Science, Faculty of
Chemistry, Department of
DSpace
UBCV
Lewis, Andrew Ross
Doctor of Philosophy - PhD
University of British Columbia
Zeolites and related microporous materials are exploited in many commercial applications because of the size and shape selectivity conferred by the molecular dimensions of their channel and cage systems. However, at present there is little direct information regarding the exact location of guest species within these materials; it is difficult to determine the structures of the host-guest complexes by X-ray diffraction techniques due to the limited availability of suitable crystals, and theoretical calculations are not always in agreement with one another. This thesis describes the application and evaluation of cross polarization (CP), rotational echo double resonance (REDOR), and transferred echo double resonance (TEDOR) solid-state N M R experiments for determining the complete three-dimensional structures of zeolite frameworks containing guests such as ions or sorbed organic molecules. In principle, these techniques permit accurate internuclear distances between spin-1/2 nuclei to be determined from measurements of the heteronuclear dipolar coupling. The viability and reliability of ¹⁹F-²⁹Si CP, REDOR and TEDOR N M R experiments was demonstrated by locating the fluoride ions within the octadecasil framework. The experimental methods were optimized and appropriate mathematical data analysis strategies developed. A comprehensive description of the mathematical methods is included. Accurate Si-F distances were determined which were in excellent agreement with those known from the single crystal structure. A series of calculations provided insight into the likelihood of being able to obtain reliable distances from REDOR and TEDOR data in cases where information regarding the number of spins, and the geometrical arrangement of these, is not known a priori. Preliminary investigations to locatep-difluorobenzene molecules within the channels of purely siliceous ZSM-5 were undertaken using these techniques. Apparatus which permitted the extended low temperature operation was developed. Powder X-ray diffraction experiments confirmed the sorbate- and temperature-induced phase changes observed for this system. Using a specially designed piece of equipment, a single crystal of ZSM-5 was loaded with a precisely controlled amount of /^-xylene and the structure successfully refined from X-ray diffraction data collected at 180 K. This represents the most accurate determination of the ZSM-5 framework to date.
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LOCATION OF GUEST SPECIES IN ZEOLITES BY SOLID-STATE NMR by ANDREW ROSS LEWIS M.Sc. (Honours) The University of Auckland, 1991 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July 1998 © Andrew Ross Lewis, 1998 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of C H E M l S T f t y The University of British Columbia Vancouver, Canada Date OcJU>a- { , H*T8 DE-6 (2/88) ABSTRACT Zeolites and related microporous materials are exploited in many commercial applications because of the size and shape selectivity conferred by the molecular dimensions of their channel and cage systems. However, at present there is little direct information regarding the exact location of guest species within these materials; it is difficult to determine the structures of the host-guest complexes by X-ray diffraction techniques due to the limited availability o f suitable crystals, and theoretical calculations are not always in agreement with one another. This thesis describes the application and evaluation of cross polarization (CP), rotational echo double resonance ( R E D O R ) , and transferred echo double resonance ( T E D O R ) solid-state N M R experiments for determining the complete three-dimensional structures of zeolite frameworks containing guests such as ions or sorbed organic molecules. In principle, these techniques permit accurate internuclear distances between spin-1/2 nuclei to be determined from measurements of the heteronuclear dipolar coupling. The viability and reliability of l 9 F - 2 9 S i C P , R E D O R and T E D O R N M R experiments was demonstrated by locating the fluoride ions within the octadecasil framework. The experimental methods were optimized and appropriate mathematical data analysis strategies developed. A comprehensive description of the mathematical methods is included. Accurate Si -F distances were determined which were in excellent agreement with those known from the single crystal structure. A series of calculations provided insight into the likelihood of being able to obtain reliable distances from R E D O R and T E D O R data in cases where information regarding the number of spins, and the geometrical arrangement of these, is not known a priori. ii Preliminary investigations to locatep-difluorobenzene molecules within the channels of purely siliceous Z S M - 5 were undertaken using these techniques. Apparatus which permitted the extended low temperature operation was developed. Powder X-ray diffraction experiments confirmed the sorbate- and temperature-induced phase changes observed for this system. Using a specially designed piece of equipment, a single crystal o f Z S M - 5 was loaded with a precisely controlled amount of /^-xylene and the structure successfully refined from X-ray diffraction data collected at 180 K. This represents the most accurate determination of the Z S M - 5 framework to date. i i i TABLE OF CONTENTS Abstract ii Table o f Contents iv List of Figures xi List o f Tables xvi Symbols and Abbreviations xvi i i Acknowledgements xx Dedication xxn Chapter 1 An Introduction to Zeolites and Solid-State N M R Spectroscopy 1 1.1 Zeolites and Related Materials I 1.1.1 General Introduction 1 1.1.2 Synthesis 2 1.1.3 Structural Topologies and Nomenclature 4 1.1.3.1 Framework Topologies and Structures 4 1.1.3.2 Nomenclature 9 1.1.4 Structural Characterization Methods 11 1.1.5 Structure Related Properties and Applications 13 1.2 Nuclear Magnetic Resonance Spectroscopy of Solids 15 1.2.1 Nuclear Magnetic Resonance Spectroscopy 15 1.2.2 Nuclear Spin Interactions in the Sol id State 16 1.2.2.1 The Zeeman Interaction 17 1.2.2.2 The Chemical Shift Interaction 20 1.2.2.3 The Dipolar Interaction 22 1.2.2.4 The Scalar Coupl ing Interaction 24 1.2.2.5 Summary of Interactions 24 1.2.3 Techniques for Obtaining "H igh Resolution" N M R Spectra from Solids 25 1.2.3.1 High Power Decoupling 26 1.2.3.2 Magic Angle Spinning 26 1.2.3.3 Cross Polarization 31 1.2.4 N M R Relaxation Processes 34 1.2.4.1 Spin-Lattice Relaxation Time (T,) 35 iv 1.2.4.2 Spin-Spin Relaxation Time (Y 2) 36 1.2.4.3 Spin-Lattice Relaxation Time in the Rotating Frame (Tip) 37 1.2.5 Internuclear Distance Measurements by Solid-State N M R 39 1.3 Investigations of Zeolite Frameworks and Guest Species 40 1.3.1 Structure Determinations by Diffraction Techniques 40 1.3.2 N M R Studies of Zeolite Frameworks and Guest Species 42 1.3.2.1 One-Dimensional N M R Studies of Zeolite Frameworks 43 1.3.2.2 Determination of Framework Connectivities by Two-Dimensional N M R 49 1.3.2.3 N M R Studies of Guest Species 53 1.3.3 Computer Model l ing of Framework Structures and Guest Species 54 1.4 Outline of Proposed Research 56 References for Chapter 1 59 Chapter 2 Experimental Details 67 2.1 Preparation of Samples used for N M R Investigations 67 2.1.1 Octadecasil 67 2.1.2 Highly Siliceous ZSM-5 . . . . 68 2.1.3 Loading of Z S M - 5 with p-difluorobenzene 68 2.2 Solid-State N M R Spectroscopy 69 2.2.1 N M R Spectrometer 69 2.2.2 N M R Probes, Rotors, and Caps 70 2.2.3 Measurement of Nuclear Relaxation Times, Pulse Lengths, and Spinning Speed 70 2.2.4 Low Temperature Operation 71 2.2.5 Cross Polarization and Setting of the Hartmann-Hahn Matching Condition 73 2.2.6 R E D O R and T E D O R Experiments 74 2.2.7 2-D I N A D E Q U A T E Experiments 75 2.2.8 N M R Data Processing 76 2.2.8.1 Peak Integration and Deconvolution of 1-D N M R Spectra 76 2.2.8.2 Processing of 2-D N M R Spectra 76 2.2.8.3 Distance Determinations from Analysis of N M R Data 77 2.3 X-ray Diffraction Experiments 77 2.3.1 Collection and Analysis of Powder X-ray Diffraction Data 77 2.3.2 Loading of Z S M - 5 Single Crystals with />-xylene 78 2.3.3 Collection and Refinement of Single Crystal Diffraction Data 80 References for Chapter 2 80 v Chapter 3 Heteronuclear Distance Determinations from Cross Polarization, R E D O R , and T E D O R N M R Experiments 81 3.1 Introduction 81 3.2 Heteronuclear Dipolar Interactions Under M A S 83 3.3 Cross Polarization 83 3.3.1 Cross Polarization for Isolated IS Spin Pairs 85 3.3.1.1 Stationary Samples 85 3.3.1.2 Samples Undergoing Magic Angle Spinning 89 3.3.2 Cross Polarization in Small Spin Clusters 92 3.3.3 Cross Polarization in a Network of Strongly Coup led /Sp ins 93 3.4 Rotational Echo Double Resonance 96 3.4.1 R E D O R for Isolated IS Spin Pairs 98 3.4.2 R E D O R Behavior for a Single S Spin Dephased by Several J Spins 103 3.4.3 R E D O R Behavior for a Single S Spin in a Network of Many / Spins 107 3.5 Transferred Echo Double Resonance 108 3.5.1 T E D O R for Isolated IS Spin Pairs 111 3.5.2 T E D O R Curve Families and Experimental Considerations 111 3.5.3 T E D O R Behavior for a Single S Spin Dephased by Several I Spins 115 3.6 Effects o f Molecular Motions 116 3.7 Summary 117 References for Chapter 3 ' 2 0 Chapter 4 1 9 F - 2 9 S i Distance Determinations in Fluoride-Containing Octadecasil from Solid-State N M R Experiments 123 4.1 Introduction 123 4.1.1 Synthesis o f Molecular Sieves in Fluoride-Containing Media 124 4.1.2 1 9 F - 2 9 S i Distance Determinations from Solid-State N M R Experiments 125 4.2 Materials and Methods 127 4.2.1 Cross Polarization Experiments 127 4.2.2 R E D O R and T E D O R Experiments 127 4.2.4 Calculations and Data Analysis 128 4.3 Results and Discussion 130 4.3.1 Octadecasil Crystal Structure 130 4.3.2 1-D l 9 F and 2 9 S i N M R Experiments 131 4.3.3 , 9 F - 2 9 S i Cross Polarization Experiments 134 vi 4.3.3.1 Hartmann-Hahn Matching Profiles 134 4.3.3.2 Variable Contact Time Experiments 136 4.3.3.3 Fitting of the Oscillatory Cross Polarization Behavior for the T - l Sil icons 139 4.3.4 l 9 F - 2 9 S i R E D O R Experiments 143 4.3.4.1 R E D O R Experiments on the D4R Sil icons (T- l Si) 145 4.3.4.2 R E D O R Experiments on the Sil icons not in the D4R (T-2 Si) 148 4.3.5 l 9 F - 2 9 S i T E D O R Experiments 153 4.3.5.1 T E D O R Experiments on the D 4 R Sil icons (T- l Si) 154 4.3.5.2 T E D O R Experiments on the Sil icons not in the D4R (T-2 Si) 160 4.4 Conclusions 160 References for Chapter 4 162 Chapter 5 Investigations into the Uniqueness of N M R Distance Determinations in Multiple Spin Systems 165 5.1 Introduction 165 5.2 Selection of Parameters 166 5.3 R E D O R Simulations 168 5.3.1 Theoretical R E D O R Behavior for 3-Spin I-S-I Systems 168 5.3.2 The R E D O R Transform Appl ied to Mult i -Spin Data 174 5.3.3 Gaussian Distribution of Dephasing Spins 176 5.4 Theoretical T E D O R Behavior for 3-spin I-S-I Systems 176 5.5 Conclusions 183 References for Chapter 5 185 Chapter 6 Preliminary Solid-State N M R Investigations of the Structure of the Low-Loaded />«ra-Difluorobenzene / ZSM-5 Complex 186 6.1 Introduction 186 6.1.1 Framework Structure of MFI-type Zeolites 188 6.1.2 Guest- and Temperature-Induced Framework Changes in Z S M - 5 190 6.1.2.1 X-ray Diffraction Studies o f Z S M - 5 Systems 190 6.1.2.2 2 9 S i N M R Studies of Z S M - 5 Systems 192 6.1.3 Other Techniques for Locating Sorbates in the Z S M - 5 Framework 196 6.1.3.1 Predictions of Sorbate Locations from Energy Minimization Calculations 196 6.1.3.2 Predictions of Sorbate Locations from Solid-State N M R Experiments 198 6.2 Materials and Methods 200 vi i 6.2.1 Sample Preparation and Sorbate Loading 200 6.2.2 N M R Experiments 200 6.2.3 Calculations to Determine Sorbate Locations and Orientations from C P data 202 6.3 Results and Discussion 204 6.3.1 1-D l 9 F and 2 9 S i M A S N M R 204 6.3.2 I N A D E Q U A T E Experiments 209 6.3.3 ' H - 2 9 S i Cross Polarization Experiments 211 6.3.4 1 9 F - 2 9 S i Cross Polarization Experiments 219 6.3.5 l 9 F - 2 9 S i R E D O R and T E D O R Experiments 225 6.4 Summary and Conclusions 225 References for Chapter 6 228 Chapter 7 Preliminary Powder X-ray Diffraction Investigations of the Low-Loaded parfl-Difluorobenzene / ZSM-5 Complex 231 7.1 Introduction 231 7.2 Materials and Methods 235 7.2.1 Sample Preparation and Data Collection 235 7.2.2 Fitting of Reflection Data 236 7.3 Results and Discussion 238 7.3.1 Phase Transitions on Cool ing 238 7.3.2 Empty Z S M - 5 at 293 K 244 7.3.3 D F B / Z S M - 5 at 260 K 247 7.3.4 D F B / Z S M - 5 at 293 K 250 7.4 Conclusions 251 References for Chapter 7 254 Chapter 8 Structure of the Low-Loaded Complex of para-Xy\ene in ZSM-5 from a Single Crystal X-ray Diffraction Study 256 8.1 Introduction 256 8.1.1 Single Crystal X-ray Diffraction Studies of Z S M - 5 Systems 258 8.1.2 Correlations Between 2 9 S i N M R Chemical Shifts and Structural Parameters 259 8.1.3 Previous Investigations of the Low-Loaded /^-xylene / Z S M - 5 Complex 260 8.2 Materials and Methods 264 8.2.1 Crystal Preparation and Sorbate Loading 264 8.2.2 Data Collection and Refinement o f Reflection Data 265 vi i i 8.2.2.1 Data Collection 265 8.2.2.2 Definitions or R-indices Used 265 8.2.2.3 Processing and Refinement of the Reflection Data 269 8.3 Results and Discussion 271 8.3.1 Geometry o f the Framework 276 8.3.2 Geometry and Packing of the />-xylene Molecules 282 8.3.3 Comparisons with /^-xylene Orientations determined by Other Methods 288 8.3.4 Predictions of 2 9 S i Chemical Shifts 288 8.4 Summary and Conclusions 293 References for Chapter 8 294 Chapter 9 Conclusions and Suggestions for Future Work 297 9.1 Summary and Conclusions 297 9.2 Suggestions for Future Work 302 References for Chapter 9 305 APPENDICES Appendix A Schematics of N M R Spectrometer Configurations 306 Appendix B Pulse and Automation Programs 312 B. 1 I ndex of Programs 313 B. 2 Program Listings 316 Appendix C Functions and Mathematica Code for Fitting Data from Cross Polarization, R E D O R , and T E D O R N M R Experiments 345 C. 1 Hartmann-Hahn Cross Polarization 346 C. 1.1 Cross Polarization Behavior for Isolated IS Spin Pairs 346 C. 1.1.1 Functions Used to Describe H H C P Behavior 346 C. 1.1.2 Nonlinear Least Squares Fitting of Experimental H H C P Data 350 C. 1.2 Cross Polarization Behavior in a Network of Strongly Coupled I Spins 352 C.2 Rotational Echo Double Resonance 353 C.2.1 R E D O R Behavior for Isolated IS Spin Pairs 353 C.2.1.1 R E D O R Functions and Nonlinear Fitting 353 C.2.1.2 The R E D O R Transform 357 ix C.2.2 R E D O R Behavior for a Single S Spin Dephased by Several / Spins 359 C.2.2.1 Exact Geometrical Analysis 359 C.2.2.2 Single S Spin Dephased by Gaussian Distribution of I Spins 363 C.3 Transferred Echo Double Resonance 366 C.3.1 T E D O R Behavior for Isolated IS Spin Pairs 366 C.3.2 T E D O R Behavior for a Single S Spin Dephased by Several / Spins 371 References for Appendix C 376 Appendix D Derivation of Equations for Calculating Heteronuclear Second Moments in the Presence of Molecular Motion 377 References for Appendix D 380 Appendix E Algorithm for Locating Molecules in Zeolite Channels from CP Data 381 E.l Program Options and Details o f Transformations Used 382 E.2 Sample Input File 384 E.3 Pseudo-Code Listing 387 References for Appendix E 391 Appendix F Supplementary Data for Chapter 6 392 Appendix G Supplementary Data for the p-Xylene / ZSM-5 Single Crystal Structure 396 x LIST OF FIGURES Figure 1.1 Representations of the framework structures of some selected zeolites 5 Figure 1.2 The secondary building units from which all known zeolite topologies can be built.. 6 Figure 1.3 Cage-like polyhedra observed in clathrasils and high si l ica clathrates 8 Figure 1.4 FID signal and real spectrum fol lowing Fourier transformation 21 Figure 1.5 Phase shift of the net magnetization induced by application of an r.f. pulse 21 Figure 1.6 Definitions of angles used to describe the orientation of an IS internuclear vector in a powder sample undergoing M A S 28 Figure 1.7 l 3 C spectra of a powder sample of ferrocene showing the effects o f M A S 30 Figure 1.8 Pulse sequence and vector representation of Hartmann-Hahn C P experiment 33 Figure 1.9 Pulse sequence and vector representation of the spin-echo experiment 38 Figure 1.10 The five possible local environments of a sil icon atom in a zeolite framework and their corresponding 2 9 S i M A S N M R chemical shifts 45 Figure 1.11 2 9 S i M A S N M R spectra of highly siliceous Z S M - 5 and the improved resolution obtained i f a very crystalline, purely siliceous sample is used 47 Figure 1.12 Framework structure of Z S M - 1 2 and contour plot of a 2 9 S i I N A D E Q U A T E experiment with the T-site connectivities shown 51 Figure 2.1 Schematic of the equipment used for low temperature N M R experiments 72 Figure 2.2 Apparatus for loading single zeolite crystals with precisely controlled amounts of volatile sorbates 79 Figure 3.1 Behavior o f the dipolar coupling as a function of the rotation under M A S 84 Figure 3.2 Cross polarization matching curves under various conditions 86 Figure 3.3 Evolution of the S spin polarization under Hartmann-Hahn cross polarization at different matching conditions 88 Figure 3.4 Theoretical C P behavior for S spins in a network of strongly coupled / spins 95 Figure 3.5 C P M A S curves for glycine showing the different behavior observed for the methylene and carbonyl carbons as a function of the contact time 95 Figure 3.6 R E D O R pulse sequences 97 Figure 3.7 Theoretical R E D O R behavior calculated for an isolated IS spin pair assuming different dipolar couplings, and the "Universal R E D O R " curve 100 xi Figure 3.8 R E D O R dephasing S /S 0 and the results o f applying a Fourier transformation and the R E D O R transform 102 Figure 3.9 Definitions of angles used to describe the orientation of the 75 internuclear vectors in an INS spin system in a powder sample undergoing M A S 106 Figure 3.10 T E D O R pulse sequences 110 Figure 3.11 Theoretical T E D O R behavior calculated for an isolated IS spin pair illustrating the effects o f varying different parameters 113 Figure 4.1 Representation of the framework structure of octadecasil showing the location of the occluded fluoride ions and the two kinds of T-sites 132 Figure 4.2 l 9 F and 2 9 S i M A S N M R spectra of octadecasil 133 Figure 4.3 Hartmann-Hahn l 9 F - 2 9 S i matching profiles for the two T-sites in octadecasil 135 Figure 4.4 1 9 F - 2 9 S i C P behavior for the two T-sites in octadecasil under M A S conditions 138 Figure 4.5 l 9 F - 2 9 S i C P behavior for the T - l Si in a stationary octadecasil sample 138 Figure 4.6 l 9 F - 2 9 S i C P behavior for the T - l Si in octadecasil at the | / | =1 sideband matching conditions under various M A S speeds 141 Figure 4.7 l 9 F - 2 9 S i C P behavior for the T - l Si in octadecasil at t h e / = +2 sideband matching condition for an M A S of 4.15 kHz 141 Figure 4.8 l 9 F - 2 9 S i R E D O R data and fits for the T - l Si in octadecasil 146 Figure 4.9 R E D O R Transform of R E D O R data acquired for the T - l Si in octadecasil 149 Figure 4.10 l 9 F - 2 9 S i R E D O R data and fits for the T-2 Si in octadecasil 149 Figure 4.11 l 9 F - 2 9 S i T E D O R spectra of octadecasil acquired with n=2, m varied and a spinning speed of 4.540 kHz 155 Figure 4.12 T E D O R data and fits for the T - l Si in octadecasil with n fixed and m varied 156 Figure 4.13 T E D O R data and fits for the T - l Si in octadecasil with n varied and m fixed 157 Figure 4.14 T E D O R data and fits for the T - l Si in octadecasil using different placement of the dephasing pulses 159 Figure 4.15 T E D O R data and fits for the T-2 Si in octadecasil with n varied and m=3 159 Figure 5.1 Pictorial representation of the I2S spin systems for which the theoretical R E D O R and T E D O R dephasing was investigated 167 Figure 5.2 R E D O R curves calculated for some 12S spin systems 170 xii Figure 5.3 R E D O R curves calculated for an I2S spin system (D,=\00 Hz, D2=\00 Hz) as a function of the I-S-I angle C, 171 Figure 5.4 R E D O R curves calculated for an I2S spin system (Z)/=100 Hz, D2=1S Hz) as a function of the I-S-I angle C, 172 Figure 5.5 R E D O R curves calculated for an I2S spin system (Z>y=100 Hz, Z)2=50 Hz) as a function of the I-S-I angle C, 173 Figure 5.6 R E D O R curves calculated for a single S spin dipolar coupled to a large number of I spins (Gaussian distribution) 177 Figure 5.7 T E D O R curves calculated for some I2S spin systems 179 Figure 5.8 T E D O R curves calculated for an I2S spin system (D,=\ 00 Hz, Z)2=100 Hz) as a function of the I-S-I angle C, 180 Figure 5.9 T E D O R curves calculated for an I2S spin system (D/=100 Hz, D2=15 Hz) as a function of the 7-5-7 angle C, 181 Figure 5.10 T E D O R curves calculated for an I2S spin system (D/=100 Hz, Z)2=50 Hz) as a function of the 7-5-7 angle t, 182 Figure 6.1 Bui lding units, topology and channel structure of the MF I framework 189 Figure 6.2 High resolution 2 9 S i M A S N M R spectra of highly siliceous Z S M - 5 showing the changes that occur with temperature or loading with p-xylene 193 Figure 6.3 High resolution 2 9 S i M A S N M R spectra of highly siliceous Z S M - 5 loaded with selected organic molecules 194 Figure 6.4 High resolution 2 9 S i M A S N M R spectra of highly siliceous Z S M - 5 loaded with 4 molecules / u.c. o f /?-dichlorobenzene,/?-chlorotoluene, or /(-xylene 195 Figure 6.5 Phase diagram for highly siliceous Z S M - 5 loaded with /7-xylene 197 Figure 6.6 1 9 F M A S N M R spectra ofp-difluorobenzene in Z S M - 5 at different temperatures . 205 Figure 6.7 2 9 S i M A S N M R spectra of the low-loaded p-difluorobenzene / Z S M - 5 complex at different temperatures 206 Figure 6.8 Contour plot of a C P - I N A D E Q U A T E experiment on Z S M - 5 loaded with 4 molecules of /?-difluorobenzene per unit cell at 245 K 208 Figure 6.9 Quantitative 2 9 S i M A S N M R spectra of/?-difluorobenzene in Z S M - 5 compared with the ' H - 2 9 S i and 1 9 F - 2 9 S i C P M A S spectra (20 ms contact time) 210 Figure 6.10 Intensities of the ' H - 2 9 S i C P M A S N M R signals as a function of the contact time for the low-loaded p-difluorobenzene / Z S M - 5 complex at 230 K. 213 xi i i Figure 6.11 Best linear fits o f 1/7CP vs. the calculated ' H - 2 9 S i second moments found from analysis of the ' H - 2 9 S i C P M A S data recorded at 230 K 215 Figure 6.12 V iew down [010] showing the location and orientation of the /7-difluorobenzene molecules found from fitting the ' H - 2 9 S i C P data recorded at 230 K 217 Figure 6.13 Location and orientation of the p-difluorobenzene molecules found from analysis o f ' H - 2 9 S i C P data recorded at 230 K 218 Figure 6.14 Intensities of the 1 9 F - 2 9 S i C P M A S N M R signals as a function of the contact time for the low-loaded p-difluorobenzene / Z S M - 5 complex at 235 K 221 Figure 6.15 Best linear fit o f 1/TCP vs- the calculated 1 9 F - 2 9 S i second moments found from analysis of the l 9 F - 2 9 S i C P M A S data recorded at 235 K 221 Figure 6.16 V iew down [010] showing the location and orientation of the /7-difluorobenzene molecules found from fitting the l 9 F - 2 9 S i C P data recorded at 235 K 224 Figure 7.1 V iew along the zig-zag channels of Z S M - 5 for structures having orthorhombic Prima, and monoclinic P2i/n.l.l symmetry 233 Figure 7.2 Powder X R D patterns of the low-loaded p-difluorobenzene / Z S M - 5 complex as the sample was cooled from 293 K to 260 K 240 Figure 7.3 Powder X R D patterns of the low-loaded p-difluorobenzene / Z S M - 5 complex at 293 K and 260 K compared with the powder pattern for empty Z S M - 5 at 293 K .. 242 Figure 7.4 Experimental and calculated powder X R D for empty Z S M - 5 at 293 K 246 Figure 7.5 Experimental and calculated powder X R D for the low-loaded /?-difluorobenzene / Z S M - 5 complex at 260 K 249 Figure 7.6 Experimental and calculated powder X R D for the low-loaded /?-difluorobenzene / Z S M - 5 complex at 293 K 252 Figure 8.1 ' H - 2 9 S i C P M A S N M R spectra of purely siliceous Z S M - 5 loaded with three molecules of /^-xylene / u.c. recorded at 173 K and 193 K 262 Figure 8.2 Numbering scheme of the Si and O atoms in the asymmetric unit of the Z S M - 5 framework with orthorhombic Prima symmetry 274 Figure 8.3 O R T E P drawings showing location of the /^-xylene in Z S M - 5 275 Figure 8.4 V iew of the low-loaded /^-xylene / Z S M - 5 complex showing the orientations and packing of the /^-xylene molecules in the straight channels 281 Figure 8.5 Labeling of the carbon atoms in /^-xylene molecules 283 Figure 8.6 Angles and coordinates used to describe the orientations of sorbates in Z S M - 5 283 Figure 8.7 N M R and X R D correlation diagrams for Z S M - 5 containing 2.85 molecules of />-xylene per u.c. at 180 K 291 xiv Figure 8.8 N M R and X R D correlation diagrams for Z S M - 5 containing 2.85 molecules of /(-xylene per u.c. at 180 K 292 Figure A . l Schematic o f spectrometer configuration used for ' H - 2 9 S i experiments 309 Figure A.2 Schematic o f spectrometer configuration used for l 9 F - 2 9 S i experiments with mixing of the F2 and F3 frequencies to generate the 2 9 S i frequency 310 Figure A.3 Schematic of spectrometer configuration used for l 9 F - 2 9 S i experiments with the 2 9 S i frequency generated directly 311 Figure C . l Theoretical H H C P behavior calculated for an isolated IS spin pair in a static powder sample using numerical integration and Bessel functions 349 Figure C.2 Theoretical R E D O R dephasing calculated for an isolated IS spin pair for different placements of the dephasing pulses 355 Figure C .3 Theoretical R E D O R dephasing calculated for an isolated IS spin pair for the indicated placements of the two dephasing pulses in the period after transfer 369 xv LIST OF TABLES Table 1.1 Pore dimensions and channel dimensionalities of selected zeotype structures 10 Table 1.2 Typical magnitudes of nuclear spin interactions for 1 3 C in a 4.7 T magnetic field 18 Table 1.3 Important N M R parameters of selected nuclei 18 Table 4.1 l 9 F - 2 9 S i dipolar couplings calculated for various Si-F interatomic distances 129 Table 4.2 2 9 S i and l 9 F relaxation parameters measured for octadecasil 129 Table 4.3 Comparison of the 2 9 S i - ' 9 F dipolar couplings and Si -F distances for octadecasil determined by various methods 144 Table 6.1 Space groups and numbers of T-sites for several Z S M - 5 structures 191 Table 6.2 Experimental and calculated parameters related to the ' H - 2 9 S i C P experiments on the low-loaded p-difluorobenzene / Z S M - 5 complex at 230 K 213 Table 6.3 Results o f fitting C P data for the low-loaded /7-difluorobenzene / Z S M - 5 complex .214 Table 6.4 Experimental and calculated parameters related to the 1 9 F - 2 9 S i C P experiments on the low-loaded />difluorobenzene / Z S M - 5 complex at 235 K 222 Table 7.1 Results from fitting of the Z S M - 5 X R D powder data using the AJUST program 245 Table 8.1 Crystal data and structure refinement for /^-xylene in Z S M - 5 at 180 K 266 Table 8.2 Atomic coordinates and equivalent isotropic displacement parameters for /^-xylene in Z S M - 5 at 180 K 272 Table 8.3 Comparison of the framework geometry in several Z S M - 5 structures determined by single crystal X-ray diffraction 278 Table 8.4 Min imum and maximum diagonal O - O distances across the 10-rings in several Z S M - 5 structures 279 Table 8.5 Comparison of the bond lengths and bond angles in /^-xylene molecules at the channel intersections in Z S M - 5 with those in crystalline /^-xylene at 180 K 284 Table 8.6 Comparison of the locations and orientations for different organic molecules adsorbed at the channel intersections in Z S M - 5 286 Table 8.7 2 9 S i chemical shifts and structural parameters for Z S M - 5 loaded with 2.85 molecules o fp- \y \em / u.c. at 180 K 290 Table 8.8 Linear regression analysis of the 2 9 S i chemical shifts against the various geometric parameters indicated for the low-loaded /7-xylene / Z S M - 5 complex at 180 K 290 xvi Table A . l Abbreviations used in the spectrometer configuration schematics 308 Table A.2 Phases of the F3 signal before and after tripling 308 Table C . l Functions describing the H H C P behavior for isolated IS spin pairs in a powder sample at various matching conditions 347 Table C.2 R E D O R dephasings calculated for a tetrahedral arrangement of 4 I spins about a central S spin using different step sizes for the numerical integration 361 Table C.3 R E D O R dephasings calculated for different I2S spin system geometries 362 Table C.4 T E D O R functions Afaj for different positions of the dephasing pulses 368 Table C .5 T E D O R dephasings calculated for different I2S spin system geometries 374 Table F . l T-sites, their occupancies and connectivities for the asymmetric unit in the monoclinic P2i/n. 1.1 phase of Z S M - 5 393 Table F.2 Fractional coordinates of the /?-difluorobenzene atoms found from fitting of the 1 H- 2 9 Si C P data at 230 K 394 Table F.3 Fractional coordinates of the p-difluorobenzene atoms found from fitting of the 1 9 F - 2 9 S i C P data at 235 K 395 Table G . l Anisotropic displacement factors for the low-loaded /(-xylene / Z S M - 5 complex at 180 K 397 Table G.2 Bond lengths for framework atoms in Z S M - 5 loaded with 2.85 molecules of /(-xylene per unit cell at 180 K 398 Table G.3 Bond angles for framework atoms in Z S M - 5 loaded with 2.85 molecules of /(-xylene per unit cell at 180 K 399 xvi i SYMBOLS AND ABBREVIATIONS a, b, c crystallographic unit cell dimensions (lattice constants) b, orientation dependent dipolar coupling (/' = 0, 1,2) B0 static magnetic field o f an N M R spectrometer B\i radiofrequency magnetic field applied to the I nuclei B\s radiofrequency magnetic field applied to the S nuclei c number o f combinations of possible spin states C P Cross Polarization D dipolar coupling / Hartmann-Hahn matching condition FID Free Induction Decay FT Fourier Transform h Planck's constant H H C P Hartmann-Hahn Cross Polarization I magnetic quantum number associated with / spins; unobserved nucleus I N A D E Q U A T E Incredible Natural Abundance Double Quantum Transfer Experiment Jj Bessel functions of the first kind n number o f rotor periods in R E D O R experiment number o f rotor periods before coherence transfer in T E D O R experiment N number o f spin pairs; number of / spins N M R Nuclear Magnetic Resonance m number o f rotor periods after coherence transfer in T E D O R experiment M macroscopic magnetization of a spin system in the presence of B0 M0 equilibrium macroscopic magnetization of a spin system in the presence of B0 M2(II) / - /homonuclear second moment M2(IS) IS heteronuclear second moment M2(SS) S-S homonuclear second moment M A S Magic Angle Spinning p probability that a given site is occupied P, Binomial probability o f that / sites are occupied r internuclear distance r.f. radio frequency R E D O R Rotational Echo Double Resonance S magnetic quantum number associated with S spins; observed nucleus Si -1 , Si-2, etc. crystallographically inequivalent T-sites (silicons) in a zeolite framework S 0 signal intensity in R E D O R experiment with no dephasing pulses applied Sf signal intensity in R E D O R experiment with dephasing pulses applied S T signal intensity in T E D O R experiment / time ti, t2 position of dephasing pulses during rotor cycle as fraction of rotor period x r T - l , T-2 crystallographically inequivalent T-sites in octadecasil framework T\ spin-lattice or longitudinal relaxation time xvi i i T\p spin-lattice relaxation time in the rotating frame T2 spin-spin or transverse relaxation time T E D O R Transferred Echo Double Resonance T G A Thermal Gravimetric Analysis u.c. unit cell v IS internuclear vector {v/, v2, v3} (unit length) x {1, 0, 0}, unit vector parallel to *-axis X R D X-ray Diffraction y {0, 1, 0}, unit vector parallel toy-axis z {0, 0, 1}, unit vector parallel to z-axis a , (3 polar angles describing orientation of IS vector in a powder sample a, [i, y crystallographic unit cell angles (lattice constants) aav average Si(OSi)4 angle al, pi, yl angles describing orientation of aromatic ring in zeolite channels a2, p2, y2 angles describing orientation of aromatic ring in zeolite channels fi, ys gyromagnetic ratios of I and S spins 8 chemical shift C, IS-I angle in a 3-spin system X nDxT dimensionless parameter ( R E D O R ) Xn nDx{ dimensionless parameter ( T E D O R ) X,„ mD\x dimensionless parameter ( T E D O R ) x contact time in cross polarization experiment x r rotor period (time for one complete rotor cycle) v r spinning speed (s"1) cor rotor frequency (rad s"') © 0 / Larmor frequency of the I spins coav Larmor frequency of the S spins coi; amplitude of the radiofrequency field applied to the / spins (0\s amplitude of the radiofrequency field applied to the S spins A O R accumulated dephasing during R E D O R experiment AS S o - S f R E D O R difference A O T „ dephasing in n rotor cycles before coherence transfer in T E D O R experiment A O T , m dephasing in m rotor cycles after coherence transfer in T E D O R experiment 9 angle between IS internuclear vector and static magnetic field B0 Q, ()>, Euler angles used to describe orientation of IS vectors 6 m the "Mag ic Angle" , 54.74° x ix ACKNOWLEDGEMENTS I have enjoyed my time at U .B .C. immensely and would like to take this opportunity to acknowledge the assistance of the many friends and colleagues who have helped and supported me during my Ph.D. studies. First and foremost, I would like to express my sincerest gratitude to Col in Fyfe for his continuous support and encouragement. His valuable advice and deep insight, as well as a seemingly endless supply of ideas, have greatly influenced my work, and continue to inspire my research efforts. I would also like to thank Hiltrud Grondey for teaching me the mechanics of experimental N M R ; without her guidance and knowledge of the Bruker software many of the experiments in this thesis would have been impossible. G .E . Barlow kindly provided the outstanding samples of Z S M - 5 used in the N M R experiments. During my Ph.D. I was truly fortunate to enjoy fruitful collaborations with several distinguished visitors to the Fyfe group: Jean-Michel Chezeau, who brought with him the truly outstanding samples prepared by Anne-Catherine Faust and Philippe Caullet, which allowed the optimization of the N M R experiments and the calculations that proved pivotal in this research project; George Kokotai lo, who possesses a contagious, boundless enthusiasm and an unparalleled knowledge of zeolites was always inspirational; Wi lhelm Schwieger, who is thanked for his great expertise in synthesizing the very high quality, large single crystals of Z S M -5 used in the X R D investigations; and Kar l Muel ler whose assistance and advice was crucial to the success of the R E D O R and T E D O R calculations. I am severely indebted to Tom Markus and Mi lan Coshizza for having the patience to repair the spectrometer and probes on the many occasions that 1 caused them to malfunction, and also for teaching me the "secrets" of the inner workings of the M S L spectrometer. I am particularly thankful to Tom, who was able to perform the seemingly magical feats of designing, modifying, improving and building N M R instrumentation required to implement all of the N M R experiments in this thesis. I would also like to thank Oskar Grenier for his skil l in altering and f ix ing many pieces of equipment, often at very short notice and much faster than could reasonably expected. Steve Rak is thanked for constructing the single crystal apparatus. Steve xx Rettig is gratefully acknowledged for his efforts to collect single crystal data and also for advice on the crystal lographic software. I would also like to express my gratitude to Hermann Gies for inviting me to visit the Institut fur Mineralogie at Ruhr-Universitat in Bochum, and for greatly improving my understanding of symmetry, X-ray diffraction, and zeolite frameworks. A t Bochum under the expert guidance of Bernd Marler, the powder X R D data was collected and I was introduced to the techniques of X-ray diffraction structure refinement. Peter Daniels and Holger Meyer zu Altenschilde are also thanked for their suggestions and assistance in the single crystal refinement work. Felix Aubke is acknowledged for careful reading of the final version of this thesis and also for his support during the initial stages of my Ph.D. work. Sabine Hediger is thanked for providing a copy of her thesis, and for having the patience to answer my many questions about the intricacies of Hartmann-Hahn cross polarization. M y present and former co-workers An ix Diaz, A lmi ra Blazek, Jim Sawada, Jerry Bretherton, K i rby Wong-Moon, Darren Brouwer, Jorgen Skibsted, Y in ing Huang, Patty Aroca-Oulette, Zhimming Me i , and Chanqing Wang are also thanked for their patience, help, enlightening discussions, and for making my time at U .B .C . so enjoyable. 1 gratefully acknowledge the Natural Sciences and Engineering Research Counci l o f Canada which funded the research reported in this thesis and also the financial assistance of the University of British Columbia. I would like to thank the many friends who visited me during my time in Vancouver and provided welcome distractions from my toil, especially L isa Simpson, J im Blanking and Ewen Anderson. Finally, I thank my family for their continued patience, support, and encouragement throughout my academic pursuits. xx i Dedicated to the memory of my Father xxi i CHAPTER 1 AN INTRODUCTION TO ZEOLITES AND SOLID-STATE NMR SPECTROSCOPY This chapter introduces the structures and physical properties of zeolites and related microporous materials, then briefly discusses some concepts and techniques used in solid-state nuclear magnetic resonance ( N M R ) spectroscopy. A n overview of previous investigations of microporous materials and guest species by solid-state N M R is also presented. 1.1 Z E O L I T E S AND R E L A T E D M A T E R I A L S 1.1.1 General Introduction Zeolites are crystalline open framework aluminosilicates which play important roles as rock-forming materials (minerals) and as synthetic products of considerable industrial and scientific interest. They have many large scale industrial applications as catalysts, ion exchangers, molecular sieves, and absorbents.' The name "zeol i te" is derived from the Swedish word zeolit coined by Cronstedt in 1756 from the Greek words ^eiv (zein = to boil) and ^.tooc; (lithos = stone) to describe the apparent "bo i l ing" he observed as the water frothed out of the mineral stillbite upon heating with a flame. Traditionally, the term zeolite was only considered to describe porous aluminosilicates, however in recent years its usage has been expanded to include crystalline inorganic materials containing elements other than sil icon and aluminium which have zeolite-like frameworks. These zeolite-like materials encompass completely siliceous analogues 1 of zeolites and clathrates (zeosils and clathrasils respectively), porous aluminophosphates (AIPO4S), and materials such as GaPOs which contain gall ium or other elements. 2 , s Several comprehensive books have been written about these materials including those by Barrer / B reck / and the more recent compilations from the International Zeolite Association Summer Schoo l s . 6 7 " 1.1.2 Synthesis Although natural mineral zeolites have been known for more than 200 years, there was relatively little interest in them until M c B a i n demonstrated their ability to selectively absorb organic molecules and coined the term "molecular sieve" in 1932. 9 In the 1940s, Barrer began the first systematic studies of zeolite synthesis, demonstrating not only their molecular sieving properties, but also producing the hydrogen forms of these materials, which act as strong acid catalysts. Within a relatively short period fol lowing the synthesis of the naturally occurring zeolites chazabite, and mordenite, the first synthetic zeolite not found in nature, zeolite A , was prepared by M i l t o n / 0 The early synthetic methods were based on hydrothermal treatments of alkaline silicate and aluminate gels and produced samples with relatively low (< 6) S i / A l ratios similar to those found in naturally occurring zeolites. Kerr pioneered the use of quaternary ammonium organic cations R ibT as "templating" or structure directing species, which allowed the direct synthesis of materials with larger S i / A l ratios and this gave rise to a whole new generation of materials, many with previously unknown structures." Zeolite compositions may be described using a simple empirical oxide formula (Eq. 1.1), where the M n + represents the exchangeable cations, the part within brackets the framework, and z H 2 0 the water of hydration. M : ; n [ ( S i 0 2 ) „ ( A 1 0 2 ) J z H 2 0 1.1 The sil icon to aluminium ratio (S i /A l = y/x) may vary from 1 to infinity, and the cations are usually metal ions or quaternary organic ammonium cations incorporated during crystallization. These cations are required to balance the net negative charges introduced by the aluminium 2 atoms in the framework. Often the large organic cations block the pores and channels and need to be removed before the materials can be used. In many cases this is simply achieved by heating the material at about 550 °C in air (oxygen) to combust the organic matter. Other species such as ammonium ions and transition metal complexes may be introduced after synthesis by ion exchange, however protons are by far the most important cations because they generate strongly acidic catalytic sites within the zeolite voids. Once it became apparent that properties such as the catalytic activity and thermal stability were related to the S i / A l ratio, other methods involving thermochemical modification, chemical treatments, and acid extraction, were developed to increase the S i / A l ratio. Where a framework can't be directly synthesized in a high S i / A l ratio (e.g. zeolite Y ) steaming of the hydrogen form can be used to remove aluminium from the framework. Heating (usually above 700 °C) in the presence of steam drives a fraction of the hydrogen ions from the zeolite crystals and causes an equal number of aluminium atoms to leave the framework. The vacancies created are somehow fi l led by sil icon atoms, thereby increasing the S i / A l ratio. Some aluminium species may remain in the pores as octahedrally coordinated cations and can act as catalytic sites. Zeolites synthesized with boron rather aluminium can also be steamed, and the boron is much easier to remove from the framework. A direct isomorphous substitution of Si for A l can be achieved by treating the sample with S iCL} / 2 In the 1980s a new class of materials, the A l P 0 4 s , whose frameworks contain aluminium and phosphorus were discovered. A l P 0 4 s have frameworks with A l / P ratios of unity and rigorous alternation of A l and P sites within their structures which means there is no net charge on the framework. However it is principally the charge balancing cations which create the catalytic sites in zeolites so the synthetic techniques were quickly extended to permit isomorphous substitution (e.g. o f P by Si or A l by Ga) and thereby introduce net framework charges in these materials. 2 , 3 A new synthetic route involving the use of non-alkaline, fluoride-containing media was introduced by Flanigen and Patton," and has been extended by Guth and co-workers, 1 4 and 3 others. J This method allows the direct synthesis of purely siliceous materials, A l P 0 4 s and isomorphously substituted and many novel materials have been prepared using this approach. A wide variety of treatments have also been successfully used to modify the as-synthesized materials. 5 1.1.3 Structural Topologies and Nomenclature 1.1.3.1 Framework Topologies and Structures Zeolites and their non-aluminosilicate analogues are microporous materials, having pore sizes and channel dimensions in the range 3-13 A , and as such are distinct from the mesoporous materials which have much larger void dimensions (up to 100 A ) . Some common frameworks, showing the channel systems which can be one, two, or three-dimensional in nature, are depicted in Figure 1.1. It is the dimensions of these channels which confers the size and shape selectivities. These frameworks contain only corner-sharing tetrahedra, al lowing them to be distinguished from layered materials such as clays, which share many of their useful physical properties (e.g. cation exchange abilities, voids of molecular dimensions and very similar elemental compositions), but also have edge-sharing ocahedra. A further, though less clear-cut distinction can be made between zeolites, which contain true "channels", and clathrates whose structures consist o f assemblies of cage-like units with intraframework cavities connected through the cage openings. The basic building blocks of zeolite-like structures are T 0 4 units, where T represents elements such as si l icon, aluminium, or phosphorus, tetrahedrally coordinated to four oxygen atoms. These positions in the framework structure are usually referred to as "T-si tes", even when, as is the case of A l in some A l P 0 4 s , up to two water molecules can be absorbed to yield five- or six-coordinated atoms. These are linked together by sharing oxygen atoms into larger finite units known as Secondary Bui ld ing Units (SBUs) which contain up to 16 T-sites (Figure 4 (a) SOD (b) LTA Figure 1.1 Representations of the framework structures of some selected zeolites. (a) Sodalite, (b) Zeolite A , (c) faujasite, (d) Z S M - 5 , (e) mordenite, and (f) VTT-5. The 3-letter codes designating the structure types are also given. 5 • o 4 - 4 / 6-6 4-1 6«1 8 8-8 6-2 5-2 5-1 4-1 4 - 4 - 1 5-3 Spiro-5 Figure 1.2 The secondary building units (SBU 's ) . A l l o f the known zeolite topologies can be built from combinations of these. In these figures, each vertex or termination represents a T-site. The oxygens (omitted for clarity) lie approximately midway between the vertices, but not on the line jo in ing them because the T-O-T angles are not 180°. After reference 17. 6 1.2). The assembly of these SBUs into three-dimensional structures through oxygen-bridges produces the familiar frameworks containing regular systems of molecular-sized, interconnected channels and cavities. The cations necessary to balance the negative charge of the framework, and other guest species including water molecules, non-silicate anions (e.g. fluoride and chloride ions), organic cations, or organic molecules may be located in the voids. A n alternative method of visualizing zeolite topologies is to consider the frameworks as being constructed from stacks of polyhedral cages. These cages, which must share faces with other polyhedra, can be either different or all alike. Some of the common polyhedra found in zeolites are depicted in Figure 1.3. These are useful for describing many structure types, especially the clathrates, but also for some of the common zeolites such as sodalite, zeolite A , and the faujasite structure of zeolites X and Y . The frameworks structures of these four materials contain the truncated octahedron (p-cage or [4 66 8] unit), sharing 4-ring faces in the case of sodalite, or linked through double 4-ring (D4R) units (zeolite A ) , or double 6-ring (D6R) units (faujasite) as shown in Figure 1.1. Representations of three other common zeolites (ZSM-5 , mordenite and VPI-5), whose frameworks are better described as being built up from chains of SBUs are shown in Figure 1.1. The channels present in many zeolites are clearly seen in the latter two examples. Variations in the framework composition (e.g. by isomorphous substitution), coupled with large number of possibilities for connecting the sub-units into 3-dimensional networks, yield an essentially infinite conceivable number of structures. A t present several hundred naturally occurring zeolites and related synthetic materials are known, with more than a hundred distinct structure types conf i rmed/ 6 Microporous materials such as zeolites and A l P 0 4 s can have many different types of channels and intrastructural cavities.' 1 5 The sizes are determined by the number of T- or O-atoms that form the rings (often circular or elliptical) and control diffusion through the channels. Generally, only those apertures which are more open than regular six-membered rings are 7 o [4 6 ] (5A 3 ) [4 45 4 ] (20A 3) [5 46 4 ] (25A 3) [4'5 8 ] (30A 3) [4356] (25 A3) [445462] (35 A3) [4 3 5V] (35 A3) [435663] (70 A3) [5 1 2 ] (80A 3 ) [4668] (130 A3) [5 I 2 6 2 ] (160A 3 ) [465683] (230 A3) [4456658'] (230 A3) [51264] (240 A3) [4 661 2](280A 3) [46546682] (300 A3) [4 35 1 26 ]8 3] (350 A3) [58612] (290 A3) [5' 26 8 ](SGT)(390A 3) [51 268](DOH) (430 A3) [46586484] (500 A3) [5 I 86 28 3] (540 A3) Figure 1.3 Compilation of the cage-like polyhedra observed in clathrasils and high si l ica clathrates. The topological code descriptor, and the free volume for the different units are indicated. After reference 18. considered to be channels, and the smaller openings are described as windows which connect larger cavities. One, two, and three-dimensional systems of channels are known, and in many cases (but not always), these are interconnected. Table 1.1 summarizes information about the nature and free diameters of the channel systems for some common structures. The void volumes of these polyhedra are given in Figure 1.3. It must be emphasized that the frameworks are not completely rigid: the T - 0 bond lengths and particularly T-O-T angles can change with temperature and in the presence of sorbed or occluded species. 7 9 2 0 1.1.3.2 Nomenclature The conventions for naming zeolites and related materials are quite diverse, principally because many groups have synthesized materials and given them "in-house" names, but also because of the many naturally occurring mineral analogues which have their own established nomenclature. There are cases where identical materials have been synthesized by several research groups and given different names, 2 ' and also of materials containing different elements but having the same framework topology. Recently however, an I U P A C Commission on Zeolite Nomenclature ruled that names consisting of three capital letters w i l l be assigned to designate the structure types o f porous framework materials. The mnemonic codes (which are generally derived from one of the established names of the material type) represent the structures and connectivities within the frameworks and a complete listing of these codes is given in the current on-line edition of the International Zeolite Associations' publication "At las of Zeolite Structure Types"." 5 These structure types do not depend on composition, distribution of the various possible atoms, cell dimensions or symmetry, and should not be confused or equated with actual materials. For example the faujasite framework type is denoted by F A U and describes the framework structure of faujasite, zeolite X , Y and others. Several more examples are given in Table 1.1. 9 Table 1.1 Pore dimensions and dimensionalities of selected zeotype structures (compiled from data listed in reference 17.) Structure Materials Pore System Channel Type Dimensionality^ Diameters [A] L T A zeolite A , Gallophosphate-A, SAPO-42 3 4.1 MF1 Z S M - 5 , Sil icate-1, TS-1 , VS-1 3 5.3 x 5.6 5.1 x 5.5 M E L Z S M - 1 1 , Silicate-2, TS-2 , V S - 2 3 5.3 x 5.4 5.3 x 5.4 M T T Z S M - 2 3 , K Z - 1 , E U - 1 3 1 4.5 x 5.2 A E L A I P O 4 - I I , SAPO-11 1 3.9 x 6.3 M T W ZSM-12 ,NU-13 ,The ta -3 1 5.5 x 6.2 T O N Theta-1, Z S M - 2 2 , K Z - 2 , NU-10 1 4.4 x 5.5 M O R Mordenite, Zeolon 1 6.5 x 7.0 1 2.6 x 5.7 B E A zeolite B 1 7.6 x 6.4 2 5.5 x 5.5 AF I A I P O 4 - 5 , SAPO-5 1 7.3 F A U Faujasite, zeolite X , zeolite Y , SAPO-37 3 7.4 A E T A I P O 4 - 8 , M C M - 3 7 1 7 .9x8 .7 C L O Cloverite 3 13 .2x4 .0 3.8 V F I VPI -5 , AIPO4-54, M C M - 9 1 12.1 t In certain structures, the different channels may be interconnected to yield 2- or 3-dimensional pore systems. 10 Aluminosil icate materials are generally referred to as zeolites or clathrates, while their purely siliceous analogues are known as zeosils and clathrasils respectively. Aluminophosphate molecular sieves are denoted as A I P O 4 S (or sometimes A l P 0 4 - n , where n denotes a specific structure type, but other names are also used) and the materials formed by isomorphous substitution into A I P O 4 S are called M e A P O s or E l A P L O s . Here M e and E l denote the metals or elements (e.g. Fe, T i , S i , Ge, B etc.) which have been introduced into tetrahedral framework positions. 2 GaPOs (Ga and P) and S A P O s (Si, A l , and P) are examples of such materials. 1.1.4 Structural Characterization Methods The main physical techniques used to characterize the structures and properties of crystalline microporous materials are diffraction, microscopy, and spectroscopy. Other methods such as thermal analysis and adsorption studies also provide valuable information about thermal stability, pore sizes, channel structure, and surface area. In recent years progress has been made in the development o f computer modelling software (e.g. packages such as Cerius22) for calculating the energies of framework structures, and properties related to the interactions between guest species and the host framework, such as their preferred locations and diffusion rates. These methods involve predicting the minimum energy configuration of the system being investigated, and the limiting factor at present is the availability o f reliable potential energy functions. Diffraction remains by far the most important technique for determining the atomic arrangements in these crystalline materials. Single crystal diffraction studies using X-rays, electrons, and neutrons are capable of yielding accurate positions for the constituent atoms, but these require single crystals of adequate quality and size, and this can often present a major obstacle because it is extremely difficult to synthesize such large zeolite crystals of sufficient quality. However, the recent availability o f area detectors and increased source beam intensities (e.g. synchrotron beam lines) now means, in principle at least, that smaller crystals may be 11 analyzed. In most cases, recourse must be made to the use of X-ray and neutron diffraction from microcrystalline or powder samples, which yield only limited information. However, Rietveld refinement 2 5 and more recently, the use of so-called "Direct Methods" 2 1 ' have proven to be effective means for structure elucidations. Rietveld refinement requires that a model structure is proposed (based on information such as elemental composition, symmetry, and unit cell dimensions derived from N M R and X-ray diffraction experiments) and then refined, usually with geometric restraints such as acceptable ranges for bond lengths and angles. Notable advances for probing the microstructure of these materials have been achieved in the last few years through the use of Transmission Electron Microscopy ( T E M ) and Scanning Electron Microscopy ( S E M ) . In a few cases these techniques have provided images at close to atomic resolution showing the pore openings and channels, as wel l as crystal defects such as dislocations, site vacancies and stacking faults. These have been reviewed by Thomas. 2 5 Spectroscopic techniques can be used to probe local structural properties such as site symmetries, coordination numbers, and to detect the presence of crystal imperfections, variations in local order, and impurities. Spectroscopic measurements generally provide details about the short-range or local order, which is complimentary to the information concerning long-range ordering obtained from microscopic and diffraction techniques. Some important methods include vibrational spectroscopy (infrared and Raman), X-ray spectroscopy (X-ray fluorescence ( X R F ) , absorption edge fine structure ( A E F S ) , extended X-ray absorption edge fine structure ( E X A F S ) ) , and electron spectroscopy (X-ray photoelectron spectroscopy ( X P S or E S C A ) . The most useful and important spectroscopic technique for characterizing microporous crystalline materials is solid-state nuclear magnetic resonance spectroscopy, since it is capable of providing unique information about both the frameworks and guest species within the void spaces of these materials. In addition it is a non-destructive technique that requires relatively small samples (ca. 100-500 mg) in the form of powders. A review of previous N M R investigations of microporous materials is presented in Section 1.3.2. 12 1.1.5 Structure Related Properties and Applications Molecular sieves have industrially important applications as catalysts, ion exchangers, adsorbents, and in gas separations.' 6 5 The wide range of applications is directly related to their unique structures, and the key to a better understanding of the chemical and physical properties of crystalline microporous materials such as zeolites lies in detailed knowledge o f their framework structures, and the locations of guest species within the channels and cavities. This is the principal goal of many current research efforts, including the investigations reported in this thesis. Each aluminium atom present in a zeolite framework introduces a net negative charge, which is balanced by cations. These cations are exchangeable, and this property is exploited in many of the industrial processes which use zeolites. By far the largest use of zeolites is as water softeners: the propensity of zeolites A and P to effectively remove C a 2 + and M g 2 + cations from "hard" water and replace them with N a + ions means these materials have replaced the potentially environmentally damaging phosphates in many detergents. The application of zeolites as adsorbents, desiccants, and in gas separations stem from their regular arrays of molecular-sized pores and channels. For example, the 4 A openings in the sodium form of zeolite A make it highly efficient desiccant that is used to dry solvents and gases in almost every laboratory in the world, while the C a 2 + exchanged form has 5 A openings and is utilized as a molecular sieve to separate nitrogen and oxygen gas. The hydrophobicity of zeolites increases with the S i / A l ratio, and materials with high sil icon contents have been used to selectively adsorb organic molecules from aqueous media. Probably the most important property o f these microporous materials after their pore size, is their acidity. Both Bronsted and Lewis acid sites may be present in zeolites, and very often these are the active catalytic sites. The acid or hydrogen form of a zeolite (often written H Z , where Z represents the zeolite framework) is obtained by ammonium ion exchange, fol lowed by calcination in air at 500 °C to drive off ammonia gas (Eqs. 1.2 and 1.3): 13 N a Z { s ) + NH4 + ( a q ) <-> NH4Z ( S ) + N a + ( a q ) 1.2 N H 4 Z ( S ) 5 0 0 ° C A 1 R > H Z ( S ) + N H 3 ( g ) 1.3 For zeolites crystallized using a quaternary ammonium cation as template, calcination of the "as-synthesized" material produces the acid form directly. The proton associates with an oxygen connected to a trivalent framework aluminium, thus producing a Bronsted acid site whose proton donor ability greatly exceeds that of amorphous silica-alumina catalysts. Further heating at 550 °C may result in the formation of Lewis acid aluminium sites. There is an extraordinary range of chemistries possible when organic reactants are in contact with zeolites and related mater ia ls / , 2 6 Although small pore (8-ring) zeolites were the first to be exploited as catalysts, it was the medium pore (10-ring) zeolites such as Z S M - 5 which provided the size- and shape-selectivity that revolutionized the oi l industry. The shape selectivity means that only molecules smaller than the aperture of the zeolite pores can reach the internal catalytic sites, and only those reactions with intermediate transition states having geometries capable of being accommodated in the cavities or pores can be formed and diffuse out. These materials are still extremely important in petroleum refining, aromatics processing, and in the production of synthetic fuels and petrochemicals. More recently applications of the larger pore (12 rings and above) molecular sieves such as the A I P O 4 , S A P O and M e A P O types have begun to appear. Isomorphous substitution has also provided new chemical applications including the use of titanium-containing M F I in the presence of hydrogen peroxide to achieve shape-selective ox idat ion/ The ability to tailor the reactivity and selectivity of zeolites and related materials to specific reactions and their characteristic physical properties make them attractive as catalysts. Addit ional benefits are gained from their heterogeneous nature, which means they may be used with a variety of reactor designs and are easily separated from liquid or gaseous reaction 14 products. Environmental advantages arise because they are reusable (although they may need to be regenerated), non-corrosive, and generally non-toxic. 1.2 NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY OF SOLIDS 1.2.1 Nuclear Magnetic Resonance Spectroscopy Over the last 50 years, high-resolution N M R has developed into one of the most powerful and useful techniques available to chemists for the investigation and elucidation of molecular structures, particularly with the availability o f superconducting high field magnets and pulse Fourier transform (FT) spectrometers. The introduction of two-dimensional techniques in the 1970s greatly expanded the kind of information available from N M R studies. Four main features characterize a high-resolution N M R spectrum of the l iquid state (i.e. solutions and isotropic liquids) and provide chemical information. These are: (/) the exact resonance frequencies of the signals (also called the "chemical shift"). These are dependent on the particular nucleus, the strength of the magnetic f ield, and are characteristic of the magnetic, and therefore the chemical, environment o f the different individual nuclei. (ii) the relative signal intensity o f each resonance which is directly proportional to the total number of nuclei undergoing resonance. (iii) the multiplet structure arising from spin-spin scalar coupling. This provides information about the numbers of closely bonded nuclei and on the geometric relationship between them. (iv) the width and line shape of the resonance. This can provide insight into molecular motions. Many of the magnetic spin interactions are averaged to zero or to their isotropic values by the rapid random molecular motions in the liquid state. In the solid-state these interactions can cause severely broadened, relatively featureless, absorption spectra. However, although additional chemical information compared to that available from liquid state spectra is present, it is usually obscured. The primary objective of high-resolution N M R spectroscopy of solid 15 samples is usually to reduce or average these interactions, thereby simplifying the spectra to recover information about the chemical shifts, intensities, and couplings. For structural investigations it is possible to recover the three-dimensional anisotropic information. The fol lowing sections provide a brief overview of the nuclear spin interactions which are important in the solid-state, and also of some techniques useful for obtaining " l iquid- l ike" N M R spectra o f solids. For more detailed treatments o f the theory and practice of solid-state N M R the reader is directed to the texts by Abragam, Ernst et al, Slichter, Engelhardt and Miche l , Mehring, and F y f e / 2 Other useful N M R theory and background can be found in references 33-39. 1.2.2 Nuclear Spin Interactions in the Solid State The interactions for nuclear spins in an applied magnetic field may be divided into five main categories: 5 2 (a) the Zeeman interaction of the nucleus with the applied magnetic f ield. (/j) the chemical shift interaction caused by magnetic shielding from the surrounding electrons. (c) dipolar interactions with other nuclei. (d) scalar coupling with other nuclei. (e) quadrupolar interactions which are present for nuclei with spins greater than 1/2. In the liquid state, rapid molecular tumbling averages these interactions to their isotropic values. However in solids, molecular motions are generally more restricted, and because these interactions are orientation dependent (anisotropic), they usually have significantly larger effects. In Table 1.2 typical magnitudes of the various interactions for 1 3 C nuclei in solids and liquids are compared. A general Hamiltonian, / / m a y be written (Eq. 1.4) which describes the total nuclear spin interactions as the sum of the individual interaction H a m i l t o n i a n s . ' ' 0 T h e subscripts Z, CS, D, SC, Q and K refer to the Zeeman, chemical shift, dipolar, scalar coupling, quadrupolar, and Knight interactions respectively. 16 H — Hz + Hcs + HD + H$c + HQ + HK 1.4 With the exception ofHz, the individual Hamiltonians in Eq . 1.4 can be generalized: Hi = C , . I - f - K 1.5 Here Ci is a constant which varies for different interactions, I is a quantum mechanical operator (with components Ix, Iy and Iz) with the eigenvalues of I 2 being / ( /+ 1). / is the spin quantum number which is often referred to as spin. The angular momentum and thus the spin is h proportional to the magnetic moment u of the nucleus, (X = y — I, where h is Planck's constant. This equation defines the gyromagnetic ratio y. K is either an external magnetic field or a nuclear spin vector. T is a second rank tensor which characterizes the magnitude and directional characteristics of the interaction. Tensors representing the chemical shift, dipolar, scalar coupling and quadrupolar interactions are denoted by <7, D , J , and Q respectively. The interaction of a spin 1/2 nucleus with its local electronic environment is incorporated in the chemical shift interaction, and in cases where the spin quantum number / is greater than 1/2, in the quadrupolar interaction. Spin-spin couplings may be either through-bond or through-space interactions, and these are represented by the scalar and dipolar coupling interactions respectively. Because quadrupolar nuclei and metals were not investigated in the present work the discussion below wi l l not include the quadrupolar and Knight interactions. 1.2.2.1 The Zeeman Interaction The Zeeman interaction is the basis of N M R spectroscopy, and occurs for all nuclei possessing a non-zero spin-quantum number. A s seen from Table 1.2 it is usually far larger than the other interactions (except for some quadrupolar nuclei). This interaction determines both the frequency of observation in a given magnetic f ield, and via the Boltzmann distribution, the 17 Table 1.2 Typical magnitudes of nuclear spin interactions for C in a 4.7 Tesla magnetic field (After reference 42). Spin Interaction Magnitude in Solids Magnitude in Liquids Zeeman 50 M H z 50 M H z Chemical Shielding up to 1 kHz isotropic value Dipolar ~ 15 kHz 0 Scalar ~ 200 Hz ~ 200 Hz Quadrupolar Coupl ing up to - 100 M H z 0 Table 1.3 Important N M R parameters of selected nuclei. (Data from reference 33). Nuclear Isotope Spin Gyromagnetic Ratio y / 1 0 7 rad T 1 s 1 N M R Frequency at 9.4 T / M H z Natural Abundance (%) ' H 1/2 26.7520 400.22 99.985 2 H 1 4.1066 61.40 0.015 , 3 C 1/2 6.7283 100.58 1.108 , 5 N 1/2 -2.7120 40.54 0.37 , 9 F 1/2 25.1810 376.30 100 2 7 A1 5/2 6.9760 104.22 100 2 9 S i 1/2 -5.3188 79.46 4.70 1/2 10.8410 161.92 100 7 9 B r 3/2 6.7228 100.22 50.54 ,27I 5/2 5.3817 80.02 100 18 fundamental detection sensitivity for a particular magnetically active isotope. The interaction of a spin with a static external magnetic f ield Bo can be described by Eq . 1.6: H z = - y , ^-1 B0 1.6 271 The Zeeman interaction is linear with the applied magnetic f ield, with larger separations of the quantized energy levels and correspondingly larger population differences occurring at higher fields, giving increased sensitivity. Different magnetically active isotopes have characteristic gyromagnetic ratios and corresponding resonance frequencies in a given magnetic field strength. Table 1.3 lists some important N M R parameters of selected nuclei o f interest in the present work. Because of their high natural abundances and large gyromagnetic ratios, ' H , 1 9 F , and 3 I P are the most sensitive common nuclei. Isotopic enrichment is often used to enhance the sensitivity of other commonly investigated nuclei such as 1 3 C and 1 5 N which are of low natural abundance as well as having lower gyromagnetic ratios. In the presence of a static magnetic field B0 the spins w i l l align themselves either parallel or antiparallel with the direction of B0. A population difference (defined by the Boltzmann populations of these two levels) creates a net macroscopic magnetization M aligned with B0. If this magnetization is tilted by some means so as to make an angle G with B0, it w i l l precess around B0 at a frequency oo0 = I y IB0 rad s"1. This frequency is called the Larmor frequency, and is in the range 10 7-10 9 Hz, which falls in the radio-frequency (r.f.) domain. The practical method for tilting the magnetization away from its equilibrium orientation is to apply an r.f. field B\ « Bo, which is perpendicular to B0 and rotates around BQ with frequency co0. To simplify the discussion of these effects, a change of reference frame from a static Cartesian axes system (x, y, z) to one that rotates about B0 at the frequency of the applied r.f. field (denoted by x', y', z') is used. In this rotating frame of reference, the magnetization w i l l precess around B\ at frequency coj = I y I B\, and i f B\ is applied for a time t, the magnetization wi l l be tipped away from the direction of B0 by an angle 9 = C0| t. After B\ is switched off, the 19 magnetization wi l l precess around Bo- In practice the sample is surrounded with a coi l (connected to an appropriately tuned r.f. circuit) which can produce an r.f. f ield B\ (a "pulse"). The coi l also detects the induced electromagnetic f ield fol lowing a pulse, which is then amplif ied and observed as the free-induction decay (FID) of the N M R signal. Fourier transformation of the FID yields the N M R spectrum (Figure 1.4). The rotation of the net magnetization by the pulse can be controlled by varying either the power or the time for which it is applied, and a pulse which causes the orientation of the magnetization to change by 90 degrees is called a n/2 pulse. The relative phase of the applied field, which determines the direction that the magnetization is tipped can also be controlled, and the usual convention is that a n/2 pulse applied along the positive x' axis is denoted as (TT/2)x and rotates the magnetization so that it lies along v ' (Figure 1.5(a)). The relationship between the time and frequency domains, coupled with the relatively broad frequency ranges that need to be excited by a pulse in solid-state N M R , means that the strength of B\ must be quite high so that typical n/2 pulses are less than 15 us. The field strength of a pulse can be deduced from the frequency at which the magnetization is rotated. For example a pulse which takes 20 ps to rotate the magnetization of spin 1/2 nuclei through 360 degrees corresponds to an r.f. field strength of 50 kHz. The ability to control the phases and amplitudes of the pulses, as well as the phase of the receiver, is crucial for the successful implementation of many N M R experiments, and schemes that cycle these phases are used to suppress instrumental artifacts and to select specific coherence pathways. 1.2.2.2 The Chemical Shift Interaction The chemical shift interaction is related to the screening or shielding of the applied magnetic field by the fields induced from the motions of the electrons surrounding the nucleus. The Hamiltonian which describes this interaction is given in Eq. 1.7. 20 FID Spectrum F igure 1.4 Free induction decay (FID) signal and resulting spectrum (real part only) fol lowing Fourier transformation. F igure 1.5 Illustration of the phase shift of the net magnetization induced by application of: (a) 7T /2 x , and (b) 7i/2_y r.f. pulses. The direction of the external magnetic field (B0) and the r.f. pulse (B\) are shown. 21 Hcs = Y i I • a • U 0 1.7 In a suitable axis frame (the principal axis system), a becomes diagonal, with principal (diagonal) elements o K , Oyy, and a H . Because rapid molecular motions occur in liquids, the three-dimensional nature of the interaction (which potentially contains diagnostic structural information) is averaged to its isotropic value viso = ( a x x + a^ , + a^ ) / 3, and a single N M R resonance is observed at the isotropic chemical shift 8Jso. Generally in solids, molecular motions do not completely average the chemical shift anisotropy ( C S A ) . For single crystals, sharp lines wi l l be observed whose resonance frequencies depend on the orientation of the crystal (and therefore the nucleus in the molecular coordinate system) relative to the applied static magnetic f ield. In the case of microcrystalline (powder) samples, every crystallite orientation is possible, and each has its own resonance frequency. The resulting spectrum is the sum of all o f these resonances, and is thus very significantly broadened. However this may not be the only interaction responsible for broadening the spectra (see below). The exact shape of the absorption observed in the spectrum wi l l depend on the principal elements of the chemical shift tensor/ ' The chemical shift interaction has a linear dependence on the strength of the applied magnetic f ield, and wi l l thus make a larger contribution relative to the dipolar interaction (which has no field dependence) at higher fields. The range of frequencies covered by the chemical shift broadening df a single resonance in solids is similar to, or larger than, the whole range of isotropic chemical shifts values found for liquids. 1.2.2.3 The Dipolar Interaction The dipolar interaction is the interaction between the magnetic moments of nuclear spins; spin / experiences the magnetic field of spin S with the Hamiltonian given by: HD = — I • D • S 1.8 71 22 In liquids the fast random molecular motions yield an isotropic value of zero for the dipolar couplings (because D is a traceless tensor). In solids, however, molecular motions are more restricted, and so the dipolar interactions are usually not averaged to zero. The dipole-dipole interaction is an entirely through-space coupling, and can be either homonuclear (e.g. ' H - ' H ) or heteronuclear (e.g. ' H - 1 3 C ) in nature. The magnitude of the dipolar coupling is dependent on the gyromagnetic ratios, the distance between the spins, and the orientation of the internuclear vector with respect to the applied static magnetic f ield. Unl ike the chemical shift interaction, the magnitude of the dipolar interaction is independent of the strength of the applied magnetic f ield. For a pair o f heteronuclear nuclei / and S the Hamiltonian can be written as: J J H E T E R O = £ h ( 3 c ( ) s 2 ft _ ] } j Q 9 471 where D is the dipolar coupling constant (in Hz) defined by: 167c 3 r 3 Po = 4TC x 10~7 kg m s~2 A~ 2 is the permitivity of free space, r is the distance between the two nuclei (in metres), the gyromagnetic ratios y/ and js have units of rad s - 1 T~', and 9 is the angle between the internuclear vector and the direction of the applied static magnetic field. The strong inverse dependence of the dipolar coupling on the internuclear distance (D <x 1 / r 3 ) means that the magnitude of the dipole-dipole interaction decreases rapidly with increasing separation of the nuclei, and thus only neighbouring nuclei w i l l experience a strong coupling. This distance dependence can be used to accurately determine distances between pairs of nuclei. Because dipole-dipole interactions are directly proportional to the gyromagnetic ratios of the two nuclei, dipolar couplings wi l l be more important for systems containing nuclei with large gyromagnetic moments such as *H and 1 9 F . Conversely, exchange of abundant spins having 23 large gyromagnetic ratios by an isotope with a lower y (e.g. replacement of *H by 2 H ) can be a very effective method for reducing dipolar broadening. 1.2.2.4 The Scalar Coupling Interaction Scalar coupling, also called ./-coupling, arises from indirect coupling between spins, and is mediated by the bonding electrons. L ike the dipolar interaction, the scalar interaction can be either homo- or heteronuclear in nature, but it is a through-bond, rather than a through-space, spin-spin coupling. The multiplet structure arising from ./-couplings between two or more spins, and the magnitudes of these couplings, often provide very useful information about the conformations and structures of molecules. The Hamiltonian for the heteronuclear scalar interaction between spins / and S can be written as: Hsc = — I j • S 1.11 271 Scalar couplings are independent of the magnitude of the applied magnetic f ield, and are usually smaller than the other interactions in solids (see Table 1.2), by which they are often overshadowed in the solid-state. The magnitude of the scalar coupling drops rapidly as the number of intervening bonds increases, but is very similar in liquids and solids, only differing i f the molecular geometry is altered with the change of state. 1.2.2.5 Summary of Interactions The relative importance of the different nuclear spin interactions which contribute to N M R spectroscopy in the solid state w i l l depend on the nucleus being observed, the static magnetic field strength, and the particular system being studied. The critical feature o f these interactions is their orientational dependence, and the relatively restricted motions in solids means they are usually not averaged to their isotropic values. Although the N M R spectra of 24 solids may have linewidths of up to several thousand hertz, they potentially contain more information than solution spectra because the individual principal components of the various tensors may be determined, and these describe the three-dimensional character o f the interactions. Usually however, N M R spectra of solids must be simplif ied by obtaining higher resolution i f structural information is to be readily extracted, and the next section introduces techniques developed for this purpose. 1.2.3 Techniques for Obtaining "High-Resolution" N M R Spectra from Solids The orientation dependence of nuclear spin interactions in the solid state means that N M R spectra of powdered solids can have linewidths of several kHz. Two main approaches are used to average or reduce these in order to obtain high resolution spectra of powders. The first kind involves the use of mechanical reorientations or rotations of the sample, and this includes the techniques of Magic Angle Spinning ( M A S ) , Dynamic Angle Spinning (DAS) and DOuble angle Rotation (DOR) . These techniques work by averaging the spatial parts o f the spin Hamiltonians, and have recently been reviewed by Chemlka and Zwanz iger / 5 D A S and D O R are specifically used for quadrupolar nuclei, where the second order terms need to be averaged. The second approach is to reduce or average the spin part o f the Hamiltonian through the use of r.f. pulses. This may be further divided into techniques used for decoupling hetero- and homonuclear interactions, which may be achieved by using high power decoupling and multiple pulse schemes, respectively. Mult iple pulse sequences including W A H U H A / 4 M R E V - 8 / j and B R - 2 4 / 6 rely on carefully chosen cycles of pulses (and the phases of these) to average the dipolar interactions to zero. The chemical shift anisotropy is scaled but not removed by these multiple pulse techniques/ 7 Combinations of mechanical reorientation and pulse techniques can be used for homonuclear decoupling (e.g. Combined Rotation and Mult ip le Pulse Scheme or C R A M P S / * M A S with h igh power decoupling is by far the most common technique for 25 heteronuclear decoupling. The fol lowing discussion wi l l be restricted to high power heteronuclear decoupling and M A S as these were the techniques employed in this research. 1.2.3.1 High Power Decoupling For most dilute spin-1/2 systems (e.g. those having a low concentration of magnetically active nuclei such as 1 3 C and 2 9 S i which are of low isotopic abundance), the major source of linebroadening in the solid-state N M R spectrum is heteronuclear dipolar coupling to other abundant spins such as ' H and 1 9 F . It is possible to eliminate these heteronuclear interactions by applying a strong r.f. f ield at the Larmor frequency of the abundant spins. This resonant irradiation causes rapid transitions of the abundant nuclei between their two spin states, with the result that their average contribution to the effective local f ield is zero, and so no net heteronuclear coupling interactions are observed for the dilute nuclei. To be effective, the strength of the applied r.f. f ield must be such that the frequency of the abundant nuclei spin-flips is comparable to (or preferably exceeds) the heteronuclear coupling frequency. In typical systems this requires r.f. fields of the order of gauss, requiring amplifier powers in the range of hundreds of Watts compared to the ca. 50 W decoupling fields used in l iquid state spectroscopy. Another consideration is that these decoupling fields often need to be applied throughout the entire pulse sequence and the data acquisition, meaning that the amplifiers must be capable of providing stable r.f. fields for hundreds of milliseconds. 1.2.3.2 Magic Angle Spinning A s discussed above, chemical shift anisotropy, dipolar and quadrupolar interactions can result in linebroadening for solids. These interactions have a first-order orientational dependence which contains the term (3 cos 2& - 1), where S is the angle between a specific molecule-fixed vector and the applied static magnetic field B0. For the dipole-dipole interactions it is convenient to use the internuclear vector r. In solution, fast, random molecular tumbling averages the value 26 of (3 cos '9 - l ) t o zero. Independently, both Andrew"' 9 and L o w e 5 0 realized that time-dependent motions could be imposed on a solid to mimic or approximate the isotropic molecular motions in liquids. A s an example we wi l l consider the dipolar interaction. Rotation of a solid sample about an axis at an angle 9 m with respect to B0 causes the vector r to trace out a conical path described by the angles a and 8 as shown in Figure 1.6. The average value of (3 cos 2 9 - 1) over the conical path is given by Eq. 1.12, where cor is the angular velocity of the rotation (sample spinning), and the brackets < > indicate that it is an average over the rotation. 5 ' < 3 c o s 2 9 - l > = ^ ( 3 c o s 2 9 m - l ) ( 3 cos 2 (3-1) 3 + — [sin29m sin2B cos(co rt + a ) + s i n 2 9 m s in 2 p cos(2co rt + a)] 1.12 In a rigid solid B wi l l be constant for a given crystal in the spinner. However for a powder sample each individual crystallite can be at a different (random) orientation with respect to B0 and s o p e [0, T C ] . A sufficiently high value of cor (i.e. "fast" spinning compared to the frequency of the interaction) w i l l average the time dependent parts cos(2oo rt) and cos(co rt) to zero. 5 7 The 1 , — (3 cos 9 m -1) term acts as a scaling factor, and the angle 9 m is under the control of the experimentalist. If 9 r a = c o s " 1 « 54.74°, then (3 c o s 2 9 m - 1 ) = 0, and so <3 cos 2 9- l> = 0 for all crystallite orientations (all values of B). This improves the resolution in the N M R spectrum by eliminating broadening arising from the chemical shift anisotropy as wel l as homo- and heteronuclear dipole-dipole interactions. The angle 54.74° is called the "Mag i c Angle" , and spinning samples about an axis inclined at the magic angle to the static magnetic field is referred to as Magic Angle Spinning or M A S . " " However, the sample rotation rate required must be greater than the frequency of the dipolar couplings which need to be averaged to zero so spinning speeds of the order tens of kHz are usually required. A t present speeds of 2-15 kHz are routinely 27 Figure 1.6 Definitions of the angles used to describe the orientation of the IS internuclear vector in a powder sample undergoing magic angle spinning. 9 m is the "Mag ic Ang le" , r is the IS distance, and 9 is the angle between the IS vector and the external magnetic field BQ. 28 available, and for small diameter spinners (< 5 mm), frequencies in excess of 30 kHz can be attained. The problem of homonuclear broadening is eliminated i f the nucleus being studied is of low natural abundance (e.g. 1 3 C , 2 9 S i , see Table 1.3) since the N M R active nuclei are dilute in the sample. For nuclei o f high isotopic abundance it is possible that physical dilution is achieved due to the nature o f the sample, or that it can be introduced through isotopic exchange as is often done for hydrogen nuclei (i.e. exchange of ' H by 2 H ) . For dilute nuclei where homonuclear interactions are weak, fast M A S and high power decoupling can be used to average the dipole-dipole interactions to their isotropic value. Spinning the sample at frequencies lower than the frequency width of the chemical shift anisotropy powder pattern does not completely average the time dependent parts of Eq. 1.12. This produces a series of "spinning sidebands" in the spectrum, centered at the isotropic chemical shift, and spaced at multiples of the spinning speed. The intensity envelope of these spinning sidebands mimics the chemical shift anisotropy observed in the spectrum of the static sample (the "powder pattern"). Figure 1.7 illustrates these effects. Since the chemical shift anisotropy is proportional to the strength of the applied magnetic field, the sideband pattern wi l l be larger at higher magnetic fields for a given spinning rate. Information about the full anisotropy (averaged by M A S ) is retained in the sideband pattern, and appropriate analysis of the sidebands can be used to determine the principal tensor components, but not their or ientat ion/ 2 Methods for suppressing these sidebands under M A S have also been reported/ 5 w A s discussed above, M A S is capable o f averaging some of the anisotropic interactions to their isotropic values. This is a time-average over each complete rotation of the sample, and the magnitude of a given interaction is not equal to the isotropic value at every instant during the rotor cycle. The anisotropic parts are still present and result in dephasing of the spins immediately fol lowing the application of an r.f. pulse. However, at the end of each rotor period fol lowing the pulse, all of the spins w i l l be back in their original positions. This refocusing of the 29 e) v r = 2000 H z JV v r = 900 H z Stationary (a) 2000 1000 1 r 0 5( 1 3 C) H z •1000 -2000 ure 1.7 C ( H decoupled) spectra obtained for a powder sample of ferrocene, (C 5H 5)2Fe The spectra were recorded: (a) for a stationary sample, and (b)-(e) using M A S at the rotation speeds v r indicated. Adapted from reference 56. 30 spins after each rotor cycle is often referred to as a "rotational echo". Because the majority of the experiments used in the research reported here were performed under M A S conditions and relied upon the dipolar interactions or involved the determination of the dipolar coupling, the effects of M A S on the dipole-dipole interactions wi l l now be discussed. Spinning the sample sufficiently fast about an axis inclined at the magic angle averages the dipolar coupling to zero over a complete rotor cycle. However the dipole-dipole interaction does not vanish - in fact only those spin pairs whose internuclear vectors are parallel to the spinning axis wi l l have a dipolar coupling of zero at all times during a rotor cycle . For al l other orientations the dipolar coupling is still present and changes continuously during the rotor period. Eq. 1.13 gives the time dependency for the dipolar coupling under M A S / 7 ooD(a, P, t) = s in 2 p cos2(cort + a ) - V2 sin2p cos(co rt + a ) ] 1.13 Here a and P are the azimuthal and polar angles respectively, and define the position of the internuclear vector as shown in Figure 1.6. The value of the dipolar coupling has a periodic dependence on the rotor cycle, and since only the time average of the dipole-dipole interactions over each cycle are zero, the dipolar coupling can still be utilized to investigate connectivities and measure distances between nuclei. Solid-state N M R techniques specifically designed for this purpose (e.g. R E D O R and T E D O R ) are discussed in detail in Chapter 3. 1.2.3.3 Cross Polarization For dilute spin-1/2 nuclei, direct one-pulse N M R experiments often suffer from two disadvantages: inherently low sensitivity and the requirement of long recycle delays due to the relatively long T\ relaxation times. The cross polarization (CP) technique, first introduced by 31 Pines, Gibby and Waugh, can often eliminate these disadvantages. During the C P experiment spin polarization, and thus net magnetization, is transferred via dipolar interactions from abundant I spins (usually 'H) to the dilute S spins (e.g. I 3 C , l 5 N , or 2 9 S i ) , which are then observed. The C P experiment provides enhancement of the S spins magnetization up to a theoretical maximum factor given by the ratio of the gyromagnetic ratios of the two spins, j/1 ys, which can be as large as 4 for ' H - 1 3 C , and 5 for ' H - 2 9 S i . The recycle delay for the C P experiment is determined by the 7\ of the (abundant) / spins, and these are often much shorter than those of the observed (dilute) nuclei. This means that more FIDs can be accumulated in a given time period, resulting in improved signal to noise in the final C P spectrum compared to a one-pulse experiment. Figure 1.8 shows the pulse sequence used to accomplish the magnetization transfer from I to S spins and a representation of the behaviour of the magnetization vectors during the C P experiment. Initially both / and 5 spins are at their equilibrium magnetization distributions. A n/2 pulse along x' is applied to the / spins, rotating the magnetization along the y ' axis in the rotating frame. The application of an on-resonance r.f. f ield with strength B\i along y ' spin-locks the / spin magnetization along this axis, which it precesses about with frequency ©i / = ji B\i. During this spin-locking pulse, an r.f field B\S is applied (along the x' axis) to the S-spins, causing them to rotate about the y ' axis with angular frequency ©is = ys B\s. The time period for which both r.f. fields are applied is known as the "contact t ime". During this contact time, x, net S spin magnetization builds up along the direction of the applied B\s f ield. Fol lowing the contact time, the B\s r.f. field is switched off and the S spin FID signal is recorded. The / spin r.f. field is left on during the acquisition and acts as a decoupling field. The process is repeated after an appropriate recycle delay, with suitable phase cycl ing of the pulses to remove instrumental and phenomenological effects. For efficient magnetization transfer to occur during the contact time, the amplitudes of the r.f. fields applied to the / and S spins must be adjusted so that the Hartmann-Hahn matching 32 (a) Tt/2, [ SPIN L O C K D E C O U P L E R E C Y C L E D E L A Y 4 T h * I P A C Q U I R E F ID (b) 71/2. Apply Z?i/ to spin lock / spins / spins precess around y' axis z ' Apply matched r.f. field Bis to 5 spins S spin magnetization builds up in direction 2 of Bis during x B Figure 1.8 (a) Pulse sequence for the Hartmann-Hahn spin-locked cross polarization experiment, (b) Vector representation showing the spin locking of the / spins and the build-up of the S spin magnetization during the contact time x. 33 condition is met. For spin-1/2 nuclei undergoing M A S , the Hartmann-Hahn match is described b y E q . 1.14:6 0 ysBls = yiBu±f(x)I 1.14 where <ar is the spinning frequency a n d / = 1 or 2. If the Hartmann-Hahn condition is satisfied then the Zeeman level separation in the rotating frame are equal for both the / and S spins, and therefore mutual spin-flips can occur. The mutual spin-flipping allows the transfer o f polarization between the two spin systems via IS dipolar interactions. The spin-locking method described above is not the only means for establishing cross polarization, and some other techniques are discussed by Slichter, 2 9 Pines et al/8 and others.* Historically, C P has been used to transfer spin polarization from abundant spins to dilute spins, with protons being used almost exclusively as the abundant spins. There have been some examples where other nuclei, particularly 1 9 F , have been used.61'63 Schaefer and co-workers'^ reported magnetization transfer between 1 3 C and l 5 N in isotopically enriched materials and successfully demonstrated elegant triple-resonance "Double Cross Polarization" experiments involving initial polarization transfer from ' H to 1 3 C followed by a second magnetization transfer to 1 5 N . Recently Fyfe et al. demonstrated the first C P experiments involving polarization transfer from quadrupolar nuclei ( A l ) to spin-1/2 nuclei ( Si and P ) . ' Several reviews of C P experiments involving less common pairs o f nuclei have been published. 1 5 7" 6 9 Further details o f the cross polarization experiment are discussed Chapter 3 and reference 70. 1.2.4 NMR Relaxation Processes The presence of molecular motions causes a fluctuation of the anisotropic magnetic interactions that provides a well-defined relaxation mechanism for the nuclei v ia modulations of the spin interactions. 7 ' Shielding anisotropy, scalar and spin rotation interactions, dipole-dipole interactions and interactions with unpaired electrons can all provide relaxation pathways under 34 the appropriate conditions. The most important relaxation mechanism in both homo- and heteronuclear spin systems in the majority of situations is via dipole-dipole interactions between the nuclei/" 5 The measurement of relaxation times is a powerful technique for the detection and quantification of molecular motions. The three relaxation times which are commonly measured wi l l be briefly discussed below. 1.2.4.1 Spin-Lattice Relaxation Time (Ti) Spin lattice relaxation is the process by which a population difference between two spin states returns to its equilibrium value after a perturbation. This is assumed to be a first order kinetic process which is exponential in nature and is described by Eq. 1.15. M0 is the equilibrium magnetization, and T\ (units of seconds) is the reciprocal of the kinetic rate constant which is referred to as the spin-lattice relaxation time. dMz (M-M0) z- = - - — z - — 1.15 dt r, The name spin-lattice relaxation is derived from the fact that the process involves a transfer of Zeeman energy from the "exci ted" spins to the surrounding environment or "lattice." Because spin-lattice relaxation involves the restoration of magnetization along the z-axis it is sometimes referred to as " longitudinal" relaxation. Five times T\ after a perturbation more than 99% of the magnetization is recovered. The Inversion-Recovery experiment is commonly used to measuring T\ is (pulse sequence: n - x - n/2 - acquire - recycle delay). T is determined from the variation of the signal intensity as a function of the delay x. A disadvantage of the Inversion-Recovery experiment is that some prior knowledge of the approximate T values is required to ensure that the recycle delay between successive scans is long enough to permit the magnetization to recover 35 sufficiently for a quantitative determination. For solids T\ can be of the order of seconds to hours which can mean very long recycle delays are needed. The use of cross polarization can dramatically improve the efficiency of the Inversion Recovery experiment through increased sensitivity (up to 4 in the case of ' H - 1 3 C ) , and because the recycle delay during a C P experiment w i l l be determined by the (usually) much shorter T\ o f the abundant spins. 7 2 1.2.4.2 Spin-Spin Relaxation Time (T2) When a n/2 pulse is applied to an ensemble of spins initially at equilibrium in a static magnetic f ield, the net z-magnetization is rotated into the x-y plane. Fol lowing this perturbation, spin-spin relaxation occurs via the exchange of spin energy brought about by mutual spin-f l ipping of the spin-states of different nuclei, and by dephasing that occurs due to inhomogeneities in the magnetic f ield. These spin-flips change the net magnetization along the x-and v-axes [Mx and My respectively), but do not change the total Zeeman energy of the spin system. Because this relaxation occurs in the x-y plane it is sometimes also called "transverse" relaxation. Assuming that we can describe this process as exponential, we can define a time constant T2 which is the reciprocal o f the first order kinetic rate constant governing the spin-spin relaxation in a perfectly homogeneous magnetic field (Eq. 1.16). A similar expression can also be written for My. Any inhomogeneity in the magnetic field w i l l cause the relaxation to proceed more rapidly, and dMx 1.16 dt the time constant T2* < T2 is used to denote the relaxation time in the presence of such inhomogeneities. 36 A spin-echo experiment (TI /2 - x - n - x - acquire - recycle delay, Figure 1.9(a)) can be used to measure T2. The initial n/2 pulse tips the magnetization into the x-y plane, then after a time x, a n pulse is applied which inverts the direction of the dephasing. This causes the spin-coherence to be refocussed, producing an "echo" at time 2x (Figure 1.9(c)). The T t -pu lse also refocusses the chemical shifts and the effects of any inhomogeneities in the applied static magnetic field Bo- In practice T2 is usually determined using the Carr-Purcel l -Meiboom-Gi l l ( C P M G ) sequence which generates a train of echoes separated by 2x, whose peak intensities decay with time constant T2. The decay of the individual FIDs is determined by T2 (Figure 1.9(b)). For solid samples under M A S conditions, it is desirable to chose the delays between 7 t pulses to be integral multiples of the rotor period x r = l /v r , (v r is the spinning frequency of the sample in Hz) to ensure that the dipolar interactions and chemical shift anisotropy are properly averaged to zero for each experiment. Cross polarization can also be used to improve the efficiency of the Spin-Echo experiment. 1.2.4.3 Spin-Lattice Relaxation Time in the Rotating Frame (Tlp) A s described above, spin-spin relaxation as described by T2 normally occurs fol lowing a 7t/2-pulse ; however i f another r.f. pulse which has its phase changed by 90° is applied immediately after the initial pulse, a different situation arises. In the rotating frame an initial n/2 pulse applied along x' w i l l rotate the magnetization from z' and generate a net magnetization a l o n g / ' . If a second pulse is applied along y' (i.e. the phase of the applied r.f. f ield B\ is shifted by 90°) then the magnetization wi l l precess about B\ (in the rotating frame) rather than decay due to T2. Because this second phase-shifted pulse effectively " locks" the magnetization along the axis parallel to B , it is called a "spin- locking" pulse, and while this B t r.f. field is applied the spins are said to be "spin- locked". However this spin-locking B\ f ield also acts as a static magnetic field in the rotating frame, and relaxation analogous to conventional spin-lattice 37 (c) z' i Apply 7i/2x pulse z- Direction reversed t — T Apply 7ty pulse t = 0 Spins dephase in x'-y' plane Spins refocus / p to form echo S " \ S ~~y' t = 2x Figure 1.9 The spin-echo pulse sequence showing: (a) the timing of the pulses, and (b) the decay and formation of the echo of the free-induction decay (FID) signal. The FID decays with a time constant T2* (< T2), while the echo amplitude decays with a time constant T2 (the true spin-spin relaxation time), (c) A vector representation showing the progressive dephasing and the refocussing of the transverse magnetization spin isochromats during the spin-echo sequence. 38 relaxation occurs, with characteristic time constant T l p . Spin-locking is an essential component o f the C P technique used for solid-state N M R , and thus Tip is an important parameter in the analysis o f C P experiments. To measure T\p the spin locking pulse is applied for a variable time x after which the FID is detected. The variation of the observed signal intensity I with x allows T\p to be determined from Eq. 1.17 where I0 is the ful l signal obtained when x = 0. I = Io exp ( \ x 1.17 1.2.5 Internuclear Distance Measurements by Solid-State N M R The combination of high power decoupling and M A S usually provides the necessary resolution to obtain chemical and structural information from dilute spins in solids. However during M A S the heteronuclear dipolar interaction is averaged to zero during each complete rotor c y c l e 5 7 J i and thus in its simplest form, the use of M A S precludes a direct measurement of D. Several techniques for measuring heteronuclear distances from determinations of the heteronuclear dipolar coupling have been reported. These include Spin-Echo DOuble Resonance (SEDOR) , 7 ^ Rotational Echo Triple ResOnance ( R E T R O ) , 7 5 Rotational-Echo DOuble Resonance ( R E D O R ) / 7 Transferred Echo DOuble Resonance ( T E D O R ) , 7 6 and others. 7 7 Techniques which utilize the homonuclear dipolar interaction to obtain information about internuclear distances between spins in solids possessing the same gyromagnetic ratio have been devised. These include R F Driven Dipolar Recoupling ( R F D R ) , 7 S Dipolar Recovery at the Magic Angle ( D R A M A ) , 7 9 Simple Echo Excitation for Dephasing of Rotational Echo Amplitudes ( S E D R A ) , * 0 Dipolar Recoupling with a Windowless Sequence ( D R A W S ) , and others. " These have been recently reviewed by Bennett et a / . t o 39 With the exception of S E D O R , all o f the techniques listed above were explicit ly designed to function under M A S conditions, and with appropriate analysis to allow the magnitude of the dipolar coupling, D to be measured. Because D is inversely proportional to the third power of the heteronuclear distance, r (Eq. 1.10), these experiments are capable of providing considerable insight into molecular structures. Moderately accurate values of dipolar couplings can yield very accurate values for the corresponding internuclear distances. Whi le the most unambiguous distance measurements wi l l come from experimental systems where the heteronuclei / and S interact as isolated spin pairs, these techniques also permit the discrimination between different structural models for complex systems. To date the most successful techniques for determining reliable (and accurate) measurements o f the heteronuclear dipolar coupling for isolated spin pairs seem to be R E D O R and T E D O R . Cross polarization also depends on the heteronuclear dipolar interaction, and can in principle be used to obtain heteronuclear distances. " These three methods were used extensively in the research presented in this thesis, and the reader is referred to Chapter 3 for detailed descriptions of the theory, pulse sequences and calculations used to extract distance information. 1.3 INVESTIGATIONS O F Z E O L I T E F R A M E W O R K S AND G U E S T SPECIES The use of diffraction techniques, solid-state N M R , and computer modell ing to determine framework structures and investigate the guest species within the channels and cages of molecular sieve materials w i l l be outlined in the fol lowing sections. Potential problems related to the application, and reliability o f the various methods wi l l also be discussed. 1.3.1 Structure Determinations by Diffraction Techniques A s discussed in Section 1.1, there is considerable interest in investigating the detailed three-dimensional lattice structures of zeolites and related materials, and locating guest species 40 within them. Although these materials are normally highly crystalline, the structural information obtainable from X-ray diffraction measurements is often severely limited for the reasons outlined in Section 1.1.4. In light of these difficulties, it is remarkable that several hundred framework structures have been solved. ' 6 However, there is relatively little direct experimental information regarding the exact location of the various guest species within the channels and cages of the microporous frameworks. A few structures have been solved for as-synthesized microporous materials where the location of the organic template has been determined: however this is not always possible, and sometimes the results are ambiguous. In general, even in cases where the framework structure is known, it is usually not possible to locate the occluded guest species. To date, there have only been six detailed single crystal structures which locate sorbed organic guest molecules (other than templating species) in the framework, all involving the M F I (ZSM-5) framework. ' 9 ' 2 0 , 8 9~ 9 2 There have been some powder X-ray and neutron diffraction investigations which have tried to locate ionic templating species or sorbed organic species, but often there is disagreement between the various studies. For example, the structures of the host-guest complexes formed by benzene in zeolite Y , and pyridine in zeolite L have been determined from neutron powder diffraction studies, 9 5 9 7 and several groups have attempted to locate /(-xylene or />-dichlorobenzene in Z S M - 5 . 9 5 However in the case of the /?-dichlorobenzene in Z S M - 5 , the location proposed from the powder data was not the same as found later by a more reliable single crystal s tudy. 2 " 8 9 Structural determinations of such host-guest systems can also be complicated by the fact that the structure can depend on both the temperature and the number of the guest molecules sorbed per unit ce l l . 9 6 " " ' 5 The sorbed species may be disordered or quite mobile at ambient temperature. Furthermore, sorbates of a similar size and shape may show powder diffraction patterns with peaks at virtually the same 26 values, but large differences in the peak intensities. Such a case was observed by Fyfe et al. for several organic sorbates in Z S M - 5 . 9 7 ' 0 2 The observation of intensity differences in the X-ray powder patterns implied that the sorbates are 41 more or less ordered (i.e. they are located at specific sites within the framework), since disordered guest molecules would only contribute to diffuse scattering, and this was later confirmed by single crystal structure determinations.' 9 ' 2 0 ' 8 9 Recent advances in the use of computer modell ing methods have meant that these techniques are beginning to correctly predict both the framework structures and the locations of guest species (see Section 1.3.3). A t present however, these calculations are not always reliable, and other techniques capable o f providing detailed structural information need to be developed. A s wi l l be outlined in the next section, solid-state N M R is capable o f providing information which is extremely helpful in structure elucidations of microporous materials and their complexes with guest species. 1.3.2 NMR Studies of Zeolite Frameworks and Guest Species Several reviews which discuss the application of solid-state N M R to microporous materials have been published including the comprehensive book by Engelhardt and M i c h e l , 3 0 and shorter reviews by Fyfe et al.,'04'105 and o the rs . ' 0 6 ' 0 7 Vir tual ly all o f the atoms making up the frameworks of zeolites and related microporous materials have NMR-ac t i ve nuclei, and can thus be studied by solid-state N M R . These include, among others, n B , 1 7 0 , 2 7 A 1 , 2 9 S i , 3 1 P , and 7 l G a . In addition, ' H nuclei may be present in the framework structure as hydroxy 1 groups. Many of the guest species which can occupy the channels and cages in molecular sieves are also amenable to investigation by N M R . For instance, the templating species and sorbed organic molecules contain ' H , l 3 C and sometimes l 5 N , and the majority o f the exchangeable charge-compensating cations have N M R active isotopes (e.g. L i , N a and Cs). This section wi l l briefly review the information that can be obtained from one and two-dimensional solid-state N M R investigations of the frameworks and the guest species. 42 1.3.2.1 One-Dimensional NMR Studies of Zeolite Frameworks The important nuclei that are commonly present in the framework structures of microporous materials (and their natural abundances) are: ' H (100%), 1 7 0 (0.04%), 2 7 A1 (100%), 2 9 S i (4.7%), and 3 1 P (100%). Other nuclei such boron, gall ium, germanium, titanium, cobalt, and vanadium, which have NMR-act ive isotopes may also be present in certain cases. M A S usually yields particularly simple N M R spectra for the spin-1/2 nuclei such as 2 9 S i and 3 I P . The N M R spectra of the quadrupolar nuclei are much more complex, but are capable of providing additional information regarding their local environments. The use of high magnetic fields, ultrafast spinning, and techniques such as Dynamic Angle Spinning and Double-Angle Rotation simplifies the N M R spectra of these quadrupolar n u c l e i / 5 ' ' 0 5 Although oxygen is a very important component of the framework, its extremely low natural abundance means that isotopic enrichment must be used i f it is to be profitably studied by N M R , and thus relatively little research has been done on it. In a few cases, D A S N M R of n O-enr iched samples has been able to resolve crystallographically distinct framework oxygen si tes. ' 0 9 The overwhelming majority of solid-state N M R studies of molecular sieve frameworks have been devoted to "H , 2 7 A 1 , 2 9 S i , and 3 I P and these wi l l be discussed below. The 2 7 A1 M A S N M R spectra of aluminosilicates generally show two types of resonances related to the usual tetrahedral and octahedral coordination geometries of A l within these materials. The tetrahedrally coordinated A l is actually in the framework, and has a chemical shift in the range 50-65 ppm (referenced to aqueous [A1(H 2 0) 6 ] 3 + ) . In virtually all cases, only a single resonance is observed for these tetrahedral aluminiums, and so crystallographically inequivalent Al-sites are not distinguishable. Only in the case of zeolite omega have crystallographically inequivalent Al-sites been resolved." 0 The octahedrally coordinated A l (which usually gives rise to a peak at about 0 ppm) is due to "extra-framework" aluminium, that is, aluminum species within the pores, and not part of the framework. The high sensitivity o f 2 7 A l N M R , and the ability to readily distinguish the two types of A l , have meant t h a t 2 7 A l N M R has been extensively used 43 to study the dealumination of zeolite lattices, and to investigate the efficiency of various treatments designed to remove any extra-framework A l species fol lowing dealuminat ion. 3 2 , " h The 2 7 A1 M A S N M R spectra of A l P 0 4 s often show single resonances due to tetrahedrally-coordinated (to four P atoms because there is strict A l / P lattice alternation in these materials), Upon hydration, some framework A l in A l P 0 4 s may also coordinate two molecules of water, changing its coordination from 4-fold to 6-fold, and this is readily detected by 2 7 A1 M A S N M R . The 3 I P nuclei in these materials are always tetrahedrally coordinated, and often only a single signal is observed in the 3 1 P M A S N M R spectrum. However, for AIPO4 -8 and VPI-5 and others which have complex unit cells, several well-resolved resonances corresponding to the different T-sites have been observed.^ 2 9 S i M A S N M R spectra have yielded a wealth of information about the framework structures of zeolites, and the temperature and sorbate induced changes they sometimes undergo. For low S i / A l ratio zeolites, the 2 9 S i M A S spectra of the simplest systems show five resonances which could be assigned to the five possible distributions of Si and A l atoms about a sil icon nucleus at the center of an S i 0 4 tetrahedron: Si [4Al ] , S i [3A l , lS i ] , Si [2Al ,2Si ] , S i [ l A l ,3S i ] , and Si[4Si]. The chemical shift ranges for these resonances are reasonably characteristic, (Figure 1.10) although they overlap and care must be taken in their use. The S i / A l ratio of the framework may be calculated from the 2 9 S i M A S spectra under the assumption that Loewenstein's r u l e m (which postulates that A l - O - A l linkages in the framework should be avoided i f possible) holds. Because this yields the S i / A l ratio for the framework, it is complementary to that provided by bulk chemical analysis, which determines the total A l content of the sample (i.e. elemental analysis also includes any Al-containing species occluded within the pores). The resonances in the 2 9 S i M A S N M R spectra of low S i / A l ratio zeolites are quite broad (5 ppm), however i f the aluminium is removed (e.g. by hydrothermal or chemical treatments), then highly siliceous frameworks can be obtained. If the lattice structures of these highly siliceous zeolites are also wel l ordered (i.e. highly crystalline), then the spectra wi l l show narrow 44 Figure 1.10 (a) The five possible local environments of a Si atom in a zeolite framework and the corresponding chemical shift ranges. (b)29Si MAS NMR spectrum of a NaY zeolite (Si/Al ratio of 2.6) with the resonances for the five different silicon environments resolved. After reference 112. resonances due only to Si[4Si]. With careful optimization of the experimental variables and instrumentation, ultra high resolution N M R spectra with peak widths of ca. 0.1 ppm can be obtained in the best cases as depicted in Figure 1.11. The excellent resolution of these spectra can be exploited to obtain very useful structural information that is not readily obtainable by other techniques. Fyfe et al. and others have reported high resolution 2 9 S i M A S N M R spectra for a number of highly siliceous zeolites and related materials including Z S M - 5 , 9 * ' " ZSM-1 l , " 7 Z S M - 1 2 , " 5 Z S M - 2 2 2 ' ) , Z S M - 2 3 , ' 0 i Z S M -3 9 , " 6 D D 3 R , " 7 decadodecasil ,"* offreti te," 9 and mordenite." 9 In these spectra, the individual resonances correspond to crystallographically inequivalent T-sites. With appropriate care, quantitative spectra can be obtained wherein the relative peak intensities reflect the populations of the different T-sites. This allows a direct l ink to be made between the N M R spectra and the information provided by diffraction methods. Whi le N M R is sensitive to the local (short range) ordering, diffraction methods reflect the long range ordering in the lattice, and the complementary nature of the two techniques has been exploited to elucidate the detailed structures of several microporous materials. ' 0" ' ' ' 2 0" ' 2 2 In a few cases the number of resonances and relative intensities may provide sufficient information to allow the individual peaks to be unambiguously assigned to specific T-sites in the lattice (e.g. zeolite offretite" 9). In other cases there may be accidental degeneracies (e.g. mordenite" 9), or several resonances with equal intensities, which means that the assignments can not be obtained from the 1-D spectra, and the use of two-dimensional N M R techniques such as I N A D E Q U A T E and C O S Y is required. These 2-D methods are discussed in Section 1.3.2.2. Several empirical correlations have been proposed which relate 2 9 S i chemical shifts to various aspects of the local geometry of the Si nuclei in the lattice. These include relationships based on the mean S i -O-S i bond angle ' 2 7 and the average Si -S i distance.' 2 5 Unfortunately, these methods are not accurate enough to provide rigorously correct assignments of the resonances to specific T-sites, especially in cases where the chemical shift differences are small, and thus 46 I I 1 1 1 1 1 1 1 1 1 " 1 0 8 ppm from T M S - 1 1 8 Figure 1.11 (a) 2 9 S i M A S N M R spectrum of calcined, highly siliceous zeolite Z S M - 5 at 79.495 M H z . (b) 2 9 S i M A S N M R spectrum obtained of a very crystalline, completely siliceous sample of Z S M - 5 after careful optimization of all experimental variables, (c) Deconvolution of spectrum (b) in terms of Lorentzian curves corresponding to the 24 individual T-sites. After reference 105. Al should only be used as a general guide. This is mainly due to the uncertainties in the exact S i -O-Si bond angles and Si-Si distances found from X-ray structure determinations. The assignment of the 2 9 S i resonances to specific T-sites is further complicated by the chemical shift variations observed as the temperature is changed, or in the presence of guest molecules within the channels, since both may induce subtle changes in the local geometry.9 7" 99.127-129 F o r e x a m p i e ) t h e 2 9 S J M A S s p e c t r a 0 f calcined (empty) Z S M - 5 at 293K contains 21 resonances which may be assigned (using 2-D I N A D E Q U A T E ) to the 24 T-sites determined from the crystal structure at the same temperature. 9 9 A t this temperature the framework has monoclinic (P2//n. 1.1) symmetry, but this changes to orthorhombic (Prima) i f the temperature is raised above 357 K. In the orthorhombic phase, there are only 12 T-sites. These changes are accurately reflected in the 2 9 S i M A S spectra and are completely reversible. Similar changes have been observed for Z S M - 1 1 1 2 9 and Z S M - 3 9 . ' 2 * The introduction of organic species into the channels can sometimes result in dramatic changes in the 2 9 S i spectra, again reflecting the slight modifications which can occur in the local environments of the T-sites. Several groups have reported 2 9 S i M A S N M R of Z S M - 5 9 * m ' m and ZSM-1 \ n o containing various organic sorbates which illustrate these changes. The spectra show a dependence on the actual number of molecules per unit cell that are present, and the nature of the adsorbed m o l e c u l e . 9 * ' 0 2 , l 2 7 The combined effects of sorbate and temperature have also been investigated. 9* ' 2 7 These effects are discussed in more detail in Chapter 6. There have been a few studies where distances between framework atoms were determined from N M R experiments. Van Eck and Veeman ' 5 ' used S E D O R to estimate average 2 7 A 1 - 3 I P distances in A l P 0 4 - 5 and S A P O - 1 1 . They measured mean 2 7 A 1 - 3 I P distances of 3.15 A and 3.17 A for the two materials respectively, by observing 2 7 A1 while dephasing 3 1 P. These distances are in good agreement with those determined from refinements of X-ray and neutron powder diffraction data. Fyfe and co-workers have reported 1-D R E D O R and T E D O R experiments on several zeolites 6 ' 5 and the A I P O 4 V P I - 5 . ' 3 2 However because these techniques 48 were designed to measure the dipolar coupling between spin-1/2 nuclei and they used A l as one of the nuclei in their experiments, Fyfe et al. were unable to determine A l - P distances. ' H nuclei are often present in the framework structures of zeolites, most commonly at the Bronsted acid sites or in hydroxyl groups at lattice defect sites. Extensive ] H M A S N M R studies have led to the assignments of the various proton resonances which are observed, and these have been reviewed by Pfeifer et al.133 Freude et al.134 were able to estimate the mean distance for A l -O H - S i acid protons in zeolites. Using the fact that the 'H- 2 7 A1 dipolar coupling dominates the proton second moment, they were able to determine ] H- 2 7 A1 distances of 2.38 A and 2.48 A from ' H N M R spectra of static samples of Z S M - 5 and zeolite Y respectively. ' H - 2 9 S i C P and R E D O R experiments have been performed to investigate the Bronsted acid protons in the NH + -exchanged forms of Z S M - 5 and zeolite Y . / J 5 Although they report that they were able to fit the experimental data satisfactorily, specific ' H - 2 9 S i distances were not given. Although one-dimensional M A S N M R spectra of microporous materials can be directly related to the crystallographically inequivalent T-sites in the asymmetric unit, assignment of the individual resonances to specific T-sites is not always straightforward for the reasons discussed above. The two-dimensional N M R techniques discussed in the next section can provide information about the connectivities between the various resonances, and thus between the T-sites in the lattice, which greatly assists the assignment. 1.3.2.2 Determination of Framework Connectivities by Two-Dimensional NMR In solution-state N M R , the application of two-dimensional techniques has furnished considerable information about the connectivities between atoms within molecules. 2*" 3 ' 7" 5 ' 5 ' 7 5 ' 5 '" 7 The assignment of resonances in the M A S spectra to specific T-sites is an essential first step in the process of locating guest species within frameworks by N M R , since it is necessary to determine exactly which T-sites the nuclei in the guest species are closest to. These 2-D techniques include Heteronuclear Shift Correlation (HSC) , which establishes heteronuclear 49 connections such as ' H - 1 3 C , and Correlation Spectroscopy ( C O S Y ) that determines homonuclear correlations (e.g. ' H / ' H , 3 1 P / 3 1 P etc.). The I N A D E Q U A T E (Incredible Natural-Abundance DoublE QUAntum Transfer Experiment) sequence was introduced to establish , 3 C / I 3 C connectivities in natural abundance samples."* Benn and co-workers" 9 successfully demonstrated the application of C O S Y and I N A D E Q U A T E to solids, showing 2 9 S i / 2 9 S i connectivities in Q 8 M 8 (the cubic octamer S i 8 O i 2 [ O S i ( C H 3 ) 3 ] 8 ) , and l 3 C / l 3 C connections in camphor. These experiments use the scalar or ./-coupling between covalently bonded spin pairs, and can be utilized to determine the three-dimensional connectivities between nuclei in microporous materials such as z e o l i t e s / 2 ' 7 2 2 Fyfe et al. were the first to apply these 2-D homonuclear correlation techniques to establish the three-dimensional S i -O-S i lattice connectivities in zeol i tes. 7 7 6 7 / 7 Because of the low natural abundance of 2 9 S i (4.7%), which means that spin pairs have only a 0.22% probability o f occurring, the initial experiments were performed on 2 9 S i isotopically-enriched (ca. 85%) samples. After optimization the experiments could be performed on samples with natural abundance 2 9 S i / * 7 2 0 7 2 y To illustrate the important aspects of these two experiments, Z S M - 1 2 wi l l be used as an example. The structure of Z S M - 1 2 is shown in Figure 1.12(a). The 2 9 S i M A S N M R spectrum of highly siliceous Z S M - 1 2 shows seven clearly separated resonances of equal intensity (Figure 1.12(b)). These reflect the seven inequivalent T-sites in the crystal lattice of Z S M - 1 2 which have equal occupancy (Figure 1.12(a)).7'70 A n important aspect of the C O S Y 2-D spectrum is the doublet splitting observed in the cross peaks, which correspond to 2 9 S i - 0 - 2 9 S i J-couplings of 9 to 16 Hz . Knowledge of the magnitude of these J-couplings is important for the efficient application of the I N A D E Q U A T E experiment. The optimal value for the fixed delay x in the I N A D E Q U A T E pulse sequence (7t/2 -T-n-i-n-ti- 3TI /4 - acquire) is \/(4J). Because of the echo portion in the sequence, there is 50 ft—Ah® T 6 T s #1[-B6-T4T5^:'-^ T4T2 T6T7— T3T7 ''T 4T 6 T3T1 T3T5 0-5 -tot.o -109.0 -iio.o -tit.o -tia.o 0 Figure 1.12 (a) Framework structure of ZSM-12 showing the seven crystallographically inequivalent T-sites. (b) Contour plot o f a 2 9 S i I N A D E Q U A T E N M R experiment on purely siliceous Z S M - 1 2 with the one dimensional M A S N M R spectrum above. Fifty-two experiments were carried out using a spectral width o f 800 Hz , a fixed delay of 20 ms and 64 scans per experiment. Adapted from reference 115. 51 the added restriction that T2<\IJ in order that acceptable S/N is obtained. Figure 1.12(b) shows the result o f a 2-D I N A D E Q U A T E experiment on Z S M - 1 2 . Compared to a C O S Y experiment, the I N A D E Q U A T E experiment has the significant advantage that there are no large signals on the diagonal. This makes it easier to observe connectivities between closely spaced resonances, which are often obscured by the single quantum resonances in a 2-D C O S Y spectrum. However, the successful implementation of an I N A D E Q U A T E experiment requires a reasonable estimate of the J-coupling. Overal l , the I N A D E Q U A T E experiment has proven itself to be superior to C O S Y in investigations of molecular sieve frameworks. 1 0 4 For example, in the case of Z S M - 5 loaded with two molecules p-xylene per unit cel l , 21 of the expected 22 connectivities were resolved from I N A D E Q U A T E experiments, but only 12 were determined using C O S Y . " Using 2-D I N A D E Q U A T E experiments, Fyfe and co-workers have successfully assigned individual 2 9 S i resonances to specific T-sites in several other highly siliceous zeolites including ZSM-22, 7 " 7 7 and ZSM-11 , " 4 More recently several techniques that yield heteronuclear framework connectivities have been reported. These include 2-D cross polarization, T E D O R and INEPT experiments on several zeol i tes' 5 ' " 2 5 and A I P 0 4 s . l 5 i 7 2 5 7 3 2 ' ^ 2 Such experiments revealed connectivities between framework 27 29 * 27 31 atoms ( A l and Si in zeolites, and A l and P in A l P 0 4 s ) that were in agreement with those anticipated from the known framework structures. 1.3.2.3 NMR Studies of Guest Species Many of the guest species that may be located within the pore and cages of microporous materials contain N M R active nuclei. Consequently, there have been a large number of N M R investigations of the various occluded species and several reviews have been publ ished. 5 0 , 7 0 l 5 ' 7 0 7 The vast majority of N M R studies of guest species have involved *H and l 3 C , mainly because many of the guest species are organic. 52 The early ' H N M R studies of guest species were devoted to the adsorption of water and alcohols on zeolites, and later small hydrocarbon molecules such as acetylene and ethylene were investigated. 5 0 However, the ' H - ' H homonuclear dipolar interactions are usually quite large which often means that the ' H spectra of static samples are very broad. The use of M A S and C R A M P S can provide *H spectra with substantially improved resolut ion. ' 0 6 The protons on sorbed organic molecules and templates are often utilized as a polarization source for improving the efficiency of N M R spectra of zeolite framework nuclei via C P . Recently, Fyfe and co-workers have used C P , T E D O R , and R E D O R experiments between the ' H nuclei in selectively deuterated, sorbed /^-xylene and 2 9 S i in highly siliceous Z S M - 5 to locate the guest molecules within the channels. ' 7 5 I 3 C N M R has also been widely used to investigate templating species, sorbed organic molecules, and to fol low chemical reactions catalyzed by microporous materials. For example, the conversion of methanol to dimethyl ether and other hydrocarbons on Z S M - 5 has been extensively studied in-situ by l 3 C N M R . ' 0 6 ' 0 7 1 3 C M A S N M R spectra of tetrapropyl ammonium cations ( T P A + ) in as-synthesized Z S M - 5 are almost identical to that of the ion in aqueous solution, proving that the template remains intact. 5 0 Reischman et al.144 observed splitting of the methyl group resonances in the 1 3 C spectrum of Z S M - 5 loaded with /^-xylene, and interpreted this as evidence for the existence of two different sorption sites. This was later confirmed by a single-crystal X-ray structure.' 9 Recently, Fyfe et al. have undertaken extensive N M R investigations of the Z S M - 5 /p-xylene system, using C P , R E D O R , and T E D O R to measure 1 3 C - 2 9 S i distances between the framework silicons and the 1 3 C-labeled methyl groups of the sorbed /^-xylene molecules, and 1 3 C Spin-Diffusion experiments to study the molecular motions. ' 7 5 2 H N M R of static samples has yielded many insights into the nature, mechanisms, and timescales of the molecular motions of sorbed species. 5 2 A good example of this is provided by the study of the temperature dependence of the 2 H spectra of selectively deuterated /(-xylenes on 53 Z S M - 5 , which allowed the temperature ranges where various molecular rotations were present or absent to be determined. 1 4 5 The potential of 1 5 N N M R to study nitrogen-containing guest species has not been ful ly exploited, mainly because of the low natural abundance of 1 5 N (0.37 %), which means that isotopic enrichment is necessary. 1 5 N chemical shifts are very sensitive to the nature of the adsorption site, and 1 5N-labeled molecules such as ammonia, acetonitrile, and pyridine have been used to probe the strength and number o f acid sites in z e o l i t e s / 0 ' 0 7 For example, the 1 5 N N M R spectra o f pyridine adsorbed on zeolite Y clearly show the conversion to pyridinium ions. ' 0 7 Many of the molecules used as templates are quaternary ammonium salts (e.g. the T P A + cations used for ZSM-5 ) , and could be more readily studied i f materials were synthesized with l 5 N -labeled templates. There have been several N M R studies of simple ions within the frameworks of zeolites and AIPO4S. Most of the charge-compensating, exchangeable cations in zeolites can potentially be studied by N M R to, but only a few (such as L i , N a , TI, and Cs) have been used to date / 0 The N M R spectra of these cations can provide insights into their location and degree of hydration. I 9 F M A S N M R has been invoked to investigate the roles played by the fluoride ions that are often encapsulated within the framework structures of microporous materials synthesized from fluoride-containing media.'""5 A n interesting N M R technique used to investigate microporous materials involves the 1 2 9 X e N M R study of sorbed xenon gas. The 1 2 9 X e chemical has proved useful as a passive probe of the pore structures, occluded metal species and other adsorbed guest m o l e c u l e s / 0 ' 7 7 1.3.3 Computer Modelling of Framework Structures and Guest Species In recent years computer modelling techniques have become well established as powerful tools in the study of microporous solids, and comprehensive commercial software packages are now avai lab le / 2 Several recent reviews have been publ ished, ' 7 8 " ' 3 ' and reference 152 contains 54 detailed accounts of the simulation techniques which have been used. Techniques which rest on the specification of interatomic potentials (Forcefield Methods) have been extensively used to model the structures of microporous materials, and to investigate the locations and diffusion o f guest species. These Forcefield methods include Energy Minimizat ion, Monte Carlo and Molecular Dynamics, and the reliability of the simulations depends critically on the quality of the interatomic potential models emp loyed . N 8 The parameters for these techniques are derived from empirical methods or ab-initio calculations. When modell ing the interactions between guest species and the framework, parameters are sometimes "borrowed" from those developed for organic systems. Using these parameters, simulations have been able to reproduce the qualitative aspects of adsorption isotherms, and yield diffusion coefficients that are in good agreement with those determined experimentally. ' 5 2 Freeman and co-workers' 5 3 have developed a "dock ing" procedure which uses a combination of Monte Carlo and Molecular Dynamics methods with energy minimization. This has been widely used for identifying low energy sites for sorbed molecules (e.g. butene in silicalite I, pyridine in zeolite L ) , and has successfully located the organic templating species in the frameworks at their X-ray determined posit ions. ' 5 7 By far the majority of the simulations of guest-host complexes in microporous materials have been performed using rigid frameworks, and often the organic species are also fixed at some predetermined configuration. Calculations which al low the (empty) framework to relax completely unrestrained to the local energy minimum have been able to reproduce the experimentally determined unit cell dimensions and fractional coordinates for zeolite A and si l ical i te. ' 5 5 Tit i loye et al.156 have simulated linear hydrocarbons adsorbed in M F I and faujasite frameworks including complete flexibil i ty of the organic component. The location of /(-xylene in purely siliceous M F I frameworks has been studied by Pickett et al.,h7 and Reischman and co-workers. ' 7 7 These calculations used rigid frameworks and similar potential functions, but different parameterizations. Whi le the adsorption sites seem to be in 55 relatively good agreement with the X-ray determined locations, the presence of the sorbate molecules changes the local symmetry of the zeolite framework, and this was not revealed by, nor included in, the simulations. In conclusion, although a considerable number of theoretical calculations have been carried out, the results are not always in agreement.' 5 8 The reliability o f the computer simulations of framework-guest systems depends critically on the quality of the potential functions and the parameters used. These problems may be compounded by the subtle geometry changes induced by the guest species. There is a definite need for experimental techniques capable of locating guest species reliably within the channels and voids and providing detailed information about the frameworks. The aim of the research presented in this thesis is to develop solid-state N M R techniques to furnish exactly this information. 1.4 OUTLINE OF PROPOSED RESEARCH A s has been described above, diffraction techniques, solid-state N M R studies and computer modell ing have been used to investigate the framework structures of crystalline microporous inorganic materials such as zeolites, and the host-guest complexes that are formed with occluded guest species. It is now possible to establish a direct relationship between the information provided by solid-state N M R , and the results of the X-ray diffraction studies using two-dimensional homonuclear solid-state N M R experiments such as C O S Y and I N A D E Q U A T E . Heteronuclear 2-D N M R techniques (e.g. INEPT, T E D O R and CP) can also provide detailed information about framework connectivites. Overal l , however, relatively little is known about the locations of the guest species within the channels and cages of microporous materials. Such information is vital i f we are to improve understanding of the many unique properties of these materials. It is also important to obtain independent, reliable experimental data to assist refinement of structures from diffraction techniques and as a test o f the correctness of solutions obtained from computer modell ing 56 methods. Solid-state N M R has considerable potential in solid-state structure investigations for directly determining internuclear distances from experiments based on the through-space IS dipolar interactions. With this in mind, the major thrust of the research was to develop the techniques of cross polarization, R E D O R , and T E D O R to allow quantitative distance determinations between nuclei in the guest species and framework atoms. It was decided to concentrate on highly crystalline, purely siliceous framework systems with fluorine-containing guest species for several reasons. Firstly, highly resolved 2 9 S i M A S N M R spectra can be obtained i f the materials are of the very highest quality, al lowing the individual N M R resonances to be assigned to specific T-sites using 2-D experiments such as I N A D E Q U A T E . This is a crucial first step in locating guest species. Secondly, 1 9 F is a spin 1/2 nucleus with a large gyromagnetic ratio, making 1 9 F - 2 9 S i experiments attractive, since the dipolar couplings wi l l be of the order of hundreds of hertz. Thirdly, although 1 9 F has 100% natural abundance, it is relatively rare, which dramatically reduces the likelihood of background interferences. Final ly, many of the samples synthesized via the "Fluoride Method" of Flanigen and Patton contain fluoride ions in their as-synthesized form, and there is considerable interest in determining the roles which these ions play in the syntheses. A n important aspect of this work wi l l be the development of appropriate protocols and analytical techniques capable of providing reliable measurements of the heteronuclear dipolar coupling in the situations typically encountered in these host-guest complexes. These techniques wi l l be tested and refined using systems where the structure is known from single crystal X-ray diffraction studies. Once the reliability is established, they can be used to achieve the overall goal o f the research: to locate guest species within framework structures where no detailed information concerning the locations is available. Chapter 2 is concerned with the experimental details, spectrometer modifications, specialized equipment required, and preparation of samples. The C P , R E D O R , and T E D O R techniques are introduced in detail in Chapter 3, before the results of 1 9 F / 2 9 S i N M R experiments 57 on octadecasil are presented in Chapter 4. Octadecasil was chosen because it is a purely siliceous, fluoride-containing framework whose structure is known from single crystal study, and it contains two types of T-sites; one which interacts with only a single fluoride ion (i.e. an isolated Si-F spin pair), and the another that is dipolar coupled to several 1 9 F nuclei. Thus octadecasil provides an ideal test case for the development of reliable fitting procedures. A critical comparison and assessment of these N M R distance determination techniques is presented in Chapter 5. In Chapter 6 the results of the I N A D E Q U A T E , C P , R E D O R , and T E D O R experiments used to locate 1,4-difluorobenzene molecules in Z S M - 5 are discussed. Preliminary investigations of the powder X-ray diffraction of the low-loaded />-difluorobenzene / Z S M - 5 complex are presented in Chapter 7. The successful single crystal refinement of the structure of the low-loaded complex of /^-xylene in Z S M - 5 is presented are detailed in Chapter 8. Chapter 9 summarizes the research results and conclusions, and outlines some proposals for future studies. Several Appendices have been included. These contain schematics of the N M R spectrometer configurations, listings of the pulse and automation programs used, as wel l as detailed information concerning the fitting procedures, equations, and Mathematica scripts used to analyze the results of the C P , R E D O R and T E D O R experiments. 58 REFERENCES FOR CHAPTER 1 1 (a) Pajado, P.R.; Rabo, J .A. ; Antos, G .J . ; Gembicki , S.A. Catal. Today, 1992,13, 113. (b) Moscou, L. in Introduction to Zeolite Science and Practice, C h . 1, van Bekkum, H.; Flanigen, E . M . ; Jansen, J .C. (Eds.), Elsevier: Amsterdam, 1991. 2 Flanigen, E . M . in Introduction to Zeolite Science and Practice, C h . 2, van Bekkum, H. ; Flanigen, E . M . ; Jansen, J .C. (Eds.), Elsevier: Amsterdam, 1991. 3 Arends, I .W.C.E.; Sheldon, R.A. ; Wal lau, M . ; Schuchardt, U . Angew. Chem. Int. Ed. Engl. 1997, 36, 1144. 4 Barrer, R . M . Zeolite and Clay Materials as Sorbents and Molecular Sieves; Academic Press, 1974. 5 Breck, D.W. Zeolite Molecular Sieves; Wi ley Interscience, 1974. 6 van Bekkum, H. ; Flanigen, E . M . ; Jansen, J .C . (Eds.), Introduction to Zeolite Science and Practice; Elsevier: Amsterdam, 1991. 7 Jansen, J . C ; Stocker, M . ; Karge, H.G. ; Weitkamp, J . (Eds.), Advanced Zeolite Science and Applications; Elsevier: Amsterdam, 1994. 8 Chon, H. ; Woo, S.I.; Park, S.E. (Eds.), Recent Advances and New Horizons in Zeolite Science and Technology, Elsevier: Amsterdam, 1996. Stud. Surf. Sci. Catal. vol . 102. 9 M c B a i n , J .W. Sorption of Gases and Vapours by Solids, Routlidge and Sons: London, 1932. 10 Quoted in Kerr, G.T. Scientific American, 1989, July, 100. 11 Quoted in Newsam, J . M . Science, 1986, 231, 1093. 12 Chang, C D . U.S. Patent N o . 4,273,753, 1981. 13 Flanigen, E . M . ; Patton, R.L . U.S. Patent No. 4073865, 1978. 14 Guth, J .L . ; Kessler, H. ; Caullet, P.; Hazm, J . ; Merrouche, A . ; Patarin, J . in Proceedings of the 9th International Zeolite Conference, Montreal, 1992. von Ballmoos, R.; Higgins J .B. ; Treacy, M . M . J . (Eds), Butterworth-Heinemann 1993, 215 15 Zhao, D.; Q iu , S.; Pang, W. in Proceedings of the 9th International Zeolite Conference, Montreal, 1992. von Ballmoos, R.; Higgins J .B . ; Treacy, M . M . J . (Eds), Butterworth-Heinemann 1993, 337. 16 Meier, W . M . ; Olson, D.H. ; Baerlocher, C h . Atlas of Zeolite Structure Types, 4th Revised Ed . ; Elsevier: London, 1996. www-iza-sc.csb.yale.edu/IZA-SC/ 17 Atlas of Zeolite Structure Types, 3rd. Revised Ed . ; Meier, W . M . ; Olson D.H. (Eds.) Butterworth-Heinemann, 1992. 18 Gies, H. ; Marler, B. in Comprehensive Supramolecular Chemistry, C h . 26, vol 26 MacN ico l , D.D.; Toda, F,; Bishop, R. (Eds.) Permagon, 1996. 59 19 van Koningsveld, H.; Tuinstra, F.; van Bekkum, H. ; Jansen, J .C. Acta Cryst. 1989, B45, 423 20 van Koningsveld, H.; Jansen, J . C ; de Man , A . J . M . Acta Cryst. 1996, B52, 131. 21 Fy fe ,C.A. ; Kokotai lo, G.T. ; Strobl, H. ; Pasztor, C .S. ; Barlow, G . ; Bradley, S. Zeolites 1989, 9, 531. 22 Cerius2 Molecular Simulations Inc. Burlington, M A . U.S.A. 23 (a) Rietveld, H . M . J. Appl. Cryst. 1969, 2, 65. (b) Young, R.A. (Ed.). The Rietveld Method, Oxford University Press, 1993 24 Giacovazzo, C . (Ed.) Fundamentals of Crystallography. Oxford University Press, 1995. 25 Thomas, J . M . in Zeolites: Facts, Figures and Future, van Santen, R.A. ; Jacobs, P.A. Eds., Elsevier: Amsterdam, 1989, p. 3 Stud. Surf. Sci. Catal. 49A. 26 Venuto, P.B. Microporous Mater. 1994, 2, 297. 27 Abragam, A . The Principles of Nuclear Magnetism; Oxford University Press: London, 1961 28 Ernst, R.R.; Bodenhausen, G . ; Wokaun, A . Principles of Nuclear Magnetic Resonance in One and Two Dimensions. Clarendon Press: Oxford, 1990. 29 Slichter, C P . Principles of Magnetic Resonance, 2nd Ed . ; Springer-Verlag: New York, 1983. 30 Engelhardt, G . ; M iche l , D. High-Resolution Solid-State NMR of Silicates and Zeolites. John Wi ley & Sons, 1987. 31 Mehring. M . Principles of High Resolution NMR in Solids, 2nd Ed. ; Springer-Verlag: New York, 1983. 32 Fyfe, C A . Solid State NMR for Chemists; C .F .C . Press: Guelph, Canada, 1983. 33 Harris, R .K . Nuclear Magnetic Resonance Spectroscopy - A Physiochemical View, 3rd Revised E d . Longmann Scientific and Technical: United Kingdom, 1987. 34 Derome, A . E . Modern NMR Techniques For Chemistry Research. Permagon Press, 1987. 35 Akitt , J .W. NMR and Chemistry - An Introduction to the Fourier Transform - Multinuclear Era. 2nd ed., Chapmann and Ha l l , 1984. 36 Sanders, J . ; Hunter, B. Modern NMR Spectroscopy: A Guide for Chemists, Oxford University Press, Oxford, England, 1987. 37 Harris, R.K. ; Mann, B .E . (Eds.) NMR and the Periodic Table. Academic Press, 1978. 38 Gunther, H. NMR Spectroscopy - Basic Principles, Concepts, and Applications in Chemistry; 2nd Ed. , John Wi ley and Sons, 1995. 39 Stejskal, E.O., Memory, J.D. High Resolution NMR Techniques in the Solid State -Fundamentals of CP/MAS. Oxford University Press, 1994. 60 40 Andrew, E.R. Int. Rev. Phys. Chem. 1981,1, 195. 41 Andrew E.R. in Encyclopedia of Nuclear Magnetic Resonance. Grant, D . M . ; Harris, R .K . (Eds.) John Wi ley & Sons, 1996. p. 2891. 42 Jel inski, L .W. ; Melchior, M.T. in NMR Spectroscopy Techniques, Dybowski , C ; Lichter, R.L. , Eds. Marcel Dekker: NewYork , 1987. 43 Chemlka, B.F. ; Zwanziger, J .W. NMR Basic Principles and Progress. 1994, 33, 80. 44 Waugh, J .S. ; Huber, L . M . ; Haeberlen, U . Phys. Rev. Lett. 1968, 20, 180. 45 Rhim, W . K . ; Elleman, D.D.; Vaughn, R.W. J. Chem. Phys. 1973, 59, 3740. 46 Burum, D.P.; Rhim, W . K . J. Chem. Phys. 1979, 71, 944. 47 Engelhardt, G . ; Miche l , D. High-Resolution Solid-State NMR of Silicates and Zeolites, p. 42, John Wi ley & Sons, 1987. 48 (a) Harris, R.K. ; Jackson, P. in Multinuclear Magnetic Resonance in Liquids and Solids -Chemical Applications, ch. 29. Granger, P.R.; Harris, R .K. (Eds.), K luwer Academic Publishers 1990 N A T O ASI Series C 322. (b) Ryan, L . M . ; Taylor, R.E. ; Paff, A . J . ; Gerstein B.C. J. Chem. Phys. 1980, 72, 508. 49 Andrew, E.R.; Bradbury, A . ; Eades, R .G . Nature. 1958,182, 1659. 50 Lowe, I.J.; Phys. Rev. Lett. 1959, 2, 285. 57 (a) Wind, R .A . in Modern NMR Techniques and Their Applications in Chemistry, Ch . 3, Popov, A.I . ; Hallenga, K. (Eds.), Marcel Dekker, 1991.(b) Mar icq, M . M . ; Waugh, J.S. J. Chem. Phys. 1979, 70, 3300. 52 Herzfeld, J . ; Berger, A . E . J. Chem. Phys. 1980, 73, 6021. 53 (a) Dixon, W.T. J. Magn. Reson. 1981, 44, 220. (b) Dixon, W.T. J. Chem. Phys. 1982, 77, 1800. 54 (a) Dixon, W.T. ; Schaefer, J . ; Sefcik, M .D . ; Stejskal, E.O. J. Magn. Reson. 1981, 45, 173. (b) Dixon, W.T. ; Schaefer, J . ; Sefcik, M.D. ; Stejskal, E . O . J . Magn. Reson. 1982, 49, 341. 55 Kolbert, A . C . ; Raleigh, D.P.; Gr i f f in, R .G. J. Magn. Reson. 1989, 82, 483. 56 Grondey, H. Ph.D. Dissertation, Universitat Gesamthochschule, Siegen, Germany 1988 57 (a) Gul l ion, T.; Schaefer, J . J. Magn. Reson. 1989, 81, 196. (b) Pan, Y . ; Gul l ion, T.; Schaefer, J . J. Magn. Reson. 1990, 90, 330. 58 Pines, A . ; Gibby, M . G . ; Waugh, J.S. J. Chem. Phys. 1973, 59, 569. 59 Hartmann, S.R.; Hahn, E .L . Phys. Rev. 1962,128, 2042. 61 60 Hediger, S.; Meier, B .H . ; Ernst, R.R. Chem. Phys. Lett. 1995, 240, 449. (b) Hediger, S.; Meier, B .H . ; Ernst, R.R. J. Chem. Phys. Lett. 1995,102, 4000. (c) Hediger, S.; Meier, B .H . ; Ernst, R.R. Chem. Phys. Lett. 1993, 213, 627. 61 Fleming, W.W. ; Fyfe, C .A . ; Kendrick, R.D. ; Lyerla, J.R.; Vanni , H. ; Yannoni , C.S. ACS Symp. Ser. 1980, 142, 206. 62 Sebald, A . , Merwin, L . H . ; Schaller, T.; Knol ler, W. J. Magn. Reson. 1992, 96, 159. 63 Peters, G . ; Preetz, W. ; Schaller, T.; Sebald, A . J. Magn. Reson. Ser. A. 1996,120, 121. 64 Schaefer, J . ; M c K a y , R.A. ; Stejskal, E.O. J. Magn. Reson. 1979, 34, 443. 65 Fyfe, C . A . ; Muel ler, K.T. ; Grondey, H.; Wong-Moon, K . C . J. Phys. Chem. 1993, 97, 13484. 66 Fyfe, C . A . ; Wong-Moon, K . C ; Huang, Y . ; Grondey, H. ; Mueller, K.T. J. Phys. Chem. 1995, 99, 8707. 67 Fyfe, C . A . ; Muel ler, K.T. ; Wong-Moon, K . C . in Nuclear Magnetic Resonance in Modern Technology, Mac ie l , G .E . , Ed , K luwer Academic Publishers : Dordiecht, The Netherlands, 1994, NATO ASISeries C 447 447. 68 Sebald, A . NMR Basic Principles and Progress, D ieh l , P.; Fluck, E. (Eds.) Springer Ver lag: Berl in 1994. vol . 31, p. 91. 69 M iche l , D.; Engelke, F. NMR Basic Principles and Progress, Fluck, E. (Eds.) Springer Verlag: Berl in 1994. Diehl , P.; vol . 32, p. 71. 70 (a) Yannoni , C.S. Acc. Chem. Res. 1982, 15, 201. (b) Voelke l , R. Angew. Chem. Int. Ed. Engl. 1988, 27, 1468. (c) Stejskal, E.O. ; Schaefer, J . ; Waugh, J.S. J. Magn. Reson. 1977, 28, 105. 71 Hallenga, K.; Popov, A.I . in Modern NMR Techniques and Their Applications in Chemistry, C h . 1, Popov, A.I . ; Hallenga, K. (Eds.), Marcel Dekker, 1991. 72 Torcia, D.A. J. Magn. Reson. 1978, 30, 613. 73 Waugh, J .S. ; Mar icq, M . M . ; Cantor, R. J. Magn. Reson. 1978, 29, 183. 74 (a) Kaplan, D.E. ; Hahn, E.L. J. Phys. Radium. 1958,19, 821. (b) Wang, P.K.; Slichter, C P . ; Sinfelt, J .H . Phys. Rev. Lett.1984, 53, 82. 75 Ho l l , S . M . ; M c K a y , R.A. ; Gul l ion, T.; Schaefer, J . J. Magn. Reson. 1990, 89, 620. 76 (a) Hing, A . W . ; Vega, S.; Schaefer, J . J. Magn. Reson. 1992, 96, 205. (b) Hing, A . W . ; Vega, S.; Schaefer, J . J. Magn. Reson. Ser. A, 1993, 103, 151. 77 (a) Schmidt, A . ; M c K a y , R.A. ; Schaefer, J . J. Magn. Reson. 1992, 96, 644. (b) Grey, C P . ; Veeman, W.S . Chem. Phys. Lett. 1992,102, 379. (c) Grey, C P . ; Veeman, W.S. ; Vega, A . J . J. Chem. Phys. 1993, 98, 7711. (d) Gul l ion.T. J. Magn. Reson. Ser. A. 1995,117, 326. (e) Gull ion.T. Chem. Phys. Lett. 1995, 246, 325. (f) Bork, V . ; Gul l ion, T.; Hing, A . ; Schaefer, J . J. Magn. Reson. 1990, 88, 523. (g) Gul l ion, T.; Pol iks, M .D . ; Schaefer, J . J. Magn. Reson. 1988, 80, 553. 62 78 Bennett, A . E . ; Ok, J .H . ; Gr i f f in, R .G . ; Vega, S. J. Chem. Phys. 1992, 96, 8624. 79 Tycko, R.; Smith, S.O. J. Chem. Phys. 1993, 98, 932. 80 Gul l ion, T.; Vega, S. Chem. Phys. Lett. 1992, 194, 423. 81 Gregory, D .M . ; Mi tchel l , D.J.; Stringer, J .A. ; K i ihne, S.; Sheils, J . C ; Callahan, J . ; Mehta, M.A. ; Drobny, G.P . Chem. Phys. Lett. 1995, 246, 654. 82 Sun, B.Q. ; Costa, P.R.; Kocisko. , D.; Lansbury, P.T.; Gr i f f in, R .G . J. Chem. Phys. 1995, 102, 702. 83 Baldus, M . ; Tomasell i , M . ; Meier, B .H . ; Ernst, R.R. Chem. Phys. Lett. 1994, 230, 329. 84 Lee, Y . K . ; Kurur, N.D. ; Helmle, M . ; Johannessen, O .G . ; Nielsen, N .C . ; Levitt, M . H . Chem. Phys. Lett. 1995, 242, 304. 85 Bennett, A . E . ; Gr i f f in, R .G . ; Vega, S. NMR Basic Principles and Progress, 1994, 33, 3. 86 Mul ler , L.; Kumar, A . ; Baumann, T.; Ernst, R.R. Phys. Rev. Lett. 1974, 32, 1402. 87 Hediger, S. Ph.D. Thesis, Eidgenossische Technische Hochschule Zurich, Switzerland, 1997 88 (a) Hawkes, G . E . ; Mantle, M.D. ; Sales, K .D . ; A ime, S.; Gobetto, R.; Groombridge, C . J . J. Magn. Reson. Ser. A. 1995,116, 251. (b) Hagaman, E.W. ; Ho, P.C. ; Brown, L.L. ; Schell , F . M . ; Woody, M . C . J. Am. Chem. Soc. 1990,112, 7445. 89 van Koningsveld, H.; Jansen, J . C ; van Bekkum, H. Acta Cryst. 1996, B52, 140. 90 van Koningsveld, H.; Jansen, J .C. Microporous Mater. 1996, 6, 159. 91 Reck, G . ; Mar low, F.; Kornatowski, J . ; H i l l , W. ; Caro, J . J. Chem. Phys. 1996,100, 1698. 92 van Koningsveld, H.; Koegler, J .H . Microporous Mater. 1997, 9, 71. 93 Fitch, A . N . ; Joboc, H.; Renouprez, A . J. Phys. Chem. 1986, 90, 1311. 94 Wright, P.A.; Thomas, J . M . ; Cheetham, A . K . ; Nowak, A . K . Nature. 1985, 318, 611. 95 (a) Gies, H.; Marler, B.; Fyfe, C .A . ; Kokotai lo, G.T. ; Cox, D.E. J. Phys. chem. Solids, 1991, 52, 1235. (b) Mentzen, B.F. ; Sacerdote-Peronnet, M . Mat. Res. Bull. 1993, 28, 1161. (c) Mentzen, B .F . ; ' Vigne-Maeder, F. Mat. Res. Bull. 1987, 22, 309. 96 Cox , D.E. Acta Cryst. 1984, A40, 369. 97 Fyfe, C .A . ; Kennedy, G .J . , DeSchutter, C.T. ; Kokotai lo, G.T. J. Chem. Soc, Chem. Commun. 1984, 541. 98 Fyfe, C .A . ; Strobl, H. ; Kokotai lo, G.T. ; Kennedy, G .J . ; Barlow, G . E . ; J. Am. Chem. Soc. 1988,110, 3373. 99 Fyfe, C .A . ; Grondey, H. ; Feng, Y . ; Kokotai lo. G.T. J. Am. Chem. Soc, 1990, 112, 8812. 63 700 West, G .W. Aust. J. Chem. 1984, 37, 455. 101 Engelhardt, G . , M iche l , D. Unpublished results reported in High-Resolution Solid-State NMR of Silicates and Zeolites, John Wi ley and Sons, 1987, 313. 102 Strobl, H. Ph.D. Thesis University of Guelph, Canada, 1991. 103 Feng, Y . Ph.D. Thesis, The University of Brit ish Columbia, Canada, 1991. 104 Fyfe, C .A . ; Feng., Y . ; Grondey, H. ; Kokotai lo, G.T. ; Gies, H. Chem. Rev. 1991, 91, 1525. 105 Fyfe, C .A . ; Mueller, K.T. ; Kokotai lo, K.T. in NMR Techniques in Catalysis, C h . 1, Be l l , A .T . ; Pines, A . (Eds.), Marcel Dekker, 1994. 106 K l inowsk i , J . Chem. Rev. 1991, 91, 1459. 707 Pfeifer, H. ; Mei ler, W. ; Deininger, D. Ann. Rep. NMR Spectros. 1983, 75, 291. 108 Muel ler, K.T., Ph.D. Thesis, University of Cal i fornia, Berkley, 1991. 709 (a) Mueller, K.T.; Wu , Y . ; Chemlka, B.F. ; Stebbins, J . ; Pines, A . J. Am. Chem. Soc. 1991, 773, 32. (b) Vermi l l ion, K .E . ; Pierre, F.; Grandinetti, P.J. J. Chem. Phys. 1998, 108,121A. (c) Bu l l , L . M . ; Cheetham, A . K . ; Anupold, T.; Reinhold, A . ; Samoson, A . ; Sauer, J . ; Bussemer, B.; Lee, Y . ; Gann, S. Shore, J . ; Pines, A . ; Dupree, R. J. Am. Chem. Soc. 1998, 720,3510. 770 Fyfe, C .A . ; Gobbi , G .C . ; Kennedy, G .J . ; Graham, J .D. ; Ozubko, R.S.; Murphy, W.J . ; Bothner-By, A . ; Dadok, J . ; Chesnick, A . S . ; Zeolites, 1985, 5, 179. 777 Loewenstein, W. Am. Mineralog. 1954, 39, 92. 112 (a) Fyfe, C .A . ; Thomas, J . M . ; K l inowsk i , J . ; Gobbi , G . C . Angew. Chem. Int. Ed. Engl. 1983, 22, 259. (b) Lippmaa, E.; Mag i , M . ; Samoson, A . ; Grimmer, A . R . ; Engelhardt, G . J. Am. Chem. Soc. 1980, 702, 4889. 773 Chezeau, J . M . ; Delmotte, L.; Guth, J .L. ; Soulard, M . Zeolites. 1989, 9, 78. 114 Fyfe, C .A . ; Feng, Y . ; Grondey, H. ; Kokotai lo, G.T. ; Mar , A . J. Phys. Chem. 1991, 55, 3141. 115 Fyfe, C . A . ; Gies, H. ; Feng, Y . ; Kokotai lo, G.T. Nature. 1989, 341, 223. 116 Fyfe, C .A . ; Gies, H.; Feng, Y . J. Am.Chem. Soc. 1989, 777, 7702. 777 Fyfe, C . A . ; Gies, H. ; Feng, Y . ; Grondey, H . Zeolites. 1990, 70, 278. 775 Alma-Zeestraten, N . C . N . ; Dorrepaal, J . ; Keijsper, J . ; Gies, H . Zeolites, 1989, 9, 81. 779 (a) Fyfe, C .A . ; Gobbi , G . C ; Kennedy, G .J . ; De Schutter, C.T. ; Murphy, W.J . ; Ozubko, R.S.; Slack, D.A. J. Am. Chem. Soc. 1984, 706, 4435. (b) Fyfe, C . A . ; Gobbi , G . C ; Murphy, W.J . ; Ozubko, R.S.; Slack, D.A. Chem. Lett. 1984, 163. 720 Fyfe, C .A . ; Gies, H. ; Feng., Y . ; Kokotai lo, G.T. Nature. 1989, 341, 223. 64 121 Fyfe, C .A . ; Feng, Y . ; Gies, H. ; Grondey, H. ; Kokotai lo, G.T. J. Am. Chem. Soc. 1990,112, 3264. 122 Fyfe, C . A . ; Feng, Y . ; Grondey, H.; Kokotai lo, G.T. ; Mar , A . J. Phys. Chem. 1991, 95, 3747. 123 (a) Fyfe, C .A . ; Wong-Moon, K . C . ; Huang, Y . ; Grondey, H. J. Am. Chem. Soc. 1995,117, 10397. (b) Wong-Moon, K . C . Ph.D. Thesis, The University of Brit ish Columbia, Canada, 124 (a) Thomas, J . M . ; K l inowsk i , J . ; Rammdas, S.; Hunter, B .K . ; Teenakoon, D.T.B. Chem. Phys. Lett. 1983,102, 158. (b) Ramdas, S.; K l inowsk i , J . Nature. 1984, 308, 521. (c) Engelhardt, G . ; Radeglia, R. Chem. Phys. Lett. 1984,108, 271. (d) Derouane, E .G . ; Hubert, R.A. Chem. Phys. Lett. 1986, 132, 315. 125 (a) Smith, J .V . ; Blackwel l , C .S. Nature, 1983, 303, 223. (b) Fyfe, C .A . ; Strobl, H.; Kokotai lo, G.T. ; Pasztor, C.T. ; Barlow, G . E . ; Bradley, S. Zeolites, 1988, 8, 132. 126 Fyfe, C .A . ; Feng. Y . ; Grondey, H. Microporous Mater. 1993, / , 393. 127 Fyfe, C .A . ; Strobl, H. ; Gies, H. ; Kokotai lo, G.T. Can. J. Chem. 1988, 66, 1942. 128 Strobl, H.; Fyfe, C . A . ; Kokotai lo, G.T. ; Pasztor, C T . J. Am.Chem. Soc. 1987,109, 7433. 129 Fyfe, C .A . ; Gies, H. ; Kokotai lo, G.T. ; Pasztor, C.T. ; Strobl, H. ; Cox , D.E. J . Am. Chem. Soc. 1989, 111, 2470. 130 Fyfe, C .A . ; Kokotai lo, G.T. ; Strobl, H.; Gies, H. ; Kennedy, G .J . ; Pasztor, C.T. ; Barlow, G . E . in Zeolites as Catalysts, Sorbents and Detergent Builders, p. 827. Karge, H.G. ; Weitkamp, J . Eds. Elsevier, 1989. 131 van Eck, E .R .H . ; Veeman, W.S . Solid State Nucl. Magn. Reson. 1992,1, 1. 132 Fyfe, C .A . ; Mueller, K.T. ; Grondey, H.; Wong-Moon. K . C . Chem. Phys. Lett. 1992,199, 198. 133 Pfeifer, H. ; Freude, D.; Karger, J . Z. Phys. Chem. 1988, 269, 320. 134 (a) Freude, D.; K l inowsk i , J . ; Hamden, H . Chem. Phys. Lett. 1988,149, 355. (b) Freude, D.; Kl inowsk i , J . ; Hamden, H. Chem. Phys. Lett. 1988, 750, 188. (c) Freude, D.; K l inowsk i , J . J. Chem. Soc. Chem. Commun. 1988, 1411. 735 Blumenfeld, A . L . ; Coster, D.; Fripiat, J .J . J. Phys. Chem. 1995, 99, 15181. 136 Benn, R.; Gunther, H. Angew. Chem. Int. Ed. Engl. 1983, 22, 250. 737 Bax, A . Two Dimensional Nuclear Magnetic Resonance in Liquids, Delft University Press, The Netherlamds, 1982. 138 Bax, A . ; Freeman, R.; Frenkiel, T .A . ; Levitt, M . H . J. Magn. Reson. 1981, 43, 478. 139 Benn, R.; Grondey, H. Brevard, C ; Pagelot, A . J . Chem. Soc. Chem. Commun. 1988, 102. 140 (a) La Pierre, R.B. Zeolites, 1985, 5, 346. (b) Fyfe, C .A . ; Gies, H.; Kokotai lo, G.T. ; Marler, B.; Cox, D.E. J . Phys. Chem. 1989, 94, 3718. 65 141 Fyfe, C .A . ; Gies, H. ; Feng, Y . ; Kokotai lo, G.T. J. Am.Chem. Soc. 1990, 112, 8812. 142 van Eck, E .R .H . ; Veeman, W.S . J. Am. Chem. Soc. 1993,115, 1168. 143 (a) Fyfe, C .A . ; Diaz, A . C ; Lewis, A . R . ; Chezeau, J . - M . ; Grondey, H. ; Kokotai lo, G.T. in Solid-State NMR Spectroscopy of Inorganic Materials. Fitzgerald, J .J . (Ed.) ACS Symposium Series. In Press, (b) Diaz, A . C ; Fyfe, C A . Unpublished Results. 144 Reischman, P.T.; Schmitt, K .D . ; Olson, D . H . J . Phys. Chem. 1988, 92, 5165. 145 Kustanovich, I.; Fraenkel, L.; Luz, Z ; Vega, S.; Zimmermann, H. J. Phys. Chem. 1988, 92, 4134. 146 (a) K lock, E.; Delmotte, L.; Soulard, M . ; Guth, J .L . in Proceedings of the 9th International Zeolite Conference, Montreal, 1992. von Bal lmoos, R.; Higgins J .B . ; Treacy, M . M . J . (Eds.), Butterworth-Heinemann 1993, 611. (b) Delmotte, L.; Soulard, M . ; Guth, F; Seive, A . ; Lopez, A . ; Guth, J .L . Zeolites. 1990,10, 778. 147 (a) Fraissard, J . Chem. Phys. Lett. 1987,136, 314. (b) Johnson, D.W.; Griff iths, L.; Zeolites, 1987, 7, 484. (c) Ito, T.; Springuel-Huet, M -A . ; Fraissard, J . Zeolites, 1989, 9, 68. (d) Ito, T.; Fraissard, J . J . Chem. Phys. 1982, 76, 5225. 148 Cheetham, A . K . ; Bu l l , L . M . Catal. Lett.1992,13, 267. 149 Catlow, C . R . A . ; Be l l , R .G . ; Gale, J .D. ; Lewis, D.W. Stud. Surf. Sci. Catal. 1995, 97, 87. 150 Kramer, C .J . ; van Santen, R.A. , Emeis, C D . A . ; Nowak, A . K . Nature. 1993, 363, 529. 151 Sauer, J . Stud. Surf. Sci. Catal. 1994, 84, 2039. 152 Modelling of Structures and Reactivity in Zeolites, Catlow, C .R .A . , (Ed.) Academic Press: London, 1992. 153 Freeman, C M . ; Catlow, C . R . A . ; Thomas, J . M . ; Brade, S. Chem. Phys. Lett. 1991,186, 137. 154 Be l l , R .G. ; Lewis, D.W.; Voigt, P.; Freeman, C M . ; Thomas, J . M . ; Catlow, C . R . A . Stud. Surf. Sci. Catal. 1994, 84, 2075. 155 Jackson, R.A. ; Catlow, C . R . A . Mol. Simul. 1988,1, 207; Demontis, P.; Suffritti, G .B . ; Quartieri, S.; Gamba, A . ; Fois, E.S. J . Chem Soc. Faraday Trans. 2 1991, 87, 1657. 756Ti t i loye, J .O. ; Parker, S . C ; Stone, F.S.; Catlow, C . R . A . J . Phys. Chem. 1991, 95, 4038. 757 Pickett, S.D.; Nowak, A . K . ; Cheetham, A . K . ; Thomas, J . M . Molec. Simul. 1989, 2, 353. 158 Cheetham, A . K . ; Bu l l , L . M . Catal. Lett. 1992,13, 267. 66 CHAPTER 2 EXPERIMENTAL DETAILS 2.1 PREPARATION OF SAMPLES USED FOR NMR INVESTIGATIONS 2.1.1 Octadecasil Highly crystalline samples of octadecasil prepared by hydrothermal crystallization (14 days at 80 °C) from a fluoride-containing medium with quinuclidine (l-azabicyclo[2,2,2] octane, [N(CH 2CH 2 )3CH]) as template in the presence of H F were kindly provided by Dr. P. Caullet and A . C. Faust o f the Laboratoire de Materiaux Mineraux, Ecole Nationale Superieure de Chimie, Universite de Haute Alsace, France. Two different samples, designated as P C 752 and A C F 2134, were used. After synthesis, the product was washed with distil led water and dried at 90 °C. The samples were checked by powder X-ray diffraction and 1 9 F and 2 9 S i M A S N M R measurements. Carbon, nitrogen and sil icon contents were determined by elemental analysis. Calculated (weight %) for 100% occupancy: C , 11.48%, N , 1.9%, Si 38.4%, Found: C , 10.5%, N , 1.78%>, S i , 38.12%. Fluorine contents were not determined for the samples used, but typical fluorine contents in these materials are in the range 2.3% to 2 .6%/ A l l experiments were performed on as-synthesized samples; no calcination was done since this is known to result in a loss of the fluoride ions from the structure in addition to removal o f the template/ 67 2.1.2 Highly Siliceous ZSM-5 Siliceous, highly crystalline Z S M - 5 was kindly provided by G . E . Barlow. The sample was crystallized from a boron-containing, aluminium-free hydrothermal synthesis. After washing with boil ing water, the sample was calcined at 500 °C overnight to remove the organic template (tetrapropylammonium), refluxed overnight with 0.2 M ammonium bifluoride solution, re-calcined at 500 °C, and then steamed at 800 °C for 6 days. Fol lowing this treatment the Z S M - 5 sample had 2 9 S i M A S N M R linewidths of ca. 0.1 ppm. Before use, samples were calcined at 500 °C for several hours to remove any adsorbed species. 2.1.3 Loading of ZSM-5 with p-difluorobenzene Controlled amounts of p-difluorobenzene were added to freshly calcined Z S M - 5 prepared as described above. For samples where ' H - 2 9 S i C P was required, /?-difluorobenzene (Aldr ich 99+ %) was used. Because simultaneous decoupling of *H and 1 9 F was not possible on the available N M R probes, 1,4-difluorobenzene-</4 (Aldr ich 98 atom% D) which was ful ly deuterated at the 2- ,3-,5-, and 6-ring positions was utilized to remove complications (e.g. line broadening) that could have arisen from *H- 2 9 Si dipolar interactions. The volume of l iquid sorbate required to achieve a specific loading (molecules / unit cell) was calculated from the known density o f the l iquid, and added to a glass vial containing the zeolite using a 25 p L glass syringe with 0.5 p L divisions. For example, to achieve a loading of 4 molecules / u .c , 20 p L of /?-diflu6robenzene-J 4 was added to 280 mg of zeolite. The glass vial was then cooled briefly in liquid nitrogen and immediately flame-sealed. To ensure an equilibrium loading was attained throughout the sample, it was put into an oven at 60 °C or left at room temperature for at least 48 hours. To verify that the desired loading had been achieved, the samples were checked using thermal gravimetric analysis and 2 9 S i M A S N M R . 68 2.2 SOLID-STATE NMR SPECTROSCOPY 2.2.1 NMR Spectrometer A l l N M R experiments were carried out using a Bruker MSL-400 N M R spectrometer running ADAKOS 89 and DISMSL 91 software. Operating frequencies were 400.13, 376.434 and 79.495 M H z for ' H , l 9 F , and 2 9 S i respectively. 2 9 S i chemical shifts were referenced with respect to tetramethylsilane (TMS) , using the highest field resonance of an Q 8 M 8 (set to -109.7 ppm) as an intermediate standard. 1 9 F N M R spectra were referenced to external C F C I 3 . The 2 9 S i offset was appropriately chosen, and ' H or l 9 F signals set on resonance. A third channel consisting of a Programmed Test Sources PTS 250 synthesizer (frequency range 0-250 M H z ) and an American Microwave Technology broad-banded r.f. amplifier (300 W) had been added to the original M S L spectrometer. The phases and amplitudes of the r.f. pulses were calibrated using a Hewlett-Packard 8405A vector voltmeter. Initial 1 9 F / 2 9 S i experiments were done using the F l synthesizer set to 376.434 M H z to drive the high-power ' H 1 k W amplifier (retuned to 376.434 M H z ) which provided about 300 W of r.f. power for the fluorine frequency. The sil icon frequency was generated by mixing a 400.13 M H z signal (from the F2 synthesizer) with a frequency-doubled 160.3175 M H z signal provided by the F3 synthesizer. The frequency doubling and mixing was provided by a home-built unit. The 2 9 S i signal was unmixed and observed at 400.13 M H z . Later experiments made use of a commercial ' H decoupling amplifier retuned to 376.434 M H z . This tripled the 125.478 M H z input frequency (from the third channel synthesizer) and produced an output o f approximately 20 W . This was sufficient to drive the (appropriately tuned) high-power amplifier, and allowed the F l synthesizer to be used for 2 9 S i . Although lower 1 9 F r.f. powers were obtained with this set-up, it provided a significant increase in the S/N ratio when observing 2 9 S i because it removed the need for frequency mixing and unmixing. Schematics detailing the components and connections needed for these experiments are given in Appendix A . 69 2.2.2 N M R Probes, Rotors, and Caps Commercial Bruker H / X double-tuned probes with either Bruker or Doty Scientific M A S stators were used. These spun 7 mm diameter zirconia rotors holding 250-300 mg of sample. In some cases a layer o f Teflon tape was packed on top to improve the spinning stability o f the samples. Spinning speeds up to 5.2 k H z were available with a stability of better than 20 H z over a period of several days. For room temperature experiments, Ny lon or Ke l -F caps were used, boron nitride stators and caps were required for low temperature work. The magic angle was set by observing the 7 9 B r resonance of K B r / and the magnetic field was shimmed using a rotor f i l led with a dilute aqueous solution of copper sulfate (0.001 M ) mixed with D 2 0 to prevent overloading the spectrometer receiver. The performance of the Bruker double-tuned ' H / X N M R probes was carefully optimized. Modif ications included soldering two or three 2 pF (5 k V ) capacitors in series across the leads of the sample coi l were often required to adjust the frequency of the ' H channel for correct matching and tuning at 376.4 M H z (for experiments involving 1 9 F) . These capacitors were " N P 0 " rated meaning they had very stable capacitance over the temperature range -55 to 125 °C. Suitable commercially-made and home-built filters were attached at the probe to improve noise rejection. The air pressure for M A S sample spinning was controlled using a Bruker M A S pneumatic unit. Temperature regulation was achieved with a Bruker B V T 1000 temperature controller and a heater coi l within the probe (insulated) bearing air supply line. A copper-constantan thermocouple positioned close to the sample allowed a temperature stability of better than ±1 °C to be maintained. 2.2.3 Measurement of Nuclear Relaxation Times, Pulse Lengths, and Spinning Speed Measurement of the nuclear relaxation parameters was achieved using the pulse programs listed in Appendix B. Analysis o f the spectra to determine T\, T2, and T\p was carried 70 out using the commercial Bruker software. Pulse lengths and r.f. f ield strengths were determined using the various pulse programs listed in Appendix B. The pulse lengths were always measured on the sample under investigation to ensure accurate values because this is crucial for the performance of the R E D O R , T E D O R and b N A D E Q U A T E experiments. If cross polarization was used then the 2 9 S i channel pulse lengths were determined after polarization transfer. Typical ly, 7i/2-pulses were in the range 6-15 ps corresponding to r.f. f ield strengths of 16.6-41.6 kHz. The spinning frequency, v r was determined using an optical spinning rate detector, or from the peak separations of the spinning sidebands in the 1 9 F M A S N M R spectra i f no spinning rate detector was available. The spinning speed was checked before and after each experiment, and could be measured to an accuracy of better than 10 Hz . Knowledge of v r was required to calculate the rotor period and the various delays needed for precise positioning of the pulses in the T E D O R and R E D O R experiments. 2.2.4 L o w Temperature Operat ion Many of the N M R experiments required stable spinning at low temperatures for extended periods. This was achieved using cold nitrogen gas as the bearing supply to the M A S rotor with further temperature regulation provided by a heating coi l inside the probe. In order to ensure stable spinning speeds, the source gas pressure had to be maintained at a level which significantly exceeded that being used, and this was accomplished by uti l izing the boil-off from a large (200 L ) self-pressurizing liquid nitrogen Dewar operating at a pressure of 1100 kPa. The bearing gas was further cooled by it passing through loop immersed in 50 L Dewar f i l led with liquid nitrogen. A schematic of the equipment set-up for low temperature M A S experiments is shown in Figure 2.1. The drive gas was either nitrogen or dry air which was pressure regulated using the Bruker M A S unit. The probe electronics were flushed continuously with nitrogen gas 71 PRESSURE REGULATOR PRESSURE LIQUID BUILDING GAS (CLOSED) (OPEN) USE SWITCH TEMPERATURE CONTROLLER ure 2.1 Schematic of the equipment required for extended low temperature MAS NMR experiments. Temperatures as low as 200 K were readily attainable and stable spinning rate of 2 kHz could be maintained for up to 45 hours if nitrogen was used as the drive gas. The programmable timer allowed automated refills providing up to 10 hours of unsupervised operation. Dry air (routed through the MAS controller) could also be utilized as drive gas. to prevent water condensation and ice formation within the probe which could result in deterioration of the probe performance during the experiment. Approximately six hours were needed for the probe electronics to reach an equilibrium temperature (and for the tuning to become constant) after cooling from room temperature. Stable 2 kHz spinning for more than 45 hours at temperatures as low as 200 K was possible using this set-up. A digital timer controlled the automatic refi l l ing of the small cooling Dewar from another liquid nitrogen Dewar, and permitted up to 10 hours of unsupervised operation. To maintain a temperature of 240 K, the timer was set to provide one minute of refi l l ing every 2 1/2 hours. During the periods when the large Dewar was being refdled, a f low of nitrogen gas was f lowed through the probe bearing supply, and after four days operating at low temperature the probe was taken out of the magnet and air dried overnight with the cover removed. It was discovered that spinning the samples for long periods of time with nitrogen gas resulted in replacement o f the air inside the spinner by nitrogen. This process was gradual but had a dramatic effect on the N M R experiments because it caused significant changes in the nuclear relaxation times. For example, over a 20 hour period, the T\ values for 2 9 S i and ' H increased from ca. 2 s and 46 ms to about 60 s and 4.5 s respectively. This problem was circumvented by using dry air as the drive gas which ensured the sample contained oxygen, providing a well-known relaxation mechanism via interactions with paramagnetic d ioxygen/ 2.2.5 Cross Polarization and Setting of the Hartmann-Hahn Matching Condition The ' H - 2 9 S i Hartmann-Hahn cross polarization ( H H C P ) matching condition was established experimentally using Q 8 M 8 with the ' H radio-frequency power set on resonance and held constant and the 2 9 S i r.f. f ield strength adjusted to maximize the observed signal for a 2 ms contact time. For l 9 F - 2 9 S i cross polarization the appropriate Hartmann-Hahn matching condition was set on the sample being investigated (octadecasil or Z S M - 5 loaded with /7-difluorobenzene). The l 9 F transmitter was set on resonance and the 1 9 F field strength set to a suitable level with 73 external attenuators. The Si r.f. power was adjusted to optimize the Si N M R signal using contact times ranging from 2 to 30 ms. Quantitative cross polarization experiments require constant r.f. f ield strengths and spinning speeds, sometimes for periods of several days at low temperature in the work reported in this thesis. Under M A S conditions the HHCP-matching condition is split into several sideband conditions which depend directly on the spinning speed, making it necessary to maintain a steady spinning speed throughout the duration of the experiment. The maintenance of correctly matched r.f. f ield strengths was also crucial, and this is affected by the amplifier performance and probe tuning. For low temperature experiments, a period of 5-6 hours was required for the tuning to stabilize; this was the time needed for probe electronics to come to an equilibrium temperature. On occasion the forward and reflected r.f. power on both channels was monitored by placing a bi-directional coaxial coupler (Narda 3020A, frequency range 50-1000 M H z ) in-line and observing the output on an oscilloscope. The Tektronix 2465 oscilloscope had a 300 M H z bandwidth and had been calibrated to compensate for roll-off at 376 and 400 M H z . Min imiz ing the reflected power was the most sensitive method for matching the probe to 50 Q , and obtaining optimal probe tuning and performance. 2.2.6 REDOR and TEDOR Experiments In all the R E D O R experiments the observed nucleus was 2 9 S i , and the trains of rotor-synchronous dephasing pulses were applied to 2 9 S i or l 9 F , depending on the pulse sequence used. The dephasing pulses were always timed to occur at half and ful l rotor periods, the l 9 F offset was exactly on resonance, and the 2 9 S i frequency was set to be approximately in the middle of the spectrum. In the R E D O R experiments which incorporated an initial cross polarization from 1 9 F to 2 9 S i to improve the efficiency, a 10 ms contact time was used. To eliminate artifacts from the effect o f small but finite switching times within the spectrometer, dephasing pulses were applied in both the So and Sf experiments rather than removing the pulses for the So as is normally done. 74 The desired effect o f either reintroducing the dipolar interactions or not was then achieved by switching the frequency on and off resonance using a frequency offset list. A variety of null experiments confirmed that the 10 M H z offset employed was sufficiently large. Appendix B contains listings of the pulse programs, as wel l as automation programs used to calculate the required delays and increment the number of rotor periods. For T E D O R experiments the , 9 F signal was set exactly on resonance and the observed nucleus was 2 9 S i . For octadecasil the 2 9 S i frequency was set so that one of the sil icon signals was on resonance since no refocussing rc-pulse was used in the period after coherence transfer. Nu l l experiments performed without the transfer pulse showed that the observed signals arose from coherence transfer. Several different versions of the T E D O R experiment were used. These included applying the dephasing pulses on 2 9 S i or 1 9 F before the coherence transfer pulse, varying the spinning speed, the positions of the dephasing pulses, and incrementing the number of rotor cycles before or after the transfer pulse. 2.2.7 2-D I N A D E Q U A T E Exper iments The 2 9 S i offset was appropriately chosen so that the individual resonances were clear of the transmitter and exact convergence of signals on either side of the central frequency was avoided if possible. The fixed delay was usually set to 15 or 16 ms based on values reported in the literature for previous 2-D I N A D E Q U A T E experiments on zeolites. 7 Typical ly, spectral widths of 800-1000 H z were used to reduce the noise in the final 2-D spectrum. Because no lock channel was available on the N M R spectrometer used, drift in the external magnetic field (< 5 Hz / day) was compensated for by acquiring several complete 2-D data sets (each containing up to 48 increments in the F l dimension) of 12-14 hours duration which were subsequently co-added. The transmitter offsets were carefully adjusted so that 1-D 2 9 S i M A S N M R spectra were exactly coincident. The number of scans in each experiment was determined by the T\ relaxation times of the 2 9 S i nuclei, or by that of the *H nuclei i f ' H - 2 9 S i cross polarization was used. When high-75 power decoupling of 1 9 F or ' H was required, the maximum allowable acquisition time was restricted to ensure the duty cycle did not exceed 10%. 2.2.8 N M R Data Processing 2.2.8.1 Peak Integration andDeconvolution of 1-D NMR Spectra For N M R spectra containing only a few well-defined and well-separated resonances, peak areas were obtained by integration of defined regions of the spectrum. This was used to measure relaxation times, and for processing of N M R data acquired for octadecasil. For the Z S M - 5 samples loaded with sorbate where up to 12 or 24 overlapping resonances were present in the 2 9 S i M A S N M R spectra, data were apodized i f necessary (using a simple exponential function), Fourier transformed, and phased using the Bruker WIN NMR ID software running on an IBM-compatible P C . If required, any baseline corrections were also done at this stage. The individual spectra were then exported using a J-Camp D X or ASCI I file format suitable for import into the Grams-386 program/ Curve fitting of the experimental N M R spectra was done using the Grams-386 software uti l izing the appropriate number of Lorentzian curves. The peak intensities were allowed to vary with the center frequencies and peak widths of the individual peaks constrained to values determined from fitting of quantitative spectra. A linear baseline was also included during the least squares fitting process (minimization of %2) to match the calculated and observed spectra. 2.2.8.2 Processing of 2-D NMR Spectra The individual 2-D data sets were zero-fil led to at least twice the number of real data points, apodized using sine-bell functions in both F l and F2 dimensions, and double Fourier transformed with a power presentation mode using Bruker DISMSL or WIN NMR 2D software. The number of real points in the time domain was often reduced to improve signal to noise in the final spectrum. 76 2.2.8.3 Distance Determinations from Analysis of NMR Data For the C P , R E D O R , and T E D O R experiments, the heteronuclear 1 9 F - 2 9 S i dipolar couplings were determined from nonlinear least squares fitting of the data in the Mathematica6 programming environment using the methods described in Chapter 3 and Appendix C. For experiments where analytical functions in terms of Bessel functions were not available, nonlinear regression was not practical, and appropriate integrals were determined and evaluated using point-by-point numerical integration over a sphere to produce a powder average as outlined in Appendix C . Prior to commencing nonlinear regression analysis, trial fittings were used to determine approximate values for the parameters that were not fixed in the experiment. Weighted nonlinear fittings of the data were carried out using the Levenberg-Marquardt algorithm in Mathematica starting from these initial parameter values. If necessary some of the parameters were constrained to realistic (positive) limits. Further details are given in Section 4.2.3. 2.3 X - R A Y D I F F R A C T I O N E X P E R I M E N T S 2.3.1 Collection and Analysis of Powder X-ray Diffraction Data Z S M - 5 powder was calcined at 550 °C for 4 hours, cooled to room temperature and loaded into Lindemann glass X-ray capillaries (0.7 mm diameter). One sample was sealed directly, another had a measured amount of />difluorobenzene (corresponding to slightly less than 4 molecules/u.c.) added before cooling in l iquid nitrogen and flame-sealing. Powder X R D patterns were acquired on a Siemens D5000 system at the Institut fur Mineralogie, Ruhr Universitat, Bochum, Germany. To avoid preferred orientation of the crystallites, the capillary was mechanically rotated about the long axis throughout the experiment. Diffraction data were collected using a focused beam of monochromatic C u Ka radiation (X = 1.5406 A) and a position sensitive detector over the range 6.0 - 40.0° 29. A step size of 0.0077° was used and each scan took approximately six hours. Up to six of these scans were co-added to yield the final X R D 77 pattern. Diffraction data was acquired at 25°C and below 0 °C, with cooling provided by a stream of air that had passed through a coiled length of copper tubing packed in dry ice and insulated within a vacuum flask. Refinement of the cell parameters from the baseline corrected X R D data was done using the program AJUST7 as described in Chapter 7. 2.3.2 Loading of ZSM-5 Single Crystals with p-Xylene Large single crystals of Z S M - 5 were grown by Dr. W. Schwieger using hydrothermal synthesis (3-5 days at 175 °C) with tetraproplyammonium chloride, then calcined at 500 °C to remove the templating species. Several large (> 0.15 mm) crystals without obvious visible defects or twinning which were suitable for single crystal X-ray diffraction experiments were selected using an optical microscope. These were loaded into 0.3 mm diameter quartz X-ray capillaries (Charles Supper Company, wal l thickness 0.01 mm) with graded quartz-Pyrex transition pieces attached at the open end, and joined to the purpose-built apparatus constructed of Pyrex glass shown in Figure 2.2. Freshly calcined highly siliceous Z S M - 5 (ca. 300 mg) was loaded into the powder reservoir, and /(-xylene ( B D H , general purpose reagent 98.5%, ca. 25 pL ) added to the liquid reservoir. After evacuating the single crystals and Z S M - 5 powder for two hours, the /(-xylene vapour was allowed to come into contact with the Z S M - 5 . Cool ing of the powder reservoir by immersion in liquid nitrogen ensured complete transfer of the /7-xylene into the part o f apparatus containing the Z S M - 5 . The l iquid reservoir was then sealed and removed. The entire apparatus was heated at 60 °C for 28 hours, then stored for two days at room temperature. Fol lwoing this the individual capillaries were isolated by closing the stopcocks and the loading of the Z S M - 5 powder verified by thermal gravimetric analysis and 2 9 S i M A S N M R of the Z S M - 5 powder. The capillaries containing the single crystals were then immersed in liquid nitrogen and flame-sealed as close as practical to the crystal. A n equilibrium loading was ensured by keeping the sealed capillary at room temperature for several days before collecting the X-ray diffraction data. 78 Clamp Figure 2.2 Apparatus for loading up to three single zeolite crystals with precisely controlled amounts of volatile sorbates. The main body (approximate volume 10 mL) is constructed from borosilicate (Pyrex) glass and can be evacuated. The stopcocks (Kontes Air-less ware) have PTFE valves with Viton O-rings and polyacetal knobs and the entire system may be heated to 100°C during the equilibration procedure. Glass wool prevents loss of zeolite powder during evacuation. 2.3.3 Collection and Refinement of Single Crystal Diffraction Data Dr. S. Rettig of the Chemistry Department at the University of Brit ish Columbia, collected X-ray diffraction data on a single Z S M - 5 crystal loaded with ca. three molecules p-xylene/u.c. at a temperature of 180 K using graphite monochromated M o Ka radiation. A Rigaku A C F 7 diffractometer equipped with an Area Detector System Corporation charge-coupled device ( C C D ) detector was utilized and a total time of 21 hours was required for the data collection. The crystal was cooled by a f low of cold nitrogen gas. The indexed diffraction data was processed using the teXsan for Windows software,* and refined using the program SHELX-979 running on an IBM-compatible P C with a Pentium 200 processor under the Windows N T operating system. Ful l details o f the refinement are described in Chapter 8. REFERENCES FOR CHAPTER 2 1 Caullet, P.; Guth, J .L . ; Hazm, J . ; Lambl in, J . M . ; Gies, H. Eur. J. Solid State Inorg. Chem. 1991, 28, 345. 2 Frye, J.S. ; Mac ie l , G .E . J. Magn. Reson. 1982, 48, 125. 3 K l inowsk i , J . ; Carpenter, T .A. ; Thomas, J . M . J. Chem. Soc, Chem. Commun. 1986, 956. 4 Fyfe, C .A . ; Grondey, H. ; Feng, Y , ; Kokotai lo, G.T. J. Am. Chem. Soc. 1990,112, 8812. 5 Grams-386, Galactic Industries Corporation, 395 Ma in Street, Salem, N H 03079 U S A . 6 Wolfram, S. The Mathematica Book. Third Edit ion. Cambridge University Press, 1996. 7 AJUST: Programa D'extraccio D'intensitats Integrades, Version 13, 1996, Rius, J . Institut de Ciencia de Materials de Barcelona (CSIC), Catalunya, Spain. 8 teXsan for Windows 1.01. Molecular Structure Corporation, 3200 Research Forest Drive, The Woodlands, T X 77381, U.S.A. 9 Sheldrick, G . SHELXL-97: Program for the Refinement of Crystal Structures. University of Gottingen, Germany. 1997. 80 CHAPTER 3 HETERONUCLEAR DISTANCE DETERMINATIONS FROM CROSS POLARIZATION, REDOR, AND TEDOR NMR EXPERIMENTS 3.1 INTRODUCTION Solid-state N M R spectroscopy has considerable potential in solid-state structure investigations via the direct determination of internuclear distances from experiments based on the through-space dipolar interactions between pairs of nuclei. The dipolar coupling, D, between two nuclei, I and S, depends on the gyromagnetic ratios of the two nuclei, yh and y$, and on the internuclear distance r (Eq. 1.10). Furthermore, since D oc r"3, moderately accurate values of dipolar couplings can yield very accurate values for the corresponding internuclear distances, with the most unambiguous distance measurements coming from experimental systems where / and S interact as isolated spin-pairs. In high-resolution solid-state N M R , magic angle spinning is used to narrow the otherwise extremely broad (up to several kHz) resonances. Under M A S conditions the heteronuclear dipolar interaction is not removed, but its average over each complete rotor cycle is z e r o / 2 Thus, in its simplest form, the use of M A S precludes a direct measurement of D. In the cross polarization (CP) experiment, spin polarization, and thus net magnetization, is transferred via dipolar interactions from abundant I spin system (usually ! H ) to the dilute S spins (e.g. 1 3 C , 1 5 N , or 2 9 S i ) , which are then observed. Commonly, C P experiments are carried out 81 where the signal intensity is monitored as a function of the spin-locking time x. The initial build-up of intensity is related to the strength of the IS dipolar couplings, and thus analysis of C P experiments should permit discrimination between different IS distances, and ideally, yield quantitative estimates for these distances. Recently, Schaefer and co-workers have introduced the Rotational-Echo DOuble Resonance ( R E D O R ) 2 , 5 and Transferred-Echo DOuble Resonance ( T E D O R ) 7 5 experiments which use radio frequency pulses applied at specific points in each rotor period to prevent the complete averaging out of the dipolar interactions, and thus permit dipolar dephasing to occur. Using appropriate analysis, 6" 8 the magnitude of the dipolar couplings can be experimentally determined and accurate interatomic distances can be determined. T E D O R and R E D O R have been applied to amino acids, 5" 6 pept ides, 5 8 , 9 p ro te ins / 0 ' " semiconductors/ 2 po lymers/ 5 and molecular sieve f rameworks/ 7 " ' 7 In cases where the distances are known independently from X -ray diffraction measurements, those obtained from R E D O R and T E D O R experiments are in very good agreement. 6 , 9 In the present Chapter, the solid-state N M R techniques of cross polarization, R E D O R , and T E D O R are introduced, and the background theory is outlined. The mathematical formalisms required to analyze the experimental data and obtain estimates for the IS distances are then developed. Appendix C contains details of the implementation of these calculations on a computer uti l izing the Mathematica18 programming environment. The case of isolated IS spin pairs, where it is possible to obtain unambiguous heteronuclear distances, is treated first. The analysis is then extended to encompass cases where multiple / spins are coupled to a single observed S spin. The effects of molecular motions that occur on the timescale of these experiments are also described. Because these experiments rely on the heteronuclear dipolar coupling, and were carried out under M A S conditions, a brief discussion of the behavior of the dipolar interaction under M A S is presented first. 82 3.2 HETERONUCLEAR DIPOLAR INTERACTIONS UNDER MAS A s discussed in Section 1.2.3.2 spinning the sample sufficiently fast about an axis inclined at 54.74° to B0 averages the effective dipolar coupling to zero over a complete rotor cycle. However the dipole-dipole interaction does not vanish - in fact only those spin-pairs whose internuclear vectors are parallel to the spinning axis (i.e. B = 0, see Figure 1.6) wi l l have a dipolar coupling of zero at all times during a rotor cycle. For al l other orientations the dipolar coupling is still present and changes continuously during the rotor period. Eq. 3.1 gives the time dependence for the dipolar coupling under M A S . 2 D(a, P, t) = D [ s in 2 p cos2(ct + cor t) - V2 sin2p cos(oc + cor t) ] 3.1 a and P are the azimuthal and polar angles respectively, and define the position of the internuclear vector as shown previously in Figure 1.6. The behavior of the dipolar coupling for an isolated spin-pair as a function of the rotor period (calculated for two different orientations of the internuclear vector relative to the external magnetic field using Eq. 3.1) is plotted in Figure 3.1. Inspection of Figure 3.1 reveals that the value of the dipolar coupling has a periodic dependence on the rotor cycle. Since only the time average of the dipole-dipole interactions over each cycle is zero, the dipolar coupling can still be utilized to investigate connectivities and measure distances between nuclei. 3.3 CROSS POLARIZATION A s discussed in Chapter 1, Hartmann-Hahn cross polarization ( H H C P ) is the most widely used technique for heteronuclear double resonance experiments in solid-state N M R . Stejskal and Memory have written an excellent book on the fundamentals of C P under M A S conditions which presents a detailed overview of the topic. ' 9 In the most common case we have abundant spins such as ' H coupled to dilute spins e.g. 1 3 C . In the present discussion we consider the phenomenon 83 Figure 3.1 Behavior of the dipolar coupling as a function of the spinner orientation under M A S for the heteronuclear spin pair orientations indicated. Curves were calculated using Equation 3.1 with D = 1000 H z and the time is given as a fraction of the rotor period. in more detail, with specific emphasis on situations involving small numbers of spins (e.g. IS, I2S, etc.) where I-S distances might be determined. The pulse sequence used to accomplish the magnetization transfer from Ito S spins via the Hartmann-Hahn spin-lock is shown in Figure 1.8. The C P experiment is selective in that only S nuclei which are dipolar coupled to the / spins w i l l show signals in the C P spectrum, and any uncoupled S spins wi l l be not be observed. Because the dipolar interaction is a through-space interaction, it is not necessary that the coupled / and S nuclei be covalently bonded; they only need to be close to one another. 84 3.3.1 Cross Polarization for Isolated IS Spin Pairs « 3.3.1.1 Stationary Samples For efficient magnetization transfer to occur during the contact time, the amplitudes of the r.f.-fields applied to the I(a)u = -y, B\i) and S (©is = - y s Sis) spins must be adjusted so that the Hartmann-Hahn matching condition is met. For spin-1/2 nuclei in a static sample the Hartmann-Hahn match is described by Eq. 3.2. 2 0 ©u = ©is 3.2 The separation of the Zeeman levels in the rotating frame is equal for both the / and S spins when this condition is satisfied, and mutual spin-flips allow the transfer of polarization between the two spin systems to occur. 2 ' Since the r.f. f ield strength (in frequency units) is equal to the reciprocal o f the 27t-pulse time, this condition corresponds experimentally to the n/2 pulse times on both channels being equal. For static samples the Hartmann-Hahn matching condition is usually broadened by the stronger/-/homonuclear interactions. The theoretical C P matching profile calculated for a static sample is shown in Figure 3.2. Matching profiles such as this represent the efficiency of the polarization transfer (signal intensity of the S spins) as a function of the mismatch of the r.f.-field strengths coi/ - ©is. The broad profile observed in this case indicates that there is still efficient polarization transfer even i f the r.f. fields are not precisely matched. A s described by Hediger, for a static single crystal in the high-field approximation (I ©i/ + ©1S| » | bo\) with matched r.f. fields (©u = ©is), the expectation value of the polarization on the S spin, <Sz>(x) i s : 2 J <SZ>(T) = ©o/ [ 1 -cos (b0 x)] / 2 3.3 85 co r / 2TC ( kHz ) 10 f= -2 -1 0 +1 +2 6.7 3.3 I I I | I I I | I I • | • I ' | • I • -40 -20 0 20 40 ©ii - cois / k H z Figure 3.2 Cross polarization matching curves calculated for a solid with relatively weak dipolar couplings. The M A S spinning rates (cor) and sideband matching conditions (/) are indicated. Adapted from reference 22. Here coo/ is the Larmor frequency of the I spin and b0 is the orientation dependent dipolar coupling defined by Eq. 3.4, whereD is defined in Eq . 1.10. b0 = D \ [3 c o s 2 9 - 1] 3.4 Eq . 3.3 describes the shuttling of the polarization back and forth between the I and S spins with a frequency corresponding to boand this wi l l depend on the orientation of the IS internuclear vector relative to the static magnetic field Bo (Figure 1.6). In a powder we must consider the orientations of the individual crystallites, and this is achieved by integrating over the angle 9. For a powder the time dependence of the polarization on the S spin is defined by : 2 J <S z>(T) = c o 0 / [ l - g 0 ( t ) ] / 2 3.5 with go(i)= j"cos(&o x) sin9 d9 3.6 9 86 This superposition of many different cosine functions in a powder gives rise to a damped oscillation as depicted in Figure 3.3(a). The Fourier transform, Go(co), o f the oscillatory part o f Eq. 3.5 yields a Pake doublet which provides information about the dipolar coupling D directly (Figure 3.3(b)). Equation 3.6 can also be expressed in terms of Bessel functions of the first kind using the mathematical formalism reported by Muel le r 7 as described in Appendix C . This results in a more efficient calculation than numerical integration and simplifies non-linear least squares fitting to experimental data with Eq. 3.5. The spin system under consideration reaches an internal quasi-equilibrium state, <Sz>qe, after a suitable time, and this is followed by further equilibration with the lattice on a longer time scale. With the Hartmann-Hahn polarization scheme for a truly isolated IS spin system (ignoring any relaxation), half o f the polarization initially on the / spin is transferred to the S spin, i.e. <S z> q e= co 0 / /2 . In real systems it is necessary to consider the case where N (not necessarily equivalent) / spins are coupled to a single S spin. These additional couplings wi l l influence the system in two ways. Firstly, there can be an additional damping due to spin diffusion among the / spins. Secondly there wi l l be an increase in the maximum polarization which the S spin can attain in the quasi-equilibrium state. For a " rea l " isolated spin system it is l ikely that the S spin is strongly coupled to one / spin, and weakly coupled to many other remote / spins. If there is a coupling to the environment which can be considered as an infinitely large temperature bath (large, open spin system), the initial polarization on the NI spins wi l l be distributed over the (N+\) spins, and ^^qe^" 00/NI {N+\), which approaches 0)0/ for large N.23 Transient oscillations in C P signal intensities as a function of the contact time were first reported by Mid ler et al. in their ' H - 1 3 C C P study of a stationary ferrocene crystal, 2 7" and they derived an equation (Eq. 3.7) which describes the oscillatory behavior observed in the build-up of the l 3 C magnetization. 87 Figure 3.3 Evolution of the S spin polarization for an isolated IS spin system in a powder sample and the Pake doublets obtained from the Fourier transform G/(co) of the oscillatory part, (a) Stationary sample at exact Hartmann-Hahn match. Samples under M A S at ( b ) / = ±1 and ( c ) / = ±2 sideband matching conditions. Adapted from reference 23. 88 <Sz>(x) = © 0 / [1 - 0.5 exp(-£, x) cos(0.5 b0t) - 0.5 exp(-&2 x)] 3.7 The first order rate constants k\, and k2 describe the decay of the transient oscillation and the increase in the net magnetization respectively. Mul ler et al24h. assumed that the spin system could be described by a Hamiltonian limited to the strongly coupled IS spin pair, with the effect o f more remote / spins represented by an isotropic random-field spin-diffusion relaxation mechanism. Under this latter assumption they proposed that k\ = 3R/2 and k2 = R where R is the relaxation rate constant. Hediger has since determined that the rate constants k\ and k2 are better treated independently. 2 5 If the spin-diffusion rate constant R is o f the same order of magnitude or larger than all heteronuclear couplings, the model used to derive E q . 3.7 is no longer valid. Eq . 3.7 can easily be extended to the case of a powder by replacing the cosine function by its integral over 9, defined by go(x) in Eq . 3.6. Considering the quasi-equilibrium polarization < S z > q e obtained for long contact times we obtain: 2 5 3.3.1.2 Samples Undergoing Magic Angle Spinning Sample rotation such as M A S introduces a time dependence in the dipolar Hamiltonian which means that it cannot be solved analytically for most systems. Using Floquet Theory, Hediger was able to obtain approximate, time-independent Hamiltonians and to predict the explicit C P M A S behaviour for isolated IS spin pairs under spin-locking (Hartmann-Hahn) C P conditions. 2 5 2 3 The relevent results from her work are summarized is this Section. A s discussed in Section 3.2, sample rotation causes the dipolar interactions to become time-modulated and averaged to zero of each complete rotor period. Stejskal et al.24 first described the effects of M A S on Hartmann-Hahn cross polarization. They showed that the <Sz>(x) = ©o/ { 0.5 [1 - exp(-£, x) g 0 ( T ) ] + <sz> 0.5 [ l -exp(-^x) ] } 3.8 01 89 matching condition centered at coi/ = coiS splits into narrow sideband conditions a u = coi.y +/co r (f = 0, ± 1 , ±2, ±3 . . . ) separated by the rotation frequency cor (Figure 3.2). These sideband matching conditions w i l l appear whenever the M A S frequency cor is comparable to, or exceeds, the width of the abundant / spin resonance and the heteronuclear dipolar coupling frequencies. If the M A S frequency is slow compared to the homogeneous linewidth of the abundant / spins, sample spinning does not significantly influence the polarization transfer obtained by H H C P . However, i f the sample rotation is sufficiently fast (cor / 2TC » D) then the C P efficiency can be dramatically affected. This can occur in solids such as hexamethylbenzene and adamantane where fast molecular motions significantly reduce the strong intramolecular homonuclear dipolar couplings, or i f there are small, relatively isolated clusters of spins. This so-called fast M A S regime can now be reached in many samples with modern high-speed spinning systems (currently capable of achieving speeds in excess of 30 kHz) , and must be taken into account in C P M A S experiments under these conditions. For an isolated IS spin system spinning sufficiently rapidly to reach the fast M A S regime, the H H C P matching condition is split into only four new sideband matching conditions (Figure 3.2(e)):2125 coi/ = © i s +/cor / = ± 1 o r ± 2 3.9 The expectation value of the polarization on the S spin at the matching cond i t ion / is then defined b y : * <Sz>(x) = co 0/[ l -gf(x)]/2 3.10 with g / ( t ) = jcos(| bf\ x) sinp dp 3.11 P The orientation dependent dipolar couplings at the first (f=±\) and second (J=±2) sideband matching conditions are given by Eqs. 3.12 and 3.13. 2 i 90 -1 D sin(2B) exp(+z'a) 3.12 2V2 b±2 = —D s in 2 p exp(±2/a) 4 3.13 The polar angles a and P describe the orientation of the internuclear vector r with respect to a M A S rotor-fixed coordinate system with its z-axis along the spinning axis as shown previously in Figure 1.6. Eq. 3.11 can also be expressed in terms of Bessel functions for convenient fitting of experimental data as described in Appendix C . The integration in Eq. 3.10 for an isolated spin system is taken over only a single angle (P) because it is not possible to detect the phase of the dipolar coupling. Note however, that i f several / spins are coupled to the S spin, the integration would be over both angles. 2 6 Figures 3.3(a-c) show the theoretical oscillatory behaviour predicted for an isolated IS spin pair by Eq. 3.10 at the M A S matching conditions and their corresponding Pake patterns. The evolution of the spin system is identical at matching conditions f o r / = 1 and -1 , and f o r / = 2 and -2. N o C P transfer is predicted to occur at the centerband position ( m l s = coi/), although this is sometimes observed due to the contribution of fl ip-flop processes between remote / spins and from polarization transfer via heteronuclear / -coup l ing. 2 3 In the high-speed limit (cor / 2TI » D), Eq . 3.8 can be extended to the case of a powder undergoing M A S by replacing the oscillatory part g0(x) by the corresponding oscillation for rotating samples, g/(t) depending on the matching condition used. Considering the quasi-equilibrium polarization <Sz>q e inside the spin system we obtain: 2 3 <Sz>(x) = co0 / { 0.5 [1 - expO-*, T) gf(x)] + <sz> 0.5 [l-exp(-feT)] } 3.14 0) 01 91 Sample spinning tends to reduce the / - / homonuclear couplings somewhat, and thus under M A S <Sz> q e can take on values between 0.5 (ideal isolated two-spin system, no k2 as a consequence) and 1.0 (significant / - /homonuclear coupl ing). 2 6 Provided the spinning speeds are not vastly different, the oscillatory behavior should be independent o f the M A S speed used. Dipolar oscillations have been reported for several different systems under M A S conditions, and attempts have been made to determine the dipolar coupling in some cases. 2 5 ' 2 7 " 5 ' However, in all but two cases the data was fitted using slight modifications of the equation derived by Mul ler et al. (Eq. 3.7) i.e. for a stationary single crystal. 2 7" Thus the effects of having a powder sample, M A S , and sideband matching conditions were not incorporated, and the couplings obtained must be viewed accordingly. Hawkes et al.32 included the effects o f M A S , but not sideband matching to qualitatively reproduce the oscillatory behavior they observed, but made no estimate of D. To date the only reliable determination of the heteronuclear dipolar coupling from the oscillatory behavior in C P M A S experiments is for ferrocene in a powder sample of co-crystallized C6o(ferrocene)2 by Hediger 2 5 using the mathematical treatment presented in this section. 3.3.2 Cross Polarization in Small Spin-Clusters Systems with small clusters o f spins which are relatively isolated from one another i.e. INS spin systems are also possible, especially in the presence of M A S and rapid molecular motions. However the equations in Section 3.3 for isolated IS spin pairs were derived using specific assumptions to define the Hamiltonian describing the interactions in such systems. The prediction of the Hartmann-Hahn C P behaviour for small spin clusters is much more complicated. The different I-S couplings w i l l behave homogeneously, and i f all o f the couplings (both I-I and I-S) are of the same order o f magnitude (e.g. in a C H 2 group) the Hamiltonian must be constructed taking into account both the number of spins and their explicit geometrical arrangement. A ful l quantum mechanical calculation could then be performed for each crystallite 92 orientation, which may be feasible for 3-spin system (i.e. I2S) but would be very time consuming. It may also be possible to apply Floquet Theory to calculate the behavior o f <Sz>(t) under the appropriate Hami l ton ian/ 6 At present no simple way to calculate the C P behavior for small spin clusters has been presented in the literature, and although the calculations could theoretically be done, this was not attempted in the present work since it was considered outside the scope of this research. In the literature, oscillatory C P behavior is apparent in samples which very likely contain INS spin systems with N < 4. Such oscillatory behavior is anticipated provided that the number of / sp ins is small, and is also observed in the theoretical behavior calculated for some I2S systems under R E D O R and T E D O R conditions (see Chapter 5). If the observed S spin is strongly dipolar coupled to many / spins, oscillations at several frequencies interfere and a smooth exponential rise to a maximum followed by a decay due to relaxation is typically observed / 3 , 3 4 The dynamics of magnetization transfer during Hartmann-Hahn C P for such a system is presented in the next section. 3.3.3 Cross Polarization in a Network of Strongly Coupled / Spins For systems with a large number of / sp ins (e.g. *H) dipolar coupled to isotopically dilute S nuclei (e.g. 1 3 C ) , the spin-lattice relaxation in the rotating frame of the abundant / spins (Ti p(/)) is usually much faster than that o f the S spins (Tip(S)). In this case T\P(I) dominates the decay and the relaxation due to T\P(S) can be i g n o r e d / 5 3 6 A n expression of the form of Eq. 3.15 describes the behaviour o f the observed S spin net magnetization in such situations. Here Mo is maximum magnetization obtainable in the absence of relaxation and M ( t ) are the net magnetization attained after matched Hartmann-Hahn C P for time x. M ( t ) = Mo [(1/TCP) / (1/TCP - 1/ T l p(/))] (exp[-x / TXp(I)] - exp[-x ITCP]) 3.15 93 In such a case the initial exponential build-up of signal intensity is characterized by the C P rate constant, TCp~\ as polarization is transferred from the / spins to the S spins during the Hartmann-Hahn m a t c h / 5 , 5 6 A n exponential decay due to loss of the spin-locked magnetization via spin-lattice relaxation in the rotating frame is superimposed on this growth (see Figure 3.4). In other cases, the equations describing the C P behaviour are more complicated, and these have been discussed by Mehr ing 5 6 and Walter et al.37 Pines et al. have reported that the time constant TCp is inversely proportional to the heteronuclear second moment, <M2(I-S)>, and thus has a direct dependence on the sixth power of the I-S internuclear distance (Eq. 3 .16) / ' TCp~l = C,s <M2(I-S)> I <M2(I-T)> 1 / 2 3.16 <M2(I-I)> is the / - /homonuclear second moment and the < > indicates an average taken over all possible orientations. The S-S homonuclear interactions are assumed to be much smaller in magnitude and have been neglected. The term C/s is a geometrical factor defined a s / ' C,s = 3TI <*j •/v ;5>J[(2A,+& Y) 2+(&,+2A,) 2' 3.17 where av = - [y/ 2 h2 (3 cos 29y -1)] / 8 K 2 r/ 3.18 and bi = [j; ys h2 (3 cos 2 9, - 1)] / 4 T C 2 rf 3.18 The ry and r, are the / - / and I-S internuclear vectors which are at angles &,y and S, to the static external magnetic field Bo, h is Planck's constant, and Nj is the number of / sp ins . Van V l e c k 5 S derived expressions for the heteronuclear and homonuclear second moments which are related to the internuclear distances r and rn respectively, and can be evaluated explicit ly i f these distances are known. For a polycrystalline sample in the absence of molecular motion, the expressions for the second moments (in s"2) a re / * ' 5 9 94 Signal Intensity Contact Time (ms) Figure 3.4 Theoretical C P behavior for S spins in a network strongly homonuclear coupled / spins. The thick line was calculated using Equation 3.15 with TCp = 5 ms and T l p = 100 ms and shows the effect o f the build up of the S spin magnetization (thin line) in the presence of the / spins T| P exponential decay (dashed line). 1 l I l I i 1 i I I i 0 10 20 30 40 50 Contact Time (ms) Figure 3.5 C P M A S curves for glycine showing the different behavior for the methylene ( C H 2 ) and carbonyl (C=0) carbons as a function of the contact time. Adapteded from reference 22. 95 <M2(I-S)> = (1 /5) (y, ys \i0h/\ 6 T C 3 ) 2 / 5> / s 6 3.20 <M2(I-I)> = (9/20) (y/ UQ A / 1 6 T C 3 ) 2 / 2>/,6 3.21 Usually some suitable cut-off distance is chosen (typically 8-10 A), after which the interactions are ignored. 7 0 The effects of molecular motion on the second moment can be accounted for using the formalism presented by Miche l et al.41 The derivation of the appropriate equations is given in Appendix D. Thus, using Eq. 3.15 (or an appropriate function which describes the behaviour in a given system), it should be possible to fit the C P signal amplitude as a function of the contact time and to determine TCp. Discriminations between different IS distances should fol low from comparisons of the TCP values; small 7CP values w i l l correspond to short heteronuclear distances while larger r C P ' s indicate longer distances. The literature contains some examples where measurements of average internuclear distances from TCP values have been made . 2 8 7 2 This behavior is wel l illustrated by the ' H - ^ C C P M A S curves measured for the carbonyl and alpha carbons in glycine (Figure 3.5). 3.4 R O T A T I O N A L E C H O D O U B L E R E S O N A N C E In the R E D O R pulse sequence, a different approach is taken to make the effect o f the dipolar coupling directly observable under M A S conditions. Trains of rotor-synchronized n-pulses which reverse the sign of the dipolar coupling are applied to reintroduce the effects of the heteronuclear dipolar coupling that are normally removed by sample rotation at the magic angle. Two dephasing pulses per rotor cycle are needed to prevent the spinning from averaging the heteronuclear dipolar interactions to zero, and to ensure the dephasing is accumulated. 2 Figure 3.6 shows R E D O R pulse sequences with and without initial cross polarization. They both consist o f a simple spin echo sequence on the observed nucleus, and a train of rotor-synchronized re-pulses on the unobserved, dipolar-coupled spins. 96 n 71 71 7t 7t 71 I I I I I I 71/2 7: I « = 0 ACQUIRE 7^ 2 'H SL DECOUPLE 71 71 71 71 Tt 71 I I I I I I I nxr nxT CP Xr 7t I n = 0 • ACQUIRE ure 3.6 R E D O R Pulse sequences. Two experiments are performed; one with no dephasing pulses (S 0 experiment) and one with dephasing (Sf experiment). A series of these two experiments is acquired using different numbers of rotor periods n. The dephasing 7t-pulses are shown at half and complete rotor periods which gives the maximum dephasing, but positions can be varied, (a) Spin-echo on observed (S) nuclei and dephasing 7i-pulses on the / spins, (b) Sequence with initial cross polarization of the S nucluei from an abundant nucleus (e.g. 'H) . 97 Two experiments are performed, one with the dephasing rc-pulses applied to the unobserved spins, and one without. The echo intensity of the experiment where no dephasing occurs is denoted by So, while that of the echo acquired under the influence of the reintroduced heteronuclear dipolar dephasing is labeled Sf. The normalized intensity difference, AS = S 0 - S& is due to the effect o f the heteronuclear dipolar coupling. The R E D O R technique has been successfully applied to determine heteronuclear distances in a number of systems including amino acids, 3 6 peptides/ proteins/ 3 semiconductors,' 2 and polymers. ' 3 Distances as large as 8 A and 16 A have been determined between isolated 1 9 F - 1 3 C and 1 9 F - 3 1 P nuclei respectively.9'"'7 3.4.1 REDOR Behavior for Isolated IS Spin Pairs For an isolated IS spin pair, AS/So shows a non-periodic oscillation (whose "per iod" is related to the heteronuclear dipolar coupling, D) when plotted against the number of rotor cycles, n, the evolution time, «x r, or the dimensionless parameter X = nDxx.2 Here x r = l /v r = 2% I cor is the time for one complete rotor revolution. The phase accumulation from dipolar dephasing for an isolated heteronuclear spin-pair may be calculated by integrating over the time of the evolution to yield the normalized R E D O R difference signal as defined by Eq. 3.22 with the integration limits a e [0, 2TC] and p e [0, T C ] . 7 AS/So = 1 - (47i)_1 J J cos [AO R (a , p, X)] sin p dp d a 3.22 a p Here a is the azimuthal angle and P is the polar angle defined by the internuclear vector in a coordinate system defined with the z axis parallel to the rotor axis as illustrated previously in Figure 1.6. The factor of (4rc)_ 1 is required to normalize this integral, and the sin B is a geometrical weighting factor required to account for the statistical (spherical) distribution of the pairs of nuclei in a powder about the spinning axis. For two dephasing rc-pulses per rotor cycle 98 positioned at one-half and complete rotations of the spinner, the R E D O R phase accumulation AR is given by Eq . 3.23. 7 Ad>R(a, p, X) = (32) , / 2 A, sinp cosp s ina 3.23 Muel ler has derived an elegant analytical mathematical formalism which allows the R E D O R behavior to be expressed in terms of Bessel functions of the first k ind. 7 Using this, Eq. 3.22 can be evaluated with a significant reduction in computation time. It also makes possible non-linear least squares fitting of experimental data. Details of this approach are presented in Appendix C . In a R E D O R experiment AS/So may be monitored as a function of either the number of rotor periods or the position during the rotor cycle at which the dephasing pulses are applied, with the number of rotor periods constant.2 Commonly, a series of dephasing 7t-pulses is applied to the unobserved heteronuclear spins, with a simple spin-echo sequence on the observed spins as shown in Figure 3.6(a), but other variations have been reported. 7 5 ' 7 6 The importance of phase cycl ing the dephasing pulse, finite pulse lengths and accurate positioning of the pulses have been investigated. 7 5" 7 9 Because the R E D O R experiment involves the formation of an echo for the observed nucleus, it is the nuclear relaxation characteristics of this nucleus which determines how quickly the sequence can be repeated (Tj), and the maximum dephasing time at which viable signal intensity can be recorded (T2). Figure 3.7 illustrates the theoretical R E D O R behaviour predicted for an isolated IS spin pair with different dipolar couplings. These R E D O R curves agree exactly with those previously published, and were calculated assuming that the spins were at f ixed positions within a rigid lattice. If the system can be described as an isolated IS spin pair, then the magnitude of the dipolar couplings can be determined by fitting of the experimental data with an appropriate expression (e.g. Eq . 3.22), and this permits accurate measurements of interatomic distances for 99 Figure 3.7 Theoretical R E D O R behavior calculated for an isolated IS spin pair, (a) Effect o f different dipolar couplings at spinning rate of 4.0 kHz: Z)=1000 H z (solid line), Z)=500 H z (dashed line), and Z)=100 H z (dotted line), (b) "Universa l " R E D O R curve with AS/So plotted as a function of the dimensionless parameter X=nDxt. 100 systems of isolated heteronuclear spins. 2 , 7 Experimentally, the requirement of isolated spin-pairs has usually been met by isotopically labelling the molecules of interest (e.g. I 3 C - ' 5 N in natural compounds) and diluting these in a large excess of the unlabelled compound. 6 8 , 9 Schaefer et al.6 have noted that the initial behavior of the universal R E D O R curve (i.e. that plotted versus the dimensionless parameter % = nDxT, (see Figure 3.7(b)) is parabolic, being described by A S / S 0 = 1.066 X2. In principle, this allows the dipolar coupling to be quickly determined from the initial dephasing, but this approach is valid only when the spin system under investigation can be described as a truly isolated IS spin pair (see Chapter 5). Positioning the dephasing pulses at half and ful l rotor periods produces the maximum dephasing/ 0 but other pulse positions can be used. If the pulses are not at x r/2 and x r then appropriate functions AO R (ct , B, X) must be determined (see Appendix C) . These may then be evaluated using point-by-point numerical integration over a sphere to produce a powder average, or alternatively derived in terms of Bessel functions using the formalism presented by Muel ler . 7 Fourier transformation of the R E D O R dephasing signal S / S 0 (Figure 3.8(a)) yields a resonance with a width proportional to the dipolar coupling (Figure 3.8(b)). In practice however, it is usually difficult to determine D precisely due to problems associated with determining the exact width of the peak. 7 Recently Mueller et al. derived a new analytical transform method, analogous to the Fourier transform, that produces resonances at the dipolar coupling frequencies present in the R E D O R s igna l / 7 They named this the R E D O R transform, and theoretically this permits direct determination of I-S distances provided that the dephasing S/So is due to isolated IS spin pairs. Figure 3.8(c) shows the dipolar spectrum resulting from a R E D O R transform of the R E D O R data in Figure 3.8(a). The R E D O R transform has been successfully applied to determine 6 L i - l 3 C distances/ 2 and for simultaneous multiple distance measurements in pept ides/ 5 Further details o f this approach are presented in Appendix C . 101 I * ' * » l , * ' ' l ' » ' ' l ' ' « * > * * * a l 0 200 400 600 800 1000 Frequency (Hz ) Figure 3.8 (a) R E D O R dephasing S / S 0 calculated for D - 300 H z and M A S spinning speed of 4 kHz. (b) Fourier transform of this signal (20 H z Lorentzian line-broadening applied), (c) R E D O R transform of the S /S 0 data (3-point Blackman-Harris apodization applied) yields a single peak at 300 Hz . After reference 57. 102 3.4.2 REDOR Behavior for a Single S Spin Dephased by Several / Spins When the observed magnetization of a single S spin is dephased by simultaneous dipolar interactions with more than one / spin, the dephasing wi l l normally be most affected by the nearest / spin (since D <x Mr 3). However, when the distances are comparable, dephasing from multiple spins wi l l be cumulative. 6 ' 8 R E D O R distance determinations are thus much more complicated i f several / nuclei contribute to the dephasing. Such a situation can arise in isotopically enriched samples when there is a significant presence of natural abundance "background" spins. Even in non-enriched samples, there can be cases where a single S spin is dipolar coupled to several / spins as w i l l be seen later in this thesis. These multiple / spins can substantially influence the observed dephasing, especially i f the nuclei under investigation have large gyromagnetic ratios. Corrections for this background dephasing may be made by subtracting the dephasing measured for a natural abundance sample 6 but this is not always feasible. Another option is to generate or propose a model structure assuming an appropriate statistical and geometric distribution of the dephasing spins, and then to calculate the multi-spin dephasing as described below. Several approaches which permit the calculation of the R E D O R behavior for systems where multiple spins are dipolar coupled to the observed spin have been reported. 6 , 8 7 2 H J J Calculations for three-spin systems indicate virtually no difference between the dephasing calculated either including or neglecting the effects o f homonuclear couplings, provided these interactions are significantly smaller than the magic angle spinning s p e e d . " J i In the equations presented here, the effects of homonuclear coupling are assumed to be averaged out by the sample spinning, and are thus not included. Naito et al.8 detailed the derivation of an expression for a three spin system based on the assumption that it could be represented as the summation of two pairwise interactions with permutations of the possible spin states. They demonstrated that the geometrical arrangement o f the spin-pairs had a measurable effect on the calculated curves. Schaefer and co-workers derived 103 a more general equation for the R E D O R behavior of an S spin dipolar coupled to any number of / spins provided that the geometric arrangement of these spins is known. 5 7 , 5 5 This is also based on the addition of pairwise interactions. Further, Schaefer et al. were able to formulate their final equations for multi-spin R E D O R in terms of a product of cosine terms, rather than as the sum of cosine sums. The product representation gives a substantial improvement in the efficiency of the computations, and this efficiency becomes more important as the number of spin pairs involved increases. The calculation of multinuclear dephasing is based on the additivity of exponential products, 5 6 and requires a knowledge of the relative geometry as wel l as the internuclear distances." 5 7 Where the structure is known this can be incorporated, otherwise a model o f the spin cluster must be proposed. The dephasing of a single observed S spin dipolar coupled to more than one / spin can be calculated directly as the powder average of a sum of independent dephasings assuming that the / nuclei are not coupled to each other, and that the / spin dephasings of the S spins are independent of one another. 5 7 5 5 The first condition can be satisfied when the sample is undergoing magic angle spinning at speeds that greatly exceeded the largest homonuclear / - /d ipo lar coupling. The second condition has not been demonstrated to date but is assumed to hold because satisfactory fits to R E D O R data under this approximation have been obtained in a few systems.* 5 5 ' 5 7 , 5 7 For a collection of two or more / spins dipolar coupled to an observed S spin, three angles are required to produce all possible relative orientations of the internuclear vectors in a spinning powder sample. Whi le it is possible to parameterize a multiple spin system by specifying the spherical polar angles (a, P) of the axis of rotation and a third angle y to define the angle of the rotation about this axis (Figure 3.9), it is more convenient to use the Euler angles ((|), 9, as this simplifies the calculations required to perform the vector rotations. To describe the R E D O R behavior for the case when two or more spin-1/2 nuclei dipolar coupled to the observed spin-1/2 nucleus, it is thus necessary to express Ad>R in terms of the three Euler angles. 104 We define v = {vj, v 2 , v3} to be a vector o f unit magnitude which lies along the heteronuclear vector, and x, y, and z to be unit vectors along the principal axes of the coordinate system (z is coincident with the spinner axis). A rotation of v through (((>, 0, gives v' = R(<j), 6, \\)) v where R(<|), 8, \\>) is a 3 x 3 rotation matrix defining a rotation about the z-axis by <j), fol lowed by a rotation about they-axis by 9, and then a rotation about the z-axis by V J / . J S The fol lowing functions of the spherical polar angles a and P can be defined in terms of the dot products o f these vectors: 5 5 sinP cosa = v'• x 3.24 sinP sina = v'• y 3.25 cosP = v' • z 3.26 Using these identities gives: sinP cosp s ina = (v' • y) (V • z) 3.27 A O R can thus be expressed (neglecting any homonuclear interactions) as: AOR(<|), 9, \|/, X) = 32 1 / 2 X (v* • y) (v' • z) 3.28 where (v' • z) = vi (cost)) sinG) + v 2 (sinG sin<))) + v 3 cosG 3.29 and (v' • y)=vi(-cos\|/ sincp - cosG cost)) sinij/) + 3.30 v2(cos<j) cosvj/ - cosG sin<)) sinvp) + v 3(sin0 s iny) For a system of N independent / nuclei interacting with a single observed S nucleus, there wi l l be N dipolar couplings, D, (i = 1 to N), needed to account for the different heteronuclear distances. We must determine the A O R ' s for all possible combinations of S ± | Z>, | , recognizing that the individual ±1/2 spin states occur with equal probability so there are 2N combinations of EZ), (or £ X,). Because the sample is a powder, we must average these sums over space (indicated by the angular brackets) to account for the possible crystallite orientations 105 A Figure 3.9 Definitions of angles used to calculate dipolar dephasing for a powder undergoing M A S . When two or more / nuclei interact with a single S nucleus three angles a e [0, 2n], Be [0 , it], and y e [0, 2n] are required to describe the possible I-S orientations. For actual calculations of the it is convenient to use the Euler angles <j), 0, and \\i since the matrices defining the rotation are simpler. (assumed to be isotropic), add them together, and divide by the number of combinations, c (Eq. 3.31). This function is thus a sum of the appropriate powder averaged sums. AS / S 0 = 1 - c"1 ly < cos [S A O R (((>, 9, v|/, A,,)] > s p a c e (j = 1 to c) 3.31 For two / spins interacting with a single observed S spin, we have two dipolar couplings (Di and D2), N = 2, and c = 2. R E D O R experiments yield only the magnitude and not the sign of D, and since I D\ + D21 = I -D/ - D21, the number of terms in the sums can be reduced by a factor of two. The averaging over space is accomplished by numerical integration over the three Euler angles, with § and \y varied from 0 to 2n, and 9 from 0 to n. Addit ional factors are needed to normalize the integral (1 /8TC 2 ) , and to account for the statistical (spherical) distribution of the spins in a powder about the spinning axis vector (sin 0). A step size of one degree (or less) is 106 desirable, but larger step sizes may be used to reduce the computation time and still provide acceptable accuracy (see Appendix C) . For such a 3-spin system Eq. 3.31 becomes: A S / S 0 =1 - (4TC2)"1 [ UeI*{cos[A0R(<t>, 0, y , + A<D(4>, 0, y , +X2] } d<|> sinG d0 d y + Ue/•{cos[A<DR(<|), 0, v|/, + AO(<|>, 0, -X2] } d«|> sin0 d0 dvp] 3.32 Schaefer et al. have shown that the dephasing can also be calculated as a product over the TV dipolar interactions, with spatial (powder) averaging. 5 7 5 5 In this form (Eq. 3.33) it is no longer necessary to consider the two possible signs of the dipolar couplings as this is implicit ly included. J J 5 6 This considerably reduces the number of calculations required, and thus the computation time. This efficiency gain in the computations gets progressively larger as the number of spin pairs increases. AS / S 0 = 1 - (%Ti2y\ J e J+ ( I L c o s [ A O R , (<|>, 0, v|/, A.,)]) d<|> sin0 d0 dv|/ (i = 1 to N) 3.33 The analysis wi l l be less straightforward for pulse placements other than iJ2 and x r described above because, in general, the functions describing the dephasing are more complex (see Appendix C) . The validity of programs written to perform the calculations based on Eqs. 3.31 and 3.33 in the present work was checked by comparing the results for a variety o f 3-spin geometries against the data presented in reference 8. Details of the implementation of these calculations using the Mathematica programming environment are given in Appendix C . The theoretical R E D O R behavior for a variety o f 3-spin I2S systems clusters is examined in Chapter 5. 3.4.3 REDOR Behaviour of Isolated S Spins in a Network of Many / Spins Blumenfeld et al.16 have proposed a formalism for calculating the R E D O R dephasing of isolated S spins in the presence of a large number of / spins where the explicit geometrical arrangement is unknown. Their approach is analogous to that used to relate Tcp to the 107 heteronuclear second moment (Eq. 3.16). They assume that the heteronuclear lineshape is inhomogeneous, and can thus be considered as a superposition of a large number o f doublet resonances with splitting 2D:. Under the further assumption that this lineshape is Gaussian, they sum the R E D O R curves calculated (vs. nxt) for the individual Z),'s with a weighting w(D,) o f each to the final curve determined by a Gaussian distribution (Eq. 3.34): 1 w(A)= pnM2(I-S) exp The resulting R E D O R curve obtained in this manner wi l l show a smooth rise to a maximum and may be considered as the response of a spin system with a given heteronuclear second moment M2(I-S). Analyt ical functions were derived to calculate the R E D O R behavior assuming a Gaussian distribution. Ful l details are presented in Appendix C together with the Mathematica scripts used to perform the calculations. R E D O R experiments may be complicated by the presence of background signals arising from uncoupled spins (e.g. natural abundance 1 3 C in natural compounds) and in some cases it is desirable to remove these interactions/ The signal intensity that has been " lost" due to dephasing in a R E D O R experiment has not vanished; it has just been transferred to another type of coherence which is not directly observable. However, the application of appropriate pulses makes it possible to recover this magnetization, and to transfer it to observable S spin magnetization. The T E D O R experiment which is specifically designed to do this is described in the next section. 3.5 TRANSFERRED ECHO DOUBLE RESONANCE T E D O R experiments were originally developed by Schaefer and co-workers 7 J as an alternative to the R E D O R experiment to measure weak dipolar coupling of heteronuclear IS spin pairs while eliminating unwanted background signals from uncoupled spins. This is particularly •D: 2M2(I-S) 3.34 108 important for l 3 C in organic and biological systems, where there wi l l always be natural abundance 1 3 C . The T E D O R experiment uses a coherence transfer analogous to the solution-state INEPT experiment. A s seen from Figure 3.10(a), a T E D O R experiment is essentially comprised of two REDOR-type sequences: an initial one on the / spins, and a subsequent one on the S spins fol lowing the application of simultaneous 7i/2-pulses to both spins. These simultaneous pulses allow for a coherence transfer of polarization from the / to the S spins. Thus, there are two time periods of dipolar dephasing; one before the transfer of coherence, and another after. The pulse sequence in Figure 3.10(b) includes an initial cross polarization transfer from a third, abundant nucleus. During the n rotor periods before the coherence transfer, a series of dephasing 7t-pulses (two per rotor cycle) are applied to prevent the refocussing of the I-S dipolar interaction by M A S . A s in the R E D O R experiment, the dephasing pulses are placed at specific points within each rotor period. T E D O R experiments are usually performed with the dephasing pulses at x r/4 and 3x r/4, but they may be placed at different fractions of the rotor period. Some other possibilities are examined in Section 3.5.2. Once an effective heteronuclear dipolar dephasing has accumulated, a coherence transfer is performed that selects only those S spins that are dipolar coupled to / spins. Because of this selective transfer, the T E D O R effectively eliminates contributions from uncoupled S spins. In the m rotor periods that fol low, the antiphase magnetization that was transferred from the / spins to the S spin is modulated by the dephasing pulses, and evolves into observable S spin magnetization. 7 The ability to vary n with m f ixed, or to vary m with n f ixed, gives more flexibil i ty to the T E D O R experiments compared to R E D O R , since it allows the selection of the experimental parameters best suited to the T\ and T2 relaxation values of a particular system, although this has not been described in the literature to date. This flexibil i ty may be especially useful i f T2 values 109 (a) 71/2 * T r • 7t/2 7t 7t Tt 71 7C I III I Coherence Transfer i i 7t 7t 71 Tt Tt 7t/2 I Ml IP «=2 m=\ ACQUIRE (b) Tt/2 H SL CP 71 1 - H T r -DECOUPLE ^ T r • n=\ Coherence Transfer 7C Tt Tt 7t 7t/2 il Ml I n=2 mzr-7t 1 OT=1 7t/2 Tt Tt Tt Tt Tt I Ml I ACQUIRE Figure 3.10 Pulse sequences for T E D O R with: (a) dephasing pulses on the observed (5) spins before coherence transfer (achieved by simultaneous 7i/2-pulses), and on the unobserved (I) nuclei after; (b) initial cross polarization from an abundant nucleus (e.g. 'H) to the unobserved spins. A series of experiments are acquired with n held constant and m varied or vice versa. The simultaneous rc-pulses ensure that the chemical shifts are refocussed. 110 are short, as can often be the case for inorganic solids. C - N distances which are in agreement with those determined from diffraction studies have been successfully determined using T E D O R experiments. 7 5 5 9 In addition, K l u g and Schaefer have demonstrated a double T E D O R experiment for the direct detection of I-S-I triads.*50 3.5.1 T E D O R Behavior for Isolated IS Spin Pairs For an isolated heteronuclear IS spin pair, the T E D O R signal, S T , arising from placement of the dephasing Tt-pulses at one-quarter and three-quarters of a rotor cycle is described by Eqs. 3.35-3 .37 / 7 The integration limits are a e [0, 2n] and P e [0, T t ] , X„ = nDit, and Xm = mDxr. S T = (471)"1 J J s in[AO T „ (a , p, X„)] sin[AO„, (a , p, X„,)] sinp dp d a 3.35 a p where A O T „ (a , P, X„) = 32 1 / 2 X„ sinp cosP cosa 3.36 and A O T m (a , P, Xm) = 3 2 , / 2 Xm sinp cosP cosa 3.37 3.5.2 T E D O R Curve Families and Experimental Considerations T E D O R dephasing behavior is best presented by plotting curves of S T versus the number of rotor periods n or the dephasing time mT i f the number of rotor periods after coherence transfer was fixed. If n was fixed then S T vs. m or m\x is appropriate. The analysis of T E D O R experiments requires that both the spinning rate and the exact value of the dipolar coupling during the period before coherence transfer are known in order to calculate the curve for the period after the transfer, and vice versa. In real situations the coupling is usually not known a priori, but can often be estimated by using known values for similar systems. A s for R E D O R , it is advantageous to use the analytical expressions in terms of Bessel functions derived by Muel ler 7 as these avoid the more complex (and time-consuming) numerical integration and permit nonlinear least squares fitting as described in Appendix C . Ill Figure 3.11 illustrates several families of theoretical T E D O R curves including variation of n with m f ixed for different values of m, n f ixed with m varied, different rotor speeds, dipolar couplings, and several values of the parameter used to "dampen" the curves to account for the homogeneous (T2) decay that occurs after the coherence transfer.5 For a T E D O R experiment, the theoretical maximum transfer of coherence (neglecting T2 decay) is predicted to occur when nDxt = 0.84. 5 Inspection of Figure 3.11(a) and (b) shows how the position of the initial maximum in the curves shifts to higher number of rotor periods as the magnitude of the dipolar interaction decreases, or as the spinning rate increases. Calculation of a series of curves with appropriate parameters corresponding to the experimental conditions prior to beginning T E D O R experiments is invaluable for selecting the best experimental variables. For a given spin system certain values of n or m may be preferable depending on nuclear relaxation parameters and available spinning speeds. Because the T E D O R signal intensity ST is not normalized as it is for R E D O R , the experimental intensities need to be scaled to match the theoretical curves. In addition to experimental constraints (such as available pulse lengths and spinning speeds), it is important to take into consideration the nuclear relaxation parameters of the nuclei as these limit the range o f n or m values that wi l l give viable signal intensities. If the T E D O R pulse sequence contains additional simultaneous rc-pulses to generate a spin-echo, it is T2 rather than T2 that is important. This wi l l be the case where a refocussed T E D O R pulse sequence is used (Figure 3.10). During the period before coherence transfer, the spin-spin relaxation rate, T2, o f the / nuclei is important, and after the transfer it is the T2 o f the observed (S) nuclei which limits the number of rotor periods after coherence transfer that signal can be detected. Other alternatives for optimizing T E D O R experiments for specific samples include using different spinning speeds, or changing the positions of the dephasing rc-pulses. For example they can be at x r /3, 2x r/3 before coherence transfer and x r/4, 3x r/4 after, or at x r/4, 3xJ4 before transfer 112 Rotor Periods After Transfer Figure 3.11 Theoretical T E D O R curves illustrating the effects of different dipolar couplings (a) and different spinning speeds (b). The curves were calculated for an isolated IS spin pair assuming n = 2 with m varied. 113 Rotor Periods After Transfer Figure 3.11 (continued) Theoretical T E D O R curves illustrating the effects of different numbers of fixed rotor periods (c) and dampening to account for T2 decay (d). The curves were calculated for an isolated IS spin pair assuming v r=4.0 kHz, D=1000 Hz , n held constant, and m varied. 114 and x r /5, 4t r /5 after. If the pulses are shifted from x r/4 and 3x r/4, appropriate theoretical functions must be determined, and numerical integration is now required to calculate the theoretical T E D O R curves. The appropriate functions for a selection of pulse placements have been derived and are presented in Appendix C . 3.5.3 T E D O R Behavior for a Single S Spin Dephased by Several / Spins The theoretical treatment presented above for the case of R E D O R multi-spin dephasing can be extended to the T E D O R experiment. For dephasing pulses positioned at x r/4 and 3x r/4, using Eqs. 3.24 and 3.25 gives: sinP cos(3 cosa = (v'• x) (v'• z) 3.38 A<DTn can thus be expressed (neglecting any homonuclear interactions) as: AOT„((|), 6, Xn) = 32m X„(v' • x) (v' • z) 3.39 where (v' • z) = vi (cos(|> sinG) + v 2 (s inG sin<))) + v 3 cosG 3.40 and (v' • x) = V i (cos9 cos<(> cosy - sin<)> sinvu) + v 2(cosG cosy sine)) + cos<|> s iny) - v 3(cosi|/ sinG) 3.41 A n identical expression is obtained for A O T m with Xm replacing X„. If the dephasing pulses are not at the one- and three-quarters points o f each rotor period, these equations wi l l become very complex (see Table C.4, Appendix C) . Since there are now contributions from several dipolar couplings, the theoretical T E D O R curves must be plotted versus the dephasing time nxT i f the number o f rotor periods before the transfer was varied (or versus mxx i f m was varied). Using the expressions derived above, it was possible to calculate the T E D O R dephasing for INS systems as a sum of sums in an analogous manner to that described for R E D O R in Section 3.4.2. Attempts to express the multi-spin 115 T E D O R dephasing in terms of a product of sums produced dephasing behavior which was not physically meaningful ( S T very small). This stems from the nature of the functions that are evaluated. The theoretical T E D O R behavior for a variety of 3-spin I2S clusters is examined in Chapter 5. 3.6 E F F E C T S O F M O L E C U L A R M O T I O N S Any relative motions of the nuclei within a heteronuclear spin system can affect the dipolar interactions since the internuclear distance wi l l vary. Clearly C P , R E D O R and T E D O R experiments w i l l al l be affected by any changes in the magnitude of the I-S dipolar couplings which occur during the course of the experiment. Such motions wi l l need to be considered i f they occur on time scales which are shorter than the reciprocal o f the heteronuclear dipole-dipole interaction i.e. o f the order of milliseconds. In systems with weak dipolar couplings where the evolution of the dephasing needs to be observed for 30 ms or more, the inclusion of the effects of motion may be very important in correctly determining D. However, the effects of motions should only be included where they are known to exist from other independent evidence. The net effect of relative motions of the / and S spins wi l l be to average the dipolar coupling, and the exact form of the averaging wi l l depend directly on the explicit nature of the geometrical displacement, and the timescale on which it occurs. Any motion wi l l reduce the magnitude of the overall dipolar coupling. In this section a qualitative description of the effects of molecular motions, and techniques for calculating the effects i f details of the motion are known is presented. For an isolated IS spin pair during a cross polarization experiment, motion wi l l result in a situation where at a given instant some S spins w i l l experience weak dipolar coupling, while others wi l l be influenced by stronger couplings. Each different coupling wi l l give rise to an oscillatory behavior whose period is determined by the dipolar coupling. The observed signal wi l l be the superposition of a large number of these oscillations and wi l l thus be a relatively 116 smooth curve without oscillations. Depending on the timescale of the motions, the couplings within each spin pair may also change during the experiment, which would also result in a smooth, non-periodic behaviour. In spin systems with a large excess of / spins which experience strong / - / homonuclear couplings, the averaged, reduced dipolar couplings wi l l mean that the TCP value wi l l increase. However, provided the motion can be modelled then the effect on the heteronuclear second moment (M2) can be calculated using the formalism presented by Miche l et al.41 (see Appendix D). Goetz and Schaefer have described how to calculate the R E D O R dephasing in the presence of such mot ions/ 5 Basical ly a three-dimensional powder average is performed in the same manner as in the multiple-spin case, except that the argument of the cosine term Eq. 3.33 is replaced by a sum of terms which depend on the trajectory of the moving spin(s). The presence of such motions wi l l result in an apparent reduction in dephasing compared to that predicted for a rigid spin system. A similar approach may also be valid for T E D O R . 3.7 S U M M A R Y R E D O R and T E D O R experiments are proven, reliable techniques for measuring IS distances from the magnitude of the heteronuclear dipolar couplings in rigid lattices. Although it is anticipated that heteronuclear distances can also be determined from C P experiments where oscillatory behavior is observed, this has only been reliably demonstrated in very few cases. Quantitative C P experiments require that the Hartmann-Hahn matching condition is sustained for the entire duration of the spin-locking pulse, which places stringent requirements on the amplifiers to provide constant r.f. fields for several tens of mill iseconds. Under M A S the requirements become even more demanding since the spinning speed must remain constant to ensure that the chosen sideband matching condition can be maintained; slight mismatching wi l l result in dramatic loses in the C P signal. Thus C P M A S is very demanding on both the mechanical and electrical instrumentation. 117 R E D O R and T E D O R require much shorter pulses than C P (typically 10-20ps) which do however, need to be quite precisely positioned to prevent the complete averaging out of the dipolar interaction. Thus in addition to maintaining a constant spinning rate, the speed must be accurately determined so that the delays between the pulses can be correctly calculated. R E D O R experiments yield normalized intensities which can provide information about the statistical occupancy of the / spin sites. Although T E D O R experiments eliminate unwanted background signals arising from observed nuclei which are not dipolar coupled to the heteronuclear spins, the analysis requires an estimate of the dipolar coupling in order to calculate the dephasing that occurs during the period where the number of rotor periods is held constant. T E D O R offers advantages because of the larger number of experimental variables available, and the corresponding increased flexibil i ty to accommodate large T\ or small T2 values of either nucleus. Another advantage of T E D O R over R E D O R is that it is possible to perform 2-D T E D O R correlation exper iments." ' 5 / 7 ' 5 / This is potentially very useful in cases where there are several resonances for both nuclei. Incorrect internuclear distances could be obtained from fitting R E D O R and T E D O R experimental data i f more than one spin is dipolar coupled to the observed spin and the fitting assumes only a single, static, isolated spin pair. The use of only a few data points acquired at small numbers of rotor periods may give incorrect answers and should thus be avoided. Independent information which verifies that the experimental data relates to an isolated spin pair should be obtained i f possible. For spin systems which cannot be considered as isolated spin pairs, it may be possible to determine the dipolar couplings (and thus distances) accurately from R E D O R and T E D O R experiments. However, because there is a strong dependence on the number of spins involved, as wel l as the specific geometrical arrangement and motions of these, direct determination of the dipolar couplings cannot be achieved as it can for isolated spin pairs, and the experimental data must be fit to a model structure. 118 Simulations with various clusters of spins have shown that the dephasing is typically dominated by the closest heteronuclear contacts when homonuclear interactions are ignored. If an accurate model which specifies the positions (and motions) of all the spins within a cluster can be proposed, then distances from observed spins to multiple heteronuclear dephasing spins may be inferred. Such a model must explicit ly include the number o f spins, any motional averaging, the statistical probability that each site is occupied by an NMR-ac t i ve isotope, the relative spatial arrangement, and the heteronuclear distances. The quality of the model wi l l be . determined by the ability o f the theoretical curve to account for the experimentally observed behavior as a function of dephasing time. Because the dephasing predicted for different geometries can be very similar at short dephasing times, it is generally important that data be acquired at sufficiently long dephasing times to discriminate between different models. However, other problems associated with the use of long dephasing times such as poor signal-to-noise, relative motions of the spins, and significant dephasing from more distant spins may complicate these analyses. Reliable distance determinations for multiple spin systems may only be obtained with knowledge of the spin cluster geometry. If unambiguous distance determinations are needed, the system under investigation should be prepared in manner that w i l l produce only isolated spin pairs (e.g. by isotopic dilution) i f at all possible. It is also desirable to ensure complete occupancy of each labeled site since this avoids further complications arising from the need to consider the statistics of different distributions of the spins. Recently, Blumenfeld et al. have reported that in cases where there are a large number of spins dephasing a single (observed) spin, it may be appropriate to assume a Gaussian distribution of isolated IS spin pairs, and calculate the R E D O R behavior as a sum of these. 7 6 The resulting curves are thus related to a single measurable variable, the heteronuclear second moment. This approach may prove useful in many cases, especially where the structure is not known, and oscillations are not seen. 119 REFERENCES FOR CHAPTER 3 7 Waugh, J.S. ; Mar icq, M . M . ; Cantor, R. J. Magn. Reson. 1978, 29, 183. 2 Gul l ion, T.; Schaefer, J . Adv. Magn. Reson. 1989,13, 57. 3 Gul l ion, T.; Schaefer, J . J . Magn. Reson. 1989, 81, 196. 4 H ing, A . W . ; Vega, S.; Schaefer, J . J. Magn. Reson. 1992, 96, 205. 5 Hing, A . W . ; Vega, S.; Schaefer, J . J. Magn. Reson. Ser. A, 1993,103, 151. 6 Pan, Y . ; Gul l ion, T.; Schaefer, J . J. Magn. Reson. 1990, 90, 330. 7 Muel ler, K.T. J. Magn. Reson. Ser. A, 1995, 773, 81. 8 Naito, A . ; Nishimura, K.; Tuz i , S.; Saito, H. Chem. Phys. Lett. 1994, 229, 506. 9 Ho l l , S . M . ; Marshal l , G.R. ; Beusen, D.D.; Kociolek, K. ; Redl inski, A . S . ; Leplawy, M.T. ; M c K a y , R.A. ; Vega, S.; Schaefer, J . J. Am. Chem. Soc. 1992,114, 4830. 10 Marshal l , G.R. ; Beusen, D.D.; Kociolek, K.; Redl inski , A . S . ; Leplawy, M.T.; Pan, Y . ; Schaefer, J . J. Am. Chem. Soc. 1990, 772, 963. 77 McDowe l l , L . M . ; Barkan, D.; Wi lson, G . E . ; Schaefer, J . Solid State Nucl. Magn. Reson. 1996, 7, 203. 72 Ho l l , S.; Kowalewski , T.; Schaefer, J . Solid State Nucl. Magn. Reson. 1996, 6, 39. 13 Pan, Y . Solid State Nucl. Magn. Reson. 1995, 5, 263. 14 Fyfe, C .A . ; Muel ler, K.T. ; Grondey, H.; Wong-Moon. K . C . Chem. Phys. Lett. 1992, 799, 198. 75 Fyfe, C . A . ; Muel ler, K.T. ; Grondey, H.; Wong-Moon, K . C . J. Phys. Chem. 1993, 97, 13484. 16 Blumenfeld, A . L . ; Coster, D.; Fripiat, J . J . J . Phys. Chem. 1995, 99, 15181. 77 Fyfe, C . A . ; Wong-Moon, K . C ; Huang, Y . ; Grondey, H. ; Muel ler, K.T. J. Phys. Chem. 1995, 99, 8707. 18 Wolfram, S. The Mathematica Book.Third Edit ion. Cambridge University Press, 1996. 19 Stejskal, E.O.; Memory, J .D. High Resolution NMR in the Solid State - Fundamentals of CP 7 MAS. Oxford University Press, New York 1994. 20 Hartmann, S.R.; Hahn, E .L . Phys. Rev. 1962,128, 2042. 27 Pines, A . ; Gibby, M . G . ; Waugh, J.S. J . Chem. Phys. 1973, 59, 569. 22 (a) Engelke, F. in Encyclopedia of Nuclear Magnetic Resonance, Grant, D .M . ; Harris, R .K . (Eds.) John Wi ley and Sons, 1996. p. 1529. (b) Burum, D.P. in Encyclopedia of Nuclear Magnetic Resonance, Grant, D .M . ; Harris, R .K. (Eds.) John Wi ley and Sons, 1996. p. 1535. 120 23 Hediger, S. Ph.D. Dissertation, Eidgenossische Technische Hochschule Zurich, Switzerland. 1996. 24a MQller, L.; Kumar, A . ; Baumann, T.; Ernst, R.R. Phys. Rev. Lett. 1974, 32, 1402. 24b Stejskal, E.O.; Schaefer, J . ; Waugh, J.S. J. Magn. Reson. 1977, 28, 105. 25 (a) Hediger, S.; Meier, B .H . ; Ernst, R.R. J. Chem. Phys. 1995,102, 4000. (b) Hediger, S.; Meier, B .H . ; Ernst, R.R Chem. Phys. Lett. 1995, 240, 449. 26 Hediger, S. Eidgenossische Technische Hochschule Zurich, Personal Communication, August 1997. 27 Walther, K .L . ; Wokaun, A . ; Baiker, A . Mol. Phys. 1990, 71, 769. 28 K le in Douwel, C . H . ; Maas, W.E.J .R. ; Veeman, W.S. ; Werumeus Buning, G . H . ; Vanken, J .M .J . Macromol. 1990, 23, 406. 29 Hagaman, E.W.; Ho, P.C. ; Brown, L .L . ; Schell , F . M . ; Woody, M . C . J. Am. Chem. Soc. 1990, 112, 7445. 30 Pratima, R.; Ramanathan, K . V . J. Magn. Reson.. Ser. A. 1996,118,1. 31 Tian, F.; Cross, T .A . J. Magn. Reson. 1997,127, 220. 32 Hawkes, G . E . ; Mantle, M.D. ; Sales, K .D . ; A ime, S.; Gobetto, R.; Groombridge, C .J . J. Magn. Reson. Ser. A. 1995,116, 251. 33 Voelke l , R. Angew. Chem. Int. Ed. Engl. 1988, 27, 1468. 34 Schaefer, J . ; Stejskal, E.O.; Garbow, J.R.; M c K a y , R.A. J. Magn. Reson. 1984, 59, 150. 35 Yannoni , C .S . Acc. Chem. Res. 1982,15, 201. 36 Mehring, M . Principles of High Resolution NMR in Solids, 2nd ed.; Springer-Verlag: New York, 1983; Chapter 4. 37 Walter, T .H . ; Turner, G .L . ; Oldf ie ld, E. J. Magn. Reson. 1988, 76, 106. 38 van Vleck, J .H . Phys. Rev. 1948, 74, 1168. 39 Harris, R .K. Nuclear Magnetic Resonance Spectroscopy - A Physiochemical View, 3rd revised ed.; Longman Scientific & Technical: United Kingdom, 1987; Chapter 6. 40 Fyfe, C A . Solid State NMR for Chemists; C . F . C . Press: Guelph, Canada, 1983; Chapter 2. 41 M iche l , J . ; Drifford, M . ; Rigny, P. J. Chim. Phys. 1970, 67, 31. 42 Aroca, P.P. Ph.D. Thesis, The University of British Columbia, 1995. 43 (a) McDowe l l , L . M . ; Ho l l , S . M . ; Quian, S.; L i , E.; Schaefer, J . Biochem. 1993, 32, 4560.(b) Christensen, A . M . ; Schaefer, J . ; Kramer, K . J . ; Morgan, T.D. ; Hopkins, T .L . J. Am. Chem. Soc. 1991,113, 6799. (c) M a r s h a l l , G . R . ; Beusen , D . D . ; K o c i o l e k , K . ; R e d l i n s k i , A . S . ; Lep lawy , M . T . ; P a n , Y . ; Schaefer, J . J. Am. Chem. Soc.1990,112, 963. 121 44 Studelska, D.R.; K lug , C .A . ; Beusen, D.D.; McDowe l l , L . M . ; Schaefer, J . J. Am. Chem. Soc. 1996,118, 5476. 45 Gul l ion T.; Schaefer, J . J. Magn. Reson. 1991, 92, 439. 46 Garbow, J.R.; Gul l ion T. J. Magn. Reson. 1991, 95, 442. 47 Naito, A . ; Nishimura, K.; K imura, A . ; Tuz i , S.; A ida , M . ; Yasuoka, N . ; Saito, H. J. Phys. Chem. 1996,100, 14995. 48 Garbow, J.R.; Gul l ion, T. Chem. Phys. Lett. 1992, 192, 71. 49 Gul l ion, T.; Baker, D.B.; Conradi, M.S. J. Magn. Reson. 1990, 89, 479. 50 Ho l l , S . M . Ph.D. Thesis, Washington University, Missour i , U .S.A. 1993. 57 (a) Muel ler, K.T. ; Jarvie, T.P. ; Aurentz, D.J.; Roberts, B.W. Chem. Phy. Lett. 1995, 242, 535. (b) Muel ler, K.T. ; Jarvie, T.P. ; Aurentz, D.J. ; Roberts, B .W. Chem. Phy. Lett. 1996, 254, 281. 52 Quist, P-O. ; Forster, H.; Johnels, D. J. Am. Chem. Soc. 1997, 779, 5390. 53 Jarvie, T.P. ; Went, G.T. ; Mueller, K.T. J. Am. Chem. Soc. 1996, 118, 5330. 54 McDowe l l , L . M . ; K lug , C .A . ; Beusen, D.D.; Schaefer, J . Biochem. 1996, 35, 5395. 55 Goetz, J . M . ; Schaefer, J . J. Magn. Reson. 1997, 727, 147. 56 Boyce, J .B. Ph.D. Thesis, University of Il l inois at Urbana-Champaign, U.S.A. , 1972. 57 van Eck, E .R .H . ; Veeman, W.S. Solid State Nucl. Magn. Reson. 1992, 7, 1. 58 Ar fken, G . Mathematical Methods for Physicists; Academic Press, 1985; Chapter 4. 59 van Eck, E .R .H . ; Veeman, W.S. J. Magn. Reson. Sr. A. 1994, 709, 250. 60 K lug , C . A . ; Schaefer, J . J. Magn. Reson. Ser. B. 1996, 770, 176. 61 Vega, A . J . J. Am. Chem. Soc. 1988, 770, 1049. 122 CHAPTER 4 F - Si DISTANCE DETERMINATIONS IN FLUORIDE-CONTAINING OCTADECASIL FROM SOLID-STATE NMR MEASUREMENTS 4.1 I N T R O D U C T I O N The framework structures of microporous materials contain regular systems of cavities and channels of molecular dimensions (3-13 A) which are critical in the application of these materials as sorbents, catalysts and molecular sieves.'"' One of their most important characteristics is the size and shape selectivity which they display towards sorbed organic molecules and thus there is considerable interest in investigating the detailed three-dimensional structures of zeolite frameworks containing intercalated species in order to understand in detail the nature of these sorbate-framework interactions. Unfortunately, there is relatively little direct experimental information regarding the exact location of sorbed molecules within these frameworks; theoretical calculations are not always in agreement with one another, and it is difficult to determine these structures by single crystal X-ray diffraction as discussed in Chapter 1. For these reasons other techniques must be developed to obtain this structural information. In this chapter results from N M R experiments and calculations which locate the fluoride ions within the framework of octadecasil are presented. The feasibility o f extending these experiments to other framework-host / fluorine-contain ing-guest systems is clearly demonstrated. 123 4.1.1 Synthesis of Molecular Sieves in Fluoride-Containing Media The fluoride-synthesis route to molecular sieves, which was originally developed by Flanigen and Patton 5 and extended by Guth and co-workers and others,6"9 produces very highly crystalline samples having high degrees of both long range and local ordering. This is indicated by the sharp reflections extending to high 29 values which are observed in their X-ray powder diffraction patterns,"'~'2 and by the narrow resonances in their 2 9 S i M A S N M R spectra." During the synthesis, fluoride anions can play several roles, acting as mineralizers, templates or structure-directing agents.6 Chemical analysis and l 9 F M A S N M R spectroscopy reveal that most of the as-synthesized materials have incorporated fluoride anions.' 7 However, it is often difficult to locate the fluoride ions by X-ray diffraction as the single crystals may be too small, or twinned, and recourse must be made to other techniques. There are additional complications in that fluoride ions and the O H groups (which can occur as defects within these framework structures) have very similar numbers of electrons making them difficult to distinguish.' 5 In several cases, however, fluoride anions have been clearly located in the double 4-ring (D4R) units of the framework. These include octadecasil, ' 6 the tetragonal variant o f AIPO4-I6,' 7 three G a P 0 4 s (cloverite,'* G a P 0 4 - L T A , ' 9 and U L M - 5 7 0 ) , and also an LTA-type A 1 P 0 4 containing some cobalt and s i l icon. 2 0 The D 4 R moiety is not the only possible location for the fluoride ions; in the triclinic C H A - l i k e A L P 0 4 - 3 4 , " and GaP0 4-34, '° fluorine is part of the framework and it apparently bridges two A l (or Ga) atoms. In A l P 0 4 - 5 , the fluoride anion has been located in the 4-ring columns of the framework, far from the organic counter-ion. 2 ' In some cases it is not localized, and for purely siliceous MFI-type zeolites a discrepancy exists: Price et al.22 reported that the F" was located close to the nitrogen of the tetrapropylammonium ion ( T P A + ) , while Mentzen et al.23 located it in the framework close to a 4-ring, but also found an unassigned site close to the T P A + . In a few cases, such as the recently reported precursor of FER-type zeoli te, 2 7 F" is not 124 incorporated, suggesting that its role in this case is restricted to that o f a mobil izing agent. Thus, there is also interest in being able to locate the fluoride ions in these types of samples to improve understanding of the various roles they play in the syntheses. 4.1.2 I 9 F - 2 9 S i Distance Determinations from Solid-State N M R Experiments Solid-state N M R in conjunction with Rietveld refinement o f powder X R D data has been successfully demonstrated to be a powerful technique for the investigation of zeolite structures.* 2 6 The 2 9 S i M A S N M R spectra o f highly siliceous zeolites can be directly related to the framework structure, the number and relative intensities of the resonances reflecting the numbers and occupancies of the crystallographically inequivalent T-sites in the asymmetric unit. 2 7" 2 9 This makes it possible, in principle, to determine the locations of species within the frameworks by determining the distances between their component atoms and specific T-sites in the framework. This can be done using experiments based on the through-space dipolar interactions between pairs of nuclei Zand S as described in Chapter 3. The magnitude of the dipolar coupling between two nuclei depends on the gyromagnetic ratios o f the two nuclei, yi, and y s , and on the IS internuclear distance (Eq. 1.10), making l 9 F attractive for these studies. Furthermore, while the 1 9 F isotope is 100% abundant, fluorine is relatively uncommon in chemical systems, and thus the likelihood of potential background interferences is minimal. In high-resolution solid-state N M R , magic angle spinning ( M A S ) , is used to narrow the otherwise extremely broad (up to several kHz) resonances. However, in addition to averaging the chemical shift to its isotropic value, the heteronuclear dipolar interactions for an isolated spin-pair are averaged to zero during each complete rotor c y c l e / 0 , 5 ' Thus, in its simplest form, the use of M A S precludes a direct measurement of D, although this interaction is responsible for the coherence transfer in the cross polarization (CP) p rocess / 2 , 5 5 In those cases where the spin system behaves essentially as an isolated heteronuclear spin-pair, an oscillatory behavior in the 125 amplitude of the C P signal at short contact times is observed for both non-rotating solid samples 5 5 , 5 7 and those undergoing magic angle spinning. 5 5 Such dipolar have been reported for several different systems under M A S conditions. 5 6" 7 7 Fitting of these oscillations with appropriate functions allows the heteronuclear dipolar coupling and thus the internuclear I-S distances to be determined as discussed in Chapter 3. If the observed spins experience dipolar coupling to several heteronuclear spins, oscillations at several frequencies interfere and a smooth exponential rise to a maximum followed by a decay due to relaxation is typically observed. 5 2 5 7 Recently, Schaefer and co-workers have introduced the R E D O R 5 7 7 2 and T E D O R 7 5 7 7 experiments. The magnitude of the dipolar couplings can be experimentally determined from these experiments using appropriate analyses. 7 7" 7" A s discussed in Chapter 3, R E D O R and T E D O R distance determinations are more complicated i f several nuclei contribute to the dephasing. In this chapter the results of Si-F distance measurements on as-synthesized octadecasil are presented. Octadecasil, chosen to be representative of molecular sieve framework structures, is the purely siliceous analogue of AIPO4-I6, and was recently synthesized by Caullet et al. from fluoride-containing media. 7 6 The crystal structure was solved using single crystal X-ray methods, the fluoride anions located, and accurate Si-F distances determined. 7 6 The low natural abundance of 2 9 S i (4.7%) in the framework, combined with the weak homonuclear couplings means that the l 9 F - 2 9 S i dipolar interactions should approximate clusters of isolated heteronuclear spin-pairs for which theoretical C P , R E D O R , and T E D O R behavior can be calculated. Octadecasil, which contains two distinct T-sites and two quite different Si-F interatomic distances, was chosen as a model case for determining the best experiments to use, as well as the optimization of these experiments and the subsequent analysis of the experimental data. 126 4.2 M A T E R I A L S AND M E T H O D S The pure, highly crystalline octadecasil sample (crystal size 80 um), was kindly provided by Dr. P. Caullet. The structure was checked by powder X-ray diffraction and l 9 F and 2 9 S i M A S N M R measurements, all o f which agreed with previously reported resu l ts . 6 ' I 6 J 9 Fluorine contents in these materials are usually in the range 2.3% to 2 . 6 % / 6 which corresponds to occupancies of 80% to 100% of the D4R units by fluoride ions. The idealized elemental composition of octadecasil is S i 2 o 0 4 0 • 2 (Q + F") where Q + is the quinuclidinium cation. The N M R experiments were carried out using a Bruker MSL-400 spectrometer, operating at frequencies of 376.434 M H z and 79.495 M H z for l 9 F and 2 9 S i respectively as described in Chapter 2. A Bruker double-tuned ' H / X M A S probe with the ' H channel tuned to the 1 9 F frequency was used, and spinning speeds of 2.0-5.2 kHz were attainable. The peak separations of the spinning sidebands in the 1 9 F M A S N M R spectra were used to determine the spinning frequency, v r , to an accuracy of better than 10 Hz . Further details are given in Chapter 2. 4.2.1 Cross Polarization Experiments For the C P experiments the Hartmann-Hahn sideband matching cond i t i on 5 5 5 0 was established experimentally by f ix ing the 1 9 F radio-frequency power and adjusting the 2 9 S i radio-frequency power to maximize the observed signal. Field strengths up to 33 kHz were available for the 1 9 F channel. For variable contact time C P experiments, spectra were acquired using contact times from 10 ps to 60 ms. The Hartmann-Hahn matches were optimized using a 2 ms contact time for non-spinning (static) samples, and 10 ms for samples undergoing M A S . 4.2.2 R E D O R and T E D O R Experiments In all the R E D O R experiments the observed nucleus was 2 9 S i , and the trains of rotor-synchronous dephasing pulses were applied to 2 9 S i or , 9 F , depending on the pulse sequence used. 127 The dephasing pulses were always timed to occur at half and full rotor periods, the F offset was exactly on resonance, and the 2 9 S i frequency was set to be approximately midway between the two sil icon resonances. In the R E D O R experiments which incorporated an initial cross polarization from 1 9 F to 2 9 S i to improve the efficiency, a 10 ms contact time was used. Further details of the experimental set-up are described in Chapter 2. For T E D O R experiments the fluorine signal was set exactly on resonance and the observed nucleus was 2 9 S i . Several variations of the T E D O R experiment were used. These included applying the dephasing pulses on 2 9 S i or 1 9 F before the coherence transfer pulse, varying the spinning speed, the positions of the dephasing pulses, and incrementing the number of rotor cycles before or after the transfer pulse. 4.2.3 Calculat ions and Data Analys is Fitting to determine the relaxation times was carried out using the commercial Bruker software. Values of the expected l 9 F - 2 9 S i dipolar coupling constants for a range of Si -F distances were calculated using Eq . 1.10 and are summarized in Table 4.1. The boldface entries in the table correspond to the experimental S i -F interatomic distances determined from the crystal structure data for octadecasil reported by Caullet et al.,'6 and the corresponding dipolar couplings. For the C P , R E D O R , and T E D O R experiments, the heteronuclear 1 9 F - 2 9 S i dipolar couplings for the T - l silicons were determined from nonlinear least squares fitting of the data in Mathematical using the methods described in Chapter 3. For all the calculations the spins were assumed to be at fixed positions within a rigid lattice and homonuclear dipolar interactions were ignored because the l 9 F - ' 9 F couplings and the much weaker 2 9 S i - 2 9 S i couplings were much less than the sample spinning speeds employed (2-5 kHz). 128 Table 4.1 19F-29Si spin-pair dipolar couplings (D) calculated for various Si-F interatomic distances (r). Boldface entries are for the distances and corresponding dipolar couplings calculated from the single crystal X-ray structure of octadecasil by Caullet et al.16 r(A) 2.775 2.733 2.692 2.655 2.632 2.585 2.552 2.521 2.492 D(Hz) 1050 1100 1150 1200 1230 1300 1350 1400 1450 r(A) 6.077 5.887 5.801 5.719 5.688 5.6420 5.568 5.433 4.824 Z)(Hz) 100 110 115 120 122 125 130 150 200 Table 4.2 Si and F MAS NMR relaxation time measurements (performed at frequencies of 79.495 MHz and 376.434 MHz respectively). Relaxation Parameter F 8(CFC1 3) = -37.8 ppm T-l Si 8(TMS) = -108 ppm T-2 Si 5(TMS) = -111 ppm r,(a) 2.6 s 22 s 20 s j^(a,b) 3.5 ms 18 ms 20 ms Values determined by fitting using the commercial Bruker software. Data acquired with rotor-synchronization. Prior to commencing nonlinear fitting, trial fittings were used to determine approximate values for the parameters that were not fixed in the experiment, the dipolar coupling and a scaling factor to match the experimental and theoretical intensities i f required. During fitting of the C P data, some constraints were necessary to prevent physically unrealistic values for some of the parameters. For T E D O R experiments there is no normalization as there is for R E D O R , so the scaling factor was arbitrary, and an exponential damping factor was incorporated to take into account T2 decay during the evolution period. 7 ' ' Weighted nonlinear fittings of the data were carried out starting from these initial parameter values, and these were constrained to realistic (positive) limits. The Levenberg-Marquardt algorithm 5 ' was utilized to minimize the value of the parameter %2 = £| F, - f 12 where F, is the value of the / * data point and f) is the value obtained from the fit. The best values for the parameters were taken as those which gave the smallest %2 values. Because the spectra acquired for small numbers of rotor cycles had better signal-to-noise ratios, they yielded more accurate intensities, and consequently these data were given more emphasis during the fitting procedure. Several data-weighting schemes were evaluated, and weighting by the inverse of the number of rotor periods proved to be the most reliable, giving very reproducible results i f the initial parameter values were varied. For experiments where the positions of the pulses were not those used for the derivations of the analytical functions reported by Mueller, 7 1 5 and also when multiple spin analysis was required (T-2 Si), the appropriate integrals 5 / 7 7 7 7 for the T E D O R and R E D O R functions were determined and then evaluated using point-by-point numerical integration over a sphere to produce a powder average as described in Chapter 3 and Appendix C . 4.3 RESULTS AND DISCUSSION 4.3.1 Octadecasil Crystal Structure The structure of octadecasil, the purely siliceous analogue of AIPO4-I6 ( IZA Structure Commission Framework Code A S T ) , has been solved by single crystal X-ray methods.' 6 The 130 framework consists of octadecahedral [4 66 1 2] cages and hexahedral [46] cages, and can be built by l inking the octadecahedra through all their common 6-membered ring faces (Figure 4.1(a)). Since these octadecahedral cages do not completely f i l l 3-dimensional space another type of void, the very small [46]-cage or double 4-membered ring (D4R) unit is created. When prepared from a fluoride-containing medium, the as-synthesized product contains the quaternary ammonium templating cation (quinuclidinium in this case) in the large cages, and the negatively charged fluoride anion (needed to balance the positive charge of the organic cation) in the D4R units, and crystallizes in a tetragonal phase (space group I4/m, No . 87 ) . M The octadecasil structure contains two types of T-sites (Figure 4.1), T - l sites at the vertices of the D4R units and T-2 sites located at the vertices of 6-rings in the ratio 4 T - l : 1 T-2. There are 20 [SiO,}] tetrahedra, and thus 16 T - l and 4 T-2 sites per unit cel l . Each T-2 links 4 T - l ' s from four different D4R units (Figure 4.1(b)). From the X-ray crystal structure data, the T - l silicons are 2.63 A from the fluoride ion inside their D 4 R unit and more than 7 A from the fluoride ions in the adjacent D 4 R units. The T-2 silicons are 5.69 A from each of four equivalent fluoride anions, and the closest F-F distance is 9.33 A. 4.3.2 1-D 1 9 F and 2 9 S i N M R Exper iments Qualitative 1 9 F and 2 9 S i M A S N M R spectra were in general agreement, both with previously reported data and the crystal structure as discussed above. In order to best implement the different experiments, a knowledge of the different nuclear relaxation parameters is essential. T\ and T2 were measured for both nuclei, and are summarized in Table 4.2. For C P experiments the value of T l p was measured using an l 9 F spin locking field of 17 or 33 kHz. The room-temperature 1-D l 9 F M A S N M R spectrum (Figure 4.2(a)) shows a single resonance at -38.2 ppm with respect to C F C I 3 . The chemical shift is indicative of a single, unique environment, and is similar to those reported for other 1 9 F / 2 9 S i systems where the fluoride ion is located within a D4R un i t / 7 ' 7 6 The static l 9 F N M R spectrum consists of a single peak with a ful l -131 Figure 4.1 (a) Schematic representation of the framework structure of octadecasil showing the packing arrangement of the two types of cages, the large [4 66 1 2]-cages, and the small [46]-cages (or D 4 R units). Si l icon atoms lie at each vertex, and oxygen atoms are located approximately midway along the lines. Thick lines indicate connections closer to the viewer. The [4 66 1 2]-cages pack in a tetrahedral arrangement by sharing all their 6-membered ring faces and [46]-cages f i l l the voids thus created. Fluoride anions lie at the center of ca. 90% the double four-ring units, (b) Portion of the octadecasil framework showing the four D4R units surrounding each T-2 sil icon. Each T - l sil icon is connected to three other T - l sites in the same D4R unit and to one T-2 sil icon. Fluoride anions are 2.63 A from each T - l sil icon in the [46]-cage and 5.69 A from the nearest T-2 si l icon. The distance between fluoride anions in adjacent D 4 R units is 9.33 A. 132 * J L * ~I -60 n -20 -30 I -40 ppm (w.r.t CFC1 3 ) -50 (b) T- l Si -104 -106 -108 -110 -112 -114 ppm(w.r.t.TMS) F igure 4.2 (a) l 9 F M A S N M R spectrum of octadecasil, obtained with 132 scans, spinning speed 4.296 kHz, pulse width 9 ps, relaxation delay 10 s (spinning sidebands marked *). (b) Quantitative 2 9 S i M A S N M R spectrum of octadecasil showing the two resonances assigned to the T - l and T-2 silicons respectively. The relative peak intensities (4:1) are as expected from the crystal structure. The spectrum was acquired with 48 scans, spinning speed 2.2 kHz, pulse width 8 ps, relaxation delay 110 s, and no *H decoupling. 133 width at half-height ( F W H H ) of 6200 Hz . The room temperature 1-D 2 9 S i M A S N M R spectrum of octadecasil shows two resonances at -107.7 ppm and -111.6 ppm with respect to tetramethylsilane (TMS) (Figure 4.2(b)). These peaks have an intensity ratio of 4:1, and can thus be assigned to the silicons in the T - l and T-2 sites respectively.' 6 The static 2 9 S i N M R spectrum shows a single resonance with a F W H H of 1700 Hz . Clearly, the known framework structure of octadecasil containing fluoride anions in the D4R units with its two different Si -F interatomic distances and two distinct sil icon environments provides an ideal test case for evaluating the reliability and robustness of 1 9 F / 2 9 S i C P , R E D O R and T E D O R N M R experiments involving molecular sieve frameworks, as wel l as for determining the optimum experimental conditions for them. For clarity the different experiments wi l l be discussed separately. 4.3.3 1 9F-2 9Si Cross Polarization Experiments 4.3.3.1 Hartmann-Hahn Matching Profiles Hartmann-Hahn matches for the 1 9 F - 2 9 S i cross polarization were determined by f ixing the 1 9 F field strength and varying the 2 9 S i r.f. power. For a non-spinning sample, a single match condition was found (Figure 4.3(a)) which corresponded to the exact Hartmann-Hahn condition (coi/ - ©is = 0) as expected. Under M A S up to four matching conditions which exhibited a clear dependence on the spinning speed were found (Figure 4.3). Moreover, under M A S almost no polarization transfer was observed at the exact Hartmann-Hahn match, but four other matching conditions separated by integral multiples of the spinning speed were found. In some cases the available 2 9 S i r.f. power range was not sufficient to observe all four conditions. For an isolated IS spin pair the heteronuclear dipolar interactions are modulated by one and two times the spinning frequency under M A S conditions, and this leads to strong first and second order sidebands in the C P matching profile i f the spinning speed exceeds the width of the abundant I spin resonance line and the heteronuclear dipolar coupling f requency/ 5 Although the 134 I I I I I • I • I 8 12 16 20 24 2 9 S i Field Strength (kHz) F igure 4.3 Hartmann-Hahn F- Si C P matching profiles for the two T-sites in octadecasil: (a) non-spinning sample, (b) 3.37 kHz M A S , and (c) 4.15 kHz M A S . The 1 9 F field strength was 17 kHz, and contact times of 2 ms and 10 ms were used for the static and M A S experiments respectively. The M A S sideband matching conditions, / , are also indicated. 135 spinning speeds employed were only approximately three times greater than the F- Si dipolar coupling calculated from the crystal structure of octadecasil for the T - l Si (1230 Hz) , the Hartmann-Hahn matching profile indicates that the T - l Si / F" ion pair is essentially behaving as an isolated spin pair with sideband matching conditions corresponding t o / = ±1 and ±2 observed as predicted by Eq. 3.9. The small amount of polarization transfer observed at the centreband (f = 0) matching condition may be due to fl ip-flop processes between remote 1 9 F spins or polarization transfer mediated through heteronuclear J -coup l i ng / 2 The matching profiles for the T-2 Si are also shown in Figure 4.3 and seem to mimic the behaviour seen for the T - l S i . The signal to noise ratio for the T-2 Si was quite poor at the 10 ms contact time employed as indicated by the relative intensities of the signals. 4.3.3.2 Variable Contact Time Experiments In variable-contact time C P experiments, the 2 9 S i signal intensity is monitored as a function of the spin-locking time t. The initial exponential build-up of intensity is usually characterized by the C P rate constant, TCP"1, as polarization is transferred from l 9 F to 2 9 S i during the Hartmann-Hahn ma tch / 7 A n exponential decay with first order rate constant Tip"' due to loss of the spin-locked magnetization via spin-lattice relaxation in the rotating frame is superimposed on this growth. For a system of isolated spin pairs, the magnetization transfer process via matched Hartmann-Hahn spin-locked cross polarization under M A S conditions should exhibit oscillatory behavior as the polarization shuttles between the connected spin-pairs, as reported previously for a few cases / 6 ~" ' 5 2 Variable contact time C P experiments from l 9 F to 2 9 S i on octadecasil were carried out at several spinning speeds and different behaviors were observed for the two types of T-sites. For the T - l silicons the variable contact time C P experiments showed a rise to a maximum, with a clear oscillatory behavior in the signal amplitude at short contact times, fol lowed by an exponential decay (Figure 4.4). On some occasions these oscillations were absent 136 and this was attributed to mismatching arising from variations in the r.f. power or the spinning speed during the course of the experiment (the C P matching sidebands become narrow at high spinning speeds, and efficient C P under M A S requires highly stable r.f. amplitudes and constant spinning rates over extended periods of t ime) / 2 The "per iod" of the oscillatory behavior was dependent on the matching condition employed, but independent of the spinning speed. Moreover, the oscillatory behavior was virtually identical under equivalent matching conditions, i.e. at / = +1 and -1 (or / = +2 and -2). For samples undergoing M A S , the dampening of the oscillations showed a noticeable dependence on the spinning speed; becoming more clearly resolved with increasing spinning rates. The rate of decay at longer contact times was found to be directly dependent on the magnitude of the 1 9 F spin locking field, becoming less with increasing l 9 F r.f. power, indicating that Tip was increasing (as would be expected). Because the silicons in the T - l sites are very close (< 3 A) to the fluoride ion which occupies their D4R, and the next-nearest 1 9 F nuclei in adjacent D4R units are much further away (> 7 A), these silicons and their corresponding F" may be considered as isolated l 9 F - 2 9 S i spin-pairs. A n oscillatory behavior is thus predicted for the T - l silicons, and is clearly seen in Figure 4.4. For the T-2 silicons a fairly smooth rise to a maximum, followed by a decay was observed (Figure 4.4). Since the T-2 silicons are surrounded by up to 4 equidistant (5.69 A) fluoride anions, they are not expected to show the pronounced oscillatory behavior predicted for isolated spin pairs. Unfortunately no explicit analytical functions are available at present to describe the cross polarization behavior of small spin clusters, however calculations for the R E D O R dephasing of an I4S system with tetrahedral geometry show oscillations (see Section 4.3.4.2). Based on the similarities in the oscillatory R E D O R and C P signal amplitudes seen for isolated spin pairs, some oscillatory behavior might be expected for the T-2 S i . This would be far less obvious than that seen for the T - l S i , and could be easily obscured (e.g. by l 9 F spin diffusion processes). A crude estimate of the period of the oscillation expected for the T-2 Si can 137 0 10 20 30 40 50 Contact Time (ms) F igure 4.4 F- Si C P behaviour for the two T-sites in octadecasil under M A S conditions as a function of the contact time at t h e / = -1 sideband matching condition. The oscillatory behaviour for the T - l Si and the decay due to Tlp are clearly seen. The theoretical fit calculated using E q . 3.14 for the T - l S i w i t h D = 1360 Hz is also shown. 0 2 4 6 8 10 Contact Time (ms) F igure 4.5 1 9 F - 2 9 S i C P behaviour for the T - l Si in a non-spinning octadecasil sample as a function of the contact time. The line shows the fit calculated using Eq. 3.8 with D = 1440 Hz , S e q = 0.9, k{x = 2.2 ms, k2A = 26.7 ms, and T l p = 2 s. The 1 9 F field strength was 17 kHz. 138 be made by assuming these behave as isolated 1 9 F - 2 9 S i spin pairs with a dipolar coupling of 120 Hz. From Figure 3.3 the oscillation period is found to be about 35 ms; much longer than the time it takes for the oscillatory behaviour to be dampened for the T - l Si (ca. 15 ms). A s described in Chapter 3, Hediger 5 2 has reported analytical functions for fitting the oscillatory C P behavior in isolated IS spin pairs at specific Hartmann-Hahn matching conditions and these were used to determine the dipolar coupling for the T - l Si as discussed in the fol lowing sections. 4.3.3.3 Fitting of the Oscillatory Cross Polarization Behavior for the T-l Silicon Non-spinning Samples at the Centerband Matching Condition Figure 4.5 shows the area of the 2 9 S i resonance for a static sample as a function of the contact time. A t short contact times a clear oscillatory behavior is seen, which is progressively damped. A n upward trend at longer contact times is also apparent. Although this resonance includes signals from both the T - l and T-2 sil icons, the contribution to the total area from the T-2 Si wi l l be small. Under M A S where the two T-sites are well resolved, an estimate of the relative areas of the contribution arising from each T-site can be made (e.g. from Figure 4.4) and is found to be less than 10 % for contact times up to 10 ms. This is about same as the uncertainty in determining the area of the static resonance by integration. On this basis the analysis and fitting of the data in terms of only T - l Si was considered val id. Fitting of the data was carried out using Eq. 3.8 in order to determine the l 9 F - 2 9 S i dipolar coupling. The increasing signal amplitude at longer contact times indicates that the spin system cannot be considered as a truly isolated spin pair, as this would level out as seen in Figure 3.3 (a)). Thus in addition to k\ (the rate constant describing the dampening of the transient oscillations), a rate constant (k2) which describes the build-up of the net magnetization is needed to allow a good fit to the experimental data, and this means <Sz>qe must be greater than 0.5. However, <Sz>qe and k2 are strongly correlated (Eq. 3.8), and in order to ensure reliable fitting 139 between different data sets the value of <Sz> q e was fixed at 0.9. This value was arrived at based on an evaluation of the number of fluoride ions surrounding the T - l Si determined from the X -ray determined structure of octadecasil. Within a 12 A-radius sphere surrounding a T - l Si (corresponding to l 9 F - 2 9 S i dipolar couplings > 15 Hz), there are eight F" ions which yields <Sz>qe = N/N + 1 « 0.9 when the statistical occupancy of the D 4 R ' s is taken into consideration. Addit ional parameters are required to match the intensities of the experimental data and theoretical curves, and to include the effects of decay due to Tip. The best fit to the envelope of experimental data was obtained with k]~l = 2.2 ms, k2~] -26.7 ms, and T| P = 2 s. The actual values of these parameters do not affect the dipolar coupling since this is defined by the period of the oscillations. Once suitable values for these five parameters were found, nonlinear least squares regression to fit the data with Eq. 3.8 (expressed in terms of Bessel functions) was undertaken and the best fit found with D = 1440 Hz. The resulting theoretical curve calculated using these values is overlaid on the experimental data in Figure 4.5 and shows quite good agreement. The largest discrepancies occur at contact times up to 1 ms, and this is attributed to the slight variation (decrease) in the output of the l 9 F amplifier power with increasing contact time; the Hartmann-Hahn match had been optimized for a 2 ms contact time. D = 1440 Hz corresponds to a Si -F distance of 2.49 A, which is slightly shorter than the 2.63 A determined from X R D . The slightly larger dipolar coupling found from fitting of the experimental data may reflect the contribution from fluoride ions in other D4R 's , and to a lesser extent the T-2 Si intensity. Spinning Samples at the f=±l Sideband Matching Conditions Under M A S conditions, the transient oscillations became significantly more pronounced than those observed for static samples. This phenomenon is readily seen by comparison of the experimental data presented in Figures 4.5, 4.6 and 4.7. According to the theoretical treatment presented by Hed iger / 2 the oscillatory behaviour at t h e / = +1 sideband matching condition 140 Peak Area (arb. units), • 3.37 kHz, / = - l • 3.37 kHz, f=+) A 4.66 kHz, / = + ! Contact Time (ms) Figure 4.6 1 9 F - 2 9 S i C P behaviour for the T - l Si in octadecasil at the I /1 =lsideband matching conditions under various M A S speeds. Curves calculated using Eq. 3.14 with D = 1340 H z (v r = 3.37 k H z , / = -1 ) , D = 1380 Hz (v r =3.37 k H z , / = +1), and D = 1360 H z (v r = 4.66 k H z , / = -1 ) are overlaid. The intensities have been arbritrarily scaled to separate the curves. Peak Area (arb. units) W I 1— 1 I 1 0 2 4 6 8 10 Contact Time (ms) Figure 4.7 1 9 F - 2 9 S i C P M A S behaviour for the T - l Si in octadecasil at t h e / = +2 sideband matching condition. The line shows the fit calculated using Eq . 3.14 with D = 1400 Hz, S e q = 0.9, k{] = 6 ms, k2A = 14 ms, and Tlp = 125 ms. The spinning speed was 4.15 kHz, and the 1 9 F field strength was 17 kHz. 141 should be identical to that observed when t h e / = -1 match is used, and should be independent of the spinning speed. A s seen from Figure 4.6, the periodicity of the transient oscillations observed for the T - l silicons is very similar at equivalent sideband matching conditions and different spinning speeds, in good agreement with the theoretical predictions. Fitting of the experimental data to Eq . 3.14 (expressed in terms of Bessel functions) was done as described for the non-spinning data. Because the oscillations were quite clearly defined at contact times of up to 8-10 ms, more periods of the oscillations were thus available to check the goodness of fit for given dipolar couplings, which reduced the uncertainty in the final D values. The reduction in the rate of damping of the oscillatory behavior with increasing spinning speeds (and the corresponding increase in the values of k\ used in the fitting) is exactly as anticipated; at higher spinning speeds the effects of the relatively weak l 9 F - ' 9 F interactions are progressively "spun out". Values of the parameters determined from the fittings were: kfx = 3 . 5 - 6 ms, &2~' = 20 -80 ms (<Sz>q e f ixed at 0.9), Tlp = 70 - 400 ms. In Figures 4.4 and 4.6 the data from three experiments are presented with the theoretical curves determined from the regression analyses. Small discrepancies are apparent at very short contact times, and are again attributed to the performance of the amplifiers; the Hartmann-Hahn matches were optimized using 10 ms contact time as a compromise to ensure the matching was maintained up to the longer contact times (50 -60 ms) needed to observe the effects of T\p decay (see Figure 4.4). The dipolar couplings determined from fits to seven experimental data sets acquired at t h e / = +1 and -1 matching conditions ranged from D = 1330 to 1400 Hz with a mean of 1360 Hz and estimated standard deviation of 50 Hz. This corresponds to Si -F distances of 2.54 (0.03) A , which is slightly shorter than the X-ray determined distance. Spinning Samples at the f=±2 Sideband Matching Conditions The oscillatory behaviour at t h e / = +2 and - 2 sideband matching conditions should be identical, but have a longer period compared to that observed at t h e / = ±1 matches. This 142 behavior was observed in the experimental data acquired for the T - l Si under M A S conditions when the field strengths were appropriately adjusted. Fitting of the data to Eq . 3.14 was carried out as described in the preceding sections and similar values of the various parameters were found. Experimental data obtained for the T - l Si at t h e / = +2 matching condition for a spinning speed of 4.15 kHz is shown in Figure 4.7 together with the curve calculated using the parameters listed in the caption. A t t h e / = ±2 matching condition only two periods of the oscillation were observed up to a contact time of 10 ms compared with the three to four seen w h e n / = ± 1 . Thus the uncertainty o f the dipolar couplings is reduced somewhat compared to those obtained from data acquired at the first sideband matches, and is similar to that determined from the static sample data. The average of the dipolar couplings determined from fitting of all the C P data at the five possible matching conditions (static and M A S ) for the T - l Si is given in Table 4.3. Comparison with Si -F distances determined from R E D O R , T E D O R , and X-ray diffraction experiments reveals that, for isolated spin pairs at least, analysis o f variable contact time data from l 9 F - 2 9 S i C P experiments can yield reliable and quite accurate interatomic distances providing oscillatory behaviour is observed. 4.3.4 1 9F-2 9Si REDOR Experiments In a R E D O R experiment the signal intensity is monitored as a function of either the number of rotor periods or the position during the rotor cycle at which the dephasing pulses are applied, with the number of rotor periods constant/ ' Commonly, a series of dephasing 7i-pulses is applied to the unobserved heteronuclear spins, with a simple spin-echo sequence on the observed sp ins / ' However when the resonance offsets are large, pulse errors can accumulate, and while phase-cycled pulse trains help to compensate for pulse imperfections, they too become ineffective at large of fsets/ 5 In such cases it is desirable to minimize the number of pulses on those nuclei having large offset effects. Garbow and Gul l ion have reported a modified R E D O R 143 Table 4.3 Comparison of the dipolar couplings (D) and F- Si interatomic distances (r) for octadecasil determined by various methods. Standard deviations are given in parenthesis. T-Site Parameter TECHNIQUE Cross Polarization*3' REDOR(a) TEDOR (a) X-ray(b) T-l (Si in D4R) Z)(Hz) 1380 (80) 1150(50) 1130(50) 1230(5) r(A) 2.53 (0.04) 2.69 (0.04) 2.70 (0.04) 2.632 (0.003) T-2 (Si not in D4R) D (Hz) n.d. ( e ) 120 (20) ( d ) 120 (20) ( d ) 122(5) i-(A) n.d . ( e ) 5.7 (0.4) ( d ) 5.7(0.4) ( d ) 5.688 (0.003) ( a ) Dipolar couplings determined from nonlinear least-squares fitting of experimental data and internuclear distances calculated from these. ( b ) Distances determined from the single crystal X-ray data of Caullet et al.16 and dipolar couplings calculated from these. ( c ) Dipolar couplings determined from visual fitting of experimental data and internuclear distances calculated from these. ( d ) Standard deviation estimated from visual f i t t ings. ( e ) Not determined. pulse sequence that requires only a single dipolar dephasing pulse on the unobserved heteronuclear spins to minimize these problems. 5 7 Several pulse sequence schemes were used to implement the R E D O R experiments, two of which are presented in Figure 3.6. R E D O R experiments were performed with either a train of dephasing pulses applied to the unobserved (7) nuclei ( l 9 F) , or by applying just a single dephasing pulse on the unobserved nuclei. Because the R E D O R experiment involves the formation of an echo for the observed nucleus, it is the spin-lattice relaxation behavior of this nucleus which determines how quickly the sequence can be repeated. A s 2 9 S i was the observed nucleus in these experiments, and the T\ values for the silicons in octadecasil are relatively long (ca. 20 s), an initial presaturation sequence was incorporated to achieve a more efficient recycling time, while still ensuring quantitative reliability. In experiments which utilized an initial cross-polarization from l 9 F to 2 9 S i prior to beginning the R E D O R portion of the sequence, the repeat time was governed by the much shorter 1 9 F T\ (see Table 4.2), and presaturation was not necessary. 4.3.4.1 REDOR Experiments on the D4R Silicons (T-l Si) Experimental R E D O R results for the Si in the T - l site using three different pulse sequences are shown in Figure 4.8. In the absence of an initial polarization transfer from 1 9 F , the experimental values of A S / S 0 did not reach the theoretical maximum of about 1.05 during the first 4.5 ms of dipolar evolution, but seemed to oscillate around 0.85 - 0.92. The explanation for this is that only about 90% of the D4R units contain a fluoride ion, as determined by elemental analysis. This would allow signals from 2 9 S i nuclei in D4R units without fluoride anions to contribute to the intensity of the peaks in the off-resonance (So) experiments, which limits the value of AS/So attainable. In the case of octadecasil then, these maximum normalized AS/So intensities provide a direct method for estimating the percentage occupancy of the D4R units by fluoride ions. 145 (a) nxr (ms) Figure 4.8 F- Si R E D O R data and fits for the T - l Si in octadecasil at the spinning speeds indicated. The theoretical curves were calculated assuming D = 1150 H z and either complete (dashed line) or incomplete (solid line) occupancy of the D 4 R by fluoride ions, (a) Dephasing pulses on 1 9 F , solid curve calculated for 85% occupancy. Data at v r = 3.950 kHz acquired with initial cross polarization from 1 9 F . (b) Dephasing pulses on 2 9 S i , solid curve calculated for 92% occupancy. 146 The oscillations observed for the T - l silicons at short contact times in the C P experiments justify the analysis of the R E D O R behavior for these silicons in terms of an isolated 2 9 S i - 1 9 F spin pair. To permit fitting of the data, the theoretical values of AS/So were multiplied by a scaling factor to account for the incomplete occupancy. This scaling factor does not affect the "per iod" of the oscillation from which the distance is determined. Nonlinear least squares fitting of the R E D O R data for the T - l Si included this scaling factor as a variable, and gave an average value for the dipolar coupling of 1150 Hz (standard deviation 50 Hz). This corresponds to a Si -F distance of 2.69 + 0.04 A, in excellent agreement with the value of 2.63 A determined from the X-ray structure. The plots in Figure 4.8 illustrate how well the scaled theoretical curves (solid lines) calculated using the dipolar couplings and scaling factors determined from the fitting match the observed experimental data. R E D O R experiments with cross polarization from l 9 F to 2 9 S i prior to the R E D O R sequence were also successful (Figure 3.6(b)). The use of an initial polarization transfer from l 9 F means that the observed R E D O R signals wi l l originate only from 2 9 S i nuclei which have F" ions in their associated D4R, and hence the incomplete occupancy wi l l not be apparent. Consequently the AS/So value should oscillate about 1.0 as was observed (see Figure 4.8(a)). A drift towards a AS/So value of unity at longer dephasing times (> 4.5 ms, n > 12) was noted (Figure 4.8(a), open circles), and this probably arises from additional dipolar couplings between the T - l silicons and the next closest (> 7 A) fluoride ions, whose contributions take a much longer time to build up. It is also apparent that data acquired using the pulse sequence with a single dephasing pulse on the unobserved nuclei attain a somewhat higher maximum AS/So ratio (ca. 0.92) compared with the value of ca. 0.85 i f the train of dephasing pulses was applied to the unobserved nuclei. This small difference in efficiency between the two pulse sequences may be due to resonance offset effects. However the curve fitting for both experiments yielded exactly the same value for the 2 9 S i - ' 9 F dipolar coupling within experimental error. It should be noted that this may not be the case for other 1 9F-containing systems, (e.g. fluoro-organic 147 sorbates), where there may exist large chemical shift anisotropies, l 9 F homonuclear and ' H - ' 9 F heteronuclear line broadening interactions. In such cases the choice of pulse sequence may be critical in obtaining the most reliable measurement of D. Figure 4.9 shows the result of applying the R E D O R transform reported by Mue l le r 5 5 to the data acquired at a spinning speed of 3.950 kHz. The peak maximum occurs at 1188 H z which corresponds to a Si -F distance of 2.663 A . The ful l width at half maximum (ca. 590 Hz) is primarily a result of the limited number of data points acquired (10), and the apodization function (three-point Blackman-Harris) used. Although several R E D O R data sets were acquired having more than ten AS/So values, the spinning speeds in these experiments were not sufficiently high for the R E D O R transform to be applied. To see a coupling of about 1200 Hz, the R E D O R data must be acquired with v r > 3 kHz since the R E D O R transform wi l l only show a range of frequencies from 0 to v r / 2. The fluctuation in the spectrum below 500 Hz is an artifact arising from the initial decay in the S /S 0 values at small numbers of rotor periods. 4.3.4.2 REDOR Experiments on Silicons not in the D4R (T-2 Si) For the T-2 sil icons, the 1 9 F - 2 9 S i dipolar coupling was estimated to be 122 Hz from the Si-F distance of 5.69 A calculated from the crystal structure. However, depending on the exact occupancy of the D4R units, there can be up to four fluoride anions in a tetrahedral arrangement about each T-2 si l icon, and therefore equidistant from it (Figure 4.1(b)). This represents a more complicated situation than for the Si in the D4R (T- l site) as the experiment no longer involves a single, isolated spin pair. Coupl ing to several fluorines can produce extra dephasing which translates into a stronger apparent dipolar coupling, and thus to an underestimate of the true heteronuclear distance. The theoretical curve calculated for a single, isolated 2 9 S i - l 9 F spin pair with a dipolar coupling of 120 H z (not shown) does not fit the experimental data at al l , but a reasonable fit at short dephasing times (< 4 ms) assuming an IS spin pair could be obtained with D = 220 Hz , corresponding to a Si-F distance of 4.67 A . This is much shorter than that known 148 0 500 1000 1500 2000 Dipolar Coupl ing (Hz) Figure 4.9 R E D O R transform of R E D O R data acquired for the T - l Si in octadecasil at a spinning speed of 3.950 kHz. Ten experimental S /S 0 data points were acquired up to n = 20, apodized with a three-point Blackmann Harris function of the form 0.424 + 0.497 COS(«TC / 10) + 0.079 cos(2wxc / 10), and zero-fil led to 128 points. The peak maximum occurs at 1188 Hz and has a F W H H of approximately 590 Hz. «x r (ms) Figure 4.10 1 9 F - 2 9 S i R E D O R data and fits for the T-2 Si in octadecasil at a spinning speed of 2.350 kHz. The curves were calculated for: a tetrahedral arrangement of four flouride ions about the T-2 Si with D = 120 H z (dashed line); a binomial distribution assuming a (partial) tetrahedral arrangement of (up to) four flouride ions having D = 120 Hz and an 85% probability that each D4R is occupied (solid line); (c) the superposition of a large number of R E D O R curves calculated for isolated 1 9 F - 2 9 S i spin pairs and weighted using a Gaussian distribution with variance defined by M 2 (S i -F ) =151450 H z 2 (dotted line). 149 from the X-ray structure, and it illustrates a potential problem when multiple spins could be involved and no clear oscillation is observed. When an observed spin magnetization is dephased by dipolar interactions with more than one other spin, the dephasing wi l l normally be dominated by the nearest one (since Dec Mr 3). However, when the distances are comparable, dephasing from multiple spins w i l l be cumulative."'5"1"* Naito et al.48 demonstrated that the geometrical arrangement of the spin pairs had a measurable effect on the calculated R E D O R curves, and Schaefer and co-workers 7 ^ 7 derived a general equation for the R E D O R behavior of an S spin dipolar coupled to any number of / spins provided that the geometric arrangement of these spins is known as described in Chapter 3. Blumenfeld et aV7 have also proposed the use of the superposition of many R E D O R curves for isolated spin pairs weighted by a Gaussian distribution with variance related to the I-S heteronuclear second moment, M2(I-S). Calculations based on these two methods are presented in the fol lowing sections. Exact Multi-Spin Calculations with Statistical Occupancy Calculation of theoretical dephasing of a single 2 9 S i by multiple l 9 F ' s was undertaken for the T-2 silicons assuming an exact tetrahedral arrangement, and additional corrections for the partial occupancy of each D4R unit were also incorporated. The dephasing of a single observed 2 9 S i spin dipolar coupled to more than one l 9 F spin can be calculated direct ly 7 7 as the powder average of a sum of independent dephasings assuming that the fluorines are not coupled to each other, and that the fluorine dephasings of the silicons are independent of one another. For octadecasil the first condition is satisfied because the sample is undergoing magic angle spinning at speeds (2-5 kHz) that greatly exceeded the largest homonuclear l 9 F - 1 9 F dipolar coupling (130 Hz for 9.3 A separation). The second condition is assumed to hold because of the good fits obtained in other sys tems 7 7 7 8 ' 5 6 and for the T - l silicons in the present work. 150 The theoretical curves calculated for an exact tetrahedral arrangement of four l 9 F nuclei about a central 2 9 S i using Eq. 3.33 with D = 120 H z fit the experimental data for the T-2 Si quite wel l (Figure 4.10, dashed line). This corresponds to complete occupancy of the D4R units. In a further refinement, the effect o f incomplete occupation of the D4R units by fluoride anions was included. This was achieved by assuming contributions from four, three, two, and one equivalent, non-interacting fluorine nuclei, coupled (D = 120 Hz) to a single T-2 2 9 S i nucleus. Curves were calculated for these four sets of 2 9 S i - l 9 F spin-pairs assuming that each T-2 sil icon was surrounded by a (partial) tetrahedral arrangement of (up to) four equidistant , 9 F nuclei. The normalized A S / S 0 values thus determined were then multiplied by an appropriate weighting factor and added together produce the final theoretical R E D O R curves. The weightings were determined assuming a binomial distribution of fluoride anions in the D4R units with a probability p that a fluoride anion occupies any given D4R. The probability, Pq that q of the four D 4 R units surrounding a given T-2 Si are occupied is: 5 * pq=cq(pn\-pf 4.1 where Cq is the number of ways of obtaining q occupied D4R units: Cq = 4\l q\(A-q)\ 4.2 Forp=0.9 Eq . 4.1 yields P4 = 0.6561, P3 = 0.2916, P2 = 0.0486, P, = 0.0036 and P0 = 0.0001. Including the effect o f incomplete (85%) occupation of the D 4 R units gives a significant improvement in the goodness of fit (Figure 4.10, solid line), however the experimental data is not o f good enough quality to permit the occupancy to be determined to an accuracy of better than 5-10%. It was apparent that the calculated multiple-spin R E D O R curves had a much stronger dependence on the magnitude of the dipolar coupling than on the occupancy, and due to the complexity of these calculations, nonlinear least squares fitting was not attempted. The 151 uncertainty in D was estimated to be less than 20 H z from inspection of curves calculated assuming 100% occupancy of the D 4 R units and a range of dipolar couplings (not shown). Thus, the R E D O R fits for the T-2 Si yield a Si-F distance of 5.7 ± 0.4 A, in very good agreement with the value of 5.69 A determined from the X-ray crystal structure. This analysis is also in good agreement with the maximum dephasing observed in the R E D O R experiments for the T - l sil icons, and indicates that the actual occupancy of the D4R units is probably slightly higher than 85%. Although in the case presented here (T-2 Si in octadecasil), all o f the I-S distances were equal, the method outlined above accommodates different distances within the group of nuclei. It should be emphasized that the possibility o f obtaining distances directly. However these results demonstrate that these exact analyses are reliable and should work for any geometrical arrangement, provided this is known. Gaussian Distribution of Isolated ,9F-29Si Spin Pairs Nonlinear leastsquares regression analysis of the T-2 Si R E D O R data in terms of a Gaussian distribution of isolated 1 9 F - 2 9 S i spin pairs was also undertaken. Using Gaussian-Hermitian quadrature integration with 180 roots of the Hermite polynomials (see Appendix C) , the best fit (lowest x2) was obtained with M 2 (S i -F ) = 151450 H z 2 and the simulated curve is shown in Figure 4.10 (dotted line). The heteronuclear second moment calculated from the X R D determined structure (assuming complete occupancy of the D4R units and a 8 A cut-off) is 305660 H z 2 . The overall fit o f the curve to the data is not good; the shape of the curve deviates quite significantly from the trend in the experimental data. This probably indicates that the Gaussian distribution model is not very appropriate in this case. 152 4.3.5 F - Si T E D O R Experiments T E D O R experiments were originally developed as an alternative to R E D O R to measure the heteronuclear dipolar coupling between nuclei while eliminating unwanted background contributions from uncoupled spins/ 3 , 7 " ' The T E D O R experiment involves two time periods of dipolar dephasing, one before the transfer of coherence (achieved by simultaneous TC / 2 pulses), and another after the coherence transfer (Figure 3.10). This allows more permutations of the experiment, which give the added flexibil i ty of being able to select the experiment best suited to the T\ and T2 relaxation parameters of a particular system. This f lexibil i ty may be particularly useful, especially i f one T2 value is unacceptably short, as is often the case for inorganic solids. The theoretical T E D O R behavior can be calculated as described in Chapter 3. Variations of the T E D O R experiment included the application of rc-pulses on 2 9 S i , or 1 9 F before the coherence transfer pulse, varying the spinning speed, the position of the pulses, and the number of rotor cycles before and after the transfer pulse. The pulse sequences used for experiments (Figure 3.10) were such that the minimum increment allowed for the number of rotor cycles before coherence transfer was two because of the use of the simultaneous rc-pulses to form an echo to ensure that the chemical shifts are refocussed at the transfer point. Larger increments are possible but only in even numbers of rotor cycles, 4, 6, 8, etc. For the number of rotor cycles after coherence transfer, increments of 1, 2, 3, or more were permitted since no simultaneous refocussing rc-pulses were applied in this part of the sequence. A l l T E D O R experiments were performed with one of the sil icon signals set exactly on resonance and several "periods" of the oscillations were acquired to verify the accuracy of the D values. It is important to take into consideration the nuclear relaxation parameters of the nuclei as these limit the range of n or m values that wi l l give viable signal intensities. During the period before coherence transfer, the spin-spin relaxation rate, T2, o f the source nuclei (e.g. I 9 F ) is important, and after the transfer it is the T2 of the observed nuclei (e.g. 2 9 S i ) that limits the maximum time (and thus the number of rotor periods) after coherence transfer that signal can be 153 detected. Because the T E D O R pulse sequences used in the present work al l contain an additional 7i-pulse which generates a spin-echo, it is T2 rather than T2 for the source nuclei that is important. 4.3.5.1 TEDOR Experiments on the Silicons in the D4R (T-l Si) Figure 4.11 shows typical T E D O R spectra obtained for octadecasil. T E D O R data obtained for the T - l silicons with all dephasing pulses at x r/4 and 3x r/4 with the number of rotor cycles after the coherence transfer varied, and the number of rotor cycles before the coherence transfer held constant are presented in Figure 4.12 for several n values. The overlaid theoretical curves were calculated from nonlinear leastsquares fitting assuming a single 1 9 F - 2 9 S i spin pair. Because the T E D O R signal intensity S T is not normalized as it is for R E D O R experiments, the experimental intensities were scaled to match the maxima of the theoretical curves. In order to obtain a good match to the experimental intensities at higher numbers of rotor periods, the theoretical curves were also damped by multiplying them by an exponential factor of 70 Hz to account for homogeneous spin-spin decay during the period after transfer which is consistent with the observed 2 9 S i linewidths ( F W H H « 60 Hz). During the analysis of data from different T E D O R experiments, this damping factor was found to vary slightly but typically it was in the range 60 ± 20 Hz . Figure 4.12(d) shows T - l Si T E D O R data for n = 2 and m varied together with theoretical curves calculated assuming dipolar couplings of 1000 Hz (dashed line), 1100 Hz (solid line) and 1200 Hz (dotted line). Clearly the quality of the fits is excellent, with less than 100 Hz uncertainty in D. Figure 4.13 shows the data obtained for the T - l Si when n was varied and m was fixed. The experimental data again agree closely with the theoretical curves determined from nonlinear fitting. Furthermore, because in these experiments there are more 154 ppm (w.r.t. TMS) Figure 4.11 19F-29Si TEDOR spectra of octadecasil acquired using a spinning speed of 4.540 kHz and the T-l Si on resonance. The number of rotor periods before the coherence transfer was fixed (n = 2), and the number of rotor periods after the transfer, m, was incremented as indicated. m, Rotor Periods A F T E R Transfer F igure 4.12 T E D O R data and fits determined from nonlinear least-squares fitting of the T - l sil icon by varying m with n held constant and all dephasing pulses at x r/4 and 3t r /4. (a) « = 2, v r o t = 4.770 kHz , D =1131 H z , (b) n = 4, v r o t = 4.770 kHz , D = 1100 Hz , and (c) n = 6, v r o t =5.244 kHz, D = 1077 Hz . (d) Indication of the sensitivity of the fit for n — 2, v r o t — 4.296 kHz: curves calculated with dipolar couplings of 1200 H z (dashed line), 1100 H z (solid line) and 1000 H z (dotted line). A n exponential damping of 70 H z was applied to all curves to account for T2 decay. The ST scales are in arbitrary units. 156 n, Rotor Periods B E F O R E Transfer Figure 4.13 T E D O R data and fits determined from nonlinear least squares fitting of the T - l sil icon as a function of n for different m values at a spinning rate of 4.540 kHz with all dephasing pulses at x r/4 and 3t r /4. (a) m = 1, D =1176 Hz, (b) m = 2, D =1207 Hz , and (c) m = 3, D = 1213 Hz . (d) Indication of the sensitivity of the fit for m = 2, spinning speed 5.244 kHz. The curves were calculated assuming dipolar couplings of 1200 Hz (dashed line), 1100 H z (solid line) and 1000 Hz (dotted line). A n exponential damping of 70 H z was applied to all curves to account for T2 decay. The ST scales are in arbitrary units. 157 "periods" of the oscillation to fit, these represent a quite stringent test o f the fit of the experimental data to the theoretically predicted behavior. This is the first time T E D O R experiments have been reported where n was varied and m f ixed. There was no discernible difference between T E D O R experiments performed with the dephasing pulses before the coherence transfer on either 2 9 S i or l 9 F . Weighted, nonlinear fittings of the T E D O R experiments with all dephasing rc-pulses at x r/4 and 3x r/4 yielded an average value of D = 1130 Hz with a standard deviation of 50 H z for the silicons in the D4R units. From these values the Si -F interatomic distance was calculated to be 2.70 ± 0.04 A , which is slightly longer than the value of 2.63 A calculated from the diffraction measurements, but still in very good agreement. A s seen from Table 4.3, the Si-F distance for the T - l silicons determined from T E D O R experiments is in very close accord to that found from R E D O R experiments, but slightly longer than found from fitting of the C P data, although all techniques have comparable accuracy. The T E D O R data obtained by changing the positions of the dephasing pulses from x r/4, 3x r/4 required integration of the appropriate functions describing the dipolar interactions, and subsequent numerical point-by-point integration of those functions. Results from these experiments were plotted versus the dimensionless parameter X„ = nDxr (or X„, = mDxr) so that "universal" curves (for isolated IS spin pairs) were obtained that could be used for fitting data acquired at different spinning speeds. The resulting curves (calculated using D = 1100 Hz and 70 Hz dampening) showed very good agreement with the experimental data. Figure 4.14 shows data for the T - l Si and the theoretical curves for T E D O R experiments performed with the dephasing pulses moved to (a) x r /5, 4x r/5 and (b) x r/6, 5x r/6 after the coherence transfer. The dephasing pulses were at x r/4 and 3x r/4 before the transfer. The dipolar coupling determined from experiments performed with the pulses moved from x r/4 and 3x r/4 was generally less (by about 50 Hz) than that determined for other T E D O R experiments and probably indicates that moving the pulses yields a less efficient T E D O R experiment. 158 mD?T Figure 4.14 T E D O R data and fits for the T - l sil icon with all dephasing pulses before the coherence transfer at x r/4 and 3x^4 and those after the transfer positioned at: (a) x r/5 and 4x r /5, and (b) x r/6 and 5x r/6. The number of rotor periods before the transfer was fixed at 2, m was varied, and the spinning speed was 4.285 kHz. The theoretical curves were calculated for D =1100 Hz with an exponential damping of 70 H z to account for T2 decay. The S T scale is in arbitrary units. «r r(ms) Figure 4.15 T E D O R data for the T-2 sil icon (n varied, m = 3, v r = 4.53 kHz, dephasing pulses at x r/4 and 3x r/4), and the theoretical curves calculated assuming an exact tetrahedral arrangement o f four fluoride ions about the T-2 Si and 1 9 F - 2 9 S i dipolar couplings of: (a) 100 Hz, (b) 120 Hz , and (c) 140 Hz . A n exponential damping of 70 Hz was applied to account for T2 decay. The S T scale is in arbitrary units. 159 4.3.5.2 TEDOR Experiments on the Silicons not in the D4R (T-2 Si) A s seen in Figure 4.15, T E D O R data for the T-2 Si were also well fit by theoretical curves calculated for a tetrahedral arrangement of four fluorides about a central T-2 sil icon (D = 120 Hz) using multiple spin analysis as outlined in Chapter 3. Statistical occupancy was not incorporated because of the arbitrary scaling between experimental data and theoretical intensities. This dipolar coupling corresponds to r = 5.71 A in good agreement with that determined from the crystal structure and the R E D O R fits. If an isolated 2 9 S i - ' 9 F spin pair was assumed, nonlinear least squares fitting to the T E D O R data for the T-2 Si yielded a value of D = 205 Hz , which corresponds to a Si -F distance of 4.78 A . This result again illustrates the danger of obtaining incorrect internuclear distances from fitting T E D O R experimental data i f more than two spins are present and the fitting assumes only a single, isolated spin pair. 4.4 C O N C L U S I O N S These results clearly establish the viabil ity of these experiments for determining the precise location of , 9F-containing species within framework structures from the magnitude of the l 9 F - 2 9 S i dipolar coupling derived from C P , R E D O R , and T E D O R . Such experiments could be extended to determine l 9 F - 3 l P interatomic distances in aluminophosphate molecular sieves (A IP0 4 s ) with fluorine-containing guests and to other framework/sorbate host-guest complexes. R E D O R experiments yield normalized intensities which are useful for testing the goodness of the fit of experimental data to the theory, and even in the present case for estimating the percentage occupancy of the D 4 R units by fluoride ions. T E D O R experiments eliminate unwanted background signals arising from observed nuclei which are not dipolar coupled to the heteronuclear spins, and can provide additional advantages because of the larger number of experimental variables available, and the corresponding increased flexibil i ty to accommodate large T\ or small T2 values of either nucleus. A n advantage of T E D O R experiments over R E D O R is that it is possible to extend them to 2-D correlation experiments/ 7" 6 0 This could be very useful 160 in cases where there are several resonances for both nuclei as it should permit a differentiation between the connectivities. This wi l l important for three-dimensional host guest-structure determinations in frameworks of the type studied here. It is possible to obtain incorrect internuclear distances from fitting R E D O R and T E D O R experimental data i f more than one spin is dipolar coupled to the observed spin and the fitting assumes only a single, static, isolated spin pair. Independent information which verifies that the experimental data relates to an isolated spin pair should be obtained. For spin systems which cannot be considered as isolated spin pairs (e.g. the T-2 Si in octadecasil), it may be possible to determine the dipolar couplings (and thus distances) accurately from R E D O R and T E D O R experiments (provided the geometry of the spin system is known) as demonstrated in the present work. In order to more fully explore the uniqueness of the R E D O R and T E D O R behavior for multi-spin systems a series of 3-spin calculations were undertaken. The results of these simulations are presented in Chapter 5. 161 R E F E R E N C E S F O R C H A P T E R 4 1 Breck, D.W. Zeolite Molecular Sieves; Wi ley Interseience, 1974. 2 Barrer, R . M . Zeolite and Clay Materials as Sorbents and Molecular Sieves; Academic Press, 1974. 3 van Bekkum, H.; Flanigen, E . M . ; Jansen, J .C. (Eds.), Introduction to Zeolite Science and Practice; Elsevier: Amsterdam, 1991. 4 Jansen, J . C ; Stocker, M . ; Karge, H.G. ; Weitkamp, J . (Eds.), Advanced Zeolite Science and Applications; Elsevier: Amsterdam, 1994. 5 Flanigen, E . M . ; Patton, R.L. U.S. Patent No. 4073865, 1978. 6 Kessler, H.; Patarin, J . ; Schott-Darie, C . Stud. Surf. Sci. Catal. 1994, 85, 75. 7 Guth, J .L. ; Kessler, H.; Caullet, P.; Hazm, J . ; Merrouche, A . ; Patarin, J . in Proceedings of the 9th International Zeolite Conference, Montreal, 1992. von Ballmoos, R.; Higgins J .B. ; Treacy, M . M . J . (Eds), Butterworth-Heinemann 1993, 215. 8 Zhao, D.; Q iu , S.; Pang, W. in Proceedings of the 9th International Zeolite Conference, Montreal, 1992. von Ballmoos, R.; Higgins J .B. ; Treacy, M . M . J . (Eds), Butterworth-Heinemann 1993, vol . 1, 337. 9 Loiseau, T.; Riou, D.; Taulelle, F.; Ferey, G . Stud. Surf. Sci. Catal. 1994, 84, 395. 10 Schott-Darie, C ; Kessler, H.; Soulard, M . ; Gramlich, V . ; Benazzi, E. Stud. Surf. Sci. Catal. 1994, 84, 101. 11 Simmen, A . Ph.D Thesis, E.T.H. Zurich, Switzerland, 1992. 12 Simmen, J . ; Patarin, J . ; Baerlocher, C h . in Proceedings of the 9th International Zeolite Conference, Montreal, 1992. von Ballmoos, R.; Higgins J .B. ; Treacy, M . M . J . (Eds), Butterworth-Heinemann 1993,433. 13 Chezeau, J . M . ; Delmotte, L.; Guth, J .L . ; Soulard, M . Zeolites. 1989, 9, 78. 14 Delmotte, L.; Soulard, M . ; Guth, F.; Seive, A . ; Lopez, A . ; Guth, J .L . ; Zeolites 1990, 10, 778. 15 Vedrine, J .C. in Guidelines for Mastering the Properties of Molecular Sieves, Barthomeuf, D,; Derouane E .G. ; Holderich, W. (Eds), Plenum Press: New York, 1989, 121. 16 Caullet, P.; Guth, J . L.; Hazm, J . ; Lambl in, J . M . ; Gies, H. Eur. J. Solid State Inorg. Chem. 1991, 28, 345. 17 Schott-Darie, C ; Patarin, J . ; Le Goff, P .Y. ; Kessler, H. ; Benazzi, E. Microporous Mater. 1994, 3, 123. 18 Estermann, M . ; McCusker, L .B . ; Baerlocher, C ; Merrouche, A . ; Kessler, H. Nature, 1991, 352, 320. 19 Merrouche, A . ; Patarin, J . ; Soulard, M . ; Kessler, H. ; Anglerot, D. in Synthesis of Microporous Materials; Occel l i , M .L . ; Robson, H.E. (Eds.), Van Nostrand Reinhold; 1992, 1, 384. 162 20 Sierra, L.; Deroche, C ; Gies, H.; Guth, J .L. Microporous Mater. 1994, 3, 29. 27 Q iu , S.; Pang, W.; Kessler, H.; Guth, J .L . Zeolites. 1989, 9, 440. 22 Price, G .D. ; Pluth, J .J . ; Smith, J .V . ; Bennett, J . M . ; Patton, R.L . J. Am. Chem. Soc. 1982,104, 5971. 23 Mentzen, B.F.; Sacerdote-Peronnet, M . ; Guth, J .L. ; Kessler, H. CR. Acad. Sci. Paris. 1991, 313, 177. 24 Schreyeck, L.; Caullet, P.; Mougenel, J - C ; Guth, J .L. ; Marler, B. J. Chem. Soc, Chem. Cow/77 .1995,2187. 25 Fyfe, C .A . ; Gies, H.; Feng., Y . ; Kokotai lo, G.T. Nature. 1989, 341, 223. 26 Fyfe, C .A . ; Feng., Y . ; Grondey, H. ; Kokotai lo, G.T. ; Gies, H. Chem. Rev. 1991, 91, 1525. 27 Fyfe, C .A . ; Strobl, H.; Kokotai lo, G.T. ; Kennedy, G .J . ; Barlow, G . E . ; J. Am. Chem. Soc. 1988, 770, 3373. 28 Fyfe, C .A . ; Feng, Y . ; Gies, H. ; Grondey, H. ; Kokotai lo, G.T. J. Am. Chem. Soc. 1990, 772, 3264. 29 Engelhardt, G . ; Miche l , D. High-Resolution Solid-State NMR of Silicates and Zeolites. John Wi ley and Sons: New York, 1987. 30 Waugh, J.S. ; Mar icq, M . M . ; Cantor, R. J. Magn. Reson. 1978, 29, 183. 37 Gul l ion, T.; Schaefer, J . Adv. Magn. Reson. 1989, 13, 57. 32 Voelke l , R.Angew. Chem. Int. Ed. Engl. 1988, 27, 1468. 33 Stejskal, E.O.; Schaefer, J . ; Waugh, J.S. J. Magn. Reson. 1977, 28, 105. 34 Mehring, M . Principles of High Resolution NMR in Solids, 2nd ed.; Springer-Verlag: New York, 1983; Chapter 4. 35 Hediger, S.; Meier, B .H. ; Ernst, R.R. J. Chem. Phys. 1995,102, 4000. 36 Hagaman, E.W.; Ho, P.C.; Brown, L .L . ; Schell , F . M . ; Woody, M . C . J. Am. Chem. Soc. 1990, 772, 7445. 37 Schaefer, J . ; Stejskal, E.O.; Garbow, J.R.; M c K a y , R.A. J. Magn. Reson. 1984, 59, 150. 38 Hawkes, G .E . ; Mantle, M.D. ; Sales, K.D. ; A ime, S.; Gobetto, R.; Groombridge, C .J . J. Magn. Reson. Ser. A. 1995, 776, 251. 39 Hediger, S.; Meier, B .H. ; Ernst, R.R Chem. Phys. Lett. 1995, 240, 449. 40 Walther, K .L . ; Wokaun, A . ; Baiker, A . Mol. Phys. 1990, 77, 769. 41 Kle in Douwel, C . H . ; Maas, W.E.J .R. ; Veeman, W.S. ; Werumeus Buning, G . H . ; Vanken, J .M .J . Macromol. 1990, 23, 406. 42 Gul l ion, T.; Schaefer, J . J. Magn. Reson. 1989, 81, 196. 43 Hing, A . W . ; Vega, S.; Schaefer, J . J. Magn. Reson. 1992, 96, 205. 163 44 Hing, A . W . ; Vega, S.; Schaefer, J . J. Magn. Reson. Ser. A, 1993, 103, 151. 45 Pan, Y . ; Gul l ion, T.; Schaefer, J . J . Magn. Reson. 1990, 90, 330. 46 Mueller, K.T. J. Magn. Reson. Ser. A, 1995, 773, 81. 47 Goetz, J . M . ; Schaefer, J . J . Magn. Reson. 1997, 727, 147. 48 Naito, A . ; Nishimura, K.; Tuz i , S.; Saito, H. Chem. Phys. Lett. 1994, 229, 506. 49 Marcucci l l i Hoffher, F.; Delmotte, L.; Kessler, H. Zeolites, 1993, 13, 60. 50 Hartmann, S.R.; Hahn, E .L . Phys. Rev. 1962, 725, 2042. 57 Wolfram, S. Mathematica. A System for Doing Mathematics by Computer. Addison-Wesley: . Massachusetts, 1991. 52 Hediger, S. Ph.D. Dissertation, Eidgenossische Technische Hochschule, Zurich, Switzerland, 1997. 53 Gul l ion T.; Schaefer, J . J. Magn. Reson. 1991, 92, 439. 54 Garbow, J.R.; Gul l ion T. J . Magn. Reson. 1991, 95, 442. 55 Mueller, K.T.; Jarvie, T.P. ; Aurentz, D.J.; Roberts, B .W. Chem. Phys. Lett. 1995, 242, 535. Chem. Phys. Lett. 1996,254, 281. 56 McDowe l l , L . M . ; K lug , C .A . ; Beusen, D.D.; Schaefer, J . Biochem. 1996, 35, 5395. 57 Blumenfeld, A . L . ; Coster, D.; Fripiat, J . J . J . Phys. Chem. 1995, 99, 15181. 58 Mendenhall, W. ; Beaver, R.J. Introduction to Probability and Statistics, 9th Edit ion; Duxbury Press: Cal i fornia, 1994, p. 167. 59 Fyfe, C . A . ; Muel ler, K.T.; Grondey, H. ; Wong-Moon. K . C . Chem. Phys. Lett. 1992,199, 198. 60 Fyfe, C .A . ; Muel ler, K.T. ; Grondey, H.; Wong-Moon, K . C . J . Phys. Chem. 1993, 97, 13484. 61 Fyfe, C .A . ; Wong-Moon, K . C ; Huang, Y . ; Grondey, H. ; Mueller, K.T. J . Phys. Chem. 1995, 99, 8707. 62 Vega, A . J . J . Am. Chem. Soc. 1988, 770, 1049. 63 Fyfe, C . A . ; Diaz, A . C ; Grondey, H.; Fahey, B. In preparation. 164 CHAPTER 5 INVESTIGATIONS INTO THE UNIQUENESS OF NMR DISTANCE DETERMINATIONS IN MULTIPLE SPIN SYSTEMS 5.1 I N T R O D U C T I O N A s discussed in the Chapter 3, the R E D O R and T E D O R behavior in INS spin systems is generally different than the dephasing for an isolated IS spin pair. Theoretical R E D O R and T E D O R curves can be calculated for multiple / spins about a single (observed) S spin as described in Sections 3.4.2 and 3.5.3, provided the precise geometrical arrangement (number and relative orientations) of the spins is specified. Naito et al. were the first to describe the mathematical framework necessary for calculating the R E D O R dephasing in a 3-spin I2S system, and demonstrated the application of this in a simple peptide system.' This methodology was later extended by Schaefer and co-workers who introduced a convenient method for performing the calculations in terms of vector dot products between the I-S vectors. 2 The expansion of these techniques to describe the dephasing in T E D O R experiments was derived and presented in Chapter 3. Using these approaches, experimental R E D O R and T E D O R data for the T-2 sil icon in octadecasil could be well fitted (Chapter 4). This study represents the only multi-spin T E D O R analysis reported to date/ Furthermore, only very few studies reported in the literature have included multi-spin R E D O R analysis, and in most of these cases the geometry of the spin system was known, or could be predicted with a fair degree of certainty, from other methods (e.g. X-ray diffraction studies) prior to the analysis of the experimental data. ' 5 "" ' 165 Any relative motions of the nuclei within a heteronuclear spin system can also affect the R E D O R and T E D O R dephasing because the internuclear distances (and thus the dipolar coupling) w i l l vary. The presence of such motions wi l l result in an apparent reduction in dephasing compared to that predicted for a rigid spin system. Goetz and Schaefer 2 have presented a mathematical formalism for calculating the dephasing where the trajectory of the motion is known, and Naito et al." have proposed a method to include the effect o f thermal motions. A t the time the experiments reported in this thesis were undertaken no systematic evaluation of the theoretical R E D O R and T E D O R behavior in INS spin systems was available. It was unclear i f the R E D O R and T E D O R dephasing in multiple spin systems could be identified and quantified directly, or whether the dephasing behavior was unique for different spin systems. In many of the systems that R E D O R and T E D O R might be utilized to characterize, the structural information available wi l l be somewhat limited. The investigations of sorbate / zeolite structures, which is the topic of this thesis, wi l l fall into this category. For this reason it is crucial to determine the situations where analysis of R E D O R and T E D O R data may be unable to furnish unambiguous, dependable distance information. A series of theoretical R E D O R and T E D O R calculations on a selection of INS spin systems assess the practicality o f extracting useful structural information from analysis of R E D O R and T E D O R experiments in such cases, and the results are summarized in this Chapter. 5.2 SELECTION OF PARAMETERS FOR SIMULATIONS A selection of 3-spin, I2S systems were chosen to simplify the calculations, and the effects of varying two parameters were investigated: (a) the IS dipolar couplings, and (b) the IS-I angle, L\. A pictorial representation of these systems is given in Figure 5.1. The full range of L, (0° < C, < 180° ) was considered, and values for the two dipolar couplings, D, and D2, (i.e. between IAS and I/rS respectively) were chosen to represent couplings in typical l 3 C - 1 5 N 166 systems. This is because many R E D O R and T E D O R experiments have focused on C - N distance determinations in biological systems such as peptides and amino acids. s Figure 5.1 Pictorial representation of the I2S spin systems for which the theoretical R E D O R and T E D O R dephasing was investigated. The dipolar coupling for IA-S (Dt) was fixed at 100 H z , while D2 (the dipolar coupling between IB and S) and the IA-S-IB angle, were varied. Three distinct IA-S-IB systems with />/ = 100 H z and D2 =100 Hz , 75 Hz , or 50 Hz were considered in detail. Preliminary calculations on a 5-spin I4S system indicated that the step size utilized (TT/20) for the 3-spin calculations provided sufficient accuracy for the integration to produce the powder average (Table C . 2, Appendix C . For clarity, the results of the R E D O R and T E D O R 3-spin simulations are discussed separately. It should be emphasized that the features of the R E D O R behavior calculated for these cases can be related directly to other I2S systems. Because the dephasing time (i.e. the product o f the number of rotor cycles (n or m) and the rotor period, x r) was used in calculations, the curves are independent of the spinning speed. Furthermore, so long as the ratio of relative magnitudes of the two dipolar couplings are in a ratio similar to those used here (1.0:1.0, 1.0:0.75 and 1.0:0.5) 167 the curves are related by a simple scaling: the larger the dipolar couplings, the shorter the time needed for a given degree of dephasing to occur. When considering the T E D O R behavior, there is the small additional complication that the dephasing time in the part o f the experiment which has a constant number o f rotor cycles must be known in order to calculate the dephasing. The theoretical curves presented in this chapter were calculated assuming a spinning speed was 2.5 kHz, with the number o f rotor periods before the coherence transfer («) varied, and the number o f rotor periods after the transfer (m) f ixed. For an isolated IS spin pair, the maximum theoretical dephasing occurs when mDxr = 0.84, / 2 On the assumption that the net dipolar coupling would be approximately 100 H z in the spin systems investigated, a value of m = 20 was selected. 5.3 R E D O R SIMULATIONS 5.3.1 Theoretical R E D O R Behavior for 3-Spin I-S-I Systems Curves calculated for Dt = D2 = 100 Hz and selected values of the angle C, (some of which are commonly encountered in chemical systems) are shown in Figure 5.2(a). The data used to generate Figure 5.2(a) are listed in Table C.3 (Appendix C) . The curve for an isolated IS spin pair with D = 100 Hz is also given. It should be emphasized that these curves are not the same as those calculated by simply adding curves calculated for the individual spin systems, IA-S and IB-S, even though the calculation involved a sum of independent S spin dephasings by the / nuclei (see Section 3.4.3). The dephasing curves are identical for £, and 180°-^ due to the symmetry o f the cosine function in the dephasing equations (Eqs. 3.31 and 3.33). The most distinctive behavior is observed when C, is small (or close to 180°), otherwise there are quite minor differences in the dephasing when C, is in the range from approximately 20° to 160°. In general the initial dephasing occurs faster in the 3-spin systems than for the IS spin pair. A lso the nearer C, is to 90°, the faster the value of AS/So approaches the equilibrium value of 1.0. Obviously, in systems with larger 168 dipolar couplings these differences would evolve more quickly, but the relative behaviors of the curves wi l l be similar. Two special cases occur i f D, = D2: (/) when L\ = 90°, and (ii) when L\ = 180°. In the first case (data not shown) the dephasing is identical to that calculated for an isolated spin pair with a dipolar coupling of V2 D/ . In the second situation, the equilibrium AS/So value is 0.5 rather than 1.0. This arises because two of the four possible combinations of the dipolar couplings cancel (+Di -D2 = -Dt + D2 = 0), and thus only the two remaining combinations contribute to the dephasing. This behavior is identical to that predicted for and isolated IS spin pair having a dipolar coupling of 2 D, with the I spins present only 50% of the time. Figure 5.2(b) shows the dephasing curves calculated for three different values of D2 with C, = 180°, and two general trends are evident. Firstly, the dephasing during the early stages is faster for larger D2. Secondly, except in the special case where Di~D2, the smaller D2, the shorter the dephasing time needed to approach the equilibrium A S / S 0 value of 1.0. A s D2 becomes a smaller fraction of Z>/, the IB-S interaction has a correspondingly smaller effect on the total dephasing. In fact when the magnitude of D2 is < 10% of 2)/, the effect o f the third spin (/«) becomes almost negligible, and the dephasing is very similar to that predicted for an isolated IS spin pair. Figures 5.3, 5.4 and 5.5 illustrate the dependence on C, where Dt = 100 H z and D2 = 100 Hz, 75 Hz, or 50 Hz, respectively. Inspection of these plots reveals that the variation between the three cases is quite small once t, is larger than about 30°. It is also apparent that a variation in C, of the order of 10° is required to effect a noticeable change, and spins systems with quite distinct geometries may exhibit very similar dephasing behavior. For example, the curve calculated for D, = D2 = 100 H z with £=20° (Figure 5.2(a)) closely mimics that obtained with Dt = 100 Hz, D2 = 50 Hz and ^=180° (Figure 5.2(b)). The relatively small changes that are observed in the calculated data wi l l be even more difficult to detect in experimental data due to uncertainties 169 (a) 1.2, A S Dephasing Time (ms) F igure 5.2 R E D O R curves calculated for some 3-spin I2S systems, (a) Di = 100 Hz , D2 = 100 Hz, and the I-S-I angle, indicated, (b) £ = 180° with Z), = 100 Hz, and D2 = 100, 75, or 50 Hz. The curve for an isolated IS spin pair with D = 100 H z is included for comparison. 170 Figure 5.3 R E D O R curves calculated for a 3-spin I2S system (Dt = 100 Hz , D2 = 100 Hz) as a function of the I-S-I angle Only curves for 0° < C, < 90° are shown since the dephasing is identical for C, and 180°-^. 171 Figure 5.5 R E D O R curves calculated for a 3-spin I2S system (Dt = 100 Hz , D2 = 50 Hz) as a function of the I-S-I angle Only curves for 0° < C, < 90° are shown since the dephasing is identical for C, and 180°-^. 173 arising from a finite signal-to-noise (S/N) ratio. Thus even in a "best-case" scenario where both interatomic distances are known (i.e. Dt and D2 can be fixed) and only C, needs to be varied, it is anticipated that C, could only be determined to an accuracy about ±15°. 5.3.2 The R E D O R Trans fo rm App l ied To M u l t i - S p i n Data The R E D O R transform is an analytic transform method, analogous to a Fourier transform, which provides a means of analyzing R E D O R data in such cases/"' When applied to Sf/So R E D O R data, the R E D O R transform produces a frequency-domain spectrum containing resonances at the dipolar coupling frequencies present in the time-domain R E D O R signal. Provided that the experimental data is of adequate quality (i.e. good signal-to-noise ratio and collected up to a sufficiently large number of rotor periods), and the spinning speed used exceeds ca. three times the largest dipolar coupling present, the R E D O R transform can successfully extract the correct dipolar frequencies from real experimental R E D O R data where the spin system contains discrete sets of heteronuclear spin pa i r s / " ' " It was not apparent from the literature what information, i f any, the R E D O R transform would yield when applied to R E D O R data acquired for samples containing multiple spin systems. In particular, it was hoped to determine whether the R E D O R transform was capable of providing correct dipolar couplings from multiple spin data. There was also interest in the actual appearance of the R E D O R transform spectrum for multiple spin systems (e.g. INS systems), to determine i f the transform spectrum contained features which might be diagnostic of the presence of multiple spins, or act as indicators that the spectrum should be interpreted with caution. Information such as this is vital to determine the validity of applying the R E D O R transform in cases where little or no information about the nature of the spin system is available prior to beginning R E D O R I-S internuclear distance determinations. For the R E D O R transform to be well behaved, the Sf/So data must decay completely to a value of 0.0. Because of a finite signal-to-noise ratio and the incomplete dephasing inherent in 174 real experimental data, an apodization function must be applied to ensure this requirement is met. Reports to date favor the use of a 3-point Blackman-Harris f u n c t i o n " " and this was used in the present work. To investigate the strengths and weaknesses of the R E D O R transform method, it was applied to Sf/So R E D O R data calculated for several I2S systems. The data were calculated in two rotor cycles increments up to 64 rotor periods for a spinning speed of 2.5 kHz using the product formalism described in Section 3.4.2. Fol lowing apodization the data were zero-fil led up to 256 rotor periods to improve the appearance of the transform spectrum. One effect o f apodization is to smooth the data, however any oscillatory fine-structure present in the data is also modified. While this is potentially troublesome for data from isolated IS pairs, it becomes a major problem in the case of I2S spin systems because the relatively minor differences which distinguish the I2S spin system geometries w i l l be further reduced. Furthermore, apodization preferentially weights the contribution of the data at short dephasing times (where the behavior is very similar for different geometries), and thus discriminates against the information present in the behavior seen at longer times. Application of the R E D O R transform to non-apodized data generally produces a periodic dipolar spectrum (due to truncation effects) which is very difficult to interpret. The appearance of the R E D O R transform was found to depend on the I-S-I angle C, and on the dipolar couplings used for the calculation of the Sf/So data. In some instances the transform spectrum indicated that only a single dipolar coupling was present, while for other values of C,, several resonances were clearly evident. The dipolar couplings determined directly from the transform spectra varied significantly; in some cases the values exceeded those assumed for the calculation of the Sf/S 0 data, while in others smaller couplings were seen. N o features were observed which might indicate that the R E D O R data was not from isolated spin pairs. In summary, the R E D O R transforms calculated for theoretical I2S data did not exactly reproduce the known dipolar couplings, and the initial apodization overshadowed any unique 175 features apparent in the raw Sf/So data in many cases. The situation w i l l be even worse for experimental data where the finite signal-to-noise ratio introduces additional uncertainties in the precise A S / S 0 values. These results were not unexpected because the R E D O R transform was developed assuming only contributions from isolated spin pairs. 5.3.3 Gaussian Distribution of Dephasing Spins Blumenfeld et al.15 have proposed an approach where the R E D O R behavior is calculated in terms of the I-S second moment, M2(I-S), for cases where a large number of I spins dephase a single S spin. The applicability o f this approach was demonstrated by these authors using the experimental 2 7 Al-observed, 'H-dephased R E D O R data for two minerals. The fitting yielded values for M2(I-S) which where in good agreement with those calculated from crystal structure." This is discussed in Section 3.4.3 and details o f the calculations are presented in Appendix C . B y using, for example, a Gaussian distribution of dephasing spins, no information regarding the specific geometrical arrangement needs to be provided. However since any dependence on the effect o f the I-S-I angles is neglected, the potential to determine specific I-S distances is relinquished. The caveat is that the number o f dephasing spins is sufficient to approximate the assumed distribution. In Figure 5.6, Gaussian R E D O R curves calculated assuming M2(I-S) = 5000 H z 2 , 10000 H z 2 , and 50000 H z 2 are shown together with that for R E D O R dephasing in an isolated IS spin pair (D = 100 Hz). The rate of dephasing increases with increasing magnitude of the heteronuclear second moment, and shows a smooth rise without oscillations; precisely the behavior expected when a large number o f oscillatory curves having different periods are added. 5.4 T H E O R E T I C A L T E D O R B E H A V I O R F O R 3-SPIN I-S-I S Y S T E M S A s for the R E D O R calculations, three spin systems with dipolar couplings of Z)/ = 100 Hz and D2 = 100 Hz , 75 Hz , or 50 H z were considered for various IA-S-IB angles. Curves 176 0 10 20 30 40 nxx Dephasing Time (ms) Figure 5.6 R E D O R curves calculated for a single (observed) S spin dipolar coupled to a large number of / sp ins and different IS heteronuclear second moments, M2(IS). A Gaussian distribution was used to weight the contributions of the individual IS dipolar couplings to the total dephasing. The curve for an isolated IS spin pair with D = 100 Hz is included for comparison. 177 calculated for Dt = D2 = 100 Hz and selected values of the angle C, are shown in Figure 5.7(a), together with that calculated for an isolated IS spin pair having D = 100 Hz. The data used to generate Figure 5.7(a) are listed in Table C.5 (Appendix C) . A s was also the case for the multi-spin R E D O R behavior, these curves are not the same as those calculated by simply adding curves calculated for the individual spin systems, IA-S and Ig-S. The I2S T E D O R curves calculated for C, and 180°-(^ are identical because of the nature of the expression (a product of the sine functions) describing the dephasing (see Appendix C) . When C, is in the approximate range 30° <C<\ 50°, the dephasing is slightly faster for the 3-spin system than for an isolated IS spin pair (Figure 5.7(a)). Figure 5.7(b) shows the dephasing curves calculated for three different values of D2 with C, = 180°, and two trends are evident. Firstly, the initial maximum for ST occurs at essentially the same dephasing time (ca. 8 ms) in all cases, and is also the same as that for an isolated IS spin pair. This could potentially be very problematic when attempting to fit experimental data, since the theoretical S T values must be multiplied by a scale factor to match the experimental T E D O R data. This need arises because, unlike AS/So values determined for a R E D O R experiment, S r is not normalized. Secondly, the time between successive maxima in S T becomes longer as D2 gets smaller. It is essentially these variations which distinguish the behavior in the different systems. However, at longer dephasing times in the T E D O R experiment, T2 induced-damping can quickly "wash-out" these oscillations. Figures 5.8, 5.9, and 5.10 illustrate the dependence on t, where/) / = 100 Hz and D2 = 100 Hz , 75 Hz, or 50 Hz , respectively. Inspection of these plots reveals that the variation between the three cases is quite small once C, is larger than about 30°. It is also apparent that, as for the R E D O R data, a variation in C, of the order of 10° is required to effect a noticeable change. Again, the relatively small changes observed in the calculated data wi l l be even more difficult to detect in real experimental data due. 178 0 10 20 30 40 «x r Dephasing Time (ms) F igure 5.7 T E D O R curves calculated for some 3-spin I2S systems, (a) Z>/ = 100 Hz, D2= 100 Hz, v r = 2.5 kHz, n varied, m = 20, and the I-S-I angle, L\, indicated, (b) C, = 180° with Di = 100 Hz , and D2 = 100, 75, or 50 Hz. The curve for an isolated IS spin pair with D= 100 Hz is included for comparison. 179 «T r Dephasing Time (ms) F,'gure5.8 TEDOR curves ^ s p m n m g l ^ f ^ " a ^ hS system (». - 1 0 0 „ n C Only curves for 0° < * = 20) as a wLn = c 1 °° C and ) 8 0 o _ C are snow n s i n c e 180 Figures., T E D O R curves calculated for a 3-spin I2S system (Df = 100 Hz D - 75 H spinning speed 2.5 kHz n varied m - o n u c ' " 2 ~ 7 5 H z ' Only curves for 0° < r < QO• T " } * f U n C t , ° " ° f t h e W a n g l e and l80 ° T ^ are shown smce the dephasing is identical f far C 181 Figure 5.10 T E D O R curves calculated for a 3-spin I2S system (Z), = 100 Hz , D2 = 50 Hz, spinning speed 2.5 kHz, n varied, m = 20) as a function of the I-S-I angle Only curves for 0° < C, < 90° are shown since the dephasing is identical for i ;and 180° - ; . 182 A major limitation with T E D O R data is that the S T intensities are not normalized which means that a scaling factor is required to match the experimental and theoretical S T values. Inspection of Figures 5.7-5.10 reveals that the shape of the curves (which is effectively what must be matched) is not completely unambiguous in many cases. In addition, any differences visible in the theoretical curves wi l l probably vanish when working with real experimental data due to finite S/N and damping of the oscillations due to spin-spin relaxation. These difficulties are compounded because the S / N decreases with increasing dephasing time. Any relative motions of the nuclei within a heteronuclear spin system can also affect the T E D O R dephasing because the internuclear distances (and thus the dipolar coupling) wi l l vary. Ove ra l l , the presence of such motions wi l l be more problematic in T E D O R experiments than in R E D O R because there are two dephasing periods. In summary, the likelihood of determining reliable distances in a I2S systems from T E D O R behavior is potentially even less than for R E D O R . Even in the "best-case" scenarios where both interatomic distances, or one distance and the angle, are known, it would be difficult to determine the complete geometry unless T2 is sufficiently long that data of adequate S/N can be obtained at large numbers of rotor cycles. 5.5 C O N C L U S I O N S In conclusion, these calculations indicate that it is highly unlikely that direct and unambiguous distance determinations can be obtained from R E D O R and T E D O R experiments on multiple spin systems when the number of spins and geometrical arrangement of these is unknown. This is true even for the simple 3-spin geometries investigated here, and the problem wi l l be compounded when more spins and/or relative motions are present. Furthermore, there is no discrimination between I2S systems with C, and 180°-^, and it is possible to obtain the wrong answer i f an isolated spin pair is assumed and multiple spins are present. R E D O R transforms of 183 data from multiple spin systems yields transform spectra devoid of features which might indicate that the spin system was not composed of isolated spin pairs, and could thus be mis-interpreted. The algorithm used to calculate the powder averaging in the present work is very computationally intensive (Appendix C) , which significantly hinders fitting experimental multi-spin data within a reasonable time period. Increasing the efficiency of the integration over the two angles to produce the powder average is thus highly desirable. This is especially true for T E D O R data where a summation must be used to performed the calculations. Methods which could be implemented include the approaches proposed by Aldermann et al.,16 Wang and H a n s o n / 7 and the recently reported R E P U L S E algor i thm/" Even with improved calculation efficiency, the best approach wi l l be to try and ensure that the spin system approximates an isolated spin pair as closely as possible, (e.g. by isotopic substitution and dilution in the unlabeled compound), or several isolated spin pairs. If this is not feasible, one possibility is to acquire several R E D O R and T E D O R data sets (with different parameters). Alternatively, C P data from groups of spins could be obtained and analyzed to obtain TCp . In both cases a model of the spin system which fully describes the relative geometric arrangement (i.e. with all angles and distances implicit ly defined) must be proposed, and the theoretical dephasing or heteronuclear second moments are calculated and compared to the experimental data. The model is modified and the calculations re-run until optimal agreement between the calculated and experimental dephasing is obtained for all o f the experimental data sets. With these approaches there wi l l be no direct determinations of distances, but structural information can still be (indirectly) obtained. This method wi l l be most efficient i f constraints can be placed upon the model which limit the possible number of spins and internuclear distances. This may be the case for sorbate molecules in zeolites since the guests must lie within the channels or voids. This approach was applied to locate />difluorobenzene in the zeolite Z S M -5 as described in the next Chapter. 184 R E F E R E N C E S F O R C H A P T E R 5 7 Naito, A . ; Nishimura, K.; Tuz i , S.; Saito, H. Chem. Phys. Lett. 1994, 229, 506. 2 Goetz, J . M . ; Schaefer, J . J. Magn. Reson. 1997,127, 147. 3 Fyfe, C .A . , Lewis, A . R , ; Chezeau, J . M . ; Grondey, H . J. Am. Chem. Soc. 1997,119, 12210. 4 Pan, Y . ; Gul l ion, T.; Schaefer, J . J. Magn. Reson. 1990, 90, 330. 5 Ho l l , S . M . ; Marshal l , G.R. ; Beusen, D.D.; Kociolek, K.; Redlinski, A . S . ; Leplawy, M.T.; M c K a y , R.A. ; Vega, S.; Schaefer, J . J. Am. Chem. Soc. 1992,114, 4830. 6 McDowe l l , L . M . ; K lug , C .A . ; Beusen, D.D.; Schaefer, J . Biochem. 1996, 35, 5395. 7 Marshal l , G.R. ; Beusen, D.D.; Kociolek, K.; Redlinski, A . S . ; Leplawy, M.T. ; Pan, Y . ; Schaefer, J . J. Am. Chem. Soc. 1990,112, 963. 8 McDowe l l , L . M . ; Barkan, D.; Wi lson, G . E . ; Schaefer, J . Solid State Nucl. Magn. Reson. 1996, 7,203. 9 Ho l l , S.; Kowalewski , T.; Schaefer, J . Solid State Nucl. Magn. Reson. 1996, 6, 39. 10 Pan, Y . Solid State Nucl. Magn. Reson. 1995, 5, 263. 11 Naito, A . ; Nishimura, K.; Kimura, S.; Tuz i , S.; A ida , M . ; Yasuoka, N . ; Saito, H. J. Chem. Phys. 1996,100, 14995. 12 Hing, A . W . ; Vega, S.; Schaefer, J . J. Magn. Reson. Ser. A. 1993,103, 151. 13 Mueller, K.T. ; Jarvie, T.P. ; Aurentz, D.J.; Roberts, B .W. Chem. Phys. Lett. 1995, 242, 535. Muel ler, K.T.; Jarvie, T.P. ; Aurentz, D.J.; Roberts, B.W. Chem. Phys. Lett. 1996, 254, 281. 14 Jarvie, T.P. ; Went, G.T. ; Mueller, K.T. J. Am. Chem. Soc. 1996,118, 5330. 15 Blumenfeld, A . L . ; Coster, D.; Fripiat, J .J . J. Phys. Chem. 1995, 99, 15181. 16 Alderman, D.W.; Solum, M.S. ; Grant, D . M . J. Chem. Phys. 1986, 84, 3717. 17 Wang, D.; Hanson, G.R. J. Magn. Reson. Ser. A. 1995, 777, 1. 18 Bak, M . ; Nielson, N .C . J. Magn. Reson. 1997, 725, 132. 185 CHAPTER 6 PRELIMINARY SOLID-STATE NMR INVESTIGATIONS OF THE STRUCTURE OF THE LOW-LOADED /MIM-DIFLUOROBENZENE / ZSM-5 COMPLEX 6.1 I N T R O D U C T I O N A s discussed in Chapter 5, the direct determinations of distances between nuclei on organic guests and the framework nuclei o f microporous hosts wi l l usually not be possible. The porous nature of the hosts means that the framework nuclei wi l l interact with several nuclei on the guest molecules, even i f they are isolated on the guests themselves. Thus a model must be postulated and tested for agreement with experimental data, the simplest such experiment is C P from a "group" of nuclei on the organic guest with no assumption of isolated spin pairs. Such experiments are described in the present chapter with the 1 9 F and ' H nuclei o f /?-difluorobenzene as independent magnetization sources. The microporous framework system chosen was purely siliceous Z S M - 5 . Z S M - 5 was selected because it is one of the few microporous materials for which single crystals suitable for single crystal X-ray diffraction experiments can be synthesized and X R D studies provide an independent a check of the appropriateness of the experimental protocol outlined in this chapter. In addition Z S M - 5 has considerable significance as a catalyst in many industrial processes, including the conversion of methanol to gasoline, the interconversion of aromatic compounds, and paraffin c rack ing. ' 2 Information on the preferred locations of sorbed 186 molecules inside the channels of zeolites would greatly aid understanding of the catalytic, diffusive, and shape-selective properties of these materials. The changes which can occur in the Z S M - 5 framework lattice due to temperature and the presence of guest species (e.g. sorbed organic molecules). Factors including the dependence on temperature, the number of guests present (loading), as well as the nature of sorbate-sorbate and sorbate-framework interactions have been studied by a variety of physical and theoretical methods as discussed in Chapter 1. Only six sorbate / Z S M - 5 single crystal structures (some closely related) have been reported to date/" 9 and at the present time, these represent the only cases where the locations of the sorbed organic molecules been reliably determined. Although sorption sites have been proposed from theoretical calculations, these are not always in agreement with one another, or the X-ray determined structures/ ' 0 " ' 5 There is a definite need to expand the database of dependable structures to improve the reliability, and verify the results, o f the calculation methods before they can be relied upon to yield accurate locations of sorbates in zeolite structures. However, it is generally difficult to synthesize zeolite crystals of adequate size and quality for single crystal X R D structure determinations, and also to load them with controlled amounts of volatile organic sorbates. Hence other techniques capable of providing locations and orientations of guest molecules must be developed. Whi le X-ray diffraction ( X R D ) studies of microcrystalline (powder) samples and single crystals of Z S M - 5 have yielded the majority of the structural information in these systems, 5""'"'"' 9 2 9 S i M A S N M R has provided critical information such as the number of T-sites, and is very sensitive method for detecting structural changes/ 9 " 2 2 Using sorbate-lattice distance information from the solid-state N M R techniques developed in the previous chapters, it should (theoretically) be possible to determine the complete three-dimensional structures of sorbate / zeolite complexes from powder samples. 187 In this chapter, the results of the preliminary attempts to determine the location and orientation ofp-difluorobenzene molecules in the low-loaded Z S M - 5 complex containing ca. four molecules per unit cell (u.c.) are presented. The ' H - 2 9 S i and 1 9 F - 2 9 S i heteronuclear dipolar couplings were probed using C P , R E D O R , and T E D O R experiments. Possible sorption sites which were consistent with these data were then determined. 6.1.1 Framework Structure of MFI-type Zeolites MFI-type zeolites include Z S M - 5 which contains Si and A l in varying ratios from about 50 through to the purely siliceous form known as silicalite, as wel l as various other materials having isomorphous substitution of A l , S i , or both by, for example B or T i . The M F I framework topology was first determined by Kokotai lo et al. from powder X-ray diffraction d a t a / 7 * and this was subsequently confirmed by a number of other investigations including several single crystal X R D s t u d i e s / " 2 7 * The basic building block of the M F I framework is the pentasil unit (Figure 6.1(a)) which consists of eight 5-membered rings. These pentasil units link together by sharing edges to form chains that run parallel to the [001] axis of the unit cell (Figure 6.1(b)). The complete 3-dimensional M F I framework is constructed from sheets of these chains and contains 4-, 5-, 6-, and 10-rings where the neighbouring chains are related by mirror planes. This produces a 3-dimensional channel system formed by two kinds of intersecting channels: sinusoidal (also called zig-zag) channels which run along the [100] axis and straight ones running parallel to [010] as illustrated in Figure 6.1(d). Both types of channels are defined by 10-membered rings which are slightly elliptical (Figure 6.1(c)), and the effective pore dimensions (determined by the oxygen van der Waals radii) are approximately 5.2 x 5.8 A. The exact symmetry of the lattice and the shapes of the channel openings can change with temperature and the presence of guest species such as sorbed organic molecules (see below). 188 (c) (d) c Figure 6.1 Bui ld ing units, framework topology, and channel structure of the M F I framework, (a) Pentasil basic building unit ( B B U ) formed by five 8-membered rings. Each vertex represents a T-atom (Si or A l ) , and oxygens are omitted for clarity, (b) Chains which run parallel to [001] in the framework formed by l inking the pentasil B B U ' s . (c) V iew down [001] showing sheets formed by joining the chains. The 10-membered ring aperatures define the straight channels. Similar sheets are present in the [100] direction, (d) Representation of the channel structure showing the interconnecting straight and sinusoidal (zig-zag) channels. After reference 14. 189 Because of the nature of the pore system, Z S M - 5 possesses very distinct sorption and diffusion properties which are exploited in its industrial applications. The channel size is intermediate between the small pore (8-ring openings e.g. the L T A framework) and large pore zeolites such as zeolites X and Y (12-ring openings, F A U framework topology). Z S M - 5 can adsorb molecules such as /^-xylene, but effectively excludes molecules with larger kinetic diameters such as l,3,5-trimethylbenzene. / : > 6.1.2 Guest- and Temperature-Induced Framework Changes in ZSM-5 6.1.2.1 X-ray Diffraction Studies of ZSM-5 Systems Z S M - 5 has been found to adopt four space groups: three with orthorhombic symmetry: Pnma (12 crystallographically inequivalent T-sites), P2/2 /2 / (24 T-sites), and Pn2,a (24 T-sites); and one having monoclinic P2i/n.l.l symmetry with 24 T-sites. As-synthesized Z S M - 5 , containing the tetrapropylammonium cation ( T P A + ) as template, exhibits orthorhombic Pnma symmetry/ ' ' ' 2 5 After calcination to remove the template, the framework shows a reversible phase transition at about 340 K (the precise temperature depends on the S i / A l ratio) and has monoclinic symmetry below and orthorhombic (Pnma) symmetry above the transition temperature. 15,17,18,21,22.26 If certain organic molecules are adsorbed into Z S M - 5 , the framework symmetry may also change. These changes were observed using powder X R D y i and 2 9 S i M A S N M R on highly crystalline, siliceous Z S M - 5 samples. • • • • Only four different sorbed molecules in Z S M - 5 have been studied by single crystal diffraction studies to date: / j - xy lene /^ -d ich lo robenzene / ' 5 />-nitroanil ine/ 7 and naphthalene/ Details of the space groups and locations of the sorbed molecules determined from these single crystal studies are summarized in Table 6.1. Whi le structure refinements from powder diffraction data have been carried out for Z S M - 5 containing /?-xylene, 2 y , 5 W/»-dichlorobenzene/ 5 ' 5 / naphthalene, 5 2 , 5 5 and several other 190 Table 6.1 Space groups and numbers of T-sites for several ZSM-5 structures as determined by single crystal X-ray diffraction. For those structures where organic guest species are present, the number of molecules per unit cell and their locations are given. Structure'3 ' reference Temp. (K) Space Group Number of T-sites Guest Location(b) (number / u.c.) Comments'0 ' MONO 18 293 P2,/n.l.l(i) 24 -crystal exhibits domain twinning HTORT 17 350 Pnma 12 -TPAORT 16 293 Pnma 12 intersection (4) TPA+ disordered HLPXY 3 293 P2,2,2 I(e) 24 intersection (4) zig-zag (4) unrestrained anisotropic refinement of all atoms HLPDCB 4 293 P2,2i2,(t) 24 intersection (4) zig-zag (4) unrestrained anisotropic refinement of all atoms. LLPDCB 5 293 Pnma 12 intersection (2.6) rigid /j-dichlorobenzene individual isotropic parms. LLPNA 6 293 Pnma 12 intersection (4) rigid />nitroaniline with individual isotropic parms. 7 293 Pn2,a(f) 24 intersection (4) framework restraints, rigid />nitroaniline, isotropic parameters LLPXY this work 9 180 Pnma 12 intersection (2.8) unrestrained anisotropic refinement of all atoms NAPH 8 293 Pnma 12 intersection (3.7) rigid napthalene with anisotropic parameters <a) MONO: monoclinic phase of empty (calcined) ZSM-5. HTORT: high temperature orthorhombic phase of empty (calcined) ZSM-5. TPAORT: as-synthesized ZSM-5 containing tetra-propylammonium ions (TPA+). HLPXY: high-loaded /^-xylene. HLPDCB: high-loaded />dichlorobenzene. LLPDCB: low-loaded /7-dichlorobenzene. LLPNA: low-loaded />nitroaniline. LLPXY: low-loaded ^-xylene /u.c. NAPH: loaded with naphthalene.<b) Intersection: in straight channel at intersection with zig-zag channel. Zig-zag: in sinusoidal channel.(c) Anisotropic and isotropic refer to the atomic displacement factors. <d) Non-standard space group to allow direct comparison with Pnma ZSM-5 structures (symmetry operators: x, y, z; -x, -y, -z; 0.5+x, 0.5-y, 0.5-z; 0.5-x, 0.5+y, 0.5+z.(e) Origin shifted to (0, 0, 0.25) to allow direct comparison with other Pnma ZSM-5 structures. The symmetry operators become: x, y, z; 0.5+x, 0.5-y, 0.5-z; -x, 0.5+y, -z; 0.5-x, -y, 0.5+z.(f) Related to Pnma by removal of the centre of symmetry which results in a loss of the mirror plane aty = 0.25. sorbates 4 J ' subsequent single crystal diffraction studies showed that the sorbate location(s) proposed from the powder studies were not always correct/ ' 8 6.1.2.2 29Si NMR Studies of ZSM-5 Systems A s discussed previously, the 2 9 S i M A S N M R spectra of highly crystalline, purely siliceous zeolite systems can be very diagnostic of the lattice structures (and symmetries) in terms of the local environments of the Si atoms. For example, subtle changes in the average S i (OSi ) 4 angles by as little 0.2° can be detected as a 2 9 S i chemical shift difference of about 0.1 ppm, which is readily observable. 8 5 7 The temperature-induced phase transition from monoclinic to orthorhombic symmetry is clearly observed in the 2 9 S i M A S N M R spectra of highly siliceous Z S M - 5 as seen in Figures 6.2(a) and (c). Two-dimensional 2 9 S i C O S Y and I N A D E Q U A T E experiments were used to assign the individual 2 9 S i N M R resonances indicated in these f igures . 2 6 5 8 Distinct changes in the 2 9 S i M A S N M R spectra are also observed upon sorption of several organic molecules including/7-xylene, pyridine, benzene, dimethylsulfoxide ( D M S O ) , acety 1 acetone,/»-chlorotoluene (Figures 6.2-6A).21,39,40 These changes are reversible (e.g. by calcination to remove the sorbate), and occur at ambient temperatures. However, no changes are seen when attempts are made to adsorb o-xylene, m-xylene, octane, cyclohexane, durene, or ethylcyclohexane. This indicates that the framework symmetry is maintained and it is only the local framework symmetry and geometry which is altered. 5 9 This is because these molecules are too small to alter the structure or are excluded. Similar temperature and sorbate induced changes have been observed for Z S M - 1 1 , but have not been seen for other highly siliceous zeolites (e.g. mordenite, omega, Z S M - 2 3 , and others), confirming that the observed changes are not caused by general susceptibility effects of the sorbed organic molecules in the cavit ies. 2 2 3 9 , 4 1 For the Z S M - 5 / sorbate systems where changes are seen, the nature of the lattice distortions seems to be relatively characteristic o f the nature of the sorbed molecule (Figure 6.3), 192 I I I I I I I I I 1 I I I I -110 -112 -114 -116 -118 -120 ppm from T M S F igure 6.2 High resolution 2 9 S i M A S N M R spectra of highly siliceous Z S M - 5 showing changes that occur with temperature or loading with/j-xylene. (a) Empty Z S M - 5 at 300 K (monoclinic, P2i/n.l.l phase), (b) Z S M - 5 loaded with 2 molecules/>xylene per u.c. at 300 K (orthorhombic, Pnma phase), (c) Empty Z S M - 5 at 403 K (orthorhombic, Pnma phase), (b) Z S M - 5 loaded with 8 molecules />xylene per u.c. at 300 K (orthorhombic, P2\2\2\ phase). The numbers indicate the assignments to specific T-sites from I N A D E Q U A T E experiments. After reference 38. 193 "i r~~i i i i i i i—t i i • i i -109 -111 -113 -115 -117 -119 i—i—i—i—i—r -109 -111 —I— I—I—I—I—I— 13 -115 -117 -119 T i i i i i i I i—i—i—i—r -109 -111 -113 -115 -117 -119 (c) J I — I — I — I — I — I — I — I — I — I — I — I — I -109 -111 -113 -115 -117 -119 \ I 1 -109 ppm from T M S T — I — I — I — I — l — I — l — I — 111 -113 -115 -117 -119 Figure 6.3 High resolution 2 9 S i M A S N M R spectra o f highly siliceous Z S M - 5 loaded with selected organic molecules: (a) pyridine (35 u.L/250 mg); (b)/7-xylene (10 u.L/250 mg); (c) dimethylsulfoxide (40 u.L/250 mg); (d) acetylacetone (20 u.L/250 mg); (e) benzene (25 uL/250 mg); and (f) toluene (24 uL/250 mg). A l l spectra recorded at room temperature at 79.495 M H z with 7 s recycle delay. After reference 40. 194 — i — I — 1 — I — I — I — I — I — I — I — I — I — I — I — -106 -108 -110 -112 -114 -116 -118 ppm from T M S F igure 6.4 High resolution 2 9 S i M A S N M R spectra of highly siliceous Z S M - 5 loaded with ca. 4 molecules per u.c. of: (a) /?-chlorobenzene, (b) /7-chlorotoluene, and (c) /(-xylene. The spectra recorded at ambient temperature. After reference 20. 195 and the observed changes are usually also affected by the precise loading and temperature. In some cases however, very similar 2 9 S i M A S N M R spectra are obtained with different molecules, indicating that the lattice geometries are closely related. For example the low-loaded forms of Z S M - 5 containing equal numbers of sorbed /^-xylene, />chlorotoluene, or p-dichlorobenzene only exhibit minor differences (Figure 6.4). From these spectra it was concluded that the locations of the molecules would likely be very similar ( C H 3 is sterically similar to CI and thus the size and shape of these molecules is comparable). 2 0 This prediction has since been confirmed by single crystal X R D stud ies/ " 5 9 Fyfe and co-workers determined phase diagrams for highly siliceous Z S M - 5 containing various amounts of sorbed /»-xylene and />dichlorobenzene at temperatures ranging from 293 to 393 K using 2 9 S i M A S N M R . 2 0 7 2 The 2 9 S i M A S N M R spectra showed that the temperature at which the phase transition between monoclinic and orthorhombic symmetry occurred was dependent on the precise loading and temperature. Furthermore, at certain loadings and temperatures a mixture of the two phases was present and it was possible to determine the fraction of each phase from the 2 9 S i M A S N M R spectra (Figure 6.5). 2 0 In attempts to assign the 2 9 S i resonances to specific T-sites within the framework based on the observed 2 9 S i chemical shifts, various correlations based on the structural geometrical parameters of the T-sites have been p roposed / 7 7 5 " 5 0 These are discussed further in Chapter 8. However, reliance on these correlations can result in erroneous assignments, 2 6 ' 5 7 5 ' and at present the only reliable methods for assigning the 2 9 S i N M R resonances to specific T-sites are the two-dimensional homonuclear N M R correlation experiments such as C O S Y and IN A D E Q U A T E . 2 6 5* 6.1.3 Other Techniques for Locating Sorbates in the ZSM-5 Framework 6.1.3.1 Predictions of Sorbate Locations from Energy Minimization Calculations Several groups have proposed sorption sites of organic molecules within the channels of zeolites from energy minimization calculat ions. ' 0" ' 2 ' 5 2" 5 5 For example, based on calculated van der 196 303 (b) (a) - *••. *••. '•. V V V v V ••. V V 383 - V 3B3*.V 373 ' • • • • • • • • • • • • • • i ;: • ^ - ^ l . \ \ ••. ••. ••. i * — & — \ — J E T -Figure 6.5 Phase diagram for highly siliceous Z S M - 5 loaded with /^-xylene from Si spectra. (a) Three-dimensional surface of the effects of the concentration of/>xylene and temperature. The percentage of the orthorhombic Pnma phase present is indicated on the vertical axis, (b) Two-dimensional projection of part (a) showing the relationship of the orthorhombic {Pnma, 12 T-sites) and monoclinic (P2t/n.l.l, 24 T-sites) phases with varying temperature and concentration of /^-xylene. After reference 20. 197 Waals interactions between the hydrocarbon and the zeolite framework and between the hydrocarbon molecules themselves, the most energetically favourable sorption sites forp-xylene at loadings up to 4 molecules/u.c. in silicalite were found to be at the channel intersections with the methyl-methyl axes lying along the straight channel . 7 0 ' " When the ^-xylene occupies only the channel intersections, the van der Waals interactions between adjacent molecules are small, and the major contribution comes from framework-oxygen //?-xylene-hydrogen interactions. Other researchers have reported similar locat ions/ 5 ' 5 6 Sorption sites in the zig-zag channel and in the straight channel between the channel intersections have also been found for different sorbates (e.g. a lkanes)/ 5 and when higher sorbate loadings were assumed/ 0 Sorbate-sorbate interactions may be significant in some cases, and should be considered, especially at higher sorbate concentrations. In the overwhelming majority of these calculations the framework has been kept rigid, and the sorbate geometry is usually maintained as a semi-rigid group having some pre-optimized conformation."'^ 2 The locations determined by these techniques are dependent on the potential functions and calculation technique used, and there is not always complete agreement between the various calculat ions."^ 2 Furthermore, there seems to be a dynamic interaction between the organic molecules and the framework because the exact framework geometry adopted is related to the nature of the sorbate p r e s e n t / 8 / 7 thus the orientations and locations determined from calculations are sensitive to the atomic coordinates used for the framework a toms/ 2 6.1.3.2 Predictions of Sorbate Locations from Solid-State NMR Experiments Recently Fyfe and co-workers have investigated the location of /^-xylene in Z S M - 5 with several solid-state N M R techniques. Using selectively deuterated/7-xylenes (deuterated at the ring or methyl groups), the locations of the sorbate molecules at a loading of 3, 6, and 8 molecules/u.c. were determined/ 7 , 5 * The inverse of the TCp values obtained from fitting of the *H-2 9 S i C P M A S data were plotted vs. the calculated 2 9 S i heteronuclear second moments. The 198 position of the /(-xylene molecules was systematically varied until a good linear correlation was found. Both the framework and thep-xylene molecules (idealized geometry) were kept rigid during these calculations. The framework symmetries and coordinates used were those reported for the single crystal X R D determinations of the low-loaded /j-dichlorobenzene complex,'' and the high-loaded form of /^-xylene in Z S M - 5 / Because 1/TCP is directly proportional to the ' H - 2 9 S i heteronuclear second moment (Eq. 3.16), a linear correlation which passes through the origin should be obtained. However the linear fit determined from the 1/TCP VS. A ^ ' H - ^ S i ) data for the high-loaded complex (i.e. containing 8 molecules/u.c.) at room temperature had a positive v- intercept/ 7 , 3 8 The cause of this disagreement was determined to be sorbate motions on the time scale (tens of milliseconds) of the C P experiment. These motions were detected by l 3 C spin-diffusion measurements on p-xylene with a 1 3 C label on one of the methyl groups/ 8 Lowering the temperature to 273 K or below reduced the diffusion sufficiently that the regression behaved exactly as expected. The final locations and orientations found for the /(-xylene molecules in the straight and zig-zag channels from these experiments were in excellent agreement with those reported for the single crystal X R D determined structure, validating the general approach/ These techniques were then applied to the low-loaded /^-xylene / Z S M - 5 complex where the sorbate location was not reliably known prior to beginning the N M R experiments. Static D N M R experiments indicated that the sorbate rings were undergoing 180° ring-flips about the methyl-methyl axis at the temperatures used, and these motions were included in the second moment calculations. In this case, temperatures below ca. 215 K were required to reduce the molecular motions sufficiently to obtain a zero intercept/ 8 The /(-xylenes were located at the channel intersections with the methyl-methyl axis along the straight channel, in agreement with the previous pred ic t ions/ " 5 6 More importantly, the sorbate location and orientation proposed from the N M R data were very close to that found by a subsequent single crystal X-ray diffraction structure determination carried out as part of the present work (Chapter 8 ) / The success of these 199 investigations indicates that analysis of C P data can be used to obtain reliable information about the location of sorbates within the Z S M - 5 framework, provided that the temperature is low enough to minimize molecular diffusion. In the best cases it is possible to obtain the precise position and orientation of the guest molecule. In the present chapter, preliminary solid-state N M R studies of the low-loaded p-difluorobenzene / Z S M - 5 complex are presented 6.2 M A T E R I A L S AND M E T H O D S 6.2.1 Sample Preparation and Sorbate Loading Crystall ine, completely siliceous Z S M - 5 was kindly provided by Ms . G .E . Bar low, The University o f Guelph. Freshly calcined Z S M - 5 (500 mg) was loaded into 5 mL glass ampoules. To this 36 u.L of 1,4-difluorobenzene (Aldr ich, 99 %) or l,4-dif luorobenzene-J 4 (Aldr ich 98 atom % D) was added (corresponding to a loading of 4 molecules/u.c.) using a micro-syringe. The sample was cooled by immersion in liquid nitrogen, and the ampoule sealed with a flame. The sample was stored at room temperature for several days to ensure an equilibrium loading had been attained before loading the rotors for the N M R experiments. The loading of the Z S M - 5 powder was verified by thermal gravimetric analysis ( T G A ) and 2 9 S i M A S N M R . The T G A measurements were performed on T A Instruments T G A 51 Thermogravimetric Analyzer using a temperature ramp of 10 °C/min. from room temperature to 600 °C under f lowing nitrogen gas. The samples showed weight losses corresponding to 3.9 (±0.3) molecules/u.c. ' H - 2 9 S i , l 9 F - 2 9 S i C P , and 2 9 S i M A S N M R experiments confirmed that the samples contained sorbedp-difluorobenzene. 6.2.2 N M R Experiments In order to minimize the molecular motions of the sorbate (which can adversely affect the dipolar-based experiments such as C P , R E D O R and T E D O R ) , the N M R experiments were performed at low temperatures using the apparatus described in Chapter 2 (Figure 2.1). Initially, 200 experiments were performed using nitrogen as the drive gas rather than air to prevent formation of ice within the probe, however it was discovered that the nitrogen replaced the molecular oxygen present within the sample. This process was gradual (occurring over a period of 12 hours or longer), and had a direct affect on the low temperature N M R experiments. A s the concentration of oxygen within the rotor was reduced, the 2 9 S i relaxation times increased dramatically. For example, at 240 K the 2 9 S i T\ relaxation times increased from ca. 2 s to greater than 35 s after the sample had been cooled for 24 hours using nitrogen gas to spin the rotor. This problem was solved by uti l izing air as the drive gas. The air was dried by passing it through several filters and a drying column (Drierite) f i l led with freshly calcined 5A zeolite A pellets and an indicator material which changed colour when wet. After less than one hour using air instead of nitrogen, the Si T\ was about 2 s again. Similar changes were seen for the 1 9 F and ' H relaxation times; at 235 K the l 9 F T\ increased from 1.5 to 10 s, while the ' H T\ increased from 45 ms to 4.5 s i f nitrogen was used. The spin-lattice relaxation times also increased with increasing temperature: from 80 ms to 105 ms for 1 9 F , and from ca. 2 s to about 4 s for 2 9 S i as the temperature was changed from 293 to 310 K. The 2 9 S i spin-spin relaxation times were 110-225 ms at 293 K and 40-150 ms at 240 K. Temperatures used for the I N A D E Q U A T E , C P , R E D O R and T E D O R experiments were selected to obtain the maximum number of resonances in the 2 9 S i M A S N M R spectra. The need to maintain a stable temperature and spinning speed for an extended time (> 2 days) was also considered. The pulse and automation programs used to acquire the N M R data are listed in Appendix B. To minimize the effect o f drift in the external magnetic f ield, the I N A D E Q U A T E experiments were performed as a series of (12-16 h) experiments which were then co-added. C P -I N A D E Q U A T E experiments which employed an initial polarization transfer from protons on the /7-difluorobenzene were also performed. The fixed delay in the I N A D E Q U A T E pulse sequence was set to 15 or 16 ms, fol lowing the typical values used for similar experiments reported in references 26 and 38. 201 The WIN-NMR software was used to perform the Fourier transformations, phase and baseline corrections of the N M R data. The real mode spectra were then exported using a J C A M P - D X format. 6 0 Curve-fitting of the spectra was achieved using the program Grams-386.6' Quantitative 2 9 S i N M R spectra were fitted to determine the appropriate parameters ( F W H H , chemical shift) for the individual Lorentzian curves, and these parameters were then used for curve-fitting the spectra from C P M A S experiments. Fitting of the variable contact time C P data to determine TCp values was performed using non linear least squares regression analysis in the Mathematica programming environment 6 2 as described in Appendix C . 6.2.3 Calculations to Determine Sorbate Locations and Orientations from C P Data Two computer programs were written to analyze the data from the 1 H - 2 9 Si and l 9 F - 2 9 S i C P experiments. The first of these (CPF9.PAS) calculated the static heteronuclear second moments, while the second program (CPH9.PAS) assumed that the sorbate molecules were undergoing 180° ring-flips about the F-F axis on the timescale of the experiments, and calculated the M2 values using the approach reported by Miche l et al.63 as described in Appendix D. Only F-Si (or H-Si) distances less than 8 A were used in the second moment analysis, except when the ring flips were assumed, in which case both sites that the H atoms occupied during the motion were included. The programs moved (and rotated) the sorbate molecule systematically thorough the channel system of the Z S M - 5 framework and performed linear regression analysis o f the 1/TC P values vs. the calculated second moments for each location and orientation. Initial calculations to determine potential sorbtion sites used a fairly coarse step size for the translations and rotations (0.25 A and 15° respectively), in order to sample a larger space within the channel system. Checks were also made to ensure that the molecules did not get too close (< 2 A) to the framework atoms. Calculations were then run using smaller step sizes (0.1 A and 5°) for the 202 rotations and translations over the region of interest. A typical calculation required in excess of 750 000 iterations, and took more than 48 hours to run. Any sorbate positions and orientations found which had acceptable regression coefficients (R2) were output. Further details of the algorithms used in these programs and a sample input file are presented in Appendix E. The Z S M - 5 framework was assumed to be rigid with monoclinic (P2/H .7.7) symmetry as deduced from the chemical shifts in the 2 9 S i M A S N M R spectra. The fractional atomic coordinates and cell parameters utilized were those reported'* for the single crystal X R D structure of calcined Z S M - 5 at room temperature, as this has the correct space group symmetry. The /7-difluorobenzene molecules were defined as rigid units having an idealized geometry: the (planar) aromatic ring was described as a regular hexagon with C - C bond lengths of 1.392 A and interior C - C - C angles of 60°, and the C - H and C - F bond lengths were fixed at 1.080 A and 1.328 A respectively. The molecules were placed in the straight channels at the channel intersections (one per intersection) with the F-F axes aligned parallel to the b axis and plane of the aromatic ring in the x-y plane. The parent molecule was positioned with the ring centroid at fractional coordinates of (0.5, 0.25, 0.0), and all other sorbate molecules in the central unit cell and surrounding 26 unit cells were generated from this by appropriate symmetry operations. The symmetry operators (general positions) for the non-standard space group P2//n.l.l are:64 x, y\ z; 0.5+x, 0.5-y, 0.5-z; -x,-y;-z; 0.5-x, 0.5+y, 0.5+z. However, to ensure the sorbate molecules remained intact after applying translations, rotations and the necessary symmetry operations to generate a complete unit cel l , the fol lowing modified symmetry operators were used: x, y; z; 0.5+x, 0.5-y, 0.5-z; 1-x, 1-y, 1-z; 0.5-x, 0.5+y, 0.5+z. Figures of the solutions found were generated using ORTEP-3 for Windows.63 Some geometrical analysis was also checked using the PLATON-98 software. 6 6 203 6.3 RESULTS AND DISCUSSION 6.3.1 1-D 1 9 F and 2 9Si MAS NMR 1-D l 9 F and 2 9 S i M A S (with decoupling) N M R data were collected at 5 degree intervals from 215 K to 300 K. The 1 9 F M A S spectra showed a series of spinning sidebands at the spinning speeds used (Figure 6.6). The isotropic chemical shift was -128.8 ppm. A t temperatures above ca. 293 K, the 2 9 S i M A S N M R spectra showed 12 resonances, and the chemical shifts indicated that the Z S M - 5 framework had orthorhombic Pnma symmetry (Figures 6.7(a,b)). This phase has been reported for several other low-loaded sorbate / Z S M - 5 complexes. 2 0 However, on cooling below ambient temperature, the appearance of the spectrum changed dramatically. The most obvious change was the appearance of a new resonance at -109.8 ppm, and also 4 new peaks in the region -114 to -117 ppm (Figure 6.7). The resonance at -109.8 ppm is characteristic o f the monoclinic P2l/n.l.J. phase. A t lower temperatures, the spectrum was very similar to that observed for the empty Z S M - 5 at room temperature (Figures 6.7(k)). It was concluded that a portion of the sample had undergone a phase transition from orthorhombic to monoclinic symmetry. Inspection of the spectra obtained for temperatures below 290 K showed a gradual increase in the intensities of these additional resonances relative to those assigned to the orthorhombic phase. The resonance at -117 ppm is diagnostic of the orthorhombic phase, and below about 260 K, this peak was no longer observed, indicating the sample had completely transformed to monoclinic symmetry. The precise 2 9 S i chemical shifts varied slightly with temperature, and the temperature at which the phase transition was complete was also found to depend on the concentration of p-difluorobenzene. A t lower loadings, the transformation occurred at higher temperatures, in agreement with the behavior reported for the low-loaded /^-xylene- and /j-dichlorobenzene / Z S M - 5 complexes. 2 0 The low-temperature (monoclinic) spectra could be deconvoluted in terms of up to 20 Lorentzian curves (Figure 6.8). This phase transition from orthorhombic to monoclinic symmetry was completely reversible, and was subsequently confirmed by powder X -204 -128.8 T=295 K -100 -110 -120 -130 ppm from C F C I 3 -140 150 Figure 6.6 1 9 F M A S N M R spectra ofp-difluorobenzene in Z S M - 5 at the temperatures indicated. 20 transients were recorded with a recycle delay of 5 s and spinning speeds of: (a) 3.12 kHz , (b) 3.07 kHz, (c) 3.03 kHz, and (d) 3.20 kHz. Spinning sidebands are marked ' * ' . -160. 205 "i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i i i i i r -110 -112 -114 -116 -118 ppm from T M S Figure 6.7 2 9 S i M A S N M R spectra of purely siliceous Z S M - 5 loaded with ca. 4 molecules of p-difluorobenzene/u.c recorded at the temperatures indicated using a recycle delay o f 20 s. 'Ortho' and 'Mono' label resonances which are diagnostic of the orthorhombic (Pnma) and monoclinic (P2l/n.J.l) phases, respectively. The spectrum of the empty (monoclinic) Z S M - 5 at 295 K is shown for comparison (k). 206 — I 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 -110 -112 -114 -116 -118 ppm from T M S Figure 6.7 (continued) 2 9 S i M A S N M R spectra of purely siliceous Z S M - 5 loaded with ca. 4 molecules of /j-difluorobenzene/u.c recorded at the temperatures indicated using a recycle delay of 20 s. 'Ortho' and 'Mono' label resonances which are diagnostic of the orthorhombic (Prima) and monoclinic (P2i/n.l.l) phases, respectively. The spectrum of the empty (monoclinic) Z S M - 5 at 295 K is shown for comparison (k). 207 T 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r -109 -111 -113 -115 -117 ppm from T M S Figure 6.8 M A S N M R spectra of the low-loaded />difluorobenzene / Z S M - 5 complex. (a) Quantitative 2 9 S i M A S spectrum and fit obtained (b) by deconvolution in terms of individual Lorentzian curves (c). C P M A S spectra obtained using 20 ms cross polarization from: ' H (d), and 1 9 F (e). The temperatures and tentative assignments of the resonances to specific T-sites are indicated. 208 ray diffraction experiments (see Chapter 7). Although the framework symmetry at low temperatures is the same as that observed for empty Z S M - 5 , the /?-difluorobenzene molecules remain inside the Z S M - 5 framework during and after the phase transition. This was confirmed by successful polarization transfer from ' H and l 9 F in C P experiments (see below). 6.3.2 I N A D E Q U A T E Exper iments It is essential to know the assignments of the different 2 9 S i resonances to specific T-sites i f information about the positions of guest molecules within zeolites is to be obtained using N M R techniques based on the dipolar interactions between the sorbed molecules and the sil icon atoms in the framework. In order to assign the resonances in the 2 9 S i N M R spectra, a series of 2-D I N A D E Q U A T E and 2-D C P - I N A D E Q U A T E experiments were performed at temperatures of 235 K, 245 K and 250 K. These temperatures were selected because the 1-D spectra showed at least 17 wel l resolved resonances, some of which had chemical shifts that changed considerably between these temperatures. It was thought that 2-D spectra obtained at these three temperatures would provide the best possible chance of achieving a complete assignment. However, due to the variation in the relaxation times induced by spinning with nitrogen gas, good quality I N A D E Q U A T E spectra were only obtained at 245 K when air was used. A contour plot o f the C P I N A D E Q U A T E acquired at 245 K is presented in Figure 6.9. The monoclinic phase of Z S M - 5 having P2//n.l.l symmetry contains 24 crystallographically inequivalent T-sites, and thus represents one of the most complicated of the known zeolite frameworks. The connectivity list for the T-sites (based on the single crystal structure7") is given in Table F.l (Appendix F). 48 different 2 9 S i - 2 9 S i connectivities are present and should theoretically be observed in a 2-D I N A D E Q U A T E spectrum. However, there are no self-connectivities, and even when the second coordination sphere of T-atoms (ignoring oxygens) is considered, no T-site has a unique connectivity pattern. This makes it difficult to find a suitable starting point to make the assignment. 209 Figure 6.9 Contour plot of a C P - I N A D E Q U A T E experiment on Z S M - 5 loaded with 4 molecules/u.c. of/>difluorobenzene at 245 K with a 1-D ' H - 2 9 S i C P M A S spectrum above. 48 experiments with 1120 scans in each experiment were carried out using a recycle delay of 3 s for a total experiment time of ca. 48 h. A spectral width of 1000 Hz , contact time of 35 ms, fixed delay of 16 ms and 256 real data points were used. Sine-bell apodization and a power calculation were used for the data processing. 210 Due to the close similarities between the Si M A S N M R spectrum of the empty (monoclinic) Z S M - 5 (for which a complete assignment has been published 2 6) and that observed for the p-difluorobenzene / Z S M - 5 complex at low temperatures, it was felt that the previous assignment provided a good starting point. Assuming that the differences between the T-sites would be maintained in the low-temperature monoclinic form, the lowest field resonance (at ca. -109.5 ppm) was tentatively assigned to Si-21, and the highest field resonance at ca. -117.1 ppm, to Si-8. From these starting points a partial assignment of the spectrum was possible (Figure 6.9). The assignment is self consistent but incomplete because there is considerable peak overlap in the center region of the 1-D spectrum. There is good internal consistency in the assignment of the best resolved peaks (i.e. the highest and lowest-field resonances), and all o f the expected connectivities between these sites are clearly observed. For example Si-5 is connected to Si-11, which is connected to Si-10, and silicons 8, 10 and 21 are all connected to Si-9 as expected from the framework connectivities. A t the present time this assignment is thought to be correct. A n important difference from the empty monoclinic Z S M - 5 at 300 K, is the interchange of the resonances assigned to Si-14 and Si-16; at 245 K sil icon 14 is to high field of Si-16 in the 2 9 S i M A S N M R spectrum of the /7-difluorobenzene / Z S M - 5 complex. The silicons in four-membered rings (T-sites 9, 10, 21 and 22) are expected to occur at lower field based on correlations between 2 9 S i chemical shifts and the geometrical parameters such as S i -O-S i bond angles and Si -S i d istances/ 7 For the resonances which have been assigned, there is also a reasonable correlation between the 2 9 S i chemical shifts and the mean Si -Si distances which supports the correctness of the assignment. 2 6 6.3.3 'H-29Si Cross Polarization Experiments Figure 6.8(d) shows ' H - 2 9 S i C P M A S spectrum of the low-loaded />-difluorobenzene / Z S M - 5 complex obtained using a 20 ms contact time at 230 K. Comparison with the quantitative 211 Si M A S N M R spectrum (Figure 6.8(a)) reveals that the intensities of the resonances in the C P spectrum are no longer equal. For example, the signals for silicons 11 and 14 are almost twice as intense as for Si-16. A lso at 230 K, the resonances assigned to Si-10 and Si-23 overlap with other peaks and thus there are only six well resolved resonances. A series of C P experiments were acquired as a function of the contact time, and deconvoluted in terms of 18 individual Lorentzian curves. Figure 6.10 shows a plot o f the intensities of the 6 outermost (best resolved) T-sites as a function of the contact time. The different T-sites seem to be divided into three groups. Sil icons 21 and 5 show the most rapid intensity increase as a function of contact time and are thus the most efficiently polarized, while Si-11, Si-14 and Si-8 show less efficient polarization, and Si-16 shows quite inefficient polarization. From this behavior it is clear that silicons 21 and 5 are closer to the ' H polarization source than silicons 11, 14 and 8, while Si-16 is relatively far from any ' H nuclei. Si-16 is located in the zig-zag channel while those silicons with largest polarization fol lowing C P are in the straight channel. Because the ' H nuclei used as the source of the polarization are on the aromatic rings, the />difluorobenzene molecules must be located somewhere within the straight channels. The TCp values determined from nonlinear least squares regression analysis of this data to Eq . 3.15 (with T\P(]H) held constant at 110 ms) are listed in Table 6.2. Sil icons which have protons in close proximity wi l l have the smaller TCp values than those which are far from the sorbate. The C P curves calculated using these time constants are overlaid on the experimental data in Figure 6.10. Using these TQP values and assuming a static sorbate molecule, the best solution found from analysis with the program CPF9.PAS had a correlation coefficient, R2, of 0.991, with a slope of 3.092 x 10~ 4, and a ^ -intercept of 45.91. The second moments calculated for this solution are listed in Table 6.2, and the parameters defining the translations and rotations applied are given in Table 6.3. Figure 6.11(a) shows the highly linear correlation found between the experimental 1/7CP values and the (static) second moments calculated for this solution. 212 Intensity (arb. units) 40 60 Contact Time (ms) Figure 6.10 Intensities of the ' H - 2 9 S i C P M A S N M R signals as a function of the contact time at 230 K for Z S M - 5 loaded with ca. 4 molecules of /?-difluorobenzene per u.c. The curves were obtained from nonlinear least squares fitting of the data to Eq. 3.15 with TipC'H) fixed at 110 ms. Table 6.2 Experimental and calculated parameters related to the ! H - 2 9 S i cross polarization experiments on the low-loaded/7-difluorobenzene / Z S M - 5 complex at 230 K. T-site Chemical Shift (ppm) ( a ) 7cp(ms) ( b ) Af 2 ( 'H - 2 9 Si ) (Hz 2 ) Static { c ) Ring F l ips ( c ) Si 21 -109.5 15.703 59408 33704 Si 5 -110.7 16.943 40903 28074 Si 11 -114.9 19.061 20264 13034 Si 16 -115.1 21.248 5914 3418 Si 14 -116.1 17.647 34539 20188 Si 8 -117.1 18.209 27551 21912 ( a ) l Referenced to T M S . ( ' C a l c u l a t e d using nonlinear least squares fitting to Eq. 3.15 with T l p ( 'H ) fixed at 110 m s . ( c ) Calculated using S i -H distances up to 8 A for the sorbate locations described by the translations and rotations given in Table 6.3. 213 Table 6.3 Results of fitting cross polarization data for the low-loaded />difluorobenzene / Z S M -5 complex at low temperature. Parameter ' H - 2 9 S i C P , 9 F - 2 9 S i C P Calculation Type Static 180° Ring Fl ips Static Temperature (K) 230 230 235 Number of Points 6 6 7 R2 0.991 0.966 0.962 Slope 3.092 x 10" 4 5.483 x 10 " 4 3.908 x 10~ 3 Intercept'3' 45.91 45.24 54.79 A X (A)(b) -0.3 -0.2 0.0 A Y (A)(b) 0.0 0.1 -0.4 AZ(A) ( b ) -0.4 -0.5 -0.4 cK°)(c) - 4 0 - 6 0 - 4 0 9 ( ° ) ( c ) - 4 0 - 4 0 0 V ( ° ) ( c ) - 25 - 2 0 40 ( 3 ) Y axis intercept. ( ' Translations along the a (AX) , b (AY) , or c (AZ) axes from the chosen starting position at the channel intersection in centre of straight channel (10.0535 A, 4.96941 A, -0.05811 A). ( c ) Euler angles defining rotation from starting orientation with aromatic ring in the x-y plane, and F-F axis parallel to b axis. 214 Figure 6.11 Best linear fits of \ITC? vs. calculated M 2 ( ' H - 2 9 S i ) values found from analysis of the ' H - 2 9 S i C P M A S data recorded at 230 K assuming the />difluorobenzene molecules were static (a), or undergoing 180° ring-flips about the F-F axis (b). See Table 6.3 for parameters. 215 The molecule was found to be shifted slightly from the center of the straight channel (0.3 A along [100] and 0.4 A along [001 ] ) and was oriented so that the plane of the aromatic ring was almost parallel to the major axis of the elliptically distorted 10-ring (Figure 6.12). The molecule was also twisted slightly away from the b axis. However, the most striking difference between the orientation found from this analysis and those reported for other sorbates in the straight channels of Z S M - 5 , is the rotation of the ring by 40° so that the fluorine atoms point towards the openings of the zig-zag channels rather than being parallel to [010] as can be clearly seen in Figure 6.13(b). The fractional atomic coordinates for the sorbate atoms for this solution are listed in Table F.2 (Appendix F). In this location Si-16 has only three ] H nuclei within an 8 A radius sphere, and these are all more than 7.1 A away. Conversely Si-21 has six protons within 8 A three of which are closer than 6 A, and Si-5 also has two protons closer than 4.6 A. A possible reason why the molecules adopt this orientation within the channels is to minimize the repulsive fluorine-fluorine and fluorine- oxygen interactions. Considering the orientations which are permitted by steric restriction between the sorbate and framework atoms, the fluorine-fluorine distances have been maximized. For the best solution found, the distance between F atoms on adjacent rings in the straight channel is 10.0 A, and the closest F-F distance between molecules in neighbouring channels is 8.31 A. This arrangement may also explain why loadings of more than 4 molecule/u.c. were not obtained at ambient temperature and pressure, even when excess /?-difluorobenzene was used. If more than 4 molecules/u.c. were present, some molecules would need to be in the zig-zag channels, and this would prevent the molecules in the straight channels from having their fluorine atoms near the openings of the zig-zag channels. When 180° ring-flips about the F-F axis were included in the ' H - 2 9 S i heteronuclear second moment calculations, the best solution (R2 = 0.966) had very similar location and orientation of the /?-difluorobenzene as seen from a comparison of the parameters for the two solutions listed in Table 6.3. The correlation obtained for the 1/TCP VS. M2 in this case is shown in Figure 6.11(b), which again does not pass through the origin. For this solution, the closest F-F 216 Figure 6.12 View down [010] showing location and orientation of /7-difluorobenzene in ZSM-5 found from fitting of'H-29Si cross polarization data at 230 K. a F igure 6.13 Location and orientation of the />difluorobenzene molecules in Z S M - 5 found from analysis of ' H - 2 9 S i C P data acquired at 230 K: V iews along the straight channel (a), and into the zig-zag channel (b) show the spatial relationship of the sorbate atoms to the different Si atoms (T-sites). 218 distances between molecules in the same channel and those in adjacent channels are 10.2 A and 8.1 A respectively. Figures 6.13 shows views down the straight channel and into the zig-zag channel for the orientation and location found from the fitting assuming stationary molecules. In these figures, the proximity o f the sorbate protons the different T-sites is seen. There are no ' H nuclei close to Si-16, while silicons 21 and 5 have several protons in close proximity, as expected from the general qualitative trends in the C P intensities as a function of contact time. The regression lines found in these experiments had large y-intercepts which from the previous work on the /^-xylene / Z S M - 5 systems, probably indicates that the /?-difluorobenzene molecules are still undergoing some slow diffusion along the channels on the time scale o f the C P experiments at 230 K. Furthermore, the reliability of the assignment o f the 2 9 S i resonances from the I N A D E Q U A T E experiments is not confirmed at the present time, and only six from the possible 24 T-sites were included in the analysis. For these reasons the location and orientation found from fitting of the ' H - 2 9 S i C P data at 230 K should be viewed as tentative, and preliminary at this time. A s a check of the location found from the ' H - 2 9 S i , a series of ' F - 2 9 S i variable contact time experiments were also performed at low temperatures. These results are presented in the next section. 6.3.4 , 9F- 2 9Si Cross Polarization Experiments Samples of purely siliceous Z S M - 5 containing ca. 4 molecules/u.c./?-difluorobenzene-t/4 were used for the l 9 F - 2 9 S i cross polarization experiments to avoid possible complications from ' H - ' 9 F dipolar interactions. Variable contact time C P experiments were performed at 235 K, 240 K, 245 K and 250 K. Figure 6.9(e) shows a 1 9 F - 2 9 S i C P M A S spectrum obtained using a 20 ms contact time at 235 K. Again the peak assigned to Si-16 shows relatively low intensity, and is thus far from the l 9 F nuclei. Conversely, the peak assigned to Si-8 is very intense, and Si-14 and 219 Si-21 are also relatively strong indicating that silicons in these T-sites must have F nuclei in close proximity. Because the resonance assigned to Si-23 is better separated than at 230 K, data from this peak was also used. Figure 6.14 shows a plot o f the intensities of the 7 outermost (best resolved) T-sites as a function of the contact time. Again, the different T-sites seem to be divided into three groups. Si l icon 8 shows the most rapid intensity increase as a function of contact time, Si-16 shows relatively inefficient polarization, and the other 5 silicons show intermediate degrees of polarization transfer. From this behavior it is clear that the l 9 F nuclei in the sorbate molecules are close to Si-8, and that silicons 14 and 21 are also closer to fluorine atoms than the other sil icons. Again these observations are consistent with the />difluorobenzene molecules being located somewhere within the straight channel. There is no obvious decay seen in the data up to the 55 ms contact time used, which indicates that r i p ( ' 9 F) is quite long. The TCp values determined from nonlinear least squares regression analysis of this data to Eq. 3.15 (with r l p ( 1 9 F ) held constant at 1800 ms) are listed in Table 6.4. The C P curves calculated using these time constants are overlaid on the experimental data in Figure 6.14, and although there is agreement between the calculated and experimental data the fits are not as good as for the ' H - 2 9 S i C P data. Using these Tc? values and assuming a static sorbate molecule, the best solutions found from analysis with the program CPF9.PAS had R2 = 0.962, a slope of 3.908 x 10~ 3, and ay-intercept of 54.79 (Figure 6.15). In this case there was a family of solutions having the same parameters for the correlations. For all of these solutions the ring centroid was shifted from the center of the straight (by 0.4 A along [010] and 0.4 A down [001]) but different rotational angles were found. This is precisely the behavior expected because any orientation of the aromatic ring plane about the F-F axis wi l l leave the Si-F distances (and hence the l 9 F - 2 9 S i heteronuclear second moments) unchanged. 220 Contact Time (ms) F igure 6.14 Intensities of the F- Si C P M A S N M R signals as a function of the contact time at 235 K for the Z S M - 5 loaded with ca. 4 molecules of /?-difluorobenzene-d 4 per u.c. The curves were obtained from nonlinear least squares fitting of the data to Eq. 3.15 with TlpC9F) fixed at 1800 ms. 110 1/Tcp 1 0 0 90 80 -70 60 -50 Si 21 y S Si 5 o- o Si 23 • y<M 5 1 8 yS Si 14 yS Si 11 Si 16 yS ys% 2000 4000 6000 8000 10000 12000 14000 Calculated Second Moment (Hz 2) F igure 6.15 Best linear fit o f \ITCP vs. calculated M 2 ( 1 9 F - 2 9 S i ) values found from analysis of the l 9 F - 2 9 S i C P M A S data recorded at 235 K. See Table 6.3 for parameters. 221 Table 6.4 Experimental and calculated parameters related to the 1 9 F - 2 9 S i cross polarization experiments on the low-loaded/>difluorobenzene / Z S M - 5 complex at 235 K. T-site Chemical Shift (ppm) ( a ) TCP (ms) ( b ) M 2 ( 1 9 F - 2 9 S i ) (Hz 2 ) Static ( c ) Si 21 -109.5 9.674 12134 Si 5 -110.8 10.248 11194 Si 23 -114.5 10.341 9424 Si 11 -115.0 11.149 8722 Si 16 -115.2 15.566 2846 Si 14 -116.1 10.271 11441 Si 8 -117.1 9.766 12758 ( a ) Referenced to T M S . ( b ) Calculated using nonlinear least squares fitting to Eq. 3.15 with r l p ( l 9 F ) fixed at 1800 ms. Calculated using Si-F distances up to 8 A for translations and rotations given in Table 6.3. 222 However, as seen from comparison of the translation and rotation parameters in Table 6.3, this solution corresponds to a position and orientation of the organic molecules which is significantly different from those found for the *H- 2 9 Si C P data. The molecule has the fluorine-fluorine axis parallel with the straight channel as shown in Figure 6.16. This position and orientation is very similar to those found for the two other low-loaded sorbate / Z S M - 5 complexes whose structures are known / ' 9 When the sorbates are at this location, the fluorine-fluorine distances between adjacent molecules in straight channel is reduced to 5.7 A. The closest F-F distance between fluorines in neighbouring channels is 11.7 A. Table 6.4 summarizes the second moments calculated for one of these (equivalent) solutions, and the fractional atomic coordinates for the sorbate atoms are listed in Table F.3 (Appendix F). A s seen from Figure 6.15, the large ^-intercept and lower R2 are a primarily due to the large displacements seen for the Si-10 and Si-16 from the overall correlation trend. This may be a result o f the overlap of the resonance corresponding to Si-10 with another peak, which would affect the intensity determined from curve fitting since there may have been a significant contribution from the next (unassigned) resonance and the TCp value obtained would be incorrect. Slow diffusion occurring on the time scale of tens of mill iseconds wi l l also affect the C P experiments, and the large ^-intercepts tend to indicate that such motions are present. Another possibility is that there are too few 1 9 F nuclei to ful f i l l the assumptions of adequate (strong) ! 9 F - I 9 F dipolar interactions (which mean that the fluorines can be treated as a large spin reservoir) required for Eq. 3.15 to be v a l i d / 7 In fact, there may be oscillatory behavior in the variable contact time C P data which indicates the system might be more appropriately described in terms of an INS spin system with N small. In the case of the ] H - 2 9 S i C P experiments this is less of a concern because the are more protons (twice the number of fluorines), and they are much closer to one another. 223 • Hydrogen © Carbon O Fluorine Figure 6.16 View down [010] showing location and orientation of />-difluorobenzene in ZSM-5 found from fitting of 19F-29Si cross polarization data at 235 K. 6.3.5 F- S i R E D O R and T E D O R Exper iments A series of R E D O R and T E D O R experiments were also performed at 240 K, and the results indicate that both experiments are viable. However these were all affected by the variation of the relaxation times caused by the gradual replacement of the oxygen gas in the sample by nitrogen described above. In addition the positives-intercepts found for the correlations between 1/7CP vs. the calculated heteronuclear second moments indicated that slow diffusions were still occurring at 240 K which would also affect the R E D O R and T E D O R experiments and they were not analyzed in detail. Although the spin system could not be considered to be composed of completely isolated l 9 F - 2 9 S i spin pairs, the low loading did minimize the number of dipolar 1 9 F - 2 9 S i interactions within an 8 A radius of any of the T-sites. It was hoped that the positions and orientations found for the /7-difluorobenzene molecules from analysis of the cross polarization experiments could provide a good starting model of the spin-system as required for the multi-spin R E D O R and T E D O R calculations (see Chapter 3). 6.4 S U M M A R Y A N D C O N C L U S I O N S Loading Z S M - 5 with 4 molecules of p-difluorobenzene per unit cell caused the framework to change from monoclinic (P2i/n.l.l symmetry, 24 T-sites) to a phase having 12 T-sites at temperatures above ca. 293 K . From the appearance of the 2 9 S i M A S N M R spectra the orthorhombic Pnma symmetry is proposed for this phase. This orthorhombic phase has been reported previously for three other low-loaded, /?ara-disubstituted aromatic / Z S M - 5 complexes. Loadings higher than 4 molecules/u.c. were not obtained for samples prepared with excessp-difluorobenzene at ambient pressure and temperature. Cool ing the sample below 290 K resulted in a transformation back to a phase having 24 T-sites, which was maintained to the lowest temperature accessible (215 K ) . The 2 9 S i N M R chemical shifts observed for this phase indicated that it was almost identical to the monoclinic 225 P2/n.Ll phase adopted by the empty Z S M - 5 framework at temperatures below ca. 340 K. The success of ' H - 2 9 S i and l 9 F - 2 9 S polarization transfer observed during Hartmann-Hahn C P experiments provided unambiguous evidence that the sorbate molecules remained within the Z S M - 5 channel system during, and after, this phase transition. It is anticipated that the transformation to monoclinic symmetry for the Z S M - 5 framework observed in the present case may also occur in other sorbate / Z S M - 5 systems at low temperatures. The general location of the sorbed /?-difluorobenzene molecules was determined to be in the straight channels at the intersection with the sinusoidal channels. However, the precise position and orientation could not be unambiguously determined from these initial studies. Two different orientations were found from analysis of the ' H - 2 9 S i and 1 9 F - 2 9 S i C P M A S N M R data. Fitting of the 1 H - 2 9 Si C P data acquired at 230 K yielded a very good linear correlation for the experimental l /T C p values versus the calculated ' H - 2 9 S i heteronuclear second moments when the />-difluorobenzene molecules were oriented so that the fluorine atoms were pointing towards the openings of the zig-zag channels and the plane of the aromatic ring was at an angle which corresponded closely to the longest cross-channel dimension of the straight channel. A much poorer linear correlation was obtained from calculations util izing the 1 9 F - 2 9 S i C P data acquired at 235 K, with the best solution(s) found when the fluorine-fluorine axis was parallel to [010]. This orientation is in accord with that previously observed for the other low-loaded Z S M - 5 / sorbate complexes. Unfortunately, the l 9 F - 2 9 S i experiments cannot provide any information about the orientation of the plane of the aromatic ring relative to the crystallographic axes. This is because the ring can rotate freely about the F-F axis without affecting the F-Si distances. In both cases the molecule centroid was shifted slightly from the center of the straight channel. When sorbate molecules are present the 10-rings defining the channels containing the sorbate distort to become more ell iptical, presumably in order to better accommodate the guest molecules/ ' 5 ' 9 In the present work, as in most of the previous investigations to determine preferred sorption sites of guests in the zeolite channel systems from theoretical calculations (e.g. 226 energy minimizations), the framework geometry was selected and kept rigid. However the precise geometry of the framework (and the channel shapes) is known to vary with different sorbates/ 9 and the chosen framework geometry may not accurately reflect the real structure, which may affect the exact position and orientation found for the sorbed molecules. Addit ional 2-D I N A D E Q U A T E experiments are required (including several at different temperatures) in order to assign all o f the resonances in the 2 9 S i M A S N M R spectra, and in addition, these preliminary results indicate that experiments need to be done at lower temperatures to slow the rate of the diffusions within the channels.. Detailed investigations of powder X-ray data and 2 9 S i M A S N M R data are invaluable aids to determining the possible symmetry, number of crystallograpically inequivalent T-sites, and space group, as wel l as the temperature and loadings at which any changes occur, and i f possible should be obtained prior to single crystal studies. Recent N M R investigations of the low-loaded p-\y\ene I Z S M - 5 complex have been utilized to predict the sorbate location and orientation, 5" and the solution found to correspond closely to that determined by the subsequent single crystal X R D structure determination (Chapter 8), thus proving the feasibility, and reliability of these N M R techniques to accurately locate the guests within the channels of zeolites. In the next chapter, the results of the preliminary powder X-ray diffraction studies undertaken to verify the space group symmetries and unit cell parameters of the two phases observed for the low-loaded />-difluorobenzene in Z S M - 5 are presented. 227 R E F E R E N C E S F O R C H A P T E R 6 7 Venuto, P. Microporous Mater. 1994, 2, 297. 2 Moscou, L. in Introduction to Zeolite Science and Practice van Bekkum, H.; Flanigen, E . M ; Jansen, J .C. (Eds.) Chapter 2. Elsevier Amsterdam, 1991. 3 van Koningsveld, H.; Tuinstra, F.; van Bekkum, H.; Jansen, J .C . Acta Cryst. 1989, B45, 423. 4 van Koningsveld, H.; Jansen, J . C ; van Bekkum, H. Acta Cryst. 1996, B52, 140. 5 van Koningsveld, H.; Jansen, J . C ; de Man, A . J . M . Acta Cryst. 1996, B52, 131. 6 Reck, G . ; Mar low, F.; Kornatowski, J . ; H i l l , W.; Caro, J . J. Chem. Phys. 1996, 100, 1698. 7 van Koningsveld, H.; Koegler, J .H . Microporous Mater. 1997, 9, 71. 8 van Koningsveld, H.; Jansen, J .C. Microporous Mater. 1996, 6, 159. 9 Single crystal X R D structure of low-loaded /(-xylene / Z S M - 5 complex. See Chapter 8. 10 Reischman, P.T.; Schmitt, K .D . ; Olson, D.U.J. Phys. Chem. 1988, 92, 5165. 11 Cheetham, A . K . ; Bu l l , L . M . Catal. Lett.1992,13, 267. 12 Be l l , R .G . ; Lewis, D.W.; Voigt, P.; Freeman, C M . ; Thomas, J . M . ; Catlow, C . R . A . Stud. Surf. Sci. Catal. 1994, 84, 2075. 13 Gies, H ; Marler, B.; Fyfe, C .A . ; Kokotai lo, G.T. ; Feng, Y . ; Cox, D.E. J. Phys. Chem. Solids, 1991,152, 1235. 14 Kokotai lo, G.T. ; Lawton, S.L. ; Olson, D.H. ; Meier, W . M . Nature 1978, 272, 437-438. 75 Wu, E.L.; Lawton. S.L. ; Olson, D.H. ; Rohrman, A . C , Kokotai lo, G.T. J. Chem. Phys. 1979, 83, 2777. 16 van Koningsveld, H.; van Bekkum, H.; Jansen, J .C. Acta Cryst. 1987, B43, 127. 7 7 van Koningsveld, H. Acta Cryst. 1990, B46, 731. 78 van Koningsveld, H.; Jansen, J . C ; van Bekkum, H. Zeolites 1990,10, 235. 19 Fyfe, C .A . ; Kennedy, G.J . , DeSchutter, C.T. ; Kokotai lo, G.T. J. Chem. Soc, Chem. Commun. 1984, 541. 20 Fyfe, C .A . ; Strobl, H.; Gies, H.; Kokotai lo, G.T. Can. J. Chem. . 1988, 66, 1942. 27 Fyfe, C .A . ; Strobl, H. ; Kokotai lo, G.T. ; Kennedy, G .J . ; Barlow, G . E . ; J. Am. Chem. Soc. 1988, 770, 3373. 228 22 Fyfe, C .A . ; Kokotai lo, G.T. ; Strobl, H.; Gies, FL; Kennedy, G .J . ; Pasztor, C.T. ; Barlow, G . E . in Zeolites as Catalysts, Sorbents and Detergent Builders, p. 827. Karge, H.G. ; Weitkamp, J . Eds. Elsevier, 1989. 23 Olson, D.H. ; Kokotai lo, G.T. ; Lawton, S.L. ; Meier, W . M . J. Phys. Chem. 1991, 85, 2239. 24 Price, G .D . ; Pluth, J .J . ; Smith, J .V . ; Bennett, J . M . ; Patton, R.L. J. Am. Chem. Soc. 1982,104, 5 25 Chao, K -J . ; L in , J - C ; Wang, Y . ; Lee, G . H . Zeolites. 1986, 6, 35. 26 Fyfe, C .A . ; Grondey, H.; Feng, Y . ; Kokotai lo. G.T. J. Am. Chem. Soc, 1990, 112, 8812. 27 West, G .W. Aust. J. Chem. 1984, 37, 455. 28 Engelhardt, G . , Miche l , D. Unpublished results reported in High-Resolution Solid-State NMR of Silicates and Zeolites, John Wi ley and Sons, 1987, 313. 29 Mentzen, B.F; Vigne-Maeder, F. Mat. Res. Bull. 1987, 22, 309. 30 Mentzen, B.F; Bosselet, F. Mat. Res. Bull. 1988, 23, 227. 31 Mentzen, B.F; Sacerdote-Peronnet, M . Mat. Res. Bull. 1993, 28, 1161. 32 Mentzen, B.F.; Sacerdote-Peronnet, M . ; Berar, J-F. ; Lefebvre, F. Zeolites 1993, 13, 485. 33 K le in H.; Fuess, H.; Ernst, S.; Weitkamp, J . Microporous Mater. 1994, 3, 291. 34 Mentzen, B.F Mat. Res. Bull. 1987, 22, 337. 35 Sacerdote-Peronnet, M . ; Mentzen, B.F. Mat. Res. Bull. 1993, 28, 767. 36 Mentzen, B.F; Favre, R.; Cauwet F. Mat. Res. Bull. 1994, 29, 587. 37 Fyfe, C .A . ; Feng. Y . ; Grondey, H. Microporous Mater. 1993,1, 393. 38 Feng, Y . Ph.D. Thesis, The University of Brit ish Columbia, 1991. 39 Kennedy, G . J . Ph.D. Thesis University of Guelph, 1985. 40 Strobl, H. Ph.D. Thesis University of Guelph, 1991. 41 Fyfe, C .A . ; Gies, H. ; Kokotai lo, G.T. ; Pasztor, C.T. ; Strobl, H. ; Cox , D.E. J. Am. Chem. Soc. 1989, 111, 2470. 42 Fyfe, C .A . ; Strobl, H. ; Kokotai lo, G.T. ; Kennedy, G .J . ; Barlow, G . E . J. Am. Chem. Soc. 1988,110, 3373. 43 High-Resolution Solid-State NMR of Silicates and Zeolites. Engelhardt, G . , M iche l , D., John Wi ley and Sons, 1987. 44 Smith, J .V . ; Blackwel l , C .S . Nature, 1983, 303, 223. 229 45 Grimmer, A . R . ; Radeglia, R. Chem. Phys. Lett., 1984,106, 262. 46 Fyfe, C .A . ; Strobl, H. ; Kokotai lo, G.T. ; Pasztor, C.T. ; Barlow, G . E . ; Bradley, S. Zeolites, 1988, 8, 132. 47 Thomas, J . M . ; K l inowsk i , J . ; Rammdas, S.; Hunter, B .K. ; Teenakoon, D.T.B. Chem. Phys. Lett. 1983,102, 158. 48 Ramdas, S.; K l inowski , J . Nature 1984, 308, 521. 49 Engelhardt, G . ; Radeglia, R. Chem. Phys. Lett. 1984,108, 271. 50 Derouane, E .G. ; Hubert, R.A. Chem. Phys. Lett. 1986, 132, 315. 51 Engelhardt, G . ; van Koningsveld, H. Zeolites, 1990, 10, 650. 52 Modelling of Structures and Reactivity in Zeolites, Catlow, C . R . A . , Ed . Academeic Press-London, 1992. 53 Pickett, S.D.; Nowak, A . K . ; Cheetham, A . K . ; Thomas, J . M . Molec. Simul. 1989, 2, 353. 54 Freeman, C M . ; Catlow, C . R . A . ; Thomas, J . M . ; Brode, S. Chem. Phys. Lett. 1991, 186. 137. 55 Smit, B.; Maesen, T . L . M . Nature, 1995, 374, 42. 56 Bosselet, F.; Sacerdote, M . ; Bouix, J . ; Mentzen, B.F. Mat. Res. Bull. 1990, 25, 443. 57 Fyfe, C A . Diaz, A . C ; Lewis. A . R . ; Chezeau, J - M . ; Grondey, H. ; Kokotai lo, G.T. in Solid-State NMR Spectroscopy of Inorganic Materials. Fitzgerald, J .J . (Ed.) ACS Symposium Series. In Press. 58 Diaz, A . C , Fyfe, C A . Unpublished Results, University of British Columbia, Canada. 59 1-D WIN-NMR, Bruker-Franzen Analyt ik G m B H , Bremen, Germany. 1996. 60 (a) McDonald , R.S.; Wi lks, P.A. Appl. Spectroscopy. 1988, 42, 151. (b) Davies, A . N . ; Lampen, P. Appl. Spectroscopy. 1993, 47, 1093. 61 Grams-386, Galactic Industries Corporation, 395 Ma in Street, Salem, N H 03079, U.S.A. 62 Wolfram, S. The Mathematica Book. Third Edit ion. Cambridge University Press, 1996. 63 M iche l , J . ; Drifford, M . ; Rigney, P. J. Chim. Phys. 1970, 67, 31. 64 International Tables for Crystallography Volume A . Hahn, T. (Ed.); K luwer Academic Publishers, Dordrecht, 1993. 65 Ortep3 for Windows, Johnson, C .K . ; Burnett, M . N . ; Farrugia, L .J . Department of Chemistry, University of Glasgow, U.K. 1998. http://www.chem.gla.ac.uk/~louis/ortep3/ 66 Platon98 for Windows, Speck, A . L ; Farrugia, L.J . Department of Chemistry, University of Glasgow, U .K . 1998. http://www.chem.gla.ac.uk/~louis/platon97/ 67 Voelke l , R.Angew. Chem. Int. Ed. Engl. 1988, 27, 1468. 230 CHAPTER 7 PRELIMINARY POWDER X-RAY DIFFRACTION INVESTIGATIONS OF THE LOW-LOADED PARA-DIFLUOROBENZENE / ZSM-5 COMPLEX 7.1 I N T R O D U C T I O N A s discussed in Chapter 6, single crystal diffraction experiments (where feasible) would provide an incisive check on the correctness of guest-host structures predicted by N M R . Powder diffraction data acquired with both synchrotron and conventional X-ray sources has provided information about the unit cell parameters, framework symmetry, and phase transitions in Z S M -5. ' ' 2 In a few cases, the location and orientation of sorbed guest species within the framework channels have been proposed from fitting of powder diffraction data. 2" 6 However, although refinement of these structures is possible, the small amount of literature data indicate that these are very complex systems. X-ray diffraction studies were initiated for the low-loaded p-difluorobenzene / Z S M - 5 complex and the progress to date is presented in this chapter. 2 9 S i M A S N M R can provide complementary information such as the number of T-sites which greatly assists the space group determination. 7"" Details of the M F I framework structure, and previous investigations of the guest- and temperature-induced changes in the framework by X-ray powder diffraction and 2 9 S i M A S N M R are discussed in Chapter 6. For the Z S M - 5 / sorbate systems where changes are seen, the lattice distortions seem to be reasonably characteristic o f the nature of the sorbed molecule. 7"" In some cases however, very similar 2 9 S i M A S N M R spectra are obtained with different molecules, indicating that the lattice 231 geometries are closely related. It may be that the locations of the molecules in these cases are similar, but this has only been verified for three systems to date (including the low-loaded form of /7-xylene in Z S M - 5 described in Chapter S).'4'18 As-synthesized Z S M - 5 has Pnma symmetry (12 T -s i tes ) / 9 , 2 0 which is transformed to monoclinic symmetry fol lowing calcination to remove the templating s p e c i e s / 2 ' Loading the calcined (empty) Z S M - 5 framework with more than two, but less than four, molecules of p-xylene per unit cell (u.c.) brings about a transformation from monoclinic P2t/n.l.l (with 24 T-sites) to orthorhombic Pnma symmetry. 2 2 2 5 The symmetry of the empty framework also changes to Pnma symmetry at temperatures above about 340 K.22,24 Increasing the loading to between 6 and 8 molecules/u.c. induces a further change to P2/2 /2 / symmetry which has 24 inequivalent T-s i tes . ' 7 2 2 These transformations are reversible, and sorbates other than/>xylene may induce similar structural t ransformat ions/ 7 * Figure 7.1(a) shows a view along the zig-zag channel o f the orthorhombic (Pnma) phase of Z S M - 5 . For the empty Z S M - 5 framework, the small increase in the cell angle (typically from 90° to 90.3-90.7°) changes the shape of the unit cel l . This results in the removal o f the symmetry elements such as the mirror planes parallel to the b axis which bisect the sinusoidal channel in the orthorhombic phase (Figures 7.1(a) and (c)). The change to monoclinic symmetry is also associated with small displacive transformations of the framework atoms, although the framework topology is maintained. Overal l , the X-ray diffraction patterns of the orthorhombic and monoclinic phases are quite similar. However there are small (but characteristic) differences which can be detected provided the samples are of high crystallinity. When the cell angles are all 90° (as is the case for orthorhombic symmetry), certain reflections wi l l overlap. For example, the reflections with Mi l le r indices (h k I) o f (-3 1 3) and (3 1 3) are coincident and occur at approximately 24.4° 29 in the orthorhombic phase (a « 20.1 A, b « 19.9 A, c « 13.3 A). When /? becomes larger than 90° (monoclinic P1.2//n.l phase), these reflections are no longer equivalent, and they are observed 232 (c) Figure 7.1 V iew along the zig-zag channels of Z S M - 5 for structures having different symmetries: (a) orthorhombic Pnma symmetry, (b) monoclinic P2t/n.l.l symmetry with domain twinning, and (c) ideal monoclinic P2i/n.l.l symmetry without twinning. The size of the twin domains was estimated to be approximately 50 unit cells (ca. 1000 A) / y After reference 21. 233 as independent peaks in the powder pattern at about 24.3° and 24.6° 20 respect ively. ' * Similar behavior is seen for other pairs of reflections, with the most obvious being those centered at ca. 11.9°, 15.5°, and 28.5° 20. The separation of the diffraction peaks into these "doublets" wi l l increase with increasing 20 and also as the deviation of the cell angle from 90° becomes larger. The observation of such "doublets" is usually taken as evidence that the sample has monoclinic symmetry.' The presence of ordered guest species within the channels of the Z S M - 5 has a relatively small effect on the appearance of the powder X R D patterns, unless the loading is sufficient to bring about a change of symmetry. The major differences between the patterns for the empty framework and a sorbate-containing sample with the same overall symmetry are usually only detected as small changes in the relative intensities of the reflections below about 30° 20, and may be associated with slight peak shifts due to changes in the cell dimensions. In general however, these changes are significant (and measurable), particularly the intensity changes for the lowest angle reflections due to the presence of sorbed organic guest. For purely siliceous Z S M - 5 , both powder X R D and 2 9 S i M A S N M R can be used to distinguish between monoclinic and orthorhombic symmetry. However only N M R can be used to determine whether the orthorhombic symmetry is Prima or P2/2/2/ since the number of T-sites and chemical shifts in the 2 9 S i M A S N M R spectra are diagnostic. Exceptions may arise i f the variations in the local framework geometry are not large enough to be observed in the N M R spectrum, or i f the unique cell angle is very close to 90° in the monoclinic phase. For the monoclinic phase, the single crystal X-ray refinement reported in the literature 2 ' was performed using the non-standard setting P2i/n.1.1 rather than P1.2i/n.l. The use of P2\/n.l.l ensures that the straight channels are aligned along the b ax is , rather than a, w h i c h permits direct comparisons with the orthorhombic structures. P2i/n.l.l symmetry with cell 234 constants a = 20.107 A, b = 19.879 A, c =13.369 A, and a = 90.67° is equivalent to the standard setting Pl.2,/n. 1 with a = 19.879 k,b = 20.107 A, c =13.369 A, and fi= 90.67°. A n additional complication for the monoclinic phase is the (apparently intrinsic) domain twinning which was observed by van Koningsveld et al. in their single crystal investigations of calcined Z S M - 5 at room temperature.2 ' They determined that the monoclinic phase consists o f an aggregate of monoclinic twin domains with domain sizes of the order o f 1000 A. A representation of the monoclinic framework structure in the presence of these twin domains is reproduced in Figure 7.1(b). A n " idea l " single-domain monoclinic crystal without twinning present is shown in Figure 7.1(c) for comparison. This chapter presents the results o f preliminary X-ray diffraction studies on the low-loaded /?-difluorobenzene / Z S M - 5 complex. Powder X R D data were collected on a Z S M - 5 sample loaded with approximately four molecules of /?-difluorobenzene/u.c. at several temperatures, and also for a sample of the empty (calcined) Z S M - 5 at room temperature. The cell constants and space group for calcined Z S M - 5 are wel l established,' ' 2 ' and provided a check of the analysis technique, before it was applied to fit the /?-difluorobenzene / Z S M - 5 data. 7.2 M A T E R I A L S AND M E T H O D S 7.2.1 Sample Preparation and Data Collection Highly crystalline, purely siliceous Z S M - 5 powder identical to that used for the N M R experiments was calcined at 825 K immediately prior to use. After cooling to room temperature it was loaded into 0.7 mm diameter glass capillaries specifically designed for X-ray use. One sample was sealed directly and a measured amount of />-difluorobenzene (corresponding to 4 molecules/u.c.) was added to another before freezing in liquid nitrogen and flame sealing. These samples are referred to as "calc ined" and " D F B " respectively in the fol lowing discussion. Powder X R D patterns were acquired with the assistance of Dr. Bernd Marler using a Siemens D5000 system at the Institute of Mineralogy, Ruhr-Universitat Bochum, Germany. The 235 diffractometer was operated in a modified Debye-Scherrer transmission geometry using monochromatized Cu Ka radiation (k = 1.540598 A ) with a position sensitive detector. The sealed capillary containing the sample was rotated to reduce preferred orientation effects and a step-scanning mode was used to produce more accurate diffraction line profiles. For both the calcined Z S M - 5 and the sample loaded with />difluorobenzene, data were recorded over the range 6.0-40.0° 29 with a step size of 0.007772° at room temperature (293 K ) . Four individual scans (ca. six hours / scan) were co-added to obtain the final powder patterns. The difluorobenzene-containing sample was then cooled using a stream of cold air. The air was cooled by passing it through a 0.5 m length of coiled copper tubing immersed in a vacuum dewar f i l led with dry ice. The cold air was directed onto the capillary through an insulated transfer tube. A series of scans over the range 21-27 ° 29 (step size 0.007772° 29) were acquired at approximately 10 minute increments (ca. 1 minute scan time) during the cooling from room temperature. After cooling for about one hour, the temperature of the air stream stabilized at approximately 260 K and data (4 scans) were collected over the range 6.0-40.0° 29 (0.007772° steps). The powder patterns were baseline corrected using the GRAMS-386 software package 2 6 and converted to ASCII-format files with the appropriate header information for the analysis program. 7.2.2 F i t t ing of Ref lect ion Data Analyses and fitting of the X R D data were done using the AJUST program 2 7 running on an IBM-compatible PC with the M S D O S operating system. The program allowed selection of the crystal system, as well as the reflection conditions to define the space group. 2* The input file contained information about the sample geometry (capillary), wavelength of the X-ray radiation used, the 29 range (and step size), initial values for the various parameters which could be 236 optimized by the least squares fitting, and " f lags" for each parameter which indicated whether the specific parameter was to be varied or held fixed during the refinement cycles. The Voigt function is a convolution of Lorentzian (L) and Gaussian (G) functions which has been shown to describe the experimental peak profiles in X-ray diffraction data quite we l l . 2 9 Although an analytical form exists for the Voigt function, this is usually approximated as a pseudo-Voigt function to reduce calculation t imes. 2 9 AJUST implements a pseudo-Voigt function to model the diffraction lineshapes with a weighted sum of the two lineshape functions L and G described by Eq. 7.1. pV=r\L + (l -r\)G 7.1 Here r\ is the mixing parameter describing the weighting of the Gaussian and Lorentzian contributions to the final peak profile. The full-widths at half-height for the diffraction ( W L and W G for the Lorentzian and Gaussian contributions, respectively) have a dependence on the scattering angle 9 which are modeled as : 2 7 W L = -yjw, + w2 tan0 + w2 tan 2 9 7.2 and W G = wx tan9 + (wy I cos9) 7.3 In addition to a zero correction (linear shift o f all 29 values), an asymmetry function was applied to the peaks up to 20° 29 to account for the diffractometer and sample-induced effects (absorption, unfocussed X-ray beam, etc.). Up to 12 parameters were refined: the cell constants (a, b, c, and the unique angle / J i f monoclinic symmetry was assumed), the lineshape contributions (w>/, w2, w3, wx, and wy), an asymmetry parameter, a zero correction, and a scale factor to match observed and calculated intensities. The variable for transparency correction (to account for absorption effects etc.) was fixed at 0.0 in all cases, and other cell angles were held constant at 90°. During the early stages of a refinement, several o f the parameters were held fixed ' 237 (e.g. lineshape parameters) while the cell constants were refined. A s the refinement proceeded (and the / ? w p decreased), the other variable parameters were progressively included in the fitting. In the final cycles all of the parameters were refined. The weighted pattern residual ('/?' factor) Rwp used is defined in Eq. 7.4. Rwp provides a numerical criterion for fol lowing the progress of the refinement as wel l as a measure of the "goodness of fit" between the calculated and observed patterns/ 0 Here y, is the intensity at the ith position in the profile, obs and calc refer to the observed and calculated intensities respectively, and w, is the weight assigned to the intensity observed at the rth step. A smaller value of Rwp indicates a smaller deviation between the observed and calculated patterns, and a better "fit". From a purely mathematical point o f view, Rwp is the most meaningful o f the possible R factors because the numerator is the residual being minimized, and thus it also reflects the progress of the ref inement/ 0 7.3 R E S U L T S AND DISCUSSION 7.3.1 Phase Transitions on Cooling The 2 9 S i M A S N M R spectra acquired in the investigations of purely siliceous Z S M - 5 loaded with 4 molecules/u.c. o f /?-difluorobenzene were presented in Chapter 6. A t temperatures above 293 K a spectrum characteristic o f orthorhombic Prima symmetry with 12 resonances was observed (Figures 6.7(a,b)). Below about 260 K, the appearance of the spectrum and chemical shifts were very similar, but not identical, to those seen for empty Z S M - 5 , which is known to be monoclinic with P2i/n.l.l symmetry (Figures 6.7(g-j)). At intermediate temperatures, a mixture of the two phases was detected (Figures 6.7(d-f)). The exact temperature of the (assumed) 7.4 238 orthorhombic to monoclinic transformation was found to depend on the precise sorbate loading, but was completely reversible. This phase transition for the D F B sample was followed as the temperature was lowered from room temperature by recording X R D powder patterns over the region 22.5° to 25.0° 29 every 10 minutes after cooling was initiated. This 29 range was chosen because it included the region around 24.5° 29 where a characteristic monoclinic "doublet" should be clearly resolved i f lower temperatures induced a phase transformation from orthorhombic to monoclinic symmetry as predicted from the N M R studies. Selected diffraction patterns obtained during this experiment are reproduced in Figure 7.2. O f particular interest is the number of peaks in the region from ca. 24.2-24.7° 29. A t 293 K a single peak centered at 24.45° 29 was clearly seen (Figure 7.2(a)). After cooling for 10 minutes the appearance of-the powder pattern changed considerably, and the doublet (peaks at 24.3° and 24.6° 29) expected for the monoclinic symmetry appeared (Figure 7.2(b)). In addition, a new reflection centered at 23.4° became visible. These observations indicated that the sample was a mixture of two phases. There was certainly a temperature gradient across the sample, but this was not the only reason for the coexistence of the two phases. Similar two-phase samples were also detected in the N M R experiments where the temperature gradient was minimized by holding the sample at a constant temperature for an extended period of time. A lso , in the N M R investigations the temperature range studied was considerably larger (230-300 K ) . It was therefore concluded that either the size of the individual crystals determined the temperature at which the phase transformation occurred, or that domains of each symmetry were present within individual crystals. A s the cooling continued, a general decrease in the intensities of reflections assigned to the orthorhombic Pnma phase, and an associated increase in those for the monoclinic symmetry, was observed. After cooling for 40 minutes the orthorhombic reflections were no longer detected (Figure 7.2(c)). The temperature of the air stream had stabilized at 260 K by this time, and after 239 22.5 23.0 23.5 24.0 24.5 25.0 Degrees 20 F igure 7.2 Powder X-ray diffraction patterns of Z S M - 5 loaded with 4 molecules per unit cell o f /)-diflurobenzene (DFB) showing the transformation, (a) to (d), from orthorhombic (Prima) to monoclinic (P1.2i/n.l) symmetry observed as the sample was cooled from 293 K to 260 K. The pattern for the calcined (empty) Z S M - 5 at 293 K (monoclinic P1.2i/n.l symmetry) is shown for comparison in (e). 240 allowing an additional 20 minutes for the sample to reach an equilibrium temperature, a series of four scans over the range 6-40° 2G (step size 0.007772°, ca. 6 hours / scan) were recorded. Comparison of the patterns recorded for the D F B sample after more than 40 minutes cooling (Figure 7.2(d)), with that obtained for the calcined Z S M - 5 at room temperature (Figure 7.2(e)), shows that the patterns are almost indistinguishable in the 22.5-25.0° 20 region. This indicates that the D F B sample almost certainly has the same (monoclinic) symmetry as the empty Z S M - 5 at low-temperatures. The powder patterns recorded over the ranges 7.0-40.0° 20 for the calcined (T=293 K ) , and /?-difluorobenzene loaded Z S M - 5 (at T=293K and 260 K ) are presented in Figure 7.3. Inspection of these diffraction patterns reveals a direct correspondence between those recorded for the calcined and low temperature difluorobenzene-loaded samples, again supporting the monoclinic symmetry postulated for the D F B sample at low temperatures from the 2 9 S i M A S N M R studies. A t room temperature, the absence of the "doublet" reflections at ca. 8.5°, 24.4°, and 28.5° 20 (as wel l as other differences) for the difluorobenzene-loaded sample, indicates that the symmetry is orthorhombic. Because only 12 resonances are observed in the 2 9 S i N M R spectrum above ca. 293 K, the framework symmetry may be unambiguously described as Pnma rather than P2/2 /2 / . Theoretically, it is also possible that monoclinic symmetry is maintained, but that all o f the cell angles are 90° (or at least very close to 90°). However, such a change would essentially make the framework virtually identical to that having truly orthorhombic symmetry, and it would be impossible to distinguish between these. The fitting of the powder diffraction data for the calcined Z S M - 5 and the D F B samples recorded at 293 K and 260 K undertaken and to determine the cell constants, and verify the symmetries of the two phases, is described in the fol lowing sections. For clarity the three samples are discussed separately. 241 8 ~]—r 10 11 12 13 14 _ | ! ^ 15 16 17 18 19 20 "i—r 21 ~i—r 22 Degrees 29 Figure 7.3 Powder X-ray diffraction patterns (7.0-22.5° 28) of ZSM-5 loaded with 4 molecules/u.c of /?-diflurobenzene at 293 K (a), and 260 K (b). The pattern recorded for calcined (empty) ZSM-5 at 293 K is shown for comparison (c). Vertical scaling has been applied to match the intensities of the reflection at 7.8° 28. No baseline corrections have been applied. All Intensities xl.5 i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i i i i i i i i i i i i i r 22.5 23.5 24.5 25.5 26.5 27.5 28.5 29.5 30.5 31.5 32.5 33.5 34.5 35.5 36.5 37.5 38.5 39.5 Degrees 20 Figure 7.3 (continued) Powder X-ray diffraction patterns (22.5-40.0° 20) of ZSM-5 loaded with 4 molecules/u.c of p-diflurobenzene at 293 K (a), and 260 K (b). The pattern recorded for calcined (empty) ZSM-5 at 293 K is shown for comparison (c). Vertical scaling has been applied to match the intensities of the reflection at 7.8° 20. No baseline corrections have been applied. 7.3.2 E m p t y Z S M - 5 at 293 K A n ideal polycrystalline material or powder is an ensemble of a very large number of randomly orientated crystals. The correct unit cell parameters and information regarding the possible space groups may not be always be readily determined from a twinned single c rys ta l / ' In a powder sample however, each of the twin domains scatters the X-ray radiation slightly differently, and effectively produces a "more random" orientation of the crystallites. Such a system wi l l therefore approximate a "perfect" powder sample more closely. For these reasons, the problems in data analysis of domain twinning which affect the single crystal data for the monoclinic phase are avoided when powder X-ray diffraction data is used. The powder X R D data recorded for the calcined Z S M - 5 at 293 K were successfully refined to # w p = 4.71% in P1.2,/n.l, and yielded cell parameters of a = 19.8823(4) A,b = 20.1085(2) A, c =13.3686(2) A, and B= 90.537(2)°. A small zero shift correction of -0.021° 29 was automatically determined, refined, and applied by the AJUSTprogram during the fitting. Because the standard setting of P1.2//n.l (i.e. with unique) rather than P2t/n.l.l (a unique) was used, the a and b cel l dimensions are swapped compared to those reported for single crystal data in the literature. 2 ' Estimated standard deviations for the cell constants and the lineshape parameters used are listed in Table 7.1. A s expected, the estimated standard deviations for the cell parameters are significantly smaller than those reported for the monoclinic single crystal structure (0.002 A and 0.01 ° ) . 2 ' The cell dimensions of Z S M - 5 are known to vary with temperature, and also with the S i / A l content, but the values found from fitting of the X R D data are within the range reported for calcined Z S M - 5 in the l i terature.' 2 ' The calculated pattern shows excellent agreement with the observed reflection data with only minor differences apparent (Figure 7.4). The major discrepancies are seen for the low angle reflections, and this is primarily due to the inability to exactly match the experimental peak profiles using the pseudo-Voigt lineshape function in this case, even when some peak asymmetry is included. This is clearly seen as "dispersion-type" peaks in the difference pattern (observed -244 Table 7.1 Results from the fitting of the Z S M - 5 X R D powder data using the program AJUST. The lineshape and zero-shift parameters used are also listed. Parameter Sample Empty (calcined) 4 molecules/u.c./? -difluorobenzene Temperature 293 K 260 K 293 K Collection time 24 h 12 h 24 h Space Group P1.2,/n.l (No. 14) P1.2,/n.l (No. 14) Pnma (No. 62) *wp (%) 4.71 6.82 6.21 a (A) 19.8823 (0.0004) ( a ) 19.8796 (0.0004) ( f l ) 20.0298 (0.0002) ( o ) 6 ( A ) 20.1085 (0.0002) ( a ) 20.0978 (0.0003) ( f l ) 19.9195 (0.0003) ( a ) - c ( A ) 13.3686 (0.0002) ( f l ) 13.3651 (0.0003) ( a ) 13.3776 (0.0003) < a ) « ( ° ) 90.000( / , ) 9 0 . 0 0 0 w 90.000 ( A ) 90.537 (0.002) ( f l ) 90.705 (0.002) ( a ) 90.000 ( / , ) r(°) 90.000 ( A ) 90.000( A ) 90.000 ( A ) Cel l Volume (A 3 ) 5344.6 5339.4 5337.4 Scale Fac tor ( t ) 1.000318 0.998945 0.999846 Zero Correction (° 29) ( l f > -0.02115 -0.01146 -0.01713 Transparency 0.000 ( A ) 0.000 ( A ) 0.000 ( A ) Asymmetry Coef f ic ient ( t ) 0.52704 0.51337 0.50215 Wx -0.286880 -0.193252 -0.194023 Wy 0.095823 0.091062 0.098729 wt 0.002238 0.002464 0.001320 w2 -0.023802 -0.022436 -0.007556 w3 0.207294 0.154197 0.087879 ( a ) Estimated standard deviations.- ' Parameter held constant during f i t t ing. ( c ) To match calculated and experimental patterns. { l t ) Linear shift o f all 29 va lues. ( e ) Appl ied up to 20° 29. 245 T 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r 6 10 14 18 22 26 30 34 38 Degrees 20 Figure 7.4 Observed (baseline corrected) and calculated powder X-ray diffraction patterns for calcined (empty) ZSM-5 at 293 K. The acquistion time for the experimental pattern was 24 hours and the calculated pattern (R^ = 4.71%) was obtained using the AJUSTprogram assuming monoclinic P1.2i/n. 1 symmetry with the parameters listed Table 7.1. calculated). The baseline correction may have also modified the peak profiles slightly. A small broad peak at ca. 21.8° 29 was not well fit and was in fact due to small amount of cristobalite in the samples used. Cristobalite is a dense si l ica phase often present as an impurity in zeolite syntheses. This was not observed in the 2 9 S i N M R spectra because it was only very minor small fraction of the sample, and more importantly, because of the long T\ relaxation times (100's of seconds) which means it was discriminated against with the relatively short recycle delays (of order of 10-20 s) used. The successful refinement of the lattice parameters for the calcined Z S M - 5 sample validates the use of the program AJUST, and the general refinement approach employed. It furnishes values for the cell constants for the purely siliceous Z S M - 5 used, and initial values for the peak profile parameters to be used in the other refinements. Furthermore, the low value indicates a very good fit, and provides a "benchmark" by which the quality of the subsequent refinements for the D F B data may be judged. 7.3.3 D F B / Z S M - 5 at 260 K A total o f four scans were acquired for the D F B sample at 260 K. The first two of the 4 six-hour scans recorded with the sample cooled showed only the characteristic monoclinic features, while the third in the series contained reflections for both phases. The fourth and final scan in the series was essentially identical to that recorded for the sample at room temperature. This transformation back to the (proposed) orthorhombic phase was attributed to a gradual warming of the sample as the dry ice sublimed and the cooling became less efficient. Consequently only the first two of the low temperature scans were added and used for the refinement of the low temperature phase. This reduced the signal-to-noise ratio compared with the other two data sets, so it was anticipated that the final Rwp should be slightly higher than that obtained for the calcined Z S M - 5 . 247 Comparison of the powder diffraction data recorded for the D F B sample at 260 K (Figure 7.3(b)), with that obtained for the calcined Z S M - 5 at room temperature (Figure 7.3(c)) reveals that the relative intensity of many of the reflections below about 25° 29 is substantially different in the presence of p-difluorobenzene. A vertical intensity scaling has been applied to ensure the peak height of the reflection at ca. 7.8° 29 is equal for al l o f the powder patterns in Figure 7.3. The peak intensities have not changed uniformly for all o f the reflections; some are almost unchanged (e.g. reflections at 14.7°, 17.6° and 17.8° 29), while others exhibit dramatic increases (see peaks in region 10-14° 29). If this intensity scaling is disregarded, the patterns are virtually indistinguishable, with the reflections occurring at almost the same 29 values in both cases. The sorbate atoms wi l l contribute to the scattering and wi l l affect the intensity of all the reflections. The contribution to the scattering from the sorbate molecules wi l l fall off quite steeply (compared to that for the framework) with increasing 29 due to significant thermal motions of the sorbate molecules. Because of this, the major intensity differences are expected at lower 29 angles, as was indeed observed. Assuming P1.2//n.J symmetry, the D F B powder data acquired at 260 K refined to a final Rwp of 6.82 % using the parameters listed in Table 7.1. Considering the reduced signal to noise ratio for these data, this indicates a very good fit to the experimental pattern. The good agreement between the calculated and observed powder patterns can be seen in Figure 7.5. For the reasons described in section 7.3.2, the largest discrepancies occur in the low angle region (as was also the case for the calcined Z S M - 5 data). The refined cell parameters refined to a = 19.8796 A,b = 20.0978 A , c =13.3651 A , and B— 90.705°. The cell dimensions are all slightly smaller than those found for the empty Z S M - 5 at 293 K, but the angle /?has become slightly larger (see Table 7.1). Overal l , the unit cell volume was reduced by about 0.1% compared to that of the empty Z S M - 5 at 293 K. Similar reductions in 248 Figure 7.5 Observed (baseline corrected) and calculated powder X-ray diffraction patterns for ZSM-5 loaded with 4 molecules/u.c. ofp-difluorobenzene at 260 K. The acquistion time for the experimental pattern was 12 hours and the calculated pattern (i?wp = 6.82%) was obtained using AJUSTassuming monoclinic P1.2i/n.l symmetry with the parameters listed Table 7.1. the unit cell volume are seen for the low-loaded/^-xylene-, />-dichlorobenzene-, andp-nitroanil ine-ZSM-5 complexes at room temperature/ 7 ' 8 However, because low temperature data was not collected for the calcined Z S M - 5 , it is unclear whether this contraction is primarily due to the presence of the sorbed guest molecules, or whether the lower temperature also changes the unit cell dimensions and angles. 7.3.4 D F B / Z S M - 5 at 293 K A s check for other cell symmetries, refinements were tried using the reflection conditions corresponding to Pnma and the lower symmetry space group Pn2/a, w h i c h is related to Pnma by removal o f the mirror plane perpendicular to the b ax is . Because p-difluorobenzene is a centrosymmetric molecule, it was decided that the higher Pnma symmetry would more likely be adopted by the D F B sample above 293 K. The only sorbate / Z S M - 5 complex which has been characterized to date (by single crystal X R D techniques) using Pn2ia symmetry is Z S M - 5 loaded with 4 molecules/u.c. of/>-nitroaniline / Z S M - 5 . ' 7 Using Pnma symmetry the data were successfully refined to an 7? w p of 6.21% using the lineshape and correction parameters listed in Table 7.1. The angles a, B, and / were all fixed at 90° during the fitting and the final cell dimensions obtained are listed in Table 7.1. The unit cell volume is less than both the empty Z S M - 5 , and the D F B at 260 K. This was caused by a reduction in the a dimension by almost 0.08 A, even though b and c both increased very slightly. These cell dimensions are in general agreement with those reported for the single crystal ' * 5 " ' 8 * and powder refinements2"15 o f the sorbate / Z S M - 5 containing ca. 4 molecules/u.c. o f single ring aromatics which exhibit Pnma symmetry. A n interesting trend in the unit cell volumes was noted for these systems. The cell volume increases from 5315 A 3 when ca. 4 molecules/u.c. o f /^-xylene are sorbed,* through 5320 A 3 for />-nitroaniline,'8 to 5324 A 3 when p-dichlorobenzene is sorbed.'*5 Although these values wi l l be affected by the exact S i /A l ratio of the Z S M - 5 used' they are perhaps a useful indicator for the strength of the sorbate-framework 250 interactions (strongest forp-xylene and decreasing with increasing unit cell volume). Assuming this to be true, the cell volume found for the low-loaded/7-difluorobenzene / Z S M - 5 complex having Pnma symmetry (5339 A 3 ) , would suggest that the sorbate-framework interactions are weaker than for the other systems. Fluorine-fluorine and fluorine-oxygen repulsive interactions may contribute to this. Further support for this argument is provided by the relatively high temperature (290 K ) below which the />-difluorobenzene / Z S M - 5 complex transforms to monoclinic symmetry. Although the i ? w p value is slightly higher than the benchmark value of 4.71% obtained for the calcined Z S M - 5 , it is still low enough to support the proposed Pnma symmetry. A s can be seen from inspection of Figure 7.6, the calculated powder pattern shows very good agreement to the experimentally determined X R D data, and with the exception of the broad peak at ca. 21.8° 29 attributed to the presence of a very small amount of cristobalite in the sample, all of the reflection features are wel l described. 7.4 C O N C L U S I O N S Accurate lattice parameters were determined from refinement of the powder X-ray diffraction data collected for calcined Z S M - 5 at 293 K, and Z S M - 5 loaded with 4 molecules of p-difluorobenzene/u.c. at 260 and 293 K. The cell parameters are summarized in Table 7.1. The calcined and low temperature D F B data sets were successfully refined in the space group P1.2f/n.l, and the room temperature D F B data was satisfactorily refined in Pnma. These X R D refinements complement the N M R investigations into the location and orientations of p-difluorobenzene molecules in the channels of Z S M - 5 at a loading of approximately 4 molecules per unit cell described in Chapter 6. In addition to furnishing accurate cell parameters, fitting of the X R D data provided an independent verification of the framework symmetries proposed from the N M R experiments, and confirmed that the framework adopts two distinct symmetries within the temperature range studied. 251 to "i 1 1 r 10 "1 T 14 18 22 n :—r 26 —r- 30 I 34 I 38 Degrees 26 Figure 7.6 Observed (baseline corrected) and calculated powder X-ray diffraction patterns for ZSM-5 loaded with 4 molecules/u.c. of p-difluorobenzene at 293 K. The acquistion time for the experimental pattern was 24 hours and the calculated pattern (R wp = 6.21%) was obtained using AJUSTassuming orthorhombic Pnma symmetry with the parameters listed Table 7.1. Above ca. 293 K, the framework has Pnma symmetry, as has been found for three other low-loaded sorbate / Z S M - 5 c o m p l e x e s / 6 J 8 , 2 S A t temperatures below about 290 K, the framework symmetry for the low-loaded form of the p-difluorobenzene / Z S M - 5 complex transforms to monoclinic (space group P1.2t/n.l) which is the same symmetry adopted by empty Z S M - 5 below 340 K. Unambiguous proof that the /?-difluorobenzene molecules remain inside the Z S M - 5 framework fol lowing this phase transition is provided by the successful ' H - 2 9 S i and l 9 F -2 9 S i cross polarization experiments described in Chapter 6. From these observations it was concluded that the sorbate / framework interactions in this system are somewhat weaker than those in the low-loaded /7-xylene / Z S M - 5 complex which maintains orthorhombic Pnma symmetry to temperatures at least as low as 173 K./ y It is predicted that sorbate / Z S M - 5 complexes other than the low-loaded from ofp-difluorobenzene in Z S M - 5 studied here may undergo similar orthorhombic to monoclinic transformations at low temperatures. Knowledge of such transitions wi l l be critical i f the N M R techniques for locating guest species in the voids of microporous materials described in this thesis are to be successfully applied to other guest / host, sorbate / zeolite systems. In general, detailed investigations of powder X-ray data and 2 9 S i M A S N M R data such as those described in this section and in Chapter 6 are invaluable aids for determining the possible crystal system, lattice parameters, the symmetry (space group), and the number of crystallograpically inequivalent T-sites. They can furnish information about the temperatures and/or loadings at which structural changes occur. If possible, these techniques should be utilized prior to beginning single crystal studies. Moreover, even in cases where the crystals are twinned or contain aggregates of twin domains, fitting of the powder X-ray diffraction data should still permit the correct unit cell parameters and possible space groups to be determined. N o attempts were made to locate the /j-difluorobenzene molecules within the Z S M - 5 framework from the powder X R D data. However, these investigations have established the space group symmetry; information that w i l l be extremely useful for future single crystal X R D 253 experiments to determine the location(s) and orientation(s) of /7-difiuorobenzene molecules in Z S M - 5 . Several single crystal X R D data sets have been acquired on/>difluorobenzene / Z S M - 5 samples prepared using the specially designed apparatus described in Chapter 2 (which permits single zeolite crystals to be loaded with precisely controlled amounts of volatile organic sorbates). Although at this point a complete structure refinement has not been possible using these data sets, (which is not surprising given the complexities of these kinds of systems), the structure of the low-loaded /(-xylene / Z S M - 5 complex has been determined from single crystal data and this is discussed in Chapter 8. R E F E R E N C E S F O R C H A P T E R 7 7 Wu , E.L.; Lawton. S.L. ; Olson, D.H. ; Rohrman, A . C . ; Kokotai lo, G.T. J. Chem. Phys. 1979, 83, 2777. 2 Gies, H.; Marler, B.; Fyfe, C .A . ; Kokotai lo, G.T. ; Feng, Y . ; Cox , D.E. J. Phys. Chem. Solids. 1991,752, 1235. 3 Mentzen, B.F; Vigne-Maeder, F. Mat. Res. Bull. 1987, 22, 309. 4 Bosselet, F.; Sacerdote, M . ; Bouix, J . ; Mentzen, B.F. Mat. Res. Bull. 1990, 25, 443. 5 Mentzen, B.F; Sacerdote, M . Mat. Res. Bull. 1993, 28, 1161. 6 Sacerdote, M . ; Mentzen, B.F. Mat. Res. Bull. 1993, 28, 767. 7 Fyfe, C .A . ; Kennedy, G .J . ; DeSchutter, C.T. ; Kokotai lo, G.T. J. Chem. Soc., Chem. Commun. 1984, 541. 8 Fyfe, C .A . ; Strobl, H. ; Gies, H. ; Kokotai lo, G.T. Can. J. Chem. 1988, 66, 1942. 9 Fyfe, C .A . ; Strobl, H.; Kokotai lo, G.T. ; Kennedy, G .J . ; Barlow, G . E . ; J. Am. Chem. Soc. 1988,770,3373. 10 Fyfe, C .A . ; Kokotai lo, G.T. ; Strobl, H.; Gies, H.; Kennedy, G .J . ; Pasztor, C.T. ; Barlow, G . E . in Zeolites as Catalysts, Sorbents and Detergent Builders, p. 827. Karge, H.G. ; Weitkamp, J . Eds. Elsevier, 1989. 77 Strobl, H.J. Ph.D. Thesis, The University of Guelph, 1989. 72 Strobl, H.; Fyfe, C .A . ; Kokotai lo, G.T. ; Pasztor, C T . J. Am. Chem. Soc. 1987, 709, 4733. 254 13 Fyfe, C .A . ; Gies, H.; Kokotai lo, G.T. ; Marler, B.; Cox, D.E. J. Phys. Chem. 1989, 94, 3718. 14 van Koningsveld, H. ; Tuinstra, F.; van Bekkum, H.; Jansen, J .C . Acta Cryst. 1989, B45, 423 15 van Koningsveld, H. ; Jansen, J . C ; van Bekkum, H. Acta Cryst. 1996, B52, 140. 16 van Koningsveld, H. ; Jansen, J . C ; de Man, A . J . M . Acta Cryst. 1996, B52, 131. 17 Reck, G . ; Mar low, F.; Kornatowski, J . ; H i l l , W.; Caro, J . J. Chem. Phys. 1996,100, 1698. 18 van Koningsveld, H.; Koegler, J .H . Microporous Mater. 1997, 9, 71. 19 Kokotai lo, Lawton, S.L.;G.T.;01son, D.H. ; Meier, W . M . Nature. 1978, 272, 437. 20 van Koningsveld, H.; van Bekkum, H.; Jansen, J .C. Acta Cryst. 1987, B43, 127. 21 van Koningsveld, H.; Jansen, J . C ; van Bekkum, H. Zeolites 1990, 10, 235. 22 Fyfe, C . A . ; Grondey, H.; Feng, Y . ; Kokotai lo, G.T. J. Am. Chem. Soc. 1990,112, 8812. 23 Lewis, A . R ; Fyfe, C .A . ; Schwieger, W. Structure of the Low-Loaded Para-Xylene / ZSM-5 Complex Determined by Single Crystal X-ray Diffraction. In preparation, (see Chapter 8) 24 van Koningsveld, H. Acta Cryst. 1990, B46, 731. 25 Collection of Simulated XRD Powder Patterns for Zeolites. Third Revised Edition. Treacy, M . M . J . ; Higgins, J . ; von Ballmoos, R. (Eds.), Elsevier, 1996. http://www.iza-sc.ethz.ch/IZA S C / 26 Grams-386 Galactic Industries Corp., 395 Main Street, Salem, N H 03079, U.S.A. 1996. 27 AJUST: P R O G R A M A D ' E X T R A C C I O D T N T E N S I T A T S I N T E G R A D E S , Version 13. Rius, J . , Institut de Ciencia de Materials de Barcelona, Catalunya, Spain. 1996. 28 International Tables for Crystallography. Hahn, T (Ed.); Kluwer Academic Publishers, Dordrecht, 1993, Volume A . 29 Snyder, R.L. in The Rietveld Method. Chapter 7. Young, R.A. , (Ed.), Oxford University Press, 1993. 30 Young, R.A. in The Rietveld Method. Chapter 1. Young, R.A. , (Ed.), Oxford University Press, 1993. 31 Diaz, A . C ; Fyfe, C A . Personal communication. 255 CHAPTER 8 STRUCTURE OF THE LOW-LOADED COMPLEX OF PARA-XYLENE IN ZSM-5 FROM A SINGLE CRYSTAL X-RAY DIFFRACTION STUDY 8.1 I N T R O D U C T I O N Although it has not been possible to date to fully refine the single crystal X R D data for the p-difluorobenzene / Z S M - 5 complex described in the preceeding chapters, the general concept of using single crystal X-ray diffraction data to check the correctness of the N M R derived structures has been checked for one other system where a structure had previously been proposed from N M R experiments identical to those described in Chapter 6.' This is the low-loaded complex of /^-xylene in Z S M - 5 , and the successful refinement of the single crystal X R D data is described in detail in this chapter. A s discussed in Chapters 1 and 6, there have been several investigations into the changes which occur in the framework lattice due to the presence of guest species such as sorbed organic molecules. However, only in a very limited number of cases has the location of the sorbed organic molecules been reliably determined (e.g. by refinement of single crystal X-ray diffraction data).2 7 Sorption sites have been proposed from theoretical calculations, but these are not always in agreement with one another, or the X-ray determined structures where these are known."''*"" In general, the successful refinement of single crystal X-ray diffraction data from Z S M - 5 single crystals is not tr ivial; there are difficulties in synthesizing single zeolite crystals of adequate size 256 and quality for single crystal X R D work (twinning is often a problem). A t the time the current investigation was undertaken, only six single crystal X-ray diffraction studies of Z S M - 5 containing organic sorbates had been reported in the literature. Whi le X-ray Diffraction ( X R D ) studies of microcrystalline (powder) samples and single crystals of Z S M - 5 have yielded much of the structural information, 2" 7 ' 7 2" 7 6 2 9 S i M A S N M R has also provided critical information. 7 6" 2 2 For the Z S M - 5 / sorbate systems where changes are seen, the nature of the lattice distortions seems to be relatively characteristic o f the nature of the sorbed molecule. 7 9" 2 2 In some cases however, very similar 2 9 S i M A S N M R spectra are obtained with different molecules, indicating that the lattice geometries are closely related. It may be that the locations of the molecules in these cases is very similar, but this has only been verified for two systems to date. 2 , 5 The increasing reliance on theoretical calculations to determine the locations of sorbates in these zeolite structures must be tempered by the relatively few accurate structures which have been determined by experiment. Moreover, the calculations rely on molecular forcefields and potential functions "borrowed" from other (often purely organic) systems. 2 5 Clearly there is a need to expand the database of dependable structures as a check on the accuracy of the proposed structures and also to improve the reliability o f the calculations methods. This chapter presents the results of the structure refinement for /(-xylene molecules in the framework of Z S M - 5 at a loading of less than four molecules per unit cell using X-ray diffraction data collected from a single crystal at 180 K. Prior to the structure determination reported here, the location and orientations of /(-xylene molecules in the low-loaded form of Z S M - 5 had been proposed from a 'f it ' o f X-ray powder diffraction data, 2 7 and also by energy minimization ca lcu la t ions . * * 2 6 Solid-state N M R experiments including ' H - 2 9 S i C P M A S and 1 3 C - 2 9 S i R E D O R had recently been completed in this research group to determine the location of the /(-xylene in Z S M - 5 for the low-loaded form by solid state N M R . 2 7 The location and orientation found in the present work for /(-xylene in Z S M - 5 by single crystal X-ray diffraction is compared to those 257 proposed from the previous investigations and those of other sorbate / Z S M - 5 complexes determined from single crystal X R D studies reported in the literature. 8.1.1 Single Crystal X-ray Diffraction Studies of ZSM-5 Systems Fol lowing the initial determination of the Z S M - 5 framework structure from powder diffraction data by Kokotai lo et al.,12'28 several refinements using single crystal X-ray diffraction data on as-synthesized samples were undertaken. O f these, the most accurate structure to date is that by van Koningsveld et al. who were able to locate the templating T P A + ion. 2 (the other structure determinations of the as-synthesized materials are discussed in reference 1). The space groups, numbers o f crystallograpically inequivalent T-sites, as well as the number and general location of guest species present (if any) found from single crystal X R D refinements on Z S M - 5 systems are summarized in Table 6.1. Z S M - 5 has been found to adopt four space groups: three with orthorhombic symmetry: Pnma (12 T-sites), P2/2 /2 / (24 T-sites), and Pn2/a (24 T-sites); and one having monoclinic P2t In. 1.1 symmetry with 24 T-sites. Four different sorbed molecules in Z S M - 5 have been studied by single crystal diffraction studies to date: /?-xylene, 2/7-dichlorobenzene, i 4/»-nitroanil ine, J fi and naphthalene.7 The latter three compounds are all solids at room temperature, al lowing the low-loaded (< 4 molecules/u.c.) forms to be relatively easily obtained. However in the case of p-xylene, which is a volatile l iquid, only the high-loaded (saturated) complex containing 8 molecules/u.c. had been previously studied by single crystal X-ray diffraction, presumably due to difficulties in controlling the amount o f volatile sorbate loaded into a single crystal. With the exception of the high-loaded /^-xylene / Z S M - 5 complex, all of the single crystal X-ray diffraction studies reported for sorbates in Z S M - 5 used crystals which were selected from a batch of crystals sufficiently large that controlled amounts o f (solid) sorbates could be added by weight. In the case of the high-loaded /7-xylene a single crystal was simply 258 exposed to excess vapor to obtain a saturated loading. It is assumed that for these studies the crystals were not loaded in capillaries since this was not discussed in the literature. Using the specially designed apparatus described in Chapter 2, precise loading of volatile organic molecules into single crystals of Z S M - 5 is now possible. This represents a major advance in this field and use of this purpose-built equipment wi l l permit the single crystal X R D investigations of many other previously unobtainable zeolite host-guest systems by X-ray diffraction, provided single crystals o f adequate dimensions and quality are available. The current availability o f image plate and C C D area detectors has dramatically reduced the minimum crystal size required (from ca. 100 um to about 20 um), thus increasing the number of zeolites for which single crystal studies should be possible. Furthermore, the improved collection efficiency of these area detectors means that data collection times are reduced from more than a week to less than 24 hours and low temperature studies are thus quite feasible. In general, collection of diffraction data at low temperatures results in smaller thermal errors, reduces the dynamic disorder, and allows more accurate bond distances and angles to be obtained. Detailed investigations of powder X-ray data and 2 9 S i M A S N M R data are invaluable aids to determining the possible crystal system and lattice parameters, the symmetry (space group), and the number of crystallograpically inequivalent T-sites. In addition they can often be used to determine the temperatures and/or loadings at which structural changes are induced. If possible, these techniques should be utilized prior to beginning single crystal studies. 8.1.2 Correlations Between 29Si NMR Chemical Shifts and Structural Parameters As discussed in Chapter 6, the 2 9 S i N M R chemical shift is a very sensitive probe of the local structure and geometry around the Si nuclei in the T-sites, and this information has been utilized as aid in selecting the correct space group for structure determination in cases where this is ambiguous. 1 7 , 1 8 In attempts to interpret and assign the 2 9 S i resonances to specific T-sites within 259 the framework lattice, various correlations based on the structural geometrical parameters of the T-sites have been presented. 2 2 , 2 9 5 " The geometrical parameters from X R D data used for interpreting the 2 9 S i M A S N M R spectra of highly siliceous zeolites are: (/') the mean S i - O - S i angle <xav and various functions based on this including cos aav I cos (a a v -1 );29,5''i36 (ii) the mean Si-Si d is tance; 2 9 i 3 0 , 3 2 and (iii) The mean Si -O bond length. 5 0 The latter is not very sensitive since the S i - O distances show little variation in siliceous zeolites. The most accepted parameters are cos otav / cos (a a v -1) and the mean S i - S i distance which has a dependence on both the bond angles and lengths. 2 9 Two problems restrict the quality of the linear correlations obtained in this manner. Firstly the quality of the positional data must be accurate (e.s.d.'s better than 0.004A and 0.02° i f possible). Secondly reliable assignments of the 2 9 S i N M R resonances to specific T-sites, with well resolved N M R spectra to provide accurate chemical shifts. The first condition can be realized from refinements of high quality single crystal X R D data, and the second criteria may be met through 2-D N M R correlation experiments such as C O S Y and I N A D E Q U A T E . 5 7 To date the main limitation preventing these correlations from being completely quantitative arises from uncertainties in the X R D derived structural parameters, rather than the precision of 29 29 38 the Si chemical shifts. However, in at least one case, reliance on these correlations produced incorrect assignments of the 2 9 S i N M R resonances. Consequently the published correlations should only be used to draw qualitative conclusions and not as a definitive method for assigning the N M R spectra. 8.1.3 Previous Investigations of the Low-Loaded /^-xylene / ZSM-5 Complex Fyfe et al. first reported changes in the powder X R D patterns and 2 9 S i M A S N M R spectra of Z S M - 5 with sorbed /^-xylene, and correctly deduced they where the result o f framework lattice distort ions. 1 6 , 3 9 It was also found that the powder X R D pattern of /^-xylene 260 sorbed in Z S M - 5 at loadings greater than two but less than four molecules/u.c. were indicative of a change to orthorhombic symmet ry . I 6 J I The 2 9 S i M A S N M R spectrum of the low-loaded /^-xylene / Z S M - 5 complex can be resolved in terms of twelve resonances of equal intensity in agreement with the proposed Pnma space group at temperatures from 173 K to 393 K . 7 0 2 9 S i 2-D C O S Y and I N A D E Q U A T E experiments at room temperature were used to assign the individual 2 9 S i N M R resonances and the connectivities found were consistent with orthorhombic space group Pnma symmetry/ 7 Figure 8.1 shows ' H - 2 9 S i C P M A S spectra for the low-loaded /7-xylene / Z S M - 5 complex acquired at 173 and 193 K with the assignments indicated. Fyfe and co-workers also reported phase diagrams for highly siliceous Z S M - 5 containing various amounts of sorbed /(-xylene at temperatures ranging from 293 to 393 K determined from 2 9 S i M A S N M R experiments/ 9" ' 0 Mentzen and Vigne-Maeder proposed locations for /^-xylene from powder X-ray diffraction data in an MFI-type zeolite containing some boron at low loadings/ 7 Using the framework coordinates of T P A + Z S M - 5 reported by Baerlocher 7 ' and space group Pnma, powder X R D patterns were simulated and compared these to the experimentally determined patterns. The best agreement was found when the centroid of the />-xylene ring was positioned on the mirror plane with the methyl groups lying along the straight channels. Several orientations of the /^-xylenes were considered and they concluded that the organic molecules might be statistically disordered with two simultaneous orientations in the channels/ 7 Reischman et al. proposed equilibrium absorption sites for/?-xylene in the channels of Z S M - 5 based on calculated van der Waals interactions between the hydrocarbon and the zeolite and between the hydrocarbon molecules themselves/ Their calculations used the Pnma framework coordinates of Olson et al.2H and indicated that the most energetically favourable sorption sites for loadings up to 4 molecules/u.c. were the channel intersections with the methyl-methyl axes along the straight channel. This configuration had a calculated energy of -82 kJ/mol, 261 T 1 1 1 1 1 1 1 1 1 1 1 r -108 -110 -112 -114 -116 -118 -120 ppm from T M S T 1 1 1 1 1 1 i 1 1 1 1 r -108 -110 -112 -114 -116 -118 -120 ppm from T M S F igure 8.1 l H - 2 9 S i C P M A S N M R spectra of the /^-xylene / Z S M - 5 complex at a loading of 3 molecules / u.c. recorded at (a) 173 K and (b) 193 K. 32 scans were acquired using a 30 ms contact time and a recycle delay of 3 s. The assignment of the resonances to specific T-sites is indicated where they could unambiguously determined from a 2-D I N A D E Q U A T E experiment at 268 K . 2 7 262 which was significantly more favorable than those calculated for several other configurations including molecules in the sinusoidal channels or molecules in both channels (> - 5 0 kJ/mol). They noted that when /(-xylene occupies only the channel intersections, the van der Waals interactions between adjacent molecules are small, and the major contribution comes from framework-oxygen //(-xylene-hydrogen interactions. Several other groups have reported theoretical calculations to determine the sorption site of /(-xylene in the MF I - framework, usually using si l ical i te. 2 j , 2 < 5 In all these calculations the framework has been rigid, and the sorbate is also usually defined as a semi-rigid group. 9 , 2 5 In some cases a wrong framework symmetry was used and the sorbate-induced framework changes can be quite substantial. 2 , 7 The locations determined are dependent on the potential functions and calculation technique used, and there is not always complete agreement between the various calculations. 9 More recently Diaz and Fyfe have investigated the location of /7-xylene in Z S M - 5 with several solid-state N M R techniques at low temperatures (down to 173 K ) uti l izing different isotopically labeled /^-xylenes. 2 7 When three molecules/u.c. /(-xylene having a single 1 3C-labeled methyl group were sorbed in Z S M - 5 , only a single 1 3 C resonance was observed for the methyl groups. 2 7 Through the use of selectively deuterated /(-xylenes the location of the sorbate molecules at a loading of 3 molecules/u.c. was determined from fitting of ' H - 2 9 S i C P M A S data for/?-xylene (deuterated at the ring or methyl groups) and correlations between TCp and the calculated 2 9 S i heteronuclear second moments (see Chapter 6). In these calculations, a rigid framework and /^-xylene molecule were assumed, using the framework coordinates reported for the single crystal X R D determination of the low-loaded form of/7-dichlorobenzene, and an ideal geometry for the sorbate molecule/ From analysis of the C P behavior it was deduced that the molecule was located near the channel intersections. Starting from a position near the channel center, the /(-xylene location was moved around in the straight channel using small steps and a range of orientations. For each orientation and position the 263 heteronuclear 2 9 S i - ' H second moments M2 were calculated (cut-off distance of 8 A ) and a plot of the reciprocal of experimentally determined Tc? values vs. M2 made. Three almost identical solutions yielded very similar, highly linear correlations, and the ' H - 2 9 S i C P M A S N M R spectra simulated (using TCp to determine the peak intensities) showed very similar agreements with the experimentally observed spectrum. The "best" solution was chosen from these and had the molecular centre exactly coincident with the mirror plane and the methyl-methyl axes parallel to [010] in accord with the observation of a single 1 3 C resonance. In the other solutions, the ring centre was displaced by less than 0.3 A from the mirror plane and the molecules showed small angular deviations from the b and c axes. 8.2 M A T E R I A L S AND M E T H O D S 8.2.1 Crystal Preparation and Sorbate Loading Large single crystals of Z S M - 5 were grown by Dr. W. Schwieger using hydrothermal synthesis (3-5 days at 175 °C) with tetraproplyammonium chloride. The molar composition of the reaction mixture was S i 0 2 (12.2) N a A 1 0 2 (0.04), N a O H (44.9), T P A B r (43.1), H 2 0 (2000). Due to the small quantity of material obtained, bulk elemental analysis was not done. The crystals were thoroughly washed with distilled water then calcined in air at 500 °C to remove the template. A n optical microscope was used to select large crystals (dimensions > 0.15 mm) having no visible defects or twinning. These were loaded into 0.3 mm diameter quartz X-ray capillaries (wall thickness 0.01 mm, graded quartz-Pyrex transition piece attached), and connected to a purpose-built apparatus constructed of Pyrex glass (see Figure 2.2). Details of the method used to load the crystal with /^-xylene are given in Section 2.3.2. The capillaries were isolated and the loading of the Z S M - 5 powder was verified by thermal gravimetric analysis ( T G A ) and 2 9 S i M A S N M R . T G A (temperature ramp 10 °C / min. to 600 °C under f lowing nitrogen gas) indicated a weight loss equal to 3.4 (0.3) molecules/u.c. A s a more sensitive check that the low-loading (< 4 molecules/u.c.) had been achieved, 2 9 S i M A S 264 N M R spectra of the Z S M - 5 powder were acquired. These were in agreement with those reported in the literature for sorbate loadings greater than two but less than four molecules /^-xylene per u.c. ' 9 , 2 0 Individual capillaries containing the single crystals were isolated, immersed in l iquid nitrogen, and sealed. They were stored at room temperature to allow an equilibrium loading to re-establish before the X-ray diffraction data were collected. 8.2.2 Data Collection and Refinement of Reflection Data 8.2.2.1 Data Collection The crystal selected for study had dimensions of 0.2 x 0.2 x 0.15 mm. Data were collected by Dr. S. Rettig at a temperature of 180 K on a Rigaku A C F 7 diffractometer equipped with an Area Detector System Corporation charge-coupled device ( C C D ) detector (size 98 x 98 mm) using graphite monochromated M o Ka radiation. 768 C C D images were stored (recording time 96 s / image) in a> and <f> scan modes with 0.3 degree steps between images up to 6 > m a x = 30.05°. A total time of 21 hours was required for the data collection during which the crystal was cooled by a f low of cold nitrogen gas. Table 8.1 summarizes other data collection parameters. 8.2.2.2 Definitions of R-indices Used A s described in the SHELXL-97 l i terature/ 2 a variety of parameters are available which can be used to monitor the success of a refinement. The diffraction experiment measures intensities and their standard deviations, which after the various corrections give F02 and o(F02). Refinement against all i^-values is demonstrably superior to refinement against F-values greater than some threshold [say 4a(F)], because more experimental information is incorporated (suitably weighted) and the chance of getting stuck in a local minimum is reduced. The progress and quality of the refinement was monitored using wR2, the weighted R-factor based on F2:42 265 Table 8.1 Crystal data and structure refinement for the low-loaded /7-xylene / Z S M - 5 complex at 180 K. CRYSTAL DATA Chemical formula Chemical formula weight Crystal system Space group Unit cell dimensions Cel l volume Reflections used to determine cell parameters Z Calculated Density Absorption Coefficient Crystal form Crystal size Crystal colour Crystal mounting C22.8 H28.6 Sig6 O192 1517.66 Orthorhombic Pnma a=19.989(4) A, 6=19.899(4) A, c=13.362(3) A 5315(2) A 3 35854 1 1.935 g/cm 3 H = 0.685 mm" 1 Block 0 . 2 0 x 0 . 2 0 x 0 . 1 5 mm Colourless (clear) Sealed quartz capillary (0.3 mm diameter) DATA COLLECTION Diffractometer Data Collection Temperature Radiation Type Wavelength Theta range for data collection Mi l le r index ranges Number of measured reflections Number o f observed reflections [ I >o(I) ] Unique reflections (after averaging) R index for symmetry equivalent reflections R index from counting statistics Completeness to 0= 30.05 Maximum and minimum transmission Number of C C D images collected Exposure time per C C D image Scan mode Scan range Background measurements Rigaku A C F 7 with A D S C C C D detector 180(2)K M o Ka (graphite monochromated) X = 0.71073 A 2.10 < 6< 30.05° -28-> h-+24, -25-> k->23,-15—>/—>18 47400 45435 7420 = 0.0398 s^igma = 0.0464 93.0% 0.9043 and 0.8752 768 96 seconds co and ^osci l lat ion, ^ = -90° -23°<co< 17.8°, 0 ° < ^ < 190.2° Determined during image integration 266 Table 8.1 (continued) Crystal data and structure refinement for the low-loaded /(-xylene / Z S M - 5 complex at 180 K. REFINEMENT Refinement method Final R indices [ I > 2ofI) ] R indices (all data) Goodness-of-fit (all data) Number of reflections used Number of restraints Number of least squares parameters H-atom treatment Weighting scheme Largest and mean least squares shift Largest e" Density Peak and Hole Absorption correction method Structure refinement program Source of atomic scattering factors Full-matrix least-squares on F2 R}(F) = 0.0437, wR2(F2) = 0.1148 i?,(F) = 0.071 =0.1238 S(F2)= 1.1080 7420 6 (to f ix hydrogen positions) 374 Fixed U at calculated positions w=\l [o2 (F2) + (0.0743 P ) 2 + 0.3534 P] where P = (F2 + 2 F C 2 ) / 3 0.002 A/cr 0.000 Ala Ap m a x = 1.038 e / A 3, Ap m i n = -0.641 e / A 3 Semi-empirical using equivalent reflections SHELXL-97 (Sheldrick, 1997V'2 International Tables for Crystallography (1992, V o l . C , Tables 4.2.6.8 and 6.1.1.4V'7 267 wR2 = { I [ w(F2-F2)2 ] 11 [ w(F2)2 ] }1 /2 8.1 Here F c is the calculated intensity and w is the weighting scheme used: w = 1 / [ o\F2) + {aP)2 + bP] 8.2 where P= [ 2 F C 2 + Max(F o 2 ,0 ) ] / 3 8.3 The use of this combination of F2 and F2 was shown by Wi l son 7 5 to reduce statistical bias. For comparison with older refinements based on F, a conventional index R{ (Eq. 8.4) based on observed F values larger than 4o(F0) was also calculated. Rx = E | | F 0 | - | F C | | / S | F 0 | 8.4 In general, the smaller the values of these i?-factors, the better the agreement between the model and the diffraction data. Another parameter which describes the quality of the final structure is the Goodness of Fit, S, and this is also based on F2: S = {2Z[w(F2-F2)2] I (n -p ) } 1 / 2 8.5 Here n is the number of reflections and p is the total number o f parameters refined. S should be close to unity when the weights o f the observations have been correctly assessed, the errors in the model are negligible in comparison with the errors in the data, and there are no significant systematic errors. 7 7 Two parameters which describe the quality o f the reflection data are i? i n t (Eq. 8.6) and - f t s i g m a (Eq- 8.7). Rmx = Z | F2 -/tf(mean) | / S [ F 2 ] 8.6 * s , f e n „ a = E [ a ( F 0 2 ) ] /2Z[F2] 8.7 268 In Eq. 8.6 both summations involve all input reflections for which more than one symmetry equivalent is averaged, and the summation in Eq. 8.7 is over all reflections in the merged list. 8.2.2.3 Processing and Refinement of the Reflection Data Intensities of the reflections were determined by three-dimensional integration of the C C D images. Initially a dynamic profile-fitting function was used to perform the peak integration, however this yielded non-positive definite thermal parameters for the framework atoms during the early stages of the refinement. Subsequently a constant volume integration technique which used fixed volumes for the individual peaks was employed and this gave wel l -behaved intensity data. Background intensities were measured from the images in the vicinity of the individual peaks and subtracted during the integration procedure. The final intensities were corrected for absorption using a semi-empirical method based on an analysis of equivalent reflections. Lorentz and polarization corrections were also applied. Cel l parameters were determined from a least squares fitting of 35854 reflections and are given in Table 8.1. The final data file contained the Mi l le r indices (indexing done by D*TREK software""), the F2 and o(F2) values for 47400 reflections (45435 with I > 1 cr). This data set was pre-processed using the teXsan for Windows software1"5 and showed systematic extinctions indicating the crystal was orthorhombic with possible space groups Pnma (No. 62) or Pn2ta (No. 3 3 ) / 7 Pnma symmetry was confirmed by successful refinement (see below). Before refinement commenced, the data were exported in the format required for the refinement program SHELXL-97.42 SHELXL-97 was run on an IBM-compatible P C with a Pentium 200 processor under the Windows N T operating system. Starting coordinates of framework atoms were taken from those reported in the literature for T P A O R T . 2 A l l framework atoms were treated as zero valent Si or O with anisotropic temperature factors. The atomic scattering factors used were taken from the International Tab les / 7 and any systematically absent reflections were automatically rejected by 269 the refinement program. After the equivalent reflections were merged and their indices converted to standard symmetry equivalents, a set o f 7420 unique (averaged) reflections was obtained. Using these data, anisotropic, full matrix least squares refinement on F2 of the framework atoms only (with site occupancies fixed to 1.0) converged to R\ = 6.64 % (wR2 = 23.03%, w = 1 / o(F2)). The Fourier difference map calculated at this stage revealed several peaks with significant electron density. The four highest were assigned to C atoms of /(-xylene (the other four C ' s are related by mirror plane aty = 0.25). A s check for reduced symmetry and/or disorder, attempts were made to refine the whole system {i.e. framework and sorbate) in Pn2ta. To achieve this a complete set o f the mirror related 12 Si and 26 O atoms was generated (using x, y, z —> x, 0.5-y, z) and several cycles of refinement in Pnma carried out using these atoms to reorient the thermal ellipsoids. The two sets were combined and refinement proceeded in Pn2ta. However during this refinement the thermal factors for several framework atoms went non-positive definite or the R factors became unstable even when constraints were applied to keep the formerly mirror-related framework atoms equivalent. To test for the presence of disorder in the /(-xylenes, several different models were used including two rigid /(-xylene molecules with separate occupancies. In this case one set moved onto the mirror plane while the other carbons became non-positive definite or the C - C bond lengths and the geometry of the molecule became unreasonable. A similar disordered model was tried in Pnma but was also badly behaved. Consequently the refinement was continued in Pnma with four C atoms having a common (refined) occupancy, the ring centre coincident with the mirror plane a t ^ = 0.25 and individual anisotropic thermal parameters for all atoms (Si, O, C) . During the final cycles, six constraints were used to f ix the five unique hydrogen atoms of the p-xylene (isotropic with occupancy equal to that of the carbons) at calculated positions ( C - H = 0.98 A, C - C - H = 120°). 270 Using this model, the refinement converged to R\ = 4.37 % (wR2 = 11.48%, weighting scheme given in Table 8.1) and a goodness-of-fit parameter S = 1.108 for 7420 reflections and 374 parameters. The average and maximum shift / e.s.d. values in the last refinement cycle were 0.002 and 0.000 respectively. The final difference synthesis showed small amounts of residual electron density with the highest peak (1.038 e / A3) located in the centre of the zig-zag channel. A possible explanation for this is residual debris not completely removed during the calcination. A small peak was also detected near the /(-xylene molecule, but all other peaks were in close vicinity of the framework atoms and attributed to "rest density" of these atoms. The occupancy of the carbon atoms refined to 0.714(7) which corresponds to 2.85(3) /(-xylene molecules / unit cel l , in close accord with the loading determined from T G A analysis of the powder sample. Heating during the sealing of the capillary may have resulted in a slight loss of sorbate, and it is also possible that the cooling of the crystal and capillary during the data collection may have had a small effect on the precise sorbate loading. Final atomic fractional coordinates and equivalent isotropic thermal displacement factors for the framework and sorbate atoms (excluding hydrogens) determined from the refinement are listed in Table 8.2. The individual anisotropic thermal parameters are listed in Appendix G . Figures were generated using ORTEP-3 for Windows48 and some geometrical analysis (e.g. of the coordination spheres) was done with the PLATON-98 sof tware/ 9 8.3 RESULTS AND DISCUSSION This structure represents a major advance since it is the first reported single crystal structure determination where a volatile organic sorbate was loaded to less than 4 molecules/u.c. in a single crystal; with the exception of the high-loaded /(-xylene / Z S M - 5 complex, the single crystal X R D structure determinations of the other sorbate / Z S M - 5 systems reported previously contained sorbates which were solids at room temperature. The crystal investigated was of comparable size to those used by other groups in previous Z S M - 5 single crystal X R D structure 271 Table 8.2 Atomic coordinates (x 104) and equivalent isotropic displacement parameters (A2 x 103) for the low-loaded /^-xylene / Z S M - 5 complex at 180 K. Ueq is defined as one third of the trace of the orthogonal ized U,, tensor. . Atom X y z Si ( l ) 4242(1) 561(1) -3506(1) 6(1) Si(2) 3045(1) 280(1) -2067(1) 7(1) Si(3) 2819(1) 640(1) 149(1) 7(0 Si(4) 1235(1) 653(1) 157(1) 6(1) Si(5) 720(1) 281(1) -1954(1) 6(1) Si(6) 1802(1) 557(1) -3475(1) 6(1) Si(7) 4215(1) -1725(1) -3342(1) 6(1) Si(8) 3030(1) -1299(1) -1951(1) 7(1) Si(9) 2704(1) -1724(1) 238(1) 7(1) Si(10) 1160(1) -1736(1) 176(1) 6(1) S i ( l l ) 670(1) -1295(1) -1946(1) 6(1) Si(12) 1810(1) -1718(1) -3312(1) 6(1) O ( l ) 3654(1) 585(1) -2697(1) 18(1) 0(2) 3013(1) 658(1) -1013(1) 14(1) 0(3) 2027(1) 576(1) 295(1) 21(1) 0(4) 1044(1) 658(1) -1006(1) 14(1) 0(5) 1078(1) 538(1) -2956(1) 11(1) 0(6) 2358(1) 396(1) -2651(1) 21(1) 0(7) 3625(1) -1656(1) -2541(1) 17(1) 0(8) 3021(1) -1598(1) -844(1) 20(1) 0(9) 1930(1) -1502(1) 219(1) 15(1) 0(10) 897(1) -1685(1) -954(1) 17(1) 0(11) 1067(1) -1590(1) -2892(1) 14(1) 0(12) 2327(1) -1446(1) -2490(1) 20(1) 0(13) 3162(1) -510(1) -1907(2) 24(1) 0(14) 831(1) -511(1) -1815(1) 15(1) 0(15) 4272(1) 1259(1) -4105(1) 15(1) 0(16) 4127(1) -38(1) -4293(1) 17(1) 0(17) 4013(1) -1347(1) -4359(1) 17(1) 0(18) 1909(1) 1288(1) -3943(1) 17(1) 0(19) 1832(1) 2(1) -4347(1) 15(1) 0(20) 1917(1) -1320(1) -4342(1) 17(1) 0(21) -60(1) 449(1) -2054(1) 12(1) 0(22) -119(1) -1401(1) -2120(1) 14(1) 0(23) 4337(1) -2500 -3600(2) 14(1) 0(24) 1925(1) -2500 -3517(2) 16(1) 0(25) 2773(1) -2500 530(2) 13(1) 0(26) 1087(1) -2500 542(1) 10(1) C ( l ) 160(4) -1787(6) -5198(5) 94(3) C(2) -296(3) -2151(5) -4643(4) 121(6) C(3) 620(3) -2135(5) -5774(5) 108(4) C(4) 166(5) -1034(8) -5191(7) 138(5) 272 determinations. 2" 5 , 5 Cel l parameters are very accurately determined since they were found from fitting of more than 35000 reflections compared to the usual 25 on conventional single crystal X R D systems. Data collection at low temperature (180 K for >20 hours) was made possible through the use of a C C D detector. This allowed the simultaneous collection of Bragg reflections from a wide angular region, and thus greatly reduced the collection time needed (in this case from more than 7 days to less than 24 hours). A n associated benefit of the C C D detector is the significant reduction in the size of crystal required, which is especially important for the type of system investigated here. Although, in general, the intensities measured for individual reflections are less accurately determined using a C C D detector compared to a conventional counter in a given time, many reflections are collected several times which allows for averaging, and thus the overall statistics are often significantly improved. Another advantage is that all of the data for a complete hemisphere (representing a complete set of reflections) is collected and stored; thus i f the wrong space group or cell is inadvertently chosen, the data can simply be re-indexed rather than having to collect the 'missed' reflections. The /^-xylene molecules were located in the straight channels at the intersection with the zig-zag channels, in agreement with other single crystal structure determinations reported for host-guest Z S M - 5 / sorbate systems. The labeling of the framework atoms is indicated in Figures 8.2 and 8.3 The orientation of the p-\y\ene molecule in the straight channel is shown in Figure 8.3, where the presence of the mirror plane through 0 2 3 , 034 , 025 and 0 2 6 can be easily seen. Van Koningsveld and co-workers found Pnma symmetry for two other single crystal X R D structures of low-loaded / Z S M - 5 complexes containing naphthalene7 or p-dicholorobenzene"' but needed to invoke a model having disordered molecules at two orientations (related by the mirror plane imposed by the Pnma symmetry). This disorder may actually be the result o f a lower symmetry which is not resolved due to limitations in the data. When a non-273 0 2 6 Figure 8.2 Numbering scheme of the Si and O atoms in the asymmetric unit of the Z S M - 5 framework in Pnma viewed approximately along (a) [100] and (b) [010]. 274 Si7 Si12 023 Figure 8.3 O R T E P drawings of/?-xylene in Z S M - 5 with numbering scheme used for Si and O atoms, (a) V iew along [010] showing the orientation of the p-xylene molecules at the intersection of the straight and zig-zag channels, (b) V i ew down [100]. 275 centrosymmetric molecule (p-nitroaniline) was sorbed in Z S M - 5 two space groups were found: 5 ' 6 Pn2ta and Pnma. In the former case the framework configuration was virtually identical to that determined previously for the unloaded high temperature (Pnma) phase of Z S M - 5 , and a large number of constraints were needed to suppress the effects of strong correlations between the (Pnma) "mirror-related" framework atoms. Although disorder might model this effectively, it is more chemically reasonable that the overall symmetry is reduced, at least in the case of non-centrosymmetric molecules (e.g. />nitroaniline and/j-chlorotoluene). This apparent contradiction can be understood i f the contributions to the scattering by the sorbate and framework atoms are considered. The scattering by the carbon atoms in a sorbate wi l l be much less than that due to the framework atoms, and may not be large enough to "violate" the Pnma symmetry. These space groups exhibit the same systematic extinctions and the presence or absence of the mirror plane perpendicular to b cannot be deduced from analysis of the reflection extinctions alone. Moreover, Pn2ia is a subgroup of Pnma and can be obtained by eliminating the inversion centre which has the effect of removing the mirror plane at y = 0.25. 8.3.1 Geometry of the Framework In Table 8.3 the framework geometry (ranges and averages for bond lengths and angles) determined for low-loaded p-xylene / Z S M - 5 in the present work is compared to those reported for previous Z S M - 5 structures. Ful l details of the S i - 0 bond lengths, as well as O - S i - O , S i - O -Si bond angles for the individual T-sites are given in Appendix G . The present structure represents the most accurate determination of the Z S M - 5 framework to date; the thermal displacement parameters for the Si and O atoms in the Z S M - 5 framework, as well as the observed variation in the S i - 0 bond lengths, are considerably smaller than any previously reported for Z S M - 5 . For example the range of S i - O bond lengths in low-loaded p-xylene form of Z S M - 5 is 0.016 A compared with ca. 0.03 A or greater for other structures, and the range of the averages for the individual S i - O - S i bond angles is narrower by more than two degrees (Table 276 8.3). The estimated standard deviations of the bond lengths and bond angles are small, being less than 0.002 A and 0.1° respectively (see Appendix G) . The more accurate determination stems primarily from the low temperature (180 K ) at which the data was acquired and large number of reflections collected (93% completeness), resulting in reduced thermal errors and a high observation / parameter ratio (« 20) respectively. The average S i - O bond length is slightly longer (by ca. 0.005 A) than that seen for the low-loaded sorbate / Z S M - 5 complexes, and significantly longer (0.015 A) than those reported for the high-loaded complexes. Another striking difference is that the minimum S i - O bond length is somewhat longer than that observed in other Z S M - 5 systems, although the maximum is very similar to those in other structures. The average S i -O-S i angle is also at least 2° lower than in other Z S M - 5 structures. These may be a result of the lower temperature at which the diffraction data was collected (all of the other structures were determined at or above room temperature) as the lattice is quite flexible and can change to accommodate thermal stresses caused by cooling or heating. The pore sizes mainly determine the molecular sieving and diffusion properties of zeolites, and while they are often referred to in terms of the number of T-atoms in the rings outlining the openings, it is really the oxygens which define the effective or " free" pore size owing to their larger van der Waals radii. One way to describe the dimensions of the channels is through use of the diagonal O - O distances across the rings. The free pore dimensions accessible to guests can easily be calculated from these by subtracting twice the van der Waals radii of oxygen (1.35 A).2 In Table 8.4 the minimum and maximum diagonal 0 — 0 distances across the 10-rings defining the channels in Z S M - 5 are listed for the low-loaded /(-xylene / Z S M - 5 complex and those reported for the other Z S M - 5 single crystal determinations. In framework structures with Pnma symmetry, the two 10-rings defining the straight channel are related by a mirror plane, and those describing the zig-zag channel share an inversion center. In the monoclinic space group Pn2/a and the orthorhombic P2 /2 /2 ; symmetry observed for the high-loaded Z S M - 5 277 Table 8.3 Comparison of the framework geometry in several ZSM-5 structures as determined by single crystal X-ray diffraction. Si-O Bond Lengths (A) O-Si-0 Bond Angles (°) Si-O-Si Bond Angles (°) Structure^ Ref. Temp (K) Range Range . Average*' AveragC Range Average Range Range Average Si(OSi)4(b) Average MONO 15 293 1.582-1.607 1.588-1.601 1.595 107.1-111.5 109.5 141.3-169.0 147.1-158.8 153.0 HTORT 14 350 1.570-1.601 1.581-1.593 1.587 107.1-111.5 109.5 145.7-177.7 150.7-163.6 155.5 TPAORT 1 293 1.567-1.605 1.584-1.591 1.586 106.0-112.0 109.5 144.9-175.9 150.5-162.8 155.4 HLPXY 2 293 1.574-1.611 1.588-1.604 1.597 107.5-112.0 109.47 138.3-172.3 148.5-162.3 154.7 HLPDCB 3 293 1.573-1.612 1.585-1.603 1.594 106.9-112.1 109.47 138.8-176.9 149.1-164.1 155.1 LLPDCB 4 293 1.577-1.607 1.584-1.596 1.592 107.7-111.1 109.47 144.4-170.7 150.0-162.8 154.0 LLPNA 5 293 1.580-1.607 1.586-1.603 1.595 107.4-111.0 109.47 142.0-169.0 148.7-162.4 153.7 LLPXY this work 180 1.594-1.610 1.597-1.604 1.601 107.4-111.1 109.47 140.5-164.7 146.8-157.6 151.0 NAPH 7 293 1.581-1.608 1.584-1.600 1.595 107.7-111.1 109.47 141.7-169.9 148.7-164.5 153.7 See Table 6.1 for description of codes. Range of the averages calculated for each crystallographically inequivalent Si atom. Table 8.4 Minimum and maximum diagonal O • O distances (A) across the 10-rings in several ZSM-5 structures. Free pore dimensions may be calculated from these by subtracting twice the oxygen van der Waals radius (i.e. 2 x 1.35 A). Structure^ MONO HTORT(b) TPAORT(b) HLPXY HLPDCB LLPDCB(b) LLPNA(b) LLPXY(b) NAPH(b) Straight Channel 10-ring 1 minimum 7.875 7.985 7.922 7.503 7.560 7.534 7.319 7.319 7.252 maximum 8.484 8.406 8.449 8.882 8.790 8.894 9.085 9.115 9.143 //5(C) 1.077 1.053 1.066 1.184 1.162 1.180 1.241 1.245 1.261 10-ring 2 minimum 7.969 7.774 7.817 maximum 8.532 8.755 8.697 l/s 1.071 1.126 1.113 Zig-Zag Channel 10-ring 1 minimum 8.054 8.061 7.992 7.456 7.461 8.002 7.990 7.991 7.895 maximum 8.593 8.308 8.250 9.071 9.060 8.292 8.285 8.329 8.255 l/s 1.067 1.031 1.032 1.217 1.214 1.036 1.037 1.042 1.045 10-ring 2 minimum 7.712 7.945 7.983 7.283 7.257 7.954 7.965 7.941 7.950 maximum 8.476 8.382 8.295 8.846 8.846 8.375 8.342 8.445 8.319 l/s 1.099 1.055 1.039 1.215 1.219 1.053 1.047 1.063 1.046 (a) See Table 6.1 for description of codes and references.(} In these structures the two 10-rings in the straight channel are equivalent because they are related by mirror plane in space group Pnma.(c) Ratio of longest over shortest diagonal distance which is related to the eccentricity (deviation from circular) of the 10-rings. / sorbate complexes, there are two independent 10-rings defining each of the straight and sinusoidal channels respectively. A s seen from the values listed in Table 8.4, there is a fair amount of variation between the three general structure types (empty framework, high- and low-loaded), but there are general similarities within each group. A useful parameter which describes the deviation of the channels from circular is the ratio of the longest over the shortest diagonal O - O distances (the eccentricity l/s). If l/s = 1.0 the Tio rings are essentially circular, while larger values of l/s indicate increasing elliptical distortion. The l/s ratios for the Z S M - 5 structures are listed in Table 8.4. Comparison of the eccentricities for the three structure types indicates that the elliptical character of the 10-rings is significantly more pronounced when there is a sorbate molecule present. This elliptical distortion of the 10-rings closely mirrors the shape of the sorbed molecule and can be clearly seen in Figure 8.4 which shows the packing of the /7-xylenes in the straight channels of Z S M - 5 . Note that the distortion produces a free pore dimension that is quite closely related to the kinetic diameter ofp-xylene (5.85 A).50 A n exception to the guest-induced eccentricity in the 10-rings is seen for the as-synthesized Z S M - 5 containing T P A + ions, where only relatively minor elliptical distortions are present. This is probably due to the smaller effective kinetic diameter of the propyl groups compared with those of aromatic ring compounds such as naphthalene and substituted benzenes, and the associated reduction in close framework-sorbate contacts. For the low loaded structures the sorbates are located at the channel intersection but lie in the straight channels, and it is these 10-rings which have l/s markedly larger than 1.0 (actually close to 1.2), while the zig-zag channels remain essentially circular. The effective pore dimensions for straight channels in Z S M - 5 containing less than 4 molecules/>xylene/u.c. (4.6 x 6.4 A) are very close to those of the other Z S M - 5 structures having sorbates at the channel intersections, although in the case ofp-dichlorobenzene, a slightly less pronounced elliptical character is observed. In the high-loaded sorbate / Z S M - 5 complexes, molecules are also present 280 Figure 8.4 View of the low-loaded ^-xylene / ZSM-5 complex down [010] showing the orientations and packing of the p-xylene molecules in the straight channels. Molecules in adjacent channels are related by inversion centers and two-fold screw axes. Note the elliptical deformation of the channels to accomodate the sorbates. in the sinusoidal channels and an elliptical distortion is observed for these 10-rings as wel l . In the empty Z S M - 5 framework, all of the 10-rings are more or less circular. These changes reflect the general f lexibil i ty of the zeolite framework, and indicate that slight changes in the geometry about each T-atom (mainly in the O - S i - O bond angles) can occur to accommodate sorbed molecules or temperature variations. In many theoretical calculations used to determine preferred sorption sites of guests in the zeolite channel systems (e.g. energy minimizations) the framework is kept rigid, and this may not accurately reflect the real structure. 8.3.2 Geometry and Pack ing of the p-xylene Molecules The C - C bond lengths and C - C - C bond angles determined for the /(-xylene molecules sorbed in Z S M - 5 at loading of 2.85 molecules/u.c. are given in Table 8.5. The labeling of the atoms in Table 8.5 is different than used in the structure determination (see Table 8.1) and the new labeling scheme is indicated in Figure 8.5. During the refinement of the X R D data, these atoms had an equal occupancy that was freely varied, and individual anisotropic thermal factors for the four independent C atoms. In the previously published single crystal determinations of low-loaded sorbate / Z S M - 5 complexes, the sorbate molecules were refined as rigid groups with ideal geometries, and sometimes with fixed occupancies as well (For the two high-loaded forms (p-xylene and p-dichlorobenzene) the sorbate geometries were unconstrained). The bond lengths and angles are in excellent agreement with those determined for a single crystal o f /(-xylene at 180 K (Table 8.5) The geometry reported 2 for /(-xylene molecules in the straight channels of the high-loaded /(-xylene / Z S M - 5 complex are also listed in Table 8.5 and a comparison reveals that the present structure determination has significantly lower e.s.d.'s in the bond lengths and a geometry that agrees very well with those found for /(-xylene at the same temperature. The anisotropic thermal displacement parameters for /(-xylene (Table G . l , Appendix G) are similar to those seen in the high-loaded form 2 and are quite elongated in the [010] direction. 282 (a) (b) C(4) ^ C ( l ) C(3) ^C(2) C7 ^ C l C6 C2 m C(3Y ^C(2) ' c(iy C$ C3 ~C4 C(4)' C8 Figure 8.5 Labeling of /^-xylene carbon atoms in (a) X-ray determined structure of low-loaded form of Z S M - 5 and (b) Table 8.5. Apostrophes indicate symmetry related atoms generated by the mirror plane m in the space group Pnma. (a) (b) Figure 8.6 Angles and coordinates used to describe orientations of sorbates in Z S M - 5 . The coordinates of the ring centre are x,y,z. (a) Angles al, Bl and yl define the orientation of the long molecular axis relative to the crystal axes a, b, and c respectively, (b) Angles a2, f32 and y2 are measured to a vector which is normal to the plane of the ring. See footnotes to Table 6.1 for further information. 283 Table 8.5 Comparison of bond lengths (A) and bond angles (°) in p-xylene molecules at the channel intersections of Z S M - 5 with those in a single crystal o f /^-xylene at 180 K. Estimated standard deviations are given in parentheses. Structure^ LLPXY ( b c ) HLPXY ( d ) /?-xylene ( c ' d ) Bond Lengths C1-C2 1.38(1) 1.37(2) 1.394(2) C2-C3 1.39(1) 1.38(3) 1.389(2) C3-C4 1.38(1) 1.43(2) 1.393(2) C4-C5 1.38(1) 1.41(2) 1.394(2) C5-C6 1.45(2) 1.44(2) 1.389(2) C6-C1 1.38(1) 1.37(2) 1.393(2) mean 1.39 1.40 1.392 C1-C7 1.50(1) 1.52(3) 1.503(2) C4-C8 1.50(1) 1.52(3) 1.503(2) mean 1.50 1.52 1.503 Endocyclic Angles C1-C2-C3 121.6(6) 122(1) 121.0(1) C2-C3-C4 121.6(6) 124(1) 121.3(1) C4 -C5 -C6 120.0(6) 122(1) 121.0(1) C5-C6-C1 120.0(6) 121(1) 121.3(1) mean 120.8 122 121.2 C2-C1-C6 118(1) 118(2) 117.7(1) C3-C4-C5 118(1) 113(2) 117.7(1) mean 118 116 117.7 Exocyclic Angles C2-C1-C7 121.7(9) 120(1) 121.2(1) C6-C1-C7 119.9(8) 121(1) 121.0(1) C3-C4-C8 121.7(9) 125(1) 121.2(1) C5-C4-C8 119.9(8) 122(1) 121.0(1) mean 120.8 122 121.1 ( a ) LLPXY: 2.85 molecules of /^-xylene / u .c ; HLPXY: 8 molecules of /j-xylene / u.c. ( b ) /?-xylene located on mirror plane (see Figure 8.5 for the labelling scheme). ( c ) />xylene molecule has a centre of symmetry. < d ) Data from reference 2. 284 N o noticeable distortions in the [100] or [001] directions are observed, indicating that the deviation of the methyl-methyl vector from the straight channel axis is quite small. A possible interpretation of the ell ipsoid shapes is that the energy minimum for the sorbate molecules is somewhat flat and we are seeing some thermal motion of the /^-xylene molecules. A s seen in Figures 8.3 and 8.4, the /(-xylene molecule lies at the intersection with the methyl-methyl axis aligned along the straight channel. The plane of the aromatic ring is tilted away from the a and c axes so that it faces the opening to the zig-zag channel (defined by Si -1 , Si-2, S i -5, Si-6 and Si-9). The /(-xylene molecules form loosely connected chains along [010], with neighbouring molecules in each straight channel related by an inversion centre, and alternating ring orientations in adjacent channels along the c direction (Figure 8.4). The C - C contact distance between terminal (methyl) carbons residing in the same channel is 4.05 A, which is very close to that reported for the high-loaded /(-xylene / Z S M - 5 complex (4.08 A) and indicates the packing along the channels is similar in these two structures. Methyl carbons of molecules residing in adjacent channels are separated by a distance of 11.75 A. The location and rotational orientation of the adsorbed /(-xylene molecules within the framework can be described by the fractional coordinates of the centre of the aromatic ring (x, y, z), and the angles between the methyl-methyl axis and the a, b, and c axes (al, J31, yl respectively), and from a vector normal to the plane of the ring to these axes (a2, 62, and y2). These variables are defined in Figure 8.6. The location and orientation of /7-xylene molecules determined in the present work, together with the corresponding values calculated from the coordinates and cell dimensions of other Z S M - 5 / sorbate systems determined by single crystal X R D are presented in Table 8.6. If the sorbate molecule is centrosymmetric, and the center is coincident with the mirror plane in space group Pnma, there wi l l only be two orientations for the molecules as seen forp-xylene within the straight channels in Figure 8.4. However i f the molecular center is not coincident with the mirror plane, then disorder wi l l be present and there wi l l be four orientations. 285 Table 8.6 Comparison of the locations and orientations ' for different organic molecules adsorbed at the channel intersections in ZSM-5. These were calculated from the unit cell dimensions and fractional atomic coordinates given in the references indicated. Structure^ HLPXY HLPDCB LLPDCB LLPNA LLPXY NAPH Method(c) crystal crystal crystal crystal crystal crystal powder NMR crystal Reference 2 3 4 5 6 this work 24 27 7 X 0.510 0.512 0.486 0.486 0.486 0.484 0.498 0.491 0.486 y 0.238 0.240 0.240 0.253 0.271 0.250 . 0.250 0.250 0.236 z -0.019 -0.025 -0.019 -0.026 -0.030 -0.019 -0.031 -0.041 -0.035 88 88 84 85 84 90 90 90 88 em 7 9 5 7 11 0 0 0 2 97 99 89 84 81 90 90 90 89 can 149 152 47 45 46 51 44 57 40 92 92 93 89 87 90 90 90 90 y2{°) 120 117 137 135 136 140 134 146 130 ( x, y, and z define the fractional atomic coordinates of the aromatic ring center (ignoring substituents) except for napthelene where they describe the molecular center. The angles are defined in Figure 8.6.(b) See Table 6.1 for definitions of the codes describing the different sorbates and loadings in ZSM-5.(c) Structures determined from single crystal X-ray diffraction (crystal), powder X-ray diffraction (powder), or 'H-29Si CPMAS NMR experiments (NMR). For the high-loaded sorbate / Z S M - 5 complexes which have P2/2 /2 / symmetry, only two orientations wi l l be observed. Only the parameters for one of these orientations is given is Table 8.6 since the others are related by the appropriate symmetry operations in each space group. The disorder observed in these cases may be a result o f the symmetry imposed on the system by the space group selected for refinement. The higher symmetry is observed occurs because the framework atoms contribute most of the scattered X-ray intensity. N M R is more sensitive to the local geometry of the individual T-sites and may provide the key to unraveling this pseudo symmetry versus disorder controversy. Comparison of the values given in Table 8.6 reveals that the location and orientation of /7-xylene are similar to that found for other low-loaded Z S M - 5 complexes. In the present work the ring centroid lies exactly on the mirror plane for /^-xylene. This is in agreement with the observation of a single i 3 C N M R resonance for the methyl carbon of the sorbed /7 -xy lene 2 7 (in the high-loaded from the methyl groups are no longer equivalent and four resonances are observed; two for the methyl's in the straight channel and two for those in the zig-zag channels). In all other cases the sorbate molecules are shifted slightly (up to 0.4 A ) from the mirror plane and thus are disordered. The angular rotation of the /7-xylene ring relative to the crystallographic axes is, overall, quite similar to those found for the other low-loaded Z S M - 5 complexes, but some differences are apparent. For /(-xylene the methyl-methyl axis is exactly parallel to the [010] axis (al = yl = 90°, (51 = 0°), compared with deviations of up to 11 0 seen for the long molecular axes of the other sorbates; only naphthalene is so closely aligned to the straight channel axes. a2 and y2 are also slightly higher for the low-loaded p-xylene / Z S M - 5 complex than in any of the other low-loaded structures. Striking differences are seen for the orientation of the aromatic ring plane in the low- and high-loaded sorbate / Z S M - 5 complexes. When the sorbate loading is less than 4 molecules/u.c. a2 is approximately 50° and y2 is nearly 140°. If eight molecules are present then a2 increases to 287 ca. 150° and y2 is reduced by about 20°. This change of almost 100° in al reflects the rotation of the sorbates in the straight channel to have a more favourable interaction with the terminal ring-substituent atoms of molecules present in the zig-zag channels in the high-loaded forms. The elliptical distortion of the straight channels (see Table 8.4) in the high loaded form also reflects the different molecular orientations and occurs in almost the opposite direction to that seen in the low-loaded complexes. 5 ' 7 8.3.3 Comparisons with p-xylene Orientations Determined by Other Methods The orientations and locations proposed from the two previous investigations of the low-loaded /(-xylene / Z S M - 5 complex by powder X-ray diffraction 2 7 and N M R 2 7 are given in Table 8.6. In both cases the centre of the aromatic ring lies on the mirror plane, and the methyl-methyl axis is exactly along the straight channel, in agreement with the present X R D structure. There are small differences in the precise position of the ring centroid relative to the channel (by up to 0.2 A ) , and the angles between the vector normal to the plane of the aromatic ring vary by about 6°. Overall the locations and rotational orientation within the channels determined from N M R and powder X R D investigations are in close agreement with the present structure. N o coordinates were published for the locations found by energy minimization calculations, so the orientational parameters could not be computed for these; however it was reported that the molecules were located at the channel intersections with the C H 3 - C H 3 axis parallel to [010] ."* 8.3.4 Prediction of 2 9 Si Chemical Shifts In previous correlations between chemical shifts and structural parameters derived from framework atoms from X R D determined structures, the limiting factor was the relatively large e.s.d.'s of X R D derived parameters. In the present work the structural parameters have been determined to a high degree of accuracy, and N M R data acquired in a similar temperature range 288 was also available, providing a sensitive test o f the correlations. Four linear correlations were considered: 8 = a [mean Si -Si distance] + b 8.8 8 = a [mean {cos a / (cos a - 1)} ] + b 8.9 8 = a [ c v ] + b 8.10 8 = a [{cos aav I (cos aav - 1)}] + b 8.11 where 8 is the isotropic 2 9 S i chemical shift in ppm referenced to T M S , a is the S i - O - S i angle and aav is the average angle for each T-site. The various geometrical parameters calculated from the coordinates in the present work for these four equations are listed in Table 8 .7 . 2 9 Si M A S N M R spectra were acquired at 193 K and 173 K (Figure 8.1) and linear interpolation was used to estimate the 2 9 S i chemical shifts at 180 K. Only those resonances which could be reliably assigned to specific T-sites (using 2-D I N A D E Q U A T E experiment obtained at 268 K, and spectra obtained at lower temperatures) were included in the fitting. The uncertainty in 5 is estimated to be better than 0.1 ppm. Plots of 8 versus the various structural parameters are presented in Figures 8.7 and 8:8, and the results of linear least-squares fitting of the data are presented in Table 8.8. The regression coefficients are greater than those previously reported and are l ikely a direct result o f the more accurate geometrical parameters determined in the present study. In Figure 8.7(b) the correlation reported in reference 29 for several Z S M - 5 structures is added for comparison (dashed line) and is in close agreement. Some scatter in the data is apparent, particularly for Si-12 and Si-1. The equations derived are in close agreement with those previously reported. However, the correlations are still not reliable enough for complete assignment of all resonances in the spectra, since distinct changes in the chemical shifts are apparent even over relatively small temperature ranges (Figure 8.1) thus it is emphasized that these correlations are not yet good enough to permit unambiguous assignments of resonances in different sorbate / Z S M - 5 systems. 289 Table 8.7 Si chemical shifts and structural parameters for Z S M - 5 loaded with 2.85 molecules of /^-xylene / u.c. at 180 K. T-Site Chemical Shift 5 (ppm) f Mean Si -O-Si angle aav (°) Mean cos a / [cos a - 1] cos a o v / [cos a a v - 1] Mean Si -Si Distance (A) S i l -112.3 150.80 0.4661 0.4661 3.094 Si2 -117.0 156.90 0.4791 0.4911 3.128 Si3 -113.6 151.89 0.4687 0.4709 3.103 Si4 -115.0 154.13 0.4736 0.4804 3.118 Si5 148.35 0.4598 0.4545 3.079 Si6 150.32 0.4649 0.4638 3.085 Si7 148.97 0.4615 0.4575 3.083 Si8 -117.4 157.47 0.4801 0.4931 3.135 Si9 149.38 0.4625 0.4595 3.086 S i lO -109.3 146.80 0.4556 0.4468 3.073 S i l 1 149.38 0.4625 0.4595 3.089 S i l 2 -113.3 150.21 0.4646 0.4634 3.092 T Chemical shifts are referenced to T M S and were estimated from interpolation of spectra acquired at 173 K and 193 K. Only those resonances which could be unambiguously assigned to specific T-sites are listed. Table 8.8 Linear regression analysis o f Si chemical shifts 8 against the various geometric parameters indicated for Z S M - 5 loaded with 2.85 molecules of /?-xylene/u.c. at 180 K. X Linear Regression Correlation Coefficient R2 Mean S i - O - S i angle aav (°) 8 = - 0 . 7 2 X - 4 . 1 2 0.967 Mean cos a 1 [cos a - 1 ] 8 = -317 .52X-35 .14 0.973 cos a a v / [cos aav - 1 ] 8 = -167 .76X-34 .62 0.973 Mean Si -S i Distance (A) 8 = -123.65 X-270.09 0.961 290 0.450 0.455 0.460 0.465 0.470 0.475 0.480 0.485 M e a n cos a / [cos a - 1] F igure 8.7 N M R and X R D correlation diagrams for zeolite Z S M - 5 containing 2.85 molecules of /7-xylene / u.c. at 180 K. Only those N M R resonances which could be unambiguously assigned to specific T-sites are included, (a) Plot of chemical shift 8 versus the mean S i - O - S i angle aav. (b) Plot o f 8 vs. the average of cos a / [cos a - 1 ]. Equations for the linear regressions (solid lines) are given in Table 8.8. The dashed line in (b) is the correlation reported in reference 29 for several Z S M - 5 structures. 291 Figure 8.8 N M R and X R D correlation diagrams for zeolite Z S M - 5 containing 2.85 molecules of /j-xylene / u.c. at 180 K. Only those N M R resonances which could be unambiguously assigned to specific T-sites are included, (a) Plot of chemical shift 5 versus cos a / [cos a - 1] for the average S i - O - S i angle aav. (b) Plot o f 5 vs. the mean S i - S i distance. Equations for the linear regressions (solid lines) are given in Table 8.8. 292 8. 4 SUMMARY AND CONCLUSIONS The structure of Z S M - 5 loaded with 2.85 molecules per unit cell o f p-xylene was determined from refinement of single crystal X-ray diffraction data. This is the first structure determined for a volatile organic sorbed in Z S M - 5 at a controlled loading and was achieved using a specially-designed, purpose-built apparatus. The diffraction data were collected at 180 K using a diffractometer with a C C D detector, and a virtually complete hemisphere of independent Bragg reflections were accumulated, al lowing the most accurate determination of the structural parameters for the Z S M - 5 framework reported to date. The sorbed /^-xylene molecules were located in the straight channels at the intersection with the sinusoidal channels, and have their methyl-methyl axes exactly parallel to [010]. The orientation is in good accord with those previously observed for the other low-loaded Z S M - 5 / sorbate complexes, and agrees closely with those proposed determined from energy minimization calculations,* 2 ' 5 and powder X R D . 2 7 Recent N M R investigations of the low-loaded /^-xylene / Z S M - 5 complex have been utilized to predict the sorbate location and orientation, and the resulting solution corresponds very closely to that determined in the present X R D structure determination. 2 7 These results prove that the N M R techniques described in this thesis can be used to determine the locations(s) and orientation(s) of guests species within the channels of microporous materials such as zeolites. With appropriate precautions and suitable data analysis strategies (for example based on the methods outlined in Chapters 3 and 6), cross polarization, R E D O R , and T E D O R N M R experiments should permit the three-dimensional structure of host-guest structures of sorbates in microporous materials to be determined. In cases when single crystal X-ray diffraction methods are not practical, the techniques developed in this thesis provide powerful and effective tools which have the potential to greatly expand the understanding of these important materials. 293 S U P P L E M E N T A R Y D A T A F O R C H A P T E R 8 The fol lowing supplementary data are listed in Appendix G : Table G . l Anisotropic displacement factors for S i , O and C. Table G.2 Bond lengths in the Z S M - 5 framework. Table G.3 Bond angles in the Z S M - 5 framework. R E F E R E N C E S F O R C H A P T E R 8 7 Diaz, A . C . ; Fyfe, C A . Personal communication. 2 (a) van Koningsveld, H.; van Bekkum, H.; Jansen, J .C. Acta Cryst. 1987, B43, 127. (b) van Koningsveld, H.; Tuinstra, F.; van Bekkum, H.; Jansen, J .C. Acta Cryst. 1989, B45, 423. 3 van Koningsveld, H.; Jansen, J . C ; van Bekkum, H. Acta Cryst. 1996, B52, 140. 4 van Koningsveld, H.; Jansen, J . C ; de Man, A . J . M . Acta Cryst. 1996, B52, 131. 5 Reck, G . ; Mar low, F.; Kornatowski, J . ; H i l l , W.; Caro, J . . / . Chem. Phys. 1996, 100, 1698. 6 van Koningsveld, H.; Koegler, J .H . Microporous Mater. 1997, 9, 71. 7 van Koningsveld, H.; Jansen, J .C. Microporous Mater. 1996, 6, 159. 8 Reischman, P.T.; Schmitt, K .D . ; Olson, D.H. J. Phys. Chem. 1988, 92, 5165. 9 Cheetham, A . K . ; Bu l l , L . M . Catal. Lett.1992,13, 267. 10 Be l l , R .G. ; Lewis, D.W.; Voigt, P.; Freeman, C M . ; Thomas, J . M . ; Catlow, C . R . A . Stud. Surf. Sci. Catal. 1994, 84, 2075. 11 Gies, H.; Marler, B.; Fyfe, C .A . ; Kokotai lo, G.T. ; Feng, Y . ; Cox, D.E. J. Phys. Chem. Solids. 1991,752, 1235. 72 Kokotai lo, G.T. ; Lawton, S.L. ; Olson, D.H.; Meier, W . M . Nature. 1978, 272, 437. 13 Wu , E.L. ; Lawton. S.L. ; Olson, D.H. ; Rohrman, A . C . , Kokotai lo, G.T. J. Chem. Phys. 1979, 83, 2111. 14 van Koningsveld, H. Acta Cryst. 1990, B46, 731. 75 van Koningsveld, H.; Jansen, J . C ; van Bekkum, H. Zeolites 1990, 10, 235. 294 76 Fyfe, C .A . ; Kennedy, G .J . ; DeSchutter, C.T. ; Kokotai lo, G.T. J. Chem. Soc., Chem. Commun. 1984, 541. 77 Strobl, H.; Fyfe, C .A . ; Kokotai lo, G.T.; Pasztor, C.T. J. Am. Chem. Soc. 1987, 709, 4733. 75 Fyfe, C .A . ; Gies, H.; Kokotai lo, G.T. ; Marler, B.; Cox, D.E. J. Phys. Chem. 1989, 94, 3718. 19 Fyfe, C .A . ; Strobl, H.; Gies, H. ; Kokotai lo, G.T. Can. J. Chem. 1988, 66, 1942. 20 Fyfe, C .A . ; Strobl, H.; Kokotai lo, G.T. ; Kennedy, G .J . ; Barlow, G . E . J. Am. Chem. Soc. 1988, 770, 3373. 21 Fyfe, C .A . ; Kokotai lo, G.T. ; Strobl, H.; Gies, H.; Kennedy, G .J . ; Pasztor, C.T. ; Barlow, G . E . in Zeolites as Catalysts, Sorbents and Detergent Builders, p. 827. Karge, H.G. ; Weitkamp, J . Eds. Elsevier, 1989. 22 High-Resolution Solid-State NMR of Silicates and Zeolites. Engelhardt, G . , Miche l , D., John Wi ley and Sons, 1987. 23 Modelling of Structures and Reactivity in Zeolites, Catlow, C .R .A . , (Ed.) Academic Press: London, 1992. 24 Mentzen, B.F; Vigne-Maeder, F. Mat. Res. Bull. 1987, 22, 309. 25 Bosselet, F.; Sacerdote, M . ; Bouix, J . ; Mentzen, B.F. Mat. Res. Bull. 1990, 25, 443. 26 Pickett, S.D.; Nowak, A . K . ; Cheetham, A . K . ; Thomas, J . M . Molec. Simul. 1989, 2, 353. 27 Diaz, A . C , Fyfe, C A . Unpublished work, Chemistry Dept., University of Brit ish Columbia, Canada. 28 Olson, D.H. ; Kokotai lo, G.T. ; Lawton, S.L. ; Meier, W . M . J. Phys. Chem. 1981, 85, 2238. 29 Fyfe, C .A . ; Feng. Y . ; Grondey, H. Microporous Mater. 1993, 7, 393. 30 Smith, J .V . ; Blackwel l , C .S . Nature. 1983, 303, 223. 31 Grimmer, A .R . ; Radeglia, R. Chem. Phys. Lett., 1984, 706, 262. 32 Fyfe, C .A . ; Strobl, H.; Kokotai lo, G.T. ; Pasztor, C.T. ; Barlow, G . E . ; Bradley, S. Zeolites, 1988, 8, 132. 33 Thomas, J . M . ; K l inowski , J . ; Rammdas, S.; Hunter, B .K. ; Teenakoon, D.T.B. Chem. Phys. Lett. 1983, 702, 158. 34 Ramdas, S.; K l inowski , J . Nature 1984, 308, 521. 35 Engelhardt, G . ; Radeglia, R. Chem. Phys. Lett. 1984, 70S, 271. 36 Derouane, E .G. ; Hubert, R.A. Chem. Phys. Lett. 1986, 132, 315. 37 Fyfe, C .A . ; Grondey, H.; Feng, Y . ; Kokotai lo. G.T. J. Am. Chem. Soc, 1990, 772, 8812. 38 Engelhardt, G . ; van Koningsveld, H. Zeolites, 1990, 70, 650. 295 39 Kennedy, G . J . Ph.D. Thesis University of Guelph, 1985. 40 Fyfe, C .A . ; Strobl, H. ; Kokotai lo, G.T. ; Kennedy, G .J . ; Barlow, G .E . J. Am. Chem. Soc. 1988,110, 3373. 41 Baerlocher, C . in "Proceedings of the V l th International Conference on Zeoli tes" 10-15 July, 1983, Reno, Nevada, U S A . Olson, D.H., Bis io, A . (eds) Butterworths, 1984 p. 823-833. 42 SHELXL-97: Program for the Refinement of Crystal Structures. Sheldrick, G . , University of Gottingen, Germany, 1997. 43 Wi lson, A . J . C . Acta Cryst. 1976, A32, 994. 44 Fundamentals of Crystallography. Giacovazzo, C . (Ed.), Oxford University Press, 1992. 45 D*TREK software for SGI Molecular Structure Corporation, 3200 Research Forest Drive, The Woodlands, Texas, T X 77381, U.S.A. http://www.msc.com/ 46 teXsan for Windows 1.01 Molecular Structure Corporation, 3200 Research Forest Drive, The Woodlands, Texas, T X 77381, U.S.A. http://www.msc.com/ 47 International Tables for Crystallography. Hahn, T. (Ed.); K luwer Academic Publishers, Dordrecht, 1993, Volume A . 48 ORTEP-3 for Windows, Johnson, C .K . ; Burnett, M . N . ; Farrugia, L .J . Department of Chemistry, University of Glasgow, U.K. 1998. http://www.chem.gla.ac.uk/~louis/ortep3/ 49 PLATON-98 for Windows, Speck, A . L ; Farrugia, L . J . Department of Chemistry, University of Glasgow, U.K. 1998. http://www.chem.gla.ac.uk/~louis/platon97/ 50 Breck, D.W. Zeolite Molecular Sieves. John Wiley, New York, 1974, pp 636-637. 296 CHAPTER 9 CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK 9.1 S U M M A R Y A N D C O N C L U S I O N S The purpose of the research reported in this thesis was to develop solid-state N M R techniques which could be used to determine the three-dimensional structures of guest-host complexes. In particular, these investigations were directed to developing an experimental protocol and the necessary data analysis techniques to locate guest species within the channels and cages of microporous materials such as zeolites. Although the results reported here are for fluorine-containing guest species in purely siliceous materials, these techniques can be readily extended to other investigate other systems containing spin-1/2 nuclei. The general strategy developed was as follows: First, the resonances in the 2 9 S i M A S N M R spectrum need to be assigned to specific T-sites within the zeolite framework. This can be accomplished using, for example, 2-D I N A D E Q U A T E experiments. The next step is to determine specific internuclear distances between nuclei in the guest species and the framework (Si) atoms. Knowledge of three or more such distances may be sufficient to locate the guest within the channels and cages of the host lattice. The approach adopted in the present work was to use the M A S N M R techniques of cross polarization (CP), R E D O R and T E D O R . In principle, these techniques allow the magnitude of the IS heteronuclear dipolar coupling to be measured, and since this is inversely proportional to the cube of the IS distance, they provide direct methods to measure the necessary distances. 297 Octadecasil, a clathrasil which contains encapsulated fluoride ions, was selected as the model compound for optimizing the experimental techniques, spectrometer configurations, and data analysis methods. 1 9 F - 2 9 S i C P , R E D O R and T E D O R N M R experiments were performed. The Si-F distances between the T - l Si and the fluoride ion in the D 4 R unit determined directly from these three techniques were in excellent agreement with that known from the single crystal X R D structure.' Because of the low natural isotopic abundance of 2 9 S i , and because the closest fluoride-fluoride distance in octadecasil is > 9.3 A , the T - l sil icon / fluoride ion closely approximates an isolated l 9 F - 2 9 S i spin pair. Nonlinear least squares fitting of the C P data was made possible by expressing the equations derived by Hediger et al.2 in terms of Bessel functions. From these experiments it was concluded that when the spin system can be described as an isolated IS spin pair, the distances determined from C P , R E D O R , and T E D O R should be, in principle, of comparable accuracy. However, the three techniques have quite different dependencies on the various relaxation properties of the nuclei in the system being investigated, and this provides some degree of f lexibil i ty for selecting the method(s) best suited to a particular sample. In any case, it is highly recommended that at least two of the techniques be used to validate the results. Because the R E D O R experiment provides normalized data, it can sometimes provide additional information about the number of S spins which are not dipolar coupled to an / spin, which may be useful to determine site occupancies for example. For the T-2 site in octadecasil, the analysis of the experimental data was complicated by the fact that up to four 1 9 F nuclei were dipolar coupled to the 2 9 S i nucleus. However, when the tetrahedral arrangement and partial occupancies (known from the crystal structure) of the D4R units by the fluoride ions was included in the theoretical calculations, good agreement was obtained between the calculated and observed R E D O R and T E D O R dephasing. It was necessary to extend the approach reported 3 for multi-spin R E D O R calculations to permit fitting of the 298 T E D O R data. These results represent the first l 9 F - 2 9 S i R E D O R and T E D O R experiments reported in the literature/ as well as the first multi-spin T E D O R analyses. A series of calculations on a selection of 3-spin, I2S systems was performed to gain insight into the likelihood of being able to obtain reliable distance information from analysis of R E D O R and T E D O R data acquired on systems where little or no information regarding the number of spins, or the geometrical arrangement of these, is available. It was apparent that even for the simple systems studied, it is highly unlikely that direct and unambiguous distance determinations can be obtained. The problem wi l l be compounded when the noise present in experimental data is considered, and more spins and/or relative motions are present. Furthermore, it is possible to obtain erroneous distances i f an isolated spin pair is assumed and multiple spins are in fact present. Thus the best approach wi l l be to try and ensure that the spin system approximates an isolated spin pair as closely as possible, (e.g. by isotopic substitution and dilution in the unlabeled compound), or several isolated spin pairs. If this is not possible, the only alternative is to acquire several R E D O R and T E D O R data sets (with different parameters), then propose a model of the spin system which fully describes the relative geometric arrangement (i.e. with all angles and distances implicit ly defined). Using this model, the theoretical dephasing can be calculated and compared to the experimental data. The model is modified and the calculations re-run until optimal agreement between the calculated and experimental dephasing is obtained for all o f the experimental data sets. With this approach, there wi l l be no direct determinations of distances, but structural information can still be (indirectly) obtained. This method wi l l be most efficient i f constraints can be placed upon the model which limit the possible number of spins and internuclear distances. This may be the case for sorbate molecules in zeolites since the guests must lie within the channel system. The low-loaded form of the p-difluorobenzene / Z S M - 5 complex was chosen as a test case for applying these N M R techniques to a system where no prior information about the 299 location of the sorbate molecules within the channel systems was available. Loading Z S M - 5 with 4 molecules of /?-difluorobenzene per unit cell caused the framework to change from monoclinic (P2i/n.l.l symmetry, 24 T-sites) to a phase having 12 T-sites at temperatures above ca. 293 K . From the appearance of the 2 9 S i M A S N M R spectra, orthorhombic Pnma symmetry is proposed for this phase, as has been reported previously for three other low-loaded, />ara-disubstituted aromatic / Z S M - 5 complexes/" 7 Loadings higher than 4 molecules/u.c. could not be obtained for samples prepared at ambient pressure and temperature, even when excess />difluorobenzene was added. Cool ing the sample below 290 K resulted in a transformation back to a phase having 24 T-sites, which was maintained to the lowest temperatures accessible (215 K ) . The 2 9 S i N M R chemical shifts observed for this phase indicated that it was almost identical to the monoclinic phase adopted by the empty Z S M - 5 framework. Equipment and an experimental protocol were developed which allowed experiments with stable M A S rates to be performed at low temperatures for periods of 2 days or longer. It was found that dry air (rather than nitrogen) should be used as the drive gas for the low temperature experiments, in order to prevent the loss of the oxygen gas from within the sample. The nuclear relaxation times of both the sorbates and framework nuclei are dependent on the concentration of paramagnetic oxygen, becoming significantly longer as the concentration decreases. The success o f ' H - 2 9 S i and l 9 F - 2 9 S polarization transfer observed during C P experiments proves that the sorbate molecules remain within the Z S M - 5 channel system during, and after, this phase transition. The orthorhombic, Pnma and monoclinic, P2i/n.1.1 symmetries proposed for these two phases were subsequently verified and the lattice constants determined from analysis of powder X R D data. A partial assignment of the 2 9 S i resonances to specific T-sites was obtained from analysis of 2-D C P - I N A D E Q U A T E experiments. The relatively high temperature (290 K ) at which the framework changed to adopt the same (monoclinic) symmetry observed for the empty Z S M - 5 indicates that the sorbate-300 framework interactions are much weaker than in the case of the low-loaded /^-xylene / Z S M - 5 complex, which maintains Pnma symmetry to temperatures at least as low as 173 K.* It is anticipated that the transformation to monoclinic symmetry for the Z S M - 5 framework observed in the present case may also occur in other sorbate / Z S M - 5 systems at low temperatures. Two programs were written as part o f the effort to locate p-difluorobenzene within the Z S M - 5 framework. These utilize the TC? values determined from fitting variable contact time C P experimental data, and calculate the heteronuclear second moments as the sorbate molecule is translated (and rotated) through the channels. The program searches for positions and orientations which have linear correlations for the \ITCV and calculated M2 values for a set of silicons. This approach had been successfully used previously to locate the /^-xylene molecules in Z S M - 5 * ' 9 Using these programs, ' H - 2 9 S i and l 9 F - 2 9 S i C P data acquired at 230 K and 235 K respectively were analyzed. It was discovered the sorbate molecules were undergoing slow diffusion that affected the C P , R E D O R and T E D O R data, and thus lower temperatures need to be used. Although the precise position and orientation of the /7-difluorobenzene molecule were not obtained, a location in the straight channel very close to the intersection with the zig-zag channels is consistent with the experimental data. A single crystal o f Z S M - 5 was loaded with a precisely controlled amount of /^-xylene using a purpose-built piece of apparatus developed as part of the present work. The low-loaded form of the /^-xylene / Z S M - 5 complex prepared contained 2.85 molecule/u.c, and single crystal X R D data collected at 180 K was successfully refined in the orthorhombic space group Pnma. The p-xylene molecules were located in the straight channels at the channel intersections, with the methyl-methyl axes aligned parallel to the b axis, in general agreement with the locations and orientations proposed previously from other techn iques.* 7 0 " This structure represents the most accurate determination of the Z S M - 5 framework distances and angles reported to date. In summary, using the N M R techniques (and analysis methods) developed in the present work, in conjunction with the general strategy proposed, determination of the complete 3-301 dimensional structures of sorbate-zeolite complexes is possible. A t the present time however, it is not routine, and care must be taken to ensure that: (/) the spin system approximates isolated spin pairs i f at all possible, (ii) the guest molecules are not moving on the time scale of the dipolar-based N M R experiments. 2 9 S i M A S N M R experiments can provide direct information about the number of T-sites for sorbate / zeolite complexes. When used in conjunction with powder X-ray diffraction data, the space group symmetry, cell parameters, and temperatures at which phase transitions (i f any) occur can be determined. This information is invaluable for determining the best loadings and temperatures for collecting single crystal X R D data. 9.2 SUGGESTIONS FOR FUTURE WORK For the />difluorobenzene / Z S M - 5 complex, additional I N A D E Q U A T E experiments are needed at several temperatures to confirm the preliminary assignment. Further experiments at temperatures lower than 230 K could slow the sorbate diffusion enough that the molecules could be reliably located using C P , R E D O R and T E D O R experiments. Static 2 D N M R investigations of /7-difluorobenzene-</4 in Z S M - 5 could provide information about the nature of the sorbate motions, and be used to probe the temperatures at which these are minimized. Several single crystals of Z S M - 5 loaded with ca. 4 molecules/u.c. of />difluorobenzene have been prepared, and X-ray diffraction data acquired at 180 K and room temperature. A structure determination wi l l be attempted in the near future. The techniques developed in this thesis could be applied to locate sorbates in other zeolite frameworks where highly crystalline, purely siliceous samples are available (e.g. mordenite, Z S M - 1 1 , and ZSM-12) . These techniques may also allow the fluoride ions to be located in other microporous materials synthesized from fluoride-containing media (e.g. the as-synthesized A l P 0 4 s and GaPOs) using l 9 F - 3 1 P C P , R E D O R , and T E D O R . It is important that methods are developed which can be used to determine i f the spin system can be treated as 302 consisting of isolated spin pairs. Although selective isotopic enrichment combined with dilution in the corresponding unlabeled compound sometimes provides a possible solution, it is not always an option. The algorithm used to perform the powder averaging needed to calculate the theoretical dephasing in the present work is very computationally intensive, which significantly hinders fitting experimental multi-spin data within a reasonable time period. Methods which could be implemented to increase the efficiency of the powder averaging include the approaches proposed by Aldermann et al.,'2 Wang and Hanson, " and the recently reported R E P U L S E algorithm.' 7 The measurement of heteronuclear dipolar couplings for isolated IS spin pairs using C P , R E D O R and T E D O R is relatively straightforward. However, once the observed nuclei are coupled simultaneously to two or more spins (i.e. INS spin systems) the determination of unambiguous distance information is virtually impossible without some prior knowledge of (fairly explicit) information regarding both the number of spins, and the relative geometrical arrangement of these. A new technique, 9 -REDOR, has recently been presented" which seeks to reduce these problems, and this should be investigated. The N M R techniques developed in this thesis to determine internuclear distances from measurements of the heteronuclear dipolar interactions may be applied to other systems containing spin-1/2 nuclei. Related techniques have been developed for non-spin 1/2 systems,'*5''7 which may allow cations such as 2 3 N a to be located, or framework-sorbate distances to be obtained in aluminium-containing materials. There are also several techniques for measuring homonuclear dipolar coupl ings," 5 ' 8 and these may provide a means to determine sorbate-sorbate distances, and investigate the problem of disordered sorbate molecules, which wi l l be very difficult or impossible to solve by diffraction techniques.. One of the most important areas which offers the potential for advancing the current knowledge is to enlarge the database of reliable sorbate / zeolite structures. A t present time, single crystal X R D structures still represent the most unambiguous method for determining the 303 positions and orientations of guest species within microporous materials. However, the experimental protocol developed in this thesis are at the stage where it is viable to determine the three-dimensional structures of sorbate / zeolite complexes from solid-state N M R investigations. Using the special apparatus developed in the present work (Chapter 2), it is now possible to load single crystals of these materials with precisely controlled amounts of volatile organic sorbates (or even mixtures). High-quality X R D data can be collected at low temperatures using a diffractometer equipped with C C D or image plate detectors, and the structures determined. A t the present time high quality single crystals of Z S M - 5 and zeolite A are available which are large enough for single crystal X-ray diffraction studies. Furthermore the synthesis of single crystals of A I P 0 4 - 5 and mordenite having dimensions suitable for single-crystal X R D studies have been reported. 7 9 These single crystal structure determinations should be carried out. 304 R E F E R E N C E S F O R C H A P T E R 9 1 Caullet, P.; Guth, J . L.; Hazm, J . ; Lambl in, J . M . ; Gies, H. Eur. J. Solid State Inorg. Chem. 1991 , 28, 345. 2 (a) Hediger, S. Ph.D. Dissertation, Eidgenossische Technische Hochschule, Zurich, Switzerland, 1997. (b) Hediger, S.; Meier, B .H . ; Ernst, R.R Chem. Phys. Lett. 1995, 240, 449. 3 Goetz, J . M . ; Schaefer, J . J. Magn. Reson. 1997,127, 147. 4 Fyfe, C . A . ; Lewis, A .R . ; Chezeau, J - M . ; Grondey, H. J. Am. Chem. Soc. 1997, 119, 12210. 5 van Koningsveld, H.; Jansen, J . C ; de Man, A . J . M . Acta Cryst. 1996, B52, 131. 6 van Koningsveld, H.; Koegler, J .H . Microporous Mater. 1997, 9, 71. 7 Single crystal X R D structure of low-loaded /^-xylene / Z S M - 5 complex. (Chapter 8). 8 Diaz, A . C , Fyfe, C A . Unpublished Results, University of British Columbia, Canada. 9 Fyfe, C A . Diaz, A . C ; Lewis. A . R . ; Chezeau, J - M . ; Grondey, H.; Kokotai lo, G.T. in Solid-State NMR Spectroscopy of Inorganic Materials. Fitzgerald, J .J . (Ed.) ACS Symposium Series. In Press. 10 Mentzen, B.F; Vigne-Maeder, F. Mat. Res. Bull. 1987, 22, 309. 11 Reischman, P.T.; Schmitt, K .D. ; Olson, D.H. J. Phys. Chem. 1988, 92, 5165. 12 Alderman, D.W.; Solum, M.S. ; Grant, D . M . J . Chem. Phys. 1986, 84, 3717. 13 Wang, D.; Hanson, G.R. J. Magn. Reson. Ser. A. 1995, 117, 1. 14 Bak, M . ; Nielson, N .C . J. Magn. Reson. 1997, 125, 132. 15 Gul l ion, T.; Pennington, C . H . Chem. Phys. Lett. 1998, 290, 88. 16 Bennett, A . E . ; Gr i f f in, R .G. ; Vega, S. in Encyclopedia of Nuclear Magnetic Resonance. Grant, D .M . ; Harris, R.K. (Eds.) John Wi ley and Sons, 1996. p. 2390. 17 (a) Schmidt, A . ; M c K a y , R.A. ; Schaefer, J . J. Magn. Reson. 1992, 96, 644. (b) Gul l ion, T. Chem. Phys. Lett. 1995, 246, 325. (c) Grey, C P . ; Veeman, W.S. ; Vega, A . J . J. Chem Phys. 1993, 98, 7711. 18 (a) Griff iths, J . M . ; Bennett, A . E . ; Gr i f f in, R.G.in NMR Basic Principles and Progress, 1994, 33, .1 (b) Lee, Y . K . ; Kurur, N.D. ; Helmle, M . ; Johannessen, O .G . ; Nielsen, N . C ; Levitt, M . H . Chem. Phys. Lett. 1995, 242, 304. (c) Bennett, A . E . ; Wel iky, D.P.; Tycko, R. J. Am. Chem. Soc. 1998,120, 4897. (d) Sun, B.-Q., Costa, P.R.; Kocisko, D.; Lansbury, P.T.; Gri f f in, R .G. J. Chem. Phys. 1995,102, 702. (e) Rayleigh, D.P.; Levitt, M .H . ; Gri f f in, R.G. Chem. Phys. Lett. 1988, 146, 71. (f) Zhu, E.; K lug , C .A . ; Schaefer, J . J. Magn. Reson. Ser. A. 1994,108, 121. (g) Gul l ion, T.; Vega, S. Chem. Phys. Lett. 1992,194, 423. 19 Linder, G . - G . ; Mar low, F.; Hoffmann, K. Proceedings of the 11th International Zeolite Conference, Seoul, Korea, August 12-17 1996. 305 APPENDIXA SCHEMATICS OF NMR SPECTROMETER CONFIGURATIONS Three different configurations of the Bruker M S L 400 N M R Spectrometer were used to perform the experiments reported in this thesis. Schematics showing the connections, amplifiers, synthesizers, filters, and attenuators are presented in this appendix. 306 Schematics for the three spectrometer configurations are given in Figures A l , A 2 and A .3 . Abbreviations used in these figures are listed in Table A . l . Many of the experiments performed in the current investigations required non-standard configurations because F3 could not be directly observed, which meant either the F1 (range 10-400.13 M H z ) or the F2 (400.13 M H z only) receivers had to be utilized. Figure A . l Schematic o f set-up used for 2 9 S i spectroscopy with high power ' H decoupling, and for 1 H - 2 9 Si cross polarization experiments. Figure A .2 Schematic o f set-up used for 1 9 F - 2 9 S i C P , R E D O R , and T E D O R N M R experiments with mixing of F2 and F3 to generate the 2 9 S i frequency. The phase control of the 2 9 S i signal was achieved using a single (constant) r.f. phase for F3 and varying the F2 phase. , 9 F could be observed directly using the F l receiver (with F l frequency set to 376.434 M H z ) i f the appropriate connections to the F2 preamplifier insert ( 'H / l 9 F ) were made. Figure A .3 Schematic o f set-up used for 1 9 F - 2 9 S i C P , R E D O R , and T E D O R N M R experiments without the need for frequency mixing. The l 9 F frequency was generated by tripling F3 and this means that the r.f. phases were also tripled (see Table A.2). The phase cycl ing used in the pulse programs needed to take this into consideration. I 9 F could be observed using the F l receiver i f the appropriate connections to the F2 preamplifier insert ( 'H / 1 9 F) were made, and the F3 carrier frequency (SFF3) and offset (03) were set to one-third of those for F l (SF and O l respectively). In this case, these frequencies had to be multiples of 100 Hz, as required by the specifications of the F3 synthesizer (Programmed Test Sources PTS-250). 307 Table A . l Abbreviations used in the Spectrometer Configuration Schematics. Abbreviation Meaning B P Band Pass E X T S T D External Standard H P High Power INT S T D Internal Standard L P Low Pass R E J Reject R F Radio Frequency Table A.2 Phases of the F3 signal before and after tripling. B E F O R E Tripl ing A F T E R Tripl ing +X (0°) +X (0°) +Y (90°) - Y (270°) - X (180°) - X (540°= 180°) - Y (270°) +Y (810°= 90°) 308 PTS-101 SYNTHESIZER (F2) PTS-200 SYNTHESIZER (F1) E X T INT 10 MHz STD STD O U T 80 MHz MAIN CONSOLE (BACK) MAIN O U T P U T 10 MHz IN ± Fl M O D U L A T O R From F1 L O W Fl Driver POWER RF IN • 3 53 I HIGH T O HP F2 I P O W E R CABINET RF IN FromFl From F2 RECEIVER IN • 6 13 ^ 80 MHz INPUT INPUT PULS PULS 1 2 From From Fl F2 T R A N S T R A N S (FRONT) BROAD BANDED POWER AMPLIFIER (Fl) POWER AMPLIFIER (F2) TUNED 70-90 TO MHz 400.13 MHz > H / 1 9 F FROM BACK (#11) PROBE 400 MHz REJ 5 2 9Si 'H 80 MHz LP 80 MHz HIGH POWER ATTENUATOR 400 MHz 3dB Figure A . l Schematic o f M S L 400 spectrometer configuration used to perform ' H / 2 9 S i experiments. The ' f l channel connections shown are those for high power decoupling or cross polarization. 309 PTS-250 SYNTHESIZER (F3) PTS-101 SYNTHESIZER (F2) PTS-200 SYNTHESIZER (F1) EXT INT 10 MHz 10 MHz STD STD OUT M A I N IN | | # OUTPUT ± EXT INT 10 MHz 10 MHz STD STD OUT M A I N IN OUTPUT F3 MODULATOR FREQUENCY DOUBLER 80- 160 160-320 MHz MHz • IN • OUT EXT INT 10 MHz STD STD OUT F2 MODULATOR MAIN OUTPUT • 10 MHz IN i Fl MODULATOR 160 MHz 400 MHz 376 MHz MAIN CONSOLE (BACK) From F1 LOW Fl Driver POWER RF IN 2"""~" —"*3 ' 53 HIGH TO HP F2 POWER CABINET RF IN • • • 4 3 44 RECEIVER IN From F1 From F2 • 13 7 70-90 NOT MHz USED • 400 80 MHz MHz REJ LP Figure A.2 Schematic of M S L 400 spectrometer configuration used to perform l 9 F / 2 9 S i experiments with mixing. The 2 9 S i frequency (79.495 M H z ) was generated by mixing F2 (400.13 M H z ) with a frequency-doubled F3 signal (160.3125 M H z ) . The 2 9 S i signal was then unmixed and observed at 400.13 M H z . The 1 9 F frequency (376.434 M H z ) was generated directly. 310 PTS-250 SYNTHESIZER (F3) PTS-101 SYNTHESIZER (F2) PTS-200 SYNTHESIZER (F1) E X T INT 10 M H z S T D S T D O U T M A I N • O U T P U T 10 M H z IN E X T INT 10 M H z S T D S T D O U T I E X T INT 10 M H z S T D S T D O U T M A I N O U T P U T » 10 M H z IN I N P U T O U T P U T BRUKER TRIPLER AND 20 W AMPLIFIER I N P U T O U T P U T HIGH POWER CABINET (BACK) I N P U T I N P U T P U L S P U L S 1 2 F rom I F rom F l 1 F2 T R A N S V T R A N S (FRONT) B R O A D B A N D E D P O W E R A M P L I F I E R ( F l ) P O W E R A M P L I F I E R (F2) T U N E D 7 0 - 9 0 T O M H z 376.4 M H z 80 MHz TEKTRONIX 2465 OSCILLOSCOPE F l M O D U L A T O R 125 MHz 80 MHz MAIN CONSOLE (BACK) I 376 MHz 80 MHz F rom F l L O W F l Dr iver P O W E R RF IN ^» • 3 53 j H I G H T O H P F2 X P O W E R C A B I N E T RF IN • * ^ 3 44 F r o m F l F rom F2 R E C E I V E R IN • • > 6 7 / 13 PREAMPLIFIER Fl F2 < H / 1 9 F PROBE FROM BACK (#11) 80 MHz PROBE FILTERS OLEKTRON DIRECTIONAL COUPLER RF R F IN O U T F W D R E V • 80 MHz 400 80 M H z M H z R E J L P 19f 376 MHz NARDA 3020A DIRECTIONAL COUPLER R F F W D R E V R F I N • • O U T Figure A.3 Schematic of MSL 400 spectrometer configuration used to perform 1 9 F / 2 9 Si experiments without mixing. The 1 9 F frequency (376.434 MHz) is obtained by tripling the F3 frequency (125.478 MHz) and amplifying it enough to drive the high power amplifier (tuned to 376.434 MHz). The reflected power could be monitored during the experiment with the oscilloscope. 311 A P P E N D I X B PULSE AND AUTOMATION PROGRAMS This appendix contains a compilation of the pulse and automation programs written to perform the N M R experiments reported in this thesis. They are written for a Bruker MSL-400 running D I S M S L 9 1 . Details of the command and programming structure may be found in the D I S M S L Manual (version 911101): Bruker Analytische Bruker Instruments, Inc. Messtechnik G M B H Fortune Drive Silberstrifen Manning Park D-7512 Rheinstetten 4 Bi l ler ica, M A 01821 Germany U.S.A. Pulse programs are included for the three spectrometer configurations shown in Appendix A : (/) ' H on F2 (400.13 M H z ) and 2 9 S i (79.495 M H z ) on F l , (//) 2 9 F on F l (376.434 M H z ) and 2 9 S i obtained by mixing F2 with (frequency-doubled) F3, and (iii) 2 9 S i on F l with l 9 F obtained by tripling and amplifying F3. The programs include examples of scripts compiled to measure pulse lengths, relaxation times, and to acquire C P , R E D O R , T E D O R , and I N A D E Q U A T E spectra. Several automation programs used to acquire or process the spectral files, and to calculate delays for R E D O R and T E D O R experiments are also given. Standard pulse programs available with the D I S M S L software have not been included. A complete listing of the filenames and a brief description of the specific function of the each program script is given below. 312 B . l INDEX O F P R O G R A M S B . l . l Single Nucleus Experiments H S O L I D C . P C One-pulse experiment for Fl. H Q U A D F 2 F . P C One-pulse experiment for F2/F3 with mixing of F2 and F3. L Q U A D F 3 . P C One-pulse experiment for F3 with frequency tripling on F3. B.l.2 Pulse Length Determination L V D 1 . A U M Automation to vary pulse length DI. L90FS1.PC Measurement of F2/F3n/2-pulse using CP from tripled F3. LI 80FS1.PC Measurement of F2/F3 n-pulse using CP from tripled F3. B.l.3 Relaxation Time Measurements C P T O N E . P C Measurement ofFl T\ using CP from F2. HCPT1 R H O . P C Measurement ofFl Tp using CP from F2. B.1.4 Cross Polarisation Experiments H C P C Y C L . P C CP from F2 to Fl with different F2 power during CP and decoupling. L V D . A U M Automation to vary contact time (VD) using a variable delay list. L F S I C P D . P C CP from F3 (tripled) to Fl with decoupling of F3 during acquistion. B.l.5 I N A D E Q U A T E Experiments HIN A D M A S . P C Program to acquire 2-D INADEQUA TE using CP from F2 to Fl. L I N A D 2 D . P C Program to acquire 2-D INADEQUATE on Fl without CP. H 2 D A Q . A U M Automation to acquire 2-D INADEQUATE serial file. H C O M B I N E . A U M Automation to add two .SER files (e.g. two INADEQUATE FID's). L A D D S M X . A U M Automation to add two .SMXfiles (e.g. two INADEQUATE plots). 313 B.1.6 R E D O R Exper iments L R E D S I F . P C REDOR experiment with all dephasing pulses on Fl (unobserved) and simple90-T-l80-Tspin-echo sequence on F2/F3 (observed). All dephasing pulses are postioned at 1/2 of the rotor cycle. L R E D C A L . A U M Automation to calculate delays for LREDSIF.PC from pulse lengths and spinning speed. L R E D O R . A U M Automation to acquire series of REDOR experiments using LREDF3F1.PC or LREDSIF.PC by reading in offsets for Fl from offset list. L R E D F 3 F1. PC REDOR experiment with dephasing pulses on F2/F3 (observed) and single 180 pulse on unobserved Fl with intialpresaturation on F2/F3. All dephasing pulses are postioned at 1/2 of the rotor cycle. L R E D C A L 2 . A U M Automation to calculate delays for LREDF3F1.PC from pulse lengths and spinning speed. L R E D 1 .PC So REDOR experiment dephasing pulses on F3 (tripled) with CP from F3. All dephasing pulses are postioned at 1/2 of the rotor cycle. L R E D 2 . P C S] REDOR experiment dephasing pulses on F3 (tripled) with CP from F3. All dephasing pulses are postioned at 1/2 of the rotor cycle. L R E D C A L 5 . A U M Automation to calculate delays for LRED1.PC and LRED2.PC from pulse lengths and spinning speed. L R E D F I D . A U M Automation to acquire series of REDOR experiments using LRED1.PC and LRED2.PC. B.1.7 T E D O R Exper iments L T E D F 1 F2.PC TEDOR experiment from Fl to F2/F3 with dephasing pulses on F2/F3 BEFORE transfer and on Fl AFTER transfer. All dephasing pulses positioned at 1/4 and 3/4 of the rotor cycle. T E D O R C A L . A U M Automation to calculate delays for LTEDF1F2.PC from pulse lengths and spinning speed. LIC4. A U M Automation to vary m (increment C4), the number of rotor cycles AFTER coherence transfer with a fixed number of rotor cycles BEFORE transfer. LIC1 . A U M Automation to vary n (increment CI), the number of rotor cycles BEFORE coherence transfer with a fixed number of rotor cycles AFTER transfer. 314 L T E D M O V B . P C TEDOR experiment from Fl to F2/F3 with dephasing pulses on F2/F3 BEFORE coherence transfer and on Fl AFTER transfer. Pulses BEFORE transfer can be MOVED (e.g. to 1/3, 2/3 of each rotor cycle using TEDCAL13. AUM). Pulses AFTER transfer are at 1/4 and 3/4 of each rotor cycle. T E D C A L 1 3 . A U M Automation to calculate delays for LTEDMOVB.PC with pulses BEFORE transfer at 1/3,2/3 and 1/4, 3/4 of each rotor cycle AFTER.. L T E D M O V A . P C TEDOR experiment from Fl to F2/F3 with dephasing-pulses on F2/F3 BEFORE transfer and on Fl AFTER transfer. Pulses AFTER transfer can be MOVED (e.g. to 1/5, 4/5 of each rotor cycle using TEDCAL15.A UM). Pulses BEFORE transfer are at 1/4 and 3/4 of each rotor cycle. T E D C A L 1 5 . A U M Automation to calculate delays for LTEDMOVA.PC with pulses BEFORE coherence transfer at 1/4,3/4 and 1/5, 4/5 of each rotor cycle AFTER.. L R E F T E D . P C 1-D refocussed TEDOR using transfer from F3 to Fl and tripling of F3. All dephasing pulses positioned at 1/4 and 3/4 of the rotor cycle. L R T C A L . A U M Automation to calculate delays for LREFTED.PC from pulse lengths and spinning speed. 315 B.2 P R O G R A M L I S T I N G S B.2.1 Single Nucleus Exper iments ; HSOL IDC.PC ; ONEPULSE ACQUISITION WITH PHASE CYCLING ; (RING DOWN DELAY IN DEPENDANT OF DW) PROT F2 START, Dl [Fl @PLS1 RGATE] D3 [STA RGATE] AQ LOOP C4 TIMES DO END LOOP ++PLS1 GOTO START ; PULSE WITH PHASE LIST 1 ; RING DOWN DELAY AND TRIGGER ; ACQUISITION BEGIN LISTS PLS1, +X-Y-X+Y RLS, +X -Y -X +Y END LISTS ; RECEIVER MODE : RPN OR QPN ; TRIGGER MODE : NT H Q U A D F 2 F . P C CREATION OF FREQUENCY BY MIXING OF F2 AND F3 ONEPULSE ACQUISITION WITH QUADRATURE PHASE CYCLE PROT F2 START, Dl [F3 +X F2 PLS1A RGATE] D3 [STA RGATE] AQ DO RING DOWN DELAY AND TRIGGER ACQUISITION RECYCLE DELAY GOTO START BEGIN LISTS PLS1, +X-Y-X+Y RLS, +X -Y -X +Y END LISTS RECEIVER MODE : RPN OR QPN TRIGGER MODE : NT REC:F2 , DECOUPLER MODE DO 316 ; LQUADF3.PC ; ONEPULSE ACQUISITION ON F3 USING TRIPLER ; TRIPLING MEANS +Y AND -Y SWAPPED ; WITH QUADRATURE PHASE CYCLE PROT F3 START, Dl [F3 PLS1A RGATE] D3 [STA RGATE] AQ DO GOTO START BEGIN LISTS PLS1, +X+Y-X-Y RLS, +X -Y -X +Y END LISTS ; RECEIVER MODE : RPN OR QPN ; TRIGGER MODE : NT ; MUST SET REC:F1, 03 = 01 / 3, SFF3 = SF /3 IN 100 HZ STEPS RING DOWN DELAY AND TRIGGER ACQUISITION RECYCLE DELAY 317 B.2.2 Pulse Length Determination ; LVD1.AUM ; TO INCREMENT Dl TO MEASURE PULSE LENGTHS ; USE WTH E.G. HSOLIDC.PC ; A LEWIS JUNE 5 1996 D1=2U ; INITIAL Dl D16=1U ; INCREMENT RF#1.001 1 ZE VDEL = Dl GO WR#1 IF #1 D1=D1 + D16 ; INCREMENT Dl BY ADDING D16 IN=1 ; LOOP TO 1 NE TIMES EXIT L90FSI.PC CROSS POLARIZATION PULSE SEQUENCE WITH PHASE ALTERNATION CP FROM F3 TO Fl, OBSERVE Fl TRIPLER MEANS F-19 BY F3 HAS +Y AND -Y INTERCHANGED DETERMINATION OF 90 DEG Fl PULSE A. LEWIS FEB 6 1997 PROT XT START, 30U Dll [F3 PLS1A] D5 [F3 -Y Fl PLS2A RGATE] 2U [RGATE] Dl [Fl @PLS3 RGATE] SOURCE 90 DEGREE CONTACT PULSE 2 US SWITCHING DELAY Fl 90 DEG PULSE ; NOTATION IMPORTANT FOR SMALL PULSES (> 0.7 US) D3 [RGATE STA] AQ DO ++ PLS3 GOTO START DEAD TIME DELAY USE NT FOR ACQUISITION INCREMENT PULSE LIST 3, AND RECYCLE DELAY BEGIN LISTS PLS1, +X-X PLS2, +X +X +Y +Y -X -X -Y -Y PLS3, -Y -Y +X +X +Y +Y -X -X RLS, +X -X +Y -Y -X +X -Y +Y END LISTS ; RECEIVER MODE : RPN, TRIGGER MODE : NT ; DECOUPLER MODE: DO, NS=8*N 318 L180FSI.PC CROSS POLARIZATION PULSE SEQUENCE WITH PHASE ALTERNATION DETERMINATION OF 180 DEG Fl PULSE WITH CP FROM F3 FOR F-19 ON F3 SO TRIPLER -Y AND +Y INTERCHANGED A. LEWIS FEB 6 1997 PROT XT START, Dll [F3PLS1A] D5 [F3 -Y Fl PLS2A RGATE] 2U DI [Fl @PLS3 RGATE] ; NOTATION IMPORTANT FOR SMALL PULSES (> 0.7 US) 2U SOURCE 90 DEGREE CONTACT PULSE 2 US SWITCHING DELAY OBSERVED 90 DEG PULSE D2 D3 AQ DO [Fl @PLS3 RGATE] [RGATE STA] ++ PLS3 OBSERVED 180 PULSE DEAD TIME DELAY USE NT FOR ACQUISITION INCREMENT PULSE LIST 3, AND RECYCLE DELAY GOTO START BEGIN LISTS PLS1, +X-X PLS2, +X +X +Y +Y -X -X -Y -Y PLS3, -Y -Y +X +X +Y +Y -X -X RLS, +X -X +Y -Y -X +X -Y +Y END LISTS RECEIVER MODE : RPN TRIGGER MODE : NT DECOUPLER MODE: DO NS=8*N 319 B.2.3 Relaxat ion T ime Measurements ; CPTONE.PC ; TI RELAXATION USING CP FROM F2 TO Fl ; SEE TORCHIA D.A., J.M.R., 30, (1978), 613-616 PROT XT START, DO [RGATE] ; RELAXATION D11 [F2 PLS1A] ; 90 DEG. PROTON PULSE D5 [Fl +XF2-Y RGATE] ; CONTACT PULSE DI [Fl +Y] ; 90 DEG. Fl PULSE LOOP 1000 TIMES ; FOR LONG TI VD ;VAR DELAY SET IN MILL1SECS IN VD LIST END LOOP ; THUS GET VD IN SECONDS DI [Fl PLS2A RGATE] ; RECOVERY PULSE D3 [F2 -Y RGATE STA] ; DEAD TIME D7 [F2 -Y] ; OBSERVATION GOTO START BEGIN LISTS PLS1, +X-X PLS2, +X+X+Y+Y-X-X-Y-Y RLS, +X -X +Y -Y -X +X -Y +Y END LISTS ; SET RPN, NT, USE NS = 8*N ; HCPT1RHO.PC ; TO MEASURE Fl Tl-RHO USING CP FROM F2 TO Fl ; WITH INVERSION OF SPIN TEMPERATURE PROT XT START, Dll [F2 @PLS1] ; F2 90 DEGREE VD [F2 -Y RGATE] D5 [F2 -Y Fl @PLS2 RGATE] ; CONTACT TIME D3 [F2 -Y STA RGATE] D7 [F2 -Y] ; USE NT FOR ACQUISITION DO ++PLS1 ++PLS2 ; RECYCLE DELAY GOTO START BEGIN LISTS PLS1, 4(+X)4(-X) PLS2, +X-Y-X+Y-X+Y+X-Y RLS, +X -Y -X +Y END LISTS ;RECEIVER MODE: RPN, TRIGGER MODE NT ;DECOUPLER MODE DO, NS=8*N 320 B.2.4 Cross Polarization Experiments HCPCYCL.PC CROSS POLARIZATION PULSE SEQUENCE POLARIZATION TRANSFER FROM F2 TO Fl WITH SPIN TEMPERATURE INVERSION DECOUPLER POWER LEVEL CAN BE CHANGED [DECPL=S1] [F2 @PLS1] [F2 -Y Fl @PLS2 RGATE] [F2 -Y STA RGATE DECPL=S2] [F2 -Y] ++PLS1 ++PLS2 PROT XT START, 10U Dl 1 D5 D3 D7 DO GOTO START BEGIN LISTS PLS1, 4(+X)4(-X) PLS2, +X -Y -X +Y -X +Y +X -Y RLS, +X -Y -X +Y END LISTS ; RECEIVER MODE: RPN, TRIGGER MODE: NT ; DECOUPLER MODE: DO, NS=8*N ; PROTON 90 DEGREE ;CONTACT TIME ; USE NT FOR ACQUISITION ; RECYCLE DELAY ; LVD.AUM ; READ IN VDEL VALUE FROM VD LIST ; AND CHECK VDEL IS LESS THAN D16 SO DON'T FRY ANYTHING ; FOR USE WITH LFSICPD.PC OR ANY CP PROG WITH D17 DELAY INCLUDED ;RF # 1.026 ; SET FILE EXTENSION 1 ZE 2 VD ; READ IN NEXT VDEL VALUE FROM VD LIST D17 = VDEL ; NOW CHECK VDEL IS OK D16= 101M ; MAXIMUM ALLOWABLE CONTACT TIME D17 = D16-D17 ; IF D17<0 SHOULD STOP ; MUST HAVE A DELAY D17 IN THE PULSE PROG !!!! 3 GO 4WR#1 ; WRITE FILE 5 IF #1 ; INCREMENT EXTENSION 6 1N=1 ; LOOP TO START NE TIMES EXIT 321 LFSICPD.PC CROSS POLARIZATION FROM F3 TO Fl FOR F19 TR1PLER AMP WITH DECOUPLING OF F3 DURING ACQUISITION TRIPLING OF F3 MEANS -Y = +Y; +Y = -Y PULSE SEQUENCE WITH QPN AND INVERSION OF SPIN TEMPERATURE A. LEWIS AUG 8 1997 USE WITH LVD.AUM TO RECORD VARIABLE CONTACT TIME GOTO START BEGIN LISTS PLS1, 4(+X) 4(-X) PLS2, +X -Y -X +Y -X +Y +X -Y RLS, +X -Y -X +Y END LISTS ; RECEIVER MODE: RPN ; REC=F1 ; TRIGGER MODE NT ; NS=8*N PROT XT START, D17 Dll [F3 @PLS1] VD [F3 +Y Fl @PLS2 RGATE] D3 [F3+Y STA RGATE] D7 [F3-Y] DO ++PLS1 ++PLS2 DELAY TO TRAP LONG VD VALUES SOURCE 90 DEGREE CONTACT TIME TRIGER RECEIVER DECOUPLE DURING ACQUISITION RECYCLE DELAY 322 B.1.4 I N A D E Q U A T E Exper iments ; H I N A D M A S . P C ; CP I N A D E Q U A T E PULSE PROGRAM FOR CPMAS SPECTROSCOPY ; H.GRONDEY A N D R.BENN ; MPI FUER K O H L E N F O R S C H U N G , M U E L H E I M A.D.RUHR PROT N O N E START, 10U [DECPL=S1] D1I [F2 PLS1 A RGATE] D5 [Fl PLS3 A F2 @PLS2 RGATE] D6 [DECPL=S2 F2 @PLS2 RGATE] ; (2N+1V4J D E L A Y D2 [Fl PLS5 A RGATE] ; 180 D E G R E E PULSE D6 [F2 @PLS2 RGATE] DI [Fl PLS4 A RGATE] D4 [F2 @PLS2 RGATE] ; 3U D E L A Y D10 [Fl PLS6 A RGATE] D3 [F2 @PLS2 STA RGATE] D7 [F2 PLS2A] DO [RGATE] G O T O START BEGIN LISTS PLS1, 32(+X-X) PLS2, -Y PLS3, 8 (-Y) 8 (+X) 8 (+Y) 8 (-X) PLS4, 8(+Y) 8(-X) 8(-Y) 8(+X) +X +X +X +X +X +x +x +x +Y +Y +Y +Y +Y +Y +Y +Y -X -X -X -X -X -X -X -X -Y -Y -Y -Y -Y -Y -Y -Y PLS5, +X +X +X +X -X -X -X -X +Y +Y +Y +Y -Y -Y -Y -Y +X +Y -X -Y +X +Y -X -Y -X -Y +X +Y -X -Y +X +Y +X -Y -X +Y PLS6, RLS, END LISTS ; RECEIVER PHASE: RPN, NS=64*N 323 LINAD2D.PC INADEQUATE PULSE PROGRAM FOR Fl DECOUPLING F3 A. LEWIS MAY 6 1998 AFTER H.GRONDEY AND R.BENN MPI FUER KOHLENFORSCHUNG, MUELHEIM A.D.RUHR SEE BAX ET AL J.A.C.S. (1980) 102, 4829 PROT Fl START, Dl [Fl PLS1A RGATE] ; INITIAL 90 D6 [F3 +X RGATE] ; (2N+1 )/4J DELAY D2 [Fl PLS3A RGATE] ; 180 DEGREE PULSE D6 [F3 +X RGATE] Dl [Fl PLS2A RGATE] D4 [F3 +X RGATE] ; 3U DELAY D10 [Fl PLS4A RGATE] ; 135 DEGREE PULSE D3 [F3 +X STA RGATE] AQ [F3 +X] DO [RGATE] GOTO START BEGIN LISTS PLS1, 8 (+X) 8 (+Y) 8 (-X) 8 (-Y) PLS2, 8 (+X) 8 (+Y) 8 (-X) 8 (-Y) PLS3, +X +X +X +X -X -X -X -X +Y +Y +Y +Y -Y -Y -Y -Y PLS4, +X +Y -X -Y +X +Y -X -Y -X -Y +X +Y -X -Y +X +Y RLS, +X -Y -X +Y END LISTS ; RECEIVER PHASE: RPN, USE NT, NS = 32 * N ; SET SW1=SW2, SI=TD, USE H2DAQ.AUM TO INCREMENT D4 ; SET ND4=1 SO D4 INCREMENTED BY IN FROM 3U ONCE EACH EXPT 324 ; H 2 D A Q . A U M ; STANDARD 2D ACQUISITION PROGRAM D4 = 3U ;RESET T 0 3U! 1 Z E 2 G O 3 WR#1 4 IF #1 5 14 6 IN=1 7 EXIT ; H C O M B I N E . A U M ; T O A D D T W O SERIAL FILES ; FILES #1 + #3 = #4 A R E SERIAL FILES ; SET DC=1 SO FILES A R E A D D E D 1 RE #1 ; FIRST SERIAL FILE WR #2 ; T E M P O R A R Y 1D FILE RE #3 ; S E C O N D SERIAL FILE A T #2 WR#4 ; O U T P U T FILE IF #1 IF #3 IF #4 2 IN=1 EXIT ; L A D D S M X . A U M ; T O A D D T W O . S M X 2D FILES ; FILES #1,3 A N D 4 A R E .SMX FILES!!! ; FILE # 2 (temporary file) must be normal file e.g. junk ; SO A D D .SMX T O T H E FILENAMES W H E N ENTERING T H E M ; SET DC = 1 SO A D D FILES ! ; SET N E E Q U A L T O SI 1 SO C O R R E C T N U M B E R OF ROWS 1 RSR#1 ; READ SUB ROW WR #2 ; WRITE T E M P O R A R Y SUB ROW FILE RSR #3 ; READ S E C O N D S M X FILE A T #2 ; A D D T W O SUB ROWS WSR #4 ; O U T P U T S M X FILE IF # 1 ; INCREMENT FILE EXTENSIONS IF #3 IF #4 2IN=1 ; LOOP T O 1 N E TIMES EXIT 325 B.2.6 REDOR Experiments LREDSIF.PC A LEWIS OCT 24 1995 1-D REDOR PULSE SEQUENCE FOR Fl - F2/F3 FREQUENCIES, E.G. F-19 AND SI-29 Y . PAN, T. GULLION, J. SCHAEFER, JMR 90, 330-340 (1990) ALLOWS DIFFERENT PULSE LENGTHS ON Fl & F2 180 PULSES ON UNOBSERVED NUCLEI AT 1/2 AND FULL ROTOR PERIODS WITHOUT PRESATURATION USE LREDCAL.AUM TO CALC DELAYS D3, D22, D23 AND D24 PROT ALL START, 10U DI [F3 +X F2 @PLS1 RGATE] D22 D12 [Fl @PLS2 RGATE] LOOP CI TIMES ;N=2*Cl+2 D23 D12 [F1@PLS3 RGATE] D23 D12 [Fl @PLS2 RGATE] END LOOP D24 D2 [F3 +X F2 @PLS4 RGATE] D24 LOOP CI TIMES D12 [Fl @PLS2 RGATE] D23 D12 [Fl @PLS3 RGATE] D23 END LOOP D12 [Fl @PLS2 RGATE] D22 D3 [STA RGATE] ; MAKE D3=Dl/2 AND USE NT D7 LOOP C2 TIMES DO END LOOP ++PLS1 ++PLS2 ++PLS3 ++PLS4 GOTO START BEGIN LISTS PLS1, +X-Y-X+Y PLS2, +X PLS3, +Y PLS4, +Y +X -Y -X RLS, +X -Y -X +Y END LISTS 326 TRIGGER MODE NT, REC = F2, USE RPN TO CALCULATE DELAYS USE LREDCAL.AUM D23 = [T(ROT)-2*D12]/2 D22 = [T(ROT)-Dl-D12]/2 D24 = [T(ROT)-D2-D12]/2 LREDCAL.AUM A LEWIS OCT 12 1995 MICROPROGRAM TO CALCULATE DELAYS FOR REDOR EXPERIMENT TO BE USED IN CONNECTION WITH LREDF1F2.PC AND LREDSIF.PC 180 PULSES ON Fl AT 1/2 AND FULL ROTOR PERIODS ENTER DI (F2 90), D2 (F2 180) AND D12 (Fl 180) AND K.3 SPINNING FREQ BEFORE RUNNING THIS!!! C2 = 2 C3 = 50 ; FOR PRESATURATION D13 = 1M D14 = D13/K3 ; TIME FOR ONE ROTOR PERIOD ; K3 IS THE SPINNING FREQUENCY IN KHZ D15 = D1 +D12 D16 = D15/C2 D17 = D12/C2 D19 = D2/C2 D20 = D17 + D19 D18 = D14/C2 PULSE PROG D3 = DI /C2 D22 = D18-D16 D23 = D18 - D12 D24 = D18-D20 D1/2 + D12/2 D12/2 D2/2 D12/2 + D2/2 1/2 OF ROTATIONAL PERIOD ;NOW CALC DELAYS USED IN Dl/2 T/2-D1/2-D12/2 T/2-D12 T/2- D12/2-D2/2 EXIT 327 ; LREDOR.AUM ; A LEWIS JAN 14 1996 . ; TO RECORD SERIES OF REDOR FID'S ; RECORDS TWO SPECTRA OFF AND ON RES ; READS IN OFFSET VALUES FROM OFFSET LIST ; INCREMENTS CI (N=2C1 +2) ; OFFSET LIST MUST HAVE 2 OF EACH OFFSET !!! C1 =6 ; SET INITIAL C1 VALUE RF#1.010 RF #2.010 2 ZE 01 ; READ IN OFF RES 01 VALUE 01 ; READ IT IN AGAIN II ; INITIALISE INTERFACE GO WR#1 IF #1 ZE 01 01 II READ IN ON RES 01 VALUE READ IT IN AGAIN INITIALISE INTERFACE GO WR#2 IF #2 3 IC1 4 IN=2 ; INCREMENT CI BY IC1 ; LOOP NE TIMES EXIT 328 ; LREDF3F1 .PC ; A LEWIS JAN 12 1996 ; 1-D REDOR SEQUENCE ; FOR Fl - F2/F3 FREQUENCIES, E.G. F-19 A N D SI-29 ; A L L PULSES ON O B S E R V E D NUCLEI (F2/F3) E X C E P T ONE ; 180 PULSES A T 1/2 A N D F U L L ROTOR PERIODS ; J.R. G A R B O W A N D T. GULLION, JMR 95, 442-5 (1991) ; A L L O W S DIFFERENT PULSE LENGTHS ON Fl & F2/F3 ; USES PRESATURATION ; USE L R E D C A L 2 . A U M T O C A L C D E L A Y S D3, D22, D23 A N D D24 PROT A L L START, 10U LOOP C3 TIMES ; SET C3 = 50 Dl [F3+X F2+X RGATE] 1M ; I M S D E L A Y END LOOP ; PRESATURATION DO ; R E L A X A T I O N D E L A Y SET T O 1 * TI D l [F3 +X F2 @PLS1 RGATE] D22 D2 [F3 +X F2 @PLS2 RGATE] LOOP CI TIMES ; N = 2*Cl+2 D23 D2 [F3 +X F2 @PLS3 RGATE] D23 D2 [F3 +X F2 @PLS2 RGATE] END LOOP D24 D12 [Fl @PLS4 RGATE] ; SINGLE 180 ON U N O B S E R V E D D24 LOOPC1 TIMES D2 [F3 +X F2 @PLS2 RGATE] D23 D2 [F3 +X F2 @PLS3 RGATE] D23 END LOOP D2 [F3 +X F2 @PLS2 RGATE] D22 D3 [STA RGATE] ; M A K E D3=Dl/2 A N D USE N T D7 10M ; D E L A Y ++PLS1 ++PLS2 ++PLS3 ++PLS4 G O T O START BEGIN LISTS PLS1,+X -Y -X +Y PLS2, +X PLS3, +Y PLS4, +Y +X -Y -X RLS, + X - Y - X + Y END LISTS 329 1 TRIGGER MODE : NT, REC = F2, USE RPN TO CALCULATE DELAYS USE LREDCAL2.AUM D23 = [T(ROT)-2*D2]/2 D22 = [T(ROT)-Dl-D2]/2 D24 = [T(ROT)-D2-D12]/2 L R E D C A L 2 . A U M A LEWIS JAN 12 1996 MICROPROGRAM TO CALCULATE DELAYS FOR REDOR EXPERIMENT TO BE USED IN CONNECTION WITH LSIFRED.PC OR LREDF3F1.PC ENTER DI (F2 90), D2 (F2 180) AND D12 (Fl 180) AND K3 SPINNING FREQ BEFORE RUNNING THIS!!! C2 = 2 C3 = 50 ; FOR PRESATURATION D13 = 1M D14 = D13/K3 ; =T, TIME FOR ONE ROTOR PERIOD ; K3 IS THE SPINNING FREQUENCY IN KHZ! D15 = D1 +D2 D16 = D15/C2 D17 = D12/C2 D20 = D2 / C2 D21 =D17 + D20 D18 = D14/C2 ; =T/2, 1/2 OF ROTATIONAL PERIOD ; NOW CALC DELAYS USED IN PULSE PROGRAM D3 = DI /C2 D22 = D18-D16 D23 = D18-D2 D24 = D18-D21 EXIT DI 12 T/2-D1/2-D2/2 T/2 - D2 T/2-D12/2-D2/2 330 ; LRED1 .PC ; S(0) EXPERIMENT WITHOUT DEPHASING, USE WITH LRED2.PC ; A LEWIS A U G 15 1997 ; REDOR PULSE SEQ WITH CP FROM F3 T O Fl (OBSERVED) ; CP-180-ACQ ON Fl (SPIN T E M P INVERSION) ; WITHOUT DEPHASING 180'S ON F3 (TRIPLED) ; A L L O W S DIFFERENT PULSE LENGTHS ON Fl & F3 ; USE L R E D C A L 5 . A U M T O C A L C T H E D E L A Y S PROT X T START, 5U Dl 1 [F3 @PLS1 RGATE] ; INITIAL 90 ON SOURCE D5 [F3 +Y Fl @PLS2 RGATE] ; C O N T A C T TIME D22 D12 [RGATE] LOOP CI TIMES ; N = 2*C1 + 2 D23 D12 [RGATE] D23 D12 [RGATE] END LOOP D24 D2 [Fl @PLS3 RGATE] D24 LOOPC1 TIMES D12 [RGATE] D23 D12 [RGATE] D23 END LOOP D12 [RGATE] D22 D3 [STA RGATE] ; M A K E D3=Dl/2 A N D USE N T D7 DO ++PLS1 ++PLS2 ++PLS3 G O T O START BEGIN LISTS PLS1, 4(+X) 4(-X) PLS2, +X -Y -X +Y -X +Y +X -Y PLS3, +X +Y +X +Y +X +Y +X +Y -X -Y -X -Y -X -Y -X -Y RLS, +X -Y -X +Y END LISTS ; USE NS = 16 * N A N D NT, RPN ; T O C A L C U L A T E D E L A Y S USE L R E D C A L 5 . A U M ; D22 = T(ROT)/2 -Dl/2 - D12/2 ; D23 =T(ROT)/2 - D12 ; D24 = T(ROT)/2 -D12/2 - D2/2 331 ; LRED2.PC ; S(F) EXPERIMENT WITH DEPHASING, USE WITH LRED1.PC ; A LEWIS AUG 15 1997 ; REDOR PULSE SEQ WITH CP FROM F3 TO Fl (OBSERVED) ; CP-180-ACQ ON Fl (SPIN TEMP INVERSION) ; DEPHASING 180'S ON F3 (TRIPLED) ; ALLOWS DIFFERENT PULSE LENGTHS ON Fl & F3 ; USE LREDCAL5.AUM TO CALC THE DELAYS PROT XT START, 5U DI I [F3 @PLS1 RGATE] ; INITIAL 90 ON SOURCE D5 [F3 +Y Fl @PLS2 RGATE] ; CONTACT TIME D22 D12 [F3+X RGATE] LOOP CI TIMES ;N = 2*Cl+2 D23 D12 [F3+Y RGATE] D23 D12 [F3+X RGATE] END LOOP D24 D2 [Fl @PLS3 RGATE] D24 LOOP CI TIMES D12 [F3+Y RGATE] D23 D12 [F3+X RGATE] D23 END LOOP D12 [F3+Y RGATE] D22 D3 [STA RGATE] ; MAKE D3=Dl/2 AND USE NT D7 DO ++PLS1 ++PLS2 ++PLS3 GOTO START BEGIN LISTS PLS1, 4(+X) 4(-X) PLS2, +X -Y -X +Y -X +Y +X -Y PLS3, +X +Y +X +Y +X +Y +X +Y -X -Y -X -Y -X -Y -X -Y RLS, +X -Y -X +Y END LISTS ;USENS= 16 * N AND NT, RPN ; TO CALCULATE DELAYS USE LREDCAL5.AUM ; D22 = T(ROT)/2 -Dl/2 - D12/2 ; D23 = T(ROT)/2 - D12 ; D24 = T(ROT)/2 -D12/2 - D2/2 332 L R E D C A L 5 . A U M A LEWIS AUG 15 1997 MICROPROGRAM TO CALCULATE DELAYS FOR REDOR EXPERIMENT TO BE USED IN CONNECTION WITH LRED1.PC AND LRED2.PC 180 PULSES ON F3 AT 1/2 AND FULL ROTOR PERIODS ENTER D1 (F1 90), D2 (F1 180), D11 (F3 90), D12 (F3 180) AND K3 SPINNING FREQ BEFORE RUNNING THIS!!! C2 = 2 C3 = 50 ; FOR PRESATURATION D13 = 1M D14 = D13/K3 ; TIME FOR ONE ROTOR PERIOD ; K3 IS THE SPINNING FREQ IN KHZ! D15 = Dl + D12 D16 = D15/C2 D17 = D2 + D12 D18 = D17/C2 D19 = D14/C2 ;Dl/2 + D12/2 ; D2/2 + D12/2 ; 1/2 OF ROTATIONAL PERIOD ; NOW CALC DELAYS USED IN PULSE PROG D3 = D1 /C2 Dl/2 T/2-D1/2-D12/2 T/2-D12 T/2-D2/2-D12/2 D22 = D19-D16 D23 = D19-D12 D24 = D19-D18 EXIT 333 ; LREDFID.AUM ; RECORDS CP REDOR S(O) AND S(F) SPECTRA ; READING IN THE PULSE PROGS LRED1.PC AND LRED2.PC ; A LEWIS AUG 15 1997 ; FOR CP FROM F3 TO Fl , OBSERVE Fl , DEPHASING ON F3 ; INCREMENTS CI (N=2*C1), CI MUST BE >= 1 !!! C1=0 ; SET INITIAL CI VALUE, C1>=1 !! ; SET IC1 THE INCREMENT FORC1 OUTSIDE !! ;RF #1.008 ; RESET FILE EXTENSIONS FOR OFF RES. FID ;RF #2.008 ; RESET FILE EXTENSION FOR ON RES. FID 1 RP LRED1 ; READ IN THE S(0) PULSE PROG II ; INITIALISE INTERFACE ZE ; ZERO MEMORY GO ; ACQUIRE OFF RES FID WR#1 ; WRITE OFF RES FID IF # 1 ; INCREMENT EXTENSION 2 RP LRED2 ; READ IN S(F) PULSE PROG II ; INITIALISE INTERFACE ZE ; ZERO MEMORY GO ; ACQUIRE ON RES FID WR #2 ; WRITE ON RES FID IF #2 ; INCREMENT EXTENSION ; NOW INCREMENT THE N LOOP COUNTER CI IC1 ; INCREMENT LOOP COUNTER IN= 1 ; LOOP TO START NE TIMES EXIT 334 B.2.7 T E D O R Exper iments LTEDF1F2.PC 1-D TEDOR PULSE PROGRAM TRANSFER FROM Fl TO F2/F3 (F-SI) PULSES AFTER TRANSFER ARE ON Fl (F) 90 DEGREE TIMES SHOULD BE ALMOST EQUAL SET DI = TRUE Fl 90 TIME AND D2 = TRUE F2/F3 180 TIME THEN SET K3 = ROTOR SPEED (KHZ) AND RUN TEDORCAL.AUM TO CALCULATE DELAYS D3, D23, D24 AND D25 PROT ALL START, DI [Fl @PLS1 RGATE] D23 D2 [F3+X F2 @PLS2 RGATE] LOOP CI TIMES ;N=2Cl+2 D24 D2 [F3+X F2 @PLS6 RGATE] D24 D2 [F3 +X F2 @PLS2 RGATE] END LOOP D24 D2 [F3 +X F2 @PLS6 RGATE] D25 D2 [Fl @PLS3 F3 +X F2 @PLS2 RGATE] D25 D2 [F3+X F2 @PLS2 RGATE] LOOP CI TIMES D24 D2 [F3+X F2 @PLS6 RGATE] D24 D2 [F3+X F2 @PLS2 RGATE] END LOOP D24 D2 [F3+X F2 @PLS6 RGATE] D23 DI [Fl @PLS5 F3 +X F2 @PLS4 RGATE] ; TRANSFER PULSE D23 D2 [Fl @PLS8 RGATE] D24 LOOP C4 TIMES ; M = C4+1 D2 [Fl @PLS7 RGATE] D24 D2 [Fl @PLS8 RGATE] D24 END LOOP D2 [Fl @PLS7 RGATE] D23 D3 [STA RGATE] ; SET D3=Dl/2 DO ; AND USE NT ++PLS1 ++PLS2 ++PLS3 ++PLS4 335 ++PLS5 ++PLS6 ++PLS7 ++PLS8 GOTO START BEGIN LISTS PLS1, +X +X -Y -Y -X -X +Y +Y PLS2, +X PLS3, +Y +Y +X +X -Y -Y -X -X PLS4, +X +X -Y -Y -X -X +Y +Y PLS5, -Y +Y -X +X +Y -Y +X -X PLS6, -Y PLS7, -Y PLS8, +X RLS, +X-X-Y+Y-X+X+Y-Y END LISTS ; RECEIVER MODE RPN, TRIGGER MODE NT, NS = 8*N ;D3 = D1 12 ; D23 = T(ROT)/4 - D2/2 - Dl/2 ; D24 = T(ROT)/2 - D2 ; D25 = T(ROT)/4 - D2 TEDORCAL.AUM MICROPROGRAM TO CALCULATE DELAYS FOR TEDOR EXPERIMENT WILL POSITION 180 PULSES AT 1/4 & 3/4 OF THE ROTOR PERIOD BEFORE AND AFTER THE COHERENCE TRANSFER TO BE USED IN CONNECTION WITH KTEDORS2.PC, HTEDNMV.PC LTEDF1F2.PC, TEDF1 F2.PC, LTEDF1 .PC AND HTEDF1.PC, ENTER Dl, D2, AND K3 = SPINNING FREQUENCY BEFORE RUNNING THIS C5 = 2 C2 = 4 C3 = 3 D13 = 1M D14 = D13/K3 ; T= ROTOR PERIOD ; K3 IS THE SPINNING FREQUENCY IN KHZ D15 = D1+D2 D16 = D15/C5 D17 = D14/C2 D18 = D14/C5 D1/2 + D2/2 1/4 OF ROTATIONAL PERIOD 1/2 OF ROTATIONAL PERIOD ; NOW CALC DELAYS USED IN PULSE PROG D3 = D1/C5 D23 = D17-D16 D24 = D18-D2 D25 = D17-D2 EXIT Dl 12 T/4-D1/2 T/2 - D2 T/4 - D2 D2/2 336 ; LIC4.AUM ; TO INCREMENT C4 ; FOR VARYING M IN TEDOR EXPERIMENT ; SET CI AND IC4=1 C4=0 ; SET INITIAL C4 VALUE RF #1.001 ; RESET FILE EXTENSION 1 ZE GO WR#1 IF # 1 IC4 ; INCR. C4 BY IC4 2 IN=1 ; LOOP TO 1 NE TIMES EXIT ; LIC1.AUM ; INCREMENTS CI BY IC1 ; USE FOR VARYING N IN TEDOR EXPERIMENTS ;SETC4 ANDIC1 = 1 RF #1.001 ; RESET FILE EXTENSION C1=0 ; SET INITIAL CI VALUE 1 ZE GO WR#1 IF #1 1C1 ; INCREMENT CI BY IC1 2 IN=1 ; LOOP TO 1 NE TIMES EXIT 337 LTEDMOVB.PC 1-D TEDOR TRANSFER FROM Fl TO F2/F3 (F-SI) FOR VARIATION OF PULSE POSITIONING ALLOWS PULSE POSITIONS BEFORE AND AFTER TRANSFER TO BE AT DIFFERENT PLACES E.G. 1/8, 7/8 AND 1/4 , 3/4 PULSES AFTER TRANSFER ARE ON Fl (F) 90 DEGREE TIMES SHOULD BE ALMOST EQUAL SET Dl = TRUE Fl 90 TIME, AND D2 = TRUE F2/F3 180 TIME THEN SET K3 = ROTOR SPEED (KHZ) AND RUN E.G. TEDCAL13.AUM TO CALCULATE FOR 1/3, 2/3, 1/4, 3/4 DELAYS D3, D23, D24 AND D25 PLUS D26, D27, D28 AND D29 PROT ALL START, Dl [Fl @PLS1 RGATE] D26 D2 [F3 +X F2 @PLS2 RGATE] LOOP CI TIMES ;N = 2Cl+2 D27 D2 [F3+X F2 @PLS6 RGATE] D28 D2 [F3 +X F2 @PLS2 RGATE] END LOOP D27 D2 [F3+X F2 @PLS6 RGATE] D29 D2 [Fl @PLS3 F3 +X F2 @PLS2 RGATE] D29 D2 [F3 +X F2 @PLS2 RGATE] LOOPC1 TIMES D27 D2 [F3 +X F2 @PLS6 RGATE] D28 D2 [F3 +X F2 @PLS2 RGATE] END LOOP D27 D2 [F3 +X F2 @PLS6 RGATE] D26 Dl [Fl @PLS5 F3 +X F2 @PLS4 RGATE] ; TRANSFER PULSE D23 D2 [Fl @PLS8 RGATE] D24 LOOP C4 TIMES ; M = C4+1 D2 [Fl @PLS7 RGATE] D24 D2 [Fl @PLS8 RGATE] D24 END LOOP D2 [Fl @PLS7 RGATE] D23 D3 [STA RGATE] ;SETD3=Dl/2 DO ; AND USE NT ++PLS1 ++PLS2 ++PLS3 ++PLS4 338 ++PLS5 ++PLS6 ++PLS7 ++PLS8 GOTO START BEGIN LISTS PLS1, +X +X -Y -Y -X -X +Y +Y PLS2, +X PLS3, +Y +Y +X +X -Y -Y -X -X PLS4, +X +X -Y -Y -X -X +Y +Y PLS5, -Y +Y -X +X +Y -Y +X -X PLS6, -Y PLS7, -Y PLS8, +X RLS, +X-X.-Y+Y-X+X+Y-Y END LISTS ; RECEIVER MODE: RPN, TRIGGER: NT, NS = 8*N ;D3 = D1 12 ; D23 = T(ROT)/4 - D2/2 - Dl/2 ; D24 = T(ROT)/2 - D2 ; D25 = T(ROT)/4 - D2 TEDCAL13.AUM A. LEWIS AUG 12 1995 MICROPROGRAM TO CALCULATE DELAYS FOR TEDOR EXPERIMENT PULSES AT 1/3, 2/3 BEFORE TRANSFER AND 1/4 , 3/4 AFTER TRANSFER TO BE USED IN CONNECTION WITH LTEDMOVB.PC ENTER DI, D2, AND K3 = SPINNING FREQUENCY BEFORE RUNNING THIS C5 =2 C2 = 4 C3 =3 C6 = 8 C7 = 6 D13 = 1M D14 = D13/K3 = R (K3 IS THE SPINNING FREQ IN KHZ) D15 = D1+D2 D16 = D15/C5 D16IS3/2 0FD1 D17 = D14/C2 1/4 OF ROTATIONAL PERIOD = R/4 D18 = D14/C5 1/2 OF ROTATIONAL PERIOD = R/2 D19 = D14/C3 R/3 D20 = D19 *C5 2R/3 D3 = D1/C5 Dl/2 D23 = D17-D16 R/4-Dl/2-D2/2 D24 = D18-D2 R/2-D2 D25 = D17-D2 R/4-D2 D26 = D19-D16 R/3 - Dl/2 - D2/2 D27 = D20 - D2 2R/3 - D2 D28 = D19-D2 R/3 -D2 D29 = D19-D2 R/3 -D2 EXIT 339 ; LTEDMOVA.PC ; 1-D TEDOR ; TRANSFER FROM Fl TO F2/F3 (F-SI) ; ALLOWS POSITION OF PULSES AFTER TRANSFER TO BE MOVED ; PULSES BEFORE ARE AT 1/4 AND 3/4 ; PULSES AFTER TRANSFER ARE ON Fl (F) ; 90 DEGREE TIMES SHOULD BE ALMOST EQUAL ; SET DI = TRUE Fl 90 TIME AND D2 = TRUE F2/F3 180 TIME ; THEN SET K3 = ROTOR SPEED (KHZ) ; AND RUN E.G.TEDCAL15.AUM (PULSES AT 1/5, 4/5) ; TO CALC DELAYS D3, D23, D24 AND D25, D26, D27 AND D28 PROT ALL START, DI [Fl @PLS1 RGATE] D23 D2 [F3+X F2 @PLS2 RGATE] LOOP CI TIMES ;N = 2Cl+2 D24 D2 [F3 +X F2 @PLS6 RGATE] D24 D2 [F3 +X F2 @PLS2 RGATE] END LOOP D24 D2 [F3 +X F2 @PLS6 RGATE] D25 D2 [Fl @PLS3 F3 +X F2 @PLS2 RGATE] D25 D2 [F3+X F2 @PLS2 RGATE] LOOP CI TIMES D24 D2 [F3 +X F2 @PLS6 RGATE] D24 D2 [F3+X F2 @PLS2 RGATE] END LOOP D24 D2 [F3+X F2 @PLS6 RGATE] D23 DI [Fl @PLS5 F3 +X F2 @PLS4 RGATE] ; TRANSFER PULSE D26 D2 [Fl @PLS8 RGATE] D27 LOOP C4 TIMES ; M = C4+1 D2 [Fl @PLS7 RGATE] D28 D2 [Fl @PLS8 RGATE] D27 END LOOP D2 [Fl @PLS7 RGATE] D26 D3 [STA RGATE] ; SET D3=Dl/2 DO ; AND USE NT ++PLS1 ++PLS2 ++PLS3 ++PLS4 340 ++PLS5 ++PLS6 ++PLS7 ++PLS8 GOTO START BEGIN LISTS PLS1, +X +X -Y -Y -X -X +Y +Y PLS2, +X PLS3, +Y +Y +X +X -Y -Y -X -X PLS4, +X +X -Y -Y -X -X +Y +Y PLS5, -Y +Y -X +X +Y -Y +X -X PLS6, -Y PLS7, -Y PLS8, +X RLS, +X-X-Y+Y-X+X+Y-Y END LISTS ; RECEIVER MODE: RPN, TRIGGER: NT, NS = 8 * N TEDCAL15.AUM A. LEWIS AUG 13 1995 MICROPROGRAM TO CALCULATE DELAYS FOR TEDOR EXPERIMENT PULSES AT 1/4, 3/4 BEFORE TRANSFER AND 1/5, 4/5 AFTER TRANSFER TO BE USED IN CONNECTION WITH LTEDMOVA.PC ENTER Dl, D2, AND K3 = SPINNING FREQUENCY BEFORE RUNNING THIS C5 = 2 C2 = 4 C3 = 3 C6 = 8 C7 = 6 C8 = 5 D13 = 1M D14 = D13/K3 D15 = D1+D2 D16 = D15/C5 D17 = D14/C2 D18 = D14/C5 D19 = D14/C8 D20 = D19 * C3 D21 =D19*C5 R (K3 IS THE SPINNING FREQ IN KHZ) D16IS3/2 0FD1 1/4 OF ROTATIONAL PERIOD = 1/2 OF ROTATIONAL PERIOD = R/5 3R/5 2R/5 R/4 R/2 D3 = D1/C5 D23 = D17-D16 D24 = D18-D2 D25 = D17-D2 D26 = D19-D16 D27 = D20 - D2 D28 = D21 -D2 Dl/2 R/4-Dl/2-D2/2 R/2-D2 R/4-D2 R/5 - Dl/2 - D2/2 3R/5 - D2 2R/5 - D2 EXIT 341 LREFTED.PC 1-D REFOCUSSED TEDOR TRANSFER FROM F3 TO Fl USING TRIPLER ON F3 SO F3 +Y AND -Y PHASES ARE INTERCHANGED A. LEWIS JAN 12 1998 PHASE CYCLING AS FOR REFOCCUSSED INEPT DEPHASING BEFORE TRANSFER ON Fl AT 1/4 3/4, N=2Cl+2 DEPHASINGAFTER TRANSFER ON F3 AT 1/4, 3/4, M=2C4+2 ALLOWS DIFFERENT PULSE LENGTHS ON Fl AND F3 D1=F1 90, D2 = F1 180, D l l = F3 90, D12 = F3 180 SET K3 = ROTOR SPEED (KHZ), USE LRTCAL.AUM TO CALC DELAYS D22, D23, D24, D25, D26, D27, D28, AND D29 PROT ALL INITIAL 90 PULSE T/4 DEPHASING ON Fl N = 2Cl+2 START, DI 1 [F3 @PLS1 RGATE] D22 D2 [Fl +X] LOOP CI TIMES D23 D2 [Fl +Y RGATE] D23 D2 [Fl +X RGATE] END LOOP D23 D2 [Fl +Y RGATE] D24 D2 [F3 @PLS2 Fl @PLS3 RGATE] ; SIMULTANEOUS 180 TO REFOCUS D24 D2 [Fl +X RGATE] LOOP CI TIMES D23 D2 [Fl +Y RGATE] D23 D2 [Fl +X RGATE] END LOOP D23 D2 [Fl +Y RGATE] D25 DI [F3 @PLS4 Fl @PLS5 RGATE ] ; COHERENCE TRANSFER D26 D12 [F3+X RGATE] ; NOW DEPHASING ON F3 LOOP C4 TIMES ; M = 2C4+2 D27 D12 [F3+Y RGATE] D27 D12 [F3 +X RGATE] END LOOP D27 D12 [F3+Y RGATE] D28 D2 [F3 @PLS2 F1 @PLS6 RGATE] ; SIMULTANEOUS 180 TO REFOCUS D28 D12 [F3+X RGATE] LOOP C4 TIMES D27 342 D12 [F3 +Y RGATE] D27 D12 [F3+X RGATE] END LOOP D27 D12 [F3 +Y RGATE] D29 D3 [STA RGATE] AQ DO ++PLS1 ++PLS2 ++PLS3 ++PLS4 ++PLS5 ++PLS6 GOTO START SET D3=Dl/2 AND USE NT ACQUIRE ECHO RELAXATION DELAY RECYCLE ON 5*T1 (F3) BEGIN LISTS PLS1, 8(+X)8(-X) PLS2, +X -X PLS3, +X -X PLS4, -Y -Y +Y +Y PLS5, 4(+X) 4(+Y) 4(-X) 4(-Y) PLS6, +X -X +X -X +Y -Y +Y -Y RLS, +X +X -X -X +Y +Y -Y -Y END LISTS RECEIVER MODE: RPN, REC:F1 TRIGGER MODE: NT NS= 16*N 343 L R T C A L . A U M A. LEWIS JAN 12 1998 MICROPROGRAM TO CALCULATE DELAYS FOR REFOC. TEDOR EXPERIMENT TO BE USED WITH LREFTED.PC Fl AND F3 PULSES ARE SIMULTANEOUS!!! ENTER DI (Fl 90), D2 (Fl 180), DI 1 (F3 90), D12 (F3 180) AND K3 = SPINNING SPEED IN KHZ, BEFORE RUNNING THIS C5 = 2 C2 = 4 D13 = 1M D14 = D13/K3 D3 = DI/C5 D17 = D2/C5 D16 = D14/C2 D15 = D14/C5 D21 =D11 /C5 D29 = D12/C5 ONE ROTOR PERIOD Dl/2 D2/2 DI 1/2 D12/2 1/4 ROTOR CYCLE 1/2 ROTOR CYCLE ; NOW CALC DELAYS USED IN PULSE PROG D22 = D16-D21 D22 = D22 - D17 ; T(ROT)/4 - DI 1/2 - D2/2 D23 = D15 - D2 ; T(ROT)/2 - D2 D24 = D16 - D2 ; T(ROT)/4 - D2 D25 = D16 - D17 D25 = D25 - D3 ; T(ROT)/4 - D2/2 -Dl/2 D26 = D16-D3 D26 = D26 - D29 ; T(ROT)/4 - D112 - D12/2 D27 = D15-D12 ; T(ROT)/2 - D12 D28 = D16-D29 D28 = D28 - D17 ; T(ROT)/4 - D12/2 - D2/2 D29 = D16-D29 D29 = D29 - D21 ; T(ROT)/4 - D12/2 - DI 1/2 EXIT 344 APPENDIX C FUNCTIONS AND MA THEM A TIC A CODE FOR FITTING DATA FROM CROSS POLARIZATION, REDOR AND TEDOR NMR EXPERIMENTS Functions used to fit data from Hartmann-Hahn C P , R E D O R and T E D O R experiments are presented in this appendix. Details of the fitting and the code used to perform this in the Mathematica programming environment 7 are also given where appropriate. 345 C.l HARTMANN-HAHN CROSS POLARIZATION C.l.l Cross Polarization Behavior for Isolated IS Spin Pairs C.l. 1.1 Functions Used To Describe HHCP Behavior The Hartmann-Hahn cross polarization ( H H C P ) behaviour for isolated IS spin pairs in a polycrystalline (powder) sample is described in Chapter 3. The signal intensity of the S spins, M{x), fol lowing H H C P for a contact time T is defined by Eq. C . l where M 0 is the net magnetization of the / spins fol lowing the initial 7t/2 pulse. where/ indicates the precise Hartmann-Hahn matching condition (cojy - cois =/a>r), and the functions 6/are defined in Eqs. 3.4, 3.12 and 3.13. For a stationary (non-spinning) sample there is only a single matching condi t ion; /= 0. Under M A S there are four sideband matching conditions the integration over a single angle 9 to produce the powder average since it is not possible to detect the phase of the dipolar coupling. 7 The functions gt(x) for the five possible matching conditions are given in Table C. 1 and can be evaluated using numerical integration but this does not permit efficient nonlinear fitting of the function. However, using the methodology reported by Muel ler, it is possible to express gj{x) in terms of Bessel functions of the first k ind. J These functions were derived for the five possible matching conditions and are given in Table C . l . The Mathematica code used to determine the theoretical H H C P behavior for isolated IS spin pair in terms of both numerical C . l For a powder sample C.2 (/= ± 1, / = ± 2) separated by the spinning speed co,..2"3 Note that it is only necessary to perform 346 Table C.l Functions g/(x) which describes the Hartmann-Hahn cross polarization behaviour for isolated IS spin pairs in a powder sample at various matching conditions,/ The functions are expressed as exact integrals and in terms of Bessel functions of the first kind. D is the heteronuclear dipolar coupling in Hz, and x is the contact time in seconds. Matching Condition / Matching Condition / Exact Integral Bessel Functions 0 (STATIC) Jo nDx (3 cos2 9 - l) sin9 1 r f 37tD^ . (nDx kn \] [(4k2-l/kl 2 JCOSl 2 + 2 Jj ± 1 (MAS) i f« 1 Jo —=r- sin 2y . V2 sinS ( nDx] 00 k=l 1 r 7t/)x^ ± 1 (MAS) i f« 1 Jo —=r- sin 2y . V2 sinS JolV2"J 00 k=l (l-4(2k)2) 2HV2"J ±2 (MAS) .Jo sin 9 2 sin9 (-l)k2 J k (nDx ] cos (UDX + kn) (1 -4k2) V 2 J V 2 2 J integration and Bessel functions of the first kind is outlined below using the static (/*= 0) matching condition in the absence of relaxation as an example. Define the function StatPowder which corresponds to numerical integration of Eq. C . 1. StatPowder utilizes the numerical integration routine NIntegrate provided with Mathematica, and because Mathematica requires arguments for trigonometric functions to be in radians, the D t I 2 term in Eq. C.2 has been multipled by 2n. StatPowder[d_, t_] := N[0.5 - (0 .25* NIntegrate[ Cos[d*t*7r (3*Cos[e] *Cos[e] - 1) ] *Sin[e] , {e, 0, TT} ] ) ] ; A list of data points (Hst3) is generated using StatPowder and a plot o f these versus the dimensionless parameter/) x is generated (plot3). 10 r maxtime maxtime = ; nurtpoints = 30; incr = N ; 1000 (nunpoints) dip = 1000; l i s t3 = {{0, 0}}; time = incr; i = 2; Do[appendTo[list3, {dip * time, StatPowder [ dip, time]}] time = time + incr; i= i + 1, {nunpoints} ] ; plot3= Lis tPlot [ l i s t3 , PlotJoiiied-> False, Prolog-> AbsolutePointSize[5], PlotRange-> {{0, maxtime * dip}, {0, 1}}, PlotLabel - > "Static Powder - no relaxation", AxesLabel-> {"D t", ""}] Define a function StatPowBess describing Eq. C . l in terms of Bessel functions as given in Table C . l : StatPowBess[d_, t_J := N[0.5 -0.5 (COS[TT*-^ * t] BesselJ[0, 3*TT* - J *t] ) + r 1 r d k * 7T , r d , Sum * Cos 7r * — * t + * BesselJ k, 3 * n * — * t , 1 (4k 2 -1) L 2 2 J L 2 J {k, 1, 5}]] 348 Here d is the IS heteronuclear dipolar coupling in Hz, t is the contact time in seconds, and the variable k determines the number of Bessel functions to include in the sums. Muel ler J had suggested that including five terms provides sufficient accuracy and thus k = 5 was used in this case. Note that the cosine argument in the Bessel functions must be converted to radians by introducing an additional factor of 2TC. A list is generated using StatPowBess and the results plotted as described above for the numerical integration. The resulting two plots are overlaid and show exact agreement as seen in Figure C . l . Similar analysis was carried out to check the validity of all expressions derived in terms of Bessel functions, and to confirm that the functions used to analyze the experimental C P , R E D O R and T E D O R data were in agreement with those reported in the literature. F igure C . l Theoretical Hartmann-Hahn cross polarization behavior calculated for an isolated IS spin pair in a static powder sample if - 0) using numerical integration of Eq. C . l (fi l led circles) and in terms of Bessel functions (curve). N o relaxation effects have been included. 349 C.l. 1.2 Nonlinear Least Squares Fitting of Experimental HHCP Data In this section the steps required for performing visual and nonlinear least squares fitting of the experimental H H C P data in the Mathematica programming environment are outlined in detail using the function for a non-spinning powder sample (f= 0) as an example. The code given is for Mathematica version 3.0, and the effects o f relaxation have been included as described in Section 3.3. The equations describing the other matching conditions given in Table C . l may also be used once the appropriate functions have been defined. First set the text style for plots and load the package required for nonlinear regression analysis: $TextStyle= {FontFamily-> "Times"}; << Statistics NonlinearFit * Next define a list S ta tDa ta l containing the experimental data points and plot the data as an object called p lo tSta t l . In this case the data are in the form {contact time (ms), peak area}. StatDatal = {{0,0}, {1.2,97.8}, {6.0, 103.6}, {0.2, 34.5}, {2.2, 103.5}, {3.2, 97.3}, {4.25, 102.9}, {5.25, 104.4} , 0.4, 84.4}, {1.4, 88.8} , {2.4, 103.5} , 3.4, 97.8}, {1.9, 90.9}, {2.0, 98.4}} ; plotStatl = ListPlot[StatDatal, PlofcJoined-> False, Prolog - > AbsolutePointSize [ 5] , PlotRange - > All, PlotLabel-> "Static CP", AxesLabel-> { "Time/ms", ""}] N o w define the equation StatBessRclax which describes the H H C P behavior for a static powder (f= 0) with full relaxation (Eq. 3.14) in terms of Bessel functions. Here d is the I-S heteronuclear dipolar coupling, t is the contact time, m is a scaling factor to match the experimental and theoretical intensities, S (0.5 < S < 1 ) is the parameter defining the degree of isolation of the / spins, r l and r2 are the parameters describing the relaxation, t l r is the spin-350 lattice relaxation of the / nuclei in the rotating frame, and the variable k determines the number of Bessel functions to include in the sums (five in this case). StatBessRelax[d_, t_, m_, S_, r l _ , r2_, t l r_] := N[m* E x p [ — * jo.5 - 0 . 5 * E x p [ - ^ ] * j c o s [ ^ | ^ - ] *BesselJ[0, 3 " * t ] -2 * V ( c o s [ ^ + ^ ] * B e s s e U [ k , 1 ^ 1 * _ ^ ) | + £ i v L 2 2 1 1 2 1 41^-1 1 J ( ( S - 0 . 5 ) * ( l - E x p [ ^ ] ) ) ) ] ; Visual fitting of the experimental data is then carried out to determine appropriate values for the various parameters. First the parameters are assigned values and a list s ta t l is created. Note that several parameter values are divided by a factor of 1000 to convert them from milliseconds to seconds. A graph of the theoretical curve is produced (p lot f i t l ) and the plot o f the experimental data (p lotStat l ) overlaid for comparison. The parameters are adjusted until an acceptable match between the experimental and theoretical plots is obtained. 10 r maxtau maxtau= ; nurrpoints = 100; inc r = N 1000 (nurrpoints) dip = 1442; mag = 182.5; Seq = 0.9; 2.2 ^ 0 26.7 2000 r a t e l = ; rate2 = ; t l rho = ; 1000 1000 1000 s t a t l = {{0, 0}}; tau = i n c r ; i = 2; Do[AppendTo[statl, {tau* 1000, StatBessBelax[ d ip , tau, mag, Seq, r a t e l , rate2, tlrho]}] ; tau = tau + i n c r ; i = i + 1, {nurrpoints} ] ; p l o t f i t l = L i s t P l o t [ s t a t l , PlofcJoined-> True, PlotRange-> A l l , PlotLabel-> " F i t " , AxesLabel-> { "Tdire/ms", ""}] Show [p lo tS ta t l , p l o t f i t l , Prolog - > AbsolutePointSize [ 5] , PlotRange - > A l l ] 351 Using these parameter values as initial starting values, nonlinear least squares fitting of the experimental cross polarization data to determine the I-S heteronuclear dipolar coupling D is then performed util izing the Mathematica procedure NonlinearRegress' which minimizes the %2 merit function. N o n l i n e a r F e g r e s s [ S t a t D a t a l , c t 2000 S t a t f i e s s F e l a x T d c , , m , 0 . 9 , r l , r 2 , 1 , L 1000 1 0 0 0 1 c t , { { d c , 1 4 4 6 ) , {m, 182} , { r l , | ^ } , { r 2 , - ^ } } , M e t h o d - > L e v e n b e r g M a r q u a r d t , S h o w P r o g r e s s -> T rue ] The Levenberg-Marquardt algorithm was found to be the most efficient method for the minimum search. In this case not all o f the parameters are allowed to vary freely during the fitting; S and tlr were fixed to values of 0.9 and 2 respectively. The output from this procedure are used as input to plot the theoretical curve and compare it to the experimental data as above. The procedure NonlinearRegress also generates a regression report containing the best fit parameters, the asymptotic standard errors and confidence interval o f the fitted parameters. C.1.2 Cross Polarization Behavior in a Network of Strongly Coupled / Spins The H H C P behavior for spins in a strongly dipolar-coupled network is different from that observed for isolated IS spin pairs. The underlying assumptions and equations describing the intensity o f the S spin signal as a function of the contact time are given in Section 3.3.3. If T\p of the S spins is much longer than that o f the / spins then T]p (I) dominates the decay and a function of the form given in Eq . 3.15 can be used to fit the experimental H H C P data. Below is the Mathematica function cpfunc which was used for nonlinear least squares fitting of H H C P data when the there was a network o f strongly coupled / spins. 352 cpfunc[a_, tcp_, tlrho_, time_] = \ * (Exp [-time / tlrho] - Exp [-time / tcp]) ; Here a is a scaling factor to match experimental and theoretical intensities, tcp defines the time constant describing the build-up of magnetization due to polarization transfer, t l r h o defines (exponential) decay in rotating frame, and t ime is the contact time. C.2 R O T A T I O N A L E C H O D O U B L E R E S O N A N C E C.2.1 R E D O R Behav ior for Isolated IS Sp in Pa i rs The R E D O R experiment is described in detail in Section 3.4. The equations and Mathematical scripts used during fitting of the experimental data, and to investigate the theoretical behavior R E D O R for different pulse positions and numbers of spins are presented below. C.2.1.1 REDOR Functions and Nonlinear Fitting The R E D O R behavior for an isolated IS spin pair is de f ined^ by Eq. C.2 where X = nDxr is a dimensionless parameter which is the product of the number of rotor cycles («), the IS heteronuclear dipolar coupling (D), and the rotor period (x r). For a mirror symmetric R E D O R pulse sequence with the dephasing pulses positioned at /, the C.2 dipolar phase accumulated over each rotor period, A O R , is: 353 A O R = J^tD„(a,p,0 dt - Jja>o(a,p,0 dt C . where a>o is defined in Eq. 1.14 and the minus sign reflects the action of the / spin pulse. The complete expression is : 7 A ® R = — J s in 2 p [s in2 a + ^ ^L - s in2a ] - 2V2 sin2P [sinl a + f ^> \ 2 71 t 2 In tx - since > C.4 Figure C.2 shows the theoretical R E D O R curves calculated for a selection of possible positions of the dephasing pulses. The Mathematica code used to generate the R E D O R curves for dephasing pulses applied at position fract (0 < fract < x r /2) is given below. In this example 30 points are calculated as a function of the dimensionless parameter nDxT with the dephasing pulses at t r / 5 . nunpoints = 30; max = 6.0; incr = max/ nunpoints; nDTr = incr; int l ist5= {{0, 0}}; fract = — ; 5 Do[sf = 1- [-——) * NIntegrate[ Sin[/3] * Cos[ (((Sin[/3] *Sin[/3] (Sin[2 (a + 2 T T * fract) ] - Sin[2a]) -2 V 2 Sin[2 /3] (Sin[a - 2 TT * fract] - Sin [a]))) + ((Sin[j3] *Sin[/3] (Sin[2 (a - 2 T T * fract)] -Sin[2a]) -2 V 2 Sin[2/3] (Sin[o+ 2 TT*fract] - Sin[a])))) ] , {/3, 0, 7 T ) , {a, 0, TT] , AccuracyGoal-> 3] ; Print [nDTr, ", ", sf ] ; AppendTo [ in t l i s tS , {nDTr, sf}]; nDTr = nDTr + incr, {nunpoints} ] When the dephasing pulse are at t\ = xrl 2, Eq. C.4 is simplified considerably and becomes: 354 0 1 2 3 4 5 6 nDxr Figure C.2 Theoretical R E D O R dephasing calculated for an isolated IS spin pair with different placements o f the dephasing Ti-pulses in a mirror symmetric R E D O R sequence. The dephasing pulses occur at l\ (indicated) during the period before the echo-forming Tc-pulse and at x r -1\ after. The curves are plotted as a function of the dimensionless parameter nDxx. 355 A O R = A, sinP cos (3 sin a C.5 Muel ler reported that Eq. C.5 can be re-expressed in terms of Bessel functions of the first kind as: J CO A S / S 0 = 1 - [Jb (V2 nDxr)f + 2 £ { [Jk(42 nDx,)]2/(16k2- 1)} C.6 k = l The Mathematical code defining a function for the theoretical R E D O R behavior for an isolated IS spin pair with dephasing pulses applied at x r/2 in terms of Bessel functions of the first kind is: sred[dip_, nTr_] := 1- BesseU[0, V 2 dip * riTr] A 2 + Sum [2. BesseU[i , dip * nTr] A 2 / ( l 6 i 2 - 1.0) , {i, 1, 5}] ; where d ip is the dipolar coupling and n T r is the product of the number o f rotor cycles and the rotor period x r. Recently Muel ler et al.H reported a further simplification which makes allows the calculation of A S / S 0 in terms of Bessel functions of order 1/4 (Eq. C.7). AS / S 0 = 1 - Jm ( V2 nDxt) J.m ( V2 nDx,) C.7 The Mathematica code defining a function for the theoretical R E D O R behavior for an isolated IS spin pair with dephasing pulses applied at x r 12 in terms of Bessel functions of order 1/4 is: newRed[n_, d_, t r j := 1 - (BesseU[l/4, Sort[2] n d t r ] * BesseU[-l /4, Sqrt[2] n d t r ] ) ; where n is the number o f rotor cycles, d is the dipolar coupling, and t r is the rotor period. 356 Either of these forms in terms of Bessel functions can be used for efficient nonlinear fitting of the experimental R E D O R data in a manner analogous to that described in Section C. 1.1.2. During the fitting procedure two parameters were varied and optimized; one corresponding to the dipolar coupling, and an additional parameter (a scaling factor) to account for incomplete or statistical site occupancies. C.2.1.2 The REDOR Transform Mueller et al.H have reported a new analytical transform which allows the dipolar coupling to be determined directly from R E D O R data for isolated IS spin pairs, as described in Section 3.4. The Mathematica code used to perform this is given below. The original code was kindly supplied by Dr. K. Mueller. First define a list which contains the experimental data in the form {n , Sf/So}. Note the use Sf/So rather than A S / S 0 so the data decays to zero, datalist = {{2, 0.101}, {4, 0.106}, {6, 0.002}, {8, 0.072}, {10, -0.008}, {12, 0.053}, {14, -0.007}, {16, 0.037}, {18, -0.001}, {20, 0.0242} Next define apodization function (three-point Blackman-Harris) used to smooth the experimental data and ensure it decays completely to zero: smooth[dat_, b j := Table[{dat[ [ j , 1] ] , N[0.424 + 0.497 Cos[Pi j / b] + 0.079Cos[2Pij/b]] datj , 2}, {j, 1, Length[dat]}]; Apodize the experimental data and zerofi l l it to 128 rotor periods: smdata = smooth [data l i s t , Length[datalist]]; zerol ist = Table[ {i, 0}, {i , 22, 128, 2}] ; z£128 = Join[smdata, zerol ist ] ; 357 Define the R E D O R transform "kernal" function and create a look-up table: kernreal[d_, t_] := -((Sqrt[2] d t) A2 * BesseU[-5/4, (Sqrt[2] d t ) ] * BesseU[-l /4, (Sqrt[2] d t ) ] ) -(Sort[2] d t) * BesseU[-l /4, (Sqrt[2] d t)] A2 + (Sqrt[2] d t) A 2 * BesselJ[-3/4, (Sqrt[2] d t) ] * BesselJ[l/4, (Sqrt[2] d t ) ] + (Sqrt[2] d t) * BesselJ[l/4, (Sqrt[2] d t)] A 2 + (Sgrt[2] d t) A 2 * BesseU[-l /4, (Sqrt[2] d t) ] * BesselJ[3/4, (Sqrt[2] d t ) ] - (Sqrt[2] d t) A2 * BesseU[l/4, (Sqrt[2] d t ) ] * BesselJ[5/4, (Sqrt[2] d t ) ] ; kreal[d_, tr_ , i i _ , i f_, iinc_] := Table[{i, kemreal [d, i tr]}, {i, i i , i f , i inc}]; makekem [dinit_, dfinal_, dinc_, tr_ , i i _ , i f_, iinc_] := Table[kreal[d, t r , i i , i f , i i n c ] , {d, d in i t , df inal , dine}] ; Define the routine to calculate the R E D O R Transform spectrum. This uses a simple summation for the integration. calcspec[data_, ktable_, ntot_, dint_, dinc_, npts_] := Do[dat2 = data; ktab = ktable; kem = ktab[ [k] ] ; integr = N[Sum[dat2[ [ j , 2]] kem[[j , 2] ] , {j, 1, npts, 1}]] ; spec = Append [spec, {dint + dine (k- 1) , integr}] , {k, 1, ntot, 1}] Calculate the R E D O R transform kernal as a look-up table kerntab. This can take several minutes. Note that we must avoid f r e q l = 0 since the function is not defined at this point, speed is the spinning speed in Hz used to acquire the experimental data. npnts = 64; rninn = 2; incr = 2; speed = 4000 ; freql = 0.0005; freq2 = (speed/2) + freql ; deltafreq = N[ (freq2 - freql) / npnts] ; kerntab = makekem [freql, freq2, deltafreq, trot , mirm, incr * npnts, incr] ; 358 N o w perform actual calculation ( R E D O R transform) to produce the dipolar spectrum from the apodized experimental data and plot it. The list specl28 contains the transform intensities as a function of the dipolar frequency, spec = {}; calcspec[zfl28, kerntab, Length[kerntab], freql , deltafreq, Length[zfl28]]; specl28 = spec; transl28 = L is tPlot[specl28, PlotJoined->True, PlotRange->All, P l o t L a b e l - > ' ' R E D C R Transform"] This analysis assumes the R E D O R data was acquired with dephasing pulses positioned at x r/2. The "wigg le" at small values of dipolar coupling in the R E D O R transform "spectrum" arises from the initial decay of the S /S 0 data. A restriction determining the applicability o f the R E D O R transform is that the maximum dipolar coupling observable is half o f the spinning speed used. This means that the spinning speed used must exceed the dipolar coupling by at least three times i f good R E D O R transform spectra are to be obtained with the maximum corresponding to the I-S dipolar coupling clearly defined. C.2.2 R E D O R Behav ior F o r a Single S Sp in Dephased by Several / Spins C.2.2.1 Exact Geometrical Analysis The background theory and approach to calculating the R E D O R dephasing for a single S spin coupled to several / spins when the explicit geometrical arrangement o f the spins is known is discussed in Section 3.4.2. The Mathematica code used to implement the formalism proposed by Goetz and Schaefer 9 in terms of a product of cosine functions containing vectorial dot products as arguments is given below. It is also possible to calculate this in terms of a sum (i.e. Eq. 3.31) as presented for the multi-spin T E D O R dephasing in Section C.3.2. 359 First define the R E D O R function A O R (Eq. 3.28) in terms of a dot product between the (rotated) internuclear vector v = {v;, v2, v3) having unit length, and unit vectors along the y and z-axes. A compiled function is used to reduce the computation time. The Mathematica package Geometry-Rotat ions is also loaded since this contains the function Rotate3D used to perform rotations of the vectors through the three Euler angles. << Geometry~Rotations * reddot= Compile [{{vect, _Real, 1}, dipcoup, nT}, Cos[4V2 * dipcoup* nT *vect[[2]] *vect[[3]]]] ; N o w define the experimental parameters such as the initial I-S vectors, the angle C, between them, and individual I-S dipolar couplings, and evaluate Eq . 3.33 using a simple summation procedure to perform the integration. In this example the dephasing is calculated for an I2S with C, = 20°, and dipolar couplings Dt=D2 = 100 Hz. The function Rotate3D[v|/, 0, <))] performs successive rotations about the three Euler angles 9, and <j>; the first by \\i about the z axis, the second by angle 0 about the x axis, and the third around the z axis by angle A series of calculations was undertaken to determine the angular step size for the integration and the computation time required to achieve suitable precision. The results are presented in Table C.2 and reveal that a step size of n/40 radians provides AS/So correct to three decimal places, and thus represents a very efficient trade-off in terms of computation time versus precision. Table C.3 lists the theoretical R E D O R dephasing A S / S 0 calculated for a 3-spin I2S system having/) / = D2 = 100 Hz for different I-S-I angles The theoretical behavior for several I2S spin systems is explored further in Chapter 5. 360 Table C.2 R E D O R A S / S 0 dephasings calculated using Eq. 3.33 for an exact tetrahedral geometry of four / spins dipolar coupled (D = 120 Hz) to a single observed S spin using various step sizes for the numerical integration. Dephasing Time nxr (ms) Step Size (radians) j t / 2 0 T U /40 T C / 60 T I / 9 0 T I / 180 Exact* 0.0 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.8 0.04069 0.03918 0.03890 0.03878 0.03867 1.6 0.14921 0.14779 0.14753 0.14742 0.14375 0.14728 2.4 0.30726 0.30599 0.30576 0.30566 0.30548 3.2 0.48658 0.48551 0.48531 0.48523 0.48517 0.48502 4.0 0.65772 0.65687 0.65672 0.65665 0.65645 Calculation time per point 1 min 8 min 27 min 1.5 h 12 h Data from Dr. J . Schaefer; personal communication, December 5, 1996. 361 Table C.3 Theoretical R E D O R A S / S 0 dephasings calculated using Eq. 3.33 for different geometries of two / spins dipolar coupled (£>/ = D2 =100 Hz) to a single (observed) S spin. C, is the angle between the two heteronuclear vectors. A step size of 7T./20 radians was used for the numerical integrations. «x r (ms) C=20° C=45° C=90° C=109° £=120° £=180° 0 0.000 0.000 0.000 0.000 0.000 0.000 2 0.083 0.084 0.084 0.084 0.084 0.082 4 0.280 0.302 0.295 0.300 0.303 0.269 6 0.490 0.577 0.553 0.572 0.585 0.445 8 0.627 0.825 0.776 0.815 0.844 0.521 10 0.672 0.984 0.920 0.980 1.019 0.497 12 0.679 1.045 0.992 1.059 1.093 0.442 14 0.709 1.036 1.022 1.079 1.090 0.426 16 0.786 1.004 1.032 1.072 1.052 0.459 18 0.882 0.985 1.027 1.058 1.016 0.500 20 0.955 0.992 1.003 1.041 0.998 0.510 22 0.985 1.013 0.964 1.022 0.997 0.486 24 0.989 1.028 0.926 1.003 1.001 0.462 26 0.997 1.027 0.907 0.991 1.002 0.464 28 1.023 1.012 0.913 0.990 0.998 0.488 30 1.052 0.993 0.937 0.997 0.996 0.505 32 1.063 0.981 0.965 1.003 0.998 0.498 34 1.046 0.980 0.986 1.001 1.005 0.475 36 1.018 0.988 0.998 0.991 1.013 0.459 38 0.999 0.998 1.002 0.981 1.019 0.462 40 0.996 1.005 1.000 0.976 1.019 0.473 362 d l = 100; d2 = 100; f = N[ 20*Degree] ; vl= {0, 1, 0};v2 =N[ Rotate3D[ v l , £ , 0, 0]] ; 2 nTrot = N[ 1 ; nunpoints = 20; numlncr = 20 ; 1 1000 J maxbeta = n; maxalpha = 7r; maxgamna = n ; 2 inc = N[ 1 ; s4 = 0; L1000 J ^ maxgamma ^ maxbeta ^ maxalpha numXncr numlncr numlncr intlist20= {{0, 0}} ; Do[a = 0 . 0 ; s 3 = 0 . 0 ; Do[/3 = 0 . 0 ; s2 = 0 . 0 ; D o [ y = 0 . 0 ; s i = 0 . 0 ; Do[newVl = K o t a t e 3 D [ v l , a , /3, y ] ; newV2 = R o t a t e 3 D [ v 2 , a , /3, r] s r = N [ r e d d o t [ n e w V l , d l , n T r o t ] * r e d d o t [ n e w V 2 , d 2 , n T r o t ] ] ; s i = s i + ( s r * dy * Sin[j8]) ; y = y + dy , { n u m l n c r } ] ; s2 = s2 + ( s i * d/3) ; p= H + 673, { n u m l n c r } ] ; s 3 = s 3 + (s2 * da) ; a = a + d a , { n u m l n c r } ] ; / s 3 i s 4 = 1 - ; v 2*TT2 r P r i n t [ n T r o t * 1000, " , " , s4] ; A p p e n d T o [ i n t l i s t 2 0 , { n T r o t * 1000 , s 4 } ] ; n T r o t = n T r o t + i n c , {nunpoints} ] ; C.2.2.2 Single S Spin Dephased by a Gaussian Distribution of I Spins Blumenfeld et al. have described a method to calculate the R E D O R dephasing for a single S spin dipolar coupled to many / spins. ' 0 This was briefly discussed in Section 3.4.3 and the full details are presented in this section. Blumenfeld and co-workers ignored the geometrical arrangement o f the heteronuclear I-S vectors, and made the assumption that there wi l l exist a distribution of dipolar couplings between the individual IS spin pairs. They proposed that a 363 Gaussian distribution could be used to weight the contribution of the individual IS spin pairs. The result is a function having a direct dependence on the heteronuclear second moment M2(I-S): A S [ M 2 ( / - 5 ) ] Jo AS[Z>,] dD C.8 where w(Z>,) is the Gaussian weighting function: w(Di) = pnM2(I-S) exp Df 2[M2(I-S)f C.9 Eq. C.8 can be evaluated numerically, but requires long computation times. Substitution of A S / S 0 by the appropriate expression in terms of Bessel functions of order 1/4 (Eq. C.7) makes it possible to obtain an analytical solution (Eq. C.10). AS[ M2(I-S)] \-iF2[\^).\±A,-A*'M2(I-S)t ] 2 2 4 5 C.10 2F2 is a hypergeometric function defined by: 2F2 [{a,b},{c,d}, z k=oV ( a i ) k O i ) k - ( a p ) k (b , ) k (b , ) k ... ( b p ) k z k where k~^(C | ) k (c , ) k - ( c p ) k (d , ) k (d , ) k ... ( d p ) k k! (a,) 0 = l , a n d ( a , ) k =(a i ) (a i+ l ) (a,+ 2 ) . . .(a,+ k - 1) etc. Unfortunately the hypergeometric function becomes unstable (due to the magnitude of the individual terms and the number of terms) when n2 M2(I -S) x2 > 3 and no longer converges. However Eq. C.8 can be re-expressed as: 364 l4M2(I-S) Jo f°° J E X P 2M2(I-S) JUA (V2 « D x r ) J.|/4 (V2 nDxr )dD C. 11 Eq. C . l 1 can be evaluated numerically using the Gaussian-Hermite quadrature method" since it is of the form: [ V / ( i ) A = t W f / ( x ( . ) + ^ C . l 2 1 = / where x,- is the /-th root o f Hn(x), the Hermite polynomial o f order n, w, is defined by Eq. C. 13, and Rn is a (small) remainder term which was not included in the calculation. 2""' n\ 4n~ ' " « 2 [//„., (x,.)]2 w, = C.13 The fol lowing Mathematica code find the nodes of the «-th order Hermite polynomials, calculates the Gaussian weights, and defines the actual G a u s s R E D O R function. Note that H n must to be large enough (typically > 150) so that the approximation is acceptable and oscillations are not present in the resulting function. This function was derived by D. Brouwer. Hn= 1 5 0 ; Hroots = NSolve[HeiamiteH[Hn, x] == 0 , x] ; node = Re[x] / . Hroots; 2 H N " 1 Hn! V~7r , weight = Be — / . Hroots; L Hn2 (HermiteH[Hn-1, x]) 2 J GuassFEDCR [ nTr_, M J : = I 71 1 1 1 — nTr 1 - - / — V weighti *Besse lJ [ l /4 , 2 V M *node[[ i ] ] l * V 2 I = I ^ 2 + 1 1 0 0 0 B e s s e U f - l / 4 , 2 V M *node[ [i] ] 1 ; L 1 0 0 0 1 Here n T r is the dephasing time in milliseconds, and M is the heteronuclear second moment in Hz 2 . A series of curves calculated for different values of the second moment are given in 365 Chapter 5. Nonlinear fitting of experimental R E D O R data can be achieved using this function as described in Section C. 1.1.2 and uses only a single parameter corresponding to M2{I-S). C.3 T R A N S F E R R E D E C H O D O U B L E R E S O N A N C E C.3.1 T E D O R Behavior for Isolated IS Spin Pairs The theory of the T E D O R experiment is discussed in Section 3.5. In this section the equations and Mathematical code used to determine functions for different positions of the dephasing pulses, and perform nonlinear least squares fitting of the experimental data are presented. The theoretical T E D O R behavior for an isolated IS spin pair i s : J " n S T .= ^ \ \ \l s in [AO T „ (a , f3 ,X n ) ] s i n [ A O T j ( B ( a , p \ X J ] ship d$da C . l 4 where n is the number of rotor periods before coherence transfer, m is the number of rotor cycles after transfer, A.,, = nDxr and A,,„= mDxx. In a T E D O R experiment there are two dephasing 7i-pulses applied per rotor period, and these are applied at times t\ and t2 (0 < t] < t2 < x r). The dipolar phase accumulated over each rotor period ( A O T , where / = n or m) is: J A O T , = {QWCX,^) dt - J^coD(a,P,/) dt + | J c o D ( a , p , 0 dt C . l 5 Eq C. 15 can be evaluated in Mathematica for various choices of t\ and t2 as fol lows: First define function describing the dipolar coupling under M A S conditions (Eq. 1.14). omega [a_, /3_, t_] : = — * {Sin[/3] *Sin[/3] * Cos[2 ( o t u r t ) ] - V2 Sin[2/3] * Cos[a+wrt]} 366 N o w this function is integrated using appropriate limits. In this example position the pulses are at one quarter and three quarters o f each rotor cycle so t\ = x r /4 and t2 = 3x r /4 . Table C.4 contains the functions A<J>T>; (/= n or m) determined for a selection of possible pulse positions using this code. Numerical integration of Eq. C . 14 (using the appropriate functions from Table C.4) was used to determine the theoretical T E D O R dephasing for selected pulse positions and several o f these are plotted in Figure C.3. The maximum dephasing occurs when t2 - t\ = x r /2 and it is apparent that the oscillations are not periodic. There is no restriction that the pulse positions before and after the coherence transfer be the same. Furthermore, it is possible to achieve the same dephasing using different pulse positions. For example, identical behavior is observed with pulses at (x r /3 , 2x r /3) and (x r /6 , 5x r /6) since the net time during which the dephasing accumulates equals x r /3 in both cases (see Figure C.3 (a)). Inspection of the equations in Table C.4 reveals that the expression for A O T , is particularly simple when the dephasing pulses are applied at (x r /4 , 3x r /4). Muel ler derived an expression for this case in terms of Bessel functions of the first k ind: J delta_ph±4 = In tegra te [omega [a, b , c] , {c, 0, -^}] -Integrate[omega[a, b , c] , {c, , —^}] + Integrate[omega[a, b , c] , {c, ^ t r , r r } ] ; ExpandAl l [Tr igReduce[del ta_phi4 / . a i r r r - > 2 7T] ] S T = - {[./„(42 {K-U)f - [MV2 {K+ K}))2 } oo Z 16k 2 -1 {[jk(42 {%„-%m})f - IM42{K+K}))2 } C.16 k = l 367 Tab le C .4 T E D O R functions A(j)T>; (/ = n or ni) defining the dephasing for the indicated positions of the two dephasing 71-pulses per rotor period as a function of the dimensionless parameter A, = iDxT. Pulse Position A(()T,/ Tr 2Xr I ' T 1— r 47i 27i n A.. . 7 „ r . 4TC . 871 -t V 2 A,,. s i n 2 p [ s i n ( a + — ) - s i n ( a + — )J + -y- sin^P [sin ( 2 a + — ) - sin ( 2a+ —)J Xr 3Tr 4 ' T -4-v/2 A.,, cos a cos P sin p Tr 4lr 7 ' T r „ r • 871 . 2TI T A. . 2 r i r . 4TI n 16K -I V 2 A,,, sin 2p [sin ( a + — ) - sin ( a + — )J + -y sin p [sin (2a + — ) - sin (2a +—— )J X, 5Xr 7 ' T r~ r 571 T t i A. 7 r 271 1 OTX T V 2 A,,. s i n 2 p [sin ( a + — ) - s i n ( a + — )J + -y sin^p [ s i n ( 2 a + — ) - s i n ( 2 a + —)J X, 6Xr 7 ' T 1— r 7TC 27X i A. , r 47t 247t n V 2 A.. s i n2B s i n ( a + — ) - sin ( a + — ) + — s u r p sin (2a + — ) - s i n ( 2 a + ) 12 7 2 7 7 Xr 7Xr I ' T V2 A,. sin 2p [sin ( a + — ) - sin ( a + —)] + A,. s in2 P cos (2a) 4 4 Xr 8Xr 7 ' T V2 A,. sin 2P [sin ( a + ) - sin ( a + — )1 + —^ sin 2 p [sin (2a + — ) - sin (2a + )1 9 9 2 9 9 x, 9x, 1 0 ' 10 1— r 971 I t n A,. 7„ r . 271 . 1871 T V2 A,. s i n 2 p [ s i n ( a + — ) - sin (a + — )J + —'- sin"p [sin ( 2a+ — ) - sin ( 2a+ —)J Figure C.3 Theoretical T E D O R dephasing for an isolated IS spin pair for the indicated placements of the two dephasing 7t-pulses in the period fol lowing coherence transfer. The curves are plotted as a function of the dimensionless parameter mDxx and were calculated assuming nDx, = 0.84 and that the dephasing pulses before coherence transfer were at x r/4 and 3x r/4. The curves are identical for x r/3, 2x r/3 and x r/6, 5x r/6 since the net dephasing time is the same (x r/3). 369 Using Eq. C . l 6, nonlinear least squares fitting of the experimental T E D O R data acquired with all dephasing pulses applied at (x r /4 , 3x r /4) was possible. In addition to a parameter for the dipolar coupling, a scaling factor was required to match experimental and theoretical intensities since T E D O R intensities are not normalized. It was found that the use of a weighting function greatly improved the fitting procedure. The best weighting scheme was one determined by the inverse of the number of rotor cycles, since the T E D O R data decay to zero and better signal to noise (and thus more reliable peak intensities) are available at small numbers of rotor periods. A damping function was also applied to account for T2 decay during the experiment. The Mathematica code used to performing nonlinear fitting of T E D O R data is given below. First define a list teddata containing the experimental data in form {number rotor cycles, peak area}, and set the other experimental parameters used to acquire the data. In this case the spinning speed was 4.77 kHz, n = 2, and m was varied from 1 to 16 (maxm) in increments o f one rotor cycle. The package for the nonlinear regression analysis is also loaded. << Statistics NonlinearFit' maxm = 16; n = 2; speed = 4770; trot= N[l/speed] ; teddata = {{0, 0), {1, 12.02}, {2, 19.20}, {3, 24.25}, {4,22.47}, {5,15.75}, {6, 8.47}, {7, 1.81}, {8, -2.52}, {9, -3.65}, {10, -2.78}, {11, -1.15}, {12, 1.24}, {13, 2.80}, {14, 2.72}, {15, 2.125}, {16, 0.54}}; Calculate a list containing the weights to be used during the nonlinear fitting: weightlist = {} ; incr = 1; maxlocp = maxm / incr; AppendTo[ weightlist, 1.0]; i = 2; Do[ w= N[l / teddatai, 1] ; AppendTo[weightlist, w] ; i = i + 1, {maxlocp}] ; 370 Define the function tedfunc describing the T E D O R behavior for isolated IS spin pair in terms of Bessel functions (Eq. C . l 6). Here dampening is dependent on m (since the number of rotor cycles after the coherence transfer was varied), and sf is a scale factor to match the theoretical and experimental intensities. tedfunc [ sfac , n b , m a , d , t r , l b ] : = sfac * Exp [-ma TT t r lb] * — * N[BesseU[0, V2 (ma- rib) d tr] ] A2- N[BesseU[0, V 2 (ma+ nb) d tr] ] A2 (N[BesseU[i, V 2 (ma - nb) d tr] ] A 2 - N[BesseU[i, V 2 (ma+ nb) d tr] ] A2) N o w do the least squares fitting of the data to obtain the best parameters: NonlinearRegress[teddata, tedfunc[sf, n, m, dipcoup, trot , damp], m, {{sf, 65}, {dipcoup, 1200}, {damp, 60}}, Method -> LervenbergMarquardt, Weights -> weightlist, ShowProgress -> True, PegressionPeport-> BestFitParameters] ; Numerical integration of Eq. C.14 (using the appropriate functions from Table C.4) was used to visually fit experimental T E D O R data acquired when the dephasing pulses were not applied at (x r / 4 , 3 x r / 4 ) . C.3.2 T E D O R Behav ior F o r a Single S Spin Dephased by Several / Spins The theoretical T E D O R behavior for a single S spin dephased by several / spins can be derived by extending the methodology presented by Naito et al.13 and Schaefer and co-workers. 7^'" ' The basis for the general approach and the underlying assumptions are described in Sections 3.4.2, 3.5.3 and C.2.2. Essentially the A O T , arguments within the sine functions in Eq. C.14 are replaced by a sum of terms expressed as the appropriate vector dot products (Eqs. 3.38-371 3.41). A l l unique combinations of the individual +Z),'s must be considered. Eq. C.l 7 gives the expression which must be evaluated for a 3-spin I2S system. In this case there are only two combinations of the dipolar couplings which need be considered: Dj + D2 and Dt - D2. These combinations are represented as ±Xtj (i = n or m, and j = 1,2, 3... c) where c is the number o f combinations of the individual Z>,'s. The expression is integrated over the three Euler angles to reproduce all possible crystallite orientations and achieve a powder average. S t = c ^ f o Jo Jo {sin[A°T.n(<l),e,v|/,+A,,„) + AoT,„((|),e,v,+A2,„)]} x {sin[AOTi„, (<|), 0, \|/, +Xhm) + AOT>m (<|>, 9, +A2,m)]} sinG dQ dy + ^ J o Jo Jo {sin[AT,«(4>, e, xu, + AOT,„((|), e, v^ , -^ 2j„)]} x {sin[AOT>„,(()), 0, t|/, +h,m) + A O T „ , (()), G, -A.2j„,)]} dif sinG dQ d\\i ] C. 17 The package Geometry 'Rotations' required to perform rotations of the vectors through the three Euler angles and is loaded using: « Geometry ~ Rotations * Define compiled functions tedsum4, tedsum3, and tedsum2 for four, three, and two / spins coupled to a single S spin respectively. The calculation can be done for the chosen values of the experimental parameters using a simple summation to perform the integration. In this example the spinning speed was 4.540 kHz, m = 2,n was varied, and there are four / spins in an exact tetrahedral arrangement about a central S spin. For this 5-spin systems there are eight unique combinations of the +D,'s (out of a possible sixteen since, for example, ID/ + D2 + D3 + D41 = I -Di - D2 - D3- D4\) which must be included. 372 tedsum4 = Compile[{ nT, mT, {g, _Beal, 1}, dipl, {h, _Real, 1}, dip2, {i, _Real, 1}, dip3, {j, _Real, 1}, dip4}, Sin[4V 2 * nT * ((dipl * gl *g[[3]]) + (dip2 * hl *h[[3]]) + (dip3 * i [ [ l ] ] *i[[3]]) + (dip4 * j [ [1] ] * j [ [3] ])) ] * Sin [ 4 V2 * mT * ((dipl * gl *g[[3]]) + (dip2 * hl *h[[3]]) + (dip3 * i [ [ l ] ] *i[[3]]) + (dip4 * jl * j[[3]])) ] ] ; tedsum3 = Compile[{ nT, mT, {g, _Real, 1}, dipl, {h, _Real, 1}, dip2, {i, _Real, 1}, dip3}, Sin[4 V 2 * nT * ((dipl * g[ [1] ] * g[ [3] ]) + (dip2 * h[ [1] ] *h[ [3] ]) + (dip3 * i [ [ l ] ] *i[[3]])) ] * Sin[4 V 2 * mT * ((dipl * g[ [1] ] * g[ [3] ]) + (dip2 * h[ [1] ] *h[ [3] ]) + (dip3 * i [ [ l ] ] *i[[3]]) ) ] ] ; tedsum2 = Conpile[{ nT, mT, {g, _Real, 1}, dipl, {h, _Real, 1}, dip2}, Sin [ 4 V2 * nT * ((dipl * gl *g[[3]]) + (dip2 * hl *h[[3]]) ) ] * Sin [ 4 V 2 * mT * ((dipl * g[[l] ] *g[[3]]) + (dip2 * hl *h[[3]]) ) ] ] ; Table C.5 lists the theoretical T E D O R dephasing S T calculated for a 3-spin I2S system having Dt = D2= 100 Hz for different I-S-I angles The theoretical behavior for several I2S spin systems is explored further in Chapter 5. If required, the statistical occupancy of the individual / spin positions can be accounted for using an appropriate function (e.g. a binomial distribution) to weight the contributions from 5-, 4-, 3-, and 2-spin systems to produce the final curve (see Section 4.3.4.2). 373 Table C.5 Theoretical T E D O R S T dephasings calculated using Eq. C. 17 for different geometries of two / spins dipolar coupled (D/ = D2 =100 Hz) to a single (observed) S spin. C, is the angle between the two heteronuclear vectors. A step size of 7 i /20 radians was used for the numerical integrations assuming a spinning speed of 2.5 kHz, and that the number of rotor periods after the coherence transfer, m, was fixed at 20 (mDxr ~ 0.84). «x r (ms) C=20° C=45° C=90° C=109° C=120° C=180° 0 0.000 0.000 0.000 0.000 0.000 0.000 2 0.091 0.203 0.183 0.204 0.216 0.025 4 0.199 0.371 0.348 0.379 0.395 0.086 6 0.312 0.475 0.469 0.497 0.503 0.172 8 0.391 0.501 0.515 0.535 0.525 0.228 10 0.399 0.450 0.471 0.486 0.465 0.209 12 0.337 0.345 0.353 0.370 0.347 0.120 14 0.247 0.217 0.205 0.225 0.206 0.020 16 0.181 0.101 0.075 0.093 0.078 -0.029 18 0.162 0.021 -0.006 0.005 -0.008 -0.016 20 0.172 -0.016 -0.039 -0.034 -0.047 0.022 22 0.171 -0.021 -0.042 -0.040 -0.047 0.039 24 0.138 -0.011 -0.033 -0.034 -0.027 0.019 26 0.081 -0.002 -0.020 -0.028 -0.005 -0.012 28 0.031 -0.002 -0.002 -0.024 0.007 -0.025 30 0.006 -0.007 0.018 -0.020 0.010 -0.012 32 0.003 -0.011 0.036 -0.013 0.008 0.005 34 0.001 -0.009 0.042 -0.005 0.006 0.004 36 -0.013 0.000 0.033 0.000 0.004 -0.012 38 -0.034 0.011 0.015 0.000 0.003 -0.025 40 -0.045 0.020 0.000 0.001 0.000 -0.019 374 d l = 120; m = 2 ; speed = 4540; mTrot = N[m / speed] ; v l = N [ { 0 , 0, l } ] ; v 2 = N[{0, - y } ] ; - V 2 - V 2 -1 V2 - V 2 -1 v 3 = N [ { - ^ , - ^ - , - ^ } ] ; v 4 = N [ { ^ | r , V3 3 3 V 3 3 3 0.25 nTro t = Nf —-— 1 ; nunpoints = 14; numlncx = 15 ; L 1000 J maxbeta = n; maxalpha = n; maxgamma = n ; i n c = N[ ^'** 1 ; s4 = 0 ; nurtComb = 8 ; 1 1000 J maxganma maxbeta maxalpha dV = — = ^ ; dS = ; da = ; numlncr numlncr numlncr i n t l i s t 4 = {{0, 0}} ; Do[a = 0 . 0 ; s3 = 0 . 0 ; Do[/3 = 0 . 0 ; s2 = 0 . 0 ; Do[y = 0 . 0 ; s i = 0 . 0 ; Do[ newVL = Rota te3D[v l , a, p, y] ; newV2 = Rotate3D[v2, a , / 3 , Y] ; newV3 = Rotate3D[v3, a , / 3 , y] ; newV4 = Rotate3D[v4, a , / 3 , y] ; s r = N[tedsum4[nTrot, mTrot, newVL, d l , newV2, d l , newV3, d l , newV4, d l ] H tedsum4[nTrot, mTrot, newVl, d l , newV2, d l , newV3, d l , newV4, - d l ] tedsum4[nTrot, mTrot, newVL, d l , newV2, d l , newV3, - d l , newV4, d l ] tedsum4[nTrot, mTrot, newVl, d l , newV2, - d l , newV3, d l , newV4, d l ] tedsum4[nTrot, mTrot, newVl, d l , neWV2, d l , newV3, - d l , newV4, - d l ] tedsum4[nTrot, mTrot, newVl, d l , newV2, - d l , newV3, d l , newV4, - d l ] tedsum4[nTrot, mTrot, newVl, d l , newV2, - d l , newV3, - d l , newV4, d l ] tedsum4[nTrot, mTrot, newVl, - d l , neWV2, - d l , newV3, d l , newV4, d l ] ] ; s i = s i + ( s r * dy * S in [£ ] ) ; y = y + d y , {numlncr}] ; s2 = s2 + ( s i * d3) ; /3= /3 +dS, {numlncr}] ; s3 = s3 + (s2 * da) ; a = a + da, {numlncr}] ; s4 = ( „ f3— ; v numComb * 2 * T T ^ ' P r i n t [ n T r o t * 1000, " , " , s4] ; AppendTo [ i n t l i s t 4 , {nTrot * 1000, s4}] ; nTrot = nTrot + i n c , {numpoints}] ; 375 REFERENCES FOR APPENDIX C / (a) Wolfram, S. The Mathematica Book. Cambridge University Press, 3rd Edition, 1996. (b) Wolfram Research, Mathematica 3.0 Standard Add-On Packages. Cambridge University Press, 1996. 2 Hediger, S.; Meier, B .H. ; Ernst, R.R Chem. Phys. Lett. 1995, 240, 449-456. 3 Hediger, S. E T H Zurich, Personal Communication, August 1997. 4 Hediger, S. Ph.D. Dissertation, Eidgenossische Technische Hochschule Zurich, Switzerland. 1996. 5 Mueller, K.T. J. Magn. Reson. Ser. A, 1995, 113, 81-93. 6 Gul l ion T.; Schaefer, J . Adv. Magn. Reson. 1989, 13, 57-93. 7 Ho l l , S . M . Ph.D. Thesis, Washington University, Missour i , U.S.A. 1993. 8 Mueller, K.T.; Jarvie, T.P. ; Aurentz, D.J.; Roberts, B.W. Chem. Phys. Lett. 1995, 242, 535-542. Mueller, K.T.; Jarvie, T.P. ; Aurentz, D.J. ; Roberts, B.W. Chem. Phys. Lett. 1996, 254, 281-282. 9 Goetz, J . M . ; Schaefer, J . J. Magn. Reson. 1997,127, 147-154. 10 Blumenfeld, A . L . ; Coster, D.; Fripiat, J .J . J. Phys. Chem. 1995,99, 15181-15191. 11 Oberhettinger, H. in Handbook of Mathematical Functions, Abramowitz, M . ; Stegun, I. A . (Eds.) Dover Publications Inc. New York, 1970, 9th printing, Chapter 15. 12 Hing, A . W . ; Vega, S.; Schaefer, J . J. Magn. Reson. Ser. A, 1993,103, 151-162. 13 Naito, A . ; Nishimura, K.; Tuz i , S.; Saito, H. Chem. Phys. Lett. 1994, 229, 506-511. 14 Pan, Y . ; Gul l ion, T.; Schaefer, J . J. Magn. Reson. 1990, 90, 330-340. 376 APPENDIX D DERIVATION OF EQUATIONS FOR CALCULATING HETERONUCLEAR SECOND MOMENTS IN THE PRESENCE OF MOLECULAR MOTION The equations necessary for evaluating the I-S heteronuclear second moments for a polycrystalline (powder) sample in the presence of molecular motion are derived in this appendix. These were incorporated in the computer programs described in Appendix E used to locate sorbed /7-difluorobenzene in the channels of Z S M - 5 from ' H - 2 9 S i cross polarization data. 377 The second moment is in fact invariant to the presence of motion; however the apparent or measured second moment is not, since part o f the the resonance is shifted far from the centre of the resonance where it is masked by the spectrometer no ise / ' 2 Michel et al.3 derived a general expression for calculating the intermolecular contribution to the second moment in the presence of molecular reorientations. A n explicit form of this expression for heteronuclear second moments convenient for calculations is derived in this appendix. The approach involves calculating the average value of M2(I-S) (Eq. D. 1) over all orientations of the I-S heteronuclear vector, rij, during the course of the motion. The calculation is over all relevant nuclei and the averaging must be over the motions and then the powder/ <M2(I-S)>col = l] JI h2 Ug / ( 3 c o s 2 9 , - l ) : ( 1 6 * 3 ) 2 D. Here 9 y is the angle between r:j and the direction of the external magnetic field B0. Because the terms in front of the cosine expression are all constants, we need only evaluate the average value of Eq. D.2 over all relevant nuclei. 3 cos 2 »„. - 1 -|2 D.2 Eq. D.2 can be re-expressed in terms of Legendre Polynomials P2 as .5.6 3cos 2 9 y - 1 2 " 2 P 2 ( c o s S t f ) " [ '1 , L rl D.3 From the addition theorem of spherical harmonics Eq. D.3 can be expressed as Eq. D.4: " 2 ^ ( c o s 9 s ) ~ 2 [ 1? \ 871 5 r, ij m=-2 D.4 where Y2m are spherical harmonics, 0y, <|),y, and 6 2 , (j)2 are the polar angles describing the orientation of the I-S vector before and after the motion, respectively, and asterix indicates the complex conjugate. Expressions for the spherical harmonics are given in references 7 and 8. 378 For a given IS spin pair, i f the / nucleus occupies q sites, and the S nucleus occupies p sites during the motion, Eq. D.3 becomes: 3 cos 2 9 , in=-2 \pg Expanding the associated Legendre polynomials yields Eq. D . 6 , where the < > indicates averaging over all possible crystallite orientations in the polycrystalline sample. 3 cos 2 9 „ - 1 7 7 q i f [871 5 (pgY1=f1=t"y ^ 5 167T (3cos 2 0 „ - l ) ( 3 c o s 2 0 2 - 1) + 8TI 5 . 5 12TI 8 n 5 5 12jU "87t 5 (3sin0y. cos0y cos<t>(y)(3sin02 cos0 2 cos<)>2) (3sin0 (y cosGy sin <)>,•,)(3sin02 cos0 2 sin<))2) ( 3 ^ e , « » 2 * , ) ( 3 ^ e 1 « « 2 f c ) ( 3 s i n 2 6 y sin2<j) y)(3sin 20 2 sin2(()2) 5 48TI y ^ ( 3 s i n 2 0 y s i n 2 < j ) , y ) ( 3 s i n 2 0 2 t I } D.5 D . 6 For a powder sample all possible crystallite orientations must be accounted for and thus we must average 02 and <j)2 over all space. Averaging these terms yields Eqs. D 7 - D 9 * <(3 cos 2 0 2 - 1 ) 2 >= -3 <(3 sin0 2 cos0 2 cos(|)2)2> = <(3 sin0 2 cos0 2 sin<|)2)2> = -D.7 D.8 <(3 s in 2 0 2 cos2<t>2)2 > = <(3 s in 2 0 2 sin2d>2)2 > = — D.9 Substitution of these terms into Eq. D . 6 allows E q . D.2 to be expressed in a convenient form for use in calculations (Eq. DAO).49 379 ' ( 3 c o s 2 S „ - 1 ) 2 \ 1 ' « 1 J 1 p q r/ . ( / « / ) / - i j-\ ( 3 c o s 2 9 , - l ) 2 + D.10 4 , 4 , —(3s in9„ cos9„ cos<b„) + —(3s in6„ cosG,, sind),,) I ^ u 'j ~ij' 15 + -l(3sin2eycos2(t)y)2 + ^ ( 3 s i n 2 6 , s i n 2 ^ ) 2 } In the case of zeolite-sorbate complexes, the framework (Si) nuclei are not undergoing motion, so p=\, and the sum is thus reduced to a sum over the q positions which the sorbate nuclei (protons) occupy over the course of the motion. We must also consider that each sil icon wi l l be dipolar coupled to N ' H nuclei (each undergoing motion) and must sum the contributions from these interactions. Thus the final form of the equation which must be evaluated for each sil icon is: (1671 J | *=l # j-\ rkj 12 2 12 i y(s ine^.cos6 t y cos«|)^) + y(sine^cose^sin<t> i y)-+ ^(sin 2 e^cos2(|)^) 2 + | (s in 2 e j t y sin2( P / t 7 ) 2 } ] REFERENCES FOR APPENDED D 1 Pake, G .E . Solid State Physics. 1956, 2, 1. 2 Andrew, E.R.; Bradbury, A . ; Eades, R.G . Nature. 1958, 182, 1659. 3 Miche l , J . ; Drifford, M . ; Rigny, P. J. Chim. Phys. 1970, 67, 31. 4 Slicter, C P Principles of Magnetic Resonance.First Edition p. 63. Harper & Row, 1963. 5 Jeffrey, A . Handbook of Mathematical Formulas and Integrals. Academic Press, 1995. 6 Spiegel, M.R. Mathematical Handbook of Formulas and Tables. Schaum's Outline Series, McGraw-H i l l Book Company, 1968. 7 Arfken G . Mathematical Methods for Physicists. Third Edit ion, Academic Press, 1985. 8 (a) Steiner, E. The Chemistry Maths Book. Oxford University Press, 1996. (b) Bronshtein, I.N.; Semendyayev, K . A . Handbook of Mathematics.^anNostrad Re inho ld . 9 Aroca, P.P. Ph.D. Thesis, The University o f British Columbia, Canada, 1995. 380 APPENDIX E ALGORITHM FOR LOCATING MOLECULES IN ZEOLITE CHANNELS FROM CROSS POLARIZATION DATA This appendix contains a descriptive outline of the logical sequence of steps necessary for calcuations used to determine the location and orientation of the /7-difluorobenzene molecule in zeolite Z S M - 5 from 1 9 F - 2 9 S i and ' H - 2 9 S i cross polarization (CP) data. The actual computer programs were developed directly from this "pseudo-code" algorithm. The approach used was to search for linear correlations between the silicon-fluorine (or silicon-proton) heteronuclear second moments and the 1 / T C p values of selected silicons in the framework as the rigid sorbate molecule was rotated and translated within the zeolite channel system. Details of the background theory, N M R experiments, fitting of the C P data, and the results of these calculations are discussed in Chapter 6. 381 E.l PROGRAM OPTIONS AND DETAILS OF TRANSFORMATIONS USED Two different programs were written. The first o f these (CPF9.PAS) calculated static second moments, while the second (CPH9.PAS) incorporated molecular motions of the sorbate molecules (180° ring-flips about the F-F axis) using the equations derived in Appendix D. The actual programs were implemented using the PASCAL programming language and contained approximately 1800 lines of code. Routines incorporated in the program allowed orthogonal and non-orthogonal space groups symmetries to be used, and also supported non-standard choices of the axes in the different crystal systems. This latter requirement was imposed by the need to use the non-standard settings for the monoclinic phase of Z S M - 5 (i.e. space group P2i/n.l.l). The source code was compiled to run under the DOS operating system using the Turbo Pascal software package 7. The pseudo-code presented here is for analysis o f l 9 F - 2 9 S i C P data but is also applicable for 1 H- 2 9 Si C P data (only the input file had to be modified). A sample input file used for the analysis o f a l 9 F - 2 9 S i C P data set is also included. The programs allowed the mode of operation to be selected from four possible options : 1. Output atomic coordinates (fractional or Cartesian) for a given rotation and/or translation 2. Output of framework-sorbate distances for a given rotation and/or translation 3. Calculation of second moments and least-squares fit for a given rotation and/or translation 4. Calculation o f second moments and least-squares fits for a range of rotations and translations Option 1 provided coordinates for subsequent viewing in an appropriate graphical environment. The programs ATOMS 4.02 and ORTEP-3 for Windows3 were used for this purpose. The option to output sorbate-framework distances was used to produce the information required for the R E D O R and T E D O R simulations (Cartesian coordinates were also output when this option was selected). The program was thoroughly checked by comparing the output distances with those obtained from the PLATON-984 crystallography software, and against manual calculations performed for selected sorbate locations and orientations. The coordinate transformations used to interconvert between fractional and orthogonal Cartesian coordinates a re / 382 X = A f x and x = M " ' X where X and x are position vectors written as column vectors, with X expressed in Cartesian coordinates (dimension of length), and x in (dimensionless) crystallographic fractional coordinates. The matrices M and M'1 are valid for all 230 space groups and are defined a s / M -a cp I sin a 0 0^ a (cos y - cos a cos ft) / sin a b sin a 0 a cos j3 b cos a c) M sin a I a cp 0 0 ^ (cos a cos ft-cosy)/ b 9) sin a Mbs'ma 0 (cos a cos y-cosfi)/ c 49 sin a - 1 / c t a n a \lc) where a, b, c, a, /?, and yare the usual cell parameters (lattice constants), and 1 - cos 2 « - cos 2 / J - cos 2 y + 2 cos a cos ft cos 7 Fractional coordinates and details o f the crystallographic unit cell parameters for the Z S M - 5 framework were taken from the single crystal X-ray structure of calcined Z S M - 5 at room temperature reported by van Koningsveld etal. (Monocl inic, P2j/n.l.l, a = 20.107 A, b = 19.879 A, c = 13.369 A, a = 90.67 0 ) . 5 The symmetry operators for this non-standard space group were obtained from reference 7. Different symmetry operators were used for the F R O M and T O atom sets to ensure that the central unit cell contained 4 complete (intact) sorbate molecules. The sorbate molecule geometry was fixed to an ideal geometry: a planar, rigid, hexagonal para-disubstituted benzene ring with C - C , C - H , and C - F bond lengths of 1.392 A, 1.080 A, and 1.328 A respectively. The matrix R used for performing the rotations about three Euler angles (()), 9, vy) is: R = cos \\i cos 0 cos <) - sin vp sin § -sin v|/ cos 0 cos (j) - cos sin (j) sin 0 cos ()) cos \\) cos 0 sin (j) + sin \\i cos (> -sin \\i cos 0 sin q> + cos cos <)> sin 0 sin \y -cos i|/ sin 0^ sin v|/ sin 0 cos 0 where the first rotation is by <j) about the z axis, followed by a rotation of 0 about the y axis, and finally a rotation about the (new) z axis by v|/. 383 Four set of atoms were used. These were subdivided into two groups; the F R O M atoms (zeolite framework Si and O), and the T O atoms (F and H atoms in sorbate molecules). In addition to a complete unit cell of S i , O, F, and H atoms, the 26 surrounding unit cells of T O atoms were generated. A l l F R O M - T O distances were checked to ensure that a given translation and rotation did not bring the sorbate too close to the framework atoms (distances less than 2 A were flagged as "too close"). The second moment calculations were only done for the 2 9 S i and the T O atoms of interest (e.g. I 9 F for 1 9 F - 2 9 S i C P data), with any T O - F R O M distances exceeding the chosen limit (typically 8-10 A) omitted. In the case of the 1 H- 2 9 Si C P data, two calculations were done; one assuming the rings were stationary (static second moments calculated, i.e. using CPF9.PAS), and another using CPH9.PAS assuming the sorbate was undergoing 180° ring-flips about the F-F axis. E.2 S A M P L E I N P U T F I L E INPUT FILE f o r CPF9.PAS TITLE F- S i CP @ 230K 4 DFB + ZSM-5 ( P 2 1 / n . l . l Z e o l i t e s 1990,10,235) C e l l parameters a b c (Angstroms) 20.107 19.879 13.369 alpha beta gamma (degrees) 90.67 90.00 90.00 "From" Atoms Data Number of known atoms to c a l c u l a t e d i s t a n c e s e t c . FROM 24 Gyromagnetic r a t i o f o r FROM N u c l e i i n rad / T e s l a sec 53188000 FROM A t o m s ( l a b e l up to 4 chars, No spaces) and FRACTIONAL coords atom X y z S i l 0 42056 0. 05546 -0. 31990 Si2 0 31368 0. 03090 -0. 16358 Si3 0 27960 0. 06249 0. 05346 Si4 0 12395 0. 06233 0. 03674 Si5 0 07678 0. 02804 -0. 17597 Si6 0 19556 0 . 05585 -0. 31331 Si7 0 42542 -0. 17148 -0. 31930 Si8 0 31225 -0. 12653 -0. 17388 Si9 0 27325 -0. 17590 0. 03597 S i l O 0 11895 -0. 17634 0. 03436 S i l l 0 07156 -0. 12939 -0. 17516 S i l 2 0 19079 -0. 16528 -0. 31408 S i l 3 0 42837 0. 44297 -0. 33456 S i l 4 0 31237 0. 47305 -0. 18814 S i l 5 0 27704 0. 43889 0. 02940 S i l 6 0 12155 0. 43563 0. 03380 S i l 7 0 07096 0. 47315 -0. 17844 S i l 8 0 18737 0. 43778 -0. 31743 384 S i l 9 0 42389 0 67204 - 0 31417 S i 2 0 0 31278 0 63130 - 0 16836 S i 2 1 0 27312 0 66892 0 04608 S i 2 2 0 11867 0 67007 0 03868 S i 2 3 0 07268 0 63082 - 0 17757 S i 2 4 0 19446 0 68070 - 0 29789 " O t h e r F r o m " A t o m s D a t a Number o f known a t o m s t o c h e c k d i s t a n c e s e t c . FROM 48 O t h e r FROM A t o m s ( l a b e l up t o 4 c h a r s , No s p a c e s ) a n d F R A C T I O N A L c o o r d s a t o m X y z 01 0 . 3 7 7 9 0 . 0588 - 0 . 2194 02 0 . 3 1 0 6 0 . 0662 - 0 . 0564 03 0 . 2018 0 . 0472 0 . 0 4 6 5 04 0 . 1032 0 . 0671 - 0 . 0784 05 0 . 1230 0 . 0 4 4 3 - 0 . 2 6 9 3 06 0 . 2 4 8 3 0 . 0477 - 0 . 2248 07 0 . 3 7 6 9 - 0 . 1533 - 0 . 2 2 8 9 08 0 . 3050 - 0 . 1 6 6 9 - 0 . 0 7 2 5 09 0 . 1960 - 0 . 1558 0 . 0316 O10 0 . 0 8 8 5 - 0 . 1 6 8 9 - 0 . 0753 O i l 0 . 1208 - 0 . 1511 - 0 . 2 6 3 0 012 0 . 2 4 8 3 - 0 . 1376 - 0 . 2424 0 1 3 0 . 3 1 8 9 - 0 . 0 4 8 5 - 0 . 1490 014 0 . 0781 - 0 . 0 5 0 9 - 0 . 1 5 2 9 0 1 5 0 . 4 1 4 5 0 . 1253 - 0 . 3771 0 1 6 0 . 3 9 2 3 - 0 . 0041 - 0 . 3892 017 0 . 4022 - 0 . 1340 - 0 . 4 1 8 6 018 0 . 2 0 0 3 0 . 1298 - 0 . 3 5 8 3 0 1 9 0 . 2 0 9 9 0 . 0026 - 0 . 4008 02 0 0 . 1948 - 0 . 1 2 7 5 - 0 . 4188 0 2 1 0 . 0 0 3 2 0 . 0 5 1 5 - 0 . 2 0 4 1 022 0 . 0 0 2 3 - 0 . 1 4 7 5 - 0 . 2098 02 3 0 . 4 2 3 9 - 0 . 2 5 0 1 - 0 . 3 4 1 3 024 0 . 1987 - 0 . 2 4 3 5 - 0 . 3 3 5 6 0 2 5 0 . 2 8 2 2 - 0 . 2 5 2 5 0 . 0 6 7 6 02 6 0 . 1101 - 0 . 2 5 2 6 0 . 0697 027 0 . 3 7 9 9 0 . 4503 - 0 . 2408 028 0 . 3.14 3 0 . 4480 - 0 . 0754 0 2 9 0 . 1991 0 . 4318 0 . 0094 O30 0 . 0812 0 . 4478 - 0 . 0 6 6 9 0 3 1 0 . 1 2 0 6 0 . 4351 - 0 . 2527 032 0. 2 5 0 5 0 . 4401 - 0 . 2 4 5 1 0 3 3 0 . 3797 0 . 6590 - 0 . 2 1 6 9 034 0 . 3148 0 . 6459 - 0 . 0508 0 3 5 0 . 1961 0 . 6513 0 . 0 2 7 0 0 3 6 0 . 0822 0 . 6559 - 0 . 0 6 5 3 037 0 . 1232 0 . 6678 - 0 . 2504 038 0 . 2497 0 . 6694 - 0 . 2144 0 3 9 0 . 3054 0 . 5530 - 0 . 1913 040 0 . 0851 0 . 5 5 1 9 - 0 . 1834 0 4 1 0 . 4186 0 . 3714 - 0 . 3 8 8 5 042 0 . 4154 0 . 5 0 1 5 - 0 . 4 1 3 5 0 4 3 0 . 3938 0 . 6320 - 0 . 4087 044 0 . 1900 0 . 3711 - 0 . 3847 385 045 0 . 1 8 6 2 0 . 5 0 3 2 - 0 . 3 8 6 3 046 0 . 2 0 7 4 0 . 6 3 2 6 - 0 . 3 9 1 4 047 - 0 . 0 0 3 9 0 . 4 5 7 6 - 0 . 2 1 0 4 048 - 0 . 0 0 1 3 0 . 6 4 8 1 - 0 . 2 1 2 0 " T o " A t o m s D a t a Number o f known a t o m s t o c a l c u l a t e d i s t a n c e s e t c . TO 2 G y r o m a g n e t i c r a t i o f o r TO N u c l e i r a d / T e s l a s e c 2 5 1 8 1 0 0 0 0 TO A t o m s (up t o 4 c h a r s , No s p a c e s ) a n d F R A C T I O N A L c o o r d s a t o m x y z F l 0 . 5 0 0 0 0 0 0 . 1 1 3 1 6 3 - 0 . 0 0 2 3 7 9 F2 0 . 5 0 0 0 0 0 0 . 3 8 6 8 3 7 0 . 0 0 2 3 7 9 Number o f O t h e r a t o m s t o c h e c k d i s t a n c e s f o r ( n o t i n c l u d e d i n c a l c ) 4 l a b e l a n d f r a c t i o n a l c o o r d s (x, y , z) f o r O t h e r a t o m s HI 0 . 3 9 3 5 3 0 0 . 1 8 7 8 1 9 - 0 . 0 0 1 0 8 1 H l l 0 . 6 0 6 4 7 0 0 . 1 8 7 8 1 9 - 0 . 0 0 1 0 8 1 H2 0 . 3 9 3 5 3 0 0 . 3 1 2 1 8 1 0 . 0 0 1 0 8 1 H22 0 . 6 0 6 4 7 0 0 . 3 1 2 1 8 1 0 . 0 0 1 0 8 1 R i n g C e n t r e ( x , y , z a s F r a c t i o n a l c o o r d s ) 0 . 5 0 0 0 0 . 2 5 0 0 0 . 0 0 0 0 Number o f " F r o m " S y m m e t r y o p e r a t i o n s 4 S y m m e t r y I n s t r u c s t o g e n e r a t e a l l FROM a t o m s i n u n i t c e l l M u s t be same n u m b e r as a b o v e a n d i n c l u d e X Y Z as F I R S T O p e r a t o r d l d2 d3 e l e2 e3 f l f2 f 3 g h i 1 0 0 0 1 0 0 0 1 0 0000 0 . 0 0 0 0 0 . 0000 1 0 0 0 -1 0 0 0 - 1 0 5000 0 . 5 0 0 0 0 . 5000 - 1 0 0 0 - 1 0 0 0 - 1 0 0000 0 . 0 0 0 0 0 . 0000 - 1 0 0 0 1 0 0 0 1 0 5000 0 . 5 0 0 0 0 . 5000 Number o f " T o " S y m m e t r y o p e r a t i o n s 4 S y m m e t r y I n s t r u c s t o g e n e r a t e a l l TO a t o m s i n u n i t c e l l M u s t be same n u m b e r as a b o v e a n d i n c l u d e X Y Z as F I R S T O p e r a t o r d l d2 d3 e l e2 e3 f l f2 f 3 g h i 1 0 0 0 1 0 0 0 1 0 . 0 0 0 0 0 0000 0 0000 1 0 0 0 - 1 0 0 0 -1 0 . 5 0 0 0 0 5000 0 5000 - 1 0 0 0 - 1 0 0 0 - 1 1 . 0000 1 0000 1 0000 - 1 0 0 0 1 0 0 0 1 0 . 5 0 0 0 0 5000 0 5000 Number o f S i l i c o n s w i t h known T c p v a l u e s i n p u t 8 S i l i c o n T c p (ms 21 9 . 674 5 1 0 . 2 4 8 10 1 1 . 7 1 6 23 1 0 . 3 4 1 11 . 1 1 . 1 4 9 16 1 5 . 5 6 6 14 1 0 . 2 7 1 8 9 . 7 6 6 END 386 E.3 P S E U D O - C O D E LISTING (Static Second Moments) START PROGRAM Get information from User about filenames and desired mode of operation get fdenames for Input and Output files determine whether to do full calculation, single calculation, output distances or coordinates get limits and step sizes for translations and rotations get cut-off distance (distances longer than this were excluded from the calculations) Read in the information from the Input fde get cell constants (a, b, c, a, fi y) get fractional coordinates for the 4 sets o f atoms (Si , O, F and H) get symmetry operators gyromagnetic ratios of 2 9 S i and 1 9 F for second moment calculations coordinates of ring centroid for rotations read in T C p data for specific silicons calculate needed constants Generate complete unit cell of Si and O atoms apply symmetry operators to fractional coordinates ensure they lie within 0 < x < l , 0 < y < l , 0 < z < 1 convert to orthogonal Cartesian coordinates Prepare H and F atoms coordinates for rotations and translations shift fractional coordinates so ring centroid lies at (0,0,0) convert H and F coordinates to orthogonal Cartesian convert coordinates of ring centroid to orthogonal Cartesian store these coordinates Open Output fi le and write header information describing output, limits selected etc. IF Output Coordinates selected T H E N Perform Rotation and Translations calculate rotation matrix for selected angles <j>, 6, and \\i rotate Cartesian coordinates shift ring atoms to proper location using ring centroid coordinates apply translations along x, y, and z axes in Cartesian system IF Output Cartesian Coordinates selected T H E N write coordinates to Output file Close Output file IF Output Fractional Coordinates selected T H E N convert rotated/translated Cartesian coordinates to fractional coordinates write coordinates to Output file Close Output file 387 IF Output Distances selected T H E N Perform Rotation and Translations calculate rotation matrix for selected angles (j), 6, and \\i rotate Cartesian coordinates shift ring atoms to proper location using ring centroid coordinates apply translations along x, y, and z axes in Cartesian system Generate 27 complete cells of F atoms convert rotated / translated F Cartesian coordinates to fractional coordinates apply symmetry operators to fractional coordinates keeping rings intact convert to orthogonal Cartesian coordinates generate the 26 surrounding unit cells of F atoms Check and output Si-F and O-F distances determine all S i -F and O-F distances IF distance is less than the selected cut-off T H E N write distance and Cartesian coordinates to Output file IF distance is less than 2.0 A T H E N add "Too C lose" flag Generate 27 complete cells of H atoms convert rotated / translated H Cartesian coordinates to fractional coordinates apply symmetry operators to fractional coordinates keeping rings intact convert to orthogonal Cartesian coordinates generate the 26 surrounding unit cells of H atoms Check and output S i -H and O-H distances determine all S i -H and O-H distances IF distance is less than the selected cut-off T H E N write distance and Cartesian coordinates to Output file IF distance is less than 2.0 A T H E N add "Too C lose" flag Close Output file 388 IF Single Calculation selected T H E N Perform Rotation and Translations calculate rotation matrix for selected angles (|), 0, and \\i rotate Cartesian coordinates shift ring atoms to proper location using ring centroid coordinates apply translations along x, y, and z axes in Cartesian system Generate 27 complete unit cells o f H atoms convert rotated/translated Cartesian coordinates to fractional coordinates apply symmetry operators to fractional coordinates keeping rings intact convert to orthogonal Cartesian coordinates generate the 26 surrounding unit cells o f H atoms Check S i -H and O-H Distances determine distances from every framework atom in unit cell to all H atoms IF any of these distances is less than 2.0 A T H E N set "Too C lose" flag IF no H atoms are too close to framework atoms T H E N Generate 27 complete unit cells of F atoms convert rotated/translated Cartesian coordinates to fractional coordinates apply symmetry operators to fractional coordinates keeping rings intact convert to orthogonal Cartesian coordinates generate the 26 surrounding unit cells o f F atoms Check Si -F and O-F Distances determine distances from every framework atom in unit cell to all F atoms IF any of these distances is less than 2.0 A T H E N set "Too C lose" flag IF no sorbate atoms (H or F) are Too Close to Si or O atoms T H E N Calculate Second Moments for each of the unique silicons determine all Si-F distances (r) IF r < cut-off T H E N add 1/ r6 to sum of 1/ r6 multiply sum of 1 / r6 by appropriate factor to obtain second moment in Hz' Perform least squares fit of second Moment vs. 1 / T C p data write results o f regression (R 2 , slope, y-intercept) to Output file write list o f second moments for all silicons to Output file Close Output file 389 IF Full Calculation selected T H E N R O T A T I O N L O O P Increment angles <)), 9, and i|/ between selected limits using appropriate steps Perform Rotation calculate rotation matrix for selected angles ((), 9, and \\i rotate Cartesian coordinates shift ring atoms to proper location using ring centroid coordinates T R A N S L A T I O N L O O P Increment translational shift parameters between selected limits using appropriate steps Perform Translation translate along x, y, and z axes in Cartesian system Generate 27 complete unit cells of H atoms convert rotated/translated Cartesian coordinates to fractional coordinates apply symmetry operators to fractional coordinates keeping rings intact convert to orthogonal Cartesian coordinates generate the 26 surrounding unit cells of H atoms Check S i -H and O-H Distances determine distances from every framework atom in unit cell to all H atoms IF any of these distances is less than 2.0 A T H E N set "Too C lose" flag IF no H atoms are too close to framework atoms T H E N Generate 27 complete unit cells of F atoms convert rotated/translated Cartesian coordinates to fractional coordinates apply symmetry operators to fractional coordinates keeping rings intact convert to orthogonal Cartesian coordinates generate the 26 surrounding unit cells of F atoms Check Si-F and O-F Distances determine distances from every Si and O atom in unit cell to all F atoms IF any of these distances is less than 2.0 A T H E N set "Too C lose" flag IF no sorbate atoms (H or F) are Too Close to Si or O atoms T H E N Calculate Second Moments for each of the unique silicons determine all S i -F distances (r) IF r < cut-off T H E N add 1 / r6 to sum of 1/ r6 multiply sum of 1 / r6 by appropriate factor to obtain second moment in Hz 2 Perform least squares fit of second Moment vs. 1 / TCp data Check and compare regression results check slope is positive IF good regression T H E N 390 write results of regression (R 2 , slope, y-intercept) to Output file write list o f second moments for all silicons to Output file compare regression results with previous best IF better regression update "best fit" T H E N store location, orientation, and regression results L O O P through all possible T R A N S L A T I O N S L O O P through all possible R O T A T I O N S Output details of "best" solution write results of best regression found (R 2 , slope, y-intercept) to Output fi le list orientation and translations used to obtain this fit Close Output file END PROGRAM ************************************************** REFERENCES FOR APPENDIX E 1 Turbo Pascal, Version 6.0, 1991. Borland International, Inc. 4585 Scouts Val ley Drive, Scotts Val ley, C A 95066, U.S.A. 2 ATOMS 4.0, Shape Software, 521 Hidden Val ley Road, Kingsport, T N 57663 U.S.A. http://www.tricon.net/comm/shape/ 3 ORTEP-3 for Windows, Johnson, C . K . ; Burnett, M . N . ; Farrugia, L.J . Department of Chemistry, University of Glascow, U.K. 1998. http://www.chem.gla.ac.uk/~louis/ortep3/ 4 PLATON-98, Speck, A . L . ; Farrugia, L .J . Department of Chemistry, University of Glascow, U.K. 1998. http://www.chem.gla.ac.uk/~louis/platon97/ 5 Diamond, R. in International Tables for Crystallography, Volume B, p. 345, Shmueli, U. (Ed.), Kluwer Academic Publishers, 1993. 6 van Koninsveld, H.; Jansen, J . C ; van Bekkum, H. Zeolites, 1990,10, 235. 7 International Tables for Crystallography, Volume A , Hahn, T. (Ed.), Kluwer Academic Publishers, 1992. 8 Arfken, G . Mathematical Methods for Physicists, Third Edit ion, Chapter 4, Academic Press, 1985. 391 A P P E N D I X F SUPPLEMENTARY DATA FOR CHAPTER 6 This appendix contains supplementary data from the low temperature N M R investigations of purely silicieous Z S M - 5 loaded with ca. 4 molecules of />-difluorobenzene per unit cell presented in Chapter 6. Three tables are included: Table F.l Occupancies and connectivities within the asymmetric unit o f the monoclinic (P2,/n.l.l) phase of Z S M - 5 . Table F.2 Fractional coordinates forp-difluorobenzene atoms for the best location and orientation found from analysis o f the ' H - 2 9 S i C P data at 230 K. Table F.3 Fractional coordinates for/>-difluorobenzene atoms for the best location and orientation found from analysis o f the l 9 F - 2 9 S i C P data at 235 K. 392 Table F. l T-sites, their occupancies and connectivities for the asymmetric unit in the monolinic (P2j/n.l.l) phase of Z S M - 5 . Each T-site is connected to the four sites listed. T-site Occupancy Connectivity 1 1 2 16 17 22 2 1 1 3 6 8 3 1 2 4 18 24 4 1 3 5 13 19 5 1 4 6 11 13 6 1 2 5 15 21 7 1 8 16 19 23 8 1 2 7 9 12 9 1 8 10 18 21 10 1 9 11 13 22 11 1 5 10 12 19 12 1 8 11 15 24 13 1 4 5 10 14 14 1 13 15 18 20 15 1 6 12 14 16 16 1 1 7 15 17 17 1 1 16 18 23 18 1 3 9 14 17 19 1 4 7 11 20 20 1 14 19 21 24 21 1 6 9 20 22 22 1 1 10 21 23 23 1 7 17 22 24 24 1 3 12 20 23 393 Table F.2 Fractional coordinates* of the y>difluorobenzene atoms found from fitting'1' o f the ' H -2 9 S i C P data recorded at 230 K. The linear regression results and the parameters defining the translation and rotation for this solution are listed in Table 6.3 Atom x/a y/b z / c F l 0.58924 0.18347 -0.11514 F2 0.38092 0.31653 0.05530 HI 0.50471 0.13032 0.00865 H2 0.56012 0.30922 -0.14594 H3 0.41004 0.19078 0.08610 H4 0.46545 0.36968 -0.06849 C I 0.53839 0.21595 -0.07353 C2 0.49613 0.18261 -0.00820 C3 0.44283 0.21665 0.03541 C4 0.43177 0.28405 0.01369 C5 0.47403 0.31739 -0.05164 C6 0.52733 0.28335 -0.09525 f For monoclinic P2,/n. 1.1 symmetry with a = 20.107 A , b = 19.879 A , c = 13.369 A and a = 90.67°. * Static second moments used. 394 Table F.3 Fractional coordinates* of the />difluorobenzene atoms found from fitting* of the l 9 F -2 9 S i C P data recorded at 235 K. The linear regression results and the parameters defining the translation and rotation for this solution are listed in Table 6.3 Atom x/a y/b z / c F l 0.50000 0.09304 -0.03265 F2 0.50000 0.36671 -0.02789 HI 0.39353 0.16770 -0.03135 H2 0.60647 0.16770 -0.03135 H3 0.39353 0.29206 -0.02919 H4 0.60647 0.29206 -0.02919 CI 0.50000 0.15985 -0.03149 C2 0.44005 0.19486 -0.03088 C3 0.44005 0.26489 -0.02966 C4 0.50000 0.29991 -0.02905 C5 0.55995 0.26489 -0.02966 C6 0.55995 0.19486 -0.03088 f For monoclinic P2i/n.l.l symmetry with a = 20.107 A, b = 19.879 A, c = 13.369 A and a~ 90.67°. + Static second moments used. 395 APPENDIX G SUPPLEMENTARY DATA FOR THE /M/t4-XYLENE / ZSM-5 SINGLE CRYSTAL STRUCTURE This appendix contains supplementary data from the X-ray diffraction refinement of a single crystal of Z S M - 5 loaded with 2.85 molecules of /7-xylene per unit cel l . Ful l details o f the structure refinement are presented in Chapter 8. Three tables are included: Table G . l Anisotropic displacement factors for S i , O and C . Table G.2 Bond lengths in the Z S M - 5 framework. Table G.3 Bond angles in the Z S M - 5 framework. 396 Table G. l Anisotropic displacement parameters (A2 x 103) for the low-loaded p-xylene / ZSM-5 complex at 180 K. The anisotropic displacement factor exponent takes the form: -2TT [h2 a*2 Uu + ... + 2 h k a* b* Ul2\. Atom U22 t /23 Ul2 Si(l) 3(1) 5(1) 9(1) Kl) -1(1) 0(1) Si(2) 6(1) 6(1) 8(1) -1(1) 0(1) 1(1) Si(3) 7(1) 7(1) 7(1) -1(1) -1(1) KD Si(4) 6(1) 6(1) 7(1) -1(1) KO -1(1) Si(5) 5(1) 5(1) 7(1) 0(1) 1(1) 0(1) Si(6) 4(1) 6(1) 9(1) Kl) 1(1) 0(1) Si(7) 5(1) 4(1) 10(1) 0(1) 0(1) 1(1) Si(8) 6(1) 5(1) 9(1) 0(1) 1(1) 0(1) Si(9) 6(1) 4(1) 9(1) 1(1) -1(1) -1(1) Si(10) 7(1) 3(1) 9(1) 0(1) 0(1) 1(1) Si(ll) 6(1) 5(1) 8(1) KO 0(1) 0(1) Si(12) 6(1) 5(1) 9(1) 0(1) 2(1) -1(1) 0(1) 11(1) 24(1) 18(1) -2(1) 5(1) -2(1) 0(2) 21(1) 12(1) 8(1) -1(1) 2(1) -1(1) 0(3) 8(1) 30(1) 26(1) HD -2(1) 2(1) 0(4) 20(1) 13(1) 10(1) 0(1) -2(1) -4(1) 0(5) 6(1) 16(1) 11(1) 3(1) 1(1) -1(1) 0(6) 9(1) 35(1) 19(1) -1(1) -5(1) 4(1) 0(7) 11(1) 21(1) 20(1) -2(1) 6(1) 1(1) 0(8) 19(1) 29(1) 13(1) ' 9(1) 5(1) 6(1) 0(9) 9(1) 9(1) 26(1) -1(1) KD 0(1) 0(10) 26(1) 13(1) 13(1) 5(1) -5(1) -2(1) 0(11) 7(1) 19(1) 17(1) -6(1) KD 2(1) 0(12) 9(1) 30(1) 22(1) -8(1) -3(1) -1(1) 0(13) 32(1) 7(1) 35(1) -2(1) -8(1) 0(1) 0(14) 14(1) 6(1) 24(1) 1(1) -1(1) 0(1) 0(15) 12(1) 8(1) 24(1) 6(1) -5(1) -1(1) 0(16) 21(1) 12(1) 17(1) -5(1) -4(1) -3(1) 0(17) 27(1) 11(1) 13(1) 4(1) -5(1) 3(1) 0(18) 19(1) 10(1) 22(1) 4(1) 10(1) -2(1) 0(19) 16(1) 13(1) 16(1) -6(1) 0(1) 3(0 0(20) 26(1) 11(1) 13(1) 4(1) 3(1) -3(1) 0(21) 7(1) 15(1) 14(1) -3(1) 4(1) 1(1) 0(22) 7(1) 15(1) 19(1) 2(1) 3(1) -1(1) 0(23) 17(1) 8(1) 17(1) 0 3(1) 0 0(24) 21(1) 5(1) 23(1) 0 9(1) 0 0(25) 16(1) 6(1) 17(1) 0 -1(1) 0 0(26) 17(1) 3(1) 10(1) 0 -2(1) 0 C(l) 61(4) 176(10) 46(3) -3(5) -17(3) 13(5) C(2) 44(3) 276(18) 45(3) -11(5) -4(3) 20(5) C(3) 56(4) 182(11) 87(5) -1(5) 18(4) 0(4) C(4) 91(7) 222(14) 101(7) 26(8) -41(5) 42(8) 397 Table G.2 Bond lengths for framework atoms in ZSM-5 loaded with 2.85 molecules of p-xylene per unit cell at 180 K. Atom 1 -Atom2 Distance / A Si (l)-O(l) 1.5975(17) Si (1)-0(21) 1.5977(16) Si (0-0(15) 1.6043(16) Si (1)-0(16) 1.6066(16) Si (2)-0(6) 1.5959(17) Si (2)-0(2) 1.5981(16) Si (2)-0(l) 1.5999(17) Si (2)-0(13) 1.6033(18) Si (3)-0(3) 1.5995(17) Si (3)-0(2) 1.6013(16) Si (3)-O(20) 1.6042(17) Si (3)-0(19) 1.6045(17) Si (4)-0(4) 1.5993(15) Si (4)-0(3) 1.6012(17) Si (4)-0(16) 1.6015(16) Si (4)-0(17) 1.6033(17) Si (5)-0(21) 1.6006(16) Si (5)-0(5) 1.6022(15) Si (5)-0(14) 1.6039(17) Si (5)-0(4) 1.6070(16) Si (6)-0(6) 1.5966(17) Si (6)-0(18) 1.5979(17) Si (6)-0(5) 1.6056(16) Si (6)-0(19) 1.6054(16) Atom 1 -Atom2 Distance / A Si (7)-0(7) 1.5986(16) Si (7)-0(23) 1.5998(9) Si (7)-0(22) 1.6022(16) Si (7)-0(17) 1.6043(16) Si (8)-0(7) 1.5941(16) Si (8)-0(8) 1.5944(17) Si (8)-0(13) 1.5943(18) Si (8)-0(12) 1.6049(16) Si (9)-0(18) 1.5967(16) Si (9)-0(8) 1.5975(16) Si (9)-0(25) 1.5984(8) Si (9)-0(9) 1.6098(16) Si (10)-O(15) 1.6013(16) Si (10)-O(10) 1.6023(16) Si (10)-O(26) 1.6038(9) Si (10)-O(9) 1.6101(16) Si (ll)-O(lO) 1.6007(16) Si (11)-0(14) 1.6011(17) Si (ll)-O(ll) 1.6046(16) Si (ll)-0(22) 1.6093(16) Si (12)-0(24) 1.5978(8) Si (12)-O(20) 1.6020(16) Si (12)-0(12) 1.6026(17) Si (12)-Q(11) 1.6069(16) 398 Table G.3 Bond angles for framework atoms of ZSM-5 loaded with 2.85 molecules of p-xylene per u.c. at 180 K. Atom 1 -Atom2-Atom3 Angle H Atom 1 -Atom2-Atom3 Angle (°) 0(1)-Si(l)-0(21) 109.24(9) 0(18)-Si(9)-0(25 • 108.42(10) 0(1)-Si(l)-0(15) 109.83(9) 0(8)-Si(9)-0(25) 109.84(11) 0(21)-Si(l)-0(15) 108.80(9) 0(18)-Si(9)-0(9) 109.10(9) 0(1)-Si(l)-0(16) 111.09(9) 0(8)-Si(9)-0(9) 108.92(9) 0(21)-Si(l)-0(16) 109.10(9) 0(25)-Si(9)-0(9) 110.55(11) 0(15)-Si(l)-0(16) 108.73(9) O(15)-Si(10)-O(10) 110.60(9) 0(6)-Si(2)-0(2) 109.16(9) O(15)-Si(10)-O(26) 109.28(9) 0(6)-Si(2)-0(l) 110.11(9) O(10)-Si(10)-O(26) 108.53(9) 0(2)-Si(2)-0(l) 108.34(9) O(15)-Si(10)-O(9) 108.82(9) 0(6)-Si(2)-0(13) 109.42(10) O(10)-Si(10)-O(9) 109.17(9) 0(2)-Si(2)-0(13) 110.44(10) O(26)-Si(10)-O(9) 110.44(10) 0(1)-Si(2)-0(13) 109.36(10) O(10)-Si(ll)-O(14) 108.96(9) 0(3)-Si(3)-0(2) 111.12(9) O(10)-Si(ll)-O(ll) 109.50(9) O(3)-Si(3)-O(20) 109.91(10) 0(14)-Si(ll)-0(11) 110.11(9) O(2)-Si(3)-O(20) 108.19(9) O(10)-Si(ll)-O(22) 109.52(9) 0(3)-Si(3)-0(19) 108.46(9) 0(14)-Si(ll)-0(22) 109.92(9) 0(2)-Si(3)-0(19) 108.67(9) 0(ll)-Si(ll)-0(22) 108.82(8) O(20)-Si(3)-O(19) 110.49(9) O(24)-Si(12)-O(20) 108.34(11) 0(4)-Si(4)-0(3) 110.40(9) 0(24)-Si(12)-0(12) 110.69(11) 0(4)-Si(4)-0(16) 110.00(9) O(20)-Si(12)-O(12) 109.63(9) 0(3)-Si(4)-0(16) 108.73(9) 0(24)-Si(12)-0(ll) 110.29(10) 0(4)-Si(4)-0(17) 108.28(9) O(20)-Si(12)-O(ll) 110.22(9) 0(3)-Si(4)-0(17) 109.94(10) 0(12)-Si(12)-0(11) 107.68(9) 0(16)-Si(4)-0(17) 109.48(9) Si(l)-0(1)-Si(2) 154.77(12) 0(21)-Si(5)-0(5) 107.41(8) Si(2)-0(2)-Si(3) 148.59(12) 0(21)-Si(5)-0(14) 110.48(9) Si(3)-0(3)-Si(4) 163.07(13) 0(5)-Si(5)-0(14) 110.36(9) Si(4)-0(4)-Si(5) 149.20(11) 0(21)-Si(5)-0(4) 111.18(9) Si(5)-0(5)-Si(6) 140.50(10) 0(5)-Si(5)-0(4) 109.30(9) Si(6)-0(6)-Si(2) 164.67(12) 0(14)-Si(5)-0(4) 108.12(9) Si(8)-0(7)-Si(7) 156.86(12) 0(6)-Si(6)-0(18) 111.12(10) Si(8)-0(8)-Si(9) 154.46(12) 0(6)-Si(6)-0(5) 108.90(8) Si(9)-O(9)-Si(10) 147.24(12) 0(18)-Si(6)-0(5) 108.07(9) Si(ll)-O(10)-Si(10) 154.62(12) 0(6)-Si(6)-0(19) 109.70(9) Si(ll)-0(11)-Si(12) 142.16(10) 0(18)-Si(6)-0(19) 109.69(9) Si(12)-0(12)-Si(8) 158.98(12) 0(5)-Si(6)-0(19) 109.31(8) Si(8)-0(13)-Si(2) 159.56(14) 0(7)-Si(7)-0(23) 109.79(10) Si(ll)-0(14)-Si(5) 156.50(12) 0(7)-Si(7)-0(22) 108.66(9) Si(10)-O(15)-Si(l) 142.37(11) 0(23)-Si(7)-0(22) 110.12(10) Si(4)-0(16)-Si(l) 158.88(11) 0(7)-Si(7)-0(17) 109.98(9) Si(4)-0(17)-Si(7) 145.37(11) 0(23)-Si(7)-0(17) 107.92(10) Si(9)-0(18)-Si(6) 145.84(11) 0(22)-Si(7)-0(17) 110.36(9) Si(3)-G(19)-Si(6) 150.25(11) 0(7)-Si(8)-0(8) 107.51(9) Si(12)-O(20)-Si(3) 145.64(11) 0(7)-Si(8)-0(13) 109.52(10) Si(l)-0(21)-Si(5) 147.19(10) 0(8)-Si(8)-0(13) 109.54(10) Si(7)-0(22)-Si(ll) 144.23(11) 0(7)-Si(8)-0(12) 110.53(9) Si(7)-0(23)-Si(7) 149.43(15) 0(8)-Si(8)-0(12) 109.80(9) Si(12)-0(24)-Si(12) 154.06(16) 0(13)-Si(8)-0(12) 109.91(10) Si(9)-0(25)-Si(9) 149.99(15) 0(18)-Si(9)-0(8) 110.01(10) Si(10)-O(26)-Si(10) 142.98(14) Symmetry transformations used to generate equivalent atoms: x+1/2, y, -z-1/2; -x+1/2, -y, z+1/2; -x+1/2, -y, z-1/2; x-1/2, y, -z-1/2; x, -y-1/2, z. 399
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Location of guest species in zeolites by solid-state NMR
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