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Location, disorder, and dynamics of guest species in zeolite frameworks studied by solid state NMR and… Brouwer, Darren Henry 2003

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LOCATION, DISORDER, AND DYNAMICS OF GUEST SPECIES IN ZEOLITE FRAMEWORKS STUDIED BY SOLID STATE NMR AND X-RAY DIFFRACTION by DARREN HENRY BROUWER B.C.S., Redeemer University College, 1997 B.Sc., The University of Guelph, 1997 A THESIS SUBMITTED IN PARTIAL FULFILMENT 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 March 2003 © Darren Henry Brouwer, 2003 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 Chemistry The University of British Columbia Vancouver, Canada Abstract Zeolites are microcrystalline framework materials with well-defined cavities and channels of molecular dimensions which enable them to act as 'molecular sieves' with size and shape selectivity towards which guest species may occupy positions within or diffuse through the pore and channel systems. Understanding the interactions between guest species and host zeolite frameworks, which are central to the synthesis and applications of zeolites, with a view to reliably modeling these systems, requires detailed structural information for these zeolite host guest complexes. For most zeolites, the application of x-ray diffraction to the structure determination of these complexes is precluded due to the microcrystalline nature of almost all zeolites and the weak scattering of the guest species. Solid state NMR, which is not limited by crystal size, offers an alternative, or at least complementary, method for structure determination of zeolite host/guest complexes. This thesis explores the potential of solid state NMR to provide information about the structure, dynamics, and disorder in zeolite guest/host complexes. A general strategy for locating guest species in zeolites was developed and implemented. This strategy consists of three main steps: (1) assign resonances (e.g. in the 2 9 Si spectrum ) to specific sites of the zeolite framework by performing two-dimensional correlation experiments, (2) experimentally probe the strengths of dipolar couplings (which are related to internuclear distances) between nuclei of the guest species (e.g. 'H or 1 9F) and the nuclei of the zeolite framework (e.g. 2 9Si), and (3) use this distance information to determine the location of the guest species with respect to the zeolite framework. The location of the fluoride ion in an as-made zeolite synthesized from fluoride-containing medium was determined by first assigning the peaks in the 2 9 Si spectrum from a two-dimensional 2 9 Si INADEQUATE spectrum, after which 'H/ 1 9 F/ 2 9 Si triple-resonance dipolar recoupling experiments were performed to measure F-Si distances to various Si sites of the zeolite framework, from which the location of the fluoride ion was deduced, along with the nature of the fluoride ion dynamics. The fluoride ions were found to be directly bonded to the zeolite framework, giving five-coordinate silicon sites whose local structure geometry was determined (due to the presence of structural disorder) only by a combination of solid state NMR distance measurements and single crystal XRD. The locations of several small organic sorbate molecules in highly siliceous ZSM-5 zeolite were determined by first assigning the peaks in the 2 9 Si spectrum, followed by relating the experimentally measured rates of 2 9Si{'H} cross-polarization to the calculated 'H/ 2 9Si dipolar coupling second moments. This solid state NMR structure determination protocol was shown to be reliable and robust over a range of sorbate loadings and temperatures and relatively insensitive to the exact nature of the zeolite framework used. The guest molecule locations determined by this solid state NMR method are in excellent agreement with the few single crystal XRD structures available. ii Table of Contents Abstract ii Table of Contents iii List of Figures ix List of Tables xiv Symbols and Abbreviations xvii Statement of Publication xx Acknowledgements xxi Dedication xxii Chapter 1 An Introduction to Zeolites, X-ray Diffraction, and Solid State NMR Spectroscopy 1 1.1 Motivation for this research 1 1.2 Zeolites 2 1.2.1 Structure and properties of zeolites 2 1.2.2 Applications of zeolites 3 1.2.3 Synthesis of zeolites 3 1.2.4 Characterization of zeolites 5 1.3 X-ray diffraction 6 1.3.1 Crystals, symmetry, and space groups 6 1.3.2 Diffraction of x-rays 8 1.3.3 The phase problem 10 1.3.4 Difference Fourier synthesis 11 1.3.5 Structure refinement 11 1.3.6 The correctness of a structure 12 1.3.7 Application of x-ray diffraction to zeolites 13 1.4 Solid state N M R spectroscopy 13 1.4.1 Nuclear spin interactions in the solid state 14 1.4.1.1 Zeeman interaction 15 1.4.1.2 Magnetic shielding (chemical shift) 16 1.4.1.3 Dipolar interaction 18 1.4.1.4 Indirect spin-spin coupling (scalar interaction) 19 1.4.2 Pulsed Fourier Transform N M R 20 1.4.3 N M R relaxation processes 22 1.4.3.1 Spin-lattice relaxation time (Ti) 22 1.4.3.2 Spin-spin relaxation time (T2) 23 1.4.3.3 Spin-lattice relaxation time in the rotating frame (T\p) 24 1.4.3.4 Temperature dependence of relaxation times 25 1.4.4 High resolution solid state N M R 26 1.4.4.1 High power decoupling 27 1.4.4.2 Magic angle spinning 27 1.4.4.3 Cross polarization 29 1.4.5 Internuclear distance measurements by solid state N M R 30 1.4.6 Application of solid state N M R to zeolites 30 1.5 Relationship between solid state N M R and X-ray diffraction 32 1.6 Outline and framework of thesis 32 References for Chapter 1 34 iii Chapter 2 Solid State NMR Experiments and Strategies for Assigning the NMR Resonances of the Zeolite Framework 37 2.1 Introduction 37 2.2 Two-dimensional NMR 37 2.3 The INADEQUATE experiment 39 2.3.1 Pulse Sequence for INADEQUATE 39 2.3.2 INADEQUATE in the solid state 40 2.3.3 Determination of zeolite framework connectivities by two-dimensional NMR 40 2.4 Peak assignments from two-dimensional NMR correlation experiments 41 2.4.1 Input for peak assignment algorithm 41 2.4.2 Testing peak assignments 44 2.4.3 Increasing efficiency 45 2.4.4 Application to the monoclinic phase of zeolite ZSM-5 48 2.4.5 Summary of peak assignment algorithm 50 2.5 Variables and functions for the algorithm 51 References for Chapter 2 53 Chapter 3 Evaluation of Solid State NMR Experiments for the Measurement of Heteronuclear Dipolar Couplings 55 3.1 Introduction 55 3.2 Cross polarization 55 3.2.1 The cross polarization pulse sequence 56 3.2.2 Dependence of CP behavior on the nature of the spin system 56 3.3 Cross polarization in an extended spin system 58 3.3.1 Thermodynamic description of cross polarization 58 3.3.2 The Hartmann-Hahn condition in an extended spin system 59 3.3.3 Thermodynamic description of cross polarization dynamics 60 3.3.4 The cross polarization drain experiment 62 3.3.5 Relationship of cross polarization rate constants to structure 63 3.4 Cross polarization in an isolated spin pair 64 3.4.1 Dipolar coupling under MAS conditions 64 3.4.2 Heteronuclear dipolar recoupling by CP MAS NMR 66 3.4.3 Practical suggestions for fitting experimental CP data 68 3.5 Rotational Echo Double Resonance (REDOR) 69 3.5.1 The REDOR pulse sequence 69 3.5.2 Explanation of the REDOR experiment 70 3.6 Transferred Echo Double Resonance (TEDOR) 74 3.6.1 The TEDOR pulse sequence 74 3.6.2 TEDOR behavior for isolated IS spin pairs 75 3.7 Comparison of CP, REDOR, and TEDOR for distance determinations 76 3.8 Conclusions 78 References for Chapter 3 79 iv Chapter 4 The Location and Dynamics of the Fluoride Ion in Tetrapropylammonium Fluoride Silicalite-1 81 4.1 Introduction 81 4.1.1 Synthesis of zeolites from fluoride-containing media 81 4.1.2 The role of fluoride ions in controlling zeolite synthesis 82 4.1.3 Diffraction studies of fluoride-containing zeolites 82 4.1.4 Solid state NMR studies of fluoride-containing zeolites 84 4.1.5 Locating the fluoride ions by solid-state NMR ...85 4.1.6 'H/ 1 9F/ 2 9Si triple frequency probe 86 4.2 Results and Discussion 87 4.2.1 29Si{'H} CP MAS spectrum 88 4.2.2 2 9Si peak assignments 89 4.2.3 Measuring l 9 F- 2 9 Si distances and determining fluoride location 90 4.2.3.1 29Si{19F} CPMAS 90 4.2.3.2 29Si{ l9F} REDOR 94 4.2.3.3 29Si{19F} TEDOR 95 4.2.3.4 Comparing CP, REDOR, and TEDOR 96 4.2.4 Dynamics of the fluoride ion 97 4.3 Conclusion 101 References for Chapter 4 102 Chapter 5 Combined Solid State NMR and XRD Investigation of the Local Structure of the Five-Coordinate Silicon in Fluoride-Containing As-Synthesized Zeolites 104 5.1 Introduction 104 5.2 Results for STF zeolite 105 5.2.1 Structure of STF 105 5.2.2 Fast spinning 2 9Si spectra 106 5.2.3 Five-coordinate silicon 108 5.2.4 Four-coordinate silicons 111 5.2.5 1 9 F MAS spectrum 114 5.2.6 Refinement of XRD data revisited 114 5.3 Results for SFF zeolite 117 5.3.1 Structure of SFF 118 5.3.2 Fast spinning 2 9Si spectrum 118 5.3.3 Measurement of F-Si distance by solid state NMR 119 5.4 Results for MFI zeolite 121 5.5 Conclusions 122 References for Chapter 5 123 Chapter 6 Locating Organic Guest Molecules in Zeolite Hosts by Solid State Cross-Polarization MAS NMR 124 6.1 Introduction 124 6.2 The zeolite ZSM-5 126 6.2.1 Structural features of the MFI framework topology 127 6.2.2 X-ray diffraction studies of ZSM-5 systems 128 6.2.3 Solid state 2 9Si NMR studies of ZSM-5 systems 129 6.3 NMR Measurements of the pDCB/ZSM-5 complex 130 v 6.3.1 Variable temperature 2 9Si spectra 131 6.3.2 Peak assignments 131 6.3.3 Cross polarization rate constants 132 6.4 Algorithm for locating guest molecules 136 6.4.1 Input 137 6.4.2 Definition of guest molecule location 137 6.4.3 Testing the locations 139 6.4.3.1 Determination of physically reasonable locations 139 6.4.3.2 Calculation of second moments and comparison to experimental data 140 6.4.3.3 Predicting and testing the intensities of the overlapping peaks 140 6.4.4 Display and summarize the results 141 6.4.5 Predicting the entire CP MAS spectrum 145 6.5 Reliability and robustness of the algorithm 146 6.5.1 Use of relative cross polarization rate constants 146 6.5.2 Sensitivity to changing the exact zeolite framework structure 147 6.5.3 Effect of temperature and motions 148 6.6 Conclusion 149 References for Chapter 6 154 Chapter 7 Investigation of the Effects of Temperature and Sorbate Loading on the Reliability of the Solid State CP MAS NMR Structure Determination Protocol 156 7.1 Introduction 156 7.2 Effect of temperature and loading on 2 9Si MAS NMR spectra 156 7.2.1 2 9Si peak assignments 157 7.2.2 Variable temperature 2 9Si MAS NMR spectra 158 7.2.3 2 9Si relaxation time measurements 160 7.3 Effects of temperature, sorbate loading, and oxygen on the 29Si{1H} CP MAS NMR dynamics 164 7.4 Effect of temperature and loading on structure determination by 29Si{'H} CP MAS NMR 170 7.5 Summary and conclusions 181 References for Chapter 7 182 Chapter 8 The Location of Naphthalene in Zeolite ZSM-5 Determined by Solid State 29Si{1H} CP MAS NMR 183 8.1 Introduction 183 8.2 NMR measurements on the naphthaIene/ZSM-5 complexes 184 8.2.1 Variable Temperature 2 9Si MAS NMR Spectra 184 8.2.2 Peak assignments 185 8.2.3 Cross polarization rate constants 186 8.3 Locating the guest molecules 191 8.4 Conclusions 196 References for Chapter 8 197 Chapter 9 Investigation of the Structure of the p-Dinitrobenzene/ZSM-5 Complex by Solid State 29Si{1H} CP MAS NMR and Single Crystal XRD 198 9.1 Introduction 198 9.2 Solid state NMR measurements 198 vi 9.2.1 Variable Temperature 2 9Si MAS NMR Spectra 199 9.2.2 Peak assignments 199 9.2.3 Cross polarization rate constants 200 9.3 Locating the guest molecules 203 9.4 Single crystal XRD results 207 9.5 Conclusions 212 References for Chapter 9 213 Chapter 10 Combined Solid State NMR and X-ray Diffraction Investigation of Order/Disorder in the p-Nitroaniline/ZSM-5 Complex 214 10.1 Introduction 214 10.2 Solid state NMR results 215 10.2.1 2 9Si MAS NMR spectra 215 10.2.2 1 5 N CP MAS NMR spectra 217 10.3 X-ray diffraction results 218 10.3.1 Possible structural models 219 10.3.2 The final structure 221 10.4 Discussion 225 10.5 Conclusions 229 References for Chapter 10 229 Chapter 11 Conclusions and Suggestions for Further Work 230 11.1 Summary and conclusions 230 11.2 Suggestions for further work 231 Chapter 12 Experimental Details 233 12.1 Preparation of samples 233 12.1.1 Reference samples 233 12.1.2 Fluoride-containing zeolites 233 12.1.3 Highly siliceous ZSM-5 234 12.1.4 Labeled organic sorbate molecules 235 12.1.5 Sorbate/zeolite complexes 236 12.2 Solid state NMR 237 12.2.1 NMR spectrometer 237 12.2.2 Probes 237 12.2.3 Magic angle spinning 239 12.2.4 Low temperature MAS 239 12.2.5 The effect of MAS on sample temperature 241 12.2.6 Shimming 242 12.2.7 Reference samples for setting up NMR experiments 242 12.2.8 2 9Si MAS and 29Si{'H} CP MAS NMR 243 12.2.9 2 9Si INADEQUATE experiments 244 12.2.10 29Si{19F} CP and REDOR experiments 245 12.2.11 'H/ 1 9F/ 2 9Si CP, REDOR, TEDOR experiments 246 12.3 Data analysis and calculations 247 12.3.1 Deconvolution of spectra 247 vn 12.3.2 Analysis of NMR peak area data 248 12.3.3 Peak assignments from INADEQUATE spectra 248 12.3.4 Sorbate/zeolite structure determination 248 12.3.5 Equations for calculating two-site exchange line shapes 248 12.4 Single crystal X-ray diffraction 249 12.4.1 Diffractometers, data collection and processing 249 12.4.2 Structure refinement 250 References for Chapter 12 250 Appendix A NMR Pulse Sequence Programs 251 A. 1 Index of NMR pulse sequence programs 251 A.2 Single pulse experiments 252 A.3 Relaxation time experiments 253 A.4 Cross polarization experiments 257 A.5 REDOR experiments 263 A.6 TEDOR experiments 269 A.7 INEPT experiment 271 A. 8 INADEQUATE experiments 272 Appendix B Supplementary Information for XRD refinements 274 B. 1 Crystal structure determination for [F,DMABO]-STF 274 B.2 Crystal structure determination for pDNB/ZSM-5 278 B. 3 Crystal structure determination for pNA/ZSM-5 283 Appendix C Mathematica Notebooks for Analysis of NMR Data 289 C. 1 Peak Assignment Algorithm 289 C.2 Spectrum Deconvolution 289 C.3 Curve Fitting 289 C.4 Structure Determination 290 C.5 Determining Error Ellipsoids for a set of 3D scatter points 291 viii List of Figures Figure 1.1 Representations of selected zeolite framework topologies 2 Figure 1.2 Illustration of the three-dimensional crystal lattice and the unit cell 6 Figure 1.3 Examples of the five types of crystallographic symmetry operations 7 Figure 1.4 Illustration of Bragg's Law 8 Figure 1.5 Direct and reciprocal lattices for a monoclinic unit cell 9 Figure 1.6 Atomic scattering factors (J) for a number of atoms as a function of sinfj/^  10 Figure 1.7 The Zeeman interaction of a spin-'/2 nucleus with a magnetic field 16 Figure 1.8 Illustration of the orientation-dependence of the chemical shift interaction 17 Figure 1.9 Calculated powder lineshapes for chemical shift anisotropy tensors 18 Figure 1.10 Illustration of the dipolar interaction 19 Figure 1.11 The vector model for NMR 20 Figure 1.12 Effect of a 'pulse' on the net magnetization in the rotating frame of reference 21 Figure 1.13 Free induction decay signal and resulting spectrum following Fourier transformation 22 Figure 1.14 Measuring T\ relaxation time by inversion recovery and saturation recovery experiments 24 Figure 1.15 Measuring T2 relaxation times by the spin-echo NMR experiment 24 Figure 1.16 Measuring T\p relaxation times by the spin-locking pulse 25 Figure 1.17 The general behavior of relaxation times as a function of temperature 26 Figure 1.18 1 3 C NMR spectra demonstrating the gain in spectral resolution and sensitivity arising from high-resolution solid state NMR techniques 27 Figure 1.19 l 3 C NMR spectra obtained for a powder sample of ferrocene demonstrating the effect of the magic angle spinning frequency 29 Figure 1.20 2 9Si MAS NMR spectra of NaY zeolite and of a very highly crystalline and completely siliceous zeolite ZSM-5 sample 31 Figure 2.1 General two-dimensional NMR experiment 38 Figure 2.2 Illustration of a two-dimensional NMR experiment (CP MAS HETCOR) 38 Figure 2.3 Pulse sequence diagram for the two-dimensional INADEQUATE experiment 39 Figure 2.4 Schematic contour plot of a two-dimensional INADEQUATE experiment 39 Figure 2.5 Framework structure of ZSM-12 42 Figure 2.6 Two-dimensional 2 9Si INADEQUATE spectrum of ZSM-12 zeolite 43 Figure 2.7 Schematic description of the peak assignment algorithm 46 Figure 2.8 Schematic of the Si connectivites in the monoclinic phase of the ZSM-5 framework 48 Figure 2.9 Two-dimensional 2 9Si INADEQUATE spectrum of the monoclinic phase of ZSM-5 49 Figure 3.1 Cross polarization pulse sequence for polarization transfer from / spins to S spins 56 Figure 3.2 Illustration of the cross polarization dynamics and matching profiles for polarization transfer from the I spins to the S spins for different types of spin systems 57 Figure 3.3 The cross polarization experiment 59 Figure 3.4. Schematic representation of the thermodynamic description of cross polarization 60 Figure 3.5. Dynamics of the observed S spin magnetization in standard S{I} cross polarization experiment 62 Figure 3.6 Pulse sequence diagrams for the collecting the 'reference' and 'drain' spectra for the CP drain experiments 63 ix Figure 3.7 Cross polarization dynamics in a S{I} cross polarization drain experiment 63 Figure 3.8 Definitions of the angles used to the describe the orientation of the IS internuclear vector under magic angle spinning conditions 66 Figure 3.9 Behavior of the dipolar coupling as a function of the spinner orientation under MAS 66 Figure 3.10 Ffartmann-Hahn CP matching profile for an isolated spin pair undergoing magic angle spinning 67 Figure 3.11 S{I} cross polarization curves for an isolated IS spin pair 68 Figure 3.12 S{I} REDOR pulse sequence 70 Figure 3.13 S{I} REDOR curves 70 Figure 3.14 Illustrations for the explanation of the REDOR experiment 72 Figure 3.15 The universal REDOR curve 73 Figure 3.16 NMR pulse sequences for refocused INEPT and refocused TEDOR 74 Figure 3.17 Calculated TEDOR curves illustrating the effects of different dipolar couplings 76 Figure 4.1 Proposed locations of the fluoride ion in [F,TPA]-MFI 84 Figure 4.2 29Si{'H} CP MAS spectra of [F,TPA]-MFI at room temperature and low temperature 85 Figure 4.3 Schematic diagram of the outer coil for the 'H/ I 9F/X probe 86 Figure 4.4 Pulse sequences used: 29Si{'H} CP MAS INADEQUATE, 29Si{19F{'H}} double cross polarization, 29Si{19F} REDOR, and l9F{29Si} TEDOR 87 Figure 4.5 MFl framework and TPA template location 87 Figure 4.6 29Si{'H} CP MAS spectrum of [F,TPA]-MFI (with deconvolution) 88 Figure 4.7. Two-dimensional 29Si{'H} CP MAS INADEQUATE spectrum of [F,TPA]-MFI 90 Figure 4.8. Comparison of the 29Si{'H} CP MAS spectrum to a 29Si{'9F{'H}} double CP spectrum 91 Figure 4.9 29Si{19F} CP curves and possible locations of the fluoride ion 92 Figure 4.10 Hartmann-Hahn 29Si{ l9F} cross polarization matching profile 93 Figure 4.11 Results of fitting the oscillations in the experimental CP data to theoretical 29Si{19F} CP curves 94 Figure 4.12 Results of the fitting of the oscillations in the 29Si{19F} REDOR curves 95 Figure 4.13 Results of the fitting of the 29Si{19F} TEDOR curves 96 Figure 4.14 Illustration of the proposed exchange process involving the fluoride ion 98 Figure 4.15 Variable temperature 1 9 F MAS NMR spectra of [F,TPA]-MFI 98 Figure 4.16 Variable temperature 29Si{'H} CP MAS NMR spectra and 29Si{19F{'H}} double CP MAS NMR spectra of [F,TPA]-MFI 100 Figure 4.17 Arhenius plot of the rate constants for fluoride ion exchange 101 Figure 5.1 Structure of as-synthesized STF zeolite 106 Figure 5.2 Fast spinning 2 9Si NMR spectra of [F,DECDMP]-STF 108 Figure 5.3 Slow spinning 2 9Si spectra of [F,DECDMP]-STF 109 Figure 5.4 Experimental and simulated 29Si{ l9F} CP-REDOR curves for Si3 for [F,DECDMP]-STF 110 Figure 5.5 Experimental and simulated 29Si{19F} CP curves for Si3 of [F,DECDMP]-STF 111 Figure 5.6 Experimental and fitted 29Si{ l9F} CP curves for the four-coordinate peaks of [F,DECDMP]-STF 113 Figure 5.7 1 9 F MAS NMR spectrum of [F,DECDMP]-STF 114 Figure 5.8 Contour plot of the difference Fourier map computed in the 01-Si3-Fl plane 115 Figure 5.9 Coordination polyhedra around the disordered Si3/Si3' pair 116 Figure 5.10 Comparison of the SFF and STF frameworks 118 Figure5.11 29Si{'H} and29Si{'9F} CP MAS spectrum of [F,DECDMP]-SFF 119 Figure 5.12 Experimental and simulated 29Si{19F} CP curves for the five-coordinate Si of [F,DECDMP]-SFF 120 Figure 5.13 Slow spinning 29Si{'H} CP MAS spectra of [F,DECDMP]-SFF, Figure 5.14 Slow spinning low temperature 2 9Si spectra of [F,TPA]-MFI 120 122 Figure 6.1 MFI framework topology 127 Figure 6.2 Single crystal XRD structures of high and low loaded pDCB/ZSM-5 complexes 129 Figure 6.3 Representative high resolution 2 9Si MAS NMR spectra of the various phases of highly siliceous ZSM-5 arising from changes in temperature or sorbate loading 130 Figure 6.4. Quantitative variable temperature 2 9Si MAS NMR of the low-loaded pDCB/ZSM-5 complex 131 Figure 6.5. Two-dimensional 2 9Si MAS INADEQUATE spectrum of the low-loaded pDCB/ZSM-5 complex 132 Figure 6.6. Comparison of quantitative 2 9Si MAS spectrum and 29Si{'H} CP MAS spectrum of the low-loaded pDCB/ZSM-5 complex at 280 K 133 Figure 6.7. Normalized 29Si{'H} cross polarization drain difference curves (AS/S0) for the low-loaded pDCB/ZSM-5 complex at 280 K 135 Figure 6.8 29Si{'H} cross polarization curves for the low-loaded pDCB/ZSM-5 complex at 280 K 135 Figure 6.9. Definition of the orientation of the molecule in terms of the Euler angles 138 Figure 6.10. Distributions of the locations of pDCB in ZSM-5 from 29Si{'H} CP drain data collected at 280 K.. . 142 Figure 6.11. Scatter plot of the atomic positions and 'average' location with 50% error ellipsoids 143 Figure 6.12 'Average' location of the pDCB molecule in ZSM-5 determined from CP MAS NMR compared to the location of pDCB molecule determined by single crystal XRD 145 Figure 6.13. Plot of the experimentally determined cross polarization rate constants (from CP drain) against the calculated heteronuclear second moments for the 'average' position of pDCB in ZSM-5 146 Figure 6.14. Comparison of experimental and predicted spectra for the 'average' location of pDCB in ZSM-5 (from CP drain) 146 Figure 6.15 Plot of the experimentally determined cross polarization rate constants (from CP curves) against the calculated heteronuclear second moments for the 'average' position of pDCB in ZSM-5 148 Figure 6.16 Comparison of experimental and predicted spectra for the 'average' location of pDCB in ZSM-5 (from CP curves) 148 Figure 6.17 Comparison of the average locations of pDCB in ZSM-5 determined from 29Si{'H} CP drain data standard CP data at the indicated temeratures, using PDCB framework coordinates 151 Figure 6.18 Comparison of the average locations of pDCB in ZSM-5 determined from 29Si{'H} CP drain data standard CP data at the indicated temeratures, using HTORT framework coordinates 152 Figure 6.19 29Si{'H} CP drain curves (AS/S0) for the low-loaded pDCB/ZSM-5 complex at 295 K 153 Figure 6.20 29Si{'H} CP curves for the low-loaded pDCB/ZSM-5 complex at 295 K 153 Figure 6.21 29Si{'H} CP drain curves (&S/S0) for the low-loaded pDCB/ZSM-5 complex at 265 K 154 Figure 6.22 29Si{'H} CP curves for the low-loaded pDCB/ZSM-5 complex at 265 K 154 Figure 7.1 Two-dimensional 2 9Si INADEQUATE spectrum of the pDBB/ZSM-5 complex at 290K 158 Figure 7.2 Quantitative variable temperature 2 9Si MAS NMR spectra of the pDBB/ZSM-5 complex with different loadings of the pDBB molecules, as indicated 159 Figure 7.3 Temperature dependence of the peak widths (at half height) of the 2 9Si MAS NMR spectra 159 Figure 7.4 Semi-logarithmic plots of the Tt and T2 relaxation times for the pDBB/ZSM-5 complexes 161 Figure 7.5 Variable temperature 2 9Si MAS NMR spectra of the pDBB/ZSM-5 complex with 4.0 mol./u.c. for sample packed in air compared to sample purged with N 2 gas and using N 2 as the drive gas 162 Figure 7.6 ZSM-5 framework with Si sites coded according to 2 9Si T\ relaxation times 163 Figure 7.7 Representative normalized 29Si{1H} CP drain difference curves (AS/So) for the pDBB/ZSM-5 complex at the sorbate loadings and temperatures indicated 165 xi Figure 7.8 Representative 29Si{'H) CP curves of the pDBB/ZSM-5 complex at sorbate loadings and temperatures indicated 165 Figure 7.9 Representative 29Si{'H} CP curves at various low temperatures of the pDBB/ZSM-5 complex with 4.0 mol./u.c. after purging with nitrogen gas and using nitrogen as bearing and drive gas to spin the sample. ... 166 Figure 7.10 Semilogarithmic plots of the temperature dependences of the parameters which describe the 29Si{'H} cross polarization dynamics 166 Figure 7.11 Comparison of the quantitative 2 9Si MAS NMR spectrum and the 29Si{'H} CP MAS NMR spectrum of the pDBB/ZSM-5 complex with 4.0 mol./u.c. at 300 K 171 Figure 7.12 ZSM-5 framework with Si sites coded according to peak intensity in the 29Si{'H} CP MAS NMR spectrum of the pDBB/ZSM-5 complex with 4.0 mol./u.c. at 300 K 171 Figure 7.13 29Si{'H} CP curves for the pDBB/ZSM-5 complex with 4.0 mol./u.c. at 300 K 172 Figure 7.14 29Si{'H} CP drain curves (AS/S0) for the pDBB/ZSM-5 complex with 4.0 mol./u.c. at 300 K 172 Figure 7.15 Distributions of the locations of pDBB in ZSM-5 from 29Si{'H} CP and CP drain data collected for the 4.0 mol./u.c. sample at 300 K 174 Figure 7.16 Scatter plot of the atomic positions of all pDBB locations consistent with the 29Si{'H} CP drain data obtained for the sample with 4.0 mol./u.c. at 300 K and average location with 50% error ellipsoids 175 Figure 7.17 'Average' location of the pDBB molecule in ZSM-5 from the 29Si{'H} CP drain data collected on the 4.0 mol./u.c. sample at 300 K 176 Figure 7.18 Plot of the measured CP rate constants against the calculated heteronuclear second moments for the average location of pDBB in ZSM-5 177 Figure 7.19 Comparison of experimental and predicted spectra for the average location of pDBB in ZSM-5 obtained from 29Si{'H} cross polarization experiments on the 4.0 mol./u.c. sample at 300K 177 Figure 7.20 Comparison of the average locations of pDBB in ZSM-5 determined from 29Si{'H} CP drain data collected at the indicated temperatures and pDBB loadings 179 Figure 7.21 Comparison of the average locations of pDBB in ZSM-5 determined from 29Si{'H} CP data collected at the indicated temperatures and pDBB loadings 180 Figure 7.22 Comparison of the average locations of pDBB in ZSM-5 determined from 29Si{'H} CP data collected on the oxygen-reduced sample with 4.0 mol./u.c. at the indicated temperatures 181 Figure 8.1 Quantitative variable temperature 2 9Si MAS NMR spectra of the ZSM-S/naph-c/o complex 185 Figure 8.2 Two-dimensional 2 9Si INADEQUATE spectrum of the ZSM-5/a-naph-J4 complex 186 Figure 8.3 Comparison of the 29Si{'H} CP MAS NMR spectra to the quantitative 2 9Si MAS NMR spectra at 220 K for the naphthalene/ZSM-5 complexes 187 Figure 8.4 Normalized difference CP drain curves for the ZSM-5/naphthalene complexes at 220K 189 Figure 8.5 29Si{'H} CP curves for the ZSM-5/naphthalene complexes at 220K 190 Figure 8.6 Distributions of the locations of naphthalene in ZSM-5 which are consistent with the 29Si{'H} CP drain data 192 Figure 8.7 Average locations of naphthalene in ZSM-5 determined from 29Si{'H} CP drain data 192 Figure 8.8 Scatter plot of the atomic positions of all naphthalene locations and 'average' location with 50% error ellipsoids 193 Figure 8.9 Average location of the naphthalene molecule in ZSM-5 for solutions consistent with all three sets of 29Si{'H} CP drain data compared to location of naphthalene molecule determined by single crystal XRD.... 194 Figure 8.10 Correlation plots between experimental CP rate constants and calculated second moments and predicted 29Si{'H} CP drain difference spectra 195 Figure 8.11 The location of naphthalene in ZSM-5 showing 'H- 2 9Si internuclear distances 196 xii Figure 9.1 Variable temperature 2 9Si MAS NMR spectra of the pDNB/ZSM-5 complex 200 Figure 9.2 Two-dimensional 2 9Si INADEQUATE spectrum of the pDNB/ZSM-5 complex at 285 K 200 Figure 9.3 Comparison of the quantitative 2 9Si MAS NMR and 29Si{'H} CP MAS NMR spectra of the pDNB/ZSM-5 complex at 285 K 201 Figure 9.4 29Si{'H} CP drain curves (AS/S0) for the pDNB/ZSM-5 complex at 285 K 202 Figure 9.5 29Si{'H} CP curves for the pDNB/ZSM-5 complex at 285 K 202 Figure 9.6 Distributions of the locations of pDNB in ZSM-5 from 29Si{'H} CP and CP drain at 285 K 204 Figure 9.7 Scatter plot of the atomic positions of all pDNB locations consistent with the 29Si{'H} CP drain data obtained at 285 K and average location with 50% error ellipsoids 204 Figure 9.8 Average location of the pDNB molecule in ZSM-5 from 29Si{'H} CP drain data collected at 285 K....205 Figure 9.9 Plot of the measured CP rate constants against the calculated heteronuclear second moments for the average location of pDNB in ZSM-5 206 Figure 9.10 Comparison of experimental and predicted spectra for the average location of pDNB in ZSM-5 obtained from 29Si{'H} cross polarization experiments at 285 K 206 Figure 9.11 Fourier electron density difference map through the molecular plane at the channel intersection 207 Figure 9.12 Structure of the pDNB/ZSM-5 structure determined by single crystal XRD showing the disorder of the pDNB molecules 209 Figure 9.13 The two locations of pDNB in ZSM-5 with anisotropic displacement parameters 210 Figure 9.14 Possible packing of the pDNB molecules along the straight channel of ZSM-5 211 Figure 10.1 Illustration of the non-linear optical properties of the pNA/ZSM-5 complex 214 Figure 10.2 2 9Si MAS spectra of ZSM-5 complexes with p-nitroaniline, p-diaminobenzene, and p-dinitrobenzene guest molecules at room temperature 216 Figure 10.3 Deconvolution of the quantitative room temperature 2 9Si MAS NMR spectrum of the pNA/ZSM-5 complex into 48 peaks of equal intensity 216 Figure 10.4 2 9 Si MAS NMR spectra of the pNA/ZSM-5 complex at 380 K and 300 K 217 Figure 10.5 15N{'H} CP MAS spectrum of the 15N-labeled pNA/ZMS-5 complex at 180 K 218 Figure 10.6 Fourier electron density difference maps at the channel intersection 219 Figure 10.7 Overlay of the pNA molecule locations on the Fourier electron density difference map 220 Figure 10.8 Overlay of the pNA molecule locations on the Fourier electron density map for the final structure refinement using four-site disorder and the Pnma space group 224 Figure 10.9 Structure of the pNA/ZSM-5 complex with four-site disorder at the channel intersection from the final structure refinement of the XRD data 224 Figure 10.10 Structure of pNA/ZSM-5 complex with anisotropic displacement parameters 224 Figure 10.11 Some possible disorder models of the pNA/ZSM-5 complex 226 Figure 10.12 Illustration that demonstrates how the 2 9Si chemical shifts can be sensitive to the orientations of the p-nitroaniline guest molecules at the channel intersection of ZSM-5 228 Figure 12.1 High-resolution 2 9Si MAS NMR spectrum of the (empty) calcined ZSM-5 sample used in the solid state NMR investigations throughout the thesis 235 Figure 12.2 Schematic diagrams for the additional outer coil for the H/F/X triple resonance probe 238 Figure 12.3 Schematic of the setup used for low temperature MAS NMR experiments 240 Figure 12.4 Difference between the actual sample temperature and the displayed temperature for the H/F/X 7 mm MAS NMR probe 242 Figure 12.5 NMR spectra of QsM8 and octadecasil reference samples 243 xm List of Tables Table 1.1 Crystallographic Crystal Systems and Bravais Lattices 7 Table 1.2 Typical magnitudes of nuclear spin interactions for common nulcei in a 9.4 Tesla magnetic field 15 Table 2.1 Known Connectivities for the Si sites in the ZSM-12 Zeolite Framework 42 Table 2.2 Observed Correlations from the 2 9Si INADEQUATE Experiment on zeolite ZSM-12 43 Table 2.3 Possible Peak Assignments for ZSM-12 Zeolite 43 Table 2.4 Rearranged Known Connectivity Table for ZSM-12 44 Table 2.5 Difference Between Observed Correlation and Rearranged Known Connectivity Tables for ZSM-12 44 Table 2.6 Following the Steps in the Peak Assignment Algorithm Applied to Zeolite ZSM-12 46 Table 2.7 Comparison of the Efficiencies of Various Approaches for Assigning the Peaks in the 2 9Si MAS NMR Spectrum of Zeolite ZSM-12 Based on its Two-Dimensional INADEQUATE Correlation Spectrum 47 Table 2.8 Known Connectivities for the Si Sites in the Monoclinic Phase of ZSM-5 Zeolite 48 Table 2.9 Observed Correlations from the 2 9Si INADEQUATE Experiment on the Monoclinic Phase of ZSM-5 ...49 Table 2.10 Possible Assignment Sets for the 2 9Si MAS Spectrum of the Monoclinic Phase of Zeolite ZSM-5 from the 2 9Si INADEQUATE Spectrum 50 Table 4.1 Fluoride ion locations in as-synthesized siliceous zeolites determined by single crystal XRD 83 Table 4.2 1 9F/ 2 9Si dipolar coupling constants and corresponding F-Si distances determined by CP, REDOR, and TEDOR, with fractional coordinates of the fluoride ion 97 Table 5.1 NMR Results and 2 9Si Peak Assignments for [F,DECDMP]-STF 113 Table 5.2 Crystal Structure and Refinement Details for As-Made [F,DMABO]-STF Zeolite 115 Table 5.3 Bond Lengths (A) and Angles (degrees) around Five-Coordinate Si3 and Tetrahedral Si3' 117 Table 6.1 Crystallographic space groups of ZSM-5 under various conditions 128 Table 6.2 Spectrum and CP Curve Fitting Parameters for the Low-Loaded pDCB/ZSM-5 complex at 280 K 136 Table 6.3 Atomic fractional coordinates and error ellipsoid parameters of the pDCB molecule for the 'average' location in ZSM-5 determined from the 29Si{'H} CP drain data at 280 K 143 Table 6.4. The location of pDCB in ZSM-5 determined by from 29Si{'H} CP drain data at 280 K compared to the location in the single crystal XRD structure 144 Table 6.5 Spectrum and CP Curve Fitting Parameters for the Low-Loaded pDCB/ZSM-5 complex at 295 K 150 Table 6.6 Spectrum and CP Curve Fitting Parameters for the Low-Loaded pDCB/ZSM-5 complex at 265 K 150 Table 7.1 2 9Si T\ relaxation times for the pDBB/ZSM-5 complex with 3.5 mol./u.c. at 300 K 163 Table 7.2 29Si{'H} cross polarization rate constants obtained for the pDBB/ZSM-5 complex at various temperatures, guest molecule loadings, and oxygen content 167 Table 7.3 Summary of trends observed for the 2 9Si MAS and 29Si{'H} CP MAS NMR data collected on the pDBB/ZSM-5 complex 169 Table 7.4 Atomic fractional coordinates and error ellipsoid parameters of the pDBB molecule for the 'average' location in ZSM-5 determined from the 29Si{'H} CP drain data for the 4.0 mol./u.c. sample at 300 K 175 xiv Table 8.1 Fitting Parameters for the NMR Data of the ZSM-5/naph-c/0 Complex 188 Table 8.2 Fitting Parameters for the NMR Data of the ZSM-5/p-naph-d, Complex 188 Table 8.3 Fitting Parameters for the NMR Data of the ZSM-5/a-naph-d4 Complex 188 Table 8.4 Atomic fractional coordinates and error ellipsoid parameters of the naphthalene molecule for the 'average' location in ZSM-5 determined from the 29Si{'H} CP drain data at 220 K 193 Table 8.5 Comparison of naphthalene locations in ZSM-5 by various techniques 195 Table 9.1 Fitting Parameters for the NMR Data of the pDNB/ZSM-5 complex at 285 K 201 Table 9.2 Atomic fractional coordinates and error ellipsoid parameters of the pDNB molecule for the 'average' location in ZSM-5 determined from the 29Si{'H} CP drain at 285 K 204 Table 9.3 Crystal Structure and Refinement Details for the pDNB/ZSM-5 complex 208 Table 9.4 Locations of pDNB molecules in ZSM-5, as ring center translations and Euler rotation angles 210 Table 10.1 Single crystal XRD structure refinement results for three models of pNA molecules at the channel intersection of ZSM-5 221 Table 10.2 Summary of refinements done for the final structure with four site disorder of the pNA molecules 222 Table 10.3 Crystal Structure and Refinement Details for the pDNB/ZSM-5 complex 225 Table 12.1 Mass Spectroscopy and 'H NMR Analyses of the Selectively Deuterated Naphthalenes 236 Table B.l Crystal data and structure refinement for [F,DMABO]-STF 274 Table B.2 Atomic coordinates and equivalent isotropic displacement parameters for [F,DMABO]-STF 275 Table B.3 Interatomic distances and angles for [F,DMABO]-STF 276 Table B.4 Anisotropic displacement parameters for [F,DMABO]-STF 277 Table B.5 Crystal data and structure refinement for pDNB/ZSM-5 278 Table B.6 Atomic coordinates and equivalent isotropic displacement parameters for pDNB/ZSM-5 279 Table B.7 Bond lengths and angles for pDNB/ZSM-5 280 Table B.8 Anisotropic displacement parameters for pDNB/ZSM-5 282 Table B.9 Crystal data and structure refinement for pNA/ZSM-5 283 Table B. 10 Atomic coordinates and equivalent isotropic displacement parameters for pNA/ZSM-5 284 Table B.l 1 Bond lengths and angles for pNA/ZSM-5 285 Table B. 12 Anisotropic displacement parameters for pNA/ZSM-5 287 xv Symbols and Abbreviations a, b, c A> Ahu ADP A possible bis K B0 B\i, B\s Bhkl C known Cobs CCD CSA CP d0, du d2, etc. d dis DIS D' DECDMP DMABO DFT £11, £22, etc. Ea AEZ e.s.d. fufi fj Fhkl FID gn h h hkl (hkl) [hkl] H HETCOR / Io hkl INADEQUATE INEPT J AJ Jk k k kd crystallographic unit cell dimensions (lattice constants) peak area of peak i real part of structure factor anisotropic displacement parameter possible peak assignments for peak i (in peak assignment algorithm) magnitude of dipolar coupling between / and S spins Fourier components of the time-dependent dipolar coupling under MAS (w = 0, ±1, ±2) static magnetic field of an NMR spectrometer radio frequency magnetic field applied to / spins, S spins imaginary part of structure factor known connectivity table (in peak assignment algorithm) rearranged known connectivity table (in peak assignment algorithm) observed correlation table (in peak assignment algorithm) charge coupled device chemical shift anisotropy Cross Polarization number of deuterium atoms in a molecule spacing between lattice planes (in Bragg's Law) dipolar coupling constant between spins / and S (radians per second) dipolar coupling constant between spins / and S (Hz) effective dipolar coupling constant N, AT-diethyl-2,5-m-dimethylpiperidinium (structure directing agent) 7Y,jV-dimethyl-6-azonium-l,3,3-trimethylbicyclo(3.2.1)octane (structure directing agent) density functional theory elements of error ellipsoid tensors activation energy Zeeman energy difference estimated standard deviation frequency domains in a two-dimensional NMR experiment atomic scattering factor of atom j structure factor for reflection hkl free induction decay powder integral of oscillations in the CP experiment at the n = ±1 or +2 spinning sidebands Planck constant (6.6262 x 10"34 J s) Planck constant (= hlln) Miller indices for a reflection Miller indices for a lattice plane Miller indices for a lattice direction Hamiltonian Heteronuclear Correlation Experiment unobserved spins, magnetic quantum number associated with / spins scaling factor in CP curves intensity of reflection hkl Incredible Natural Abundance Double Quantum Experiment Incredible Natural Abundance Polarization Transfer Experiment scalar coupling anisotropy in the scalar coupling Bessel functions of the first kind Boltzmann constant (1.3807 x 10"34 J K"1) exchange rate constant rate constant for damping of CP oscillations k,,ks kis kjs kis m m M M2 M2{II) Mo MSL Mx Mz MR MT MAS MFl mol./u.c. naph NMR Pi pDBB pDCB pDNB pNA ppm r r2 R R, r.f. REDOR S So Sd Sf AS/So Sep ST ^isolated ^network S{I} S/N Si/Al SDA SDR [Si0 4 / 2 F]-Si0 4 / 2 t rate constant for spin-lock relaxation for the / and S spins. (absolute) cross polarization rate constant obtained from CP drain experiments (relative) cross polarization rate constant obtained from CP curves predicted CP rate constant based on linear regression between k/s and M 2 spin state of a nucleus (m = ±1/2 for spin-1/2 nuclei) number of rotor cycles after coherence transfer in TEDOR experiment matrix to convert between Cartesian and fractional coordinates heteronuclear dipolar coupling second moment homonuclear dipolar coupling second moment initial magnetization in relaxation time experiments magnetization in spin lock experiment for measuring T\p relaxation time magnetization in spin echo experiment for measuring T2 relaxation time magnetization in saturation or inversion recovery experiments for measuring T\ scaling factor for REDOR curves scaling factor for TEDOR curves magic angle spinning framework topology code for ZSM-5, Silicalite-1 molecules per unit cell number of rotor periods in REDOR experiment number of rotor periods before coherence transfer in TEDOR experiment Fourier index, spinning sideband number (n = 0, ±1, ±2) naphthalene Nuclear Magnetic Resonance position of peak i p-dibromobenzene p-dichlorobenzene /?-dinitrobenzene /?-nitroaniline parts per million (chemical shift) internuclear distance degree of linear correlation gas constant (8.3145 J moi"1 K"1) three dimensional rotation matrix conventional R factor for XRD refinements against F radio frequency Rotational Echo Double Resonance observed spins, magnetic quantum number associated with S spins reference experiment for REDOR or CP drain 'drain' experiment for CP drain 'dephased' experiment for REDOR normalized difference intensity for CP drain or REDOR signal intensity in CP experiment signal intensity in TEDOR experiment contribution to CP signal intensity from isolated spin pairs contribution to CP signal intensity from extended spin network S spin observed, / spin unobserved in CP, REDOR, TEDOR experiments signal to noise ratio silicon to aluminum ratio structure directing agent standard deviation of regression five coordinate silicon with attached fluoride ion tetrahedral silicon time xvii t\, t2 time domains in two-dimensional NMR experiments /(a/2) /-value from Student's t distribution (1-a confidence) T temperature T\ spin-lattice relaxation time T2 spin-spin or transverse relaxation time T2* time constant for decay of FID (including inhomogeneous effect) T\p spin-lattice relaxation time in the rotating frame r d a m p time constant for damping of TEDOR curves TEDOR Transferred Echo Double Resonance TEOS tetraethylorthosilicate TMS tetramethylsilane TPA tetrapropylammonium Vc volume of unit cell w, peak width at half height of peak / weighting value for refection hkl wR.2 weighted R value for refinements against F2 x, y, z fractional coordinates of the ring center of sorbate molecules a , p polar angles describing orientation of IS internuclear vector a , p, y crystallographic unit cell angles (lattice constants) (Xhu phase of reflection hkl y / ; ys magnetogyric ratios of spin / and spin S 5]! 8 22, 833 principal elements of the chemical shift anisotropy tensor 8anlso anisotropy parameter of the CSA tensor h'a„iSO effective anisotropy of the CSA tensor 8, i 0 isotropic chemical shift g ratio of 'heat capacities' of the rare and abundant spins (|),8,V|/ Euler rotation angles describing the orientation of sorbate molecules <))(a,p,T) dephasing angle in REDOR experiment <DR accumulated dephasing in REDOR experiment O T „ dephasing in n rotor cycles before coherence transfer in TEDOR experiment O x m dephasing in m rotor cycles after coherence transfer in TEDOR experiment rj asymmetry parameter of the CSA tensor 9. angle between IS internuclear vector and magnetic field X wavelength X n Dtr dimensionless parameter (REDOR) X„ n Dxr dimensionless parameter (TEDOR) Xm m Dxr dimensionless parameter (TEDOR) u 0 permitivity of free space {An x 10"7 kg m s"2 A 2) v 0 Larmor frequency (Hz) v r spinning speed (Hz) 0m 'magic angle' (54.74°) p(X, Y,Z) electron density at point X, Y, Z x delay time, incremented pulse time T correlation time xr rotor period m0 Larmor frequency (rad s"') m 1 / ; m 1 5 nutation frequency for the /and S spins arising from applied r.f. field (rad s"1) ($r spinning rate (rad s'1) Q span of the CSA tensor (Sn - 833) xviii Statement of Publication Portions of this thesis present data and conclusions previously issued in the following publications: C A . Fyfe, D.H. Brouwer, A.R. Lewis, L.A. Villaescusa, and R.E. Morris. Combined solid state NMR and X-ray diffraction investigation of the local structure of the five-coordinate silicon in fluoride-containing as-synthesized STF zeolite. Journal of the American Chemical Society 2002, 124, 7770-7778. C A . Fyfe, D.H. Brouwer, A.R. Lewis, and J.M. Chezeau. Location of the fluoride ion in tetrapropylammonium fluoride silicalite-1 determined by 'H/ 1 9 F/ 2 9 Si triple resonance CP, REDOR, and TEDOR NMR experiments. Journal of the American Chemical Society 2001, 123, 6882-6891. C A . Fyfe and D.H. Brouwer. Solid state NMR and X-ray diffraction structural investigations of the />-nitroaniline/ZSM-5 complex. Microporous andMesoporous Materials 2000, 39, 291-305. xix Acknowledgements I am most grateful to Prof. Colin Fyfe for his excellent supervision and constant interest in this project. I have learned so much from his vast knowledge of chemistry and solid state NMR. I have appreciated his seemingly endless supply of ideas, his incredible efficiency in proof-reading manuscripts, and enjoyable lunch-time conversations. I am indebted to Anix Diaz and Andrew 'Lui ' Lewis upon whose work much of this thesis is built upon. I would especially like to thank Lui for teaching me how to run the NMR spectrometer, how to refine X-ray diffraction data sets, and for his constant enthusiasm and excitement about everything. I would like to thank Milan Coschizza and Tom Markus from Electronic Engineering Services and Oscar Grenier from Mechanical Engineering Services for their work in designing, building, trouble-shooting, and fixing the various pieces of equipment for the solid state NMR spectrometer, particularly the design and modification of the triple-resonance H/F/X MAS probe. I have greatly appreciated their willingness to help at any time. Brian Patrick and the late Steve Rettig are thanked for collecting the single crystal XRD data sets. I would like to acknowledge and thank the scientists who visited the Fyfe research group over the course of my Ph.D. and with whom some of this work was done in collaboration. Jean-Michel Chezeau provided the excellent [F,TPA]-MFI sample (synthesized by A.C. Faust) and the octadecasil reference sample and was a gracious host when I visited. Russell Morris is thanked for the micro-crystal XRD work on the STF zeolite system. The fluoride-containing zeolite samples were synthesized by Luis Villeascusa. The solid state NMR work on the SFF zeolite was done with Richard Darton. I would like to thank Peter Tekely for discussions and insight into cross polarization dynamics. W. Schwiegger provided the large crystals of ZSM-5 with which the single crystal XRD studies were carried out. Prof. H. Gies and Michael Fechtelkord are thanked for their helpful discussions about XRD structure refinements. My present and former co-workers in the Fyfe research group, Hiltrud Grondey, Andrew Lewis, Jerry Bretherton, Jeff Alvaji, Glenn Wong, Almira Blazek, Jim Sawada, Michael Fechtelkord, Heiko Morell, Florin Marica, Joseph Lee, Wu Lan, and Seung-Yeop Kwak are thanked for their help and discussions. I thank Jonathan and Jen Patrick for allowing me to work at their beautiful home on Bowen Island to get this thesis started. I gratefully acknowledge the Natural Science and Engineering Research Council for financial support in the form of Post Graduate Scholarships (PGS A and PGS B). I also thank the University of British Columbia for the Gladys Estella Laird Research Fellowship. Lastly, I would like to humbly thank God for creating such an amazing and awesome world and gifting me with the capacity to discover and understand one little part of it. xx to Paula xxi Chapter 1 An Introduction to Zeolites, X-ray Diffraction, and Solid State NMR Spectroscopy This chapter outlines the motivation of this thesis research and describes how solid state NMR is an alternative and complementary method to X-ray diffraction, especially for the study of zeolite host/guest complexes. Some general background information about zeolites, diffraction, and solid state NMR is provided. A general strategy for locating guest species in zeolite hosts by solid state NMR techniques is outlined and described as a framework for the thesis. 1.1 Motivation for this research Zeolites are inorganic microcrystalline framework materials with well-defined cavities and channels of molecular dimensions, resulting from syntheses in the presence of structure directing 'template' molecules or ions. The resulting pores and channels enable zeolites to act as 'molecular sieves' with size and shape selectivity towards which guest species may occupy positions within or diffuse through the pore and channel systems. The applications of zeolites are many and include ion exchange, size and shape selective separations and catalysis, and as potential non-linear optical materials. Central to the synthesis of zeolites and to their applications are the interactions between the guest species and the host zeolite framework. In order to understand how guest species (e.g. ions, organic sorbates or template molecules) interact with host zeolite framework, with a view to reliably modeling these systems, it is necessary to have detailed structural information about these complexes. For most zeolites, the application of single crystal X-ray diffraction (XRD) to these complexes is precluded due to their microcrystalline nature. Powder XRD performs quite well for determining zeolite framework topologies, but does not reliably locate the usually weakly scattering guest species. Solid state NMR, which is independent of crystal size, offers an alternative, or at least complementary, method for structure determinations of zeolite host/guest complexes. This thesis explores the potential of solid state NMR to provide information about the structure, dynamics, and disorder in zeolite guest/host complexes. Chapter 1 references begin on page 34. 1 Chapter 1. Introduction 1.2 Zeolites 1.2.1 Structure and properties of zeolites The main structural feature of zeolites'"6 is the well-defined porosity of molecular dimensions. There are over 200 types of zeolite 'framework topologies', each having a unique three-dimensional arrangement of atoms giving rise to differences in the size, shape, and interconnectivities of the zeolites cages, channels, cavities, and pores. A number of zeolite framework topologies, each denoted by a three-letter code, are illustrated in Figure 1.1. A complete compilation of the known zeolite topologies can be found in the International Zeolite Association's Atlas of Zeolite Framework Types.1 (a) LTA (Zeolite A) (b) FAU (Faujasite, Zeolite Y) (c) MOR (Mordenite) (d) MFl (ZSM-5, Silicalite-1) Figure 1.1 Representations of selected zeolite framework topologies. The three-letter code indicates the 'topology' or 'structure type' and the names of zeolites with these structure types are given in parentheses. A second, and equally important, aspect of zeolite structure is the composition of the framework structure. The framework topology refers only to the 'shape' of the zeolite framework and does not indicate which atoms are present in the framework. The framework composition determines many of the properties of the zeolite. For example, the presence of framework A l atoms of an aluminosilicate zeolite gives rise to an overall negative charge of the zeolite framework and to the presence of hydrated extra-framework charge-balancing cations (M"+). The general chemical formula for an aluminosilicate zeolite is: When the framework charge is balanced by H , aluminosilicates are powerful acid catalysts. The thermal stabilities of zeolites tend to increase as the Si/Al increases. Purely siliceous zeolites (no A l present in the framework) are hydrophobic materials with no catalytic activity. It is possible to substitute framework atoms with other metals such as iron, titanium, and copper leading to interesting catalytic properties. Aluminophosphate8 and gallophosphate zeolite materials have frameworks made up of strictly alternating Al or Ga and P sites, with no net framework charge. To summarize, the structure and properties of zeolites are determined both by the framework topology and the types of atoms present in the framework and the extraframework cavities. Chapter 1 references begin on page 34. 2 Equation 1.1 Chapter 1. Introduction 1.2.2 Applications of zeolites The three main areas of application of zeolites are for catalysis, separations, and ion exchange.3-6,9,10 Aluminosilicate zeolites are 'activated' to be acid catalysts by ion exchanging with N H / cations, followed by heating which removes N H 3 and leaves behind a proton (H+) bound to the framework. The combination of the well-defined channels and cavities, high surface area, and high acidity make aluminosilicate zeolites powerful shape-selective acid catalysts. These materials are of tremendous importance in the petroleum industry where they are used for hydrocarbon cracking, isomerization, and fuel synthesis. Zeolite Y , Z S M - 5 , and mordenite are some of the more important zeolites in the petroleum industry.6 Zeolites which have metals substituted in the framework are used as shape-selective oxidation or reduction catalysts." Zeolites are now becoming increasingly important for shape-selective catalysis in the production of fine chemicals.12 The shape selective properties of zeolites are also the basis for their use in molecular adsorption and separation applications. Cation-containing zeolites are used extensively as dessicants due to their high affinity for water. These materials also find application in gas separation (e.g. O2 and N2 from air) where the molecules are differentiated on the basis of their electrostatic interactions with the metal ions. High silica zeolites are hydrophobic and preferentially adsorb organic molecules and have found application as deodorizers (e.g. in kitty litter) and for removal of ethanol from water. A classic example of zeolite separation is the preparation and separation of xylene isomers by Z S M - 5 in which the desired p-xylene isomer can diffuse through the pore system at a much faster rate than the ortho and meta isomers.13 The structure and properties of zeolites thus allow them to separate molecules based on differences of size, shape, and polarity. The charge-balancing extra-framework metal cations can be readily exchanged with other cations in aqueous solution. The major ion-exchange application of zeolites is the use of Zeolite A as a water-softener in phosphate-free laundry detergent powder. Other applications include water purification and waste-water treatment. Recently, zeolite host/guest complexes have been explored as potential non-linear optical materials in which non-centrosymmetric guest species are aligned in the channels of the zeolite due to intermolecular interactions between the guest species or due to coulombic interactions between the guest species and negative framework charges. , 4'15 The key to most of these zeolite applications is the interactions which exist between the guest species and the host zeolite framework. 1.2.3 Synthesis of zeolites Many zeolites are naturally occurring minerals. However, the number of zeolite types has been greatly expanded by several synthetic techniques. Early zeolite synthetic methods were based on hydrothermal treatments of alkaline silica and alumina gels, by analogy to the formation of natural Chapter 1 references begin on page 34. 3 Chapter 1. Introduction zeolites, and produced zeolites with relatively low Si/Al ratios and hydrated, exchangeable metal cations. Many new zeolite topologies have been synthesized with quaternary ammonium organic cations R4N4" introduced as 'template molecules' into the synthesis mixture. Zeolites synthesized with organic 'template' molecules generally have higher Si/Al ratios and larger pore sizes. The interaction between the 'template' molecules and the zeolite framework is one of the important factors in the type of zeolite topology produced in a given synthesis. These organic template molecules can often be removed from the voids of the zeolite framework by 'calcination' in which the material is heated in air at about 550°C to combust the organic matter. The International Zeolite Association Synthesis Commission has compiled a database of Verified Syntheses ofZeolitic Materials}6 In order to obtain high resolution solid state 2 9 Si NMR spectra of zeolites,17-19 it is necessary that the material be very highly siliceous (free of aluminum), ordered, and free of structural defects. Hydrothermal crystallization of alkaline silica gels and organic template cations leads to substantial numbers of Si-O" and Si-OH defect sites which balance the charge of the quaternary ammonium template cations. Highly siliceous zeolites can be obtained if the synthesis is carried out in the presence of small amounts of aluminum or boron, followed by steam treatment at about 700 to 800°C of the acid forms of these materials which drives the aluminum or boron out of the framework. This strategy was employed by Fyfe and co-workers to obtain highly siliceous forms of several zeolite materials in order to perform detailed high resolution solid state 2 9 Si MAS NMR experiments,17"20 including the ZSM-5 material used in this thesis research for the study of the structures of zeolite/sorbate complexes. From the early to middle 1970s, an alternate synthesis route for the direct synthesis of highly siliceous zeolites has been developed that can be carried out at neutral pH and employs fluoride ions as the mineralizing agent rather than hydroxide ions. The 'fluoride synthesis' of zeolites was first introduced by Flanigen and Patton for the synthesis of fluoride silicalite-1,21 The scope of this synthetic route has subsequently been extended by Guth, Kessler, and co-workers22"25 and more recently by Camblor26 and Morris.14-15 The most notable difference between the fluoride and hydroxide synthetic routes is that pure silica zeolites synthesized in fluoride media have been shown to have substantially fewer defects.27-28 Another important aspect of the fluoride synthetic route is that larger crystals can be made29 and it has also afforded new zeolite topologies with low framework densities.26 In addition, the fluoride route can be used to prepare catalytically active materials by incorporating other elements such as B, Al , Fe, Ga, Ge, and Ti into the framework22"24 and to prepare non-silicon based microporous aluminophosphate and gallphosphate materials.25 Morris and co-workers have shown that a number of zeolites synthesized va the fluoride route have non-linear optical properties.14-15 Because of the superior quality and interesting properties of these materials, there is considerable interest in understanding the role(s) that the fluoride ions play in the synthesis of zeolites under these conditions. Structural studies indicate that the many of the 'as-synthesized' zeolites incorporate the fluoride ions into their structure. Therefore it is thought that the fluoride ions are important for charge Chapter 1 references begin on page 34. 4 Chapter 1. Introduction balance and may act as templates or structure directing agents. By determining the location of the guest fluoride ions in the host zeolite frameworks, it is hoped that significant insight into the role(s) of fluoride ions in zeolite synthesis can be gained and used in a predictive manner. 1.2.4 Characterization of zeolites The structure and properties of zeolites can be characterized by an array of techniques. The most important technique for determining the structure of zeolites is diffraction. Due to the microcrystalline nature of most zeolites, diffraction experiments are usually limited to powdered samples. Most zeolite framework topologies have been determined from powder XRD experiments.30 The International Zeolite Association has compiled a Collection of Simulated XRD Powder Patterns for Zeolites.^ However, reliably locating weakly scattering guest species by powder XRD is usually not feasible. In a few exceptional cases, zeolite crystals of suitable size and quality are available for study by single crystal X-ray diffraction, as described further in Section 1.3.7. Solid state NMR is also an important technique for the characterization of zeolite structures.19-32 It is not limited by crystal size nor the extended ordering of the sample since it probes the local structure and dynamics. Therefore, solid state NMR provides important complementary structural information to diffraction experiments. Section 1.4.6 describes some examples of the type of structural information of zeolites available from solid state NMR experiments. Throughout this thesis, the potential of solid state NMR to provide information about the structure, dynamics, and disorder of zeolite host/guest complexes will be explored. In recent years, computer modeling has become an important tool for the study of zeolite structure.33 These methods are used to predict the minimum energies of zeolite frameworks and zeolite host/guest structures. The limiting factor, at present, in computer modeling is the availability of reliable potential energy functions, particularly for the non-bonding interactions between guest molecules and the zeolite frameworks. It is hoped that the availability of reliable structures of zeolite/sorbate complexes, determined by X-ray diffraction and/or solid state NMR techniques, will assist in the development of more reliable potential energy functions. Another important characterization technique is high resolution electron microscopy which can provide images at close to atomic resolution, showing the pore openings and channels of zeolites, as well as crystal defects such as dislocations, site vacancies, and stacking faults.34 Thermal analysis and adsorption studies can also provide valuable information about thermal stability, pore sizes, and surface area. Since the focus of this thesis is the use and development of solid state NMR and X-ray diffraction techniques for the structural study of zeolite host/guest complexes, the remainder of this introductory chapter provides additional background information for these two important techniques. Chapter 1 references begin on page 34. 5 Chapter 1. Introduction 1.3 X-ray diffraction X-ray diffraction has become the most important tool for the structural characterization of crystalline solids. If a single crystal of suitable size and quality can be obtained and a proper structure refinement performed, an enormous amount of structural information is available from a single crystal XRD data set. With the recent availability of CCD area detectors and more powerful computers, the speed at which XRD data can be collected and processed has increased dramatically. The following describes some of the basic concepts behind the X-ray diffraction experiment35"37 and how structural information is extracted from the data. 1.3.1 Crystals, symmetry, and space groups The fundamental characteristic of the crystalline state is a very high degree of internal order. This order arises from the atoms, molecules, or ions which make up a crystal being arranged in a precisely regular way that is repeated 'infinitely' in all directions. A 'crystal' can thus be regarded as being built up by the continuing three-dimensional translational repetition of a basic structural pattern called the 'unit cell', which may comprise a single atom or molecule or a complex assembly of molecules. The 'crystal lattice' is the basic network of points on which the repeating unit cell may be imagined to be laid down so that the regularly repeating structure of the crystal is obtained, as illustrated in Figure 1.2. There are seven possible types of unit cells or 'crystal systems', classified according to their rotational symmetry, which can be repeated to fill all space in all three dimensions ranging from the least symmetric triclinic to the most symmetric cubic (see Table 1.1). There are fourteen distinct crystal lattices called the 'Bravais lattices'. The seven crystal systems make up 'primitive' lattices in that the lattice points are only at the comers of the unit cells such that there is an equivalent of one lattice point per unit cell. There are seven non-primitive lattices which contain two or more lattice points per unit cell. These additional lattice points may be either 'face-centered' or 'body-centered'. Figure 1.2 Illustration of the three-dimensional crystal lattice and the unit cell. Chapter 1 references begin on page 34. 6 Chapter I. Introduction Table 1.1 Crystallographic Crystal Systems and Bravais Lattices. Crystal System Unit Cell Parameters Lattice Symmetry Lattice Type* (Bravais Lattices) Triclinic Monoclinic Orthorhombic Tetragonal Trigonal/ Rhombohedral Hexagonal Cubic a*b*c; 1 a * P * y (no rotational symmetry) a*b*c; 21m a = y; p > 90° (two-fold rotation axis parallel to b) a±b±c; mmm a = p = y = 90 (three mutually perpendicular two-fold rotation axes) o a = b* c\ Almmm a = p = y = 90° (four-fold rotation axis parallel to c, two-fold rotation axes perpendicular to c) a = b = c; 2/m a = p = Y * 90° (three fold rotation axis along one body diagonal of the unit cell) a = b^c; 6/mmm a = p = 90°; Y = 120° (six-fold rotation axis parallel to c, two-fold rotation axes perpendicular to c) a = b = c; m3m a = p = Y = 90° (three-fold rotation axes along all four body diagonals of the unit cell) P,C P, C, I, F P, I P, I,F *P (primitive) - one lattice point per unit cell, I (body centered) - two lattice points per unit cell, C (face centered on the ab face) - two lattice points per unit cell, F (face centered on all faces) - four lattice points per unit cell, R (rhombohedral primitive) - one lattice point per unit cell. In additional to the translational symmetry (described by the Bravais lattice), there is additional 'point-symmetry' in a crystal. There are 32 possible 'crystallographic point groups' which involve combinations of the following point-symmetry operations: w-fold rotation axes, w-fold roto-inversion axes, and mirror planes. Combination of these point symmetry operations with translations gives rise to the following 'space symmetry' operations: «-fold screw axis and glide planes. Examples of the crystallographic symmetry operations are illustrated in Figure 1.3. It is possible to combine these symmetry operations (pure rotations, rotary inversions, screw axes, mirror planes, glide planes, and translations) in exactly 230 ways that are compatible with the geometric requirements of three-dimensional lattices. Each of these 230 crystallographic 'space groups' consists of a distinct set of symmetry operators which describe an infinitely extended, regular repeating pattern in three dimensions. n-fold rotation axis (rotation) & rotate 3607n • © n-fold roto-inversion axis (rotation + inversion) n-fold screw axis (rotation + translation) J3> <Ss> z+2/3 z+1/3 mirror plane (reflection) glide plane (reflection + translation) y+1/2 ® Figure 1:3 Examples of the five types of crystallographic symmetry operations (excluding simple translations). Chapter 1 references begin on page 34. 7 Chapter 1. Introduction A crystal is therefore essentially described by (1) a set of unit cell parameters which describe the dimensions of the repeated unit cell, (2) a set of symmetry operators defined by the crystallographic space group, (3) the atomic positions of the unique atoms which make up the 'asymmetric unit'. Each symmetry operation of the space group is applied on each of the unique atoms to give all of the atoms in the unit cell. The extended crystal is then made up by translations of all the atoms in the unit cell in all three dimensions. The aim of structure determination by X-ray diffraction is to determine each of these three sets of information. 1.3.2 Diffraction of X-rays X-ray radiation is scattered by electrons. The periodicity of the electron density in a crystal leads to coherent scattering of the X-rays and gives rise to a 'diffraction pattern' in a similar manner to the diffraction patterns obtained from the interaction of optical light with diffraction gratings. A convenient way to describe the diffraction of X-rays from crystals is to consider that X-ray beams are 'reflected' from planes in the crystal lattice. Diffraction maxima or 'reflections' arise from the constructive interference of the 'reflected' X-rays when the additional path traveled by X-rays 'reflected' in successive planes is an integer multiple of the X-ray wavelength. The relationship between the angle of coincidence 0, the wavelength X, and the distance between planes d that leads to constructive interference is Bragg's Law : nX = 2d sin0 Equation 1.2 This expression can be derived from basic trigonometry, as illustrated in Figure 1.4. The diffraction pattern consists all of the 'reflections' arising from all of the lattice planes present in the crystal. The lattice planes in the crystal (the 'direct lattice') are assigned by Miller indices (hkl) where each index is the reciprocal of intersection with the unit cell vectors a, b, and c. Each set of lattice planes gives rise to a 'reflection' in the diffraction pattern which is assigned by the corresponding Miller index hkl. The spacings between the 'reflections' in the diffraction pattern are related to the reciprocals of Chapter 1 references begin on page 34. 8 Figure 1.4 'Reflection' of X-rays from crystal lattice planes. Constructive interference occurs if the path difference is an integer multiple of the X-ray wavelength (Bragg's law). Chapter I. Introduction the unit cell constants. The lattice on which the 'reflections' in the diffraction pattern lie is thus termed the 'reciprocal lattice'. Figure 1.5 illustrates the relationship between the direct and reciprocal lattices for a monoclinic unit cell. With the geometry of the X-ray diffraction experiment and the wavelength of the X-rays (X) known, it is possible to determine the lattice type and the unit cell parameters of the crystal from the reciprocal lattice diffraction pattern. A careful inspection of which reflections are absent in the diffraction pattern provides detailed information about the symmetry of the crystal since each space group has a unique set of 'systematic absences'. Therefore, from the positions and systematic absences of the reflections in the diffraction pattern, it is possible to determine the unit cell parameters and the crystallographic space group of the crystal. Direct Lattice Reciprocal Lattice Figure 1.5 Direct and reciprocal lattices for a monoclinic unit cell in the xz and x*z* planes. The Miller indices of the direct lattice planes are indicated by (hkl) and the Miller indices of the reflections in the reciprocal lattice are indicated by hkl. The atomic positions of the atoms in the asymmetric unit are determined from the intensities of the reflections. The intensity of a reflection hkl is proportional to the square of the 'structure factor amplitude' IkkiK\Fhki\2 Equation 1.3 The 'structure factor' FMI for reflection hkl is FM = ^  fj exp[2rc i {h Xj +k yy- +1 Zj)] Equation 1.4 j where f is the 'atomic scattering factor' of atom j corresponding to the value of sinG/A, for the reflection in question (29 is the angle between the incident X-rays and the scattered X-rays of reflection hkl), modified to take into account any thermal vibration of the atom (Figure 1.6). Chapter 1 references begin on page 34. 9 Chapter 1. Introduction Figure 1.6 Atomic scattering factors (/) for a number of atoms as a function of sinG/X. s'\nQ/X The structure factor can be expressed as a combination of the amplitude, \Fhki\, and phase, a„ki, of the scattered radiation: Phki = K, | e'0"" = Ahkl + iBhkl Equation 1.5 where \Fhki|2 = 4ki + B2hkl and ahkl = tan' 1 {Ahkl/Bhkl) Equation 1.6 .The Ahki and Bm terms are functions of the positions and types of all the atoms in the unit cell Ahkl = ^ fj cos 2n(h Xj +k yj +1 Zj) and Bm = ^ / y . sin 2n{h Xj + k yi +1 Zj ) Equation 1.7 j j The aim of structure determination by X-ray diffraction is to determine the positions of the atoms in the unit cell from the measured intensities of the reflections according to these equations. 1.3.3 The phase problem In order to obtain an image of the scattering matter in three dimensions (the electron density distribution), a Fourier transform from structure factors in 'hkl space' to electron density in 'XYZ space' is performed. The electron density at any pointX, Y, Z represented by p(X,Y,Z), is given by the following expression: p(X, Y, Z) = — £ ^ £ F h k l exp[- 2ni{hX + kY + IZ)] Equation 1.8 h k l where Vc is the volume of the unit cell and Fha is the structure factor for the particular set of indices h, k, and /. By substituting Equation 1.5 for Fhkh this electron density function can be expressed in terms of amplitudes and phases of the structure factors: 9{XJ,Z) = ^ YJllY}Fhki\C0AMhX + kY + lZ)-ahk^ Equation 1.9 c h k l Therefore, if amplitude \Fha\ and phase a.nU were known for each reflection hkl, it would be possible to calculate the electron density at all values of X, Y, and Z and plot the values to give a three dimensional Chapter 1 references begin on page 34. 10 Chapter 1. Introduction electron density difference map. Then, assuming atoms to be at the centers of the peaks, the structure could be worked out directly. However, there is a problem. Experimentally, it is only possible to measure the amplitude of the structure factor for a given reflection and not its phase. The phase of each reflection must be derived from values of Ahu and Bnki that are calculated from a 'trial structure' or by purely analytical methods. The difficulty of getting estimates of the phase angles so that the electron density can be calculated directly is called the 'phase problem'. The most difficult challenge in X-ray diffraction is to come up with a 'trial structure' from which estimates of the phase angles can be calculated. In the early years of X-ray diffraction, these trial structures were obtained by trial and error methods, model building, Patterson maps, the heavy-atom method, or the isomorphous replacement method. Recently, with more powerful computers, 'direct methods' have been increasingly employed to give phase information directly from the reflection data. The phase problem is not an issue for the single crystal XRD structures of zeolite host/guest complexes reported in this thesis since a suitable initial trial structure is available from the known zeolite framework topology. Consequently, the techniques available to obtain initial trial structures are not described in detail. 1.3.4 Difference Fourier synthesis From a suitable trial structure (which may not contain all of the atoms in the structure), it is possible to obtain Fourier electron density difference maps which reveal the positions of the missing atoms. This is accomplished by calculating the phases ahk! and structure factor amplitudes \Fhk!\c for each reflection hkl from the atomic parameters in the trial structure and using the following equation (modified from Equation 1.9): 9diff(XJ,Z) = ^ YLH^i lo - 1 ^ / \c)cos[2n{hX + kY + lZ)-ahkl) Equation 1.10 V c h k I where \Fhki\o is the experimentally observed structure factor amplitude for reflection hkl and \Fhki\c is calculated according to Equation 1.6. Although the calculated phases may not be absolutely correct (due to the missing atoms in the trial structure), the resulting Fourier electron density difference maps will usually be quite meaningful and useful if the trial structure is reasonably close to the actual structure. For the zeolite host/guest structures reported in the this thesis, the Fourier electron density difference maps calculated using the empty zeolite framework as the trial structure provide a clear picture of the electron density of the guest molecules. These maps clearly reveal the location of the guest molecules and even the disorder of the molecules, if present. 1.3.5 Structure refinement After approximate positions have been determined or proposed for most, if not all, of the atoms, refinement of the structure can be started. In this process, the atomic parameters are varied systematically Chapter 1 references begin on page 34. 11 Chapter I. Introduction so as to give the best possible agreement between the observed structure factor amplitudes and those calculated for the proposed structure. In a 'least-squares refinement', the following function is minimized: YJ WM (I Fhki \l ~ I Fhki \l )2 Equation 1.11 all hkl where \Fhki\0 is the experimentally observed structure factor amplitude for reflection hkl, \Fhkt\c is the structure factor amplitude for reflection hkl calculated from the proposed structure according to Equation 1.6 and Whki = 1 la(\Fhkt\ I f Equation 1.12 is a weighting factor equal to the inverse square of the standard deviation of the experimental value of \FhU\ I. The variable parameters that are normally used in the least squares refinement include the atomic position parameters (xj, yjt zj) from each atom j, the temperature displacement parameters which may be up to six parameters if the vibrations are anisotropic and represented by an ellipsoid, and an overall scaling factor to match the observed and calculated values. In some cases, the occupancy or population of atom j may also be refined. Thus, in a general case, there may be as many as KW+1 parameters to be refined for a structure with N independent atoms. It is desirable that there be many more observations than parameters, in order for the least-square refinement method to be successful. The least-squares refinement of a structure is usually coupled with difference Fourier syntheses to ensure that all atoms are included in the structural model. 1.3.6 The correctness of a structure There are several criteria available for judging the 'correctness' of a structure arrived at from a least-squares refinement procedure. Firstly, the refinement must be stable and converge to a minimum. Secondly, there should be good agreement between the observed and calculated structure factor amplitudes. This agreement is measured by the weighted R factor (for refinements against \Fhki\ 20): X WM ( I Fhkl Io ~ I Fhkl Ic ) wR2 = P*-= 7 ~y Equation 1.13 y z^whki\\Fhki\o) I hkl or by the conventional R factor (for comparison to refinements against \F„ki\ )'• V\\Fhki\o-\F, y,I Fhkl Io hkl A 'good' structure is considered to have a wR2 value of < 0.15 and a R\ value of < 0.05. It is important to note that a good R factor does not necessary indicate that the correct structure has been reached and it is necessary to ensure that the other criteria are also met. A third indicator of the correct Chapter 1 references begin on page 34. 12 hkl Ic | Rl = ——^ . Equation 1.14 Chapter 1. Introduction structure is that a Fourier electron density difference map, calculated with the phases of the final structure, should reveal no large discrepancies in the electron density. A good structure should have no residual electron density differences greater than about 1 eA"3. Finally, it is important to ensure that the geometry (bond lengths and angles) and that the resulting anisotropic displacement parameters of the final structure are not unreasonable. 1.3.7 Application of X-ray diffraction to zeolites Due to the micro-crystalline nature of most zeolites, structure determination by diffraction is most often limited to powder samples. Rietveld refinement38-39 of high-quality powder X-ray diffraction data has led to the elucidation of many zeolite framework structures, but is much less reliable in locating weakly scattering guest species. Single crystal diffraction is capable of reliably determining accurate atomic positions for the both the framework and guest species, but requires single crystals of suitable quality and size. Unfortunately, the synthesis of large and untwinned zeolite crystals is extremely challenging and presents a significant obstacle for zeolite structure determination. One notable exception to this problem is the zeolite ZSM-5 or Silicalite-1 (MFI framework topology), for which single crystals can be synthesized which are of sufficient size and quality for collection of acceptable XRD data on a standard X-ray diffractometer. Consequently, this zeolite has been the focus of most of the structural investigations of zeolite/sorbate complexes. A limited number of reliable crystal structures of zeolite/sorbate complexes of ZSM-5 are available from single crystal XRD studies by van Koningsveld and co-workers.40-45 With the recent availability of CCD area detectors, increased source beam intensities (e.g. synchrotron beam lines), and data analysis software to deal with crystal twinning, the threshold of crystal size and quality requirements is being lowered. Morris and co-workers have recently reported on the structures of several fluoride-containing zeolites, synthesized via the fluoride route, determined from X -ray diffraction experiments using synchrotron radiation on single micro-crystals with dimensions of the order of 10 urn.14-15 1.4 Solid state NMR spectroscopy Nuclear magnetic resonance (NMR) spectroscopy46-53 is one of the most powerful and useful techniques available to chemists for the investigation and elucidation of molecular structures and dynamics. NMR deals with the interaction of the nuclear spins of atoms with magnetic fields. These interactions provide a great deal of information about the local magnetic environments of nuclei, from which information about local structure and dynamics can be obtained. The power and importance of NMR for the study of the structure and dynamics of proteins and organic and inorganic molecules in solution is well known. Chapter 1 references begin on page 34. 13 Chapter I. Introduction NMR experiments can also be performed on solid materials. The great deal of information available from solution NMR is not accessible for many materials since they may not soluble or the solution structure may be appreciably different from the solid state structure. There are also many systems which must be studied in the solid state because that is the state in which they function, for example polymers, zeolites, heterogeneous catalysts, semiconductors, resins, glasses, coal, wood, cellulose, soils, and minerals.54 Although many solid materials can be studied with diffraction techniques that probe long-range order, solid state NMR may provide additional complementary information about short range order and dynamics. In cases where diffraction experiments are not feasible (e.g. amorphous materials) or difficult (e.g. microcrystalline materials), solid state NMR is clearly a very important structure determination technique.54-56 The main difference between solution and solid state NMR is the fact that in solution molecules are free to diffuse and tumble isotropically, while in the solid state the structure is much more rigid and experiences much less motion. As a result of the motional freedom in the solution state, many of the orientation dependent nuclear spin interactions are averaged out, resulting in narrow, highly resolved signals. In the solid state, the nuclear spin interactions are not averaged, and (with the exception of single crystal NMR) the result is often broad and relatively featureless signals. However, by using 'high resolution solid state NMR techniques', in particular 'magic angle spinning' (MAS), it is possible to reduce or remove many of the line-broadening nuclear spin interactions and obtain solution-like narrow resonances. One of the main advantages of solid state NMR is that these nuclear spin interactions which lead to broad, featureless NMR signals also contain a great deal of structural information and can be selectively re-introduced and observed. Consequently, solid state NMR experiments potentially have access to more structural information than solution state NMR. In this brief introduction to solid state NMR, the nuclear spin interactions in the solid state are described, along with some of the techniques which make high resolution solid state NMR possible. A brief overview of solid state NMR study of zeolite structure is also provided. The specific NMR experiments used to study guest/host zeolite structures (two-dimensional NMR and solid state NMR experiments to measure intemuclear distances), are described in detail in Chapters 2 and 3. 1.4.1 Nuclear spin interactions in the solid state The interactions of nuclear spins in an applied magnetic field can be divided into five main types, the relative magnitudes of which are listed in Table 1.2 for both solution and the solid state. The observed NMR resonance frequency for a given nucleus will depend on all of these interactions. A general Hamiltonian H can be written which describes the total nuclear spin interactions as the sum of the individual interaction Hamiltonians: H=HZ + Hcs + HD + Hsc + HQ Equation 1.15 Chapter I references begin on page 34. 14 Chapter 1. Introduction Table 1.2 Typical magnitudes of nuclear spin interactions for common nulcei in a 9.4 Tesla magnetic field. Nuclear Spin Interaction Hamiltonian Description of Interaction Magnitude in Solids Magnitude in Solution Zeeman Hz interaction with static magnetic field 50 - 400 MHz 50 - 400 MHz Magnetic Shielding (Chemical Shift) Hcs shielding due to local electronic environment up to several kHz isotropic value Dipolar Coupling HD through-space interactions with neighboring nuclei up to ~ 30 kHz 0 Indirect Spin-Spin Coupling Hsc through-bond interactions with neighboring nuclei ~ 200 Hz -200 Hz Quadrupolar HQ interaction with electric field gradient for spins > 'A up to - 100 MHz 0 Many of these interactions are 'anisotropic' or orientation-dependent, such that the observed NMR resonance frequency for a given nucleus will depend on its orientation with respect to the applied magnetic field. In solution, the rapid isotropic tumbling motions of the molecules remove any orientation-dependence, so that the observed NMR resonance frequency for each nucleus of a given type will be at the 'isotropic' frequency. In comparison, the nuclei in a solid powder will experience every possible orientation, so there will be many overlapping NMR resonance frequencies for each type of nucleus, resulting in broad peaks. In the following, these nuclear spin interactions are introduced and described conceptually without resorting to rigorous mathematical descriptions. Because quadrupolar nuclei were not investigated in the present research, the discussion will not include the quadrupolar interaction. 1.4.1.1 Zeeman interaction When a nuclear spin (of spin I) is placed in a magnetic field, the normally degenerate magnetic spin energy states become split into 27+1 non-degenerate states, as shown in Figure 1.7. This is called the 'Zeeman splitting' which arises from the 'Zeeman interaction' of nuclear spins with a static magnetic field. The energy difference between these spin states is a function of the type of nucleus and the strength of the magnetic field (Bo): AEZ = yhB0 Equation 1.16 where y is the magnetogyric ratio of the nucleus. Transitions between these energy levels occur at the frequency: AE7 co0 = — — - y B 0 Equation 1.17 h where co0 is the 'Larmor frequency' in rad s"1 and v0 = co0/27i is the Larmor frequency in Hz. For a superconducting NMR magnet with a field strength of B0 « 10 T, the Larmor frequencies of commonly Chapter 1 references begin on page 34. 15 Chapter 1. Introduction occurring nuclei are on the order of 50 to 400 MHz, in the radio-frequency (r.f.) range. The population difference between the energy levels is governed by the Boltzmann distribution: AE7 An = n+U2 -n_U2=N- 2kT Equation 1.18 where TV is the total number of nuclei, k is Boltzmann constant, and T is the temperature. For 'H nuclei in a B0 w 10 T magnetic field, the population difference is very small, An/N « 3 x 10"5, making NMR quite an insensitive technique. m = -1/2 m = +1/2 m = -1/2 AEz=yhB0 m = +M2 magnetic field strength (6 0) Figure 1.7 The Zeeman interaction of a spin-'A nucleus with a magnetic field. The population difference between the energy levels is governed by the Bolzmann distribution. NMR spectroscopy deals with the transitions between these energy levels caused by the application of radio-frequency radiation. All of the other spin interactions are small perturbations of the Zeeman interaction in that they cause small variations in the Zeeman energy levels. It is these smaller perturbations that yield structural information about the system under study. 1.4.1.2 Magnetic shielding (chemical shift) Nuclei are not isolated entities since they are surrounded by electrons and other nuclei. The surrounding electrons can 'shield' a nucleus from the static magnetic field so that the nucleus experiences a local magnetic field slightly different that the applied static magnetic field. Consequently, the energy levels will deviate slightly from the Zeeman splitting, giving rise to transitions at slightly different frequencies than the Larmor frequency. This deviation from the Larmor frequency arising from magnetic shielding by the local electronic environment is usually represented by the 'chemical shift'. Thus, a spectrum containing these different transition frequencies provides information about the local environments of the nuclei within the system. The shielding of a nucleus by the surrounding electrons is usually anisotropic; that is, the chemical shift depends on the orientation of the nucleus with respect to the static magnetic field. This orientation dependence is called the 'chemical shift anisotropy' (CSA). As a result, the position of the resonances in the NMR spectrum of a single crystal will depend on the orientation of the crystal with respect to the magnetic field (Figure 1.8a). For a solid powder, in which all possible orientations are possible, the spectrum is a sum of many frequencies arising from many chemical shifts, resulting in broad Chapter I references begin on page 34. 16 Chapter 1. Introduction lines (Figure 1.8b). In solution NMR, the rapid isotropic tumbling of molecules leads to a time-averaging of all possible orientations and the observed chemical shift is the 'isotropic chemical shift' (Figure 1.8c). • 1 i i 1 1 1 — i — r chemical shift Figure 1.8 Illustration of the orientation-dependence of the chemical shift interaction, (a) In a single crystal, the resonance frequency will depend on the orientation of the carbonyl l 3 C nucleus with respect to the static magnetic field B0. (b) In a powder, all orientations are possible, leading to a range of resonance frequencies, the sum of which is a broad signal reflecting the anisotropy of the chemical shift interaction, (c) In solution, the rapid isotropic tumbling motions leads to a single resonance frequency at the isotropic chemical shift. Adapted from reference 55. Mathematically the chemical shift anisotropy is described by a second-rank tensor (a 3 by 3 matrix), which consists of six independent components. Generally, the CSA tensor is expressed in a coordinate frame where all off-diagonal elements vanish. In this 'principal axis system', the CSA tensor is fully described by the three diagonal 'principal components' (8n, 822, 833) and three Euler angles describing the orientation of the principal axes system with respect to some arbitrary frame. The CSA can also be expressed in terms of the isotropic chemical shift (8iso), the anisotropy parameter (baniso), and the asymmetry parameter (r)) where: 8i«, =7(811+522 +833) 5aniso- 53 3 -oiso r l = " _ f ~ Equation 1.19 " aniso with |833 - 8,so| > |S 11 - 8jS0\ > |82  - 5,JO|. Examples of some powder line shapes with different CSA tensors are presented in Figure 1.9. In certain cases, it is possible to extract the CSA parameters from these 'wide-line' static NMR spectra of powders, but the spectra become unmanageable when there are several overlapping wide lines. For high resolution solid state NMR, the CSA can be reduced or removed by magic angle spinning, as will be described later. When the CSA is not fully removed by magic angle spinning, an analysis of the resulting spinning sideband pattern57 can yield the principal components of the CSA tensor (see Figure 1.19). Chapter 1 references begin on page 34. 17 1.4.1.3 Dipolar interaction The dipolar interaction is the through-space spin-spin coupling between the magnetic moments of nuclear spins. It describes the local magnetic field that a nucleus experiences from its neighboring nuclei (Figure 1.10a). Each nucleus creates a small magnetic field that influences the local magnetic fields of its neighbors, causing small perturbations of the Zeeman energy levels. The dipolar interaction can be a homonuclear interaction (between nuclei of the same type, e.g. 'H-'H) or a heteronuclear interaction (between different nuclei, e.g. 'H - 1 3 C ), The magnitude of the heteronuclear dipolar coupling (bis) between nucleus I and nucleus S is a function of the magnetogyric ratio of the two nuclei, the intemuclear distance between them, and the orientation of the intemuclear vector with respect to the applied state magnetic field (defined by the angle S): b]S=±^-(3cos2 S -1) Equation 1.20 where the 'dipolar coupling constant', dis or D/s, is defined by: 4B.*M£ (inrads"') 4nr Equation 1.21 rf^i^M ( i n H z ) where uo = An x 10"7 kg m s"2 A"2 is the 'permitivity of free space', y/ and js are the magnetogyric ratios (in units of rad s"1 T"1) of the I and S nuclei, h =h/2n where h - 6.6262 x 10"34 J s is the 'Planck constant', and r is the intemuclear distance (in meters). From the dependence of bis on S, it is apparent that the dipolar interaction is also orientation dependent. In a manner similar to the chemical shift anisotropy, the dipolar interaction in solution is averaged, in this case, to zero by rapid isotropic tumbling. The dipolar interaction in a single crystal results in peak splitting (one peak arising from 'spin-up' and the other from 'spin-down' of the coupled nucleus) that is dependent on the orientation of the crystal with respect to the static magnetic field (Figure Chapter 1 references begin on page 34. 18 Chapter 1. Introduction 1.10b). In a powder, the dipolar interactions result in line broadening since the frequencies arising from the dipolar interactions of all possible orientations are summed (Figure 1.10c). Figure 1.10 Illustration of the dipolar interaction, (a) The S nucleus experiences a magnetic field arising from a neighboring / spin that is dependent on the orientation of the IS internuclear vector with respect to the static magnetic field S0. (b) For an isolated spin pair in a single crystal, the dipolar coupling leads to a peak splitting that reflects the strength of the dipolar interaction and the crystal orientation, (c) For many spins in a powder sample, the dipolar interactions lead to broad featureless lines and can be major source of line-broadening (adapted from reference 58). For high resolution solid state NMR, the line-broadening effects of the dipolar couplings can be removed or reduced by magic angle spinning and high power decoupling, as described later. Chapter 3 describes how these distance-dependent dipolar couplings can be selectively re-introduced in MAS experiments in order to directly measure internuclear distances. 1.4.1.4 Indirect spin-spin coupling (J coupling) The indirect spin-spin coupling interaction involves the indirect spin-spin or 'J-coupling' between two nuclei which occurs via the bonding electrons. Like the dipolar interaction, the /-coupling can be either homonuclear or heteronuclear in nature, but it is a through-bond, rather than through-space, internuclear spin-spin coupling. This coupling to neighboring bonded nuclei results in additional perturbations to the Zeeman energy levels, and gives rise to additional resonance frequencies separated by the magnitude of the J-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, particularly in solution. The J-coupling is usually much smaller than the corresponding dipolar coupling and its anisotropy is almost always ignored. Scalar couplings are independent of the applied magnetic field strength and are not removed or reduced by isotropic tumbling in the solution state or by magic angle spinning in the solid state (assuming the anisotropy of the J coupling is zero), but may be scaled by homonuclear line-narrowing multiple pulse techniques. The magnitude of the J-coupling drops rapidly as the number of intervening bonds increases. In Chapter 2 , the 2 9 S i - 0 - 2 9 S i J-couplings between Si sites in the zeolite framework are used in the INADEQUATE experiment in order to establish the framework bonding network, so that 2 9 Si peak Chapter 1 references begin on page 34. 19 A ; s = ± M i M ( 3 c o s 2 8 8n r isolated /Ssp in pairs in single crystal isolated IS spin pairs in powder Chapter 1. Introduction assignments can be made. In Chapter 5, 1 9 F- 2 9 Si ./-couplings are observed and used by the INEPT experiment in fluoride-containing as-synthesized zeolites to demonstrate the existence of F-Si covalent bonds. 1.4.2 Pulsed Fourier Transform NMR A helpful description of the pulsed Fourier transform NMR experiment is the 'vector model' in which the 'net magnetization' arising from all of the nuclear spins is considered as a vector which is rotated by the application of r.f. pulses. A more rigorous description of an NMR experiment requires a density matrix treatment.59'60 The interaction between the nuclear magnetic moment of a nucleus with the static magnetic field B0 results in 'precession' of this magnetic moment about B0 at the Larmor frequency of the nucleus, as illustrated in Figure 1.11a. For a spin / = 1/2 nucleus, there are 2/+1 = 2 possible 'precession cones', depending on the spin state of the nucleus (w/ = +1/2 or m/ = -1/2), as shown in Figure 1.11b. When all nuclei are considered, there is an excess population of nuclei in the lower energy m/ = +1/2 spin state (according to the Boltzmann distribution). When all the nuclear magnetic moment vectors are summed, the result is an equilibrium 'net magnetization' along B0 (defined as the z direction), as illustrated in Figure 1.1 lc. m=-M2 Figure 1.11 The vector model for NMR. (a) the magnetic moment p. of a single nucleus precesses about the static magnetic field B0 at the Larmor frequency co0. (b) For an ensemble of spin-Vi nuclei, there are two possible precession cones, with the lower energy m=+\/2 spin state more populated according to the Boltzmann distribution, (c) The sum of all the magnetic moment vectors in this ensemble of spins is a 'net magnetization' vector in the direction of the static magnetic field. In order to observe an NMR signal, it is necessary to perturb the nuclear spins away from this equilibrium state. This is accomplished by applying an r.f. field B\ « Bo which is perpendicular to B0 and at the Larmor frequency of the observed nucleus. Experimentally, this is accomplished by passing an alternating current (of the appropriate frequency) through a coil which surrounds the sample and is connected to an appropriately matched and tuned r.f. circuit. In order to follow the fate of the net magnetization vector, it is convenient to change from a static Cartesian frame of reference to a 'rotating frame' of reference which rotates around B0 at the frequency of the applied r.f. field. A 'merry-go-round' is a helpful analogy for this rotating frame of reference. In this rotating frame, the application of the B\ field causes the net magnetization vector to precess about this applied 5, field at the 'nutation frequency'm, = y B{ (Figure 1.12b). If this field is Chapter 1 references begin on page 34. 20 Chapter 1. Introduction applied for a time / (an r.f 'pulse'), the net magnetization vector will be rotated about B\ by an angle 6 = ©1 t. A '90° pulse' refers to the application of the B\ field for time t such that the net magnetization is rotated 90° into the xy plane. (Figure 1.12c) (c) 7 % coi =yB| Figure 1.12 Effect of a 'pulse' on the net magnetization in the rotating frame of reference, (a) net magnetization vector before pulse, (b) application of an r.f. field Bx at the Larmor frequency results in 'nutation' about 5, with frequency ©i, (c) net magnetization vector after a 90° pulse along the x axis. After the B\ field is turned off, the net magnetization in the xy plane of the rotating frame will undergo a 'free induction decay' (FID) in which the magnetization decays with time constant T2 or T2* and rotates (in the xy plane of the rotating frame) at the frequency difference between the rotating frame frequency and the Larmor frequency of the observed nuclei. When an FID decays with time constant T2, the decay (and the resulting peak width in the spectrum) is considered to be 'homogeneous', arising only from spin-spin relaxation. The time constant T2* for the decay in the FID denotes an 'inhomogeneous' decay, arising from additional dephasing mechanisms such as magnetic field inhomogeneities and chemical shift distributions. Experimentally, this precession of the net magnetization in the xy plane induces an electrical current in the coil which is amplified and then detected. The NMR spectrum is obtained by a Fourier transformation of the time-domain FID signal into the frequency domain, as illustrated in Figure 1.13. The Fourier transformation of an exponentially decaying FID with time constant T2 or T2* is a Lorentzian peak with a line width of (nTf^)'1. Figure 1.13 Free induction decay (FID) signal and resulting spectrum (real part only) following Fourier transformation. time frequency Chapter 1 references begin on page 34. 21 Chapter 1. Introduction 1.4.3 NMR relaxation processes The relaxation properties of the nuclei in a sample can have significant experimental implications. The T\ relaxation times determine the delay time required between collection of successive FIDs, affecting the degree of S/N that can be achieved during a given time. T2 and T\P relaxation times can often be limiting factors in NMR experiments involving spin-echoes (Y2) or spin-locking (T\P) components. Relaxation describes the return of a perturbed spin system to equilibrium population levels. Relaxation arises from nuclear spin transitions stimulated by fluctuations of local magnetic fields resulting from motions which cause changes in the nuclear spin interactions. Motionally-induced changes in the shielding anisotropy, dipole-dipole interactions, quadrupolar interactions, as well as interactions with unpaired electrons can all provide relaxation pathways under the appropriate conditions. The measurement of relaxation times can be a powerful technique for the detection and quantification of molecular motions. The dominant relaxation mechanism in the highly siliceous zeolites studied in this work involves the interactions with the unpaired electrons of paramagnetic 0 2 molecules which fill unoccupied cavities in the zeolite framework.61'62 As the channel system of the zeolites fills up with sorbate or template molecules and the oxygen molecules are displaced, the relaxation times become longer and more dependent on the motions of the 'H nuclei of the guest molecules. The relaxation behaviors of the 'H and 2 9 Si nuclei for a sorbate/zeolite complex are studied in detail in Chapter 7. 1.4.3.1 Spin-lattice relaxation time (T:) Spin-lattice relaxation, or 'longitudinal relaxation', is the process by which a perturbed spin system returns to equilibrium population levels. The T\ relaxation time determines the delay time required between the collection of successive FIDs. In terms of the vector model of NMR, it describes the rate at which the net magnetization vector returns to its full magnitude along the z axis after a pulse (or series of pulses). This relaxation process is assumed to be a first order kinetic process, described by the differential equation. j^MZ= -(MZ - M Q ) I T { Equation 1.22 where MQ is the equilibrium magnetization and T\ is the time constant (reciprocal of the rate constant) referred to as the 'spin-lattice relaxation time.' T\ relaxation times can be measured by the Inversion Recovery or Saturation Recovery experiments, as illustrated in Figure 1.14. Chapter 1 references begin on page 34. 22 Chapter 1. Introduction Inversion Recovery Saturation Recovery Figure 1.14 Measuring Tx relaxation time by inversion recovery (left) and saturation recovery (right) experiments: (a) pulse sequences, (b) vector representation of the net magnetization, (c) observed magnetization as a function of the delay time x from which T\ is determined. 1.4.3.2 Spin-spin relaxation time (7"2) Spin-spin relaxation, or 'transverse relaxation', describes the rate at which net magnetization is lost in the xy plane after a pulse. Following a 90° pulse, the magnetization will be dephased by inhomogeneous effects such as magnetic field inhomogeneities and the rate of dephasing is described by T2 . In order to remove the effects of inhomogeneous broadening, the spin-echo experiment is applied in order to 'refocus' these inhomogeneities. The decay of the magnetization at the end of the spin echo is a result of spin-spin relaxation. This relaxation process is also described by first order kinetics: j-tMx= -Mx IT2 Equation 1.23 The measurement of T2 relaxation times by the spin echo experiment is illustrated in Figure 1.15. The T2 relaxation times are very important parameters in NMR experiments such as INADEQUATE, REDOR, and TEDOR (see Chapters 2 and 3) which depend on conserving transverse magnetization. Chapter J references begin on page 34. 23 Chapter I. Introduction t=0 t = T f = 2T Figure 1.15 Measuring T2 relaxation times by the spin-echo NMR experiment: (a) pulse sequence, (b) decay and formation of the echo of the FID signal, (c) vector representation showing the dephasing and refocusing of the spins, (d) observed magnetization as a function of the delay time x from which T2 is determined. 1.4.3.3 Spin-lattice relaxation time in the rotating frame (71p) As described above, spin-spin relaxation (T2) in the x-y plane normally occurs following a 90° pulse. However, the spins experience a different type of relaxation if the they are 'spin-locked' in the xy plane. In the rotating frame, an initial 90° pulse in the x direction will rotate the net magnetization from the z axis to the y axis. The magnetization can be 'spin-locked' along the y axis by then applying the r.f. field (B\) along y. In this 'spin-locked' state, the spins precess about B\ in the rotating frame rather than decaying due to T2 or T2. In the rotating frame, this spin-locking B\ field acts as a static magnetic field, and relaxation analogous to conventional spin-lattice relaxation occurs. The decay of the spin-locked magnetization (MSL) is described by the T\p relaxation time: f MSL = -MSL 17ip Equation 1.24 The measurement of T\p relaxation times by the spin-locking experiment is illustrated in Figure 1.16. The Tip relaxation times are very important parameters in the cross polarization experiment in which spin-locking fields are applied simultaneously at the Larmor frequencies of two different types of nuclei in order to achieve polarization transfer between them (Chapter 3). Chapter 1 references begin on page 34. 24 Chapter 1. Introduction (a) 90°(x) B,jy) spin-lock (C) M(x) M(T) = M 0 e T/?ip (b) apply 90°(x) pulse apply spin-lock B, r.f. field along y spins precess about B, relaxation in the spin-lock field 7~\ t = 0 t = T Figure 1.16 Measuring Tip relaxation times by the spin-locking pulse sequence: (a) pulse sequence, (b) vector representation of the spins in the spin-locking experiment, (c) observed magnetization as a function of the spin-lock time x from which T\p is determined. 1.4.3.4 Temperature dependence of relaxation times As mentioned previously, NMR relaxation arises from motions which cause fluctuations in the local magnetic fields of nuclei. Therefore the different relaxation times described above have a strong dependence on temperature, as illustrated in Figure 1.17. Assuming a dipolar mechanism for the relaxation process and a single molecular reorientation motion, characterized by a 'correlation time' (TC) which describes the mean time between reorientation jumps and is inversely related to temperature, the dependence of the spin-lattice relaxation time T\ on the correlation time xc and Larmor frequency ©o is represented by: f . \ Equation 1.25 -c J where C is a constant which contains the second moment parameter. As illustrated in Figure 1.17, the variation of the T\ relaxation time with inverse temperature consists of a 'V'-shaped curve with a minimum which depends on the resonance frequency (determined by the magnetic field strength), with lower fields shifting the minimum to lower temperatures. The T\p relaxation time has a similar behaviour, except the minimum in the curve occurs at lower temperatures and is therefore sensitive to lower frequency motions. For this particular relaxation mechanism, the T2 relaxation times continue to decrease to the rigid lattice value (xc —»<x>). As for the relative values of these relaxation times: T2 < T\, T\p and 7V <r,. l = c l + co 0 2 x c 2 l + 4co 0 2x c 2 Chapter 1 references begin on page 34. 25 Chapter 1. Introduction Figure 1.17 The general behavior of the Tu T2 and T\p relaxation times as a function of temperature, assuming a single thermally-activated motion and a dipolar relaxation mechanism. Adapted from reference 55. T2 1/7 • 1.4.4 High resolution solid state NMR The orientation dependence of nuclear spin interactions in the solid state means that the NMR spectra of powdered solids can have line widths of several kHz. Two main approaches are used to average or reduce these interactions in order to obtain high resolution solid state NMR spectra of solids. The first approach involves the use of mechanical rotations of the sample (such as magic angle spinning) in order to average the spatial parts of the nuclear spin Hamiltonians. The second approach is to reduce or average the spin part of the Hamiltonian through the use of r.f. pulses. Heternonuclear dipolar interactions can be reduced or removed by high-power decoupling. Homonuclear dipolar interactions can be reduced or removed by multiple pulse sequences such as WAHUHA, 6 3 MREV-8, 6 4 BR-24,65 or FSLG 6 6" 6 8 . These types of experiments are particularly important for obtaining high-resolution solid state 'H spectra, since the homonuclear 'H- 'H dipolar interactions are typically very large. Magic angle spinning, combined with high-power decoupling (if needed), is the most common technique for achieving high-resolution spectra of dilute nuclei in solids. The CP MAS NMR experiment,56'58-69 which combines these two techniques with cross polarization (to enhance the signal of rare spins) has revolutionized the field of solid state NMR. The spectra in Figure 1.18 demonstrate the incredible gain in resolution and sensitivity obtainable in high-resolution 1 3C{'H} CP MAS solid state NMR. Chapter 1 references begin on page 34. 26 Chapter 1. Introduction 250 200 150 100 50 0 5^0 1^00 ppm ITMS) Figure 1.18 l 3 C NMR spectra demonstrating the gain in spectral resolution and sensitivity arising from high-resolution solid state NMR techniques (from reference 58). 1.4.4.1 High power decoupling For most dilute spin-1/2 systems (those nuclei having a low concentration of magnetically active nuclei, such as 1 3 C or 2 9 Si which have low natural abundance and no homonuclear dipolar couplings), a major source of line broadening in the solid state NMR spectrum arises from the heteronuclear dipolar couplings to abundant nuclei such as 'H. It is possible to eliminate these heteronuclear interactions by applying a strong and continuous r.f. field at the Larmor frequency of the abundant spins. This resonant irradiation causes rapid transitions of the abundant nuclei between the two spin states, with the result that the average contribution to the effective local field at the dilute nuclei is zero. To be effective, the strength of the applied r.f. field must be such that the frequency of the transitions between spin states for the abundant nuclei is comparable (or preferably exceeds) the heteronuclear dipolar coupling frequency. Because the dipolar interactions can be quite large, especially in systems which contain many 'H nuclei, it is necessary to apply high power decoupling fields. The effect of high power 'H decoupling can be seen by comparing Figure 1.18b and Figure 1.18c. Experimentally, solid state NMR spectrometers require amplifiers which can produce several hundred watts of power (compared to about 50 W of power for a solution state NMR spectrometer) and provide stable, high-power, r.f. fields up to several hundred milliseconds. 1.4.4.2 Magic angle spinning Magic angle spinning (MAS) 7 0" 7 2 is the key technique to obtaining high resolution solid state NMR spectra. The technique consists of rapidly rotating the solid sample about an axis inclined 54.74° Chapter I references begin on page 34. 27 Chapter 1. Introduction with respect to the static magnetic field. If the spinning frequency is fast enough, the result of MAS is the same as rapid isotropic molecular motions in solution in that the nuclear spin interactions are averaged to their isotropic values. The result of magic angle spinning is high-resolution solid state NMR spectra with narrow resonances (dipolar interactions removed) at the isotropic chemical shift frequencies (chemical shift anisotropy removed). Figure 1.18d shows the dramatic improvement in resolution in an NMR spectrum when MAS is applied. What is it about the 54.74° angle that is 'magic'? As described earlier, the chemical shift and dipolar interactions depend on the orientation of a nucleus or pair of nuclei with respect to the applied magnetic field (defined by the angle &). For both the chemical shift anisotropy and the dipolar coupling, this orientation dependence is defined by the term: Consider the dipolar interaction between nucleus I and nucleus S. When the sample is rotated rapidly about an angle 9 with respect to the static magnetic field, the intemuclear vector maps out a cone. The time-average of the orientation dependence of the dipolar coupling is therefore which means that the orientation dependence of the dipolar coupling is removed. A similar argument can be made for the averaging of the chemical shift anisotropy. In order to completely remove the chemical shift anisotropics and all heteronuclear and homonuclear dipolar couplings, the sample rotation rate must be greater than the strengths of these interactions. In situations where MAS cannot completely remove large dipolar interactions, it is important to couple MAS with high-power heteronuclear decoupling or homonuclear decoupling techniques. When the spinning frequency is less than the chemical shift anisotropy, a series of 'spinning sidebands' result which are centered about the isotropic chemical shift and are spaced at multiples of the spinning frequency. The intensity envelope of these spinning sidebands maps out the chemical shift anisotropy observed in the non-spinning 'powder spectrum', as illustrated in Figure 1.19. Information about the chemical shift anisotropy is retained in the sideband pattern, and appropriate analysis of the sideband intensities can be used to determine the principal tensor elements, but not their orientation.57 3 cos2 S-1. which equals zero when Chapter 1 references begin on page 34. 28 Chapter 1. Introduction vr=2000 Hz Figure 1.19 1 3 C ('H decoupled) spectra obtained for a powder sample of ferrocene demonstrating the effect of the magic angle spinning frequency. At slower spinning rates, the spinning sideband manifold maps out the chemical shift anisotropy observed in the non-spinning spectrum. At faster spinning rates, when the spinning rate exceeds the width of the chemical shift anisotropy, the orientation dependence of the chemical shift is averaged out and the isotropic chemical shift is observed (adapted from reference 73). - | 1 1 1 1 . 1 . \ r 2000 1000 0 -1000 -2000 ic('JC) Hz Magic angle spinning provides a tremendous gain in resolution, as the chemical shift anisotropies and dipolar couplings are reduced or even removed. However under such conditions, the dipolar interactions which are of interest for measuring internuclear distances are averaged out. In Chapter 3, the time dependence of the dipolar interaction under magic angle spinning conditions is described in more detail, along with NMR experiments designed to 're-introduce' the dipolar couplings so that internuclear distances can be determined. 1.4.4.3 Cross polarization The cross polarization experiment74 is commonly employed for increasing the sensitivity of the NMR signal of the dilute spins (e.g. l 3 C, 2 9 Si , l 5N) by transferring the magnetization or 'polarization' from the abundant spins (e.g. 'H) to the dilute spins via the dipolar interactions which exist between the nuclei. Briefly, this polarization transfer is achieved by applying simultaneous 'spin-locking' r.f. fields (with 'matched' r.f. field strengths) at the Larmor frequencies of the abundant and dilute nuclei. A detailed description of the mechanism and dynamics of the cross polarization experiment is given in Chapter 3. The gain in S/N of a CP experiment over a standard pulse experiment arises from two factors. Firstly the 'polarization' (population difference between the Zeeman energy levels) of the abundant spins is transferred to the dilute spins such that the polarization of the dilute spins is enhanced by up to a factor Chapter 1 references begin on page 34. 29 Chapter 1. Introduction of Y//ys where y7 and y s denote the magnetogyric ratios of the abundant and dilute spins respectively. For cross polarization from 'H to l 3 C , the polarization of the l 3 C can be enhanced by a factor of about y//y5 = 4, while cross polarization from 'H to 2 9 Si results in a polarization enhancement by a factor of about y//y5 = 5 (in the absence of relaxation effects). Secondly, the delay time between collecting successive FIDs in the CP experiment depends on the T\ relaxation time of the abundant nuclei, which is typically much shorter than the T\ relaxation time of the rare spins. This means that more FIDs can be collected in a given amount of time, resulting in further increased S/N. When cross polarization is combined with high-power decoupling and magic angle spinning, the resulting CP MAS NMR experiment56'58-69 provides an enormous gain in sensitivity and resolution, as demonstrated in Figure 1.18. In addition, as described in Chapter 3, the dynamics of the cross polarization process can provide a great deal of information about structure, since the CP dynamics are a function of the heteronuclear dipolar couplings which are, in turn, related to the intemuclear distances. 1.4.5 intemuclear distance measurements by solid state NMR There has been a great deal of recent solid state NMR research into the development of experiments to measure dipolar couplings under magic angle spinning conditions. Since the dipolar coupling constant is related to the intemuclear distance, these solid state NMR experiments have a great of potential for structure determination of systems which may not be accessible by diffraction techniques. As described earlier, the effects of the dipolar couplings are usually removed by the time-averaging brought about by magic angle spinning. Therefore, these solid state NMR pulse sequences are designed to prevent this time-averaging to occur in such a way as to measure the dipolar coupling constant between two nuclei, and thus the intemuclear distance. The pioneering heteronuclear dipolar 'recoupling' experiments, Rotational Echo Double Resonance (REDOR)7 5 and Transferred Echo Double Resonance (TEDOR)76, were first performed by Schaefer and co-workers and have been further developed and applied by many other researchers. It has also been shown that the cross polarization experiment can be used to measure intemuclear distances when isolated spin pairs exist.77-78 These experiments to measure intemuclear distances under MAS conditions form the basis of the strategy described in this thesis to determine the structures of zeolite host/guest complexes by solid state NMR and are described and evaluated in detail in Chapter 3. 1.4.6 Application of solid state NMR to zeolites Several reviews which discuss the application of solid state NMR to zeolites and related microporous materials have been published including the book by Engelhardt and Michel,3 2 and shorter reviews by Fyfe et al, 1 9 and Klinowski.79 The following provides a very general overview of the type of information about zeolite structures available from solid state NMR experiments. Chapter 1 references begin on page 34. 30 Chapter 1. Introduction Virtually all of the atoms which make up zeolite frameworks are NMR active and can therefore be studied by solid state NMR. These nuclei include n B , 1 7 0, 2 7A1, 2 9 Si , 3 1P, and 7 1Ga. The chemical shifts in one-dimensional MAS NMR spectra yield information about the local structure of the nuclei. For example, the 2 9 Si spectra of aluminosilicate zeolites provide information about the fractions of 2 9 Si nuclei with 0, 1, 2, 3, or 4 27A1 nuclei in the coordination spheres, from which the framework Si/Al ratio of the zeolite can be worked out 8 0 8 2 (see Figure 1.20a). High resolution 2 9 Si MAS NMR spectra of highly siliceous zeolites,17'18 reveal the number and occupancy of crystallographically unique silicon atoms, providing information about the crystallographic space group of the zeolite18-20-83'84 (see Figure 1.20b), The crystallographic phase changes induced by changes in temperature or sorbate molecule loading have been studied in detail by high resolution 2 9 Si MAS NMR. 1 8 - 8 5 Two-dimensional NMR experiments probe the connectivities between the nuclei in the framework, yielding a great deal of information about the zeolite framework. For example, the Si-O-Si connectivities in highly-siliceous zeolites can be probed with the two-dimensional 2 9 Si INADEQUATE experiment20-86 (see Chapter 2) and the Al-O-P connectivities in microporous aluminophosphate materials can be probed by two dimensional 2 7A1/ 3 1P INEPT or CP experiments.87 T I I I I 1 1 1 1 1 1 1 1 1 1 -80 -90 -100 -110 -108 -110 -112 -114 -116 -118 29 29 Si chemical shift (ppm from TMS) Si chemical shift (ppm from TMS) Figure 1.20 (a) 2 9Si MAS NMR spectrum NaY zeolite (Si/Al ratio of 2.6) with the resonances for the five different Si environments resolved, (b) Ultra-high resolution 2 9Si MAS spectrum of a very highly crystalline and completely siliceous zeolite ZSM-5 sample, after careful optimization of all experimental parameters, showing resonances for the 24 crystallographically distinct Si sites in the framework (monoclinic phase), from reference 18. Guest species in zeolites can also be studied by solid state NMR. The structure and dynamics of various organic sorbate and template molecules can be studied by *H, 2 H , 1 3 C, and 1 5 N NMR experiments. The acid sites in catalytically active zeolites and adsorbed water can be studied by 'H NMR experiments. Also, 1 9F, 2 3Na, 6 L i / 7 L i , and 1 3 3Cs NMR experiments can provide information about the location, dynamics, and degree of hydration of ionic guest species. 1 2 9 Xe NMR can be used to probe microporous Chapter 1 references begin on page 34. 31 Chapter 1. Introduction materials since the , 2 9 Xe chemical shift of adsorbed Xe gas is sensitive to pore structure and the presence of guest species.88 This thesis extends the study of highly siliceous zeolites to double resonance experiments in which the dipolar couplings between nuclei of the guest species and the 2 9 Si nuclei of the framework are probed in order to obtain information about structure of the host/guest complexes. 1.5 Relationship between solid state NMR and X-ray diffraction Solid state NMR and X-ray diffraction are complementary techniques and form a powerful combination when used together for the study of the structure, dynamics, and disorder of solid materials. X-ray diffraction arises from the long range and periodic order of electron density in materials while solid state NMR probes the local magnetic environments of the nuclei present in the material. NMR is a powerful tool for studying the dynamic time-dependent processes that occur in a material while XRD provides only the average structure over time. With regard to order/disorder, XRD provides the average structure over the entire crystal and indicates the presence of disorder, but may not provide the information about the nature of the disorder which solid state NMR may provide. When crystals of sufficient size and quality are available, XRD is by far the superior technique for determining structure and solid state NMR can provide important complementary information. However, when these conditions are not met, solid state NMR often provides a wealth of information which diffraction experiments cannot provide. In the case of zeolite host/guest complexes, the limiting factor in the study of their structures is the availability of crystals which are of sufficient size and quality since zeolites are typically microcrystalline and often twinned. Furthermore, the guest species are often weakly scattering and do not contribute a great deal to the X-ray scattering compared to the contribution of the atoms in the zeolite framework. These structures are therefore well-suited for study by a combination of XRD and solid state NMR. 1.6 Outline and framework of thesis The common theme throughout this thesis is how solid state NMR provides an alternative and complementary technique for the study of the structure of zeolite host/guest complexes. Solid state NMR experiments are described by which the location of guest species can be determined from NMR data alone, independent of XRD data. In addition, examples are provided in which solid state NMR experiments provide important complementary information to XRD with regard to structure, disorder, and dynamics. The chapters are structured around a general strategy for locating guest species in zeolite frameworks. This strategy consists of three main steps: (1) assign resonances in the NMR spectrum of the zeolite host to specific sites of zeolite framework by performing two-dimensional NMR correlation experiments, (2) experimentally probe the strengths of the heteronuclear dipolar couplings (which are Chapter 1 references begin on page 34. 32 Chapter 1. Introduction related to internuclear distances) between nuclei of the guest species (e.g. 'H or 1 9F) and the nuclei of zeolite framework (e.g. 2 9Si), and (3) use this distance information to determine the location of the guest species with respect to the zeolite framework. Examples of information concerning dynamics and disorder in these zeolite host/guest structures available from solid state NMR that is complementary to XRD are interspersed throughout the thesis. Chapter 2 describes the two-dimensional INADEQUATE experiment by which the 2 9Si-0- 2 9Si scalar couplings between Si sites in the zeolite framework can be probed. From these correlations, the resonances in the 2 9 Si spectra are assigned to specific framework Si sites using a peak assignment algorithm which compares the observed correlations to the known connectivities in the zeolite framework. Chapter 3 describes in detail and evaluates a number of solid state NMR technique available for measuring heteronuclear dipolar couplings, which provide information about distances. In Chapter 4, this general strategy is implemented to locate the fluoride ion in an as-made zeolite, synthesized via the fluoride route, by measuring 1 9 F- 2 9 Si internuclear distances to various Si sites in the framework. The dynamics of the fluoride ion at this location are also described. In Chapter 5, it is shown conclusively for a number of fluoride-containing as-synthesized zeolites that the fluoride ions are covalently bonded to a particular Si site of the framework, giving a five-coordinate Si site whose local structural geometry was determined, due to the presence of structural disorder, only by a combination of solid state NMR distance measurements and single microcrystal XRD. In Chapter 6, this general strategy for locating guest species in zeolites is extended to organic sorbate/zeolite complexes in which exact internuclear distances cannot be measured directly. With the peaks in the 2 9 Si spectrum assigned from two-dimensional NMR experiments, the rates of 2 9Si{'H} cross polarization reflect the relative distances between the 'H nuclei of the organic sorbate molecule and the different 2 9 Si nuclei of the framework. This chapter describes a protocol for determining guest sorbate molecule locations from 2 9Si{'H} CP MAS NMR spectra. In Chapter 7 the reliability and robustness of this protocol is examined over a wide range of temperatures and sorbate molecule loadings. In Chapters 8 and 9, the structures of a number of zeolite/sorbate complexes detennined by this solid state 2 9Si{'H} CP MAS NMR are presented and compared with single crystal XRD structures. Chapter 10 is a combined solid state NMR and single crystal XRD study of the order/disorder of the /?-nitroaniline/ZSM5 complex, which has been shown to have non-linear optical properties. Finally Chapter 11, describes some suggestions for future work and concludes the thesis while Chapter 12 provides the experimental details for the various experiments carried out and presented in this thesis. Chapter I references begin on page 34. 33 Chapter 1. Introduction References for Chapter 1 (1) Barrer, R. M. Zeolite and Clay Materials as Sorbents and Molecular Sieves; Academic Press:, 1974. (2) Breck, D. W. Zeolite Molecular Sieves; Wiley Interscience:, 1974. 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Chapter 1 references begin on page 34. 36 Chapter 2 Solid State NMR Experiments and Strategies for Assigning the NMR Resonances of the Zeolite Framework This chapter introduces two-dimensional NMR correlation experiments that can be used to probe the 'connectivities' in the zeolite framework. A general strategy and algorithm for working out the peak assignments from two-dimensional NMR correlation experiments is described in detail, with a focus on the assignment of the 2 9 Si resonances of highly siliceous zeolites from two-dimensional INADEQUATE experiments. 2.1 Introduction The first step towards locating guest species in zeolite frameworks is to assign the peaks in the NMR spectra to the magnetically inequivalent sites of the host framework. Two-dimensional NMR correlation experiments can provide a great deal of information about the 'connectivities' that exist in the structure that is being probed. For highly siliceous zeolites, the 2 9 Si MAS COSY and INADEQUATE experiments1 are powerful tools for investigating the three-dimensional connectivity pattern of the zeolite framework as they probe Si-O-Si bonding.2-12 This chapter begins with a brief introduction to two-dimensional NMR 1 3 " 1 7 and a description of the INADEQUATE experiment18"20 and its application to zeolite structures.5"7'9"12 The remainder of the chapter describes a new efficient and automated algorithm for assigning peaks in the 2 9 Si NMR spectrum based on the observed correlations in two-dimensional INADEQUATE NMR spectra. 2.2 Two-dimensional NMR The basic idea of two-dimensional NMR was first proposed as a concept by Jeener in 197121 and was initially explored and developed by Ernst and co-workers.22"24 It has become a very powerful standard tool in high-resolution solution NMR for peak assignment, structure confirmation, and even structure elucidation.25"27 The concept has been extended to three and even four dimensions for the determination of protein structures in solution. In a one-dimensional NMR experiment, a free induction decay (FID), S(t2), is recorded during a time t2 and the frequency spectrum S(f2) is obtained by Fourier transformation of this signal. The basic principle of two-dimensional NMR is that there is an additional 'evolution' period during which the Chapter 2 references begin on page 53. 37 Chapter 2 Peak Assignments from Two-Dimensional NMR 'prepared' nuclear spins evolve for a time t\ before an FID is collected such that the observed signal is a function of both t\ and t2, S(t\,t2). The basic structure of two-dimensional NMR experiment is illustrated in Figure 2.1. In general, a series of FIDs are collected with incremented values of the evolution period t\ and the two-dimensional spectrum S(f\f2) is the two-dimensional Fourier transformation of S(tut2). Although the order in which the transformations are applied is arbitrary, the concept of two-dimensional NMR is best illustrated by first transforming the series of FIDs collected in t2 which gives a series of spectra in which the peaks are modulated by the interactions which 'evolved' during t\. The second Fourier transformation of these modulations will then yield the two-dimensional spectrum. An example of a two-dimensional NMR experiment in the solid state is illustrated in Figure 2.2. preparation evolution mixing detection (U) {t2) Figure 2.1 General two-dimensional NMR experiment. Figure 2.2 Illustration of a two-dimensional NMR experiment, (a) Pulse sequence for a two-dimensional solid state CP MAS heteronuclear correlation (HETCOR) experiment in which the chemical shifts of the I nuclei evolve before polarization is transferred to the S nuclei via a I{S} cross polarization transfer, (b) Series of spectra after Fourier transformation of the FIDs collected in t2 in which the peak intensities are modulated by the frequencies of the / nuclei which evolve in t\. (c) Two-dimensional spectrum after Fourier transformation of t\. The modulations in b show up as a frequency in the f dimension. Chapter 2 references begin on page 53. 38 Chapter 2 Peak Assignments from Two-Dimensional NMR 2.3 The INADEQUATE experiment The /ncredible /Vatural Abundance DoublE QUAnTum Experiment (INADEQUATE) was first proposed by by Bax and Freeman as a one-dimensional solution NMR experiment to observe the double quantum coherences arising from pairs of ./-coupled 1 3 C nuclei in natural abundance in organic compounds.18 When extended to a second dimension19-20 in which these double quantum coherences are allowed to evolve and be 'encoded' in the observed FIDs, the two-dimensional INADEQUATE experiment becomes a homonuclear chemical shift correlation experiment which is a very powerful tool for peak assignment and structure determination as the observed correlations can be related to the bonding 'connectivities' in the structure under study. The applications of the INADEQUATE experiment in solution and solid state have recently been reviewed.28 2.3.1 Pulse Sequence for INADEQUATE The basic pulse sequence for the two dimensional INADEQUATE experiment is illustrated in Figure 2.3. The preparation period consists of an echo with delays of 1/(47) by which the double quantum coherences arising from pairs of J-coupled nuclei with chemical shifts coy and co* are excited. The double quantum coherences then evolve during t\ with a frequency equal to the sum of the chemical shift frequencies of the coupled nuclei (coy + co*). The final pulse converts the double quantum coherences into observable magnetization (with frequencies co,- ± Jjkl2 and co* ± Jjkl2) which is collected as an FID during t2. After Fourier transformation in both dimensions, each coupled spin pair gives rise to two sets of signals in the two-dimensional spectrum which are present as anti-phase doublets separated by JJk at chemical shifts coy and co* in thef2 domain respectively while they appear at coy + co* in the double quantum (fi) dimension. The two sets of signals are equally-spaced on both sides of the diagonal of the plot, as shown in Figure 2.4. These correlations provide a wealth of information about the connectivities present in the structure under study. 90° 180° 90° ^ 135° I I I I L convert to observable magnetization Figure 2.3 Pulse sequence diagram for the two-dimensional INADEQUATE experiment Figure 2.4 Schematic contour plot of a two-dimensional INADEQUATE experiment on a J-coupled two-spin system. Chapter 2 references begin on page 53. 39 Chapter 2 Peak Assignments from Two-Dimensional NMR 2.3.2 INADEQUATE in the solid state The INADEQUATE experiment can be extended to the solid state under magic angle spinning conditions in which the chemical shift anisotropies and dipolar couplings are reduced or even eliminated, leaving only isotropic chemical shifts and J couplings as in solution. In appropriate samples, sensitivity can be enhanced by replacing the initial 90° pulse with cross polarization from 'H. The CP MAS INADEQUATE experiment was first applied to the plastic crystal camphor by Benn and co-workers.1 When chemical shift anisotropies are not completely removed by MAS, it is necessary that the delays in the experiment be synchronized with the spinning rate to ensure correct echo formation. Narrow linewidths are an important prerequisite for solid state MAS INADEQUATE experiments since the anti-phase doublets begin to cancel each other out as the linewidth increases. The refocused INADEQUATE experiment,29'30 which has an additional echo after the t\ evolution period, yields in-phase doublets and avoids this problem, but can be limited by the rate of T2 relaxation since the total echo time is doubled. Recently, solid state INADEQUATE-type experiments have been developed which are based on through-space dipolar couplings.31"34 In these experiments, the preparation and mixing periods consist of pulse schemes which recouple the dipolar interactions under MAS conditions.35 Since the dipolar couplings are typically much stronger than the ./-couplings, the preparation and mixing periods can be shorter, allowing samples with shorter T2 values to be studied. 2.3.3 Determination of zeolite framework connectivities by two-dimensional NMR The two-dimensional 2 9 Si MAS INADEQUATE experiment is a very powerful tool for probing the Si-O-Si bonding or 'connectivity' patterns in highly-siliceous zeolite frameworks. Although the 2 9Si-0-2 9 Si J-couplings in zeolites are weak (9 to 16 Hz) 3 6 and the natural abundance of 2 9 Si is low (4.7%) such that only about 1% of the silicon atoms occur as 2 9 Si spin pairs (4x0.047x0.047, where the factor of four arises from each Si being connected to four other Si), it is still possible to collect two-dimensional spectra within a reasonable amount time (1 to 2 days). The two-dimensional 2 9 Si INADEQUATE spectra have been used to provide valuable information about the crystallographic space group of zeolites8-37'38 and to provide peak assignments in order to relate 2 9 Si chemical shifts to structural parameters determined by XRD such as bond lengths and angles.39 In the work described in this thesis, the assignment of 2 9 Si resonances made possible by the 2 9 Si INADEQUATE experiment is a crucial first step towards locating guest species in zeolites by solid state NMR techniques. Chapter 2 references begin on page 53. 40 Chapter 2 Peak Assignments from Two-Dimensional NMR 2.4 Peak assignments from two-dimensional NMR correlation experiments The interpretation and analysis of two-dimensional correlation spectra in order to determine peak assignments is not always straightforward. As the number of magnetically inequivalent sites in the structure increases and in situations where there is little information in addition to the correlation spectrum (such as characteristic chemical shifts, relaxation times, and relative intensities), it becomes increasingly difficult to work out peak assignments and to be confident that all possible sets of peak assignments have been tested. In comparison to organic compounds, for which there exists a great deal of additional information in the form of chemical shifts and coupling patterns, the unambiguous assignment of the peaks in the 2 9 Si spectra of highly siliceous zeolites is often a very difficult task. For most highly siliceous zeolites, all 2 9 Si are tetrahedrally coordinated and site occupancies often identical, so there is usually very little additional information (e.g. in the form of characteristic chemical shifts or relative intensities) to assist in assigning the peaks. Usually, the only source of information to work with is the 2 9 Si-0- 2 9 Si correlations oberserved in a two-dimensional correlation experiment such as INADEQUATE. Each 2 9 Si peak could potentially be assigned to any silicon site in the structure, so it is necessary to test all possible combinations of assignments against the experimental data. Since the number of possible assignments to test is 7Y! where N is the number of peaks or magnetically inequivalent sites, this task becomes very tedious to perform manually and is well suited for analysis by computer. The remainder of this chapter describes an efficient algorithm for relating experimental correlation spectra to the known connectivities that are present in the structure under study in order to find all possible sets of assignments of the individual resonances in the NMR spectrum to the magnetically inequivalent sites in the structure. Although this algorithm is particularly useful for working out peak assignments for situations in which there exists little information beyond the correlation spectra, we think that it could be a useful tool for easily, reliably, and efficiently working out peak assignments from any type of correlation experiment (solution or solid state) on any type of sample. Since this algorithm was developed for determining the peak assignments of high-resolution solid-state 2 9 Si MAS NMR spectra of highly siliceous zeolites from two-dimensional 2 9 Si MAS INADEQUATE spectra, the peak assignment algorithm is described in detail using data from zeolite ZSM-12 as a working example. The algorithm was written as a Mathematica (version 3.0)40 notebook, the code for which is supplied in Appendix C, along with sample input files. 2.4.1 Input for peak assignment algorithm The algorithm requires three tables of information as input: (1) a table of the connectivities known from the structure (Cknown), (2) a table of the observed correlations from the two-dimensional correlation experiment (C0&), and (3) a list of the possible sites to which each peak could be assigned (•<4p0SSjDie). From this information, all possible sets of peak assignments which are consistent with the experimental data are generated. Chapter 2 references begin on page 53. 41 Chapter 2 Peak Assignments from Two-Dimensional NMR The table of known connectivities (Q„0M,„) contains the information about which sites are 'connected' to one another via the coupling mechanism under investigation. In this example of 29Si INADEQUATE on zeolite ZSM-12, the table of known connectivities from the framework topology lists which framework Si sites are 'connected' to one another via 29Si-29Si /-couplings through the bridging Si-O-Si bonds (Table 2.1). For example, Si site 3 is connected twice to site 1 and once to each of sites 5 and 6. Figure 2.5 Framework structure of ZSM-12 showing the seven crystallographically inequivalent Si sites. From reference 5. Table 2.1 Known Connectivities for the Si sites in the ZSM-12 Zeolite Framework (Ckmwn).5 1 2 3 4 5 6 7 1 0 2 2 0 0 0 0 2 2 0 0 2 0 0 0 3 2 0 0 0 1 0 1 4 0 2 0 0 1 1 0 5 0 0 1 1 0 2 0 6 0 0 0 1 2 0 1 7 0 0 1 0 0 1 0 ° There actually exists two self-connectivities for Si site 7, but self-correlations do not appear in INADEQUATE spectra. The table of experimentally observed correlations (Cobs) contains the observed correlations from the two-dimensional NMR experiment. An entry of zero indicates that the correlation between peaks is definitely absent. A value of one indicates that there exists exactly one correlation and a value of two indicates exactly two correlations. In situations where there may be ambiguity or uncertainty concerning whether or not the correlation is actually present or not, half-integer values can be used. These indicate that the correlation may or may not be present. For example, an entry of 1.5 indicates that there definitely exists one correlation between the two peaks, but there may or may not be a second correlation. For the ZSM-12 example, the correlation table shown in Table 2.2 can be constructed from the experimental 2 9Si INADEQUATE spectrum (Figure 2.6). The strong correlations between peaks A-D, A-F, B-E, and D-G were given values of 1.5, the correlations between C-G and E-F were given values of 1, and the weak correlations between peaks B-F, B-G, and C-E were given values of 0.5. Note that the diagonal values are zero due to the fact that self-correlations do not show up in the INADEQUATE experiment. Chapter 2 references begin on page 53. 42 Chapter 2 Peak Assignments from Two-Dimensional NMR G F E D C B A Figure 2.6 Two-dimensional 2 9Si INADEQUATE spectrum of ZSM-12 zeolite.5 The table of possible peak assignments contains information about possible peak assignments using any experimental information in addition to the connectivity pattern from the two-dimensional NMR spectrum. Chemical shifts, relaxation times, and relative peak intensities are some examples of information that can used to narrow down the assignments. In the ZSM-12 example, the 2 9 Si T\ relaxation time for peak B is significantly longer than the rest of the peaks. The ZSM-12 framework structure has six silicon sites on the surface of the channels and one site (Si site 5) 'buried' in the walls of the framework. Since the T\ relaxation is primarily due to paramagnetic oxygen in the channels of the zeolite, peak B can be assigned to the 'buried' 5 site. As for the rest of the peaks, they could possibly be any of the remaining six silicon sites. The table of possible peak assignments (Table 2.3) reflects this information, using a value of 1 if the assignment is possible, and a value of 0 if the assignment is not possible. From this table, Apossible, a list containing the possible assignments for each peak is constructed. For example, Apossible= {5} mdAp0Ssibie = {1, 2, 3, 4, 6, 7}. Table 2.3 Possible Peak Assignments for ZSM-12 Zeolite. 1 2 3 4 5 6 7 A 1 1 1 1 0 1 1 B 0 0 0 0 1 0 0 C 1 1 1 1 0 1 1 D 1 1 1 1 0 1 1 E 1 1 1 1 0 1 1 F 1 1 1 1 0 1 1 G 1 1 1 1 0 1 1 Chapter 2 references begin on page 53. 43 Chapter 2 Peak Assignments from Two-Dimensional NMR 2.4.2 Testing peak assignments With this information, it is possible to propose a set of peak assignments and test it against the experimentally observed correlation table. The proposed peak assignments should be consistent with the possible peak assignments, Apossibie. For example, the following set of peak assignments is proposed: Peak in Si spectrum: A B C D E F G Crystallographic Si site: 2 5 7 1 3 6 4 To test this proposed assignment set against the experimental correlation table, the rows and columns of the Cknown table are first rearranged according to this assignment to give C'known (Table 2.4). Table 2.4 Rearranged Known Connectivity Table for ZSM-12 (C'know„ = rearranged Cknow„).a 2 5 7 1 3 6 4 2 0 0 0 2 0 0 2 5 0 0 0 0 1 2 1 7 0 0 2 0 1 1 0 1 2 0 0 0 2 0 0 3 0 1 1 2 0 0 0 6 0 2 1 0 0 0 1 4 2 1 0 0 0 1 0 " C k m w n is Table 2.1. This rearranged table, C'know„, is then compared to Cobs. If the peak assignments are correct, then these two tables should be the same and if the peak assignments are incorrect, then there will be differences between the two tables. Recall that half-integer values can be used if there is uncertainty in the experimental spectrum. Therefore, the maximum tolerated difference between the two tables is ±0.5. To efficiently compare Cobsto the C'known for a proposed set of peak assignments, the table Cobs - C'known is searched for any elements less than -0.5 or greater than +0.5. The difference table, Cobs - C'known (Table 2.5), for this particular proposed set of peak assignments clearly shows that the peak assignments are not consistent with the experimentally observed correlations, as illustrated by the elements in bold-face type. Table 2.5 Difference Between Observed Correlation Table and Rearranged Known Connectivity Table for ZSM-12 {Cobs - C Icnown)' A/2 B/5 C/7 D/l E/3 F/6 G/4 A/2 0 0 0 -0.5 0 1.5 -2 B/5 0 0 0 0 0.5 -1.5 -0.5 C/7 0 0 0 0 -0.5 -1 1 D/l -0.5 0 0 0 -2 0 1.5 E/3 0 0.5 -0.5 -2 0 1 0 F/6 1.5 -1.5 -1 0 1 0 -1 G/4 -2 -0.5 1 1.5 0 -1 0 Cobs *s Table 2.2 and C known is Table 2.4. Chapter 2 references begin on page 53. 44 Chapter 2 Peak Assignments from Two-Dimensional NMR In this manner, every possible set of peak assignments can be proposed and tested. In the absence of any additional information, the total number of proposed assignments that need to be tested is 7Y! where N is the number of peaks or magnetically inequivalent sites. In this example of ZSM-12, where the identity of one of the peaks is known, the total number of possible assignment sets is reduced from 7! = 5040 to 1 x 6! = 720, a reasonable number of combinations to test. However as 7V gets larger, the number of possible assignments becomes too many to test in a reasonable amount of time. For example, solving the INADEQUATE spectrum in this manner for the monoclinic phase of ZSM-5 in which there are 24 Si sites is just not possible as 24! = 6.2 x 1023. Therefore a strategy must be developed to greatly reduce the number of combinations tested, making even the situation with N = 24 possible to solve. 2.4.3 Increasing efficiency To reduce the number of combinations tested, the algorithm takes advantage of the fact that there needs to be only one element different between C0BS and the rearranged C\nown table (i.e. one element of the Cobs - C'known table that is less than -0.5 or greater than +0.5) for that set of assignments to be ruled out. Therefore, is if far more efficient to introduce and test peak assignments one peak at a time, rather than propose complete sets of assignments. For example, only the assignments {1,5}, {2,5}, and {7,5}for peaks {A,B} give agreement between the observed correlations and known connectivities. Therefore, it is only necessary to further test assignments sets with {1,5}, {2,5}, or {7,5} assigned to peaks {A,B} since all assignment sets with {3,5}, {4,5}, or {6,5} assigned to peaks {A,B} will all have at least one contradiction between the observed correlations and known connectivities. By introducing and testing peak assignments in this step-wise manner, all good assignments for which there is agreement between the observed correlations and the known connectivities are kept and passed on to the next step, whereas all bad assignments for which there is disagreement are immediately removed. This approach dramatically cuts down on the number of proposed assignment sets to be tested, yet still guarantees that all acceptable assignment sets are found. The algorithm is schematically described in the Figure 2.7. Its application to the ZSM-12 example is shown in Table 2.6 where the values for each variable at each step are tabulated in order to illustrate the 'flow' of the algorithm. Chapter 2 references begin on page 53. 45 Chapter 2 Peak Assignments from Two-Dimensional NMR V = « ) l su={} n for / = 1 to N S1 = AddPeak [ S M , Pl ] Aproposed = ConstructProposedAssignments[ A^od, APpossihle\ Agood = SelectGoodAssignments[ A'proposed, S' ] / = /+l Figure 2.7 Schematic description of the peak assignment algorithm. See Section 2.5 for a detailed description of the functions and variables. Table 2.6 Following the Steps in the Peak Assignment Algorithm Applied to Zeolite ZSM-12. i Added Peak Set of Peaks to be Tested Possible Peak Assignments for Added Peak Proposed Assignments Good Assignments (P') (S') pi (^ possible) ( ^proposed ) ( Ag0od ) 0 {} {{}} 1 A {A} {1,2, 3, 4, 6,7} {{1}, {2}, {3}, {4}, {6}, {7}} {{1},{2}, {3}, {4},{6},{7}} 2 B {A,B} {5} {{1,5}, {2,5}, {3,5}, {4,5}, {6,5}, {7,5}} {{1,5}, {2,5}, {7,5}} 3 C {A,B,C} {1,2, 3, 4, 6,7} {{1,5,2}, {1,5,3}, {1,5,4}, {1,5,6}, {1,5,7}, {2,5,1}, {2,5,3}, {2,5,4}, {2,5,6}, {2,5,7}, {7,5,1}, {7,5,2}, {7,5,4}, {7,5,4}, {7,5,6}} {{1,5,7}, {2,5,7}, {7,5,1}, {7,5,2}} 4 D {A,B,C,D} {1,2, 3, 4, 6,7} {{1,5,7,2}, {1,5,7,3}, {1,5,7,4}, {1,5,7,6}, {2,5,7,1}, {2,5,7,3}, {2,5,7,4}, {2,5,7,6}, {7,5,1,2}, {7,5,1,3}, {7,5,1,4}, {7,5,1,6}, {7,5,2,1}, {7,5,2,3}, {7,5,2,4}, {7,5,2,6}} {{1,5,7,2}, {2,5,7,1}} 5 E {A,B,C,D,E} {1,2,3, 4, 6, 7} {{1,5,7,2,3}, {1,5,7,2,4}, {1,5,7,2,6}, {2,5,7,1,3}, {2,5,7,1,4}, {2,5,7,1,6}} {{1,5,7,2,6}, {2,5,7,1,6}} 6 F {A,B,C,D,E,F} {1,2, 3, 4, 6,7} {{1,5,7,2,6,3}, {1,5,7,2,6,4}, {2,5,7,1,6,3}, {2,5,7,1,6,4}} {{2,5,7,1,6,4}} 7 G {A,B,C,D,E,F,G} {1, 2, 3, 4, 6, 7} {{2,5,7,1,6,4,3}} {{2,5,7,1,6,4,3}} This calculation yields one unique assignment set for which there is agreement between the experimentally observed correlations and the connectivities known from the ZSM-12 structure: Peak in 2 9Si spectrum: A B C D E F G Crystallographic Si site: 2 5 7 1 6 4 3 Chapter 2 references begin on page 53. 46 Chapter 2 Peak Assignments from Two-Dimensional NMR An additional gain in efficiency can be obtained by changing the order in which the peaks are added in the algorithm. By using the peaks for which more information is known in the beginning stages of the algorithm, the total number of combinations tested is further reduced. The peaks are ranked primarily by the number of possible peak assignments. In the ZSM-12 example, peak B has one possible assignment so it is ranked first while the other peaks are ranked equally since they all have six possible peak assignments. The peaks can then be ranked secondarily by the number of 'definite' correlations (i.e. by the number of integer values in the Coos table, including zeros). Peak C has six integer values and the remaining others have five, so the ranked order is then P = {B, C, A, D , E , F, G} . In Table 2.7, the efficiencies of various approaches for solving the peak assignments for ZSM-12 from the INADEQUATE correlation experiment are compared. It is important to note that each of these approaches gives the same unique assignment set as given above. However, it is the efficiency with which these different approaches yields the answer that is of interest. This table demonstrates the large gain in efficiency in testing the peak assignments in the step-wise manner employed by this algorithm and the further gains in efficiency that are obtained by including the additional information about peak B and by ranking the peaks according to the amount of information available. For the ZSM-12 example, this peak assignment algorithm results in a gain of efficiency of about two orders of magnitude over testing all possible assignment combinations, and still guarantees that all assignment sets which agree with the experimental correlation data are found. Table 2.7 Comparison of the Efficiencies of Various Approaches for Assigning the Peaks in the 2 9Si MAS NMR Spectrum of Zeolite ZSM-12 Based on its Two-Dimensional INADEQUATE Correlation Spectrum." Method of Calculation Number of Assignment Sets Tested Calculation Time (seconds) All possible combinations of assignments. 5040 8.7 All possible combinations of assignments with peak B assigned to Si site 5. 720 1.4 Step-wise with order P ={A,B,C,D,E,F,G}. 294 0.38 Step-wise with order P = {A, B, C, D, E, F, G} and peak B assigned to Si site 5 54 0.17 Step-wise with ranked order P = {B, C, A, D, E, F, G} and peak B assigned to Si site 5 49 0.11 " The algorithm was implemented as a Mathematica (version 3.0)40 program and was run on a PC equipped with a 500 MHz Intel Pentium III processor and 256 MB of RAM. Chapter 2 references begin on page 53. 47 Chapter 2 Peak Assignments from Two-Dimensional NMR 2.4.4 Application to the monoclinic phase of zeolite ZSM-5 The 2 9 Si MAS NMR spectrum of the monoclinic phase of zeolite ZSM-5, in which there are 24 unique tetrahedral Si sites, is one of the more challenging spectra to assign since there are many peaks, all of equal intensity, and there is little information outside the two-dimensional 2 9 Si INADEQUATE spectrum which can be used for assigning the peaks. This challenging example clearly demonstrates the usefulness of the peak assignment algorithm. The 2 9 Si MAS NMR spectrum of the monoclinic phase of ZSM-5 was previously assigned from the observed correlations in the two-dimensional INADEQUATE spectrum.6-7 This assignment rested on the assumption that four of the lowest field peaks (peaks S-X) could be assigned to the silicons in the four-membered rings (sites 9,10, 21, and 22). Although the same assignment is reached using the present computational approach, no such initial assumptions are made and all possible assignments which agree with the experimental correlations are found. The table of known connectivities (Table 2.8) was constructed from the known topology of the monoclinic phase of ZSM-5 (Figure 2.8) where each Si atom is connected via S i -O-Si bonds to four different Si atoms. The table of observed correlations (Table 2.9) was constructed from the correlation peaks in the two-dimensional 2 9 Si INADEQUATE spectrum (Figure 2.9) in the same manner as for the previous example of ZSM-12. The table of possible peak assignments consists entirely of values of 1 since all peaks can potentially be assigned to any Si site. Figure 2.8 Schematic of the Si connectivites in the monoclinic phase of the ZSM-5 framework. From reference 6. Table 2.8 Known Connectivities for the Si Sites in the Monoclinic Phase of ZSM-5 Zeolite.6 1 2 3 4 5 6 7 8 9 1011 12131415161718192021222324] 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 2 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 4 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 5 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 6 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 7 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 8 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 10 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 11 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 12 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 13 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 14 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 15 0 0 0 0 0 1 0 0 0 0 0 1 0 I 0 1 0 0 0 0 0 0 0 0 16 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 17 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 18 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 19 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 20 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 21 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 22 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 23 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 24 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 Chapter 2 references begin on page 53. 48 Chapter 2 Peak Assignments from Two-Dimensional NMR 0,P,Q,R l,J,K,L -110 -112 -114 -116 ppm Figure 2.9 Two-dimensional 2 9Si INADEQUATE spectrum of the monoclinic phase of ZSM-5 zeolite, from reference 6. Table 2.9 Observed Correlations from the 2 9Si INADEQUATE Experiment on the Monoclinic Phase of ZSM-5 Zeolite." A B C D E F G H I K L M N O P Q R S T U V W X A 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 2 0 0 0 0 0 B 0 0 0 0 0 2 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 C 0 0 0 0 0 2 0 0 1 1 1 1 1 0 0 0 0 0 0 2 0 0 0 0 D 0 0 0 0 0 0 0 0 1 1 1 1 1 2 0 0 0 0 0 0 0 2 2 0 E 0 0 0 0 0 0 2 0 1 1 1 1 1 0 1 1 1 1 0 0 2 0 0 0 F 0 2 2 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 G 0 1 0 0 2 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 H 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 2 2 I 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 J 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 K 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 L 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 M 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 2 0 N 0 0 0 2 0 0 0 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 O 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 P 1 1 1 0 1 0 1 1 1 I 1 1 1 1 1 0 1 1 1 1 1 0 0 1 Q 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 R 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 S 2 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 0 0 2 0 2 T 0 0 2 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 0 0 2 2 0 U 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 2 0 2 V 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 W 0 0 0 2 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 X 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 1 1 1 2 0 2 0 0 0 " The elements in this table have been multiplied by a factor of two: 0 = connection definitely absent, 1 = connection may or may not be present, 2 = connection definitely present. With the above input, the algorithm finds 18 sets of peak assignments which are consistent with the observed correlations and the known connectivities in 4 hours by testing 6.2 x 106 of 24! = 6.2 x 1023 possible assignment sets as presented in Table 2.10. Upon closer inspection, these assignment sets are closely related to one another. There are essentially four groups of assignments in which the assignment of the 16 resolved peaks are identical, but there are differences in the assignment of the peaks which make up the two groups overlapping peaks. Furthermore, there is a relationship between assignments 1-5 and 10-14 and between assignments 6-9 and 15-18 in that there is an exchange of site / with site z'±12. When the 2 9 Si chemical shifts are correlated with the mean Si-Si distances39 (from the single crystal XRD structure41), the group consisting of assignment sets 1-5 is clearly shown to be superior over the others. The assignment which gives the best correlation is chosen as the correct assignment and is identical to that reported from the previous 'manual' analysis.6'7 Chapter 2 references begin on page 53. 49 Chapter 2 Peak Assignments from Two-Dimensional NMR Table 2.10 Possible Assignment Sets for the Si MAS Spectrum of the Monoclinic Phase of Zeolite ZSM-5 from the 2 9Si INADEQUATE Spectrum. No. A B C D E F G H (I, J,K,L} 6 M N {0,P,Q,R}6 S T U V W X 1 0.915 8 16 14 11 23 15 17 6 {3,12,18,24} 4 19 {1,2,7,20} 9 13 22 10 5 21 2 0.903 8 16 14 11 23 15 17 6 {2,3,12,24} 4 19 {1,7,18,20} 9 13 22 10 5 21 3 0.899 8 16 14 11 23 15 17 6 {2,3,12,18} 4 19 {1,7,20,24} 9 13 22 10 5 21 4 0.894 8 16 14 11 23 15 17 6 {2,12,18,24} 4 19 {1,3,7,20} 9 13 22 10 5 21 5 0.892 8 16 14 11 23 15 24 6 {2,3,12,18} 4 19 {1,7,17,20} 9 13 22 10 5 21 6 0.254 19 3 8 22 14 2 15 6 {1,12,16,17} 20 23 {4,7,18,24} 11 9 13 10 21 5 7 0.245 19 3 8 22 14 2 15 6 {1,7,12,16} 20 23 {4,17,18,24} 11 9 13 10 21 5 8 0.247 19 3 8 22 14 2 15 6 {1,7,16,17} 20 23 {4,12,18,24} 11 9 13 10 21 5 9 0.211 19 3 8 22 14 2 15 6 {1,7,12,17} 20 23 {4,16,18,24} 11 9 13 10 21 5 10 0.096 20 4 2 23 11 3 5 18 {6,14,15,24} 16 7 {5,8,13,19} 21 1 10 22 17 9 11 0.070 20 4 2 23 11 3 5 18 {6,14,15,24} 16 7 {8,12,13,19} 21 1 10 22 17 9 12 0.068 20 4 2 23 11 3 5 18 {12,14,15,24} 16 7 {6,8,13,19} 21 1 10 22 17 9 13 0.067 20 4 2 23 11 3 5 18 {6,12,14,24} 16 7 {8,13,15,19} 21 1 10 22 17 9 14 0.056 20 4 2 23 11 3 5 18 {6,12,15,24} 16 7 {8,13,14,19} 21 1 10 22 17 9 15 0.004 7 15 20 10 2 14 3 18 {4,13,19,24} 8 11 {5,6,12,16} 23 21 1 22 9 17 16 0.002 7 15 20 10 2 14 3 18 {4,5,13,24} 8 11 {6,12,16,19} 23 21 1 22 9 17 17 0.001 7 15 20 10 2 14 3 18 {4,5,13,19} 8 11 {6,12,16,24} 23 21 1 22 9 17 18 0.000 7 15 20 10 2 14 3 18 {5,13,19,24} 8 11 {4,6,12,16} 23 21 1 22 9 17 " The possible assignments are ranked according to the degree of linear correlation between chemical shift and mean Si-Si distance. b The brackets indicate a group of overlapping peaks for which all permutations of the assignments are possible. 2.4.5 Summary of peak assignment algorithm This algorithm, which efficiently assigns resonances in NMR spectra to the magnetically inequivalent sites based on information from two-dimensional NMR correlation experiments and the 'connections' known from the structure under study, can potentially be applied to any type of sample and any type of two-dimensional NMR experiment, whether it be on solution or solid state samples based on homonuclear or heteronuclear correlations via either dipolar or /-couplings. The algorithm has been applied for assigning resonances in 3 1P and 1 9F spectra from solid state homonclear and heteronuclear dipolar coupling-based correlation experiments.32-42 The algorithm is particularly well-suited for situations in which there is little or no additional information to distinguish the peaks from one another (e.g. characteristic chemical shifts, relative intensities, relaxation times). As the examples presented here show, this situation often arises in solid-state extended framework systems in which the nuclei are found in very similar local environments. This algorithm finds all possible set of assignments which are consistent with the known connectivities and observed correlations in a very efficient manner. Thus when ambiguous and no single unique assignment is possible, the availability of all the possible assignments will give a clear picture of the ambiguity and be a useful aid in planning further specific experiments to distinguish between them. This algorithm has proven to be a very useful tool for reliably assigning the peaks in the 2 9 Si MAS NMR spectra of siliceous zeolites, since peak assignment is a pre-requisite to determining the location of ions or sorbate molecules by double-resonance NMR techniques such as CP, REDOR, or TEDOR. Chapter 2 references begin on page 53. 50 Chapter 2 Peak Assignments from Two-Dimensional NMR 2.5 Variables and functions for the algorithm The following is a description of the variables and functions used in the peak assignment algorithm (see Figure 2.7). These variables and functions are described and explained in the context of the described ZSM-12 working example (see Table 2.6). Variables: / = 1,2, ... N where /Vis the number of peaks (N = 7 in the ZSM-12 example). Pl is the added peak in step / and is the /* element of the list P which describes the order by which the peaks will be tested. (P ={A, B, C, D, E, F, G} in the ZSM-12 example described in Table 6). S' is the set of peaks to be tested at the /* step and is constructed by appending P' to the set of peaks from the previous step (S 1 ' - 1 ) with the function AddPeak. •^'proposed*s m e s e t of proposed assignments to be tested against S' at the i t h step and is constructed with the ConstructProposedAssignments function using the good assignments from the previous step (Agood) and the possible peak assignments for the added peak ( A p o s s i b l e ) where A p o s s i b i e is the set of lists of the possible peak assignments for each peak. A'good is the set of assignments selected by the SelectGoodAssignments command from the set of proposed assignments ( A ' p r o p o s e d ) . Only those assignments for which there is agreement between the observed correlation table (rearranged according to the set of peaks iS*') and the known connectivity table (rearranged according to the assignment AlpJroposed being tested) are selected. Functions: AddPeak[5, P] This function appends peak P to the existing set of peaks S. For example in step / = 6 of the ZSM-12 example (see Table 2.6), the command AddPeak[{A,B,C,D,E}, F ] yields the set {A,B,C,D,E,F}. ConstructProposedAssignments[G, Q] This function makes a list of the proposed assignments by combining the good assignments G and the possible peak assignments Q for the added peak. Each element from list Q is appended to each assignment set in G and only those lists without duplicated numbers are selected. For example, in step i = 6 of the ZSM-12 example (see Table 2.6), when peak F is added and G = {{1,5,7,2,6}, {2,5,7,1,6}} and Q = {1,2,3,4,6,7}, the command Chapter 2 references begin on page 53. 51 Chapter 2 Peak Assignments from Two-Dimensional NMR ConstructProposedAssignments[{{1,5,7,2,6}, {2,5,7,1,6}}, {1,2,3,4,6,7}] yields the following list of proposed assignments: {{1,5,7,2,6,3}, {1,5,7,2,6,4}, {2,5,7,1,6,3}, {2,5,7,1,6,4}} RearrangeTable[r, order] This function selects and arranges the rows and columns of table T so that they are arranged in the given order. For example, the command RearrangeTable[Q„olv„, {2,5,7}] (where Cknown is Table 2.1) will return the following 3x3 table: 2 5 7 2 0 0 0 5 0 0 0 7 0 0 2 Another example is RearrangeTable[CoAi, {A,B,C}] (where Cobs is Table 2.2) which will return the following 3x3 table: A B c A 0.5 0 0 B 0 0.5 0 C 0 0 1.5 GoodAssignmentQ[t9, K] This boolean function tests whether or not there is agreement between the observed correlation table O and the known connectivity table K. The function examines the elements in the table O - K and returns the value True if the absolute values of all elements are equal to or less than 0.5 or returns the value False if the absolute value of any one element is greater than 0.5. For example, if O = RearrangeTabIe[C0£S, {A,B,C}] andAT= RearrangeTable[Cfaovv„, {2,5,7}], the command GoodAssignmentQJ RearrangeTable[Cofa, {A,B,C}], RearrangeTable[Q„0lv„, {2,5,7}] ] returns the value True since O - K= RearrangeTable[Cofa, {A,B,C}] - RearrangeTabIe[CWn, {2,5,7}] = A/2 B/5 C/7 A/2 -0.5 0 0 B/5 0 -0.5 0 C/7 0 0 -0.5 SelectGoodAssignmentsb4, S] This function selects the good assignments from a list of proposed assignments A tested against the set of peaks S. It selects those assignments which return the value True for the command GoodAssignmentQJ RearrangeTable[Cofa, S], RearrangeTable[CtoOW„, Aj] ] For example, in step i = 2 of the ZSM-12 example (see Table 2.6), where S = {A, B} and A = {{1,5}, {2,5}, {3,5}, {4,5}, {6,5}, {7,5}}, the command SelectGoodAssignments[{{l,5}, {2,5}, {3,5}, {4,5}, {6,5}, {7,5}}, {A, B}] returns the set of good assignments {{1,5}, {2,5}, {7,5}}. Chapter 2 references begin on page 53. 52 Chapter 2 Peak Assignments from Two-Dimensional NMR References for Chapter 2 (1) Benn, R.; Grondey, H.; Brevard, C ; Pagelot, A. J. Chem. Soc, Chem. Commun. 1988, 102. (2) Fyfe, C. A.; Gies, H.; Feng, Y.; Kokotailo, G. T. Nature 1989, 341, 223. (3) Fyfe, C. A.; Gies, H.; Feng, Y. J. Chem. Soc., Chem. Commun. 1989, 1240. (4) Fyfe, C. A.; Gies, H.; Feng, Y. J. Am. Chem. Soc. 1989, 111, 7702. (5) Fyfe, C. A.; Feng, Y.; Gies, H.; Grondey, FL; Kokotailo, G. T. J. Am. Chem. Soc. 1990,112, 3264. (6) Fyfe, C. A.; Grondey, H.; Feng, Y.; Kokotailo, G. T. J. Am. Chem. Soc. 1990,112, 8812. (7) Fyfe, C. A.; Grondey, H.; Feng, Y.; Kokotailo, G. T. Chem. Phys. Lett. 1990,173, 211. (8) Fyfe, C. A.; Gies, H.; Kokotailo, G. T.; Marler, B.; Cox, D. E. J. Phys. Chem. 1990, 94, 3718. (9) Fyfe, C. A. Zeolites 1990,10, 278. (10) Fyfe, C. A.; Feng, Y.; Grondey, H.; Kokotailo, G. T.; Mar, A. J. Phys. Chem. 1991, 95, 3747. (11) Fyfe, C. A.; Grondey, H.; Feng, Y.; Kokotailo, G. T.; Ernst, S.; Weitkamp, J. Zeolites 1992, 12, 50. (12) Morris, R. E.; Weigel, S. J.; Henson, N. J.; Bull, L. M.; Janicke, M . T.; Chmelka, B. F.; Cheetham, A. K. J. Am. Chem. Soc. 1994,116, 11849. (13) Bax, A. Two Dimensional Nuclear Magnetic Resonance in Liquids; Delft University Press and D. Reidel Publishing Co.: Dordrecht, Holland, 1982. (14) Benn, R.; Guenther, H. Angew. Chem. Int. Ed. Engl. 1983, 22, 350. (15) Ernst, R. R.; Bodenhausen, G.; Wakaun, A. Principles of Nuclear Magnetic Resonance in One and Two Dimensions; Clarendon Press: Oxford, 1987. (16) Derome, A. E. Modern NMR Techniques for Chemistry Research; Pergamon Press: New York, 1987. (17) Sanders, J.; B., H. Modern NMR Spectroscopy, A Guide for Chemists; Oxford University Press:, 1987. (18) Bax, A.; Freeman, R.; Kempsell, S. P. J. Am. Chem. Soc. 1980,102, 4849. (19) Bax, A.; Freeman, R.; Kempsall, S. P. J. Magn. Reson. 1980, 41, 349. (20) Bax, A.; Freeman, R.; Frenkiel, T. A.; Levitt, M. H. J. Magn. Reson. 1981, 43, 478. (21) Jeener, J. Ampere International Summer School Basko Polje, Yugoslavia, 1971. (22) Aue, W. P.; Bartholdi, E.; Ernst, R. R. J. Chem. Phys. 1976, 64, 2229. (23) Ernst, R. R. Chimia 1975, 29, 179. (24) Kumar, A.; Welti, D. D.; Ernst, R. R. J. Magn. Reson. 1975,18, 69. (25) Christie, B.; Munk, M. E. J. Am. Chem. Soc. 1991,113, 3750. (26) Funatsu, K.; Sasaki, S. J. Chem. Inf. Comp. Sci. 1996, 36, 190. (27) Munk, M. E. J. Chem. Inf. Comp. Sci. 1998, 38, 997. (28) Buddrus, J.; Lambert, J. Magn. Reson. Chem. 2002, 40, 3. (29) Lesage, A.; Mardet, M. ; Emsley, L. J. Am. Chem. Soc. 1999,121, 10987. (30) Nakai, T.; McDowell, C. J. Magn. Reson. Ser. A 1993, 104, 146. (31) Hohwy, M. ; Rienstra, C. M.; Jaroniec, C. P.; Griffin, R. G. J. Chem. Phys. 1999,110, 7983. Chapter 2 references begin on page 53. 53 Chapter 2 Peak Assignments from Two-Dimensional NMR (32) Dollase, W. A.; Feike, M.; Forster, H.; Scalier, T.; Schnell, I.; Sebald, A.; Steuernagel, S. J. Am. Chem. Soc. 1997,119, 3807. (33) Hong, M. J. Magn. Reson. 1999,136, 86. (34) Bennett, A. E.; Ok, J. H.; Griffin, R. G. J. Chem. Phys. 1992, 96, 8624. (35) Lee, Y. K.; Kurur, N . D.; Helmle, M.; Johannessen, O. G.; Nielsen, N . C.; Levitt, M. H. Chem. Phys. Lett. 1995, 242, 304. (36) Fyfe, C. A.; Gies, H.; Feng, Y.; Kokotailo, G. T. Nature 1989, 341, 223. (37) Marier, B.; Deroche, C.; Gies, H.; Fyfe, C. A.; Grondey, H.; Kokotailo, G. T.; Feng, Y.; Ernst, S.; Weitkamp, J.; Cox, D. E. J. Appl. Cryst. 1993, 26, 636. (38) Fyfe, C. A.; Gies, H.; Kokotailo, G. T.; Pasztor, C ; Strobl, H.; Cox, D. E. J. Am. Chem. Soc. 1989, 7/7,2470. (39) Fyfe, C. A.; Feng, Y.; Grondey, H. Microporous Mater. 1993, 7, 393. (40) Wolfram, S. Mathematica: A System for Doing Mathematics by Computer v. 3.0; Wolfram Media: Champaign IL, 1996. (41) van Koningsveld, H.; Jansen, J. C ; van Bekkum, H. Zeolites 1990,10, 235. (42) Munch, V.; Taulelle, F.; Loiseau, T.; Ferey, G.; Cheetham, A. K.; Weigel, S.; Stucky, G. D. Magn. Reson. Chem. 1999, 37, SI00. Chapter 2 references begin on page 53. 54 Chapter 3 Evaluation of Solid State NMR Experiments for the Measurement of Heteronuclear Dipolar Couplings This chapter describes and evaluates a number of solid state NMR experiments to measure heteronuclear dipolar couplings between nuclei of the guest species and nuclei of the host framework. Cross polarization, REDOR, and TEDOR experiments for measuring distances between isolated spin pairs are explained and compared. Cross polarization and cross polarization drain experiments for measuring cross polarization rate constants for extended spin networks are also explained and compared. These experiments will provide the structural information necessary to determine the locations of guest molecules with respect to the zeolite frameworks. 3.1 Introduction In order to locate guest species in the zeolite framework, it is necessary probe the distances between the guest species and the zeolite framework. This can be accomplished by solid state NMR experiments which measure the distance-dependent dipolar couplings between nuclei. With the peaks in the NMR spectrum of the zeolite framework assigned from two-dimensional NMR correlation experiments, it is possible to measure multiple distances between the guest species and different positions in the zeolite framework, allowing for a reliable determination of the location of the guest species. This chapter describes some of the solid state NMR experiments available for measuring heteronuclear dipolar couplings under magic-angle spinning conditions. 3.2 Cross polarization As described in Chapter 1, the solid state cross polarization (CP) experiment1"7 is commonly employed for increasing the sensitivity of the NMR signal of rare spins. In the CP experiment, magnetization or 'polarization' is transferred from the abundant / spins (e.g. 'H) to the rare S spins (e.g. 1 3 C, I 5 N , 2 9Si) via the dipolar interactions which exist between the nuclei. The usual gain in S/N of a CP experiment over a standard single pulse experiment arises from two factors. Firstly, the population difference between the 'spin-up' and 'spin-down' states (the polarization) of the rare spins is increased by a maximum factor of y7 /ys. Secondly, the delay time between collecting successive FIDs depends on the T\ relaxation time of the abundant spins which is typically much shorter than the 7i relaxation time of the rare spins. Chapter 3 references begin on page 79. 55 Chapter 3. Solid state NMR distance measurement techniques In addition to the gain in sensitivity available in the CP experiment, the dynamics or time-dependence of the magnetization transfer can provide infonnation about structure. In this chapter, the cross polarization process and the resulting dynamics of the magnetization transfer are explained for spin systems in which there exists an extended network of coupled abundant spins and for spin systems which consist of an isolated I-S spin pair. For both cases, the cross polarization dynamics can be related to the heteronuclear dipolar couplings and therefore provide infonnation about intemuclear distances and structure. 3.2.1 The cross polarization pulse sequence The cross polarization pulse sequence for polarization transfer from / spins to S spins is illustrated in Figure 3.1. The / spins are first excited by a 90° pulse and then are 'spin-locked' by applying an r.f. field at the resonance frequency of the / spins with nutation frequency ©i/ which is phase shifted from the excitation pulse by 90°. Polarization transfer from the spin-locked / spins to the S spins is achieved by applying a simultaneous r.f. field at the resonance frequency of the S spins (contact pulse) with a nutation frequency coi.« which is 'matched' to ©u. The dynamics of the polarization transfer can be followed by performing a series of experiments with incremented values of the contact time T . The plot of polarization transferred as a function of contact time is termed the 'CP curve'. 90°. (<>>„)„ 1 recycle H spin lock decoupling delay Figure 3.1 Cross polarization pulse sequence for polarization transfer from / spins to S spins. 3.2.2 Dependence of CP behavior on the nature of the spin system The matching conditions and the CP dynamics will depend on the nature of the spin system, as illustrated in Figure 3.2. For spin systems which consist of a strongly coupled network of the source / spins, the CP matching profile is a very broad peak centered at a>u = cow which is called the Hartmann-Hahn match condition.1 The dynamics of the polarization transfer in such a spin system follows a growth-decay curve for which the rate of growth usually (but not always, see later) reflects the strength of the l-S dipolar interactions and the decay usually arises from the Tlp relaxation of the / spins during the spin-lock period. For spin systems in which the homonuclear /-/ dipolar couplings between the source / spins are reduced, the CP matching profile breaks into a spinning sideband pattern where the maxima are polarization transfer (Oils) acquire FID . • * "contact pulse Chapter 3 references begin on page 79. 56 Chapter 3. Solid state NMR distance measurement techniques separated by the spinning frequency and the CP efficiency at the Hartmann-Hahn condition is reduced.4 8-1 4 The reduction of the homonuclear couplings can arise from the nature of the spin system, the presence of molecular motion, or from increased spinning rates. Under these circumstances, the dynamics of the polarization transfer still retains the smooth growth-decay curve characteristic of an extended spin system. If the spin system consists of isolated I-S pairs, the polarization transfer takes on a very different behavior. The polarization 'shuttles' between the / and S nuclei, which results in oscillations in the CP curves the frequency of which is a function of the heteronuclear dipolar coupling and thus, the distance between the / and S nuclei. 4 1 2 1 7 The CP matching profile for an isolated spin pair consists of four maxima at toi/ - a>is = n oir where n = ±1 or +2 and cor is the spinning rate. Strongly Coupled Weakly Coupled Extended Spin System Extended Spin System Isolated Spin Pairs Contact Time Contact Time Contact Time CP Matching Profile: Figure 3.2 Illustration of the cross polarization dynamics and matching profiles for polarization transfer from the / spins (filled circles) to the S spins (open circles) for different types of spin systems. The effects of the heteronuclear dipolar coupling strengths on the CP dynamics are illustrated for two spins; the heteronuclear dipolar interactions are larger for the spin represented by the solid red lines compared to the spin represented by the dashed green lines. As the homonuclear dipolar couplings between the I spins are reduced, the CP matching profiles split into spinning sidebands where the match conditions are separated by the spinning rate. Chapter 3 references begin on page 79. 57 Chapter 3. Solid state NMR distance measurement techniques 3.3 Cross polarization in an extended spin system As described above, the dynamics of the polarization transfer in an extended spin system where there exist homonuclear couplings between the source / nuclei follows a smooth growth-decay curve, in which the rate of polarization transfer reflects the strength of the I-S heteronuclear dipolar interactions.2 For such a spin system, the cross polarization experiment is often explained and described in terms of a thermodynamic analogy in which a reservoir with a large heat capacity (the abundant / spin system) is put into a low 'spin temperature' state (spin locking) and is then put into 'thermal' contact (Hartman-Hahn matching) with a reservoir which has a small heat capacity (the rare S spins system), during which the S spin system will be 'cooled' towards the (spin) temperature of the I spins.2-5-7 Since the concept of 'spin temperature' is inversely related to magnetization, the result is a transfer of magnetization from the abundant / spins to the rare S spins. The dynamics of cross polarization can thus be understood in terms of the flow of heat between the / and S spin reservoirs and can be described by an appropriate set of coupled differential equations. As long as the spinning frequency is less than the static linewidth of the / spin spectrum (this linewidth reflects the strength of the /-/ homonuclear dipolar interactions), the effects of magic angle spinning on the CP matching profile and the CP dynamics can be ignored. 3.3.1 Thermodynamic description of cross polarization The amount of signal observed in an NMR experiment involving spin-1/2 nuclei ('magnetization') is proportional to the difference in population ('polarization') of the two energy levels arising from the Zeeman interaction of the spins with the strong magnetic field B0. The relative populations of these two energy levels are governed by the Boltzmann distribution N-\n/N+m =exp{-hyBQ/kTL) Equation3.1 where TL is the temperature of the lattice. The first step in the cross polarization experiment is to prepare the abundant / spin system in a low spin temperature state. This is done by applying the spin-locking field Bu along the y axis of the rotating frame immediately following the initial 90° pulse applied along the x axis. In this spin-locked state (in the rotating frame), the relative populations of the two energy levels are N_i/2 /N+i/2 = e x p( - frysi/ /kTj) Equation 3.2 where 7) is the 'spin temperature' of the spin-locked abundant / spins. A comparison of these two expressions shows that the spin temperature of the spin-locked / spins is related to the temperature of the lattice by 7) / TL = Bu IB0 Equation 3.3 Since Bu « B0, this means that T, « TL. Therefore, there exists a large polarization of the abundant / spin system spin locked along the y axis of the rotating frame and precessing about the y axis with an angular frequency u>\I = yIBu. Chapter 3 references begin on page 79. 58 Chapter 3. Solid state NMR distance measurement techniques 3.3.2 The Hartmann-Hahn condition in an extended spin system The S spin system is put into 'thermal contact' with the low spin temperature spin-locked abundant / spin system by applying an r.f. field at the resonance frequency of the S spins at the same time as the spin-locking field is applied to the / spins. The S spins precess (in the rotating frame) about the applied field BiS with angular frequency coi.y = y.s B\s. If the r.f. fields applied to the / and S spins are adjusted so that the Hartmann-Hahn match condition1 "li Bu = y.v B\s Equation 3.4 is satisfied such that the angular frequencies of the precession about the applied fields are equal W|/ =C0is, Equation 3.5 then the / and S spins have the same time dependence in the rotating frame. (a) / 9o; (wi/)y 1 recycle spin lock decoupling delay 1 polarization transfer .-•'contact pulse T • acquire FID (c) / spins S spins J|Sii=«>i/ = «>is=rAs lab frame spin-locked rotating frame lab frame (b) apply 90°(x) pulse • apply spin-lock S 1 ( r.f. field along y • spins precess about BU with frequency co,, • apply matched 8,S r.f. field to S spins spins precess about B, s with frequency to1 s and net magnetization builds up <E^' Figure 3.3 The cross polarization experiment: (a) pulse sequence, (b) vector representation showing the spin locking of the / spins and the build-up of S spin magnetization during the contact time x, (c) energy level diagram of the / and S spins illustrating that the differences in the energy levels in the spin-locked rotating frame are equal at the Hartmann-Hahn condition and that mutual spin flips allow for transfer of polarization from the / to the S spins. Chapter 3 references begin on page 79. 59 Chapter 3. Solid state NMR distance measurement techniques Essentially, the energy difference between the levels of the I and S spins in this spin-locked rotating frame have been equalized under the Hartmann-Hahn condition, as shown in Figure 3.3c. Under this Hartmann-Hahn condition, a resonance exchange of energy between the two spin systems can take place readily through a mutual spin flip mechanism mediated by the I-S dipolar couplings, as illustrated in Figure 3.3c. Since the abundant / spin system is highly polarized ('cold' spin temperature), these mutual spin flips will increase the polarization of the S spin system which corresponds to a significant cooling of its spin temperature. The polarization is transferred until the spin temperatures of the I and S spin systems are equalized. Since the heat capacity of the abundant / spin system is much larger than the heat capacity of the rare S spins, the S spin system is cooled to the initial spin temperature of the / spin system (in the absence of spin-lock relaxation): TS=T,= (Bu I Bo) TL = (ys / y,) (Bls IB0) TL Equation 3.6 The spin temperature of the S spin system is therefore reduced by a factor ys I yt which corresponds to an increase in the magnetization by a factor of y/ / ys. At end of this 'contact time', there will exist observable S spin magnetization in the x-y plane which is detected by collecting an FID. 3.3.3 Thermodynamic description of cross polarization dynamics The dynamics of cross polarization can be described in terms of the flow of heat between the / and S spin systems and can be described by the set of coupled differential equations2-6-7 in Equation 3.7 (schematically described in Figure 3.4). S'(t) = -kIS(S(0-m)-ksS(t) / Equation 3.7 r(0 = -*kls{i(t)-s(tj)-k1i(t) where S(t) and 1(f) are the inverse spin temperature (magnetization) of the I and S spin systems, e = AfcS(S+l)//Y/I(I+l) is the ratio of the 'heat capacities' of the two spin reservoirs, k!S = Tc?'x is the rate constant for 'heat flow' or magnetization transfer between the / and S spin systems, and k, = 7^"' and ks = T i^p"1 are the rate constants for Tlp (spin lock) relaxation of the / and S spins respectively. Lattice Figure 3.4. Schematic representation of the thermodynamic description of cross polarization. For the standard S{Pj cross polarization experiment in which the magnetization is transferred from the abundant / spins to the observed rare S spins after an initial excitation pulse on the / spins, the initial conditions to the differential equations in Equation 3.7 are S(0) = 0 and 1(0) = I0. If it is assumed Chapter 3 references begin on page 79. 60 Chapter 3. Solid state NMR distance measurement techniques that s « 0, then the expressions which satisfy the differential equations in Equation 3.7 and describe the cross polarization dynamics are: S{t) = /„ ^ (e"*'' - eHk"+ks)') (kIS +ks)-kj Equation 3.8 I(t) = I0e-k>' The expression for S(t) in Equation 3.8 indicates that the S spin magnetization (the CP curve) grows to a maximum intensity and then decays (see Figure 3.5), while the / spin magnetization decays with rate constant k;. A few words of caution are merited at this point. Firstly, it is often assumed that the Tlp relaxation of the S spins is negligible. It is valid to make this assumption if ks is much less than kiS, but incorrect measurements of ks may result if this is not the case. Secondly, when cross polarization data are fit in order to extract the rate constants, it is usually assumed that the growth of the S spin magnetization depends on the kIS rate constant and the decay depends on the ki rate constant. It is important to note that this assumption is only true if ks + ks> kh as shown in Figure 3.5a. Tekely and co-workers18 have pointed out that when there is fast T\p relaxation of the / spins (k/ > kIS + ks), the rate constants for the growth and decay of the S spin magnetization are reversed from the usual assumptions: the CP curve grows with rate constant kj to a maximum that is very dependent on the value of k/s and then decays with rate constant kiS + ks, as shown in Figure 3.5b. Under these conditions, it is difficult, for a number of reasons, to obtain reliable values of the cross polarization rate constant (k/S) from S{I} CP curves. The kIS term is found in two parts of the expression for S(t) in Equation 3.8: in an exponential term and in the pre-exponential scaling factor. When the / spin Tip relaxation is fast, the exponential term in which k/s is found describes the decay of the CP curve. There are two problems here. Firstly, the rate constant for the decay is kIS + ks and nothing is known about ks from a standard S{I} CP experiment. Secondly, even if ks could be ignored, it is experimentally difficult to acquire enough reliable data points at long contact times to define this exponential decay and fit it since there is a limit in how long the contact pulses can be applied without heating the sample or damaging the amplifiers or probe at the short recycle delays required to acquire suitable S/N. The ks term is also present in the pre-exponential scaling factor. Since ki is large with respect to kIS +ks, this factor is approximately equal to IQ(k,slki). The difficulty in obtaining reliable k!S values is that kIS is very highly correlated to the I0 value which also needs to be fit to the data. Even though reliable absolute values of kis cannot be obtained from the CP curves under these conditions, it is possible to obtain reliable relative values of k/s since I0 is a constant that is identical for the CP curves of all the Si sites. In the next section, a modification to the standard CP experiment is described with which reliable absolute values of the cross polarization rate constants can be obtained. Chapter 3 references begin on page 79. 61 Chapter 3. Solid state NMR distance measurement techniques CO CO (b) k, >kIS+ks Figure 3.5. Dynamics of the observed S spin magnetization in standard S{I} cross polarization experiment in which (a) the rate of / spin T l p relaxation is slow compared to the rate of cross polarization, and (b) the rate of / spin T| P relaxation is fast compared to the rate of cross polarization. These curve were generated using Equation 3.8. 3.3.4 The cross polarization drain experiment The cross-polarization drain experiment8-19 is a 'reverse' cross polarization experiment in which the excitation pulse and spin lock field are applied to the rare S spins and the 'drain' of magnetization from the S spins is observed with and without a Hartmann-Hahn matched field applied to the I spins, as illustrated in Figure 3.6. In this case, the initial conditions to the set of differential equations in Equation 3.7 are S(0) and 1(0) = 0 and the solution to these equations (assuming e w 0) which describe the dynamics of the CP drain experiment is S(t) = S(0)e-^+k«)' . Equation 3.9 /(/) = 0 The exponential decay resulting from the CP drain experiment without the contact pulse applied on the / spins ('reference' experiment So) is due entirely to S spin T\p relaxation and has the rate constant ks since kiS = 0 (see Figure 3.5a). S0(t) = S(0)e~ks' Equation 3.10 The exponential decay resulting from the CP drain experiment with the contact pulse applied on the / spins ('drain' experiment SJ) has the rate constant k!S+ks (see Figure 3.5a). 5^(0 = 5(0) e _ ( * s + * a ) ' Equation 3.11 The analysis of the CP drain dynamics can be simplified by plotting the data as a normalized difference plot (AS/So,where AS = S0 - Sd), such that the cross polarization rate constant is the only variable to fit (see Figure 3.5b). AS/S0(t) = l-e-k,s' Equation 3.12 In many cases, this analysis is clearly superior for measuring absolute cross polarization rate constants compared to fitting standard CP curves since these normalized difference curves depend only on k^. There is no dependence on the initial magnetization of the I spins (I0), nor the T\p relaxation of the / and S Chapter 3 references begin on page 79. 62 Chapter 3. Solid state NMR distance measurement techniques spins (k; and ks). However, the disadvantage of the CP drain experiment is that the recycle delay of the experiment is determined by the Tx relaxation time of the S nuclei which is usually much longer than that of the / nuclei. 90? I 'Reference' experiment (S0) decoupling spin lock acquire FID recycle delay 90? 'Drain' experiment (S„) contact pulse decoupling polarization transfer spin lock acquire FID r e c y c | e delay Figure 3.6 Pulse sequence diagrams for the collecting the 'reference' and 'drain' spectra for the CP drain experiments. In the 'reference' experiments (S0), the matched 'H r.f. field is not applied during the 2 9Si spin lock, while in the 'drain' experiment (Sd), it is applied. S0(/) = S(0)e-(b) 1.0 i 0.8 -,— s o 0.6 -CO 0.4 -< 0.2 -0.0 -AS/Sa(t) = \-e Figure 3.7 Cross polarization dynamics in a S{I} cross polarization drain experiment: (a) reference (So) and drain (Sd) decays, (b) normalized difference curve (AS/So). 3.3.5 Relationship of cross polarization rate constants to structure As described earlier, the cross polarization process occurs via the heteronuclear dipolar couplings which exist between the / and S spins. The rate of cross polarization depends on the strength of these heteronuclear dipolar couplings. It is this relationship between cross polarization rate constants and heteronuclear dipolar coupling strengths which provides infonnation about structure. Pines et al. have shown2 that there exists a proportional relationship between the cross polarization rate constant and the strength of the I-S dipolar couplings expressed as the heteronuclear dipolar coupling second moment, M2(IS): Chapter 3 references begin on page 79. 63 Chapter 3. Solid state NMR distance measurement techniques k[SozM2(IS). Equation 3.13 This proportionality exists because k!S=CISM2(IS)/^M2(II) Equation 3.14 where Qy is a constant geometrical factor and the homonuclear second moment, M2(II), is constant for a given system of source spins.2 The heteronuclear dipolar coupling second moment20 is a pair-wise summation, namely the sum of the squares of the dipolar couplings, and as such does not depend on the angular relationship between the spin pairs and can be calculated from the I-S internuclear distances: If cross polarization rate constants to several unique S nuclei in the structure can be measured, it may be possible to locate the positions of the source / nuclei with respect to the S nuclei by comparing the experimentally measured kis values to calculated second moments.21-22 This approach is employed in Chapter 6, in which a method to locate small organic sorbate molecules in a host zeolite framework based on 2 9Si {'H} cross polarization rate constants is described in detail. 3.4 Cross polarization in an isolated spin pair As mentioned briefly earlier in the chapter, the CP curve for an isolated spin pair has oscillations whose frequency is a function of the heteronuclear dipolar coupling constant between the / and S spins. An analysis of these CP curves will yield the I-S internuclear distance directly. Since DIS oc l /o 5 3 , a moderately accurate measurement of the dipolar coupling constant will yield quite an accurate internuclear distance. Oscillations in CP signal intensity were first reported for 1 3C{'H} CP experiments on a non-spinning single crystal of ferrocene by Miiller et al. 1 5 It was shown that the frequency of this oscillation is related to the dipolar coupling constant.16 Stejskal and Schaefer8 reported oscillations under magic angle spinning conditions in 'H/ 1 3 C/ 1 5 N double CP experiments and demonstrated the effects of MAS on the CP matching conditions. Hediger13 incorporated the effects of sideband matching, MAS, and powder averaging using Floquet theory to give a sound theoretical basis for heteronuclear distance determination by CP MAS NMR. This analysis was employed by Fyfe et al. to determine the 1 9 F- 2 9 Si distance in the clathrasil octadecasil.23 Marica and Snider14 have also derived an exact expression for CP between two spin-1/2 nuclei derived from the quantum Liouville equation. 3.4.1 Dipolar coupling under MAS conditions As described in Chapter 1, the dipolar interaction is the through-space interaction between the magnetic moments of nuclear spins. It describes the magnetic field that a nucleus experiences as a result of a neighboring nucleus. The magnitude of the heteronuclear dipolar coupling between an isolated I-S spin pair, b!S, is dependent on the magnetogyric ratio of the two nuclei, the internuclear distance between Chapter 3 references begin on page 79. 64 Equation 3.15 Chapter 3. Solid state NMR distance measurement techniques them, and the orientation of the intemuclear vector with respect to the applied static magnetic field (defined by the angle $): bis = — ( 3 c o s 2 Equation3.16 2 where dIS — (in angular frequency units) 4nr 15 2n Sn2r3 K ' Equation 3.17 As described in Chapter 1, magic angle spinning of solid samples can provide a tremendous gain in resolution, as the chemical shift anisotropics and dipolar couplings are reduced or even removed, and is a necessity to resolve the signals of the magnetically inequivalent sites in a sample. However under such conditions, the dipolar interactions which are of interest for measuring intemuclear distances are averaged out over each rotor period. Therefore, in order to measure dipolar couplings under MAS conditions, they must be reintroduced or 'recoupled' so that their effect can be observed in some manner. As the sample is spun about the magic angle with respect to the static magnetic field (B0), the dipolar interactions have a time dependence since the orientations of the intemuclear vector with respect to B0 changes as the sample spins. Equation 3.18 gives the time dependence for a dipolar coupling under MAS. b,s (a, P, 0 = jdIS (sin2 Pcos2(a + &rt) - V2 sin 2pcos(a + cor/)) Equation 3.18 where a and P are the azimuthal and polar angles respectively and define the orientation of the intemuclear vector with respect to the spinning axis (see Figure 3.8). The periodic behavior of a dipolar coupling as a function of the rotor period according to Equation 3.18 is plotted in Figure 3.9. It is important to note that although the time-average value of the dipolar coupling over each rotor period is zero, the dipolar coupling is still present and can be manipulated or disrupted so that it does not average to zero over a rotor period. Chapter 3 references begin on page 79. 65 Chapter 3. Solid state NMR distance measurement techniques Periods Figure 3.8 Definitions of the angles used to the describe the orientation of the I-S internuclear vector under magic angle spinning conditions, (see Equation 3.18). Figure 3.9 Behavior of the dipolar coupling as a function of the spinner orientation under MAS for the heteronuclear spin pair orientations indicated. Curves were calculated using Equation 3.18 with D1S = 2000 Hz and the time is given as a fraction of the rotor period. 3.4.2 Heteronuclear dipolar recoupling by CP MAS NMR The time dependence of the heteronuclear dipolar coupling in Equation 3.18 can be rewritten in terms of Fourier components: +2 n=-2 where b0=0 b±l = -^-V2sin2pV b±2 = ^ L s i n 2 pe ±/2a Equation 3.19 From this expression of the time dependence of the heteronuclear dipolar coupling under MAS conditions, the CP MAS behaviour of isolated spin pairs can be derived by Average Hamiltonian Theory12, Floquet theory13, or by solving the quantum Liouville equation.14 The derivation of this expression for CP MAS NMR of isolated spin pairs is beyond the scope of this thesis, but can be found in the references indicated above. The expression derived by Marica and Snider14 fully describes the dependence of the CP behavior on time, the strength of the applied r.f. fields, spin rate, and the orientation of the internuclear vector: S(0 = ± /oZ b„ +{A + rmr): -(l-cos(/„0)-bn\2 +{-L + n(or): -(l-cos(F„0) where A = coi/-co 1 5 and E = co1/ + co 1 5 Chapter 3 references begin on page 79. 66 Chapter 3. Solid state NMR distance measurement techniques f„ = ^ \b„\2 +(A + «co,)2 and .F„ = ^ j\b„\2 + (s + «co r) 2 Equation3.20 If it is assumed that Z » 2mr, then the second term which depends on the sum of the applied r.f. fields can be dropped: S(0 = ± /oZ: -(l-cos(/„0) Equation 3.21 «t^2|6„|2 +(A + «m r ) 2 This expression indicates that there will only be efficient cross polarization between the I and S spins when A = ±cor or A = ±2ov This expression describes how the Hartmann-Hahn CP matching profile for isolated spin pairs is 'broken' into four spinning sidebands, as illustrated in Figure 3.10. +2(Dr +C0 r 0 - M r A = co,/- co is -2cor Figure 3.10 Hartmann-Hahn CP matching profile for an isolated spin pair undergoing magic angle spinning. At these matching conditions, the heteronuclear dipolar coupling is no longer averaged by the magic angle spinning, but is 'recoupled' by the application of the matched r.f. fields. The dynamics of the cross polarization at any of the n = ±1 or ±2 matching conditions will reflect the strength of the dipolar coupling, as the signal oscillates at a frequency which is a function of the dipolar coupling constant: s » (0 = 2 7o f1 _ c o s (\K 10) Equation 3.22 This expression describes the CP dynamics for a single orientation of the I-S internuclear vector. For a powder sample, it is necessary to average over all possible orientations. Since there is no dependence on the angle a, an average over all possible values of p is required: (S„)(0 = / 0 ( i - g „ ( 0 ) Equation 3.23 where g„(0 = ijcosj6„|/)sinp dp- Equation 3.24 By integrating over all values of P, the expression for the powder average in Equation 3.23 becomes a superposition of many different frequencies, leading to a CP curve with damped oscillations as illustrated in Figure 3.11. By fitting the oscillations in an experimental CP curve, it is possible to measure the heteronuclear dipolar coupling constant and thus determine the internuclear distance. It is preferable to Chapter 3 references begin on page 79. 67 Chapter 3. Solid state NMR distance measurement techniques collect CP curves at the ±1 matching condition since the oscillations have a shorter period, leading to reduced uncertainty in the measurement of D,s. (a) ±1 matching condition (S ± 1 ) A = co iy - co15 = ±co r 1 0.5 b 1 - Jcos(^-sin2p) sinp^ p 8 12 16 20 D,st (b) ±2 matching condition ± 2 / A = co17 — oo l s = ±2 co,. 1 r (S + ) 1- J"cos(^ sin2 P) sinpjp 8 12 16 20 D,st Figure 3.11 S{I} cross polarization curves for an isolated I-S spin pair at (a) the ±1 matching condition and (b) the ±2 matching condition. These curves were calculated using Equation 3.23 with I0 =1. From reference 13. 3.4.3 Practical suggestions for fitting experimental CP data Integrating over all values of p can be cumbersome and is not well-suited to least-squares fitting to experimental data. Following the general methodology of Mueller,24'25 the integrals g„ can be expressed in terms of an infinite series of Bessel functions of the first kind:23 g±l (0 = i }cos(^ sin 2p)sin p d$ o k=\ Equation 3.25 g + 2 (0 = ^{cos(-^sin2p)sinp# o - -teK y - 2± ( - D * (i - 4 * 2 y J k y c o S ( ^ + f ) k=\ Truncating these series at k = 10 is sufficient to approximate the exact integral over all possible orientations. In practice, the spin pairs are never completely isolated and experience relaxation effects. In order to fit the experimental CP curves, the expression in Equation 3.23 is expanded to include a term for the damping of the oscillations (kd), spin lock relaxation (&/), and contributions from the extended network of spins (after Equation 3.8): Chapter 3 references begin on page 79. 68 Chapter 3. Solid state NMR distance measurement techniques {Sn )(0 - 7 0 {(•*) $ isolated + 0 ~ x) S „ e t w o r k } -*/' _ e-kis> 1 Equation 3.26 These extra parameters serve only to ensure a good fit to the experimental data and do not affect the measurement of the internuclear distance, since it is the frequency of the oscillation described by g„(t) which determines the distance. 3.5 Rotational Echo Double Resonance (REDOR) The REDOR experiment,26-27 originally developed by Gullion and Schaeffer, employs radio frequency pulses applied at specific points in each rotor period to prevent the complete averaging of the dipolar interactions after each rotor period. With the dipolar coupling re-introduced or 'recoupled', the observed magnetization is reduced or 'dephased' by an amount which depends on the value of the dipolar coupling constant and the amount of time the dipolar coupling is recoupled and allowed to dephase the observed signal. 3.5.1 The REDOR pulse sequence The REDOR experiment is carried out as a normalized difference experiment in which two spectra are obtained for each dephasing time as illustrated in Figure 3.12. The reference spectra (the S0 experiments) are collected with an echo pulse sequence and without the rotor-synchronized dephasing pulses. The single TC pulse on the observed nucleus serves to refocus the chemical shifts. The decay in the signals of the reference spectra arises only from T2 relaxation as illustrated in Figure 3.13a. The dephased spectra (the S/ experiments) are collected with a train of rotor-synchronized TC pulses applied at the middle and end of the rotor periods (usually on the unobserved nucleus) which serve to re-introduce the dipolar interactions and cause a dephased or reduced signal, as shown in Figure 3.13a. The effect of the dipolar coupling is observed in a plot of AS/S0 against dephasing time where AS = S0 - Sf (Figure 3.13b). The REDOR and CP drain experiments are similar in the sense that a loss of the signal is measured with respect to a reference signal. Chapter 3 references begin on page 79. 69 Chapter 3. Solid state NMR distance measurement techniques s 0 Experiment Sf Experiment M l Ml 4 f tV • -4 f i r • -4 jXr • 4 f T r • Figure 3.13 S{I} REDOR curves: (a) experimentally collected reference (S0) and dephased (SJ) curves, (b) normalized difference curve (AS/S0). 3.5.2 Explanation of the REDOR experiment Consider a single crystallite of the powder sample such that the intemuclear vector between spin / and spin S is defined by the angles (a, P) as depicted in Figure 3.8. As the sample is spun around on the axis which is at the magic angle with respect to the static magnetic field B0, the magnitude of the dipolar interaction becomes time dependent as the angle 9 between the intemuclear vector and B0 changes as the sample is rotated. bIS(a,$,t) = ±±dls(pm2 Pcos2(a + a>rt) - V2 sin2pcos(a + corf)) Equation 3.27 The cumulative effect of the time-dependent dipolar coupling on the observed magnetization at time x is described by the 'dephasing angle' <))(a,p,x) which is the integral of Equation 3.27: Chapter 3 references begin on page 79. 70 Chapter 3. Solid state NMR distance measurement techniques X 4>(a,p,T)= jbis(a,$,t)dt 0 Equation 3.28 = ± { s i n 2 p[sin 2(a + corr) - sin 2a] - 2V2 sin 2p[sin(a + corr) - sin a]} such that cos (j)(a,p,x) is observed magnetization arising from crystallite a,p at time x. The time dependence of the magnitude of the dipolar interaction, the dephasing angle, and the observable magnetization for a single crystallite for the reference S0 experiment are plotted in Figure 3.14. The magnitude of the dipolar interaction has a periodic behavior as the sample rotates and its sign is reversed after the refocusing pulse on the S nuclei at the midway point. However, at the end of the each rotor period (x = n xr), the dephasing angle which represents the cumulative effect of the dipolar coupling is zero, demonstrating that the dipolar interactions are averaged or removed under normal magic-angle spinning conditions: mr <Ka,p,«Tr)= J6 / 5 (a,p ,0d/ = 0 Equation 3.29 0 Another way of illustrating this effect is to map out trajectory of the dipolar interaction in the transverse xy plane in the rotating frame of the S spin (bottom of Figure 3.14). When x = 0, the spin is along the x axis ((j) = 0) and then moves away from the x-axis as it acquires a dephasing angle according to Equation 3.28. and then returns to the x-axis at the end of each rotor period (x = nxr) to form the 'rotational echo' from which the REDOR experiment derives its name. The decay that is observed in the reference spectra is due only to T2 relaxation. It is important to note that the formation of these rotational echoes arising from the averaging of the dipolar interaction over each rotor period occurs for all values of a and p. The time dependence of the magnitude of the dipolar interaction, the dephasing angle, and the observable magnetization for a single crystallite orientation for the dephased Sf experiment are plotted in Figure 3.14. The effect of each TC pulse (on either the I or S nuclei) is to change the sign of the dipolar interaction and reverse its trajectory. The pulses applied at the middle of each rotation prevent the averaging of the dipolar coupling over each rotor period, prevent formation of rotational echoes, and lead to non-zero values of the dephasing angle. The dephasing angle for crystallite a,p at the end of one complete rotation is: Xr/2 T <Ka,p,xr)= J6 /5(a,p,/)d/+ J-& /s(a,p,/)d/ 0 T - / 2 Equation 3.30 = — 2V2sinasin2p where the negative sign in the second integral arises from change in sign of the dipolar interaction due to the TC pulse applied at xr/2. The dephasing angle after n rotor periods is Chapter 3 references hegin on page 79. 71 Chapter 3. Solid state NMR distance measurement techniques 4»(a,p,/7ir ) = nD,s xr 2V2 sinasin2(3 Equation 3.31 which can be expressed with as a function of the dimensionless parameter X = n Dxr sin a sin 2p Equation 3.32 The observed signal arising from crystallite a,P is cos <J>R(a,p,A.) which oscillates with a period that is a function of the dipolar coupling constant (Figure 3.14). S 0 Experiment 1 2 3 n rotor p e r i o d s Sf Experiment i l l Ml 1 2 3 n rotor pe r iods / f y I / L Figure 3.14 Illustrations for the explanation of the REDOR experiment (see text). From top to bottom: pulse sequence, time dependence of the dipolar coupling for one particular orientation (bjs), accumulated dephasing angle (cj)), observed magnetization for this particular orientation (cos §), trajectory of dipolar interaction. Chapter 3 references begin on page 79. 72 Chapter 3. Solid state NMR distance measurement techniques The dephased signal Sf arising from the entire powder sample is calculated by averaging over all possible a,(3 orientations: Mueller and co-workers have determined an elegant analytical expression to this integral in terms of Bessel functions:24'25 The expression for the 'universal' normalized difference REDOR curve which is plotted in Figure 3.15 is then: The dipolar coupling constant, and thus the intemuclear distance, can be determined from an experimental REDOR curve by simply by adjusting the value of D/s so that the data points fit the universal REDOR curve. In situations where not every S spin is dipolar coupled to an / spin (due to incomplete occupancy of the / spins, for example), the signal intensity of the S nuclei will not be fully dephased and the REDOR curve will not reach the full intensity. In these situations, a scaling factor which reflects the occupancy of the / spins should be applied to the S{I} REDOR curve.28 This problem can be overcome by performing a S{I} CP-REDOR experiment in which the initial 90° excitation pulse on the S channel is replaced with S{I} cross polarization so that only the S spins which are coupled to / spins are observed. In practice, this has additional difficulties, since the S{I} CP match condition will usually be a narrow spinning sideband since the spin system is an isolated spin pair, as described in Section 3.4.2. Equation 3.33 Equation 3.34 Equation 3.35 0.0 Figure 3.15 The universal REDOR curve (Equation 3.35). The normalized difference between the S0 and Sf experiments is plotted as a function of the dimensionless parameter X = n Dxr. 0 2 4 6 8 X = nD x r Chapter 3 references begin on page 79. 73 Chapter 3. Solid state NMR distance measurement techniques 3.6 Transferred Echo Double Resonance (TEDOR) The TEDOR experiment29-30 was originally developed by Schaefer and co-workers as an alternative to the REDOR experiment to measure weak dipolar couplings of heteronuclear I-S spin pairs while eliminating the background contributions from uncoupled spins. The TEDOR experiment is similar to the CP-REDOR experiment in the sense that there is a polarization transfer from / to S so that only S nuclei which are coupled to / nuclei are observed. The advantage of TEDOR over the CP-REDOR experiment is that the polarization transfer is achieved with rotor-synchronized 90° and 180° pulses, which is experimentally less demanding than being matched on a narrow spinning sideband of the CP matching profde. 3.6.1 The TEDOR pulse sequence The TEDOR experiment is essentially a dipolar based INEPT experiment31-32 in which rotor-synchronized n pulses are applied to re-introduce the dipolar interactions during magic angle spinning. The pulse sequences for refocused INEPT and TEDOR experiments are displayed in Figure 3.16. In the INEPT experiment, polarization is transferred from the I to S nuclei via the I-S J-coupling. The experiment is most efficient when the delay between the pulses is 1/(4J). The TEDOR experiment follows the same general pulse sequence as INEPT, except that dipolar recoupling n pulses are applied at % and lA of each rotor period, in order to re-introduce the I-S dipolar couplings in a similar fashion to the REDOR experiment. (a) INEPT (refocused) coherence transfer 1 1 1 1 1 < -T-. *•< -Tl IT-, M -H • AJ AJ AJ AJ (b) TEDOR (refocused) 4 ( I T , • / n = 0 I I Ml I Figure 3.16 NMR pulse sequences for (a) refocused INEPT and (b) refocused TEDOR. Both pulse sequences perform a coherence transfer from the / spins to the S spins. The black pulses represent n pulses while the white pulses represent nil pulses. The INEPT experiment operates via the I-S J-coupling while the TEDOR experiment operates via the I-S dipolar coupling. The n pulses at 'A and 3A of each rotor period in the TEDOR experiment serve to re-introduce the dipolar couplings. The n pulses at nxjl and mxjl refocus the chemical shifts. During the n rotor periods before the coherence transfer, the application of a series of n pulses leads to an accumulation of dipolar dephasing. The simultaneous n/2 pulses bring about a coherence transfer from the / spins to the S spins. In the m rotor periods that follow, the antiphase magnetization Chapter 3 references begin on page 79. 74 Chapter 3. Solid state NMR distance measurement techniques that was transferred from the I spins to the S spins is modulated by the dipolar dephasing pulses, and evolves into observable S spin magnetization. Because of the selective transfer, the TEDOR experiment eliminates contributions from S spins that are not dipolar coupled to I spins. During the n rotor periods before the coherence transfer, the signal decays due to T2 relaxation of the I spins, while the signal decays during the m rotor periods after the coherence transfer due to T2 relaxation of the S spins. Like the CP experiment, the TEDOR experiment can be extended to two dimensions33 by having an evolution time after the initial n/2 pulse on the I spins and before the rotor-synchronized dipolar dephasing pulses are applied. The resulting two-dimensional spectrum will be a heteronuclear correlation spectrum in which the chemical shifts of the I nuclei are correlated with the chemical shifts of the S nuclei. 3.6.2 TEDOR behavior for isolated I-S spin pairs For an isolated heteronuclear I-S spin pair, the TEDOR signal (ST) arising from placement of the dephasing n pulses at % and 3A of the rotor cycles is: ST = — JJsin[o7-j„(a,p,A.n)]sin[4>r>OT(a,P,A,m)]sinP dfida Equation3.36 n o o where O r „(a,P,A.„)= Xn2-42 sin2Pcosa £> r OT(a,p,A,w) = Xm2-\[2 sin 2p cos a Equation 3.37 and X„ = nDxr and Xm = mDxr. Equation 3.38 In order to facilitate least-squares fitting of experimental data, the integral in Equation 3.36 can be expressed in terms of Bessel functions:25 ST = ^ ([J0 (V2 ( » - m) D xr )]2 - [J0 (42 {n + m) D xr )]2) - X \ kJk(V2 (n-m)Dxr)}2-[Jk(42 (n + m) D xr)]2) k=]l6k -1 Equation 3.39 In practice, this function in Equation 3.39 is usually multiplied by a scaling factor (since this experiment is not normalized like REDOR) and an exponential decay to reflect the T2 relaxation. The TEDOR experiment is usually performed with one of n or m held constant while the other is incremented. Usually the choice will depend on the T2 relaxation properties of the nuclei: if T2 of the I nuclei is shorter, then n is held constant and m is varied, while if T2 of the S nuclei is shorter, then m is held constant and n is varied. Figure 3.17 displays TEDOR curves for several different values of the I-S dipolar coupling constant DiS calculated assuming n = 2 and m incremented. By fitting the oscillations in these curves, the dipolar coupling constant and thus the internuclear distance can be determined directly. Chapter 3 references begin on page 79. 75 Chapter 3. Solid state NMR distance measurement techniques ST Z) / s = 1000Hz tor=4.0kHz Figure 3.17 Calculated TEDOR curves illustrating the effects of different dipolar couplings. The curves were calculated for an isolated I-S spin pair assuming n = 2 with m incremented. Rotor Periods After Transfer (m) 3.7 Comparison of CP, REDOR, and TEDOR for distance determinations The techniques described above for the determination of intemuclear distances each have their advantages and disadvantages and the choice of the appropriate experiment in a given situation will depend on a number of factors. In general, the distances obtained from CP MAS NMR tend to be shorter than the actual distance, while the distances obtained from REDOR and TEDOR tend to be longer than the actual distance.23 REDOR and TEDOR are effected by finite pulse lengths, r.f. field inhomogeneities, and variations in the spinning frequency, all of which reduce the efficiency of the dipolar dephasing, yielding a smaller apparent dipolar coupling constant and longer intemuclear distance. However, with modem equipment it is possible to control the spinning frequency to ± 5 Hz and the problems associated with r.f. field homogeneity can be reduced by appropriate phase cycling of the dephasing n pulses.34 To reduce the effects of finite pulse lengths, high power pulses are required. This is one of the main disadvantages of REDOR and TEDOR experiments, especially at faster spinning rates when the pulse lengths can be greater than 10% of the rotor cycle. The CP experiment is very sensitive to the stability and setting of the r.f. field strengths35 and the stability of the magic angle spinning rate, as any deviation from the spinning sideband matching condition tends to not only reduce the CP efficiency, but gives oscillations which are at a greater frequency. The frequency of the oscillation for a given orientation is described in Equation 3.21 by the cosine term cos(/"„ 0 where /„ = y|/3„ | 2 + (A + n(or f . When the r.f. fields are perfectly matched at a spinning sideband condition, then A + «cor = 0 and f„ = \b„\ which depends only on the dipolar coupling constant and orientation (see Equation 3.19). However, when the r.f. fields are not perfectly matched at a spinning sideband condition, then A + «cor 0 and f„ > \bn\, which means the oscillation occurs at a greater frequency, yielding a larger apparent dipolar coupling constant (since the analysis assumes that the r.f. fields are perfectly matched) and thus a shorter Chapter 3 references begin on page 79. 76 Chapter 3. Solid state NMR distance measurement techniques intemuclear distance. This high sensitivity to the r.f. field strength stability is the major disadvantage of measuring intemuclear distances by CP MAS NMR. With regard to the ease of experimental set-up, the REDOR and TEDOR experiments tend to be simpler experiments to optimize and set-up, as it is only necessary to measure pulse lengths and the spinning frequency, compared to the CP MAS experiment which requires very careful setting of the CP matching condition, often on the actual sample under investigation. In general, in the CP MAS experiment is better for measuring large dipolar coupling constants (short distances) while the REDOR and TEDOR experiments are preferred for measuring smaller dipolar coupling constants (longer distances). Since the REDOR and TEDOR experiments are rotor-synchronized experiments in which data points can only be collected at multiples of the rotor period, larger dipolar couplings require faster spinning rates in order to collect enough data points to define the oscillations in the curves which determine the dipolar coupling constant. In addition, at these faster spinning rates the finite pulse lengths become more problematic. In comparison, the CP MAS experiment is not rotor-synchronized so there is no limit on the number of experimental data points which can be collected to define the dipolar oscillations. However, the CP MAS experiment is much more sensitive to the homonuclear interactions between the / spins, so the CP curves begin to take on more of the characteristics of an extended spin system (smooth exponential growth-decay curves) for smaller heteronuclear I-S dipolar couplings (especially at slower spin rates), resulting in less prominent dipolar oscillations. Another advantage of the CP MAS experiment is that the dipolar oscillations are sensitive only to the angle p, while the dipolar oscillations in the REDOR and TEDOR experiments depend on both a and p. The significance of this different orientational dependence is that when the powder-averages are taken, the amplitudes of the dipolar oscillations in the CP curves are much greater than that of REDOR and TEDOR, meaning the that the effect of the dipolar coupling constant is more pronounced, enabling greater reliability in distance determination. Another factor to consider when choosing the appropriate experiment is the relaxation times. The CP MAS experiment is dependent on the spin lock T\p relaxation of the / and S nuclei, while the REDOR and TEDOR experiments depend on T2 relaxation. An important distinction between the REDOR and TEDOR experiments is that REDOR depends on the T2 relaxation of the observed S nuclei and is not effected by the T2 relaxation of the dephasing / nuclei, while TEDOR depends on the T2 relaxation of both nuclei. The TEDOR experiment allows for a degree of flexibility since it allows the selection of experimental parameters best suited to the T2 relaxation values of a particular system, as described earlier in Section 3.6.2. Since CP MAS and TEDOR experiments involve a polarization transfer, the observed signal comes only from heteronuclear dipolar coupled spins, so there is no need for normalization and there is no contribution from uncoupled spins as there is in the REDOR experiment. An additional advantage of Chapter 3 references begin on page 79. 77 Chapter 3. Solid state NMR distance measurement techniques there being a polarization transfer is that the CP and TEDOR experiments can be performed as two-dimensional experiments in which the chemical shifts of the / nuclei are correlated to the chemical shifts of the S nuclei. This is potentially very useful in cases where there are several resonances for both nuclei. The advantage of the REDOR experiment being normalized is that the effects of relaxation are completely removed and do not need to be fit, as is required in the CP and TEDOR experiments. The curve thus depends only on the value of the dipolar coupling constant (unless there are uncoupled spins, in which case a scaling factor must be applied). For all of these experiments, direct distance determination becomes very difficult and unreliable when the spin system is more complicated than an isolated spin pair.36 There is a strong dependence on the number of spins involved as well as the specific geometrical arrangement and motions of the spins. It is not possible to obtain direct distance information from such spin systems, but it may be possible to fit the experimental data with a model structure. In general, extracting structural information out of CP MAS, REDOR, and TEDOR curves for multi-spin systems is very difficult.36 The cross polarization rate constants in CP MAS experiments can be used to provide geometry independent information about the strengths of the dipolar couplings in the form of heteronuclear dipolar coupling second moments,21'22 but these data provide no direct information about structure and must be compared to model structures. 3.8 Conclusions CP, REDOR, and TEDOR experiments provide information about internuclear distances by measuring the strength of the heteronuclear dipolar couplings. For isolated spin pairs, it is possible to directly determine the dipolar constant, and thus the internuclear distance by these three experiments. Each of these experiments has its advantages and disadvantages. For extended spin systems, the cross polarization rates measured in the CP or CP drain experiments reflect the strength of the dipolar interactions and these rate constants can be related to the heteronuclear dipolar coupling second moments. The rest of this thesis describes how these experiments can be used to measure distances between guest species and zeolite frameworks, in order to determine their location in the zeolite framework. The locations of fluoride ions in an as-synthesized zeolite frameworks are determined by directly measuring several 1 9 F- 2 9 Si distances by 2 9Si{ 1 9F} CP, REDOR, and TEDOR experiments (Chapter 4). The locations of small organic sorbate molecules in sorbate/zeolite complexes are determined by comparing the cross polarization rate constants measured in 2 9Si{'H} CP experiments to calculated heteronuclear dipolar coupling second moments (Chapters 6-9). These results illustrate how solid state NMR can be a powerful tool for structure determinations in complex systems. Chapter 3 references begin on page 79. 78 Chapter 3. Solid stale NMR distance measurement techniques References for Chapter 3 (1) Hartmann, S. R.; Hahn, E. L. Phys. Rev. 1962,128, 2042. (2) Pines, A.; Gibby, G.; Waugh, J. S. J. Chem. Phys. 1973, 59, 569. (3) Schaefer, J.; Stejskal, E. O. J. Am. Chem. Soc. 1976, 98, 1031. (4) Stejskal, E. O.; Schaefer, J.; Waugh, J. S. J. Magn. Reson. 1977, 28, 105. (5) Yannoni, C. S.Acc. Chem. Res. 1982, 75, 201. (6) Mehring, M. Principles of High Resolution NMR in Solids; 2nd ed.; Springer-Verlag: Berlin, 1983. (7) Stejskal, E. O.; Memory, J. D. High Resolution NMR in the Solid State, Fundamentals of CP MAS NMR; Oxford University Press:, 1994. (8) Schaefer, J.; Stejskal, E. O.; Garbow, J. R.; McKay, R. A. J. Magn. Reson. 1984, 59, 150. (9) Sardashti, M.; Maciel, G. E. J. Magn. Reson. 1987, 72, 467. (10) Engelke, F.; Kind, T.; Michel, D.; Pruski, M.; Gerstein, B. C. J. Magn. Reson. 1991, 95, 286. (11) Meier, B. H. Chem. Phys. Lett. 1992, 188, 201. (12) Wu, X.; Zilm, K. J. Magn. Reson. Ser. A 1993, 104, 154. (13) Hediger, S., Improvement of Heteronuclear Polarization Transfer in Solid-State NMR, Ph.D. Dissertation, Eidgenossishe Technische Hochschule, Zurich, Switzerland, 1997. (14) Marica, F.; Snider, R. F. Solid State NMR 2003, in press. (15) Muller, L.; Kumar, A.; Baumann, T.; Ernst, R. Phys. Rev. Lett. 1974, 32, 1402. (16) Levitt, M. H.; Suter, D.; Ernst, R. R. J. Chem. Phys. 1986, 84, 4243. (17) Fyfe, C. A.; Lewis, A. R.; Chezeau, J. M. Can. J. Chem. 1999, 77, 1984. (18) Klur, I.; Jacquinot, J.-F.; Brunet, F.; Charpentier, T.; Virlet, J.; Schneider, C ; Tekely, P. J. Phys. Chem. B 2000,104, 10162. (19) Schaefer, J.; McKay, R. A.; Stejskal, E. O. J. Magn. Reson. 1979, 34, 443. (20) van Vleck, J. H. Phys. Rev. 1948, 74, 1168. (21) Fyfe, C. A.; Diaz, A. C ; Lewis, A. R.; Chezeau, J.-M.; Grondey, H.; Kokotailo, G. T. In Solid State NMR Spectroscopy of Inorganic Materials; Fitzgerald, J. J. (Ed.); ACS Symposium Series, , 1999; Vol. 717, p 283. (22) Fyfe, C. A.; Diaz, A.; Lewis, A. R.; Forster, H. J. Am. Chem. Soc. 2002, in press. (23) Fyfe, C. A.; Lewis, A. R.; Chezeau, J. M. Can. J. Chem. 1999, 77, 1984. (24) Vogt, F. G.; Aurentz, D. J.; Mueller, K. T. Moi. Phys. 1998, 95, 907. (25) Mueller, K. T. J. Magn. Reson. Ser. A 1995, 773, 81. (26) Gullion, T.; Schaefer, J. Adv. Magn. Reson. 1989,13, 57. (27) Gullion, T.; Schaefer, J. J. Magn. Reson. 1989, 81, 196. (28) Fyfe, C. A.; Lewis, A. R.; Chezeau, J. M.; Grondey, H. J. Am. Chem. Soc. 1997, 779, 12210. (29) Hing, A. W.; Vega, S.; Schaefer, J. J. Magn. Reson. 1992, 96, 205. (30) Hing, A. H.; Vega, S.; Schaefer, J. J. Magn. Reson. Ser. A 1993,103, 151. (31) Morris, G. A.; Freeman, R. /. Am. Chem. Soc. 1979,100, 760. Chapter 3 references begin on page 79. 79 Chapter 3. Solid state NMR distance measurement techniques (32) Fyfe, C. A.; Wong-Moon, K. C; Huang, Y.; Grondey, H. J. Am. Chem. Soc. 1995,117, 10397. (33) Fyfe, C. A.; Diaz, A. C. J. Phys. Chem. B 2002,106, 2261. (34) Gullion, T.; Baker, D. B.; Conradi, M. S. J. Magn. Reson. 1990, 89, 479. (35) Bertani, P.; Raya, J.; Reinheimer, P.; Gougeon, R.; Delmotte, L.; Hirschinger, J. Solid State Nucl. Magn. Reson. 1999,73,219. (36) Fyfe, C. A.; Lewis, A. R. J. Phys. Chem. B 2000,104, 48. Chapter 3 references begin on page 79. 80 Chapter 4 The Location and Dynamics of the Fluoride Ion in Tetrapropylammonium Fluoride Silicalite-1 In this chapter, the general strategy for locating guest species in zeolites is demonstrated for determining the location of fluoride ions in as-synthesized zeolites. In this particular example, the fluoride ions in an as-synthesized zeolite with the MFl topology are unambiguously located using a combination of two-dimensional 2 9 Si correlation experiments and triple-resonance 'H/ 1 9 F/ 2 9 Si CP MAS, REDOR, and TEDOR NMR distance measurement experiments. With the location of the fluoride ion established, it was possible to study its dynamics over a wide range of temperatures. 4.1 Introduction 4.1.1 Synthesis of zeolites from fluoride-containing media Zeolites and related microporous materials are commonly prepared by hydrothermal crystallization of alkaline reaction mixtures. For highly siliceous materials, this synthetic route generally leads to substantial numbers of Q 3 Si-O' and Si-OH defect sites which can be observed by 'H and 2 9 Si magic angle spinning (MAS) NMR. 1 During the past twenty years, an alternate synthetic route has been developed that can be carried out near neutral pH and employs fluoride ions as the mineralizing agent rather than hydroxide ions, as first reported by Flanigen and Patton for the synthesis of fluoride silicalite-1.2 In subsequent years, the scope of this synthesis route has been further extended by Guth, Kessler, and co-workers3-6 and more recently by Camblor and co-workers.7 The most notable difference between the fluoride and hydroxide synthetic routes is that materials synthesized in fluoride media have been shown to have substantially fewer defect sites.8'9 Another important aspect of the fluoride synthetic route is that larger crystals can be made4-10 and it has also afforded pure silica phases with low framework densities.7 Morris and co-workers have shown that a number of fluoride-containing zeolites have non-linear optical properties.11 In addition, the fluoride route can be used to prepare catalytically active materials by incorporating other elements such as B, Al , Fe, Ga, Ge, and Ti into the framework4-6 and to prepare non-silicon based microporous materials such as A I P O 4 S and GaP04s.3 Chapter 4 references hegin on page 102. 81 Chapter 4. Location offluoride ions in [F,TP A]-MFI zeolite 4.1.2 The role of fluoride ions in controlling zeolite synthesis Because of the superior quality of the products and potentially interesting applications, there is considerable interest in understanding the role that the fluoride ions play in the synthesis of zeolites under these conditions. The initial motivation for including fluoride ions in the synthesis mixture was for F" to replace OH" as the mineralizing agent since the solid silica sources are not soluble near neutral pH. It has also been proposed that the fluoride ions may catalyze the condensation reaction involved in Si-O-Si bond formation.12 However, chemical analysis,4'13 solid state 1 9F and 2 9 Si MAS NMR spectroscopy,14"17 and X-ray diffraction (XRD) studies11'18"20 reveal that many of the as-synthesized zeolites incorporate the fluoride ions into their structure. Therefore, it is thought that the fluoride ions may play additional roles such as charge balancing and acting as templates or structure directing agents (SDAs).6 For the non-linear optical materials, it is thought that the fluoride ions align and order non-centrosymmetric SDA cations via electrostatic interactions.11-21 By probing the location of the fluoride ions in zeolite frameworks, it is hoped that significant insight into these additional roles of fluoride ions in zeolite syntheses can be gained and perhaps used in a predictive manner. 4.1.3 Diffraction studies of fluoride-containing zeolites Despite the importance of the role that fluoride ions play in this synthesis method, there are very limited structural data concerning the location of fluoride ions in purely siliceous zeolite frameworks. Single crystal XRD, the method of choice for determining structures of crystalline solids, is limited in its application to zeolites due to their microcrystalline nature and to problems arising from crystal twinning.22 There are additional complications in that fluorine and oxygen have very similar numbers of electrons making them difficult to distinguish. In particular, F" anions are isoelectronic with the OH groups which can occur as defects within zeolite frameworks. There are only five crystal structures of as-synthesized purely siliceous zeolite materials made via the fluoride route which unambiguously locate the fluoride ions: two conventional single crystal structures of clathrasil materials and three zeolite structures determined by synchrotron XRD on very small single crystals. The single crystal structure of the clathrasil octadecasil19 revealed a fluoride ion location in a small interstitial cavity of the framework: a double four-ring or [46] cage (cages are denoted as [nmn'm ...] according to the number m of windows consisting of n Si atoms). This location is quite far away from the SDA cation, demonstrating that the fluoride ions are not found exclusively as intimate ion pairs with the SDA cation, and hence that their locations may be determined by other effects, perhaps related to templating or structure-directing roles. In the single crystal structure of another clathrasil nonasil,18 the fluoride ion is also located a considerable distance away from the SDA in a small [4'5462] cage of the framework. Furthermore, in this case, the fluoride ion was found to be directly covalently bonded to one of the silicon atoms in the four-ring of this cage, creating a five-coordinate [Si04/2F]" silicon site. This phenomenon of five-coordinate [Si04/2F]" sites in the four-rings of small interstitial Chapter 4 references begin on page 102. 82 Chapter 4. Location offluoride ions in [F, TP AJ-MF1 zeolite cavities of zeolite frameworks has also been observed recently in the crystal structures of zeolite SSZ-232 0, ITQ-411-21, and SSZ-3521 determined from low temperature synchrotron XRD data collected on very small crystals. A summary of the fluoride ion locations in fluoride-containing siliceous zeolites determined by XRD is presented in Table 4.1. The observation of fluoride ions located in small cages of the framework is not limited to purely siliceous zeolites, as fluoride ions have been found in the frameworks of several A1P04 and GaP0 4 materials synthesized in a similar fashion via the fluoride route.3 The fluoride ions in these materials have been found to occupy three different types of environments: in the small double four-ring structural units, as a bridging atom between gallium or aluminum atoms, or as a terminal Ga-F group.323 Table 4.1 Fluoride ion locations in as-synthesized siliceous zeolites determined by single crystal XRD. Cage structure Zeolite* F" location F-Si distance XRD data Reference Octadecasil [F,Q]-AST [46] cage 2.67 A Nonasil [4l5462] cage 1.84 A [F,Cocp2]-NON single crystal (295 K) single crystal (220 K) 19 SSZ-23 [F,TMAda]-STT ITQ-4 [F,BQol]-IFR R . 3-4 N 1.94 A [4 5] cage ] 95 A 1.96 A [43526']cage 1.92 A micro-crystal 20 (synchrotron, 160 K) SSZ-35 [4'5262]cage 1.87 A [F,DMABO]-STF micro-crystal (synchrotron, 30 K) micro-crystal (synchrotron, 150K) 11 * Structure directing agents: Q = quinuclidine, Cocp2 = cobaltacene, TMAda = AWN-trimethyl-l-adamantammonium, BQol = hydroxybenzylquinuclindinium, DMABO = Af,JV-dimethyl-6-azonium-1,3,3-trimethybicyclo(3.2. l)octane Although tetrapropylammonium fluoride silicalite-1 ([F,TPA]-MF1), an as-synthesized siliceous zeolite with the MFl topology,24 was the first material synthesized via the fluoride route and one where the improvements in the quality of the crystals due to this synthesis method are most apparent, the location of the fluoride ion within this framework was still unknown. There have been attempts to locate it but however the answer remained ambiguous as there were several proposed locations (see Figure 4.1). In an XRD study of a twinned crystal, Price et al. proposed the fluoride ion to be in the channel intersection, 2.45 A away from the positively charged nitrogen of the TPA template.22 Using published Chapter 4 references begin on page 102. 83 Chapter 4. Location offluoride ions in [F. TP A]-MFl zeolite atomic coordinates for the MFl framework and TPA cation template,25 Mentzen et al. constructed Fourier electron density difference maps from powder X-ray diffraction data collected on a [F,TPA]-MFI sample and observed two extra-framework sites: one in a [4*5262] cage of the framework and the other in the channel intersection, 2.32 A from the nitrogen of the template cation.26 Although the site in the framework cage was assigned to the fluoride ion, no satisfactory explanation could be given for the site in the channel intersection. One of the aims of the present research is to resolve this discrepancy and present an unambiguous location of the fluoride ion in [F,TPA]-MF1. 4.1.4 Solid state NMR studies of fluoride-containing zeolites Koller and co-workers showed that the presence of five-coordinate [Si0 4 2F]" sites in a purely siliceous zeolite could also be detected by solid state 2 9Si{'H} CP MAS NMR spectroscopy (see Figure 4.2), as these five-coordinate silicon sites give resonances that are shifted to high field (around -145 ppm) and are substantially enhanced by 29Si{1<:)F} cross polarization.15 In the case of some materials, a broad peak between -115 and -150 ppm appears in the 2 y Si spectrum due to an exchange process involving the fluoride ions in which they are thought to be mobile between different S i 0 4 2 tetrahedra.15 This motion gives rise to an average chemical shift for silicon sites whose environments change between four-coordinate Si0 4 / 2 and five-coordinate [Si0 4 / 2F]\ By lowering the temperature, this motion can be 'frozen out', yielding a narrow peak at around -145 ppm. 1 4 1 5 Thus far, five-coordinate [Si0 4 2 F f sites have been detected by 2 9 Si CP MAS NMR spectroscopy in some seven structures in total, including [F,TPA]-MFI.14 The low temperature spectrum of [F,TPA]-MF1 in Figure 4.2 shows only a single peak at the five-coordinate chemical shift. The reason for the lack of a doublet (arising from the F-Si J-coupling) is explained in detail in Chapter 5. • Price et al. 2.45 A from N atom of TPA+ • Mentzen et al. 'X' 2.32 A from N atom of TPA+ • Mentzen et al. 'F' [4 15 26 2] cage of framework Figure 4.1 Proposed locations of the fluoride ion in [F,TPA]-MFI: XRD of a twinned crystal (Price et al27) and powder XRD (Mentzen et al.26). Chapter 4 references begin on page 102. 84 Chapter 4. Location offluoride ions in [F,TP A]-MFl zeolite 5-coordinate S i Figure 4.2 29Si{'H} CP MAS spectra of [F,TPA]-MFI at room temperature (top) and low temperature (bottom) showing the peaks arising from the five coordinate Si when the fluoride ion is dynamic (top) and when it is static (bottom). 4.1.5 Locating the fluoride ions by solid-state NMR Although 1 9F MAS and 2 9 Si CP MAS NMR can detect the presence of fluoride ions and [Si0 4 / 2F]' sites, these techniques alone cannot determine the location of fluoride ions within zeolite frameworks. These materials are thus ideal candidates for the general strategy to locate guest species in zeolites outlined in the introductory chapter. Using two-dimensional NMR spectroscopy, it is possible to assign the resonances in the 2 9 Si spectrum to each of the unique silicon sites in a zeolite framework. Because the fluoride ions are relatively dilute in the zeolite and the 2 9 Si nuclei have a relatively low natural abundance, there will be isolated l 9 F/ 2 9 Si spin pairs. This is ideal for the CP, REDOR, and TEDOR experiments described in Chapter 3, since it is therefore possible to directly measure the l 9 F/ 2 9 Si dipolar couplings and thus F-Si internuclear distances. With several F-Si internuclear distances measured, the fluoride ions are easily located with respect to the zeolite framework. These dipolar recoupling experiments have been demonstrated to be reliable in measuring internuclear distances between isolated l 9 F/ 2 9 Si spin pairs in the clathrasil octadecasil.28-30 The aim of the present work is to unambiguously determine the location of the fluoride ion in as-synthesized [F,TPA]-MFI zeolite using these solid state NMR techniques. In structural studies of small molecules or ions occluded in zeolites such as this, solid state NMR has advantages over XRD in the many cases where single crystals of sufficient size and quality are not available for XRD. If samples of sufficient quality (for NMR) can be synthesized, this general approach using solid state NMR techniques can be extended to any other fluoride-containing zeolite frameworks. Chapter 4 references begin on page 102. 85 Chapter 4. Location of fluoride ions in [F.TPA]-MFI zeolite AA .6 1H/1 9F/2 9Si triple frequency probe Because the as-synthesized [F,TPA]-MFI zeolite still contains the organic template cation and there exist relatively strong ' H / 2 9 S i dipolar couplings, it is necessary to apply ' H decoupling during acquisition in order to obtain high-resolution 2 9 S i N M R spectra. Therefore, an H/F/X triple-resonance probe capable of operating at ' H , l 9 F , and 2 9 S i frequencies simultaneously was required to carry out the N M R experiments which probe the interactions between 1 9 F and 2 9 S i . This was achieved by a relatively straightforward modification of an existing H / X double resonance probe. A separate radio frequency (r.f.) channel with matching and tuning capabilities for l 9 F was added to an existing double resonance M A S N M R probe, having an additional r.f. coil which was mounted externally on the cylindrical M A S stator, as depicted in Figure 4.3. This additional coil has an r.f. field orthogonal to both the inner solenoid coil and the external magnetic field. Although this outer coil is quite large, it is relatively efficient due to its being part of a single frequency circuit and its r.f. field being orthogonal to the static magnetic field. Further details about this probe design can be found in Chapter 12 which describes the experimental details in greater depth. Figure 4.3 Schematic diagram of the outer coil for the 'H/ 1 9 F/X probe. See Chapter 12 for more details. With this probe, it is possible to perform the CP, REDOR, and TEDOR experiments as ' H / ' 9 F / 2 9 S i triple resonance experiments in which the experiments can begin on ' H to take advantage of its shorter T\ and the gain in S/N arising from 2 9 Si{'H} cross polarization. Also, it is possible to apply ' H decoupling during the experiments in order to obtain highly resolved 2 9 S i spectra. The pulse sequences for the ' H / 1 9 F / 2 9 S i triple resonance CP, REDOR, and TEDOR experiments are illustrated in Figure 4.4. Chapter 4 references begin on page 102. 86 Chapter 4. Location offluoride ions in [F, TP AJ-MFI zeolite (3) na (b) 'H I spin lock decouple recycle delay *Si contact pulse X xu I I H j spin lock sp contact pulse decouple spin lock ' M 1 SP'n n I lock decouple