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Investigation of the three-dimensional structures of zeolite molecular sieves by high resolution solid… Diaz Garcia, Anix C. 1999

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INVESTIGATION OF THE THREE-DIMENSIONAL STRUCTURES OF ZEOLITE M O L E C U L A R SIEVES B Y HIGH RESOLUTION SOLID STATE N M R by A N I X C. DIAZ G A R C I A Lie. in Chemistry, Central University of Venezuela, 1985 A THESIS SUBMITTED IN P A R T I A L F U L F I L M E N T OF THE REQUIREMENTS FOR THE D E G R E E OF DOCTOR OF PHILOSOPHY in THE F A C U L T Y OF G R A D U A T E STUDIES (Department of Chemistry) We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH C O L U M B I A December 1998 © Anix. C. Diaz Garcia, 1998  In presenting degree  at the  this  thesis  in partial fulfilment  of the  and study. I further  copying of this thesis for scholarly purposes or  for an  advanced  University of British Columbia, I agree that the Library shall make it  freely available for reference department  requirements  by  his  or  her  representatives.  agree that permission for extensive  may be granted It  is  by the head  understood  that  of my  copying  or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department The University of British Columbia Vancouver, Canada Date  DE-6 (2/88)  11  ABSTRACT  This thesis work describes the use of solid state N M R experiments to obtain important structural information about zeolite complexes with organic guest molecules. A highly siliceous zeolite ZSM-5 loaded with p-xylene was chosen for the detailed study. A methodology to investigate the zeolite complexes of highly siliceous ZSM-5 with pxylene molecules by locating the organic molecules inside the framework using only N M R techniques was developed. In this way a complete three-dimensional characterisation of these systems was obtained. The application of the double and triple resonance dephasing experiments of CrossPolarization (CP), Rotational Echo Double Resonance (REDOR), and Transferred Echo Double Resonance (TEDOR), to attain internuclear distances from the dipolar interaction between the guest molecules nuclei and the silicon nuclei in the zeolite framework was investigated. Specifically deuterated and  1 3  C labelled p-xylenes were used in these studies. Triple resonance  dephasing experiments of REDOR and TEDOR were performed on the complex of the high loaded form of zeolite ZSM-5 with p-xylene [ C,CH3] to obtain structural information through 13  the dipolar interaction between the labelled  1 3  C methyl group of the guest molecules and the  silicon atoms. The unambiguous assignment of the  1 3  C N M R spectra of the guest p-xylene  molecules was done using 2D-TEDOR experiments. The acquisition of reliable quantitative data from these techniques was complicated due to the dynamics of the absorbed molecules within the zeolite framework. The motional characteristic of the molecules was investigated by H N M R and chemical-exchange spectroscopy. The 2  application of high resolution  1 3  C C P / M A S 2D N M R exchange spectroscopy to investigate the  molecular motions of guest molecules inside zeolite catalysts and to obtain critical kinetic information on these processes was demonstrated for the first time.  J  Ill  By application of the CP experiment and the protocol developed in this thesis a threedimensional structure of the low-loaded complex of p-xylene in ZSM-5 was obtained. This structure was derived without any previous x-ray diffraction information. The N M R results indicated that the p-xylene molecules were located in the intersection of the sinusoidal and straight channels of the zeolite.  iv Table of Contents Abstract  ii  Table of contents  iv  List of Tables  xii  List of Figures  •  xv  Symbols and Abbreviations  xxiii  Acknowledgements  xxvi  Dedication  xxvii  C H A P T E R 1:  INTRODUCTION...  1  1.1.  ZEOLITE M O L E C U L A R SIEVES  1  1.1.1  Introduction  1  1.1.2  Zeolite Structures  2  1.1.2.1  6-Membered Oxygen Ring Systems  5  1.1.2.2  8-Membered Oxygen Ring Systems  5  1.1.2.3  10-Membered Oxygen Ring Systems  5  1.1.2.4  12-Membered Oxygen Ring Systems  7  1.1.2.5  Larger than 12-Membered Oxygen Ring Systems  7  1.1.3  Applications of Zeolites  8  1.1.3.1  8  As Molecular Sieves  V  1.1.3.2 1.1.4  As Catalysts  9  Methods for the Characterization of Zeolite Structures  15  1.1.4.1  Adsorption Studies  18  1.1.4.2  Powder Diffraction Methods  19  1.1.4.3  Electron Microscopy  20  1.1.4.4  Nuclear Magnetic Resonance  20  1.2.  PRINCIPLES OF SOLID STATE N M R SPECTROSCOPY  22  1.2.1  Magnetic Interactions in Solid State N M R  22  1.2.1.1  Zeeman Interaction  23  1.2.1.2  Dipole-Dipole Interaction  24  1.2.1.3  Chemical Shift Interaction  25  1.2.1.4  Spin-Spin Interaction  27  1.2.1.5  Quadrupolar Interaction  28  1.3.  R E L A X A T I O N TIME M E A S U R E M E N T S IN N M R  30  1.3.1  Spin-Lattice Relaxation Time (T i)  30  1.3.2  Spin-Spin Relaxation Time (T2)  31  1.3.3  Spin-Spin Relaxation Time in the Rotating Frame (Ti )  34  1.3.4  Dependence of Relaxation Times on Molecular Motions  35  1.4.  METHODS IN HIGH RESOLUTION SOLID STATE N M R  37  1.4.1  Magic Angle Spinning  37  p  1.4.2  High Power Decoupling of Protons  39  1.4.3  Cross Polarization (CP)  40  1.4.3.1  Cross Polarization Dynamics  46  1.4.3.2  Geometrical Information from Cross-Polarization Rate  47  1.4.3.3  Second Moments  48  1.5.  TWO-DIMENSIONAL N M R SPECTROSCOPY  53  1.5.1  Representation of the Two-Dimensional Data  54  1.5.2  Classification of Two-Dimensional N M R Experiments  55  1.5.2.1  J-Resolved Spectroscopy  55  1.5.2.2  2D Correlated Spectroscopy  55  1.5.3  Processing of Two-Dimensional N M R Experiments  56  1.6.  HIGH RESOLUTION SOLID STATE N M R SPECTROSCOPY OF ZEOLITE M O L E C U L A R SIEVES  59  1.7.  G O A L OF THE THESIS  67  1.8.  REFERENCES  69  C H A P T E R 2:  EXPERIMENTAL  75  2.1  INTRODUCTION  75  2.2  S A M P L E PREPARATION  76  2.2.1  Zeolite Synthesis  76  2.2.2  Synthesis of the Labelled Compounds  77  2.2.2.1  Deuterium Labelledp-Xylenes  77  Vll  2.2.2.2  1 3  C Labelled p-Xylenes  78  2.2.3  Loading of Sorbates in the Zeolite Materials  78  2.3  SAMPLE ANALYSIS  78  2.3.1  Determination of the Zeolite Loadings  78  2.3.1.1  By Thermogravimetric Analysis  78  2.3.1.2  By Si NMR Spectroscopy  79  29  2.4  OPTIMIZATION OF THE N M R EXPERIMENT  79  2.4.1  Shimming, Probes and Reference Samples for Setting Up  79  2.4.2  29  S i Cross Polarization Setting  80  2.4.3  1 3  C Cross Polarization Setting  83  2.4.4  Low Temperature M A S Spinning  83  2.5  M E A S U R E M E N T OF R E L A X A T I O N P A R A M E T E R S  84  2.6  A N A L Y S I S OF THE N M R D A T A  84  2.6.1  Programs used for processing N M R experimental data  84  2.6.2  Analysis of the variable contact times cross-polarization data  84  2.7  REFERENCES  87  CHAPTER 3 INVESTIGATION OF THE STRUCTURE OF THE HIGH LOADED FORM OF P-XYLENE IN ZSM-5 BY W S i CROSS POLARIZATION EXPERIMENTS AT ROOM TEMPERATURE 88 3.1  INTRODUCTION  '.  88  3.1.1  Molecular Mobility of p-Xylene in Complexes of ZSM-5 Studied by Deuterium N M R Spectroscopy 93  vm 3.2  EXPERIMENTAL.....  100  3.2.1  Sample Preparation  100  3.2.2  Deuterium N M R Experiments  100  3.2.3  Cross-Polarization Experiments  100  3.3  RESULTS A N D DISCUSSION  100  3.3.1  Deuterium N M R Spectroscopy  100  3.3.2  Variable Contact Time ' H / S i N M R CP/MAS Experiments  104  3.4  REFERENCES  126  29  '.  CHAPTER 4: INVESTIGATION OF SLOW M O L E C U L A R MOTIONS AND DIFFUSIONAL BEHAVIOR IN T H E HIGH LOADED FORM OF ZSM-5 WITH P-XYLENE BY TWO-DIMENSIONAL C SOLID STATE NMR CHEMICAL EXCHANGE EXPERIMENTS 128 1 3  4.1  INTRODUCTION  128  4.1.1  Rate processes in a system with two sites  132  4.1.1.1  Two Site System with Pure Slow Chemical Exchange  134  4.1.2  Multiple Site Chemical Exchange  135  4.2  EXPERIMENTAL  136  4.2.1  Sample Preparation  136  4.2.2  1 3  C CP/MAS Experiments  136  4.3  RESULTS A N D DISCUSSION  138  4.3.1  Possible Mechanisms for the Chemical Exchange ofthe p-Xylene molecules  160  4.4  REFERENCES  166  ix  CHAPTER 5: INVESTIGATION OF THE STRUCTURE OF THE HIGH LOADED FORM OF P-XYLENE IN ZSM-5 BY H/ Si CROSS POLARIZATION EXPERIMENTS AT LOWER TEMPERATURE 168 J  29  5.1  INTRODUCTION  168  5.2  EXPERIMENTAL  169  5.3  RESULTS A N D DISCUSSION  170  5.4  CONCLUSIONS  186  5.5  REFERENCES  188  CHAPTER 6: INVESTIGATION OF AN UNKNOWN STRUCTURE: THE LOW LOADED FORM OF P-XYLENE IN ZSM-5 STUDIED BY W'Si CROSS POLARIZATION EXPERIMENTS 188 6.1  INTRODUCTION  188  6.2  EXPERIMENTAL  191  6.2.1  Sample Preparation  191  H N M R Spectra at Variable Temperature  191  6.2.3  I N A D E Q U A T E Experiments at 268 K  191  6.2.4  l  W Si  CP Experiments  192  6.3  RESULTS A N D DISCUSSION  193  6.3.1  Deuterium N M R Spectroscopy  193  6.3.2  Variable Contact Time S i C P / M A S N M R Experiments  196  6.4  CONCLUSIONS  227  6.5  REFERENCES  228  6.2.2  2  29  29  X  CHAPTER 7: PRELIMINARY STUDIES OF THE STRUCTURE OF THE HIGH LOADED FORM OF P-XYLENE IN ZSM-5 BY DOUBLE RESONANCE W'Si DIPOLAR DEPHASING REDOR EXPERIMENTS 229 7.1  INTRODUCTION  229  7.1.1  Calculation of REDOR Dephasing  232  7.1.1.1  Isolated Spin System  232  7.1.1.2  Collection of Isolated I-S Spin Pairs  236  7.1.1.3  Many S Spins Coupled to an I Spin  236  7.2  EXPERIMENTAL  238  7.2.1  Sample preparation  238  W Si REDOR Experiments  238  7.2.2  ]  29  7.3  RESULTS A N D DISCUSSION  240  7.4  CONCLUSIONS  252  7.5  REFERENCES  253  CHAPTER 8: PRELIMINARY STUDIES OF THE STRUCTURE OF THE HIGH LOADED FORM OF P-XYLENE IN ZSM-5 BY TRIPLE RESONANCE ^"C/^Si DIPOLAR DEPHASING EXPERIMENTS 255 8.1.  INTRODUCTION  255  8.2.  EXPERIMENTAL  260  8.2.1  Sample Preparation  260  8.2.2  ' H / C / S i CP-REDOR Experiments  260  8.2.3  ' H / ^ C / ^ S i CP-TEDOR Experiments  261  13  29  xi 8.2.4  ' H / C / S i Two-Dimensional Heteronuelear Correlation CP-TEDOR 13  29  Experiments  261  8.3.  RESULTS A N D DISCUSSION  264  8.3.1  REDOR Experiments  264  8.3.2  TEDOR Experiments  286  8.3.3  Two Dimensional TEDOR Experiments  288  8.4.  CONCLUSIONS  293  8.5  REFERENCES  295  APPENDICES: TURBO PASCAL COMPUTER PROGRAMS WRITTEN TO CALCULATE IMPORTANT VALUES USED IN THIS THESIS  296  A P E N D I X 1. Program to Calculate Static Internuclear Si-H Second Moments for the Aromatic Hydrogens in the System of Orthorhombic ZSM-5 High Loaded with p-Xylene Space Group P2j2,2i 297 A P E N D I X 2. Program to Calculate Internuclear Si-H Second Moments for Methyl Hydrogens Rotating about their C 3 axis in the System of Orthorhombic ZSM-5 High Loaded with p-Xylene Space Group P2,2,2i 306 A P E N D I X 3. Program to Rotate and Translate the p-Xylene and Calculate Internuclear Si-H Second Moments for the Aromatic and Methyl Hydrogens in the System of Orthorhombic ZSM-5 Low Loaded with p-Xylene Space Group Pnma 326 A P E N D I X 4: Program to Calculate Lorentzian Signals from the CP Correlation in the System of Orthorhombic ZSM-5 Low Loaded with p-Xylene Space Group Pnma 341 A P E N D I X 5: Program to Calculate Average Internuclear Si-H Second Moments for the Aromatic Hydrogens Flipping about the C2 Axis in the System of Orthorhombic ZSM-5 Low Loaded with p-Xylene Space Group Pnma 356  Xll  List of Tables Table 1.1  Classification of some zeolites  4  Table 1.2  Commercially available zeolites  11  Table 1.3  Some commercial processes using zeolite catalysts  14  Table 1.4  Adsorption capacities of hydrocarbons on HZSM-5  19  13  Table 1.5  C nuclear spins interactions in a 4.7 Tesla field  23  Table 1.6  Classification of some standard 2D experiments and areas of application in high resolution N M R spectroscopy 56  Table 1.7  Description of the phase changes occurring in zeolite ZSM-5 with temperature and sorbate loading 64  Table 2.1  Pulse sequences used for the determination of Ti and T2 values  Table 3.1  Shortest calculated Si-H distances from the single crystal X R D data for the complex of p-xylene in ZSM-5 with 8 molecules per u.c  85  111  Table 3.2  Selected relaxation parameters for the *H and S i nuclei in the p-xylene/ZSM-5 complex 117  Table 3.3  Experimental and calculated parameters related to the ' H / S i cross-polarization experiments on the complex of p-xylene-d<5 in ZSM-5 with 6 molecules per u.c. at room temperature 118  Table 3.4  Experimental and calculated parameters related to the H / Si cross-polarization experiments on the complex of p-xylene-d^ in ZSM-5 with 6 molecules per u.c. at room temperature 122  Table 4.1  Calculated Si-C distances for the complex of 8 molecules of p-xylene in ZSM-5  2 9  29  1  Table 4.2  9Q  144  Expected cross peaks according to the strength of the dipolar couplings given in Table 4.1 145  Xlll  Table 4.3  Kinetic constants at different temperatures for the intramolecular exchange of the p-xylene molecules in the straight and zig-zag channels in the system of 8 molecules of p-xylene per u.c. in ZSM-5 154  Table 4.4  Pore opening (0...0 distances, A) for the double 10-rings in the straight and sinusoidal channels of the complex of 8 molecules of p-xylene per u.c. in. ZSM-5 (From reference 15). The O numbering is for use in this table only and is defined as given in the diagram below 161  Table 5.1  Selected relaxation parameters for the ' H and S i nuclei in the specifically deuterated xylenes of the p-xylene/ZSM-5 complexes at 273 K 2 9  174  Table 5.2  Experimental and calculated parameters related to the H / S i cross polarization experiment on the complex of p-xylene-^ in ZSM-5 with 6 molecules per u.c. at 273 K 176  Table 5.3  Experimental and calculated parameters related to the H / Si cross-polarization experiment on the complex of p-xylene-d<5 in ZSM-5 with 8 molecules per u.c. at 273 K 178  Table 5.4  Experimental and calculated parameters related to the W Si cross-polarization experiment on the complex of p-xylene-^ in ZSM-5 with 6 molecules per u.c. at T=273 K 183  Table 5.5  Table 6.1  Table 6.2  1  1  l  29  *  Experimental and calculated parameters related to the H / Si cross-polarization experiment on the complex of p-xylene-c/4 in ZSM-5 with 8 molecules per u.c. at T=273 K 183 Selected relaxation parameters for the ' H and S i nuclei in the specifically deuterated p-xylene/ZSM-5 complexes at 233 K 2 9  202  Experimental and calculated parameters from the least squares fit to the data from the H / S i cross-polarization experiments on the complex of p-xylene-^ in ZSM-5 with 3 molecules per u.c. at different temperatures 207 29  Experimental and calculated parameters from the least squares fit to the data from the H / S i cross-polarization experiments on the complex of p-xylene-<^ in ZSM-5 with 3 molecules per u.c. at different temperatures 212 1  Table 6.4  90  29  1  1  Table 6.3  29  29  Fractional atomic coordinates for the complex of ZSM-5 loaded with 3 molecules per u.c. of p-xylene. The p-xylene coordinates were calculated from the N M R data and correspond to solution 58 226  xiv Table 7.1  Calculated dipolar coupling and Si-H distancefromthe experimental REDOR data for the complex of ZSM-5 with 8 molecules per u.c. of p-xylene-(4 at 273 K 249  Table 7.2  Calculated dipolar coupling and Si-H distancefromthe experimental REDOR data for the complex of ZSM-5 with 8 molecules per u.c. of p-xylene-J^ 250  Table 8.1  Selected relaxation parameters for the H and Si nuclei in the complex of 8 molecules per u.c. of p-xylene in ZSM-5 at 273 K 266  Table 8.2  Shortest calculated Si-C distances for the complex of 8 molecules of p-xylene per u.c. in ZSM-5 determined by the XRD structure, up to a distance of 7 A 268  Table 8.3  Calculated dipolar couplings and Si-H distance from the experimental REDOR data for the complex of ZSM-5 with 8 molecules per u.c. of p-xylene [ C, CH3] (99.5 at. %) 271  !  29  13  Table 8.4  Calculated dipolar couplings and Si-H distances from the experimental REDOR data for the complex of ZSM-5 with 4 molecules of unlabeled p-xylene and 4 molecules of p-xylene [ C, CH ] (99.5 at. %) per u.c 280 13  3  Table 8.5 Table 8.6  Transversal relaxation times (T2) for the Si nuclei in the p-xylene/ZSM-5 complex at 273 K 29  287  Expected cross peaks according to the strength of the dipolar couplings given in Table 4.1 292  XV  List of Figures Figure 1.1  Secondary building units commonly occurring in zeolite  3  Figure 1.2  Sheet projection of ZSM-5  3  Figure 1.3  The framework structures of selected zeolites together with the aperture of their channels as defined by the linking oxygen atoms  6  Figure 1.4  Proposed mechanism for the hydrothermal dealumination of zeolites  16  Figure 1.5 Figure 1.6  Different kinds of size and shape selectivity in reactions within zeolite cavities.... 17 Powder pattern arising from dipolar interaction effects for a two-spin system 26  Figure 1.7  A schematic representation of the chemical shift anisotropy  Figure 1.8  Schematic representation of the Carr-Purcell spin echo pulse sequence for measuring T2 relaxation times  29  33  Figure 1.9  Pulse sequence for measuring T i ( Si) relaxation times  Figure 1.10  General behaviour of the relaxation times, T\, T , and T i , as a function of the temperature 36 Schematic representation of the geometric arrangement for mechanical sample spinning 38  Figure 1.11  Figure 1.12  36  p  2  p  Single-contact spin-lock cross-polarization pulse sequence showing the time dependence of the proton and silicon magnetization  41  Figure 1.13  Spin locking dynamics viewed in the rotating frame on resonance  41  Figure 1.14  Large H , small  Si, and infinite lattice reservoirs, each characterized by a heat  capacity and temperature: C H , T ; Csi, Tsi; C L , T L ; respectively  43  Figure 1.15  The geometric relationship of two spins I and S in an external magnetic field  52  Figure 1.16  Angles important in describing the rotation of a molecule  52  h  xvi Figure 1.17  Common time domain apodization functions used in the processing of 2D N M R spectra 57  Figure 1.18  (a) Si M A S N M R spectrum of the zeolite analcite. (b) Characteristic chemical shift ranges of the five different local silicon environments 62  Figure 1.19  (a) S i M A S N M R spectrum of ZSM-5 at 300 K . (b) S i M A S N M R spectrum of the low loaded form of ZSM-5 (2 molecules of p-xylene per u.c.) at 300 K . (c) S i M A S N M R spectrum of the low loaded form of ZSM-5 at 403 K . (d) S i M A S N M R spectrum of the high loaded form of ZSM-5 (8 molecules of p-xylene per u.c.) at 293 K 63 2 9  2 9  2 9  29  Figure 1.20  Figure 1.21  S i 2D I N A D E Q U A T E spectrum of the low loaded form of ZSM-5 (2 molecules of p-xylene per u.c.) at 300 K 65 29  29  S i 2D I N A D E Q U A T E spectrum of the high loaded form of ZSM-5 (8 molecules of p-xylene per u.c.) at 300 K 66  Figure 2.1  T G A plots which shows the desorption of p-xylene sorbed in ZSM-5, from room temperature to 300 °C with a rate of 2 °C/s 81  Figure 2.2  (a) Si M A S N M R decoupled spectra of ZSM-5 with increasing concentration of pxylene. (b) S i CP M A S N M R decoupled spectra of the same samples 82 29  29  Figure 2.3  Experimental setting to run M A S N M R spectra at low temperatures  86  Figure 3.1  (A) A secondary building unit of the 5-1 type. (B) A n asymmetric unit of orthorhombic form with the space group Pnma. (C) Chain-type building block....89  Figure 3.2  (a) Skeletal diagram of a pentasil layer formed by linking the chain type building blocks, (b) Stacking sequence of layers in ZSM-5 (layer shaded), (c) The channel system in ZSM-5 90  Figure 3.3  Variation of peak separation with the angle 0 formed between the principal component of the electric field gradient (EFG) tensor and the magnetic field vector  94  Figure 3.4  Theoretical H N M R powder spectrum of a methyl group: motional averaging of the electric field gradient tensor by rapid single axis rotation 96  Figure 3.5  Calculated deuterium N M R line shapes of p-xylene under various dynamic conditions  97  XVII  Figure 3.6  Figure 3.7  2  H N M R spin echo spectra of deuterated p-xylene adsorbed in Na-ZSM-5 (6 wt %) as a function of the temperature 99 (a) Ff N M R spectrum of p-xylene-^ in ZSM-5 at a loading of 8 molecules per u.c. (b) H N M R spectrum of p-xylene-cfc in ZSM-5 at a loading of 6 molecules per u.c 102 2  Figure 3.7  (c) Ff N M R spectrum of p-xylene-^ in ZSM-5 at a loading of 8 molecules per u.c. (d) H N M R spectrum of p-xylene-^ in ZSM-5 at a loading of 6 molecules per u.c 103 2  Figure 3.8  S i CP M A S N M R spectra of the complex of p-xylene-^ in ZSM-5 (a) ait a loading of 6 molecules per u.c, (b) 7 molecules per u.c, and (c) 8 molecules per u.c 105  2 9  •  1  90  Figure 3.9  Cross-polarization pulse sequence for polarization transfer from Ff to  Si  107  Figure 3.10  (a) S i CP M A S N M R spectrum of ZSM-5 loaded with 8 molecules p-xylene-c/,5 per u.c. (b) Quantitative S i M A S N M R spectrum of the same sample.... 109 2 9  9  Figure 3.11  Schematic representation of a view down the straight channel of the ZSM-5 lattice showing the locations of the p-xylene molecules in the sinusoidal channel (XYL2), and in the intersection of the channels (XYL1) 112  Figure 3.12  Schematic representation of a view along the sinusoidal channel (100) ofthe ZSM-5 lattice showing the location of the p-xylene molecule (XYL2)  113  Figure 3.13  Intensities of the S i CP M A S N M R signals as functions of the contact time at room temperature for: (a) ZSM-5 with a loading of 6 molecules p-xylene-i/<5 per u.c, (b) ZSM-5 with a loading of 8 molecules p-xylene-^ per u.c 115  Figure 3.14  Plot of experimental T C P values vs. the calculated second moment (Aro )is values for the complexes of p-xylene-Je in ZSM-5 at room temperature 116  Figure 3.15  Intensities of the Si CP M A S N M R signals as functions of the contact time at room temperature for: (a) ZSM-5 with a loading of 6 molecules p-xylene-^ per u.c, (b) ZSM-5 with a loading of 8 molecules p-xylene-J^ per u.c 120  Figure 3.16  Plot of experimental T C P values vs. the calculated second moment (Aco )is values for the complexes of p-xylene-c/4 in ZSM-5 at room temperature 125  Figure 4.1  Pulse sequence for 2D exchange spectroscopy (experiment 2D-CPNOESY)  2 9  90  2  131  XVlll  Figure 4.2  C C P - M A S N M R spectra of the complex of 8 molecules per u.c. of p-xylene [methyl, C ] in ZSM-5at different temperatures 139  1 3  13  Figure 4.3  Schematic representation of a view down a straight channel of the ZSM-5 lattice showing the locations of the p-xylene molecules in the sinusoidal channel (XYL2), and in the intersection of the channels (XYL1) 140  Figure 4.4  Countour plot of a 2D-CPTEDOR experiment on the complex of 8 molecules per u.c. of p-xylene [methyl, C ] in ZSM-5 at 273 °K 142 13  Figure 4.5  Countour plots of 2D-CPNOESY experiments at the mixing time indicated on the complex of 8 molecules per u.c. of p-xylene [methyl, C ] in ZSM-5 carried out at 297 °K 147 13  Figure 4.6  Countour plots of 2D-CPNOESY experiment on the complex of 8 molecules per u.c. of p-xylene [methyl, C ] in ZSM-5 carried out at 273 °K 148 13  Figure 4.7  Cross section plots from the 2D N O E S Y spectrum of the complex of 8 molecules of p-xylene[methyl, C ] in ZSM-5 at 297 °K at different mixing times for the exchange between Z l and Z2 152 13  Figure 4.8  Cross section plots from the 2D N O E S Y spectrum of the complex of 8 molecules of p-xylene[methyl, C ] in ZSM-5 at 297 °K at different mixing times for the exchange between SI and S2 153 13  Figure 4.9  Graphs of the ratio of intensities for the intramolecular exchange involving the molecules located in the zig-zag channels obtained from the 2D-CPNOESY spectra of the complex of 8 molecules per u.c. of p-xylene [methyl, C ] in ZSM-5 as a function of the mixing time x at the different temperatures indicated 155 13  m  Figure 4.10  Graphs of the ratio of intensities for the intramolecular exchange involving the molecules located in the straight channels obtained from the 2D-CPNOESY  13 spectra of the complex of 8 molecules per u.c. of p-xylene [methyl, C] in ZSM-5 as a function of the mixing time x at the different temperature indicated 156 m  Figure 4.11  Arrhenius plots of the rate constant vs. the inverse of absolute temperature used to obtain the activation energy for the intramolecular exchange of the molecules located in the zig-zag channels 158  Figure 4.12  Contour plots of 2D-CPNOESY experiments on the complex of 6 molecules per u.c. of p-xylene [ C H , C ] in ZSM-5 carried out at 297 °K 159 13  3  xix Figure 4.13  Graph of the ratio of intensities for the intramolecular exchange of the molecules located in the zig-zag channels obtained from the 2D-CPNOESY spectra of the complex of 6 molecules per u.c. of p-xylene [methyl, C ] in ZSM-5 as a function of the mixing times x at 297 °K 160 l3  m  Figure 4.14  Figure 5.1  Schematic representation of the p-xylene molecule with its C 2 and C 3 rotation axes 163 S i CP M A S N M R spectrum of ZSM-5 loaded with 8 molecules of p-xylene-ek per u.c, contact time 5 ms at (a) 293 K , (b) 273 K 171  29  Figure 5.2  Intensities of the S i CP M A S N M R signals as functions of the contact times at a temperature of 273 K for the complexes of xylene-afc: (a) with a loading of 6 molecules per u.c, (b) with a loading of 8 molecules per u.c 173  Figure 5.3  Intensities of the S i CP M A S N M R signals as functions of the contact times at a temperature of 273 K for the complexes of xylene-J^: (a) with a loading of 6 molecules per u.c, (b) with a loading of 8 molecules per u.c 177  Figure 5.4  Plot of experimental Tcp values vs. the calculated second moment (Aco )is values for the complexes of p-xylene-^ in ZSM-5 at a temperature of 273 K , (a) with a loading of 6 molecules per u.c. (b) with a loading of 8 molecules per u.c 181  Figure 5.5  Plot of experimental T C P values vs. the calculated second moment (Aco )is values for the complexes of p-xylene-<£/ in ZSM-5 at a temperature of 273 K , (a) with a loading of 6 molecules per u.c. (b) with a loading of 8 molecules per u.c 182  Figure 5.6  (a) S i CP M A S N M R spectrum of ZSM-5 loaded with 8 molecules p-xylene-^ per u.c. at a temperature of 273 K , calculated from the Tcp/(Aco )is correlation, (b) The experimental S i CP M A S N M R spectrum obtained at a temperature of 273 K with a contact time of 5 ms 184  2 9  29  29  29  Figure 5.7  (a) S i CP M A S N M R spectrum of ZSM-5 loaded with 8 molecules p-xylene-^ 29  2  ,  per u.c. at a temperature of 273 K , calculated from the Tcp/(Aco )is correlation, (b) The experimental S i CP M A S N M R spectrum obtained at a temperature of 273 K with a contact time of 5 ms 185 29  70  Figure 6.1  (a) Quantitative Si M A S N M R spectra of ZSM-5 with increasing concentrations of p-xylene. The numbers indicate the number of p-xylene molecules sorbed per 96 T atom and proton decoupling during acquisition (b) S i CP/MAS N M R spectra of the same samples 190 29  XX  Figure 6.2  2  Figure 6.3  2  Figure 6.4  H N M R spectra of p-xylene-d* in ZSM-5 at a loading of 3 molecules per u.c. at the temperatures indicated 194 H N M R spectrum of p-xylene-d<; in ZSM-5 at a loading of 3 molecules per u.c.. at 193 K 195  (a) S i CP M A S N M R spectrum of ZSM-5 loaded with 3 molecules p-xylene-cfc per u.c. at 233 K., contact time 5 ms, recycle delay 2 s. (b) Quantitative S i M A S N M R spectrum of the same 197 2 9  2 9  Figure 6.5  1 3  Figure 6.6  2 9  Figure 6.7  C C P / M A S N M R spectra of the complex of [ CH ] p-xylene in ZSM-5 at the different temperatures indicated 198 13  3  S i M A S N M R spectra of the complex of ZSM-5 with 3 molecules of p-xylene-d<5 per u.c. at the different temperatures indicated 200 Contour plot of an I N A D E Q U A T E on ZSM-5 with 3 molecules per u.c. of pxylene at 263 K  201  Figure 6.8  Intensities of the S i CP M A S N M R signals as functions of the contact time for ZSM-5 with a loading of 3 molecules of p-xylene-dg per u.c. at the temperatures indicated 204  Figure 6.9  Intensities of the S i CP M A S N M R signals as functions of the contact time for ZSM-5 with a loading of 3 molecules of p-xylene-d^ per u.c. at the temperatures indicated 206  Figure 6.10  2 9  2 9  S i CP M A S N M R spectra of ZSM-5 loaded with 3 molecules p-xylene-ds per u.c. at 233 K , calculated from the Tcp/ (Aco )is correlation 215  2 9  2  Figure 6.11  S i CP M A S N M R spectra of ZSM-5 loaded with 3 molecules p-xylene-^ per u.c. at 233 K , calculated from the Tcp/(Aco )is correlations 216  2 9  2  Figure 6.12  Three-dimensional representation of the structure of the low-loaded ZSM-5 with 3 molecules of p-xylene from solution 14 seen (a) along the y axis, (b) along the x axis 217  Figure 6.13  Three-dimensional representation of the structure of the low-loaded ZSM-5 with 3 molecules of p-xylene from solution 58 seen (a) along the y axis, (b) along the x axis 218  xxi Figure 6.14  Three-dimensional representation of the structure of the low-loaded ZSM-5 with 3 molecules of p-xylene from solution 96 seen (a) along the y axis, (b) along the x axis 219  Figure 6.15  Plots of experimental T C P values vs. the calculated second moments (Aco )is values for the complex of 3 molecules per u.c. of p-xylene-^ in ZSM-5 at 233 K , for the best solutions 220  Figure 6.16  Plots of experimental Tcp values vs. the calculated second moments (Aco )is values for the complex of 3 molecules per u.c of p-xylene-^ in ZSM-5 at 233 K , for the best solutions, as indicated in the figure 221  Figure 6.17  Plots of experimental Tcp values vs. the calculated second moments (Aco )is values with motion for the complex of 3 molecules per u.c. of p-xylene-de in ZSM-5 for solution 58 at the temperatures indicated in the figure 224  Figure 6.18  Plots of experimental Tcp values vs. the calculated second moments (Aco')is values for the complex of 3 molecules per u.c. of p-xylene-^ in ZSM-5 for solutions 14, 58, and 96 at 213 K 225  Figure 7.1  Pulse sequence for rotational echo double-resonance (REDOR) S i N M R . In the first experiment, a conventional spin echo acquired after n rotor cycles provides the reference signal, So, and no pulses are applied on the ' H channel. In the second experiment, 180° pulses are applied to the ' H channel twice per rotor cycle, and the modified signal S, is recorded 231  Figure 7.2  Diagram showing the relationship between the spinning axis, the external magnetic field Bo, and the I-S heteronuclear dipolar vector 233  Figure 7.3  The 79.48 M H z REDOR S i N M R spectra of ZSM-5 loaded with 8 molecules of p-xylene-dg per u.c. at 273 K . (a) Full spin echo spectrum, So. (b) Rotational-echo spectrum, Sf. (c) Difference spectrum (AS) between the full spin echo spectrum, So and the rotational-echo spectrum, Sf. 242  Figure 7.4  Evolution ofthe REDOR Si('H) signals for the S i peaks in ZSM-5 loaded with 8 molecules of (a) p-xylene-^ per u.c. at 273 K , with v = 2.1 kHz, (b) p-xylene-^ per u.c. at 273 K , with v = 2.08 kHz 243  2  2  2  29  29  29  2 9  r  r  Figure 7.5  Evolution ofthe REDOR Si('H) AS/S ratios for the sample of ZSM-5 loaded with 8 molecules p-xylene-fifc per u.c. at 273 K , with v = 2.1 kHz 244 29  0  r  Figure 7.6  Evolution ofthe REDOR Si('H) AS/S ratios for the sample of ZSM-5 loaded with 8 molecules p-xylene-c/^ per u.c. at 273 K , with v = 2.8 kHz 247 29  0  r  XXII  Figure 7.7  Evolution of the REDOR Si('H) AS/S ratios for the sample of ZSM-5 loaded 29  0  with 8 molecules p-xylene-dg per u.c. at 273 K , with v = 2.8 kHz  251  Figure 8.1  Pulse sequence for rotational echo double-resonance (REDOR) S i N M R  259  Figure 8.2  Pulse sequence for transferred echo double-resonance (TEDOR) S i N M R , in  Figure 8.3  which 180 pulses are applied for n rotor cycles to the C (I) spins, shown here at x/4 and 3T/4 in each rotor cycle 262 Pulse sequence for two-dimensional heteronuclear correlation TEDOR experiment with preliminary evolution of I spin magnetization during the ti time period, and detection of S spin magnetization during the ti time period 263  r  2 9  z y  0  Figure 8.4  1 3  The 79.48 M H z REDOR S i N M R spectra of ZSM-5 loaded with 8 molecules of p-xylene [ C, CH ]per u.c. at 273 K 267 2 9  13  3  Figure 8.5  Evolution of the REDOR S i ( C ) AS/S ratios for the sample of ZSM-5 loaded with 8 molecules p-xylene-[ C, CH ] per u.c. carried out at 273 270 29  13  0  13  3  Figure 8.6  Evolution of the REDOR S i ( C ) AS/S ratios for the sample of ZSM-5 loaded with 8 molecules p-xylene-[ C, CH ] per u.c. carried out at 273 K 278 29  13  0  13  3  Figure 8.7  Evolution of the REDOR S i ( C ) AS/S ratios for the diluted sample of ZSM-5 loaded with 4 molecules p-xylene-[ C, CH ] per u.c. and 4 molecules p-xylene (natural abundance) carried out at 273 K 279 29  13  0  13  3  Figure 8.8  Evolution of the REDOR S i ( C ) AS/S ratios for the diluted sample of ZSM-5 loaded with 4 molecules p-xylene-[ C, CH ] per u.c. and 4 molecules p-xylene (natural abundance) carried out at 273 K 285 29  13  0  3  Figure 8.9  S i N M R spectra of ZSM-5 loaded with 8 molecules of p-xylene [ C, CH ]per u.c. at 273 K , showing the evolution of the TEDOR S i ( C ) S signal 290  2 9  13  3  29  13  f  Figure 8.10  Evolution of the TEDOR S i ( C ) AS/S ratios for the sample of ZSM-5 loaded with 8 molecules p-xylene-[ C, CH ] per u.c. at 273 K 291 29  13  0  3  XX111  Symbols and Abreviations A  Angstrom unit; 1 A = 10" m.  Bo  strength of the static magnetic field.  Bi  strength of the radiofrequency field during a pulse.  COSY  chemical shift correlation spectroscopy.  CP  cross polarization.  x  correlation time.  c  10  D  Dipolar coupling constant.  F i , F2  frequency dimensions corresponding to ti and t2.  FID  free induction decay.  FT  Fourier transformation.  h  (i) hour. (ii) Planck constant.  Hz  Hertz (unit of frequency).  I, S  (i) general representation for nuclear spins, where I and S refer to two different types of nuclei. (ii) spin quantum numbers for I and S nuclei, respectively.  INADEQUATE  incredible natural abundance double quantum transfer experiment.  J  scalar J-coupling.  MAS  magic angle spinning.  m  number of rotor cycles of dipolar dephasing after the transfer of coherence in TEDOR experiments.  ms  millisecond.  xxiv Mo  equilibrium macroscopic magnetization of a spin system in the presence of Bo  MHz  megahertz ( l x l O Hz).  n  (i) number of rotor cycles of dipolar dephasing in a REDOR experiment.  6  (ii) number of rotor cycles of dipolar dephasing before the transfer of coherence in TEDOR experiments. NMR  nuclear magnetic resonance.  NOESY  nuclear Overhouser effect spectroscopy.  ppm  parts per million frequency scale = (signal frequency/SF)* l x l 0 .  REDOR  rotational echo double resonance,  r.f.  radiofrequency.  s  second.  SF  spectrometer frequency, e.g. 400.13 M H z for *H in a magnetic field of 9.4 T.  Sf, So  signal intensities in the REDOR experiment with and without dephasing pulses, respectively.  AS  REDOR difference siganl; AS= S - S .  S/N  signal to noise ratio.  6  f  0  van Vleck heteronuclear second moment for the Si-H dipolar coupling. van Vleck homonuclear second moment for the H - H dipolar coupling. TEDOR  transferred echo double resonance.  ti  variable evolution time period in two-dimensional N M R experiments.  t2  detection period in two-dimensional N M R experiments.  XXV  Ti  spin-lattice relaxation time.  Tip  spin-lattice relaxation time in the rotating frame.  T2  spin-spin relaxation time.  T2*  spin-spin relaxation time including the effects of magnetic field inhomogeneity.  Tcp  cross-polarization time constant.  TGA  thermogravimetric analysis.  TMS  tetramethyl silane (chemical shift zero reference for ' H , C , and S i N M R ) .  T-site  tetrahedral crystallographic site in the zeolite framework.  5  chemical shift (usually in ppm).  13  2 9  y  x  v  r  frequency of sample rotation (in Hz).  x  r  rotational period (time for one complete rotor cycle, T =l/v ).  a>o  gyromagnetic ratio of nucleus X .  r  Larmor precession frequency.  r  xxvi Acknowledgement I would like to take this opportunity to thank the many people who helped and supported me throughout my Ph.D. studies, and who make possible the culmination of my thesis. I would like to sincerely thank Dr. Colin Fyfe for his guidance, ideas, advice and support through all my research work. I am sincerely indebted to Dr. Hiltrud Grondey for all her time and patience in helping me learn more about N M R and also for being a great friend who always supported and provided me with her excellent advice. I want to thank Tom Markus of the Electronic Engineering Service whose great skills and knowledge helped us to solve all our instrument problems, and his cheerful personality always provided hope when things looked a little bleak. Also I want to thank Cedric and Ron of the Mechanical Engineering Service who helped me to build the low temperature system I used in this work. I gratefully acknowledge the financial assistance of P D V S A INTEVEP for my scholarship. I am also very grateful to all the people in our group, specially to Almira, Kirby, Andrew (Lui), Patty and Holger, who make my time in U B C so enjoyable and help me so much to adapt to a new city. And finally, I would like to thank my family for all their support, specially to my husband Anibal, who always gave me his support, help and love to follow my dream of finishing this Ph. D. and also for being there in my moments of great joy and sadness. And finally to my little girls Adriana and Alexandra who did not see too much of my face when I was working but gave me the inspiration to finish this big job. God bless them.  To Adriana and Alexandra my sweet inspirations  1  CHAPTER ONE INTRODUCTION  1.1. 1.1.1  Z E O L I T E M O L E C U L A R SIEVES INTRODUCTION  Zeolites are very important microporous inorganic materials widely used in industrial applications as catalysts, molecular sieves, ion exchange resins, and adsorbents. ' ' '  1 2 3 4  Zeolites were first recognized as a new type of mineral in 1756 with the discovery of stilbite. The word zeolite has Greek roots and means "boiling stones", an allusion to the visible loss of water noted when natural zeolites are heated. In the thirties, long before zeolites were used as catalysts, the molecular sieving properties of zeolites and their potential as selective sorbents in separation processes were recognized by McBain  5  who in 1932 selectively adsorbed molecules in zeolites and coined the  term "molecular sieves". Barrer in 1941 also extensively studied the molecular sieving ability of zeolites ' , and derived the hydrogen forms of zeolites which are strong acid catalysts. 6  7  8  From a chemist's stand point, zeolites are crystalline inorganic polymers based on a framework of XO4 tetrahedra linked to each other by the sharing of oxygen atoms, where X may be trivalent A l or tetravalent Si atoms. The aluminium tetrahedra in the structure determine the charge. This is balanced by cations that occupy non-framework positions.  A representative  empirical formula is written as: M (A10 ) (Si0 ) .mH 0 x/n  2  x  2  y  2  Where M represents the exchangeable cations of valence n, which neutralize the net negative charge of the zeolite framework arising from the A I O 4 " tetrahedra, and mHiO represents the 5  2  water molecules of hydration.  The zeolite frameworks are very open and contain a regular  system of channels and/or cavities in which the ions and water molecules are located. The Si/Al ratio is invariably found to be equal to or greater than one and can approach infinity for completely "aluminium free" zeolites. 1.1.2  ZEOLITE STRUCTURES 239  There are about 39 different natural occurring aluminosilicate zeolites ' ' . Successful application of several of these natural zeolites for ion exchange stimulated interest in producing their synthetic analogs. To date these sustained efforts in zeolite synthesis have produced at least 100 synthetics species with no known natural counterparts. Numerous attempts have been made to group or classify zeolites on the basis of different structural elements. As stated earlier zeolite frameworks consist of tetrahedral T atoms linked through common oxygen atoms to form a three-dimensional structure. Zeolite frameworks can also be thought of as consisting of finite or infinite (i.e. chain- or layer- like) component units. The recurring finite units are called secondary building units (SBU). One simple way of classifying zeolite structures is based on the SBUs, which describe all known zeolites frameworks as arrangements linking the 16 possible SBUs. The commonly occurring SBUs are shown in Figure 1.1. In a SBU, a tetrahedral (Si, Al) is present at each corner or termination, but the oxygen atoms are not shown. These bridging oxygen atoms are located approximately halfway between the tetrahedral atoms but not usually on the line joining them. The way in which these SBUs link to generate a structure is shown in Figure 1.2 for zeolite Z S M - 5 . Table 1.1 lists 10  some known structures classified by their S B U content, structure type (IUPAC nomenclature), and common names.  3  O  CD-  •  (a)  (b)  (f)  (c)  (g)  (h)  Figure 1.1 Secondary building units commonly occurring in zeolite frameworks (a) single four ring (S4R), (b) single six ring (S6R), (c) single eight ring (S8R), (d) double four ring (D4R), (e) double six ring (D6R), (f) complex 4-1, (g) complex 5-1 and (h) complex 4-4-1. (From reference 27).  (b)  (c)  Figure 1.2 Sheet projection of ZSM-5. (a) S B U in pentasil zeolites, (b) linkage of SBUs to form chains (c) Linkage of chains to generate layers in the ZSM-5 structure. (From reference 46)  4  Table 1.1  Classification of some zeolites  Secondary Building Units (SBU)  Structure Type (IUPAC nomenclature)  Name  S4R  ANA GIS PHI  Analcime Gismondine Phillipsite  S6R  ERI LTL MAZ OFF  Erionite Zeolite L Zeolite Omega Offretite  S8R  Occurs in many structures (i.e. chabazite, zeolite A) but with other SBU's  D4R  LTA  Zeolite A  D6R  CHA FAU FAU GME KFI  Chabazite Faujasite Zeolite X , Y Gmelinite zeolite ZK-5  4-1  NAT SCO THO  Natrolite Scolecite Thomsonite  5-1  MOR DAC MFI MEL  Mordenite Dachiardite Zeolite ZSM-5 Zeolite ZSM-11  4-4-1  HEU STI  Heulandite Stilbite  The kind of building units most suitable for the classification of zeolites depends on the properties under consideration. Where interest in a particular zeolite is based on its ability to selectively adsorb one component of a mixture over another, a detailed structure is not necessary.  5  It is however important to identify the size of the pore opening necessary to achieve the desired selectivity. In Figure 1.3 are shown some selected zeolites together with the apertures of their respective channels. Zeolites can be grouped into six categories according to the number of oxygen atoms in their largest pore ring as indicated below. 1.1.2.1  6-Membered Oxygen Ring Systems: In almost all 6-membered oxygen ring systems, the apertures are actually windows  rather than channels. These windows typically connect largest cavities or "cages". Examples of zeolites in this group are: sodalite, afghanite, dodecasil 1H, liottite, Linde N , melanophlogite, ZSM-39, nonasil, sigma-2 and AIPO4-I6. None of these are of any catalytic significance since their apertures are too small even for molecules such as methane to enter. These materials can ion exchange smaller ions such as N a , C a , L a , as long as they are not hydrated. +  2+  2+  1.1.2.2 8-Membered Oxygen Ring Systems: The 8-membered oxygen ring systems include most of the earliest known shape selective small pore zeolites such as Linde A , erionite, and chabazite. Member of this group adsorb straight chain molecules, such as n-paraffins and olefins and primary alcohols. The pore/channel systems of these zeolites also contain interconnecting supercages, which are much larger than the size of the connecting windows. 1.1.2.3 10-Membered Oxygen Ring Systems: The 10-membered oxygen ring systems are also known as medium pore zeolites. 11  Among the varieties of unique crystal structure types in this group are ZSM-5  12  and ZSM-11  (which are known as pentasils), Theta 1 (which is isostructural with ZSM-22, KZ-2, ISI-1, and Nu-10), ZSM-23, ZSM-48, partheite, and laumontite.  6  ZEOLITE A  Figure 1.3 The framework structures of selected zeolites together with the apertures of their channels as defined by the linking oxygen atoms (From reference 9).  7  Except for partheite and laumontite, which have puckered 10-membered oxygen rings in their structure, almost all medium pore zeolites are synthetic in origin. Zeolites with ten oxygen atoms in their largest rings are more siliceous than previously known zeolites. Among the zeolites in this group, only ZSM-5, ZSM-11, and NU-87 have bidirectional intersecting channels.  The others have non-intersecting unidirectional channels.  ZSM-5 has received the most attention by far, and serves as a prime example of the unique role of medium pore zeolites in catalysis. ZSM-5 can be synthesized by using organic molecule ions such us tetrapropyl ammonium bromide, as directing agents in the reaction mixtures (templates). When the zeolite is crystallized from solution , the organic molecules are incorporated into the 13  zeolite crystals, filling the intracrystalline void space either as organic cations or as occluded salt molecules . 14  1.1.2.4 12-Membered Oxygen Ring Systems: Zeolites in the group of 12-membered oxygen ring systems are also known as large pore zeolites. Prior to the discovery of VPI-5, these materials had the largest pores of all molecular sieves. They include the faujasite family of zeolites: zeolites X , zeolite Y , mordenite, zeolite L , zeolite beta, etc. Several of these have been the focus of much catalysis research because of their unique pore structure. Zeolite beta was the first synthetic high silica zeolite (SiO2/Al2O3>20). For catalytic applications, the most widely used zeolite remains the synthetic faujasite, zeolite Y . 1.1.2.5 Larger than 12-Membered Oxygen Ring Systems: In recent years systems with more than 12-membered oxygen rings have been discovered. Beginning with the announcement of VPI-5, a crystalline aluminophosphate with an 18-membered oxygen ring system in 1988 ' , extensive research into very large pore molecular 15 16  8  sieves was undertaken. The structure of VPI-5 is defined by an uni-dimensional channel of 18membered oxygen rings with a free diameter of 12.5 A  12  '  17  . The VPI-5 structure is not  particularly stable especially at high temperatures and when exposed to steam. Other very large 18  structures include AIPO4-8 (MCM-37), which contains 14-membered oxygen rings , and cloverite, a gallophosphate, which contains 20- and 8-membered oxygen ring dual pore systems . Strictly speaking these materials are not zeolites, although some authors include them 19  as zeolites . To date, however, no aluminosilicate zeolites containing more than 12- membered 20  oxygen rings have been identified.  1.1.3 APPLICATIONS OF ZEOLITES: 1.1.3.1 As Molecular Sieves: The remarkable sorptive properties of zeolites have been recognized, as have their ionexchange capacities ' ' . They are capable of ionic and molecular sieving, the size and shape of 2 8 21  the admitted species being selected by the dimension of the aperture openings in the zeolite. The size of the zeolite pore openings is determined by: (1) The number of tetrahedral units, or, alternately, the number of oxygen atoms required to form the pores. (2) The nature and the locations of the cations that are present. (3) The Si/ A l ratio. Table 1.2 lists some commercially available zeolites along with their pore sizes, compositions, and sorption capacities toward different molecules. The application of zeolites as molecular sieves is based in their ability to adsorb one component of a mixture over others. This property depends on the internal dimension of the intracrystalline channel structure. For example zeolites A and X differ in their adsorption  9  properties toward organic molecules. In a process that requires the separation of linear from branched paraffins, Ca exchanged zeolite-A would be the preferred zeolite. The size of the pore opening of this zeolite (4.5 A) results in selective adsorption of the small unbranched molecules. However the large pore of zeolite X (7.4 A) would not be selective in such as process, as it will adsorb both linear and branched hydrocarbons. The ease by which zeolites undergo ion exchange, replacing the cations held in their structures by ions present in a external solution, is used commercially in many industrial 2 8 22  processes ' ' . Some examples of these processes are: • As components in detergent for water softening (exchanging C a  2+  for Na ). +  • Treatment of brackish water to remove ammonia. • Recovery of precious metals (as complex cations). • Treatment of liquid nuclear effluent (to remove radioactive species from solution). By appropriate adjustment of their cations very delicate size exclusion separations can be done, for example: • Gas separation, e.g. n-paraffins are accepted by Molecular Sieve 5 A (CaA) while i-paraffins are excluded by virtue of their larger kinetic diameters. • Gas purification, e.g. 13X zeolite (Na faujasite) is used to remove sulphur and nitrogen containing molecules from gaseous environments. 1.1.3.2 As Catalysts: Zeolite molecular sieves have very important applications in many areas of catalysis, generating intense interest in these materials in industrial and academic laboratories ' ' ' . 1 4 20 23  Their importance to industrial catalysis can be attributed to their unique combination ofthe following properties:  10 • High internal surface area (>600 m7g). • Uniform pores with one or more discrete sizes. • Presence of ion exchangeability produces highly dispersed catalytically active sites, such as highly acidic sites when the exchangeable cations are replaced by protons. • Good thermal stability to withstand harsh industrial environments. • Ability to adsorb and concentrate hydrocarbons. Because the pores of the zeolites are similar in size to many organic molecules of practical interest, it was possible to design novel catalysts on a molecular level by controlling the ingress or egress of reactants and products through them, originating a new type of catalyst known as shape selective catalyst. Beginning with the original discovery of selective conversion of long straight chain molecules into smaller molecules using small-pore zeolites, the realm of industrial applications of shape selective catalysis has been extended by the discovery of ZSM-5 and other medium pore zeolites ' . Medium pore zeolites can selectively convert both linear and 22 23  selected branched molecules, single ring aromatics, and naphthalenes with critical molecular dimensions less than about 6 A. Some major commercial processes making use of zeolite catalysts are listed in Table 1.3. Faujasitic zeolites are amongst the most widely used of all commercial zeolites. They far surpass the performance of their silica-alumina gel predecessors, and possess the useful property of being sufficiently thermally stable to withstand regeneration at high temperatures . 24  The reactivity and selectivity of molecular sieve zeolites as catalysts are determined by active sites provided by an imbalance of charges between the silicon and the aluminium atoms in the framework. Each aluminium atom contained within the framework structure has the potential to produce an active acid site . Classical Bronsted and Lewis acid models have been  Table 1.2 Commercially available zeolites (from ref. 26) Pore Size Zeolite  Composition  Sorption Capacity CH  Cation  H0  n-C6Hi4  2-3  Na  28  14.5  16.6  7.4  3-6  Na '  26  18.1  19.5  USY  7.4  >3  Na  11  15.8  18.3  A  3  2  Na/K  22  0  0  A  4  2  Na  23  0  0  A  4.5  2  Na/Ca  23  12.5  0  Beta  6.8  20  H  22  15  20  Chabazite  4  8  "N"  15  6,7  1  Clinoptilolite  4x5  1.1  "N"  10  1.8  0  Erionite  3.8  4  "N"  9  2.4  0  Ferrierite  5.5x4.8  10-20  H  10  2.1  1.3  L-type  6  6-7  K  12  8  7.4  Mazzite  5.8  7  Na/H  11  4.3  4.1  Mordenite  6x7  10-12  Na  14  4  4.5  Mordenite  6x7  10-20  H  12  4.2  7.5  Offretite  5.8  8  K/H  13  5.7  2  Phillipsite  3  4  "N"  15  1.3  0  ZSM-5  5.5  >20  H  4  12.4  5.9  (A)  Si0 /Al 0  X  7-4  Y  2  2  3  2  "N" = mineral zeolite, cations variable and usually Na, K, Ca, Mg. USY = ultrastable Y.  6  I2  12  used to classify the active sites on zeolites. Bronsted acidity is proton-donor acidity; this occurs in zeolites when the cations balancing the framework anionic charge are protons. Lewis acidity is electron acceptor  acidity, for example, a trigonally coordinated aluminium atom is 27  electrodeficient and can accept an electron pair, thus it behaves as a Lewis acid . The Bronsted acidity can be obtained by: (a) Decomposition of the N H 4 ion-exchanged form: +  calcine  NaZ + NH4CI —> N H Z — > N H + H Z 4  3  500°C  (b) Hydrogen-ion exchange: H + NaZ —> HZ + N a +  +  The "protonated" form contains protons associated with negatively charged framework oxygens linked into aluminium tetrahedra creating acidic Bronsted sites. At 550 °C protons can be lost in the form of water with the consequent formation of Lewis sites as shown below:  Bronsted sites  Lewis sites  The acid strength and number of acid centers (both Bronsted and Lewis acid centres) can be adjusted in a controlled way during synthesis and/or by subsequent treatments. The framework (or lattice) Si/Al ratio is a reflection of the number of potential acid sites (protons). In general zeolites with larger Si/Al ratios have stronger acid sites and better  13  thermal and hydrothermal stability. Also they are more organophilic and therefore have different sorption selectivities. Zeolites can be synthesized in a range of different Si/Al ratios or they can be modified by post-synthesis chemical treatment to increase the Si/Al ratio and stabilize the framework structure . 23  The treatment of large pore zeolites, particularly zeolite Y , with silicon hexafluoride or ammonium hexafluorosilicate at relatively low temperature (<100 °C) has become a widely accepted and commercially practiced method for producing high silica zeolites ' . The 28 29  problems with these procedures are: (1) Aluminium is preferentially removed from the outside of the zeolite crystal. (2) It is necessary to remove every trace of fluoride in order to preserve thermal and hydrothermal stability . 30  Other halides such as SiCU have also been used for simultaneous aluminium extraction and isomorphous silicon substitution. In NaY nearly perfect substitution of silicon from framework aluminium has been obtained by treating the zeolite with gaseous SiCLj at 480 31  °C  . The substitution appears to proceed according to the following reaction:  Sr  0 -Si  O  Al  0  0 O  Sf  SiCl  -Si  O  Si  0  O  Si  + M[A1C1].  Table 1.3:  Some commercial processes using zeolite catalysts (from ref. 40)  Process  Catalyst  Advantage  Catalytic cracking  R E Y (REX, R E H Y , H Y , REMgY)*  Selectivity and high conversion rates  Hydrocracking  X , Y , mordenite loaded with Co, Mo, W, N i , also H Y , Ca Mg Y and H - ZSM-5  High conversion rates  Selectoforming  Ni-clinoptilolite / erionite, Ni-erionite  Increase in octane number  Hydroisomerization  Pt-mordenite  Converts low octane and hexane feed to higher octane materials  Dewaxing  Pt-mordenite  Removes long chain paraffins  Benzene alkylation  ZSM-5  Ethylbenzene and styrene production with low by-product yield  Xylene isomerization  ZSM-5  Increase in p-xylene yield with low by-product yield  Methanol to gasoline conversion  ZSM-5  High gasoline yield with high octane rating  NOx reduction  H-mordenite  Effluent clean-up in nitric acid and nuclear reprocessing plants  * R E Y stands for zeolite Y materials with rare earth metal cations  15  Hydrothermal treatments are also used in the dealumination of zeolites. It is well known that steaming converts framework tetrahedral aluminium to nonframework octahedral aluminium via hydrolytic cleavage, with the concomitant production of extra-lattice aluminium 23  in the pores. Further treatment will then produce reinsertion of silica into the framework . In Figure 1.4 is shown a schematic representation for the proposed mechanism of hydrothermal dealumination. In the case of low Si/Al ratio zeolites, steaming can make the framework more robust and resistant to thermal damage and acid attack. This is usually the procedure used to obtain highly siliceous and crystalline ZSM-5. The other very important and unique feature of zeolites is their shape selective properties. The shape selectivity of zeolites means that only molecules smaller than the aperture of the channels can react with the zeolite catalyst.  In addition, only those molecules whose  transition state geometry is smaller than the cavity and/or pore diameter can be formed or released. This is described schematically in Figure 1.5. 1.1.4  METHODS FOR THE CHARACTERIZATION OF ZEOLITE STRUCTURES  The previous discussion about the molecular sieves and catalytic properties of zeolites has shown that the unique combination of chemical reactivity, size and shape selectivity of these materials is intimately related to their structures. Thus for a complete understanding of the catalytic properties of specific zeolites, it is essential to have a complete description of the zeolite lattice framework and also of complexes of the framework with organic molecules. Ideally all zeolite structures should be capable of solution by the use of modern X-ray single crystal techniques and indeed naturally occurring species have been so studied. However in the case of synthetic materials, very few of them are available as suitable single crystals for  16  Si  0  b Si  0  0  0 0  b  NH;  Al  0  o  0  Si  Si  Si-  0  p  Si  Sr  0  0  Si  0  p  Si  Al  NHt  0  0  Si  p  0  0  0  Si  0  Si  0  Si  O  Si  0  Si  0  Si  0  Si  0  Si  0  Si  0  0  Al"  0  Si  Si  0  STEP 1:  [-NH, ]  H- ZEOLITE  0  0  ZEOLITE  deammoniation  0  Si  0  Si-  Si  0  0  Al  Si  0  STEP 2: Si  0  0  Si  Si  0  Si  0  0  Si  Si  0  hydrolysis [Al(OH^ ]  Si  0  0  Si  if Si  0 Sr  Si  0  H  0  H  0 Si  Si  0  0  Si  si  H  OH  0-  H  0  O  o — s i — o — s i — o — s i — o -  Si  0  Si  Si  Si  0  if  H  0  O  0  Si  0  0  if OH  Si  UNSTABLE INTERMEDIATE  Si  0 O  0  Si  0  Si  0  STEP:  DEALUMINATED ZEOLITE  Figure 1.4  Proposed mechanism for the hydrothermal dealumination of zeolites.  17  REACT ANT SELECTIVITY  PRODUCT SELECTIVITY  RESTRICTED TRANSITION STATE SELECTIVITY  Figure 1.5 Different kinds of size and shape selectivity in reactions within zeolite cavities. (From reference 27)  18  conventional X R D measurements. These materials are usually microcrystalline, with individual crystals of the order of a few microns. Even in the case of a suitable single crystal, it is extremely difficult to distinguish between the Si and A l atoms in the lattice by diffraction techniques, as they are relatively high atomic mass and differ by only one mass unit (28 and 27, respectively) and have almost identical X-ray scattering intensities. When single crystal X-ray methods are inapplicable, other techniques have been used for the investigation of zeolites structure. These mainly involve the following four different approaches. 1.1.4.1 Adsorption Studies A property that has been used extensively in characterizing molecular sieve materials is the ability to adsorb selected molecules. From an examination of adsorption properties, substantial structural information can be deduced about these materials. The most fundamental characteristic is the pore volume of the individual molecular sieve. Several probe molecules have been routinely used to determine the pore volume, including oxygen, n-hexane, and H 2 O . Other adsorbates that have been used include C O 2 , Ar, N 2 , and n-butane. Typically, several different probe molecules are utilized to provide a more meaningful determination of the pore volume. The adsorption measurements are taken on samples that have been previously calcined to remove the organic molecules used in their synthesis (templates) and/or hydration water. The adsorption ^9  -5-5  isotherms can be used to calculate the void volume using the Gurvistch rule ' . Adsorption capacities have been reported for selected organic molecules in zeolites ZSM-5 by several authors , as shown Table 1.4. Only p-xylene appears to show significant 34  discrepancy in capacity measurements that can be attributed to crystal size and quality.  19  Table 1.4 Adsorption capacities of hydrocarbons on HZSM-5 (from ref. 33) Hydrocarbon  HZSM-5/(a) T = 25 HZSM-5/(b) T = 25 HZSM-5/(c) T = 25 °C (molecules per °C (molecules per °C (molecules per u/c) u/c) u/c)  n-Hexane  7.6  8.14  8.2  3-Methyl pentane  6.0  6.74  5.7  Benzene  -  -  7.6  Toluene  6.6  -  -  p-Xylene  5.8  5.84  8.2  o-Xylene  -  -  5.4  1.1.4.2  Powder Diffraction  Methods' '™. 3  In this method, X-ray irradiation of zeolite powders (1-50 pm crystalline diameter) produces a scattering pattern from the regular arrays of atoms (or ions) within the structure. It reflects the framework and non-framework symmetry of the constituents of each zeolite to produce a diagnostic fingerprint. These diagnostic patterns can provide the identification of a known zeolite structure, and have an obvious use as quality control for known synthetic zeolites, but must be used with extreme caution, especially in the case of new zeolite structures. Recently, improvements in X-ray fluxes using synchrotron sources and development in data analysis techniques based on Rietveld methods '  have had a considerable impact in the area of zeolite  structure determination . X-rays from these sources are very intense, polarized and sharply 39  focused, and give therefore a great improvement in resolution and signal to noise in a powder diffraction experiment.  The Rietveld refinement method predicts the X R D pattern from  proposed structures, refines the structure to optimize the agreement with experimental and  20  presents data output of the closeness of fit between the experimental and computed patterns. The method can predict framework atom positions as well as the siting of cations . 40  1.1.4.3 Electron Microscopy  41  The technique of Scanning Electron Microscopy (SEM) is extensively used to characterize zeolite crystal morphologies. It is used in synthesis and quality control for the detection of mixed and new zeolite phases. High Resolution Electron Microscopy (HREM) can provide details of zeolite crystal symmetries, yielding information in real space at the subnanometer level. In some circumstances the high resolution makes it possible to observe the pore structure. It is the most appropriated way of examining defect and mixed phases in zeolites. 1.1.4.4 Nuclear Magnetic Resonance '  42 43  In recent years, high resolution solid state N M R spectroscopy has emerged as a very important technique in the characterization of zeolite structures. This method is complementary to X-ray diffraction measurements with the advantage of no having limitations regarding the zeolite crystal size.  N M R probes short range ordering and local structure, while X R D is  sensitive to long range ordering and periodicities. In principle, each of the three basic atomic constituents of the aluminosilicate framework of zeolites, silicon, aluminium, and oxygen are amenable to N M R measurements by *7 Q  the naturally occurring isotopes  *7 "7  1*7  Si, A l , and  1*7  O, respectively. However, the  O isotope has  very low natural abundance (0.037 %) and has a nuclear quadrupole moment (giving rise to line broadening), which make the application of 0 N M R very difficult, although some interesting 1 7  studies of 0 enriched silicates and zeolites have been published ' ' . 1 7  44 45 46  21  The  Al  27  isotope is 100% abundant, but also has a quadrupolar moment which  complicates the spectrum. In spite of that, Al N M R spectroscopy has been widely used in the 27  study of zeolite ' . 41 42  The  2 9  S i isotope has a natural abundance of 4.7 %, and no quadrupolar moment and thus  gives rise to relatively narrow resonance lines.  Si N M R spectroscopy has yielded the most  information about zeolite structure. Due to the importance of this technique in the present thesis, details of its applications in the study of zeolite structures will be discussed more extensively in Section 1.4.  22  1.2.  1.2.1  PRINCIPLES O F SOLID S T A T E N M R SPECTROSCOPY  MAGNETIC INTERACTIONS IN SOLID STATE N M R : The more important interactions in the solid state for a nucleus with a magnetic  moment located in a magnetic field B are: 0  (i) Zeeman interaction of the nucleus with the magnetic field. (ii) Dipolar interactions with other nuclei. (iii) Magnetic shielding interaction by the surrounding electrons giving rise to chemical shift. (iv) Scalar J-coupling to other nuclei. (v) Quadrupolar interaction present for nuclei with spin > 1/2. A general Hamiltonian for the interactions experienced by a nucleus of spin I in the solid state may thus be written as: H =H +H +H T  z  D  c s  + Hj + H  (1. 1)  Q  In a particular solid state system some interactions usually dominate the total Hamiltonian determining the characteristics of the spectrum. In Table 1.5 typical values for these different interactions are listed. In solution, molecules and ions reorient rapidly on the N M R time scale.  As a  consequence, the direct dipole-dipole and quadrupolar interactions are averaged to zero by yhe molecular motion, and the chemical shift is averaged to an isotropic value. The Hamiltonian in the liquid state is reduced to: H =H +H z  c s  + Hj  (1. 2)  23  Consequently in liquids the measurements of chemical shift 8 and indirect coupling J are significantly easier than in solids in which the interactions are anisotropic (orientation dependent) because of the relatively fixed positions of the molecules and have a stronger effect.  Table 1.5:  C nuclear spins interactions in a 4.7 Tesla field  Spin Interaction  Hamiltonian  Zeeman  H  Chemical Shift  Magnitude in Solution Magnitude in Solid  50 MHz  50 MHz  Hcs  isotropic value  up to 10 kHz  Dipolar  H  0  *15kHz  Scalar Coupling  Hj  «200 Hz  «200 Hz  0  up to 1 MHz  Dipolar Coupling to  • H  z  D  Q  Quadrupolar Nuclei  1.2.1.1 Zeeman Interaction  The Zeeman interaction occurs between the magnetic moment of the nucleus and the applied magnetic field B , yielding 21+1 energy levels (where I is the nuclear spin quantum 0  number) separated by h&o = yhBo, where y is the gyromagnetic ratio and coo is the Larmor precession frequency. Only nuclei with odd atomic mass or atomic number have a magnetic moment.  24  The Hamiltonian for this interaction may be written as Hz =  ftyB 'Iz. 0  (1.3)  This interaction is directly proportional to the magnetic field; thus the energy separations between the quantized levels are larger at higher magnetic fields. As a consequence the sensitivity of the N M R technique is improved due to the increase of the population difference between the energy levels. 1.2.1.2 Dipole-Dipole Interaction The dipolar interaction arises from the direct through space dipole-dipole interaction between two nuclei.  It is based on the interaction of the small local fields of the nuclear  magnetic moments; therefore the dipole-dipole coupling is independent of the applied magnetic field and depends on the spatial arrangement of the nuclei. For two isolated and different spins I and S (heteronuclear dipolar interaction), the interaction may be written as  H =h  2  D  I D S  (1.4)  where the factor h — ^ — - is called the dipolar coupling constant (in frequency units Hz), and  ris is the internuclear distance between the I and S spins, and po is the permeability constant (47ixlO" kgms" A" ) 7  2  2  A  The tensor D is a traceless tensor, thus its isotropic value is zero. This is the case for isotropic liquids where the random molecular motion averages it to zero.  25  The distance dependence of the dipolar interaction can be used to determine accurately distances between pairs of nuclei, and is the principle of the methodology derived in this thesis to get structural information about the location of sorbed molecules in host-guest complexes of zeolites.  The strong inverse distance dependence (1/r ) means that only close nuclei will 3  experience a strong interaction and because this is a through space interaction, atoms need not be bonded. The dependence of the dipolar interaction on the gyromagnetic ratios means that it is more important for nuclei with spin 1/2 with larger magnetic moments. For a single crystal with only one orientation for r i s , there are two lines in the spectrum of each different nuclear type with the resonance frequency given by Equation (1.5): v =v  0  ± ^ | ^ ^ ( l - 3 c o s 4 r AJT  2  ^ )  (1.5)  where 0is is the angle between the internuclear vector and the magnetic field, po is the magnetic permeability constant, and vo the resonance frequency in absence of dipolar interactions for the appropiate case. In a polycrystalline sample, where there are random orientations of the internuclear vector, the spectrum shows a dipolar powder pattern, as shown in Figure 1.6. The dotted curve is the powder pattern obtained by the averaging of Equation 1.5 for an isolated pair of spins and is called a Pake doublet . Inclusion of a broadening function to take into account smaller dipolar 47  interactions with other nuclei produces the full curve shown in Figure 1.6.  1.2.1.3 Chemical Shift Interaction The chemical shift is due to the screening of the applied magnetic field at a given nucleus by the surrounding electrons. In the solid state, the shift will be dependent on the orientation of  26  the molecule in the magnetic field. The three-dimensional nature of the shielding may be expressed as H = ^-TaB cs  (1.6)  Yl  A  where / and B are both vector quantities, a is a 3x3 matrix or second rank tensor called the A  chemical shift tensor. By a suitable choice of the coordinate system a may be converted to a diagonal form with three principal elements a n , G22, and 0-33.  chemical shift Figure 1.6 Powder pattern arising from dipolar interaction effects for a two-spin system. The dotted curve represents the spectrum for an isolated pair of nuclei and the solid trace shows the effect of neighbouring nuclei on the isolated system. (From reference 42)  27  In solution, the random tumbling of the molecules averages the chemical shift to its isotropic value a ., defined as av  a .= 1/3(011 + 022+033)  (1.7)  av  The chemical shift interaction (in frequency units) is linear with the magnetic field strength and is thus more important and proportionately larger at higher fields. The orientation dependence of the chemical shift interaction is illustrated in Figure 1.7. In a single crystal, an isolated nucleus will give rise to a sharp signal whose frequency is dependent upon the orientation of the crystal with respect to the applied magnetic field. However, the spectrum of a single nucleus in a polycrystalline material is a broad line whose exact shape depends on the principal elements of the shielding tensor. 1.2.1.4  Spin-Spin Interaction The spin-spin interaction is also called J-coupling or scalar coupling and arises from  indirect coupling between the two spins via bonding electrons. identical (homonuclear) or different (heteronuclear) spins.  This interaction can be with  For the heteronuclear case, the  interaction Hamiltonian for a pair of spin S and I may be written as H =2 D  7rhIJS  (1.8)  A  where J is the scalar coupling tensor. This interaction is independent of the magnetic field and is usually smaller than the other interactions under consideration (e.g. dipolar). In contrast to the direct dipolar interaction, the mechanism is through-bonds rather than through-space.  28  1.2.1.5 Quadrupolar Interaction In addition to the magnetic dipole moment, nuclei with spin quantum number I>l/2 exhibit an electric quadrupole moment eQ, which reflects the deviations from spherical symmetry of the electric charge distribution at the site of the nucleus. The quadrupolar interaction arises from the electrical interaction between the nuclear quadrupole moment eQ with the non-spherical symmetric electric field gradient (EFG) around the nucleus. It is magnetic field independent and may be described as in Equation 1.9: H = Q  / g i  (1.9)  A  where Q is the quadrupolar coupling tensor characterizing the three dimensional nature of the interaction. The magnitude of the interaction is such that it usually dominates the spectra of most nuclei with a quadrupole moment.  The quadrupolar coupling is a traceless tensor, i.e. its  isotropic value is zero. This is observed in solution due to the random isotropic molecular motion.  I  I  I  I  I  c h e m i c a l shift  Figure 1.7 A schematic representation of the chemical shift anisotropy: (a) A single crystal with two different orientations of a carbonyl function with respect to the external magnetic field 13  produces two different C resonances, (b) A polycrystalline sample results in the superposition of peaks resulting from all possible orientations, (c). A solution shows only the isotropic average as a result of rapid molecular motion. (From reference 42).  30 1.3.  RELAXATION TIME MEASUREMENTS IN NMR  The presence of molecular motion in solids provides a well defined relaxation mechanism for the nuclei via a modulation of the dipolar interactions; alternatively the measurement of relaxation times provides a very powerful technique for the detection and quantification of molecular motions. The determination of the spin lattice relaxation time (Ti), spin-spin relaxation time (T2), and spin-spin relaxation time in the rotating frame (Ti ) were very p  important in the evaluation of the experiments presented in this thesis and will be discussed in more detail. 1.3.1  SPIN-LATTICE RELAXATION TIME (Ti)  When a group of nuclear spins is placed in a static magnetic field Bo, a small but measurable magnetization M develops along the direction of Bo from a net alignment of the z  individual nuclear magnetic moments. At equilibrium, when the populations of spin-energy levels are given by the Boltzmann distribution, the net magnetization in the z direction, Mo, is given by the Curie law: 2N I(I + 1) 2  M =h 0  7  3kT  B  (1.10)  where N is the number of spins, y is the gyromagnetic ratio, h is the Planck's constant divided by 2TC, I is the nuclear spin quantum number, k is the Boltzmann's constant, and T is the absolute temperature. The rate at which M approaches Mo is generally given by a first-order differential z  equation as shown: dM _ -1 ( dt T,1 z  M -M ) Z  0  (1.11)  where Ti is the spin-lattice relaxation time. Integration of Equation 1.11 gives  31  M -M =Ce  (1.12)  Tl  Q  z  where C depends on the initial conditions. Several ingenious pulse sequences have been developed to measure j j ' ' ' ' 4 8  4 9  5 0  5 1  5 2  of  these, the Inversion Recovery Fourier Transform (IRFT) pulse sequence is the most commonly used technique and probably the most reliable. The following sequence is used: (180° - x - 90° -1 - acquisition),, where T is a variable delay and / is the waiting time which allows the system to return to thermal equilibrium. The values of t must be greater than 5Ti for quantitative reliability. The intensity of the signal for each i is related to Ti by Equation 1.12. 1.3.2  SPIN-SPIN RELAXATION TIME (T ) 2  When an isolated spin system is at equilibrium in a static magnetic field Bo, there is no net magnetization in the xy plane. If the spins are subjected to a (7t/2) RF pulse B i , the net z x  magnetization is rotated into the xy plane along the positive y axis. In a perfectly homogeneous magnetic field, Bo, the decay of magnetization in the xy plane is governed by T , the spin-spin or 2  transverse relaxation time  dt  T ' dt  T  2  2  and  M;- = M e y  Ti  0  (1.14)  Under these conditions, the rate of spin-spin relaxation, R =l/T , is related to the line 2  width at half-height v i / , for a Lorentzian line, by: 2  2  32  ^/2=4-=— 7rT  2  ( L i 5 )  n  In practice, the magnetic field is not perfectly homogeneous, nuclei in different regions of the sample experience slightly different applied fields, causing them to precess at slightly different frequencies. This results in an enhanced dephasing (see Figure 1.8) of the spins in the xy plane, and thus an effectively shorter spin-spin relaxation time T* . The observed line width 2  results from both field inhomogeneity and the natural T of the nuclei: 2  *  where T  2  is sometimes called the effective spin-spin relaxation time, and vi/ (obs) = vi/ (natural) + vi/ (inhomo) 2  2  J ^ ^ _ 1 _ 7lT  2  +  7lX  2  Z  (1-17)  2  A B ^  (  l  l  g  )  2K  where yABo/27t is the magnetic field inhomogeneity in Hertz. In general, measurements of T are much more difficult than those of T\. The errors in T 2  2  determination have been discussed in detail in references 53 and 54 Several novel techniques for measuring T when yABo/27i > 1/T have been devised. Most 2  2  of these are based on the famous Hahn spin-echo technique , 90 - T - 180 -T [echo], depicted in 55  Figure 1.8. The discussion that follows applies to a system with a single-line N M R spectrum and detection on resonance, unless otherwise stated. In 1954, Carr and Purcell reported the following multiple-pulse sequence: 56  90 - x - 180 -x [echo] - x -180 -x [echo] - x -180 -x [echo]-....  33  Figure 1.8 Schematic representation of the Carr-Purcell spin echo pulse sequence for measuring T relaxation times. 2  depicted in Figure 1.8. A l l pulses are applied along the x axis. The initial preparation pulse tips Mo to be along the positive y axis. Spins in different regions of the applied field Bo precess at frequencies slightly different from the Larmor frequency, causing a dephasing of M . The x y  slower-moving components  of M  x y  , labelled S in Figure 1.8, will appear to move  counterclockwise, while those faster moving components (F) appear to move clockwise in the xy plane. At time x after the 180° pulse (2x after the initial 90° pulse), the magnetization will refocus along the negative y axis. The refocusing and subsequent dephasing of the magnetization along the y axis are known as spin echoes. After a further time delay, x, the spins again lose coherence and another 180° pulse is required to refocus them. This sequence is repeated until  34  M  x y  has essentially decayed to zero. The intensity of each echo at t=2x, 4x, 6x, ... will depend on  T2 in the following way:  h) = he^2 1.3.3  (1.19)  SPIN-SPIN RELAXATION TIME IN THE ROTATING FRAME ( T ) JP  The spin-lattice relaxation time in the rotating frame, T i , is a first order time constant p  that characterizes the decay of Mo in a field B i that is generally much smaller than Bo. The measurement of this value is important in the investigation of molecular motions because it is sensitive to lower frequency molecular motions than is T i . It is also an important factor in many of the investigations of dilute spin system by cross-polarization techniques as discussed in Section 1.3. T i is the characteristic time constant for the decay of the magnetization along the p  on-resonance radio frequency field (Bi) in the rotating frame. The experimental technique used to obtain the T i relaxation time is called Forced Transitory Precession or 'Spin Locking' and is p  illustrated in Figure 1.9. A n on-resonance 90° pulse is first applied along x to bring the magnetization along y. The phase of this pulse is then shifted by 90°, thus it is now applied along y, that it, in the same direction that the magnetization vector. This second pulse is called the 'spin locking' pulse and while it is being applied, the spin are said to be 'spin locked'. In the absence of this pulse it would be a simple decay of the y magnetization due to T2 relaxation processes. The second pulse acts as a static field and the relaxation of the y magnetization is thus analogous to conventional spin-lattice relaxation and is called 'spin-lattice relaxation in the rotating frame'. The spin-locking is applied for a time x, during which there will be some decay of the y magnetization which may be detected by recording the FID immediately after the locking  35  pulse as shown in Figure 1.9.  The T j values can be obtained from the variation of signal p  intensity with x , as given by Equation (1.20) I =I e ^ . p (t)  1.3.4  0  (1-20)  DEPENDENCE OF RELAXATION TIMES ON MOLECULAR MOTIONS  The T i , T2, and T i p relaxation times are strongly dependent on the presence of molecular motions, which are all dependent on the correlation time x c of the motion. The general dependence of the relaxation times on motion is shown in Figure 1.10, assuming a dipolar mechanism for relaxation. The T i curves depend on the Larmor precession frequency as indicated, with v i > v 2 . The two curves differ at low temperatures but are identical in the high temperature limit. The spin-spin relaxation time ( T i ) curves are related to the spin-spin relaxation time T 2 curve, as shown in Figure 1.10. Since T 2 is proportional to 1/Av, the changes in T 2 curves mirror the changes in linewidth and second moment. Also shown in Figure 1.10, is T i p , the spin lattice relaxation time in the rotating frame. As it can be seen from the figure, its importance in the investigation of molecular motion is that its minimum occurs at temperatures much closer to the linewidth changes and it is thus sensitive to much lower frequency motions than T i .  36  Figure 1.10 General behaviour of the relaxation times, T\, T2, and T i , as a function of the temperature. (From reference 42). p  37  1.4.  1.4.1  M E T H O D S IN H I G H R E S O L U T I O N SOLID S T A T E N M R  MAGIC ANGLE SPINNING  As early as 1958, Andrew, Bradbury, and Eades used rapid sample rotation to narrow dipolarbroadened lines, and a year later'Andrew and Lowe independently recognized the significance of the magic angle (54.7°) ' . Although Andrew and Eades showed in 1962 that magic angle 57 58  spinning (MAS) could remove the broadening caused by chemical shift anisotropy, it remained for Schaefer and Stejskal in 1976 to combine magic angle spinning with cross polarization and dipolar decoupling to obtain high resolution C N M R of solids . 1 3  59  M A S subjects the solid to a motion which produces, to a first approximation, the same net averaging effect as rapid isotropic molecular tumbling in solution. The basis of this experiment is the observation that most of the spin interactions (e.g. chemical shift and dipolar interaction) depend on a term of the form of (3cos 9 - 1) where 8 is the angle between a vector r 2  and the magnetic field Bo. In the case of the dipolar interaction, the vector r is the internuclear vector ry, and in the chemical shift interaction, the vector r represents the principal axis of the shielding tensor. If coherent rotation of a solid sample is considered about an axis R that is inclined at an angle P to Bo (see Figure 1.11), the average of (3cos 0 - 1) about the conical path 2  indicated for the internuclear vector r is given by Equation 1.21 : 60  (3cos 0 - l ) 2  = l/2(3cos p - l)(3cos a -1) 2  avg  2  (1.21)  where the extremes of the angle 0 are a+(3 and o>p. The parameter a is fixed in a rigid solid, though (like 0) it takes all possible values i f the material is a powder. The term l/2(3cos p - 1), therefore, acts as a scaling factor on the dipolar powder pattern. Fortunately the angle a is under  38  Figure 1.11 Schematic representation of the geometric arrangement for mechanical sample spinning. The solid sample is rotated with an angular velocity co about an axis R, which is inclined at an angle a to the external magnetic field Bo. The specific molecule-fixed vector r makes an angle (5 with the rotation axis, and is inclined to the magnetic field by an angle 0, which varies periodically as the sample rotates. r  the control of the experimentalist. If 13=0 (i.e. rotation about Bo), l/2(3cos a - 1)=1, so there is no net effect on the spectrum. If (3=90° (i.e. rotation about an axis perpendicular to Bo), l/2(3cos a l)=l/2, so the powder pattern is scaled down by a factor of 2. The more interesting case is when p=54.7°, because: 3cos a=W3 and l/2(3cos a - 1)=0. Thus, (3cos 0 - l) g=0 for all the 2  2  2  av  orientations of 0. Therefore, the magic angle spinning reduces or eliminates dipolar interactions, reduces quadrupolar interactions to first order, and yields isotropic values for chemical shift. However, problems can arise because the rate of rotation required to average the dipolar interaction completely has to be greater than the static bandwidth expressed in Hz. This can be several tens of kHz (e.g. for ' H - ' H homonuclear interactions); and because such a speed cannot  39  be achieved in practice a broadening of the spectrum due to residual dipolar interaction may be observed. The same limitation applies to the averaging of the chemical shift anisotropy, resulting in spinning sidebands, located on each side of the isotropic chemical shift position and separated by distances equal to the spinning frequency. 1.4.2  HIGH POWER DECOUPLING OF PROTONS The concept of high power decoupling is analogous to that in solution-state N M R  spectroscopy in which decoupling (generally proton noise or W A L T Z decoupling) is employed to remove the scalar or J-couplings. In the solid state dipolar decoupling with much higher power levels is used to remove the much higher dipole-dipole interactions. For most dilute spin systems (e.g.  1 3  C , Si), in which the magnetically active nuclei of 29  interest are present in low concentration, the major line broadening interaction for the dilute spins is the heteronuclear dipolar coupling with the abundant spin system (usually protons). The local field, B | , at a nucleus I in the dilute spin system is altered by a nucleus j in the abundant 0C  spin system, as described in Equation (1.11): B  = Bo ± Lijrij- (3cos eij -1) 3  l o c  2  (1.22)  where Bo is the external magnetic field, p.j is the magnetic moment of a nucleus j , ry is the internuclear distance, 9y is the angle between the internuclear axis and the static field, and the plus and minus signs arise because the spins which modulate the local field may be oriented parallel or antiparallel to the applied external field. It is possible to eliminate this interaction by irradiating the abundant spin system with a strong RF field at its Larmor frequency. The effect of this decoupling irradiation is to induce rapid transitions in the abundant nuclei which cause their contribution to the effective local field to become zero on the N M R time scale. Since the interactions may be of the order of tens of kHz  40  in the solid state, the decoupling power level has to be much higher («lkW) than the relatively low decoupling power of ~5 W or less, commonly used in solution N M R 1.4.3  CROSS POLARIZATION (CP) The line narrowing techniques of dipolar decoupling and magic-angle spinning provide  the resolution necessary to obtain chemical and structural information on individual dilute spins in the solid state. However, in solid state, the conventional one-pulse Fourier transform N M R experiment suffers the disadvantage of requiring lengthy recycle delays because of the very often long spin-lattice relaxation time (Ti) and the low sensitivity that characterize rare spins such as 13  C or  29  S i . The technique of cross polarization, first introduced by Pines, Gibby, and  Waugh ' ' , provides both signal enhancement, and much shorter recycle delays. In this 61  62  63  experiment, spin polarization, and thus net magnetization, is transferred from the abundant spins to the dilute spins via the dipolar interaction. The magnetization transfer is accomplished using the pulse sequence showed in Figure 1.12, in which the abundant spins are *H and the rare spins  90 are  90  1  Si. The vector diagrams illustrating the behaviour of the H and  Si magnetization during  this pulse sequence are illustrated in Figure 1.13. The CP pulse sequence begins with a 90° pulse to the protons, which rotates the magnetization along the y axis in the rotating frame (see Figure 1.12 and 1.13). Then the proton magnetization is spin-locked by an on-resonance rotating frame radio frequency field, B i , along the y axis in the rotating frame. This state represents a high H  degree of polarization along  BIH,  which will decay with a characteristic time  TI H. P  At the  beginning of the contact period a RF field, Bisi, is applied to the S i nuclei, and its magnitude is 2 9  adjusted so that the Hartmann-Hahn condition is satisfied: YHBiH = YsiBisi (1.23)  41  Figure 1.12 Single-contact spin-lock cross-polarization pulse sequence showing the time dependence of the proton and silicon magnetizations.  B  t  (b)  0  00 90°phase shift of B 1H spin-lock protons W  H =YH 1H B  T <t<t  t=T  2  So apply rf power B 29  1 S i  Si «srYsi isi B  Figure 1.13 Spin locking dynamics viewed in the rotating frame on resonance: (a) just after the 7T./2 pulse and (b) after the 90° phase shift of the RF field. Precession of individual proton moments around B m results in an oscillatory component along the z axis. The times indicated refer to the pulse sequence shown in Figure 1.12.  42  When the Hartmann-Hahn condition is fulfilled, the 'pf and S i spins have the same 2 9  transition frequencies in their respective rotating frames and rapid transfer of spin polarization 90  1  from H to  Si is possible by the dipolar spin-flip mechanism. Experimentally this conditions is  met by setting the 90° pulses for both channels to be equal. 90  After the contact time, when both RF fields are on, the  Si spin free induction decay  signal is recorded in the presence of B I H for decoupling the H spins. The C P experiment is l  90  selective in that the 1  Si nuclei which are dipolar-coupled (i.e. close in the space or "connected"  •  •  to the H nuclei will show signals in the spectrum, while uncoupled  29  •  •  *  Si nuclei will be absent or  severely discriminated against. The following is a discussion of the fundamentals of cross polarization using the concept of spin thermodynamics, spin temperature and the variation of proton spin temperature during the C P sequence shown in Figure 1.12. When a solid is placed in a magnetic field Bo, individual protons populate Zeeman levels with energies ±(YH/47I)BO, corresponding to spin alignment parallel or antiparallel to Bo. The protons also interact with each other via dipolar couplings and experience the mutual spin flips characteristic of the spin diffusion process. If a single proton in an abundant spin system changes Zeeman levels by exchanging energy with the lattice, this information is transmitted in a short time, typically <100ps, to a large number of neighbouring protons by a propagation of such mutual flips. Thus the protons will soon (<100ps) be found in a state of internal equilibrium, which can be considered a single thermodynamic reservoir (Figure 1.14) characterized by a temperature 7H, with Zeeman levels populated according to a Boltzmann distribution. After several spin lattice relaxation times (Tm), the proton reservoir will come to equilibrium with the  43  lattice, and 7H will be equal to the lattice temperature, 7L- The proton magnetization is given by the Curie law according to Equation (1.24) M  = C B /7  0 H  //  (  Where CH is the proton Curie constant: C  H  (1.24)  i  = N y h1 2  H  H  2  Ak ,NH is the number of protons and k  is the Boltzmann constant. The heat capacity of the corresponding proton reservoir depends on the number of spins, and is given by: eu=N y B IA H  2  H  (1.25)  2  Q  L  T  IpSi  CP  l s i  Lattice  Figure 1.14 Large ' H , small S i , and infinite lattice reservoirs, each characterized by a heat capacity and temperature: fa, 7 ; ^si, 7si; fa, 7 ; respectively. Temperatures in parenthesis are those at the start (t=0) of the CP sequence. The T (Si) and Tcp connections are made during the CP time, while Ti (H) processes are operative during the entire proton spin-lock (see Figure 1.12). Dashed lines signify weak coupling (long relaxation times) 29  H  L  ]p  p  44  The first step (after proton polarization) in the CP experiment is a proton spin-lock along the RF field (Figure 1.12). The proton reservoir is perturbed by this sequence, but shortly after the 90° phase shift of the RF field (t=x, Figure 1.12 and 1.13), the protons regain internal equilibrium. In this equilibrium condition in the rotating frame the spin states have energy ±(YH/2TC)BI /2, determined by the strength of the RF field . The population of these states is 64  H  given by a Boltzmann distribution characterized by a spin temperature in the rotating frame. Under this condition the proton magnetization, which is conserved during the spin lock, is given by: MOH =  (1.26)  CHBXWIH  where TH is the proton spin temperature in the rotating frame that can be calculated by combining Equations (1.24) and (1.26). Since BiH=10mT while Bo>lT, this temperature is very low, e.g., for a sample at room temperature, 7H =3 K . The rotating frame reservoir established by a spinlock sequence is a quasi-equilibrium state , since the proton magnetization decays with a time 65  constant T i , which is typically in the milliseconds range. p H  90  At t=x (Figure 1.12), the silicon magnetization (Msi) is small, since  Si nuclei will  generally take much longer than the protons to polarize in Bo (i.e. Tisi >. TIH). The corresponding 70  Si spin temperature is given by: 7 =C iB /Msi Sl  S  where Csi is the Curie constant, C  (1.27)  0  =Ny h 2  S I  Si  Si  2  /4k. Since Msi is small, 7si will be large; the  silicon reservoir is "hot". A thermal link between the hot silicon and cooled proton reservoirs (Figure 1.14) is then established by irradiating the silicon atoms on resonance during the first part  45  of the proton spin lock (CP time, x<t<ti) and adjusting the RF field amplitudes so that the Hartmann-Hahn condition (Equation (1.23)) is satisfied. 1  29  •  *  As shown in Figure 1.13 (b) and (c), the CP dynamics for an isolated H - Si pair can be understood in terms of oscillating z components of the precessing spin, viewed simultaneously in the silicon and proton rotating frame which have coincident z axes (along B ). The proton spin0  locked moment has a z component (p ) which oscillates at a frequency H  z  COIH,  producing a dipolar  field. The S i moment precessing about Bo, has a z component oscillating at a frequency ©isi, 2 9  and experiences a resonant perturbation from p , since H  z  COIH=  coisi, when Equation (1.23) is  satisfied. Thus the silicon and proton spins, with identical oscillatory components in their respective rotating frame, can cross relax efficiently by the energy-conserving spin flips mechanism normally reserved for nuclei of the same type. When Equation (1.23) is satisfied the cross relaxation time Tcp, depends mainly on the strength of the ' H - S i dipolar coupling. After 29  several Tcp, the 'Ff and S i reservoirs come to equilibrium at a spin common temperature. This 2 9  temperature will be close to the spin-locked proton magnetization, because the silicon spin •  •  9  reservoir (with a relatively small number of nuclei, i.e., Nc~10" N H ) does not have enough heat capacity to significantly raise the temperature of the proton reservoir. Assuming that there has not been decay of the spin-locked proton magnetization at the end during CP time (i.e. TipH-^Tcp), the proton, and thus, the silicon spin temperature at the end of the cross polarization period (t=ti) will be very low:  7 =7 = Si  H  7L(B  1 h  /  Bo)~10- 7 3  l  (1.27)  This reduction of the silicon spin temperature translates into a growth, during the CP time, of 90  Si magnetization along the RF field B i o The result is that the enhanced polarization is M =(YH/Ysi)Mosi«4 Mosi (1.28) si  46  Where Mosi is the polarization which would be generated in Bo after waiting several Tisi (i.e. M si=CsiBo/7 ). L  0  The CP sequence can be repeated following a proton re-polarization period of several TIH- Typically Tisi > Tm, thus in a given period of time, more FIDs can be accumulated by using the CP technique. 1.4.3.1 Cross Polarization Dynamics For a coupled spin system Si-H with a relaxation rate 1/TI SJ(H), which is slow with P  respect to the cross polarization rate 1/Tcp, when the Hartmann-Hahn condition is fulfilled the spin magnetization for the dilute spin evolves according to Equations (1.29)  M (t) = Sl  {MJX)e'^(\-e^)  65  (1.29)  where (1.30)  In this thesis Ti (Si) was large enough for its effect to be neglected; thus Equation (1.29) p  simplifies to:  M (t) = M.o a  (1.31)  The cross polarization time, TCP, can be determined by fitting the change in intensity of the  90  Si signals as a function of the contact time using Equation (1.31).  47  1.4.3.2 Geometrical Information from Cross-Polarization Rate A suitable description of the cross-polarization transfer rate T'CP is necessary in order to obtain quantitative information about Si-H distances from the determined values. The T"'CP decreases monotonically to zero for increasing mismatch of the Hartmann-Hahn condition, i.e. = COisi - C O I H  ACO  coij = YjBij  (j = S i , H )  As mentioned before Bisi and B m are the amplitudes of the RF fields of the Si and H spins , respectively, in the rotating frame. The transfer rate, T"'CP, is proportional to the spectral distribution function J(<o) for the e  cross-polarization process'  66  T'cp-JCAcOe) Where Aco = (co e  2  - co ) 2  1Si  1/2  si  - (co  2  - co ) 2  1H  (1.31)  1/2  H  Under spin-lock conditions, T cp was calculated by the density matrix perturbation by _1  McArthur, Hahn, and Walstedt -1  C1>  T  and by Demco, Tegenfeldt and Waugh :  1 =2^ °  2  AC  )siH (&G>e) J  (1-32) J(Ao) )= e  JC (r)CosAo) Tdt x  e  o Where (Aco )siH is the van Vleck heteronuclear second moment for the Si-H dipolar coupling. The correlation function C (x) can be determined empirically. In their work McArthur x  Demco used a Gaussian shaped function: 69  C (x) = exp(x /x ) 2  x  where x is the correlation time. c  2  c  (1.33)  and  48  To calculate T"'cp, second and higher order approximations are used to determine C (x). x  If a second order approximation is used, the correlation time (T ) introduced in Equation (1.33) is c  expressed by the second moment N of the correlation function C (x) according to Equation 2  (1.34)  x  69  x = (2/N V* c  (1.34)  2  For a polycrystalline sample N can be expressed by the van Vleck homonuclear second 2  2  67  moment (Aco )HH of the abundant nuclei , N = 5/36(Aco )  (1-35)  2  2  HH  A simple expression for Tcp results i f the Hartmann-Hahn condition is fulfilled, i.e. i f the spectral density function in Equation (1.32) reduces to J (0)= Vi x Vrc, thus: x  c  - U ^ r T s ( > >™ Afl  TCP  2  (1.36)  2  J(&0)>HH ) 2  f  This rather simple formula for TCP" has been used to derive information on the local 1  structure around the rare S spin (i.e. interpretation of (Aco )is) in polycrystalline materials from 2  the analysis of cross-polarization rate in combination with lineshape data (i.e. determination of (Aco )n) for the abundant nuclei. Such selective measurements were reported in the case of 19  F - V C CP transfer , and for polymers . 3  65  69  1.4.3.3 Second Moments The two experimental variables used to characterize the broad featureless absorptions obtained in static solid state N M R spectra are the linewidth and the second moment. This latter is defined mathematically as the mean square width of the curve. The theoretical expressions for calculating the second moment, Equation (1.37) and (1.38), were first published by J. H . van Vleck . He developed the method of moments to calculate the properties of a resonance line  49  without knowing the energy Eigenstates and Eigenvalues. The homonuclear second moment for the abundant nuclei I (e.g. 'H) in a rigid lattice is given by a summation of pairwise internuclear interactions over the lattice ' : 61 71  „(l-3cos ^) 2  (A*> )„=^ 2  v  ^  J  I(I +  1)XT  2  e-^-  ( ) L37  r~  where po is the permeability constant, I is the spin quantum number, ry is the internuclear distance between two spins i,j, and 9y is the angle formed between the internuclear distance vector and the external magnetic field Bo (see Figure 1.15). The interaction is very strongly distance dependent. If two different types of spins I and S (e.g. Si and H) are dipolar coupled in a rigid lattice, the heteronuclear second moment (Aco )is is given by Equation (1.38) ' 2  1  ( A «  ifYcYihUnY 2  ) I S 4 PATT T ^ 3  9  61 71  2  ^(1~3C0S  SCS + 1 ) £ -  In a powder sample, the term (l-cos 0jj) 2  2  #;;)  2  (1.38)  4  is averaged for all orientations of the crystal  axes with respect to Bo i.e. for a rigid lattice, <(l-cos 0jj) >=4/5 (where the symbol < > means 2  2  averaged value). For convenience, the second moment is often divided into two parts; the intramolecular part arising from interactions within the molecule, which can be calculated from the knowledge of the molecular structure, and an intermolecular part consisting of the interactions with surrounding molecules, whose exact calculation requires a knowledge of the crystal structure. The presence of motion is important and it has to be considered in the calculation of the second moments. Any rapid molecular motion will tend to partially average the dipolar interactions, so that the second moment will appear to be decreased . The total second moment 60  is in fact invariant to the presence of motion, but the measured second moment is not, because  50  part of the resonance is shifted far from the centre of the resonance where it is hidden in the noise and consequently not observed. •y  o  'y  In the presence of motion, the term [(3cos 0ij-l)/r ] in Equations (1.36) and (1.37) must be averaged over the motion. The intramolecular contribution maybe expressed very simply in terms of the angles defined in Figure 1.16. For a pair of nuclei j,k fixed in a molecule, the axis of rotation of the molecule making an angle 0' with respect to the static field Bo and the internuclear vector rjk inclined yjk with the rotation axis. Then, as the molecule rotates, the angle 0jk (between Bo and the internuclear vector) which occurs in the factor (l-cos 0jk) in the expression for the 2  second moment (Equation 1.37), varies with time. Since the frequencies of rotation are high compared with the frequencies of interest in the resonance, it is the time average of (1-cos 0jk) that affects the second moment. Assuming that the motion is over a potential well of threefold or higher symmetry, this average can be shown to be independent of the details of the motion, and is given by: / •> \ (l-3cos 0 ) j k  ^ (3cos r -1) = (l-cos 0')2  ik  2  2  a v g  (1.39)  Equation (1.39) shows that if the axis of rotation is parallel to the internuclear axis (Yjk 0), in which the relative position of the nuclei is unaffected by the rotation, the angular =  factor is unaffected by the rotation. On the other hand if yjk = n/2, then (l-3cos 0 } 2  jk  = -^(l-cos 6>') 2  avg  (1.40)  In a powder sample, all orientations of the crystal axes with respect to Bo are found. For a rigid lattice, it must be averaged over all the ramdon crystal orientations. When motion •y  sets in, (1-cos 0jk) must be first averaged over the motion, to obtain the second moment  51 70  of a given orientation. Then it must be averaged over all the crystal orientations . The expression for the homonuclear second moment with intramolecular motion (for example rotation of CH3 group) is given by Equation (1.41) (l-3cos x ) 2  1 1  1(1 + 1)1  20  2  jk  r  j  (1.41)  6  For the intermolecular contribution, the term [(3cos 0jj-l)/rjj ] in Equations (1.37) and 2  3  (1.38), must again be averaged over the motion. However, in this case, both the angle, 0y, and the internuclear distance, ry , vary with the motion. Michel and co-workers  have shown that  averaging over all the positions occupied by the two atoms in the reorientation, and then averaging over the powder yields Equation (1.42). 4(3cos ^-l) 2  2  4 +—(3cos(9 sin6' sin^) 15 ij  ((i-3cos 0 ) ) 2  Jk  x  x  /  m  m  /  p  = - ^ ± i pq WH ".  ij  j  +—(3cos^sin0 cos^) +—(3sin G^cosl^. a  (1.42)  1  + ^(3sin ^sin2^) 2  2  The summations are made over the N positions occupied by the internuclear vector corresponding to the p sites occupied by. atom i and the q sites occupied by atoms j , £ind 6y, cpy, are the polar angles made by the vector iv to an arbitrary origin.  Figure 1.16 Angles important in describing the rotation of a molecule.  53  1.5.  TWO-DIMENSIONAL N M R SPECTROSCOPY One of the more important developments in high resolution N M R spectroscopy was the  introduction of two-dimensional experiments. The concept of extending N M R spectroscopy into two frequency dimension was first proposed in 1971 by Jeener , who suggested that two73  dimensional (2D) correlation spectroscopy (COSY) experiment should be possible. Since then, there has been a rapid growth in the development and application of high resolution 2D N M R techniques after Ernst and co-workers demonstrated a large variety of 2D N M R experiments in solution . 74  A l l multidimensional N M R pulse sequences consist of three parts: preparation, evolution, and detection periods. The preparation period can include one or more pulses to initiate or "prepare" the magnetization for the experiment. The prepared magnetization then evolves under the influence of different interactions, depending on the experiment, during the evolution period (ti). Finally, after a 'transfer' or 'mixing' period i f needed the signal is acquired during the detection period. In a 2D N M R experiment the second time domain is introduced by acquiring a series of ID experiments where the evolution time, ti, is incremented. The incrementation of ti creates a second frequency domain reflecting the interactions which occur within the spin system during this time. The data are arranged in a two-dimensional matrix, S(ti,t2) with n rows (number of FIDs gathered i.e. number of increments of ti) and k columns (number of data points collected in t ). 2  After Fourier transformation of these data in one dimension S(ti,t ) -> S(ti,F ), a series of spectra 2  2  is obtained that are phase modulated. A second Fourier transformation of corresponding columns in the data set yields a 2D data matrix, S(Fi,F ). 2  54  A 2D N M R experiment is always possible i f a systematic change in the evolution period results in a periodic change of the phase and/or amplitude in the magnetization at the end of the evolution period. The second Fourier transform determines the frequency of these modulations and provides the second dimension for the spectrum (Fi). The spreading of the N M R spectrum in a second orthogonal dimension provides information about the spin interactions occurring during the evolution period, t\. Often this will involve J-couplings, chemical shifts, etc. 1.5.1  REPRESENTATION OF THE TWO-DIMENSIONAL DATA  The 2D data are usually represented in the form of a contour plot in which the two frequencies form the horizontal and vertical axes, and contour levels are drawn through points of equal intensity (see Figure 4.5, Chapter 3). The contour lines define the shape of the resonances, while intensity information is indicated by the number of contour levels. The 2D contour plot S(Fi,F2) is composed of  n rows and k columns in the F i and F dimensions, respectively, where 2  n is the number of separate one-dimensional N M R experiments performed and k is the number of data points acquired during the acquisition time t . The number of experiments n is usually 2  kept to the minimum number required to obtain the desired resolution in F i , since the total experiment time is proportional to n (k is generally not limited in size since the acquisition period occurs during usually much longer recycle delay of the experiments). In addition to contour plots, cross sections and projections are also used to examine displays and interpret 2D data. Cross sections of the 2D spectrum consist of rows and columns in the F i and F dimensions, respectively. In practice, the peaks which contain information of 2  interest lie on a limited number of cross sections, and it is often informative to plot them as separate one-dimensional spectra to obtain, for example, intensity information, as shown in Chapter 4, Figure 4.7.  55  The projections in the 2D experiments are generated by a computer algorithm "projecting" the intensities of the cross sections onto each of the 2D axis (Fi and F2). These are displayed with a contour plot (see Figure 4.12, Chapter 8). Usually in the presentation of the 2D spectrum, much better resolved one-dimensional spectra are substituted for the projections.  1.5.2  CLASSIFICATION OF TWO-DIMENSIONAL N M R EXPERIMENTS There are two prominent classes of 2D N M R experiments: classified according to their  objectives (some examples are presented in Table 1.6). 1.5.2.1 J-Resolved Spectroscopy In conventional ID solution N M R , the multiplets often overlaps rendering assigment of the spectrum difficult. In 2D J-resolved spectra one frequency axes contains the coupling information (J) and the second one contains the chemical shifts (8). 1.5.2.2 2D Correlated Spectroscopy Two types of 2D correlated spectra can be distinguished: •  Both dimensions may be coupled through coherent transfer of magnetization; hetero (e.g. ^ ^ C ) or homo (e.g. S i / S i ) correlated 2D N M R involving single and multiple quantum 29  29  precession periods. •  Incoherent transfer of magnetization (2D N O E or chemical exchange). The concept of coherence transfer is more direct and general than the conventional  double resonance techniques. It is usually applied to obtain correlations between the chemical shifts of nuclei that are coupled and for identification of the topology of homo or heteronuclear coupling networks. Besides that it is also possible to elucidate the connectivities of transitions in the energy level diagram and to determine the magnitude and relative signs of the J-couplings.  56  Table 1.6: Classification of some standard 2D experiments and areas of application in high resolution N M R spectroscopy (from reference 75).  2D N M R experiments  Application  Variables  J-correlated Homonuclear J-Resolved  J(H,H)  8( H)  Determination of coupling constants  Heteronuclear J-Resolved  J(X,H)  5(X)  Determination of coupling constants  J  Heteroscalar correlated HETCOR or HETCOSY  8(X)  8('H)  Assigment of resonances  RELAY  8(X)  8('H)  Assigment of molecule fragments  Homoscalar correlated INADEQUATE  8(Xi)+8(Xj)  8(X)  X connectivities through bonds  8(X)  8(X)  X connectivities through bonds  Dipolar correlated  8(X)  8(X)  Spatial relationships  Chemical exchange  8(X)  8(X)  Mechanisms and kinetics of reversible reactions  COSY  1.5.3  PROCESSING OF TWO-DIMENSIONAL N M R EXPERIMENTS The processing of data obtained from 2D experiments is more demanding than is  customary with ID experiments. In order to obtain sufficient digital resolution in the ti dimension, the number of experiment (which determines the number of data points in the ti  57  dimension) must not be too small. However, as explained before, the digital resolution in the F i domain is usually kept to a minimum in order to reduce the total time of the experiment. To improve digital resolution in both Fi and F domains, "zero filling" is carried out in each domain. 2  Figure 1.17 Common time domain apodization function used in the processing of 2D N M R spectra (shown for a time domain of 256 ms): (a) Exponential multiplication with LB=1, 3, and 5 Hz. (b) Lorentz-Gaussian function with LB=-5 Hz and GB=0.1, 0.3, and 0.5 times the timedomain, (c) Sine-bell shifted by 0,7i/2, n/4, and TT/8. (d)) Sine-bell square shifted by 0, n/2, n/4, and 7t/8. (From reference 76).  Apodization is the step which gives the operator most control over the final presentation of the data. To enhance the S/N ratio, the time-domain FID in each dimension is multiplied by an appropriate apodization function. Fourier transform and phase correction are then performed in  58  each dimension. Some examples of apodization function commonly used are shown in Figure 1.17. For example, the sine-bell apodization shifted by 7t/2 (Figure 1.17 c) is a cosine function which starts at one and ends at zero. Sine-bell apodization is commonly used in 2D processing, and is optimally shifted and/or squared (see Figure 1.17 c,d) in order to produce the desired S/N ratio and resolution . 76  59  1.6.  HIGH RESOLUTION SOLID STATE NMR SPECTROSCOPY OF ZEOLITE MOLECULAR SIEVES High resolution solid state N M R spectroscopy has emerged as a powerful complementary  technique to x-ray diffraction for structural investigations of molecular sieves systems ' ' . The 43 77 78  techniques are complementary in that x-ray diffraction is most sensitive to long range ordering and periodicities, and less sensitive to the perfection of and nature of short-range ordering. On the other hand, N M R spectroscopy is affected by the local magnetic environments of the nuclei, and thus is extremely sensitive to short range order and local structure. Since there are usually no protons covalently bonded to the zeolite framework, cross polarization cannot be carried out, and high power proton decoupling is not necessary. Therefore, the experiment most often reduces to the very simple one-pulse magic angle spinning (MAS). After the initial work of Lippmaa and co-workers , there have been many studies in low 79  Si/Al ratio zeolites that have clearly established that S i N M R signals in zeolites are sensitive to 2 9  the atoms attached to the oxygens of the silicon tetrahedron. Thus, to a first approximation, for a given zeolite a maximum of five signals are expected corresponding to Si[4Al]; Si[3Al,lSi]; Si[2Al,2Si]; Si[l Al,3Si]; and Si[4Si], the term in parenthesis indicating the atoms attached to the oxygens of the tetrahedron.  This is illustrated in Figure 1.18, which also shows the typical  chemical shift ranges of low Si/Al ratio zeolites. Under Loewestein's rule , which postulates 29  that A l - O - A l linkages are not possible in zeolites, the Si/Al ratio can be calculated from the N M R spectrum from the intensities of these five signals according to Equation (1.43) 4  _Si_ Al  ^I(nAl) n=0  4  0.25^nl(nAl) n=0  (1.43)  Si  60  where I is the peak intensity and n is the number of coordinated A l atoms for a given peak. This formula includes only those A l bonded to Si atoms in the zeolite framework, since the A l concentration is detected indirectly from its effect in the S i N M R spectrum. Thus, the method 2 9  has the advantage that the Si/Al ratio is determined exclusively for the zeolite framework. On the other hand, the ratio from chemical analysis will include framework A l and any aluminium occluded in the cavities or present as impurities and not integral parts of the framework. Both analyses are complementary and can be used together to calculate the  extrafrarnework  aluminium. Because of the lack of Si/Al ordering in the zeolite framework, the  Si resonances are  relatively broad, with linewidths on the order of 5 ppm. When the aluminium atoms are removed from the framework to produce a completely siliceous zeolite framework which is perfectly ordered, the  Si M A S N M R spectrum shows very sharp resonances (linewidths less than 1 ppm)  whose number corresponds to the number of crystallographically inequivalent sites in the unit 81  cell and whose relative intensities correspond to the populations of these sites . Thus, a direct link can be made between the N M R and diffraction methods. S9  Fyfe and co-workers  90  have used two-dimensional  experiments such as C O S Y and I N A D E Q U A T E  •  Si homonuclear correlation  in highly siliceous zeolites to establish the  three-dimensional S i - 0 - S i bonding connectivities within the framework. 29  29  High resolution N M R investigations have demonstrated that the room temperature form of the completely siliceous ZSM-5 material is monoclinic with 24 silicon sites in the asymmetric unit, and that a structural change to an orthorhombic form, space group Pnma, with 12 silicon sites is induced by addition of two molecules of p-xylene per unit cell, or by increasing the temperature. In the first case the change is gradual, both forms being crystalline and coexisting at  61  intermediate conversions while for the thermally induced change the turnover occurs in a very small temperature range. If more p-xylene molecules are added the structure changes to an orthorhombic form with 24 silicon sites, space group P2/2/2/. These phase changes on ZSM-5 are summarized in Table 1.7. In Figure 1.19 the one-dimensional spectra of the four described systems are shown. The unambiguous assignments of the S i N M R signals were done by two2 9  dimensional S i homonuclear correlation experiments such as I N A D E Q U A T E . The substantial 2 9  82  changes in the peak positions for the different systems reflect clearly the changes in local T-site geometries induced in the structural transformations. In Figures 1.20 and 1.21 the 2D I N A D E Q U A T E experiments for the complexes of ZSM-5 loaded with 2 and 8 p-xylene molecule per u.c, respectively, are shown. The two-dimensional Si homonuclear correlation experiments utilize the J-couplings in  Si-O- Si spin pairs, which  have only a 0.22% probability of occurring. As a result, the experiments are inherently insensitive. Determination of the scalar couplings is important in that it facilitates the application of the I N A D E Q U A T E experiment ' . The conventional pulse sequence is: 83 84  [(90°) —T— (180° ) -x-(90°) - t i - (135°) -t , acquire] x  2  where the maximum signal is obtained when x=l/(4J), assuming that T » l / J . 2  Zeolite ZSM-5 has the most complicated unit cell of any zeolite system, with either 12 or 24 T-sites depending on the phase, and thus is a very demanding candidate for these 2D connectivity experiments. C O S Y and I N A D E Q U A T E experiments have been performed for the orthorhombic form of low-loaded ZSM-5 (2 molecules of p-xylene per 96 T-atoms unit cell).  62  Si[4Al]  '  (b)  i  I  I  I  L  -80  -90 -100 PPM from TMS  Al 0 AKKKMI 0 Al  Al 0 AJ090S 0  Al 0 SiOSiOSI 0  s  SI 0 SiOSiOSI 0 Si  SK«*0  Al 0 Atosiosi 0 Al SK3AI)  •KSAI)  SKtAO  SI(QAJ)  4:0  3:1  Z2  Id  0:4  s  I Sl(OAI)  Sl(IAl) SI(2AI)  Si(3AJ)  1 I 80  »(4AJ)  I  I I I I I I -90 -100 -110 PPM from TMS  I  Figure 1.18 (a) Si M A S N M R spectrum of the zeolite analcite. (b) Characteristic; chemical shift ranges of the five different local silicon environments, (from ref. 42)  63  4,18,12,24,3  I — i  1  -110  1  1  -112  "  1—| 1  I  -114  -116  1  -118  1  1  r  -120  PPM  Figure 1.19 (a) S i M A S N M R spectrum of ZSM-5 at 300 K . (b) S i M A S N M R spectrum of the low loaded form of ZSM-5 (2 molecules of p-xylene per u.c.) at 300 K . (c) S i M A S N M R spectrum ofthe low loaded form of ZSM-5 at 403 K . (d) S i M A S N M R spectrum ofthe high loaded form of ZSM-5 (8 molecules of p-xylene per u.c.) at 293 K . (From ref. 77). 2 y  2 y  2 9  2 9  64  From single crystal x-ray refinements  ' , a total of 22 connectivities are expected for this  phase. While the COSY spectrum (not shown) shows only 12 of these connectivities, the I N A D E Q U A T E experiment (Figure 1.21) is superior with 21 of the 22 connectivities clearly visible ' 75  79  From the knowledge that only four silicons have self-connectivities, and using the  expected connectivities from the x-ray structure, a complete self-consistent assignment of all the N M R resonance was obtained.  Table 1.7: Description of the phase changes occurring in zeolite ZSM-5 with temperature and sorbate loading.  Sample  Condition  Space Group  T-Sites in the Asymmetric Unit  room temperature (300 K )  monoclinic form P2,/n  24  high temperature (403 K )  (85) orthorhombic form Prima  ZSM-5  ZSM-5 with sorbed p-xylene  low loading with p-xylene (2 molecules/u.c.) 300 K high loading with p-xylene (8 molecules/u.c.) 300 K  (86) orthorhombic form Prima  12  12  (87) orthorhombic form P2,2,2, (88)  24  65  ms  Figure 1.20 S i 2D INADEQUATE'spectrum of the low loaded form of ZSM-5 (2 molecules of p-xylene per u.c.) at 300 K . (From ref. 77). z y  66  4,18,12,24,3  T  1  -110  1  -111  1  1  1  1  -112  -113  -114  -115  1  T  -116 -117  PPM Figure 1.21 S i 2D INADEQUATE spectrum of the high loaded form of ZSM-5 (8 molecules of p-xylene per u.c.) at 300 K . (From ref. 77). 2y  67  1.7.  G O A L OF T H E THESIS The goal of the work described in this thesis was to develop a methodology to investigate  further the zeolite complexes of highly siliceous ZSM-5 with p-xylene molecules by locating the organic molecules inside the framework using only N M R techniques that are based on the dipolar interactions between the atoms of the guest molecules and the silicon nuclei in the zeolite framework. In this way a complete three-dimensional characterization of these system could be obtained. Chapter 2 describes the experimental work, synthesis of material, and instrument settings, used in these experiments. Chapter 3 investigates the application of cross-polarization experiments to obtain information about the location of p-xylene molecules in the high loaded form of zeolite ZSM-5. Chapter 4 describes chemical exchange experiments to study the molecular dynamics of the p-xylene molecules inside the zeolite framework in the high loaded complex. Chapter 5 validates the applicability of the CP experiments to locate p-xylene molecules i f a complete knowledge of the mobility of the organic molecules is obtained. In Chapter 6 the CP experiment and the protocol developed in this thesis are used to obtain the three-dimensional structure of a sample without any previous information of the structure from x-ray diffraction. This was the low loaded complex of p-xylene in ZSM-5. The p-xylene molecules were determined to be located in the intersection of the sinusoidal and straight channels of the zeolite, and fractional coordinates for the molecules were obtained. Chapter 7 explores the application of the double resonance dephasing technique REDOR to obtain structural information about the location of the p-xylene molecules in the high loaded form of zeolite ZSM-5, again through the dipolar interactions between the protons of the guest molecules and the silicon atoms of the zeolite framework. In Chapter 8 some preliminary results are presented of the application of the triple resonance dephasing experiments of REDOR and  68 1  T  TEDOR on the complex of the high loaded form of zeolite ZSM-5 with p-xylene [ C,CH3] to 13  obtain structural information through the dipolar interaction between the labelled group of the guest molecules and the silicon atoms of the zeolite framework.  C methyl  69  1.8. REFERENCES  1 Barrer, R. M . , Chem. Ind., (London), pg. 1203, 1968 2 Breck, D. W., "Zeolites Molecular Sieves", John Wiley, New York, 1974. 3 Meier, W, N . , "Molecular Sieves"; Barrer, R. M . Ed.; Soc. Chem. Ind. London, 1968. 4 Smith, J. V . , "Zeolites Chemistry and Catalysis", Rabo, J. A . Ed.; A.C.S. Monograph, 171, 1976. 5 McBain, J. M . , "Sorption of Gases and Vapours by Solids", Routlidge and Sons. London, 1932 6 Barrer, R. M . , U.S. Patent, 2,306,610; 1942 7 Barrer, R . M . , J. Soc. Chem. Ind, 64, 130, 1945. 8 Barrer, R. M . , Nature, 164, 112, 1949. 9 Meier, W. 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(a) Lippmaa, E; Magi, M . ; Samoson, A . ; Tarmak, M . ; Engelhardt, G., J. Am. Chem. Soc, 103, 4992, 1981. 80 Loewestein, W.,^4m. Mineralog., 39, 92, 1954. 81 Kokotailo, G. T.; Fyfe, C.A.; Kennedy, G.C., Gobbi, G.C.; Strobl, H . ; Pasztor, C: T.; Barlow, G.E.; Bradley, S.; Murphy, W.J.; Ozubko, R. S., Pure Applied Chem., 58,1367,1986. 82 Fyfe, C.; Grondey, FL; Feng, Y Kokotailo, G. T., J. Am. Chem. Soc, 112, 8813, 1990. 83 Bax, A.; Freeman, R.; Frenkiel, T.A.; Levitt, M.H., J. Mag, Reson., 43, 478, 1981. 84 Mareci, T.H.; Freeman, R., J. Mag, Reson., 48, 478, 1982. 85 van Koningsveld, H., Jansen, J . C ; van Bekkum, H., Zeolites, 10, 235, 1990. 86 van Koningsveld, H.; van Bekkum,H.; Jansen, J . C , Acta Crystallogr. Sect. B, 46, 731, 1990. 87 Olson. D.H.; Kokotailo, G. T.; Lawton, S.L., J. Phys. Chem., 85, 2238, 1981. 88 van Koningsveld, H.; Tuinstra, F.; van Bekkum,H.; Jansen, J . C , Acta Crystallogr. Sect. B, 45, 423, 1989.  75  CHAPTER TWO EXPERIMENTAL  2.1.  INTRODUCTION N M R spectroscopy has developed, through the introduction of two-dimensional  methods and double and triple resonance dephasing experiments, into the most important technique for the investigation of molecular structure and dynamics. The very recent application of these experiments into the high resolution solid state N M R methodology constitutes a very important development in the study of catalysts, particularly in their application to the study of zeolite materials. The general application of 2D N M R techniques to solids is considerably more complex than in liquids, mainly because the dipolar interactions and chemical shift anisotropy, which are averaged in liquids, produce the very broad lines typical of solid state N M R spectra. In addition, the short T relaxation times characteristic of solids restrict the use of long evolution 2  times which are required in some experiments. In the case of zeolites, the experiments are also insensitive due to the low natural abundance of the  Si nucleus and its long Ti times.  In the study of zeolite complexes with organic guest molecules, the application of double and triple resonance dephasing experiments of Cross-Polarization (CP), Rotational Echo Double Resonance (REDOR), and Transferred Echo Double Resonance (TEDOR), to obtain reliable quantitative internuclear distance from the dipolar interaction between the guest molecules nuclei and the lattice atoms can be complicated due to the dynamics of the sorbed molecules within the zeolite framework. The accuracy of the measurements depends critically on the motional characteristic of the absorbed molecules. Many motions (like ring flipping, etc) can  76  be taken into account in the calculations, but many others (like diffusion) have to be stopped to obtain valid measurements. Therefore in many experiments is necessary to work at low temperatures to obtain meaningful data leading to structure determination. Working at low temperature in high resolution solid state N M R is experimentally very demanding because it is necessary to keep the sample spinning at a constant speed for long periods of time due to the low sensitivity of the N M R experiment. In this thesis a methodology which allows spinning of a sample at a stable speed and low temperature (up to -80 °C) for up to six days was designed. The application of high resolution solid state 2D and dipolar dephasing N M R experiments in the study of zeolite complexes with organic guest molecules is very demanding and time consuming in term of sample preparation, the spectroscopy involved and experimental setting. The important factors in the experiments will be discussed in this chapter. 2.2.  2.2.1  SAMPLE PREPARATION  ZEOLITE SYNTHESIS It has been demonstrated that highly siliceous zeolites yield S i M A S / N M R spectra 29  with very narrow resonances since the structures are now perfectly ordered, all silicons having the same Si[4Si] local environment ' ' . The numbers of these resonances and their intensities 1 2 3  reflect directly the numbers and occupancies of the crystallographically inequivalent T-sites in the asymmetric unit in the unit cell ' ' . 4 5 6  The  samples of ZSM-5 used in this thesis were obtained by the complete  hydrothermal dealumination of a highly siliceous sample. The hydrothermal treatment adopted in this work was first demonstrated by McDaniel and Maher . A calcined sample of ZSM-5 is 7  ammonium exchanged with a 1 M aqueous solution of NH4F and then this sample is subjected to  77  a steaming treatment, by passing water vapor over the sample at -750 °C for several days. The formula for the unit cell of this completely dealuminated zeolite is Si960i92. 2.2.2  SYNTHESIS OF THE LABELED COMPOUNDS  2.2.2.1 Deuterium Labeledp-Xylenes  ;  The sample p-xylene d<j (deuterated in the methyl groups) is commercially available, and was purchased as 99.9 % isotopically pure from Aldrich. The p-xylene d (deuterated in the aromatic ring) was synthesized by acid, exchange 4  with deuterium oxide as follows: approximately 1 ml of p-xylene and 9 ml of a solution of 4 % 8  DC1 in D2O was introduced into an approximately 10 cm long Pyrex glass tube with 15 mm o.d. (8 mm i.d.). The reaction mixture was degasified by repeatedly freezing with liquid nitrogen, evacuation, and thawing to room temperature. The tubes were sealed with a flame. The sealed tubes were then placed into stainless steel bombs containing approximately 2 ml of water to ensure that the pressure inside and outside of the glass reaction tubes would be approximately equal during heating. The bombs were closed and placed in an oven at 200 °C for 48 hours. The exchanged p-xylene was separated from the water solution by decanting, washed several times with D 0 , and purified by distillation. The progress of the reaction was followed by ' H N M R 2  spectroscopy, measuring the ratio of aromatic protons to methyl protons. The exchange procedure was repeated several times and the best exchange ratio obtained was approximately 0.2 residual aromatic protons, corresponding to a 95 % exchange of the aromatic hydrogens.  78  2.2.2.2 C Labeled p-Xylenes 13  The compound [ C, CH3] p-xylene was synthesized by Dr. Ralph Ambrust from the 13  metal-mediated reaction of labeled C H I (99.5 % isotopically pure from Aldrich) and p13  3  bromotoluene with Li[C(CH3)3]. 2.2.3  LOADING OF SORBATES IN THE ZEOLITE MATERIALS  The p-xylene loaded samples were prepared by activation of highly siliceous ZSM-5 at 400 °C for approximately four hours. After the samples were cooled down to room temperature, measured amounts of liquid p-xylene were added to weighed samples of ZSM-5 in glass vials. The vials were sealed and kept in an oven at approximately 80 °C for at least 8 hours to ensure an equilibrium distribution of the sorbates through the samples.  2.3. 2.3.1  SAMPLE ANALYSIS DETERMINATION OF THE ZEOLITE LOADINGS  2.3.1.1 By Themogravimetric Analysis The exact number of molecules loaded in a sample can be measured by thermogravimetric analysis (TGA) by heating from room temperature to 400 °C with a rate of 2 °C/s. The number of molecules per unit cell sorbed in the sample is obtained by subtraction of initial and final sample weight, according to Equation (2.1):  (2.1)  79  where MW iit is the molecular weight of the zeolite ZSM-5, which can be calculated for a zeo  e  completely siliceous material according to the empirical formula  (SiO*2)96,  and  is the  MW . i ne p  x y  e  molecular weight of p-xylene. Figure 2.1 shows two typical T G A plots for the desorption of a high loaded sample of ZSM-5 with p-xylene. The maximum loading of p-xylene molecules inside the zeolite channels is approximately 7.5 molecules per u.c, for the samples studied in this thesis. When more p-xylene is added, the molecules in excess are sorbed at the surface, as can be seen in Figure 2.1 (b). This T G A plot shows that the surface molecules are easily desorbed at 28 °C.  2.3.1.2 By Si NMR Spectroscopy 29  90  Si N M R spectra are very sensitive to changes in the loading of p-xylene molecules in a highly siliceous ZSM-5 and can be used to determine the number of molecules adsorbed inside the zeolite structure ' ' . Figure 2.2 shows how the 5 6 7  29  S i N M R spectra change with different  loadings of p-xylene in a highly siliceous zeolite ZSM-5 from a calcined sample to a loading of ~8 molecules per u.c. 2.4.  2.4.1  OPTIMIZATION OF T H EN M R EXPERIMENT  SHIMMING, PROBES AND REFERENCE SAMPLES FOR SETTING UP To obtain well resolved spectra with a good signal to noise ratio in the shortest  possible measurement time, some practical aspects of the N M R experiments have to be considered. First the proper setting of the magic angle is very important to obtain high resolution solid state experiments. This was done by observing the B r resonance of a sample of K B r . The 79  9  number and intensities of the sidebands in the resonance are very sensitive to the angle of the spinning axis and maximum intensity is reached when the angle is set to exactly 54.7°.  80  Good homogeneity in the static field is also an important factor for obtaining good resolution in the resulting spectra. In order to obtain the maximum S/N, the probe must be precisely tuned to resonance. The tuning is very sensitive to changes in temperature and sample spinning; variations in these parameters during the experiment can decrease the resolution and intensities considerably, and lead to unsatisfactory data. This is particularly important because basically all the experiments done in this thesis are intended to yield quantitative data. Very high homogeneity of the magnetic field is required in order to observe the narrow resonances characteristic of these siliceous samples. This is done by careful shimming on the FID of an approximately 50:50 mixture of water and deuterium oxide. A very small amount of CuSO*4 is added to the sample to reduce the relaxation time of the ' H , and consequently shorter repetition times (~1 s) can be used, facilitating the observation of small changes in the FID during shimming. 2.4.2  2 9  S i CROSS POLARIZATION SETTING  The cross polarization experiment for S i is set with a sample of QjMs (cubic 29  octamer silicic acid trimethylsilyl ester) using a contact time of 8 ms, and recycle delay of 8 s. The proton BIH is fixed, and the Bisi is adjusted to give maximum cross-polarization S i signal 29  1  which can be seen with a single scan. To check the matching, the H and  90  Si 90° pulse widths  are measured: i f the Hartman-Hahn condition is satisfied both pulse widths are the same. Small correction of the CP setting is done with the analyzed sample, using the same procedure to obtain •  90  maximum cross-polarization  Si signal of the zeolite.  90  All  Si N M R chemical shifts given in this thesis are indexed with respect to T M S  (tetramethylsilane), using QsMg as intermediate standard and taking the highest field resonance in the S i N M R spectrum of the reference to be -109.7 ppm . 2 9  10  81  Figure 2.1 T G A plots which shows the desorption of p-xylene sorbed in ZSM-5, from room temperature to 300 °C with a rate of 2 °C/s. The amount of p-xylene molecules sorbed in the sample is obtained by subtraction of initial and final sample weights, (a) Sample prepared with 7 molecules of p-xylene per u.c. The first inflexion point corresponds to the loss of approximately half of the sorbed molecules (3.7 molecules per u.c). (b) Sample prepared with 9 molecules of pxylene per u.c. The first inflexion point corresponds to the loss of excess p-xylene sorbed on the surface.  82  (a)  I  -110  (b)  1  T -  -115 -120 5 / ppm  1  -110  |  |  -115 8 / ppm  -120  Figure 2.2 (a) Si M A S N M R decoupled spectra of ZSM-5 with increasing concentration of p-xylene, the numbers of p-xylene molecules sorbed per u.c. are indicated in the figure. A 350 s delay time between pulses ensures the spectra are quantitative, (b) S i CP M A S N M R decoupled spectra of the same samples with a 20 ms contact time and 5 s delay time 29  29  83  2.4.3  1 3  C CROSS POLARIZATION SETTING The Hartmann-Hahri condition for the cross polarization experiments with  13  C is set  with a sample of adamantane in the same way described for S i in Section 2.4.2, above. A l l 2 9  1 3  C  N M R spectra in this thesis are indexed with respect to TMS, using adamantane as intermediate standard and taking the highest field resonance in the C N M R spectrum of the reference to be 1 3  29.5 ppm . 11  2.4.4  Low TEMPERATURE M A S SPINNING The low temperature experiments were done using a 7 mm HP/BB M A S Bruker  probehead, using zirconia spinners with boron nitride caps. The low temperature experimental set-up is shown in Figure 2.3. In this arrangement the cooling air is also the bearing gas. A pressurized 200 liter liquid nitrogen Dewar was used as the cold bearing gas reservoir. This precold bearing gas is cooled down further by going through a coil submerged in a 25 1 Dewar filled with liquid nitrogen. The drive gas can be dry compressed air when working at temperatures above 243 K . For lower temperatures dry nitrogen gas is required to avoid stopping the sample spinning due to ice formation. The pressurized 200 liters liquid nitrogen can also be used as the drive gas because the Dewar utilized for this set-up has another output in which the gas comes out at room temperature under the control of a pressure regulator. The temperature is regulated within the probe with the VT-100 Bruker Temperature Control Unit. The liquid nitrogen level in the 25 1 Dewar tank has to be controlled to keep the temperature regulated. Because some of the experiments require keeping the sample cold for many days (and nights), the refilling of the small Dewar was done automatically using a solenoid valve which opened or closed the supply  84  of liquid nitrogen from a second storage Dewar (see Figure 2.3). This valve was programmed with a digital timer. 2.5.  MEASUREMENT OF RELAXATION PARAMETERS  In all the N M R sequences, it is necessary to allow the spin system to relax back to equilibrium between the acquisition of one FID and the start of the next pulse train, the waiting time being characterized by the spin-lattice relaxation time, T i . In addition the multiple pulse sequences (e.g. 2D, REDOR, TEDOR, etc) have a finite length of evolution and fixed delays during which the magnetization decays due to the spin-spin relaxation, characterized by the time constant T . 2  The S i , 29  1 3  C , and H relaxation time measurements, Ti and T were performed on a J  2  Bruker MSL-400 spectrometer operating at 79.49, 100.59, and 400.13 MHz, respectively, using the pulse sequences listed in Table 2.1.  2.6.  2.6.1  ANALYSIS OF T H E N M R DATA  PROGRAMS USED FOR PROCESSING N M R EXPERIMENTAL DATA The N M R data were transferred and converted from Bruker Aspect 3000 format to  PC format through the N M R L I N K software from Bruker. The PC N M R data were processed (Fourier transform) using the programs WINNMR from Bruker.  2.6.2  ANALYSIS OF THE VARIABLE CONTACT TIMES CROSS-POLARIZATION DATA The ' H / S i M A S N M R CP spectra were deconvoluted into individual Lorentzian 29  curves using the software G R A M S . This program was preferred over WINNMR because it is possible to fix some parameters during the deconvolution of the spectrum, for example the  85  linewidth of the individual resonance signals. It was found to be more accurate in the zinalysis of the variable contact time C P spectra to use the linewidth of the individual signals obtained from the deconvolution of the quantitative  2 9  S i M A S N M R spectrum that was carried out under the  same experimental conditions as the C P spectra. This procedure provides the correct linewidths of the S i N M R signals. These linewidths are then fixed during the deconvolution of the variable 2 9  contact time C P spectra. The deconvoluted peak areas are used in a non-linear fitting of the C P signals using Equation (1.31) (Section 1.4.2.2), with the software package Mathematica 3.1 and Mathematica for Windows 95.  Table 2.1: Pulse sequences used for the determination of T i and T values. 2  Relaxation Time  Pulse Sequence  Equation for Calculation  T,  180°-T-90°(FID)  ln[I(oo)-I(t)]=ln(2)+ln[I(oo)] -x/Ti  T  90 -[x-180 °-T]n(FID)  ln[I(t)]- ln[I(0)] = -2x/T  o  2  x  Tiof'H  'H:  with C P  T i o f S i or with C P 2 9  1 3  1 3  C  2 9  180°-T-90°-CP-HPD  C:  C:  ln[I(oo)-I(t)]=ln(2)+ln[I(oo)] -x/Ti  CP-(FID)  'H: 90°-CP 1 3  2  x  H P D  CP-90°-T-90°-(FID)  ln[I(t)]=ln(2)+ln[I(0)] -x/T,  phase cycle: 180° shift of ' H pulse  T of Si o r C with C P 2  Y  'H:  1 3  1 3  C:  90°-CP  T  H P D  CP-T-180 —c-(FID) 0  phase cycle: 180° shift of * H pulse  ln[I(t)]- ln[I(0)] = -2x/T  2  86  Regulator  a  for Drive Gas Supply  Cool Nitrogen Output for Bearing Gas Suply  SerfPressurizing Dewar  for Refilling of Small Dewar  To Probe Head Bearing Input  For Drive and Bearing Gas Supply  25 Its Dewar for Cooling down Bearing Gas  To Bruker MAS pneumatic input unit  Figure 2.3  Experimental set-up to run M A S N M R spectra at low temperatures.  87  2.7.  REFERENCES  1 Fyfe, C. A . ; Gobbi, G . C ; Murphy, W.J.; Ozubko, R.S.; Slack, D.A., J. Am. Chem. Soc, 4435,(1984). 2 Fyfe, C. A . ; Strobl, FL; Kokotailo, G.T.; Kennedy, G.J.; Barlow, G.E., J. Am. Chem. Soc, 3373,(1988).  106,  110,  3 Fyfe, C. A . ; Strobl, H.; Kokotailo, G.T.; Pasztor, C.T.; Barlow, G.E.; Bradley, S., Zeolites, 8, 132,(1988). 4 Fyfe, C. A . ; Grondey, H.; Feng, Y.; Kokotailo, G.; Mar, A., J. Phys. Chem., 95, 3747, (1991). 5 Fyfe, C. A . ; Grondey, H . ; Feng, Y.; Kokotailo, G.; Giess, H . , Chem. Review, 91, 1525, (1991). 6 Fyfe, C. A . ; Feng, Y.; Grondey, FL, Microporous Materials, 1, 393, (1993). 7 McDaniel, C.V., Maher P.K., in "Molecular Sieves", R. M . Barrer, Ed, Soc. Chem. Ind., London, (1968). 8 Hawthorne, S. B.; Miller, D. J.; Aulich, T. R., Fresenius ZAnal. Chem., 334, 421, 1989. 9 Frye, J. S.; Maciel, G.E., J. Magn. Reson., 48, 128, (1982). 10 Engelhardt, G.; Michel, D.; "High Resolution Solid State NMR of Silicates and Zeolites ", John Wiley & Sons, Chichester, 1987. 11 Jelinski, L. W.; Melchior, M . T., "High Resolution NMR of Solid", in N M R Spectroscopy Techniques, M.D. Bruch ed., Marcel Dekker, New York, 1996.  88  CHAPTER THREE INVESTIGATION OF THE STRUCTURE OF THE HIGH LOADED FORM OF P-XYLENE IN ZSM-5 B Y ' W S i CROSS POLARIZATION EXPERIMENTS AT ROOM TEMPERATURE i  3.1. INTRODUCTION Among the many zeolites known to date zeolite ZSM-5 occupies a unique place because of its high catalytic activity and the extreme size and shape selectivity it displays towards organic molecules'. These properties have been applied in various important industrial processes such as the conversion of methanol to high quality gasoline, the synthesis of ethylbenzene, and the catalytic production of p-xylene for the polymer industry . The high catalytic selectivity of Z S M 2  5 is attributed to the unique topology and the dimensions of the inner channels and cavities in the zeolite framework. This open framework allows the penetration and diffusion of molecules selected according to their molecular sizes ' . 3 4  Zeolite ZSM-5 is the best known of a whole family of zeolites called pentasils, which have closely related structures . The pentasil framework can be constructed from the secondary 5  building unit (SBU) of the 5-1 type as shown in Figure 3.1a. Pairs of 5-1 units are joined to form a building unit of the framework (Figure 3.1b), which is the asymmetric unit of the phase with the space group Pnma or half of the asymmetric unit of the other phases (see on). These units can be linked to form chains (Figure 3.1c), and such chains interconnected to form a layer, as shown in Figure 3.2A. Different ways of linking the layers form two different members of the pentasil family, ZSM-5 and ZSM-11. The ZSM-5 framework with 96 silicon sites per unit cell is formed when the sheets are connected such that neighboring pairs are related by an inversion center  89  (Figure 3.2b). The layers link together to form a three-dimensional network with two interconnected sets of 10-ring opening channels . One set consists of straight nearly circular 6  channels (5.4-5.6 A in diameter) that run parallel to the crystallographic (010) axis. The second set of elliptical 10-ring openings called zigzag or sinusoidal channels (cross section of 5.1-5.5 A) run along the perpendicular (100) direction. These are undulating channels with an angle of 112° between segments and are connected at right angles to the straight channels at the intersections.  (b)  (c)  Figure 3.1 (a) A secondary building unit of the 5-1 type, (b) A n asymmetric unit of orthorhombic form with the space group Pnma. (c) Chain-type building block. (From reference 6).  The structure of ZSM-5 was first deduced from powder diffraction studies by Kokotailo and co-workers in an "as synthesized form" containing template molecules and was found to 5  have orthorhombic symmetry and space group Pnma. Removal of the template molecules by calcination reduces the symmetry of the framework to monoclinic, space group P2i/n . These 6  90  Figure 3.2 (a) Skeletal diagram of a pentasil layer formed by linking the chain type building blocks, (b) Stacking sequence of layers in ZSM-5 (layer shaded), (c) The channel system in ZSM-5. (From reference 5). The adsorption properties of ZSM-5 toward hydrocarbons have been studied in detail. Recently, the adsorption desorption isotherms of p-xylene in H-ZSM-5 (Si/Al=132) at 313 K and  91 323 K were published . For sorbate loadings greater than 4 molecules per u.c. there is a sudden 9  increase in the adsorption from 4 to 7.6 molecules per u.c, at constant P/Po, with a hysteresesis loop as earlier observed by Olson . In this "high coverage" p-xylene/ZSM-5 system the 6  molecules were located by X-ray powder diffraction assuming orthorhombic Pnma symmetry . 10  In the straight channel, four p-xylene molecules are at the intersection of the channels with their long molecular axes perpendicular to the crystallographic mirror plane m and with their molecular center in m. In the sinusoidal channel, the other four p-xylene have their molecular plane coincident with the crystallographic mirror plane. A recent single crystal X-ray study by van Koningsveld and co-workers solved the structure which has orthorhombic symmetry 7  P2]2i2j  with an asymmetric unit of 24 silicon sites and Z=4. One of the two independent p-  xylene molecules lies at the intersection of the straight and sinusoidal channels with its long molecular axis nearly parallel to the straight channel axis. The second p-xylene molecule is in the sinusoidal channel with its long molecular axis nearly parallel to (100). This structure is very reliable and was used in all the data analysis in the present work. As described in the introduction, Fyfe and co-workers have followed the structural changes in zeolite ZSM-5 induced by the adsorption of p-xylene ' ' . A l l of the previous N M R work 11 12 13  was concerned with studying the three-dimensional frameworks of the zeolites but no quantitative work had been done to define the locations of the guest molecules by N M R . However, as will be seen, it is essential to know the assignments of the different  Si resonances  to specific T-sites and the assignments from previous studies were used in the present work. In order to obtain information about the positions of the guest molecules by N M R it is necessary to use experiments based on the dipolar interactions between the sorbed molecules and the silicon atoms in the zeolite framework. In this chapter we describe investigations which demonstrate the  92  potential of the Cross-Polarization (CP) M A S N M R technique to define the three-dimensional geometric relationship between sorbed organic molecules and the molecular sieve framework. The CP experiment is based on the heteronuclear dipolar interaction which is through-space and very strongly distance dependent, making it possible, in principle at least, to obtain quantitative structural data.  The system chosen for study was the orthorhombic form of zeolite ZSM-5  containing eight molecules of p-xylene per u.c. as there is considerable literature data available against which to measure the viability and reliability of this approach, and most importantly, there is an excellent single crystal X-ray diffraction derived structure . In addition, the  Si M A S  N M R spectrum shows highly resolved signals and all of them have been assigned to specific Tsites from I N A D E Q U A T E experiments ' . Samples of ZSM-5 loaded with 6, 7 and 8 molecules 14 15  of p-xylene per u.c were studied. Previous N M R studies showed that the phase transformation was complete at loadings equal to or higher than 6 molecules per u.c. Different loadings were studied to investigate possible differences in the three-dimensional framework structures and the dynamics and locations of the guest molecules inside the framework. In order to use the cross-polarization data to obtain quantitative information it is necessary to know the motional characteristics of the sorbate molecules. Some motions of the sorbed molecules such as ring flipping, or rotation about their molecular axes, can be taken into account in the second moment calculations. However diffusion of the molecules will average the dipolar interactions in an unknown manner, and therefore cannot be tolerated in structural studies of this type. In this chapter we use deuterium N M R spectroscopy of deuterated p-xylenes to obtain valuable information about the dynamics of the guest molecules in these complexes.  93  MOLECULAR MOBILITY OF P-XYLENE IN COMPLEXES OF Z S M - 5 STUDIED BY  3.1.1  DEUTERIUM N M R SPECTROSCOPY. Deuterium N M R spectra of stationary samples can be used to study molecular motions in solids . This technique has been extensively applied to study the dynamics of guest molecules 16  sorbed in zeolites  ' ' .The dominant interaction determining the line-shapes of solid state  1718 19 20  deuterium N M R spectra is the nuclear quadrupole interaction and the powder resonance lineshapes obtained can be a critical test for models of molecular motions. The basic theory supporting this topic is described briefly below. The deuterium magnetic resonance frequency in a magnetic field of intensity Bo is given by (3 cos (0) - 1 - 77 sin (0) cos(20))« 2  <o = y B ± D  2  0  0  ^  (3.1)  where yo denotes the magnetogyric ratio of the deuteron and cog the static quadrupole coupling constant (QCC):  here, eQ is the electric quadrupole moment of the deuteron, and eq=W represents the zz zz  component of the electric field gradient (EFG) tensor in its principal axis system. The angles 0 and <X> describe the orientation of the E F G tensor with respect to Bo in this system, and r| is the so-called asymmetry parameter, defined by  o<n<i  V -V ^ ^V^ =  (3.3)  zz  For deuterium bonded to carbon, the asymmetry parameter has been found to be approximately zero, and the z axis lies along the C-D bond. Hence equation 3.1 simplifies to  94  (3cos (0)-l) 2  ® = //A ±  2  w  e  (-) 3  4  where 0 is the angle between the principal component of the electric field gradient and the magnetic field vector. For a powder the resulting signal reflects the averaging of equation 3.4 over 0. The spectrum of a single type of deuteron in a polycrystalline material is a "Pake doublet" where the frequencies between both the inner and outer singularities yield the quadrupolar coupling constant as shown in Figure 3.3. When the molecules in the sample undergo a fast 21  reorientational motion, the quadrupolar interaction is averaged, resulting in a reduced and, in general, a biaxial, quadrupole tensor. The exact nature of the averaging depends on the details of the motion. Often this involves reorientional jumps of the molecule (and thus the principal quadrupole axis) between sites that are equally populated.  Figure 3.3 Variation of peak separation with the angle 9 formed between the principal component of the electricfieldgradient (EFG) tensor and the magneticfieldvector. (From reference 21).  95  The quadrupolar coupling constant (QCC) is very sensitive to the correlation time (x ) of r  the quadrupole energy fluctuations brought about by an anisotropic molecular motion. This results in an averaging of the electric field gradient (EFG) tensor at the  H nucleus. The  averaging of the QCC is dependent on the angle A formed between the rigid E F G tensor and the 99  •  •  rotation axis , as shown in Figure 3.4. Vega and co-workers studied the system of p-xylene sorbed at different loadings in ZSM-5 *  23  and calculated the theoretical deuterium N M R spectra for different kinds of averaging motions . The zeolite used was a synthetic material somewhat different from that used in the present work, with the unit cell formula Na Al Si96- Oi92, with n«3. Their studies used two isotopomers of pn  n  n  xylene, viz., p-xylene deuterated in the aromatic (p-xylene-c/^) and in the methyl (p-xylene-cfc) sites. Since the two deuteration sites are inequivalent, they are sensitive to different modes of motion of the p-xylene molecules and provide complementary information. The deuterium N M R line shapes calculated by Vega and co-workers for various possible motions are shown in Figure 3.5. In the calculation of the methyl group motion, it was assumed 19  that the methyl groups were freely rotating around their C 3 symmetry axes, resulting in an average axially symmetric quadrupole tensor of l/2(3cos (109)-l)=0.34 of the rigid value. 2  Further information concerning the molecular reorientation can be obtained from the deuterium line shape. When a particular motion occurs with a correlation time much less than T =10" s, which is the inverse of the quadrupole coupling constant cog«135 kHz, then the 5  c  spectrum will be narrowed from that observed in the rigid lattice. The deuterium spectrum of a CD3 group that is rapidly reorienting about its C3 axis (shown in Figure 3.5) has the shape of a powder pattern but the effective quadrupole splitting is reduced to usually cog«35-40 kHz in molecular solids. The effect of slow motions which occur with correlation times x >10" s, i.e., 5  c  96 those having a frequency less than co , are not observed in these experiments. The N M R time e  scale in the present case is defined by oo e , which represents an upper limit for slow motion.  Figure 3.4 Theoretical H N M R powder spectra of a methyl group: motional averaging of the electric field gradient tensor by rapid single axis rotation. (From reference 22)  97  Figure 3.5 Calculated deuterium NMR line shapes of p-xylene under various dynamic conditions. The traces on the left are for aromatic deuterons with COQ =3/4(e'qQ//0=135 kHz, r]=0, while those on the right are for methyl deuterons. In the calculation of the latter it was assumed that the methyl groups were rotating freely about their C3 axes, resulting in an average axially symmetric quadrupole tensor with COQ =-36 kHz. Traces (a) are for static molecules, (b) for molecules undergoing 7t-flips about their para axes, and (c) for molecules rotating freely about their para axes. Traces d-f are for molecules that in addition to free rotation about their para axis undergo discrete two or three site jumps. In (d) the molecules undergo two-site jumps by 112°. Traces e are as d but for 90° jumps. Traces (f) correspond to three-site jumps. In all calculations a line-width parameter 1/T2=1 kHz was used. (From reference 19).  98  When the correlation time is T «10" S, a broadening of the spectrum is observed and the 5  c  sharp features of the spectrum lost. For molecules undergoing very rapid isotropic reorientations as in a liquid, the quadrupole interaction is averaged to zero and a single narrow peak at zero offset frequency is observed.  The quadrupolar echo spectra of p-xylene d.4 and df, adsorbed on Na-ZSM-5 (6 wt % loading, equivalent to ~3 molecules per u.c.) at different temperatures are shown in Figure 3.6 . 19  It is easy to observe the changes occurring in the motional state of the molecules. By comparing the experimental and simulated spectra the following conclusions can be drawn. At low temperatures (-125 and -70 °C), the methyl groups are rapidly rotating about their threefold axis, while the benzene rings are either rigid (broad spectrum) or undergoing discrete 180° flips about their para axes (narrower lines). Above -70 °C the spectra of both the aromatic and methyl deuterons become strongly temperature dependent. The aromatic spectrum is composed of a narrow component, corresponding to free continuous rotation of the molecules about their para axis and also shows broader features due to static rings as well as molecules undergoing 180° ring flips. The spectra of the methyl groups can be interpreted as being composed of a broad component due the rapid rotation of the methyl groups in static molecules, and in molecules whose phenyl groups undergo either discrete 180° flips or free continuous rotation about their para axis. In addition, the narrow component in the spectrum characterizes molecules which undergo two site jumps of either 112° and 90° of their para axis. The latter motion was attributed to p-xylene molecules located near the channels intersections and jumping back and forth between neighboring segments in the straight and zigzag channels . 19  99  D  D D C-\£^-CD 3  D static K - flip free rotation around para axis  D  f r e e r o t a t l o n 3  methyl groups  1A1 25°C  static TI - flip  •70°C  static n - flip  -125°C  + two site jumps  + two site jumps  150 kHz  Figure 3.6  2  H N M R spin echo spectra of deuterated p-xylenes adsorbed in Na-ZSM-5 (6 wt  %) as a function of the temperature. (From reference 23).  100  3.2.  EXPERIMENTAL:  3.2.1  SAMPLE PREPARATION: Samples of ZSM-5 loaded with 6, 7 and 8 molecules per u.c. of p-xylene-Jg, and p-  xylene-c^ were prepared following the procedure described in Chapter 2, Section 2.2.3. 3.2.2  DEUTERIUM N M R EXPERIMENTS: Wide-line deuterium N M R spectra were obtained using a home-built probe which  accommodated both 10 mm and 5 mm horizontal solenoid coils. A quadrupolar echo sequence (90 -x-90 -x-acq ) x  y  24  was used and typical 90° pulse times were ca. 2.8 ps and 6 ps for the 5 mm  and 10 mm coils, respectively. 3.2.3  CROSS-POLARIZATION EXPERIMENTS: The Hartmann-Hahn condition was adjusted using Q M 8  8  (cubic octamer silicic acid  trimethylsilyl ester) according to the procedure described in Chapter 2, Section 2.4.2. Typical 90° pulse times were 11 ps ( H) and 11.2 ps ( Si). The S i spectra were referenced to TMS using !  Q M 8  8  29  2 9  as an intermediate external reference standard. The samples were rotated in the magic  angle between 2300 Hz and 3000 Hz.  3.3.  3.3.1  R E S U L T S A N D DISCUSSION:  DEUTERIUM N M R SPECTROSCOPY: As mentioned in the introduction, the p-xylene/ZSM-5 system has previously been studied  in detail by Vega and coworkers . Although the system studied was Na-ZSM-5 and is thus 23  significantly different from that studied here, the theoretical spectra for the different molecular  101 motions such as methyl group rotation and 180° ring 'flips' provide excellent reference points for the present work and were used in the interpretation of the spectra described below. The H spectra of the present samples are shown in Figure 3.7. The spectrum of the p2  xylene-^/8 molecules per u.c. intercalate (Figure 3.7 a) shows a very narrow central component, broadened by the line-broadening used to enhance the very broad main signal. The line shape of the broad component and the splitting of 130 kHz is indicative that the rings of p-xylene molecules are rigid at this temperature and this loading of p-xylene. The intensity of the major broad component in the spectrum is greatly underestimated in the quadrupolar echo experiment because of its very short T value. The narrow central line is indicative of completely isotropic 2  motion but the fraction of molecules involved is small (its concentration is estimated to be less than 10%) and most probably reflects molecules on the exterior surfaces of the crystallites or at defect sites at this maximum loading. Because ofthe mobility of the p-xylene molecules giving rise to this minor component, they will not participate in the cross-polarization experiments. The spectrum of the 6 molecules per u.c. loading shows the characteristic pattern of rigid rings (Figure 3.7 b), and does not show the narrow component, supporting the conclusion that the narrow signal is due to excess p-xylene on the exterior surface of the zeolite. This minor component was also observed in the T G A experiments (Figure 2.1 b) In the case of the p-xylene-c^ intercalates, Figures 3.7 c, d, the splitting in the H spectra is 2  now reduced to 44 kHz indicating free rotation of the methyl groups about their C 3 axes but there is no evidence of free rotation of the molecule or of large scale diffusion. Again a small, very narrow central resonance is observed for the 8 molecules per u.c. intercalate (Figure 3.7 c) which is again assigned to a small percentage of freely diffusing molecules adsorbed on the exterior  102  surface. The spectrum of the 6 molecules per u.c. form (Figure 3.7 d) is very similair to the 8 molecules per u.c. loading but does not show this narrow component.  Figure 3.7 (a) H N M R spectrum of p-xylene-c/4 in ZSM-5 at a loading of 8 molecules per u.c. at 293 K . The 90° pulse length was 2.8 ps, echo delay 12 ps, and 5204 scans were accumulated with a recycle delay of 12 s. The spectrum was processed with a line broadening of 2500 Hz. Due to the line broadening, the intensity of the narrow line is enhanced, (b) H N M R spectrum of p-xylene-d4 in ZSM-5 at a loading of 6 molecules per u.c. at 293 K . The 90° pulse length was 2.8 ps, echo delay 12 ps, and 912 scans were accumulated with a recycle delay of 6 s. The spectrum was processed with a line broadening of 6000 Hz. 2  2  103  44 KHz  u  (d)  6 molec./u.c.  ( c )  8 molec./u.c.  200000  +  i  100000  0  ^  H  -100000  -200000  Figure 3.7 (c) H N M R spectrum of p-xylene-de in ZSM-5 at a loading of 8 molecules per u.c. The 90° pulse length was 6 ps, echo delay 8 ps, and 3676 scans were accumulated with a recycle delay of Is. The spectrum was processed with a line broadening of 200 Hz. (d) H N M R spectrum of p-xylene-d6 in ZSM-5 at a loading of 6 molecules per u.c. The 90° pulse length was 3.5 ps, echo delay 9 ps, and 128 scans were accumulated with a recycle delay of Is. No line broadening was used in processing this spectrum. 2  104  Thus, both p-xylene molecules have rigid rings and rotating methyl groups at sorbate loadings between 6 and 8 molecules and this must be taken into account in the calculations of second moments and distances. It should be emphasized that the location of discrete atomic positions in diffraction experiments does not necessarily indicate the absence of molecular reorientations as these are often between equivalent positions, i.e. positions of minimum potential, as in the case of 180° ring flips, and as such are not detected by diffraction experiments which reflect the positions which most of the atoms occupy most of the time. Even where 25  diffraction experiments detect disorder, this could still be either static or dynamic in nature . It must be noted that the above results provide information about the dynamics of the pxylene molecules "on the deuterium time scale" i.e. for motions occurring at correlation times smaller than the quadrupolar splitting constant co =120 kHz, i.e. T <10" S. Slower motions are 5  Q  c  not detected in these experiments, as will be discussed later. 3.3.2  VARIABLE CONTACT TIME 'H/ SI N M R C P / M A S EXPERIMENTS: 29  Figure 3.8 shows the S i CP M A S spectra for zeolite ZSM-5 loaded with 6, 7, and 8 molecules 2 9  of p-xylene. As can be seen, the spectra indicate that the framework structure is the same at all loadings. As previously reported, the 8 molecule per u.c. form is orthorhombic, space group P2j2i2i, and has 24 T-sites in the asymmetric unit . The assignment of the different resonances 7  to the appropriate silicons shown in the Figure 3.10, inset, comes from previously reported I N A D E Q U A T E experiments ' . In the spectra, the resonances corresponding to silicons 1, 3, 12 13  10, 12, 16 and 17 are reasonably well-defined and these will be used in the structure determinations.  105  Figure 3.8: Si CP M A S N M R spectra of the complex of p-xylene-^ in ZSM-5 (a) at a loading of 6 molecules per u.c., (b) 7 molecules per u.c, and (c) 8 molecules per u.c. A l l the spectra were obtained under the same experimental conditions: contact time 5 ms, recycle delay 5s.  106 In order to obtain meaningful information from the cross-polarization experiments with respect to the structure of the sorbate/ framework complex the distances between the protons on the guest molecules and the silicon nuclei in the framework must be reasonably well defined. This was achieved in the present work by investigating two closely related partially deuterated systems; p-xylene-d,/ (1), where the polarization source is the protons in the methyl groups and p-xylene-J(5 (2), where the polarization source is the four protons on the aromatic ring. Although the proton spin systems do not qualify as "isolated nuclei" which is obviously the optimum situation for obtaining unambiguous structural data from these experiments, their isolation was good enough to obtain reliable data.  The cross-polarization experiments were carried out using the standard spin-lock sequence shown in Figure 3.9 with spin temperature inversion to suppress artifacts  . During the spin-  locking step, there is coherence transfer from ' H to S i via the heteronuclear dipolar interaction 2 9  when the two spin-locking fields H  J ( H )  and H  1 ( G J )  satisfy the Hartmann-Hahn match condition,  Equation 3.5  ^HH](H)  =  ^siHi(si)  (3-5)  107  In the present work the two r.f. fields were matched experimentally. The experimental Hartmann-Hahn match conditions for the sample studied were relatively broad.  contact time  to allow protons to ireequilibrate  •  1  29  Figure 3.9: Cross-polarization pulse sequence for polarization transfer from H to Si.  Quantitatively, the cross-polarization process is usually described as in Equation 3.6 with the assumptions that T  l p ( H )  « T  time in the rotating frame and T  lp(Si  ) and T  l p ( S i )  l p ( S i )  is very long, where T  l p ( H )  is the proton relaxation  is the silicon relaxation time in the rotating frame. Also the  number of ' H nuclei must be much larger than the number of S i nuclei. This latter condition is 29  at least approximately satisfied in the present cases because of the low natural abundance of S i 2 9  (4.6%). However, in samples of this type, the protons are present at quite low concentrations and there may be relatively small homonuclear dipolar couplings between protons on different molecules, so the proton reservoir may not be a strongly coupled homogeneous spin system.  108  Thus, Equation (3.6) is expected to give an approximate description of the behavior of the S nucleus magnetization only. -1 - CP.  exp -t/  T  X  i (//)J  7  exp  \p(H)J  T  P  v /  cpJ )  (3.6)  T  I represents the theoretical maximum signal intensity obtainable from the polarization 0  transfer in the absence of any loss due to relaxation processes.  Of particular importance, the  cross-polarization rate constant 1/Tcp is proportional to the second moment of the dipolar line 27  shapes  according to Equation 3.7 and hence has a dependence on the internuclear distance of  l/r6. C(Aa>%  1/TCP  (Aco ) 2  9  172  (3.7)  //  9  where C is a constant and (Aco ).„and (Aco ) „ a r e the heteronuclear (I, S) and homonuclear (1,1) second moments, respectively. The second moments can be calculated from the van Vleck equation as described in Chapter 1, section 1.2.3.3.1. 2  1/TCP  a  (Aco )  It is anticipated then that the  2  29  / s  a  2  ^J-If-  (3.9)  S i CP M A S N M R spectra of these systems will show  substantial differences in the enhancements of the different signals based on their distances from the proton magnetization sources and that these effects might be used to determine the geometric relationship between the host lattice and the organic guest molecules. The effects of the distance dependence can be seen qualitatively from a comparison of the CP spectrum with that from a  109  simple quantitative one-pulse experiment as shown in Figure 3.10. The structure is orthorhombic with 24 T-sites of equal occupancy  and the assignment of the resonances comes from the  previous 2D I N A D E Q U A T E experiments ' . 15 16  I  1  1  1  1  1  1  1  1  1  1  1  -110 -111 -112 -113 -114 -115 -116 -117 -118 -119 -120 -121 Figure 3.10: (a) Si CP M A S N M R spectrum of ZSM-5 loaded with 8 molecules p-xylene-J per u.c, contact time 5 ms, recycle delay 5 s. (b) S i M A S N M R spectrum of the same sample obtained using a recycle delay of 350 s to ensure complete relaxation of the silicon nuclei. The 90° pulse length was 13 ps.  6  2 9  110  In the CP experiment some signals are obviously enhanced compared to the others. The resonances due to silicons 1, 3, 10, 12, 16, and 17 are quite well resolved and these were used in the further investigations. Since the structure is known in the present instance, it will be possible to compare calculated second moment values from this structure with the Tcp values deduced experimentally from Equations (3.6) and (3.7). Table 3.1 lists the closest Si-H distances calculated from the X R D structure . The hydrogen 7  positions were determined indirectly from the X R D data using a C-H distances of 0.98 A for the aromatic hydrogens and 1.1 A for the methyl hydrogens, and the appropriate geometry for the C H 3 group. The numbering of the hydrogen atoms reflects the two different kinds of p-xylene molecules, X Y L 2 (3) located in the sinusoidal channels and XYL1(4) located at the intersection of the sinusoidal and straight channels as shown in Figure 3.11. The figure also shows the locations of silicons 1,3, 10 , 12, 16, and 17, as does Figure 3.12 which gives a clearer picture of the immediate environment of X Y L 2 .  X Y L 2 (3)  X Y L 1 (4)  Ill  Table 3.2 presents some important relaxation parameters for the 1H and 29Si nuclei in the p-xylene/ZSM-5 complex.  T a b l e 3.1:  Shortest calculated S i - H distances ' from the single crystal X R D data for the 1  complex of p-xylene in Z S M - 5 with 8 molecules per u.c..  2 9  S i T-Site  Si  Si  Si  Si  Si  Si  1  10  1  12  17  16  3  Harom.  atom  r i-H (A) S  HCH3  atom  rsi-H (A)  H-2  4.318  H-5  3.596  H-13  5.413  H-9  3.804  H-l  5.889  H-8  5.858  H-13  3.963  H-19  3.566  H-l  5.166  H-8  3.586  H-3  5.354  H-5  4.103  H-3  3.205  H-18  4.494  H-12  3.386  H-10  4.990  H-4  3.915  H-8  5.400  H-l  3.607  H-5  3.778  H-13  3.572  H-19  4.089  H-2  5.044  H-20  4.495  H-l  4.344  H-5  3.508  H-4  4.758  H-7  4.463  H-2  5.318  H-6  5.016  H-3  3.132  H-18  4.101  H-4  3.619  H-19  4.408  H-12  4.627  H-15  4.795  ' The hydrogen atomic positions were calculated using a C - H distances of 0.98 A for the  aromatic hydrogens and. 1.1 A for the methyl hydrogens, and the appropriate geometries for a tetrahedral C H 3 group and planar aromatic ring.  112  Figure 3.11: Schematic representation of a view down the straight channel of the ZSM-5 lattice showing the locations of the p-xylene molecules in the sinusoidal channel (XYL2), and in the intersection of the channels (XYL1). Oxygens are omitted for clarity. Representations are based on the structural data of reference 7.  113  10  22  Figure 3.12. Schematic representation of a view along the sinusoidal channel (100) ofthe Z S M 5 lattice showing the location of the p-xylene molecule (XYL2). Oxygens are omitted for clarity. Representations are based on the structural data of reference 7.  2 9  S i C P / M A S spectra were obtained as a function of the contact time (CT) up to a  maximum of 60 ms for samples of ZSM-5 loaded with 6 and 8 molecules of the specifically deuterated p-xylenes (1) and (2). The spectra were deconvoluted in terms of Lorentzian functions and the intensities of the reasonably well resolved resonances due to silicons 1, 3, 10, 12, 16, and  114  17 tabulated. Figure 3.13 shows plots of these data for the p-xylene-^ sorbate (1) and Figure 3.15 for the p-xylene-^ (2) system. In general terms, the curves in Figures 3.13 and 3.14 approximate the behaviour expected from Equation (3.6). That is, there is an exponential growth due to polarization transfer and a decay from the loss of proton magnetization due to T  l p ( H )  . The  curves which grow fastest have the highest maxima and the maxima in the series shift to longer contact time values as they become lower. There are also consistencies between the different two data sets. Thus, in Figure 3.13, the curves for both sorbate loadings indicate that silicons 12, 3, and 17 are much more efficiently polarized (and hence closer to the H polarization source) than !  silicons 16, 10, and 1. Qualitatively this is in excellent agreement with the Si-H distances shown in Table 3.1. In the 8 molecules per u.c. case (Figure 3.13 b) the distinction is clearest in the early part of the curves where the growth is dominated by T . For the case of 6 molecules per C P  u.c. (Figure 3.13 a) this agreement becomes more evident. The corresponding curves for a loading of 7 molecules per u.c. (not shown) exhibit intermediate behavior. A similar trend is seen for the p-xy\ene-d system (Figure 3.15) where silicons 10, 1, 17, 4  and 3 polarize much more efficiently than silicons 16 and 12. ). Once more, this is in agreement with the Si-H distances from X R D shown in Table 3.1. Again the effect is more obvious for the loading of 6 molecules per u.c (Figure 3.15 a). Also, the behavior observed at a loading of 7 molecules per u.c. (not shown) is again intermediate. It should be noted that in the figure for a loading of 6 molecules per u.c. the maximum observed for the curve corresponding to Si 10 is very similar to the one from Si 17, although the Si 10 curve is the one which grows faster and has shorter Tcp value and consequently we should expect a higher maximum. The difficulty is that the peaks corresponding to Si 1 and Si 10 are very close together, and since they have very  115  Figure 3.13. Intensities of the Si CP M A S N M R signals as functions of the contact time at room temperature for: (a) ZSM-5 with a loading of 6 molecules p-xylene-^ per u.c, (b) ZSM-5 with a loading of 8 molecules p-xylene-d^ per u.c.  116  0.00  50000.00  100000.00 150000.00 200000.00 250000.00  Calculated second moment (Hz ) 2  ( b )  120  T  04 0.00  1  1  1  1  1  50000.00 100000.00 150000.00 200000.00 250000.00  Calculated second moment (Hz ) 2  Figure 3 . 1 4 : Plots of experimental TCP values vs. the calculated second moment (A® ) is values for the complexes of p-xylene-J<j in Z S M - 5 at room temperature, (a) 6 molecules per u.c. (b) 8 molecules per u.c. 2  117  similar TCP values it is not possible to have a completely accurate deconvolution and their intensities could be somewhat in error. However this problem affects the accuracy of the Tcp values obtained only very slightly because they are mainly determined from the initial rise of the curves.  Table 3.2: Selected relaxation parameters for the H and Si nuclei in the p-xylene/ZSM5 complex. !  8 molecules/u.c.  6 molecules/u.c. ca. 5T[ (s)  29  ca. 5Ti (s)  Tlp(H)  (ms) 12.0  8.0  T (ms) 0.034  H (ring)  5.0  T (ms) 0.0409  'HCCHs)  6.0  0.0531  58.0  8.0  0.053  >800  350.0  6.0 - 22.0  -  -350.0  6.0 - 60.0  -  Nuclei !  Si (framework)  2  2  T  lp(H)  (ms) >800  The variable contact time cross-polarization curves were fitted to Equation 3.6, with T , fixed. The fittings were done using the non-linear statistics package in the  p ( H )  Mathematica  program. The program also calculates the asymptotic standard errors for the parameters determined in the fitting. The differences in behavior between the six and eight molecule loadings are due mainly to differences in the T  l p ( H )  values (see Table 3.3). At loadings of 8 molecules per u.c, the T  values are too long relative to the T  C P  values for clear decays to be observed for the curves and  Equation 3.6 simplifies to  WW,  l p ( H )  f 1 -exp V  W  / CPJJ T  (3.10)  118  Table 3.3: Experimental and calculated parameters related to the ^ ^ S i cross-polarization experiments on the complex of p-xylene-rf in ZSM-5 with 6 molecules per u.c. at room temperature. 6  (a) Io varied, TI (H> fixed at 12 ms. (b) I , Tip(H) fixed. P  0  Resonance (ppm)  Si 10  (a.u.)  T (ms)  x  -111.6  77±4  17±1  204.0  42,548  Si 1  -112.0  64±3  13±1  213.8  58,338  Si 12  -116.7  104±2  2.5±0.1  278.7  231,890  Si 17  -117.3  71±1  4.5±0.2  83.8  129,398  Si 16  -117.6  71±3  18±1  156.6  46,716  Si 3  -118.9  92±1  2.8±0.1  113.9  193,823  (a) T-Site  (a)  Io  ( a )  C P  (Aco ) calc  2  2  (b)  /s  (Hz ) 2  Calculated using a non-linear fitting program, fixing Ti ( )=12.0 ms in Equation 3.6. p H  (b)  Calculated from the XRD data taking into account all Si-H interactions up to a distance of 8  A.  (b)  "Si  T-Site  (c)  Resonance (ppm)  (a.u.)  T (ms)  x  Io  .  ( C )  C P  (Aco ) calc  2  2  (d)  /?  (Hz ) 2  Si 10  -111.6  103.7  28±2  439.8  42,548  Si 1  -112.0  103.7  30.5±3  725.3  58,338  Si 12  -116.7  103.7  2.5±0.1  279.0  231,890  Si 17  -117.3  103.7  10±1  1775  129,398  Si 16  -117.6  103.7  32±2  442  46,716  Si 3  -118.9  103.7  3.2±0.2  569  193,823  Calculated using a non-linear fitting program, fixing Ti (H)=12.0 ms and I =103.7 in Equation p  o  3.6. (d)  A.  Calculated from the XRD data taking into account all Si-H interactions up to a distance of 8  119  In the case of ZSM-5 loaded with 6 molecules of p-xylene- d per u.c. (Figure 3.13 a), 6  values for T  l p ( H )  and I were obtained from least squares fits to the linear decays of plots of log I 0  vs. CT for Si 12 and Si 3. The average value of T  lp(H)  =12.0 ms was used in fitting all of the  curves (Table 3.3 a). Estimates of I = 103.7 are also obtained for these two sites (Table 3.3 b). 0  Using the fixed value of T  ] p ( H )  and fitting the curves using a non-linear least squares fit to  Equation (3.6) to obtain I and T 0  C P  gives the data in Table 3.3 a. The calculated curves from  these fits are those shown together with the experimental data points in Figure 3.13 a. There is some variation in I  0  (the theoretical maximum magnetization) for the different silicon sites.  Although all are of equal occupancy in the structure, it is possible that I could vary as there is 0  some degree of isolation of the groups of proton spins, and different silicon sites may be in contact with different numbers of protons. Keeping, both I and T 0  for Si 12 yields a slightly different set of T  c p  fixed at the value found  l p ( H )  values (Table 3.3 b) but the order is unchanged.  From the known structure, the second moment values can be calculated as indicated in Tables 3.3 and 3.4. The motional characteristics observed in the H N M R spectra were 2  considered in the calculation of the intermolecular heteronuclear second moments (I,S). The total second moment for the interactions of the methyl hydrogens with the silicon atoms was averaged for a rotation around the methyl C 3 axis (Table 3.4) and a static model was used in the case of 28  28 29  the interactions between the aromatic hydrogens and the silicons in the zeolite framework ' (Table 3.3). The programs written to calculate the second moments are shown in Appendix 1 for interactions of the static aromatic protons, and in Appendix 2 for the methyl group interactions.  120  Contact tlmo (ms)  Figure 3.15: Intensities of the Si CP M A S N M R signals as functions of the contact time at room temperature for: (a) ZSM-5 with a loading of 6 molecules p-xylene-^ per u.c, (b) ZSM-5 with a loading of 8 molecules p-xylene-c/4 per u.c.  121  Since T  is directly related to the H / S i heteronuclear second moment via Equation (3.9), 1  C P  a plot of 1/T  CP  vs (Aco )  / 5  29  should be a straight line that goes through the origin. Such  correlations are shown in Figure 3.14 for p-xylene-d (1). Linear correlations are obtained for 6  both loadings; however in the 8 molecules case, the straight line deviates considerably from the origin. Similar results are obtained for the complexes of ZSM-5 with p-xylene-^ (2). In the sample containing 8 molecules per u.c. (Figure 3.15 b) there is no clear decay of the contact time curves due to a long T,  ( H )  value, but qualitatively the order of the signal enhancements is as  expected. The situation is much clearer for the case of 6 molecules per u.c. (Figure 3.15 a). Here, the most intense signals (silicons 1 and 10) show a linear decay when log I is plotted vs. CT, and can be used to determine T  l p ( H )  . If T  l p ( H )  is fixed to the average value of 58 ms in a non-linear  least squares fitting of Equation (3.6) for all of the data, the curves shown together with the experimental data in Figure 3.15 (a) are obtained. As in the p-xylene-d case, there is some small 6  variation in T  C P  depending on whether I is fixed at the value found for Si 10 or used as a 0  variable (Table 3.4). Again the plots of 1/T  CP  vs. the calculated second moments (averaged for  three-fold reorientation of the methyl groups) (Figure 3.16) give linear correlations for both loadings but in the case of the 8 molecules per u.c. loading the straight line does not pass through the origin. Thus the general behavior observed in the CP experiments is in reasonably good agreement with that expected from theory.  122  Table 3.4: Experimental and calculated parameters related to the 'H/ Si cross-polarization experiments on the complex of p-xylene-rf^ in ZSM-5 with 6 molecules per u.c.. at room temperature. 29  (a) Io varied, TI (H>fixedat 12 ms. (b) I , Tip(H) fixed. P  0  (a)  (a)  Resonance (ppm)  Io (a.u.)  T (ms)  Si 10  -111.6  43.70.4  6.210.2  35.2  (Hz ) 41,735  Si 1  -112.0  41.1+0.2  6.310.1  11.0  38,985  Si 12  -116.7  34.7±0.5  14.710.5  17.5  10,751  Si 17  -117.3  44.610.4  9.010.2  20.2  29,425  Si 16  -117.6  33.510.5  11.710.4  18.9  24,547  Si 3  -118.9  43.310.4  9.410.3  22.7  16,783  Si T-Site 2 y  (a)  ( a )  C P  2(a)  (Aco ) calc 2  (b)  /s  2  Calculated using a non-linear fitting program, fixing Ti ( )=58.0 ms in Equation 3.6. P  (b)  x  H  Calculated from the X R D data taking into account all Si-H interactions up to a distance of 8  A.  (b)  Resonance (ppm)  Io (a.u.)  T () ICP  Si 10  -111.6  43.7  6.210.2  35.2  (Hz ) 41,735  Si 1  -112.0  43.7  7.210.2  49.0  38,985  Si 12  -116.7  43.7  20+1  128.7  10,751  Si 17  -117.3  43.7  13.010.2  25.0  29,425  Si 16  -117.6  43.7  1811  231.0  24,547  Si 3  -118.9  43.7  9.810.2  23.0  16,783  Si T-Site i y  (c)  c  x  2(c)  (ms)  (Aco ) calc 2  (d)  /s  2  Calculated using a non-linear fitting program, fixing Ti (H)=58.0 ms and Io=43.7 in Equation 3.6. Calculated from the X R D data taking into account all Si-H interactions up to a distance of 8 (c)  (d)  A.  P  123  The linear correlation for the p-xylene-fi^ case (Figure 3.16) does not appear to be as good as those for p-xylene-^ (Figure 3.14). However, it should be noted that due to the motional averaging of the methyl interactions, the second moments are much smaller and the TCP values are spread over a smaller range. Another source of error is the p-xylene-^ isotopic purity. This compound was synthesized as described in Chapter 2, Section 2.2.2.1, by deuterium exchange of the p-xylene's aromatic protons with a mixture of D2O/DCI. The reaction is a chemical equilibrium between protonated and deuterated p-xylene, thus in order to shift this equilibrium toward the complete deuteration of the aromatic protons, a large excess of D2O was used and the exchange process was reapeated several times on the same material. The exchange yielding was followed by *H N M R , however the best isotopic purity obtained was 0.2 aromatic hydrogen for every 6 methyl hydrogens, i.e. equivalent to having a 5 % of p-xylene molecules with one residual proton. Because of the larger second moments for the aromatic heteronuclear interactions, this residual proton would affect the enhancement of the measured intensities for the silicon atoms, specially for Si 12 and Si 3 which have the larger dipolar interactions (and the larger second moments) with the aromatic protons. This could explain slightly higher TCP values obtained for these silicons than those expected from the linear regression (Figure 3.16). We suspected that the problems with the fitting of the CP data in the case of 8 molecules of p-xylene per u.c. loadings might possibly be due to a very slow diffusion process of the p-xylene molecules occurring within the channels. This motion could be too slow to be detected on the time scale of the deuterium N M R experiment but it could be of critical importance in the CP experiments when working with contact times as long as 60 ms. Any such diffusion process could produce substantial errors in the CP curves. In the fitting of the CP curves for the 8 molecules per u.c. loading, these would be magnified due to the long T,  ( H )  where the signal  124  intensities do not decay for contact times longer than 10 ms (unlike the case of the 6 molecules per u.c. loadings), therefore, these intensities at longer contact timesare heavily weighed during the fitting process. Because the problem of slow motions not detected by deuterium N M R could be quite general and would be of critical importance for reliable structure determinations, this was investigated is some detail as described in Chapter 4.  125  Figure 3.16: Plots of experimental TCP values vs. the calculated second moment (Aco'')/s values for the complexes of p-xylene-^ in ZSM-5 at room temperature, (a) 6 molecules per u.c.. (b) 8 molecules per u.c.  126  3.4. REFERENCES  1. (a) Breck, D. W. "Zeolites Molecular Sieves"., John Wiley, New York, (1974). (b) Meier, W.N. 'Molecular Sieves'", Barrer, R . M . Ed., Soc. Chem. Ind. London, (1968). 2. Chen, N . Y . , Degnan, T.F.Jr., Smith, C M . , "Molecular Transport and Reaction in Zeolites. Design and Application of Shape selective Catalysis", V C H , New York, pg 33, (1994). 3. Smith, J.V., "Zeolites Chemistry and Catalysis". Rabo, J.A. Ed., A.C.S. Monograph, 171, (1976). 4. Barrer, R. M . , "Zeolites and Clay Minerals as Sorbents and Molecular Sieves". Academic Press, London, (1978). 5. Kokotailo, G.T., S.L., Olson, D., Meier, W., Nature, 272, 437, (1978). 6. Olson, D.H., Kokotailo, G.T., Lawton, S.L., Olson, D., Meier, W., J. Phys. Chem., 85, 2238, (1981). 7. van Koningsveld, H., Jansen, J . C , van Bekkum, H., Acta Cryst., B43, 127, (1987). 8. van Koningsveld, H., Jansen, J . C , van Bekkum, H., Zeolites, 10, 235, (1990). 9. Richards, R. E., Rees, L. V . C , Zeolites, 8, 35, (1988). 10. Mentzen, B. F., Bosselet, F., Bouix, J., C. R. Acad. Sci., 305, 581, (1987). 11. Fyfe, C.A., Strobl, H., Kokotailo, G.T., Kennedy, G.J., Barlow, G.E., J. Am. Chem. Soc, 110, 3373, (1988). 12. Fyfe, C.A., Feng, Y., Grondey, H . Microporous Materials, 1, 393, (1993). 13. Fyfe, C.A., Grondey, H., Feng, Y . , Kokotailo, G.T., Giess, H. Chem. Review., 91, 1525, (1991). 14. Fyfe, C.A., Grondey, H . , Feng, Y . , Kokotailo, G.T., Mar, A . J. Phys. Chem., 95, 3747, (1991).  127  15. Fyfe, C.A., Grondey, H., Feng, Y., Kokotailo, G.T., Ernst, S., Weitkamp, J. Zeolites, 12, 50, (1992). 16. Hentschel, D., Sillescu, H., Spiess, H.W., Macromolecules, 103, 7707, (1981). 17. Eckman, R., Vega, A.J., J. Am. Chem. Soc, 105, 4841, (1983). 18. Eckman, R., Vega, A.J., J. Phys. Chem., 90, 4679, (1986). 19. Luz, Z., Vega, A.J., J. Phys. Chem., 90, 4903, (1986). 20. Stepanov, A . G . , Maryasov, A.G., Vyacheslav, N.R., Zamaraev, K., Mag. Reson. Chem., 32, 16, (1994). 21. Fyfe, C A . Solid State NMR for Chemists, CFC Press, Guelph, ON, (1984). 22. B.Nagy, J., in "Multinuclear Magnetic Resonance in Liquids and Solids-Chemical Applications", Grander, P. and Harris, R.K., Eds. N A T O ASI Serie C, V o l 322. Kluwer Academic Publishers, Dordrecht, The Netherland, pg 371, (1990). 23. Kustanovich, I., Fraenkel, D., Luz, Z., Vega, S., J. Phys. Chem., 92, 4134, (1988). 24. Bloom, M . , Davis, J.M., Valic, M.I., Can. J. Phys., 58, 1510, (1980). 25. Fyfe, C.A., Veregin, R.P., Amer. Cryst. Assoc., 43, (1970). 26. Stejskal, E.O., Schaefer, J., J. Mag. Reson., 34, 443, 1979. 27. (a) Pines, A., Gibby, M.G., Waugh, J. S., J. Chem. Phys., 59, 569, (1973). (b) Yannoni, C.S., Acc. Chem. Res., 15, 201, (1982). 28. Michel, J., Drifford, M . , Rigny, P., J. Chim. Phys., 67, 31, (1970). 29. Slichter, C P . , Principles of Magnetic Resonance, Springer-Verlag, New York., pg. 65, (1990).  128  CHAPTER FOUR INVESTIGATION OF SLOW MOLECULAR MOTIONS AND DIFFUSIONAL BEHAVIOR IN THE HIGH LOADED FORM OF ZSM-5 WITH p-XYLENE BY TWO-DIMENSIONAL 13  C SOLID STATE NMR CHEMICAL EXCHANGE EXPERIMENTS  4.1. I N T R O D U C T I O N : The deuterium N M R spectra discussed in Chapter 3 for the system of 8 molecules of pxylene in ZSM-5 showed no evidence of diffusion or of free rotation of the organic guest molecules within the channels, the p-xylene molecules having rigid rings and rotating methyl groups at sorbate loadings between 6 and 8 molecules. However the detailed cross polarization studies described in that chapter could not be fitted exactly to the theoretical equations suggesting, perhaps, the presence of some very slow molecular motions not detected on the time scale of the deuterium N M R experiments (x =10~ s). Because of the small dipolar couplings 5  c  involved and the corresponding long contact times of up to 60 ms, very slow motions could have an appreciable effect on the fits particularly for the 8 molecule loading. In this chapter we demonstrate how 2D C N M R exchange spectroscopy can be used to study the complex slow 1 3  molecular dynamics of this system. Neutron and X-ray diffraction investigations can give information on long range order for sorbate configurations'' . However, locating discrete  atomic positions  in diffraction  experiments does not necessarily indicate the absence of molecular reorientations as these are  129  often between equivalent positions. Even where disorder is detected, it could be either static or dynamic in nature. Information on the dynamics of local guest species is difficult or impossible to obtain from these methods because of their very fast timescales, i.e. they detect where most of the atoms are most of the time. Pulsed field gradient N M R methods have been applied to measure long time motions such as large scale molecular self diffusion (ca. 1 pm) ' over long times and solid state 2D 4 5  deuterium exchange N M R spectroscopy has been successfully used by Spiess and co-workers for studying the reorientation mechanisms and timescales of slow motional processes in polymers ' ' . 6 7 8  Very few applications of 2D exchange spectroscopy to zeolite systems have been published: One reason for this could be that in these complicated systems the N M R signals of the guest sorbates very often do not show chemical shift differences. In some recent studies, 2D 129  X e exchange N M R on static samples has been used to measure the slow intercage migration of  xenon atoms physically adsorbed in NaA zeolite, relying on the high mobility of the xenon atoms within the cages to produce narrow isotropic N M R lines ' . In a recent communication Chmelka 9 10  and co-workers have reported 2D exchange C N M R spectra of adsorbed benzene molecules in 1 3  a static sample of powdered Ca-LSC. The benzene molecules bind to Ca  adsorption sites,  causing the observed C N M R spectra to depend on the orientation of the benzene molecules l 3  with respect to the external magnetic field Bo making possible the observation of molecular exchange between different benzene sites . 11  The results presented in this chapter demonstrate for the first time the application of high resolution C C P / M A S 2D N M R exchange spectroscopy to investigate the molecular motions of 1 3  guest molecules inside zeolite catalysts and to obtain critical kinetic information on these  130  processes. Particularly important in the context of the present work, the method detects very slow motions which do not affect the deuterium N M R spectra but which can have large effects on techniques such as CP, REDOR, and TEDOR when they are used to determine internuclear distances. The application of the 2D-CP-NOESY technique to study exchange in solid state systems was first proposed by Maciel and co-workers . This method is completely analogous to the two12  dimensional experiment introduced by Ernst and coworkers to study chemical exchange and spin diffusion processes in the liquid state . The two pulse sequences are identical except that the 13  first 90° pulse applied to the C spins in the liquid state N O E S Y experiment is replaced by a CP 1 3  sequence to make use of the favorable relaxation and sensitivity properties of the abundant nuclei ('H in this case) to generate observable magnetization in the less abundant spin system ( C in 13  this case) as shown in Figure 4.1. The pulse sequence depicted in Figure 4.1 can be visualized in terms of four discrete time periods. In the preparation period the ' H magnetization is transferred to the dilute spins ( C) 13  through cross polarization, resulting in observable magnetization for the dilute nucleus. The various components of the transverse magnetization created by CP are chemical shift labeled when they precess with proton decoupling at their characteristic resonance frequencies during the "evolution period" tj. The 90° pulse following the evolution period transfers the shift encoded x,y magnetization into  1 3  C chemical  C z magnetization, which therefore depends on the  1 3  C  precessional frequency, making it possible to keep track of each chemically shifted  C  isochromat during the subsequent mixing period . •  *  •  *  *  *  •  13  The mixing period is a fixed time interval x which allows communication between  C  m  spins. This communication may take the form of chemical exchange in which a particular C 1 3  131  nucleus experiences a new chemical shift as the result of relocation to a different environment in the molecular or crystal structure. Another possibility includes spin diffusion via dipolar coupling. However for dilute nuclei (e.g. C ) this mechanism proceeds via the protons and can 13  be quenched i f proton decoupling is carried out during the mixing period. The resulting distribution of longitudinal magnetization components is converted back into observable x,y magnetization by the second 90° pulse and the FID recorded with proton decoupling, generating a second C chemical shift scale. 1 3  preparation  13  C  Figure 4.1  decouple  (spin lock) evolution  90  contact time  tl  j  GO C  X  90  ^  acquisition  90  Pulse sequence for 2D exchange spectroscopy (experiment 2D-CPNOESY).  As is usual in 2D N M R techniques, the experiment has to be repeated for a number of equally incremented values of the evolution time ti. The result is a data matrix S(ti,t2), the double Fourier transform of which yields the desired 2D spectrum S(coi,co ), where both 2  frequency axes, Fi and F are C chemical shift scales. The appearance of off diagonal peaks at 1 3  2  coi,co frequencies in this 2D spectrum indicates that an exchange process is occurring during the 2  132  mixing period and has transferred magnetization components of precession frequency coi to a precession frequency ©2. This experiment can provide not only qualitative information but also quantitative kinetic data for the exchange process as will be discussed below. We limit the analysis of this experiment to a particularly simple situation where each of the N nuclear sites j is characterized by a single characteristic frequency co (corresponding to its chemical shift) and spin-spin y  coupling effects are absent. The treatment follows that originally given by Ernst ' . 13 14  4.1.1  RATE PROCESSES IN A SYSTEM WITH TWO SITES We consider here a system with two sites (or it could also be two molecules A and B ) . A  first order slow chemical exchange process is assumed,  A  kAB -  B  (4.1)  BA  which is described by the kinetic matrix K K =  - k AB • AB  BA  -k  (4.2)  BA  Longitudinal relaxation is introduced to the model and may involve two different processes: (a) The two nuclei may relax independently with relaxation rates R I A and R I B due to external relaxation. (b) In addition, there may be a direct dipolar interaction between the two nuclei A and B leading to dipolar cross relaxation with the relaxation rate R D .  133  If the exchange is slow, i.e., k~AB, ks «\G)A-<DB\, A  the lineshapes are not noticeably  affected by the transport of transverse magnetization from a site to another so the contribution of the exchange can be neglected in the evolution and detection periods. After 2D Fourier transformation, the integrated amplitude of a signal with frequency coordinates (01,002) is hj (TJ = a (T^MJQ  (4.3)  kj  where r is the mixing time, and the mixing coefficient  a\g(is  m  %  (W =[exp{L r }]ig  (4.4)  m  The equilibrium magnetization Mjo = «/ Xj M 0 is proportional to the number n, of magnetically equivalent nuclei in site j, and to the mole fraction X , (X =1 for pure cross 7  relaxation between two nuclei within one molecule; X , =0.5 for symmetrical two site chemical exchange). The exchange matrix L is L = -R + K  (4.5)  which expresses the effect of spin-lattice relaxation (the diagonal elements of R are equal to 1/T j), cross relaxation (off diagonal elements of R), and chemical exchange (kinetic matrix K). k  For the simple system represented in Equation 4.1, the exchange matrix L which governs the mixing process is given by ^ _ L  AA  L  AB  AA  _  R  B  X  R  C  X  ~  A  R  C  (4.6)  BB  R  with R =R  + 2X R  D  +Xk  (4.7)  RBB=RIB+ 2X R  D  +X k  (4.8)  AA  IA  B  A  B  A  134  Rc=R -k  (4.9)  D  For the mixing coefficients a^it^, which describe the exchange process, the following expressions are found : 13  ^ ( ^ ) = ^"  CTrm  [cosh(Z)r )-^sinh(/JrJ]  (4.10)  ra  *BBM = X e-^[cosh(Dt )-^sinh(DTj] B  a (T ) = a ( ) = -X X ^-e- '  sinh(/JrJ]  aT  M  m  BA  (4.11)  m  Tm  A  B  (4.12)  where  cr = ±(R R )  (4.13)  S = -\(R -R )  (4.14)  AA+  M  BB  BB  D = (S +X X R / 2  2  A  B  (4.15)  2  C  The mixing coefficients %(x ) determine the integrated intensities of the two diagonal m  peaks and the two cross peaks of the resulting 2D spectrum according to Equation 4.3. The two cross peaks have identical intensities.  4.1.1.1 Two Site System with Pure Slow Chemical Exchange We consider here a single spin system (i.e. the number of magnetically equivalent nuclei in site j is one) with a pure symmetrical chemical exchange between two sites equal concentrations of the two sites: X A = X B = 1/2  1314  ( ^ B = ^ =  k) with  . In addition we take into account an  external relaxation mechanism acting equally on both sites, i.e.  R I A =  R I B  =  R I -  It should be noted  that chemical exchange will also cause some exchange of the transverse magnetization during  135  the evolution and detection periods. However for slow chemical exchange i.e.,  JCAB,  kA B  \(o -  <<  A  CDB\, this exchange effect will be very small and will only affect the linewidth and cause the following effective transverse relaxation rates: R 2A=R2A+l/2k,  (4.16)  EFF  andR  EFF  =R2B+l/2k  2B  (4.17)  The behavior during the mixing period is determined by substituting RD= 0 (no dipolar relaxation) and XA=XB=1/2 into Equations 4.7, 4.8 and 4.9, to obtain RAA=RBB  =  <J=R,+l/2k  (4.18)  Rc = -k  (4.19)  8=0, D=l/2k  (4.20)  which leads to the peak amplitudes  <^(r ) = a (r J m  a  AB  BB  (r ) = a  4.1.2  m  BA  = ± e " * - [1 + r  ( r ) = I « T * ' - [1 m  ]  (4.21)  ]  (4.22)  MULTIPLE SITE CHEMICAL EXCHANGE In larger exchange systems Equation 4.4 cannot be solved analytically. However, for a  sufficiently short mixing period T , an approximate expression for the amplitude can be obtained m  by invoking the initial rate approximation. Since exp(Lx ) & 1+ Li m  m  (4.21)  we obtain cikk(T )= 1+ L k r m  k  a i(rj = L t k  k!  m  m  (4.22) (4.23)  136  Thus the cross peak amplitudes are directly proportional to the corresponding matrix elements. In absence of cross relaxation (pure chemical exchange), we obtain a direct measure of the exchange rates . 14  MO  =  MO  =ytw  ( 4 2 4 )  Thus, in the case of a system with chemical exchange to different sites, the exchange rate kkj can be directly determined from the amplitude of the corresponding cross peaks.  4.2.  4.2.1  EXPERIMENTAL:  SAMPLE PREPARATION:  Samples of ZSM-5 loaded with 6 and 8 molecules per u.c. of [ C,CH ] p-xylene were 13  3  prepared following the procedure described in Chapter 2, Section 2.2.3. The preparation of [ C,CH3] p-xylene is given in Section 2.2.2.1. 4.2.2  , 3  All  C C P / M A S EXPERIMENTS  CP/MAS N M R experiments were carried out using a Bruker M S L 400  spectrometer and standard probe. Typical 90° pulse times were 5 ps for H and ^C. The C A  1 3  spectra were referenced to T M S using adamantane as an intermediate external reference standard. The magic angle was set using the B r spectrum of K B r and samples were spun at 79  3.0-3.5 kHz. The experiments at low temperatures were done using cold nitrogen as the bearing gas. As most of the experiments presented in this thesis required maintaining a sample spinning for very long periods (days) at low temperatures, liquid nitrogen was used as the source for the bearing gas. A detailed description of the apparatus designed for the low temperature  137  experiments in the thesis was presented in Chapter 2, Section 2.4.4. The temperature was regulated using the standard commercial Bruker V T unit. The 2D-NOESY experiments were carried out using decoupling during the mixing time to quench possible spin diffusion via the proton nuclei. Because of the use of the decoupler during the mixing time, the longest mixing time used was 120 ms.  138  4.3. R E S U L T S A N D DISCUSSION: I 3  C N M R spectroscopy was used to study the motional behaviour of the high loaded 13  complexes of zeolite ZSM-5 with p-xylene. The p-xylene was specifically labelled in C (98%) 1 J  in one methyl group. The use of this enriched compound is advantageous because of the much higher sensitivity of the experiment and the correspondingly much shorter experimental times required. Figure 4.2 shows the C CP/MAS N M R spectra ofthe complex of 8 molecules C[C-1] 1 3  13  p-xylene in ZSM-5 as a function of temperature. The linewidths of the peaks change with temperature and they tend to broaden and coallesce at higher temperatures. At 273 K . four well resolved peaks can be distinguished in the spectrum corresponding to four  different  environments for the methyl groups of the p-xylene molecules within the zeolite framework as expected from the x-ray structure. No further changes in the spectrum are observed at lower temperatures. Figure 4.3 shows a sketch of the structure of this complex as determined by single crystal XRD  1 5  as discussed in the previous chapter. The p-xylene molecule labelled as X Y L 1 , located in  the intersection of the channels has two chemically different carbons indicated, for simplicity, as SI and S2 in structure (3). The p-xylene in the sinusoidal or zig-zag channel is identified as X Y L 2 , and in structure (4), the two distinct methyl carbons are labelled as Z l and Z2. The numbering of the atoms in (3) and (4) is the same as used in the x-ray structure of this complex published by van Koningsveld . 15  139  28  26  24  22  20  18  16  14  12  (ppm) 0  Figure 4.2  1 3  C C P - M A S N M R spectra, at the temperature indicated, of the complex of 8 13  molecules of p-xylene [methyl,  C] in ZSM-5  140  Figure 4.3 Schematic representation of a view down a straight channel of the ZSM-5 lattice showing the locations of the p-xylene molecules in the sinusoidal channel (XYL2), and in the intersection of the channels (XYL1). (From ref. 15)  The changes in the lineshapes of the N M R signals with temperature indicate slow motion(s) of the p-xylene molecules within the channels (correlation time x < 10 ms). The c  separation of the lines is of the order of -100 Hz, and any exchange processes of this frequency will be expected to affect the spectra. Although there is a clear evidence for chemical exchange in the spectra, it is unclear which sites the exchange(s) is (are) between and it is not possible to unambiguously interpret the spectral changes.  141  Z1  *1  7CH-  70 CH. JO  60 50  40  1  20 30  4  80CH,  8CH,  XYL1  XYL2  (3)  (4)  In order to investigate these motions in detail by 2D N O E S Y spectroscopy, it is first necessary to assign the  1 3  C N M R signals observed in the spectrum to the four different methyl  groups of the p-xylene molecules the zeolite channels. The unambiguous assignment of these resonances was done using 2D-TEDOR (Transferred Echo Double Resonance) [see Chapter 8, Section 8.3.3]. In this experiment the C spins are correlated to the S i spins through the dipolar 1 3  2 9  interactions between them. Because the dipolar interaction has a very strong dependence on the internuclear distance (1/r ), only those pairs of nuclei with relatively large dipolar couplings will 3  show cross peaks in the spectrum; C atoms that are too far away from the S i nuclei will not 1 3  2 9  show any cross peaks. The intensity of a cross peak is a measure of the strength of the dipolar interaction; thus, for a given silicon atom a more intense cross peak indicates that a carbon is closer to that silicon in the zeolite lattice. Therefore in the 2D-TEDOR spectra shown in Figure 4.4 only those carbon close to the different silicon atoms will show a cross peak. Since the silicon resonances have been assigned to specific sites, the carbon resonances can be assigned. Table 4.1 shows the shortest Si-C distances and dipolar couplings calculated from the X R D data  142  Figure 4.4 Contour plot of a 2D-CPTEDOR experiment on the complex of 8 molecules per u.c. of p-xylene [methyl, C ] in ZSM-5 at 273 °K with the ID C P / M A S N M R spectra shown above, 32 experiments were acquired with a contact time of 3 ms and 1568 scans in each experiment with 5 s delay between pulses, for a total experimental time of aproximately 70 hours. Sine bell apodization was used. 13  143  within a distance of 7 A and the expected cross peaks for each of the resolved silicon signals in the spectrum according to the individual dipolar coupling from Table 4.1 are given in Table 4.2. The S, M , and W nomenclature used in Table 4.2 to indicate strong, medium and weak dipolar couplings gives an approximate indication of the expected cross peak intensities. Thus, for example, for Si 10, Table 4.1 only indicates two C - S i interactions which are relatively strong 13  29  (78.8 and 78.3 Hz) involving the methyl carbons Z l and Z2 corresponding to the p-xylene in the zig-zag channel. The 2D TEDOR spectrum in Figure 4.4 shows only two strong cross peaks for that silicon, which must correspond to these Z l and Z2 interactions. The assignments of Z l and Z2 are obtained from the expected cross peaks for Si 16. From Table 4.1 and 4.2 a very strong interaction between Si-16 and Z l is predicted, and this is observed in the 2D-TEDOR spectrum. The assignments of the methyl signals from the p-xylene in the straight channel are more difficult because those signals are very close in the  1 3  C N M R spectrum. However for Si 17, the  dipolar coupling for the interaction between Si 17 and S2 is almost twice that for Si 17 and SI (which is very small), and thus, an intense cross peak between Si 17- S2 and a weak correlation at all or no cross peak for SH7-S1 are expected. This is observed in the 2D TEDOR spectrum (Figure 4.4). A l l these assignments are self consistent with other S i - C interactions observed in 2 9  l 3  the spectrum as indicated in Figure 4.4. A more detailed discussion of the fundamentals of the 2D TEDOR experiment is postponed until Chapter 8 in which the triple resonance dipolar dephasing experiments are described.  Table 4.1: Calculated Si-C distances for the complex of 8 molecules of p-xylene in ZSM-5  29  Si T-site  Sil  Si3  Si4 SilO Sil2 Sil6  Sil7  Sil8  Carbon atoms  rsi-x(A) from XRD  Dipolar coupling (Hz)  S2  4.459  67.73  Z2  4.491  66.30  Zl  4.972  48.87  SI  5.950  28.51  S2  4.685  58.41  SI  5.296  40.43  Z2  5.380  38.56  Zl  6.139  25.96  Zl  4.537  64.31  Z2  6.954  17.86  Zl  4.240  78.77  Z2  4.248  78.32  S2  5.207  42.5  Z2  5.428  37.56  Zl  4.179  82.28  Z2  6.314  23.85  Zl  4.598  61.79  S2  4.696  58.00  SI  5.893  29.35  Z2  6.595  20.93  S2  4.481  66.75  Z2  5.650  33.29  Zl  5.652  33.26  SI  5.988  27.97  Calculated from the X R D data from reference 15, up to a distance of 7 A.  .  145  Table 4.2: Expected cross peaks in the 2D TEDOR spectrum according to the strength of the dipolar couplings given in Table 4.1.  29  Zl  Z2  SI  S2  Si 1  M  s  w  s  Si 3  W  w  M  M  Si 4  S  w  -  -  Si 10  s  s  Si 12  -  w  -  W  Si 16  s  w  -  -  Si 17  s  w  w  M  Si 18  w  w  w  S  Si T site  -  S = strong dipolar coupling (between 60-85 Hz). M = medium dipolar coupling (between 40-59Hz). W = weak dipolar coupling (between 20-39 Hz).  The assignment of the C N M R signals from these data given in Figure 4.4 agrees with a 1 3  previous assignment by Olson and co-workers . However, they only detected three signals in the 16  1 3  C N M R spectrum and assigned the signal observed at highest field to the methyl group in the  sinusoidal channel (carbon Z2) based on qualitative chemical shift arguments because of the close interaction with the anisotropic shielding cone of the aromatic ring from the p-xylene molecule located in the intersection (see Figure 4.4). However a completely unambiguous  146  assignment of all the signals is only possible using the 2D-TEDOR experiment as described above.  Figure 4.5 presents a series of 2D-CP-NOESY experiments carried out at 297 K with  different mixing times to show the three different exchange regimens observed. At short mixing times (20 ms) no exchange is detected in the 2D spectrum at this temperature, at intermediate times (40 ms) considerable intramolecular exchange is observed between the two methyl groups of the molecule in the zig-zag channel (Zl and Z2), and between the two methyl groups of the molecule in the straight channel (SI and S2). At long mixing times (90 ms) an additional very slow exchange process is detected that interchanges methyl group environments between molecules in the zig-zag channel and molecules in the straight channels, S1,S2 to Z1,Z2, (intermolecular exchange). A l l of these motions will undoubtedly affect CP experiments at longer mixing times such as these described in the previous chapter. In addition there may be other motions with comparable or even faster rates which are not detected in these experiments because they involve exchange between equivalent sites. As expected, these exchange processes are slowed down by reducing the temperature, confirming the exchange mechanism. 2D-CP-NOESY spectra (Figure 4.6) carried out at 273 K showed that no appreciable exchange is observed between the p-xylene molecules even at very long mixing times (90 ms), indicating that is possible to quench the observed motions of these molecules by decreasing the temperature.  147  x =20 ms no exchange  x =40 ms m  intra molecular exchange  (ppm)  20.0  19.0  18.0  (ppm)  S1Z2 S2Z2  18.0 18.5 19.0  x =100ms  S2Z1 O  •19.5  m  S1Z1 intra molecular and intermolecular exchange  20.0 20.5  •21.0  •i•i•  (ppm)  111 • 1111 • • 11 % 11  20.0  19.0  18.0  Figure 4.5 Countour plots of 2D-CPNOESY experiments at the mixing time indicated on the complex of 8 molecules of p-xylene [methyl, C ] in ZSM-5 carried out at 297 °K. The ID C P / M A S N M R spectrum is shown above. Each plot is the result of 32 experiments, 80 scans in each experiment, with a 5 s delay between pulses, sweep width of 800 Hz, and 128 data points collected during acquisition. The spectra show the three regimens of exchange observed in this system at the different mixing times indicated. 13  148  t  m  = 9 0 ms  i  (pom)  21.0  T = 273 K  20.5  20.0  19.5  i  19.0  i  16.5  18.0  17.5  Figure 4.6 Countour plots of 2D-CPNOESY experiment on the complex of 8 molecules of pxylene [methyl, C ] in ZSM-5 carried out at 273 °K with the ID C P / M A S N M R spectrum shown above. The plot is the result of 32 experiments, 64 scans in each experiment, with 5 s delay between pulses, sweep width of 800 Hz, and 128 data points collected during acquisition, mixing time 90 ms. The spectrum shows that no appreciable exchange is observed at this temperature even for a mixing time of 90 ms. 13  2D-CP-NOESY experiments at different temperatures (313 K , 297 K , 283 K , and 273 K ) were carried out as a function of the mixing time to determine the rate constants for the chemical exchanges and the activation energies of these processes.  149 The intramolecular exchanges observed between carbons Z l and Z2 of the p-xylene in the zig-zag channel, and between carbons SI and S2 of the p-xylene in the straight channels can be described quantitatively by the two spin chemical exchange mathematical treatment derived in Section 4.1.1.1, because the other exchange process (intermolecular exchange) is much slower and the error in not taking the intensities of these cross-peaks into account is negligible (see later). Any cross-relaxation effects can be neglected in this analysis, because the 2D-NOESY experiments were taken using decoupling during the mixing time to quench spin diffusion through the proton nuclei.  1 3  C - C spin diffusion can also be neglected because the large 1 3  internuclear distances between these nuclei and their spin dilution. This last assumption was experimentally corroborated by investigating the behaviour of a sample substantially diluted in 1 3  C (50 % p-xylene and 50 % [ C , C H ] p-xylene). l3  3  Thus, for the intramolecular exchange of the methyl carbons from the p-xylene molecules in the zig-zag channel: kziz2  Zl «  " Z2  (25)  ^Z2Z1  Since k z i z 2 kz2zi~kz, the intensities of the diagonal peaks are given by: =  Iz  l Z l  ( r ) = I z 2 z 2 (rm) m  =V  RlTm  [1 + e -  k z T m  ]M  0  (4.26)  The intensities of the cross peaks are given by:  hz x  2  ( * ) = I z z , ten) = ^ e m  2  R , r m  [1- e -  k z r m  ]M  0  (4.27)  150  As can be seen from Figure 4.5 where there is no symmetrization applied, the measured relaxation rate R i was the same for the two methyl groups, as expected. The intramolecular chemical exchange rate can be determined by the ratio of the peak intensities given by Equations 4.26 and 4.27, according to: Iz,Z I  Z Z ( ^ m ) + 1  ( m) r  2  I  2  ==-[l-e"  Z 2^2 Z ( 7  7  7  m )  k z r m  ]  (4.28)  2  which simplifies to:  2^2  In ZZ  ( m)  l  2  T  2  l  (4.29)  kz^m  ~ ZZ  ( m)  I  T  2  These intensities can be measured directly by integration of the spectra obtained from the cross section plots of the 2D N O E S Y spectrum as shown in Figures 4.7 and 4.8 for the 2D experiment at room temperature (297 K). These 2D spectra were taken in magnitude mode and thus the measured intensities can be used directly in a quantitative evaluation. Z z (T )  +  J  The plot of In  l  2  m  Z z . zA m)  I 2  T  7  2  versus x should be a straight line with slope m  ^Z Z 2  ( m)~ T  2  Iz,Z? -1^2  ( m) T  kz and intercept zero. These plots are shown in Figure 4.9, for the different N O E S Y experiments at various temperatures. Similar expressions can be obtained for the intramolecular, exchange of the methyl groups Si and S for the p-xylene molecules in the straight channels: 2  k  SI <  S1S2  "  S2S1  l  and  S2  (29)  151  SS  ( m)  ^S S  ( m) ^S,S  J  In  {  T  2  2  _  SS  ( /w)  h S  ( m)~ S S  J  Again plots of In  T  J  r  2  ISTS-, 2 2 ( m)  +  {  2  r  2  T  2  T  2  ^ S ,2°2 5 i m)  +  (4.30)  ( m)  T  7  I  l  as a function of x for the 2D C P N O E S Y m  ( m) T  2  experiments at different temperatures should yield straight lines with slopes equal to the intramolecular exchange rate constants of the p-xylene molecules in the intersection of the channels at those temperatures and should have intercepts of zero. The linear correlations shown in Figure 4.10 are not as good as those obtained for the intramolecular exchange in the zig-zag channels, because the signals corresponding to SI and S2 in the C N M R spectrum are very 1 3  close, resulting in some giving peak overlap. This results in overstimates of the peak areas determined for the cross peaks, which is more noticeable at very short mixing times, because the very small intensities of the cross peaks for the exchange between SI and S2 are somewhat enhanced by the tails of the diagonal peaks. As a consequence of this all the initial points in the plots shown in Figure 4.10 are higher than the general trend. The calculated rate constants for the intramolecular exchange of the methyl groups inside the channels are listed in Table 4.3 together with their experimental errors. These experimental ^S,S ( m ) T  errors were calculated by differentiating the expression In  2  +  Is S (m ) r  2  2  with respect to  the intensities. The errors in measuring the intensities were determined to be approximately 4-5 % of the integral values. The errors in the rate constants were determined from the maximum and minimum slopes obtained when  152  Figure 4.7 Cross section plots from the 2D N O E S Y spectrum of the complex of 8 molecules of p-xylene[methyl, C ] in ZSM-5 at 297 °K at different mixing times for the exchange between Z l and Z2. These spectra show how intensity is drained with increasing mixing times x from the diagonal peaks to the cross peaks due to the chemical exchange. 13  m  153  S2 Mixing time= 20 ms  Mixing time= 40 ms  Mixing time= 60 ms  Mixing time= 80 ms  Figure 4.8 Cross section plots from the 2D N O E S Y spectrum of the complex of 8 molecules of p-xylene[methyl, C ] in ZSM-5 at 297 °K at different mixing times for the exchange between SI and S2. These spectra show how intensity is drained with increasing mixing times x from the diagonal peaks to the cross peaks due to the chemical exchange. 13  m  154  considered the errors calculated for the expression In  Is,S ( m ) T  ^S S ( m )  +  T  2  -^S S ( m ) T  2  2  2  —  as shown by the  2  As,S ( m ) 7  2  error bars in Figures 4.9 and 4.10. The intramolecular exchange rate constant between the methyl groups on the molecules in the straight channel could not be obtained from the 2D-CP-NOESY experiment at 313 K and above because the signals corresponding to Si and S2 collapsed into a single peak at this temperature. Further, there are substantial errors introduced at shorter diffussion times from the contributions from the wings of the larger diagonal peaks which make the data at 273 K unreliable.  Table 4.3:  Kinetic constants at different temperatures for the intramolecular exchange of  the p-xylene molecules in the straight and zig-zag channels in the system of 8 molecules of  p-xylene per u.c. in ZSM-5. Temperature (K)  Intramolecular  Exchange  Zig-Zag Channel kz  (s ) 1  Intramolecular  Exchange  Straight C h a n n e l (s )  ks  1  313  75 ±2  -  297  19.710.4  21.610.2  283  7.2 + 0.8  7.010.6  273  1.810.3  In the mathematical treatment presented above for the intramolecular exchange a two site pure exchange mechanism was assumed to be operating. Thus an exact analytical expression could be calculated for Equation 4.4. However there is another process that exchanges positions  155  Figure 4.9 Graphs of the ratio of intensities for the intramolecular exchange of the molecules located in the zig-zag channels obtained from the 2D-CPNOESY spectra of the complex of 8 molecules of p-xylene [methyl, C ] in ZSM-5 as a function of the mixing times x at the different temperatures indicated. The linear correlations yield the rate constants for this exchange. 13  m  156  2,9  j  T = 297 K  Mixing time (ms) 1 T  0 •  1  1  1  1  0  20  40  60  80  1 100  Mixing time (ms) Figure 4.10 Graphs of the ratio of intensities for the intramolecular exchange of the molecules located in the straight channels obtained from the 2D-CPNOESY spectra of the complex of 8 molecules of p-xylene [methyl, C ] in ZSM-5 as a function of the mixing times x at the different temperature. The linear correlations yield the rate constants for this exchange. 13  m  of the molecules in the straight and the zig-zag channels (intermolecular exchange). This process is slow enough that the cross peak intensities due to this exchange are visible only at very long mixing times. Consequently, the errors introduced by neglecting these intensities are very small.  157  The rate constant of the much slower intermolecular exchange cannot be calculated exactly and the approximation developed in Section 4.1.1.2 for multiple site exchange has to be used. Because this exchange is so slow, the only rate constant that could be calculated using the initial rate approximation (Section 4.1.1.2) was for the intermolecular exchange at high temperature (313 K ) . At lower temperatures and shorter mixing times the intensities of the cross peaks due to the intermolecular exchange are negligible. At 313 K , the rate constant &,> ,=15.5 ± lte  0.3 s" for the intermolecular exchange was calculated using the data from the experiments taken 1  with mixing times of 20 ms, and 40 ms using Equation 4.24. The error was calculated by differentiating Equation 4.24 with respect to the intensities. The error in the measured intensities was estimated to be 5 %. The activation energies for the intramolecular exchange can be calculated from the data shown in Table 4.3 according to the Arrhenius equation  k=Ae"  , as shown in Figure 4.11.  The value determined was 65 ± 2 kJ/mol (15.4 kcal/mol) for the intramolecular exchange in the zig-zag channels. If only the two temperature K s values (Table 4.3) are used, an activation energy of 56 kJ/mol for the exchange in the straight channel can be calculated. However this values comes from a linear regression of only two data points, thus it might have a big error that cannot be estimated. The errors in the activation energy for the intramolecular exchange in the zig-zag channels was determined from the maximum and minimum slopes obtained with the errors calculated for the rate constants. To investigate effects of the sample loadings, 2D CPNOESY experiments on the complex of 6 molecules of p-xylene [methyl, C ] in ZSM-5 were carried out at 297 K and the 13  contour plots for these experiments are presented in Figure 4.12. The rate constant obtained from the slope of the plot of the ratio of intensities as a function of the mixing time (Figure 4.13) for  158  the chemical exchange of the methyl in the zig-zag channel is 89.5 ± 0.5 s" . This value is much 1  larger than that calculated for the 8 molecules per u.c. complex at the same temperature (19.7 s1), perhaps due to the larger number of unoccupied sites in the system. The rate constant for the intramolecular exchange of the p-xylene molecule in the straight channels was not calculated because of the poorer resolution of the signals corresponding to the methyl carbons SI and S2 in the 2D spectrum.  6,00315  0,0033  0,00345  0,0036  0,00375  1/T ( K ) 1  Figure 4.11 Arrhenius plots of the rate constant vs. the inverse of the temperature to obtain the activation energy for the intramolecular exchange of the molecules located in the zig-zag channels.  159  Figure 4.12 Contour plots of 2D-CPNOESY experiments on the complex of 6 molecules of pxylene [methyl, C ] in ZSM-5 carried out at 297 °K with the ID projection shown above. Each plot consists of 32 experiments, 32 scans in each experiment, with 5 s delay between pulses, sweep width of 800 Hz, and 128 data points collected during acquisition. The mixing times are indicated for each contour plot. 13  160  3,5  T  Mixing time (ms)  Figure 4.13 Graph of the ratio of intensities for the intramolecular exchange of the molecules located in the zig-zag channels obtained from the 2D-CPNOESY spectra of the complex of 6 molecules per u.c. of p-xylene [methyl, C ] in ZSM-5 as a function of the mixing times x at 297 °K. The linear correlation yields the rate constants for this exchange. 13  m  4.3.1  POSSIBLE MECHANISMS FOR T H E CHEMICAL EXCHANGE OF T H E P-XYLENE MOLECULES  The elliptical cross section of p-xylene has main axes lengths of ~ 6.1 and 4.0 A, as calculated using the Van der Waals radii of the atoms. The reported kinetic diameter is 5.85 15  A . 18  Table 4.4 lists the sizes of pore openings (O .. O distances) for the double 10-rings in the straight and sinusoidal channels, obtained from the X R D data . 15  161  Table 4.4: Pore opening (O'O distances, A) for the double 10-rings in the straight and sinusoidal channels of the complex of 8 molecules of p-xylene per u.c. in ZSM-5 (From reference 15). The O numbering is for use in this table only and is defined as given in the diagram below. 6 7  5 — ^ \  4  3  8  2 9  10  1  10-rings  l->6  2->7  3->8  4->9  5->10  Max. *  Min.*  straight  7.774f  7.949  8.615  8.755$  8.099  6.06  5.07  channel  7.503f  7.968  8.489  8.882$  8.071  6.18  4.80  sinusoidal  9.071$  8.606  7.578  7.456t  8.302  6.37  4.76  channel  8.846$  8.533  7.447  7.278f  5.891  6.15  4.58  $ Maximal O O distances f Minimal O O distances * Max. and min. pore sizes are calculated using 1.35 A for the O-atom radius.  The p-xylene molecules in the straight channels (XYL1) can be involved in two different motions. The first and most obvious one is where the p-xylene in the channel intersection (XYL1) jumps (diffuses) along the straight channel to the next intersection site (assuming that the molecule at the channel intersection has diffused to another positions e.g. defect, so the intersection is empty). However this motion does not exchange the crystallographic positions of SI to S2, and S2 to SI; because of the symmetry present within the straight channels, the p-  162  xylene molecules are equivalent. Therefore even although this motion could well occur, it would not show up as cross peaks in the NOESY experiment The second possible mechanism is when the molecule turns around by 180° around the C axis (see Figure 4.14). This motion, which could be by a series of small steps involving both 2  translation and rotation, effectively exchanges the positions of SI to S2, and S2 to SI. Although the maximum pore size in the straight channel (6.18 A), is about the same value as the long molecular axis length of the p-xylene molecule (6.1 A), it is still possible that this turning motion could occur because the channel intersections produce a "cage" with a larger volume. Derouane and Vedrine have observed that the channel intersections afford afreevolume of somewhat larger size . 19  In the case of the molecules in the zig-zag channels, translational diffusion (jumping) of the p-xylene molecules within the sinusoidal channel (assuming that the molecule at the channel intersection has diffused to another positions e.g. defect, so the intersection is empty), will again locate the molecule in an equivalent crystallographic position. Although this diffusion process very likely occurs again, it will not show up as cross peaks in the 2D CPNOESY experiment. Consequently, the only possibility by which the intramolecular exchange of the methyl groups can occur is again by rotating the molecule 180° around the C2 axis. Comparing the effective maximum size of the pore openings for the sinusoidal channel listed in Table 4.4 (6.37A) with the long molecular axis calculated for the p-xylene molecule (~6.1 A), we can conclude that it is again difficult for the rotation of the molecule around the C2 axis to occur at the position of minimum potential energy that the molecule occupies in the zigzag channels. However if the molecule (XYL2) diffuses to the (empty) larger cage formed by the intersection of the channels (possible only when the molecule XYL1 has diffused to a  163  "vacancy"), the molecule can rotate around the C2 axis exactly as described for X Y L 1 , so the carbon atom Z2 exchanges with Z l . The intersection of the channels is bigger in the direction of the undulating zig-zag channel because the two arms of the undulation make an angle of 112° angle with each other, so the space for the flipping is not determined by the 10-rings pore openings. After the rotation, the molecule can reenter the zig-zag channel and occupy its original site.  H  !  H  Figure 4.14. Schematic representation of the p-xylene molecule with its C2 and C3 rotation axes.  The fact that the exchange process is highly accelerated when the loading is lowered to 6 molecules per u.c. (kz = 89.5 + 0.5 s" ) is consistent with this mechanism for the exchange, 1  because it is necessary to have void spaces (vacancies) in order for the intramolecular exchange to occur. The ID N M R spectra (Figure 3.8, Chapter 3) indicate that the framework consist of volumes of 8 molec./u.c. and volumes of 0 molec./u.c, both with exactly the framework structure (P2/2/2/). Although it is not clear from N M R how large these volumes are, there is  164  obviously a large potential reservoir of empty lattice sites to promote the exchange processes described here. The activation barrier for the intramolecular exchange in the straight channel should be smaller than that in the zig-zag channel, because only a 180° rotation around the C axis of the p2  xylene molecule is required. On the other hand the exchange in the zig-zag has to be a concerted process in which the p-xylene molecule at the channel intersection moves to another position in the straight channel and the p-xylene in the sinusoidal (XYL2) moves to the intersection and undergoes 180° rotation around its C 2 axis. The other possibility is that the p-xylene in the sinusoidal (XYL2) moves to a defect and undergoes 180° rotation around its C 2 axis. Therefore is expected that the exchange of the sinusoidal p-xylene should have a larger activation barrier because the molecules must undergo diffusion and 180° rotation around their C 2 axis. However, experimentally it was determined that the activation energy for both intramolecular exchanges are similar, which could indicate that the limiting high energy step is the rotation at the channel intersection in both cases. Nevertheless, due to the larger error in the determination of the activation energy for the exchange in the sinusoidal, it is not possible to draw a definitive conclusion. In other reported studies of the dynamics of the p-xylene molecules in ZSM-5, the activation energy for rotation about the long axis of p-xylene in ZSM-5 (not detected in the present experiment) has been found to be approximately 20 kJ/mol ' . Activation energies for 16  20  jumps between the two sites have been estimated at around 30-70 kJ/mol . There are no 19  previous data relevant to the intramolecular exchange studied here. The results presented in this chapter demonstrate that very slow chemical exchanges are occurring involving the p-xylene guest molecules in ZSM-5. These exchanges will undoubtedly  165  affect the CP experiments because they occur on a time scale significant for this experiment. However the exchange is slowed down when the temperature is lowered and it was shown that at 273 K , no observable chemical exchange was detected even at long mixing times (90 ms). Therefore in the next chapter the CP experiments on the high loaded samples are repeated at 273 K to ensure that any possible exchange processes will not affect the results.  166  4.4.  REFERENCES  1 Wright, P.A.; Thomas, J.M.; Cheetham, A . K . ; Nowak, A . K . , Nature, 318, 611,..  1985.  2 Fitch., A . N . ; Jobic, H.; Renouprez, A., J. Phys. Chem., 90, 131, 1986. 3 Parise, J.B.; Hriljac, J.A.; Cox, D.E.; Corbin, D.R.; Ramamurthy, Y., J. Chem. Soc, Chem. Commun., 3, 226, 1993. 4 Karger, J.; Pfeifer, H.., Zeolites., 7, 90, 1987. 5 Karger, J.; Pfeifer, FL. "NMR Techniques in Catalysis" . Bell, A.T. & Pines, A . Eds. Marcel Dekker, New York, pg.69-137, 1994. 6 Schmidt, C ; Wefing; S.; Blumich, B.; Spiess, H . W., Chem. Phys. Letters, 130, 84, 1986. 7 Wefing, S.; Kaufmann, S.; Spiess, H . W., J. Chem. Phys., 89, 1234, 1988. 8 Schmidt, C ; Blumich, B.; Spiess, H. W., J. Mag. Reson., 79, 269, 1988. 9 Larsen, R.G., Shore, J.; Schmidt-Rohr; K . ; Emsley, L.; Long, FL; Pines, A . ; Janicke, M . ; Chmelka, B.F.; Chem. Phys. Letters, 214, 220, 1993. 10 Janicke, M . ; Chmelka, B.F ; Larsen, R.G.; Shore, J.; Schmidt-Rohr, K.; Emsley, L.; Long, FL; Pines, A., Stud. Surf. Sci. Catal. , 84, 519, 1994. 11 Wilhelm, M . ; Firouzi, A . ; Favre, D.E.; Bull, L . M . ; Schaefer, D.J.; Chmelka, B.F., J. Am. Chem. Soc.,117, 2923, 1995. 12 Szeverenyi, N . M . ; Sullivan, M.J.; Maciel, G.E., J. Magn. Reson. 47, 462, 1982. 13 Jeener, J.; Meier, B.H.; Bachmann, P.; Ernst, R.R., J. Chem. Phys.. 71, 11, 4546, 1979. 14 Ernst, R.R.; Bodenhausen, G.; Wokaun, A . , "Principles of Nuclear Magnetic Resonance in One and Two Dimensions", Chapter 9, Claredon Press, Oxford, 1987. 15 van Koningsveld, LL; Tuinstra, F.; van Bekkum, LL; Jansen, J . C ; Acta Cryst, B46, 423-431, 1989.  167  16 Reischman, P.T.; Schmitt, K.D.; Olson, D.H.; J. Phys. Chem., 92, 5165, 1988. 17 Brady, J.E.; Humiston, G.E. "General Chemistry, Principles and Structure". 4th ed. John Wiley & Sons, New York, pg.508, 1986. 18 Hing, A.W.; Vega, S.; Schaefer, J., J. Magn. Reson, Ser. A„ 103, 1511, 1993. 19 (a) Derouane, E.G.; Vedrine, J . C , J. Mol. Catal, 8, 479, 1980. (a) Derouane, E.G., Stud. Surf. Sci. Catal, 5, 5, 1980. 20 Bnagy, J.; Derouane, E.G.; Resing, H.A.; Miller, G.R., J. Phys. Chem., 87, 833, 1983.  168  CHAPTER FIVE INVESTIGATION OF THE STRUCTURE OF THE HIGH LOADED F O R M OF P-XYLENE IN ZSM-5 B Y W Si CROSS POLARIZATION l  29  EXPERIMENTS AT L O W E R TEMPERATURE  5.1.  INTRODUCTION In Chapter 4 it was shown that the p-xylene molecules inside ZSM-5 move very slowly  within the same channels (intramolecular exchange) and also between the two channel systems (intermolecular exchange). These motions are very slow and could not be detected by H N M R spectroscopy which only detects motions occurring with correlation times, T <10° S (for a c  quadrupolar coupling constant of -150 kHz) . They were however, detected by  1 3  C chemical  exchange experiments, whose time scale makes it possible to observe much slower motions (in this case it was possible to measure correlation times of x <10" s). c  The chemical exchange experiments presented in Chapter 4 demonstrated that these motions were slowed down at lower temperatures and were basically "frozen out" at 273 K . Thus, at this temperature no significant chemical exchange could be detected even at a mixing time as long as 90 ms, as shown in Figure 4.6. This means they would not affect N M R experiments with evolution times up to this value. In the present chapter the results of the CP dynamics study of the high loaded form of ZSM-5/P-xylene at 273 °K are presented. These results give a completely reliable structure for the sorbate/framework complex for all loadings of p-xylene between six and eight molecules per u.c. because the experiments are now unaffected by any motions of the organic guests.  169  5.2.  EXPERIMENTAL  A l l the experiments were conducted at 273 °K. Because these experiments require keeping the samples at 273 °K for long periods of time (typically for a CP experiment about 24 h), a special low temperature set up had to be constructed for these, as shown in Chapter 2, Section 2.4.4. The probehead tuning is very sensitive to changes in temperature and spinning speed and must be re-tuned when the system (probehead + sample) reaches a uniform temperature. The temperature of the sample was regulated using a Bruker VT-100 temperature control unit. The low temperature arrangement used in this work proved to be successful in keeping the temperature and spinning speed constant by maintaining a steady flow of cold nitrogen gas as the bearing source for both cooling and spinning the sample . Using this setup a sample can be kept spinning at a constant speed of -3000 Hz and at a regulated temperature of 273 K for 6 days, without refilling the pressurized liquid nitrogen gas used as the source of the bearing gas. This is extremely important in these experiments because it completely avoids the introduction of any humidity into the system due to water condensation which would adversely affect the probehead tuning.  170  5.3. R E S U L T S A N D DISCUSSION: Figures 5.1 a and b show the S i CP M A S spectra for zeolite ZSM-5 loaded with 8 29  molecules of p-xylene at 293 °K and 273 °K, respectively. As can be seen, the spectra are basically identical indicating that the framework structure has not changed on lowering the temperature. As previously reported, the 8 molecule per u.c. form is orthorhombic, space group P2/2/2/, and has 24 T-sites in the asymmetric unit . To our advantage, in the  Si N M R  spectrum at 273 °K the resonances corresponding to silicons 1,3, 10, 12, 16 and 17 (indicated in the figure) are even better resolved than in the room temperature spectrum. These small differences between the spectra can be explained in terms of very small changes in distances and angles involving O-Si-0 bonds of the zeolite framework on lowering the temperature. The assignment of the different resonances to the appropriate silicons shown in the Figure 5.1 comes  23 from the previously reported I N A D E Q U A T E experiments ' . The cross-polarization experiments were carried out using the standard spin-lock sequence shown in Figure 3.9 (see Chapter 3) with spin temperature inversion to suppress artifacts .The 4  relaxation parameters relevant to these experiments are presented in Table 5.1. S i C P / M A S 29  spectra were recorded as a function of contact time (CT) up to a maximum of 60 ms for samples of ZSM-5 loaded with 6 and 8 molecules of the specifically deuterated p-xylenes (1) and (2) at 273 °K. The spectra were deconvolved as previously in terms of Lorentzian functions and the intensities of the well resolved resonances due to silicons 1, 3, 10, 12, 16, and 17 tabulated. Figure 5.2 shows plots of these data for the p-xylene-J sorbate (1) and Figure 5.3 for the p6  xylem-d (2) system. 4  171  ppm from TMS  Figure 5.1 Si CP M A S N M R spectrum of ZSM-5 loaded with 8 molecules of p-xylene-dt per u.c, contact time 5 ms, at (a) 293 K , and (b) 273 K .  172  (2)  (3)  The variable contact time cross-polarization curves were fitted according to Equation 5.1, with T (  29  S i )  l p ( H )  and  T  l p (  fixed. This equation describes the dynamics of the CP experiment when T i 29  S i )  p ( H )  < T  l p  is very long. The fittings of the CP data were done in the same manner as for the  room temperature experiment (using the non-linear statistic package in the  Mathematica  program, version 3.0). -1 I(t) = I  1- CP, l  a  exp  -exp  y/ cp; T  (5.1)  As previously, I represents the theoretical maximum signal intensity obtainable from the 0  polarization transfer in the absence of any loss due to relaxation processes In general terms, the curves in Figures 5.2 and 5.3 approximate the behavior expected from Equation 5.1 and are similar to those obtained at room temperature. That is, there is an exponential growth due to polarization transfer and a decay from the loss of proton magnetization due to T  l p ( H )  . The curves which grow fastest have the highest maxima and the  maxima in the series shift to longer contact time values as they become lower. There are also qualitative consistencies between the data sets at the different temperatures. Thus, in Figure 5.2,  173  Figure 5.2 Intensities of the Si CP MAS NMR signals as functions of the contact times at a temperature of 273 K for: (a) ZSM-5 with a loading of 6 molecules p-xylene-^ per u.c, (b) ZSM-5 with a loading of 8 molecules p-xylene-d<5 per u.c.  174  the curves for both sorbate loadings at 273 °K indicate that silicons 12, 3, and 17 are much more efficiently polarized (and hence closer to the ' H polarization source) than silicons 16, 10, and 1 in the same way as was observed when the experiments were conducted at 293 °K. The effect is more obvious for the loading of 6 molecules per u.c. (Figure 5.2a) because the  TI H P  is much  shorter than the 8 molecules per u.c. case (Figure 5.2b).  Table 5.1: Selected relaxation parameters for the H and Si nuclei in the specifically deuterated xylenes of the p-xylene/ZSM-5 complexes at 273 K !  8 molecules/u.c.  6 molecules/u.c. (ms) 22.0  ca. 5Ti (s) 8.0  T (ms) 0.0422  T, pH (ms) very long  -  22.2  8.0  -  very long  6.0 - 22.0  -  350.0  6.0 - 60.0  -  T (ms) 0.0422  T,pH  ^(ring)  ca. 5Ti (s) 5.0  ^(CHa)  6.0 350.0  Nuclei  Si (framework)  29  2  2  A similar trend is seen for the p-xy\ene-d systems with the 6 and 8 molecules 4  per  u.c.(Figure 5.3). In this case silicons 10, 1, are much more efficiently polarized (and hence closer to the ' H polarization source) than silicons 17 16, 12, and 3.. Again the effect is more obvious for the loading of 6 molecules per u.c. (Figure 5.3a). Once more this is in qualitative agreement with the Si-H distances from the X R D structure determination shown in Table 3.1.  175  Again, the differences in the shapes of the curves between the six and eight molecule loadings are due mainly to differences in the T molecules per u.c., the T  l p ( H )  l p ( H )  values (Table 5.1). At a loading of 8  values are too long relative to the T  C P  values for clear decays to be  observed for the curves and Equation 5.1 can be simplified to Equation 5.2 f  ( 1 - exp  \  y/  CP) )  In the case of ZSM-5 loaded with 6 molecules of p-xylene- d per u.c. (Figure 5.3a), a 6  value for T  ] p ( H )  was obtained from least squares fits to the linear decays of plots of ln(I) vs. CT  for Si 12 and Si 3 (Table 5.2). The average value of T  l p ( H )  other curves. Table 5.2. presents the values of I and T 0  C P  = 21.0 ms was used in fitting all of the obtained from a least square fitting of  these curves. The CP curves indicated in Figure 5.2 show that better fittings are obtained for all the data points of all the different silicon sites. The CP experiment at room temperature (Figure 3.13) could not be fitted very well with Equation 5.1, particularly the curves for those silicons with long T p values (Si 1, Si 10 and Si 16). In contrast, at 273 K all the data points for every C  silicon can be fitted perfectly with Equation 5.1. Table 5.2 shows the values of I  0  and T  C P  obtained from a non-linear least squares fit of the data points shown in Figure 5.2a to Equation 5.1. The variation in the I values in Table 5.2 for the different silicon sites is about 8 %, which 0  is much smaller that the variation obtained at room temperature (about 30 %). The Io values are expected to be similar if not identical for all the silicon atoms because all the T sites are of equal occupancy in the structure. It is possible that I could vary slightly as there is some degree of 0  176  isolation of the groups of proton spins, and different silicon sites may be in contact with different numbers of protons, but these are not expected to be significant effects. 1  70  Table 5.2: Experimental and calculated parameters related to the Wl Si cross polarization experiments on the complex of p-xylene-rfg in ZSM-5 with 6 molecules per u.c. at 273 K.  29  Si T-Site  Resonance (ppm)  Io (a.u.) (a)  T p (ms) (a)  C  (Aco ) calc 2  (b)  IS  (Hz ) 2  Si 10  -111.6  506±9  13.6±0.5  42548  Si 1  -112.0  448±3  10.5±0.2  58338  Si 12  -116.7  474±6  2.9±0.1  231890  Si 17  -117.3  508±6  5.2±0.1  129398  Si 16  -117.6  385±7  16.3±0.6  46716  Si 3  -118.9  547±7  3.5±0.1  193823  Calculated using a non-linear least square fitting program, fixing Ti (H)=21 ms in Equation 5.1. The program also calculates the asymptotic standard errors for the parameters determined in the fitting. (a)  p  ( b )  Calculated from the X R D data taking into account all Si-H interactions up to a distance of 8 A.  Again, for the loading of 8 molecules per u.c. of p-xylene-^, the whole data set can be fitted exactly using Equation 5.2 for the different resolved silicon resonances. The calculated curves from these fits are those shown together with the experimental data points in Figure 5.2 b. The values of I and T 0  C P  obtained by the a non-linear least squares fit of the CP data with  Equation 5.2 are presented in Table 5.3. Again the variation in I is less than 9 %. 0  The theoretical intermolecular Si-H second moment values calculated from the known structure and indicated in Tables 5.2 and 5.3 for Si 1, Si 3, Si 10, Si 12, Si 16 and Si 17 are the same as previously used in Chapter 3.  177  Figure 5.3 Intensities of the Si CP M A S N M R signals as functions of the contact times at a temperature of 273 K for the complexes of xylene-^: (a) with a loading of 6 molecules per u.c, (b) with a loading of 8 molecules per u.c.  178 As previously, the Trjp values are expected to be directly related to the *H/ Si 29  heteronuclear second moments via Equation 5.3:  C(Aco ) 2  I/TCP =  where C is a constant, and ( A C O  2  ) H H  s i H  (5.3)  (AC0 ) HH 2  1/2  and (Ato ) iH are the homonuclear second moment for the 2  S  protons and the heteronuclear second moment for the silicon resonances, respectively.  Table 5.3: Experimental and calculated parameters related to the H/ Si cross-pollarization experiments on the complex of p-xylene-rfg in ZSM-5 with 8 molecules per u.c. at 273 K. 1  29  Si T-Site  Resonance (ppm)  I 0 (a.u.)  T p (ms)  29  Si 10  -111.6  147±4  26±2  (A(o )is calc (Hz ) 42548  Si 1  -112.0  142±2  20±0.6  58338  Si 12  -116.7  161±2  5.2±0.2  231890  Si 17  -117.3  150±1  9.3±0.2  129398  Si 16  -117.6  166±6  22±2  46716  Si 3  -118.9  156±1  6.2±0.2  193823  (a)  C  2  (b)  2  Calculated using a non-linear least square fitting program to Equation 5.1. The program also calculates the asymptotic standard errors for the parameters determined in the fitting. (a)  (b)  Calculated from the X R D data taking into account all Si-H interactions up to a distance of 8 A  A plot of 1/T vs. (Aco ) should be a straight line that goes through the origin. Such CP  fS  correlations are shown in Figure 5.3. In contrast to the room temperature plots excellent linear correlations with intercepts of zero are obtained for loadings of both 6 and 8 molecules per u.c.  179  in the CP experiments carried out at 273 K . In the room temperature experiment, the intercept of the correlation for the 8 molecules per u.c. loading deviated very significantly from zero (see Figure 3.15). Similar results are obtained for the complexes of ZSM-5 with p-xylene- d (2). In the 4  sample containing 8 molecules per u.c. (Figure 5.3 b) there is no clear decay of the contact time curves due to a long T  l p ( H )  value, but qualitatively the order of the signal enhancements is as  expected. The situation is much clearer for the case of 6 molecules per u.c. (Figure 5.3 a). Here, the most intense signals (silicons 1 and 10) show a linear decay when ln(I) is plotted vs. CT, and can be used to determine T  l p ( H )  . If T  l p ( H )  is fixed to the average value of 22 ms in a non-linear  least squares fitting of all of the data, the curves shown together with the experimental points in Figure 5.3a are obtained. In Table 5.4 the Io and Tcp values obtained from these fittings are presented. From the curves in Figure 5.4 it can be seen that all the data points can be fitted very well to Equation 5.1. Also the variation in the Io values shown in Table 5.4 is less than 8 %, significantly smaller that the dispersion found in the room temperature data (12 %). In the 8 molecules per u.c. case no decay is observed in the CP curves because the proton relaxation time in the rotating frame ( T i ) is too long. Thus Equation 5.1 is simplified to pH  Equation 5.2. The non linear least square fit of all the data is shown together with the experimental points in Figure 5.4b. The Io and Tcp values obtained from these fittings are presented in Table 5.5. Again all the CP data points can be represented with Equation 5.2. Plots of 1/T  CP  vs (Aco )  SiH  should be straight lines with intercepts of zero. Such  correlations are shown in Figure 5.5. Again, good linear correlations with intercepts of zero are obtained for loadings of both 6 and 8 molecules per u.c., in contrast to the room temperature  180  data where the linear correlation for the 8 molecules per u.c. case deviated considerably from zero. The larger scatter in these data reflect the much smaller dipolar interactions involved because of the methyl group and also the the p-xylene- d.4 isotopic purity, as discussed previoualy in Chapter 3, Section 3.3.2. Now that the relationships between TCP and (Aco )/^ are established for the complexes of the 2  two deuterated p-xylenes, it is possible to calculate the intensities of all of the silicon resonances in any CP spectrum, even if they are not clearly resolved. Thus, for any given contact time value, the intensity distribution of the complete spectrum can be simulated using Equation 5.1. As a test of the correctness of the experimental protocol, the calculated CP spectra for the complexes of 6 molecules per u.c. of p-xylene-^ and p-xylene-^ are compared to the experimental ones for a contact time of 5 ms, in Figure 5.6 and 5.7, respectively. These calculated spectra are from the TCP vs. (Aco )/s linear correlations. For each of the 24 Si-sites, the 2  second moments were computed from the X R D data in reference 1, and using the graphs in Figure 5.4 b, and 5.5 b, the TCP values were predicted. Thus, each signal intensity can be determined from Equation 5.2 for any given contact time. Excellent agreement between the observed and simulated spectra is found, indicating that the method can predict accurately the intensities of the silicon signals in a CP experiments. Conversely, it also provides strong evidence that the method can be used with confidence to determine unknown structures i f care is taken to eliminate any very slow motion which might be present.  •y  Figure 5.4: Plot of experimental TCP values vs. the calculated second moment (Aco )is values for the complexes of p-xylene-^ in ZSM-5 at a temperature of 273 K , (a) with a loading 6 molecules per u.c. (b) with a loading 8 molecules per u.c.  182  240  T  0  5000  10000  15000  20000 25000  30000  35000 40000 45000  Calculated second moment (Hz ) 2  Figure 5.5: Plot of experimental Tcp values vs. the calculated second moment (Aco )/,? values for the complexes of p-xylene-^ in ZSM-5 at a temperature of 273 K , (a) with a loading 6 molecules per u.c. (b) with a loading 8 molecules per u.c. 2  183  Table 5.4: Experimental and calculated parameters related to the H7 Si cross-polarization experiments on the complex of p-Xylene-rf* in ZSM-5 with 6 Molecules per u.c. at T=273 K. Si T-Site  Resonance (ppm)  I (a.u.)  T p (ms)  Si 10  -111.6  293±5  5.0±0.3  (Aco ), calc (Hz ) 41735  Si 1  -112.0  333±5  5.4±0.2  38985  Si 12  -116.7  321±6  14.8±0.6  10751  Si 17  -117.3  367±4  8.5±0.2  29425  Si 16  -117.6  346±7  10.4±0.5  24547  Si 3  -118.9  352±5  8.5±0.3  16783  29  0  <a)  2  C  (b)  s  2  Calculated using a non-linear fitting program, fixing Tlp(H)=22.3 ms in Equation 5.1 Calculated from the X R D data taking into account all Si-H interactions up to a distance of 8  ( }  A.  Table 5.5: Experimental and calculated parameters related to the H/ Si cross-polarization experiments on the complex of p-xylene-rf^ in ZSM-5 with 8 molecules per u.c. at 1-273 K. 1  Si T-Site  Resonance (ppm)  Io (a.u.)  T r (ms)  29  Si 10  -111.6  94.5±0.4  6.2±0.1  (Aco ), calc (Hz ) 41735  Si 1  -112.0  96.1±0.6  5.9±0.2  38985  Si 12  -116.7  98.1±0.5  14.0±0.2  10751  Si 17  -117.3  100.1±0.5  7.8±0.1  29425  Si 16  -117.6  105.8±0.6  12.1±0.2  24547  Si 3  -118.9  96.3±0.5  9.6±0.2  16783  29  (a)  C  2  (b)  s  2  Calculated using a non-linear fitting program to Equation 5.2 ( }  A.  Calculated from the X R D data taking into account all Si-H interactions up to a distance of 8  T = 273 K  -110  -112  -114  -116  -118  -122  T=273 K experim ental  )  -110  -120  -112  -114  -116  -118  -120  -122  p p m fro m T M S  Figure 5.6: (a) Si CP M A S N M R spectrum of ZSM-5 loaded with 8 molecules p-xylene-^ per u.c. at a temperature of 273 R, calculated from the Tcp / (Aco )/,? correlation. Here, the Tcp values were predicted using the graph in Figure 5.4 b; the contact time was chosen to 5 ms. (b) The experimental S i CP M A S N M R spectrum obtained at a temperature of 273 K with a contact time of 5 ms. 2  2 9  185  -110  -112  -114  -116  -118  -120  -122  -110  -112  -114  -116  -118  -120  -122  ppm from TMS Figure 5.7: (a) S i CP M A S N M R spectrum of ZSM-5 loaded with 8 molecules p-xylene-^ per u.c. at a temperature of 273 K , calculated from the Tcp / (Aco )/? correlation. Here, the TCP values were predicted using the graph in Figure 5.5 b; the contact time was chosen to 5 ms. (b) The experimental S i CP M A S N M R spectrum obtained at a temperature of 273 K with a contact time of 5 ms. 29  2  2 9  186  5.4.  CONCLUSIONS Cross polarization experiments can provide very valuable structural information about the  locations of guest molecules in zeolites. In order to get accurate distance information between the sorbed molecules and the zeolite framework, it is necessary to have information about the possible molecular motions of these molecules. In the present case deuterium N M R provided very useful information about molecular motions such as ring flipping and free rotation of the methyl groups about their C3 axis. However in these systems was shown that very slow motions can still occur at correlation times too slow to be detected by deuterium N M R (x < 9 ps). In the c  present work, these slow motion were detected using the success of this technique depends on different  1 3  C N M R exchange spectroscopy. However  C sites being observed, which may be not the  case for other systems, particularly i f only one molecule per asymmetric unit is present and it is of high symmetry. Very slow motions occurring on a time scale of up to 100 ms, can be significant source of errors in the CP studies of these systems, and cannot be allowed in accurate distance determinations. Therefore it is necessary always to work at low temperatures where these motions can be "frozen out". If this is the case the results of the present chapter indicate that the CP technique is a reliable method for organic sorbate/zeolite framework structure determination.  187  5.5.  REFERENCES  1 - van Koningsveld, H.; Jansen, J . C ; van Bekkum, FL, Acta Cryst., B 4 3 , 127, 1987. 2 - Fyfe, C.A.; Feng, Y.; Grondey, FL, Microporous Materials, 1, 393, 1993. 3 - Fyfe, C.A.; Grondey, FL; Feng, Y.; Kokotailo, G.T.; Gies, LL, Chem. Review, 91, 1525, 1991. 4 - Stejskal, E.O.; Schaefer, J., J. Mag. Reson., 34, 443, 1979.  188  CHAPTER SIX INVESTIGATION OF AN UNKNOWN STRUCTURE: THE LOW LOADED FORM OF P-XYLENE IN ZSM-5 STUDIED BY W S i CROSS POLARIZATION EXPERIMENTS 6.1.  INTRODUCTION Previous chapters have demonstrated that detailed structural information in exact  agreement with the known x-ray structure could be obtained for the high loaded complex of pxylene in ZSM-5 from solid state N M R techniques based on the dipolar interactions between nuclei of the organic guest molecule and the silicon nuclei of the zeolite lattice. In Chapters 3 and 5 the application of the CP/MAS technique to locate the p-xylene molecules was demonstrated. In all these previous chapters the high loaded complex of p-xylene/ZSM-5 was used to develop and test protocols that could be used to study samples with unknown crystal structures. In this chapter the application of the cross-polarization technique to the study of a sample of unknown crystal structure, the low loaded complex of p-xylene/ZSM-5 is described and from these data a crystal structure for this complex is proposed. This study completes the work of this thesis and demonstrates the feasibility of using only solid state N M R techniques to obtain the three-dimensional structures of sorbate-molecular sieve complexes. As mentioned earlier in the thesis, Fyfe and co-workers have previously used high resolution S i N M R to study the effects of temperature and sorbed organic molecules on the 29  ZSM-5 framework ' ' . Increasing the temperature has been shown to induce a change from the 1 2 3  monoclinic form with 24 T-sites to an orthorhombic form with 12 T sites . A similar phase 4  189  change is produced by the sorption of p-xylene, the change being complete at approximately two molecules per unit cell, and with high enough resolution, the complete three-dimensional phase diagram of the combined effects of temperature and p-xylene concentration can be determined by N M R . In Figure 6.1 the S i N M R spectra of ZSM-5 are shown as a function of increasing p3  2 9  xylene concentration. The spectra indicate that the 12 T-site orthorhombic phase (Pnma) is kept up to a loading of ~4 molecules of p-xylene per u.c . Further addition of p-xylene changes the 5  structure to an orthorhombic form with 24 T-sites (P2/2/2/) . It must be noted that the C P / M A S 5,6  spectrum shown in Figure 6.1 b indicates that at a loading of 4 molecules per u.c. there is a small fraction of the orthorhombic phase of ZSM-5 with space group P2]2]2i. This fraction is very small and can be detected only in the C P / M A S spectrum (compare with the quantitaitive M A S spectrum shown in Figure 6.1 a, at the same loading). This is because it has a more efficient 1  H7 Si cross-polarization transfer compared to the low loading phase. For this reason, in the 29  present work a loading of 3 molecules per u.c. was used to eliminate possible problems resulting from a mixture of phases.  190  (a)  1  -110  1  (b)  -I—  -115 -120 5 / ppm  I  -110  i  r-  -115 5 / ppm  -120  Figure 6.1 (a) Si M A S N M R decoupled spectra of ZSM-5 with increasing concentration of p-xylene; the numbers of p-xylene molecules sorbed per u.c. are indicated in the figure. A 350 s delay time between pulses ensures the spectra are quantitative, (b) S i CP M A S N M R decoupled spectra of the same samples with a 20 ms contact time and 5 s delay time 29  2 9  191  6.2.  EXPERIMENTAL  6.2.1  SAMPLE PREPARATION  Samples with a loading of three molecules per u.c. of p-xylene de and p-xylene d^ were prepared following the procedure previously outlined in Chapter 2, Section 2.2.3. 6.2.2  2  H N M R SPECTRA AT VARIABLE TEMPERATURE  Wide-line deuterium N M R spectra were obtained using a home-built probe which accommodated both 10 mm and 5 mm horizontal solenoid coils. A quadrupolar echo sequence (90 -T-90 -T-acq ) was used and typical 90° pulse times were ca. 2.8 ps and 6 ps for the 5 mm 7  x  y  and 10 mm coils, respectively. The low temperature measurements were carried out with a flow of cold nitrogen gas. The temperature was regulated using the Bruker VT-1000 temperature control unit. 6.2.3  I N A D E Q U A T E EXPERIMENTS AT 268 K .  I N A D E Q U A T E experiments were performed using the pulse sequence in which the last 90° pulse was replaced by a 135° pulse to provide quadrature detection in the double quantum frequency domain The experiment was carried out at a temperature of 268 K , using the 8  experimental arrangement for working at low temperatures described in Chapter 2. The spectra were acquired with a S i / ' H double tuned probe with 7 mm spinners. The determined 90° pulse 2 9  length was 8.25 ps. The collected data were processed and plotted using the program 2D-WIN N M R from Bruker.  192  6.2.4  ' H / ^ S i C P EXPERIMENTS Variable contact time experiments on the complexes of 3 molecules of p-xylene dg and d  4  in ZSM-5 were carried out at 243 K and 233 K, using the experimental arrangement for working at low temperatures described in Chapter 2. Experiments at contact times of up to 60 ms were carried out. Typical 90° pulse times were 11 p.s. (^H) and 11.2 p.s. ( Si). The number of scans 29  accumulated for each contact time varied between 1000-3000. Additional experiments were carried out at even lower temperatures. We thanks Dr. Hans Forster from Bruker Germany for the variable contact time experiments on the complexes of 3 molecules of p-xylene de and d in ZSM-5 carried out at 213 K 193 K and 173 K . 4  193  6.3.  6.3.1  R E S U L T S A N D DISCUSSION  DEUTERIUM N M R SPECTROSCOPY In Chapter 3, Section 3.1.2, the fundamentals of H N M R spectroscopy and the work of 2  Vega and co-workers on the system of p-xylene adsorbed on Na-ZSM-5 were described. 9  Although the system studied by Vega and co-workers is significantly different from that used here, the theoretical spectra for the different molecular motions such as methyl group rotation and 180° ring 'flips' provide excellent reference points and were used in the interpretation of the spectra described below. The quadrupolar echo H N M R spectra of p-xylene ^ and dg adsorbed on ZSM-5 at a 2  loading of 3 molecule per u.c. obtained at different temperatures are shown in Figures 6.2 and 6.3, respectively. From these spectra the changes in the motional states of the molecules can be deduced. By comparing the experimental spectra with the simulated spectra shown in Figure 3.6, Chapter 3, the following conclusions can be drawn: The spectrum of p-xylene-J* at room temperature (293 K), shows that all the benzene rings in the sample are undergoing discrete 180° flips around the C 1 - C 4 molecular axis on the deuterium N M R time-scale. Lowering the temperature to 243 K produces a broadening of the spectrum and the appearance of a splitting of 130 kHz characteristic of rigid phenyl rings. The spectrum indicates the presence of a mixture of molecules with rigid benzene rings and molecules whose phenyl groups undergo 180° flips around the C i - C4 molecular axis. Reducing the temperature increases the proportion of p-xylene molecules with rigid phenyl rings as shown in the spectra at 213 K and 193 K .  194  500000  300000  100000  -100000  -300000 -500000  Figure 6.2 H quadrupolar echo N M R spectra of p-xylene-G^ in ZSM-5 at a loading of 3 molecules per u.c. at the temperatures indicated. The 90° pulse length was 3.45 ps, echo delay 30 ps, and between 1000-4000 scans were accumulated with a recycle delay of 20 s. The spectra were processed with a line broadening of 1000 Hz. 2  195  In the case of the p-xylene-d<5 intercalate, Figure 6.3, the splitting is 40 kHz indicating free rotation of the methyl groups about their C 3 axes, as expected, but with no evidence for diffusional motion on this time scale. Therefore the p-xylene molecules in the low loading complex have freely rotating methyl groups and aromatic rings that are static or undergoing 180° flips around the C 3 axis, the proportion of which depends strongly on the temperature. These molecular motions have to be considered in the calculation of the second moments, and in general, it must kept in mind that these conclusion are valid only in the context of the timescale of the deuterium experiments (x <.10" s). It is 5  c  anticipated that the phenyl rings must be considered to all be flipping on the timescale of the CP experiments and it is possible that even more extensive motions might occur at some temperatures on this timescale.  40 kHz  —•  250000  150000  50000  -50000  -150000  -250000  Figure 6.3 H quadrupolar echo N M R spectrum of p-xylene-d<5 in ZSM-5 at a loading of 3 molecules per u.c. at the temperatures indicated. The 90° pulse length was 3.45 ps, echo delay 12 ps, and 376 scans were accumulated with a recycle delay of 20 s. The spectrum was processed with a line broadening of 1000 Hz. 2  196  6.3.2  VARIABLE CONTACT TIME SI C P / M A S N M R EXPERIMENTS 29  Because of the strong dependence (1/r ) between the Si-H internuclear distance and the 6  cross-polarization rate it was anticipated that the S i CP/MAS N M R spectra of this system 2 9  would show substantial differences in the enhancements of the different signals. The effect ofthe distance dependence can be seen qualitatively from a comparison of the CP spectrum of the complex of p-xylene-ck at 233 K with that from a quantitative one pulse experiment at the same temperature as shown in Figure 6.4: some signals which must be closer to the aromatic hydrogens are strongly enhanced. As in the case of the 8 molecules per u.c. complex, it is expected for the low loading sample that the p-xylene molecules could undergo very slow molecular motions inside the zeolite framework similar as those studied in Chapter 4. This kind of motion is important on the time scale of the cross polarization experiments used in the present work (up to 60 ms), and they cannot be allowed i f quantitative information on the location of these molecules is to be obtained. In order to solve this problem, it was previously shown in Chapters 4 and 5 that it is necessary to reduce the temperature until these motions are slowed down so they are negligible on the CP time scale, which is the time usually required in the dipolar dephasing experiments. The difficulty in the present case is that for this system there is no difference in the chemical shifts between the two methyl groups as shown in Figure 6.5. Thus the application of chemical exchange spectroscopy to study slow motional processes in this system is precluded. Consequently, in order to assess whether diffusion of the guest molecules is occurring but at too slow a rate to affect the deuterium N M R experiments, a series of CP experiments must be conducted at decreasing temperatures until no appreciable changes in the behaviour of the contact time curves is observed between successive temperatures.  197  I  -110  i 1  i  l  -112  1  I  1  I  1  -114 (ppm)  I  1  I  1  -116  l  1  l  -118  Figure 6.4: (a) Si CP M A S N M R spectrum of ZSM-5 loaded with 3 molecules p-xylene-cfe per u.c. at 233 K , contact time 5 ms, recycle delay 2 s. (b) S i M A S N M R spectrum of the same sample obtained using a recycle delay of 350 s to ensure complete relaxation of the silicon nuclei. The S i 90° pulse length was 13 ps. 2 9  2 9  198  T = 233 K  |  I I I I  I 1 I I I I  I I I I I I I  40  I I I 1 I I I  30  I I  I I 1 1 T-I-T-T  r 1 I 1 T r n  1 T 1 I  I I  I | T  20 10 (ppm)  l l l l  0  I I I I I 1 I  1 1 1  -10  Figure 6.5: C CP/MAS N M R spectra of the complex of [ C H ] p-xylene in ZSM-5 at the different temperatures indicated. The ' H 90° pulse length was 9.0 ps, contact time 2 ms, and between 72-264 scans were accumulated with a recycle delay of 1 s. 1 3  13  3  A n additional problem is that the  Si N M R spectra of the system ZSM--5 with 3  molecules of p-xylene are sensitive to changes in the temperature, and the chemical shifts of some signals are significantly affected when lowering the temperature, as seen from the series of 2 9  S i N M R M A S spectra carried out at different temperatures shown Figure 6.6. The spectrum at  199  room temperature has been assigned previously using the I N A D E Q U A T E experiment (see Chapter 1, Figure 1.20). However, because some signals are shifted considerably and their shifts possibly crossing over each other when lowering the temperature, a new I N A D E Q U A T E experiment was done to unequivocally assign the signals. Figure 6.7 shows the I N A D E Q U A T E spectrum for this sample at 268 K . This temperature was chosen after close examination of all the spectra in Figure 6.6 because it gives the largest number of clearly resolved signals. The analysis of the I N A D E Q U A T E spectrum gives the assignment of the signals corresponding to Si 11 and Si 12 which were clearly resolved in the spectrum at low temperature, compared to the previously assigned room temperature spectrum. The assignment of the signals is indicated in the 1-D spectrum shown in Figure 6.7. Now that the assignment of the resolved signals in the S i N M R M A S spectra a lower 2 9  temperature is known, the cross polarization experiments can be carried out and interpreted. As the presence of slow motions could not be directly detected in this study, variable 29  contact time cross-polarization experiments were conducted at different temperatures.  •  Si  CP/MAS spectra were obtained as a function of the contact time up to a maximum of 60 ms, at different temperatures for the samples with 3 molecules per u.c. of p-xylene dg and d . The 4  spectra were deconvoluted in terms of Lorentzian functions and the intensities of the reasonably well resolved resonances due to silicons 2, 3, 4, 8, 10, and 12 tabulated. Figure 6.8 (a) and (b) shows plots of these data for the p-xylene dg system at 293 K , 243 K , 233 K , 213 K , 193 K , and 173 K . 1  Table 3.2 lists some important relaxation parameters for the specifically deuterated p-xylene/ZSM-5 complexes.  H and  29  Si nuclei in the  200  410  '  412  '  414 ' (ppm)  416  '  418  Figure 6.6: Si M A S N M R spectra of the complex of ZSM-5 with 3 molecules of p-xylene-Gk per u.c. at the different temperatures indicated. The S i 90° pulse length was 7.0 ps and between 32 and 56 scans were accumulated with a recycle delay of 12 s. 2 9  201  Figure 6.7: Contour plot of an I N A D E Q U A T E on ZSM-5 with 3 molecules per u.c. of p-xylene at 263 K with a ID M A S N M R spectrum shown above. 36 experiments with 480 scans in each experiment were performed with a recycle delay of 14 s. A sweepwidth of 820 Hz, fixed delay of 15 ms, and 140 real data points were used. Sine-bell and trapezoidal apodization in the F2 and F l dimensions, respectively, and a power calculation were used for the data processing.  202 1  Table 6.1 Selected relaxation parameters for the deuterated p-xylene/ZSM-5 complexes at 233 K.  5q  H and  Si nuclei in the specifically  ca. 5Ti (s)  T  (ms)  (ms)  'HCring)  0.8  0.04  76.9  'H(CH )  0.8  0.05  59.5  30  11.4-18.0  -  Nuclei  3  Si (framework)  Tlp(H)  2  Quantitatively, the cross-polarization process is usually described as in Equation (6.1) with the assumptions that T  l p ( H )  time in the rotating frame and T  « T  lp(Si  ) and T  l p ( S i )  is the silicon relaxation time in the rotating frame. Also the  l p ( S i )  is long, where T  l p ( H )  is the proton relaxation  number of ' H nuclei must be "much" larger than the number of S i nuclei. This latter condition 29  is at least approximately satisfied in the present cases because of the low natural abundance of 2 9  S i (4.6%). However, in samples of this type, the protons are present at quite low concen-  trations (in this case the ratio is approximately 4 protons for 12 S i nucleus) and there may be 2 9  relatively small homonuclear dipolar couplings between protons on different molecules, so the proton reservoir may not be a strongly coupled abundant homogeneous spin system. Thus, Equation (6.1) is expected to give only an approximate description of the behaviour of the S nucleus magnetization.  ( I(t) = I  0  T 1-'cp/  /  vV  (  cxp-/  /  \  / Y»  ( -txA~/  T  (6.1)  Here, I represents the theoretical maximum signal intensity obtainable from the polariza0  tion transfer in the absence of any loss due to relaxation processes  203  The CP data in Figure 6.8 (a), for the experiment carried out at room temperature cannot be fitted properly with Equation 6.1. Although some signals are evidently enhanced compared the others, the order of the curve maximas for the different resolved silicons changes compared to that of the CP plots at lower temperatures (e.g. 243 K , Figure 6.8 (a)). This behaviour is an indication of molecular motions in the system that affects the CP data obtained at different contact times. In fact, at temperatures above RT, all the signals are enhanced to the same degree, indicative of free diffusional averaging of the interactions. These spectra thus cannot be used for distance determination as have been claimed by Mentzen . 10  In general terms, the curves shown in Figures 6.8 (a) and (b) for the CP data measured at 243 K 233 K , 213 K , 193 K , and 173 K , approximate the general behaviour expected from Equation (6.1). That is, there is an exponential growth due to polarization transfer and a decay from the loss of proton magnetization due to T  l p ( H )  . The curves which grow fastest have the  highest maxima and the maxima in the series shift to longer contact time values as they become lower. There are clear consistencies between the different temperature data sets. Thus, in Figures 6.8 (a) and (b), the curves for all the temperatures below or equal than 243 K indicate that silicon 8 is much more efficiently polarized (and hence closer to the ' H polarization source) than the other silicons. Silicons 3, 2 and 12 have an intermediate enhancement, and Si 4 and 10 are only weakly polarized, and therefore are much further away from the aromatic protons. A similar trend is seen for the p-xylene-c^ system at low temperature (Figure 6.9) where silicons 3 and 2, polarize much more efficiently than silicons 8, 12, 4 and 10.  204  T = 293 K  1.0E+1 9.0E+0 8.0E+0 7.0E+0 6.0E+0 5.0E+0  Si 3  4.0E+0 3.0E+0  ° Si  2.0E+0 1.0E+0  4«  10  •  o  Si 4  fin  O.OE+O 10  15  20  25  30  35  40  45  Contact time (ms)  T = 243 K  Si 3 Si 2 Si 4  10  20  30  40  50  60  Contact time (ms)  233 K  Si 4  O.OE+O 20  30  40  60  Contact time (ms)  Figure 6.8: (a)Intensities of the S i CP M A S N M R signals as functions of the contact time for ZSM-5 with a loading of 3 molecules of p-xylene-Gk per u.c. at the temperatures indicated. The lines represent the best fits calculated using Equation 6.1 in a non-linear least squares fitting program. 2 9  205  T=213 K  1.0E+39.0E+28.0E+2.—. 9  OB  7.0E+2-  Si 12 Si 3  6.0E+2 -  a  5.0E+2 -  a  4.0E+2 3.0E+22.0E+2 • 1.0E+2 O.OE+O40  60  Contact time (ms)  1.0E+3-9.0E+2 -• ,—,  s  8.0E+2-7.0E+2--  00  >, '«  a a  6.0E+2-5.0E+2-4.0E+23.0E+2-2.0E+2 -1.0E+2 -O.OE+O J 40  60  Contact time (ms)  Figure 6.8 (b) Intensities of the Si CP M A S N M R signals as functions of the contact time for ZSM-5 with a loading of 3 molecules of p-xylene-^ per u.c. at the temperatures indicated. The lines represent the best fits calculated using Equation 6.1 in a non-linear least squares fitting program.  206  4.0E+6  T = 243 K  20  30  40  Contact time (ms)  5.0E+7  Si 3  T = 233 K  0.0E+0 20  30  40  Contact time (ms)  T=213 K  10  20  30 40 50 60 Contact time (ms)  70  80  Figure 6.9 Intensities of the Si CP M A S N M R signals as functions of the contact time for ZSM-5 with a loading of 3 molecules of p-xylene-^ per u.c. at the temperatures indicated. The lines represent the best fits calculated using Equation 6.1 in a non-linear least squares fitting program.  207  Table 6.2 Experimental and calculated parameters from the least squares fit to the data from the W Si cross-polarization experiments on the complex of p-xylene-</<5 i i n ZSM-5 with 3 molecules per u.c. at different temperatures. l  29  (a)T=233K. > Si T-Site Si 2  Resonance (ppm) -117.7  Si 3  9  ' ~ Io  icp  Tlp(H  x  2  (a.u.) 47.1±0.9  (ms) 7.4±0.5  (ms) 76.9  119  -114.6  45.1±0.5  6.9±0.4  76.9  44  Si 4  -115.5  24.0±0.2  11.8±0.3  76.9  27  Si 8  -118.1  76.7±0.6  4.2±0.2  76.9  131  Si 10  -110.4  34.9±0.6  9.2±0.5  76.9  140  Si 12  -113.8  46.0±0.7  7.7±0.4  76.9  132  (b) T=213 K. Si 2  -117.7  928±15  21.4±0.8  245  12482  Si 3  -114.6  854±16  20.9±0.9  245  14923  Si 4  -115.5  367±20  45±4  245  4115  Si 8  -118.1  942±39  12.2±0.9  245  15121  Si 10  -110.4  567±13  36±2  245  3105  Si 12  -113.8  894±13  23.2±0.8  245  8304  (c) T=193 K Si 2  -117.7  916±17  32±1  278  9777  Si 3  -114.6  819±17  28±1  278  12688  Si 4  -115.5  609±43  114±11  278  1095  Si 8  -118.1  847±39  15±1  278  12736  Si 10  -110.4  707±23  58±3  278  3215  Si 12  -113.8  865±18  31.8±0.9  278  4120  (d) T=173 K. Si 2  -117.7  373±9  24.5±1.2  541  1988  Si 3  -114.6  580±12  20.2±1.3  541  11349  Si 4  -115.5  291±22  48±6  541  1681  Si 8  -118.1  859±67  14.7±1.7  541  14241  Si 10  -110.4  496±23  44±3  541  2515  Si 12  -113.8  581±20  22.4±1.7  541  12530  208  The variable contact time cross-polarization curves were fitted to Equation (6.1), with T ( H )  l p  fixed. The fittings were done using the non-linear statistics package in Mathematica; the  program also provides a statistical asymptotic standard error for the fitted parameters (% ). In principle % values reflects the "goodness of fitting" to the experimental data. However, the 2  values depend on the absolute magnitudes of the data which in the present instance are arbitrary. Thus comparisons cannot be made between different sets and even within a set, the data curves should be normalized and x  2  values corrected. Also, no indication of the error in the  experimental signal intensities is obtained from these x, values. The calculated curves from these 2  fits are those shown together with the experimental data points in Figure 6.8 (a) and (b), for the complexes of p-xylene-^ and in Figure 6.9 for p-xylene- d . 4  In the case of ZSM-5 loaded with 3 molecules of p-xylene- d per u.c. (Figures 6.8 a,b), the 6  value for T  l p ( H )  was obtained from least squares fits to the linear decays of plots of ln(I) vs. CT  for Si 8 (Table 6.1) for each different temperature CP data. Thus, for example, for the data carried out at 233 K , the value of 76.9 ms was used in fitting all of the other curves at that temperature. Using this value of T  l p ( H )  to Equation (6.1) to obtain I and T 0  and fitting the curves using a non-linear least squares fits c p  values gives the data in Table 6.2 (a). The calculated  fitting values for the 213 K , 193 K and 173 K CP experiments are presented in Table 6.2 (b), (c) and (d), respectively. There is some variation in I (the theoretical maximum magnetization) for the different 0  silicon sites for all different temperature CP data. Although all the silicon sites are of equal occupancy in the structure, it is possible that I could vary as there is some degree of isolation of the 0  209  groups of proton spins, and different silicon sites may be in primary contact with different numbers of protons. In the case of ZSM-5 loaded with 3 molecules of p-xylene- d per u.c. (Figure 6.9), the 4  values for T  l p ( H )  were obtained from least squares fits to the linear decays of plots of ln(I) vs. CT  for Si 3 (Table 6.3) for all different temperature CP data. For example, for the data obtained at 233 K , the value of 59.5 ms calculated from the decay of Si 3 was used in fitting all of the other curves at that temperature. Using this value of T  l p ( H )  squares fits to Equation (6.1) to obtain I and T  c p  G  and fitting the curves using non-linear least  values gives the data in Table 6.3 (a). In this  case the lowest temperature CP data available were 213 K and the calculated fitting values for this temperature are presented in Table 6.3 (b). In principle, the p-xylene molecules in this system can be located anywhere in both the sinusoidal or the straight channels. Qualitatively, the CP data show that the aromatic protons are closer to Si 8, than to Si 12, Si 2, Si 3, Si 4 and Si 10, and therefore the p-xylene molecule cannot be located in the sinusoidal channel. A more quantitative approach can be taken by calculating the theoretical CP spectra for different locations of the p-xylene molecules by using the experimentally determined Tcp values (shown in Tables 6.2 and 6.3) for the complexes of 3 molecules per u.c. of p-xylene-efo and pxylene-^ in ZSM-5 at 233 K to determine the positions of the p-xylene molecules in the framework. The T  values are directly related to the ' H / S i heteronuclear second moment via 29  c p  Equation 6.2:  210  C(Aco ) 2  1/T = CP  where C is a constant and (Aco ) and JS  /5  (Aco ) // 2  (6.2)  172  (Aco ) are the heteronuclear (LS) and homonuclear (1,1) u  second moments, respectively. The second moments can be calculated for a given structure from the van Vleck equation as described in Chapter 1, Section 1.2.3.3.1. The approach taken to locate the p-xylene molecules in the complex was as follows: the pxylene molecule was located at a specific position inside the zeolite, and all the S i - H distances between the guest molecule and the zeolite framework calculated (the atomic positions from the silicon framework were taken for the published ZSM-5 orthorhombic structure, space group Pnma ). The initial atomic coordinates for a p-xylene molecule were calculated from an origin 11  (0,0,0) in the centre of the aromatic rings with the atomic distances as in (1).  -<a9A (1) Because of the fast rotation of the methyl groups about its C3 axis, the three hydrogens of the C H 3 were reduced to the point at the centre of the triangle formed by the three hydrogens, as shown in (1). A computer program (given in Appendix 3) was written in the turbopascal language to systematically apply rotation matrixes about the x, y, and z crystallographic axes to the starting coordinates of the p-xylene molecule. The new rotated coordinates (centre {0,0,0}) are translated  211  to the Cartesian coordinate reference system used for the reported Pnma structure  11  so the p-  xylene molecule is initially located with the long molecular axis along the along the y axis and its centre in the mirror plane ({x,l/4,z}). In this reference system the x axis runs parallel to the sinusoidal channels, and the y axis runs parallel to the straight channels. The program was written to systematically rotate the molecule up to 180° about y, and up to 60° about x and z. The p-xylene is also methodically translated from the initial position in the mirror plane along x, y, and z. The translation along x, and z was constrained to be from 0 to 0.6 A because the molecule touches against the zeolite framework for larger values. Translation along the y axis moved the molecule from the mirror plane up to 5 A along the straight channel. Therefore with the program given in Appendix 3, all possible positions and orientations of the p-xylene molecule in the straight channel can be calculated. The calculated atomic positions for the molecule are then used in another subroutine of the program to calculate the heteronuclear second moments between the guest molecules and the silicon atoms in the zeolite framework. For a methyl group undergoing fast rotation about its C 3 axis, the motionally averaged second moments were calculated using the distances from the silicon atoms to the point in the centre of the triangle formed by the three hydrogens, as shown in (1). For the aromatic protons, motional averaging due to ring "flips" should be used, however this was not done in the program that calculates the heteronuclear second moment for all the possible orientations and position of the p-xylene molecule (Appendix 3), because the additional matrixes required to average the second moments could not be implemented in this computational platform due to memory limitations. The averaged Si-H second moments for the aromatic protons were calculated for every solution in an independent program, given in Appendix 5.  212  Table 6.3: Experimental and calculated parameters from the least squares fit to the data from the W s i cross-polarization experiments on the complex of p-xylene-^ in ZSM-5 with 3 molecules per u.c. at different temperatures.  (a) T=233 K Si T-Site Si 2  Resonance (ppm)  (a)  -117.7  • Io (a.u.) 53.2±0.6  (ms) 5.3±0.2  Si 3  -114.6  54.5±0.4  Si 4  -115.5  Si 8  2 y  T  Tlp(H  x  2  (ms) 59.5  137  4.2±0.1  59.5  69  24.6±0.4  12.0±0.5  59.5  24  -118.1  33.3±0.6  7.7±0.4  59.5  99  Si 10  -110.4  19.9±0.5  11.6±0.8  59.5  46  Si 12  -113.8  37.7±0.5  6.7±0.3  59.5  107  (b) T=213 K Si 2  -117.7  1239±16  7.6±0.3  76.5  27446  Si 3  -114.6  1327±21  5.7±0.2  76.5  10932  Si 4  -115.5  485±19  12±1  76.5  28769  Si 8  -118.1  694±16  11.3±0.6  76.5  20837  Si 10  -110.4  421±26  14±2  76.5  43836  Si 12  -113.8  767±15  8.5±0.5  76.5  24022  In the automated program given in Appendix 3, the aromatic heteronuclear second moments are calculated for a static molecule. This is not expected to introduce big errors in finding the best solution for the p-xylene molecule because there are not large differences in the R  2  correlation values for the plots of 1/TCP vs averaged or static second moments for the  aromatic protons, and also because the H N M R spectra (see Figure 6.2) show that there are a 2  large proportion of static p-xylene ring molecules at temperatures lower than 243 K . Structure determinations were carried out using an automated version of the general protocol described in Chapter 3 and Chapter 5. At this time the lowest temperature data sets were at 233 K and were used in the analysis.  213  Since T is related to the H/ Si heteronuclear second moment via Equation (6.2), a plot 1  29  cp  9  of 1/T vs (Aco ) CP  IS  should be a straight line. This was included in the program by using a least  square linear regression subroutine to quantify the linearity of the plots of the calculated second moments from the atomic coordinates for every possible orientation of the p-xylene molecules versus the experimental Tcp values. The program output only the p-xylene positions and orientations with the best linear regression (in this case was chosen as the cut-off point a values of R >0.98) for acceptable fits for both the aromatic and methyl protons. These solutions were further reduced by considering the Si-H distances of all the 12 silicon atoms. Any solutions with Si-H distances shorter than 2.8 A were rejected as reflecting repulsive interactions. In spite of these constraints there are 106 possible solutions with R correlation values between 0.98-0.995. The computer time necessary to calculate the correlations for the whole range of possible orientations of the p-xylene molecule in the zeolite was approximately 120 h, using a Pentium pro 200 MHz C.P.U.. Because of the experimental error in the measurements of the Tcp values, it is not valid just to select the location of the p-xylene molecule with the best R correlation value as the only 2  criterion for the best solution. In order to further narrow the range of possible solutions, the theoretical individual Lorentzian lines for the 12 silicon sites were calculated to obtain the simulated NMR spectra for each of the 106 solutions using the program given in Appendix 4. The total area of the theoretical spectra (obtained by adding the 12 individual Lorentzian lines) as well as the individual Lorentzian areas for the best resolved peaks (Si 10, Si 4, and Si 3) were compared with the experimental values for complexes of both p-xylene d and dg. The three best 4  matching according to the Lorentzian simulated spectra are shown in Figures 6.10 and 6.11 for the 3 molecule per u.c complexes of p-xylene dg and d respectively. They are identified as 4  214  solutions 14, 58, and 96. These three solutions are very similar as can be seen from their threedimensional structures shown in Figures 6.12, 6.13 and 6.14. In solution 58 (Figure 6.14) the molecular mirror plane of the p-xylene molecule coincides exactly with the crystallographic mirror plane, with the long molecular axis parallel to the y axis [1,0,0] and the aromatic ring oriented with an angle of 33° about the axis y. In solutions 14 and 96, the molecules have the aromatic rings oriented almost identically to solution 58 (with an angle of 36° along y) but they are shifted respectively, by 0.1 and 0.3 A from the mirror plane. Also in solutions 14 and 96, the long molecular axis of the p-xylene molecule are shifted, respectively, 9° and 12° from the [0,1,0], and 15° and 6° from [0,0,1]. Figures 6.15 and 6.16 show the plots of the Tcp values vs. the calculated second moment at 233 K for the three best solutions, for the complexes of ZSM-5 loaded with 3 molecules of pxylene d and d& respectively. It must be noted that none of the linear regressions that were 4  obtained for the 233 K data, including the three shown in Figures 6.15 and 6.16, had intercepts of zero. A similar situation was found for the corresponding data at room temperature for the complex of ZSM-5 with 8 molecule of p-xylene per u.c. at room temperature (Figure 3.15 and 3.16) and it is possible that the reason for the deviation of the intercepts from zero in the present case is also due to very slow molecular motions of the sorbed molecules. To investigate this further, Si CP/MAS experiments as a function of the contact time at 29  temperatures lower than 233 K were carried out for the samples with 3 molecules per u.c. of pxylene de and d and these data are presented in Figure 6.8 (b) and 6.9 (see Section 6.2.4.1). 4  215  Solution 96  a8  Figure 6.10 Si CP MAS NMR spectra of ZSM-5 loaded with 3 molecules p-xylene-cfc per u.c. at 233 K , calculated from the TCP / (Aco )/s correlations. For each of the 12 Si-sites, the second moments were computed using program given in Appendix 4, and the TCP values predicted using the appropriate graph from Figure 6.12. Thus, each signal intensity can be determined from Equation 6.1 for any given contact time; here CT = 10 ms was chosen. The individual Lorentzian lines for each signal and the experimental Si CP MAS NMR spectrum at 233 K obtained with a contact time of 10 ms are also shown in the figure. 2  29  216  -108  -110  -112  -114  -116  -118  -120  -108  -110  -112  -114  -116  -118  -120  A  f  Solution 14  10  Si  Si 10  -108  A  /  I  I  -110  -112  AA \y\  i  Si  A  12  A  1 -114  Si  3  Si4  J  -116  Si2  Si 8  A  1 -118  -120  Figure 6.11: Si CP M A S N M R spectra of ZSM-5 loaded with 3 molecules p-xylene-^ per u.c. at 233 K , calculated from the TCP / (Aco )/s correlations. For each of the 12 Si-sites, the second moments were computed using program given in Appendix 4, and the Tcp values predicted using the appropriate graph from Figure 6.13. Thus, each signal intensity can be determined from Equation 6.1 for any given contact time; here CT = 10 ms was chosen. The individual Lorentzian lines for each signal and the experimental S i CP M A S N M R spectrum at 233 K obtained with a contact time of 10 ms are also shown in the figure. 29  2  2 9  217  Figure 6.12. Three-dimensional representations of the structure of the low-loaded ZSM-5 with 3 molecules of p-xylene from solution 14 seen (a) along the y axis, (b) along the x axis  Figure 6.13. Three-dimensional representations of the structure of the low-loaded ZSM-5 with 3 molecules of p-xylene from solution 58 seen (a) along the y axis, (b) along the x axis  219  Figure 6.14. Three-dimensional representations of the structure of the low-loaded ZSM-5 with 3 molecules of p-xylene from solution 96 seen (a) along the y axis, (b) along the x axis  220  -I  1  1  1  1  1  1  0  5000  10000  15000  20000  25000  30000  35000  0  5000  10000  15000  20000  25000  30000  35000  1  Figure 6.15: Plots of experimental Tcp values vs. the calculated second moment (Aco )/^ values for the complex of 3 molecules per u.c. of p-xylene-^ in ZSM-5 at 233 K , for the best solutions, as indicated in the figure. 2  221  0  -I 0  1 5000  1 10000  1 15000  1 20000  1 25000  1 30000  1 35000  Calculated second moment (Hz ) 2  Figure 6.16: Plots of experimental Tcp values vs. the calculated second moment (AG> )JS values for the complex of 3 molecules per u.c of p-xylene-^ in ZSM-5 at 233 K , for the best solutions, as indicated in the figure.  222  The same protocol used for the CP data at 233 K was carried out with the automated program given in Appendix 3 for the p-xylene-d<$ CP data at 193 K and the p-xylene-c/^ CP data at 213 K . The best solution found was identical to solution 58, but the aromatic ring is inclined 27° about y instead of 33°. This difference is explained as a thermal effect because at lower temperature the p-xylene rings are more rigid. Figures 6.17 and 6.18 show the plots of Tcp vs. calculated second moments for the best solution, for the complexes of ZSM-5 loaded with 3 molecules of p-xylene-^ and d^, respectively. In the plots for the complex of p-xylene-^ at lower temperatures shown in Figure 6.17, there is a clear trend of the intercepts crossing closer to zero when the temperature is lowered. However the data for the CP experiment obtained at 173 K have a worse correlation that at 193 K . The possible reason is that at lower temperatures the positions of the silicon signals shift and in the case of Si 8 and Si 2, and Si 12 and Si 3, an almost complete overlapping of their resonances is observed, making the deconvolution of these signals very inaccurate. In the case of the complex of p-xylene d^ the lowest temperature data available is at 213 K (Figure 6.18) and it can be seen again that there is a trend of the intercepts crossing closer to zero as the temperature is lowered, suggesting as previously that some residual slow motions are being quenched. It must be noted that the former analysis was done on two different and independent samples of the same complex (3 molecules per u.c.) of p-xylene deuterated in different positions (methyl and aromatic hydrogens), and the CP experiments show different sensitivities to different silicon atoms in the framework. Both sets of data independently indicate that the best solutions for the complex structure are those presented before. Therefore it is felt that these represent a very good approximation to the structure of the complex.  223  From examination of these data it is not possible to decide with certainty the single best solution, because the small differences between them are comparable with the experimental error. From a point of view of symmetry, the best possible solution is 58, because it has the higher symmetry, and therefore is the best solution for the space group Pnma. Also this solution is consistent with there being only one signal in the  C N M R spectrum (Figure 6.5) because  both methyl group are equivalent. The fractional atomic coordinates for solution 58 are given in Table 6.4. The numbering used in the table is indicated in (2) for the p-xylene molecule and in (3) for the zeolite framework.  (3)  224  90  Figure 6.17: Plots of experimental TCP values vs. the calculated second moment (Aco )/s values with motion at the temperatures indicated in the figure, for the complex of 3 molecules per u.c. of p-xylene-cfc in ZSM-5 for the best solution determined with the data at 193 K (which is identical to 58 but the aromatic ring is inclined 27° about y). 2  225  Figure 6.18: Plot of experimental Tcp values vs. the calculated second moment (Aco )/s values for the complex of 3 molecules per u.c. of p-xylene-^ in ZSM-5 for the best solution determined with the data at 193 K (which is identical to 58 but the aromatic ring is inclined 27° about y).at 213 K . 2  226  Table 6.4: Fractional atomic coordinates for the complex of ZSM-5 loaded with 3 molecules per u.c. of p-xylene. The p-xylene coordinates were calculated from the NMR data and correspond to solution 58. The framework coordinates are those reported for the single crystal XRD structure reported in reference 11.  Atom  x/a  y/b  z/c  H-l H-2 H-3 H-4 H-5 H-6 C-l C-2 C-3 C-4 C-5 C-6 C-7 C-8 Si-1 Si-2 Si-3 Si-4 Si-5 Si-6 Si-7 Si-8 Si-9 Si-10  -0.09451 -0.09451 0.076395 0.076395 -0.00906 -0.00906 -0.00906 -0.05932 -0.05932 -0.00906 0.041209 0.041209 -0.00906 -0.00906 0.304498 0.281183 0.12328 0.304198 0.119277 0.182819 0.423075 0.071246 0.181418 0.421774  0.309802 0.190198 0.190198 0.309802 0.411124 0.088876 0.320355 0.285178 0.214822 0.179645 0.214822 0.285178 0.394731 0.105269 0.028586 0.062968 0.064068 -0.12924 -0.17341 -0.17251 0.056572 0.027686 0.057371 -0.17221  0.624237 0.624237 0.458196 0.458196 0.541216 0.541216 0.541216 0.590052 0.590052 0.541216 0.492381 0.492381 0.541216 0.541216 -0.20226 0.020226 0.019124 -0.19345 0.021728 -0.32902 -0.34604 -0.19234 -0.34234  Si-11 Si-12  0.274178 0.068444  -0.17241  0.025032 -0.19044  -0.13013  -0.33362  227  6.4.  CONCLUSIONS Solid State N M R experiments can be used to obtain important structural information  about sorbates-molecular sieves complexes. In particular it was demonstrated in this chapter that the CP experiment can provide accurate information that can be used to determine the threedimensional structure of the low loaded p-xylene complex of ZSM-5. The major limitation in the method is the presence of very slow motions which in the present case were eliminated at temperature below 213 K . NOTE: After this work was completed, a single crystal x-ray diffraction investigation of this system has been carried out. The structure obtained agrees with that derived here from N M R data 12  alone, further confirming the validity of the method .  228  6.5.  REFERENCES  1 Fyfe, C.A., Strobl, H.J., DeSchutter, C.T., Kokotailo, G.T., J. Chem. Soc. Chem. Commun., 547, 1984. 2 Fyfe, C.A., Kokotailo, G.T., Lyerla, J.R., Flemming, W.W J. Chem. Soc. Chem. Commun., 740, 1985. 3 Fyfe, C.A., Strobl, H.J., Kokotailo, G.T., Kennedy, G.J., Barlow, G.E., J. Am. Chem. Soc, 110, 3373, 1988. 4 Olson, D.H., Kokotailo, G.T., Lawton, S.L., Meier, W . M . , J. Phys. Chem., 85, 2238, 1987. 5 Fyfe, C.A., Feng, Y . , Grondey, H., Kokotailo, G.T., J. Chem. Soc. Chem. Commun., 1224, 1990. 6 van Koningsveld, H . , Jansen, J . C , van Bekkum, FL, Acta Cryst., B43, 127, (1987). 7. Bloom, M . , Davis, J.M., Valic, M.I., Can. J. Phys., 58, 1510, (1980). 8 Mareci, T.H., Freeman, R., J. Mag. Reson., 48, 158, (1982). 9 Kustanovich, I., Fraenkel, D., Luz, Z., Vega, S., J. Phys. Chem., 92, 4134, (1988). 10 Lefebvre, F.; Mentzen, B . F., Material Research Bull, 29, (10), 1049, (1994). 11 van Koningsveld, FL, Jansen, J . C , van Bekkum, FL, Acta Cryst., B52, 131, (1996). 12 Andrews, L., PhD Thesis,UBC, 1998  229  CHAPTER SEVEN PRELIMINARY STUDIES OF THE STRUCTURE OF THE HIGH LOADED FORM OF P-XYLENE IN ZSM-5 BY DOUBLE RESONANCE W S\ DIPOLAR DEPHASING REDOR EXPERIMENTS  l  7.1.  29  INTRODUCTION If possible, the determination of internuclear distances would be the most direct approach  to structural studies of solids. Solid state N M R spectroscopy can provide this information by measurement of the dipolar coupling between two nuclei. As discussed previously, in a static polycrystalline sample the dipolar coupling between two magnetically dilute nuclei results in the characteristic Pake pattern . This was first observed in the ' H spectrum of gypsum, CaSO^FfcO, 1  where it arises from the interaction between the two protons in the water molecule of hydration. The splitting between the singularities provides a straightforward measurement  of the  homonuclear dipolar coupling, and therefore of the internuclear distance between the two proton spins. Unfortunately, in the more general case, the structural information revealed by internuclear distances cannot be obtained from spectra of static samples due to line-broadening mechanisms such as the overlapping of signals from multiple sites, multiple dipolar interactions, and chemical shift anisotropics that complicate the lineshape seen for an isolated spin pair due to through space dipolar coupling. As a consequence of these problems, various methods have been developed that can measure the dipolar couplings even in the presence of other interactions in static samples,  230  particularly the chemical shift term present in the spin Hamiltonian. These techniques include Separated Local Field (SLF) spectroscopy ' , Spin Echo DOuble Resonance (SEDOR) ' and 2 3  4 5  nutation N M R . 6  These approaches are useful for the determination of distances between spin pairs in static solids, including powders. However, when there are several chemically inequivalent sites, high resolution solid state N M R spectra are required and the application of magic angle spinning (MAS) is essential. M A S efficiently averages out weak heteronuclear and homonuclear dipoledipole couplings, as well as the anisotropic part of the chemical shift, resulting in well resolved spectra of the isotropic chemical shifts. Thus, in order to observe selected dipolar couplings in rotating solids it is necessary to reintroduce them in the experiment by some method that reverses their averaging by M A S . Newer dipolar-dephasing techniques  seek to maintain the heteronucleair dipolar  dephasing while averaging the chemical shift anisotropy with magic angle spinning (MAS). Rotational-Echo DOuble Resonance (REDOR) '  7 8  and Transferred-Echo DOuble Resonance  ( T E D O R ) ' N M R experiments use 180° pulses synchronized with the sample rotation to retain 9  10  the dipolar dephasing. Without the extra pulses, the dipolar couplings are averaged to zero over each rotor period by the sample spinning. The main applications of REDOR techniques have • •  been in the measurement of weak  J  J  C  7  8  11  17  C- N dipolar couplings in proteins' ' ' ' ' 13  experiments have demonstrated that REDOR can be used to measure  I? 1  while other •  2 *  *  C- D distances in organic  systems ' ' ' . Application of both REDOR and TEDOR experiments to inorganic framework 14 15 16 17  materials have been successful in investigating the local environments of 18 19  spin pairs ' .  27  31  A l / P and  27  29 *  A l / Si  231 The scheme of the REDOR pulse sequence is shown in Figure 7.1. Two experiments are carried out: In the first experiment, a 90° pulse is applied to the S nuclei to create transverse magnetization. After an integral number of rotor cycles has passed (t=nx /2, with n even), a 180° r  Tt  TI  %  III nx  n  ii  n  I I II nx  r  r  ACQUIRE  Figure 7.1. Pulse sequence for rotational echo double-resonance (REDOR) N M R . In the first experiment, a conventional spin echo acquired after n rotor cycles provides the reference signal, So, and no pulses are applied on the H channel. In the second experiment, 180 pulses are applied to the I channel twice per rotor cycle, and the modified signal Sf, is recorded. !  0  refocusing pulse is applied to the S spins and a spin echo is formed at time t= nx . The amplitude r  of this spin-echo is designated So, the full signal with no dipolar dephasing. A second experiment is then carried out under exactly the same conditions as the first, but two 180° pulse are applied to the I spins at each one-half and full rotor cycle, resulting in the reversal of the sign of the dipolar coupling term each half rotor period and preventing its averaging to zero. The effect of  232  the coupling is to cause dephasing of the S-spin magnetization in this experiment. A 180° refocusing pulse applied to the S spins replaces the 180° pulse to the I spins in the middle of the dephasing period and refocuses the isotropic S spin chemical shifts at the beginning of the data acquisition, as in the first experiment. The outcome is a signal Sf that differs from the So signal due to dephasing caused by the non-zero averaged dipolar coupling. When the signal Sf is subtracted from the full echo intensity So, the difference signal AS= So - Sf is due solely to spins that have I-S dipolar interactions. In this chapter the potential of H(I)/ Si(S) REDOR experiments to obtain Si-H 1  29  distance and structural information is examined, again using the high loaded complex of pxylene in ZSM-5 (of known structure) as test system. In the present REDOR experiments the dephasing of the silicon magnetization is obtained by the application of ' H 180° pulses. To eliminate any effects due to the slow molecular motions described for this system in Chapter 4, the REDOR experiments were carried out at a temperature of 273 K .  7.1.1  CALCULATION OF R E D O R DEPHASING  7.1.1.1 Isolated Spin System For a static sample, the dipolar transition frequencies of an isolated I-S spin pair (spin A l  nuclei) are given by  20  C0 (6) = ± / D(3cos e-l) 1  D  2  2  (7.1)  where 0 is the angle between the internuclear I-S vector and the magnetic field Bo, and D is the dipolar coupling given by (7.2)  233  where yi and ys are the gyromagnetic ratios for the I and S spins, respectively, po is the magnetic permeability constant in vacuum (po 47tlO" K g m s" A" ), h is Planck's constant divided by 2TX, =  7  2  2  and ris is the internuclear distance between the I and S spins.  Figure 7.2 Diagram showing the relationship between the spinning axis, the external magnetic field Bo, and the I-S heteronuclear dipolar vector. For magic angle spinning, the spinning axis is inclined at an angle 0 = 54.7° with respect to the external field. The heteronuclear dipolar vector forms a polar angle P and an azimuthal angle a with respect to the spinning axis.  234  Under magic angle spinning at a frequency co, the dipolar frequencies become  21  r  u) (a,P,t) = ±'/2D{sin p cos2(a+co t)- V2 sin(2p) cos( a+ cot)} 2  D  r  r  (7.3)  where a is the azimuthal angle and p the polar angle defined by the internuclear vector in a coordinate system with the z axis parallel to the rotor axis (Figure 7.2). For a given spin in the transverse plane, the average dipolar coupling evolution over a time period t is given by Equation 7.4.  co (a,p,0 = — fco (a,p,0<* D  D  T X  +  J  r  (7.4)  0  (sin P[sin2(a + co t) - sin2a| - 2V2 sin2p[sin(a + co t) - sinaj  71  2  r  2T,.co I  T  r  Over one full rotor cycle x , the evolution of the dipolar coupling averages to zero, i.e. r  co (a,p,O = 0. D  A single 180° dephasing pulse on the I-spins at a time, ti, during a rotor cycle changes the average dipolar frequency for that cycle as:  1  co = — 1, D  ti  |co (a,p,/)^- Jco (a,P,?)cfr D  D  (7.5)  where the minus sign is due to the reversal of the sign of the I-S dipolar coupling at ti . In 7  contrast, the homonuclear interaction is not affected by the 180° pulse because of the bilinear property of the spin part of the Hamiltonian, leading to the averaging of the interaction over the spin coordinate. In a normal REDOR experiment, the I-spin 180° pulses are applied at every half rotor cycle (i.e. ti=x /2) and Equation 7.4 simplifies to r  235  co (a,(3,0 = ±4 V2 sin a sin (5 cos p  (7.6)  D  If n is the total number of dephasing rotor cycles, then the phase accumulation of each Ispin is: A O „ = ® (a$, /^)m  = 4V2«Dx sinasinpcosp  Xr  r  D  r  (7.7)  r  This means diminished echo intensity at the end of the rotor cycle during which the I-spin pulse occurred. The diminution is proportional to the length of the rotor period so there is more dephasing at slower spinning rates. The total loss in signal can be measured by the ratio of the difference signal (with and without dephasing) to the full signal ' :  M <*zM  .  =  (7 8)  The expected difference signal, normalized to the full echo intensity at that echo time, is calculated for a powder by averaging over all possible orientations of the internuclear vector (over the surface of a sphere): 2TC T C / 2  AS  I r e  — =1 0  S  j 2 7 l a  }cos(AO )sinpjpcia R n  (7.9)  =0(3=0  where cos(AOR ) represents each spin's contribution to the observed signal. >n  o  Schaefer and co-workers have noted that the initial behaviour of the REDOR curves is a parabola, described by — = W66(nDx )  2  o  r  (7.10)  s  This equation is obtained by expanding the cosine function within the integral (Equation 7.9) in the limit of small dephasing angle, and integrating the first few terms.  236  7.1.1.2 Collection of Isolated I-S Spin Pairs  In the case of a collection of isolated spin-pairs with different internuclear distances, and therefore different dipolar couplings D,, the observed REDOR dephasing is a sum of REDOR „22  curves  2n  0  S  47X  n  cos ^ J I a=OP=0  cosl 471 H  J  7V D C  2  c D l  2V2sin(2p)sin(a) L/asin(p)dp (7.11)  2V2 sin(2P)sin(a) a?asin(P)dp+  J  a=0P=0  Each of the terms in the sum of Equation 7.11 represents the REDOR dephasing for an individual I-S spin pair. The observed dephasing is therefore a sum of the REDOR curves. In this case, the experimentally measured dephasing can be fitted using a structural model to calculate the internuclear distances and the REDOR curves. Mueller has shown that it is possible and easier to simulate these curves using a Bessel function as the REDOR curve . 7.1.1.3 Several S Spins Coupled to an I Spin  If more than one S spin is coupled to the observed I spin, a much more complicated mathematical treatment has to be considered. Several approaches have been recently reported ' , and it has been demonstrated that the geometrical arrangement of the spin-pairs has 12 24  a measurable effect on the calculated curves. Very recently a mathematical treatment for the calculation of the REDOR curves in the case of dephasing by multiple spins has been published  237  by Schaefer and Goetz . In this treatment i f only the I-S heteronuclear dipolar interaction is 22 considered and the total dephasing for a multiple spin system is a product of cosine terms :  2V2sin2/J sina (i)  So  (i)  dad/3  (7-12)  STT  Since the sample is a powder it is necessary to average over all possible orientations of the collections of S spins. The calculations using Equation 7.12 are very complex and time consuming, and the results not unambiguous when it is necessary to consider several interactions. Recently, a semiempirical approach to the problem of calculating REDOR responses in the extreme case of SI , with large n was proposed ' . This approach is based on the assumption 25 26  n  that the heteronuclear dipolar lineshape is completely unresolved and Gaussian. In that case the REDOR response can be fitted with a single parameter only, namely, the Gaussian linewidth, or TO  the square root of the heteronuclear second moment (M2 ).  238  7.2. 7.2.1  EXPERIMENTAL SAMPLE PREPARATION:  Samples with a loading of eight molecules of p-xylene-^ and p-xylene-^ were prepared following the procedure described in Chapter 2, Section 2.2.3.  7.2.2  1  H 7 S i R E D O R EXPERIMENTS 29  The REDOR experiments were carried out at a temperature of 273 K using the experimental arrangement described in Chapter 2, Section 2.4.4. The pulse program used for the REDOR experiments was similar to that illustrated in Figure 7.1 but the initial 90° pulse was replaced by a CP pulse sequence to create the transverse magnetization of the dilute S i nuclei by transferring the magnetization from the abundant ' H 29  spins, thus taking advantage of the favourable relaxation and sensitivity properties of the abundant nuclei. The REDOR experiments were carried out on a Bruker MSL-400 spectrometer operating at 79.495 and 400 M H z for S i and *H, respectively. A 7 mm triple-tuned Bruker probe was l9  used in double-tuned mode for S i and ' H . Typical 90° pulse times were 10.0 us C !!) and 9.5 ps 19  1  (29si). The rotational frequency of the M A S spinner was kept constant to within ± 1 % during each experiment. The spinning speeds in different experiments were between 2.1 and 3.1 kHz and 200 scans were accumulated for each experiment with a recycle delay of 7 s. During the Sf spin echo experiment the *H 180° dephasing pulses were applied on resonance. During the So spin echo experiment, in which there should be no dephasing of the Si nuclei, the ' H 180° dephasing pulses were applied 10 M H z off resonance. It was necessary to apply these pulses off resonance instead of simply not applying them to preserve the timing of  239  the experiment exactly. The resonance frequency was switched between the S and S 0  experiments using a frequency offset list.  f  240  7.3.  R E S U L T S A N D DISCUSSION ' H / S i REDOR spectra were obtained as a function of the number of rotor cycles for the 29  samples of ZSM-5 loaded with 8 molecules per u.c. of p-xylene de and d . The spectra were 4  deconvoluted in terms of Lorentzian functions and the intensities of the reasonably well resolved resonances due to silicons 1, 3, 10, 12, 16, and 17 determined as previously. The AS values for each of the six well resolved silicon signals were obtained by subtracting the appropriate deconvoluted areas of the So and Sf spectra. The different REDOR S i N M R spectra of ZSM-5 loaded with 8 molecules per u.c. of 2 9  p-xylene d are shown in Figure 7.3. As expected, the signal intensities are reduced in the Sf 4  spectrum at 273 K after 10 rotor cycles, because of the reintroduced Si-H dipolar interactions. This is easier to see in the difference spectrum AS which shows only signals due to dipolar dephased S i nuclei. Normalization of AS, as the ratio, AS/So, eliminates the decrease in signal 29  intensity due to transversal relaxation (T2) during the experiment. Because the initial So signal is generated from a CP experiment, the relative signal intensities in it are already discriminated by the H / S i dipolar couplings, but this is also compensated by the normalization of AS as the 1  29  ratio, AS/SoThe REDOR data for the complexes of Z S M loaded with 8 molecules per u.c. of p-xylene de and p-xylene d are shown in Figure 7.4 a and b, respectively. The data points are interpolated 4  as a visual guide only and do not indicate curve fitting. Qualitatively, these data show the same trend found in the CP experiments, i.e. for the complex of p-xylene de, the signals which dephase faster are Si 12, Si 3 and Si 17, indicating that these silicons are closer to the aromatic protons than Si 1, Si 10, and Si 16. On the other hand, for the complex of p-xylene d , Si 1 and Si 10, are 4  241  closer to the methyl groups than Si 12, Si 3, Si 17 and Si 16, and in the REDOR experiment they show the fastest dephasing. The experimental data points together with the calculated REDOR curves for the complex of ZSM-5 with 8 molecules per u.c of p-xylene d$ are shown in Figure 7.5. The theoretical REDOR curves were calculated using Equation 7.9 for only one Si-H dipolar interaction corresponding to the closest Si-H distance as indicated in the figure. From the detailed study of these plots is possible to draw the following conclusions: 1. The initial portion of the experimental data are reasonably well reproduced by the theoretical REDOR curve calculated for only the closest Si-H interaction. 2. The experimental data do not show the characteristic oscillations expected for an isolated spin system. This is as expected, as there are Si-H dipolar interactions from several aromatic protons. The accumulated dephasing from the weaker dipolar interactions becomes important at longer dephasing times. Because of the observation that at small number of rotor cycles, the dephasing ratio AS/So is dominated by the strong dipolar couplings it is possible that the application of Equation 7.10 (valid only at short dephasing times) might provide some information about the shortest Si-H distances in the complex. The data from two REDOR experiments carried out at different spinning speeds (2326 and 2857 Hz) for 2 and 4 rotor cycles for the complex of ZSM-5 with 8 molecules per u.c. of pxylene df, are shown in Table 7.1. The dipolar couplings and the Si-H interatomic distances calculated from them using Equation 7.9 are also listed, together with the closest Si-H distances from the published X R D structure , (the second closest distance are also shown in parentheses). 27  -109  -111  -113  -115  -117  -119  -121  Figure 7.3: The 79.48 M H z CP REDOR S i N M R spectra of ZSM-5 loaded with 8 molecules of p-xylene-cfc per u.c. at 273 K , 200 scans were accumulated for each experiment with a recycle delay of 7 s. The experiments were carried out with 10 rotor cycles at a spinning speed of 2890 Hz. (a) Full echo spectrum, So. (b) Rotational-echo Si N M R spectrum Sf. (c) Difference spectrum (AS) between the full echo spectrum So and the rotational-echo spectrum, Sf. 2 y  243  Figure 7.4: Evolution ofthe REDOR Si('H) signals for the S i peaks in ZSM-5 loaded with 8 molecules of (a) p-xylene-<3?6 per u.c. at 273 K , with v = 2.1 kHz, (b) p-xylene-<^ per u.c. at 273 K , with v = 2.08 kHz. The data points are joined for clarity only. 29  2 9  r  r  244  Si 1, 1 interaction (3.96 A)  !  4  6  Si 10, 1 interaction (4.32 A)  8  10  i  12  D ephasing time (m s)  Si 3, 1 interaction (3.13 A)  l  i  i  4  £  0  10  12  D ephasing time (m s)  Si 17, 1 interaction (3.572 A)  9  10  12  2  D ephasing time (m s)  1  t  9  10  12  D ephasing time (m s)  Figure 7.5: Evolution of the REDOR S i ( H ) AS/S ratios for the sample of ZSM-5 loaded with 8 molecules p-xylene-dg per u.c. at 273 K , with v = 2.890 kHz. The solid lines represent the calculated REDOR curves using Equation 7.9 for only one dipolar coupling corresponding to the closest Si-H distance determined from X R D in each case, as indicated in the plots. 29  !  0  r  245  From the table it can be seen that the closest Si-H distances calculated in this way are in good agreement with those known from the X R D structure, with relative deviations from 1 to 12 %. There are also variations in the calculated distances between experiments carried out at the same spinning speeds, but with different number of rotor cycles, and also between experiments at different spinning speed. These variations could be due to the large errors in the determination of very small AS intensities, and also in the validity of the application of Equation 7.9 to data taken at longer dephasing times. A similar approach was used for the REDOR data measured for the complex of ZSM-5 with 8 molecules per u.c. of p-xylene d (Table 7.2). The calculated REDOR curves for this 4  complex together with the experimental data points are shown in Figure 7.6. These curves were again calculated using Equation 7.9 for only one isolated pair interaction corresponding to the closest Si-H distance as indicated. Again, the initial rise of the curves is dominated by the strongest dipolar coupling, and the theoretical REDOR curve for only one isolated spin-pair interaction fits the initial experimental data points for small dephasing angle, using the closest Si-H distance. However for Si 3 and Si 12, there is an appreciable deviations from this behavior. Perhaps this is because for these silicons atoms there are not close Si-H interactions, but a group of spins at longer Si-H distances. Therefore there is not one dominant interaction, and consequently the approximation of the isolated spin-pair treatment fails. Again, the application of Equation 7.10 (valid only for short dephasing angles) provides some information about shortest Si-H distances involving the methyl groups. In Table 7.2 the data for the REDOR experiments carried out with 2, 4 and 6 rotor cycles for the complex of ZSM-5 with 8 molecules per u.c. of p-xylene d are shown. The dipolar couplings, and the Si-H 4  interatomic distances calculated from these data using Equation 7.10 are also listed together with  246  the three closest Si-H distances determined from the published X R D structure. Inspections of this table indicates some agreement between the Si-H distances calculated from the REDOR data with those determined from the X R D structure. The deviations are larger than for the aromatic hydrogen case (in this case the deviations are between 8 to 20 %). There are also variations between calculated REDOR Si-H distances between experiments carried out at different number of rotor cycles. These variations could be again due to the large errors in the determination of very small AS intensities, and also to the validity of the application of Equation 7.9 to data obtained at longer dephasing times. In the analysis of the REDOR data for the complex of ZSM-5 with 8 molecules per u.c. of p-xylene d.4, the rotation of the C H 3 about the C 3 axis was not considered. Some authors have applied an 8-10 % reduction of the dipolar interaction measured in REDOR by motional modulation ' ' . In this case there will be a reduction of the Si-H dipolar couplings due to the 28 29 30  fast rotation of the methyl groups, which is not considered when using Equation 7.10. The proton homonuclear interaction was neglected in the present study because the M A S averages it to zero. This assumption is approximately true, but it is quite possible that there is some residual homonuclear interaction not averaged out at the rotation speed used in this work (2.1 kHz). This interaction is another possible source of error that is not taken into account in the REDOR simulations. In spite of the use of partially deuterated p-xylene molecules, the complexes of 8 molecules of p-xylene-^ and p-xylene-^ in ZSM-5 are not isolated spin systems, and each silicon nucleus has between 3 to 5 hydrogen nuclei surrounding at distances less than 6 A. Thus for an exact quantitative analysis of the REDOR data of these complexes, a multiple spins system will have to be considered.  247  Si 10, 1 interaction (3.596 A)  Si 1, 1 interaction (3.566 A)  I  o.$  0.4 0.2  2  4  £  6  $  1  l •  o.s.  0.8 •  °  6  Si 3, 1 interaction (4.101 A)  Si 12, 1 interaction (4.494 A)  S  4  D ephasing time (ms)  D ephasing time (ms)  -2.  f 0.6f  S  T 0.6 0.4  0.4  0.2  0.2  2  4  £  6  D ephasing time (ms)  4  6  D ephasing time (ms)  Figure 7.6: Evolution ofthe REDOR Si('H) AS/S ratios for the sample of ZSM-5 loaded with 8 molecules p-xylene-^ per u.c. at 273 K , with v = 2.8 kHz. The solid lines represent the calculated REDOR curves using Equation 7.9 for only one dipolar coupling corresponding to the closest Si-H distance determined from X R D as indicated in the plots. 29  0  r  248  As was discussed in the introduction, Section 7.1.1.3, very recently Schaefer and Goetz published a mathematical approach to treat the case of many I-spins dipolar coupled to an S-spin. Figure 7.7 shows the theoretical curves from considering the interactions of each Si with the 99  three closest hydrogen atoms using the mathematical approach proposed by Schaefer . As can be seen the fits still do not represent the data at longer dephasing times, consistently larger than the observed effect. In this approach the homonuclear interaction was again neglected. This may be an important interaction for the systems studied here, as the protons are close and dipolar interaction relatively large. Work in this area is currently in progress , which may make a more quantitative analysis of these data possible. It is also possible that the experimental data are lower than they should be because of some unoccupied sites (-10 %) and inefficiencies in the experiment in terms of rf inhomogeneity, finite pulse length, etc. These should all be investigated in further work.  249  Table 7.1: Calculated dipolar coupling and Si-H distance from the experimental REDOR data for the complex of ZSM-5 with 8 molecules per u.c. of p-xylene d$ at 273 K  2 4 2 4  0.00043 0.00043 0.00035 0.00035  0.1428 0.2571 0.0248 0.1894  2 4 2 4  0.00043 0.00043 0.00035 0.00035  0.0925 0.3276 0.0637 0.2351  340.00 320.00 353.26 339.27  4.13 4.21 4.07 4.13  4.14  2 4 2 4  0.00043 0.00043 0.00035 0.00035  0.3510 0.6703 0.2426 0.5913  662.44 457.73 689.35 538.09  3.30 3.74 3.26 3.54  3.46  2 4 2 4  0.00043 0.00043 0.00035 0.00035  0.1837 0.4585 0.1260 0.3989  479.22 378.56 496.83 441.96  3.68 3.98 3.64 3.78  3.77  2 4 2 4  0.00043 0.00043 0.00035 0.00035  0.1083 0.2854 0.0176 0.2597  368.01 298.66 185.76 356.63  4.02 4.31 5.05 4.06  4.36  2 4 2 4  0.00043 0.00043 0.00035 0.00035  0.3142 0.5868 0.2634222 0.5529  626.75 428.30 718.32 520.34  3.37 3.82 3.22 3.58  3.50  (b)  Si T-site  n  ' 10  1  12  17  16  3  (a)  (b)  average r< s, (A) from REDOR  Dredor (Hz) calculated from REDOR 422.60 283.50 220.41 304.57  X (a)  r  (Hz)  S -S ^ c 0  f  exp  r V (A) calculated from REDOR 3.84 4.38 4.77 4.28 (  H  d)  H  r  ( e ) S i  -H  (A) from XRD 4.32  4.32  (5.41) 3.96 (5.17) 3.21 (3.39) 3.61 (3.57) -  4.34 (4.76) 3.13 . (3-62)  Number of rotor cycles Dipolar coupling constant calculated from (So-Sf)/So using Equation 7.9  Calculated Si-H distances from the dipolar coupling constant determined from the REDOR data.  (c)  Averaged Si-C distances from the Si-C distances determined from the REDOR data at different dephasing times.  (d)  (e)  Shortest Si-H distances calculated from the X R D data from reference 27.  250  Table 7. 2: Calculated dipolar coupling and Si-H distance from the experimental REDOR data for the complex of ZSM-5 with 8 molecules per u.c. of p-xylene d 4  Dredor (Hz) ^ 0 Kxp calculated from REDOR 0.3507 600.00 0.6115 396.12 0.7377 290.05 417.52 0.1698 0.3252 288.85 0.4426 224.66 0.2667 523.24 0.5348 370.46 0.6149 264.83 0.2439 500.36 0.4337 333.59 0.5564 251.91 0.2571 513.71 0.4705 347.47 0.6172 265.30 0.2001 453.15 0.3729 309.34 0.5427252 248.79 (b)  Si T-site  10  1  12  17  16  3  w  (b)  n  (a)  2 4 6 2 4 6 2 4 6 2 4 6 2 4 6 2 4 6  (Hz)  0.00048 0.00048 0.00048 0.00048 0.00048 0.00048 0.00048 0.00048 0.00048 0.00048 0.00048 0.00048 0.00048 0.00048 0.00048 0.00048 0.00048 0.00048  S  r s, (c)  H  (A)  calculated from REDOR 3.41 3.92 4.35 3.85 4.36 4.74 3.57 4.01 4.48 3.63 4.15 4.56 3.60 4.10 4.48 3.75 4.26 4.58  average r si. (d)  H  r s,H (e)  (A)  (A)  from REDOR  from XRD  3.89  3.60 (3.80)  4.32  3.57 (3.59)  4.96  4.49 (4.99)  4.12  3.78 (4.09)  4.33  3.51 (4.46)  4.43  4.10 (4.41)  Number of rotor cycles Dipolar coupling constant calculated from (So-Sf)/So using Equation 7.9  Calculated Si-H distances from the dipolar coupling constant determined from the REDOR data. (c)  Averaged Si-C distances from the Si-C distances determined from the REDOR data at different dephasing times.  (d)  (e)  Shortest Si-H distances calculated from the X R D data from reference 27.  251  Si 12, 3 interactions 3.20 A, 3.39 A, 3.92 A  Si 10, 3 interactions 4.32 A, 5.41 A, 5.78 A  1 0.8 ^0  0.6  0.4 0.2  1  4  6  8  10  2  Dephasing time (ms) Si 3, 3 interactions 3.13 A, 3.62 A, 4.63 A  1  4  6  2  4  6  8  10  Dephasing time (ms) Si 1, 3 interactions 3.96 A, 5.17 A, 5.35 A  2  10  Dephasing time (ms)  4  6  8  10  Dephasing time (ms)  Si 16, 3 interactions 4.34 A, 4.76 A, 5.32  Si 17, 3 interactions 3.61 A, 3.57 A, 5.04  0.6  1  4  6  S  2  10  Dephasing time (ms)  4  6  8  1.0  Dephasing time (ms)  Figure 7.7: Evolution ofthe REDOR Si('H) AS/S ratios for the sample of ZSM-5 loaded with 8 molecules p-xylene-6?<5 per u.c. at 273 K , with v = 2.8 kHz. The solid lines represent the calculated REDOR curves using Equation 7.12 for three dipolar couplings corresponding to the closest Si-H distances determined from X R D as indicated in the plots. 29  0  r  252  7.4.  CONCLUSIONS  The REDOR experiment which re-introduces the dipolar coupling averaged out by M A S while maintaining the high resolution needed for a spectrum with multiple sites can provide important structural information of the complex of zeolites with guest molecules as illustrated by the application of Equations 7.9 and 7.10 to the experimental data for the complexes of ZSM-5 with 8 molecules per u.c. of p-xylene 0*4 and df,. This treatment corresponds to the case of an isolated spin pair for the strongest Si-H interaction, which is clearly not the case in these samples. However it was shown that the dephasing of the REDOR signals at short times is dominated by the strongest interactions and some valuable Si-H interatomic distances can be determined using Equation 7.9. This information is valuable because it could perhaps be used to propose a structural model of the complexes that can be used in combination of other N M R techniques (e.g. cross-polarization) to reduce the number of possible structures. However, it has to be kept in mind that these distance estimates are only semi-quantitative. When a more complicated mathematical analysis of the data using multiple spin interactions was done for the sample with only aromatic hydrogens, a better fit for the experimental data points was not obtained suggesting, perhaps, that the homonuclear interaction is not completely averaged out by M A S for the present system at the experiment spinning speeds used. It is also possible that inefficiencies in the REDOR pulses lead to a less efficient experiment causing the experimental data points to be lower than they should be. In any case, an important conclusion from these experiments is that the interpretation of the REDOR experiments on these system must involve postulating a structure just as do the corresponding CP experiments.  253  7.5.  REFERENCES  1 Pake, G.E., J. Chem. Phys., 16, 317, 1948. 2 Stall, M.E., Vega, A.J., Vaughan, R.W., J. Chem. Phys, 65, 4093, 1976. 3 Munowitz, M.G., Huang, T.H., Dobson, C M . , Griffin, R.G., J. Mag. Reson., 57, 56, 1984. 4 Kaplan, D.E., Hahn, E.L., J. Phys. Radium., 19, 821, 1956. 5 Slichter, C P . , Principles of Magnetic Resonance, Springer-Verlag, New York., 1990. 6 Yannoni, C.S., Kenderick, R.D., J. Chem. Phys., 74, 747, 1981. 7 Gullion, T.; Schaefer, J., J. Mag. Reson., 81, 196, 1989 8 Pan, Y.; Gullion, T.; Schaefer, J., J. Mag. Reson., 90, 330, 1990. 9 Hing, A.W.; Vega, S.; Schaefer, J. J. Mag. Reson., 96, 205, 1992. 10 Hing, A.W., Vega, S., Schaefer, J., J. Mag. Reson. Series A, 103, 151, 1993. 11 Gullion, T.; Schaefer, J., Advan. Mag. Reson., W.S. Warren, Ed., vol 13, pg 57, 1989. 12 McDowell, L . M . , Klug, C.A., Beusen, D.D., Schaefer, J., Biochemistry., 35, 5395, 1996. 13 Naito, A , Nishimura, S., Kimura, S., Tuzi, S., Aida, M . , Yasuoka, N . , Saito, H . , J. Phys. Chem., 100, 14995,1996 14 Schmidt, A., McKay, R.A., Schaefer, J. J. Mag. Reson., 96, 644, 1992. 15 Schmidt, A., Kowalewski,T., Schaefer, J. Macromolecules., 26, 1729, 1993 16 Lani Lee, P.,Xiao, C , Wu, J., Yee, A., Schaefer, J. Macromolecules., 28, 6477, 1995. 17 Lani Lee, P., Schaefer, J. Macromolecules., 28, 2577, 1995. 18 Fyfe, C.A., Mueller, K.T., Grondey, H . , Wong-Moon, K . C , Chem. Phys. Lett., 199, 198, 1992.  254  19 Fyfe, C.A., Mueller, K.T., Grondey, FL, Wong-Moon, K.C., J. Phys. Chem., 91, 13484, 1993. 20vanVleck, J.H., Phys. Rev., 74,168, 1948. 21 Lowe, I.J., Phys. Rev. Lett, 2, 285, 1959. 22 Goetz, J.M., Schaefer, J., J. Magn. Reson., 127, (2), 147, 1997. 23 Mueller, K.,T., J. Magn. Reson. Series A, 113, 81, 1995. 24 Naito, A , Nishimura, S., Tuzi, S., Saito, FL, Chem. Phys. Lett., 229, 506, 1994. 25 Blumenfeld, A . L . ; Coster, D.J.; Fripiat, J.J., J. Phys. Chem., 99, 15184, 1995. 26 Blumenfeld, A . L . ; Fripiat, J.J., Topics in Catalysis, 4, 119, 1997. 27 van Koningsveld, FL, Jansen, J . C , van Bekkum, FL, Acta Cryst., B43, 127, 1987. 28 Marshall, G.R, Beusen, D.D., Kociolek, K., Redlinski, A.S., Leplawy, M.T., Pan, Y . , Schaefer, J., J. Am. Chem. Soc, 113, 963, 1990. 29 Holl, S.M., Marshall, G.R, Beusen, D.D., Kociolek, K., Redlinski, A.S., Leplawy, M.T., McKay, R.A., Vega, S., Schaefer, J., J. Am. Chem. Soc Cryst., 113, 4830, 1992 30 Garbow, J.R., McWherter, C.A., J. Am. Chem. Soc. , 115, 238, 1993. 31 Fyfe, C.A., Lewis, A.R., Chezeau, J.M., Grondey, FL, J. Am. Chem. Soc, in press.  255  CHAPTER EIGHT PRELIMINARY STUDIES OF THE STRUCTURE OF THE HIGH LOADED FORM OF P-XYLENE IN ZSM-5 BY TRIPLE RESONANCE W C/ Si  l  8.1.  u  29  DIPOLAR DEPHASING EXPERIMENTS  INTRODUCTION In the previous chapter the solid state REDOR experiment was applied to the system  of ZSM-5 loaded with 8 molecules of p-xylene. In this system the guest molecules were specifically deuterated in the aromatic or methyl positions in order to have some spin isolation to obtain preliminary information about the Si-H distances. However, it was found that the studied system was still too complicated because of the multiple dipolar interactions from different *H spins on the p-xylene molecules and perhaps also because of incomplete averaging of the ' H - ' H homonuclear interactions. In this chapter the application of REDOR experiments is further investigated using the system of ZSM-5 loaded with 8 molecules of p-xylene. In this case the sorbed molecules are specifically labelled with C in one methyl group to allow the measurement 1 3  of S i - C interactions. The REDOR experiment applied to this system is essentially the 29  13  same as that described in Chapter 7 with the difference that three radiofrequency channels i^  i  are used ' ' . The dephasing of the silicon magnetization is now obtained through the application of two C 180° pulses per rotor cycle (Figure 8.1). ' H decoupling suppress all 1 3  !  H - C and H - S i interactions. Protons are the source of polarization in REDOR, but 1 3  1  29  otherwise are not an important part of the experiment. The theoretical background of the  256  REDOR experiment described in Section 6.1.1.1 can be applied to calculate the REDOR dephasing of the  Si signals by the dipolar interactions with the  C nuclei.  The application of TEDOR (Transferred-Echo DOuble Resonance) to the system of 1^  90  ZSM-5 loaded with 8 molecules of p-xylene [ C, CH3] to obtain information about  Si -  C distances was also investigated in the present chapter. The TEDOR experiment was originally introduced as an alternative to R E D O R to measure weak I-S dipolar couplings of heteronuclear I-S pairs of spin 1/2 nuclei while eliminating unwanted background signals from uncoupled I and S spins . 4,5  The basic pulse sequence for the TEDOR experiment introduced by Schaefer and co-workers is shown in Figure 8.2. In the first step of the experiment, dephasing 180° 5  pulses are introduced to prevent M A S refocusing of the I-S dipolar interaction. The 180° dephasing pulses on the S channel are still one half rotor cycle apart but they occur at onequarter and three-quarter of each cycle. Once an effective I-S dipolar coupling has been created by the 180° dephasing pulses, a transfer of coherence is performed (achieved by simultaneous 90° pulses in both I and S channels) to select S spins dipolar-coupled to I spins in a sample that also contains uncoupled S spins. A n observable signal arising from the selected S spin is then created and modulated by REDOR-type, 180° dephasing pulses. This allows the I-S dipolar coupling of the heteronuclear I-S pair to be measured from the modulation pattern of the S-spin signal. Such an experiment is not complicated by the presence of signals from uncoupled S spins because the selection procedure obtained by the coherence transfer step allows observable magnetization to be generated only by S spins that are dipolar-coupled to I spins. After the S spins dipolar-coupled to the I spins have been selected by coherence transfer, the subsequent evolution of the magnetization is governed  257  by the average dipolar interaction created by the I-spin 180° dephasing pulses. A n observable S-spin signal forms which is modulated according to the strength of the heteronuclear dipolar coupling. The I-S dipolar coupling of the heteronuclear I-S pair can be measured from the modulation pattern of the selected signal. This last step corresponds 23  essentially to a REDOR experiment' . Thus, the TEDOR experiment involves two periods of dipolar dephasing; one period before the transfer of coherence, and another period after the coherence transfer where the antiphase magnetization is allowed to evolve back into observable signal. The expected signal for the TEDOR experiment can be calculated in an analogous manner to the REDOR experiment. The dipolar dephasing in the first part of the TEDOR experiment evolves over n rotor periods as: cosasinPcosP with similar dephasing ( A O  T  m  (8.1)  ) during the m rotor periods of evolution after the  coherence transfer. From a comparison of Equations (8.1) and (7.7) for the REDOR phase dephasing, it can be seen that the TEDOR dephasing now contains a coscc rather than the sina dependence of the REDOR signal due to the movement of the 180° pulses by one quarter of a rotor cycle. The complete TEDOR signal after n periods of preparative dephasing and m periods of evolution after the transfer for pulse placement at one quarter and three-quarters of a rotor cycle is ' : 3 4  271  S =— r  Z 1 1  f 0  7t/2  fsin(AO )sin(AO r/?  0  r/M  )sinpfi?p^a  (8.2)  258  This pulse sequence was optimized by adding a simultaneous refocusing 180° pulses on both I and S channels at exactly half of the evolution period after the transfer of coherence to produce an echo. In this way, all the signals in the spectrum are in phase because the chemical shift anisotropy and magnetic field inhomogeneity are refocused at the end of the evolution. Since the TEDOR experiment evolves a coherence transfer step, it can be extended into a two dimensional heteronuclear correlation (HETCOR) experiment. The twodimensional TEDOR experiment involves an extra period of encoding of the I spin magnetization (Figure 8.3). The experiment is performed by preparing the I spins with a 90° pulse, and then encoding their evolution frequencies in an initial (ti) time period. At the end of ti, a second 90° pulse is used to remove one orthogonal component of the magnetization by returning it to the z-axis, effectively selecting only one component for the rest of the experiment and making possible the use of TPPI ' . A TEDOR experiment is then performed on the magnetization that remains in the xy-plane. The S signal is acquired for each of a set of ti values, and the data array is subjected to a two-dimensional Fourier transformation, which produces a two-dimensional correlation spectrum of the dipolar connected spins in the sample. In this thesis, a two-dimensional TEDOR experiment was carried out for the sample of ZSM-5 loaded with 8 molecules of p-xylene [ C, CH ] to assign unequivocally the four 13  3  13  signals of the  C N M R spectrum to the crystallographically unequivocal methyl groups of  the p-xylene molecules in the straight and zig-zag channels, with cross-polarization from the protons to the carbon nuclei, and dephasing 180° pulses applied on the before the coherence transfer and on the C channel after the transfer. 1 3  Si channel  259  TC/2  H  SL  DECOUPLE  I IIII I It  ( C) 13  / «,  7T  7t  It  It  nT 2  7t  r  .  2  i.  V  |I r  7  PSi) S . c P *r  4  4  :  nT  *\ ACQUIRE  '  r  Figure 8.1. Pulse sequence for rotational echo double-resonance (REDOR) Si( C) N M R . In the first experiment, a conventional spin echo acquired after n rotor cycles provides the reference signal, So, and no pulses are applied on the C (I) channel. In the second experiment, 180 pulses are applied to the C (I) channel twice per rotor cycle, and the modified signal Sf, is recorded. Cross polarization from protons to silicons is used to take advantage of the favorable magnetization of the proton nuclei and faster relaxation. 1 3  0  1 3  260  8.2.  EXPERIMENTAL  8.2.1  SAMPLE PREPARATION 13  Samples with a loading of eight molecules per u.c. of p-xylene [ C, CH3] (99.5 at. %), were prepared following the procedure previously outlined in Chapter 2, Section 2.2.3. A n isotopically diluted sample was prepared by measuring exact amounts of unlabeled pxylene and p-xylene [ C, CH3] (99.5 at. %) to obtain a sample with 4 molecules of 13  unlabeled p-xylene and 4 molecules of p-xylene [ C, CH3] (99.5 at. %), equivalent to 13  having a sample with 25.7 % of its methyl carbon abundance). 8.2.2 W C/ Si l  u  29  CP-REDOR  1 3  C labelled (including natural  EXPERIMENTS  The REDOR experiments were carried out at a temperature of 273 K using the pulse 13  sequence illustrated in Figure 8.1, with the dephasing 180° pulses applied on the  C  channel. A l l N M R experiments were carried out with a Bruker M S L 400 spectrometer 1  29  modified to include a third channel. A 7-mm triple tune Bruker probe operating for H / Si / C was used. The resonance frequencies were 79.495 M H z for S i , 400.13 M H z for ' H l 3  and 100.608 M H z for  29  C . Typical 90° pulses were 9.5 ps for U, 7.8 ps for S i (FI  1 3  l  29  1  channel) and 11.5 ps for  C (F3 channel). The initial silicon magnetization (90° pulse) was  obtained using a CP pulse sequence with a contact time of 10 ms. The rotational frequency of the M A S spinner was kept constant with a variation of ± 1 % during each experiment. The spinning speed in different experiments ranged from 2.5 to 3.1 kHz. 336 scans were accumulated for each experiment for the undiluted sample and 664 for the diluted sample, with a recycle delay of 6 s.  261  During the Sf spin echo experiment the C 180° dephasing pulses were applied on resonance. During the So spin echo experiment, in which there should be no dephasing of the Si nuclei, the  1 3  C 180° dephasing pulses were applied 10 M H z off resonance. It was  necessary to apply these off resonance pulses (instead of simply no apply them) to keep an accurate timing during the experiment. The resonance frequency was switched between the So and Sf spin echoes using a frequency offset list.  8.2.3  'H/ C/ Si CP-TEDOR EXPERIMENTS 13  29  The TEDOR experiments were carried out at a temperature of 273 K using the pulse sequence illustrated in Figure 8.2, varying the number of cycles after the magnetization transfer. A fixed number of rotor cycles (n=22) before the coherence transfer was used. The sample was kept to a constant spinning speed of 2668 ± 1 %, and 544 scans were accumulated for each experiment with a repletion delay of 6 s. Typical 90° pulses were 9.5 ps for *H, 7.8 ps for S i (FI channel) and 11.5 ps for 2 9  1 3  C (F3 channel). The transfer of  magnetization from the protons to the carbon nuclei was done using a CP pulse sequence with a contact time of 3 ms. 8.2.4  L  U /  U  C /  2  9  S I  TWO-DIMENSIONAL HETERONUCLEAR CORRELATION CP-TEDOR  EXPERIMENTS The TEDOR experiments were carried out at a temperature of 273 K using the pulse sequence illustrated in Figure 8.3 with TPPI. The number of cycles before the transfer of coherence was n=22, and after the transfer was m=22. These numbers were the optimal values (determined in the previous one-dimensional CP-TEDOR experiments, Section 8.2.3) to get maximum signal intensity in the spectra. The sample was kept to a constant  262  spinning speed of 2600 ± 1 %, and 1200 scans were accumulated for each experiment with a repetition delay of 6 s. Typical 90° pulses were 9.5 ps for ' H , 7.8 ps for S i ( F l channel) 2 9  and 11.5 ps for  l 3  C (F3 channel). The transfer of magnetization from the protons to the  carbon nuclei was done with a CP pulse sequence using a contact time of 3 ms.  Jt/2  •H  SL  DECOUPLE  1 Mill 7t/2  71  ( C) 13  /  CP  Tt  -M-  Jt  7T  -mx  Jt  7T  r  Coherence Transfer  HIM n  PS)  s  TI  T,  7t  TI  I I  Tt  nil  •  ACQUIRE  Figure 8.2. Pulse sequence for transferred echo double-resonance (TEDOR) S i ( C ) N M R , in which 180° pulses are applied for n rotor cycles to the C (I) spins, shown here at T/4 and 3x/4 in each rotor cycle. Simultaneous 90° pulses then transfer the spin coherence from the I spins to the S spins, and further evolution for m rotor cycles under dipolar dephasing produces observable ST magnetization. Cross polarization from protons to carbon is used to take advantage of the favourable magnetization and relaxation behaviour of the proton nuclei. 29  1 3  13  263  TC/2  it/2  CP  7t  n  t  t  n  V  - nTr  mi r  M  Coherence Transfer Jl  (2Si)  1t  5t  B  II  1t/2  11  S T.  tH  ACQUIRE  Figure 8.3. Pulse sequence for the two-dimensional heteronuclear correlation TEDOR experiment with preliminary evolution of I spin magnetization during the ti time period, and detection of S spin magnetization during the t time period. Cross polarization from protons to carbons is to take advantage of the favorable magnetization and relaxation properties of the proton nuclei. 2  264  8.3.  8.3.1  R E S U L T S A N D DISCUSSION  REDOR 13  EXPERIMENTS  H / C / S i REDOR spectra were obtained as a function of the number of rotor 13  29  cycles for the samples of ZSM-5 loaded with 8 molecules of p-xylene [ C, CH3] (99.5 at. %) per u.c. and the for the isotopically diluted sample with 4 molecules of unlabeled pxylene and 4 molecules of p-xylene [ C, CH3] (99.5 at. %). The spectra were deconvoluted 13  in terms of Lorentzian functions and the intensities of the reasonably well resolved resonances due to silicons 1, 3, 10, 12, 16, and 17 determined. The AS values for each of the six well resolved silicon signals were obtained by subtracting the corresponding deconvoluted areas of the So and Sf spectra. The different REDOR S i N M R spectra of ZSM-5 loaded with 8 molecules per u.c. 2 9  of p-xylene xylene [ C, CH3] at 273 K are shown in Figure 8.4. As expected, the signal 13  intensities are reduced in the Sf spectrum after 96 rotor cycles (Figure 8.4b), because ofthe reintroduced  Si- C dipolar interactions. This is easier to see in the difference spectrum,  AS, which shows only signals due to dipolar dephased  2 9  S i nuclei (Figure 8.4c).  Normalization of AS, as the ratio, AS/So, eliminates the decrease in signal intensity due to transversal relaxation (T2) during the experiment. Table 8.1 lists some important relaxation parameters for the C and S i nuclei in 1 3  2 9  the complexes of 8 molecules of p-xylene in ZSM-5, determined to best design and interpret the experiments. The shortest Si-C distances for this complex calculated from the X R D structure in a range of up to 7 A for Si 1, Si 3, Si 10, Si 12, Si 16, and Si 17, are listed in Table 8.2 The  265  numbering of the atoms in X Y L 1 and X Y L 2 is the same as used in the x-ray structure of this complex published by van Koningsveld . . The identification of the methyl carbons is 9  according to:  XYL1  XYL2  As can be seen from the table, there are at least three nearby methyl carbons dipolar coupled to each Si atom. Therefore, the analysis of the REDOR data for this system is still complicated, because (in spite of the sorbed molecules being labeled in only one methyl carbon) the complex of 8 molecules of p-xylene per u.c. does not provide the "ideal" " Si9  13  C isolated spin systems. The Si-C distances were calculated from the X R D structure in the following way: a complete unit cell was built from the reported X R D fractional coordinates of the complex of ZSM-5 loaded with 8 molecules per u.c. using the proper symmetry operators for a 8  space group P2i2]2]. To make sure of determining all the possible Si-C distances, 26 other unit cells were built around the central unit cell under consideration. The Si-C distances were calculated from the silicon atoms of one asymmetric unit in the central unit cell with respect to all the 8 p-xylene molecules in the central unit cell and the 26x8=208 p-xylenes in the other 26 unit cells. Only those Si-C distances equal to or less than 7A were output.  266  In Table 8.2, the unit cell and the asymmetric unit for each different p-xylene methyl carbons of the zeolite complex are also indicated. This information is important to determine which carbons interacting with a given silicon atom of the zeolite framework are from the same p-xylene molecule. If they are from the same molecule they both must be in the same unit cell and asymmetric unit as is, for example, the case for Si 12. 1  29  Table 8.1: Selected relaxation parameters for the H and 8 molecules per u.c. of p-xylene in ZSM-5 at 273 K . ca. 5Ti (s) T2 Nuclei (ms)  'H  Si nuclei in the complex of  Ti pH (ms)  6.0  0.0422  very long  C (CH )  35-50  21-15  -  Si (framework)  350.0  6.0 - 60.0  -  13  3  As can be seen from Table 8.2, there are up to 4 Si-C dipolar interactions within 7 A that should be considered in an exact and accurate REDOR analysis. As a first approximation in the analysis of the data, the REDOR curves considering only the closest Si-C interaction were calculated. In this case, as only one methyl carbon is labelled C l3  (99.5 at %), the probability of a given methyl carbon being C labelled is: 13  p = 0.5(0.995) = 0.4975  (8.3)  There still is a probability of 1.1 % (the natural abundance) that the other carbon in the methyl group will be C (in that case there would be not an isolated spin-pair system), but this is neglected here for simplicity, and also because its contribution to the total REDOR dephasing will be very small.  267  i  1  -108  i -110  i  1  -112  1  i -114  [  i  '  -116  (ppm)  i  -118  i  i -120  1  i -122  Figure 8.4: The 79.48 M H z REDOR S i N M R spectra of ZSM-5 loaded with 8 molecules of p-xylene [ C, CH ] per u.c. at 273 K . 336 scans were accumulated for each experiment with a recycle delay of 6 s and the spectra were obtained with 98 rotor cycles at a spinning speed of v = 2.586 kHz. (a) Full spin echo spectrum, So. (b) Rotational-echo spectrum, Sf. (c) Difference spectrum (AS) between the full spin echo spectrum, So, and the rotationalecho spectrum, Sf. 2 y  13  3  r  268  Table 8. 2: Shortest calculated Si-C distances for the complex of 8 molecules of pxylene per u.c. in ZSM-5 within a distance of 7 A from the XRD structure ,. 8  Si T-site 29  Sil  Si3  SilO  Sil2  Sil6  Sil7  Carbon atoms  Unit cell  Asymmetric unit  S2 Z2 Zl SI S2 SI Z2 Zl Zl Z2 S2 S2 Z2 Zl SI Zl Z2 S2 Zl S2 SI Z2  1 1 1 8 1 8 1 1 5 1 1 19 19 19 19 1 1 12 1 3 24 3  1 1 2 4 1 4 1 1 4 3 3 3 3 3 3 1 1 2 1 2 3 2  (A)  Dipolar coupling (Hz)  4.459 4.491 4.972 5.950 4.685 5.296 5.380 6.139 4.240 4.248 6.780 5.207 5.428 6.585 6.980 4.179 6.314 6.696 4.598 4.696 5.893 6.595  67.73 66.30 48.87 28.51 58.41 40.43 38.56 25.96 78.77 78.32 19.20 42.5 37.56 21.03 17.68 82.28 23.85 20.01 61.79 58.00 29.35 20.93  I*Si-X  If only one Si-C interaction is considered, Equation (1.9), in Chapter /, Section /. 1.1.1.1, which describe the REDOR signal dephasing for an isolated spin pair has to be multiplied by the probability, p, of having a labelled methyl carbon, as shown in Equation (8.4): 1  — = p(l-— -  v  In  2  n  j  7 1 / 2  fcos(AO )sinpjpja)  a=0p=0  M  (8.4)  269  The experimental data points together with the calculated REDOR curves for only the closest interaction using Equation (8.4) for the complex of ZSM-5 with 8 molecules per u.c of p-xylene [ C, CH3] (99.5 at. %) are shown in Figure 8.4. The experimental data 13  shown correspond to two REDOR data sets obtained using two different spinning speeds (2.586 kHz, and 3.024 kHz), to have more experimental data points for the same number of rotor cycles. From the figure, it can be seen that the calculated curves do not represent the complete experimental data well. At small dephasing times the fitting is reasonably good, which is expected because here the dephasing is dominated by the strongest interaction, as observed previously in Chapter 7 for the Si-H REDOR data. However for longer dephasing times, the Si-C dipolar interactions from other methyl carbons start adding up considerably, and the experimental AS/So ratios continue to increase. There are large experimental errors in the determined AS values for this system because the Si-C dipolar couplings are very small and therefore, the observed signal dephasings are correspondingly small and the S/N ratio at longer dephasing time poor. Because the dephasing ratio AS/So at small number of rotor cycles is dominated by the strongest dipolar coupling, it was thought that the application of Equation (7.10), Section 7.1.1.1.1 (valid only for short dephasing frequency) might provide information about the shortest Si-C distances in the complex. In this case, because the probability of one methyl carbon being  C labelled is 0.503, Equation (7.10) has to be multiplied by this  probability factor, as indicated in Equation (8.5). ^ - = p[\.066(nDT ) ] 2  r  (8.5)  270  Si 1 0 , 1 i n t e r a c t i o n  *  0.01  O.Ot  Si 1 2 , 1 interaction  0.03  • ^  0.04  D ephasing time (s)  Si 1 6 , 1 i n t e r a c t i o n  0.01  0.02  0D1  OO*  0  (  l  D ephasing time (s)  *  Si 1 7 , 1 interaction  0.03  0.04  0  D ephasing time (s)  0  1  o  o  i  0  0  3  0  0  4  D ephasing time (s)  Figure 8.5: Evolution of the REDOR S i ( C ) AS/S ratios for the sample of ZSM-5 loaded with 8 molecules of p-xylene-[ C, C H 3 ] per u.c. at 273 K for two data sets obtained at two different spinning speeds (v i = 2.586 kHz and v 2 = 3022 kHz). The solid lines represent the calculated REDOR curves using Equation (8.4) for only one dipolar coupling corresponding to the closest S i - C distance determined from the X R D structure, as indicated in the figure. 2 y  u  0  r  r  29  13  271  Table 8.3: Calculated dipolar coupling and Si- C distance from the experimental R E D O R data for the complex of ZSM-5 with 8 molecules per u.c. of p-xylene [ C, CH ] (99.5 at. %) l3  3  Si T-site  10  1  12  17  16  3  n  (a)  Time x (ms)  r  Dredo/  S  J  (c)  r ,c s  (Hz) calculated from  calculated from  (A)  20  0.331  0.1149  REDOR 69.99  REDOR 4.62  26  0.331  0.1835  68.03  4.66  14  0.387  0.0470  54.71  5.01  18  0.387  0.1536  76.88  4.48  20  0.331  0.1382  76.76  4.48  26  0.331  0.1647  64.47  4.75  14  0.387  0.0864  74.13  4.53  18  0.387  0.1356  72.24  4.57  20  0.331  0.0578  49.63  5.18  26  0.331  0.1276  56.73  4.95  14  0.0465  54.42  5.02  18  0.387 0.387  0.0505  44.10  5.39  14  0.331  0.0965  91.66  4.22  26  0.331  0.1478  61.05  4.83  10  0.387  0.0790  99.24  4.11  14  0.387  0.1199  87.35  4.29  20  0.331  0.1637  83.54  4.35  26  0.331  0.2147  73.61  4.54  14  0.387  0.1119  84.38  4.34  18  0.387  0.1829  83.90  4.35  20  0.331  0.1284  73.99  4.53  26  0.331  0.1896  69.16  4.64  10  0.387  0.0810  100.51  4.09  14  0.387  0.1125  84.61  4.34  Average Shortest (e) Vc Si-C ( d  (A)  (A)  from  from  REDOR  XRD  4.68  4.24  4.57  4.46  5.13  5.21  4.36  4.60  4.39  4.18  4.39  4.69  Number of rotor cycles. (  ' Dipolar coupling constant calculated from (So-Sf)/So using Equation (8.5).  Calculated Si-C distances from the dipolar coupling constant determined from the REDOR data. (c)  ^ Averaged Si-C distances from the Si-C distances determinedfromthe REDOR data at different dephasing times. (e)  Shortest Si-C distances calculated from the XRD data from reference 8.  272  The data for two REDOR experiments carried out at different spinning speeds (2586 and 3024 Hz) for small signal dephasings (i.e. small number of rotor cycles) for the complex of ZSM-5 with 8 molecules per u.c. of p-xylene [ C, CH3] (99.5 at. %) are shown in Table 8.3. The dipolar couplings, and the Si-C interatomic distances calculated from these data using Equation (8.5) are also listed, together with the shortest Si-C distances determined from the published X R D structure . 8  From the table it can be seen that the Si-C distances calculated in this way are close to the values determined from the X R D data. The values for the REDOR calculated interatomic distances are within 10 % of the values obtained from X R D . There are some variations in the calculated distances between experiments carried out at the same spinning speeds, but with different number of rotor cycles, and also between experiments at different spinning speed. These variations are probably dued to the large errors in the determination of very small AS intensities in the spectra. For a more accurate analysis of this system it is necessary to include the contributions from other further away carbon spins, and to add all contributions weighted by the proper probability factors. A multiple spin treatment as described in Section 7.1.1.3 was implemented for Si 16, Si 12 and Si 17, as described below. When more than one Si-C dipolar interaction is to be taken into account, the probability that a given Si atom has a certain number of C labelled methyl carbons will 1 3  depend on the specific silicon site considered. For example, for Si 16, there are three Si-C interactions within 7 A, and two of them are from methyl carbons on the same p-xylene molecule ( Z l and Z2), as depicted below:  273  This is the simplest case for this system. As indicated in the scheme, there are only two nearby p-xylene molecules; one in the straight channel and the other in the zig-zag channel. Therefore there are four different carbons interacting with Si 16, but as only one carbon is labeled in each molecule (the C natural abundance is neglected in this treatment 13  because its contribution is very small compared to the labelled nuclei), only four possible cases in which Si 16 is dipolar coupled to two methyl carbons are possible, as indicated below: Z l - S i 16--S2  with a probability of 25 %  (I)  Z2 - S i 16--S2  with a probability of 25 %  (II)  Z l -- S i 16- SI  with a probability of 25 %  (III)  Z2- - Si 16- SI  with a probability of 25 %  (IV)  However, the cases described in (III) and (IV) correspond to interactions with carbon SI, which is too far (Si-C>7 A) and is neglected in the present treatment. Thus, situations (III) and (IV) actually correspond to a contribution of 25 % each of Si 16 with a single interaction to Z l and with a single interaction to Z2, respectively. There is a 50 % contribution of single spin dipolar dephasing (equivalent to having isolated spin pairs)  274  corresponding to cases (III) and (IV), and a 50 % contribution of double spin dipolar dephasing (equivalent to having three spin systems), from cases (I) and (II). Similarly, for Si 12 there are four close methyl carbons (in the radius range of up to 7 A) from one p-xylene molecule in the zig-zag channel, ( Z l and Z2), and one p-xylene molecule in the straight channel, (S1 and S2), as indicated below:  5.428 A  5.207 A  However, in this case all the interactions are important (because all the Si-C distances are smaller than the cut off of 7 A);thus, all the four possible cases (I), (II), (III) and (IV) described before for Si 16, are double interactions (three spin systems) for Si 12. For Si 1, Si 10, and Si 17, all the Si-C interactions are from different p-xylene molecules and thus, the probability of finding a labeled methyl group is given by the binomial probability distribution : 9  P(x) = c: "  x n-x  P q  x\(n -  (8.6) x)\  where x, the number of successes in n trials, make take values 0,1,2,...,n.  275  In the formula for P(x), the quantity p q " represents the probability of observing a x  n  x  simple event with x successes and (n-x) failures, the term C , counts the number of such as n  x  simple events, i.e. the number of ways to combine a given number of interacting spins, as shown below. If four S i - C dipolar interactions D i , D2, D 3 , D 4 are considered, the probability of 29  13  one given Si atom having interactions with no C methyl carbons is P(0), one 1 3  1 3  C methyl  carbons is P(l), two C methyl carbons is P(2), three C methyl carbons is P(3), and four 1 3  1 3  1 3  C methyl carbons is P(4). P(0)=l*(0.503)°*(0.497) =0.0610 4  P(l)=4*(0.503) *(0.497) =0.2470 1  3  P(2)=6*(0.503) *(0.497) =0.3750 2  2  P(3)=4*(0.503) *(0.497) =0.2530 3  1  P(4)=l *(0.503) *(0.497)°=0.0640 4  In this case the contributions from 4 spin and 5 spin systems, given by P(3) and P(4), respectively, represent 31.7 % of the total signal dephasing AS/SoThe REDOR curves for Si 12, Si 16 and Si 17, using the multiple spin analysis are shown together with the experimental data points in Figure 8.6. As can be seen from the figure, the calculated fit for each silicon with the interactions listed from a radius of up to 7 A, represents better the whole behaviour of the REDOR data than the fitting considering only one closest Si-C interaction (Figure 8.5), i.e. the oscillations predicted for an isolated spin-pair are lost in the multiple spin fitting for Si 17 and Si 16 due to the contributions from more distant nuclei. However, the calculated fits are higher in intensity than the experimental data. One possible reason for this could be the evaporation of some p-xylene  276  molecules in the sample, in which case there would be some silicon atoms in the zeolite with no close p-xylene molecules, i.e. like small pockets with no p-xylene molecules in the channels, and consequently there would be less interactions than calculated assuming a full loading. In order to have a sample with less multiple spin interactions i.e. more similar to an isolated spin-pair system, a 50 % isotopically diluted sample was prepared with p-xylene natural abundance and p-xylene[ C, CH3] (99.5 at. %). These data are presented in Figures 13  8.7 and 8.8. In a first approximation for the analysis of these data, the REDOR curves for only the closest Si-C interaction were calculated. In this case as only one methyl carbon is labeled C (99.5 at %), and the sample is diluted by 50 %, the probability of a given methyl 1 3  carbon being C i s : p = 0.25(0.995) = 0.249  (8.7)  and the probability of a given methyl carbon not being C is 1 3  q=\-p = 0.751  (8.8)  Therefore i f only one Si-C interaction is considered, Equation (8.5) which describes the signal dephasing for an isolated spin pair has to be multiplied by the probability factor p=0.249, for this sample. The experimental data points together with the calculated REDOR curves for a single interaction using Equation (8.5) with a probability, />=0.249, for the complex of ZSM-5 4 molecules of unlabeled p-xylene and 4 molecules of p-xylene [ C, C H 3 I (99.5 at. %), are shown in Figure 8.7.  277  As expected, the experimental REDOR responses are lower than those for the undiluted case. As can be seen, the calculated theoretical curves for a single isolated spin system do not represent well the whole experimental data. Again, at small dephasing times the fitting is better, which is expected because the dephasing is dominated by the strongest interaction. However, for longer dephasing times, S i - C dipolar interactions from other 2 9  l 3  methyl carbons start adding up and the experimental AS/So ratios continue to increase. The experimental errors in the determined AS/So ratios are larger than for the "undiluted" case because in addition to the very small Si-C dipolar couplings, the sample is now isotopically diluted, and therefore, there are less  l 3  C interactions in this sample giving less dephasing  and lower S/N ratios. Because of the observation that at small number of rotor cycles, the dephasing ratio AS/So is dominated by the strong dipolar couplings, the application of Equation (8.5) (valid only for short dephasing times) should again provide the same information about the shortest Si-C distances in the complex. In this case, because the probability of one methyl carbon being  C is 0.249, Equation (8.5) has to be multiplied by this factor.  The data for two REDOR experiments for small signal dephasings (i.e. small number of rotor cycles) for the complex of ZSM-5 with 4 molecules of unlabeled p-xylene and 4 molecules of p-xylene[ C, CH3] per u.c. are shown in Table 8.4. The dipolar couplings, and the Si-C interatomic distances calculated from these data using Equation (8.5) are also listed, together with the closest Si-C distances determined from the published X R D structure . 8  278  Si 12, 4 interactions Dl=42.5 H z ; D2=37.6 Hz: D3=21.0 H z : D4=17.7 H z  0.8 0.6  AS/S  0  0.4 0.2  5  10  15  20  25  30  35  Dephasing time (ms) Si 16,3 interactions Dl=82.3 Hz; D2=23.8 H z ; D3=20.0 H z  AS/S  r  5  10  15  20  25  30  35  Dephasing time (ms) Si 17, 4 interactions Dl=61.8 H z ; D2=58.0 Hz; D3=29.3 Hz; D4=20.9 H z  AS/S  fl  5  10  15  20  25  30  35  Dephasing time (ms)  Figure 8.6: Evolution ofthe REDOR S i ( C ) AS/S ratios for the sample of ZSM-5 loaded with 8 molecules p-xylene-[ C, CH3] per u.c. at 273 K for two data sets carried out at two different spinning speeds (v i = 2.586 kHz and v = 3.022 kHz) to obtain more data points. The solid lines represent the calculated REDOR curves using multiple spin interactions, Equation (7.12), as indicated in the plots. 2y  1J  0  13  r  r2  279  Si 10,1 interaction 0^78.77. H i  Si 1,1 interaction Dj=67.7 H i  .U  I  ..  m  0.03  0.04  0.05  0.06  »•<"•  °"  Dephasing time (s)  E  °»  3  "  Dephasing time (s)  Si 12,1 interaction  Dephasing time (s)  Dephasing time (s)  Figure 8.7: Evolution of the REDOR S i ( C ) AS/S ratios for the diluted sample of ZSM-5 loaded with 4 molecules p-xylene-[ C, CH3] per u.c. and 4 molecules p-xylene (natural abundance) carried out at 273 K and at a spinning speed of v = 2.483 kHz. The solid lines represent the calculated REDOR curves using Equation (8.4) for only one dipolar coupling corresponding to the closest Si-C distance determined from X R D as indicated in the plots. 2 y  u  0  13  r  280  Table 8. 4: Calculated dipolar coupling and Si-H distance from the experimental R E D O R data for the complex of ZSM-5 with 4 molecules of unlabeled p-xylene and 4 molecules of p-xylene [ C, CH3] (99.5 at. %) per u.c.. 13  Si T-site  n  (a)  Xr  S -S ^ 0  f  (Hz)  Dredor'  (Hz) calculated  r  (c) Sl  -c  (A)  calculated  Average ( d  Wc  (A) from  r .c (A) from X R D (d)  Si  REDOR  10  1  12  17  16  3  w  (b)  16  0.403  0.0848  92.02  4.22  22  0.403  0.2039  103.79  4.05  28  0.403  0.1573  71.62  4.58  16  0.403  0.0954  97.63  4.13  22  0.403  0.2787  121.34  3.84  28  0.403  0.1684  74.11  4.53  16  0.403  0.0467  68.33  4.66  22  0.403  0.0478  50.27  5.16  28  0.403  0.0791  50.79  5.14  16  0.403  0.0571  75.50  4.50  22  0.403  0.1709  95.01  4.17  28  0.403  0.1383  67.17  4.68  16  0.403  0.0258  50.75  5.14  22  0.403  0.2207  107.97  4.00  28  0.403  0.1589  72.00  4.57  16  0.403  0.0846  91.91  4.22  22  0.403  0.2105  105.47  4.03  28  0.403  0.1472  69.29  4.63  4.28  4.24  4.17  4.46  4.99  5.21  4.45  4.60  4.57  4.18  4.29  4.69  Number of rotor cycles Dipolar coupling constant calculated from (S -S)/So using Equation 8.5 0  f  Calculated Si-C distances from the dipolar coupling constants determined from the REDOR data. (c)  (d)  Shortest Si-C distances calculated from the XRD datafromreference 8.  281  From the table it can be seen that the Si-C distances calculated in this way are again close to those determined from the X R D structure, in the same way that for the "undiluted sample". The relative errors between the averaged Si-C distances determined by REDOR compared with the values obtained from the X R D data are smaller than 10 %. There are variations in the calculated REDOR distances between experiments with different number of rotor cycles. Some of these variations could be due to the large errors in the determination of very small AS intensities. For the diluted sample this is more important because of the smaller number of C nuclei contributing to the dephasing of the S i N M R l 3  29  signals. For a more accurate analysis of this system it is necessary to include the contributions from other further away carbon spins, and to add all contributions weighted by the proper probability factor. A multiple spin treatment as described in Section 7.1.1.3 was implemented for Si 16, Si 12 and Si 17, as described below. As the system studied is isotopically diluted, the probabilities are very different to those calculated for the 8 molecules [ C, CH3] per u.c. complex. Thus, for Si 16, the population distributions for the different dipolar interactions for the diluted sample are as indicated below.  282  Si 16 with no labeled methyl carbons  37.5 %  18.75% of Z1-SH6 Si 16 with one C spin interactions 1 3  18.75 % o f Z 2 - S i l 6 12.5 % o f S2-SH6  Si 16 with two C spin interactions  6.25% of Z l - S U 6 - S 2  1 3  6.25 % o f Z 2 - S i 16 - S2  In the case of Si 12, the population distributions for the different dipolar interactions is now as indicated below: Si 12 with no labeled methyl carbons  25%  12.5%ofZl-Sil2 Si 12 with one C spin interactions  12.5 % o f Z 2 - S i l 2  1 3  12.5 % o f S2-SH2 12.5 % o f S1-SH2 6.25 % o f Z l - S U 2 - S 2  Si 12 with two C spin interactions  6 . 2 5 % o f Z 2 - S i 12 - S 2  1 3  6.25% of Z l - Si 1 2 - SI 6.25%ofZ2-Si  16-SI  283  In the case of Si 17 with 4 different p-xylene molecules nearby, the different probabilities are: Si 17 with no labeled methyl carbons  40/128  13/128 o f Z l - S i l 7 Si 17 with one C spin interactions  13/128 o f Z 2 - S i l 7  1 3  13/128 of S 2 - S U 7 13/128 of SI - S i l 7 24/128 o f Z l - S i l 7 - S 2 24/128 o f Z 2 - S i 1 7 - S 2  Si 17 with two C spin interactions  24/128 o f Z l - Si 1 7 - SI  1 3  24/128 o f Z 2 - S i 1 7 - S I 24/128 o f Z 2 - S i 1 7 - Z l 24/128 o f S 2 - S i 1 7 - S I  1/128 o f S i l 7 - Z l - Z 2 - S l Si 17 with three C spin interactions  1/128 o f S i l 7 - Z l - Z 2 - S 2 1/128 o f S i l 7 - Z 2 - S l - S 2 1/128 o f S i l 7 - Z l - S 1 - S 2  Si 17 with four C spin interactions  8/128 o f S i l 7 - Z l - Z 2 - S 1 -  284  The REDOR curves for Si 12, Si 16 and Si 17, using the multiple spin analysis with the population distributions indicated above are shown together with the experimental data points in Figure 8.8. As it can be seen from the figure, the calculated fits for each silicon atom with the interactions listed better represent the general behaviour of the REDOR data than the fitting considering only one closest Si-C interaction (Figure 8.7), i.e. the oscillations in the AS/So ratios predicted for an isolated spin-pair are lost in the multiple spin fittings due to the contributions of other further away interactions. However, again the calculated fits are higher in intensities than the experimental data and further studies should be carried out to investigate this discrepancy. One most important conclusion from this work is that the porous nature of these materials means that the framework silicons will be involved in multiple dipolar interactions with nuclei on organic sorbates even i f single site isotopic enrichment is used. Although this is worse in the present instance than it would be at lower loadings (e.g. 4 molecule/u.c), it means that direct distance determinations in these complexes will not be possible, unlike active sites in enzymes which are the case of isolated from each other. This means that a model must be postulated and the fit to the experimental data evaluated. There is not advantage over the H / Si CP experiments discussed earlier (Chapter 3 to 6) which are simpler and have higher S/N and these will, in most cases, be the most attractive in structural studies.  285  Si 12,4 interactions  Dl=42.5 H z : D2=37.6 Hz: D3=21.0 Hz: D4=17.7 Hz  10  20  30  40  50  Dephasing time (ms) Si 16, 3 interactions  Dl=82.3 Hz; D2=23.8 Hz; D3=20.0 Hz  10  20  30  40  50 60  Dephasing time (ms) Si 17, 4 interactions  Dl=61.8 H z ; D2=58.0 Hz; D3=29.3 Hz; D4=20.9 H z  *  10  20  30  40  50  Dephasing time (ms)  Figure 8.8: Evolution of the REDOR S i ( C ) AS/S ratios for the diluted sample of ZSM-5 loaded with 4 molecules p-xylene-[ C, CH3] per u.c. and 4 molecules p-xylene (natural abundance) at 273 K and at a spinning speed of v = 2.483 kHz. The solid lines represent the calculated REDOR curves using multiple spin interactions Equation (7.12) for the of interactions indicated in the figure. 29  13  0  13  r  286  8.3.2  T E D O R EXPERIMENTS  Like REDOR, TEDOR is a solid state N M R experiment that has been used to measure internuclear distances between isolated pairs of spin Vi nuclei. In this section the application of the TEDOR experiment to study the high loaded complex of p-xylene [ C, CH3] (99.5 at. %) is presented. As discussed previously, the TEDOR experiment was initially introduced to overcome the contribution of uncoupled natural abundance spins to the echo signal measured in a REDOR experiment. " H / , J C r ' S i TEDOR spectra were obtained as a function of the number of rotor cycles after the transfer of coherence (m), for the sample of ZSM-5 loaded with 8 molecules of p-xylene [ C, CH3] (99.5 at. %) per u.c. at 273 K with a fixed number of rotor cycles before the transfer of coherence (n=22). The spectra were deconvoluted in terms of Lorentzian functions and the intensities of the reasonably well resolved resonances due to silicons 1,3, 10, 12, 16, and 17 determined. The TEDOR S i N M R spectra of ZSM-5 loaded with 8 molecules per u.c. of p29  xylene [ C , CH ] (99.5 at. %) at 273 K as a function of the number of rotor cycles, m, are ,J  3  shown in Figure 8.9. The antiphase magnetization (initially unobservable) evolves during the additional dephasing period into the in-phase magnetization that is detected. The application of the simultaneous 180° pulses after the transfer (at m/2, see Figure 8.2) to produce an echo, refocus all the  Si signals and the final N M R spectrum can be properly  phased, as shown in the spectra indicated in Figure 8.9. In these spectra it can be seen how the intensities of the signals increase, reach a maximum and then decrease as a function of the number of rotor cycles, m. This behaviour can be more easily seen in the plots of the individual signal areas, presented in Figure 8.10.  287 Variation of the number of rotor cycles before or after the transfer of coherence in the TEDOR experiment leads to different amounts of dipolar-dephasing which will accumulate in time as shown in Equations (8.1) and (8.2). For individual pairs of isolated dipolar coupled nuclei, these equations can be used to generate universal curves. The experimental data points together with the calculated TEDOR curves using Equations (8.1) and (8.2) as a function of the number of cycles m after the transfer for the complex of ZSM-5 with 8 molecules per u.c. of p-xylene [ C, CH3] (99.5 at. %) are shown 13  in Figure 8.10. The TEDOR curves were calculated considering one S i - C isolated spin29  13  pairs corresponding to the closest interactions. For TEDOR experiments, there is no normalization as there is for REDOR, so an arbitrary scaling factor was applied to Equation (8.2) to mach the experimental intensities. This eliminates the intensity mismatch seen previously in the corresponding REDOR plots. Also, an exponential dampening function of mi  r  T  exp  was used to take into account transversal relaxation (T2) during the evolution  2  period . The transversal relaxation (T2) for the S i nuclei used in the fitting are listed in 10  29  Table 8.5.  Table 8. 5: Transverse relaxation times (T2) for some Si nuclei in the p-xylene/ZSM5 complex at 273 K. 29  29  Si site T (ms) 2  Sil  Si 3  Si 10  Si 12  Si 16  Si 17  32.6  38.6  37.0  44.5  44.5  35.6  288  From Figure 8.9 it can be seen that the calculated TEDOR curves assuming only one strong interaction represent in a semi-quantitative way the experimental data, because in reality each silicon atom is dipolar coupled to several carbon nuclei. However these experiments show that there are differences in the positions of the maxima positions of the calculated TEDOR curves for the different silicon nuclei, indicating their potential to yield structural information. For example, Si 1 and Si 10, which have the largest S i - C dipolar 29  13  couplings, reach the intensity maxima at approximately m=22, however in the case of Si 12, with the smallest S i - C dipolar coupling, the maxima is reached at at approximately 29  13  m=40. The experimental data is a little scattered due to the large errors in the determination of small intensity variations because of the from very small S i - C dipolar couplings. 29  13  The main purpose of this TEDOR experiment was to find the best combination of number of rotor cycles before and after the transfer to carry out a two-dimensional TEDOR experiment. 22 rotor cycles before and after the transfer for the 2D experiment were chosen, because all the signals in the spectrum have relatively good intensities, but there is clear differentiation between the different framework sites.  8.3.3  TWO-DIMENSIONAL T E D O R EXPERIMENTS  The TEDOR experiment is amenable to extension into a second spectral dimension since it involves coherence transfer to a heteronucleus, rather than spin-echo detection of dipolar coupling via the excited nucleus. The two-dimensional C - » S i TEDOR spectrum 13  29  of the complex of ZSM-5 with 8 molecules per u.c. of p-xylene [ C, C H ] (99.5 at. %) 13  3  shown in Figure 4.4 was acquired using the optimized conditions of 22 rotor cycles of preparative dephasing and 22 rotor cycles of antiphase to in-phase evolution after the  289  transfer (n=22, m=22). This experiment was carried out to make an unambiguous assignment of the C N M R spectrum for this system, as previously discussed in Chapter 4. 1 3  The cross peaks in the spectrum indicate the S i nuclei that are dipolar coupled to the 29  different  1 3  C spins. Because the dipolar interactions have a very strong dependence on the  internuclear distance (1/r ), only those C atoms with relatively large dipolar couplings to 3  1 3  the different silicon sites will show cross peaks in the spectrum;  l 3  C atoms that are too far  away from the S i nuclei will not produce cross peaks. The cross peak intensity is a relative 2 9  measure of the strength of the dipolar coupling, since as was shown in the one dimensional TEDOR experiment (Figure 8.10) the positions of the maxima intensity shift for the different silicon atoms. Thus, for example, for a fixed number of cycles before the transfer of n=22, the maxima for Si 1 and Si 10 are at m=22 after the transfer, but it is at m=40 for Si 12. Therefore at the fixed conditions used in the 2D experiment all resolved silicon signals used for the assignment exhibit good intensity but  there are variations in the  observed cross peaks which are intrinsic to the experiment conditions and the dipolar connectivities. These intensities give a good approximation about the strengths of the  Si-  C dipolar interaction that can be used to analyze the 2D TEDOR data. 1X  The assignment of the  C spectrum was already discussed in Chapter 4, and is  presented in Figure 4.4. In Table 8.6, the expected cross peaks according to the strengths of the dipolar couplings are indicated.  I  i  1  -172  1  I  1  -176  I  i  i  1  -180  i  1  I  1  -184  I  '  i  ~!  -188  r  1  i  1  I  -192  1  i  -196  (ppm)  Figure 8.9: ^ Si N M R spectra of ZSM-5 loaded with 8 molecules of p-xylene [ C, CH ]per u.c. at 273 K , showing the evolution of the TEDOR S i ( C ) Sf signal. 512 scans were accumulated for each experiment with a recycle delay of 6 s between them. A fixed number of cycles (n=22) before the transfer of magnetization was used. The spectra were obtained y  U  3  29  13  varying the number of rotor cycles m after the transfer from 8 to 30. The 7C dephasing pulses were applied on the S i channel before the transfer and on the C channel after the transfer. The sample was spun at the magic angle with a speed of v = 2.668 kHz. 2 9  1 3  r  291  Si 3, D=58.4 H z  Si 10, D=78.8 H z J  5X10 3X10  2.5X10 2x10 1.5x10 1X10  Sxlo' 10  20  SO  40  50  10  Rotor cycles after transfer  20  30  tO  50  60  Rotor cycles after transfer  Si 16, D=82.3 H z  Si 17, D=61.8 H z  3.5X10 3X10  s  2.5x10  f  2X10 1.5X10 lxio SxU 20  30  10  50  10  Rotor cycles after transfer  20  30  3D  40  50  50  Rotor cycles after transfer  Si 12, D=42.5 H z  10  20  Si 1, D=67.8 H z  40  50  10  60  20  30  40  50  60  Rotor cycles after transfer  Rotor cycles after transfer  Figure 8.10: Evolution ofthe TEDOR S i ( C ) S for the sample of ZSM-5 loaded with 8 molecules p-xylene-[ C, CH3] per u.c. at 273 K for the experiment carried out at v = 2.668 kHz,and with a fixed number of cycles, n=22, before the transfer of coherence. The solid lines represent the calculated TEDOR curves using Equation 8.2 for only one dipolar coupling corresponding to the closest Si-C distance determined from X R D as indicated in the plots. 29  13  f  r  292  Table 8. 6: Expected cross peaks intensities according to the strengths of the dipolar couplings given in Table 4.1.  29  Si T site  Zl  Z2  SI  S2  w w  s M  -  -  -  -  Si 1  M  Si 3  W  Si 4  S  Si 10  s  w w s  Si 12  -  M  -  -M  Si 16  s s w  W  -  -  W  w w  -M  Si 17 Si 18  •v;  W  S = strong dipolar coupling (between 85-60 Hz). M = medium dipolar coupling (between 59-40 Hz). W = weak dipolar coupling (between 39-20 Hz).  S  293  8.4.  CONCLUSIONS  The solid state  Cl Si REDOR and TEDOR experiments which re-introduce the  dipolar coupling averaged out by M A S maintaining the high resolution desirable for spectrum with multiple sites can provide important structural information on the complexes of zeolites with guest molecules. The mathematical approach using the closest  29  Si- C 13  interaction in the analysis of the experimental REDOR and TEDOR data for the complexes of ZSM-5 with 8 molecules per u.c. of p-xylene [ C, C H ] (99.5 at. %) provided a semi13  3  quantitative interpretation of these data. These treatments correspond to a case of isolated spin pairs for the strongest Si-C interactions, which is not the case in these samples. However, it was shown that the dephasing of the REDOR signal at short number of rotor cycles is dominated by the strongest interaction and the application of Equation (8.5) yields a good estimation of the shortest Si-C interatomic distances. This information is valuable because it might be used to propose structural model of the complexes that can be used to reduce the number of possible structures in these complexes. However, a model must be proposed as in the case of ' H T S i cross-polarization which also provides structural information and this experiment is less demanding and can easily be applied to non isolated spin systems. Another possibility is the application of isotopic dilution of the sample to obtain truly isolated spin pairs. The problem, of course, is sensitivity due to the very small number of  C available for dipolar dephasing which will adversely affect the S/N ratio of the  spectra. But even in this case it will be necessary to use structural models to include several Si-C interactions.  294  There is a discrepancy between the absolute values of the observed and calculated data which has not been resolved in the present REDOR work although the general profiles of the curves are well reproduced by the multiple spin calculations. There are several possible reasons for this and further studies should be carried out on this system. The TEDOR experiments were very useful to obtain structural informaition of these system because it can be extended into a second spectral dimension which 13  can be used to assign  C spectra of the guest molecules sorbed in zeolites, and  consequently a better understanding of these complex system can be obtained.  295  8.5.  REFERENCES  1 Gullion, T.; Schaefer, J. J. Mag. Reson., 81, 196, 1989 2 Pan, Y.; Gullion, T.; Schaefer, J. J. Mag. Reson., 90, 330, 1990. 3 Gullion, T.; Schaefer, J. Advan. Mag. Reson., W.S. Warren, Ed., vol 13, pg 57, 1989. 4 Hing, A.W.; Vega, S.; Schaefer, J. J. Mag. Reson., 96, 205, 1992. 5 Hing, A.W.; Vega, S.; Schaefer, J. J. Mag. Reson. Series A, 103, 151, 1993. 6 Marion, D., Wuthrich, K., Biochem. Biophys. Res. Commun., 113, 967, 1983. 7 Drobny, G., Pines, A., Sinton, S., Weitekamp, D., Wemmer, D., Symp. Faraday Div. Chem. Soc, 174, 49, 1979. 8 van Koningsveld, H.; Tuinstra, F.; van Bekkum, H.; Jansen, J . C ; Acta Cryst., B46, 423431, 1989 9 Mendenhall, W., Beaver, R.J., 'Introduction to Probability and Statistics", Duxbury Press, California, 9 edition, pg 167. 19 th  10 Mueller, K.,T., J. Magn. Reson. Serie A, 113, 81, 1995.  296  Appendices: Turbo Pascal Computer Programs written to Calculate Important Values Used in this Thesis:  A P E N D I X 1.  Program to Calculate Static Internuclear Si-H Second Moments for the Aromatic Hydrogens in the System of Orthorhombic ZSM-5 High Loaded with p-Xylene Space Group P2/2/2/.  A P E N D I X 2.  Program to Calculate Internuclear Si-H Second Moments for Methyl Hydrogens Rotating about their C 3 axis in the System of Orthorhombic ZSM-5 High Loaded with p-Xylene Space Group P2/2/2/.  A P E N D I X 3.  Program to Rotate and Translate the p-Xylene and Calculate Internuclear Si-H Second Moments for the Aromatic and Methyl Hydrogens in the System of Orthorhombic ZSM-5 Low Loaded with p-Xylene Space Group Pnma.  A P E N D I X 4:  Program to Calculate Lorentzian Signals from the CP Correlation in the System of Orthorhombic ZSM-5 Low Loaded with p-Xylene Space Group Pnma.  A P E N D I X 5:  Program to Calculate Average Internuclear Si-H Second Moments for the Aromatic Hydrogens Flipping about the C2 Axis in the System of Orthorhombic ZSM-5 Low Loaded with p-Xylene Space Group Pnma.  297  APENDIX 1. Program to Calculate Static Internuclear Si-H Second Moments for the Aromatic Hydrogens in the System of Orthorhombic ZSM-5 High Loaded with p-Xylene Space Group P2i2j2i. program SMHETARO;{ STATIC SECOND MOMENT FOR Si-AROMATIC HYDROGENS) uses winCrt;  { FOR PXYLENE HIGH LOADING ORTHORHOMBIC P212121}  const nhidr=8; nsi=24; a=20.121; b=19 . 82; c=13.438; var 1 , i , j , k, m: integer smtstl,smtst2,dist:real; staticrad,staticgauss,statichz,DCtHHHZ, DCtHZ,DCt,secondrnoment:real; xh,yh,zh : a r r a y [ 1 . . 2 7 , 1 . . 4 , 1 . . n h i d r ] of r e a l ; x S i , y S i , z S i :array[1..nSi] of r e a l ; output:text;  PROCEDURE FINDCOOR;  var i,j,k:integer; input:text; x l , y l , z l : real;  begin {FILE FOR FRACTIONAL COORDINATES AROMATIC HYDROGENS xyzcora2.TXT) assign(input,'xyzcora2.txt') ; { f i l e with the atoms coordenates, must be f i r s t hydrogen, then s i l i c o n coordinates, x y z) reset(input); for i:=l to nhidr do {Calculates the other positions for the space group P212121, to create the complete unit c e l l ) begin k:=l; read(input,XI); XH[1,k,i]:=xl; read(input,Yl); YH[l,k,i]:=yl; readln(input,zl) ; ZH[l,k,i]:=zl; inc(k); X H [ l , k , i ] =0.5+xl; YH[1,k,i] =0.5-yl; ZH[l,k,i] = - z l ;  298  inc(k) ; XH[l,k,i]:=0.5-xl; YH[l,k,i]:=-yl; ZH[l,k,i]:=0.5+zl; i n c (k) ; XH[l,k,i]:=-xl; YH[l,k,i]:=0.5+yl; Z H [ l , k , i ] : = 0 . 5 - z 1; writeln('H',l,k,i, ' • ,ZH[l,k,i) :6:4); end; for i:=l  ',XH[1,k,i]:6:4 ,  ',YH[1,k,i]:6:4,  1  t o n s i do  begin k:=l; read(input,xl); XSi[i]:=xl; read(input,yl); YSi[i]:=yl; readln(input, zl) ; ZSi[i]:=zl; end; close(input) ;  for  i:=l  P212121,  to  to nhidr  do  { C a l c u l a t e s the {create  f o r k:=l begin  other  positions  for  the space  group  for  the space  group  for  the space  group  } to  the complete  2nd u n i t  cell}  4 do  XH[2,k,i]:=XH[1,k,i]-1 ; YH[2,k,i]:=YH[l,k,i]-1; ZH[2,k,i):=ZH[l,k,i]; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other {create  f o r k:=l begin  positions  } to  the complete 3th u n i t  cell}  4 do  XH[3,k,i]:=XH[l,k,i]-l; YH[3,k,i]:=YH[l,k,i]; ZH[3,k,i]:=ZH[l.k,i]; end; for  i:=l  P212121,  to  to nhidr }  do  { C a l c u l a t e s the other  positions  299 {create the complete 4th unit cell} for k:=l to 4 do begin XH[4,k,i]:=XH[l,k,i]-l; YH[4,k,i]:=l+YH[l,k,i]; ZH[4,k,i]:=ZH[l,k,i] ;  ! | I  end ; for i : = l to nhidr do P212121, to } for k:=l to begin  4  {Calculates the other positions for jthe space group j {create the complete 5th unit cell} i  do  I  j I  i  XH[5,k,i]:=XH[l,k,i]; YH[5,k,i]:=YH[l,k,i]-l; ZH[5,k,i]:=ZH[l,k,i];  ;  end ; for i : = l to nhidr do P212121, to } for k:=l to 4 do begin  {Calculates the other positions for'the space group I {create the complete 6th unit c e l l ) . ! I  X H [ 6 , k , i ] =XH[1,k, i ] ; Y H [ 6 , k , i ] = l+YH[l,k, i) ZH[6,k,i] = Z H [ l , k , i ] ; end; {Calculates the other positions for the space group for i : = l to nhidr do P212121, to } {create the complete 7th unit cell} for k:=l to 4 do begin XH[7,k,i]:=l+XH[l,k,i]; YH[7,k,i]:=YH[l,k,i]; ZH[7,k,i]:=ZH[l,k,i]; end; for i : = l to nhidr do P212121, to } for k:=l to 4 do begin  {Calculates the other positions for jthe space group {create the complete 8th unit cell}  j  300  XH[8,k,i]:=l+XH[l,k,i]; YH[8,k,i]:=YH[l,k,i]-l; ZH[8,k,i]:=ZH[l,k,i];  .  end ; for i : = l to nhidr do P212121,  to  {Calculates the other positions for the space group  }  {create the complete 9 t h unit cell} for k:=l to begin  4  do  XH[9,k,i):=l+XH[l,k,i]; YH[9,k,i]:=l+YH[l,k,i]; ZH[9,k,i]:=ZH[l,k,i]; end; for i : = l to nhidr do P212121,  to  {Calculates the other positions for the space group  }  {create the complete 1 0 t h unit cell} for k:=l to begin  4  do  XH[10,k,i]:=XH[l,k i]; YH[10,k,i]:=YH[l,k,i]; ZH[10,k,i]:=1+ZH[1,k,i]; (  end; for i : = l to nhidr do P212121,  to  {Calculates the other positions  for the space group  }  {create the complete 1 1 t h unit cell} for k:=l to begin  4  do  XH[ll,k,i]:=XH[l,k,i]-l; YH[ll,k,i]:=YH[l,k,i]-l; Z H [ l l , k , i ] : = l + ZH[l,k,i] ; end; for i : = l to nhidr do P212121,  to  {Calculates the other positions for the space group  }  {create t h e complete 1 2 t h u n i t for k:=l to 4 do begin XH[12,k,i]:=XH[l,k i]-l; YH[12,k,i]:=YH[l,k,i]; ZH[12,k,i]:=l+ZH[l,k,i]; end; (  cell}  301  for  i:=l  P212121,  to nhidr  to }  for k:=l begin  do  {Calculates {create  the other  the complete  positions  13th unit  f o r the space  group  cell}  t o 4 do  XH[13,k,i]:=XH[l,k,i]-1; YH[13,k,i]:=l+YH[l,k,i]; ZH[13,k,i]:=l+ZH[l,k,i]; end; i n c (1) ; for  i:=l  P212121,  to  to nhidr  do  {Calculates  positions  f o r the  space  group  f o r the space  group  } {create  for k:=l begin  the other  the complete  14th u n i t  cell)  t o 4 do  XH[14,k,i]:=XH[l.k,i]; YH[14,k,i]:=YH[l,k,i]-1; ZH[14,k,i]:=l+ZH[l,k,i]; end ; for  i:=l  P212121,  to nhidr  do  {Calculates  the other  positions  to } {create  for k:=l begin  the complete  15th u n i t  cell}  t o 4 do  XH[15,k,i]:=XH[l,k,i]; YH[15,k,i]:=l+YH[l,k,i]; ZH[15,k,i]:=l+ZH[l,k,i]; end; for  i:=l  P212121,  to nhidr  do  {Calculates  the other  positions  f o r the space  group  to } {create  for k:=l begin  the complete  16th u n i t  cell}  t o 4 do  XH[16,k,i]:=l+XH[l,k,i]; YH[16,k,i]:=YH[l,k,i]; ZH[16,k,i]:=l+ZH[l,k,i]; end;  f o r i : = l to nhidr do P212121,  {Calculates the other positions for the space group  to } {create  for k:=l begin  t o 4 do  the  complete  17th u n i t  cell)  302  XH[17,k,i]:=l+XH[l,k,i]; YH[17,k,i] :=YH[l,k,i)-l; ZH[17,k,i]:=l+ZH[l,k,i]; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other  f o r the space  group  } {create  f o r k:=l begin  positions  to  the complete  18th u n i t  cell}  4 do  XH[18,k,i]:=l+XH[l,k, i]; YH[18,k,i]:=l+YH[l,k,i]; ZH[18,k,i]:=l+ZH[l,k,i]; end ; for  i:=l  P212121,  to  to .nhidr  do  {Calculates the other  {create f o r k:=l begin  positions  for  the space  group  } to  the complete  19th u n i t  cell)  4 do  XH[19,k,i]:=XH[l,k,i]; YH[19,k,i):=YH[l,k,i]; ZH[19,k,i]:=ZH[l,k,i]-l; end; for  i:=l  P212121,  to  to nhidr  do  { C a l c u l a t e s the {create  f o r k:=l begin  other  positions  for  the space  group  space  group  } to  the complete  20th u n i t  cell}  4 do  XH[20,k,i]:=XH[l,k,i]-l; YH[20,k,i]:=YH[l,k,i]-l; ZH[20,k,i]:=ZH[l,k,i]-l; end; for  i:=1  P212121,  to  to nhidr  do  { C a l c u l a t e s the {create  f o r k:=l begin  other  positions  for  }  to  4  do  XH[21,k,i):=XH[l,k,i)-l; YH[21,k,i]:=YH[l,k,i]; ZH[21,k,i]:=ZH[l,k,i]-l; end;  the complete 21th  unit cell}  the  303  for  i:=l  P212121,  to nhidr  do  {Calculates  the other  positions  f o r the space  group  to ) {create  f o r k:=l begin  the complete  22th u n i t  cell)  t o 4 do  XH[22,k,i]:=XH[l,k,i]-l; YH[22,k,i]:=l+YH[l,k,i]; ZH[22,k,i]:=ZH[l,k.i]-l; end; for  i:=l  P212121,  to nhidr  do  {Calculates  the other  positions  f o r the space  group  to } {create  for k:=l begin  the complete  23th u n i t  cell}  t o 4 do  XH[23,k,i]:=XH[l,k,i]; YH[23,k,i]:=YH[l,k,i]-l; ZH[23,k,i]:=ZH[l,k,i]-l; end ; for  i:=l  P212121,  to nhidr  do  {Calculates  the other  positions  f o r the space  group  to } {create  f o r k:=l begin  the complete  24th u n i t  cell}  t o 4 do  XH[24,k,i]:=XH[l,k,i]; YH[24,k,i]:=l+YH[l,k,i]; ZH[24,k,i]:=ZH[l,k,i]-l; end ; for  i:=l  P212121,  to nhidr  do  {Calculates  the other  positions  f o r the space  group  to ) {create  f o r k:=l begin  the complete  25th unit  cell}  t o 4 do  XH[25,k,i]:=l+XH[l,k,i} ; YH[25,k,i]:=YH[l,k,i]; ZH[25,k,i]:=ZH[l,k,i]-l; end; for  i:=l  P212121,  to nhidr  do  {Calculates  the other  positions  f o r the space  to } (create the complete  f o r k:=l begin  t o 4 do  26th u n i t  cell}  group  304  XH[2 6 , k , i ] : = l + X H [ l , k , i ] ; YH[26,k,i]:=YH[l,k,i]-l; ZH[26,k,i]:=ZH[l,k,i]-l;  end; for  i:=l  P212121,  to nhidr  to  do  { C a l c u l a t e s the other p o s i t i o n s  the space  group  } {create  f o r k:=l begin  for  to  the complete 27th u n i t  cell}  4 do  XH[27,k,i]:=l+XH[l,k,i]; YH[27,k,i]:=l+YH[l,k,i]; ZH[27,k,i]:=ZH[l,k,i]-l; end ;  end ; p r o c e d u r e  S M i n t e r s t a t i c ;  {calculate intermolecular  static  s e c o n d moments}  var rHH,vx,vy,vz:real; vSimjx,vSimjy,vSimjz,vSix,vSiy,vSiz:real; dist,r:real; DCtHH, s u d i s h : R E A L ; H:array[1..nhidr,1..nhidr]  of  real;  begin assign(output,'smhetaro.txt'); rewrite(output) ; f o r j:=1 BEGIN  t o NSI do  smtstl:=0; f o r 1:=1 f o r k:=l for i:=l begin  t o 27 d o t o 4 do t o NHIDR d o  vx:=(XSi[j]-XH[1,k,i])* a; {calcule distances vy:=(YSi[j]-YH[l,k,i])*b; vz:=(ZSi[j]-ZH[l,k,i])*c; rHH:=sqrt(sgr(vx)+sqr(vy)+sqr(vz)) ; r:=sqrt(sqr(vx/a)+sqr(vy/b)+sqr(vz/c)); i f rHH<8 t h e n begin write(' writeln;  Si  ',j, ' H ' , i , '  ' , X S i [ j ] : 6:4, '  b e t w e e n S i a n d H}  ' , Y S i [ j ] :6 : 4 , '  •,ZSi[j]:6:4);  write(output,  'Si' , j , '  -  1  . ' H ' . i , '  :  ',XSi[j] : 6 : 4 , '  ',YSi[j]:6:4,  '  ' , Z S i [ j ] :6:4) ; writeln(output, ','  ' , X H [ 1 , k , i ) : 6 : 4, •  '  R Ang S i - H : ' ,  ' , Y H [ 1 , k , i ] :6 : 4 , '  1  ,ZH[1,k,i] :6:4, '  rHH:4:3);  sudish:=1/(rhh*rhh*rhh); smtstl:=sqr(sudish)+smtstl; DCtHHHZ:=23881.78012*sudish;  {DIPOLAR COUPLING  inherzt  garamaH*gamrnaHi ( h / 4 p i ^ 2 * u o / 4 p i ) { writeln(output,'  R Si-H: ',rhh:6:4,'  DSi-H(Hz):','  ',DCtHHHz:6:4);  end; end ; s t a t i c r a d : = (smtstl)*4.5032903&9 ; staticHz:=( s m t s t l ) * 1 1 4 . 0 6 9 6 7 5e6; staticgauss:=(smtstl)*159.19; writeln(output, sumatory 1  writeln(output,'static  of  l/r~6  for S i ' , j , '  =  ',  DCtHH:6:4);  internuclear  total  s e c o n d moment o f S i * , j , ' ( r a d 2 H z 2 )  internuclear  total  s e c o n d moment  internuclear  total  s e c o n d moment o f  ' ,staticrad:6:4); writeln(output,'static  of S i ' , j , ' ( H z 2 )  =  ',staticHz:6:4); writeln(output,'static ' ,staticgauss:6:4) ; end; close(output); E N D ;  begin findcoor; SMintrastatic ; end.  Si',j,'(gauss2)  306  APENDIX 2. Program to Calculate Internuclear Si-H Second Moments for Methyl Hydrogens Rotating about their C axis in the System of Orthorhombic ZSM-5 High Loaded with p-Xylene Space Group P2i2i2i. 3  p r o g r a m  a e c o n d n o m e n t c a l ;  MOTION} uses w i n C r t ;  {INTERMOLECULAR SECOND MOMENT S i - H FOR {FOR PXYLENE HIGH LOADING ORTHORHOMBIC,  CH3 WITH P212121}  const nhidr=6; nsi=24; a=20.122; b=19.82; c=13.438;  var smtotal:real ; secondrad,secondhz,secondgauss,secondstaticHz:real; smstatic,sudis:real ; j,k,n,m:integer ; dist:real ; x s i l , y s i l , z s i l : a r r a y [ 1 . . n s i ] of r e a l ; xh,yh,zh : a r r a y [ 1 . . 2 7 , 1 . . 4 , 1 . . n h i d r ] of r e a l ; x S i , y S i , z S i :array[1..nSi] of r e a l ; output:text; s m l : a r r a y [ 1 . . n h i d r , 1 . .4,1. . 27] of r e a l ; s m 2 : a r r a y [ 1 . . n h i d r , 1 . . 4 , 1 . . 2 7 ] of r e a l ; s m 3 : a r r a y [ 1 . . n h i d r , 1 . . 4 , 1 . . 2 7 ] of r e a l ; s m 4 : a r r a y [ 1 . . n h i d r , 1 . . 4 , 1 . . 2 7 ] of r e a l ; s m 5 : a r r a y [ 1 . . n h i d r , 1 . . 4 , 1 . . 2 7 ] of r e a l ,• ml, m2 , m3 , m4 , m5 : r e a l ; soprom2,soprom:array[1..nsi] of r e a l ; {array of second moment average f every S i , to the 4 CH3 groups} smsta2,smstal:array[1..nsi] of r e a l ; PROCEDURE  PINDCOOR;  var input:text ; xl,yl,zl: real; begin  { X Y Z C H 3 1 . t x t , f i l e w i t h t h e f i r s t 6 h y d r o g e n a t o m s CH3 h i g h l o a d i n g } { X Y Z C H 3 2 . t x t , f i l e w i t h t h e s e c o n d 6 h y d r o g e n a t o m s CH3 h i g h l o a d i n g }  assign(input,'XYZCh31.txt'); {the h y d r o g e n s ,  { f i l e w i t h t h e atoms c o o r d e n a t e s , must he t h e n t h e s i l i c o n c o o r d i n a t e s , x y z}  first}  reset(input); for  i:=l  t o n h i d r do {P212121,  {Calculates the other p o s i t i o n s f o r to create the complete u n i t c e l l }  t h e s p a c e group}  307  begin  k:=l; read(input,XI);  XH[l,k,i]:=xl; read(input,Yl); YH [ 1 , k , i ]  :=yl;  readln(input,zl); ZH[l,k,i]:=zl;  inc(k); XH[l,k,i]:=0.5+xl; YH[l,k,i]:=0.5-yl; ZH[l,k,i]:=-zl; inc(k); XH[l,k,i]:=0.5-xl; YH[l,k,i]:=-yl; ZH[l,k,i]:=0.5+zl; inc(k); XH[l,k,i):=-xl; YH[l,k,i):=0.5+yl; ZH[l,k,i]:=0.5-zl; writeln('H',1,k,i, ',ZH[l,k,i):6:4); end; for i:=l  t o n s i do  begin k:=l; read(input,xl); XSi[i]:=xl; read(input,yl); YSi[i]:=yl; readln(input,zl) ; ZSi[i]:=zl; end; close(input);  '  ' , X H [ l , k , i ] :6 : 4 , '  ' , Y H [ l , k , i ] :6:4, '  308  for i : = l to nhidr do {Calculates the other positions for the space group P212121, to create the complete 2nd unit cell} for k:=l to 4 do begin  XH[2,k,i]:=XH[l,k,i]-l; YH[2,k,i]:=YH[l,k.i]-1; ZH[2,k,i]:=ZH[l,k,i];  end ;  for i : = l to nhidr do {Calculates the other positions for the space group P212121, to create the complete 3th unit c e l l ) for k:=l to 4 do begin XH[3,k,i]:=XH[l,k,i)-l; YH[3,k,i]:=YH[l,k,i]; ZH[3,k,i]:=ZH[l,k,i]; end;  for i : = l to nhidr do {Calculates the other positions for the space group to create the complete 4th unit cell}  P212121,  for k:=l to 4 do begin  XH[4,k,i]:=XH[l,k,i)-l;  309  YH[4,k,i]:=l+YH[l,k,i]; Z H [ 4 , k , i ] : = Z H [ l , k , i] ;  end;  for i : = l to nhidr do P212121, to }  {Calculates the other positions for the space; group {create the complete 5 t h unit cell}  for k:=l to 4 do begin XH[5,k,i]:=XH[l,k,i]; YH[5,k,i]:=YH[l,k,i]-l; ZH[5,k,i]:=ZH[l,k,i); end ; for i : = l to nhidr do P212121,  to  {Calculates the other positions for the space group  }  {create the complete 6 t h unit c e l l } for k:=l to 4 do begin XH[6,k,i]:=XH[l,k,i]; YH[6,k,i]:=l+YH[l,k,i}; ZH[6,k,i]:=ZH[l,k,i]; end; for i : = l to nhidr do {Calculates the other positions for the space group to create the complete 7 t h unit cell} for k:=l to 4 do begin  P212121,  XH[7,k,i]:=l+XH[l,k,i]; YH[7,k,i]:=YH[l,k,i]; ZH[7,k,i]:=ZH[l,k,i] ; end; for i : = l to nhidr do {Calculates the other positions for the space group to create the complete 8 t h unit cell} for k:=l to 4 do begin  P212121,  XH[8,k,i]:=l+XH[l,k,i]; YH[8,k,i]:=YH[l,k,i]-l; ZH[8,k,i]:=ZH[l,k,i] ; end; for i : = l to nhidr do {Calculates the other positions for the space group P 2 1 2 1 2 1 , t o create the complete 9 t h unit cell}  310  f o r k:=l t o 4 do begin XH[9,k,i]:=l+XH[l,k,i]; YH[9,k,i]:=l+YH[l,k,i]; ZH[9,k,i]:=ZH[l,k,i]; end; f o r i : = l t o n h i d r do {Calculates the other p o s i t i o n s P212121, t o c r e a t e the complete 10th u n i t c e l l } f o r k:=l t o 4 do begin  f o r the space  group  f o r the space  group  f o r the space  group  XH[10,k,i]:=XH[l,k,i] ; YH[10,k,i]:=YH[l,k,i]; ZH[10,k,i):=l+ZH[l,k,i]; end; f o r i : = l t o n h i d r do {Calculates the other p o s i t i o n s P212121, t o c r e a t e t h e complete 1 1 t h u n i t c e l l } f o r k:=l t o 4 do begin XH[ll,k,i]:=XH[l,k,i]-l; YH[ll,k,i]:=YH[l,k,i]-l; ZH[ll,k,i]:=l+ZH[l,k,i]; end ; f o r i : = l t o n h i d r do {Calculates the other p o s i t i o n s P212121, t o c r e a t e t h e c o m p l e t e 1 2 t h u n i t c e l l } f o r k : = l t o 4 do begin XH[12,k,i]:=XH[l,k,i]-l; YH[12,k,i]:=YH[l,k,i]; ZH[12,k,i]:=l+ZH[l,k,i}; end ; for  i:=l  P212121,  to nhidr  do  {Calculates  positions  f o r t h e space group  to } {create  for  the other  k:=l  to  4 do  begin XH[13,k,i]:=XH[l,k,i)-l; YH[13,k,i]:=l+YH[l,k,i] ; ZH[13,k,i]:=l+ZH[l,k,i] ; end; i n c (1) ;  the complete  13th u n i t  cell}  311  for i : = l to nhidr do {Calculates the other positions for the space group P212121, to create the complete 14th unit c e l l ) for k:=l to 4 do begin  XH[14,k,i] :=XH[l,k,i] ; YH[14,k,i):=YH[l,k,i]-l; ZH[14,k,i] :=l + Z H [ l , k , i ] ; end; for i : = l to nhidr do {Calculates the other positions for the space group P212121, to create the complete 15th unit cell} for k:=l to 4 do begin XH[15,k,i]:=XH[l,k,i); YH[15,k,i]:=l+YH[l,k,i); ZH[15,k,i]:=l+ZH[l,k,i]; end; for i : = l to nhidr do {Calculates the other positions for the space group P212121, to create the complete 16th unit cell} for k:=l to 4 do begin XH[16,k,i]:=l+XH[l,k,i]; YH[16,k,i] :=YH[l,k,i] ; ZH[16,k,i]:=l+ZH[l,k,i); end; for i : = l to nhidr do {Calculates the other positions for the space group P212121, to create the complete 17th unit cell} for k:=l to 4 do begin XH[17,k,i]:=l+XH[l,k,i]; YH[17,k,i]:=YH[l,k,i]-l; ZH[17,k,i):=l+ZH[l,k,i]; end; for i : = l to nhidr do {Calculates the other positions for the space group P212121, to create the complete 18th unit cell} for k:=l to 4 do begin  312  XH[18,k,i]:=l+XH[l,k,i]; YH[18,k,i]:=l+YH[l,k,i]; ZH[18,k,i]:=l+ZH[l,k,i]; end; for i : = l to nhidr do {Calculates the other positions for the space group P212121, to create the complete 19th unit cell} for k:=l to 4 do begin  XH[19,k,i):=XH[l,k,i]; YH[19,k,i] :=YH[l,k,i] ; ZH[19,k, i ] : = Z H [ l , k , i ] ~ l ; end ; for i : = l to nhidr do {Calculates the other positions for the space group P212121, to create the complete 20th unit cell} for k:=l to 4 do begin  XH[20,k,i]:=XH[l,k,i]-l; YH[20,k,i]:=YH[l,k,i]-l; ZH[20,k,i]:=ZH[l,k,i]-l; end ; for i : = l to nhidr do {Calculates the other positions for the space group P212121, to create the complete 21th unit cell} for k:=l to 4 do begin  XH[21,k,i]:=XH[l,k,i]-l; YH[21,k,i]:=YH[l,k,i]; ZH[21,k,i]:=ZH[l,k,i]-l; end;  313  for i:=l P212121, t o  for  k:=l  t o n h i d r do {Calculates the c r e a t e the complete 22th u n i t  to  other p o s i t i o n s for cell}  the  space group  other positions for cell}  the  space group  other p o s i t i o n s for cell}  the  space group  the  other  the  space group  complete 25th u n i t  cell}  4 do  begin  XH[22,k,i]:=XH[l,k,i]-l; YH[22,k,i]:=l+YH[l,k,i]; ZH[22,k,i] :=ZH[l,k,i]-l; end; for i:=l P212121, t o  for  k:=l  t o n h i d r do {Calculates the c r e a t e the complete 23th u n i t  to  4 do  begin  XH[23,k,i]:=XH[l,k,i]; YH[23,k i]:=YH[l,k,i]-l; ZH[23,k,i]:=ZH[1,k,i]-1; end ; (  for i:=l P212121, t o  for  k:=l  t o n h i d r do { C a l c u l a t e s the c r e a t e the complete 24th u n i t  to  4 do  begin  XH[24,k,i]:=XH[l,k,i]; YH[24,k,i]:=l+YH[l,k,i]; ZH[24,k,i]:=ZH[l,k,i]-l; end; for  i:=1  P212121,  for  to  k:=l  begin  to  nhidr  create  to  4 do  do  the  {Calculates  positions for  314  XH[25,k,i]:=l+XH[l,k,i]; YH[2 5,k,i} :=YH[1,k,i] ; ZH[25,k,i]:=ZH[l,k,i]-l; end; for i : = l to nhidr do {Calculates the other positions for the space group P212121, to create the complete 26th unit c e l l ) for k:=l to 4 do begin  XH[26,k,i] :=l+XH[l,k,i] ; YH[26,k,i]:=YH[l,k,i]-l; ZH[26,k,i]:=ZH[l,k,i]-l; end; for i : = l to nhidr do {Calculates the other positions for the space group P212121, to create the complete 27th unit c e l l ) for k:=l to 4 do begin  XH[27,k,i] =l+XH[l,k,i]; YH[27,k,i) = l + Y H [ l , k , i ] ; ZH[27,k,i] = Z H [ l , k , i ] - l ; end; end; PROCEDURE  DISTANCES;  var theta,phi:real; r,vx,vy,vz:real; begin assign(output,'smavech3.sm'); rewrite(output); for j:=1 to n s i do begin  315  f o r 1:=1 t o 27 d o f o r k : = l t o 4 do f o r i : = l t o 6 do begin sml[i,k,1]:=0; s m 2 [ i , k , 1 ] : =0; sm3[i,k,1]:=0; sm4[i,k l]:=0; sm5[i,k,1]:=0; end; ml = 0 m2 = 0 m3 = 0 m4 = 0 m5 = 0 soprom[j]:=0; soprom2[j]:=0; (  {**lst  methyl group a v e r a g i n g * * )  f o r 1:=1 t o 27 d o f o r k : = l t o 4 do f o r i : = l t o 6 do begin vx:=(XSi[j]-XH[l,k,i])*a; vy:=(YSi[j]-YH[l,k,i])*b; vz:=(ZSi[j]-ZH[l,k,i])*c; r:= s q r t ( s q r ( v x ) + s q r ( v y ) + s q r ( v z ) ) ; i f r<8 t h e n begin write('Si',j,' ','H',1,k,i,' '); w r i t e l n ( X H [ l , k , i ] :6:4, ' ' , Y H [ 1, k , i ] : 6 : 4 , ' write(output,'Si', j ,'  -  ','H',l,k,i,'  :  ' , Z H [ 1 , k , i ] : 6 : 4, ' ',Xsi[j]:6:4,'  r:4:3);  ',Ysi[j):6:4,'  ',Zsi[j]:6:4); writeln(output,'  ',XH[1,k,i]:6:4,'  ',YH[1,k,i]:6:4,'  ' , r : 4:3 ) ; theta:=arctan(sqrt(1-sqr(vz/r))/(vz/r)); phi:=arctan(vy/vx); sml[i,k,l]:=1/(r*r*r)*((1/2)*(3*sqr(cos(theta))-l)); sm2[i,k,l]:=1/(r*r*r)*(3*cos(theta)*sin(theta)*cos(phi)); s m 3 [ i , k , l ] - . = 1 / ( r * r * r ) * (3*cos ( t h e t a ) * s i n ( t h e t a ) * s i n ( p h i ) ) ; sm4[i.k.l]:=1/(r*r*r)*(3*sqr(sin(theta))*cos(2*phi)); sm5[i,k,1]:=1/(r*r*r)*(3*sqr(sin(theta))*sin(2*phi)); sudis:=1/(r*r*r); smstal[j]:=smstal[j]+sqr(sudis) end; end;  {averaging) f o r 1:=1 t o 27 d o  ',ZH[1,k,i]:6:4,'  316  f o r k:=l begin  to  4 do  ml:=sqr((smlll,k,l)+ sml[4,k,l]+  sml[2,k,l]  sml[5,k,1])/3)  m2:=sqr((sm2[1,k,1]+  sm2[2,k,l]  sm2[ 4 , k, 1 ] + s m l [ 5 , k , 1 ] ) / 3 ) m3:=sqr((sm3[l,k,l]+ sm3[4,k,1]+  sml[5,k,1])/3)  sm4[4,k,l]+  m5:=sqr((sm5[l,k,lj+  sm2[3,k,1])/3)+sqr((sm2[6,k,1]+  +  sm3[3,k,1])/3)+sqr({sm3[6,k,1]+  +  sm4[3,k,1])/3)+sqr((sm4[6,k,1]+  +  sm5[3.k,1])/3)+sqr((sm5[6.k,1]+  ; sm5[2.k.l]  sml[5,k,1])/3)  soprom[j]:=soprom[j]  +  ; sm4[2,k,l]  sml[5,k,1])/3)  sm5[4,k,l]+  sml[3,k,1])/3)+sqr({sml[6,k,1]+  ; sm3[2,k,l]  m4:=sqr((sm4[l,k,l]+  +  ;  ; + ml+(1/3)*(m2+m3)+  (1/12)*(m4+m5);  end ; {to  have  the t o t a l  s e c o n d moment i n r a d 2 H z 2 , m u l t i p l y f o r  5.6291128e9,  which  is sqr((gamma)H*(gamma)Si*h/2pi*Uo/4pi)  *1/  3 *  3/4  (1/3*1(1+1)(heteronuclear  sm) ) writeln(output); writeln(output) ; end; end ; PROCEDURE  FINDCOOR2;  var input:text; xl,yl,zl: real; begin  {XYZCH31.txt,  file  with  the  first  6 h y d r o g e n a t o m s CH3  highloading) {XYZCh32.txt,  file  w i t h t h e s e c o n d 6 h y d r o g e n a t o m s ch3  highloading) assign(input,'XYZCh32.txt'); hydrogen,  {file  w i t h t h e atoms c o o r d e n a t e s ,  must be  first  then) {silicon coordinates,  x y  z}  reset(input); for  i:=l  P212121,  to nhidr to  do  }  begin k:=l; read(input,XI); XH[l,k,i]:=xl; read(input,Yl) ; YH[l,k,i]:=yl; readln(input,zl)  {Calculates the other p o s i t i o n s {create  the complete u n i t  cell)  for  the space  group  317  ZH[l,k,i]:=zl; inc(k) ; XH[l,k,i):=0.5+xl; YH[l,k,i]:=0.5-yl; ZH[l,k,i]:=-zl; inc(k) ; XH[l,k,i]:=0.5-xl; YH[l,k,i]:=-yl; ZH[l,k,iJ :=0.5+zl; inc(k); XH[l,k,i]:=-xl; YH[l,k,i]:=0.5+yl; ZH[l,k,i]:=0.5-zl; writeln('H',1,k,i, ' ' , Z H [ 1 , k , i ] :6:4) ;  ',XH[1,k,i]:6:4, '  ',YH[l,k,i] :6:4, '  end ; for i : =1 to n s i do begin k:=l; read(input,xl); XSi [i] :=xl; read(input,yl); YSi[i]:=yl; readln(input,zl); ZSi [i] :=zl; end; close(input); f o r i : = l t o n h i d r do {Calculates the other P212121, t o c r e a t e t h e c o m p l e t e 2nd u n i t cell) f o r k : = l t o 4 do begin  p o s i t i o n s f o r the space  group  p o s i t i o n s f o r the space  group  XH[2,k,i]:=XH[l,k,i]-1; YH[2,k,i]:=YH[l,k,i]-l; ZH[2,k,i]:=ZH[l,k,i]; end; f o r i : = l t o n h i d r do {Calculates the other P212121, t o c r e a t e t h e complete 3 t h u n i t cell) f o r k : = l t o 4 do begin  XH[3,k,i] =XH[l,k,i]-1; YH[3,k,i] =YH[l,k,i]; ZH[3,k,i] =ZH[l,k,i];  318  end; for i:=l P212121, t o f o r k:=l begin  t o n h i d r do { C a l c u l a t e s the other c r e a t e the complete 4th u n i t cell) t o 4 do  positions for  the  space  group  t o n h i d r do {Calculates the other p o s i t i o n s f o r c r e a t e the complete 5th u n i t c e l l } t o 4 do  the  space  group  the  space  group  positions for  the  space group  t o n h i d r do { C a l c u l a t e s the other p o s i t i o n s f o r c r e a t e the complete 8th u n i t c e l l } t o 4 do  the  space  XH[4,k,i]:=XH[l,k,i]-l; YH[4,k,i]:=l+YH[l,k,i]; ZH[4,k,i]:=ZH[l,k,i]; end; for i:=l P212121, t o f o r k:=l begin  X H [ 5 , k , i ] : = X H [ 1, k, i ] ; YH[5,k,i):=YH[l,k,i)-l; ZH[5,k,i]:=ZH[l,k,i]; end; for i:=l P212121, t o f o r k:=l begin  t o n h i d r do { C a l c u l a t e s the o t h e r p o s i t i o n s f o r c r e a t e the complete 6th u n i t c e l l } t o 4 do  XH[6,k,i]:=XH[1,k,i]; YH[6,k,i]:=l+YH[l,k,i]; ZH[6,k,i] :=ZH[l,k, i] ; end;  for  i:=l  P212121, t o f o r k:=l begin  t o n h i d r do {Calculates the other c r e a t e the complete 7th u n i t c e l l ) t o 4 do  XH[7,k,i]:=l+XH[l.k,i); YH[7,k.i]:=YH[l,k,i]; ZH[7,k,i]:=ZH[l,k,i]; end;  for i:=l P212121, t o f o r k:=l begin  group  319  XH[8,k,i]:=l+XH[l,k,i); YH[8,k,i]:=YH[l,k,i]-l; ZH[8,k,i]:=ZH[l,k,i]; end; f o r i : = l t o n h i d r do {Calculates the other P212121, t o c r e a t e t h e c o m p l e t e 9 t h u n i t c e l l ) f o r k : = l t o 4 do begin  p o s i t i o n s f o r the space  group  f o r i : = l t o n h i d r do {Calculates the other p o s i t i o n s f o r the space P212121, t o c r e a t e t h e c o m p l e t e 1 0 t h u n i t c e l l ) f o r k : = l t o 4 do begin  group  XH[9,k,i]:=l+XH[l,k,i] ; YH[9,k,i]:=l+YH[l.k,i] ZH[9,k,i]:=ZH[l,k,i]; ;  end;  n  XH[10,k,i]:=XH[l,k,i]; YH[10,k,i]:=YH[1,k,i]; ZH[10,k,i]:=l+ZH[l,k,i]; end; f o r i : = l t o n h i d r do {Calculates the other p o s i t i o n s f o r the space P212121, t o c r e a t e t h e c o m p l e t e 1 1 t h u n i t c e l l ) f o r k : = l t o 4 do begin  group  XH[ll,k,i]:=XH[l,k,i]-l; YH[ll,k,i]:=YH[l,k,i]-l; ZH[ll,k,i]:=l+ZH[l,k,i]; end; f o r i : = l t o n h i d r do {Calculates the other p o s i t i o n s f o r the space P212121, t o c r e a t e t h e c o m p l e t e 1 2 t h u n i t c e l l ) f o r k : = l t o 4 do begin  group  XH[12,k.i]:=XH[l,k,i]-l; YH[12,k,i]:=YH[l,k,i]; ZH[12,k,i]:=l+ZH[l,k,i]; end; f o r i : = l t o n h i d r do {Calculates the other p o s i t i o n s f o r the space P212121, t o c r e a t e t h e c o m p l e t e 1 3 t h u n i t c e l l ) f o r k : = l t o 4 do  group  320  begin  XH[13,k,i]:=XH[l,k,i)-l; YH[13,k,i]:=l+YH[l,k,i]; ZH[13,k,i]:=l+ZH[l,k,i]; end inc(l); for i:=l t o n h i d r do { C a l c u l a t e s the P212121, t o c r e a t e the c o m p l e t e 14th u n i t f o r k : = l t o 4 do begin  other positions for cell)  the  space  group  other p o s i t i o n s for cell)  the  space  group  other p o s i t i o n s for cell)  the  space  group  positions for  the  space  group  positions for  the  space  group  XH[14,k,i]:=XH[l,k,i]; YH[14,k,i]:=YH[l,k,i)-l; ZH[14,k,i]:=l+ZH[l,k,i); end; for i:=l P212121, t o f o r k:=l begin  t o n h i d r do { C a l c u l a t e s the c r e a t e the complete 15th u n i t t o 4 do  XH[15,k,i]:=XH[l,k,i); YH[15,k,i]:=l+YH[l,k,i]; ZH[15,k,i]:=l +Z H [ l , k , i ] ; end; for i:=l P212121, t o f o r k:=l begin  t o n h i d r do {Calculates the c r e a t e the complete 16th u n i t t o 4 do  XH[16,k,i]:=l+XH[l,k,i]; YH[16,k,i]:=YH[l,k,i] ; ZH[16,k,i]:=l+ZH[l,k,i]; end;  for  i:=l  P212121, for  to  k:=l  to nhidr create to  do  the  {Calculates complete 17th  the  other  unit  cell)  the  other  unit  cell)  4 do  begin  XH[17,k.i]:=l+XH[l,k,i]; YH[17,k,i]:=YH[l,k,i]-l; ZH[17,k,i]:=l+ZH[l,k,i]; end; for  i:=l  P212121,  to  to  nhidr  create  do  the  {Calculates complete 18th  321  f o r k:=l begin  to  4 do  XH[18,k,i):=l+XH[l,k,i]; YH[18,k,i]:=l+YH[l,k,i]; ZH[18,k,i]:=l+ZH[l,k,i]; end ; for i:=l t o n h i d r do {Calculates the other P212121, t o c r e a t e t h e c o m p l e t e ' 1 9 t h u n i t c e l l } f o r k : = l t o 4 do begin  positions  f o r the space  group  XH[19,k,i]:=XH[l,k,i]; YH[19,k,i]:=YH[l.k,i]; ZH[19,k,i]:=ZH[l,k,i]-l; end ; for i:=l P212121, t o for k:=l begin  t o n h i d r do { C a l c u l a t e s the other p o s i t i o n s c r e a t e the complete 20th u n i t c e l l } t o 4 do  for  the space  group  for  the space  group  for  the space  group  XH[20,k,i]:=XH[l,k,i]-l; YH[20,k,i]:=YH[l,k,i]-l; ZH[20,k,i]:=ZH[l,k,i}-l; end; f o r i:=1 t o n h i d r do {Calculates the other p o s i t i o n s P212121, t o c r e a t e t h e c o m p l e t e 2 1 t h u n i t c e l l } f o r k:=1 t o 4 d o begin  XH[21,k,i]:=XH[l,k,i]-1; YH[21,k,i]:=YH[l,k,i]; ZH[21,k,i]:=ZH[l,k,i]-l; end ; for  i:=l  P212121, for  to  k:=l  to nhidr  do  {Calculates the other p o s i t i o n s  c r e a t e the complete 22th u n i t to  4 do  begin  XH[22,k,i]:=XH[l,k,i]-l; YH[22,k,i]:=l+YH[l,k,i]; ZH[22,k,i]:=ZH[l,k,i]-l; end;  cell}  322  f o r i : = l t o n h i d r do {Calculates the other p o s i t i o n s f o r the space P212121, t o c r e a t e t h e c o m p l e t e 2 3 t h u n i t c e l l ) f o r k : = l t o 4 do begin  group  XH[23,k,i]:=XH[l,k,i]; YH[23,k,i]:=YH[l,k,i)-l; ZH[23,k,i]:=ZH[l,k,i]-l; end; f o r i : = l t o n h i d r do {Calculates the other p o s i t i o n s f o r the space P212121, t o c r e a t e t h e c o m p l e t e 2 4 t h u n i t c e l l ) f o r k:=l t o 4 do begin  group  XH[24,k,i]:=XH[l,k,i] ; YH[24,k,i]:=l+YH[l,k,i]; ZH[24,k,i]:=ZH[l,k,i]-l; end; f o r i : = l t o n h i d r do {Calculates the other p o s i t i o n s f o r the space P212121, t o c r e a t e t h e c o m p l e t e 2 5 t h u n i t c e l l ) f o r k : = l t o 4 do begin  group  XH[25,k,i]:=l+XH[l,k,i]; YH[2 5 , k , i ] : = Y H 1 1 , k , i ] ; ZH[25,k,i]:=ZH[l,k,i]-l; end; f o r i : = l t o n h i d r do {Calculates the other p o s i t i o n s f o r t h e space P212121, t o c r e a t e t h e c o m p l e t e 26th u n i t c e l l ) f o r k : = l t o 4 do begin  group  XH[26,k,i]:=l+XH[l,k,i]; YH[26,k,i]:=YH[l,k,i]-l; ZH[26,k,i]:=ZH[l,k,i]-l; end; for  i:=l  P212121, for  to nhidr  to create  k:=l  do  t o 4 do  begin  XH[27,k,i]:=l+XH[l,k,i]; Y H [ 2 7 , k , i ] : = l + Y H [ l , k , i} ; ZH[27,k,i]:=ZH[l,k,i]-l; end;  {Calculates  the other p o s i t i o n s f o r the space group  the complete 27th u n i t  cell}  323  end; PROCEDURE DISTANCES2;  var theta,phi:real; r,vx,vy,vz:real; begin for j:=l to n s i do begin for 1:=1 to 27 do for k:=l to 4 do for i : = l to 6 do begin sml[i,k,1]:=0; sm2[i,k,1]:=0; sm3[i,k,1]:=0; sm4[i,k,1]:=0; sm5[i,k,1]:=0; end; ml:=0; m2:=0; m3:=0; m4:=0; m5:=0; {**lst methyl group  averaging**}  for 1 =1 to 27 do for k =1 to 4 do for i =1 to 6 do begin vx: = ( X S i [ j ] - X H [ 1 , k , i ] ) * a; vy:=(YSi[j]-YH[l,k,i])*b; vz: = ( Z S i [ j ] - Z H [ l , k , i ] )*c; r:=sqrt(sqr(vx)+sqr(vy)+sqr(vz) i f r<8 then begin write ('Si', j , • - \ ' H M , k , i , ' • ) ; w r i t e l n ( X H [ l , k , i ] :6:4, ' ',YH[1,k,i] :6 : 4,  1  write(output,'Si',j,'  ',Zsi[j]:6:4);  -  ','H',1,k,i,'  :  1  ,ZH[1,k,i] :6:4, '  r:4:3);  ',Xsi[j]:6:4,' ',Ysi[j]:6:4,'  writeln(output, ' ',XH[1,k,i] :6: 4, ' ',YH[1,k,i] :6:4, ' ', ZH[1,k,i] :6:4, ' ', r:4:3); theta:=arctan(sqrt(1-sqr(vz/r))/(vz/r)); phi:=arctan(vy/vx); sml[i,k,1]:=1/(r*r*r)*((1/2)*(3*sqr(cos(theta))-1)); sm2[i,k,1]:=1/(r*r*r)*(3*cos(theta)*sin(theta)*cos(phi));  sm3[i,k,l]:=1/(r*r*r)*(3*cos(theta)*sin(theta)*sin(phi)); sm4[i,k,1]:=1/(r*r*r)*(3*sqr(sin(theta))*cos(2*phi)); sm5[i,k,1]:=1/(r*r*r)*(3*sqr(sin(theta))*sin(2*phi)); sudis:=l/(r*r*r); smsta2[j]:=smstal[j]+sqr(sudis) end; end;  for 1:=1 to 27 do for k:=l to 4 do begin ml:=sqr((sml[1,k,1]+ sml[2,k,l] sml[4,k,l]+ sml [5, k, 1] )/3) ; m2:=sqr((sm2[1,k,1]+ sm2[2,k,l] sm2[4,k,l]+ sml [5, k, 1] )/3) ; m3:=sqr((sm3[1,k,1]+ sm3[2,k,l] sm3[4,k,l]+ sml[5,k,1])/3) ; m4:=sqr((sm4[1,k,1]+ sm4[2,k,l] sm4[4,k,l]+ sml[5,k,1])/3) ; m5:=sqr((sm5[1,k,1]+ sm5[2,k,l] sm5[4,k,l]+ sml [5, k, 1] )/3) ;  + sml[3,k,1])/3)+sqr((sml[6,k, 1] + + sm2[3, k, 1] )/3)+sqr((sm2[6,k,1]+ + sm3[3,k,1])/3)+sqr((sm3[6, k, 1] + + sm4[3,k,1])/3)+sqr((sm4[6, k,1] + + sm5[3,k,1])/3)+sqr((sm5[6, k, 1] +  soprom2[j]:=soprom2[j] +ml+(l/3) (m2+m3) +(1/12)*(m4+m5); end;  smtotal:= soprom[j]+soprom2[j] ; smstatic:=smsta2[j]+smstal[j]; {to have the t o t a l second moment i n rad2Hz2, m u l t i p l y f o r 5.6291128e9, which is sqr((gamma)H*(gamma)Si*h/2pi*Uo/4pi) * (1/3*S (S+l) (heteronuclear sm) } secondrad:=(smtotal)*4.503298e9; secondHz:=(smtotal)*114.06967e6; secondgauss: = (smtotal)* 159.19; secondstaticHz:=(smstatic)*114.06967e6; writeln(output, 'motion internuclear t o t a l ',secondrad:4:6); writeln(output,'motion internuclear t o t a l ',secondHz:4:6); writeln(output,'motion internuclear t o t a l ' , secondgauss:4:6); w r i t e l n ( o u t p u t , ' s t a t i c internuclear t o t a l ',secondstaticHz:4:6); writeln(output); end; close(output) end; begin findcoor; distances;  second moment of S i ' , j , ' (rad2Hz2) second moment of Si',j,'(Hz2)  =  second moment of Si',j,'(gauss2) second moment of Si',j,'(Hz2)  =  2  findcoor2; distances2; end.  325  326  APENDIX 3. Program to Rotate and Translate the p-Xylene and Calculate Internuclear Si-H Second Moments for the Aromatic and Methyl Hydrogens in the System of Orthorhombic ZSM-5 Low Loaded with p-Xylene Space Group Pnma. program pxylene; uses w i n C r t ;  {INTRAMOLECULAR SECOND MOMENTS S i - H FOR P - X Y L E N E HYDROGENS) {ROTATES AND TRANSLATES THE MOLECULE TO D I F F E R E N T POSITIONS) { FOR PXYLENE LOW LOADING ORTHORHOMBIC Pnma) { I N T I T I A L P - X Y L E N E POSITIONS IS IN MIRROR PLANE)  mirror plane) const nhidr=6; nsi=6; a=20.022; b=19.899; c=13.383 ; TYPE vec = ARRAY[1..3]' of r e a l ; A S C I I _ F i l e = TEXT; a t o m _ c o o r d = .RECORD x_pos, y _ p o s , z_pos : r e a l ; END; {of RECORD a t o m _ c o o r d ) var movex,movey,movez,X,Y,Z:real; varx,vary,varz:integer,• l,i,j,k,n,m,h:integer; dist:real; smtstl,SMtl,smtst2,SMt2:real ; x h , y h , z h : a r r a y [ 1 . . 2 7 , 1 . . 8 , 1 . . n h i d r ] of r e a l ; x i n , y i n , z i n : a r r a y [ 1 . . n h i d r ] of r e a l ; { i n i t i a l x a t , y a t , z a t : a r r a y [ 1 . . n h i d r ] of r e a l ; x S i , y S i , z S i : a r r a y [ 1 . . n S i ] of r e a l ; S M : a r r a y [ l . . 6 , 1 . . 2 ] of r e a l ; i n T c p : a r r a y [ 1 . . 6 , 1 . . 2 ] of r e a l ;  coordinates  of  H from  output:text; FileNamel, FileName2: s t r i n g ; {for i n p u t and o u t p u t ) Titlel, title2 : string; InFile, OutFile,0utFile2 : ASCII_File; { Disk f i l e s ) cutcorr,cutoff:real; {maximum i n t e r a t o m i c d i s t a n c e t o c o n s i d e r calculations} degree_x,degree_y,degree_z,rot_x,rot_y,rot_z :integer; S l o p e , I n t e r c e p t , C o r r C o e f f : REAL; Slopech3, Interceptch3,CorrCoeffch3 : REAL;  in  p-xylene)  the  procedure presentation; begin { MAIN BODY ) { OPEN A S C I I f i l e  (with  .dmc e x t e n s i o n )  writeln('  containing  crystal  data  )  smarlo2m.PAS');  writeln; writeln(' writeln; writeln('This  program w i l l  rotate  by  A.C.  Diaz');  the  molecule  around x,  y OR z  by');  327  w r i t e l n ( ' s p e c i f i c d e g r e e s i n t e r v a l s a n d a l s o w i l l move t h e m o l e c u l e i n and z ' ) ; w r i t e l n ( ' i t w i l l w r i t e an output f i l e f o r alchemy and an o u t p u t file'); writeln(' w i t h Interatomic D i s t a n c e s , D i p o l a r C o u p l i n g s , Second Moments'); w r i t e l n ( ' s p a t i a l g r o u p Pnma, 12 S i , a n d 4 h y d r o g e n a t o m s , s e c o n d moments is averaged'); w r i t e l n ( ' f o r m o t i o n , needs a i n p u t f i l e w i t h c o o r d i n a t e s i n angtron and arigen (0,0,0)'); writeln; writeln; w r i t e l n ( ' E n t e r Name o f t h e A S C I I c r y s t a l I n p u t F i l e ( w i t h f u l l p a t h ) : ' ) ; writeln; w r i t e ( ' I n p u t Filename : ' ) ; readln(FileNamel); Assign(InFile, FileNamel); writeln;  x,  y,  writeln;writeln; w r i t e l n ( ' E n t e r Name o f .sm:  the  ASCII  File  for  output  '); writeln; w r i t e ( ' O u t p u t F i l e n a m e f o r s e c o n d moments: readln(FileName2); A s s i g n ( O u t F i l e , FileName2); writeln; writeln('Enter Cut-off distance for w r i t e l n ( ' A l l i n t e r a c t i o n s which are writeln; write('  CUT-OFF D i s t a n c e  data  (with  full  ');  Moment C a l c u l a t i o n s ' ) ; s h o r t e r than t h i s w i l l be  (Angstroms)  path)  :=  output');  ');  readln(cutoff); w r i t e l n ( ' E n t e r Cut-off for best R"2'); w r i t e l n f ' A l l c o r r e l a t i o n s b e t t e r than t h i s w i l l writeln; write(' C U T - O F F c o r r e l a t i o n ( e g . 0 . 9 9 6 ) := readln(cutcorr);  be  output');  ');  end;  procedure getdata; var xl,yl,zl:real;  begin { Open t h e  input  file  for  read only,  and r e s e t  pointer  to  reset(InFile); { Now r e a d i n t h e C r y s t a l d a t a , a n g l e s a n d d i m e n s i o n s e t c readln(InFile); ; {skip h e a d i n g and word TITLE) readln(InFile, Titlel); readln(InFile, Title2); readln(InFile); { s k i p comments) { Now r e a d s i n t h e d a t a f o r t h e a t o m c o o r d i n a t e s }  )  beginning }  add  f o r h:=l begin  to nhidr  do  read(InFile,XI); Xin[h]:= x l ; read(InFile,YI) ; yin[h]:= y l ; readln(InFile,zl) ; zin[h]:= z l end; for  i:=1  t o n s i do  begin read(InFile,xl); XSi[i]:=xl; read(InFile,yl); YSi[i]:=yl; readln(InFile, zl) ; ZSiti]:=zl; end; close(InFile); end;  Procedure rotationx; begin { Now r e a d s i n t h e d a t a f o r h : = l t o n h i d r do begin  for  the  atom c o o r d i n a t e s  )  Xin[h]; X: Z: (-Yin[h]* sin(degree_X*3.14159/180)+Zin[h]*cos(degree_X*3.14159/180)) Y: (Yin[h]*cos(degree_X*3.14159/180)+Zin[h]*sin(degree_X*3.14159/180)); Xat[h] = X; Yat[h] = y; Zat[h] = z end; end;  Procedure rotationy; begin f o r h:=l . begin  to nhidr  do  Y = (Yat[h]); Z = (Zat[h]*cos(degree_Y*3.14159/180)-Xat[h]*sin(degree_Y*3.14159/180)); (Xat[h]*cos(degree_Y*3.14159/180)+Zat[h]*sin{degree_Y*3.14159/180)); X = Xat[h] = X; Yat[h] = y ; Zat[h] = z end; end;  Procedure rotationZ;  329  Begin for h:=l begin  to nhidr  do  Z:= Z a t [ h ] ; Y:= ( - X a t [ h ] * s i n ( d e g r e e _ Z * 3 . 1 4 1 5 9 / 1 8 0 ) + Y a t [ h ] * c o s ( d e g r e e _ Z * 3 . 1 4 1 5 9 / 1 8 0 ) ) ; X : = ( X a t [h] * c o s ( d e g r e e _ Z * 3 . 1 4 1 5 9 / 1 8 0 ) + Y a t [h) * s i n ( d e g r e e _ Z » 3 . 1 4 1 5 9 / 1 8 0 ) . ) ; Xat[h]:= X; Yat[h]:= y; Zat[h]:= z end; end;  Procedure movemolecule; begin f o r h:=l begin Zat[h]:= Yat[h]:= Xat[h]:= end; end;  to nhidr  do  Zat[h]+(0.5188*c)+movez; Yat[h]+(0.25*b)+movey; Xat[h]+(-0.014 05*a)tmovex;  procedure findcoor;  begin for  i:=l  to nhidr  do  (Calculates  the other p o s i t i o n s  for  P212121, t o } (create  the complete u n i t  cell)  begin k:=l; XH[l,k,i):=xat[i)/a; YH[l,k,i]:=yat[i)/b; ZHtl.k,i]:=zat[i]/c;  writeln('H',l,k,i,' •,XH[1,k,i]:6:4,* •,ZH[l,k,i):6:4); i n c (k) ; XH[l,k,i]:=0.5-xat[i]/a; YH[l,k,i]:=-yat(i]/b; .ZH[l,k,i]:=0.5+zat[i]/c; writeln('H',l,k,i,' ',XH[1,k,i):6:4,' • , Z H [ l , k , i ] :6:4) ; inc(k) ; XH[l,k,i]:=-xat[i]/a YH[l,k,i):=0.5+yat[i)/b; ;  1  ,YH[1,k,i]:6:4,'  ',YH[1,k,i]:6:4,'  the  space  group  330  ZH[l,k,i]:=-zat[i]/c; writeln('HM,k,i, ' ' , XH [ 1, k, i ] : 6 : 4 , ' ' , Z H [ 1 , k , i ] :6:4) ; i n c (k) ; XH[l,k,i]:=0.5+xat[i]/a; YH[l,k,i]:=0.5-yat[i]/b; ZH[l,k,i]:=0.5-zat[i]/c; writeln('H',l,k,i, ' •,XH[1,k,i]:6:4,' ',ZH[l,k,i]:6:4); i n c (k) ; XH[1,k,i]:=-xat[i]/a; YH[l,k,i]:=-yat[i]/b; ZH[l,k,i]:=-zat[i]/c; writeln('H',1,k,i,' ',XH[1,k,i]:6:4,' • , Z H [ 1 , k , i ] :6:4) ; inc(k); XH[l,k,i]:=0.5+xat[i]/a; YH[1,k,i] :=yat[i] / b ; ZH[l,k,i] :=0.5-zat[i]/c; writeln {' H M , k , i , ' ' , XH [ 1, k, i ] : 6 : 4 , ' ',ZH[1,k,i]:6:4); inc(k); XH[l,k,i]:=xat[i]/a; YH[l,k,i]:=0.5-yat[i]/b; ZH[l,k,i]:=zat[i]/c; writeln('H',l,k,i, ' ',XH[1,k,i] :6:4, ' ',ZH[1,k,i]:6:4); inc(k); XH[l,k,i]:=0.5-xat[i]/a; YH[1,k,i]:=0.5+yat[i]/b; ZH[l,k,i]:=0.5+zat[i)/c; writeln('H',l,k,i,' ',XH[l,k,i]:6:4,' ',ZH[1,k,i]:6:4); end ;  for  i:=l  P212121,  to  to nhidr  do  ' , YH [ 1 , k , i ] : 6 : 4 , '  ',YH[1,k,i]:6:4,'  ' , YH [ 1, k, i ) : 6 : 4 , '  1  , Y H [ 1 , k , i ] :6:4 , '  ',YH[1,k,i]:6:4,'  {Calculates the other  positions  for  the space  group  for  the space  group  } {create  f o r k:=l begin  ' , YH [ l , k , i ] : 6 : 4 , '  to  the complete  2nd u n i t  cell)  8 do  XH[2,k,i]:=XH[l,k,i]-l; YH[2,k,i]:=YH[l,k,i)-l; ZH[2,k,i]:=ZH[l,k,i]; end ; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other {create  f o r k:=l begin  positions  } to  8 do  XH[3,k,i]:=XH[l,k,i)-l;  the complete 3th u n i t  cell)  331  YH[3,k,i]:=YH[l,k,i] ; ZH[3,k,i]:=ZH[l,k,i]; end; for  i:=l  P212121,  to nhidr  to  do  {Calculates the other  positions  for  the space  group  for  the space  group  for  the space  group  f o r the space  group  } {create  f o r k:=l begin  to  the complete  4th u n i t  cell)  8 do  XH[4,k,i]:=XH[l,k,i]-l; YH[4,k,i]:=l+YH[l.k,i]; ZH[4,k,i]:=ZH(l,k,i]; end; for  i:=l  P212121,  to nhidr  to  do  { C a l c u l a t e s the other {create  f o r k:=l begin  positions  ) to  the  complete  5th u n i t  cell}  8 do  X H [ 5 , k , i ] : = X H [ 1 , k, i ] ; YH[5,k,i]:=YH[l,k,i)-1; ZH[5,k,i]:=ZH[l,k,i]; end; for  i:=l  P212121,  to  to nhidr  do  { C a l c u l a t e s the other  } {create  f o r k:=l begin  positions  to  the complete  6th u n i t  cell}  8 do  XH[6,k,i]:=XH[1,k,i]; YH[6,k,i]:=l+YH[l,k,i]; ZH[6,k,i]:=ZH[l,k,i]; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other  } {create  f o r k:=l begin  to  8 do  XH[7,k,i]:=l+XH[l,k,i] ; YH[7,k,i]:=YH[l,k,i]; ZH[7,k,i]:=ZH[l,k,i]; end;  positions  the complete 7th u n i t  cell}  332  for  i:=l  P212121,  to  to nhidr  do  {Calculates  the other p o s i t i o n s  f o r the space  group  f o r the space  group  f o r the space  group  } {create  for k:=l to begin  the complete  8th u n i t  cell}  8 do  XH[8,k,i] :=l+XH[l,k,i] ; YH[8,k,i]:=YH[l,k,i]-l; ZH[8,k,i}:=ZH[l,k,i] ; end ; for  i:=l  P212121,  to nhidr  do  {Calculates  the other p o s i t i o n s  to } {create  for k:=l to begin  the complete  9th unit  cell}  8 do  XH[9,k,i] :=l+XH[l',k,i) ; YH[9,k,i]:=l+YH[l,k,i]; ZH[9,k,i]:=ZH[l,k,i]; end; for  i:=l  P212121,  to nhidr  do  {Calculates  the other positions  to } {create  for k:=l to begin  the complete  10th u n i t  cell)  8 do  XH[10,k,i]:=XH[l,k,i]; YH[10,k,i]:=YH[l,k,i]; ZH[10,k,i]:=l+ZH[l,k,i]; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates  the other p o s i t i o n s  f o r the space  group  } {create  for k:=l to begin  the complete  11th u n i t  cell}  8 do  XH[ll,k,i]:=XH[l,k,i]-l; YHtll.k.i]:=YH[l,k,i]-l; ZH[ll,k,i]:=l+ZH[l,k,i]; end; for  i:=l  P212121, for  to  to nhidr }  k:=l to  do  {Calculates {create  8 do  the other p o s i t i o n s  the complete  12th u n i t  f o r the space  cell}  group  333  begin  XH[12,k,i]:=XH[l,k,i]-l; YH[12,k,i] :=YH[l,k,i] ; ZH[12,k,i]:=l+ZH[l,k,i]; end; for  i:=l  P212121,  to nhidr  do  {Calculates  the other  positions  f o r the space  group  to } {create  f o r k:=l begin  the complete  XH[13,k,i]:=XH[l,k,i]-l; YH[13,k,i]:=l+YH[l,k,i]; ZH[13.k,i]:=l+ZH[l,k,i]; end; inc(1); f o r i:=l t o n h i d r do {Calculates P212121,  13th unit  cell}  t o 8 do  the other  positions  f o r the space  group  to } {create  for k:=l begin  the complete  14th u n i t  cell)  t o 8 do  XH[14,k,i]:=XH[l,k,i] ; YH[14,k,i]:=YH[l,k,i]-l; ZH[14,k,i]:=l+ZH[l,k,i]; end; for  i:=l  P212121,  to nhidr  do  {Calculates  the other  positions  f o r the space  group  to } {create  f o r k:=l begin  the complete  15th u n i t  cell}  t o 8 do  XH[15,k,i):=XH[l,k,i]; YH[15,k,i] :=l+YH[l,k,i] ; ZH[15,k,i]:=l +ZH[l,k,i) ; end; for  i:=l  P212121,  to nhidr  do  (Calculates  the other  positions  f o r the space  to } {create  for k:=l begin  t o 8 do  XH[16.k,i]:=l+XH[l,k, i ] ; YH[16,k,i]:=YH[l,k,i]; ZH[16,k,i]:=l+ZH[l,k,i]; end;  the complete  16th unit  cell}  group  334  for  i:=l  P212121,  to  to  nhidr  do  {Calculates {create  f o r k:=l begin  the  other  positions for  the  space  group  the  space  group  } to  the  complete 17th  unit  cell)  8 do  XH[17,k,i] :=l+XH[l,k, i] ; YH[17,k,i]:=YH[l,k,i]-l; ZH[17,k,i):=l +ZH[l,k,i] ; end ; for  i:=l  P212121,  to  to  nhidr  do  {Calculates {create  f o r k:=l begin  the  other p o s i t i o n s for  } to  the  complete 18th  unit  cell)  8 do  XH(18,k,i]:=l+XH[l,k,i] ; YH[18,k,i]:=l+YH[l,k,i]; ZH[18,k,i]:=l+ZH[l,k,i]; end; for  i.-=l  P212121,  to  to nhidr  do  {Calculates  {create f o r k:=l begin  the  other p o s i t i o n s for  the  space  group  ) to  the  complete 19th  unit  cell)  8 do  XH[19,k,i]:=XH[l,k,i) ; YH[19,k,i]:=YH[l,k,i); ZH[19,k,i]:=ZH[l,k,i]-l; end; for  i:=l  P212121,  to  to  nhidr  do  {Calculates  other p o s i t i o n s for  the  space  group  the  space  group  ) {create  f o r k:=l begin  the  to  the  complete 20th u n i t  cell)  8 do  XH[20,k,i]:=XH[l,k,i]-l; YH[2 0 , k , i ] : = Y H [ l , k , i ] - l ; ZH[20,k,i]:=ZH[l,k,i]-l; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates {create  for  k:=l  the  other p o s i t i o n s for  ) to  8 do  the  complete 21th  unit  cell)  335  begin  XH[21,k,i]:=XH[l,k,i]-l; YH[21,k,i]:=YH[l,k,i]; ZH[21,k,i]:=ZH[l,k,i]-1; end; for  i:=l  P212121,  to  to  nhidr  do  {Calculates  other  positions  for  the  space  group  the  space  group  the  space  group  the space  group  } {create  f o r k:=l begin  the  to  the  complete  22th u n i t  cell)  8 do  XH[22,k,i]:=XH[l,k,i]-l; YH[22,k,i]:=1+YH[1,k,i]; ZH[22,k,i]:=ZH[1,k,i]-1; end ; for  i:=l  P212121,  to  to  nhidr  do  {Calculates {create  for k:=l begin  the  other  positions  for  } to  8  the  complete  23th u n i t  cell)  do  XH[23,k,i]:=XH[l,k,i]; YH[23,k,i]:=YH[l,k,i]-l; ZH[23,k,i]:=ZH[l,k,i]-l; end ; for  i:=l  P212121,  to  to  nhidr  do  {Calculates  k:=1  other  positions  for  } {create  for  the  to  the  complete  24th u n i t  cell)  8 do  begin  XH[24,k,i]:=XH[l,k,i); YH[24,k,i]:=l+YH[l,k,i]; ZH[24,k,i]:=ZH[l,k,i)-l; end; for  i:=l  P212121,  to  to  nhidr  do  {Calculates  k:=l  to  8 do  begin  XH[25,k,i):=l+XH[l,k,i]; YH[25,k,i]:=YH[1,k,i]; ZH[25,k,i]:=ZH[l,k,i)-l; end;  other  positions  for  } {create  for  the  the  complete  25th u n i t  cell)  336  for  i:=l  P212121,  to  to nhidr  do  {Calculates {create  f o r k:=l begin  the other  positions  for  the space  group  the space  group  } to  the complete  26th u n i t  cell}  8 do  XH[26,k,i]:=l+XH[l,k,i]; YH[26,k,i]:=YH[l,k,i]-1; ZH[26,k,i]:=ZH[l,k,i]-l; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates {create  f o r k:=l begin  to  the complete  8 do  XH[27,k,i]:=l+XH[l,k,i]; YH[27,k,i]:=l+YH[l,k,i]; ZH[27,k,i]:=ZH[l,k,i]-l; end ;  end;  procedure secondmomentaro; var theta,phi:real ; r,vx,vy,vz:real; DCtHHKZ : r e a l ; sumr,static:real; sototal:real ; begin  f o r j:=1 begin  the other  positions  for  }  t o n s i do  sumr:=0 ; sm[j,1]:=0; f o r 1:=1 t o 27 d o f o r k : = l t o 8 do for i:=l t o 4 do begin vx:=(XSi[j]-XH[l,k,i)*a); vy:=(YSi[j]-YH[l,k,i]*b) ; vz:=(ZSi[j)-ZH[l,k,i)*c); r:=sgrt(sqr(vx)+sqr(vy)+sqr(vz)); i f r<cutoff then.  27th u n i t  cell}  337  begin sumr:=sumr+l/sqr(r*r*r); {writeln(outfile, 'si ' ,j, ' H ' , l , k , i , ' ,  ' , Z H [ l , k , i ] :4:4, '  r=  ',r:2:2) ;  ',xH[1,k,i]:4:4, ',  ',YH[1,k,i]:4:4, '  }  end; end ;  {to  have  the  total  s e c o n d moment i n r a d 2 H z 2 , m u l t i p l y f o r  sgr((gamma)H*(gamma)Si*h/2pi*Uo/4pi)  *1/  3 *  3/4  5.6291128e9,  which  is  (1/3*1(1+1)(heteronuclear  sm) } SM[j,l]:=(sumr)*114.06967e6/2; s t a t i c : = 114.06967e6*sumr/2; w r i t e l n ( ' S E C O N D MOMENT S i ' , j , ' =  ' , S M [ j , 1 ] :4 : 4) ;  end; end; p r o c e d u r e  *econdmon»entch3;  var r,vx,vy,vz:real ; DCtHHHZ : r e a l ; sumr,static:real ; begin  f o r j:=1 begin  t o n s i do  sumr:=0 ; sm[j,2]:=0; {**lst  methyl group a v e r a g i n g * * )  f o r 1:=1 t o 27 do f o r k:=l t o 8 do f o r i:=5 t o 6 do begin vx:=(XSi[j)-XH[l,k,i]*a); vy:=(YSi[j]-YH[l,k,i]*b); VZ:=(ZSi[j]-ZH[l,k,i]*c); r:=sgrt(sgr(vx)+sgr(vy)+sgr(vz)); i f r<cutoff then begin  sumr:=sumr+l/sgr(r*r*r); {writeln(outfile, ' s i ' . j . ',ZH[l,k,i]:4:4,' end; end;  r=  ' H M.k.i,'  ',r:2:2);  )  ' .xH [ 1 ,  k,  i] :4  :4,  1  , " ,YH[l.k,i]  : 4 : 4 , '  338  {to  have  the  total  s e c o n d moment  in  rad2Hz2,  sgr((gamma)H*(gamma)Si*h/2pi*Uo/4pi)  *1/  multiply  3 *  3/4  for  5.6291128e9,  ( 1 / 3 * 1 (1 + 1)  sm) } SM[j,2]:=(sumr)*114.06967e6/2; w r i t e l n ( ' S E C O N D MOMENT S i ' , j , ' =  ' , S M [ j , 2 ] : 4 : 4) ;  end; end;  PROCEDURE DoLeastSquares; const n=6;  {number  of  VAR I : INTEGER; Sumx, Sumy, Sumxx, Sumxy, Sumyy, Denom :  BEGIN inTcp[l,1] inTcp[2,1] inTcp[3,1] inTcp[4,1] inTcp[5,1] inTcp[6,1] Sumx  :=  Sumxy  :=  0.0;  data  point)  REAL;  1000/21.4 1000/20.9 1000/45.0 1 0 0 0 / 1 2 .2 1000/36 . 0 1 0 0 0 / 2 3 .2 Sumy  0.0;  :=  Sumyy  0.0; :=  Sumxx  :=  0.0;  0.0;  FOR I := 1 TO n DO BEGIN Sumx := Sumx+SM[I,1]; Sumy := Sumy+inTcp[I,1]; Sumxx := S u m x x + S M [ 1 , 1 ] * S M [ 1 , 1 ] ; Sumxy := Sumxy+SM[I,1]*inTcp[I,1]; Sumyy := S u m Y Y + S Q R ( i n T c p [ 1 , 1 ] ) ; END; Denom :=' S Q R ( S u m x ) - N * S u m x x ; S l o p e := (Sumx*Sumy-N*Sumxy)/Denom; I n t e r c e p t := (Sumx*Sumxy-Sumy*Sumxx)/Denom; C o r r C o e f f := sgr((Sumx*Sumy-N*Sumxy)/SQRT((SQR(SumY)-N*SumYY) * (SQR(Sumx) - N * S u m x x ) ) ) ; END;  PROCEDURE DoLeastSquaresch3; const n=6;  {number  VAR I : INTEGER; Sumx, Sumy,  of  data  point)  which  (heteronuclear  is  339  Sumxx, Sumyy,  Sumxy, Denom :  BEGIN inTcp[1,2] inTcp[2,2] inTcp[3,2) inTcp[4,2] inTcp[5,2] inTcp[6,2]  REAL;  1000/7.6; 1000/5.7; 1000/12.0 1000/11.3 1000/14.0 1000/8.5;  0.0;  :=  Sumx := 0 . 0 ; Sumy := 0 . 0 ; Sumxx Sumxy : = 0 . 0 ; Sumyy : = 0 . 0 ;  FOR I := 1 TO n DO BEGIN Sumx := S u m x + S M [ 1 , 2 ] ; Sumy : = Sumy+ i n T c p [ 1 , 2 ] ; Sumxx := S u m x x + S M [ I , 2 ] * S M [ I , 2 ] ; S Sumxy := Suum mxxyv++SSM M[[II,,22]]**iinnTTccpp[[I I, , 2 ] Sumyy := S u m Y Y + S Q R ( i n T c p [ I , 2 ] ) ; END; Denom := S Q R ( S u m x ) - N * S u m x x ; S l o p e c h 3 := ( S u m x * S u m y - N * S u m x y ) / D e n o m ; I n t e r c e p t c h 3 := ( S u m x * S u m x y - S u m y * S u m x x ) / D e n o m ; C o r r C o e f f c h 3 := s q r ( ( S u m x * S u m y - N * S u m x y ) / S Q R T ( ( S Q R ( S u m Y ) - N * S u m Y Y ) * (SQR(Sumx) - N * S u m x x ) ) ) ; END; ( * * s t a r t s main program**) begin presentation; getdata; rewrite(OutFile); writeln(OutFile,'FILE = ',FileName2); writeln(OutFile); writeln(OutFile,Titlel) ; writeln(OutFile,Title2); writeln(OutFile) ; writeln(OutFile,'molecule.PAS  output  for  input  file  ',FileNamel);  writeln(OutFile) ; writeln(OutFile, ' Cut-off ', cutcorr:5:2) ; writeln(OutFile); write(outfile,'Si,j,  );  distance  •SM[j]  ',  cutoff:5:2,'  '.  '  1/Tcp[j]  Angstroms  ',•  ','  R"2  C u t - o f f R~2 =  ','  intercept  1  writeln(OutFile,'  slope  f o r v a r x : = 0 t o 6 do f o r v a r y : = 0 t o 12 d o for varz:=0 to 6 do f o r r o t _ x : = 0 t o 8 do f o r r o t _ y : = 0 t o 18 d o f o r r o t _ z : = 0 t o 8 do begin movex:=varx/10 ;  ' ,'  rotation(x,y,z)=  ','  t r a n s l a t i o n ^ , y , z) = ') ;  340  movey:=vary/10 ; movez:=varz/10 ; d e g r e e _ x : = r o t _ x * 3; degree_y :=rot_y*3 ; degree_z:=rot_z * 3 ; rotationx; rotationy; rotationz; movemolecule; writeln;writeln; writeln('rotation (',degree_x,',',degree_y,',',degree_z,') ','move=(',movex:1:1,•,',movey:1:1,',•,movez:1:1,')'); writeln;writeln; findcoor; secondmomentaro; DoLeastSquares; writeln;writeln; writeln('correlation ' , C o r r C o e f f : 4 : 4) ; writeln;writeln; i f CorrCoeff>cutcorr then begin secondmomentch3 ; DoLeastSquaresch3 ; i f CorrCoeffch3>cutcorr then begin for  j:=1 begin  to  6 do  write(OutFile,j,'  ',SM[j,1]:10:2,'  ',inTcp[j,1]:10:2,  '  '.CorrCoeff:10:4,' ',intercept:10:4); write(OutFile,' ',slope:10:6,' '); write(outfile,degree_x,' ',degree_y,' ',degree_z,' '); writeln(OutFile,movex:2:2,' ,movey:2:2,' ',movez:2:2); e n d ; { c l o s e l o o p f o r SM 1 a n d 2} w r i t e l n ( O u t F i l e , ' r e s u l t s f o r t h e CH3 g r o u p ' ) ; 1  for  j:=1 t o begin  6 do  write(OutFile,j,j,  '  ' ,SM[j,2] :10:2, '  ' ,inTcp[j,2]  :10:2 ,  '  '.CorrCoeffch3:10:4); write(OutFile,' ',interceptch3:10:4,' ',slopech3:10:6,' '); write(outfile,degree_x,' ',degree_y,' ',degree_z,' '); writeln(OutFile,movex:2:2,' '.movey:2:2,' ',movez:2:2); e n d ; { c l o s e l o o p f o r S M 1 a n d 2} w r i t e l n ( O u t F i l e , ' r e s u l t s f o r the aromatic p r o t o n s ' ) ; end; {close i f corrcoeffch3) end; {close i f corrcoeff for aromatics) END; { c l o s e a l l l o o p o f r o t a t i o n a n d t r a n l a t i o n }  close(OutFile); writeln('calculations end.  successfully  completed');  341 A P E N D I X 4: Program to Calculate Lorentzian Signals from the C P Correlation in the System of Orthorhombic ZSM-5 Low Loaded with p-Xylene Space Group Pnma. program lorenzian;  uses winCrt; const nhidr=6; nsi=12; a=20.022; b=19.899; c=13.383; TYPE  ASCII_File = TEXT;  var movex,movey,movez,X, Y, Z:real; varx,vary,varz:integer; 1,i,j,k,n,m,h:integer; dist:real; smtstl,SMtl,smtst2, SMt2:real; xh,yh,zh :array[1..27,1..8,1..nhidr] of r e a l ; x i n , y i n , z i n :array[1..nhidr] of r e a l ; { i n i t i a l coordinates of H from p-xylene} xat,yat,zat :array[1..nhidr] of r e a l ; x S i , y S i , z S i :array[1..nSi] of r e a l ; SM:array[1..nsi,1..2] of r e a l ; Tcp:array[1..nsi,1..2] of r e a l ; output:text; FileNamel, FileName2,FileName3: s t r i n g ; {for input and output} T i t l e l , title2 : string; I n F i l e , I n f i l e 2 , O u t F i l e , O u t F i l e 2 : A S C I I _ F i l e ; { Disk f i l e s } c u t c o r r , c u t o f f : r e a l ; {maximum interatomic distance t o consider i n the calculations} degree_x,degree_y,degree_z,rot_x,rot_y, r o t _ z : r e a l ; Slope, Intercept, CorrCoeff : REAL; Slopech3, Interceptch3,CorrCoeffch3 : REAL; areatotal,areatotalch3:real; junk,cutdis:real; t a u , r : r e a l ; {contact time i n ms} procedure presentation;  begin { MAIN BODY } { OPEN ASCII f i l e  (with .dmc extension) containing c r y s t a l data }  ClrScr; writeln(' smarlo2m.PAS'); writeln; writeln(' by A.C. Diaz'); writeln; w r i t e l n ( ' T h i s program w i l l rotate the molecule around x, y OR z b y ) ; w r i t e l n ( ' s p e c i f i c degrees i n t e r v a l s and also w i l l move the molecule i n x, y, and z ' ) ; 1  342  is  w r i t e l n ( ' i t w i l l w r i t e an o u t p u t f i l e f o r alchemy and an o u t p u t file'); writeln(' w i t h I n t e r a t o m i c D i s t a n c e s , D i p o l a r C o u p l i n g s , Second M o m e n t s ' ) ; w r i t e l n ( ' s p a t i a l g r o u p Pnma, 12 S i , a n d 4 h y d r o g e n a t o m s , s e c o n d moments averaged'); writeln('for  arigen  motion,  needs a input  file  with coordinates in  angtron  and  (0,0,0)'); writeln; writeln; writeln('Enter  Name o f  the  ASCII  writeln; w r i t e ( ' I n p u t Filename : '); readln(FileNamel); Assign(InFile, FileNamel); writeln; w r i t e l n ( ' E n t e r Name o f t h e writeln; w r i t e ( ' I n p u t Filename : '); readln(FileName3); Assign(InFile2, FileName3); writeln; writeln;writeln; writeln('Enter Cut-off writeln('All  interactions  crystal  Input  Input  File  for  distance for  which are  File  (with f u l l  rotation  path):  parameters  ');  ');  Moment C a l c u l a t i o n s ' ) ;  shorter  than  this  will  be  output');  writeln; write!  CUT-OFF D i s t a n c e  1  (Angstroms)  :=  ');  readln(cutoff); writeln('Enter Cut-off shortest Si-H distance allowed'); w r i t e l n ( ' A l l c o r r e l a t i o n s l o n g e r t h a n t h i s w i l l be o u t p u t ' ) ; writeln; write! ' CUT-OFF d i s t a n c e (eg. 2.6) := '); readln(cutdis); writeln('Enter writeln; w r i t e ( ' Contact readln(tau); writeln('Enter •sm:  contact  time= Name o f  time  for  area  File  for  end;  procedure getdata; var xl,yl,zl:real;  begin  ms');;  ' ) ; the  ASCII  '); writeln; write('Output Filename for l o r e n z i a n area: readln(FileName2); Assign(OutFile, FileName2); writeln;  calculation in  output  ');  data  (with  full  path)  add  { Open the input f i l e reset(InFile) ;  for read only, and reset pointer to beginning }  { Now read i n the Crystal data, angles and dimensions etc ) r e a d l n ( I n F i l e ) ; ; {skip heading and word TITLE) readln(InFile, T i t l e l ) ; readln(InFile, T i t l e 2 ) ; r e a d l n ( I n F i l e ) ; {skip comments) { Now reads i n the data for the atom coordinates } for h:=l to nhidr do begin read(InFile.Xl); Xin[h]:= x l ; read(InFile,Yl); yin[h]:= y l ; readln(InFile,zl); zin[h]:= z l end ; for i:=1 to nsi do begin read(InFile,xl); XSi [i] :=xl; read(InFile,yl); YSi[i]:=yl; readln(InFile,zl); ZSi[i]:=zl; end; close(InFile); end ; Procedure rotationx; begin { Now reads i n the data for the atom coordinates for h:=l to nhidr do begin  )  = Xin[h] ; = (-Yin[h]*sin(degree_X*3.14159/180)+Zin[h]*cos(degree_X*3.14159/180)) (Yin[h)*cos(degree_X*3.14159/180)+Zin[h]*sin(degree_X*3.14159/180)); Xat[h] = X; Yat[h] = y; Zat[h] = z end; end; Procedure rotationy; begin for h:=l begin Y:= Z:=  to nhidr do  (Yatth]); (Zat[h]*cos(degree_Y*3.14159/180)-Xat[h]*sin(degree_Y*3.14159/180));  344  X:=  (Xat[h]*cos(degree_Y*3.14159/180)+Zat[h]*sin(degree_Y*3.14159/180));  Xat[h]:= Yat[h]:= Zat[h]:= end; end;  Procedure Begin f o r h:=l  X; y; z  rotationZ;  to nhidr  do  begin Z: = Y:= X:=  Zatth]; (-Xat[h]*sin(degree_Z*3.14159/180)+Yat[h]*cos(degree_Z*3.14159/180)); (Xat[h]*cos(degree_Z*3.14159/180)+Yat[h]*sin(degree_Z*3.14159/180));  Xat[h]:= Yat[h]:= Zat[h]:= end ; e n d ,-  Procedure begin f o r h:=l begin Zat[h]:= Yat[h]:= Xat[h]:= end ; end ;  X; y; z  movemolecule;  to nhidr  do  Zat[h]+(0.5188*c)+movez; Yat[h]+(0.25*b)+movey; Xat[h]+(-0.01405*a)+movex;  procedure  findcoor;  begin for  i:=l  P212121,  to  to nhidr  do  {Calculates  the  other  positions  for  ) {create  the complete  unit  cell)  begin k:=l; XH[l,k,i]:=xat[i]/a; YH[l,k,i]:=yat[i]/b; ZH[l,k,i]:=zat[i]/c;  writeln ( ' H M . k . i . ,ZH[l,k,i):6:4);  '  ' , XH [ l , k , i ] : 6 : 4 ,  ' , YH [ 1, k, i ] : 6 : 4 , •  the  space  group  345  inc(k); XH[l,k,i]:=0.5-xat[i]/a; YH[l,k,i]:=-yat[i]/b; ZH[1,k,i]:=0.5+zat[i)/c; writeln('H',1,k,i , ' ' , X H [ 1, k, i ] : 6 : 4 , '  ',YH[1,k,i]:6:4,'  ' , Z H [ 1 , k , i ] :6:4) ; inc(k); XH[l,k,i]:=-xat[i]/a; YH[l,k,i]:=0.5+yat[i]/b; ZH[l,k,i]:=-zat[i]/c; writeln('H'.l.k.i,' ",XH[1,k,i]:6:4,' • , Z H [ 1 , k , i ] : 6 : 4) ; inc(k) ; XH[l.k,i]:=0.5+xat[i]/a; YH[l,k,i]:=0.5-yat[i]/b; ZH[l,k,i]:=0.5-zat ti]/c; writeln('H',l,k i, ' ' , X H [ 1 , k , i ) :6:4, • •,ZH[l,k,i]:6:4); inc(k); XH[l,k,i]:=-xat[i]/a; YH[l,k,i]:=-yat[i]/b; ZH[l,k,i]:=-zat[i]/c; writeln! ' H ' , l , k , i , ' ',XH[1,k,i]:6:4,' ' , Z H [ 1 , k , i ] :6 : 4) ; inc(k); XH[l,k,i]:=0.5+xat[i]/a; YH[l,k,i]:=yat[i]/b; ZH[l,k,i]:=0.5-zat[i]/c; writeln('H',l,k,i,' ' , X H [ 1 , k , i ] :6 : 4 , ' ' , Z H [ 1 , k , i ] : 6 : 4) ; inc(k); XH[1,k,i]:=xat[i]/a; YH[l,k,i]:=0.5-yat[i]/b; ZH[l,k,i]:=zat[i]/c; (  writeln('H',l,k,i,'  ',YH[l,k,i]:6:4,'  ' , Y H [ 1 , k , i ] :6 : 4 , '  ',YH[1,k,i]:6:4, '  ' , Y H [ l , k , i ] :6:4, '  ',XH[1,k,i]:6:4,'  ',YH[l,k,i]:6:4,'  ' , Z H [ 1 , k , i ] :6:4) ; inc(k); XH[l,k,i]:=0.5-xat[i]/a; YH[l,k,i]:=0.5+yat[i]/b; ZH[l,k,i]:=0.5+zat[i]/c; writeln('H',1,k,i,' ',XH[1,k,i]:6:4,'  ',YH[1,k,i]:6:4,'  ',ZH[l,k,i]:6:4); end; for  i:=l  P212121,  to  to nhidr  do  { C a l c u l a t e s the other {create  for  k:=l  to  8 do  begin  XH[2,k,i]:=XH[l,k,i]-l; YH[2,k,i]:=YH[l,k,i]-l; ZH[2,k,i]:=ZH[l,k,i]; end;  positions  ) t h e c o m p l e t e 2nd u n i t  cell)  for  the space  group  346  for  i:=l  P212121,  to nhidr  do  {Calculates  the other  positions  f o r the space  group  to } {create  f o r k:=l begin  the complete  3th unit  cell}  t o 8 do  XH[3,k,i]:=XH[l,k,i]-l; YH[3,k,i]:=YH[l,k,i]; 2H[3,k,i]:=ZH[l,k,i] ; end; for  i:=l  P212121,  to nhidr  do  {Calculates  the other  positions  f o r the space group  to } {create  for k:=l begin  the complete  4th unit  cell}  t o 8 do  XH[4,k,i]:=XH[1,k,i]-1; YH[4,k,i]:=l+YH[l,k,i]; ZH[4,k,i}:=ZH[l,k,i]; end; for  i:=l  P212121,  to nhidr  do  {Calculates  the other  positions  f o r the space  group  f o r the space  group  f o r the space  group  to } {create  for k:=l begin  the complete  5th unit  cell}  t o 8 do  XH[5,k,i]:=XH[l,k,i]; YH[5,k,i]:=YH[l,k,i]-l; ZH[5,k,i]:=ZH[l,k,i]; end; for  i:=l  P212121,  to nhidr  do  {Calculates  the other  positions  to } {create  for k:=l begin  the complete  6th unit  cell}  t o 8 do  XH[6,k,i]:=XH[l,k,i]; YH[6,k,i]:=l+YH[l,k,i]; ZH[6,k,i]:=ZH[l,k,i]; end; for  i:=l  P212121, for  to nhidr  to }  k:=l  t o 8 do  do  {Calculates  {create  the other  the complete  positions  7th unit  cell}  347  begin  XH[7,k,i]:=l+XH[l,k,i]; YH[7,k,i]:=YH[l,k,i]; ZH[7,k,i]:=ZH[l,k,i]; end;  for  i:=l  P212121,  to  to nhidr  do  { C a l c u l a t e s the other {create  f o r k:=l begin  positions  for  the space  group  for  the space  group  for  the space  group  the space  group  } to  the complete  8th u n i t  cell}  8 do  XH[8,k,i]:=l+XH[l,k,i]; YH[8,k,i]:=YH[l,k,i]-l; ZH[8,k,i]:=ZH[l,k,i]; end ; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other {create  f o r k:=l begin  positions  } to  the complete  9th u n i t  cell}  8 do  XH[9,k,i]:=l+XH[l,k,i]; YH[9,k,i]:=l+YH[l,k,i]; ZH[9,k,i]:=ZH[l,k,i]; end ; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other {create  f o r k:=l begin  positions  } to  the complete  10th u n i t  cell}  8 do  XH[10,k,i]:=XH[l,k,i]; YH[10,k,i]:=YH[l,k,i] ; ZH[10,k,i):=l+ZH[l,k,i]; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other  for  } {create  f o r k:=l begin  positions  to  8 do  XH[ll.k,i]:=XH[l,k,i]-l;  the complete  11th u n i t  cell}  348  YH[ll,k,i]:=YH[l,k,i]-l; ZH[ll,k,i]:=l+ZH[l,k,i]; end; for  i:=l  P212121,  to  to  nhidr  do  {Calculates {create  f o r k:=l begin  the  other  positions for  the  space group  the  space group  the  space group  the  space group  the  space group  } to  the  complete 12th  unit  cell}  8 do  XH[12,k,i]:=XH[l,k,i]-l; YH[12,k,i]:=YH[l,k,il; ZH[12,k,i]:=l+ZH[l.k,i]; end; for  i:=1  P212121,  to  to  nhidr  do  {Calculates {create  f o r k:=l begin  the  other  positions for  } to  the  complete 13th  unit  cell}  8 do  XH[13,k,i]:=XH[l,k,i]-l; YH[13,k,i]:=l+YH[l,k.i]; ZH[13,k,i] :=l+ZH[l,k,i] ; end ; inc(1) ; for  i:=l  P212121,  to  to  nhidr  do  {Calculates  other  positions for  } {create  f o r k:=l begin  the  to  the  complete 14th  unit  cell}  8 do  XH[14,k,i]:=XH[l,k,i]; YH[14,k,i]:=YH[l,k,i]-l; ZH[14,k,i]:=l+ZH[l,k,i]; end; for  i:=l  P212121,  to  to  nhidr  do  {Calculates  other  positions for  } {create  f o r k:=l begin  the  to  the  complete 15th  unit  cell)  8 do  XH[15,k,i]:=XH[l,k,i]; YH[15,k,i]:=l+YH[l,k,i]; ZH[15,k,i]:=l+ZH[l,k,i]; end ; for  i:=l  P212121,  to  to }  nhidr  do  {Calculates {create  the  the  other  complete 16th  positions for unit  cell}  349  f o r k:=l begin  to  8 do  XH[16,k,i]:=l+XH[l,k,i]; YH[16,k,i]:=YH[l,k,i]; ZH[16,k,i]:=l+ZH[l,k,i]; end;  for  i:=l  P212121,  to  to nhidr  do  {Calculates the other {create  f o r k:=l begin  positions  for  the space  group  the  group  } to  the complete  17th u n i t  cell}  8 do  XH[17,k,i]:=l+XH[l,k,i]; YH[17,k,i]:=YH[l,k,i)-l; ZH[17,k,i]:=l+ZH[l,k,i]; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other {create  f o r k:=l begin  positions  for  space  } to  the complete  18th u n i t  cell}  8 do  XH[18,k,i]:=l+XH[l,k,i]; YH[18,k,i]:=l+YH[l,k,i]; ZH[18,k,i]:=l+ZH[l,k,i]; end; for  i:=l  P212121,  to  to nhidr  do  { C a l c u l a t e s the  {create f o r k:=l begin  other  positions  for  the space  group  } to  the complete  19th u n i t  cell}  8 do  XH[19,k,i):=XH[l,k,i]; YH[19,k,i]:=YH[l,k,i]; ZH[19,k,i]:=ZH[l,k,i]-l; end ; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other {create  f o r k:=l begin  positions  for  } to  8 do  XH[20,k,i]:=XH[l,k,i]-l;  the complete 20th u n i t  cell}  the space  group  350 YH[20,k,i]:=YH[l,k,i]-l; ZH[20,k,i}:=ZH[l,k,i]-l; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other {create  f o r k:=l begin  positions  for  the  space  group  the space  group  the  space  group  the space  group  the space  group  } to  the complete  21th u n i t  cell}  8 do  XH[21,k,i]:=XH[l.k,i]-l; YH[21,k,i]:=YH[1,k,i]; ZH[21,k,i]:=ZH[l,k,i}-l; end ; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other {create  f o r k:=l begin  positions  for  } to  the complete 22th u n i t  cell}  8 do  XH[22,k,i]:=XH[l,k,i]-1; YH[22,k,i]:=l+YH[l,k,i]; ZH[22,k,i]:=ZH[l,k,i]-l; end ; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other {create  f o r k:=l begin  positions  for  } to  the complete  23th u n i t  cell}  8 do  XH[23,k,i]:=XH[l,k,i]; YH[23,k,i]:=YH[l,k,i]-1; ZH[23,k,i]:=ZH[l,k,i]-l; end ; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other {create  f o r k:=l begin  positions  for  } to  the complete  24th u n i t  cell}  8 do  XH[24,k,i]:=XH[l,k,i]; YH[24,k,i]:=l+YH[l,k,i]; ZH[24,k,i] : = Z H U , k . i ] - l ; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other  positions  for  } {create  the complete  25th u n i t  cell}  351  for k:=l to 8 do begin XH[25,k,i]:=l+XH[l,k,i]; YH[25,k,i]:=YH[l,k,i]; ZH[25,k,i]:=ZH[l,k,i]-l; end; for i : = l to nhidr do P212121, to }  {Calculates the other positions for the space group {create the complete 26th unit c e l l )  for k:=l to 8 do begin XH[26,k,i]:=l+XH[l,k,i]; YH[26,k,i):=YH[l,k,i)-l; ZH[26,k,i]:=ZH[l,k,i]-l; end ; for i : = l to nhidr do P212121, to }  {Calculates the other positions for the space group {create the complete 27th unit  for k:=l to 8 do begin XH[27,k,i]:=l+XH[l,k,i]; YH[27,k,i]:=l+YH[l,k,i); ZH[27,k,i]:=ZH[l,k,i]-1; end; end; procedure  secondmomentaro;  var vx,vy,vz:real; DCtHHHZ : r e a l ; sumr,static:real; sototal:real; begin for j:=1 to n s i do begin sumr:=0 ; sm[j,1]:=0; sototal:=0 ; (**lst methyl group averaging**}  cell}  352  f o r 1:=1 t o 27 d o f o r k:=l t o 8 do f o r i : = l t o 4 do begin vx:=(XSi[j]-XH[l,k,i]*a); vy:=(YSi[j]-YH[l,k,i]*b); vz:=(ZSi[j]-ZH[l,k,i]*c); r:=sqrt(sqr(vx)+sqr(vy)+ sqr(vz)); i f r<cutdis then begin writeln(outfile,'error end; i f r<cutoff begin  ,  S i - H for aromatic  is=  ',r:2:2);  then  s u m r : = sumr + l / s q r ( r * r * r ) ; {writeln(outfile, ' s i ', j , ' H ' , l , k , i , ' ' , Z H [ l , k , i ] : 4 : 4 , ' r= ' , r : 2 : 2) ; ) end; end;  ' , x H [ 1 , k , i ] :4 : 4 , ' ,  ',YH[1,k,i]:4:4, '  { t o h a v e t h e t o t a l s e c o n d moment i n r a d 2 H z 2 , m u l t i p l y f o r 5 . 6 2 9 1 1 2 8 e 9 , w h i c h i s s q r ( ( g a m m a ) H * ( g a m m a ) S i * h / 2 p i * U o / 4 p i ) * 1 / 3 * 3 / 4 ( 1 / 3 * I (1 + 1) ( h e t e r o n u c l e a r sm) ) SM[j,l]:=(sumr)*114.06967e6/2; s t a t i c : = 114.06967e6*sumr/2; w r i t e l n ( ' S E C O N D MOMENT S i ' , j , ' =  end; end;  p r o c e d u r e secondmomentch3; var vx,vy,vz:real; DCtHHHZ : r e a l ; sumr,static:real; begin  f o r j:=1 begin  t o n s i do  sumr:=0 ; sm[j,2]:=0; f o r 1:=1 t o 27 d o f o r k : = l t o 8 do f o r i:=5 t o 6 do begin  ' , S M [ j , 1 ] :4 : 4) ;  353  vx:=(XSi[j]-XH[l,k,i]*a); vy:=(YSi[j]-YH[l,k,i)*b); vz:=(ZSi[j)-2H[l,k,i]*c); r:=sqrt(sqr(vx)+sqr(vy)+sqr(vz)); i f r<cutdis then begin writeln(outfile,'error end ; i f r<cutoff begin  ,  Si-H for  CH3 i s =  *,r:2:2);  then  sumr:=sumr+l/sgr(r*r*r); {writeln(outfile, ' s i ' , j , ' H ' , l , k , i , ' ' , Z H [ l , k , i ] : 4 : 4 , ' r= ' , r : 2 : 2 ) ; ) end; end ;  ',xH[1,k,i]:4:4, , 1  ',YH[1,k,i]:4:4, '  ( t o h a v e t h e t o t a l s e c o n d moment i n r a d 2 H z 2 , m u l t i p l y f o r 5 . 6 2 9 1 1 2 8 e 9 , w h i c h i s s q r ( ( g a m m a ) H * ( g a m m a ) S i * h / 2 p i * U o / 4 p i ) * 1 / 3 * 3 / 4 ( 1 / 3 * 1 (1 + 1) ( h e t e r o n u c l e a r sm) ) SM[j,2]:=(sumr)*114.06967e6/2; w r i t e l n ( ' S E C O N D MOMENT S i ' , j , ' =  ',SM[j,2]:4:4);  end; end ;  PROCEDURE: l o r e n z i a n a ; const n=6;  (number o f  data  point)  Tlrhod63=76.9;(T1RH0 of  aromatic protons,  Tlrhod43=59.5;(T1RH0 of methyl protons,  from s l o p e  from slope  of  of  Tcp decay)  Tcp decay)  VAR area:real;  BEGIN a r e a t o t a l : =0 ,areatotalch3:=0; { c a l c u l a t e s a r e a f o r d63) for i:=l t o n s i do begin Tcp[i,l]:=1000/(slope*SM[i,1]+intercept); area:=76692216.67*(Tlrhod63/(Tlrhod63-Tcp[i,1)))*(exp(-tau/Tlrhod63)-exp(tau/Tcp[i,l])); areatotal:=areatotal+area;  end; {calculates area for for i:=l t o n s i do begin  d43}  Tcp[i,2]:=1000/(slopech3*SM[i,2]+interceptch3); area:=37187300*(Tlrhod43/(Tlrhod43-Tcp[i,2]))*(exp(-tau/Tlrhod43)-exp(tau/Tcp[i,2])); areatotalch3:=areatotalch3+area; end;  END; { * * s t a r t s main program**} begin presentation; getdata; reset(infile2) ; {open i n f i l e F o r i : = 1 t o 10 d o begin readln(InFile2);  {skip  end ; rewrite(OutFile); writeln(OutFile,'FILE = writeln(OutFile); writeln(OutFile,Titlel); writeln(OutFile,Title2); writeln(OutFile);  with rotation  comments f r o n  coordinates)  infile2)  ',FileName2);  writeln(OutFile,'molecule.PAS  output  for  input  file  ',FileNamel);  writeln(OutFile); w r i t e l n ( O u t F i l e , ' C u t - o f f d i s t a n c e between ' , c u t o f f : 5 : 2 , ' cutdis:5:2 C o n t a c t time= ',tau:2:l); writeln(OutFile); writeln(OutFile); write(outfile,' R"2(aro f i r s t ) ',' intercept ' , ' slope '); w r i t e l n ( O u t F i l e , ' areatotald63= ' , ' rotation(x,y,z)= ' , ' translation(x,y,z) {open  file  with rotation  c o o r d i n a t e s and r e a d s i n  REPEAT read(InFile2,junk); read(InFile2,junk); read(InFile2,junk);  {label  read(InFile2,corrCoeff); read(InFile2,intercept); read(InFile2,slope); read(InFile2,degree_x); read(InFile2,degree_y); read(InFile2,degree_z); read(InFile2,movex); read(InFile2,movey); r e a d l n ( I n F i l e 2 ,move.z) ;  }  slope,  intercept}  355  for i:=l t o 6 do begin readln(infile2); end; { of i loop) read(InFile2,junk); read(InFile2,junk); read(InFile2,junk);  {skip  the  (label  6  next  lines}  }  read(InFile2,corrCoeffch3); read(InFile2,interceptch3); readln(InFile2,slopech3);  for i:=l t o 6 do begin readln(infile2); end; { of i loop}  {skip  the  next  6  lines}  rotationx; rotationy; rotationz; movemolecule ; writeln;writeln; writeln('rotation (',degree_x,',',degree_y,',',degree_z,') ','move=(',movex:1:1,',',movey:1:1,',',movez:1:1,')'); writeln;writeln; findcoor; secondmomentaro ; secondmomentch3; lorenziana ; write(OutFile,' d63 ' , c o r r C o e f f : 1 0 : 4 , ' ',intercept:10:4); write(OutFile,' ',slope:10:6,' ',areatotal,' '); write(outfile,degree_x:2:0,' ',degree_y:2:0,' ',degree_z:2:0,' writeln(OutFile,movex:2:2,' ',movey:2:2,' ',movez:2:2); write(OutFile,' d43 ' , c o r r C o e f f c h 3 : 1 0 : 4 , ' ',interceptch3:10:4); write(OutFile,' ',slopech3:10:6,' ',areatotalch3,' '); write(outfile,degree_x:2:0,' ',degree_y:2:0,' ',degree_z:2:0,' writeln(OutFile,movex:2:2,' ',movey:2:2,' ',movez:2:2); { f o r j : = 1 t o 2 do for i:=l t o n s i do begin writelnfOutfile,'Tcp=',i,j,'=  ',Tcp[i,j]:5:2);  end; ) writeln(outfile);  UNTIL  EOF(InFile2);  (of  EOF l o o p  }  close(InFile2); close(OutFile); writeln('calculations end.  successfully  completed');  ');  ');  356 APENDIX 5: Program to Calculate Average Internuclear Si-H Second Moments for the Aromatic Hydrogens Flipping about the C 2 Axis in the System of Orthorhombic ZSM-5 Low Loaded with p-Xylene Space Group Pnma. program PXYLFLIP const nhidr=6; nsi=6; a=20.022; b=19.899; c=13.383; TYPE  vec = A R R A Y [ 1 . . 3 ] of r e a l ; A S C I I _ F i l e = TEXT; a t o m _ c o o r d = RECORD x_pos, y_pos, z_pos : r e a l ; END; {of RECORD a t o m _ c o o r d } var movex,movey,movez, X Y, Z : r e a l ; varx,vary,varz:integer; l,i,j,k,n,m,h:integer; dist:real,smtstl,SMtl,smtst2,SMt2:real; x h , y h , z h : a r r a y [ 1 . . 2 7 , 1 . . 8 , 1 . . n h i d r ] of r e a l ; x i n , y i n , z i n : a r r a y [ 1 . . n h i d r ] of r e a l ; { i n i t i a l c o o r d i n a t e s x a t , y a t , z a t : a r r a y [ 1 . . n h i d r ] of r e a l ; xSi,ySi,zSi :array[1..nSi] of r e a l ; SM . - a r r a y [ 1 . . 6 , 1 . . 2 ] o f r e a l ; inTcp:array[1..6,1..2] of r e a l ; output:text; FileNamel, FileName2: s t r i n g ; {for i n p u t and o u t p u t ) (  Titlel, InFile, cutcorr,  title2 : string; OutFile,0utFile2  : ASCII_File;  cutcorrCH3,cutoff:real;  { Disk  files  of  H from  }  {maximum i n t e r a t o m i c  distance  to  the c a l c u l a t i o n s ) d e g r e e _ x , d e g r e e _ y , d e g r e e _ z , r o t _ x , rot__y, r o t _ z : i n t e g e r ,S l o p e , I n t e r c e p t , C o r r C o e f f : REAL; Slopech3, Interceptch3,CorrCoeffch3 : REAL; s m l : a r r a y [ 1 . . 4 , 1 . . 8 , 1 . . 2 7 ] of r e a l ; s m 2 : a r r a y [ 1 . . 4 , 1 . . 8 , 1 . . 2 7 ] of r e a l ; s m 3 : a r r a y [ 1 . . 4 , 1 . . 8 , 1 . . 2 7 ] of r e a l ; s m 4 : a r r a y [ l . . 4 , 1 . . 8 , 1 . . 2 7 ] of r e a l ; s m 5 : a r r a y [ 1 . . 4 , 1 . . 8 , 1 . . 2 7 ] of r e a l ; theta,phi:real; r,vx,vy,vz:real; soprom:array[1..6] of r e a l ; ml,m2,m3,m4,m5,m6:real;  procedure presentation; begin { MAIN BODY ) { OPEN A S C I I f i l e  (with  .dmc e x t e n s i o n )  containing  p-xylene)  crystal  data  )  consider  in  357  writeln('  smarlo2m.PAS');  wri t e l n ; writeln('  by  A.C.  Diaz');  writeln; writeln('This  program w i l l  writeln('specific x,  is  degrees  rotate  the  intervals  molecule around x,  and a l s o w i l l  y OR z  move t h e  by');  molecule  in  y,  and z ' ) ; w r i t e l n ( ' i t w i l l w r i t e an o u t p u t f i l e f o r alchemy and an o u t p u t file'); writeln(' w i t h Interatomic D i s t a n c e s , D i p o l a r C o u p l i n g s , Second Moments'); w r i t e l n ( ' s p a t i a l g r o u p Pnma, 12 S i , a n d 4 h y d r o g e n a t o m s , s e c o n d moments averaged'); writeln('for  arigen  motion,  needs a input  writeln('Enter  Name o f  the ASCII  writeln; w r i t e ( ' I n p u t Filename : '); readln(FileNamel); Assign(InFile, FileNamel); writeln; writeln;writeln; w r i t e l n ( ' E n t e r Name o f t h e A S C I I .sm:  file  with coordinates in  angtron  and  (0,0,0)'); writeln; writeln; crystal  File  Input  for  output  '); writeln; w r i t e ( ' O u t p u t F i l e n a m e f o r s e c o n d moments: readln(FileName2); Assign(OutFile, FileName2); writeln; writeln('Enter Cut-off distance for w r i t e l n ( ' A l l i n t e r a c t i o n s which are writeln; write('  CUT-OFF D i s t a n c e  File  (with f u l l  data  (with  full  writeln('All  Cut-off  for  correlations better  R*2  :=  ');  for  than  the  aromatic  this  will  0.996)  :=  data  ');  b e o u t p u t ' ) ,-  writeln; writer  CUT-OFF c o r r e l a t i o n  (eg.  readln(cutcorr); w r i t e l n ( ' E n t e r C u t - o f f f o r b e s t R~2 w r i t e l n ( ' A l l c o r r e l a t i o n s b e t t e r than writeln; write(*  CUT-OFF c o r r e l a t i o n  readln(cutcorrCH3);  end;  procedure getdata; var xl,yl,zl:real;  (eg.  path)  S e c o n d Moment C a l c u l a t i o n s ' ) ; s h o r t e r than t h i s w i l l be o u t p u t ' ) ;  (Angstroms)  best  ');  '),-  readln(cutoff); writeln('Enter  path):  ' ) ,-  f o r CH3 d a t a ' ) ; t h i s w i l l be o u t p u t ' ) ; 0.996)  :=  ') ;  add  358  begin { Open the input f i l e for read only, reset(InFile);  and reset pointer  { Now read i n the C r y s t a l data, angles and dimensions etc r e a d l n ( I n F i l e ) ; ; {skip heading and word TITLE) readlndnFile, Titlel) ; readln(InFile, T i t l e 2 ) ; r e a d l n ( I n F i l e ) ; {skip comments) { Now reads i n the data for the atom coordinates } for h:=l to nhidr do begin  to beginning } }  read(InFile,XI); Xin[h]:= x l ; read(InFile,Yl); yin[h]:= y l ; readln(InFile,zl); zin[h]:= z l ; end; for i:=l  to nsi do  begin read(InFile,xl); XSi[i]:=xl; read(InFile,yl); YSi[i]:=yl; r e a d l n d n F i l e , zl) ; ZSi[i]:=zl; end; close(InFile); end; Procedure r o t a t i o n x ; begin { Now reads i n the data for the atom coordinates } for h:=l to nhidr do begin X:= Xin[h] ; Z:= (-Yin[h]*sin(degree_X*3.14159/180)+Zin[h]*cos(degree_X*3.14159/180)); Y:= (Yin[h)*cos(degree_X*3.14159/180)+Zin[h]*sin(degree_X*3.14159/180)); Xatth):= X; Yat[h]:= y; Zat[h]:= z; end; end; Procedure r o t a t i o n y ; begin for h:=l  to nhidr do  359 begin Y: = (Yat[h]); Z: = (Zat[h]*cos(degree_Y*3.14159/180)-Xat[h]*sin(degree_Y*3.14159/180)); X:= (Xat[h]*cos(degree_Y*3.14159/180)+Zat[h]*sin(degree_Y*3.14159/180)); Xat[h]:= X; Yat[h]:= y; Zat[h]:= z; end; end; Proceduxe r o t a t i o a Z ;  Begin for h:=l to nhidr do begin Z:= Zat[h]; Y:= (-Xat[h]*sin(degree_Z*3.14159/180)+Yat[h)*cos(degree_Z*3.14159/180)); X:= (Xat[h]*cos(degree_Z*3.14159/180)+Yat[h]*sin(degree_Z*3.14159/180)); Xat[h]:= X; Yat[h]:= y; Zat[h]:= z; end ;  end ;  Procedure movemolecule;  begin for h:=l to nhidr do begin Zat[h]:= Zat[h]+(0.5188*c)+movez; Yat[h]:= Yat[h]+(0.25*b)+movey; Xat[h]:= Xat[h]+(-0.01405*a)+movex; end ; end; procedure  findcoor;  begin for i : = l to nhidr do P212121, to }  {Calculates the other positions for the space group {create the complete unit c e l l )  begin k:=l; XH[l,k,i]:=xat[i]/a; YH[l,k,i]:=yat[i]/b; ZH[l,k,i]:=zat[i]/c;  360  ',XH[l,k,i] :6:4,' writeln( H' , l , k , i , ' ' , Z H [ l , k , i ] : 6 : 4) ; inc (k) ; XH[1,k,i]:= 0.5-xat[i]la; YH[1,k,i]:= -yat[i]/b; Z H [ l , k , i ] : = 0.5 + z a t [ i ] I c ; ',XH[l,k,i]:6:4, writeln('H' , l , k , i , ' , Z H I 1 , k , i ] : 6 : 4) ; inc(k); XH[1,k,i]:= -xat[i]/a; Y H [ l , k , i ] : = 0.5+yat[i]lb; ZH[l,k,i]:= -zat[i]Ic; writeln('H' , l , k , i , • ' , X H [ l , k , i ] 6:4, ' ' , Z H [ l , k , i ] : 6 : 4) ; inc(k); X H [ l , k , i ] : =0 . 5 + x a t [ i ] / a ; YH[1,k,i):=:0.5-yat[i]lb; Z H [ l , k , i ] : =^0.5-zat[i]Ic; ',XH[1,k,i]:6:4, writeln('H' , 1 , k , i , ' ' , Z H [ 1 , k , i ] : 6 : 4) ; inc(k); X H [ 1 , k , i ] : =: - x a t [ i ] l a ; Y H [ 1 . k , i ] : =- y a t [ i ] l b ; Z H [ l , k , i ] : =- z a t [ i ] I c ; writeln('H' , l , k , i , ' ',XH[l.k,i]:6:4, • , Z H [ l , k , i J : 6 : 4) ; inc(k); XH 1 1 , k , i ] : =0.5+xat[i]/a;• YH [ 1 , k, i )•: =y a t [ i ] l b ; ZH[l,k,i]:= 0.5-zat[i]Ic; ',XH[l,k,i]:6:4, writeln('H' , 1 , k , i . ' , Z H [ l , k , i ] : 6 : 4) ; inc(k); XH[1,k,i]:= xat[i]/a; YH[1,k,i]:= 0.5-yat[i]/b; ZH[l,k,i]:= zat[i]Ic; writeln('H' , l , k , i , ' ',XH[l,k,i):6:4, ' , Z H [ l , k , i ] : 6 : 4) ; inc(k); X H [ l , k , i ] : = 0.5-xat[i]/a; Y H [ l , k , i ] : = • 0.5+yat [i] lb; Z H t l . k , i ] : = •0.5+zat[i]Ic; writeln('H' , l , k , i , ' ',XH[l,k,i):6:4, ' , Z H [ l , k , i ] : 6 : 4) ; end; 1  1  1  for i : = l P212121,  to  to nhidr do  1  ,YH[l,k,i] :6:4, '  ,YH[l,k,i] :6:4, '  ',YH[l,k,i] :6:4, '  ,YH[l,k,i]:6:4,'  ,YH[l,k,i]:6:4,'  ,YH[l,k,i] :6:4, '  ,YH[l,k,i]:6:4,'  ,YH[l,k,i) :6:4, '  {Calculates the other positions  }  .  {create the complete 2 n d unit c e l l } for k:=l to 8 do begin XH[2,k,i]:=XH[l,k,i]-l;  for the space group  361  YH[2,k,i]:=YH[l,k,i]-1; ZH[2,k,i]:=ZH[l,k,i]; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other p o s i t i o n s {create  f o r k:=l begin  f o r the space  group  for  the space  group  f o r the space  group  for  group  } to  the complete 3th u n i t  cell)  8 do  XH[3,k,i):=XH[l,k,i]-l; YH[3.k,i):=YH[l,k,i]; ZH[3,k,i]:=ZH[l,k,i]; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other p o s i t i o n s  } {create  f o r k:=l begin  to  the complete  4th u n i t  cell)  8 do  XH[4,k,i):=XH[l,k,i]-l; YH[4,k,i):=l+YH[l,k,i]; ZH[4,k,i]:=ZH[l,k,i]; end; for  i.-=l  P212121,  to  to nhidr  do  {Calculates the other p o s i t i o n s  ) {create  f o r k:=l begin  to  the complete  5th u n i t  cell)  8 do  XH t 5 , k , i ) : = X H [ 1 , k , i ] ; YH[5,k,i):=YH[l,k,i)-l; ZH[5,k,i]:=ZH[l,k.i]; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other p o s i t i o n s  } {create  f o r k:=l begin  to  8 do  XH[6,k,i]:=XH[l,k,i]; YH[6,k,i):=l+YH[l,k,i]; ZH[6,k,i]:=ZH[l,k,i]; end;  the complete  6th u n i t  cell)  the space  362  for  i:=l  P212121,  to  to  nhidr  do  {Calculates  other  positions for  the  space  group  the  space  group  the  space  group  the  space  group  the  space  group  } {create  f o r k:=l begin  the  to  the  complete 7th  unit  cell)  8 do  XH[7,k,i]:=l+XH[l,k,i]; YH[7,k, i] :=YHU,k, i] ; ZH[7,k,i]:=ZH[l,k,i] ; end;  for  i:=l  P212121,  to nhidr  to  do  {Calculates {create  f o r k:=l begin  the  other p o s i t i o n s for  } to  the  complete 8th  unit  cell)  8 do  XH[8,k,i]:=l+XH[l,k,i]; YH[8,k,i]:=YH[l,k,i]-l; ZH[8,k,i]:=ZH[l,k,i); end; for  i:=l  P212121,  to  to nhidr  do  {Calculates  other p o s i t i o n s for  } {create  f o r k:=l begin  the  to  the  complete 9th u n i t  cell)  8 do  XH[9,k,i]:=l+XH[l,k,i]; YH[9,k,i]:=l+YH[l,k,i]; ZH[9,k,i]:=ZH[l,k.i]; end; for  i:=l  P212121,  to  to n h i d r  do  {Calculates  other  positions for  ) {create  f o r k:=l begin  the  to  the  complete 10th  unit  cell)  8 do  XH[10,k,i]:=XH[l,k,i]; YH[10,k,i]:=YH[l,k,i]; ZH[10,k,i):=l+ZH[l,k,i); end; for  i:=l  P212121, for  to  k:=l  to nhidr ) to  do  {Calculates {create  8 do  the  the  other p o s i t i o n s for  complete 11th  unit  cell)  363 begin  XH[ll,k,i]:=XH[l,k,i]-1; YH[ll,k,i]:=YH[l,k,i]-l; ZH[ll,k,i]:=l+ZH[l,k,i]; end; for i:=l to nhidr P212121, t o }  do  {Calculates  the other  {create the complete f o r k:=l begin  positions  12th unit  f o r the space  group  cell}  t o 8 do  XH[12,k,i]:=XH[l,k,i]-l; YH[12,k,i]:=YH[l,k,i]; ZH[12,k,i]:=l+ZH[l,k,i]; end; for  i:=l  P212121,  to nhidr  do  {Calculates  the other  positions  f o r the space  group  to } {create  f o r k:=l t o begin  the complete  13th unit  cell}  8 do  XH[13,k,i]:=XH[l,k,i]-l;  YH[13,k, i ] . : = l + Y H [ l , k , i ] ; ZH[13,k,i]:=l+ZH[l,k,i]; end; inc(1); f o r i:=l t o n h i d r do {Calculates P212121,  the other  positions  f o r the space  group  to } {create  f o r k:=l t o begin  the complete  14th unit  cell}  8 do  XH[14,k,i] =XH[l,k,i]; YH[14,k,i]:=YH[l,k,i]-l; ZH[14,k,i]:=l+ZH[l,k,i]; end ; :  for  i:=l  P212121,  to nhidr  do  {Calculates  the other  f o r the space  to } {create the complete  for k:=l begin  t o 8 do  XH[15,k,i]:=XH[l,k,i); YH[15,k,i]:=l+YH[l,k,i]; ZH[15,k,i):=l+ZH[l,k,i]; end;  positions  15th unit  cell}  group  364  for  i:=l  P212121,  to  to nhidr  do  {Calculates {create  f o r k:=l begin  the other p o s i t i o n s f o r  the space  group  the space  group  the space  group  } to  the complete 16th u n i t  cell)  8 do  XH[16,k,i]:=1+XH[1,k,i]; YH[16,k,i]:=YH[l,k,i]; ZH[16,k,i]:=l+ZH[l.k,i]; end;  for  i:=l  P212121,  to  to nhidr  do  {Calculates {create  f o r k:=l begin  the other p o s i t i o n s f o r  } to  the complete 17th u n i t  cell)  8 do  XH[17,k,i]:=l+XH[l,k,i]; YH[17,k,i]:=YH[1,k,i]-1; ZH[17,k,i]:=l+ZH[l,k,i]; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates  positions for  } {create  f o r k:=l begin  the other  to  the complete 18th u n i t  cell)  8 do  XH[18,k,i]:=l+XH[l,k,i]; YH[18,k,i]:=l+YH[l,k,i]; ZH[18,k,i]:=l+ZH[l,k,i]; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates  the space group  } {create  f o r k:=l begin  the other p o s i t i o n s f o r  to  the complete 19th u n i t  cell)  8 do  XH[19,k,i]:=XH[l,k,i] ; YH[19,k,i]:=YH[l,k,i] ; ZH[19,k,i]:=ZH[l,k,i]-l; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates  ) {create  for  k:=l  the other p o s i t i o n s for  to  8 do  the complete 20th u n i t  cell)  the space group  365  begin  XH[20,k, i ] : = X H [ l , k , i ] - 1 ; YH[20,k,i]:=YH[l,k,i]-1; ZH[20,k,i]:=ZH[l,k,i]-1; end ; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other {create  f o r k:=l begin  positions  for  the space  group  the space  group  the space  group  the space  group  } to  the complete 21th u n i t  cell}  8 do  XH[21,k,i]:=XH[l,k,i]-l; YH[21,k,i]:=YH[l,k,i]; ZH[21,k,i]:=ZH[l,k,i]-l; end; for  i:=l  P212121,  to  to nhidr  do  { C a l c u l a t e s the other {create  f o r k:=l begin  positions  for  } to  the complete  22th u n i t  cell}  8 do  XH[22,k,i]:=XH[l,k,i]-l; YH[22,k,i]:=l+YH[l,k,i]; ZH[22,k,i]:=ZH(l,k,i]-1; end ; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other {create  f o r k:=l begin  positions  for  } to  the complete  23th u n i t  cell}  8 do  XH[23,k,i):=XH[l,k,i]; YH[23,k,i]:=YH[l,k,i]-l; ZH[23,k,i]:=ZH[l,k,i]-1; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other {create  f o r k:=l begin  to  8 do  XH[24,k,i]:=XH[l,k,i]; YH[24.k,i]:=l+YH[l,k,i]; ZH[24,k,i]:=ZH[l,k,i]-1; end;  positions  for  } the complete 24th u n i t  cell}  366  for  i:=l  P212121,  to  to nhidr  do  { C a l c u l a t e s the other {create  f o r k:=l begin  positions  for  the space  group  the space  group  the space  group  } to  the complete 25th u n i t  cell)  8 do  XH[25,k,i]:=l+XH[l,k,i]; YH[25,k,i]:=YH[l,k,i]; ZH[25,k,i]:=ZH[l,k,i]-l; end; for  i:=l  P212121,  to  to nhidr  do  {Calculates the other {create  f o r k:=l begin  positions  for  } to  the complete  26th u n i t  cell)  8 do  XH[2 6 , k , i ] : = l + X H [ l , k , i ] ; YH[26,k,i]:=YH[l,k,i)-l; ZH[26,k,i]:=ZH[l,k,i]-l; end; for  i:=l  P212121,  to  to nhidr  do  { C a l c u l a t e s the other {create  f o r k:=l begin  positions  for  } to  8 do  XH[27,k,i]:=l+XH[l,k,i]; YH[27,k,i]:=l+YH[l,k,i]; ZH[27,k,i]:=ZH[l,k,i]-l; end ;  end;  p r o c e d u r e seeondmomentaro;  begin f o r n : = l t o n s i do begin { f o r 1:=1 t o 27 d o f o r k:=l t o 8 do for i:=l t o 4 do begin sml[i,k,l]:=0; sm2[i,k,1]:=0; sm3[i,k,l]:=0; sm4[i,k,l]:=0; sm5[i,k,1]:=0;  the complete 27th u n i t  cell)  367  end; soprom[j]:=0;} {**aromatic f o r 1:=1 for k:=l for i:=l begin  hydrogen a v e r a g i n g * * )  t o 27 d o t o 8 do t o 4 do  vx:=(XSi[j]-XH[l,k,i]*a); vy:=(YSi[j]-YH[l,k,i)*b); vz:=(ZSi[j]-ZH[l,k,i]*c); r:=sqrt(sqr(vx)+sqr(vy)+sqr(vz)); i f r<2.8 then begin writeln(OutFile,'DISTANCE end ; i f r<cutoff begin  Si',J,'-H  IS  ',r:4:2);  then  write(OutFile, ' S i ' , j , ' ', 'H',1,k,i, ' : '); write(OutFile,XH[l,k,i] :6:4, ' ' , Y H [ 1 , k , i ) :6 : 4 , ' ' , Z H [ 1 , k , i ] :6 : 4 , ' ' , r 4:3 ) ; theta:=arctan(sqrt(1-sqr(vz/r))/(vz/r)); phi:=arctan(vy/vx); sml[i,k,1):=1/(r*r*r)*((1/2)*(3*sqr(cos(theta))-1) ); sm2[i,k,l]:=l/(r*r*r)*(3*cos(theta)*sin(theta)*cos(phi)); sm3[i,k,l]:=l/(r*r*r)*(3*cos(theta)*sin(theta)*sin(phi)); sm4[i,k,1]:=1/(r*r*r)*(3*sqr(sin(theta))*cos(2*phi)); sm5[i,k,l]:=l/(r*r*r)*(3*sqr(sin(theta))*sin(2*phi));  r  :  end ; end;{end loop  {**averaging  l,k,i:=4)  of the aromatic hydrogen  positions**)  for 1:=1 to 27 do for k:=l to 8 do begin  ml:=sqr((sml[1,k,1] + m2:=sqr((sm2[1,k, 1] + m3:=sqr{(sm3[1, k, 1 ] + m4:=sqr((sm4[1,k,1]+ m5:=sqr((sm5[1,k,1]+  sml[2,k,l])/2) sm2[2,k,l])12) sm3[2,k,l])/2) sm4[2,k,l])/2) sm5[2,k,l])/2)  sqr{(sml[3,k,l]+ sqr((sm2[3,k,l]+ sqr((sm3[3,k,l]+ sqr((sm4[3,k,1]+ sqr((sm5[3,k,1]+  sml[4,k,l])/2) sm2[4,k,l])/2) sm3 [ 4 , k , l ] ) 1 2 ) sm4[4,k,l])/2) sm5[4,k,l])/2)  soprom[j] :=soprom[j] + ml+(l/3) * (m2-t-m3) ••• (1/12) * (m4+m5) end; SM[j,1]:=(soprom[j])*114.06967e6/2 ; end;  {close begin  from n s i )  { c a l c u l a t e s s e c o n d moment i n H z )  (A) =  368  f o r j : = 1 t o n s i do begin w r i t e l n ( ' S E C O N D MOMENT S i ' , j , '= end; end; p r o c e d u r e  ' ,SM[j,2] : 4 : 4 ) ;  secondmomentch3;  var r,vx,vy,vz:real; DCtHHHZ : r e a l ; sumr,static:real; begin  for j:=l begin  t o n s i do  {sumr:=0 ; sm[j,2]:=0;  }  f o r 1:=1 t o 27 d o f o r k : = l t o 8 do f o r i : = 5 t o 6 do begin vx:=(XSi[j]-XH[l,k,i]*a); vy:=(YSi[j]-YH[l,k,i]*b); vz:=(ZSi[j]-ZH[l,k,i)*c); r:=sgrt(sqr(vx)+sqr(vy)+sqr(vz)); i f r<cutoff then begin  ,  sumr:=sumr+l/sqr(r*r*r); {writeln(outfile, 'si ' ,j , ' H ' , Z H [ l , k , i ] : 4 : 4 , ' r= ' , r : 2 : 2 ) ; end; end ;  {to  have t h e  total  \ l , k , i , ' }  ' , xH [ 1 , k, i ] : 4 :4 , • ,  s e c o n d moment i n r a d 2 H z 2 ,  sqr((gamma)H*(gamma)Si*h/2pi*Uo/4pi)  *1/  multiply  3 *  3/4  sm) } SM[j,2]:=(sumr)*114.06967e6/2; w r i t e l n ( ' S E C O N D MOMENT S i ' , j , ' =  end; end;  ',SM[j,2):4:4);  for  ' , YH [ 1 , k, i ] : 4 : 4 , '  5.6291128e9,  which  (1/3*1(1+1)(heteronuclear  is  369  PROCEDURE DoLeastSquares; const n=6;  {number  of  data  VAR I : INTEGER; Sumx, Sumy, Sumxx, Sumxy, Sumyy, Denom :  BEGIN inTcp[1,1] inTcp[2,1] inTcp[3,1] inTcp[4,1] inTcp[5,1] inTcp[6,1]  point}  REAL;  1000/31.95; 1000/28; 1000/113.7 1000/15.48 1000/58.06 1000/31.8;  Sumx := 0 . 0 ; Sumy := 0 . 0 ; Sumxx Sumxy := 0 . 0 ; Sumyy := 0.0;  0.0;  FOR I := 1 TO n DO BEGIN Sumx := S u m x + S M [ 1 , 1 ] ; Sumy := S u m y + i n T c p [ I , 1 ] ; Sumxx := S u m x x + S M [ 1 , 1 ] * S M [ 1 , 1 ] ; Sumxy := Sumxy+ S M [ 1 , 1 ] * i n T c p [ 1 , 1 ] ; Sumyy := SumYY+ S Q R ( i n T c p [ 1 , 1 ] ) ; END; Denom : = S Q R ( S u m x ) - N * S u m x x ; write('denom= ',denom:4:4); S l o p e := (Sumx*Sumy-N*Sumxy)/Denom; I n t e r c e p t := (Sumx*Sumxy-Sumy*Sumxx)/Denom; C o r r C o e f f := sqr((Sumx*Sumy-N*Sumxy)/SQRT((SQR(SumY)-N*SumYY) * (SQR(Sumx) - N * S u m x x ) ) ) ; END; PROCEDURE  const n=6;  DoLeastSguaresch3;  {number o f  VAR I : INTEGER; Sumx, Sumy, Sumxx, Sumxy, Sumyy, Denom :  data  point}  REAL;  BEGIN inTcp[1,2] inTcp[2,2] inTcp[3,2] inTcp[4,2] inTcp[5,2] inTcp[6,2]  1000/7.61; 1000/5.67; 1000/11.98 1000/11.24 1000/14.24 1000/8.54;  370  Sumx := 0 . 0 ; Sumy := 0 . 0 ; Sumxx := Sumxy := 0 . 0 ; Sumyy := 0 . 0 ;  0.0;  FOR I := 1 TO n DO BEGIN Sumx := Sumx+SM[1,2] ; Sumy := Sumy+ i n T c p [ 1 , 2 ] ; Sumxx := S u m x x + S M [ I , 2 ] * S M [ I , 2 ] ; Sumxy := Sumxy+SM[1,2]*inTcp[1,2]; Sumyy := S u m Y Y + S Q R ( i n T c p [ 1 , 2 ] ) ; write('sumax= ',sumx:4:4); END; Denom := S Q R ( S u m x ) - N * S u m x x ; write('denom= ',denom:4:4); S l o p e c h 3 := ( S u m x * S u m y - N * S u m x y ) / D e n o m ; Interceptch3 := ( S u m x * S u m x y - S u m y * S u m x x ) / D e n o m ; C o r r C o e f f c h 3 := s q r ( ( S u m x * S u m y - N * S u m x y ) / S Q R T ( ( S Q R ( S u m Y ) - N * S u m Y Y ) * (SQR(Sumx) - N * S u m x x ) ) ) ; END; { * * s t a r t s main program**} begin presentation; getdata; rewrite(OutFile); writeln(OutFile,'FILE = ',FileName2); writeln(OutFile); writeln(OutFile,Titlel); writeln(OutFile,Title2); writeln(OutFile); w r i t e l n ( O u t F i l e , ' m o l e c u l e . P A S output for writeln(OutFile); writeln(OutFile,' ' , cutcorr:5:2) ; writeln(OutFile);  Cut-off  write(outfile,'Si,j, ' ) ; writeln(OutFile,'  ','SM[j] slope  f o r v a r x : = 0 t o 6 do f o r v a r y : = 0 t o 12 do for varz:=0 to 6 do f o r r o t _ x : = 0 t o 8 do f o r r o t _ y : = 0 t o 18 do f o r r o t _ z : = 0 t o 8 do begin movex:=varx/10 ; movey:=vary/10 ; movez:=varz/10 ; d e g r e e _ x : = r o t _ x * 3; degree_y:=rot_y*3 ; degree_z:=rot_z*3 ; rotationx; rotationy; rotationz; movemolecule; writeln;writeln;  distance  ','  ',  input  file  cutoff:5:2,'  ',  '  1/Tcp[j]  rotation(x,y,z)=  ','  ',FileNamel); Angstroms ' , '  ','  R"2  Cut-off  ','  R"2=  intercept  translation(x,y,z)=');  371  writeln('rotation (',degree_x,',',degree_y,',',degree_z,') ','move=(',movex:1:1,',',movey:1:1,',',movez:1:1,')'); writeln;writeln,• findcoor; secondmomentch3; DoLeastSguaresch3; writeln;writeln; writeln('correlation= ', CorrCoeffch3:4:4); writeln;writeln; i f CorrCoeffch3>cutcorrch3 then begin secondmomentaro ; DoLeastSquares; i f CorrCoeff>cutcorr then begin for  j:=1 t o 6 do begin write(OutFile,j,' ',SM[j,1]:10:2,' ',inTcp[j,1]:10:2, • ',CorrCoeff:10:4,' ',intercept:10:4); write(OutFile,' ',slope:10:6,' ' ) ; write(outfile,degree_x,' ',degree_y,' ' degree_z, '); writeln(OutFile,movex:2:2,' ',movey:2:2,' ',movez:2:2); e n d ; { c l o s e l o o p f o r SM 1 a n d 2} w r i t e l n ( O u t F i l e , ' r e s u l t s f o r t h e CH3 g r o u p ' ) ; ,  /  for  j:=1 t o 6 do begin write(OutFile,j,j,' ',SM[j,2]:10:2,' ',inTcp[j,2]:10:2, ' • ,CorrCoeffch3:10:4); write(OutFile,' ',interceptch3:10:4,' ',slopech3:10:6,' '); write(outfile,degree_x,' ',degree_y,' ',degree_z,' '); writeln(OutFile,movex:2:2,' ',movey:2:2,' '.movez:2:2); e n d ; { c l o s e l o o p f o r SM 1 a n d 2) w r i t e l n ( O u t F i l e , ' r e s u l t s f o r the aromatic p r o t o n s ' ) ; end; {close i f corrcoeffch3) end; {close i f c o r r c o e f f for aromatics) END; { c l o s e a l l l o o p o f r o t a t i o n a n d t r a n l a t i o n )  close(OutFile); writeln('calculations end.  successfully  completed');