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UBC Theses and Dissertations

Study of molecular motion on main group III and V addition complexes by broadline and pulse NMR. Ang, Tian Tse 1972

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13 »^>1 STUDY OF MOLECULAR MOTION ON MAIN GROUP I I I AND V ADDITION COMPLEXES BY BROADLINE AND PULSED NMR by TIAN TSE ANG B . S c , Nanyang U n i v e r s i t y , S i n g a p o r e , 1967 A THESIS SUBMITTEQ IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Chemistry We a c c e p t , t h i s t h e s i s as conforming t o the r e q u i r e d s tandard THE UNIVERSITY OF BRITISH COLUMBIA August , 1972. In present ing t h i s thes is in p a r t i a l f u l f i l m e n t of the requirements fo r an advanced degree at the Un ive rs i t y of B r i t i s h Columbia, I agree that the L ib ra ry sha l l make i t f r e e l y a v a i l a b l e for reference and study. I fu r ther agree that permission for extensive copying of th i s t h e s i s fo r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s representat i ves . It is understood that copying or p u b l i c a t i o n o f t h i s thes i s f o r f i n a n c i a l gain s h a l l not be allowed without my wr i t ten permiss ion . Department of The Un ive rs i t y of B r i t i s h Columbia Vancouver 8, Canada A b s t r a c t The proton magnetic resonance a b s o r p t i o n and s p i n - l a t t i c e r e l a x a t i o n measurements have been c a r r i e d out on Me^NrBMe^i Me3N-A£Me3, Me 3P-A£Me 3, M e 3 P - B M e 3 , M e ^ M e g B , Me 2 NH-BMe 3 , Me 2 NH-AjiMe 3 , Me 3NBC£ 3, Me^NBB^, and t r i m e t h y l a m i n e - h a l o g e n complexes i n o r d e r to study the m o l e c u l a r motion and phase t r a n s i t i o n s of these complexes i n the s o l i d s t a t e between 77 K to t h e i r m e l t i n g p o i n t s . The a c t i v a t i o n energies and r a t e parameters a s s o c i a t e d w i t h these motional processes are r e p o r t e d . The second moment data o f a l l the t r i m e t h y l amine a d d i t i o n complexes i n d i c a t e the methyl groups at tached to n i t r o g e n are a l l r i g i d (as f a r as the nmr second moment i s concerned) a t l i q u i d n i t r o g e n temperature and at h i g h e r temperature the methyl groups as w e l l as the t r i m e t h y l a m i n e moiety r o t a t e w i t h a frequency g r e a t e r than about 10 kHz. The methyl groups r o t a t e p r i o r to the r o t a t i o n o f the t r i m e t h y l a m i n e moiety i n a l l but the M e 3 N - B r 2 and Me 3 N-BMe 3 complexes. The present study concludes t h a t i f the i n t e r m o l e c u l a r c o n t r i b u t i o n s t o the a c t i v a t i o n energ ies f o r methyl group r e o r i e n t a t i o n s are o f the same o r d e r , the a c t i v a t i o n energies f o r the methyl groups f o l l o w the t r e n d of the s t a b i l i t y o f the t r i m e t h y l amine complexes. The second moment data show t h a t the methyl groups a t tached t o b o r o n , phosphorus and aluminium are a l l r e o r i e n t a t i n g a t 77 K at a r a t e f a s t e r than about 10 kHz. The r e l a x a t i o n s t u d i e s conclude t h a t the a c t i v a t i o n energies f o r the three methyl groups a t tached to v a r i o u s c e n t r a l atoms decrease i n the o r d e r N > C > B > S i > hi. - i i i -Comparison o f the c a l c u l a t e d and exper imenta l mim'mum f o r methyl group r e o r i e n t a t i o n suggests t h a t there i s smal l d i s t o r t i o n of the C 3 p o t e n t i a l w e l l , and comparison o f the c a l c u l a t e d and exper imental p r e - e x p o n e n t i a l f a c t o r s suggests t h a t the a c t i v a t i o n energy f o r r o t a t i o n o f the whole molecule o r the moiety i s temperature dependent. Table o f Contents PAGE ABSTRACT - - i i TABLE OF CONTENTS—— — — - i v LIST OF TABLES - x LIST OF FIGURES - x i i i ACKNOWLEDGMENTS - x v i i D E D I C A T I O N — CHAPTER I INTRODUCTION - 1 A. I n t r o d u c t i o n to A d d i t i o n Complexes 1 B. V a r i o u s S t u d i e s on A d d i t i o n Complexes 2 C. NMR S t u d i e s on A d d i t i o n Complexes 3 References (Chapter I) 4 CHAPTER II INTRODUCTION TO NMR THEORY- - - 6 A. Elementary Resonancy Theory 6 B. The L i n e Shape F u n c t i o n - - 7 C. Second Moment of A b s o r p t i o n L i n e Shape 10 D. S p i n - l a t t i c e R e l a x a t i o n T i m e — 15 E. D i s t r i b u t i o n o f C o r r e l a t i o n Times and t h e i r E f f e c t on T, and E , — 20 i a F. A c t i v a t i o n Energy 23 References (Chapter I I ) - - - — 24 - V -CHAPTER I I I APPARATUS AND METHODS OF MEASUREMENT — 27 A. Continuous Wave (CW) Measurements : — 27 1. CW Spectrometer 27 2. C a l i b r a t i o n o f Spectrometer 27 3 . L i n e Width and Second Moment M e a s u r e m e n t s - - — - 28 4 . V a r i a b l e Temperature Assembly 29 B. S p i n - l a t t i c e R e l a x a t i o n Measurements 30 1. Pu lsed S p e c t r o m e t e r — 30 2. L i n e a r i t y o f R e c e i v e r — - 32 3. V a r i a b l e Temperature Assembly— — 32 4. Measurement of S p i n - l a t t i c e R e l a x a t i o n T i m e — 33 C. The Dry Box - 35 References (Chapter I I I ) 36 CHAPTER IV AN NMR STUDY OF TRIMETHYLAMINE OR PHOSPHINE COMPLEXED WITH TRIMETHYLBORANE OR ALUMINIUM — - 37 A. I n t r o d u c t i o n 37 B. Exper imental 37 B . l M a t e r i a l s - — - — - 37 B.2 P r e p a r a t i o n o f A d d i t i o n Complexes 37 B. 3 Measuring Procedures- — 38 C. T r i m e t h y l a m i n e - t r i m e t h y l b o r a n e 38 C. l L i n e Widths and Secqnd Moments- 38 C.2 C a l c u l a t i o n o f Second Moment and D i s c u s s i o n of M o l e c u l a r Motion 39 - v i C.3 I n t e r p r e t a t i o n o f the Observed Second Moment -•*•<-- 41 C. 4 S p i n - l a t t i c e R e l a x a t i o n 47 D. T r i methyl a m i n e - t r i methyl aluminium Complex— 52 D. 1 L i n e Width and Second Moment 52 D.2 C a l c u l a t i o n o f Second Moment and D i s c u s s i o n o f M o l e c u l a r M o t i o n - 54 D. 3 S p i n - l a t t i c e R e l a x a t i o n 56 E. T r i m e t h y l p h o s p h i n e - t r i m e t h y l a l u m i n i u m 63 E. l L i n e Widths and Second Moments 63 E.2 C a l c u l a t i o n o f Second Moment 63 E. 3 S p i n - l a t t i c e R e l a x a t i o n Time 67 F. T r i m e t h y l p h o s p h i n e - t r i m e t h y l b o r a n e 69 F. l Exper imenta l L i n e Width and Second Moment 69 F . 2 C a l c u l a t i o n o f Second Moment and D i s c u s s i o n of M o l e c u l a r Motion 71 F . 3 S p i n - l a t t i c e R e l a x a t i o n Times 73 References (Chapter I V ) - - - 79 CHAPTER V AN NMR STUDY OF TRIMETHY^PHOSPHINE AND TRIMETHYL-BORANE — - - - 81 A. I n t r o d u c t i o n 81 B. Exper imental • 81 B . l M a t e r i a l s - - - 81 B.2 Measuring Procedures 82 - v i i -C. T n m e t h y l p h o s p h i n e 82 C . l Exper imental L i n e Widths and Second Moments — 82 C.2 C a l c u l a t i o n o f Second Moment and D i s c u s s i o n o f M o l e c u l a r Mot ion — 82 C. 3 S p i n - l a t t i c e R e l a x a t i o n Times • 86 D. T r i methyl borane 90 D. l Exper imental Second Moments and L i n e Widths 90 D.2 C a l c u l a t i o n o f Second Moment and D i s c u s s i o n o f M o l e c u l a r M o t i o n - • 90 D.3 S p i n - l a t t i c e R e l a x a t i o n Times 95 References (Chapter V ) — • 96 CHAPTER VI AN NMR STUDY OF DIMETHYLAMINE COMPLEXED WITH TRIMETHYLALUMINIUM OR TRIMETHYLBORANE 97 A. I n t r o d u c t i o n 97 B. E x p e r i m e n t a l - 97 B . l P r e p a r a t i o n o f Complexes 97 B. 2 Procedure o f measurement 98 C. Dime thy 1 ami n e - t r i m e t h y l a l uminium 98 C. l Exper imental L i n e Widths and Second Moments 98 C.2 C a l c u l a t i o n o f Second Moments and D e t e r m i n a t i o n o f M o l e c u l a r Motion 98 C.3 S p i n - l a t t i c e R e l a x a t i o n Times 102 D. Dimethyl ami n e - t r i m e t h y l borane 106 - v i i i -D . l Exper imenta l L i n e Widths and Second Moments . 106 D.2 C a l c u l a t i o n o f Second Moments and D e t e r m i n a t i o n o f M o l e c u l a r Motion 106 D.3 S p i n - l a t t i c e R e l a x a t i p n Times--- • 109 References (Chapter VI) 113 CHAPTER VII SPIN-LATTICE RELAXATION STUDY OF TRIMETHYL-BORON TRIHALIDES COMPLEXES 114 A. I n t r o d u c t i o n - — 114 B. Experimental 114 B . l M a t e r i a l s and P r e p a r a t i o n - 114 B. 2 Procedure 115 C. R e s u l t s and D i s c u s s i o n - 115 C. l Tr imethylamine-boron t r i b r o m i d e C o m p l e x — - 115 C.2 Tr imethy lamine-boron t r i c h l o r i d e Complex 118 References (Chapter V I I ) — - 123 CHAPTER VII SPIN-LATTICE RELAXATION STUDY OF TRIMETHYL-AMINE-HALOGENS COMPLEXES - 124 A. I n t r o d u c t i o n - - 124 B. E x p e r i m e n t a l - - - r 124 C. R e s u l t s and D i s c u s s i o n 125 C . l T r i m e t h y l ami n e - i o d i n e Complex- 125 i x -C.2 T r i m e t h y l a m i n e - i o d i n e C h l o r i d e Complex - >, — — 128 C.3 T r i methyl ami ne-brpmine C o m p l e x - — - 129 D. Summary 1 129 References (Chapter V I I I ) - - — 131 CHAPTER IX CONCLUSION AND SUGGESTIONS FOR FURTHER WORK-- - 132 A. C o n c l u s i o n o f the Present Work- — 132 B. Suggest ions f o r F u r t h e r W o r k — 137 References (Chapter IX) 139 APPENDIX A Computer Programme to c a l c u l a t e T.| from exper imental data -. 141 APPENDIX B Computer Programme to c a l c u l a t e second moment from exper imenta l d a t a — - — 143 APPENDIX C Computer Programme to f i t the exper imental T 1 data u s i n g two BPP curves 144 -X-L i s t o f Tables TABLE TITLE PAGE 4.1 T h e o r e t i c a l second moment f o r t r i m e t h y l a m i n e - t r i -methylborane ( i n G^) and comparison w i t h exper iment-a l va lues : 44 4 .2 T h e o r e t i c a l second moment f o r t r i m e t h y l a m i n e - t r i -methyl aluminium ( i n G ) and comparison w i t h experimental v a l u e s - 55 4 . 3 T h e o r e t i c a l second moment f o r t r i m e t h y l p h o s p h i n e -t r i m e t h y l a l u m i n i u m ( i n G ) and comparison w i t h experimental values 65 4 . 4 Energy and Rate Parameters f o r t r i m e t h y l p h o s p h i n e -t r i m e t h y l aluminium 69 4 .5 T h e o r e t i c a l second moment f o r t r i m e t h y l p h o s p h i n e -2 t r i m e t h y l b o r a n e ( i n G ) and comparison w i t h exper imenta l values 72 4 .6 Energy and Rate Parameters f o r t r i m e t h y l p h o s p h i n e -t r i m e t h y l borane • 77 - x i -5.1 Comparison o f t h e o r e t i c a l and exper imenta l second moments o f t r i m e t h y l p h o s p h i n e (second moment i n G } 85 5.2 Comparison o f t h e o r e t i c a l and exper imental second moments o f t r i m e t h y l b o r a n e (second moment i n G 2 ) — 92 6.1 C a l c u l a t i o n o f second moments f o r d imethyl amine-t r i m e t h y l a l u m i n i u m complex and comparison w i t h the exper imenta l values (second moment i n G ) 101 6.2 C a l c u l a t i o n o f second moments f o r d imethyl amine-t r i m e t h y l b o r a n e complex and comparison w i t h the 2 exper imenta l values (second moment i n G ) • 108 7.1 R e s u l t s o f combustion a n a l y s i s on t r i m e t h y l a m i n e -boron t r i h a l i d e s complexes 115 8.1 R e s u l t s o f combustion a n a l y s i s on t r i m e t h y l a m i n e -halogens complexes 125 9.1 A c t i v a t i o n energ ies ( i n kca l/mole) and r a t e parameters f o r v a r i o u s motions i n a d d i t i o n complexes ; 133 - x i i -Values o f T-j minimum f o r methyl group r e o r i e n t a t i o n - x i i i -L i s t o f F i g u r e s FIGURE TITLE PAGE 3.1 R e l a t i o n o f i n p u t s i g n a l and output v o l t a g e o f the r e c e i v e r o p e r a t i n g a t 30 MHz 33 4.1 L i n e w i d t h and second, moment of t r i m e t h y l a m i n e -t r i m e t h y l b o r a n e as a f u n c t i o n o f temperature 40 4 .2 The s p i n - l a t t i c e r e l a x a t i o n t i m e , T^, o f t r i m e t h y l -a m i n e - t r i m e t h y l b o r a n e as a f u n c t i o n o f i n v e r s e temperature • 48 4 . 3 P l o t o f w T c versus i n v e r s e o f temperature o f t r i m e t h y l a m i n e - t r i m e t h y l b o r a n e (a) f o r r o t a t i o n o f the methyl groups a t tached t o boron (b) f o r r o t a t i o n o f the methyl group a t tached to n i t r o g e n p lus the r e o r i e n t a t i o n of the whole molecule about the B-N bond — 49 4 .4 L i n e width and second moment o f t r i m e t h y l a m i n e -t r i m e t h y l a l u m i n i u m as a f u n c t i o n o f t e m p e r a t u r e — 5 3 - x i v-4 . 5 The s p i n - l a t t i c e r e l a x a t i o n time o f t r i m e t h y l -a m i n e - t r i m e t h y l a l u m i n i u m as a f u n c t i o n o f i n v e r s e temperature 57 4 .6 P l o t o f w T versus r e c i p r o c a l o f temperature o f t r i m e t h y l a m i n e - t r i m e t h y l a l u m i n i u m (a) f o r r o t a t i o n of the methyl groups a t tached to n i t r o g e n (b) f o r r e o r i e n t a t i o n o f the whole molecule about the N-A bond - 60 4.7 Temperature dependence o f l i n e w i d t h and second moment of t r i m e t h y l p h o s p h i n e - t r i m e t h y l a l u m i n i u m - — — 64 4 . 8 The s p i n - l a t t i c e r e l a x a t i o n time o f t r i m e t h y l -p h o s p h i n e - t r i m e t h y l a l u m i n i u m as a f u n c t i o n o f r e c i p r o c a l o f temperature 68 4 .9 Temperature dependence o f l i n e w i d t h and second moment o f t r i m e t h y l p h o s p h i n e - t r i m e t h y l b o r a n e 70 4.10 S p i n - l a t t i c e r e l a x a t i o n time of t r i m e t h y l p h o s p h i n e -t r i m e t h y l borane as a f u n c t i o n o f i n v e r s e temperature < 74 - X V -5.1 L i n e w i d t h and second moment o f t r i m e t h y l p h o s p h i n e as a f u n c t i o n o f temperature • 83 5.2 S p i n - l a t t i c e r e l a x a t i o n t ime o f t r i m e t h y l p h o s p h i n e as a f u n c t i o n o f i n v e r s e t e m p e r a t u r e — - - - — - — — - 87 5.3 P l o t o f iiiQTc versus r e c i p r o c a l o f temperature o f t r i m e t h y l phosphine 88 5.4 L i n e w i d t h and second moment of t r i m e t h y l b o r a n e as a f u n c t i o n of temperature 91 5.5 S p i n - l a t t i c e r e l a x a t i o n t ime of t r i m e t h y l b o r a n e as a f u n c t i o n o f i n v e r s e o f temperature 94 6.1 L i n e w i d t h and second, moment o f d imethyl ami ne-t r i m e t h y l aluminium as a f u n c t i o n o f temperature 99 6.2 S p i n - l a t t i c e r e l a x a t i o n time o f dimethyl amine-t r i m e t h y l a l u m i n i u m as a f u n c t i o n o f i n v e r s e of temperature • 103 6.3 P l o t o f co T versus i n v e r s e o f temperature f o r the o c r r o t a t i o n o f the methyl groups a t tached to n i t r o g e n i n d i m e t h y l a m i n e - t r i m e t h y l a l u m i n i u m 104 - x v i 6.4 L i n e w i d t h and second moment o f dimethyl amine-t r i m e t h y l borane versus temperature 107 6.5 S p i n - l a t t i c e r e l a x a t i o n time o f dimethyl amine-t r i m e t h y l borane versus i n v e r s e of temperature 110 7.1 S p i n - l a t t i c e r e l a x a t i o n time o f t r i m e t h y l a m i n e boron t r i b r o m i d e complex as a f u n c t i o n o f i n v e r s e o f temperature-- • 116 7.2 S p i n - l a t t i c e r e l a x a t i p n time o f t r i m e t h y l a m i n e boron t r i c h l o r i d e complex as a f u n c t i o n o f i n v e r s e temperature 119 7.3 DSC curve f o r t r i m e t h y l a m i n e boron t r i c h l o r i d e complex 121 8.1 S p i n - l a t t i c e r e l a x a t i o n time o f t r i m e t h y l a m i n e -i o d i n e c h l o r i d e complex as a f u n c t i o n o f i n v e r s e o f temperature 127 8.3 S p i n - l a t t i c e r e l a x a t i o n time of t r i m e t h y l a m i n e -bromine complex as a f u n c t i o n of i n v e r s e o f temperature 128 - x v i i -Acknowledgments I would l i k e t o express my s i n c e r e g r a t i t u d e t o P r o f e s s o r B . A . Dunel l who i n t r o d u c e d me to the f i e l d o f b r o a d l i n e and p u l s e d NMR. I am g r e a t l y indebted to him f o r h i s k i n d h e l p , g u i d a n c e , r e s e a r c h f a c i l i t i e s and constant encouragement. The he lp and courage he gave to me and my f a m i l y d u r i n g my c r i t i c a l i l l n e s s i s beyond repayment. A l s o I would l i k e to express my s i n c e r e g r a t i t u d e t o D r s . K . S . Chan, W.A. Young and h i s medical group, H. Chuan, I . H . P l e n d e r l e i t h , A . I . Munro and h i s medical group who have saved my l i f e . S p e c i a l thanks are due to Dr. A . I . Munro and h i s medical group who performed an e x c e l l e n t thoracotomy. F u r t h e r I would l i k e to thank P r o f e s s o r C .A. McDowell f o r h i s c o n t i n u i n g i n t e r e s t i n the f i e l d o f b r o a d l i n e and pulsed NMR, h i s k i n d help and h i s generous r e s e a r c h f a c i l i t i e s . ; I would l i k e to thank Dr . A. S t o r r f o r p r o v i d i n g M e 3 N - B M e 3 , Drs . R. I k e d a , A.W. Khanzada, S . E . U l r i c h and W.R. Janzen f o r t h e i r h e l p f u l d i s c u s s i o n s , f r i e n d s h i p and c h e e r , and members o f the e l e c t r o n -i c shop f o r t h e i r i d e a l s e r v i c e and adv ice i n keeping the spectrometers i n good Operat ing c o n d i t i o n . My debt to my w i f e f o r her constant encouragement and e s p e c i a l l y f o r the courage and care she gave me d u r i n g my c r i t i c a l i l l n e s s i s beyond repayment. I 'j - x v i i i -F i n a l l y , I would l i k e to acknowledge the r e c e i p t o f an a s s i s t a n t s h i p from the Department o f C h e m i s t r y , a U n i v e r s i t y o f B r i t i s h Columbia Graduate F e l l o w s h i p . - 1 -CHAPTER I I n t r o d u c t i o n A. I n t r o d u c t i o n to A d d i t i o n Complexes A d d i t i o n complex f o r m a t i o n i s an a s s o c i a t i o n w i t h d e f i n i t e s t o i c h i o m e t r y between two o r more m o l e c u l e s . This a s s o c i a t i o n i s s t r o n g e r than an o r d i n a r y van der Waals i n t e r a c t i o n . A d d i t i o n complexes are f r e q u e n t l y formed when e l e c t r o n a c c e p t o r molecules i n t e r a c t w i t h e l e c t r o n donor m o l e c u l e s . These complexes are recognized by the almost i n v a r i a b l e appearance o f new i n t e n s e broad s p e c t r a l bands i n the v i s i b l e o r u l t r a v i o l e t spectrum, g e n e r a l l y accompanied by p e r t u r b a t i o n s o f the s p e c t r a l bands a r i s i n g from e l e c t r o n i c t r a n s i t i o n s o f the component molecules and by i n d i c a t i o n s o f compound f o r m a t i o n i n phase d iagrams. Most : complexes have smal l heats o f f o r m a t i o n and d e f i n i t e f o r m a t i o n c o n s t a n t s . D i p o l e moments and semi c o n d u c t i v i t y are d i f f e r e n t from those o f the component m o l e c u l e s , and marked a n i s o t r o p i c s i n l i g h t a b s o r p t i o n , c o n d u c t i v i t y , c o m p r e s s i b i l i t y and other p h y s i c a l p r o p e r t i e s are f r e q u e n t l y observed. A d d i t i o n complexes may be c l a s s i f i e d i n t o three c l a s s e s . They are o - a , a-7T and TT-TT, r e f e r r i n g t o complexes where the o r b i t a l s are i n v o l v e d i n f o r m a t i o n of complexes are both a o r b i t a l s , one a and one TT, both TT o r b i t a l s r e s p e c t i v e l y . Examples a r e : 1. a o r b i t a l donors : amines, p h o s p h i n e s , a r s i n e s , e t c . 2. TT o r b i t a l donors: aromat ic hydrocarbons. • - 2 -3 . a o r b i t a l a c c e p t o r s : B F 3 > B C j ^ , Me 3B e t c . 4 . IT o r b i t a l a c c e p t o r s : aromat ic o r e t h y l e n i c hydrocarbons w i t h e l e c t r o n - w i t h d r a w i n g s u b s t i t u e n t s such as NOg and CN groups. The present study i n v o l v e d o n l y o-a a d d i t i o n complexes. T h e r e f o r e o n l y r e l e v a n t t o p i c s w i l l be d i s c u s s e d . B. Var ious S t u d i e s on A d d i t i o n Complexes The e a r l i e r work on a d d i t i o n complexes has concerned the p r e p a r a t i o n of the complexes and s t u d i e s on the p h y s i c a l c h e m i s t r y and thermodynamic p r o p e r t i e s o f complexes. There have been s e v e r a l reviews concerned w i t h a d d i t i o n complexes, l a r g e l y complex compounds formed by one s p e c i f i c a c c e p t o r m o l e c u l e , o r by one c l a s s o f acceptor m o l e c u l e s , u s u a l l y b o r o n - c o n t a i n i n g , e . g . boron t r i b r o m i d e [ 1 . 1 ] , boron t r i c h l o r i d e [ 1 . 2 ] , b o r o n t r i f l u o r i d e [1.3 - 1 . 5 ] , borane [1 .6 -1.7] and t r i a l k y l b o r a n e s [ 1 . 8 ] . The s t a b i l i t y r e l a t i o n s h i p s among analogous m o l e c u l a r a d d i t i o n compounds o f Group I I I elements have been reviewed by Stone [ 1 . 9 ] . M u l l i k e n [1 .10] i n 1952 gave a t h e o r e t i c a l b a s i s f o r i n t e r p r e t i n g m o l e c u l a r complex f o r m a t i o n , and the treatment immediately p r o v i d e d the t h e o r e t i c a l b a s i s f o r i n t e r p r e t a t i o n o f s p e c t r o s c o p i c and f o r m a t i o n constant d a t a , and i n i t i a t e d research on semi c o n d u c t i v i t y and magnetic p r o p e r t i e s o f m o l e c u l a r complexes [ 1 . 1 1 ] . V a r i o u s methods have been used to study the s t r u c t u r e o f a d d i t i o n complexes. They a r e : X - r a y d i f f r a c t i o n , i n which the c r y s t a l s t r u c t u r e i n the s o l i d s t a t e can be s t u d i e d , E l e c t r o n D i f f r a c t i o n and Microwave - 3 -S p e c t r o s c o p y , i n which the m o l e c u l a r s t r u c t u r e can be s t u d i e d i n the gaseous phase, v i b r a t i o n a l s p e c t r o s c o p y , i n which the f o r c e constant o f the bond formed can be determined and the s t a b i l i t i e s o f complexes can be compared, and e l e c t r o -chemical s t u d i e s and e q u i l i b r i u m p r o p e r t i e s . A l l these methods have been reviewed by Coyle and Stone [1.12] f o r boron complexes. C. NMR S t u d i e s on A d d i t i o n Complexes N u c l e a r Magnetic Resonance measurements have been performed on a number o f 7T-o, TT—TT and o-o a d d i t i o n complexes [1.13 - 1.20] t o study the m o l e c u l a r motion 35 i n the s o l i d s t a t e . CI NQR has been s t u d i e d to i n v e s t i g a t e the c- and TT-c h a r a c t e r i n the B-C& bonds [1.21] and temperature v a r i a t i o n study on - P C £ NQR was used i n an attempt to study the r e o r i e n t a t i o n o f the BC£ 3 moiety i n t r i m e t h y l a m i n e - b o r o n t r i c h l o r i d e complexes [ 1 . 2 2 ] . The e a r l i e r nmr work i s most ly l i m i t e d to l i n e w i d t h and second moment measurement. The present study i n v o l v e s the a d d i t i o n complexes o f main Groups I I I and V. Besides ; making l i n e w i d t h and second moment measurements t o determine the m o l e c u l a r motion f o r those complexes, we have a l s o used pulsed nmr t o study the k i n e t i c s o f the m o l e c u l a r motion i n the s o ] i d s t a t e . Most o f t h i s work i n v o l v e s the a d d i t i o n complexes o f a l k y l a m i n e s and a l k y l p h o s p h i n e s w i t h a l k y l b o r a n e s and a l k y l a l u m i n i u m s . S i n c e most o f them are a i r and mois ture s e n s i t i v e , they must be handled i n an extremely dry and oxygen f r e e atmosphere. -4-References [1.1] D,R. N a r t i n , Chem. R e v s . , 42 (1948) 581 [1.2] D.R. M a r t i n , Chem. R e v s . , 34 (1944) 461 [1.3] H . S . Booth and D.R. M a r t i n , Boron T r i f l u o r i d e and i t s D e r i v a t i v e s , W i l e y , New Y o r k , 1949. [1.4] N . N . Greenwood and R . L . M a r t i n , Q u a r t . R e v s . , 8 (1954) 1 [1 .5] A . V . T o p c h i e v , S .V . Z a v g a r d n i i and Y . A . M . P a u s h k i n , Boron T r i f l u o r i d e and i t s Compounds as C a t a l y s t s i n Organic C h e m i s t r y , Pergamon, London, 1959 [1 .6] F . G . A . S t o n e , Quart . Revs. ,9 (1955) 174 [1 .7] F . G . A . S t o n e , Adv. I n o r g . Chem. and Radiochem. ( E d s . H . J . Ernie us and A . G . Sharpe) 2 (19C0) 279 [1 .8] M . F . L a p p e r t , Chem, R e v s . , 5 6 v 1956) 959 [1 .9] F . G . M . S t o n e , Chem. R e v s . , 58 (1958) 107 [1.10] R . S . M u l l i k e n , J . Amer. Chem. S o c , 74 (1952) 811 [1.11] R.S . M u l l i k e n and W.B. P e r s o n , M o l e c u l a r Complexes, A L e c t u r e and R e p r i n t Volume [1.12] T . D . Coyle and F . G . A . S t o n e , Progress i n Boron Chemistry ( E d . H. S t e i n b e r g and A . L . McClosky) Pergamon Press Book, New York 1 (1964) 8 3 , and the re ferences t h e r e i n [1.13] D. Pendred and R . E . R i c h a r d s , T r a n s . Faraday S o c , 5_1 (1955) 468 [1.14] B . A . D u n e l l , C.A. F y f e , C .A. McDowell and J . i p m e e s t e r , T r a n s . Faraday S o c , 65 (.1969) 1153 •v 5-1.15] D . F . R . G i l s o n and C.A. M c D o w e l l , Can. J . Chem., 44 0 9 6 6 ) 945 1.16] D . F . R . G i l s o n and C.f\. M c D o w e l l , J . Chem. P h y s . , 39 (1963) 1825 1.17] D . F . R . G i l s o n and C.A. McDowel l , J . Chem. P h y s . , 40 (1964) 2413 1.18] J . Ripmeester , P h . D . T h e s i s , Chemistry Department, U n i v e r s i t y o f B r i t i s h Columbia , 1970 \ 1.19] C.T. Yim and D . F . R . G i l s o n , Can. J . Chem., 48 (1970) 515 1.20] C.A. Fyfe and J . R i p m e e s t e r , Can. J . Chem., 48 (1970) 2283 i 1.21] J . A . S . Smith and D.A. Tong, J . Chem. S o c . ( A ) , (1971) 178 1.22] D . F . R . G i l s o n and R.M. H a r t , Can. J . Chem., 48 (.1970) 1976 - 6 -CrfAPTER I I I n t r o d u c t i o n t o NMR Theory I t i s the i n t e n t i o n of t h i s chapter t o g i v e a b r i e f i n t r o d u c t i o n t o the theory o f n u c l e a r magnetic resonance, A d e t a i l e d theory i s beyond the scope o f t h i s t h e s i s and w i l l not be g i v e n , but t h e r e are many e x c e l l e n t books [2.1 - 2 .5] and reviews [ 2 . 6 , 2 .7] on the nmr theory and r e s u l t s . The work i n v o l v e d i n t h i s t h e s i s concerns the study o f protons i n diamagnet ic s o l i d s and t h e r e f o r e o n l y r e l e v a n t s e c t i o n s o f theory are rev iewed. A. Elementary Resonance Theory , , When a nucleus p o s s e s s i n g a non-zero s p i n a n g u l a r momentum i s p l a c e d i n a magnetic f i e l d , the s p a t i a l degeneracy o f the a n g u l a r momentum i s removed, y i e l d i n g 21 + 1 e q u a l l y spaced energy l e v e l s w i t h a s p l i t t i n g AE = ytitt0. Here I i s the n u c l e a r s p i n quantum number, y i s a s c a l a r q u a n t i t y r e l a t i n g the n u c l e a r s p i n and magnetic moment v e c t o r s , h" i s P l a n c k ' s c o n s t a n t d i v i d e d by 2TT and H 0 i s the a p p l i e d magnetic f i e l d . When the n u c l e a r s p i n s are i n thermal e q u i l i b r i u m w i t h the l a t t i c e , the r e l a t i v e p o p u l a t i o n s n-j, n-j, o f adjacent l e v e l s are governed by the Boltzman d i s t r i b u t i o n ! i = e « E / K T ( 2 „ 3 Thus- there w i l l be a p o p u l a t i o n d i f f e r e n c e between adjacent s t a t e s . I f an o s c i l l a t i n g r f f i e l d p e r p e n d i c u l a r t o H 0 i s now a p p l i e d to the system such t h a t h\j = AE =yr1Ho , a b s o r p t i o n o f energy o c c u r s . -7-Equat ion (2.1) shows t h a t i f H c = 0, n-j = nj . The e s t a b l i s h m e n t o f thermal e q u i l i b r i u m between the two s t a t e s a f t e r a p p l i c a t i o n o f H 0 must i n e v i t a b l y r e q u i r e t h a t t h e r e are i n t e r a c t i o n s between the n u c l e i and t h e i r s u r r o u n d i n g s ; these i n t e r a c t i o n s cause the s p i n o r i e n t a t i o n to change, w h i l e the excess magnetic energy i s t r a n s f e r r e d to o t h e r degrees o f freedom. T h i s process i s c a l l e d s p i n - l a t t i c e r e l a x a t i o n and the t ime constant t o e s t a b l i s h the thermal e q u i l i b r i u m between s t a t e s a f t e r a p p l i c a t i o n of H Q i s c a l l e d the s p i n - r l a t t i c e r e l a x a t i o n time T-j. Besides i n t e r a c t i n g w i t h the magnetic f i e l d , the r f f i e l d and the l a t t i c e , the n u c l e a r s p i n s a l s o i n t e r a c t w i t h each o t h e r . The i n t e r a c t i o n s w i t h i n the s p i n system w i l l broaden the resonance l i n e shape and a l s o dephase the n u c l e a r m a g n e t i z a t i o n i n the xy p l a n e . A measure o f the phase memory t ime o f the n u c l e a r m a g n e t i z a t i o n i n the xy plane i s u s u a l l y termed the s p i n - s p i n r e l a x a t i o n time T2. B. The L i n e Shape F u n c t i o n C a l c u l a t i o n o f the nmr l i n e shape i s a most d i f f i c u l t task i n the s o l i d s t a t e where the resonance l i n e s are broadened by the l o c a l f i e l d produced by n e i g h b o r i n g s p i n s and by the c o r r e s p o n d i n g s p i n - f l i p process among s p i n s o f the same n u c l e a r s p e c i e s . Of a l l the d i f f e r e n t causes o f broadening o f resonance l i n e s , the one important one f o r our case (protons) i s the d i p o l a r b r o a d e n i n g . The H a m i l t o n i a n o f i n t e r e s t can be w r i t t e n as H = H z + H d (2.2) - 8 -where H z i s the Zeeman H a m i l t o n i a n and i s g iven by ( 2 . 3 ) Here H 0 i s the a p p l i e d magnetic f i e l d i n the z - d i r e c t i o n and I z i s the quantum number f o r the Z component o f the i t h n u c l e a r s p i n . H^ i s the d i p o l a r H a m i l t o n i a n and f o r two n u c l e i i and j w i t h magnetic moment ^ and ^ r e s p e c t i v e l y and j o i n e d by a v e c t o r _r . . i s g iven by where z i <J Ri ' Ri - 3 ( M . • r . .) (u. . r . .) 3 r . . i J Y2 f i 2 . Z . A . . + B. . + C . + D. . + E. . + F. . Y i < J 1 J i j T J i J U T J A. . 1 J = I 1 I J (1 - 3 c o s 2 e . .)r~.3. Z Z l j ' 1 J = ( i j l J + f i j ) (1 - 3 c o s 20 . ) rT 3 i j " i J C. " 1 J T ^ z 1 ; + I + I z ) s i n 0 i j c o s 0 i j e x p ( - % ' > r i j - f s i n 2 0 i . e x p ( - 2 i 4 , i j ) r T j 3 (2 .4) l i C. . * , F. . = E. .* 1 J T J T J where F ,0.., <b. . are the p o l a r c o o r d i n a t e s o f the v e c t o r between s p i n i and i j i J T J j , l j , 1^  e t c . are the usual r a i s i n g and l o w e r i n g o p e r a t o r s f o r e i g e n f u n c t i o n of I z e t c . , and the * s i g n s denote the complex conjugates o f the f u n c t i o n . In H ^ , the terms A and B commute w i t h H z and are c a l l e d the s e c u l a r terms. - 9 -They g i v e the s o - c a l l e d t r u n c a t e d d i p o l a r H a m i l t o n i a n H ^ , i . e . = -(StflZ)?! (I, • I j - (1 - 3 cos 2 G,.) r ' | (2.5) I t i s the Zeeman and t r u n c a t e d d i p o l a r Hairri l tonians t h a t determine the p o s i t i o n and shape o f the resonance l i n e . The resonance l i n e shape f q r t w o - s p i n systems was f i r s t s t u d i e d f o r gypsum ( C a S O ^ r ^ O ) by Pake [ 2 . 8 ] , and e x t e n s i v e work on a wide range o f c r y s t a l hydrates has r e c e n t l y been reviewed [ 2 . 9 ] . T h e o r e t i c a l s t u d i e s o f l i n e . s h a p e i n t h r e e - s p i n systems have a l s o been made. Systems s t u d i e d i n c l u d e compounds c o n t a i n i n g the CH^ group, w i t h o u t and w i t h t a k i n g account o f the t u n n e l l i n g e f f e c t f o r the C H 3 group [2.10 - 2 . 1 2 ] , and the H 3 0 + [2.13] and HF j^ [2.14] i o n s . Some f o u r - s p i n systems have been s t u d i e d , a s , f o r example, NH^ i o n [ 2 . 1 5 , 2.16] and barium bromide d i h y d r a t e [2.17] . One f i v e - s p i n system y i e l d i n g a h i g h l y s t r u c t u r e d spectrum has been examined i n d e t a i l . That i s the H 2 F 3 " i o n i n i t s sodium and potassium s a l t s [ 2 . 1 8 ] . Some p r o m i s i n g r e s u l t s have.been o b t a i n e d f o r S F g c l a t h r a t e deuterate ,where because o f • v e r y weak 19 i n t e r m o l e c u l a r i n t e r a c t i o n s , the F a b s o r p t i o n l i n e shows a good f i n e s t r u c t u r e [2.19] a t l i q u i d he l ium temperature . For c o m p l i c a t e d systems, f o r which exact l i n e shape c a l c u l a t i o n i s too d i f f i c u l t , the w e l l known Van Vleck formula [2.20] f o r second moment o f a b s o r p t i o n l i n e shape i s very u s e f u l i n o b t a i n i n g s t r u c t u r a l i n f o r m a t i o n . -10-C. Second Moment o f Absorptior] L i n e Shape C . l Second Moment from A b s o r p t i o n L i n e Shape. We d e f i n e the nth moment, M n , o f a resonance a b s o r p t i o n curve ( n o r m a l i z e d to u n i t area by the r e l a t i o n [ 2 . 2 , p. 106] . M n = r ° A n g(A)dA ( 2 . 6 ) YOO where A = W q - to 1 The second moment M 2 i s then g iven by M 2 =f A 2 g(A)dA (2 .7) For p o l y c r y s t a l l i n e m a t e r i a l , the second moment i s [ 2 . 1 , p. 160] " z - l l ^ 2 ^ ' \ l f t . • T A Y f W J ' f o ? ( 2 - 8 ) where I i s the n u c l e a r s p i n number f o r n u c l e i a t resonance , g i s the n u c l e a r g f a c t o r , B i s the n u c l e a r magneton and r . . i s the d i s t a n c e between i t h and j t h n u c l e i . S u b s c r i p t f r e f e r s to o t h e r n u c l e i not at resonance. The second moment can be c a l c u l a t e d by numerical i n t e g r a t i o n o f the a b s o r p t i o n c u r v e , from the l i n e w i d t h o f the d i s p e r s i o n mode o f the a d i a b a t i c r a p i d passage (ARP) s i g n a l [ 2 . 2 1 , 2.22] o r from the f r e e i n d u c t i o n decay ; o b t a i n e d by p u l s e methods. C a l c u l a t i o n o f second moment from the a b s o r p t i o n curve i s a long and tedious procedure and c a u t i o n must a l s o be e x e r c i s e d to avo id s a t u r a t i o n from and the modulat ion f i e l d [ 2 . 4 , p . 109] , C a l c u l a t i o n of second moment from the ARP d i s p e r s i o n s i g n a l i s a r a p i d method, the s i g n a l - t o - n o i s e r a t i o i s much b e t t e r than t h a t i n c o n v e n t i o n a l w i d e - l i n e nmr, and, i n a d d i t i o n , s a t u r a t i o n and modulat ion e f f e c t s are e l i m i n a t e d . However, i f the s p i n - l a t t i c e r e l a x a t i o n time i n the r o t a t i n g frame, T-j p , i s s h o r t , the r e l a x a t i o n i n the r o t a t i n g frame d i m i n i s h e s the s i g n a l to an unusuable l e v e l . T h e r e f o r e i t i s not a p p l i c a b l e to the whole temperature range o f i n t e r e s t [ 2 . 2 2 , 2 . 2 3 ] . I t i s w e l l known t h a t the s i g n a l v o l t a g e of the FID curve can be expanded i n terms o f even powered moments o f the resonance a b s o r p t i o n curve [ 2 . 2 4 , 2 . 2 , p. 110] i . e . 2 4 V ( t ) = 1 - | y M 2 + £ r M 4 - ( 2 . 9 ) Equat ion (2 .9) shows t h a t the moments of even number can be c a l c u l a t e d from the FID c u r v e . But the main d i f f i c u l t y here i s t h a t the important i n i t i a l p a r t o f V ( t ) i s b u r i e d i n the dead time of the r e c e i v e r . A method has been d e s c r i b e d by Barnaal and Lowe [2.25] to c o r r e c t the b e g i n n i n g o f the FID curve f o r the d i s t o r t i o n due to s low recovery o f the r e c e i v e r from s a t u r a t i o n , but i t i s a l a b o r i o u s procedure . Powles and Strange [ 2 . 2 6 ] , and M a n s f i e l d [2.7] have developed a method to overcome t h i s s i t u a t i o n by u s i n g two 90° p u l s e s , the second p u l s e being 90° out o f r f phase w i t h the f i r s t (_90° - x -90°g Q o)» t o produce a s o l i d echo. They have shown t h a t the s i g n a l v o l t a g e o f the s o l i d echo a f t e r a time T ' from the second p u l s e i s V ( T + T ' ) . { i . i L ^ i M g t i L - L U i ^ . :..} { (2.10) where the l a s t term M ^ x i s an a t t e n u a t i o n term o f the FID. T h i s method has been used s u c c e s s f u l l y i n polymethylbenzenes [2.28] where the second moment 2 i s s m a l l e r than 20 G . Rhim, Pines and Waugh [2.29] have r e c e n t l y developed a new method u s i n g a sequence o f pulses t o produce a "magic echo" . The "magic echo" method seems to be the best s i n c e i t i s p r a c t i c a l l y f r e e o f the, n o n l i n e a r a t t e n u a t i o n e f f e c t s unavoidable i n the case o f the s o l i d echo. C.2 E f f e c t of M o l e c u l a r Motion on Second Moment and L i n e W i d t h . The second moment was shown by Pake [2.30] and Andrew and Newing [2.31] to be i n v a r i a n t to m o l e c u l a r m o t i o n . F u r t h e r i t was shown i n the l a t t e r paper t h a t r o t a t i o n produces i n the spectrum weak s i d e bands which are u s u a l l y unobservable e x p e r i m e n t a l l y , because they are b u r i e d i n the n o i s e i n the wings and hence a reduced second moment i s observed. A l i n e narrowing t r a n s i t i o n i s expected t o be completed when [ 2 . 2 , p. 425] ( ^ ) 1 / 2 x c « l C 2 . l l ) 2 where ina i s the r i g i d l a t t i c e second moment expressed as an angular frequency and T i s the c o r r e l a t i o n time f o r the random m o t i o n a l p r o c e s s . I f the motion i s t h e r m a l l y a c t i v a t e d and the l i n e shape i s the same before and a f t e r the mot ional narrowing (which i s u s u a l l y not e x a c t l y the c a s e ) , a r e l a t i o n between l i n e width and c o r r e l a t i o n time i s g i v e n by [2.32] T c = tan rr(6H 2 - B 2 ) / 2 ( C 2 - B 2 ) ] / (ofYfiH) (2.12) where a i s an i l l - d e f i n e d constant and i s a p p r o x i m a t e l y equal t o u n i t y , 6H i s the l i n e width i n the narrowing r e g i o n , B i s the narrowed l i n e w i d t h and C i s the unnarrowed l i n e w i d t h . T C obeys the A r r h e n i u s a c t i v a t i o n energy and temperature r e l a t i o n s h i p where E 3 i s the a c t i v a t i o n energy f o r the b a r r i e r h i n d e r i n g the r o t a t i o n , a Equations (2.12) and (.2.13) can p r o v i d e an e s t i m a t e o f the a c t i v a t i o n energy from the l i n e width versus temperature measurement. The e f f e c t o f m o l e c u l a r r o t a t i o n on second moment can be c a l c u l a t e d from Gutowsky and Pake's formula [2 .33] where y i s the angle between the i n t e r n u c l e a r v e c t o r r. and the a x i s o f r o t a t i o n , M£ and are the reduced and r i g i d l a t t i c e second moments r e s p e c t i v e l y . I f the motion i s o s c i l l a t o r y , Andrew's e x p r e s s i o n [2 .34] should be used: x c = T ° exp ( E a / R T ) (2.13) (2.14) -14-Wosc = ^ where p = 1 - | ((1 - J Q 2 ( a ) ) S i n 2 Y + (1 - J Q 2 ( 2 a ) ) S i n 4y] (2.15) where J Q i s a Besse l f u n c t i o n o f f i r s t k i n d , a i s the ampl i tude o f o s c i l l a t i o n , and Y i s the angle between the p a i r d i r e c t i o n and the a x i s o f r o t a t i o n a l o s c i l l a t i o n . For small angle a,p reduces to p = 1 - | a 2 S i n 2y (2.16) C.3 T u n n e l l i n g E f f e c t on the Second Moment. S t u d i e s on polymethyl benzenes [ 2 . 2 8 , 2 . 3 5 , 2.36] and ammonia [2.37] have i n d i c a t e d t h a t second moments keep t h e i r reduced values down to very low temp-2 1/2 e r a t u r e , which means (Aw ) T « 1, whereas the s p i n - l a t t i c e r e l a x a t i o n time 2 1/2 s t u d i e s show (Aw ) ' T » 1. T h i s apparent c o n t r a d i c t i o n has been i n t e r p r e t e d as i n d i c a t i n g the e x i s t e n c e o f a t u n n e l l i n g a s s i s t e d pheonomenon i n the l i q u i d h e l i u m temperature range. A l l e n [2.38] has d e r i v e d an e x p r e s s i o n f o r M 2 f o r an i s o l a t e d t u n n e l l i n g Ch* 3-group account ing f o r the reduced second moment at low temperature . For a b a r r i e r h e i g h t of 3 k c a l / m o l e , the second moment i s j u s t 1/4 o f the r i g i d l a t t i c e v a l u e . For a h igher b a r r i e r (3 - 3.5 kcal/mole) h i s e x p r e s s i o n i s M 2 = f o ( Y 2 R 2 / r 6 ) [ l - 0 . 1 1 ( r / A ) T / 2 - 0 . 6 4 ( r / A ) ] (2.17)' Pi.? 3 wher;e r = ( r n / r ) and A i s the t u n n e l l i n g s p l i t t i n g o f t o r s i o n a l ground s t a t e . In a more recent paper Clough [2 .29] has shown by c a l c u l a t i o n t h a t the -15-t u n n e l l i n g e f f e c t can decrease the r i g i d l a t t i c e second moment but the second moment due to t u n n e l l i n g i s h i g h e r than the second moment reduced by c l a s s i c a l r e o r i e n t a t i o n about the Cg a x i s ; i . e . i t i s more than 1/4 o f the r i g i d l a t t i c e v a l u e . He has shown t h a t the i n c r e a s e o f second moment from 2 the c l a s s i c a l reduced va lue may be as great as 5 G . D. - S p i n - l a t t i c e R e l a x a t i o n Time In g e n e r a l , two c o n d i t i o n s are necessary f o r a s u c c e s s f u l s p i n - l a t t i c e r e l a x a t i o n mechanism. F i r s t l y , there must be some i n t e r a c t i o n which a c t s d i r e c t l y on the s p i n s ; s e c o n d l y , i t must be time dependent. I t can be shown [ 2 . 5 , Chap. 4] t h a t any i n t e r a c t i o n which f l u c t u a t e s s t r o n g l y at the resonance frequency produces powerful s p i n - l a t t i c e r e l a x a t i o n . ; A number o f p h y s i c a l i n t e r a c t i o n s have been found to be important i n c o u p l i n g the n u c l e i to the l a t t i c e and hence p r o v i d i n g a l i n k through which energy can be changed between the s p i n s and l a t t i c e . These processes a r e : 1. magnetic d i p o l e - d i p o l e i n t e r a c t i o n ! 2. e l e c t r i c quadrupole i n t e r a c t i o n 3 . chemical s h i f t a n i s o t r o p y i n t e r a c t i o n 4 . s c a l a r - c o u p l i n g i n t e r a c t i o n 5. s p i n - r o t a t i o n i n t e r a c t i o n . To d e s c r i b e the motion and/or the p o s i t i o n o f a r i g i d body i t i s customary, h e l p f u l and convenient to i n t r o d u c e f u n c t i o n s r e l a t e d to the s p h e r i c a l harmonics . -16-They are d e f i n e d as f o l l o w s : Y Q = r " 3 (1 - 3 c o s 2 e ) Y-j = r s i n e cose exp(i<{>) Y 2 = r ~ 3 s i n 2 G exp(2i<|>) (2 .18) where r , 0, <j> are the usual s p h e r i c a l c o o r d i n a t e s . As the molecule moves, the r , 0, <f> become f u n c t i o n s o f time and so do the f u n c t i o n s Y^ ( i = 0 , 1 , 2 ) . S i n c e the r e l a x a t i o n times and are r e l a t e d t o the average behaviour o f a c o l l e c t i o n o r ensemble o f n u c l e i , we are p a r t i c u l a r l y i n t e r e s t e d i n , t h e average way i n which the n u c l e i move about. The s o - c a l l e d c o r r e l a t i o n f u n c t i o n s K . ( T ) ( i = 0 , 1, 2) g ive us t h i s i n f o r m a t i o n ; they are d e f i n e d as K . ( T ) = < Y . ( T ) Y J * (T + T)> ( 2 . 1 9 ) . where Y > i s the complex conjugate o f Y^ and < > denotes the ensemble, average. A common and f r e q u e n t l y used c o r r e l a t i o n f u n c t i o n i s o f e x p o n e n t i a l f o r m , i . e . ^•(x) = Y . ( T ) Y . * ( T ) e x p(-x / T C ) (2 .20) where x c i s the c o r r e l a t i o n t ime c h a r a c t e r i s t i c of the m o t i o n . The i n t e n s i t y of the not ion a t frequency w, the s o - c a l l e d s p e c t r a l d e n s i t y f u n c t i o n , can be obta ined by F o u r i e r T r a n s f o r m a t i o n of the c o r r e l a t i o n f u n c t i o n , i . e , -17-i V w ) = T K.(T) exp(i(Or)dx (2 .21) The s p i n - l a t t i c e r e l a x a t i o n r a t e , T ^ " \ t h e r e f o r e depends on the va lue of 0(w Q ) and a l s o the s t r e n g t h o f the c o u p l i n g between the s p i n system and the l a t t i c e . In a diamagnetic s o l i d , the d i p o l e - d i p o l e i n t e r a c t i o n s are important and the s p i n - l a t t i c e r e l a x a t i o n time T^ was shown [ 2 . 2 , p . 291] to be f - = | 1(1 + 1 ) Y 4 R 2 E [ J - / ^ ) + J - ^ 2 % ) ] (2 .22) where i and j are now the n u c l e i o f i n t e r e s t . For t w o - s p i n systems T^ due to i s o t r o p i c r o t a t i o n was g i v e n by [ 2 . 2 , p .300] i _ 2 Y 4 k 2 K I +1) r T c x 4 t c L 2 2 u . 2 2 U+M T l+4ai T J T l 5 r 6 . _ . . _ . 0 C 0 c The s p i n - l a t t i c e r e l a x a t i o n time f o r 3 - s p i n systems has been s t u d i e d e x t e n s i v e l y . The c a l c u l a t i o n o f r e l a x a t i o n time i n v o l v e s two c o r r e l a t i o n f u n c t i o n s f o r each mutual d i p o l e - d i p o l e i n t e r a c t i o n . I f we are examining the r e l a x a t i o n o f proton 1 i n a t h r e e proton system, the c o r r e l a t i o n f u n c t i o n f o r i n t e r a c t i o n s 1, 2 and 1,3 i s c a l l e d the " a u t o - c o r r e l a t i o n f u n c t i o n " and the c o r r e l a t i o n f u n c t i o n f o r i n t e r a c t i o n s 2 , 3 , which a l s o a f f e c t s the r e l a x a t i o n o f proton 1, i s c a l l e d the " c r o s s - c o r r e l a t i o n f u n c t i o n " . H i l t and Hubbard [2.40] -18-have shown t h a t i n the case o f 3 - s p i n systems undergoing h indered r o t a t i o n , i f cross c o r r e l a t i o n s are n e g l e c t e d , the r e l a x a t i o n f u n c t i o n i s e x p o n e n t i a l , and f o r p o l y c r y s t a l l i n e m a t e r i a l they d e r i v e d an e x p r e s s i o n f o r T-j 1 = ! _ i V 4T 20 2 2 0 c 2 2 1 "*"4u) T 0 c The r e s u l t i s the same as t h a t o b t a i n e d by O ' R e i l l y and Tsang [2,41] who used a much s i m p l e r approach. . H i l t and Hubbard [2.40] a l s o t r e a t e d the 3 - s p i n system by c o n s i d e r i n g both the c r o s s - c o r r e l a t i o n and a u t o - c o r r e l a t i o n f u n c t i o n s . They found the m a g n e t i z a t i o n M ( t ) a f t e r a pulse o f w i d t h 0 i s not e x p o n e n t i a l , but a sum of 4 e x p o n e n t i a l s g i v e n by 4 MjrCt) - % = (cos0 - 1) My l C. e x p ( - q . t / T ' ) (2 .23) ' j=l J J where C , q . are c o m p l i c a t e d f u n c t i o n s o f to x and the angle S between the j j * o c C 3 ~ a x i s and H , and T ' i s a measure o f the s t r e n g t h of i n t e r a c t i o n between the magnetic d i p o l e s g iven by I = C y 2 n / r 3 ) 2 ]- ( 2 . 2 4 ) f ' ^o where r i s the i n t e r p r o t o n d i s t a n c e i n the CHo-group. For p o l y c r y s t a l l i n e -19-m a t e r i a l and a 180° - T - 90° p u l s e sequence, Equat ion (2 .23) becomes 4 R A / t ) = {[M o - M z ( t ) ] /2Mq } A v = I j T M C j e x p ( - q j t / T ' ) S i n 3 d B (2 .25) More r e c e n t l y A l l e n and Clough [2.42] have c a l c u l a t e d the temperature depend-ence o f T.| t a k i n g i n t o account the t u n n e l l i n g s p l i t t i n g o f the t o r s i o n a l -o s c i l l a t o r ground s t a t e o f the h i n d e r e d CH 3 ~group. T h i s t u n n e l l i n g s p l i t t i n g accounts f o r more than one minimum at very low temperature (below 100 K ) . The,, e x p r e s s i o n o b t a i n e d by these authors i s [ 2 . 4 2 , 2 . 4 3 ] 1 9 4 £ 2 T r + 4 t T - 2tr "^ nfr (~ I 2 7 — § - ? • <»0> • «"«-?T,>> <2-26> 1 r 1 + tiL T l+4(i) T 0 c 0 c where f(w) = 8Y/ {6T0 X 4 + 2 X 2 ( 2 Y 2 - 1) + 1 } w i t h X = <JO/3J , Y = ( 3 J x t ) _ 1 . In X and Y , 3jR i s the t u n n e l l i n g s p l i t t i n g and i s a c o r r e l a t i o n time obeying the equat ion x. = x exp(E /RT) . At hiqh temperature where the T, o a t u n n e l l i n g e f f e c t i s not i m p o r t a n t , the l a s t two terms can be o m i t t e d and one o b t a i n s the BPP e q u a t i o n [2.44, 2 . 4 5 ] - 2 0 -E . D i s t r i b u t i o n o f C o r r e l a t i o n Times and T h e i r E f f e c t on T-j and E a . The m o d i f i e d BPP Equat ion (2 .27) i s o n l y s a t i s f a c t o r y f o r one c o r r e l a t i o n t i m e , T . The a c t i v a t i o n energy can be e x t r a c t e d from the s lopes o f a In T^ vs T"^  p l o t on e i t h e r s i d e o f the minimum, where 1. i n the low temperature r e g i o n ( W 0 T C » 1 ) , In T-j « E f l/RT 2. i n the high temperature r e g i o n ( W 0 T c « 1 ) , In T.| « - E a / R T i I t can a l s o be o b t a i n e d from a p l o t o f O J 0 T c versus i n v e r s e o f temperature where w o T c a ^ temperature T can be o b t a i n e d from the exper imenta l T-j minimum and the experimental va lue o f T-j a t temperature T . However, i f there i s a l a c k o f a unique c o r r e l a t i o n t i m e , a broad and f l a t T^ minimum e x i s t s , i n c o n t r a s t w i t h a sharp T-j minimum p r e d i c t e d by the BPP Equat ion ( 2 . 2 7 ) . The presence o f more than one c o r r e l a t i o n time may a r i s e i n t h r e e d i f f e r e n t ways. The f i r s t case i s where we may have a number o f independent types o f r o t a t i o n proceeding a t n e a r l y the same temperature but w i t h d i f f e r e n t r a t e s and each c o n t r i b u t i n g towards T^. A known example o f t h i s case i s the t e r t - b u t y l group, which may e x h i b i t both methyl and t e r t - b u t y l group r o t a t i o n . The f i r s t work to separate these two s p e c i f i c c o n t r i b u t i o n s i s t h a t o f A l l e n and Johnson [2.46] on l - t e r t - b u t y l - 4 - m e t h y l - b e n z e n e . The second case i s t h a t there e x i s t s the same type o f motion proceeding at d i f f e r e n t ra tes i n a l i m i t e d number (o f the order o f t h r e e o r f o u r ) o f d i f f e r e n t environments and c o n t r i b u t i n g towards T, at the same temperature . - 2 1 -This may come about because the r o t a t i n g groups are a t tached t o d i f f e r e n t c e n t r a l atoms, or the r o t a t i n g groups are l o c a t e d a t d i f f e r e n t c r y s t a l s i t e s . The d i f f e r e n t c o n t r i b u t i o n s o f each motion to T-| may be separated under f a v o r a b l e c i r c u m s t a n c e s . Examples w i l l be seen i n the f o l l o w i n g C h a p t e r s . The t h i r d case i s t h a t t h e r e e x i s t s a d i s t r i b u t i o n o f c o r r e l a t i o n t i m e s , perhaps a l l due to the same type o f m o t i o n , f o r example, methyl group r e o r i e n t a -t i o n . T h i s d i s t r i b u t i o n r e s u l t s from a continuous d i s t r i b u t i o n o f environments w i t h i n the sample a t t r i b u t a b l e to s t a t i c c r y s t a l inhomogenei t ies o r thermal f l u c t u a t i o n o f environment. This c a s e , which i s c h a r a c t e r i s t i c o f polymer systems, has been reviewed by Odajima [2.47] and Connor [2.48] and we w i l l summarize the main p o i n t s o f t h e i r review here . In o r d e r to e x p l a i n the broad T^ minimum, the m o d i f i e d BPP e q u a t i o n has been f u r t h e r m o d i f i e d [2.49] to i n c l u d e a continuous d i s t r i b u t i o n o f c o r r e l a t i o n t i m e s , d e s c r i b e d by a d e n s i t y f u n c t i o n G ( T c ) where , d x c = 1 ( 2 . 2 8 ) , t o g i v e [2.50] i = c r r Tc G ( xc ) d Tc + 4 r ^ c ^ c i (2.29) The d e n s i t y f u n c t i o n can be expressed i n terms o f a l o g a r i t h m i c c o r r e l a t i o n time s c a l e . I f T i s the c e n t e r o f the d i s t r i b u t i o n on the l o g a r i t h m i c s c a l e , - 2 2 -then d e f i n e S - In C x c / x 0 ) G ( x c ) can then be r e p l a c e d by F(S) w i t h c o n d i t i o n s £ F ( S ) d S = l , G ( x c ) d x c = F ( S ) d S , x c G ( x c ) = F(S) ( 2 . 3 0 ) There are v a r i o u s types o f d i s t r i b u t i o n f u n c t i o n s which g i v e r i s e t o a symmetric curve o f In T^ versus T~^. They a r e : the r e c t a n g u l a r d e n s i t y f u n c t i o n , Gaussian d i s t r i b u t i o n f u n c t i o n , L o r e n z t i a n d e n s i t y f u n c t i o n , Fuoss and K i r k w o o d , and Cole and Cole d i s t r i b u t i o n f u n c t i o n s . The In T-j versus T~^ curves d e r i v e d from the f i r s t t h r e e f u n c t i o n s have the f o l l o w i n g p r o p e r t i e s : the l i m i t i n g s lopes are the same as those o b t a i n e d from the BPP e q u a t i o n , but the curve g e n e r a l l y shows a broad ^ minimum. The In T-j versus T ^ curves d e r i v e d from Fuoss and Kirkwood and Cole and Cole d i s t r i b u t i o n s have, i n g e n e r a l , a broad T-j minimum, and the l i m i t i n g s l o p e s are s m a l l e r than those o b t a i n e d from the BPP e q u a t i o n . The o n l y d i s t r i b u t i o n f u n c t i o n which g i v e s an asymmetric curve o f In T-j versus T~^ i s the Cole-Davidson f u n c t i o n . The h i g h e r temperature l i m i t i n g s l o p e i s the same as t h a t from the BPP e q u a t i o n , whereas the lower temperature s l o p e i s m o d i f i e d by the w i d t h o f the d i s t r i b u t i o n , and T-j minimum i s s h i f t e d s l i g h t l y downward. The T, minimum i n t h i s case i s not very b r o a d . - 2 3 -F. A c t i v a t i o n Energy Even i n the gaseous s t a t e , i t i s d i f f i c u l t to make c o r r e c t e m p i r i c a l p r e d i c t i o n s o f b a r r i e r h e i g h t s because many f a c t o r s can a f f e c t the p o t e n t i a l b a r r i e r . These i n c l u d e the bond l e n g t h a s s o c i a t e d w i t h the r o t a t i o n a l m o t i o n , m o l e c u l a r symmetry, e l e c t r o n e g a t i v i t y o f the s u b s t i t u e n t s and the type o f bonding ( f o r example, the p o s s i b l e e x i s t e n c e o f Tr-bonding). In the s o l i d s t a t e , t h e r e are a l s o i n t e r m o l e c u l a r f o r c e s , which a f f e c t the a c t i v a t i o n energy f o r the r o t a t i o n a l m o t i o n . The s t r e n g t h o f i n t e r m o l e c u l a r f o r c e s depends on the type o f c r y s t a l . I o n i c and c o v a l e n t network c r y s t a l s may have the b i n d i n g energy as high as 300 k c a l / m o l e . M e t a l l i c c r y s t a l s may have the b i n d i n g energy as high as 100 k c a l / m o l e . Hydrogen-bonded c r y s t a l s l i k e i c e have about 12 kca l/mole b i n d i n g energy. The compounds s t u d i e d i n t h i s t h e s i s are m o l e c u l a r c r y s t a l s whose b i n d i n g energies are n o r m a l l y l e s s than 10 k c a l / m o l e . A p o i n t worth ment ioning i s t h a t i n a molecule l i k e Me^A-BMe^ o r Me-jA-BXg, where A , B are c e n t r a l atoms and X i s a halogen atom, we are unable to d i s t i n g u i s h between the C 3 r e o r i e n t a t i o n o f the molecule as a whole and u n c o r r e l a t e d r e o r i e n t a t i o n o f each h a l f o f the molecule about the A-B bond u s i n g the nmr t e c h n i q u e . However, the a c t i v a t i o n energy f o r the r e o r i e n t a t i o n o f the molecule as a whole i n v o l v e s merely i n t e r m o l e c u l a r i n t e r a c t i o n s whereas u n c o r r e l a t e d r e o r i e n t a t i o n o f each h a l f of the molecule about the A-B bond i n v o l v e s both i n t e r m o l e c u l a r and i n t r a m o l e c u l a r i n t e r a c t i o n s . Thus the , a c t i v a t i o n energy f o r the l a t t e r case should be h i g h e r than t h a t f o r the former case i f o t h e r parameters o f the systems being compared are very s i m i l a r o r i f one can d i s t i n g u i s h both motions i n the same system. - 2 4 -References [2.1] E . R . Andrew. N u c l e a r Magnetic Resonance, Cambridge U n i v . P r e s s , 1955 [2 .2] A. Abragram, The P r i n c i p l e s o f N u c l e a r Magnetism, Oxford U n i v . P r e s s , 1961 [2.3] C P . S l i c h t e r , P r i n c i p l e s o f Magnetic Resonance, H a r p e r , N . 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P h y s i c s , 30 (1959) 1272 -27-CHAPTER I I I Apparatus and Methods o f Measurement This chapter i s intended to g i v e some d e t a i l s o f apparatus used and methods o f measurement of second moment, and s p i n - l a t t i c e r e l a x a t i o n t i m e , T.j . The p r e p a r a t i v e methods f o r a d d i t i o n ' complexes are not d i s c u s s e d h e r e , because they w i l l be g i v e n i n d e t a i l i n l a t e r c h a p t e r s . A. Continuous Wave (CW) Measurements 1. CW Spectrometer The spectrometer used f o r CW measurements was a c o n v e n t i o n a l c r o s s - c o i l V a r i a n VF-16 w i d e l i n e spectrometer equipped w i t h a V a r i a n s i x i n c h magnet. The t r a n s m i t t e r and r e c i e v e r u n i t was a V a r i a n V4210A v a r i a b l e frequency r f u n i t o p e r a t i n g at 16 MHz i n a l l exper iments . The usual l o c k - i n d e t e c t i o n method was used. The modulat ing f i e l d was s u p p l i e d by a V a r i a n V4250B sweep u n i t and a V4240 sv/eep a m p l i f i e r u n i t , and i n a l l experiments the modulat ion frequency was kept a t 80 Hz. The f i r s t d e r i v a t i v e o f the a b s o r p t i o n mode s i g n a l was recorded by means of V a r i a n V4270B l o c k - i n a m p l i f i e r u n i t . S p e c t r a were recorded by a HP Model 680 s t r i p c h a r t r e c o r d e r . 2. C a l i b r a t i o n o f Spectrometer The 'H resonance f i e l d H Q was l o c a t e d from the p o s i t i o n o f the a b s o r p t i o n s i g n a l o b t a i n e d from a doped water sample. A s i d e band t e c h n i q u e was used f o r - 2 8 -c a l i b r a t i o n o f the scanning r a t e . J o produce these s i d e bands, the r f c a r r i e r frequency ("16 MHz) was modulated by a known audiofrequency generated from a H . P . Model 200CD wide range o s c i l l a t o r , the frequency o f which was measured by a H . P . Model 3734A e l e c t r o n i c c o u n t e r . The scan r a t e was c a l i b r a t e d i n gauss per cm. along the base l i n e o f the r e c o r d e r . The modulat ion ampl i tude was c a l i b r a t e d by d i r e c t l y r e c o r d i n g the f i r s t d e r i v a t i v e o f the overmodulated doped water sample. The observed peak-to-peak l i n e w i d t h was taken equal t o 2Hm, where Hm i s the modulat ion ampl i tude i n gauss . 3. L i n e w i d t h and Second Moment Measurements The l i n e w i d t h was taken as the d i s t a n c e between the extreme maximum and m i n -imum of the recorded spectrum. The second moment o f the exper imental a b s o r p t i o n d e r i v a t i v e curve a f t e r s u b t r a c t i n g the wel l -known modulat ion c o r r e c t i o n due to Andrew [3.1] i s where g(h) = g ( H Q -H) = y " g(w o-aj) = y " g ( A ) , H 0 i s the resonance f i e l d , H the f i e l d away from resonance and Hm i s the modulat ion a m p l i t u d e . For numerical i n t e g r a t i o n purposes Equat ion (3.1) reduces t o n=N (3.1) ( 3 . 2 ) - 2 9 -where n i s the number of s e c t i o n s on the x - a x i s , Y n i s the y - a x i s h e i g h t of the d e r i v a t i v e c u r v e , N i s the maximum number o f s e c t i o n s on the x - a x i s and S i s the scanning r a t e i n G / s e c t i o n . A computer programme was used t o c a l c u l a t e the second moments u s i n g Equat ion ( 3 . 2 ) . At l e a s t two s p e c t r a were recorded at each temperature and the average second moment and l i n e w i d t h was o b t a i n e d . The r f f i e l d used was 0.005 mG to 0.10 mG depending on the T^ and o f the sample. The r e p o r t e d second moment has i n most cases a d e v i a t i o n o f l e s s than 10%. The. important source o f e r r o r comes from the s i g n a l a t each wing where the s i g n a l / n o i s e r a t i o i s s m a l l e r than 1. The modulat ion ampl i tude was always kept much s m a l l e r than 1/3 o f the l i n e w i d t h t o avoid modulat ion broadening and to s a t i s f y the f i r s t two c o n d i t i o n s o f P r o v o t o r o v ' s Theory [3.2] . However, when s e l f - d i f f u s i o n o c c u r s , the modulat ion frequency may exceed the l i n e w i d t h , and the s i g n a l i s overmodulated. The inhomogeneity o f the magnetic f i e l d H Q becomes s i g n i f i c a n t when the l i n e w i d t h i s l e s s than about 0.5G. Consequently the l i n e w i d t h i n the r e g i o n o f s e l f - d i f f u s i o n i s a f f e c t e d by f i e l d inhomogeneity. 4. V a r i a b l e Temperature Assembly Temperature c o n t r o l was achieved by immersing the sample d i r e c t l y i n l i q u i d n i t r o g e n to a t t a i n 77°K. Temperatures below 77°K were o b t a i n e d by pumping on l i q u i d n i t r o g e n , and temperatures can be adjusted by changing the r a t e of pumping. For temperatures from 110°K t o room temperature c o l d gas f low methods were used. The l i q u i d n i t r o g e n was b o i l e d o f f w i t h a 400 Watt heater immersed i n a 50 l i t e r tank. The c o l d n i t r o g e n gas was l e d from a. -30-Dewar system to the probe. The temperature was v a r i e d e i t h e r by v a r y i n g the v o l t a g e across the heater o r , f o r f a s t e r response , by h e a t i n g the c o l d gas w i t h an a d d i t i o n a l h e a t e r p l a c e d i n s i d e the Dewar system. To get minimum temperature g r a d i e n t , the v o l t a g e on the heater immersed i n l i q u i d n i t r o g e n was h e l d f i x e d at a value which g ives a good high f low r a t e o f c o l d gas and n e g l i g i b l e thermal g r a d i e n t . The temperature o f the sample was measured us ing a copper-constantan thermocouple p l a c e d a p p r o x i m a t e l y 1-2 cm. below the sample, and a Leeds and Nor^hrup Type G s t r i p c h a r t r e c o r d e r , o r a p o t e n t i o m e t e r . For temperatures between 77°K and 110°K, the c o l d gas from the 50 l i t e r tank was f i r s t passed through a copper heat exchanger p l a c e d i n l i q u i d n i t r o g e n before r e a c h i n g the Dewar system. The temperatures were c o n t r o l l e d by a Versa-Therm p r o p o r t i o n a l e l e c t r o n i c temperature c o n t r o l l e r Model 2156 w i t h a Veco 05A11 t h e r m i s t o r . For temperatures from room temperature upwards, hot a i r was used. The s t a b i l i t y o f the temperature ; w i t h t h i s system i s about ±0.5° . The sample was a l l o w e d t o e q u i l i b r a t e f o r at l e a s t f o r t y minutes before the s p e c t r a were t a k e n . B. S p i n - L a t t i c e R e l a x a t i o n Measurements , 1. Pu lsed Spectrometer The pulsed spectrometer used f o r T^ measurements was a Bruker v a r i a b l e frequency (.16 to 62 MHz) pulsed spectrometer . The frequency at which a l l our T-j measurements were performed was 30 MHz. This spectrometer c o n t a i n s a b a s i c 1 MHz q u a r t z o s c i l l a t o r w i t h a - 8 -9 frequency s t a b i l i t y l y i n g between 10" - 10 . A l l the measurement times - 3 1 -are d e r i v e d d i g i t a l l y from t h i s o s c i l l a t o r and t h e i r accuracy i s o f the same order as t h a t o f the o s c i l l a t o r f requency . Three separate p u l s e channels are a v a i l a b l e to gate the high frequency i n the o s c i l l a t o r u n i t . The b a s i c 1 MHz frequency from the main o s c i l l a t o r i s taken i n t o a frequency s y n t h e s i z e r , where h a l f o f the resonance frequency i s produced. T h i s h a l f h igh frequency i s then fed to t h r e e channels a f t e r a m p l i f i c a t i o n . The f i r s t channel i s gate channel I , where the h i g h frequency s i g n a l i s fed a f t e r be ing phase s h i f t e d , doubled and a m p l i f i e d . In the second c h a n n e l , which i s gate channel I I , the h igh frequency i s fed d i r e c t l y a f t e r being doubled and a m p l i f i e d . In the t h i r d c h a n n e l , termed the r e f e r e n c e c h a n n e l , the high frequency serves as a phase coherent frequency f o r the phase s e n s i t i v e d e t e c t o r . The gate channel I i s opened o n l y by p u l s e I and the gate channel I I i s opened by pulses II and. I I I . The high frequency i n the form o f pulses i s l e d , a f t e r p a s s i n g through the gates opened by d . c . pulses I , I I and I I I , through a f i v e - s t a g e r f power a m p l i f i e r which i s capable o f d e l i v e r i n g a power o f 2-3 ysec f o r a 180° p u l s e to the t r a n s m i t t e r c o i l i n the probe where i t e x c i t e d the nmr frequency s i g n a l . T h i s nmr s i g n a l combined w i t h the s i g n a l produced by r f pulses i s passed through a p r e a m p l i f i e r and a f t e r a t t e n u a t i o n i s d e t e c t e d by the r e c e i v e r e i t h e r by diode o r phase s e n s i t i v e d e t e c t i o n . > The maximum band w i d t h o f the r e c e i v e r i n the spectrometer i s 1 MHz.. The dead time o f the r e c e i v e r a f t e r an r f p u l s e i s a p p r o x i m a t e l y 5-6 ysec at 30 MHz . Most o f the experiments i n t h i s work were done u s i n g a band ; width o f 1 MHz, but i n some cases where n o i s e l e v e l was high and the T 2 was l o n g , a band width of 300 kHz was used. i, - 3 2 -The magnet used f o r the p o l a r i z i n g magnetic f i e l d H Q v/as a V a r i a n 1 2 - i n c h high r e s o l u t i o n e lec tromagnet . The s i g n a l ampl i tudes were recorded on a T e k t r o n i x Type 549 s t o r a g e o s c i l l o s c o p e w i t h Type 1A1 Dual Trace p l u g - i n u n i t . The o s c i l l o s c o p e has a band w i d t h o f 30 MHz. 2. L i n e a r i t y o f R e c e i v e r In a l l experiments we have used a diode d e t e c t o r . To c a l i b r a t e the l i n e a r i t y o f the r e c e i v e r at 30 MHz we used a H . P . Model 606A s i g n a l g e n e r a t o r o p e r a t i n g at 30 MHz. The output o f the s i g n a l generator was f e d to the i n p u t o f the r e c e i v e r p r e a m p l i f i e r . The output v o l t a g e from the r e c e i v e r was measured w i t h a T e k t r o n i x Type 549 o s c i l l o s c o p e . The i n p u t v o t l a g e was read from the meter o f the s i g n a l g e n e r a t o r . The o s c i l l o s c o p e was c a l i b r a t e d by the b u i l t i n v o t l a g e c a l i b r a t o r . F i g . 3.1 shows the output v o l t a g e as a f u n c t i o n o f the i n p u t v o l t a g e from the H . P . s i g n a l generator at 30 MHz. Most o f the T-j measurements were taken i n the range o f l i n e a r i t y . Those which were o u t s i d e were c o r r e c t e d f o r n o n - l i n e a r i t y o f the diode d e t e c t o r . , 3 . V a r i a b l e Temperature Assembly The q u a r t z v a r i a b l e temperature i n s e r t was d i f f e r e n t from the Bruker i n s e r t and was designed by A l l e n * . With the redesigned i n s e r t , the temperature o f the sample can be taken as low as the l i q u i d n i t r o g e n temperature . To prevent condensat ion i n the probe , the used n i t r o g e n gas was r e c y c l e d , heated to about 50°C, and blown i n t o the probe. The c o o l i n g system i s s i m i l a r to the system used i n CW measurement except t h a t temperatures above 105°K were c o n t r o l l e d by a B-ST 100/700 temperature c o n t r o l l e r i n the p u l s e work. * V i s i t i n g P r o f e s s o r from Department of P h y s i c s , U n i v e r s i t y o f Nott ingham, England. i n p u t v o l t a g e F i g . 3.1. R e l a t i o n o f i n p u t s i g n a l and output v o l t a g e of the r e c e i v e r o p e r a t i n g a t 30 MHz. - 3 4 -To o b t a i n the necessary accuracy i n temperature measurement, temperatures between 77° and 105°K were monitored and measured by copper-constantan thermocouple connected w i t h a p o t e n t i o m e t e r . The sample was a l l o w e d to e q u i l i b r a t e f o r a t l e a s t twenty minutes before measurement was made. 4 . Measurement o f S p i n - L a t t i c e R e l a x a t i o n Time S p i n - l a t t i c e r e l a x a t i o n time was measured by e i t h e r a 180° - x - 90° p u l s e sequence o r a n90° - x - 90° p u l s e sequence. I f the r e l a x a t i o n i s e x p o n e n t i a l , the r e l a x a t i o n f u n c t i o n R(x) i s g i v e n by R(x) = [Mo - MZCT)] /2Mo = e x p C - x / T ^ ( 3 . 3 ) f o r a 180° - x - 90° p u l s e sequence. Where Mo i s p r o p o r t i o n a l to the v o t l a g e a f t e r a s i n g l e 90° p u l s e , and Mz(x) i s p r o p o r t i o n a l to the v o l t a g e a f t e r a 180° - x - 90° p u l s e sequence. For d i f f e r e n t x ' s , we get d i f f e r e n t values of Mz(x) and a p l o t o f l n R ( x ) versus x should g i v e a s t r a i g h t l i n e w i t h s l o p e (-1 /T-j). A l t e r n a t i v e l y one can choose x i n the sequence 180° - x - 90° i n such a way so as to g i v e , a t x = x Q , Mz(x) = 0 . In t h a t case ( N u l l method) Equat ion (.3.3) g i v e s R(T Q) = 1/2 and T ] = x Q / l n 2 = 1 .443x Q ( 3 . 4 ) However, t h i s method i s not very a c c u r a t e , e s p e c i a l l y when the r f f i e l d i s not homogeneous and a diode d e t e c t o r i s used f o r s i g n a l d e t e c t i o n . A method f o r c o r r e c t i n g the H, inhomogeneity has been proposed by van P u t t e [ 3 . 3 ] . The - 3 5 -T-j o b t a i n e d from the s l o p e of the p l o t o f R(x) versus x always g i v e s a r e l i a b l e va lue [ 3 . 4 ] . However, a^ a matter o f good exper imenta l p r a c t i c e , i t i s always d e s i r a b l e to achieve good H^ homogeneity. For a sample w i t h long T-j, i t i s more convenient to use a n90° - x - 90° p u l s e sequence. For t h i s sequence the r e l a x a t i o n f u n c t i o n R(x) i s g i v e n by R(.x) = [ Mo - Mz(x)] /Mo = e x p C - x / T ^ ( 3 . 4 ) A p l o t o f R(x) versus x should a l s o g i v e a s t r a i g h t l i n e w i t h s l o p e (-1/T.j). A computer programme w i t h l e a s t square f i t t i n g was used to c a l c u l a t e . The s tandard d e v i a t i o n o f the s l o p e o f the s t r a i g h t l i n e was found to be l e s s than 5% f o r a l l the samples s t u d i e d . C. The Dry Box S i n c e a l k y l a l u m i n i u m and a l k l y l b o r a n e compounds and t h e i r complexes are a i r s e n s i t i v e , they must be handled i n a dry and oxygen f r e e atmosphere. A glove bag , o b t a i n e d from Instruments f o r Research and I n d u s t r y , was used as a dry box. The oxygen f re e dry n i t r o g e n gas was blown i n t o the g love beg f o r at l e a s t twenty minutes before the g love bag was s e a l e d . A f t e r s e a l i n g , two smal l holes were punched on the top o f the g love bad so t h a t n i t r o g e n g a s , c o u l d be blown c o n t i n u o u s l y i n t o the glove bag t o m a i n t a i n h i g h e s t p u r i t y o f the n i t r o g e n atmosphere. -36-References [ 3 . 1 ] E . R . Andrew, Phys. Rev. 9J_ (1953) 425 [ 3 . 2 ] M. Goldman, S p i n Temperature and N u c l e a r Magnet ic Resonance i n S o l i d s , O x f o r d : Clarendon P r e s s , 1970 , p . 109 . [ 3 . 3 ] K. van P u t t e , J . Mag. Res. 2 (1970) 174 [ 3 . 4 ] T . C . F a r r a r and E . D . B e c k e r , P u l s e and F o u r i e r Transform NMR, Academic P r e s s , 1 9 7 1 , Chapter 3 . -37-CHAPTER IV An NMR Study o f Tr imethylamine o r phosphine complexed w i t h T r i m e t h y l -borane o r aluminium A. I n t r o d u c t i o n This chapter d e s c r i b e s the d e t a i l s o f an nmr study o f the a d d i t i o n complexes o f t r i m e t h y l a m i n e and t r i m e t h y l p h o s p h i n e w i t h t r i m e t h y l b o r a n e and t r i m e t h y l a l u m n i urn. The a d d i t i o n complexes have been reviewed by Stone [4.1] and have been d i s c u s s e d i n Chapter I . The complexes are on the one hand very s i m i l a r to hexamethylethane and h e x a m e t h y l d i s i l a n e i n m o l e c u l a r s t r u c -t u r e and on the o t h e r hand, they p r o v i d e v a r i a t i o n o f the l e n g t h o f the bond between the methyl groups and the c e n t r a l atoms. I t i s p o s s i b l e t o use the nmr technique to study the m o l e c u l a r motion o f these a d d i t i o n complexes and the e f f e c t o f the c e n t r a l atoms on m o l e c u l a r m o t i o n . B. Experimental  B . l M a t e r i a l s T r i m e t h y l amine (anhydrous) was o b t a i n e d from Eastman Kodak. T r i m e t h y l -phosphine was o b t a i n e d from P f a l t z and Bauer , I n c . T r i m e t h y l b o r a n e and t r i m e t h y l a l u m i n i u m were purchased from A l f a I n o r g a n i c s . T r i m e t h y l a m i n e -t r i m e t h y l borane was k i n d l y p r o v i d e d by Dr . A. S t o r r . B.2 P r e p a r a t i o n o f A d d i t i o n Complexes The complex t r i m e t h y l a m i n e - t r i m e t h y l a l u m i n i u m [ 4 . 2 ] was prepared by i n t r o d u c i n g an excess o f t r i m e t h y l a m i n e t o t r i m e t h y l a l u m i n i u r n which was a t - 3 8 -l i q u i d n i t r o g e n temperature . The t r a n s f e r was made i n a vacuum system, the mixture of compounds warmed s l o w l y from l i q u i d n i t r o g e n temperature t o room temperature , and the excess t r i m e t h y l a m i n e pumped o f f at room temperature . The product which remained was subl imed i n t o a vacuum and c o l l e c t e d on a c o l d f i n g e r which was a t about 1Q°C. The c o l d f i n g e r was then warmed s l o w l y to room temperature and the sample was kept under vacuum o v e r n i g h t . T r i m e t h y l -p h o s p h i n e - t r i m e t h y l a l u m i n i u m [4 .2] was prepared by m i x i n g t r i m e t h y l p h o s p h i n e and t r i m e t h y l a l u m i n i u m at room temperature w i t h t r i m e t h y l p h o s p h i n e s l i g h t l y i n excess and was then p u r i f i e d by vacuum s u b l i m a t i o n . T r i m e t h y l p h o s p h i n e -t r i m e t h y l b o r a n e [ 4 . 3 , 4 . 4 ] was prepared by i n t r o d u c i n g a smal l amount o f t r i m e t h y l b o r a n e t o t r i m e t h y l p h o s p h i n e which was trapped a t l i q u i d n i t r o g e n temperature . The m i x t u r e o f the compounds was warmed to dry i c e acetone temperature. The procedure was repeated u n t i l a manometer showed the r e a c t i o n was completed. The r e s i d u a l gas was pumped o f f and the product which remained was p u r i f i e d by vacuum s u b l i m a t i o n . Samples were t r a n s f e r r e d i n a dry box to 10 mm O.D. sample tubes f o r CW measurement and to 7.5 - 8 .0 mm O.D. t h i n w a l l tubes f o r s p i n - l a t t i c e , r e l a x a t i o n time measurement. ; B. 3 Measuring Procedures Both CW and T^ measurements have been d e s c r i b e d i n Chapter I I I . C. Tr imethylami n e - t r i m e t h y l b o r a n e C. l L i n e vijdths and Second Moments The exper imenta l second moments and l i n e widths are p l o t t e d v s . temperature - 3 9 -i n F i g u r e 4 . 1 . The second moment has a p l a t e a u va lue o f 22.2 ± 0 . 6 G 2 between 63 and 95 K. Then i t decreases from 19.6 G a t 100 K to a va lue o f 2 ? 2.6 ± 0 . 3 G a t 138 K, and cont inues to decrease very s l o w l y to 2.0 ± 0 . 3 G at the h i g h e s t observed temperature , 350 K. The shape o f the l i n e w i d t h v s . temperature i s s i m i l a r t o t h a t o f the second moment v s . temperature . C.2 C a l c u l a t i o n o f Second Moment and D i s c u s s i o n o f M o l e c u l a r Mot ion C.2.1 N o t a t i o n Before c a l c u l a t i n g the t h e o r e t i c a l second moment f o r v a r i o u s degrees o f motion i n the l a t t i c e , l e t us i n t r o d u c e some n o t a t i o n f o r second moments. We denote the r i g i d l a t t i c e second moments as f o l l o w s : S , the t o t a l second moment; S j , second moment a r i s i n g from i n t e r a c t i o n between protons w i t h i n the same methyl group; S J J , second moment a r i s i n g from i n t e r a c t i o n s between d i f f e r e n t methyl groups i n the same m o l e c u l e ; S J J J , second moment due to i n t e r a c t i o n s between protons and n i t r o g e n and boron atoms i n the same, m o l e c u l e ; S j y , i n t e r m o l e c u l a r second moment. When the t h r e e methyl groups a t tached to one o f the c e n t r a l atoms are r o t a t i n g r a p i d l y , whereas the methyl groups a t tached to the o t h e r are s t i l l " f i x e d " , the second moments are denoted by S " , S ' j , S ' J J , S ' J J J , S ' j y , r e s p e c t i v e l y , as above. When a l l methyl groups i n the molecule are r o t a t i n g r a p i d l y , the second moments are denoted by S " , S " j , S " I ] R , S " J J J , s " i v ' r e s P e c t i v e l y . When the whole molecule r o t a t e s about i t s B-N bond and a l l the methyl groups are a l s o r o t a t i n g , the second moments are denoted as above by S " S " ' j , S " ' j j , S ' " I T T > ^ " ' I V r e s P e c t i y e l y . C . 2 . 2 . R i g i d l a t t i c e second moment S ince the c r y s t a l s t r u c t u r e o f t r i m e t h y l a m i n e - t r i m e t h y l b o r a n e Fig. 4.1. Line width and second nonent of trimethylamine-trimethylborane as a function of temperature. - 4 1 -i s not known, the t h e o r e t i c a l second moment can o n l y be e s t i m a t e d . The t o t a l r i g i d second moment, S , o f t r i m e t h y l a m i n e - t r i m e t h y l b o r a n e may be c o n s i d e r e d as the sum of f o u r components: S j , S J J , s j j l ' s I V a s c ' e f i n e c ' b e f o r e . Of the four components, on ly Sj can be c a l c u l a t e d w i t h p r e c i s i o n ^ Assume t h a t the C-H bond d i s t a n c e i s 1 . 1 0 8 and t h a t the carbon bonds are d i r e c t e d t e t r a h e d r a l l y . 2 Then Sj i s 2 1 . 3 G . Al though the atomic c o o r d i n a t e s o f t r i m e t h y l a m i n e - t r i m e t h y l -borane are not known at very low temperature , an e s t i m a t e o f bond l e n g t h s can be made by u s i n g t a b l e s o f i n t e r a t o m i c d i s t a n c e s [ 4 . 5 ] o r from c o v a l e n t r a d i i [ 4 . 8 ] . Good es t imates appear to be r (C-N) = 1 . 4 7 8 and r ( C - B ) = 1 . 5 6 8 . The B-N bond l e n g t h c a l c u l a t e d from c o v a l e n t r a d i i i s 1 . 5 5 ft, which i s 0 . 0 1 8 l o n g e r than the C-C bond l e n g t h . However, i n hexamethylethane, the c e n t r a l C-C bond l e n g t h i s 1 . 5 8 8 a c c o r d i n g to e l e c t r o n d i f f r a c t i o n s t u d i e s [ 4 . 7 ] . From the f a c t t h a t t r i m e t h y l a m i n e - t r i m e t h y l b o r a n e w i l l d i s s o c i a t e r a t h e r ; e a s i l y a t h igh temperature [ 4 . 8 ] , i t i s presumed t h a t the B-N bond l e n g t h should not be l e s s than 1 . 5 8 ft. We assume i t i s 1 . 6 0 ft. This va lue i s lower than 1 . 8 0 ± 0 . 1 5 ft o b t a i n e d by microwave [ 4 . 2 4 ] . However, the c o n c l u s i o n o f microwave has been c r i t i c i z e d [ 4 . 2 5 ] on the grounds t h a t t h i s B-N bond . d i s t a n c e i s s u b s t a n t i a l l y g r e a t e r than t h a t observed i n a number o f s o l i d complexes by X - r a y d i f f r a c t i o n . Changes i n t h i s va lue by about 0 . 0 5 ft w i l l , 2 however, a f f e c t S J J by o n l y 0 . 1 G . We assume a l s o t h a t at low temperature the methyl groups a t t a c h e d to the n i t r o g e n atoms are staggered w i t h r e s p e c t t o the methyl groups a t tached to boron. Smith [ 4 . 9 ] found t h a t S J J would be reduced by a f a c t o r 0 . 9 0 / 1 . 0 4 i f he assumed t h a t the e f f e c t o f the methyl group v r e o r i e n t a t i o n i s to c o n c e n t r a t e the C H , protons a t t h e i r c e n t r e o f r o t a t i o n . - 4 2 -In our c a l c u l a t i o n o f S J J a r e v e r s e l i n e o f reasoning was f o l l o w e d . Assuming t h a t a l l methyl groups r o t a t e , we c a l c u l a t e d the c o n t r i b u t i o n to the second moment by c o n c e n t r a t i n g the CH^ protons a t t h e i r c e n t r e o f r o t a t i o n . Then 2 i s o b t a i n e d by m u l t i p l y i n g by a f a c t o r 1 . 0 4 / 0 . 9 0 , and we get = 4 . 3 5 G . The c o n t r i b u t i o n to the second moment a r i s i n g from i n t e r a c t i o n s between protons 2 and n i t r o g e n i s s m a l l , be ing about 0 . 0 1 G , which can be n e g l e c t e d . However, the c o n t r i b u t i o n to the second moment a r i s i n g from i n t e r a c t i o n s between protons 11 2 and B i s not n e g l i g i b l e . C a l c u l a t i o n g ives 0 . 3 G f o r t h i s c o n t r i b u t i o n . The c o n t r i b u t i o n due to ^ B was n e g l e c t e d . We conclude t h a t S J J J i s a p p r o x i m a t e l y 2 2 0 . 3 G . A reasonable es t imate [ 4 . 9 , 4 . 1 0 ] f o r S j y i s 7 ± 1 G , and thus the 2 t o t a l r i g i d l a t t i c e second moment i s S = 3 3 . 0 ± 1 G . C . 2 . 3 . E f f e c t o f r o t a t i o n o f t h r e e methyl groups i n e i t h e r the t r i m e t h y l - amine or t r i m e t h y l b o r a n e moiety From Powles and Gutowsky's formula [ 4 . 1 1 ] , S ' j i s found t o be 2 1 3 . 3 G . S m i t h ' s method [ 4 . 9 , 4 , 1 2 ] was used to c a l c u l a t e S ' J J , and we found i t 2 to be S J J = 4 . 0 G . S ' j j j i s the same as S j j j i f the methyl groups a t tached to n i t r o g e n are r o t a t i n g . I f the methyl groups a t tached to boron are r o t a t i n g , 2 S ' j j j becomes 0 , 2 G . By l i n e a r i n t e r p o l a t i o n between the v a l u e S " ^ = 2 . 4 ± 2 2 0 . 8 G (see below) and the r i g i d l a t t i c e va lue o f 7 ± 1 G we o b t a i n S' IV 4 . 7 ± 0 . 8 G 2 . As a r e s u l t , the t o t a l c a l c u l a t e d S' i s 2 2 . 3 + 0 . 8 G 2 . C . 2 . 4 . E f f e c t o f r o t a t i o n o f a l l methyl groups ; The e f f e c t o f the r o t a t i o n o f the methyl groups about t h e i r 2 3 - f o l d a x i s i s to reduce Sj by a f a c t o r o f 4 . Thus S"j = 5 . 3 G . S " j j i s o b t a i n e d by the method of S m i t h , mentioned i n the s e c t i o n on r i g i d l a t t i c e second moment. - 4 3 -and i s 3 . 8 G . $"m i s the same as S ' m - F o l l o w i n g S m i t h ' s summary [ 4 . 9 ] o f es t imates made i n the l i t e r a t u r e o f f i n d i n g r e d u c t i o n f a c t o r s o f 0 . 4 2 -0.25 f o r second moment c o n t r i b u t i o n s from i n t e r a c t i o n s between two r o t a t i n g groups, we e s t i m a t e d a value f o r S " j y fo 2.4 + 0 . 8 G 2 . Thus S'1 = 11.7 ± 0 .8 G 2 . C . 2 . 5 . E f f e c t o f methyl r e o r i e n t a t i o n plus r e o r i e n t a t i o n about the c e n t r a l bond The c o n t r i b u t i o n to the second moment o f a methyl group r e o r i e n t a t i n g r a p i d l y about i t s C^ a x i s and a l s o about an a x i s making an angle \p t o the C^ a x i s has been c o n s i d e r e d by Powles and Gutowsky [4 .11 ] . In t h i s case we can 2 c a l c u l a t e S " ' j = 0 . 6 G . S J J can be c a l c u l a t e d by assuming a l l C H 3 protons 2 concentrate at the c e n t r e o f the c i r c l e o f r o t a t i o n . Thus S' J J = 0 .5 G . S" ' j j j w i l l be reduced to a p p r o x i m a t e l y z e r o . A c c o r d i n g to Chezeau e t a ] . [ 4 . 1 0 ] , S " ' I V should not be l e s s than 0.9 G 2 and they es t imated S " ' I V = 1.4 G 2 . 2 We a l s o assume S " ' j y = 1.4 G fop t r i m e t h y l a m i n e - t r i m e t h y l b o r a n e , and t h e r e f o r e conclude t h a t S" ' = 2.5 ± 0 .5 G 2 . C.3 I n t e r p r e t a t i o n o f the observed second moment The c a l c u l a t e d values f o r the proton resonance second moments are compared w i t h exper imental r e s u l t s i n Table 4 . 1 . Even a t the lowest temperature a t t a i n e d , 2 63 K, the l a t t i c e i s not r i g i d s i n c e the measured va lue o f 22.5 G i s c o n s i d e r a b l y 2 l e s s than the c a l c u l a t e d value o f 33 G . The p l a t e a u value observed below 95 K corresponds reasonably w e l l w i t h r e o r i e n t a t i o n o f three methyl g r o u p s . I t has a l r e a d y been i n d i c a t e d t h a t the C-B bond l e n g t h i s g r e a t e r than C-N bond l e n g t h . I t seems p l a u s i b l e , t h e r e f o r e , t h a t s t e r i c h indrance to r o t a t i o n o f the methyl groups a t tached to boron w i l l be l e s s than t h a t f o r the methyl groups a t t a c h e d t o - 4 4 -• . . - TABLE 4.1 p T h e o r e t i c a l second moments f o r t r i m e t h y l a m i n e - t r i m e t h y l b o r a n e ( i n G ) and the Comparison w i t h experimental values Group Me3N Motion Me3B T h e o r e t i c a l Second Moment C o n t r i b u t i o n I n t e r C H 3 P r o t o n t 0 " I n t r a C H 3 I n t r a m o l e c u l a r N and B I n t e r m o l e c u l a r T o t a l Experimental Second Moment Temperature T°K SS SS 21.3 4 .35 0 . 3 7 ± 1 33 ± 1 SS RS 13.3 4 . 0 0 .2 4 . 7 ± 1 22.2 ± 1 22.5 63 - 95 RS SS 13.3 3.9 0 . 3 4 . 7 ± 1 22.2 ± 1 RS RS 5.3 3 . 8 0 .2 2.4 ± 1 11.7 ± 1 RR RR 0.6 0 . 5 0 . 0 1.4 ± 0.5 2.5 ± 0.5 2.6 - 2.0 138- - 350 SS = methyl group s t a t i o n a r y and whole moiety s t a t i o n a r y RS = methyl group r o t a t i n g but moiety s t a t i o n a r y RR = methyl group r o t a t i n g and whole moiety r o t a t i n g -45-n i t r o g e n and t h a t r e o r i e n t a t i o n o f the methyl groups i n the t r i m e t h y l b o r a n e moiety w i l l a f f e c t the nmr l i n e w i d t h and second moment a t lower temperatures than w i l l r e o r i e n t a t i o n o f methyl groups i n the t r i m e t h y l a m i n e m o i e t y . Thus 2 we i n t e r p r e t the second moment p l a t e a u o f 22.5 G below 95 K as i n d i c a t i n g r e o r i e n t a t i o n o f methyl groups i n the t r i m e t h y l b o r a n e moiety and " f i x e d " ( m e t h y l groups i n the t r i m e t h y l a m i n e m o i e t y . The q u e s t i o n can a r i s e o f whether the r e o r i e n t a t i o n o f methyl groups a t low temperatures i s a s s i s t e d by quantum mechanical t u n n e l l i n g [4.26 - 4 . 2 9 ] . As d i s c u s s e d i n Chapter I I , the second moment r e d u c t i o n which occurs when t h e r e i s t u n n e l l i n g may be d i f f e r e n t from t h a t which occurs f o r c l a s s i c a l r e o r i e n t a t i o n , but a c c o r d i n g to A l l e n [4 .13] the quantum mechanical and c l a s s i c a l mechanisms both g i v e a r e d u c t i o n f a c t o r o f \ when the b a r r i e r h e i g h t i s l e s s than about 3 k c a l / m o l e , a va lue which i s i n excess o f most o f the b a r r i e r s to methyl group r e o r i e n t a t i o n observed i n t h i s work. In these cases the magnitude o f the second moment g ives no evidence f o r the e x i s t e n c e o f t u n n e l l i n g . For N-methyl gr ou ps , f o r which the b a r r i e r i s more than 3 k c a l / m o l e , we have found the observed second moments to be c o n s i s t e n t w i t h r i g i d l a t t i c e c o n d i t i o n s at the lowest observed temperatures . T u n n e l l i n g mechanisms do not come i n t o q u e s t i o n , t h e n , i n the case o f N-methyl groups i n our compounds. A n a l y s i s of the T-j data [see l a t e r ) shows t h a t the T-j minimum can be e x p l a i n e d s a t i s f a c t o r i l y by the m o d i f i e d BPP e q u a t i o n [ 4 . 1 6 , 4 .17] which assumes the d i p o l e - d i p o l e r e l a x a t i o n i s t h e r m a l l y a c t i v a t e d . I t has been shown t h a t the l i n e narrowing t r a n s i t i o n i s expected to be completed when [4 .14] -46-( A U ) 0 2 ) 1 / 2 T C « 1 ( 4 . 1 ) 2 whereat^ i s the r i g i d l a t t i c e second moment and T c i s the c o r r e l a t i o n t ime f o r the motional p r o c e s s . Using the T-j d a t a , a l i n e w i d t h and second moment t r a n s i t i o n i s expected to occur a t about 5 1 K i f the methyl groups a t t a c h e d to boron are r i g i d . This temperature i s lower than the lowest temperature we can a t t a i n . I t would be i n t e r e s t i n g to see i f t h e r e i s t u n n e l l i n g a s s i s t e d r e o r i e n t a -t i o n below 5 0 K i n t r i m e t h y l a m i n e - t r i m e t h y l b o r a n e . S i n c e no h a l t i n the decrease o f second moment between 9 5 K and 1 4 0 K 2 i s observed near 1 2 G , one concludes t h a t r o t a t i o n o f methyl groups i n the t r i m e t h y l a m i n e moiety and r o t a t i o n o f the whole molecule about the boron-n i t r o g e n a x i s occur w i t h comparable f r e q u e n c i e s i n t h i s temperature range. T h i s o b s e r v a t i o n corresponds to t h a t f o r hexamethylethane [ 4 . 1 0 ] , f o r which no p l a t e a u which would correspond t o methyl group r e o r i e n t a t i o n but no s i g n i f -i c a n t r e o r i e n t a t i o n about the c e n t r a l C-C bond i s observed i n the second moment. This o b s e r v a t i o n agrees w i t h e a s i e r methyl group r e o r i e n t a t i o n about the longer C-Si bond [ 4 . 1 5 ] and lends c r e d i b i l i t y t o our i n t e r p r e t a t i o n o f the second moment v s . temperature curve o f t r i m e t h y l a m i n e - t r i m e t h y l b o r a n e . The 2 l e v e l l i n g o f f o f second moment above about 1 4 0 K to a va lue o f some 2 . 6 G agrees w e l l w i t h the c a l c u l a t e d second moment f o r r e o r i e n t a t i o n o f a l l methyl groups as w e l l as r o t a t i o n o f the whole molecule about the B-N a x i s . The study was not pursued above 3 5 0 K because the compound begins t o subl ime and d i s s o c i a t e to a s i g n i f i c a n t e x t e n t beyond t h a t temperature . -47-C.4 S p i n - L a t t i c e R e l a x a t i o n F i g u r e 4 . 2 shows the temperature dependence o f s p i n - l a t t i c e r e l a x a t i o n times of t r i m e t h y l a m i n e - t r i m e t h y l b o r a n e . The m o d i f i e d 14.16] e q u a t i o n o r i g i n a l l y developed by Bloembergen J 4 . 1 7 ] U i x M U l + 1 ) I r - 6 / _ V c + ^ V c _ A ( 4 ; 2 ) T, % j " \ l + " 0 2 V 1 + 4 ^ 3 . i s used t o analyze our T^ d a t a . The symbols are c o n v e n t i o n a l and have been d e f i n e d i n Chapter I I , The c o r r e l a t i o n time x c i s assumed t o have a s imple A r r h e n i u s dependence on an a c t i v a t i o n energy, E = , and on temperature a x c =T c ° exp (E a /RT) ( 4 . 3 ) T h i s equat ion can a l s o be w r i t t e n as V c =Vc° e x P ( E a / R T ) C 4 ' 4 ) We a t t r i b u t e the low temperature minimum i n the InT-j vs T"^ curve t o r e o r i e n t a t i o n about t h e i r C^ axes o f those methyl groups which are a t t a c h e d to the boron atom. Using a va lue ( T , ) • = 37 ms to e v a l u a t e the p a r t o f Equat ion 3 1 min r (4 .2) o u t s i d e the square b r a c k e t s , we o b t a i n e d a value o f w Qx c f o r each experimental T-j p o i n t between 79 and 130 K. A p l o t o f l n w 0x c vs T~^ i s shown by l i n e a i n F i g u r e 4 . 3 . A l e a s t squares f i t o f the l i n e gave - 4 8 -~ i r 1 1 1 12 10 8 6 A 1 0 0 0 / T ° K F i g . 4 . 2 . The s p i n - l a t t i c e r e l a x a t i o n t i m e , T , , of t r i m e t h y l a m i n e - t r i m e t h y l -borane as a f u n c t i o n of i n v e r s e temperature . The broken l i n e s i n d i c a t e the r e s o l u t i o n of the observed T, i n t o tv/o mechanisms. ~I 1 1 1 1 1 1 1 1 1— 1 1 13 12 11 IO 9 8 7 6 5 4 3 2 T O O O / T ° K F i g . 4.3 P l o t o f u^x versus i n v e r s e of temperature of t r i m e t h y l a m i n e - t r i m e t h y l b o r a n e . (a) f o r r o t a t i o n o f the methyl groups a t tached to boron (b) f o r r o t a t i o n o f the methyl groups a t tached to n i t r o g e n plus the r e o r i e n t a t i o n o f the whole molecule about the B-N bond. - 5 0 -l n V c = C" 9 , 6 8 ± 0 - 2 1 5 + ^ , 8 9 * 0 , 0 4 ) x 1 q 3 / R T (4 .5) The a c t i v a t i o n energy was thus found to be 1.89 ± 0.04 kca l/mole f o r r e o r i e n t a t i o n of the methyl groups a t tached to the boron atom. We a t t r i b u t e the h i g h temp-e r a t u r e minimum i n the InT-j vs T~^ curve to r e o r i e n t a t i o n of methyl groups at tached to n i t r o g e n and the r e o r i e n t a t i o n o f the whole molecule about the B-N a x i s . Between 130 and 165 K the s p i n - l a t t i c e r e l a x a t i o n time i s b e l i e v e d to be c o n t r o l l e d by t h r e e mechanisms; namely the r e o r i e n t a t i o n o f the three methyl groups at tached to the boron atom, the r e o r i e n t a t i o n o f methyl groups at tached to the n i t r o g e n atom, and the r o t a t i o n of the whole molecule about the B-N a x i s . The change o f second moment w i t h temperature between 100 and 1 3 8 K i n d i c a t e s t h a t the l a t t e r two mechanisms cannot be separated from each o t h e r i n the frequency range i n which they are e f f e c t i v e i n changing the l i n e w i d t h o f the CW spectrum. We assume t h a t these two r o t a t i o n a l motions are l i k e w i s e i n s e p a r a b l e i n t h e i r c o n t r i b u t i o n to s p i n - l a t t i c e r e l a x a t i o n a t the Lamor frequency of 30 MHz, and we have lumped them t o g e t h e r as a s i n g l e process w i t h a common a c t i v a t i o n energy and a common value o f T c ° . In the temperature range 130 to 165 K, the observed s p i n - l a t t i c e r e l a x a t i o n time can be expressed as ^T^obs ^VcH - j + TO (4 .6) 1 mol where ( T , ) i s the r e l a x a t i o n time c o n s t a n t o f the r e o r i e n t a t i o n mechanism -51-f o r the t h r e e methyl groups a t tached to boron. I t s va lue can be c a l c u l a t e d from Equat ion ( 4 . 5 ) and ( 4 . 2 ) , and i t i s shown i n F i g u r e 4 . 2 by the broken l i n e o f p o s i t i v e s l o p e . (T-|) -| i s the r e l a x a t i o n time c o n s t a n t of the r e o r i e n t a t i o n mechanisms f o r the methyl groups a t tached to n i t r o g e n combined w i t h r o t a t i o n of the whole molecule about the B-N a x i s . Using Equat ion ( 4 . 6 ) , one can o b t a i n i t from the observed T-j and c a l c u l a t e d values o f ( t - ] )Q | • The broker, l i n e o f n e g a t i v e s l o p e i n F i g u r e 4 . 2 shows the c a l c u l a t e d value o f ^ l V i o l ' U s^ n9 a v a ^ u e ° f ( T - ] ) m i n = ^ m s ' c a l C L | 1 a t e c l va lues o f ( T ] ) m o i i n the temperature range from 145 to 165 K, and observed va lues above 165 K, we c a l c u l a t e d GO T f o r each T, p o i n t between 145 and 335 K. These values are o c 1 p l o t t e d as l i n e b i n F i g u r e 4 . 3 . A l e a s t square f i t o f the l i n e gave l n V c = ("10-71 ± °-08) 4 (3-63 1 °'03' x 1 q 3/ r t (4-?) The a c t i v a t i o n energy was thus found to be 3.63 ± 0 .03 kca l/mole f o r r e o r i e n t a -t i o n of methyl groups a t tached to n i t r o g e n and r o t a t i o n o f the whole molecule about the B-N a x i s . The ass igned r e l a x a t i o n mechanism can be checked from n . m . r . l i n e width and second moment. Decrease i n n . m . r . l i n e width o r second moment due to the combined r o t a t i o n motion o f methyl groups a t tached to n i t r o g e n and whole molecule should occur i n a c o r r e l a t i o n t ime range near T c ~ ( Y * ^ ^ O R (ySH) where and 6H are the second moment and l i n e width a t about the mid-2 3 p o i n t o f n a r r o w i n g . M 2 = 12 G (see F i g u r e 4.1) g ives C O 0 T c = 2.0 x 10 and SH = o 11 G g i v e s (JO QT c = 6.4 x 10 . From F i g u r e 4.3b o r Equat ion ( 4 . 7 ) , one p r e d i c t s that the temperature o f second moment o r l i n e width decrease should be at about 100 o r 106 K, r e s p e c t i v e l y , va lues which agree s a t i s f a c t o r i l y w i t h the exper imenta l - 5 2 -temperature f o r l i n e n a r r o w i n g . I f i n Equat ion ( 4 . 2 1 , k^rT.. i s put equal to j r " /s f o r an i s o l a t e d methyl group r o t a t i n g abput i t s C 3 a x i s [ 4 . 1 8 ] , where r , the i n t e r -proton d i s t a n c e , i s taken as 1.80 %, one o b t a i n s (J-,) • = 17.8 ms. We b e l i e v e 1 mm t h a t at the lower temperature minimum i n T-| o n l y the methyl groups on boron are r o t a t i n g r a p i d l y enough to c o n t r i b u t e to s p i n - l a t t i c e r e l a x a t i o n . The o t h e r ha l f , o f methyl groups i n the molecule are presumably r e l a x e d through spin,-d i f f u s i o n [4.19] t o the B-methyl groups and the observed minimum i n T-j would be expected to be twice [4.19] t h a t f o r the B-methyl groups a l o n e , hence 35.6 ms, n e g l e c t i n g i n t e r - g r o u p c o n t r i b u t i o n s t o T-j. D e s p i t e the f a c t t h a t one would expect the p r e d i c t e d T^ minimum to be l a r g e r than the observed va lue (37 ms) i n view o f the neglect o f i n t e r - g r o u p c o n t r i b u t i o n , the agreement w i t h experiment i s good enough to suggest t h a t the low temperature minimum has been c o r r e c t l y ass igned to r o t a t i o n o f t h r e e o f the s i x methyl groups. For r o t a t i o n o f the whole m o l e c u l e , k . r T . becomes fir" /45 f o r an i s o l a t e d methyl group [ 4 . 2 0 ] . At the temperature o f the 19 ms minimum i n T-j, r e l a x a t i o n by r o t a t i o n o f the B-methyl groups i s c o n s i d e r e d n e g l i g i b l e and the minimum i n T-j f o r the combined motion i s c a l c u l a t e d to be 22.4 ms, n e g l e c t i n g i n t e r - g r o u p c o n t r i b u t i o n . This compares reasonably w i t h the experimental va lue o f 19,ms. D. T r i methyl ami n e - t r i m e t h y l a l u m i n i urn complex D . l L i n e Width and second Moment The experimental l i n e w i d t h and second moment of t r i m e t h y l a m i n e -t r i m e t h y l aluminium are p l o t t e d a g a i n s t temperature i n F i g u r e 4 . 4 . The second 24 n 5 0 Fig. 4.4. • Second moment o Line width T.P T.P r 2 4 - 2 0 M 6 CD I 12 Q h 8 h4 UJ z _ J 1 0 0 150 2 0 0 250 3 0 0 3 5 0 4 0 0 T E M P E R A T U R E (°K ) Line width and second moment of trimethylamine-trinethylaluminium as a function of temperature. 1 cn CO I -54" moment i s constant at 20.3 + 0 . 5 G between 65 and 80 K and then decreases 2 r a t h e r r a p i d l y to 9 . 8 + 0.3 G a t about 120 K. I t remains a t t h i s v a l u e f o r 2 s e v e r a l degrees and then decreases s l o w l y to about 2 G a t 240 K, above which i t changes o n l y very l i t t l e except near 313 K, where t h e r e i s a sharp and c o m p a r a t i v e l y l a r g e change i n l i n e w i d t h . Above 313 K, the second moment i s e s s e n t i a l l y zero and the l i n e w i d t h i s determined by the ampl i tude o f the modulat ion f i e l d and the magnetic f i e l d inhomogeneity . D.2 C a l c u l a t i o n o f Second Moment and D i s c u s s i o n o f M o l e c u l a r M o t i o n Using the methods f o r c a l c u l a t i n g t h e o r e t i c a l second moments which were d e s c r i b e d i n d e t a i l b e f o r e , we have o b t a i n e d the t h e o r e t i c a l second moments, which are l i s t e d i n Table 4 . 2 , f o r r i g i d l a t t i c e c o n d i t i o n s and f o r v a r i o u s kinds o f m o l e c u l a r m o t i o n . For the c a l c u l a t i o n on t r i m e t h y l a m i n e -t r i m e t h y l a l u m i n i u m we have taken i n t e r a t o m i c d i s t a n c e s as f o l l o w s [ 4 . 5 ] : . r ( C - H ) = 1.10 ft, r ( C - N ) = 1.47 ft, r(C-Afc) = 2.00 ft and r ( N - A a ) = 1.93 ft.* I t i s c l e a r from Table 4 . 2 t h a t even at the lowest observed temperature the r i g i d l a t t i c e va lue o f the second moment o f t r i m e t h y l a m i n e - t r i m e t h y l a l u m i n i u m has .not been reached. The exper imental va lue of the second moment between 65 and 80 K agrees very w e l l w i t h the va lue c a l c u l a t e d on the assumption t h a t three of the s i x methyl groups i n the molecule are r e o r i e n t i n g . S i n c e the C-A& bond i s much l o n g e r than the C-N bond i t seems probable t h a t the r a p i d l y ; r e o r i e n t i n g groups are those a t tached to a luminium. This c o n c l u s i o n i s supported by the f a c t t h a t the methyl groups i n h e x a m e t h y l d i s i l a n e [4.15] r o t a t e e s s e n t i a l l y *r(N-A£) o b t a i n e d f r o m r ( C - N ) , r ( C - A A ) and r ( C - C ) -55-TABLE 4 . 2 T h e o r e t i c a l second moments f o r t r i m e t h y l a m i n e - t r i m e t h y l a l u m i n i u m ( i n G^) and the Comparison w i t h experimental values T h e o r e t i c a l Second Moment C o n t r i b u t i o n Group Motion I n t e r C H 3 b u t Proton to Exper imenta l Temperatur Me,N Me^A£ I n t r a C H , ' I n t r a m o l e c u l a r N and A£ I n t e r m o l e c u l a r T o t a l Second Moment T°K SS SS 21.3 2.5 0 . 3 6 ± 1 30.1 + 1 - -SS RS 13.3 2.3 0.1 4 . 3 + 0.5 20.0 + 0.5 20.3 ± 0 .5 65 - 80 RS SS 13.3 2.2 0 .3 4 . 3 + 0.5 20.1 + 0.5 20.1 ± 0 .5 RS RS 5 .3 2.2 0.1 2.4 + 0.5 10.0 + 0.5 9 . 8 ± 0.3 120 - 130 RR RR 0.6 0 . 3 0 1.0 + 0.3 1.9 + 0.3 2.0 ± 0 . 5 220 - 313 d i f f u s i o n 0 0 0 0 0 0 313 - m.p. SS = methyl group s t a t i o n a r y and whole moiety s t a t i o n a r y RS = methyl group r o t a t i n g but moiety s t a t i o n a r y RR = methyl group r o t a t i n g and whole moiety r o t a t i n g -56-f r e e l y a t l i q u i d n i t r o g e n t e m p e r a t u r e , whereas the methyl groups i n hexa-methylethane 14,10] are s e v e r e l y l i m i t e d i n t h e i r r o t a t i o n a l freedom at 85 K, and a l s o t h a t the bond lengths are r(C-A£) > r ( C - S i ) and r (C-C) > r ( C - N ) . This c o n c l u s i o n f u r t h e r supports the p r e v i o u s c o n c l u s i o n on t r i m e t h y l a m i n e -t r i methyl borane s i n c e r(C-Aji) > r ( C - B ) , The p l a t e a u a t 9 . 8 ± 0 .3 G , which we observed between 120 and 130 K, corresponds to the second moment c a l c u l a t e d on the assumption t h a t a l l the methyl groups r o t a t e f r e e l y about t h e i r axes . The f u r t h e r gradual decrease i n l i n e w i d t h and second moment which takes p lace above 130 K i s a t t r i b u t e d to r e o r i e n t a t i o n o f the whole molecule about 2 the N-AJl a x i s . The exper imental second moment of 2.0 G found over the c o n s i d e r a b l e temperature range centred about 250 K agrees w i t h the v a l u e ; c a l c u l a t e d on the assumption t h a t the methyl groups are r o t a t i n g and the whole molecule r o t a t e s about i t s N-A£ a x i s . Narrowing o f the l i n e w i d t h and decrease o f second moment e s s e n t i a l l y to zero above the t r a n s i t i o n temperature o f 313 K i s b e l i e v e d to be caused by d i f f u s i o n of the whole molecule i n the c r y s t a l 1 a t t i ce. D.3 S p i n - l a t t i c e R e l a x a t i o n A p l o t o f T-j a g a i n s t r e c i p r o c a l temperature i s shown i n F i g u r e 4 . 5 . Below 290 K two minima are observed i n T-|, one a t about 183 K and one a t a b o u t 276 K. Sudden changes i n T-j at 290 and 313 K are a t t r i b u t e d t o phase t r a n s i t i o n s i n the s o l i d , and the sharp change at 375 K i s due t o m e l t i n g , a l though i t i s 2° below the m e l t i n g p o i n t g iven by Davidson and Brown [ 4 . 2 ] . The s o l i d down to 313 K i s des ignated as phase I , between 313 and 290 K as phase I I , and below 290 K as phase I I I . 13 F i a . 4.5. 1 11 9 7 1 0 0 0 / T ° K The s p i n - l a t t i c e r e l a x a t i o n time of t r i m e t h . y l a m i n e - t r i m e t h . y l a l u n i n i u n as a f u n c t i o n of i n v e r s e temperature. The broken l i n e s i n d i c a t e the r e s o l u t i o n o f ob.serv.ed-I-j. , The..open, eir.c.1 es..are,the-.:r-e-s.o]ved-T-j f o r r o t a t i o n about N - A l bond. - 5 8 -The a n a l y s i s o f the data f o r t r i m e t h y l a m i n e - t r i m e t h y l a l u m i n i u m i s s i m i l a r to t h a t f o r t r i m e t h y l a m i n e - t r i m e t h y l b o r a n e . We analyze the T-j data i n the v a r i o u s phases as f o l l o w s . Phase I I I We a t t r i b u t e the i n c r e a s e o f T-| w i t h i n c r e a s i n g temperature i n the range o f 77 to 88 K to the r e o r i e n t a t i o n about t h e i r C 3 axes o f those methyl groups at tached to the aluminium atom. In t h a t temperature range the c o n t r i b u t i o n t o the o v e r a l l r e l a x a t i o n t i m e , T-j, made by the mechanism which produces a minimum at 183 K i s s m a l l . E x t r a p o l a t i o n of the l i n e a r l y d e c r e a s i n g InT^ w i t h d e c r e a s i n g T~^ (.that p o r t i o n o f the curve which i s due to t h i s second mechanism) back to T = 88 K shows t h a t the c o n t r i b u t i o n o f the second process to T.| i s over 30 times l a r g e r than the observed a t 88 K. The e r r o r i n t r o d u c e d by i g n o r i n g the c o n t r i b u t i o n o f the second mechanisms to the v a l u e o f T^ observed at and below 88 K i s , t h e r e f o r e w i t h i n the exper imenta l u n c e r t a i n t y i n T.|. The broken l i n e s i n F i g u r e 4 . 5 between 88 and 125 K are the v a l u e s o f T.| f o r the two r e s o l v e d r e l a x a t i o n mechanisms. The r e s u l t a n t T-j o b t a i n e d by recombining the r e s o l v e d values agrees very w e l l w i t h the observed T^. A l e a s t squares d e t e r m i n a t i o n o f the s l o p e o f the best s t r a i g h t l i n e f o r the InT-j p o i n t s p l o t t e d a g a i n s t T"^ between 77 and 88 K g ives an a c t i v a t i o n energy o f 0.7 ± 0.1 kca l/mole f o r r e o r i e n t a t i o n o f the methyl groups a t tached t o a luminium. T h i s va lue i s s m a l l e r than t h a t r e p o r t e d f o r methyl groups a t t a c h e d to s i l i c o n , 1.56 ± 0 . 0 8 kcal/mole [ 4 . 1 8 ] , and i s e s s e n t i a l l y the same as the v a l u e , u n c o r r e c t e d f o r any temperature dependence o f the p r e - e x p o n e n t i a l f a c t o r i n T , of 653± 29 cal/mole g iven by Smith [ 4 . 9 ] f o r tetramethylgermane, i n which -59-the C-Ge bond l e n g t h - 1 . 9 9 % i s c l o s e to the C-A£ bond l e n g t h i n t r i m e t h y l -aluminium 1 4 . 5 ] . The minimum i n T^ a t 183 K i s due to r e o r i e n t a t i o n about t h e i r C 3 axes o f methyl groups a t t a c h e d t o the n i t r o g e n atom. Us ing a va lue o f 36 ms, we o b t a i n e d aj Q T c f o r each T^. A p l o t o f those v a l u e s o f co 0 x c a g a i n s t T~^ i s shown i n l i n e a i n the F i g u r e 4 . 6 , and from the l e a s t squares f i t o f t h i s 1 i ne l n V c = t " 9 - 0 6 ± 0.17) + (3.10 ± 0.06) x 1 0 + 3 / R T ( 4 . 8 ) the a c t i v a t i o n energy f o r the r e o r i e n t a t i o n o f the methyl groups a t tached t o n i t r o g e n i s found t o be 3.1 ± 0.1 k c a l / m o l e . S p i n - l a t t i c e r e l a x a t i o n between 210 and 290 K i s b e l i e v e d to be a r e s u l t of two p r i n c i p a l mechanisms, namely, r e o r i e n t a t i o n o f the methyl groups on n i t r o g e n and r e o r i e n t a t i o n of the whole molecule about i t s N-A& a x i s . ' T h e observed r e l a x a t i o n r a t e , rT\ , can be expressed as the sum o f the r e l a x a t i o n u l ' o b s , r a t e due to r e o r i e n t a t i o n o f methyl groups at tached to n i t r o g e n atom, (T-|)^_Q^ > and the r e l a x a t i o n r a t e due t o the r e o r i e n t a t i o n o f the whole molecule Values o f ( T - ] ) ^ . ^ w e r e o t ) t a i n e d f o r the s e v e r a l temperatures c o r r e s p o n d i n g to experimental p o i n t s from Equat ion ( 4 . 8 ) and ( 4 . 2 ) and the va lue ( T - j ) m i -36 ms. Values of O y ) m o i were then c a l c u l a t e d f o r those temperatures by , 1 1 1 1 1 1 8.0 T.O 6.0 5D 4.0 3.0 1 0 0 0 / T ° K F i g . 4 . 6 . P l o t of U ) O T c versus r e c i p r o c a l of temperature o f t r i m e t h y l a m i n e - t r i m e t h y l a l u m i n i u m (a) f o r r o t a t i o n o f the methyl groups attached to n i t r o g e n , (b) f o r r e o r - j e n t a t i o n o f the whole-molecule about the , N - A t bond . . .. , . . . - 6 1 -Equat ion (.4.9). These va lues o f CT-j)m 0-| are p l o t t e d as open c i r c l e s and connected w i t h a broken l i n e i n F i g u r e 4 . 5 . T h e minimum o f 49 ms f o r CT-| ) m o -j can then be used to o b t a i n a p l o t of co T a g a i n s t T " \ where T i s now the r 0 c c c o r r e l a t i o n time f o r r e o r i e n t a t i o n about the N-A^ a x i s . This p l o t i s shown i n l i n e b i n the F i g u r e 4 . 6 , and from the l e a s t squares f i t l n w 0 T C = C-10.20 ± 0.34) + (5 .42 ± 0.18) x 10" 3 /RT we o b t a i n an a c t i v a t i o n energy o f 5 .4 ± 0 .2 kca l/mole f o r r e o r i e n t a t i o n o f the whole molecule about i t s N-A£ a x i s . The a s s i g n e d r e l a x a t i o n mechanisms i n phase I I were checked w i t h the second moment and l i n e w i d t h data and they agree very w e l l . Phase I I The sudden change i n T-j at 290 K i n d i c a t e s t h a t here t h e r e i s a phase t r a n s i t i o n which a l l o w s a sudden change i n the c o r r e l a t i o n f r e q u e n c i e s o f the r e l a x a t i o n p r o c e s s e s . L i n e b i n F i g u r e 4 .6 shows t h a t on the low temperature s i d e o f the t r a n s i t i o n oo0xc i s a p p r o x i m a t e l y equal t o 0.4 f o r r e o r i e n t a t i o n o f the whole m o l e c u l e . S i n c e V q i s 30 MHz, we f i n d t h a t the c o r r e l a t i o n frequency j u s t below the t r a n s i t i o n temperature i s about 75 MHz f o r t h a t p r o c e s s . T h i s i s much l a r g e r than the mot ional frequency which would a f f e c t the l i n e w i d t h and second moment. Consequently no change appears i n these parameters a t the t r a n s i t i o n between phase II and I I I . Al though the InT^ a g a i n s t T"^ p o i n t s between 290 and 313 K can be f i t t e d by a s t r a i g h t l i n e whose s l o p e corresponds to an a c t i v a t i o n energy o f 3.9 ± 0 . 4 k c a l / m o l e , i t i s probably i n c o r r e c t t o a s s i g n - 6 2 -t h i s t o the r e o r i e n t a t i o n o f the whole molecule i n s o l i d phase I I . The va lue o f 310 ms f o r ( T ^ ^ L , a t 290 K, w h i l e CTj} b i s 900 ms a t 291 K, shows t h a t 3 t h e r e must be a sudden i n c r e a s e i n c o r r e l a t i o n frequency f o r N-methyl group r o t a t i o n as w e l l as f o r the r o t a t i o n o f the whole m o l e c u l e . The r e l a t i v e c o n t r i b u t i o n o f the two processes i s unknown i n the range 290 to 313 K. The f a c t t h a t t h e r e i s a d i s c o n t i n u o u s change i n c o r r e l a t i o n frequency f o r N-methyl group r o t a t i o n at the phase t r a n s i t i o n emphasizes t h a t the r e o r i e n t a t i o n : process must be at l e a s t p a r t l y c o n t r o l l e d by i n t e r m o l e c u l a r i n t e r a c t i o n s . Phase I There i s a sudden jump i n T^ a t 313 K. T h i s corresponds t o the r a p i d change i n l i n e w i d t h and second moment which was observed a t t h i s t e m p e r a t u r e , and,we c o n s i d e r t h a t a t r a n s i t i o n between two s o l i d phases occurs h e r e , and t h a t 1 i n the h i g h e r temperature phase I d i f f u s i o n a l jumps occur w i t h s u f f i c i e n t frequency to decrease the l i n e w i d t h and second moment to very smal l v a l u e s . At h i g h e r temperatures i n phase I the r a t e o f d i f f u s i o n a l jumping has i n c r e a s e d t o the p o i n t where, above about 350 K, i t causes T^ to decrease once aga in u n t i l the m e l t i n g p o i n t i s reached. I t i s not known what c o n t r i b u t i o n N-methyl group r e o r i e n t a t i o n makes to the observed T^ i n phase I . I f we assume i t t o be n e g l i g i b l e and' c o n s i d e r o n l y whole molecule r o t a t i o n and d i f f u s i o n as the e f f e c t i v e r e l a x a t i o n mechanisms, we can r e s o l v e the InT^ a g a i n s t T""' curve i n the range 313 to 375 K i n t o a s t r a i g h t l i n e o f 1 n(T-| ^ Q - J a g a i n s t T - 1 ( w i t h i n c r e a s i n g T-j f o r i n c r e a s i n g T) f o r the c o n t r i b u t i o n o f the r o t a t i o n o f the whole molecule about i t s N-A£ a x i s to the observed s p i n - l a t t i c e r e l a x a t i o n , and a second s t r a i g h t l i n e o f l n ( T , ) . . . a g a i n s t T " 1 ( w i t h d e c r e a s i n g T, f o r i n c r e a s i n g T) f o r the c o n t r i b u t i o n -63-o f d i f f u s i o n a l motion t o the r e l a x a t i o n , t h e observed be ing assumed t o be o f the form The s lopes o f these l i n e s , which are shown i n F i g u r e 4 . 5 , correspond t o a c t i v a t i o n energies o f 4 .7 ± .2 kcal/mole f o r m o l e c u l a r r o t a t i o n and 19.5 ± .2 kca l/mole f o r s e l f - d i f f u s i o n . The l a t t e r agrees very w e l l w i t h the a c t i v a t e d energy o f s e l f -d i f f u s i o n f o r hexamethylethane, which Chezeau et a l [4.10] found from l i n e w i d t h , T.| and T-jp s t u d i e s . E_. T r i m e t h y l p h o s p h i n e - t r i m e t h y l a l u m i n i u m E . l L i n e Widths and Second Moments The experimental second moment and l i n e w i d t h are p l o t t e d vs temperature 2 i n F i g u r e 4 . 7 . The second moment has a value of 10.0 + 1.0 G at 65 K. I t de-2 creases s l o w l y to a p l a t e a u value o f 4 . 5 ± 0 . 5 G a t 132 K, and aga in decreases 2 s l o w l y above 180 K to another p l a t e a u va lue o f 1.75 ± 0 .2 G a t about 240 K. The shape of the l i n e w i d t h vs temperature curve i s s i m i l a r to t h a t o f the second moment vs temperature . E .2 C a l c u l a t i o n o f Second Moment The m o l e c u l a r parameters and c r y s t a l s t r u c t u r e o f t r i m e t h y l p h o s p h i n e -t r i m e t h y l aluminium are a l l unknown. The t h e o r e t i c a l second moment h a s , however, been c a l c u l a t e d by the methods d e s c r i b e d e a r l i e r i n t h i s c h a p t e r , and i t s values are l i s t e d i n Table 4 .3 f o r r i g i d c o n d i t i o n s and v a r i o u s types o f m o l e c u l a r 60 100 140 180 220 260 3 ° 0 340 T E M P E R A T U R E (°KJ F i g . 4 . 7 . Temperature dependence o f l i n e width and second moment o f t r i m e t h y l p h o s p h i n e -t r i m e t h y l a luminium. - 6 5 . TABLE 4 . 3 T h e o r e t i c a l second moments f o r t r i m e t h y l p h o s p h i n e - t r i m e t h y l -aluminium ( i n G^) and comparison w i t h experimental values Group Motion T h e o r e t i c a l Second Moment C o n t r i b u t i o n Experimental Temperature M p Mo Ao I n t r a I n t e r CFL Proton t o I n t e r - T o t a l Second Moment T°K Me 3P M.3A£ ^ _ ^ 3 _ p a n d ^ m o l e c u l a r m o l e c u l a r SS SS 21 .3 1.2 0.2 7 ± 1 2 9 . 8 + 1 -RS SS 1 13.2 1.1 0.1 4 . 5 + 0 . 8 18.9 + 0.8 _ SS RS J RS RS 5.3 1.0 0.1 2.4 + 0 . 8 8.8 + 0 . 8 10.0 + 1 66 - 77 RR RS ' 2.9 0 .6 0 1.7 + 0 . 8 5.2 + 0 . 8 4.5 + 0.5 132 - 180 RS RR J RR RR 0.6 0 . 3 0 1.2 + 0 . 3 2.1 + 0.3 1.8 + 0 . 2 240 - m.p SS RS RR = Methyl groups and the moiety are both s t a t i o n a r y = The methyl groups are r o t a t i n g but the moiety i s s t a t i o n a r y = Methyl groups and moiety are r o t a t i n g - 6 6 -mot ion . For c a l c u l a t i o n o f seconcj moments, the f o l l o w i n g bond d i s t a n c e s have been t a k e n . r(C-H) = 1.10 ft^CC-p) <= 1.84 ft [ 4 . 1 9 , 4 . 2 0 , 4 . 2 1 ] , r(C-A£) = 2.0 ft J 4 . 5 ] , r(p-A£) = 2.30 ft.* Table 4 . 3 shows t h a t even a t the lowest temperature a t t a i n e d , t r i m e t h y l -p h o s p h i n e - t r i m e t h y l a l u m i n i u m i s not r i g i d , nor does i t behave s i m i l a r l y to t r i m e t h y l a m i n e - t r i m e t h y l b o r a n e and t r i m e t h y l a m i n e - t r i m e t h y l a l u m i n i u m , i n which the methyl groups i n one of the m o i e t i e s a r e e f f e c t i v e l y r i g i d a t 77 K. The second moment o b t a i n e d at 65 K corresponds t o a l l methyl groups r o t a t i n g . This i s expected s i n c e r ( C - P ) > r ( C - B ) > r ( C - N ) . The second moment above 240 K agrees very w e l l w i t h the v a l u e es t imated on the assumption t h a t a l l methyl groups are r o t a t i n g about t h e i r t h r e e f o l d axes and the whole m o l e c u l e i s ' r o t a t i n g about the P-A& bond. The p l a t e a u va lue between 132 and 180 K agrees q u i t e w e l l w i t h the c a l c u l a t e d va lue on the assumption t h a t a l l methyl groups as w e l l as one o f the m o i e t i e s are r o t a t i n g w h i l e the o t h e r moiety i s f i x e d . One cannot determine which moiety i s r o t a t i n g i n t h i s temperature r e g i o n from o n l y the r e s u l t s o b t a i n e d f o r t r i m e t h y l p h o s p h i n e - t r i m e t h y l a l u m i n i u m . The best, way to s o l v e t h i s problem would be to study a compound such as ( C D 3 ) 3 P - A & ( C H 3 ) 3 o r ( C H 3 ) 3 P - A * i C D 3 ) 3 . Another p o s s i b i l i t y i s t o c o n s i d e r the r e s u l t s f o r Me2PH-A£Me3 and Me2NH-A£Me3. The second moments o f Me2NH-A£Me3 (see Chapter VI) suggest t h a t the r o t a t i o n o f the t r i m e t h y l a l u m i n i u m moiety s t a r t s a t about 240 K. Thus i n the temperature r e g i o n o f 132 - 180 K, the moiety which r o t a t e s may p o s s i b l y be t r i m e t h y l p h o s p h i n e . , * 0 b t a i n e d from K C - P ) , KC-A£) and K C - C ) - 6 7 -E . 3 S p i n - l a t t i c e R e l a x a t i o n Time F i g u r e 4 . 8 shows the v a r i a t i o n o f exper imenta l T^ w i t h i n v e r s e o f temperature. I t shows m u l t i p l e minima, and at low temperature the T^ curve i s n e a r l y f l a t . The a n a l y s i s o f the T-| data i s s t r a i g h t f o r w a r d . We a t t r i b u t e the T-j minimum at about 290 K t o r e o r i e n t a t i o n o f the t r i m e t h y l a luminium m o i e t y , and the T^ minimum at about 157 K to r o t a t i o n o f t r i m e t h y l p h o s p h i n e . I f we assume a T^  minimum due to some r e l a x a t i o n mechanism occurs w e l l below l i q u i d n i t r o g e n temperature , the T^ r e s u l t s can be r e s o l v e d i n t o t h r e e p a r t s as shown by the broken l i n e s . The r e s u l t a n t T^ from t h i s r e s o l u t i o n i s w i t h i n 15%, o f the experimental T^ v a l u e s . Thus t h e r e are t h r e e r e l a x a t i o n mechanisms which c o n t r i b u t e d to the observed s p i n - l a t t i c e r e l a x a t i o n r a t e i n the temperature i range of 77 - 157 K. One of them must be the r o t a t i o n o f the t r i m e t h y l p h o s p h i n e moiety . The prev ious two s t u d i e s have shown t h a t methyl groups a t t a c h e d to d i f f e r e n t k inds o f c e n t r a l atoms have d i f f e r e n t c o r r e l a t i o n t i m e s . In t r i m e t h y l -p h o s p h i n e - t r i m e t h y l a l u m i n i u m , s i n c e r(C-A«,) > r ( C - P ) , the methyl groups a t t a c h e d to aluminium are expected t o r o t a t e p r i o r to the r o t a t i o n o f methyl groups a t tached to phosphorus. We thus a s s i g n the T^ minimum at about 112 K from the r e s o l v e d curve to the r o t a t i o n o f methyl groups a t tached to phosphorus and i n the range 77 to 120 K, the i n c r e a s e o f T-j w i t h i n c r e a s i n g temperature t o the r o t a t i o n o f methyl groups a t tached t o a luminium. The r e s u l t s are summarized i n Table 4 . 4 . , I I I I 1 I 1 1 1 1 12 10 8 6 4 1 0 0 0 / T ° K F i g . 4 . 8 . The s p i n - l a t t i c e r e l a x a t i o n time o f t r i m e t h y l p h o s p h i n e - t r i m e t h y l a l u m i n i u m as a f u n c t i o n o f r e c i p r o c a l of temperature . The broken curves i n d i c a t e the r e s o l u t i o n of observed T, i n t o more than one mechanism. 1 - 6 9 -TABLE 4 . 4 Energy and Rate Parameters f o r T r i m e t h y l p h o s p h o n e - t r i m e t h y l a l u m i n i u r r i E 0 Type o f motion A (kca l/mole) T c (sec) R o t a t i o n o f Me^AJl moiety 9.95 + 0.19 1.03 x I O " 1 6 R o t a t i o n o f Me 3P moiety 3 .28 + 0.06 7.63 x I O " 1 4 R o t a t i o n o f methyl groups at Me 3 P 1.15 + 0.1 1.86 x I O " 1 ' R o t a t i o n o f methyl groups at Me3AA 0.75 + 0.1 -We have checked the c o r r e l a t i o n t imes f o r the r o t a t i o n s o f the t r i m e t h y l -aluminium and t r i m e t h y l p h o s p h i n e m o i e t i e s u s i n g the T^ data at t h e i r l i n e width and second moment t r a n s i t i o n temperatures . The c o r r e l a t i o n times o b t a i n e d a t these temperatures from the T-j data show they agree w i t h the c o r r e l a t i o n times o f narrowing the l i n e widths and second moments. T h i s confirms t h a t the assignment i s c o r r e c t f o r the r e l a x a t i o n mechanisms i n the t r i m e t h y l p h o s p h i n e - t r i m e t h y l a l u m i n i u n complex i n the temperature range o f 157, K to i t s m e l t i n g p o i n t . Fj T r i m e t h y l p h o s p h i n e - t r i m e t h y l borane F . l Exper imental L i n e Width and Second Moment The l i n e widths and second moments are p l o t t e d as f u n c t i o n s o f temp-e r a t u r e i n F i g u r e 4 . 9 . Below 100 K the second moment i n c r e a s e s s l o w l y as the 2 temperature decreases . I t has a va lue of about 9 . 8 ± 0.5 G i n the temperature I , T 1 T 1 1 1 ' ' 1 1 ' 1 « 100 180 260 340 420 T E M P E R A T U R E °K F i g . 4 . 9 . Temperature "dependence o f T i n e width and second moment of t r i m e t h y l p h o s p h i n e - t r i m e t h y l borane. -71-range 100 - 125 K. I t decreases, s l o w l y as the temperature i s i n c r e a s e d and then reaches a p l a t e a u v a l u e o f 2.3 ± 0.4 G 2 a t about 200 K. A t 324 K, t h e r e i s a sudden change i n l i n e width and second moment and above t h i s temperature the l i n e w i d t h i s the same as the l i n e w i d t h o f doped w a t e r . The shape o f l i n e w i d t h versus temperature curve i s s i m i l a r to t h a t o f second moment versus temperature. F. 2 C a l c u l a t i o n o f Second Moment and D i s c u s s i o n o f M o l e c u l a r M o t i o n C a l c u l a t i o n o f the t h e o r e t i c a l second moment has been made i n the same way b e f o r e , and w i t h the assumption t h a t r ( C - H ) = 1.10 ft, r ( C - P ) = 1.84 % [4 .19 , 4 . 2 0 , 4 . 2 1 ] , r(c-B) = 1.56 8 [ 4 . 5 , 4 . 6 ] , r ( P - B ) = 1.83 fl.* The r e s u l t s are shown i n Table 4 . 5 . Table 4 . 5 shows t h a t even at the lowest temperature a t t a i n e d , the r i g i d second moment has not been reached. The experimental second moment i n the range 100 - 125 K agrees q u i t e w e l l w i t h the va lue c a l c u l a t e d on the assumption t h a t a l l methyl groups are r o t a t i n g . The second moment between 200 - 324 K agrees very w e l l w i t h the c a l c u l a t e d va lue assuming t h a t a l l methyl groups as w e l l as the whole molecule i s r o t a t i n g about i t s P-B bond. The second moment above 324 K i s b e l i e v e d to be determined by the s e l f - d i f f u s i o n mechanism i n the s o l i d s t a t e . The i n c r e a s e of second moment w i t h d e c r e a s i n g temperature below 100 K i s almost c e r t a i n l y due to the decrease i n r o t a t i o n a l frequency o f the methyl groups. Obtained from r ( C - P ) , r ( C - B ) , r ( C - C ) -72-TABLE 4 . 5 T h e o r e t i c a l second moment ( i n G^) f o r t r i m e t h y l p h o s p h i n e -t r i m e t h y l b o r a n e and comparison w i t h experimental values Group Motion T h e o r e t i c a l Second Moment C o n t r i b u t i o n Me 3P Me 3B I n t r a ChL I n t e r C H 3 but i n t r a -m o l e c u l a r Proton to P and B I n t e r -m o l e c u l a r T o t a l Experimental Second Moment Temperature T°K SS SS 21 .3 2.9 0 .5 7 ± 1 31 .8 + 1 - -RS SS SS ' RS J 13.2 2.4 0 .5 4 .5 + 0.8 30.6 + 0.8 - -RS RS 5.3 2.4 0 .5 2.4 + 0.8 10.6 + 0 . 8 9.8 ± 0 . 5 100 - 125 RR RR 0.6 0.6 0 . 2 1.2 + 0.3 2.6 + 0.3 2.3 ± 0 .4 200 - 324 S e l f - 0 0 0 0 0 0.1 324 - m.p D i f f u s i o n SS RS RR = Methyl groups and the moiety are both s t a t i o n a r y = The methyl groups are r o t a t i n g but the moiety i s s t a t i o n a r y = Methyl groups and moiety are r o t a t i n g - 7 3 -F . 3 S p i n - l a t t i c e R e l a x a t i o n Times F i g u r e 4.10 i s a p l o t o f T^  versus the i n v e r s e o f temperature . There i s a sudden jump o f T^ at 310 K and 324 K. The change i n T-j a t 324 K i s not as g r e a t as the change at 310 K. However, t h e r e i s a sudden change i n t ime constant o f the FID curve which i n d i c a t e s t h e r e i s a sudden change i n l i n e width or T 2 a t t h i s temperature . There are two minima i n the T^ curve below 310 K. The s o l i d down to 324 K i s ass igned as phase I , between 324 and 310 K as phase I I , and below 310 K as phase I I I . We w i l l analyse the T-j data i n d i f f e r e n t phases. Phase I I I The s p i n - l a t t i c e r e l a x a t i o n r a t e between 200 and 290 K i s a f f e c t e d by the r e l a x a t i o n mechanism at h igh temperature and by the r e l a x a t i o n mechanism at low temperature. The two c o n t r i b u t i o n s were r e s o l v e d as shown by the broken l i n e s i n F i g u r e 4 . 1 0 . From the r e s o l v e d T-j, and the T^ data above 250 K as w e l l as the T, minimum at 250 K, oo x can be o b t a i n e d f o r each 1 o c temperature a t which a T^ value has been found,and a l e a s t squares f i t g i v e s Thus the a c t i v a t i o n energy f o r the r e l a x a t i o n mechanism i n t h i s temperature range i s found to be 8.00 ± 0.08 k c a l / m o l e . A n a l y s i s o f the second moments has suggested t h a t t h i s r e l a x a t i o n mechanism be ass igned to the r o t a t i o n o f the whole molecule about i t s P-B bond. Decrease i n n . m . r . l i n e width o r second moment due to the r o t a t i o n o f the whole molecule about i t s P-B bond should T P M . P 1 0 0 0 / T ° K i i F i g . 4 .10. S p i n - l a t t i c e r e l a x a t i o n time o f t r i m e t h y l p h o s p h i n e - t r i m e t h y l b o r a n e as a f u n c t i o n o f i n v e r s e temperature . The broken l i n e s show the r e s o l u t i o n o f observed T-j a t about 250 K. The open c i r c l e s . s n o w the r e s o l u t i o n o f observed T-j a t each p o i n t i n t o more than one mechanism. -75-occur i n a c o r r e l a t i o n t ime range near x c = (yfivf^) o r (Y<$H) where Mg 2 and 6H are the same as d e f i n e d b e f o r e , f i , = 6 G Csee F i g u r e 4.9} g ives 3 3 ^o T c ~ ^ a n d ^ = 5 , 5 ^ g i v e s w 0 T c 10 . Values o f o^x o b t a i n e d from the r e l a x a t i o n data i n the temperature range of 140 - 170 K are o f the o r d e r o f 5 3 10 to 10 . This i n d i c a t e s t h a t the assignment o f the r e l a x a t i o n mechanism i n the temperature range o f 200 to 310 K i s c o r r e c t and the r e l a x a t i o n mechanism i s the r o t a t i o n o f the whole molecule about i t s P-B bond. The T-j minimum at lower temperature i s very broad and the T^ curve cannot be d e s c r i b e d by a BPP e q u a t i o n w i t h a s i n g l e c o r r e l a t i o n t i m e . However, a good f i t can be obta ined i f we assume t h e r e are two c o r e l a t i o n t i m e s . a n d the r e l a x a t i o n processes can be d e s c r i b e d by two BPP e q u a t i o n s . The s o l i d p o i n t s on the curve are the exper imenta l p o i n t s , the open p o i n t s are the r e s o l v e d T-j p o i n t s and the s o l i d l i n e i s the r e s u l t a n t T^  c a l c u l a t e d from the two separate mechanisms. The c a l c u l a t e d va lues agree q u i t e w e l l w i t h the exper imental d a t a . The r e s o l v e d curve f o r which the T-j minimum occurs a t 104 K has a (T-| ) m 1 - n = 52 ms and an a c t i v a t i o n energy o f 1.46 k c a l / m o l e . The o t h e r r e s o l v e d curve which the T n minimum occurs a t 124 K has (T,} . = 1 1 mm 53 ms and an a c t i v a t i o n energy o f 2.14 k c a l / m o l e . The va lues o f (T.|) - n suggest t h a t the two r e l a x a t i o n mechanisms are the same but d i f f e r i n ; a c t i v a t i o n energy o n l y . The previous s t u d i e s have shown t h a t methyl groups a t tached to d i f f e r e n t c e n t r a l atoms have d i f f e r e n t r o t a t i o n a l c o r r e l a t i o n t i m e s . In t r i m e t h y l p h o s p h i n e -t r i m e t h y l b o r a n e , the methyl groups a t t a c h e d to phosphorus and the methyl groups a t tached to boron exper ience d i f f e r e n t environments . I f these -76-environments do not d i f f e r too much, the c o r r e l a t i o n times f o r r o t a t i o n o f the methyl groups w i l l not d i f f e r s i g n i f i c a n t l y . There fore both c o r r e l a t i o n times make a c o n t r i b u t i o n to the s p i n - l a t t i c e r e l a x a t i o n r a t e and a broad minimum i n T-j was o b t a i n e d . S i n c e the C-P bond l e n g t h i s g r e a t e r than the C-B bond l e n g t h , the a c t i v a t i o n energy o f 1,47 kca l/mole can probably be ass igned to the r o t a t i o n o f methyl groups a t t a c h e d to phosphorus and 2.14 kcal/mole can be ass igned to the r o t a t i o n o f methyl groups a t tached t o b o r o n . This assignment o f a c t i v a t i o n energ ies i s a l s o supported by the f a c t t h a t values o f a c t i v a t i o n energy f o r the r e o r i e n t a t i o n o f methyl groups a t t a c h e d to phosphorus i n t r i m e t h y l p h o s p h i n e - t r i m e t h y l a l u m i n i u m (1 .2 kcal/mole) and to boron i n t r i m e t h y l a m i n e - t r i m e t h y l b o r a n e (1.9 kca l/mole) are q u i t e c l o s e to the a c t i v a t i o n energ ies a s s i g n e d . Phase II Although an a c t i v a t i o n energy o f 1.00 + 0.45 kcal/mole was o b t a i n e d from the t h r e e experimental p o i n t s between 310 and 324 K, i t i s dangerous to a s s i g n t h i s a c t i v a t i o n energy to the r e o r i e n t a t i o n o f the whole molecule a long i t s P-B bond. The r e l a x a t i o n r a t e i n t h i s phase may be the r e s u l t o f two o r more mechanisms, namely, the r o t a t i o n o f the whole molecule about i t s P-B bond, the r o t a t i o n o f methyl groups, and o t h e r mechanisms, which may i n v o l v e i s o t r o p i c r o t a t i o n o f the whole m o l e c u l e . Phase I The s p i n - l a t t i c e r e l a x a t i o n time i n c r e a s e s w i t h the i n c r e a s i n g o f temperature i n the temperature range o f 324 - 358 K. The a c t i v a t i o n energy o b t a i n e d from the s l o p e o f the l e a s t squares f i t t e d s t r a i g h t l i n e i s 2.84 ± -77-0.24 k c a l / m o l e . Above 358 K, the s p i n - l a t t i c e r e l a x a t i o n t ime decreases w i t h i n c r e a s i n g temperature u n t i l i t reaches the m e l t i n g p o i n t . The a c t i v a t i o n energy o b t a i n e d from the s l o p e i s 4 .3 ± 0.6 k c a l / m o l e . No attempt was made t o r e s o l v e the T^ data s i n c e , i n phase I , t h e r e i s no assurance t h a t t h e r e are o n l y two r e l a x a t i o n mechanisms i n v o l v e d . In a d d i t i o n , the r a n g e ' o f T*"^  i s so smal l i n phase I t h a t we do not know which i s the predominant mechanism. The sample melts s h a r p l y at 391 K. The m e l t i n g p o i n t c i t e d i n the l i t e r a t u r e was 391 - 394 K. The a c t i v a t i o n energy o f 4 . 3 ± 0.6 kca l/mole might be ass igned to the s e l f - d i f f u s i o n process o f t r i m e t h y l p h o s p h i n e - t r i m e t h y l -borane. This v a l u e , however, i s extremely low when compared w i t h the a c t i v a t i o n energy f o r the s e l f - d i f f u s i o n process o f other compounds s t u d i e d [ 4 . 1 0 , 4 . 1 5 , 4 . 2 0 J . The va lue i s somewhat doubtful because we do not know the c o n t r i b u t i o n to the r e l a x a t i o n r a t e from o t h e r mechanisms. The a c t i v a t i o n energy 2.84 ± 0.24 kcal/mole i n the range o f 324 - 358 K i s not a s s i g n e d . Table 4 .6 g i v e s a summary of energy and r a t e parameters f o r t r i m e t h y l -p h o s p h i n e - t r i m e t h y l b o r a n e i n the temperature range s t u d i e d . - 7 8 -TABLE 4 . 6 Energy and Rate Parameters f o r T r i m e t h y l p h o s p h i n e - t r i m e t h y l b o r a n e Type o f Motion E^Ckeal/mole) T c ° ( s e c ] Temperature R o t a t i o n o f methyl groups a t Me 3P R o t a t i o n o f methyl groups a t Me 3B R o t a t i o n o f the whole molecule ? ? S e l f - d i f f u s i o n 1.47 2.14 8 .00 ± 0 . 0 8 1.00 ± 0.45 2.84 ± 0.24 4 .3 ± 0.6 2.65 x 10 5.45 x 10 9.87 x 10' -12 •13 •16 77 - 200 77 - 200 200 - 310 310 - 324 324 - 358 358 - m.p. - 7 9 -References [4.1] F . G . A . S t o n e , Chem. R e v . , 58 (1958)101 [4 .2] N . Davidson and H . C . Brown, J . A . C . S . , 64 (1942)-316 [4 .3] S. S u j i s h i , P h . D . 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Abragam, P r i n c i p l e s o f N u c l e a r Magnetism, Oxford U n i v . P r e s s , 1961 [4.15] . T . Y u k i t o s h i , H. Suga, S . S e k i and J , I t o h , J . Phys. Soc. J a p a n , 12 (1957) 506 -80-14.16] R. Kubo and K. T o m i t a , J . Phys. Soc. J a p a n , 9_ 0 9 5 4 ] 888 [4.17] N. Bloerabergen, E . M . P u r c e l l and R.V. Pound, Phys. R e v . , 73 0 9 4 8 ) 679 [4.18] D . E . O ' R e i l l y and T. Tsang , Phys. R e v . , 157. 0 967 ) 417 [4.19] J . E . Anderson and W.P. S l i c h t e r , J . Phys. Chem.,69 (1965) 3099 [4.20] S. A l b e r t , H . S . Gutowsky and J . A . R i p m e e s t e r , J . Chem. P h y s . , 56 0 9 7 2 ) 1332 [4.21] H.D. S p r i n g a l l and L . O . Brockway, J . A . C . S . , 60_ 0 9 3 8 ) 996 [4.22] L . S . B a r t e l l and L . O . Brockway, J . Chem. P h y s . , 32 0 9 6 0 ) 512 [4.23] D.R. L i d e , J r . , and D . E . Mann, J . Chem. P h y s . , 29 (.1958) 914 [4.24] D.R. L i d e , J r . , R.W. T a f t , J r . , and P. Love , J . 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Jhe m o l e c u l a r s t r u c t u r e o f t r i m e t h y l p h o s p h i n e has been s t u d i e d by e l e c t r o n d i f f r a c t i o n [ 5 . 1 , 5 . 2 ] and microwave s p e c t r o -scopy [ 5 . 3 ] , and the r o t a t i o n b a r r i e r f o r the methyl groups was o b t a i n e d i n the gaseous phase from these s t u d i e s . The m o l e c u l a r s t r u c t u r e o f t r i m e t h y l -borane has been s t u d i e d by e l e c t r o n d i f f r a c t i o n [ 5 . 4 ] , but no energy o r r a t e parameters were o b t a i n e d f o r t h i s compound. I t i s our purpose t o study the a c t i v a t i o n energy and c o r r e l a t i o n time o f the methyl group r o t a t i o n and other p o s s i b l e m o l e c u l a r motions i n these two compounds i n the s o l i d s t a t e . B_. Exper imental B . l M a t e r i a l s T r i m e t h y l p h o s p h i n e was o b t a i n e d from P f a l t z and Bauer , I n c . , and was d i r e c t l y t r a n s f e r r e d i n a dry box to a 10 mm O.D. sample tube f o r b r o a d l i n e work and to a 7.5 - 8.0 mm t h i n w a l l sample tube f o r pulsed nmr measurement. The d i s s o l v e d oxygen was pumped o f f by the freeze-pump-thaw method. T r i -methylborane was purchased from A l f a I n o r g a n i c s and was trapped i n the sample tubes a t l i q u i d n i t r o g e n temperature w i t h the a i d o f a vacuum l i n e . Samples were s e a l e d i n the sample tube immediately a f t e r being trapped.; - 8 2 -B. 2 Measuring Procedures These were the same as d e s c r i b e d i n Chapter I I I . T^ va lues f o r t r i m e t h y l -phosphine were o b t a i n e d by u s i n g a 180° - T - 90° p u l s e sequence w i t h a 180° p u l s e l e n g t h o f 2-3 y s e c . The same method was used t o o b t a i n T^ values f o r t r i m e t h y l b o r a n e when these were s h o r t e r than 5 s e c . For T-j values which were longer than 5 s e c , a n90°- T - 90° pulse sequence was used. The T-j values were c a l c u l a t e d from the s l o p e o f a l e a s t squares f i t s t r a i g h t l i n e o f M ° 2 ~ o ^ T ^ versus T . The s tandard d e v i a t i o n o f the s l o p e i s ; l e s s than 5% i n a l l cases . C. T r i m e t h y l p h o s p h i n e C. l Exper imental L i n e Widths and Second Moments The exper imental second moments and l i n e widths o f t r i m e t h y l p h o s p h i n e are p l o t t e d versus temperature i n F i g u r e 5 . 1 . The second moment has a va lue o f 29.0 ± 1 G 2 a t 65 K. I t decreases t o a p l a t e a u va lue o f 9 .5 ± 0 .5 G 2 , a t 2 105 K. At about 155 K the second moment decreases again from 8.5 G to a 2 p l a t e a u v a l u e o f 2.2 ± 0.4 G at about 175 K. Superimposed s o l i d and l i q u i d l i n e s appear between 186 and 189 K. Above 189 K no s o l i d s i g n a l was o b s e r v e d . The m e l t i n g c i t e d i n CRC handbook i s 187.8 - 188.8 K. This agreed q u i t e w e l l w i t h our o b s e r v a t i o n . The shape o f the l i n e w i d t h versus temperature curve i s s i m i l a r to t h a t o f the second moment versus temperature c u r v e . C.2 C a l c u l a t i o n of Second Moment and D i s c u s s i o n o f M o l e c u l a r Motion Although the m o l e c u l a r s t r u c t u r e o f t r i m e t h y l p h o s p h i n e has been s t u d i e d by e l e c t r o n d i f f r a c t i o n [ 5 . 1 , 5 .2J and microwave spectroscopy [ 5 . 3 ] , no c r y s t a l s t r u c t u r e study has been made on the s o l i d s t a t e . Thus the c a l c u l a t i o n T E M P E R A T U R E (°K) F i g . 5 .1 . L i n e width and second moment o f t r i m e t h y l p h o s p h i n e as f u n c t i o n o f temperature . - 8 4 -o f the i n t r a m o l e c u l a r second moment i s based on the s t r u c t u r e parameters o b t a i n e d from the microwave s t u d i e s , which agree very w e l l w i t h the e l e c t r o n d i f f r a c t i o n s t u d i e s . For c a l c u l a t i o n o f the i n t r a m o l e c u l a r second moment, the f o l l o w i n g bond lengths and bond angles from the microwave study are used: r(C-H) = 1.09 ft, r ( C - P ) = 1.84 ± 0.003 8, ):HCH = 107.0° + 1 . 0 ° , ):CPC = 9 9 . 1 ° ± 0 . 2 ° . The i n t e r m o l e c u l a r second moment cannot be c a l c u l a t e d w i t h o u t a knowledge o f the c r y s t a l s t r u c t u r e . I t i s , however, e s t i m a t e d t h a t the i n t e r m o l e c u l a r second moment o f t r i m e t h y l p h o s p h i n e would be a p p r o x i m a t e l y the same as the i n t e r m o l e c u l a r second moment o f t r i m e t h y l a m i n e [ 5 . 5 , 5 . 6 ] . Haigh e t a l . [5.5] e s t i m a t e d the i n t e r m o l e c u l a r second moment f o r t r i -2 2 methylamine to be about 2.1 G w h i l e Fyfe [5.6] es t imates i t t o be 4 . 8 G . Both workers may have had s a t u r a t i o n problems w h i l e r e c o r d i n g the spectrum s i n c e a s p i n - l a t t i c e r e l a x a t i o n time study [5.7] shows the T^ at l i q u i d n i t r o g e n temperature i s extremely l o n g . Our e s t i m a t e o f i n t e r m o l e c u l a r second 2 moment f o r t r i m e t h y l p h o s p h i n e i s t h e r e f o r e 3.5 ± .5 G . Table 5.1 shows the r e s u l t s o f the c a l c u l a t i o n and e s t i m a t i o n and t h e i r comparison w i t h the experimental v a l u e s . The observed second moment at 65 K agrees q u i t e w e l l w i t h the c a l c u l a t e d r i g i d l a t t i c e second moment. We a l s o found from our T^ study (see l a t e r ) t h a t the c o r r e l a t i o n frequency o f methyl group r e o r i e n t a t i o n at t h i s temperature i s about 1 KHz, which i s s m a l l e r than the l i n e w i d t h of the r i g i d l a t t i c e spectrum expressed i n f requency. Thus at 65 K, the t r i m e t h y l -phosphine can be regarded as a " r i g i d " m o l e c u l e . The second moments between 105 - 145 K agree very w e l l w i t h the c a l c u l a t e d va lues when a l l methyl groups are r o t a t i n g . The decrease o f second moment above 145 K shows t h a t - 8 5 -TABLE 5.1 Comparison o f t h e o r e t i c a l and exper imenta l second moments o f t r i m e t h y l p h o s p h i n e (second moments i n G^) I n t e r -Kind of motion a c t i o n C H 3 C H 3 -C H 3 Proton to phosphorus I n t e r -m o l e c u l a r T o t a l Experimental Second Moment Temperature T°K SS 24.7 ± 0 .9 1.5 0 . 2 3.5 ± 0.5 29.9 ± 1.4 29.1 ± 1 65 RS 6 . 2 ± 0 . 2 1.3 0 . 2 1.3 ± 0.4 9.0 ± 0.6 9.5 ± 0.5 105 - 145 RR 0 .2 0 . 3 0.1 1.2 ± 0 . 3 1.8 ± 0 . 3 3 .2 ± 0.4 175 - 186 SS = s t a t i o n a r y RS = methyl groups r o t a t i n g w h i l e the molecule i s s t a t i o n a r y . RR = methyl groups as w e l l as the whole molecule are r o t a t i n g about t h e i r Co a x i s - 8 6 -there i s an a d d i t i o n a l motion i n the m o l e c u l e . Comparison o f the e x p e r i m e n t a l second moment and c a l c u l a t e d va lue suggests t h a t the a d d i t i o n a l motion i s the r e o r i e n t a t i o n o f the whole molecule about i t s m o l e c u l a r a x i s . The a c t i v a t i o n energy o f the motion determined from the l i n e w i d t h measurements was 7 .5 ± 2 k c a l / m o l e . The accuracy o f a c t i v a t i o n energy o b t a i n e d from l i n e width measurement i s not good because when the l i n e w i d t h <5H at t r a n s i t i o n temperature approaches the l i n e w i d t h a f t e r t r a n s i t i o n , the u n c e r t a i n t y i n c o r r e l a t i o n times o r f r e q u e n c i e s o b t a i n e d becomes so l a r g e . In a d d i t i o n , the temperature range o f the l i n e w i d t h t r a n s i t i o n i s smal l and hence the range o f c o r r e l a t i o n times o r f r e q u e n c i e s which are o b t a i n e d i s f a i r l y s m a l l . C .3 S p i n - L a t t i c e R e l a x a t i o n Time F i g u r e 5 .2 i s a p l o t o f exper imenta l values o f T^ f o r t r i m e t h y l -phosphine versus the i n v e r s e o f temperature . For a r e l a x a t i o n process c h a r a c t e r i z e d by a s i n g l e c o r r e l a t i o n t i m e -T , the T^ can be expressed by the m o d i f i e d BPP e q u a t i o n [ 5 . 8 , 5 .9 ] 1 c u o T c A 4 V c T co -i . 2 2 i . / i 2 2 1 o L l + w 0 T c 1 + H T c J ( 5 . 1 ) where c i s a constant and c o 0 x c are convent iona l symbols. x £ i s assumed t o have an A r r h e n i u s dependence on an a c t i v a t i o n energy E 3 and on temperature T . a x c = x c ° exp ( E a / R T ) which can be w r i t t e n as V c =Vc° e x P ( E a / R T ) C 5 " 2 ) - 8 7 -1 3 — i — 1 1 9 1 G O O / T ° K i — 5 F i g . 5 . 2 . S p i n - l a t t i c e r e l a x a t i o n time o f t r i m e t h y l p h o s p h i n e as a f u n c t i o n o f i n v e r s e temperature. -88--89-The c o n s t a n t c i n Equat ion (5.1) can be c a l c u l a t e d from the exper imental ( T j ) m i n ando^x, can be o b t a i n e d f o r each p o i n t from E q u a t i o n (5.1). F i g u r e 5.3 i s a p l o t o f OJ QT c versus the i n v e r s e o f temperature. A l e a s t squares f i t o f the s t r a i g h t l i n e gave 1 n V c = t " 7 " 9 5 ± °- 1 7) + (- 2- 0 8 1 °-4) x 1°3/RT The a c t i v a t i o n found f o r t h i s r e l a x a t i o n process i s thus 2.08 ± 0 . 0 4 kca l/mole and i t can be ass igned unambiguously t o the r o t a t i o n of methyl groups i n t r i m e t h y l p h o s p h i n e . The c o r r e l a t i o n time o f the r o t a t i o n o f the whole molecule about i t s m o l e c u l a r a x i s i s too long to a f f e c t T-j below the m e l t i n g p o i n t . Thus i t i s not p o s s i b l e to determine the a c t i v a t i o n energy from T-j measurement. However, we found from the l i n e widths an a c t i v a t i o n energy o f 7.5 + 2 kca l/mole f o r t h i s p r o c e s s . A more p r e c i s e va lue might be o b t a i n e d from T^p measurements, but t h i s i s beyond the c a p a b i l i t y o f our equipment. A microwave study [5 .3] has shown t h a t the r o t a t i o n a l b a r r i e r f o r the methyl groups i s 2.6 ± 0 . 5 k c a l / m o l e . An e l e c t r o n d i f f r a c t i o n study [5 .2] has shown t h a t the b a r r i e r , which depends on the assumed s k e l e t a l ampl i tudes f o r gauche and t r a n s C-H i n t e r a c t i o n s , i s g r e a t e r than 1.5 k c a l / m o l e . Our r e s u l t , which i s 2.08 ± 0.04 k c a l / m o l e , agrees q u i t e w e l l w i t h these s t u d i e s . The agreement w i t h the microwave study suggests t h a t the r o t a t i o n b a r r i e r f o r methyl groups i s predominant ly an i n t r a m o l e c u l a r i n t e r a c t i o n . - 9 0 -D_. T r i methyl borane D.I Exper imenta l Second Moments and L i n e Widths The exper imental second moments and l i n e widths are p l o t t e d as f u n c -t i o n s o f temperature i n F i g u r e 5 . 4 . The second moment has a p l a t e a u va lue o f 2 12.5 ± 0 . 5 G from 65 K to 77 K. I t then decreases to a p l a t e a u va lue of 2 2.5 ± 0 .2 G at about 90 K. The p l a t e a u va lue remains constant up to the m e l t i n g p o i n t o f t h i s compound. D.2 C a l c u l a t i o n o f Second Moment and D i s c u s s i o n o f M o l e c u l a r Mot ion The c r y s t a l s t r u c t u r e o f t r i m e t h y l b o r a n e i s unknown. The i n t r a m o l e c u l a r second moment t h e r e f o r e was c a l c u l a t e d from the s t r u c t u r a l parameters o b t a i n e d from an e l e c t r o n d i f f r a c t i o n study [ 5 . 4 ] . The e l e c t r o n d i f f r a c t i o n study shows t h a t t r i m e t h y l b o r a n e i s a p l a n a r molecule and the bond lengths and bond angles are r ( B - C ) = 1.56 ft, r ( C - H ) = 1.05 ft, £ CBC = 120° . The r ( C - H ) assumed by Le*vy and Brockway seems somewhat s h o r t , and t h e r e f o r e another set o f c a l c u l a t i o n s u s i n g r (C-H) = 1.10 ft was o b t a i n e d f o r comparison. The i n t e r m o l e c u l a r second moment cannot be o b t a i n e d w i t h o u t knowledge o f the c r y s t a l s t r u c t u r e . We thus e s t i m a t e d i t from the known i n t e r m o l e c u l a r second moment o f another p l a n a r m o l e c u l e , hexamethylbenzene, whose i n t e r m o l e c u l a r 2 second moment i s 5.6 G [5 . 11 ] . However, the d e v i a t i o n o f the i n t e r m o l e c u l a r 2 second moment o f t r i m e t h y l b o r a n e from 5.6 G may be q u i t e l a r g e . We t h e r e f o r e 2 adopt a va lue o f 5.6 ± 2G . Smith [5.10] has summarized e s t i m a t s s made i n the l i t e r a t u r e o f r e d u c t i o n f a c t o r s f o r second moment c o n t r i b u t i o n s from i n t e r a c t i o n s between two r o t a t i n g groups. These range from 0.42 to 0 . 2 5 , and we choose a f a c t o r o f 0 .33 :± 0 . 0 9 . Thus a va lue o f 2 .0 ± 0 . 5 G 2 was o b t a i n e d f o r the i n t e r m o l e c u l a r second moment when a l l methyl groups are r o t a t i n g . 14-12-0 w LU O 1 0 -8-6 -O o LU CO 4 -2 -o o LINE WIDTH & SECOND MOMENT °^ _ a o _ 2 o o - — o — o — o - o -60 80 100 -14 -12 -10 - 8 - 6 0 i — i Q U J ,2 120 F i g . 5 . 4 . T E M P E R A T U R E (°K) . L i n e w i d t h and second moment of t r i m e t h y l b o r a n e as f u n c t i o n o f temperature. - 9 2 -TABLE 5.2 Comparison o f t h e o r e t i c a l and experimental second moments of t r i m e t h y l b o r a n e (second moment i n G2) T h e o r e t i c a l Second Moment C o n t r i b u t i o n Type of Motion I n t r a CH, I n t e r C H , Proton to I n t e r - T o t a l Experimental Temperature but i n t r a - B o r o n m o l e c u l a r Second Moment T K m o l e c u l a r SS 29.1 2.4 0.6 5.6 ± 2 38.1 ± 1 RS 7.3 2.1 0 .6 1 . 9 + 1 11.1 ± 1 12.5 ± 0 .5 6 5 - 7 7 I RR 1.8 0 . 5 0 . 2 0.7 ± 0.6 3.2 ± 0.6 2.5 ± 0 .2 90 - m.p. SS 21.3 2.4 0.6 5.6 ± 2 29.9 ± 2 -RS 5.3 2.1 0.6 1 . 9 + 1 9.9 ± 1 12.5 ± 0 .5 6 5 - 7 7 RR 1.3 0 .5 0 .2 0.7 ± 0.6 2.7 ± 0.6 2.5 ± 0 . 2 90 - m.p. SS = Methyl groups and the moiety are both s t a t i o n a r y RS = Methyl groups are r o t a t i n g w h i l e the molecule i s s t a t i o n a r y RR = Methyl groups and moiety are r o t a t i n g A = C a l c u l a t i o n base"on r ( C - H ) = 1.05 % B = C a l c u l a t i o n base on r (C-H) = 1.10 8 - 9 3 -The r e d u c t i o n f a c t o r f o r the i n t e r m o l e c u l a r c o n t r i b u t i o n f o r methyl group r o t a t i o n p lus the r o t a t i o n o f the whole molecule about i t s m o l e c u l a r a x i s , which i s p e r p e n d i c u l a r to the C 3 a x i s o f the methyl groups , i s unknown. I f we assume the same f a c t o r s a l s o apply to the reduced second moment, then the i n t e r m o l e c u l a r second moment f o r r o t a t i o n o f methyl groups p lus r o t a t i o n of 2 whole molecule about i t s m o l e c u l a r a x i s becomes 0.7 ± 0 . 3 G . Table 5.2 shows the comparison o f the c a l c u l a t e d second moment and exper imenta l second moment. Set A r e f e r s to the c a l c u l a t i o n on the assumption t h a t r (C-H) = 1.05 ft and s e t B r e f e r s to the c a l c u l a t i o n on the assumption t h a t r ( C - H ) = 1.10 ft. Table 5.2 shows t h a t even at the lowest temperature o b t a i n e d , the t r i m e t h y l borane i s not r i g i d . The p l a t e a u va lue between 65 and 7.7 K corresponds to the r o t a t i o n o f the t h r e e methyl groups , and the p l a t e a u v a l u e between 90 K and the m e l t i n g p o i n t corresponds to the r o t a t i o n o f methyl groups p lus the r o t a t i o n o f whole molecule about the m o l e c u l a r a x i s . Comparison of the c a l c u l a t e d va lue and experimental va lue f o r methyl group r o t a t i o n shows the agreement o f the experimental second moment w i t h the c a l c u l a t i o n based on r(C-H) = 1.05 ft i s b e t t e r than the c a l c u l a t i o n based on r ( C - H ) = 1.10 ft. However, the agreement of s e t B i s b e t t e r than s e t A when the methyl groups and the whole molecule r o t a t e . This may be due on the one hand t o the i n a c c -u r a c i e s i n the v a r i o u s approximat ions we have assumed f o r c a l c u l a t i o n o f the t h e o r e t i c a l second moments, o r on the o t h e r hand to i n a c c u r a c y i n the experimen second moments because o f s a t u r a t i o n at low temperature . I t should be noted t h a t T, i s about 20s a t 77 K. - 9 4 -1 0 0 0 / T ° K F i g . 5.5. S p i n - l a t t i c e r e l a x a t i o n time o f t r i m e t h y l b o r a n e as a f u n c t i o n o f i n v e r s e o f temperature. - 9 5 -D.3 S p i n - l a t t i c e R e l a x a t i o n Time The s p i n - l a t t i c e r e l a x a t i o n t ime T^ f o r t r i m e t h y l b o r a n e i s p l o t t e d versus i n v e r s e o f temperature i n F i g u r e 5 . 4 . The T-j minimum i s not reached before the sample m e l t s . Therefore i t i s hopeless to t r y to o b t a i n the c o r r e l a t i o n t ime f o r the mot ional p r o c e s s . However, the energy parameter can be o b t a i n e d from Equat ion (5.1) i f wT_ » 1, o r w T « 1. The T, values f o r t r i m e t h y l b o r a n e between 90 K and m e l t i n g p o i n t a r e on the lower temperature s i d e o f a minimum and t h e r e f o r e u>qtc » 1. E q u a t i o n (5.1) can be w r i t t e n as 11 V c where C| = 2 c / w o . Thus the a c t i v a t i o n energy can be o b t a i n e d from a p l o t o f lnT^ versus T ~ l . The a c t i v a t i o n energy o b t a i n e d i n the range o f 90 - 112 K i s 2.87 ± 0.18 k c a l / m o l e . T h i s v a l u e i s h i g h e r than the a c t i v a t i o n energy f o r r e o r i e n t a t i o n of methyl groups a t t a c h e d t o boron i n t r i m e t h y l a m i n e - t r i m e t h y l -borane. S i n c e r e o r i e n t a t i o n o f the methyl groups a t t a c h e d t o boron which i s bonded t e t r a h e d r a l l y has a lower a c t i v a t i o n energy than 2.87 + 0.18 k c a l / m o l e , we conclude t h a t 2.87 ± 0.18 kca l/mole cannot be ass igned to the r o t a t i o n o f methyl groups i n t r i m e t h y l b o r a n e i n which the $CBC bond angle i s 120°. The a c t i v a t i o n energy, 2.87 ± 0.18 kca l/mole can p o s s i b l y be ass igned t o the r o t a t i o n o f the whole molecule about i t s m o l e c u l a r a x i s . The T^ curve below 90 K i s probably due to the c o n t r i b u t i o n o f methyl group r o t a t i o n to the r e l a x a t i o n r a t e . But we have not attempted to e x t r a c t the a c t i v a t i o n energy f o r t h i s mechanism because the u n c e r t a i n t y w i l l be q u i t e l a r g e from the o n l y r e s u l t s a t t h i s temperature range. - 9 6 -References [5.1] H.D. S p r i n g a l l and L . O . Brockway, J . A . C . S . , 60 (1938) 996 [5.2] L . S . B a r t e l l and L . O . Brockway, J . Chem. P h y s . , 32 (1960) 512 [5 .3] D.R. L i d e , J r . , and D . E . Mann, J . Chem. P h y s . , 29 (1958) 914 [5.4] H.A. Le*vy and L . O . Brockway, J . A . C . S . , 59 (1937) 2085 [5.5] P . J . H a i g h , P . C . Canepa, G.A. Matzkanin and T . A . S c o t t , J . Chem. P h y s . , 48 (1968) 4234 [5 .6] C.A. Fyfe and J . Ripmeester , Can. J . Chem.,48(1970) 2283 [5.7] A .W.K. Khanzada, Ph.D. T h e s i s , U n i v e r s i t y of B r i t i s h Columbia [5 .8] R. Kubo and K. T o m i t a , J . Phys. Soc. J a p a n , 9 (1954) 888 [5 .9] N . Bloembergen, E . M . P u r c e l l , and R.V. Pound, Phys. R e v . , 73 (1948) 679 [5.10] G.W. S m i t h , J . Chem. P h y s . , 42 (1965) 4229 -[5.11] E . R . Andrew, J . Chem. P h y s . , 18 (1950) 607 - 9 7 -CFjAPTER VI An NMR Study of Pi methyl amine Complexed w i t h T r i m e t h y l  aluminium o r T r i m e t h y l b o r a n e A; I n t r o d u c t i o n T h i s c h a p t e r d e s c r i b e s the nmr study o f the a d d i t i o n complex o f dimethylamine w i t h t r i m e t h y l a l u m i n i u m and t r i m e t h y l b o r a n e . B r o a d l i n e nmr s t u d i e s o f dimethylamine have been made by Haigh et a l . [ 6 . 1 ] , who found the methyl groups r e o r i e n t more r a p i d l y than the methyl groups i n t r i m e t h y l a m i n e . Khanzada [ 6 . 2 ] has a l s o s t u d i e d the s p i n - l a t t i c e r e l a x a t i o n t ime o f d i m e t h y l -amine and the c l a t h r a t e dimethylamine h y d r a t e , and found the a c t i v a t i o n energy f o r the methyl group r e o r i e n t a t i o n i s l e s s than t h a t i n t r i m e t h y l amine. Our purpose i s to study the dimethylamine when i t forms a d d i t i o n complexes w i t h t r i m e t h y l aluminium and t r i m e t h y l b o r a n e . B_. Experimental B . l P r e p a r a t i o n o f the Complexes Dimethylamine (anhydrous) was o b t a i n e d from Eastman Kodak C h e m i c a l s . T r i m e t h y l a l u m i n i u m and t r i m e t h y l b o r a n e were purchased from A l f a I n o r g a n i c s . The d i m e t h y l a m i n e - t r i m e t h y l a l u m i n i u m complex was prepared [ 6 . 3 ] by mix ing the amine and t r i m e t h y l a l u m i n i u m at l i q u i d n i t r o g e n temperature and warming the mixture s l o w l y t o room temperature . The excess amine was pumped o f f and the complex was p u r i f i e d by vacuum s u b l i m a t i o n . The same method was used f o r - 9 8 -p r e p a r a t i o n o f the d i m e t h y l a m i n e - t r i m e t h y l b o r a n e complex [ 6 . 4 ] . The m e l t i n g p o i n t s agree very w e l l w i t h the m e l t i n g p o i n t s c i t e d i n the l i t e r a t u r e [ 6 . 3 , 6 . 4 ] . Samples were t r a n s f e r r e d to 7.5 - 8 .0 mm.O.D. t h i n w a l l sample tubes f o r s p i n - l a t t i c e r e l a x a t i o n time, measurement and to 10 mm. O.D. sample tubes f o r b r o a d l i n e nmr measurement. B. 2 Procedure o f measurement The method o f measurement has been d e s c r i b e d i n Chapter I I I , except t h a t i n the case o f the dimethyl a m i n e - t r i m e t h y l b o r a n e complex the s p i n - l a t t i c e r e l a x a t i o n t imes were recorded w i t h a Bruker B-KR 300 Z15 boxcar i n t e g r a t o r w i t h a gate t ime o f 0 . 5 ysec . The output s i g n a l from the boxcar i n t e g r a t o r was d i s p l a y e d on a d i g i t a l v o l t m e t e r . C. Dimethyl ami n e - t r i m e t h y l a l umi ni urn C. l Exper imenta l L i n e Widths and Second Moments The exper imenta l second moments and l i n e widths are p l o t t e d versus 2 temperature i n F i g u r e 6 . 1 . The second moment has a p l a t e a u va lue o f 9 . 4 ± 0.5 G 2 between 77 K and 235 K. Then i t decreases from 7.5 G a t 250 K to a p l a t e a u 2 value of 3 . 8 ± 0 .5 G a t 294 K. Jhe change o f l i n e widths versus temperature i s s i m i l a r to t h a t of the second moment versus temperature . C.2 C a l c u l a t i o n o f Second Moments and D e t e r m i n a t i o n o f M o l e c u l a r Motion S ince no m o l e c u l a r parameters o r c r y s t a l s t r u c t u r e i s known f o r the d i -methyl ami n e - t r i m e t h y l aluminium complex, o n l y an es t imated second moment can be o b t a i n e d . The c a l c u l a t i o n o f second moment has been d e s c r i b e d i n Chapter I V , and f o r c a l c u l a t i o n o f second moment i n the dimethyl a m i n e - t r i m e t h y l a l u m i n i u m o- 80 120 160 200 240 "" "Temperature °K — i 1— 280 320 •O F i g . 6.1. L ine width and second moment of d imethy lamine - t r imethy la lumin ium as a f u n c t i o n o f temperature . -100-complex, we have taken r(N-H) = 1.00 8, r (C-N) = 1.47 8, r(C-Afc) = 2.00 8 and r(N-A&) = 1 .93 , r ( C - H ) = 1.10 8. The bond angles are assumed to be t e t r a h e d r a l . The r e s u l t s o f the c a l c u l a t i o n are shown i n Table 6.1 and are compared w i t h the experimental second moments. From Table 6 . 1 , i t i s c l e a r t h a t even at l i q u i d n i t r o g e n t e m p e r a t u r e , d i methyl ami n e - t r i m e t h y l a l u m i n i urn, 1i ke t r i m e t h y l ami n e - t r i m e t h y l a l u m i ni urn, cannot be c o n s i d e r e d to be r i g i d , . C o n t r a r y to the s i t u a t i o n i n t r i m e t h y l ami ne-t r i m e t h y l a l u m i n i u m , the methyl groups a t t a c h e d t o n i t r o g e n i n dimethyl amine-t r i m e t h y l a l umi n i urn are not r i g i q 1 , f o r the observed second moment agrees q u i t e w e l l w i t h the va lue c a l c u l a t e d on the assumption t h a t a l l methyl groups i n the molecule are r o t a t i n g f r e e l y . This can be e x p l a i n e d i n terms o f the s t e r i c h indrance o f methyl groups i n the t r i m e t h y l a m i n e moiety being l a r g e r than t h a t i n the dimethylamine m o i e t y . The decrease o f second moment about 235 K i s due to some a d d i t i o n a l motion and t h i s motion c o u l d be the r e o r i e n t a t i o n o f the whole molecule along i t s N-A£ bond as i n t r i m e t h y l a m i n e - t r i m e t h y l a l u m i n i u m o r the r e o r i e n t a t i o n o f e i t h e r the dimethylamine o r the t r i m e t h y l a l u m i n i u m moiety . The r o t a t i o n o f the dimethylamine moiety w h i l e the t r i m e t h y l a l u m i n i u m i s f i x e d seems l e s s probable because the dimethylamine moiety i s asymmetric and a l s o f o r a r o t a t i n g dimethylamine moiety the t h e o r e t i c a l second moment i s much h igher than the observed second moment. The observed va lue o f the second moment i s h i g h e r than the va lue c a l c u l a t e d on the assumption t h a t the whole molecule i s r o t a t i n g about i t s N-A£ bond, but i s l e s s than the va lue c a l c u l a t e d on the assumption t h a t the dimethylamine moiety i s f i x e d . Comparing the exper imenta l and t h e o r e t i c a l va lues of the second monent f o r a l l the methyl groups r o t a t i n g but the -101-TABLE 6.1 C a l c u l a t i o n o f Second Moments f o r D i m e t h y l a m i n e - t r i m e t h y l -aluminium complex and Comparison w i t h the Experimental Values (second moment i n G 2 ) T h e o r e t i c a l Second Moment C o n t r i b u t i o n CH Group Motion 3" Proton at N Proton to I n t e r - Experimental Temperature Me2NH Me 3 Ail C H 3 CHg to C H 3 N and A£ m o l e c u l a r T o t a l Second Moment T K SS SS 20 1.6 2.0 0.4 6 ± 1 30.0 ± 1 - -RS RS 5 1.4 1.8 0 .2 2.2 ± 1 10.6 ± 1 9 .4 ± 0 .5 77 -RR RR 0.6 0.2 0 . 2 0 .0 1.2 2.2 3 .8 + 0 .5 294 -RS RR 2.3 0.7 0.7 0 .0 1.6 5.3 RR RS 3.2 0 .9 1.0 0.2 1.7 7.1 _ _ SS = s t a t i o n a r y RS = methyl groups are r o t a t i n g but the moiety i s s t a t i o n a r y RR = methyl groups and the moiety are both r o t a t i n g -102-m o i e t i e s s t a t i o n a r y , we f i n d t h a t the c a l c u l a t e d va lue i s h i g h e r than the exper imental v a l u e , a l though the two va lues agree w i t h i n the u n c e r t a i n t i e s of each. The h i g h e r v a l u e f o r the t h e o r e t i c a l second moment c o u l d a r i s e from an o v e r e s t i m a t e o f i n t e r m o l e c u l a r c o n t r i b u t i o n , n e g l e c t o f v i b r a t i o n a l m o t i o n s , o r i n c o r r e c t assumptions concerning bond a n g l e s . The c a r r y i n g over o f these p o s s i b l e e r r o r s to the c a l c u l a t e d second moment f o r the case o f r o t a t i n g . m o i e t i e s c o u l d account f o r a t l e a s t p a r t o f the disagreement between the observed 2 second moment o f 3 . 8 ± 0 .5 G between 294 and 320 K and any o f the t h e o r e t i c a l l y c a l c u l a t e d v a l u e s . The most probable motion above 235 K, i n a d d i t i o n to methyl group r o t a t i o n , would seem to be r o t a t i o n o f the t r i m e t h y l a l u m i n i u m m o i e t y , w h i l e the dimethylamine moiety remains " f i x e d " . A second moment study o f ( C D 3 ) 2 N D A C ( G H 3 ) 3 and (CH 3 ) 2 NHA£(CD 3 ) 3 would he lp to c l e a r t h i s u n c e r t a i n t y . C.3 S p i n - l a t t i c e R e l a x a t i o n Times F i g u r e 6 .2 shows the v a r i a t i o n o f the exper imental s p i n - l a t t i c e r e l a x a t i o n times w i t h the i n v e r s e of temperature . The curve was r e s o l v e d i n t o three p a r t s and the r e s o l u t i o n i s i l l u s t r a t e d by the broken l i n e i n the f i g u r e . The a c t i v a t i o n energy from the r e s o l v e d s t r a i g h t l i n e p o r t i o n i n the r e g i o n 290 - 315 K, i n which T^ decreases as the temperature i n c r e a s e s , i s 9.68 ± 0 . 3 k c a l / m o l e . This va lue agrees very w e l l w i t h the a c t i v a t i o n energy f o r the r o t a t i o n o f the t r i m e t h y l a l u m i n i u m moiety i n the t r i m e t h y l p h o s p h i n e -t r i m e t h y l a l u m i n i u m complex (9 .95 ± 0.19 k c a l / m o l e ) . I t i s h i g h e r than the a c t i v a t i o n energy f o r r o t a t i o n o f the whole molecule about i t s N-A£ bond i n the t r i m e t h y l a m i n e - t r i m e t h y l a l u m i n i u m complex (5 .42 ± 0.18 k c a l / m o l e ) . The to i TJ C o o <D if) O.l o CO 8 ~r-4 2 13 12 11 IO 7 6 1 0 0 0 / T 0 K F i a . 6.2. S p i n - l a t t i c e r e l a x a t i o n time of d imethy lamine - t r imethy la lumin ium as a f u n c t i o n o f i n v e r s e temperature . The broken l i n e s i n d i c a t e the r e s o l u t i o n of observed T-. i n t o more than one mechanism. -104-1 1 1 1 1 1 9 8 7 6 5 4 1 0 0 0 / T ° K F i a . 6.3. P l o t of to x versus inve rse of temperature f o r the r o t a t i o n of the methyl groups at tached to n i t r o g e n i n dimeth.ylamine-t r imeth .y la l uminium. -105-second moment study a l s o shows t h a t above 235 K, the t r i m e t h y l a l u m i n i u m moiety r o t a t e s w i t h a frequency g r e a t e r than the narrowed l i n e w i d t h . The a c t i v a t i o n energy, 9 .68 ± 0 . 3 k c a l / m o l e , o b t a i n e d from the h igh temperature p a r t o f the curve can probably be a s s i g n e d to the r o t a t i o n o f the t r i m e t h y l a l u m i n i u m moiety . The T.| minimum which occurs at about 132 K i s due to some o t h e r k i n d o f molec-u l a r mot ion . Using (T . | ) m . | n = 52 msec f o r t h i s second m o t i o n a l process and the exper imental T-j values between 135 and 250 K, values o f IO 0T c were o b t a i n e d from the BPP [ 6 . 5 , 6 . 6 ] equat ion and have been shown i n F i g u r e 6 . 3 . A l e a s t squares f i t o f the s t r a i g h t l i n e gave 1 n V c = ( - 1 0 - 8 8 1 + t 2 - 7 4 1 ° - 0 4 ) x 1° 3 /RT (6.1) Thus the a c t i v a t i o n energy found i s 2.74 ± 0.04 kca l/mole and i t can be ass igned to the methyl group r o t a t i o n i n the dimethylamine m o i e t y . Equat ion (6 .1) shows t h a t i f a) T i s o f the o r d e r o f 1 0 2 - 1 0 3 , T should be between 89 and 77 K. o c ' Therefore a c c o r d i n g to the s p i n - l a t t i c e r e l a x a t i o n s t u d y , there should be a l i n e w i d t h o r second moment t r a n s i t i o n between 77 and 89 K. However, there i s no such t r a n s i t i o n observed i n the l i n e width and second moment s t u d y . T h i s c o n t r a r i n e s s was a l s o observed i n ammonia [ 6 . 7 ] and some polymethyl benzenes [6 .8 - 6 .10] and can be e x p l a i n e d by the p o s t u l a t e t h a t there i s t u n n e l l i n g motion of the methyl groups at low temperature [ 6 . 1 1 ] . The s l o p e o f the r e s o l v e d s t r a i g h t l i n e p o r t i o n i n the r e g i o n 77 - 108 K corresponds t o an apparent a c t i v a t i o n energy o f 0.89 + 0.10 k c a l / m o l e . Al though the decrease i n T-j w i t h -106-d e c r e a s i n g temperature below 100 K i s probably p r i m a r i l y due t o motion o f the methyl groups i n the t r i m e t h y l a l u m i n i u m m o i e t y , the probable e x i s t e n c e o f m u l t i p l e minima i n T-j at low temperatures due t o t u n n e l l i n g motion o f the methyl groups i n the dimethylamine moiety may a l s o c o n t r i b u t e t o the o b s e r v a b l e Tj i n t h i s r e g i o n . D. P i methyl ami n e - t r i m e t h y l borane D.I Exper imental L i n e Widths and Second Moments F i g u r e 6.4 i s a p l o t o f second moments and l i n e widths versus temp-2 e r a t u r e . The second moment has a p l a t e a u va lue o f 11.7 ± 0 .5 G between 100 and 220 K. Below 100 K the second moment i n c r e a s e s as the temperature d e c r e a s e s . 2 The second moment decreases s l o w l y from 11.3 G at 227 K to a v a l u e o f approx-2 i m a t e l y 4 G near the m e l t i n g p o i n t . The change o f l i n e widths versus temp-e r a t u r e i s s i m i l a r to t h a t o f second moment versus temperature . P.2 C a l c u l a t i o n o f Second Moments and D e t e r m i n a t i o n o f M o l e c u l a r Motion S i n c e no m o l e c u l a r s t r u c t u r e and c r y s t a l s t r u c t u r e i s known f o r the dimethyl a m i n e - t r i m e t h y l b o r a n e complex, the t h e o r e t i c a l second moment can o n l y be e s t i m a t e d . The c a l c u l a t i o n o f second moment has been d e s c r i b e d i n Chapter I V , and f o r c a l c u l a t i o n o f second moment i n the dimethyl a m i n e - t r i m e t h y l b o r a n e complex, we have taken r(N-H) = 1.00 ft, r (C-N) = 1.47 8, r ( C - B ) = 1.56 8 and r ( N - B ) = 1.60 r(.C-H) = 1.10 8. The bond angles are assumed to be t e t r a h e d r a l . The r e s u l t s of the c a l c u l a t i o n s are shown i n Table 6 . 2 , and are compared w i t h the exper imental second moments. 14-CM o 12H L U o 10-4 8H O O LU CO 60 @ S E C O N D M O M E N T Q L I N E W I D T H O o 100 H 4 H 2 10 f— Q h8 L U h-6 —I 300 340 140 180 220 260 T EMP E R A T URE (°K) F i g . 6.4. L i n e w i d t h and second moment of dimethyl amine-tr imethylborane versus temperature. o -108-TABLE 6.2 C a l c u l a t i o n o f Second Moments f o r Dimethyl amine- tr imethy lborane Complex and Comparison w i t h the Experimental Values (second moment i n G 2 ) T h e o r e t i c a l Second Moment C o n t r i b u t i o n Group Me2NH Motion Me 3B C H 3 C H 3 -C H 3 Proton a t . N t o C H 3 Proton to N and B I n t e r -m o l e c u l a r T o t a l Experimental Second Moment Temperature T°K SS SS 20 3 .3 2.2 0.6 6 ± 1 31.9 ± 1 - -RS RS 5 2.9 1.9 0.2 2.2 ± 1 12.4 ± 1 11.7 ± 0 .5 100 - 220 K RR RR .6 0.4 0 . 3 0 .0 1.3 2.6 4 . 0 ± 0 .5 290 - 306 K RS RR 2.3 1.4 1.0 0 .0 1.6 6 .3 RR RS 3.2 1.9 1.3 0.2 1.7 8 .3 _ SS = s t a t i o n a r y RS = methyl groups are r o t a t i n g but the moiety i s s t a t i o n a r y RR = methyl groups and the moiety are both r o t a t i n g -109-Table 6.2 shows t h a t the exper imenta l second moments between 100 and 220 K correspond t o the r o t a t i o n o f a l l methyl groups i n the d imethyl amine-t r i m e t h y l borane complex. The i n c r e a s e of second moments below 100 K i s due to l e s s m o b i l i t y of the methyl groups . The r i g i d l a t t i c e second moment i s not reached at temperatures down t o 77 K. The decrease o f second moment above 220 K i s due t o some a d d i t i o n a l motion i n the molecule and t h i s motion c o u l d be the r o t a t i o n o f the whole molecule a long i t s N-B bond, o r the r o t a t i o n o f e i t h e r the dimethylamine moiety o r the t r i m e t h y l b o r a n e m o i e t y . The r o t a t i o n o f the dimethylamine moiety w h i l e the t r i m e t h y l b o r a n e moiety i s f i x e d seems l e s s p r o b a b l e , because the es t imated second moment f o r t h i s 2 c o n d i t i o n i s much h i g h e r than the observed v a l u e , 4 G . The second moment near the m e l t i n g p o i n t i s h i g h e r than the e s t i m a t e d v a l u e f o r the whole molecule r o t a t i n g about the N-B bond, but i s l e s s than the es t imated va lue f o r the t r i m e t h y l b o r a n e moiety r o t a t i n g w h i l e the dimethylamine moiety i s f i x e d . L i k e the d i m e t h y l a m i n e - t r i m e t h y l a l u m i n i u m complex, the a d d i t i o n a l motion may be due t o the r e o r i e n t a t i o n o f t r i m e t h y l b o r a n e m o i e t y . A second moment study on ( C D 3 ) 2 N D - B ( C H 3 ) 3 and ( C H 3 ) 2 N H - B ( C D 3 ) 3 would he lp t o c l e a r t h i s argument. D.3 S p i n - l a t t i c e R e l a x a t i o n Times F i g u r e 6.5 i s a p l o t o f the exper imental s p i n - l a t t i c e r e l a x a t i o n times versus i n v e r s e o f temperature . The T-j minimum i s b r o a d , and the apparent a c t i v a t i o n energies o b t a i n e d from the low and h igh temperature p a r t s o f the curve are 2.04 + 0.07 kca l/mole and 2.68 ± 0.04 kcal/mole r e s p e c t i v e l y . I t i s obvious t h a t the motion cannot be d e s c r i b e d w i t h a unique c o r r e l a t i o n I 1 I I 1 1 1 1 1 1 1 1 I I I I 13 12 11 IO 9 8 7 6 5 4 3 2 1 0 0 0 / T ° K F i g . 6 . 5 . S p i n - l a t t i c e r e l a x a t i o n time of d imethy lamine - t r imethy lborane versus i n v e r s e o f temperature . The broken curve between 95 and 180 K shows the c a l c u l a t e d T-, curve as d i s c u s s e d i n d e t a i l i n the t e x t . The broken l i n e s at h iah temperature par t show the r e s o l u t i o n of T n i n t o two mechanisms. - I l l -t i m e . The broadening i n the T^ minimum may a r i s e from two types o f independent m o t i o n s , which i n our case are the r o t a t i o n s o f methyl groups at tached on the one hand to n i t r o g e n and on the o t h e r to b o r o n , a t the same temperature but proceeding at d i f f e r e n t r a t e s and each c o n t r i b u t i n g towards the e f f i c i e n c y o f the s p i n - l a t t i c e r e l a x a t i o n . An attempt was made to f i t the T.| curve by assuming t h e r e are two types o f m o t i o n , each c h a r a c t e r i z e d by a c o r r e l a t i o n t i m e , and t h a t the r a t i o o f the T-j minima of the two motions i s about 2 : 3 . Reasonable va lues o f a c t i v a t i o n e n e r g i e s , T.| minima, and temperatures a t which the T-| minima o c c u r f o r each o f the tv/o mot ional processes were put i n t o a computer programme (Appendix C ) which c a l c u l a t e d T^ values from these a d j u s t a b l e parameters and compared them w i t h experimental T^ v a l u e s . The c a l c u l a t e d values agree very w e l l w i t h the exper imental T^ values i n both the low and the high temperature p a r t s but d e v i a t e q u i t e s i g n i f i c a n t l y i n the r e g i o n where the broad T^ minimum occurs i f we assume the a c t i v a t i o n energy f o r the r e o r i e n t a t i o n o f methyl groups a t tached to boron i s 2.04 k c a l / m o l e , t h a t ( T - | ) m i n = 34 msec a t 110 K,, t h a t the a c t i v a t i o n energy f o r r e o r i e n t a t i o n o f methyl groups a t t a c h e d t o n i t r o g e n i s 2.689 k c a l / m o l e , and t h a t the ( T , ) . = 50 msec at 142 K. The broken 1 mi n l i n e i n F i g u r e 6.5 shows the c a l c u l a t e d values i n the r e g i o n where the: broad T-j minimum o c c u r s . Another p o s s i b i l i t y may account f o r the presence o f more than one c o r r e l a t i o n time i n d i s a e t h y l a m i n e - t r i m e t h y l b o r a n e . A d i s t r i b u t i o n of c o r r e l a t i o n times may e x i s t i f , f o r a s i n g l e type o f motion which produces r e l a x a t i o n , there i s a d i s t r i b u t i o n o f environments w i t h i n the sample. The o n l y known d i s t r i b u t i o n f u n c t i o n t h a t d e s c r i b e s an asymmetric InT, curve i s -112-the Cole-Davidson d i s t r i b u t i o n f u n c t i o n [ 6 . 1 2 , 6 . 1 3 ] . However, the minimum i n T.j c a l c u l a t e d from the Cole-Davidson d i s t r i b u t i o n i s not as broad as the experimental minimum o b t a i n e d h e r e . As a r e s u l t o f the f a i l u r e to o b t a i n a complete ly s a t i s f a c t o r y f i t o f exper imental and c a l c u l a t e d va lues by e i t h e r two d i s c r e t e r e l a x a t i o n processes o r a Cole-Davidson d i s t r i b u t i o n , a c t i v a t i o n energies o b t a i n e d from the low and h igh temperature s i d e s cannot be ass igned w i t h o u t any a m b i g u i t y . The a c t i v a t i o n energy o b t a i n e d from the r e s o l v e d T-j, where T-j decreases w i t h i n c r e a s e o f temperature , i n the temperature r e g i o n o f 280 - 308 K, i s 14.03 ± 1.51 k c a l / m o l e . This a c t i v a t i o n energy may be ass igned t o the r e o r i e n t a t i o n o f the t r i m e t h y l b o r a n e m o i e t y . -113-References [6 .1 ] P . J . H a i g h , P . C . Canepa, G.A. Matzkanin and T . A . S c o t t , J . Chem. P h y s . , 48 (1968) 4234 [6 .2] A . U . K . Khanzada, P r i v a t e Communication [ 6 . 3 ] N. Davidson and H . C . Brown, J . A . C . S . , 64 (1942) 316 [ 6 . 4 ] H.C. Brown, H. Bartholomay, J r . , and M.D. T a y l o r , J . A . C . S . , 66 (1944) 435 [6 .5] N. Bloembergen, E . M . P u r c e l l and R.V. Pound, P h y s i c . R e v . , 73 (1948) 679 [ 6 . 6 ] R. Kubo and K. T o m i t a , J . P h y s i c . Soc. J a p a n , 9_ (1954) 888 [6 .7] J . L . C a r o l a n and T . A . S c o t t , J , Mag. R e s . , 2 (1970) 243 [ 6 . 8 ] P . S . A l l e n and A . Cowking, J . Chem. P h y s . , 47 (1967) 4286 [ 6 . 9 ] E .R. Andrews and P . S . A l l e n , J . Chim. O h y s . , 3 (1966) 85 [6.10] P . S . A l l e n and A . Cowking, J . Chem. P h y s . , 49 (1968) 789 [6.11] P . S . A l l e n , J . Chem. P h y s . , 48 (1968) 3031 [6.12] D.W. Davidson and R . H . C o l e , J . Chem. P h y s . , 1_9 (1951) 1484 [6.13] T . M . Connor, T r a n s . Faraday S o c , 60 (1964) 1574 -114-CHAPTER V I I S p i n - l a t t i c e R e l a x a t i o n Study o f T r i m e t h y l amine- Boron T r i h a l i d e s Complexes A^ I n t r o d u c t i o n This chapter d e s c r i b e s the study o f proton s p i n - l a t t i c e r e l a x a t i o n times f o r t r i m e t h y l a m i n e - b o r o n t r i c h l o r i d e and t r i m e t h y l a m i n e - b o r o n t r i -bromide. The w i d e - l i n e n u c l e a r magnetic resonance study o f m o l e c u l a r motion i n complexes o f t r i m e t h y l a m i n e w i t h boron t r i h a l i d e s [ 7 . 1 , 7 .2] and borane [7.1] has a l r e a d y been made. These e a r l i e r i n v e s t i g a t o r s a t t r i b u t e d l i n e width and second moment t r a n s i t i o n s t o methyl group r e o r i e n t a t i o n i n the temperature range below 110 K, f o l l o w e d by r o t a t i o n of t r i m e t h y l a m i n e group about the B-N a x i s a t h i g h e r temperatures . The temperature dependence o f 35 the C£ NQR spectrum i n the t r i m e t h y l a m i n e - b o r o n t r i c h l o r i d e complex has a l s o been s t u d i e d [ 7 . 3 ] . We have not chosen t r i m e t h y l a m i n e - b o r o n t r i f l u o r i d e i n our study s i n c e the proton and f l u o r i n e resonance f r e q u e n c i e s are very c l o s e and t h i s f a c t w i l l c o m p l i c a t e the i n t e r p r e t a t i o n of the r e s u l t s [ 7 . 4 ] . B. Experimental B . l M a t e r i a l s and P r e p a r a t i o n Anhydrous t r i m e t h y l a m i n e was o b t a i n e d from Eastman Kodak C h e m i c a l s . Boron t r i c h l o r i d e was purchased from Matheson and boron t r i b r o m i d e was purchased from A l f a I n o r g a n i c s . Complexes were prepared a c c o r d i n g to the methods d e s c r i b e d i n the l i t e r a t u r e [ 7 . 5 , 7 . 6 ] . Tr imethy lamine-boron t r i c h l o r i d e complex was r e c r y s t a l l i z e d three t imes from a b s o l u t e a l c o h o l . T r i m e t h y l a m i n e -boron t r i b r o m i d e complex was r e c r y s t a l l i z e d from benzene. Table 7 shows the -115-r e s u l t o f a combustion a n a l y s i s f o r H , C, and N . TABLE 7.1 R e s u l t s o f Combustion A n a l y s i s on Tr imethy lamine-boron t r i h a l i d e s Complexes Sample C C a l c . Found H C a l c . Found N C a l c . Found Me3NBCJc3 20.44 20.48 5.15 5.09 7.94 8.07 Me 3NBBr 11.62 11.46 2.9 3.11 4 . 5 2 4.63 Samples were s e a l e d i n 7 .5 - 8.0 mm O.D. t h i n w a l l tubes under vacuum, B. 2 Procedure The method o f measurement has been d e s c r i b e d i n Chapter I I I . Values o f T^ were measured by a 180 - T - 90° p u l s e sequence. The s tandard d e v i a t i o n o f the s lope o f the s t r a i g h t l i n e which T^  i s o b t a i n e d i s l e s s than 5%. £. R e s u l t s and D i s c u s s i o n C. l Tr imethy lamine-boron t r i b r o m i d e Complex F i g u r e 7.1 shows a p l o t o f proton T-j va lues f o r t r i m e t h y l ami ne-boron t r i b r o m i d e complex versus i n v e r s e o f temperature . I t e x h i b i t s two minima i n the T^ c u r v e . The T^ minimum a t high temperature i s sharp whereas the T.| minimum at low temperature i s v e r y b r o a d . No study was made.beyond 450 K s i n c e we^did not want to r i s k i n j u r y to the probe head. I I I I 8 7 6 5 4 3 2 1 0 0 0 / T ° K F i g . 7. 1. S p i n - l a t t i c e r e l a x a t i o n time o f t r i m e t h y l a m i n e boron t r i b r o m i d e complex as a f u n c t i o n o f i n v e r s e temperature. The broken l i n e s show the r e s o l u t i o n o f observed T-j i n t o more than one mechanism as d i s c u s s e d i n d e t a i l i n the t e x t . -117-The broad minimum i n T-j i n d i c a t e s the r e l a x a t i o n process cannot be d e s c r i b e d w i t h o n l y a s i n g l e c o r r e l a t i o n t i m e . The a c t i v a t i o n energy o b t a i n e d from the s l o p e of the low temperature p a r t of the curve i s 2.86 ± 0 .08 k c a l / m o l e , w h i l e the a c t i v a t i o p energy o b t a i n e d from the s l o p e o f the h i g h temperature p a r t i s 3.23 + 0.07 k c a l / m o l e . An attempt was made to f i t the exper imental T-j data us ing a Co le-Davidson [ 7 . 7 , 7.8] d i s t r i b u t i o n f u n c t i o n w i t h the width o f the d i s t r i b u t i o n g iven by 6 = 2 . 8 6 / 3 . 2 3 . The c a l c u l a t e d values agreed very w e l l on both s i d e s o f the T^ minimum. However, the c a l c u l a t e d ( T , ) . was much lower than the exper imenta l ( T , ) . and the I min r 1 min minimum i n the c a l c u l a t e d curve was not as broad as the exper imental minimum. W i t h i n 10% e r r o r we get a very good f i t w i t h the exper imenta l T-j d a t a , i f we assume t h e r e are two c o r r e l a t i o n t i m e s , each having an A r r h e n i u s temp-e r a t u r e and a c t i v a t i o n energy dependence, and i f the r e l a x a t i o n r a t e can be d e s c r i b e d by the BPP [ 7 . 9 , 7.10] e q u a t i o n . The r e s o l u t i o n o f the exper imenta l T i curve i s shown by the two d o t t e d BPP c u r v e s , one w i t h ( T , ) „•„ = 60 ms I 1 min at about 162 K and w i t h an a c t i v a t i o n energy of 2.86 k c a l / m o l e , and the o ther w i t h ( T - | ) m i - n = 55ms at about 198 K and w i t h an a c t i v a t i o n energy o f 3.24 k c a l / m o l e . The l i n e width and second moment [7.1] study suggests t h a t i n t h i s temperature range the probable mechanisms f o r s p i n - l a t t i c e r e l a x a t i o n i s the r e o r i e n t a t i o n o f methyl groups. A s imple p i c t u r e to e x p l a i n the, r e s u l t s i s to assume t h e r e are two types o f c r y s t a l l o g r a p h i c s i t e f o r the t r i m e t h y l a m i n e - b o r o n t r i b r o m i d e complexes. The methyl groups i n each c r y s t a l l o g r a p h i c s i t e exper ience a d i f f e r e n t environment. There fore t h e r e e x i s t two c o r r e l a t i o n times and d i f f e r e n t a c t i v a t i o n energ ies f o r the methyl group r e o r i e n t a t i o n . However, o t h e r e x p l a n a t i o n s f j r the e x i s t e n c e o f two -118-r e l a x a t i o n mechanisms might p o s s i b l y be found. The l i n e w i d t h and second moment [7 .1] study shows t h a t the whole molecule i s r o t a t i n g a t a frequency o f the o r d e r o f l i n e w i d t h a t about 260 K. The high temperature minimum i n T-j can t h e r e f o r e be a t t r i b u t e d t o the r e o r i e n t a t i o n o f the whole molecule about i t s B-N bond. The T 1 i n the r e g i o n o f 300 - 400 K i s a f f e c t e d by the r e o r i e n t a t i o n of methyl groups as w e l l as the r e o r i e n t a t i o n o f the whole molecule about i t s B-N bond. The r e s o l u t i o n of the two c o n t r i b u t i o n s i s shown i n the F i g u r e 7 . 1 . The r e s o l v e d T-| f o r the r e o r i e n t a t i o n o f the whole molecule a long i t s N-B bond can be c h a r a c t e r i z e d by a motion w i t h a s i n g l e c o r r e l a t i o n time x c = (4 .24 ± 0.49) x 1 0 ~ 1 6 exp (12.80 ± 0.55) x 10 3 /RT Thus the a c t i v a t i o n energy f o r the r e o r i e n t a t i o n o f the whole molecule a long i t s N-B bond i s 12.80 ± 0.55 k c a l / m o l e . The a c t i v a t i o n e n e r g i e s found f o r methyl groups r e o r i e n t a t i o n and the r e o r i e n t a t i o n of the whole molecule about i t s N-B bond by our pulsed nmr study are both h i g h e r than the a c t i v a t i o n energies found from l i n e w i d t h measurement [ 7 . 1 ] ' . T h e i r values are 1.7. - 2.0 kcal/mole f o r methyl groups r e o r i e n t a t i o n and 9.1 kca l/mole f o r the r o t a t i o n o f the whole molecule about the N-B bond. C.2 Tr imethylamine-boron t r i c h l o r i d e The temperature dependence o f proton T-j f o r t r i m e t h y l amine-boron t r i c h l o r i d e complex i s shown i n F i g u r e 7 . 2 . The T-j minimum at low temperature i s s l i g h t l y b r o a d , but i t i s not as broad as the minimum i n the t r i m e t h y l a m i n e -boron t r i b r o m i d e complex. There i s a sudden change i n T, a t 390 K and we 1 1 1 1 1 1 H 1 1 1 1 1 1 5 8 7 6 5 4 3 2 1 0 0 0 / T ° K F i g . 7.2. S p i n - l a t t i c e r e l a x a t i o n time o f t r i m e t h y l a m i n e boron t r i c h l o r i d e complex as a f u n c t i o n o f i n v e r s e temperature . The broken l i n e s at about 300 K show the r e s o l u t i o n o f observed T-. i n t o two mechanisms. 1 -120-a t t r i b u t e t h i s to a phase t r a n s i t i o n . T h i s phase t r a n s i t i o n i s conf irmed by our DSC s t u d y . F i g u r e 7.3 i s the DSC cruve f o r t r i m e t h y l a m i n e - b o r o n t r i c h l o r i d e complex. Below 380 K, normal FID s i g n a l s were observed f o r the t r i m e t h y l amine-boron t r i c h l o r i d e complex, but a t h i g h e r temperatures t h e r e i s a r e l a t i v e l y s t r o n g high frequency n o i s e superimposed on the FID s i g n a l . This phenomenon p e r s i s t e d and d i d not d i s a p p e a r a t 430 K, the h i g h e s t temperature o f measurement. The h igh temperature phase may be p i e z o e l e c t r i c [7.11 i n nature and the n o i s e generated by the r f p u l s e on the sample. T h i s phenomenon was a l s o observed i n tetramethylammonium c h l o r i d e [ 7 . 1 1 ] . There was no such phase t r a n s i t i o n observed i n the l i n e w i d t h and second moment measurement. Probably the m o l e c u l a r motions are the same i n both phases and the c o r r e l a t i o n f r e q u e n c i e s o f the motions are h i g h e r than the l i n e widths expressed i n f requency. The a n a l y s i s o f the T-j data i s s t r a i g h t f o r w a r d . We a t t r i b u t e the T.j minimum at low temperature to the methyl group r e o r i e n t a t i o n . The s o l i d curve i s the f i t t e d BPP curve w i t h a s i n g l e c o r r e l a t i o n t i m e : x c = (1.35 ± 0.16) x 1 0 " 1 2 exp (2.79 ± 0.04) x 10 3 /RT Thus the a c t i v a t i o n energy f o r methyl group r e o r i e n t a t i o n was found t o be 2.79 ± 0.04 k c a l / m o l e . S i n c e both nmr [7.1] and nqr [7 .3] s t u d i e s have shown the r e o r i e n t a t i o n of both amine and boron t r i c h l o r i d e m o i e t i e s , we a s s i g n the T-j minimum which occurs a t about 350 K t o the r e o r i e n t a t i o n o f the whole molecule about i t s N-B bond. In the r e g i o n o f 290 - 340 K, the s p i n - l a t t i c e r e l a x a t i o n r a t e , T , " \ F i g . 7.3. DSC curve o f t r i m e t h y l a m i n e - b o r o n t r i c h l o r i d e . -122-i s the sum o f two r e l a x a t i o n r a t e s , namely the s p i n - l a t t i c e r e l a x a t i o n r a t e , due to the methyl group r o t a t i o n and the s p i n - l a t t i c e r e l a x a t i o n r a t e due to the r o t a t i o n of the whole molecule about i t s N-B bond. The two c o n t r i b u t i o n s to the experimental T-| were r e s o l v e d and are shown i n F i g u r e 7.2 by d o t t e d l i n e s . The r e s o l v e d T^ f o r the r e o r i e n t a t i o n o f the whole molecule about i t s N-B bond can be c h a r a c t e r i z e d by a s i n g l e c o r r e l a t i o n time x c = (9 .45 ± 0.5) x 1 0 " 1 8 exp (13.79 ± 0.91) x 10 3 /RT The a c t i v a t i o n energy f o r the r e o r i e n t a t i o n o f the whole molecule about i t s N-B bond was t h e r e f o r e found t o be 13.79 ± 0.91 k c a l / m o l e . The a c t i v a t i o n energies o b t a i n e d from the T^ study f o r methyl group r e o r i e n t a t i o n and the r e o r i e n t a t i o n o f the whole molecule about i t s N-B bond are h i g h e r than those o b t a i n e d from l i n e w i d t h measurement (1 .6 - 1.9 kca l/mole and 9 . 3 kcal/mole [ 7 . 1 ] ) . The a c t i v a t i o n energy o b t a i n e d from the T^ p o i n t s above 390 K i s 3.72 ± 0.39 k c a l / m o l e . This a c t i v a t i o n energy i s not a s s i g n e d and i s p o s s i b l y o n l y an apparent value a r i s i n g from more than one mechanism. -123-References [7.1] C .T . Yim and D . F . R . G i l s o n , Can. J . Chem., 48 (.1970) 515 [7 .2] B .A. D u n e l l , C .A. F y f e , C .A. McDowell and J . R i p m e e s t e r , T r a n s . Faraday S o c , 65 (1969) 1153 [7.3] D . F . R . G i l s o n and R.M. H a r t , Can. J . Chem., 48 (1970) 1976 [7.4] J . E . Anderson and W.P. S l i c h t e r , J . Chem. P h y s . , 43 (1965) 433 [7.5] E. Wiberg and W. S U t t e r l i n , Z . Anorg . u . A l l gem. Chem., 202 (1931) 31 [7 .6] R .C . O s t h o f f , C .A. Brown, and H. C l a r k , J . A . C . S . , 7_3 (1951) 4045 [7 .7] D.W. Davidson and R . H . C o l e , J . Chem. P h y s . , 19_ (1951) 1484 [7 .8] T . M . Connor, T r a n s . Faraday S o c , 60 (1964) 1574 [7.9] N. Bloembergen, E . M . P u r c e l l and R.V. Pound, P h y s i c R e v . , 7_3 (1948) 679 [7.10] R. Kubo and K. T o m i t a , J . P h y s i c . Soc. J a p a n , 9_ (1954) 858 [7.11] S. A l b e r t , H . S . Gutowsky and J . A . Ripmeester , J . Chem. Phys. 56 (1972) 3672 -123a-A d d i t i o n a l Note A f t e r the complet ion o f t h i s t h e s i s , a r e p o r t on c r y s t a l and m o l e c u l a r s t r u c t u r e s o f t h r e e t r i m e t h y l a m i n e - b o r o n h a l i d e a d d u c t s : Me 3 NBCJl 3 , M e 3 N B B r 3 and M e 3 N B I 3 which appeared i n J . o f C r y s t . and M o l . S t r u c t u r e , J_ (1971) 363, came t o our a t t e n t i o n . In M e 3 N B B r 3 t h e r e i s s l i g h t d i s t o r t i o n from C 3 symmetry i n the t r i m e t h y l a m i n e m o i e t y . T h i s might account f o r the two va lues o f a c t i v a t i o n energy f o r the methyl group r e o r i e n t a t i o n s . -124-CHAPTER VII S p i n - l a t t i c e R e l a x a t i o n Study o f T r i m e t h y l a m i n e - halogens Complexes A. I n t r o d u c t i o n There has been c o n s i d e r a b l e i n t e r e s t r e c e n t l y i n the s t r u c t u r e and bonding i n a d d i t i o n complexes i n which t r i m e t h y l a m i n e acts as the e l e c t r o n donor and halogen acts as an e l e c t r o n a c c e p t o r . X - r a y measurement on t r i -methy lamine- iodine and t r i m e t h y l a m i n e - i o d i n e c h l o r i d e [ 8 . 1 , 8 . 2 ] have shown t h a t the n i t r o g e n - h a l o g e n - h a l o g e n l i n k a g e i s l i n e a r and the n i t r o g e n - h a l o g e n and halogen-halogen bond lengths are l o n g e r than t h e i r ' n o r m a l ' c o v a l e n t bonds. Fyfe and Ripmeester [ 8 . 3 ] have measured the proton nmr l i n e w i d t h and second moment f o r these complexes. I t i s our purpose t o study the s p i n -l a t t i c e r e l a x a t i o n times of these compounds a t v a r i o u s temperatures and to e x t r a c t the a c t i v a t i o n energ ies and r a t e parameters f o r the motions i n the s o l i d s t a t e . B_. Exper imenta l Anhydrous t r i m e t h y l a m i n e was o b t a i n e d from Eastman Kodak C h e m i c a l s , i o d i n e c h l o r i d e from BDH, and bromine from A l f a I n o r g a n i c s . The i o d i n e used was reagent grade. Complexes were prepared a c c o r d i n g t o the method d e s c r i b e d i n the l i t e r a t u r e [ 8 . 1 , 8 . 2 ] . Table 8.1 shows the r e s u l t s o f the combustion a n a l y s i s f o r C, H , and N. -125-TABLE 8.1 R e s u l t s o f Combustion A n a l y s i s on T r i m e t h y l a m i n e -halogen complexes SAMPLE C a l c . Found C a l c . Found C a l c . Found 11.52 11.20 2.90 2.76 4 . 4 8 4.32 16.27 16.16 4.10 4.17 6.32 ' 6.29 16.45 16.32 4.15 4.13 6.45 6.60 ( C H 3 ) 3 N - I 2 (CH 3 ) 3 N-IC£ ( C H 3 ) 3 N - B r 2 A l l samples were s e a l e d i n 7.5 - 8 . 0 mm O.D. t h i n w a l l tubes under vacuum and s t o r e d i n l i q u i d n i t r o g e n i n the dark when not i n use . S p i n - l a t t i c e r e l a x a t i o n times were measured by a TT - TT/2 p u l s e sequence and the procedure d e s c r i b e d i n Chapter I I I . C. R e s u l t s and D i s c u s s i o n C . l T r i m e t h y l a m i n e - i o d i n e Complex The exper imental va lues o f the proton T^ f o r the t r i m e t h y l a m i n e - i o d i n e complex are p l o t t e d versus i n v e r s e o f temperature i n F i g u r e 8 . 1 . The s o l i d l i n e has been c a l c u l a t e d u s i n g the m o d i f i e d BPP e q u a t i o n [ 8 . 4 , 8 . 5 j and the r e l a t i o n x c = (2 .13 ± 0.06) x 1 0 " 1 2 exp (3.57 ± 0.11) x 1 0 3 / R T , which was i n t u r n o b t a i n e d from the exper imenta l p o i n t s , ( T ] ) m j n = 3 0 and the BPP e q u a t i o n . From the second moment and l i n e width study I 8 .3 ] -126-1000/T°K F i g . 8 . 1 . S p i n - l a t t i c e r e l a x a t i o n times o f t r i m e t h y l a m i n e - i complex as a f u n c t i o n o f i n v e r s e temperature . odine -127-5 g i 5 1000/T°K F i g . 8 . 2 . S p i n - l a t t i c e r e l a x a t i o n times o f t r i m e t h y l a m i n e - i o d i n e c h l o r i d e complex as a f u n c t i o n of i n v e r s e temperature . -128-F i g . 8 . 3 . S p i n - l a t t i c e r e l a x a t i o n times o f t r imethy lamine-bromine complex as a f u n c t i o n o f i n v e r s e temperature . -129-the r e l a x a t i o n mechanism can probably be ass igned to methyl group r e o r i e n t a -t i o n . The a c t i v a t i o n energy, 3.57 ± 0.11 k c a l / m o l e , o b t a i n e d from our measurement i s lower than the va lue o b t a i n e d by Fyfe and Ripmeester [ 8 . 3 ] . They o b t a i n e d 6.9 ± 0.4 kcal/mole from l i n e w i d t h measurement. C.2 T r i m e t h y l a m i n e - i o d i n e c h l o r i d e Complex The temperature dependence o f proton T-j f o r t r i m e t h y l a m i n e - i o d i n e c h l o r i d e complex i s shown i n F i g u r e 8 . 2 . The s o l i d l i n e i s the f i t t e d BPP curve w i t h Tc = (1.64 ± 0.07) x 1 0 ' 1 2 exp(4.25 + 0.17) x 10 3 /RT From second moment and l i n e width s t u d y , the r e l a x a t i o n mechanism can probably be ass igned to methyl group r e o r i e n t a t i o n . The a c t i v a t i o n energy o b t a i n e d i s 4.25 ± 0.17 k c a l / m o l e . This va lue i s again lower than the v a l u e , 6 .2 ± 0 .5 k c a l / m o l e , o b t a i n e d from l i n e w i d t h measurement [ 8 . 3 ] . C.3 T r i methyl ami ne-bronrjne Complex The temperature dependence o f proton T-j f o r t r i m e t h y l ami ne-bromine complex i s shown i n F i g u r e 8 . 3 . The s o l i d l i n e i s the f i t t e d BPP curve w i t h x c = (4 .38 ± 0.07) x 10" 1 3 exp (4.31 ± 0.08) x 10 3 /RT Second moment and l i n e w i d t h study had shown t h a t the r e o r i e n t a t i o n o f methyl groups as w e l l as the r e o r i e n t a t i o n o f the t r i m e t h y l a m i n e moiety o c c u r s i m u l t a n e o u s l y . The r e l a x a t i o n mechanism i n the temperature r e g i o n s t u d i e d can probably be ass igned to the r e o r i e n t a t i o n o f both methyl groups and the t r i m e t h y l amine moiety . In f a c t we cannot d i s t i n g u i s h the r o t a t i o n o f the t r i -methylamine moiety o r the rotat-jon o f the whole molecule a long the m o l e c u l a r a x i s . The a c t i v a t i o n energy, 4.31 + 0 .08 k c a l / m o l e , o b t a i n e d from our pulsed -130-nmr study i s lower than the v a l u e , 6 . 8 ± 0 .5 k c a l / m o l e , o b t a i n e d from l i n e w i d t h measurement. b. Summary Values o f a c t i v a t i o n energy f o r methyl group r e o r i e n t a t i o n were o b t a i n e d by a pulsed nmr technique f o r t r i m e t h y l a m i n e - h a l o g e n complexes. They are s y s t e m a t i c a l l y lower than the values o b t a i n e d from l i n e w i d t h measurement. The d i f f e r e n c e i s p a r t i c u l a r l y l a r g e f o r the i o d i n e complex. T h i s i s probably because i n the l i n e w i d t h study o f the i o d i n e complex, the two reg ions o f motional narrowing o v e r l a p more than f o r the bromine and i o d i n e c h l o r i d e complexes. -131-References [8.1] K.O. Strtfmme, A c t a Chemica S c a n d . , j_3 (1959) 268 [ 8 . 2 ] 0 . Hassel and H. Hope, A c t a Chemica S c a n d . , 14 (1960) 391 [ 8 . 3 ] C.A. Fyfe and J . Ripmeester , Can. J . Chem., 48 (1970) 2283 [ 8 . 4 ] N . Bloembergen, E . M . P u r c e l l and R.V. Pound, Phys. R e v . , 73 (1948) 679 [8 .5] R. Kubo and K. T o m i t a , J . Phys. Soc. J a p a n , 9 (1954) 888 -132-CHAPTER IX C o n c l u s i o n and Suggest ions f o r F u r t h e r Work A . C o n c l u s i o n o f the Present Work The a c t i v a t i o n energies and r a t e parameters f o r v a r i o u s types o f motion f o r the compounds s t u d i e d have been summarized i n Table 9 . 1 . Table 9.2 shows the va lues o f the c a l c u l a t e d and exper imenta l T-j minima f o r methyl group r e o r i e n t a t i o n . In a l l c a s e s , the exper imental T-j minimum f o r methyl group r e o r i e n t a t i o n i s h i g h e r than the p r e d i c t e d value even though we n e g l e c t e d the c o n t r i b u t i o n f o r i n t e r m e t h y l group c o n t r i b u t i o n s and i n t e r m o l e c u l a r i n t e r a c t i o n s . Look and Lowe [9.11 and B l i n c 19.21 have c o n s i d e r e d the e f f e c t o f h indered m o l e c u l a r r o t a t i o n between unequal p o t e n t i a l w e l l s f o r two s p i n systems upon nmr s p i n - l a t t i c e r e l a x a t i o n t i m e s . They showed t h a t s p i n - l a t t i c e r e l a x a t i o n r a t e due to such h indered r o t a t i o n i s a f f e c t e d by any d i f f e r e n c e i n the depths o f the p o t e n t i a l w e l l s of the o r d e r of kT (about 0.1 to 0 . 6 kca l/mole at 50 K to 300 K) and f o r such a case the s p i n - l a t t i c e r e l a x a t i o n r a t e should be 4a m u l t i p l i e d by a f a c t o r o f — • where a = exp ( E R - E J/kT. (Itar B 0 1 Here E^ - E^ i s the d i f f e r e n c e i n depth o f the unequal p o t e n t i a l w e l l s and i s at the o r d e r of kT. I t was thus shown t h a t the e f f e c t of hav ina E_ 4= E i s a l e n g t h e n i n g o f s p i n - l a t t i c e r e l a x a t i o n t i m e . The theory has been a p p l i e d [n an a n a l y s i s o f the s p i n - l a t t i c e r e l a x a t i o n TABLE 9.1 Activation energies (in kcal/mole) and rate parameters for various motions in addition cor^ plexes Compounds (c3)p « VB < C 3V (c3)„ '4'B Cj Diffusion £ A - 3 ' 6 3 •[••1.2x10-" EA-1.89 T ' - 3 . 4 X 1 0 - " T c c - 3 . 0 X 1 0 - " EA-3.63 -• = 1.2x10-" I c c . 1 . 7 x l 0 - " E A .3. ,0 t° .6 .16x10"" , c c . 2 . 3 x ! 0 -EA-0.7 EA-5.42 EA.19.S t l . 2 . 0 x l 0 - " c T c c - 1 . 6 x l 0 - " Me3P-A:Me3 EA-1.15 .86x10"" T .3.8x10-"-cc EA-0.75 EA=3.28 63x10"'• , c c - 1 . 5 x l 0 -EA-9.95 T £ - 1 . G 3 X 1 0 - " I c c - 9 . 6 x l O - " «* 3P-BMe 3 EA.1.47 ^-2.65x10"" T -3.4x10-" cc EA=2.14 ^•5.45x10-" , c c - 2 . S x l O - " EA.6.C0 iJ=9.8xlC"" T -1.45x10-" cc Me^H-A;y« ; 3 EA-0.89 EA-9.95 T * = D . 2 £ X 1 0 _ ) ' : c c . 9 . 6 x l 0 -- -2.5x10-" cc Me2riH-3Hc3 E.-2.69 EA-2.04 Ef-14.03 TJ-2.37x10-" T^-2.89x10"" T c c . 2 . 5 , 1 0 - " T -2.9x10-" He3P EA.2.08 T J-1.9xlO"" T - 2 . 9 x l 0 - " 7.5:2 (£H) «e3S <1 E A = 2 - 8 7 Ne3;i-BC;3 EA-2.79 E A - 1 3 - 7 9 i j -1 .3x l0"" -••9.4>1C"S* Me3N-BBr3 EA-2.68-3.24 T" - (4 .5 -8 .1)X10"" i c c - (2 .5 -2 .3)x lO-" EA-12.S0 1^-4.2x10"" , c c - 2 . 0 , 1 0 - " « e 3 N - I 2 EA-3.57 i = - 2 . 1 x l 0 " ; : •2.2x10-" cc He3N-ICl E f i'4-25 : ° - 1 . 6 x l 0 - " 4 -2 .0,10-" He3N-Br2 EA-4.31 - ' -4 .4x10-" c T c ( . - l . l x l 0 - " - Calc. t -134-TABLE 9.2 Values o f T-, minimum f o r methyl group r e o r i e n t a t i o n Compounds Methyl Group Attached to ^ T l ^ m i n . e x p t . ^ V m i n , c a l c . Me 3 N-BMe 3 Boron 36 ms 35.6 ms Me3N-A£Me3 N i t r o g e n 36 ms 35.6 ms Me 3 P-A&Me 3 Phosphorus 50 ms 35.6 ms Me 3 P-BMe 3 iPhosphorus 50 ms 35.6 ms 'Boron 52 ms 35.6 ms Me2NH-A£Me3 Ni trogen 52 ms 47 .5 ms Me 2 NH-BMe 3 ( N i t r o g e n 50 ms 47.5 ms ' Boron 34 ms 31.7 ms Me 3P Phosphorus 26 ms 17.8 ms Me3B Boron -Me3N-BC£3 N i t r o g e n 28 ms 17.8 ms M e 3 N - B B r 3 N i t r o g e n 55 - 60 ms 17.8 ms M e 3 N - I 2 N i t r o g e n 29 ms 17.8 ms Me3N-IC£ N i t r o g e n 27 ms 17.8 ms M e 3 N - B r 2 N i t r o g e n --135-i n the low temperature phase o f s o l i d hydrogen s u l f i d e £ 9 . 3 j . Although the e f f e c t o f h indered m o l e c u l a r r o t a t i o n between unequal p o t e n t i a l w e l l s upon nmr s p i n - l a t t i c e r e l a x a t i o n times has not been worked out f o r a t h r e e s p i n system, the same e f f e c t , i . e . the l e n g t h e n i n g of s p i n - l a t t i c e r e l a x a t i o n t i m e , i s expected . A d i f f e r e n c e i n p o t e n t i a l w e l l s f o r groups which undergo r e o r i e n t a t i o n can a r i s e i f v a r i o u s p o s i t i o n s of the group are non e q u i v a l e n t w i t h r e s p e c t to l a t t i c e symmetry. I t i s c o n c e i v a b l e t h a t i n some cases the energ ies might d i f f e r by kT or more. T h i s d i f f e r e n c e i n energy b a r r i e r s i s smal l compared to the observed va lues o f a c t i v a t i o n energy f o r methyl group r e o r i e n t a t i o n and i s not detected by s p i n - l a t t i c e r e l a x a t i o n s t u d y . A number o f e x p r e s s i o n s have been proposed f o r the p r e -e x p o n e n t i a l f a c t o r x 0 o f the A r r h e n i u s e q u a t i o n x = x „ ° exp (Ea/RT) , c c c the best known be ing t h a t o f E r y i n g { 9 . 4 J . R e c e n t l y , t h e r e has been renewed i n t e r e s t [9.5, 9 . 6 ] i n B a u e r ' s [9 .7] p u r e l y c l a s s i c a l t r e a t -ment. A t h i r d approach expresses the p r e - e x p o n e n t i a l f a c t o r i n terms o f frequency o f l i b r a t i o n o f the molecule i n i t s p o t e n t i a l w e l l [ 9 . 8 ] . B r o t [ 9 . 9 ] has demonstrated t h a t the t h r e e approaches a r e , i n the c l a s s i c a l l i m i t , s t r i c t l y e q u i v a l e n t . We t h e r e f o r e c a l c u l a t e the x c ° u s i n g the t h i r d approach. The l i b r a t i o n a l frequency o f the mole-c u l e i n i t s p o t e n t i a l w e l l can be c a l c u l a t e d [9 .10] by -136-f o r a molecule o r group which has a C 3 symmetry.- Here V i s the depth o f p o t e n t i a l w e l l and I i s the moment o f i n e r t i a o f the r o t o r . The c o r r e l a t i o n time f o r r e o r i e n t a t i o n o f the group s h o u l d be g i v e n by x 0 = l / 2 l T v , . The c a l c u l a t e d va lues are w i t h i n one o r two orders c l i b o f magnitude o f the exper imenta l values f o r the r e o r i e n t a t i o n o f methyl groups and are always s m a l l e r , as one should e x p e c t , than the experimental v a l u e s . For the r e o r i e n t a t i o n o f a moiety o r a molecule about the c e n t r a l bond, however, the d i f f e r e n c e i s , i n some c a s e s , very l a r g e , and the c a l c u l a t e d va lue i s o f t e n l a r g e r than the experimental v a l u e . This l a r g e d e v i a t i o n i n an improbable d i r e c t i o n may be due to l a t t i c e expansion and thus t o temperature dependence o f the a c t i v a t i o n energies [ 9 . 1 1 ] . A q u a l i t a t i v e c o n c l u s i o n can be made t h a t the a c t i v a t i o n energy f o r methyl group r e o r i e n t a t i o n depends to a f i r s t approximat ion on the c e n t r a l atom to which the three methyl groups are a t t a c h e d . The l o n g e r the c a r b o n - c e n t r a l atom bond i s the lower the a c t i v a t i o n energy i s . Thus the a c t i v a t i o n energies f o r the t h r e e methyl groups a t t a c h e d to v a r i o u s c e n t r a l atoms are i n the o r d e r N > C > B > S i > A£ 19 .12 , 9 . 1 3 , 9 . 1 4 ] . We may now t u r n to the a c t i v a t i o n energies of methyl groups i n t r i m e t h y l amine complexes. The a c t i v a t i o n energ ies f o r methyl group r e o r i e n t a t i o n i n the t r i m e t h y l a m i n e complexes f o l l o w the t r e n d o f s t a b i l i t y o f the complexes ,* i . e . the a c t i v a t i o n energy decreases when the s t a b i l i t y o f the complex i n c r e a s e s , i f we assume t h a t the i n t e r m o l e c u l a r i n t e r a c t i o n s f o r the methyl group r e o r i e n t a t i o r * M e 3 N - B r 2 , Me 3 N-ICA decompose at about 25°C, K p = 0.47 f o r Me 3 N-BMe 3 a t 100°C, M e 3 N - I 2 decomposes at 66°C, K p f o r Me3N-A£Me3 i s too smal l to measure a t 150°C and Me 3NBC£ 3, M e 3 N - B B r 3 are s t a b l e at 240 C [9.21 - 9.23.]. -137-are smal l and have the same o r d e r . T h i s t r e n d i s not s u r p r i s i n g s i n c e the a c t i v a t i o n energy f o r methyl group r e o r i e n t a t i o n i n a t r i m e t h y l -amine moiety i s a f f e c t e d predominant ly by the CNC bond angle and C-N bond l e n g t h . As the n i t r o g e n forms a new a bond, the CNC bond angle w i l l expand and the C-N bond w i l l lengthen [ 9 . 1 5 ] . Bj Suggest ion f o r F u r t h e r Work The prev ious chapters have shown the r e s u l t s o f s p i n - l a t t i c e r e l a x a t i o n time and second moment s t u d i e s on some a d d i t i o n complexes of main group I I I and V elements between 77K and t h e i r m e l t i n g p o i n t s . The r e s u l t s can be e x p l a i n e d q u i t e s a t i s f a c t o r i l y i n terms o f v a r i o u s types o f m o l e c u l a r motion i n the s o l i d s t a t e , and the a c t i v a t i o n energies and r a t e parameters o f the m o l e c u l a r motions were e x t r a c t e d . However, there are some r e s u l t s which are u n c e r t a i n , e s p e c i a l l y the a c t i v a t i o n energy o f the d i f f u s i o n process i n some compounds. The s p i n - l a t t i c e r e l a x a t i o n t imes cannot be r e s o l v e d w i t h o u t unambiguity immediately below the m e l t i n g p o i n t because the frequency o f the d i f f u s i o n process i s not h igh enough t o g i v e an overwhelming r e l a x a t i o n mechanism below the m e l t i n g p o i n t . The a c t i v a t i o n energy f o r the d i f f u s i o n process i n t r i m e t h y l p h o s p h i n e - t r i m e t h y l b o r a n e i s abnormal ly low i n comparison to t h a t i n h e x a m e t h y l d i s i l a n e , hexamethyl-ethane, o r t r i m e t h y l a m i n e - t r i m e t h y l a l u m i n i u m , f o r a l l o f which the m o l e c u l a r s t r u c t u r e s are very s i m i l a r . To determine the a c t i v a t i o n energy a c c u r a t e l y f o r d i f f u s i o n p r o c e s s , a study o f r e l a x a t i o n times i n the r o t a t i n g frame, T^p, i s necessary . T h i s technique f -138-enables one to s tudy the low frequency m o l e c u l a r motions [ 9 . 1 6 , 9 . 1 7 ] , and t o exc lude o t h e r high frequency m o l e c u l a r m o t i o n s . Another t e c h n i q u e , which i s a v a i l a b l e i n our l a b o r a t o r y , i s to s tudy the d i f f u s i o n constant by the p u l s e d - g r a d i e n t , sp in-echo method [9.18 - 9 . 2 0 ] , More i n f o r m a t i o n on the nature o f methyl group r e o r i e n t a t i o n can be o b t a i n e d f o r those a t t a c h e d to b o r o n , phosphorus and aluminium i f the study i s pursued down to l i q u i d he l ium temperature , where the t u n n e l l i n g e f f e c t may become i m p o r t a n t . Very l i t t l e nmr study has been done i n the s o l i d s t a t e on the a d d i t i o n complexes of group I I I and group V , or group I I I and group VI e lements . A d e t a i l e d study o f these complexes would l e a d to the a c t i v a t i o n energ ies and r a t e parameters f o r methyl groups at tached to a wide range o f c e n t r a l atoms, as w e l l as to a c t i v a t i o n energies and r a t e parameters r o t a t i o n about the bond formed by . groups I I I and V , and by groups I I I and VI elements i n the s o l i d s t a t e . -139-References [9.11 D.C. Look and I . J . Lowe, J . Chem. Phys. 44 (1966) 3437 [9.23 R. B l i n c , Advances i n Magnetic Resonance, e d . Waugh, A . P . , 1968, v o l . 3 , p . 166 [9.31 D.C. Look, I . J . Lowe and J . A . N o r t h b y , J . Chem. Phys. 44 (1966) 3411 19.4] S. G l a s s t o n e , K . J . L a i d l e r and H. E y r i n g , The Theory o f Rate P r o c e s s , McGraw H i l l , New Y o r k , 1941 B . 5 ] M. D a v i e s , J . Chim. Phys. 63 (1966) 67 B . 6 ] A . B o n d i , J . A . C . S . 88 (1966) 2131 B . 7 ] E. Bauer , C a h i e r Phys. No. 20 (1944) 1 [9 .8] H. F r b h l i c h , Theory o f D i e l e c t r i c s , Clarendon P r e s s , Oxford 1949, p.78 [9 .9] C. B r o t , Chem. Phys. L e t t . 3 (1969) 319 [9 . IO] I . Darmon and C. B r o t , M o l . C r y s t . 2 (1967)301 1 9 . I l l C. B r o t , D i s c , o f Faraday Soc. 48 (1969) 213 [9.12] S. A l b e r t , H . S . Gutowsky and J . A . R i p m e e s t e r , J . Chem. Phys. 56 (1972) 1332 I9 .13J J . M . Chezeau, J . Dufoureq and J . H . S t r a n g e , M o l , Phys. 20 (1971) 305 I9 .14J Present S t u d i e s l 9 . 1 5 J M.C. Day and J . S e l b i n , T h e o r e t i c a l I n o r g a n i c C h e m i s t r y , R e i n h o l d , 1965, p. 210 -140-[9.16] D.C. Look and I . J . Lowe, J . Chem. Phys. 44 (1966) 2995 [9.17] D.C. Look and I , J . Lowe, J . Chem. Phys, 44 (1966) 3437 [9.18] E.O. S t e j s k a l and J . E . Tanner , J . Chem. Phys. 42 (1965) 288 [9 .19] J . E . Tanner , J . Chem. Phys. 52 (1970) 2523 19.20.] J . E . Tanner, J . Chem. Phys. .56 (1972) 3850 [9.21] K.O. Str^mme, A c t a Chemica S c a n d . , 1_3 (1959) 268 [9.22] 0 . Hassel and H. Hope, A c t a Chemica S c a n d . , J_4 (1960) 391 [9.23] F . G . A . S t o n e , Chem. R e v . , 58 (1958) 101, and the re ferences t h e r e i n -141-APPENDIX A > 2 " .'. D I M E N S I O N X(31 ) , Y(30),MZ(30 ) , J T(30 ) , F(30),RMZ(3Q) > 3 hG5 READ ( 5 , 2 0 ) M,MO, TEMP, SCALE > k 20 FORf 1AT ( 2 I 3, F 1 1 . 0 , A ' i ) > 3 ;;RI TLC C # i * 3 ) T E M P > G !»3 F 0 R i ! A T ( / / , 2 X , F 7 . 1, ' IC' ) > 7 Rf10=|10 > C, RM2 = 2.*RfSn > 9 READ, ( J T ( I ), I = l,fi) > 10 v.R I TL ( C, 14 0 ) (JT ( I ), I = 1,i) > 11 !»•" FORMAT(251 5) > 12 R E A D , ( M Z ( I ) , I - 1 , M ) > 17 W R I T F C / i l ) (MZ( I ), I =1 ,10 > lh kl FOR,'.AT (251 5) > 15 no so 1=1,11 > 1 5 X ( I ) = J T ( I ) > 17 P.MZ( l ) = M Z ( I ) > 1 2 F( I ) = (RM0-Rf1Z( I ) ) /RM2 > m Y ( 1 ) = A L O H ( F ( 1 ) ) > 2 0 30 COLT r u e > 7 1 l - ' R I " ' r ( r / ; L 2 ) ( F d ) , i « i , M ) > 22 U2 F O R t i A T ( 2 5 F 5 . 3 ) > 23 S U M » n . > 2h S U M V - n . > 2 5 PO 2 .™ 1 = 1 , ? ' > ?G SUJ1X«SUU>. + X( I ) > 2 7 SUMY = StJ«":Y + Y ( I ) > 2 3 2 0 0 CONTINUE > 2 1 Af i=f > 3 0 ;.,w=suf::;/.\i" > 31 YAV = SU?'-Y/Af-: > 32 D I ! : A Y = ^ . > 3 3 n i F X S f s O . > 3't 00 3 " 1 1=1,;' , > 3 5 0 I FX Y = D I F X Y + ( X ( I ) - X A V ) * Y ( I ) > 3n 3 ™ Dl F X S O * P I FXr»f;+(X( I ) - X A V ) * * 2 > 3 7 C = D I F ; ; Y / D I F ; ^ U > 5r> B O Y A Y - O X A V > 3 : 1 D 3 Q = 1 . > uo y s - > i . ' ; 1 DO 3 : U 1=1,:' > f* 2 PSO = [)hQ+ (BB + C* X (I ) - Y ( I ) ) * * ? . > !*3 311 / r»i>-X5(.i + X ( I ) * * 2 > ?t5 nF.t>A.- i*xs^ - ( A f :*xAY ) * * ? > U'\ noVRTD = ^ /?-rT (D!;r) > H7 STDniC=onvr7r*f : "PT(.*r) > »»3 STIll ,s i ; (V/RTP*W.T(Xr>r ; ) -142-> It 9 E R R = - S T D E R C / C * 1 0 0 . > 50 T l=-1 . / C > 51 V.'P 1 T E ( 0 ,50 ) T l , S C A L E > 52 50 FORf'AT( / , 2X , ' T l = IN \Ah) > 57, W R I T E(n,51) ERR I r; • F r 7J \ / 5U 51 FORMAT(2X, ' ERROR 1 H SLo r r / 5 5 CO TO hC5 > 56 i:!JD > 5 7 $ DATA APPENDIX B > 1 $ COMPILE > 2 C MX PER I HEl-.'TAL SECOND MOM! NT 5 > 3 DIMENSION Ji ( 52 ), A (2 ) , B (7 ) , 5 ( 2 ) > k WRI TE ( C ; , 2 7) > 5 27 FOP...AT(i:<, 'TRACE',2X, 'TEnP ' , i>X , ' S ( l ) ' , 3 X , ' S ( 2 ) ' , ' s X , ' SECOWP MO.MFVT' > H 1,UX,'LI.\'F V.' I DTI! 1 , f> X, 'SCAN',5X, ' MOODLAT I OTJ 1 ) > 7 READ ( 5 , ? n ) K, L , J , X , Y , KTFNP, DE LTA ; !, (fi ( I ) , l = l , 5 2 ) > Z 2?) FORHAT(AU,2 H i , FH . 3,F7.3,I 5,Ffi . ? / ? GI3/2GI 3 > > ) AL I f'i:=2. °*X*0ELTA!! > 10 DO 1 !.= 1 , 2 > 11 A(r,)=n. > 12 1 E (!,)=•!. > 13 DO 21 1 = 1 ,L > l i t A ( l ) = A ( i ) + F L O A T ( i * i * i *r;{ I }) > 15 D ( l ) = B ( l ) + F L O A T ( l * K ( l ) ) > li> 21 CONTINUE • > 17 DO 22 ! = 1 , J £ > 18 A(2)=A(2)+ FLOAT ( 1 * 1 * 1 * N (1+2 CO) V* > i n C(2 ) = B(2)+ FLOAT ( l * N ( l + 2 E ) ) > 2 0 2 2 CONTINUE > 21 DO 2b M = l , 2 > 22 S(M)= 0.333*X*X*A(f - i)/B(f1)-0.?5*Y*Y > 23 2P CONTINUE > ?h SM= 0 .5* ( 5 ( 1 ) + S(2>) > 2 5 WRI TE (P , , 2C)K, KTEMP, S ( 1 ) , S( 2 ), SM, AL I NE, X , Y > 26 23 FORnAT(lX,A5JE,lX,2F7.2,5X,F7.2,5X,Fll.?,5X,F7.3,5X,F3.3) > 27 CO TO 19 > 2 3 END > 21 $DATA > 30 SSTOP -144-U J a U. c: IT c a. o cc C J CM + + i i i i I i i U ) R - C cr. ~* IT, cc CO o C : LT. U l < I— Li. o o c-U~| LTl 1 ^ h- U. — s c-<-» s — cr *-» S w\ o a. «— < ::: <J o U J H C ' (- I- a zz :_: u. o c r. to </: < CO a. a. * * ro co c:. . c* r i N i n • — . zz \~ z. <-< cz u. - o G t: M < y—\ - — i c ' w s h -i n «"i u : n u. u < < 1 U l I c o c a: Of. <; ca a, a. 1Z c-i ZZ o h H h o «. s O < O a r H r - ZZ * R - T ~ < < O ^ •>> ui ui c a. i r > C III r H C" r l H \ t_l o • O Ls_ (._> CM c K> H — L.n . L"> I— • I— <x s - » <c o - D U D » 3 < ^ < CZ 't y L u. L' o O * cc C" a. UJ R -* co < CJ X X * * • • I + + *—. ^ CM * -K c o o o ^» * • < ca w — rH >i >< <C w w + + H H . . 1—1— w v-> V , cn "*N * s . « - < ^ cz *—• — — * rH a. i - H * a. x x W W * o r H I— I CO < a. i ; P ' s «. f j ^> < IJJ U l • I— -t I I I i n r H rH Ul o X II c-.!. . r-i • o • * cz o II —^» II II < ca f-H rH (— t_ < r H r H | -l ~ II r~- r H f ' zzz C ! r H U l \ w <^ w J ~ •—• < — E; H-1~ c: — c C a: I X . c u. c r i to c-. » w % ir~- I-i_- < w u. :~ U J h- c i o — a: u. cz liz C X > I A N UJ «. w c. tc :— i w < i ui zz i h- OZ I — o I o: U. I a. « U . L U I— ^ r_ c-^  C-J \ Ct r H r H ^ . ti-ll * o UJ — t:r w 2 w H L J >C — CM h r i h O a- o O o ::: u. o o o y— o c. CJ CJ c CM O r H o rA CM N*l CM rH H CM K>, in ' j s t o cr c-i u-\ e: r- C J cn o r H CM K> J LA ta i - - <>- c- c: H N I A j w a s to c o rH r H rH rH r H r H rH r H C1 C) C-J C-J C-J C-J CJ M n ^ f A n i ' M A ^ r A ^ K M ' l _-f / \ /"s / \ / " \ . ' \ / \ / ' N / * • . / \ ^ /^S / \ / \ / \ / \ / \ / * \ / \ / \ /^V ^ 

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