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NMR studies of molecular dynamics of some organic salts and charge transfer complexes Williams, Donald Shanthakumaran 1978

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NMR STUDIES OF MOLECULAR DYNAMICS OF SOME ORGANIC SALTS AND CHARGE TRANSFER COMPLEXES by DONALD SHANTHAKUMARAN WILLIAMS B.Sc. (Hons.), University of S r i Lanka, Colombo Campus, 1971 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Chemistry) We accept t h i s thesis as conforming to the required standards. THE UNIVERSITY OF BRITISH COLUMBIA October, 1.97 7 © Donald Shanthakumaran Williams, 197 7 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f f//g»7/J in^y  The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook P l a c e V a n c o u v e r , B. C , Canada V6T 1W5 Da t e /i^v- 3-~3f / ? 7 7 S u p e r v i s o r : C. A. McDowell ABSTRACT Nuclear 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 time measurements have been c a r r i e d out on the tro p o l o n e s a l t of t-butylamine, (CH 3) 3CNH 3Tr~ (Tr = t r o p o l o n a t e i o n , C 7 H 5 0 ~ ) , the c h o l i n e s a l t s , (CH 3) 3NCH 2CH 2OH. X~ (x~ = C l ~ , Br , I , ClO^ ) and the trimethylamine-phosphorous penta-f l u o r i d e adduct, (CH 3) 3NPF,-, i n order to study molecular motion and phase t r a n s i t i o n s i n these systems i n the s o l i d s t a t e . 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 the motional processes are r e p o r t e d . Proton magnetic resonance (pmr) a b s o r p t i o n second moments and proton s p i n - l a t t i c e r e l a x a t i o n times i n the Zeeman frame (T^) i n the temperature range 66K - 425K f o r + the s o l i d (CH 3) 3CNH 3Tr show t h a t the molecule i s r i g i d on the nmr t i m e s c a l e a t the lowest temperature s t u d i e d , w h ile at higher temperatures r o t a t i o n of methyls about t h e i r C 3 symmetry axes i s found to s e t i n f i r s t , f o l l o w e d by an a d d i t i o n a l composite motion i n v o l v i n g r e o r i e n t a t i o n of both the t - b u t y l group and the NH 3 group about the C-N bond. A proton study i n the p a r t i a l l y d e u t e r a t e d (-ND3) analogue has enabled the r e l a x a t i o n e f f e c t s of the l a t t e r two motions to be separated, and, by f i t t i n g the T, data f o r the two compounds to appropriate relaxation rate expressions, a c t i v a -t i o n a l energy barriers for the abovementioned motional processes have been determined. It has also been suggested that the + t-butyl group and the NH^ group rotate independently about the C-N bond rather than as one unit. Proton s p i n - l a t t i c e relaxation time measurements in both the Zeeman and rotating frames of reference (T^ and T^ p) for the four choline s a l t s and second moments of the pmr absorption for the perchlorate have enabled the following motional processes to be i d e n t i f i e d : (i) rotation of the methyl groups at low temperatures followed successively by, ( i i ) the onset of motion of the NMe^ moiety about the long chain C-N axis (denoted C^), ( i i i ) general reorientation of the whole choline cation, (iv) additional slow motion of the long chain (CF^CI^OH in the case of the chloride and bromide, and (v) d i f f u s i o n of the choline ion i n the case of the iodide and perchlorate. From a quantitative analysis of the and data, a c t i v a t i o n energies for the above types of motion are determined. A c r y s t a l - c r y s t a l phase t r a n s i t i o n known to occur at 353, 364 and 362K in the chloride, bromide and iodide, respectively, has been confirmed. A similar t r a n s i t i o n has been discovered in the perchlorate, and i s found to occur at a much lower temperature (272K). Evidence has also been presented for a further c r y s t a l -c r y s t a l phase t r a n s i t i o n i n choline iodide at 430K, at which - i v -point a "quenching" of the d i f f u s i o n a l process i s found i n th i s structure. In the adduct (CH^J^NPF,-, studies of proton and flu o r i n e nmr absorption spectra and measurements have shown that (i) at 4.2K the molecule i s ' r i g i d 1 , ( i i ) reorientation of one of the methyls and reorientation of the PF,. group 1 19 about the P-N bond cause a H and F nmr l i n e narrowing, ( i i i ) t h i s i s followed by the rotation of the other two methyl groups together with the rotation of the (CH-^^N group about the P-N bond. These are confirmed by a success-f u l simulation of the observed pmr lineshapes at 4.2K and at 7 7K. The proton and flu o r i n e T^ data show the ~*"H and 19 F spins to be strongly coupled. A study of f l u o r i n e T^ in the f u l l y deuterated compound, (CD^J^NPF^ has enabled the analysis of the o v e r a l l T^ data to be s i m p l i f i e d . The observed trends in the T^ data are seen to be well explained by the theory for a coupled spin system of two unlike spins. - v -TABLE OF CONTENTS Page ABSTRACT i i LIST OF FIGURES v i i i LIST OF TABLES x ACKNOWLEDGEMENTS x i CHAPTER I: INTRODUCTION . 1 CHAPTER I I : BASIC THEORY OF NUCLEAR MAGNETIC RESONANCE 6 2.1 Elementary magnetic resonance theory 6 2.2 Dipolar i n t e r a c t i o n 11 2.3 Absorption spectra for r i g i d structures. ... 13 2.4 Complicated systems - method of moments. ... 16 2.4.1. Second moment and VanVleck formula. 16 2.4.2. Second moment and the free induction decay 18 2.5 Molecular motion 20 2.6 Spin l a t t i c e relaxation 24 2.6.1. Correlation functions, spectral densities 24 2.6.2. Relaxation of a system of l i k e nuclei i n laboratory frame 26 2.6.3. Relaxation of a system of l i k e nuclei i n the rotating frame 34 2.6.4. Relaxation of a system of unlike nuclei 35 2.6.5. Correlation times and ac t i v a t i o n energies from relaxation time measurements 37 - v i -Page References. 4 0 CHAPTER I I I : APPARATUS AND METHODS OF MEASUREMENT 44 3.1 Continuous wave measurements 44 3.1.1. Wideline NMR spectrometer 1 44 3.1.2. Calibr a t i o n of the spectrometer 45 3.1.3. Variable temperature assembly 4 5 3.1.4. Wideline spectrometer II 46 3.1.5. Linewidth and second moment measurements 47 3.2 Pulsed NMR measurements 48 3.2.1. Pulse spectrometer 48 3.2.2. Variable temperature assembly 52 3.2.3. Measurement of T^ 53 3.2.4. Measurement of Tj 54 References 55 CHAPTER IV: MOLECULAR MOTION IN T-BUTYLAMMONIUM TROPOLONATE 56 4.1 Introduction 56 4.2 Experimental 58 4.2.1. Sample preparation 58 4.2.2. Spectrometers 59 4.3 Results 60 4.3.1. Continuous wave measurements 6 0 4.3.2. Relaxation time measurements 7 0 4.4 Discussion 88 References 92 CHAPTER V: MOLECULAR MOTION AND PHASE TRANSITIONS IN SOLID CHOLINE CHLORIDE, BROMIDE, IODIDE AND PERCHLORATE 9 6 5.1 Introduction 96 - v i i -Page 5.2 Experimental 101 5.2.1. Sample preparation 101 5.2.2. Spectrometers 102 5.3 Results. 103 5.3.1. Second moments 103 5.3.2. Relaxation time measurements 108 a) Choline chloride 108 b) Choline bromide 121 c) Choline iodide 125 d) Choline perchlorate 138 5.4 Summary 14 3 References 144 CHAPTER VI: MOLECULAR MOTION IN PHOSPHOROUS PENTA-FLUORIDE-TRIMETHYLAMINE ADDUCT 14 7 6.1 Introduction 147 6.2 Experimental 148 6.2.1. Sample preparation 148 6.2.2. Spectrometers 149 6.3 Results 150 6.3.1. Second moments 150 6.3.2. Lineshape analysis 156 6.3.3. Relaxation time measurements 159 a) Overall relaxation data 159 b) 1 9 F relaxation i n (CD 3) 3NPF 5 (II). 163 c) *H and 1 9 F relaxation i n (CH3) 3NPF5 (I) 165 (i) High temperature region (T>150K) 165 ( i i ) Low temperature region (T<140K) 171 References 174 CHAPTER VII: CONCLUSIONS 175 APPENDIX NMR ABSORPTION LINESHAPE FOR A TRIANGULAR CONFIGURATION OF NUCLEI .. 182 - v i i i - -LIST OF FIGURES Figure Page 2.1 Theoretical magnetic resonance lineshapes for a triangular configuration of protons. ... 15 2.2 Motional model assumed i n Dunn and McDowell ca l c u l a t i o n 31 3.1 Block diagram for the pulse spectrometer 49 3.2 C i r c u i t diagram for the s i n g l e - c o i l nmr probe used in the pulse spectrometer 51 4.1 Temperature dependence of the linewidths and second moments of the proton magnetic reson- .. ance absorption for tropolone s a l t of t-butylamine 61 4.2 Representative proton magnetic resonance lineshapes for tropolone s a l t of t-butylamine at four selected temperatures. 62 4.3 Temperature dependence of the proton spiiji l a t t i c e relaxation times, T x for (CH 3) 3CNH 3Tr , (CH 3) 3CND 3Tr - and NH3 71 4.4 Temperature dependence of c o r r e l a t i o n times for C 3 reorientation of methyls 81 4.5 Temperature dependence of c o r r e l a t i o n times for C 3 motion o_f the t-butyl group and C 3 motion of the NH 3„ group 82 5.1 Temperature dependence of the proton second moment in choline perchlorate 104 5.2 Temperature dependence of the proton Ti and T i of choline chloride 109 5.3 Temperature dependence of c o r r e l a t i o n times for methyl reorientation i n choline chloride, bromide, iodide, and perchlorate I l l 5.4 Temperature dependence of the proton T± and T 1 d of choline bromide 122 - ix Figure Page 5.5 Temperature dependence of the proton Ti and Tip of choline iodide 126 5.6 Oscillograph traces of the FID's for choline iodide at s ix selected temperatures. 131 5.7 Temperature dependence of proton T 2 and second moments for choline iodide i n phases II and III 132 5.8 Temperature dependence of the c o r r e l a t i o n times for s e l f d i f f u s i o n of the choline ion in phases II and III of the iodide 136 5.9 The DTA thermograms for choline iodide 139 5.10 Temperature dependence of the proton Tj and T i p of choline perchlorate 140 6.1 Temperature dependence of the proton second moment for trimethylamine-PF 5 adduct 151 6.2 Simulation of pmr lineshapes for trimethyl-amine-PF5 adduct 157 6.3 Temperature dependence of the proton and flu o r i n e T1's for (CH 3) 3NPF 5 and (CD 3) 3NPF 5 160 6.4 The high temperature proton Tiiminimum i n (CH 3) 3NPF 5 a f t e r removing the e f f e c t of the fluorines 170 A . l Energy l e v e l diagram for three spin-1/2 nuclei 183 X LIST OF TABLES Table Page 4.1 Proton coordinates (in Angstrom units) of the t-butylammonium cations and the tropolonate anion 64 4.2 Calculated second moment contributions (Gauss 2) for the t-butylamine-tropolone adduct 68 4.3 Experimental T x minima for t e r t i a r y butylamine-tropolone adduct 7 3 4.4 Calculated minima (in millisecond) for t e r t i a r y butylamine-tropolone adduct 7 8 4.5 ' B e s t - f i t ' parameters to the T x data for t-butylamine-tropolone adduct 8 6 5.1 Theoretical 1R second moments for various possible motional models of the choline ion 105 5.2 Experimental and calculated values for T l p minima in phase I of choline chloride, bromide, iodide and perchlorate 116 5.3 Summary of acti v a t i o n energies in kcal mole" 1 for the molecular motions proposed for choline ion i n the chloride, bromide, iodide and perchlorate 120 6.1 Theoretical *H second moments for trimethyl-amine-PF5 adduct. -. . . . . 154 - x i -ACKNOWLEDGEMENTS I would l i k e to thank my research dir e c t o r , Professor C. A. McDowell, for introducing me to the f i e l d s of broad-l i n e and pulsed nmr, and for his guidance, encouragement and support. My most sincere thanks to Dr. P. Raghunathan for his continual int e r e s t and guidance throughout t h i s work and for the many unt i r i n g hours devoted during the writing of this thesis. I also wish to express my gratitude to Professor B. A. Dunell and Professor E. E. Burnell for the i r useful discus-sions and suggestions. I g r a t e f u l l y acknowledge the s k i l l f u l technical assistance of the electronic, mechanical, glassblowing and microanalysis services; a special word of thanks to Mr. T. Marcus of the Electronics Shop for the maintenance of the spectrometers. I am indebted to my wife, Mangay for her constant encouragement and moral support, and her help in the preparation of t h i s manuscript. I am thankful to the Canadian Commonwealth Scholarship and Fellowship Commission for a scholarship and to the University of S r i Lanka for granting me leave of absence. F i n a l l y , I wish to thank a l l my colleagues and friends for t h e i r encouragement and help. My thanks are also due to Ms. P h y l l i s Moore for neatly typing t h i s manuscript. - x i i -To my m o t h e r - 1 -CHAPTER I INTRODUCTION Many o f t h e most f a s c i n a t i n g p r o b l e m s i n p h y s i c s and c h e m i s t r y a r e c o n c e r n e d w i t h t h e m o t i o n o f atoms and m o l e c u l e s . G ases and l i q u i d s , on t h e one hand, p o s s e s s much r o t a t i o n a l and t r a n s l a t i o n a l f r e e d o m and s o l i d s , on t h e o t h e r , g e n e r a l l y p o s s e s s v e r y l i t t l e . T h e r e a r e , however, e x c e p t i o n s t o t h e s e g e n e r a l i z a t i o n s , and some s o l i d s have been known t o e x h i b i t r o t a t i o n o f i n t r a m o l e c u l a r g r o u p s as w e l l as o f who l e mole-c u l e s (or i o n s ) and t r a n s l a t i o n a l d i f f u s i o n o f atoms, i o n s and m o l e c u l e s . O ver t h e p a s t t h r e e d e c a d e s , n u c l e a r m a g n e t i c r e s o n a n c e (nmr) has p r o v e d t o be a v a l u a b l e and p o w e r f u l t o o l i n t h e s t u d y o f a t o m i c and m o l e c u l a r m o t i o n i n t h e s o l i d s t a t e [ 1 . 1 - 1 . 3 ] . A t o m i c and m o l e c u l a r m o t i o n m o d u l a t e s t h e m a g n e t i c d i p o l a r i n t e r a c t i o n between t h e a t o m i c n u c l e i , w i t h t h e r e s u l t o f n a r r o w i n g t h e nmr s p e c t r u m i n a manner w h i c h depends on t h e n a t u r e o f t h e m o t i o n . Thus, t h e s t u d y o f r e s o n a n c e a b s o r p -t i o n s p e c t r u m g i v e s i n s i g h t i n t o t h e n a t u r e o f t h e m o t i o n , - 2 -w h e t h e r i t be o n l y v i b r a t i o n a l h i n d e r e d r o t a t i o n o f a g r o u p o r o f a whole m o l e c u l e , r e o r i e n t a t i o n p r e d o m i n a n t l y a b o u t one a x i s , i s o t r o p i c t u m b l i n g , o r t r a n s l a t i o n a l d i f f u s i o n . S i n c e t h e s e m o t i o n s a r e u s u a l l y t h e r m a l l y a c t i v a t e d , t h e s t u d y o f m a g n e t i c r e s o n a n c e s p e c t r a o f t h e n u c l e i i n v o l v e d i n t h e m o t i o n f r o m a v e r y low t e m p e r a t u r e , where t h e s e m o t i o n s a r e f r o z e n (on t h e nmr t i m e s c a l e o f ^10 ~* s e c ) , t o h i g h e r t e m p e r a t u r e s (up t o t h e m e l t i n g p o i n t where e x t e n s i v e m o t i o n i s e x p e c t e d t o p r e v a i l ) show t h e p r o g r e s s i v e a p p e a r a n c e o f d i f f e r e n t modes o f m o t i o n . M o t i o n becomes p r o g r e s s i v e l y more g e n e r a l as t h e t e m p e r a t u r e i s i n c r e a s e d . The t e m p e r a t u r e d e pendence o f t h e nmr s p e c t r u m f r e q u e n t l y s u f f i c e s t o e s t a b l i s h t h e e x i s t e n c e and t h e n a t u r e o f t h e m o t i o n . The f l u c t u a t i o n s i n t h e d i p o l a r i n t e r a c t i o n , b r o u g h t a b o u t by m o l e c u l a r m o t i o n , a l s o i n d u c e t r a n s i t i o n s between t h e n u c l e a r m a g n e t i c e n e r g y s t a t e s and t h u s s e r v e as t h e a l l -i m p o r t a n t s o u r c e o f t h e mechanism f o r e n e r g y t r a n s f e r between t h e s p i n s y s t e m and t h e o t h e r d e g r e e s o f f r e e d o m [ 1 . 4 ] . T h i s e n e r g y exchange 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 i s c h a r a c t e r i z e d by t h e q u a n t i t y " 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 " . Measurements o f t h e t e m p e r a t u r e d e p e n d e n c e o f t h i s r e l a x a t i o n t i m e p r o v i d e a measure o f t h e r a t e o f n u c l e a r m o t i o n and hence e n a b l e t h e k i n e t i c s o f t h e m o l e c u l a r m o t i o n ( r a t e s o f r e o r i e n t a t i o n and a c t i v a t i o n e n e r g y b a r r i e r s ) t o be s t u d i e d . I n a d d i t i o n , s i n c e c r y s t a l - c r y s t a l p h a s e t r a n s i t i o n s u s u a l l y - 3 -accompany a change i n t h e r a t e s o f m o l e c u l a r r e o r i e n t a t i o n s i n t h e c r y s t a l , r e l a x a t i o n t i m e measurements a l s o p r o v i d e a good means o f d e t e c t i n g t h e s e . The nmr method f o r s t u d y i n g m o l e c u l a r m o t i o n has s e v e r a l a d v a n t a g e s o v e r t h e o t h e r known methods s u c h as t h e r m o d y n a m i c measurements, X - r a y d i f f r a c t i o n , d i e l e c t r i c measurements, e t c . Thermodynamic and X - r a y methods a r e o n l y s e n s i t i v e t o r e o r i e n t a t i o n p r o c e s s e s w h i c h i n t r o d u c e d i s o r d e r . F o r example, m o t i o n o f a m o l e c u l e between e q u i v a l e n t p o s i t i o n s where no d i s o r d e r i s p r o d u c e d w i l l n o t be d e t e c t e d by t h e a b o v e - m e n t i o n e d t e c h n i q u e s . T h i s i s i n d e e d a s e r i o u s l i m i t a -t i o n s i n c e many r e o r i e n t a t i o n a l p r o c e s s e s i n t h e s o l i d s t a t e a r e f a v o u r e d by h i g h symmetry. D i e l e c t r i c measurements, on t h e o t h e r hand, r e q u i r e a change i n t h e e l e c t r i c d i p o l e moment t o be b r o u g h t a b o u t by t h e m o t i o n and t h u s e x c l u d e t h e sym-m e t r i c a l m o l e c u l e s l i k e b e n z e n e . The nmr method, however, i s n o t hampered by any o f t h e above l i m i t a t i o n s , and has t h e added a d v a n t a g e t h a t i t d i r e c t l y m e a sures t h e "jump f r e q u e n c y " o f t h e m o t i o n . The f a c i l i t y w i t h w h i c h t h e "*"H n u c l e u s may be s t u d i e d by nmr makes i t a good s u p p l e m e n t a r y t e c h n i q u e f o r X - r a y d i f f r a c t i o n , w h i c h does n o t 'see' h y d r o g e n atoms. The h i g h s e n s i t i v i t y o f t h e nmr s p e c t r u m t o t h e r e l a t i v e d i s p o s i t i o n o f t h e s p i n sometimes a l l o w s s t r u c t u r a l i n f o r m a t i o n t o be o b t a i n e d [ 1 . 5 ] . - 4 -I n t h i s d i s s e r t a t i o n , t h e t e m p e r a t u r e d e p e n d e n c e s o f a b s o r p t i o n s p e c t r a a r e i n g e n e r a l u s e d t o d e t e c t and i d e n t i f y any m o l e c u l a r m o t i o n s t a k i n g p l a c e , and t h e t e m p e r a t u r e d e p e n d e n c e s o f t h e 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 a r e u s e d t o c o n f i r m and p r o v i d e k i n e t i c d a t a o f t h e s e m o t i o n a l p r o c e s s e s . The s y s t e m s c h o s e n a r e s m a l l , n e a r l y s p h e r i c a l , m o l e c u l e s c o n t a i n i n g CH_ g r o u p s and a h i g h i n t e r n a l symmetry, namely, + _ + _ _ _ _ _ _ ( C H 3 ) 3 C N H 3 C-H 0_ f (CH 3) 3NCH 2CH 2OH X (X =C1 , B r ,1 ,C1C>4) and (CH 3) 3NPF,-. The h i e r a r c h y o f m o t i o n s i s s t u d i e d i n t h e s e s y s t e m s o v e r a r a t h e r wide t e m p e r a t u r e r a n g e , and t h e v a r i o u s m o t i o n a l p r o c e s s e s c h a r a c t e r i z e d . References [1.1] E.R. Andrew and P.S. A l l e n , J . Chim. Phys. 63, 85 (1966). [1.2] P.S. A l l e n , M.T.P. I n t e r n a t i o n a l Review of Science, P h s y i c a l Chemistry S e r i e s I, V o l . 4, p. 41 (1972). (C.A. McDowell, ed.). [1.3] C.A. F y f e , M o l e c u l a r Complexes (R. F o s t e r , ed.) (Elek Science, London (1973)), V o l . 1, p. 209. [1.4] A. Abragam, P r i n c i p l e s o f Nuclear Magnetism (Oxford Clarendon), Chapter V I I I . [1.5] P.J. Wheatley, Determination of M o l e c u l a r S t r u c t u r e Oxford: Clarendon Press (1959). - 6 -CHAPTER II BASIC THEORY OF NUCLEAR MAGNETIC RESONANCE The purpose of t h i s chapter i s to present a b r i e f i n t r o -duction to the theory of nuclear magnetic resonance with p a r t i c u l a r emphasis on the effects of molecular motion on the nmr absorption lineshape and s p i n - l a t t i c e relaxation. A detailed theory w i l l not be attempted since i t i s found in many excellent text books [2.1-2.5]. Recent advances in the theory and applications have been covered in many reviews [2.6-2.8]. This thesis involves the study of only 1 19 H and F nuclei in diamagnetic so l i d s and therefore only relevant sections of the theory w i l l be presented. 2.1 ELEMENTARY MAGNETIC RESONANCE THEORY. The general theory of magnetic resonance can be developed from two d i f f e r e n t viewpoints—quantum mechanical and c l a s s i c a l . The two approaches are complementary, certain aspects of magnetic resonance:being explained more s a t i s f a c t o r i l y by one approach than the other. - 7 -In a quantum mechanical sense, the Hamiltonian f o r a nucleus of magnetic moment y = y'hl i n t e r a c t i n g with a magnetic f i e l d H i s - y H = -ytiH I . The eigenvalues m of I take -o - -o o z ^ z the 21+1 value s - I , -1+1.... through 0 to 1-1, I, r e s u l t i n g i n the p o s s i b l e e n e r g i e s of the system given by the d i s c r e t e energy l e v e l s E = -YhH m, c a l l e d the Zeeman energy l e v e l s . m o ^ Resonance corresponds to t r a n s i t i o n s between these l e v e l s governed by the s e l e c t i o n r u l e Am = ±1 e f f e c t e d by a r a d i o -frequency f i e l d of a p p r o p r i a t e energy. The above d e s c r i p t i o n i s a p p l i c a b l e to a s i n g l e s p i n , but i n r e a l i t y , i t i s necessary to c o n s i d e r an ensemble of nuc l e a r s p i n s . In an i s o l a t e d ensemble of n u c l e a r s p i n s a t thermal e q u i l i b r i u m , the s p i n s may be assumed to be d i s t r i b u t e d among the p o s s i b l e energy l e v e l s a c c o r d i n g to Boltzmann s t a t i s -t i c s . I f the p o p u l a t i o n s of the neighbouring s p i n s t a t e s |m> and |m+l> are denoted by n m and n m + 1 r e s p e c t i v e l y , then, JEl+A = . YtiH o/kT L ( 2 > 1 ) m where i s the e q u i l i b r i u m temperature o f the sample, u s u a l l y c a l l e d the ' l a t t i c e ' temperature. However, i t i s p o s s i b l e to d i s t u r b t h i s e q u i l i b r i u m , e i t h e r s t e a d i l y , by a p p l y i n g a weak s a t u r a t i n g r . f . f i e l d , or t e m p o r a r i l y f o r i n s t a n c e , by (i) suddenly changing the va l u e of the steady magnetic f i e l d or ( i i ) a p p l y i n g a str o n g r a d i o f r e q u e n c y p u l s e . I t i s s t i l l - 8 -p o s s i b l e t o a s s i g n f o r m a l l y a s p i n t e m p e r a t u r e T , d i f f e r e n t f r o m t h e l a t t i c e t e m p e r a t u r e T , and d e f i n e d by t h e r e l a t i o n n 1 and n'..,, b e i n g t h e p o p u l a t i o n s o f l e v e l s |m>and |m+l> m m+1 z> r r I I i n t h e p e r t u r b e d s y s t e m . A s p i n s y s t e m w i t h T g ^ T L i s s a i d t o be i n a m e t a s t a b l e e q u i l i b r i u m , and s u c h a s y s t e m w i l l " c o o l down" t o t h e l a t t i c e t e m p e r a t u r e . F o r t h i s a p p r o a c h t o e q u i l i b r i u m t o t a k e p l a c e , t h e r e s h o u l d be some f o r m o f h e a t c o n t a c t between t h e s p i n s y s t e m and t h e s u r r o u n d i n g s , and t h i s i s p r o v i d e d by a l l t h e o t h e r d e g r e e s o f f r e e d o m o f t h e s u b s t a n c e c o n t a i n i n g t h e n u c l e i i n q u e s t i o n . The a p p r o a c h o f t h e s p i n and l a t t i c e s y s t e m s t o t h e r m a l e q u i l i b r i u m i s t e r m e d s p i n - l a t t i c e r e l a x a t i o n . A more q u a n t i t a t i v e c o n s i d e r a t i o n b a s e d on t h e above arguments shows t h a t t h e a p p r o a c h t o e q u i l i b r i u m i s e x p o n e n t i a l w i t h a c h a r a c t e r i s t i c t i m e , t h e 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^) d e f i n e d by, m+1 e Y * V k T s (2.2) n' m T -1 (Wt + W|) (2.3) 1 where W| and WJ. a r e t h e upward and downward r a d i a t i o n l e s s t r a n s i t i o n p r o b a b i l i t i e s . Under t h e i n f l u e n c e o f a r . f . f i e l d , t h e r a t e o f a b s o r p t i o n o f e n e r g y i s g i v e n by, - 9 -= n A E dt o P (2.4) where n Q i s the population difference at thermal equilibrium, A E i s the energy difference between the two l e v e l s and P i s the p r o b a b i l i t y of simulated t r a n s i t i o n s between the two levels under the influence of the r . f . Time dependent per-turbation theory gives the t r a n s i t i o n p r o b a b i l i t y per unit time that a time dependent perturbation V causes t r a n s i t i o n s between states |a> and |b? as, where g(v')~ i s the normalised lineshape function representing the d i s t r i b u t i o n in energy of the t r a n s i t i o n s between states |a> and |b>. Applying t h i s to the nmr case, we get, (2.5) P = P -> P m+1 = P m+1 -* P m m - %Y 2H 1 2(I+m)(I-m+1)g(v). (2.:.6) For a spin with 1 = h, (2.7) The broadening of the resonance l i n e s , represented by g(v) i s brought about i n addition to l i f e t i m e broadening due - 10 -to processes, by other interactions that change the r e l a t i v e energies of the states. From a c l a s s i c a l point of view, t h i s spread i s a measure of how quickly,the precessing spins w i l l get out of phase destroying the component of magnetization i n the XY plane, and i s represented by a Transverse Relaxation  Time ( T 9 ) . By d e f i n i t i o n , T2 = ^ ( v ) m a x • (2.8) dE For an unsaturated absorption l i n e , i . e . g^O, equation (2.4) requires 2PT^<<1. Substituting for P as i n equation (2.7) and r e a l i s i n g that saturation i s maximum at the centre of resonance, i . e . at g(v) , we get the condition for an ^ max ^ unsaturated l i n e as, Y 2H 1 2T 1T 2<<1 . (2.9) 2 2 1+Y T i T 2 -""s c a x x e < 3 the 'saturation factor'. Experimentally, one avoids saturation by using a low enough r . f . l e v e l (H^). Quite frequently, the shape function i s defined i n terms of an angular frequency scale g(oj). Magnetic resonance l i n e s i n solution almost always show a 'Lorentz' lineshape :[2.9.]., T2 1 = — " 2 2 ' ( 2' 1 0> 1+T 2 Z (co-co o r - 11 -a f a c t w h i c h a u t o m a t i c a l l y f o l l o w s f r o m B l o c h ' s p h e n o m e n o l o g i c a l e q u a t i o n s [2.2, p. 3 0 ] . F o r s o l i d s , o t h e r t y p e s o f d i s t r i b u t i o n f u n c t i o n s a r e more a p p r o p r i a t e . The most common one i s t h e ' G a u s s i a n ' l i n e s h a p e [ 2 . 1 0 ] , T 0 0 g (OJ) = — — .e 2 o' (2.11) /2lT 2.2 DIPOLAR INTERACTION. The phenomena w h i c h c a u s e a b r o a d e n i n g o f m a g n e t i c r e s o n a n c e l i n e s i n c l u d e : (a) t h e l a c k o f a homogeneous f i e l d H q, (b) l i f e t i m e b r o a d e n i n g due t o t h e s p i n - l a t t i c e r e l a x a t i o n , (c) n u c l e a r q u a d r u p o l e c o u p l i n g , and (d) m a g n e t i c d i p o l e -d i p o l e c o u p l i n g . A s s u m i n g t h a t t h e m a g n e t i c f i e l d i n h o m o g e n e i t y e f f e c t s a r e u n i m p o r t a n t , f o r a s p i n o f I = h t h e most domin-a n t o f t h e s e i s t h e m a g n e t i c d i p o l e - d i p o l e i n t e r a c t i o n s . The t w o - s p i n d i p o l a r s y s t e m may be d i s c u s s e d as a c o n v e n i e n t i l l u s t r a t i o n . The t o t a l H a m i l t o n i a n f o r a s y s t e m o f two i n t e r a c t i n g s p i n s i n an e x t e r n a l l y a p p l i e d m a g n e t i c f i e l d H q may be w r i t t e n a s , (2.12) - 12 -w h e r e ^ ^ i s the Zeeman p a r t g i v e n by, " ^ V i z " Y 2 f e H o I 2 z < 2- 1 3> a n d ^ ^ i s the d i p o l a r p a r t given by, J ? d = Y 1 Y 2 ^ 2 [ A + B + C + D + E + F] Here, A = I l z I 2 z ( 1 _ 3 C o s 2 0 ) r - 3 B = - ^ [ I 1 + I 2 ~ + I l ~ I 2 + ] ( 1 ~ 3 C o s 2 e ) r ~ 3 C = - | [ I 1 + I 2 z + I i z I 2 + ] s i n 9 C o s 0 e " 1 ( ) ) r ~ 3 D = C 3 T +_ +_. 2 Q -2±4>..-3 E = - j l j . I2 ' (2.14) F = E* where a s p h e r i c a l p o l a r c o o r d i n a t e system has been used w i t h p o l a r angle 0 between r' and H q and an azimuthal angle $. * r e p r e s e n t s complex conjugate and I + and I are the u s u a l quantum mechanical " r a i s i n g " and "lowering" o p e r a t o r s d e f i n e d i n a c a r t e s i a n r e f e r e n c e frame by, - 13 -I + + i l y (2.15) I In a matrix representation |m.>|m.>, the term A i s diagonal and corresponds to the case of two in t e r a c t i n g dipoles considered c l a s s i c a l l y . Term B connects states |m^ m2> with either |m^-l, m2+l> or |m1+l, m2~l> with no change i n the sum of the two eigenvalues and i s c a l l e d the ' f l i p f l o p ' term. C and D f l i p one spin only such that A(m1+m2) = ±1 whereas E and F terms f l i p both the spins i n the same d i r e c t i o n such that A(m^+m2) = ±2. The net e f f e c t of terms C to F i s to produce s a t e l l i t e l i n e s at frequencies 0 and 2CO q; these peaks are very weak and may be disregarded. Thus, for lineshape c a l c u l a t i o n s one uses a truncated Hamiltonian c o n s i s t i n g of only A and B terms, namely, However, as w i l l be seen l a t e r , the terms C to F are important when considering s p i n - l a t t i c e r e l a x a t i o n . 2.3 ABSORPTION SPECTRA FOR RIGID STRUCTURES. The simplest case of a lineshape, that of two i n t e r -acting protons, was elegantly studied by Pake [2.11] i n CaSO.•2H„0 where the protons may be considered to a f i r s t (2.16) - 14 -approximation to occur in isola t e d pairs. In order to explain the experimentally observed spectrum, i t was necessary to include the interaction of the more remote neighbours. This e f f e c t has been well demonstrated by Pederson et a l . [2.12]. Further work on hydrates by nmr have been reviewed by Reeves [2.13], The lineshape i s a double-humped curve and i s t y p i c a l of many substances where the pair interaction i s dominant. The lineshape for the case of three i d e n t i c a l spins (e.g. isolat e d CH^, NH^, H^ O, etc.) has been worked out by Andrew and Bersohn [2.14], and the essence of t h e i r c a l c u l a t i o n i s pre-sented in the Appendix. For a p o l y c r y s t a l l i n e sample, the lineshape i s a t r i p l e t (Figure 2.1) and t h i s has been observed in numerous experiments. Ammonium s a l t s are t y p i c a l examples of the four-spin configuration, the lineshape of which has been investigated by Gutowsky et a l . Taking intragroup contributions alone a complicated lineshape i s predicted but as i n the case of the three spin system, inclusion of the interactions of the remote neighbours smears out the fine structure. The calculations have been extended to a f i v e spin configuration [2.16] for which calculations are even more complex and the lineshape hardly shows any structure. I t i s therefore very complex and unrewarding to carry these calculations to higher spin systems. In fact, to proceed further, we are forced to resort to the so-called method of moments, a clever technique due to Van Vleck, which enables one to compute properties of the resonance - 15 -(c) (d) FIGURE 2.1 Theoretical magnetic resonance lineshapes for a triangular configuration of protons. (a) absorp-ti o n lineshape for r i g i d t r i a n g l e , (b) absorption lineshape for a rotating t r i a n g l e , (c) derivative of absorption lineshape for a r i g i d t r i a n g l e , (d) derivative of absorption lineshape for a rotating t r i a n g l e . - 16 -l i n e s w i t h o u t s o l v i n g e x p l i c i t l y f o r t h e e i g e n s t a t e s and e i g e n v a l u e s . 2.4 COMPLICATED SYSTEMS - METHOD OF MOMENTS. 2.4.1 S e cond moment and Van V l e c k ' s f o r m u l a . The n t h moment o f a n o r m a l i z e d a b s o r p t i o n l i n e s h a p e a b o u t a p o i n t CO q i s d e f i n e d a s [2.1, p. 106] M n = / (oco-co Q ) n g (co)dto . (2.17) F o r s o l i d s , t h e p r o p e r t y o f t h e r e s o n a n c e a b s o r p t i o n l i n e o f most r e l e v a n c e i s u s u a l l y t h e s e c o n d moment, M 2 = / (w- co ) 2 g ( c o ) d a ) . (2.18) Van V l e c k 1 s?..'[.2.17] c a l c u l a t i o n o f t h e s e c o n d moment o m i t s t h e e f f e c t o f terms C t o F i n t h e H a m i l t o n i a n , t h e r e b y e x c l u d i n g t h e c o n t r i b u t i o n s n o t n e a r co . T h e r e f o r e , t h e ^ o l i m i t s o f i n t e g r a t i o n i n e q u a t i o n (2.18) a r e s u c h a s t o i n c l u d e t h e a b s o r p t i o n i n t h e r e g i o n o f C O q b u t t o e x c l u d e any c o n t r i b u t i o n s i n t h e r e g i o n o f 0 and 2 C O q . The s e c o n d moment M 2 may be w r i t t e n i n t e r m s o f t h e 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 a c c o r d i n g t o [2.1, p. 1 1 1 ] ^ , T r { [ ^ ' , I ]2:} M 2 = - r-5 * (2.19) 1 Ti T r {I 2,} % T h i s e x p r e s s i o n i s d i f f e r e n t f r o m Abragram's e x p r e s s i o n by a f a c t o r o f n 2 as Abragram's H a m i l t o n i a n i s d e f i n e d i n u n i t s o f "h. - 17 -Evaluation of the traces lead to the well known Van Vleck expression [2.17], M_ = - ^ y ^ I (1+1) (^)-C (l-3Cos 29. . ) 2 r T 6 2 4' \ N / i , j x3 .ID (2.20) + ¥ ^ ) ^ / f x f { 1 f + 1 ) ( 3 C o s 2 e i f 1 ) 2 r i f where the f i r s t term arises from the N resonant nuclei in the sample and the second comes from th e i r interactions with the non-resonant spins f. In the case of a p o l y c r y s t a l l i n e material where internuclear vectors r are randomly oriented w.r.t. H , the 2 2 4 term (3Cos 0-1) i s replaced by i t s s p a t i a l average of — giving, (2.21) Experimentally, the most d i r e c t method of obtaining the second moment i s by numerical integration of the nmr absorption curve. However, t h i s i s a slow and painstaking process and care must be taken to avoid signal d i s t o r t i o n due to saturation brought about by high r . f . l e v e l s (see equation (2.9)) and overmodulation [2.18], and also to ensure that - 18 -slow passage conditions are maintained [2.19]. A second method of obtaining moments i s from the free induction decay [2.20]. 2.4.2 Second moment and the free induction decay. It i s well known [2.1, p.110, 2.21] that the l i n e -shape function g(to) i s the Fourier transform of the corres-ponding free induction decay (FID) function F(t) which represents the amplitude of the magnetization following a TT/2 r . f . pulse. Consequently, oo F(t) = ~/ Cos (wt)g(o)).dwx (2.22) 6 and, therefore, f t 2 t 4 \ F(t) = F(0) I l-fj-M2- + Jj-M4 - 1 (2.23) It has been shown that the o r i g i n t = 0 i s at the middle of the pulse [2.22]. In p r i n c i p l e , i t i s possible to f i t the FID to an expression of the form i n equation (2.23) and obtain moments of the absorption l i n e . A l t e r n a t i v e l y , one can also write, M2n " < - 1 » n ( § H m ; / F<°» < 2- 2 4' - 19 -from which the moments may be obtained. As seen from these equations, information on M2 i s contained i n the i n i t i a l part of the FID which i s usually obscured by the 'dead time' of the receiver of a pulse spectrometer. However, certain 'pulse t r i c k s ' are available to overcome th i s d i f f i c u l t y by pushing the FID well out of the dead time region. The technique of s o l i d echo [2.23,2.24) involves the application of a pulse sequence 0-T-(^-) _ _ 0 sequence (sub-2.. o z y u s c r i p t outside parenthesis denotes r e l a t i v e phase of the pulse,) . .. The signal amplitude V at a time x' after the second pulse i s given by, 1, V(T-M-) = j; 1 - i l ^ - L . M 2 + i l z l _ ^ „ 4 [ + \ ' 6 \ ] M4x + •••• • ( 2 - 2 5 ) I t i s seen then, that the f i r s t three terms i n equation (2.25) are just the FID but centred at a time 2T a f t e r the second pulse i . e . , at the echo maximum. Therefore, up to the f i r s t TT three terms, the signal after the second pulse i n a (^'QO - 1" ^2^90° s e < 3 u e n c e i - s a F I D r e l a t i v e to the time 2x. Assuming the higher terms to be in accordance with th i s conjecture, the fourth term has been taken as an error term s i g n i f y i n g the deviation of the echo from the FID. I t has been shown that = 0 for isola t e d spin pairs and not for other - 20 -geometries. It i s therefore necessary to use the i n i t i a l part of the echo for moment analysis. Another method using the Jeener echo [2.25] has been discussed in a recent publication [2.26]. 2.5 MOLECULAR MOTION In many so l i d s , i t i s known that there i s often consid-erable motion of the whole molecules about preferred axes or of intramolecular groups about chemical bonds. This motion renders the magnetic dipole-dipole interactions time dependent (i . e . , A and B fluctuate in time). It i s then the average value of these interactions over a time i n t e r v a l which may or may not be large compared to the fluctuation time that determine the nmr lineshape. If the fluctuation time i s less than the time over which i t i s averaged, the average value of the dipolar f i e l d w i l l be less than the instantaneous value, giving r i s e to a narrower absorption l i n e . The c r i t e r i o n for l i n e narrowing i s , ( K 2 ) i i x c « 1 (2.26) where i s the second moment for the 'motionless' molecule (expressed i n angular frequency units) and T ^ i s the cor r e l a -tion time for the fluctu a t i o n . In practice, for a proton resonance l i n e of ^ 10G, for l i n e narrowing to occur, T_<< 2x10 ^  sec. - 21 -If such a motion i s thermally activated, the reorienting frequency may be assumed to vary according to an Arrhenius type relationship, o E/RT T- = T °e (2.27) where E i s the ac t i v a t i o n energy governing the motion. If the lineshape remains unchanged during a l i n e narrowing process, x c for the motion causing the t r a n s i t i o n may be related to the linewidths by [2.27] r = tan[Tr(6H 2-B 2)/2(C 2-B 2) ] c ay(6H) (2.2») where B and C are the r i g i d l a t t i c e and narrowed linewidths and a i s a constant calculable as (81n 2) ^. From equations (2.27) and (2.28) one may extract a value for the a c t i v a t i o n energy. However, such a procedure i s sometimes l i k e l y to be erroneous since the assumption that no lineshape change takes place during the t r a n s i t i o n i s often not true. The shape of resonance absorption in the presence of molecular motion i s modified through the averaging of the 2 (3Cos 0-1) terms in A and B terms of the Hamiltonian. The two-spin h system undergoing molecular reorientation has been studied by Gutowsky and Pake [2.28]. The case of t r i -angular groups of nuclei of spin h reorienting about any given - 22 -axis has been worked out by Andrew and Bersohn [2.14], The special case frequently encountered, i n which the axis of reorientation i s normal to the plane of the tr i a n g l e i s out-lined in the Appendix and the re s u l t i n g lineshape i s shown in Figure 2.1. As pointed out e a r l i e r , the calculations for higher spin systems are complicated and a second moment analysis i s used. Molecular motion brings about a reduction in the observable second moment by time averaging of the 2 (3Cos 6-1) term and a measurement of thi s reduction enables one to i d e n t i f y the type of motion causing i t . For a pair of nuclei reorienting i n an n-fold potential (ng.3) , the reduction factor to the second moment i s given by [2.28], ^(3Cos 20 - l ) 2 (2.29) where 0 i s the angle between the internuclear vector r and the axis of rotation. The case of a general two-fold reorientation i n a double-minimum potential i s s l i g h t l y more complex and has been treated for the cases where the nuclear pairs spend equal [2.29] and unequal [2.30] resident times in the two potential wells. If the motion i s only o s c i l -latory, the reduction factor i s given by, ( l - J Q 2 (5)) Sin 220 + ( l - J Q 2 (26))sin 46 ,J (2.30) - 23 -where 6 i s the angular amplitude of o s c i l l a t i o n and J i s a o Bessel function of the f i r s t order. For small angles 6, t h i s gives the approximate r e s u l t i 3-2_. 2 1 - 2 6 S i n Y • (2.31) In the present study, the group of most intere s t i s the methyl group. The r i g i d l a t t i c e second moment for a methyl group in a p o l y c r y s t a l l i n e sample i s given by [2.31]. M2 = | a 2 (2.32) where, 3y a = — 2 r 3 with r being the interproton distance and y the proton magnetic moment. If the methyl group rotates about an axis which makes an angle \p with the symmetry axis, the reduced second moment M ! , i s given by [ 2 . 3 1 ] , ' 2 2 27 4 2 M2 = 5 a' LIT S i n ^ ~ 3Sin + l j (2.33) If i n addition, the CH^ group also rotates about i t s symmetry axis, the reduced second moment i s given by - 24 -M 2 = TO ( 3 C o s 2 ^ - 1 ) 2 • (2.34) As sample t e m p e r a t u r e s much l o w e r t h a n t h a t o f l i q u i d n i t r o g e n a r e u s e d , quantum e f f e c t s [2.32] become s i g n i f i c a n t . I n p a r t i c u l a r , t h e e f f e c t s o f r o t a t i o n a l t u n n e l l i n g o f m e t h y l g r o u p s on t h e o b s e r v e d p r o t o n r e s o n a n c e l i n e s h a p e s [2.33, 2.36] and s e c o n d moments [2.35] have been s t u d i e d e x t e n s i v e l y i n r e c e n t y e a r s . 2.6 SPIN LATTICE RELAXATION. 2.6.1 C o r r e l a t i o n f u n c t i o n s , s p e c t r a l d e n s i t i e s . Two c o n d i t i o n s a r e n e c e s s a r y f o r an e n e r g y t r a n s f e r between a s p i n - s y s t e m and t h e l a t t i c e . F i r s t l y , t h e r e s h o u l d be an i n t e r a c t i o n a c t i n g d i r e c t l y on t h e s p i n s and s e c o n d l y , i t must be t i m e d e p e n d e n t . I n g e n e r a l , any i n t e r a c t i o n f l u c t u a t i n g a t t h e r e s o n a n c e f r e q u e n c y o f t h e n u c l e i w i l l c a u s e e f f i c i e n t s p i n - l a t t i c e r e l a x a t i o n . The v a r i o u s i n t e r a c t i o n s w h i c h c o u p l e t h e s p i n s y s t e m t o t h e l a t t i c e a r e , 1. m a g n e t i c d i p o l e - d i p o l e c o u p l i n g 2. e l e c t r i c q u a d r u p o l e c o u p l i n g 3. c h e m i c a l s h i f t a n i s o t r o p y 4. s c a l a r c o u p l i n g 5. s p i n r o t a t i o n . Of t h e s e , t h e most d o m i n a n t mechanisms a r e t h e f i r s t two. I n t h e a b s e n c e o f q u a d r u p o l a r n u c l e i , t h e r e l a x a -- 25 -t i o n i s m a i n l y , g o v e r n e d by m a g n e t i c d i p o l e - d i p o l e i n t e r a c t i o n s . The H a m i l t o n i a n f o r a s y s t e m o f two i n t e r a c t i n g s p i n s /(^^j7 has been g i v e n i n e q u a t i o n ( 2 . 1 4 ) . The t i m e d e p endence tot/l^ i s b r o u g h t a b o u t by any t i m e d e p e n d e n c e i n r , 9 and §. T h e r e f o r e , i t i s c o n v e n i e n t t o s e p a r a t e t h e t i m e - d e p e n d e n t p a r t s i n t h e t e r m s A t o F by w r i t i n g , Y Q = r ~ 3 ( l - 3 C o s 2 6 ) (2.35) -3 . Y1 = r S m e C o s G e x p (i<j>) (2.36) Y 2 = r ~ 3 S i n 2 9 e x p (2i<f>) • (2.37) M o l e c u l a r m o t i o n r e n d e r s Y Q , Y^ and r a n d o m l y v a r y i n g f u n c t i o n s o f t i m e ; c o n s e q u e n t l y , one may d e f i n e an a s s o c i a t e d s e t o f c o r r e l a t i o n f u n c t i o n s KCT) d e f i n e d by, K i ( t ) = < Y ± ( t ) Y ± * ( t + x ) > (2.38) where * d e n o t e s complex c o n j u g a t e and <> d e n o t e s ensemble a v e r a g e . F o r s t a t i o n a r y random functions-:sof t h e t y p e Y Q , Y^ and i t i s common t o assume a c o r r e l a t i o n f u n c t i o n o f t h e e x p o n e n t i a l form, i . e . , — T / T K i ( x ) = <Y i 2>e C (2.39) - 26 -where x i s the c o r r e l a t i o n time c h a r a c t e r i s t i c of the motion. (i) The spectral density J(w) of the random function i s given by the Fourier transform of K^(x), (i) f.oo J(o>) = / K. (x) exp (iojx)dx . (2.40) — 00 1 If K(x)- has the form i n equation (2.39), (i) 2 2x J (ui) = <Y. > --5- (2.41) - 1 (1+x x ) c 2.6.2 Relaxation of a system of l i k e nuclei i n laboratory frame. The s p i n - l a t t i c e relaxation rate for a pair of l i k e nuclei i , j due to dipole-dipole interactions i s given by [ 2 . 1 , p. 2 9 1 ] , i - = f l d + D y V [ j ^ > (a,o) + j { 2 ) ( 2 W q ) ] ( 2 . 4 2 ) The spectral densities J's usually have the form given in equation ( 2 . 4 1 ) and therefore the relaxation i s most e f f i c i e n t when a) x ^ 1. o c The relaxation rate expression for any given mole-cular motional s i t u a t i o n may now be worked out, provided that expressions for J's are calculable. This, however, i s the most d i f f i c u l t task in the whole exercise. - 27 -For a spin pair undergoing i s o t r o p i c reorientation, the spectral densities have been calculated as [2.10, 2.38, 2.39] . j<°> ( W) = | ^ (2.43) 1+tB T C J ( 1 ) (03) = ~ — ^ | j (2.44) 1+C0 T c J ( 2 ) M = TT — 9 (2.45) c The spectral densities for the case of a spin pair undergoing anisotropic reorientation about an axis making an i angle 9 with the interspin vector are given by [2.39], J ( 0 ) ( U) = ^ ( f s i n 2 e ' C o s V + | s i n 4 9 6T < 2 ' 4 6 > c 2 2 I + . U T T c J ( 1 ) (co) = I _ ^ l S i n 2 0 cos 28 + ± S i n V ) r T c -j , f 2 2 1+CO T c j < 2 ) ( u ) = 1_ (4 s i n2 e« C o s2 e« + l s i n 4 ' r \ 2 2 l+co •t c (2.47) 4 x (2.48) - 28 -On the other hand, i f the s p i n p a i r undergoes 180° f l i p s , the J's are g i v e n by [2.40], J ( 2 , ( » ) 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 of any p a r t i c u l a r s p i n by another s p i n may now be c a l c u l a t e d by sub-s t i t u t i n g i n equation (2.42) the s p e c t r a l d e n s i t i e s a p p r o p r i a t e to the motion. For a system of three or more sp i n s undergoing a c o r r e l a t e d motion, t h i s i s not s t r i c t l y v a l i d , as has been shown f o r the case of a methyl group [2.41, 2.42]. Here, the c a l c u l a t i o n o f 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 of nucleus 1, 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 are termed " a u t o c o r r e l a t i o n f u n c t i o n s " and t h a t due to i n t e r a c t i o n 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 of nucleus 1 i s termed " c r o s s - c o r r e l a t i o n f u n c t i o n " . However, i n a group c o n t a i n i n g more than two s p i n s , i f the Z component of the magnetization has a simple e x p o n e n t i a l dependence on time i n the experimental d e t e r m i n a t i o n of T^, and i f the groups are not i s o l a t e d i n the c r y s t a l , c r o s s -c o r r e l a t i o n may be n e g l e c t e d and then T^ may be c a l c u l a t e d as though the motion of s p i n p a i r s were independent [2.42]. Under 4 2 1 2 |-Sin 9 Cos ( 1+0) T c (2.49) 4 . 2 ' 2 1 |-Sin 0 Cos 0 D T C - i ^ 2 2 1+ca T c (2.50) these c i r c u m s t a n c e s , one may w r i t e ( 1 ^ ) ^ f o r the i t h s p i n as, j . ( 2 , < 2 U )" . l ] o J (2.51) Assuming a common s p i n temperature, the o b s e r v a b l e 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 f o r an N s p i n system i s g i v e n by, For the r o t a t i o n o f a methyl group about i t s a x i s of symmetry, n e g l e c t i n g c r o s s - c o r r e l a t i o n s , H i l t and Hubbard have o b t a i n e d the r e l a x a t i o n r a t e e x p r e s s i o n as, T h i s e x p r e s s i o n was a l s o o b t a i n e d by O ' R e i l l y and Tsang [2.43] F u r t h e r , H i l t and Hubbard have shown t h a t , i f the c r o s s -c o r r e l a t i o n s a r e i n c l u d e d , the r e l a x a t i o n o f the s p i n system i s not e x p o n e n t i a l , but a sum o f f o u r e x p o n e n t i a l s , and t h a t the concept o f T, i s no l o n g e r v a l i d . ^ methyl group r e o r i e n t a t i o n t o i n c l u d e s u p e r p o s i t i o n o f d i f f e r -ent motion. T h e i r c a l c u l a t i o n i s a p p l i c a b l e to a complex Another e f f e c t which i s important i s symmetry r e s t r i c t e d s p i n d i f f u s i o n i n t r o d u c e d by Wind e t a l . ( J . Chem. Phys. 67_, 2436 (1977)). These e f f e c t s a r e , however, not expected t o be impor-t a n t i n t h i s study i n view of. the l a r g e i n t e r m e t h y l i n t e r a c t i o n s p r e s e n t . (2.52) (2.53) Dunn and McDowell [2.44] have extended the work on - 30 -motion of a methyl group rotating about i t s threefold axis (C^) simultaneous with the rotation of the axis i t s e l f about another axis fixed in the molecular framework and i s o -tropic tumbling of the whole molecule [see Figure 2.2]. Their f i n a l equation for the relaxation rate i s , 1 9 Y 4 k 2 f k * * * V" v^V + Bf(V + c f ( T c 4 ) + D f ( T c ) | (2.54) where A = i (l-3Cos 2S) , B = -|sin 46, C = Sin 226 + Sin 46 and 1 4 D = 2-(8-3Sin 6); 6 i s the angle between the symmetry axis and the axis about which i t rotates, x .. i s the c o r r e l a t i o n c l time for is o t r o p i c tumbling, x.... i s the c o r r e l a t i o n time for c2 the rotation of the C~ symmetry axis and x . ; x .. and x... 3 4 5 are defined as where x i s the c o r r e l a t i o n time for C, rotation of methyls. The form of the spectral density function i s given i n the - 31 -FIGURE 2.2 M o t i o n a l model assumed i n Dunn and M c D o w e l l c a l c u l a t i o n [ 2 . 3 8 ] . The r e l e v a n t r o t a t i o n a x e s a r e i n d i c a t e d by d o t t e d l i n e s ; t h e T C ' S i n p a r a n t h e s i s a r e t h e c o r r e l a t i o n t i m e s c o r r e s -p o n d i n g t o t h e m o t i o n ( r e p r e s e n t e d by c u r l y a r r o w s ) . - 32 -usual way as, f (co T) = ^ — 7 - + o " 2 2 1 ^ . * 2 2 1 + CO T 1 + 4C0 T o o This master equation (2.54) i s quite useful i n examining a variety of intramolecular motion. For example, in groups t y p i f i e d by t-butyl ((CH 3) 3C-), trimethylamino ((CH 3) 3N-), etc. (which are of importance i n th i s study), where the methyl groups are attached to an atom in a t e t r a -hedral configuration, a possible motion for the axis i s the motion of the whole group about a three-fold axis (C^ 1) with 6 = 70.5° and equation (2.52) reduces to, 1 9 yV (4 . ^ 32., . TFT - = ~a7\ r~ \ (CO T ) + • — f (CO T ) 1 r J 27 o c^ 27 o c^ + | | f (u> T ) + | f f (co x ) I . (2.55) 27 o c 4 2/ o c ^ j For the simultaneous motion of of methyls and rotation of the axis about a ' axis taking place at comparable frequencies, substitution of T = 0 0 and T = x i n equation c l c c2 (2.55) gives 1 _ 1 yV 16f (co T ) + 19f (0> x /2) \ (2.56) Tn 60 6 K v o c' ' J - " v o c' 1 r If , on the other hand, the 1 motion i s superposed on very fast ( i . e . , COQTC<<I) c 3 rotation of methyls, substituting - 33 -T = 0 One o b t a i n s , 1 2_ 15 Y (2.57) 6 r In g e n e r a l , the r e l a x a t i o n r a t e f o r any one type of motion may be w r i t t e n as a g e n e r a l i z e d BPP equation of the type, where C r e p r e s e n t s the s t r e n g t h o f the r e l a x a t i o n i n t e r a c t i o n and depends on the d e t a i l s o f the motion. shows a minimum when co T =0.62. o c As seen from the f o r e g o i n g d i s c u s s i o n , s p i n - l a t t i c e r e l a x a t i o n measurements i n the l a b o r a t o r y or "Zeeman" frame are u s e f u l i n st u d y i n g molecular motions t a k i n g p l a c e w i t h a c o r r e l a t i o n time T ^ CO . I t i s i n p r i n c i p l e p o s s i b l e to c o study slower motions by making measurements a t lower r e s -onance f r e q u e n c i e s , but, an experimental problem i n v o l v e d i n the o b s e r v a t i o n of r e l a x a t i o n i n a weak a p p l i e d f i e l d i s t h a t the magnetic resonance s i g n a l i s g r e a t l y reduced i n a weak f i e l d . T h i s problem can be circumvented by a p p l y i n g a s t r o n g r . f . f i e l d and then o b s e r v i n g the r e l a x a t i o n i n the " r o t a t i n g frame". (2.58) - 34 -2.6.3 R e l a x a t i o n of a system of l i k e n u c l e i i n the r o t a t i n g frame. The theory of s p i n - l a t t i c e r e l a x a t i o n i n a r o t a t i n g frame of r e f e r e n c e has been w e l l reviewed by A i l i o n [2.45]. In the weak c o l l i s i o n l i m i t [2.46] namely, H^ ??>?6H or H, >6H and T >>x , where H, i s the r . f . magnetic f i e l d , 6H i s the l o c a l d i p o l a r f i e l d and T 0 i s the r i g i d l a t t i c e T„, Z RJ-J Z s p i n l a t t i c e r e l a x a t i o n i n the r o t a t i n g frame, f o r a s p i n p a i r with T=h i s g i v e n by, 1 9 4X2 ( 1 _ (0) , . 5 -T (1) . , ¥77p = 8 Y * j ? J i j ( 2 a ) l } + 2 J i j ( (V + r J ± \ 2 ) (2u o) | (2.59) where, U l = Y H 1 Equation (2.59) shows a s p e c t r a l d e n s i t y c o n t r i b u t i o n a t 20^, and thus any molecular f l u c t u a t i o n with a c o r r e l a t i o n time TCM2CO-^) ^ w i l l cause e f f i c i e n t s p i n - l a t t i c e r e l a x a t i o n i n the r o t a t i n g frame; i n a t y p i c a l experiment, to^MOkHz (com-pared to (JOq which i s u s u a l l y of the order of tens of Megahertz) , and t h i s makes the technique a powerful t o o l i n the study -4 of slow ( i . e . , t y p i c a l l y ^10 sec) motions. To c a l c u l a t e the - 35 -relaxation rate expression for a reorienting molecule or molecular group, an argument similar to that for c a l c u l a -tions (see Sec. 2.6.2) may be developed. Similar to equation (2.58), a generalised equation may be written as, - c I Is + T= T i ) 2 ,, 2 2 ' . 2 2 lp ( (l+coo x c ) ( l + 4 u o x c 3 T c ) + T TT- \ (2.60) The constant C here i s i d e n t i c a l to that i n equation (2.58) for the same motional s i t u a t i o n . Tn shows a minimum at lp 2co, T = 1. 1 c 2.6.4 Relaxation of a system of unlike n u c l e i . Following Abragam [2.1] the time evolution of the nuclear magnetizations of spins I and S caused by relaxation may be written as a set of coupled d i f f e r e n t i a l equations, namely, dt = - e n * - 3 I S Y % = ^ s i x " 3ssY (2.61) where, - 36 -x = < I > - I z o y = <S > - S 2 z o The observable relaxation rates X + = (T.^ ) 1 and X = -1 (T 1) are eigenvalues of the secular determinant • 3 Z I - X - 3 s i IS " 3 s s " A = o, (2.62) namely, K = M - ( 3 I T _ + 3 S S ) * V ( 3n + B s s } - 4 3 n e s s + 4 3 i s e s i } • (2.63) The above eigenvalues determine the time development of the general solution of the system [2.47, 2.48]: X+t A - t x = A^e +B^e y = A 2e +B2e (2.64) where A and B c o e f f i c i e n t s for a system following a 180° pulse are given by - 37 -( 3 T T+A_) (3 Q Q+A_) A n = 21 x A„ = 2S b b 1 o(A +-A_) "2 " (A +-A_0; B, = -21 t B. = -2S. S S + (2.65) '1 o(A +-A_) D2 ~ "°o(A +-A_) Again, foil-owing Abragam, the 8's are w r i t t e n as, = f Y j V l d + D Z ' J i j 1 5 (a)z) + 2 J . j 2 ) ( 2 ^ ) + l 2^^ 2 s< S + 1>^ Jik° )< ui - u s ) + " J i k 1 ^ " ^ (2) + 9 J ± ] ; ' (O31+oas) ] (2.66) 3 l S ( i ) = l 2 ^ l S 2 t 2 l < I + 1 ^ [ - J i i ° ) ^ i - " s ) + 9 J ± ] ^ 2 ) (coj+ajg)] (2.67) The other 3's, 3 g g and 3 g j , are o b t a i n e d by i n t e r c h a n g i n g I and S i n the a p p r o p r i a t e e x p r e s s i o n s (2.66) and (2.67). 2.6.5 C o r r e l a t i o n times and a c t i v a t i o n e n e r g i e s from r e l a x a t i o n time measurements. The temperature dependence of T^ and T^ . may be r e l a t e d to an a c t i v a t i o n energy f o r the motional process c a u s i n g the r e l a x a t i o n i f one assumes x to have an Arrhenius-^ c type temperature dependence as i n equation (2.26). - 38 -The act i v a t i o n energy E may be extracted from the l i m i t -ing slopes of the l n ( T l f T l p ) vs. T plot; 1. In the low temperature region (tooxc>>l for T^ and W..T >>1 for T, ) , Jl c 1P slope = E/R . 2. In the high temperature region (U OT c<<1 for T^ and TIP»' slope = -E/R. The a c t i v a t i o n energy may also be obtained from a plot of l n x c vs. T ^ where at temperature T can be obtained from the experimental T^ (or minimum and the experimental value of T 1 (or ) at temperature T using equations (2.58 or 2.60). Symmetric sharp minima w i l l , however, be observed only i f the motion can be characterized by a single c o r r e l a t i o n time. The absence-of a unique c o r r e l a t i o n time leads to a broad, f l a t and non-symmetric minimum [2.49 -2. 51] . It must be pointed out that the nmr method determines theuactivation energy and not d i r e c t l y the ba r r i e r height as in some other methods (2.52, 2.53). Activation energy for rotation i s the average energy of those molecules or molecular groups which pass over the b a r r i e r to rotation. The r e l a t i o n of the quantity E to the poten t i a l energy b a r r i e r (V) to rotation of the molecular group i s uncertain. Smith [2.54] - 3 9 -h a s a t t e m p t e d t o r a t i o n a l i z e t h e a c t i v a t i o n e n e r g i e s o f some f o u r - s p i n t e t r a h e d r a i n t e r m s o f t h e i r t o r s i o n a l e n e r g y s t a t e s , a n d s u g g e s t s t h e a c t i v a t i o n e n e r g y t o b e t h e e n e r g y d i f f e r e n c e b e t w e e n t h e g r o u n d h a r m o n i c l e v e l a n d t h e e n e r g y l e v e l j u s t a b o v e - t h e h i g h e s t a n h a r m o n i c l e v e l . The a c t i v a t i o n e n e r g y i s o f t e n l i k e l y t o be l e s s t h a n V a n d t h e r e f o r e may be t a k e n a s a l o w e r l i m i t t o t h e b a r r i e r s h e i g h t . A g o o d d i s -c u s s i o n o f t h i s s u b j e c t i s a l s o f o u n d i n r e f e r e n c e [ 2 . 5 5 ] . - 40 -References [2.1] A. Abragam, The Pr i n c i p l e s of Nuclear Magnetism, Oxford University Press, 1961. [2.2] E.R. Andrew, Nuclear Magnetic Resonance, Cambridge University Press, 1955. [2.3] C P . S l i c h t e r , P r i n c i p l e s of Magnetic Resonance, Harper, N.Y., 1963. [2.4] T.C. Farrar and E.D. Becker, Pulsed and Fourier Transform NMR, Academic Press, N.Y., 1971. [2.5] N. Goldman, Spin Temperature and Nuclear Magnetic Resonance in Solids, Oxford University Press, 1970. [2.6] MTP International Review of Science, Series 1, V.4 (1972) and Series 2, V.4 (1975). (C.A. McDowell, Ed.), Butterworths, London. [2.7] Advances i n Magnetic Resonance, v o l . 1-7 (J.S. Waugh, Ed.), Academic Press, N.Y., London (1965-1974). [2.8] Nuclear Magnetic Resonance, v o l . 1-5, Journal of Chemical Society, s p e c i a l i s t p e r i o d i c a l reports (1972-1976). [2.9] J.G. Powles and B. Carazza, Magnetic Resonance, (CK. Coogan, N.S. Ham, S.N. Stuart, J.R. Pilbrow and G.V.H. Wilson, Eds.), Plenum Press, N.Y.-London (1970). [2.10] N. Bloembergen, E.M. Pu r c e l l and R.V. Pound, Phys. Rev. 73, 679 (1948) . - 41 -[2.11] G.E. Pake, J. Chem. Phys. 16, 327 (1948). [2.12] B. Pederson and D.F. Holcomb, J. Chem. Phys. 3_8, 61 (1963). [2.13] L.W. Reeves, Progress in NMR Spectroscopy, v o l . 1 (J.W. Emsley, J. Feeney and L.H. S u t c l i f f e , Eds.), Pergamon Press, Ltd. (1969). [2.14] E.R. Andrew and R. Bersohn, J. Chem. Phys. 18_, 159 (1950) . [2.15] H.S. Gutowsky, G.E. Pake and R. Bersohn, j . Chem. Phys. T2, 643 (1954) . [2.16] R. Bli n c , Z. Trontelj and B. Volarsek, J. Chem. Phys. 4_4, 1028 (1966) . [2.17] J.H. van Vleck, Phys. Rev. 74, 1168 (1948). [2.18] 0. Haworth and R.E. Richards, Progress i n NMR Spectro-scopy, v o l . 1 (J.W. Emsley, J. Feeney and L.H. S u t c l i f f e , Eds.), Pergamon Press, Ltd. (1966). [2.19] M. Weger, B e l l System Technical Journal^ 3_9, 1013 (1960). [2.20] F. Bloch, Phys. Rev. 7/3, 460 (1946). [2.21] I.J. Lowe and R.E. Norberg, Phys. Rev. 107, 46 (1957). [2.22] D. Barnall and I.J. Lowey Phys. Rev. Lett. 11, 258 (1963). [2.23] J.G. Powles and J.H. Strange, Proc. Phys. Soc. 82, 6 (1963). [2.24] J.G. Powles and P. Mansfield, Phys. Lett. 2, 58 (1962). [2.25] J. Jeener and P. Broekaert, Phys. Rev. 157, 232 (1967). - 4 2 -[ 2 . 2 6 ] M. Bloom, E . E. B u r n e l l , S.B.W. Roe d e r and M.J. V a l i c , J . Chem. P h y s . 6_6, 3 0 1 2 ( 1 9 7 7 ) . [ 2 . 2 7 ] G.W. S m i t h , J . Chem. Phys. £ 2 , 4 2 2 9 ( 1 9 6 5 ) . [ 2 . 2 8 ] H.S. Gutowsky and G.E. Pake, J . Chem. Phys. 1J3, 1 6 2 ( 1 9 5 0 ) . [ 2 . 2 9 ] E.R. Andrew and J.R. Brookeman, J . Mag. Res. 2, 2 5 9 ( 1 9 7 0 ) . [ 2 . 3 0 ] E.R. Andrew, J . Mag. Res. 9_, 1 0 8 ( 1 9 7 3 ) . [ 2 . 3 1 ] J.G. Powles and H.S. Gutowsky, J . Chem. Ph y s . 2 1 , 1 6 9 5 ( 1 9 5 3 ) ; 2 1 , 1 7 0 4 ( 1 9 5 3 ) ; 22_, 1 6 9 2 ( 1 9 5 5 ) . [ 2 . 3 2 ] R. S r i n i v a s a n , MTP I n t e r n a t i o n a l Review o f S c i e n c e , P h y s i c a l C h e m i s t r y , S e r i e s two, V o l . 4 ( C A . Mc D o w e l l , E d . ) , B u t t e r w o r t h s , London ( 1 9 7 5 ) . [ 2 . 3 3 ] F. A p a y d i n and S. C l o u g h , J . Phys. C . l , 9 3 2 ( 1 9 6 8 ) . [ 2 v 3 4 ] T.B. Cobb and C.S. J o h n s o n , J r . , J . Chem. Ph y s . 5 2 , 6 2 2 4 ( 1 9 7 0 ) ; 5 3 , 4 1 2 2 ( 1 9 7 0 ) . [ 2 . 3 5 ] H.M. M c l n t y r e and C.S. J o h n s o n , J r . , J . Chem. Phys. 5 5 , 3 4 5 ( 1 9 7 1 ) . [ 2 . 3 6 ] C. M o t t l e y and C.S. J o h n s o n , J r . , J . Chem. Ph y s . 6 1 , 1 0 7 8 ( 1 9 7 4 ) . [ 2 . 3 7 ] P.S. A l l e n , J . Chem. Phys. £ 8 , 3 0 3 1 ( 1 9 6 8 ) . [ 2 . 3 8 ] R. Kubo and K. T o m i t a , J . Phys. S o c . J a p a n 9, 8 8 8 ( 1 9 5 4 ) . [ 2 . 3 9 ] D.E. Woessner, J . Chem. Phys. 3_6, 1 ( 1 9 6 2 ) . [ 2 . 4 0 ] B.A. D u n e l l and S.E. U l r i c h , J . Chem. S o c . F a r a d a y T r a n s . I I , 6 9 , 3 7 7 ( 1 9 7 3 ) . - 43 -[2.41] R.L. H i l t and P.S. Hubbard, Phys. Rev. 134, A392 (1964). [2.42] M.F. Baud and P.S. Hubbard, Phys. Rev. 170, 384 (1968). [2.43] D.E. O'Reilly and T. Tsang, Phys. Rev. 157, 417 (1967). [2.44] M.B. Dunn and CA. McDowell, Mol. Phys. _2_4, 969 (1972). [2.4 5] D.C A i l i o n , Advances in Magnetic Resonance, (ed. J.S. Waugh), Academic Press, N.Y., London, Vol. 5, (1971). [2.46] C P . Jones, Phys. Rev. 148, 332 (1966). [2.47] R. Blinc and G. Lahajnar, j . chem. Phys. £7, 4146 (1967). [2.48] A.P. Caron, D.J. Heuttner, J.L. Ragle, L. Sherk and T.R. Stengle, J. Chem. Phys. 47_, 2577 (1967). [2.49] A. Odajima, Progr. Theoret. Phys. (Kyoto) Suppl. 10, 142 (1959). [2.50] T.M. Connor, Trans. Faraday S o c , 60^, 1574 (1964). [2.51] A.W.K. Khanzada, CA. McDowell and P. Raghunathan, J. Chem. Phys. 60, 3025 (1974). [2.52] J.P. Lowe:, .Progress i n Physical Organic Chemistry, (A. Streitweiser, J r . , R.W. Taft, Eds.), V.6, Inter-science, N.Y. (1968). [2.53] J.R. Durig, S.M. Craven and W.C Harris, V i b r a t i o n a l  Spectra and Structure, Edited by J.R. Durig, Dekker, N.Y. (1972). [2.54] D. Smith, J. Chem. Phys. 62^ , 4497: (1975). [2.55] A. Kumar and C.S. Johnson, J r . , J. Chem. Phys. 60, 137 (1974). - 44 -CHAPTER III APPARATUS AND METHODS OF MEASUREMENTS This chapter i s intended to give some d e t a i l s of apparatus and methods of measurements used i n t h i s study. 3.1 CONTINUOUS WAVE MEASUREMENTS 3.1.1 Wideline NMR Spectrometer I. The spectrometer used for a l l variable temperature measurements down to 77K was a conventional c r o s s - c o i l Varian 4200 wideline spectrometer equipped with a 6 inch e l e c t r o -magnet. The transmitter/receiver section was a Varian 4210A variable frequency r f unit. A l l measurements were ca r r i e d out at 8 MHz. The usual 'l o c k - i n 1 detection method was used. The modulating f i e l d was supplied by a Varian V4250B sweep unit and, in a l l experiments, the modulating frequency was kept at 80 Hz. The f i r s t derivative of the absorption mode signal was recorded by means of Varian V4270B lo c k - i n amplifier unit. Spectra were recorded on an HP Model 68 0 s t r i p chart recorder. - 45 -3.1.2 C a l i b r a t i o n of the Spectrometer. The resonance f i e l d H was adjusted from the o absorption signal obtained from a doped water sample. A side band technique was used for c a l i b r a t i o n of the scanning rate. To produce these side bands, the main r f c a r r i e r frequency (8 MHz) was modulated by a known audiofrequency generated from an HP model 2 00CD wide range o s c i l l a t o r , the frequency of which was measured by an H.P. model 3734A electronic counter. The scan rate was calib r a t e d i n gauss per cm along the base l i n e of the recorder chart paper. The modulation amplitude was calib r a t e d by d i r e c t l y recording the f i r s t derivative of an overmodulated doped water sample. The observed peak-to-peak l i n e width was taken equal to 2 Hm, where Hm i s the modulation amplitude in gauss. 3.1.3 Variable temperature assembly. Temperature control was achieved by a gas-flow method. For temperatures below room temperature, l i q u i d nitrogen was boiled o f f with a variac-controlled 400 watt heater immersed in a 50 l i t r e l i q u i d nitrogen tank, and led through a dewar system to the probe. To get minimum temper-ature gradient, the voltage on the heater was kept at a fixed value which gives a good high flow rate of cold gas. The temperature was varied by varying the voltage across an additional heater placed inside the dewar system. The temperature of the sample was constantly monitored by a - 46 -copper-constantan thermocouple placed approximately 0.25 -0.5 inches below the sample, and a Leeds and Northrup Type G s t r i p chart recorder. For temperatures between 7 7K and 110K, nitrogen from the 50 l i t r e tank was passed through a copper heat exchanger c o i l placed in l i q u i d nitrogen before reaching the dewar system. For temperatures from room temperature upwards, a hot a i r flow was used. The s t a b i l i t y of the temperature with th i s system i s about ±0.5°. Samples were allowed to equi l i b r a t e at least for 20 minutes before spectra were run. 3.1.4 Wideline spectrometer I I . The spectrometer was used to obtain a l l spectra at 4.2K, and also at 77K when the use of very low r . f . levels became necessary to avoid saturation. The temperatures 4.2 and 77K are achieved by immersing the sample i n l i q u i d helium and l i q u i d nitrogen, respectively. The temperature was monitored by a calibrated gold (0.03% atomic Fe)-chromel thermocouple and read out on a FLUKE 34 7 d i g i t a l micro-voltmeter. The spectrometer consists of a variable frequency Robinson r . f . o s c i l l a t o r [3.1] capable of sustaining o s c i l l a t i o n s in the nmr c o i l at very low r . f . l e v e l s . The resonant frequency was constantly monitored on a HP frequency counter. The signal following nmr absorption i s phase detected by means of a PAR model 121 lock-in amplifier and i s recorded on a HP Moseley 7035B X-Y recorder. - 47 -The magnet u s e d h e r e i s a V a r i a n 9 i n c h e l e c t r o -magnet w i t h a V a r i a n F i e l d i a l Mark I I power s u p p l y . The F i e l d i a l a l s o d r i v e s t h e r e c o r d e r i n t h e X d i r e c t i o n s y n c h r o n o u s w i t h t h e f i e l d sweep, w h i c h e n a b l e s t h e d i r e c t c a l i b r a t i o n o f s p e c t r a . Whenever S/N r a t i o was p o o r , s i g n a l s w ere a v e r a g e d o n a V a r i a n C-1024 c o m p u t e r o f a v e r a g e t r a n -s i e n t s ( C A T ) . 3.1.5 L i n e w i d t h and s e c o n d moment m e a s u r e m e n t s . The l i n e w i d t h was t a k e n a s t h e p e a k - t o - p e a k d i s t a n c e i n t h e f i r s t d e r i v a t i v e o f t h e u n s a t u r a t e d ^ a b s o r p t i o n c u r v e . F o r a d e r i v a t i v e t r a c i n g o f t h e a b s o r p t i o n s i g n a l , t h e s e c o n d moment e q u a t i o n g i v e n i n E q u a t i o n (2.18) may be r e w r i t t e n a s _ J f ' (H) (H-Ho) dH M = i (3.1) Z 3 +00 ; f ' (H) (H-Ho)dH — oo where f ' ( H ) i s t h e d e r i v a t i v e o f t h e a b s o r p t i o n i n t e n s i t y a t f i e l d H. F o r n u m e r i c a l i n t e r g r a t i o n p u r p o s e s , e q u a t i o n (3.1) may be w r i t t e n a s E n 3 Y n 2 )  W 2 3 EnYn ^ Z > t C a r e was t a k e n t o employ r . f . (H-j^ ) f i e l d s low enough t o e n s u r e t h i s c o n d i t i o n . - 48 -where Yn i s the signal height n units away from the centre of resonance, and S i s the scan rate i n gauss per unit. Any small broadening of the experimental spectra due to "overmodulation" by the modulating f i e l d H was J 3 m corrected according to the well known expression of Andrew [3.2]: M 2(true) - M 2(expt) - j H 2 (3.3) A FORTRAN programme employed the summation (3.2) and the modulation correction (3.3) to y i e l d accurate second moments from derivative tracings. ^ 3.2 PULSED NMR MEASUREMENTS 3.2.1 Pulse spectrometer. The pulse spectrometer used was a Bruker B-KR322S variable frequency (16 to 62 MHz) pulse spectrometer. A l l the measurements reported here were performed in the neighbourhood of 30 MHz. A schematic block diagram of the spectrometer i s shown in Figure (3.1). The pulse generator contains b a s i c a l l y a very stable 1 MHz quartz o s c i l l a t o r , from which a l l the measuring times are derived d i g i t a l l y ; t h e i r accuracy i s of the same order as that of the o s c i l l a t o r frequency. The basic 1 MHz frequency from the main o s c i l l a t o r i s taken Heathkit r.f. power amp)if ier Bruker r.f. power amp!i f ier For T, ( — o P Reference phase shifter For^j Transmitter Phase shifter l + l l + l I I HF Pulse amplif ier Frequency Gate Gate synthes izer 1 1 1 II + I I I * Pulse generator & Programmer Preampli f ier Attenuator Gated amp] i f ier Probe head Power supply Tr i gger Time index Receiver Signal processi ng Pu1se gated integrator Trigger relay 1 Teletype 1, T imer DVM JEOL computor I nterface Automated data processing FIGURE 3.1 Block diagram for the pulse spectrometer. - 50 -i n t o a f r e q u e n c y s y n t h e s i z e r where i t i s u s e d as a r e f e r e n c e t o p r o d u c e t h e r e q u i r e d r a d i o f r e q u e n c y f o r t h e NMR e x p e r i -ment. The r . f . i s now f e d i n t o t h r e e c h a n n e l s : ( i ) t o g a t e I (opened by p u l s e I) v i a a p h a s e s h i f t e r , ( i i ) t o g a t e I I (opened by p u l s e s I I and I I I ) d i r e c t l y , and ( H i ) t o t h e ph a s e s e n s i t i v e d e t e c t o r ( V i a a n o t h e r phase s h i f t e r ) t o s e r v e as a phase c o h e r e n t r e f e r e n c e f r e q u e n c y f o r t h e p h a s e s e n s i t i v e d e t e c t o r . The h i g h f r e q u e n c y , i n t h e f o r m o f p u l s e s f r o m g a t e s I and I I , i s t h e n f e d t o a b r o a d b a n d HF power a m p l i f i e r w h i c h d r i v e s a f i v e - s t a g e , t u n e d r . f . power a m p l i f i e r . A f t e r t h e s e s t a g e s o f power a m p l i f i c a t i o n , 180° p u l s e s t y p i c a l l y 2-3ysec l o n g c o u l d be d e l i v e r e d t o t h e p r o b e c o i l f o r t h e nmr p u l s e e x p e r i m e n t . The p r o b e u s e d i n t h e s e e x p e r i m e n t s was a d a p t e d i n t h i s d e p a r t m e n t f o r u s e w i t h a s i n g l e c o i l a r r a n g e m e n t ( i n s t e a d o f t h e ' d o u b l e c o i l ' c o n f i g u r a t i o n s u p p l i e d by B r u k e r ) ; i t s c i r c u i t d i a g r a m i s shown i n F i g u r e (3.2), w i t h b r i e f n o t a t i o n s on t h e c i r c u i t f u n c t i o n . The s i g n a l f r o m t h e p r o b e now p a s s e s t h r o u g h 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 f e d t h r o u g h a g a t e d a m p l i f i e r i n t o t h e r e c e i v e r where i t i s a m p l i f i e d and p h a s e s e n s i t i v e d e t e c t e d . The g a t e d a m p l i f i e r m e n t i o n e d above was added as a m o d i f i c a t i o n t o t h e o r i g i n a l B r u k e r c i r c u i t r y i n o r d e r t o p r o t e c t t h e r e c e i v e r f r o m t h e e f f e c t s o f t h e s t r o n g r . f . p u l s e s , t h e r e b y p r e v e n t i n g o v e r l o a d o f t h e r e c e i v e r . - 51 -p r e a m p l i f i e r A R.F. power[ a m p l i f i e r •M-FIGURE 3.2 C i r c u i t d i a g r a m f o r t h e s i n g l e - c o i l nmr p r o b e u s e d i n t h e p u l s e s p e c t r o m e t e r . - 52 -The dead time of the receiver a f t e r an r . f . pulse i s about 7-10 ysec at 30 MHz. The maximum bandwidth of the receiver unit i s 1 MHz and a l l measurements were ca r r i e d out using t h i s value of bandwidth. The set up described above was used for T^ measure-ments. For T.. measurements, where the use of long r . f . lp • . ^ pulses in the rotating frame- becomes necessary, i t was found that the Bruker r . f . amplifier was not capable of deli v e r i n g steady pulses of long duration. Therefore, for T^p measurements, the Bruker r . f . amplifier was replaced by a Heathkit^ DX60 r . f . power amplifier. The DX60's power supply i s replaced by an HP model 712B.regulated power supply. With t h i s modification steady pulses of long duration were attainable. The maximum H^ f i e l d obtainable was 8.4 G. 3.2.2 Variable temperature assembly. The quartz variable temperature ins e r t used i n these experiments was d i f f e r e n t from the commercially a v a i l -able Bruker i n s e r t and was designed in t h i s department. The temperature regulation method was sim i l a r to that used i n the CW measurements except that the temperatures here were contolled by a Bruker B-ST 100/700 temperature c o n t r o l l e r . The Heathkit was modified to introduce screen-grid modula-ti o n at the f i n a l stage of amplification. - 53 -The o r i g i n a l form of the Bruker c o n t r o l l e r i s capable of co n t r o l l i n g temperatures only down to 100K. To control temperatures between 77 and 100K, the Cu-constantan thermo-couple voltage was increased by inser t i n g a battery. The temperatures d i r e c t l y read from the Bruker c o n t r o l l e r were calibra t e d against a temperature measurement made by another thermocouple embedded i n a sample. 3.2.3 Measurement of T^. Spin l a t t i c e relaxation time in the Zeeman frame, T^, was measured by either a 180°-T-90° or a n90°-T-90° [3.4] pulse sequence. If the relaxation i s exponential, the relaxation function, R(x), i s given by, R(T) = [M -M (T)]/2M = exp(-i/T 1) (3.4) for a 180-T-90 pulse sequence, and R(x) = [M -Ml/NI = exp(-x/T 1) (3.5) for a n90-x-90 pulse sequence, where M q i s proportional to the signal following a pulse sequence with x>>T,, and M (x) J- z i s proportional to the signal height following either sequence - 54 -f o r a p a r t i c u l a r v a l u e o f T. Thus, a p l o t o f l n R ( x ) v s . x g i v e s a s t r a i g h t l i n e w i t h s l o p e A l e a s t - s q u a r e s 1 f i t o f t h e d e c a y a m p l i t u d e s f o l l o w i n g a p u l s e s e q u e n c e t o E q u a t i o n s (3.4) o r (3.5) were p e r f o r m e d by a JEOL computor. The r e s u l t i n g T ^ 1 s a r e a c c u r a t e t o w i t h i n ± 4 % . F o r T 1 < 2 s e c , t h e 1 8 0 ° - T - 9 0 ° s e q u e n c e was u s e d whereas f o r T^>2sec, t h e s a t u r a t i o n s e q u e n c e , n 9 0 ° - x - 9 0 ° was u s e d . 3.2.4 Measurement o f T-j_ . 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 n t h e r o t a t i n g f r a me, T'lp' was m e asured u s i n g t h e f o l l o w i n g p u l s e s e q u e n c e : a 90° p u l s e was i m m e d i a t e l y f o l l o w e d by a ' s p i n l o c k i n g " 9 0 ° -p h a s e - s h i f t e d p u l s e o f v a r i a b l e d u r a t i o n [ 3 . 4 ] . R e l a x a t i o n i s now g o v e r n e d by t h e e q u a t i o n , M -T/T, R(T) = ^ = e ± p (3.6) o where M z i s p r o p o r t i o n a l t o s i g n a l h e i g h t f o l l o w i n g t h e s e c o n d p u l s e and M q i s p r o p o r t i o n a l t o t h e s i g n a l h e i g h t i n t h e a b s e n c e o f t h e s e c o n d p u l s e . A p l o t o f lnR.(vx) v s . x g i v e s a s l o p e o f -1/T^ . The s t r e n g t h o f t h e s p i n - l o c k i n g f i e l d was d e t e r m i n e d by m e a s u r i n g t h e l e n g t h o f a 180° p u l s e . R e f e r e n c e s [3.1] F.N.H. R o b i n s o n , J . S c i . I n s t r . 3_6, 481 (1959). [3.2] E.R. Andrew, Phys. Rev. 91, 425 (1953). [3.3] The JEOL computer was programmed by Dr. E.E. B u r n e l l o f t h i s d e p a r t m e n t . [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 T r a n s - f o r m NMR, A c a d e m i c P r e s s , ( 1 9 7 1 ) . [3.5] D.C. Look and I . J . Lowe,. J . Chem. Ph y s . 4_4, 2995 (1966). - 56 -CHAPTER IV M o l e c u l a r M o t i o n i n t-butylammonium t r o p o l o n a t e 4.1 INTRODUCTION I n C h a p t e r I I , t h e b a s i c t h e o r y o f n u c l e a r m a g n e t i c r e s o n a n c e was p r e s e n t e d and i t s p o t e n t i a l u s e s i n d i c a t e d . The t e c h n i q u e has been f u l l y e x p l o i t e d i n s t u d y i n g a v a r i e t y o f a s p e c t s o f c h e m i c a l p h y s i c s o f t h e s o l i d s t a t e and o r i e n t e d s y s t e m s (see f o r example, R e f . [4.1]). I n p a r t i c u l a r , i t has p r o v e d t o be a p o w e r f u l t o o l i n s t u d y i n g s t r u c t u r e and m o l e c u l a r m o t i o n s i n t h e s e s y s t e m s . The c h e m i c a l s y s t e m s so f a r s t u d i e d i n t h i s r e s p e c t a r e d i v e r s e , r a n g i n g f r o m s m a l l m o l e c u l e s i n c o n d e n s e d [4.2 ,4.3], g l a s s y [4.4-4.6], l i q u i d -c r y s t a l l i n e [4.7,4.8] and c l a t h r a t e [4.9-4.11] p h a s e s , a d d i t i o n compounds between two s m a l l m o l e c u l e s [4.12,4.13], t o t h e more c o m p l i c a t e d c a s e s o f p o l y m e r s [4.14,4.15], s o a p s [4.16] and b i o l o g i c a l s y s t e m s [4.17]. T h i s c h a p t e r d e s c r i b e s t h e s t u d y o f m o l e c u l a r m o t i o n i n t h e a d d i t i o n compound fo r m e d between t - b u t y l a m i n e , (CH3)gCNH2 and t h e seven-membered r i n g t r o p o l o n e , C-,HrO_. The s y n t h e s i s o f t h e compound has been r e p o r t e d r e c e n t l y [4.18] a l o n g w i t h - 57 -addition compounds of several other amines with tropolone. The molecular structure of the compound i s s a l t - l i k e and i s shown below. I I I From the point of view of motional dynamics, t h i s com-pound i s of interest because, (i) the cati o n i c fragment i s highly symmetrical and may therefore be expected to exhibit extensive molecular motion, ( i i ) the motional behaviour of t-butylamine [4.19] and of a system similar to that of tro-polonate ion, that of tropilium cation [4.20] have been studied by NMR, and i t would be of intere s t to examine how thei r behaviour i s modified in the "adduct" structure, + ( i i i ) the NH^ fragment i s also of intere s t per se, espe c i a l l y in view of i t s importance in amino acid structures, and has not been studied i n many environments. - 58 -4.2 EXPERIMENTAL 4.2.1 Sample preparation. .Tropolone obtained from A l d r i c h Chemicals and t-butylamine from Eastman Kodak were used without further p u r i f i c a t i o n . D^O (99.7%) was obtained from Merck, Sharp and Dohme, Canada Ltd. + The tropolone s a l t of t-butylamine (CH 3) 3CNH 3C 7H 50 2 (I) was prepared by adding stoichiometric quantities of tropolone in CCl^ to t-butylamine in CCl^. The compound precipitated immediately as a yellow s o l i d and was p u r i f i e d by vacuum sublination. Microanalysis for C, H and N yielded the following r e s u l t s : C = 68.4%, H = 8.98% and N = 6.87% (calculated, C = 67.6%, H = 8.78% and N = 7.17%). The melting point of 190°C agreed well with that reported e a r l i e r [4.18]. + The deuterated compound, (CH3) 3CND3C7H,-02, or compound II, was prepared by r e c r y s t a l l i z i n g I i n D 20 several times u n t i l the s p i n - l a t t i c e relaxation time data stayed v i r t u a l l y constant for two successive preparations. The samples were ground to a fine powder and trans-ferred to 10 mm O.D. glass tubes for c.w. measurements and to 7 mm 0 : . i D . thin wall glass tubes for s p i n - l a t t i c e relaxa-t i o n time measurements. They were then pumped on a vacuum l i n e for at least 12 hours and sealed under vacuum. - 59 -4.2.2 S p e c t r o m e t e r s . C o n t i n u o u s wave measurements down t o 10OK were p e r f o r m e d a t 8 MHz on t h e w i d e l i n e nmr s p e c t r o m e t e r I d e s c r i b e d i n S e c t i o n 3.1.1, and t h o s e a t 77K and 68K were c a r r i e d o u t a t 17.3 MHz on t h e w i d e l i n e s p e c t r o m e t e r I I d e s c r i b e d i n S e c t i o n 3.1.4. The t e m p e r a t u r e o f 68K was a c h i e v e d by pumping on l i q u i d n i t r o g e n . 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 s i n Zeeman fra m e (T^) were m e a s u r e d on t h e p u l s e s p e c t r o m e t e r d e s c r i b e d i n S e c t i o n 3.2.1 a t 30.00 MHz. - 6 0 -4 . 3 RESULTS 4.3.1 Continuous wave measurements. The observed temperature dependence of the l i n e -widths and second moments of the proton magnetic resonance absorption for the tropolone s a l t of t-butylamine (I) i s shown i n Figure (4.1). The second moment has a 'plateau 1 2 value of 25.5 G from the lowest temperature studied, (66K) u n t i l about 100K, at which temperature i t undergoes a sudden 2 t r a n s i t i o n reaching a second plateau of 15.5 G . Again, at ^190K, the second moment undergoes a further t r a n s i t i o n 2 reaching a f i n a l plateau of 3.5 G . The linewidths show a similar behaviour to the second moments. The representative proton magnetic resonance lineshapes for compound I at four selected temperatures are shown in Figure (4.2). The spectrum at 77K has the familiar ' t r i p l e t ' lineshape c h a r a c t e r i s t i c of dipolar interactions among protons i n a r i g i d triangular configuration. To r a t i o n a l i z e these res u l t s , various motional models are considered and estimates of the corresponding the o r e t i c a l second moments made. Case of the 'rigid lattice1. 1 14 For a p o l y c r y s t a l l i n e sample containing H and N nuclei, substitution of appropriate nuclear constants i n equation (2.21) leads to the r e s u l t , 100 2 0 0 3 0 0 4 0 0 Temperature CK] FIGURE 4.1 Temperature dependence of the linewidths (open c i r c l e s ) and second moments ( f i l l e d c i r c l e s ) of the proton magnetic resonance absorption for tropolone s a l t of t-butylamine (I). FIGURE 4.2 R e p r e s e n t a t i v e p r o t o n m a g n e t i c r e s o n a n c e x l i n e s h a p e s f o r t r o p o l s a l t o f t - b u t y l a m i n e a t .four s e l e c t e d t e m p e r a t u r e s . - 63 -M 2 = 716.164 N + 2.216 N (4.1) where, N i s the number of protons per molecule, r^_. i s the distance i n Angstrom units between protons i and j , and r_^ N i s the distance i n Angstrom units between proton i and the nitrogen atom. The ' r i g i d ' l a t t i c e second moment may be considered to be a sum of two contributions: M2, the intramolecular part II i and M2, the intermolecular part. M2 may further be broken down into contributions within each group such as, CH,,, NH^ and Tr , and the intergroup contributions. Since no s t r u c t u r a l information on t h i s compound i s available, i t i s reasonable to assume a molecular structure with standard bond, distances and bond angles. For the + o (CH 3) 3CNH 3 cation, bond distances of C-C---= 1.54 A, C-H = 1.09 A, C-N = 1.47 A and N-H = 1.03 A and tetrahedral angles at the four carbon atoms and at the nitrogen atom were assumed;' the parameters for the tropolonate anion, Tr were assumed to be the same as those of Tr i n sodium tropolonate [4.21], Using these parameters and an 'unhindered' conformation for the cation, the proton coordinates were generated by a com-puter program employing a procedure due to Thompson [4.22], and are shown in Table 4.1. The interproton distances are now r e a d i l y calculated and substitution of these in Equation + - 64 -TABLE 4.1 Proton Coordinates (in Angstrom units) of the t-butylammonium cation X Y Z -1.243 -2.082 0.515 -2.931 -1.501 0.515 -2.087 -1.792 -l:.i031 -1.243 0. 595 -2.061 -2.931 0.304 -1.558 -2.087 1.788 -1.036 -1.600 1.753 1. 251 -3. 061 0.728 1. 261 -1.600 0.207 2.14 3 0.335 0.487 0. 843 0. 335 -0.974 0.000 0. 335 0.487 -0.843 methyl methyl methyl NH-, Proton Coordinates (in Angstrom units) of the • tropolonate anion  (Axes as shown in figure below) Y* x 0.98 3.28 4.11 0. 96 3.22 2.61 2.14 0. 00 -2.58 -2.12 - 65 -1 2 (4.1) gives a second moment, M2 of 22.87 G . The contributions from various groups to t h i s value are shown in column 1 of Table 4.2. The intergroup contributions depend on the r e l a t i v e orientations of the three CH^ and the NH^ groups. However, i t was found that the values are not very sensitive to the r e l a t i v e orientation of the groups. This has also been pointed out by Powles and K a i l [4.23] elsewhere i n a study of isobutyl bromide. For a precise estimate of the intermolecular contribution it to the second moment, M , one requires a knowledge of the c r y s t a l structure. However, several methods are available II to obtain approximate estimates for M2 i n t n e absence of stru c t u r a l information [4.24] of which the method described below i s most suitable for our purposes. Assuming the proton density to be dis t r i b u t e d on the surface of a sphere, Smith [4.24] has obtained an approximate expression for M2, namely, M2 = 3 5 8 - 1 X ( ^ ) R ^ ( 4 * 2 ) where n^ i s the number of protons per unit c e l l , V i s the volume of the unit c e l l , and R i s the molecular radius. Writing V i n terms of the density of the material, we get \ / R 1( M = 358.1 x l ^ f P — ^ (4.3) " \0 En.M. i i i - 66 -where i s t h e number o f m o l e c u l e s o f t y p e i i n t h e u n i t c e l l and NL t h e i r gram m o l e c u l a r w e i g h t ; ^yVis t h e A v a g a d r o ' s number. I n a s o l i d where o n l y one t y p e o f m o l e c u l e e x i s t s , E q u a t i o n (4.3) r e d u c e s t o , rV l \ / N p / \ " A R 3 A l 0 2 4 x M y M 2 = 358.1 x l ^ | [ - ^ ] ( - ^ ] . (4.4) where M i s t h e gram m o l e c u l a r w e i g h t o f t h e s u b s t a n c e and i s t h e number o f p r o t o n s p e r m o l e c u l e . o F o r a c a l c u l a t e d m o l e c u l a r r a d i u s o f 4 A and a measured -3 d e n s i t y o f ^ 2 g ; c m f o r compound I, u s e o f E q u a t i o n (4.4) 2 " g i v e s a v a l u e o f 2.5 G f o r M.^' g i v i n g a t o t a l s e c o n d moment o f 25.4 G 2 . Motional models. V a r i o u s p o s s i b l e dynamic modes a r e n e x t c o n s i d e r e d . A s s u m i n g t h e s e m o t i o n s r t o t a k e p l a c e a t a r a t e r a p i d enough t o c a u s e an NMR l i n e n a r r o w i n g , t h e c o r r e s p o n d i n g r e d u c e d s e c o n d moments were t h e n c a l c u l a t e d . R o t a t i o n o f m e t h y l g r o u p s a b o u t t h e i r symmetry a x e s r e d u c e s t h e i n t r a m e t h y l s e c o n d moment c o n t r i b u t i o n by a + f a c t o r o f 4. R o t a t i o n o f t h e NH^ g r o u p a b o u t i t s symmetry + a x i s r e d u c e s t h e H-H ( i n NH^) c o n t r i b u t i o n by a f a c t o r o f 4 + and t h e N-H ( i n NH^) c o n t r i b u t i o n by t h e f a c t o r g i v e n i n E q u a t i o n (2.29) w i t h e " = 7 0 . 5 ° . F o r t h e r o t a t i o n o f t h e - 67 -whole t-butyl group about the C-N bond, the reduction factor i s obtained from Equation (2.34) with \p = 70.5°. The reduction factors for the intergroup second moment contributions cannot be calculated p r e c i s e l y . Here again, approximations have been made [4.24-4.27] to estimate these quantities. The possible motional modes that could account for the proton resonance l i n e narrowing observed in adduct I, and the i r corresponding residual second moments computed using the above mentioned procedures, are set out in Table 4.2. Upon comparing the observed second moment;:values corresponding to the 'plateau' regions of Figure (4.1) with those calculated (Table 4.2), the following motional processes may^ .be assigned: (i) In the temperature region 6 6K-100K, the observed 2 'plateau' value of 25.5 G i s consistent with the r i g i d 2 l a t t i c e value of 25.4 G , suggesting a r e l a t i v e l y r i g i d structure. The observed t r i p l e t lineshapes in t h i s temperature range indeed support t h i s assignment. ( i i ) As the temperature i s raised, the f i r s t motion most l i k e l y to produce l i n e narrowing i s the reorienta-tion of the methyl groups about th e i r symmetry axes. The value of the residual second moment expected for 2 th i s motion .(15.4 G , Table 4.2) agrees well with the 2 plateau value of 15.5 G observed between 110K and 220K, TABLE 4.2 C a l c u l a t e d Second Moment Contributions (Gauss 2) for the T e r t i a r y Butylamine-Tropolone Adduct Type of I n t e r a c t i o n R i g i d S t r u c t u r e Motional Models CH 3 Rotation about C3 Axis CH3 Rotation + NH3 Rotation about t h e i r C3 axes C3 Rotation of CH 3 + NH 3 r o t a t i n g + CH3 + C 3 of t - b u t y l group o v e r a l l r o t a t i o n of t - b u t y l about the molecular cl a x i s Intragroup: H-H i n Methyls 11.72 2.93 2.93 2.93 0.34 H-H i n NH* 5.48 5.48 1.37 5.48 1.37 N-H i n NH* 0.33 0.33 0.05 0.33 0.05 H-H i n Tr" 1.13 . 1.13 1.13 1.13 1.13 Intergroup: Inter-Methyl 1.64 1.42 1.42 0.15 0.15 Methyl-NH* 2.57 ^2.4 ^2.2 ^0.5 0.30 Inter-Molecular I n t e r a t i o n : ^ 2.50 %1.75 ^1.0 /v,0.75 ^0.5 TOTAL: ^25.4 ^15.4 ^10.1 ^11.3 ^3.84 - 69 -confirming that the l i n e narrowing at ^10 OK i s indeed caused by methyl group reorientation. ( i i i ) Two other internal motions are l i k e l y to occur about the C-N bond. These are, + a) rotation of the NH^ group about i t s threefold symmetry axis b) rotation of the (bulkier) t-butyl group about the C-N bond axis (labelled as C^). The expected residual second moments for either of these 2 motions i s around 10 G (Table 4.2). However, the observed 2 second moment shows no plateau in the region of 10 G , but 2 shows a f i n a l plateau of 3.5 G , which agrees well with a s i t u a t i o n where both of the above-mentioned motional processes taking place concomitantly at comparable frequencies. It i s thus possible that the (CH^^C-NH^ cation rotates about the C-N bond as one unit (without any int e r n a l rotation about the C-N bond) causing a single l i n e narrowing at ^210K. Further confirmation of t h i s p o s s i b i l i t y may be sought from T^ measurements which give more accurate values for the c o r r e l a t i o n times. The T^ data are discussed i n the next section. It i s to be noted that, from our data, no conclusion could be derived regarding the motion, i f any, of the tropolonate anion (Tr ). This i s because of the fact that the i n t e r -proton distances involved i n the tropolonate ion are much - 70 -larger?.arid y i e l d a second moment contribution of only 1.13 Gz even for the ' r i g i d l a t t i c e ' structure of the anion (Table 4.2) . The most l i k e l y motions would be rapid f l i p p i n g of the tropolonate ring about a axis of symmetry and re-orientation about an axis perpendicular to the plane of the ring . Even i f either of these motions were to be occurring, the corresponding reduction factor to the second moment of the o v e r a l l NMR absorption would be so small as to be hardly noticeable. 4.3.2 Relaxation time measurements. The temperature dependence of the s p i n - l a t t i c e + relaxation times (T 1) for the compound (CH^-jCNH^Tr (I) i s shown i n Figure 4.3 ( f i l l e d c i r c l e s ) . The data show a minimum of 41.4 msec centred at 208K and a second broad and f l a t minimum of 50.5 msec in the temperature range 375-395K. In accordance with our deductions from second moment measurements, the low temperature minimum i s assigned to the rotation of the three methyl groups about th e i r symmetry axes. The high temperature minimum i s broad and i s charac-t e r i s t i c of the absence of a unique c o r r e l a t i o n time. Again, using the second moment r e s u l t s , t h i s i s r a t i o n a l i z e d as being due to rotation of the t-butyl group and the NH^ group about the C-N bond axis, these motions taking place at comparable frequencies. To v e r i f y these assignments further, the c o n t r i -1 1 ! 1 1 1 * 3 4 5 6 7 8 1000/T CK"'] .3 Temperature dependence of the proton s p i n - l a t t i c e relaxation times, T x for (a) ^CH 3) 3CNH 3Tr~ ( f i l l e d c i r c l e s ) , (b) (CH 3) 3CND 3Tr" (open c i r c l e s ) , and (c) NH3 (triangles) derived from the data sets (a) and (b) . The s o l i d l i n e s through the data points are theoretical lines with 'best-f i t 1 parameters in Table 4.5. - 72 -+ bution to the relaxation from the NH^ group was removed by studying the s p i n - l a t t i c e relaxation times for the deuterated compound, (CH^^CND^Tr (compound I I ) , and these re s u l t s are represented by the open c i r c l e s i n Figure 4.3. As expected, the low temperature minimum which i s due to methyl rotation undergoes very l i t t l e change, whereas the high temperature minimum i s now due to the rotation of the t-butyl group alone about the C-N bond. The narrow and symmetric nature of t h i s minimum i s i n support of t h i s assignment. The experimental T^ minima and t h e i r respective assignments are summarized i n Table 4.3. We now turn to a more quantitative discussion of the relaxation data. Neglecting cross-correlation e f f e c t s , and assuming the presence of a common spin temperature, Equation (2.52) i s rewritten for t h i s p a r t i c u l a r case as, 1 1_ ( 9 3 5 \ ( 4 5 ) T x 17 y T 1 ( t - B u ) + T 1(NH 3) + T^Tr") J for (CH 3) 3CNH 3Tr~ (I) and, 1_ = 1_ / 9 5 \ T± 14 lT 1(t-Bu) T x(Tr-) J  (q' b> for (CH 3) 3CND 3Tr (II), TABLE 4.3 Experimental T^ Minima for Ter t i a r y Butylamine-Tropolone Adduct Temperature Assignment Compound at Minimum T-^  Minimum of (Kelvin) (milliseconds) Motion (CH3) 3'CNH3Tr 208 41.4 C 3(CH 3) 375..- 395 50.5 C 3(t-Bu) + C3(NH*) (CH 3) 3CND 3Tr 208 38.25 C 3(CH 3) 370 65. 9 C 3 (t-Bu) -NH. .425 (a) 14.35 (a) C 3(NH 3) Values estimated by difference -- see text. - 74 -where, (t-Bu) , T^NH.^) and T-^T.r") a r e t h e c o n t r i b u t i o n s t o t h e o v e r a l l r e l a x a t i o n f r o m (Z(CE^) ^ , NH^ and t h e t r o p o l o n a t e a n i o n T r r e s p e c t i v e l y ; t h e s e q u a n t i t i e s may now be d e s c r i b e d i n d i v i d u a l l y u s i n g t h e BPP t h e o r y . The e f f e c t o f t h e NH^ r o t a t i o n w i l l be b e s t s e e n i n t h e r e l a x a t i o n d a t a f o r t h e d e u t e r a t e d compound (CD^^CNH^Tr , b u t s i n c e t h i s compound was n o t a v a i l a b l e t o u s , we r e s o r t e d t o t h e f o l l o w i n g a p p r o a c h . From E q u a t i o n s (4.5) and (4.6), we o b t a i n , i = I ( j j . 1 4 _ _ \ ( 4 7 ) T l ( N H 3 ) 3 \ T 1 ( I ) T 1 ( I I ) / where, T ^ I ) and T 1 ( I I ) a r e t h e d a t a f o r compounds I and I I , r e s p e c t i v e l y , a t some p a r t i c u l a r t e m p e r a t u r e . U s i n g E q u a t i o n (4.7), t h e NH^ c o n t r i b u t i o n t o t h e r e l a x a t i o n i n t h e n e i g h b o u r h o o d o f t h e h i g h t e m p e r a t u r e minimum i s e v a l u a t e d f r o m t h e e x p e r i m e n t a l T ^ ( I ) and T ^ ( I I ) v a l u e s a t a s e r i e s o f t e m p e r a t u r e s i n t h e r a n g e 320-465K, and t h e s e r e s u l t s a r e r e p r e s e n t e d by f i l l e d t r i a n g l e s i n F i g u r e (4.3). As e x p e c t e d , t h e d a t a show a w e l l - d e f i n e d minimum c o r r e s p o n d i n g t o t h e r o t a t i o n o f t h e NH-, g r o u p (see a l s o T a b l e 4 .3) . Tj minima. As m e n t i o n e d i n S e c t i o n 2.6.2, t h e d e p t h o f a minimum depends on t h e d e t a i l s o f m o t i o n c a u s i n g i t . We s h a l l t h e r e f o r e -,75 -attempt to confirm our assignments of the minima (Table 4.3) by comparing the experimental T^ (minimum) values with those expected t h e o r e t i c a l l y for the p a r t i c u l a r motion proposed. The possible motional modes are considered in turn, and i t i s assumed that the o v e r a l l relaxation i s dominated by only the p a r t i c u l a r motion considered, with the other spins coming to a common spin temperature by spin d i f f u s i o n ; i . e . , in Equations (4.5) and (4.6), for the group undergoing the motion under consideration, the expression for T^ relevant to that motion i s substituted while the other motions are assumed not to contribute ( i . e . , other T^°°) . For the reorientation of a methyl group about i t s symmetry axis, the relaxation rate expression was given i n Equation (2.53). Using t h i s expression for (t-Bu) in Equations (4.5) and (4.6) with the other T^'s set to i n f i n i t y , the T^(min) values for the relaxation governed by methyl rotation i n compounds I and II were calculated as 33.2 and 27.3 msec, respectively. I t i s to be noted that t h i s calcu-l a t i o n includes only the interactions within a methyl group; inclusion of the other interactions i s expected to lower the T^ minimum. Sim i l a r l y , for the motion of the t-butyl group about the molecular threefold axis (C^) superposed on fas t motion:.: of methyls, using Equation (2.57), (min) values for I and II were 112.0 and 92.2 msec respectively. In t h i s case, i t i s also possible to estimate the intermethyl contribution to the o v e r a l l relaxation. This i s done [4.28,4.29] by assuming that when x <<x „ (x and x 9 as defined i n Equation (2.54)), the protons of each methyl group are concentrated on t h e i r respective C 3 symmetry axes as point dipoles. Thus, the intermethyl contribution i s brought about by a motion of the three point dipoles, similar to the motion of a methyl group, the rate expression for which was given i n Equation (2.53). The intermethyl contribution to the relaxation govern by a threefold rotation of the t-butyl group, may be thereby written as, = 3 x ?r f (0J x „ ) (4.8) T1 (intermethyl) " A 20f* 6 i V U , o L c 2 where r^ i s now the distance between two methyl groups which are collapsed into points. In (4.8), expression (2.53) i s mu l t i p l i e d by a factor 3 since there are now three protons at each point dipole. When thi s correction i s added, with o r* = 3.10 A, the T^(min) values-for I and II were found to be 80.6 and 66.4 msec, respectively. The rotation of the NH^ group i s s i m i l a r to the rotation of a methyl group, and using the expression (2.53) o with r = 1.6 8 A, for compound I, a value of 7 3.1 msec i s obtained. For an i s o l a t e d NH^ group, a value of 12.9 msec i s obtained. -.77 -The possible motional modes for the tropolonate ion are considered next. The relaxation rate expressions for the tropolonate ion are derived from Equations (2.51) and (2.52) with the appropriate expressions for the spectral densities, J's. The geometry of the tropolonate ion i s assumed to be the same as that i n sodium tropolonate [4.21]. The only axis of symmetry i t possesses i s a C 2 axis. For a 180° ' f l i p p i n g 1 of the rin g about i t s twofold symmetry axis, using spectral densities (Equations (2.49) and (2.50)) i n Equations (2.51) and (2.52), the ^(min) values for compounds I and II were calculated as 1005 and 828 msec, respectively. I f , on the other hand, the c r y s t a l structure around the tropolonate ring were to be such as to provide an n f o l d b a r r i e r (n>3), leading e s s e n t i a l l y to a continuous stepwise jumps of the tropolonate ring, the spectral densities in Equations (2.47) and (2.48) have to be used. Considering t h i s model, T^(min) values of 275 and 226 msec are obtained for the compounds I and II, respectively. For reorientations of the rin g about an axis perpendicular to i t , again, use of spectral densities in Equations (2.47) and (2.48) give T^(min) values of 416 and 342 for compounds I and II, respectively. The calculated T^(min) values for various motional models are summarized i n Table 4.4, and these are to be com-pared with the experimental values in Table 4.3. The low temperature 1^ minima in both compounds are somewhat higher TABLE 4.4 Calculated T1 Minima (in milliseconds) for Tertiary Butylamine-Tropolone Adduct Compound C 3(CH 3) C 3(t-Bu) C 3(t-Bu) C-(NH') C 2(Tr ) C 2(Tr ) Rotation of correctedt Free Jump T r - about a perpendicular axis (CH 3) 3CNH 3Tr 3 3.2 112.0 80.6 73.1 oo 275. 0 1005.0 416.0 (CH 3) 3CND 3Tr 27.3 92.2 66.4 226. 0 828. 0 342. 0 -NH3 group 12. 9 The correction takes into account inter-methyl contributions, Eq. 9 of text. - 79 -than the t h e o r e t i c a l values expected for motion of methyls, es p e c i a l l y considering the neglect of the contributions from outside the methyl group. However, in view of the number of simplifying assumptions made, the agreement i s s t i l l quite reasonable. The high temperature T^(min) i n compound II i s i n excellent agreement with the calculated value for motion of the t-butyl moeity in which a correction for the intermethyl contribution has been made. Furthermore, T^(min) value for the i s o l a t e d NH^ group extracted from the experimental data i s in excellent agreement with the expected value. Thus, we may now conclude that our assignments of the minima are correct. Correlation times and activation energies. For the relaxation governed by any singleutype of motion, the rate expression was given by the generalized BPP Equation (2.58). At the T^ minimum, c u ^ n r i = 0.616, and substitution of t h i s value i n Equation (2.58) leads to 1 = C x 1.425 . (4.9) T.^(min) Thus, C may be evaluated from a knowledge of the depth of the minimum. Once C i s known, the c o r r e l a t i o n time at any given temperature can be calculated by substituting T^ at that temperature in Equation (2.58). - 80 -Using the above-mentioned procedure, the c o r r e l a t i o n times for motion of methyl groups derived from the data in the neighbourhood of the low temperature minima i n compounds I and II are shown i n Figure (4.4). F i l l e d c i r c l e s are data points for compound I and open c i r c l e s are for compound II. The data points are found to l i e on a straight l i n e in the l n x c vs. 1/T plot, showing an Arrhenius-type a c t i v a t i o n law to be obeyed. A least-squares f i t to the data points gives an ac t i v a t i o n energy of 2.90 ± 0.05 kcal mole . The c o r r e l a t i o n times for the motion of the t-butyl moeity about i t s threefold axis of rotation (C^) are obtained from the data near the high temperature minimum i n compound II, and are represented by open c i r c l e s in Figure (4.5). From the data derived for the case of an is o l a t e d NH^ group, we have obtained the co r r e l a t i o n times for the motion of the NH^ group, and these are also presented i n Figure (4.5) ( f i l l e d c i r c l e s ) . Again, the l n i c vs. 1/T plot i s found to be l i n e a r . Least-squares f i t s to the data points of Figure (4.5) gives a c t i v a t i o n energies of 8.45 ± 0.19 and 7.60 ± 0.25 kcal.mole respectively, for the motion of t-butyl group and NH^ group about the C-N bond. One question to be answered at t h i s point i s whether the t-butylammonium cation rotates about the C-N bond as one unit, or, whether the t-butyl group and the NH., group - 81 -FIGURE 4.4 Temperature dependence of co r r e l a t i o n times for C 3 reorientation of methyls. F i l l e d c i r c l e s : from Ti data for compound I; open c i r c l e s : from Ti data for compound I I . FIGURE 4.5 Temperature dependences of c o r r e l a t i o n times f o r C 3 motion of the t-bu^yl group (open c i r c l e s ) and C 3 motion of the NH3 group ( f i l l e d c i r c l e s ) . - 83 -r o t a t e i n d e p e n d e n t l y o f e a c h o t h e r a b o u t t h e C-N bond. As s e e n i n F i g u r e ( 4 . 5 ) , t h e c o r r e l a t i o n t i m e s f o r t h e NH^ g r o u p a r e l o n g e r t h a n t h o s e f o r t h e t - b u t y l g r o u p by a f a c t o r o f 4, s u g g e s t i n g t h e r o t a t i o n o f t h e NH 3 g r o u p t o be s l i g h t l y s l o w e r t h a n t h a t o f t h e t - b u t y l g r o u p . T h i s i s a l s o s u g g e s t e d i n F i g u r e ( 4 . 3 ) , where t h e T^ minimum due t o NH^ m o t i o n a p p e a r s a t a h i g h e r t e m p e r a t u r e t h a n t h a t due t o t h e t - b u t y l g r o u p m o t i o n . A l s o , t h e a c t i v a t i o n e n e r g i e s f o r t h e two g r o u p s a r e d i f f e r e n t by ^1 k c a l mole 1 (a more a c c u r a t e d e t e r m i n a t i o n o f a c t i v a t i o n e n e r g i e s show a d i f f e r e n c e o f ^3 k c a l mole . See l a t e r . ) . I f t h e c a t i o n r o t a t e s as one u n i t , t h e a c t i v a -t i o n e n e r g i e s o b t a i n e d f o r m o t i o n o f e i t h e r o f t h e g r o u p s s h o u l d be t h e same. We a r e t h u s l e d t o c o n c l u d e t h a t t h e r e i s i n t e r n a l r o t a t i o n a b o u t t h e C-N bond and t h a t t h e c a t i o n d o e s n o t r o t a t e as one u n i t . I n o b t a i n i n g t h e c o r r e l a t i o n t i m e s i n F i g u r e s (4.4) and ( 4 . 5 ) , i t was assumed t h a t t h e r e l a x a t i o n i n t h e t e m p e r a t u r e r e g i o n c o n s i d e r e d was due t o a s i n g l e t y p e o f m o t i o n and t h a t c o n t r i b u t i o n s f r o m o t h e r t y p e s o f m o t i o n s were a b s e n t . However, as s e e n i n F i g u r e ( 4 . 3 ) , t h e two minima o b s e r v e d i n e i t h e r o f t h e compounds I o r I I a r e n o t v e r y f a r a p a r t i n t e m p e a r t u r e , and i t i s , t h e r e f o r e , p o s s i b l e t h a t r e l a x a t i o n n e a r one minimum may a l s o have a c o n t r i b u t i o n f r o m t h e m o t i o n c a u s i n g t h e o t h e r minimum. I n s u c h a c a s e , t h e t r u e c o r r e l a t i o n t i m e s and a c t i v a t i o n e n e r g i e s w i l l have t o be o b t a i n e d o n l y by l e a s t -- 84 -s q u a r e s f i t t i n g t h e e n t i r e s e t o f d a t a p o i n t s t o a p p r o p r i a t e e x p r e s s i o n s . T h i s , we s h a l l p r o c e e d t o do as f o l l o w s . The r e l a x a t i o n o f compound I may be d e s c r i b e d by a sum o f t h r e e BPP e x p r e s s i o n s o f t h e t y p e , k7 = C l f ("oV + C 2 f ( V c 2 } + S ^ V c ' ( 4- 1 0 ) where f ( a j Q T ) has t h e f o r m g i v e n i n E q u a t i o n (2.54). T , x c 2 and x c , a r e t h e c o r r e l a t i o n t i m e s f o r t h e m o t i o n o f m e t h y l s , m o t i o n o f t h e t - b u t y l g r o u p and m o t i o n o f t h e NH^ g r o u p r e s p e c t i v e l y , and C^, C 2 and a r e c o n s t a n t s r e p r e s e n t i n g t h e s t r e n g t h o f e a c h r e l a x a t i o n mechanism. E a c h x i s assumed t o have an A r r h e n i u s t e m p e r a t u r e d ependence as i n E q u a t i o n (2.26) w i t h an a s s o c i a t e d a c t i v a t i o n e n e r g y , E. T r e a t i n g t h e c o n s t a n t s , C's and x Js and E's o f E q u a t i o n (2.26) as a d j u s t a b l e p a r a -O :J> m e t e r s , t h e e n t i r e s e t o f T^ d a t a p o i n t s f o r compound I a r e f i t t e d t o e x p r e s s i o n (4.10) by a n o n - l i n e a r l e a s t - s q u a r e s p r o c e d u r e [4.30]. The s o l i d l i n e ( l a b e l l e d a) t h r o u g h t h e d a t a p o i n t s i n F i g u r e (4.3) i s drawn u s i n g E q u a t i o n (4.110) and t h e ' b e s t - f i t ' p a r a m e t e r s r e s u l t i n g f r o m t h e l e a s t - s q u a r e s f i t . The p r o c e d u r e was r e p e a t e d f o r t h e e n t i r e s e t o f T^ v a l u e s f o r compound I I , where t h e r e l a x a t i o n i s now d e s c r i b e d by a sum o f two BPP e x p r e s s i o n s , namely, - = C l f ( a , 0 T c ) + C 2 f ( u V c 2 ) (4.11) - 85 -The s o l i d l i n e ( l a b e l l e d b) i s t h e t h e o r e t i c a l ' b e s t - f i t ' c u r v e . The T^ v a l u e s e x t r a c t e d f o r an i s o l a t e d NH^ g r o u p were f i t t e d t o a s i n g l e BPP e x p r e s s i o n o f t h e t y p e shown i n E q u a t i o n ( 2 . 5 8 ) , r e s u l t i n g i n t h e t h e o r e t i c a l b e s t - f i t l i n e ( l a b e l l e d c) t h r o u g h t h e d a t a p o i n t s . The ' b e s t - f i t ' p a r a m e t e r s r e s u l t i n g f r o m t h e l e a s t - s q u a r e s f i t t i n g p r o c e d u r e s f o r t h e t h r e e c a s e s a r e summarized i n T a b l e 4.5. As s e e n i n F i g u r e ( 4 . 3 ) , t h e o v e r a l l f i t t o t h e d a t a i s q u i t e good. A l s o , e a c h p a r a m e t e r l i s t e d i n T a b l e 4.5 has been o b t a i n e d f r o m two d i f f e r e n t s e t s o f d a t a p o i n t s (namely, f o r m o t i o n o f m e t h y l s and m o t i o n o f t - b u t y l g r o u p f r o m d a t a f o r compounds I and I I , and f o r m o t i o n o f NH^ g r o u p f r o m d a t a f o r I and c a l c u l a t e d d a t a f o r an i s o l a t e d NH^ g r o u p ) ; t h e v a l u e s o f e a c h p a r a m e t e r a g r e e w e l l w i t h one a n o t h e r w i t h i n t h e e r r o r l i m i t s q u o t e d . A l s o , t h e a c t i v a t i o n e n e r g i e s o b t a i n e d e a r l i e r f r o m p l o t s o f l n x c v s . T 1 f o r m o t i o n o f m e t h y l s and m o t i o n o f t h e NH^ g r o u p a r e i n good a g r e e m e n t w i t h t h o s e shown i n T a b l e 4.5. However, t h e a c t i v a t i o n e n e r g y f o r m o t i o n o f t h e t - b u t y l g r o u p , o b t a i n e d e a r l i e r , does n o t a g r e e w i t h t h e c o r r e s p o n d i n g v a l u e i n T a b l e 4.5. Due t o r e a s o n s d i s c u s s e d e a r l i e r , we t a k e t h e p a r a m e t e r s i n T a b l e 4.5 t o be t h e more r e l i a b l e o n e s . The i n t e r n a l c o n s i s t e n c y o f t h e v a l u e s i n T a b l e 4.5, n o t o n l y t e s t i f y t o t h e c o r r e c t n e s s TABLE 4 . 5 ' 3 e s t - F i t ' Parameters t o the Data f o r t-Butylamine Tropolone Adduct L a b e l s ( F i g . 3) Motion o f Methyl C ( s e c ) T ° ( s e c ) 1 c E, K c a l mole Motion of t - b u t y l group C (sec T ° ( s e c ) c E, K c a l mole C 3 Motion o f NH 3 C(sec ) T ° (sec) E, K c a l mole Curve a. (CK 3) 3CN'K 3Tr 17.58±1.06 (I) Curve b, (CH 3) 3CND 3Tr" ( I D Curve c, N K ; -5 ( e x p e r i m e n t a l v a l u e s e s t i -mated by d i f f e r e n c e --see t e x t ) 19.34±1.53 (1.81+0.89) x 10 1 " (2.31±1.32)| x I D " 1 2 3.07±0.20 2.94±0.23 . 03 + 1.12 9.34±1.34 (4.00±5.97) x 1 0 " 1 5 (3.52±7.53) 15 x 10 10.22il.10 7.66±0.91 (6.41±1.49) x 1 0 " 1 3 10.29±1.56 46.13+1.33 (6.90±5.30) x 1 0 " 1 3 7.23±0.15 7.23±0.59 - 87 -o f o u r a n a l y s i s o f t h e r e l a x a t i o n d a t a , b u t a l s o add more c o n f i d e n c e t o t h e p a r a m e t e r s o b t a i n e d by t h i s method. The p r o t o n s e c o n d moment and r e l a x a t i o n t i m e d a t a , w h i l e l e a d i n g t o a r a t h e r c l e a r - c u t a n a l y s i s o f t h e d y n a m i c s o f t h e t-butylammonium c a t i o n , do n o t e n a b l e us t o draw any d e f i n i t i v e c o n c l u s i o n s r e g a r d i n g t h e t r o p o l o n a t e a n i o n . T h i s i s b e c a u s e o f t h e r e l a t i v e l y i n e f f i c i e n t r e l a x a t i o n mechanisms p r o v i d e d by t h e p o s s i b l e m o t i o n s o f t h e t r o p o l o n a t e a n i o n a s see n f r o m t h e h i g h c a l c u l a t e d T^(min) v a l u e s i n T a b l e 4.4. S i n c e t h e s p i n s y s t e m i s e f f i c i e n t l y r e l a x e d by o t h e r mechanisms o v e r t h e e n t i r e r a n g e o f t e m p e r a t u r e s s t u d i e d , any m o t i o n o f t h e t r o p o l o n a t e i o n w o u l d be e x p e c t e d t o make a somewhat i n s i g n i f i c a n t c o n t r i b u t i o n t o t h e o v e r a l l m e a s u r e d T^. However, s t u d i e s on t h e compound w i t h t h e f u l l y d e u t e r a t e d c a t i o n , ( C D ^ ^ N D ^ T r w o u l d e n a b l e one t o o b t a i n d e f i n i t i v e i n f o r m a t i o n r e g a r d i n g t h e m o t i o n , i f any, o f t h e t r o p o l o n a t e r i n g . - 88 -4.4 DISCUSSION The a c t i v a t i o n a l energy b a r r i e r governing the methyl group motion, obtained ..as an average of the two values i n Table 4.5, i s 2.99 ± 0.28 kcal mole" 1. S i m i l a r l y , from the data of Table 4.5, one may assign mean ac t i v a t i o n energies of 10.5 ±±1.5 kcal mole" 1 and 7.23 ± 0.6 kcal mole" 1 for the rotation of the t-butyl group and of the NH^ group, respectively. A study of molecular motion of the t-butylammonium cation, in the h a l i d e - s a l t s (CI , Br , I. ) using proton T^ measurements was reported recently by R a t c l i f f e and Dunell [4.31]. From th e i r study, they suggest one methyl group i n the t-butyl group to be d i f f e r e n t from the other two, and have obtained two d i f f e r e n t activation energies for the two types of methyls. No such behaviour was found i n our study. For C^ motion of the i r less hindered methyl groups, they obtain a c t i v a t i o n energies of 2.51 ± 0.02, 2.54 ± 0.02 and 2.87 ± 0.02 kcal mole" 1 for the chloride, bromide and iodide s a l t , respectively. For the unique methyl group, which i s more hindered, a c t i v a t i o n energies of 5.4 ± 0.4, 5 20 ± 0.3 and 4.2 ± 0.4 kcal mole - 1 for chloride, bromide and iodide, respectively, are obtained. The act i v a t i o n energy of 2.99 ± 0.28 kcal mole 1 obtained by us for the Tr s a l t , i s i n good agreement with values reported by R a t c l i f f e and Dunell for the less hindered methyl groups. For the C^ rotation of the t-butyl groups, R a t c l i f f e and Dunell obtain ac t i v a t i o n energies of 9.4 ± 0.3, 8.1 ± 0.2 and - 89 -5.4 ± 0.2 kcal mole for chloride, bromide and iodide, respectively; for motion of the NH^ group, 8.96 ± 0.26, 7.93 + 0.19 and 6.52 ± 0.24 kcal mole - 1 are obtained. The a c t i v a t i o n energies obtained by us for these two motions i n Tr are also s i m i l a r to t h e i r values. R a t c l i f f e and Dunell have not discussed the p o s s i b i l i t y of i n t e r n a l rotation about the C-N bond. However, as in our case, t h e i r high temperature minimum for the deuterated com-pounds (CH 3) 3CND 3X (X = C l ~ , Br~, I~) appears to occur at a lower temperature than the corresponding minima for the undeuterated compounds, suggesting that NH^ motion i s s l i g h t l y slower than the t-butyl motion. It i s also useful to compare our a c t i v a t i o n energies with those reported for other similar compounds. Our ac t i v a -t i o n energy of 2.99 ± 0.28 kcal mole 1 for the methyl group reorientation seems to be t y p i c a l of methyl groups attached to a carbon atom and reorienting against a threefold b a r r i e r . For instance, i n p i v a l i c acid, (CH3)3COOH [4.32], E = 2.35 ± 0.15 kcal mole and i n (CH 3) 3CND 2 [4.33], an upper l i m i t estimate of E = 3.2 ± 0.1 kcal mole 1 has been reported. In the series of compounds CH 3CC1 3, (CH 3) 2CC1 2, (CH 3) 3CC1 and (CH3)^C [4.34], the a c t i v a t i o n energies have been reported as 4.1, 4.1, 3.6 and 3.0 kcal mole respectively. For the C'^ motion of t e r t i a r y butyl groups rotating against a threefold i n t e r n a l b a r r i e r , we are not aware of any - 90 -a c t i v a t i o n energy va l u e s other than those of R a t c l i f f e and Du n e l l d i s c u s s e d e a r l i e r . The a c t i v a t i o n energy f o r C'^ motion i n (CH^CCOOH [4.32], of 4.00 ± 0.25 k c a l m o l e - 1 , i s lower than our value, as expected f o r the case o f a t h r e e f o l d r o t o r a g a i n s t a twofold i n t e r n a l b a r r i e r . The NH 3 motion has been s t u d i e d i n a v a r i e t y of chemical systems. Andrew, et a l . [4.35] s t u d i e d the NH 3 r e o r i e n t a t i o n i n a s e r i e s of amino a c i d s and found the a c t i v a t i o n energy to be i n the range 6.9 k c a l m o l e - 1 f o r g l y c i n e NH3CH2COO~~ to 11.9 k c a l mole 1 i n DL Leucine. McElroy, e t a l . [4.36] s t u d i e d f i v e more amino a c i d s where the a c t i v a t i o n e n e r g i e s were found to range from 4 k c a l m o l e 1 i n DL.Lysine-HCl to 9.5 k c a l mole 1 i n homocystine. In 6 and y phases of methylammonium c h l o r i d e , A l b e r t and Ripmeester 04.37] r e p o r t v a l u e s of 5.7 ± 0.3 and 7.65 ± 0.4 k c a l mole 1 , r e s p e c t i v e l y . Our a c t i v a t i o n energy of 7.23 ± 0.6 k c a l mole 1 f a l l s w i t h i n the range o f the value s summarized above. As p o i n t e d out by R a t c l i f f e and Dun e l l [4.31], the f a c t t h a t we see a r o t a t i o n of the t - b u t y l c a t i o n about the C-N bond but not the i s o t r o p i c tumbling of the (nearly s p h e r i c a l ) i o n , p o i n t s to some s i g n i f i c a n t e x t e r n a l b a r r i e r a t the NH^ end. The r e l a t i v e l y l a r g e a c t i v a t i o n energy o b t a i n e d f o r the C^ r o t a t i o n of the NH^ group which i s s i m i l a r i n s i z e to the CH 3 group, i s a l s o i n support of a l a r g e e x t e r n a l b a r r i e r . I t should be remembered, however, t h a t the b a r r i e r to r o t a t i o n has - 91 -a c o n t r i b u t i o n from the i n t e r n a l b a r r i e r , which should be + higher f o r a NH^ group than f o r a CH^ group, i n view of the C-N bond d i s t a n c e being s h o r t e r than the C-C bond d i s t a n c e . A p a r t of these r e s u l t s have been p u b l i s h e d elsewhere [4.38] . - 92 -References [4.1] Nuclear Magnetic Resonance, Vol. 1-5, Journal of Chemical Society, S p e c i a l i s t p e r i o d i c a l Reports (1972-1976). [4.2] P.S. Allen, Magnetic Resonance (C.A. McDowell, ed.), MTP International Review of Science, Physical Chemistry Series I, Butterworths, London, Vol. 4 (1972). [4.3] J.D. Graham and R.H. Hannon, J. Chem. Phys. 64, 1204 (1976) and references^therein. [4.4] H.M. Mclntyre and C.S. Johnson, J r . , J. Chem. Phys. 55, 345 (1971). [4.5] C. Mottley and C.S. Johnson, J r . , J. Chem. Phys. 61, 1078 (1974). [4.6] P. Diehl, Nuclear Magnetic Resonance, Vol. 5, Journal of Chemical Society, S p e c i a l i s t P e r i o d i c a l Reports (1976) . [4.7] J.W. Emsley and J.C. Lindon, NMR Spectroscopy Using Liquid Crystal Solvents, Pergamon Press (1975). [4.8] P. Diehl, NMR - Basic P r i n c i p l e s and Progress, Vol. 1, Springer-Verlag, B e r l i n , Heidelberg, N.Y. [4.9] D.W. Davidson, Water: A Comprehensive Treatise, Vol. 2, (F. Franks, ed.), Plenum Press (1973). [4.10] A.W.K. Khanzada, C.A. McDowell and P. Raghunathan, J. Chem. Phys. 60^ 3025 (1974) and references therein. - 93 -[4.11] P.S. Al l e n , A.W.K. Khanzada and CA. McDowell, Mol. Phys. 2J5, 1273 (1973) . [4.12] B.A. Dunell, CA. Fyfe, CA. McDowell and J. Ripmeester, Trans. Faraday Soc. 6j>, 1153 (1969). [4.13] CA. Fyfe and D. Harold-Smith, J. Chem. Soc. Faraday Trans. II 72, 2269 (1976). [4.14] I. Ya. Slonim and A.N. Lyubimov, The NMR of Polymers, Plenum Press, N.Y. (1970). [4.15] V.J. McBrierty, Polymer, 1J5, 503 (1974). [4.16] C L . Khetrapal, A.C Kunwar, P. Diehl and A.S. Tracey, NMR - Basic P r i n c i p l e s and Progress, Vol. 9, Springer-Verlay, B e r l i n . Heidelberg, N.Y. (1975). [4.17] R.A. Dwek, Nuclear Magnetic Resonance (N.M.R.) i n Biochemistry, Clarendon Press, Oxford (1973). [4.18] Bo Long Poh, Can; J. Chem. 52, 3428 (1974). [4.19] P.S. Allen, A.W.K. Khanzada and CA. McDowell, J. Chem. Phys. 59, 470 (1973). [4.20] CA. Fyfe and CA. McDowell, Chem. Phys. Lett. _2, 170 (1968). [4.21] Table of Interatomic Distances, Chemical Society Special Publication, Vol. 18 (1965). [4.22] H.B. Thompson, J. Chem. Phys. Al_, 3407 (1967). [4.23] J.G. Powles and J.A.E. K a i l , Proc. Phys. Soc. (London) 73, 833 (1959). [4.24] G.W. Smith, J. Chem. Phys. 42:, 4229 (1965) and references therein. - 94 -[4.2 5] J.G. Powles and H.S. Gutowsky, J. Chem. Phys. 2_1, 1695 (1953); 21, 1704 (1953). [4.26] C.A. Fyfe and J. Ripmeester, Can. J. Chem. 4_8, 2283 (1970). [4.27] R. Bli n c , S. Zumer and G. Lahajnar, Phys. Rev. B l , 4456 (1970). [4.28] S. Albert, H.S. Gutowsky and J. Ripmeester, J. Chem. Phys. 5_6, 3672 (1972) . [4.29] T.T. Ang and B.A. Dunell, Can. J. Chem. _52, 1840 (1974) . [4.30] The non-linear least-squares f i t uses the minimiza-tion program MINUIT (F. James and M. Roos, C.E.R.N. Document (1971)), which involves the minimization sub-routines SIMPLX (J.A. Nelder and R. Mead, Computer J. 1_, 308 (1967)) followed by MIGRAD (W.C. Davidon, Computor J. 1(3, 406 (1968)). Errors quoted correspond to standard deviations. My sincere thanks to Mr. D. Garner for his kind assistance with t h i s program..^ [4.31] C.I. R a t c l i f f e and B.A. Dunell, J. Chem. S o c , Faraday Trans II, 73r 493 (1977). [4.32] S. Albert, H.S. Gutowsky and J.A. Ripmeester, J. Chem. Phys. 64, 3277 (1976). [4.33] P.S. Allen, A.W.K. Khanzada and C.A. McDowell, J. Chem. Phys. 59, 470 (1973). - 9 5 -[ 4 . 3 4 ] E.O. S t e j s k a l , D.E. Woessner, T.C. F a r r a r and H.S. Gutowsky, J . Chem. Phys. 3 J L , 5 5 ( 1 9 5 9 ) . [ 4 . 3 5 ] E.R. Andrew, W.S. Hinshaw, M.G. Hutchins and R.O.I. Sjoblom, Mol. Phys. 3 1 , 1 4 7 9 ( 1 9 7 6 ) . [ 4 . 3 6 ] R.G.C. McElroy, R.Y. Dong, M.M. P i n t a r and W.F. Forbes, J . Mag. Res. 5 , 2 6 2 ( 1 9 7 1 ) . [ 4 . 3 7 ] S. A l b e r t and J.A. Ripmeester, J . Chem. Phys. 5 8 , 5 4 1 ( 1 9 7 3 ) . [ 4 . 3 8 ] C A . McDowell, P. Raghunathan and D.S. W i l l i a m s , J . Mag. Res. 2 4 , 1 1 3 ( 1 9 7 6 ) . - 96 -CHAPTER V MOLECULAR MOTION AND PHASE TRANSITIONS IN SOLID  CHOLINE CHLORIDE, BROMIDE, IODIDE AND PERCHLORATE 5.1 INTRODUCTION + Systems containing the choline head group, (CH3) .JNCH2CH2O-have been the subject of active research i n recent times because of t h e i r b i o l o g i c a l importance [5.1-5.3] and because of the anomalously high r a d i a t i o n s e n s i t i v i t y of c r y s t a l l i n e choline chloride [5.4]. We report here a study, of molecular motion and ba r r i e r s to i n t e r n a l r o t a t i o n i n the choline ion, + (CH 3) 3NCH 2CH 2OH, i n four of i t s p o l y c r y s t a l l i n e s a l t s , . a s such a study i s expected to add to the present knowledge of the b i o l o g i c a l a c t i v i t y of re l a t e d systems and of the radia-t i o n s e n s i t i v i t y of choline chloride. For example, since the conformation of the choline head group i n b i o l o g i c a l systems has been related to t h e i r b i o l o g i c a l a c t i v i t y , information on the ba r r i e r s to i n t e r n a l r o t a t i o n i n t h i s group should be of much importance [5.5,5.6]. With regard to the problem of r a d i a t i o n s e n s i t i v i t y of choline chloride, too, an involvement of molecular r o t a t i o n of the choline ion has been suggested. In the following paragraphs, presently a v a i l a b l e - 97 -background information on choline s a l t s i s presented. + S o l i d choline halides, (CH3)3NCH2CH2OHX (X = CI, Br, I) have been subjected to a variety of i n t e r e s t i n g studies. C r y s t a l l i n e choline chloride i s the most ion i z i n g - r a d i a t i o n sensitive compound known [5.7], i t s exposure to i o n i z i n g radiation r e s u l t i n g in decomposition into trimethylamine hydrochloride, (CH3)3N-HC1 and acetaldehyde, CH3CHO [5.8]. For example, in the r a d i o l y s i s of s o l i d choline chloride, the G value for r a d i c a l production (radicals produced /100 eV absorbed) i s only about 2, while the G for r a d i o l y s i s (molecules of choline chloride destroyed /100 eV absorbed) can be as high as 55,000 [5.9]. This anomalous radiation s e n s i t i v i t y i s shown only by the c r y s t a l l i n e form; i n solution, the compound exhibits normal radiation s t a b i l i t y [5.10]. The r a d i o l y s i s mechanism in choline chloride i s believed to be of a chain reaction type involving detrapped electrons [5.7, 5.11,5.12]. X-ray crystallographic studies of choline chloride have shown a c r y s t a l - c r y s t a l phase t r a n s i t i o n at approximately 353K, above which the compound shows normal radiati o n sensi-t i v i t y [5.13,5.14]. The low temperature polymorph i s found to have orthorhombic symmetry [5.15] while the high temperature one has a distorted f.c.c. structure [5 .16, 5.:.I7] . Other evidence for the above phase t r a n s i t i o n comes from infrared [5.12,5118], positron a n n i h i l a t i o n [5.19] and e l e c t r i c a l con-d u c t i v i t y measurements [5.11,5.12]. - 98 -The r a d i a t i o n s e n s i t i v i t y o f c h o l i n e b r o m i d e i s a b o u t a t h i r d o f t h a t o f t h e c h l o r i d e [ 5 . 1 0 ] . I n t h i s compound, t o o , a c r y s t a l - c r y s t a l p hase t r a n s i t i o n a t 364K has been s u g g e s t e d by i n f r a r e d [5.12] and e l e c t r i c a l c o n d u c t i v i t y measurements [ 5 . 1 2 ] , X - r a y s t u d i e s [5.15] show t h e c r y s t a l s t r u c t u r e i n t h e low t e m p e r a t u r e p h a s e t o be b a s e d on an o r t h o r h o m b i c u n i t c e l l . C h o l i n e i o d i d e i s d i f f e r e n t f r o m t h e o t h e r two h a l i d e s i n t h a t i t p o s s e s s e s n o r m a l r a d i a t i o n s e n s i t i v i t y . E l e c t r i c a l c o n d u c t i v i t y measurements on t h e i o d i d e [5.12] show a s h a r p i n c r e a s e a t 367K s i g n i f y i n g a c r y s t a l - c r y s t a l p h a s e t r a n s i t i o n . X - r a y d i f f r a c t i o n s t u d i e s [5.15] a t room t e m p e r a t u r e show i t s symmetry t o be m o n o c l i n i c . W i t h r e s p e c t t o c h o l i n e p e r c h l o r a t e , we a r e n o t aware o f any s t u d i e s i n t h e s o l i d s t a t e . R e t u r n i n g t o t h e q u e s t i o n o f c h o l i n e c h l o r i d e ' s e x t r e m e r a d i a t i o n s e n s i t i v i t y i n i t s low t e m p e r a t u r e p o l y m o r p h , a l t h o u g h mechanisms have been p r o p o s e d f o r t h e r a d i o l y s i s p r o c e s s , i t has s t i l l n o t been p o s s i b l e t o e s t a b l i s h what u n i q u e p r o p e r t y o f t h i s low t e m p e r a t u r e p h a s e c r y s t a l s t r u c t u r e makes p o s s i b l e t h e r e m a r k a b l y e f f i c i e n t c h a i n mechanism f o r d e c o m p o s i t i o n . The i n e r t n e s s t o r a d i a t i o n o f t h e h i g h t e m p e r a t u r e p h a s e i s b e l i e v e d t o be due t o r e a c t i o n o f r a d i c a l s p r o d u c e d by i r r a d i a t i o n w i t h m o b i l e p r o t o n s , t h e r e b y i n h i b i t i n g a c h a i n r e a c t i o n [ 5 . 1 1 ] . T h i s p r o p o s a l i s b a s e d on e l e c t r i c a l - 99 -c o n d u c t i v i t y measurements w h i c h s u g g e s t t h e t r e m e n d o u s l y i n c r e a s e d c o n d u c t i v i t y i n t h e h i g h t e m p e r a t u r e p h a s e o f c h o l i n e c h l o r i d e t o be p r o t o n i c i n o r i g i n [ 5 . 1 1 ] . P r o t o n i c c o n -d u c t i v i t y n e c e s s a r i l y means e a s y i n t e r m o l e c u l a r t r a n s f e r o f p r o t o n s t h r o u g h h y d r o g e n b o n d s . As p o i n t e d o u t by Daycock, e t a l . [5.20] i n c o n n e c t i o n w i t h p r o t o n i c c o n d u c t i v i t y i n i m i d a z o l e , i n o r d e r t o m a i n t a i n a n e t f l o w o f c h a r g e a l o n g t h e d i r e c t i o n o f t h e e l e c t r i c f i e l d , i t i s u s u a l l y n e c e s s a r y f o r i n d i v i d u a l m o l e c u l e s , a f t e r t h e y have t r a n s f e r r e d a p r o t o n , t o u n d e r g o r o t a t i o n so as t o be s u i t a b l y d i s p o s e d f o r t h e n e x t p r o t o n t o be a c c e p t e d . I n v i e w o f t h e f o r e g o i n g d i s c u s s i o n , a s t u d y o f m o l e c u l a r m o t i o n i n c h o l i n e s a l t s s h o u l d s h e d c o n s i d e r a b l e l i g h t on t h e p r o b l e m o f r a d i a t i o n damage i n c r y s t a l l i n e c h o l i n e c h l o r i d e and b r o m i d e . A l s o , m o t i o n a l b e h a v i o u r o f t h e c h o l i n e f r a g m e n t i n v a r i o u s c h e m i c a l e n v i r o n m e n t s w o u l d p r o v i d e a good com-p a r i s o n w i t h i t s b e h a v i o u r i n b i o l o g i c a l e n v i r o n m e n t s . The f i r s t s t e p s t o w a r d s an i n v e s t i g a t i o n o f m o l e c u l a r d y n a m i c s i n s o l i d c h o l i n e h a l i d e s were t a k e n by Graham and Hannon [5.21] who r e p o r t e d a s t u d y o f t h e t e m p e r a t u r e d e p e n d e n c e o f p r o t o n m a g n e t i c r e s o n a n c e l i n e w i d t h s i n t h e s e compounds. We have u n d e r t a k e n a s t u d y o f m o l e c u l a r d y n a m i c s i n c h o l i n e h a l i d e s u s i n g 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 measurements i n b o t h Zeeman and r o t a t i n g r e f e r e n c e f r a m e s . By way o f c o m p a r i s o n w i t h t h e h a l i d e s , and w i t h a v i e w o f o b t a i n i n g more i n f o r m a t i o n - 100 -o n t h e b e h a v i o u r o f c h o l i n e i o n , we h a v e e x t e n d e d o u r s t u d y t o c h o l i n e p e r c h l o r a t e i n w h i c h i t i s e x p e c t e d t h a t t h e l a r g e r s i z e o f t h e a n i o n w o u l d l e a d t o a l a r g e r c r y s t a l s t r u c t u r e a n d p r o v i d e more room f o r r e o r i e n t a t i o n s o f t h e c h o l i n e i o n . Graham and H a n n o n [ 5 . 2 2 ] h a v e s i n c e p u b l i s h e d a p r e l i m i n a r y T n s t u d y o f t h e c h l o r i d e a n d i o d i d e . - 101 -5.2 EXPERIMENTAL 5.2.1 Sample p r e p a r a t i o n . The f r e e c h o l i n e b a s e and i t s c h l o r i d e , b r o m i d e and i o d i d e were p u r c h a s e d f r o m Sigma C h e m i c a l Co. The h a l i d e s were g r o u n d t o a f i n e powder, t r a n s f e r r e d t o 7mm O.D. t h i n -w a l l g l a s s t u b e s and d r i e d a t 100°C on a vacuum l i n e f o r a t l e a s t 12 h o u r s . They were t h e n s e a l e d u n d e r vacuum and s t o r e d i n a r e f r i g e r a t o r p r i o r t o u s e . + C h o l i n e p e r c h l o r a t e , ( C H 3 ) 3 N C H 2 C H 2 0 H C 1 0 4 was p r e -p a r e d by t r e a t i n g c h o l i n e b a s e w i t h p e r c h l o r i c a c i d , e v a p o r a t i n g t h e s o l u t i o n t o d r y n e s s , and r e c r y s t a l l i z i n g t h e r e s i d u e i n 95% e t h a n o l . I t was g r o u n d and t r a n s f e r r e d t o a 10mm O.D. g l a s s t u b e f o r C.W. measurements and a 7mm O.D. t h i n - w a l l g l a s s t u b e f o r r e l a x a t i o n t i m e measurements. The s a m p l e s were d r i e d on a vacuum l i n e f o r a t l e a s t 24 h o u r s a t room t e m p e r a t u r e , s e a l e d u n d e r vacuum and s t o r e d i n a r e f r i g e r a t o r . - 102 -5.2.2 S p e c t r o m e t e r s C o n t i n u o u s wave measurements were p e r f o r m e d on t h e NMR s p e c t r o m e t e r I d e s c r i b e d i n S e c t i o n 3.1.1. 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 i n t h e Zeeman r r o t a t i n g r e f e r e n c e f r a m e s were p e r f o r m e d on t h e B r u k e r s p e c t r o m e t e r d e s c r i b e d i n S e c t i o n 3.2.1. A l l T^ measurements were made a t 30.20 MHz. The r o t a t -i n g f i e l d s t r e n g t h s u s e d f o r measurements a r e m e n t i o n e d i n t h e t e x t . - 103 -5.3 RESULTS 5.3.1 Second moments. Our d e t a i l s of second moment measurements for choline perchlorate are shown in Figure (5.1). As regards the three halides, although Graham and Hannon [5.21] have carried out detailed measurements of second moments as a function of temperature, a s a t i s f a c t o r y interpretation of the results on the halides (as well as on the perchlorate) becomes possible only after a detailed discussion of the expected second moments for a variety of motional models. The expected t h e o r e t i c a l second moments are therefore d i s -cussed next. The heavy atom coordinates of c r y s t a l l i n e choline chloride at room temperature have been reported [5.15]. Using these, o and assuming a C-H bond distance of 1.09 A and tetrahedral bond angles at Nitrogen and the Carbon atoms, the proton coordinates were generated by a computer program as described in Chapter IV. Considering only proton-proton interaction, the intramolecular second moment calculated using Equation 2 (4.1) i s 22.73 G . The contributions to t h i s value from various groups i n the molecule are summarized in Table 5.1. Our value for the t o t a l intramolecular second moment i s 2 s l i g h t l y lower than 24.78 G reported by Graham and Hannon [5.21]. For the intermolecular contribution, Graham and 2 Hannon report a second moment contribution of 4.93 G . Use FIGURE 5.1 Temperature dependences of the proton second moment i n choline perchlorate. TABLE 5.1 Theoretical "*"H Second Moments for Various Possible Motional Models of the Choline Ion Motional Model Type of inte r a c t i o n Rigid Methyl Methylene Intermethyl Intermethylene Methyl-methylene Intermolecular 14. 50 3. 21 1. 98 0.63 2.41 4.93 3 Methyls 2 Methyls 1 Methyl 3 Methyls r o t a t i n g rotating rotating rotating , + + C^ of NMe^ group . 3.62 7.25 10.87 0.62 3.21 3.21 3.21 3.21 1.71 1.80 1.89 0.43 0.63 0.63 0.63 0.63 ^2.25 ^2.30 ^2.36 0.50 1.23 2.47 3.70 ^0.5 TOTAL 27. 66 12.66 17.66 22.66 5.89 - 106 -of t h i s value gives a t o t a l ' r i g i d l a t t i c e ' second moment of 27.66 G 2. The possible motional modes are next considered. Let us assume that the chain CH2CH2OH remains r i g i d and that the l i n e narrowing i s caused by the reorientation of methyl groups. The second moment values expected for rotation of one, two and a l l three methyl groups have been calculated and the resu l t s are shown i n Table 5.1. Once again, precise second moment values could be calculated only for the intragroup contributions. As discussed i n Chapter II, reorientation of each methyl group about i t s symmetry axis reduces i t s second moment contribution by a factor of 4. Rotation of a l l three methyl groups about t h e i r C^ symmetry axes super-posed on a rotation of the whole NMe^ group about i t s three-f o l d rotation axis (denoted C^) reduces the second moment by a factor given in Equation (2.34); with = 70.5°. The reduction factors for the intergroup contributions cannot be calculated precisely and approximations [5.23-5.25] have been used to estimate these. The t o t a l second moment values expected for rotation of one, two and a l l three methyl groups 2 i are 22.66, 17.66 and 12.66 G , respectively. For the C^ + rotation of the NMe^ group, together with the rotation of 2 a l l three methyls, a value of 5.89 G i s obtained. Graham and Hannon [5.21] have made th e i r motional assign-ments on the basis of previously reported calculations for - 107 -compounds containing only methyl groups. It i s to be noted that these calculations are not d i r e c t l y applicable to a structure l i k e that of the choline ion, where the non-methyl protons i n -CE^CH^OH have an independent contribution to the second moment which w i l l depend, of course, on whether or not there i s motion of t h i s chain CH2CH2OH (see Table 5.1). For 2 the chloride, the second moment plateau of 16.0 G observed by Graham and Hannon, following the f i r s t linewidth t r a n s i t i o n 2 i s in agreement with our calculated value of 17.66 G for rotation of only two of the methyls while the rest of the molecule remains r i g i d . The plateau following the above 2 t r a n s i t i o n in the bromide, of value 14.0 G , i s closer to the expected value for a l l three methyls rotating. However, the 2 value of 9.2 G found for the iodide in t h i s temperature 2 region i s considerably smaller than the value of 12.66 G expected for rotation of a l l three methyls with the CH2CH2OH chain remaining r i g i d . This suggests some additional motion causing the l i n e narrowing - probably some motion of the chain. As the samples are warmed up, a second linewidth tran-s i t i o n occurs in a l l three halides [5.21]. The second moment 2 following this t r a n s i t i o n , namely 4.3, 4.0 and 3.5 G i n the chloride, bromide and iodide, respectively, are a l l smaller 2 i than our calculated value of 5.89 G for the onset of + reorientation of the NMe^ group. This again s i g n i f i e s some additional motion of the chain CH„CH„0H. - 108 -For the perchlorate, the second moment plateau 2 of 29±2 G at 77K i s consistent with that expected for a r i g i d molecule. The plateau following the f i r s t transition,. 2 of ^9 G , suggests the rotation of a l l three methyl groups about t h e i r symmetry axes, together with some motion of the chain. The plateau following the second t r a n s i t i o n suggests the additional motion of the NMe^ group about i t s threefold rotation axis (C3) . The second moment values follow-ing the c r y s t a l - c r y s t a l phase t r a n s i t i o n at 272K, are con-sis t e n t with i s o t r o p i c tumbling of the choline ion in t h i s phase. Proton spin relaxation times for a l l the above choline s a l t s are discussed i n the following section. It w i l l be seen that these data not only confirm the essential results of the second moment measurements, but indeed provide additional information on the rates and ac t i v a t i o n energies for these motional processes. 5.3.2 Relaxation time measurements. a) Choline Chloride. The temperature dependences of the s p i n - l a t t i c e relaxation times in the laboratory frame (T^) and rotating frame (T.. ) for choline chloride are shown, in.Figure 5.2. lp The T^ data ( f i l l e d c i r c l e s ) show a single minimum centred at 278K and undergo a sudden increase at 353K, the temperature of the previously reported c r y s t a l - c r y s t a l phase t r a n s i t i o n - 109 -A A A . A A A j ! A 1 u-j j j , : [ 2 3 4 5 6 . 7 1000 / T (K"1) FIGURE 5.2 Temperature dependence o£ the proton Ti and T l p o£ choline chloride. F i l l e d c i r c l e s : T x data at 30.20 MHz; f i l l e d t r i a n g l e s : T l p data at Hi = 8.4 G. S o l i d l i n e through the T x data points i s the t h e o r e t i c a l l i n e drawn with b e s t - f i t parameters. - 110 -[5.11-5.14]. In the high temperature phase, phase II, increases l i n e a r l y up to the highest temperature studied. Our T 1 r e s u l t s are in general agreement with those of Graham and Hannon [5.22]. The data ( f i l l e d triangles) show a well-defined minimum at 3 00K and appear to be going down to another minim at lower temperatures. At 353K, T 1 also undergoes a sudden increase of nearly two orders of magnitude, which i s immediately followed by a shallow minimum with T, (min) = 150 msec. lp In accordance with the linewidth data of Graham and Hannon [5.21], the low temperature T^ minimum should be assignable to reorientation of methyl groups about t h e i r C 3 symmetry axes. Assuming t h i s motion to be governed by a single c o r r e l a t i o n time, the relaxation in the region of the minimum i s described by a BPP expression of the type i n Equation (2.58), and the co r r e l a t i o n times at various temperatures are extracted from the experimental T^ value at that p a r t i c u l a r temperature (see Chapter IV). These c o r r e l a -tion times are shown by f i l l e d c i r c l e s i n Figure (5.3). The plot of l n x c vs. T 1 i s nearly l i n e a r , showing that the assumption of a single c o r r e l a t i o n time i s good and that T C follows an 'Arrhenius' type of dependence on temperatures. A le a s t squares f i t to these data points in Figure (5.3) gives an ac t i v a t i o n energy of 4.40±0.03 kcal mole 1 . - I l l -1000 /T(K") FIGURE 5.3 Temperature dependence of c o r r e l a t i o n times for methyl reorientation i n choline chloride ( f i l l e d c i r c l e s ) , bromide (open c i r c l e s ) , iodide ( f i l l e d triangles) and perchlorate (open t r i a n g l e s ) . S o l i d l i n e s are l i n e a r least-squares f i t s to the data. - 112 -A n o n - l i n e a r l e a s t s q u a r e s f i t o f t h e e n t i r e s e t o f d a t a p o i n t s i n phase I t o an e x p r e s s i o n o f t h e t y p e i n E q u a t i o n (2.56) g i v e s 2 4 . 7 6±1.17 s e c 1 f o r t h e c o n s t a n t C and ° -12 t h e a c t i v a t i o n p a r a m e t e r s T c = (1.16±0.52) x 10 s e c and E = 4.34+0.23 k c a l mole 1 . The s o l i d l i n e t h r o u g h t h e T^ d a t a p o i n t s i n F i g u r e (5.2) i s drawn u s i n g E q u a t i o n (2.58) and t h e a b o v e - m e n t i o n e d p a r a m e t e r s . The f i t t o a s i n g l e BPP e x p r e s s i o n i s r e a s o n a b l y good. Graham and Hannon, f r o m t h e i r l i n e w i d t h s t u d i e s [5.21] had s u g g e s t e d one o f t h e m e t h y l g r o u p s i n c h o l i n e c h l o r i d e t o be d y n a m i c a l l y n o n - e q u i v a l e n t t o t h e o t h e r two. T h i s w o u l d mean t h e p r e s e n c e o f two 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 f o r t h e two t y p e s o f m e t h y l s , r e s u l t i n g i n two d i f f e r e n t T.-^  minima. i t i s n o t p o s s i b l e t o s a y w i t h c e r t a i n t y w h e t h e r t h e low t e m p e r a t u r e T^ minimum i s c a u s e d by t h e r e o r i e n t a t i o n o f a l l t h r e e m e t h y l g r o u p s o r by o n l y t h e two l e s s h i n d e r e d g r o u p s . I f t h e minimum i s c a u s e d by r e o r i e n t a t i o n o f t h e two e q u i v a l e n t and t h e one u n i q u e Me g r o u p s , t h e minimum i s l i k e l y t o be a s y m m e t r i c . However, t h i s asymmetry i n t h e o b s e r v e d T^ minimum i s n o t v e r y l a r g e as s e e n f r o m t h e good f i t t o a s i n g l e BPP and t h e l i n e a r i t y o f t h e l n x v's~. T 1 p l o t ( F i g u r e s 5.1, 5 . 2 ) . Thus, T^ d a t a f o r t h e c h l o r i d e s u g g e s t ( i ) e i t h e r a n e a r e q u i v a l e n c e o f a l l m e t h y l g r o u p s , c a u s i n g t h e n e a r l y s y m m e t r i c T^ minimum, o r ( i i ) one o f t h e m e t h y l g r o u p s b e i n g d y n a m i c a l l y v e r y d i f f e r e n t f r o m t h e o t h e r two, w i t h t h e c o n s e q u e n c e t h a t - 113 -the phase t r a n s i t i o n i s reached before t h i s hindered methyl group rotates fa s t enough to cause a T^ minimum. It i s useful to compare the minimum value with that expected for the proposed motion. This i s done by assuming that the chief mechanism responsible for relaxation of proton spins in the choline ion i s the reorientation of methyl groups, the other spins (e.g. methylene and OH) then coming to a common spin temperature by spin d i f f u s i o n [5.26]. Thus, we may write, 1_ = ! _ R ( N M e 3 ) , (5.1) + + wherein the relaxation rate of the NMe^ group, R(NMe^), i s described by Equations (2.52,2.53). For reorientation of the three methyls about th e i r symmetry axes, use of Equation (2.51) for R(NMe3) with r = 1.78 A gives 27.3 msec for the T^ minimum at 3 0.20 MHz. For only two of the methyl groups reorienting, a T^ minimum of 40.95 msec i s obtained. The apparent agreement- of the observed value of 28 msec with that calculated for reorientation of a l l three methyls i s fortuitous, as the above c a l c u l a t i o n does not take into account the contribution from interaction outside the methyl groups which are l i k e l y to lower the T^ minimum. Thus, a model of two equivalent methyls and a unique more hindered methyl i s more favoured. - 114 -The T.. minimum a t 282K i s a s s i g n e d t o r o t a t i o n lp o f t h e w h o l e NMe g r o u p above i t s t h r e e f o l d r o t a t i o n a x i s (C^). To v e r i f y t h i s a s s i g n m e n t , t h e e x p e c t e d T^ minimum v a l u e i s c a l c u l a t e d . Once a g a i n , t h e s p i n s y s t e m i s assumed t o be r e l a x e d by t h e m o t i o n o f m e t h y l g r o u p s , i . e . r e l a x a t i o n d e s c r i b e d by E q u a t i o n (5.1) w i t h T^ r e p l a c e d by T l p • F o r T, measurements, o u r e x p e r i m e n t a l c o n d i t i o n s meet t h e 'weak lp c o l l i s i o n ' r e q u i r e m e n t [5.27] and a g e n e r a l i z e d t h e o r e t i c a l e x p r e s s i o n f o r T, u n d e r t h e s e c o n d i t i o n s was g i v e n i n lp E q u a t i o n (2.56). Near t h e T n minimum, o> T >>1 and t h u s , ^ lp o c t h e q u a n t i t y w i t h i n p a r e n t h e s e s may be r e p l a c e d by 3 T c 7y « "' (5.2) (1 + 4o)^x^) The expressions for any given molecular motion i s the same as that for T^, except that f ( 0 J o T c) 1 S n o w replaced by expression (5.2). Thus, for motion of the NMe^ group superposed on fast (OJOTc<<1) motion of methyls, use of Equation (2.55) with the appropriate change gives, \2 T 3 * * c 2 (5.3) T n (NMe.,) 1 5 r 6 1 + 4W2T 2 lp 3 1 c2 i where x „ i s the c o r r e l a t i o n time for the C_ motion of the c2 3 + o NMe^ group. With an inter-proton r = 1.78 A and a spin lock-ing f i e l d of 8.4 G in Equation (5.3), a T - j _ p : m i n value of 390 ysec i s obtained. This value i s considerably higher than - 115 -t h e o b s e r v e d minimum v a l u e o f 265 y s e c . Once a g a i n , t h e c a l c u l a t i o n does n o t i n c l u d e . - i n t e r a c t i o n s o u t s i d e t h e m e t h y l g r o u p , b u t as i n t h e c a s e o f T, minimum c a l c u l a t i o n s f o r m o t i o n d e s c r i b e d i n C h a p t e r IV ( E q u a t i o n ( 4 . 8 ) ) , i t i s p o s s i b l e t o i n c l u d e an i n t e r m e t h y l c o n t r i b u t i o n t o t h e r e l a x a t i o n . R e p l a c e m e n t o f ^(^0TC2^ ky t h e e x p r e s s i o n (5.2) i n E q u a t i o n (4.8) g i v e s t h e c o r r e s p o n d i n g e x p r e s s i o n f o r T, and u s e o f t h i s e x p r e s s i o n w i t h r = 3.08 A, g i v e s a T n lp * lp minimum o f 283 y s e c w h i c h i s i n good a g r e e m e n t w i t h t h e e x p e r i m e n t a l v a l u e o f 265 p s e c . T h i s adds s u p p o r t t o o u r a s s i g n m e n t . The e x p e r i m e n t a l and c a l c u l a t e d v a l u e s a r e summarized i n T a b l e ( 5 . 2 ) . A t l o w e r t e m p e r a t u r e s , T^ p shows a f l a t r e g i o n (182K t o 166K) f o l l o w e d by a downward t r e n d (T<166K) i n d i c a t i n g p o s s i b l y a n o t h e r minimum. T h i s low t e m p e r a t u r e r e g i o n o f t h e r e l a x a t i o n i s g o v e r n e d by t h e m o t i o n o f m e t h y l s a b o u t t h e i r C^ symmetry a x e s . To v e r i f y t h i s , we c a l c u l a t e t h e p o s i t i o n o f t h e minimum c o r r e s p o n d i n g t o t h e m o t i o n c a u s i n g t h e T^ minimum a t 278K. A T^ minimum i s o b s e r v e d when a) x ~ 1, whereas a T n minimum i s o b s e r v e d when o c lp CO^Tc « 1. A s s u m i n g an A r r h e n i u s - t y p e o f d e p e n d e n c e o f on t e m p e r a t u r e , we may t h u s w r i t e , o (5.4) TABLE 5.2 Experimental and Calculated Values for Minima i n Phase I of Choline Chloride, Bromide, Iodide and Perchlorate Calculated T-\ minimum (psec) Compound R.F. f i e l d Temperature Observed Without With (G) of Tjp minimum Intermethyl Intermethyl Minimum(K) (psec) choline c h l o r i d e 3.4 300 265 390 283 choline bromide 5.9 253 260 274 199 choline iodide 5.9 282 260 274 199 choline perchlorate 5.9 205 208 274 199 - 117 -where T ( T ^ min) and T ( T ^ p min) a r e t h e t e m p e r a t u r e s o f and minima, r e s p e c t i v e l y . U s i n g E q u a t i o n \ (5.4) w i t h E = 4.34 k c a l mole 1 t h e t e m p e r a t u r e o f t h e T, minimum a t lp a s p i n - l o c k i n g f i e l d o f 8.4 G c o r r e s p o n d i n g t o t h e m o t i o n c a u s i n g t h e minimum a t 278K i s c a l c u l a t e d as 150K (1000/T = 6.67K - 1). I n d e e d , T± d a t a p o i n t s a t t h e l o w e s t t e m p e r a t u r e s t u d i e d (153K) a p p e a r t o be g o i n g down t o w a r d s a minimum. The f l a t r e g i o n i s p o s s i b l y due t o t h e m o t i o n o f t h e u n i q u e , i . e . , more h i n d e r e d , m e t h y l g r o u p . A l e a s t -s q u a r e s f i t t o t h e d a t a p o i n t s on t h e h i g h t e m p e r a t u r e s i d e o f t h i s r e g i o n (190K t o 222K) g i v e s an a c t i v a t i o n e n e r g y o f 4.50±0.27 k c a l m o l e - 1 . Use o f E q u a t i o n (5.4) w i t h t h i s a c t i v a t i o n e n e r g y shows t h e T^ minimum c o r r e s p o n d i n g t o t h i s m o t i o n t o o c c u r a t 360K (1000/T = 2.77K - 1) w h i c h i s above t h e t e m p e r a t u r e o f t h e p h a s e t r a n s i t i o n . The s l i g h t change i n c u r v a t u r e o f T^ p o i n t s i n p h a s e I c l o s e t o t h e phase t r a n s i t i o n a l s o s u g g e s t s a n o t h e r r e l a x a t i o n mechanism b e c o m i n g e f f i c i e n t -p o s s i b l y t h e m o t i o n o f t h e t h i r d m e t h y l . F l a t r e g i o n s i n T.^  i n s t e a d o f minima have been p r e v i o u s l y o b s e r v e d [5.28]. I n t - b u t y l ammonium c h l o r i d e , f o r example, where t h e e x p e r i m e n t a l e v i d e n c e shows one o f t h e m e t h y l g r o u p s t o be d i f f e r e n t f r o m t h e o t h e r two, a v e r y s i m i l a r b e h a v i o u r o f T, has been lp o b s e r v e d [5.28]. Our r e s u l t s t h e r e f o r e show r a t h e r c l e a r l y t h a t i n c h o l i n e c h l o r i d e , two o f t h e m e t h y l g r o u p s a r e - 118 -dynamically equivalent, while the t h i r d methyl i s unique, with the a c t i v a t i o n energies for reorientation of the two types of methyl groups about th e i r symmetry axes being 4.34+0.23 and 4.50±0.27 kcal mole respectively. We refer again to Figure (5.2). In the high temperature phase, phase II, increases up to the highest temperature studied and the lnT^ vs. T 1 plot i s l i n e a r . A least-squares f i t to these data points gives an act i v a t i o n energy of 6.7 9+0.12 kcal mole 1 . This region of T^ relaxa-tion i s a l i t t l e more d i f f i c u l t to be characterized. We rule out rotation of methyls about th e i r symmetry axes as being responsible for T^ relaxation in phase II, as the measured a c t i v a t i o n energy i n t h i s phase of 6.79±0.12 kcal mole 1 i s much higher than that measured for methyl rotation in phase I. The change in act i v a t i o n energy for methyl rotation i n going from phase I to phase II i s expected to be in the opposite sense, as in phase II, the choline ion is known to exhibit a greater molecular freedom [5.21]. The linewidth r e s u l t s of Graham and Hannon show a sharp drop in linewidth at the temperature of the c r y s t a l - c r y s t a l phase t r a n s i t i o n , and the corresponding second moments i n phase II indicate i s o t r o p i c tumbling of the choline ion. From our Figure 5.2, T^'s i n phase II increase with temperature, which i s diagnostic of some motion taking place at a co r r e l a t i o n time x such that co x <<1. We therefore believe the T.. c o c . 1 relaxation i n phase II to be governed by a general reorienta-- 119 -t i o n o f t h e c h o l i n e i o n r a t h e r t h a n s i m p l e m e t h y l r o t a t i o n a s has b e e n s u p p o s e d by Graham and Hannon [5.22]. T h i s g e n e r a l r e o r i e n t a t i o n c o u l d e i t h e r be t h e i s o t r o p i c t u m b l i n g o f t h e c h o l i n e i o n o r t h e r o t a t i o n o f t h e NMe^ g r o u p a b o u t i t s t h r e e f o l d r o t a t i o n a x i s ( C ^ ) . I t i s n o t p o s s i b l e t o a s s i g n t h e T^ r e l a x a t i o n t o e i t h e r o f t h e s e mechanisms u n a m b i g u o u s l y . However, t h e l a c k o f any t e n d e n c y f o r a downward d i p i n T^ d a t a p o i n t s up t o t h e h i g h e s t t e m p e r a t u r e s t u d i e d , l e a d s us t o b e l i e v e t h a t i s o t r o p i c t u m b l i n g i n p h a s e I I i s t a k i n g p l a c e w i t h a c o r r e l a t i o n t i m e s u c h t h a t to x <<1. I n summary, t h e r e f o r e , we a s s i g n t h e T, r e l a x a t i o n o c 2 ^ 1 i n p hase I I t o i s o t r o p i c t u m b l i n g o f t h e c h o l i n e i o n w i t h an a c t i v a t i o n e n e r g y o f 6.79±0.12 k c a l mole \ In p h a s e I I , T, v a l u e s do n o t c o i n c i d e w i t h t h e lp T^ v a l u e s , s h owing t h a t r e l a x a t i o n i s n o t e f f e c t e d by t h e same mechanism i t h a t e f f e c t s T n r e l a x a t i o n . The T, v a l u e s 1 lp a l s o show a v e r y s h a l l o w minimum o f 150 msec. The r e l a t i v e l y h i g h v a l u e o f t h i s minimum s u g g e s t s t h a t t h e mechanism g o v e r n -i n g t h e T, r e l a x a t i o n c o u l d be r a t h e r i n e f f i c i e n t . We lp q u a l i t a t i v e l y a s s i g n t h i s t o some m o t i o n o f t h e c h a i n -CH2CH2OH, f o r example, c o n f o r m a t i o n a l c h a n g e s [5.6] a t t h e two c a r b o n atoms. From t h e d a t a on t h e h i g h t e m p e r a t u r e s i d e o f t h e T-j^p minimum, an a c t i v a t i o n e n e r g y o f 4.34 + 0.27 k c a l mole 1 i s c a l c u l a t e d f o r t h i s m o t i o n . The a c t i v a t i o n e n e r g i e s o b t a i n e d f o r t h e v a r i o u s m o t i o n s p r o p o s e d a r e shown i n T a b l e 5.3. TABLE 5.3 Summary of A c t i v a t i o n E n e r g i e s a i n kcalmole" 1 for the Molecular Motions Proposed f o r Choline Ion i n the Chloride, Bromide, Iodide and Perchlorate Compound Methyl motion Motion of fNMe 3 General D i f f u s i o n Chain about C 3 about c ' r e o r i e n t a t i o n Motion Symmetry Axis Chloride Phase I Phase II 4.34 ± 0.23 4.50 ± 0.27 c 11.00 ± 0.01 6.79 ± 0.12 4.34 ± 0.27 Bromide Phase I Phase II 4.38 ± 0.0? 1.09 ± 0.19 5.13 ± 0.0? 3.99 ± 0.21 Iodide Phase I Phase II Phase III 3.84 ± 0.26" 11.12- ± 0.33 9.10 ± 0.21" 21.4 ± 0.5 11.2 + 0.5 Perchlorate Phase I Phase II 3.17 + 0.34 7.42 + 0.15 6.95 ± 0.56 b ^17 c a. Errors quoted are standard deviations c. Value's obtained from T, data. lp b. Values obtained from T^ data. - 121 -b) Choline bromide. The temperature dependences of spin l a t t i c e relaxa-tion times in the laboratory reference frame ( f i l l e d c i r c l e s ) and in the rotating reference frame ( f i l l e d t r i a n g l e s ) , are shown in Figure (5.4). The re s u l t s are i n general very similar to those of the chloride. T^ shows a minimum centred at 282K. This minimum appears to be very asymmetric with an apparent shoulder on the low temperature side around 238K. Again, at the temperature of the phase t r a n s i t i o n (364K), a very sharp increase i n T^ i s observed, above which T^ continues to increase i n phase I I . T, shows a minimum of 260 usee at 253K. A sharp lp upward jump i n the values i s observed at 3 64K, above which T.. continued to increase in phase I I . lp Once again, in accordance with Graham and Hannon's linewidth data [5.21], we assign the T^ minimum in phase I to reorientation of methyl groups about th e i r symmetry axes. Assuming the motion to be governed by a single c o r r e l a -tion time, the c o r r e l a t i o n times at a series of temperatures were calculated from the T^ values at those temperatures and the re s u l t s are represented by open c i r c l e s in Figure (5.3). A least-squares f i t to the data points gives an activation energy of 4.45±0.05 kcal mole 1 . From the l i n e a r low temperature region of T^ alone, an ac t i v a t i o n energy of 4.38±0.08 kcal mole - 1 i s obtained. Although Graham and Hannon - 122 -C O o CD CO H lxlO-^J 1x10-1x10* r4 n Choline Bromide A o • J} (30 MHz) A Tj^HrSSG) A A A A A A A 4 5 DOO^K-1) 7 J11 GURE 5.4 Temperature dependence of the proton T x and T l p of choline bromide. F i l l e d c i r c l e s : T x data at 30.20 MHz; f i l l e d t r i n a g l e s : 5.9 G. T± data at Hx - 123 -[5.21] have s u g g e s t e d t h e m e t h y l s i n t h i s compound a l s o t o be n o n - e q u i v a l e n t , o u r s e c o n d moment c a l c u l a t i o n s f a v o u r t h e m e t h y l s t o be e q u i v a l e n t . The weak s h o u l d e r on t h e low t e m p e r a t u r e s i d e o f t h e T^ minimum a r o u n d 25OK (10 0.0/T = 4.00) a p p e a r s t o be a s s i g n a b l e t o t h e n o n - e q u i v a l e n c e o f m e t h y l s [ 5 . 2 9 ] , However, r e c e n t c a l o r i m e t r i c s t u d i e s on s o l i d c h o l i n e b r o m i d e [5.17] show a p o s s i b l e c r y s t a l - c r y s t a l p h a s e t r a n s i t i o n a r o u n d 270K (1000/T = 3.70). I n t h e l i g h t o f t h i s f i n d i n g , i t i s n o t p o s s i b l e t o s a y w i t h c e r t a i n t y w h e t h e r t h e asymmetry i n t h e T^ minimum i s due t o t h e non-e q u i v a l e n c e o f m e t h y l s o r t o t h e p h a s e t r a n s i t i o n a t 270K. i The T n minimum i n p h a s e I i s a s s i g n e d t o C 0 l p 3 + r o t a t i o n o f t h e NMe^ g r o u p . A l e a s t - s q u a r e s f i t t o t h e l i n e a r p o r t i o n o f d a t a p o i n t s on t h e h i g h t e m p e r a t u r e s i d e o f t h i s T, minimum g i v e s an a c t i v a t i o n e n e r g y o f 8.09±0.19 l p k c a l mole 1 . As i n t h e c a s e o f t h e c h l o r i d e , t h e T, lp minimum v a l u e s e x p e c t e d were c a l c u l a t e d w i t h and w i t h o u t i n t e r m e t h y l c o n t r i b u t i o n s f o r a s p i n - l o c k i n g f i e l d o f 5.9 G, and were f o u n d t o be 199 and 274 y s e c , r e s p e c t i v e l y . The o b s e r v e d v a l u e o f 260 y s e c i s i n good agreement w i t h t h e c a l c u l a t e d r a n g e , t h e r e b y v e r i f y i n g o u r a s s i g n m e n t . I n p h a s e I I , t h e T^ v a l u e s i n c r e a s e w i t h t e m p e r a -t u r e up t o t h e h i g h e s t t e m p e r a t u r e s t u d i e d , and f r o m t h e l i n e a r p l o t o f l n T ^ v s . T ^, an a c t i v a t i o n e n e r g y o f 5.13± 0.18 k c a l mole 1 i s o b t a i n e d . Once a g a i n , s i n c e t h i s v a l u e - 1 2 4 -i s t o o h i g h t o be a s s i g n e d t o m e t h y l r o t a t i o n , and s i n c e v a l u e s do n o t d i p t o w a r d s a n o t h e r minimum up t o t h e h i g h e s t t e m p e r a t u r e s t u d i e d , we a s s i g n t h i s ( 5 . 1 3 ± 0 . 1 8 k c a l mole "S t o t h e a c t i v a t i o n a l e n e r g y b a r r i e r g o v e r n i n g i s o t r o p i c t u m b l i n g o f t h e c h o l i n e i o n . Here, t o o , a s i n t h e c a s e o f t h e c h l o r i d e , v a l u e s do n o t c o i n c i d e w i t h t h e v a l u e s i n p h a s e I I , s u g g e s t -i n g t h a t and r e l a x a t i o n s a r e n o t g o v e r n e d by t h e same mechanism. However, u n l i k e i n t h e c a s e o f t h e c h l o r i d e , we do n o t o b s e r v e a T, minimum and i t i s n o t p o s s i b l e t o s a y l p a n y t h i n g r e g a r d i n g t h e e f f i c i e n c y o f t h e r e l a x a t i o n mechanism i n t h i s p h a s e . A l e a s t - s q u a r e s f i t t o t h e T^ d a t a p o i n t s i n p h a s e I I g i v e s an a c t i v a t i o n e n e r g y o f 3 . 9 9 ± 0 . 2 1 k c a l m o l e - 1 . I n k e e p i n g w i t h t h e v e r y s i m i l a r b e h a v i o u r o f t h e r e l a x a t i o n o b s e r v e d i n o t h e r t e m p e r a t u r e r e g i o n s o f c h l o r i d e and b r o m i d e , and b e c a u s e o f t h e v e r y s i m i l a r a c t i v a t i o n e n e r g i e s m easured f o r t h e two compounds f r o m T i d a t a i n p h a s e I I , we a s s i g n t h e T, r e l a x a t i o n i n J-p ^ ^ l p phase I I o f t h e b r o m i d e a l s o t o be g o v e r n e d by some m o t i o n o f t h e c h a i n CH 2CH 2OH. A summary o f a c t i v a t i o n e n e r g i e s o b t a i n e d f o r t h e v a r i o u s m o t i o n s p r o p o s e d i n t h e b r o m i d e i s f o u n d i n T a b l e 5 . 3 . - 125 -c) Choline iodide. The relaxation time data for choline iodide are presented in Figure (5.5). T^'s are represented by f i l l e d c i r c l e s and T n 's measured at 5.9 and 2 . 0 G are represented lp by f i l l e d and open triangles respectively. The relaxation time data are seen to d i f f e r from those of the chloride and bromide in several important respects. T^ shows a symmetrical minimum of 24 msec centred at 283K; the T 1 data appear to f l a t t e n at temperatures lower than 140K. At 362K, under-goes a sharp upward jump and continues to increase up to 430K, at which temperature i t takes a further sharp jump. T^ then continues to increase up to about 48OK when i t registers a down-turn dip ind i c a t i n g the presence of another T^ minimum at higher temperatures. T^ res u l t s for choline iodide have also been reported by Graham and Hannon [5.22]. Their data are in general agreement with ours. T, values measured with H, = 5.9 G, show a minimum lp 1 of 260 ysec at 282K and appear to be going down to another minimum at the lowest temperature studied. At 362K, T^ shows a sharp discontinuity and goes through another minimum of 1.85 msec at 392K. Again at 430K, they show a discon-t i n u i t y and are found to be decreasing at the highest temperature studied, indicating the existence of another T, minimum. Indeed, T, data measured at a low spin locking lp lp f i e l d of 2.0 G c l e a r l y manifest t h i s minimum. Choline Iodide • T, (30 MHz) A T1/0(Hf5.9G) A ^(Hp20G) 7 8 l O O O Z - l K ' 1 ) T FIGURE 5.5 Temperature dependence of the proton T i and Ti of choline iodide. F i l l e d c i r c l e s : T i data at 30.20 MHz; f i l l e d t r i a n g l e s : T l p data at H : = 5.9 G; open t r i a n g l e s : T l p data at = 2.0 G. S o l i d l i n e through the T^ data i s the t h e o r e t i c a l ' b e s t - f i t ' l i n e . - 127 -As in the case of the chloride and bromide, the minimum i n phase I i s assigned to reorientations of methyl groups about th e i r symmetry axes. The c o r r e l a t i o n times derived from there T^ data assuming the presence of a unique co r r e l a t i o n time are shown i n Figure (5.3) by f i l l e d t r i a n g l e s . The l n x c vs. T 1 plot i s l i n e a r showing the v a l i d i t y of the assumption of a single c o r r e l a t i o n time and also an Arrhenius-type of dependence of x c on temperature. A least-squares f i t to l n x c vs. T - 1 data points gives an ac t i v a t i o n energy of 3.80±0.04 kcal mole" 1. A non-linear least squares f i t of the T^ data points in the temperature range 175K - 340K to an expression of the type in Equation (2.56) gives the best f i t parameters C = 29.65±1.51 sec" 1 x ° = (5.88±3.09) x 10~ 4 sec and c E = 3.84±0.26 kcal mole - 1. The s o l i d l i n e through the points in Figure (5.5) i s drawn using Equation (2.56) and the best-f i t parameters. It i s seen that the f i t of the T 1 data points around the minimum to a single BPP expression i s excellent, supporting the presence of equivalent methyls and the presence of a unique c o r r e l a t i o n time. Graham and Hannon [5.22] have obtained ac t i v a t i o n energies of 4.0 and 4.5 kcal mole 1 for methyl reorientation from the low and high temperature sides of t h e i r T 1 minimum. Our value of 3.84±0.26 kcal moles i s in good agreement with t h e i r value from the low temperature side of the minimum. - 128 -The l e v e l - o f f of T^ values at very low tempera-tures has also been observed by Graham and Hannon [5.22]. They att r i b u t e i t to either the presence of an impurity or to the presence of a low temperature phase t r a n s i t i o n . However, recent calorimetric studies have not shown any evidence for such a t r a n s i t i o n [5.17]. The sharp increase i n T^ at 362K also has been observed by Graham and Hannon [5.22] and i s in d i c a t i v e of a c r y s t a l - c r y s t a l phase t r a n s i t i o n . No X-ray or heat capacity data are available for t h i s phase t r a n s i t i o n , but the sharp increase in e l e c t r i c a l conductivity at 367K [5.5] lends support to t h i s . The Tn minimum in phase I i s attributed to the lp • + reorientation of the NMe^ group, and a least-squares f i t to the l i n e a r portion of the data points on the high temperature side of t h i s minimum gives an act i v a t i o n energy of 11.12±0.33 kcal mole - 1. A least-squares f i t to the T^ data points i n the temperature range 362K to 430K gives an act i v a t i o n energy of 9.10±0.21 kcal mole 1 . As in the case of the chloride and bromide, t h i s i s assigned to iso t r o p i c reorientation of the choline ion. Linewidth studies by Graham and Hannon [5.21] have shown that from 359 to 372K the second moment decreases to 2 <1G and then approaches a value of zero, i n d i c a t i v e of - 129 -g e n e r a l r e o r i e n t a t i o n f o l l o w e d by s e l f d i f f u s i o n . S i n c e minima and l i n e w i d t h t r a n s i t i o n s g e n e r a l l y t a k e p l a c e a p p r o x i m a t e l y a t t h e same t e m p e r a t u r e r e g i o n , we a s s i g n o u r T, minimum o f 1.85 msec a t 392K t o s e l f - d i f f u s i o n o f t h e l p c h o l i n e i o n . From t h e d a t a on t h e low and;'high t e m p e r a t u r e s i d e o f t h i s minimum, a c t i v a t i o n e n e r g i e s f o r d i f f u s i o n o f 18.2±0.3 and 25.0±1.4 k c a l m o l e " 1 a r e o b t a i n e d . The s h a r p i n c r e a s e i n T^ and t h e d i s c o n t i n u i t y i n T.. v a l u e s a t 430K i n d i c a t e a n o t h e r p h a s e t r a n s i t i o n , l p a l t h o u g h no m e n t i o n o f s u c h a p h a s e t r a n s i t i o n i s made i n p r e v i o u s l y p u b l i s h e d r e s u l t s . I n t h e f o l l o w i n g , we s h a l l p r e s e n t more e v i d e n c e f o r t h e I I + I I I p h a s e t r a n s i t i o n a s w e l l as f o r a ' d i f f u s i o n a l l y q u e n c h e d ' c h o l i n e i o n f o l l o w i n g t h i s t r a n s i t i o n . S i n c e Graham and Hannon had r e p o r t e d l i n e -w i d t h d a t a o n l y up t o 4 0 0 K , a s t u d y o f l i n e w i d t h c h a n g e s i n t h e h i g h t e m p e r a t u r e r e g i o n ( p h a s e s I I and I I I ) a l o n e was u n d e r t a k e n by m o n i t o r i n g t h e f r e e i n d u c t i o n d e c a y (FID)... I n p a s s i n g f r o m p h a s e I t o p h a s e I I , t h e FID u n d e r g o e s a s h a r p change r e s u l t i n g i n a s l o w e r d e c a y c o r r e s -p o n d i n g t o a n a r r o w e r a b s o r p t i o n l i n e . W i t h f u r t h e r i n c r e a s e o f t e m p e r a t u r e i n p h a s e I I , t h e FID becomes l o n g e r and l o n g e r , f i n a l l y r e a c h i n g a d e c a y shape e x p e c t e d f o r a l i q u i d -l i k e a b s o r p t i o n l i n e s h a p e s u g g e s t i n g t h a t d i f f u s i o n was o c c u r r i n g . - 130 -However, at 43OK the temperature of the proposed phase t r a n s i t i o n , the FID shortens in a spectacular way, corresponding to a broader absorption lineshape in phase I I I . A further increase of temperature i n phase III r e s u l t s i n longer FID's tending towards one expected i f d i f f u s i o n was occurring. The observed FID's at six selected temperatures are shown in Figure (5.6). To further i l l u s t r a t e the changes in the FID's, the values of transverse relaxation times (T 2) measured as the time taken for the FID to reduce to l/e of i t s o r i g i n a l value, are shown i n the top portion of Figure (5.7). The free induction decay i s the Fourier transform of the absorption lineshape and i s related to the even moments of the absorption lineshape by Equation (2.21). From the 2 i n i t i a l slopes of the plots of FID signal amplitude vs. t , values of second moments M.^ were obtained and are shown on the lower half of Figure (5.7). It i s seen that the second moment reduces to zero in phase II, showing d i f f u s i o n of the choline ion to be taking place. However, at 430K, the l i n e broadens abruptly, suggesting a p a r t i a l "quenching" of d i f f u s i o n in the new phase, phase I I I . Further increase: of temperature re s u l t s in l i n e narrowing, the proton absorption again tending towards a zero second moment as a r e s u l t of d i f f u s i o n becoming faster in phase I I I . - 131 -Phase I \ 350 K \ 360 K \ i — i \ V 10 p Sec. \ ^ // 1 1 lOpSec. / / Phase II , 370 K \ 420 K. \ • — • ^ \ \ 50 pSec ^ 1 // 1 1 ^ 500pSec — / / Phase III 440 K 500 K \ i — i ^\ \ 50 p Sec. i — i v 100pSec. 1 ^ / / — FIGURE 5.6 O s c i l l o g r a p h t r a c e s of the FID's f o r c h o l i n e i o d i d e a t s i x s e l e c t e d temperatures. - 132 -FIGURE 5.7 Temperature dependence o f proton T„ ( f i l l e d t r i a n g l e s ) and second moments ( f i l l e d c i r c l e s ) f o r c h o l i n e i o d i d e i n phases II and I I I . - 133 -The T^p results i n phase III (Figure 5.5) are also seen to support the above-mentioned behaviour. T, lp values i n phase III measured at an r . f . f i e l d of 5.9 G are seen to decrease up to the highest temperature studied. This i s explained as the d i f f u s i o n a l process in phase III becoming faster with r i s e in temperature and tending towards the condition oo, x sal for a T, minimum. T, values measured 1 c lp lp at a lower spin locking f i e l d of 2.0 G indeed shows the T. c ^ lp minimum corresponding to d i f f u s i o n in phase I I I . An ac t i v a -tion energy f o r ( d i f f u s i o n in phase III obtained from values measured at H.^  = 5.9 G was found to be 10.1±0.4 kcal mole 1 . A th e o r e t i c a l description of the spin relaxation caused by s e l f d i f f u s i o n , has been worked out by Torrey [5.30-5.32]. Two models have been considered, the ' l a t t i c e d i f f u s i o n ' model and the 'isotropic d i f f u s i o n ' model. In the case of the ' l a t t i c e d i f f u s i o n ' model, molecules are assumed to undergo t r a n s l a t i o n a l jumps of equal length to the nearest neighbour l a t t i c e s i t e s . The spin relaxation rate equations for t h i s model are dependent on the symmetry of the unit c e l l , and only the cases of f.c.c. and b.c.c. have so far been treated [5.30-5.32]. The second model, the 'isotropic d i f f u s i o n ' model, assumes an appropriate p r o b a b i l i t y d i s t r i b u t i o n for the jump distance of the molecules. This model i s applicable to l i q u i d s , or to sol i d s in which the - 134 -d i f f u s i o n a l mechanism i s more complex than jump ;to a descrete vacant s i t e . The rate equations for t h i s model do not require a knowledge of the c r y s t a l structure [5.30]. It has been pointed out [5.33] that the difference i n the relaxation rates predicted by the two models i s quite small and there-fore spin relaxation measurements are usually not very sensi-t i v e to the model chosen. In view of t h i s fact, and because no c r y s t a l structure data on the choline iodide in the high temperature phases (II and III) are available, we assume the i s o t r o p i c d i f f u s i o n model to describe the spin relaxation rates in the high temperature phases of choline iodide. When the mean square jump distance i s long, i . e . 2 2 (r )>>d , where d i s the distance of closest approach between two molecules, i n the neighbourhood of the minimum has the form, 1 T c - i - = C ° 2 2 (5.5) lp 1 + 0)-, T 1 C where, C = | Y V I ( I + 1 ) ^ 5 d 3 In the above equation, n i s the uniform spin density. From the measured T, minimum of 1.85 msec with lp Hn = 5.9 G, the constant C in Equation (5.5) i s evaluated - 135 -and the c o r r e l a t i o n times x c at a series of temperatures i n phase I I were calculated from the corresponding values at these temperatures. The values are shown in Figure 5.8 (closed c i r c l e s ) . For the T^ relaxation in phase I I I , the constant C of Equation (5.5) was evaluated from the observed T, minimum of 750 usee at H, =2.0 G. The c o r r e l a t i o n lp 1 times in phase I I I were then obtained from T n data at both lp = 5.9 G ( f i l l e d triangles) and H 1 = 2.0 G (open triangles) and are also shown i n Figure (5.8). As seen i n Figure (5.8), the c o r r e l a t i o n time for the d i f f u s i o n a l process increases by about two orders of magnitude in going from phase I I to phase I I I , thus demonstrating very well the ' d i f f u s i o n a l quenching' we have proposed. Least-squares f i t s to the data points in Figure 5.8 in phases I I and I I I give activation energies of 21.35±0.47 and 11.16±0.50 kcal mole" 1 for the d i f f u s i o n a l processes in phases:.:il:.ahd I I I , respectively. As we have done for the other relaxation time minima, i t i s now useful to compare our experimental T^ minima with those expected t h e o r e t i c a l l y for a s e l f - d i f f u s i o n mechanism. Using Equation (5.5) and r e l a t i n g the constant C to lA^i the second moment pr i o r to l i n e narrowing by d i f f u s i o n , one gets [5.33], M = 0.25 — . (5.6) Tlp(min) w l - 136 --10 c 4 •10 -5 o (D cn CD c o -6, D10J CD t_ i_ o O 10 r7 Choline Iodide ^ M i n i m u m (Ht = 2.06) 2.0 -> Tj. Minimum (H, = 5.96) 2.2 2M 2.6 2.8 -1 1 0 0 0 / T (K ' ) FIGURE 5.8 Temperature dependence of the co r r e l a t i o n times for s e l f - d i f f u s i o n of the choline ion i n phases II and III of the iodide obtained from T l p data at Ei = 5.9 G ( f i l l e d c i r c l e s ) and H^  = 2.0 G (open c i r c l e s ) . S o l i d l i n e through data points are l i n e a r least-squares f i t s . - 137 -The value of M^ ,. the residual second moment of the absorption l i n e narrowed by is o t r o p i c tumbling of molecules, cannot be calculated for phases II and III of choline iodide as the c r y s t a l structure i s not known. An experimental value of i s also not available, because at the low temperature ends of both phases II and III, the nmr absorption l i n e i s already narrowed by the d i f f u s i o n a l process (see Figure 2 5.7; also ref. [5.21]). However, using the value of 0.88 G for obtained by Graham and Hannon for the high temperature cubic phase of choline chloride,[5.21], a T, . . . value of ^ ' lp (mm) 1.10 msec with H^ = 5.9 G i s calculated, which i s in f a i r agreement with the experimental value. Our experimental Tn , . . value i s also of the same order of magnitude as lp (mm) those obtained for the d i f f u s i o n a l processes in similar compounds such as p i v a l i c acid [5.34]. In order to investigate whether there i s any difference i n the T, relaxation mechanism between phases II and III in choline iodide, the following procedure i s adopted. From the T.. , . , value of 750 ysec obtained at ^ lp (mm) H^ = 2.0 G in phase III, that expected at H^ = 5.9 G was calculated using Equation (5.6) to be 2.21 msec. This i s in good agreement with the T n , . . value of 1.8 5 msec 3 ^ lp (mm) observed at = 5.9 G in phase II, lending support to the idea that in both of the phases II and I I I , relaxation i s governed by the same motional mechanism. -M38 -One o f t h e i m p o r t a n t r e s u l t s i n t h i s c h a p t e r i s t h e e v i d e n c e f o u n d f o r a c r y s t a l - c r y s t a l p h a s e t r a n s i t i o n ( I I ^ - I I I ) i n c h o l i n e i o d i d e a t 430K. F u r t h e r c o n f i r m a t i o n o f t h e p r o p o s e d phase t r a n s i t i o n i s s o u g h t f r o m D i f f e r e n t i a l t T h e r m a l A n a l y s i s e x p e r i m e n t . The DTA thermogram f o r c r y s t a l l i n e c h o l i n e i o d i d e i s shown i n F i g u r e (5.9). I t shows two w e l l - d e f i n e d e n d o t h e r m i c t r a n s i t i o n s b e g i n n i n g a t 361K and 427.5K, r e s p e c t i v e l y , on warming and s t a r t i n g a t 411K and 353K, r e s p e c t i v e l y , on c o o l i n g . T h i s has a l s o been o b s e r v e d by P e t r o u l e a s [5.17]. The a c t i v a t i o n e n e r g i e s o b t a i n e d f o r t h e v a r i o u s m o t i o n s p r o p o s e d i n c h o l i n e i o d i d e a r e summarized i n T a b l e 5.3. d) C h o l i n e p e r c h l o r a t e . The r e l a x a t i o n t i m e r e s u l t s f o r c h o l i n e p e r -c h l o r a t e a r e shown i n F i g u r e (5.10). T^ v a l u e s ( f i l l e d c i r c l e s ) show a s i n g l e minimum o f 32 msec w h i c h i s immed-i a t e l y f o l l o w e d by a s h a r p upward jump a t 272K above w h i c h t h e y c o n t i n u e t o i n c r e a s e w i t h t e m p e r a t u r e . T, measured a t = 5.9G ( f i l l e d t r i a n g l e s ) l p 1 shows a minimum o f 208 y s e c a t 205K and a f l a t r e g i o n a t The d i f f e r e n t i a l t h e r m a l a n a l y s i s e q u i p m e n t c o n s i s t e d o f FISHER T h e r m a l y s e r model 262, L i n e a r t e m p e r a t u r e programmer model 370, D.C. m i c r o v o l t a m p l i f i e r model 500 and r e c o r d e r s e r i e s 2 00. H e a t i n g r a t e u s e d was 5°/min. My t h a n k s t o Dr. Y. Koga o f t h i s d e p a r t m e n t f o r h i s k i n d a s s i s t a n c e i n r u n n i n g t h e thermograms. - 139 -FIGURE 5.9 The DTA thermograms for choline iodide. - 140 -10" d o 0 C D v Ul h 1 " 1 11 j 1 Choline Perchlorate • : • e © : e: A A ' / A A4 A \ A j A A A • T, (30MHz) * A A A ^(H^5.9G) A A A A ) . A A A A A a A A A A A A A 4 1000/T ( K " ' ) 6 FIGURE 5.10 Temperature dependence of the proton Ti and T l p of choline perchlorate. F i l l e d c i r c l e s : T x data at 30.20 MHz; f i l l e d t r i a n g l e s : T 1 o data at Hj = 5.9 G; open t r i a n g l e s : H! = 2 . 0 G. data at - 141 -lower temperatures. also shows a sharp jump at 2 72K, following which the downward trend of values at both f i e l d s examined (H^ = 5.9 G - f i l l e d t r i a n g l e s , = 2.0 G - open t r i a n g l e s ) , i s i n d i c a t i v e of another minimum at higher temperatures. The sharp increase in T, and Tn values at 1 lp 272K i s taken as s u f f i c i e n t evidence for the existence of a c r y s t a l - c r y s t a l phase t r a n s i t i o n at 272K. Once again, the T^ minimum at 205K i s assigned to reorientation of the three methyl groups about t h e i r symmetry axes. The cor r e l a t i o n times extracted from the T^ data using Equation (2.56) are shown by open trian g l e s i n Figure (5.3). A least-squares f i t to the data points give an ac t i v a t i o n energy of 3.26±0.12 kcal mole" 1. F i t t i n g the entire set of T^ data points in phase I by the non-linear least-squares procedure gives the best f i t parameters of C = 22.18±1.29 s e c - 1 , T q = (5.55±4.55) x -12 -1 10 sec and E = 3.18±0.34 kcal mole . The s o l i d l i n e through the T^ data points i n Figure (5.10) i s drawn using the above parameters. The T^(min) value of 32 msec observed i n the perchlorate i s higher than that observed for the halides but i s s t i l l i n good agreement with the expected 28 msec for methyl reorientation. - 142 -The T n minimum a t 205K i s a s s i g n e d t o t h e c' lp ^ 3 r o t a t i o n o f t h e NMe^ g r o u p . A l e a s t - s q u a r e s f i t t o t h e l i n e a r p o r t i o n o f d a t a p o i n t s o n - t h e h i g h t e m p e r a t u r e s i d e o f t h i s T ^ p minimum g i v e s an a c t i v a t i o n e n e r g y o f 7.42+0.15 k c a l mole ^. The o b s e r v e d T, (min) v a l u e o f 208 y s e c i s lp i n good a g r e e m e n t w i t h t h e c a l c u l a t e d t h e o r e t i c a l v a l u e o f 199 y s e c , w h i c h i n c l u d e s t h e i n t e r m e t h y l c o n t r i b u t i o n ( see T a b l e 5 . 2 ) . The f l a t T ^ p r e g i o n a t t h e l o w e s t t e m p e r a t u r e s i n v e s t i g a t e d i s p r o b a b l y due t o t h e r o t a t i o n o f m e t h y l g r o u p s b e c o m i n g i m p o r t a n t i n t h e r e l a x a t i o n . A l e a s t - s q u a r e s f i t t o t h e p o i n t s i n t h e h i g h t e m p e r a t u r e phase g i v e s an a c t i v a t i o n e n e r g y o f 6.95+0.56 k c a l mole 1 , w h i c h i s a s s i g n e d t o i s o t r o p i c t u m b l i n g o f t h e c h o l i n e i o n i n t h e p e r c h l o r a t e s t r u c t u r e . I n t h e h i g h t e m p e r a t u r e p h a s e (phase I I ) , t h e downward t r e n d o f T n v a l u e s w h i c h i n d i c a t e s a n o t h e r minimum lp i s a s s i g n e d t o d i f f u s i o n b e c o m i n g e f f e c t i v e i n c a u s i n g r e l a x a t i o n . T h i s i s s u p p o r t e d by t h e l i n e n a r r o w i n g w h i c h b e g i n s t o a p p e a r a t 300K ( F i g u r e 5.1). From t h e l i n e a r p o r t i o n o f T, d a t a m e a s u r e d a t H, = 2.0 G, an a c t i v a t i o n e n e r g y f o r lp 1 3 J d i f f u s i o n o f ^17 k c a l m o l e 1 i s o b t a i n e d . - 1 4 3 -5 . 4 SUMMARY I n summary , o u r a n a l y s i s o f t h e t e m p e r a t u r e d e p e n d e n c e o f t h e Zeeman and r o t a t i n g f r a m e 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 (T^ a n d T ^ p ) i n c h o l i n e c h l o r i d e , b r o m i d e , i o d i d e a n d p e r -c h l o r a t e h a s e n a b l e d us t o i d e n t i f y t h e f o l l o w i n g m o t i o n a l p r o c e s s e s : ( i ) r o t a t i o n o f t h e m e t h y l groups f o l l o w e d + s u c c e s s i v e l y by ( i i ) t h e o n s e t o f r e o r i e n t a t i o n o f t h e NMe^ m o i e t y a b o u t t h e l o n g c h a i n C - N ( d e n o t e d a s C^) a x i s , ( i i i ) g e n e r a l r e o r i e n t a t i o n o f t h e w h o l e c h o l i n e c a t i o n , a n d ( i v ) a d d i t i o n a l s l o w m o t i o n o f t h e l o n g c h a i n C E ^ C F ^ O H i n t h e c a s e o f t h e c h l o r i d e a n d b r o m i d e , and (v) d i f f u s i o n o f t h e c h o l i n e i o n i n t h e c a s e o f t h e i o d i d e a n d p e r c h l o r a t e . T h e a c t i v a -t i o n e n e r g i e s d e t e r m i n e d f o r t h e a b o v e m o t i o n a l p r o c e s s e s w e r e s u m m a r i z e d i n T a b l e ( 5 . 3 ) . A c r y s t a l - c r y s t a l p h a s e t r a n s i t i o n w h i c h i s known t o o c c u r a t 3 5 3 , 3 6 4 a n d 3 6 2 K i n t h e c h l o r i d e , b r o m i d e and i o d i d e r e s p e c t i v e l y , i s f o u n d t o o c c u r a t a much l o w e r t e m p e r a t u r e ( 2 7 2 K ) i n t h e p e r c h l o r a t e l a t t i c e . E v i d e n c e h a s a l s o b e e n p r e s e n t e d f o r a new h i g h t e m p e r a t u r e c r y s t a l - c r y s t a l p h a s e t r a n s i t i o n a t 4 3 5 K i n t h e i o d i d e , a t w h i c h p o i n t a ' q u e n c h i n g ' o f t h e d i f f u s i o n a l p r o -c e s s i s f o u n d i n t h i s s t r u c t u r e . A p a r t o f t h e s e r e s u l t s h a s b e e n p u b l i s h e d e l s e w h e r e [ 5 . 3 5 ] . - 144 -R e f e r e n c e s [ 5 . 1 ] A. D a n i e l s , R.J.P. W i l l i a m s and P.E. W r i g h t , N a t u r e (London) 2 6 1 , 3 2 1 ( 1 9 7 6 ) and r e f e r e n c e s t h e r e i n . [ 5 . 2 ] D. Nachmanson, Handb. Sens. P h y s i o l . 1, 18 ( 1 9 7 1 ) and r e f e r e n c e s t h e r e i n . [ 5 . 3 ] R.B. B a r l o w , I n t r o d u c t i o n t o C h e m i c a l P h a r m a c o l o g y , 3 r d e d . , Methuen, London ( 1 9 6 4 ) , [ 5 . 4 ] B.M. T o l b e r t , P.T. Adams, E.L. B e n n e t t , A.M. Hughes, M.R. K i r k , R.M. Lemmon, R.M. N o l l e r , R. O s t w a l d and M.. C a l v i n , J . Amer. Chem. S oc. 7J5, 1 8 6 7 ( 1 9 5 3 ) . [ 5 . 5 ] R.W. B a k e r , C H . C h o t h i a , P. P a u l i n g and T . J . P e t c h e r , N a t u r e 2 3 0 , 439 ( 1 9 7 1 ) . [ 5 . 6 ] D. L i c h t e n b e r g , P.A. Kr o o n and S . I . Chan, J . Amer. Chem. S o c . 96, 5934 ( 1 9 7 4 ) . [ 5 . 7 ] Y. T o m k i e w i c z , R. A g a r w a l and R.M. Lemmon, J . Amer. Chem. S oc. 9_5, 3144 ( 1 9 7 3 ) . [ 5 . 8 ] ; : M . Ackerman and R.M. Lemmon, J . Phys. Chem. 7 1 , 3 3 5 0 ( 1 9 6 7 ) . [ 5 . 9 ] R.O. L i n d b l o m , R.M. Lemmon and M. C a l v i n , J . Amer. Chem. Soc. 8J3, 2484 ( 1 9 6 1 ) . [ 5 . 1 0 ] R.M. Lemmon, P.K. Gordon, M.A. P a r s o n s and F. M a z z e t t i , J . Amer. Chem. S oc. 8 0 , 2 7 3 0 ( 1 9 5 8 ) . [ 5 . 1 1 ] A. N a t h , R. A g a r w a l , L. M a r t o n , V. Subramanyan and R.M. Lemmon, J . Amer. Chem. S o c . 93, 2 1 0 3 ( 1 9 7 1 ) . - 145 -[5.12] A. Nath, R. Agarwal and R.M. Lemmon, J. Chem. Phys. 61f 1542 (1974). [5.13] I. S e r l i n , Science 127, 261 (1957). [5.14] R.L. C o l l i n , J. Amer. Chem. Soc. 7_9, 6086 (1957). [5.15] M.E. Senko and D.H. Templeton, Acta Cryst. 13, 281 (1960). [5.16] P. Shanley and R.L. Collin./ Acta Cryst. 14, 79 (1961). [5.17] V. Petrouleas, personal communication. [5.18] A. Theoret and C. Sandorfy, Spectrochim. Acta 22, 1527 (1966) . [5.19] C. Wang and H. Ache, J. Chem. Phys. 52, 5492 (1970). [5.20] J. Daycock, G. Jones, J. Evans and J. Thomas, Nature-(London), 218, 672 (1968). [5.21] J.D. Graham and R.H. Hannon, J. Chem. Phys. 64, 1204 (1976). [5.22] J.D. Graham and R.H. Hannon, J. Mag. Res. 23, 97 (1976). [5.23] G.W. Smith, J. Chem. Phys. 42_, 4229 (1965). [5.24] J.G. Powles and H.S. Gutowsky, J. Chem. Phys. 21, 1695 (1953); 21, 1704 (1953). [5.25] R. Blin c , S. Zumer and G. Lahajner, Phys. Rev. B l , 4456 (1970). [5.26] J.E. Anderson and W.P. S l i c h t e r , J. Phys. Chem. 69, 3099 (1965). [5.27] G.P. Jones, Phys. Rev. 148, 332 (1966). - 146 -[5.28] C.I. R a t c l i f f e and B.A. Dunell, J. Chem. Soc. Faraday Transactions I I , 7_3, 493 (1977). [5.29] T. Kodama, J. Mag. Res. 1_, 137 (1972). [5.30] H.C. Torrey, Phys. Rev. 9_2, 962 (1953). [5.31] H.C. Torrey, Phys. Rev. 9_6, 690 (1954). [5.32] H.A. Resing and H.C. Torrey, Phys. Rev. 131 1102 (1963). [5.33] N. Boden, J. Cohen and R.T. Squires, Mol. Phys. 31, 1813 (1976). [5.34] R.L. Jackson and J.H. Strange, Mol. Phys. ,2_2, 313 (1971)%. [5.35] CA. McDowell, P. Raghunathan and D.S. Williams, J. Chem. Phys. 66, 3240 (1977). - 147 -CHAPTER VI MOLECULAR MOTION IN PHOSPHORUS PENTAFLUORIDE- TRIMETHYLAMINE ADDUCT 6.1 INTRODUCTION Phosphorus pentafluoride, PF,_ forms a d d i t i o n a l complexes with many oxygen-, sulphur-, and nitrogen-containing compounds [6.1), but the motional behaviour of none of these appears to have been inv e s t i g a t e d previously. The addition compound of PF,. with trimethylamine i s chosen f o r our study of mole-cular motion here f o r the following reasons: (i) the high symmetry of the trimethylamine group ' and the nearly s p h e r i c a l nature of the adduct may lead to extensive i n t e r n a l motional processes with but small energy b a r r i e r s to them, ( i i ) the adduct i s r e l a t i v e l y stable, with a''reported melting point of 148 °C [6.2] , ( i i i ) the study may provide a good comparison with that of boron t r i f l u o r i d e - t r i m e t h y l a m i n e adduct (BF^:N (CH^)^) which has been investigated i n t h i s laboratory [6.3]. 1 19 (iv) the H and F spins may be expected to be strongly coupled, thereby showing i n t e r e s t i n g e f f e c t s i n t h e i r spin re l a x a t i o n behaviour. - 148 -High resolution nmr has shown [6.1] the geometry of the PF r group to be octahedral with four equivalent equatorial o fluorines and a unique a x i a l f l u o r i n e . The structure of the adduct i s shown below. (I) (ID 6.2 EXPERIMENTAL 6.2.1 Sample preparation. The adduct, (CH^) ^ N-PF(I) was prepared by con-densing phosphorus pentafluoride into a solution of trimethyl-amine i n toluene, held at -78°C [6.1,6.2]. A white s o l i d deposited immediately from the solution, and when no further absorption of PF,- occurred, the v o l a t i l e products were removed by pumping. The powdery white residue was then p u r i f i e d by sublimation at ^60°C i n vacuo. The product was then ground to a fine powder and transferred to evacuated flamed-out glass tubes and sealed under vacuum. They were stored i n l i q u i d nitrogen u n t i l used for measurements. A l l transfers were carried out either in the vacuum l i n e or i n a glove bag under an atmosphere of nitrogen. - 149 -The adduct (CB^)3N-PF5(II), was also prepared by the above procedure using the f u l l y deuterated trimethyl-amine (CD^J^N. Phosphorus pentafluoride (Matheson of Canada Ltd.) was used d i r e c t l y from the cylinder without further p u r i f i -cation; toluene (reagent grade) was d i s t i l l e d over calcium hydride, and trimethylamine (Eastman Kodak) was dried over lithium aluminum hydride p r i o r to use. d9-Trimethylamine (CD^^N (Merck, Sharpe and Dohme, 99% pure), was used d i r e c t l y from the cylinder without further p u r i f i c a t i o n . Microanalysis of the undeuterated adduct (I) corresponded to C = 20.00%, H = 4.97% and N = 7.32% (Calc: C = 19.47%, H = 4.90, N = 7.57%). It's melting point was 19 found to be 130°C. The high resolution F spectrum of the adduct I run i n a c e t o n i t r i l e (0.3% water) on a Varian T60 Spectrometer, showed the presence of PFg ion to be neg l i g i b l e (<5%). 6.2.2 Spectrometers. absorption spectra down to 77K were run on wide-l i n e spectrometer I described i n Section 3.1.1. "*"H spectra at 4.2K and that used for lineshape analysis at 77K, and a l l 19 F absorption spectra were run on wxdelxne spectrometer II described i n Section 3.1.4. A l l T^ measurements were measured on the Bruker Spectrometer described in Section 3.2.1 at 31.00 MHz. - 150 -6.3 RESULTS 6.3.1 Second moments. The temperature dependence of the second moments of the "^H absorption for compound I i s shown i n Figure 6.1. 2 It i s found to have a 'plateau' value of 18 G i n the temper-ature range 77-90K; t h i s i s followed by a single linewidth 2 t r a n s i t i o n i n the range 90-150K, reaching a value of 1.8 G which remains unchanged up to room temperature. A proton magnetic resonance absorption spectrum was also run at 4.2K, 2 which gave a second moment value of ^2 5 G . To r a t i o n a l i z e these re s u l t s i t i s necessary to calculate the expected second moments for the r i g i d molecule and for various possible motional modes. However, these values cannot be calculated p r e c i s e l y since no s t r u c t u r a l information i s a v a i l a b l e ' f o r t h i s compound. The following procedure i s , therefore, used to estimate the ~*"H second moments. The proton magnetic resonance lineshape of compound I i s assumed to be dominated by the interactions within the methyl groups, the 'other interactions' (intermethyl, i n t e r -molecular and H-F interactions) causing a further broadening with a second moment contribution which we s h a l l represent by 2 2 3 (this i s the same 3 given i n the Appendix). For r i g i d methyl groups, assuming a C-H bond distance of 1.09 A and tetrahedral angles at the methyl Catoms, the contribution to 20 —1 T 1— I I 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 Temperature (K ) FIGURE 6.1 Temperature dependence o f t h e p r o t o n second moments f o r t r i m e t h y l a m i n e -P F c adduct. - 152 -the second moment from the'-: methyl groups i s c a l c u l a t e d u s i n g 2 Equation (2.19) as 22.14 G . The c o n t r i b u t i o n to the second 2 2 moment from 'other i n t e r a c t i o n s ' ( 3 ) was found to be 2.5 G by means of a l i n e s h a p e f i t t i n g procedure (see l a t e r ) , g i v i n g 2 a t o t a l r i g i d l a t t i c e second moment of 24.6 G , i n e x c e l l e n t 2 agreement w i t h the second moment value of ^25 G observed at 4.2K. Var i o u s motional modes are c o n s i d e r e d next. Bearing i n mind t h a t the r o t a t i o n o f a methyl group about i t s symmetry a x i s reduces i t s second moment c o n t r i b u t i o n by a f a c t o r o f 4, the i n t r a m e t h y l second moment c o n t r i b u t i o n s r e s u l t i n g from the r o t a t i o n o f one, two and a l l t h r e e 2 methyl groups were c a l c u l a t e d as 16.61, 11.07 and 5.54 G , r e s p e c t i v e l y . The r e d u c t i o n f a c t o r s used f o r the c o n t r i b u -t i o n from 'other i n t e r a c t i o n s ' are approximate.; , .Using the r e s u l t of Powles and Gutowsky [6.4] t h a t methyl r o t a t i o n 2 reduced 3 by a f a c t o r of 4, the c o n t r i b u t i o n s to the second moment from i n t e r a c t i o n s o u t s i d e the methyl group when one, two and a l l three methyls r o t a t e are estimated to be 1.9, 1.3 and 0.6 G , r e s p e c t i v e l y . The t o t a l second moments f o r r o t a t i o n o f one, two and a l l three methyl groups are thus 2 18.5, 12.4 and,6.1 G , r e s p e c t i v e l y . For the r o t a t i o n of the NMe^ group about the N-P bond a x i s (denoted C^ 'I together w i t h the r o t a t i o n of O methyls, use of Equation (2.32) with = 70.5- ( r e s u l t i n g from - 153 -t e t r a h e d r a l geometry at the ni t r o g e n ) g i v e s a value o f 0.6 G f o r the i n t r a m e t h y l c o n t r i b u t i o n , which suggests the t o t a l 2 second moment to be ^1 G . Comparison of the experimental second moments (Figure 6.1) w i t h those c a l c u l a t e d f o r v a r i o u s motional models (summarized i n Table 6.1) allows one to i n f e r the f o l l o w i n g d e t a i l s r e g a r d i n g motion: (i) a t 4.2K, the TMA group i s r i g i d , ( i i ) a t 77K, the proton nmr a b s o r p t i o n l i n e i s narrowed by the r o t a t i o n of o n l y one of the th r e e methyl groups about i t s C^ symmetry a x i s , ( i i i ) the l i n e narrowing i n the temperature range 90-150K i s caused by the C^ r o t a t i o n of the oth e r two methyl groups together w i t h C^ r o t a t i o n o f the NMe^ group about the N-P bond a x i s . 19 The F nmr a b s o r p t i o n s p e c t r a were run a t 4.2K, 77K and a t room temperature, and were found to have second 2 moment value s of 11.0, 3.7 and 2.0 G , r e s p e c t i v e l y . 19 The t h e o r e t i c a l F second moments are c a l c u l a t e d i n the f o l l o w i n g manner. Since no s t r u c t u r a l i n f o r m a t i o n on t h i s compound was a v a i l a b l e , the P-F bond le n g t h s i n the PF,. group were assumed to be the same as those i n PF^ i o n , i . e . , P-F = 1.58 A and P-F = 1.73 A [6.5]. Use of these v a l u e s eq ax 19 i n Equation (2.19) y i e l d s a r i g i d l a t t i c e F second moment TABLE 6.1 T h e o r e t i c a l "'"H Second Moments f o r Trimethylamine - P F 5 Adduct RIGID R o t a t i o n R o t a t i o n R o t a t i o n C 3 of 3 Methyls of of of + 1 one methyl two methyls three methyls of (CH^^N Intramethyl 22.1 16.6 11.1 5.5 0.6 Other i n t e r a c t i o n s ^2.5 v L . 9 ^1.2 ^0. 6 ^0. 4 TOTAL ^24 . 6 ^18.5 ^12. 3 ^6.1 - 155 -2 4 19 c o n t r i b u t i o n o f 9.0 G f r o m t h e PF,. g r o u p 1 . F o r t h e F s e c o n d moment c o n t r i b u t i o n f r o m o t h e r i n t e r a c t i o n s , u s e o f 2 1 t h e same 3 v a l u e s as o b t a i n e d f o r H s e c o n d moments, i . e . 2 19 2.5 G g i v e s t h e t o t a l F a b s o r p t i o n s e c o n d moment o f 2 11.5 G , i n good a g r e e m e n t w i t h t h e e x p e r i m e n t a l l y o b s e r v e d v a l u e o f 11 G 2 a t 4.2K. The most l i k e l y m o t i o n t o o c c u r i n t h e PF,. m o i e t y i s r o t a t i o n a b o u t i t s symmetry a x i s . F o r t h i s m o t i o n , t h e F -F c o n t r i b u t i o n and t h e P-F c o n t r i b u t i o n s a r e eq eq eq r e d u c e d by a f a c t o r o f 4, and t h e F -F c o n t r i b u t i o n i s J ax eq r e d u c e d by a f a c t o r g i v e n by E q u a t i o n (2.27) w i t h ©' = 4 2 . 4 ° , w h i l e t h e P-F c o n t r i b u t i o n r e m a i n s u n c h a n g e d . The above r e d u c t i o n f a c t o r s r e s u l t i n a s e c o n d moment c o n t r i b u t i o n f r o m 2 t h e P F 5 g r o u p o f 1.9 G . 19 C o m p a r i s o n o f t h e e x p e r i m e n t a l and c a l c u l a t e d F s e c o n d moments s u g g e s t s t h a t : ( i ) a t 4.2K t h e PF,. g r o u p i s r i g i d , 19 ( i i ) a t 77K t h e F a b s o r p t i o n l i n e i s n a r r o w e d by t h e f o u r f o l d r o t a t i o n o f t h e PF,. g r o u p a b o u t t h e P-N bond a x i s , 19 ( i i i ) f u r t h e r n a r r o w i n g o f t h e F a b s o r p t i o n l i n e s h a p e a t h i g h e r t e m p e r a t u r e s i s p r o b a b l y c a u s e d by t h e a v e r a g i n g T h i s i n c l u d e s a c o n t r i b u t i o n f r o m F- P i n t e r a c t i o n s as w e l l . - 156 -of the H-F c o n t r i b u t i o n s brought about by the motion of the protons ( e a r l i e r d i s c u s s e d ) . 6.3.2 Lineshape a n a l y s i s . The "*"H magnetic resonance a b s o r p t i o n spectrum o b t a i n e d a t 4.2K i s shown i n F i g u r e 6.2a. I t shows the f a m i l i a r ' t r i p l e t ' l i n e s h a p e expected f o r a r i g i d methyl group (see the Appendix and F i g u r e 2.1). To examine t h i s l i n e s h a p e 2 f u r t h e r and to o b t a i n a v a l u e f o r the broadening f a c t o r , fj , t h e o r e t i c a l l i n e s h a p e s f o r a r i g i d t r i a n g l e o f protons are simulated a c c o r d i n g t o the procedure i n the Appendix, f o r a 2 s e r i e s of 3 v a l u e s . The f i t between the experimental and 2 2 t h e o r e t i c a l l i n e s h a p e s i s found to be b e s t f o r 3 = 2.5 G . The 'smooth' l i n e drawn through the experimental spectrum a t 4.2K i n F i g u r e 6.2a i s t h i s b e s t - f i t t h e o r e t i c a l l i n e s h a p e . I t i s seen t h a t f o r the f i r s t h a l f of the spectrum, the agree-ment i s e x c e l l e n t , thereby c o n f i r m i n g t h a t the t h r e e methyl groups remain r i g i d a t 4.2K, .and a l s o p r o v i d i n g a v a l u e f o r B2.* The poor agreement between the experimental and t h e o r e t i c a l l i n e s h a p e s i n the second h a l f of the spectrum i s b e l i e v e d to be due to s a t u r a t i o n of the nmr s i g n a l a t the v a l u e of the Hn f i e l d used. EXPERIMENTAL THEORETICAL ko 20 A •20 A -40 2 G j 2 = =2.5 G< R o t a t i n g m e t h y l , g 2=0.6 G 2 x R i g i d + 1 x r o t a t i n g 5 G •15 -I R i g i d methyl FIGURE 6.2 S i m u l a t i o n o f the p.m.r. l i n e s h a p e s f o r (CH 3) 3NPF 5: (a) experimental l i n e s h a p e a t 4.2K ( t h i n l i n e ) and computed ' f i t 1 ( t h i c k l i n e ) ; (b) experimental l i n e s h a p e a t 77K ( t h i n l i n e ) and computed ' f i t ' ( t h i c k l i n e ) ; (c) computed l i n e s h a p e f o r a r i g i d t r i a n g l e ; (d) computed l i n e s h a p e f o r a r o t a t i n g t r i a n g l e ; (e) computed li n e s h a p e f o r two' r i g i d + one r o t a t i n g case. - 158 -The proton nmr a b s o r p t i o n spectrum a t 77K i s a l s o d i s p l a y e d i n F i g u r e (6.2b) and t h i s spectrum remains unchanged throughout the p l a t e a u r e g i o n (77-90K). Now, our second moment measurements have suggested t h a t the nmr l i n e i n the temperature range 77-90K i s narrowed by the r o t a t i o n of one o f the methyls. To v e r i f y t h i s suggestion, we simulate the l i n e s h a p e expected t h e o r e t i c a l l y f o r a system c o n t a i n i n g two r i g i d and one r o t a t i n g methyl groups. T h i s c o u l d be done by adding, i n the r a t i o of 2:1, the t h e o r e t i c a l l i n e s h a p e s f o r r i g i d and r o t a t i n g methyl groups. Assuming the methyl group environment to remain unchanged i n going from 4.2K 2 to 77K, 3 f o r a r i g i d methyl group a t 77K may be taken as 2 . 2.5 G , the v a l u e which g i v e s the best f i t w ith the e x p e r i -mental l i n e s h a p e a t 4.2K. On the other hand, i n the case 2 of the r o t a t i n g methyl group, 3 may be assumed to be reduced by a f a c t o r of 4 [6.4]. The t h e o r e t i c a l l i n e s h a p e s computed a c c o r d i n g to the procedure i n the Appendix, u s i n g the above-2 mentioned values of 3 , are shown i n F i g u r e (6.2 c & d ) . The l i n e s h a p e i n F i g u r e (6.2e), o b t a i n e d by adding l i n e s h a p e s a and b i n the r a t i o 2:1, i s t h a t expected f o r a model of two r i g i d and one r o t a t i n g methyl groups. S u p e r p o s i t i o n of t h i s on the experimental l i n e s h a p e a t 77K leads to a very good f i t indeed, (Figure 6.2b) thus adding support to the i d e a t h a t there are two kinds of methyl groups i n the s o l i d s t a t i s t i c a l l y weighted i n the r a t i o 2:1. I t i s , however, not p o s s i b l e to - 159 -say whether t h i s non-equivalence suggests the presence of one unique and two equivalent methyl groups within a molecule, or the presence of two non-equivalent s i t e s i n the c r y s t a l l a t t i c e , s t a t i s t i c a l l y weighted i n the r a t i o 2:1. The answer to t h i s question can only be obtained from a study of the c r y s t a l structure of t h i s compound. Similar findings of non-equivalence of methyls have been reported [6.6, 6.7 and Chapter 5, t h i s t h e s i s ) . 6.3.3 Relaxation time measurements. a) Overall relaxation data: The experimental proton spin l a t t i c e relaxation H 19 times, T^ , for the adduct I ( f i l l e d c i r c l e s ) , and the F spin l a t t i c e relaxation times for the adducts I and II (open c i r c l e s and f i l l e d t r i a n g l e s , respectively) are shown i n Figure (6.3). T^ shows a highly asymmetric minimum centred at 213K ("L^00 = 4.69 K - 1 ) and another minimum centred at 98K ( 1^°° = 10.20 K _ 1 ) . The proton relaxation was found to be s l i g h t l y non-exponential i n the temperature range 110-165K ( 1 0^° = 9.09 - 6.06 K _ 1 ) and became markedly non-exponential at temperatures <110K. However, i n these temperature regions, the i n i t i a l decay of the magnetization was found to be exponential, and the T^ values shown for these temperature regions in Figure (6.3) are those extracted from the i n i t i a l decay. FIGURE 6.3 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 i n trimethylamine-PF 5 adduct. F i l l e d c i r c l e s : proton T x data f o r (CH 3) 3N:PF 5; open c i r c l e s : f l u o r i n e T : data f o r (CH 3) 3N:PF 5; f i l l e d t r i a n g l e s : f l u o r i n e T : data f o r (CD 3) 3N:PF 5. - 161 -19 The F 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 adduct I show a very broad minimum i n the range 77-100K C ^ 0 0 = 12.99 -10.00 K - 1 ) and another minimum c e n t r e d a t 173K ( 1 ^ Q 0 = 5.81 K - 1 ) wi t h a r e p r o d u c i b l e 'hump' a t ^220K =4.55 K _ 1 ) . The T^ v a l u e s f o r the adduct I I show a s i n g l e minimum c e n t r e d at 87K = 11.49 K _ 1 ) . Two p o i n t s are noteworthy i n F i g u r e (6.3):, F (x) the T^ data f o r the f u l l y d e u t e r a t e d adduct, adduct I I , do not show a hi g h temperature minimum, F ( i i ) as seen from the T^ data f o r adduct I I , deutera-t i o n has the e f f e c t of s h i f t i n g the depth as w e l l as the * p o s i t i o n o f the low temperature minimum. 1 19 These o b s e r v a t i o n s suggest t h a t i n adduct I, the H and F spins are s t r o n g l y coupled so t h a t the e f f i c i e n t r e l a x a t i o n of one k i n d o f nucleus a c t s as a si n k f o r the r e l a x a t i o n o f the o t h e r . Keeping t h i s o b s e r v a t i o n i n mind, and i n accordance w i t h the b r o a d l i n e r e s u l t s d i s c u s s e d e a r l i e r , the observed s p i n r e l a x a t i o n behaviour may be assig n e d to the f o l l o w i n g r e l a x a t i o n mechanisms:-F (i) The s i n g l e minimum of T^ f o r the f u l l y d e uterated adduct (II) i s caused by the f o u r f o l d r e o r i e n t a t i o n of the PF^ group about the N-P bond, w i t h u>Fx>F«l ( x F i s the c o r r e l a t i o n time f o r t h i s motion). In other words, the T-^_ data f o r the adduct I appear to be ' p u l l e d down' towards the r e g i o n s where T i shows a minimum. - 162 -( i i ) The r e o r i e n t a t i o n o f the 'unique' methyl group at a c o r r e l a t i o n time T such t h a t 10 rel causes the H low temperature T^ minimum. ( i i i ) The h i g h temperature T^ minimum i s probably due to C 3 r e o r i e n t a t i o n o f the other two methyls together w i t h the r e o r i e n t a t i o n of the TMA group about the P-N bond w i t h a c o r r e l a t i o n time such t h a t to x ^ ^ i l . F (iv) The hi g h temperature minimum i n T^ v a l u e s f o r adduct I i s s o l e l y due to the ' c r o s s - r e l a x a t i o n ' of the f l u o r i n e s through the more e f f i c i e n t l y r e l a x i n g protons; the broader T^ minimum observed i n adduct I compared w i t h t h a t i n adduct I I i s a l s o due to the ' c r o s s - r e l a x a t i o n ' o f the f l u o r i n e s through proton r e l a x a t i o n . For a vigorous q u a n t i t a t i v e treatment [6.8] of the above o v e r a l l r e l a x a t i o n data, i t i s necessary to c o n s i d e r the s p i n system as one of th r e e u n l i k e s p i n s , namely, "'"H, 19 31 . . F and P. However, as w i l l become apparent i n the ensuing d i s c u s s i o n , most of our data are i n t e r p r e t a b l e by t r e a t i n g the system as c o n s i s t i n g o n l y o f two u n l i k e s p i n s , the theory f o r which was presented i n S e c t i o n 2.6.4. We s h a l l now d i s c u s s the s e t s o f r e l a x a t i o n data r e p o r t e d above i n a more q u a n t i t a t i v e manner. - 163 -b) l 9 F relaxation in (CD„) „NPE,. (II). .5 6 .' t>  By the simple a r t i f i c e of d e u t e r a t i o n , the c o n t r i -19 b u t i o n to the r e l a x a t i o n o f F s p i n s by protons i s reduced by 98%. Thus, the s p i n system may now be t r e a t e d as one of 19 31 two u n l i k e s p i n s , , namely, F and P, f o r which the equations i n S e c t i o n 2.6.4 are now a p p l i c a b l e . The s p e c t r a l d e n s i t i e s J's i n Equations (2.66) and (2.67) depend on the type of motion. For the f o u r f o l d r e o r i e n t a t i o n of the PF<-group about the P-N bond, these s p e c t r a l d e n s i t i e s are given by Equations (2.46-2.48). The r e l a x a t i o n r a t e s g . i n Equations (2.66) and (2.67) f o r the two types of f l u o r i n e s ( e q u a t o r i a l and a x i a l ) are now c a l c u l a t e d by s u b s t i t u t i n g the a p p r o p r i a t e e x pressions f o r the s p e c t r a l d e n s i t i e s and c a r r y i n g out the summation. The o v e r a l l observable r a t e s are then taken as, i ( B a X + 4 g e q ) . (6.1) Once again, assuming the PF^ group to have the same bond lengths as those i n PFg* i o n [6.5], we get, T 4 9 1 F T F = 1.9124x10 f + FF - - - - - - 2 2 ' , . 2 2 1 + 0 3 F T F 1 + 4U> FT F -V 3 T F + 3.1858x10"! — ~ *• + 2 2 2 2 l + ( u F - u ) p ) T P * . . . The B here and i n the ensuing d i s c u s s i o n i s not to be con-fused w i t h the B 2 (broad energy f u n c t i o n ) used e a r l i e r . - 164 -, 6 T F ,. , . .2 2 ) (6.2) > p p = 3.1858x10° g 2 + ^ 2 " l ( 6 - 3 ) l + ( 0 ) F - 0 ) p ) T F l + ( 0 ) F + 0 3 p ) T p * p p - 1.5929x10* — - ^ - j + 2 2 y i + ( u F - U ) p ) T F l + 0) p T F + _ \ (6.4) l + ( 0 ) F + 0 ) P ) 2 T F 2 ! = 5g (6.5) PF PFP 19 31 o)„ and oj_ r e f e r to the Larrnor f r e q u e n c i e s of F and P , r P r e s p e c t i v e l y , i n r a d i a n s / s e c . A l l r e l a x a t i o n r a t e s ( g ) i n the above Equations (6.2-6.5) are of the same order of magnitude, and a non-e x p o n e n t i a l r e l a x a t i o n i s t h e r e f o r e p r e d i c t e d . A s l i g h t non-e x p o n e n t i a l i t y was indeed observed, but the i n i t i a l p a r t of the (M -M )/2M decay p l o t s were found to be e x p o n e n t i a l , and the F values shown i n F i g u r e (6.3) are the v a l u e s e x t r a c t e d from t h i s i n i t i a l decay. I t i s e a s i l y seen from Equations (2.63) and (2.64) t h a t f o r e x t r a c t e d from the i n i t i a l decay, T F = —^— . (6.6) 1 *FF - 165 -From Equations (6*2) and (6.6), one c a l c u l a t e s f o r r o t a t i o n of the PFJ. group a minimum o f 4 9 msec. T h i s i s t o be com-pared w i t h the observed v a l u e of the minimum of 70 msec. F The e n t i r e s e t o f T^ data p o i n t s f o r adduct I I were then l e a s t - s q u a r e s f i t t e d to an e x p r e s s i o n o f the type, 1 / T F 4 ? F i - = C ^ 7 + T l V 1 + " F T F ' ^ 4 4 ' / T F 3 T F 6 T F + C I 2 2 + ~ 2—2 + 2 2 / (<~>,"~) 1 + U F - U ) P ) T F 1 + l + ( 0 ) F + 0J P) T F to g i v e an a c t i v a t i o n energy o f 1.13 ± 0.11 k c a l mole 1 and a T ° of (5.37 ± 2.77) x 10~ 1 2 sec. f o r the r o t a t i o n of the P F C group about the P-N bond. The ' b e s t - f i t ' v a l u e s o b t a i n e d f o r the ' r e l a x a t i o n s t r e n g t h ' parameters C and c' were (1.21 ± 0.09) 9 8 — 2 x 10 and (2.64 ± 0.36) x 10 sec , r e s p e c t i v e l y , i n f a i r agreement with the c a l c u l a t e d values shown i n f r o n t of the pa r a n t h e s i s i n Equation (6.2). 1 H and 1 9 F relaxation in (CH7)„NPF (I). u i2 0 (i) High temperature r e g i o n (T>150K). We have assigned the T-j^  r e l a x a t i o n i n t h i s temperature r e g i o n to the r e o r i e n t a t i o n of two of the methyls t o -gether w i t h r e o r i e n t a t i o n of the TMA group a t f r e q u e n c i e s comparable w i t h the Larmor frequency o f protons, OJ H - 166 -19 The F r e l a x a t i o n i n t h i s temperature r e g i o n was assigned to ' c r o s s - r e l a x a t i o n ' through the "'"H s p e c i e s . Since the motion of the f l u o r i n e atoms i s f a s t i n t h i s temperature r e g i o n , and t h e r e f o r e do not c o n t r i b u t e to the o v e r a l l 1 31 r e l a x a t i o n e f f i c i e n c y , and s i n c e H - P i n t e r a c t i o n s are n e g l i g i b l e , the s p i n system may now be t r e a t e d as one of 1 19 . two u n l i k e s p i n s , namely H and F. Once again, u s i n g the theory set out i n S e c t i o n 2.6.4, one may w r i t e ! = C.M.(intra TMA) HH 1 2. 4T. + 2 2 2 2 1 + U H T 2 1 + 4 V 2 J + C 2M 2(H-F) 3T. + 2 2 ' 2 2 l+(uo -a>F) T 2 l + o ) H x 2 T2 2 2 1+(0) H+W F) T 2 (6.8) HF 9 PFH C 3M 2(H-F) -T . 2 2 l+(ai -a) F) T 2 6T + 2 2 1+(CJ H+0) F) T 2 (6.9) lFF = 5 C 2 M 2 ( H " F ) 2 2 _l+(o) -aip) T 2 3x. 1 + 0 ) F T 2 + 1 2 2 l+(a, H+u, F) x 2 j (6.10) - 167 -where C^, C 2 and are now dimensionless c o n s t a n t s which depend on the geometry o f the motion and are of the same order "of magnitude. M 2 ( i n t r a TMA) i s the "*"H second moment c o n t r i b u t i o n from i n t e r a c t i o n s w i t h i n the TMA group and M 2 (H-F) i s the c o n t r i b u t i o n to "*"H second moment 1 19 from H- F i n t e r a c t i o n s . i s the c o r r e l a t i o n time f o r the motion o f protons. The f a c t o r 5/9 appears i n Equations (6.9) and (6.10) due to the f a c t t h a t there a r e nine protons to every f i v e f l u o r i n e atoms. In the above equations, the most dominant second moment term i s M 2 ( i n t r a TMA) and t h i s leads t o , S > 8 ^ B ^ B (6.11) HH FF HF FH With the above approximation, one gets s o l u t i o n s to Equation (2.63) as, X+ = ~ e F F a n d X - = " PHH ( 6 - 1 2 ) In t h i s l i m i t , i n s p e c t i o n of the exp r e s s i o n s f o r A's and B's (Equation 2.65) y i e l d , A1 -> 0 and B 2 0 or, (6.13) A 2>>A 1 and B_L>>B2 - 168 -The r e f o r e , i n t h i s temperature r e g i o n (T>150K), the r e l a x a t i o n f o l l o w i n g a 18 0° p u l s e would be governed by s i n g l e e x p o n e n t i a l s , I H-<I H> -B t - 2 - — = e H H (6.14) 2 I H o F F I o - < I z > r^FF* p = e (6.15) 21 o 1 19 and, indeed, both H and F r e l a x a t i o n s were found to be e x p o n e n t i a l . From Equations (6.14) and (6.15), the measured s p i n - l a t t i c e r e l a x a t i o n times are giv e n by, H "HH and, (6.16) 1 • F "FF 1 w h e r e B „ „ a n d 3_„ a r e d e f i n e d i n E q u a t i o n s ( 6 . 8 ) a n d ( 6 . 1 0 ) , r e s p e c t i v e l y . The t h e o r e t i c a l t r e n d s o f t h e p r o t o n and f l u o r i n e r e l a x a t i o n t i m e s e x p e c t e d f r o m E q u a t i o n s ( 6 . 8 ) a n d ( 6 . 1 0 ) , r e s p e c t i v e l y , a r e s e e n t o be w e l l r e p r o d u c e d i n t h e e x p e r i -m e n t a l d a t a ( F i g u r e 6 . 3 ) ; i n p a r t i c u l a r , t h e min imum a t (oo —oo ) T _ « 1 a n d t h e ' h u m p ' a t o o o ^ x - ~ 1 w h i c h a r e e x p e c t e d H F Z i z - 169 -from the form of Equation (6.10) [6.9], are w e l l reproduced i n the experimental f l u o r i n e r e l a x a t i o n time curve (open c i r c l e s ) . The T^ minimum i s very asymmetric, the low temperature arm of the minimum g i v i n g a much s m a l l e r s l o p e due to a c o n t r i b u t i o n to the "'"H r e l a x a t i o n i n t h a t temper-t u r e r e g i o n from the (ui - U O T - term i n Equation (6.8). H E c z We now attempt to examine the e f f e c t of e l i m i n a t i n g the ' c r o s s - r e l a x a t i o n ' c o n t r i b u t i o n from the T^ data. I t i s seen from Equations (6.16), (6.8) and (6.10) t h a t the value o f T^ without the c r o s s - r e l a x a t i o n c o n t r i b u t i o n (denoted T^ (co r r e c t e d ) ) i s given by, 1 1 5 1 (6.17) T^ (corrected) T-^  The v a l u e s of T^ (corrected) e v a l u a t e d from the e x p e r i -H F mental T^ and T^ v a l u e s a t a s e r i e s of temperatures are shown i n F i g u r e (6.4). I t i s seen t h a t much of the asymmetry has now been reduced, but the T^ minimum i s s t i l l not p e r f e c t l y symmetric. Least-squares f i t s to the data p o i n t s on the low and high temperature s i d e s o f the T^ (corrected) minimum give a c t i v a t i o n e n e r g i e s of 2.36 ± 0.57 and 3.51 ± 0.11 k c a l mole r e s p e c t i v e l y . . T h i s may suggest the "'"H r e l a x a t i o n to be governed by more than one c o r r e l a t i o n time; t h i s , indeed, i s i n agreement with our e a r l i e r assignment of t h i s minimum to the r o t a t i o n o f two of the methyls together w i t h the motion of the NMe^ - 170 -FIGURE 6.4 The high temperature proton T x minimum i n (CH 3) 3NPF 5 after.removing the e f f e c t of the f l u o r i n e s . - 171 -group about the P-N bond, which are expected to take p l a c e w i t h two d i f f e r e n t c o r r e l a t i o n times. Thus, the v a l u e of 2.36 ± 0.57 k c a l mole 1 may be taken as an upper l i m i t to the a c t i v a t i o n energy f o r the r o t a t i o n of the two e q u i v a l e n t methyls whereas the value 3.51 ± 0.11 k c a l mole 1 may be taken as i n lower l i m i t t o the a c t i v a t i o n energy f o r the r o t a t i o n of the NMe^ group. ( f o r analogous c o n c l u s i o n s , see r e f . 6.10). One sees from Equations (6.8) and (6.10) t h a t i n the h i g h temperature s i d e of the T^ n and T^ minima, t h e i r r e s p e c t i v e s l o p e s should y i e l d the same va l u e f o r the a c t i v a t i o n energy. Indeed, the high temperature l i n e a r p o r t i o n of the T^ data (open c i r c l e s , F i g u r e (6.3)), g i v e an a c t i v a t i o n energy of 3.35 ± 0.11 k c a l mole ^, i n e x c e l l e n t agreement w i t h t h a t o b tained from the high H 1 temperature T^ data ( f i l l e d c i r c l e s , F i g u r e (6.3)), of 3.32 ± 0.10 k c a l mole" 1. ( i i ) Low temperature r e g i o n (T<14 0K)• In t h i s temperature r e g i o n , the motion of the f l u o r i n e s (C^ r o t a t i o n of the PF,.) , as w e l l as t h a t of the protons (C^ r o t a t i o n of unique methyl) c o n t r i b u t e to the r e l a x a -t i o n of the s p i n system. T h e r e f o r e , i t i s necessary to t r e a t the s p i n system here as one of three u n l i k e s p i n s , namely, "^"H, "^F and 3 1 P , which would r e q u i r e the s o l u t i o n of three coupled equations. However, the mathematical - 172 -manip u l a t i o n s here are t e d i o u s , and the a n a l y s i s o f the r e l a x a t i o n data would be q u i t e complex. For t h i s reason, H F no q u a n t i t a t i v e treatment of the and data f o r compound I i s attempted i n t h i s temperature r e g i o n . A l l the c o n c l u s i o n s r e g a r d i n g motion i n TMA-PF,. i n the temperature r e g i o n s t u d i e d are summarized below:-a) There are two types of methyl groups i n the s o l i d , s t a t i s t i c a l l y weighted i n the r a t i o 2:1. b) At 4.2K the s t r u c t u r e i s ' r i g i d 1 , a t l e a s t on the nmr time s c a l e . c) The unique type of methyl group i s the more mobile one, causing a proton nmr l i n e narrowing between 4.2K and 77K and a proton T^ minimum a t 98K. d) Subsequent r o t a t i o n of the other two methyl groups to g e t h e r w i t h the motion o f the TMA group cause a f u r t h e r l i n e narrowing i n the temperature range 90-150K and a T^ minimum at 213K. A c t i v a t i o n energy l i m i t s of E<2.36±0.57 k c a l mole 1 f o r the r o t a t i o n of methyls -1 ' and of E>3.51+0.11 k c a l mole f o r the C 3 motion of the TMA group are measured from the T^ data a t the above-mentioned minimum. e) R o t a t i o n of the PF,. group about the P-N bond i s 19 f a s t enough a t 77K to cause a narrowed F a b s o r p t i o n l i n e a t 77K.• I t causes a f l u o r i n e T^ minimum a t 87K i n the deuterated adduct. A c t i v a t i o n energy measured f o r t h i s - 173 -motion from data f o r II i s 1.13 ± 0.11 k c a l mole f) The r e l a x a t i o n time data show, i n g e n e r a l , t h a t the 1 19 H and F d i p o l e s are s t r o n g l y coupled. - 174 -References [6.1] E.L. M u e t t e r t i e s , T.A. B i t h e r , M.W. Farlow and D.D. Coffman, J . Inorg. N u c l . Chem. 1_6, 52 (1960). [6.2] F.N. Tebbe and E.L. M u e t t e r t i e s , Inorg. Chem. 6^, 129 (1967). [6.3] B.A. D u n e l l , C.A. Fy f e , C A . McDowell and J . Ripmeester, Trans. Faraday Soc. 6.5, 1153 (1969). [6.4] J.G. Powles and H.S. Gutowsky, J . Chem. Phys. 21, 1695 (1953). [6.5] "Table o f i n t e r a t o m i c d i s t a n c e s and c o n f i g u r a t i o n i n molecules and i o n s " , Chemical S o c i e t y , London, S p e c i a l p u b l i c a t i o n No. 11 (1958). [6.6] J.D. Graham and R.H. Hannon, J . Chem. Phys. 6jl, 1204 (1976) . [6.7] C.I. R a t c l i f f e and B.A. D u n e l l , J . Chem. Soc. Trans. Faraday I I , 73, 493 (1977). [6.8] A. Abragam, 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 e r s i t y P ress, N.Y. (1961). [6.9] A.P. Caron, D.J. Heuttner, J.L. Ragle, L. Sherk and T.R. Stengle, J . Chem. Phys. 2577 (1967). [6.10] P.S. A l l e n , A.W.K. Khanzada and C A . McDowell, J . Chem. Phys. 59, 470 (1973). - 175 -CHAPTER V I I C o n c l u s i o n s The c o n c l u s i o n s o f t h e work p r e s e n t e d i n t h e f o r e g o i n g c h a p t e r s may now be summarized. In t h e t r o p o l o n e s a l t o f t - b u t y l a m i n e t h e m o t i o n a l p r o c e s s e s t a k i n g p l a c e i n t h e c a t i o n i c f r a g m e n t were d e t e r -mined t o be as f o l l o w s . A t 66K, t h e f r a g m e n t was f o u n d t o be ' r i g i d ' on an nmr t i m e s c a l e . As t h e t e m p e r a t u r e i s i n c r e a s e d , m e t h y l r o t a t i o n s e t s i n f i r s t , f o r w h i c h an a c t i v a t i o n e n e r g y o f 2.99 ± 0.28 k c a l mole 1 i s m e a s u r e d . T h i s i s f o l l o w e d by t h e r o t a t i o n o f t h e ( C H 3 ) 3 C - and t h e + NH 3~ g r o u p s a b o u t t h e C-N bond a x i s w i t h a c t i v a t i o n e n e r g i e s o f 10.5 ± 1.5 and 7.23 ± 0.60 k c a l mole 1 , r e s p e c t i v e l y . From t h e d i f f e r e n c e between t h e l a t t e r two a c t i v a t i o n e n e r g i e s and f r o m a d e t e r m i n a t i o n o f c o r r e l a t i o n t i m e s , some i n t e r n a l m o t i o n a b o u t t h e C-N bond a x i s has been s u g g e s t e d , w i t h t h e + NH 3 g r o u p r o t a t i n g a t a s l i g h t l y s l o w e r r a t e t h a n t h e t -b u t y l g r o u p . T h i s f a c t , t a k e n t o g e t h e r w i t h t h e r e l u c t a n c e o f t h i s n e a r l y s p h e r i c a l c a t i o n t o u n d e r g o i s o t r o p i c t u m b l i n g , + may p o i n t t o some h y d r o g e n b o n d i n g a t t h e NH 3 g r o u p . A - 176 -c r y s t a l l o g r a p h i c study of t h i s compound should be u s e f u l i n v e r i f y i n g t h i s suggestion. As regards the motion of the t r o p o l o n a t e i o n , C^H^-C^ , i t has not been p o s s i b l e to draw any c o n c l u s i o n s . We are not aware of any other i n s t a n c e where the motion of t h i s i o n has been s t u d i e d . R e o r i e n t a t i o n of t h i s seven-membered r i n g around i t s o n l y a x i s of symmetry, a 0.^ a x i s , seems u n l i k e l y because o f the high a c t i v a t i o n e n e r g i e s t h a t would be i n v o l v e d . An i n - p l a n e r o t a t i o n i s p o s s i b l e , although t h i s r o t a t i o n i s not about a symmetry a x i s , and once again, a v e r i f i c a t i o n of t h i s c o u l d be sought from a c r y s t a l l o g r a p h i c study which would show such a motion as a p o s i t i o n a l d i s o r d e r . Such a motion has been found i n azulene, which has a geometry very s i m i l a r to t h a t of the t r o p o l o n a t e i o n [7.1]. In the four c h o l i n e s a l t s s t u d i e d , our r e l a x a t i o n time measurements i n the Zeeman and r o t a t i n g frames of r e f e r e n c e have enabled us to draw s e v e r a l important c o n c l u s i o n s . A c r y s t a l - c r y s t a l phase t r a n s i t i o n (I-^II) which i s known to occur a t 353, 364 and 362K i n the c h l o r i d e , bromide and i o d i d e , r e s p e c t i v e l y , has been confirmed by our study. F u r t h e r -more, i n the p e r c h l o r a t e s a l t o f c h o l i n e , a c r y s t a l - c r y s t a l phase t r a n s i t i o n (272K) has been d i s c o v e r e d , which occurs a t a much lower temperature. In a d d i t i o n , we have s u p p l i e d ample evidence f o r a f u r t h e r c r y s t a l - c r y s t a l phase t r a n s i t i o n i n c h o l i n e i o d i d e (II+III) a t 430K, which has not been so f a r r e p o r t e d . - 177 -With r e s p e c t to motional behaviour, the c h l o r i d e and bromide have been found i n g e n e r a l to be very s i m i l a r . T h i s i s c o n s i s t e n t with the r e s u l t s of other s t u d i e s [7.2]. However, the c h l o r i d e d i f f e r s from the bromide i n one r e s p e c t : i n the c h l o r i d e , evidence has been found f o r the presence of two types of methyls, a suggestion f i r s t made by Graham and Hannon [7.3]. The a c t i v a t i o n e n e r g i e s f o r motion of the two types o f methyls, namely, 4.34 ± 0.23 and 4.50 ± 0.27 k c a l mole 1 , r e s p e c t i v e l y , i n the c h l o r i d e are very s i m i l a r to the methyl motion a c t i v a t i o n energy of 4.38 ± 0.08 k c a l mole 1 i n the bromide. In the i o d i d e and the p e r c h l o r a t e , the methyl motion appears l e s s hindered, as evidenced by the lower a c t i v a t i o n e n e r g i e s of 3.84 ± 0.26 and 3.17 ± 0.34 k c a l mole \ r e s p e c t i v e l y . In phase I of a l l f o u r s a l t s , methyl motion i s f o l l o w e d + by a r e o r i e n t a t i o n of the NMe^ group about a r o t a t i o n a x i s , f o r which a c t i v a t i o n e n e r g i e s of 11.00 ± 0.01, 8.09 ± 0.19, 11.12 ± 0.33 and 7.42 ± 0.15 k c a l mole" 1 have been o b t a i n e d f o r the c h l o r i d e , bromide, i o d i d e and p e r c h l o r a t e . These values are t y p i c a l f o r such a motion. In the high temperature phase, phase I I , the c h l o r i d e and the bromide show i s o t r o p i c tumbling of the c a t i o n with a c t i v a t i o n e n e r g i e s of 6.79 ± 0.12 and 5.13 ± 0.08 k c a l mole \ r e s p e c t i v e l y . In t h i s phase, the r a d i a t i o n s e n s i t i v i t y of c h o l i n e c h l o r i d e has been r e p o r t e d [7.4] to be 'normal 1, and - 178 -i t has been suggested t h a t t h i s i s a r e s u l t of mobile protons i n h i b i t i n g the c h a i n r e a c t i o n t h a t i s b e l i e v e d to be the cause of the extreme r a d i a t i o n s e n s i t i v i t y of the c h l o r i d e i n phase I. T h i s proton m o b i l i t y may be thought of as being brought about by i n t e r m o l e c u l a r proton t r a n s f e r through hydrogen bonds, a phenomenon f a c i l i t a t e d by o v e r a l l molecular r e o r i e n t a -t i o n . Thus, the i s o t r o p i c tumbling observed i n the c h l o r i d e adds support to the e x p l a n a t i o n given f o r the r a d i a t i o n s t a b i l i t y of the c h l o r i d e i n phase I I . X-ray c r y s t a l l o g r a p h i c s t u d i e s a l s o have shown a d i s o r d e r e d s t r u c t u r e i n t h i s plane [7.5] , which i s c o n s i s t e n t with g e n e r a l r e o r i e n t a t i o n of the i o n s . In phase I I o f the i o d i d e and p e r c h l o r a t e , too , i s o t r o p i c tumbling has been observed ( a c t i v a t i o n e n e r g i e s 9.10 ± 0.21 and 6.95 ± 0.56 k c a l mole 1 , r e s p e c t i v e l y ) ; t h i s motion i s followed by s e l f d i f f u s i o n of the c h o l i n e i o n w i t h a c t i v a t i o n e n e r g i e s 21.4 ± 0.5 and ^17 k c a l mole r e s p e c t i v e l y . I n t e r e s t i n g o b s e r v a t i o n s have been made r e g a r d i n g the phase t r a n s i t i o n II->III of i o d i d e . In going from phase II+III, an abrupt l i n e broadening has been observed, sugg e s t i n g a p a r t i a l 'quenching' of the d i f f u s i o n a l p r o c e s s . T h i s d i f f u s i o n i n phase I I I i s t h e r m a l l y a c t i v a t e d i n the u s u a l way but w i t h a lower a c t i v a t i o n energy (11.2 ± 0.5 k c a l mole "*") com-pared to t h a t i n phase I I . We are aware o f o n l y one other case, t h a t of 2-methyl - 2-propanethiol, (CH^)^CSH-where a - 179 -s i m i l a r d i f f u s i o n a l quenching behaviour has been observed [7.6], where the behaviour i s r a t i o n a l i z e d i n terms of s t e r i c crowding around a d i f f u s i n g molecule f o l l o w i n g the phase t r a n s i t i o n . We cannot, however, pursue our d i s c u s s i o n along s i m i l a r l i n e s without having a knowledge of the c r y s t a l s t r u c t u r e before and a f t e r the phase t r a n s i t i o n I I + I I I . In phase II of the c h l o r i d e and bromide, an a d d i t i o n a l motion with a c t i v a t i o n e n e r g i e s o f 4.34 ± 0.27 and 3.99 ± 0.21 k c a l mole r e s p e c t i v e l y , have been observed and have been assi g n e d to the probable motion of the c h a i n -CH^CI^OH. Such a motion has been supported by the r e c e n t c r y s t a l l o -g r a p hic s t u d i e s of P e t r o l e a s [7.7]. I t i s noteworthy t h a t although the r e s u l t s o b t a i n e d i n the p e r c h l o r a t e l a t t i c e are e s s e n t i a l l y s i m i l a r to those observed f o r the h a l i d e s , the a c t u a l temperatures o f the motional and c r y s t a l - c r y s t a l phase t r a n s i t i o n s i n the former are s h i f t e d to much lower temperatures and the a c t i v a t i o n e n e r g i e s o btained f o r the former are a l s o g e n e r a l l y lower. T h i s i s o n l y t o be expected as the l a r g e r s i z e o f the ClO^ would p r o v i d e more room f o r the r e o r i e n t a t i o n of the c a t i o n . In the adduct of trimethylamine and PF,., our l i n e s h a p e a n a l y s i s r e s u l t s show r a t h e r c l e a r l y t h a t t h e r e are two types of methyl groups i n the s o l i d s t a t i s t i c a l l y weighted i n the r a t i o 2:1, with the unique type of methyl being much l e s s hindered than the other two, causing a proton l i n e narrowing - 180 -between 77 and 4.2K. This i s f o l l o w e d by the motion of the other two methyls together with the r e o r i e n t a t i o n of the NMe3 group about the P-N bond. An upper l i m i t f o r the a c t i v a t i o n a l energy governing r e o r i e n t a t i o n of the two e q u i v a l e n t methyls of 2.36 ± 0.57 k c a l mole 1 and a lower l i m i t to the a c t i v a t i o n a l energy governing the NMe^ group of 3.51 ± 0.11 k c a l mole 1 have been o b t a i n e d . The r o t a t i o n of the PF,. group about the P-N bond was found to be 19 f a s t enough to cause a narrowed F a b s o r p t i o n l i n e a t 77K. A c t i v a t i o n energy f o r t h i s motion has been measured as 1.13 ± 0.11 k c a l mole 1 . The r e l a t i v e l y low a c t i v a t i o n e nergies measured f o r the v a r i o u s motions suggest r e l a t i v e l y low hindrances to motion i n the c r y s t a l packing; t h i s i s c o n s i s t e n t with the r e l a t i v e l y low second moment c o n t r i b u -2 t i o n (of 2.5 G ) from i n t e r a c t i o n s o u t s i d e the methyl group ob t a i n e d from l i n e s h a p e f i t t i n g . Furthermore, i n t h i s 1 19 s t r u c t u r e , the H and F sp i n s have been found to be s t r o n g l y coupled, r e s u l t i n g i n i n t e r e s t i n g r e l a x a t i o n e f f e c t s . - 181 -R e f e r e n c e s [7.1] C.A. F y f e , M o l e c u l a r Complexes - V o l . 1. (ed. R. F o s t e r ) , E l e k S c i e n c e , London (1973) . [7.2] A. N a t h , R. A g a r w a l and R.M. Lemmon, J . Chem. Ph y s . 61, 1542 (1974). [7.3] J.D. Graham and R.H. Hannon, J . Chem. Phys. 64, 1204 (1976). [7.4] I . S e r l i n , S c i e n c e 127, 261 (1957). [7.5] P. S h a n l e y and R.L. C o l l i n , A c t a C r y s t a l l o g r . 14_, 79 (1961). [7.6] G.W. S m i t h , J . Chem. Phys. 51, 3569 (1969). [7.7] V. P e t r o u l e a s , p e r s o n a l c o m m u n i c a t i o n . - 182 -APPENDIX NMR ABSORPTION LINESHAPE FOR A TRIANGULAR  CONFIGURATION OF NUCLEI The H a m i l t o n i a n f o r t h e i n t e r a c t i o n o f t h r e e i d e n t i c a l n u c l e i i s , 3 « I z i + E ( l i ' I j " 3 I z i I z j ) A . 1=1 K l J J J where, 2t 2 , A. . = (3Cos 0. .-1) ( A l ) 1 3 2 r 3 . ^ 1 3 i s t h e a n g l e between t h e e x t e r n a l m a g n e t i c f i e l d H and t h e v e c t o r c o n n e c t i n g n u c l e i i and j . W r i t i n g t h e H a m i l t o n i a n i n a m a t r i x r e p r e s e n t a t i o n , 2 2 2 ^2 u s i n g a s b a s i s s t a t e s e i g e n f u n c t i o n s o f 1 ,,1^, ^2 ' I and I , where .J = I. + I „ , I = , / + I_ and I = I n + z -1 - 2 - -3 z l z I 9 + I_ , and s o l v i n g t h e e i g e n v a l u e e q u a t i o n s g i v e s t h e e n e r g y l e v e l d i a g r a m shown i n F i g u r e A l . - 183 -- 2 x x + y 0 x - y x + y 0 x - y - 2 x FIGURE A . l Energy l e v e l diagram f o r three s p i n h n u c l e i . Arrows i n d i c a t e allowed t r a n s i t i o n s . (Levels are l a b e l l e d i n frequency u n i t s . ) - 184 -For an e q u i l a t e r a l t r i a n g u l a r c o n f i g u r a t i o n of n u c l e i , the v a l u e s x and y i n F i g u r e A l are given by, y a ( | - |cos2<M (A2) y = y a ( | ^ - S i n % - 3Sin 2 l( J + 1)% (A3) where, a = ^ yR and ip i s the angle between the normal to the plane o f the t r i a n g l e and the magnetic f i e l d . The t r a n s i t i o n p r o b a b i l i t i e s are p r o p o r t i o n a l to 2 |<n|l |n'>| where n and n' are s t a t e s between which magnetic d i p o l e t r a n s i t i o n s are allowed a c c o r d i n g to s e l e c t i o n r u l e s A^/= 0, A l = 0 and AM = ±1. I f a p a r t i c u l a r resonance f i e l d p o s i t i o n h i s d e f i n e d as h = H-H* where H i s the a p p l i e d f i e l d and H* i s the c e n t r e of resonance f o r each nucleus, the f i n e s t r u c t u r e then c o n s i s t s of seven l i n e s a t f i e l d p o s i t i o n s g i v e n by h = 0, h = ±y/y, h = +(-3x+y)/2y and h = ±f-3x-y)/2y. For a p o l y c r y s t a l l i n e m a t e r i a l , t a k i n g s p a t i a l averages over IJJ leads to the f o l l o w i n g r e s u l t s : i ) For the l i n e component at h = 0, t r a n s i t i o n p r o b a b i l i t y - 185 -i s the same as i n the s i n g l e c r y s t a l case, namely, I I I + 3x 8 r 2 (A4) i i ) For the l i n e component h = y/u, the powder l i n e s h a p e F(h) i s given by, F(h) = h m 2 2 12a 1 -4h 2 ( f ± 3 Y i ) ] ( ^ ± Y i ) (A5) where, 2 ( ™ * 1 9 \ 2 > a - 2 2 The + s i g n i s to be taken f o r (-j) 2a<h<a The - s i g n i s to be taken f o r (-^) 2a<h< (19) 2/2a. i i i ) For the l i n e components h = (3x ± y)/2u, F(h) = 24a 9\ a ( •h 1 - 2p 1 - 3p (A6) where, 2 9 3h' + + 4 a - 186 -and P = 4h 2h _ 3Y-In the above, the upper .signs are to be taken f o r , -a<h<a 4 (1(19 j 2•: + 3 ) , and the lower signs are to be taken f o r , -2a<h<-a/4( (19)^ - 3) . iv) For the l i n e components h = -y/u, - ( 3 x ± y ) / 2 u , i t i s on l y necessary t o r e p l a c e h by -h i n Equations (A5) and (A6). T h i s l i n e s h a p e i s f o r an i s o l a t e d t r i a n g u l a r group of n u c l e i . In a c t u a l s t r u c t u r e s , however, neighbouring groups broaden the l i n e s h a p e . T h i s broadening by neighbouring groups may be represented by 3 and i s i n t r o d u c e d i n t o the c a l c u l a t i o n by m u l t i p l y i n g the l i n e s h a p e f u n c t i o n s F(h) by the Gaussian e~~ and t h i s leads t o the l i n e s h a p e shown i n F i g u r e (2.1). For the case of a t r i a n g l e of protons r o t a t i n g about 2 i t s C, symmetry a x i s , averaging of the (3Cos 6 ..-1) term i n Equation (Al) leads to a l i n e s h a p e c o n s i s t i n g of a c e n t r a l l i n e a t h = 0 wit h p r o b a b i l i t y h and the l i n e s h a p e on e i t h e r s i d e d e s c r i b e d by, F (h) = (l/8/3a) (1 ± h / a ) h - 187 -f o r -a<±h<2a 2 2 h / 2 6 M u l t i p l y i n g t h i s by the broadening f u n c t i o n e g i v e s the l i n e s h a p e shown i n F i g u r e (2.1). The l i n e s h a p e s were simulated by a FORTRAN computor program on an IBM 370/168. The program was w r i t t e n by Dr. P. Raghunathan of t h i s department. 

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