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Nuclear magnetic resonance study of molecular motion in some solids Ripmeester, John Adrian 1970

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A NUCLEAR MAGNETIC RESONANCE STUDY OF MOLECULAR MOTION IN SOME SOLIDS  BY  JOHN A. RIFMEESTER B.Sc.  (ions)) University of B.C., 1965  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  IN THE DEPARTMENT OF CHEMISTRY  vWe accept t h i s t h e s i s as conforming t o the required standard  THE UNIVERSITY OF BRITISH C0LUM3IA M February, 1970  In  presenting  this  an a d v a n c e d  degree  the  shall  I  Library  further  for  scholarly  by h i s of  agree  this  written  thesis  in p a r t i a l  fulfilment  of  at  University  of  Columbia,  the  make  tha  it  freely  permission  available  thesis  for  It  financial  is  gain  Depa r t m e n t The U n i v e r s i t y  of  British  Canada  by  the  Columbia  shall  not  requirements  reference copying of  I  agree  and  copying or  be a l l o w e d  for  that  study.  this  thesis  Head o f my D e p a r t m e n t  understood that  permission.  V a n c o u v e r 8,  for  for extensive  p u r p o s e s may be g r a n t e d  representatives.  British  the  or  publication  without  my  ABSTRACT A number of s o l i d substances ware examined by nuclear magnetic resonance methods with a view t o i n v e s t i g a t i n g possible molecular motion. The p o s s i b i l i t y of using the a d i a b a t i c r a p i d passage technique as a method f o r i n v e s t i g a t i n g the molecular motion i n the s o l i d state was s t u d i e d .  Two systems, namely benzene and furan were studied.  I t was found that s p i n - l a t t i c e r e l a x a t i o n times and i n some cases, second moments could be obtained using the a d i a b a t i c r a p i d passage technique; the r e s u l t s obtained were i n good agreement w i t h values obtained using standard techniques.  Also i t was found that the  presence of a c e r t a i n type of molecular motion severely a f f e c t s the shape and amplitude of the a d i a b a t i c r a p i d passage s i g n a l . A number of charge-transfer complexes were i n v e s t i g a t e d using 1  standard broadline *H and  1  19 F nuclear magnetic resonance techniques.  Some strong charge-transfer complexes studied i n t h i s manner i n c l u d e : a number of amine complexes of BF^ and some halogen complexes of trimethylamine.  Second moment and l i n e w i d t h changes with temperature  were i n t e r p r e t e d i n terms of r e o r i e n t a t i o n s of molecular groups w i t h i n the complexes. A l s o studied were a number of weak complexes of benzene.  Linewidth,  second moment, and a l s o s p i n - l a t t i c e r e l a x a t i o n time measurements showed that the benzene r i n g s were r e o r i e n t a t i n g about t h e i r hexad axes -5 -1 at frequencies greater than about 10 120%.  sea  at temperatures above  The a c t i v a t i o n energies f o r t h i s motion depended s t r o n g l y on  the environment of the benzene r i n g i n the complex.  - i i-  A study of some arene-chromium-tricarbonyl compounds i n d i c a t e d that the motional p r o p e r t i e s of t h e arene rings i n the complexes resembled very much the motional properties o f the free r i n g compounds; t h i s suggests that s p e c i f i c bonding e f f e c t s are r e l a t i v e l y inimportant. F i n a l l y , l i n e w i d t h , second moment and s p i n - l a t t i c e r e l a x a t i o n time measurements are reported f o r some soap systems, the a l k a l i metal stearates and oleates.  T r a n s i t i o n temperatures observed could i n  some cases be c o r r e l a t e d w i t h values obtained by d i f f e r e n t methods. Some motional models were suggested i n order t o explain decreases i n l i n e w i d t h s and second moments w i t h i n c r e a s i n g temperature.  I t was  shown that methyl group r o t a t i o n provides a r e l a x a t i o n mechanism i n the low temperature phase f o r a l l the soaps studied.  Activation  energies found f o r t h i s process ranged from 1.8-2.5 Kcal/mole. The e f f e c t of thermal h i s t o r y on phase t r a n s i t i o n s i n the a l k a l i metal stearates was a l s o i n v e s t i g a t e d .  Thermograms were obtained  using samples with d i f f e r e n t thermal h i s t o r i e s using a d i f f e r e n t i a l scanning calorimeter.. I t was found that thev thermal h i s t o r y of a sample may a f f e c t t r a n s i t i o n temperatures, and a l s o the absence of presence of some t r a n s i t i o n s .  - iii -  TABLE OF CONTENTS Page No. Abstract  ^ m  Table of Contents List of Tables List of Figures Acknowledgements  v  i  i  viii ^  Chapter I Nuclear Magnetic Resonance Theory l ) Elementary Resonance Theory  1  2$ The Dipolar Interaction and Resonance Line Shapes  3  3) Second Moments  5'  4) Effect of Molecular Motion on Line Shapes and Second Moments  7  5) Spin-Lattice Relaxation  10  6) Adiabatic Rapid Passage  11  7) Molecular Motion i ) Motional Models  12  i i ) Tunnelling  14  i i i ) Activation Energies  14  iv) NMR Terminology  15  Bibliography Chapter II NMR Experimental Details 1) Continuous Wave (CW) Experiments i) Instrumentation i i ) Spectra 2) Adiabatic Rapid Passage (ARP) Experiments i) Instrumentation and Methods of Measurement Bibliography  16  18 18 20 20 24  - iv -  Table of Contents (Continued) Page No. Chapter I I I Adiabatic Rapid Passage Experiments 1) Introduction  25  2) Experimental  26  3) Results and Discussion  27  Bibliography  32  Chapter IV Complexes of Benzene 1) Introduction  33  2) Experimental 3)) Results  34  i ) Benzene-B^  35  i i ) Benzene-CBr^  38  i i i ) Benzene-N 0^  39  iv) Benzene-S0  41  2  2  Bibliography  46  Chapter V Borontrifluoride-Amine Complexes 1) Introduction  48  2) Experimental  49  3) Results and Discussion i ) Molecular Motion i n BF^.NH^  50  i i ) Molecular Motion i n BF^.NCC^  53  i i i ) Molecular Motion i n BF^.Pyridine  55  iv) Molecular Motion i n BF^. NMe^  58  Bibliography  62  -  V  -  Table of Contents (continued) Page No. Chapter VI Trimethylamine-Halogen Complexes 1) Introduction  63  2) Experimental 3) Results and Discussion  63  i) Molecular Motion i n Trimethylamine  64  i i ) Molecular Motion i n Trimethylamine-Bromine Complex  65  i i i ) Molecular Motion in Trimethylamine-Iodine Complex  65  iv) Calculated Second Moments  66  v) Motional Effects  68  vi) Activation Energies  71  Bibliography  75  Chapter VII Arene-Chromium-Tricarbonyl Compounds 1) Introduction  76  2) Experimental  76  3) Results and Discussion i ) Benzene-Chromium-Tricarbonyl  77  i i ) Mestitylene-Chromium-Tricarbonyl  79  i i i ) Hexamethylbenzene-Chromium-Tricarbonyl  80  Bibliography Chapter VIII Studies on Soaps l ) Introduction  84  85  i) Structure of fatty acids and their salts  85  i i ) Transitions i n soaps and methods of study  88  i i i ) Molecular Motion i n soaps  93  - vi -  Table of Contents (continued) Page No. Chapter VIII (cont) 2) Experimental i ) Preparation of A l k a l i Metal Soaps  93  i i ) NMR experiments  94  i i i ) Thermal experiments  94  3) Results i ) Thermal Studies  95  i i ) T-i measurements on A l k a l i metal stearates  97  i i i ) Results f o r Oleates  100  4) Discussion i ) Low temperature second moments  106  i i ) Molecular Motion i n the low temperature region  107  i i i ) S p i n - l a t t i c e relaxation i n the low temperature phase  112  i v ) The low temperature t r a n s i t i o n  115  v) Linewidths and second moments between t r a n s i t i o n s  116  v i ) T^ values between t r a n s i t i o n s  117  v i i ) The high temperature phase t r a n s i t i o n  118  v i i i ) Correlation between t r a n s i t i o n  observed by  NMR and other methods  119  ix) General Observations  120  x) Summary  121  Bibliography  123  Appendix A  126  Appendix B  133  Appendix D Appendix C  135 134  - vii L i s t o f Tables page 42  IV-1 Summary of T-^ r e s u l t s f o r Benzene Complexes. IV-2 Summary of CW NMR Motional Data f o r Benzene Complexes.  43  V - l Calculated and observed second moments f o r borontrifluoride-ammonia complex.  51  V-2 C a l c u l a t e d and observed second moments f o r b o r o n t r i f l u o r i d e - a c e t o n i t r i l e complex.  55  V-3 C a l c u l a t e d and observed second moments f o r b o r o n t r i f l u o r i d e - p y r i d i n e complex.  57  V-4 Observed and c a l c u l a t e d second moments f o r b o r o n 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 complex.  59  VI-1 Observed second moment values above and below motional t r a n s i t i o n s f o r NMe-j, NMe^.Br , NMe<j.I and NMe-j.ICl and c a l c u l a t e d values f o r d i f f e r e n t molecular motions. 2  2  72  VI-2 Motional types, l i m i t i n g l i n e w i d t h s and a c t i v a t i o n energies f o r NMe-j, NMe^Br , NMe3l 2  V I I I - 1 Melting P o i n t s f o r some c i s C  l g  2  and NMe^ICl.  acids.  74 87  VIII-2 T r a n s i t i o n Scheme f o r Sodium soaps according t o V o i d . ">90 V I I I - 3 Some t r a n s i t i o n s observed f o r the a l k a l i - m e t a l stearates by powder X-ray methods. 92 VTII-4 T r a n s i t i o n s observed f o r the a l k a l i - m e t a l stearates using the DSC method.  96  VIII-5 Summary of r e l a x a t i o n data f o r the a l k a l i - m e t a l stearates and oleates. 103 V I I I - 6 Summary of broadline NMR t r a n s i t i o n temperatures f o r a l k a l i metal stearates and oleates and s t e a r i c and o l e i c a c i d s . 104 V I I I - 7 Summary of broadline NMR second moments f o r the stearates and oleates at various temperatures. 105  - Vlll  -  L i s t of Figures to follow page 1. Amplitude of the ARP signal versus temperature f o r benzene,  27  2. ARP signal shapes observed f o r benzene at various temperatures.  27  3. Some magnetization decay curves observed f o r benzene  28  4(a and b ) . Inverse temperature plots of l o g  9  and l o g TT f o r t  benzene,  28  5. Amplitude of the ARP signal versus temperature f o r furan.  29  6. Log  29  as a function of temperature f o r furan.  7(a and b) Linewidth versus temperature plots f o r benzene-Brj (a) and benzene-^O^ (b). 8j(a and b) Inverse temperature plots of l o g  35 f o r benzene-Br  2  (a)  and benzene-SC^ (b). 9(a and Vb) Inverse temperature plots of l o g and logTL<.f° benzene-CBr^. 10(a and b) Inverse temperature plots of l o g T-^ and l o g * C f or benzene-^O^.  36  r  38  t  l l ( a and b)  39  F lineshapes f o r borontrifluoride-ammonia at 77°K  and 295°K.  50  12. % and ^9F linewidths as a function of temperature f o r borontrifluoride-ammonia.  50  13. % and 9 F second moments as a function of temperature f o r borontrifluoride-ammonia.  50  14. ^"H and ^^p linewidths as a function of temperature f o r borontrifluoride-acetonitrile.  53  15. "*"H and''"'^ second moments as a function of temperature f o r borontrifluoride-acetonitrile.  53  1  16.  linewidths and second moments as a function of temperature f o r borontrifluoride-pyridine.  17. ^"H linewidths and second moments as a function of temperature f o r borontrifluoride-trimethylamine.  55 58  18. hi lineshapes observed f o r borontrifluoride-trimethylamine at various temperatures. 19. Linewidths and second moments as a function of temperature f o r trimethylamine and (inset) representative lineshapes at various temperatures.  58  64  - ix to f o l l o w page 20. Linewidths and second moments as a f u n c t i o n of temperature f o r trimethylamine-Br2 and ( i n s e t ) representative lineshapes at various temperatures. 65 21. Linewidths and second moments as a f u n c t i o n of temperature f o r trimethylamine-Ig and ( i n s e t ) representative lineshapes at various temperatures.  65  22. Linewidths and second moments as a f u n c t i o n of temperature f o r trimethylamine-ICl and ( i n s e t ) representative lineshapes at various temperatures.  65  23. Linewidths and second moments as a f u n c t i o n of temperature f o r benzene-chromium-tricarbonyl.  77  24(a and b) Log and l o g inverse temperature p l o t s f o r benzene-chromium-tricarbonyl.  78  25. Second moment and l i n e w i d t h v a r i a t i o n w i t h temperature f o r hexamethylbenzene-chromium-tricarbonyl.  81  26. C r y s t a l s t r u c t u r e of potassium palmitate.  86  27. DTA and DSC r e s u l t s obtained f o r a number of sodium soaps.  89  28. L i t h i u m Stearate: L i n e w i d t h , second moment and s p i n - l a t t i c e r e l a x a t i o n time as a f u n c t i o n of temperature.  97  29. Sodium Stearate: Linewidth, second moment and s p i n - l a t t i c e r e l a x a t i o n time as a f u n c t i o n of temperature.  98  30. Potassium Stearate: L i n e w i d t h , second moment and s p i n - l a t t i c e r e l a x a t i o n time as a f u n c t i o n of temperature.  98  31. Rubidium Stearate: L i n e w i d t h , second moment and spin-^lattice r e l a x a t i o n time as a f u n c t i o n of temperature.  99  32. Cesium Stearate: L i n e w i d t h , second moment and s p i n - l a t t i c e r e l a x a t i o n time as a f u n c t i o n of temperature.  99  33. L i t h i u m Oleate: L i n e w i d t h , second moment and s p i n - l a t t i c e •? r e l a x a t i o n time as a function of temperature.  100  34. Sodium Oleate: L i n e w i d t h , second moment and s p i n - l a t t i c e r e l a x a t i o n time as a f u n c t i o n of temperature.  101  35. Potassium Oleate: L i n e w i d t h , second moment and s p i n - l a t t i c e r e l a x a t i o n time as a f u n c t i o n o f temperature.  101  36. Rubidium Oleate: L i n e w i d t h , second moment and s p i n - l a t t i c e r e l a x a t i o n time as a f u n c t i o n o f temperature.  101  37. Cesium Oleate: L i n e w i d t h , second moment and s p i n - l a t t i c e r e l a x a t i o n time as a f u n c t i o n o f temperature.  102  - X to follow page 133  38. DSC curves f o r Lithium Stearate. 39. DSC curves f o r Sodium Stearate.  133  40. DSC  curves f o r Potassium Stearate.  133  41. DSC  curves f o r Rubidium Stearate.  133  42. DSC  curves f o r Cesium Stearate  133  43. Inverse temperature plots of l o g stearates.  f o r alkali-metal  44. Inverse temperature plots of l o g  f o r alkali-metal  134  oleates.  134  45. Representative spectra for Lithium and Sodium Oleate.  136  46. Representative spectra f o r Potassium Oleate.  136  47. Representative spectra f o r Rubidium and Cesium Oleate.  136  - xi ACKNOWLEDGEMENTS I would l i k e t o express my sincere g r a t i t u d e t o Professor B.A. Dunell who introduced me t o the f i e l d of broadline NMR and a l s o provided guidance and assistance as my research d i r e c t o r . A l s o I would l i k e t o thank Dr. C.A. Fyfe, who spent two years i n the Chemistry Department as a Post Doctoral Fellow and who during h i s stay  c o l l a b o r a t e d w i t h me on some of the work reported here.  Both  Professor Dunell and Dr. Fyfe provided many h e l p f u l suggestions. Further I would l i k e t o thank Professor C.A. McDowell f o r h i s continuing i n t e r e s t i n the f i e l d of broadline NMR. I would l i k e t o acknowledge the e x c e l l e n t work done by Mr. P. Borda who performed microanalyses  on some of the compounds prepared  and a l s o Messrs. E. F i s h e r and J . S a l l o s w i t h whose able assistance the spectrometers were kept i n operating c o n d i t i o n .  - 1-  CHAPTER I  NUCLEAR MAGNETIC RESONANCE THEORY A d e t a i l e d theory of nuclear magnetic resonance i s beyond the scope o f t h i s thesis and w i l l not be given. books (1,2,3) and reviews (4,5) e x i s t .  Many excellent  This work has been  concerned with the study of spin ^ nuclei i n diamagnetic s o l i d s and only relevant sections of theory are reviewed.  1.  Elementary Resonance Theory When a nucleus possessing a non-zero spin angular momentum  i s placed i n a magnetic f i e l d , the s p a t i a l degeneracy i s removed, y i e l d i n g 21 4» 1 equally spaced energy l e v e l s with a s p l i t t i n g H ,Here I i s the nuclear s p i n quantum number, v i s a 0  s c a l a r quantity r e l a t i n g the nuclear s p i n and magnetic moment vectors,"^ i s Planck's constant divided by iTT and H applied magnetic  Q  i s the  field.  Transitions between these energy l e v e l s may be induced by a l i n e a r l y polarized radio frequency f i e l d H^, with the frequency of the f i e l d V such that  When the nuclear  spins are i n thermal equilibrium (with the l a t t i c e ) , populations of the adjacent Boltzmann f a c t o r  l e v e l s Aw, Hj  the r e l a t i v e  are governed by the  ,  he ^eAcr M 3  The radio frequency f i e l d induced t r a n s i t i o n s tend to disturb the r e l a t i v e populations from t h e i r equilibrium values.  - 2 -  Besides the interactions of the nuclear spins with the magnetic and RF f i e l d s , there are two other basic types of i n t e r actions:  those of the nuclear spins with the l a t t i c e and those  with other nuclear spins.  How these interactions a f f e c t the  properties of the spin system w i l l be mentioned b r i e f l y . The tendency t o return the aforementioned populations from t h e i r disturbed values to t h e i r equilibrium values i s termed s p i n - l a t t i c e relaxation with an attendant time constant u s u a l l y termed T^.  S p i n - l a t t i c e relaxation takes place through the  i n t e r a c t i o n of the spins with fluctuating magnetic f i e l d s due to electron spins, r e l a t i v e motion of nuclear spins and a number of other mechanisms.  Saturation i s said t o occur when  the RF f i e l d supplies more energy then can be dissipated by the s p i n - l a t t i c e relaxation process. The i n t e r a c t i o n of the spins with each other affects the system i n two ways.  „  Each nucleus sees a magnetic f i e l d due to  i t s neighbours; t h i s f i e l d i s usually termed the l o c a l f i e l d , Hi,. line.  One e f f e c t of the l o c a l f i e l d i s t o broaden the resonance A dephasing of the spins also r e s u l t s , causing the l i f e t i m e  of a spin i n a c e r t a i n energy l e v e l t o be l i m i t e d .  A measure of  t h i s phase memory time of a spin state i s usually termed Tg, the spin-spin r e l a x a t i o n time. Information of i n t e r e s t t o the chemist and physicist may be obtained from the measurement of spin-spin, as well as s p i n - l a t t i c e relaxation times and the s h i f t i n g , as w e l l as broadening or s p l i t t i n g of the resonance l i n e .  In this work, the l i n e s p l i t t i n g s and  broadening observed, and also the s p i n - l a t t i c e relaxation time  measurements, could a l l be explained i n terms of d i p o l a r i n t e r actions between n u c l e i .  A more d e t a i l e d account of the dipolar  i n t e r a c t i o n w i l l now be given. 2.  The Dipolar Interaction and Resonance Line Shapes A system of i d e n t i c a l s p i n ^ nuclei i n a magnetic f i e l d may  be described by the Hamiltonian  where / i j  the Zeeman term, describes the i n t e r a c t i o n between  the nuclear spins and the magnetic f i e l d , and Via i s the dipolar term due t o i n t e r a c t i o n amongst the spins.  A^.A+B , A - H I j B . - j . (Iel1  T>  - 4 (tl)  I =. I* ±c' Xy Here, I i s the spin angular momentum operator and the internuclear vector magnetic f i e l d ")"^D with  may  0ij*and  (Pcj  fix  orientation with respect to the  Hg.  be s i m p l i f i e d considerably by neglecting the terms  C j s i i j Z since t h e i r contribution to the resonance l i n e shape  i s n e g l i g i b l e . Also i f the nuclear spins are d i f f e r e n t ( i e . ^ ^ j the B term may  be dropped as well.  dipolar i n t e r a c t i o n may  The simplest system where the  be analysed i s the two-spin system, where  the i n t e r a c t i o n between two c l o s e l y spaced n u c l e i i s much greater than any other i n t e r a c t i o n . four unperturbed singlet l e v e l s .  The dipolar i n t e r a c t i o n s h i f t s the Zeeman l e v e l s to give t r i p l e t  and  This causes the resonance l i n e to be s p l i t i n t o  a doublet with separation  AH~ ^ Y^^"  3  ^  005*6— l)  Interactions other than the i n t r a p a i r interactions tend to broaden each component l i n e .  The separation of the l i n e s i s  seen to be angle dependent, and i f a single c r y s t a l containing such nuclear pairs i s rotated i n a magnetic f i e l d , the r e s u l t i n g rotation patterns may  y i e l d information about the length as well  as orientation of the internuclear vector i n the c r y s t a l . I f , however, a powdered sample i s examined, where the c r y s t a l l i t e s , and thus also the internuclear vectors, are randomly oriented, the angular term must be averaged over a l l c r y s t a l l i t e orientations and a doublet with a separation of  Wa.  3 Y\\  Z results.  Q  f"^  -  5  -  Two-spin systems that have been studied extensively by  NMR  include many c r y s t a l hydrates, the work on which has recently been reviewed (6). Three-spin systems have also been studied, u s u a l l y i n compounds i n powdered form, and t h e i r spectra analysed.  Although  the calculated spectrum for an i s o l a t e d three-spin system i s complex, broadening by neighbouring spins s i m p l i f i e s the observed spectrum, and generally takes the form of a t r i p l e t .  Again,  information regarding the internuclear distances within the three-spin system may  be extracted from the spectra.  Systems  studied include compounds containing the CH^ group (7), and U0 3  + (8) and HF~  the  (9) ions.  Some four-spin systems have been treated, as i n the  NH"*"  k i o n (10,11) but the calculations become quite lengthy.  Also  the powder spectrum does not usually have much structure and the l i n e shape i s then of limited value. One  f i v e - s p i n system y i e l d i n g a highly structured spectrum  has been examined i n d e t a i l , that of the H , ^ and potassium s a l t s  -  ion i n the sodium  (12).  A c t u a l l y , f o r complex s p i n systems, where no f i n e structure i s ob ervable, i t i s more convenient to use second moments f o r S  obtaining s t r u c t u r a l 3.  information.  Second Moments The development of the method of moments for obtaining  s t r u c t u r a l information i s due to Van Vleck (13). second moments may  Experimental  be calculated from the resonance l i n e from  - 6 -  the expression:  where f (H) i s the l i n e shape function and (H-H ) measures 0  distance from the center of resonance.  The expression obtained  by Van Vleck f o r the t h e o r e t i c a l second moment i s :  5«  ^I(I-H).  where the indices j and k r e f e r to the n u c l e i at resonance and the index f refers to other non-zero spin n u c l e i .  I t can be seen  that when the spins are d i f f e r e n t , the numerical factor i n front 9  of the sum signs i s smaller by a factor of  This i s due to the  absence of a broadening process which exists only f o r l i k e spins, the spin exchange or f l i p - f l o p process. The above second moment expression i s i n the correct form to be used f o r the analysis of single c r y s t a l spectra. time there i s some uncertainty whether the formula may  At t h i s be  applied i n t h i s form to the analysis of highly structured resonance l i n e s .  Recently i t was proposed (14) that large dipolar  s p l i t t i n g s would render normally equivalent nuclei s l i g h t l y  non-  equivalent, the extent of the equivalence depending on the overlap of the component l i n e s .  However, i t was  found that t h i s work •  had been i n error (15)•  There are several cases (11,16) where  some doubt s t i l l exists as t o the correctness of use of the Van Vleck second moment formula.  Pederson (15) has  suggested  that these cases should be reexamined. Recently i t also has been shown (17,18) that i f a spin greater than one h a l f nucleus i s present, the Van Vleck formula  - 7 must be modified i n some cases.  I f the quadrupolar spin contributes  significantly to the second moment and the quadrupolar energy i s of the same order or larger than the Zeeman energy i n the applied f i e l d , an extra term must be retained i n the dipolar Hamiltonian thus modifying the second moment also.  Some instances where  this effect has been found to be important are the studies of HMn(CO) , HCo(CO) (18) and tf B!(OCD ) (19). U  5  4  3  2  Again, i f the second moment i s to be calculated for a powdered sample, the angular term must be averaged over the powder, since the internuclear vectors w i l l be randomly oriented. After averaging, the second moment expression becomes:  S-fcTM  V^£n^|*gIfMrf«l?  4  (6)  4. Effect of Molecular Motion on Lineshapes and Second Moments So far i t has been assumed that the spins were rigidly fixed i n the crystal lattice.  When sufficient molecular motion  is present, be i t i n the form of vibrations or rotations of parts or a l l of a molecule, the nuclei i n this molecule see the time averaged magnetic moments of their neighbours, thus generally decreasing the resonance line width. Most types of molecular motion can be assigned a characteristic correlation  timeTTc or alternatively  a correlation frequency  /^c —  Zfc)"^  Molecular motion becomes effective i n narrowing resonance lines in solids when the frequency of the motion becomes of the same order of magnitude as the linewidth of the resonance line i n frequency units i.e.  JV <^ Side;  fluorine nuclei i n most solids.  \0*L\O* Hertz for protons or  On a molecular scale, thus,  the broadline NMR method i s sensitive to molecular motion of  - 8 a f a i r l y low frequency (compare, f o r example, 1 0 ^ i l infrared, IO ® 1  H"£X-rays.)  A two spin system rotating about an axis  perpendicular to the internuclear axis may be taken as an example of the e f f e c t of molecular motion i n a simple s p i n system.  The spectrum s t i l l consists of a doublet, but the  separation i s only h a l f of what i t was  f o r the r i g i d case.  Attempts have been made to extract information about the magnitude of the hindering potential from molecular motion resonance l i n e narrowing.  A v a r i e t y of expressions has • been  developed, some of the more common being  V vrT  (20)  (7)  =  where T i s the temperature of linewidth t r a n s i t i o n and  $"H{Wtr( JH\B ) /2 1  (21)  (C -B )))-' ( 8 ) l  1  together with  Here o(  i s a constant approximately equal to unity, S"H i s the  linewidth i n the narrowing region, B i s the f u l l narrowed l i n e width, and C i s the unnarrowed linewidth. Use of the other equations has been i l l u s t r a t e d i n ref. (22).  Activation  energies and b a r r i e r heights obtained i n this manner are usually taken to be correct to a f a c t o r of two or so only, as many assumptions enter into the derivation of the equations.  However, the  values obtained are i n t e r e s t i n g f o r comparison purposes. In some early work (23), i t was  found that decreases i n  observed second moments as a function of temperature could be interpreted i n terms of molecular motion.  For instance, the  e f f e c t of simple rotation of a group of n u c l e i around an axis  - 9 -  which makes an angle y  w i t h the i n t e r n u c l e a r a x i s i s simply t o I )^.  m u l t i p l y the powder second moment formula by £ ( 3 CoS^-  Andrew ( 2 4 ) has c a l c u l a t e d the e f f e c t o f t o r s i o n a l o s c i l l a t i o n s on the angular parts o f second moments. f a c t o r of p  p  m  These are reduced by a  where  |- f | (,  Si^+O-T^iirff}  vol  where ^ i s the angle between the i n t e r n u c l e a r vector and the a x i s o f o s c i l l a t i o n and ec i s the amplitude o f the o s c i l l a t i o n . The Jo's are B e s s e l f u n c t i o n s .  Second moment  reductions have  been c a l c u l a t e d f o r more complex motions by Andrew and Eades (25) Dmitreva and Moskalev (26,27), Kroon (28) and others. On examining the expression from which second moment formulas are  l  i t can be seen that a c t u a l l y there should be no motional dependence o f the second moment(29).  P r e v i o u s l y i t was stated  that molecular motion narrows the resonance l i n e .  However,  t h i s i s not the only e f f e c t o f molecular motion on the NMR spectra.  I t was shown by Andrew and Newing (30) that sidebands  are produced as w e l l , a t frequencies t \\^ (n i s an i n t e g e r ) , the r  more c e n t r a l sidebands having greater i n t e n s i t y .  As the motional  frequency increases, the sidebands have the e f f e c t o f t r a n s f e r i n g i n t e n s i t y from the center of the resonance l i n e i n t o the wing3, where i t i s f r e q u e n t l y obscured by random noise.  When the  motional frequency i s much greater than the r i g i d l a t t i c e l i n e width, the experimentally observable second moment has the reduced value.  - 10 Thus second moments may be calculated from NMR spectra and interpreted i n terms of static or dynamic internuclear interactions provided these moments are not taken near a line narrowing region. 5.  Spin-Lattice Relaxation In diamagnetic solids, there are two main nuclear relaxation  mechanisms. The f i r s t of these i s relaxation by paramagnetic impurities, where the nuclear spins relax by spin-diffusion to the impurity sites.  Thi3 process i s of interest i n ionic solids  as well as i n organic substances when more efficient processes are absent.  It has been the subject of a number of recent  investigations (31,32).  The second process i s the one of interest  here and i t involves relaxation of the nuclear spins through the interaction of the spins with fluctuating magnetic fields produced by molecular motions of neighbouring spins. The relaxation time of a spin system which i s described by a spin temperature i s given by  where Wmn  i s the transition probability between two energy levels  separated by an energy (Em-En). Expressions for the transition probability may be found i n terms of ensemble averages over dipolar Hamiltonian matrix elements.  The T^ expression so  found is(fior like spins)  where thevJ(w( are spectral densities inverses of correlation functions functions of the dipolar Hamiltonian  ' and are Fourier i n turn are  where the I  are given i n eqn. 3.  I f cross c o r r e l a t i o n effects  are neglected, the c o r r e l a t i o n functions are u s u a l l y taken to be  . The  r(p)  (ft. F<*fe e - * 4  must be evaluated and depend on the system of spins  as w e l l as the model chosen f o r the motion, although the expressions f o r T j w i l l a l l have the general form  I f a single c o r r e l a t i o n time,"tic »  c  a  n  he chosen as repre-  sentative of the motion i t i s u s u a l l y assumed that the temperature behaviour i s described by  where E  a  again represents an a c t i v a t i o n energy associated with  the b a r r i e r to rotation.  With t h i s form f o r the c o r r e l a t i o n  time-temperature behaviour a V shaped curve i s predicted when  Jlto  T^ i s p l o t t e d versus inverse temperature, with a minimum  occurring when  6Jotcs0.6^  A complete treatment  and with l i m i t i n g slopes Jt  E c t / R  of dipolar s p i n - l a t t i c e r e l a x a t i o n  including cross c o r r e l a t i o n e f f e c t s , has been given by Hubbard and others (33). 6.  Adiabatic Rapid Passage (ARP) A l l of the relevant theory may be found i n Abragam's  text ( l ) , but some of the equations used as w e l l as some of the passage conditions w i l l be introduced here. The conditions f o r observing an adiabatic rapid passage 3ignal i n a s o l i d are given by (34)  and have been v e r i f i e d experimentally (35).  The f i r s t condition  - 12 insures t h a t r e l a x a t i o n e f f e c t s can be neglected during the time of passage, and the second i s the a d i a b a t i c c o n d i t i o n ; i t insures that the magnetization vector w i l l f o l l o w the e f f e c t i v e magnetic field.  I t i s usual t o work i n the w e l l known r o t a t i n g reference  frame (36) f o r analyzing r a p i d passage experiments.  The s i g n a l  observed i s p r o p o r t i o n a l t o the x component o f the magnetization i n the r o t a t i n g reference frame Midland  M where H  e  <  R  (18)  M o H e / ( H e + H c )  =  i s the e f f e c t i v e f i e l d i n the r o t a t i n g frame given by  He=  C ( H . - H n "  1  (19)  ARP s i g n a l s may be characterized by the width a t h a l f height  SH=C>i(H,\Hi]'  /i  (zo\  The second moment S may be found simply from  5«3Hu  (2.1)  E f f e c t s of incomplete i n v e r s i o n of the magnetization as w e l l as i r r e v e r s i b i l i t y e f f e c t s have been discussed elsewhere  (35,37)»  I t should be pointed out that f o r systems containing s e v e r a l types of spins the simple r e l a t i o n s h i p i n eqn. (21) does not hold. 7.  Molecular Motion  i)  Motional Models I t i s of i n t e r e s t t o go i n t o some more d e t a i l regarding  molecular motion i n the s o l i d s t a t e .  Two types o f motional  models e x i s t f o r molecules w i t h r e o r i e n t a t i o n a l freedom. One i s due t o Pauling and Fowler (38): the molecules a r e assumed to be i n a s t a t e o f continuous r o t a t i o n . F r e n k e l (39):  The other i s due t o  the molecules may have only a f i n i t e number  - 13 of o r i e n t a t i o n s i n the c r y s t a l .  Most of the time the molecule  spends near the bottom of the p o t e n t i a l minimum. For molecules w i t h no, or p o s s i b l y one, heavy atom such as NH^, CH^, e t c . , the r o t a t i o n may be almost f r e e , or  alternatively tunnelling  may be an e f f e c t i v e motional process. However, f o r most other molecular systems, the step-wise r e o r i e n t a t i o n model i s more satisfactory.  In many instances methods such as d i e l e c t r i c  r e l a x a t i o n and NMR second moment and s p i n - l a t t i c e r e l a x a t i o n measurements reveal dynamic s t r u c t u r e s , while X-ray measurements show an e s s e n t i a l l y s t a t i c s t r u c t u r e . the F r e n k e l model.  This i s consistent w i t h  The molecules perform l i b r a t i o n a l movements  i n s i d e the p o t e n t i a l w e l l s and cross the b a r r i e r s at such a rate as t o narrow the NMR resonance l i n e .  Recently a p u b l i c a t i o n (40)  appeared which discussed some of the i m p l i c a t i o n s of the F r e n k e l model w i t h a view t o c o r r e l a t i n g thermal and NMR data.  I t was  shown that the c o n t r i b u t i o n to the^energy and entropy of the molecules while they are " i n a s t a t e of jump" i s n e g l i g i b l e . This implies that when the molecules undergo such r e o r i e n t a t i o n s , and when the molecule has a G  n  symmetry a x i s and the hindering  p o t e n t i a l i s n f o l d , thermodynamics presence of the motion.  i s very i n s e n s i t i v e to the  However, i f the molecule i n i t s r o t a t o r  phase has a greater number of allowed o r i e n t a t i o n s than the molecule has n f o l d symmetry, a thermal t r a n s i t i o n should be required to l i b e r a t e t h i s motion, e n t i r e l y because of configurat i o n a l entropy e f f e c t s .  - 14 ii)  Tunnelling No d i r e c t evidence of quantum mechanical t u n n e l l i n g was  observed i n t h i s work, but as a l o t of the work included  studies  i n v o l v i n g small molecular groups such as ^CH^ and -NH^ i t was thought that some mention of t h i s should be made. There has been a l o t of i n t e r e s t i n the p o s s i b i l i t y o f small molecular groups t u n n e l l i n g through p e r i o d i c r o t a t i o n a l b a r r i e r s (41) but not u n t i l r e c e n t l y have some of the d i f f i c u l t i e s been resolved.  Studies on polymethyl benzenes (42-45) have i n d i c a t e d  that second moments kept t h e i r reduced values down t o very low temperatures ( a few degrees K ) ; This has been i n t e r p r e t e d as a tunnelling effect.  A t h e o r e t i c a l a n a l y s i s of the problem (46)  has shown that t u n n e l l i n g e f f e c t s may be present f o r r o t a t i o n a l b a r r i e r s lower than 5 keal/mole. In some studies o f r e l a x a t i o n times i n pdlymethylbenzenes, two or more r e l a x a t i o n  time minima were observed, whereas the d i p o l a r  mechanism (as described by eqn. (15)) i s u s u a l l y able t o explain only one of these.  The extra minima have been i n t e r p r e t e d  (47)  as t u n n e l l i n g a s s i s t e d phenomena. i i i ) A c t i v a t i o n Energies I n the normal course of events a c t i v a t i o n energies are obtained from Arrhenius p l o t s of c o r r e l a t i o n frequencies or c o r r e l a t i o n times.  Recently (48) a t t e n t i o n has been drawn  t o the f a c t that s t r i c t l y one measures an a c t i v a t i o n  enthalpy,  and that a true i n d i c a t i o n of b a r r i e r heights i s not obtainable i n t h i s manner unless the b a r r i e r height i s temperature independent.  -  One  15  -  can expect that to a certain degree barriers are dependent  on the density or s p e c i f i c volume of a s o l i d , which usually  are  temperature dependent, so that caution must be used i n interpreting a c t i v a t i o n energies, unless the experiment i s c a r r i e d out under constant volume  iv)  NMR  conditions.  Terminology  In a n t i c i p a t i o n of possible d i f f i c u l t i e s a r i s i n g from the terminology used i n l a t e r chapters, some of the more commonly used expressions should be explained at t h i s point. Controversy may  a r i s e from the use of the word " t r a n s i t i o n " ,  meaning linewidth and second moment narrowing regions.  This w i l l  just mean that the frequency of the motion has reached a value of the order of the unnarrowed linewidth  i n frequency u n i t s .  Below  the t r a n s i t i o n the p a r t i c u l a r motion can be said to have stopped, although t h i s i s s t r i c t l y incorrect.  Any  references to  the  "onset" of molecular motion w i l l also be stated with t h i s i n mind. Such NMR  t r a n s i t i o n s do not necessarily coincide with thermal or  thermodynamic t r a n s i t i o n .  - 16 BIBLIOGRAPHY CHAPTER I 1  A. Abragam, The Principles of Nuclear Magnetism, Clarendon Press, Oxford, 1962  2 C P . Slichter, Principles of Magnetic Resonance. Harper and Row, New York, 1963 A. Carrington and A.D. McLachlan, Introduction to Magnetic Resonance, Harper and Row, New York, 1967 3 E.R. Andrew, Nuclear Magnetic Resonance, Cambridge University Press, 1955 4  E.R. Andrew, Ber. der Bunsengesellschaft 67, 295 (1963)  5 E.R. Andrew, and P.S. Allen J . de Chim. Phys. 65 (1966) 6  L.W. Reeves, Progress i n NMR Spectroscopy Vol.4, ed. J.W. Ensley, J Feeney and L.H. Sutcliffe, Pergamon Press (1969)  7  J.G. Powles and H.S. Gutowsky J. Chem Phys. 21, 1695 (1953) i b i d . 21, 1704 (1953)  8 R.E. Richards and J.A.S. Smith Trans. Farad. Soc. 47, 1261 (1951) 9  J.S. Waugh, F.B. Humphrey and D.M. Yost J . Phys. Chem. 57, 486 (1953)  10 R. Bersohn and H.S. Gutowsky J. Chem. Phys. 22, 651 (1954) 11 J . Itoh, R. Kusaka and Y. Saito J . Phys. Soc. Japan 17, 463 (1962) 12 R. Blinc, Z. Trontelj and B Volavsek J. Chem. Phys. 44, 1028 (1966) 13  J.H. van Vleck Phys. Rev. 74, 1168 (1948)  14  B. Pederson J. Chem. Phys. J 2 , 720 (1963)  15  B. Pederson Chem. Phys. Lett. 1, 373 (1967)  16 R. Chidambaram Acta. Crysta. 15, 619 (1962) 17 G.M. Sheldrick Mol. Phys. 13_, 399 (1967) 18  T.C. Farrar and T. Tsang J . Res. Nat. Bur. Standards ]3K, 195 (1969)  19  D.L. Vander Hart, H.S. Gutowsky and T.C. Farrar J. Am Chem. Soc. 89, 5056 (1967)  20  J.S. Waugh and E.I. Fedin Sov. Phys. Sol. State 4_, 1633 (1963)  21  G.W. Smith J . Chem. Phys. 42, 4229 (1965)  22 H. Levy II J . Inorg. Nucl. Chem. 2g, 1859 (1967)  - 17 23 H.S. Gutowsky and G.E Pake J. Chem. Phys. 18, 162 (1950) 24 E.R. Andrew J. Chem. Phys 18, 607 (1950) 25 E.R. Andrew and R.G. Eades Proc. Roy. Soc. A216, 398 (1953) 26 L.V. Dmitrieva and V.V. Moskalev Sov. Phys. Sol. State 5, 1623 (1964) 27  V.V. Moskalev Sov. Phys. Sol. State 3_, 2218 (1962)  28  D.J. Kroon Philips Res. Reports 15, 501 (i960)  29 P.W. Anderson J. Phys. Soc. Japan 9, 316 (1954) 30 E.R. Andrew and R.A. Newing Proc. Phys. Soc. 72, 959 (1959) 31  J . Haupt and W. Mtiller-Warmuth Z. Naturforschg 234-. 643 (1967)  32  I.J. Lowe and D.Tse Phys. Rev. 166, 279 (1968) R. van Steenwinkel and P. Zegers Z. Naturforschg 23$, 818 (1968)  33 L.K. Runnels Phys. Rev. 134, A28 (1964) R.L. Hilt and P.S. Hubbard Phys. Rev. 134, A392 (1964) 34  J.G. Powles.Proc. Phys. Soc. 71, 497 (1958)  35  W.R. Janzen, T.J.R. Cyr and B.A. Dunell J. Chem. Phys. 48, 1246 (1968)  36  I.I. Rabi, N.F. Ramsey and J . Schwinger Rev. Mod. Phys. 26, 167 (1954)  37 M. Goldman, M. Chapellier and V.H. Chau Phys. Rev. 168, 301 (1968) 38 L. Pauling Phys. Rev. ^6, 430 (1930) R.H. Fowler Proc. Roy. Soc. 149, 1 (1935) 39  J . Frenkel Act. Phys. Chim. 555R, 3 no 123 (1935)  40  I. Darmon and C. Brot Mol. Cryst. 2, 301 (1967)  41 E.0. Stejskal and H.S. Gutowsky J. Chem. Phys. 28, 388 (1958) E.0. Stejskal, D.E. Woessner, T.C. Farrar and H.S. Gutowsky J. Chem. Phys. 31, 55 (1959) 42  P.S. Allen and A. Cowking J. Chem. Phys. ^7, 4286 (1967)  43  P.S. Allen and A. Cowking J . Chem. Phys. 49, 789 (1968)  44  J . Haupt and W. Muller-Warmuth Z. Naturforschg.23&, 208 (1968)  45  G.P. Jones, R.G. Eades, K.W. Terry and J.P. Llewellyn J. Phys. C 1, 415 (1968)  46  P.S. Allen J. Chem. Phys. 4jJ, 3031 (1968)  47  P.S. Allen and S. Clough Phys. Rev. Lett. 22, 1351 (1969)  48  C. Brot Chem. Phys. Lett. J3, 319 (1969)  - 18 -  CHAPTER II  NMR EXPERIMENTAL DETAILS  This chapter w i l l deal with the instruments and methods used t o obtain the data and also describe some of the methods of data treatment.  1.  Continuous Wave (CW) Experiments  i ) , Instrumentation The NMR spectometers used were conventional crossed c o i l instruments, composed mainly of Varian u n i t s .  Basically,  there were two instruments, a Varian DP60 spectrometer with a 12" magnet, and a Varian V4200B spectrometer equipped with a 6  M  magnet.  Three transmitter-receiver units were a v a i l a b l e ,  with operating frequencies of 56.4, 30, and 2-16 MHz. were recorded with the l o c k - i n detection method,  and  Spectra the  derivative of the true absorption curve.-was recorded. F i e l d sweep methods were used and c a l i b r a t i o n was achieved by audio modulating a narrow signal such as given by a doped water s o l u t i o n .  Modulation amplitudes were also measured from  the peak to peak width of a n a t u r a l l y sharp s i g n a l . i i ) Spectra Spectra were recorded oh s t r i p - c h a r t recorders, and care was taken to optimize the RF f i e l d amplitude and the modulation amplitude t o avoid d i s t o r t i o n due to saturation or excessive modulation amplitude.  Temperature control was achieved by  immersing the samples d i r e c t l y i n l i q u i d nitrogen or oxygen  to a t t a i n temperatures of 77°K and 90°K r e s p e c t i v e l y . Temperatures below 77 K were obtained by pumping on l i q u i d n i t r o g e n . F o r G  temperatures between 90°K and room temperature a conventional gas flow cryostat was used, w i t h l i q u i d nitrogen as coolant.  Tempera-  t u r e v a r i a t i o n was achieved by e i t h e r varying the gas flow r a t e , or varying the current i n a small heater c o i l present i n the flow system.  F o r temperatures greater than room temperature  heated a i r was passed over the samples.  Two  copper-constantan  thermocouples placed up and downstream from the sample  monitored  the temperature, the thermocouple voltages being displayed continuously on a s t r i p - c h a r t recorder.  Temperature measurements  are estimated t o be i n e r r o r by not more than 2C°. Linewidths were taken t o be the distances between the d e r i v a t i v e curve minima and maxima.  Second moments were  computed d i r e c t l y from the absorption d e r i v a t i v e using the formula:  For compution purposes, the i n t e g r a l s a r e replaced by sums g i v i n g  where X measures distance from the center of resonance,Y i s the value o f the d e r i v a t i v e a t t h a t point and A i s a s c a l e f a c t o r . Second moments were a l s o corrected f o r modulation e f f e c t s ( l )  Sbwe» St*?. - —• H m where rL^ i s the peak modulation amplitude.  (3) Normal procedure was  to record a t l e a s t two spectra at each temperature a f t e r a period of e q u i l i b r N a t i o n .  Second moments were then c a l c u l a t e d from both  halves of each d e r i v a t i v e , since the spectra were symmetrical,  - 20 y i e l d i n g a t l e a s t f o u r second moment values which were subsequently averaged.  A  F o r t r a n IV program was w r i t t e n t o c a l c u l a t e second  moments using equations (2) and ( 3 ) . I t i s extremely d i f f i c u l t t o generalize as t o the accuracy of the second moments, as t h i s depended on the q u a l i t y of each i n d i v i d u a l -spectrum.  Where s i g n a l t o noise r a t i o s were good i t  i s thought t h a t errors are probably l e s s than 5%.  I f , however,  s a t u r a t i o n problems were encountered, errors could be as large as 10-157°.  Normally maximum d e v i a t i o n s from the mean f o r a number  of second moments obtained a t the same temperature were l e s s than 10%. 2.  A d i a b a t i c Rapid Passage (ARP) Experiments  i)  Instrumentation and Methods o f Measurement ARP measurements were c a r r i e d out using the Varian V4211  2-16 MHz R.F. u n i t and the 6" electromagnet mentioned p r e v i o u s l y F i e l d sweep rates of 200-300 gauss/see. were a t t a i n e d by applying the square wave or square step output of a  Servomex LF51  MKII  waveform generator d i r e c t l y t o the sweep input of the e l e c t r o magnet power supply. L i n e a r i t y of the sweep r a t e was checked by sweeping through a water s i g n a l and a number of i t s sidebands produced by audiomodulation. To avoid d i s t o r t i o n o f the ARP s i g n a l by AC a m p l i f i e r s , the s i g n a l was taken from the diode detector stage of the r e c e i v e r , and applied d i r e c t l y t o the d i f f e r e n t i a l a m p l i f i e r of a Hewlett Packard 130C o s c i l l o s c o p e .  A low pass f i l t e r was  i n s e r t e d between the a m p l i f i e r input and the r e c e i v e r i n order to remove some o f the high frequency n o i s e .  - 21 The frequency normally used was 8MHz, with a RF f i e l d amplitude of 0.6 gauss. calibrate  Anderson's method (2) was used t o  f i e l d amplitudes.  I t was found that i f high  f i e l d values were used, say ^ 1 gauss, s i g n i f i c a n t sample heating r e s u l t e d . For the l o c a l f i e l d measurements, a s i n g l e r a p i d passage was used, and the r e s u l t i n g o s c i l l o s c o p e d i s p l a y was then photographed w i t h a Hewlett Packard 197A o s c i l l o s c o p e camera. The s i g n a l width a t h a l f height i s given by  for a l i q u i d  providing a c a l i b r a t i o n i n gauss/cm. L o c a l f i e l d s may be r e l a t e d t o the second moment by the simple r e l a t i o n  For T^ measurements, two methods were used.  The f i r s t  was a two-pass method and has been described elsewhere (3).  On  the f i r s t passage through resonance, the magnetization i s i n v e r t e d , while the second passage samples later.  the magnetization a t a time t  A number of such sequences are repeated, varying t ,  and a l s o w a i t i n g a time  long compared t o T^ between sequences.  I f a s i n g l e r e l a x a t i o n time e x i s t s , the magnetization M^. a t time t can be r e l a t e d ! t o - t h e e q u i l i b r i u m magnetization M b y Q  Mt-  Mo  (i.i  When T^ values o f s e v e r a l tens of seconds are found, the w a i t i n g time becomes very long i n the above method, and an a l t e r n a t i v e  - 22 technique was used.  The ARP signal amplitude was reduced to  zero by a number of successive passages.  The growth of the  signal back to i t s equilibrium value could then be monitored by an additional passage a time t later. For the two-pass or IT- "H^JL experiment, a single square wave was taken directly from the waveform generator and applied to the sweep input of the magnet power supply. When t, the time between passages was greater than about one second, t was essentially equal to the square wave half period. However, when t was less than one second, i t was found that t was significantly shorter than the square wave half period piftgsumably because of the effects of magnet inductance.  Values for t were then obtained by timing  the passage between signals using the calibrated sweep times on the oscilloscope.  Normal procedure was to obtain  a number of S^ values (heights of the ARP signal during the sampling passage) and to obtain the T^ value from the 3lope of a log (S^.-S~) versus t plot.  S*and S~ refer to  ARP signal amplitudes obtained after the magnetization attained equilibrium at high and low fields respectively. A third possible method, the T^ null method is less satisfactory, although somewhat more facile.  The experi-  ment i s essentially a two-pass experiment and t , the time between passages is adjusted so that the second signal has zero amplitude.  T^ should then just be equal to t/ln2.  However, for this value to be the true T^ f u l l inversion of the magnetization is required (see ref (3)).  Sometimes  - 23 n u l l measurements are used as approximate  values  when the magnetization does not follow a simple exponent i d l decay (4).  - 24 BIBLIOGRAPHY CHAPTER I I  1  E.R. Andrew Phys. Rev. 91, 425 (1953)  2  W.A. Anderson, N.M.R. and E.P.R. Spectroscopy, Varian 3 Workshop, Pergamon Press, New York, I960, p. 164  3  W.R. Janzen, T.J.R. Cyr and B.A. Dunell J . Chem. Phys. 48, 1246 (1968)  4  M.F. Baud and P.S. Hubbard Phys. Rev. Y[0, 384 (1968)  d  Annual  - 25  -  CHAPTER III  ADIABATIC RAPID PASSAGE EXPERIMENTS  1.  Introduction Some recent work ( l ) i n t h i s laboratory has been concerned  with studying the p o s s i b i l i t y of using the ARP method as a technique f o r investigating s o l i d s .  The emphasis of the work was placed tm  obtaining the right conditions f o r observing a true rapid passage s i g n a l i n a s o l i d sample.  Also some techniques f o r  measuring T-p the s p i n - l a t t i c e relaxation time were discussed. I t was also found that the ARP two-pass or  experiment  gave T^ values i n good agreement with values obtained by standard;; methods. Additional experiments  have now been performed on some  s o l i d systems i n which molecular motion takes place, with view to determining the f e a s i b i l i t y of using the ARP method as an a l t e r n a t i v e technique f o r f i n d i n g second moments as well as s p i n - l a t t i c e r e l a x a t i o n times as function of temperature.  In  p r i n c i p l e , t h i s method should provide a very f a c i l e method f o r obtaining second moments, since i t i s independent of saturation effects and no corrections have to be made f o r modulation effects. The compounds chosen f o r study were benzene and furan and these were taken for a p a r t i c u l a r reason.  Some anomalous effects were  noticed during the i n v e s t i g a t i o n of a number of compounds by the ARP method.  In p a r t i c u l a r , these effects were observed near CW  linewidth and second moment t r a n s i t i o n s i n compounds where  - 26 molecular motion occurred.  I t was suspected that these e f f e c t s  involved the presence of molecular motion, p o s s i b l y with the generation of motional sidebands causing the problem.  The  d e c i s i o n was made t o i n v e s t i g a t e t h i s phenomenon f u r t h e r . Benzene was chosen as one of the compounds, because i t has been i n v e s t i g a t e d p r e v i o u s l y , by both CW (2) and pulse methods (3). The conclusions drawn from these studies i n d i c a t e that the benzene 5  rings s t a r t r o t a t i n g a t frequencies greater thdn about 1 0 cps around 100°K.  The motion i s probably a cooperative phenomenon,  w i t h the rings r o t a t i n g around t h e i r hexad axes between equivalent positions.  The a c t i v a t i o n energy obtained from the T-L measurements  was 3 . 9 5 keal/mole.  The l i n e w i d t h change was smooth and continuous  and could a l s o be f i t t e d i n terms of an a c t i v a t i o n energy. thermodynamic t r a n s i t i o n s are observed f o r benzene.  No  Now furan i s  a molecule s i m i l a r i n shape and s i z e and i t a l s o has s i m i l a r motional p r o p e r t i e s .  That i s , the furan molecule r o t a t e s about  an a x i s perpendicular t o the molecular plane, but i n t h i s case the r o t a t i o n a x i s does not coincide w i t h a symmetry a x i s .  Also,  the motion i s l i b e r a t e d suddenly, and the motional onset i s accompanied by a phase t r a n s i t i o n a t  150 K. G  Only CW  NMR  measurements have been performed on t h i s compound ( 4 ) . 2. Experimental The instruments and the techniques used f o r obtaining the data have been mentioned p r e v i o u s l y i n Chapter I I . The benzene used was spectroscopic grade obtained from F i s h e r , and the furan was A l d r i c h "PURISSJ*.gradej these m a t e r i a l s were used without f u r t h e r p u r i f i c a t i o n .  The samples were placed  - 27 i n t h i n walled 10mm  od glass tubes and were degassed t o remove  oxygen by using a number of freeze-pump-thaw cycles. 3.  R e s u l t s and Discussion Figure 1 shows a p l o t of the amplitude of the ARP  of benzene vs. temperature.  signals  The amplitude of the ARP s i g n a l was  chosen as v a r i a b l e t o be p l o t t e d r a t h e r than a width parameter since i t i s much easier t o measure d i r e c t l y from an o s c i l l o s c o p e screen.  However, i t i s evident that changes i n H^ w i l l a f f e c t the  amplitude o f the s i g n a l as w e l l as the width.  On the same  temperature scale the CW linewidth and second moment measurements (2)  are p l o t t e d .  Figure 1 shows that the amplitude of the s i g n a l  goes through a minimum where the l i n e w i d t h and second moment change. Figure (2)  shows some of the ARP s i g n a l s observed and the d i s t o r -  t i o n of the s i g n a l shape i s obvious; the amplitudes i n f i g u r e are not t o s c a l e .  (2)  The ARP conditions were s a t i s f a c t o r y i n the  e n t i r e region of study except r i g h t near the T^ minimum, a t 140°K and i n t h i s region a second type of d i s t o r t i o n i s obvious although no l o s s of s i g n a l amplitude was evident. The d i s t o r t i o n of the s i g n a l shape and the l o s s of s i g n a l amplitude i s presumably t o be a t t r i b u t e d to motional e f f e c t s .  I n t h i s region then, l o c a l  f i e l d values and, t h e r e f o r e , second moments could not be found. However, at 77°K and 194°K the ARP s i g n a l was not d i s t o r t e d and  2 the second moments found at those temperatures were 10.0 gauss  2 and 1.55 gauss  r e s p e c t i v e l y , i n good agreement w i t h CW study  2 values of 9.80 and 1.60  gauss  (2).  Another e f f e c t noted i n t h i s r e g i o n was that the second s i g n a l normally obtained w i t h the ARP T^ two-pass experiment  Figure 1 Amplitude f o r ARP signal versus temperature f o r benzene; — O — • in. i l i n e widths and ..-.second moments from ref,(2.^  TEMP. (°KJ  ARP measurements,  Figure 2 ARP s i g n a l shapes observed f o r benzene at various temperatures; the amplitudes are a r b i t r a r y ; r e l a t i v e amplitudes may be found from the previous f i g u r e .  115  102  /  120  L 161  J  194  /  128  I  o  - 28 could not be observed unless t , the time between passages was greater than <r>* T^. set o f S^-S~  This caused some d i f f i c u l t y i n that a complete  values could not be obtained.  However, g e n e r a l l y T^  values were obtainable over the e n t i r e temperature range of i n t e r e s t , except r i g h t near the T^ minimum, where T^ was too short f o r our p a r t i c u l a r instrumentation. Figure (3) i z a t i o n decay curves obtained.  shows some of the magnet-  Curve A was obtained i n the region  of anomalous e f f e c t s , and no second s i g n a l could be seen f o r the two-pass experiment when t was l e s s than about 0.4  sec.  Another  observation of i n t e r e s t involves the extrapolated S^-S~ t = o and the experimentally obtained S^-S" be equal i d e a l l y .  curves to  values, which should  This i s seen t o be the case f o r curve B, which  was obtained at a temperature f a r away from the line-narrowing region.  F a i l u r e f o r the S^-S" when tss o and the S*-S~ values t o  coincide has been i n t e r p r e t e d i n terms of an incompletely i n v e r t e d magnetization because of an i n s u f f i c i e n t l y intense H-^ f i e l d  (1).  This i s not the case here, because curves A and B were obtained under i d e n t i c a l c o n d i t i o n s , and t h i s again then may point t o molecular motional e f f e c t s as the cause of the anomalous behaviour. The T^ values obtained are p l o t t e d i n f i g u r e (4a) together with Andersons 50 MHz r e s u l t s obtained by pulse methods  (3).  The d i f f e r e n c e s i n T^ min. values and the temperatures at the minimum are due t o the d i f f e r e n c e s i n measuring frequencies. The "Cc values c a l c u l a t e d assuming a value of 0.01  sec. f o r  T^ a t the minimum are shown i n f i g u r e (4b) together w i t h Anderson's (3) energy*  and a l s o Andrew and Eades' (2)"Cc values.f A c t i v a t i o n  found from the c o r r e l a t i o n time p l o t was 3.95  keal/mole,  i n good agreement w i t h the values found p r e v i o u s l y , 3.95 and 3.70  kcq|/mole  kco(/mole r e s p e c t i v e l y .  The anomalous e f f e c t s observed i n the line-narrowing region most l i k e l y are governed by a s i m i l a r c o n d i t i o n to that which governs the observance of CW or a l t e r n a t i v e l y and SH  Hu  i s the CW l i n e width.  I f t h i s hypothesis i s c o r r e c t , the anomalies observed near the benzene r o t a t i o n a l t r a n s i t i o n should be absent f o r furan, since the phase t r a n s i t i o n causes the r i n g r o t a t i o n t o take place The  suddenly so that i n no f i n i t e temperature  height of the ARP s i g n a l f o r furan p l o t t e d v s . temperature i s shown i n f i g . (5).  On the same temperature s c a l e are shown the CW l i n e w i d t h  and second moments (4).  No d i s t o r t i o n of the ARP s i g n a l was evident  and a l s o no major l o s s of s i g n a l amplitude was observed, as was expected.  Second moments found from the ARP signals were 4.95  gauss at 136°K and 1.42 2  values of 5.7 gauss  2  gauss at 163°K and compare with CW 2  9  and 1.3 gauss* r e s p e c t i v e l y .  The low  temperature phase second moments obtained by the two methods do not agree very w e l l .  There i s the p o s s i b i l i t y that s a t u r a t i o n  problems were encountered while recording the CW spectra however, since T^ i n the low temperature phase i s greater than 100 seconds, causing large p o s s i b l e errors i n second moments. The T-j_'s obtained f o r furan by the ARP method are shown i n f i g u r e (6). The low temperature phase T^'s are a l l quite long, i n agreement w i t h the f a c t that major d i p o l a r r e l a x a t i o n mechanisms are  absent due to the r i g i d condition of a l l the molecules.  Spin-  l a t t i c e r e l a x a t i o n i n t h i s region probably takes place bgr a s p i n  Figure 5  - 30 d i f f u s i o n process t o paramagnetic impurity s i t e s .  At the  temperature at which the phase t r a n s i t i o n occurs, a d i s c o n t i n u i t y occurs i n the  p l o t , and i n the high temperature phase the  important r e l a x a t i o n mechanism w i l l be provided by the r o t a t i o n of the furan r i n g s . From the slope of the l o g i t i s evident that 2.35  keal/mole.  vs tyT p l o t  and the a c t i v a t i o n obtained i s  No Tj. data are a v a i l a b l e f o r f u r a n , but d i e l e c t r i c  measurements (5) i n d i c a t e an a c t i v a t i o n energy of 2.00 and a r e o r i e n t a t i o n frequency of 6x10^  keal/mole,  Hz. at 171°K. These  r e s u l t s are i n s u b s t a n t i a l agreement w i t h the NMR  results.  One other i n t e r e s t i n g observation i s that the ARP  signal  amplitude decreased j u s t below the melting points f o r both benzene and furan.  I t appears that t h i s i s due t o the presence  of some motions w i t h frequency components such that A  Hu  I n concluding, then, t h i s work has shown that i n favourable cases the ARP method can give second moments and s p i n - l a t t i c e r e l a x a t i o n times and information equivalent t o CW l i n e w i d t h s . Results obtained suggest that an a d d i t i o n a l c o n d i t i o n must be added t o the normal ARP conditions f o r compounds i n which molecular motion•exists.  A c t u a l l y , i t was not e n t i r e l y un-  expected that second moment values could not be obtained i n the r e g i o n of l i n e w i d t h narrowing.  Second moments obtained  from CW spectra i n t h i s region have not r e a l l y any s i g n i f i c a n c e because the a c t u a l values w i l l depend on how much the motional sidebands generated contribute t o the observed s i g n a l .  The  ARP method i s e s p e c i a l l y w e l l s u i t e d t o obtaining second moments i n systems w i t h very long r e l a x a t i o n times, where  - 31 s a t u r a t i o n problems are encountered with CW methods.  Another  advantage of the ARP method i s t h a t the equipment necessary i s very simple and e a s i l y a v a i l a b l e . Some l i m i t s on the measurements by the ARP method may  be  given at t h i s p o i n t . With the present equipment, where the sweeping of the f i e l d i s l i m i t e d l a r g e l y by the inductance of the magnet system,  values down t o about 0.02 seconds could  be measured, although the ARP s i g n a l was not e n t i r e l y symmetric under these c o n d i t i o n s . A l s o a complete set of S^,-S~ values i s not a v a i l a b l e w i t h such short T^'s and values found here are not as accurate as those found f o r l a r g e r  values (> 0.5 s e c ) .  Another d i s t i n c t disadvantage of the ARP method i s the presence of the anomalous e f f e c t s observed near regions of motional narrowing. I t i s f e l t t h a t c e r t a i n l y the present experimental arrangement could be improved s u b s t a n t i a l l y .  One  such  improvement would i n v o l v e p r o v i d i n g f o r a separate set of sweepcoils f o r sweeping the magnetic f i e l d , so that greater c o n t r o l over the a c t u a l sweep conditions could be excercised.  - 32 -  BIBLIOGRAPHY CHAPTER III 1 W.R. Janzen, T.J.R. Cyr, and B.A. Dunell J . Chem. Phys. 48, 1246 (1968) 2 E.R. Andrew and R.G. Eades Proc. Roy. Soc. A218. 537 (1953) 3 J.E. Anderson J. Chem. Phys. 4J, 3575 (1965) 4  F. Fried Comptes Rendu Acad. Sci. Paris 262, 1497 (1966)  5 F. Fried and B.J. Lassier J . Chim. Phys. 63_, 1 (1966)  CHAPTER IV  COMPLEXES OF BENZENE 1.  Introduction The structure o f charge-transfer complexes i s a t o p i c of  much recent i n t e r e s t .  Spectroscopic studies of the charge-  t r a n s f e r i n t e r a c t i o n i n s o l u t i o n are numerous and have r e c e n t l y been reviewed ( 1 , 2 ) .  However, the studies o f the s o l i d  complexes are more r a r e , and the r e s u l t s i n d i c a t e that  structures  deduced from s o l u t i o n studies do not n e c e s s a r i l y agree with the s o l i d state structures.  Recently ( 3 ) , the importance of the  charge-transfer i n t e r a c t i o n r e l a t i v e t o c l a s s i c a l forces, such as the Coulomb and p o l a r i z a t i o n i n t e r a c t i o n s i n s o l u t i o n has been examined.  The bonding i n the 1:1 s o l u t i o n complexes of  benzene i s generally described as " s a c r i f i c i a l , " where charget r a n s f e r takes place from a bonding TT o r b i t a l on the donor benzene molecule t o an antibonding T molecule.  orit  o r b i t a l on the acceptor  Charge-transfer i n t e r a c t i o n s are expected t o be weak  f o r complexes of t h i s type.  M u l l i k e n and Person (3) have  concluded that the c l a s s i c a l e l e c t r o s t a t i c forces and the charget r a n s f e r forces are about equally important i n weak complexes. I n s o l i d s , c r y s t a l packing e f f e c t s as w e l l as the other forces mentioned are expected t o be a major f a c t o r i n determining the structures. 81 Br pure quadrupole measurements (4) performed on some o f  - 34 these complexes have brought some authors t o conclude that any s h i f t s due t o c h a r g e i t r a n s f e r are g e n e r a l l y hidden, because these are o f the same order as s h i f t s expected j u s t from nonequivalence e f f e c t s i n the c r y s t a l . NMR measurements have been performed on a number of benzene and s u b s t i t u t e d benzene complexes o f hexafluorobenzene, carbontetrabromide, antimony pentachloride (5) (6).  and s i l v e r perchlorate  From the temperature e v o l u t i o n of the l i n e w i d t h and second  moment i t i s evident that the benzene r i n g reorientates about i t s s i x f o l d a x i s a t frequencies greater then about 10-* sec"* a t 1  temperatures near 100°K. Normally a c t i v a t i o n energies found from l i n e w i d t h changes f o r the complexes are smaller than the value found f o r benzene i t s e l f from s p i n - l a t t i c e r e l a x a t i o n time measurements.  NMR r e s u l t s obtained from the study of the AgClO^  complex caused some controversy (7,8)  as t o whether the benzene  r i n g i s d i s t o r t e d from s i x - f o l d symmetry as reported i n an X-ray study (9).  A d d i t i o n a l references t o X-ray studies on charge-  t r a n s f e r complexes may be found i n some recent reviews (10,11). In t h i s work NMR measurements have been performed on some a d d i t i o n a l complexes of benzene, those o f SO2, ^0^, measurements are a l s o reported f o r the CBr^ complex.  and B r and 2  T-^ measure-  ments were made because o f t e n l i n e w i d t h changes f o r these complexes occur i n r e l a t i v e l y i n a c c e s s i b l e temperature regions and a c t i v a t i o n energies are then d i f f i c u l t t o e x t r a c t . 2.  Experimental CW NMR measurements were c a r r i e d out as described i n Chapter I I  - 35 at a frequency of 30 MHz.  For t h e T-^ measurements, the two-pass  ARP method was used, where p o s s i b l e . Tfe«.ai*t©rials used were reagent grade or b e t t e r and were used without f u r t h e r p u r i f i c a t i o n .  The complexes were prepared by  weighing out equimolar q u a n t i t i e s of each component, mixing them i n 10mm outside diameter glass tubes and quenching them i n l i q u i d nitrogen.  To remove d i s s o l v e d oxygen, the benzene was outgassed  by bubbling dry nitrogen through i t before use.  A f t e r samples  were mixed, each was f u r t h e r subjected t o s e v e r a l freeze-pumpthaw c y c l e s . The melting points of the N 0^, SO2 and B r complexes agreed 2  2  with the reported l i t e r a t u r e values (12,13,14). 3.  Results  i)  Benzene-Br  2  The temperature dependence of the second moment and l i n e w i d t h are  shown i n f i g u r e ( 7 a ) .  A t r a n s i t i o n i n l i n e w i d t h s and second  moments can be seen t o occur around 118°K.  The second moment  was 5.9 gauss a t 77°K and 1.4 g a u s s a t 140°K. 2  the  2  From there,  second moment decreased very s l o w l y u n t i l a value of 1.0 2  gauss  was reached near the melting p o i n t .  A narrow component  was observed i n the spectrum near 210°K, the i n t e n s i t y of which increased as t h e temperature was r a i s e d . The CW NMR r e s u l t s are consistent with the benzene r i n g s s t a r t i n g t o r e o r i e n t a t e a t frequencies greater t h a n ^ l O ^ s e c T  1  2  around 110°K.  The second moment a t 77°K of 5.9 gauss  the r i g i d l a t t i c e value, of which 3.16 gauss  2  w i l l be  (15) 1® due t o  intramolecular i n t e r a c t i o n s i f the benzene r i n g has s i m i l a r dimensions t o those of the free compound. The T^ measurements are shown i n f i g u r e (8a).  The r e l a x a t i o n  of the magnetization could be f i t t e d by a s i n g l e exponential decay at temperatures below about 210°K. Above t h i s temperature a more complex behaviour was evident, most l i k e l y due t o the presence of the narrow component observed i n the CW spectra.  An a n a l y s i s of  the complex T^ behaviour was not c a r r i e d out, and a weighted average value was p l o t t e d , namely the T-^ value determined by the n u l l method.  The a c t i v a t i o n energy obtained from the low  temperature slope of the T^ was 5.8 greater than the value of 3.95  keal/molejsignificantly  keal/mole (16) found f o r s o l i d  benzene. A c r y s t a l s t r u c t u r e has been reported f o r t h i s complex (12). X-ray measurements at -5G°C i n d i c a t e that the complex consists of i n f i n i t e chains o f a l t e r n a t i n g benzene and bromine molecules. The bromine molecules were found t o be e x a c t l y over the center of the r i n g s w i t h the bromine-bromine a x i s perpendicular t o the r i n g plane, and the bromine-bromine same as i n the free molecule.  distance was found t o be the  The chains of a l t e r n a t i n g donor  and acceptor molecules are arranged i n such a manner  that the  benzene r i n g i n one chain i s next t o a bromine molecule i n the other.  Large a n i s o t r o p i c temperaturesfactors were evident. A  recent i n f r a r e d study (17) of the complex a t 77°K g e n e r a l l y agrees w i t h the X-ray r e s u l t s , i f the bromine molecule i s displaced t o be s l i g h t l y nearer one of the benzene r i n g s .  (a)  „ (b) '•  100L  >  100  M.P.  M.P.  10 -  A  10  T,  (SEC)  (SEC)  j  Cr  .01  .01  4  6 1000/  H>  JL  JL  8 T  10  12  4  o  6 1000/  (°Kr'  8 T  10  12  ( ° K )•'  —  % p>  TO  Figure 8 I n v e r s e temperature p l o t s of l o g T-^ f o r (a) benzene-Brg, v a l u e s determined by two-pass method and —Q—  dO  CD  and (b) benzene-SO^; n u l l method.  r  - 37 Up t o t h i s time the b a r r i e r s t o benzene r i n g r o t a t i o n f o r weak charge-transfer complexes studied have always been lower thanIboSS observed f o r benzene i t s e l f ( 5 ) . One other case i s known where the a c t i v a t i o n energy i s higher, and t h i s i s f o r the benzene-dicyanin-nickel-ammine-clathrate  (18).  Nakajima a t t r i b u t e d  the high b a r r i e r t o the absence of cooperative motions which p o s s i b l y occur i n s o l i d benzene, but not i n the c l a t h r a t e , where the b a r r i e r i s caused by the r e l a t i v e l y r i g i d d i c y a n i n n i c k e l ammine cage.  Since the benzene r i n g s are surrounded by bromine  molecules, a s i m i l a r explanation may be given f o r the high b a r r i e r observed i n the complex.  I f maximum overlap f a c i l i t a t i n g the charge-transfer i n t e r a c t i o n i s taken as the c r i t e r i o n f o r the r e l a t i v e o r i e n t a t i o n of the donor and acceptor m o i e t i e s , an e n t i r e l y d i f f e r e n t s t r u c t u r e i s predicted. The brojnine molecule should be placed w i t h i t s a x i s e i t h e r p a r a l l e l o r a t a s l i g h t angle t o the plane of the benzene r i n g .  So f a r , no explanation has been given f o r  t h i s , and the e l e c t r o n i c d e s c r i p t i o n of the bonding i n t h i s complex i n the s o l i d s t a t e remains a puzzle (19).  A ®^Br MQR  study (20) has a l s o been c a r r i e d out on t h i s complex, and the frequencies found d i f f e r e d l i t t l e from those found i n s o l i d bromine.  Hooper concluded that l i t t l e or no charge-transfer  took place i n the complex a t 77°K, although t h i s i n t e r p r e t a t i o n has been questioned more r e c e n t l y ( 4 ) .  - 38 i i ) Benzene-CBr. 4  NMR l i n e w i d t h s and second moments measurements obtained f o r t h i s complex were i n good agreement w i t h values obtained i n an e a r l i e r study (5).  The r e s u l t s show a l i n e w i d t h and second moment  t r a n s i t i o n near 90°K, and these parameters had not reached t h e i r r i g i d l a t t i c e values a t 77°K. Again the l i n e w i d t h and second moment changes may be i n t e r p r e t e d i n terms o f a r e o r i e n t a t i o n of the benzene r i n g around i t s hexad a x i s . The T^ measurements are shown i n f i g u r e (9a).  A simple  exponential expressed the magnetization decay i n the e n t i r e temperature range.  Using a value o f 0.02 sec f o r the T^ value  a t the minimum, c o r r e l a t i o n times T c were c a l c u l a t e d u s i n g eqn. 15 i n Chapter I , and are shown as a f u n c t i o n of inverse temperature i n f i g u r e (9b).  The slope of the p l o t i n d i c a t e s an a c t i v a t i o n  energy of 2.76 keal/mole.  Near 220°K the T^ values deviated  from the predicted curve and decreased with i n c r e a s i n g temperature, i n d i c a t i n g that a new r e l a x a t i o n process i s becoming e f f e c t i v e . The presence o f a narrow component i n the CW spectrum suggests t h a t motion responsible f o r t h i s r e l a x a t i o n process might be a d i f f u s i o n , although the broad component p e r s i s t e d u n t i l the m e l t i n g point was reached  j u s t above room temperature.  The c r y s t a l s t r u c t u r e f o r t h i s complex i s not known, but i t can be assumed that i t i s s i m i l a r t o the p-xylene-carbon t e t r a bromide complex (21).  The benzene r i n g has two bromine atoms  coordinating t o the center of the r i n g , one t o each side. Zig-zag s t r i n g s o f the a l t e r n a t e donor and acceptor moieties run p a r a l l e l t o the c r y s t a l c a x i s .  A value of 3.34 ? i s found  1000/T  (OK)-  1  0  0  0  /  T  ,o .. K)  Figure 9 Inverse temperature p l o t s of (a) l o g T  and l o g "tc f o r benzene-CBr,  - 39 for  the bromine-ring center distances, 0.2%  the Vander Waals' r a d i i .  A  8 1  l e s s than the sum of  B r NQR study (4) i n the s o l i d  complex gave frequencies l i t t l e d i f f e r e n t from those of s o l i d CBr^.  The authors concluded that s h i f t s due t o charge-transfer  were of the same order as s h i f t s due t o c r y s t a l packing e f f e c t s , so that l i t t l e may be s a i d about the extent of charge-transfer. The a c t i v a t i o n energy of 2.76  kcal/mole observed f o r the  complex i s s i g n i f i c a n t l y lower than that obtained f o r benzene. This i s t o be expected on the basis of a l o o s e r s t r u c t u r e i n the complex.  Yet, i t i s l i k e l y that cooperative e f f e c t s are  present, since u n l i k e the bromine complex, the aromatic r i n g s are probably arranged i n a plane, as i n the p-xylene-carbon tetrabromide complex. i i i ) Benzene-N^ Linewidth;. and second moment' changes w i t h temperature; are shown i n f i g u r e (7b) and are s i m i l a r to those observed f o r the other two complexes, w i t h the t r a n s i t i o n s taking place near 105°K.  The second moment at 77°K i s 6.0 gauss^ and  o 1.3 gauss  a t 120°K.  From there, the second moment decreased  slowly w i t h i n c r e a s i n g temperature t o a value of about 1 gauss^, and i t stayed a t t h i s value u n t i l the m e l t i n g point was reached. The CW r e s u l t s are again consistent w i t h the benzene r i n g s s t a r t i n g to r e o r i e n t a t e around t h e i r hexad axes at rates greater than about 105 secT  a t a temperature of 110°K.  T^ r e s u l t s are shown i n  f i g u r e (10a). A T^ minimum i s evident and c o r r e l a t i o n times were c a l c u l a t e d t a k i n g a T. minimum value of .020  sec.  100  Figure 10 Inverse temperature p l o t s of (a) l o g T, and (b) l o g t c f o r benzene-N-0  - 40 -  Below 140°K, an a c t i v a t i o n energy of 5.0 keal/mole i s obtained.  At t h i s temperature, a change i n slope i n the l o g  and log"C c vs ^/T  p l o t s i s evident. The high temperature  a c t i v a t i o n energy was 2.0 keal/mole.  Since no d i s c o n t i n u i t y  was found t o be present i n the T^ curve, and no d i s t i n c t second minimum was observed, i t i s thought t h a t t h i s change i n slope simply r e f l e c t s a change i n the b a r r i e r t o r o t a t i o n , r a t h e r than s i g n i f y i n g the presence of a new r e l a x a t i o n mechanism.  Also  no major changes were observed i n the CW spectra near t h i s 9  temperature, although a slow decrease from 1.3 gauss gauss  2  t o 1.0  occurred between about 115°K and 140°K  A phase study (14) of ^ 0 ^ and various donor compounds i n c l u d i n g benzene i n d i c a t e d that a 1:1 complex formed w i t h benzene and various other "TT  donors.  The ^ 0 ^ molecule i s g e n e r a l l y  regarded as an e l e c t r o n d e f i c i e n t molecule ( 1 4 , 2 2 ) , w i t h 8 electrons i n the IT  molecular o r b i t a l system, so that 4 more  electrons p o s s i b l y could be accommodated. X-ray studies ( 2 2 ) i n d i c a t e a rather complex s t r u c t u r e e x i s t s at temperatures above about 170°K.  The a l t e r n a t e  donor  and acceptor molecules are arranged i n l i n e a r chains, w i t h the chain axes p a r a l l e l t o the t r i g o n a l axes of the u n i t c e l l , and the molecular axes perpendicular t o the chain axes.  The  molecules are a l s o s t a t i s t i c a l l y d i s t r i b u t e d between two c r y s t a l l o g r a p h i c a l l y non-equivalent s i t e s , w i t h the s i t e s interconverting.  The ^ 0 ^ molecules are placed over the  benzene r i n g s so that the n i t r o g e n atoms are e q u i d i s t a n t from two and two carbons.  Stromme(25.)also suggested that at the  - 41 temperature a t which the X-ray s t r u c t u r e was determined, both component molecules are quite mobile, and the motion i s l i k e l y f u l l y cooperative.  I t was a l s o suggested that the high temperature  s t r u c t u r e would not be stable a t lower temperatures and a s t r u c t u r e of lower symmetry was observed at -100°C, although the s t r u c t u r e was not i n v e s t i g a t e d i n d e t a i l . change i n slope i n the  I t i s possible then that the  curve and the small change i n second  moment observed near 140°K correspond t o a minor change i n structure.  P o s s i b l y the NgO^ moiety i s able t o r e o r i e n t a t e  above t h i s temperature.  The change i n a c t i v a t i o n energy from  5.0 t o 2.0 keal/mole would then correspond t o a lower b a r r i e r t o r o t a t i o n because of the motion of both types of molecules becoming f u l l y cooperative. i i ) Benzene-SOg Second moments and linewidths d i d not change s i g n i f i c a n t l y between 77°K and the m e l t i n g p o i n t . gauss^.  The second moment was 1.3  The T-^ measurements are shown i n f i g u r e (8b); only part  of t h e T^ curve could be obtained, but an a c t i v a t i o n energy could s t i l l be extracted.  The value found was 2.0 keal/mole.  No other experiments have been c a r r i e d out on the s o l i d complex except f o r a phase study (13) i n d i c a t i n g the 1:1 complex. Spectroscopic studies on s o l u t i o n s have been c a r r i e d out- (23,24) and some s t r u c t u r e s have been suggested, p o s i t i o n i n g the molecules favouraSly so that Charge-transfer i s f a c i l i t a t e d .  The acceptor  o r b i t a l on the s u l f u r atom has been suggested t o be an antibonding  - 42 pIT o r b i t a l with someMlT character, w i t h 2 major lobes o f opposite s i g n p o s i t i o n e d at an angle of 105° t o the S-0 bonds, and i n a plane perpendicular t o the molecular plane.  The s u l f u r  atom i s then p o s i t i o n e d d i r e c t l y over the benzene r i n g center, and the S 0 molecular plane should be e i t h e r p a r a l l e l t o the r i n g 2  plane, or i n c l i n e d a t a s l i g h t angle t o i t .  The T^ measurements have been summarized i n table IV-1, g i v i n g T^ min. values and a c t i v a t i o n energies.  Included are T^  measurements performed on benzene (see Chapter I I I , a l s o r e f . 15, 16) and Benzene-Chromium-Tricarbonyl (see Chapter V I I ) . Table IV-1 Summary of T^ r e s u l t s f o r Benzene Complexes Compound  T^ min.  Temperature at Eact  (sec.)  (kcal/mole)  minimum ( K)  Benzene  .01  143  3.95  Benzene-Br  .026  159  5.8  .020  112  2.76  .020  119  5.0, 2.0  Tricarbonyl  .025  149  3.6  Benzene-S0  .025  80  2.0  2 Benzene-CBr. 4  Benzene N 0^ 2  Benzene-Chromium-  o  CW measurements have been summarized i n t a b l e IV-2 i n c l u d i n g previous work ( r e f . 5, 6, 1 8 ) i  - 43 Table IV-2 Summary of CW nmr Motional Data f o r Benzene Complexes Compound  State  of ring  at 77°K.  Temperature o f l i n e w i d t h t r a n s i t i o n s (°K)  Benzene  S  100  Benzene-Br2  S  116  Benzene-^O^  s  95  Benzene-AgClO^  s s  103  s  150  Benzene-SO^  R  >77  Benzene-SbCl^  R  X77  Benzene-CBr^  S-R  80  Benzene-Hexafluorobenzene  S-R  80  Benzene-Chromium-Tricarbonyl Benzene-dicyaninammine-nickel c l a t h r a t e  a.  S=sStationary, R«Reorientating, S-R = I n T r a n s i t i o n Now, from the t a b l e s i t i s evident that there i s a l a r g e  v a r i a t i o n i n a c t i v a t i o n energies and motional onset temperatures which depends on the environment o f the r i n g s . Also evident i s an increase i n values of T^ min. on going from benzene t o the complexes.  This  r e f l e c t s the decrease i n intermolecular proton-proton i n t e r a c t i o n s i n the complexes. P r e v i o u s l y i t has been proposed (16) that the r o t a t i o n a l motion of the benzene r i n g i s a cooperative process, where the r e o r i e n t a t i o n between equivalent p o s i t i o n s of a large number of molecules w i t h i n a c l u s t e r i s t r i g g e r e d by a s i n g l e event,  - 44 -  and some experimental evidence was obtained i n support of t h i s . I t i s quite l i k e l y that the r e o r i e n t a t i o n a l a c t i v a t i o n energies found depend on the e f f i c i e n c y of the cooperative e f f e c t , a3 w e l l as c r y s t a l packing e f f e c t s .  The lowest a c t i v a t i o n energies would  then be expected t o be found f o r a f a i r l y loosely packed s o l i d , where some contact between the rings i s maintained, so that cooperative e f f e c t s can be present.  Generally f o r the complexes f o r which both X-ray and NMR r e s u l t s are a v a i l a b l e i t i s found that the Frenkel model mentioned i n Chapter I applies quite well.  There also exists the problem of d i s t o r t i o n from  s i x f o l d symmetry of the benzene rings, of which the structure o f the benzene-AgClO^  as determined by the X-ray method i s an example.  A l l benzene rings undergo hindered r o t a t i o n at temperatures at which X-ray structures are normally determined.  Distortionsy  then, i f they are r e a l , are properties of the c r y s t a l l a t t i c e s i t e rather than of the molecule.  The only model which would then  agree with both X-ray and NMR results would have the benzene rings reorientating between p o t e n t i a l minima, and the rings would have t o go from one distorted form t o another during the reorientation. Gilson and McDowell (6) previously argued that i f c r y s t a l l a t t i c e forces were able t o d i s t o r t a benzene molecule i n the benzene-AgClO^ complex from s i x f o l d symmetry, these forces should also be able t o hold the molecule r i g i d l y i n the l a t t i c e .  From  the NMR second moment at room temperature i t was shown that the  - 45 benzene molecule was rotating and hence i t was suggested that a d i s t o r t i o n of the benzene molecule was u n l i k e l y . However, there i s some N M R  experimental evidence f o r the  presence of molecular motion i n a system where the molecules are distorted by c r y s t a l l a t t i c e forces. A study of s o l i d UF^ (26) showed that at low temperatures the  l a t t i c e i s e f f e c t i v e l y r i g i d , with the UF  0  molecule distorted  tetragonally so that there are 2 inequivalent types of f l u o r i n e s . X-ray studies showed the presence of 4 short and 2 long U-F bonds, and the NMR  studies show that the two types of fluorines have  d i f f e r e n t chemical s h i f t s . even as reorientations occur  This chemical nonequivalence p e r s i s t s (ie J/r«£ t  but becomes  averaged out at somewhat higher temperatures (when I V & ^  ).  X-ray studies show that fluorine s i t e inequivalence s t i l l persists,at temperatures where the UF^ chemical inequivalence i s averaged out. Distortions, then, should modify the shape and height of the reorientational b a r r i e r s to some extent, but at t h i s time data on r e o r i e n t a t i o n a l b a r r i e r s i n systems which are known t o be d i s t o r t e d are  not generally a v a i l a b l e . It  of  appears then that reorientational barriers i n complexes  benzene are s t i l l governed l a r g e l y by c r y s t a l packing forces  and cooperative e f f e c t s , as i n benzene i t s e l f , with possible contributions fromithe presence of d i s t o r t i o n s and charge-transfer interactions.  - 46 BIBLIOGRAPHY CHAPTER IV 1  G. Briegleb, Elektronen-Donator-Acceptor-Komplexe, Springer-Verlag, B e r l i n , 1961  2  L . J . Andrews and L.M. Keefer, Molecular Complexes i n Organic Chemistry, Holden Day, Inc., San Francisco, 1964  33  R.S. Mulliken and W.B. Person J . Am. Chem. Soc. 9JL, 3409 (1969)  4  D.F.R. G i l s o n and C T . O'Konski J . Chem. Phys. 48, 2767 (1968)  5  D.F.R. Gilson and C.A. McDowell Can. J . Chem. 44, 945 (1966)  6  D.F.R. Gilson and C.A. McDowell J . Chem. Phys. 3_2, 1825 (1963)  7  H.G. Smith J . Am. Chem. Soc. 2k,  8  D.F.R. G i l s o n and C.A. McDowell J . Chem. Phys. 40, 2413 (1964)  9  H.G. Smith J . Chem. Phys. UO, 2412 (1964)  811 (1952)  10  H.S. Bent Chem. Rev. 68, 587 (1968)  11  C.K. Prout and J.D. Wright Angew, Chemie (Int. Ed.) It  12  0. Hassel and K.O. Stromme Acta. Chem. Scand. 12, 1146 (1958)  13  B.C. Smith and G.H. Smith J . Chem. Soc. 5514 (1965)  14  C C . Addison and J.C. Sheldon J . Chem. Soc. 1941 (1956)  15  E.R. Andrew and R. G. Eades Proc. Roy. Soc. A218, 537 (1953)  16  J.E. Anderson J . Chem. Phys.  17  W.B. Person, C F . Cook and H.B. F r i e d r i c h J . Chem Phys. 46, 2521 (196?)  18  H. Nakajima J . Phys. Soc. Japan 20, 555 (1965)  19  R.S. Mulliken and W.B. Person Ann. Rev. Phys. Chem. 13_, 107 (1962)  20  H.O. Hooper J . Chem Phys. 41, 599 (1964)  °59 (1968)  3775 (1965)  21 i'F.J. S t r i c t e r and D.H. Templeton J . Chem. Phys. 3J£, 161 (1962) 22  K.O. Stromme Acta. Crysta B 2 4 . 1607 (1968)  23  P.A.D. de Maine J . Chem. Phys. 26, 1036 (1957)  - 47 24 D. Booth, F.S. Darnton and K.J. I v i n Trans. Farad. Soc. 55_, 1293 (1959) 25  I. Darmon and C. Brot Mol. Cryst.  301 (1967)  26 R. B l i n c , E. Pirkmajer, J . S l i v n i k and I. Zupancic J . Chem. Phys. 4J>, 1488 (1966  - 48 -  CHAPTER V  BORONTRIFLUORIDE-AMINE COMPLEXES  1.  Introduction Borontrifluoride (BF^) combines with nitrogen 8 -donor  molecules t o form complexes of the type BF^-NR^R^R^ ( l ) which can be regarded as extreme cases of charge-transfer complexes where the degree of t r a n s f e r of charge approximates t o covalent bond formation i n the ground state.  In the main these complexes  are r e l a t i v e l y stable c r y s t a l l i n e s o l i d s and the c r y s t a l structures of a number have.been determined ( 2 - 6 ) with s p e c i a l emphasis on the nature of the bonding between the two components and possible intermolecular hydrogen-bonding i n the s o l i d state.  On formation  of the complex, the geometry of the BF^ moiety changes s i g n i f i cantly.  A change i n hybridization from Sp* t o Sp'  changes the  configuration around the boron from t r i g o n a l planar t o approximately tetrahedral ( l ) .  Since the bonding o f the amine involves  the lone p a i r , changes i n geometry are r e l a t i v e l y minor. The r e l a t i v e donor strengths of the amines have been correlated with the B-N bond lengths; r e l a t i v e donor strengths^obtained are ( 4 ) J Py>  NMe > NH > 3  3  NCCH^.  The BF^ moiety bond lengths and angles r e f l e c t the r e l a t i v e donor strengths as w e l l . *  A broadline NMR investigation should  The content of t h i s chapter has recently been published i n Trans. Farad. Soc. 6 5 , 5 5 7 ( 1 9 6 9 ) , "A Broadline Nuclear Magnetic Resonance Study of some s o l i d B o r o n t r i f l u o r i d e Amine Complexes" by B.A. Dunell, C.A. Fyfe, C.A. McDowell and J.A. Ripmeester  -  4 9  -  reveal the motional properties of each moiety i n the complexes and these should r e f l e c t differences i n c r y s t a l packing as w e l l as hydrogen bonding e f f e c t s . 2.  Experimental CW spectra were obtained using a frequency of 30 MHz. The complexes were prepared by l i t e r a t u r e methods (l). The  usual procedure was t o bubble BF^ gas into an ice-cold dry ether solution of the amine i n case;the amine was a l i q u i d .  For the  ammonia complex, a dry, i c e - c o l d ether s o l u t i o n was f i r s t saturated with BF^ gas, and the ammonia gas was passed over the s t i r r e d solution. In a l l cases the complexes were w h i t e c r y s t a l l i n e s o l i d s . 0  These were f i l t e r e d , dried and packed into 10mm outside diameter thin-walled glass tubes.  Spectra were obtained as described i n  Chapter I I . Melting points and sublimation points obtained were consistent with published values.  A l l samples gave analyses i n  good agreement with the proposed structures. Correlation frequencies were obtained i n the regions of linewidth change using the modified BPP equation (see equation & i n Chapter I ) . A c t i v a t i o n energies were obtained from the c o r r e l a t i o n frequencies assuming Arrhenius type behaviour. The calculations were performed using a s l i g h t l y modified version of a program o r i g i n a l l y written by G.W. Smith (!§). A l l of the complexes contained f i v e types of n u c l e i with non-zero spin angular momentum: ^H, ^ F , ^ B , ^*B and ^ N , Account had t o be taken of a l l of these nuclei i n the second moment calculations.  Hv^Jhc-r^-c^ 0  - 50 Second moment calculations were carried out using Fortran IV programs written f o r an IBM 7044 computer.  Separate programs were  written f o r the pyridine, a c e t o n i t r i l e and ammonia complexes.  One  of these i s presented i n appendix A. 3.  Results and Discussion  i)  Molecular Motion i n BF^NH^ Both the  L 19 n and F resonances i n s o l i d BF^-NH^ are smooth  1° curves showing no fine structure.  The  7  F resonance at room  temperature ( f i g . 11a) i s markedly different from that observed at 77°K ( f i g . l i b ) i n d i c a t i n g the presence of some motion i n the c r y s t a l . resonance.  There i s a s i m i l a r but smaller change i n the The nature of the motion can be investigated i n more  d e t a i l by consideration of the temperature dependence of the l i n e widths and second moments of the resonance. a) Linewidth V a r i a t i o n The variations i n linewidth of the *ft and ~'F resonances with temperature over the range 77°K t o just below the melting point of the complex are shown i n f i g . (12). at  200°K i n the  the BF^ component.  The large change  resonance suggests that the motion involves In f i g . (12), the curve i n the region of the  t r a n s i t i o n has been f i t t e d i n terms of an approximate a c t i v a t i o n energy f o r the r e o r i e n t a t i o n process using the modified BPP eqn., (7) (See experimental).  This yields a value of E s f t  4.2*  0.5 keal/mole  f o r the process. b)  Second Moment Variations The temperature dependences of the second moments of both  19  F —O"  ^  10  < O  9  CO CO ZD  X  H Q  N<>H LINEWIDTH CHANGES •CALC. CURVE  8  E -4-2±0-5Kca!.m.' a  LU  2? 7  H —O  m.p.  80  JL  120  160  200  240  280  320  360  400  440  . o,  TEMP..(°K).Figure 12 1 19 H and F linewidths as a function of temperature f o r borontrifluoride-ammonia.  480  o «» o M  .8  % TO CD  \J1  O  40  80  120  160  200  240  280  320  •  '  360  400  1  *  440  TEMP. (°K) Figure 13 H and !9F second moments as a function of temperature for borontrifluoride-ammonia.  »  480  the  and  resonances are shown i O f i g . (13). Again the  dominant change i s i n the  resonance.  T h e o r e t i c a l values of  the second moments were computed f o r various cases from formulas mentioned i n Chapter I and the c r y s t a l s t r u c t u r e found by Hoard, G e l l e r and Cashin (2).  These are compared with the experimental  values i n Table V - l Table V - l C a l c u l a t e d * and observed second moments (gauss ) f o r b o r o n t r i f l u o r i d e - ammonia complex 2  F resonance BF  NH k 3  b  3  S S  Calculated  S R  c  ;.R  R  C  Observed  c  Calculated  Observed  37.8  22.6 c  H resonance  20.3-20.7  18.0(77°K)  11.4-10.3  10.5(77°K)  4.4-5.5  4.5(250°K)  9.2-10.3  8.0(260 K)  a.  Calculated from c r y s t a l structure o f Hoard, G e l l e r and Cashin, Acta Cryst. 4, 396 (1951).  b.  S  c.  Approximate reduction f a c t o r s used f o r intermolecular contributions (see t e x t ) .  s  G  s t a t i o n a r y , R as r o t a t i n g  Assuming a r i g i d l a t t i c e model, and using the molecular s t r u c t u r e and proton co-ordinates  suggested by Hoard (2), the  various contributions t o the second moments were c a l c u l a t e d using the Van Vleck formula, contributions over distances greater than being estimated by an i n t e g r a l .  The various contributions were:  ( g a u s s ) : I n t r a B-F = 10.72, I n t r a F-Fse 4.7, I n t r a H-F sr 1.14, 2  I n t r a H-H =* 32.24, I n t r a N-H » 1.90, I n t r a F-H » 1.00, I n t e r F - F ss 2.33, I n t e r H-F s* 3.62, I n t e r B-Fa» 0.12, I n t e r H-H =c 2.16, I n t e r F-H as 3.34, I n t e r B-F«s 0.19, g i v i n g the t o t a l second moments shown i n Table 1.  - 52 The reductions i n the intramolecular H-H  and N-H contributions  i n NH^ and i n the intramolecular F-F and B-F contributions i n BF^ can be calculated exactly f o r reorientation of these groups about the 3-fold molecular axis, giving F(BF,')* 2.67 G 19  \i(Wj)ss  7.54 G . 2  2  and  However, the various intermolecular c o n t r i -  butions and F-H and H-F intramolecular contributionsSare more d i f f i c u l t to estimate, though not as c r i t i c a l , as t h e i r c o n t r i bution to the o v e r a l l values of the second moments are r e l a t i v e l y small.  Smith ( l ) records estimates made i n the l i t e r a t u r e ,  f i n d i n g reduction factors of 0.65 - 0.5 interactions and 0.42 - 0.25  f o r stationary-rotating  f o r rotating-rotating interactions.  Calculated second moments using t h i s range of reduction factors f o r rotating NH^ and stationary BF^ are given i n table V - l . o The agreement between these and the observed values at 77 K suggests that a t t h i s temperature  there i s perhaps some r e s i d u a l  motion (e.g. t o r s i o n a l o s c i l l a t i o n ) as indicated by the s l i g h t upward slope i n the second moment curve.  I t i s , however, d i f f i c u l t  to reconcile these values with the value of 25 G  2  f o r the  resonance at 90°K reported by Richards ( S i ) , although t h i s would perhaps seem somewhat large even f o r a r i g i d l a t t i c e from the structure of Hoard (2).  There i s a s i m i l a r large difference  i n the ^H values at room temperature.  The values reported here  were invariant within experimental error over several d i f f e r e n t samples, and the experimental procedure gave good agreement with the r e s u l t s of Richards (11) and Caron et a l . (13) on the related system BF ~ NH* *  4  *  4  A private communication from Dr. D.F.R. Gilson (McGill University) reports that he and Mr. C T . Yim have found values f o r the BF3.NH3 complex system i n disagreement with those reported by Richards (13) and i n very substantial agreement with those reported here.  - 53 Reorientation of both the BF-j and NH^ groups around the 19 3-fold molecular axis leads to a reduction i n the calculated second moment to ( 4 . 1 - 5.2)G  2  and the  F  second moments to  (9 - 10.1)G which are (table l ) i n reasonable agreement with 2  the observed values after the transition. The second moments observed experimentally are then consistent  the  with^transition and associated activation energy being for the reorientation —  non reorientation around the molecular axis  of the BF^ group i n the complex while the NH^ group i s rotating at a l l temperatures down to 77°K, the small changes in the % resonance being due to a reduction i n the F-H contributions to the ^"H second moment.  The X-ray structure shows no evidence of motion  at a l l at room temperature^suggesting strongly a "jump" mechanism for the reorientation process (ie. the Frenkel model). ii)  Molecular Motion i n BF3.NC-CH3 The  1 9  F and hi resonance i n the above complex show changes  with temperature similar to those described abov% for the BF^.NH^ complex, but with the transition at a much lower temperature. a)  Linewidth Variations 19  1  The variations i n linewidth of both the H and  F  resonances with temperature are shown i n f i g . ( 1 4 ) , the curve i n the region of the transition at around 130°K being a least squares f i t as before i n terms of an approximate activation energy.  The activation energy obtained i n this way (Ea=s 3 . 4 *  0.4 keal/mole) i s significantly lower than that for BF^.NH^, i n agreement with the lower transition temperature.  From a comparison  10  P  19,  Fs>B  O  N^C—C<JH  F" LINEWIDTH  \°  CHANGES rl  CALCULATED  b  1  d  **H  CURVE  E  =3-4±0-5k.cal.m.  b 1 \ Q \  op o "CT  o o 40  80  120  160  200  TEMR(°K) Figure 1 4 1  H and  19  240  280  • '  •  320  360  400  F line widths as a function of temperature for borontrifluoride-acetonitrile.  9 CD  80  120  160  200  240  TEMP (°K)  280  320  360  400  H,  •  Figure 15  I .  •  T> TO  •'•H and  1  9  F s e c o n 3  moments as a function of temperature f o r b o r o n t r i f l u o r i d e - a c e t o n i t r i l e .  ®  54  -  -  of the two X-ray structures, i t has been suggested that the much closer packed structure of BF^NH^ i s due to intermolecular F-H bonding.  The differences i n the a c t i v a t i o n energies and t r a n s i t i o n  temperatures reported here r e f l e c t this closer packed structure and are i n accord with some degree of intermolecular i n t e r a c t i o n , but cannot be considered substantial evidence i n favour of H-bonding as the s p e c i f i c i n t e r a c t i o n . b)  Second Moment Measurements  19  1 The v a r i a t i o n s of the second moments of both the ni and  F  resonances with temperature are shown i n f i g . (15). Below temperatures of about 126°K, saturation i s a serious problem with the 19 F resonance, making accurate measurement of second moments impossible by steady state methods. I t i s thought that at t h i s 19 temperature, the second moment of the  F resonance i s i n excess  2 of 18 G .  The observed values are compared with t h e o r e t i c a l  values calculated from the structure of Hoard et a l . ,(3) i n table V-2. Calculations of second moments were carried out using the Van Vleck formula as before, contributions from distances> 8? being estimated by an i n t e g r a l .  The value of the CH bond length  assumed (3) i n the X-ray data (1.07&) i s somewhat less than that normally used f o r CH bonds, and the calculations were made using a CH bond length of 1.09A. for a r i g i d l a t t i c e are: H-F = .03, F-H ao 1.69,  F-H a .02;  The various i n d i v i d u a l contributions  INTRA H-H at 22.0,  INTER H-H = .60,  B-Fss 0.5, B-H ss .13.  F-F-r 5.38,  F-F % .93, H-F «•  B-F ar-13.70, 1.90,  Approximate reduction factors  were used i n estimating the intermolecular contributions as before.  Table V-2  Calculated  8  and Observed second moments (gauss ) f o r 2  b o r o n t r i f l u o r i d e - a c e t o n i t r i l e complex  19 BF^NCCH^  Calculated  S  21.89  S  S  c  R  c  21.13-20.94  R  c  R  c  3.73-3.26  a.  1 H resonance  F resonance Observed  Calculated  Observed  24.34 >18.0 (77°K) 3.4 (180°K)  6.89-6.59  6.5 (77°K)  6.48-6.08  5.0 (180°K)  Calculated from reference (3) except C-H bond length was increased t o 1.09 X.  b.  S sc S t a t i o n a r y , R sr R e o r i e n t a t i n g  c.  Approximate reduction f a c t o r s used f o r intermolecular c o n t r i b u t i o n s . The correspondence between the observed and c a l c u l a t e d second  moments i n t a b l e V-2 i s consistent with the t r a n s i t i o n being f o r BF^ r e o r i e n t a t i n g - BF^ r i g i d , while the CH^ group i s r o t a t i n g at a l l temperatures down t o 77°K.  Again there i s no evidence f o r  r o t a t i o n from X-rays, suggesting a "jump" mechanism f o r the r e o r i e n t a t i o n process. i i i ) Molecular Motion i n BF^.Pyridine There i s l i t t l e change i n the ^tt resonance of thi3  complex  between room temperature and 77 K. There a r e , however, large changes G  19 i n both the l i n e w i d t h and second moments o f the  F absorption  at about 100°K. f i g . ( l 6 ) . The l i n e w i d t h t r a n s i t i o n i n f i g . (l6)  1 9  Figure 16 F linewidths and second moments as a function of temperature for borontrifluoride^pyridine.  CM—  CO CO  18  r  11< F R E S O N A N C E o  —  SECOND MOMENTS LINEWIDTHS  § 12  o o  '  CALCCURVE, E = 2 - 3 t O - 4 k . c o l ^ !  LU  co  10  "2 o  co  8  CO  Z)  <  —  6  ^  4  X  LU  80  120  160  2 0 0  TEMR (°K)  2 4 0  280  320  3 6 0  - 56 was f i t t e d as before using the modified BPP equation, g i v i n g E  a  s 2.3 ± 0.4 keal/mole.  That t h i s a c t i v a t i o n energy i s  smaller than those of the preceding two complexes i s consistent with the lower temperature a t which the t r a n s i t i o n occurs. T h e o r e t i c a l values f o r the second moments were computed as before from the c r y s t a l s t r u c t u r e reported by Zvonkova (4) and are compared w i t h the observed values i n t a b l e V-3. A CH bond length o f 1. 08 was used f o r the p y r i d i n e r i n g hydrogens as suggested by Zvonkova (4,i&).  The t h e o r e t i c a l values f o r a  completely r i g i d l a t t i c e are F = 1 9  16.6 G  and ^H = 15.8 G .  2  2  Using approximate reduction factors as before, these can be recomputed f o r motion of the BF^ group around i t s 3 - f o l d a x i s (table V-3). There i s reasonable agreement i n the two values f o r the 19  1  F resonance, but poor agreement i n the H values. However, the major c o n t r i b u t i o n t o the computed ^H second moment ( 9*5 G ) comes from a s i n g l e type of intermolecular H-H contact between p y r i d i n e rings i n d i f f e r e n t u n i t c e l l s , the hydrogen p a i r s being separated by the unusually s m a l l distances 1.72 and 1.86 A*. The two sets of r e s u l t s can be brought i n t o agreement i f one assumes that there i s a t o r s i o n a l o s c i l l a t i o n of the p y r i d i n e rings of about 20° about the B-N-C a x i s .  A simple t w i s t i n g of  the r i n g s (to about 15°) would give the same r e s u l t , but t h i s would seem t o be precluded by the X-ray data.  I t i s , however,  d i f f i c u l t t o understand why adjacent r i n g s should be coplanar w i t h r e s u l t i n g H-H separations o f 1.7 and 1.8/ X, values which 2  - 57 are s i g n i f i c a n t l y smaller than the vamder Waals diameter o f 2.4 H. (55) There may, however, be more c r i t i c a l contacts between non magnetic species i n the molecules which do not show up i n a resonance study, but make t h i s the p o s i t i o n of lowest p o t e n t i a l f o r the molecules as a whole. Table V-3  C a l c u l a t e d * and observed second moments (gauss ) f o r 2  b o r o n t r i f l u o r i d e - p y r i d i n e complex. F resonance B F  3°  Py  S R  S S  c  a.  c  b  Calculated  H resonance  Observed  Calculated  Observed  16.6  14.7(68°K)  15.8  6.8(77°K)  3.3-3.7  3.5(130°K)  14.3-14.6 5.5(120°K)  Calculated from the c r y s t a l s t r u c t u r e of Zvonkova, Sov. Phys. Crystallography 1, 54 (1956) using a C-H distance o f 1.0 A*, Zvonkova, Sov. P h y s J - Crystallography, 2, 403 (1957).  b.  S s Stationary, R  c.  Approximate reduction f a c t b  s  Rotating r s  used.  There i s some evidence f o r motion i n the temperature dependence of ^H resonance i n t h a t the second moment decreases w i t h i n c r e a s i n g temperature, dropping from 6.8 G  2  a t 77°K t o a value of 4.5 G a t 2  295°K. 19 Proton motion has no l a r g e e f f e c t on the F second jaoment due t o a r e l a t i v e l y small H-F intermolecular i n t e r a c t i o n , making 19 the  F spectrum r e l a t i v e l y i n s e n s i t i v e t o the hydrogen  co-ordinates  - 58 IQ and the agreement i n c a l c u l a t e d and observed F second moments i s reasonable. T h i s , and the large l i n e w i d t h changes, suggest that the motion observed i s the r e o r i e n t a t i o n - non r e o r i e n t a t i o n of the BF moiety while the p y r i d i n e r i n g i s r e l a t i v e l y f i x e d . 3 iv)  Molecular Motion i n BF^-NMe^ I n contrast t o the r e s u l t s f o r the preceding three complexes, 19  there i s no s u b s t a n t i a l change i n the  F resonance of s o l i d  BF^-NMe^ between room and l i q u i d nitrogen temperature.  There  are, however, very s u b s t a n t i a l changes i n the "*H spectrum, beginning a t about 150°K,fig. (17). The t r a n s i t i o n region c o n s i s t s o f two p a r t s ; f i r s t there i s a rather slow t r a n s i t i o n between 150°K and 100°K where the second moment r i s e s from O 2 2 G t o 8 G but the s i g n a l i s s t i l l a broad featureless curve, f i g . (I8)^and then a very sharp t r a n s i t i o n between 100°K and 70°K which involves an increase i n the % 2  second moment t o  o  30 i 3 G . At 68 K the t r a n s i t i o n seems t o be complete, the resonance having the general appearance of a s t a t i o n a r y three-spin system^fig. (18). A l e a s t squares f i t as before on the low temperature  l i n e w i d t h t r a n s i t i o n i n g . (17)^  y i e l d s an a c t i v a t i o n energy of 4.2 ± 0.5 k e a l m"  1  Although the second moment of the F resonance i s r e l a t i v e l y 1 9  i n v a r i a n t t o down t o 77 K, between 77 and 68°K i t increases from G  6.7 G  2  t o a value of 14 G . 2  This d i f f e r e n c e i s too large t o be  reasonably accounted f o r i n terms o f increased intermolecular H-F contributions and would seem t o i n d i c a t e that the BF^ moiety i s a l s o undergoing a motional t r a n s i t i o n a f t e r the second t r a n s i t i o n i n v o l v i n g the NMe^ moiety.  The temperature dependences o f the  second moments are shown i n t a b l e V-4.  t o follow page 58  C--H  /  M  H  H  H  RESONANCE SECOND. MOMENTS LINEWIDTHS CALC. CURVE  XX  80  120  150  200  TEMR (°K) Figure  E=4-2±0-5k.calm  -o—& 240  280  320  360  400  »  17  ^ H linewidths and second moments as, a function of temperature f o r borontrifluoride-trimethylamine.  to.follow page 58  H  RESONANCE  H  C - H  160  H /  ° K  /  N<iC-i  H  i-i  v  C - H H  H  /  V  / \  103 ° K  Y  V  /  f  /  /  68°!-  I*  t.\-'ty}<.>.("• !  •10  o  -J  10  SCAL.E (GAUSS) Figure 18 H lineshapes observed f o r borontrifluoride-trimethylamine at various temperatures.  Table V-4  Observed and C a l c u l a t e d second moments (gauss ) f o r 8  2  BF^ Trimethylamine Complex. 1 9  F resonance  resonance Calculated  Observed  S S  28 ± 2  30 ± 3(68°K)  R  R S  7.0 - 8.0  7.6 (109°K)  R  R R  1.6-2.5  2.0 ( 160°K)  a.  See t e x t .  b.  R * R o t a t i n g , S = S t a t i o n a r y , RS = methyls r o t a t i n g ,  BF,  NMe,  R  Calculated  3 i l  Observed  3 ( 100°K)  NMe^ s t a t i o n a r y , RR a methyls', r o t a t i n g , NMe^ r o t a t i n g The hydrogen p o s i t i o n s , which are not given by the X-ray determination ( 5 ) , w i l l be q u i t e c r i t i c a l i n determining the second moments. However, a s a t i s f a c t o r y q u a l i t a t i v e i n t e r p r e t a t i o n of the observed second moments can be given using the p o s i t i o n s o f some of the other atoms.  Such an approach  has been used very s u c c e s s f u l l y by Smith (7)  f o r a series  of s o l i d tetramethyl compounds. Using the approximations of Smith, the second moment f o r 2 a r i g i d CH^ group should be  22 G  and the c o n t r i b u t i o n from  other methyl groups both on the same molecule and elsewhere 6 ± 2 G , g i v i n g a r i g i d l a t t i c e ^H second moment o f 28 4: 2 G , 2  i n good agreement with the observed value of 30 * 3 G  2  (table  Further, Powles and Gutowsky (US) have i n t e r p r e t e d the lineshapes of s e v e r a l t h r e e - s p i n systems i n terms of an intra-methyl c o n t r i b u t i o n t o the second moment and a s i n g l e term corresponding t o  - 60 a l l other contributions t o the second moment. shape a t 68°K gives a value of 6 * 2 G  The observed l i n e -  f o r t h i s term, g i v i n g a 2  r i g i d l a t t i c e second moment o f 28 ± 2 G  i n agreement w i t h t h a t  found above by the approximations o f Smith. R o t a t i o n o f the methyl groups round t h e i r t h r e e - f o l d axes w i t h the r e s t of t h e molecule s t a t i o n a r y reduces the intra-methyl 2  c o n t r i b u t i o n t o 5.5 G . Using the approximate reduction f a c t o r s f o r i n t e r a c t i o n between two r o t a t i n g components as before, the other contributions are ( l . 5 4" 2.5)G , g i v i n g a t o t a l second moment 2 2  of (7.0 - 8.0)G , which i s i n good agreement w i t h the experimentally observed value o f 7.6 G  2  a t 100°K (table V-4).  Further good  evidence that t h i s t r a n s i t i o n involves r o t a t i o n of the methyl groups i s that the f i n e s t r u c t u r e observed a t 68°K disappears during the t r a n s i t i o n f i g . (18). R o t a t i o n of the whole NMe^ moiety round the B-N a x i s , assuming B-N-C =, 105°, f u r t h e r reduces the  second moment t o (1.6 - 2.5)G^ 2  i n good agreement w i t h t h e value of 2G  observed experimentally  f o r temperatures above 160°K. Using the B and F p o s i t i o n s given i h s t h e X-ray s t r u c t u r e , 19 2 an intramolecular F second moment of X5.04G i s c a l c u l a t e d f o r a r i g i d BF^ group.  This i s much l a r g e r than observed  experimentally except a t 68°K and suggests r o t a t i o n of the BF^ group a t temperatures above 77°K. c o n t r i b u t i o n f o r reduction  The reduced intramolecular  o f the BF^ group around i t s t h r e e - f o l d  o a x i s i s 2.1 G , i n reasonable agreement w i t h the experimental value o f 3 G  2  a t temperatures above 100°K, assuming the  difference t o come from intermolecular i n t e r a c t i o n s .  - 61 The t r a n s i t i o n s can then be r a t i o n a l i s e d i n terms of a model where at room temperature, both the BF^ and CH^ rotate round t h e i r three-fold axes and the NMe^  groups  rotates round  the B-N bond and, with decreasing temperature, f i r s t the stops, then the CH^ , then the BF^. ,S  NMe^  Although the molecule  approximates closer than previous one to a globular shape, the r o t a t i o n of the whole molecule i s s t i l l round the three-fold molecular axis.  At  373°K a narrow component appeared i n the  broadline spectrum, which grew as the temperature was At 391°K the remaining  increased.  broadline disappeared suddenly, leaving  a narrow l i n e with a linewidth and second moment determined by the modulation amplitude.  This t r a n s i t i o n at  confirmed using the DSC technique.  390°K was  It i s l i k e l y that the  t r a n s i t i o n i s to a p l a s t i c c r y s t a l phase (17), where i s o t r o p i c rotations occur, as w e l l as s e l f - d i f f u s i o n .  - 62 -  BIBLIOGRAPHY CHAPTER V 1 N.N. Greenwood and R.L. M a r t i n Quart. Rev., V.8 No. 1 (1954) 2 J.L. Hoard, S. G e l l e r , and W.M. Cashin Acta. Cryst.  396 (1951)  3 J.L. Hoard, T.B. Owen, A. B u z z e l l , and O.N. Salmon Acta, • Cryst. 3_, 130 (1950) 4 Z.V. Zvonkova Sov. Phys.  Crystallography 1, 54 (1956)  5 S. G e l l e r and J.L. Hoard Acta 6 S. G e l l e r and J.L. Hoard A c t a  Cryst. ^ :  399 (1951)  Cryst. 3_, 121 (1950)  7 G.W. Smith J . Chem. Phys. ^2, 4229 (1965) 8 G.W. Smith General Motors Res. Pub. No. G.M.R.-540 9 E.R. Andrew Phys. Rev. 92, 425 (1953) 10 J.H. Van Vleck Phys.i Rev. 2kt  l l 6  S (1948)  11 J.B. Leans and R.E. Richards Spectrochimica Acta. 10, 154 (1957) 12^ D. Pendred and R.E. Richards Trans. Farad. Soc. 5JL, 468 (1955) 13 A.P. Caron, D.J. Huettner, J.L. Ragle, L. Sherk, and T.R. Stengle J . Chem. Phys. /£, 2577 (1967) 14 A.V. Zvonkova Sov. Phys. Crystallography 2, 403 (1957) 15 L. P a u l i n g Nature o f the Chemical Bond 3rd E d i t i o n , C o r n e l l U n i v e r s i t y Press, Ithaca, N.Y. 260. (i960) 16 J.G. Powles, and H.S. Gutowsky J . Chem. Phys. 21, 1695 (1953) 17 J . Timmermans. J . Phys. Chem. S o l i d s 18, 1, (1961)  - 63 -  CHAPTER VI  TRIMETHYLAMINE-HALOGEN COMPLEXES 1.  Introduction Considerable interest has been shown, in recent years, i n  the structure and bonding i n charge-transfer complexes in which the trimethylamine moiety acts as the electron donor. With halogen acceptors such as iodine, bromine and iodine monochloride, the complexes formed are solids at room temperature.  Single  crystal X-ray measurements (1,2) indicate?that the nitrogenhalogen-halogen linkage i s essentially linear and that the nitrogen-halogen and halogen-halogen bond lengths are slightly larger than their "normal" convalent values.  Further impli-  cations of these studies, as well as additional experimental data, have been discussed and reviewed (3,4,5). The purpose of the present work was to investigate possible molecular motions about 77°K in the (NMe )-(Halogen) complexes 3 2 by the broadline NMR method. For comparison, a study was made of NMe^ i t s e l f between 77°K and i t s melting point, as at the time the work was done no literature results were available (see on). 2. i)  Experimental Materials Consistent results were obtained from the following method  of preparation of the complexes:  An ice-cold solution of trime-  thylamine i n absolute ethanol was added to an ethanolic solution of the appropriate halogen. Fine crystals of the complex separated from the solution immediately, and addition of the trimethylamine  - 64 s o l u t i o n was continued u n t i l the c h a r a c t e r i s t i c halogen colour disappeared.  The product c r y s t a l s were then f i l t e r e d , washed w i t h  dry ether and a i r d r i e d .  Two samples of each complex were thus  prepared; one sample was sealed i n a 10 mm od t h i n - w a l l e d glass tube under nitrogen.  The second sample was r e c r y s t a l l i z e d from  methylene c h l o r i d e at -40°C, d r i e d and sealed i n a s i m i l a r tube. The samples were a l l kept under l i q u i d nitrogen when not i n use, since there was some tendency towards decomposition at room temperature.  The thermal decomposition of the complexes has  been studied (6) and the products characterized.  One complex  i s a l s o reported t o be l i g h t s e n s i t i v e (2). Both samples of each complex gave analyses i n s a t i s f a c t o r y agreement w i t h the proposed s t r u c t u r e .  Complete temperature  runs were c a r r i e d out on both samples of each complex, and both gave i d e n t i c a l r e s u l t s . i i ) Equipment and Procedure Broadline spectra were obtained using a frequency of 30 MHz. 3. Results and Discussion i)  Molecular Motion i n Trimethylamine The changes i n l i n e w i d t h and second moment o f the proton  resonance l i n e of trimethylamine from 77°K up t o i t s melting point are shown i n f i g u r e (19).  I t i s evident from the temperature  behaviour of these parameters that a marked motional t r a n s i t i o n takes place, which i s q u i t e d i s t i n c t from the melting t r a n s i t i o n . At 77°K the spectrum showed the c h a r a c t e r i s t i c f i n e s t r u c t u r e of a broadened, r i g i d , three-spin system ( f i g . 19 i n s e t ) .  This f i n e  Figure 19  TEMP. (°Kl  - 65 structure disappeared a t about 110°K. The second moments change r e g u l a r l y from 30.5 gauss a t 77°K t o 2.7 gauss a t 140°K. The 2  2  general properties of the t r a n s i t i o n are s i m i l a r t o those reported r e c e n t l y by Haigh and co-workers (8).  However, although there i s  good agreement i n the reported l i n e w i d t h s , there i s a s i g n i f i c a n t d i f f e r e n c e i n the l i m i t i n g high-temperature second moment values (4.7 gauss from reference (8) c . f . 2.7 gauss i n the present 2  2  study), which w i l l be important i n determining the i n t e r p r e t a t i o n of the present r e s u l t s . i i ) Molecular Motion i n Trimethylamine-Bromine Complex (NMe^'B^). Linewidth and second moment changes with temperature are shown together w i t h some representative spectra i n f i g u r e (20). As i n the case o f trimethylamine, the c h a r a c t e r i s t i c f*»ine structure of the broadened three-spin system observed a t 77°K disappears at about 130 K near the l i n e w i d t h t r a n s i t i o n .  The second moment  changes r e g u l a r l y from a value of 27.7 gauss  2  G  a t 77°K t o 1.8 gauss  at 170°K and remains constant from t h i s temperature up t o room temperature.  The o v e r a l l shape o f the t r a n s i t i o n , and the  l i m i t i n g high and low temperature values of the linewidths and second moments, are very s i m i l a r t o those of trimethylamine itself. i i i ) Molecular Motion i n Trimethylamine-Iodine (NMe^-Ig) and Trimethylamine-Iodinemonochloride (NMe^-ICl)  Complexes.  Figures (21); and (22) show the l i n e w i d t h and second moment changes f o r NMe^'I^ and NMe^'ICl r e s p e c t i v e l y .  Again there are  l a r g e s p e c t r a l changes i n d i c a t i v e of motional t r a n s i t i o n s , but  2  Figure 20 Linewidths and second moments as a function of temperature f o r trimethylamine-Bij, and (inset)lineshapes observed at varinas temperatures.  100  200  TEMP.(°K)  300  Figure21  Liiiewidths and second moments as a function of temperature f o r t r i m e t h y l a m i n e - I and-(inset) lineshapes observed at various temperatures.  2  Figure 22  TEMP. (°K)  -  66  -  these are quite different from those of NMe^ i t s e l f and the NMe^'Br^ complex.  The spectra at 77° both show fine structure K  characteristic of a r i g i d three-spin system, and this disappears during the linewidth transition.  However, the linewidths and  second moments do not decrease directly to their limiting hightemperature values, but show an intermediate step with a second moment value of 7-8 gauss . 2  At h|igher temperatures, there i s a  second transition where the linewidths and second moments attain their limiting values (S.M.  s  1.7G , L.W. = 3.3G for NMe.j*I 2  2  and S.M. a 1.9G , L.W.« 3.3G for NMeylCl). 2  iv) Calculated Second Moments , Complete theoretical second moments cannot be calculated a priori using Van Vleck's formula (9) because of lack of structural data i n the solid state for NMe^ and NMe^'Br^ and the lack of data on the hydrogen co-ordinates of NMe^'I^ and NMe^'ICl whose structures are known. However, the data can be successfully interpreted by several more empirical approaches (table Vl-1). The relative hydrogen positions i n the four complexes are similar enough for the four molecules to be considered together. It i s convenient to divide the second moment into three contributions:  the contribution due to the interactions within a  methyl group - SI, from interactions between methyl groups on the same molecule - S 2 , and between methyl groups on different molecules - S3. There are only two configurations of the hydrogens i n an NM^ moiety which are consistent with C^  symmetry:  a form  where three of the hydrogens are eclipsed with the C. atoms  - 67 and a form where they are staggered.  The former involves  hydrogen-hydrogen contacts less than the sum of the Vander Waals r a d i i , and only the l a t t e r i s considered.  Using t h i s assumption  and the microwave data f o r trimethylamine (10), the contributions S l and S2 can be calculated exactly for t h i s molecule ( S l  S2»  25.6 gauss ) . The contribution S3 can, however, only be estimated. A value of 6.5 gauss i n SiMe^ (11).  was found by Smith f o r the S3 contribution  Since there i s one fewer methyl group i n NMe^,  and nitrogen-methyl as w e l l as methyl-methyl contacts exist, an approximate reduction by a f a c t o r of £ may be reasonable, giving S3B  4 . 8 j t l gauss . Since S3 i s a r e l a t i v e l y small contribution  to the t o t a l , the exact value w i l l not be c r i t i c a l . p  The t o t a l  second moment f o r NMe^ w i l l then be 30.4i 2 gauss , i n good agreement with the experimental value of 30.5±1 gauss  2  (table V l - l ) .  It i s also possible to obtain some information about the r e l a t i v e magnitudes of the intramethyl and intermethyl second moment contributions from the f i n e structure of the resonance l i n e at 77°K (12), although i t i s not known to what extent the approximations used hold i n systems with a large intermethyl broadening.  gaus3  2  Assuming the intramethyl second moment of 23.6±1.2  calculated from the microwave parameters, the best f i t  to the observed lineshape (figure (19) inset) i s given by an 2 intermethyl second moment contribution of (5.3-6.3) gauss ,  o giving a t o t a l second moment value of 29.4*2 gauss . For the three halogen complexes, complete calculations can be performed  f o r trimethylamine-iodine and trimethylamine-iodine  monochloride, using the c r y s t a l structures.data (1,2), and assuming  - 68 that the hydrogen atoms can be placed t e t r a h e d r a l y around the carbons with a CH bond length of 1.09A* t o give an o v e r a l l C^ symmetry.  This procedure y i e l d s o v e r a l l second moments of o  2  28.18 gauss  and 29.29 gauss* f o r the i o d i n e and i o d i n e mono-  c h l o r i d e r e s p e c t i v e l y , i n good agreement w i t h the values found experimentally ( t a b l e V l - 1 ) .  Consideration of the lineshapes  at 77°K as before ( f i g u r e s X\ a n d M , i n s e t ) , t a k i n g the intramethyl c o n t r i b u t i o n as 23.6 gauss , gives t o t a l estimated second moments 2  2  of 2 8 * 1 gauss  f o r both complexes, i n approximate agreement  with the above values. In the case of the trimethylamine-bromine  complex, there a r e  no s t r u c t u r a l data a t a l l . However, i t lis expected t o have a structure s i m i l a r t o the other two complexes, and i t s second moment could be approximated  by using a value roughly equivalent t o t h e i r  values (^28 g a u s s ) .  There i s some j u s t i f i c a t i o n f o r t h i s i n the  2  s i m i l a r i t y of the second moments o f the above two complexes t o each other, and a l s o t o trimethylamine, and i n the f a c t that the experimental values are very s i m i l a r f o r a l l the complexes (table V l - 1 ) .  The i n t e r p r e t a t i o n of the lineshape a t 77°K can,  however, be made even though s t r u c t u r a l data are not a v a i l a b l e . Assuming only that the intramethyl c o n t r i b u t i o n i s 22.4 gauss o  g i v i n g a t o t a l second moment of 28 gauss , s i m i l a r t o the other complexes. v)  Motional E f f e c t s In the case of the motional t r a n s i t i o n s of trimethylamine  i t s e l f and i t s bromine complex figures (19,20), the l i m i t i n g high temperature second moments of 2.7 and 1.8 gauss  respectively  - 69 are  too low t o be explained simply by a r o t a t i o n of the methyl  groups around t h e i r t h r e e - f o l d axes.  The most s a t i s f a c t o r y model  would seem t o be one where the methyl groups are r o t a t i n g around t h e i r t h r e e - f o l d axes, and the whole molecule i s r o t a t i n g about the molecular t h r e e - f o l d symmetry a x i s .  The intramethyl reduction  factors may be c a l c u l a t e d f o l l o w i n g Powles and Gutowsky (12). Assuming an angle of 71.3° between the N-C bonds and the molecular symmetry a x i s f o r trimethylamine (10), the reduced c o n t r i b u t i o n i s 0.7 gauss2.  The corresponding value f o r bromine complex i s  a l s o 0.7 gauss . 2  The reduction i n the remaining contributions  f o r doubly r o t a t i n g groups i s more d i f f i c u l t t o estimate. Koide (13) has c a l c u l a t e d a reduction f a c t o r of £ f o r these i n t e r a c t i o n s i n hexamethylethane.  Using t h i s reduction f a c t o r y i e l d s intermethyl  second moments of 2.0 and 1.4 gauss , and t o t a l reduced second 2  moments of 2.7 and 2.1 gauss  2  f o r NMe^ and NMe^.B^ r e s p e c t i v e l y .  The s a t i s f a c t o r y agreement between these values and those found experimentally ( t a b l e V l - l ) i s taken as evidence that the motional t r a n s i t i o n i n these two species i s i n f a c t the onset of simultaneous r o t a t i o n of the methyl groups, about t h e i r t h r e e - f o l d axes, and the whole molecule about i t s molecular symmetry a x i s .  The r e c e n t  i n v e s t i g a t i o n of trimethylamine by Haigh and co-workers (8), r e f e r r e d t o i n the i n t r o d u c t i o n , gave a value of 4.6 gauss , and 2  was i n t e r p r e t e d  as motion of the methyl groups with p o s s i b l y a  c o n t r i b u t i o n from some other motion.  However, i t i s f e l t that the  experimental value quoted here i s i n accord both w i t h the c a l c u l a t e d reduced value, and w i t h the values found f o r the three halogen complexes (vide i n f r a ) .  - 70  -  I n the cases of the complexes with iodine and iodine monoc h l o r i d e figures (21,22), the f i r s t motional transitiomireduces the second moments t o 7-8 gauss . 2  This value i s i n accord w i t h  a r e o r i e n t a t i o n of the methyl groups about t h e i r t h r e e - f o l d axes, the r e s t of the molecule being s t a t i o n a r y .  Such a motion would  reduce" the intramethyl c o n t r i b u t i o n by a f a c t o r of  and the  intermethyl c o n t r i b u t i o n by a f a c t o r of 0.25 - 0.42 (13), 2 a t o t a l reduced second moment of 7-8 gauss  giving  f o r both complexes,  i n s a t i s f a c t o r y agreement w i t h the experimentally observed values. The second m o t i o n i a l t r a n s i t i o n causes the second moments t o o  drop t o 1.8 gauss* i n both cases, and can be i n t e r p r e t e d as the onset of motion of the whole molecule around the molecular symmetry axis ( t a b l e V l - l ) g i v i n g a reduced second moment of 2 1.7 gauss  as discussed above f o r the bromine  complex.  Thus (table V l - 1 ) , two d i s t i n c t types of behaviour are observed.  In NMe^ and NM^-Br , the methyl group r o t a t i o n and 2  the r o t a t i o n of the whole NMe^ moiety seem t o be very s t r o n g l y coupled, and only one l i n e w i d t h t r a n s i t i o n i s observed.  This  type of motional t r a n s i t i o n i s s i m i l a r to that observed f o r Me CBr, Me^CCl (12) and Me^C-CMe^ (13). 3  I n the NMe^'Ig and NMe^vICl complexes, however, the methyl group r o t a t i o n and NMe^ r e o r i e n t a t i o n take place i n two q u i t e d i s t i n c t steps.  This type of behaviour i s observed f o r NJ^-BF^  ( 7 ) , Me^S I~, Me.jS0 I~, Me^NO (14) and has a l s o been observed +  +  r e c e n t l y i n s e v e r a l complexes of the type NMe^'BX^ (15).  The  reasons f o r t h i s d i f f e r e n c e i n behaviour are d i f f i c u l t to determine.  Unfortunately, i n most cases the c r y s t a l s t r u c t u r e s  - 71 — are not known, and no c o n c l u s i o n s can be drawn about s t r u c t u r a l d i f f e r e n c e s , which might account f o r those e f f e c t s . The? X-ray i n v e s t i g a t i o n s of these complexes 3how no evidence of motion which t h e NMR i n d i c a t e s i s t a k i n g place a t room temperature. Thus, i n these complexes, t h e motion must take p l a c e a t room temperature.  Thus, i n these complexes, the motion must take place  by a "jumping" mechanism between e q u i v a l e n t methyl s i t e s .  In  view of the s t r u c t u r a l s i m i l a r i t i e s between the compounds and the s i m i l a r i t i e s i n t h e i r s p e c t r a , t h i s i s probably tnso compounds s t u d i e d .  f o r a l l the  I n view o f the molecular motions found, however,  i t would seem t h a t t h e d i f f e r e n c e s i n bond lengths and angles t o the d i f f e r e n t methyl groups found i n t h e complexes (1,2) a r e not r e a l , but may be due t o t h e e r r o r s i n h e r e n t i n the two dimensional analysis,  vi)  A c t i v a t i o n energies A c t i v a t i o n energies were c a l c u l a t e d f o r a l l the m o t i o n a l  t r a n s i t i o n s observed by a l e a s t square f i t t i n g o f t h e l i n e w i d t h t r a n s i t i o n s t o t h e m o d i f i e d Bloeriibergen, P u r c e l l and Pound r e l a t i o n s h i p (16).  These are shown i n t a b l e V l - 2 t o g e t h e r w i t h t h e d e s c r i p -  t i o n o f t h e t r a n s i t i o n s d e r i v e d above.  Good f i t s were obtained i n  a l l cases, but t h e r e s u l t s must be approached w i t h some degree of caution.  F i r s t l y , t h e r e l a t i o n s h i p - u s e d i s an e m p i r i c a l ono, and  the energies i t gives have no a b s o l u t e s i g n i f i c a n c e except f o r purposes o f comparison w i t h i n a s e r i e s o f r e l a t e d compounds. Furthermore,  i n t h e compounds s t u d i e d here, t h e r e i s a severe  change i n l i n e s h a p e which accompanies the l i n e w i d t h narrowing and i n some cases, d i f f e r e n t m o t i o n a l e f f e c t s overlapped.  For  TABLE VI-1:  Observed second moment values (gauss ) above and below motional t r a n s i t i o n s f o r NMe^, NMe^'Br^, NMe and NMeo'ICl, and calculated values f o r d i f f e r e n t molecular motions. 2  NMe^  NMe^'B^  MOTIONAL TYPE  Obs.  Calc.  RIGID LATTICE  30.5  3 0 . 4 ± 2 . 0 77°K  METHYL ROTATION  a  Temp.  Obs.  27.7  Calc.  NMe^'^  a  28.0±2.0  Temp.  Obs.  Calc.  77°K  27.1  7-8  —  NMeo'ICl  Temp.  Obs.  Calc.  28.18  77°K  28.0  2 9 . 2 9  77°K  7-8  148°K  7-8  7-8  195°K  1.7  2.1  295°K  a  a  Temp.  -  METHYL ROTATION AND ROTATION ROUND NC, SYM. AXIS.  2.7  2.7  143°K  1.8  2.1  170°K  1.7-1.9  J  a See text f o r details of the assumptions and approximation involved.  2.1  295°K  - 73 t h i s reason, an even more empirical estimate of the energies using the Waugh estimate (17) of V o =  37T (where T i s the temperature  of the t r a n s i t i o n ) i s also included i n the table. f o r the a c t i v a t i o n energies f o r methyl  The high values  group rotation would tend  to suggest that quantum mechanical tunneling through the potential b a r r i e r s to rotation i s r e l a t i v e l y unimportant i n the cases studied here. The b a r r i e r t o methyl group rotation i n NMe^ by a number of methods (10, 18, 19).  has been found  Thus a themodynamic study,  assuming a one dimensional p o t e n t i a l energy b a r r i e r , yielded a value of 4.27  keal/mole"  1  (18).  A value of 4.4  keal/mole  -1  was found from a study of the v i b r a t i o n a l s a t e l l i t e s i n the microwave spectrum (10), and an i n f r a - r e d study of NMe^ yielded values of 4.13  - 5.19  chosen f o r the b a r r i e r .  keal/mole  -1  at 77°K (20)  depending on the model  TABLE VT-2: Motional types, l i m i t i n g linewidths (gauss) and a c t i v a t i o n energies (keal/mole" ) derived from the modified BPP equation and a c t i v a t i o n energies (keal/mole~l) estimated from Waugh's equation.  SAMPLE  NMe  MOTIONAL  LOW TEMP. LINEWIDTH  HIGH TEMP. LINEWIDTH  Ea (MOD. BPP)  Ea (WAUGH EST.)  CH  3  NMe^  19.0  4.0— 4.5  NMe *Br 3 2  CH  3  NMe  18.0  3.4  6.8^0.5  5.1  NMe ' I 3 2  CH  3  17V8  7.2  6.9±0.4  4.4  7.2  3.3  9.5*1.0  5.4  17.9  6.6  6.2±0.5  5.6  6.0  3.3  11.0 ±1.3  7.8  3  NMe *IC1 3  3  NM e CH  3  NMe 3  (6.6-8.4)±0.5  a Value i s very dependent on the value of the l i m i t i n g l i n e w i d t h .  a  4.25  * 75 -  BIBLIOGRAPHY CHAPTER VI 1„ K.O. Str^mme Acta. Chem. Scand. 1/3, 268 (1959) 2 0. Hassel and H. Hope Acta. Chem. Scand. l ^ , 391 (i960) 3 0. Hassel and Chr. Ramming Quart. Rev. 16, 1 (1962) 4  C.K. Prout and J.D. Wright Angew. Chemie. (International Edition) 7, 659 (1968)  5 H.A. Bent Chem. Rev. 68, 587 (1968) 6 H. Bohme and W. Krau3se Ber. 84, 170 (1950) 7  B.A. Dunell, CA. Fyfe, CA. McDowell and J.A. Ripmeester Trans. Farad. Soc. 65, 1153 (1969)  8 P.J. Haigh, P.C Canepa, G.A. Matzkanin and T.A. Scott, J . Chem. Phys. 48, 4234 (1968) 9  J.H. Van Vleck Phys. Rev. 74, 1168 (1948)  10  D.R. Lide and D.E. Mann J. Chem. Phys. 28, 572 (1958)  11  G.W. Smith J . Chem. Phys. 4J2, 4229 (1965)  12  J.G. Powles and H.S. Gutowsky J. Chem. Phys. 2|, 1695 (1953)  13  T. Koide Bull. Chem. Soc. Japan £0, 2026 (1967)  14  G.A. Fyfe and J.A. Ripmeester, unpublished work.  15  D.F.R. Gilson and C.T Yim, personal communication.  16 H.S. Gutowsky and G.E. Pake J . Chem. Phys. ig,  162 (1950)  17  J.S. Waugh and E.I. Fedin Sov. Phys. Solid State  1633 (1963)  18  J.G. Aston, M.R. Sagenkahn, G.J. Szasz, G.W. Moesser and H.F. Zuhr, J.A.C.S. 66, 1171 (1944)  19  T.D. Goldfarb and B.N. Khare J. Chem. Phys. 4£, 3379 (1967)  - 76 -  CHAPTER VII  ARENE-CHROMIUM-TRICARBONYL COMPOUNDS  1.  Introduction Compounds o f the sandwich type have been extensively studied  e s p e c i a l l y using X-ray methods ( l ) with the point of view of elucidating the structure and bonding.  S o l i d state NMR studies  have been performed on a number of compounds of the TT-cyclopentadienyl type, both diamagnetic ( 2 ) and paramagnetic  ( 3 ) systems.  These studies revealed that b a r r i e r s to the r o t a t i o n of the rings around an axis perpendicular to the r i n g plane were quite low, of the order of 0 . 9 - 2 . 3 kcal/mole. X-ray studies have been performed on a number of arene-chromiumt r i c a r b o n y l compounds (6,7).  An e a r l i e r study (4) on dibenzene-  chromium revealed a d i s t o r t i o n of the r i n g from s i x - f o l d symmetry, but t h i s was l a t e r shown not t o be so (5). the arene-chromium-tricarbonyl compounds  The X-ray studies on (6,7) were performed  i n order t o see i f the aromatic rings i n the3e compounds would show any d i s t o r t i o n s from s i x - f o l d symmetry due t o p r e f e r e n t i a l bonding of the metal t o the rings.  S o l i d state NMR studies of these  compounds were thought t o be i n t e r e s t i n g , since the motional properties of the rings i n the compounds could then be compared with those of the free rings, 2.  Experimental  i)  Compounds Benzene-and Mesitylene-Chromium-Tricarbonyl were obtained from  A l f a Inorganies and were used without further p u r i f i c a t i o n .  - 77 The Hexamethylbenzene-chromium-tricarbonyl was prepared by heating together hexamethylbenzene  ( A l d r i c h Chemical Co.) and  Chromium Hexacarbonyl ( A l f a I n o r g a n i e s ) , i n dimethoxyethane ( 8 ) . The compound was p u r i f i e d chromatographically.  F i n a l traces of  solvent were removed by heating under vacuum at 50°C. i i ) Instrumental Broadline spectra were obtained as described p r e v i o u s l y using frequencies o f 16 and 5614 MHz. T^ measurements were made using the two-pass ARP method at a frequency of 8 MHz. 3. Results and Discussion i)  Benzene-Chromium-Tricarbonyl The CW NMR r e s u l t s are shown i n f i g u r e (23). The second moment  was 6.2 gauss a t 77°Kj a l i n e w i d t h and second moment change was 2  evident near 100°K. Above the t r a n s i t i o n the second moment was 1.2 gauss and decreased slowly t o a value o f 0.9 gauss a t room 2  2  temperature. The c r y s t a l s t r u c t u r e of benzene-chromium-tricarbonyl has been determined (7). No evidence o f any d i s t o r t i o n from s i x - f o l d symmetry of the r i n g was found.  A Fortram IV program was w r i t t e n t o c a l c u l a t e  the intramolecular second moment c o n t r i b u t i o n and a l s o the i n t e r molecular c o n t r i b u t i o n l e s s than 5 & using the proton coordinates given i n the X-ray study. Values found were 3.7 gauss and 1.6 2  gauss . 2  Contributions from distances greater than 5 A* were 2  estimated by an i n t e g r a l , g i v i n g a value of 0.4 gauss . The t o t a l r i g i d l a t t i c e second moment found then i s 5.7 gauss . I f 2  one considers that t h e X-ray s t u d y was made a t room temperature,  - 78 -  the d i f f e r e n c e between the c a l c u l a t e d r i g i d l a t t i c e second moment and the experimental second moment a t 77°K may be explained by lattice  contraction.  The most common gotion of rings of t h i s type i s a r e o r i e n t a t i o n of the rings about an a x i s at r i g h t angles t o the r i n g plane.  A  motion of t h i s type reduces the intramolecular second moment c o n t r i 2 bution by a f a c t o r of 4, g i v i n g a value of 0.92 gauss . The reduction f a c t o r f o r the intermolecular  c o n t r i b u t i o n may be estimated  to be the same as that used f o r benzene, where a value of 12 was calculated (9).  Using t h i s reduction f a c t o r , a c o n t r i b u t i o n of  2  0.17 gauss  9  i s found, g i v i n g a t o t a l second moment of 1.09 gauss  for rotating rings.  This i s i n s a t i s f a c t o r y agreement with the  experimental second moment of 1.2 gauss  above the t r a n s i t i o n .  These r e s u l t s then are consistent then with the benzene rings r o t a t i n g at frequencies greater than 105 Hz above a temperature of approximately  120°K. Since no motions except f o r v i b r a t i o n s  e t c , were observed i n the X-ray s t r u c t u r e , the r e o r i e n t a t i o n takes place between equivalent  p o s i t i o n s , i n agreement with the  model, as described previously.  Frenkel  The a d d i t i o n a l decrease i n  second moment t o 0.9 gauss^ a t room temperature i s most l i k e l y due t o a d d i t i o n a l v i b r a t i o n s , o s c i l l a t i o n s , e t c . The T values measured are shown i n1 f i g u r e (24a). A simple T^ , minimum can be seen i n the l o g T^ v s . /T curve, as predicted by 1  eqn.  (15) i n Chapter I f o r an a c t i v a t e d d i p o l a r r e l a x a t i o n process.  C o r r e l a t i o n times were c a l c u l a t e d and these are presented i n f i g u r e (24b).  The r e s u l t s can be f i t t e d reasonably w e l l by a  s t r a i g h t l i n e , with the a c t i v a t i o n energy obtained from the slope  •479 being 3.6 kcal/mole.  This i s somewhat l e s s than the value found  f o r benzene i t s e l f , 3.90 kcal/mole (10). A c t u a l l y the l i n e w i d t h , second moment and a l s o the s p i n - l a t t i c e r e l a x a t i o n time r e s u l t s f o r the benzene-chromium-tricarbonyl f o r benzene i t s e l f .  resemble the r e s u l t s obtained  There i s a reduction i n the intermolecular  second moment c o n t r i b u t i o n which r e f l e c t s the decrease i n the i n t e r a c t i o n s between protons on d i f f e r e n t r i n g s .  At f i r s t i t  may seem s u r p r i s i n g that i n view of t h i s decrease the r e o r i e n t a t i o n a l b a r r i e r value i s approximately the same as the value found f o r benzene i t s e l f .  However, from the c r y s t a l s t r u c t u r e i t i s evident  that van der Waals  1  contacts are present which probably contribute  t o the b a r r i e r heightj there i s an 0-H contact a t 2.58 8 and a benzene C-0 contact a t 3.1 At t h i s point the p o s s i b i l i t y that the e n t i r e complex molecule reorientates about i t s t h r e e - f o l d a x i s has been neglected.  From  the geometry of the complex t h i s seems a rather u n l i k e l y s i t u a t i o n s i n c e the carbonyl groups s t i c k out w a l l beyond the benzene r i n g i n the plane at r i g h t angles to the molecular t h r e e - f o l d a x i s . P r e v i o u s l y (16) i t was shown that independent r i n g r o t a t i o n takes place i n a r e l a t e d system.  Broadline NMR studies on b i s (cycle—  pentadienyl-molybdenum-tricarbonyl)  showed that some type of  molecular motion took place, and the geometry of the complex precluded a l l types of motion except intramolecular r i n g r o t a t i o n . Most l i k e l y independent  r i n g r o t a t i o n takes place i n the benzene-  chromium-tricarbonyl as w e l l . ii)Mes itylene-Ghromium-Tricarbonyl Linewidths and second moments d i d not show any major changes between 77°K and the melting point near 450°K.  Second moments were  9.6 gauss a t 77°K and 8.9 gauss2 a t room temperature. 2  The c r y s t a l  s t r u c t u r e of t h i s compound i s not known, but by comparing the experimental r e s u l t s f o r the mesitylene complex w i t h those f o r free mesitylene, (11,12) relevant information about p o s s i b l e types of molecular motional models may be obtained. The r i g i d l a t t i c e second moment c a l c u l a t e d f o r mesitylene was 2 4 i 2 gauss  2  (12), o f which 18 gauss were due t o intramolecular  contributions.  2  However, i t was found that the experimental second  moment remained constant a t 10 gauss between 4°K and the melting 2  point.and i t was then concluded that the methyl groups were mobile 2 and a second moment of 9^6 2 gauss (12).  was c a l c u l a t e d f o r t h i s s i t u a t i o n ,  I f i t i s assumed that the intermolecular second moment  c o n t r i b u t i o n increases somewhat on going from the complex t o the free r i n g compound, the experimental second moment value at 77°K f o r the mesitylene-chromium-tricarbonyl i s not i n c o n s i s t e n t with the presence of methyl group r o t a t i o n .  I n the mesitylene study  no motions except methyl group r o t a t i o n was found t o be present and a l s o a very low frequency motion observed by T-^^j  methods (12)  j u s t below melting p o i n t . From the small decrease i n second moment from 77°K t o room temperature i t i s l i k e l y that s m a l l amplitude o s c i l l a t i o n s are t a k i n g place i n the complex. iii)  Hexamethylbenzene-chromium-Tricarbonyl Second moment and l i n e w i d t h v a r i a t i o n s with temperature are  shown i n . f i g u r e (25). At 77°K, the second moment was 11.8 gauss and remained a t t h i s value u n t i l a t r a n s i t i o n occured between 150°K and 230°Kj the l i m i t i n g high temperature second moment p was 2.0 gauss .  2  - 81 A c r y s t a l s t r u c t u r e f o r t h i s compound i s a v a i l a b l e (6) but no hydrogen p o s i t i o n s were found.  The authors note a twofold  d i s t o r t i o n of the hexamethylbenzene r i n g , but i n a recent review ( l ) some doubt was expressed as t o the r e a l i t y of t h i s d i s t o r t i o n . Extensive NMR data on hexamethylbenzene i t s e l f are a v a i l a b l e (12,13-15), so t h a t relevant conclusions may be drawn by comparing r e s u l t s f o r the two compounds. Hexamethylbenzene  r e s u l t s have been obtained down t o 2°K, and  above t h i s temperature the second moment i s always much l e s s than the predicted r i g i d l a t t i c e second moment of 32.7 gauss (13). 2  From t h i s i t was concluded that methyl group r o t a t i o n took place, andthe second moment c a l c u l a t e d f o r t h i s s i t u a t i o n was found t o be 16.4 gauss . Experimental second moment values between 50 K and 150°K were obtained v a r i o u s l y as about 13-14 gauss (13-15), 2  consistent w i t h methyl group r o t a t i o n plus some a d d i t i o n a l motion, probably l a t t i c e v i b r a t i o n s and o s c i l l a t i o n s .  B y t a k i n g i n t o account  a s m a l l decrease i n the intermolecular c o n t r i b u t i o n , the second moment of the complex compound may be explained by having present the same types of motion as f o r the f r e e  hexamethylbenzene.  •Second moments showed a decrease between 150°K and 210°K to a value of 2.5 gauss  f o r hexamethylbenzene, and t h i s values i s  consistent w i t h t h e e n t i r e r i n g r o t a t i n g around i t s hexad a x i s . The a c t i v a t i o n energy f o r t h i s motion was found t o be 6.7 kcal/mole from T^ measurements (13). Again a s i m i l a r motion w i l l e x p l a i n the second moment value of t h e complex compound at temperatures greater than 220°K.  I f the Waugh estimate f o r the a c t i v a t i o n  energy i s used, namely Va- 37T, where T i s the l i n e w i d t h t r a n s i t i o n temperature, approximately equal a c t i v a t i o n energies o f 6.6 Kcal/mole  - 82 are found f o r hexamethylbenzene and the complex, i n good agreement with the value found from  measurements (13).  Linewidth and  second" moment t r a n s i t i o n s are again quite s i m i l a r f o r the complexed and f r e e r i n g s , as noted before f o r the 'benzene' case. I n the X-ray studies mentioned on the  arene-chromium-  t r i c a r b o n y l (6,7) i t was suggested that the coordination of the c e n t r a l metal atom may be thought of as octahedral.  Three a l t e r -  nate carbons on the r i n g may then be regarded as "bonding" s i t e s . Now f o r benzene and hexamethylbenzene the s e l e c t i o n of the three bonding s i t e s i s not important as only one type of rotamer e x i s t s . However, i f such s p e c i f i c bonding was important, some d i s t o r t i o n from s i x - f o l d symmetry would be expected, most l i k e l y a t h r e e - f o l d distortion.  No such d i s t o r t i o n was evident i n the X-ray s t u d i e s ,  and the NMR studies i n d i c a t e motional properties s i m i l a r t o those of the f r e e aromatic r i n g compounds.  Any s p e c i f i c bonding e f f e c t s ,  then, i n the symmetric rings a t l e a s t , are of the same order of magnitude as c r y s t a l packing f o r c e s . Now i n the case of mesitylene, two possible rotamers e x i s t . One rotamer has the bonding s i t e s a t the carbons to which the methyl groups are attached and the other has the bonding s i t e s at the remaining three carbons.  I t has been proposed (16) that  since the m e t a l - t r i c a r b o n y l moiety has e l e c t r o n withdrawing p r o p e r t i e s (18), the rotamer with the bonding s i t e s at thee carbons w i t h the methyl groups should be more s t a b l e since methyl groups have e l e c t r o n r e l e a s i n g p r o p e r t i e s .  However, s o l u t i o n NMR  studies  (17) on para and meta-xylene-chromium-tricarbonyl between -30°C and o , . 35 C y i e l d e d only averaged spectra. The authors (17) concluded then  - 83  -  that f o r the p-xylene complex, where two types of rotamers are p o s s i b l e , the b a r r i e r to r e o r i e n t a t i o n should be l e s s than 10 kcal/mole. The broadline NMR  study showed that the mesitylene r i n g i n  the complex compound d i d not r o t a t e i n the s o l i d phase.  Unfortu-  n a t e l y , mesitylene i t s e l f shows s i m i l a r behaviour, although the melting point i s much lower, near 220°K; the b a r r i e r t o r e o r i e n t a t i o n i n t h i s case i s i n t e r m o l e c u l a r i n o r i g i n .  In the complex  compound, u n f o r t u n a t e l y no d e c i s i o n can be made as t o what proport i o n of the b a r r i e r i s i n t r a m o l e c u l a r i n nature. We can conclude, then, that t o a good approximation the r i n g s i n the complex compounds behave much l i k e the free r i n g compounds themselves.  For the benzene and hexamethylbenzene complexes i t  may be s a i d that s p e c i f i c bonding e f f e c t s are probably q u i t e small. The upper l i m i t of the c o n t r i b u t i o n t o the r o t a t i o n a l b a r r i e r due to s p e c i f i c bonding e f f e c t s should not be greater than a few kcal/mole.  No conclusions about s p e c i f i c bonding can be reached  f o r the mesitylene complex from the broadline resonance  studies.  - 84 -  BIBLIOGRAPHY CHAPTER V I I 1  P.J. Wheatley Perspect. S t r u c t . Chem. 1,-1.1 (1967)  2  C H . Holm and J.A. Ibers J . Chem. Phys. 3j0, 885 (1959)  3  H. Nakajima Nuclear Magnetic Resonance and Relaxation i n S o l i d s , ed. L. van Gerven North Holland P u b l i s h i n g Co. Amsterdam, 1965 p. 259  4  F. J e l l i n e k J . Organometallic Chem. 1, 43 (1963)  5  F.A. Cotton, W.A. Dollase and J.S. Wood J.A.C.S. 85, 1543 (1963)  6  M.F. B a i l y and L.F. Dahl Inorg. Chem. 4, 1298  7  M.F. B a i l y and L.F. Dahl Inorg. Chem.  (1965)  1314 (1965)  8- B. N i c h o l l s and M.C. Whiting J . Chem. Soc. 551 (1959) 9  E.R. Andrew and R.G. Eades Proc. Roy. Soc. A218, 537 (1953)  10  J.E. Anderson J . Chem. Phys. 4^3, 3775 (1965)  11 12  E.R. Andrew J . Chem Phys. 18^ 607 (1950) G.P. Jones, R.G. Eades, K.W. Terry and J.P L l e w e l l y n J . Phys. C 1, 415 (1968)  13  P.S. A l l e n and A. Cowking J . Chem. Phys. 47, 4286 (1967)  14  Z.M. E l Z a f f a r J . Chem. Phys. 3 . 6 , 1093 (1962)  15  B. Lemanceau, J . Chezeau and J . Hache J . de Chim. Phys. 94 (1966)  16  J.S. Waugh, J.H. L o e h l i n , F.A. Cotton and D.P. Shoemaker J . Chem. Phys. 3 1 , 1434 (1959)  17  J.T. P r i c e and T.S. Sorenson Can. J . Chem. 46, 515 (1968)  18  D.S. C a r r o l l and S.P. McGlynn Inorg. Chem. 7, 1285 (1968)  CHAPTER V I I I  STUDIES ON SOAPS 1.  Introduction One o f the t r a d i t i o n a l i n t e r e s t s i n t h i s l a b o r a t o r y has  been the study of phase-transitions and molecular motion i n f a t t y acids and t h e i r a l k a l i metal s a l t s using NMR methods. Compounds which have been studied by the CW NMR method include the even numbered ^2.2~^1^  a  c  ^  s  (^> ) 2  a s  w e  H  a s  the c i s and  trans 4^, ^ . , o l e f i n i c C-^g a c i d s , (3) the potassium s a l t s of C^ 0  to C^£ even numbered acids (4,5), the sodium s a l t s of the ^12~^18  e v e n  numbered acids ( 6 ) , the a l k a l i metal stearates (7)  and the sodium 3,5,5 trimethylhexanoate  (8).  A l s o some p r e l i m i n a r y  studies have been made using an a d i a b a t i c r a p i d passage technique (9,10), r e c e n t l y adapted f o r use i n t h i s l a b o r a t o r y . This present work i s a continuation of the aforementioned studies.  Compounds studied were the a l k a l i metal oleates and  stearates; both CW as w e l l as ARP NMR methods were used. Before the experimental r e s u l t s w i l l be presented and discussed, some o f the relevant s t r u c t u r a l features o f f a t t y acids and t h e i r s a l t s as w e l l as some o f the methods used t o study these compounds w i l l be reviewed. i)  Structure of f a t t y acids and t h e i r s a l t s I t has been shown (11,12) that f o r i n f i n i t e chains composed  of methylene u n i t s there are only a few independent ways of e f f i c i e n t l y packing these chains.  Each type o f packing i s  characterized by an appropriate 3ubcell.  End packing e f f e c t s  such as those of methyl groups and carboxylate groups, as w e l l  - 86 as the e f f e c t s of substituents and double bonds i n the middle of the chain, perturb the chain packing, and i t u s u a l l y becomes less e f f i c i e n t . X-ray d i f f r a c t i o n r e s u l t s (13,14) have shown that at low temperatures a l k a l i metal soaps have a l a y e r s t r u c t u r e i n which the carboxylate ions l i e i n p a r a l l e l sheets.  The a l k a l i metal  ions hold these sheets together, forming a l a y e r .  The hydro-  carbon chains s t i c k out p a r a l l e l t o each other on both sides of the carboxylate groups.  Examples of t y p i c a l soap s t r u c t u r e s  are provided by X-ray studies of potassium caprate (13), and potassium palmitate (14) (see f i g . (26)).  I t i s obvious, then,  that i n a l k a l i metal soaps there are two main types of bonding: i o n i c i n the carboxylate ends of the molecules and Vander Waals bonding between the hydrocarbon; chains.  M e l t i n g of t h i s type  of compound takes place when molecular motions such as v i b r a t i o n s ^ r o t a t i o n s , e t c . break up the regular ordering of the l a t t i c e . When the bonding of the end groups i s very strong, as i t i s i n the a l k a l i metal s a l t s , the Vander Waals bonding between the chains i s broken up long before the soap a c t u a l l y melts.  The r e s u l t s  of t h i s i s that a number of phase t r a n s i t i o n s occur before the soap f i n a l l y melts, quite often accompanied by a rearrangement of the c r y s t a l s t r u c t u r e or the l i b e r a t i o n of a motional mode. I t i s i n t e r e s t i n g t o look at some examples of lowering of t r a n s i t i o n temperatures,  i n t h i s case the melting point t r a n s i -  t i o n s , of a s e r i e s of compounds due t o chain packing e f f e c t s . One such s e r i e s i s formed by the saturated and mono unsaturated C-^g a c i d s .  The melting point a l t e r n a t i o n of f a t t y acids as a  f u n c t i o n of the number of methylene segments i s w e l l known.  to follow page 86  X  •  c  •  c  Xi ^  (b)  (a)  a=4.15 | b>5.60 X 0*37.82 A *»93° „ P-91.4 f=92.4°  V <  a *4.15 £ b »5.30 J c »2.56 A c^»=65»2 g s  g  /4 3K>8.5° S  ^=110.4°  /  <  50 ) (  In IP (c) .  0  5A i  Figure 26  T h e crystal structure of potassium palmitate ( B form); (a) a-axis projection; (£) ESS p r o ^ c t i L ; (c? arrangements of atoms i n one half of the ionic double layer.  This has been explained (15) by the f a c t that the even numbered acids have a more favourable packing arrangement because of a t i l t i n g of the hydrocarbon chain w i t h respect to the planes of the carboxyl and t e r m i n a l methyl groups.  For the G-^g a c i d s ,  the melting points f o l l o w the trend C^g t r a n s . unsat.>  C^g  c i s t unsat., because the l e s s severe d i s r u p t i o n of the chain a x i s i n the trans unsaturated a c i d gives a more l i n e a r  arrange-  ment f o r the trans than the c i s a c i d . Two more trends may be observed i n the melting points of the c i s a c i d s . (See t a b l e V I I I - l ) Table V I I I - 1  M e l t i n g points f o r some c i s C-^g a c i d s .  P o s i t i o n s of double bond  a  length of methylene chains  a  M.P.  2-3  14  51  6-7  10,4  28.6  8-9  8,6  23.8  10-11  6,8  22.8  12-13  4,10  27.6  7-8  9,5  12.5  9-10  7,7  17-18  14  (°C)  13.4,16.3 56.1  see r e f . (16) F i r s t there i s a r e l a t i o n s h i p l i k e that of the even-odd  melting point a l t e r n a t i o n f o r the saturated a c i d s , and t h i s be explained i n a s i m i l a r manner.  may  The melting points i n t h i s  case depend on whether the double bond i s between odd-even o r even-odd carbons.  The other trend shows a dependence of the  melting point on the maximum number of uninterrupted methylene  - 88 u n i t s i n the two chain segments of the molecule. i i ) T r a n s i t i o n s i n soaps and methods of study I t w i l l now be necessary t o discuss the c l a s s i f i c a t i o n of the mesomorphic t r a n s i t i o n s i n the a l k a l i metal soaps w i t h a view t o the many d i f f e r e n t methods used f o r observing them. F o r instance t r a n s i t i o n temperatures determined by d i f f e r e n t methods do not n e c e s s a r i l y agree, or sometimes t r a n s i t i o n s observed using one method are not observed a t a l l u s i n g another. I n some cases t h i s may be explained by the f a c t t h a t d i f f e r e n t samples a r e used o r even that t h e same sample has been subjected t o a d i f f e r e n t thermal treatment.  Quite often soap  t r a n s i t i o n temperatures are very s e n s i t i v e t o impurity or thermal history effects.  F o r i n s t a n c e , there i s some question whether  supposedly anhydrous soap samples are t r u l y anhydrous (l7,18)j soaps quite o f t e n form a s e r i e s of hydrates, s t a r t i n g w i t h the hemihydrate.  A study has been made of i m p u r i t y and thermal  h i s t o r y e f f e c t s on the premelting behaviour of s t e a r i c a c i d by the NMR method  (19).  The other reason f o r the observed d i f f e r e n c e s i n phase behaviour i s inherent i n the experimental method used; d i f f e r e n t methods measure q u i t e d i f f e r e n t properties of the soaps.  I t i s sometimes important t h a t the experimental  methods used employ e n t i r e l y d i f f e r e n t timescales (20). Some of the methods used t o observe phase behaviour i n soaps include i n f r a r e d spectroscopy, thermal methods such as the d i f f e r e n t i a l thermal a n a l y s i s (DTA) and d i f f e r e n t i a l scanning c a l o r i m e t r y (DSC) techniques, d i l a t o m e t r y , microscopic methods,  - 89 l i g h t transmission, and powder X-ray methods. Void and Void (21-25) and coworkers were the f i r s t authors who t r i e d t o f i t the observed phase t r a n s i t i o n s i n t o a scheme. Thy used a number of methods, i n c l u d i n g thermal, microscopic and d i l a t o m e t r i c techniques, t o study the sodium soaps of the even numbered  - ^g c  a c i d s , and l a t e r included some of the other  a l k a l i metal s t e a r a t e s . This was done w i t h some success, although some of the trends observed i n phase t r a n s i t i o n temperatures  and  enthalpies could not be i n t e r p r e t e d i n terms of s t r u c t u r a l features. T r a n s i t i o n s observed f o r the even numbered sodium soaps i n Voids' study are shown i n t a b l e VIII-2. Recently the sodium soaps from C^Q t o C using DTA and DSC methods (17).  have been reexamined  Trends i n t r a n s i t i o n  temperatures  and enthalpies observed i n t h i s study are shown i n f i g u r e  (27).  I n f r a r e d spectroscopy may be used t o obtain information about the lengths of hydrocarbon chains, as w e l l as t h e i r r e l a t i v e o r i e n t a t i o n and s t a t e of motion.  For instance, the s p l i t t i n g  of the methlene r o c k i n g and t w i s t i n g mode near 720 cm~  x  was  shown to be due to the presence of two types of chains oriented p a r a l l e l to each other but with the chain zig-zags a t r i g h t angles (26).  At low temperatures, the extended trans c o n f i g u r a t i o n i s  the s t a b l e form i n c r y s t a l l i n e long chain compounds. As the temperature  increases, the band progressions due t o , f o r instance,  the CH^ wagging mode, f i r s t weaken i n i n t e n s i t y and then e i t h e r s h i f t or disappear as the compound melts.  This i s because of  the appearance of d i f f e r e n t r o t a t i o n a l isomers, which reduces the number of CH  0  groups trans t o each other.  Compounds studied  to follow page Transition tc.Tpcrjture(*C) 350 '*V  I S O I R O P C SOLUTION AH (cat mole" ) 300  250 SUB NEAT SOAPS NEY/ PHASE  • • •  200  SUPLWAXY"  150  SUBWAXY  CURD  a fa  too  W  11  12  13  U  15  ——*•  IS  :  17  13  ]• 19  Number of C-atc-Tis  S  11  O  I? 13  li E B p ~n ,3° • Nyrnber c f C-alorr.s  (b)  (a)  411 (cM rr.olc"')  5000 ISOVKOPC  <000 2000  3000  3000  /  •  EAT SOBM-. NEAT  1500  V.'AXY SUBNEAT 2000  2000  woo' SUPcRWAXV SU3MEAT  1000  1000  SUFERV/AXY • NEW PHASE  500  / ' /  E  II  12  13 •  U  fi IS p 13 19 •- Number of C-atc.T.s  ,  WAXY  • ' " M T W PHASE SUa.\'EAT  'SUTIR.VAXY  0 10  (d)  (c)  tl  12  13  K  ,0  K  1 7  Number of  8  C-atoms  Figure 27 DTA and DSC results for a number of sodium soaps ( ref. 17) (a) transition temperatures; (b) total enthalpy and entropy} (cr and d) enthalpies for various transitions.  - 90 Table VIII-2 T r a n s i t i o n Scheme f o r Sodium Soap3 according to V o l d . -  a  laurate  myristate  palmitate  curd-subwaxy  100  107  117  117  68  subwaxy-waxy  141  141  135  132  118  waxy-superwaxy  182  176  172  167  178  superwaxy-subneat  220  217  208  198  218  subneat-neat  255  245  253  257  neat-isotropic  336  310  295  288  stearate  oleate  256  a see r e f . (22) i n t h i s manner include sodium palmitate (27), theoC-w d i c a r b o x y l i c acids and t h e i r esters (28), and the even numbered C^(2).  A review of i n f r a r e d studies on long  C-^g acids  chain compounds may  be found i n r e f . (29). An extensive study o f the s t r u c t u r e and polymorphism of a large number of even numbered a l k a l i metal soaps has been made using the X-ray powder method (30-34)•  The phase t r a n s i t i o n s  i n soaps may be thought of as a stepwise melting process, w i t h i n c r e a s i n g disorder i n each successive phase.  At low temperatures,  where the soaps are e s s e n t i a l l y c r y s t a l l i n e , the e n t i r e structure w i l l contribute f a i r l y evenly to the X-ray s c a t t e r i n g .  At higher  temperatures, the hydrocarbon chains are e s s e n t i a l l y i n a l i q u i d l i k e s t a t e of motion and as such s t r u c t u r a l rearrangements observed by the X-ray method i n t h i s temperature r e g i o n are probably due to changes i n the i o n i c groupings. The phases characterized by the X-ray method f o r the a l k a l i metal stearates are shown i n t a b l e VIII-3 together w i t h changes i n specifie.volume and s t r u c t u r a l  - 91 parameters. In broadline NMR  studies, interactions between the protons  govern resonance l i n e widths, so that hydrocarbon chain configurations as well as the state of motion of the chains determine the magnitude of the interaction.  The broadline NMR method i s convenient  for studying resonance l i n e s with width greater than a few tenths of a gauss.  Experimentally linewidths of t h i s order are found i n  the phases occurring at lower temperatures,(below about 50°C-200°C depending on the i n d i v i d u a l soap).  Above these temperatures, the  hydrocarbon chains are i n an e s s e n t i a l l y l i q u i d - l i k e 3 t a t e of motion, so that high resolution methods are more convenient to use i n t h i s temperature region. drawn from broadline NMR  Now what information may be  data?  R i g i d l a t t i c e second moments may be calculated and compared with experimental low temperature second moments.  Studies of t h i s  nature (4) have shown, however, that minor differences i n proton p o s i t i o n a l parameters do not a f f e c t second moments much, e s p e c i a l l y i n the lc*jer chain compounds.  Also i n f o r m a t i o n may be obtained  about the motional state of the chain.  Major changes i n chain  motion may be followed by observing the NMR  linewidths and  second moments as a function of temperatures, and i n favourable cases these changes coincide with transitions observed by other methods.  A c t i v a t i o n energies may be extracted from linewidth  change data, but the exact meaning of t h i s parameter i s not clear, since c o r r e l a t i o n frequencies found from linewidths do not usually give a single straight l i n e .  Also some d i f f i c u l t y  resuts from not knowing exactly what type of motion causes the linewidth change.  Table VIII-3  Some transitions observed for the alkali-metal stearates by powder X-ray methods d wrlong spacing; transition temperatures i n °C.  Lithium Stearate  122 190 crystal I — * - crystal I I — » » waxy ribbon-like phase 1.04 0.96 0.87  specific volume  (X)  d  42.0  Sodium Stearate specifie volume  (&/ca?)  crystal  45.0 133 f> waxy  d <f) Potassiqm Stearate specific volume (*/<») d  (i)  42.0  Rubidium Stearate specific volume (S/cm ) 3  d  (i)  d  (&/cm?)  (X)  a ses ref. (30-34)  45.1  46.3  84 177 crystal I-»» crystal II-a» semicrystalline 1.15 1.07 1.02 40.6  Gesium Stearate specific volume  139 69 crystal I -»» crystal I I — * . crystal I I I — * waxy ribbon-like phase 1.02 0.97 -'\®Sffc, 0.91  44.1  disclike phase  42.4  , 70 104 206 crystal I-e*. crystal II-*» crystal I I I — w a x y phase 1.27 1.22 1.14 1.11 38.7  40.4  42.6  42.1  - 93 S p i n - l a t t i c e relaxation time measurements can give information about the dynamics of the a c t i v e dipolar relaxation mechanisms, and a c t i v a t i o n energies may be found as w e l l .  i i i ) Molecular Motion i n Soaps Some of the d i f f i c u l t y with the study of molecular motion i n long chain hydrocarbon compounds l i e s i n f i n d i n g an appropriate motional model.  Evidence f o r extensive molecular motion e x i s t s ;  for instance, r o t a t i o n as well as t o r s i o n a l o s c i l l a t i o n of the entire hydrocarbon chain has been proposed (35,36), f o r some paraffins.  C a l c u l a t i o n (37)  of intermolecular p o t e n t i a l barriers  to rotation f o r r i g i d , c y l i n d r i c a l hydrocarbon chains indicate that .such a model i s f e a s i b l e . f  Rotational t r a n s i t i o n temperatures  and b a r r i e r s may be calculated i n f a i r agreement with experimental results.  However, i n long chain carboxylic acids and e s p e c i a l l y  t h e i r s a l t s , one end of the chains i s r i g i d l y held, so that a model such as that used f o r paraffins cannot be used here.  For  s i m i l a r reasons, the model where the entire hydrocarbon chain performs t o r s i o n a l o s c i l l a t i o n s about the chain axis as a r i g i d unit cannot be considered as a s a t i s f a c t o r y motional model.  2.  Experimental  i)  Preparation of A l k a l i Metal Soaps The o l e i c a c i d used i n the preparation of the a l k a l i metal  oleates was obtained from the Hormel Foundation, Austin, Minn, and was quoted to be better than 99$  pure.  The a l k a l i metal  hydroxides used were reagent grade or better. To prepare the soaps a hot aqueous ethanol solution of the hydroxide was used to neutralize a hot solution of o l e i c acid i n  -  94  -  ethanol, using phenolphthalein as i n t e r n a l i n d i c a t o r .  On cooling,  the s o l u t i o n normally deposited white flakey soap c r y s t a l s , which were f i l t e r e d , washed with cold ethanol, then with acetane and a i r dried.  The soaps were dried at 100°C under vacuum f o r ,  about a day, ground into a f i n e powder, packed into t h i n walled 10mm od glass tjjbes, and again heated under vacuum a t 110°C f o r another day.  After sealing under vacuum, the samples were ready  for use i n the NMR experiments. The other soaps studied were prepared i n a s i m i l a r way, Kodak white l a b e l grade acids were used, without further purification.  Before being dried each soap was r e c r y s t a l l i z e d  once from absolute or aqueous ethanol. I t should be mentioned here that not a l l soaps precipitated as f l a k e y white c r y s t a l s .  The sodium stearate normally came down  as a g e l , and t o some extent also the sodium oleate, although on drying these soaps resembled the other f a t t y a c i d s a l t s .  The  cesium oleate was a s t i c k y white s o l i d , and was rather d i f f i c u l t to handle.  These materials d i d not improve p h y s i c a l l y on recry-  s t a l l i z a t i o n and were used without further treatment. i i ) NMR experiments The CW as w e l l as ARP NMR experiments were carried out as described i n Chapter I I . Frequencies used f o r the CW experiments were 30 and 16 MHz and f o r the ARP experiments 8 and 16 MHz. i i i ) Thermal experiments While the NMR work was i n progress, a Perkin-Elmer DSC 1-B scanning calorimeter was made available f o r use i n the department. I t was thought then that i t would be i n t e r e s t i n g t o compare the  - 95 t r a n s i t i o n s observed using the NMR the DSC method.  method with those seen using  At t h i s point a c l a r i f i c a t i o n should be made as  to the differences between the DTA and DSC methods.  For the DTA  experiment the quantity measured i s the difference i n temperature between the sample and a standard, while i n the DSC method the difference i n the heat required to keep the sample and the standard at .the same temperature i s recorded.  Now,  whereas f o r the DTA  method peaks are observed normally f o r both f i r s t and second order t r a n s i t i o n s , f o r the DSC method peaks should accompany only f i r s t order t r a n s i t i o n s ; second order t r a n s i t i o n s should cause only a s h i f t i n the baseline.  The decision was made t o  determine to what extent the t r a n s i t i o n s observed i n the stearates were thermal h i s t o r y dependent.  Samples of each of  the stearates were r e c r y s t a l l i z e d and subjected to d i f f e r e n t thermal treatments.  The d i f f e r e n t i a l thermogram was then run,  always at 10°C/min., up to a temperature of 200°C. 3.  Results  i)  Thermal measurements The DSC thermal studies are summarized i n table VIII-4.  Only transitions which gave d i s t i n c t peaks were taken into account, so that a l l t r a n s i t i o n s l i s t e d should be f i r s t order. Transitiomtemperatures i n column 1 are f o r samples which were kept under vacuum f o r one day at room temperature.  Samples  used f o r the column 2 temperatures were kept under vacuum f o r 14 hrs. at 110-120°S and run 24 hrs. l a t e r .  Column 3 samples  received s i m i l a r treatment as f o r those under column 2, but were  - 96 Table V I I I - 4  Li  T r a n s i t i o n s observed f o r the a l k a l i metal stearates using the DSC method.  1  2  3  4  112 191  112 195  112 195  110 173  — —  —  —  116  ——  48 82 116 132 72 96 104 132 —  130  '67,75 95 104 132 —  90 111 133  —  67,74  63 96 102 130 138 149 153  - —  ___  132 —  149  152  — -  —  59 82 128  137  141 186  60 72 101 114 129 184  152  — -  —  58 78  —  80 129 135 141 172  62  ^72 100 115 132 —  —  81  122 190  108 194  117 193  — —  —  ——  93 118 136  113  —_  133  — —  69  - —  139  —  —  170  148 163 174  170  ____  84  75* 130 — ——  a  r e f . (30-34)  d  dilatometry values; r e f . (38)  60  — -  177  —  —  — -  —— —  59 71 101 114 128 184  85  d  136  63 71 102 114 129 182  C  68,77 90 106 134  —  140 189  b  NMR  a  —  137 142 191  —  DTA  X-rays  d  75  — —  143  —  —  70 104  70 100 d  d  70 100  —  —  —  —  —  206  r e f . (18)  c r e f . (7)  - 97 kept heated under vacuum f o r 28 hrs. and run 24 hrs. l a t e r .  Samples  used f o r the column 4 r e s u l t s were fused under vacuum and run about a week l a t e r .  Representative DSC thermograms are presented i n  Appendix B. Also l i s t e d i n table VTII-4 are transitions observed by d i f f e r e n t authors using a number of methods.  ii)  Measurements on A l k a l i Metal Stearates CW measurements on the a l k a l i - m e t a l stearates have been discussed  previously (7).  * t i s unfortunate that the same samples as were  used i n that study were no longer a v a i l a b l e , as the thermal history, and to some extent, the preparative methods which are used are extremely important, a)  Lithium Stearate Figure (28) shows a plot of l o g  vs. temperature.  A single  low temperature minimum was observed, with T- min.=s 0.042 sec at 112°K.  I f the l o g of  i s plotted versus VT,  a minimum results  as predicted by eqnj^iS^in Chapter I, with the a c t i v a t i o n energies found from the l i m i t i n g slopes approximately equal. d i s c o n t i n u i t y was observed i n the lower value at t h i s temperature.  curve, with  At 387°K a dropping to a  The CW linewidth and second  moments (7) show a t r a n s i t i o n near t h i s temperature at 390°K. DSC studies ( t h i s work) show the t r a n s i t i o n to be 385°K; other temperatures at which t h i s t r a n s i t i o n has been observed by various other techniques are: DTA  395°K, X-rays (30), 381°K, DTA  (24), 387°K, dilatometry (38).  (18), 385°K,  This t r a n s i t i o n has been shown  to be a true phase change between two c r y s t a l phases.  -  98  -  I n the high temperature c r y s t a l phases  values again increase  w i t h temperature, and an a c t i v a t i o n energy of 1.4 kcal/mole i s obtained i n t h i s region (see appendix C f o r l o g  vs ^-/T p l o t s ) .  Near 3o3°K, another d i s c o n t i n u i t y occurs, with the the higher temperature phase.  lower i n  Transition" temperatures from  other methods are: 3 6 3 % NMR ( 7 ) , 3 6 7 % X-rays (30), 4 6 7 % DTA (18). A l l the parameters c h a r a c t e r i z i n g the l o g T^ vs temperature curve have been summarized i n t a b l e V I I I - 5 . b)  Sodium Stearate As mentioned p r e v i o u s l y , sodium stearate e x h i b i t s an extremely  complicated phase behaviour.  T^ studies over the e n t i r e temperature  region o f i n t e r e s t were not obtained, because the magnetization decays could not be f i t t e d with a s i n g l e exponential.  Figure (29)  shows the T^ values which could be e x t r a c t e d from the data.  Between  150°K and 360°K more complex behaviour was observed, but a T^ value could s t i l l be found.  The T^ p l o t t e d i n t h i s temperature region  i s the shorter one observed. Again at low temperatures, a simple T^ minimum i s evident at 119°K although a weak secondary minimum i s a l s o observed near 220°K.  P l o t t e d on t h e same graph are the CW r e s u l t s , ,('Y) but no  features are found t o r e l a t e d i r e c t l y t o the T^ r e s u l t s . explanations f o r t h i s behaviour w i l l be mentioned c)  Possible  later.  Potassium Stearate The p l o t of T^ vs temperature as w e l l as CW r e s u l t s (7) are  shown i n f i g u r e (30). The r e s u l t s resemble those obtained f o r l i t h i u m s t e a r a t e , w i t h one low temperature minimum at 122°K and  140  220  300  TEMP. (°Kl  380  460  -  Figure 29 Sodium Stearate: Linewidth, second moment and s p i n - l a t t i c e r e l a x a t i o n time as a f u n c t i o n of temperature.  £  g. H n t» (8  O CO'  - 99 d i s c o n t i n u i t i e s occurring at 342°K and near 426°K.  The low  temperatures discontinuity corresponds t o another c r y s t a l t r a n s i t i o n ; transitions temperatures observed by other methods are 342°K, X-rays (32), 333°K NMR (7) 3 4 1 %  DTA (18). The second discontinuity,  near 420°K, does not correspond t o a linewidth or second moment t r a n s i t i o n i n the CW studios (7). The present DSC studies indicate v.,. t r a n s i t i o n s at 422°K and 426°K, and several other studies indicate t r a n s i t i o n s near t h i s temperature:  433-438°K, l i g h t transmissions  (39), 4 2 1 % DTA (18). Transitions i n t h i s region seem to be very dependent on the thermal history of the sample. Again the parameters characterizing the T^ behaviour are summarized i n table VTII-5. d) Rubidium Stearate The CW linewidths and second moments (#) are shown i n figure (36), together with the T^ measurements.  Again, a single low temperature  minimum i s observed at 131°K, and d i s c o n t i n u i t i e s at 355°K and 415°K which correspond f a i r l y w e l l with the NMR t r a n s i t i o n s at 348°K and 416°K.  Other studies reveal the low temperature t r a n s i t i o n at 3 5 3 %  DSC (this work), 3 5 7 % X-rays (34), 3 4 8 %  dilatometry (38), and  the high temperature t r a n s i t i o n at 414°K, DSC (this work) and 403°K, dilatometry (38). The X-ray work (34) d i d not show the high temperature t r a n s i t i o n . e)  Cesium Stearate Figure (32) shows the CW (7) as well as ^  results.  The l i n e -  width and second moment t r a n s i t i o n s occur at 343 and 375°K. The T^ results show a single T^ minimum at 116°K.  No discontinuity  was observed t o occur near the low temperature CW linewidth  V  - 100 t r a n s i t i o n , although a small decrease i n range was observed.  over a wider temperature  The low temperature t r a n s i t i o n has a l s o been  observed with other methods: (33), 3 4 3 % dilatometry (38).  344°K, DSC ( t h i s work), 3 4 3 % X-rays The high temperature t r a n s i t i o n , a t  375°K was accompanied by a discontinuous change i n the T^ curve. Other methods r e v e a l t h i s t r a n s i t i o n t o be a t 3 7 4 % DSC ( t h i s work), 377°K, X-rays (33), and 375°K, 3 7 3 % dilatometry (38). i i i ) Results f o r Oleates a)  L i t h i u m Oleate. The CW l i n e w i d t h s and second moments are p l o t t e d as a function  of temperature i n f i g u r e (33); on the same p l o t are shown the T^ values obtained. Linewidths and second moments change smoothly from 16.0 gauss  and 25.0 gauss at 77°K t o 8.0 gauss, and 15 gauss 2  at 290°K r e s p e c t i v e l y .  2  At t h i s temperature the second moment: and  l i n e w i d t h decreased more r a p i d l y t o values of U  gauss and 5.5 2  gauss . Further slow decreases i n these parameters then took place,to 4.0 gauss and 7.0 gauss at 410°K. A sharper change 2  occurred near 418°K and the l i n e w i d t h above t h i s temperature was determined by the modulation amplitude. The second moment at t h i s point was of the order of about 0.7 gauss . The T^ study revealed a low temperdaw* minimum a t 130°K. Where the low temperature l i n e w i d t h t r a n s i t i o n takes place, a dip i n the T-^ curve can be seen, although there i s no c l e a r d i s c o n t i n u i t y at t h i s point.  A d i s c o n t i n u i t y i n the T^ curve i s observed however,  at the temperature where the second l i n e w i d t h t r a n s i t i o n occurs. Representative spectra are shown i n appendix B. DSC studies revealed a rather weak peak near the temperature of the high temperature l i n e w i d t h t r a n s i t i o n .  - 101 b)  Sodium Oleate Figure (34) shows the linewidth, second moment and  obtained for sodium oleate.  results  The linewidth and second moments  at 77°K were 15.6 gauss and 25.6 gauss2.  The sharper changes  in linewidth and second moment took place near 260°K and 335°K. A T-^ minimum i s evident at 110°K., and another shallow minimum near 260°K.  Near 335°K a discontinuity was observed in the  curve.  Near this temperature also a peak resulted i n the DSC thermogram. t) Potassium Oleate The CW and T^ results are shown in Figure (35) and to some degree resemble those obtained for lithium oleate. was observed to be at 120°K.  The T^ minimum  Linewidth and second moment transitions  were found near 280°K and 408°K.  Again, the f i r s t transition was  accompanied by a slight dip i n the T^ curve, and the second by discontinuity i n the T^ curve as well as a peak i n the DSC thermogram. d)  Rubidium Oleate Figure (36) shows results obtained for Rubidium oleate.  The  second moments and linewidth at 77°K are 25.8jpuss and 15.3 gauss respectively.  The T^ minimum value occurs at 132°K. Linewidth  and second moment transitions occur near 280°K and 348°K.  The  second moment change near 280°K, however, i s not very distinct; also there i s no apparent T^ transition at this point.  The  second change, near 348°K, was extremely sharp, and the soap sample was observed to become slightly translucent at this temperature.I A large DSC peak_was observed to accompany this transition, ,—  - -  and a smaller peak occured near 319^K,  - 102 e)  Cesium Oleate CW as well as  results are shown i n figure ( 3 7 ) . Line-  widths and second moments at 77°K were 15.0 gauss and 25.7 gauss'' respectively.  I t appeared as though a small t r a n s i t i o n was  present r i g h t near 80°K;  the linewidth and second moment a t  90°K were 14.2 gauss and 23.8 gauss  respectively.  Decreases  i n these parameters between 90°K and the low temperature t r a n s i t i o n near 300°K were rather more rapid then for the other soaps. values, a f t e r reaching a  minimum value of 0.050 sec. remained  very low u n t i l temperatures near 320°K from where i t increased steadily.  Near the t r a n s i t i o n a t 300°K, linewidths and second o  moments reached the quite low values of 2.4 gauss and 1.8 gauss respectively.  A narrow component obscured the broader l i n e near  430°K, and the second moments dropped further t o reach a value of 0.88 gauss  2  at 468°K.  I t should be mentioned at t h i s point that f o r a l l the oleates studied, the f i r s t linewidth and second moment t r a n s i t i o n was quite gradual, with no great changes i n lineshapes^taking place. The second t r a n s i t i o n was preceded by the appearance o f a narrow component, which then gradually grew at the expense of the broad component u n t i l a t the t r a n s i t i o n temperature only the narrow l i n e remained.  Nosspecial study was made o f t h i s phenomenon  as the appearance o f t h i s narrow component i s very much dependent on sample p u r i t y and thermal h i s t o r y . The appearance o f t h i s narrow component may a f f e c t the T-^ values t o some extent, since the broad and narrow components are l i k e l y to have somewhat d i f f e r e n t T,*s.  This would explain  - 103 Table VIII-5  Summary of r e l a x a t i o n data f o r the a l k a l i metal stearates and o l e a t e s .  Low temperature phase Temperature a t T-jmin. ^minimum (°K) (sec)  High temperature phase Ea(kcal/mole) low temp-high temp  T-, (sec) miaplateau  Ea  oleates Li  134  .035  1.7  2.4  1.0  3.0  Na  110  .056  1.7  -  -  4.6  K  122  .037  2.3  1.7  1.5  Rb  132  ;033  1.5  2.1  2.0  0.8  Cs  115  .050  1.7  -  -  6.1  Li  115  .042  1.8  2.3  0.8  1.4  Na  118  .058  1.7  -  -  K  122  .045  2.1  2.4  3.0  Rb  132  .050  2.3  2.5  4.4  Cs  116  .059  2.2  1.8  3.0  stearates  3.2  - 104 Table VIII-6  Summary of broadline NMR transition temperatures for alkali metal stearates and oleates and stearic and oleic acid.  Transition temperatures Oleates  (°K)  (°K)  Li  295  418  Na  260  337  K  280  407  Rb  280  348  Cs  297  Oleic acid  268  Stearates  286(M.P.)  . :,  Li  387  443  Na  358  386  K  353  443  Rb  348  416  Cs  343  373  Stearic Acid  -  34l(M.P.)  - 105 Table VTII-7  Summary o f broadline NMR second moments f o r the stearates and oleates a t various temperatures.  o at 77 K  below low temp, transition  above low temp, transition  below high temp, transition  Oleates Li  25.1  16  11  6-7  Na  26.0  20  14  10-11  K  25.4  18  12  4-5  Rb  26.0  18-20  13  6  Cs  25.8  8-10  1.8 •  22.5  19  14  14  Li  26  20  8-9  4  Na  28  20  12  K  27  20  12  4  Rb  25  22  6  4  Cs  27  16  4  4  -  -  20  Oleic Acid Stearates  S t e a r i c A c i d 21.5  9-10  - 106 the s l i g h t drop-off i n T^'s observed somewhat below the discont i n u i t i e s , as w e l l as m u l t i p l e r e l a x a t i o n times found i n t h i s region.  U s u a l l y the p r i n c i p a l  P l o t s of l o g  value was measured and recorded.  versus ^~/T f o r a l l soaps studied are shown i n  appendix C. i v ) Discussion i)  Low temperature second moments The second moments observed at 77°K f o r the oleates studied,  as w e l l as the stearates and the parent acids have been summarized i n table V I I I - 7 . gauss  2  There i s l i t t l e v a r i a t i o n and a value o f ~  25.5  can be chosen t o be representative of a l l the 77°K oleate  second moments.  Normal procedure f o r comparing t h e o r e t i c a l  second moments w i t h experimental values i s t o separate the second moment c o n t r i b u t i o n s i n t o an intra-molecular and inter-molecular part.  Complete c r y s t a l s t r u c t u r e determinations  f o r any of the a l k a l i metal oleates.  have not been made  However, o l e i c a c i d i t s e l f  has been studied u s i n g X-ray methods (40), and since a t low temperatures a l l long chain compounds tend t o be i n the extended trans c o n f i g u r a t i o n (except around the double bond), the i n t r a molecular c o n t r i b u t i o n t o the second moment should be the same as f o r the o l e a t e s .  C a l c u l a t i o n s o f t h i s quantity have been made  ( 3 ) , g i v i n g an intra-molecular second moment c o n t r i b u t i o n o f 15.9  gauss . 2  For the inter-molecular second moment contributions the value c a l c u l a t e d f o r the stearates may be used, which has been found t o be about 8 gauss .(36). 2  The t o t a l second moment found  i s then 24.9 gauss . U s u a l l y attempts are made t o correct second  momenta c a l c u l a t e d from room temperature parameters f o r bond and l a t t i c e shrinkage when a low temperature second moment i s t o be compared w i t h the c a l c u l a t e d value.  Another e f f e c t which may  s l i g h t l y change second moments i s that of l a t t i c e v i b r a t i o n s . Some data were a v a i l a b l e on the v a r i a t i o n of the o l e i c a c i d l a t t i c e parameters w i t h temperature, and i t was then p o s s i b l e to c a l c u l a t e that the second moment found from parameters obtained near room temperature should be increased by about 9 $ t o take account of l a t t i c e contraction down t o 7 7 ° K .  It is  estimated, then, that the r i g i d l a t t i c e second moment f o r the oleates should be about 2 6 gauss . Previous studies on stearates ( 7 ) and other soaps ( 6 ) i n d i c a t e that a t 7 7 ° K the hydrocarbon chain i s not n e c e s s a r i l y rigid.  For most soaps b e t t e r agreement between c a l c u l a t e d  and experimental second moments r e s u l t e d i f i t was assumed that the end methyl group was r o t a t i n g about i t s t h r e e f o l d axis.  A motion of t h i s type should reduce the second moment  by 1 . 9 gauss . 2  F o r the oleates then, i f methyl group r o t a -  t i o n i s present, a second moment o f about 2 4 gauss should 2  result. A l l o f the experimental values (see t a b l e %) l i e between the  r i g i d and r o t a t i n g methyl group second moments, so that no  d e c i s i o n can be made which of the two models i s c o r r e c t a t 7 7 ° K . From observations of the Cesium oleate second moment and l i n e widths a t 7 7 ° K i t appears as though a small change i s evident near t h i s temperature, i n d i c a t i n g that the r o t a t i o n a l frequency of the motion near t h i s temperature i s approximately the same as  - 107 the l i n e w i d t h i n frequency u n i t s ( about 1 0 ^ - 1 0 ^ Hz). Some a d d i t i o n a l d i f f i c u l t y w i t h deciding on e i t h e r the r i g i d or r o t a t i n g methyl group models l i e s i n the f a c t that there i s a p o s s i b i l i t y that the second moment w i l l not n e c e s s a r i l y go t o i t s r i g i d value.  lattice  Studies on some polymethyl benzenes ( 4 1 ) , i n d i c a t e t h a t i f  t u n n e l l i n g of the methyl group i s present the second moment may keep i t s reduced value down to l i q u i d helium temperature.  Also,  for long chain compounds the change i n second moment f o r methyl group r o t a t i o n i s quite s m a l l , of the order of 1 0 $ of the t o t a l or l e s s , and may be q u i t e d i f f i c u l t t o observe.  Some preliminary  studies have been performed on some short chain a c i d s a l t s ( 4 2 ) and i n d i c a t i o n s are that the methyl groups r o t a t i o n t r a n s i t i o n f o r some of these compounds occurs near 80°Kj r i g i d  lattice  conditions are not yet a t t a i n e d a t 77°K. i i ) Molecular motion i n the low temperature region (below about 273°K) Between 77°K and the low temperature l i n e w i d t h and second moment t r a n s i t i o n s , second moments decrease s t e a d i l y , somewhat more r a p i d l y f o r l i t h i u m oleate than f o r the other soaps. T y p i c a l l y the second moments have values of about 16-B-20 gauss below the t r a n s i t i o n , except f o r the cesium soap, which shows a much greater decrease t o 8 - 1 0 gauss . 2  A somewhat s i m i l a r trend  i s observed f o r the a l k a l i metal s t e a r a t e s , where t y p i c a l second 2 moment values below the t r a n s i t i o n are 20-22 gauss  9  and 1 6 gauss''  f o r the cesium stearate. This second moment decrease has p r e v i o u s l y been i n t e r p r e t e d i n terms of motional narrowing, i n p a r t i c u l a r t o r s i o n a l o s c i l l a t i o n s  - 108  of the hydrocarbon chains (36).  -  The simplest model i s that where  the entire chain o s c i l l a t e s as a r i g i d u n i t .  As previously mentioned,  the d i f f i c u l t y with t h i s model i s that one end of the chain i s t i g h t l y held by the i o n i c groupings.  E s p e c i a l l y f o r the oleates  t h i s model i s quite unsatisfactory because of the c i s configura- . t i o n of the chain about the double bond.  A more r e a l i s t i c model  would introduce some independence i n t o the o s c i l l a t i o n of each methylene group.  For a straight chain, the methylenes furthest  from the i o n i c grouping might then be able to o s c i l l a t e through angles of 360° or more, sometimes i n one d i r e c t i o n , then i n the other.  Calculations for a model such as t h i s are p r o h i b i t i v e ,  however, because f o r each type of i n t e r a c t i o n motional reduction factors have to be calculated f o r both<C©s  and <r~^>  averaging.  I t i s of i n t e r e s t to explore some of the results obtained with other methods to study molecular motion i n long chain compounds. Extensive studies have been made of d i e l e c t r i c and mechanical r e l a x a t i o n phenomena i n paraffins, t h e i r derivatives such as ethers, ketones, esters and alcohols, and also polymers, but unfortunately no studies of soaps are a v a i l a b l e . As i t turns out, NMR  measure-  ments and also the physical properties of the soaps generally indicate that the f a t t y acid s a l t s do not have properties t y p i c a l of the compounds l i s t e d above.  I t may  be then be d i f f i c u l t to  draw p a r a l l e l s between the soaps and otherAlong chain compounds. From d i e l e c t r i c measurements on long chain ketones, esters, and ethers (43), Hoffman concluded  (44) that chains with length  up to 37 methylene units i n length behave as r i g i d rods, with no extensive chain twisting taking place.  - 109 -  1  A low temperature  ^ relaxation process has been observed for s  parafins; for polymers, this process exits as well and has been associated with the occurrence of a kink in the chain and the reorientation of a chain segment.  In polymers, the  relaxation  process i s much stronger i n samples with a high percentage of amorphous character. In fact i t has been proposed (15) the  ^  that i f  process takes place i n totally crystalline material,  i t i s associated entirely with effects at the crystal grain , boundaries.  Then, i f large relaxation phenomena are observed,  these should be associated with amorphous regions in the solid. Also, quite often dielectric and mechanical measurements are made with the molecules of interest dissolved in a matrix of a different material, and i t i s probable that results obtained in this manner apply more directly to amorphous than to crystalline materials. Illers (46) proposed that the ^  process observed for paraffins  as well as fatty acids could be associated with the occurrence of rotational isomers.  Now, from I l l e r s  1  mechanical measurements  i t i s found that the correlation time i s about 1 second at 110°K  for the stearic acid i n polystyrene matrix.  An activa*  tion energy for the ^ process of 60 cal/ Ch* unit i s found 2  from Hoffman's tabulation of mechanical and dielectric data. For a C^g soap chain, then, an activation energy of about kcal/mole i s found.  1.0  From an  application of the modified B.P.P. equation (see eqn. 8, Chapter l ) correlation frequencies were calculated for the changes of linewidth with temperature i n the low temperature phase.of potassium stearate (36).  An activation energy of 1.1  kcal/mole was found,  - 110 i n reasonable agreement with the values predicted f o r  r e l a x a t i o n . F o r soaps the low temperature phase  l i n e w i d t h changes are u s u a l l y associated with t o r s i o n a l o s c i l l a tions.  I t i s quite possible that motions responsible f o r the low  temperature phase l i n e w i d t h and second moment changes are the same as those responsible f o r the y  r e l a x a t i o n process.  A second r e l a x a t i o n process has been observed,using mechanical and d i e l e c t r i c methods, t o occur i n polymers, p a r a f f i n s and long chain ester3, ethers and ketones.  This process has been associated  w i t h c r y s t a l defects, where chains can r e o r i e n t over low b a r r i e r s ; an a c t i v a t i o n energy of 700 c a l / CBj u n i t , together with a c o r r e l a t i o n time of about 1 second a t 180°K p r e d i c t s an a c t i v a t i o n energy of about 11 kcal/mole with'Co^s he*"*' seconds f o r a stearate chain. I l l e r s (46)  found that f o r associated chain compounds such as the  c r y s t a l l i n e alcohols and a c i d s t h i s OC process i s absent because of the high hindering b a r r i e r associated with the polar groups, so that t h i s process should be absent f o r soaps. Another i n t e r e s t i n g comparison can be made between second At 77°K the soap  moments of the soaps and t h e i r parent a c i d s .  second moments are of the order of 3-6 gauss l a r g e r than the 2  a c i d second moments because of increased intermolecular second moment c o n t r i b u t i o n s . This would i n d i c a t e a t i g h t e r packing of t h e chains f o r the soaps, with smaller i n t e r p r o t o n distances. Now below t h e low temperature t r a n s i t i o n , oleate second moments have decreased 6-9 gauss gauss  and the stearate second moments 3-6  (the cesium s a l t s a l i t t l e more than t h i s ) .  At equivalent  temperatures, the parent a c i d second moments show l i t t l e decrease,  - Ill -  for oleic acid 3.5 gauss and for stearic acid there i s almost no 2  change.  This indicates that i n the soaps extensive motion takes  place, but very much less motion is evident for the acids. It seems therefore, although at low temperatures the soap chain packing is, much tighter, i t i s less efficient, with more unfavourable proton-proton contacts.  When sufficient thermal  energy becomes available, these unfavourable proton-proton contacts may be alleviated somewhat by the motion of the chain fragments to which these protons are attached. It may be necessary then to look for motional processes quite different from those observed for the more efficiently packed chain compounds. Most of the soaps show only a slight decrease i n linewidth and second moment i n this temperature region, but for sodium stearate ( 3 6 ) and cesium oleate, and to a lesser extent, sodium oleate, a narrow component also was evident with a linewidth much less than one gauss.  There i s the possibility, then, of  correlating the appearance of the narrow component at a low temperature with the physical state of the samples on preparation. As mentioned i n the experimental section, sodium soaps have a marked tendency to form gels, and the cesium oleate was a sticky white solid, and on i n i t i a l preparation these soaps did not at a l l resemble the other salts.  However, on filtering and drying  the sodium soap gels, these materials appeared to be typically soap-like powders. Narrow components have been observed previously i n maEy different instances, eg. i n paraffins (47), acids (19), and  - 112 polymers (48).  Quite often these narrow peaks appear shortly  before melting of the compound and then are interpreted a3 premelting phenomena (19).  In polymers, narrow components  are associated with amorphous regions within the s o l i d or the presence of extensive motion along grain boundaries.  In  these amorphous regions i n the s o l i d state, the chains e x i s t i n a disordered state, and more molecular motion i s present than i n the c r y s t a l l i n e regions at the same temperatures. For the three aforementioned  soaps, then, i t seems that the  presence of amorphous regions i s more prominent thdn f o r the other soaps.  Further evidence for t h i s - w i l l be mentioned i n the  section on  measurements.  i i i ) Spin l a t t i c e relaxation i n the low temperature phase. For a l l the soaps except the sodium s a l t s and cesium oleate, only one minimum exists i n the  curve (at  110-130°K),  and this  may be attributed to a dipolar relaxation mechanism involving methyl group rotation. n-alkanes  S i m i l a r minima have been observed f o r  (49), polymers (48,50,51) and  t a i n i n g methyl groups (52).  other compounds con-  Use of equation^"?) i n Chapter I  allows the extraction of activation energy values from the l i m i t i n g high and low temperature slopes of the minimum, which, i n favourable cases, may be related to r o t a t i o n a l b a r r i e r s . Only one  value was found usually, indicating that a l l protons  are relaxed e f f e c t i v e l y by the same process. K\„alkanes (49)  Studies on  showed that the methyl group r o t a t i o n provided  a "sink" f o r the relaxation of the methylene protons by means of a s p i n - d i f f u s i o n process, with the r e l a x a t i o n at the methyl group as the l i m i t i n g process, i n high magnetic f i e l d s  (52).  -  In t h i s case,  1 1 3 -  a t the minimum depends on the r a t i o of the t o t a l  number of protons i n a? chain t o the number o f methyl protons per chain.  Now since  min. values are d i r e c t l y p r o p o r t i o n a l t o t h e  measuring frequency, values f o r the stearates may be predicted from the  r e s u l t s obtained f o r the n-alkanes at 5 0 MHz ( 4 9 ) by c o r r e c t i n g  for the change i n measuring frequency. 0.041  For  The value predicted was  sec, and values found were 0 . 0 4 2 - . 0 5 9  seconds (see t a b l e V T I I - 5 )  the n-alkanes, T^ r e s u l t s could be explained using a s i n g l e  c o r r e l a t i o n time "Ct, but t o obtain meaningful r e s u l t s f o r polymers, i t i s u s u a l l y necessary t o invoke a d i s t r i b u t i o n of c o r r e l a t i o n times ( 5 1 , 5 3 ) ,  the e f f e c t of which i s t o make the T-^ minimum  f l a t t e n out, g i v i n g a higher T^ min. value than predicted, and a l s o lower apparent a c t i v a t i o n energies. A c t i v a t i o n energies obtained from two independent evaluations ( 4 9 , 5 2 ) group r o t a t i o n i n p a r a f f i n s were 2 . 6 + 0 . 2 independent of chain lengths.  f o r t h e methyl  kcal/mole, and were  For the soaps, values varying  from 1 . 7 - 2 . 5 kcal/mole were found ( t a b l e V I I I - 5 ) and a c t i v a t i o n energies from the l i m i t i n g high and low temperature slopes of the  T^ minimum should be the same, but here, as elsewhere  t h i s was not found t o be the case.  ( 5 4 , 5 5 ) ,  No c l e a r explanation f o r t h i s  e x i s t s , although i n some cases t h i s may be explained by the presence of a second e f f e c t i v e r e l a x a t i o n process. There a l s o e x i s t s the p o s s i b i l i t y t h a t , despite precautions taken t o degas the  samples some molecular oxygen i s present i n the sample,  which should decrease the T^ values e s p e c i a l l y i n the low temperature region.  Oleate a c t i v a t i o n energies ranged from  1 . 7 - 2 . 4 kcal/mole, and T^ min. values from 0 . 0 3 3 - 0 . 0 5 6  seconds,  -  1 1 4 -  (table V T I I - 5 ) , so that the low temperature r e l a x a t i o n processes for  the oleates and stearates are very s i m i l a r .  The presence of  the  double bond does not seem t o a f f e c t the e f f i c i e n c y of the  s p i n - d i f f u s i o n process, although some authors ( 5 2 ) favour a onedimensional process along l i n e a r paths.  The observation of & s i n g l e  r e l a x a t i o n times i n polymers ( 5 0 ) at low temperatures has caused other authors t o conclude that s p i n - d i f f u s i o n was e f f e c t i v e i n such systems as w e l l , and c e r t a i n l y l i n e a r paths along a s i n g l e chain are not f e a s i b l e f o r the d i f f u s i o n process here.  Indeed f o r polyethylene,  a "three-dimensional random walk with s i n k s " was found t o provide a reasonable mode!.! f o r the d i f f u s i o n process t o methyl s i t e s 1  d i s t r i b u t e d throughout the l a t t i c e . Sodium oleate and sodium stearate T-^ r e s u l t s i n d i c a t e a shallow secondary low temperature minimum near 2 6 0 ° K and the cesium oleate T-^'s remained at a v e r y low value at temperatures aboV£ the T^ minimum. T^ minima i n t h i s temperature region have been observed i n polyethylene ( 4 8 , 5 0 )  and other polymers ( 5 4 , 5 0 ) .  The value of Tj_  at t h i s minimum was found t o be d i r e c t l y p r o p o r t i o n a l t o the percentage c r y s t a l l i n i t y of the sample ( 4 8 ) and therefore the minimum has been assooiated w i t h chain motion i n Vsjt, amorphous regions i n the s o l i d .  To be more exact, t h i s i s the same motion as  t h a t responsible f o r the V" r e l a x a t i o n process observed by mechanical measurements.  The absence of m u l t i p l e r e l a x a t i o n times suggests  that a s p i n - d i f f u s i o n process operates i n t h i s case as w e l l , with the  amorphous regions a c t i n g as r e l a x a t i o n s i n k s . Although i s some cases ( 4 8 , 5 0 ^  s i n g l e r e l a x a t i o n times are  - 115 found, studies on very similar systems (56) revealed that multiple relaxation times were present. was noted.  In t h i s study similar behaviour  For the sodium and cesium oleates, a single relaxation  time was observed i n the temperature region of i n t e r e s t , and f o r sodium stearate multiple relaxation times were found to be present. I t i s probable, then, that the presence or absence of multiple relaxation phenomena depends on the size and also the number and the d i s t r i b u t i o n of t h i s type of relaxation sink i n the s o l i d . I t appears, then, that i n the sodium soaps studied and a l s o in cesium oleate, molecular motion s i m i l a r to that causing relaxat i o n i n amorphous regions i n polymers i s present. iv) The low temperature t r a n s i t i o n For  a l l the stearates, except the sodium s a l t , X-ray measure-  ments (30-34) have indicated that the low temperature NMR  transi-  t i o n corresponds to a true phase change between two c r y s t a l phases, with a decrease i n t e n s i t y (see table VIII-3) of about accompanying the t r a n s i t i o n .  4-8$  DSC evidence exists which suggests  that the low temperature t r a n s i t i o n observed f o r sodium stearate may be f i r s t or second order, depending on thermal h i s t o r y .  No  trends i n t r a n s i t i o n temperatures with the size of the cation are obvious. For  the oleates, no DSC evidence exists f o r a phase t r a n s i t i o n  accompanying the NMR  t r a n s i t i o n and no X-ray study has been made.  Most l i k e l y i f there i s a phase t r a n s i t i o n i t probably i s not f i r s t order, as noo strong peaks were observed i n the DSC thermogram.  The linewidth and second moment changes are also much more  gradual than f o r the stearates, other than sodium stearate f o r  -  1 1 6 -  which no low temperature c r y s t a l t o c r y s t a l phase X-ray t r a n s i t i o n i s observed. The T^ studies f o r the stearates a l s o show a d i s c o n t i n u i t y i n the T^ vs temperature curve where the phase t r a n s i t i o n occurs. For the oleates, no t r u e d i s c o n t i n u i t y was found, but a s l i g h t d i p i n the curve was seen f o r some of the soaps.  This i s a f u r t h e r  i n d i c a t i o n that the t r a n s i t i o n s f o r the oleates and stearates are of a d i f f e r e n t nature. v)  Linewidths and second moments between t r a n s i t i o n s Below the low temperature t r a n s i t i o n the second moments f o r  most of the soaps have values of 9 - 1 4 gauss' , with the values f o r 1  the rubidium stearate and the cesium soaps s i g n i f i c a n t l y lower. The cesium oleate i s unique i n that i t does not show a second NMR transition.  The second moments a t t a i n a value of 1 . 8 gauss above 2  the low temperature t r a n s i t i o n and from there decreases only very slowly; near 4 2 0 ° K the decrease becomes more rapid and a value o f 0 . 8 8 gauss  2  i s found at 4 6 5 ° K .  For the other soaps second moments  were 1 0 gauss f o r the sodium soaps and 4 - 7 gauss f o r the other 2  2  soaps below the high temperature t r a n s i t i o n . For a l l the s t e a r a t e s , X-ray measurements ( 3 0 - 3 4 ) another c r y s t a l l i n e phase e x i s t s between the two NMR  showed that transitions.  The decrease i n density of about 8% i n going from the low t o the high temperature c r y s t a l phase should allow a s u b s t a n t i a l increase i n molecular motion, i n agreement w i t h the decrease i n second moment. Previous CW NMR studies ( 7 ) i n d i c a t e d that second moment above the low temperature phase t r a n s i t i o n were consistent w i t h complete chain r o t a t i o n about the chain a x i s .  - 117 There i s evidence f o r another type of motion from an i n f r a r e d study of sodium palmitate (26).  Near 90°C (near the low temperature  t r a n s i t i o n ) the appearance of a s i g n i f i c a n t number of d i f f e r e n t r o t a t i o n a l isomers i s i n d i c a t e d .  Low temperature mechanical studies  (46) i n d i c a t e d that such r o t a t i o n a l isomers were i n t e r c o n v e r t i n g between d i f f e r e n t c o n f i g u r a t i o n s .  I f these interconversions are  r a p i d enough they may be t r e a t e d as motional modes e f f e c t i v e i n decreasing NMR l i n e w i d t h s and second moments.  Now the low temp-  erature mechanical studies have i n d i c a t e d that t h i s motional process should be c l a s s i f i e d as a y  process. I f i t i s assumed that the  c o r r e l a t i o n times are v l sec at 1 0 0  o K  a n d  "^10"^  3 e  c . at 370°K  from the mechanical and NMR measurements r e s p e c t i v e l y an a c t i v a t i o n energy of 2.5 - 3.5 kcal/mole r e s u l t s , not too unreasonable from an energy point of view. vi)  T^ values between t r a n s i t i o n s For the s t e a r a t e s , except the cesium and sodium soaps, a  w e l l defined d i s c o n t i n u i t y appeared at the low temperature t r a n s i t i o n , with the high temperature phase T^ values being lower.  The  cesium stearate and most oleates g e n e r a l l y showed a s l i g h t decrease or a s m a l l d i p i n the T^ curve i n the region of the low temperature t r a n s i t i o n .  For the sodium o l e a t e , the T^'s v a r i e d continuously  i n both low and higher temperature phases, w i t h no d i s c o n t i n u i t y present. A new r e l a x a t i o n process must become e f f e c t i v e f o r the soaps which e x h i b i t a decrease i n T^ values on going through the t r a n s i tion.  I f methyl group r o t a t i o n was s t i l l the main e f f e c t i v e  r e l a x i n g motion, the T  values should show an increase on entering  - 118 -  the h i g h e r temperature  phase, c o n s i s t e n t w i t h an i n c r e a s e i n  c o r r e l a t i o n t i m e due t o a lower b a r r i e r temperature decrease  phase.  i n t h e l e s s dense, h i g h e r  I t i s unlikely that correlation  on g o i n g through t h e t r a n s i t i o n i n d i c a t i n g  times  should  a higher  b a r r i e r i n t h e h i g h e r temperature  phase.  c o r r e l a t i o n t i m e s s h o u l d decrease  on g o i n g through t h e t r a n s i t i o n  indicating  a higher b a r r i e r  I n the second  I t i s unlikely that  i n t h e h i g h e r temperature  c r y s t a l l i n e phase,  values again increase with  indicating thatWoCt-^Clfor t h e e f f e c t i v e r e l a x i n g  temperatures, motion.  No d i s t i n c t i v e minima were e v i d e n t .  straight  l i n e s c o u l d be f i t t e d t o t h e l o g T^.vs V  activation  phase.  Approximately T  d a t a , and  e n e r g i e s a r e summarized i n t a b l e 5, a l t h o u g h t h e s i g -  n i f i c a n c e o f t h e s e v a l u e s i s not o b v i o u s . the hydrocarbon of c o r r e l a t i o n  Any motions i n v o l v i n g  c h a i n s a r e l i k e l y t o have a l a r g e times.  distributions  I t i s j i p o s s i b l e t h a t some o f t h e m o t i o n a l  modes r e l e a s e d d u r i n g the phase t r a n s i t i o n and e f f e c t i v e i n narrowing  the resonance  l i n e a t t h e t r a n s i t i o n temperature a r e  r e s p o n s i b l e f o r t h e r e l a x a t i o n i n t h i s c r y s t a l phase. The on  going  still  cesium and sodium o l e a t e T^ v a l u e s showed l i t t l e  change  through t h e t r a n s i t i o n , and t h e r e l a x a t i o n p r o c e s s i s  t h e same one t h a t governs t h e r e l a x a t i o n i n t h e low tempera-  t u r e phase.  T h i s absence o f any major change i s c o n s i s t e n t w i t h  t h e r e l a x a t i o n b e i n g due t o amorphous r e g i o n s , as a c r y s t a l change s h o u l d n o t a f f e c t amorphous r e g i o n s .  v i i ) The h i g h temperature A h i g h temperature  phase t r a n s i t i o n  NMR t r a n s i t i o n was observed f o r a l l t h e  soaps s t u d i e d except t h e cesium o l e a t e .  F o r some o f t h e s t e a r a t e s  - 119 t h i s t r a n s i t i o n has been characterized by X-ray methods (30-34).. L i t h i u m and potassium stearate t r a n s i t i o n s correspond to true phase changes from the c r y s t a l phase t o a waxy phase.  For the cesium  stearate, the t r a n s i t i o n i s again t o another c r y s t a l phase.  Nor  t r a n s i t i o n was observed by the X-ray method f o r the sodium and rubidium stearate i n the region where the NMR t r a n s i t i o n s were observed.  However, a peak i n the DSC thermograms accompany a l l  the high temperature NMR t r a n s i t i o n s so that even f o r the sodium and rubidium stearate a f i r s t order t r a n s i t i o n i s i n d i c a t e d .  For  the oleates, the high temperature phase t r a n s i t i o n a l s o was accompanied by a peak i n the DSC thermograms, but t h i s t r a n s i t i o n has not been c h a r a c t e r i z e d .  NMR  second moments above t h i s phase  t r a n s i t i o n are normally i n the 0.5 - 1.0 gauss range. 2  Values  l i k e t h i s are normally associated w i t h the presence of motions about a number of axes, o n l y t r a n s l a t i o n a l motions being excluded. The t r a n s i t i o n could then be c l a s s i f i e d as a c r y s t a l phase-subwaxy phase t r a n s i t i o n i n terms of Void's c l a s s i f i c a t i o n . rl  v i i i ) C o r r e l a t i o n between t r a n s i t i o n observed by NMR F a i r l y good c o r r e l a t i o n e x i s t s between the NMR  and other methods transitions  observed f o r the soaps and those seen using the DSC method. A l l temperature regions of l i n e narrowing f o r the stearates observed by the NMR method correspond t o peaks i n the DSC thermograms, and the same may be s a i d f o r the high temperature t r a n s i t i o n s i n the o l e a t e s . However, f o r the stearates many more t r a n s i t i o n s were observed using the DSC method, than were observed using NMR, and  - 120 supposedly a l l the DSC peaks correspond to f i r s t order phase changes. Since most of these phase changes do not correspond to transitions observed by X-rays, no major changes in unit c e l l parameters accompany these transitions.  Also, no major changes i n chain interaction take  place, since these should be evident from studies by the NMR method. These phase changes observed by DSC remain somewhat mysterious. The fact that no large peaks were observed to accompany the low temperature transitions for the oleates tends to suggest that possibly a higher order transition takes place here.  The DSC method  also reveals that the oleates exhibit fewer transitions than the corresponding stearates.  This has also been observed for branched  soaps (17), where fewer possibilities of mesomorphic transitions exist. ix) General Observations From the complexity of the phase structure of the soaps as determined by the X-ray as well as the other methods mentioned, i t would seem rather futile to try to place each transition observed for the soaps into a rigid scheme, as was attempted for the sodium soaps (22). The number of transitions increases with chain length,, and also varies with the cation. The differences i n phase behaviour of the stearates must be attributable largely to the effect of the ionic groups.  Although  close packing arguments usually are applied to small spherical systems, the arrangement of the oxygen and positive ions in the ionic layer might be expected to resemble conventlally packed solids.  In  the potassium palmitate each potassium ion i s surrounded by aix oxygens at distances between 2.73& aad 2.78 8,  approximately equal  - 121 to the sum of the oxygen and potassium ionic r a d i i .  The  coordination i s expected t o change from 4^4 to 6:6 and f i n a l l y to 8:8 as the cation t o anion radius r a t i o increases. the  Similarly  coordination i n the i o n i c groups i n the soaps might be expected  to change f rom 4.2  to 6:3 and 8 : 4  changes from L i * to Cs*. considerably.  coordination as the cation  This might then change the chain packing  No other soap structures are known i n d e t a i l ; the  only other s t r u c t u r a l parameters that are known f o r a number o f soaps are d, the distance between ionic layers and S, the projected area available per carboxylate group.  In going from the l i t h i u m  stearate t o the cesium stearate (excepting the sodium s a l t ) these parameters f o r the low temperature c r y s t a l phase are  42.6A, 40.6)? and 38.7A;Ss  22.lS , 2  25.0A" , 26.L? 2  2  and  :ds42.o8, 28.ifl . 2  These data indicate that there are minor differences i n structure, but the implications as f a r as the motional and phase properties of the soaps are concerned are not clear.  3$  Summary A short summary of the results obtained for the 3oaps w i l l  now be given. I t was found that methyl group r o t a t i o n takes place at a l l temperatures down t o about 77°K at frequencies greater than 10^105 Hz. Methyl group rotation also was the effective relaxation mechanisraTidn the low temperature phase.  Activation energies  obtained f o r t h i s process varied from 1.7 - 2.5 kcal/mole. For several soaps a second low temperature relaxation process was found t o be important and t h i s process was thought t o be similar to the one associated with amorphous regions i n polymers. Various  - 122 types of molecular motion were proposed to e x p l a i n l i n e narrowing observed i n both the high and low temperature phases of the soaps. For the stearates a l l of the low temperature t r a n s i t i o n s observed by NMR accompanied known X-ray t r a n s i t i o n s from one c r y s t a l l i n e pbase t o another.  The o r i g i n of the oleate low temperature  NMR t r a n s i t i o n s remains unknown.  The high temperature MMR t r a n s i -  t i o n s f o r the oleates as w e l l as stearates a l l accompanied  first  order t r a n s i t i o n s observed using the DSC method, and some of the stearate NMR t r a n s i t i o n s a l s o corresponded to known X-ray transitions.  I n the high temperature phase a new  process becomes e f f e c t i v e f o r some of the soaps.  relaxation The nature  of t h i s process i s uncertain; i n some cases a c t i v a t i o n energies could be obtained i n t h i s temperature region, but the s i g n i ficance of the values i s not known. The DSC studies showed that the thermal h i s t o r y of the s oaps may a f f e c t some of the t r a n s i t i o n s severely.  Many more t r a n s i -  tions were observed w i t h t h i s technique than could be accounted f o r by e i t h e r the NMR on the X-ray methods. I f any f u t u r e studies on soaps are undertaken, i t might be i n t e r e s t i n g t o i n v e s t i g a t e the thermal h i s t o r y e f f e c t s and a l s o the e f f e c t of the presence of amorphous regions i n more d e t a i l using l i n e w i d t h , second moment and a l s o s p i n - l a t t i c e r e l a x a t i o n time measurements.  -  1 2 3 -  BIBLIOGRAPHY CHAPTER V I I I 1  R.F. 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Blears Polymer 6, 385 (1965) 54 T.M. Connor Polymer 4., 263 (1963) 55* T.M. Conner Trans. Farad. Soc. 60, 1574 (1964) 56,W.P. S l i c h t e r J . Appl. Phys. 3J2, 2339 (1961)  -  1 2 6 -  APPENDIX A Although t h i s computer program i s by no means general,  this  presentation may be of some a i d t o anyone w r i t i n g a t h e o r e t i c a l second moment program. The program i s meant t o c a l c u l a t e proton and f l u o r i n e r i g i d l a t t i c e second moments f o r BF^MH^ from the c r y s t a l structure  information.  The input data required are AO, BO, CO, the u n i t  cell  dimensions, A X ( l ) , BI( I ) , C Z ( l ) , the f r a c t i o n a l coordinates f o r a BF^NH-j molecule as given by the c r y s t a l s t r u c t u r e study, A-F, parameters t o generate the remaining 7 molecules i n the unit c e l l obtained from X-ray t a b l e s f o r the space group i n question, and A l , B l , C l , parameters t o generate 2 6 u n i t c e l l s surrounding the c e n t r a l c e l l . The out-put the program provides includes:  B-F, B-N, N-H  bond lengths, B-N-H bond angles, the F-F, F-B, F-H, N-H, H-F, H-H intramolecular F-H,  second moment c o n t r i b u i t o n s , and the F-F, H-H, F-H,  H-B, F-B intermolecular  second moment contributions from  distances l e s s than 8 A . Also given are a l l the atomic coordinates w i t h i n the c e n t r a l unit  cell. Further, I l a b e l s the 8 molecules w i t h i n the c e n t r a l u n i t  c e l l , J = l i n d i c a t e s a boron nucleus, J = 2 ^ N , J = 3 - 5  1 ]  ^ F and  and J = 6 - 8 ^H. Also, K l a b e l s the 2 7 u n i t c e l l s and N l a b e l s the molecules w i t h i n the 2 6 p e r i p h e r a l u n i t c e l l s .  Reproduced on  the f o l l o w i n g pages are the Fortran IV deck contents, input data and a p a r t i a l output  listing.  - 127 UNIVERSITY ; j i ? S * -i v i S ^ i 4 - f 5 *  $  ifHr. -k v * j6r * # ."V A A &  OF  B.  * W* # * * t * *  C.  COMPUTING  L I S T I NG  * A '¥ A. 5. ^ $ A « *• * A -it* * « £ *  CENTRE  * * * * * * * * * * * * * * * * * * * * < s * * * r - i : A f c A s :  ^ at vj< i- =r -if v. J:JX A $  *  DIMENSION A X { 8 ) , BY ( 3 ) , C Z ( 8 ) , X ( 8 , 8 ) , Y I 3 , 8 ) , Z ( 8 , 8 )' C , Z 1 ( 1 , 8 ) , 0 I T ( 8 ) , D IN ( 3) , TM E T A ( 3 ) COMMON X , Y , Z READ I,AO,80,CO FORMAT (3F8.4) R FAD  1 ,  __  ( AX ( I ) , BY ( T ) , C Z (  I  ) ,  1=1,  A  r-i' M i: & * $  # j|t # * * * #  , X 1 { 1, 8 ) , Y 1 ( 1 , 8 >  _  8 )  '  "  1=0 1=1+1 READ 2,A,B,C,D,E,F FORMAT ( 6F5.2) K=0 . PRINT 52 F O R M A T < / , 2 7H I J DO 2 0 J =l,8 r X {I , J )- ( AX ( J ) ) * A 0 Y(I,J)=(C+D-BY(J))«3C Z ( I> J )•= ( E + F - C Z ( J ) ) * C 0 IFfl.GE.2) GO TO 6 0 0  :  _ X  Y  Z)  A  xn r , j)=x< i , j)  1 ( I , ,1 ) = Y ( I t J ) Z H I , J )=Z ( I, J ) CONTINUE P R I N T 51 , ! , J , X { I , J ) , Y ( I , J ) , Z I I , J ) FORMAT ( / / , 2 I 3 , 3 F 8 .4 ) CONTINUE  V  10  )  10  I F ( I . G F . 8 ) GO T O 7 5 GO T O 1 0 DO 7 0 0 L=?,5 D I M L ) = 0 I S T ( 1, 1 , L ) SUM=Q. CONTINUE DO 8 0 0 L=6,8 O I N l L )= D I S T ( 2 , 1 , L ) SUM=SUMM 1 . / D I N ( L ) )^ 6 : J  T H F T = A R C 0 5 ( ( ( X ( L , 2 ) - X ! 1 , 1 I ) M X( i , ! I - K I ] , Z ) ) H 1 ( Y( 1 , L ) - Y ( 1 , 2 )  )0  ) M Z ( 1 ,2) - Z( 1 ,1 ) ) • { Z( 1 , L ) - l l 1 . 2 )  )1  *  !  ) ) / I 0.1 S T ( 1 , 1 , 2  )*  2 D I S T ( 2 , 1 , U )) TH-ETACL ) - T H F T * 5 7 . - 2 9 6 CONTINUE S D = ( 2 . 2 6 / 3 . ) * SUM ADI'ST=< 1 . / D I - S T l 1 , 1 , 3 ) I « 6 M l . / 0 I S T ( l , l , 4 ) ) * * 6 + ( l . / O I S T j 1 , 1 , 5 ) ) * * 6 „ . BB=72. SC=8R*A0.I S T / 3 . P R I N T 701 ( O I T ( L ) , L =2 , 5 ) , S C F O R M A T ( / / / , 6H 8 - N = , F 8 . 4 , 6 H R - F = , 3 F 8 . 4 8HSM' B - F = , F 8 . 4 ) PRINT 8 0 1 , I1.HNIL) , T K E T A ( L ) , L =6 , 8 ) , S D F O R M A T ( / / / , I 7H N - H AND O - N - H = , 2 F 8 . 4 , 4 X , 2 F 8 . 4 , 4 X , 2 F 8 . 4 , 9 H S.M.N-H 1 = , F 3 . 4) PRINT•53 •• F O R M A T( / / / I 7 H C A L C O F I N T R A S M ) ' f  )1  Y( 1 , 2 | - Y ( I , 1 ) ) «  t  P R O TON  -PROTON  ~  i: Kh  J T» ;  128 -  AD I S T = ( l . / 0 I S T ( 6 , l , 7 ) SA = 7 1 6 . * AD I S T / 3 . FLUORINE-FLUORINE  ;  ADI ST=  l « 6 f (  ( 1 . / O I S T ( 3 , 1 , 4) )  1 . / O 1ST < 6 ,  + { 1 . / O I ST{ 7 , 1 , 3 )  P  6 f ( I . / OI S T ( 3 , 1 , 5 H * * 6 + ( 1 . / OT S T ( 4 ,  S8=634. AQIST/3.  '  M  :  1,3)  )* * (, :  I , 5 ) )' •• 6  -  FLUOR.INF-PROTON  ~  ~  ~  SUM=0. DO  21  J =3 , 5  DO  21  L=6,8  ADIST=( I . / D I S K J , 1 , L ) ) * * 6 :l  SlJM=SUM + AO.I S T CONTINUE Sl=(159./3.)*SUM S 2 = ( 1 4 0 . 9 / 3 . ) SUM  ~~  ~ ~  SF=sa+si+sc SP=SA+S2+SD PRINT 2  22,SA,S3,SNS2,SP,SF  FORMAT 1. , 1 G H  {///10H  S.M.P-F  S.M.P-P  =»F8.4,1CH  = ,F8.4,18H  S M . INTRA  S.M.F-F PROTON  =,F8.4,9  =,F3.4,14H  H  S.M.F-P=,F».4  SM  INTRA  F.  =,  . 2 F 8 . 4> PR I N T 4  54  '  FORMAT  <///23H  PROTON  -PROTON  "'  INTERMOLECULAR  SUM T O 3 = 0 .  "  CONTR.)  ,.  :  SUMT04=0. SUMT05=0. SUMT06=0. SUMT07=0.  02  SUMT03=0.  K-K+1 IFIK.F0.1J  N=l  IF(K.GT.l)  N=0  PR I N T 00  300,K  F O R M A T ( 5 H - — K = , 13 ) N= N + 1 SUM=0. DO  31  DO  31  CALL 1  J = 6,8 L=fi,8 FINDIS(.J,N,L,X,Y,  Z , X1 , Y 1, 7 1 , SUM )  CONTINUE S3=(3 5 3 . / 3 . )  SUM  F-F SUM=9. DO  3.3  J =3 » 5  DO  33  1=3,5  CALL 3  .  _'  '  FIN0IS(J,N,L,X,Y,Z,XL,Y1,Z1,SUM>  CONTINUE S4={  3 1 7 . / 3 . MSU.M  F-P SUM=0. DO  34  .  . _  '_  DO 3 4 L=6,8 CALL F I ND I S ( J t N i L »X V  .  J=3,5 f  v , Z t X 1 , Y 1 t ? 1 » SU M »  CONTINUE S5-(159./3.)*SUM p-F  ;  SUM=0.~ DO  3 5  DO  3 5  CALL  ~ J=6,3  •  ^ '  . " ~  '  1 = 3,5 FINDlS(J»N,LtX,  _____ Y, Z , X 1 , Y 1 . » Z . 1 t SUM)  ^  :  ;  ~  ~  "  ?  CONTINUE S6=(140.9/3.MSUM F-3 SUM=0. 00 130 L = 3 , 5 . CALL FINDIS( I , N , L , X , Y , Z , X 1 , Y I , Z 1 , S U M ) CONTINUE S7 = ( B 3 / 3 . ) SUM H-B ' ' SUM=0. DO 140 L = 6 , 8 CALL F I N D I S t 1 , N , L , X , Y, Z , X I , Y 1 , Z 1 , S U M ) CONTINUE S8=(BB/3.)*SUM IF ( S3 . E Q . (0 . ) . AND . S4 . F Q . (0 . ) . A N D . S 5 . F Q . ( 0."")' . AND . So . EQ ."{ 6V> ) GO "TO C 900 P H I N T 2 0 0 , N , S 3 , S 4 , S 5 , S 6 , S 7, S 8 FORMAT ( / / , 3H N=,J 3 , 8H SM P - P = , F 3 . 3 , 8H SM F - F = , F 8 . 3 , 8H SM F - P = C , F 8 . 3 , 8 H SM P - F = , F 8 . 3 , 8 H SM F - B = , F 8 . 3 , 8 H SM H - B = , F 8 . 3 ) SUMT03=SUMT03+S3 _ _ SUMT04=SUMT04+S4 ' " SUMT05=SUMT05+S5 SUMT06=SUMT06+S6 Sl)MT07=SUMT07 + S7. SUMTD8=SUMT03+S8 I F ( N . G E . B ) GO TO 79 GO TO 8 >• ~~ ;  :  >  > >  IFIK.GE.27) GO TO 7  >  READ 5 0 0 , A 1 , B 1 , C 1 FORMAT {3F4. 1 ) DO 97 1=1,3 DO 97 J = 1 , 3 X.( I f J ) = X ( I ,.J )+Al*AO Y(I,J)=Y<I,J)+81*B0 Z ( I., J) = Z.( I t J )+Cl*CO CONTINUE GO TO 502 PRINT 70,SUMT0 3,SUMT04,SUMTO 5,SUMTO6,SUM TO7,SUMTOH FORMAT ( / / / , 1 0 H S . M . P-P = , F 3 . 4 , 1 0 H S . M . F - F = , F8 . 4 , 1 OH " s". ?•*. F - » = , F 3 C.4,10.H S . M . P - F -= F8.3,10H S . M . F - B = , F 3 . 3 , 1 0 H S.M.H-B = , F 8 . 3 ) SF=SUMT04+SUMT0 5+SUMT07 S?=SUMT03+SUMT06+SUMT08 PRINT 71,SP,SF FORMAT ( / / / , 1 5 H INTER S . M . P = , F 8 . 4 , 4 X , 1 5 H INTER S . . F _ = , F 8 . 4 J S T O P " ' END SUBROUTINE F 1 N D I S ( J , N , L , X , Y , Z , X 1 , Y 1 , Z 1 , S U M ) DIMENSION X( 1 0 , 2 0 ) ,Y ( 10,20 ) , Z M O ,20 ) , X l ( 1 , ? 0 > , Y l ( 1 ,20 I , 71 ( 1, 20 ) D I S = SQR T ( ( X1 { 1 , J ) - X ( N, L ) ) **2 + ( Y 1 ( 1 , J ) - Y ( N, L ) ) * 2 + ( Z 1 ( 1, J ) - Z K N , L ) ) f  M  C**2)  ..  I F ( D l S . G T . ( 3 . ) ) GO TO 1 1 F ( D IS . GT . ( 3 . ) ) GO TO 2 PRINT 3 , P I S FORMAT ( F 8 . 4 ) AOIST=(1./DIS)-?6 SUM= SUM + ADI ST _ _ RETURN ' END :  FUNCTION T H E T A I J , K , L )  "  ~  ."  DIMENSION XI 1 0 , 2 0 ) Y ( l O , 20) ,7< 1 0 , 2 0 ) -130COMMON X , Y , Z THFTA-=57.296*ARC0S( ( ( X (1 , K ) - X { I , J ) ) M X ( 1 , L ) - X ( 1 . K( Y) ()l +,:<)- Y ( 1 , J ) 1 ) M Y( 1 ,L) -Y< 1 , K ) ) + ( Z (1 , K )-? ( I , J ) ) M It 1 ,L ) - Z( I , KD) I) S) K / (J , 1,K)*n i 2ST( K, 1, L 5 ) ) RETURN "~ FND FUNCTION O t S T l J N , L ) DIMENSION X ( 1 0 , 2 0 ) , Y ( 1 0 , 2 0 ) ,Z( 10, 2 0 ) COMMON X,Y,Z DIST^SQRT ( ( X ( l , J ) - X ( N , L ) ) - 2 K Y ( l , J ) - Y ( N , L ) ) ' 2 M Z ( I , J ) - Z ( N , L ) ) " ' 2 C) RETURN END . 22 3.1 1 9.31 . 160 0 .105 0. 169 .046 0 . 241 0.095 DATA - 0 . 040 .0 78 0.167 0. 0 9 4 .305' 0.093 0. 156 0.308 . 188 0. 10 0 .3 5 .11 0.15 0. 25 .06 -0.01 0. 20 .025 0. 1. ). 1. 0. 1. }, .5 -1 . 0.5 1. 0 . 1 . 0.5 - 1 . ) 1 . 0.5 I. 0.5 - 1 . 0. 1. )5 1 . ). -1 . 0. -1. 0. - 1 . ), 5 0. - I. 1 . -0.5 - 1 . - 0 . 5 + 1. - 0 . 5 - 1. ). -1 . -1. -0.5 1. 0. ), 5 -1 . 0• 0. 0. 0 . 1. -2 . 0. 1 . 1. C . -?. 1. 0. 0. 0. 0. 0. 0 . -1. 0. -1. 0 . 0. 0 . o. 0. 1. 1. 1. 0. 0. -2 . 0 . 0. 0. 0. 1. 1. 0. 0. 1. 0. 0. 0 . 0. 0. -1. 0. -1. 0.' 0. f  t  v  t  j  D I M F N S I ON X ( 1 0 , 2 0 ) , Y ( 1 0 , 2 ^ > ,/<10,20) " ^ " COMMON X , Y , Z T H F T A = 5 7 . 2 9 6^ ARCOSt I (XI l , K | - « l l , J I ) M X f 1 , L ) - X { U K ) ) H Y (1 , '< ) - Y { 1 » J ) 1) ( Y ( 1 , L ) - Y ( 1 , K ) )+(Z (1 , K ) - 7 ( I , J ) ) ( Z ( I , L ) - Z ( I , K ) ) ) / ( O I S T ( J , 1 , K ) * 0 I ? S T ( K , 1,1 n . i RETURN ~ ~ END F U N C T I O N DI S T ( J N,L) DIMENSION X(1C,20),Y(10 2^),Z(10,20) COMMON X,Y,Z D I S T ^ S Q R T I ( X ( 1 , J ) - X ( N , L )) 2 + ( Y ( 1,J ) - Y < N , L ) ) • 2 H Z ( 1 , J ) - Z ( N , L ) ) ^ 2 t  t  —  - .  RETURN END 8.11 8. 22 9.31 0.1050. 160 0. 169 0.241 0 .r>46 0.095 0.0 78 -0.040 0.167 0.305 0.094 0.093 0. 188 0.156 0.308 0.11 0.35 0.10 -0.06 0.25 0.15 0.20 0.025 -0.01 0. 1. 0. 1L. 0. 1. 0.5 - I . 0.5 1 0. 1. 0.5 -]L. 0. 1. 0.5 I . 0.5 1. 0. 1 C.5 - 1 . 0. -I . 0. -11. 0. - 1 . 0.5 1. - 0 . 5 -1 0. - 1 . 0. -1 . - 0 . 5 +1L . -0.5-1. 0.5 - 1 . 0. -1L. - 0 . 5 1. 0. 1. 0. 2. 0. 0. 0. U 1. 0. - 2 . 0. 1 . 1. 0. 0. - 2 . 0. 1. 1. 1. 0. 0. 1. 0. 0. 0. -1 . 0. 0. - 1 . 0. 0. 1. 0. 1. 0. 0. 0. 1. 0. 0. 1. 1. 2. 0. 0. 0. - 2 . 0.  c.  2.  0. 0.  0.  Do 3. !_.  1  0.  3.  1,  1.  0. 1. 0 . _0. CU 0. 0. - 1 . 0. - 1 . 0. 0. 0. I.  .  0.  N-H  AND B - N - H =  1.0297 7 4 . 1 8 0 8  1.0133 7 0 . 4 2 2 8  72.0000 73.7887 S.M.N-H=  .'  2  1.9002  .  CALC OF INTRA SM  S.M.P-P  = 29.3344 S . M . F - F  INTERMOLECULAR  =  4.6993 S.M.F-P=  1.1355  S.M.P-F  =  1.0062  SM.INTRA  PROTON = 3 2 . 2 4 0 7 SM INTRA  CONTR.  — K=  1  N=""2  SM P-P = " 0 . 0 5 5 ' SM "F-F="  '  0".253~~SM F-P= \  0.010SM  P-F=  0 . 7 3 9 SM F - B = 0 . 0 1 9 '  SM H-B=" _  0.001  \  ;  \ M  N=  3 SM P-P=  , 0 . 1 9 9 SM F - F =  0 . 0 9 0 SM F-P=  0.401  SM P-F=  0 . 0 1 2 SM F-B=  0.003  SM H-B=  0.019  N=  4 SM P-P=  0.096  0.255  SM F-P=  0.583  SM P-F=  0.010  SM F-B=  0.011  SM H-B=  0.033  N=  5 SM P-P=  0.208SM F-F=  0 . 1 4 0 SM F-P=  0.662  SM P - F =  0 . 5 8 7 SM F - B =  0.012  SM H-B=  0.026  N=  6 SM P-P=  0.000  SM F - F =  0.008  SM F-P=  0.000  SM P-F=  0.002  0.000  SM H-B=  0.000  N=  7 SM P-P=  0 . 0 0 8 SM F - F =  0.000  SM F-P=  0.002  SM P - F =  0 . 0 0 0 SM F - B = " 0 . 0 0 0  SM H-B=  0.000  N=  8 SM P-P=  0 . 0 0 5 SM F-F==  0.002  SM F-P=  0.001  SM P-F=  0.003  SM H-B=  0.000  SM F - F =  SM F - B =  SM F - B =  0.000  N=  6 SM P-P=  0.001 SM F*F =  0.007 SM F-P =  0.001 SM P-F=  0.003 SM F-B=  0.000 SM H-B=  0.000  N=  7 SM P-P =  0.076 SM F-F=  0.117 SM F-P=  0.011 SM P-F=  0.414 SM F-B=  0.010 SM H-B=  0.002  N=  8 SM P-P=  0.005 SM F-F=  0.000 SM F-P=  0.000 SM P-F=  0.000 SM F-B=  0.000 SM H-B=  0.000  — K=  24  — K = 25  —K=  26  —K=  27  N=  VO  2 SM P-P=  0.C00 SM F-F =  S.M.P-P -  1.8702 S.M.F-F  INTER  P =  S.M.  TIME 22HRS  56MIN  5.1589  26.8SEC  =  0.000 SM F-P =  2.0792 S.M. F-P =  INTER  S.M.  F =  0.000 SM P-F=  3.4926  5.6903  S.M.P-F =  0.000 SM F-B =  3.095__S,.H,. f-ft  0.000 SM M-B*  *  O..J 1 8  0.00C  *t «Tfi._U-..&«  - 133 APPENDIX B  o  On the next f i v e pages are reproduced t r a c i n g s of the thermograms obtained f o r the thermal h i s t o r y study of the a l k a l i metal stearates.  The thermal h i s t o r i e s of the d i f f e r e n t soap  samples w i l l be repeated at t h i s p o i n t : curves 1: Samples were kept under vacuum curves 2'- samples were kept under vacuum at 110-120°K f o r 14 hours and run 24 hours later. curves 3  1  samples were kept under vacuum a t 110-120°K f o r 28 hours and run 24 hours later,  curves 4* samples were fused under vacuum and run about a week l a t e r . The purpose of t h i s study was t o demonstrate that thermal h i s t o r y a f f e c t s both the shapes and heights of the peaks, and sometimes t r a n s i t i o n s may appear or disappear on heating or fusing.  T r a n s i t i o n temperatures l i s t e d are only approximate  as the peaks were often broad, with long l e a d i n g edges.  c  Figure 4 1 DSC  curves  f o r Rubidium S t e a r a t e  - 134 APPENDIX C Reproduced on the next two pages are l o g  versus inverse  temperature p l o t s f o r the a l k a l i metal stearates ( f i g . (43) ) and oleates ( f i g . (44) ). The l o g T^ values have appeared p r e v i o u s l y p l o t t e d as a f u n c t i o n of temperature ( see Chapter V I I I ) . The inverse temperature p l o t s are included here t o i l l u s t r a t e the s t r a i g h t l i n e segments of the curves from which a c t i v a t i o n energies were obtained.  to follow page 134  Figure 43 Inverse temperature plots of l o g T  1  3  5  7 1 0 0 0 / T (°K  f o r alkali-metal  9  11  stearates  13  t o follow page 1 3 4  1000/T (°K.)-• Figure 44 Inverse temperature plots of l o g T  f o r alkali-metal.oleates  - 135 APPENDIX D  Inithis section w i l l be shown some representative spectra obtained for the oleates. The spectra are also listed i n the following table together with the second moment at the corresponding temperature. Uncertainties listed are maximum deviations from the averaged second moment obtained from at leas* four experimental second moment values.  No.  Lithium Oleate Temp. (°K) Second Moment (gauss ) 2  1  77  25.1*1  2  162  18.7* .2  ,;3  295  13.44.4  4  419  5.1 *.2  5  434  0.65*.l  Sodium Oleate 6  77  26.0 ±.8  7  240  18.0 41  8  293  11.9*1  9  331  4.0 ±.4  10  374  0.8 4.1  Potassium Oleate M  77  25.4* .5  12  261  17.5 ±15  13  295  11.6 ±.3  14  401  3.87 ±.3  15  408  2.89 ±.3  16  414  1.85 ±.1  -136 -  No.  Temp. (°K)  Second Moment (gauss ) 2  Rubidium Oleate  17  77  18  258  26.0*1 16 i l  Cesium Oleate  19  77  :> 25.8 ± 1  20  23k  12.3 ± 1  21  270  8.3 i . 8  22  335  1.7*.2  to follow page 136  A  v  i  io  3  iff  o  IO  4-  _ / . 1 i.ntJ'.jjAllj.ij..  T  TH»f»  (O  10  8  >  Figure 45 Representative spectra f o r Lithium ( 1-5 ) and Sodium ( 6-10 ) Oleate.  t o f o l l o w page 136  Figure 46 Representative spectra f o r Potassium Oleate  \ 11  •0K  J It  *  *8  if  13 10  t o f o l l o w page 136  Figure 47 Representative spectra f o r Rubidium ( 17-18  ) and  Cesium Oleate ( 19-22  )  

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