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UBC Theses and Dissertations

Deuterium nuclear magnetic resonance study of water in model and biological membrane systems Wei, C.M. 1979

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D E U T E R I U M N U C L E A R MAGNETIC RESONANCE I N MODEL AND  BIOLOGICAL  STUDY  MEMBRANE  OF WATER  SYSTEMS  by C. M.  A THESIS  WEI  SUBMITTED I N P A R T I A L F U L F I L L M E N T  THE R E Q U I R E M E N T S MASTER  FOR THE DEGREE OF  OF  SCIENCE  in THE DEPARTMENT  OF  PHYSICS IF THE FACULTY OF GRADUATE STUDIES  We  accept to  this  thesis  the required  as  conforming  standard  THE U N I V E R S I T Y OF B R I T I S H October, 1979  (DfeC.M. Wei, 1979  COLUMBIA  OF  In p r e s e n t i n g t h i s  thesis  an advanced degree at the L i b r a r y I  further  for  of  this  freely  available  for  agree t h a t p e r m i s s i o n f o r e x t e n s i v e  the requirements  Columbia,  I agree  reference and copying o f  this  representatives. thesis for  It  financial  i s understood that gain s h a l l  Department of The U n i v e r s i t y o f B r i t i s h  2075 Wesbrook Place Vancouver, Canada V6T 1W5  Columbia  not  copying or  for  that  study. thesis  purposes may be granted by the Head of my Department  written permission.  G  fulfilment of  the U n i v e r s i t y of B r i t i s h  s h a l l make it  scholarly  by h i s  in p a r t i a l  or  publication  be allowed without my  ii Abstract A d e u t e r o n magnetic resonance s t u d y o f w a t e r has been c a r r i e d o u t i n the l a m e l l a r phase o f t h e egg y o l k l e c i t h i n - w a t e r and o u t e r membrane o f E. C o l i - w a t e r systems i n excess w a t e r ( a b b r e v i a t e d t o EYL/EXCD2O and EC/EXCD 0, r e s p e c t i v e l y ) and egg y o l k l e c i t h i n - w a t e r i n 2 2 % (by w e i g h t ) 2  water (EYL/22%WD20).  S p e c t r a o f these systems were t a k e n as a f u n c t i o n o f  t e m p e r a t u r e , and t h e i r moments were c a l c u l a t e d .  A n a l y s i s of the i n t e g r a t e d  s i g n a l i n t e n s i t i e s r e v e a l e d t h a t the e x c e s s f r e e ( b u l k ) w a t e r i n t h e EC/EXCD 0 and EYL/EXCD^O f r o z e a t -1°C and -2°C, r e s p e c t i v e l y (pure _ © 2  f r e e z e s a t 4°C).  2  The w a t e r from b i l a y e r s i n t h e two e x c e s s w a t e r systems  was f r o z e n i m m e d i a t e l y a f t e r i t was squeezed o u t , whereas t h e w a t e r squeezed out from b i l a y e r s i n the EYL/22%WD20 remained u n f r o z e n down t o -10°C. A l l the squeezed out w a t e r i n t h e EYL/22%WD 0 was f r o z e n a t -15°C. 2  w a t e r i n t h a t s y s t e m was u n f r e e z a b l e i n t h e r e g i o n under s t u d y .  The bound The amount  o f w a t e r f r o z e n o u t i n t h e EC/EXCD 0 a t -2°C and i n t h e EYL/EXCE^O a t -3°C 2  was found t o be a p p r o x i m a t e l y 85% o f t h e t o t a l w a t e r c o n t e n t o f t h e systems. The w a t e r f r o z e n o u t i n t h e EYL/22%WD 0 a t -15°C was determined t o be 50% 2  of t h e t o t a l w a t e r i n that-;system. A minimum i n the second moment vs temperature o f t h e EYL/22%WD20 was o b s e r v e d and a s c r i b e d t o t h e p r e s e n c e o f i s o t r o p i c f r e e w a t e r squeezed out from t h e b i l a y e r s .  P r o t o n magnetic  resonance r e s u l t s showed t h a t t h e r e was no l i p i d phase t r a n s i t i o n i n t h e EYL/22%WD 0 i n t h e r e g i o n from -10°C t o 48°C.  iii T a b l e o f Contents Page Abstract  i i  L i s t of Figures  vi  Acknowledgements  ix  Chapter 1  Introduction 1.1.  F u n c t i o n s o f B i o l o g i c a l Membranes  1  1.2.  S t r u c t u r e o f B i o l o g i c a l Membranes  1  1.3.  Model Membranes  1.4.  Membrane F l u i d i t y and T r a n s p o r t C a r r i e r s  1.5.  Involvement o f L i p i d Component o f Membrane i n Phase Transition  1.6.  2  '5 5  6  B i o l o g i c a l S i g n i f i c a n c e o f Phase T r a n s i t i o n i n Membrane System  7  1.7.  Study of Membrane System by NMR Technique  8  1.8.  Water i n Membrane System  9  1.9.  M o t i v a t i o n f o r the R e s e a r c h P r o j e c t  11  NMR Theory F o r N u c l e i I n L y o t r o p i c A m p h i p h i l i c L i q u i d C r y s t a l / Water System 2.1.  B a s i c P r i n c i p l e s o f N u c l e a r M a g n e t i c Resonance  12  2.2.  Quadrupole . I n t e r a c t i o n s and The F i r s t Order P e r t u r b a t i o n  12  2.3.  Deuterium M a g n e t i c Resonance  15  a) Deuteron on t h e Hydrocarbon C h a i n  15  b) DMR on D~0  21  P r o t o n M a g n e t i c Resonance  22  a) A Two-Spin System  23  2.4.  XV  Page b) PMR on a p r o t i a t e d L i p i d System 3  4  Experimental 3.1.  The M a t e r i a l s  27  3.2.  Samples P r e p a r a t i o n  27  3.3.  NMR Apparatus  27  3.4.  NMR Measurements  28  The R e s u l t s 4.1.  5  25  DMR R e s u l t s a) Quadrupole S p l i t t i n g s  30  b) E v a l u a t i o n s o f t h e DMR s p e c t r a i n terms o f t h e i r moments  3Q  4.2.  PMR R e s u l t s  31  4.3.  Sources o f E r r o r  32  D i s c u s s i o n And C o n c l u s i o n 5.1.  r  DMR S p e c t r a o f D-0  \  a) S p e c t r a o f D~0 i n t h e EYL/EXCD.0 and EC/EXCD 0 systems  33  b) S p e c t r a o f D-0 i n t h e EYL/22%WD 0 system  39  2  2  5.2.  The Moments o f t h e DMR S p e c t r a a) The i n t e g r a t e d s i g n a l  intensities  (M ) o f t h e DMR s p e c t r a  of D-0 i n t h e EYL/EXCD-0 and EC/EXCD 0 systems  ". 42  2  b) The i n t e g r a t e d i n t e n s i t y o f the DMR s p e c t r a o f D 0 i n t h e 2  EYL/22%WD 0 system  44  2  c) The f i r s t and t h e second moments o f t h e DMR s p e c t r a o f D 0 i n 2  the EYL/EXCD-0 and EC/EXCD 0 systems  44  2  d) The f i r s t and second moments o f t h e DMR s p e c t r a o f D 0 i n 2  the EYL/22ZWD-0  55 2  e) The temperature dependence o f t h e A  2  and t h e M^/M  2  the EYL/22%WD 0, EYL/EXCD 0 and EC/EXCD 0 2  2  2  for 60  Page 5.3.  Comparison W i t h Other Work  64  5.4.  PMR R e s u l t s F o r The EYL/22%WD 0 2  66  Appendix A  Moments Of N u c l e a r M a g n e t i c Resonance S p e c t r a  71  Appendix B  C o n t r i b u t i o n s To The Second Moment  76  References  78  vi L i s t of F i g u r e s Figure 1  Page A schematic r e p r e s e n t a t i o n of d i p o l m i t o y l - 3 - s n phosphatidylcholine l i p i d molecule.  2  2  A schematic r e p r e s e n t a t i o n o f l a m e l l a r and v e s i c u l a r s t r u c t u r e s i n a l i p i d - w a t e r system.  3.  4  A schematic r e p r e s e n t a t i o n of t h e geometry and t h e c o o r d i n a t e system i n a l i p i d b i l a y e r .  14  4  T h e o r e t i c a l powder p a t t e r n f o r a d e u t e r i u m n u c l e u s .  20  5.  Energy l e v e l s and t h e c o r r e s p o n d i n g  spectrum o f a t w o - s p i n  system o r i e n t e d a t an a n g l e 8.  24  6  Logarithmic  26  7  DMR s p e c t r a o f D 0 i n t h e E. C o l i / E X C D 0 o b t a i n e d a t (a) 20°C,  PMR l i n e s h a p e as d e r i v e d by Bloom e t a l . 2  2  (b) 4°C, ( c ) -1°C, (d) -2°C. 8  37  DMR s p e c t r a o f D 0 i n t h e EYL/EXCT> 0 o b t a i n e d a t (a) 18°C, 2  2  (b) 4°C, ( c ) -2°C, (d) -3°C.  38  DMR s p e c t r a o f D 0 i n t h e EYL/22%WD 0 o b t a i n e d 2  2  a t (a) 25°C,  (b) 4°C, ( c ) -3°C, (d) -4°C, (e) -5°C, ( f ) -10°C, (g) -15°C, (h) -20°C, ( i ) -25°C. 10  41  Temperature dependence of t h e i n t e g r a t e d s i g n a l i n t e n s i t y ,  M , Q  of DMR of D 0 i n t h e EYL/EXCD 0 and t h e E. C o l i / E X C D 0 . 2  11  2  Temperature dependence o f t h e i n t e g r a t e d s i g n a l i n t e n s i t y , of DMR of D 0 i n t h e EYL/22%WD 0. 2  12  M , Q  45  2  Temperature dependence of t h e f i r s t moment M^ o f t h e DMR spectrum o f D 0 i n t h e EYL/EXCD 0 and E. C o l i / E X C D 0 . 2  13  43  2  2  Temperature dependence o f t h e second moment M  2  2  o f t h e DMR  spectrum o f D 0 i n the EYL/EXCD 0 and E. C o l i / E X C D 0 . 2  2  50  2  51  Second moments of the DMR spectra of D 0 i n the EYL/EXCD 0 2  2  plotted against that i n the EYL/22%WD 0. 2  Temperature dependence of the l i n e width A v of the DMR spectrum of D 0 i n the E. Coli/EXCD 0 and EYL/EXCD 0. 2  2  2  Temperature dependence of the fourth moment M^ of theDMR spectrum of D 0 i n the EYL,/EXCD 0 and E. Coli/EXCD 0. 2  2  2  Temperature dependence of the f i r s t and the fourth moments, M  1S  M^, of the DMR spectrum of D 0 i n the EYL/22%WD 0. 2  2  Temperature dependence of the second moment M  2  of the DMR  spectrum of D 0 i n the EYL/22%WD 0. 2  2  2 Temperature dependence of the r a t i o M^/M  and the r e l a t i v e  2  mean square deviation A  2  of the DMR spectrum of D 0 i n the 2  E. Coli/EXCD 0. 2  2 Temperature dependence of the r a t i o M^/M,, and the r e l a t i v e mean square deviation A  2  of the DMR spectrum of D 0 i n the 2  EYL/EXCD 0. 2  Temperature dependence of the r e l a t i v e mean square deviation 2 A  2  and the r a t i o K^/M^ of the DMR spectrum of D 0 i n the 2  EYL/22%WD 0. 2  Temperature dependence of the quadrupole s p l i t t i n g A v which i s measured d i r e c t l y from the DMR spectrum of D 0 i n the 2  EYL/22%WD 0. 2  2 Temperature dependence of the r a t i o M^/M  2  and the second  moment of the PMR spectrum of the EYL/22%WD 0. 2  Temperature dependence o f t h e second moment o f PMR spectrum of (a) t h e o u t e r membrane o f E. C o l i i n t h e EC/EXCD-O, (b) the EYL i n t h e EYL/EXCD-0, ( C ) temperature dependence o f M^/M  2  of t h e PMR spectrum o f t h e EYL i n t h e EYL/EXCD-0.  (a) Second moments v s temperature o f t h e DMR s p e c t r a o f o u t e r membranes of E. C o l i grown on a medium c o n t a i n i n g p e r d e u t e r a t e d p a l m i t i c a c i d and o l e i c a c i d as w e l l as perdeuterated p a l m i t i c a c i d .  (b) The parameter Av v s  temperature o f t h e DMR s p e c t r a o f t h e o u t e r membranes of E. C o l i grown on a medium c o n t a i n i n g o l e i c a c i d as w e l l as Perdeuterated p a l m i t i c  acid.  ix  Acknowledgements First enthusiasm enriched his  and f o r e m o s t , o f my  I  am v e r y  grateful  the technical  for  t h e many  is  regard  greatly  to Dr. A l e x  greatly  benefited greatly  from  Mackay  a n d D r . James  H.  i n the experiments  d i s c u s s i o n s and u s e f u l s u g g e s t i o n s .  the continued  support  of Alex  i n many o t h e r  Davis and In  respects  appreciated. I t h a n k my w i f e , May  f o r her patience  support.  I have  c o n s u l t a t i o n s and h e l p  fruitful  Finally, and  experience.  B l o o m , who h a s  a n d t h e many d i s c u s s i o n s we h a v e h a d .  for  this  t o acknowledge t h e p a t i e n c e and  s u p e r v i s o r , D r . Myer  my m a s t e r s  instruction  I wish  San, f o r t y p i n g the t h e s i s  and c o n t i n u i n g encouragement  and m o r a l  1 Chapter 1  Introduction  1.1.  Functions  o f B i o l o g i c a l Membranes  Every l i v i n g c e l l i s e n c l o s e d as a s t u r d y e n c l o s u r e  by a membrane t h a t s e r v e s n o t o n l y  i n s i d e which t h e c e l l can f u n c t i o n , b u t i t can a l s o  p e r f o r m a l a r g e number o f b i o l o g i c a l f u n c t i o n s .  F o r i n s t a n c e , i t can  f u n c t i o n as a d i s c r i m i n a t i n g g a t e , e n a b l i n g n u t r i e n t s and o t h e r t i a l agents t o e n t e r and waste p r o d u c t s t o l e a v e .  essen-  The c y t o p l a s m i c  cell  membrane can "pump" s u b s t a n c e s from one s i d e o f the membrane where such substance's c o n c e n t r a t i o n Thus t h e c y t o p l a s m i c  i s low t o the o t h e r where i t i s much h i g h e r .  membrane s e l e c t i v e l y r e g u l a t e s t h e f l u x o f n u t r i -  e n t s and i o n s between t h e c e l l and i t s e x t e r n a l environment. h i g h e r organisms have, i n a d d i t i o n t o a c y t o p l a s m i c  The c e l l s o f  membrane, a number o f  i n t e r n a l membranes t h a t i s o l a t e t h e s t r u c t u r e s termed o r g a n e l l e s , which play various s p e c i a l i z e d roles ( 1 ) .  1.2.  S t r u c t u r e o f B i o l o g i c a l Membranes A l l o f the b i o l o g i c a l membranes mentioned above a r e remarkably s i m i -  l a r i n their basic s t r u c t u r a l features.  I t i s c l e a r t h a t any model formu-  l a t e d t o d e s c r i b e membrane s t r u c t u r e s must be a b l e t o account f o r such an e x t r a o r d i n a r y range o f f u n c t i o n s . Membranes a r e composed almost e n t i r e l y o f two c l a s s e s o f m o l e c u l e s : p r o t e i n s and l i p i d s ( p o l y s a c c h a r i d e s i c a l membranes).  etc. are also associated with b i o l o g -  The p r o t e i n s p r o v i d e  t h e membrane w i t h i t s d i s t i n c t i v e  f u n c t i o n a l p r o p e r t i e s , whereas the l i p i d s g i v e t h e g r o s s s t r u c t u r a l p r o p e r t i e s o f t h e membrane ( 1 ) .  A dipalmitoyl-3-sn-phosphatidylcholine  l i p i d m o l e c u l e i s shown i n F i g . 1.  (DPPC)  The l i p i d s found i n membranes a r e  2  +  N ( C H 3 ) 3 P o l a r head group (hydrophilic)  Chain 1  Figure  1.  Chain 2 (Hydrophobic  tail)  A schematic r e p r e s e n t a t i o n of D i p a l m i t o y l - 3 - s n phosphatidylcholine l i p i d molecule.  3  a m p h i p a t h i c , meaning t h a t one end o f t h e m o l e c u l e i s h y d r o p h o b i c , o r i n s o l u b l e i n w a t e r , and t h e o t h e r end h y d r o p h i l i c , o r w a t e r - s o l u b l e .  The h y d r o p h i l i c  r e g i o n o f t h e l i p i d m o l e c u l e i s p o l a r , and t h e h y d r o p h o b i c r e g i o n i s nonpolar.  I n most membrane l i p i d s t h e n o n p o l a r r e g i o n c o n s i s t s o f h y d r o c a r b o n  chains o f f a t t y a c i d s : at  one end.  h y d r o c a r b o n m o l e c u l e s w i t h a c a r b o x y l group  (COOH)  I n a t y p i c a l membrane l i p i d two f a t t y a c i d m o l e c u l e s a r e  c h e m i c a l l y bonded through t h e i r c a r b o x y l ends t o a backbone o f g l y c e r o l . g l y c e r o l backbone,  The  i n t u r n , i s a t t a c h e d t o a p o l a r head group c o n s i s t i n g o f  phosphate and o t h e r groups.  P h o s p h a t e - c o n t a i n i n g l i p i d s o f t h i s type a r e  c a l l e d p h o s p h o l i p i d s , w h i c h a r e found i n a l l membranes. Because ities,  the two p a r t s o f a membrane l i p i d have i n c o m p a t i b l e s o l u b i l -  t h e l i p i d m o l e c u l e s i n t h e presence o f w a t e r s p o n t a n e o u s l y o r g a n i z e  themselves i n t h e form o f a v a r i e t y o f l y o t r o p i c mesophases c h a r a c t e r i z e d by the e x i s t e n c e o f l o n g range o r d e r and s h o r t range d i s o r d e r ( 1 - 4 ) .  The  c o n v i n c i n g e v i d e n c e f o r t h e e x i s t e n c e o f these mesophases have been p r o v i d ed by X-ray s t u d i e s ( 5 ) , n u c l e a r magnetic resonance (NMR) s t u d i e s  (6-7),  and o t h e r p h y s i c o c h e m i c a l t e c h n i q u e s ( 8 - 1 2 ) . Of p a r t i c u l a r i n t e r e s t i s t h e l a m e l l a r l i q u i d c r y s t a l (L^) phase where t h e l i p i d m o l e c u l e s form b i l a y e r s and a l t e r n a t e i n a r e g u l a r w i t h l a y e r s o f w a t e r and c o u n t e r i o n s as shown i n F i g . 2.  lattice  I n t h i s way the  h y d r o p h o b i c r e g i o n o f each m o l e c u l e i s s h i e l d e d from w a t e r , whereas the h y d r o p h i l i c p o l a r head groups f i n d themselves i n a lower e l e c t r o s t a t i c energy by a s s o c i a t i n g i n t i m a t e l y w i t h w a t e r .  The h y d r o c a r b o n c h a i n s a s s o -  c i a t e themselves i n t h e form o f b i l a y e r s as a r e s u l t o f t h e above i n t e r a c t i o n s and t h e a t t r a c t i v e Van der Waal's f o r c e s . Most b i l a y e r s i n l i p i d - w a t e r system i n l a m e l l a r l i q u i d  crystalline  phase n a t u r a l l y arrange themselves i n t o an o n i o n r i n g c o n f i g u r a t i o n , so  4  (b)  r~S-n  Water  r^TZ.  Water  mm F i g u r e 2. (a) The p h o s p h o l i p i d b i l a y e r forms the fundamental s t r u c t u r a l m a t r i x o f a membrane. The l i p i d s a r e arranged c h a i n t o c h a i n so t h a t o n l y t h e h y d r o p h i l i c p o l a r heads ( t h e c i r c l e s ) a r e exposed t o t h e aqueous s o l u t i o n on b o t h s i d e s o f t h e membrane. L i p i d m o l e c u l e s can d i f f u s e l a t e r a l l y a t a h i g h f r e q u e n c y , b u t can r a r e l y e x e c u t e a f l i p - f l o p t r a n s i t i o n from one l a y e r t o the o t h e r . The w i g g l y l i n e s r e p r e s e n t t h e h y d r o c a r b o n c h a i n . (b) S p h e r i c a l b i l a y e r  (vesicle).  5 t h a t nowhere i n the b i l a y e r s the h y d r o p h o b i c t a i l s a r e i n c o n t a c t w i t h ter.  wa-  These b i l a y e r s form the b a s i c s t r u c t u r e of most b i o l o g i c a l membranes.  1.3. Model Membranes^ Due t o the c o m p l e x i t y of r e a l b i o l o g i c a l membranes, the NMR  spectrum  o b t a i n e d i s a s u p e r p o s i t i o n o f a l a r g e number of powder p a t t e r n s w h i c h a r e not w e l l r e s o l v e d .  Thus, i n o r d e r t o u n d e r s t a n d the fundamental p h y s i c a l  p r o p e r t i e s w h i c h determine the p r o p e r f u n c t i o n o f membranes, workers i n _ the f i e l d l o o k f o r s i m p l e r membrane systems t h a t c o u l d be used as  "models".  S i n c e l i p i d s a r e the fundamental " b u i l d i n g b l o c k s " o f . t h e - c e l l membrane, model membrane systems have been made w i t h l i p i d s o b t a i n e d from n a t u r a l s o u r c e s such as egg y o l k l e c i t h i n (13-14) as w e l l as from s y n t h e t i c n i q u e s such as DPPC ( 1 5 ) .  tech-  These model membranes a r e s i m i l a r (not i d e n t i -  c a l ) i n t h e i r s t r u c t u r a l p r o p e r t i e s t o b i o l o g i c a l membranes and they can be much b e t t e r c h a r a c t e r i z e d p h y s i c a l l y and c h e m i c a l l y than membranes from l i v i n g c e l l s , w h i c h have a c o m p l i c a t e d assortment o f d i f f e r e n t  lipids.  The phase t r a n s i t i o n s a r e a l s o much s h a r p e r w i t h p u r i f i e d l i p i d s o f a s i n g l e homogenous t y p e , t h i s makes q u a n t i t a t i v e measurement and i n t e r p r e t a t i o n much e a s i e r .  F u r t h e r m o r e , NMR  theoretical  s p e c t r a g i v e n by model mem-  branes a r e s i m p l e r t o i n t e r p r e t than those g i v e n by n a t u r a l ones.  There  have been numerous s t u d i e s on model and b i o l o g i c a l membranes c o n c e r n i n g the importance of the h y d r o p h o b i c p a r t s of the p h o s p h o l i p i d m o l e c u l e s i n d e t e r m i n i n g the g e n e r a l p r o p e r t i e s of the i n t e r i o r o f the p h o s p h o l i p i d b i l a y e r (5-7, 16)..  1.4.  Membrane F l u i d i t y and T r a n s p o r t C a r r i e r s S i n c e the phenomenon o f l i f e o c c u r s i n s i d e the c e l l , w h i c h i s e n c l o s e d  by a membrane, how do s u b s t a n c e s pass through the membrane t o p r o v i d e the c e l l with life-supporting nutrients?  The h y d r o p h o b i c n o n p o l a r f a t t y a c i d  6 hydrocarbon chain region of a phospholipid b i l a y e r i s p h y s i c a l l y  incompat-  i b l e w i t h s m a l l w a t e r - s o l u b l e s u b s t a n c e s such as m e t a l i o n s , sugars and amino a c i d s , and thus a c t s as a b a r r i e r t h r o u g h which they cannot f l o w ".• freely.  Bangham e t a l o f t h e A g r i c u l t u r a l Research C o u n c i l i n Cambridge,  England, and C h a p p e l l e t a l o f t h e U n i v e r s i t y o f Cambridge (17) measured the r a t e a t w h i c h g l u c o s e passes through t h e p h o s p h o l i p i d - b i l a y e r w a l l s o f l i p o s o m e s ( v e s i c l e s ) and found t h a t i t was f a r t o o low t o account f o r t h e r a t e a t which g l u c o s e p e n e t r a t e s b i o l o g i c a l membranes.  They demonstrated  t h a t a h i g h l y s e l e c t i v e c a r r i e r p r o t e i n e x i s t s i n b i o l o g i c a l membranes t o f a c i l i t a t e t h e passage o f m e t a l i o n s and s m a l l p o l a r m o l e c u l e s through t h e p e r m e a b i l i t y b a r r i e r p r e s e n t e d by t h e p h o s p h o l i p i d b i l a y e r . S i n c e t r a n s p o r t c a r r i e r s must be m o b i l e i n o r d e r t o move substances from one s i d e o f t h e c e l l membrane t o t h e o t h e r , i t i s n e c e s s a r y f o r t h e r e g i o n c o n t a i n i n g t h e f a t t y a c i d c h a i n s t o have a h i g h degree o f f l u i d i t y i n which each b i l a y e r behaves as a two d i m e n s i o n a l f l u i d w i t h t h e l i p i d c h a i n s p r e f e r e n t i a l l y o r i e n t e d a l o n g t h e normal t o the b i l a y e r  surface.  W i t h i n the b i l a y e r the hydrocarbon chains of the l i p i d molecules are f l e x i b l e (melted) and t h e m o l e c u l e s undergo r a p i d l a t e r a l d i f f u s i o n and r o t a t i o n about t h e i r l o n g a x i s .  D i f f e r e n t p a r t s o f t h e hydrocarbon c h a i n can  a l s o undergo s m a l l and r a p i d a n g u l a r e x c u r s i o n s such as b e n d i n g , t w i s t i n g and f l o p p i n g p e r p e n d i c u l a r t o t h e m o l e c u l a r a x i s ( t h e l o n g a x i s o f t h e molecule) .  X-ray d i f f r a c t i o n p a t t e r n s o f membrane systems above t h e t r a n s i t  t i o n temperature a r e d i f f u s e and q u i t e s i m i l a r t o those o b t a i n e d from l o n g c h a i n l i q u i d hydrocarbons found i n p a r a f f i n , w h i c h i n d i c a t e s t h a t t h e f a t t y a c i d s o f membranes a r e i n f a c t d i s o r d e r e d a t p h y s i o l o g i c a l temperature ( 5 ) .  1.5.  Involvement o f L i p i d Component o f Membrane i n Phase T r a n s i t i o n Experiments have c o n c l u s i v e l y demonstrated t h a t t h e phase t r a n s i t i o n  7 i n membrane systems  (such as Acholeplasma l a i d l a w i i and model membranes)  i s due e x c l u s i v e l y to the l i p i d  component o f the membrane (18-19).  fore p h y s i c a l techniques that e l u c i d a t e w i t h phases are a p p r o p r i a t e  s t r u c t u r e , and t h e o r i e s  t o o l s to study t h i s phenomenon.  n a t u r e of the phase t r a n s i t i o n i n m u l t i b i l a y e r d i s p e r s i o n s  deal  basic  i s revealed  X-ray d i f f r a c t i o n and n u c l e a r magnetic  Calorimetric  data (18-19) showed t h a t the t r a n s i t i o n s i n l i p i d  s t r u c t u r a l changes i n l i p i d  that  The  calorimetry,  mainly i n v o l v e hydrocarbon-chain d i s o r d e r i n g  There-  resonance  by  (16-18). bilayers  (phase t r a n s i t i o n s i n v o l v i n g  b i l a y e r s such as l a m e l l a r  to hexagonal phase  t r a n s i t i o n had been observed by X-ray t e c h n i q u e ( 5 ) ) . X-ray d i f f r a c t i o n and o t h e r p h y s i c a l t e c h n i q u e s s t u d i e s w i t h low and v a r y i n g  water c o n c e n t r a t i o n ,  show t h a t ,  l i p i d s have a r i c h v a r i e t y o f  phase behaviour i n a d d i t i o n to the phase t r a n s i t i o n i n the presence o f excess water, which i s of primary b i o l o g i c a l i n t e r e s t ( 1 8 ) .  1.6.  B i o l o g i c a l S i g n i f i c a n c e o f Phase T r a n s i t i o n i n Membrane System The o r d e r - d i s o r d e r  change i n the dynamical s t a t e of hydrocarbon c h a i n s  i n b i l a y e r membranes g i v e s  r i s e to a phase t r a n s i t i o n t h a t o c c u r s i n many  c e l l membranes as w e l l as model membranes.  Much work (18) has been done  on the c y t o p l a s m i c membrane o f Acholeplasma l a i d l a w i i , which i s a p r i m i t i v e orgamism w i t h a l a r g e s u r f a c e - t o - v o l u m e r a t i o .  A f t e r the c e l l  was  grown, a t a p a r t i c u l a r temperature T , the membrane w a s c e x t r a c t e d and c a l o r i m e t r i c measurements were made.  Data show a s p e c i f i c heat anomaly,  about 20°C broad, c e n t e r e d near or s l i g h t l y below T ,  When these c e l l s  were grown a t d i f f e r e n t growth temperatures T ', the c a l o r i m e t r i c anomaly i s s h i f t e d towards  the  temperature  T '.  This  suggests t h a t  the phase  t r a n s i t i o n i s not j u s t some p h y s i c a l phenomenon t h a t happens to o c c u r , but t h a t i t has r e a l b i o l o g i c a l r e l e v a n c e .  There a r e many o t h e r examples  8 of  p h y s i c a l l y i n d u c e d b i o l o g i c a l changes r e l a t e d t o t h e membrane phase  transition.  Organisms t h a t e x i s t i n c o l d environments have membrane compo-  nents g i v i n g r i s e t o reduced p h a s e - t r a n s i t i o n t e m p e r a t u r e s .  1.7.  Study o f Membrane System by NMR  Technique  N u c l e a r magnetic resonance i s a v e r y u s e f u l t e c h n i q u e f o r s t u d y i n g the  s t r u c t u r e and t h e d y n a m i c a l s t a t e o f t h e membrane systems ( 3 , 2 0 ) .  By s t r u c t u r e , we mean t h e average o r i e n t a t i o n o f t h e h y d r o c a r b o n c h a i n s , the  p o l a r groups, and the a m p l i t u d e s o f f l u c t u a t i o n o f t h e l i p i d  segments.  The s t u d y o f t h e d y n a m i c a l s t a t e o f a membrane system i s concerned w i t h t h e r a t e o f segmental motions and t h e r a t e o f d i f f u s i o n o f t h e l i p i d s w i t h i n each monolayer.  I n terms o f e x p e r i m e n t a l NMR p a r a m e t e r s , t h e problems o f  membrane s t r u c t u r e and d y n a m i c a l p r o p e r t i e s o f t h e b i l a y e r a r e s o l v e d i f the  complete s e t o f segmental second rank o r d e r parameter t e n s o r s ( s e e Sec-  t i o n 2.3a, Chapter 2) and t h e r e l a x a t i o n times a r e measured, and i f a cons i s t e n t m o l e c u l a r i n t e r p r e t a t i o n o f the e x p e r i m e n t a l d a t a can be p r o v i d e d . The o r d e r parameter S ^ o f a d e u t e r i u m bond v e c t o r and, f o r a s p e c i a l c a s e , S o f a H-H bond v e c t o r can be measured from the quadrupole tin  splitting,  A V Q , i n t h e d e u t e r i u m n u c l e a r magnetic resonance (DMR) spectrum and from the  n u c l e a r d i p o l a r s p l i t t i n g i n the p r o t o n magnetic resonance (PMR) spec-  trum r e s p e c t i v e l y , s i n c e they a r e 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 s p l i t t i n g s (Appendix A ) .  The o r d e r parameter can then be i n t e r p r e t e d i n terms o f  s t a t i s t i c a l models f o r the b i l a y e r s t r u c t u r e .  The o n s e t o f motions o r t h e  phase t r a n s i t i o n from one form o f l a t t i c e s t r u c t u r e t o t h e o t h e r w i t h a h i g h e r degree o f l a t t i c e symmetry (such as a c u b i c phase) w i l l , due t o m o t i o n a l a v e r a g i n g , reduce t h e o r d e r parameters S  and S CD  quently the s p l i t t i n g s i n the s p e c t r a . the  , and conseHH  The o t h e r NMR parameters such as  l i n e w i d t h o f a s i n g l e t a b s o r p t i o n spectrum a r e a l s o reduced due t o  9  motional averaging of d i p o l a r or quadrupolar i n t e r a c t i o n s .  T h e r e f o r e , phase  t r a n s i t i o n s o r onset o f motions i n t h e s e systems a r e d e t e c t e d by t h e a b r u p t change i n the NMR parameters as t h e temperature i s v a r i e d . Much work has been done on t h e c o n f o r m a t i o n s and motions o f t h e l i p i d m o l e c u l e s i n membrane system (21-30).  D a v i s e t a l (23) s t u d i e d t h e  hydrocarbon c h a i n d i s o r d e r i n t h e p o t a s s i u m p a l m i t a t e - w a t e r system.  I n the  l i q u i d c r y s t a l l i n e phase t h e C-D o r d e r parameters o f t h e f i r s t few methy l e n e c h a i n segments were found t o i n c r e a s e w i t h i n c r e a s i n g temperature t o a maximun o f 100°C and then d e c r e a s e a t h i g h e r t e m p e r a t u r e s . the  C-D o r d e r parameters f o r t h e r e s t o f the methylene  c r e a s e d w i t h i n c r e a s i n g temperature.  In contrast,  c h a i n segments de-  I n t h e same system H i g g and Mackay  (30) have determined t h e complete o r d e r parameter t e n s o r s f o r t h e a-methy l e n e group by measuring t h e a-CH p e r d e u t e r a t e d c h a i n and t h e a-CD deuterated chains.  2  2  d i p o l a r s p l i t t i n g s i n an o t h e r w i s e splittings  (23) i n t h e s p e c i f i c a l l y  The temperature dependence o f the a-CH  s i m i l a r t o t h a t o f the a-Ci>  2  2  s p l i t t i n g s was  splittings.  B u r n e l l e t a l (31) s t u d i e d the o r d e r i n g o f water i n t h e p o t a s s i u m p a l m i t a t e / D 0 system. 2  They found t h a t t h e o r d e r parameter o f t h e d e u t e r i u m  i n D 0 had the same temperature dependence as t h e f i r s t few methylene 2  as e s t a b l i s h e d by D a v i s e t a l d e s c r i b e d p r e v i o u s l y .  pairs  T h i s c o r r e l a t i o n was  a s c r i b e d t o the l i p i d - w a t e r i n t e r a c t i o n v i a hydrogen bonding between t h e water and the p o l a r heads near t h e l i p i d - w a t e r  1.8.  interface.  Water i n Membrane System Water ( H 0 ) c o n s t i t u t e s a major component o f c e l l s o f a l l l i v i n g o r 2  ganism, and p l a y s an i m p o r t a n t r o l e i n l i f e p r o c e s s a t t h e c e l l u l a r  level.  The o r d e r i n g o f water a t t h e l i p i d - w a t e r ( D 0 ) i n t e r f a c e can be observed 2  because o f t h e i n t e r a c t i o n s between t h e n u c l e a r quadrupole moments o f  10 d e u t e r i u m i n B^O and the e l e c t r i c f i e l d g r a d i e n t s a t t h e n u c l e a r The a n i s o t r o p y e x p e r i e n c e d  sites.  by w a t e r m o l e c u l e s i n the l i p i d - w a t e r system i s  f a r s m a l l e r than t h a t i n t h e h y d r o c a r b o n c h a i n s , b u t i s s t i l l l a r g e enough to g i v e a w e l l r e s o l v e d quadrupole s p l i t t i n g f o r w a t e r deuterons i n D2O. I n t h e DMR s p e c t r a o f D^O i n l a m e l l a r phases o f egg y o l k l e c i t h i n , egg phosphatidylethanolamine,  ox b r a i n sodium p h o s p h a t i d y l s e r i n e (32) and  d i p a l m i t o y l p h o s p h a t i d y l c h o l i n e (33), a sharp c e n t r a l l i n e was o b s e r v e d . F i n e r e t a l a s c r i b e d t h i s sharp c e n t r a l l i n e t o t h e presence o f i s o t r o p i c water.  One s h o u l d be c a u t i o u s o f t h i s e x p l a n a t i o n .  As p o i n t e d o u t by  Wennerstrom e t a l (34) and L i n d b l b m e t a l (35) t h a t f o r some samples, t h e sharp c e n t r a l l i n e was independent o f t h e added w a t e r c o n c e n t r a t i o n , and may be due t o double quantum t r a n s i t i o n s , w h i c h i s u n o b s e r v a b l e a t low RF power, w h i l e i t i s much more i n t e n s e than t h e powder p a t t e r n a t h i g h RF f i e l d strengths.  Thus i t i s v e r y easy t o determine t h e n a t u r e o f t h e peak  by i n v e s t i g a t i n g t h e dependence o f t h e s i g n a l i n t e n s i t y on t h e RF f i e l d strength. A p p l i c a t i o n o f F i n e r ' s method o f a n a l y s i s (36), F i n e r and Darke were a b l e t o d i s t i n g u i s h 2, 3 and 4 d i f f e r e n t k i n d s o f water f o r egg phosphatidylethanolamine, tively.  egg l e c i t h i n and sodium p h o s p h a t i d y l s e r i n e  respec-  These water types were i d e n t i f i e d as t i g h t l y bound i n n e r h y d r a t i o n  s h e l l , weakly bound w a t e r , t r a p p e d w a t e r , w i t h exchange between them b e i n g r a p i d on the NMR time s c a l e , and f r e e w a t e r .  The c h a r a c t e r i s t i c  splitting  of t h e main h y d r a t i o n s h e l l o f egg y o l k l e c i t h i n i s 0.37 kHz, and t h a t o f the i n n e r h y d r a t i o n s h e l l o r t h e most t i g h t l y bound s h e l l o f t h e same system i s 6.9 kHz, which a r e c o n s i d e r a b l y s m a l l e r  than  the s p l i t t i n g o f  170 kHz t y p i c a l l y found f o r p o l y c r y s t a l l i n e i c e and h y d r a t e s (56).  11 1.9.  M o t i v a t i o n f o r t h e Research P r o j e c t Deuterium magnetic resonance o f D^O i n EYL/D^O system has been done  by F i n e r e t a l (32) and o t h e r s .  A l l o f them measured t h e quadrupole  s p l i t t i n g s o f DMR s p e c t r a o f water ( D 0 ) as a f u n c t i o n o f t e m p e r a t u r e . 2  T h i s method o f e v a l u a t i n g DMR s p e c t r a i s s u b j e c t e d t o a s y s t e m a t i c e r r o r and i s d i f f i c u l t t o a p p l y when t h e s p e c t r a a r e broadened. I n t h i s r e s e a r c h , t h e moments (Appendix A) w i l l be c a l c u l a t e d from the  DMR s p e c t r a o f V^O i n t h e EYL/D^O and E. C o l i / D 0 systems, and the 2  s p l i t t i n g s from t h e moments thus d e t e r m i n e d .  The l a t t e r w i l l be compared  to t h e s p l i t t i n g s d i r e c t l y o b t a i n e d from measuring t h e s e p a r a t i o n s between the  d o u b l e t peaks o f t h e s p e c t r a . A c c o r d i n g t o t h e d a t a ( A l e x Mackay, u n p u b l i s h e d ) o b t a i n e d from PMR  s t u d i e s o f the p r o t i a t e d o u t e r membrane o f E. C o l i / D 0 and EYL/D^O i n 2  excess w a t e r , t h e temperature dependence o f t h e second moments and t h e 2 M^/M^  c a l c u l a t e d from t h e PMR s p e c t r a o f t h e two systems showed an anomalous  d i s c o n t i n u i t y a t 4°C t h a t i s n o t observed i n D a v i s ' d a t a (37) o b t a i n e d from DMR s t u d y o f the d e u t e r a t e d o u t e r membranes o f E. C o l i .  S i n c e PMR i s s e n s i -  t i v e t o i n t e r m o l e c u l a r motions w h i l e DMR i s n o t , t h e d a t a seem t o suggest t h a t the anomalous d i s c o n t i n u i t y was due t o onset o f l a t e r a l d i f f u s i o n o f the  phospholipid molecules.  Because pure D 0 f r e e z e s a t 4°C, t h e l a t e r a l 2  o d i f f u s i o n below 4 C might have been stopped by f r e e z i n g o f t h e w a t e r .  The  p o s s i b l e c o r r e l a t i o n between t h e d i s a p p e a r a n c e o f t h e l a t e r a l d i f f u s i o n and f r e e z i n g o f t h e water w i l l be c o n f i r m e d o r d i s m i s s e d by t h e r e s u l t s o f my experiments.  12 Chapter 2  NMR  2.1.  Theory For N u c l e i I n L i p i d / W a t e r System  B a s i c P r i n c i p l e s of N u c l e a r Magnetic Resonance N u c l e i h a v i n g a non-zero n u c l e a r s p i n p o s s e s s a magnetic d i p o l e moment  •]_, which i s r e l a t e d t o the n u c l e a r s p i n j by-(38)  '— -  -  y = yfil  where y I  s  t n  e  {  gyromagnetic r a t i o , and I  i s a vector operator.  2  .i}  In  a s t a t i c magnetic f i e l d H^, a magnetic n u c l e u s may e x i s t i n one of the  21+1  s p i n s t a t e s w i t h s p i n quantum number m = I , I - 1, ... - I and energy l e v e l s E_(m)  = -yhH m = -fico^m, w h i c h a r e the e i g e n v a l u e s of the Zeeman H a m i l t o n i a n o  H  Z  =  where I  -v-h  -^Vz  { 2  i s the Z-component of the n u c l e a r s p i n o p e r a t o r I .  -  2 }  Thus, when  ZJ  an a p p r o p r i a t e r a d i o f r e q u e n c y e l e c t r o m a g n e t i c r a d i a t i o n (RF f i e l d ) i s a p p l i e d to  the n u c l e u s p e r p e n d i c u l a r t o the a p p l i e d magnetic f i e l d H , a t r a n s i t i o n q  between two s p i n s t a t e s i s i n d u c e d by a c o u p l i n g o f the magnetic d i p o l e moment t o the RF f i e l d , and the phenomenon o f n u c l e a r magnetic resonance o c c u r s .  2.2.  Quadrupolar I n t e r a c t i o n s and The F i r s t Order P e r t u r b a t i o n In a d d i t i o n t o a magnetic d i p o l e moment, a n u c l e u s o f s p i n I > _  p o s s e s s e s an e l e c t r i c quadrupole moment which has i t s o r i g i n i n a n o n s p h e r i c a l l y symmetric n u c l e a r charge d i s t r i b u t i o n .  C o n s e q u e n t l y , the n u c l e u s has  an e l e c t r o s t a t i c i n t e r a c t i o n w i t h i t s environment when i t i s i n an e l e c t r o s t a t i c f i e l d g r a d i e n t (EFG) w h i c h does not p o s s e s s too h i g h a degree o f symmetry.  T h i s i n t e r a c t i o n depends on the o r i e n t a t i o n of the n u c l e a r s p i n .  Hence,,  the  magnetic H  where due  H  to  Hamiltonian  f i e l d Hq = Hz  is  z  the  gradient and  total  is  the  i n t e r a c t i o n between at  the  the  applied  s t a t i c magnetic  perturbation  to  c o u p l i n g of  the  and H  site.  the the  field,  Q  is  the  quadrupole  terms  c o u p l i n g between the  the  nuclear  interaction  than  in  an  applied  quadrupolar  moment  and  H e r e we h a v e  Hamiltonian  the  electric  field  ignored  chemical  shift  etc.  nuclear  quadrupole  nuclear magnetic  it  can be  shown  Zeeman e n e r g y  levels  due  moment  EFG  is  to  the  d i p o l e moment  (38-41)  to  and  H^  are  that  the  given  first  in  much  order  frequency  by  m  E  the  > \  by  Zeeman H a m i l t o n i a n ,  smaller  where  spin I  {2.3}  dipole-dipole  units  a nucleus with  + HQ  existing  If  given  for  1 }  the  = 4  h  I(2I-l)  angles  { 3 C Q  quantum  2 9  "  $ specify  6,  p r i n c i p a l coordinate  magnetic  2  number  1  +  the  system of in  the  2Sin2ecos2$}{3m2-I(I+l)}  magnetic the  EFG  field  {2,4}  direction with  as  shown  in  Fig.  representation  where  I  is  respect  3a,  m is  diagonal,  to  the and  Li  2 e qQ/h  is  component quadrupole  the of  quadrupole the  EFG  moment  eQ  coupling  q = V'  is  called  the  the  associated with  n ={|V | - | V J } / yy  /'e i n  constant  x  asymmetry  involving  the  product  principal coordinate the  spin  I  nucleus.  of  system, The  the and  ZZ the  quantity:  {2.5}  |V J z  parameter,  where  2 2 = 9 V/9x etc.,  V  and V i s  the  XX  net  electrostatic potential  principal  IVz z 1  axes  I=  are 1  IVy y '  ordered  I—>  | Vx x '  at so  I  the  nuclear  site.  Conventionally,  the  EFG  that i {^ 2. .u6j}.  14  (b)  (a)  F i g u r e 3. (a) O r i e n t a t i o n o f the s t a t i c magnetic f i e l d w i t h r e s p e c t t o the p r i n c i p a l coordinate  system o f the e l e c t r i c f i e l d  gradient.  (b) Schematic r e p r e s e n t a t i o n o f the geometry and the c o o r d i n a t e system i n a l i p i d b i l a y e r . field H  q  6 i s the a n g l e between t h e magnetic  and the b i l a y e r normal f i , 6 i s t h e a n g l e between the  C-D bond d i r e c t i o n and H , and 9 i s the a n g l e between t h e C-D o n bond d i r e c t i o n and n.  /  15 and,^consequently, 0 <_ n <_ 1.  In I t s p r i n c i p a l a x i s system, the EFG  at the n u c l e a r s i t e i s determined by  the parameters q and n.  parameter ri i s a measure of the d e v i a t i o n of the EFG  The  from a x i a l  tensor  asymmetry  symmetry.  The parameter Q , which i s a measure of the d e v i a t i o n of the n u c l e a r  charge  d i s t r i b u t i o n from s p h e r i c a l symmetry, i s the p r o p e r t y of the nucleus and  i s the same f o r a l l compounds i n which a g i v e n nucleus  alone,  i s found.  For a  p r o l a t e s p h e r o i d a l d i s t r i b u t i o n ( f o o t b a l l l i k e ) Q i s p o s i t i v e , f o r an  ( f l a t t e n e d at the p o l e s and b u l g i n g a t the equator) Q i s n e g a t i v e .  spheroid  Q vanishes  f o r a s p h e r i c a l l y symmetric charge d i s t r i b u t i o n .  l e v e l s of the t o t a l H a m i l t o n i a n  i n frequency {2.3}  o r d e r p e r t u r b a t i o n s o l u t i o n of eqn.  E  = E m m  ( 0 )  + E  E  2.3.  m  {2.7}  by  {2.7}  ( 1 )  and V  o  i s the Larmor  frequency. ^ J  as  e 2  - _ 4'hI(2I-l)  Then eqn.  first  m  L e t us d e f i n e a parameter  Q  Thus the energy  u n i t s as a r e s u l t of the  are given  where E ^ = E_(m)/27Tn = • ( — Y H / _ T T ) _ = - v m, m Z o o  v V  oblate  - __ _ qQ 2TT 4 h l ( 2 l - l )  (  o)  2  t  Z  -  O  J  i s w r i t t e n as  = -v m + \ o J  3  c  o  s  z  Q-  1  + 5sin ecos2$}{3m -I(I+l)} z  Deuterium Magnetic Resonance  {2.9}  2  2  (DMR)  a) Deuteron on the hydrocarbon c h a i n . Assume t h a t the a m p h i p h i l i c membrane system i s i n the r i g i d phase so t h a t the c h a i n motion i s suppressed.  lattice  L e t us c o n s i d e r one.of  the  th deuterons i n the n  p o s i t i o n of the hydrocarbon c h a i n as d e p i c t e d i n F i g . 3b.  Since the deuterium nucleus  has  a spin 1 = 1 ,  by the g e n e r a l p e r t u r b a t i o n r e s u l t expressed  i t s energy l e v e l s as i n eqn.  {2.9}  are  given  16 M  -  V  + i v  q  2 ••  (  n  3 c o s 9-1  +  s  i  n  2  Q  c  o  s  2  $  {2.10}  )  n E  = Zi  o  T-. E  + 1  _ =  v  -V  (  Q  3cpsVl  n . 2  +  s  n  9 c o s 2 $ )  {  2  /3cos2 9- 1 +, n . 29cos2$) ( 2  ^ 1 +  2  >  1  1  }  /o io\ {2.12}  s l n  TI  and t h e c o r r e s p o n d i n g resonance f r e q u e n c i e s a r e 2 E - - E = V + V ( ° s 9-1 -1 o o Q 2 n  3sin 6cos2$) 2  {2.13}  + 5sin ecos2$) z  {2.14}  3c  A  E  where V  O  2 = V - v. ( °^ +1 o u z n  - E  3C  x  x  6  -  1  -13 2 = (2rr) ^ e q Q/h, and q n  2  +  2  n  i s t h e ZZ component o f t h e EFG a t t h e  th deuteron s i t e i n the n  p o s i t i o n of the chain.  Thus t h e NMR spectrum  a r i s i n g from t h e p a r t i c u l a r d e u t e r o n w i l l c o n s i s t o f two sharp peaks c e n t e r e d about t h e c e n t r a l f r e q u e n c y V and s e p a r a t e d by 2 2 Av = v _ (3cos 9-1) + n v _ s i n 9 o s 2 $ n n q  {2.15a}  C  N o t i c e t h a t , i n t h e absence o f c y l i n d r i c a l symmetry ( n i- 0) t h e resonance f r e q u e n c i e s and t h e s p l i t t i n g depend on t h e a n g l e s 9 and $.  The e f f e c t o f  non - z e r o n on t h e powder p a t t e r n spectrum has been e x p l o r e d i n g r e a t d e t a i l by Barnes (41) and Cohen e t a l ( 4 0 ) . Suppose t h a t t h e membrane system i n a! l a m e l l a r l i q u i d  crystalline  phase i s o r i e n t e d so t h a t a l l t h e o p t i c a l axes ( i n a l i p i d b i l a y e r they a r e the  normals t o the b i l a y e r s u r f a c e s ) o f the microdomains  i n the m a c r o s c o p i c  sample a r e p a r a l l e l t o each o t h e r , making an a n g l e 9 w i t h t h e a p p l i e d -»magnetic f i e l d H^.  I f t h e l i p i d m o l e c u l e s i n t h e o r i e n t e d sample undergo a  r a p i d a n i s o t r o p i c m o t i o n w i t h a c o r r e l a t i o n time T c much s h o r t e r than t h e  17. . i n v e r s e o f the s t a t i c q u a d r u p o l a r s p l i t t i n g s , then the r e o r i e n t a t i o n o f the C - D bond w i l l modulate 0 and hence 6_ as d e p i c t e d i n F i g . 3b, and the a n g u l a r dependent  Av  n  f a c t o r s i n eqn. ( 2 . 1 5 a } . i s t a k e n as the time average.  = v  n  Q n  Thus:  2 2 <3cos 6-l> + T)\) < s i n Gcos2$> Q n  {2.15b}  n  The EFG a t a d e u t e r o n s i t e on a h y d r o c a r b o n c h a i n i n l i q u i d c r y s t a l l i n e phase has, t o a good a p p r o x i m a t i o n , a c y l i n d r i c a l symmetry*, thus the asymmetry parameter r) i s p r a c t i c a l l y z e r o .  T h e r e f o r e , n e g l e c t i n g n, eqn.  {10b} i s reduced to a much s i m p l e r form: 2 A V  n  =  V  <  Q  3  c  o  s  9 _ 1 >  ^2.15c} th  The a n i s o t r o p i c motion o f the C D i n the n 2  p o s i t i o n o f the h y d r o c a r b o n  c h a i n can be s e p a r a t e d i n t o two independent components:  (a) r e o r i e n t a t i o n  of the C D ^ group about a symmetry a x i s and (b) f l u c t u a t i o n s o f the d i r e c t i o n of t h i s a x i s ( t h e average d i r e c t i o n o f t h i s a x i s has been shown to be normal to the l a m e l l a i n r e l a t e d systems ( 4 2 ) ) .  W i t h the motions s e p a r a t e d i n t o  these two independent components, and u s i n g the w e l l known a d d i t i o n theorem 2 f o r s p h e r i c a l harmonics (Abragam book, p. 4 5 4 ) , <3cos 8-l> can be w r i t t e n 2 ? 3cos 6 - 1 „ <3cos 9-l> = < ^ - 2 — > ( 3 c o s 0.-1) {2.16} and the f i r s t o r d e r quadrupole s p l i t t i n g i n the DMR spectrum a r i s i n g from til  the d e u t e r o n i n the n  p o s i t i o n o f the h y d r o c a r b o n c h a i n i s g i v e n by  2  3 c o s 6 -1 Av = V < _2 n _ > ( 3 c o s z a - l ) n Q ^n  {2-.1.7}  n  *The Z p r i n c i p a l a x i s of the EFG a t the s i t e of a d e u t e r i u m n u c l e u s on the hydrocarbon c h a i n i s almost always w i t h i n a few degrees of the C - D c o v a l e n t bond d i r e c t i o n and t h a t the asymmetry parameter i s r\ <^ 0.05  (41)  18 where t h e a n g l e s 6  n  and Q are d e f i n e d i n F i g . 3.  The formulae  {2.15a}-.and  {2.17}are t h e fundamental equation's f o r t h e e v a l u a t i o n o f D M R s p e c t r a . We d e f i n e a C - D bond o r d e r parameter S 2 3cos 6 -1 S  CD  = <  r  5  as n  "  {  *  2  -  1  8  }  n th where t h e s u b s c r i p t n on D denotes t h e d e u t e r o n i n t h e n the  hydrocarbon c h a i n . Av  n  p o s i t i o n along  Then eqn. {2.17} i s s i m p l i f i e d t o  S „ _ (3cos e-l) U LD — n n 2  = V  {2.19}  n  To a good a p p r o x i m a t i o n , a l l t h e h y d r o c a r b o n c h a i n - CD^ deuterons are  assumed t o be c h e m i c a l l y e q u i v a l e n t and hence w i l l have t h e same quadru  pole coupling constant.  Furthermore, s i n c e t h e quadrupole c o u p l i n g V n  of  the d e u t e r o n on t h e h y d r o c a r b o n c h a i n i s p r e d o m i n a n t l y o f i n t r a m o l e c u l a r  o r i g i n ( C - D bond), i t depends m a i n l y on t h e s t a t e o f t h e c o v a l e n t C - D bond. Thus V  depends on temperature through bond v i b r a t i o n . However, i n the n temperature range o f i n t e r e s t i n t h i s s t u d y , t h e temperature v a r i a t i o n o f V  i s e x p e c t e d t o be n e g l i g i b l y s m a l l , and thus can be assumed c o n s t a n t i n t h a t range.  C o n s e q u e n t l y , t h e o r d e r parameter f o r the methylene  deuterons  can be o b t a i n e d d i r e c t l y from t h e measured quadrupole s p l i t t i n g s u s i n g eqn. {2.19} i f V  i s known.  An o r i e n t e d sample i s d i f f i c u l t  t o p r e p a r e , so i n s t e a d one u s u a l l y  uses a powder sample made o f many s m a l l c r y s t a l s o r i e n t e d randomly w i t h r e s p e c t t o t h e l a b o r a t o r y frame whose Z - a x i s i s o r i e n t e d a l o n g t h e a p p l i e d s t a t i c magnetic f i e l d d i r e c t i o n .  I n our c a s e , t h e b i l a y e r normals a r e r a n -  domly o r i e n t e d w i t h e q u a l p r o b a b i l i t y f o r a l l d i r e c t i o n s , and t h e s u p e r position  o f t h e l i n e s a r i s i n g from t h e d i f f e r e n t o r i e n t a t i o n s g i v e s r i s e  19 to a broad a b s o r p t i o n c u r v e c h a r a c t e r i s t i c o f a powder p a t t e r n o f t h e form  f (w) = 2 |{g_(w) + g_ <-<*>)} n  '{2.20}  U B  where _  Aw  -J  Aw  -_  Aw 0 < w <  n  -7T-  n 1  = ^  Aw  -  <HT  +  W  1  )  A  ^n ,  n  . < w < Aw  —7T-  2 = 0  —  —  n  otherwise  {2.21}  2  A W  n  =  3 e 0 4 ^ l i CD S  =  2 7 T V  n  S  0 CD '  a  n  d  S  n  CD  ±  S  g  ±  V  e  n  b  y  e q i U  n  2  1 8  { - ^'  T  h  e  spectrum has two i n t e n s e peaks s e p a r a t e d by an amount g i v e n by t h e s p l i t t i n g i n t h e DMR spectrum o f t h e c o r r e s p o n d i n g sample o r i e n t e d a t 0 = 90°, i . e . the  peaks s e p a r a t i o n i n t h e powder p a t t e r n , i s Aw = 2ir|v "S | {2.22} TI n as g i v e n by eqn.{2*19} w i t h 0 =90°. T h i s f i r s t o r d e r powder p a t t e r n spectrum n  i s shown i n F i g . 4 a . When d i p o l a r l i n e b r o a d e n i n g i s t a k e n i n t o a c c o u n t , t h e powder p a t t e r n assumes t h e form (43) AN Tf f (w) = -=A f'M-^-y 2 n ° T ,. 2n T  2  0  -1 + {to+2Trv S__ P (cos9)} ) n °n n  Q  C  2  -1 +  (~^_-  T„ 2n  +'  {W-2TTV  S n  2  P (cos0)} )  C D  2  }sin0d0  {2.23}  n t _1  where N ^ i s t h e number o f d e u t e r o n s i n t h e n  p o s i t i o n o f the hydrocarbon  chains, T i s t h e s p i n - s p i n r e l a x a t i o n time o f t h e d e u t e r o n s i n t h a t zn 0  p o s i t i o n , and A i s a n o r m a l i z a t i o n c o n s t a n t .  The f u n c t i o n P ( c o s 0 ) i s t h e 2  20  l>  ll  Frequency  ( i n kHz)  st F i g u r e 4. (a) T h e o r e t i c a l 1  o r d e r powder p a t t e r n f o r a d e u t e r i u m n u c l e u s  i n a symmetric e l e c t r i c f i e l d g r a d i e n t (n = 0 ) .  The dashed  lines  show the i n d i v i d u a l components o f the m = -1 f-> m = 0 and m = 0 •*-»- m = +1  t r a n s i t i o n s , w h i l e the s o l i d l i n e i n d i c a t e s the sum  the two components.  Note t h a t the s e p a r a t i o n o f t h e  of  180°  " s h o u l d e r s " i s t w i c e the d o u b l e t s e p a r a t i o n Av. (b) The same spectrum as (a) but q u a d r u p o l a r and d i p o l a r b r o a d e n i n g has been t a k e n i n t o a c c o u n t . unbroadened spectrum i n ( a ) .  line  The d o t t e d curve i s the  21 2 Legendre p o l y n o m i a l d e f i n e d as P2(cos0) = (3cos 9-1)/2.  N o t i c e t h a t the  i n t r i n s i c s p l i t t i n g i n t h i s broadened powder p a t t e r n i s Aco = n  |.  2TT|V  % T h i s broadened  f i r s t o r d e r powder p a t t e r n i s d e p i c t e d i n F i g . 4b.  n For a  p e r d e u t e r a t e d l i p i d system c o n s i s t i n g of M n o n - e q u i v a l e n t d e u t e r o n p o s i t i o n s a l o n g the c h a i n s , the r e s u l t a n t spectrum c o n s i s t s of a s u p e r p o s i t i o n of M broad a b s o r p t i o n c u r v e s g i v e n by  f (  (43)  ) = X^Co.)  U  each w i t h two sharp edges ( 9 0 ° ) s e p a r a t e d by an a n g u l a r f r e q u e n c y Au>  S  = 2rr|v  |.  C D  n  n  In an i s o t r o p i c l i q u i d , i f the m o t i o n i s f a s t compared to the s t a t i c s p l i t t i n g f r e q u e n c y , the o r d e r parameter i s averaged t o zero and no s p l i t t i n g i s observed.  However, s i n c e the motion i n a l a m e l l a r l i q u i d  t a l system i s i n g e n e r a l a n i s o t r o p i c , S  4 0 and a s p l i t t i n g o f the  crysfirst  n o r d e r spectrum w i l l u s u a l l y be o b s e r v e d ,  b) DMR  on  D 0. 2  The p r i n c i p l e s of d e u t e r o n magnetic resonance of D 0 2  a r e the same as  those o u t l i n e d i n the l a s t s e c t i o n , e x c e p t t h a t i n d e u t e r o n s i t e s , a l t h o u g h the  major c o n t r i b u t i o n t o the e l e c t r i c f i e l d  m o l e c u l a r 0-D  g r a d i e n t i s from the i n t r a -  bond, t h e r e can be c o n t r i b u t i o n s w h i c h a r e of i n t e r m o l e c u l a r  o r i g i n such as the charge d i s t r i b u t i o n i n the v i c i n i t y of the p o l a r head groups as w e l l as o t h e r o r i g i n s .  Furthermore, a d e c r e a s e o f  i n c r e a s i n g hydrogen-bond s t r e n g t h has been observed (44) . quadrupole c o u p l i n g c o n s t a n t  with  T h e r e f o r e the  c o u l d be d i f f e r e n t from s i t e t o s i t e .  F u r t h e r c o m p l i c a t i o n a l s o a r i s e s due to c h e m i c a l exchange between deuterons i n w a t e r m o l e c u l e s i n d i f f e r e n t s i t e s .  I f the c h e m i c a l exchange  22 r a t e i s much more r a p i d than the quadrupole s p l i t t i n g , the o b s e r v e d s p l i t t i n g i s a w e i g h t e d average over t h e d i f f e r e n t s i t e s and i s g i v e n by (36, 45-46)  Av = I ^ P ^ S J  {2.24}  where P^ i s the p r o b a b i l i t y ( d e f i n e d by the f r a c t i o n of n u c l e i i n s i t e i ) t h a t a n u c l e u s i s i n s i t e i w i t h a c h a r a c t e r i s t i c quadrupole c o u p l i n g constant VQ  i  and o r d e r parameter S ^ .  The l a r g e s t c o n t r i b u t i o n to V ^  i  is  assumed to come from the i n t r a m o l e c u l a r 0-D bond (44) , which means t h a t V ^ remains a p p r o x i m a t e l y the same f o r the d i f f e r e n t s i t e s .  If VQ  1  1  does not  v a r y s i g n i f i c a n t l y w i t h temperature e i t h e r , t h e n , as shown by eqn.  {2.24},  the measured s p l i t t i n g s a r e a p p r o x i m a t e l y p r o p o r t i o n a l to an average o r d e r parameter  <S> = Z.P.S.  {2.25}  w i t h a c o n s t a n t o f p r o p o r t i o n a l i t y e q u a l to V ^ - ^ Q * 1  Thus Av can then be  w r i t t e n as  Av = l l . P . V . V l l x Q x 1  1  = IvJlE.P.S.I Q' x x x 1  1  {2.26}  1  w h i c h can p r o v i d e u s e f u l i n f o r m a t i o n f o r a 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 o f the quadrupole s p l i t t i n g s of the f i r s t o r d e r DMR  2.4.  spectrum of water system.  P r o t o n M a g n e t i c Resonance For the purpose o f comparing the r e s u l t s o f B^O i n the p r o t i a t e d  E Y L / ^ O sample ( i n 22% water by w e i g h t ) o b t a i n e d t h r o u g h DMR  t e c h n i q u e to  those o b t a i n e d from the p r o t o n magnetic resonance o f EYL i n the same sample, a b r i e f - r e v i e w of.PMR t h e o r y i s p r e s e n t e d h e r e . The t o t a l H a m i l t o n i a n o f N p r o t o n s system i s g i v e n by (39)  23 H = H  z  + H  d  •} {2.27>  where the f i r s t term i s the Zeeman energy and the second term i s the sum of the pairwise interaction energy between two magnetic dipoles y. and y,. 3  k  When the protons i n the N-body spin system form small groups within which the proton separations are d i s t i n c t l y  smaller than those between two  neighbouring groups, to a f i r s t order approximation one may consider such a group as an isolated system and calculate i t s energy l e v e l s i n the presence of an applied f i e l d H treating the rest of the protons i n the system as o>  being a perturbation on these energy l e v e l s , because the dipole-dipole interaction decreases rapidly with distance, a) A two-spin system For  a pair of strongly coupled protons on a a-CH^  group i n an other-  wise deuterated hydrocarbon chain i n a sample oriented at an angle 6, and assuming that the l a t t i c e i s r i g i d and dipolar broading by the neighbouring protons i s neglected, solution of eqn. {2.2-7} gives a doublet of i n f i n i t e l y sharp peaks centered about the Larmor frequency U J  q  = yH  Q  with separation  between them given by  A(JJ =  (l-3cos 0) 2  TT  2  3  {2.28}  r each of which are broadened by the dipolar i n t e r a c t i o n with the neighbouring dipoles. the  The dipolar energy levels of the two-spin system oriented at 6 and  corresponding f i r s t order spectrum are given i n F i g . 5. For  a powder sample, a similar argument as that i n Section 2.3 on  DMR  (47-48) w i l l give a well-known Pake doublet, which i s identical.with that  24 Zeeman  Dipolar Coupling  2.2 (1 - 3cos"6) /  4r  E = YhH o  m = -1  (a)  3  »=0  " TT  a  v  ~  3 c O S  6  >  2 2 + ^ - ( 1 - 3cos 9) 4r 2  E = -YhH m = +1  r  r  Figure 5. (a) Zeeman energy ( l e f t ) and dipolar coupling (right) of the t r i p l e t states of a two-spin system oriented at an angle 6. (b) The f i r s t order spectrum of the two-spin system oriented at 0 whose energy levels are given by (a). The dashed l i n e s are the unbroadened resonance l i n e s and the s o l i d curves are dipolar broadened doublets.  25 3 "Y^ri shown i n F i g . 4 w i t h the peak s e p a r a t i o n r e p l a c e d by AOJ = -z -^—Is I, where L J Hn r S i s the component o f t h e second o r d e r , s y m m e t r i c , t r a c e l e s s o r d e r rlri parameter t e n s o r a l o n g the H-H d i r e c t i o n .  b) PMR For  on a p r o t i a t e d l i p i d  system  a p e r d e u t e r a t e d l i p i d system, the a - d e u t e r i u m NMR  signal i s easily  d i s t i n g u i s h e d from t h e o t h e r d e u t e r o n r e s o n a n c e s , c d u e _ t o t h e . l a r g e a - d e u t e r o n quadrupolar s p l i t t i n g .  I n c o n t r a s t , i n a n o n - d e u t e r a t e d l i p i d system i n  l i q u i d c r y s t a l l i n e phase, the i n t r a - m e t h y l e n e and i n t e r - m e t h y l e n e p r o t o n d i p o l a r i n t e r a c t i o n s are comparable, and a r e much l a r g e r t h a n the range of proton chemical s h i f t s . shapes PMR  (30).  C o n s e q u e n t l y , t h e s p i n systems have complex l i n e -  For i n s t a n c e , f o r p h o s p h o l i p i d b i l a y e r v e s i c l e s t h e o b s e r v e d  l i n e s h a p e i s a s u p e r p o s i t i o n o f L o r e n t z i a n c u r v e s ( 4 9 - 5 0 ) , and f o r the  l a m e l l a r b i l a y e r i n l i q u i d c r y s t a l l i n e mesophase the PMR  lineshape i s  c h a r a c t e r i z e d by e x t r e m e l y b r o a d wings w i t h a s i n g u l a r i t y a t t h e c e n t r a l (Larmor) f r e q u e n c y ( 5 1 ) .  T h e o r i e s have been d e v e l o p e d by Bloom e t a l (52)  and Wennerstrom (53) to e x p l a i n the l i n e s h a p e o b s e r v e d i n l i q u i d lamellar bilayer. i n F i g . 6, c u r v e d.  crystal  The l o g a r i t h m i c l i n e s h a p e g i v e n by the t h e o r y i s shown  26  F i g u r e 6.  PMR  l i n e s h a p e s f o r v a l u e s of m„(0)/oj. (0) to be - 2 - 1  (b) 10  , (c) 10  and  (a) 10  (d) 1 (Bloom, e t a l ( 5 2 ) ) .  Spectrum  (d) i s the type o f a b s o r p t i o n l i n e s h a p e f i r s t observed Lawson and F l a u t t ( 5 1 ) .  ,  by  Chapter 3  Experimental 3.1.  The M a t e r i a l s a) The D 0 (99.7% enrichment) was purchased from Merck Sharpe and 2  Dohme ( M o n t r e a l ) . b) The p r o t i a t e d EYL (egg y o l k l e c i t h i n ) , t y p e 3E was p u r c h a s e d from Sigma C o r p o r a t i o n and used w i t h o u t f u r t h e r p u r i f i c a t i o n . 3.2.  Samples P r e p a r a t i o n a) To g e t r i d o f t h e water i n t h e EYL, we d i s s o l v e d t h e m a t e r i a l i n  benzene and r e c r y s t a l l i z e d i t by b l o w i n g n i t r o g e n through t h e s o l u t i o n a t room temperature a t a r a t e f a s t enough t o m i n i m i z e exposure t o l i g h t and p r e v e n t i t from o x i d a t i o n .  The sample was then k e p t under vacuum a t room  temperature o v e r n i g h t t o e l i m i n a t e t h e l a s t t r a c e s o f benzene.  The p r o t i a t e d EYL  sample was made by w e i g h i n g t h e c o r r e s p o n d i n g molar amount o f V^O i n t o t h e sample tube which c o n t a i n e d t h e d r i e d EYL. The sample was mixed by s t i r r i n g w i t h a s p a t u l a and s e a l e d .  I t was then wrapped i n t i n f o i l and k e p t i n a  r e f r i g e r a t o r a t -20°C. b) D e s c r i p t i o n o f t h e p r e p a r a t i o n o f E. C o l i sample has been g i v e n by D a v i s e t a l ( 3 7 ) .  3.3.  NMR Apparatus a) The d e u t e r i u m s p e c t r a were t a k e n a t 34.44 MHz i n a h i g h r e s o l u t i o n  s u p e r c o n d u c t i n g s o l e n o i d s u p p l i e d by N a l o r a c , I n c . , C o r c o r d , C a l i f o r n i a w i t h a B r u k e r SXP4-100 NMR s p e c t r o m e t e r .  The t r a n s i e n t d i g i t i z a t i o n and a v e r a g i n g  was a c c o m p l i s h e d w i t h a N i c o l e t 1090AR d i g i t a l o s c i l l o s c o p e i n t e r f a c e d t o an I n t e l 8080A m i c r o p r o c e s s o r - b a s e d d a t a a c q u i s i t i o n system.  The F o u r i e r  t r a n s f o r m s and moment c a l c u l a t i o n s were done w i t h a BNC-12 minicomputer.  The  28 BNC-12 computer i s equipped w i t h a D i a b l o D i s k D r i v e ( s e r i e s 31 d e n s i t y ) and was  used f o r s t o r a g e and a n a l y s i s o f the d a t a .  single  The  Spectro-  meter i s c a p a b l e of p u t t i n g out a t r a i n of up to 4 RF p u l s e s o f c o n t r o l l e d amplitude  and whose phases and l e n g t h s can be v a r i e d  A programable t i m e r ( N i c o l e t 293 I/O computer was  used to automate the NMR  independently.  c o n t r o l l e r ) i n t e r f a c e d to the  measurements.  Thus the  triggering  o f the i n d i v i d u a l RF p u l s e s , the s p a c i n g between them, and the r e p e t i t i o n r a t e were computer c o n t r o l l e d . The probe c o n s i s t e d of a RF c o i l i n t o which the sample was i n s e r t e d . The c o i l ( t o g e t h e r w i t h the sample) was oven.  C o o l i n g was  the oven.  The  a c h i e v e d by b l o w i n g c o o l a n t ( l i q u i d n i t r o g e n )  temperature g r a d i e n t a c r o s s the sample volume was  to be c o n s i d e r a b l y l e s s than  3.4.  e n c l o s e d i n a c y l i n d r i c a l copper through estimated  1°C.  NMR  Measurements  The  c o n v e n t i o n a l method o f o b t a i n i n g NMR  s p e c t r a c o n s i s t s of a p p l y i n g  a 90° RF p u l s e and then F o u r i e r t r a n s f o r m i n g the f r e e i n d u c t i o n decay ( F I D ) . D u r i n g the a p p l i c a t i o n o f the RF p u l s e , the r e c e i v e r o f the NMR g e t s s a t u r a t e d and  spectrometer  a c e r t a i n l e n g t h o f time ( c a l l e d the r e c o v e r y time o r  dead time) has to e l a p s e b e f o r e i t r e t u r n s to i t s normal o p e r a t i n g c o n d i t i o n s . Therefore  the e a r l y p a r t of the FID cannot be observed  time o f the r e c e i v e r .  due  to the  The u s u a l method, d e l a y i n g d a t a a c q u i s i t i o n  recovery until  the r e c e i v e r has r e c o v e r e d , r e s u l t s i n l o s s of the i n f o r m a t i o n c o n t a i n e d i n the e a r l y p a r t o f the FID  (which i s v e r y i m p o r t a n t f o r wide l i n e s )  i n v a r i a b l y l e a d s to d i s t o r t i o n o f the spectrum ( 5 4 ) .  I t also introduces  f i r s t o r d e r phase s h i f t s and a p o o r l y d e f i n e d base l i n e . problem the NMR  and  To c i r c u m v e n t  this  s p e c t r a were o b t a i n e d u s i n g the s o l i d echo by the method o f  Davis e t a l ( 5 4 ) .  T h i s method c o n s i s t s of a p p l y i n g a 90° p u l s e (whose phase  29 i s 0° w i t h r e s p e c t t o the r e f e r e n c e frequency)  f o l l o w e d by a n o t h e r  90° p u l s e  whose phase i s s h i f t e d by 90° w i t h r e s p e c t t o the f i r s t p u l s e a t a time x ( t y p i c a l l y 100-200 Us) l a t e r .  An echo i s formed a t 2x due to the r e f o c u s i n g  o f the n u c l e a r m a g n e t i z a t i o n .  By F o u r i e r t r a n s f o r m i n g the echo s t a r t i n g  a t t = 2T t h e f u l l spectrum i s o b t a i n e d . To enhance s i g n a l t o n o i s e , an a l t e r n a t i n g phase p u l s e sequence • O  O  O  (9O ) _ -T-(9O ) _ o-T -(9O ) _ E  O  quadrupolar  e  g o  r  e  O  1 8 O  o-T-(9O ) _ o 0  9 O  was u s e d , where the second  echo p u l s e sequence was phase s h i f t e d by 180° w i t h r e s p e c t t o  the r e f e r e n c e f r e q u e n c y .  F i v e hundred scans f o r DMR on D^O and 1000  f o r PMR on EYL a r e s u f f i c i e n t t o o b t a i n good s i g n a l a v e r a g i n g . were d e t e c t e d i n q u a d r a t u r e .  scans  The s i g n a l s  30 Chapter 4  The 4.1.  DMR  Results  Results  F o r c o n v e n i e n c e , t h e egg y o l k l e c i t h i n / D ^ O i n 22% (by w e i g h t ) o f w a t e r (D 0) , egg y o l k l e c i t h i n / ^ O and E. C o l i / ^ O 2  abbreviated  i n excess w a t e r a r e r e s p e c t i v e l y  t o EYL/22%WD 0, EYL/EXCD 0 and EC/EXCD 0. 2  2  2  A l l the r e s u l t s  mentioned h e r e w i l l be d i s c u s s e d more f u l l y i n Chapter 5 where t h e f i g u r e s are  placed. a) Quadrupole  splittings  When l i n e b r o a d e n i n g i s a b s e n t , the quadrupole s p l i t t i n g s can be obtained  from the peak p o s i t i o n s i n the DMR  spectra.  However, i n t h e p r e s -  ence o f d i p o l a r b r o a d e n i n g , the p o s i t i o n s o f t h e maximum i n t e n s i t y a r e no l o n g e r c o i n c i d e n t w i t h the p o s i t i o n s o f the 90° edges o f t h e quadrupole powder p a t t e r n (Appendix A ) .  I n t h i s s i t u a t i o n , the " s p l i t t i n g s " a r e  e m p i r i c a l l y d e f i n e d as t h e average o v e r two measurements;  namely,  the  s e p a r a t i o n between t h e peaks and the s e p a r a t i o n between two p o i n t s on the o u t e r edges o f the powder p a t t e r n a t 75% o f t h e peak a m p l i t u d e o f t h e experimental  DMR  spectra.  By t h e method d e s c r i b e d above, quadrupole  " s p l i t t i n g s " were measured d i r e c t l y from t h e DMR  s p e c t r a o f t h e EYL/22%WD 0 2  sample, t h e r e p r e s e n t a t i v e s o f w h i c h are shown i n F i g . 9. between -6°C  In the region  and -10°C, the l i n e s h a p e s a r e s i n g l e t s , and o n l y t h e l i n e  w i d t h s a t half-maximum i n t e n s i t y were measured.  The r e s u l t s o f the measure-  ments are p r e s e n t e d i n F i g . 22. b) E v a l u a t i o n o f the DMR  s p e c t r a i n terms o f t h e i r moments  The v a l u e s of t h e moments M f r o m th_e DMR  n  ( A p p e n d i x A) can r e a d i l y be c a l c u l a t e d  s p e c t r a s u c h as those shown i n F i g . 7-9.  A l t h o u g h i n the  31 experiment the f i r s t eight mements were routinely calculated by integrating over the spectrum, only the f i r s t few moments of the spectra (M_ to M^) are r e l i a b l e i n the l i q u i d c r y s t a l l i n e phase, and at lower temperature only M -M^ Q  can be accurately determined, because the accuracy of the higher  moments depends c r i t i c a l l y on the f i d e l i t y of the broad part of the spectrum. The results of the calculations of -the integrated signal i n t e n s i t i e s  ,  the  f i r s t , the second and the' fourth moments for the three samples  (namely,  the  EYL/22%WD 0, the EYL/EXCD^O and the EC/EXCD^O) are given i n F i g . 10-13 2  and F i g . 16-18. In order to compare the results of quadrupole s p l i t t i n g s obtained by direct measurements from the DMR spectra of the EYL/22%WD 0 sample ( F i g . 22), 2  the  f i r s t moment M^ (which gives the average s p l i t t i n g ) as given by eqn. A.6  i n Appendix A, namely, M  1  4 it- . = —T <Av> 3/3  was used to calculate the quadrupole s p l i t t i n g s i n the DMR spectra of the EYL/22%WD 0 i n the region from 5°C to 25°C. 2  Below 5°C l i n e broadening may  become too severe to render v a l i d i t y to the equation given above.  The  results of the calculations are shown i n F i g . 22. + 4.2.  PMR Results The second and the fourth moments were calculated from the PMR spectrum  of the EYL/22%WD 0 system, and the r e s u l t s are shown i n F i g . 23. 2  4.3.  Sources of Error There i s no severe problem of d i s t o r t i o n i n the DMR spectrum of D 0 2  due to 90° pulse length, because the spectral width of D 0 i s small (as 2  32 compared t o t h a t o f PMR and DMR spectrum o f t h e l i p i d s ) .  F o r o u r PMR  e x p e r i m e n t , we o b t a i n e d a p u l s e l e n g t h o f 0.9 m i c r o s e c o n d f o r t h e 90° p u l s e , w h i c h i s s h o r t enough t o r o t a t e a l l m a g n e t i z a t i o n s i n a l l p a r t s o f the NMR spectrum through t h e same a n g l e . One o f t h e s i g n i f i c a n t s y s t e m a t i c e r r o r i n t h e DMR experiment f o r B^O was magnetic inhomogeneity, w h i c h cannot be t o t a l l y e l i m i n a t e d .  Another  s o u r c e o f e r r o r a r o s e from image f o r m a t i o n due t o i n a c c u r a t e q u a d r u t u r e phasing.  F o r i n s t a n c e , t h e asymmetries i n t h e base o f t h e s p e c t r a o f t h e  EC/EXCD 0 a t -1°C t o 10°C as shown i n F i g . 7 were due t o the f o r m a t i o n o f 2  images.  T h i s work w, s done i n c o l l a b o r a t i o n w i t h Dr. A. L. Mackay. a  33 Chapter 5  D i s c u s s i o n And C o n c l u s i o n 5.1.  DMR S p e c t r a o f D 0 2  a) S p e c t r a o f D 0 i n t h e EYL/EXCD 0 and EC/EXCD 0 systems 2  2  2  As shown i n F i g . 7-8, the DMR s p e c t r a o f D 0 i n t h e EYL/EXCD 0 (whose 2  2  w a t e r c o n c e n t r a t i o n l i e s between 50% and 60%) a r e q u a l i t a t i v e l y s i m i l a r t o those i n t h e EC/EXCD 0 (whose water c o n c e n t r a t i o n > 9 0 % ) .  U n l i k e t h e DMR  2  s p e c t r a o f D 0 i n the EYL/22%WD 0, w h i c h c o n s i s t o f powder p a t t e r n 2  2  doublets  w i t h quadrupole " s p l i t t i n g s " i n t h e o r d e r o f 1 kHz i n t h e temperature range between -3°C and 25°C as shown i n F i g . 9, t h e quadrupole " s p l i t t i n g s " i n these s p e c t r a a r e absent.  F o r T >_ -2°C, the s p e c t r a o f t h e EYL/EXCD 0 c o n s i s t o f 2  an e x t r e m e l y narrow s i n g l e t c h a r a c t e r i s t i c o f i s o t r o p i c w a t e r .  Like the  EYL/EXCD 0, the s p e c t r a o f t h e EC/EXCD 0 f o r T _> -1°C a l s o c o n s i s t o f a v e r y 2  2  narrow s i n g l e t . Q u a n t i t a t i v e l y , the s p e c t r a o f D 0 i n t h e EYL/EXCD 0 and t h a t i n the 2  EC/EXCD 0 a r e d i f f e r e n t . 2  2  The observed l i n e w i d t h s o f t h e s p e c t r a o f t h e  EYL/EXCD 0 range from 81 Hz a t -2°C t o 110 Hz a t 20°C, w h i l e those o f t h e 2  EC/EXCD 0 s t a y c o n s t a n t 2  a t 30 Hz f o r T >^ -1°C.  Thus,Lthe l i n e w i d t h s o f t h e  DMR s p e c t r a o f the EC/EXCD 0 a r e s m a l l e r than those o f t h e EYL/EXCD 0 by a 2  2  f a c t o r o f 3 t o 4. The  r e d u c t i o n i n quadrupole s p l i t t i n g s from 1 kHz f o r t h e s p e c t r a o f  the EYL/22%WD 0 ( F i g . 9) t o the z e r o s p l i t t i n g i n the s p e c t r a o f t h e 2  EYL/EXCD 0 ( F i g . 8) c a n be u n d e r s t o o d as f o l l o w s : 2  Case I . Assume t h a t t h e system i s i n w a t e r c o n c e n t r a t i o n C j< the maximum h y d r a t i o n  (40%).  A l l concentrations  per gram o f l i p i d and w a t e r m i x t u r e .  a r e e x p r e s s e d by grams o f w a t e r  F o r a crude a p p r o x i m a t i o n ,  the two-site  model proposed by Wennerstrom e t a l (34) i s adopted f o r t h e system.  The two  34  s i t e s correspond  t o the t r a p p e d water (water w h i c h i s i n c o r p o r a t e d between  b i l a y e r s , b u t i s weakly a s s o c i a t e d t o the p o l a r head groups (34b)) and bound w a t e r (water w h i c h i s s t r o n g l y bound t o the s u r f a c e s formed by the p o l a r head groups).  The s p l i t t i n g i n t h e DMR  spectrum of t r a p p e d w a t e r cannot be r e -  s o l v e d , w h i l e t h a t f o r the bound w a t e r has a v a l u e i n the o r d e r of s e v e r a l kHz.  S i n c e the maximum w a t e r i n c o r p o r a t e d between b i l a y e r s i n the l i q u i d  c r y s t a l l i n e l a m e l l a r phase i s 40% by w e i g h t ( 1 6 ) , a l l the w a t e r i n the EYL/22%WD20 system i n l i q u i d c r y s t a l l i n e l a m e l l a r phase i s i n c o r p o r a t e d  into  the b i l a y e r s , and t h e r e i s p r a c t i c a l l y no b u l k w a t e r ( f r e e i s o t r o p i c w a t e r t h a t i s not i n c o r p o r a t e d between b i l a y e r s and exchanges s l o w l y w i t h w a t e r t h a t i s i n c o r p o r a t e d between b i l a y e r s ( 3 2 ) ) .  I n the l a m e l l a r phase where C _< 40%,  the b i l a y e r s s w e l l i n two ways (namely, i n c r e a s e i n t h i c k n e s s o f t h e b i l a y e r s and moving-apart o f the p o l a r head groups) as w a t e r i s added, so t h a t a l l the w a t e r , t r a p p e d or bound, i s i n c r e a s e d .  However, i n our crude model, we assume  t h a t the change i n the bound w a t e r i s n e g l i g i b l e so t h a t o n l y the amount o f trapped w a t e r i s i n c r e a s e d when the t o t a l w a t e r c o n t e n t of the system i s increased (54).  On the b a s i s o f t h i s model, and, s i n c e the exchange between  the two s i t e s i s f a s t as i n d i c a t e d by the e x i s t e n c e o f o n l y a s i n g l e powder p a t t e r n ( r a t h e r than two o r more superimposed s p e c t r a ) shown i n F i g . 9a, the q u a d r u p o l e s p l i t t i n g A v i n t h e o b s e r v e d DMR EYL/22%WD„0 i s g i v e n by eqn.  =  Av  i=t,b where A v  t  «  {2.24}:  W - W, I-—^-Av W t 1  spectrum o f w a t e r d e u t e r o n i n the  W, + T ^ A V ^ |1  W  b  A v ; W and W a r e t h e mole f r a c t i o n s o f the t°tal D-0 b b 2  {5.1}  content  of  the system and bound w a t e r , r e s p e c t i v e l y ; A v , = V ^ s , i s the c h a r a c t e r i s t i c b Q b s p l i t t i n g i n the DMR s p e c t r u m of D„0 when i t i s s t r o n g l y bound t o the i n t e r f a c e  35 formed by p o l a r head groups, w h i l e  Av  V  f c  t  = Q ^  1 S t  the c h a r a c t e r i s t i c  i n t h e DMR s p e c t r u m o f D^O when i t i s i n t h e t r a p p e d w a t e r s i t e .  splitting  The above  f o r A v demonstrates t h a t , f o r low w a t e r c o n c e n t r a t i o n , t h e o b s e r v e d  equation  s p l i t t i n g i s p r e d o m i n a n t l y t h a t o f A v , , s i n c e A v « A v , . As more w a t e r i s b t b added t o t h e system, t h e f r a c t i o n a l c o n t r i b u t i o n from A v , ( A v , may depend on b  b  w a t e r c o n c e n t r a t i o n , b u t h e r e we assume i t t o be c o n s t a n t ) becomes s m a l l e r . C o n s e q u e n t l y , an o v e r a l l r e d u c t i o n i n t h e s p l i t t i n g o f t h e o b s e r v e d spectrum o c c u r s w i t h i n c r e a s i n g w a t e r c o n c e n t r a t i o n u n t i l t h e s p l i t t i n g cannot be resolved.  I n a more r e a l i s t i c model, more t h a n one type o f bound s i t e  should  be assumed. Case I I . F o r C > 40%, two phases o f D^O a r e formed:  t h e maximum amount  of w a t e r t h a t i s i n c o r p o r a t e d i n t o t h e b i l a y e r s , and b u l k o r i s o t r o p i c e x c e s s f r e e w a t e r i n a s e p a r a t e phase e x c h a n g i n g s l o w l y w i t h t h e maximum w a t e r o f hydration.  I n t h i s s i t u a t i o n , t h e observed s p e c t r u m i s a s u p e r p o s i t i o n o f  the two s p e c t r a a r i s i n g from t h e w a t e r w i t h i n t h e b i l a y e r s and the b u l k w a t e r . The second moment o f t h e o b s e r v e d spectrum i s g i v e n by (Appendix B) r.i H „, EX M  2  "  1  +  H Here  A  E X  /  A  H  +  1  +  V  /  A  E X  { 5  2  ' '  EX and  a r e r e s p e c t i v e l y the second moments o f t h e s p e c t r a o f t h e  w a t e r o f maximum h y d r a t i o n and t h e e x c e s s f r e e w a t e r .  A^ and A ^ a r e the  i n t e g r a t e d i n t e n s i t i e s o f t h e s p e c t r a o f t h e w a t e r o f maximum h y d r a t i o n f  H and o f t h e e x c e s s f r e e w a t e r f„„: EX 00  AJJ = /  \  x  f (fl) H  dft  = / f W) « £X  {5.3}  {5.4}  36 00  F o r C -> , A _  M  2  -»•  x  = M  00  and, c o n s e q u e n t l y , eqn. {5.2} i s reduced t o  E X 2  i . e . t h e second moments and t h e l i n e w i d t h s a r e m a i n l y t h a t o f t h e i s o t r o p i c excess f r e e w a t e r as o b s e r v e d i n t h e DMR spectrum o f t h e EC/EXCD 0 system 2  ( F i g . 7, 13 and 1 5 ) .  N o t i c e t h a t the second moments  and t h e l i n e w i d t h s  f o r T 2_ -1°C shown i n F i g . 13 and 15 a r e m a i n l y those o f t h e magnet inhomogeneity (~30 Hz ± 2 0 % ) . For T < -2°C, t h e DMR s p e c t r u m o f D 0 i n t h e EC/EXCD 0 c o n s i s t s o f a 2  2  b r o a d and s t r u c t u r e l e s s l i n e whose l i n e w i d t h v a r i e s from 240 t o 700 Hz.  The  s p e c t r u m f o r t h e EYL/EXCD 0 i n t h e r e g i o n T <_ -3°C i s a l s o b r o a d and i t s l i n e 2  w i d t h v a r i e s from 380 t o 400 Hz.  N o t i c e t h a t t h e enormous drop i n t h e DMR  s i g n a l i n t e n s i t y shown i n F i g . 10 i s due t o d i s a p p e a r a n c e o f t h e DMR s i g n a l of a l l  the e x c e s s f r e e w a t e r as a r e s u l t o f t h e f r e e z i n g out o f t h i s w a t e r  ( t h i s w i l l be d i s c u s s e d l a t e r on).  The s p e c t r u m o f t h e f r o z e n e x c e s s f r e e  f D0 2  ( t h e i c e ) i s too b r o a d t o be d e t e c t a b l e .  Thus, t h e DMR s p e c t r a o b s e r v e d  i n t h i s temperature r e g i o n a r i s e s o l e l y from the w a t e r i n c o r p o r a t e d between the b i l a y e r s .  The o b s e r v e d b r o a d l i n e s can be u n d e r s t o o d i n terms o f eqn. {5.2}.  When t h e e x c e s s f r e e w a t e r has been f r o z e n o u t , A_„ = 0, and, because t h e i c e s i g n a l cannot be d e t e c t e d , t h e e q u a t i o n i s e f f e c t i v e l y reduced t o M  M  H 2  2  -  M  H 2  i s e x p e c t e d t o be l a r g e r than M  EX 2  , and c o n s e q u e n t l y a b r o a d e r l i n e w i d t h  t The i c e spectrum has a quadrupole s p l i t t i n g o f 160 kHz. To observe t h e e n t i r e DMR s p e c t r u m o f p o l y c r y s t a l l i n e i c e , a s p e c t r a l w i d t h o f a t l e a s t 300 kHz i s r e q u i r e d . The s p e c t r a l w i d t h used f o r my w a t e r DMR e x p e r i m e n t s was o n l y 10 kHz f o r t h e EC/EXCD 0 and t h e EYL/EXCD.O systems, and 20 kHz f o r t h e EYL/22%WD 0. 2 z  37  F i g u r e 7.  Deuterium n u c l e a r magnetic resonance s p e c t r a o f D 0 i n the E. C o l i / D 0 system i n excess w a t e r 90% by w e i g n t ) o b t a i n e d a t 2  (a) 20°C, (b) 4°C, ( c ) -1°C, (d) -2°C and 34.42 MHz, 300 scans u s i n g the q u a d r u p o l a r echo and q u a d r a t u r e d e t e c t i o n method. R e p e t i t i o n r a t e = 1 second, s p e c t r a l w i t h = 10 kHz. A l l the s p e c t r a a r e 5 kHz p l o t .  EYL/D 0 IN EXCESS WATER 5 kHz PLOT  Figure 8.  38  Deuterium nuclear magnetic resonance spectra of D^O i n the egg yolk l e c i t h i n / ^ O system i n excess water concentration (>>40%) obtained at (a) 18°C, (b) 4°C, (c) -2°C, (d) -3°C and 34.42 MHz, 500 scans using the quadrupolar echo and quadrature detection method.  Spectral width = 10 kHz.  A l l the spectra are 5 kHz plot.  39 below t h e f r e e z i n g p o i n t .  The absence o f s t r u c t u r e  tt  i n t h e o b s e r v e d spectrum  i n t h i s r e g i o n may be caused by inhomogeneous b r o a d e n i n g ; t h e p r e s e n c e o f i c e i n t h i s temperature r e g i o n may have c r e a t e d d i f f e r e n t r e g i o n s i n t o which the unfreezable water i s d i s t r i b u t e d . ly.  Water i n d i f f e r e n t r e g i o n s exchanges s l o w -  Each o f these r e g i o n s may have t h e same T^, b u t t h e o r d e r parameter o f  the 0-D bond d i r e c t i o n i n t h e D^O m o l e c u l e s v a r i e s from r e g i o n t o r e g i o n , so t h a t w a t e r i n d i f f e r e n t r e g i o n s g i v e s r i s e t o DMR s p e c t r u m w i t h quadrupole s p l i t t i n g .  different  A s u p e r p o s i t i o n o f a l l o f these s p e c t r a a r i s i n g  from  w a t e r i n a l l t h e r e g i o n s y i e l d s a s p e c t r u m whose s t r u c t u r e cannot be r e s o l v e d . b) S p e c t r a o f D 0 i n t h e EYL/22%WD 0 2  2  F o r temperatures between 25°C and -3°C, t h e DMR spectrum o f D 0 i n t h e 2  EYL/22%WD 0 c l e a r l y e x h i b i t s t h e w e l l known d o u b l e t powder p a t t e r n w i t h 2  quadrupole " s p l i t t i n g " v a r y i n g from 1.3 kHz f o r t h e system i n l a m e l l a r c r y s t a l l i n e phase ( L ) t o 0.72 kHz a t -3°C. a  The q u a d r u p o l e s p l i t t i n g  liquid ( i n the  o r d e r o f 1 kHz) i n t h e d o u b l e t powder p a t t e r n o b t a i n e d f o r t h i s system i s much l e s s than t h a t t y p i c a l l y found (55) f o r p o l y c r y s t a l l i n e i c e and h y d r a t e s ( i n the o r d e r o f 150 k H z ) .  The l a r g e r e d u c t i o n i n t h e s p l i t t i n g i s an i n d i c a t i o n  o f t h e g r e a t e r t i m e a v e r a g i n g o f t h e e l e c t r i c f i e l d g r a d i e n t s due t o a r a p i d but a n i s o t r o p i c r e o r i e n t a t i o n o f t h e w a t e r m o l e c u l e s a s s o c i a t e d w i t h the l e c i t h i n p o l a r groups w h i l e d i f f u s i n g a l o n g t h e i n t e r f a c e .  The v a l i d i t y o f  S t r u c t u r e i n t h e s p e c t r a i n t h e r e g i o n I < -2 C f o r t h e EC/EXCT^O and I < -3 C f o r t h e EYL/EXCD 0 i s e x p e c t e d , s i n c e , as t h e t r a p p e d w a t e r d e c r e a s e s , and, 2  as w i l l be shown l a t e r , the squeezed out w a t e r i n t h e s e systems i s f r o z e n as soon as i t i s squeezed o u t , eqn. {5.1} i n t h i s c h a p t e r p r e d i c t s t h a t the DMR s i g n a l o f t h e bound w a t e r , w h i c h has c h a r a c t e r i s t i c s p l i t t i n g o f s e v e r a l kHz, s h o u l d predominate.  40 t h i s i n t e r p r e t a t i o n i s f u r t h e r s u p p o r t e d by t h e work o f F i n e r e t a l (32) and C h a r v o l i n et a l (56). The presence o f sharp edges i n the d o u b l e t powder p a t t e r n s shows t h a t the asymmetry parameter n = 0.  The growth o f t h e s i g n a l a t the c e n t r e o f the  spectrum i s d i s c e r n i b l e a t -3°C, w h i c h becomes more pronounced i n t h e s p e c t r u m a t -4°C.  The spectrum a t -5°C  i s d e f i n i t e l y a s u p e r p o s i t i o n o f two  spectra:  one i s t h e powder p a t t e r n d o u b l e t due t o the t i g h t l y bound w a t e r and the o t h e r i s c h a r a c t e r i s t i c of free i s o t r o p i c water.  I n t h e spectrum at -10°C, the  i d e n t i t y of t h e powder p a t t e r n d o u b l e t i s l o s t .  T h i s spectrum c o n s i s t s o f  a narrow s i n g l e t w i t h an i n t r i n s i c l i n e w i d t h o f 90 Hz. component o f t h e spectrum a t -5°C  The sharp c e n t r a l  a r i s e s from t h e i s o t r o p i c " f r e e " , w a t e r  w h i c h has been squeezed out from t h e b i l a y e r s .  As shown i n F i g . 9 g - i , the  zero degree s h o u l d e r s and 90 degree edges a r e absent i n t h e powder p a t t e r n s f o r T £ -15°C.  The s p l i t t i n g s i n these s p e c t r a range from 160 t o 360  which are very smail values.  Hz,  However, due to l a c k o f e x p e r i m e n t a l c e r t a i n t y  about the o r i g i n o f t h e b r o a d e n i n g mechanism, we s h a l l n o t attempt t o i n t e r p r e t t h e observed s p e c t r a i n t h i s r e g i o n .  Note t h a t the drop i n s i g n a l t o  n o i s e i n t h e spectrum f o r the EYL/22%WD20 a t -25°C i s not due t o drop i n t h e DMR  s i g n a l i n t e n s i t y as can be seen from F i g . 11, b u t due t o the b r o a d e n i n g  of t h e l i n e .  The a r e a o f the spectrum M  q  ( i n t e g r a t e d s i g n a l i n t e n s i t y ) , which i s  p r o p o r t i o n a l t o the s p i n p o p u l a t i o n , s h o u l d be c o n s t a n t except f o r a s m a l l change i n t h e Boltzmann f a c t o r , because the s p i n p o p u l a t i o n i s unchanged during the experiment.  F i g u r e 9.  DMR s p e c t r a o f  i n t h e Ei*L/22%tfD 0 o b t a i n e d a t (a) 25°C, (b) 4°C, b  (c) -3°C, "(d) -4 C,  (e) -5°C, ( f ) -10°C, (g) -15°C, (h) -20°C,  ( i ) -25°C and 34.46 MHz, 1000 scans a c c u m u l a t i o n f o r s i g n a l a v e r a g i n g u s i n g t h e q u a d r u p o l a r echo and q u a d r a t u r e d e t e c t i o n method. P v e p e t i t i o n r a t e = % second, s p e c t r a l w i d t h = 20 kHz. A l l t h e s p e c t r a a r e 5 kHz p l o t . Spectrum i n F i g u r e 1 0 - j i s t h e same as t h a t i n F i g u r e 1 0 - i except i t i s a 10 kHz p l o t .  42 5.2.  The Moments o f t h e DMR S p e c t r a a) The i n t e g r a t e d s i g n a l i n t e n s i t i e s ( M ) o f t h e DMR s p e c t r a o f D^O i n q  the  EYL/EXCD 0 and EC/EXCD 0 2  The i n t e g r a t e d s i g n a l i n t e n s i t y (M ) VS T f o r D 0 i n t h e two systems a r e q  shown i n F i g . 10.  2  I n t h e t e m p e r a t u r e range d e f i n e d by T > -2°C, t h e s i g n a l  i n t e n s i t y o f D 0 i n b o t h systems i n c r e a s e s as t e m p e r a t u r e d e c r e a s e s . 2  This i s  p a r t l y due t o t h e Boltzmann f a c t o r ( s i g n a l i n t e n s i t y i s p r o p o r t i o n a l t o t h e p o p u l a t i o n d i f f e r e n c e i n s p i n s t a t e s , which i s i n t u r n p r o p o r t i o n a l t o the Boltzmann f a c t o r ) , and p a r t l y due t o the f a c t t h a t s i g n a l i n t e n s i t y i s s e n s i t i v e t o change i n Q o f t h e RF c o i l c o n t a i n i n g t h e sample, because as T d e c r e a s e s , Q i n c r e a s e s , s o does t h e s i g n a l i n t e n s i t y . to  I t i s also sensitive  the change i n t h e d i e l e c t r i c c o n s t a n t o f t h e water and t h e l i p i d s . The enormous drop i n i n t e n s i t y o f t h e DMR s i g n a l o f D 0 i n t h e EYL/EXCD 0 2  2  i s due t o f r e e z i n g out o f a l l t h e e x c e s s f r e e w a t e r i n t h e system.  Note  w i t h i n e x p e r i m e n t a l e r r o r , the M  Q  VS T i s l i n e a r f o r T >^ -2°C, thus i t i s  permissible to extrapolate the M  Q  VS T l i n e down t o T = -3°C.  the at  value of M  q  that,  The r a t i o o f  a c t u a l l y measured a t T = -3°C t o t h e e x t r a p o l a t e d v a l u e o f M  t h e same t e m p e r a t u r e i s 0.15.  Q  T h i s means t h a t t h e w a t e r t h a t remained un-  f r o z e n a t -3°C comprises 15% o f t h e o r i g i n a l t o t a l w a t e r c o n t e n t o f t h e sample. F u r t h e r m o r e , f o r T <_ -3°C, t h e r e i s s y s t e m a t i c and g r a d u a l r e d u c t i o n i n s i g n a l i n t e n s i t y as temperature d e c r e a s e s , as shown by t h e smooth c u r v e on t h e l e f t of  t h e M v s T d i s c o n t i n u i t y i n F i g . 10. q  f r e e z i n g out o f w a t e r .  That i s an i n d i c a t i o n o f f u r t h e r  As w i l l be s u b s t a n t i a t e d i n S e c t i o n 5.2d, i t i s t h e  f r e e z i n g out o f t h e w a t e r squeezed out from t h e b i l a y e r s t h a t l e a d s t o t h e g r a d u a l decrease i n t h e s i g n a l i n t e n s i t y i n t h e r e g i o n below the f r e e z i n g p o i n t as temperature d e c r e a s e s . The t e m p e r a t u r e dependence o f t h e DMR s i g n a l i n t e n s i t y o f D„0 i n t h e  43  44 EC/EXCD 0 i s s i m i l a r t o t h a t i n t h e EYL/EXCD^O. 2  a t -1°C.  The e x c e s s f r e e w a t e r f r e e z e s  T h i s f r e e z i n g p o i n t and t h a t of 1> 0 i n t h e EYL/EXCD 0 (which f r e e z e s 2  a t -2°C) d i f f e r o n l y by 1°C.  2  The f r a c t i o n o f water t h a t remained u n f r o z e n a t  -2°C i s 16% o f t h e t o t a l w a t e r . b) The i n t e g r a t e d i n t e n s i t y o f t h e DMR spectrum o f D 0 i n t h e EYL/22%WD 0 2  2  system The g e n e r a l temperature dependence o f t h e DMR s i g n a l i n t e n s i t y o f D 0 2  i n t h e EYL/22%WD 0 f o r T >_-10°C ( F i g . 11) i s s i m i l a r t o those mentioned e a r l i e r . 2  There i s an enormous drop i n i n t e n s i t y as temperature changes from -10°C t o -15°C, i n d i c a t i n g t h a t t h e w a t e r squeezed out from t h e b i l a y e r s -10°C and -15°C.  f r e e z e s between  The f r a c t i o n o f w a t e r r e m a i n i n g u n f r o z e n a t -15°C i s 0.50.  Note t h a t t h e f r e e z i n g p o i n t o f t h e squeezed out i s o t r o p i c w a t e r i n t h i s system i s 8°C l o w e r than t h a t o f D 0 i n t h e o t h e r two systems. 2  c) The f i r s t and t h e second moments o f t h e DMR s p e c t r a o f D 0 i n t h e 2  EYL/EXCD 0 and EC/EXCD 0 2  2  systems  The temperature dependence o f M EYL/EXCD 0 i s shown i n F i g . 13. 2  2  o f t h e DMR s p e c t r u m o f D 0 i n t h e 2  To r a t i o n a l i z e t h e o b s e r v e d M  2  f o r t h e system  EYL/EXCD 0, t h e model proposed i n Appendix B i s assumed f o r t h e d i s t r i b u t i o n 2  o f w a t e r i n t h i s system.  S i n c e w a t e r c o n c e n t r a t i o n i n t h e EYL/EXCD 0 l i e s 2  between 50% and 60% ( r e c a l l t h a t w a t e r c o n c e n t r a t i o n c i s e x p r e s s e d as c = W/(W+L), where L and W a r e r e s p e c t i v e l y t h e w e i g h t o f t h e l i p i d s and o f the water),  a maximum amount W  o f t h e w a t e r w h i c h g i v e s W /(W  i n c o r p o r a t e d i n t o the l i p i d b i l a y e r s  17lJ  +L) = 0.4 i s  i n l i q u i d c r y s t a l l i n e l a m e l l a r phase,  f o r m i n g t h e w a t e r o f maximum h y d r a t i o n .  The r e s t o f t h e w a t e r forms t h e i s o t r o p i c  excess f r e e w a t e r e x i s t i n g i n a s e p a r a t e phase and exchanging s l o w l y w i t h t h e w a t e r i n c o r p o r a t e d between t h e b i l a y e r s .  I n such a model, t h e second moment,  M ( E Y L / E X C D 0 ) , o f t h e observed NMR spectrum o f the. w a t e r i n t h e EYL/EXCD 0 i s 2  2  2  8x10 _  6h  2h  i  I  -25  0  -10  T  i  i  10 (°C)  Figure 11. Temperature dependence of the integrated  i  u  i  25  signal i n t e n s i t y , M o  of deuteron magnetic resonance of D O i n the EYL/22%WD 0. o  46 g i v e n by eqn. { B . l } i n Appendix B:  M (EYL/EXCD 0) = f M ^ + (1 - f ) M 2  2  H  {5.5}  2  where  i s the f r a c t i o n o f t h e water o u t s i d e t h e b i l a y e r s . EX independent o f t e m p e r a t u r e .  M  2  Here f i s assumed t o be  H , M  2  a r e r e s p e c t i v e l y t h e second moments o f  the i s o t r o p i c e x c e s s f r e e w a t e r and the w a t e r o f maximum h y d r a t i o n as d e f i n e d i n Appendix B. = pM  Assume t h a t (EYL/22%WD 0)  2  {5.7}  2  where M (EYL/22%WD 0) 2  2  i s the second moment o f t h e DMR s p e c t r u m o f D 0 i n t h e 2  EYL/22%WD 0, and t h a t p i s independent o f t e m p e r a t u r e .  S u b s t i t u t i n g eqn. {5.7}  2  i n t o eqn. {5.5} g i v e s  M (EYL/EXCD 0) = f M ^ + ( 1 - f)pM (EYL/22%WD 0) 2  2  2  {5.8}  2  EX S i n c e the observed second moment M EX magnet i n h o m o g e n e i t y , M seen i n t h e  2  o f t h e f r e e w a t e r i s v i r t u a l l y t h a t o f the  i s i n s e n s i t i v e t o change  2  i n temperature as can be  v s T p l o t f o r t h e EC/EXCD 0 shown i n F i g . 13 where the s p e c t r u m 2  i s dominated by t h e e x c e s s f r e e w a t e r f o r T _> -1°C. I f t h e model under c o n s i d e r a t i o n i s v a l i d , t h e n , a c c o r d i n g t o eqn. {5.8}, we e x p e c t t o o b t a i n a s t r a i g h t l i n e f o r a p l o t o f t h e M (EYL/EXCD 0) v e r s u s EX 2  M (EYL/22%WD 0) w i t h s l o p e (1 - f ) p and i n t e r c e p t fM2 2  2  .  2  The p l o t o f t h e  M (EYL/EXCD 0) f o r T _> -2°C ( r e p r e s e n t e d by p o i n t s marked by o i n F i g . 13) 2  2  a g a i n s t t h e M (EYL/22%WD 0) 2  2  i n t h e same t e m p e r a t u  r e  range ( p r e s e n t e d i n F i g . 18)  i s shown i n F i g . 14 where t h e M2 (EYL/EXCD 0) i s i n d e e d l i n e a r l y r e l a t e d t o t h e 2  M (EYL/22%WD 0). 2  2  The s l o p e and t h e i n t e r c e p t o f t h e s t r a i g h t l i n e o b t a i n e d by  47 the p r i n c i p l e o f l e a s t squares f i t t o t h e e x p e r i m e n t a l d a t a a r e determined t o be:  (1 - f ) p = 0.073 ± 0.0036  fM  E X  6  = 0.63 x 1 0 s e c "  2  2  {5.9}  ± 0.038 x 1 0  6  sec"  2  {5.10}  mx Let W, be t h e amount o f w a t e r found i n t h e bound s i t e , and W. be t h e b iso maximum amount o f w a t e r added t o t h e EYL/22%WD 0 t o make i t f u l l y h y d r a t e d , 2  mx i . e . W,-, = W, + W. i s t h e amount o f w a t e r s o t h a t C = W _ . / ( ™ ) = 40%. FH b iso FH FH W  + L  T  The upper and l o w e r bounds f o r t h e p r o p o r t i o n a l c o n s t a n t p can be c a l c u l a t e d on t h e b a s i s o f t h e t w o - s i t e model proposed i n S e c t i o n 5.1a and t h e f o l l o w i n g assumptions: (a) The s u r f a c e a r e a p e r p o l a r head group s t a y s c o n s t a n t when more w a t e r i s added t o t h e system EYL/22%WD 0, so t h a t 2  remained c o n s t a n t and t h a t a l l  the w a t e r added t o t h i s system c o n t r i b u t e s o n l y t o t h e i s o t r o p i c  site.  (b) There i s o n l y one v a l u e o f o r d e r parameter i n t h e bound s i t e , and t h u s o o n l y one v a l u e o f s p l i t t i n g A v , f o r t h i s s i t e .  The s p l i t t i n g i n t h e  :  D  i s o t r o p i c s i t e i s zero. C o n s e q u e n t l y , t h e average o v e r a l l s p l i t t i n g s  o b s e r v e d i n t h e systems  EYL/22%WD 0 and EYL/40%WD O a r e r e s p e c t i v e l y g i v e n by eqn. {5.1}: 2  2  W, <Av>  = Av  <Av>  = Av  5  - ^2 2 - A vb , r  + W b iso W = +  b  W = rf22 W  W k Av, E mx,, b W iso  -f-  w  ra  A bv ,  {5.11}  Av,  {5.12}  b  2  22  Here W„. = W, + W. i s t h e t o t a l w a t e r i n t h e EYL/22%WD 0 and W ' i s the 22 b iso 2 iso mx i s o t r o p i c w a t e r between t h e b i l a y e r s . W „ = W, + W. i s t h e t o t a l amount o f FH b iso o  J  T  48 water i n t h e EYL/40%WD 0. 2  The second moment M  as g i v e n by eqn. A.3 o r A.6 i n Appendix A can be  2  w r i t t e n as M  2  = K <(AV) > = K { A v }  2  2  {5.13}  where K i s a c o n s t a n t . Eqn. {5.13} g i v e s M (EYL/22%WD 0) and 2  = M (EYL/40%WD O) t h e f o l l o w i n g  2  2  2  expressions: W M_(EYL/22%WD 0) = K {r^~ A v , } 2 Z W b  2  {5.14}  o  2 2  M„  H  2  = K & - AV. } FH  2  {5.15}  b  From eqn. {5.7}, p i s g i v e n by H  M _ " M„(EYL/22%WD 0) ~  W  2  P  o  Z  (  22 W~7  2 }  {5.16}  rri  Z  Note t h a t a s assumption (a) i s r e l a x e d ,  tends t o i n c r e a s e w i t h i n c r e a s i n g c,  so t h a t p g i v e n by eqn. {5.16} r e p r e s e n t s t h e l o w e r bound, P-J^J ^ expressions W  W W„/W ZZ  22  FH  O R  P'  From t h e  f o r t h e water c o n c e n t r a t i o n s o f t h e systems EYL/22%WL> 0 and EYL/40%WD O: 2  W  ??  + L = 0.22  and  TT W f  was found t o be 0.42 and p,. = 0.18. ib  r  2  FH  _ = 0.4 +, L  {5.17}  The assumption t h a t t h e water added  t o t h e EYL/22%WD 0 does n o t c o n t r i b u t e t o t h e second moment, but i t makes t h e 2  average environment more i s o t r o p i c p u t s an upper bound on p so t h a t 0.18 < p < 1  {5.18}  Eqn. {5.9} and i n e q u a l i t y {5.18} g i v e 0.59 ± 0.02 < f < 0.93 ± 0.0036  {5.19}  and from {5.10} and {5.9}, t h e upper and t h e lower bounds on M 6  (0.68 ± 0.014) x 1 0 s e c "  2  < M  E  X  6  E X 2  < (1.07 ± 0 . 0 7 4 ) x l 0 s e c "  2  a r e g i v e n by: {5.20}  From eqn. {5.5} or {5.8}, i t i s c l e a r t h a t the i n c r e a s e i n  f o r the  EYL/EXCD2O w i t h i n c r e a s i n g temperature ( t h i s i s a l s o observed i n EYL/22%WD 0 as 2  shown i n F i g . 1 8 ) , a b e h a v i o u r unexpected when compared w i t h most s t u d i e s o f m o t i o n a l n a r r o w i n g , i s due t o l i p i d - w a t e r i n t e r a c t i o n , w h i c h imposes a c o n s t r a i n t on the o r d e r i n g of the time average e f g a t the l i p i d - w a t e r i n t e r f a c e .  The  o r d e r i n g e f f e c t i s assumed t o be such t h a t a t low t e m p e r a t u r e s , the p r i n c i p a l a x i s e f g , w h i c h i s a l o n g the 0-D  bond d i r e c t i o n , assumes an o r i e n t a t i o n w i t h  -r  r e s p e c t t o t h e b i l a y e r normal n, g i v i n g an average 0-D  bond o r d e r parameter  which i s smaller than that f o r the high-temperature c o n f i g u r a t i o n . changes from -2°C  t o -3°C,  As  temperatur<  t h e r e i s a sharp i n c r e a s e i n the v a l u e of M  f a c t o r o f t h r e e , c o r r e s p o n d i n g t o t h e b r o a d e n i n g o f the DMR  2  by a  a b s o r p t i o n l i n e by  the mechanism e l u c i d a t e d i n S e c t i o n 5.1a, namely, the sudden d i s a p p e a r a n c e of the d o m i n a t i o n by t h e i s o t r o p i c e x c e s s f r e e w a t e r . The v a r i a t i o n of t h e M  of the DMR  2  spectrum of D 0 2  i n the EC/EXCT> 0 as a 2  f u n c t i o n of temperature i s s i m i l a r t o t h a t f o r t h e EYL/EXCD 0, except t h a t f o r 2  T 2_ -1°C,  the M  2  i s independent of temperature because the observed DMR  signal  i s d o m i n a n t l y t h a t of the i s o t r o p i c e x c e s s f r e e water as d i s c u s s e d i n S e c t i o n 5.1a.  As shown i n F i g . 13, t h e v a l u e o f M  2  i n t h e r e g i o n T >^ -1°C  f o r the  EC/EXCD 0, w h i c h i s d o m i n a n t l y t h a t of t h e magnet inhomogeneity, i s found t o 6 —^ 6 —2 be 0.45 x 10 sec *" ± 0.15 x 10 sec , w h i c h i s s m a l l e r t h a n the l o w e r bound 2  of the M  E X 2  f o r the EYL/EXCD 0 g i v e n by t h e i n e q u a l i t y {5.20}. 2  T h i s i s not  FX unexpected, because M  2  depends on the sample and i t s geometry and t h e s t a t e  of t h e magnet inhomogeneity i n the space o c c u p i e d by t h e sample. t h i s system, t h e d i s c o n t i n u i t y i n t h e M the e x c e s s f r e e water i s f r o z e n o u t . as temperature changes from -1°C  2  Again, i n  occurs at the temperature at which  The f i v e - f o l d i n c r e a s e i n t h e  t o -2°C  r e f l e c t s the  M  2  51  F i g u r e 13.  Temperature dependence o f t h e second moment M  2  of t h e DMR  spectrum o f D 0 i n t h e EYL/EXCD 0 ( c i r c l e s ) and the 2  EC/EXCD„0 ( t r i a n g l e s ) .  2  52  x10 M ( EYL/22°/oWD 0) 2  F i g u r e 14.  2  Second moments, M (EYL/EXCD 0), o f t h e DMR s p e c t r a o f D 0 i n t h e 2  2  2  system EYL/EXCD 0 p l o t t e d a g a i n s t t h e second moments, M (EYL/22%WD 0), 2  2  of D 0 i n t h e EYL/22%WD 0. 2  2  The s o l i d l i n e i s t h e l e a s t squares f i t  2  to t h e e x p e r i m e n t a l d a t a ( c i r c l e s ) where a two parameter f i t o f t h e form M (EYL/EXCD 0) = f M 2  was used.  2  E X 2  + (1 --f)pM (EYL/22%WD-0) 2  53  8 2 x10 L 6 N  A A AAA  0  F i g u r e 15.  i*r  oooooooo O O O Q Q O O T  -10  0  10  T  (°C)  Temperature dependence o f t h e l i n e w i d t h Av of t h e DMR spectrum of D 0 i n the E. C o l i / E X C D 0 ( c i r c l e s ) and 2  .  20  EYL/EXCD 0 2  (triangles).  2  54  15 -  13 X10 -  (°C)  T F i g u r e 16.  Temperature dependence o f the f o u r t h moment M. o f the 4 spectrum o f D^O i n the EYL/EXCD 0 ( c i r c l e s ) and 2  E. C o l i / E X C D 0 9  (triangles).  DMR  55 d i s a p p e a r a n c e of t h e d o m i n a t i o n by the e x c e s s f r e e water due t o f r e e z i n g out of  the w a t e r .  S i m i l a r remarks can be made about the temperature dependence  of  the f i r s t moment M  ( F i g . 12) and the l i n e w i d t h A v  I  spectrum of the  ( F i g . 15) of the D M R  x  2  EYL/EXCL> 0  and  2  EC/EXCD 0. 2  d) The f i r s t and second moments of the D M R s p e c t r a of D 0 i n the E Y L / 2  22%WD 0 2  Comparison o f the M EXCD 0  2  v s T f o r the E Y L / 2 2 % W D 0 w i t h t h a t f o r the E Y L / 2  p r e s e n t e d i n F i g . 13 and 18 shows t h a t the v a l u e s o f the  2  f i r s t system a r e 6 ( a t second.  -2°C)  to 9 ( a t  20°C)  M  f o r the  2  t i m e s l a r g e r than those f o r the  T h i s d i f f e r e n c e i s e x p e c t e d , because when more water i s added t o a  system w i t h maximum h y d r a t i o n , the amount of i s o t r o p i c water i n c r e a s e s , and t h u s , as p o i n t e d out i n S e c t i o n 5.1a and Appendix B, the average for  environment  the D 0 m o l e c u l e s becomes more i s o t r o p i c due t o the i n c r e a s e d d o m i n a t i o n 2  by the excess f r e e w a t e r , l e a d i n g t o the s m a l l e r M i n Appendix  2  as d i c t a t e d by eqn.  {B.1}  B.  The o b s e r v a t i o n o f the phenomenon of l i p i d - w a t e r i n t e r a c t i o n i n t h i s system  (EYL/22%WD 0) 2  EC/EXCD 0. 2  i s much more pronounced  than t h a t i n the  EYL/EXCD 0 2  and  I n a system where the water c o n c e n t r a t i o n i s w e l l below the maximum  h y d r a t i o n , eqn.{5.l} d e r i v e d from the t w o - s i t e model i n t h i s c h a p t e r i n d i c a t e s t h a t the bound w a t e r , w h i c h i s i n v o l v e d i n the l i p i d - w a t e r  interaction,  dominates the observed D M R s i g n a l , g i v i n g r i s e to s p e c t r a w i t h s p l i t t i n g s i n the  o r d e r o f s e v e r a l kHz.  C o n s e q u e n t l y , the M  2  of the spectrum i s v e r y  s e n s i t i v e t o the 0 - D bond o r i e n t a t i o n a l o r d e r parameter whose magnitude pends on the l i p i d - w a t e r In  de-  interaction.  the r e g i o n - 1 0 ° C _< T _< - 3 ° C , the most s t r i k i n g c o n t r a s t between the  b e h a v i o u r o f the  M  2  f o r t h i s system  (EYL/22%WD 0) 2  and the  EYL/EXCD 0  as temperature d e c r e a s e s , the former d e c r e a s e s whereas the l a t t e r  2  i s that,  increases.  F u r t h e r m o r e , as temperature d e c r e a s e s , the M  (and c o r r e s p o n d i n g l y the l i n e  2  w i d t h as shown i n Fig.22) f o r the EYL/22%WD 0 i n the r e g i o n d e c r e a s e s much 2  more r a p i d l y than t h a t f o r the same system i n the r e g i o n T >^ -3°C. p e r a t u r e dependence of the M  The tem-  f o r the EYL/22%wT> 0 i n t h i s r e g i o n i s not unt  2  2  e x p e c t e d , because the t r a p p e d w a t e r i n t h i s r e g i o n i s g r a d u a l l y squeezed out from the b i l a y e r s . to -10°C  The squeezed out i s o t r o p i c water remains u n f r o z e n down  as shown i n S e c t i o n 5.2b,  and the DMR  s i g n a l o f t h a t i s o t r o p i c water  becomes more and more dominant as temperature d e c r e a s e s , l e a d i n g t o a d e c l i n e i n the M  2  much more r a p i d than t h a t e x p e c t e d from l i p i d - w a t e r i n t e r a c t i o n i n  the r e g i o n T >^ -3°C.  On the o t h e r hand, as shown i n F i g . 10, a l l the i s o t r o p i c  excess f r e e water i n the EYL/EXCD 0 has been f r o z e n out i n t h i s r e g i o n , and, 2  i n the range -3°C _< T <^ -2°C, -10°C  <^ T <_ -3°C,  the l i p i d i s f u l l y h y d r a t e d .  t h e t r a p p e d water i s e x p e c t e d to be squeezed out from the  b i l a y e r s g r a d u a l l y as temperature i s l o w e r e d . M  2  Thus, f o r  However, the b e h a v i o u r o f the  f o r the EYL/EXCD 0 i s o b v i o u s l y i n c o m p a t i b l e w i t h the e x i s t e n c e o f such 2  i s o t r o p i c water.  T h i s means t h a t the i s o t r o p i c w a t e r i s f r o z e n as soon as  i t i s squeezed out from the b i l a y e r s .  T h i s h y p o t h e s i s i s s u p p o r t e d by the  e v i d e n c e p r o v i d e d by t h e d e c r e a s e i n t h e DMS EXCD 0 i n t h i s r e g i o n as shown i n F i g . 1Q. 2  the spectrum f o r the EYL/EXCD 0 a t -10°C  s i g n a l i n t e n s i t y f o r the EYL/ Thus, we expect t h a t the M  t h a t of the spectrum f o r the EYL/22%WD 0 a t the same t e m p e r a t u r e . 2  This i s  i n d e e d the case as shown i n F i g . 1-3 and F i g . 18, where the r a t i o of M the EYL/EXCD 0 t o t h a t f o r the EYL/22%WD 0 i s 53:5 o r 11. 2  o f the spectrum f o r the EYL/EXCD 0 i n t h e range from -3°C 2  of  s h o u l d be c o n s i d e r a b l y l a r g e r t h a n  2  2  2  2  for  The i n c r e a s e i n M t o -10°C  as  2  tempera-  t u r e d e c r e a s e s may be a s c r i b e d t o the f o l l o w i n g mechanisms: (a) The s q u e e z i n g out o f t h e t r a p p e d w a t e r r e s u l t s i n a p o p u l a t i o n r e d u c t i o n i n the i s o t r o p i c s i t e s between the b i l a y e r s , w h i l e the p o p u l a t i o n i n the a n i s o t r o p i c s i t e s  may  57 remain f i x e d .  C o n s e q u e n t l y , a c c o r d i n g t o eqn,{5.l} i n t h i s c h a p t e r , t h e Av^  i n t h a t e q u a t i o n g a i n s more and more w e i g h t , w h i l e the c o n t r i b u t i o n from t h e Av^ fades away, r e s u l t i n g i n t h e i n c r e a s e i n  as temperature d e c r e a s e s ,  (b) As temperature i s l o w e r e d , t h e average 0-D bond o r d e r parameter a t each s i t e i n c r e a s e s , g i v i n g r i s e t o a b r o a d e r l i n e w i d t h , ( c ) When temperature i s d e c r e a s e d , t h e motions o f the l i p i d p o l a r head group, t o w h i c h t h e w a t e r m o l e c u l e s a r e bound, a r e reduced ( 3 6 ) , r e s u l t i n g i n a l e s s e r m o t i o n a l a v e r a g i n g of  t h e e l e c t r i c f i e l d g r a d i e n t s and t h e d i p o l a r i n t e r a c t i o n , so t h a t the s p i n -  s p i n r e l a x a t i o n time T ing  occurs.  2  i s shortened.  I t i s very d i f f i c u l t  C o n s e q u e n t l y , a l i f e time l i n e broaden-  t o d i s t i n g u i s h between t h e p r o c e s s d e s c r i b e d  i n (a) and t h a t i n ( b ) . The M  v s T p l o t f o r the EC/EXCD 0 ( F i g . 13) i n t h e r e g i o n between -3°C  2  2  and -10°C i s s i m i l a r t o t h a t f o r t h e EYL/EXCD 0, and i s a l s o d i c t a t e d by t h e 2  same mechanism as s u p p o r t e d by t h e e x p e r i m e n t a l f a c t s shown i n F i g . 10. The f r e e z i n g o f t h e squeezed o u t w a t e r i n t h e EYL/EXCD 0 arid EC/EXCD 0 2  2  i n t h e r e g i o n mentioned above i s i n g r e a t c o n t r a s t t o t h e squeezed o u t water i n t h e EYL/22%WD 0, w h i c h d i d n o t f r e e z e u n t i l below -10°C. 2  This difference  i s n o t s u r p r i s i n g , because, i n t h e neighborhood o f -2°C, l a r g e s u r f a c e s o f ice  a r e formed due t o the f r e e z i n g o f t h e e x c e s s f r e e w a t e r i n t h e EYL/EXCD 0 2  and EC/EXCD 0. 2  These s u r f a c e s enhance f r e e z i n g o f w a t e r pushed o u t from the  b i l a y e r s i n t h e temperature r e g i o n from -2°C t o -10°C.  I n t h e EYL/22%WD 0 2  sample, no such i c e s u r f a c e s e x i s t a t -2°C, so t h a t t h e r e i s no s u r f a c e o f c r y s t a l l i z a t i o n i n the r e g i o n . As temperature d e c r e a s e s , t h e M,> f o r t h e EYL/22%WD 0 r e a c h e s a minimum 2  a t -10°C.  From t h e s p e c t r a o f t h i s system i n t h e r e g i o n from -3°C t o -10°C  as shown i n F i g .  9 c - f , i t i s e v i d e n t t h a t t h e presence o f i s o t r o p i c w a t e r  squeezed out from the b i l a y e r s i s one o f t h e most l i k e l y mechanisms  ,58  F i g u r e 17.  Temperature dependence o f t h e f i r s t  ( t r i a n g l e s ) and t h e f o u r t h  ( c i r c l e s ) moments, M^, M^, o f t h e DMR spectrum o f B^O i n the EYL/22%WD 0. 2  60 r e s p o n s i b l e f o r t h e minumum.  A complete phase diagram o f egg y o l k  lecithin-  w a t e r system has been p r o v i d e d by S m a l l and Chapman (57) and R e i s s - H u s s o n ( 5 8 ) . However, s i n c e t h e phase l i n e  i s i l l - d e f i n e d , i t i s dangerous t o draw any  c o n c l u s i o n r e g a r d i n g the phase b e h a v i o u r o f o u r sample s o l e l y on t h e b a s i s o f t h e i r phase diagram.  ( t h e EYL/22%WD 0) 2  U n f o r t u n a t e l y , our PMR experiment  o d i d n o t cover t h e r e g i o n below -10 C, so t h a t no i n f o r m a t i o n c o n c e r n i n g t h e phase b e h a v i o u r o f o u r EYL/22%WD 0 sample i s a v a i l a b l e . 2  Due t o l a c k o f  e x p e r i m e n t a l c e r t a i n t y , i t i s v e r y d i f f i c u l t t o know whether a phase  transition  i s a l s o i n v o l v e d a t -10°C. 2 e) The temperature dependence o f t h e  and the M^/M^  f o r t h e EYL/  22%WD 0, EYL/EXCD 0 and EC/EXCD 0 2  2  2 The temperature dependence o f t h e parameters Ag and M^/M  f o r the three  2  systems a r e p l o t t e d i n F i g . 19-21. 2 The shapes o f the A„ v s T and M./M„ v s T f o r t h e EYL/EXCD 0 and 2 4 2 2 2 EC/EXCD^O a r e v e r y s i m i l a r . A sharp drop i n A and m^/M^ o c c u r s as temperature o  2  changes from -2°C t o -3°C and -1°C t o -2°C f o r t h e EYL/EXCD 0 and EC/EXCD 0, 2  respectively.  2  The v a l u e s o f t h e s e parameters f o r temperatures below the ':  f r e e z i n g p o i n t a r e s m a l l e r than those a t t e m p e r a t u r e s above i t . 2 The shapes o f t h e A v s T and M^/M v s T f o r t h e EYL/22%WD 0 a r e v e r y d i f f e r e n t from those f o r t h e o t h e r two systems. A sharp anomalous i n c r e a s e i n t h e v a l u e s o o f A„ and M./M o c c u r s around -10°C. Note t h a t t h e anomalous 2 4 2 2 2  2  2  2  increase i n either A  2  o r M^/M^  (Appendix A) does n o t c o r r e s p o n d t o the c o -  e x i s t e n c e o f i c e and water phases, s i n c e i c e does n o t c o n t r i b u t e t o t h e moments o f t h e spectrum.  However, s i n c e t h e s t a t e o f w a t e r depends on t h e  environment ( t h e l i p i d s ) i n w h i c h t h e water e x i s t s , i t i s v e r y l i k e l y  that  the anomalous b e h a v i o u r o f t h e two parameters f o r t h e EYL/22%WD 0 a t -10°C 2  c o r r e s p o n d s t o the c o e x i s t e n c e o f d i f f e r e n t phases o f w a t e r .  61  (°C)  T  2  F i g u r e 19.  Temperature  dependence o f the r a t i o M^/M^  r e l a t i v e mean square d e v i a t i o n A spectrum o f D 0 o  2  ( c i r c l e s ) and the  ( t r i a n g l e s ) of the  i n the E. C o l i / E X C D 0 . o  DMR  62  F i g u r e 20.  Temperature  dependence o f t h e r a t i o M^/M^  ( c i r c l e s ) and t h e  r e l a t i v e mean square d e v i a t i o n A,, ( t r i a n g l e s ) o f t h e DMR spectrum o f D„0 i n t h e EYL/EXCD„0.  63  -25  0  -10  T F i g u r e 21.  Temperature  10  25  (°C)  dependence o f t h e r e l a t i v e mean square d e v i a t i o n 2  ( c i r c l e s ) and t h e r a t i o M^/M^  ( t r i a n g l e s ) o f t h e DMR  spectrum o f D 0 i n the EYL/22%WD 0. o  o  .64 5.3.  Comparison W i t h Other Work The temperature dependence o f t h e f i r s t moment  (which g i v e s t h e  average quadrupole s p l i t t i n g , and hence average o r d e r p a r a m e t e r ) , t h e second moment  and t h e quadrupole s p l i t t i n g measured d i r e c t l y from t h e DMR spectrum  of D^O i n t h e EYL/22%WD20 as shown i n F i g . 18 and 22 have t h e same g e n e r a l shape as t h e quadrupole s p l i t t i n g v s temperature o f t h e DMR spectrum f o r t h e EYL/QD^O (19% by w e i g h t o f w a t e r c o n c e n t r a t i o n ) p r e s e n t e d by F i n e r e t a l (32) as shown i n F i g . 22, b u t they do n o t agree i n d e t a i l .  For convenience, l e t  us denote EYL/9D 0 as EYL/19%WD 0. 2  2  At -20°C, t h e spectrum o f t h e EYL/19%WD 0 (Fig.22). has a quadrupole 2  s p l i t t i n g o f 1.8 kHz, w h i l e t h a t o f t h e EYL/22%WD 0 ( F i g . 22) has a much s m a l l 2  s p l i t t i n g o f o n l y 0.37 kHz, a d i f f e r e n c e by a f a c t o r o f f i v e .  The s p l i t t i n g  a t -10°C i n t h e spectrum o f t h e EYL/19%WD 0 i s 0.81 kHz, and t h a t o f t h e 2  EYL/22%WD 0 i s o n l y 0.1 kHz, a f a c t o r o f e i g h t s m a l l e r . 2  But t h e s p l i t t i n g  i n t h e s p e c t r a a t 25°C f o r t h e s e two systems a r e n e a r l y i d e n t i c a l ; namely, 1.2 kHz f o r t h e s p l i t t i n g i n t h e spectrum o f t h e EYL/19%WD 0, and t h a t o f t h e 2  EYL/22%WD 0 i s 1.02 kHz. A minimum i n t h e A y v s T o f t h e EYL/19%WD 0 and 2  2  EYL/22%WD 0 o c c u r s a t -2°C and a t -10°C, r e s p e c t i v e l y , w i t h a m i n i m a l v a l u e 2  of 0.52 kHz f o r t h e former and 0.12 kHz f o r t h e l a t t e r .  The phase diagrams  p r o v i d e d by S m a l l (57) and F. R e i s s - H u s s o n (58) i n d i c a t e t h a t t h e phase behavi o u r o f t h e EYL/water ion, of the  system i s s e n s i t i v e t o s m a l l change i n w a t e r concentra-:'.  so t h e d i f f e r e n c e i n t h e temperature a t which t h e minimum i n t h e A v v s T  t h e two systems o c c u r s i s n o t unexpected. onset of chain m e l t i n g .  F i n e r a s c r i b e d t h e minimum t o  However, no such t r a n s i t i o n i n t h e EYL/22%WD 0 2  i s o b s e r v e d i n t h e range from -10°C t o 48°C as demonstrated by o u r PMR d a t a g i v e n i n F i g . 23.  65  F i g u r e 22.  (a) Temperature  dependence o f t h e quadrupole s p l i t t i n g Av w h i c h i s  measured d i r e c t l y from t h e DMR spectrum o f D^O i n t h e EYL/22%WD 0 ( c i r c l e s ) .  The p o i n t s marked by t r i a n g l e s a r e t h e  quadrupole s p l i t t i n g s A v ^ c a l c u l a t e d  from t h e f i r s t moment M^ o f  the DMR spectrum o f D^O i n t h e s a i d system. calculated  s p l i t t i n g s are systematically  Note t h a t t h e  l a r g e r than t h o s e o b t a i n e d  by d i r e c t measurement, i n d i c a t i n g t h e e x i s t e n c e o f l i n e b r o a d e n i n g . I f l i n e b r o a d e n i n g i s a b s e n t , t h e two c u r v e s s h o u l d be  coincident,  (b) The i n s e r t shows t h e quadrupole s p l i t t i n g v s T i n t h e DMR s p e c t r a o f egg y o l k phosphatidylethanolamine/21%WD 0 2  (triangles)  and EYL/19%WD 0 = EYL/9P 0 ( c i r c l e s ) p r e s e n t e d by F i n e r e t a l ( 3 2 ) . 2  2  66 5.4.  PMR Results for the EYL/22%WD 0 2  2 Temperature dependence of the M  2  and M^/M  2  of PMR spectrum of EYL In the  EYL/22%WD 0 system are given i n F i g . 23. 2  The M -10°C  2  decreases monotonically and smoothly as temperature r i s e s from  to 48°C.  The value of M  compared to that at -10°C.  2  at 48°C i s smaller by a factor of f i v e as  The reduction i n M  2  at higher temperature region  arises from motional narrowing due to increase i n time averaging of the d i p o l e dipole i n t e r a c t i o n . 2 Within experimental  error, the M^/M  i s independent of temperature. I f  2  we assume the existence of t r a n s l a t i o n a l d i f f u s i o n of the phospholipid molecules along the bilayer surfaces and r o t a t i o n about the normal to the b i l a y e r s , and, furthermore,  i f the powder pattern lineshape i s assumed to be given by a super-  p o s i t i o n of the lineshape 2  _ls  f(co,9) = {27TM (P (cos6)) } exp{-(a)-uJ ) 2  2  o  2  2  /2M (P (cos0) } } 2  {5.21}  2  by summing over the o r i e n t a t i o n angle 8 (52), we obtain 6.45 for the value of 2 , which i s consistent with the data for F i g . 23 within 2  the M^/M  2  error.  Thus, t h i s p a r t i c u l a r value of M^/M  2  experimental  may suggest that there are s t i l l  a l o t of motions at a temperature as low as -10°C.  Furthermore, since M^/M  2  2  i s very s e n s i t i v e to coexistence of phases (Appendix A), the absence of anomalous increase i n that parameter indicates that there i s no phase t r a n s i t i o n i n the entire region under investigation. However, as shown i n F i g . 24, the preliminary PMR r e s u l t s for EYL i n the EYL/EXC_ 0 (Alex Mackay, unpublished) exhibit some unusual behaviour near 4°C, 2  This work was done i n collaboration with Dr. A. L. Mackay.  67 which c o u l d be a s s o c i a t e d w i t h a change i n t h e o r d e r i n g o f the water m o l e c u l e s . T h i s phenomenon a l s o o c c u r s i n the EC/EXCT^O a t 4°C as shown i n t h e same f i g u r e 2 ( t h e M^/M  2  f o r t h i s system i s n o t shown).  S i n c e t h e DMR d a t a on t h e E. C o l i  o u t e r membrane (37) does n o t show any anomaly a t 4°C ( F i g . 2 5 ) , and no anomaly i s observed i n t h e EYL/22%WD 0 as shown above, t h e phenomenon observed by A l e x 2  t Mackay i n t h e two systems i n excess water  has been a s c r i b e d t o t h e onset of  t r a n s l a t i o n a l d i f f u s i o n of the phospholipid molecules.  The p o s s i b l e c o r r e l a t i o n  between t h i s phenomenon and t h e f r e e z i n g out o f water i n t h e two systems i n excess water has been r u l e d out on t h e e v i d e n c e p r o v i d e d by my DMR presented i n t h i s  results  thesis.  When the w r i t e up o f t h i s t h e s i s i s completed, A l e x Mackay r e p e a t e d the PMR experiment f o r t h e EYL/EXCD 0 sample, and found t h a t t h e r e s u l t s a r e n o t 2  reproducible.  68  F i g u r e 23.  Temperature  dependence o f t h e r a t i o M^/M^  ( c i r c l e s ) and t h e  second moment ( t r i a n g l e s ) o f t h e PMR spectrum o f t h e EYL/22%WD 0.  69  -5  0  10  20  35  T (°C)  F i g u r e 24.  Temperature  dependence of the second moment IL^ °f  P  M  R  spectrum o f  (a) the outer membrane o f E. C o l i i n the EC/EXCD 0 ( c i r c l e s ) , (b) 2  the EYL i n the EYL/EXCT^O ( t r i a n g l e s ) ,  (c) temperature dependence  2 of M^/M  2  o f the PMR spectrum o f the EYL i n the EYL/EXCD 0 (squares)  (Alex Mackay's u n p u b l i s h e d d a t a ) .  2  70  (a)  0  10  20 T  Figure  25.  (a)  The  outer as  of acid  E.  10  20  temperature grown  of  the  DMR  30  (°C)  spectrum of  on a medium c o n t a i n i n g  40  outer  perdeuterated  (triangles).  parameter  as  vs  Coli  membranes  well  0  T  Second moments  palmitic  40  (°C)  membranes  (b)  30  of  A  2  E.  vs  temperature  Coli  perdeuterated  grown  of  the  DMR  s p e c t r a of  the  on a medium c o n t a i n i n g o l e i c  palmitic acid  (37).  acid  71 Appendix A  Moments Of N u c l e a r Magnetic Resonance S p e c t r a When l i n e broadening  i n NMR  a b s o r p t i o n s p e c t r a becomes  the sharp s p e c t r a l f e a t u r e s d i s a p p e a r . p o l e -J s p l i t t i n g s orientational  (see S e c t i o n 2.3a,  o r d e r parameters  substantial,  Thus, the t r u e o r i n t r i n s i c quadru-  Chapter 2 ) , and c o n s e q u e n t l y  the  cannot be determined p r e c i s e l y from the  u s u a l s p e c t r o s c o p i c t e c h n i q u e ; namely by measuring the s e p a r a t i o n between the peaks (peak s p l i t t i n g ) i n a spectrum d i r e c t l y .  That i s , the i n t r i n s i c  s p l i t t i n g s can no l o n g e r be i d e n t i f i e d w i t h the peak s p l i t t i n g s . the i n t r i n s i c s p l i t t i n g s can be determined by matching each  However,  experimental  spectrum w i t h a computer s i m u l a t e d spectrum (Bloom e t a l , 1978a, u n p u b l i s h ed) , where a known broadening  i s i n t r o d u c e d i n t o a powder p a t t e r n of known  splittings. Alternatively, s y s t e m a t i c way  the moments of a NMR  of d e t e r m i n i n g  a b s o r p t i o n spectrum p r o v i d e a  the o r d e r parameter  distribution,  th The n  moment of a spectrum i s d e f i n e d as  where f (co-oo^) i s the l i n e s h a p e of the NMR the Larmor frequency  u)  a b s o r p t i o n spectrum c e n t e r e d about  ( i n a n g u l a r frequency  units).  Moments of Deuterium N u c l e a r Magnetic Resonance Spectrum For a f i r s t o r d e r quadrupole  powder p a t t e r n , the DMR  spectrum  f(oo-0) ) i s symmetric about the a n g u l a r Larmor f r e q u e n c y , ( J J , i . e . o  q  f (] to—u> | ) = f (-1 o  lineshape vanish. d e f i n e d as  (JO-U)^  | ) (Abragam, 1961), c o n s e q u e n t l y  I t i s convenient  the odd moments of  to use the moments of the  this  half-spectrum  oo  ri  M = / (w-w ) n w o o oo  n  for  = w-w  o  o  f(w-w ) dco w o  °°  = / n where  oo  f(w-w ) dw / / o  f(Q) dn / / f ( f t ) d^  {  o  .  In t h i s case both odd and even moments e x i s t .  even moments, eqn.fA.l) i s reduced  Ai2  }  Notice that  to eqn.{ .2} because of the symmetry A  i n f(fi). The DMR lineshape f(fl) of a simple system having only one type of deuterium s i t e (and hence one value of order parameter) i s a single quadrupole  powder pattern given by eqns. {14} and {15} i n Section 2.3a, Chapter  2, and the moments of this spectrum as defined by eqn.{A.2} hassbeen shown (Bloom et a l , 1978a) to be  M  n  _ A (-  e  2  V4  q  Q  fi)  n  n  }  = A_(2Tr)  n  b  S CD  (Av)  when l i n e broadening  n {  can be neglected, i . e . when there i s no l i n e  or the i n t r i n s i c l i n e width i s much smaller than the quadrupole The c o e f f i c i e n t A  N  ±  >  3  }  broadening splitting.  can be calculated from the expression for the spin 1  powder pattern linshape (Bloom et a l , 1978a). are given as A  A  = 2/3/3 and A  2  = 1/5.  The f i r s t  In eqn{A.3},  two c o e f f i c i e n t s i s the C-D bond ..  order parameter previously defined (Chapter 2), and Av i s the quadrupole s p l i t t i n g i n the powder spectrum.  Thus, f o r a single spin 1 = 1  quadru-  pole.. powder pattern, when-broadening i s n e g l i g i b l e , the moments of the spectrum are functions only of the quadrupole . s p l i t t i n g Aw =  2TTAV,  and the  measurement of any one of the moments i s equivalent to a measurement of the quadrupole  splitting.  In deuterium-labelled phospholipids.'.in b i o l o g i c a l membranes, large numbers of inequivalent deuterium s i t e s may e x i s t , because most b i o l o g i c a l  73 membranes have a v a r i e t y o f p h o s p h o l i p i d s c o r r e s p o n d i n g t o d i f f e r e n t p o l a r head groups and c o m b i n a t i o n s of p a i r s of a c y l c h a i n s h a v i n g v a r i o u s l e n g t h s and degrees of s a t u r a t i o n . i n the v a l u e of C-D  These d i f f e r e n c e s may  bond o r d e r parameter  g i v e r i s e to v a r i a t i o n s  among the d i f f e r e n t  lipids  even i f a l l l i p i d s were l a b e l l e d a t the same p o s i t i o n on a hydrocarbon Larger v a r i a t i o n s i n S the sample.  chain.  o c c u r between g e l and l i q u i d c r y s t a l r e g i o n s o f  At p h y s i o l o g i c a l temperature,  these d i f f e r e n t thermodynamic  phases a r e expected to c o e x i s t i n b i o l o g i c a l membranes, which a r e r e l a t i v e l y inhomogeneous s i n c e they c o n s i s t o f m i x t u r e s of l i p i d s and p r o t e i n s . Furthermore, system may  the l i p i d - p r o t e i n i n t e r f a c e i t s e l f i n a b i o l o g i c a l membrane  give r i s e to observable v a r i a t i o n s i n S  .  Thus, the i n f o r m a -  t i o n r e q u i r e d t o c h a r a c t e r i z e the o r i e n t a t i o n a l o r d e r of such a complex system i s not s i m p l y an o r d e r parameter S, but r a t h e r an o r d e r parameter distribution function P(S). th The n  moment of the o r d e r parameter d i s t r i b u t i o n P(S) i s d e f i n e d  S  S P ( S ) dS  as  n  = f°  o  {A-.4}  n  where, f o r a q u a s i - c o n t i n u o u s d i s t r i b u t i o n o f S , P(S)dS  i s the p r o b a b i l i t y  of f i n d i n g an o r i e n t a t i o n a l o r d e r parameter between S and S + dS f o r the deuterium s i t e s of the complex  system.  For a d i s t r i b u t i o n o f o r d e r parameters r e s u l t a n t DMR  spectrum  c h a r a c t e r i z e d by P ( S ) , the  i s a s u p e r p o s i t i o n o f powder p a t t e r n s .  shown (Bloom e t a l , 1978,  unpublished)  that  I t has been  74 Mn = An ( 4 r  S  4 ^  = A (2TTV ) n Q  n  n  n  <S. > CD  n  = A (2rr)  n  <(Av) > n  n  n  {A.5}  where 2  V  3 e gQ 4 h  Q  A V  V  S  = Q CD  For t h e f i r s t two moments, eqn.{A.5} g i v e s  M  =  l  173  <  A  V  >  =  V  373 Q  2  4TT = ^ < ( A v )  2  <  S  CD  2  4ir  2  >  = ^ V  2  >  2  <S  Q  2  2 C D  >  { A  .6}'  The r e l a t i v e meain square d e v i a t i o n from t h e mean A^ o f t h e d i s t r i b u t i o n of o r i e n t a t i o n a l o r d e r parameters i s d e f i n e d as 2 S  . 2  S  "  s  2 < S  2 - l 2  CD  '  -  2 < S  CD  <s >  1 1.35M 2  >  >  2  CD 2  M  1  -1  {A.7}  A s i m p l e system h a v i n g o n l y a s i n g l e o r d e r parameter (and c o n s e q u e n t l y , i t s DMR spectrum c o n s i s t s o f o n l y a s i n g l e powder p a t t e r n ) has t h e p r o p e r t y t h a t S = S_ n 1  n  = S„_ giving A „ = 0 (neglecting l i n e broadening). CD z n  s i m p l e c a s e , eqn. iA.5} i s reduced The parameter A  2  In this  t o eqn. {A.3}.  i s a v e r y u s e f u l one i n t h a t i t c h a r a c t e r i z e s t h e  w i d t h o f t h e d i s t r i b u t i o n o f quadrupole  splittings.  T h i s parameter i s v e r y  s e n s i t i v e t o inhomogeneity i n t h e k i n d o f sample under c o n s i d e r a t i o n such as  75 the  c o e x i s t e n c e of phases ( 5 9 ) .  Proton Magnetic  Resonance  U n l i k e d e u t e r i u m - l a b e l l e d p h o s p h o l i p i d s i n model and b i o l o g i c a l membrane systems where d e u t e r o n - d e u t e r o n d i p o l a r i n t e r a c t i o n s a r e n e g l i g i b l e , A f o r 2  s p e c i f i c a l l y p r o t o n a t e d o r p r o t i a t e d p h o s p h o l i p i d s i n membrane system i s d i f f i c u l t t o i n t e r p r e t , because i n t h i s system p r o t o n - p r o t o n d i p o l a r a c t i o n s a r e l a r g e and cannot be i g n o r e d . the  inter-  However, t h e r a t i o o f the f o u r t h t o  square of t h e second moments o f a PMR spectrum i s s t i l l u s e f u l and has  p h y s i c a l meaning.  F o r example, c o n s i d e r a p r o t i a t e d system i n a s t a t e i n w h i c h  t h e r e i s n e i t h e r t r a n s l a t i o n a l d i f f u s i o n n o r r o t a t i o n o f the p h o s p h o l i p i d m o l e c u l e s , then t h e PMR l i n e s h a p e i s assumed t o be a s i m p l e G a u s s i a n g i v e n by  {A.8} 2  which g i v e s M^/M  2  =3.  motions a r e p r e s e n t .  I n a l a m e l l a r l i q u i d c r y s t a l l i n e phase, b o t h of t h e s e  I f t h e l i n e s h a p e o f t h e o r i e n t e d sample i s g i v e n by (52)  {A.9}  where 0 i s t h e a n g l e between the magnetic f i e l d H the  and the a x i s o f symmetry f o r  q  m o t i o n ( t h e normal t o t h e b i l a y e r ) , P ( c o s 0 ) i s t h e second o r d e r Legendre 2  2 p o l y n o m i a l (3cos 0 - l ) / 2 , and M (0) i s the second moment o f t h e spectrum when 2  the  sample i s o r i e n t e d a t 8 = 0.  The second and t h e f o u r t h moments of t h e  powder p a t t e r n a r i s i n g from eqn. {A.9} a r e r e s p e c t i v e l y ^M (0) and -~M^(0), 2 2 c o n s e q u e n t l y , M^/M = 6.45. The parameter M^/M i s very sensitive to 2  2  2  c o e x i s t e n c e o f phases such as g e l and l i q u i d c r y s t a l l i n e phases.  An anomalous  2 b e h a v i o u r i n t h e temperature dependence o f M^/M  2  over t h e r e g i o n of c o -  e x i s t e n c e o f phases has been observed i n t h e DPL/D 0 system ( A l e x Mackay, 2  unpublished).  Appendix B  C o n t r i b u t i o n s To The Second Moment L e t us c o n s i d e r a l i p i d / w a t e r system i n a water c o n c e n t r a t i o n , c, w h i c h i s much h i g h e r than 40% by w e i g h t (the maximum h y d r a t i o n ) . maximum amount (by w e i g h t ) , W  I n t h i s system, a  , of the water which g i v e s W  /(W rH  in  + L i p i d s ) = 40% rH  i s i n c o r p o r a t e d i n t o t h e b i l a y e r s ( 3 3 ) , w h i l e the r e s t of the water forms what i s c a l l e d b u l k or i s o t r o p i c excess f r e e water e x i s t i n g i n s e p a r a t e phase and exchanging s l o w l y w i t h t h e water i n c o r p o r a t e d between t h e b i l a y e r s (32-33, 36, 61).  Thus, t h e observed NMR spectrum of t h e w a t e r , F ( f t ) , i s a s u p e r p o s i t i o n o f  two s p e c t r a :  a spectrum ( f ) a r i s e s from t h e water a s s o c i a t e d w i t h t h e l i p i d , n  and t h e o t h e r  (f„„) i s the NMR a b s o r p t i o n spectrum o f t h e excess f r e e water;:  u  that i s :  F(ft) = f („) + f ( f i ) R  {B.l}  E X  From t h e d e f i n i t i o n o f moments g i v e n i n Appendix A, 9  oo  M  =  2  ft  oo  F(ft)  dft  / /_ F(ft) dft  2  2  /ft f„(ft) dft + / f t f fft) dft n hX /f  (ft) dft + /f„ (ft) dft v  M_  H  2  1  A  + EX  = fM  E X  + /  h  1 +  + (1 - f ) M  2  M„ ?  E X  {B.2}  ^ I ^  H 2  {B.3}  where M.  H  2  = / f t f ( f t ) dft / /£_(„) dft u  {B.4}  77  M  E X 2  = / ^ f g j C f i ) dti I / f ( ^ ) dtt  {B.5}  E X  = / f ( f l ) dft  {B.6}  H  f = 1 / {1 + Ag / A^}  {B.8}  For c > 40% by weight, addition or reduction i n the amount of water i n the system w i l l not a l t e r the amount of water incorporated between the bilayers, consequently, A^ and  are constant.  00  Thus, for c -»- , A ^  consequently, EX M  2  ->M  2  On the other hand, when c -> 40% by weight, A ^  M  2  -* M  H 2  0.  Hence:  °° and, s  78 References (1) Harvey F. L o d i s h & James E. Rothman, i n : The Assembly o f C e l l Membranes, S c i e n t i f i c American, J a n u a r y , 1979. (2) Helmut Hanser, i n : L i p i d s , e d . by F e l i x F r o u k s , Plemum P r e s s . (3) Joachim S e e l i g , Q u a r t e r l y Reviews o f B i o p h y s i c s 10, _3 (1977), 353-418. (4) John F. Nagle and Hugh L. 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