UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The lipid-water interaction in lyotropic measophases : an NMR study 1978

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
UBC_1978_A1 A23.pdf
UBC_1978_A1 A23.pdf [ 6.11MB ]
Metadata
JSON: 1.0085755.json
JSON-LD: 1.0085755+ld.json
RDF/XML (Pretty): 1.0085755.xml
RDF/JSON: 1.0085755+rdf.json
Turtle: 1.0085755+rdf-turtle.txt
N-Triples: 1.0085755+rdf-ntriples.txt
Citation
1.0085755.ris

Full Text

THE LIPID-WATER INTERACTION IN LYOTROPIC MEASOPHASES AN NMR STUDY by KHALED ABDOLALL B. Sc., University of Waterloo, 1972 M. Sc. University of B r i t i s h Columbia, 1974 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA in the Department of PHYSICS In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree l y ava i l ab le for reference and study. I further agree that permission for extensive copying of th i s thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thes is fo r f inanc ia l gain sha l l not be allowed without my writ ten permission. Department of The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date V 5 7 t 6 Abstract A nuclear magnetic resonance study of the lipid-water interaction has been carried out i n the lamellar mesophase of the sodium laurate-water system. Deuterium quadrupole s p l i t t i n g s and spin l a t t i c e relaxation time measurements of perdeuterated fatty acid chains and the quadrupole s p l i t t i n g s of water (D2O) and the sodium counter ion are used to study the effects of this i n t e r a c t i o n . The results indicate that the lipid-water i n t e r a c t i o n has a strong influence on the conformations and motions of the. l i p i d chains, p a r t i c u l a r l y those chain segments near the l i p i d water interface. The d e t a i l s of this i n t e r a c t i o n are not included i n the theories which attempt to explain hydrocarbon chain ordering i n b i l a y e r membranes i n terms of chain-chain (or l i p i d - l i p i d ) interactions only. A thermodynamic analysis of the results indicates that a description of the ordering of the hydrocarbon chains e n t i r e l y i n terms of chain-chain interactions i s not complete, and that a complete theory should include the lipid-water i n t e r a c t i o n e x p l i c i t l y . The f i r s t experimental evidence for a spin l a t t i c e relaxation mechanism between water protons and l i p i d protons i n a l i p i d water system i s also reported. The e f f e c t of isotopic modification of the methylene hydrogen n u c l e i on the proton spin l a t t i c e relaxation rate i n l^O and also of the e f f e c t of the isotope modification of the water on the relaxation rates of the l i p i d protons i s investigated. Although the measurements show that protons deep i n the b i l a y e r make a substantial contribution to the s p i n - l a t t i c e relaxation rate of the water protons, a detailed theore- t i c a l analysis demonstrates that the experimental results can be accounted for without invoking deep penetration of the water i n the b i l a y e r . Table of Contents Page Abstract L i s t of Figures i L i s t of Tables 1 1 1 Acknowledgements i v Chapter 1 Introduction 1 2 Theory 2.1 Quadrupolar Interactions 13 2.1.1 Deuterium Magnetic Resonance 15 a) Chain deuterons b) Deuterium i n D2O 17 2.1.2 2 3Na NMR 13 2.2 Spin-Lattice Relaxation 19 2.2.1 Deuterium Spin-Lattice Relaxation 23 2.2.2 Chain Protons. ( L i p i d ^ O mixtures) 24 2.2.3 Chain Protons and H2O Protons (Lipid/H 20 mixtures) 26 3 Experimental 27 3.1 Fatty acids 27 3.2 D 20 27 • 3.3 Deuteration of the fatty acids 27 3.4 Proton l a b e l l i n g of deuterated fat t y acids 27 3.5 Samples 29 3.6 NMRApparatus. 30 A) The Spectrometer 30 B) Probehead and Variable Temperature Oven 30 3.8 NMR Measurements 32 A) Spectroscopy 32 B) Relaxation Measurements 33 4 Results 4.1 Quadrupole S p l i t t i n g s 35 4.2 Spin-Lattice Relaxation Times 36 A) Deuterium Results 36 B) a-Protons 38 C) H20 Results 38 4.3 Sources of Error 38 5 The Lipid-Water Interaction . . . -. A Microscopic Interpretation 52 5.1 Quadrupole S p l i t t i n g s 52 5.2 Spin-Lattice Relaxation (Perdeuterated Chains) 56 5.3 A Model for Molecular Motions Mediated by the Lipid-Water Interaction 58 5.4 Isotope Effects 59 6 The Lipid-Water Interaction ?Anylysis In terms of 62 , Macroscopic Variables '• ' i 6.1 Quadrupole S p l i t t i n g s . 62 Discussion i n r e l a t i o n to e x i s t i n g theories 77 6.2 Spin-Lattice Relaxation 78 7 Spin-Lattice Relaxation between Water protons and L i p i d Protons 84 7.1 Analysis and Discussion of the H 20 results 84 The Model 85 7.2 a-CH2 Results 92 Appendix A. The temperature Dependence of Water and Counter Ion order i n Soap-Water Mesophases. A deuterium and Sodium NMR study . 9 6 Appendix B. Determination of The equation of State for the Sodium Laurate-Water system Using low angle X-ray Scattering 104 Appendix C. Water s e l f Diffusion and spin-spin relaxation i n Sodium Laurate/H 20 113 References 117 i L i s t of Figures Figure Page 1 A Schematic representation of the lamellar l i q u i d c r y s t a l phase of a lipid-water system. 3 2 A schematic representation of the geometry i n a l i p i d b i l a y e r . 14 3 Experimental arrangement for the deuteration of the fat t y acids 28 4 Variable temperature oven and sample holder. 31 5 Representative deuterium p a r t i a l l y relaxed spectra 34 6 Representative deuterium, proton and ̂ 3^a J J ^ R spectra . 40 7 v n versus T 41 8 V n versus n 42 9 v n versus C 43 10 Quadrupole s p l i t t i n g s versus temperature for D2O , 23fla and the f i r s t few positions on the hydrocarbon chain 44 11 1/Ti as a function.of position on the hydrocarbon chain 45 12 1/Tln Versus 103/T 46 13 versus n 47 14 1/Ti versus C 48 15 1/Ti versus 103/T for the ct-CD2 i n d__C._-Na/6H20 and d 2 3C 1 2-Na/6D 20 ^ 1 49 16 '1/Ti versus 103/T for the C1-CH2 protons i n d„ C12-Na/6H20 and d 2 ]C 1 2-Na/6D 20 Z X " 50 17 1/Ti versus 103/T for H 20 i n d 0C 1 2-Na/6H 20 , d 2 1C 1 2-Na/6H 20 and d 2 3C 1 2-Na/6H 20 51 18 l / v n Ov n/8C) T versus n 55 i i Figure Page 19 1/ Tln versus n 61 20(a,b) (a) Order parameter curves obtained for two di f f e r e n t lamellar phases of dC^K-I^O » having the same A value, (b) Order parameter curves variations for different a values i n the lamellar phase of dC^2K-H20 . 65 20C Quadrupole s p l i t t i n g s curves for two samples of dC^2~Na/H20 having the same A value. 66 21 The f r a c t i o n a l v a r i a t i o n of the quadrupole s p l i t t i n g with temperature keeping the area per polar head constant and keeping the water concentration constant. 71 22 The f r a c t i o n a l v a r i a t i o n of the quadrupole s p l i t t i n g s with temperature keeping the area per polar head constant. 73 23 The f r a c t i o n a l v a r i a t i o n of the quadrupole s p l i t t i n g s with water concentration keeping the area per polar head constant. , 24 The f r a c t i o n a l v a r i a t i o n of the quadrupole s p l i t t i n g with water concentration keeping the area per polar head constant for di f f e r e n t C values at a fixed temperature. 25 The ration of the change i n V n with T keeping A f i x e d to the change i n v n with T keeping C fixed. 75 26 A semilog plot of roo-rn . 76 27 Ratio of the activation energies for the chain deuterons at constant surface area per polar head to that at constant water concentration. 8 1 28 Effect of systematic errors due to the X-ray : measurements 29 Schematic representation of the different s p a t i a l regions, i n which water protous and l i p i d protons move 8 3 8 6 3 0 Log A versus Log C for the sodium laurate water system. 1 1 0 3 1 The dependence of AQ on temperature 1 1 1 3 2 The dependence of A on temperature for the sodium laurate-water system. 1 1 2 3 3 Log, (S/S Q) + 2T/T2 versus T 3 116 ) III L i s t of Tables Table Page Ratio of the change i n the s p i n - l a t t i c e r elaxation rate of protons due to the -CH2 protons to the change of the relaxation rate of the -CH2 protons due to the water protons i n dj-jC^-Na/SI^O . 94 Temperature dependence of the lamellar repeat distance, thickness of the b i l a y e r and the mean area per polar head for the sodium laurate water system. 109 Dependence on the water concentration of the lamellar repeat distance, the b i l a y e r thickness and the area per polar head. 109 Ratio D/D0 of the s e l f d i f f u s i o n c o e f f i c i e n t of water i n the sodium laurate-water system to that of pure water at 100 °C for several G values. 115 Quadrupole s p l i t t i n g s of chain deuterons i n the sodium laurate water system; dependence on temperature and water concentration. 1-20 S p i n - l a t t i c e relaxation times of chain deuterons i n the sodium laurate water system; dependence on temperature and water concentration. 121 i v Acknowledgements I am very grateful to my research supervisor Professor Myer Bloom who provided the stimulus and continuing help through-out the course of this work. I have benefited greatly from his i n s t r u c t i o n and the many discussions we had. I thank my wife Khadija for typing the thesis and for her patience and continuing encouragement and moral support. I express my sincere gratitude to the following people who through i n d i v i d u a l help have contributed to this work: Dr. E l l i o t Burnell of the Chemistry Department for many discussions and useful suggestions and for providing the help and equipment i n f sample preperation. Dr. J. Charvolin of the Laboratoire de Physique de Solides, Orsay for the useful discussions we had and for suggesting the work on the sodium laurate-water system. Dr. Alex Mackay, Dr J . Davis and Dr M. I. V a l i c for the technical consultations and help i n the experiments and for the many discussions and useful suggestions. In this regard the continued support of Alex i n many other respects i s greatly appreciated. Dr. T. P.Higgs for his assistance i n preparing the s p e c i f i c a l l y protonated samples. Dr. W. N. Hardy for the useful suggestions he gave for explaining the dependence of the deuterium relaxation rates on water concentration. Dr. K. Jeffrey of the University of Guelph for providing the assistance and f a c i l i t i e s to do the X-ray measurements. 1 Chapter 1 Introduction Water i s a major component of c e l l s and tissues of a l l l i v i n g organisms. The importance of i t s role i n l i f e processes on the c e l l u - l a r l e v e l i s w e l l recognised but has not yet been f u l l y understood. Many of the properties of the c e l l membrane involve water d i r e c t l y or i n d i r e c t l y . For example most of the transport mechanisms i n the c e l l membrane are mediated by water. Another example i s the membrane action of some anesthetics which i s believed by some to involve membrane associated water i n a physical way rather than causing chemical changes i n the c e l l membrane. From such examples i t is, apparent that an under- standing of how the water interacts with the "building blocks" of the c e l l membrane i s very important to the understanding of membrane processes. The complexity of r e a l b i o l o g i c a l membranes has motivated s c i e n t i s t s i n the f i e l d to look for simpler systems that could be used as "models". Since l i p i d s form a large f r a c t i o n of the "building blocks" of the c e l l membrane, l i p i d bilayers have been used as such models because of t h e i r s i m i l a r i t y i n structure to r e a l b i o l o g i c a l membranes. The purpose of t h i s work i s to contribute to the understanding of the mechanism of the l i p i d - water interaction i n a l i p i d b i l a y e r membrane. In the presence of water, l i p i d molecules form a variety of ly o t r o p i c mesophases characterized by the existence of long range order and short range disorder. These phases have been i d e n t i f i e d by X-ray studies ( 1 ) , 2 nuclear magnetic resonance (2,3) and other techniques (4). Of p a r t i c - ular interest i s the lamellar l i q u i d c r y s t a l (L Q) phase where the l i p i d molecules form bilayers of i n d e f i n i t e extent and alternate i n a regular l a t t i c e with layers of water and counter ions as shown i n f i g . 1 . Each b i l a y e r can be thought of as a two dimensional f l u i d with the l i p i d chains p r e f e r e n t i a l l y oriented along the normal to the b i l a y e r surface. Within the b i l a y e r the hydrocarbon chains of the molecules are f l e x i b l e (melted) and the molecules undergo rapid l a t e r a l d i f f u s i o n (5) and the rotation about t h e i r long axis. Different parts of hydrocarbon chain can also undergo small and rapid angular excursions (such as bending, twisting and flopping) perpendicular to the molecular axis (the long axis of the molecule). The ordering of the hydrocarbon chains within the b i l a y e r i s then described i n terms of averages over the fast molecular motions. A measure of t h i s ordering w i l l thus give information on the physical state and f l u i d i t y of the b i l a y e r . There have been numerous studies on model and b i o l o g i c a l membranes using X-rays (1) nuclear magnetic resonance (2,3), and other techniques (4). With few exceptions (6,Appendix A) most of these studies are either concerned with the structure and properties of water i n these systems per se (7-11), or with the dynamics and structure of the amphilic region. The influence of the interaction between the water and the l i p i d on the structure and dynamics of the two regions has not yet been developed appreciably. The a b i l i t y of water to form hydrogen bonds which i s simply under- stood as an e l e c t r o s t a t i c a t t r a c t i o n between the e l e c t r o p o s i t i v e hydrogen of one water molecule and the electronegative oxygen of another water or Figure 1. The lamellar l i q u i d c r y s t a l phase of a lipid-water system. The c i r c l e s represent the polar portions (polar heads) of the molecules, and the zig-zag l i n e s represent the hydro- carbon chains. 4 l i p i d molecule, can have profound influence on the ordering and dynamics of the hydrocarbon chains within the b i l a y e r . Thus l i p i d and water mutually affect each other v i a hydrogen bonding (Appendix A). The deta i l s of such an interaction have not been included i n many of the theories which attempt to explain hydrocarbon chain disorder i n b i l a y e r membranes (12, 13, 14). The central questions that w i l l be highlighted i n t h i s work are: how does the water between the b i l a y e r s influence the ordering of the hydrocarbon chains and how deeply does i t penetrate into the bilayer? To answer such questions i t i s necessary to use l o c a l probes that are sensitive to t h e i r environment as w e l l as to the dynamics of the system. An NMR study has been carried out on the lamellar l i q u i d c r y s t a l (L^) phase of the sodium laurate/water system. There are two reasons for choosing t h i s system: ( i ) a very d e t a i l e d phase diagram i s available (15), and ( i i ) one can obtain complementary information on the sodium counter ion. Interactions between the nuclear quadrupole moments of deuterium 23 i n D̂ O or Na and the e l e c t r i c f i e l d gradients at the nuclear s i t e s w i l l provide information on 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 sodium and/or the structure and ordering of water at the lipid-water interface. The conformations and. motion of the lipidrmolecules can be studied by measuring the quadrupole s p l i t t i n g s i n the deuterium magnetic resonance spectrum for deuterons along the hydrocarbon chain of a perdeuterated molecule (16-18), or the proton di p o l a r s p l i t t i n g s i n a a-CH^ group (19) i n an otherwise deuterated hydrocarbon chain. The deuterium s p l i t t i n g s are related to order parameters S r n which give a 5 measure of the or i e n t a t i o n a l order of the C-D bond direction i n a methy- lene group while the proton dipolar s p l i t t i n g s are related to order parameters S which give a measure of the o r i e n t a t i o n a l order of the proton-proton vector i n a 01-CH2 group. Thus a knowledge of and w i l l completely specify the o r i e n t a t i o n a l order of the methylene chain segment. Information on the l i p i d water i n t e r a c t i o n can also be obtained by relaxation measurements which can y i e l d information regarding the nature and the strength of the interaction of the nuclear spin system with i t s molecular environment. Parameters such as co r r e l a t i o n times (x ) associated with the molecular motions can be determined from relaxation measurements. Complementary information on the l i p i d water interaction can also be obtained from correlations i n the quadrupole s p l i t t i n g s of 23 Na, water (D2O), and chain (Appendix A) deuterons. Deuterium magnetic resonance has been used by several workers i n the study of the conformation and motion of the l i p i d molecules i n b i l a y e r membranes (16-18, 20-26). The most prominent of these studies are those by Charvolin et a l (17) and Mely et a l (18) on the potassium laurate-water system, Seelig and Niederberger (23) on sodium deconate-water, Seelig and Seelig (23, 26) on phospholipid b i l a y e r s , and Davis and Jeffrey (19) on the potassium palmitate-water system. In these studies the order parameter p r o f i l e for the hydrocarbon chains i n the l i q u i d c r y s t a l phase was determined by measuring the quadrupole s p l i t t i n g s for deuterons on s p e c i f i c a l l y deuterated (24) or perdeuterated chains (16, 17, 18). A ch a r a c t e r i s t i c feature common to a l l of these results i s the appearance of a "plateau" region where about h a l f of the chain methylenes a f t e r the a position have v i r t u a l l y the same order parameter. This plateau 6 disappears at higher temperature and water concentration with a decrease i n the quadrupole s p l i t t i n g s . The plateau was believed to have some origins i n the s t e r i c repulsions between neighbouring chains (27, 28). Some models have been proposed where the s t e r i c interactions are taken into account i n terms of the crosssectional area of a given chain conformation (13). This crosssectional area i s characterized by the l a t e r a l space occupied by a l i p i d molecule, or the mean area (A) per polar head at the l i p i d water interface. Mely et a l (17) have studied the order of the l i p i d chains i n potassium laurate-water mesophases as a function of the temperature i n samples having constant water concentrat- ion and as a function of water concentration at constant temperature. They have found that the deuterium quadrupole s p l i t t i n g s decreased with increasing temperature or water concentration. The same authors have also measured the quadrupole s p l i t t i n g s for samples having the same area polar head but at different water concentration and temperature. The s p l i t t i n g s for such samples }though not identical,were s i m i l a r . On the basis of these results the authors concluded that A i s a "good parameter to represent the average microscopic order". They believe that the v a r i a t - ion of the quadrupole s p l i t t i n g s with temperature and/or water concentrat- ion depends primarily on the variation of A with these parameters Davis and Jeffrey (18) studied the hydrocarbon chain disorder i n the potassium palmitate-water system. In the l i q u i d c r y s t a l l i n e phase the C-D order parameters of the f i r s t methylene chain segments were found to increase with increasing temperature to a maximum of 100°C and.then decrease at higher temperature. In contrast the C-D order parameters for the rest of the methylene chain segments decreased with increasing temperature. In the same system Higgs and Mackay (19) have determined the complete ordering tensor for the a-methylene group by measuring the CI-CH2 dipolar s p l i t t i n g s i n an otherwise perdeuterated chain and the 0.-CD2 s p l i t t i n g s i n s p e c i f i c a l l y deuterated chains. The temperature dependence of the a-CI^ s p l i t t i n g s was s i m i l a r to that of the a-CD^ s p l i t t i n g s . However the order parameters and S^, d i f f f e r e d by 0-20% L U t in i n the temperature range studied (40-100°C), in d i c a t i n g that the motion of t h i s p a r t i c u l a r segment i s not t r u l y a x i a l l y symmetric around the normal to the b i l a y e r . From these studies the behaviour of the methylene chain segment near the l i p i d water interface was believed to be due to a l i p i d water i n t e r a c t i o n . A b d o l a l l , Burnell and V a l i c (Appendix A) 23 studied the hydrocarbon chain, D20 and Na counter ion order i n the potassium palmitate/D20 and sodium palmitate/D20 systems. There was a s t r i k i n g correlation between the ordering of the f i r s t few methylenes of 23 the hydrocarbon chain, deuterium i n D20 and the Na counter ion. This correlation was ascribed to the structuring effect of the water v i a hydrogen bonding with the polar heads. A model consistent with the experimental results was proposed (Appendix A). In terms of t h i s model the l i p i d water structure at low temperatures imposes a di r e c t i o n for which a l l the order parameters are smaller than for the higher temperature structure for purely geometric reasons. At higher temperatures the structuring effect of water decreases and there i s an "apparent" increase i n order u n t i l the i n t r i n s i c decrease i n order parameters r e s u l t i n g from the thermal excitations dominates at s t i l l higher temperatures. There have been many the o r e t i c a l studies on the chain ordering i n l i q u i d crystals and b i l a y e r membranes (12-14, 29-32). One of the most successful of these i s Marceljas (13) molecular f i e l d c a l c u l a t i o n . In the mean f i e l d approximation the inte r a c t i o n energy of a single chain i n the molecular f i e l d i s given by the sum of the i n t e r n a l energy of the single chain, the Vander Waals interactions of the chain with i t s neighbors v i a the molecular f i e l d and a l a t e r a l pressure term which i s proportional to the cross sectional area per polar head. The l a t e r a l pressure term takes into account the s t e r i c repulsions between the hard cores of the atoms. S t a t i s t i c a l averages are then calculated by summing over a l l conformations of a single chain i n the molecular f i e l d of i t s neighbours. This model has been successfully u ed to interpret the deuterium NMR results for the sodium-deconate-deconol-water (13) and other NMR data (33). However the resu l t s do depend on the assumed orientation of the i n i t i a l chain segment, which implies that a descrip- tion of the ordering of the hydrocarbon chains i n a b i l a y e r membrane e n t i r e l y i n terms of chain-chain interactions i s incomplete. What has been ignored i n these t h e o r e t i c a l calculations i s the lipid-water i n t e r - action. Empirical evidence that such a l i p i d water interaction has a strong influence on the ori e n t a t i o n a l order of the hydrocarbon chains i n a l i p i d b i l a y e r , e s p e c i a l l y those chain segments near the polar head i s , as already mentioned, demonstrated by the s t r i k i n g s i m i l a r i t y i n the temperature dependence of the quadrupole s p l i t t i n g s of the f i r s t few 23 methylene chain deuterons, and Na counter ion i n the palmitates- water systems (Appendix A) and i n the sodium laurate-water system studied i n th i s thesis. 9 In order to investigate the interactions that are most important i n determining the o r i e n t a t i o n a l ordering of the hydrocarbon chains i n the l i p i d b i l a y e r i n a quantitative way we have made a systematic study on the sodium laurate-water system i n the l i q u i d c r y s t a l (L^) phase. The quadrupole s p l i t t i n g s of the methylene chain deuterons were measured as a function of temperature and water concentration. An equation of state r e l a t i n g the area per polar head, temperature and water concentrat- ion was determined by X-rays for t h i s system. Using elementary thermodynamics the results were analysed by examining the s e n s i t i v i t y of the quadrupole s p l i t t i n g s to variations i n the different thermodynamic variables. The results of the analysis indicate that a description of the disorder of the hydrocarbon chain e n t i r e l y >'n terms of chain-chain interactions i s indeed not complete. A complete theory should include the l i p i d water i n t e r a c t i o n e x p l i c i t l y . S p i n - l a t t i c e relaxation measurements i n l i p i d b i l a y e r membranes using deuterium NMR i s f a i r l y recent. Using a series of f a t t y acid probes of different lengths and la b e l l e d at several positions Stockton et a l (34) showed thac the molecular motions within the phosphotldyl- choline bilayers increase rapidly with distance from the l i p i d water interface. More recently Davis, Bloom and Jeffrey (35) measured the s p i n - l a t t i c e relaxation times as a function of temperature and position on the hydrocarbon chain for the methylene deuterons i n perdeuterated chains of the potassium palmitate-water system. In the l i q u i d c r y s t a l - l i n e (k^) phase, t h e i r results indicate the presence of complex molecular motions of the different methylene chain segments. A simple model 10 proposing two different types of motions (a fast and a slow motion) with different correlation times was considered. In terms of t h i s model they were able to explain i n a q u a l i t a t i v e way the change i n relaxation times p r o f i l e with increasing temperature. In the present thesis the s p i n - l a t t i c e relaxation rates for methylene chain deuterons of perdeuterate d chains i n the l i q u i d c r y s t a l (L^) phase of the sodium laurate-water system were measured as a function of temperature, water concentration and position on the hydrocarbon chain. The results obtained suggest that complex molecular motions mediated by a lipid-water i n t e r - action must be taken into account. A model i s proposed to explain the influence of the l i p i d water interaction on the relaxation rates of the methylene chain deuterons. While deuterium quadrupole s p l i t t i n g s and spin l a t t i c e relaxation time measurements can be used to study the ef f e c t of the lipid-water i n t e r a c t i o n on the o r i e n t a t i o n a l ordering and mobility of the hydro - carbon chains, i t i s not possible to obtain from such measurements information on the extent of water penetration into the l i p i d b i l a y e r . In order to obtain such information i t i s necessary to measure quantities that depend on the s p a t i a l location of the l o c a l probe used and on the strength of the interaction between the probe and i t s molecular environment. The spin l a t t i c e relaxation rate for a proton due to dipolar couplings (which i n most cases are the main relaxation mechanisms for protons) with another nuclear spin depends on the inverse of the 6 t n power of the separation between the spins and on the product of the square of t h e i r magnetogyric r a t i o s . Thus a study of the ef f e c t of isotope modification of the l i p i d region on the spin l a t t i c e relaxation rates of the water protons should i n principle give useful information on the extent of water penetration into the b i l a y e r . Complementary information can also be obtained by studing the effect of isotope modification of the water on the spin l a t t i c e relaxation rates of proton spin labels i n otherwise perdeuterated chains. We have performed such studies on the sodium laurate-water system. The results obtained suggest at f i r s t glance that water penetrates much further into the b i l a y e r than the a-position. However, a detailed t h e o r e t i c a l a n a l y s i s , shows that the experimental results can be accounted for without invoking deep penetration of the water i n the b i l a y e r . Information on the extent of water penetration i n the b i l a y e r can also be obtained from neutron d i f f r a c t i o n measurements. Just recently Buldt et a l (37) reported some results on phospholipid b i l a y e r s . The authors conclude that water penetrates i n t o the b i l a y e r up to the glycerol back bone of the l i p i d molecules. E a r l i e r studies by Schoenborn (36) on a s i m i l a r system did not have s u f f i c i e n t resolution to detect such water penetration. 12 Thesis Outline This thesis w i l l consist of 6 more chapters. The second chapter w i l l include the relevant NMR theory i n lyotropic mesophases . Experimental d e t a i l s and results are given i n chapters 3 and 4. In chapter 5 an interpretation of the results w i l l be discussed i n terms of a microscopic model for the lipid-water i n t e r a c t i o n . In chapter 6 a thermodynamic analysis of the results i s used to investigate the interactions that are important i n determining the state of the l i p i d chains i n a l i p i d water system. The l a s t chapter deals with the mechanism of spin l a t t i c e relaxation between water protons and methyl- ene protons i n a l i p i d water system and the problem of water penetration into the b i l a y e r . 1 3 Chapter 2 Theory 2.1 Quadrupolar Interactions The t o t a l Hamiltonian for a nucleus with spin i n an applied magnetic f i e l d H i s given by (ignoring chemical s h i f t terms etc.) H = H z + H Q [ l ] where H z i s the Zeeman Hamiltonian and H Q i s the quadrupolar Hamiltonian due to the interaction of the quadrupole moment eQ associated with the spin I and the e l e c t r i c f i e l d gradients (efg) e x i s t i n g at the s i t e of the nucleus. , I f H Q <(<( H z i t can be shown ( 3 8 ) that the f i r s t order perturbat- ion to the Zeeman energy levels due to H Q are given by ( i n frequency units) where the angles G , $ specify the magnetic f i e l d d i r e c t i o n r e l a t i v e to the p r i n c i p a l coordinate system of the efg as shown i n f i g . 2b ,m i s the magnetic quantum number i n the represention where I z i s diagonal, e^qQ i s the quadrupole coupling constant and n i s an asymmetry parameter h f , defined such that 0<n<l and i s a measure of the deviation of the efg from a x i a l symmetry. I f r|=0 then the energy levels of the t o t a l Hamiltonian i n frequency units are E . E<°> • E <» m m T m 14 Figure 2. (a) Schematic representation of the geometry i n a l i p i d b i l a y e r . n i s the normal to the b i l a y e r . i s the angle between the magnetic f i e l d H* and n, 0 i s tlje angle between the C-D bon§ d i r e c t i o n and H and 9 i s the angle between the C-D bond d i r e c t i o n and n. (b) Orientation of the magnetic f i e l d d i r e c t i o n r e l a t i v e to the p r i n c i p a l coordinate system of the e l e c t r i c f i e l d gradient. 15 - - v + F( i £ 24^)(3" 2-i« +i)) w where v. i s the Larmor frequency YH and v n _ 3e^qQ L 2n 4 h2I(2I-l) 2.1.1 Deuterium Magnetic Resonance. a) chain deuterons. The deuterium nucleus has a nuclear spin 1=1. I f we concentrate on one deuteron on the n position of the hydrocarbon chain and assume for the moment that the chain i s not moving ( r i g i d l a t t i c e ) then the energy levels as given by eqn. [5] are n - v T + VQ_ (3cos20-lA - 1 6 \ 2 ) E = I 3cos 20-l 0 3 V 2 E. = -VT + VQ /3cos 20-l 1 L 6 1 2 The corresponding resonance frequencies are E 0-E x = V L _ Vp. ^3cos20-l ^ and the NMR spectrum w i l l consist of two sharp peaks separated by. AV, = V Q ^ 3 c o s 2 e - l ^ [ 4 ] The efg at the s i t e of a deuterium nucleus on the hydrocarbon chain i s along the C-D bond d i r e c t i o n . I f the molecules are undergoing fast anisotropic motion at frequencies much greater than those of the quadru- polar s p l i t t i n g s , then the reorientation of the C-D bond w i l l modulate 16 2 0 and a time average of 3cos Q-l has to be considered. For the 2 molecules i n a l i p i d b i l a y e r , the symmetry axis of the motion i s the normal n to the bi l a y e r . Thus for a deuteron on the n t n position of the hydrocarbon chain eqn. [4] w i l l give for the quadrupole s p l i t t i n g s S / 3 c o s 2 f t - l \ £ 5 ] U S  cos2jMQ n [ — J where as shown i n f i g . 2a on page \t\ Qn i s the angle between the C-D bond di r e c t i o n and the normal n to the b i l a y e r i s the angle between n and the magnetic f i e l d d i r e c t i o n and the quantity g z 3 c o s 2 V l \ 0 ] 3 = / 3 c o s - Q n - l y i s defined as the order parameter, normally denoted i n the * . l i t e r a t u r e by SQJJ • A l l the hydrocarbon chain -CD2 deuterons are chemically equivalent and therefore w i l l have the same V Q . Since the bilayers are randomly oriented, the d i f f e r e n t values of cosft are equally probable and the superposition of the l i n e s a r i s i n g from the di f f e r e n t orientations gives r i s e to a broad absorption curve c h a r a c t e r i s t i c of a powder pattern of the form (39) g(v) = / d cosft [7] with two intense peaks separated by 17 = |—|v QS n) [8] For a perdeuterated hydrocarbon chain, the spectrum w i l l consist of a number of overlapping powder patterns a r i s i n g from the various deuterons situated along the hydrocarbon chain. A representative spectrum i s shown i n fig.6a on page 40 • Since V Q i s of intramolecular o r i g i n (C-D bond) i t i s not expected to be temperature dependent. Consequently the order parameters for the methylene chain deuterons can be obtained d i r e c t l y from the measured quadrupole s p l i t t i n g s using equation [8] . b) Deuterium i n D20 For water deuterons although the main contribution to the efg i s from the intramolecular 0-D bond, there can be other contributions of intermolecular o r i g i n such as the charge d i s t r i b u t i o n near the polar heads and other interactions (Appendix A ). Moreover, hydrogen bonding can reduce the contribution of the 0-D bond from 312 KHz (as measured i n the gas phase) to 213 KHz (40). For such reasons V Q could be di f f e r e n t for d i f f e r e n t s i t e s . Also chemical exchange can take place between nucl e i i n d i f f e r e n t environments. I f the exchange rate i s much faster than the s p l i t t i n g difference, the observed s p l i t t i n g i s a weigh- ted average over the d i f f e r e n t s i t e s and i s given by. D,o - i l p i v Qi s i l M V ;2' where Pj_ i s the f r a c t i o n of n u c l e i i n s i t e i with associated quadrupole coupling constant | V Q ± and order parameter S ± defined by 18 S ± . 3cos 29 1 -1 [10] 2 where i s the angle between ri and the efg p r i n c i p a l axis and the bar denotes a time average. As discussed i n Appendix A the separation of the various terms i n eqn. [9] i s not possible without making certain assumptions. The largest contribution to V Q ^ i s assumed to come from the intramolecular 0 -D bond. This could mean that V Q ^ remains roughly the same for the different s i t e s . I f i n addition to Vq i being independent of i i t i s further assumed that does not vary s i g n i f i c a n t l y with tempers ture then the measured s p l i t t i n g s are roughly prportional to an average order parameter S=£ P^S^ which can provide useful information i n a i q u a l i t a t i v e way. 2.1.2 2 3Na NMR The Na nucleus has a spin 1= ^ • From eqn. £3] the resonance frequencies are given by E-3/2 ~ E - l / 2 " *L + VQ ( 3 c o s 2 e - l ^ E - l / 2 " E l / 2 = V L and the corresponding NMR spectrum w i l l consist of 3 peaks separated by A vNa Since rapid exchange can take place between the sodium ions i n 19 dif f e r e n t s i t e s i n the aqueous region then as outlined i n the previous section the observed s p l i t t i n g i s a weighted average given by ^ i The efg at the s i t e of a sodium nucleus i s of intermolecular o r i g i n and i s largely due to the charge d i s t r i b u t i o n near the polar head groups and the asymmetric d i s t r i b u t i o n of waters of hydration (see appendix A page 77)• Thus i t i s expected that there w i l l be a d i s t r i b u t i o n of Vqi , p^ and S^ that can be quite temperature dependent making the 23 interpretation of the Na NMR s p l i t t i n g s i n terms of an order parameter rather d i f f i c u l t . However i f correlations e x i s t i n the temperature 23 dependence of the methylene chain deuterons 1 . and , changes i n 23 the Na s p l i t t i n g s w i l l give a measure of the order of the surrounding charge groups. 2.2 Spin -L a t t i c e Relaxation The general problem of s p i n - l a t t i c e relaxation i n l y o t r o p i c mesophases i s complicated and not completely understood. Only the general aspects of the relevant theory w i l l be discussed here. The t o t a l Hamiltonian for a nuclear spin system i s , i n most cases, given by H = H z + H ±(t) [12] where H z i s the Zeeman Hamiltonian and H^(t) i s a time dependent Hamiltonian corresponding to quadrupole or dipolar couplings (for some 19 n u c l e i , such as F , large chemical s h i f t terms must also be included) 20 These couplings are modulated by the l a t t i c e : The quadrupolar couplings depend on the e l e c t r i c f i e l d gradients at the s i t e of a nucleus and dipolar couplings depend on the r e l a t i v e positions of the spins. H^(t) can always be decomposed into an average and a fluct u a t i o n about the average as follows (41) Hi(t) = <H ±> + ( H ^ t ) - ^ ^ ) = < H i > + HiCt) [13] For an anisotropic environment i s nonzero and causes s p l i t t i n g s i n the NMR spectrum and H^(t) i s a spin l a t t i c e coupling responsible for the relaxation of the spin system toward thermal equilibrium with the l a t t i c e . H ^ t ) can be writ t e n (38) H ±(t) = ^ F ( m ) ( t ) A ( m ) [14] m=-2 m (m) where the F (t) are random functions of time and the A are operators acting on the spin variables. F^m^ and A ^ transform under rotations as the spherical harmonics of order two. The s p i n - l a t t i c e relaxation rate - which describes the rate of energy T l transfer from the nuclear spin system to the l a t t i c e may be expressed i n the form 2 [15] i =<o*i\zy <% j(mo)0) m=0 where ̂  l ^ i^ ^ P ^ I s t n e 1 1 1 6 3 1 1 squared value of the s p i n - l a t t i c e coupling, are numerical factors, OJQ i s the Larmor frequency and Jn/^o) i s t n e Fourier transform of the reduced c o r r e l a t i o n function gjjjCx) defined by g j x ) = G M(T) _ < F W ( t ) > 2 [ 1 6] Gm(0) - < F ( m ) ( t ) > 2 G m(x) i s c a l l e d the correlation function of F ^ ( t ) defined by G^x) = < F ( m ) ( t ) F ( m ) ( t + T ) > [17] and describes how F^ m^(t) at time t i s correlated to i t s value at some l a t e r time t+T . The time v a r i a t i o n of F ^ m \ t ) i s due to some physical motions i n the system. For times x much shorter than some c r i t i c a l time T C ( c a l l e d the correlation time), the motions are ne g l i g i b l e and F ^ (t) = F ^ ( t + x ) . For times ' uch greater than T C there i s no correlation between F ^ (t) and F ^ (t+x) and G m(x) = ^ F ^ ( t ) y 2. Therefore the reduced correlation function g m(x) has a maximum value of unity at x=0 and f a l l s off to zero for T » T C . The correlation time x c may then be used as a measure or time scale for the motions. Thus i f there i s a model for the molecular motions, the correlation function can be calculated, which i n turn would allow the calculation of the relaxation rates. On the other hand, measurements of spin l a t t i c e relaxation rates allow the determination of the reduced spectral density functions which can be used to test models for the molecular motions. In most cases the calc u l a t i o n of g^x) i s n o n t r i v i a l . A crude assumption that i s often made i s to assume that g m(x) decays exponentially, i . e. g M(T) - e - T / T * [18] 22 then, the reduced spectral density j m ( u ) i s oo -OO 2?c [19] c 2 For very short corre l a t i o n times, a) xf 1 and a l l the spectral density functions j m(mu) 0) are independent of frequency and equal., to JiCo) = J 2(o) = j (o) = 2T C [20] In t h i s case the expression for ̂  as given by eqn. 15 reduces to a T l product of an i n t e n s i t y factor and a cor r e l a t i o n time T c • For example the s p i n - l a t t i c e relaxation rate for a p a i r of dipolar coupled protons undergoing i s o t r o p i c motion i s given by (38) i - a L ± y ? T , [21] Another example i s the quadrupole relaxation through i s o t r o p i c molecular reorientation. For a nuclear spin with 1=1, the relaxation rate jj- i s (for an a x i a l l y symmetric e l e c t r i c f i e l d gradient) T l 1 ( is&Y T [22] T i °\~ir-j "c In equations 21 and 22 , the quantities - -^-5- and e qQ are the dipole- 2 r h dipole and the quadrupolar coupling constants respectively. I f these coupling constants are known the measurements w i l l provide T c . I f the fluctuations i n the in t e r a c t i o n H^(t) arise from molecular motion that varies with temperature, relaxation measurements can be used to study the temperature va r i a t i o n of T . Often there i s a 23 "b a r r i e r " to motion and an ac t i v a t i o n energy E a such that T c . x w e V k T [ 2 3 ] where Too i s the correla t i o n time at i n f i n i t e temperature. Thus the temperature v a r i a t i o n of ̂  should give a measure of the a c t i v a t i o n energy. 2.2.1 Deuterium Spin-Lattice Relaxation. For the deterium nucleus, the coupling Hq(t) of the nuclear quadrupole moment with the fluctuating e l e c t r i c f i e l d gradients at the nuclear s i t e i s almost always the main relaxation mechanism. Since the effectiveness of a relaxation mechanism depends on the magnitude (or intens i t y ) of the corresponding s p i n - l a t t i c e coupling (see eqn. 15 ), the magnetic dipolar couplings, which are very e f f e c t i v e f o r protons make a n e g l i g i b l e contribution to the deuterium relaxation rates. This i s due to the fact that the dipolar i n t e r a c t i o n between a deuterium neucleus and another nucleus S depends on the product 2 2 " Y-r Y » where Y^ and Y are the magnetogyric r a t i o s of the deuterium I S I S nucleus and the S nucleus respectively (Abragam p.2^5"). Thus the 2 deuteron-proton dipolar interactions are weaker by _3_(YH/YD^ — . 24 8 than the corresponding proton-proton di p o l a r i n t e r a c t i o n . Therefore considering the large value of the deuterium quadrupole coupling constant (^170 KHz) i n the systems studied here d i p o l a r interactions make at most a minor contribution to the deuterium relaxation rates. 1/T^ for deuterons i s then given by 24 T L < I " Q I 2 > ( H*o) + J 2 ( 2 « O ) ) PQ where ^ |HQ | 2 >̂ i s the mean square value of Hg(t) and J J ^ Q ) and ^(^Uq) are the reduced spectral density functions associated with Hq(t). For deuterons on the hydrocarbon chain these spectral density functions are expected to be f a i r l y complicated receiving contributions from the reorientation of the C-D bond around a given chain segment, single molecule motions r e l a t i v e to the director as w e l l as c o l l e c t i v e motions of many molecules which are associated with the motions of the direc t o r i t s e l f about i t s equilibrium orientation. For a single type of motion i t can be shown that, i n the short correl a t i o n time l i m i t (W2T.2 « 1 » where T„ i s the c o r r e l a t i o n time O n " ch a r a c t e r i s t i c of the motion of the n*"*1 methylene chain segment)* 1 t"h the relaxation rates ^ f o r deuterons on the n p o s i t i o n of the X l n hydrocarbon chain are given by (35) 2 where S n i s the order parameter defined by eqn. 6 . The factor 1-Sn takes into account the anisotropy of the system. For Sn=0 eqn. 25 becomes the usual expression (eqn. 22) for deuterium quadrupole relaxation i n i s o t r o p i c f l u i d s (38). 2.2.2 Chain Protons. (Lipid/D 20 mixtures) For protons on the hydrocarbon chain, the problem i s less simple than that for deuterons. In t h i s case the spin l a t t i c e coupling responsible for relaxation i s 25 HdU> = H d (t) - <H d> [26] Where H<j(t) i s the time dependent dipolar Hamiltonian for the spin system. Due to the large magnetic moment of the proton, the dipolar interactions between protons on the neighbouring methylenes of the hydrocarbon chain are quite strong and tBnd to cause a fast e s t a b l i s h - ment of a common spin temperature for a l l the protons on the hydro- carbon chain. This makes the interpretation of proton relaxation measurements rather d i f f i c u l t . This d i f f i c u l t y can be made easier by having protons only i n one position i n an otherwise perdeuterated chain. This e s s e n t i a l l y eliminates the i n t e r .-CH2 dipolar contribution to the relaxation rates for methylenes on the same chain. The contribution of the i n t e r molecular dipolar interactions to the relaxation rates of the methylene protons i s expected to be much weaker than that due to the i n t r a molecular dipolar interactions. This i s because the magnitude of the dipolar interactions depends on r (where r i s the proton-proton distance so that the contribution to ̂  f a l l s o f f very rapidly ( r ~ ^ ) with increasing r. Thus i n the short correlation time l i m i t , the main relaxation mechanism for a pa i r of methylene protons i n an otherwise perdeuterated chain, i s mainly due to the reorientation of the H-H vector j o i n i n g the proton p a i r . The proton relaxation rate i n t h i s case i s , i n analogy with the deuterium case, given by where Sut. i s an order parameter defined by tin « v 3 c o s 2 0 - l \ [28] HH \ 2 / where 0 i s the angle between the H-H vector and the normal n to the b i l a y e r . 2.2.3 Chain protons and protons (Lipid/H^O mixtures). The theory of s p i n - l a t t i c e relaxation f o r water and chain protons i n lipid/H20 samples prepared with nondeuterated, perdeuterated and s p e c i f i c a l l y protonated chain w i l l be dealt with i n chapter 7 . 27 Chapter 3 Experimental. 3.1 Fatty acids The f a t t y acids (reagent grade) were purchased from the Eastman Kodak Co. and used without further p u r i f i c a t i o n . 3.2 P20 The (99.7% enrichment) was purchased from Merck Sharpe and Dohme (Montreal). 3.3 Deuteration of the f a t t y acids. The procedure of deuterating the f a t t y acids i s the same as that of Hsiao et a l (42). The f a t t y acid and palladium on charcoal, as a c a t a l y s t , i n the r a t i o of 5:1 by weight, are placed i n a two neck fla s k as shown i n f i g . 3 and heated- to 180°C, with deuterium gas (obtained by e l e c t r o l y s i s of D̂ O) passing over the surf ace continually at the rate of 35 cc. per. minute for 1 week. The palladium on charcoal was removed by d i s s o l v i n g the mixture of f a t t y acid and palladium on charcoal i n chloroform, f i l t e r i n g through a c e l i t e column, and then evaporating the chloroform using a rotary evaporator. Mass spectral analysis revealed better than 99.2% deuteration. 3.4 Proton l a b e l l i n g of deuterated f a t t y acids. Laurie ($,-W)d2i acid having a -CH2 group at the. a p o s i t i o n i n an otherwise deuterated chain was prepared by exchange with KOH/^O at 230°C. Equimolar amounts of the fat t y acid and KOH (reagent grade) with .25 moles/litre of water excess KOH were dissolved i n ^ 0 and heated for 24 hours at 220°C i n a sealed s t a i n l e s s s t e e l tube. The 28 c o l d w a t e r D 2 g a s E L H Y G E N M A R K IV Milton R o y Figure 3. Experimental arrangement for the deuteration of the fat t y acids. 29 exhanged f a t t y acid s a l t solution was a c i d i f i e d with concentrated HC1 to p r e c i p i t a t e the f a t t y acid. Separation of the f a t t y acid was accomplished by shaking-with d i e t h y l ether i n a separating funnel. The ether layer was dried over anhydrous sodium su l f a t e and the ether was then evaporated i n a rotary evaporator. Further p u r i f i c a t i o n of the f a t t y acid was accomplished by s i l i c a gel chromotography. Mass spectral and NMR analysis of the d 23 and d 2 j acids indicated better than 99% H atthea position and 99.2%D at the (3-w) p o s i t i o n of the l a u r i c - d 2 1 acid sample. 3.5 Samples The f a t t y acid s a l t s were prepared by d i s s o l v i n g equimolar amounts of the f a t t y acid and the corresponding base (KOH or NaOH) i n ethanol and slowly c r y s t a l l i z i n g the f a t t y acid s a l t s . A f t e r f i l t r a t i o n and washing with ethanol, the p r e c i p i t a t e d s a l t was r e c r y s t a l l i z e d , washed with ethanol, and dried under vacuum at 140°C . The samples were made by weighing the corresponding molar amounts of the dry s a l t and H 20 or D20 and sealed i n a glass tube. Mixing was accomplished by centrifuging back and forth through a c o n s t r i c t i o n i n the glass tube. The samples were further homogenized by leaving them 4 days i n an oven at 120°C. Notation; Different samples w i l l be referred to by the number of < deuterated positions on the hydrocarbon chain, the concentration of water and whether.it i s prepared with H 20 or D20. For example d 2iCi 2-Na/6H20 stands for a sample prepared to have 6 moles of water per 1 mole of sodium laurate with one p a i r of protons at the a p o s i t i o n i n an 30 otherwise perdeuterated chain; s i m i l a r l y c^-jC^2_Na/6D20 stands f o r a sample with 6 moles of D2O per 1 mole of perdeuterated sodium laurate. 3.6 NMR Apparatus. A) The Spectrometer. The NMR measurements were carried out on a Bruker SXP4-100 NMR pulse spectrometer with a Nicolet BNC-12 computer. The spectrometer i s capable of putting out a t r a i n of up to 4 RF pulses of controlled amplitude and whose phases and lengths could be'varied independently. The computer i s equipped with a Diablo Disk Drive (series 31 single density) and was used for storage and analysis of the /. data. A programable timer (Nicolet 293 I/O controller) interfaced to the computer was used to automate the NMR measurements. Thus the triggeri n g of the i n d i v i d u a l RF pulses, the spacing between theia, the re p e t i t i o n rate as w e l l as the changing of the sample temperature was computer controlled. Automation of the measurements, especially the measurement of the spin l a t t i c e relaxation rates resulted i n a tremendous saving of time. The accumulation of the thesis data would have other- wise taken another 2VJ years. B) Probehead and Variable Temperature Oven. The probehead and the a i r flow heating system provided with the spectrometer were found to be unsatisfactory due to the large temperature gradient across the sample. To circumvent t h i s problem a variable temperature oven was b u i l t . The diagram i s shown i n f i g . (4). The oven was connected to the temperature control unit supplied with the 31 RF connector RF to probe arm Figure A . Variable temperature oven and sample holder. (a) Heater arrangement, (b) Oven with sarnie holder. On the inside of the copper block there i s a sh i e l d (not shown i n the diagram )made up of afihe brass screen to prevent ringing and eddy current effects after the application of an RF pulse. 32 spectrometer. Automatic temperature control was also made possible by in t e r f a c i n g the temperature control unit to the computer. Temperature gradients over a sample space of 1 cm diameter and 3 cm i n height were undetectable (less than .2°C at 100°C ) The temperature stability was within 1°C over a 24 hour period. The time required for the sample to reach thermal equilibrium was less than 20 minutes for an increment i n temperature of 10°C . 3.8 NMR Measurements A) Spectroscopy. The conventional method of obtaining NMR spectra consists of applying a 90° RF pulse and then Fourier transforming the free induction decay (FID). During the application of the R.F.. pulse, the receiver of the NMR spectrometer gets saturated and a certain time (ca l l e d the recovery time or dead time) has to elapse before i t returns to i t s normal operating condition. Therefore the early part of the FID cannot be observed due to the recovery time of the receiver. The usual method, delaying data acquisition u n t i l the receiver has recovered, results i n the loss of the information contained i n the early part of the FID (which i s very important f o r wide l i n e s ) and in v a r i a b l y leads to d i s t o r t i o n of the spectrum. I t also introduces f i r s t order phase s h i f t s and a poorly defined base l i n e . To circumvent this problem the NMR spectra were obtained using the s o l i d echo by the simple method of Davis et a l (43). This method consists of applying a 90^ 0 pulse followed by another 90° pulse whose phase i s s h i f t e d by 90 with respect to the f i r s t pulse at a time ( t y p i c a l l y 100-200V|s) later.An echo i s formed at 2T due to the refocusing of the nuclear 33 magnetization. By Fourier transforming the echo s t a r t i n g at t=2x the f u l l spectrum i s obtained. B) Relaxation measurements. Sp i n - l a t t i c e relaxation times, T j , were measured using a 180- T - s o l i d echo pulse sequence where the 180° pulse was applied on only every second cycle and alternate scans were subtracted from the computer memory. The i n t e n s i t i e s of the i n d i v i d u a l peaks of the Fourier transformed spectra decay according to M 0 - M z ( t ) = 2MQe _ T / T l n where MQ i s theequilibrium magnetization • and n i s the p o s i t i o n on the hydrocarbon chain. Fig. 5 shows p a r t i a l l y relaxed Fourier transformed spectra for different x values. The r e p e t i t i o n rate , or time between pulse . sequences, was chosen to be at least 5 times longer than the longest Tj i n the spectrum. The Tj's were obtained from semilog plots of T versus peak amplitudes. For H 20 T̂  measurement the conventional 180-T-90 pulse sequence was used. Figure 5. Representative deuterium p a r t i a l l y relaxed spectra for sodium laurate/water at 13.8 MHz and 90 C. Repetition rate = 10 seconds; 90 pulse length = 4.5 us; number of scans = 200. The spectra were obtained using the quadrupolar echo method as described i n the text. 35 Chapter 4 Results 4.1 Quadrupole S p l i t t i n g s . The deuterium quadrupole s p l i t t i n g s of the (-CT>^) groups on perdeuterated hydrocarbon chains i n the l i q u i d Crystal (L a) phase of the sodium laurate-water system, were measured as a function of temperature , position on the hydrocarbon chain and water concentration. Fig. 6a i s a representative spectrum fronr.which the s p l i t t i n g s are obtained. I t consists of 11 overlapping powder patterns a r i s i n g from deuterons at the di f f e r e n t positions on the hydrocarbon chain. At high temperatures and water concentration i t i s possible to resolve 10 of the 11 peaks i n the spectrum. The assignment of the peak positions was t distance , made assuming that the order decreases with ^ from the head groups (39)i F i g . 7 i s a representative diagram showing the temperature dependence of the quadrupole s p l i t t i n g s for '^^j^-^/GH 0, '^ie quadrupole s p l i t t i n g s for the 01-CD2 and the 3,4 positions show a temperature dependence that i s quite d i f f e r e n t from the rest of methyl- ene chain deuterons: The s p l i t t i n g s increase with temperature reach a maximum at /vL25°C and then show a s l i g h t decrease at higher temperatures. In contrast, the s p l i t t i n g s for the rest of the chain deuterons decrease with increasing temperature. Fig 8 . shows the quadrupole s p l i t t i n g s as a function of position on the hydrocarbon chain at two d i f f e r e n t temperatures. These s p l i t t i n g s are large for the a, and the f i r s t few methylenes and become progressively 3 6 smaller for the methylene pairs at the t a i l of the hydrocarbon chain. In the same figure i t i s inte r e s t i n g to note the absence of the "plateau" observed i n other systems ; for example (17, 18) . A representative diagram for the dependence of the quadrupole s p l i t t i n g s on water concentration i s shown i n f i g . .9 . At low water concentrations the s p l i t t i n g s are large for the f i r s t few hydrocarbon chain segments and decrease rapidly with increasing water concentration. Near the t a i l of the hydrocarbon chain the s p l i t t i n g s are progressively smaller and seem to have a somewhat weaker dependence on water . concentration. The eff e c t of water isotope composition on the quadrupole s p l i t t i n g of the chain deuterons was investigated for two samples prepared with 1^0 and D20 respectively but having the same molar r a t i o of water to fa t t y acid s a l t . There was no observable difference i n the measured quadrupole s p l i t t i n g s of the two samples to within the experimental error . The quadrupole s p l i t t i n g s as a function of temperature for 2 3 deuterium i n D£0 , Na and the f i r s t 3 positions on the chain are shown i n f i g . 10 . They a l l . have a s i m i l a r temperature dependence suggesting a correlation i n the ordering of water, counter ion and the hydrocarbon chain segments close to the polar head. A s i m i l a r behaviour was observed f o r the potassium palmitate-water system (see appendix A) . A.2 Spin-Lattice Relaxation Times, A) Deuterium Results: The spin l a t t i c e relaxation time T j , for each-CD2 group of a perdeuterated f a t t y acid chain i n the sodium laurate-water 37 system were measured at 13.8 MHz as a function of temperature and water concentration. Fig. 11 shows 1/Tp as a function of chain position at 105°C » The relaxation rates ) are large for the methylenes close to the r l n polar region and progressively get smaller towards the centre of the b i l a y e r . In f i g . 12 the temperature dependence of -j- i s shown. I t i s T l n clear from f i g . 12 that a l l the T^'s are characterised by an a c t i v a t i o n energy. Except f o r the methyl (-CD3) group, the ac t i v a t i o n energies are approximately the same. Fig. .13 i s a plot of the ac t i v a t i o n energy versus chain position • The dependence of 1/T-j, on water concentration i s shown i n f i g . 14 for the 2 and 10 positions and for the CD^-group. The relaxation rates for the 3-9" positions (not shown i n the diagram) also increase with increasing water concentration. The relaxation rates for the methylenes near the polar head seem to be more sensitive to the water concentration than the methylenes near the centre of the b i l a y e r . In fact ^ for the CD3 i s almost independent of water concentration. The effect of water isotope composition on the relaxation rates of the methylene chain segments was studied for two samples prepared with H2O and D2O respectively but with same molar r a t i o of H2O or D2O to the f a t t y acid s a l t . The results are shown i n f i g . 15 for the 01-CD2 . The relaxation rates for the chain deuterons were not measurably affected by changing the isotope composition of the water • 38 B) ct-protons: The spin l a t t i c e relaxation time f o r the cc-C^ i n a n other- wise perdeuterated chain were measured as a function of temperature f o r two samples prepared with Ĥ O and D̂ O respectively but with the same molar r a t i o of water to f a t t y acid s a l t . For b r e v i t y they w i l l be refered to as d„ C -Na/6H 0 and d C -Na/6D 0 . T here was a small but 21 12 2 21 12 2 measureable difference i n the T 's of the a protons of the two samples . 1 the results are shown i n f i g . 16 . To ensure that the state of the two samples was the same, the quadrupole s p l i t t i n g s of the chain deuterons i n the two samples were measured and were found to be i d e n t i c a l , c) Ĥ O Results The effect of isotope composition on the Ĥ O T^ i n the sodium laurate-water system was measured for i n 3 d i f f e r e n t samples: Ĥ O with perdeuterated chains, Ĥ O with orprotonated chains and Ĥ O with a l l protonated chains. These samples w i l l be refered to by d,,C, -Ka/6H0, (JB-U) d„,C -Na/6H 0 and d C -Na/6H 0 . Where the 23 12 2 21 12 2 o 12 2 subscript on the d stands for the number of deuterated positions on the hydrocarbon chain. The results are shown i n f i g .17 -. For a l l the temperatures studied the relaxation rate (1/Tj) f o r the H20 protons increase with increasing number of protons on the hydrocarbon chain. 4.3 Sources of error Quadrupole s p l i t t i n g s were obtained from the peak positions i n the NMR spectra. In the presence of dipo l a r broadening of the quadrupolar spectra, the positions of maximum i n t e n s i t y are no longer coincident with the positions of the 90° edges of the powder patterns. This introduces a small decrease i n the measured quadrupole s p l i t t i n g s . 39 Ih addition for spectra consisting of a superposition of quadrupolar powder patterns, e.g. of the perdeuterated chains, the overlap between neighbouring patterns causes a small apparent increase i n the measured quadrupole s p l i t t i n g s . Due to the small magnetic moment of the deuteron and i n view of the large quadrupole s p l i t t i n g s considered here such effects were assumed to introduce only a n e g l i g i b l e systematic error i n the measurements. The accuracy of determining the peak positions of maximum in t e n s i t y i s e s s e n t i a l l y l i m i t e d by the spectral resolution of the computer, which i s 12.5 Hz for a 50 KHz spectrum. However, the signal to noise r a t i o i s diffe r e n t for the different positions on the hydrocarbon chain and ranges from about 400:1 for the CD3 to 50:1 for the a posit i o n . Therefore i t i s more d i f f i c u l t to locate the positions of maximum int e n s i t y for the 2-4 positions, thus introducing an additional error of about 50 Hz i n the s p l i t t i n g s of those positions. The main sources of error i n the measurements of the deuterium relaxation rates are the reduction i n the sig n a l to noise r a t i o at long T values and interference between overlapping powder patterns. Since the deuterium magnetic resonance spectrum i s a superposition of powder patterns, then the peak in t e n s i t y of a certain position w i l l contain contributions from those powder patterns with the larger s p l i t t i n g s . These contributions are only s i g n i f i c a n t for short xvalues because the relaxation rates increase with increasing s p l i t t i n g s . For t h i s reason the T^'s for the overlapping peaks were obtained from the plots of T versus peak amplitudes at longer T values. 4 0 Figure 6. (a) A deuterium magnetic resonance spectrum for d23 C12~ N a^ 6 H2° o b t a i n e d a t 120°C and 13.8 MHz using the quadrupolar echo method. (b) A proton magnetic resonance spectrum of the a-protons i n a d2^-laurate water sample obtained at 90 MHz and 90 C using the s o l i d echo and quadrature detection. The central peak i s due to water and residual protons on the chain. (c£ A 2 3Na spectrum of d 23C 1 2-Na/6H 20 at 23.8 MHz and 86 C obtained using the echo method. See text for abbreviations. 80 100 120 140 T E M P E R A T U R E ( ° C ) Figure 7. Temperature dependence of the quadrupole s p l i t t i n g s for d 23Cj 2-Na/6H 20. The numbers beside the curves denote the positions on the hydrocarbon chain. The s o l i d curves are least square f i t s to the experimental data (dots and c i r c l e s ) where a three parameter f i t of the form v ( T ) = a< n ) + a 5 n ) ( T - T ) + a n o 1 v o (n) (T - T ) o was used. 42 16.0 IM X 6.0 4.0 2.0 1 — A 1 — • at 105 °C — A A at 135 °C — • A 9 —. A • — A - • A I . . 1 . 1 . 1 1 A 1 2 (3,4) 6 8 10 12 n (CARBON NUMBER) Figure 8. The quadrupole s p l i t t i n g s as a function of po s i t i o n on the hydrocarbon chain for d22Cj2~^ a/^2^* 43 3 4 5 6 7 C ( MOLES OF H^IMOLE OF dC-Na) Figure 9. Dependence of the quadrupole s p l i t t i n g s on water concentrations at 120 C. The s o l i d curves are least square f i t s to the experimental data ( c i r c l e s ) where a f i t of the form . »2 v (c) = b + b- (c - c ) + b_ x-, n o 1 o i l . was used. 44 T E M P E R A T U R E (°C) Figure 10. The quadrupole s p l i t t i n g s as a function of temperature for deuterium i n D^O ( t r i a n g l e s ) , 2 3Na (squares), the a (open c i r c l e s ) and the 3 and 4 positions ( s o l i d c i r c l e s ) . The D 20 s p l i t t i n g s are for d23Ci2-Na/6D20 and the rest are for d23Ci2~ N a/^ H 2^* 45 2 (3,4) 6 8 10 12 n (CARBON NUMBER) Figure 11. T as a function of position on the hydrocarbon chain at 13.8 MHz and 105°C for d 2 3C 1 2-Na/6H 20. 2.5 2.6 2.7 2.8 I0 3/T ( K H ) Figure 12. Temperature dependence of the relaxation rates of the chain deuterons i n d23C12-Na/6H20 at 13.8 MHz. The s o l i d lines are the least square f i t s to the experimental data where a f i t of the form Log L l n = a + b -J n n T was used. The numbers appearing beside the s o l i d lines indicate the position n on the hydrocarbon chain. 47 4.0 — • -< I ? 3.0 ro g . 1 T T i c o LU 2.0 — T I 1.0 1 1 1 1 1 , 1 , 1 2 (3,4) (5,6) 8 10 12 n (CARBON NUMBER) Figure 13. A c t i v a t i o n energy versus chain p o s i t i o n for the deuterium relaxation rates i n d O QC, o-Na/6Ho0. 48 l O L U CO 14.0 — o 2 12.0 IQO o 8.0 — 6.0 • 4.0 • • o © 10 2.0 - a i ft X i i A 1 A CD 3 I 3 4 5 6 7 C (MOLES OF H20/1M0LE OF C )2-Na) Figure 14. Dependence of the relaxation rates for the chain deuterons on water concentration at 13.8 MHz and 105°C. Positions 3-9 are not shown i n the diagram (see text) . 49 Figure 15 . Dependence of the relaxation rates on inverse temperature for the 01-CD2 i n d23Ci2 _ N a/ 6 H2° (open c i r c l e s ) and d23 c12~ N a/ 6 D2° ( triangles ) at 13.8 MHz . 50 1 ° - (K) Figure 16 . Dependence of the relaxation rates of the (X-CH2 protons on inverse temperature i n ($-w)d2]C12~Na/6H2° (open c i r c l e s ) and (B-w)d2iC 1 2" N a/ 6 l )2 0 ( s o l i d c i r c l e s ) at 90 MHz . 51 Figure 17 . Dependence of the relaxation rates on inverse temperature for H 20 i n d0Ci2-Na/6H2O ( s o l i d c i r c l e s ) , (3-w)d 2iC 1 2- N a/ 6 H2° (triangles) and d 23Ci2- N a/6H 20 (open c i r c l e s ) at 90 MHz 52 Chapter 5 The Lipid-Water Interaction A Microscopic Interpretation. 5.1 Quadrupole S p l i t t i n g s , I t was pointed out e a r l i e r that the quadrupole s p l i t t i n g s are proportional to order parameters which can provide inform- tion on the conformations and motion of the l i p i d molecules within the b i l a y e r as w e l l as on the ordering of water and counter ions at the lipid-water interface. The results shown i n f i g . 10 on page indicate a correlation between the quadrupole s p l i t t i n g s of the deuterons on the f i r s t few methylene chain segments, the deuterons i n D20 and the 2 % a counter ion. The s p l i t t i n g s increase with temperature, reach a maximum o at 125 C and then decrease at higher temperature. In contrast the s p l i t t i n g s for the rest of the hydrocarbon chain segments shown i n f i g . 7 on page 41 decrease with increasing temperature. A s i m i l a r behaviour was observed for the potassium palmitate-water system where this correlation was ascribed to the structuring e f f e c t of the water v i a hydrogen bonding. A model consistent with the experimental results (see Appendix A for details) proposes two configurations which i n t e r - change rapidly compared with NMR s p l i t t i n g s . At lower temperatures, the water, v i a some complicated hydrogen bonded structures with the oxygens of the l i p i d carboxyl groups, imposes a constraint on the f i r s t C-C bond di r e c t i o n causing i t to be p a r a l l e l to the normal n to the b i l a y e r , leaving the t a i l on the average some what t i l t e d . This, for 53 purely geometric reasons, results i n smaller quadrupole s p l i t t i n g s than those at the high temperatures (see table 1 Appendix A ). Since the lipid-water i n t e r a c t i o n tends to t i l t the hydrocarbon chain, i t i s i n competition with chain-chain ( i . e . l i p i d - l i p i d ) interactions whose influence i s to cause the hydrocarbon chain to be p a r a l l e l to n . When the molecular axis i s p a r a l l e l to n , the quadrupole s p l i t t i n g s are larger than for the structure imposed by the lipid-water i n t e r a c t i o n . Therefore when the hydrogen bonded structures tend to break up at higher temperatures and the chain-chain interactions become more dominant, the quadrupole s p l i t t i n g s for deuterons near the head of the chain increase even though the order of the system as a whole decreases. The D20 and 2 % a results could also be explained i r terms of t h i s model. For the deuterons i n D2O and the 2 % a counter ion the average environment i n the low temperature configuration are such that t h e i r p r i n c i p a l parameters which are smaller than those for the high temperature configuration (see table 1 appendix A'). The dependence of the quadrupole s p l i t t i n g s on water concentration i s shown i n f i g . 9 on page 43 . There i s a marked decrease i n the quadrupole s p l i t t i n g s with increasing water concentration. I t i s important to note that the f r a c t i o n a l v a r i a t i o n i n the quadrupole s p l i t t i n g s at high water concentrations shown i n f i g . 18 i s greater f o r the methylene chain segments close to the polar head than those near the centre of the b i l a y e r . This res u l t i s e a s i l y accounted for i n terms of the proposed model. Near the surface of the b i l a y e r i t i s the e l e c t r i c f i e l d gradients (ej .es with n giving average order 54 lipid-water interaction that i s responsible for the va r i a t i o n i n the order parameters. The more water there i s between the bilayers the more degrees of freedom there are for forming dif f e r e n t hydrogen bonded structures which would resu l t i n an average conformation of the hydro- carbon chains that would lead to a reduction i n the quadrupole s p l i t t i n g s . On the other hand, near the centre of the b i l a y e r , i t i s the in t e r a c t i o n between the chains, which i s less dependent on water concentration, that controls the var i a t i o n of the quadrupole s p l i t t i n g s . Samples prepared with H2O and D2O respectively but having the same molar r a t i o of water to fa t t y acid s a l t show no observable difference i n the measured quadrupole s p l i t t i n g s of the two samples. This indicates that the average o f (3cos 20-l) over n thylene motions i s not 2 measurably affected by modification of the isotope composition of the hydrogen i n the water. 2 (3,4) 6 8 10 12 n CARBON NUMBER Figure 18. Fractional variations of the quadrupole s p l i t t i n g s of.the chain deuterons with water concentration at fixed temperature (120 C). P a r t i a l derivatives are evaluated at C= 6 56 5.2 Spin-Lattice Relaxation (Perdeuterated Chains) While deuterium quadrupole s p l i t t i n g s give information on the or i e n t a t i o n a l ordering and degree of motion of the l i p i d chains, spin- l a t t i c e relaxation measurements allow the determination of a time scale and an i n t e n s i t y factor for the molecular motions. In chapter 2 i t has been already stated that for chain deuterons quadrupolar interactions are the main relaxation mechanism. The spin- l a t t i c e relaxation rate }• , was expressed i n the form (eqn. 24 chapter 2) A l T l  = O N * > ( j l ( u o > + J 2 ( 2 o ) o ) z where <̂ |HQ|̂  i s the mean square value of the spin l a t t i c e coupling Hq(t) due to the quadrupolar interactions and Ji ( w 0 ) , ,J2(2w0) are the reduced spectral density functions associated with Hq(t) . Thus 1 / - j j - measurements allow the determination of J i ( w 0 ) and J2(2co0) which can be used to define a correlation time for the molecular motions occurring at the Larmor frequency w0 and at 2u)0 . Figure'11 on page 45 shows ^ as a function of position on the hydrocarbon chain. The relaxation rates are large for the -CD2 groups near the polar head and become progressively smaller towards the centre of the b i l a y e r . This indicates that the motions of the chain segments near the l i p i d water interface are considerably d i f f e r e n t from those of the methylene chain segments of the t a i l of the hydrocarbon chain. The temperature dependence of ̂  i s shown i n f i g . 12 on page 46 A l n for the dif f e r e n t positions on the hydrocarbon chain. A l l the relaxation 57 rates are characterized by an act i v a t i o n energy. Except for the methyl (-CD3) group, a l l the activation energies are roughly the same as shown i n f i g . 13 on page 47 . The decrease i n the relaxation rates with increasing temperatures indicates that the short correl a t i o n time 2 2 l i m i t (w0T<s.l ; where T N i s the correlation time characterizing the motion of the n*"*1 methylene chain segment) i s s a t i s f i e d . Further evidence that t h i s l i m i t i s s a t i s f i e d comes from the direct comparison, as w i l l be discussed below, of the relaxation rates of the a-CH2 at 90 • MHz and the a-CD2 at 13.8 MHz . The detection of d i s t i n c t types of molecular motion as manifested by different c o r r e l a t i o n times requires a study of the dependence of ̂ on the nuclear Larmor frequency w0 . The larg r proton magnetic moment would permit ^ measurements at much higher values of u Q thus making 1 possible the detection of shorter c o r r e l a t i o n times. However, i n the short correlation time l i m i t , the relaxation rates are independent of frequency (see chapter 2, section 2.2 ) and the expression for ̂  reduces to a product of an i n t e n s i t y factor and a correla t i o n time. From the experimental data of figures 12 and 16 , the relaxation rates of the a-CD2 at 13.8 MHz and of the a-CH2 at 90 MHz were found to be i n the r a t i o of 17.8 as compared with 18.7 for the r a t i o of the square of the coupling constants.This implies that the correlation times associated with the motions occuring at these frequncies are short For a single type of fast motion, i t was previously shown (eqn. 25 chapter 2 ) that i n the short co r r e l a t i o n time l i m i t , the relaxation rates are given by 58 where S n i s the order parameter for the n t h C-D bond defined by equation, 2 6 i n chapter 2 and the factor 1 -S n takes into account the anisotropy of the system. A logarithmic p l o t of ^ versus v n ( r e c a l l the V_ i s proportional to S n ) i s shown i n f i g . 19 for 4 different temperatures. Except for the f i r s t few positions, the dependence of ^ on V n seems 1 l n to obey a power law ( = ^ ) where p = 1.1 at 90°C and becomes smaller In at higher temperatures. I t i s l i k e l y that more complex motions must be taken into account. I f the above equation i s v a l i d .however,the factor 1-S nhardly changes since Sn~.2 . Therefore changes i n the relaxation rates ~ are expected to be l a r g e l y due to changes i n the c o r r e l a t i o n i l n times x n . The dependence of J- on water concentration i s shown i n f i g . 14 In on page 48 . The relaxation rates for the methylenes near the polar haad increase with increasing amounts of water more than the relaxation rates of the methylenes near the centre of the b i l a y e r . For the -CD^ ^ i s almost independent of water concentration. In contrast, the quadrupole s p l i t t i n g s a l l decrease with increasing water concentration. This i s further evidence that complex molecular motion mediated by the lipid-water interaction must be taken into account. A simple model explaining the influence of the water on the relaxation rates of the methylene chain deuterons w i l l be discussed below. 5.3 A Model for Molecular Motions Mediated by The lipid-Water Interaction. The increase i n the relaxation rates with increasing water 59 concentration maybe due to the interaction of the water with the polar heads v i a hydrogen bonding. Increasing the water concentration w i l l r e s u l t i n greater formation of hydrogen bonded structures ( l i p i d - molecules and the water engaged i n hydrogen bonding with the polar heads). Therefore, i t i s the motion of the combination ( l i p i d +water hydrogen bonded to the polar heads) that has to be taken into account. I t i s quite possible that increasing water concentration w i l l increase the ef f e c t i v e mass of the hydrogen bonded structures and re s u l t i n slowing down of the r o t a t i o n a l motion as w e l l as the twi s t i n g , bending and wiggling motions about the long axis of the molecules and thus give r i s e to higher relaxation rates. In addition , increasing water concen- t r a t i o n w i l l increase the area per polar head (£ee appendix B f i g . 29). This w i l l increase the available space occupied by the hydrocarbon chains which would allow for single molecule motions of larger amplitude also around the d i r e c t o r v r e s u l t i n g i n larger relaxation rates. However, an increase i n the area per polar head would also give more freedom of movement for the i n d i v i d u a l chain segments causing a reduction i n the observed quadrupole s p l i t t i n g s (see f i g . 9 on page 43 ) 5.4. Isotope e f f e c t s . The isotope modification of the water may influence the relaxation rates of the chain deuterons i n two ways: ( i ) by changing the spectral densities (or correla t i o n times) through modification of the motions or ( i i ) by af f e c t i n g the contribution of the dipolar i n t e r - actions to the relaxation rates. In the previous section i t has been pointed out that, due to the 60 hydrogen bonding of the water with the polar heads, the motion of the combination ( l i p i d + water hydrogen bonded to the polar heads) should be considered. Since the deuteron i s heavier than the proton, then replacing H2O with D20 would r e s u l t i n an increase i n the mass of the hydrogen bonded structures r e s u l t i n g i n the slowing down of the motions ( l o c a l bending and twisting around the chain segments as w e l l as the o v e r a l l t r a n s l a t i o n a l and ro t a t i o n a l motion of the hydrogen bonded structure). This would increase the correla t i o n times and therefore r e s u l t i n larger relaxation rates. However, an examination of the relaxation data for two samples prepared with H 20 and D20 respectively but with the same molar r a t i o of water to f a t t y acid s a l t , reveals that t h i s effect i s n e g l i g i b l e , since there was no measurable difference (within the experimental error) i n the relaxation rates of the two samples as shown i n f i g . 15 on page 49 for the a-CD2 . The r e s u l t s also indicate that the contribution to the relaxation rates due to dipolar interactions i s also n e g l i g i b l e . This r e s u l t i s not su r p r i s i n g since, as was discussed e a r l i e r , the quadrupolar interactions of the chain deuterons are much larger than deuteron-proton dipolar interactions and hence are much more e f f e c t i v e i n s p i n - l a t t i c e r e l a x a t i o n . We - conclude that j u s t as isotope modification of water does not change the average quadrupolar i n t e r a c t i o n , as discussed e a r l i e r , the fluctuations of the quadrupolar interactions about the average which are responsible for spin l a t t i c e - r e l a x a t i o n are not affected s i g n i f i c a n t l y . 1 2 4 6 4 v n ( k H z ) Figure 19. A log-log plot of the relaxation rates versus quadrupole s p l i t t i n g s for the chain deuterons i n d 2 3C 1 2-Na/6H 20 at 80°C ( s o l i d dots), 105°C (open c i r c l e s ) , 125°C ( t r i a n g l e s ) , and 135 C (squares). 62 Chapter 6 The Lipid-Water Interaction Analysis i n terms of Macroscopic Variables 6.1 Quadrupole S p l i t t i n g s The order parameters of the C-H bonds along a hydrocarbon chain i n a l i p i d b i l a y e r give a quantitative measure of the nature of the f l u i d i t y of the b i l a y e r . These order parameters are proportional to the deuterium quadrupole s p l i t t i n g s of the -CD2 groups on the different positions of the hydrocarbon chain. In t h i s chapter a systematic investigation i s made of the dependence of these l o c a l order parameters on the macroscopic thermodynamic parameters which characterise the l i p i d - water system. I t has been suggested by Mely et a l (17) that A , the mean area per polar head, i s a "good parameter to represent the average microscopic order" i n the b i l a y e r . Their conclusion i s based on measurements on the potassium laurate -water system which show that where-as the p r o f i l e of the quadrupole s p l i t t i n g s changes appreciably when the temperature T i s varied with the water concentration C kept constant and also when C i s varied with T kept f i x e d , the va r i a t i o n i s much less than when both T and C are varied i n such a way as to keep A constant.As may be seen from t h e i r data which are reproduced i n f i g . 20 (a.b)the quadrupole s p l i t t i n g s i n the samples having i d e n t i c a l surface area are not i d e n t i c a l . Rather the p r o f i l e s of S n versus n for these samples resemble each other more closely i n a q u a l i t a t i v e sense than do the p r o f i l e s i n which C and T are separately varied without keeping A constant . As shown i n fig.20C the curves for the quadrupole s p l i t t i n g s 63 X -X 30 5= <J 20 \A at c "3." 10 w» u a 9 £X •o a s 3 a A*32.8A' \ . :247.HjO-50*C . :21V.HjO-74*C _ l _ J L 1_ 2 4 S 3 10~ 12 Carbon number (from polar head) -JO 02 2 i 6 8 10 12 Carbon number (from polar head) Figure 20 . (a) Order parameter curves obtained for two dif f e r e n t lamellar samples of dC^K-R^O,having the same A value. (b) Order parameter curves variations as the area per polar head i s increased i n the lamellar phase of dC 1 2K-H 20 (• :21%-31°C;A :24%-50°C;§ :30%-51°C;-r- :30%-110 C). (The white dots come from computer simulation of the unresolved line s . ) Reproduced from reference (17) . 64 16 14 N i 12 CM \ 1 0 8 0 9 O o c = 6 j T = 105°C — © C = 5 j T=13 5C : HIM - o • — o — 8 o Q S o • _ i I i I I . I I i i i 2 (3,4) 6 8 10 12 n ( C A R B O N NUMBER) Figure 20C . Quadrupole s p l i t t i n g s curves for two samples of dC..-Na/R^O having the same A value. 65 for two samples of dC^-Na/l^O having the same A are also s i m i l a r . The hypothesis of Mely et a l that the quadrupole s p l i t t i n g s v^CC.T) depend on C and T i n such a way that they vary only i f the surface area varies, i . e . v n(C,T) i s a function of A(C,T) makes good physical sense i f the dominant interactions responsible for the o r i e n t a t i o n a l order of the hydrocarbon chain segments are the chain-chain i n t e r a c t i o n s . These i n t e r - actions are expected to be sensitive to the average separation of the hydrocarbon chains, which would be simply related to the surface area per polar head. In view of the fact that we have strong empirical evidence that the l i p i d water interaction has a strong influence on the or i e n t i o n a l order of the hydrocarbon chains, e s p e c i a l l y those chain segments near the polar head, i t i s of great i n t e r e s t to examine the v a l i d i t y of t h e i r hypothesis i n a systematic manner f o r another system. In order to do t h i s , i t i s not necessary to compare samples having the same values of A at d i f f e r e n t C and T as has been done by Mely et a l . Since A i s related to C and T through an equation of s t a t e , as w i l l be discussed l a t e r , i t i s a simple procedure, using elementary thermodynamics, to examine the dependence of V n for any s p e c i f i e d v a r i a t i o n of the thermodynamic variables so long as data i s available over a wide range of any set of independent variables. In t h i s section we carry through such a thermodynamic analysis using the measured values of V n over a range of C and T which were presented i n chapter 3 and the experimentally determined empirical equation of state presented i n Appendix B. Thermodynamic Formulation. I f the quadrupole s p l i t t i n g of the -CD2 groups on the n t Q 66 position of a hydrocarbon chain i s a function of several independent thermodynamic variables {Qj} where Qj could be water concentration, temperature, PH, pressure or i o n i c species. A d i f f e r e n t i a l change dv, i n V n i s given by : \ f3vn(...tQ±,..) \ i In t h i s work the NMR measurements were carried out on samples of different water concentration at different temperatures but always under the constraint of the equilibrium water vapor pressure because the samples were sealed. Therefore i t w i l l be assumed that there are only two independent thermodynamic variables that have to be considered i n this analysis: the water concentration and the temperature. Eqn. [ l ] then s i m p l i f i e s to. where T and C are the temperature and water concentration respectively. In order to test for the s e n s i t i v i t y of the quadrupole s p l i t t i n g s V n to changes i n the di f f e r e n t thermodynamic variables, i t i s s u f f i c i e n t to examine the p a r t i a l derivatives of v n with T and C keeping A the surface area per polar head constant. That i s , to determine whether v n depends on T and C only through A . I f these variations are di f f e r e n t from zero then A i s not necessarily "a good parameter" which [ 1 ] 67 characterises the state of the b i l a y e r as proposed by Mely et a l . From [2] the p a r t i a l derivatives of v n with respect to T and C keeping A, the surface area constant are given by A l l the p a r t i a l derivatives on the r i g h t of equations [3]»[4] are obtained from the NMR experiments except for OC/3T) Aand OT/3C)A which have to be determined independently from an equation of state. In appendix B the equation of state for the Cj^-Na/H^O system was found to be A = A C(T)C P [5] where A i s the surface area per polar head, C i s the water concentration, p i s a constant equal to .24 and A Q(T) i s the area per polar head i n the l i m i t of zero water concentration and i s only a function of temperature. From [3], [4] and [5] ..we obtain: / 3Vn \ - C . 1 / 9Vn \ [6] \ 3 T )c P A b dT V 8 C ; T / ^ L \ . P . A Q . J _ 7 \ \ [7] V 3 C ) C dAo h i / N XT dT C A l l the p a r t i a l derivatives [ \ and ( ̂ n j were obtained V a T jc \ a c JT from l i n e a r least square f i t s to the experimental data as indicated i n . 68 the captions of figures 7 and 9 on pages 41 and 43. Due to the wide v a r i a t i o n i n the quadrupole s p l i t t i n g s of the methy- lene deuterons on the hydrocarbon chain, i t i s the r e l a t i v e quantities 1 (9vn \ , 1 ( 3 v n \ that are meaningful. 311(1 v£\Tc)i 1 / 8v n \ i f 3v n \ Figure 21 i s a plot of ^ [ ] A and ~ [jT IC V e r s u s position number n on the hydrocarbon chain. I t i s clear that 1 ( 9v n \ — I -̂ "Y" K does not vanish except for the n=7 position which may' be just accidental. In fact keeping A constant seems to be less e f f e c t i v e i n c o n t r o l l i n g the f r a c t i o n a l v a r i a t i o n of the quadrupole s p l i t t i n g s of the f i r s t few -CD2 groups than keeping C constant. In f i g . 22 a plot of 1 (3v n \ \T~ \1TT~ JA versus n the position number on the hydrocarbon chain i s shown for four di f f e r e n t temperatures. I t can be seen that the f r a c t i o n a l varation of v n with T keeping A constant for the f i r s t 6 positions depends on temperature but i s independent of temperature for positions (7-12) i n c l u s i v e . A s i m i l a r observation can be made for 1 ( 3Vn \ 1 / 3v n \ — ^ JA. A S S N O W N I N ^S* 23.Fig 24 shows that \ Xc~ /A depends on C only for the f i r s t 6 positions. This suggests that the ordering of the hydrocarbon chain segments close to the polar head i s influenced by the constraints which water imposes on the f i r s t C-C bond v i a hydrogen bonding. The influence of the water gets weaker towards the centre of the b i l a y e r . This ef f e c t can be seen more c l e a r l y i n f i g . 25 where the r a t i o 69 (_3Vn_\ V 9T /C i s plotted aganist the position number for d i f f e r e n t temperatures. Again t h i s r a t i o i s a function of temperature for the f i r s t few chain segments but i s independent of temperature for the chain segments close to the centre of the b i l a y e r and asymptotically approaches a constant value of .7. This indicates that the v a r i a t i o n with temperature i n the ordering of the hydrocarbon chain segments near the lipid-water interface keeping A constant i s much greater than i t i s keeping C constant. However i n the centre of the b i l a y e r A tends to be s l i g h t l y more ef f e c t i v e than C i n c o n t r o l l i n g the v a r i a t i o n i n the ordering of the methylene chain segments. This v a r i a t i o n i s consistent with the model mentioned i n the preceding chapter. At lower temperatures hydrogen bonding of the water with the polar head groups i s more favourable than at higher temperature where the hydrogen bonding structures tend to break up. "An e f f e c t i v e range" <1JI> which i s a measure of the extent of the persistence of the influence of the water can be obtained from f i g 25. A semilog p l o t of r -r„ versus n i s shown i n f i g . 26 where r = l i m i t r ° oo « oo n->oo- n r corresponds to an i n f i n i t e l y long chain. I t was f i t t e d by inspection to a value of .8 assuming an exponential dependence of r Q on n and an e f f e c t i v e range of 4<v5 chain segments was obtained. The above observations imply that insofar as the system studied i n t h i s thesis i s concerned, A i s not the best parameter to characterise the state of the b i l a y e r p a r t i c u l a r l y for the methylene chain segments that are close to the l i p i d water interface . The 70 conformations of these chain segments are dictated by the hydrogen bonded structures of water at the surface. However i n the centre of the b i l a y e r keeping A constant but varying T or C does not influence the v a r i a t i o n of the order parameters s i g n i f i c a n t l y . This i s i n agreement with the i n t u i t i v e physical picture where i n the centre of the b i l a y e r i t i s chain chain interactions and the available, area per polar head which determines the ordering and conformations of the hydrocarbon chains, whereas i n the v i c i n i t y of the polar head i t i s the l i p i d water i n t e r - action v i a hydrogen bonding that controls the v a r i a t i o n of the order parameters. 71 CVJ I O x - 2 >-4 TO ;?~6 - 8 e o Q = A o A Q = C -A • _ — A 9 — A • A A • • - A • • A — A e — A 1 i 1 1 1 1 1 • 1 (3,4) 6 8 10 n (CARBON NUMBER ) 12 Figure 21. The f r a c t i o n a l v a r i a t i o n of the quadrupole s p l i t t i n g s with temperature keeping the area per polar head constant (open c i r c l e s ) , and keeping the water concen- trations constant (triangles) . P a r t i a l derivatives are evaluated at T=105°C and C= 6 . 72 I o o CM I o <r C 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 5 1 - o - 2 C = 6 l 1 9 8 6 °C A 1 0 5 ° C °12 5°C A 1 3 5 ° C 1 o A A 9 O 6 i 1 2 3,4 6 8 10 12 n ( C A R B O N N U M B E R ) Figure 22. The f r a c t i o n a l v a r i a t i o n of the quadrupole s p l i t t i n g s with temperature keeping the area per polar head constant. 73 0.3 0.2 0.1 c -0.1 -0.2 • 8 6 °C o 105°C n X A 12 5 °C a 8 • 1 3 5 °C A ° — • s 8 e @ - 0 o o • C = 6 • 1 I I i i i 2 (3,4) 6 8 10 12 n ( C A R B O N N U M B E R ) Figure 23. The f r a c t i o n a l v a r i a t i o n of the quadrupole s p l i t t i n g s with water concentration keeping the area per polar head constant. 74 c O - 1 ^ 2 3,4 6 8 10 12 n ( C A R B O N N U M B E R ) Figure 24. The f r a c t i o n a l v a r i a t i o n of the quadrupole s p l i t t i n g s with water concentration keeping the area per polar head constant. 75 c <T5 C 6.0 4.0 2.0 2.0 -4.0 -6.0 -8.0 — -°- o — _ X - x - C = 6 — A . a a a a 4 ° m - i - — x — * o 1 A "T X * 86°C o 105°C A 12 5°C — d 135°C i i . 1 , I . I . I (3,4) 6 8 10 n ( C A R B O N N U M B E R ) 12 Figure 25. The r a t i o of the change in.v with T keeping A fixed to the change i n V r with T keeping G fi x e d . 76 Figure 26. A semilog plot of r abbreviations. r . See text for n 77 Discussion i n re l a t i o n to ex i s t i n g theories. There have been many th e o r e t i c a l calculations on the chain ordering i n l i q u i d crystals and b i l a y e r membranes (12-14, 29-32). The most successful of these i s Marcelja's (13) molecular f i e l d c a l c u l a t i o n . In the mean f i e l d approximation, the inte r a c t i o n energy of a single chain i n the molecular f i e l d i s given by. E - E. fc + E + PA i n t disp where E. i s the i n t e r n a l energy of a single chain and depends on i n t the p a r t i c u l a r conformation, E ^ i s due to Vander Waal's interactions of the chain with i t s neighbors v i a the molecular f i e l d . The l a s t term i s due to the l a t e r a l pressure on each chain and stems from the s t e r i c repulsions among the hard coresf'of the atoms. I t i s proportional to the pressure P and the average cross sectional area A of the chain. S t a t i s t i c a l averages are then evaluated by summing over a l l conformations of a single chain i n the molecular f i e l d of i t s neighbors. By adjusting P and assuming an i n i t i a l orientation for the f i r s t C-C bond t h i s model i s able to predict the order parameter p r o f i l e of some NMR (13, 33)data. of However the results do depend on the assumed orientation^the i n i t i a l chain segment, which implies that a description of the ordering of the hydro- carbon chain i n b i l a y e r membranes e n t i r e l y i n terms of chain chain interactions i s incomplete. Instead of f i x i n g the orientation of the f i r s t C-C bond i n an ad hoc way a more complete theory should, as could be seen from the thermodynamic analysis, include the l i p i d water in t e r a c t i o n e x p l i c i t l y . 78 6.2 Spin-Lattice Relaxation In the previous section i t was found that the lipid-water interaction played an important role i n co n t r o l l i n g the ordering and f l u i d i t y of the hydrocarbon chains within the b i l a y e r . In t h i s section, the same thermodynamic approach w i l l be used to see to what extent the l i p i d - water in t e r a c t i o n affects the dynamics of the l i p i d chains. Using the same formalism of the previous section, the relaxation rate R n of the -CH2 group i n the n t n position of the hydrocarbon chain i s assumed to be a function of several thermodynamic variables Qj Since a l l the relaxation rates i n t h i s work were found to have an acti v a t i o n energy, i t would bei more convenient to consider log RQ instead of R n (since the ac t i v a t i o n energies a* proportional to (31og Rn/31/T) and are independent of temperature) . A d i f f e r e n t i a l change i n log R n i s then given by I f the same assumptions of the previous section are made i . e . the only independent thermodynamic parameters that have to be cons- idered are the temperature and water concentration then 9 reduces to [9] [10] where 3 = - From (10) we immediately obtain 3 79 A l l the p a r t i a l derivatives on the right of equation (11) are obtained from the NMR results except for (3C/33) A which i s readily obtained from the equation of state and i s given by \ 3B/A \ 38/C/ \dC /3 = T 2 C I dAo [12] P A dT o Substituting 12 into 11 gives 31°g M = f ^ i M , T2_C I ^ / 3 logJR^X 33 /A \ 33 /C P AodT \ 3C / 3 In 13 we i d e n t i f y {^\°^ ^ k a n d {^^~~^)c b y a c t i v a t i o n energies (E ). and .(E ) r and. 13 becomes. ( Ean }A - <%m>C * P A Q d T \ 3 C /g L 1* J where E a n i s the activation energy for the relaxation process fo'r the deuterons on the n t n position of the hydrocarbon chain. Analysis of the re s u l t s . In order to test for the s e n s i t i v i t y of the dynamical state of the hydrocarbon chain on the different thermodynamic parameters we examine the following r a t i o ( y 2 C . 1 . ̂ 0 f 3 log *n) r 1 5 l ( Ean }A = * P A 0 dT V 3 C / ft L J (Ean)c (^an)c The quantity ^3 log ̂ n\ was obtained from the dependence of \ 3 C /8 the relaxation rates on water concentration. (E„n)-, was obtained from 80 semilog plots of versus - for each position on the chain. Fig. 27 shows ( E a n ) A / ( E a n ) c for the dif f e r e n t positions on the hydrocarbon chain. This r a t i o i s greater than 1. for the f i r s t few positions but tends towards unity i n the centre of the b i l a y e r . ,This result i s somewhat s i m i l a r to those obtained for the order parameters. Near the polar head i t i s the lipid-water i n t e r a c t i o n that controls the dynamics of that part of the chain but i n the centre of the b i l a y e r i t i s chain chain i n t e r a c t i o n that i s the c o n t r o l l i n g factor which i n turn i s dependent on the available area per polar head. 81 2 (3,4) (5,6) 8 10 12 n ( C A R B O N N U M B E R ) Figure 27. Ratio of the act i v a t i o n energies f o r the chain deuterons at constant surface area per polar head to that at constant water concentration. 82 Error Analysis In estimating the error associated with the various V n V 3 T A v n V 9 C .... . u • . * , I* i , ••• etc, the standard quantities — [ — ^ — formula for c a l c u l a t i n g the error i n a function f of several variables Xj was used, 2 2 6 X j where e i s the error i n f and 6Xj i s the error i n Xj . I t should be noted that only the errors i n the quantites obtained from the NMR / 3v n\ /3v n \ measurements such as \"g"Y"/ a \3~C~ / **' e t c » w e r e included i n C T computing the error i n the derived quantities where the equation of state (eqn. 5 ) was used. This was done because errors a r i s i n g from the use of the equation of state ( i . e . error i n p, A , dAo ) as dT determined by X-rays are propagated only i n a systematic manner. This i s i l l u s t r a t e d i n f i g . 28 where as an example the value of _1_ dAo P A 0 dT has been increased by 1 standard error i n c a l c u l t i n g the quantity 1 / H i \ — ^ -jpjT J . As can be seen from the comparison of figures 22 28 such errors only s h i f t the whole family of curves without changing the q u a l i t a t i v e v a r i a t i o n with n and T. 83 • • © 8 6 °C A A A 105°C o12 5°C — o A ° A « A 1 3 5 ° C - A — 4 A 1 A O ' '•"» A • A O — A • 1 i i l l 1 1 1 • I (3,4) 6 8 n ( C A R B O N 10 12 NUMBER ) Figure 28. Effect of systematic errors due to the X-ray measurements on the f r a c t i o n a l v a r i a t i o n of the quadrupole s p l i t t i n g s with temperature keeping the area per polar head constant. The parameters P, A b and dAe/dT obtained from the X-ray measurements have been increased by 1 standard error. A comparison of the data shown above with those of f i g . 22 shows that the eff e c t of th i s systematic error i s to s h i f t the whole family of curves without changing the q u a l i t a t i v e variation with n and T. 84 Chapter 7 Spin-Lattice Relaxation between Water Protons and L i p i d Protons In the previous chapters i t was found out that water does play an important role i n the ordering of the hydrocarbon chains within the bi l a y e r v i a hydrogen bonding with the polar heads. The remaining question to be answered i s : does water penetrate into the b i l a y e r and i f so how deeply? In an attempt to answer th i s question, the eff e c t of iso t o p i c modification of the methylene hydrogen n u c l e i on the proton s p i n - l a t t i c e relaxation rate i n H2O and also of the eff e c t c" the isotope modification of the water on the methylene protons on the hydrocarbon chain was studied. 7.1 Analysis and Discussion of the H2O r e s u l t s . Fig. 17 on page 51 shows the temperature dependence of ̂  for the protons i n H 20 i n d 2 3C 1 2~Na/6H 20 , (3-w)d 2 1C 1 2-Na/6H 20 and d^C^-Na^R^O , where the f i r s t sample contains no methylene protons, the second has -CH2 groups only i n the a-position and the t h i r d has protons a l l along the hydrocarbon chain. The subscript on the d indicates the number of deuterons on the hydrocarbon chain. I t can be seen that for a l l the temperatures studied, the relaxation rate ^ for the H 20 protons increase with increasing number of protons. This r e s u l t indicates that the dipolar interactions between the -CrL, and H 20 protons contribute appreciably to the relaxation rate of the protons i n the R̂ O V t This work was done i n collaboration with Dr. A.L. Mackay and professor M. Bloom. 85 In fact the increase i n the relaxation rate of the H2O protons A ( i ) i n the d sample due to the -CH2 protons and the increase i n r l _ C H 2 0 l the relaxation rate of the R~0 protons A ( — — V i n the doi sample due to the a-CH2 protons were found to be i n the r a t i o R - ^4^CH* " 6 W A ( f 1 ) a - C H 2 As discussed i n the t h e o r e t i c a l section, the contribution to the relaxation rate due to dipolar interactions between a pair of spins i s proportional to r - ^ for two spins at a fixed separation r . I t would appear, therfore, that i n order to account for the large contribution to \ of the HoO protons due the l i p i d protons far from the l i p i d water 1 interface, appreciable penetration of the b i l a y e r by H 20 molecules would have to be involved. However, a detailed t h e o r e t i c a l analysis (M. Bloom private communication) shows that this experimental result can be accounted for without invoking deep penetration of the water i n the b i l a y e r . The mathematical d e t a i l s of t h i s analysis are rather lengthy and w i l l not be presented here. Only the results and a description of the model used and the d i f f e r e n t assumptions made w i l l be discussed. The Model. Fig. 29 shows a schematic representation of the d i f f e r e n t s p a t i a l regions of the water and l i p i d separated by a plane at the l i p i d - water interface. The relaxation rates are proportional to the spectral density 86 Region 1 (water region) Region 2 ( l i p i d region) Region 2 ( l i p i d region) Region 1 (water region) 1 Figure 29 . Schematic representation of the different s p a t i a l regions i n which a spin of type l ( a water proton ) and a spin of type 2 (a l i p i d proton ) move. The position of the two spins i s s p e c ified by the space cordinates {z,p ,<f> , £ } i n a coord- inate system having the z axis normal to the planes separating regions 1 and 2 . L j i s the thickness of the water layer,L2 i s the thickness of the l i p i d b i l a y e r , I i s the thickness of a proton layer i n i n the l i p i d region , d g i s the lamellar repeat spacing and d i s the distance of closest approach between spins 1 and 2 . Note that z + £ , p, <J> are the r e l a t i v e positions of the two spins i n c y l i n d r i c a l cordinates. The cordinate <J> i s not shown i n the diagram. 87 functions of the s p a t i a l part of the dipolar i n t e r a c t i o n between the two spins d i f f u s i n g i n the different regions. These spectral density functions are the Fouler transforms of the c o r r e l a t i o n functions defined by G m(T) = / Y 2 m ( r 0 ) Y 2 m ( r ( t ) ) \ ^ r 3 ( o ) r 3 ( t ) / [2] where the Y2m's are the spherical harmonics of order 2. The following assumptions are made i n t h i s model: 1) A spin of type 2 (a proton on the hydrocarbon chain) has a uniform p r o b a b i l i t y of being i n any of the regions of volume 2 and i s given by r pdpdfldg , d<C<d+& L2-d-i<l Q otherwise P 2(p, <j>, O = =<(' A£ ' ' 2-d-£<£<L2-d A spin of type 1 (a water proton) w i l l have a uniform p r o b a b i l i t y of of being i n any of the regions of volume 1 dz 0<Z<L. p 1 ( z ) d z = <; L j O otherwise 2) The conditional p r o b a b i l i t y that the two spins are i n the po s i t i o n specified by the space coordinates Z,p,<{>,£ at time t , knowing that they were i n the position s p e c i f i e d by Z0,P0»<l>o ?o a t t i m e z e r o i s given by. • ' ' - P(p,<j>,C ,z,t;p0,<J>0,C0,ze) = P(C,?0,t)P(p,4.,p0,4>o»t)P(z,z0,t) [3] where P(C,C 0,t) = 6(C-C 0) ' 88 and i s equivalent to assuming that type 2 spins do not move perpendicular to the b i l a y e r , P C P . ^ . P Q . ^ Q ' O i s the solution to the two dimensional d i f f u s i o n equation with a d i f f u s i o n coeffiencient DH = D l + D2 | ( M given by the sum of the d i f f u s i o n c o e f f i c i e n t s of spins 1 and 2 p a r a l l e l to the plane of the b i l a y e r and P ( z , z 0 , t ) i s the solut i o n to the d i f f u s i o n equation characterised by a di f f u s i o n c e f f i c i e n t Dj_ for the d i f f u s i v e motion perpendicular to the plane of the b i l a y e r with r e f l e c t i o n s at the Z=0 and Z=L^ boundaries. Mathematical procedures f o r P(p,(j>,p0,<|>0,t) and P ( z , z Q , t ) can be found i n ( 4 4 ) . We f i r s t consider some l i m i t i n g cases which are never met i n practice but nevertheless w i l l give some insig h t into the nature of the problem. In a l l of the cases that w i l l be considered the short 2 2 correlation time l i m i t (oariT«l) w i l l be assumed. The experimental u c result that r a t i o of the relaxation rates of the 0C-CH2 at 90 MHz and of the 01-CD2 at 13.8 MHz are i n the r a t i o of the coupling constants squared (see chapter 2 ) together with the fact that the relaxation rates decrease with increasing temperature support t h i s assumption. Case i : A l i p i d b i l a y e r of i n f i n i t e extent i n contact with an i n f i n i t e reservoir of water. This corresponds to the case where Lj»d . The spins of type 1 (water protons) are assumed to have a d i f f u s i o n c o e f f i c i e n t much greater than the d i f f u s i o n c o e f f i c i e n t of the l i p i d . ( D j j > 10 D2y ) and that D j ^ . Under these assumption the spectral density 89 functions at zero frequency (short correlation time l i m i t ) were found to be M where the a m's are normalization constants given by a* = 5/16TT , a\ = 5/24TT , a* = and i s the number of spins per unit volume i n region 2. To calculate the r a t i o R defined by eqn. 1 i t i s s u f f i c i e n t to compare the r a t i o of two J m ( o ) values for &=.8A° and £=9.2A° respect- i v e l y . The two different values of Z correspond to the thickness of the layer of protons i n the d2l and d Q samples and were estimated- from the thickness of the b i l a y e r and the mean area per polar head as determined by X-ray measurements (Appendix B). A value of 5.75 was obtained for the r a t i o R, which i s i n very close agreement with the experimental value of ̂ 6 . However a rough calculation for the absolute values of ̂  , by putting 2A° for d ; 1.73xlO~"5cm2/see for and 2 2 ^ 1 7.08.x 10 /cmJ = •—- for the density of protons i n the l i p i d containing a-CH2,gave results that were an order of magnitude too small (.014 sec*~l as compared with the experimental value of .08 sec-"'" for 01-CH2). The results for t h i s case were insensitive to the r a t i o of D,,/̂ Case i i P a r a l l e l d i f f u s i o n of water molecules i n a f i n i t e water layer. J n(o) 3TTP a 2 m 8 L lD 1 Lo g(—j-) L 2-d-Jl •)! 90 In t h i s case the water molecules are assumed to be d i f f u s i n g i n a f i n i t e region 0 z L^with a constant d i f f u s i o n c o e f f i c i e n t i n the p a r a l l e l d i r e c t i o n , i . e D,^(z)=D|j= constant and D^c 0 . The expressions for the spectral density function are then given by where now the contribution from the successive bilayers has been included. From 6 a r a t i o R=497 was obtained. Again the calculations for the absolute values of ~ gave results that are an order of magnitude *1 shorter than the experimental values (.02 sec--'- as. compared with the ('•> experimental value of .08;sec ). Case i i i Slow d i f f u s i o n of a boundary water layer. In view of the fact that the model i n the previous two cases could predict the correct value for R but gave results that are an order of magnitude too small for the absolute value of the relaxation rates suggests that other mechanisms that could be e f f e c t i v e i n relaxing the water protons should be considered. One such mechanism could be that a small f r a c t i o n f of the water binds to the l i p i d at the w a t e r - l i p i d interface for a long time compared with the correlation times considered here (<~10~^see) and thus would diffuse more slowly than the bulk water with a d i f f u s i o n c o e f f i c i e n t . By incorporating t h i s into the theory the contribution to the relaxation rates from the boundary layer 91 can be shown to be proportional to m ds°b !Cotir(A)-.CotTr(d±^-)4cotTr(y± )-cotTr( Li!^+i) d s dS d s . [9] where a delta function was used for the p r o b a b i l i t y d i s t r i b u t i o n of the bound water layer. In order for t h i s model to predict the correct absolute value for the relaxation rates and also for the r a t i o R , Djj has to be about t h i r t y times less than the measured d i f f u s i o n c o e f f i c i e n t f o r the water (1.73 xlO c n r / s e c ; Appendix C ). A lower l i m i t for Db i s the d i f f u s i o n c o e f f i c i e n t for the l i p i d molecules themselves. The di f f u s i o n c o e f f i c i e n t of the l i p i d chains i n the l i q u i d c r y s t a l phase of potassium laurate ±s^2.^Xl6^ cm2/sec(45)-As far as we know the d i f f u s i o n c o e f f i c i e n t of the l i p i d molecules i n the sodium laurate- wacer system has not yet been measured. Such a measurement, together with the measurement of the d i f f u s i o n c o e f f i c i e n t of H2O as w e l l as the relaxation rate as a function of i t s concentration should be useful i n formulating a successful theory. From the preceeding analysis i t seems that the question of whether water does penetrate into the b i l a y e r or not remains to be resolved. However, the r a t i o R=6 does not imply water penetration. Further th e o r e t i c a l and experimental work i s required to resolve t h i s problem. I t should be noted that information on the extent of water penetration into the b i l a y e r can also be obtained from neutron d i f f r a c t i o n 92 measurements. Buldt et a l (37) have recently reported some measurement on a phospholipid water system where they conclude that water penetrates into the b i l a y e r up to the glycerol backbone of the l i p i d molecules. E a r l i e r measurements by Schoenborn on a s i m i l a r system did not have s u f f i c i e n t resolution to detect such water penenetration. 7.2 CC-CH2 Results The temperature dependence of the relaxation rate for -̂ CR̂  i n the d2j-laurate for two samples containing R̂ O and D2O respectively i s shown i n f i g . 16 on page 50 . There i s a measurable difference i n the CA-CH2 relaxation rates for the two samples, i n d i c a t i n g the influence of the dipolar i n t e r a c t i o n between the H2O protons and OC-CH2 protons. The fact that the a-CH2 protons and the H 20 protons s t i l l have d i s t i n c t T^ values when they interact with each other excludes the p o s s i b i l i t y of long correlation times for the dipolar i n t e r a c t i o n between the -CH2 protons which would otherwise bring the two spin systems to a common temperature. Short c o r r e l a t i o n times for the dipolar interactions between H2O and CV-CH2 protons are expected because of rapid d i f f u s i o n of water and also of the hydrocarbon chains. The model used to interpret the rela x a t i o n of the H2O protons due to the dipolar interactions with 1 the l i p i d protons can also be used to calculate the relaxation rate of the l i p i d protons due to the same inter a c t i o n . Denoting the number of H2O and -CH2 protons by and NB respectively, the model assumes each of the A spins to be equivalent and independent of each other and the same f o r each of the B spins. I t i s then easy to show that for small perturbations to the s p i n - l a t t i c e 93 relaxation rate of the A system (H 20) , A(1 / T 1 ) A i s related, to that of the B system (CH2) by / M " l ^ ' ~ N B R = " ~ % since the gyromagnetic ratios and spins of the A and B systems are exactly the same. For the d 2 i sample used here NB/N A = 1/6 . In a previous publication ( 46 ) we have reported a value for R of .. 6 ± . 3 which was the average value calculated from the data of figures 16 and 17 over the temperature range 80-115 °C . I t was i n i t i a l l y argued that t h i s large discrepency could not be at t r i b u t a b l e to sample differences or systematic errors i n the experiment. This argument was based on the fact that the measured deuterium quadrupole s p l i t t i n g s f o r the (3-u) positions of the d„ C -Na/6H 0 , d C -Na/6D 0 and 21 12 2 21 12 2 d C -Na/6H 0 were found to be i d e n t i c a l , implying that the hydrocarbon chains have the same f l e x i b i l i t y gradient and therefore i t would be un l i k e l y that the molecular motions which cause s p i n - l a t t i c e relaxation i n each of the samples are appreciably d i f f e r e n t . Since t h i s paper was written we have made a c r i t i c a l estimate of the relaxation data which has led us to the conclusion that the difference between the experimental and predicted values of R may not be inconsistent with each other within the experimental error. From figures 16 and 17 the measured values of R* are shown i n table 1 for several temperatures. In the high temperat- ure region i t i s d i f f i c u l t to make any conclusions about t h i s r a t i o due Temperature (*C ) 120 115 105 90 80 Table. (1) Ratio of the change i n of H2O protons due to a-protons ti the a-protons due to the water pr< / R 2.6 + 2.2 1.0 + .7 .7 + .3 .6 + .3 • k ± .1 the spin l a t t i c e relaxation rate rate < the change of the relaxation^of tons i n d2]C-Na/6H20 . 95 to the large uncertainties involved. At lower temperatures this r a t i o i s almost twice the predicted value of J_ within the experimental 6 uncertainties. These large uncertainties a r i s e mainly from the fact that A[ -j- ) and A( ̂  ) are obtained by subtracting large number of comparable magnitudes. Moreover systematic errors i n the T^ measure- ments cannot be exluded. In view of the large uncertainties i n It'we believe that further experimental work i s needed. Such work should involve experiments where the contribution to the spin l a t t i c e relaxation rates due to the i n t r a molecular dipolar interactions are reduced. For the 1^0 molecule the i n t r a molecular dipolar interaction between the two protons makes an important contribution to s p i n - l a t t i c e relaxation: The proton Tj f o r HDO i n D20 i s much longer than that for D20 . Therefore the contribution of the intramolecular dipolar interaction to the water relaxation can be eliminated by carrying out experiments analogous to those described above using samples which contain a small amount of HDO i n D20 . A study of R.' for higher values of should also be carried out, since t h i s would give a larger effect which would be e a s i t r to measure. I t should be noted that the value of NB/NA predicted by the model calculations for R does not take into account the correlated motions of the two CH2 protons. General coupled equations for an AB 2 system are available, for example (47,48 ). The parameters thereby introduced maybe examined by measuring quantities such as the dipolar relaxation of the CH 2 spin system (49 ) or by the equivalent methods of " s e l e c t i v e inversion recovery" ( 50 )• Summary and Conclusions The flow chart shown below summarizes the areas of inv e s t i g a t i o n i n the thesis and the conclusions reached. PROBLEM: To understand the lipid-water i n t e r a c t i o n How deep does water penetrate into the b i l a y e r 7 i QUESTIONS How does the lipid-water i n t e r a c t i o n influence the conformations and motions of the l i p i d chains ? F l u i d i t y of the b i l a y e r NMR relaxation measurements of H.O and l i p i d protons;effeet o f l s o t o p i c modification on the relaxation rates I-Water ( %c a, H 2 0 w i t h H 2 0 w i t h H O w i t h a l l p r o -p e r d e u t - a - p r o t o - e r a t e d n a t e d t o n a t e d c h a i n s c h a i n s c h a i n s - p r o t o n a t d c h a i n s H 2 0 with D 20 (b) (c) (d) (e) Sp i n - l a t t i c e relaxation between water protons and l i p i d protons; Protons deep i n the b i l a y e r make a substantial contribution to the spin l a t t i c e relaxation rates; Theoretical analysis accounts for the results without Invoking deep penetration of water In the b i l a y e r . -{ NMR experiments}- 1 S p i n - l a t t i c e relaxation —>Information on the dynamics of the l i p i d chains l/T J n(C,T) The nnodynamic V n < C , T ) a n a l y s i s Spectroscopy Quadrupole s p l i t t i n g s — ^ I n f o r m a t i o n on the ordering of the l i p i d chains,water'(D20) and counter ions Perdeuterated chains D 20 2 3Na Correlations.empirical evidence for a lipid-water Interaction The lipid-water Interaction has a strong Influence on the conformations and motions of the l i p i d chains Microscopic model f o r the llpld-water interaction V A description of the state of the b i l a y e r e n t i r e l y i n terms of chain-chain Interactions ,as done i n e x i s t i n g theories,Is not complete. A complete theory should include the l i p i d water Interaction e x p l i c i t l y . APPENDIX A Chemistry and Physics of Lipids 20 (1977) 115-129 ©Elsevier /North-Holland Scientific Publishers, Ltd. THE TEMPERATURE DEPENDENCE OF WATER AND COUNTER ION ORDER IN SOAP-WATER MESOPHASES. A DEUTERIUM AND SODIUM NMR STUDY* K. ABDOLALL, E.E. BURNELL3 and M.I. VALIC Department of Physics and Department of Chemistry", University of British Columbia, Vancouver, B.C., Canada, V6T1W5 Received January 3, 1977 accepted March 23, 1977 Deuterium magnetic resonance ( D M R ) spectra o f the water and hydrocarbon chains in potas- sium and sodium palmitates and sodium magnetic resonance spectra of sodium in sodium palmitate demonstrate correlations between water, hydrocarbon chain and counter ion order. In the lamellar phase of potassium palmitate the order parameters inferred from D M R splittings of D , 0 and the first few methylene chain segments initially increase and then decrease with increasing temperature. This is explained in terms o f a model where the lipid-water structure at low temperatures imposes a direction for which all the order parameters are smaller than for the higher temperature structure for purely geometric reasons. As temperature increases the structuring effect of water decreases and there is an "apparent" increase in order until at even higher temperatures there is an intrinsic decrease in order parameter. In addition, for potassium palmitate the D M R splittings of D , 0 and the first few methylene segments indicate a "phase transition" within the l iquid crystalline phase. I. Introduction In order to understand the role played by water near biological membranes, it is essential to understand the mechanism of lipid-water interaction. In the presence of water, lipid molecules form a variety of lyotropic mesophases characterized by the existence of long range order and short range disorder. These phases have been identif- ied by X-ray studies [1 ], nuclear magnetic resonance [2,3] and other techniques [4]. Their description has received considerable attention in the literature [5] and will not be elaborated on here. Of particular interest are the three lamellar phases: liquid crystal (L a), gel (L^) and coagel. In these phases the soap molecules form bilayers which are stacked parellel to one another and separated from each other by water and counter ions. In the L a phase the chains are flexible (melted) and the soap molecules undergo rapid lateral diffusion and rotations abcu» their long axis, while in the lower tempera- * Research supported by the National Research Council of Canada and a special Killam-Canada Council Interdisciplinary Grant. US A'. Ahdolall el al.. NMR studies in potassium ami solium palmilales lure 1.0 phase (he chains arc slil'f(frozen), fully cxlcndcd, lightly packed, and interdig- ilaled. In the cnagcl phase Ihc lamellar structure is relained but waler is squeezed out into pockets of hulk or "lice" waler. To obtain infoiniation about ilic ordering of cither the water at the lipid water interface or the lipid molecules within the bilayer, it is necessary to use microprobes that are sensitive to their local environment as well as to the dynamics of the system. Interactions between nuclear quadrupole moments and the electric field gradients arising from the surrounding charges affect the NMR spectra in a dear-cut way and enable such information to be obtained. From such studies there is considerable evid- ence that water near model and biological membranes possesses significantly more strucluic than bulk water |(>|. This is paper III of a series of three papers on the NMR of soap water mesophascs. Paper I | 7 | discusses hydrocarbon chain disorder as observed using DMR, and paper II | 8 | discusses the proton magnetic resonance (I'MK) from potassium palmitate (/}Lo)-dj». In this paper, results as a function of temperature of an NMR study of waler,sodium counter ion and hydrocarbon chains in potassium and sodium palmitates are reported. In particular, we demonstrate a striking correlation between the ordering of water and the first few methylenes of the hydrocarbon chain. An explanation for this correlation in terms of a simple model is given in section IV. We also report a new - fluid fluid "phase transition" within the lamellar phase of a potassium palmitatc-water system. This ttansition manifests itself in the order parameters of the water and the methylenes near the polar end of the hydrocarbon chain. II. Experimental Palmilic(C| 6)acid was purchased from Hormel Institute or Calbiochem (California), and was used without further purification. Dcuterated compounds were prepared in our laboratory. The fatty acid salt was prepared by dissolving in ethanol stoichiometric amounts of dry fatty acid and sodium or potassium hydroxide, and slowly crystallizing the fatty acid salt. After filtration and washing with ethanol the precipitated soap was dried at I00°C under vacuum for several hours. The soap-water mixtures were made by weighing the corresponding amounts of dry soap and D 2 0 or HjO into a glass tube and scaling under dry nitrogen gas. For the sodium soap a quartz tube was used. The samples were mixed by ccntrifuging back and forth through a constriction in the tube. Before each cenlrifugation the samples were heated well above the gel-liquid crystalline phase transition temperature. Further homogenizalion was accomplished by leaving the sample in an oven for several days at a temperature above its gel-fluid phase transition. It was found that the variable temperature unit (gas flow system) suppled with the spectrometer was not adequate when dealing with soap-water mixtures. Therefore, a temperature controlled oven (paper 1) with greatly reduced temperature gradients in the sample was constructed and used for the measurements. K. Abdokll el al., NMR studies in potassium and sodium palmilales 117 The NMR measurements were carried out on a Bruker SXP 4-100 pulsed NMR spectrometer. The quadrupole splittings were obtained using the quadrupolar echo by the method of Davis et al. | 9 | . 111. Results ^The interaction between nuclear quadrupole moments and electric field giadients efg at nuclei gives rise to splittings in deuterium and sodium magnetic resonance spectra. For water deuterons chemical exchange takes place between nuclei in different sites and. if the exchange is much faster than the splitting difference, the observed splitting is a weighted average over the different sites |10] .For an oriented sample, where the normal n to the bilayer makes a uniform angle f l with the magnetic field direction, the high field deuterium (or sodium) NMR spectrum consists of two (or three) peaks separated by A v = l £ PiK)iSj (3 cosJ a- 1) I (I) where p, is the fraction of nuclei occupying site i with associated quadrupole coupling constant VQ and order parameter Sj (discussed more fully in paper II). For an axially symmetric efg. S t is given by Si = 3/2cos J i J j -1 /2 , (2) where i>; is the angle between n and the efg principal axis and the bar denotes a time average. Hq. (I) can be applied to (he case of hydrocarbon chain and water deuterons and counter ions. However, there are differences among these three cases. For example, all hydrocarbon chain C D 2 deuterons are chemically equivalent and will therefore have the same I>Q, . Furthermore, since I>Q is of intramolecular origin ( C - D bond) it is not expected to vary with temperature. Consequently, the splittings Ai> yield order para- meters directly. If the efg is axially symmetric about the C - D direction, ^ equals S Q J , the order parameter for the bond direction. The case of water and counter ions is more difficult because p j r I*Q and Sj may all differ from site to site, hence the separation of the various terms in eq. (I) is not possible without assumptions. For DjO the largest contribution to I>Q is from the intramolecular 0-1) bond, and its value is close to that for ice. Therefore, all fg . are similar and are not expected to vary significantly with temperature. The measured splittings are thus roughly proportional to an average order parameter S = ?P,S,, enab- ling a qualitative comparison of the experimental Ac with model calculations. Also, we do not expect p; to vary greatly with temperature in the narrow temperature region of interest, and hence the temperature dependence of the observed splittings reflects mainly changes in order parameter. v© 118 K. Ahdolall ttal., NMR studies In potassium and sodium pahnltates In contrast, theefg at a counter ion (e.g. sodium) nucleus arises from intermolccular sources (polar head group changes and water dipoles, i.e., via the asymmetric distribu- tion of waters of hydration). Therefore, one expects to have a distribution of fy (as well as pj and S,) which can be quite temperature dependent, thus making the inlcrpre- tation of Av in terms of definite order parameters rather difficult. However, should the counter ion splittings correlate with those of hydrocarbon chain and water deuterons then llie temperature changes of counter ion Av should give an indication of changes in order parameters. It will be shown that this is the case for the sodium splittings of perdeuterated sodium palmitate dC 1 6 Na. A. Potassium palmitate Non-oriented samples yield essentially the same information as oriented samples. For an unoriented sample there is a random distribution of all values of and the deuterium magnetic resonance spectrum (see fig. I for representative half spectra) consists of a broad absorption curve with major peaks separated by Avj2 (paper I and Bloom el al. (111). The spectra of fig. I show"the presence of residual quadrupolar splittings indicating that the water molecules are located in an anisotropic environment in which they experience non-zero time averageikelectric field gradients and are said to be partially oriented. The anisotropy is imposed by the presence of the interface and the charge distribution near it, as well as by the hydrogen bonding of the water mole- cules and hydialed ions with the polar heads. For the liquid crystalline (fig. I a) and the gel (fig. lb) phases the D 2 0 deuterium spectrum is the usual "power doublet", the Fig. 1. Representative half spectra for D , 0 In C„K In (•) lamellar phase, (b) gel phase and (c) mixture of ge! and coagel phases (see text). K. Abdolall tt al., NMR studies In potassium and sodium pclmilalet 119 TEMPERATURE ("CI TEMPERATURE l"C) Fig. 2a.The temperature dependence of the D , 0 and hydrocarbon chain deuteion quadrupole splittings for a perdeuterated, d C „ K sample. In this case the splittings were measured from the centre to the corresponding peaks in the absorption spectrum. It should be noted that the experi- ments reported in Fig. 2a were performed to study lipid-water correlation effects, and that the signal to noise ratio was not as good as that for the spectra reported in paper 1. Quantitative diff- erences in the CDj order parameters between Fig. 2 and paper I should therefore not be taken seriously. Fig. 2b. Temperature dependence of the quadrupole splittings of D , 0 and a-CD, in the perdeuter- ated d C l t K sample. The insert is the temperature dependence of the D , 0 splittings in a protorutcd C, ,K sample. lower temperature spectrum of fig. lc contains in addition a central peak due to the isotropic "bulk" (free) water squeezed out from the water layers of the lamellar phase. This isotropic water is indicative of a coagel phase, and, in principle, the number of water molecules associated with different phases can be determined from NMR inten- sity measurements. It is likely that fig. Ic is a spectrum of a sample containing a mix- ture of gel and coagel phases. Alternatively, this spectrum could represent different phase separation zones within the gel region. More work, including X-ray studies, i i needed for a complete understanding of soap structures in the solid phase. The quadrupole splittings, Av, as a function of temperature for the water deuterons as measured from spectra similar to those in fig. I are shown in fig. 2 for perdeuterated potassium palmitate dC,„K. The splittings are appreciable in the low temperature coagel and gel phases and the sudden decrease in splitting denotes the coagel or gel to liquid crystalline phase transition. This decrease may be due to lesser intrinsic order of the - ) 120 K. Abdotatl et at., NMR studies In potassium and sodium palmitate* water at the lamellar surface, changes in the average direction of water ordering, and reduction of long-range order throughout the water layer. As shown in fig. 2 the splittings for DjO as a function of temperature in the liquid crystalline phase increase with temperature at first, exhibit a maximum between 70— I00°C. and then decrease. The deuterium splittings of the chain deuterons were also measured as a function of temperature. The results, shown in fig. 2a, indicate that the splittings of the first few methylene pairs exhibit a temperature dependence similar to that of D 2 0 . This suggests a strong correlation between the ordering of the water mol- ecules and the first few links of the hydrocarbon chain. A model explaining this correl- ation will be discussed below. The results in fig. 2a at ~ 50-60°C indicate a discontinuity in the splittings which is ascribed to a liquid crystalline-liquid crystalline "phase transition". The discontinuity occurs only for the water and the first several CD 2 ' s of the hydrocarbon chain and is thus suggestive of changes in the lipid-water structure and possibly a conformational change in the hydrocarbon chain near the lipid-water interface. Since this transition is a new phenomenon, the experiment was repeated and the temperature was -iried in smaller intervals. The results for the o-CDj and DjO are displayed in fig. 2b. The insert in the same figure shows the results for a protonated C , 6 K sample. It is clear that the Fig. 3a. Spectra taken at three different temperatures showing the D , 0 splittings near the "fluid- fluid" phase transition in the dC„K sample. The two smaller peaks are due to -CD, groups. The shoulders of the D,0 signal are also visible. Fig. 3b. Representative half spectra at three different temperatures for the perdeuterated dC„K sample showing the water peak and the peaks due to the methylene pairs on the hydrocarbon chain. The right hand part of the spectra is expanded vertically 16-limes. The arrows Indicate the splittings from the a-CD,. K. Abdolatl tt at., NMR studies In potassium and sodium palmitates 121 fluid-fluid transition occurs at somewhat different temperatures in different samples; these differences may be due to sample preparation techniques and/or to isotope effects. Representative spectra for D 2 0 and chain deuterons of dC„,K in the region of this fluid-fluid phase transition are shown in figs. 3a and b. These spectra show the water line (fig. 3a) as well as the lines due to all chain deuterons (fig. 3b). Note thai the or-CD2 and the D 2 0 lines are each split near 50°C indicating the co-existence of two fluid phases. (See also the results of paper 1 where the a-CD 2 splitting is more clearly shown, and paper II). B. Sodium palmitate Sodium has a nuclear spin of 3/2 and the high field NMR spectrum for an unoriented sample is similar to that for deuterium with two major peaks separated by Ac but in- cludes a sharp orientation independent central line (if chemical shift anisotropy is neglected); fig. 4 is a plot of the quadrupole splittings of D 2 0 , " N a counter ion, and chain deuterons as a function of temperature for dC, 6Na. As seen in fig. 4 the temper- ature dependence of the Na, D 2 0 , and first several CD 2 exhibit the same slope which demonstrates a definite correlation between the water, " N a counter ion and the first few hydrocarbon chain segments. All of these splittings decrease less rapidly with tem- perature than those from CD 2 ' s near the methyl end of the chain; this agrees with pre- dictions of the Marcelja mean field calculations for chain order parameters [12] be- 10 i W i •op I I I 100 110 120 OO TFMPF.RATURE (*C ) Fig 4 Temperature dependence or the quadrupolar splittings for D , 0 . " N a counter ion and deuterons on the hydrocarbon chain in a dC,.Na sample. (The C,. results were obta.ned from a H,0 * dC„ Na sample because the -CD, line overlaps with that of D , 0 making the separation or the two very difficult.). 122 cause increased temperature yields increased area per polar head and decreased lateral pressure. In contrast t o C l t K no fluid-fluid phase transition is detected,and no increase in splittings with temperature is observed in the lamellar phasefor the DjO, Na* or CDj's. Below the coagel-lamcllar phase transition temperature (~ 83°C), we were unable to observe quadrupolar split lines for Na' or D , 0 . contrary to the case for d C ) 6 K . Only central Na* and D 3 0 lines were observed. Further work is needed on this phase. IV. Discussion Water exists as various hydrogen bounded structures, and also interacts with the polar head groups of fatty acid salts via hydrogen bonding and other electrostatic in- teractions. These phenomena give rise to structuring effects: i.e. lipid and water struc- tures mutually affect each other (13]. The details of such an interaction have not been included in many of the theories [12, 14] which attempt to explain hydrocarbon chain order parameters. The interaction between lipid and water is demonstrated in a particularly interesting way by the results of this and papers I and II which show that the NMR splittings of DjO, a-Cllj , a-CDj and the first few CD2's of the alkyl chain for the lamellar fluid phase of C | S K all increase with temperature to a maximum value, and then slowly decrease (figs. 2, 3 of I and fig. 2 of II). In general, such an increase in splitting might be though of as an increase in order. However, this is not necessarily true; a strong interaction between lipid and water might well impose a constraint where all the observed order parameters (eq. (2)) are small for purely geometric reasons. A decrease in the strength of this interaction at higher temperatures could lead to larger observed values of S even though the system may be inherently less ordered. To dem- onstrate how such ideas lead to new information about lipid structure and lipid-water interaction, we present here a simple model which explains qualitatively the results of this and the preceding two papers. A. A model consistent with the experimental results of papers Our model proposes two rapidly (compared with NMR splittings) interchanging configurations, A and B, for the lipid-water interface [15]. The main idea here is that at lower temperatures (configuration A) the lipid-water interaction imposes ordering effects near the polar head region. In particular, the first C - C bond is more or less normal to the interface leaving the tail on the average somewhat tilted. At higher tem- peratures (configuration B) the lipid-water structuring effects are reduced and the dominant steric interaction imposes lipid ordering such that the chain is more or less parallel to n, the normal to the lamellar surface, leaving the first C - C bond at an angle to the surface. The two configurations are now described in more detail. 1. Configuration A As an example, suppose that at low temperatures a lipid-water structure similar to 123 Fig. 5. Model for the lipid-water Interfac* 1A\ B ^ • B) P-domta . , , c o n n p u r a t l o n ' * ^ > a C T T ^ " " ' ' 0 " " l o w " m ' ™ ' u " - '•on, with one puch* rotation are .hownTn a1,1 ?' l " confo'°»<™ «* conform.- See text To, further e x p i a t i o n . " " , h e ° " C H . 'HH '» Perpendicular to n. 124 K. Ahdotall et al. NMR studies in potassium and sodium palmltates that shown in fig. 5a (where two of the molecular conformations of the first five car- bons are shown) is energetically favoured. For this configuration: (i)The first C - C bond vector r c f . is aligned at some angle to n, such that for the o>CII} both the proton-proton vector r ( l ( | and the carbon-deuteron vector r c n make an angle some- what less than 00° with n. (For simplicity the diagram shows the first C - C bond par- allel to nr. a tilt out of the plane of the paper must be introduced to explain the Q-CHJ results), (ii) The average environment of the water deuterons (and of the sodium coun- ter ions) are such that their principal elg axes make angles with n giving average order parameters which are smaller than those for configuration B. The diagram is drawn with the water deuteron-deuteron vector r D D perpcndicrhr to n and the bisector of the angle DOD parallel to n. 2. Configuration B At higher temperatures the extra thermal energy allows fewer hydrogen bonds lead- ing to a decrease in the lipid-water interaction. As an example we suppose (fig. 5b) that the long axis of the hydrocarbon tail for the all-trans conformation lies along n such that for the a-carhon both r ( p and are perpendicular to n. This configuration should lead to minimum free energy if hydrocarbon intermolecular interactions are dominant. For the purposes of illustrative calculation we allow isotropic rotation of DjO about the hydrogen bonded OD bond shown in fig. 5b. Two lipid molecular con- formations are shown. B. Simple calculations based on the model To illustrate the effects of different structures on the observed NMR splittings, we have listed in table I calculated values of the various order parameters (eq. (2)) for each of configurations A and B. The a-Crl^ has not been included in this simplified model; however, similar qualitative results will obtain for all order parameters (includ- ing cr-CH)) if the first C - C bond makes some appropriate angle with n. The values in table I are averaged over the various molecular conformations of the hydrocarbon chain. The following assumptions have been made for the calculations: (i) All CCC and.CCD angles are tetrahedral. For water, angle MOM is 105°. and the angle between lone pair electrons is 120° (16). For ease of calculation, conformer rotations of 120° are used rather than the more likely value of 112.5° | I 7 ] ; this does not significantly modify the calculated order parameters, (ii) There arc rapid (at least threefold symmetric) motions of lipids, water and counter ions about n such that the anisotropic interactions are motionally narrowed and the residual projected along n | I0 , 18]. (iii) The average order parameter is given by eq. 2, with 0 being the angle between n and the vector of interest (tIM, T(-n, r 0 0 , q n ) . All efg tensors are assumed to be axially symmetric along the bond directions. For sodium the efg used is Ihat̂ from the oriented water lone pair electrons .with the principal axis q n indicated as efg in fig. 5. (iv)pji (pji) is the probability that the bond between carbons i and j is trans (gauche) to the precedingCj-2-Cj-| bond, with pjJ + 2p'J = 1. K. A bdohtt et al., NMR studies In potassium and sodium palmltates 125 Table I Calculated order parameters2 Configuration A Configuration B 1 1 " 3 * 2 3 F ' 3 V 2 P l D , 0 006 0.15 d efg - i - 0 . 1 8 d "Calculations are averaged over conformations t^i^t^, tafl'M**' W A T S * *ni W&U- I'or A g^j and tQ0 give equal contributions to order parameters. b Assumes that the C - C bond is at an angle 35V,° to n. Motions about C O O - C 0 axis are not con- sidered (i.e. p°f - 0). c For gauche conformation S • Vi (P, cos (90) + P, 00s (35M)) • 0. ''Assumes hydrogen bond parallel to first C - C bond and free rotation about 0. . . . D - 0 axis. C. Discussion 1. . ie lamellar La phase As shown in Fig. 2 (and papers I and II) the experimental order parameters for DjO, or-CHj and the first several CDj's of the hydrocarbon chain in the liquid crystalline phase of CmK increase with temperature at first to a maximum and then gradually decrease. On the basis of ourmodel these results can be explained in the following way. We note that the calculated order parameters (table I) associated with configuration B are all of larger absolute value than those for A. According to the model the observed order parameters are the average over rapid exchange between both configurations, A being favoured at low, and B at higher temperatures. Hence, as temperature is raised we expect the observed order parameters to increase with (he increasing probability of structure B, until such a point that the probability of configuration A becomes small. In addition, with increasing temperature the thermal motions lead to an overall intrinsic decrease of the "molecular" order parameters, as observed for nematic liquid crystals (19). Thus, the model indeed predicts the experimentally observed temperature dep- endence of order parameters. Incidentally, for dC| 6 Na (fig. 4) no increase in order parameters is observed, suggesting that configuration B already dominates at temper- atures just above the coagcl-lamellar phase transition. 126 K. Abdolcll etal.NMR ttudiet in potassium and sodium palmitates 2. "Plateau" The experimental order parameters for -CDj ' s along the hydrocarbon chains in soap-water systems (paper I [7, 20)) exhibit a constant value for the first several —CDj's at low temperatures in the L 0 phase. This observation, referred to as the "plateau" in the literature, is usually associated with the influence of "kinks" [21 ], but it can also be accounted for with the proposed model if the lipid-water interaction in the liquid crystalline phase affects to a progressively lesser extent those CD] groups further removed from the polar head region. Let us assume that there is minimum free energy for the intermolecular forces between hydrocarbon chains when the long axis of the hydrocarbon tail lies along n(a situation facilitating the rapid rotational motions about n in the lamellar phase (10, 18]).For configuration B where, as discussed earlier, the water has little or no ordering influence, the steric forces are dominant. However, for configuration A where the first C - C bond lies along (or close) to n. the long axis of the hydrocarbon tail for the all-trans conformation does not lie along n. Since the influence of the surface becomes progressively less as we go down the chain, the steric forces will tend to align parallel to n, that part of the chain which is further from the polar head. This could involve molecular conformations which are slightly distorted from normal trans and gauche. Thus, the orientation of the molecular axis gradually changes from that of configuration A to that like configuration B, and according to table 1 this corresponds to an increase in the observed SCD- On the other hand,because of the extra conformations available to those carbons far removed from the polar head, a general decrease in order parameters is expected as we go down the chain. Thus, the increase predicted above and the general decrease act oppositely and cancel each other in the region of the first few - C D 2 links leaving a constant value for the SCD as ob- served experimentally. 3. "Odd-even"effect Measured values (figs 2 and 4 of this paper and fig. 3 of paper I) of the order par- ameters Sen at lower temperatures in the L;, phase show that Sjj = Sy > Sa * S e , etc. This applies all along the chain except for those -CDj's near the - C D 3 end where each successive -CD] has lower order parameter. This low temperature behaviour of SCD' S is referred to in the literature as the "odd-even" effect (7, 20]. With increasing temp- erature, the "odd-even" effect is observed to disappear progressively in the tail-head direction until at sufficiently high temperatures each successive - C D 2 has lower order parameter (fig. 3 of paper I shows that all except (J and y peaks have separated at ~90°C). This effect is readily accounted for by our model. Indeed, i f the high energy conformationsg*g* are neglected [17], thenconfiguration A predicts equal values for Sfl and Sj. However, ISjjl and ISy I are also predicted to be smaller than ISQI due to the term 2/3 p^7 (table 1). Similar results would obtain for Sj and S e (if the confor : mation gy5'{ e gf j is neglected), and for each pair of carbons down the hydrocarbon chain to a progressively lesser extent (depending on the probabilities of certain confor- mations for which the order parameters for both members of the pair are different), thus giving rise to the "odd-even" effect. On the other hand configuration B predicts K. Abdolatl etal., NMR studies in potassium and sodium palmitates 127 (table 1) that each successive CDj will have lower order parameter. Hence, as temper- ature increases the experimental ratio Sg/SE increases from the low temperature (con- figuration A) value of 1, where the 6-CD 2 and e-CD2 peaks overlap completely, to a higher value where separate peaks are observed. This is consistent with configuration B becoming more probable at higher temperature. Further down the chain the ratio differs from 1 for all temperatures; this is consistent with the long molecular axis be- coming aligned along n as one leaves the polar region. 4. The gel phase The experimental order parameters for the Q-deuterons and a-protons in the gel phase are of slightly lower value thart-those for other chain deuterons [papers 1,11). Furthermore, the experimental valuesare such that ISHH ' K slightly smaller than ISrjD both being < M. However, in the lamellar phase ISHH I is equal to or slightly greater than ISCD The results for the gel phase can be explained by the model if a gauche rotation near the polar head (between 0- and 7-carbons, say) is invoked. Such a rotation might accomodate more readily the water and counter ion structure and leave the rest of the tail all-trans and roughly parallel to n, hence facilitating a rotation about a symmetry axis m (not necessarily 1 n). As a result, the first C - C bond will be inclined to n in such a way that both TQ) and r i ( H for the cr-position make an angle with n f somewhat less than 90" in agreement with the experimental values ISHH I ~ ISCD V4- Assuming that in the gel phase the soap molecules are rigid and consist of two rapidly interconverting g | j to g^g conformations* and that the only other motion is rapid rotation about m then the results of paper I and II allow the calculation of the angles 0, that various vectors r make with m. The values SQ-CHJ = - u-34 (fig. 5, paper II) gives = 109° for the a-CH 2;the value Sa<:D} = -036 (paper I) in the conjunc- tion with SO>CH2 gives Syy = - 0.40 where y is thehisector of angle HCH. This value of " y y gives Oy = 105°. Using the values for angles CCC = 112°, CCH = HCH = 109° [17) and the result that the value for Sct>, for most of the chain is -0.44 (paper I) leads to a rotation of either 21° or 76° about the Cg-C7 bond for formation of the gauche con- formation. The latter is close to the "most probable" value of 112.5° for the dihedral angle, and distortions from this value are not unexpected [I7J. The above calculations are crude, and a more plausible picture might be a rotation about C^-C-y of somewhat more that 90° followed by rotations of a degree or so in the opposite sense about bonds further down the chain, hence yielding a distribution of order parameters for different CD 2 's as indicated by the results of paper I. The fact that for the cr-position the order parameter SHH is less than SCD in 'he gel phase, while in the lamellar phase S H T| is larger than or equal to Sr-ry, depends on ho-v close to n the first C - C bond lies and on the particular motions involved in the averaging. In general, a hydrocarbon chain, even in the all-trans conformation, has no three-fold or •Cfl-Cy is the closest C-C bond to the o-carbon around which a gauche rotation will leave the molecular axis roughly parallel to m. We neglect other possible fluctuatiunJ or the molecular axis about m in this rigid molecule calculation. 128 K. Abdotatl tt al., NMR audits in potassium and sodium palmltatts greater axis of symmetry, and hence there is no reason to expect that SHU D e equal to SCD (See paper II for further discussion on this point). V . Conclusions This paper has demonstrated that the magnetic resonance spectra of deuterium in water and hydrocarbon chains of potassium and sodium palmitates and of sodium in sodium palmitate indicate correlations between water, hydrocarbon chain and counter ion order. For the lamellar phase of potassium palmitate the order parameters of D a O and the first few methylene chain segments are shown to increase and then decrease with increasing temperature. This has been explained in terms of a model where the lipid-water structure at low temperatures imposes a direction on the first C—C bond for which all the order parameters are small for purely geometric reasons. At higher temperatures the structuring effect of water is decreased and there is an increase in the splittings. Details of the lipid-water structure at lower temperatures may involve con- siderations of a-CH 2 - C O O conformation and complicated hydrogen bonded structures such as two lipid molecules being bridged by one water molecule, and hydrogen bond- • ingof more than one water per lipid oxygen. Also, some water superstructure (possibly tetrahcdral) is likely to persist throughout the water layer. The above qualitative arguments should be checked with a more complete theory, using for example an intermolecular force mean field to account for fluctuations of the molecular axis about n for each conformation. In such calculations the lipid-water interaction should not be neglected and attention should be given to the first C - C bond orientation which might well depend on both conformation and water structure. A fluid-fluid phase transition is detected within the lamellar phase of C , 6 K and involves the water and first several segments of the hydrocarbon chain. This transition may well indicate a change in the water superstructure, or a conformational change fas trans to gauche) near the polar head. The presence of such a gauche conformation in the gel phase is suggested by a rigid molecule calcul:.-ion. Furthermore, these studies demonstrate that NMR is a very sensitive method of detecting different phases and phase transitions in lipid-water systems. Acknowledgements We thank Dr. T.P. Higgs for synthesizing the deuterated fatty acids and for assisting in sample preparation. We are grateful to the authors of papers I and II for careful criticism of our work. We are indebted to Myer Bloom for many fruitful discussions. References | 1 | V. Luzzati, in: Biological Membranes, ed. by D. Chapman. Academic Pre*. N.Y. (1948) K. A bdohtll tt al, NMR studies in potassium and sodium palmltatts 129 (2) A. Johansson and B. Lindman, in: Lipuid Crystals and Plastic Crystals, Vol . 2, ed. by G.W. Cray and P.A. Winsor, Kliss llorwood, Chichester (1974); G.J.T. Tiddy, in: Specialist Periodical Reports on NMR, Vol. 16 (1977) [ 31 B. Mely and J. Charvolin, Chem. Phys. Lipids (in press) | 4 | B.D. Landbionke and D. Chapman,Chem. Phys. Lipids 3 (1969) 304 | 5 | P.G. de Genncs, in: The Physics of Liquid Crystals, Clarendon Press. Oxford (1974) |6] II.A. Rcsing, A.N. Garroway and K.R. roster, in: Magnetic Resonance in Colloid and Interface Science, ed. by II.A. Rising and C.G. Wade, ACS Symposium, 34 (1976) 516 (7| J . l l . Davis and K.R. Jeffrey, Chem. Phys. Lipids 20 (1977) 87 [8] A . L . MacKay and T.P. Higgs, ChJm. Phys. Lipids 20 (1977) 105 | 9 | J . l l . Davis, K.R. Jeffrey, M. Bloom, M.I. Valic and T.P. Higgs, Chem. Phys. Letters 42 (1976) 390 [10} G. Lindblom. N.O. Persson and B. Arvidson. in: Lyotropic Liquid Crystals and the Structure of Biomembranes, Chapter 9, ed. by S. Friberg, Adv. Chem. Set. 1976; H. Wennerstrdm, G. Lindblom and B. Lindman, Chem. Scripta 6 (1974) 97 ( I I I M. Bloom, E E . Burncll. S.B.W. Roeder and M.I. Valic, J. Chem. Phys. (in press) 112) S. MarCelja, Biochim. Biophys. Acta 367 (1974) 165 [13] F.Y. Fujiwaraand L.W. Reeves, J. Am. Chem. Soc. 98 (1976) 6790 |14 | J.F. Nagle, J. Chem. Phys. 58 (1973) 252; P. Bothorel, J. Belle and B. Lamaire. Chem. Phyt. Lipids 12 (1974 ) 96; H. Schindler and J. Seelig, Biochemistry 14 (1975) 2283: M L . Scott. J. Chem. Phys. 62 (1975) I 347; R E . Jacobs, B. Hudson and II.C. Anderson, Proc. Nad. Acad. Sci. U.S.A., 72 (1975) 3993; J.A. McCammon and J.M. Deutch, J. Am. Chem. Soc. 97 (1975) 6675: M B . Jackson, Biochemistry 15 (1976) 2555 (15) A two site model has been used previously to explain the NMR of acetylene [P. Diehl. S- Sykora.W. Niedcrbcrger and E.E. Bumell, J. Mag. Res. 14 (1974) 260] and methyl fluoride | E . E . Bumell, J R . Council andS.E. Ulrich, Chem. Phys. Letters, 31 (1975) 3951 dissolved in nematic solvents |16 | D. F.isenberg and W. Kauzmann, in: The Structure and Properties of Water, Oxford University Press (1969) [17] P.J. Flory.in: Statistical Mechanics of Chain Molecules. Interscicnce, N.Y. (1969) [18] M. Bloom, in: Proc. First Specialized "Colloque Ampere1' ed. by J.W. Hennel. Krakow, Poland (1973), p. 80 M. Bloom, E.E. Bumell, M. l . Valic and G. Weeks, Chem. Phys. Lipids 14 (1975) 107 (19| W.Maierand A. Saupe.Z. Naturforsch. A13 (1958)564; A M , (1959) 882; A15 (1960)287 [20] B. Mely, J . Charvolin and P. Keller, Chem. Phys. Lipids 15 (1975) 161; J . Charvolin, P. Manneville and B. Deloche. Chem. Phys. Letters 23 (1973) 345 [ 211 A . Seelig and J . Seelig. Biochemistry 13 (1974) 4839 104 APPENDIX B Determination of The Equation of State for The sodium Laurate-Water system Using low Angle X-ray Scattering^ In order to determine the equation of state r e l a t i n g the d i f f e r e n t thermodynamic parameters (mean area/polar head, temperature and water concentration) for the lamellar l i q u i d c r y s t a l (L a) of the sodium laurate-water system the lamellar repeat distance for t h i s system was measured using low angle X-ray scattering as a function of temperature and water concentration. Following the procedure of Gallot and Skoulious (51) the area per polar head was derived from the measured lamellar repeat spacings. Experimental Results and Discussion Due to the random orientations of the l i q u i d c r y s t a l domains of bi l a y e r of the sodium laurate-water system i n the lamellar l i q u i d c r y s t a l phase i n the samples used the X-ray d i f f r a c t i o n patterns are concentric rings whose diameters are related to the lamellar repeat spacing by Bragg's law mA = 2 dsin0 [ l ] where m = 0, 1, 2, .... d i s the lamellar repeat distance, X Is the wavelength of the X-ray radiation used (1.54A ) and 0 i s the scattering angle. I f d^ i s the measured diameter of the m t n ring , f i s distance between the sample "''The X-ray measurements were carried out i n collaboration with L. Wood and K. Jeffrey at the University of Guelph Ontario. 105 and the f i l m the 0 i s given by tan 20 = ^ ' i [ 2 l 2 f 1 J Due to instirumental l i m i t a t i o n s only the rings corresponding to 1/2 , 1/3 , ... of the fundamental spacing ( i . e for m-2,3,...) were observed. Using equations 1 and 2 the fundamental spacing was obtained from the rings corresponding to m=2 and 3 . Table 2 shows the temperature dependence for the lamellar repeat spacing i n the temperature range (85^145*0 ) for a sample having 6 moles of water/1 mole of sodium laurate. I t remains roughly the same between 86 and 125 C and then shows a decrease at higher temperatures. Table 3 shows the concentration dependence for d at two d i f f e r e n t temperatures. There i s a s l i g h t increase i n d with increasing water concentration. Calculation of the b i l a y e r thicVjiess da and the area per polar head A In the model used by Gallot and Skoulious the simplifying assumption that water does not penetrate into the b i l a y e r i s made .'. i m p l i c i t l y . I f v a and v e are the s p e c i f i c volumes of soap and water respectively, c a and c e = l - c a are the f r a c t i o n a l concentrations (per unit mass) then d c v + (1-c )v -a a a e which gives -1 w 106 v a has only been measured for the potassium Myristate-water system (51). For the other soaps v a was derived by assuming the a d d i t i v i t y of p a r t i a l molar volumes i n the following way. I f a soap molecule C nX of the ion type X with n carbons on the hydrocarbon chain then i t s molar volume V n(X) i s given by. V n ( X ) = V C H 3 + (n-2) V C H 2 + [5] Where VcR$ i s t n e p a r t i a l molar volume of the methyl group, Is the p a r t i a l molar voulme of one..methylene group and V ^ Q^ i s the volume of the carboxyl group and the X ion. In terms of the molar volume for 0^-K eqn. 5 can be rewritten., as V X ) = V U ( K ) + ( n - 1 4 ) V C R 2 +(V X-V K) [>] Where V X-V K i s the difference i n p a r t i a l molar volumes of ion X and the potassium ion. The se p e c i f i c volume v a i s then given by the ,\ re l a t i o n V n(X) =Mava where M a i s the molecular weight of the soap. Gallot and Skpulious (51) have v e r i f i e d that eqn. 6 yields results that are.in good agreementwith experimental values for v a . For the Cj^-Na eqn. 6 becomes V 1 2(Na) „ V 1 A ( K ) - 2 V C H z + (V N a-V^) [l\ The value of VcH2 a t a given temperature was arrived at by comparing the s p e c i f i c volumes of the normal alkanes as a function of the number of the carbon atoms (52). V N a-V K was put equal to the difference of the molar volumes of NaCl and KC1 i n water (53). 107 Using the calculated v a values as outlined above and the s p e c i f i c volume of water i n equilibium with i t s own vapour pressure for v e , d a was calculated using 4 . The results are shown i n table 2 To calculate the mean surface are per polar head the following equation was used. where N i s Avogadro's number. Fig.30 i s a log-log plot of the dependence of A on water concentration f o r three temperatures. The results at 86°C are those of Gallot and Skoulious (51). Like a l l the other sodium soaps studied i n (51) the following empirical r e l a t i o n O was found to hold. C i s the water concentration i n moles of water/1 mole of soap and P i s a constant = .24. Fig.31 i s a plot of A Q versus T. In fig.32 the temperature dependence of A i s shown for 0=6 i t increases l i n e a r l y with temperature i n the range 86-120 °C and then increases at a faster rate at higher temperatures with a break i n the slope at-125 °C. We believe that this i s probably an a r t i f a c t due to s l i g h t perturbations i n the experimental arrangement. Furthermore there were no anomalies i n the deuterium quadrupole s p l i t t i n g s of the perdeuterated sample of the same composition. The fact that d a i s almost independent of temperature and depends very weakly on concentration can imply two things : ( i ) water penetration A Where A Q(T) i s a function of temperature only ,T i s the temperature. 108 i n between the chains or ( i i ) shrinkage of the chains resulting from bending and twisting motionsi In the model used for calculations the f i r s t p o s s i b i l i t y has been excluded. I t must be kept i n mind, however, that the p o s s i b i l i t y of some penetration of the water into the bi l a y e r s cannot be excluded on the basis of our experiments. This w i l l i n no doubt introduce some uncertainty i n the experimental r e s u l t s . 109 o :rature (C) d(A) d a(A) A (A ) 86 30.6 20.4 36.2 91 30.8 20.2 36.6 96 30.4 20.3 36.6 105 30.6 20.4 36.9 112 30.4 20.3 37.3 117 30.5 20.4 37.3 122 30.5 20.4 37.5 127 29.7 19.8 38.8 132 29.1 19.4 39.8 137 28.4 18.9 41.0 142.5 29.4 18.9 41.2 Table 2 . Temperature dependence of the lamellar repeat distance d, the thickness of the b i l a y e r d a and the mean area per polar head A for the sodium laurate-water system. The water concentration i s 6 moles of water/1 mole of sodium laurate. (§105 °C @135°C °c d(A) d a(A) A(A 3 29.6 23.7 31.8 4 29.9 22.4 33.5 5 30.3 21.4 35.2 6 28.8 19.2 36.9 7 28.1 17.7 39.4 2 30.0 25.8 30.0 3 29.1 23.3 33.3 4 29.1 21.8 35.5 5 30.3 21.4 36.2 6 27.1 18.1 40.0 7 28.2 17.8 44.0 Table 3 . Dependence on the water concentration C(moles of water/ 1 mole of sodium laurate) of the lamellar repeat spacing d, the bi l a y e r thickness d a and the mean are per polar head A at 105 °C and 135 °C . 110 0.3 0.4 0.5 0.6 0.7 0.8 0.9 LOG C (MOLES OF H20/1-M0LE OF C^-Na) Figure 30 . A log-log plot of the mean area per polar head versus water concentration for the sodium laurate-water system at 86 C (open c i r c l e s , obtained from ref.51 ), 105 C ( s o l i d dots) and 135°C ( t r i a n g l e s ) . Figure 31 The dependence of A q on temperature. 112 Figure 32. The dependence of the mean area polar head on temperature at a fixed concentration for the sodium laurate-water system. 113 Appendix C Water s e l f Diffusion and Spin-Spin relaxation In sodium laurate/H 20 . The s e l f - d i f f u s i o n c o e f f i c i e n t and the spin-spin relaxation time T 2 of H 20 were measured, i n the sodium laurate water system. The spin echo method with an externally applied f i e l d gradient (38) was used. Theory For an i s o t r o p i c l i q u i d sample the amplitude of a spin echo i n an NMR experiment i s given by S(2T) = S(0) exp (-2T/T 2), exp (- I Y V D T 3 ) [ l ] 3 ' where T i s the spacing between the 90° and 180° pulses, G i s the applied magnetic f i e l d gradient and D i s the d i f f u s i o n c o e f f i c i e n t . The term involving D i n equation 1 takes, into account the extra damping to the transverse nuclear magnetization due to the change i n the Larmor frequency as a result 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 molecules across an inhomogenous applied magnetic f i e l d . I f G and T 2 are known D can be obtained from the slope of a semilog plot of log (S(2T) + 2T/T 2) versus T For water i n an anisotropic enviroment eqn. [ l j has to be modified. In the sodium laurate water system the d i f f u s i o n of water between the bilayers i s mainly p a r a l l e l to the b i l a y e r s . For an oriented sample i t can be shown (54) that the angular dependence i n the lab frame of the di f f u s i o n tensor i s given by D l l - < D 1 > + (< D..> - < D j > ) s i n 2 0 DO 114 where ^Dx̂ > and are the components of the d i f f u s i o n tensor : i n the frame of the b i l a y e r and 9 i s the angle between the normal ri to gradient the b i l a y e r and the magnetic f i e l d d i r e c t i o n . Since the water molecules are confined to narrow regions between the b i l a y e r , the d i f f u s i v e motion perpendicular to the lamellae does not transport the water molecules very f a r and therefore i t w i l l be assumed that <^D^— 0 . Equation 2 then becomes % - <Dn > s i n 2 Q = d ( i _ u 2 ) c 3 J where D = <^D^and y = cos 0 . and the echo amplitude w i l l be given by: S(2x) = S Q exp (-2T/T2). exp (- | Y 2 G 2 D ( l - y 2 ) ) [ 4 ] In randomly oriented samples a l l values of y=cos0 are equally probable and an average over a l l arientations has to be considered giving S(2T) = S Q exp (-2T/T2) / d y exp (- | y 2 G 2 D ( l - y 2 ) x 3 ) = S 0exp(-2x/T 2). exp(- 1 Y 2 G 2 D T 3 ) X (\/| Y V D T ) [ 5 ] 3 J 1 y 2 where x(y) = ~ f dx. exp (x ). / 2 2 2 3 — Y G D. T ) i s a correction term for lamellar systems to equation 1 , the expression for S(2T) for i s o t r o p i c systems. Experimental Results Using a Bruker B-KR 300Z18 f i e l d gradient u n i t , rtie echo Amplitude was measured for several T values at d i f f e r e n t values of G for the water i n the sodium laurate water sample. To c a l i b r a t e G the same measurements were made on pure water (R^O) • The sample sizes and diameters of the tubes (.5cm) were chosen to be i d e n t i c a l . T 2 for 115 rLjO i n the sample was measured using the 90°-T-180 pulse sequency i n the absence of a f i e l d gradient and was found to be 30. msec. To calculate D equation 5 was f i t t e d to the data by a 2 parameter non l i n e a r least squares f i t where the i n t e g r a l was evaluated numerically. Fig. 33 i s a representative f i t for eqn. 5 . The r a t i o of D to the s e l f d i f f u s i o n c o e f f i c i e n t i n pure water D / D Q , i s shown i n table 4 for d i f f e r e n t G values. 2 2 2 9 2 2 " . • G | y G D Q 3 Y G D D/DQ _ 0 _2 q —2 (Gauss/cm) (msec )xl0 (msec - J)xlO 19.4 1.55. .30 .19 27.3 3.08: ' .59 .19 34.4 4.90 1.03 .21 41.0 6.93 1.50 .22 Table 4. Ratio D/Da of the s e l f , d i f f u s i o n c o e f f i c i e n t of water i n the sodium laurate water system to that of pure water at 100°C for several G values. D/D0 was obtained from the r a t i o of 2y2G2D/3 calculated by f i t t i n g eqn. 5 to the experimental data (column 3), to the slope of log S(2x) + 2T/T 2) versus x 3 plot for pure water (column.-2). G was calculated using the results i n column 1 and the known d i f f u s i o n c o e f f i c i e n t of pure water at 100°C (55 ). The water concentration for the sample i s 6 moles of water per 1 mole of sodium laurate. Figure 33 . Log(S/S0 )+2T/T2 versus T 3 . The s o l i d l i n e represents the f i t of equation 5 to the experimental data (dots)for the water s e l f d i f f u s i o n c o e f f i c i e n t measurement i n the lamellar phase of the sodium laurate water system at 100*0. 117 References (1) V. L u z z a t i , i n : B i o l o g i c a l Membranes , ed. by D. Chapman, Academic Press, N.Y. (1968) (2) A. Johanson and B. Lindman, i n : Li q u i d c r y s t a l s and P l a s t i c Crystals, Vol. 2, ed. by G. W. Gray and P.A. Winsor, E l i s s Harwood, Chichester (1974) ; G.J.T. Tiddy, i n : S p e c i a l i s t P e r i o d i c a l Reports on NMR, Vol. 16 (1977) (3) B. Mely and J. Charvolin, Chem. Phys. L i p i d s ( i n press) (4) B.D. Ladbrooke and D. Chapman, Chem Phys. Li p i d s 3 (1969) 304 (5) S.B.W. Roeder E.E. Burnel l , An-Li Kuo and C.G. Wade, J. Chem. Phys., 1976, 64 , 1848 (6) J. Charvolin and P. Rigny, Chem. Phys. l e t t . 1973, 18, 515 (7) W. Drost-Hansen, i n "Chemistry of the C e l l Interface", ed. H.D. Brown, Chapter 6, Part B, P . l . Academic Press, N.Y. ,1971 (8) J.A. Walter and A.B. Hope, Progr. Biophys. Mol. B i o l . 23 ,3 (1971) (9) J . J . Tait and E. Franks, Nature (London) 230,91 (1971) (10) E.G. Finer and A. Darke, Chem. Phys. L i p i d s . 12, (1974) (11) Werner Neiderberger, Yves T r i c t o t , J . Mag. Res. 28, 313-316 (1977). (12) J.F. Nagle, J . Chem. Phys. 58 (1973) 252 (13) S. Marcelja, Biochem. Biophys. Acta. 367 (19 74) 165 (14) P. Botherel, J . Bel l e and B. Lemaire, Chem. Phys. Lipids 12 (1974) 96 (15) C. Madelmon and R. Perron. C o l l o i d & polymer S c i . 254 (1976) 581 (16) J. Charvolin, P. Manneville and B. Deloche, Chem . Phys. Letters 23 (1973) 345 (17) B. Mely, J . Charvolin and P. K e l l e r , Chem. Phys. Lipids 15 (1975) 161 (18) J.H. Davis and K.R. Jeff r e y , Chem . Phys. Li p i d s 20 (1977) 87 (19) T.P. Higgs and A.L. Mackay, Chem. Phys. Li p i d s 20 (1977) 105 (20) O l d f i e l d , E., Chapman, D., and Derbyshire, W. (1971), FEBS Lett. 16, 102 . 118 (21) Charvolin, J . , Mannevllle, P., and Deloche, B. (1973), Chem. Phys. Lett. 23, 345 . (22) Se e l i g , J . , and Niederberger, W. (1974), J. Am. Chem. Soc. 96, 2069 . (23) Seelig, J . , and Niederberger, W. (1974), Biochemistry 13, 1585. (24) Se e l i g , J . , and Seelig, A. X1974), Biochem. Biophys. Res Commun. 57, 406. (25) Seelig, A., and Seelig, J . (1974), Biochemistry 13, 4839 . (26) Neiderberger, W., and Seelig, J. (1974), Ber. Bunsengerns. Phys. Chem. 78, 947 . (27) J.F.Nagle, J . Chem. Phys. 58 (1973) 252 . (28) J . Se e l i g , Quartterly Reviews of Biophysics 10, 3 (1977) 353 . (29) H.L. Scott, J . Chem. Phys. 62 (1975) 1347 . (30) R.E. Jacobs, B. Hudson and H.C. Anderson, Proc. N a t l . Acad. S c i . USA 72 (1975) 3993 (31) J.A. McCammon and J.M. Deutch, J. Am. Chem. Soc. 97 (1975) 6675 . (32) M.B. Jackson, Biochemistry (1976) 2555 (33) H. Schindler and J. Seelig. Biochemistry 14 (1975) 2283 . (34) G.W. Stockton, C.F. Polanzek, L.C. L e i t c h , A.P. Tulloch, and I. C P . Smith. Biochem. Biophys. Res. Commun. 60 (1974) 844 (35) J.H. Davis , K.R. Jeffrey and M. Bloom, J. Mag. Res. (in press) (36) B.P. Schoenborn, Biochin, Biophys. Acta 457 41 (1976) (37) G. Buldt, H.V. Galley, A Seelig, J. Seelig and G. Zaccai Nature, 271 (Jan. 1978)182 (38) A. Abragam, "The princ i p l e s of Nuclear Magnetism," Clarendon, Oxford, 1961 (39) G.WL Stockton, C.F. Polanszek, A.P. Tullock, F. Hassan and I.CP. Smith, Biochemistry 15 (1976) 954 / 119 (40) P. Waldstein, S.W. Rabideau and J.A. Jackson, J . Chem. Phys. 41 (1964) 3407 (41) J. Charvolin and P. Rigny, J . of Chemical Physics 58 (1973) 3 999 (42) C.Y.Y.Hsiao, C.A. Ohaway, and D.B. Wetlaufer, Lipids 9, 913 (1974). (43) J . J . Davis, K.R. Je f f r e y , M. Bloom, M.I. V a l i c , and T.P. Higgs. Chem. Phys. Lett. 42 (19 76) 390 (44) S. Chandrasekhar. Rev. of Mod. Phys., 15 (1943) 1 . (45) R.T. Roberts. Nature 242 (1973) 348 . (46) K. A b d o l a l l , A.L. Mackay, and M. Bloom J . of Mag Res. (In press). (47) R.L. Void and R.R. Void, J . Chem. Phys. 66, 1202 (1977) (48) L.G. Werbelow and D.M. Grant, J . Chem. Phys. 63,. 544 (1976) (49) J . Jeener and P. Broekaert, Phys. Rev. 157, 232 (1976) . (50) R.R. Void and R.L. Void, J . Chem. Phys. 66, 1202 (1977) . (51) P.B. Gallot and Antoine Skoulios. K o l l o i d - Z e i t s c h r i f t und Z e i t s c h r i f t fur Polymers, 208 (1965) 37. (52) D o o l i t t l e , A.K., J. Appl. Phys. 22 (1951) 1471 . (53) Handbook of Physics and Chemistry. P. , Chemical Rubber Company. (54) R. B l i n c , M. Burger, M. Luzar, J. P i r s , I. Zupancic and S. Zumer. Phy. Rev. Lett. 33 (1974) 1192 . (55) J . J . Simpson and H.Y. Carr. The Physical Review ser. 2,111 (1958) 1201 . P. 120 1-3 CD c f M CD d 2 3C 1 2-Na/2H 20 Vn (kHz ) 2 •yn 2 3,4 5 6 7 8 9 10 11 12 100 20.45 16.05 14.83 *..: 7 13.02' 10.53 9.12 5.93 2.06 105 20.84 16.44 15.42 13. 90 11.36 9.80 6.43 2.26 108 20.90 16.46 15.41 13.83 11.32 9.68 6.38 2.22 110 20.85 16.33 15.23 13.67 11.21 9.59 6.32 2.17 111 20.83 16...33 15.27 13.66 11.16 9.62 6.29 2.19 112 20.80 16.26 15.19 13. 61 11.07 9.51 6.24 2.14 115 20.78 16.11 15.05 13.42 10.93 9.36 6.12 2.09 116 20.78 16.17 15.10 13. 45 10.95 9.34 6.12 2.11 117 20.78 16.13 14.98 13.31 10.84 6.03 2.08 120 20.64 16.04 14.94 13.26 10.72 9.18 5.98 2.05 125 20.65 15.99 14.76 13. 16 10.57 9.01 5.83 1.97 130 20.52 15.88 14.65 13.10 12.71 10.39 8.87 5.74 1.90 135 20.40 15.72 14.45 12.85 12.41 10.14 8.64 5.58 1.84 140 20.36 15.66 14.31 12.67 12.28 9.99 8.56 5.46 1.78 145 20.28 15.52 14.17 12.51 12.11 9.84 8.36 5.33 1.75 150 20.19 15.36 14.01 12.38 11.99 9.67 8.23 5.20 1.67 d23 C12 _ N a / 3 H2° v n (kHz ) 2 2 3,4 5 6 7 8 9 10 11 12 100 19.63 14.89 13.24 11.39 10,71 8.70 7.35 4.82 1.61 102 19.54 14.86 13.16 11.38 10.62 8.62 7.30 4.74 1.59 103 19.57 14.86 "".13.15"1 7" 11.33 10760 8.59 7.24 4.72 1.57 105 19.59 14.78 13.10 11.22 10.51 8.46 7.18 4.64 1.56 110 19.45 14.67 12.93 11.11 10.34 8.36 6.99 4.53 1.50 115 19.36 14.53 12.81 10.86 10.13 8.15 6.82 4.41 1.43 120 19.25 14.47 12.63 10.10 9.97 8.04 6.68 4.27 1.37 125 19.17 14.38 12.50 10.62 9.84 7.89 6.52 4.15 1.33 130 19.06 14.23 12.32 10.46 9.68 7.74 6.38 4.06 1.29 135 18.97 14.16 12.16 10.28 9.51 7.51 6.25 3.96 1.22 140 18.85 14.01 12.04 10.14 9.35 7.40 6.10 3.86 1.17 145 ' 18.79 13.93 11.91 10.00 9.23 7.25 5.98 3.77 1.12 150 18.67 13.82 11.77 9.84 9.08 7.13 5.86 3.69 1. 11 pj £ ct- fO CO 4 2 << o CD I—1 ct- CD CO B CO M PL H- CO c+ •d ct- CD H- 0 CS ci , rjq CD m t i o o CO Hj o o & to c+ H" CD 0 & CD CD 4 0 c+ CD ^ 2 CD t3 03 P3 pu 3 s; t+ P tr- et- CD CO l-J CO O O O M-O £ o B CD t i i— 1 <+ fo 4 0 ps H ct- 03 H- ct- O CD 3 d 25C 1 2-Na/6H 20 ^SL (kHz ) 2 n 2 3,4 5 6 7 8 9 10 11 12 C 70 14.49 10.58 9 .55 8.42 7.91 6.59 5.66 3.91 1.34 75 14.66 10.73 9 .53 8.29 7.80 6.43 5.51 3.78 1.29 80 14.84 10.79 9 .54 8.20 7.69 6.25 5.37 3.64 1.23 85 14.99 10.89 9 .52 8.15 7.52 6.10 5.18 3.52 1.18 90 15.10 10.99 9 .47 8.06 7.42 5.96 5.03 3.42 1.15 95 15.25 11.10 9 .39 7.93 7.24 5.80 4.87 3.30 1.10 100 15.38 11.08 9.67 9.33 7.86 7.18 5.71 4.74 3.22 1.06 105' 15.43 11C13 9.67 9.18 7.71 7.08 5.37 4.54 3.13 1.03 110 15.43 11.13 9.57 9.18 7.67 6.93 5.42 4.49 3.03 .98 115 15.52 .11.17 9.51 9.07 7.56 6.82 5.31 4.38 2.92 .95 120 15.58 11.18 9.55 9.05 7.45 6.65 5.15 4.27 2.86 .92 125 15.58 11.18 9.42 8.94 7.40 6.57 5.04 4.16 2.75 .87 130 15.59 11.17 9.46 8.86 7.29 6.45 4.96 4.05 2.70 .85 135 15.50 11.11 9.38 8.81 7.20 6.35 4.87 3.99 2.60 .78 140 15.45 11.01 9.25 8.67 7.06 6.18 4.71 3.83 2.50 .74 145 15.42 11.00 9.24 8.61 6.95 6.09 4.60 3.75 2.44 .73 150 15.33 10.94 9.13 8.50 6.84 5.96 4.49 3.66 2.39 .70 d 2 3C 1 2-Na/7H 20 (kHz ) 2 n 2 3,4 5 6 7 8 9 10 11 12 C 70 12.18 8.86 8. 20 7.39 7.02 5.90 5.10 3.58 1.20 73 12.21 8.90 8. 20 7.32 6.95 5.83 5.03 3.52 1.17 75 12.38 8.98 8. 19 7.30 6.90 5.77 4.97 3.48 1.16 81 12.38 8.98 8. 15 7.20 6.79 5.62 4.81 3.34 1.11 91 12.51 9.11 8. 09 7.03 6.52 5.33 4.53 3.13 1.03 95 12.66 9.14 . 8. 04 6.95 6.41 5.21 4.41 3.03 .99 100 12.77 9.20 8. 01 6.84 6.32 5.10 4.30 2.93 .95 106 12.83 9.22 8.21 7.92 6.77 6.19 4.97 4.16 2.82 .90 110 12.92 9.28 8.15 7.89 6.70 6.09 4.85 4.06 2.75 .88 120 13.00 9.34 8.09 7. 76 6.53 5.87 4.63 3.83 2.59 .81 130 13.06 9.38 8.03 7.67 6.35 5.66 4.42 3.64 2.43 .74 141 13.05 9.36 7.97 7.51 6.19 5.48 4.21 3.43 2.26 .67 150 13.09 9.33 7.91 7.40 6.05 5.30 4.04 3.25 2.11 .61 P. 17 d 2 3C 1 2-Na/4H 20 (kHz ) 2 n 2 3,4 5 6 7 8 9 10 11 12 °c > 90 18.49 13.78 11. 73 9.83 9.03 7.18 6.03 3.96 1.34 92 18.52 13.76 11. 69 9.79 8.96 7.10 5.93 3.93 1.33 95 18.47 13.71 11. 58 9.70 8.87 6.99 5.85 3.85 1.32 100 18.51 13.62 11. 45 9.62 8.74 6.88 5.74 3.78 1.26 105 18.35 13.48 11. 30 9.42 8.59 6.74 5.62 3.66 1.21 110 18.32 13.46 11. 16 9.33 8,50 6.62 5.52 3.61 1. 12 120 18.24 13.26 10. 91 9.11 8.24 6.40 5.27 3.42 1.10 126 18.02 13.18 11. 23 10. 79 8.91 8.08 6.23 5.11 3.31 1.05 130 17.93 13.07 11. 17 10. 73 8.87 8.02 6.19 5.08 3.27 1.03 135 17.81 13.06 11. 11 10. 64 8.79 7.91 6.05 4.97 3.20 .98 140 17.74 12.93 10. 93 10. 49 8.70 7.73 5.97 4.87 3.14 .94 145 17.66 12.87 10. 89 10. 41 8.61 7.68 5.87 4.76 3.05 .90 150 , 17.64 12.78 10. 80 10. 31 8.48 7.56 5.80 4.68 2.99 .88 d23 C12 _ N a / 5 H2° ( kHz ) 2 2 3,4 5 6 7 8 9 10 11 12 C 80 17.32 12.72 10. 74 8.98 8.20 6.51 5.48 3. 70 1.22 85 17.38 12.66 " 10. 62 8.85 8.04 6.34 5.33 3.58 1.18 90 17.33 12.61 11.01 10.47 8.72 7.89 6.18 5.20 3.47 1.14 95 17.37 12.64 10.91 10.44 8.61 7.76 6.09 5.09 3.42 1.11 100 17.27 12.62 10.85 10.34 8.53 7.67 5.97 4.97 3.32 1.07 105 17.30 12.54 10.68 10.22 8.44 7.48 5.82 4.87 3.21 1.04 110 17.26 12.50 10.64 10.11 8.30 7.37 5.71 4.74 3.14 1.01 120 17.09 12.33 10.47 9.89 8.07 7.17 5.49 4.51 2.98 .95 128 16.86 12.10 10.14 9.56 7.73 6.87 5.19 4.21 2.77 .87 130 16.99 12.16 10.27 9.70 7.89 6.96 5.30 4.35 2.86 .89 135 16.89 12. 18 10.18 9.59 7.76 6.86 5.19 4.22 2.77 .85 140 16.76 12.05 10.08 9.59 7.69 6.74 5.09 4.14 2.70 .84 145 16.70 11.96 10.03 9.40 7.59 6.66 5.03 4.06 2.64 .81 150 16.67 11.87 9.94 9.35 7.54 6.57 4.93 3.98 2.59 .78 Table 6. Sp i n - l a t t i c e relaxation times of chain deuterons i n the sodium laurate water system; dependence on temperature and •Water concentration. OO o CO IN CM TJ w c CM CO  cd cu J25 cn 1 *—s vo CN a •—1 t—i in u H co c o m >-i CM O CM vO co in o IN m •—< <t in N m in î - CO <r CM v o m co IN IN IN 00 o m • 00 i—i vO CM m ON «* i-H i-H CM CM CM CO m vO CO ON <* TJ rN o IN m O o CM co o C IN r-H m ON i-H m i-H CM O r—1 i-H i-H CM CM CO a o CO OJ "N. CO cd 1—̂ S3 d o IN 1 r-H vO CO CM <r m in IN i-H CM H I—1 CM o •—i m ON CM CO I—1 in i-H •—i CM CM CM CM • u -CO CM TJ O ON CO CO rN | N in o IN r-H i-H O O i—1 VO CM CO CO i-H r-H CM CM CM CO m o m v o H CM CO CO oo <r v o v o co CM r*» vo o "-H co -vi- vo vO • • • • r-« m m r~- O oo oo co oi H oo CM CM o- m fN IN m m IN f"» co o oo CM co ON m co i-H CM co co <f m N ci vo rs r> ffl O Csl 0> H <f •-H CM CM CM CO -sT CO 00 vO CM o m 1—' CM CM m m v o *-H r-H CM CM CM CO C / m m m / H r » CO / U -H -< m m m m O O O H N C O C_) 00 CJ> i-H i-H i-H i-H o m O CM o CM vO ON i-H CM CO vo 00 ON • • • o vo o co <f <r ON I IN vo m < • o o ON I CM co -o- m vo IN m co IN IN o r~-oo vo es IN <r H r-H CM co co <j" m CM O CM i-H <r m 00 i-H IN r-H fN vO i-H CM CM CO CO vT | N CM m O fN ID oo | co oo CM m co <r i-H i-H CM CM CO CO 00 TJ C IN O o CM O EC cu CO '—. N - / eg c S r-H VO I H CM m r-H o CO CM TJ <r CO rN CM m CM O O CM vO O -J" CO CM •-H r-H CM CM CM CO o m m m CM in o m v o o •-H CM CM CM tO o ON IN m m o CM m ON in IN o r-H rH r-H CM CM CO o vo m co IN in co vo o m oo m r-H i-H CM CM CM CO / m m m m o o o -H CM CO CJ 00 ON rH i—I r-H r-H o P.- n t * . d^C 1 2-Na/5H 20 (seconds) n o 2 3,4 5,6 7 8 9 10 11 12 C 80 . 0822 C9096 .097 .0977 .117 .148 .187 .290 .750 90 .116 .135 .137 . 138 . 155 .184 .243 .335 .815 105 . 173 . 183 .177 .200 .220 .325 .327 .370 1.01 115 .220 .224 .228 .242 .267 .320 .375 .537 1.24 125 .260 .273 .266 .285 .312 .370 .445 .614 1.19 135 .342 .309 .310 .345 .380 .437 .510 .735 1.42 d -T -23^12 •Na/6H20 T. (seconds) in > n o 2 3,4 5,6 7 8 9 10 11 12 C 80 .057 .067 .060 .067 .070 .090 . 107 .158 .68 90 .066 .077 .080 .088 .095 . 123 .150 .200 .76 105 .097 .110 . 117 .126 .137 .172 .210 .277 .89 115 .118 .140 .150 .167 .178 .230 .275 .385 1.05 125 .168 . 160 .173 .212 .230 .315 .370 .493 1.22 135 .204 .212 .257 .295 .310 .405 .470 .595 1.36 d23 C12-•Na/7H20 T, (seconds) In . n 2 3,4 5,6 7 8 9 10 11 12 C 80 .043 .048 .048 .056 .057 .076 .100 .163 .600 90 .052 .062 .064 .073 .083 .112 .140 .235 . 760 105 .076 .085 .097 .107 .118 .147 .210 .329 .946 115 .098 . 112 . 120 .135 .145 .187 .245 .353 1.02 125 .113 . 138 .147 .163 . 182 .250 .317 .458 1.15 135 .144 . 156 .187 .223 .210 .280 .368 .555 1.31

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
United States 3 0
France 3 0
China 2 15
Japan 1 0
City Views Downloads
Ashburn 3 0
Unknown 3 5
Beijing 2 0
Tokyo 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}

Share

Share to:

Comment

Related Items