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NMR studies of carboxylic acids : an investigation of head group behaviour in lyotropic and nematic phases Delikatny, Edward James 1987

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NMR STUDIES OF CARBOXYLIC ACIDS - AN INVESTIGATION OF HEAD GROUP BEHAVIOUR IN LYOTROPIC AND NEMATIC PHASES by EDWARD JAMES DELIKATNY B.Sc. (University of Winnipeg) A THESIS SUBMITTED IN PARTIAL FULFD1MENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Chemistry We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1987 c Edward James Delikatny, 1987 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia 1956 Main Mall Vancouver, Canada DE-6(3/81) ABSTRACT The orientational order of the methylene segments adjacent to the head group in the lamellar liquid crystalline phase of potassium palmitate/D20 was investigated using multinuclear magnetic resonance. Previous studies had shown that the orientational order near the soap—water interface decreased with decreasing temperature, contrary to intuition. To investigate this phenomenon, three isotopically substituted species of palmitic acid were synthesized: palmitic acid-d 3 1, 1- 1 3C-2,2-H 2- palmitic acid-d 2 9, and 2,2,3,3-H4- palmitic acid—d 27. These compounds were treated in two complementary fashions: the acids were dissolved in the liquid crystal 4 —(octyloxy)—benzoic acid (p-OOBA) and the corresponding potassium salts were dispersed in D 20 at a constant water concentration. Dipolar and quadrupolar couplings were obtained from the *H, -^C, and H nmr spectra of these molecules, in nematic and lamellar liquid crystalline phases, as a function of temperature. In a parallel study, nmr spectra of acetic, propionic, and butyric —2,2 — d 2 acids dissolved in p —OOBA were recorded. In order to observe *H — *H dipolar couplings, a two dimensional spin echo (JJ72 — tj/2 — it—tj/2—echo) was necessary to remove heteronuclear dipolar couplings to the chain deuterons. A refocussing pulse applied simultaneously to the spins allowed observation of the heteronuclear *H— ^ C dipolar couplings in the carbon 13 labelled compound. The complete orientational order matrix of the alpha methylene segment of potassium paImitate/D20 and of palmitic acid/p—OOBA was determined from the dipolar and quadrupolar couplings. As the temperature is decreased from 110°C to a temperature just above the gel-liquid crystalline phase transition (45°C), ii the orientation of the methylene segment of potassium palmitate is rotated by 3° towards a configuration in which the first C—C bond is parallel to the bilayer normal. This is in direct agreement with a previous model, the Abdollal model of lipid—water interaction, in which the decrease in orientational order was postulated to be a strictly geometric effect arising from electrostatic interactions of the lipid with the water. A mean field equilibrium statistical mechanical model, based on the Samulski Inertial Frame Model, was developed to simulate the experimental dipolar and quadrupolar nmr couplings. In potassium palmitate, electrostatic interactions, approximately constant at higher temperatures, increase dramatically as the phase transition is approached. In contrast mean field steric repulsive forces remain constant over the entire temperature range studied. This evidence also supports the Abdollal model of lipid — water interaction. The electrostatic interaction was shown to be of greater importance in the orientational ordering of the solutes in the liquid crystal than in potassium palmitate and this was attributed to intermolecular H —bonding between solute and p —OOBA. The ordering of the head group of carboxylic acids dissolved in p—OOBA was demonstrated to be remarkably similar regardless of the chain length of the solute. iii TABLE OF CONTENTS Abstract ii Table of Contents iv List of Figures vii List of Tables xi List of Abbreviations xii Acknowledgements xiv I. INTRODUCTION 1 A. THEORY 3 1. THE ZEEMAN HAMILTONIAN 4 2. THE INDIRECT SPIN SPIN COUPLING 5 3. THE DIPOLAR HAMILTONIAN 5 a. THE ORIENTATIONAL ORDER MATRIX 7 b. SOLVING DIPOLAR COUPLED SPECTRA 9 4. THE QUADRUPOLAR INTERACTION 11 a. THE ORIENTATIONAL ORDER PARAMETER 13 b. THE POWDER PATTERN 14 c. THE QUADRUPOLAR ECHO 15 d. DEPAKING 16 5. TWO DIMENSIONAL SPIN ECHO SPECTROSCOPY 17 a. THE DENSITY MATRIX FORMALISM 19 b. CALCULATION OF THE ECHO SPECTRUM 21 c. EFFECTS OF IMPERFECT REFOCUSSING PULSES .. 22 B. SOAPS 23 1. PHASE BEHAVIOUR 23 2. X-RAY STUDIES 27 3. NMR STUDIES OF SOAPS 29 a. GENERAL 29 b. SPECIFIC NMR STUDIES 32 c. RESEARCH INSPntING THE PRESENT WORK 39 C. NEMATIC LIQUID CRYSTALS AS AN ORIENTING MEDIUM 49 D. MOLECULAR MODELLING 50 1. INTERNAL POTENTIAL 51 2. SEELIG 52 3. INCLUSION OF EXTERNAL FORCES 55 4. THE MARCELJA MODEL 55 5. THE SAMULSKI INERTIAL FRAME MODEL 61 EL MATERIALS AND METHODS 66 A. NOMENCLATURE 66 B. PREPARATION OF PERDEUTERATED FATTY ACIDS 67 C. PREPARATION OF 2,2,3,3-H4-HEXADECANOIC ACTD-d27 70 iv 1. REDUCTION OF TETRADECANOIC ACID 70 a. PREPARATION OF REACTANT 70 b. PREPARATION OF REAGENT 70 2. PREPARATION OF 1,1-H2~ 1-TETRADECANOL METHANESULFONATE -c?27 71 3. PREPARATION OF 2,2,3,3-H4-HEXADECANOIC ACTD-d27 •• 72 a. PREPARATION OF SODIUM DIETHYL MALONATE . 72 b. PREPARATION OF 2,2,3,3-H4-HEXADECANOIC ACID . 73 D. PREPARATION OF 1- 13C-2,2-H2-HEXADECANOIC ACID-d29 •••• 74 E. PREPARATION OF 4-(OCTYLOXY)-BENZOIC ACDD—di 75 F. SHORT CHAIN CARBOXYLIC ACIDS 76 G. PREPARATION OF FATTY ACTD SALTS 76 H. SAMPLE PREPARATION 77 1. SOAPS 77 2. LIQUID CRYSTALS 77 I. NMR 78 1. DEUTERON NMR 78 2. PROTON NMR 79 3. CARBON 13 NMR 82 HI. SOAPS 84 A. DEUTERON NMR 84 B. 1-13C-2,2-H2-POTASSIUM PALMITATE—d29 92 1. PROTON AND CARBON 13 NMR 92 2. CALCULATION OF THE ORDER MATRIX 101 C. 2,2,3,3-H4-POTASSIUM PALMITATE - d2 7 I l l 1. PROTON NMR I l l D. THE INERTIAL FRAME MODEL 121 E. RESULTS FROM THE D? CALCULATION 130 1. SIMULATION OF EXPERIMENTAL NUMBERS 130 2. THE ADJUSTABLE PARAMETERS 140 3. THE ORDER MATRIX AND THE MOMENT OF INERTIA TENSOR 148 4. WATER AND COUNTER IONS 153 5. CALCULATION OF THE ALPHA METHYLENE ORDER MATRIX 154 6. IMPROVING THE CALCULATION 157 F. CONCLUSIONS 160 1. COMMENTS ON CLEANLINESS AND REPRODUCIBILITY 162 IV. SHORT CHAIN CARBOXYLIC ACIDS 169 A. ACETIC ACTD 170 B. PROPIONIC ACTD 175 C. BUTYRIC ACTD-2,2-d2 181 1. CALCULATION OF THE ORDER MATRIX 187 v 2. THE INERTIAL FRAME MODEL 189 V. LONG CHAIN CARBOXYLIC ACIDS 192 A. DEUTERON NMR 192 B. 1-13C-2.2-H2 PALMITIC ACDD-d29 197 1. PROTON AND CARBON 13 NMR 197 2. CALCULATION OF THE ORDER MATRIX 203 C. 2,2,3,3-H4-PALMITIC ACID-d27 • 2 0 9 D. THE INERTIAL FRAME MODEL 211 E. CONCLUSIONS 215 VI. REFERENCES 219 vi List of Figures FIGURE 1.1: Structures of Lipid Phases . 25 FIGURE 1.2: The Phase Diagram of Potassium Palmitate/H20 28 FIGURE 1.3: The Abdollal Model of the Lipid Water Interface 42 FIGURE 3.1: 2H nmr Spectrum of Perdeuterated Potassium Palmitate-d3i 85 FIGURE 3.2: 2H Order Parameter Profiles of Perdeuterated Potassium Palmitate 87 FIGURE 3.3: Temperature Dependence of the 2 H Quadrupolar Splittings of Perdeuterated Potassium Palmitate 89 FIGURE 3.4: Temperature Dependence of the 2 H Quadrupolar Splittings of l-13c-2,2-H2 Potassium Palmitate)-d29 90 FIGURE 3.5: Temperature Dependence of the 2 H Quadrupolar Splittings of 2,2,3,3-H4 Potassium Palmitate-d27 91 FIGURE 3.6: IH nmr Spectra of l-13C-2,2-H2 Potassium Palmitate-d29 ..93 FIGURE 3.7: 13C nmr Spectra of l-13C-2,2-H2 Potassium Palmitate-d29 .96 FIGURE 3.8: i H Dipolar Coupling Constants for l-13C-2,2-H2 Potassium Palmitate-d29 98 FIGURE 3.9: 13C Dipolar Coupling Constants for 1-13C-2.2-H2 Potassium Palmitate-d29 99 FIGURE 3.10: Axis Systems for Acetic, Propionic and Butyric Acids 103 FIGURE 3.11: Order Parameters for the a —Methylene Segment of 1-13C-2.2-H2 Potassium Palmitate-d29 105 FIGURE 3.12: Temperature Dependence of Szz and S 3 3 106 FIGURE 3.13: Temperature Dependence of the Diagonalized Order Parameters 108 FIGURE 3.14: Rotation Angle Needed to Diagonalize the Order Matrix of the Rigid o—Methylene Segment of the 1—13c Labelled Potassium Palmitate 110 FIGURE 3.15: i H Single Pulse and Spin Echo nmr Spectra of 2,2,3,3-H4 Potassium Palmitate-d2 7 112 vii FIGURE 3.15C.D: Depaked and Simulated nmr Spin Echo Spectra of 2,2,3,3-H4 Potassium Palmitate-d27 114 FIGURE 3.16: Temperature Dependence of the Dipolar Splittings of 2,2,3,3-H4 Potassium Palmitate-d27 115 FIGURE 3.17: Temperature Dependence of the Dipolar Couplings of 2,2,3,3-H4 Potassium Palmitate-d27 116 FIGURE 3.18: The Parameterization of Potassium Palmitate 127 FIGURE 3.19: The D? Model: Calculated and Experimental Dipolar Couplings 131 FIGURE 3.20: The D? Model: Calculated and Experimental Quadrupolar Couplings 135 FIGURE 3.21: The IF Model: Quadrupolar Coupling Profile 136 FIGURE 3.22: The D7 Model: Effect of Increasing The Chain Length on The Calculated Quadrupolar Coupling Profile (110°C) 138 FIGURE 3.23: The IF Model: Effect of Increasing The Chain Length on The Calculated Quadrupolar Coupling Profile (45°C ) 139 FIGURE 3.24: The TF Model: Variation of Cylinder Radius with Temperature 141 FIGURE 3.25: The IF Model: Variation of Head Group Parameter with Temperature 142 FIGURE 3.26: The IF Model: Effect of Changing The Head Group Mass on the Head Group Parameter Length 149 FIGURE 3.27: The D? Model: Effect of Changing The Head Group Mass on the Cylinder Radius 150 FIGURE 3.28: Recalculation of the a-Methylene Order Matrix from the IF Calculation 155 FIGURE 3.29: Recalculation of the Diagonalized a—Methylene Order Matrix from the D? Calculation 156 FIGURE 4.1: 1H nmr Spectrum of 11 mole % Acetic Acid in p-OOBA 171 FIGURE 4.2: lH nmr Spin Echo Spectrum of 11 mole % Acetic Acid in p-OOBA 174 FIGURE 4.3: l H nmr Spectrum of 11 mole % Propionic Acid in p-OOBA .. 176 FIGURE 4.4: lH Spin Echo nmr Spectrum of 11 mole % Propionic Acid in p-OOBA 178 viii FIGURE 4.5: Axis Systems for Acetic, Propionic and Butyric Acids 180 FIGURE 4.6: IH nmr Spectrum of 11 mole % Butyric Acid-2,2-d2 in p-OOBA 183 FIGURE 4.7: i H Spin Echo nmr Spectrum of 11 mole % Butyric Acid-2,2-d2 in p-OOBA 185 FIGURE 4.8: Effect of Refocussing Pulse Length on i H Spin Echo nmr Spectrum of Butyric Acid-2,2-d2 in p-OOBA 186 FIGURE 5.1: 2H nmr Spectrum of Perdeuterated Palmitic Acid in p-OOBA . 193 FIGURE 5.2:Temperature Dependence of the 2H nmr Quadrupolar Splittings in Palmitic Acid 194 FIGURE 5.3: 2H nmr Quadrupolar Splitting Profile as a Function of Chain Position 195 FIGURE 5.4: iH Spin Echo nmr Spectra of 11 mole % 1-13C-2.2-H2 Palmitic Acid-d29 in p-OOBA 198 FIGURE 5.5: 13C Single Pulse nmr Spectrum of 11 mole % l-13c-2,2-H2 Palmitic Acid-d29 in p-OOBA 200 FIGURE 5.6: Temperature Dependence of the Heteronuclear Dipolar Couplings of 11 mole % l-13C-2,2-H2 Palmitic Acid-d29 in p-OOBA 201 FIGURE 5.7: Temperature Dependence of the Homonuclear Dipolar Couplings of 11 mole % l-13C-2,2-H2 Palmitic Acid-d29 in p-OOBA 202 FIGURE 5.8: Order Parameters for the a—Methylene Segment of 1-13C-2.2-H2 Palmitic Acid-d29 in p-OOBA 204 FIGURE 5.9: Temperature Dependence of S z z and S 3 3 205 FIGURE 5.10: Temperature Dependence of the Diagonalized Order Parameter Matrix for the a-Methylene Segment of 13c Labelled Palmitic Acid-d29 in p-OOBA 207 FIGURE 5.11: Rotation Angle Needed to Diagonalize the Order Matrix of the a—Methylene Segment of the 13C Labelled Palmitic Acid-d29 in p-OOBA 208 FIGURE 5.12: IH Spin Echo nmr Spectra of 11 mole % 2,2,3,3-H4 Palmitic Acid-d27 in p-OOBA 210 ix FIGURE 5.13: The IF Model: Quadrupolar Coupling Profile for Palmitic Acid in p-OOBA 214 x List of Tables TABLE 1.1: Calculated Order Parameters From The Abdollal Model 44 TABLE 3.1: Calculated Dipolar Couplings for 2,2,3,3-H4-Potassium Palmitate-d27 117 TABLE 32: The D? Model: The Parameterization of Potassium Palmitate 124 TABLE 3.3: The D? Model: Experimental and Calculated Dipolar and Quadrupolar Coupling 132 TABLE 3.4: The D? Model: Variation of Adjustable Parameters with Temperature 143 TABLE 3.5: The IF Model: Variation of Adjustable Parameters with Head Group Mass 151 TABLE 4.1: Dipolar Couplings and Order Parameters for the Short Chain Acids in p-OOBA 172 TABLE 5.1: The IF Model: Palmitic Acid in p-OOBA 11 mole% 212 xi LIST OF ABBREVIATIONS 2D J two dimensional J-resolved spectroscopy amu atomic mass unit COM Centre of Mass D i j dipole—dipole coupling between nuclei i and j DPPC dipalmitoyl phosphatidylcholine DSC differential scanning calorimetry e2qQ/h Quadrupole coupling constant efg Electric Field Gradient FID Free Induction Decay g + gauche plus g~ gauche minus H a the hexagonal phase D7 Inertial Frame La the lamellar liquid crystalline phase the lamellar gel phase nmr nuclear magnetic resonance PMI Principal Moment of Inertia P2(cos0) Second Legendre Polynomial = i(3 cos2 6 — 1) ppm parts per million RIS Rotational Isomeric States RMS Root Mean Square Qa the cubic phase % nuclear quadrupole moment of deuteron xii q internal electric field gradient tensor at the site of the deuteron r Cyl Mean Field Cylinder Radius, an adjustable parameter of the Samulski model rHG Head group Interaction Length, an adjustable parameter of the Samulski model San a/Jth element of the order matrix Sjj orientational order parameter SD Standard Deviation T r ed Reduced Temperature t trans p —OOBA 4 —(octyloxy)—benzoic acid, p—n—octyloxybenzoic acid, a liquid crystal. p—BOB A p —n—butyloctyloxybenzoic acid. EBBA N—(4—ethoxybenzylidene) — 4" — n—butylaniline 1132 Merck ZLI 1132: A mixture of three phenylcyclohexanes and one biphenylcyclohexane nCB, n = 4,5,8 n—cyanobiphenyl, a liquid crystal. Phase V Merck Phase V: A SchifFs base liquid crystal 7i gyromagnetic ratio of nucleus i xiii ACKNOWLEDGEMENTS I would like to thank my supervisor, Elliott Burnell, the man who would not let me quit even when I wanted to so desperately. This thesis is proof of his dedication and support. Thanks to John Rendell, my constant companion and fellow solvent inspector, an endless supply of fact and fancy, and to Art van der Est, our pragmatic revolutionary, for his keen insight and sense of humour. Thanks to all and sundry who have crossed the portals of 159: to Peter Beckmann, for giving me a good boot when I needed it, to Alexandra Weaver, who taught me to love science again, to Thomas K. Pratum, chimiste et spectroscopiste extraordinaire, to Gina L. Hoatson, for being Gina, to Mei Kok, Peter B. Barker, John Ripmeester, and David Gin. These people have all made my stay worthwhile. Thanks to Myer Bloom for confusing me over the years and making me think, and thanks to Tony Day and T.P.Higgs for patiently watching over a physical chemist stumbling through the wonderful world of organic chemistry. Words cannot express how grateful I am to the people in the shops: Kam Sukul, and Tom Markus in electronics, Emil Matter, Cedric Neale, and Big Bill Henderson in the mechanical shop, Steve Rak and Steve Takacs in glassblowing. Without them, this thesis could not have been completed. Thanks to Dr. W.R Cullen for the use of his bomb. My parents, Alison and Ted, have given me much support over these years, emotional and moral, as well as financial. Thanks mom, dad, Brenda, Bruce, xiv little Markie and Frere. My deepest thanks and appreciates to Hazel, who typed this monster, and who defused my darkest moods with grace and humour. Hazel gets the h in Ph.D. xv I. INTRODUCTION The simplest model of a biomembrane is the soap—water system. It fits the prerequisites — it is a system consisting of solvent and amphiphile which when mixed together at appropriate concentrations forms the familiar bilayer structures which are the structural basis of the fluid mosaic model of the cell membrane. Yet it is free of other complicating influences — it is a two component system and it is devoid of membrane soluble cholesterol, extrinsic and intrinsic proteins, glycolipids and glycoproteins. In fact, it is simpler in structure than the phospholipids which are the main component of cell membranes in that there is only one hydrophobic chain per molecule and the head group consists of a simple carboxylate anion, rather than the more complex phosphatidyl ethanolamine, choline or serine. It is, as Charvolin says, "an extreme oversimplification, a fragmentary representation of actual membranes" [1]. In spite of this, or perhaps because of this, the soap—water systems are extremely well studied. Investigators are careful to draw the analogy to the cell membrane without ever making direct comparisons. Throughout this thesis this approach shall be followed. One of the primary techniques used in the study of these systems is deuteron nuclear magnetic resonance (nmr). Its main advantage is that due to the largely intramolecular nature of the quadrupolar interaction, deuteron nmr spectra yield information about each distinct methylene group in the hydrocarbon chain. One can then speak about different regions of the bilayer structure on a molecular level rather than drawing conclusions from bulk macroscopic properties. 1 INTRODUCTION / 2 There have been anomalies observed in the deuteron nmr spectra of the lamellar phase of the soaps. For methylene groups near the lipid—water interface the deuteron order parameter, S Q Q , rather than exhibiting the intuitive strict monotonic increase with decreasing temperature, comes to a maximum and then decreases [2]. In some cases, two distinct deuteron nmr peaks have been observed for deuterons near the polar head group [2] implying two slowly exchanging configurations at lower temperatures [3]. In addition, what could be interpreted as lamellar — lamellar phase transitions have been observed [4, 5]. Obviously, near the interface there are electrostatic interactions to consider as well as the steric effects present elsewhere in the chain. This thesis is an attempt to investigate these phenomena, to understand the forces that come into play near these interfaces and to gain insight into the lamellar phases of amphiphilic molecules. The method used in this study has been to isotopically substitute perdeuterated soap molecules with protons and carbon 13 near the head group. Then the *H, 2 1 H, and C nmr spectra can be examined to obtain information on orientation of the head groups and the conformational preferences of the first few methylene segments of the chain. A molecular modelling scheme based on the Bamulski Inertial Frame model [6,7,8,9] was used to simulate the experimental quadrupolar and dipolar nmr couplings. In the course of these experiments, the complete order matrix of the first segment of potassium palmitateT^O has been determined as a function of temperature. This is an improvement on the determination of the order matrix previously reported by Higgs and Mackay [10]. In developing the spin echo methods necessary to extract the information, it was INTRODUCTION / 3 necessary to orient a series of long and short chain fatty acids in the liquid crystal p—OOBA (p—octyloxybenzoic acid). The multinuclear nmr spectra of these compounds then consist of relatively sharp peaks instead of the Pake doublets characteristic of randomly oriented samples. These results are also presented in this thesis. The introduction will proceed as follows: first nmr theory relevant to the project will be discussed. Secondly, an overview on the soaps will be presented including the experimental evidence which led to this project. This will be followed by a section on the use of nematic liquid crystals as an orienting medium. Finally, molecular modelling of lipid membrane systems will be discussed. A. THEORY This discussion is restricted to partially oriented molecules in uniaxial (thermotropic or lyotropic) phases. No attempt will be made to discuss orientational ordering in biaxial phases. The theory has largely been gleaned from many fine textbooks [11, 12, 13, 14], review articles [15, 16, 17, 18] and graduate thesis [19, 20, 21, 22, 23] and in general no references will be given except where specifically warranted. For nuclei in an anisotropic environment (i.e. in a liquid crystalline phase), the nuclear spin Hamiltonian can be written as the sum of several terms: X = Xz + XD + Xj + # Q (l.l) INTRODUCTION / 4 The first term is the Zeeman term describing the interaction of the spins with the magnetic field. The second term is the dipolar Hamiltonian describing the direct dipole—dipole interaction between the spins. The third term is the J coupling or indirect coupling and the last term is the quadrupolar Hamiltonian, valid only for nuclei with I a l , which describes the interaction between the nuclear quadrupole moment and the electric field gradient at the nucleus. In isotropic solution, the value of the dipolar and quadrupolar terms average to zero, and the spin Hamiltonian reduces to the familiar form used in high resolution nmr spectroscopy. Each of these interactions will now be outlined in some detail, with emphasis on the dipolar and quadrupolar terms which are especially relevant to this thesis. In the course of this section the order matrix will be defined and its properties discussed. 1. T H E Z E E M A N HAMILTONIAN When nuclei with spin are placed in a static magnetic field, the degeneracy of their magnetic energy levels is lifted, and the spins interact with the field in a way described by the Zeeman Hamiltonian. This Hamiltonian can be written: *z = 2vT * * I * < 1 - o l " - o Z 2 i ) H 0 where y- is the gyromagnetic ratio of spin i, I 2j is the z component of the total spin of nucleus i, and H Q is the strength of the static magnetic field which is by definition, along the z direction. The a's are elements of the nuclear chemical shielding tensor: < 7 j l s 0 is equal to l/3(Tr(a)) and is equivalent to the isotropic chemical shift, INTRODUCTION / 5 is the partially averaged component of the anisotropic chemical shift tensor, equal to zero in isotropic phases. 2. T H E INDIRECT SPIN SPIN COUPLING The indirect spin —spin coupling Hamiltonian is given by: (1.3) where Jy is the isotropic part of the indirect coupling equal to l/3(Tr(J)), I zj and I2j have been defmed previously, and I j + , Ij + , \~, Ij~ are the raising and lowering operators for the i and j spins. This term gives rise to the scalar or J coupling observed in high resolution nmr. This is only mentioned because it is important in the discussion of the dipolar interactions which follows. There is also an anisotropic contribution to the spin—spin coupling, which has a form identical to the dipolar Hamiltonian (see equation 1.4). The anisotropic J coupling, also known as the "pseudo dipolar coupling constant", is negligible for protons due to the spherical symmetry of the contact interaction, and is generally ignored. 3. T H E DIPOLAR HAMILTONIAN The direct through space dipole—dipole interaction between a system of interacting spins is described by the dipolar Hamiltonian: #D = ^  D,j (31zil2j - \ • ip (1.4) INTRODUCTION / 6 where D^ is the time averaged component of the direct dipolar coupling and Ij and Ij are the total spin operators of nuclei i and j respectively. Expanding the total spin operator into its components, and regrouping gives: 2 D i j [ i 2 i i 2 j - 1 + j r j ; )] (1.5) (1.3) and (1.5) may be combined to give the following form for the Hamiltonian: In a dipolar coupled nmr spectrum of an oriented molecule, the quantities Dy and Jjj often cannot be separated. In these cases, rather than measure a scalar coupling from the nmr spectrum, the value for the J coupling is usually assumed to be the same as the value obtained from high resolution nmr. The quantity D^ is called the dipolar coupling constant and is defined as : _ < 1 ^ A i l i > where 7j and 7j are the gyromagnetic ratios of nuclei i and j respectively, h is Planck's constant, rjj is the distance between the two nuclei i and j, and 6^ is the angle between the magnetic field direction and the internuclear vector between nuclei i and j. If the molecule is rigid, or if the segment of the molecule containing the two nuclei i and j is rigid, then (1.7) becomes: INTRODUCTION / 7 If the main symmetry axis of the phase (i.e. the optic axis of the liquid crystal or the lamellar director) is parallel to the magnetic field, then (1.8) is rewritten as: where Sy defines the orientational order parameter or degree of orientation of an axis joining the two nuclei i and j relative to the external magnetic field direction. For liquid crystals in which the optic axis is perpendicular to the magnetic field, or in randomly oriented samples where the measured quantity is the 9 0 ° edge of the powder pattern, the dipolar coupling constant in (1.9) must be scaled by a factor of £ < 3 c o s ^ 9 0 ° —1> = — £. The range of Sy is defined as — i ^ S j j < l where the limits correspond to values of 9 of 9 0 ° and 0 ° respectively. An order parameter of 1 describes perfect orientation parallel to the magnetic field direction, and an order parameter of — £ defines perfect orientation perpendicular to the magnetic field direction. Note that an order parameter of >i must by definition be positive, and that the order parameter passes through zero at an angle equal to 5 4 . 7 4 ° — the magic angle. (1.9) o. THE ORIENTATIONAL ORDER MATRIX For a rigid segment of an oriented molecule the Saupe orientational order matrix may be defined: INTRODUCTION / 8 where a,/? are the molecule fixed x, y, and z axes defined in the rigid segment of the molecule, cos#a is the cosine of the angle between the axis and the magnetic field direction and 8aQ is the Kronecker delta ($ a 0 = l for a = 0, 8 a 0 = O otherwise). The order matrix can be related to the experimentally measured order parameters (or to any other axis system) by a coordinate transformation: (1.11) where the sum is over a/3=x,y,z and where cos#a is the direction cosine between the molecule fixed (a = x, y, z) axis and the vector joining the i ^ n th and j nuclei. The order matrix is by definition traceless, symmetric, and characterized by five independent elements. The limits of the elements of the order matrix are — i s S a £ < l for a = 0 and - 3 / 4 s S a ^ < 3 / 4 for a*/?. Judicious choice of the molecule fixed axis system can reduce the number of independent elements of the order matrix needed to describe the orientation of the molecule if the molecule contains the appropriate elements of symmetry. For example, a plane of symmetry reduces the number of independent elements in the order matrix to 3 , 2 perpendicular planes of symmetry or a C 2 axis of rotation symmetry will reduce the number to 2 and with a C 3 or greater axis of symmetry, only one element of the order matrix is necessary to describe the orientation if the molecule fixed axis system is chosen to coincide with the symmetry axis. The order matrix can be diagonalized, which is equivalent to a rotation of the rigid molecule segment about its three molecule defined axes into the principal orientation axis frame of the molecule. The orientation is then described by two independent elements of the order matrix (the third is INTRODUCTION / 9 unnecessary, since the matrix is traceless by definition) and the up to 3 angles necessary to perform the rotation. b. SOLVING DIPOLAR COUPLED SPECTRA The procedure for analysis of spin i dipolar coupled nmr spectra parallels very closely the solution of high resolution nmr spectra. The secular determinant is set up from the stationary state nuclear spin wave functions and from the appropriate Hamiltonian: H m n = < <Pm I # I <Pn > ( 1 12) where in the case of dipolar coupled nuclei the Hamiltonian is the sum of (1.2) and (1.6). The secular determinant is diagonalized to determine the energy levels of the system and the selection rules and transition intensities are determined by the relative transition probability: l « |< ^ m U I X 1I V „ >l 2 d-13) where \pm, ^ n are the eigenfunctions of the diagonalized Hamiltonian, and the sum is over all nuclei with the same gyromagnetic ratio. Examination of (1.2) and (1.6) reveals that, for two coupled spin £ nuclei, the diagonal elements of the secular determinant will have terms involving the sum of dipolar coupling (2Dy+Jy) and the chemical shift, whereas the off diagonal elements will contain only terms involving (Jy—Dy). When the determinant is diagonalized, and the transition energies (E m, E n) and frequencies (w m n=(E m-E n)27r/h are calculated, INTRODUCTION / 10 it is found that for two strongly coupled nuclei (in which the dipolar coupling is much greater than the chemical shift, Dy>>(aj— Oj) the dipolar splitting is equal to three times the dipolar coupling: Ai/jj = 3Djj (1.14) On the other hand, for weakly coupled nuclei, in which the chemical shift difference cannot be ignored, the dipolar splitting is instead given by: - u n = (2D,j + Jy) ( L 1 5 ) The strongly coupled case applies to nuclei of the same species physically close together (recall that Dy « <l/ry^>) whereas the weakly coupled case applies to heteronuclei (e.g. ^ C and *H dipolar coupling) and spatially separated homonuclei of different chemical shift. For small numbers of spins, with the assistance of molecular symmetry, the nmr spectra can sometimes be solved analytically. However, in dipolar coupled spectra, the complexity rapidly increases with the number of spins, and most spectra must be solved with computer assistance. The computer program LEQUOR [24, 25] was used extensively to solve dipolar coupled spectra. A suitable set of starting parameters (dipolar couplings, J couplings, and chemical shifts) are chosen, either from inspection, intuition or literature values. The secular determinant is solved and assuming a decent choice of starting parameters, calculated transitions are assigned to experimental lines. The spectrum is recalculated, iteratively fitting the calculated to the experimental spectrum until convergence is reached. More lines are assigned, and the procedure is repeated until the spectrum is deemed solved. The calculated dipolar couplings INTRODUCTION / 11 are reported with an RMS error which is the sum of the squared differences between calculated and experimental couplings. 4. THE QUADRUPOLAR INTERACTION For a static deuteron in an anisotropic environment, the nmr spectrum is dominated by the quadrupolar interaction. The quadrupolar Hamiltonian describes the interaction of the nuclear electric quadrupole moment with the electric field gradient that arises due to asymmetric charge distribution at the nucleus. In the principal coordinate system of the efg this is given by: where e qQ/h is the quadrupole coupling constant, e is the charge of the proton, Q is the nuclear quadrupole moment, eq is the electric field gradient equal to V 2 Z, TJ is the asymmetry parameter of the efg equal to (V x x — Vyy)/Vzz, and the I's are nuclear spin operators defined previously. The electric field gradient is a traceless symmetric tensor quantity with the principal axis system defined such that: rQ = 4h!(2 qi-l) [3I, 2-I(] + 1) + j^(I + 8+I_ 8)] (1.16) iv 2 Z 1*1 v x x 1*1 V y y| (1.17) which limits the asymmetry parameter to: (1.18) For an axially symmetric electric field gradient, (17 = 0), (1.16) reduces to: INTRODUCTION / 12 2 * q_Q . r*i 2 _ i / u i ^ i d.i9) This is very similar to the expression given for two dipolar coupled spin i nuclei (1.4). A transformation of (1.16) from the efg principal axis reference frame to the laboratory fixed reference frame yields: 2 * Q = 4hI(21-l)'t 3 Ii 2- 10-'-l)3 [ § ( 3 c o s V l ) + \f) s i n 2 * cos20] (1.20) where 6 and 0 are the polar angles of the efg relative to the magnetic field. To first order, ( ) and ignoring chemical shift and dipolar interaction the energies of a static deuteron in a magnetic field are given by: 2 E m = ->hH0m + 4^ 2 (jg l ) [3m2-I(I + l)] [£(3cos20-l) + ± v s i n 2 * cos20] < L 2 1) where m = —1,0,1 for 1=1. The transition frequencies for the single quantum spectrum (Am = ±1) are given by: u0 = - 7 H 0 ± ^ ( 3 c o s 2 0 - l ) + y, sin26 cos20] d- 2 2) There are two allowed transitions and this gives rise to a doublet with a separation & V Q , the quadrupolar splitting: A l / Q = [ ( 3 c o s 2 0 - l ) + 7j s i n 2 * cos20] ( 1 ' 2 3 ) For a deuteron in a C—D bond, the only relevant quadrupolar nucleus in this thesis, TJ is typically on the order of 0.04 [26] so that to a good approximation, 17 =0 in which case: INTRODUCTION / 13 2 = ^ T ^ 5 [ ( 3 c o s 2 c 9 - l ) ] (1-24) Since ezqQ/h = 167 kHz for a deuteron in a C-D bond [16, 27], the maximum deuteron quadrupolar splitting, which occurs in a rigid lattice when 8 — 0, is 250.5 kHz. In the presence of molecular motion more rapid than the inverse rigid lattice quadrupolar splitting, i.e. motions with a correlation time T>>1/2TTA»>Q, the quadrupolar interaction is modulated, and a reduced quadrupolar splitting is observed: a. THE ORIENTATIONAL ORDER PARAMETER In analogy to the dipolar interaction, an orientational order matrix may be defined for the quadrupolar interaction (1.10). For a deuteron in a C —D bond with n = 0, there is only one independent element of the order matrix and (1.25) becomes: = — T T P < 3 C O S 6? — 1 > (1.25) <Av Q> CD (1.26) where S Q Q is called the carbon deuteron order parameter. b. THE POWDER PATTERN INTRODUCTION / 14 For dipolar or quadrupolar coupled nuclei in a rigid solid where all orientations of the internuclear vectors (or C-D bond vectors) are equally probable, the resonance frequencies of the nuclei are orientation dependent and the Hamiltonian is scaled by: #(/?) = #(0) P 2(cos/?) = #(0) (3cos*/3-l)/2 d.27) where /3 = the angle between the external magnetic field and the internuclear (or C—D) vector of interest. The resulting resonance line, which is a superposition of many doublets of varying frequency, is inhomogeneously broadened into a characteristic lineshape called the Pake doublet [28] or powder pattern. The splitting now corresponds to those nuclei oriented at 90° to the magnetic field, the outer edge of the pattern to those oriented at 0° to the field. This is a strictly geometric effect arising from the relative probability of finding any orientation with respect to some axis. In other words, there is a much higher probability of rinding the spins at the equator than it is at the poles. In uniaxial lamellar liquid crystalline phases randomly dispersed, where the normal to the plane of the bilayer is a symmetry axis of the phase, the orientation dependent Pake doublet is often considered to arise from the random orientation of the lamellar director with respect to the field. Then (1.25) can be rewritten: " ^ ( 3 C O S 2 ^ ' ) < ^ S t l = A > (1-28) INTRODUCTION / 15 where 8 is now the angle between the C —D bond vector and the symmetry axis of the phase and 0 is the angle between the symmetry axis and the magnetic field. A similar expression can be written for dipolar splittings. The measured splitting in an nmr spectrum, corresponding to 0 = 90° (i(3cos^/3 — 1)= — i) reduces this equation to: <^Q> = " ^ g 5 S C D (1-29) In general, the sign of the coupling constant is unknown and can only be determined with certainty if SQJJ > $. c. THE QUADRUPOLAR ECHO The acquisition of deuteron nmr spectra of powder samples is severely hindered by the the problem of receiver deadtime. By the time the spectrometer has recovered from the effects of the radiofrequency pulse (up to 40 Msec), a substantial fraction of the deuteron nmr signal has decayed. To overcome this problem, a two pulse sequence known as the quadrupolar echo has been developed [29]. A ir/2 pulse is applied to the spins in thermal equilibrium, and after a time T, a second ir/2 pulse 90° shifted in phase is applied. At a time 2r, the quadrupolar interaction is refocussed as an echo well outside the deadtime of the spectrometer. If the phase difference of the two pulses is exactly 90°, then the refocussing of the quadrupolar interaction is complete. Fourier transformation of the signal from the peak of the echo then yields the true deuteron nmr spectrum. INTRODUCTION / 16 d. DEPAKING For powder pattern spectra which arise from randomly oriented samples, a numerical procedure has been developed which calculates the spectrum of the oriented molecule. This procedure is called depaking [30, 31] because it effectively removes the orientation dependent Pake doublet. The procedure is valid for any second rank tensor interaction which is axially symmetric and which scales with P£(cos0). This includes all dipolar interactions, axially symmetric quadrupolar and anisotropic chemical shift interactions. In the case where no axial symmetry is present, depaking generates recognizable artifacts [31] which can be used in the assignment of spectra. In addition, depaking can be applied, essentially as a deconvolution technique, to a superposition of overlapping powder patterns as in the case of perdeuterated soap or lipid spectra. Here depaking can be useful in resolving overlapping peaks arising from different deuterons, and the depaked spectrum can be integrated [23] to aid in the assignment of deuteron lines. This is especially useful at temperatures near the liquid crystalline—gel phase transition for resonances arising from nuclei near the polar head group where often many lines overlap due to steric constraints placed on the molecule. Depaking is now often used in lieu of simulation of powder spectra. In this thesis depaking has been used for the first time to 1) depake dipolar coupled spectra consisting of more than two dipolar coupled nuclei and 2) depake dipolar coupled spectra in a lamellar (motionally averaged) phase. INTRODUCTION / 17 5. TWO DIMENSIONAL SPIN ECHO SPECTROSCOPY This thesis is concerned primarily with the measurement of dipolar couplings in perdeuterated fatty acids isotopically substituted near the head group with *H and It was found that precise measurement of the dipolar couplings was hampered by the presence of heteronuclear dipolar couplings to the deuterons on the rest of the chain. Some method had to be found to remove the unwanted couplings, while leaving the important information intact. It would be nice if that method conveniently removed the effects of chemical shift as well. The method chosen is a variation on 2D J spectroscopy commonly in use in high resolution nmr. The pulse sequence is simple, a 90° pulse followed after a time T with a 180° refocussing pulse. There are two main differences between this method, dubbed two dimensional spin echo spectroscopy [32], and conventional 2D J spectroscopy [33, 34]. The first is that the delay time between the two pulses in the echo pulse sequence is considerably shortened. This decreases the dwell time (i.e. increases the spectral width) in the second time domain which is necessary to observe the broader signals obtained from dipolar coupled nuclei. The other difference is that rather than collect a full free induction decay (FID) in both of the time domains, only a single point in the normal time domain is collected for each condition in the second time domain. As a result, only a single FID is collected for each experiment rather than a complete two dimensional data set. The saving in computer time in data processing and disk space for data storage is enormous, at least 3 orders of magnitude, and in most cases the discarded information was not of any use. INTRODUCTION / 18 The easiest way to discuss the spin echo experiment is to use a density matrix approach since the time evolution of the spins must be followed in response to the spin echo pulse sequence. A complete discussion of two dimensional nmr spectroscopy [35,36] and the density matrix [37,38] is not warranted within the scope of this thesis, so a "seat of the pants" approach will be used, bringing in the necessary concepts only as they are needed. The two dimensional nmr experiment is normally divided into four regions or time periods called the preparation, evolution, mixing, and detection periods. The two dimensional spin echo experiment, essentially a two dimensional version of Hahn's spin echo [39], can be similarly categorized as follows: The spin system is "prepared" by the use of a 90° pulse to generate transverse magnetization. Evolution is allowed under the appropriate Hamiltonian, in this case a sum of Zeeman, homonuclear dipolar and heteronuclear dipolar terms. The evolution time is systematically incremented in successive applications of the pulse sequence — this gives the pulse sequence its dependence on a second time variable. The mixing period consists of a 180° refocussing pulse applied after a time r = tj/2. Terms which are linear in spin operators reverse their direction of precession, those bilinear in spin operators are invariant to the effects of a 180° pulse. At a time t=2r, the detection period starts with the accumulation of the spin echo caused by the refocussing of the terms linear in spin. The two time domains are termed tj (the variable time domain) and t 2 (the normal time domain). Collection of a t 2 signal as a function of varying tj (or T) produces a two dimensional data matrix, which upon double Fourier transformation yields the normal FT spectrum in the f 2 (frequency) domain and a spectrum devoid of INTRODUCTION / 19 effects from chemical shift and heteronuclear dipolar couplings in the fj dimension. A more detailed explanation using the density matrix formalism follows. a. THE DENSITY MATRIX FORMALISM The high temperature high field form of the density matrix at thermal equilibrium is proportional to I z: p(O) oc — ° 1 2 (1-30) ' 2nkT Application of a (7l72)v pulse generates x magnetization. The density matrix following a perfect (n/2)y pulse is proportional to I x: p(0)+ « 1 (1.31) where I x = I I x j (1.32) where the sum is over all nuclei excited by the rf pulse. The spins are then allowed free precession for a time tj/2 under the appropriate Hamiltonian which includes terms for chemical shift, homo and heteronuclear dipolar couplings: p ( t , / 2 ) _ « e x p [ - i ^ d ) t , / 2 ] l x exp[iJ^ d ) t , / 2 ] ( 1 - 3 3 ) At time t-j/2, application of a refocussing pulse of duration 0 radians produces INTRODUCTION / 20 the density matrix: p(l ,/2) + « exp(-i/?F ) exp[-iy d )t,/2] I x exp[i^ d )t ,/2] exp(i/?Fy) (1.34) where F y = £ ] y k (1.35) and where the sum is again over all nuclei excited by the refocussing pulse. In the case of heteronuclear dipolar couplings, this operator will extend over all species of nuclei to which a refocussing pulse is applied. For /3 = 180°, the exponential operator exp(—iir Fy) can be written as: exp ( - i 7 T F y ) = n exp ( - i 7 T ] y k ) (1.36) = {J I (2i) I y k | = i N P y (1.37) where P y is a product of spin operators Iy for all nuclei affected by the it pulse and N is the number of nuclei. Substituting (1.37) into (1.34) and then allowing the spins to refocus under the influence of a Hamiltonian K^T^ will give rise to the spin echo which will then dephase in the t 2 time domain. p(t,.t 2) « e x p [ - i ^ 2 ) t 2 ] exp[-ij/ r ,i ,/2] P y e x p l - i f l ^ t ,/2] ] x ( 1 - 3 8 ) x exp[iV d )t,/2] P y exp[i^ r )t ,/2] e x p [ ^ 2 ) t 2 ] The signal at any time (tj,t2) is given by the trace of I x with the density INTRODUCTION / 21 matrix. The signal after the pulse sequence ig complete is given by: S(t,.t 2) = Tri I, exp[-iV2)t2] eXp[-i^r)t ,/2] P y exp[-i^ d )t ,/2] 1, U-39) x exp[i^ d )t ,/2] P y exp[i^r)t,/2] exp[i^ 2 )t 2] j Using a basis set in which the Hamiltonians are diagonal, the transition frequencies can be written as the eigenvalues of the Hamiltonian. The signal is now given by: s ( i > * t 2 ) = k . L ( p y ) l m ( p y ) n k e x P t ^ E k - E'I) t 2 ] ( 1 4 0 ) x exp[i(E k - E,) t,/2] exp[!(En - E m ) t ,/2] Double Fourier transformation of this expression will yield the two dimensional frequency spectra. The spectral frequencies in the f 2 domain are: " 2 = ( E k - E , ) / - h ( 1 - 4 1 ) and in the f^ domain: « , = ( (E k - E,) + ( E m - E n ) / " t , ( 1 ' 4 2 ) 6. CALCULATION OF THE ECHO SPECTRUM In practice, it is not necessary to use the density matrix to calculate the frequencies and intensities of the echo spectrum. Using the results of the previous section, the program LEQUOR can be modified to perform the INTRODUCTION / 22 simulations. [32, 40, 41, 42] The energies of the system are calculated exactly the same way as for a normal dipolar coupled spectrum, by diagonalizing the secular determinant and solving for the eigenvalues of the Hamiltonian. Instead of calculating transition frequencies using (1.41), equation (1.42) is used. The relative transition intensities are now calculated as: I « ( l x ) k , ( P y ) j m 0 x) m n ( py)nk (1.43) where ( 1*)k) = l< V'k M x I V'l >l ( P y ) ] m = |< V) I P y I i>m >l Modifications of this sort are easily made to the program LEQUOR. LEQUOR can be further modified to include the effects of a refocussing pulse on other nuclei. For the systems studied in this thesis, the spectra are simple enough to be solved analytically, and these modifications were never made. c. EFFECTS OF IMPERFECT REFOCUSSING PULSES In the event that the rf field is not perfectly homogeneous over the entire sample, different spins will experience a different length of refocussing pulse. This leads to extra transitions in the spin echo spectrum which can be calculated quantum mechanically. In this case (1.36) can be replaced by: exp(-i/3F y) = n exp(-i/SI y k) (1.44) where /? is the length of the refocussing pulse. Expansion of the exponential for INTRODUCTION / 23 a single spin k, and regrouping gives: exp(-i/SFy) = cos | 1 + 2i sin | I y k d-45) where 1 is the unit operator. Switching from Iy to the ladder operators yields: exp(-i/SFy) = cos | 1 + sin | [I + - I _] (1.46) Equation (1.46) is now substituted into (1.36, 1.37) and into (1.43) for calculation of the spin echo intensities in the presence of an inhomogeneous rf field. It can now be seen that the phase of the refocussing pulse was chosen to be y in order to avoid the problem of complex arithmetic. In practice, the phases of the two pulses are cycled through an 8 pulse phase cycling routine to eliminate effects of inhomogeneous ir/2 pulses and receiver baseline drift. For calculation purposes it is sufficient to calculate the intensities for only one set of phases. B. SOAPS 1. PHASE BEHAVIOUR Soap is the generic term for alkali salts of long chain fatty acids. In general this includes molecules with 7 to 22 carbons, saturated or unsaturated, and any alkali metal counterion from lithium down to cesium. Soaps are amphiphiles, that is they have hydrophilic polar head groups in the form of carboxylate anions attached to hydrophobic hydrocarbon tails. This amphiphilic nature leads to a variety of phases when the molecules are dispersed in water. When added to INTRODUCTION / 24 •water at concentrations greater than the critical micelle concentration (CMC), the molecules will aggregate into micelles (see Figure 1.1), approximately spherical, with the polar head groups in contact with the aqueous solvent and the hydrophobic chains inside. The aggregation is a self assembly process in order to minimize the free energy of the phase. As the amphiphile concentration is increased, the molecules undergo a number of phase transitions — first into a regular hexagonal (H a) phase in which the molecules are packed into "infinite" cylinders with hydrophilic head groups exposed to the aqueous media and hydrophobic tails congregating in the centre. The phase is called hexagonal because the packing of the cylinders is in a hexagonal array. Further decrease of water concentration results in a cubic phase (Qa) in which the aggregates pack in a cubic arrangement. This phase is bicontinuous i.e. the water and soap each form infinite intertwining networks. With increased soap concentration a liquid crystalline lamellar or L f l phase is formed in which the molecules are arranged in lamellar or bilayer structures — water on the outside, hydrophobic chains inside. This phase is of considerable interest due to the structural similarities to cell membranes and this thesis is mainly concerned with potassium palmitate in the lamellar phase. If the temperature is decreased, the L a phase undergoes a disorder—order phase transition to the or gel phase. This phase is also lamellar in overall structure but the methylene chains lose considerable flexibility and become stiff and extended in the gel phase. The next low temperature phase is the coagel phase which consists of areas of crystalline soap/r^O 1:1 and pockets of dilute soap solution in water. In addition there are a number of intermediate phases formed by mixtures of INTRODUCTION / 25 FIGURE 1.1 Structures of Lipid Phases Legend: A) micellar, B) hexagonal (Ha), C) lamellar (L a) (Adapted from Reference 43) INTRODUCTION / 26 amphiphiles of differing chain length. Charvolin [44] has observed a cubic phase in combinations of potassium caprate and potassium stearate at water concentrations that normally produce a lamellar phase. Doane and Chidichimo [45 — 51] have done considerable work on a ribbon phase — an intermediate phase between a hexagonal and lamellar phase—formed by 1% potassium laurate in potassium palmitate at a higher water concentration than the regular lamellar phase. The existence of these intermediate phases can be explained in terms of the packing constraints imposed on the molecules by molecules of differing chain length, and on geometric arguments based on the overall structure of the phase. Tang et al. [22, 52] and Beckmann et al. [53] have used similar packing arguments to explain the quadrupolar splittings of lamellar phases of mixtures of soaps of differing chain lengths. The experiments in this thesis were mainly performed at a relatively low but constant water content: 70% by weight potassium palmitate: 30 weight % D 20 equivalent to a molar ratio of 6.3 moles water/mole soap. Commonly this concentration has been chosen because it is approximately in the middle of the lamellar phase region and phase transitions to the gel or coagel phase can be effected simply by changing the temperature. This study however, focuses on the lamellar liquid crystalline phase and this concentration was selected to make comparison to past studies [2, 3, 4, 5, 10, 54 — 64] easier. INTRODUCTION / 27 2. X-RAY STUDIES The original x—ray studies on potassium palmitate were done by McBain and Sierichs [65]. Their phase diagram, reproduced from reference [66], is shown in Figure 1.2. Extensive x-ray work on the soaps has been done by Gallot and Skoulios [67 — 70] and x-ray studies have been reviewed many times [66, 71, 72]. In the lamellar phase, the soap molecules form bilayer structures, a one dimensional lattice separated by regions of water. X —ray diffraction studies show that these bilayer structures exhibit long range (macroscopic) order and short range (molecular) disorder [71]. Small angle reflections, used to characterize the long range order have been used to measure the repeat distance between bilayers [67, 68]. The bilayers are approximately planar and equidistant. As the temperature is increased the thickness of the bilayer and of the lamellar repeat distance decreases accompanied by an increase in the area per polar head group reflecting the increased disorder of the hydrocarbon chains. The area per polar head group and the increase in interfacial area depends only on the counterion of the soap and not on the chain length. For potassium palmitate at 86°C, at water concentrations near those studied in this thesis (5.72 moles water per mole o soap), Gallot and Skoulios report a lamellar thickness of 26.8 A and a repeat o distance between lamellae of 36.0 A corresponding to an area per polar head group of 37.0 A . The area per polar head group in potassium soaps at a o water concentration of 6.3 moles water/mole soap changes from 39.3 A at 104°C to 34.1 A at 45°. X—ray diffraction studies of all lipids in the lamellar phase exhibit a diffuse INTRODUCTION / 28 FIGURE 1.2 The Phase Diagram of Potassium Palmitate/H20 1 1 1 I I I 100 80 60 40 20 10 SOAP WT % Legend: Isotropic solution —• micelkvr, middle soap = hexagonal (HQ), neat Boap = lamellar liquid crystalline (L a), curd = lamellar gel (L.0). Adapted from Reference 66 INTRODUCTION / 29 0 — 1 band in the x-ray diffraction pattern at (4.6 A) [71, 72]. This is almost identical to the diffraction pattern of liquid paraffin and reveals that the hydrocarbon chains are in a extremely disordered state. The average chain orientation, however is perpendicular to the lipid water interface especially at low temperatures/water contents when the average area per polar head group is decreased. ° — 1 At the gel-liquid crystalline phase transition, the diffuse band at (4.6 A) 0 — 1 changes to a sharp reflection at (4.26 A) . This is accompanied by an increase of the lamellar repeat distance. This is attributed to the transition of the hydrocarbon chains in the gel phase into an ordered all trans state. Investigation of the short range disorder characteristic of lamellar phases in lipid water systems is better accomplished by a technique which is sensitive to the molecular disorder. One technique which has been applied with particular success is magnetic resonance. 3. NMR STUDIES OF SOAPS a. GENERAL Soaps have long been the subject of nmr spectroscopic investigation. Nmr has been used to study both the static (spectroscopic) and dynamic (relaxation) properties of these systems, on a number of different nuclei. The spectral changes associated with phase transitions are dramatic, hence phase properties are easily studied by this method. INTRODUCTION / 30 Analysis of the solid state proton nmr spectra of lyotropic liquid crystals is not trivial. The plethora of unaveraged anisotropic dipolar interactions arising from the ubiquitous proton give broad formless lineshapes from which little information can be gleaned. Even in the lamellar phase, where intermolecular dipolar interactions are averaged by diffusion in the plane of the membrane and rapid reorientation about the director axis, individual dipolar couplings cannot be measured due to intramolecular dipolar broadening. Early nmr studies of lyotropic mesophases were severely hindered by these factors and by instrumental limitations. The most common technique was to disperse lipid in D 20 and then measure the deuteron resonance on the solvent and the proton resonance on the amphiphile. Since resolution of dipolar couplings was not attainable, experimentalists relied on relaxation studies and measurement of the moments of the lineshape. Two developments occurred which drastically altered this scenario. The first was the discovery of a facile synthesis for deuterated fatty acyl chains [73, 74]. This allowed the measurement of intramethylene deuteron order parameters at various sites in the bilayers. The second was the advent of pulse Fourier transform nmr and especially the quadrupolar echo pulse sequence [29] used to refocus the quadrupolar interactions outside the spectrometer dead time. Suddenly high fidelity deuteron nmr spectra were available with good signal to noise and little or no distortion. Since then, deuteron nmr has become one of the most popular and fruitful techniques in this field. The deuteron nmr spectra are distinct and very striking. In the lamellar phase, at sufficiently high temperatures, the unaveraged intramolecular quadrupolar coupling gives rise to a distinct doublet for almost every methylene group along INTRODUCTION / 31 the chain. At low temperatures just above the gel—liquid crystalline phase transition, the deuteron quadrupole nmr splittings of deuterons near the head group exhibit an approximately constant quadrupolar splitting. This is called the "plateau" of the order parameter profile. The quadrupolar splitting is directly related to the orientational order parameter of the deuteron in a carbon—deuteron bond (1.26). The order parameter is a measure of the time average of the orientational fluctuations of the bond. In unoriented dispersions, the H nmr spectrum for each methylene group consists of a superposition of doublets reflecting the random distribution of orientations with respect to the magnetic field. This characteristic spectral shape is termed the Pake doublet or the powder pattern. Hexagonal phase spectra exhibit similar general structure to lamellar phase spectra except the splitting is reduced by a factor of approximately — i due to extra averaging resulting from diffusional motion of the molecules about the long axis of the cylinders — an axis perpendicular to the symmetry axis of the individual molecules [75 — 77]. Gel phase deuteron spectra show only two distinct hydrocarbon quadrupolar splittings: a smaller one for the deuterated methyl groups which experience an extra degree of averaging due to rapid molecular motion about the ultimate carbon bond axis, and a broad formless larger splitting reflecting the not quite identical order parameters of a methylene chain frozen into an all—trans state [2, 76]. In a perfect all trans state, all methylene C—D bond vectors would make an angle of 90° with respect to the normal to the bilayer. The spectra in the coagel phase are similar in shape to the gel phase except that the methylene peak is considerably sharper owing to the freezing of the residual motions of the chains into a crystalline state. The methyl groups continue to rotate and display a reduced splitting of P2(cos70.5) = INTRODUCTION / 32 — 1/3 relative to methylene groups. On the deuteron nmr timescale, the methyl group rotation persists down to at least — 92°C in potassium palmitate/H^O [2] and down to — 113°C in rubidium stearate/H^O [56] which is well below the freezing temperature of the water (—60°C). In cubic liquid crystalline phases of amphiphiles neither amphiphile nor water molecules show orientational dependent quadrupolar or dipolar splittings [59 — 62, 78, 79]. Rapid translation of the amphiphiles within the cubically symmetric phase effectively average all anisotropic couplings to zero. (It is well known that molecules with tetrahedral or greater symmetry dissolved in liquid crystals exhibit no orientational order and hence no dipolar or quadrupolar splitting except for small effects due to asymmetric vibrations of the molecules [80, 81]. This is also true for molecules in a phase of cubic symmetry.) Micellar phases also give high resolution nmr spectra, but in this case it is the rapid tumbling of the micelles in solution which averages out residual quadrupolar and dipolar couplings [82 — 84]. b. SPECIFIC NMR STUDIES Much of the early magnetic resonance work on the anhydrous soaps was performed by Dunell et al. [85 — 88]. They investigated phase behaviour in a series of long chain fatty acids and their alkali metal salts. Second moments and linewidths were measured as a function of temperature and correlated with the phase behaviour. Relaxation measurements were also made and results correlated with X—ray data and calorimetry. One of the first nmr studies on the soap—water systems was done by Lawson INTRODUCTION / 33 and Flautt [89] in 1966. They described the shape of the 1H absorption line in sodium palmitateT^O and anhydrous sodium stearate as super—Lorentzian referring to the extremely broad wings in the lineshape. They attributed this to "a distribution of correlation times in the hydrocarbon chains" arising from restricted motion at the head group and freer movement farther down the chain. The super—Lorentzian lineshape was later observed by Lawson and Flautt [90] in dimethyldodecylamine oxide/T^O mesophases and Charvolin [61,62] in studies of potassium laurate/T^O later concluded that the proton FID consisted of 3 components, two solid like and one liquid like corresponding to three motional regions of the chain. The origin of the super — Lorentzian line was later clarified by WennerstrSm [91] and Bloom et al. [92], who suggested that the characteristic shape was due to rapid diffusion in the plane of the bilayer and to rapid axial motions of the hydrocarbon chains about the axis normal to the bilayer. The lineshape is then the typical lineshape of residual dipolar interactions projected along a symmetry axis (the bilayer normal). These motions have two additional effects. They average out the intermolecular dipolar couplings and give rise to an effective axial symmetry. This has important consequences which will be discussed later. Lawson and Flautt [89] and Charvolin [59,60,63] also observed two distinct D 20 resonances in the lamellar and hexagonal phases: one "bound" to the mesophase, exhibiting a quadrupolar splitting, and the other arising from free bulk water which gave a single resonance line. The quadrupolar splitting is not observed in micellar or cubic phases. It has since been realized that the water is not in the strictest sense bound to the interface, but rather in exchange on a timescale slow compared to the deuteron quadrupolar interaction. In addition, it may be the deuteron double quantum transition which is responsible for the INTRODUCTION / 34 central line [17, 93]. Following the discovery of a synthetic deuteration technique, Charvolin, Manneville and Deloche [64] oriented perdeuterated potassium laurate/TH^O by sandwiching the mixture between approximately 30 glass plates. This replaces the distribution of orientation dependent splittings by the relatively sharp lined spectra characteristic of a single orientation. In this paper a number of key points about these systems were demonstrated. They resolved for the first time a number of peaks in the nmr spectrum and attributed these to different positions on the hydrocarbon chain. They showed the angular dependence of the deuteron spectra by rotating the glass plates and demonstrated that the quadrupolar splitting truly does follow a P2(cos0) dependence, with maximum splitting at zero degrees orientation and no splitting at the magic angle. (The orientation dependence of the dipolar splitting had been previously reported by de Vries and Berendsen [94] who oriented potassium oleateyT^O between glass plates.) From the narrow, symmetric nature of the lines, they conclude that no appreciable static angular distribution is present and therefore the average electric field gradient is axially symmetric. In addition, the normal to the lamellae is shown to be a symmetry axis for the reorientational motions. They show the first order parameter profile with order parameters decreasing from the polar head group to the methyl end of the chain with plateau region. The small values of the quadrupolar splitting indicate that there is sufficient orientational disorder to appreciably average the quadrupolar interaction. In subsequent publications, Charvolin examined the phase behaviour of oriented INTRODUCTION / 35 deuterated potassium laurate [75] and potassium stearate [76] using deuteron magnetic resonance. In these papers, the existence of the plateau region was confirmed in the lamellar and hexagonal phases of both these amphiphiles. The plateau was suggested to arise from steric interactions with the other chains and was observed to disappear at higher temperatures. The gel phase was also examined [76] and magnetic resonance results were correlated with the area per polar head group of the molecules as determined by x—ray techniques. The technique of macroscopically aligning samples has been used numerous times with lyotropic liquid crystals to examine proton [95—100] and deuteron [4, 5, 75, 76] spectra. Artificial line narrowing to produce high resolution spectra in ordered phases can be achieved by orienting the glass plates at the magic angle, 54.74°. If the molecular motion projected along the normal to the phase (the bilayer for lamellar phases, the long cylindrical axis for hexagonal phases) is rapid enough, then all interactions which scale with P2(cosi9) are effectively removed without magic angle spinning. With the use of external magnetic field gradients, diffusion measurements have been made on the oriented systems [98—100]. In a series of elegant publications, which somewhat inspired this thesis, the nmr spectra of a series of fluorinated potassium myristates [101, 102] and their corresponding phosphatidylcholines [103 — 105] have been investigated. The fluoromyristates were originally synthesized to study orientational order in E.coli. and phospholipid model membranes [106, 107]. However, the nmr spectra were dominated by the anisotropic chemical shift and heteronuclear F—H dipolar coupling and in order to measure the F — F dipolar coupling in potassium INTRODUCTION / 36 4,4-difluoromyristate a pulsed spin echo technique was necessary. Rather than use a two—dimensional spin echo technique as is done in this study, Post et al. employed a Carr-Purcell-Meiboom-Gill (CPMG) sequence (90 x-(r-180°y-r) n) to refocus the heteronuclear dipolar interaction and chemical shift. A single point was deftly plucked from the peak of each echo and a free induction decay was composed from the collection of points. The resulting spectra, like those obtained using the two dimensional method, exhibited only a homonuclear dipolar coupling. The advantage to this method is that the entire free induction decay can be collected in a single shot, the disadvantage is that due to sample heating arising from the high duty cycle of the transmitter [108], problems with baseline drift [109—111], and cumulative pulse imperfections [112] only a limited number of points can be collected and this limits the digital resolution. The CPMG method was attempted numerous times in the present study to observe proton — proton dipolar couplings, but in order to obtain the necessary spectral width, the 180° refocussing pulses (~6 usee in duration) had to be placed 10 usee apart. The combination of transmitter power droop, cumulative pulse imperfections, receiver saturation and sample heating from the excessive numbers of pulses made measurement of the proton dipolar couplings impossible. Post measured the complete order matrix for the fluorines in potassium 4,4—difluoromyristate using the F — F dipolar coupling and the principal values of the fluorine chemical shift tensor [101]. On the basis of comparison of the proton spectra of fluorinated and unfluorinated potassium myristate and on the comparison of the S^p order parameter with S^jj's from other work, they concluded that the introduction of a single fluorinated methylene group has a INTRODUCTION / 37 negligible effect on the orientational order. Assuming the off diagonal elements of the order matrix to be zero, the order matrix for the 4 —fluoro methylene segment was found to be not axially symmetric at 50°C (S x x= -0.209, Syy= —0.155). In a temperature dependent fluorine nmr study of the fluorinated myristate [102], they report the existence of a new phase at temperatures below the gel phase. The phase is characterized by a sharpening of the F powder patterns and a reduction in F — F dipolar splitting of ~ i from the L f l phase. They postulate the existence of a low temperature hexagonal phase to explain these results. The water concentration was higher in these systems (77 wt% soap = 4.5 moles D20/mole soap), but this is still below concentrations that would normally produce a hexagonal phase. Rendall et al. (not John) have reported a low temperature hexagonal phase in sodium and potassium palmitate [113], however they report no gel phase in these systems and this may be due to confusion in nomenclature. In a series of review articles [1,114, and especially 71], Charvolin chronicled the work on the soaps to date and presented a summary of the types of motions present in the various phases. This is a view which has persisted to this day and has been confirmed by numerous relaxation studies in potassium palmitate, protonated [56] and perdeuterated [115], sodium laurate [21, 116] and rubidium stearate [58]. The liquid crystalline lamellar phase of the soaps is thought of as being a two dimensional fluid. Long range order is exhibited by the overall structure of the lamellae, whereas within each of the lamellae, the individual molecules possess a INTRODUCTION / 38 considerable degree of disorder. This orientational disorder arises from chain deformations (rotameric isomerizations), the effect of which increases towards the methyl end of the chain. This result is confirmed by numerous deuteron nmr studies which show quadrupolar coupling constants decreasing towards the end of the chain [2, 5, 64, 75, 76]. In addition to rotameric isomerizations, the hydrocarbon chains in the lamellar phase are believed to undergo a number of different motions including rapid rotation about the long axis of the molecule [56], and translational diffusion in the plane of the bilayer. Rapid rotation about the instantaneous director of the phase i.e. the long axis of the molecule projects the C—D order parameters (or the intramolecular dipolar interactions) along this direction [2, 76, 92] which is an effective 3 — fold or greater axis of symmetry. This also means that angular fluctuations from this symmetric state cannot last longer than a few jisec. Translational diffusion of oriented potassium oleate in the lamellar phase has been measured with constant and pulsed field gradient nmr experiments [99] and found to be 1.1 ±0.1 XlO cm /sec, rapid enough to average intermolecular dipolar couplings between neighbouring amphiphiles. This translational diffusion is believed to persist even into the gel phase [56]. Other low frequency motions possibly exist such as collective reorientations of the entire molecules, and long range director fluctuations, a rippling of the bilayer surface like the surface of a washboard [56]. As the temperature is lowered, rotational isomerizations are inhibited by steric interactions causing the plateau in quadrupolar splittings and a change in the INTRODUCTION / 39 activation energy as measured from deuteron relaxation [115]. At the liquid crystalline—gel phase transition, the chains freeze into a rigid all trans state and the overall width of the bilayer increases. Rotation about the long axis is still present in the gel phase and gauche —trans isomerizations near the head group have been invoked to explain relaxation data [56, 58]. The gel phase is known to be metastable and over a period of hours—days will change into a crystalline coagel state. c. RESEARCH INSPIRING THE PRESENT WORK The plateau, the region of constant quadrupolar splitting in the deuteron order parameter profile, is believed to arise from restrictions placed on segments near the interface by the steric influences of the neighbouring chains or by electrostatic interactions with the polar head groups. At higher temperatures the quadrupolar splittings decrease monotonically with chain position reflecting the removal of these influences due to increased average area/polar head group and increased thermally activated fluctuations of the molecules. The most dramatic demonstration of this has been given by Davis and Jeffrey [2] in the first of a series of three papers [2, 10, 3], who presented quadrupolar order parameter profiles for potassium palmitate—d3]/H.20 at 42° and 178°C, just above the gel—liquid crystalline phase transition and well into the L f l phase. The lower temperature spectra clearly display the plateau, the higher temperatures the characteristic exponential decrease. Davis and Jeffrey also observed unexpected behaviour in the temperature dependence of the deuteron order parameter profiles in the potassium palmitate/r^O system. At temperatures just above the gel to INTRODUCTION / 40 liquid crystalline phase transition the order parameters of the first four or five segments were observed to increase with increasing temperature. The D 20 splittings in potassium palmitate were observed to behave in a similar fashion [3] indicating that a correlation exists between the bilayer and the solvent. One would have expected the order parameter to decrease with increasing temperature as the molecular fluctuations which average the static quadrupolar splitting are increased. In addition, two distinct quadrupole splittings were observed for the deuterons at the alpha position of the molecule. This result was confirmed by measuring the quadrupole splitting in a sample of potassium palmitate deuterated only at the alpha position. In the selectively deuterated sample the increase — decrease of the order parameter was again observed (with maximum splittings at about 85°C) as were the two quadrupole splittings at intermediate temperatures (54±5°C). As the temperature was raised through this region the relative amplitudes of the two peaks change with the peak with larger splitting growing in intensity at the expense of the other. Values of the second moment, M2, for the selectively deuterated spectra followed the same trend. They termed this phenomenon a lamellar - lamellar "phase transition" (the quotations are theirs) and observed that the transition was reversible with no hysteresis. The characteristic temperature dependence of the order parameters is observed consistently in potassium palmitate, although with minor variations [2 — 5, 10, 54] and is also observed in sodium palmitate [21] but has not been reported in detailed temperature dependence studies of sodium laurate [3] or rubidium stearate [57,58]. In sodium palmitate [21] the temperature dependence of the ^ 3Na quadrupolar splittings parallels the increase —decrease of the deuteron quadrupolar splittings. Other nmr experiments on soaps have not been detailed INTRODUCTION / 41 enough to really tell. The two deuteron peaks for the alpha position seem to be exclusive to potassium palmitate. Others [4, 5, 117] have reported two alpha peaks whose temperature dependent intensity remains constant — these have been attributed to deuteron—deuteron dipolar couplings. Abdollal, Burnell and Valic [3] have postulated that the decrease in order parameter at lower temperatures and the two alpha deuteron splittings observed by Davis and Jeffrey may arise from structuring imposed upon the first few methylene groups by water molecules near the interface. The effect would be to pull the First C—C bond away from the most stable trans position towards a direction parallel to the bilayer director. The resulting order parameters would be reduced strictly owing to a geometric effect and if the structuring resulted in two configurations which exchanged slowly on the nmr timescale, two deuteron peaks could be observed. This disruption could be collective in nature — the two configurations occurring in separate domains of the sample possibly with slightly different transition temperatures due to sample inhomogeneity. A model based on the idea of two exchanging configurations was rendered in another of the three proximate articles in the same journal [2]. The article, penned by Abdollal, Burnell, and Valic presented a model based on geometric arguments, hitherto referred to as the Abdollal model, which explained the anomalous results of Davis and Jeffrey. The salient features of the Abdollal model can be best comprehended by examination of Figure 1.3. The model proposed two interchanging configurations, A and B, at the lipid—water interface. At lower temperatures, the lipid—water interaction imposes a structuring effect on the carboxyl group of the palmitate as is shown in Figure 1.3A. Here the first INTRODUCTION / 42 FIGURE 1.3 The Abdollal Model of the Lipid Water Interface-gouche (&r) trons (or gauche r * ) (A) Predominant configuration at lower temperature. (B) Predominant configuration at higher temperature. The all trans conformation and conformations with one gauche rotation are shown. In all cases the a — CH2 rHfj is perpendicular to the bilayer director. The efg represents the principal axis of the sodium efg tensor, (from Reference 3). INTRODUCTION / 43 C —C bond is shown to be parallel to the bilayer normal. This induces a tilt in the tail of the molecules which would persist down through the first few methylene segments. The placement of the polar head groups allow water molecules to hydrogen bond simultaneously to more than one lipid molecule. At higher temperatures, thermally activated fluctuations break the hydrogen bonds and the main interaction becomes the steric constraints (hydrocarbon intermolecular interactions) of the neighbouring chains. This leaves the first bond of the molecule in the trans state and leaves both r^ T j and rjjjj for the a—carbon perpendicular to the bilayer normal. Calculations based on this model were presented and are reproduced here in Table 1.1 Several simplifying assumptions were made: all CCC and CCD angles are tetrahedral, the HOH angle in water is given as 105°, the angle between lone pairs is 120°. Conformer rotations of 120° are used and rapid axially symmetric motion is assumed to project residual quadrupolar interactions along the director. All efg tensors were assumed axially symmetric about their bond directions. The C —D order parameters for each conformation (not to be confused with configuration) are calculated and averaged over the conformations scaled by their probabilities. In the all trans conformation (configuration B, no rotational isomers) all C —D order parameters are equal to P2(cos90)= — £. Conformational motions will lessen a particular SQTJ value by an amount dependent on the probability of gauche rotations up to that C—D bond. This leads to progressively decreasing quadrupolar splittings. However for configuration A, the absolute value of the segmental order parameters are less than the corresponding order parameters for configuration B. The overall order parameters which are the INTRODUCTION / 44 TABLE 1.1 Calculated Order Parameters From The Abdollal Model Configuration A Configuration B I I " 3 " 2 3 p t 3 p g ± 2 P t 3 F t 3 *g± pt F t >g± F g± D,0 0.06 0.15d efg -0.18 d aCa!culations are averaged over conformations t^t^t^, t^t^g^, t a / J g| t 6 and t^g^g^. For A g j^ and tap give equal contributions to order parameters. Assumes that the C - C bond is at an angle 35Vi° to n. Motions about C O O - C a axis are not con-sidered (i.e. Pgf = 0). cFor gauche conformation S = Vi (P, cos (90) + P2 cos (35V4)) = 0. d Assumes hydrogen bond parallel to first C - C bond and free rotation about 0. . . . D-0 axis. INTRODUCTION / 45 scaled sum of the configurational order parameters (S = P ^ A + PJJSJJ) would be smaller at lower temperatures due to the predominance of configuration A, increase with temperature as Pg increased, and then start to decrease as increasing thermal motions cause a lessening of the molecular order. The structuring effect would have progressively less influence going down the chain as rotational isomerizations relieve the induced stress and further average the quadrupolar interaction. The two effects act in an opposite fashion, cancelling each other out in the intermediate regime of the first few methylene groups leading to a constant S Q Q value — a possible explanation for the so called plateau. Another interesting feature of this model is that it adequately predicts the "odd—even" effect [2, 64, 75] which manifests itself as equal splitting for odd —even (e.g. C3 — C4) pairs of methylene groups near the polar head group at low temperatures in the L f l phase. If certain high energy g^g^tg^g4") conformations are ignored [118—120] then the calculated order parameters for S^ and Sy are equal in configuration A. Similarly Sg = S f if the conformation g^,ygtg eg^ e£ is neglected. This effect decreases down the chain as more conformations are made available. In configuration B, the calculated order parameters decrease progressively down the chain. Hence as temperature increases, and configuration B predominates, the ratio Sg/Sf increases from a value of 1 (i.e. the peaks overlap) to a larger value where the two have separate resolvable splittings. This model is remarkably simple — based on only a few geometric arguments, INTRODUCTION / 46 and involving calculations that, for segments near the head group, are easily performed on the back of an envelope. Yet it predicts the experimental results surprisingly well, not only the quadrupolar couplings, but the low temperature plateau, the odd—even effect and the high temperature behaviour, with only two adjustable parameters — the probability of a gauche rotation about C —C bonds and the probability of either configuration A and B. In oriented samples of potassium palmitate — dgj/I^O 72:28 by weight, Vaz and Doane [4, 5, 55] observed similar behaviour — the rise and fall of the order parameters near the head group, the constant decrease in the rest of the chain. However they reported two breaks in the slope of the temperature curves which they attribute to two lamellar—lamellar phase transitions, one just above the L^—L f l gel —liquid crystalline phase transition and one 25° higher at the maximum quadrupolar splitting. Doublets were observed for many of the quadrupolar resonances, but these were attributed to dipolar couplings between deuterons on each methylene group. No mention was made of the dependence of their intensities on temperature. The existence of three phases was confirmed by Differential Scanning Calorimetry (DSC) although the results were not actually reported. The phase transitions are postulated to arise from a change in the symmetry of the methylene chains — from axial symmetry at high temperatures to biaxial symmetry in the lower two temperature phases. This change in symmetry may entail a collective tilt of the chains away from perpendicularity to the bilayer surface or from a biased rotation about the long molecular axis. The high temperature phase transition has not been observed in any other study and this behaviour may arise from surface effects induced by the glass plates or INTRODUCTION / 47 may be a consequence of increased water concentrations. In a subsequent pubbcation [55], the behaviour of potassium palmitate-udg/I^O 70:30 wt% in lamellar dispersions was investigated. Deuteron powder patterns of the terminal methyl group were carefully recorded in a temperature range ±10°C about the lower temperature lamellar—lamellar phase transition. As the temperature is lowered, the deuteron powder patterns changed from axially symmetric through a two phase region where a superposition of axially and nonaxially symmetric spectra was evident (two quadrupole couplings), to a region of non — axiallity characterized by an asymmetry parameter of n = 0.5 —0.8. The quadrupolar splitting reached a maximum at the lower end of the two phase region and then fell off as the temperature is further lowered. This is in direct contrast to the work of Davis and Jeffrey [2], Abdollal, Burnell and Valic [3], and the previous work of Doane himself [4,5] in which the methyl group quadrupolar coupling was observed to increase continuously as the temperature was lowered with no onset of biaxiallity. AU previous studies were performed on perdeuterated soaps in which the numerous overlapping powder spectra may have obscured this behaviour. It is also possible that the low temperature measurements were made in the gel phase, although this would normally cause the a>—SQJ-J coupling to increase dramatically [2]. An attempt was made to clarify the head group behaviour in a paper by Higgs and Mackay, the third of the aforementioned triad [10]. A partially deuterated potassium palmitate was prepared in which the two a-deuterons were replaced with protons, the proton dipolar coupled spectra recorded, and in conjunction with INTRODUCTION / 48 the quadrupolar coupling measured from a—deuterated potassium palmitate, the order matrix for the first methylene segment was determined. The proton nmr spectra consisted of a single Pake doublet, characteristic of 2 dipolar coupled spin i nuclei [ll,p216ff] separated by a splitting A»>JJJJ=3/2DJJJJ broadened by intramolecular dipolar interactions with the remaining deuterons. The behaviour of the proton dipolar couplings is similar to that of the deuterons — rising to a maximum and then falling off with decreasing temperature with accompanying behaviour of the proton second moment. The value Spjjj was calculated directly from the dipolar splitting using (1.9) scaled by a factor of — £ since the samples were randomly dispersed. Assuming that the CH^ unit has two planes of symmetry — one in the plane of the three atoms and a second plane bisecting the HCH angle, the number of independent elements needed to describe the orientation of the methylene group is two [12]. If the molecule fixed axis system is carefully chosen, these are two of the diagonal elements of the order matrix (the third is uniquely determined since the matrix is traceless). The chosen axes were x, the H—H direction, y, the bisector of the HCH angle, and z, the normal to the HCH plane. Using this definition, S X X = SJJJJ, and S Y Y was determined from S Q Q and SJJJJ by a rotation about the z axis: S C D = S H H s i n 2 0 + S y y c o s 2 0 (1.47) where <p is one half the HCH bond angle. The magnitudes of the order parameters SQTJ and SJJJJ were found to differ somewhat, SQTJ being smaller in absolute magnitude than SJJJJ throughout most of the temperature range, crossing at lower temperatures. The values for S J Q J and Syy differ by a greater amount — up to almost 50% in the region where two deuteron peaks were observed. INTRODUCTION / 49 The difference in these elements of the order matrix reveals that the molecules are not axially symmetric at the alpha methylene groups — although axial symmetry is almost achieved at higher temperatures (>80°C). This evidence rules out a simple model where reduction in order parameters is reduced strictly by rapid symmetrical rotations about the long axis of the molecule and by director fluctuations about the rotation axis. This determination is actually incomplete since the assumptions made about the symmetry of the molecule are not entirely true [26]. While the plane of symmetry bisecting the HCH angle is vabd for the all trans conformation and may even be valid when the time average of all conformations is considered, the HCH plane is not a plane of symmetry if adjacent groups are considered: the methylene on one side and the carboxyl on the other. In order to determine the complete order matrix for the molecule, at least one extra nmr coupling must be measured. In the present study a similar molecule was synthesized — alpha protonated, but with a carbon—13 label at the carboxyl group. Now an off—diagonal element of the order matrix is available from the * 3C —H dipolar coupling and a truer test of axial symmetry and the validity of the Abdollal model may be made. C. NEMATIC LIQUID CRYSTALS AS AN ORIENTING MEDIUM Nematic liquid crystals, which align spontaneously in magnetic fields, have long been used as solvents for small molecules [121,122]. The solutes then exhibit a small average orientational order due to the influence of the anisotropic medium of the liquid crystal. The dipolar and quadrupolar (for I>1) interactions, normally averaged to zero by rapid molecular tumbling in liquids, now become the INTRODUCTION / 50 dominant interaction in the nmr spectrum. The dipolar interactions have been of particular interest in nmr [12,123-125] since they are related to the time averaged distance between nuclei. Therefore the dipolar coupled nmr spectra can be used as a probe of molecular geometry. Normally, in solid phases where the spins are dipolar coupled to all the other spins in the sample, the spectra consist of broad amorphous lines. In partially oriented systems, intermolecular dipolar couplings are eliminated as a result of low solute concentration and the rapid molecular motion of the solute relative to the liquid crystal. The resulting nmr spectra have contributions only from the intramolecular dipolar (or quadrupolar) interaction and appear as sharp lines superimposed on a broad background signal which arises from the liquid crystal. The experimental couplings can be related to the orientational order parameters as discussed previously (1.7). This has proved to be a powerful method to solve molecular geometries and to probe the mechanisms of orientational order in both solutes and liquid crystals. D. MOLECULAR MODELLING Most molecular modelling schemes for methylene chains in a bilayer or in a liquid crystal rely upon the modelling of the intramolecular and intermolecular potential and the use of this potential to calculate order parameters or some other quantity that can be compared to experimental values. In general, the potential is broken down into the sum of a number of different contributions. E total = E l n l + E e x t U-«> The first term, INTRODUCTION / 51 E m t , is the intramolecular potential that arises from the conformational rotations of the chain about the C—C bonds. The second term, E e x t , is the orientation dependent intermolecular potential arising from external forces, which may include steric effects of the other chains, hard sphere repulsive forces, weak attractive dispersion forces, electrostatic interactions, and surface effects. These forces are often modelled by a mean field surrounding a particular chain of interest. The advantage of a mean field approach is the considerable saving in computer time. In molecular dynamics [126,127] or Monte Carlo calculations [128 — 130], the behaviour of a statistically significant number of chains must be calculated, whereas with a mean field only the fluctuations of one chain in the mean field of its neighbours is important. 1. INTERNAL POTENTIAL The most common model for the internal potential is the Flory rotational isomeric state model (RIS) [118]. In this model, only a discrete number of conformers or rotational isomers about each C—C bond are allowed. These correspond to minima in a chosen internal potential, usually a 3—fold potential with the minima occurring at 0° and ±112.5° [118,p51]. These 3 conformations are termed the trans, gauche plus, and gauche minus conformers, represented as t, g + , and g~~ respectively. For liquid n—alkanes, the gauche minima have energies 2.1 ±0.5 kJ/mole greater than the trans minima with a potential energy barrier of about 14.6 kJ/mole at room temperature. For each conformer of the chain, the internal energy can be calculated by summing the contributions from each bond in the chain. Certain high energy conformers, for example g + g ~ and INTRODUCTION / 52 g — g + , are not allowed or are assigned high potential energies (e.g 10.5 kJ/mole) due to steric repulsion effects. This is called the pentane effect as it was first derived for n—pentane. The internal energy is then averaged over all possible conformers of the chain which is 3^ where (N+1) is the number of methylene segments. A partition function is calculated in the standard way, as the sum of the Boltzmann factors: Z = I e x p [ ( - E l o l ) i / R T ] . (1.49) Then a probability of each conformer can be defined as: P i = 2 e x P K - E t o t ) i / R T ] d.50) and from this starting point, all thermodynamic and experimental properties can be calculated. 2. SEELIG Early attempts to calculate nmr splittings in deuterated lipid chains were made by Seelig [131,132]. In his scheme, external effects were ignored and gauche rotations in the chains were considered in pairs separated by one or more trans linkages. These were called kinks ( g + t g — or g — t g + ) or jogs (g +tttg -, g —tttg +) in the chains. The kinks and jogs were invoked because a single gauche conformation in a chain would induce a reorientation of all segments in the chain down to the terminal methyl group. As Seelig pointed out [131], this would lead to an exponential decrease in order parameter, which although observed in spin INTRODUCTION / 53 label studies, is not observed in deuteron nmr studies of lipid bilayers. All studies of soaps [2, 4, 5, 52, 53, 64] show the characteristic plateau region of the order parameter profile at temperatures near the gel —liquid crystalline phase transition with exponential decrease only occurring towards the methyl group. In these early molecular models, the kinks and jogs were used intuitively to restrict the fluctuations of the chain rather than explicitly stating an intermolecular potential. In Seelig's papers, methylene chains (decanol or DPPC) were held in an all trans position and small angular fluctuations of the rigid molecule were allowed to reduce the molecular order parameter, S m o j , from the rigid all trans value of 1, according to the formula: S Q = | ( 3 < c o s 2 a > - l ) (1.51) where a is the angular fluctuation from the bilayer normal. They then define an experimental order parameter in terms of a kink probability as: Smol = S 0 [ P A ( ^ ) ( 3 c o s 2 0 o - l ) + P 4)(3cos 260 ° - 1 ) ] ^ where: P A + P B = 1 (1.53) The value P^ is the probability of finding the normal to the DCD plane at an angle of 0° with respect to the bilayer normal (which is defined as the first C —C bond direction) and the value of Pg is the probability of finding the normal to the DCD plane at an angle 60° to the bilayer normal. In the first paper, where only an isolated kink is specifically allowed, this was equivalent to INTRODUCTION / 54 being the probability of a trans conformation and Pg = 2?^^. In the second paper where a number of kinks and jogs were allowed in the same chain, then these strict probability definitions do not hold since a trans linkage in the middle of a jog, can be inclined at an angle of 60° to the bilayer normal. In the first paper [131] using this simple scheme with a value of S m o j = ~ 2 S C D = 0.57 they calculate P A = P t = 0.83 for S 0 = 0.7 and P t = 0.62 for S 0 = 1.0. A change in bilayer thickness as a result of kinking is discussed and compared with x—ray data. In the second paper [132], the value of S 0 is taken to be unity and the probabilities P^ and Pg were never explicitly calculated. Instead they postulated fluctuating kinks and jogs in the molecule with increased gauche isomers towards the end of the chain and they estimated 3 — 6 gauche isomers per chain at 50°C based on a Boltzmann type argument. In addition using a geometric argument, they estimated the decrease in bilayer thickness from the fully extended all trans chain to the disordered chain o o as 11.2 A compared with an x—ray value of 11.6 A. Seelig calculates the average segment length by: < ] i > = [PiA 1 + P»B * c o s 6 0 ° ] = I (1-0.5 P i B) (1-54) o where I = 1.25 A is the effective length of the segment and / cos60° is the projected length of a segment in the B state. The total length of <L> of the hydrocarbon chain was then found by: <L> = I <Jj> = I (15-0.5 I. P i B ) ] (1.55) For such a simple model, the results are good. However it was soon realized INTRODUCTION / 55 that specific intermolecular forces must be included for a complete description of the chain statistics. 3. INCLUSION OF EXTERNAL FORCES Various theoreticians have employed a number of external forces to model lipid chains or liquid crystals. These models are discussed in a number of recent reviews [133—136]. For the problem at hand, which involves interactions between the aqueous solvent and the polar region of the molecules, it is important to use a model in which the initial restrictions placed on the head group are minimal. Many models ignore the head group either choosing a small number of initial conformations (1-3) or choosing initial orientations at random. With this in mind, selected lipid modelling schemes will be discussed, some for their seminal nature and others for their direct applicability. 4. THE MARCELJA MODEL Marcelja's theory of chain ordering in liquid crystals [137] and in bilayers [120] is based on summation of the potential over all the conformations of the chain in a molecular field of neighbouring molecules. He writes the total potential as: E total + E ext = E int + E disp + E steric (1.56) The first term is the Flory type RIS energy defined as: E i n l = E 0 + I E ( | i . (1.57) INTRODUCTION / 56 where £ = t, g4-. E Q is the energy of the first three groups of the chain which are somehow rigidly affixed to a surface. The values E(£ ,t) =0, E(t,g±) = 1.67 kJ/mole and E (g4- ,g+) = 9.20 kJ/mole were used in his calculations. Marcelja used three initial conformations of the head group and generated all conformations based on these initial orientations. Conformations where the chain bent back into the aqueous region were not allowed. The second term, E^gp, is an effective attractive interaction energy that arises from dispersive van der Waals interactions between chains: Edisp = ~ * ( n t r / n ) I (|cos 2^-^) (1.58) where <p is the angle between the normal to the HCH plane and the normal to the plane of the bilayer and where ntr/n is the fraction of bonds in the trans state (included for the bilayer calculations, but not for the liquid crystal work). The strength of the molecular field is defined by the parameter $ where: * = V D <(n t r/n) I <|cos (1.59) Therefore $ depends on the average order of the system and on a coupling constant, V Q = 2.84 kJ/mole based on the freezing energy of polyethylene. The third term, E g t e r j c results from lateral pressure on each chain — it is essentially a steric repulsion term based on a hard sphere repulsive interaction: F - P A d - 6 0 ) L steric ~ PA INTRODUCTION / 57 where A is the cross sectional area of the chain and P is the pressure — estimated to be between 18—20 dyne/cm. The area per polar head is almost independent of chain length but very dependent on the concentration of the lipids dispersed in water. The area is approximated by: A = A 0 l 0 / l ( i ) (1-61) where 1Q and A Q are the length and area of the chain frozen in the all trans state and is the effective length of a particular conformation i.e. the length projected on the bilayer normal. Then the partition function can be calculated using (1.48) where the sum is over all conformations. The equation for the molecular field $ is given by: * = $ {[ ( n l r / n ) I (|cosV;3)] exp[-E(4». P ) / k B T ] | <l-«2) Note that this equation is self consistent — the calculated value of $ depends on E($). Values of V Q and P are chosen and $ calculated as a function of E($). The only valid solutions are where $ c a ] c = $chosen* Then the self consistent mean field energies can be calculated along with the partition function and relative probabilities of each conformation using (1.49) and (1.50). Knowing the conformational probabilities and choosing reasonable geometric parameters, the order parameters can be calculated as a weighted average of the order parameters of each conformation: S C D = I PiS; = I { ( e " E i / k T ) (S.) d.63) The Marcelja model has only one adjustable parameter — the lateral pressure P, INTRODUCTION / 58 but it has a number of parameters that must be chosen, the coupling constant, VQ, the energies of the trans and gauche conformers and the geometry of the molecule. The Marcelja model has been criticized on a number of points — his simplistic treatment of repulsive interactions as a lateral pressure and the fixed orientation of the first three segments of the chain. The term n^n in the attractive potential has been questioned since the intermolecular potential should not depend on the fraction of trans linkages. Marcelja claims it is necessary to model the lipid chains which freeze during the liquid crystalline—gel phase transition, as opposed to liquid crystalline chains which only reach a common average orientation. Marcelja also used an attractive (dispersive) force as the major contribution to his mean field. In more modern theories, the main part of the intermolecular potential is usually a repulsive term based on excluded volume or steric effects. However, Marcelja was the first to use the mean field approach to model behaviour in lipid bilayers, and his work inspired a number of investigators to continue in this vein. Schindler and Seelig were among the first to use the Marcelja model [119] with only minor changes in the numerical values. The values that Schindler and Seelig used (with the corresponding Marcelja values in brackets) are V Q = 2.47 (2.84) kJ/mol, surface energy P =18.5 (25) dyne/cm, E g = 2.09 (1.67) kJ/mole and the gauche rotation angle for the RIS approximation g4- = 120° (112.5°). The initial orientations that Seelig used are also different from Marcelja's. Seelig presents order parameters in good agreement with 2 H nmr experiments on DPPC although the fit is better towards the centre of the bilayer. They also use the model to calculate the trans, gauche and kink probability in the hydrocarbon INTRODUCTION / 59 chain. They find Pfc = 0.69 which lead to values of 9.7, 4.3, 0.6 and 0.2 for the average number of trans bonds, gauche bonds, kinks and jogs per palmitic acyl chain. The Marcelja model forms a basis for modelling of lipid chains. In general, the RIS approximation is used to describe the angular fluctuations, but Dill and Flory [138, 139] and the group of Gelbart [140, 141] have performed calculations in which the chains are placed on a two or three dimensional rectangular (cubic) lattice. In addition, a two dimensional triangular (hexagonal) lattice [134, 142, 143] has been used to model the alkyl chains. The conformations of a number of chains must then be considered, but a partition function may still be calculated as the sum over all the chains in the lattice, as opposed to a sum over all the conformations of a single chain. Dill considered the external intermolecular potential to be primarily repulsive and included this as a chain stretch which promotes linear chain conformers. Gelbart also used a repulsive intermolecular potential, which he considered to be a lateral pressure, which is determined by solving the equations for the packing constraints. The lateral pressure is not necessarily held constant from layer to layer in the lattice. In later work, Gelbart [144] applies the same theory to RIS chains. Again the intermolecular potential depended on packing constraints which depend on an average area per polar head (i.e. the lateral pressure) and on a density profile within the bilayers. Gruen [145, 146] adapted the Marcelja model, included a specific head group interaction, and calculated two lateral pressure terms, one for the head group INTRODUCTION / 60 and one for the chains. In later work [147, 148] Gruen used a model very similar to that of Gelbart. The internal potential was calculated as a sum of an RIS term and a hydrophobic contact term which reduces the probability of methylene segments exposed to water. The mean field is again assumed to be repulsive in nature, largely due to packing constraints and interpreted in terms of a straightening of chains. All of the models discussed above adequately reproduce experimental order parameter profiles. The plateau of deuteron quadrupolar splittings is adequately represented and is a result of the repulsive, steric packing constraints considered in the mean field interaction potential. In simulations of the soaps, however, no model can adequately reproduce the large value of the order parameter at the methylene group adjacent to the head group [138, 144, 148]. This arises because the forces included to model the interactions at the head group do not include any specific intermolecular interaction which would influence the head group orientation. In other words, the orientation of the head group is either chosen to lie in one of a few initial conformations [119, 120, 131, 132, 137, 146], or is forced into restricted initial conformations by the chain modelling procedure [134, 138—143], or the conformations are generated at random [144, 147, 148]. The proper procedure would be to integrate over all initial head group orientations. For anything but a very limited number of conformers, this would be prohibitively expensive. In order to calculate the dipolar and quadrupolar couplings for methylene segments near the head group in lamellar phase soaps a model must be chosen in which the head group orientation is not restricted by the imposed initial conditions. 5. THE SAMULSKI INERTIAL FRAME MODEL INTRODUCTION / 61 The model upon which calculations in this thesis are based is the Samulski inertial frame (D?) model [6 — 9]. The approach is similar to the other mean field models — the RIS approximation is used, the partition function and order parameters are calculated in the same fashion. The Samulski model relies on one approximation: that the axis system that diagonalizes the moment of inertia tensor of a particular conformation diagonalizes the order matrix for that same conformation. Samulski's interaction potential is divided into three terms: E = EDA + E N B + E c(r) (1.64) where E p ^ is the dihedral angle energy (equivalent to the internal energy of the conformations discussed previously), Ej^g is the nonbonded interaction energy between atom pairs. Based on a Lennard—Jones 6-12 potential, this term prevents the molecule from coiling back on itself. The third term, E^(r) is the mean Field part of the potential assumed to be a primarily repulsive Lennard—Jones potential characterized by a hypothetical cylinder of variable radius, r. The radius of this cylinder is the sole adjustable parameter of this model. The method employed is to generate all possible RIS conformations, calculate the internal energies, and then for each conformation perform rotations about the centre of mass to rotate the molecule into the principal moment of inertia (PMI) axis frame. From the principal moments of inertia for a particular conformation, the semiaxes of an ellipsoid with uniform mass distribution having the same INTRODUCTION / 62 inertia tensor as the conformation are easily calculated as: A a = {]„ + \ y y - l a a ) 5 / 2 m (1.65) where m is the mass of the molecule, a,p\7=x,y,z and A x f i A y < A z by definition. Then the conformation dependent molecular diagonal order matrix is assumed to be proportional to the ellipsoid semiaxes: S « = 1 " ( A x + A y ) / 2 A 2 d.66a) S x x = _ 2 + A X/2A 2 S yy = _ ^ "f A y/2A Thus the order matrix is defined to be traceless, and the elements of the order matrix are defined such that — 0.5<Sxx,SyyS0 and 0sSzzi<1.0. The limits on S Z 2 describe the limiting geometries of the ellipsoid: S z z = l for an infinitely thin cylinder (A x=Ay = 0) and 8^=0 for a perfect sphere (A x=A y=A z). This reflects the orientational order of each conformation, and in effect allows for small amplitude rigid fluctuations of the molecules which reduce the overall value of the order parameter matrix. Then the external contributions to the potential are calculated, Ej^g from the position of the chain methylene groups relative to each other and —Q(T) from the positions of the methylene groups relative to the constraining cylinder. The distance between each atom and the nearest point on the cylinder is determined, and the interaction is calculated as a Lennard—Jones 6 — 12 potential. This potential is summed over all methylene groups in the (1.66b) (1.66c) I N T R O D U C T I O N / 63 molecule and added to the total potential. Then the partition function, statistical weights and probabilities of each conformation can be calculated as described previously using (1.48) and (1.49). The segmental order parameters for each conformation are determined using (1.11). For a diagonal molecular order matrix and noting that z=r cos#2 and x 2+y 2 + z 2=r 2 (1.11) becomes: S|j = —2 [ S ^ X i f + S y y y i j 2 + S z z Z i 2 ] (1.68) r ij where x^ , yy, and z^ are the distances between the resonant nuclei (or between C —D for the deuteron measurements). Assuming an axially symmetric field gradient, the deuteron quadrupole splittings are easily determined: 2 3e qQ 1 0 0 „ = — — — [ S ^ x , 8 + S y y y u 2 + S 2 z Z j j 2 ] 4n r jj Calculation of the dipolar couplings, while never explicitly done by Samulski, is completely analogous: D i j = — T — [ S x x X i j + S y y y j j 2 + S 2 z Z i j 2 ] (1.70) 47T r ij The dipolar or quadrupolar splittings are then scaled by the conformer probability which takes into account both internal and external forces and summed over all conformations to get a predicted coupling. The "goodness of fit" is tested by a "Reliability Factor" which is defined as: R = ^ A l / i ca lc ~ Lux obs ) ( L 7 1 ) I obs The cylinder radius is varied and the calculation performed iteratively in order to INTRODUCTION / 64 minimize R. There are a number of advantages to using this molecular modelling scheme. The orientation of the head group is determined separately for each conformation dependent upon a physical property (the moment of inertia tensor) rather than choosing a discrete number of orientations or generating initial orientations randomly. Specific head group solvent interactions like hydrogen bonding can be easily included in such a model through the addition of an extra term in the potential. The model deals with conformational motion simultaneously with reorientation of the molecule. Small amplitude fluctuations which reduce the values of all order parameters equally are included by calculation of a conformer order matrix. However the IF model has no self consistent calculation of the mean field and therefore cannot o priori predict the temperature dependence of experimental quantities. In this sense it is cruder than the Marcelja and other mean field models. The appeal lies in the conceptual simplicity of the modelling of external forces and especially in the treatment of the head group orientation which is critical in the study of orientational order near the lipid water interface. This concludes the introduction, which has been a discussion of the systems studied, the methods used to study them and the models needed to interpret the results. The next chapter will consist of experimental details. The following three chapters will discuss the results obtained and their interpretation in the three isotopically substituted potassium palmitates, the corresponding three acids dissolved in a liquid crystal, and the series of short chain acids dissolved in the same liquid crystal. A short discussion at the end will tie these three chapters INTRODUCTION / 65 together and summarize the major findings of this thesis. TL. MATERIALS AND METHODS A. NOMENCLATURE Part of this section describes the synthesis of three partially deuterated species of palmitic acid. Their IUPAC names are hexadecanoic — 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 16-d 3 1 acid, hexadecanoic- 1- 1 3C- 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 16-d 2 9 acid and hexadecanoic- 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 16—d 2y acid. These names, which draw attention to the deuterated portions of these molecules, are obviously too unwieldy to be used consistently throughout the course of this thesis. Since this is primarily a study which deals with nmr interactions near the carboxyl group of these molecules, and therefore largely with the protons and carbon 13 present, liberty has been taken with the nomenclature to emphasize the lack of deuterons at the head group. The new names become hexadecanoic acid — d 3 j , 1 — * 3C — 2, 2 — H 2 — hexadecanoic acid-d 2g and 2, 2, 3, 3 —H4~hexadecanoic acid-d2y. These names are used throughout this chapter. However, there is a large body of literature on the study of the potassium salts of compounds very similar to these. In keeping with tradition, the common names of the fatty acid salts are adopted throughout the rest of the thesis: potassium palmitate—dgj, 1 —* 3C—2, 2—H2~potassium palmitate—d2g and 2, 2, 3, 3—H^—potassium palmitate—d 27 or, in less lucid moments, perdeuterated potassium palmitate, alpha protonated palmitate and alpha beta palmitate. To maintain consistency, the short chain acids are also given 66 MATERIALS AND METHODS / 67 common names: ethanoic, propanoic and butanoic-2,2—d2 acids becoming acetic, propionic and butyric—2,2—d 2 respectively. B. PREPARATION OF PERDEUTERATED FATTY ACIDS Fatty acids were obtained from Calbiochem—Behring or Merck Sharp and Dohme and used without further purification. Perdeuterated acids were prepared using the method of Hsiao, Ottaway, and Wetlaufer [74]. Typically 10-20 g of fatty acids were mixed with 3-5 g of 10% Pd on charcoal catalyst (MCB# PX5 5865) in a 2 neck 250 mL round bottom flask. This mixture was melted in an oil bath on a magnetic stirrer. The round bottom flask was connected to a water condenser which was connected to an oil bubbler to monitor the gas flow and the system was flushed with nitrogen gas. The melt was heated to 150—180°C and deuterium gas was passed over the surface of the stirring mixture at a rate of 1 bubble/2 sec. Deuterium gas was generated by electrolysis of D 20 (MSD 99.8%D) using an Elhygen Mark TV hydrogen generator. The electrolyte consisted of 200 mL of 40% NaOD in 99.0%D D 20 (MSD #MD 358). Reaction mixtures were heated with stirring for 7—14 days and progress was monitored with high resolution *H nmr and mass spectroscopy. Deuterations could be run in series by inserting a dry ice or ice—methanol cold trap in between reflux apparati to trap volatile components. After the desired degree of deuteration had been achieved, (>98%) the reaction mixture was allowed to cool and solidify. The reaction flask was wrapped in a clean dry cloth and the flask was broken by mechanical shock with a hammer. The highly deuterated cake of solid fatty acid was removed leaving behind isotopically impure fatty acid which had splashed MATERIALS AND METHODS / 68 and dried on the walls of the flask. The fatty acid was dissolved in warm ethanol and the catalyst removed by vacuum filtration either through a medium glass frit (which tended to clog) or through diatomaceous earth/Whatman #1 filter paper in a Buchner funnel. Increasingly apolar solvents were used to remove the perdeuterated acid from the catalyst: ethanol, diethyl ether and hexanes. In later preparations a Soxhlet extractor was used for this purpose — what a marvelous invention. Extracts were refiltered to remove traces of catalyst and the solvent was removed by rotary evaporation. Yields of 90% were not uncommon. The perdeuterated acid was then recrystallized from hexane and/or ethanol/water. The final extent of deuteration was determined by high resolution proton nmr and mass spec. For the nmr determination, acid was weighed into a 5 mm nmr tube and a small amount of benzene was added by weight. Percent deuteration was calculated from the integration of the proton signal. The mass spectra of the perdeuterated fatty acids are very characteristic consisting of a series of envelopes of peaks separated by 16 amu (the mass of a CD 2 group). Only the intensities of the envelope surrounding the parent peak are reported, since these are the peaks used to determine percent deuteration. Perdeuterated acids were purified using silica gel flash chromatography [149]. For each gram of fatty acid approximately 10 grams of silica gel 230 — 400 mesh was used. For 2.5 g of fatty acid it was necessary to use a 2 cm diameter X 70 cm in length column fitted with a 250 mL solvent reservoir and ground glass joint. Into the bottom of the column was placed a plug of glass wool and approximately 2 cm of sand to prevent clogging. The silica gel was poured in dry and packed under pressurized nitrogen gas with freshly distilled hexane. MATERIALS AND METHODS / 69 About 200 — 300 mL was used to pack the column. Solvent was then drawn down to just above the surface of the silica gel bed. Sample, dissolved in a minimum amount of solvent, was applied with a Pasteur pipette to the top of the column, being careful not to disturb the surface of the gel. The sample was drawn inside and several 10 mL aliquots of packing solvent were added to the surface and drawn into the column. Pressurized N 2 was used when the going was slow. This procedure keeps the sample localized in a small region of the column which helps give better separation. The column was eluted under pressure (~8 psi=10 cm/min) with hexane until nothing comes off and then with hexane/toluene 1:1. Aliquots of 50—150 mL were collected into weighed round bottom flasks and the solvent removed by rotary evaporation. The progress of the column was monitored by thin layer chromatography on silica gel plates using high boiling petroleum ethendiethyl ethenglacial acetic acid 70:30:2 as the developing solvent. Chromatograms were developed in an iodine chamber (the organic compounds absorb the sublimed iodine from I 2 crystals and appear as brown spots) or observed under ultraviolet light. In general, nothing came off the column until the solvent was changed. The first hexane - toluene fractions contained an oil which was the decarboxylated fatty acid, the major side product of the reaction, Rf = ~0.70. This was followed by the purified fatty acid with an R^  of ~0.30. Fractions showing only one spot in the chromatogram were dissolved in methyl alcohol, pooled and rotovapped. Fatty acids were recrystallized at least twice from hexane or ethanol/water and stored in a vacuum desiccator for at least 12 hours before use. MATERIALS AND METHODS / 70 C. PREPARATION OF 2,2,3,3-H 4-HEXADECANOIC ACID-D 2 7 1. REDUCTION OF TETRADECANOIC ACID [150] a. PREPARATION OF REACTANT Tetradecanoic acid (myristic acid) was deuterated by Dr. T.P. Higgs described in section UB. The extent of deuteration was found to be >99% by mass spec and high resolution nmr. Perdeuterated myristic acid was recrystallized twice from freshly distilled acetone and dried overnight in a vacuum desiccator. Rf : 0.38 (h.b.petroleum ethendiethyl ethenglacial acetic acid, 70:30:2); ms m/z: 257(1.7), 256(16.3), 225(M + ,100), 254(9.6); JH nmr (60 MHz, CDC13) 6: 9.30 ppm (s, IH, COOH). b. PREPARATION OF REAGENT 1.5 equivalents lithium aluminum hydride (LiAlH^, LAH), 1.74 g, was added to 100 mL anhydrous ether in a dry round bottom flask in dry ice in the fume hood. The flask was gently heated to facilitate dissolving the LAH. In fact, the LAH did not dissolve but formed a murky suspension. A reflux condenser with a CaCl2 drying tube was fitted to the flask. Perdeuterated tetradecanoic acid (6.73 g 0.0264 moles) was dissolved in 100 mL anhydrous ether and added dropwise to the cooled reaction flask with a dropping funnel. The reaction mixture was refluxed for 3 hours. The reaction was quenched by adding solid Na2S0 4 • 10H2O slowly to the cool reaction mixture in the hood. Na2SO 4«10H2O was prepared MATERIALS AND METHODS / 71 by suspending Na2SO^ in water and decanting off the excess water. The residue was removed by gravity filtration and washed thrice with 100 mL aliquots of ether. Solvent was removed by rotary evaporation and the resulting white powder was recrystallized once from diethyl ether. The 1,1—H2 —1~ tetradecanol—d27 crystallized as white gleaming leaflets from diethyl ether at dry ice temperature and was stored overnight in the vacuum desiccator. The yield was 5.45 g (85.7%). Rf : 0.19 Qi.b.petroleum ether:diethyl ethenglacial acetic acid, 70:30:2); ms m/z: 224(1.2), 223(12.7), 222(M + -HDO,100), 221(44.9), 220(2.5); *H nmr (60 MHz, CDClg) 6: 3.6 ppm (s, 2H, -CH2OH), 4.7 ppm (s, 1H, -OH); mp: 32.9-34.4°C (uncorrected). 2. PREPARATION OF 1,1- H 2 - 1 - TETRADECANOL METHANESULFONATE - d 2 7 [151-153] To a solution of 5.45 g (0.0226 moles) of 1,1-H2 tetradecanol—d27 in 110 mL methylene chloride was added a 50% molar excess of triethylamine (3.47 g, 0.0343 moles) in 50 mL methylene chloride. The mixture was cooled to — 10°C in an ice/water/NaCl bath. A 45% molar excess of methanesulfonyl chloride (3.73 g, 0.0327 moles) was dissolved in 40 mL methylene chloride and was added to the reaction mixture slowly with a Pasteur pipette. The reaction was stirred for 3.5 hours at —10 — — 5°C resulting in a yellow solution. The completed reaction was extracted with cold 150 mL aliquots of deionized water, 10% HCl, saturated NaHCOg and saturated NaCl. The organic layer was dried overnight over Na2S04. The drying agent was removed by gravity filtration and the MATERIALS AND METHODS / 72 solvent was removed by rotary evaporation. The product was an oil which crystallized in the fridge into white translucent needles. Recrystallization from 95% ethanol gave a dense white fibreglass like mat of crystals, which when dried overnight in vacuo yielded 6.59 g of tetradecanol methanesulfonate, a 91.4% yield. Rf : 0.25 (h.b.petroleum ethendiethyl ethenglacial acetic acid, 70:30:2); ms m/z: 224(3.1), 223(15.8), 222(M+-mesyl-D,100), 221(8.5), 220(0.2); JH nmr (60 MHz, CDC13) 6: 2.9 ppm (s, 3H, -O-SOg-CHg), 4.1 ppm (s, 2H, -0-CH 2-CD 2-); mp 38.8-41.3°C (uncorrected). 3. PREPARATION OF 2,2,3,3-H4-HEXADECANOIC ACID-d 2 7 [152,154] a. PREPARATION OF SODIUM DIETHYL MALONATE Into a IL round bottom flask flushed with nitrogen gas and fitted with a reflux condenser and CaCl 2 drying tube was put 250 mL thoroughly dried xylene. Xylene was dried by distillation from P 2Og and stored over CaH2. 0.540 g (0.0235 moles) of sodium metal was added to the xylene and the flask was heated to 120°C in an oil bath with vigorous stirring in order to melt the sodium. The mixture was cooled to room temperature while stirring. Diethyl malonate (4.34 g, 0.0271 moles) was dissolved in 80 mL xylene and added to the stirring reaction mixture drop wise through a dropping funnel. The reaction was allowed to proceed overnight at room temperature under a small positive nitrogen pressure. A white gel like precipitate formed. MATERIALS AND METHODS / 73 b. PREPARATION OF 2,2,3,3—H4—HEXADECANOIC ACID 1,1—H2_ 1—tetradecanol methanesulfonate—d27 (6.10 g, 0.01911 moles) was dissolved in 80 mL clean dry xylene and added slowly to the reaction mixture through a dropping funnel. The temperature was raised to 120°C with the use of an oil bath and the solution was refluxed for 5 hours. Rotary evaporation of the solvent yielded a yellow oil which did not crystallize when stored overnight under nitrogen gas in the freezer. The oil was saponified for 1 hour in 150 mL of 5% KOH in 80% ethanol on a steam bath at 80°C. 2N H 2S0 4 (72 mL) was added slowly to the solution at 80°C until acidic (pH = 4). Stirring and heating was continued for 30 minutes resulting in a clear slightly yellow solution with a white precipitate. Most of the ethanol was removed by rotary evaporation and 200 mL of deionized H 20 was added. This solution was extracted four times with diethyl ether and the ether extracts were stored overnight over Na 2S0 4. The drying agent was removed by filtration and washed with ether. The ether extracts were rotovapped, redissolved in a small amount (10 mL) ether and transferred to a 100 mL 2—neck round bottom flask. The ether was removed by evaporation under a stream of nitrogen. The flask was connected to a water aspirator and a gentle stream of nitrogen (2 psi) was passed through the flask. The flask was heated in an oil bath at 170°C for 2 hours. Effervescence was observed as the decarboxylation takes place. The result was an amber coloured liquid that solidified to a yellow—white sludge in the freezer under nitrogen. The yellow solid was recrystallized thrice from freshly distilled acetone, and then MATERIALS AND METHODS / 74 recrystallized from ethanol using Norit decolourizing charcoal before the hot filtration step. The fatty acid was recrystallized from hexane and then from acetone — water using decolourizing charcoal. Flash chromatography was performed using hexane and hexane:toluene 1:1 as the eluting solvents. The final yield was 1.80 g 2,2,3,3—H^—hexadecanoic acid—d 2 7 (2,2,3,3-H^ —palmitic acid-d 2 7) (33.3%). The overall reaction yield was 26.1%. Rf : 0.31 (h.b.petroleum ethendiethyl ethenglacial acetic acid, 70:30:2); ms m/z: 286(0.2), 285(3.5), 284(17.0), 283(M+,100), 282(8.5); JH nmr (400 MHz, CDCI3) 6: 1.57 ppm (t, 3 J 2 3 = 7.0 Hz, 2H, - C D 9 - C H 9 - C H 9 ) , 2.30 ppm (t, 3 J 2 3 = 7.0 Hz, 2H, -CH 2-CH2-COOH); mp 57.8-59.4°C (uncorrected). D. PREPARATION OF 1- 1 3C-2,2-H 2"HEXADECANOIC ACID-D 2 9 [155] 1— C hexadecanoic acid (1— C palmitic acid), 99.4 atom% C was purchased from Merck Sharp and Dohme, Montreal (MS-3124 lot 2269-J). 1 3 C hexadecanoic acid (1.08 g 0.00420 moles) was mixed with 0.27 g 10% Pd on charcoal catalyst and deuterated as described in section HB. The yield was 0.90 g (74.1%). Mass spec and high resolution nmr showed greater than 97% deuteration. * 3C hexadecanoic acid —d 2g (0.20 g, 6.9X10 - 4 moles) was dissolved in 5 mL of a 0.57M KOH/H20 solution and this solution was pipetted into a thick walled Carius tube (10 cm X 2 cm). The tube was approximately half full. The solution was frozen in liquid nitrogen, the air removed carefully to prevent foaming and replaced with 0.5 atm of nitrogen. The tube was flame sealed and put into a glass jacket inside a 0.5 inch thick stainless steel high pressure reaction vessel (bomb). The bomb was filled with water to the level of MATERIALS AND METHODS / 75 the solution in the Carius tube, sealed, placed into a heating mantle containing sand and wrapped successively in heating tape, glass wool, and aluminum foil. The reaction vessel was heated and the pressure gauge was used to monitor the temperature. The reaction was maintained at 245 psi (approximately 205°C) for two days and four hours (52 hours). The bomb was cooled, the sealed glass ampoule removed, wrapped in a clean dry cloth and the ampoule opened by mechanical shock with a hammer. The gel inside was removed and dissolved in water. The mixture was acidified with HCl and extracted thrice with diethyl ether. The ether was removed by rotary evaporation leaving a white powder which was recrystallized from hexane and dried in a vacuum desiccator. The yield was 0.16 g (80.6%). This procedure was repeated with 0.30 g of fatty acid at a slightly higher temperature (460 psi 240°C) with a yield of 0.25 g (82.7%). Rf : 0.28 QJi.b.petroleum ethendiethyl ethenglacial acetic acid, 70:30:2); ms m/z: 288(6.9), 287(31.2), 286(M + ,100), 285(73.3) 284(28.1), 283(6.4), 282(2.0); *H nmr (400 MHz, CDCI3) 6: 2.33 ppm (d, 2 J C H = 7.8 Hz, 2H, -CD^CHg-COOH), residual proton peaks due to incomplete deuteration at: 0.87 ppm (methyl), 1.20 ppm (methylene), 1.27 ppm (methylene), 1.61 ppm (0 — methylene); 1 3 C nmr (75.4 MHz, CDCI3) 6: 179.13 ppm (t, 2 J C H = 6.8 Hz, 2H, -CH 2- 1 3COOH). E. PREPARATION OF 4 - (OCTYLOXY) - BENZOIC ACED-Dj 3.0 g of 4 —(octyloxy)—benzoic acid (p—octyloxybenzoic acid, p—OOBA), purchased from Frinton Laboratories, Vineland N.J., was dissolved in 100 mL hexane and 2 mL D 20 with heating. The mixture was refluxed for one hour, the flask was MATERIALS AND METHODS / 76 cooled below the boiling point, the D 20 was drawn from the bottom with a Pasteur pipette and replaced with fresh D 20. This process was repeated. Upon cooling the p—OOBA—d^ crystallizes. OOBA was recrystallized from hexane and dried in vacuo. The yield was 2.5 g (84%). The absence of the carboxyl proton was confirmed by *H nmr and mass spec. F. SHORT CHAIN CARBOXYLIC ACIDS Glacial acetic acid, propionic acid and butyric acid were obtained from Fisher Scientific (Canada) and used without further purification. Butyric acid—2,2 — d 2 was prepared by Dr. T.P. Higgs using the method of Atkinson et al. [155] by refluxing in KOD/ D 20. The acid was recovered by acidification of the reaction mixture followed by vacuum distillation. The extent of deuteration was determined to be 97.4% by 1H nmr. ms m/z: 91(73.3), 90(M + ,100), 89(58.9), 88(2.2), 75(1818.6), 62(7315.7). G. PREPARATION OF FATTY ACID SALTS To a solution of fatty acid dissolved in a minimal amount of ethanol was added 1.05 equivalents of an IM KOH/H20 solution. The mixture was stirred for at least 15 minutes and the solvent removed by rotary evaporation. Fatty acid salts were slowly recrystallized at least twice from ethanol and washed with ice cold solvent. Fatty acid salts were dried in vacuo for at least 24 hours before use. H. SAMPLE PREPARATION MATERIALS AND METHODS / 77 1. SOAPS Soaps were weighed into an 8 mm borosilicate glass tube sealed at one end and with a constriction —1.5 cm from the bottom. Excess soap was removed from the walls of the tube with a cotton applicator. A second constriction was made in the glass tube with a torch, being careful not to char the sample. D 20 (100%D) was added to the surface of the soap with a Hamilton syringe in the ratio 6.3 moles D20/mole soap. The tube was placed onto the vacuum line and frozen in liquid nitrogen. The air was removed and replaced with 0.5 atm nitrogen gas. The tube was thawed and the freeze—pump —thaw procedure was repeated four times. The frozen tube was then sealed by torch at the second constriction which produces a dumbbell shaped sample tube. The sample was heated in a 110°C oven and the soap was centrifuged through the constriction at least one hundred times to ensure homogeneity. The sample was then frozen and flame sealed at the constriction. At each stage of this procedure the tube was weighed to ensure that no water was lost to evaporation. The samples were stored in a 110°C oven for a minimum 3 day period prior to use. 2. LIQUID CRYSTALS Liquid crystal samples were prepared by weighing 11 mole% of the appropriate solute into the liquid crystal (p —OOBA—dj) in either a standard 5 mm nmr tube or an 8 mm (diameter) by 2 cm tube attached to a ground glass joint by a narrow constriction. Samples were then degassed as above and sealed under MATERIALS AND METHODS / 78 0. 5 atm nitrogen gas. Before each experiment, the mixtures were twice heated to a temperature above the nematic — isotropic phase transition and mixed thoroughly in order to assure sample homogeneity. 1. NMR 1. DEUTERON NMR Deuteron nmr experiments were performed using a Bruker BKR 322 —s high power pulsed nmr spectrometer equipped with a 4.7T Oxford instruments superconducting magnet. The deuteron resonance frequency was 30.7 MHz. The 90° pulse length was typically 5 — 9 usee. The quadrupolar echo method (90 x—T — 90y—T —echo) [29] was used to avoid the effects of receiver deadtime. The pulses were cycled through a 4—pulse phase cycling sequence: xy, —xy,x—y, —x—y and the resulting echoes were alternately added and subtracted from the computer memory. Echoes were digitized with a Nicolet 2090 —HA Digital oscilloscope and signal averaging was accomplished using an Intel 8080 computer. Normally 3000 — 9000 transients were collected. Data were processed despite the aid of a Nicolet 1280 data station. No great care was taken to ensure that digitization started at the top of the echo — rather an interpolation technique based on a five point smoothing was used to adjust the data so that this condition was met [16]. This prevents the spectral distortion which can occur if the signal digitization is not started right at the peak of the echo. The spectrometer reference phase was set so that the signal in the imaginary channel was essentially but not perfectly zero, hence the imaginary MATERIALS AND METHODS / 79 data were kept and a quadrature Fourier transform was performed from the peak of the echo. Normally a zero order phase correction of less than 10° was needed to phase the frequency spectrum. No first order phase correction was applied. 2. PROTON NMR Proton nmr experiments were performed on a Bruker CXP — 200 solid state nmr spectrometer equipped with a wide bore 4.7T Oxford instruments superconducting magnet and either a high resolution (saddle coil) or a solid state (solenoidal coil) probe. In the solid state probe the 90° pulse length ranged from 3 — 5 Msec, while in the high resolution probe the 90° pulse length was kept between 10 and 15 usee. For single pulse experiments the phases of the pulses and the receiver were cycled through a four pulse phase cycling scheme (CYCLOPS): x, —x,y, —y in order to reduce the effects of pulse and receiver imperfections [156]. Adequate signal to noise could be obtained with less than 1000 scans. The proton spin echo experiments were performed using the method of Turner [32,108,157,158] and of Kumar [40-42,159]. A 90° pulse was used to generate transverse magnetization. This was followed after a time T by a 180° refocussing pulse which produced a spin echo at a time 2T. One point was collected at the peak of the echo, the delay time T was incremented and the pulse sequence was repeated. Continued incrementation of tau generates a free induction decay totally devoid of effects due to chemical shift, heteronuclear dipolar couplings, or magnet (HQ) inhomogeneities. Generally 1024 increments of T were used to produce a IK data set. The initial value of r (equal to the MATERIALS AND METHODS / 80 increment time) ranged from 5 — 20 ^sec depending on the desired spectral width. The phases of the pulses were then cycled through an eight pulse phase cycling scheme (xx,xy,x—x,x —y,—xy,—xx,—x —y,— x —x, alternately added and subtracted) designed to cancel pulse imperfections [108, 160]. Spectra were processed by baseline correction, zero filling to 4K and quadrature Fourier transformation. Unfortunately, this method will generate additional peaks in the spectrum if the spin system is strongly coupled or if the refocussing pulse is not perfectly homogeneous over the sample. The latter problem can be eliminated to a great extent through the use of a solid state probe equipped with a solenoidal coil. The sample then sits entirely within the coil and the Hj homogeneity is greatly improved. The first problem is slightly more difficult in that it is a function of the spin system itself. In this case strongly coupled refers to the ratio of intergroup to intragroup dipolar couplings and chemical shift, not to the ratio of scalar couplings to chemical shift, as the term is more commonly used. These problems can be overcome with the use of computer programs designed to calculate these extra transitions [32, 40, 41], The proton—carbon double resonance echo experiments were performed in a similar manner, except that the 180° refocussing pulse was applied simultaneously to both the carbon spins and the proton spins [40,161 — 163]. This is similar to the so called "proton flip" [164,165] experiment except that the nucleus of observation is the proton rather than carbon —13. Then the resulting free induction decay depends on proton homonuclear dipolar couplings and H— C heteronuclear dipolar couplings and not on H- H dipolar couplings or chemical shift. The probe used for these experiments was a standard Bruker MATERIALS AND METHODS / 81 1 I q cross polarization probe doubly tuned to both H and C. Observation of the proton signal was done through the decoupling coil. To observe protons in this fashion on the CXP-200, modifications to the spectrometer were necessary. In order to generate 1 3 C rf pulses at 50.3 MHz and JH rf pulses at 200.0 MHz •I q 1 the spectrometer had to be set up like a normal C experiment with AH decoupling. However, the receiver supplied with the decoupler was not adequate to collect the proton signals — it is a single channel receiver with low signal/noise characteristics designed mainly for tuning purposes. To overcome this, the 60 MHz and 140 MHz reference frequencies needed to observe protons at 200 MHz were spliced from the decoupler receiver and into the main receiver [166] and the main receiver was used to collect the FID's. Due to spectrometer limitations the phases of the heteronuclear refocussing pulse could not be cycled through four phases (one pulse must be reserved as a trigger pulse), so only a 2 phase cycle was used (x, —x) corresponding to the sign of the proton refocussing pulse. The proton homo and heteronuclear experiments were analyzed using a modified version of LEQUOR discussed in the Introduction which takes into account 1) additional transitions which arise due to the strongly coupled nature of the spin systems and 2) additional lines which result from incomplete refocussing of the magnetization due to imperfect 180° pulses. The spin echo experiments are completely analogous to the technique of 2D J spectroscopy used in high resolution nmr. The main differences are that shorter pulse lengths must be used to excite the greater spectral range of the liquid MATERIALS AND METHODS / 82 crystalline spectra, and that shorter delay times, T, must be used to effectively increase the spectral width. Rather than collect the complete two dimensional data set, only one point in t 2 was collected for each T value. This greatly reduced the disk space needed for data acquisition, allowing overnight spectrometer runs of many temperatures. Simultaneously, the data processing time is reduced — the time needed to Fourier transform a IK data set in the tj dimension being orders of magnitude less than the time it takes to double Fourier Transform a IK X 128 point two dimensional data set. Since this particular technique has never been applied to randomly oriented liquid crystalline systems, there was a temptation to christen the pulse sequence with some inane acronym that nmr spectroscopists are so fond of inventing. Happily this temptation has been resisted, and the nomenclature of Turner was adopted instead — referring to these experiments simply as "the spin echo experiment", or "the two dimensional spin echo experiment". The resulting spectra are termed "the spin echo spectra" or "the spectra in the fj dimension". Since this is the only fancy pulse sequence used in this thesis, there should be no confusion. 3. CARBON 13 NMR Carbon 13 nmr experiments were executed on the CXP—200 nmr spectrometer using the 1 3 C cross polarization probe. The 13 C pulse length ranged from 3 to 5 usee. The pulses were cycled through the 4 phase cycling scheme mentioned previously (CYCLOPS). The proton decoupled C nmr experiments were done using on resonance broadband decoupling, with a decoupling pulse of 2.2 msec duration. MATERIALS AND METHODS / 83 Temperature control for all nmr experiments was effected using the standard Bruker forced air flow device. Temperature was monitored with the use of a regulating thermocouple and up to three additional thermocouples. The temperature gradient across the sample using this method is estimated to be less than a degree. HI. SOAPS Three partially protonated species of potassium hexadecanoate (potassium palmitate) were synthesized: dgj (perdeuterated), 1— C —2,2-H2—d2o, (alpha protonated) and 2,2,3,3—H^—d2 7 (alpha beta protonated). These potassium palmitates were dispersed in D 20 in a lamellar liquid crystalline phase at a constant water concentration (6.3 moles D 20 /mole soap) and their deuteron, proton, and carbon 13 nmr spectra were recorded as a function of temperature. The temperature ranged from 110°C (well into the lamellar L f l phase) to 45°C (just above the L a ~ liquid crystal —gel phase transition) and were only recorded as a function of decreasing temperature. This chapter discusses the results obtained, their interpretation and the results of the model calculation used to describe the head group behaviour in these systems. A. DEUTERON NMR The deuteron quadrupolar echo nmr spectrum of potassium palmitate — dgj/D 20 is presented in Figure 3.1. The spectrum is approximately symmetric, a full quadrature Fourier transform was used, and consists of a number of overlapping Pake doublets. The spectrum is a typical high temperature lamellar phase spectrum of a soap — axially symmetric with almost all separate deuteron resonances resolved. The deuteron nmr spectra of the other two species of potassium palmitate are similar. The alpha protonated soap displays no alpha splitting (the largest quadrupolar splitting), the aP shows no splitting at the two or three position. Since the quadrupolar splitting for the three and four positions 84 SOAPS / 85 FIGURE 3.1 2H nmr Spectrum of Perdeuterated Potassium Palmitate—d 3i Temperature = 110°C, 90° pulse length = 5 usee, T = 96usee., Relaxation Delay = 0.5 sec, 3600 Acquisitions. SOAPS / 86 overlap this is not always apparent in the deuteron spectra. The quadrupolar frequencies were consistently measured from the outside of the peak in order to offset the effects of line broadening. The effect of a broadening function superimposed on a lineshape is to shift the apparent resonance frequency towards the centre of the spectrum [ 1 1 , 17 , 9 2 ] . Rather than simulate lineshapes with broadening functions for every quadrupole coupling or depake all the deuteron spectra, this simple correction was made. This unfortunately introduces a small systematic error into the measurements. The measured distance between the doublets is called the quadrupolar splitting, AJ»Q, which is directly related to the carbon—deuteron order parameter, SQTJ, by equation (1.29). Assignment of resonances was made assuming that the quadrupolar splitting is progressively averaged towards the methyl end of the chain. The smallest quadrupolar splitting is due to the deuterons on D2O. Small peaks which appear on the edge of the D 2 0 peak in some spectra are assigned to the methyl deuterons, which are at the most disordered end of the chain and possess an extra degree of motional averaging from the methyl group rotation. The largest quadrupole splitting, significantly larger than the rest and only observed in the perdeuterated soap, arises from the two deuterons alpha to the carboxyl, the next largest from the deuterons at the 3 , 4 positions (they overlap even at high temperatures) and the next peak from the 5 , 6 positions. Each deuterated methylene group from the 7 position down gives rise to a separate Pake doublet at high temperatures. Typical order parameter profiles as a function of chain position for two temperatures in the lamellar phase are shown in Figure 3 . 2 . At low temperatures (just above the gel-liquid crystalline phase transition) deuterons FIGURE 3.2 2 H Order Parameter Profiles of Perdeuterated Potassium Palmitate Legend: n 110C v 45C SOAPS / 88 from the 2 — 8 position display an approximately constant quadrupolar splitting. This is called the "plateau" in the order parameter profile and arises from the steric constraints placed on the top half of the chains in the bilayer by other soap molecules. As the temperature is increased, the steric effects are decreased as a result of increased angular fluctuation of the molecules and increased area per polar head group and the quadrupolar splittings decrease exponentially down the chain. The cross in the order parameter profiles of different temperatures only occurs at the high water concentration end of the lamellar phase [54]. Temperature dependences of the deuteron order parameters are shown in Figures 3.3, 3.4, 3.5. These show the expected temperature dependence: almost exponential decrease of the quadrupolar splittings as the temperature is raised for deuterons buried in the centre of the bilayer, the increase—decrease for those near the lipid—water interface. Each of these order parameter plots is the average of two sets of measurements on different samples (for the C salt each sample is from a different preparation). The error in the measurement is within the size of the points. While the salient features of all the order parameter plots are the same, there are minor differences between the different isotopically substituted palmitates. This is especially evident in Figure 3.4 (*3C—2,2 — H2). The differences could be the result of an isotope effect, or due to small variations in water content, temperature homogeneity, or sample homogeneity. Most likely it is a result of purchasing soaps from different chemical companies. Water content was carefully monitored by weighing samples at every stage of the sample preparation procedure, temperature homogeneity was assured by the use of three copper constantan thermocouples separate from the regulating thermocouple, and sample homogeneity was achieved by excessive centrifugation SOAPS / 89 FIGURE 3.3 Temperature Dependence of the 2H Quadrupolar Splittings of Perdeuterated Potassium Palmitate 40 60 80 100 120 Temperature (C) The labels represent the assignment of deuteron splittings to chain position. Two peaks were observed for the 2 position at lower temperatures. The intensity of these peaks were not temperature dependent and these are believed to be ^H—^H dipolar couplings. At higher temperatures the methyl group coupling is hidden under the D2O resonance. A separate methyl group coupling is only observed below 65"C. The D2O coupling parallels that of the 2 position, the methyl group that of the 11 through 15 positions. The line is drawn to aid the eye. SOAPS / FIGURE 3.4 Temperature Dependence of the 2JJ Quadrupolar Splittings of 1 — 13c — 2,2 — H 2 Potassium Palmitate—d29 N I c a (/) L. 0 0 a 3 L. "D D 3 o 120 Temperature (C) No quadrupolar splitting is observed for the 2 position. SOAPS / 91 FIGURE 3.5 Temperature Dependence of the 2H Quadrupolar Splittings of 2,2,3,3-114 Potassium Palmitate—d2 7 N I c a w w 0 0 a u •o 0 3 o 120 Temperature (C) No quadrupolar splitting is observed for the 2. Since the quadrupolar splittings for the 3 and 4 positions overlap at all temperatures, it is difficult to tell if the 3 splitting is present or not. SOAPS / 92 along with storing samples at temperatures well into the L F L phase. Calbiochem—Behring supplied the palmitic and myristic acids used to synthesize the d 3 1 and 2,2,3,3-H4 — d 2 7 , Merck, Sharp and Dohme supplied the 1 3 C labelled palmitic. Variations of this genre have been reported before [53,167] and are possibly due to contamination of the compounds with trace amounts of fatty acids of differing chain length. See the section on cleanliness and reproducibility for further discussion on these points. B . 1 - 1 3 C - 2 , 2 - H 2 - P O T A S S I U M P A L M I T A T E - D 2 9 1. P R O T O N A N D C A R B O N 1 3 N M R Representative proton single pulse and spin echo spectra of the carbon —13 labelled soap are presented in Figure 3.6. The single pulse spectra appear as broad Pake doublets with central peak(s) which arise from residual protons on the deuterated hydrocarbon chain and in the D 20. Broadening of the line by heteronuclear dipolar couplings to the deuterons on the alkyl chain masks the C—H dipolar couplings In fact, the apparent splitting of the powder pattern does not change over the temperature range studied. More sophisticated nmr techniques are necessary if the desired information is to be extracted. The spin echo spectra (Figure 3.6 B,C) are more informative. Removal of magnet inhomogeneities, heteronuclear dipolar couplings and chemical shift results in a symmetric nmr spectrum with a single dipolar coupling DJJJJ, equal to 1/3 of the measured splitting. Application of a 180° pulse simultaneously in the * 3C SOAPS / 93 FIGURE 3.6 IH Single Pulse nmr Spectrum of 1-130—2,2 —H2 Potassium Palmitate —d29 40000 30000 -1—1—j—1—r 20000 1 1 I ' ' 10000 -I—1—1—r 1 1 1 1 -1—1—1—r -1—j—1—1—r-0 -10000 -20000 -30000 -40000 Hz A) Single Pulse. Temperature = 60°C, 90° pulse length = 3 psec, Relaxation Delay = 5.0 sec. 300 Acquisitions. B) Spin Echo (see next page) — no refocussing pulse. Temperature = 60°C, 90° pulse length = 3 psec, T = 10 psec, Relaxation Delay = 0.5 sec, 8 Acquistions. C) Spin Echo (see next page) — with refocussing pulse. Temperature = 60°C, 90° pulse length = 3 psec, r = 10 usee, Relaxation Delay — 0.5 sec, 8 Acquisitions. SOAPS / 94 FIGURE 3.6 B and C 1 1 1 1 I 1 ' 1 1 | 1 1 1 ' | ' ' ' • | i i i i | • i i i 15000 10000 5000 0 -5000 -10000 -15000 Hz B)Proton Spin Echo Spectrum without l^C refocussing pulse. ~* 1 1 1 | 1 1 1 1 | 1 1 1—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i— 15000 10000 5000 0 - 5 0 0 0 -10000 -15000 Hz OProton Spin Echo Spectrum with 1&C refocussing pulse. For Legend see previous page. S O A P S / 9 5 •I q 1 channel prevents refocussing of the C — H dipolar couplings (but not the 1 2 •"•H — d i p o l a r couplings) which appear as the small splitting equal to ( 2 D C H + J C H ) in Figure 3 . 6 C . Carbon proton dipolar couplings were also obtainable from the carbon—13 single pulse spectrum shown in Figure 3 . 7 A . This spectrum consists of a 1:2:1 triplet separated by 2DQJJ+JQJJ superimposed onto the chemical shift anisotropy ( C S A ) 13 pattern of the C nucleus. High power decoupling of the protons removes the 1 3 C — *H dipolar coupling leaving only this C S A pattern behind (Figure 3 . 7 B ) . The C S A pattern appears axially symmetric in nature, although the signal to noise ratio is poor enough to obscure all but one singularity (°\\~a22> ^n's peak is shifted 2 1 4 8 Hz = 4 2 . 7 ppm downfield relative to isotropic benzene (external reference) and it is estimated that the other singularity (033) appears at 2 2 4 6 Hz = 4 4 . 7 ppm downfield from O J J . The shape of the spectrum remains constant throughout the temperature range studied. Not much emphasis has been placed on this result except that it demonstrates that the carboxyl carbon is in an axially symmetric anisotropic environment throughout the entire lamellar phase. The disruption in the baseline at 5 0 0 0 Hz in Figure 3 .7 results from residual carbon signal in the probe. This signal is from a porcelain coil support designed for high power proton work. Originally, the carbon—13 experiments and the H— C double resonance experiments were performed on a Bruker CXP—2 0 0 using the standard Bruker cross polarization probe. No cross polarization was necessary since the molecule was enriched in carbon—13. However the sample SOAPS / 96 FIGURE 3.7 13c nmr Spectra of 1 —13C-2,2-H2 Potassium Palmitate — d29 T 1 j 1 1 1 1 j 1 1 1 1 J 1 1 1 1 J 1 1 1 1 1 1 1— 10000 5000 0 -5000 -10000 Hz T 1 1 1 1—1 1 1 1 1 1 1 1 1 1 1 r—j 1 1 1 1 1 1 r 10000 5000 0 -5000 -10000 Hz A) Single Pulse. No decoupling. Temperature = 110° C, 90° pulse length = 5 psec, Relaxation Delay = 0.5 sec, 2500 Acquisitions. B) Single Pulse with proton decoupling. Temperature = 110° C, 90° pulse length = 5 psec, Relaxation Delay = 0.5 sec, 2500 Acquisitions. SOAPS / 97 coil support in the probe had been replaced with a block of teflon which gave a dandy natural abundance carbon—13 spectrum. The carbon—13 nmr spectrum of 13 the C labelled acid dissolved in p —OOBA with the probe signal will be shown in Chapter 5, Figure 5.5. A substantial proton nmr signal was also obtainable from the same probe, probably arising from residual protons on the teflon. This would not affect normal operation of the probe as the cross polarization between the low natural abundance 13 C and the residual protons present in the teflon would statistically be- negligible. However for natural abundance or carbon—13 enriched work the effect was deadly. To circumvent this problem, the teflon block in the probe was replaced with a porcelain coil support originally supplied with the Bruker high power proton probe. While this reduced the background signal immensely, the problem was not entirely solved. The porcelain insert was coated in some sort of glaze to prevent chipping, a substance rich in protons and carbon. Mechanical abrasion was used to remove this glaze, but a residual proton and carbon—13 signal was still present. This is the disruption in the baseline in Figures 3.7A and B. The remaining proton signal was of sufficient magnitude that a separate proton probe was necessary for single pulse experiments. No spurious signal was evident in the *H spin echo experiments using either probe. The temperature dependence of the proton and carbon —13 dipolar couplings are displayed in Figures 3.8 and 3.9. The proton—proton dipolar couplings are the average result of four measurements of the dipolar splittings, single and double resonance spin echoes performed on two separate samples. The proton dipolar couplings follow a similar trend to that observed by Higgs and Mackay [10], rising with decreasing temperature, peaking at ~65°C and dropping off below this SOAPS / 98 FIGURE 3.8 Temperature Dependence of iH Dipolar Coupling Constants for 1—13c — 2,2-H2 Potassium Palmitate—d29 This is the average of two single resonance and two double resonance measurements. Error bars are the standard deviation of those couplings. The line joining the points is drawn to aid the eye. SOAPS / 99 210 -200 40 60 80 Temperoture (C) 100 120 This is the average of two 1&C single pulse and two lH double resonance spin echo measurements. Error bars are the standard deviation of the four couplings. SOAPS / 100 temperature. Dipolar coupling was measurable just into the gel phase at a temperature at which no deuteron quadrupolar echo spectra were obtainable (40°C). These spectra were low in signal to noise, and measurement of dipolar couplings was difficult. The estimated dipolar couplings from these spectra give a DJJJJ = —1827 Hz and DQJJ = 253 Hz. These are considerably smaller than the corresponding liquid crystalline phase couplings. No spectra were obtainable below 40°C. The spectra at 40°C probably represent the dipolar couplings in a 2 phase region near the transition. Both Higgs and Mackay [10] and Davis and Jeffrey [2] observed an increase in proton and deuteron couplings upon transition into the gel phase. Carbon—proton dipolar couplings are averaged over four sets of experiments, * 3C single pulse and H— C double resonance spin echoes for each of two samples. The * 3C—*H coupling constants show almost no temperature dependence which implies that the average orientation of the C— H internuclear vector does not change appreciably over a 70° temperature range. Any change in l^Q—lpj dipolar couplings would be reduced from the corresponding change in the *H — *H dipolar couplings by at least a factor of ~7 times as a result of reduced gyromagnetic ratio and increased distance between resonant nuclei. This measurement is therefore not as sensitive to molecular orientation as is the *H— *H coupling. 2. CALCULATION OF THE ORDER M A T R K SOAPS / 101 From the three measured nmr couplings (the 1 H - 1 H , the C - D and the 13 C_ 1 H), the order matrix for the rigid alpha methylene group can now be calculated. The expression for the dipolar couplings has been given previously (1.7). Since the amphiphiles are dispersed randomly in D2O, the measured splitting corresponds to the most probable orientation relative to the bilayer director (0 = 90°) and this expression is reduced by a factor of P2(cosp')= — i : T) -llLl_ 3 C O S 2 G ~ 1 (3-D Because the segment is rigid i.e. because the positions of the resonant nuclei do not change relative to one another, the time average over order parameters and internuclear distance in the expression for dipolar couplings can be separated into two independent terms. If small vibrational effects can be ignored, (3.1) may be rewritten as: l7l7 2h 1 3cos 2f?-l = < a> < > (3-2) J 2 4TT 2 r u 3 2 ' The first thing to do is calculate dipolar couplings from measured splittings in the carbon-13 and proton echo spectra. For the protons, D J T H = 1/3(APJJJJ) and for the heteronuclear dipolar coupling, D c H ^ ^ ^ C H - ^ C H ^ - "^ he v a ^ u e f ° r ^CH is 7 Hz as determined from the high resolution nmr spectrum. The sign of the coupling is taken from References [168,169]. Next, SQQ, the deuteron order parameter for the alpha position is determined from the deuteron quadrupolar echo spectra using Equation (1.29). It is important to know the relative signs of SOAPS / 102 the dipolar and quadrupolar couplings, especially for the heteronuclear coupling which depends also on J. The methylene H—H and C —D order parameters are known to be of approximately the same size [10] and are probably negative [119,131,132]. For a randomly oriented sample, where 90° edges of the powder pattern are measured, this would make A P Q positive and DJJJJ negative. For any reasonable geometry and initial orientation of the palmitate head group, the C—H internuclear vector makes an angle with the bilayer director that would result in a positive order parameter and therefore a positive dipolar coupling. (In the all trans state 6Z = 125.55, P2(cosl25.55) = 0.007; for the first C-C bond parallel to the bilayer director 6Z = 154.64 P2(cosl51.64) = 0.662). If the average value <P2(cos0)> changed sign with temperature, then a spectrum with zero dipolar splitting would be observed which is not the case. The order parameters SQT), SJJJJ and SQJJ can then be calculated from Equations (3.2) and o o (1.29). Internuclear distances of rjjjj=1.78 A and r£jj=2.163 A were used. A fixed axis frame is chosen in the rigid methylene group such that one measured order parameter is along an axis. The scheme of Higgs and Mackay [10] is followed: the x —axis is along the H-H bond vector, the y —axis is the bisector of the HCH angle and the z—axis is mutually perpendicular and in the general direction of the lipid water interface (see Figure 3.10). On average over the conformational motions of the rest of the molecule the yz plane is a plane of symmetry in the molecule fixed axis system. As a result, the number of independent elements in the order matrix is reduced from 5 to 3. For this rigid group, in this axis system S x y=S^=S x z=S^=0, S X X = S J J J J and the other elements of the order matrix can be calculated using (1.11). Since the C-D FIGURE 3.10 Molecule Fixed Axis System for Potassium Palmitate SOAPS / 103 This is the molecule fixed system axis system used for the calculation of the order matrix for the alpha methylene segment of potassium palmitate (and for palmitic acid/p — OOBA in Chapter V). Transformation to the principal axis system of the order matrix involves a rotation about the x axis in the yz plane, the plane of symmetry. SOAPS / 1 0 4 bond vector is in the xy plane (cos# Z=0), SQD is given by: 2 2 SfJD = S X XCOS ^jj + SyyCOS <Py + 2 S y y C O S <f) JJ C O S <P y (2.3) S C D = S H H c o s 54.8 + SyyCOS 35.2 + 0 (3-4) where # x is the angle between the molecule fixed x axis and the C—D bond vector. This expression can be rearranged to calculate Syy. The off diagonal element, S v z, of the order matrix is calculated similarly: 2 2 2 SCH = S x x C O S 0x + SyyCOS <f)y + S z z c o s 0 2 + 2S COS0yCOS0z (3 .5 ) therefore: S y z = t s CH - ( s x x c o s 2 0 x + S y ycos 2# y + S Z 2cos 20 z)] / 2cos0ycos0z (3.6) The third diagonal element, S^, is determined by S z z = " ( S ^ + ^yy^ These three elements determine the complete order matrix for the alpha methylene segment of potassium palmitate. The order matrix as a function of temperature is presented in Figures 3 . 1 1 and 3 . 1 2 . The results are similar to those of Higgs and Mackay for 2 , 2 - H 2 potassium palmitate—d2g, apparent axial symmetry at high temperature, with the absolute values of SQTJ and S J Q J decreasing as the temperature is lowered. The value of S v z remains approximately constant throughout the temperature range with a slight absolute decrease at temperatures near the phase transition. The profile of Syy is approximately equal to S ^ at high temperatures, but falls off more rapidly as the temperature is lowered. In contrast Higgs and Mackay observed that SOAPS / 105 FIGURE 3.11 Temperature Dependence of the Order Parameters for the a—Methylene Segment of l- 1 3C-2,2-H2 Potassium Palmitate-d29 - 0 . 3 5 - 0 . 3 0 -Ul - 0 . 2 5 -- 0 . 2 0 --0 .15 40 60 80 100 Temperature (C) 120 Legend: Measured Order Parameters: Q = S x x S ^ ~ l ~ — S QQ Calculated Order Parameters: Q = Syy A = SyZ Sxx and SQD a r e measured from the and %H spectra respectively. ScH c a n be measured from both the and the 1$C spectra. The molecule fixed axis system has been presented in Figure 3.10. FIGURE 3.12 Temperature Dependence of S z z and S 3 3 SOAPS / 106 0.60 0.55 -~ 0.50 0.45 -0.40 40 60 80 100 T e m p e r a t u r e (C) 120 S:;: m=Szz 0=S 3 3 Szz and S33 (diagonalized) for the a—methylene segment of l — 1^C—2,2—H2 Potassium Palmitate—d29- Presented on the same figure to conserve space. SOAPS / 107 Syy reached a minimum and then increased again. This is because their experimental values of SQT) and S J J J J cross each other at low temperatures. This discrepancy could be due to their use of carbon-deuteron order parameters from potassium palmitate-2,2 — d instead of from the perdeuterated soap. The order matrix was diagonalized and these results are displayed in Figures 3.12 and 3.13. Now it can be easily seen that the order matrix is not axially symmetric, as the values of S J J and S 2 2 differ at all temperatures. Since the only off diagonal element in the order matrix is SyZ, the value for S-^ j is identically S^. No special significance is given to the fact that the order parameters S ^ and S 2 2 cross. It does demonstrate that the principal ordering axes of the rigid alpha methylene segment are temperature dependent, and that the ordering of the segment in the 1 (read x) direction is relatively constant compared to the segment orientational order in the 2 direction. The values of S 2 2 are extremely sensitive to the measured D Q J J dipolar coupling, which is the least accurately measured coupling, and minor variations in the CH coupling will have a large effect on the temperature at which these order parameters cross. However as long as the relative magnitude of D Q J J as a function of temperature remains the same, the shape of the profile is constant. The orientation of the alpha methylene segment in the diagonalized order matrix frame is still described by three independent parameters — two of the principal elements of the order matrix and a third which is the Euler angle calculated from the eigenvector of the diagonalization. The angle represents the rotation of the order matrix in the plane of symmetry, which for the axis system defined is the yz plane. This is equivalent to the degree of rotation about an axis parallel to x, or the degree of SOAPS / 108 FIGURE 3.13 Temperature Dependence of the Diagonalized Order Parameters - 0 . 3 5 120 Temperature (C) Legend: CD — S -JI CD — SOAPS / 109 rotation of the alpha methylene group away from the trans state. This rotation angle changes from about 13° to 16° over the temperature range studied (see Figure 3.14). This is the difference in average angle between the molecule fixed axis frame and the diagonal order matrix axis frame, which in general increases with decreasing temperature. This implies that as the temperature is decreased the molecule is being pulled towards a configuration where the first C —C bond is more parallel to the bilayer normal. This is in direct agreement with the Abdollal model [3]. However the change in orientation is very subtle, only 3° over a 65° temperature range. The effect of diagonalizing the order matrix is to decrease the curvature in the plot of two of the diagonal elements, S 2 2 and S33 (relative to S v v and S^). The value of S j g ^ S j j remains unchanged. The origin of the curvature is postulated to be a geometric effect arising from the interaction of the soaps with the water. If the effect of the interaction is to restrict the average direction of the head group in the yz plane (i.e. to induce an overall rotation in the yz plane), then the transformed (diagonal) order matrix (Figure 3.13) should display no temperature dependence and the curves S 2 2 and S33 should now increase monotonically with decreasing temperature. This is clearly not the case. The remaining curve in the order parameters S 2 2 and S33 must arise from a different source. It still makes no logical sense to postulate a decrease in molecular order with decreasing temperature so it must be some other angular factor, which could cause the decrease of the order parameters of the alpha methylene group while the overall "molecular" order parameter increased. The angular factor could possibly be a trans—gauche isomerization about the first or SOAPS / 110 This angle represents the direction cosine between molecule fixed axis system (see Figure 3.10) and principal orientation axis system. The rotation angle, as the axis system is defined, is the yz plane. SOAPS / 111 second C —C bond, or a rotation about the alpha group fixed y axis (which would tend to push the head group into the bilayer). It would be possible to include such rotations in a molecular modelling scheme. Some knowledge of the intergroup dipolar couplings would be helpful in designing such a model. The experimental deuteron couplings seem to indicate (and the Abdollal model predicts) that the structuring effect of the water persists at least a few methylene segments into the bilayer. Therefore, information on the orientational ordering at the next methylene segment could be useful in sorting out the problem of lipid water interaction. C. 2,2,3,3-H 4-POTASSIUM P A L M I T A T E - D 2 ? 1. PROTON NMR 2,2,3,3 — H4 — potassium palmitate—d 2 7 (alpha beta palmitate, a/3 palmitate) was dispersed in D 20 at a concentration of 6.3 moles water/moles soap and the deuteron quadrupolar echo, the proton single pulse, and the proton spin echo spectra were recorded as a function of temperature. A representative proton single pulse spectrum is presented in Figure 3.15A. Again the heteronuclear dipolar couplings broaden the spectrum to the point where individual transitions are obscured. The proton spin echo spectrum in the fj dimension is displayed in Figure 3.15B. The spectra are symmetric, and a number of transitions are clearly apparent. It appears that the spectra are a superposition of a number of axially symmetric SOAPS / 112 FIGURE 3.15 lH Single Pulse and Spin Echo nmr Spectra of 2,2,3,3-H4 Potassium Palmitate-d2 7 I A: 20000 15000 10000 5000 0 -5000 -10000 -15000 -20000 Hz | 1 1 1 1 | 1 1 1 ' | 1 1 1 1 | 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 15000 10000 5000 0 -5000 -10000 -15000 -20000 Hz A) Single Pulse. Temperature = 50° C, 90 degree pulse length = 4.4 usee, Relaxation Delay = 2.0 sec, 512 Acquisitions. B) Spin Echo. Temperature = 50° C, 90 degree pulse length = 3.45 u sec, T = 5 usee, 180 degree pulse length = 6.9 usee, Relaxation Delay = 2.0 sec, 16 Acquisitions. SOAPS / 113 powder patterns. These orientation dependent powder patterns can be removed using the numerical procedure depaking (discussed in the Theory section) and the depaked spectrum is shown in Figure 3.15C. The spectra retain their symmetry about the central frequency, but the transitions now appear as individual resonance lines. This spectrum was simulated using the modified version of LEQUOR previously discussed in the Introduction and the simulated spectrum is shown in Figure 3.15D. This simulation is for a refocussing pulse of 166°. A total of nine lines were fitted to half of the symmetric experimental spectrum and the RMS error of this was 69.0 Hz, just outside the experimental digital resolution of 50 Hz. When the transitions from the other half of the spectrum are included in the simulation the effect on the calculated dipolar couplings and the RMS error is negligible. Small intensity peaks in the simulation arising from the inhomogeneous refocussing pulse were not fit even though there appear to be corresponding peaks in the depaked spectrum. The two peaks just on the outside of the large central peak were not assigned either. These lines consistently appear in the spin echo spectra, and along with the central peak, are inhomogeneous H j artifacts. The temperature dependence of the dipolar splittings and dipolar couplings are presented graphically in Figure 3.16 and 3.17 and the calculated dipolar couplings are given in Table 3.1. There are several points to note. Close examination of the dipolar couplings reveal a similar type of temperature dependence, the characteristic rise and fall, as was observed in the deuteron and proton spectra of the other isotopes of potassium palmitate. The effect here appears to be very small, but this is partly because of the scale on which Figure 3.17 is plotted. SOAPS / 114 FIGURE 3.15 C-D Depaked and Simulated nmr Spin Echo Spectra of 2,2,3,3-H4 Potassium Palmitate-d2 7 C: _) , , , , 1 , , , , —1 0.0 S.O 10.0 1S.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 FREQUENCY (KHZ) C) The depaked spectrum is calculated for 0° orientation, therefore frequencies are out by a factor of 2. D) Calculated: D22 = -2794 Hz, D23 = -691 Hz, D23' = -228 Hz, 1*33 = —2120 Hz, RMS Error = 69.0 Hz, 166° refocussing pulse, Lorentzian linewidth - 50 Hz. SOAPS / 115 FIGURE 3.16 Temperature Dependence of the Dipolar Splittings of 2,2,3,3-rU Potassium Palmitate-d2 7 12 1H 10 9H 8 7 -6 -5 -B B B B B- -B B - ^ j • B — f l B B B B B B~ Br -B~ -fi g B B B ~ -B-—B B— • f l B B B-- 6 B B B B B B B B B B B B Q B B B B B B B B B B B B B 40 60 80 100 Temperature (C) 120 Dipolar splittings measured from the spectra shown in Figure 3.15B. The error in the measurement is within the size of the points. SOAPS / 116 FIGURE 3.17 Temperature Dependence of the Dipolar Couplings of 2,2,3,3-H4 Potassium Palmitate —d2 7 3.5 Dipolar couplings calculated from the spectra shown in Figure 3.1SB. These couplings are also displayed in Table 3.1. The error in the measurement is within the size of the points. SOAPS / 117 TABLE 3.1 Calculated Dipolar Couplings for 2,2,3,3-H4- Potassium Palmitate-d27 DIPOLAR COUPLINGS(Hz) TOTAL TEMP(°C) D 2 2 ( D a a ) D 3 3(Dpp) D 2 3,(D ap,) D 2 3(D ap) RMS ERROR(Hz) 45 -2822136 -2082133 -242131 -628138 57.6 50 -2842±62 -2108156 -288156 -608169 96.6 55 -2878142 -2108138 -237135 -666143 66.3 60 -2794146 -2120146 -228134 -691143 69.0 65 -2811134 -2094131 -231126 -689133 51.5 70 -2783142 -2064138 -231132 -693140 64.1 75 -2780136 -2067133 -232127 -702135 54.8 80 -2755141 -2056138 -226131 -705138 62.2 85 -2758136 -2042133 -217127 -716134 55.0 90 -2718134 -2028136 -231130 -697135 62.2 95 -2710137 -2026134 -246128 -688135 54.7 100 -2703140 -2001136 -215130 -718137 60.5 105 -2671143 -1974139 -223131 -712139 63.9 110 -2610144 -1964145 -224135 -710144 72.1 SOAPS / 118 The difference between the high temperature value and the maximum alpha dipolar splitting is actually greater here than it was in the carbon—13 labelled soap (see Figure 3.8). The drop off at lower temperatures, however, is more pronounced in the carbon—13 labelled compound. These discrepancies are attributed to differences between samples. The dipolar coupling constants obtained from the simulation are all of the same sign and by comparison with the previous section on the carbon—13 labelled soap, must all be negative. The largest dipolar coupling, attributed to the two alpha protons, is of the same order as was observed in the alpha protonated soaps (the difference is about 6%). The beta protons have the next largest dipolar coupling, this value is reduced from the alpha coupling by a factor of about 1.4, almost exactly equivalent to the corresponding reduction observed between alpha and beta deuterons in the deuteron spectra. The increased orientational averaging arises from increased motional freedom of the /3 methylene segment. The intergroup couplings are much smaller and of the same sign. These dipolar couplings are averaged by rotational freedom (gauche—trans isomerizations) about the Ca~ bond. The fact that one intergroup coupling is three times smaller that the other is a function of the time averaged distance between these protons — the protons on the same side of the molecule (hereafter called a/3) are on average closer together than those on the opposite side of the molecule (hereafter called ap"). Since the dipolar coupling constant depends on <S^/r]$>, a larger coupling will result for the a/3 protons than the ap" unless the average orientation of the a/3 protons is such that it is reduced by a smaller value of the order parameter, S i j -SOAPS / 119 Interpretation of these dipolar couplings is more difficult than in the previous case. The first temptation is to proceed as before — intelligently choose an axis system, determine the order matrix in this axis system, and diagonalize to obtain rotation angles of the matrix. If the a$ segment was rigid, this would yield a single set of order parameters for this segment of potassium palmitate. However, the afi segment of potassium palmitate is not rigid — there is considerable conformational motion about the C f l — b o n d . In addition, this conformational freedom removes the plane of symmetry of the two groups. The problem of treating orientational order in non rigid molecules is not as simple as for rigid ones [170-173]. A second approach would be to calculate separate order matrices for both segments of the molecule using the proton, deuteron and carbon—13 nmr couplings. The analysis for the alpha segment would be similar to the calculation presented previously. For the beta segment, at least 3 independent order parameters would need to be specified assuming a plane of symmetry bisecting the HCH segment. From the present data only two are available, Spjpj^ and SQ-Q^ . An alternate element to the beta order matrix could be obtained from the intermethylene group couplings if the time average of < S j j / r j j 3 > m t e r g r 0 U p could be separated. For non rigid segments, this is impossible using magnetic resonance, unless the exchange rate is slow relative to the dipolar interaction (Tex<<l/27rDij). A third approach is to treat all the available information together in a single analysis, include the conformational motion and use equilibrium statistical SOAPS / 120 mechanics. For a/3 palmitate in the all trans conformation there is one plane of symmetry, hence three independent order parameters are needed to describe the orientation. For a palmitate molecule with a g + or g~ conformation at the a/3 linkage, there is no symmetry and five independent elements are needed in the orientational order matrix. However, as long as conformational changes at other C—C linkages are ignored, the g + and g~ conformers are mirror images of each other, and the absolute value of their order matrices are the same. This leaves a total of 3 + 5 = 8 independent order parameters necessary for the complete description of the alpha beta segments of the palmitate molecule. The order matrix for each conformation consists of the sum of the order matrices in the fixed axis system of each conformation weighted by the probability of that conformation. If the probability of g~*~ and g~ conformers are the same, this adds one more unknown to the problem (Pt, Pg±) bringing the total to 9. From nmr measurements, a total of seven experimental quantities are available — one C— H coupling, four H dipolar couplings and two deuteron quadrupolar couplings. Hence this is an underdetermined problem — more unknowns than equations, so the elements of the order matrix cannot be determined analytically. An additional problem is that the conformer order parameter can never be separated from their probabilities: S = I P i S i = P t S t + P g + S g + + P g _ S g _ = P t S t + 2 P g S g (3.7) Instead some sort of modelling scheme must be used and the calculated order parameters fit to the experimental data. Hopefully, the model will contain a minimum number of adjustable parameters, certainly no more than two, one would be preferable, and the adjustable parameters should be related to the physical forces acting on the palmitate molecules. SOAPS / 121 D. THE INERTIAL FRAME MODEL The model chosen to simulate the experimental dipolar and quadrupolar couplings is a modified version of the Samulski Inertial Frame (D?) Model [6—9], which was discussed in the Introduction. The Samulski IF model relies on the assumption that the order matrix is diagonal when the moment of inertia tensor is diagonal. A number of conformers are generated using the RIS approximation, and rotated about their centres of mass to a position in which the above condition is met. A diagonal order matrix is calculated from the principal moments of inertia. The molecule is placed in a cylinder of variable radius, r Cyj, and a mean Field interaction potential is calculated depending on the distance from the cylinder. From the mean field interaction potential, the internal potential of the molecule, and a non—bonded interaction term, a conformer probability is calculated. A transformation from the PMI frame to a local frame yields a set of couplings which are scaled to the conformer probabilities, summed over all conformations, and compared with experiment. The modifications to the Inertial Frame Model reflect the interactions specific to the lipid water interface in potassium palmitate. Conformations in which the hydrocarbon chain protrude into the aqueous medium are discarded. Rather than explicitly deal with hydrogen bonding to individual water molecules, the electrostatic interactions are mimicked by the attachment to the carboxyl group of a weight on a rod of variable length along the direction of the first C —C bond. SOAPS / 122 This is one of the two adjustable parameters in the model, the other being the radius of the constraining cylinder. The addition of the weight affects the moment of inertia of a particular conformation — the longer the attaching rod, the larger the value of the minor principal moment of inertia. As a result the first C—C bond direction lies closer to the minor principal moment of inertia axis which in the model is also one principal axis of the conformer order matrix. The change in relative orientation would effectively decrease the values of the alpha and beta deuteron nmr couplings. Therefore the increased hydrogen bonded interactions at lower temperatures are modelled by increasing the rod length. Neither one of the adjustable parameters, the radius of the constraining cylinder or the length of the rod, can be directly related to any physical property. They are ad hoc parameterizations designed to test the relative importance of what is believed to be the two most important forces acting at the lipid —water interface. Therefore it is only the relative change in these two parameters as a function of temperature which has any meaning in this study. What follows is a recap of the IF model with special emphasis on the details of the calculation, the parameterization of potassium palmitate, and the modifications made to the Samulski version of the model. The IF model calculation was written as a subroutine to a modified version [174] of the established computer program SHAPE [175]. The original SHAPE program calculates dipolar couplings from a set of Cartesian coordinates and performs the least squares and iterative part of the calculation to minimize the RMS error between experimental and calculated nmr couplings. The initial modifications made to the SHAPE program were to incorporate a subroutine SOAPS / 123 called LINUS [176]. LINUS can determine molecular coordinates from a set of bond lengths, bond angles and dihedral angles. Once these initial coordinates have been determined, the modified SHAPE can calculate the moment of inertia tensor and perform the coordinate transformation into the PMI frame. The additional subroutine must set up the required number of conformations, calculate the conformer order matrix, and calculate the internal and external energies of the palmitate molecule in the mean field. It was also necessary to rewrite the calculation of the couplings to include calculation of both homo and heteronuclear dipolar couplings and quadrupolar couplings. In order to deal with the inherent flexibility of the palmitate molecule, a model must be chosen for the internal potential. The Flory rotational isomeric state (RIS) model is used, three rotational states (t, g + , and g — with dihedral angles 0, 112.5°, —112.5° respectively) are allowed about each C—C bond. These three states are assigned arbitrary potential energies of t = 0 kJ/mole and g~^  = g~ — 1.67 kJ/mole. These values and others which will follow are summarized in Table 3.2. For a particular conformer, the total internal potential is calculated as the sum of the internal potential from each bond. Even with only three RIS states per C—C bond, the number of internal rotations soon becomes prohibitively high. Ignoring rotations about the HOOC—CH 2 and CH2-CH3 bonds, which have no effect on the nmr couplings of interest, potassium palmitate has 13 flexible C —C bonds for which there are 3—1.59 million RIS states. If high energy g + g — conformers are assigned a zero probability and if the symmetry of the rotational isomers is taken into account —every conformer has a mirror image except for the all trans — the number of conformers drops to ~55,000. This is SOAPS / 124 TABLE 3.2 THE IF MODEL The Parameterization of Potassium Palmitate INTERNAL POTENTIAL dihedral angles 4>t 0° • g+,<t>g- 112.5° conformational energy E(t) (kJ/mole) 0.00 E(g +)=E(g") 1.67 E(g +g") i n f i n i t y GEOMETRIC PARAMETERS bond lengths (A) rCD :C0 :CH 1.53 1.00 1.24 1.095 bond angles (degrees) <CCC 112.50 <CCH 108.82 <0CC 120.00 EXTERNAL POTENTIAL LENNARD-J0NES PARAMETERS A(kJ/mol) 8.309*lo!? B(kJ/mol) -4.724*10 3 TRUNCATION PARAMETERS regular extended number of carbons 7 9 number of flexible CC bonds 5 7 number of conformers 50 288 chain mass(amu) 64 64 HG mass(amu) 500 500 tot mass(amu) 704 704 ADJUSTABLE PARAMETERS r c y l rHG still too many to do a reasonable calculation. Since it is the head group behaviour of the molecule that is of primary interest, perhaps the methyl half of the molecule could be ignored. If, starting with the C3 linkage, only rotations about 5 C —C bonds are considered, the calculation would encompass the first seven carbons and the number of conformers would drop to 50. In place of the eighth and subsequent carbons, a mass is attached to mimic the rest of the SOAPS / 125 chain. The mass is chosen and kept constant at 64 amu — the mass of 4 deuterated methylene groups. Test calculations in which this mass was varied showed little change in the calculated splittings near the head group. Molecular geometries are calculated from the parameters in Table 3.2. The geometric parameters were taken from Samulski's work and from [176a]. Minor alterations in all parameters (except r^jj) have minimal effect on the calculated couplings. The proton dipolar couplings are particularly sensitive to T Q J J since the dependence of the couplings on interproton distance goes as 1/r3 (1.70). Electrostatic forces are simulated by the addition of a weight on a rod of variable length. In the model the rod is attached directly to the carboxyl carbon atom and the direction of the rod is coincident with the first C —C bond direction. A mass of 500 amu is affixed to the rod. This distance will be referred to as TJJQ, a head group interaction length. Attachment of the rod directly to the carboxyl carbon, rather than to one of the adjacent oxygen atoms where hydrogen bonding would normally take place is an attempt to simulate the effects of hydrogen bonding that might be expected to impose a direction on the chain, such that the first C—C bond is more parallel to the director. As a bonus, this modelling scheme preserves the symmetry of mirror image conformations which helps keep the cost of computing down. While the mass of 500 amu may seem a bit extreme, this number is chosen to ensure that the head group parameter has a noticeable effect on the moment of inertia tensor. As will be shown later, the effect of reducing this mass is only to increase the length of the attaching rod, it has little effect on the calculated couplings. The SOAPS / 126 all —trans conformer of the doctored potassium palmitate, resplendent in its severed glory is shown in Figure 3.18. From these starting parameters, the moment of inertia tensor is calculated. First the centre of mass of the molecule is determined: m • r • r C o M 0 ) = I -J—1 (3-8) m t o t where m^  is the mass of the i t n nuclei, rj is the cartesian coordinate of that atom, n\ot is the total mass of the molecule, and where rj is over x,y, and z. The three potassium palmitates from which the experimental numbers were measured all differ slightly in mass but only by a total of 4 amu, so the mass of the doctored perdeuterated potassium palmitate (204 + 500 = 704 amu) was used in all spectral simulations. The molecule is translated to the centre of mass (COM) coordinate system by subtraction of the 3 components (i"C0M^^' a n c* t n e moment of inertia tensor determined by: l*fi = 1 m i fia r „ (3-9) where the sum is over all atoms in the molecule, r^a, r ^ are now the components of the fo atom in the COM coordinate system and a/3 is over x,y,z. The moment of inertia tensor is diagonalized and the principal values obtained. Transformation of the coordinates to the PMI frame is easily accomplished using the eigenvectors of the inertia tensor diagonalization: (3.10) SOAPS / 127 F I G U R E 3 .18 The Parameterization of Potassium Palmitate The seven methylene segments closest to the head group are included in the calculation. Rotations in a three fold potential are allowed about the five CH2 — CH2 bonds. The two adjustable parameters are the cylinder radius, r^/, and the length of the rod attached to the carboxyl group, rjjQ. SOAPS / 128 The molecule is now in a frame in which its moment of inertia tensor is diagonalized. This frame, within the scope of the IF model, also diagonalizes the order matrix. The semiaxes of an ellipsoid with uniform mass distribution having the same inertia tensor as the conformer are calculated using (1.65) and from the semiaxes the diagonal molecular conformer order matrix is determined using (1.66a—c). The value of S__ for the various conformers ranges from ~0.5 to 0.9 depending on the relative degree of disorder in the chain. The non—bonded interactions between methylene groups greater than 4 carbons away is calculated as a Lennard—Jones 6—12 potential using "united atom parameters". [6—9,177] For two methylene (CD2) groups the non—bonded energy is calculated from the following expression: A + — « (8.11, " NB ~~ 12 6 r r where A = 8.309X106 kJ/mole and B=-4.724X103 kJ/mole. The non-bonded interaction prevents the palmitate chain from coiling back on itself, an excluded volume interaction. The molecule is now constrained in a hypothetical cylinder of variable radius, r c y j . The constrained molecule in its cylindrical cage is presented, in Figure 3.18. The cylinder simulates the steric repulsion or excluded volume forces primarily responsible for the orientational behaviour of these molecules. The cylinder is thought of as a mean field of methylene groups and the interaction between each carbon atom and the nearest point on the cylinder is calculated as a Lennard-Jones 6—12 potential using (3.11) with the same values for A and B. SOAPS / 129 The total non—bonded (Ej^g) and cylinder (EQO")) potential energies are the sum over the contributions from each carbon atom in the chain. The chain is not allowed to project beyond the interface into the aqueous o medium. A cut off of 2.0 A beyond the carboxyl carbon is imposed and any e conformer which exceeds this 2.0 A limit is assigned zero probability. The choice e of 2.0 A is arbitrary and is based on similar calculations done by Gelbart et al. [140, 144]. Gelbart picks a number of initial orientations at random for the amphiphiles in his calculations and allows the position of the head group to vary o up to 1.5 A at random in the direction parallel to the direction of the phase. When the first C—C bond direction is parallel to the bilayer director, the o hydrophobic cutoff extends 1.38 A beyond the oxygen atoms into the medium — close to the value chosen by Gelbart. In the course of the calculations, very few conformations are rejected on this basis. Those that are tend to be of the most twisted variety, the type that would have a low internal and non—bonded probability anyway. Now that the various contributions to the potential energy have been included, the total potential of the conformers is calculated as the sum of the three contributions, the internal, the non—bonded and the cylinder potential (1.64). The statistical weight of each conformation is the Boltzmann factor of the potential, the partition function is calculated as the sum of the Boltzmann exponentials (1.49) and the conformer probability is defined as the statistical weight divided by the partition function (1.50). SOAPS / 130 The calculation of order parameters and dipolar and quadrupolar splittings has been described in the Introduction (1.68-1.70). The calculated nmr couplings for each conformer are scaled by the total conformer probability and then the individual couplings are summed over all conformations. All splittings are then scaled to one experimental splitting, chosen in imitation of Samulski to be the a — CD 2 deuteron quadrupolar splitting and compared to experiment. A least squares procedure is used to calculate a weighted RMS error. The squared difference in each set of couplings is weighted by (1/SD)^ where SD is the standard deviation in the experimental numbers. In order to maintain consistency between calculations, SD for the dipolar couplings is taken as an approximate average from the LEQUOR spectral simulations. The SD for the quadrupolar couplings is estimated from the uncertainty in the measurement of the deuteron quadrupolar splittings. Since it is the simulation of the couplings near the head group that is most important, quadrupolar splittings from methylenes farther down than position 4 were given zero weight in the error calculation. The program is run iteratively, allowing the two adjustable parameters r Cyj and TJJQ to vary until convergence is reached. The cost of one run on low priority Batch ranges from 70 cents to ~$1.50. E. RESULTS FROM THE IF CALCULATION 1. SIMULATION OF EXPERIMENTAL NUMBERS A plot of experimental and calculated dipolar couplings as a function of temperature is displayed in Figure 3.19 and in Table 3.3. Considering the SOAPS / 131 FIGURE 3.19 The IF Model: Calculated and Experimental Dipolar Couplings N I c a n L. o a -1 --2 --3 --4 fl D D TJ—0—•—o—D—D—•—13—0—6—6 D C H • g D D D D D D O D o D D D D , D Q- "D 0 O^D D D D D D D D D 23 23 D D • • D D D-0 • 0 D • • 32 • • D D D D 2 2 40 i r 1 1 60 80 Temperature (C) 100 120 Legend: • experimental calculated These experimental couplings have been displayed before in Figures 3.3, 3.8 and 3.9. The couplings of Figure 3.9 have been scaled by a factor such that the alpha dipolar couplings of Figures 3.3 and 3.8 are identical. THE IP MODEL EXPERIMENTAL AND CALCULATED DIPOLAR AND QUADRUPOLAR COUPLINGS DIPOLAR COUPLINGS(Hz) 13 c_lH(a) 1H_1H D C H D 2 3 ( D a p ) D23'<DaP'> >>2 2(Da a) ^ ^ p ) TEMP('C) EXPT CALC EXPT CALC EXPT CALC EXPT CALC EXPT CALC RMS ERROR 45 256 317 -628 -670 -242 -471 -2822 -2618 -2082 -1787 186 50 254 314 -608 -642 -288 -479 -2842 -2762 -2108 -1814 177 55 259 314 -666 -632 -237 -488 -2878 -2879 -2108 -1870 188 60 252 307 -691 -604 -228 -485 -2794 -2936 -2120 -1893 203 65 251 307 -689 -596 -231 -486 -2811 -2968 -2094 -1898 202 70 241 305 -693 -587 -231 -484 -2783 -2969 -2064 -1886 205 75 243 308 -702 -595 -232 -487 -2780 -2964 -2067 -1881 205 80 242 307 -705 -591 -226 -485 -2755 -2959 -2056 -1870 209 85 250 309 -716 -597 -217 -488 -2758 -2955 -2042 -1863 209 90 242 305 -697 -582 -231 -483 -2718 -2942 -2028 -1838 209 95 239 305 -688 -581 -246 -481 -2710 -2931 -2026 -1826 204 100 237 307 -718 -589 -215 -483 -2703 -2917 -2001 -1822 210 105 233 304 -712 -580 -223 -480 -2671 -2904 -1974 -1804 209 110 211 300 -710 -567 -224 -474 -2610 -2885 -1964 -1781 217 QUADRUPOLAR COUPLINGS(Hz)(c) CARBON 2 3 4 5 6 7 TEMP("C) EXPT CALC EXPT CALC EXPT CALC EXPT CALC EXPT CALC EXPT CALC 45 28668 28868 21802 21710 22438 21802 20875 13915 20875 12291 19238 5642 50 30859 30859 22901 22731 23697 22901 21362 14677 21361 12883 19727 6632 55 32495 32495 23951 23749 24814 23951 21851 15820 21851 13853 19800 7486 60 33460 33460 24536 24324 25429 24536 22049 16719 22049 14606 19654 8214 65 33923 33923 24756 24527 25699 24756 22144 17027 22124 14873 19434 8467 70 33984 33984 24698 24458 25643 24698 21729 17101 21729 14940 19092 8542 75 33859 33859 24585 24356 25509 24858 21729 17091 21410 14954 18774 8459 80 33819 33819 24488 24261 25409 24488 21485 17142 21313 15007 18457 8490 85 33704 33704 24365 24143 25268 24365 21069 17097 20996 14989 18262 8387 90 33643 33643 24170 23943 25092 24170 20752 17043 20752 14937 17871 8459 95 33496 33496 24023 23803 24935 24023 20459 17038 20459 14946 17725 8424 100 33252 33252 23877 23670 24573 23877 20068 17038 20068 14971 17383 8297 105 33130 33130 23706 23496 24581 23706 20288 16998 19922 14940 17213 8310 110 32975 32975 23502 23294 2485 23502" 20117 16968 19742 14914 17009 8360 (a) These numbers have been scaled so that the D 2 2 dipolar couplings of the two species match. (b) The error In the experimental dipolar couplings have previously been reported In Table 3.1. (c) Quadrupolar couplings are from the perdeuterated potassium palmitate. The estimated experimental error In the deuteron couplings ls less than 5%. SOAPS / 133 crudeness of the model, the fit to the experimental dipolar couplings is good. The numbers are of the right order of magnitude, the right sign, the right relative magnitude and show the appropriate trends: the C— H dipolar couplings and D23, D23' intergroup couplings show little change over the temperature range whereas the D22 and D33 intragroup couplings demonstrate the rise and fall at lower temperatures. The error in the experimental couplings, generally less than 100 Hz, would fall almost inside the size of the points. Given a ~50 Hz RMS error in the spectral simulation and an up to 10% deviation between samples in the deuteron order parameters at low temperatures, these numbers fit rather well. The calculated alpha couplings are too large and the beta couplings too small possibly implying that in the model calculation, the restriction on the head group is somewhat too stringent and the amount of freedom about the C2 — C3 linkage too liberal. The intergroup couplings are out by almost 25%. However, these couplings depend not only on the angular excursions of the palmitate molecule, but on the time averaged distance between the intermethylene protons. Therefore these numbers are especially sensitive to some of the angular parameters in the model, for example the dihedral angle used to define the RIS states and the internal energy assigned to each of the three rotational isomers. It is difficult to say even if the assignment of these two couplings is correct, since there is no a priori knowledge of the relative probabilities of the three rotational states of this segment, or even whether the RIS model as it is used here is particularly appropriate to model flexible segments so near an interface. In other words, a combination of rotational isomers could be imagined in which the distance between the a and 0 protons (the a/3' protons), farthest apart in the trans state, are on the average closer than the a/? protons. Alternately an SOAPS / 134 average orientation could be imagined in which the order parameter of the ap" protons exceeds that of the a/3 protons. Test calculations in which the assignments of these two couplings are switched show an increase in RMS error, so within the scope of the IF model, intuition seems to prevail. The numbers presented here are the best fit found for all the parameters in the model. A plot of the temperature dependence of experimental and calculated quadrupolar couplings is displayed in Figure 3.20. The a — CD 2 couplings fit perfectly, as they must since all couplings are scaled to these numbers. The fit for the 3 and 4 (/3 and 7) positions is adequate, and the fit degenerates from there. This will be discussed later. However, there are some features to note. The characteristic rise and fall of the deuteron couplings is predicted. The rise and fall is greater near the head group for both the calculated and experimental numbers. The calculated numbers peak at the appropriate temperature for all but the 7 position. The IF model predicts the odd —even effect. The 3 and 4 couplings, indistinguishable in the experimental spectrum, are calculated to be very close. Again, the 5 and 6 deuteron couplings, which through much of the temperature range overlap experimentally, are also calculated by the model to be quite close, although too small. The 7 coupling is farther removed from the 5 and 6 in both the calculated and experimental quadrupolar couplings. This can also be seen in a plot of quadrupolar splittings as a function of chain position at one temperature (Figure 3.21). The odd—even effect is easily seen in this plot, as well as the fact that the calculated splitting at the 4 position is greater than at the 3 position! While this behaviour has never been observed for lamellar phase soaps or lipids, this increase in orientational order has been observed before in liquid SOAPS / 135 Legend: 0 experimental calculated Experimental couplings are numbered on the left, calculated couplings are numbered on the right of the figure. Experimental numbers are taken from perdeuterated potassium palmitate (see Figure 3.3). The average of the 2 position quadrupolar splittings are used. SOAPS / 136 FIGURE 3.21 The IF Model: Quadrupolar Coupling Profile 40 - i 35 -5 -i i i i 1 r 1 3 5 7 carbon number 0 experimental (110C) calculated Legend: This calculation is for 110°C, with an RMS error of 217 Hz. The values for the adjustable parameters are r^i = 5.90A, and rftQ = 2.71A. S O A P S / 1 3 7 crystals [ 1 7 8 — 1 8 1 ] and has been predicted by other theoretical calculations on liquid crystal systems [6 , 9 , 1 8 0 ] . The extreme drop off in the calculated couplings away from the head group is rather disconcerting. This is due to the simplistic modelling of the rest of the chain past the seven position as a ball with a mass of four deuterated methylene groups. This brutal amputation of the palmitate molecule was invoked parsimoniously in an attempt to keep the computing time and costs down. In the truncated chain, the "terminal" methylene group is allowed much more orientational freedom than if it were under the influence of the remaining 9 segments of the molecule. As a result, conformations (generally of the more disordered variety) which would have reduced probability as a result of non—bonded or cylinder interactions from the remainder of the chain, are assigned a higher probability. This leads to increased orientational or conformational freedom which decreases the quadrupolar couplings. To test this idea, some sample calculations were run in which the chain length was increased by two methylene segments. The calculations were performed iteratively, varying rCyj and T J J Q , but with no adjustment of any of the other starting parameters. In theory, the cost of the computation increased by a factor of 2 . 4 for every carbon atom added; in practice, the number of iterations increased along with the number of conformations and the cost of these runs leapt to the 7 to 1 0 dollar region on low priority Batch. Two plots from the extended calculation of the quadrupolar splittings as a function of chain position are shown in Figure 3 . 2 2 and 3 . 2 3 . These figures show results from both the 7 and 9 carbon calculation at two different temperatures. Note that the fit of the 5 and 6 positions is greatly improved and that at the 7 , 8 , and 9 positions, the fit decreases in a similar fashion as the "terminal" methylenes of the shorter chain. However the S O A P S / 138 carbon number Legend: • experimental (HOC) calculated The results of the extended chain calculation at 110°C. The regular calculation (identical to Figure 3.21) isgshown for comparison. The values for the adjustable parameters are rCy[ = 6.43A, and r^Q = 3.82A SOAPS / 139 FIGURE 3.23 The IF Model: Effect of Increasing The Chain Length on The Calculated Quadrupolar Coupling Profile 40 - i — 3 5 -/-s N I ~ 3 0 -0 -| 1 1 1 1 1 1 1 r 1 3 5 7 9 carbon number Legend: n experimental (45C) calculated The results of the extended chain calculation at 45 "C. The regular calculation is shown for comparison. The values for the ^adjustable parameters for the extended^ (and regular) calculation are r^i = 6.52A (5.85A), and rtfQ = 4.63A (3.55A). Notice the plateau in the extended calculation at 45 "C which is not present at higher temperatures (Figure 3.22). SOAPS / 140 agreement at the 3 and 4 positions is not as good. Better agreement could probably be obtained by modifying the initial parameters. An interesting point is that the extended calculation predicts a plateau, a region of constant splitting, in the quadrupolar splittings from positions 3 to 6 at lower temperatures, temperatures just above the gel—liquid crystalline phase transition. 2. THE ADJUSTABLE PARAMETERS Figures 3.24 and 3.25 and Table 3.4 show the temperature variation of the two adjustable parameters in the LF model — the radius of the constraining cylinder (rCyj) and the length of the head group interaction parameter ( F ^ Q ) . The cylinder radius is almost constant over the whole range of temperatures — changing from 5.90 A at 110°C to 5.94 A at 50°C before an abrupt drop to 5.85 A. at 45°C. The cylinder radius is constant over a 20 range from 50-70°C. The head o group length, on the other hand, is essentially constant at 2.71 A from 110° o down to 65 C but below this temperature it rises rapidly to 3.55 A at 45°C. The maximum change in rCyj over the temperature range is 1.5% (0.7% not including the lowest temperature point), whereas T J J Q varies by almost 30% in the same range. The increased length in rjjQ represents increased structuring of the head group methylene segments of potassium palmitate by some interaction, i.e. H—bonding to water molecules and/or counterions, at temperatures below a critical temperature of 65°C. Steric effects, represented by rCyj, remain constant throughout the entire lamellar phase region studied, becoming more important at temperatures just before the phase transition. SOAPS / 141 FIGURE 3.24 The IF Model: Variation of Cylinder Radius with Temperature 6.2 -i • 6.1 -6 -5.8 -5.7 -5.6 -j 1 1 1 1 1 1 1 40 60 80 100 120 Temperature (C) This is the variation in the steric forces, characterized by a mean field cylinder, with temperature. The percent change from 110°—45"C is about 1.5%. SOAPS / 142 FIGURE 3.25 The IF Model: Variation of Head Group Parameter with Temperature This is the variation with temperature in the electrostatic interactions, characterized by a mass on a rod of variable length. The rod length affects the minor principal moment of inertia which in turn affects the orientation of the head group. The percent change from 110° — 45°C is about 30%. SOAPS / 143 TABLE 3.4 THE IF MODEL Variation of Adjustable Parameters with Temperature TEMP(°C) r H G ( A ) r c y l ( A ) 4 5 3 . 5 5 5 . 8 5 5 0 3 . 2 0 5 . 9 4 5 5 2 . 9 8 5 . 9 4 6 0 2 . 7 9 5 . 9 4 6 5 2 . 7 4 5 . 9 4 7 0 2 . 7 2 5 . 9 4 7 5 2 . 7 5 5 . 9 3 8 0 2 . 7 3 5 . 9 3 8 5 2 . 7 6 5 . 9 2 9 0 2 . 7 4 5 . 9 3 9 5 2 . 7 4 5 . 9 2 1 0 0 2 . 7 6 5 . 9 0 1 0 5 2 . 7 4 5 . 9 0 1 1 0 2 . 7 1 5 . 9 0 Is the drop in r c y i at 45°C significant? It is hard to tell with certainty. There is no disruption at this temperature for any of the other computed values: rjjQ, the dipolar, or the quadrupolar splittings. This would suggest that perhaps there is some significance to the sudden increased steric effects. It is known that as the hydrocarbon chains undergo the liquid crystalline—gel phase transition they lose considerable flexibility and become stiff and extended [2, 75]. This has been SOAPS / 144 correlated with an increase in the overall bilayer thickness at the expense of the surface area per polar head group [66 — 68, 71]. In other words, the steric constraints imposed by other lipid chains in the bilayer increase at the phase transition. At temperatures just above the phase transition, the deuteron nmr spectra often display a broad underlying component, believed to be the onset of the gel phase. Separate local regions of gel phase have been postulated, possibly arising from inhomogeneities in the sample [2]. If the drop in rCyj is to be believed, it is possible that there is an increase in overall steric effects just before the phase transition not necessarily directly associated with phase separation. However, it is possibly a computational aberration. A more careful temperature dependence study in this region would probably tell. Why does rjjQ remain constant over most of the temperature range and then rise almost exponentially at lower temperatures? It would seem that the H—bonding effects suddenly become more important in determining the ordering of the palmitate head group at a temperature of ~65°C. This temperature coincides with the maximum quadrupolar splitting of the 3 — 6 deuterons and is only 5° away from the maximum splitting at the 2—position. Therefore the increase in rHG corresponds directly to the fall of the quadrupolar splittings of the 2 — 6 deuterons. These results lend credence to the predictions of the Abdollal model — the decrease in quadrupolar splittings is due to a strictly geometric effect imposed on the surface by interactions with the water at the interface. There is no evidence here to indicate that the conclusions of Doane [4, 5] are correct — that the change in slope of the quadrupolar order parameter profile is due to a change in the principal molecular axis system (essentially a removal of the axial SOAPS / 145 symmetry accompanied by a "lamellar — lamellar" phase transition). The temperature of maximum quadrupolar splitting is also known to correspond to a change in slope in an Arrhenius plot of the Tj spin lattice relaxation time vs. 1/T [115]. This corresponds to an increased activation energy which is greater for deuterons near the polar head group region. The authors of Reference [115] propose that the preferential increase in activation energies at decreased temperatures arises from unspecified "constraints on the chain motion". These model calculations indicate that such constraints may be explainable solely in terms of the interaction with the water with no change in the steric forces. However the temperature of maximum splitting observed by Davis [2, 115] and by Doane [4, 5] is almost 20° higher than the corresponding temperature observed in this study. A detailed Tj relaxation study on the samples used in this thesis would need to be done before any definite conclusions could be drawn. Of what significance is the cylinder radius? The cylinder radius throughout the o calculation remains relatively constant at ~5.92 A. This is in general larger than the cylinder radii calculated by Samulski. For example, in a study of n—octane o 0.5 wt% in Merck Phase V [7L the optimum cylinder radius is 4.58 A; for the liquid crystals 4CB and 8CB, the optimum cylinder radius is calculated as 5.3 e and 5.9 A respectively [6]; for 3 discotic liquid crystals (in which only one chain attached to the central core is considered), rCyj is calculated to range from 4.8 e to 5.1 A [8]; for octanoic acid (lwt%) in Merck Phase V, rCyj is reported as e 4.55 A [9]. The larger radii determined for potassium palmitate imply that steric restraint is less important in lamellar mesophases than in nematic and discotic liquid crystals. Intuitively, this concept seems correct since thermotropic liquid SOAPS / 146 crystals consist of a rigid aromatic core to which floppy alkyl chains are attached, as opposed to the flexible chains of potassium palmitate. Additionally, a decrease in the steric effects might be expected because ordering at the interface is described by the second adjustable parameter in the model, rpjQ. The cylinder radius should in general increase for longer chains, as more conformations become accessible to the molecule. Samulski has shown this for nematic [6] and discotic [8] liquid crystals, and it is demonstrated here as well — in the extended chain o calculations, the cylinder radius increased from 5.90 to 6.43 A at 110°C and from 5.85 to 6.52 A at 45°C. It is the presence of TJJQ which gives the calculated a —CD 2 splitting its characteristic increased value relative to the other quadrupolar splittings. This o behaviour is unique to the soaps [2, 21, 57, 75] — it is not observed in H nmr studies of other amphiphiles [119, 182, 183]. In fact, the large order parameter at the alpha position is observed not only in lamellar dispersions, but in fatty acids dissolved in liquid crystals as well [9,184]. This includes not only liquid crystals in which there is a specific intermolecular interaction like the electrostatic interactions in p —OOBA, but in other liquid crystals as well. It is believed that the extra order arises from dimerization of the solutes forming a relatively rigid central core compared to the floppy alkyl chains. Recent publications demonstrate that the alpha deuteron splittings of methyl myristate and methyl octanoate [9,184], solutes which cannot form H—bonded dimers, dissolved in Merck phase V and ZLI—1167 do not demonstrate an increased order parameter relative to the beta position. Other theoretical calculations on the soaps [9,138,148], while adequately reproducing the rest of the order parameter SOAPS / 147 profile, including the plateau at low temperatures, have not been able to simulate the alpha deuteron coupling. This study demonstrates that while the plateau is due to the steric effects of the other chains, the increased order parameter at the alpha position and the odd even effect can be reasonably reproduced by the inclusion of electrostatic interactions with the water. Samulski, in a publication titled "The Deuterium Nmr Order Parameter Signature" [184] has independently arrived at a similar modelling scheme for head group behaviour of myristic acid dissolved in ZLI—1167. To model dimerization of the acid in the liquid crystal he o places an additional oxygen atom at the distance of 2.7 A from the carboxyl hydrogen. Using this scheme, he can also reproduce the deuteron order parameter profile of myristic acid/ZLI—1167. In the present work, however the additional mass is attached to the carboxyl carbon in order to preserve the symmetry of mirror image conformations. It must be emphasized that the two adjustable parameters in the modified IP model, r c v i and TJJQ, measure only the relative change in steric and electrostatic forces. Nothing can be said about the magnitude or nature of these forces from the model calculations. One would suspect that H—bonding is important in deterrnining head group orientation at all temperatures — if it wasn't, presumably the calculation of T J J Q would yield a very small number. However, to calculate the energy involved in H—bonding or to estimate the number of H—bonded water molecules per amphiphile is impossible from this calculation. Similarly for the cylinder radius — the model only shows that packing constraints remain constant as a function of temperature. SOAPS / 148 What is the effect of changing the mass on the end of the • rod? In test calculations, the mass on the end of TJJQ was varied from 1000 to 50 amu and the dipolar and quadrupolar couplings calculated. The effect of decreasing the o mass is to increase the rod length 0"JJQ) from 2.59 to 4.53 A as shown in Figure 3.26, 3.27, and in Table 3.5. Over the same range, the cylinder radius o remains relatively constant, changing from 5.91 to 5.78 A and the RMS error in the calculation increases from 219 to 261 Hz. The effect on the dipolar couplings is almost negligible — the maximum change in the *3C — *H and *H— *H (^22'^33'^23'^23^ dipolar couplings is 10, 47, 8, 5, and 6 Hz respectively. The effect on the quadrupolar couplings is slightly more dramatic. Decreasing the head group mass tends to pull all the quadrupolar couplings up except for the 3 position, which decreases. The effect is to improve the deuteron fit at all carbons except for 3 and 4 where the increase at the 4 position is emphasized. As it was stated before the mass of 500 amu was chosen to ensure that this parameter has a definite effect on the head group couplings. 3. THE ORDER MATRLX AND THE MOMENT OF INERTIA TENSOR How good is the underlying assumption of the D? model — that the order matrix is diagonalized by diagonalizing the moment of inertia tensor? The idea is that the orientation of molecules in liquid crystalline phases is dominated by steric repulsive interactions which in turn are governed by the shape of the molecule itself. The shape of the molecule is assumed to be characterized by the moment of inertia tensor. There is substantial circumstantial evidence that this assumption is valid. In a study of 27 substituted aromatic solutes in nematic SOAPS / 149 FIGURE 3.26 The IF Model: Effect of Changing The Head Group Mass on the Head Group Parameter Length 5 - r 4.8 -4.6 -2.4 -2.2 -2 -| 1 1 1 1 1 1 1 1 1 0.00 0.20 0.40 0.60 0.80 1.00 Head Group Moss (kg /N ) N = Avogadro's Number. As a test of the calculation, the mass on the end of the rod was varied. This, and the following graph show the change in adjustable parameters with the variation in head group mass. SOAPS / 150 FIGURE 3.27 The LF Model: Effect of Changing The Head Group Mass on the Cylinder Radius 6.2 N = Avogadro's Number, see Figure 3.26. SOAPS / 151 TABLE 3.5 THE IF MODEL Variation of Adjustable Parameters with Head Group Mass HEAD GROUP MASS(AMU) r H G(A) r c y l(A) 1000 2.59 5.91 500 2.71 5.90 A 00 2.78 5.90 300 2.88 5.89 200 3.07 5.87 100 3.61 5.83 75 3.93 5.81 50 4.53 5.78 liquid crystals, Anderson [185] notes a correlation between the largest principal element of the order matrix and the minor principal element of the inertia tensor. Even for asymmetrically substituted benzenes (e.g. 1,4—dichloro — 2,5—difluoro) the difference in axis systems is only 10°. In similar studies of allyl halides [186], cyclopentene [187] and trimethylene oxide and sulphide [188], dissolved in liquid crystals, the differences between PMI and SOAPS / 152 principal order axis are reported as 8° or less. In more symmetric molecules, like benzoyl fluoride [174] and p—substituted benzaldehydes [189], the two axis systems are coincident to within a degree! The assumption is not universally correct, however. Emsley et al. [190] in a study of dibromoacetophenone in Merck Phase V calculate a difference in axis system of almost 30° and in a later publication Counsell et al. [191] conclude that "there is no sound relationship between the components of the inertial tensor, which is a single molecule property, and those of the ordering matrix which is determined by anisotropic intermolecular interactions". This concept is supported by a recent studj' on o — dichlorostyrene in EBBA [192] in which the difference between axis systems is concentration dependent and ranges from 4 to 18°. The order matrix is, as it should be, concentration dependent, whereas the moment of inertia tensor, the molecular property, is not. In addition, the studies where good agreement is quoted all refer to highly symmetric molecules with limited flexibility in nematic melts as opposed to the highly flexible lyotropic mesophases dealt with in this thesis. Still, the anisotropic intermolecular interactions referred to in reference [191] consist primarily of short range repulsive interactions between individual molecules. If these interactions are not related to the moment of inertia tensor, they are certainly related to the size and shape of the molecules [193, 194] which would explain, at least crudely, why an assumption of this nature might give reasonable results in compounds with relatively uniform mass distribution. The final question to be asked about ambiguous assumptions like these is "Do they work?". It has worked numerous times for Samulski [6-9] and in the present application it gives answers of the same quality to experiments of much finer detail. SOAPS / 153 4. WATER AND COUNTER IONS What do these results say about the water and counter ions? Since no measurements were made on the potassium counterion, nothing definite can be said about its behaviour near the head group. For the water, on the other hand, the change in the D 20 deuteron couplings with temperature parallel those of the a—methylene segments. This has been observed before in 2H nmr spectra of sodium palmitate/I^O [21,116] and of potassium palmitate D 20 [2, 3]. In fact the ^3Na spectrum in sodium palmitate also demonstrates this behaviour. Hence there is a definite correlation between the amphiphile and solvent. The small value of the quadrupolar splitting in D 20 demonstrates that the water molecules enjoy considerable motional freedom in the bulk phase, yet that this motion is restricted by interactions with the bilayer. The virtual absence of any central isotropic water line in the deuteron spectra indicates that exchange between bound and free water layers as discussed by Charvolin [59 — 62] must be rapid compared to the nmr splitting. It is also possible that the central line reported by Charvolin results from excitation of the deuteron double quantum transition caused by high rf intensity in continuous wave spectroscopy [17, 93, 195]. Drawing any conclusions on the water "structure" based on this present study is dangerous. The efg for D in an OD bond varies depending on the electronic environment of that bond. For water, in which the deuterons are presumably involved in hydrogen bonding with associated deuteron transfer, the efg of the OD bond is in constant flux. As a result, the quadrupole coupling constant is not known exactly, and calculation of order parameters becomes meaningless. Abdollal et al. [3] has roughly calculated a relative change in the D 20 order SOAPS / 154 no parameters and the Na efg as a result of his proposed configurational change (see Table 1.1). In order to do this, they assume all efg tensors are axially symmetric, that the value of the OD efg tensor is the same as in ice, that the hydrogen bond is parallel to the first C—C bond in the high temperature configuration, that rotation about the hydrogen bonded OD bond is free, rapid, and of threefold or greater symmetry, and that the principal axes of the sodium efg tensor lies along the direction of the oriented water lone pair electrons. With these assumptions, the order parameters for D 20 and the efg tensor for configuration B, (the low temperature configuration) are calculated to be of a smaller magnitude in agreement with the quadrupolar splittings. No conclusions will be drawn on the water orientation in this thesis. 5. CALCULATION OF THE ALPHA METHYLENE ORDER MATRIX Can the calculated nmr couplings from the IF model explain the strange temperature dependence of the order matrix for the alpha methylene segment of potassium palmitate (see Figure 3.13). The calculated dipolar and quadrupolar couplings from the IF model were used to recalculate an order matrix for the alpha methylene segment in the 1— C — 2,2—H2 — potassium palmitate. The results of this calculation are shown in Figure 3.28 and Figure 3.29. The calculated elements of the order matrix now have similar temperature dependence and do not cross. The orientational order in the 2 direction exceeds that of the 1 (or x direction) at all temperatures. Hence the modified IF model does not explain the subtleties of the orientational ordering at the alpha segment. In order to explain the odd decrease and cross of the experimental profile, perhaps an SOAPS / 155 FIGURE 3.28 Recalculation of the a-Methylene Order Matrix from the IF Calculation -0.35 Legend: S jji • = S x x , S H H 0 = S y y A = S y z + = S C D The dipolar and quadrupolar couplings calculated using the IF model were used to recalculate Figure 3.11. The qualitative features of the two figures are the same, although the details are different. The largest discrepancy is in SyZ, the least accurately measured coupling. SOAPS / 156 FIGURE 3.29 Recalculation of the Diagonalized a-Methylene Order Matrix from the IF Calculation -0.35 120 Temperature (C) Sij: • = S 1 1 0 = S 2 2 The dipolar and quadrupolar couplings calculated using the IF model were used to recalculate Figure 3.13. It can be seen that the two order parameter profiles no longer cross. The IF model does not explain the subtle details of the orientational ordering. SOAPS / 157 angular dependence about a second rotation angle could be invoked. This would be rotation through an angle about the y (or 2) axis of the methylene group. To test a hypothesis like this, the angular rotation must be included in the molecular modelling process. Using the IF model, a second angle could be included by allowing the electrostatic parameter (the mass on the end of the rod) to vary from its position coincident to the first C—C bond. This destroys the symmetry of related conformers, doubles the computational time and also introduces a third adjustable parameter to the model. Well, as the saying goes, with enough parameters you could fit an elephant, but perhaps the introduction of the new adjustable parameter could be at the expense of one of the other adjustable parameters — the cylinder radius. The cylinder radius varied by only 1.5% through the temperature range, so it could be held at a constant value, or the values determined in the previous calculation could be used. 6. IMPROVING THE CALCULATION How could the model calculations be improved? A better method of generating chain conformations is necessary in order to simulate the deuteron quadrupolar couplings of the rest of the chain. One method would be to pick a number of conformations at random, for example the 10 state model used by Pink [196]. Calculations are performed on a limited number of conformers one "totally ordered" (the all trans state), one totally disordered (the no trans state) and the remainder of intermediate disorder. Pink, who uses this scheme to generate lipid conformations for Monte Carlo calculations, weights each conformation with a degeneracy, however an internal probability could be used in a mean field SOAPS / 158 calculation. Another method would be to generate all conformations of the lipid chain but to reject conformations which exceed a certain number of gauche conformers (for example 4). This would exclude highly disordered conformers i.e. conformers of intrinsically low internal probability. If conformer generation was started at the head group, as it would have to be for a study dealing with head group behaviour, the resulting rotational isomers would tend to be disordered near the interface and rigidly ordered at the end. This is contrary to intuition, so a scheme of this sort would have to be used judiciously. A third method would be to use a Monte Carlo procedure to generate a specific number of chain conformations at random. Samulski has used the Monte Carlo method to generate 80,000 conformations in a simulation of quadrupolar splittings of perdeuterated hexadecane [197]. Although the experimental numbers are adequately reproduced, the form of the external potential could be improved. It seems that the right forces have been chosen to model the lamellar phase of potassium palmitate, but their description is rather crude. The external potential, represented by the constraining cylinder carries no intrinsic temperature dependence (except in the Boltzmann factor). In addition, the calculation of the mean field is not self consistent. As a result, the model can only be used to calculate the relative dipolar and quadrupolar couplings at each temperature, the numbers must then be scaled to an experimental coupling. This makes calculation of thermodynamic functions from the partition function meaningless. In order to improve the calculation, the intermolecular potential must be stated explicitly as the sum of the physical forces acting on the molecule. For example, Marcelja [120,137] used two terms SOAPS / 159 in the intermolecular potential, a steric repulsion term based on lateral pressures between chains (1.60) and an anisotropic attractive dispersion term calculated self consistently. The dispersion term carries a temperature dependence (1.62) and the lateral pressure term depends on the cross sectional area of the chain which is temperature dependent. One must still consider how to deal with the orientation of the molecule, specifically the head group. This is one of the main reasons why the Samulski model was initially chosen, not only does it adequately predict deuteron order parameters but the head group orientation is determined not at random, or by choosing a few specific orientations, but by the conformer moment of inertia tensor. Some physical property must be chosen to model the head group orientation whether it be moment of inertia, polarizability, or size and shape of the molecule. Since moment of inertia seems to predict orientational order in symmetric molecules of uniform mass distribution, the suggestion has been made of using a unit mass inertial tensor [198] in which the atoms of the molecule are replaced with atoms of mass 1 amu. In the context of the model presented here, this could easily be done. The interaction of the head group with the water is crudely represented as a mass on a rod. To attempt to model an electrostatic interaction with a number of water molecules and/or counterions would be expensive and probably foolhardy, but if successful could simulate H order parameters and the efg at the Na or 39 K nucleus. A more sensible approach is to model an interaction of an amphiphile chain with a single water molecule and calculate a potential of SOAPS / 160 interaction between the two. One example could be in the form of a restoring potential such that when the soap molecule is displaced from some equilibrium (say, with the first C—C bond parallel to the bilayer director) by a rotation into the principal moment of inertia frame, the electrostatic potential would exert a restoring force based on a Hooke's Law force constant. An immediate disadvantage to this scheme would be the calculation of two sets of molecular coordinates for each conformer — one from rotation to the PMI frame, and the other from back rotation as a result of the influence of the electrostatic potential. F. CONCLUSIONS In order to obtain precise information on head group interactions, three isotopically substituted species of potassium palmitate were synthesized: potassium palmitate—dr^, 1— C —2, 2—potassium palmitate—d2g and 2, 2, 3, 3 —H^—potassium palmitate —d 2 7. The proton, carbon—13 and deuteron nmr spectra of these three species dispersed in a lamellar phase were recorded as a function of temperature at a constant water content. A two dimensional spin echo technique designed to remove heteronuclear dipolar couplings was necessary to extract the dipolar couplings in the proton spectra. An extra refocussing pulse applied simultaneously to the *3C spins allowed observation of the *H-13C dipolar couplings. This is believed to be the first application of this pulse sequence to observe nuclei coupled to protons. The proton spin echo spectra of the four spin system (2,2,3,3 —H^) is believed to be the first purely dipolar coupled four spin nmr powder spectrum. The dipolar powder lineshape is shown SOAPS / 161 to possess the expected P2(cos0) dependence by removal of the powder patterns using the numerical depaking procedure. With the assumption of a single plane of symmetry, the complete orientational order matrix (consisting of three independent elements) for the rigid a—methylene segment of potassium palmitate in a lamellar phase was determined. The individual order parameters were calculated from the nmr splittings in the perdeuterated and carbon 13 labelled soap. The a—methylene segment is shown to be not axially symmetric at any temperature in the lamellar phase. The average rotation angle necessary to diagonalize the orientational order matrix of the alpha methylene segment was calculated as a function of temperature and found to change by 3° over the range 110° —45°C. This is an improvement on a previous determination of the order matrix by Higgs and Mackay, who with the assumption of an extra plane of symmetry in the a —methylene HCH plane, calculated only two independent elements of the order matrix. The change in orientational angle of the methylene group confirms the Abdollal model of lipid water interaction. A conceptually and mathematically simple model based on the Samulski Inertial Frame model was devised to determine the effects of water on the structuring of the methylene segments near the soap-water interface of potassium palmitate. Two forces were included in the calculation, the steric forces of the neighbouring chains, modelled as a constraining cylinder, and the electrostatic interactions of the carboxyl head groups with the water, modelled as a ball on a rod. Using the modified IF model, the deuteron quadrupolar splittings and the *H— *H, SOAPS / 162 13 1 C— H dipolax splittings of three isotopically substituted potassium palmitates were simulated. The radius of the constraining cylinder (i.e. the steric effects) remained relatively constant over the temperature range 110° —45°C, whereas the electrostatic interaction (the length separating the ball from the soap molecule) remained constant from 110° —65°C and then increased by ~30% over the temperature range 65° — 45°C. This is in agreement with an earlier model proposed by Abdollal et al. in which an anomalous increase - decrease of the deuteron order parameter profile for deuterated methylenes near the interface was postulated to arise from a strictly geometric effect imposed on the methylene segments by interaction with the water. 1. COMMENTS ON CLEANLINESS AND REPRODUCIBILITY The soap —water systems, although well studied by nmr, are notoriously irreproducible. Almost all published articles involving these systems carry some sort of disclaimer as to the results therein. For example, "we believe these discrepancies to be due to differences in sample preparations" [61], "The spectra obtained...differ slightly from those obtained previously" [53], "Since the details of sample preparation can influence the results" [5], "considerable alterations in behaviour before and after recrystallization from acetone" [113], "the difficulty in preparing a truly homogeneous sample" [2], "different transition temperatures due to impurities of sample inhomogeneities" [2], "these differences may be due to sample preparation techniques and or isotope effects" [3], "character of this particular phase transition is concentration or purity dependent" [4], "There is also the problem that the samples may not be exactly similar as to soap-water SOAPS / 163 ratio and impurity content" [56] etc.etc. The differences between experiments may arise from contamination of the fatty acids, possibly with other fatty acids of differing chain length. Alternately, the differences may be due to inhomogeneity in the sample due to improper mixing, or to minor variations in water content. For these reasons a number of precautions were taken to nunimize the experimental error. Soaps, as the name implies, are soaps. Therefore to avoid contamination all glassware must be kept scrupulously clean. The glassware used for the soap studies was purchased new, washed in conventional detergent and water, then rinsed at least forty times with tap water, followed by rinsings with solvent, usually acetone and ethanol. The glassware was re—rinsed with water, followed by 2 — 3 rinsings in deionized water and thoroughly dried in a 110°C oven before use. This set of glassware was kept pristine — solely for the use of the soaps, and never washed with detergents again. Instead traces of fatty acid salts were removed by repeated washings with solvents and water. Since all studies in this thesis were performed on potassium palmitate, any residual contamination would be due to a different isotope of the same molecule, and therefore negligible. All fatty acids were purchased from the same supplier (Calbiochem—Behring) with the exception of the *3C labelled fatty acid which was purchased from Merck Sharp and Dohme. This nunimizes differences due to synthetic and purification methods. Even recrystallization solvents may make a difference [113, 167]. Soap samples were prepared using a standard method [5, 53, 61] by weighing fatty acid salts into a constricted sample tube. A second constriction is made, D 20 is SOAPS / 164 added to the surface of the soap and the tube is flame sealed. Water content was monitored by weighing of the sample tubes at every step of the preparation. Samples in which the weight changed significantly were discarded. This precaution nunimizes loss due to evaporation of water and ensures constant water content from sample to sample. To prevent sample inhomogeneity, samples were stored in a 110°C oven, and daily centrifuged back and forth through the constriction in the sample tube. After a minimum one hundred centrifugings, the sample tubes were flame sealed at the constriction and stored in a 110°C oven for at least 3 days prior to use. Just before insertion into the probe, the samples were centrifuged again to remove bubbles and to concentrate the soap into one end of the tube. To minimize experimental error, the nmr experiments were performed in a consistent manner. Since hysteresis may be a factor, especially near the phase transition, experiments were always started at 110°C and temperature was decreased in regular intervals. Samples were allowed to equilibrate in the probe at the initial temperature until a consistent nmr spectrum was observed before data acquisition was begun. The spectrum was collected, the temperature was decremented and the samples allowed to equilibrate at the new temperature for one hour before data acquisition was begun again. An attempt was made to keep all samples at the same temperature for the same time period. This was difficult to do because of the length of time necessary for the spin echo experiments and the need to efficiently utilize the allotted spectrometer time. Decent proton single pulse spectra could be collected in half an hour, deuteron quadrupolar echo spectra could easily be obtained in three hours, the time needed SOAPS / 165 for proton and proton—carbon—13 echo spectra ranged from 5 — 12 hours/temperature. As a compromise, deuteron spectra were collected at two temperatures for every proton spin echo spectrum. The temperature increments were 2 — 3 degrees for the deuteron spectra, and 5 degrees for the spin echo spectra. Thus the time taken to cover the entire temperature range was kept approximately constant. Temperature at the sample was monitored with up to three thermocouples separate from the regulation thermocouple. Using these prescribed precautions, it was found that dipolar and quadrupolar splittings in a particular sample were reproducible from day to day. It was also found that quadrupolar splittings could be reproduced up to two years later in a sample which had been stored in the liquid crystalline phase at 110°C. In addition quadrupolar and dipolar splittings were easily reproducible in different samples of the same isotopically substituted palmitate. The error in the quadrupolar splittings in Figures 3.3 — 3.5 is generally within the size of the points. In the case of the 1 3 C labelled soap, the splittings were reproducible between two samples from two different preparations of the same compound. However, isotopic differences are observed in the quadrupolar coupling temperature profiles. These are most easily ascertained by close examination of Figures 3.3 — 3.5. Near the methyl end, the profiles are almost superimposable but at the head group there are apparent discrepancies in the shape of the profile. As the temperature is decreased the quadrupolar splittings fall off more rapidly in the perdeuterated sample than in either the C—2,2—H 2 or 2,2,3,3—H4~ samples. 1 ^ The differences are most obvious in the C —2,2—H2 sample, the other two exhibit very similar temperature dependence. This supports the notion that the SOAPS / 166 variations are the result of purchasing starting materials from different suppliers. A number of attempts were made to eliminate small systematic temperature errors by scaling the nmr couplings to the values measured on the monitoring thermocouples placed near the sample. It was found that the temperature homogeneity within the samples and temperature variation between samples were sufficiently small as to negligibly affect the splittings. The next attempt was to scale the deuteron splittings by matching order parameter profiles from the various isotopes at different temperatures. The idea is to correct for small variations in water content and sample composition which would slightly offset the temperature profile and the phase transition temperature. Again the best fit was determined to be at the same temperature for all isotopes. Subsequently, the deuteron splittings were scaled by dividing all the numbers in a particular order parameter profile by a constant, then comparing relative splittings of the various isotopes at different temperatures. The scaling factor was chosen to be the quadrupolar splitting from the deuterons at the 10 position — the splitting closest to the headgroup that does not overlap any other quadrupolar splitting at any temperature. In other words, deuteron resonances from the 34, 56, and 78 positions overlap at low temperatures. This leads to broader lines from which the measurement of the precise quadrupolar coupling is difficult. In contrast, at positions farther down the chain, the lines sharpen considerably. Scaled order parameter profiles (AVJAV^Q) were compared for the three potassium palmitates and temperature corrections made based on the shape of the profile, rather than on the absolute value of the splittings. Splittings were S O A P S / 167 1 *3 then adjusted to coincide with the C —2,2 — H 2 values. Interestingly enough, at low temperatures this scaling worked rather well, the best fit for all three isotopes was at the same temperature. However at higher temperatures, the efficacy of this fitting process waned, at 110°C it was necessary to match order parameter profiles from up to 20° away. This was obviously incorrect. The gel to liquid crystalline phase transition temperature between samples differed by no more than 3°C — orientational order could not differ this drastically at higher temperatures — especially since the fit at these temperatures for the unsealed data was already adequate. An orientational order matrix calculated for the rigid alpha methylene segment using these doctored numbers showed little change in SQTJ over the entire temperature range studied, as compared to Figure 3.11 and consequently little change in Syy. S ^ , which is determined solely from the a—methylene dipolar splitting in the ^C — 2,2 — H 2 sample, remained unchanged. In the scaled diagonalized order matrix, in comparison to Figure 3.13, S J J and S 2 2 no longer crossed, in fact the general trend is for S 2 2 to increase, rather than decrease as the temperature is dropped. S 3 3 looked similar to before, although the trend was not so dramatic. It is possible that the cross observed in order parameters S ^ j and S 2 2 i s due entirely to differences between samples. It has already been noted that the temperature at which the crossing takes place is very dependent on S ^ J J which is the coupling measured with least accuracy. When the rotation angle of the scaled order matrix was calculated, there was no significant change over the entire temperature range. Therefore, this method of data correction removed all interesting trends in the data. However, given the drastic measures needed to adjust the higher temperature splittings, it is safe to conclude that these "corrected" results have no validity. SOAPS / 168 Eventually it was decided to live with the up to ten percent discrepancy in the quadrupolar splittings and follow the established procedure of including a (somewhat extended) disclaimer, warning all potential investigators of the hazards and pitfalls involved in the study of soap/water systems. In the Inertial Frame model calculations one small correction was made. The C— H and alpha *H— *H dipolar splittings were adjusted so that the alpha proton dipolar couplings from the two were identical. This correction ranged from 0.65 to 6.4% and had little to no effect on the final results of the model calculation. It is interesting to note that for the corresponding systems dissolved in the nematic liquid crystal p —OOBA, the deuteron order parameter profiles from sample to sample are essentially superimposable. There are no problems arising from minor differences in sample preparation, concentration, composition etc. No special care is needed in handling and preparation, no correction factors are necessary. Dipolar and quadrupolar splittings are reproducible from day to day regardless of thermal history. This is more likely a property of the liquid crystal, the major component of these samples, than of the solute. IV. SHORT CHAIN CARBOXYLIC ACIDS Several long and short chain fatty acids were dissolved in the liquid crystal p—octyloxybenzoic acid (p-OOBA). p—OOBA forms a liquid crystalline phase by virtue of its ability to form dimers via intermolecular hydrogen bonding [199]. The dimers then have the approximate molecular shape characteristic of many thermotropic liquid crystals, the "rigid" aromatic core attached to floppy alkyl chains. This ability to dimerize leads to an interesting side effect: the liquid crystal can form hydrogen bonds with appropriate solutes, for example other carboxylic acids. The first bonds of the solute then lie parallel to the benzoic acid moiety of the solvent, approximately along the long axis of the liquid crystal, which leads to a large molecular solute orientation. Large orientation results in large order parameters which result in large dipolar splittings and hence more easily resolvable spectra. The main disadvantage to using p —OOBA as a nematic solvent is its high nematic temperature range (108 — 147°C) [200, 201] which is often lowered by the presence of solutes, but which still leads to some experimental difficulties. These difficulties include maintenance of high temperatures on commercial nmr spectrometers, and temperature gradients incurred using commercial temperature regulation devices. The series of short chain acids, acetic, propionic, and butyric —2,2—d2 were dissolved in the liquid crystal p-OOBA at a concentration of approximately 11 mole %. The proton single pulse and spin echo nmr spectra were recorded at 110°C for each sample. For acetic and propionic acids, the single pulse spectra are readily analyzable and the echo spectra were used only as a test of the 169 SHORT CHAIN CARBOXYLIC ACIDS / 170 method. For the deuterated butyric acid, all information results from the echo spectroscopy, the proton single pulse spectrum is sufficiently complicated and remains intractable to this day. Throughout this chapter the spin systems are described with the designation A n B m referring to the number of equivalent nuclei. All solutes contain a methyl group, and the description of spin systems consistently refers to the methyl group as A 3 . A. ACETIC ACID The H nmr single pulse acetic acid spectrum is shown in Figure 4 .1 . Acetic acid is an A 3 spin system. The three protons in the methyl group give rise to a triplet with " a dipolar splitting of 3 D J Q J = D^A = 1 6 6 6 5 ± 3 6 Hz corresponding to a dipolar coupling constant of = 5 5 5 5 Hz. The methyl group possesses C 3 V symmetry and this symmetry allows the description of the orientation of the methyl group using a single order parameter. The order parameter, S^, can easily be calculated using (1.9). For an interproton distance o o of 1.78 A calculated assuming a C—H bond length of 1.09 A and a HCH bond angle of 1 0 9 . 5 ° [202], the order parameter for the methyl group of acetic acid is S^ = - 0 . 2 6 0 9 ± 0 . 0 0 0 6 (see Table 4.1). The other elements of the order matrix are easily determined as S x x = Syy and S M = -(S^+Syy) since the order matrix is traceless. In a previous study [203], acetic acid dissolved in liquid crystals with no specific intermolecular interactions yielded dipolar coupling constants ranging from 1691 — 2 6 6 9 Hz which would correspond to order parameters of 0 . 0794 — 0 . 1 2 5 4 respectively. The additional orientational order observed in p —OOBA arises from the specific electrostatic H—bonding between SHORT CHAIN CARBOXYLIC ACIDS / 171 FIGURE 4.1 l H nmr Spectrum of 11 mole % Acetic Acid in p-OOBA Experimental: Temperature = 110°C, 90° pulse length = 5usee, Relaxation delay = 4 sec, 1700 Acquisitions. Recorded on the CXP—200. The large background hump is the dipolar couplings of the liquid crystal. SHORT CHAIN CARBOXYLIC ACIDS / 172 TABLE 4.1 Dipolar Couplings and Order Parameters for the Short Chain Acids in p-OOBA acetic acid propionic acid (single pulse) propionic acid (spin echo) butyric acid-2,2-d2 D <a> AA 5555112 -561±3 -53113 204015 DIPOLAR COUPLINGS(Hz) DBB 561913 546214 1581112 AB 75412 71913 -71616 ORDER PARAMETERS xx acetic acid propionic acid (single pulse) propionic acid (spin echo) acetic acid propionic acid (single pulse) propionic acid (spin echo) yy zz yz -0.260910.0006 -0.263810.0001 -0.260910.0006 0.521910.0011 -0.219910.0004 0.483710.0005 -0.144510.0005 -0.256410.0002 -0.212410.0003 0.468810.0005 -0.137610.0008 Sll S22 S33 ROTATION ANGLE (b) -0.260910.0006 -0.260910.0006 0.521910.0011 — -0.263810.0001 -0.2509+0.0008 0.514710.0007 11.1710.05 -0.256410.0002 -0.239110.0010 0.495510.0008 11.0010.07 (a) consistently refers to the methyl group couplings. (b) ROTATION ANGLE in the yz plane needed to diagonalize the order matrix. SHORT CHAIN CARBOXYLIC ACIDS / 173 solvent and solute. Note that the sign of the order parameter, S,_, is uniquely determined to be positive since — i s S z z s l , by definition. This also uniquely determines the sign of D J J J J to be positive. The * 9F nmj- spectrum of 15 mole% trifluoroacetic acid in p —OOBA has been measured by Dunn [204]. At 105°C, the 1 9 F - 1 9 F dipolar coupling was found to be 5818 Hz corresponding to an order parameter of 822=0.373. The orientational order parameter is again very large reflecting the intermolecular hydrogen bonding. The fact that the value is smaller than in this study of acetic acid is probably due to the concentration difference. Dunn also found that as the temperature was lowered the value of S z z increased to 0.532 at 90°C and 0.598 at 85°C. In a study of trimethylacetic acid (5.1 mole%) in a mixture of p —OOBA and p-BOBA (p-butyloxybenzoic acid) 22:78 by weight at 64°C [202] the order parameter, S^, was determined to be 0.33. p—BOB A was used to lower the temperature range of the nematic phase. No direct comparisons of order parameters are now possible, but note that the orientation is again very large for an acid in this solvent. The echo spectra for acetic acid dissolved in p—OOBA, experimental and calculated are shown in Figure 4.2. Several features are worth note: because there is no chemical shift of one methyl proton relative to the others, both single pulse and echo spectra are symmetric about the centre of the spectrum. The central peak is of much larger intensity in the echo spectrum, a result of SHORT CHAIN CARBOXYLIC ACIDS / 174 FIGURE 4.2 IH nmr Spin Echo Spectrum of 11 mole % Acetic Acid in p —OOBA T 1 1 1 1 1 1 1 1 "I 1 1 1 1 1 1 1 1 1 1 1 1 j 1 1-20000 10000 0 - 1 0 0 0 0 - 2 0 0 0 0 Hz A) Experimental: Temperature=110°C, 90° pulse length = lOpsec, T = 5 psec, 180° pulse length = 20 psec, Relaxation Delay = 2.0 sec, 16 Acquisitions. B) Calculated: D}{H = 5555 Hz, 146° refocussing pulse, Lorentzian linewidth = 150 Hz. SHORT CHAIN CARBOXYLIC ACIDS / 175 an inhomogeneous refocussing pulse. Extra transitions which result from poor H^ homogeneity are evident as the small peaks at approximately one half the dipolar coupling frequency. These transitions can be simulated using the modified version of LEQUOR discussed previously in the Introduction and this is shown in Figure 4.2B. The intensity of the extra transitions depend on the length of the refocussing pulse and the simulation shown here are for a pulse length of 146°. These experiments were performed on a Bruker CXP 200 nmr spectrometer using a high resolution probe equipped with a standard saddle coil arrangement. The H^ field is then very inhomogeneous over the sample volume, i.e. different parts of the sample experience different length refocussing pulses and this gives rise to the extra lines. B. PROPIONIC ACID The experimental single pulse proton nmr spectrum and the calculated spectrum for propionic acid dissolved in p —OOBA at 110°C are shown in Figures 4.3. The spectrum is almost first order in nature (i.e. ((a^—Og), |D^g|< <|D^ |^, |Dgg|) but must be analyzed as an A 3 B 2 system. The large central line results from the carboxyl protons on the propionic acid which are in rapid exchange with the carboxyl proton of the liquid crystal. Exchange is sufficiently rapid that no coupling is observed between these protons and the rest of the molecule. This peak is reduced in intensity because the acid protons of the liquid crystal have been removed by exchange with D 2 O . The spin echo spectrum of propionic acid in p—OOBA in the fj dimension is SHORT CHAIN CARBOXYLIC ACIDS / 176 FIGURE 4.3 ! H nmr Spectrum of 11 mole % Propionic Acid in p -OOBA JLJJL_JJUUJ JLIU l i i i i | i i i i | i i i i | i i i i | i ' ' ' | • ' i t i 1 1 1 1 i 1 1 1 *" 20000 15000 10000 5000 0 -5000 -10000 -15000 -20000 Hz A) Experimental: Temperature=U0°Ct 90° pulse length = 2.1 usee, Relaxation Delay = 0.5 sec, 50 Aquisitions. B) Calculated: DAA = -561 Hz, DAB = 754 Hz, DBB = 5619 Hz, RMS Error = 22 Hz. Lorentzian linewidth = 100 Hz. DAA is the methyl group coupling. SHORT CHAIN CARBOXYLIC ACIDS / 177 shown in Figure 4.4 along with a calculated spectrum. This spectrum, recorded at the same time as the single pulse spectrum in Figure 4.3, was used as a test of the spin echo method. Since the chemical shift is refocussed at the peak of the echo, no chemical shift difference is observed between methyl and methylene protons and the spin echo spectrum is completely symmetric. The magnet inhomogeneities are also refocussed by the echo sequence. Thus their contribution to the line width is removed and this gives rise to sharper peaks. In addition the good Hj homogeneity over the whole sample gives the true dipolar coupled spectrum with no extra transitions. These experiments were done on the CXP—200 in a solid state probe with a solenoidal coil. The spectrum was analyzed using the iterative computer program LEQUOR [24,25] and yielded dipolar coupling constants of D^j^ = — 561(—531) Hz, Dgg = 5619(5462) Hz and D A B = 754(719) Hz with an RMS error of 22(25) Hz (see Table 4.1). The coupling constants calculated from the echo spectrum are given in brackets. The chemical shift of the B protons relative to the A protons was calculated in the single pulse spectrum to be 334 Hz which at 200 MHz corresponds to 1.67 ppm downfield, slightly higher than the high resolution nmr value of 1.30 ppm. Throughout the calculation the J coupling was held constant at 3 JAJ3 = 7-05 Hz. The large values of the dipolar coupling Dgg reflects the increased orientational order imparted to the solute by the specific electrostatic solute—solvent interaction. The methyl group coupling, D^A^, and the intergroup coupling are reduced by rapid molecular motion of the methyl group about the C 9 —Co bond axis. SHORT CHAIN CARBOXYLIC ACIDS / 178 FIGURE 4.4 iH nmr Spin Echo Spectrum of 11 mole % Propionic Acid in p-OOBA JLJ1JL_JLJ^^ r I i !• -r—i—I—T" i - i — i — r T—r 15000 10000 5000 -5000 -10000 -15000 -20000 Hz A) Experimental: Temperature=110°C, 90° pulse length = 2.1 psec, r = 5 usee, 180° pulse length = 4.2 usee, Relaxation Delay = 0.5 sec, 8 Aquisitions. B) Calculated: DAA = -531 Hz, DAB = 719 Hz, DBB = 5462 Hz. RMS Error = 25 Hz, 180" refocussing pulse, Lorentzian linewidth = 40 Hz. SHORT CHAIN CARBOXYLIC ACIDS / 179 Order parameters for propionic acid were calculated from the iterative computer program SHAPE [174, 175]. These results are presented in Table 4.1. Tetrahedral geometry was assumed for all HCH, HCC, and CCC bond angles. o o Bond lengths were taken to be 1.09 A for a C-H bond and 1.54 A for a C—C bond. A molecule fixed axis system was chosen such that the z—axis lies along the H2C—COOH bond. The molecule fixed axis system used for propionic (and butyric) acid is shown in Figure 4.5. The methyl group was allowed to rotate in a 3—fold classical potential with a potential barrier of 12.6 kJ/mole. The geometry of the molecule was calculated in 10° steps — because of 3 —fold symmetry of the methyl group, only a total of 12 steps had to be calculated. Each of these steps were weighted with a relative probability based on a barrier to rotation of 12.6 kJ/mole. There is a plane of symmetry in the molecule defined by the Cj — C 2 — C 3 plane if the methyl group is in the most probable conformation, a staggered conformation relative to the methylene segments. In this case, the number of independent order parameters needed to describe the orientation of propionic acid in p —OOBA is reduced from 5 to 3. [12]. Because of the way the axis system was chosen (with the plane of symmetry in the yz plane), these three order parameters are Szz, S^, and Syz. Their calculated values are S B = 0.4837(0.4688), S n = -0.2638(-0.2564) and S y z = -0.1445(-0.1376). Note that S y y is uniquely determined since S^+Syy + S^ = 0 and therefore Syy = -0.2199(-0.2124). The numbers in brackets are calculated from the echo spectrum. The signs of the order parameters are not uniquely determined since now Szz<0.5. By comparison with acetic acid, S^ is probably positive and all other elements of the order matrix are negative. S^ has the largest absolute value of the order parameters and this makes sense in SHORT CHAIN CARBOXYLIC ACIDS / 180 FIGURE 4 . 5 Axis Systems for Acetic, Propionic, and Butyric Acids These are the molecule fixed system axis systems used for the calculation of the order matrices. For acetic acid, this is also the principal orientation axis system. For propionic acid, the transformation to the principal axis system involves a rotation about the x axis in the yz plane, the plane of symmetry. For butyric acid, the axis system is only a starting point for the IF calclation. The molecule is then rotated about its centre of mass into the principal moment of inertia (PMI) frame. SHORT CHAIN CARBOXYLIC ACIDS / 181 that is representative of the ordering along the z axis of the molecule fixed axis system, which is approximately the nematic director of the phase. The value of in liquid crystals is usually in the range of 0.5 to 0.8 [158,205] so the ordering of the solute is of the same magnitude as that of the liquid crystal. These values of the order matrix are higher and of a different sign than those reported by Heldman [201]. However, the higher solute concentration in that study (17 mole%) would reduce the value of the order parameter, and a different choice of axis system changes the sign of the off diagonal elements. The order matrix can be diagonalized and this is equivalent to rotating the axis system in the yz plane into the principal orientation axis system. The order of the system is still described by 3 independent order parameters, but these are now any two of the principal values of the order matrix (the trace is still zero) and an angle calculated from the eigenvector of the diagonalization process. The diagonal elements of the order matrix (also given in Table 4.1) are S^ = -0.2638(-0.2564) S 2 2 = -0.2509(-0.2391) and S 3 3 = 0.5147(0.4955). Diagonalization pushes one of the order parameters over the 0.5 limit and uniquely determines its sign. The average rotation of the molecule in the yz plane calculated from the eigenvectors is 11.17° (11.00°). This describes the average tilt of the entire solute—liquid crystal complex away from the molecule fixed axis frame. C. BUTYRIC ACID-2,2-D 2 The analysis of the nmr spectrum of butyric acid in a liquid crystal has proved to be a formidable task. Butyric acid is only a seven spin system (AqBB'CC) SHORT CHAIN CARBOXYLIC ACIDS / 182 yet the nmr spectrum of the oriented acid is much more complicated than the corresponding five spin system, propionic acid. It was in an attempt to simplify the nmr spectrum that butyric acid was deuterated at the alpha position. This is still a seven spin system although now it is a AgBB'XX' system. The orientational order of the two solutes should be the same — the two deuterons are not expected to produce much of an isotope effect. Therefore the DAJ^, D^g, and Dggt dipolar couplings should be approximately the same. The couplings to the alpha protons (deuterons) should be reduced by a factor T J J ^ D = ^-51 times in the partially deuterated analog. While initially, the reduced deuteron couplings may seem to be of assistance in solving the spectrum, the small couplings actually seem to make the analysis more difficult. The single pulse nmr spectrum of butyric acid —2,2—d 2 dissolved in p —OOBA at 110°C at a concentration a 11 mole % is shown in Figure 4 .6. The spectrum is very complicated with about five envelopes of reasonably sharp lines in the centre of the spectrum. Transitions in the wings are broad, of low intensity, and difficult to measure to any accuracy. Good quality spectra of solutes in liquid crystals at these temperatures are not easily attainable due to poor temperature homogeneity in the samples. This effect manifests itself in broader lines which obscure some of the transitions in the wings of the spectrum. Other investigators have avoided this problem by mixing p—OOBA with similar compounds with a lower melting point like p—butoxybenzoic acid 78 :22 [202] in order to lower the nematic range. In any event, the spectrum is sufficiently intractable that no reasonable set of dipolar couplings has been found for either of the isotopically substituted butyric acids. If any information is to be obtained on the oriented butyric acid, some method must be found to measure the dipolar coupled proton nmr spectrum free SHORT CHAIN CARBOXYLIC ACIDS / 183 FIGURE 4 . 6 l H nmr of 11 mole % Butyric A c i d - 2 , 2 - 0 2 in p-OOBA Experimental: Temperature = 110°C, 90° pulse length = 5 usee, Relaxation Delay = 0.5 sec, 48 Acquisitions. Recorded on the WH—400. The background signal is unresolved dipolar couplings from the liquid crystal. SHORT CHAIN CARBOXYLIC ACIDS / 184 of the complicating influence of the deuterons. The proton spin echo spectrum of butyric acid-2,2—d2 in p —OOBA is shown in Figure 4.7. This is now, effectively, the proton nmr spectrum of a five spin system AgB2, and is much simpler in nature than the corresponding one pulse spectrum. The calculated spectrum was simulated using the modified version of LEQUOR discussed in the Introduction. The dipolar coupling constants calculated for this spectrum (shown in Table 4.1) are D^^ = 2040 Hz, Dgg = 1581 Hz, D^g = —716 Hz with an RMS error of 23 Hz. The scalar coupling constant q was assumed to be 7.05 Hz for J^B* Because chemical shift is not observed due to the refocussing pulse, variation of chemical shift had no effect on the calculated spectrum, so rather than vary chemical shift in the calculation as an adjustable parameter, the chemical shift was held constant at the isotropic value of 0.58 ppm = 116 Hz [157]. The effects of the refocussing pulse can clearly be seen in Figure 4.8. These are experimental and calculated spectra of butyric acid —2,2—d2 in p—OOBA with a purposely inhomogeneous refocussing pulse. The difference between the two experimental spectra 4.7 A and 4.8A is that the first was recorded on the Bruker CXP—200 using a solid state probe equipped with a solenoidal coil, the second on the same spectrometer using a high resolution probe equipped with a saddle coil. The large broad central hump in Figure 4.8 arises from unaveraged intramolecular dipolar couplings in the liquid crystal. The calculated spectrum in Figure 4.8B shows that the extra transitions induced by imperfect refocussing pulses can be calculated quantum mechanically. This calculation is for a SHORT CHAIN CARBOXYLIC ACIDS / 185 FIGURE 4.7 IH nmr Spin Echo Spectrum of 11 mole % Butyric Acid-2,2-d2 in p-OOBA V U - T — i 1—t—r 10000 -1 j — 1 — 1 — 1 — r 5000 -1 1 1 r—1 1 1 1 1 1 1 r* -5000 -10000 Hz A) Experimental: Temperature=110°C, 90° pulse length = 3.0 psec, T = lO.Ousec, 180° pulse length = 6.0 psec, Relaxation Delay = 0.5 sec, 4 Acquistions. Recorded on the CXP—200 B) Calculated: DAA = 2040 Hz, DAB = '716 Hz, DBB = 1581 Hz, RMS Error = 23 Hz 180° refocussing pulse, Lorentzian linewidth = 100 Hz. SHORT CHAIN CARBOXYLIC ACIDS / 186 FIGURE 4.8 Effect of Refocussing Pulse Length on lH Spin Echo nmr Spectrum of Butyric Acid-2,2-d2 in p-OOBA T — i 1—i 1 — i — t — r — r — i — r — i r — i — ' — i — r — | — i — r I r | i r -10000 5000 0 -5000 -10000 Hz A) Experimental: Temperature= 100°C, 90° pulse length = 10 usee, T = 10 usee, 180° pulse length = 19.0 usee, Relaxation Delay = 0.5 sec, 64 Aquisitions. B) Calculated: DAA = 2396 Hz, D^B = -843 Hz, DBB = 1906 Hz. 146" refocussing pulse, Lorentzian linewidth = 50 Hz. SHORT CHAIN CARBOXYLIC ACIDS / 187 refocussing pulse of 145°. The intensity of the extra transitions is affected by the length of the refocussing pulse[142,146]. The deuteron nmr quadrupolar echo spectrum of butyric acid—2,2—d2 consists of a doublet from the deuterons in the deuterated methylene group with a quadrupolar splitting of 46,386 Hz. This is of the same order of magnitude as the alpha quadrupolar splitting measured in perdeuterated palmitic acid in p-OOBA (50,245 Hz). 1. CALCULATION OF THE ORDER MATRIX For acetic and propionic acid, calculation of the order matrix was relatively simple. The symmetry of the hydrocarbon part of the molecules could be used to reduce the number of independent elements of the order matrix to one and three for acetic and propionic acid respectively. For butyric acid, the description of orientational order becomes more difficult. The inherent flexibility of butyric acid, flexibility which changes the relative positions of dipolar coupled nuclei, means that the orientation of the molecule can no longer be described by a single order matrix. There are two approaches to a problem like this. The first is to define an order matrix for each rigid subunit in the molecule, the second is to try and determine a single order matrix for the entire molecule. For long flexible molecules, the first approach is often used. The deuteron quadrupolar coupling constants measured from nmr experiments lend themselves to this sort of description in that a separate deuteron coupling is often available for each methylene segment. The second approach is more dangerous, in that a flexible SHORT CHAIN CARBOXYLIC ACIDS / 188 molecule can exist in many different conformations, each of which would have a separate order matrix. The molecular order matrix must then be averaged over all conformations. Using spectroscopic measurements to define a single order parameter for a flexible molecule is not often done anymore. For butyric acid, there is only a single bond about which conformational rotation will affect the orientational order — the &2~ ^ 3 bond. If & Flory RIS approximation is used, there are only 3 conformations to butyric acid — the t, g + and g — related by rotations about the C2 — Cg bond. For the trans conformer, which has a plane of symmetry bisecting the HCH plane, the number of independent elements in the order matrix is reduced to 3. For the g + and g conformers, the symmetry of the molecule is destroyed and 5 elements are needed for each conformation. However, the two conformers are mirror images of each other, so one order matrix will suffice for the two gauche conformers. In addition, each conformer is associated with a probability, so an extra two (one if Pg + = Pg -) parameters are needed. The conformer order parameters can never be separated from their probabilities (3.7) so this reduces the number of parameters by one. Thus a total of 8 parameters are needed to describe the orientation of this marginally flexible molecule. These arguments are similar to those presented in the previous chapter in an analysis of order matrix of the a—methylene segment of potassium palmitate. In that section, the additional assumption of ignoring conformational motions at other C —C bonds was necessary. From nmr four couplings are obtained — the three proton couplings from the spin echo spectrum and a deuteron coupling from the quadrupolar echo. If the single pulse spectrum of either isomer of butyric were tractable, another SHORT CHAIN CARBOXYLIC ACIDS / 189 up to 4 couplings would be available. This is exactly enough for a complete description of the orientation of butyric acid, although this does not guarantee that such a calculation would work. With only four measured couplings, however, a molecular modelling scheme is necessary. 2. T H E INERTIAL F R A M E MODEL Keeping with tradition, the butyric acid molecule is subjected to analysis with the Inertial Frame Model. The geometric parameters were kept constant from the previous analysis on the soaps, as were the conformational energies and the head group mass. Only the cylinder radius (rcyj) and the head group rod length (rpjrj) are varied. Since only three conformations exist, the entire molecule can be treated with the RIS approximation and there is no need to model the methyl tail. The methyl group was allowed to rotate in a 3 —fold symmetric potential with a potential energy barrier of 12.6 kJ/mole. The conformational probabilities and dipolar couplings were calculated in 10° steps. Similar to the calculation of order parameters in propionic acid, it was only necessary to consider 12 conformations due to the three fold symmetry of the rotation. The best fit of the proton dipolar couplings using the model yielded dipolar coupling constants of D f i B= 1581(1581) Hz, DAB=-884(-716), and 0^=2034(2040) Hz where the numbers are scaled to the experimental coupling Dgg, and the numbers in brackets are the experimental numbers. This calculation gave a cylinder radius of o o rcyl=4.96 A a n e a (* S1*0"? interaction length of 11.19 A with 133 Hz RMS o error. The cylinder radius is ~1 A smaller than in the calculation on the soaps at the same temperature (110°C). In view of the previous discussion on the SHORT CHAIN CARBOXYLIC ACIDS / 190 effect on chain length on cylinder radius, this is seen to be correct. The cylinder radius is of the same order as that determined for larger solutes in liquid crystals [6—9], but again this could be because of the second adjustable parameter in the model. The length of the rod, TJJQ, which determines the head group ordering is much larger than rjjQ calculated for potassium palmitate. This reflects the influence of the liquid crystal on the orientational order of the solute. The specific intermolecular interaction between solvent and solute has a much greater effect than the influence of water in the lamellar phase soaps. Attempts to include the deuteron quadrupolar coupling in the TP calculation have failed. Calculation of the deuteron coupling using the parameters described above yield deuteron coupling constants of —27,481 Hz compared to the experimental — 46,386 Hz. Scaling the calculation to the alpha deuteron coupling, as was done with the soaps, gives proton dipolar couplings that are much too high. No reasonable explanation for these observances are proffered at this time. The deuteron quadrupolar coupling is similar in magnitude to that measured for perdeuterated palmitic acid in the same liquid crystal at the same temperature (the difference is 7.6%), and as it will be demonstrated the alpha proton dipolar couplings for the solutes acetic, propionic and two isotopically substituted palmitic acids differ by only 4%. The orientational order at the head group of carboxylic acids dissolved in p—OOBA seems to be the same regardless of chain length. In addition, analysis of palmitic acid using the D? model (as will be shown in the o next chapter) gives a head group interaction length of 10.16 A, on the same order as that for butyric acid. The proton dipolar couplings of the beta segment of butyric acid (Dgg) are much smaller than the corresponding couplings in SHORT CHAIN CARBOXYLIC ACIDS / 191 palmitic acid. While this is probably due to increased isomeric freedom about the C 2 — Cg bond, this could be where the discrepancy lies. In the analysis of palmitic acid and potassium palmitate there are two measured couplings at the alpha position, plus the carboxyl carbon—alpha proton coupling and this may lend stability to the calculation. Butyric acid, as a seven or five spin system, has proved to be a formidable molecule to analyze. This is not surprising, only a few dipolar coupled nmr spectra of seven spin systems have ever been analyzed. These tend to be highly symmetric rigid solutes usually containing one or two methyl groups. For butyric acid, which is a flexible molecule of limited symmetry, the problem is inherently of much greater difficulty. Still, since it is the system on which the methods used in this thesis were developed, it has proved to be a useful vehicle to get at other problems. To complete a project like this, other isotopes of butyric acid could be synthesized involving the replacement of various protons and carbons with deuterons and carbon 13. This would aid in the analysis of the single pulse spectrum of both the butyric and butyric —2,2—d2 acids. In addition, the extra couplings available from the C spectra may be needed for the complete determination of the order matrix for this molecule. As the next chapter involves the solubilization of palmitic acid in the same liquid crystal system as has been discussed here, conclusions on the short chain acids will be deferred until the palmitic acid results have been presented. V. LONG CHAIN CARBOXYLIC ACIDS The main thrust of this thesis is the study of the orientational behaviour in lamellar phase soaps near the lipid—water interface. However, a number of spectroscopic difficulties were encountered in this endeavour, most notably the difficulty in separating the various nuclear interactions present in the partially protonated soap molecules. The proton—proton and proton—carbon 13 dipolar coupling had to be separated from the chemical shift, and more importantly from the proton — deuteron dipolar couplings which were of sufficient magnitude to broaden the lines and obscure the dipolar couplings of interest. It was in an attempt to simplify this problem that the series of molecules were oriented in the liquid crystal p —OOBA. In this way the nmr spectra could be observed without the complicating influence of the Pake doublets that arise from unoriented lamellar phase samples. Since similar experiments were performed on both systems, the lamellar lyotropics and the acids in p —OOBA, this discussion closely parallels Chapter 111 on the soaps. A. DEUTERON NMR Perdeuterated palmitic acid (hexadecanoic acid—dgj) was dissolved in p —OOBA at a concentration of 11 mole %. The quadrupolar echo deuteron nmr spectra of the perdeuterated acid at 100°C is shown in Figure 5.1. The variation of quadrupolar splittings as a function of temperature and chain position are shown in Figures 5.2 and 5.3. The spectra are symmetric and consist of a number of relatively sharp peaks corresponding to the quadrupolar splittings of CD 2 groups 192 LONG CHAIN CARBOXYLIC ACIDS / 193 FIGURE 5.1 2H nmr Spectrum of Perdeuterated Palmitic Acid in p —OOBA Experimental: Temperature = 100°C, 90° pulse length = 5 psec, r = 96 psec, Relaxation Delay = 0.5 sec. Spectrum recorded on the BKR 322-s at 30.7 MHz. The assignment of these peaks is detailed on the next two figures. LONG CHAIN CARBOXYLIC ACIDS / 194 FIGURE 5.2 Temperature Dependence of the 2H nmr Quadrupolar Splittings in Palmitic Acid 80 0 H 1 1 1 1 1 1 1 75 85 95 105 115 Temperature (C) The assignment of the deuteron peaks is shown on the left side of the figure. Assignment is based on integration and assuming that the quadrupolar interaction is progressively averaged towards the methyl end of the alkyl chain. Legend: D 1 1 0 C 0 9 0 C * 80C The splitting for the methyl group (16) is reduced due to extra motional averaging. The splitting for the 2 position is increased as as result of H— bonding to the liquid crystal. At higher temperatures, separate peaks for the 3 — 6 and for the 7—10 are not resolvable. The error in the measurement is within the size of the points. LONG CHAIN CARBOXYLIC ACIDS / 196 along the methylene chain. The difference in quadrupolar splittings reflect the difference in orientational order down the chain. Near the head group where angular fluctuations are restricted due to electrostatic interactions with the liquid crystal, the quadrupolar splittings are large. Further down the chain, the quadrupolar splittings decrease as angular excursions from the all trans configuration increase. The methyl group, which experiences additional motional averaging due to rapid rotation about the local Cg v axis, has the smallest quadrupolar splitting. The assignment of the peaks to the positions on the chain is also shown in Figures 5.2 and 5.3. These assignments were based on integration of the deuteron spectra and on the assumption that the quadrupolar splitting decreases monotonically towards the methyl end of the molecule. This is not necessarily the case in liquid crystals [206]. For example in the liquid crystal 5CB (5 — cyanobiphenyl) the quadrupolar splitting at the 3 position in the alkyl chain is greater than the quadrupolar splitting at the 2 position [179, 180]. In the fatty acids, however, the 2—position has a characteristically large quadrupolar splitting relative to the rest of the molecule. This is true in lamellar lyotropic phases, and in the acids oriented in thermotropic liquid crystals [184, 201]. The alpha quadrupolar splitting in potassium soaps dissolved in lyotropic liquid crystal phases shows this behaviour whereas the corresponding fatty acids do not [207 — 210]. The deuteron splitting of the 2 position is unambiguously assigned by comparison with the deuteron spectra of the corresponding protonated acid. Close examination of the deuteron nmr peaks at the 2 position reveals fine structure. These are the intramethylene deuteron-deuteron dipolar couplings. LONG CHAIN CARBOXYLIC ACIDS / 197 These should be reduced from the proton — proton dipolar couplings by a ratio of —36. These have been observed before [117] and have been used to describe orientation (Srjj)) in decanol/sodium decanoate/water multilayers. However these couplings are considerably broadened by intermethylene deuteron—deuteron dipolar interactions and to base conclusions upon them is difficult. Normally, in liquid crystal work, data are scaled to a reduced temperature defined as: (5.1) For these samples, the exact nematic—isotropic transition temperatures were never measured. Instead, since all experiments were performed on isotopes of the same molecule dissolved in the same liquid crystal at the same temperatures, the data were simply scaled to their deuteron quadrupolar splitting profiles. In general, these were sufficiently reproducible as to warrant no numerical alterations. B. l - 1 3 C - 2 , 2 - H 2 PALMITIC ACID-D 2 9 1. PROTON AND CARBON 13 NMR The proton spin echo spectra of 11% C —2,2—H2 palmitic acid dissolved in p —OOBA, with and without a double resonance refocussing pulse, are displayed in Figure 5.4. Proton single pulse spectra were obscured by the heteronuclear dipolar couplings to the deuterons on the chains and the single pulse spectrum consisted of a broad background triplet characteristic of the liquid crystal. With LONG CHAIN CARBOXYLIC ACIDS / 198 FIGURE 5.4 iH Spin Echo nmr Spectra of 11 mole % l-13c-2,2-H2 Palmitic Acid-d29 in p-OOBA ' I 1 10000 B: 20000 10000 "1 1 1 1 r--10000 0 — ' — I — - 1 0 0 0 0 — i 1 . r-- 2 0 0 0 0 Hz A) Without *3C Refocussing Pulse: Temperature=110°C, 90° pulse length = 3.0 psec, T — 5 psec, 180° pulse length = 6.5 psec, Relaxation Delay = 0.5 sec, 8 Acquisitions. B) With Refocussing Pulse: Parameters as above. The central peak is an artifact due to Hj inhomogeneities. The large splitting in both spectra is the lH—lH dipolar coupling. The small splitting in B is the 1H—13C dipolar coupling. LONG CHAIN CARBOXYLIC ACIDS / 199 the heteronuclear couplings removed, the proton single pulse spectrum appears as a triplet, the central peak arising from the inhomogeneous refocussing pulse and the two outer peaks from the alpha protons with a dipolar splitting of 3DJQJ. The second refocussing pulse at the *3C Larmor frequency allows observation of the C— H heteronuclear dipolar couplings, the smaller couplings in Figure 5.4B, which have a spacing of (2DQJJ+JQJJ). *3C — *H dipolar couplings were also measured from the 13C single pulse spectrum and a representative spectrum is shown in Figure 5.5. In this oriented sample, the resonances appear as single peaks (with no CSA pattern as observed in the soap) and the triplet intensity pattern of 1:2:1 is easily seen. The peak separation is also (2DQJJ+JQJJ). The large background signal upon which the triplet sits arises from the teflon in the probe. The linewidth of the triplet is broadened by long range ^ 3C— *H and i q o C- H dipolar couplings. In Figures 5.6 and 5.7, the temperature dependence of the dipolar couplings is shown. The proton and carbon—13 dipolar couplings rise steadily with decreasing temperature until 92°C. Below this temperature, no *H— *H dipolar couplings were observable using the spin echo method, possibly due to the appearance of intermolecular dipolar couplings between the solute and liquid crystal. The *3C — *H dipolar couplings can be measured from the *3C spectra below this temperature and show a dramatic drop. Below 87°C no *3C dipolar couplings are observable. The temperature at which the *H dipolar couplings disappear corresponds to a levelling off in the deuteron quadrupolar couplings. This is attributed to a nematic—smectic C phase transition which normally occurs at 108°C. The transition temperature is lowered by the presence of the solute. The fall off in dipolar couplings upon entry to a smectic C phase has been observed before in C H 2 C I 2 dissolved in p —OOBA at 2.1 mole% [211]. LONG CHAIN CARBOXYLIC ACIDS / 200 FIGURE 5.5 13C Single Pulse nmr Spectrum of 11 mole % 1-13C-2.2-H2 Palmitic Acid-0*29 in p-OOBA Temperature = 110°C, 90° pulse length = 3.0 psec, Relaxation Delay = 1.0 sec, Size = 2K, 2500 Acquisitions. The triplet shows the carbon proton dipolar coupling. The large broad central peak is residual carbon signal from the teflon in the probe. LONG CHAIN CARBOXYLIC ACIDS / 201 FIGURE 5.6 Temperature Dependence of the Heteronuclear Dipolar Couplings of 11 mole % l- 1 3C-2,2-H2 Palmitic Acid-d29 in p-OOBA N I V) CP c a 3 0 0 0 0 a 96 100 Temperature. (C) 112 Legend: 0 1H-13C Couplings o 13C-1H Couplings The figure shows I3C—JH dipolar couplings measured from the 13C single pulse spectrum and the spin echo spectrum. Dipolar couplings were resolvable in the 13C spectrum 7" lower than in the *H spectrum. Each line is the average of two measurements. LONG CHAIN CARBOXYLIC ACIDS / 202 FIGURE 5.7 Temperature Dependence of the Homonuclear Dipolar Couplings of 11 mole % 1_13c-2,2-H2 Palmitic Acid-d29 in p-OOBA 10 - T 9 -8 -N I b 4 -3 -2 H 1 1 1 1 1 — i — i — i — i — i — i — i — i — i — i — 80 84 88 92 96 100 104 108 112 Temperature (C) The temperature scale is the same as in Figure 5.6. The couplings are the average of four measurements. The error in the measurement is within the sign of the points. LONG CHAIN CARBOXYLIC ACIDS / 203 The presence of CH2CI2 lowers the nematic — smectic C phase transition to 98°C and the smectic C —solid phase transition to 76°C. Below 76°C no couplings were observed. Orientational order is difficult to describe in smectic phases due to the biaxiallity of the phase and no attempt will be made. 2. CALCULATION OF THE ORDER MATRIX p —OOBA is a Type I liquid crystal i.e. it has a positive diamagnetic anisotropy and the nematic phase aligns with its director parallel to the magnetic field. The order parameters can be directly calculated from (1.9) and (1.26). Since the orientation of the palmitic acid molecule at the head group will be along the long axis of the liquid crystal, the order parameters SJJJJ, SQJJ will be negative in sign and SQJJ will be positive. Therefore the dipolar and quadrupolar couplings DJQJ, DQJJ and A^Q will have signs of positive, negative, and negative respectively. The molecule fixed axis system for the alpha methylene is chosen as described in the Soaps section, see Figure 3.10), such that SJJJJ = S^ and S v v is calculated as a linear combination of SJJJJ and SQJJ according to (3.3) and (3.4). S,,„ is calculated by a coordinate transformation (3.5 and 3.6). The order matrix is traceless by definition, and the third diagonal element is obtained by simple subtraction. The plane of symmetry in the a—CH2 segment determines the number of independent elements in the order matrix as 3. The complete order matrix for all temperatures at which all dipolar coupling are measurable is shown in Figure 5.8 and 5.9. Several trends are evident: S__, representative of LONG CHAIN CARBOXYLIC ACIDS / 204 FIGURE 5.8 Temperature Dependence of the Order Parameters for the a-Methylene Segment of l- 1 3C-2,2-H2 Palmitic Acid-d29 in p-OOBA 0.4 90 95 100 105 110 115 Temperature (C) Legend: Measured Order Parameters: D —SxX,S |_|H _r" = SQQ<C> = S^ H Calculated Order Parameters: Q = S y y A = S y Z Sxx and SQD ar* measured from the *H and 2H spectra respectively. ScH can be measured from both the JH and the 13Q spectra. The molecule fixed axis system has been presented in Figure 3.10. LONG CHAIN CARBOXYLIC ACIDS / 205 FIGURE 5.9 Temperature Dependence of S z z and S 3 3 Szz and S33 (diagonalized) for the a—methylene segment of l — 13C—2,2—H2 Palmitic Acid—d29- Presented on the same figure to conserve space. LONG CHAIN CARBOXYLIC ACIDS / 206 the ordering of the methylene group along approximately the nematic director of the phase, is large and increases steadily with decreasing temperature. In addition, the absolute values of S-™, S„,, and S„, increase through the same " JJ J1-temperature range. The values of S^ and Syy differ by approximately 0.2 throughout the entire temperature range. The order matrix is diagonalized and the results are presented in Figures 5.9 and 5.10. The angle of rotation in the yz plane necessary to diagonalize the order matrix is shown in Figure 5.11. The average angle of rotation at high temperatures (110°C) is 26.1° — on average the first C—C bond is only 8.9° away from coincidence with the principal orientation axis direction. This angle decreases with decreasing temperature and drops abruptly at 70°C to 23.0°. The onset of a smectic C phase is accompanied by a tilt in the director of the phase and the drop in rotation angle could represent the onset of the tilt. The value of S 3 3 , the major principal diagonal element of the order matrix, ranges from approximately 0.5 to 0.65. This is a huge order parameter for a solute and represents the ordering imparted onto the alpha methylene segment by electrostatic H—bonding to the liquid crystal. The values of S 3 3 are similar to measured order parameters for liquid crystals. The fact that S 3 3 exceeds 0.5 determines the sign of S 3 3 (and therefore S_„) to be positive. This lends credence to the assignment of the signs of the order parameters in both this and the previous section on the soaps (Chapter ELT). The absolute values of S^j and S22 both increase with decreasing temperature, and at low temperatures appear to approach axial symmetry. Note that the axis system used to describe the alpha methylene segment is slightly different than the one used in the description of propionic acid: in the palmitic system the z direction is defined as the perpendicular to the HCH plane, in LONG CHAIN CARBOXYLIC ACIDS / 207 FIGURE 5.10 Temperature Dependence of the Diagonalized Order Parameter Matrix for the a-Methylene Segment of 1 3C Labelled Palmitic Acid-d29 in p-OOBA 00 - 0 . 4 0 -0.35 - 0 . 3 0 -- 0 . 2 5 -- 0 . 2 0 --0 .15 85 90 95 100 105 Temperature (C) S i j : E N S n Q = S 2 2 Notice that the ordinate is inverted relative to Figure 5.8. LONG CHAIN CARBOXYLIC ACIDS / 208 FIGURE 5.11 Rotation Angle Needed to Diagonalize the Order Matrix of the a —Methylene Segment of the 1 3C Labelled Palmitic Acid-d29 in p-OOBA This angle represents the direction cosine between molecule fixed axis system (see Figure 3.10) and principal orientation axis system. The rotation angle, as the axis system is defined, is the yz plane. LONG CHAIN CARBOXYLIC ACIDS / 209 propionic acid it is defined as the HOOC — C H 2 bond direction. The difference is a rotation of 35° in the yz plane. Therefore the rotation angle of 11.08° calculated for propionic acid should be compared to a value of 8.9° here. C. 2,2,3,3-H4-PALMITIC ACID-D 2 7 The proton spin echo spectra of 11% 2,2,3,3—H^—palmitic acid—d 2 7 (a/3 palmitic acid) in p—OOBA is shown in Figure 5.12. The simulated spectrum displayed in the same figure is calculated for a refocussing pulse of 156°. The spectrum of this compound was only recorded at a single temperature (110°C) and the dipolar couplings calculated for this temperature are D 2 2 = 5788, D 2 3 = 1312, D2gi = 938 and D33 = 3430 Hz with an RMS error of 6 Hz. The numbering of the protons is the same as in the previous section, 23' representing the two protons farthest apart in the all trans position, 23 representing the two closest together. The values of the alpha proton dipolar couplings for the two isotopes differ by ~200 Hz — a less than 4% difference. The ratio of alpha/beta dipolar couplings is 1.7 whereas the same ratio obtained from the deuteron spectra is 1.4. In contrast the ratios obtained from the proton and deuteron spectra in the soap were both identically 1.4. Again, this difference arises from increased orientational averaging of the D33 couplings due to conformational motions about the C 2 — C 3 bond. The value of the alpha coupling is quite high (5788 Hz), but of the same order of magnitude as that of acetic acid (5555 Hz) and propionic acid (5619 Hz) in the same liquid crystal at the same concentration at the same temperature. This would indicate that the ordering of the solute, at least near the central aromatic region of the liquid crystal, is not vastly different regardless LONG CHAIN CARBOXYLIC ACIDS / 210 FIGURE 5.12 IH Spin Echo nmr Spectra of 11 mole % 2,2,3,3-H2 Palmitic Acid-d27 i n p-OOBA JJLA. -r -1—1—|——1 r—i—1—j 1 — 1 — T — 1 j—1—1 r—1—1—t—1—r—1 r~ 20000 10000 0 -10000 -20000 -Hz A) Experimental: Temperature = 110°C, 90° pulse length = 2.5 psec, T = 5 p 180° pulse length = 5.1 psec, Relaxation Delay = 0.5 sec, 8 Aquisitions. B) Calculated: D22 = 5788 Hz, D23 = 1312 Hz, D23 = 938 Hz, D33 = 3430 Hz, 156" refocussing pulse, Lorentzian linewidth = 30 Hz. LONG CHAIN CARBOXYLIC ACIDS / 211 of the length of the solute chain. On the other hand, the D33 proton dipolar coupling is markedly smaller in butyric acid-d2 than in a/3 palmitic. This is due to restricted conformational motion of the 8 palmitic segment imposed by the rest of the chain. By comparison, the freedom of movement of the B and 7 segments of butyric acid is large. These are broad statements, and do not take into account factors like the change in phase diagram (i.e. reduced temperatures are not used) associated with the different solutes. D. THE INERTIAL FRAME MODEL In a similar analysis to that described previously, the entire palmitic acid/p —OOBA complex is treated using the modified IF Model. The coordinates of the liquid crystal are not explicitly calculated, rather the liquid crystal is replaced by a mass on a rod of variable length. This is equivalent to T J J Q in the previous chapter. Calculation of the two adjustable parameters at 110°C yields a o cylinder radius of 5.98 A and a head group interaction parameter rjjg = 10.16 o A with an RMS error of 147 Hz between calculated and experimental nmr couplings, (see Table 5.1) The cylinder radius is almost identical to the previous o calculated rCyj for the lamellar phase (the difference is 0.04 A). The head group o o interaction length however has leaped from 2.71 A to 10.16 A — an almost 4 fold increase from the soap. Obviously, the intermolecular H—bonding between solute and liquid crystal will be of much greater magnitude than between the potassium palmitate molecule and water. In other words, the orientation of the head group is much more influenced by hydrogen bonding to a large, rigid, ordered liquid crystal than it is by hydrogen bonding to relatively disordered LONG CHAIN CARBOXYLIC ACIDS / 212 TABLE 5.1 THE If Model: Palmitic Acid in p-OOBA 11 mole% DIPOLAR COUPLINGS(Hz) UCH D22 v"a<x-D23 <DaB> D23.(Dap,) D33 <DBB> EXPT 792 -5788 -1312 -918 -3430 CALC 866 -5238 -1708 -1072 -3374 QUADRUPOLAR COUPLINGS(Hz) CARBON 2 3 4 5 6 7 50246 36262 36262 32960 32960 32960 50246 35950 36910 17194 16292 3422 TEMPERATURE = 110°C CALCULATED ADJUSTABLE PARAMETERS r n r = 10.16A - 5 - 9 W RMS error 147 Hz LONG CHAIN CARBOXYLIC ACIDS / 213 water molecules in the lamellar phase. This is confirmed by both the large alpha dipolar splitting and the long calculated T J J Q . The similar cylinder radius implies that the steric constraints placed on a long chain fatty acid are similar in a uniaxial nematic mean field and in a lamellar liquid crystalline phase. If anything, the constraints of the lyotropic phase of a single molecular species are slightly greater than the two component liquid crystal/solute mixture. The fit of the calculated deuteron dipolar couplings is similar to before — good for the first three spbttings and degenerating from there, (see Figure 5.13) These discrepancies are again attributed to the truncation of the palmitic acid model at the seventh carbon. In this case, no extended calculation has been attempted. Deuteron couplings past the 4 t n carbon were again given no weight in the calculation of couplings or of the RMS error. The RMS error calculated for the acid in p—OOBA is lower than the for the corresponding soap calculation. In p —OOBA, the RMS error is 147 Hz, in the soap calculation, it ranges from 177 to 217 Hz. It is the consistency between liquid crystal samples, not always present in the soaps, that is the reasons for reduced RMS error. The next stage in these experiments would be a temperature dependence study of the 2,2,3,3—H^ — palmitic acid in p—OOBA. The resulting numbers could be used to calculate the temperature dependence of r c y j and T J J Q in the liquid crystal. From the C data and the calculated rotation angle, it would appear that T J J Q would probably decrease with temperature. An interesting point for future experiments is that it is not absolutely necessary LONG CHAIN CARBOXYLIC ACIDS / 214 FIGURE 5.13 The IF Model: Quadrupolar Coupling Profile for Palmitic Acid in p —OOBA 60 -i 1 0 H 1 1 1 1 1 T 1 3 5 7 carbon number Legend: D experimental (110C) calculated o e Adjustable Parameters: rjjQ = 10.16A, rcyi = 5.98A, RMS error = 147 Hz. LONG CHAIN CARBOXYLIC ACIDS / 215 to use a liquid crystal with which the fatty acids can form intermolecular hydrogen bonds. Other experimentalists [184] have demonstrated that fatty acids in liquid crystals will dimerize and give order parameters of similar magnitude to those observed here. E. CONCLUSIONS A series of short chain (acetic, propionic, and butyric —2,2—d2) and long chain (palmitic —dgj, 1 —*3C —2, 2 —H 2~ palmitic —d 2g and 2, 2, 3, 3 — H^ — palmitic) carboxylic acids were dissolved in the liquid crystal p —OOBA at a concentration of 11 mole % and their nmr spectra recorded. The dipolar couplings for the acetic acid and the alpha methylene segment of propionic, 1— ^C — 2,2—H2_ and 2,2,3,3,—H4—palmitics were found to be very similar (5555, 5640, 5543 and 5788 Hz a 4.0% total difference) as were the quadrupolar couplings for butyric acid -2,2-d2 and palmitic acid-d 3 1 (46,386, 50,245 Hz, a 7.7% difference). Dipolar couplings dropped off much more rapidly in the short chain acids than in the palmitics and this is attributed to reduced conformational freedom in the long palmitic acid chain. The orientational order matrix for acetic and propionic acid at 110°C were determined. Due to lack of symmetry and the presence of conformational freedom, the order matrix of butyric acid —2,2,—d2 was unsolvable. From the nmr spectra of palmitic acid—dgj and 1— *3C — 2,2-H2—palmitic acid—d2g, the order matrix of the rigid alpha methylene segment of palmitic acid/p-OOBA was calculated as a function of temperature. The order matrices of propionic acid and the rigid LONG CHAIN CARBOXYLIC ACIDS / 216 alpha methylene segment of palmitic acid, both of which contained an off diagonal element, could be diagonalized to obtain the rotation angle of the principal axis of the order matrix relative to the molecule fixed axis system. These were found to differ by only two degrees between the two solutes. The diagonal principal order axes define the average orientation of the first C—C bond to be only 8.9 (11.0) degrees away from coincidence with an axis system in which the z axis is defined as first C—C bond direction. The order matrix for the three solutes was found to be quite similar at 110°C. The value of the diagonalized order matrix in the 3 direction was found to be 0.5219, 0.5051 and 0.4750 for acetic acid, propionic acid and the alpha methylene segment of palmitic acid respectively. These order parameters are noted to be huge and this is attributed to the H—bonding interaction of the carboxyl groups on the solute and liquid crystal. The fact that the order parameters of acetic and propionic acids exceed 0.5 uniquely determines the sign of S 3 3 , a rare feat in studies of oriented solutes, and by implication the signs of the order parameters of the other solutes are assigned as well. With the aid of the couplings from 2,2,3,3 —H 4 —palmitic acid—d2y, the modified Samulski Inertial Frame Model was used to simulate the dipolar couplings and quadrupolar couplings at 110°C. The same model was used to simulate the dipolar couplings of butyric acid —2,2—d2 at the same temperature. The RMS error in the D? calculation was found to generally decrease in the liquid crystal studies relative to the same calculations done in the soaps. The value of the o head group interaction length was found to differ by ~1 A between the two o solutes: 11.19 and 10.16 A for butyric and palmitic respectively, but this is still LONG CHAIN CARBOXYLIC ACIDS / 217 a factor of ~4 greater than the value of the same parameter in the calculation o involving potassium palmitate (2.71 A). The large value of rjjQ compared to the soaps is believed to reflect the relative interaction strengths of the head groups with the liquid crystal p —OOBA and with D 20 in the lamellar phase. On the other hand, the other adjustable parameter in the model, r c y j , is shown to be remarkably similar between palmitic acid and potassium palmitate at the same o temperature (5.90 and 5.94 A, although to some extent this is probably o coincidental) whereas the value for butyric acid is 4.96 A. The difference arises from the difference in chain length of the two solutes, the steric effects of the liquid crystal have more influence on the short chain acids than on the long. The analysis of butyric acid was shown to be incomplete as not all couplings could be fitted. These results demonstrate that the orientational order of the head group of carboxylic acids dissolved in the liquid crystal p —OOBA are very similar regardless of the chain length of the acid. The similarities and differences in orientational ordering in related lyotropic and nematic liquid crystalline phases have been investigated and discussed. 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W . , D e l i k a t n y , E . J . , a n d L a m , W . C . : I n d u c t i o n o f m e s e n t e r i c tumor m e t a s t a s i s by i n t r a p e r i t o n e a l c h e m o t a c t i c f a c t o r . F e d . P r o c . 40.:782 ( 1981 ). ( A b s t r a c t ) . O r r , F . W . , V a r a n i , J . , D e l i k a t n y , E . J . , J a i n , N . , a n d W a r d , P . A . : Chemotac t i c responses of f i b r o s a r c o m a s u b p o p u l a t i o n s to a complement d e r i v e d f a c t o r . F e d . P r o c . 3_9:777 (1980 ). ( A b s t r a c t ) . Awards and S c h o l a r s h i p s M . R . C . P o s t d o c t o r a l F e l l o w s h i p 1987 B . C . P o s t s e c o n d a r y S c h o l a r s h i p 1986 NSERC Pos tgraduate S c h o l a r s h i p 1981-1985 UBC U n i v e r s i t y Graduate F e l l o w s h i p 1983 ( d e c l i n e d ) U n i v . o f Winnipeg Board of Regents G e n e r a l P r o f i c i e n c y S c h o l a r s h i p 1977,1978 S h e l l Canada S c h o l a r s h i p 1976,1977 

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