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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 degree  at the  this thesis  in partial fulfilment  University of British Columbia, I agree  freely available for reference  or  by  his  or  requirements  for an  advanced  that the Library shall make it  and study. I further agree that permission for extensive  copying of this thesis for scholarly purposes department  of the  her  may be granted by the  representatives.  It  is  understood  that  head  of my  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 using  multinuclear  orientational  order  temperature,  magnetic near  contrary  resonance.  the  to  isotopically  substituted  species  acid-d ,  1- C-2,2-H 2  acid—d 7.  These  2  studies had  interface  acid  acid-d , 29  compounds were treated in two  shown  decreased  investigate  palmitic  palmitic  1 3  31  of  To  was investigated  2  Previous  soap—water  intuition.  palmitate/D 0  this  were and  that  with  the  decreasing  phenomenon,  three  synthesized:  palmitic  2,2,3,3-H -  palmitic  4  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 0  at a  2  constant water  concentration. Dipolar and quadrupolar couplings were obtained from the *H, and  H  nmr  spectra of these molecules, in nematic and lamellar liquid crystalline  phases, as a function of temperature. In a parallel study, nmr propionic, and order  to  -^C,  butyric —2,2 — d  observe  *H — *H  acids dissolved in p —OOBA  dipolar  (JJ72 — tj/2 — it—tj/2—echo) was to the chain deuterons. A  2  couplings,  a  two  spectra of acetic, were recorded. In  dimensional  spin  echo  necessary to remove heteronuclear dipolar couplings  refocussing pulse applied simultaneously  spins allowed observation of the heteronuclear *H— ^ C  to the  dipolar couplings in the  carbon 13 labelled compound.  The  complete  potassium  orientational  paImitate/D 0 and  dipolar and  2  quadrupolar  order  matrix  of the  alpha  methylene  of palmitic acid/p—OOBA was  couplings. As  determined  the temperature is decreased  to a temperature just above the gel-liquid  ii  segment of from the  from  110°C  crystalline phase transition (45°C),  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  Inertial Frame Model, was developed to simulate quadrupolar  nmr  couplings.  In potassium  on the Samulski  the experimental  palmitate,  dipolar and  electrostatic interactions,  approximately constant at higher temperatures, increase dramatically as the phase transition is approached. In contrast mean constant the  field  steric repulsive forces remain  over the entire temperature range studied. This evidence also supports  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  remarkably similar regardless of the chain length of the solute.  iii  to be  T A B L E 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 A. NOMENCLATURE B. PREPARATION OF PERDEUTERATED FATTY ACIDS C. PREPARATION OF 2,2,3,3-H4-HEXADECANOIC ACTD-d27  iv  66 66 67 70  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  PREPARATION OF 4-(OCTYLOXY)-BENZOIC ACDD—di SHORT CHAIN CARBOXYLIC ACIDS PREPARATION OF F A T T Y ACTD SALTS SAMPLE PREPARATION 1. SOAPS 2. LIQUID CRYSTALS I. NMR 1. DEUTERON NMR 2. PROTON NMR 3. CARBON 13 NMR  E. F. G. H.  75 76 76 77 77 77 78 78 79 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 Ill 1. PROTON NMR Ill D. T H E 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 A. ACETIC ACTD B. PROPIONIC ACTD C. BUTYRIC ACTD-2,2-d2 1. CALCULATION OF THE ORDER MATRIX v  169 170 175 181 187  2. THE INERTIAL FRAME  MODEL  V. LONG CHAIN CARBOXYLIC ACIDS A. DEUTERON NMR B. 1-13C-2.2-H2 PALMITIC ACDD-d29 1. PROTON AND CARBON 13 NMR 2. CALCULATION OF THE ORDER MATRIX C. 2,2,3,3-H4-PALMITIC ACID-d27 D. THE INERTIAL FRAME MODEL E . CONCLUSIONS VI. REFERENCES  189 192 192 197 197 203 •  2  0  9  211 215 219  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 H Perdeuterated Potassium Palmitate 2  Quadrupolar Splittings of 89  FIGURE 3.4: Temperature Dependence of the H Quadrupolar Splittings of l-13c-2,2-H2 Potassium Palmitate)-d29 2  FIGURE 3.5: Temperature  Dependence of the H 2  90  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 FIGURE  3.11: Order Parameters for the a —Methylene 1-13C-2.2-H2 Potassium Palmitate-d29 FIGURE 3.12: Temperature Dependence of Szz and S 3 3 FIGURE  3.13: Temperature  103  Segment  Dependence of the Diagonalized Order  of 105 106  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  vii  112  FIGURE FIGURE  FIGURE  3.15C.D: Depaked and Simulated nmr 2,2,3,3-H4 Potassium Palmitate-d27  Spin  Echo  Spectra of 114  3.16: Temperature Dependence of the Dipolar 2,2,3,3-H4 Potassium Palmitate-d27  Splittings of  3.17: Temperature  Couplings of  Dependence  of the Dipolar  115  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 FIGURE 3.20: The D? Model: Calculated and Experimental Quadrupolar  131  Couplings  135  FIGURE 3.21: The IF Model: Quadrupolar Coupling Profile FIGURE 3.22: The D7 Model: Effect of Increasing The The Calculated Quadrupolar Coupling Profile FIGURE 3.23: The IF Model: Effect of Increasing The The Calculated Quadrupolar Coupling Profile  136  Chain Length on (110°C) Chain Length on (45°C )  138 139  FIGURE 3.24: The TF Model: Variation of Cylinder Radius with Temperature 141 FIGURE  3.25: The IF Model: Temperature  Variation  of Head  Group  Parameter  with 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 Calculation  Order Matrix  from  the IF 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: l H nmr p-OOBA  Spin  Echo  Spectrum  of 11 mole  %  Acetic  Acid in 174  FIGURE 4.3: l H nmr Spectrum of 11 mole % Propionic Acid in p-OOBA FIGURE  4.4: l H Spin Echo nmr p-OOBA  Spectrum  viii  of 11 mole %  .. 176  Propionic Acid in 178  FIGURE 4.5: Axis Systems for Acetic, Propionic and Butyric Acids FIGURE  4.6: IH nmr p-OOBA  FIGURE  4.7: i H Spin Echo nmr Spectrum Acid-2,2-d2 in p-OOBA  FIGURE  Spectrum  of 11 mole  %  Butyric  180  Acid-2,2-d2 in 183  of 11 mole  %  Butyric 185  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 FIGURE  5.3: 2H nmr Position  Quadrupolar Splitting  Profile  as a Function  194  of Chain 195  FIGURE 5.4: i H Spin Echo nmr Spectra of 11 mole % 1-13C-2.2-H2 Palmitic Acid-d29 in p-OOBA 198 FIGURE FIGURE  5.5: 13C Single Pulse nmr Spectrum of 11 l-13c-2,2-H2 Palmitic Acid-d29 in p-OOBA  mole  % 200  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 1-13C-2.2-H2 Palmitic Acid-d29 in p-OOBA  FIGURE 5.9: Temperature Dependence of S  z z  Segment  of  and S 3 3  204 205  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 Palmitic Acid-d27 in p-OOBA  ix  of 11 mole % 2,2,3,3-H4 210  FIGURE 5.13: The IF Model: Quadrupolar Coupling Profile for Palmitic Acid in p-OOBA  x  214  List of Tables T A B L E 1.1: Calculated Order Parameters From The Abdollal Model TABLE  3.1: Calculated Dipolar Palmitate-d27  Couplings  44  for 2,2,3,3-H4-Potassium 117  TABLE 32: The D? Model: The Parameterization of Potassium Palmitate TABLE TABLE  3.3: The D? Model: Experimental Quadrupolar Coupling 3.4: The D? Model: Temperature  Variation  124  and Calculated Dipolar and 132  of Adjustable  Parameters  with 143  TABLE 3.5: The IF Model: Variation of Adjustable Parameters Group Mass TABLE 4.1: Dipolar Couplings and Order Parameters Acids in p-OOBA  151  for the Short Chain  TABLE 5.1: The IF Model: Palmitic Acid in p-OOBA 11 mole%  xi  with Head  172 212  LIST OF 2D  J  ABBREVIATIONS  two dimensional J-resolved spectroscopy  amu  atomic mass unit  COM  Centre of Mass  ij  dipole—dipole coupling between nuclei i and j  DPPC  dipalmitoyl phosphatidylcholine  DSC  differential scanning calorimetry  e2 Q/h  Quadrupole coupling constant  efg  Electric Field Gradient  FID  Free Induction Decay  g  gauche plus  D  q  +  g~  gauche minus  H  the hexagonal phase  a  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  ppm  parts per million  RIS  Rotational Isomeric States  RMS  Root Mean Square  Qa  the cubic phase  %  nuclear quadrupole moment of deuteron  xii  =  i(3  cos  2  6  — 1)  q  internal electric field gradient tensor at the site of the deuteron  r yl  Mean Field Cylinder Samulski model  rHG  Head group Interaction Length, an adjustable parameter Samulski model  Sn  a/Jth element of the order matrix  Sjj  orientational order parameter  SD  Standard Deviation  T d  Reduced Temperature  t  trans  p —OOBA  4 —(octyloxy)—benzoic 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  C  a  r e  Radius,  acid,  xiii  an  adjustable parameter  p—n—octyloxybenzoic  acid,  of the  of the  a  liquid  ACKNOWLEDGEMENTS  I would like to thank my me  quit even  supervisor, Elliott Burnell, the man  who  would not let  when I wanted to so desperately. This thesis is proof of his  dedication and  support. Thanks to John  Rendell, my  fellow solvent inspector, an endless supply of fact and  constant companion fancy, and  and  to Art van  der Est, our pragmatic revolutionary, for his keen insight and sense of humour. Thanks  to all and  sundry  Beckmann, for giving me who  taught  me  to  who  have crossed the portals  of 159:  to Peter  a good boot when I needed it, to Alexandra Weaver,  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 and  stay worthwhile. Thanks to Myer Bloom for confusing me making me  watching  over  think, and a  physical  thanks to Tony chemist  stumbling  Day  and  through  over the years  T.P.Higgs for patiently the  wonderful  world  of  organic chemistry.  Words cannot express how Sukul, and Tom  grateful I am  to the people in the shops:  Kam  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  emotional and  Ted, have given me  much support over these years,  moral, as well as financial. Thanks mom,  xiv  dad, Brenda, Bruce,  little Markie and Frere. My this monster, and who  deepest thanks and appreciates to Hazel, who  defused my  typed  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 — and  it is a two component system  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  choline or serine. It is, as Charvolin  complex  says,  phosphatidyl  ethanolamine,  "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 can  about each distinct methylene group in the hydrocarbon chain. One  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  deuteron  soaps.  order  For methylene  groups near the  S Q Q , rather  parameter,  than  lipid—water interface the  exhibiting  the  intuitive  strict  monotonic increase with decreasing temperature, comes to a maximum and then decreases  [2].  observed  In  for  some  deuterons  cases, near  two  the  distinct  deuteron  polar head  exchanging configurations at lower temperatures interpreted  as  lamellar — lamellar  phase  Obviously, near the interface there well  as  the  steric  effects  present  nmr  group  [2]  peaks  have  implying two  been slowly  [3]. In addition, what could be  transitions  have  are electrostatic  been  observed  [4,  interactions to consider  elsewhere in the  chain. This  5]. as  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 order  dipolar nmr couplings. matrix  determined  as  of a  the  In the  first  function  course  segment of  of  temperature.  of these experiments, potassium This  is  the  complete  palmitateT^O has an  improvement  on  been 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. T H E O R Y  This  discussion  (thermotropic  or  is restricted  to  lyotropic) phases.  partially No  oriented  attempt  will  molecules be  in uniaxial  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 = X  z  + X  D  + 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 direct  dipole—dipole interaction  term  is the dipolar Hamiltonian  between  the spins. The third  coupling or indirect coupling and the last term valid  only for nuclei  nuclear  quadrupole  with  I a l , which  moment  is the J Hamiltonian,  describes the interaction  between the  and the electric field  Hamiltonian  term  is the quadrupolar  gradient at the nucleus. In  isotropic solution, the value of the dipolar and quadrupolar zero, and the spin  describing the  reduces  to the familiar  terms average to  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 *  *  where y- is the gyromagnetic spin of nucleus i, and H  Q  I * < 1 - ol" - o  Z 2 i  ) H  0  ratio of spin i, I j is the z component of the total 2  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: chemical  <7j  l s 0  is equal to l/3(Tr(a)) and is equivalent to the isotropic 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 j z  and  I j have been defmed previously, and I j , Ij , \ ~ , I j ~ are the raising  and  lowering operators for the i and j  +  +  2  scalar or J coupling  spins. This  term  observed in high resolution nmr. This  gives  rise to the  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 coupling, also known as the "pseudo dipolar coupling  1.4). The anisotropic J  constant", is negligible for  protons due to the spherical symmetry of the contact interaction, and is generally ignored.  3. T H E D I P O L A R HAMILTONIAN  The  direct through space dipole—dipole interaction between a system of interacting  spins is described by the dipolar Hamiltonian:  # = ^ D,j (31 l - \ • ip D  zi 2j  (1.4)  INTRODUCTION / 6 where D^ is the time averaged component of the direct dipolar coupling and  and Ij  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 i 2 i  - 1  2 j  +  jrj;  )]  (1.5)  (1.3) and (1.5) may be combined to give the following form for the Hamiltonian:  In and  a dipolar coupled nmr spectrum of an oriented  molecule, the quantities Dy  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. or  the lamellar director) is parallel to the  the optic axis of the liquid crystal  magnetic  field,  then  (1.8)  is rewritten  as:  (1.9)  where Sy defines  the orientational order parameter or degree of orientation of an  axis  two  joining  direction.  the  For liquid  nuclei crystals  i  and  in  j  which  relative the  to  optic  magnetic field, or in randomly oriented samples the  9 0 ° edge of the  the  external  axis  where  is  perpendicular  the  the  limits  =  correspond  where  respectively.  A n order parameter of 1 describes  to  >i  the  magnetic  field  must by definition be positive,  zero at an angle equal to 5 4 . 7 4 °  o. THE ORIENTATIONAL  For  the  in (1.9)  9  of  direction.  must  perfect  orientation parallel to the  and that the — the magic  that  an  and  as  of  Note  90°  is  values  magnetic field direction, and an order parameter of — £ defines to  to  — £ . The range of Sy is defined  — i^Sjj<l  perpendicular  field  measured quantity  powder pattern, the dipolar coupling constant  be scaled by a factor of £ < 3 c o s ^ 9 0 ° —1>  magnetic  0°  perfect orientation  order parameter  of  order parameter passes through angle.  ORDER MATRIX  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#  is the cosine of the angle between the  a  magnetic  field  8 0 =O  otherwise). The  a  measured  direction  and  8Q  order matrix  order parameters  ($ 0 = l  is the Kronecker delta  a  can  (or to any  be  related  other axis  axis and the a  to the  system)  by  for a = 0,  experimentally a  coordinate  transformation: (1.11)  where  the sum  is over  a/3=x,y,z and  between the molecule fixed (a  =  where  cos#  a  is the direction  cosine  x, y, z) axis and the vector joining the i ^  n  th  and  j  nuclei. The  order matrix is by  definition  characterized by five independent elements. The order matrix are — i s S £ < l a  for a = 0 and  traceless, symmetric,  and  limits of the elements of the  - 3 / 4 s S ^ < 3 / 4 for a*/?. 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  plane of symmetry matrix to 3, symmetry  2  of symmetry. For example,  a  reduces the number of independent elements in the order  perpendicular planes of symmetry  will reduce the number  to 2  and  C2  or a  with a  axis of rotation  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  described  by  two  axis frame  independent  of the molecule. The  elements  of the  order  orientation  matrix  is then  (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  = < <Pm I  mn  # 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  where \p , ^ m  n  «  |< ^  m  U IX1I  V„  >l  2  d-13)  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 , E ) and frequencies ( w = ( E - E ) 2 7 r / h are calculated, m  n  mn  m  n  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 =  On  the  other  hand, for weakly  3Djj  coupled  (1.14)  nuclei, in which  the  chemical  shift  difference cannot be ignored, the dipolar splitting is instead given by:  -u  The  +  (2D,j  =  n  Jy)  ( L 1 5 )  strongly coupled case applies to nuclei of the same species physically close  together  (recall that Dy  heteronuclei (e.g. ^ C  « <l/ry^>) whereas the weakly coupled case applies to  and  *H  dipolar coupling) and spatially separated  homonuclei  of different chemical shift. For  small numbers of spins, with the assistance of  molecular  spectra  symmetry,  the  nmr  can  However, in dipolar coupled spectra, the  sometimes  be  solved  analytically.  complexity rapidly increases with the  number of spins, and most spectra must be solved with computer assistance. The computer coupled  program spectra.  couplings,  and  LEQUOR A  suitable  chemical  literature values. The  [24, set  25] of  shifts) are  was  used  extensively  starting parameters chosen, either from  secular determinant is solved and  solve dipolar  (dipolar couplings,  J  inspection, intuition or  assuming a decent choice  of starting parameters, calculated transitions are assigned The  to  to experimental lines.  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. T H E QUADRUPOLAR  For  a static  deuteron  INTERACTION  in an anisotropic  dominated by the quadrupolar  environment, the nmr spectrum is  interaction. The quadrupolar  the interaction of the nuclear electric quadrupole  Hamiltonian describes  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:  Q r  =  q  2  Q is the nuclear quadrupole 2Z  8  8  +  where e qQ/h is the quadrupole  V ,  (1.16)  4h!(2 i-l) [3I, -I(] + 1) + j ^ ( I + I _ ) ]  coupling constant, e is the charge of the proton,  moment, eq is the electric field gradient equal to  TJ is the asymmetry parameter of the efg equal to ( V  x x  — Vyy)/V , and the zz  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:  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 *  This is very  similar  nuclei (1.4). A  2  q_Q  r*i  .  2  _ i / u i ^ i  d.i9)  to the expression given for two dipolar coupled  transformation of (1.16) from  the efg principal  spin i  axis reference  frame to the laboratory fixed reference frame yields:  *Q  2 4hI(21-l)'t i - 0-'-l)3 [ § ( 3 c o s V l ) + \f) s i n * cos20] 3I  =  2  1  (1.20)  2  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  = ->hH m +4 0  where m spectrum  u  There  0  =  ^ jg (  2  [3m -I(I + l)] [£(3cos 0-l) + ± 2  l)  2  s i n * cos20] < 2  v  L 2 1  )  —1,0,1 for 1=1. The transition frequencies for the single quantum  (Am =  = -  ±1) are given by:  H  7  0  ±  are two allowed  separation & V Q ,  A l /  ^(3cos 0-l) 2  + y, sin 6 2  transitions and this gives rise  cos20]  to a doublet  d-  2 2  )  with a  the quadrupolar splitting:  Q  For a deuteron  =  [ ( 3 c o s 0 - l ) + 7j s i n * 2  2  cos20]  ( 1  '  2 3 )  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:  2 = ^ T ^  Since  e qQ/h z  =  167  kHz  for a  INTRODUCTION / 13 [(3cos c9-l)]  5  (1-24)  2  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 T>>1/2TTA»>Q,  the  quadrupolar quadrupolar  splitting, i.e. motions interaction  is  with  modulated,  a correlation and  a  time  reduced  quadrupolar splitting is observed:  =  a. THE  In  ORIENTATIONAL  analogy  ORDER  — T T P  <3COS  (1.25)  6? — 1 >  PARAMETER  to the dipolar interaction,  an  orientational  order matrix  may  defined for the quadrupolar interaction (1.10). For a deuteron in a C —D  be bond  with n = 0, there is only one independent element of the order matrix and (1.25) becomes: <Av > Q  CD  where S Q Q is called the carbon deuteron order parameter.  (1.26)  INTRODUCTION / 14 b. THE  For  POWDER  PATTERN  dipolar or quadrupolar coupled nuclei in a rigid solid where all orientations  of the  internuclear  vectors (or  C-D  bond  vectors) are  equally  resonance frequencies of the nuclei are orientation dependent and is scaled  the Hamiltonian  by:  #(/?)  where /3 = (or  probable, the  C—D)  the  =  #(0)  P (cos/?) =  #(0)  2  angle between the external  vector  of  interest.  The  (3cos*/3-l)/2  magnetic field and  resulting  resonance  d.27)  the  line,  internuclear  which  is  a  superposition of many doublets of varying frequency, is inhomogeneously broadened into a characteristic lineshape called the The  splitting now  Pake doublet [28] or powder  corresponds to those nuclei oriented  at 90°  pattern.  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  orientation with respect  the  relative probability of finding any  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  normal to  lamellar the  liquid  crystalline phases  plane of the  bilayer is a  randomly  symmetry  dispersed,  axis  of the  where  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  axis of the phase and magnetic field. A measured  0  bond vector and  the symmetry  is the angle between the symmetry  axis and  the  similar expression can be written for dipolar splittings. The  splitting  in  an  nmr  spectrum,  corresponding  0  to  =  90°  (i(3cos^/3 — 1)= — i) reduces this equation to:  <^Q>  In  general, the  =  " ^ g  The by  QUADRUPOLAR  the the problem from  a  spectra of powder samples is severely hindered  of receiver deadtime.  the effects  two  pulse  developed [29]. A  only be  $.  of the  sequence  By  the time  the spectrometer  radiofrequency pulse (up  substantial fraction of the deuteron nmr problem,  can  ECHO  acquisition of deuteron nmr  recovered  (1-29)  C D  sign of the coupling constant is unknown and  determined with certainty if SQJJ >  c. THE  S  5  known  to 40  signal has decayed. To as  the  quadrupolar  has  Msec),  a  overcome this  echo  has  been  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  transformation of the signal from deuteron nmr  spectrum.  interaction  is complete.  Fourier  the peak of the echo then yields the true  INTRODUCTION / 16 d.  DEPAKING  For  powder  pattern  spectra  numerical procedure has  which  arise  from  been developed which  randomly  oriented  samples,  calculates the spectrum  a  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  transition for resonances arising from nuclei near the polar head often  many  Depaking  lines  is now  overlap  due  to steric  constraints  placed  on  phase  group where the molecule.  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 E C H O SPECTROSCOPY  This thesis is concerned primarily with the measurement of dipolar couplings in perdeuterated and  fatty  It was  acids isotopically substituted near the head group with  *H  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 chosen is a variation on 2D  J spectroscopy  commonly in use in high resolution  pulse sequence is simple, a 90° pulse followed after a time T with a  nmr.  The  180°  refocussing pulse. There  dubbed  method  two  dimensional  are  spin echo  two  main  differences between this method,  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 collected for each experiment rather than The  a result, only a single FID is  a complete two  dimensional  data set.  saving in computer time in data processing and disk space for data storage  is enormous, at least 3 orders of magnitude, and information was  not of any  use.  in most cases the discarded  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  spectroscopy  sequence. A  complete discussion of two dimensional  [35,36] and the density matrix  nmr  [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 Evolution is allowed  under the appropriate  Hamiltonian,  Zeeman, homonuclear dipolar and heteronuclear  magnetization.  in this case a sum of  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 tj/2.  Terms  which  are linear  in spin  operators  reverse  their  r  =  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  t j (the variable time domain) and t  domain). Collection of a t two  dimensional  2  2  (the normal time  signal as a function of varying t j (or T) produces a  data matrix, which upon double Fourier transformation yields the  normal F T spectrum in the f  2  (frequency) domain and a spectrum  devoid of  INTRODUCTION effects  from  dimension.  chemical  A  more  shift  detailed  and heteronuclear  dipolar  explanation  the density  using  couplings matrix  / 19  in the  fj  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  '  Application  of a (7l72)  v  pulse  —  °  1  2nkT  (1-30)  2  generates  x magnetization.  The density  matrix  following a perfect (n/2)y pulse is proportional to I : x  p(0)+  «  (1.31)  1  where  I  =  x  I  I  x  (1.32)  j  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)_  «  exp[-i^  d )  t,/2]  l  exp[iJ^ t , / 2 ] d)  x  ( 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 ) e x p [ - i y t , / 2 ] d)  +  I  e x p [ i ^ t ,/2] d )  x  exp(i/?F ) y  (1.34)  where  F  and  where the sum  the  case of heteronuclear  y  = £  ]  yk  (1.35)  is again over all nuclei excited by the refocussing pulse. In dipolar couplings, this operator  will  extend  species of nuclei to which a refocussing pulse is applied. For /3 =  over all 180°, the  exponential operator exp(—iir Fy) can be written as:  exp(-i7TF ) y  {J I (2i) I  =  where P  y  = n exp(-i7T] )  y k  |  = i  is a product of spin operators  pulse and N  (1.36)  y k  N  P  (1.37)  y  Iy for all nuclei affected by the it  is the number of nuclei. Substituting (1.37) into (1.34) and then  allowing the spins to refocus under the influence of a Hamiltonian rise to the spin echo which will then dephase in the t p(t,.t ) « e x p [ - i ^ t ] 2 )  2  2  x exp[iV t,/2] d)  The  e x p [ - i j / i ,/2] P r,  P  e x p [ i ^ t ,/2] r)  y  signal at any time (tj,t ) is given 2  y  2  K^ ^ will give T  time domain.  e x p l - i f l ^ t ,/2]  ]  x  ( 1 - 3 8 )  exp[^ t ] 2 )  2  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 ) = T r i I, 2  exp[-iV t ] e p[-i^ t 2)  x e x p [ i ^ t ,/2] d)  Using  a  basis  r)  2  X  P  ,/2] P  e x p [ - i ^ t ,/2]  U-39)  exp[i^ t,/2] e x p [ i ^ t ] j r)  y  1,  d )  y  2 )  2  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  )  x exp[i(E - E,) t,/2] exp[!(E k  n  n  k  e x  Pt^ k E  -  E'I) t ] 2  (  1  4  0  )  - E ) t ,/2] m  Double Fourier transformation of this expression will yield the two dimensional frequency spectra. The spectral frequencies in the f domain are: 2  " 2 = (E  k  - E,)/-h  ( 1  -  4 1 )  ( 1  '  4 2 )  and in the f^ domain:  «,  6. CALCULATION  In  = ((E  k  - E,) + ( E  OF THE ECHO  practice, it is not necessary  frequencies previous  and intensities  section,  - E )/"t, n  SPECTRUM  to use the density matrix  of the echo  the program  m  LEQUOR  spectrum. Using can be  to calculate the  the results  modified  of the  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 ) , (P )j x  where  (1  k  y  0 ) x  m  ( y)nk p  m n  (1.43)  * ) 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  In the event that the rf field  PULSES  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 ) = n exp(-i/SI ) y  yk  (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/SF ) = cos | y  1 + 2i sin | I  d-45)  y k  where 1 is the unit operator. Switching from Iy to the ladder operators yields:  exp(-i/SF ) = cos | y  Equation  1 + sin |  [I  +  - I _]  (1.46)  (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  effects of inhomogeneous ir/2 pulses  phase cycling routine to eliminate  and receiver baseline drift. For calculation  purposes it is sufficient to calculate the intensities for only one set of phases.  B. SOAPS  1. P H A S E 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 with  the polar  head  groups  in contact  with  1.1), approximately spherical,  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 ) phase in which the molecules are packed into "infinite" a  cylinders  with  hydrophobic  hydrophilic  tails  head  congregating  groups  exposed  in the centre.  to the aqueous  The phase  media  and  is called hexagonal  because the packing of the cylinders is in a hexagonal array. Further decrease of water concentration results in a cubic phase (Q ) in which the aggregates a  pack in a cubic arrangement. This phase is bicontinuous i.e. the water and soap each  form  infinite  intertwining  liquid crystalline lamellar or L  networks. With f l  phase is formed  arranged in lamellar or bilayer structures — chains  inside.  This  phase  increased  soap  concentration a  in which the molecules are  water on the outside, hydrophobic  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 undergoes a disorder—order phase transition to the  a  phase  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 (H ), (Adapted from Reference 43) a  C) lamellar ( L ) a  INTRODUCTION / 26 amphiphiles in  of differing chain length. Charvolin [44] has observed  combinations  concentrations  of  potassium  that normally  caprate  produce a  and  potassium  stearate  lamellar phase. Doane and  [45 — 51] have done considerable work on  a  ribbon phase  phase between a hexagonal and lamellar phase—formed by in potassium phase. The  — 1%  an  water  Chidichimo intermediate  palmitate at a higher water concentration than the regular lamellar existence of these intermediate phases can be explained in terms of  length, and et  at  potassium laurate  the packing constraints imposed on the molecules by molecules  Tang  a cubic phase  on geometric  al.  [22,  52]  of differing chain  arguments based on the overall structure of the phase. and  Beckmann  arguments to explain the quadrupolar  et  al.  [53] have  used  similar  packing  splittings of lamellar phases of mixtures of  soaps of differing chain lengths.  The  experiments in this thesis were mainly  constant water content: 70% equivalent  to  a  molar  ratio  performed at a relatively low  by weight potassium of  6.3  moles  palmitate: 30  water/mole  soap. Commonly  concentration has been chosen because it is approximately lamellar phase region and  phase transitions  weight %  but D 0 2  this  in the middle of the  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  comparison to past studies [2, 3, 4, 5, 10, 54 — 64] easier.  selected to make  INTRODUCTION / 27 2. X - R A Y  The  STUDIES  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  Skoulios [67 — 70] and x-ray  work on the soaps has been done by Gallot and 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 F I G U R E 1.2 The Phase Diagram of Potassium Palmitate/H20  1  100  1  1  I  I  I  80  60  40  20  10  SOAP WT %  Legend: Isotropic solution —• micelkvr, middle soap = hexagonal (HQ), neat Boap = lamellar liquid crystalline (L ), curd = lamellar gel (L.0). Adapted from Reference 66 a  INTRODUCTION / 29 0  band in the x-ray identical  to  the  hydrocarbon  diffraction pattern at (4.6  diffraction  chains  are  pattern  in a  of  liquid  extremely  A)  —1  [71, 72]. This is almost  paraffin and  disordered  reveals  state. The  that  average  the 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 0  lamellar  repeat  distance. This  at (4.6  A)  —1  changes to a sharp reflection at (4.26 A) of the  diffuse band  . This is accompanied by an increase 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  a.  STUDIES OF  SOAPS  GENERAL  Soaps have long been the subject of nmr been  used  properties  to  study  of these  both  the  systems, on  changes associated with  static a  spectroscopic investigation. Nmr  (spectroscopic) and  number  phase transitions are  are easily studied by this method.  of  different  dynamic  has  (relaxation)  nuclei. The  spectral  dramatic, hence phase properties  INTRODUCTION / 30 Analysis of the solid state proton nmr trivial. The  plethora of unaveraged  spectra of lyotropic liquid crystals is not  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  measured due to intramolecular dipolar broadening. Early nmr mesophases  were  limitations. The  severely  hindered  by  these  most common technique was  factors  be  studies of lyotropic  and  by  instrumental  to disperse lipid in D 0 2  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 The first was [73,  74].  developments occurred which drastically altered this scenario.  the discovery of a facile synthesis for deuterated fatty acyl chains  This  allowed  the  measurement  of  intramethylene  parameters at various sites in the bilayers. The second was Fourier transform nmr  and  deuteron  order  the advent of pulse  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 at  sufficiently  spectra are distinct and very striking. In the lamellar phase,  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  transition, the deuteron quadrupole  above  nmr  the gel—liquid  crystalline  splittings of deuterons near  phase  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 orientational spectrum  fluctuations  for each  is a measure of the time average  of the bond. In unoriented dispersions, the  methylene  group  consists  of a  superposition  of the H  nmr  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 — the  individual molecules  distinct  hydrocarbon  methyl  groups  molecular motion  [75 — 77]. Gel phase  quadrupolar  which about  an axis perpendicular to the symmetry axis of  splittings:  experience an extra  a  deuteron  spectra  show only two  smaller one for the deuterated  degree  of averaging due to rapid  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, methylene  C—D  all  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 and  down to — 113°C  in rubidium stearate/H^O  [2]  [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  amphiphiles  within  splittings  the  cubically  [59 — 62,  78,  symmetric  79]. Rapid phase  translation  effectively  of the  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  asymmetric  dipolar  or  quadrupolar  splitting  except  for small  effects  due  to  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  Much  of the  performed  by  STUDIES  early  magnetic  Dunell et  al.  resonance  work  [85 — 88]. They  on  the  anhydrous  soaps  was  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 H 1  sodium  palmitateT^O  and  anhydrous  sodium  stearate  absorption line in  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 0 2  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  the mixture between approximately of  orientation  dependent  potassium laurate/TH^O by  sandwiching  30 glass plates. This replaces the distribution  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  orientation and  P2(cos0) dependence, with no  maximum  splitting  splitting at the magic angle. (The  at  zero  degrees  orientation dependence of  the dipolar splitting had been previously reported by de Vries and Berendsen [94] who  oriented  potassium  symmetric nature  oleateyT^O  between  glass  plates.) From  of the lines, they conclude that no  distribution is present and  the  appreciable static  narrow, angular  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  magnetic resonance.  laurate [75] and potassium  stearate [76] using  deuteron  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 nmr  a series of elegant publications, which somewhat inspired this thesis, the 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  use a two—dimensional employed  than  spin echo technique as is done in this study, Post et al.  a Carr-Purcell-Meiboom-Gill  (CPMG) sequence (90 -(r-180°y-r) ) x  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 saturation  of transmitter power droop, cumulative and sample  heating  from  pulse imperfections, receiver  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  comparison concluded  and unfluorinated  of the S^p order  potassium  parameter with  S^jj's  myristate from  and on the  other  work, they  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  segment  matrix was  to be  found  to  zero, the order  matrix  be  symmetric  not  axially  for the 4 —fluoro  Syy= —0.155). In a temperature dependent fluorine nmr myristate [102], they report the existence of a new the gel phase. The phase is characterized by patterns and a reduction in F — F  at  50°C  methylene  ( S = -0.209, xx  study of the fluorinated  phase at temperatures below  a sharpening of the F powder  dipolar splitting of ~ i  from the L  phase.  fl  They postulate the existence of a low temperature hexagonal phase to explain these results. The soap would  =  water concentration was  higher in these systems (77  wt%  4.5 moles D20/mole soap), but this is still below concentrations that 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 phase i.e. the long axis of the molecule projects the C—D  director of the  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  Translational  this  symmetric  state cannot  diffusion of oriented potassium  last longer  than  a few jisec.  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  dipolar couplings between neighbouring  amphiphiles.  to average  intermolecular  This translational diffusion is  believed to persist even into the gel phase [56]. Other low frequency possibly exist such as collective reorientations of the entire molecules,  motions 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  The  plateau, the region of constant quadrupolar splitting in the deuteron order  parameter the  INSPIRING THE PRESENT WORK  profile, is believed to arise from restrictions placed on segments near  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 temperature  crystalline phase transition and well into the L spectra  clearly  display  f l  the plateau, the higher  characteristic exponential decrease. Davis  and Jeffrey  phase. The lower temperatures the  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 0 2  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  increase — decrease of the order parameter  was  deuterated  again observed  sample  the  (with maximum  splittings at about 85°C) as were the two  quadrupole splittings at intermediate  temperatures  was  (54±5°C). As  the temperature  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, M, 2  for the selectively deuterated spectra followed the same trend. They termed  this phenomenon a lamellar - lamellar "phase transition" (the quotations are theirs) and  observed  characteristic  that  the  temperature  transition  was  dependence  reversible  of  the  order  with  no  hysteresis.  parameters  The  is observed  consistently in potassium palmitate, although with minor variations [2 — 5, 10, 54] and  is also observed  in sodium palmitate [21] but has  detailed  temperature  stearate  [57,58]. In sodium palmitate [21] the temperature  ^ Na 3  quadrupolar  dependence  splittings  studies  parallels  quadrupolar splittings. Other nmr  of  the  sodium  not been reported in  laurate  increase —decrease  experiments  [3] or  rubidium  dependence of the of  the  deuteron  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 peaks whose temperature  dependent  intensity  remains  constant —  alpha  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  slowly  on  if the structuring the  nmr  resulted  timescale, two  in two  deuteron  disruption could be collective in nature separate  domains  of  the  sample  —  configurations which peaks  the two  possibly  with  could  be  exchanged  observed.  This  configurations occurring in slightly  different  transition  temperatures due to sample inhomogeneity.  A  model based on the idea of two  another of the three proximate penned by  referred  to  Valic presented a model based as  anomalous results of Davis and model can  be  configurations was  rendered in  articles in the same journal [2]. The  Abdollal, Burnell, and  arguments, hitherto  exchanging  best comprehended  the  Abdollal  Jeffrey. The by  on geometric explained the  salient features of the Abdollal  examination  proposed two interchanging configurations, A  model, which  article,  of Figure 1.3.  The  model  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  F I G U R E 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 Hfj is perpendicular to the bilayer director. The efg represents the principal axis of the sodium efg tensor, (from Reference 3). r  INTRODUCTION / 43 C —C the  bond is shown to be parallel to the bilayer normal. This induces a tilt in tail  of the  methylene  molecules  segments.  The  molecules to hydrogen  which  would  placement  persist  of the  down  polar  through  head  the  main  groups  first  allow  few water  bond simultaneously to more than one lipid molecule. At  higher temperatures, thermally activated fluctuations break and  the  interaction  becomes  the  steric  the hydrogen  constraints  bonds  (hydrocarbon  intermolecular interactions) of the neighbouring chains. This leaves the first bond of  the molecule  in the trans state and  r ^ T j and  leaves both  rjjjj for the  a—carbon perpendicular to the bilayer normal.  Calculations based  on  this model were presented and  are reproduced  Table 1.1 Several simplifying assumptions were made: all CCC are lone  tetrahedral, the HOH pairs  symmetric the  and CCD  angles  angle in water is given as 105°, the angle between  is 120°. Conformer motion  here in  rotations of 120°  are used  and  rapid  axially  is assumed to project residual quadrupolar interactions along  director. All efg tensors were assumed axially symmetric  directions. The C —D  about their bond  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 isomers) all C —D motions  order parameters  will lessen a particular  rotational  are equal to P2(cos90)= — £. Conformational  SQTJ  value by  probability of gauche rotations up to that C—D  an  amount dependent  on the  bond. This leads to progressively  decreasing quadrupolar splittings. However for configuration A, the absolute value of  the  segmental  parameters  order  parameters  for configuration  B.  The  are  less  overall  than  the  corresponding order  order parameters  which  are the  INTRODUCTION / 44 T A B L E 1.1 Calculated Order Parameters From The Abdollal Model  Configuration A  Configuration B  I  I  "3  "2  3 t p  F 3  D,0  t  2 t  3 g±  P  p  3  *g±  p  0.06  t  F  t  >g± g ± F  0.15  d  efg  -0.18  Ca!culations are averaged over conformations t^t^t^, t ^ t ^ g ^ , t g | t For A g^j and t p give equal contributions to order parameters.  and t ^ g ^ g ^ .  a  a/J  d  6  a  Assumes that the C - C bond is at an angle 35Vi° to n. Motions about C O O - C axis are not considered (i.e. Pgf = 0). a  c  For gauche conformation S = Vi (P, cos (90) + P cos (35V4)) = 0. 2  d  Assumes hydrogen bond parallel tofirstC - C bond and free rotation about 0. . . . D - 0 axis.  INTRODUCTION / 45 scaled sum of the configurational order parameters smaller  at lower  increase  with  increasing  temperatures  temperature  thermal  due to the predominance  as Pg  motions  (S = P ^ A + PJJSJJ) would be  increased, and then  cause  a  lessening  of configuration  start  A,  to decrease as  of the molecular  order. The  structuring effect would have progressively less influence going down the chain as rotational  isomerizations relieve  quadrupolar each  the induced  stress  and further  average the  interaction. The two effects act in an opposite fashion, cancelling  other out in the intermediate regime  leading to a constant S Q Q value  —  of the first few methylene  groups  a possible explanation for the so called  plateau.  Another  interesting  "odd—even"  effect  feature of this  model  [2, 64, 75] which  is that  manifests  it adequately  itself  as equal  predicts the 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^g ") 4  conformations are ignored [118—120] then the calculated order parameters for S^ and  Sy  are equal in configuration  g^,ygtg g^ £ e  conformations parameters  e  A. Similarly  Sg = S  is neglected. This effect decreases are made  decrease  available.  progressively  down  In configuration down  the chain.  if the conformation  f  the chain as more  B, the calculated Hence  increases, and configuration B predominates, the ratio Sg/S value of 1 (i.e. the peaks overlap) to a larger  f  as  order  temperature  increases from a  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  L^—L  f l  gel —liquid  maximum  crystalline  quadrupolar  phase  splitting.  phase  transitions, one just  transition  Doublets  were  above the  and one 25° higher at the 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 reported. The phase  (DSC) although the results were not actually  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 about  the  temperature symmetric  lower  temperature  is lowered, through  nonaxially symmetric  lamellar—lamellar  the deuteron  a two phase  powder  region  where  phase  patterns  transition. changed  a superposition  ±10°C  As the  from  axially  of axially and  spectra was evident (two quadrupole couplings), to a region  of non — axiallity characterized by an asymmetry parameter quadrupolar splitting reached a maximum  of n = 0.5 —0.8. The  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  quadrupolar coupling was observed to increase continuously  the methyl  group  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  measurements were made in the gel phase, although this would  temperature  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  potassium palmitate was prepared in which  partially deuterated  the two a-deuterons were replaced  with protons, the proton dipolar coupled spectra recorded, and in conjunction with  INTRODUCTION / 4 8 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  broadened by  A»>JJJJ=3/2DJJJJ  intramolecular dipolar interactions with the remaining deuterons. The behaviour of the proton dipolar couplings is similar to that of the deuterons maximum  and then falling off with decreasing temperature  —  rising to a  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  symmetry — the HCH  dispersed. Assuming  that  the CH^  unit  has two planes of  one in the plane of the three atoms and a second plane bisecting  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 normal  direction, y, the bisector of the HCH  to the HCH  determined from  SQQ  S  where  plane. Using and  C D  SJJJJ  = S  sin 0  SQTJ  and  SJJJJ  absolute magnitude than  bond  X X  SJJJJ  and S  = SJJJJ,  cos 0 2  y y  Y Y  was  (1.47)  angle. The magnitudes  were found to differ somewhat,  SQTJ  of the order  being smaller in  throughout most of the temperature range, crossing  at lower temperatures. The values for —  + S  2  H H  definition, S  by a rotation about the z axis:  <p is one half the HCH  parameters  this  angle, and z, the  SJQJ  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 all trans conformation and conformations  may  is considered, the  angle is vabd for the  even be valid when the time HCH  plane  is not a  plane  average  of all  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 molecule was  coupling must be measured. In the present study a similar  synthesized —  carboxyl group. Now from the * C —H 3  alpha protonated, but with a carbon—13 label at the  an off—diagonal element  of the order matrix is available  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 particular  interest  in nmr  spectrum. The  dipolar interactions have been of  [12,123-125] since  they  are  related to the  averaged distance between nuclei. Therefore the dipolar coupled nmr be used as a probe of molecular spins are  dipolar coupled  consist of broad  spectra can  geometry. Normally, in solid phases where the  to all the other  amorphous lines. In  spins in the  partially  sample, the  solute concentration and  rapid molecular motion of the solute relative to the liquid crystal. The spectra  have  contributions  quadrupolar) interaction  and  only  appear  as  spectra  oriented systems, intermolecular  dipolar couplings are eliminated as a result of low  nmr  time  from  the  sharp  lines  intramolecular superimposed  background signal which arises from the liquid crystal. The  the  resulting  dipolar on  experimental  a  (or  broad  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. M O L E C U L A R MODELLING  Most molecular  modelling  schemes for methylene chains  liquid crystal rely upon the potential and other  the use  modelling  intramolecular and  intermolecular  of this potential to calculate order parameters or some  quantity that can  be  compared  potential is broken down into the sum  E total =  The  of the  in a bilayer or in a  to experimental  values. In  general, the  of a number of different contributions.  E  l n l  first  +  E  e x t  U-«>  term,  INTRODUCTION / 51 E ,  is the intramolecular  m t  of the chain  about the  dependent intermolecular  potential that arises from the conformational rotations  C—C  bonds. The  second term, E  e x t  , is the orientation  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 often modelled by  surface  effects. These forces  a mean field surrounding a particular chain of interest. The  advantage of a mean field approach is the considerable In  molecular  behaviour  of  dynamics a  are  [126,127] or  statistically  Monte  Carlo  significant number  saving in computer time.  calculations  of chains  whereas with a mean field only the fluctuations of one  [128 — 130],  must  be  the  calculated,  chain in the mean field  of its neighbours is important.  1. INTERNAL POTENTIAL  The  most  isomeric  common  state  conformers  model  model (RIS)  or  for  the  internal potential  [118]. In  rotational isomers  is the  this model, only  about  each  C—C  a  bond  Flory  discrete are  rotational number  of  allowed. These  correspond to minima in a chosen internal potential, usually a 3—fold potential with the minima occurring at 0° and are termed the trans, gauche plus, and t, g , +  and  g~~  energies 2.1 ±0.5  respectively. For  ±112.5° [118,p51]. These 3 conformations gauche minus conformers, represented as  liquid  n—alkanes, the  gauche minima have  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 derived for n—pentane. The  internal energy is then averaged  conformers of the chain which is 3^ segments. A  where (N+1)  first  over all possible  is the number of methylene  partition function is calculated in the standard way,  as the sum  of  the Boltzmann factors:  Z = Iexp[(-E  l o l  )i/RT].  (1.49)  Then a probability of each conformer can be defined as:  Pi = 2  and  e x  PK- tot)i/RT]  d.50)  E  from this starting point, all thermodynamic and experimental properties can  be calculated.  2.  SEELIG  Early attempts to calculate nmr by  splittings in deuterated lipid chains were made  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  —  in  were  +  the  chains. The  kinks  and  jogs  or g t g ) or jogs ( g t t t g , g t t t g ) —  +  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 j , from the rigid all trans m o  value of 1, according to the formula:  S  = | (3<cos a>-l)  (1.51)  2  Q  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  [P (^)(3cos 0 -l) + 2  0  o  A  P4)(3cos 60°-1)] 2  ^  where: P  The  A  + P  B  =  1  (1.53)  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  normal to the DCD  of Pg  is the probability  of finding the  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 second  paper  Pg  =  2?^^.  In the  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 =  ~2S  0.62  =  C D  for S  0  0.57 =  they calculate P  1.0. A  =  A  P  t  =  0.83  for S  0  =  0.7 and P  t  m o  j =  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  explicitly  to be  unity  and  calculated. Instead they  the  probabilities  P^  and  Pg  were  never  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  as  11.2  A  o  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 )  (1-54)  i B  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> hydrocarbon chain was  then found by:  <L>  For  of the  = I <Jj> =  I (15-0.5 I. P ) ] i B  such a simple model, the results are good. However it was  (1.55)  soon realized  INTRODUCTION / 55 that specific intermolecular forces must be included for a complete description of the chain statistics.  3. INCLUSION OF  E X T E R N A L 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  E total  +  E ext  =  E int  +  writes the total potential as:  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, g -. E 4  Q  is the energy of the first three groups of the chain  which are somehow rigidly affixed to a surface. The values E(£ ,t) =  1.67 kJ/mole and E (g - ,g+) =  9.20 kJ/mole were used in his calculations.  4  Marcelja used  three initial  conformations based  =0, E(t,g±)  conformations of the head  group  and generated  all  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:  E  disp = ~ * ( n r / ) I (|cos ^-^) n  (1.58)  2  t  where <p is the angle between the normal to the HCH plane and the normal to the  plane of the bilayer and where n /n is the fraction of bonds in the trans tr  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  (1.59)  <(n /n) I <|cos tr  Therefore $  depends on the average order of the system  constant, V  = 2.84 kJ/mole based on the freezing energy of polyethylene.  The  third  Q  term, E  g t e r  j  c  results from  and on a coupling  lateral pressure on each chain  —  it  is  essentially a steric repulsion term based on a hard sphere repulsive interaction:  F L  -  PA  steric ~ PA  d- ) 60  INTRODUCTION / 57 where A  is the cross sectional area of the chain and  estimated  to be between 18—20 dyne/cm. The  P  is the pressure  —  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 l /l 0  where 1  and A  Q  state and  are the length and area of the chain frozen in the all trans  Q  is the effective length of a particular conformation  projected on using  (1-61)  ( i )  0  i.e. the length  the bilayer normal. Then the partition function can  (1.48) where the  sum  is over  all conformations.  The  be  calculated  equation  for the  molecular field $ is given by:  *  =  $ {[  (n  l r  /n) I  (|cosV;3)]  Note that this equation is self consistent — on  E($). Values  E($). The  of V  only  valid  Q  and  P  <l-«2)  B  the calculated value of $ depends  are chosen and  solutions are  exp[-E(4». P ) / k T ] |  where  $ ] c a  $ c  calculated as a function of =  $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  = I PiS; = I {  ) ( .)  d.63)  The Marcelja model has only one adjustable parameter —  the lateral pressure P,  C D  (e" i E  / k T  S  INTRODUCTION / 58 but it has a number of parameters that must be chosen, the coupling constant, V, Q  the energies of the trans and  molecule. The  gauche conformers and  the geometry of the  Marcelja model has been criticized on a number of points —  simplistic treatment of repulsive interactions as a lateral pressure and orientation of the  first three  segments of the  attractive potential has been questioned  chain. The  term  his  the fixed  n^n  in the  since the intermolecular potential should  not depend on the fraction of trans linkages. Marcelja claims it is necessary to model  the  lipid  transition, as  chains  which  freeze  during  the  opposed to liquid crystalline chains  average orientation. Marcelja  also used  an  liquid  crystalline—gel  which only reach  attractive  phase  a common  (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  and  model  behaviour  in lipid  bilayers,  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  Seelig used (with the corresponding (2.84) kJ/mol, surface energy P  values. The  values  that  Schindler  Marcelja values in brackets) are V  =18.5  (25) dyne/cm, E  g  =  approximation g -  Q  =  and 2.47  2.09  (1.67) kJ/mole  =  120° (112.5°).  and  the gauche rotation angle for the RIS  The  initial orientations that Seelig used are also different from Marcelja's. Seelig  4  presents order parameters in good agreement with H 2  although  nmr  experiments on DPPC  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 P  =  fc  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  Flory  [138,  139]  is used and  to describe the  the  rectangular  (cubic) lattice. In addition, a two 142,  143]  has  are  Gelbart  in which  [134,  chains  of  calculations  lattice  the  group  angular  been  placed  used  to  fluctuations, but  [140,  on  a  141]  two  or  dimensional model  have three  Dill  and  performed dimensional  triangular (hexagonal)  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  opposed to a sum  over all the chains in the lattice, as  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  which is determined by  solving the equations  lateral pressure  necessarily held constant  lattice. In  is not  later work, Gelbart  to be  a lateral pressure,  for the packing  [144] applies the  from  layer to layer in the  same theory  Again the intermolecular potential depended on packing  constraints. The  to RIS  chains.  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]  interaction, and  adapted the  calculated two  Marcelja model, included a lateral pressure  terms, one  specific head group 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 any  forces included to model the interactions at the head group do not include 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.  INTRODUCTION / 61 5. T H E SAMULSKI INERTIAL F R A M E  The  model upon which  MODEL  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  tensor of a particular conformation diagonalizes  the moment  of inertia  the order matrix for that same  conformation. Samulski's interaction potential is divided into three terms:  = DA  E  E  + E  N B  + E (r)  (1.64)  c  where E p ^ is the dihedral angle energy (equivalent to the internal energy of the conformations between  discussed  atom  previously),  pairs. Based  Ej^g is the nonbonded  on a Lennard—Jones  6-12  interaction  energy  potential, this term  prevents the molecule from coiling back on itself. The third term, E^(r) is the mean  Field  part  Lennard—Jones  of the  potential  potential  characterized  assumed by  a  to be hypothetical  a  primarily cylinder  radius, r. The radius of this cylinder is the sole adjustable  repulsive  of variable  parameter  of this  model.  The method employed internal energies,  is to generate all possible RIS conformations, calculate the  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  where  m  a  =  {]„ + \  is the mass  definition. Then  - l  y y  a a  )5/2m  of the molecule,  (1.65)  a,p\7=x,y,z  the conformation dependent  and  A fiA <A x  y  z  by  molecular diagonal order matrix is  assumed to be proportional to the ellipsoid semiaxes:  S«  =  S  1 " (A  = 2 _  x x  S yy =  _  +  x  + A )/2A y  A /2A X  d.66a)  2  (1.66b) 2  (1.66c)  ^ "f A y/2A  Thus the order matrix is defined to be traceless, and the elements of the order matrix are defined such that S  Z 2  — 0.5<S ,SyyS0 and 0sS i<1.0. The limits on  describe the limiting geometries of the ellipsoid: S  cylinder (A =Ay = 0) and 8^=0 x  the  zz  xx  orientational  order  of each  z z  =l  for an infinitely thin  for a perfect sphere ( A = A = A ) . This reflects x  y  conformation, and in effect  z  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  INTRODUCTION  / 63  molecule and added to the total potential. Then the partition function, statistical weights  and probabilities of each  previously  conformation  can be calculated  using (1.48) and (1.49). The segmental  as described  order parameters  for each  conformation are determined using (1.11). For a diagonal molecular order matrix and noting that z=r cos# and x + y + z = r 2  2  2  (1.11) becomes:  2  2  S|j = —2 [ S ^ X i f r  + S  + S  2 y y y i j  2 z z Z i  ]  (1.68)  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 — — — [S^x, 4n r jj  =  0  8  + S  y y  y  0  + S  2  u  „ 2 z Z j j  2  ]  Calculation of the dipolar couplings, while never explicitly done by Samulski, is completely analogous:  D  ij  = — T  —  r ij  47T  [SxxXij  + S  2 y  y  y  j  j  + S  2 2 z Z i j  ]  (1.70)  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 offit"is tested by a "Reliability Factor" which is defined as:  R  =  ^  A  l  /  i  calc  I  ~  x  Lu  obs )  (  L  7  1  )  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 potential.  The  reorientation  model  deals  with  of the molecule.  conformational  Small  amplitude  motion fluctuations  simultaneously which  in the with  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, 1 6 - d  acid, hexadecanoic- 1 -  3 1  C-  1 3  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, 1 6 - d hexadecanoic-  2 9  acid and  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 y 2  acid. These names, which draw attention  to the deuterated portions of these molecules, are obviously too unwieldy used consistently throughout study  which  deals  with  to be  the course of this thesis. Since this is primarily a  nmr  interactions  near  the carboxyl  molecules, and therefore largely with the protons and carbon  group  of these  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 j ,  1 — * C — 2, 2 — H — 3  3  2  hexadecanoic acid-d g and 2, 2, 3, 3 —H ~hexadecanoic acid-d y. These names 2  4  2  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—d g 2  palmitate—dgj, 1 — * C — 2 , 3  and 2, 2, 3, 3—H^—potassium  2—H ~potassium 2  palmitate—d 7 or, in less lucid 2  moments, perdeuterated potassium palmitate, alpha protonated palmitate and alpha beta palmitate. To maintain  consistency, the short chain acids are also given  66  MATERIALS AND common names: ethanoic, propanoic and butanoic-2,2—d  METHODS / 67  acids becoming acetic,  2  propionic and butyric—2,2—d respectively. 2  B. P R E P A R A T I O N  OF P E R D E U T E R A T E D F A T T Y  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 were mixed with 3-5 a 2 neck 250 mL on  a  magnetic  g of 10% Pd on charcoal catalyst (MCB# PX5  round bottom flask. This mixture was  stirrer.  The  round  bottom  flask  was  was  the system was  flushed with nitrogen gas. The melt was  (MSD  water  gas was  99.8%D) using an Elhygen Mark TV  generated by hydrogen  of 40% NaOD in 99.0%D D 0 2  mixtures were heated with stirring for 7—14 with high resolution *H  heated to 150—180°C  passed over the surface of the stirring mixture at a  sec. Deuterium  consisted of 200 mL  to a  connected to an oil bubbler to monitor the gas flow and  deuterium gas was  rate of 1 bubble/2  5865) in  melted in an oil bath connected  condenser which  and  g of fatty acids  nmr  electrolysis of  generator. The (MSD  #MD  D 0 2  electrolyte  358). Reaction  days and progress was  monitored  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 reaction flask was  allowed to cool and solidify. The  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 and  dried on  ethanol and  the walls of the flask. The  fatty  acid was  the catalyst removed by vacuum filtration  METHODS / 68 dissolved in warm  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 was  removed by  rotary evaporation. Yields of 90%  perdeuterated acid was final  were not uncommon.  The  then recrystallized from hexane and/or ethanol/water.  The  extent of deuteration was  mass spec. For the nmr and  determined  by  determination, acid was  a small amount of benzene was  fatty  acids  are  envelopes of peaks separated by intensities of the envelope  high resolution proton nmr weighed into a 5 mm  nmr  and tube  added by weight. Percent deuteration  calculated from the integration of the proton perdeuterated  the solvent  very  signal. The  characteristic  16 amu  was  mass spectra of the  consisting  (the mass of a C D  2  of  a  series  of  group). Only the  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 was 70  10  used. For 2.5 g of fatty acid it was cm  in length column fitted  with  grams of silica gel 230 — 400  necessary to use a 2 cm  a 250  glass joint. Into the bottom of the column was approximately dry  and  2 cm  packed  mL  mesh  diameter  solvent reservoir and  X  ground  placed a plug of glass wool and  of sand to prevent clogging. The  under pressurized nitrogen gas  with  silica gel was freshly  poured in  distilled  hexane.  MATERIALS AND About 200 — 300  mL  was  down to just above the  used to pack the surface of the  minimum amount of solvent, was  column. Solvent  silica gel bed.  METHODS / 69 was  Sample, dissolved in a  applied with a Pasteur pipette to the top of  the column, being careful not to disturb the surface of the gel. The drawn inside and surface was  and  several 10 mL  drawn into the column. Pressurized  was  N  was  2  used when the going  slow. This procedure keeps the sample localized in a small region of the  psi=10  hexane/toluene  cm/min) with 1:1.  bottom flasks and the  sample  aliquots of packing solvent were added to the  column which helps give better separation. The (~8  then drawn  column was  hexane  until  nothing  Aliquots of 50—150 mL the  solvent removed by  monitored  by  column was comes  eluted under pressure off and  then  with  were collected into weighed round rotary evaporation.  thin layer chromatography on  The  progress of  silica  gel plates  using high boiling petroleum ethendiethyl ethenglacial acetic acid 70:30:2 as the developing organic  solvent. Chromatograms were  compounds absorb the  developed  in an  sublimed iodine from I  2  iodine chamber  crystals and  appear  (the as  brown spots) or observed under ultraviolet light. In general, nothing came off the column  until  contained  the  solvent  an oil which was  of the reaction, Rf = an  R^  was  changed.  The  the decarboxylated  ~0.70. This was  first  hexane - toluene  fractions  fatty acid, the major side product  followed by the purified fatty acid with  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 for at least 12 hours before use.  stored in a vacuum desiccator  MATERIALS AND C. PREPARATION  1. REDUCTION  OF 2,2,3,3-H -HEXADECANOIC 4  OF TETRADECANOIC  a. PREPARATION  METHODS / 70  ACID-D  2 7  ACID [150]  OF REACTANT  Tetradecanoic acid (myristic acid) was deuterated by Dr. T.P. Higgs described in section UB. The extent of deuteration high  was found to be >99% by mass spec and  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  257(1.7), 256(16.3), 225(M ,100), 254(9.6); H +  J  nmr  (60 MHz,  CDC1 ) 6: 3  m/z: 9.30  ppm (s, IH, COOH).  b. PREPARATION  1.5 equivalents 100 mL  OF REAGENT  lithium aluminum hydride (LiAlH^, LAH), 1.74 g, was added to  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 L A H did not dissolve but formed a murky suspension. A reflux condenser with a CaCl2 drying tube was fitted to the flask. Perdeuterated tetradecanoic g 0.0264 moles) was dissolved in 100 mL to the cooled  acid (6.73  anhydrous ether and added dropwise  reaction flask with a dropping funnel. The reaction mixture was  refluxed for 3 hours. The reaction was quenched by adding solid Na2S0 • 10H O 4  slowly  2  to the cool reaction mixture in the hood. N a 2 S O « 1 0 H 2 O was prepared 4  MATERIALS AND by suspending Na2SO^ in water and was  removed by  METHODS / 71  decanting off the excess water. The  gravity filtration and  washed thrice with  100  mL  residue  aliquots of  ether. Solvent was  removed by rotary evaporation and the resulting white powder  was  once  recrystallized  from  diethyl ether.  The  1,1—H2 1~ tetradecanol—d 7 —  2  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  224(1.2), 223(12.7), 222(M -HDO,100), 221(44.9), 220(2.5); *H  nmr  +  CDClg)  6:  3.6  32.9-34.4°C  2.  ppm  (s,  2H,  -CH OH), 2  ppm  (s,  1H,  (60  MHz,  -OH);  mp:  (uncorrected).  PREPARATION  METHANESULFONATE - d  To a solution of 5.45 methylene  4.7  m/z:  1,1- H  added a  mL  50%  - 1 - TETRADECANOL  45%  2  tetradecanol—d 7 in 110 2  molar excess of triethylamine  methylene chloride. The  in an ice/water/NaCl bath. A g, 0.0327 moles) was  2  [151-153]  2 7  g (0.0226 moles) of 1,1-H  chloride was  0.0343 moles) in 50  OF  mixture was  (3.47  g,  cooled to — 10°C  molar excess of methanesulfonyl chloride  dissolved in 40 mL  mL  methylene chloride and  was  (3.73  added to  the reaction mixture slowly with a Pasteur pipette. The  reaction was  stirred for  3.5  solution. The  completed  hours  at  reaction was saturated over  —10  —  — 5°C  resulting in  extracted with cold 150  NaHCOg and  Na2S0 . The 4  saturated  drying  mL  yellow  aliquots of deionized  NaCl. The  agent was  a  water, 10%  organic layer was  removed  by  gravity  HCl,  dried overnight  filtration  and  the  MATERIALS AND solvent was  removed  by  rotary  evaporation. The  METHODS / 72  product was  an  oil which  crystallized in the fridge into white translucent needles. Recrystallization 95%  ethanol gave a dense  white fibreglass like mat  from  of crystals, which when  dried overnight in vacuo yielded 6.59 g of tetradecanol methanesulfonate, a  91.4%  yield. Rf : 0.25 224(3.1), MHz,  (h.b.petroleum ethendiethyl ethenglacial acetic acid, 70:30:2); ms 223(15.8),  CDC1 ) 3  6:  222(M -mesyl-D,100), +  2.9  - 0 - C H - C D - ) ; mp 2  2  ppm  38.8-41.3°C  3. PREPARATION OF  a. PREPARATION  (s, 3H,  221(8.5),  220(0.2);  -O-SOg-CHg),  4.1  J  H  nmr  ppm  (s,  m/z: (60 2H,  (uncorrected).  2,2,3,3-H -HEXADECANOIC A C I D - d 4  OF SODIUM DIETHYL  2 7  [152,154]  MALONATE  Into a IL round bottom flask flushed with nitrogen gas and fitted with a reflux condenser  and  Xylene was  CaCl  2  dried by  drying tube was distillation from  (0.0235 moles) of sodium heated to 120°C sodium. malonate the was  The  in an  metal was  put 250 P Og 2  added  and  mL  thoroughly dried xylene.  stored over CaH . 0.540 g 2  to the xylene and the flask  was  oil bath with vigorous stirring in order to melt the  mixture was  cooled  to room temperature  (4.34 g, 0.0271 moles) was  dissolved in 80 mL  while stirring. Diethyl xylene and added to  stirring reaction mixture drop wise through a dropping funnel. The reaction allowed to proceed overnight at room temperature under  nitrogen pressure. A white gel like precipitate formed.  a small positive  MATERIALS AND b. PREPARATION  OF 2,2,3,3—H —HEXADECANOIC  ACID  4  1,1—H2 1—tetradecanol _  dissolved in 80 mL  methanesulfonate—d 7  (6.10  2  clean dry xylene and  through a dropping funnel. The  g,  0.01911  moles)  was  added slowly to the reaction mixture  temperature was  of an oil bath and the solution was  METHODS / 73  raised to 120°C with the use  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 of 5% was  KOH  added  heating was  in 80%  ethanol on  slowly to the  saponified for 1 hour in 150  a steam bath at 80°C. 2N  solution  at 80°C  until  200  times  mL  with  (72  mL)  (pH = 4). Stirring  and  2  4  continued for 30 minutes resulting in a clear slightly yellow solution  with a white precipitate. Most of the ethanol was and  acidic  H S0  mL  of deionized H 0 2  diethyl  ether  and  was the  removed by rotary evaporation  added. This solution ether  extracts were  was  extracted four  stored overnight  over  Na S0 . 2  The  4  drying agent was  removed by  extracts were rotovapped, transferred to a 100 mL  filtration and  redissolved in a  washed with ether. The ether  small amount (10  of nitrogen. The  flask was  aspirator and a gentle stream of nitrogen (2 psi) was flask was  observed  as the decarboxylation takes place. The  solid  connected  was  recrystallized  and  removed by to a water  passed through the flask.  heated in an oil bath at 170°C for 2 hours. Effervescence  liquid that solidified to a yellow—white yellow  ether  2—neck round bottom flask. The ether was  evaporation under a stream  The  mL)  result was  was  an amber coloured  sludge in the freezer under nitrogen. The  thrice from  freshly  distilled  acetone,  and  then  MATERIALS AND recrystallized filtration  from  ethanol using  step. The fatty  acid  Norit  decolourizing  was recrystallized  from  METHODS / 74  charcoal  before  the hot  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  27  (2,2,3,3-H^ —palmitic  acid-d ) 27  (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:  CDCI3)  286(0.2), 285(3.5), 284(17.0), 283(M ,100), 282(8.5); H nmr (400 MHz, +  6: 1.57 ppm (t, J 3  J  = 7.0 Hz, 2H, - C D 9 - C H 9 - C H 9 ) , 2.30 ppm (t, J 3  2  3  7.0 Hz, 2H, -CH -CH2-COOH); mp 57.8-59.4°C 2  13  2  C hexadecanoic acid (1— C palmitic acid), 99.4 atom%  from  Merck  Sharp  and  Dohme,  Montreal  3  =  (uncorrected).  D. P R E P A R A T I O N OF 1- C - 2 , 2 - H " H E X A D E C A N O I C A C I D - D  1—  2  (MS-3124  hexadecanoic acid (1.08 g 0.00420 moles) was mixed  2 9  [155]  C was purchased lot 2269-J).  1 3  C  with 0.27 g 1 0 % Pd on  charcoal catalyst and deuterated as described in section HB. The yield was 0.90 g  (74.1%).  Mass  spec  and high  resolution  deuteration. * C hexadecanoic acid — d g 3  2  in 5 mL  nmr  showed  (0.20 g, 6 . 9 X 1 0  - 4  greater  than  97%  moles) was dissolved  of a 0.57M KOH/H 0 solution and this solution was pipetted into a 2  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 prevent foaming  carefully to  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 The  wrapped successively in heating tape, glass wool, and  reaction vessel was  temperature. The two  days and  heated and the pressure gauge was  reaction was  maintained at 245  four hours (52  hours). The  ampoule removed, wrapped in a clean dry mechanical shock with a hammer. The water. The  mixture was  ether. The  ether  which was  recrystallized from  yield was  0.16  was  acidified  removed by  cooled, the sealed glass  cloth and  the  and  removed and  extracted  rotary evaporation  dissolved in  thrice with diethyl  vacuum  repeated with 0.30  desiccator.  (400  g (82.7%).  QJi.b.petroleum ethendiethyl ethenglacial acetic acid, 70:30:2); ms  CDCI3) 6:  MHz,  COOH), residual proton (methyl), 1.20 1 3  C  nmr  ppm  (75.4  2.33  ppm  peaks due  (methylene), 1.27 MHz,  CDCI3)  6:  (d,  J  2  C  =  H  7.8  to incomplete ppm  Hz,  (methylene), 1.61  179.13  ppm  (t,  2H,  deuteration  2  J  C  ppm H  =  The  g of fatty acid  288(6.9), 287(31.2), 286(M + ,100), 285(73.3) 284(28.1), 283(6.4), 282(2.0); nmr  by  leaving a white powder  dried in a  g (80.6%). This procedure was  ampoule opened  at a slightly higher temperature (460 psi 240°C) with a yield of 0.25 Rf : 0.28  205°C) for  bomb was  HCl  hexane and  used to monitor the  psi (approximately  gel inside was  with  aluminum foil.  m/z: *H  -CD^CHgat: 0.87  ppm  (0 — methylene); 6.8  Hz,  2H,  -CH - COOH). 13  2  E. P R E P A R A T I O N OF  3.0  4 - (OCTYLOXY) - BENZOIC A C E D - D j  g of 4 —(octyloxy)—benzoic acid (p—octyloxybenzoic  from Frinton Laboratories, Vineland N.J., was 2 mL  D 0 2  with heating. The  mixture was  acid, p—OOBA), purchased  dissolved in 100  mL  hexane and  refluxed for one hour, the flask  was  MATERIALS cooled below the boiling point, the D 0 2  AND METHODS / 76  was drawn from  the bottom with a  Pasteur pipette and replaced with fresh D 0 . This process was repeated. Upon 2  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 C H A I N C A R B O X Y L I C 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 0 . The acid was recovered by acidification of the reaction 2  mixture followed by vacuum distillation. The extent of deuteration was determined to be 97.4% by H nmr. 1  ms m/z: 91(73.3), 90(M ,100), 89(58.9), 88(2.2), 75(1818.6), 62(7315.7). +  G. P R E P A R A T I O N 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/H 0 solution. The mixture 2  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.  MATERIALS AND H. S A M P L E  METHODS / 77  PREPARATION  1. SOAPS Soaps were weighed into an 8 mm with a constriction —1.5  cm  borosilicate glass tube sealed at one end and  from the bottom. Excess soap was  the walls of the tube with a cotton applicator. A  removed from  second constriction was  made  in the glass tube with a torch, being careful not to char the sample. (100%D) was  2  added to the surface of the soap with a Hamilton syringe in the  ratio 6.3 moles D20/mole soap. The tube was frozen  D 0  in liquid  nitrogen gas. The  nitrogen. The tube was  repeated four times. The constriction which  air was  removed  thawed and  a  dumbbell  and  replaced  with  0.5  the freeze—pump —thaw procedure  frozen tube was  produces  placed onto the vacuum line and atm was  then sealed by torch at the second  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 weighed  to ensure that no water  was  lost to evaporation. The  samples  was 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 tube or an 8 mm a narrow  (diameter) by 2 cm  nmr  tube attached to a ground glass joint by  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. D E U T E R O N  Deuteron power  NMR  nmr  experiments  pulsed  nmr  were performed  spectrometer  equipped  using a Bruker with  superconducting magnet. The deuteron resonance 90°  pulse  length  was  typically  a  4.7T  322 — s  Oxford  frequency was  usee. The  5— 9  BKR  instruments  30.7 MHz.  quadrupolar  high  echo  The  method  ( 9 0 — T — 90y—T —echo) [29] was used to avoid the effects of receiver  deadtime.  The  sequence:  x  pulses  were  xy, —xy,x—y, — x — y  cycled and  the  the computer  through  a  resulting  echoes  subtracted  from  2090 —HA  Digital oscilloscope and signal  Intel 8080 computer. Normally  4—pulse  memory. Echoes  phase  were were  cycling  alternately digitized  averaging was  added  with  accomplished  and  a Nicolet using an  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 interpolation technique based on a five point smoothing  —  rather an  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  imaginary  spectrometer channel was  reference phase  was  set so that  the signal  in the  essentially but not perfectly zero, hence the imaginary  MATERIALS AND METHODS / 79 data  were kept  and a quadrature  peak of the echo. Normally  Fourier transform  was performed  from the  a zero order phase correction of less than  needed to phase the frequency  10° was  spectrum. No first order phase correction was  applied.  2. P R O T O N  NMR  Proton nmr experiments were performed on a Bruker nmr  spectrometer  equipped  with  a  wide  bore  CXP — 4.7T  200 solid state  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  (CYCLOPS): x, —x,y, — y  cycled  through  in order  a  four  pulse  phase  cycling  to reduce the effects of pulse  and receiver  imperfections [156]. Adequate signal to noise could be obtained with 1000  less than  scans. The proton spin echo experiments were performed using the method  of Turner to  scheme  [32,108,157,158] and of Kumar [40-42,159]. A  generate  90° pulse was used  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 pulse sequence was repeated. Continued induction  decay  totally  devoid  T was incremented  incrementation of tau generates  of effects  due to chemical  and the a free  shift, heteronuclear  dipolar couplings, or magnet (H ) inhomogeneities. Generally 1024 increments of T Q  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  quadrature  to 4K  and  Fourier transformation.  Unfortunately, this method will generate additional peaks in the spectrum if the spin  system  is strongly  coupled or if the refocussing  homogeneous over the sample. The  pulse is not perfectly  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 H j 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  similar  manner,  double except  resonance that  the  echo 180°  experiments  were  refocussing  performed  pulse  was  in a 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 H—  induction  decay  depends  on  proton  homonuclear  C heteronuclear dipolar couplings and not on  chemical shift. The  probe used  H-  for these experiments  dipolar  couplings  and  H  dipolar couplings or  was  a standard Bruker  MATERIALS AND METHODS / 81 1  cross polarization probe doubly tuned to both proton signal was done through  I  H  and  q  C. Observation of the  the decoupling coil. To observe protons in this  fashion on the CXP-200, modifications to the spectrometer were necessary. In order to generate the spectrometer  1 3  C rf pulses at 50.3 MHz and H rf pulses at 200.0 MHz •I q 1 J  had to be set up like  a normal  C experiment  with  A  H  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 200  and 140 MHz  reference frequencies needed to observe protons at  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  data set, only one reduced  the  point in t  disk  space  2  than  was  needed  collect the complete two T  collected for each for  data  acquisition,  dimensional  value. This greatly allowing  overnight  spectrometer runs of many temperatures. Simultaneously, the data processing time is reduced dimension Fourier  —  the time needed to Fourier transform a IK  being  orders  Transform  a  of magnitude IK  X  128  less  than  point two  the  time  dimensional  data set in the t j it takes data  to  double  set. Since this  particular technique has never been applied to randomly oriented liquid crystalline systems, there was acronym  that  a temptation to christen the pulse sequence with some inane  nmr  spectroscopists are  temptation  has  instead —  referring to these experiments  or "the two  been  resisted,  and  the  so  fond  of  nomenclature  inventing. Happily of Turner  simply as "the spin echo  was  this  adopted  experiment",  dimensional spin echo experiment". The resulting spectra are termed  "the spin echo spectra" or "the spectra in the f j dimension". Since this is the only fancy pulse sequence used in this thesis, there should be no confusion.  3. C A R B O N 13  Carbon  13 nmr  using the  1 3  C  NMR  experiments  were executed  cross polarization probe.  on the CXP—200 nmr  spectrometer  The 13  C  pulse length ranged from 5 usee. The  pulses were cycled through the 4 phase cycling scheme mentioned  previously (CYCLOPS). The using on resonance duration.  3 to  proton decoupled  C  nmr  experiments  were done  broadband decoupling, with a decoupling pulse of 2.2 msec  MATERIALS AND Temperature  control for all nmr  experiments was  Bruker forced air flow device. Temperature  was  effected  METHODS / 83  using the standard  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  palmitate)  were  protonated)  and  protonated  species  potassium  synthesized: dgj (perdeuterated), 2,2,3,3—H^—d 7  (alpha  2  palmitates were dispersed in D 0  beta  hexadecanoate 1—  (potassium  C —2,2-H —d o, 2  protonated).  2  These  (alpha  potassium  in a lamellar liquid crystalline phase at a  2  constant  of  water concentration (6.3 moles D 0 2  /mole soap) and their  deuteron,  proton, and carbon 13 nmr spectra were recorded as a function of temperature. The (just  temperature ranged from 110°C (well into the lamellar L above  recorded  the L ~  liquid  a  crystal —gel  as a function of decreasing  phase  f l  phase) to 45°C  transition) and were  temperature. This  chapter  only  discusses the  results obtained, their interpretation and the results of the model calculation used to describe the head group behaviour in these systems.  A. D E U T E R O N  NMR  The deuteron quadrupolar  echo nmr spectrum of potassium  in Figure  quadrature  Fourier transform was used, and consists of a number of overlapping  doublets.  spectrum resonances potassium  The spectrum  of a soap  —  spectrum  2  presented  Pake  3.1. The  palmitate — dgj/D 0 is  is a  axially  is approximately  typical  symmetric  resolved. The deuteron  nmr  high with  temperature almost  all  spectra of the other  palmitate are similar. The alpha protonated  splitting (the largest quadrupolar  symmetric,  a  full  lamellar phase separate  deuteron  two species of  soap displays no alpha  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 i 3  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 [ 1 1 , 1 7 , 9 2 ] . Rather than simulate lineshapes with  the centre of the spectrum  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 resonances  order  was made  parameter, assuming  SQTJ,  by  equation  (1.29).  Assignment  that the quadrupolar splitting  of  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 0 2  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  temperatures  in the lamellar  temperatures  (just  above  as a  phase  the gel-liquid  function  are shown crystalline  of chain  position  for two  3.2.  At low  in Figure  phase transition) deuterons  2  Legend:  FIGURE 3.2 Order Parameter Profiles of Perdeuterated Potassium Palmitate  H  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  only occurs at the high water concentration end  temperatures  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  substituted The  same, there  minor  differences  between  the  different  palmitates. This is especially evident in Figure 3.4  differences  variations  are  could be  in water  the  result  of an  content, temperature  isotope effect, or  isotopically  (* C—2,2 — H ). 3  2  due  homogeneity, or sample  to small  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 use  of three  thermocouple,  copper and  constantan  homogeneity was  thermocouples  sample homogeneity was  separate  achieved by  from  assured by the the  regulating  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 /  Temperature  FIGURE 3.4 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 H Quadrupolar Splittings of 2,2,3,3-114 Potassium Palmitate—d2 7 2  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  Calbiochem—Behring the  d  3 1  and  samples  at  temperatures  supplied the palmitic and  2,2,3,3-H — d , 4  into  L  the  F L  phase.  myristic acids used to synthesize  Merck, Sharp  2 7  well  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.  PROTON  1  3  C - 2 , 2 - H  2  A N D  Representative  - P O T A S S I U M  C A R B O N  proton  single  labelled soap are presented broad  Pake doublets with  the deuterated heteronuclear C—H  13  PALMITATE-  D  2  9  N M R  pulse  and  spin  echo  in Figure 3.6. The  spectra  of the  carbon —13  single pulse spectra appear as  central peak(s) which arise from residual protons  hydrocarbon chain and  in the D 0. 2  dipolar couplings to the deuterons on  Broadening of the the  line  on by  alkyl chain masks the  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  symmetric nmr  spectrum with  dipolar couplings and  chemical  shift results in a  a single dipolar coupling DJJJJ, equal to 1/3 of  the measured splitting. Application of a  180°  pulse simultaneously  in the  *C 3  SOAPS / 93 FIGURE 3.6  IH Single Pulse nmr Spectrum of 1-130—2,2 —H2  -1—1—j—1—r  40000  30000  20000  1  1  I ' '  10000  -1—j—1—1—r-  0  A)Single Pulse. Temperature = 60°C, Delay = 5.0 sec. 300 Acquisitions.  -I—1—1—r  Potassium Palmitate —d29  1 1 1 1  -1—1—1—r  -10000 -20000 -30000 -40000  Hz  90° pulse length = 3 psec, Relaxation  B) Spin Echo (see next page) — no refocussing pulse. Temperature = 90° pulse length = 3 psec, T = 10 psec, Relaxation Delay = 0.5 sec, 8 Acquistions.  60°C,  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  I  1  15000  '  1  1  |  1  10000  1  1  1  5000  '  |  ' 0  '  '  • |  i  i  -5000  i  i  |  • i  -10000  i i -15000  Hz  B)Proton Spin Echo Spectrum without l^C refocussing pulse.  ~*  1  1  15000  OProton page.  1  |  1  1  10000  1  1  |  1  1  5000  1  —i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i— 0  -5000  -10000  -15000  Hz  Spin Echo Spectrum with 1&C refocussing pulse. For Legend see previous  SOAPS •I  channel 1  prevents refocussing  95  1  q  C— H  of the  /  dipolar  couplings (but not the  2  •"•H — d i p o l a r ( 2 D  C  H  + J  C  H  )  couplings) which  in Figure  appear  as  the  small  splitting  equal  to  3.6C.  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 C nucleus. High power decoupling of the protons removes the  pattern of the *H  1 C— 3  dipolar coupling leaving only this C S A  C S A pattern appears axially  The  symmetric  pattern behind (Figure  in nature, although the signal to  noise ratio is poor enough to obscure all but one peak is shifted  2 1 4 8 Hz  =  42.7  ppm  3.7B).  singularity  (°\\~ 22 a  ^'  >  n  s  downfield relative to isotropic benzene  (external reference) and it is estimated that the other singularity (033) appears at  2246  Hz  =  44.7  ppm  downfield from  OJJ.  The  shape  of the spectrum  remains constant throughout the temperature range studied. Not much has been placed  on  this result except that it demonstrates  carbon is in an axially symmetric  emphasis  that the carboxyl  anisotropic environment throughout the entire  lamellar phase. The disruption in the baseline at  5000  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  H— using  C double resonance experiments were performed on the standard Bruker cross polarization probe. No  necessary since the molecule was  a Bruker  and  the  CXP—200  cross polarization  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  10000  T  1 1 10000  1  1  j  1  1  1  1  5000  1—1  1 1 5000  1  J  1  1  1  0  1  1  1  1 0  1  J  1  1  1  1  1  -5000  1  1  1  r—j  -5000  1  1 1 1 1— - 1 0 0 0 0 Hz  1 1 1 r -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 enriched work the effect was in the probe was the Bruker  deadly. To circumvent this problem, the teflon block  replaced with a porcelain coil support originally supplied with  high power proton probe. While  immensely, the problem in  abundance or carbon—13  was  this reduced  the background signal  not entirely solved. The porcelain insert was  some sort of glaze to prevent  carbon. Mechanical abrasion was  chipping, a substance  rich  coated  in protons  and  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  remaining proton signal was  and  B. The  that a separate proton probe was spurious signal was The  temperature  necessary  evident in the *H  and  for single pulse experiments.  3.9. The  carbon —13  proton—proton  dipolar couplings are  dipolar couplings are the  average result of four measurements of the dipolar splittings, single and resonance  spin echoes performed  on  No  spin echo experiments using either probe.  dependence of the proton and  displayed in Figures 3.8  of sufficient magnitude  two  separate samples.  couplings follow a similar trend to that observed  by  Higgs  The and  double  proton dipolar Mackay [10],  rising with decreasing temperature, peaking at ~65°C and dropping off below this  SOAPS / 98 FIGURE 3.8 Temperature Dependence of i H 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  100  120  Temperoture (C)  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 temperature  at  coupling  which  no  was  deuteron  (40°C). These spectra were low couplings was DJJJJ  =  difficult. The  —1827 Hz  the corresponding below 40°C. The  and  measurable just quadrupolar  into the  echo  spectra  in signal to noise, and  estimated DQJJ =  gel phase were  at  a  obtainable  measurement of dipolar  dipolar couplings from these spectra give a  253  Hz.  These are considerably smaller than  liquid crystalline phase couplings. No  spectra were obtainable  spectra at 40°C probably represent the dipolar couplings in a 2  phase region near the transition. Both Higgs and Jeffrey [2] observed an increase in proton and  Mackay [10] and  Davis  and  deuteron couplings upon transition  into the gel phase.  Carbon—proton dipolar couplings are averaged over four sets of experiments, single pulse and The  H—  C double resonance spin echoes for each of two  * C — * H coupling constants  show almost no  3  implies that the average orientation of the change  appreciably  over  a  70°  C—  temperature  couplings  gyromagnetic measurement *H— *H  by  ratio  at and  is therefore  coupling.  least  a  factor of ~7  increased not  as  distance  3  samples.  temperature dependence which H  internuclear vector does not  range. Any  change  dipolar couplings would be reduced from the corresponding dipolar  *C  change in the *H — *H  times as between  sensitive to molecular  in l ^ Q — l p j  a  result  resonant  of reduced  nuclei.  orientation as  This is the  SOAPS / 101  2. CALCULATION OF THE ORDER M A T R K  From  the  three  measured  nmr  couplings  (the  1  H- H,  the  1  C-D  and  the  13 _ C  1  H),  the order matrix for the rigid alpha methylene  calculated.  The expression  (1.7). Since splitting  the  for the  amphiphiles  corresponds  to  the  dipolar couplings  are  dispersed  most  probable  has  been  randomly in orientation  group can now be given previously  D 2 O , the  relative  to  measured  the  bilayer  director (0 = 90°) and this expression is reduced by a factor of P2(cosp')= — i : -llLl_  T)  3  C  O  S  2  G  ~  (3-D  1  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:  J  The  =  l7l7 h 2  2 4TT  <  2  3cos f?-l  1 r  2  a> < 3 u  2  '  (3-2)  >  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  parameter  alpha position is  for the  References  [168,169]. Next, determined from  SQQ, the the  deuteron order  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 known to be of approximately  and C —D order parameters are  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 6  Z  =  125.55, P (cosl25.55) 2  bond parallel to the bilayer director 6  Z  =  0.007; for the first C - C  = 154.64 P (cosl51.64) = 0.662). If the 2  average value <P (cos0)> changed sign with temperature, then a spectrum 2  zero  dipolar  splitting  would  be observed  which  with  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 =S^=S =S^=0, x y  x z  S =SJJJJ X X  and the other  elements of the order matrix can be calculated using (1.11). Since the C-D  SOAPS / 103 FIGURE 3.10 Molecule Fixed Axis System for Potassium Palmitate  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# =0), SQD  is given by:  Z  2  SfJD  CD  =  S  H H  vector. This expression can element, S , =  CH  54.8  S y y C O S 35.2  +  S  be  (2.3)  y  +  0  fixed x axis and  rearranged to calculate Syy.  (3-4)  the C—D The  bond  off diagonal  of the order matrix is calculated similarly:  vz  S  cos  is the angle between the molecule  x  2 S y C O S <f) JJ C O S <P y  SyyCOS <Py +  +  X X  S  where #  2  S C O S ^jj  =  xx  2  0x  C O S  2  SyyCOS <f)y +  +  S  z z  2  cos  0  +  2  2S  COS0 COS0 y  z  (3.5)  therefore: S  The three  yz  =  t CH s  -  ( xx s  c o s 2  0  + S cos # y y  third diagonal element, S^, elements  determine  segment of potassium  + S c o s 0 ) ] / 2cos0 cos0  2  x  the  2  y  Z 2  is determined complete  palmitate. The  order  Mackay for 2 , 2 - H  2  potassium  matrix  is  lowered.  The  =  "(S^  for the  +  z  (3.6)  ^yy^ These  alpha  methylene  results are similar to those of Higgs  palmitate—d g, apparent 2  high temperature, with the absolute values of S Q T J temperature  zz  y  order matrix as a function of temperature  is presented in Figures 3 . 1 1 and 3 . 1 2 . The and  by S  z  value  of  S  v z  and S J Q J  remains  axial symmetry at decreasing as the  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 - C - 2 , 2 - H 2 Potassium Palmitate-d29 13  -0.35  Ul  -0.30  -  -0.25  -  -0.20  -  -0.15  40  60  80  100  Temperature  Legend: Measured Order Parameters: Calculated Order Parameters:  120  (C)  Q = Sxx S ^  ~ l ~ — S QQ  Q = Syy  SyZ  A =  S and SQD measured from the and %H spectra respectively. ScH be measured from both the and the 1$C spectra. The molecule fixed axis system has been presented in Figure 3.10. a r e  xx  c a n  SOAPS / 106 FIGURE 3.12 Temperature Dependence of S  z z  and S 3 3  0.60  0.55  -  ~ 0.50  0.45  0.40  -  40  60  80  100  120  Temperature (C) S : m = S z z 0 = S3 3 :;  S and S33 (diagonalized) for the a—methylene segment of l — ^C—2,2—H2 Potassium Palmitate—d29- Presented on the same figure to conserve space. 1  zz  SOAPS / 107 Syy  reached  a  minimum  experimental values of  and then and  SQT)  SJJJJ  increased  again. This  The  palmitate-2,2 — d  order matrix  instead of from the perdeuterated soap.  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.  only off diagonal element in the order matrix S^.  parameters S ^  order parameters from  was diagonalized and these results are displayed in Figures  3.12 and 3.13. Now  identically  their  cross each other at low temperatures. This  discrepancy could be due to their use of carbon-deuteron potassium  is because  No  special  and S  2 2  significance  is Sy , the value  is given  Z  to the fact  Since the for S-^j  is  that the order  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  DQJJ  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  DQJJ  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  -0.35  120  Temperature  Legend: CD — S -JI  CD —  (C)  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. the molecule  This implies that as the temperature is decreased  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 The  of the diagonal elements, S  value  of S j g ^ S j j  2 2  and  S33 (relative to S  remains unchanged. The  origin  of the  and  v v  S^).  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 plane), then the transformed no  (diagonal) order matrix  temperature dependence and  monotonically remaining different  with  curve  decreasing  in the  source. It still  the curves  temperature.  order makes  parameters no  logical  S  2 2  overall rotation in the yz (Figure 3.13)  and  S33  This is clearly S  2 2  and  sense  S33  should display  should now not must  the  increase case.  arise  to postulate a  The  from  decrease  a 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 intergroup dipolar couplings would  modelling scheme. Some knowledge of the  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 -POTASSIUM 4  1. P R O T O N  deuteron spectra single  in D 0 2  pulse  palmitate—d  (alpha beta  27  at a concentration  quadrupolar were  2 ?  NMR  2,2,3,3 — H4 — potassium dispersed  PALMITATE-D  recorded spectrum  echo, the proton  palmitate, a/3 palmitate) was  of 6.3 moles water/moles soap and the single pulse, and the proton  as a function of temperature. A is presented  in Figure  spin echo  representative proton  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 f j 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 l H 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  | 1111| 111' | 1111| 1111I 1111I 1111I 1111I 111 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 about  the  central  resonance  frequency,  lines. This  but  spectrum  the  was  spectra retain their symmetry  transitions  simulated  now  using  LEQUOR previously discussed in the Introduction and  appear  the  as  modified  individual version of  the simulated spectrum is  shown in Figure 3.15D. This simulation is for a refocussing pulse of 166°. total of nine lines were fitted to half of the symmetric experimental and  the RMS  error of this was  resolution of 50  69.0  A  spectrum  Hz, just outside the experimental  digital  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 of the  large central  peak  were  appear  in  echo  spectra,  the  spin  not  assigned and  two  peaks just on the outside  either. These  along  with  the  lines consistently central  peak,  are  inhomogeneous H j artifacts.  The  temperature dependence of the dipolar splittings and  presented graphically in Figure 3.16  and 3.17  dipolar couplings are  and the calculated dipolar couplings  are given in Table 3.1. There are several points to note. Close examination the  dipolar couplings  reveal  a  similar  characteristic rise and fall, as was of the other isotopes of potassium  type  observed  of temperature  in the deuteron  palmitate. The  of  dependence, the  and  proton spectra  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:  _)  ,  0.0  S.O  , 10.0  , 1S.0  ,  1  20.0  25.0  FREQUENCY (KHZ)  ,  30.0  ,  35.0  ,  40.0  ,  45.0  —1  50.0  C) The depaked spectrum is calculated for 0° orientation, therefore frequencies are out by a factor of 2. D) Calculated: D22 = -2794 Hz, D 3 = -691 Hz, D23' = -228 Hz, 1*33 = —2120 Hz, RMS Error = 69.0 Hz, 166° refocussing pulse, Lorentzian linewidth - 50 Hz. 2  SOAPS / 115 FIGURE 3.16 Temperature Dependence of the Dipolar Splittings of 2,2,3,3-rU Potassium Palmitate-d2 7  12  1H  -B  B  B  B  B-  B  B  B-^j  -B  10 •  9H  B—fl  B  B  8  B  Br -B~  B~  -fi g B ~ -B-—B  B B B—  •fl  7 6B  5 B--  Q  40  6  B  B  B  B  B  B  60  B  B  B  B  B  B  B  B  B  B  B  B  80  B  B  B  B  B  B  100  B  B  120  Temperature (C)  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 T A B L E 3.1 Calculated Dipolar Couplings for 2,2,3,3-H4- Potassium Palmitate-d27  DIPOLAR COUPLINGS(Hz) TEMP(°C)  45 50 55 60 65 70 75 80 85 90 95 100 105 110  D  )  D (Dpp)  -2822136 -2842±62 -2878142 -2794146 -2811134 -2783142 -2780136 -2755141 -2758136 -2718134 -2710137 -2703140 -2671143 -2610144  -2082133 -2108156 -2108138 -2120146 -2094131 -2064138 -2067133 -2056138 -2042133 -2028136 -2026134 -2001136 -1974139 -1964145  2 2  (D  a a  3 3  D ,(D p,) 2 3  a  -242131 -288156 -237135 -228134 -231126 -231132 -232127 -226131 -217127 -231130 -246128 -215130 -223131 -224135  TOTAL D  2 3  ( D p ) RMS a  -628138 -608169 -666143 -691143 -689133 -693140 -702135 -705138 -716134 -697135 -688135 -718137 -712139 -710144  ERROR(Hz)  57.6 96.6 66.3 69.0 51.5 64.1 54.8 62.2 55.0 62.2 54.7 60.5 63.9 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 pronounced  in the  carbon—13  labelled  temperatures,  however, is more  compound. These  discrepancies are  attributed to differences between samples. The dipolar coupling constants obtained from  the simulation are all of the same  previous  section on the carbon—13  sign and by comparison  labelled  soap, must  with the  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  6%).  protons  have the next  the alpha  coupling by  The beta  reduced  from  equivalent deuterons from  to the corresponding in the deuteron  increased motional  soaps (the difference is about  largest dipolar coupling, this value is a factor  reduction  of about  observed  1.4, almost  between  alpha  exactly  and beta  spectra. The increased orientational averaging  arises  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  C~ a  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 $>,  a larger coupling will  ]  result for the a/3 protons than the ap" unless the average orientation of the a/3 protons is such that it is reduced by a smaller value of the order parameter, S  ij-  SOAPS / 119 Interpretation of these dipolar couplings is more difficult than case. The first temptation is to proceed as before —  in the previous  intelligently choose an axis  system, determine the order matrix in this axis system, and diagonalize to obtain rotation angles of the matrix. If the a$  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  conformational motion about the C freedom  removes the plane  f l  —bond.  of symmetry  treating orientational order in non  —  there is considerable  In addition, this conformational  of the two  groups. The  problem of  rigid molecules is not as simple as for rigid  ones [170-173].  A  second  segments  approach of  couplings. The presented  the  would  molecule  be  to  using  calculate the  separate  proton,  order  deuteron  matrices  and  for both  carbon—13  nmr  analysis for the alpha segment would be similar to the calculation  previously. For  the  beta  segment,  at  least  3  independent  order  parameters would need to be specified assuming a plane of symmetry bisecting the HCH SQ-Q^. An  segment. From the present data only two  separated.  resonance,  and  alternate element to the beta order matrix could be obtained from the  intermethylene group couplings if the time average be  are available, Spjpj^  For  non  rigid  segments,  this  is  of S j j / r j j > <  3  impossible  m t e r  g  using  r 0 U  p could magnetic  unless the exchange rate is slow relative to the dipolar interaction  (T <<l/27rDij). ex  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~  +  at the a/3  conformation  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  each other, and  and  +  g~  conformers are mirror images of  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. order matrix for each conformation consists of the sum  The  of the order matrices in  the fixed axis system of each conformation  weighted by  conformation. If the probability of g~*~ and  g~  the probability of that  conformers are the same, this  adds one more unknown to the problem (P , Pg±) bringing the total to 9. From t  nmr  measurements, a total of seven experimental quantities are available —  C— H  coupling, four  H  couplings. Hence this is an  dipolar  couplings  underdetermined  and  two  problem  —  deuteron  additional  problem  is that the  conformer  order  quadrupolar  more unknowns than  equations, so the elements of the order matrix cannot be determined An  one  parameter  analytically.  can  never  be  separated from their probabilities:  S  = I  PiSi  =  P S t  t  + P  g  +  S  g  +  + P _S _ g  g  =  P S t  Instead some sort of modelling scheme must be used and parameters fit to the experimental  number of adjustable parameters, certainly  would  preferable, and  the  + 2P S g  (3.7)  g  the calculated order  data. Hopefully, the model will contain a  minimum be  t  no  more than  adjustable parameters should  be  two,  related  one  to the  SOAPS / 121 physical forces acting on the palmitate molecules.  D. T H E INERTIAL F R A M E  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  condition  about  their  is met. A  centres of mass to a position  diagonal order  matrix  in which  is calculated  from  the above  the principal  moments of inertia. The molecule is placed in a cylinder of variable radius, r yj, C  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  moment of inertia of a particular conformation  —  affects the  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  interactions at lower  nmr  couplings. Therefore  temperatures  the increased  are modelled  hydrogen  bonded  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  parameterization  with  special  emphasis  of potassium  on the details  of the calculation, the  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 program  calculates dipolar couplings from  SHAPE  [175]. The original  SHAPE  a set of Cartesian coordinates and  performs the least squares and iterative part of the calculation to minimize the RMS  error  between  experimental  modifications made to the SHAPE  and  calculated  program  nmr  couplings. The  initial  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  subroutine  the coordinate transformation into the PMI  must  set up  the  conformer order matrix, and palmitate  molecule  required number  of conformations,  calculate the internal and  in the mean  frame. The  field. It was  additional  calculate  the  external energies of the  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  (RIS) model is used, three rotational states (t, g , +  rotational isomeric state  and g  —  0, 112.5°, —112.5° respectively) are allowed about each C—C states are assigned arbitrary potential energies of t = —  1.67  kJ/mole. These values and  with dihedral angles bond. These three  0 kJ/mole and g~^  =  g~  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  states per C—C  bond, the number of internal rotations soon becomes prohibitively  high. Ignoring rotations about the H O O C — C H no effect on the nmr C —C g g +  2  and  CH2 CH3 -  couplings of interest, potassium  bonds for which there are 3 — 1 . 5 9 —  RIS  rotational isomers is taken into account except for the all trans —  palmitate has  million RIS  conformers are assigned a zero probability and —every  bonds, which have 13 flexible  states. If high energy if the symmetry of the  conformer has  a mirror image  the number of conformers drops to ~55,000. This is  SOAPS / 124 T A B L E 3.2 THE IF MODEL The Parameterization of Potassium Palmitate  INTERNAL POTENTIAL  EXTERNAL POTENTIAL LENNARD-J0NES PARAMETERS  dihedral angles 4>t 0° • g+,<t>g112.5°  A(kJ/mol) B(kJ/mol)  conformational energy E ( t ) (kJ/mole) 0.00 E(g )=E(g") 1.67 E(g g") infinity  TRUNCATION PARAMETERS regular 7 number of carbons  GEOMETRIC PARAMETERS  number of f l e x i b l e CC bonds  +  +  bond lengths (A) 1.53 1.00 1.24 1.095  CD C0 CH  r : :  bond angles (degrees) <CCC 112.50 <CCH 108.82 <0CC 120.00  8.309*lo!? -4.724*10 3  extended 9  7  5  number of conformers  50  288  chain mass(amu)  64  64  HG mass(amu)  500  500  tot mass(amu)  704  704  ADJUSTABLE PARAMETERS r r  still  too many  to do  a  cyl HG  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  deuterated methylene  amu  groups. Test calculations in which  —  the mass of 4  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/r (1.70). 3  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. A referred  direction  of the rod  mass of 500  amu  to as TJJQ, a head  is coincident with  is affixed  group  the first  C —C  bond  to the rod. This distance will be  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 bonus,  this  modelling  C—C  scheme  bond is more parallel to the director. As preserves  the  symmetry  of  mirror  a  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 o 0) = I -— J  C  1  (3  M  m  where m^ is the mass of the i  t  n  -  8)  tot  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^^'  anc  *  t n e  moment of inertia tensor determined by:  l*fi = 1  where  the sum  is over  m  all atoms  i fia r „  in the molecule,  (3-9)  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 FIGURE  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  diagonalized. This frame, within the scope of the IF model, also diagonalizes  is 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  away  is  calculated  as  a  between methylene  groups greater  Lennard—Jones 6—12  parameters". [6—9,177] For two methylene  (CD ) 2  potential  than 4 carbons  using  "united  atom  groups the non—bonded energy  is calculated from the following expression:  " NB ~~  where  A = 8.309X10  6  kJ/mole  and  A  r  12  + — «  r  (8.11,  6  B=-4.724X10  3  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 j . The constrained molecule in its cylindrical cage is presented, in Figure 3.18. c y  The  cylinder simulates the steric repulsion or excluded volume forces primarily  responsible  for the  thought of as each  orientational behaviour of these molecules.  a mean field of methylene  carbon atom  and the  Lennard-Jones 6—12  groups and the  nearest point on the  cylinder  The cylinder is  interaction between is  calculated  as  a  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 e  conformer which exceeds this 2.0  A  limit is assigned zero probability. The  any choice  e  of 2.0 A [140,  is arbitrary and  144].  Gelbart picks  is based on similar calculations done by Gelbart et a  number of initial  amphiphiles in his calculations and  orientations  at random  for  al. the  allows the position of the head group to vary  o  up  to 1.5  When  the  A  at random in the direction parallel to the direction of the phase.  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 the  that the  various contributions  total potential of the  to the potential energy have been  conformers is calculated  contributions, the internal, the non—bonded and  as  the  sum  included,  of the  three  the cylinder potential (1.64). The  statistical weight of each conformation is the Boltzmann factor of the potential, the  partition function  (1.49) and  is calculated  as  the  sum  the conformer probability is defined  by the partition function (1.50).  of the as the  Boltzmann exponentials statistical weight divided  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  individual couplings are summed  conformer  probability  and then the  over all conformations. All splittings are then  scaled to one experimental splitting, chosen in imitation of Samulski to be the a — CD 2  deuteron  squares  procedure  quadrupolar is used  splitting  and compared  to calculate  a weighted  difference in each set of couplings is weighted  to experiment.  RMS  A  least  error. The squared  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  down  than  position  important, quadrupolar 4 were  splittings  given zero weight  from  methylenes  in the error  farther  calculation. The  program is run iteratively, allowing the two adjustable parameters r yj and TJJQ C  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 T H E IF C A L C U L A T I O N  1. SIMULATION  A  plot  OF E X P E R I M E N T A L  of experimental  temperature  is displayed  NUMBERS  and calculated  dipolar  couplings as a  in Figure 3.19 and in Table  function of  3.3. Considering the  SOAPS / 131 FIGURE 3.19 The IF Model: Calculated and Experimental Dipolar Couplings  fl  N  I  D  •  g  D  Q-  D TJ—0—•—o—D—D—•—13—0—6—6 D  CH  D  "  D  D  0  D  D  D  O^D  D  O  D  o  D  D  D  D  , 23  D D D D D D D D  23  -1 -  c  a n L.  -2 -  o a  0  •  0  D •  D  D •  •  •  •  D D  •  D  D  D  D  -  32  D 2  2  -3 -  -4  i 60  40  r  1  1  80  100  120  Temperature (C)  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 _l (a) c  D TEMP('C) 45 50 55 60 65 70 75 80 85 90 95 100 105 110  1 _1  H  H  D (D )  CH  2 3  D 3'< aP'> D  a p  2  H  >> (D ) 22  aa  ^ ^ p )  EXPT  CALC  EXPT  CALC  EXPT  CALC  EXPT  CALC  EXPT  CALC  256 254 259 252 251 241 243 242 250 242 239 237 233 211  317 314 314 307 307 305 308 307 309 305 305 307 304 300  -628 -608 -666 -691 -689 -693 -702 -705 -716 -697 -688 -718 -712 -710  -670 -642 -632 -604 -596 -587 -595 -591 -597 -582 -581 -589 -580 -567  -242 -288 -237 -228 -231 -231 -232 -226 -217 -231 -246 -215 -223 -224  -471 -479 -488 -485 -486 -484 -487 -485 -488 -483 -481 -483 -480 -474  -2822 -2842 -2878 -2794 -2811 -2783 -2780 -2755 -2758 -2718 -2710 -2703 -2671 -2610  -2618 -2762 -2879 -2936 -2968 -2969 -2964 -2959 -2955 -2942 -2931 -2917 -2904 -2885  -2082 -2108 -2108 -2120 -2094 -2064 -2067 -2056 -2042 -2028 -2026 -2001 -1974 -1964  -1787 -1814 -1870 -1893 -1898 -1886 -1881 -1870 -1863 -1838 -1826 -1822 -1804 -1781  CALC  EXPT  13915 14677 15820 16719 17027 17101 17091 17142 17097 17043 17038 17038 16998 16968  20875 21361 21851 22049 22124 21729 21410 21313 20996 20752 20459 20068 19922 19742  RMS ERROR 186 177 188 203 202 205 205 209 209 209 204 210 209 217  QUADRUPOLAR COUPLINGS(Hz) ) (c  CARBON 2 TEMP("C) EXPT 45 50 55 60 65 70 75 80 85 90 95 100 105 110 (a) (b) (c)  28668 30859 32495 33460 33923 33984 33859 33819 33704 33643 33496 33252 33130 32975  CALC  EXPT  28868 30859 32495 33460 33923 33984 33859 33819 33704 33643 33496 33252 33130 32975  21802 22901 23951 24536 24756 24698 24585 24488 24365 24170 24023 23877 23706 23502  3 CALC  EXPT  21710 22731 23749 24324 24527 24458 24356 24261 24143 23943 23803 23670 23496 23294  22438 23697 24814 25429 25699 25643 25509 25409 25268 25092 24935 24573 24581 2485  4  CALC  EXPT  21802 22901 23951 24536 24756 24698 24858 24488 24365 24170 24023 23877 23706 23502"  20875 21362 21851 22049 22144 21729 21729 21485 21069 20752 20459 20068 20288 20117  5  6  CALC 12291 12883 13853 14606 14873 14940 14954 15007 14989 14937 14946 14971 14940 14914  7 EXPT 19238 19727 19800 19654 19434 19092 18774 18457 18262 17871 17725 17383 17213 17009  These numbers have been scaled so that the D dipolar couplings of the two species match. The error In the experimental dipolar couplings have previously been reported In Table 3 . 1 . Quadrupolar couplings are from the perdeuterated potassium palmitate. The estimated experimental error In the deuteron couplings ls less than 5%. 2 2  CALC 5642 6632 7486 8214 8467 8542 8459 8490 8387 8459 8424 8297 8310 8360  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 D23,  D23'  show the appropriate trends: the  and  lower temperatures.  D33  The  dipolar couplings and the  temperature range  intragroup couplings demonstrate the rise and fall at  error in the experimental  couplings, generally less than  Hz, would fall almost inside the size of the points. Given a ~50  error in the spectral simulation and an up to 10% the  H  intergroup couplings show little change over  whereas the D22  100  C—  deuteron  well. The  order  parameters at low  Hz  RMS  deviation between samples in  temperatures,  these  calculated alpha couplings are too large and  numbers fit rather  the beta  couplings too  small possibly implying that in the model calculation, the restriction on the head the amount of freedom about the C2  group is somewhat too stringent and linkage too liberal. The  intergroup couplings are out by  these  not  couplings  depend  only  on  the  angular  almost 25%.  excursions  of the  —  C3  However, palmitate  molecule, but on the time averaged distance between the intermethylene  protons.  Therefore  angular  these  numbers  are  especially  sensitive  to  some  of  the  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 since there is no  couplings is correct,  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 the distance between the a  of rotational isomers could be imagined in which  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  assignments of these two couplings are switched show an increase in RMS  the  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  1  i  3  i  i  1  5  r  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.  SOAPS  crystals [ 1 7 8 — 1 8 1 ] and  /  137  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 r yj and C  TJJQ,  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) is shown for comparison. The values for the adjustable parameters are r y[ = 6.43A, and r^Q = 3.82A g  C  SOAPS / 139 FIGURE 3.23 The IF Model: Effect of Increasing The Chain Length on The Calculated Quadrupolar Coupling Profile 40  /-s N I  ~  - i  —  35-  30-  0 -|  1  1  1  1  3  1  1  5  1  1  7  r 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 (r yj) and the length of the head group interaction parameter  The cylinder  (F^Q).  C  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 r yj over the temperature range is 1.5% (0.7% not C  including the lowest temperature point), whereas  TJJQ  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 r yj, remain constant C  throughout the entire lamellar phase region studied, becoming more important at temperatures just before the phase transition.  SOAPS / 141  FIGURE 3.24  The  I F Model: Variation  of Cylinder Radius with Temperature  6.2 - i  •  6.1 -  6-  5.8 -  5.7 -  5.6 -j 40  1  1  60  1  1  80  1  1  100  1  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 The  IF  Model:  Variation  of  FIGURE 3.25 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 T A B L E 3.4 THE IF MODEL Variation of Adjustable Parameters with Temperature  TEMP(°C)  r  H G  (A)  r  c y l  (A)  45 50  3.55  5.85  3.20  5.94  55 60 65 70  2.98  5.94  2.79  5.94  2.74  5.94  2.72  5.94  75 80 85 90 95 100 105 110  2.75  5.93  2.73  5.93  2.76  5.92  2.74  5.93  2.74  5.92  2.76  5.90  2.74  5.90  2.71  5.90  Is the drop in r i at 45°C significant? It is hard to tell with certainty. There c y  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 r yj is to be C  believed, it is possible that there is an increase in overall steric effects just before  the  phase  transition  not  necessarily  directly  associated  separation. However, it is possibly a computational aberration. A  with  phase  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 r  HG  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 T j 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  temperatures  the preferential  increase in activation  energies  at decreased  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 T j 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), r yj is calculated to range from 4.8 C  e  to 5.1 A [8]; for octanoic acid (lwt%) in Merck Phase V, r yj is reported as C  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  characteristic increased  value  which  gives  the calculated a — C D  relative to the other  2  splitting its  quadrupolar splittings. This o  behaviour is unique to the soaps [2, 21, 57, 75] — nmr  studies of other  amphiphiles  it is not observed in  H  [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  which  methyl  octanoate  [9,184], solutes  dissolved in Merck phase V  cannot  form  H—bonded  dimers,  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 i and c v  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 deterrnining  head  group  would suspect that H—bonding  orientation  presumably the calculation of  TJJQ  at  is important in  all temperatures —  if it wasn't,  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 Similarly  for the  cylinder  radius  —  the  model only  constraints remain constant as a function of temperature.  this calculation.  shows  that packing  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 * C — *H 3  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 deuteronfitat 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 -| 0.00  1  1  0.20  1  1  1  0.40 Head G r o u p M o s s  1  0.60  1  1  0.80  1  1.00  (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 (A)  1000 500 A 00 300 200 100 75 50  2.59 2.71 2.78 2.88 3.07 3.61 3.93 4.53  HG  r  c y l  (A)  5.91 5.90 5.90 5.89 5.87 5.83 5.81 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  systems are coincident to within a degree! The  axis  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  publication Counsell et al. between the  [191] conclude that "there is no  components of the  sound relationship  inertial tensor, which is a  single molecule  property, and  those of the ordering matrix which is determined by  intermolecular  interactions". This  concept is supported by  a  in a later  anisotropic  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 [191]  interactions referred to in reference  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  What  COUNTER IONS  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 0 deuteron couplings with temperature parallel those of the 2  a—methylene  segments. This has been observed before in H 2  sodium palmitate/I^O [21,116] and of potassium palmitate D 0 2  nmr spectra of [2, 3]. In fact  the ^ Na spectrum in sodium palmitate also demonstrates this behaviour. Hence 3  there is a definite correlation between the amphiphile and solvent. The small value of the quadrupolar splitting in D 0 demonstrates that the water molecules 2  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 0 order 2  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 0  and  2  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  Can  the  calculated  nmr  ALPHA METHYLENE ORDER MATRIX  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—H — potassium 2  results of this calculation are shown in Figure 3.28 calculated elements of the order matrix now  and  palmitate. The  Figure 3.29.  The  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=Syy  A=Syz  +=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 Sy , the least accurately measured coupling. Z  SOAPS / 156  FIGURE 3.29  Recalculation of the Diagonalized a-Methylene Order Matrix from the IF Calculation  -0.35  120 Temperature Sij:  •=S  1  1  (C)  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 symmetry  of  related conformers, doubles the  bond. This destroys 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  How  CALCULATION  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 degeneracy, however an  internal probability could be  with a  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 conformers (for example 4).  a certain number of gauche  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 couplings  only be  at each  used  to calculate  temperature,  the relative dipolar  the numbers  must  then  be  and  quadrupolar  scaled  to an  experimental coupling. This makes calculation of thermodynamic functions from the partition  function  meaningless.  In  order  to  improve  the  intermolecular potential must be stated explicitly as the sum  calculation,  the  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  disadvantage  based  on  a  Hooke's  Law  force  constant.  An  immediate  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^, 3 —H^—potassium  1—  C —2,  2—potassium  palmitate — d .  The proton,  27  palmitate—d g 2  carbon—13  and  2, 2, 3,  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 * C spins allowed 3  observation of the *H13  C  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  individual order parameters  lamellar  The  splittings in the  perdeuterated and carbon 13 labelled soap. The a—methylene  segment is shown  at any  from  determined.  the nmr  to be not axially symmetric  were calculated  phase was  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 calculated only two  independent elements of the order matrix. The  plane,  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 Two  interface of potassium palmitate.  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  C—  1  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  temperature range  65° — 45°C. This is in agreement with  proposed by Abdollal et al.  and  then increased by  in which an  ~30% an  over the  earlier model  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  The  soap —water  CLEANLINESS AND  systems,  although  REPRODUCIBILITY  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" sample preparation techniques  and  [2], "these differences may  be due to  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 * C labelled fatty acid which was purchased from Merck 3  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 0 is 2  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  consistent manner. Since hysteresis may transition, experiments were always  experiments were performed  in a  be a factor, especially near the phase  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 data acquisition was  begun. The spectrum was  spectrum was observed before collected, the temperature  decremented and the samples allowed to equilibrate at the new one hour before data acquisition was  begun again. An  was  temperature for  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  hours/temperature. As  echo  spectra  ranged  from  5 — 12  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 between two  samples  1 3  C  from two  labelled soap, the splittings were reproducible 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—H ~ samples. 4  1^  The differences are most obvious in the  C —2,2—H  2  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  SOAPS  then adjusted to coincide with the low  temperatures  isotopes was  1 *3  C —2,2 — H 2  /  167  values. Interestingly enough, at  this scaling worked rather well, the best fit for all three  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  consequently  little change in Syy. S ^ ,  which is determined  a—methylene dipolar splitting in the ^C — 2,2 — H  2  and  solely from the  sample, remained unchanged.  In the scaled diagonalized order matrix, in comparison to Figure 3.13, S J J and S 2 2  than  no longer crossed, in fact the general trend is for S 2 2 to increase, rather 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 due entirely to differences between samples. It s  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  thermotropic  shape characteristic of many  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 crystal, which leads to a large molecular  the long axis of the liquid  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  temperatures  on  difficulties. These commercial  nmr  difficulties  spectrometers,  include and  maintenance of high temperature  gradients  incurred using commercial temperature regulation devices.  The  series of short chain acids, acetic, propionic, and butyric —2,2—d  2  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 / 1 7 0 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 B n  All  solutes  contain  a  methyl  m  referring to the number of equivalent nuclei.  group, and  the  description  of spin  systems  consistently refers to the methyl group as A 3 .  A. ACETIC ACID  The  H  single pulse acetic acid spectrum is shown in Figure 4 . 1 . Acetic  nmr  acid is an A 3 spin system. The a  triplet  with " a  dipolar  three protons in the methyl group give rise to  splitting  of  3DJQJ  =  D^A  corresponding to a dipolar coupling constant of group possesses C 3 orientation  of the  parameter, S^,  V  =  = 5555  methyl group using a  Hz. The methyl  single order parameter. The  can easily be calculated using  order  For an interproton distance  (1.9).  o  of 1.78 A calculated assuming a C—H  is S ^  Hz  symmetry and this symmetry allows the description of the  o  angle of  16665 ± 3 6  109.5°  =  [202],  bond length of 1.09 A and a HCH  the order parameter for the methyl group of acetic acid  -0.2609±0.0006  (see Table  matrix are easily determined as S  xx  =  4.1).  Syy  The  liquid crystals with no specific intermolecular  parameters  ranging of  from  1691  0.0794 —0.1254  — 2669  Hz  respectively.  other elements of the order  and S  order matrix is traceless. In a previous study  constants  bond  M  [203],  =  -(S^+Syy) since the acetic acid dissolved in  interactions yielded dipolar coupling which The  would  correspond  additional  to  order  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  DIPOLAR COUPLINGS(Hz)  DAA <> a  D  BB  AB  acetic acid  5555112  propionic acid (single pulse)  -561±3  561913  75412  propionic acid (spin echo)  -53113  546214  71913  butyric acid-2,2-d2  204015  1581112  -71616  ORDER PARAMETERS yy  xx -0.260910.0006  -0.260910.0006  zz 0.521910.0011  propionic acid (single pulse)  -0.263810.0001  -0.219910.0004  0.483710.0005  -0.144510.0005  propionic acid (spin echo)  -0.256410.0002  -0.212410.0003  0.468810.0005  -0.137610.0008  Sll  S22  S33  ROTATION ANGLE (b)  acetic acid  -0.260910.0006  -0.260910.0006  0.521910.0011  —  propionic acid (single pulse)  -0.263810.0001  -0.2509+0.0008  0.514710.0007  11.1710.05  propionic acid (spin echo)  -0.256410.0002  -0.239110.0010  0.495510.0008  11.0010.07  acetic acid  (a)  yz  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 s l , z z  by definition. This also uniquely  determines the sign of D J J J J to be positive.  The  * F nmj- spectrum of 15 mole% trifluoroacetic acid in p —OOBA has been 9  measured by Dunn [204]. At 105°C, the F 1 9  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  temperature was lowered the value of S  zz  also found  that as the  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 temperature  range  to be 0.33. p—BOB A  of the nematic  phase. No  direct  was used to lower the 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 20000  10000  "I  1 1 1 1 0  1  1 1 1 1 1 1 1 -10000  j  11  -20000  -  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 2 0 0 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 / FIGURE 4.3 ! H nmr Spectrum of 11 mole % Propionic Acid in p - O O B A  l  JLJJL_JJUUJ JLIU i  20000  i  i  i  |  i  i  15000  i  i  |  i  10000  i  i  i  |  i  i  i  i  5000  | i '  '  0  -5000  '  |  •  '  i i *" -10000 -15000 -20000 i t  1  1  1  1  1  1  1  Hz  A) Experimental: Temperature=U0°C 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. t  176  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  methylene protons and the spin echo spectrum  between methyl and  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 H j 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 J A J 3 3  =  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 —Co 9  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 !•  15000  10000  -r—i—I—T"  5000  i-i—i—r  T—r  -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  Tetrahedral geometry was  results  are  assumed for all HCH,  presented in Table  HCC,  and CCC  bond angles.  o  o  Bond lengths were taken to be 1.09 A for a C-H C—C  4.1.  bond and 1.54 A for a  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 — C2 — 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 S , S^, zz  values  are S  B  =  0.4837(0.4688),  -0.1445(-0.1376). Note that S 0  and  therefore Syy  =  S  n  =  and S . yz  Their calculated  -0.2638(-0.2564) and  S  yz  is uniquely determined since S^+Syy + S^  y y  -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  S <0.5. By comparison with acetic acid, S^ is zz  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 elements  from of  the  the  -0.2638(-0.2564)  eigenvector  order S  matrix =  22  Diagonalization pushes one uniquely determines  (also  diagonalization process. The given  -0.2509(-0.2391)  in and  Table S33  of the order parameters over  its sign. The  plane calculated from  of the  4.1) =  are  diagonal S^  =  0.5147(0.4955).  the 0.5  limit  and  average rotation of the molecule in the yz  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  The analysis of the nmr  2  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 / 1 8 2 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  TJJ^D  times in the partially deuterated analog. While initially, the reduced couplings may  =  ^-51  deuteron  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  concentration a  acid — 2 , 2 — d  11 mole %  2  dissolved  in p —OOBA  is shown in Figure 4.6. The  at  110°C  spectrum  at  a  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 - O O B A  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—d Figure 4.7. This is now,  effectively, the proton nmr  2  in p —OOBA is shown in spectrum  of a five spin  system AgB , and is much simpler in nature than the corresponding one pulse 2  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^^ D^g  =  —716  Hz with an RMS  = 2040 Hz, Dgg  =  1581 Hz,  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—d purposely  inhomogeneous refocussing pulse. The  experimental spectra 4.7 A  and  4.8A  2  in p—OOBA with a  difference  is that the first was  between  the  two  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  be  can  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 - O O B A  V U -T—i  1—t—r 10000  -1  j—1—1—1—r  5000  -1  1  1  r—1 1  -5000  1  1  1  1  1  r*  -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 l H 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  10000  5000  r—i—'—i  0  —  r — | — i — r  I  -5000  r  |  i  -10000  r  -  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 =  refocussing pulse, Lorentzian linewidth = 50 Hz.  1906  Hz.  146"  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—d consists of 2  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  approximation is used, there are only 3 conformations to butyric acid — g  and  +  g  related  —  by  rotations about the  C2 Cg —  bond. For  conformer, which has a plane of symmetry bisecting the HCH  the t,  the trans  plane, the number  of independent elements in the order matrix is reduced to 3. For the g g  RIS  +  and  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 be  +  = Pg ) parameters are needed. The conformer order parameters can never -  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 assumption  palmitate. In that section, the additional  of ignoring conformational  necessary. From nmr  motions  at  other  C —C  bonds  was  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 (r j) and the head group rod length (rpjrj) cy  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  fiB  = 1581(1581) Hz, D =-884(-716), and 0^=2034(2040) Hz AB  numbers are scaled to the experimental coupling Dgg,  and  where the  the numbers in  brackets are the experimental numbers. This calculation gave a cylinder radius of o  r l=4.96 cy  A  o a  nea(  * S * "? interaction length of 11.19 A with 133 Hz 1  0  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  reasonable  dipolar couplings that are much too high. No  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 — Cg 2  bond, this could be  palmitic acid and potassium  where the discrepancy  lies. In the analysis of  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—d couplings available from the  C  spectra may  2  acids. In addition, the extra 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 192  2  groups  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 F I G U R E 5.2 Temperature Dependence of the 2H nmr Quadrupolar Splittings in Palmitic Acid  80  0  H  75  1  1  85  1  1  95  1  1  105  1  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  quadrupolar splittings  splittings  decrease  as  are large. Further down the chain, the angular  excursions  from  the  all trans  configuration increase. The methyl group, which experiences additional motional averaging due  to rapid rotation about the local Cg  axis, has the smallest  v  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 structure. These  peaks at the 2 position reveals fine  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  orientation  have been observed before [117] and have been used (Srjj)) in decanol/sodium  couplings are considerably broadened  decanoate/water  to describe  multilayers. However these  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. P R O T O N AND C A R B O N 13 NMR  The  proton spin echo spectra of 11%  C —2,2—H  2  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 10000 1  "1  1  1  1  r-  -10000  B:  —  20000  10000  0  '—I— -10000  —i  1 .  -20000  r-  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 * C 3  H  Larmor frequency allows observation of  the  C—  heteronuclear dipolar couplings, the smaller couplings in Figure  5.4B,  which have a spacing of (2DQJJ+JQJJ). * C — *H 3  dipolar couplings were  also measured from the 13  C  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 i  q  linewidth of the triplet is broadened by long range ^ C— *H 3  and  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  * C — *H  dipolar couplings can be measured from the  *C  spectra below this temperature and show a dramatic drop. Below 87°C no  *C  3  dipolar couplings are observable. The couplings disappear corresponds  temperature at which the  to a levelling off in the deuteron  couplings. This is attributed to a nematic—smectic  C  *H  3  3  dipolar  quadrupolar  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- C-2,2-H2 Palmitic Acid-d29 in p-OOBA 13  N  I  V) CP  c a  3 0 0 0 0  a  96  112  100  Temperature. (C)  Legend:  0  1 H - 1 3 C Couplings  o  1 3 C - 1 H Couplings  The figure shows C— H dipolar couplings measured from the C 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. I3  J  13  LONG CHAIN CARBOXYLIC ACIDS / 202 FIGURE 5.7  Temperature Dependence of the Homonuclear Dipolar Couplings of 11 mole % _13c-2,2-H2 Palmitic Acid-d29 in p-OOBA 1  10  - T  9 -  8 N  I  b  4-  3 -  2 H  80  1  1  84  1  1  88  1 — i — i — i — i — i — i — i — i — i — i —  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—CH  2  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- C-2,2-H2 Palmitic Acid-d29 in p-OOBA 13  0.4  90  95  100  105  110  115  T e m p e r a t u r e (C)  Legend: Measured Order Parameters:  D —SxX,S |_|  Calculated Order Parameters: Q = S y y  H  _r  " SQQ C> = S ^ =  <  H  A = SyZ  S and SQD * measured from the *H and 2H spectra respectively. ScH can be measured from both the H and the 13Q spectra. The molecule fixed axis system has been presented in Figure 3.10. ar  xx  J  LONG CHAIN CARBOXYLIC ACIDS / 205 FIGURE 5.9 Temperature Dependence of S  zz  and S 3 3  S 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. zz  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  "  temperature range. The  values of S ^  J1  and  Syy  throughout the entire temperature range. The  differ by  approximately  0.2  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 the first C—C  bond is only 8.9°  (110°C) is 26.1° —  on average  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 This is a huge order parameter for a  solute and  0.5 to 0.65.  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 S 2 2  temperature, and at low temperatures  both increase with decreasing  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 C Labelled Palmitic Acid-d29 in p-OOBA 1 3  -0.40  -0.35  -0.30  -  -0.25  -  -0.20  -  00  -0.15  85  90  95  100  105  Temperature (C) S  i j :  ENSn  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 C Labelled Palmitic Acid-d29 in p-OOBA 1 3  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-H -PALMITIC A C I D - D 4  27  The proton spin echo spectra of 11% 2,2,3,3—H^—palmitic acid—d  27  (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, D gi 2  938 and D 3 3 = 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 D 3 3 couplings due to conformational motions about the C — C 3 bond. The value of the alpha coupling is quite high (5788 Hz), but 2  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 p-OOBA  i n  JJLA. -1—1—|——1  20000  r—i—1—j  1—1—T—1  10000  j—1—1  0  r—1—1—t—1—r—1  -10000  A) Experimental: Temperature = 110°C, 90° pulse length = 180° pulse length = 5.1 psec, Relaxation Delay = 0.5 sec, B) Calculated: D22 = 5788 Hz, D23 = 1312 Hz, D23 = 3430 Hz, 156" refocussing pulse, Lorentzian linewidth = 30  r~  -r  -20000 -Hz 2.5 psec, T = 5 p 8 Aquisitions. 938 Hz, D33 = 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 r yj for the lamellar phase (the difference is 0.04 A). The head group C  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)  CH 22 "a<x23 <aB> D .(D ,) 33 <BB> U  D  v  D  D  23  ap  D  QUADRUPOLAR COUPLINGS(Hz)  D  CARBON 2 3 4 5 6 7  EXPT 792 -5788 -1312 -918 -3430  CALC 866 -5238 -1708 -1072 -3374  50246 36262 36262 32960 32960 32960  50246 35950 36910 17194 16292 3422  TEMPERATURE = 110°C CALCULATED ADJUSTABLE PARAMETERS r = 10.16A n r  -  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  TJJQ.  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  tn  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 to 217  error is 147 Hz, in the soap calculation, it ranges from 177  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 crystal. From the that  TJJQ  dependence of r j and c y  TJJQ  in the liquid  C data and the calculated rotation angle, it would appear  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  0  1  1  H  1  1  1  1  3  1  5  T  7  carbon number Legend:  D  experimental (110C)  calculated o  Adjustable Parameters: rjjQ = 10.16A, r i cy  e  = 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—d ) and long chain 2  (palmitic —dgj, 1 —* C —2, 3  2 —H ~ 2  palmitic —d g  and  2  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—H  _ 2  and  2,2,3,3,—H4—palmitics were found to be very similar (5555, 5640, 5543 and 5788 Hz a 4.0% acid -2,2-d  2  total difference) as were the quadrupolar couplings for butyric  and  palmitic acid-d  31  (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,—d was unsolvable. From the nmr spectra 2  of palmitic acid—dgj and  1— * C — 2,2-H —palmitic 3  2  acid—d g, the order matrix 2  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  diagonal element, could  be  acid, both of which contained  diagonalized  to obtain  the  an  off  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 for the three solutes was  bond direction. The  order matrix  found to be quite similar at 110°C. The  value of the  diagonalized order matrix in the 3 direction was 0.4750 for acetic acid, propionic  acid and  found to be 0.5219, 0.5051 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 Samulski Inertial Frame Model was  —palmitic acid—d y, the modified 2  used to simulate the dipolar couplings and  quadrupolar couplings at 110°C. The  same model was  dipolar couplings of butyric acid —2,2—d  2  error in the D? calculation was  4  used to simulate the  at the same temperature. The  RMS  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 0  in the lamellar phase. On  2  the  other hand, the other adjustable parameter in the model, r j , is shown to be cy  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 from the difference in chain length of the two  A. The  difference arises  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  nematic  liquid  differences in orientational ordering in related lyotropic and  crystalline  phases have been investigated  and  discussed.  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M o k a s h i , S . , D e l i k a t n y , E . J . , and O r r , F . W . : R e l a t i o n s h i p s b e t w e e n c h e m o t a x i s , c h e m o t a c t i c m o d u l a t o r s , and c y c l i c n u c l e o t i d e l e v e l s i n tumor c e l l s . C a n c e r R e s e a r c h 43.: 1980-1983 ( 1 9 8 3 ) . O r r , F . W . , M o k a s h i , S . , a n d D e l i k a t n y , E . J G e n e r a t i o n of a complement d e r i v e d c h e m o t a c t i c f a c t o r f o r tumor c e l l s i n e x p e r i m e n t a l l y i n d u c e d p e r i t o n e a l e x u d a t e s and i t s e f f e c t on t h e l o c a l m e t a s t a s i s o f c i r c u l a t i n g tumor c e l l s . A m . J . P a t h . 1 0 8 : 1 1 2 - 1 1 8 ( 1 9 8 2 ) . L a m , W . C . , D e l i k a t n y , E . J . , O r r , F . W . , W a s s , J . , V a r a n i , J . ,and W a r d , P . A . : The c h e m o t a c t i c r e s p o n s e o f tumor c e l l s : a m o d e l f o r c a n c e r m e t a s t a s i s . A m . J . P a t h . 104:69-76 (1981). Orr,F.W.,Varani,J.,Delikatny,E.J.,Jain,N.,and Ward,P.A.: C o m p a r i s o n o f t h e c h e m o t a c t i c r e s p o n s i v e n e s s o f two f i b r o s a r c o m a p o p u l a t i o n s of d i f f e r i n g m a l i g n a n c y . A m . J . P a t h . 102 :160-167 ( 1 9 8 1 ) . Orr,F.W.,Lam,W.C.,Delikatny,E.J.,Mokashi,S.,and Varani,J.: L o c a l i z a t i o n o f i n t r a v e n o u s l y i n j e c t e d tumor c e l l s i n t h e r a t m e s e n t e r y a f t e r i n t r a p e r i t o n e a l a d m i n i s t r a t i o n of c h e m o t a c t i c s t i m u l i . I n v a s i o n and M e t a s t a s i s 1.: 239-247 (1981 ) . D a n c h u r a , W . , W a s y l i s h e n , R . E . , D e l i k a t n y , E . J . , a n d Graham,M.R. : Conformational p r e f e r e n c e s of the syn—pyridine c a r b o x a l d e h y d e o x i m e s . C a n . J . C h e m . 5_7_: 2135-2139 ( 1 9 7 9 ) .  Published  Abstracts  D e l i k a t n y , E . J a n d B u r n e l l , E . E . : D e u t e r i u m magnetic resonance of l y o t r o p i c l i q u i d c r y s t a l s : m i x t u r e s o f s a t u r a t e d and u n s a t u r a t e d fatty acyl Society of  chains. 30 Annual Conference Canada. O c t . 6,1983. t h  of  the  Spectroscopy  O r r , F . 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 of mesenteric tumor m e t a s t a s i s b y 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 factor. F e d . P r o c . 40.:782 ( 1981 ). (Abstract). 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 Ward,P.A.: Chemotactic r e s p o n s e s 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 ). (Abstract). Awards and  Scholarships  M.R.C. Postdoctoral Fellowship B.C. Postsecondary Scholarship NSERC P o s t g r a d u a t e S c h o l a r s h i p UBC U n i v e r s i t y G r a d u a t e F e l l o w s h i p U n i v . of Winnipeg Board of Regents General P r o f i c i e n c y Scholarship S h e l l Canada S c h o l a r s h i p  1987 1986 1981-1985 1983 ( d e c l i n e d ) 1977,1978 1976,1977  

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