Science, Faculty of
Chemistry, Department of
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UBCV
Grant, Rowland Frederick
Doctor of Philosophy - PhD
University of British Columbia
The proton magnetic resonance absorption has been measured in stearic acid, anhydrous sodium stearate and anhydrous potassium stearate. The temperature dependence of the widths and second moments of the proton magnetic resonance absorption lines of these compounds is discussed. The proton magnetic resonance absorption in the C-form of stearic acid has been measured between -188°C and the melting point. The results suggest that the methyl end groups may be free to rotate about their C₃ axes above -77°C and that pre-melting becomes significant above 40°C. The proton magnetic resonance absorption in anhydrous sodium stearate has been investigated between -182°C and 200°C. An abrupt change in the line width and second moment has been observed between 113°C and 114°C, the supercurd to subwaxy phase transition. The results suggest that, at temperatures below 114°C, the motion of the hydrocarbon chain portion of the sodium stearate molecule is chiefly one of oscillation or rotation about the chain longitudinal axis. The hydrocarbon chains may be free to move about other axes above 114°C, although the molecule as a whole retains a fixed position in the crystal lattice. The proton magnetic resonance absorption in anhydrous potassium stearate has been measured from -190°C to 182°C. Abrupt changes in the line width have been observed between 55°C and 62°C and at 171°C; these changes correspond to known phase transitions. The second moment results suggest that some torsional oscillation may occur about the longitudinal axes of the hydrocarbon chain portion of the potassium stearate molecule, at temperatures below 55°C. Above 62°C, contact between the molecules may have decreased enough to allow some lateral motion of the hydrocarbon chains.
AN INVESTIGATION OF PROTON MAGNETIC RESONANCE IN STEARIC ACID, SODIUM STEARATE AND POTASSIUM STEARATE by ROWLAND FREDERICK GRANT B.A., University of Brit i s h Columbia, 195S ffi.Sc, University of Br i t i s h Columbia, 1955 A THESIS SUBMITTED IN PARTIAL FUI^IIMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY In the Department of Chemistry We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA ; December, 1959 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department of Chemistry The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8 , Canada. Date December 5, 1959. GRADUATE STUDIES Field of Study: Chemistry Physical Chemistry Seminar Quantum Chemistry Thermodynamics Molecular Structure Chemical Kinetics Molecular Rearrangements . Others Studies: C. Reid H. M. Daggett, Jr. { B. A. Dunell W. A. Bryce A. Rosenthal Electricity and Magnetism J. M. Daniels Theoretical Mechanics F. A. Kaempffer Differential Equations T. E. Hull PUBLICATIONS 1. Nuclear Magnetic Resonance Study of Phase Transitions in Anhy-drous Sodium Stearate, R. F. Grant, N. Hedgecock, and B. A. Dunell, Can. J. Chem., 34, 1514- 1517 (1956) 2. Proton Magnetic Resonance Absorption in the C-form of Stearic Acid, R. F. Grant and B. A. Dunell, Can. J. Chem., 38, 359 - 364 (1960). Faculty of Graduate Studies PROGRAMME OF THE FINAL ORAL E X A M I N A T I O N FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of ROWLAND FREDERICK GRANT B.A., University of British Columbia, 1952 M.Sc. University of British Columbia, 1955 IN ROOM 225, CHEMISTRY BUILDING THURSDAY, APRIL 14th, 1960 at 4:00 P.M. COMMITTEE IN CHARGE DEAN G. M. SHRUM: Chairman B. A. DUNELL G. M. VOLKOFF C. A. McDOWELL M. F. McGREGOR C. REID J. S. FORSYTH G. G. S. DUTTON B. N. MOYLS External Examiner: E. R. ANDREW University of Wales, University College of North Wales Bangor, Wales AN INVESTIGATION OF PROTON MAGNETIC RESONANCE IN STEARIC ACID, SODIUM STEARATE, AND POTASSIUM STEARATE ABSTRACT The proton magnetic resonance absorption has been measured in stearic acid, anhydrous sodium stearate and anhydrous potassium stearate. The temperature dependence of the widths and second moments of the proton magnetic resonance absorption lines of these compounds is discussed. The proton magnetic resonance absorption in the C-form of stearic acid has been measured between -188°C and the melting point. The results suggest that the methyl end groups may be free to rotate about their C a axes above -77°C and that premelting be-comes significant above 4 0 ° C The proton magnetic resonance absorption in anhydrous sodium stearate has been investigated between -182°C and 200°C. An abrupt change in the line width and second moment has been observed betwen 113°C and 114°C, th supercurd to subwaxy phase transition. The results suggest that, at temperatures below 114°C, the motion of the hydrocarbon chain portion of the sodium stearate molecule is chiefly one of oscillation or rotation about the chain longitudinal axis. The hydrocrabon chains may be free to move about other axes above 114°C, although the molecule as a whole retains a fixed position in the crystal lattice. The proton magnetic resonance absorption in anhydrous po-tassium stearate has been measured from -190°C to 182°C. Abrupt changes in the line width have been observed between 55°C and 62°C and at 171°C; these changes correspond to known phase transi-tions. The second moment results suggest that some torsional oscilla-tion may occur about the longitudinal axes of the hydrocarbon chain portion of the potassium stearate molecule, at temperatures below 55°C. Above 62 °C, contact between the molecules may have de-creased enough to allow some lateral motion of the hydrocarbon chains. - 1 1 -ABSTRACT The proton magnetic resonance absorption has been measured i n stearic acid, anhydrous sodium stearate and anhydrous potassium stearate. The temperature dependence of the widths and second moments of the proton magnetic resonance absorption lines of these compounds i s discussed. The proton magnetic resonance absorption i n the C-form of stearic acid has been measured between -188°C and the melting point. The results suggest that the methyl end groups may be free to rotate about their C 3 axes above -75J°C and that pre-melting becomes significant above 40°C. The proton magnetic resonance absorption i n anhydrous sodium stearate has been investigated between -182°C and 200°C. An abrupt change i n the line width and second moment has been observed between 113°C and 114°C, the supercurd to subwaxy phase transition. The results suggest that, at temperatures below 114°C, the motion of the hydrocarbon chain portion of the sodium stearate molecule i s chiefly one of o s c i l l a t i o n or rotation about the chain longitudinal axis. The hydrocarbon chains may be free to move about other axes above 114°C, although the molecule as a whole retains a fixed position i n the crystal l a t t i c e . The proton magnetic resonance absorption i n anhydrous potassium stearate has been measured from -190°C to 182°C. Abrupt changes i n the line width have been observed between 55°G and 62GC and at 171°C; these changes correspond to known - I l l -phase transitions. The second moment results suggest that some torsional o s c i l l a t i o n may occur about the longitudinal axes of the hydrocarbon chain portion of the potassium stearate molecule, at temperatures below 55°C. Above 62°C, contact between the molecules may have decreased enough to allow some l a t e r a l motion of the hydrocarbon chains. - i v -TABLE OF CONTENTS CHAPTER I CHAPTER I I CHAPTER I I I CHAPTER IV Page Number 1 2 IntroquetIon References In Chapter I Theory General Principles of Nuclear Magnetic Resonance 3 Nuclear Magnetic Resonance of Rigid Structures 6 Molecular Motion i n Solids 9 References i n Chapter I I 15 Apparatus General Description 17 Arrangement of the Nuclear Magnetic Resonance Spectrometer 18 The Oscillating Detector 19 The Phase-sensitive Detector 24 Magnetic F i e l d Control and Modulation 25 The Sample Container and Temperature Control 27 References i n Chapter I I I 30 Method Purification of Stearic Acid 31 Preparation of Sodium Stearate 32 Preparation of Potassium Stearate 33 Treatment of Results 34 References i n Cnapter IV 38 V -CHAPTER V CHAPTER VI CHAPTER VII Page Number A Proton Magnetic Resonance Investigation of Sodium Stearate Introduction 39 The Structure of Sodium Stearate 45 Experimental Results 50: Discussion 54 References i n Chapter V 68 A Proton Magnetic Resonance Investigation of Stearic Acid Introduction 72 The C-Form Structure of Stearic Acid 73 Experimental Results 75 Discussion 79 References i n Chapter VI 86 A Proton Magnetic Resonance Investigation of Potassium Stearate Introduction 89 The Structure of Potassium Stearate 91 Experimental Results 95 Discussion 97 References i n Chapter VII 103 APPENDIX 1. Line Widths"of Sodium Stearate Used i n Figure X 105 2. Line Widths of Sodium Stearate Used in Figure XI 105 - v l -Page Number 3. Second Moments of Sodium Stearate Used i n Figure XIII 107 4. Line Widths of Stearic Acid Used i n Figure XX 109 5. Second Moments of Stearic Acid Used in Figure XXII 109 6. Line Widths of Potassium Stearate Used i n Figure XXIV 110 7. Second Moments of Potassium Stearate Used i n Figure XXV l i s - v l l -LIST OF ILLUSTRATIONS Following Page Figure I The Motion of an Internuclear Vector about an Axis 9 Figure II Block Diagram of Apparatus 18 Figure III Oscillating Detector 22 Figure IV Phase-sensitive Detector 24 Figure V Narrow Band Amplifier 24 Figure VI F i e l d Sweep Unit, Modulation Control and Phase Shift Network 25 Figure VII Details of Probe Sample Case and Arrangement of Thermostat 27 Figure V I H General Arrangement of Apparatus around Magnet 27 Figure IX Unit Ce l l Cross Section of Silver Stearate and a Potential Barrier to Chain Rotation 47 Figure X Sodium Stearate, Line Width vs Temperature 50 Figure XI Sodium Stearate, Line Width vs Temperature 51 Figure XII Sodium Stearate, Some F i r s t Derivative Curves 52 Figure XIII Sodium Stearate, Second Moment vs Temperature 53 Figure XIV The Effect of Torsional Oscillation on the Second Moment of Sodium Stearate 57 Figure XV Correlation Frequencies from Line Width Results 63 Figure XVI Correlation Frequencies from Second Moment Results 65 Figure XVII A Representative Cross Section of a Fatty Acid Unit C e l l 75 - v l i i -Following Page Figure XVIII Stearic Acid, F i r s t Derivative Curves Showing Fine Structure 76 Figure XIX Stearic Acid, h^/hg vs Temperature 76 Figure XX Stearic Acid, Line Width vs Temperature 76 Figure XXI High Resolution Spectra of Stearic Acid Solidifying at 69°C 77 Figure XXII Stearic Acid, Second Moment vs Temperature 78 Figure XXIII Potassium Stearate, Some Possible Arrangements of Hydrocarbon Chains 93 Figure XXIV Potassium Stearate, Line Width vs Temperature 95 Figure XXV Potassium Stearate, Second Moment vs Temperature 96 Figure XXVI Change i n F i r s t Derivative of Resonance Absorption i n a High Temperature Phase 96 Figure XXVII Potassium Stearate, Correlation Frequencies from Line Width Results 100 Figure XXVIII Potassium Stearate, Correlation Frequencies from Second Moment Results 100 - Ix -I am indebted to Dr. B.A. Dunell for introducing me to the f i e l d of nuclear magnetic resonance and for guiding this work. I am grateful to Professor C.A. McDowell for his aid i n obtaining the excellent electromagnet essential for this study. I would also l i k e to thank Dr. M. Bloom and Dr. L.B. Robinson for their invaluable help and advice. I am particularly Indebted to my colleagues Dr. T.M. Connor, Mr. w. Corfield and Dr. A. Horsfield for their aid i n various aspects of this work and to my wife Tania for her assistance i n preparing and typing this thesis. Financial aid i n the form of a National Research Council Studentship for 1956-57 and for 1957-58, i s gratefully acknowledged. - 1 -CHAPTER I INTRODUCTION The thermal activation of molecular motion i n solid long chain hydrocarbon compounds has sometimes been related to phase transitions and premelting effects ( i ) . In recent years nuclear magnetic resonance techniques have been employed to study th i s molecular motion i n a few long chain hydrocarbons (2,3,4,5). Since the nuclei of the hydrogen atoms i n the hydrocarbon chains usually account for almost a l l the nuclei with magnetic moments i n these molecules, the nuclear magnetic resonance of the hydrogen atoms, usually called proton magnetic resonance, must be employed. This study describes the construction and assembly of a broad line nuclear magnetic resonance spectrometer of conven-tional design and i t s use i n obtaining the proton magnetic resonance spectra of some long chain hydrocarbon compounds at various temperatures. These compounds are sodium stearate, potassium stearate and stearic acid. The proton magnetic resonance of sodium stearate has already been b r i e f l y reported (6); however, Chapter V of this work i s devoted to a more detailed discussion. The proton magnetic resonance of stearic acid, discussed i n Chapter VI, i s of an exploratory nature, for only a l i t t l e independent information exists which might suggest that there i s any extensive molecular motion i n this compound (7). Chapter VII deals with the proton magnetic resonance of potassium stearate which i s also investigated for the f i r s t time. References in Chapter I (1) Daniel, V., Advances in Physics, 2, 450 (1953). (2) Andrew, E*R., J. Chem. Phys., 18, 607 (1950). (3) Rushworth, F.A., Proc. Roy. Soc. (Lond.), A222, 526 (1954). (4) Kojima, S. and Ogawa, S., J. Phys. Soc. Japan, 8 , 283 (1953). (5) Komatsu, H., J. Phys. Soc. Japan, 11, 755 (1956). (6) Grant, R.F., Hedgecock, N. and Dunell, B.A., Can. J. Chem., 34, 1514 (1956). (7) Singleton, W.S., Ward, T.L. and Dollear, F.G., J. Am. Oil Chem. Soc, 27, 143 (1950). - 3 -CHAPTER I I THEORY General Principles of Nuclear Magnetic Resonance Nuclear magnetic resonance has been the subject of several books (1,2,3) or significant parts of books (4,5) and numerous review a r t i c l e s . The author i s particularly indebted to the books by Andrew and by Saha and Das (1,3), for much of the material i n the following discussion. Many atomic nuclei possess a magnetic moment which may be considered to arise from the angular momentum of the positive-l y charged nucleus. This angular momentum i s described, by a spin quantum number I. When such a nucleus i s placed i n a uniform magnetic f i e l d H 0, i t s spatial degeneracy i s removed, and 21+1 equally spaced Zeeman energy levels are established. These energy levels correspond to different orientations of the nuclear magnet with respect to the f i e l d H0. Transitions between these levels may be induced by a weak magnetic f i e l d o s c i l l a t i n g at the resonance frequency which i s applied at right angles to the direction of the main f i e l d H 0. The frequency at which resonance occurs i s given by V o = M HQ I K where i s the magnetic moment of the nucleus and h i s Planck's constant. The probability of the induced transition i s the same for a l l the energy levels. However, i n thermal - 4 -equilibrium, the population of the l e v e l s corresponds to a Boltzmann d i s t r i b u t i o n and there i s a net absorption of energy when the weakly o s c i l l a t i n g f i e l d i s applied. An assembly of nuclear spins maintains thermal equi-l i b r i u m with i t s environment, usually c a l l e d the l a t t i c e , i n the following manner. Thermal motions of the l a t t i c e produce o s c i l l a t i n g f i e l d s at the n u c l e i . Some o s c i l l a t i o n s may occur at the resonance frequency and cause t r a n s i t i o n s , hence energy can be transferred between the n u c l e i and the l a t t i c e . I f a sample were abruptly transferred from a very weak magnetic f i e l d to a very strong f i e l d , the suddenly non-degenerate energy l e v e l s of the nuclear spins would have p r a c t i c a l l y i d e n t i c a l populations. In order to obtain thermal equilibrium, some of the nuc l e i i n i t i a l l y i n the higher energy states give up energy to the l a t t i c e . This equilibrium i s approached ex-ponentially with a time constant T 1 } the spin l a t t i c e relaxa-t i o n time. An i s o l a t e d nucleus i n . a uniform f i e l d absorbs energy at the resonance frequency over a very narrow range, and a sharp absorption l i n e w i l l be observed. However, for nu c l e i i n a r i g i d c r y s t a l l a t t i c e the magnetic resonance absorption l i n e i s broadened or s p l i t by the i n t e r a c t i o n of the nuclear magnets themselves. These co-called spin-spin interactions a r i s e i n two di f f e r e n t ways. F i r s t l y , the t o t a l magnetic f i e l d at any single nucleus consists not only of the applied f i e l d H 0 but also includes the resultant of the l o c a l f i e l d s produced by the s t a t i c components of neighbouring magnetic - 5 -n u c l e i . The d i r e c t i o n and magnitude of the l o c a l f i e l d may not he the same at each nucleus, depending on the r e l a t i v e arrangement of the neighbouring n u c l e i i n the l a t t i c e . The eff e c t i v e magnetic f i e l d w i l l vary somewhat on either side of H 0 f o r d i f f e r e n t n u c l e i , so that resonance absorption through-out the sample w i l l occur over a range of frequencies and a broadened l i n e w i l l be obtained. The second way l i n e broaden-ing may a r i s e i s by spin exchange between l i k e n u c l e i . A given nucleus precesses about the main f i e l d H 0 at the Larmor frequency which i s the resonance frequency. This pre-cessing nucleus gives r i s e to o s c i l l a t i n g magnetic f i e l d s which can induce t r a n s i t i o n s among the energy l e v e l s of another nearby nucleus. When t h i s occurs, the f i r s t nucleus must I t s e l f undergo t r a n s i t i o n s , with the result that the two nuc l e i interchange t h e i r orientations with respect to the main f i e l d H 0. This spin-exchange process reduces the l i f e t i m e of a nucleus i n any p a r t i c u l a r spin energy l e v e l . Then, accord-ing to the Heisenberg uncertainty p r i n c i p l e , t h i s reduction i n l i f e t i m e should produce a broadening of the energy l e v e l s which leads t o a broadening of the nuclear magnetic resonance absorption l i n e . This spin-exchange broadening i s of the same order of magnitude as the effe c t of l o c a l f i e l d s . Spin-spin r e l a x a t i o n has a c h a r a c t e r i s t i c time Tg, which has been pre-c i s e l y defined i n terms of the maximum value of the normalized l i n e shape function. T 2 i s approximately the re c i p r o c a l of the magnetic resonance l i n e width i n frequency u n i t s . The resonance absorption l i n e may also be broadened by non-- 6 -uniformity of the main magnetic f i e l d H 0 over the sample, or hy nuclear e l e c t r i c quadrupole interactions i f the nuclear spin quantum number I exceeds £. Nuclear Magnetic Resonance of R i g i d Structures Since the nuclear environment influences the width and shape of a resonance l i n e , the resonance absorption spectrum can provide information about the chemical structure and molecular arrangement i n the sample. Suppose the external f i e l d H 0 i s s u f f i c i e n t l y homogeneous that the true l i n e width and shape a r i s i n g from a given.sample can be observed. Possible quadrupole i n t e r a c t i o n can be disregarded since t h i s work i s devoted to a study of the proton resonance i n s o l i d s , and the spin I of the proton i s one h a l f . The source of l i n e broadening i s therefore the magnetic i n t e r a c t i o n of the nuclear dipoles. A simple experimental s i t u a t i o n i n which the nuclear dipoles l i e close together i n pairs occurs f o r the protons of the water molecule i n many c r y s t a l l i n e hydrates. Such a s i t u a t i o n was f i r s t studied by Pake, who found that the resonance obtained from a single c r y s t a l of hydrate consisted of a pa i r of l i n e s f or each value © of the angle between the external f i e l d H 0 and the vector length r , between the protons ( 6 ) . By a f i r s t order quantum-mechanical perturbation c a l c u l a -t i o n , Pake found that the resonance l i n e s should be symmetric-a l l y disposed about the point at which a single resonance would have been expected i f no s p l i t t i n g occurred. This - 7 -s p l i t t i n g was found to be AH = ! A * A : 3 (3 C o / e - i ) . I f the s o l i d i s not a single c r y s t a l , but instead i s p o l y c r y s t a l l i n e , the averaging out of the angle © over a l l directions tends 1 to smear out t h i s structure. Evidence of the pair s p l i t t i n g s t i l l remains, however (6, 7 ) . Resonance l i n e s p l i t t i n g of a more complicated nature has been studied f o r systems of three v i r t u a l l y i s o l a t e d n u c l e i (8,9). The th e o r e t i c a l c a l c u l a t i o n of the resonance absorption l i n e shape has also been c a r r i e d f o r a tri a n g u l a r array of three nuclei (10). In general, the d i r e c t c a l c u l a t i o n of the l i n e shape i s tedious f o r the simple systems described, and v i r t u a l l y im-possible f o r any complex array of n u c l e i . Furthermore, the re s u l t would be le s s rewarding since the m u l t i p l i c i t y of interactions between groups w i l l smear out a l l detailed f i n e structure i n the l i n e shape. Comparison between a s t r u c t u r a l model and experiment i s possible i f the second moment of the resonance l i n e shape i s employed (11). The second moment AH|, expressed i n terms of the magnetic f i e l d i s defined by 7 < wf(H) J H s-co where 7(H) i s the absorption i n t e n s i t y , i n a r b i t r a r y u n i t s , as a function of the magnetic f i e l d H, and H 0 i s the resonance - 8 -f i e l d f o r an i s o l a t e d nucleus at a given frequency. The expression f o r the second moment given by Van Vleck f o r the in t e r a c t i o n of an assembly of nuclear spins i n a r i g i d l a t t i c e i s In t h i s equation >Uf i s the magnetic moment, and I f i s the spin of any other nuclear species f . Here r i J K i s the magni-tude of the vector connecting n u c l e i j and k, and Bj* i s the angle between t h i s vector and the d i r e c t i o n of the applied f i e l d . Subscripts j and k r e f e r to the nuclear species at resonance and subscript -f refers to a l l other nuclear species present. N i s the t o t a l number of nuclei at resonance i n the unit c e l l to which broadening interactions are considered to be confined. With c r y s t a l l i n e powders the terms i n 0 are averaged over a l l d i r e c t i o n s and the second moment becomes (7) J>K - 9 -Molecular Motion In Solids As the sample temperature i s raised, molecules or parts of molecules i n many solids may begin to rotate about one or more axes. ?/hen the frequency of rotation i s about the same as the line width, the resonance line begins to narrow (12). Gutowsky and Pake have described a simple system where the isolated nuclear pair, discussed previously, rotates freely about a single axis (13). In such a case the angular factor p 3 cos - 1 i s averaged i n time so that the resonance absorption l i n e becomes half as wide and correspondingly more intense than i t was with the non-rotating pair. More com-plicated systems involving the rotation of three nuclei about one axis have also been considered (10,14). Gutowsky and Pake have derived an expression for the second moment of a system of nuclei which rotate about a single axis and make an angle 0' with H 0, the static f i e l d (13): The angle YJK i s t n e angle between the axis of rotation and the internuclear vector The motion of the internuclear vector i s shown i n Figure I. In polycrystalline samples the T H E M O T I O N O F A N I N T E R N U C L E A R V E C T O R K.u A B O U T A N AXIS 0 N axes of rotation are randomly distributed i n a l l directions so that the factor (3 cos 2 0 - l ) 2 must be replaced by i t s mean value 4/5. The second moment for a polycrystalline sample i s therefore: J>K > which i s exactly the same as i f the individual terms In the summations for the r i g i d lattice were multiplied by the factor F 0 0 = i (3 < v r J l t -Andrew has calculated the effect of rotational oscillation on the second moment (15). The result i s expressed i n terms of the ratio of the second moments for the oscillating and r i g i d cases given as C . For a polycrystalline sample this i s : where o( i s the angular amplitude of oscillation and J 0 i s a Bessel function. The calculation of the second moment for several l i k e nuclei i n an isolated molecule rotating about some axis i s f a i r l y straightforward. However, when molecules are f a i r l y close together, there may be significant inter-action between nuclei of the different molecules. This gives an intermolecular component to the second moment. In the case of molecular rotation, the calculation of the intermolecular - 11 -component i s complicated by the fact that both r\JK and 9 J K vary during motion. A general method has been developed for this problem, however, the calculation i s formidable (16). Rotation of a molecule about more than one axis w i l l of course reduce the second moment further and isotropic rotation w i l l reduce the second moment almost to zero. However, the inter-molecular contribution does not average to zero as long as the centers of mass of the molecules remain fixed. When sel f -diffusion through the l a t t i c e begins, the overall second moment becomes zero (17). It has been argued, from theoretical considerations, that molecular motion should cause a change i n the nuclear magnetic resonance l i n e shape such that the second moment remains constant (18,19). As the line width narrows due to the motion, the t a i l s of the line are predicted to increase i n size. In the case of rotation with a uniform angular velocity co a about a single axis, side bands are predicted to be found at angular frequencies ± 2 coa on either side of the main peak. However, these side bands and t a i l s w i l l be smeared out and unobservable i f molecular rotation i s irregular or random, which seems to be the case (20)-. The foregoing discussion of the changes i n second moment due to molecular motion i s therefore s t i l l v a l i d . Since uniform molecular rotation does not seem to occur i n solids, the term molecular reorientation w i l l be used i n describing rotational motions of molecules. The line width narrowing due to molecular motion has been discussed by Bloembergen, Purcell and Pound (12) i n terms of - 12 -the Debye correlation time Tt . The correlation time i s defined as the average time required for the reorientation of the molecule or part of the molecule containing the inter-acting nuclei i n question. When there i s a rapid reorienta-tion of molecules, the local f i e l d set up by the nuclear magnets i s now rapidly fluctuating. For such a case the second moment formula of Van Vleck has been expressed as: 4s tz i 3 ( i t -Jo(Y» A)) J_ JL. irr x where J 0 ( V ) i s the static portion of the local f i e l d spectrum. This function i s i n turn defined i n terms of the Debye correla-tion.time Tc (12). The equation for the second moment f i n a l l y becomes: Gutowsky and Pake have redefined t h i s equation i n terms of frequency and have introduced Vc, the correlation frequency: Here i s the line width i n the case of reorientation and A i s the r i g i d l a t t i c e line width (13). The factor £ i s intro-duced to cover the uncertainties which arise from the li m i t s of integration employed and also the inaccurate definition of AVwith respect to line shape. The lin e width i s usually defined as the separation between points of maximum and minimum - 13 -slope on the absorption curve.* Kubo and Tomlta (19) have developed a general theory of magnetic resonance and from a rigorous treatment of the foregoing discussion, have assigned a value of (8 In 2)""1 to £ . The correlation time can also be determined from measurements of Tp the spin l a t t i c e relaxa-tion time, and the constant £ can therefore be calculated directly for a particular experiment. Values of £. range from 0.03 to 0.9 i n studies of various hydrocarbons (16,21). It would seem that to take £ as unity should not affect the use-fulness of the results on application of t h i s theory. To treat a transition from one definite line width C to a narrower line B characteristic of a specialized motion, the equation of Gutowsky and Pake (13) can be adjusted to give: (AV)*= Bx * C J A T „ - ' The r i g i d l a t t i c e line width A i s taken to be: A = (B 2 + C 2)*, and i s the line width at any point within the transition. The experimental l i n e width versus temperature curve can be f i t t e d to the above equations i f the reorientation process i s governed by an activation energy A E , and i f Vc varies with temperature T as: AE Vc = U e R T The activation energy A E per mole i s related to the height of - 14 -the p o t e n t i a l h a r r i e r r e s t r i c t i n g reorientation and R i s the gas constant. - 15 -References In Chapter II (1) Andrew, E.R., Nuclear Magnetic Resonance, Cambridge University Press, 1955. (2) Grivet, P., La Resonance Paramagnetique Nuclealre, Centre National de la Recherche Scientifique, Paris, 1955. (3) Sana, A.K. and Das, T.P., Theory and Applications of Nuclear Induction, Sana Institute of Nuclear Physics, Calcutta, 1957. (4) Pake, G.E., Solid State Physics, Academic Press, New York, 1956, Vol. 2, p.l. (5) Ramsey, N.F., Nuclear Moments, John Wiley and Sons, New York, 1953. (6) Pake, G.E., J. Chem. Phys., 16, 327 (1948). (7) Gutowsky, H.S., Kistiakowsky, G.B., Pake, G.E. and Purcell, E.M., J. Chem. Phys., 17, 972 (1949).. (8) Richards, R.E. and Smith, J.A.S., Trans. Faraday Soc, 47, 1261 (1951). (9) Waugh, J.S., Humphrey, F.B. and Yost, D.M., J. Phys. Chem., 57, 486 (1953). (10) Andrew, E.R. and Bersohn, R., J. Chem. Phys., 18, 159 (1950). (11) Van Vleck, J.H., Phys. Rev., 74, 1168 (1948). (12) Bloembergen, N., Purcell, E.M. and Pound, R.V., Phys. Rev., 73, 679 (1948). (13) Gutowsky, H.S. and Pake, G.E., J. Chem. Phys., 18, 162 (1950). - 16 -(14) Powles, J.G. and Gutowsky, H.S., J. Chem. Phys., 21, 1695 (1953). (15) Andrew, E.R., J. Chem. Phys., 18, 5 (1950). (16) Andrew, E.R. and Eades, R.G., Proc. Roy. Soc. (Lond.), A216, 398 (1953). (17) Andrew, E.R., Conference on Defects in Crystalline Solids, Bristol, 1954, The Physical Society, London, p.60. (18) Anderson, P.W., J. Phys. Soc. Japan, 9, 316 (1954). (19) Kubo, R. and Tomita, K., J. Phys. Soc. Japan, 9, 888 (1954). (20) Andrew, E.R., Chemical Society Symposia, Bristol, 1958, The Chemical Society, London, Special Publication No. 12, p.177. (21) Rushworth, F.A., Proc. Roy. Soc. (Lond.), A222, 526 (1954). - 17 -CHAPTER I I I APPARATUS General Description The apparatus used for this work: i s a broad line nuclear magnetic resonance spectrometer of conventional design. I t consists of a large, s t a t i c , homogeneous magnetic f i e l d H Q i n which a solenoidal c o i l i s placed with i t s axis perpendicular to the large f i e l d H Q. The sample under investigation i s placed inside this solenoidal c o i l . The c o i l i t s e l f i s part of a pa r a l l e l resonant c i r c u i t . Energy i s supplied to this c i r c u i t from a constant current source which i s a weakly o s c i l l a t i n g o s c i l l a t o r . The frequency of the os c i l l a t o r i s held constant and the large magnetic f i e l d i s slowly varied. As the f i e l d passes through the resonance conditions for the nuclei of interest in the sample, radio frequency energy i s absorbed from the c o i l , thereby decreasing the amplitude of the radio frequency voltage across i t . This decrease i n amplitude can, i n principle, be observed by amplifying and rectifying the radio frequency voltage and recording the re c t i f i e d voltage. In order to avoid direct current amplifica-tion, which might be necessary i n such an arrangement to obtain an observable signal, the large f i e l d H Q i s modulated s l i g h t l y at a low audio frequency. Now the resonance frequency of the nuclei oscillates about the value determined by the large f i e l d . As this f i e l d H Q i s swept slowly through - 18 -resonance, the radio frequency voltage across the c o i l i s modulated at t h i s audio frequency. The modulated radio frequency voltage i s amplified and detected within the o s c i l l a t o r i t s e l f g i v i n g the audio s i g n a l and noise. This i s amplified further and passed through a narrow band am p l i f i e r , tuned to the modulation frequency, which reduces the noise while passing the s i g n a l . The signal i s passed through a phase-sensitive detector and on to a recording milliammeter. To decrease the noise present with the s i g n a l s t i l l f urther, a long time constant i s included a f t e r the phase-sensitive detec-t o r . In order to study the nuclear magnetic resonance spectra of the sample over a range of temperatures, means are provided to heat and cool the sample i n the strong magnetic f i e l d . The Arrangement of the Nuclear Magnetic Resonance Spectrometer The arrangement of the nuclear magnetic resonance spectro-meter i s outlined i n Figure I I . The large magnet i s a Varian model V-4007 electromagnet supplied with s i x inch diameter pole pieces separated by a gap of 1.75 inches. This magnet i s energized by a Varian model V-2200 A regulated magnet power supply. The f i e l d can be both swept and modulated by i n j e c t i n g the required a.c. and d.c. voltages i n the sweep input jack with the sweep control switch turned to the attenuated po s i t i o n . A Heathkit model AO-1 audio o s c i l l a t o r was constructed to supply a 27 cycles per second voltage to the magnet power supply and to the h o r i z o n t a l input of a Heathkit model OM-l oscilloscope. Another portion of t h i s audio signal i s changed B L O C K D I A G R A M O F A P P A R A T U S RECEIVER FREQUENCY 1 METER OSCILLATING DETECTOR AUDIO PREAMP. MAGNET POWER SUPPLY F I ELD SWEEP — AND MODULATION CONTROL ELECTRO AUDIO OSCILLATOR P H A S E SH IFT NETWORK MAGNET C R. 0. NARROW BAND AMPLIFIER PHASE SENSITIVE DETECTOR RECORDING MILLIAMMETER F I G U R E II TO FOLLOW P A G E 18 - 19 -i n phase by a phase s h i f t network: and sent to the phase-sensitive detector. The audio component from the o s c i l l a t i n g detector i s amplified by a r e s t r i c t e d band preamplifier tuned to pass 27 cycles per second. The output of the narrow band amplifier goes to the v e r t i c a l input of the oscilloscope and to the phase-sensitive detector. The f i r s t derivative of the nuclear magnetic resonance absorption s i g n a l , from the phase-sensitive detector, i s recorded on an E s t e r l i n e Angus model AW recording d.c. milliammeter. The frequency of the o s c i l l a t i n g detector was monitored by a Hammarlund HQ-100 communications receiver. The frequency was measured by weakly coupling the o s c i l l a t i n g detector to a Lampkin type 105B frequency meter. The O s c i l l a t i n g Detector In an o s c i l l a t i n g detector the sample c o l l i s part of the p a r a l l e l tuned element i n the g r i d c i r c u i t of the radio frequency o s c i l l a t o r i t s e l f . Apparently almost any standard o s c i l l a t o r c i r c u i t i s suitable ( l ) . The frequency of o s c i l l a -t i o n i s l a r g e l y determined by the values of the p a r a l l e l tuned element i n the g r i d c i r c u i t , commonly c a l l e d the 'tank c i r c u i t ' . In a l l nuclear magnetic resonance spectrometers of the o s c i l l a t i n g detector type, the resonant impedance Z 0 of the tank c i r c u i t i s : Z 0 = L/CR, where L i s the inductance, C i s the capacitance and R the series resistance of the tank c i r c u i t . When resonance occurs, - 20 -the impedance i s reduced to the value: Z F K * ( / + HIT S Q P / c j , ( H J * ) where JT i s the sample f i l l i n g factor, P i s the power absorbed by the nuclei In the sample at resonance, C J o i s 2TfVowhere Vo i s the resonance frequency, and Q i s the figure of merit of the resonant circuit given by: Q » CJE/R. The amplitude of the weak radio frequency magnetic f i e l d i s HT_. The reduction i n the resonant impedance therefore i s given by: ¥TT Q Jr p <** (Hi) x Now V 0 s IZ 0 i n such a system, where V 0 i s the operating voltage level of oscillation and"i i s the current in the tank cir c u i t which i s a constant. A change i n the resonant impedance Z 0 by magnetic resonance absorption w i l l therefore change the voltage level of the oscillator (2). The optimum absorption of power by the nuclei occurs, at the condition (3): The optimum operating voltage of the oscillator has been shown (4) to be proportional to H-^ : - 21 -In cases where TjTg i s very small, R± must he large and the radio frequency voltage level may he relatively high. In cases where T]T 2 i s large, the voltage level required for optimum conditions may he too low for stable os c i l l a t i o n . In practice, the voltage level of oscillation available i s usually more than sufficient to meet the demands for the case where TT_T 2 i s very small, and attention i s usually given to ways and means of lowering the oscillation level. There are other reasons for keeping this o s c i l l a t i o n voltage level low: for example, the curvature of the oscillator tube characteristic i s small for a small oscillation ampli-tude, hence the o s c i l l a t i o n voltage level i s most sensitive to a given change of impedance at resonance. Also the tube characteristics are more linear at lower levels so that noise components originate i n a smaller band of frequencies than i s the case for operation at higher osc i l l a t i o n voltage levels. In short, the voltage level of the oscillator i s usually adjusted to be at the threshold of stable oscillation i n order to obtain greatest sensitivity, lowest noise and optimum absorption of power ( l ) . If the steady magnetic f i e l d H 0 i s modulated sinusoid-a l l y at 27 cycles per second, Z 0 and therefore V 0 w i l l be modulated at this frequency as the steady f i e l d i s swept through resonance. This amplitude-modulated, radio frequency voltage i s r e c t i f i e d within the oscillator i t s e l f . Spectro-meters employing such grid detection are called oscillating detectors or autodynes (5). The nuclear magnetic resonance - 22 -absorption signal appears as an audio component of the modula-tion frequency of 27 cycles per second i n the plate voltage of the oscillator tube and only requires suitable audio amplifi-cation to be observed on an oscilloscope or be fed into a , phase-sensitive detector. The osci l l a t i n g detector used in this work i s almost identical to one described by Gutowsky, Meyer and McClure ( 6 ) ; a schematic diagram of the oscillator i s shown i n Figure H I . It consists of a one tube os c i l l a t i n g detector followed by several stages of audio amplification. This oscillator i s rather similar to an earlier design by Hopkins (7), and i t differs mainly by addition of capacitors C 3 and C 4 i n the grid c i r c u i t . Previous experience with the autodyne circuit of Hopkins and the marginal oscillator c i r c u i t of Pound and Knight (4) showed that a stable voltage level of oscillation could not be obtained that would not cause saturation of the proton resonance i n some solids. The addition of the capa-cit i v e feed-back control by Gutowsky et a l . ( 6 ) seemed to allow a much lower stable oscillation level. <The radio frequency voltage across the tank cir c u i t could, with careful adjustment, be reduced below 0.01 volts (R.M.S.), which seems to be an order of magnitude lower than the other types of oscillating detectors t r i e d . The oscillator c i r c u i t and the f i r s t two stages of audio amplification were mounted together on a standard sheet steel chassis; the audio amplifier components arranged around the 12AU.7 ? double triode were shielded from the oscillator F I G U R E III T O F O L L O W P A G E 2.2 O S C I L L A T I N G D E T E C T O R - 23 -components by a sheet metal partition. The last three stages of the apparatus in Figure III were on a separate chassis a few feet from the oscillating detector and connected to i t by a long coaxial cable. This additional audio amplification was only needed i f a recording galvanometer, such as the Esterline Angus milliammeter, was used with the spectrometer. The frequency of the oscillator will depend on the In-ductance of the sample coil and the setting of the variable capacitors Clt C2, C 3 and C 4. The approximate frequency was fir s t established by the capacity of C 2 and the size of the sample c o i l . In this work: the oscillator frequency was in the vicinity of 28 megacycles per second. The sample coil was 1 centimeter inside diameter, 1.5 centimeters long and con-sisted of 8 turns of No. 18 B and S copper wire. It was found that less noise and greater stability resulted i f condenser C 3 was adjusted to a minimum. Condenser C 4 controlled the level of oscillation and was adjusted to the oscillation threshold. The 10K variable resistor R was used as a fine adjustment for the oscillation level. The exact frequency desired was then obtained by adjusting the trimmer ^ and the oscillation level was readjusted to a minimum by adjusting resistor- R. The Hammarlund HQ 100 communications receiver "S" meter was used to monitor the oscillation level. The high voltage to the oscillator and amplifier in Figure III was supplied by a Lambda Electronics Corp. Model 28 regulated power supply, and the filament voltage was supplied by 6 volt storage batteries. - 24 -The Phase-sensitive Detector The circuit diagram of the phase-sensitive detector used in this work i s shown in Figure IV. The circuit diagram of the narrow hand amplifier that supplies it with signal is shown in Figure V. This phase-sensitive detector is almost identical to one described by Schuster (8). The operation of this type of circuit has been well described by Andrew (1). In this type of circuit the signal voltage is combined vec-torially with a reference voltage at the modulation frequency and the resultant voltage is rectified. In Schuster's circuit shown in Figure IV, the amplified signal from the oscillating detector is fed from the anode of the 6SH7 pentode in the narrow band amplifier to the phase-sensitive detector at A. The reference voltage, delivered by the Heathkit audio oscillator at modulation frequency, enters the detector via the cathode follower at B and is applied to the grids of the 6SN7 double triode V-|_ through the secondary of the Hammond 448 transformer. The reference voltage alternately cuts off one half of the tube V]_ and causes the other half to conduct. This switching takes place at the modulation frequency so that tube V]_ serves as a synchronous rectifier for the incoming signal. The difference in voltage between the outputs C and D is proportional to the modulation frequency component of the voltage applied at the signal input A, multiplied by a phase angle factor. For a maximum output the phase angle between the signal and reference voltages should be 0 or TT ( l ) . This rectified output is applied to a high-impedance vacuum tube F I G U R E IV P H A S E S E N S I T I V E TO FOLLOW PAGE 24 D E T E C T O R F I G U R E V TO FOLLOW PAGE 24 O TO A N A R R O W B A N D A M P L I F I E R - 25 -voltmeter, represented by the circuit about V 2 in Figure IV, and the recording miliiammeter is connected between terminals E and F. If harmonics of the modulation frequency are present in the noise or modulated signal coming in at A, the phase-sensitive detector will also respond to them. To avoid this, and to lower the noise level, the audio amplifier in Figure V has an LC f i l t e r tuned to the modulation frequency in the grid circuit of the f i r s t stage. The phase-sensitive detector also responds to noise at or near the modulation frequency. To prevent this appearing as fluctuations at terminals E and F, a selection of RC filters are placed between the phase-sensitive detector and the vacuum tube voltmeter. This allows the band-width of the noise to be reduced to values between 2 cycles per second and 0.05 cycles per second. In this work a band-width of 0.4 or 0.2 cycles per second was employed. Also the modulation amplitude was adjusted to less than one sixth of the line width so that the incoming sinusoidal signal, when rectified, would be proportional to the f i r s t derivative of the line shape. Magnetic Field Control and Modulation The magnetic field , HQ, was swept by an arrangement shown in Figure VI. The 2K Beckman Helipot is a voltage divider for a 22 volt dry ce l l which supplied a bias voltage to the refer-ence cell in the Varian regulated magnet power supply. The Helipot was slowly turned by a clock motor which in turn I F I E L D S W E E P U N I T OFF m 4 7 0 I C J.70K U o K S I K J 3 K I 5 K 1 K 3 K IK TO S W E E P INPUT OF M A G N E T POWER S U P P L Y o SOK XK HELIPOT C L O C K M O T O R DR IVE M O D U L A T I O N C O N T R O L 9 TO S W E E P I N P U T O F MAG P O W E R S U P P L Y ? 0 N E T V C X C I N St fo- so MICROAMPS HjOK *SOK I 9 « K If H.JK T E N OF T H E S E i 9 Q FROM AUDIO osc. 333 ~ P H A S E S H I F T N E T W O R K — t i n TO R E F E R E R E N C E INPUT OF P H A S E S ENS IT IVE D E T E C T O R o! L i Q F R O M o Q A U D I O H A N H O M O I 3 3 3 I r F I G U R E VI TO FOLLOW PAGE 25 - 26 -caused the magnetic f i e l d to slowly change. The range and the rate of f i e l d sweep was adjusted by the selection of resistors which altered the voltage across the Helipot. The magnetic f i e l d H 0 can be calibrated easily for a given sweep range by measuring the f i e l d with a mineral o i l sample and plotting the f i e l d values against the voltage i n -jected by the sweep arrangement. It was found i n practice that very frequent calibrations were necessary since a small change i n the dry c e l l voltage or switching the magnet off and on, altered the whole calibration range. Since a given ex-perimental run was always repeated at least twice i n succession i t was found convenient to adopt the following procedure. The o s c i l l a t o r was set at a given frequency and precisely measured by the Lampkin frequency meter. Then a nuclear magietic resonance signal was recorded and the recording meter and f i e l d sweep were stopped simultaneously by one switch. The osc i l l a t o r frequency was then altered by about 150 kilocycles per second; the frequency was increased or decreased depend-ing on whether the f i e l d was being increased or decreased. The frequency was measured again and another resonance signal was recorded. The difference i n frequency between the two signals provides a calibration of the chart, and although errors probably arose due to slippage of gears and couplings i n the clock motor and the recording meter, line widths measured by either calibration method mentioned above differed by less than two percent. The magnetic f i e l d H 0 could also be modulated by driving - 27 -the grids of the current regulating tubes in the magnet power supply with the output of the audio oscillator. In order for the magnet to he able to follow the voltage swing of the grids, the modulation frequency was made as low as possible; in this case i t was 27 cycles per second. The modulation amplitude was controlled by the series of voltage dividers and measured on the meter as shown in Figure VI. The modulation amplitude was calibrated by observing a narrow resonance on the oscillo-scope while placing the modulation voltage on the horizontal sweep. The horizontal sweep was calibrated by measuring the radio frequency change for a given shift of the signal trace on the oscilloscope. This gave the peak to peak calibration of the modulation amplitude. The Sample Container and Temperature Control The sample container used in this work is illustrated in Figure VII and its arrangement in the magnetic field i s shown in Figure VIII. The sample co i l , previously described, was placed near the bottom of a brass cylinder at the end of the probe. The coil leads were held in place by a teflon cylinder in the brass sample container. Long openings were cut in the upper part of the container and a hole was drilled through the teflon cylinder to facilitate the changing of samples. The upper end of the probe was connected to a thick bakelite plate. This plate rested on a platform built above the magnet as shown in Figure VIII. Small adjustments of the position of the sample container in the magnet gap were made by three F I G U R E D E T A I L S O F P R O B E S A M P L E C A S E VII TO FOLLOW PAGE 27 A R R A N G E M E N T O F T H E R M O S T A T i i • TEFLON SPACER SAMPLE ACCESS PORT TEFLON CYLINDER SAMPLE COIL PROBE SAMPLE CASE CYLINDRICAL^ DEWAR "~ HOT AIR DUCT HEATER COILS COMPRESSED AIR INLET F I G U R E VIII TO FOLLOW PAGE 27 G E N E R A L A R R A N G E M E N T O F A P P A R A T U S A R O U N D M A G N E T OSCILLATING ^DETECTOR BAKELITE SHEET PLATFORM BUILT ABOVE MAGNET DEWAR FOR LOW TEMPERATURE MEASUREMENTS MAGNET POLE PIECES LEVELLING SCREW DEWAR "HOLDER PROBE COAXIAL LEAD PROBE SAMPLE CASE 3 - 28 -levelling screws at the edge of the bakelite plate. Temperatures up to about 300°C could be attained and controlled i n the following manner. A regulated Jet of a i r was blown over the heating c o i l arrangement shown i n Figure VII. The temperature of the heating c o i l was controlled by-two Powerstat variable transformers arranged i n tandem. The heated a i r was led up through an unsilvered cylindrical dewar which surrounded the sample container in the magnet gap. Small or rapid variations i n the a i r temperature were greatly damped by the brass of the sample container. It was found that temperature fluctuations during one measurement seldom exceeded! 0.5QC at temperatures below 100°C and kept within tl.O°C up to 200°C. Low temperatures were obtained by immersing the probe directly in the refrigerant. In order to prevent the refrigerant from getting Into the probe, i t was placed in a long close-fitting brass tube which was sealed at the lower end. A cork at the top of this tube also prevented the dis-ruptive condensation of moisture in the probe at low tempera-tures. The refrigerants were liquid a i r for the lowest tem-perature and acetone-dry ice slush baths for the higher tem-peratures. The temperatures did not d r i f t more thantl.O°C during a given resonance measurement. The temperature was measured by a calibrated copper-constantan thermocouple placed directly in the sample, but clear of the sample c o i l . The samples themselves were poly-crystalline powders contained in 10 x 75 mm pyrex test tubes. - 29 -It was sometimes necessary to protect the samples from atmos-pheric oxygen, i n which case they were sealed, i n the test tubes under dry nitrogen. In such cases the thermocouple could not, of course, be placed directly i n contact with the sample. However, i f a melting point tube, closed at one end, was sealed into the wall of the test tube i n such a way that i t protruded into the sample, the contact between the thermo-couple and the sample seemed adequate. - 30 -References in Chapter III (1) Andrew, E.R., Nuclear Magnetic Resonance, Cambridge University Press, 1955, p.50,51. (£) Das, T.P. and Hahn, E.L., Nuclear Quadrupole Resonance Spectroscopy, Solid State Physics, Supplement 1, Academic Press, New York:, 1958, p.85. (3) Bloembergen, N., Purcell, E.M. and Pound, R.V., Phys. Rev., 73, 679 (1948). (4) Pound, R iV. and Knight, W.D., Rev. Sci. Inst., 21, 219 (1950). (5) Roberts, A.; Rev. Sci. Inst., 18, 845 (1947). (6) Gutowsky, H.S., Meyer, L.H. and McClure, R.E., Rev. Sci. Inst., 24, 644 (1953). (7) Hopkins, N.J., Rev. Sci. Inst., 20, 401 (1949). (8) Schuster, N.A., Rev. Sci. Inst., 22, 254 (1951). - 31 -CHAPTER IV METHOD Purification of stearic Acid The stearic acid used in this work was Eastman Kodak white lahel grade. It was purified hy repeated crystalliza-tions at low temperatures according to the procedure of Brown and Kolb (1). About six grams of acid in a t a l l , one lite r beaker was dissolved in 200 ml. of freshly distilled acetone. The beaker of solution was placed in a cooling bath of a dry ice-acetone mixture maintained at -20°C, and the solution was slowly stirred for about one hour. The solvent was removed by suction through a sintered glass, f i l t e r stick. Homologous series of acids differing by only two carbon atoms are very difficult to separate by simple crystallization since their solubilities are too much alike. However, Brown and Kolb have found that i f one component of a binary mixture of adjacent saturated acids Is present in large excess, and the major component is the less soluble, the separation can be accomplished simply by a series of crystallizations. Even i f the major component is the more soluble, part of i t can eventually be obtained pure, provided the less soluble com-ponent .is present in a small enough amount ( l ) . The progress of purification was followed by freezing point measurements. The freezing point of a fatty acid is held to be much easier to reproduce than the melting point, - 32 -and i s considered a reliable Indication of the purity of the sample (2). The recrystallized stearic acid was dried over phosphorous pentoxide in a vacuum dessicator. A sample was then melted in a test tube in a water bath and allowed to freeze while being constantly stirred with a thermometer. A calibrated thermometer, graduated to 0.1°, was used to measure the freezing point. The low temperature crystallization pro-cedure was repeated until the freezing point ceased to rise after further purification. Close agreement with the accepted freezing points for the pure fatty acids usually means that the homologous impurities have been reduced to less than 0.1 percent (3). A maximum freezing point of 69.3°C, found for carefully purified stearic acid, agreed exactly with the value reported by Markley (2). A sample for proton magnetic resonance measurements was prepared by melting the stearic acid in an open 10 x 75 mm test tube and allowing i t to slowly solidify. A capillary tube, sealed at one end, was placed in the sample to act as a thermocouple well. In a l l the proton magnetic resonance measurements, the temperature was maintained constant at least an hour before the resonance spectrum was obtained. At the temperature of liquid air.the sample was given at least three hours to come to thermal equilibrium. Preparation of Sodium Stearate The sodium stearate was prepared from Eastman Kodak white label stearic acid which had been purified in the manner - 33 -previously described ( l ) . The freezing point of this stearic acid reagent was raised to 69.2°C which is slightly less than the accepted value of 69.3°C (2). This stearic acid was dissolved in hot 95 percent ethanol and titrated to a phenol-phthalein end point with a 60 percent aqueous ethanol solution of sodium hydroxide. The sodium stearate was filtered by suc-tion on a Buchner funnel, washed several times with warm ethanol and allowed to dry in air between several leaves of f i l t e r paper. The fluffy sodium stearate crystals were melted under vacuum to remove residual water and ethanol, and to render the soap more compact. At 165-170°C sodium stearate became translucent and at about 260°C i t became transparent, however, i t did not melt until 275-280°C. The fused soap was cooled and then crushed.into a powder. A sample tube supplied with a thermocouple well was f i l l e d with this dense powdered soap. The soap was melted under vacuum once more and slowly cooled. The vacuum system was f i l l e d with dry nitrogen and the sample tube was sealed off. Preparation of Potassium Stearate The method of preparation of potassium stearate was similar to that of sodium stearate. Purified stearic acid (1) with a freezing point of 69.2°C was dissolved in hot 95 per-cent ethanol and titrated to a phenolphthalein end point with a 50 percent aqueous ethanol solution of potassium hydroxide. Potassium stearate precipitated out of the cooled solution as small crystals. These were filtered by suction on a Buchner - 34 -funnel, washed with cold ethanol and dried in an oven at 105°C. The potassium stearate was melted and sealed under dry nitro-gen In a sample tube in the same manner as sodium stearate. On heating, the potassium stearate showed no visible change until 265-270°C when i t became translucent, and as the tem-perature was raised further i t became more and more trans-parent; at 340-345°C i t appeared to melt. Treatment of Results The line width in this work i s defined as the distance along the fiel d axis between points of maximum and niinimum slope of the nuclear magnetic resonance absorption line. This corresponds to the distance along the field axis between the positive and negative" peaks of the derivative curve. The second moment may be calculated directly from the derivative of the resonance absorption curve by using the following equation (4): where +(H) is the intensity of the derivative of the absorp-tion curve in arbitrary units. The other symbols have been defined in Chapter II. For integration, the resonance lines are divided up into many small equal portions along the field axis. As the resonance lines were found to be symmetrical about the center, the center of the line was taken as zero. - 35 -These divisions follow an arbitrary scale which can be related to the magnetic f i e l d by a factor n. The second moment can now be expressed as . , , i i _ z A A 5 G + a + 8b + 27c B = 0 + a + 2b + 3C where a, b, c, etc. are the values of f (H) at positions 1, 2, 3, etc. along from the center of the trace. Originally the separation between the divisions a, b, c, etc. were made very small and the arithmetic was carried out with the help of a desk calculator. An alternative method used, which i s just as accurate, involves plotting A and B on graph paper and weighing the cut-outs to determine the areas. With a fairly regular shaped line, the separation between a, b, c, etc. can be made larger. This procedure can apparently be further simplified (5). A" small broadening of the resonance line i s caused by the modulation field IL^. Andrew has calculated the extent of broadening due t o ' % (6): A H a \ R u e = A H l o 8 S - I f ( H O where A H | t r u e is the real second moment, A H ^ o b g is the observed value and H M is the peak to peak modulation amplitude. A l l second moments reported in this work have been corrected for modulation broadening. 7/hen a number of measurements were made at one particular temperature for a given compound, the line widths and second - 36 -moments were averaged. A standard deviation, £, w a s calculated for such cases using the following formula: 6 = 1 rLLzl!*] 4 where S is the actual value, S is the average value of a l l the results and n is the number of measurements. In most cases only two measurements were made at a given temperature, hut several values of line widths for each compound were available from room temperature measurements. The standard deviations found for line widths are given in Table I. The standard de-viations found for the second moments are given in Table II. Table I . Compound Temperature °C AH gauss 6 Sodium stearate 23 12.8 t o . 2 Potassium stearate 28 12.9 t O.i Stearic acid 24 14.2 t o . 2 Table II Compound Temperature °C AH 2(gauss) 2 6 & ' Sodium stearate 23 19.8 t o . 9 Potassium stearate 28 20.2 ±0.5 Stearic acid 24 19.6 t o . 6 - 37 -On the graphs in the following chapters, these uncertain-ties in the second moments and line widths are only very approximately represented by the size of the points. In the case of sodium stearate line widths, the large number of points made i t undesirable to represent the uncertainty. - 38 -References in Cnapter IV (1) Brown, J.B. and Kolb, D.K., Progress in the Chemistry of Pats and other Lipids, Pergamon Press, London, 1955, vol. 3, p.58. (2) Markleyj K.S., Patty Acids, Intersclence, New York, 1947, p.118. (3) Francis, P., Collins, F.J.E. and Piper, S.H., Proc. Roy. Soc. (Lond.), A158, 691 (1937). (4) Pake, G.E. and Purcell, E.M., Phys. Rev., 74, 1184 (1948). (5) Powles, J.G., Brit. J. App. Phys., 9, 277 (1958). (6) Andrew, E.R., Phys. Rev., 91, 425 (1953). - 39 -CHAPTER V . A PROTON MAGNETIC RESONANCE INVESTIGATION OF SODIUM STEARATE Introduction Anhydrous sodium stearate, C 1 7H 3 5C00Na, i s a white opaque solid which becomes translucent and plastic above 130°C, part-ly transparent above 200°C and completely transparent above 265°C. These changes represent different liquid crystalline phases (1). Sodium stearate undergoes other phase transitions which are not so easily detected. These are li s t e d below i n Table III. The range of temperatures shown for each transi-tion indicates the agreement between different investigations that employed different methods. Table I I I Name of Transition Transition Temperature References Genotyplc Point 65 - 70°C 2,3,4,5 Curd:to Supercurd 89 - 93°C 6,7,8 Supercurd to Subwaxy UO ri 117°C 3,4,5,8 Subwaxy to Waxy 125 - 134°C 3,5,7,8,9 Waxy to Superwaxy 165 - 175°C 5,6,8,9,10 Superwaxy to Subneat 198 - 209°C 3,5,6,8,10,11 Subneat to Neat 226 - 262°C 3,5,6,8,10,11,12 Melting Point 278 - 298°C 5,8,10,12,13 - 40 -To discuss these mesomorphic phases and phase transitions i t i s f i r s t necessary to indicate the general structure of a soap. The x-ray diffraction analysis of most solid fatty acid salts (soaps) shows that they have a layer structure i n which the carboxyl ion ends l i e i n parallel sheets. Two such sheets form a double layer, and both individual sheets and the double layer are held together by positive ions. The long hydro-carbon chains stick out parallel to each other from both sides of this e l e c t r i c a l l y balanced double layer, with their longi-tudinal axes slightly inclined at an angle T to i t ( 8 ) . This arrangement i s illustrated i n the following sketch. Investigations on a series of sodium soaps showed that a given transition temperature i s only slightly dependent on chain length (7,8). It was inferred that similar changes i n structure are involved at a given transition i n a l l the sodium soaps. At the transitions from curd to subwaxy and from sub-- 41 -waxy to waxy the heat effect i s large and varies with the chain length. At higher temperature transitions, the : heat effect i s small and relatively independent of the chain length. It was concluded that low temperature transitions are due mainly to changes i n the arrangement of the hydrocarbon chains while the high temperature transitions are due more to a re-arrangement at the ionic ends of the molecule (7). The genotypic transition was f i r s t reported by Thiessen and Ehrlich (14). Dilatometric curves for sodium palmitate and sodium stearate showed abrupt changes i n slope and certain lines i n the x-ray pattern of sodium palmitate disappeared between 62 and 80°C. An abrupt change i n dielectric constant and a change i n the optical double refraction of sodium pal-mitate at about the melting point of the parent acid gave rise to speculation that part of the cohesive force between the hydrocarbon chains of sodium soap might be overcome at the melting point of the parent acid (2,15). Other observations of a genotypic transition were reported (3,4,8,16). However, there were also cases where the transition was not found (7, 16). Wirth and Wellman did not detect the genotypic point In anhydrous sodium palmitate in the course of their dielectric constant measurements (17). However, they did see a small change i n beta sodium palmitate which contains about three percent water. When beta sodium palmitate contained five per-cent palmitic acid, Wirth and Wellman obtained very much the same results as Thiessen and his coworkers. It was therefore concluded that the genotypic point is due to impurities (17). - 42 -The curd to supercurd transition, which occurs about 90°C, Is usually observed only by differential thermal analysis, and is accompanied by a heat of transition of about one kilocalorie per mole (7,8,20). There seems to be no abrupt change in the density of sodium stearate at the curd to supercurd transition (11,18). Existing structural data are not sufficiently detailed within this temperature.range to indicate precisely what mechanism requires this small amount of heat at 90°C (8,19,21). However, the hydrocarbon chains may have considerable freedom of motion in the supercurd phase. For instance, i t has been reported that the distribution of bands of the infrared spectrum arising from methylene wagging modes in sodium palmitate becomes less well resolved as the temperature approaches 100°C. This i s taken to mean that the sodium palmitate lattice has expanded sufficiently to allow the hydrocarbon chains to flex and twist (19). Such a motion will produce some rotational isomerism, each isomer having its own chain wagging and twisting frequencies. Hence.the infra-red spectrum no longer consists of sharp bands in the 1250 cm"1 region. Analogous spectral changes for sodium stearate were also observed (19). The transition from the supercurd to the subwaxy phase occurs at about 114°C. At this temperature there i s an abrupt change in plasticity, and soap mixed with o i l will swell (4, 22). These changes have been attributed to a loosening of the sodium stearate lattice at the methyl group ends of the hydro-carbon chains, for this would provide easier slip planes (4,22). - 43 -An abrupt decrease in the unit cell long spacings of sodium palmitate at the supercurd to subwaxy transition confirms the fact that there is a change in structure (23). In sodium stearate this change has a latent heat of five kilocalories per mole, which is larger than any of the other heats of tran-sition in this soap (7,8,23). Infrared studies on sodium palmitate show that as the temperature is raised to the v i c i -nity of the supercurd to subwaxy transition there is a large decrease in the intensity of the band, associated with the in-phase motion of a l l the methyl groups. This indicates that many more methylene groups are free to move incoherently about the long axis. A l l the fine structure due to the methylene wagging modes vanishes, while bands assigned to other methyl-ene rocking modes become diffuse or disappear (19). Although there seems to be a significant change of structure at the supercurd to subwaxy transition, there i s again no abrupt change in the density of sodium stearate. However, there is a great change in the slope of the density versus temperature curve in the subwaxy phase (11,18). It would seem then, that the change of the lattice parameters of sodium stearate at the supercurd to subwaxy transition is sufficient to allow con-siderable freedom of motion to the hydrocarbon chains. The subwaxy to waxy transition around 130°C represents the loss of crystalline properties. The soap becomes trans-lucent (9), there i s a relatively abrupt decrease in density (11,18), and according to one investigation the x-ray diffrac-tion lines,representing the short spacings of the unit cell - 44 -disappear (8). Furthermore, the infrared spectrum around 130°C becomes almost identical to that observed for molten fatty-acids (19). There is s t i l l some structure of course, for sodium stearate is s t i l l fairly solid in the waxy phase. How-ever, a great decrease in the short range order of the hydro-carbon chains seems to occur at the subwaxy to waxy transition. The next transition, waxy to superwaxy at about 165°C, is accompanied by a small decrease in density and. an increase in transparency (9,18). A further decrease in the long spacings probably means that the hydrocarbon chains have more room in which to f l a i l about than they had at lower temperatures (21).. Contrary to most of the foregoing evidence, i t has sometimes been held that the waxy to superwaxy transition in sodium stearate, rather than the previous transition, represents the beginning of the liquid-like state for the hydrocarbon chains (1,21,24). It has been suggested that this disagreement may be due to the lack of complete conversion of the samples from one phase to another (25). In one case i t has been noted that the complete conversion of a given phase to the next phase at a higher temperature may require several hours (23). The superwaxy to subneat transition at around 200°C in sodium stearate appears to be similar in kind, but perhaps greater in magnitude, than the waxy to superwaxy transition. In particular, the density decrease is greater and a heat of transition of about one kilocalorie per mole has been reported (7,11,18). The neat type phases show the typical structures of smectic mesornorphs such as focal cones and Grandjean - 45 -terraces (1,7,25). At the subneat to neat transition, about 250°C, sodium stearate will flow under its own weight (13). The transition is also marked by further changes in density and transparency (9,18). Considerable changes in the structure of the ionic layer portion are believed to take place at this transition (7). At about 280°C the remaining long range structure of the neat phase breaks down completely and the soap melts to an isotropic liquid (10,12,13). The Structure of Sodium Stearate X-ray diffraction studies have been carried out on poly-crystalline anhydrous sodium stearate (8,26). The unit cell of sodium stearate at room temperature has been reported as being monoclinic with the following dimensions (42): a 4.16 A b 4.62 A C 44.83 A T 61.53° where the angle of t i l t T is the angle between the. axis of the molecule and the base plane of the unit c e l l . . Density measurements require that each unit ce l l contain only two molecules. Reliable.and reproducible results are difficult to obtain from x-ray studies of sodium stearate and details of the molecular arrangement in the unit cell have not been de-termined (27). On the other hand, the structure of silver stearate has been well defined by x-ray measurements (28). - 46 -The silver stearate unit cell is t r i c l i n i c with the following parameters: a 4.69 A b 4.12 A C 50.35 A <X 104°35' £ 93°59' T 76°1'~ T 68° There are two molecules in this unit c e l l . They are arranged in the usual manner such that there i s an ionic layer or sheet with the hydrocarbon chains extending out from both sides of i t . The planes of these chains are approximately parallel to the a axis, and the longitudinal axes of the hydrocarbon chains are tilted in a plane perpendicular to the a axis. Information concerning the structure of sodium stearate is available from infrared spectroscopic studies. An import-ant feature about the main methylene rocking vibration in the spectra of the higher sodium soaps is that this band i s single. However, many long chain compounds show a doublet in this region (19). It has been suggested that the presence of a doublet is indicative of orthorhombic packed hydrocarbon chains, while a single band in this region is indicative of tric l i n i c packed chains (19). It is probable then, that the sodium stearate unit ce l l is t r i c l i n i c like the unit cell of silver stearate. It should be noted that the unit c e l l cross sections of sodium stearate and silver stearate are almost - 47 -identical. In view of these similarities i t seems reasonable to assume that the arrangement of sodium stearate molecules in the crystal lattice i s very much the same as the arrangement of the silver stearate molecules. The data of Vand, Aitken and Campbell (£8) appear sufficiently complete to allow the construction of a model of the unit cell of silver stearate. For the hydrocarbon chain portion i t has been assumed that the bond angles are tetra-hedral throughout. This assumption agrees with the bulk of experimental results, although there is some evidence suggest-ing that carbon-carbon bond angles may deviate slightly from the tetrahedral in some soaps (28). The carbon-hydrogen bond o length is taken as 1.094 A and the carbon-carbon distance is taken as 1.54 A (29). The hydrocarbon chains are arranged in the zig-zag configuration found in most solid hydrocarbon com-pounds (30). An illustration of a unit ce l l cross section constructed from the dimensions given by Vand, Aitken and Campbell for silver stearate at 20°C (28) is shown in Figure IX. In this illustration i t is assumed that the plane of the carbon zig-zag is exactly parallel to the a axis. Vand et al. (28) could not determine the arrangement of this plane direct-ly and relied upon comparisons with other hydrocarbon com-pounds. It might be profitable therefore to calculate whether or not the hydrocarbon chains, as arranged, are near a minimum of potential energy with respect to rotation about their longitudinal axes. A simple method for such a calculation has been used by F I G U R E IX TO FOLLOW PAGE 47 BARRIER TO ROTATION OF HYDROCARBON CHAIN ABOUT ITS LONGITUDINAL AXIS FOR SILVER STEARATE 0 40 80 120 160 ANGULAR POSITION IN DEGREES - 48 -Lauritzen (31). This method defines the potential harrier in terms of overlapped van der Waals spheres. The energy has its minimum value when the van der Waals spheres are In contact hut do not overlap. Only the hydrocarbon chain portion is considered for the purpose of this calculation; the end groups of the molecule will be ignored. The atoms which are closest to each other are the hydrogen atoms; the van der Waals radius for hydrogen is taken as 1.2 A (29). The potential energy arising from an overlap of van der Waals spheres is given by: V = C £(27.7 - 17.3 r + r 3 ) where C is a constant and r is the internuclear distance* In angstroms, of a pair of hydrogen atoms. When the hydrocarbon chains, arranged as in a silver stearate unit c e l l , are rotated about their longitudinal axes, the potential energy fluctuates with angular position to the a axis in the manner shown in Figure DC. With the help of models and projections of the unit c e l l , i t was found that the potential minimum occurred when the zig-zag plane of a hydrocarbon chain is rotated about seven degrees. Since the effect of the end groups has not been accounted for, the potential minimum might easily be closer to zero degrees rotation. The assumption of Vand et a l . (28) seems to be correct. If i t i s assumed that sodium stearate molecules are packed in the crystal lattice with the same internuclear distances as silver stearate molecules, then i t should be possible to predict the theoretical second moment (32) for the proton magnetic resonance of sodium stearate. The contribution - 49 -of the sodium nucleus to the second moment of sodium stearate w i l l he ignored since i t i s relatively far removed from the hydrogen of the hydrocarbon chain. For a powder sample the expression for the second moment A H| of an assembly of one nuclear species alone i s : The symbols have been defined.in Chapter II. The proton resonance i n a polycrystalline sample i s : where r i s In centimeters (33). The calculation of the theoretical second moment i s s p l i t into two parts; one part i s the contribution of the interaction of the protons i n the same molecule, called the intramolecular contribution, and the other is the contribution of the interactions between protons of different molecules, called the intermolecular contribution. The following table contains the predicted second moments for sodium stearate at two temperatures. In each case r i g i d l attice conditions are assumed; that i s , molecular motions at frequencies comparable to or greater than the resonance line widths are absent. 4. " 5 N I J>K - 50 -Table IV Second Moment of Sodium Stearate Temperature °C Intramolecular contribution (gauss)2 Intermolecular contribution (gauss)2 Total (gauss)d 20° -182° 18.9 18.9 11.4 9.4 30.3 28.3 Vand et al . (28) give an extrapolation formula for the lattice parameters of silver soaps at different temperatures. It is possible therefore to estimate the second moment at -182°C; this i s given in the table above. However, the extra-polation formula i s based upon experimental measurements at 20°C and 78°C only, and may not apply in the region of -182°C. In view of the assumptions involved in arriving at inter-nuclear distances for sodium stearate, i t would not seem un-reasonable to consider the two values for the total second moment as approximate limits, within which the experimental second moment might be found. Experimental Results In a preliminary Investigation, the proton magnetic resonance line width of sodium stearate was measured at several different temperatures. The results of this investiga-tion seemed to agree fairly well with the results of a similar study made some years previously (24). The line widths observed in the present study are plotted against temperature in Figure X. The course of the results of the previous study - 51 -Is represented in Figure X by the heavy line. Next, the sample of sodium stearate was left at 138°C for about twelve hours, during which time the line width narrowed from 4.1 gauss to 2.6 gauss. The sample was then allowed to cool slowly to room temperature. A second Investigation of the temperature dependence of the sodium stearate line width was made. This time, however, the temperature was maintained for more than two hours before the proton magnetic resonance was recorded, rather than thirty minutes as before. Under these new conditions, the line width began to narrow at a lower temperature than i t did before. A second sample was obtained which had been used in the original investigations (24). Under the new conditions, the proton magnetic resonance line widths from this sample also showed a narrowing at a lower temperature and agreed well with the new results. To find whether or not the maintenance of temperature for even longer times would cause a narrowing of the line width at even lower temperatures, a third sample was kept about four hours at each temperature before a measurement was made. The results from this third sample agreed closely with the other two, hence thermal equilibrium had probably been established after the temperature was maintained for about two hours. As an extra precaution, the temperature was usually held constant about twelve hours i f i t was in the vicinity of a known phase transi-tion. Investigations;were now extended to lower temperatures with the third sample. The line width results from a l l samples are shown in Figure XI. It seems evident that the original - 52 -proton magnetic resonance studies on sodium stearate (24) reported a situation where thermal equilibrium had not been properly established, although the line width changes had seemed reproducible. A similar condition has occurred in the course of x-ray studies on sodium stearate and the same kind of misleading results have been reported. (21,23,25) The line width of sodium stearate at -182°C was found to be 16.1 gauss. As the temperature was raised, this line width was observed to decrease in a regular manner. The behaviour of the line width with temperature from -70°C to 130°C is shown in Figure XI. The line width appears to decrease with temperature linearly up to about 45°C where the line width is about 12.5 gauss. Above this temperature the line width de-creases much more rapidly and at 90°C i t is about 5 gauss. From 90°C to 113°C the line width versus temperature curve changes slope and decreases to 2.8 gauss. This temperature range coincides with the supercurd phase. Between 113°C and 114°C the line width abruptly narrows from 2.8 gauss to a width which appears to be limited only by fi e l d homogeneity. This abrupt narrowing coincides with the supercurd-subwaxy phase transition. Some first derivative curves of the proton magnetic resonance absorption of sodium stearate which are character-is t i c of particular temperature regions are shown in Figure XII. The curve at -182°C is very similar to low temperature proton resonance curves reported for octadecane (34) and poly-ethylene (35). As the temperature i s raised to 23°C, the F I R S T D E R I V A T I V E C U R V E S F O R S O D I U M S T E A R A T E a. >v (o a 10 i & i t i 6 GAUSS F I G U R E XII TO FOLLOW PAGE 5 2 - 53 -narrowing of the resonance derivative curve at the tails is about twice the narrowing at the maximum slope peaks. From 23°C to the curd-supercurd transition in the vicinity of 90°C the line width decreases considerably, but the width between the tails changes scarcely at a l l . Throughout the supercurd phase the tails begin to decrease in width, but even at the supercurd-subwaxy transition, where the line width becomes very narrow, the ta i l s are s t i l l quite broad. Here the actual line shape would be a narrow spike mounted on a comparatively broad, low pedestal. At 130°C, in the vicinity of the subwaxy-waxy transition, this pedestal decreases in width and ampli-tude and becomes difficult to measure accurately; i t seems to persist up to about 200°C, however. The fine structure on the derivative curve at 23°C in Figure XII is also apparent at -51°C. It reaches its maximum amplitude at 23°C, whereupon i t quickly decreases and dis-appears as the temperature i s raised further. The amplitude of this fine structure seems to depend upon the thermal history of the sample. The line width of the fine structure at 23°C is very narrow and is limited by the fiel d homogeneity and the operation of the oscillator. The second moment of the proton magnetic resonance of sodium stearate at -182°C was found to be 28.0 * 1.5 gauss2. The behaviour of the second moment over the temperature range -70°C to 130°C is shown in Figure XIII. These values were obtained from Investigations with the third sample only. The second moment decreases from 21.2 gauss2 at -69°C to 19.9 S E C O N D M O M E N T I N ( G A U S S ) * 0 * ® o w ^ © a o po cr> 1 i i i i i i i i i i i i i i i i i i i i i i i i i i i » - 54 -gauss2 at -28°C and then remains almost constant up to 23°C. Above room temperature the second moment decreases in a regular manner to just below the supercurd-subwaxy transition point, where, at 111°C i t has a value of 7.8 gauss2. The second moment decreases fairly abruptly between 113°C and 114°C, the supercurd-subwaxy transition, where i t goes from 6.7 gauss2 to 1.2 gauss2. At 118°C the second moment has de-creased even more to 0.6 gauss2 and at 130°C, around the subwaxy-waxy transition, i t is 0.4 gauss2. The tails on the absorption line up to 200°G would indicate that the second moment i s finite at least up to that temperature. However, the small size of these tails makes i t difficult to determine a reliable second moment, although i t is likely to be con-siderably less than 0.4 gauss2. Discussion The decrease in the proton magnetic resonance line width of sodium stearate as the temperature is Increased can, in general, be said to be due to molecular motion. Since a l l the protons in the molecule are in the hydrocarbon chains, the line width is to some extent a function of the amount of motion that the chains are undergoing. The motions responsible for noticeable narrowing of the resonance line correspond to -frequencies of the order of the rigid lattice line width, that i s , about 70 kilocycles per second (36). From the details of the hydrocarbon chain packing already discussed, the most likely motion would seem to be rotation or rotational oscilla-- 55 -tion about the chain longitudinal axis. The line width versus temperature change shown in Figure XI would then suggest that there is a gradual increase in the amount of chain reorienta-tion up to 45°C. Above this temperature the magnitude of re-orientation about the chain axis grows rapidly. The very narrow line at 114°C -must represent considerable freedom of motion of the hydrocarbon chain (37). The rapid change of line width above 45°C seems to be accompanied by a change in line shape-, as is indicated by Figure XII. Some consequence of this line shape change will be discussed later. The fine structure on the derivative curve at, 23°C is of a kind that has been previously observed in long chain hydrocarbons (34,38). Fine structure observed in the proton magnetic resonance line of methyl chloroform has been shown to be due to impurities (39); in iso-butyl bromide fine structure seems to arise from the coexistence of crystal and supercooled liquid (40). Impurities probably play an im-portant role in giving rise to the fine structure of the resonance line of sodium stearate. However, since this fine structure shows some dependence on the thermal history of the sample, i t might also represent amorphous regions in the sample. It may be that sodium stearate molecules in the vicinity of an impurity molecule have difficulty in orienting themselves into the usual soap structure and may instead get tangled up or be forced apart so that rapid motion leading to a narrow line is possible. At -182°C the experimental second moment for sodium - 56 -stearate i s 28.0 gauss2. This value is at the lower limit for the calculated values given previously. It cannot be said that motion, as defined for this work, is completely absent at -182°C in sodium stearate. On the other hand, considering the assumptions involved in arriving at a theoretical rigid lattice second moment, the experimental value probably re-presents only a slight departure from rigid lattice conditions. In this discussion 28.0 gauss2 will be taken as the rigid lattice second moment for sodium stearate. It i s evident then that some motion of the hydrocarbon chains exists at -69°C where the second moment is 21.2 gauss2. It is possible to predict the reduction of the second moment caused by certain regular types of motion by using the equations set forth in Chapter II. The free reorientation of the methyl end group about its C3 axis will reduce the intramolecular contribution by 1.9 gauss2. For some kinds of motion likely in solid long chain hydrocarbons, Andrew (34) has found that the intra- and intermolecular contributions are reduced by about the same factor. • The reorienting methyl end group will reduce the intermolecular contribution from 9.1 gauss2 to 8.2 gauss2 and the total predicted second moment for sodium stearate with the methyl end groups reorienting freely about their C 3 axes is 25.2 gauss2. This reduction is not sufficient to account for the observed second moment at -69°C. The approximate potential energy diagram in Figure IX shows that considerable torsional oscillation about the longi-tudinal axes of the hydrocarbon chains i s possible. Assuming - 57 -that the rigid lattice second moment of sodium stearate is 28.0 gauss2, the effect of torsional oscillation on the second moment can he predicted. The predictions, shown in Figure XIV, were computed hy means of Andrew's equation for the reduction in second moment due to torsional oscillation. It can he seen from Figure XIV that an average torsional oscillation of 29 degrees is sufficient to account for the second moment of 21.2 gauss2 at -69°C. Furthermore, the average angle of oscillation need only he increased to 32 degrees to account for the 19.8 gauss2 observed at room temperature. It might be possible to account for the second moment of 16.1 gauss2 found at 62°0 i f torsional oscillation of 41 degrees was assumed. The potential energy diagram indicates that further oscilla-tion of this type is unlikely. However, i f the methyl end group is assumed to reorient freely.about its C 3 axis, then less torsional oscillation will be necessary to account for the observed second moments. For example, i t has been shown that the rotation of the methyl end group reduces the rigid lattice second moment by 2.8 gauss2, that i s , by one tenth. If i t is assumed that the second moment versus angle of oscillation curve in Figure XIV is reduced by one tenth, then about 22 degrees average torsional oscillation is sufficient to explain the second moment at -69°C, 26 degrees average tor-sional oscillation at 23°C and 36 degrees at 62°C. Now suppose the sodium stearate molecules become free to reorient about their longitudinal axes. The intramolecular second moment for this condition can be calculated by means of the T H E E F F E C T O F T O R S I O N A L O S C I L L A T I O N O N T H E S E C O N D M O M E N T O F S O D I U M S T E A R A T E en 0 I i i i i i i i i i i 0 40 80 120 160 TORSIONAL OSCILLATION <* IN DEGREES F I G U R E X I V TO F O L L O W PAGE 57 - 58 -treatment outlined, by Gutowsky and. Pake (36) and is found to be 5.5 gauss . The intermolecular second moment is determined as before by assuming the rigid lattice Intermolecular second moment is decreased by the motion in the same proportion as the intramolecular second moment. The intermolecular second moment becomes 2.6 gauss2 and the total second moment i s 8.1 gauss2. If the whole chain can rotate about its longitudinal axis i t seems reasonable to assume that the methyl end group can also rotate about its C 3 axis independently. This corres-ponds to rotation about two axes and will reduce the intra-molecular second moment contribution from the methyl end group s t i l l further. The change in second moment due to the rota-tion of methyl groups about two or more axes has been de-scribed by Powles and Gutowsky (39,48) and is applied to sodium stearate to give an intramolecular second moment of 5.3 gauss2 and a total second moment of 7.8 gauss2. This corresponds to the experimental second moment found around 111°C. It must be noted that the experimental second moments have an accuracy of ±5 percent, therefore the temperature referred to for a particular form of molecular motion is only approximate. So far the possible effect of the ionic layer formed at the carboxyl ends of sodium stearate has been ignored. It would seem reasonable to suppose that the portions of the hydrocarbon chain nearest the strongly bonded ionic layer would be able to undergo torsional oscillation to a somewhat lesser extent than the portions of the chain farthest away - 59 -from the ionic layer. In other words, the hydrocarbon chain should twist about i t s longitudinal axis rather than undergo a simple torsional oscillation of the whole molecule. It has been shown that twisting of the chain may facilitate the tran-sition from torsional oscillation to complete rotation (41,42). If the hydrocarbon chain is assumed to be rigid, then on rotating, the whole chain has to be lifted over the potential barrier at the same time. If V-j^ is the energy required to l i f t a single link over the barrier, the total energy will be V m = mVp where m is the number of carbon atoms in the chain. If the chain has a certain flexibility, then i t may be gradually lifted over the potential barrier so that a total energy less than mV^ nay be required. A twisting of the hydro-carbon chain will also require a certain energy, but this has been shown to decrease with increasing chain length for a given angle of twist of the end of the chain (42). For a short chain the potential barrier, Vm, is proportional to the number of methylene links, but for long chains V m will tend to a constant value independent of chain length. For a twisting hydrocarbon chain i t has been shown that (42) vm = v l ^ T a n l 1 " The value m is a constant which separates short chains from long chains and is taken to be 26. If the methyl end group is assumed to be reorienting freely and is ignored, m may be taken as 16 for sodium stearate. Application of the formula shows that the energy barrier opposing the rotation of the - 60 -hydrocarbon chain about its longitudinal axis in sodium stearate i s , for a twisting chain, seven eighths as large as for a rigid chain. In view of favourable lowering of the potential barrier and the particular constraint imposed upon the hydrocarbon chains by the ionic layer in the sodium stearate, i t would seem most probable that the chain is undergoing rotation by stages along the chain until complete rotation is achieved at 111°C. If the torsional oscillation and twisting are in phase, as might be expected, a few degrees of torsion around the longitudinal axis at the chain end nearest the ionic layer might allow complete rotation of some groups at the opposite end. For instance, suppose that the carboxyl carbon is kept rigid by the ionic layer, but that the rest of the chain is free enough to twist about its longitudinal axis. Suppose each methylene group rotates by ten degrees more than it s neighbour nearest the carboxyl end, and that the methyl end group is free to reorient about its C 3 axis. If the second moments taken from Figure XIV at ten degree Intervals are altered for methyl end group rotation, and i f the first sixteen of these are averaged (starting from <X - 0), then the second moment is 12.2 gauss2. This corresponds roughly to the experimental values found between 80°C and 90°C. More twist-ing than this will be necessary to account for the experimental values in the supercurd phase where the second moment is found to decrease from about 12 gauss2 to about 7 gauss2. It has already been mentioned that a second moment value around 7.8 gauss2 corresponds to a situation where the chains reorient - 61 -freely about their longitudinal axes. Hence, the experimental results for the supercurd phase might represent an increasing amplitude of chain twisting until the whole molecule is able to rotate. Now such a rotation seems to require that the carboxyl groups be free to rotate also, i f the original crystalline packing is to be maintained. This rotation seems unlikely, for the unit cell parameters given for silver stearate by Vand^ Aitken and Campbell show that the metal and carboxyl ions must be fitted together compactly (28). On the other hand, the sodium stearate lattice i s probably expanding as the temperature is raised; this is born out by dilatometric measurements (11,18). And i f , in the expanded lattice of the supercurd phase, the carboxyl groups cannot rotate, perhaps the hydrocarbon chains will have enough room to oscillate slightly in a direction at right angles to the chain axis. A small lateral oscillation of the twisting hydrocarbon chains might be sufficient to account for the second moment of 6.7 gauss2 at 113°C, which is smaller than that predicted for com-plete chain rotation even with the t 5 percent uncertainty. Between 113°C and 114°C the second moment decreases from 6.7 gauss2 to 1.2 gauss2. Such a reduction is usually taken to indicate that the ihole of the molecule is reorienting about more than one axis (33). If a molecule is free to reorient about axes in any direction, that i s , i f molecular tumbling i s isotropic, the intramolecular contribution to the second moment should average to zero. However, so long as,the centers of mass of the molecules remain fixed, the inter-- 62 -molecular contributions w i l l not average to zero and a small but f i n i t e second moment should be observed (43). The super-curd to subwaxy transition at 114°C in sodium stearate appears to involve a change from rotation or twisting about the longi-tudinal axis of the hydrocarbon chain to a condition where re-orientation may be possible about other axes. Yet the second moment of 1.2 gauss 2 suggests that the sodium stearate mole-cules are s t i l l fixed in the crystal l a t t i c e . There may now be room enough for the hydrocarbon chains to f l a i l about; the ionic layer probably remains.intact, however. The smaller, but s t i l l f i n i t e second moment of 0.4 gauss 2 found at 130°C i n the v i c i n i t y of the subwaxy-waxy transition would indicate, s t i l l greater freedom of motion for the hydrocarbon chains. Perhaps this i s due to some alteration i n packing of the ionic layer. Above 130°C there i s s t i l l some suspicion of structure and the zero second moment indicative of diffusion i s probably not reached below 200°C. These results seem to agree with the conclusions drawn from recent x-ray studies on sodium stearate (44). Above the supercurd-subwaxy transition the la t t i c e structure consists of a set of parallel ribbons,>Indefinite in length, packed i n a rectangular array. The sodium carboxylate ends of the molecules f i t into the ribbon and the hydrocarbon chains, i n a li q u i d - l i k e state (19), f i l l up the rest of the latt ic e. The thermal activation of molecular motion i n long chain hydrocarbon derivatives and some polymers has been studied by measurements of dielectric relaxation (45). Nuclear magnetic - 63 -resonance measurements may also be used for these studies and have the added advantage that polar groups need not be in motion or even be present in the c cm pounds. The method for calculating the activation energy of the motion from the narrowing of the resonance envelope due to this motion has been discussed in Chapter II of this work. The equation of . Gutowsky and Pake (36) is expressed again in terms of the line width A H in gauss: Vc - f f A H / T ™ [ I (AH*- 6';/(A'- 8l) where £ is taken as unity, A H is the line width in the tran-sition region, B is the line width at a temperature above the transition and A is the line width below this region. For sodium stearate B is taken as 2.8 gauss, which is the line width just prior to the super cur d-subwaxy transition at 114°C, and A is 16.1 gauss which is considered to be the rigid lattice line width at -182°C. These values for A and B were chosen because second moment studies previously discussed indicated that the motion is likely to be about the longitudinal axis of the hydrocarbon chains in the temperature range between these values. Gutowsky and Pake (36) assume an Arrhenius relation for the correlation frequencies so that a graph of \TK VC versus l/T is used to evaluate the thermal activation energy A E of the motion. The application of this method to sodium stearate line widths is shown in Figure XV. Two activation energies were found by this method for sodium stearate, one F I G U R E X V TO FOLLOW PAGE 6 3 - 64 -represents the temperature region above 65°C and the other the range below i t . Table V Range A E kcal/mole Vo c/sec. Below 65°C 0.8 Above 65°C 19.2 Finding two activation energies by this method may not be unusual, for a similar situation has been reported for poly-ethylene (35,46). A physical interpretation for the activa-tion energies i n polyethylene has been suggested. For the small energy at low temperatures a small amplitude torsional oscillation i s postulated, while at high temperatures the large activation energy i s ascribed to rotational and trans-lational modes of large amplitude (46). The case for sodium stearate may be similar, although the known crystal structure would not be expected to allow large translational modes below the supercurd-subwaxy transition at 114°C. It has been shown that the magnetic resonance line shape of sodium stearate changes with temperature. Powles states that the line width i s not a good measure of temperature effects l f the line shape changes (47) and the use of the second moment for such calculations i s suggested (48). Hence the correlation frequency i s expressed as: u = ^ (AH:)VT„ I AH: - (AHP. * (AH:)A-(AH:)8 8.9 X 10* 7.6 X 10 1 6 - 65 -p Here AHg Is the second, moment at any temperature in the tran-sition region. The subscripts A and B indicate the low and high temperature limiting values respectively. The second moment (AH | ) a was taken as 28.0 gauss2 at -182°C and (AH | ) B was taken as 6.7 gauss2 at 113°C. The graph of In Vc versus l/T in Figure XVI yielded a series of points through which two intersecting straight lines can be drawn, though not without some uncertainty. The two activation energies derived from the slopes are given below in Table VI. Table VI Temperature Range A E in kcal/mole -182°G to 34°C * 0.5 84°C to 113°C 22 The activation energies A E in Table VI suggest that there is reorientation over a relatively large potential barrier and that this motion begins in the vicinity of the curd-super curd transition temperature. Below this transition temperature some molecular motion involving a relatively small activation energy may be taking place. The second moment results, pre-viously discussed at length, indicated that the hydrocarbon chains of sodium stearate may be rotating or twisting about their longitudinal axes and that this rotational motion is somewhat more violent in the supercurd phase above about 90°C. It seems probable that the larger value of A E from the line width results in Table V and the second moment results in F I G U R E X V I TO FOLLOW PAGE 6 5 - 66 -Table VI, represents the activation energy required for this twisting of the hydrocarbon chains. The exact temperature range of the activation energies in Table V and Table VI probably have l i t t l e significance, and the differences in the two cases may be due to the change in shape of the proton magnetic resonance line. Activation energies from 6 kcal/mole to 13 kcal/mole, obtained from the narrowing of the resonance lines in poly-ethylene, have been ascribed to rotational modes of motion of large amplitude (35,46). A similar line narrowing mechanism is proposed for sodium stearate in the temperature range from about 60°C to about 114°C. However, activation energies of 19 to 22 kcal/mole were obtained for sodium stearate, and these are almost, twice as large as the activation energies reported for polyethylene. In polyethylene the greatest line narrowing seems to be due to molecular motion in amorphous regions in the solid where the contact between the hydrocarbon chains is relatively small (35). Sodium stearate, on the other hand, seems quite crystalline below the.supercurd-subwaxy transition (21), so that any motion taking place must overcome a larger barrier due to the greater lattice energy. The approximate activation energy, Vm, for the twisting of a hydrocarbon chain about its longitudinal axis, can be calculated from Frohlich's equation discussed previously in this chapter. (42). For most simple, substituted hydrocarbons, V 1 is taken as about 0.8 kcal/mole (42) and hence V m is about 11 kcal/mole. The potential energy barrier opposing such twisting in sodium - 67 -stearate must therefore he about twice as large as in most hydrocarbon compounds of the same chain length. - 68 -References In Chapter V Doscher, T.M. and Void, R.D., J. Phys. and Colloid Chem. 52, 97 (1948). Thiessen, P.A., Klenck, J., Gockowinck, H. and Stauff, J Z. physik. Chem. A, 174, 335 (1935). Void, R.D., J. Phys. Chem., 49, 315 (1945). Southam, F. and Puddington, I.E., Can. J. Research, B25, 121 (1947). Ravich, G.B. and Nechitaylo, N.A., Doklady Akad. Nauk, 83, 117 (1952). Void, M.J., J. Am. Chem. Soc, 63, 160 (1941). Void, R.D., J. Am. Chem. Soc, 63, 2915 (1941). Kokotailo, G., Thesis, Temple University, 1955. Benton, D.P., Howe, P.G. and Puddington, I.E., Can. J. Chem., 33, 1384 (1955). Void, R.D., Macomber, M. and Void, M.J., J. Am. Chem. Soc, 63, 168 (1941). StainsPy, G., Farnand, R. and Puddington, I.E., Can. J. Chem., 29, 838 (1951). Void, R.D. and Heldman, M.J., J. Phys. and Colloid Chem. 52, 148 (1948). Powell, B.D. and Puddington, I.E., Can. J. Chem., 31, 828 (1953). Thiessen, P.A. and Ehrlich, E., Z. physik. Chem., B19, 299 (1932). Thiessen, P.A. and Kienck, J., Z. physik. Chem., A174, 335 (1935). - 69 -(16) Gallay, W. and Puddington, I.E., Can. J. Research, B21, 202 (1943). (17) Wirth, H.E. and Wellman, W.W., J. Phys. Chem., 60, 921 (1956). (18) Benton, D.P., Howe, P.G., Farnand, R. and Puddington, 1. E., Can. J. Chem., 33, 1798 (1955). (19) Chapman, D., J. Chem. Soc, 784 (1958). (20) Stross, F.H. and Abrams, S.T., J. Am. Chem. Soc, 73, 2825 (1951). (21) De Bretteville, A. and McBain, J.W., J. Chem. Phys., 11, 426 (1943). (22) Gallay, W. and Puddington, I.E., Can. J. Research, B22, 90 (1944). (23) Nordsieck, H., Rosevear, F.B. and Ferguson, R.H., J. Chem. Phys., 16, 175 (1948). (24) Grant, R.F., Hedgecock, N. and Dunell, B.A., Can. J. Chem., 34, 1514 (1956). (25) Brown, G.H. and Shaw, W.G., Chem. Rev., 57, 1109 (1957). (26) Vand, V. and de Boer, J.H., Proc. K. Akad. Wet. Amst., 50, 991 (1947). (27) Stosick, A., J. Chem. Phys., 18, 1035 (1950). (28) Vand, V., Aitken, A. and Campbell, R.K., Acta Cryst., 2, 398 (1949). (29) Pauling, L., The Nature of the Chemical Bond, Cornell University Press, 1948, p.161, 189. (30) Miiller, A., Proc. Roy. Soc (Lond.), A124, 317 (1927). (31) Lauritzen, J.I., J. Chem. Phys., 28, 118,(1958). - 70 -Van Vleck, J.H., Phys. Rev.,..74, 1168 (1948). Andrew, E.R. and Eades, R.G., Proc. Roy. Soc. (Lond.), A216,398 (1953). Andrew, E.R., J. Chem. Phys., 18, 607 (1950). Rempel, R.C., Weaver, H.E., Sands, R.H. and Muller, R.L. J. Appl. Phys., 28, 1082 (1957). Gutowsky, H.S. and Pake, G.E., J. Chem. Phys., •18, 162 (1950). Bleombergen, N., Purcell, E.M. and Pound, R.V., Phys. Rev., 73, 679 (1948). Rushworth, F.A., Proc. Roy. Soc. (Lond.), A222, 526 (1954). Powles, J.G. and Gutowsky, H.S., J. Chem. Phys., 21, 1695 (1953). Powles, J.G. and Kail, J.A.E., Proc. Phys. Soc, ]373 , 833 (1959). Hoffmann, J.D., J . Chem. Phys., 20, 541 (1952). Frohlich, H., Theory of Dielectrics, Oxford University Press, Second Edition, 1958, p.128. Andrew, E.R., Nuclear Magnetic Resonance, Cambridge University Press, 1956, p.173. Skoulios, A. and Luzzoti, V., Nature (Lond.), 183, 1310 (1959). Smyth, CP., Dielectric Behavior and Structure, McGraw-Hill, New York, 1955, p.139-191. McCall, D.W. and Slichter, W.P., J. Poly. Sci., 27, 171 (1957). - 71 -(47) Powles, J.G., Proc. Phys. Soc. (Lond.), B69, 281 (1956). (48) Powles, J.G. and Gutowsky, H.S., J. Chem. Phys., 23, 1692 (1955). - 72 -CHAPTER VI A PROTON MAGNETIC RESONANCE INVESTIGATION OF STEARIC ACID Introduction The normal saturated fatty acids each consist of a hydro-carbon chain with a carboxyl group at one end. In the s o l i d state the hydrocarbon chain i s an extended zig-zag arrangement of carbon atoms i n one plane, and a l l the carbon bonds are arranged with a tetrahedral angle. The acids c r y s t a l l i z e with the long axes of the hydrocarbon chains p a r a l l e l ; the terminal groups become associated In planes throughout the crystal. Moreover, the molecules exist as dlmers such that p a r a l l e l planes of carboxyl groups and of methyl groups may occur. The hydrocarbon chains themselves are not necessarily perpendicu-l a r to these planes and indeed, they are usually t i l t e d (1,2, 3). The normal fatty acids exhibit polymorphism. The forma-tion of a particular polymorph seems to depend on the purity of the acid and the conditions of c r y s t a l l i z a t i o n (4). Acids with an even number of carbon atoms may occur i n three d i f f e r -ent crystal forms designated A, B and C. X-ray diffraction examinations of these acids have shown that the long spacings decrease and the t i l t of the chains increases i n the order A to B to C (5). From the melt, the even-numbered acids crys-t a l l i z e i n the C-form. The fact that but one melting point i s observed for these acids would indicate that the A and the B - 73 -forms transform readily to the C-form upon heating; this is also borne out by x-ray studies (6). Reverse transformations apparently do not occur, so although crystallization from sol-vents often leads to a mixture of polymorphic forms, a sample made up entirely of the C-form can be obtained by crystalliza-tion from the melt. Dielectric measurements on the C-form of stearic acid suggest that there is no rotational phase below the melting point of the kind observed in the corresponding esters (7). However, the specific volume of stearic acid exhibits a marked increase between 60°C and the melting point (6). There is also no abrupt change In the slope of the specific volume versus temperature curve at the melting point of stearic acid, such as is usually found for pure organic compounds (6). This kind of behaviour in long chain hydrocarbon compounds has some-times been attributed to premelting (8). This possibility is investigated in the following study. The C-Form Structure of stearic Acid The intramolecular distances are taken from the model of a long hydrocarbon chain described by Muiler (9). The average ii distance between alternate carbon atoms was taken by Muiler as 2.51 Aj and he assumed that the bond angles in the hydrocarbon chain were a l l equal to the tetrahedral angle 109°28'. How-ever, Malkin reported this distance to be about 2.6 A in the B-form of stearic acid, so that the angles of the planar carbon zig-zags would be 116° (10). The electron density - 74 -projection for the C-form of lauric acid reveals that the hydrocarbon chain i s slightly bent i n a bow shape (11). The results of a similar study on the B-form of stearic acid show that the portion of the hydrocarbon chain nearest the carboxyl group i s deformed (12). The distance between alternate carbon atoms reported by Malkin must be an average value, for his x-ray studies only gave unit c e l l dimensions (10), and since the hydrocarbon chain of the B-form of stearic acid i s now known to be distorted (12), Malkin 1s value i s probably not significant. The bond angles i n the hydrocarbon chain w i l l therefore be taken as the tetrahedral angle. The unit c e l l of the C-form of stearic acid i s a long monoclinic prism. Two stearic acid molecules, associated at the carboxyl groups, l i e along each of the four edges of the prism, surrounding a f i f t h pair i n the center. Two of these pairs belong to the unit c e l l , the remaining three pairs are associated with adjoining c e l l s (10). The unit c e l l dimen-sions for the C-form of stearic acid (13) are given below: a 9.36 A b 4.96 A C 50.8 A £ 128°14' From a detailed structural determination of lauric acid the hydrocarbon chain was found to be t i l t e d by an angle T of 54°52' i n the ac plane (11). It i s assumed that T i s about the same for a l l the acidsj since B differs only slightly i n the series given above. The angle that the plane of the - 75 -carbon zig-zags makes with the a axis is taken as 45° (11). The unit ce l l cross section for stearic acid (13) is shown in Figure XVII. The dimensions of the carboxyl dlmer portion of lauric acid are assumed to apply to a l l the acids (11). The 0-H bond length is taken as 1.04 A (14), hence the inter-proton distance in the dimer is 2.40 A. The carbon-hydrogen bond length is 1.094 A and the carbon-carbon bond length is taken as 1.54 A (15). The packing of the carboxyl groups in lauric acid is known from the work of Vand, Morley and Lbmer (11) and is,assumed to apply to stearic acid. If the distance between alternate carbon atoms in the hydrocarbon chain is o taken as 2.52 A, the length of each molecule can be determined. On this basis, the distance between the planes passing through the carbon nuclei of the end methyl groups of adjacent unit cells is found to be 2.18 A. From these data the rigid lattice second moments for the proton magnetic resonance of the C-form of stearic acid can be calculated (16). By employ-ing the procedure used for sodium stearate, the intramolecular second moment was found to be 18.4 gauss2, the intermolecular second moment was found to be 6.0 gauss2, giving a total of 24.4 gauss2. Experimental Results As the temperature of stearic acid is raised from the liquid air temperature of -188°C to about 24°C, the derivative of the proton magnetic resonance absorption line begins to show a vestige of a narrow peak along with the usual broad F I G U R E XVII TO FOLLOW PAGE 75 A R E P R E S E N T A T I V E C R O S S S E C T I O N O F A F A T T Y A C I D U N I T C E L L - 76 -peak expected for a solid hydrocarbon. Above room temperature the narrow peaks become much more pronounced until about three degrees below the melting point the broad peaks have almost disappeared. The selection of fi r s t derivative lines in Figure XVIII serves to illustrate this behaviour. The growth of the narrow peaks at the expense of the broad peaks is shown in Figure XIX. Here the amplitude of the narrow peak h N is divided by the amplitude of the broad peak h B and this ratio is plotted as a function of the number of degrees centigrade from the freezing point. The temperature is represented in this way for convenience when comparing the narrow peak growth of different fatty acids or of samples of one acid which differ in purity. The results from three different purities of stearic acid are represented in Figure XIX. The sample with a freezing point of 69.3°C is probably quite pure and, according to Francis and Piper (18), may have less than 0.1 percent of homologous impurities (17,18). The sample with the freezing point of 68.1°C is the unpurlfied Eastman Kodak white label grade acid which may have as much as 5 percent of homo-logous impurities (19,20). The change of the peak amplitude ratios with temperature from the freezing points appears to be the same for a l l the stearic acid samples. In this respect, the narrow peaks seem to be independent of small quantities of impurities in the sample. The variation of line width with temperature for the broad peak of stearic acid F.P. 69.3°C is given in Figure XX. At -188°C the line width is 15.5 gauss, i t narrows to 14.2 F I G U R E XVIII TO FOLLOW PAGE 7 6 STEARIC ACID O N E H A L F O F F I R S T D E R I V A T I V E C U R V E S S H O W I N G F I N E S T R U C T U R E 0 2 4 6 8 10 12 14 G A U S S 0 2 4 6 8 10 12 14 G A U S S F I G U R E XIX TO FOLLOW PAGE 7 6 S T E A R I C A C I D FREEZING POINT — T °G L I N E W I D T H IN G A U S S m TJ m > a m o 00 o 00 o O O I o ro o o cv o ro en oo T l C7> CD C O H m > o o o o ro ZD m X X O o r -i -o "D > m O 1 O 0 - 77 -gauss by -42°C and remains approximately at this value until 66°C. Above this temperature, the resonance absorption of the broad peak: component is so weak: that i t s width is difficult to measure accurately. However, a trace of the broad component remains until 69°C. The true width of the narrow component was not obtained directly. The narrow peaks of small ampli-tude became indistinct when the modulation amplitude was lowered below 0.5 gauss peak to peak. The widths of the narrow peaks at 54°C, 61.5°C and the melting point a l l were governed by the modulation amplitude and the inhomogeneity of the magnetic field. A certain amount of dispersion was noticed in the narrow line below a width of 0.1 gauss. This is apparently caused by a slight change in the operating fre-quency of the marginal oscillator due to the change in the magnetic susceptibility of the sample at resonance. The maxi-mum frequency change due to this dispersion phenomenon is in-versely proportional to the width of a simple absorption line and is ordinarily negligible in solids (21). This inherent defect in the marginal oscillator method makes i t unprofitable to investigate nuclear magnetic resonance lines narrower than 0.1 gauss. A Varian Model V-4300A high resolution nuclear magnetic resonance spectrometer with a sample thermostat was made available for a short time. Stearic acid in a cylindrical 5 mm. outer diameter glass tube was melted and then allowed to solidify slowly. At the same time a number of high resolution spectra were obtained which are shown in Figure XXI. No TO FOLLOW PAGE 7 7 F I G U R E XXI H I G H R E S O L U T I O N P R O T O N R E S O N A N C E S P E C T R A O F S T E A R I C A C I D S O L I D I F Y I N G A T 6 9 °C - 78 -proton magnetic resonance absorption could be detected below the freezing point in this case, and the line width observed just below freezing was approximately 0.01 gauss. The true width of the narrow peak in the broad line spectrum is there-fore between 0.1 and 0.01 gauss. The various peaks in the high resolution proton magnetic resonance spectra, rather in-distinctly shown in Figure XXI,- are chemical shift peaks (22). The main peak in the high resolution spectrum is due to the methylene hydrogen in the long chain. The small peak to the right and about 18 cycles per second from the main peak is assigned to the methyl end group protons. The small peak about 39 cycles per second to the\eft of the center peak is assigned to the protons of the alpha methylene group. The earboxyl proton is not shown in Figure XXI as i t is about 445 cycles per second to the left of the main peak. Preliminary studies on the rather impure stearic acid sample, F.P. 68.1°Cj showed that the second moment decreases as the melting point i s approached. However, i f the narrow peaks on the broad resonance line are removed by the procedure outlined for polymers by Wilson and Pake (23), then the second moments are almost constant. The second moment results, from the broad lines, for the pure sample, F.P. 69.3°C, are shown as a function of temperature in Figure XXII. Some scattering of the second moment values may be due to the somewhat arbitrary method used to decompose the resonance lines (23). For example, the narrow peaks are cut off along the dotted lines drawn on the proton resonance curves of Figure XVIII. F I G U R E XXII TO FOLLOW PAGE 7 8 O n O S T E A R I C A C I D F P 6 9 . 3 °C S E C O N D M O M E N T S F R O M B R O A D C O M P O N E N T O F R E S O N A N C E C U R V E S • ' » ' • » • l i i i i 1 1 1 1 1 - 8 0 - 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0 T E M P E R A T U R E "C - 79 -The experimental second moment at -188°C is 28.0 gauss2, at 24°C i t has become 19.6 gauss2 and remains about this value up to 66°C, at which temperature the broad component had almost disappeared. Discussion The experimental results seem to suggest that stearic acid above 24°C and below the melting point is a two phase system* The nearly constant line width and second moment for the broad component of the proton magnetic resonance deriva-tive curves suggests that there i s no recognizable phase tran-sition below the melting point, and that the hydrocarbon chains maintain their positions fairly rigidly throughout the crystal lattice. This agrees with the dielectric studies of Crowe and Smyth (7) who found no evidence of a rotational transition below the melting point of stearic acid. The cal-culated rigid lattice second moment for stearic acid at room temperature is 24.4 gauss2. At -188°C, the 28.0 gauss2 second moment probably indicates that the lattice has contracted, since, as the sample warmed up to room temperature, the reson-ance line narrowed gradually. The predicted rigid lattice value for the second moment in the vicinity of room tempera-ture is roughly 3 gauss2 larger than the mean experimental values found below -30°G, so that seme molecular motion must be present. Rushworth (26) has shown that the methyl groups at the ends of n-pentane and n-hexane molecules may undergo reorientation about their C 3 axes at temperatures well below - 80 -the melting points. If unhindered reorientation of the methyl end groups takes place in stearic acid* the intramolecular second moment will he reduced to 16.5 gauss2, and i f the intermolecular second moment i s reduced by the same fraction (27), the total second moment becomes 21.8 gauss2. This value agrees within experimental error with the results found between -26°C and -78°C. Even above room temperatures the second moment from the broad portion of the resonance curve ranges between 19.3 gauss2 and 20.5 gauss2. It seems possible therefore that the broad portion of the resonance curve re-presents an almost rigid lattice and that the existing molecular motion probably concerns mainly the ends of the molecules. This conclusion ignores the possible effect of zero-point energy oscillations of the protons In the stearic acid hydro-carbon chain. The reduction In the second moment due to this effect can be calculated by means of the method of Gutowsky, Pake and Bersohn (28). The angle of oscillation, 0 * , is defined (29) as: \ *TT*CI S? / where c is the velocity of light, I is the moment of inertia of the oscillating group of atoms, and V is the frequency of oscillation in cm"1. For a single mode of motion, the second moment correction factor is ( I - 81 -The only motion of the protons In stearic acid, which has a frequency \) low enough to be of great importance, is the methylene rocking mode, where V i s about 720 cm"1 (30). The moment of inertia of the methylene group is open to some speculation, for i t is suspected that the methylene rocking may be coupled to some motion of the carbon skeleton of the hydrocarbon chain. At worsts however, I is 3.98 x 10" 4 0 2 gm.cm. and the reduction in the second moment is 3 percent or about 0.7 gauss2. Where the methylene rocking also involves motion of the carbon skeleton about the chain longitudinal axis, I is 10*43 x 10" 4 0 gm.cm.2, and the second moment is reduced by 1 percent» Thus the zero-point energy oscillations do not account for the observed second moments. Moreover, the rather low moment of inertia of the methyl group Itself (31) lends support to the proposal that reorientation of the methyl end group about its C 3 axis may occur f i r s t , before motion of the rest of the hydrocarbon chain. However, the reduction in the second moment can also be brought about by torsional oscillation of the hydrocarbon chain about i t s longitudinal axis as was shown in Chapter V. Therefore, the evidence for methyl end group reorientation cannot be considered conclusive. The narrow component of the proton magnetic resonance line is not quite as narrow as i s usually found in liquids; i t is less than 0.1 gauss, which would suggest a molecule in rapid, but slightly hindered motion. Such a situation has - 82 -been reported for some high polymers, and It has been shown that a decrease of the narrow line width to the same order of magnitude as is found for liquids may indicate a diffusion process (24). In polymers, however, the so-called amorphous phase narrow line usually decreases from a width comparable to that of the broad component (23,25). Such a behaviour Is not observed in stearic acid, where the narrow component is about 0.1 gauss in width, as far as could be determined, regardless of temperature. The change is mainly in the amplitude of the narrow line, which would suggest that more and more molecules begin moving rapidly as the temperature increases. The two phases are then a comparatively rigid, crystalline structure and an amorphous structure. The phases appear to be in equi-librium and as the temperature is raised, the amorphous phase becomes favoured over the crystalline phase. A comparison of the Integrated areas from the broad and the narrow components of the proton resonance lines is shown below in Table VII. Table VII Temperature °C Percentage area of narrow component 40 0.9 45 1.1 54 2.5 58 5.9 66 27.4 - 83 -Fine structure, such as the narrow line found in stearic acid spectra, has been observed by Andrew in the proton magnetic resonance spectra of octadecane and lauryl alcohol (27). Similar fine structure has also been reported for n-pentane and n-hexane by Rushworth (26) and in cetyl alcohol by Kojlma and Ogawa (32). Andrew has advanced a tentative ex-planation for the fine structure of the resonance line (27). The methyl end group line, considered separately, is. a triplet with a fair l y strong central line. If the methyl group is free to rotate about its C 3 axis, the amplitude of the center line will increase. Normally the methyl contribution to the total proton magnetic resonance line w i l l be broadened by interaction with the neighbouring rigid protons. However, i f the molecule rotates or undergoes torsional oscillation of large amplitude, the broadening effect of the neighbouring protons will be reduced and the central line of the methyl group contribution may show up as fine structure. This would probably not represent more than the contribution of one proton In the stearic acid molecule or about three percent of the area of the integrated resonance curve. Rotation of the end methyl group therefore does not explain the magnitude of the fine structure above 58°G. The growth of the narrow line in stearic acid appears to be an example of premelting (33). It has been pointed out that many long chain hydrocarbon compounds do not necessarily melt by some sudden catastrophic process (8). Also the presence of impurities has been shown to be an insufficient - 84 -explanation for the considerable melting range exhibited by many long chain compounds (8). This Is supported by the apparent lack of influence of small amounts of impurities on the 1%/hg ratio with change in temperature. Premeltlng in seme cases has been thought to be due to rotation of the hydrocarbon chains below the final melting point. It might also be a cooperative increase in the number of holes and interstitial molecules in the solid which culminates at the melting point with the break-up of long range order (34). Oldham and Ubbelohde have presented evidence which suggests that near the melting point of long chain hydrocarbons, the number of holes in equilibrium in the lattice i s abnormally large, and that i t may increase progressively with rising tem-peratures (35,36) . Near the melting point the number of holes seems to increase cooperatively, hence genuine premeltlng takes place. Such a process could be imagined to take place in stearic acid. Lattice defects due to dislocations and im-purities in the crystal might allow a few of the stearic acid hydrocarbon chains to rotate about their longitudinal axes and also perhaps to flex and whip about. This could correspond to motion about many axes and lead to the observed narrow proton magnetic resonance line. As the temperature rises, these zones of motion and disorder grow in size at the expense of the surrounding ordered structure, until just below the melt-ing point the crystalline structure is completely transformed to an amorphous structure. The melting point of stearic acid will correspond to the break-down of this amorphous structure. - 85 -The anomalous specific volume change between 60°C and the melting point (6) is probably due to this Increasing disorder in the structure of stearic acid. - 86 -References in Chapter VI Langmuir, I., J. Am. Chem. Soc, 39, 1848 (1917). Mailer, A., J. Chem. Soc, 123, 2043 (1923). Muller, A. and Shearer, G., J. Chem. Soc, 123, 3156 (1923). Sydow, E. von, Arkiv Kemi, 9, 231 (1956). Piper, S., fflallcin, T. and Austin, H.E., J. Chem. Soc, 2310 (1926). Singleton, W.S., Ward, T.L. and Dollear, P.G., J. Am. Oil Chem. Soc, 27, 143 (1950). Crone, R.W. and Smyth, CP., J. Am. Chem. Soc, 73, 5401 (1951). Ubbelohde, A.R., Trans. Faraday Soc, 34, 272 (1938). Muller, A., Proc. Roy. Soc. (Lond.), A154, 624 (1936). Malkin, T., Progress in the Chemistry of Fats and other Lipids, Pergamon Press, London, 1952, vol. I, p.l* Vand, V., Morley, W.M. and Lomer, T.R., Acta Cry S t . , 4, 324 (1951). Sydow, E. von, ActaCryst., 8, 557 (1955). Ahrahamsson, S. and Sydow, E. von, Acta Cryst., 7, 591 (1954). Davies, M.M. and Sutherland, G.B.B.M., J. Chem. Phys., 6, 755 (1938). Pauling, L., The Nature of the Chemical Bond, Cornell University Press, Ithaca, 1948, p.161. Van Vleck:, J.H., Phys. Rev., 74, 1168 (1948). - 87 -Francis, F., Collins, F.J;E. and Piper, S.H., Proc. Roy. Soc. (Lond.), A158, 706 (1937). Francis, F. and Piper, S.H., J. Am. Chem. Soc, 61, 577 (1939). Markley, K.S., Fatty Acids, Interscience, New York, 1947, p.118. Kokotailo, G., Thesis, Temple University, 1955. Nolle, A.W. and Henneke, H.L., Rev. Sci. Instv,, 28, 930 (1957). Hopkins, C.Y. and Bernstein, H.J., Can. J.'Ghem., 37, 775 (1959). Wilson, C.W. and Pake, G.E., J. Chem. Phys., 27, 115 (1957).' Collinsj R.L.,'J. Poly* Sci*, 28, 67 (1958). HcCall, D.W. and Silenter, W.P*, J. Poly. Sci., 26, 171 (1957). Rushworth, F.A., Proc Roy. Soc (Lond*), A222, 526 (1954). Andrew, E.R., J. Chem. Phys., 18, 607 (1950). Gutowsky, H.S., Pake, G.E. and Bersohn, R., J* Chem. Phys., 22, 643 (1954). Ibers, J J L and Stevenson, D.P., J. Chem. Phys., 28, 929 (1958). Corlsh, P.J. and Chapman, D., J. Chem. Soc, 1746 (1957). Das, T.P./J. Chem. Phys., 27, 763 (1957). Kojima, S. and Ogawa, S.* J. Phys. Soc. Japan, 8, 283 (1953). - 88 -(33) Ubbelohde, A.R., Quart. Revs., 4, 356 (1950). (34) Lennard-Jones, J.E. and Devonshire, A.P., Proc. Roy. Soc. (Lond.), A170, 464 (1939). (35) Oldham, J.W.H. and Ubbelohde, A.R., Trans. Faraday Soc, 35, 328 (1939). (36) Oldham, J.W.H. and Ubbelohde, A.R., Proc. Roy. Soc. (Lond.), A176, 50 (1940). CHAPTER VII A PROTON MAGNETIC RESONANCE INVESTIGATION OF POTASSIUM STEARATE Introduction Anhydrous potassium stearate Is known to pass through several thermal transitions between successive phases below the melting point. These transition temperatures are listed below in Table VIII. Unlike the phase transitions of sodium stearate discussed in Chapter V, the potassium stearate tran-sitions have not been classified in detail. And in general, the potassium salts of fatty acids have not been studied as extensively as the sodium salts. Table VIII Name of Transition Transition Temperature °C References Crystal B to C 51,57,78 1,2,3 108 2 Subneat group 162,170,160,165 1,2,4,5 235-249, 242 1,4 Neat group 265,258,267,270 1*2,4,5 345,346,345 1,2,4 Melting point 353, 360 4,5 X-ray diffraction measurements have shown that the lowest temperature transition in potassium stearate involves a change from one crystal structure, called the B phase, to another, - 90 -called the C phase (3). The transition temperature of 78°G reported by Lomer (3) Is probably an error, for his own x-ray diffraction work shows that the higher temperature C phase exists at 75°C. Other investigators (1,2) seem to place the transition temperature between about 50°C and 60°G. Most potassium soaps have an analogous B phase to 0 phase transi-tion and for potassium palmitate the heat of transition is known to be 4.9 kilocalories per mole (6). It seems likely that potassium stearate will have a heat of transition of the same order of magnitude. The transition at 108GC has only been observed by differential calorimetry (2) and i t s sig-nificance is obscure. On the other hand, a l l methods of In-vestigation agree that there is a marked transition between 160°C and 170°C (1,2,4,5). Some investigators (5) have suggested that this transition represents the beginning of a phase similar in properties to the subneat:"/ phase of sodium stearate; others (1) have intimated that it may be more analogous to the waxy phases. The transition reported to occur around 240°C (1,4) has not been detected by differential calorimetrlc measurements (2), but may be another subneat transition. There is again general agreement on the existence of a phase transition around 265°C (1,2,4). At this tempera-ture potassium stearate begins to flow and shows typical smectic liquid crystalline behaviour of the neat phase. It has been pointed out that the temperature of the formation of the neat phase is influenced only slightly by the length of the hydrocarbon chain or the size of the alkali metal cation - 91 -(6). The melting point of potassium stearate has usually been taken as 345GC (1,2), however, i t has been suggested that a true isotropic liquid does not form until about 360°C and that there may be another neat-type phase transition at 345°C (4,5). No suggestions have been offered as to the kinds of molecular motion which might exist in these high temperature phases in potassium stearate. The Structure of Potassium Stearate A somewhat detailed x-ray diffraction investigation of the A crystalline phase of potassium caproate has shown that the alternate,carbon atoms in the zig-zag hydrocarbon chain are separated by 2.60 A (7). This would suggest that the bond angles might differ slightly from the tetrahedral angle usually considered for long hydrocarbon chains (8). Electron diffraction measurements on some straight-chain hydrocarbon compounds in the vapour phase also show the alternate carbon distance as about 2.60 A (9,10). They also suggest that the H-C-H bond angle may be 107° and the C-H bond length may be about 1.12 A (9), while the C-C bond length is 1.54 A (10). These new intramolecular parameters may not apply to the B or 0 phases of solid potassium stearate, however, they will be considered along with the usual tetrahedral case described in Chapters V and VI. The unit c e l l of both the B and the C phase of potassium stearate has been determined by x-ray diffraction (3). The unit ce l l parameters are given below in Table IX. - 92 -Dimension Table IX B phase at 25°C C phase at 75°C a A 4.16 8.07 b A 5.57 5.67 c.k 42.1 45.5 «° 91.5 90 91.6 93.2 r 94 90 T " 53 55.5 There are two potassium stearate molecules per unit cell in the B phase and four molecules per unit c e l l in the C phase (3). As in sodium stearate, described in Chapter V, the molecules of potassium stearate are arranged so that the potassium carboxylate ends form an electrically balanced ionic double layer; the long hydrocarbon chains stick out parallel to each other from both sides of this layer. Unfortunately, a l l the details as to the arrangement of the potassium stearate molecules in the B phase and C phase unit cells have not been reported. For instance, l t is not known i f the hydrocarbon chain portion is inclined in the be plane or the ac plane of the unit c e l l . Also the angle that the plane of the carbon-carbon zig-zags makes with the a or the b axis is open to conjecture. Some possible projections of the B phase unit c e l l were constructed. It was found that i f the chains were inclined in, or parallel to, the ac plane, then some hydrogen atoms on adjacent chains were brought within 1.7 A of - 93 -each other. Since this internuclear distance is well within the van der laals radius of hydrogen (11), i t seems likely that the hydrocarbon chains are not inclined in the ac plane. Three possible arrangements for the hydrocarbon chains in-clined parallel to the be plane are shown in Figure XXIII. In Figure XXIII (a) the hydrocarbon chains are arranged in a criss-cross fashion as in the A phase of potassium caprate (7). In Figure XXIII (b) the hydrocarbon chains are a l l inclined in the same direction, but the plane of the carbon-carbon zig-zags is parallel to the a axis and in Figure XXIII (c) the plane of the zig-zags is parallel to the b axis. The intermolecular second moments (12), calculated for the proton magnetic resonance in the manner described in Chapter V, are given in Table X for each of the three arrange-ments shown in Figure XXIII. The intramolecular second moment for the case where the carbon bond angles are tetrahedral throughout the chain i s the same as was found for sodium stearate in Chapter V, namely 18.9 gauss2. For the non-tetra-hedral case, discussed previously in this chapter, the intra-molecular second moment was found to be 18*0 gauss2. These differences in the hydrocarbon chains had no sigaifleant effect on the intermolecular second moments. The effect of the potassium nuclei oh the second moments of the proton magnetic resonance of potassium stearate is very small and will be ignored. F I G U R E XXIII TO FOLLOW PAGE 33 P O T A S S I U M S T E A R A T E - 94 -Table X The B Phase of Potassium Stearate at 25°C Molecular Intermolecular Total second moments arrangement second moment tetrahedral non-tetrahedrai Figure XXIII . . case case (a) 5.9 24.8 23.9 (b) 6.6 25.5 24.6 (c) 8.1 27.0 26.1 The a axis In the A phase of potassium caproate is known to increase with temperature with a coefficient of expansion of 1.75 x 10"4 per degree Centigrade (3). Assuming that this coefficient of lattice expansion applies to the B phase of potassium stearate, the second moments at -190°C were calcu-lated and are given in Table XI. Table XI The B Phase of Potassium Stearate at -190°C Molecular Intermolecular Total second moments arrangement second moment tetrahedral non-tetrahedrai Figure XXIII case case (a) 6.2 25.1 24.2 (b) 8.7 27.6 26.7 (c) 8.9 27.8 26.9 The plane of the carbon-carbon zig-zags might make some angle other than 90° or 0° with the a or b axes. However, the ex-treme cases considered here should serve to give an order-of-- 95 -magnitude estimate of the rigid lattice second moment. Similar arrangements of the hydrocarbon chains shown in Figure XXIII are also possible in the C phase of potassium stearate. For instance, i f the hydrocarbon chains are in-clined in the be plane and the plane of the carbon-carbon zig-zags is parallel to the b axis of the C phase unit ce l l in Table IX, then the intermolecular second moment is 6.1 gauss2. This rigid lattice value is 2 gauss2 less than the 8.1 gauss2 calculated for the corresponding B phase at 25°C. Experimental Results The variation of the proton magnetic resonance line width of potassium stearate as a function of temperature is shown in Figure XXIV. The line width seemed to change linearly with temperature from 15.7 gauss at -190°C to 12.6 gauss at 37°C. Between 55°C and 62°C an abrupt transition took place and the line width decreased from 12.0 gauss to about 9 gauss. Above 62°C the line width again decreased linearly with temperature until at 170°C i t was 2.5 gauss. At 171°C the line width narrowed to a value which appeared to be governed by the ampli-tude of modulation and the inhomogeneity of the magnetic field. Thus there are two line width transitions in potassium stearate. One is between 55°C and 62°0 and may correspond to the change from the B to the C crystalline phase. The other, at 171°Cj probably represents the phase transition which ranges between 160°C and 170°C in Table VIII. The change in second moment of the proton magnetic - 96 -resonance absorption as a function of temperature is shown in Figure XXV. In general, the second moment changed in much the same manner as the line width. The second moment was 26.8 gauss2 at -190°C and decreased in a fairly regular manner to about 20 gauss2 around 0°C; i t then levelled off, and at 55°C was 18.9 gauss2. The B to C phase transition was represented by a fairly sharp reduction in second moment between 55°G and 62°C, for at 62°C the second moment was 12.0 gauss2. The second moment decreased linearly with increasing temperature, however, i t did not show an abrupt change at 171°C such as occurred in the line width. This seems to be due to a change in shape of the proton magnetic resonance absorption curve. This resonance absorption curve or line narrowed to a great degree at 171°C, but the tails of the curve did not narrow as much as the center. Since the contribution to the second moment is greatest from the t a i l portion of the resonance curve (12), the second moment in this case should not decrease proportionately as much as the line width. The selection of fir s t derivative resonance absorption curves for potassium stearate, shown in Figure XXVI, serves to illustrate this line shape change. It is possible that the narrowing of the line width between 170°C and 171°C is actually the appearance of fine structure, such as is discussed in Chapter VI, for in-stance. However, this was not clear from the experimental results. S E C O N D M O M E N T IN ( G A U S S ) i ro o o o ro o i 03 o ^ o "D m JO > H o c JO m o o o a> o ro o o ro o o 03 I I I 1— T—1—1— O T — r ro oo ro o T — T -ro ro i i i ro ro 0) 1—i—i O / O H > CO CO <z CO H m > JO > H m ° S i- 73 o m 2 x o X m < o - 97 -Discussion The observed, second, moment of 26.8 gauss2 at -190GC is quite close to some of the predicted rigid lattice values in Table XI. The criss-cross chain arrangement ((a) in Figure XXIII) seems to be ruled out. Unfortunately, the difference between the second moments of the other hydrocarbon arrange-ments ((b) and (c) in Figure XXIII) is too small to decide between them. Furthermore, the intramolecular second moment, when the hydrocarbon chain bond angles are tetrahedral, i s only 0.9 gauss2 larger than when they are not tetrahedral, so that no decision can be made on this question either. It seems likely, nevertheless, that the observed second moment at -190°C represents a rigid lattice structure. For the purposes of discussion the hydrocarbon chain bond angles will be con-sidered as tetrahedral and the experimental rigid lattice Intermolecular second moment will therefore be 7.9 gauss2. The reduction in second moment-:as the temperature is raised cannot be due entirely to lattice expansion. The predicted second moments of potassium stearate at 25°C, given in Table X, are a l l larger than the observed values in this temperature range. In Chapter VI i t was pointed out that reorientation of the end methyl^groups about their C 3 axes might occur while the molecule is relatively motionless (13). Such a condition would reduce the Intramolecular second moment from 18.9 gauss2 to 17.0 gauss2 and i f the intermolecular second moment were reduced proportionately (14), the total would be 24.1 gauss2. - 98 -It Is evident from Figure XXV that even at -77°C the molecular motion must involve more than the methyl end group. In Chapter V, the possibility of torsional oscillation of the hydrocarbon chain about its longitudinal axis was discussed in some detail. The graph in Figure XIV, which shows the effect of torsional oscillation on the second moment of sodium stearate, should apply approximately to potassium stearate. The second moment of 18.9 gauss2 which was found for the B phase just below the B to C transition represents an amplitude of torsional oscillation between 30 and 40 degrees. For one particular arrangement of the hydrocarbon chains i t was shown that the rigid lattice second moment decreased 2 gauss2 in going from the B phase at 25°C to the G phase at 75°C. It can be seen in Figure XXV that the observed second moment changes by approximately 9 gauss2 between these tem-peratures. Furthermore, in going from the B phase to the C phase of potassium stearate between about 50°C and 60°C the second moment is reduced by about 7 gauss2, hence increased molecular motion accompanies this change in structure. The fairly linear change in line width and second moment with temperature in the C phase, suggests that molecular motion also changes linearly with temperature. The second moment for the complete reorientation of the potassium stearate chains about their longitudinal axes in the C phase is 7.3 gauss2 i f reorientation of the methyl end group about its C 3 axis is assumed, and i f the C phase rigid lattice intermolecular second moment is taken as 6.1 gauss2. The - 99 -second moment of 7.3 gauss2 was found at about 125°C. It is apparent then that the hydrocarbon chains must undergo rather extensive twisting in the C phase. It was suggested in Chapter V that the rather strongly bonded ionic layer in a fatty acid salt might resist such motion that would allow simple reorientation of the whole molecule about its longi-tudinal axis. If this is so, then some lateral motion of the hydrocarbon chains might also take place around 125°. In any case, the lower second moments observed at temperatures above 125°C must indicate molecular motion other than a simple rota-tion or twisting of the chain. At these temperatures there must be reorientation about other axes in the molecule (15) which is brought about by, say, a slight bending of the twist-ing or rotating chain. The narrow line width, which occurs at temperatures above the transition at 171°C, must indicate a comparatively large freedom of molecular motion in a l l direc-tions for most of the interaction between proton pairs has been averaged out (16). However, the s t i l l finite second moment is usually thought to signify that the molecules s t i l l maintain their mean positions in the lattice and are not free to diffuse (17). In Chapter V this same condition was shown to occur at the supercurd-subwaxy transition around 114°C in sodium stearate. Evidently then, the transition at 171°C in potassium stearate is a transition from the curd to the waxy type ..phase. As this transition occurs about 55°C higher in potassium stearate than in sodium stearate, i t would seem that the intermolecular attraction i s stronger in potassium 100 -stearate than in sodium stearate. This in turn may arise from a somewhat better packing of the potassium ions in the metal-carhoxylate layer than of the sodium ions. Thermal activation energies and correlation frequencies for the molecular motion i n potassium stearate were obtained from line width and second moment results in the same general manner as for sodium stearate in Chapter V. However, the equation of Gutowsky and Pake (18) is applied separately to the B phase and the C phase in potassium stearate. The correlation frequencies obtained from the change in line width in both the B and C phases of potassium stearate are shown plotted against the reciprocal of the absolute temperature in Figure XXVII. Similarly, the correlation frequencies obtained from the second moment results are shown in Figure XXVIII. The thermal activation energy of the motion, AE, and the frequency factor Vo derived from the line width results are shown in Table XII, and these values derived from the second moment results are shown in Table XIII. Table XII Results from Line Widths Phase A E kcal./mole Vo c/sec. B C 1.1 6.6 7w7 X 105 2.5 X 108 F I G U R E XXVII TO FOLLOW PAGE IOO P O T A S S I U M S T E A R A T E O CORRELATION FREQUENCIES FROM LINE WIDTH RESULTS ' ' ' i i i — i — J —i— i — i — i i • . . . . . . . . . . . 2 3 4 5 6 T'CKr'x io 3 F I G U R E XXVIII TO FOLLOW PAGE IOO P O T A S S I U M " S T E A R A T E CORRELATION FREQUENCIES FROM SECOND MOMENT RESULTS 1 1 1 1 1 1 1 * * i i . i . i 2 3 4 5 6 T - ' ( ° K ) " x l 0 3 - 101 -Table XIII Results from Second. Moments Phase A E kcal./mole Uc/sec. B 1.3 4.1 X 10° 1.2 x 108 C 6.8 The reasonably good agreement between the activation energies obtained from the line width and second moment results probably indicates that there is l i t t l e change in line shape over most of the temperature range considered. The lower value of A E between 1.1 and 1.3 kcal./mole found in the B phase of potassium stearate probably represents the barrier to the torsional oscillation of small amplitude which is possible in this phase. The value of A E between 6.6 and 6.8 kcal./mole found in the C phase of potassium stearate must re-present the barrier to rather extensive motion of the chains, for l t was pointed out previously in this discussion that the small second moments could yield no other conclusion. The value of A E for motion in sodium stearate as l t approached the supercurd-subwaxy transition was shown in Chapter V to.be of the order of 20 kcal./mole. And yet only a A E of 6 kcal./mole was found for molecular motion in potassium stearate as i t approached a similar kind of transition. Since molecular motion in the B phase of potassium stearate below 55°G does not seem to be much greater than i n sodium stearate around 55°C, this smaller value of A E in the C phase must be due to the changes in structure at the B to C transition. It - 102 -was shown in the discussion in Chapter V that the harrier to extensive twisting of a hydrocarbon chain in a typical hydro-carbon compound might be about 11 kcal./mole (19). The 'typical 1 barrier to reorientation of the hydrocarbon chains must therefore have been reduced by at least 4 to 5 kcal./mole at the B to C transition in potassium stearate. Although i t may be a coincidence, this reduction of about 4 to 5 kcal*/mole is around the same as the expected value for the heat of tran-sition from the B to the C phase in potassium stearate (6). Finally, the activation energy A E of around 6 kcal./mole found for potassium stearate in the C phase is about the same as the activation energy for molecular motion in the amorphous zones of polyethylene (20,21). In these amorphous zones the hydrocarbon chains are arranged in a somewhat disordered manner and contact between the chains i s small compared to the crystalline arrangement. This may also be the case for the hydrocarbon chains in the C phase of potassium stearate. Also, like polyethylene, potassium stearate might be considered to behave as a viscous liquid rather than a solid at the high temperature end of the C phase (20). - 103 -References in Chapter VII Void, M.J., Macomber, M. and Void, R.D., J. Am. Chem. Soc, 63, 168 (1941). Ravich, G.B. and Nechltaylo, N.A., Doklady Akad. Nauk 83, 117 (1952). Lomer, T.R., Acta Cryst., 5, 11 (1952). Benton, D.P., Howe, P.G. and Puddington, I.E., Can. J. Chem., 33, 1384 (1955). Benton, D.P., Howe, P.G., Parnand, R. and Puddington, 1. E., Can. J. Chem., 33, 1798 (1955). Void, R.D. and Void, M.J., J. Phys. Chem., 49, 42 (1945). Vand, V., Lomer, T.R. and Lang, A., Acta Cryst., 2, 214 (1949). Muller, A., Proc. Roy. Soc. (Lond.), A154, 624 (1936) Bonham, R.A., Bartell, L.S. and Kohl, D.A., J. Am. Chem. Soc, 81, 4765 (1959). Kuchitsu, K., Bull. Chem. Soc Japan, 32, 749 (1959). Pauling, L., The Nature of the Chemical Bond, Cornell University Press, 1948, p.189. Van Vleck, J.H., Phys. Rev., 74, 1168 (1948). Rushworth, P.A., Proc. Roy. Soc. (Lond.)* A222, 526 (1954). Andrew, E.R., J. Chem. Phys., 18, 607 (1950). Powles, J.G. and Gutowsky, H.S., J. Chem. Phys., 21, 1704 (1953). - 104 -(16) Bloembergen, N., Purcell, E.M. am Pound, R.V., Phys. Rev., 73, 679 (1948). (17) Andrew, E.R., Bristol Conference on Defects In Crystal-line Solids, July 1954, The Physical Society, London, p.60. (18) Gutowsky, H.S. and Pake, G.E., J. Chem. Phys., 18, 162 (1950). (19) Frohlich, H., Theory of Dielectrics, Oxford University Press, Second Edition, 1958, p.128. (20) McCall, D.W. and Slichter, W.P., J. Poly. Sci., 26, 171 (1957). (21) ?filson, C.W. and Pake, G.E., J. Chem. Phys., 27, 115 (1957). - 1G5 -APPENDIX 1. Line Widths of Sodium Stearate Used in Figure X. Temperature °C Line Width in Gauss 25 12.0 54 11.9 75 10.2 94 9.2 105 8.8 115 7.1 128 4.5 138 4.1 138 2.6 2. Line Widths of Sodium Stearate Used In Figure XI. (a) First Sample Temperature °C Line Width in Gauss 24 13.3 30 13.2 41 12.0 45 12.2 58 11.8 67 10.8 79 8.5 92 4.8 98 .-* 103 3.7 108 3.5 - 106 -2. (Continued) Second Sample Temperature °C Line Width in Gauss 21 L3.4 46 12.3 55 11.8 71 10.6 77 8.1 84 6.8 93 4.8 99 4.6 102 4.0 Third Sample Temperature °C Line Width in Gauss -182 16.1 -68.5 13.8 -51 13.8 -28 13.5 -17 13.4 -2 13.2 4 13.0 23 12.8 35 12.7 44 12.5 62 11.5 74 9.3 (cont'd) - 107 -(c) (Continued) Temperature °C Line Width : 80 8.1 85 5.5 86 6.5 89 4.6 92 4.5 94 4.5 99 3.9 103 3.8 105 3.7 107 3.7 111 3.2 113 2.8 114 0.5 118 0.5 130 0.5 Second Moments of Sodium Stearate Used in Figure XIII, Temperature °C Second Moment in Gauss2 -182 28.0 -68.5 21.2 -51 20.7 -28 19.9 -17 19.7 -2 19.8 4 19.8 (cont'd) - 108 -(Continued) Temperature °C Second Moment in Gauss 23 19.8 35 18.8 44 17.6 62 16.1 74 15.1 80 13.0 85 s 12.4 86 12.6 89 12.2 92 11.2 94 11.9 99 10.3 103 9.9 105 10.2 107 8.1 111 7.8 113 6.7 114 1.2 118 0.6 130 0.4 - 109 -4. Line Widths of Stearic Acid Used In Figure"XX. Temperature °C Line Width In Gauss -188 15.5 -77 14.5 -68 14.7 -42 14.2 -26 14.0 -14 14.4 5 14.5 19 14.0 24 14.2 34 14.0 40 14.2 45 14.2 544 14.2 58 14.2 66 14.2 5 . i Second Moments of Stearic Acid Used In Figure XXII. Temperature °C Second Moment In Gauss2 -188 28.0 -77 21.1 -68 21.8 -42 21.4 -26 21.7 -14 20.5 5 20.6 (cont'd) - 110 -(Continued) 19 19.9 24 19.6 34 20.5 40 20.1 45 19.4 54 20.5 58 19.9 66 19.3 Widths of Potassium Stearate Used in Fierui Temperature °C Line Width in Gauss -190 15.7 -77 14.1 -65 14.1 -56 14.0 -41 13.7 -7 13.3 8 13.2 28 12.9 37 12.6 42 12.4 51 11.9 55 12.0 58 10.0 62 8.7 (cont'd) - I l l -6. (Continued) Temperature °C 70 83 88 90 95 97 112 122 126 136 140 154 160 166 170 171 179 182 Line Width in Gauss 8.6 8.0 7.6 7.9 7.3 7.0 6.1 5.8 5.6 4.9 4.7 4.0 3.4 3.4 2.5 0.3 0.3 0.3 - 112 -Second Moments of Potassium Stearate Used In Figure XXV. Temperature °C Second Moment -190 26.8 -77 22.6 -65 22.7 -56 21.6 -41 21.2 -7 20.1 8 19.9 28 20.2 37 19.7 42 18.9 51 17.4 55 18.9 58 14.9 62 12.0 70 12.1 83 10.4 88 9.7 90 10.2 95 9.3 97 10.0 112 8.0 122 7.8 126 7.2 136 6.3 (cont'd) - 113 -7. (Continued) Temperature °C Second Moment In Gauss2 140 5.6 154 4.7 160 4.6 166 4.0 170 3.8 171 3.6 179 2.6 182 1.9 F I G U R E I T O F O L L O W PAGE 3 T H E M O T I O N O F A N I N T E R N U C L E A R V E C T O R JlJK A B O U T AN AXIS 0 N B L O C K D I A G R A M O F A P P A R A T U S RECEIVER FREQUENCY METER 1 OSCILLATING DETECTOR AUDIO PRE AMP. MAGNET POWER SUPPLY FIELD SWEEP — AND MODULATION CONTROL ELECTRO AUDIO OSCILLATOR PHASE SHIFT NETWORK MAGNET C. R. 0. NARROW BAND AMPLIFIER PHASE SENSITIVE DETECTOR RECORDING MILLIAMMETER F I G U R E II TO FOLLOW P A G E 18 F I G U R E III T O F O L L O W PAGE 22 O S C I L L A T I N G D E T E C T O R F I G U R E IV T O F O L L O W P A G E 24-P H A S E S E N S I T I V E D E T E C T O R + ZSO o— 6 S N 7 V4. H . O K C SXOK H7H 1 JOK AAA A A A , 3 0 K 50K - A A A . - H A M M O N D 4 4 8 f ' 6 C 4 6 A 6 S N 7 Vi F I G U R E V TO FOLLOW PAGE 24 O TO A INPUT O •JfTOK •3.50 K M AAA. 8 J L K 33K {5 K UTC g.iK " t i - * 3 K l-SK I S © I 5 K 50K (3K lis© 5 6 9 3 6 0 5 6 S H 7 O + 2 5 0 6-3 N A R R O W B A N D A M P L I F I E R F I E L D S W E E P UNIT O F F <n 4 7 0 K & . 7 0 K iloK 51 K 33K I S K Ik J K I K TO S W E E P INPUT OF M A G N E T POWER S U P P L Y o s' > HELIPOT C L O C K M O T O R DR IVE TO S W E E P INPUT O F M A G N E T P O W E R S U P P L Y M O D U L A T I O N C O N T R O L HAM n ONO 333 ^ Q FROM O g AUDIO o O o s c r P H A S E S H I F T N E T W O R K TO R E F E R E R E N C E INPUT O F P H A S E S ENS IT IVE D E T E C T O R F I G U R E VI TO FOLLOW PAGE 25 9 Q F R O M o Q A U D I O O S C . • 3 5 H A H H O M O I 3 33 j F I G U R E VII TO FOLLOW PAGE 27 D E T A I L S O F P R O B E A R R A N G E M E N T O F S A M P L E C A S E T H E R M O S T A T J L TEFLON SPACER SAMPLE ACCESS PORT TEFLON CYLINDER SAMPLE COIL PROBE SAMPLE_ CASE CYLINDRICAL DEWAR HOT AIR DUCT HEATER COILS COMPRESSED—* AIR INLET F I G U R E VIII TO FOLLOW PAGE 27 G E N E R A L A R R A N G E M E N T O F A P P A R A T U S A R O U N D M A G N E T OSCILLATING DETECTOR BAKELITE SHEET PLATFORM BUILT ABOVE MAGNET DEWAR FOR LOW TEMPERATURE MEASUREMENTS MAGNET POLE PIECES LEVELLING SCREW 3 _DEWAR HOLDER PROBE COAXIAL LEAD PROBE SAMPLE CASE F I G U R E IX TO FOLLOW PAGE 47 BARRIER TO ROTATION OF HYDROCARBON CHAIN ABOUT ITS LONGITUDINAL AXIS FOR SILVER STEARATE ANGULAR POSITION IN DEGREES F I R S T D E R I V A T I V E C U R V E S F O R S O D I U M S T E A R A T E 103 »C G A U S S F I G U R E XII TO FOLLOW PAGE 52 S E C O N D M O M E N T IN ( G A U S S ) * ^ „ _ — - _ _ _ ' r o r o r o ' - r o o r o ^ o > o o 0 r o ^ o > o o o r o j > ^ i i i i i i i i i i i i i i i i i i i i i i i i i i i i T H E ON T H E S E C O N D M O M E N T O F S O D I U M S T E A R A T E F I G U R E XIV TO FOLLOW PAGE 57 F I G U R E X V TO FOLLOW PAGE 6 3 F I G U R E X V I TO FOLLOW PAGE 6 5 FIGURE XVII TO FOLLOW PAGE 75 A R E P R E S E N T A T I V E C R O S S S E C T I O N O F A F A T T Y A C I D U N I T C E L L 6 6 FIGURE XVIII TO FOLLOW PAGE ? Q S T E A R I C A C I D O N E H A L F O F F I R S T D E R I V A T I V E C U R V E S S H O W I N G F I N E S T R U C T U R E 0 2 4 6 8 10 12 14 GAUSS F I G U R E XIX TO FOLLOW PAGE 76 S T E A R I C A C I D NARROW COMPONENT AMPLITUDE h„ FROM FIRST DERIVATIVE RESONANCE CURVE IS DIVIDED BY BROAD COMPONENT AMPLITUDE ha Q F P 6 9 . 3 °C Q F P 69-1 °C F P 68-1 °C 0 4 8 12 16 2 0 2 4 2 8 F R E E Z I N G P O I N T — T °C L I N E W I D T H IN G A U S S m ~o m J> H C 3) m o 0 0 o 0 0 o O I O I ro o ro o 4> o o ro 0) oo ro TI CD CD OJ co —I m > JO o o o o Z! o cz 3} m x X —i o -n o o > O m O J G G O 3 TO FOLLOW PAGE 77 F I G U R E XXI H I G H R E S O L U T I O N P R O T O N R E S O N A N C E S P E C T R A O F S T E A R I C A C I D S O L I D I F Y I N G A T 6 9 °C 2 8 2 6 CO * CO 3 2 2 < £ 2 0 z I 8 6 4 O " 2 % « 8 6 LU co 4 - o F I G U R E XXII TOFOLLOWPAGE 78 LU —xy o o S T E A R I C A C I D F P 6 9 . 3 °C SECOND MOMENTS FROM BROAD COMPONENT OF R E S O N A N C E CURVES • • • i l i i 1 1 1—i——i 1 1 - 1 8 0 - 8 0 - 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0 T E M P E R A T U R E °C FIGURE X X IIP TO FOLLOW PAGE 93 P O T A S S I U M S T E A R A T E b I ro o o CD o ro o i 00 O i o SECOND MOMENT IN (GAUSS) 4> o> <*> r ro T " i — r n — r ro _ — — ro ro ro ro 4* o> oo o ro J> o> O H > CO CO c CO H m > 70 > H m T—r—«—i—i—III—i—i—i—i—i O —i o •n o o r~ c r- 30 o m "D > X © X m < O / / F I G U R E X X V I TO FOLLOW PAGE96 P O T A S S I U M S T E A R A T E F I G U R E XXVII TO FOLLOW PAGE IOO POTASSIUM S T E A R A T E O CORRELATION FREQUENCIES FROM LINE WIDTH RESULTS 1 1 1 1 • 1 1 ' ' • * • • • « 2 3 4 5 6 T-'CKJ-'X 10* F I G U R E XXVIII TO FOLLOW PAGE 1 0 0 P O T A S S I U M * S T E A R A T E CORRELATION FREQUENCIES FROM SECOND MOMENT RESULTS 1 1 1 1 1 i i i t 2 3 4 5 6 T ( °K ) "x I 0 3
Thesis/Dissertation
eng
Chemistry
Vancouver : University of British Columbia Library
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Graduate
An investigation of proton magnetic resonance in stearic acid, sodium stearate and potassium stearate
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