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A study of molecular motion in potassium caproate, caprylate, and caprate and lithium stearate by proton… Janzen, Wayne Roger 1963

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A STUDY OF MOLECULAR MOTION IN POTASSIUM CAPROATE, CAPRYLATE, AND CAPRATE AND LITHIUM STEARATE BY PROTON MAGNETIC RESONANCE by WAYNE ROGER JANZEN B.Sc., University of B r i t i s h Columbia, 1961 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of Chemistry We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1963 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 for 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 for reference and study. I f u r t h e r agree that per-mission for extensive copying of t h i s t h e s i s for s c h o l a r l y purposes may be granted by the Head of my Department or by h i s representatives. 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 for 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. / teJQ.Ut- ^ 3 - i i -ABSTRACT Proton magnetic resonance has been measured i n the temperature range -196° to 295°C for potassium caprylate, from -196° to 230°C for lithium stearate, and at -196° and 27°C for potassium caproate. Theoretical second moments for potassium caproate, caprylate and caprate at -196°C were computed using various molecular parameters and were compared with experimental values. Unfortunately the th e o r e t i c a l values were s u f f i c -i e n t l y a l i k e for any one soap so that i t could not be decided which of the parameters were applicable. The re s u l t s do show, however, that the end methyl group rotates i n potassium cap-roate at -196°C and probably does so i n potassium caprylate and caprate. A sharp decrease i n l i n e width and second moment takes place i n potassium caprylate between 50° and 55°C and between 283° and 286°C. The f i r s t t r a n s i t i o n corresponds to a known c r y s t a l phase change at 55°C. The second moment res u l t s suggest that some to r s i o n a l o s c i l l a t i o n about the longitudinal axes of the hydrocarbon chain portion of the o potassium caprylate molecules takes place below 50 C. Above 55°C to r s i o n a l o s c i l l a t i o n of large amplitude or possibly even rotation of the hydrocarbon chain occurs. The t r a n s i t i o n between 283° and 286°C corresponds to onset of motion i n the - i i i -hydrocarbon chain r e s t r i c t e d only by continued ordering of the polar end groups i n the ionic layer of the soap. The proton magnetic resonance r e s u l t s i n lithium stearate indicate t r a n s i t i o n s at 115°, 171+°, and 225°C. These pmr tr a n s i t i o n s correspond to known phase t r a n s i t i o n s . The second moment re s u l t s suggest that the methyl group of the hydrocarbon chain i n lithium stearate begins to rotate between-183° and -136°C. The second moment above 115°C i s approximately equivalent to that estimated for rotation of the hydrocarbon chain about i t s long axis. Above 171°C very extensive motion of the chains occurs, although they are s t i l l held i n pos i t i o n by the ionic layer. The io n i c layer begins to break up i n the region 215° to 218°C, with the compound becoming an is o t r o p i c l i q u i d at about 225°C. ACKNOWLEDGEMENTS I would l i k e to thank Dr. B. A. Dunell for introducing me to the f i e l d of nuclear magnetic reson-ance and for guiding and encouraging me i n t h i s work. I am also indebted to my colleague, Mr. Donald Ware, for his aid i n keeping the spectrometer i n working condition. F i n a l l y I would l i k e to thank a l l the people in the nmr group for t h e i r good humor and company, without which the tedious task of obtaining numbers from the wide-line spectrometer would have been insupportable. - i v -TABLE OF CONTENTS Page Number INTRODUCTION Nuclear magnetic resonance Fatty acid s a l t s chapter 1. NUCLEAR MAGNETIC RESONANCE General p r i n c i p l e s Structural investigation chapter 2. METHOD Preparation of potassium caprylate Preparation of potassium caproate Preparation of lithium stearate Spectrometer Treatment of re s u l t s Temperature control Experimental, potassium caprylate Experimental, lithiu m stearate chapter 3. POTASSIUM SOAPS POTASSIUM CAPROATE (KCg) Cry s t a l structure Structure of the hydrocarbon chain Theoretical second moments Experimental r e s u l t s POTASSIUM CAPRATE (KC 1 0) Cry s t a l structure Theoretical second moments POTASSIUM CAPRYLATE (KC 8) Cry s t a l structure Theoretical second moments Experimental r e s u l t s DISCUSSION chapter 4. LITHIUM STEARATE ( L i C l g ) Introduction Experimental r e s u l t s Discussion 1 2 4 5 9 9 10 11 12 14 15 15 18 20 21 22 25 26 26 27 29 29 31 36 38 41 REFERENCES 49 APPENDIX 1. Line Widths and S econd Moments of Potassium Caprylate used i n Figure 3.3 2. Line Widths and Second Moments of Lithium 'Stearate used i n Figure 4.1 3. Line Widths of Lithium Stearate by High Resolution used i n Figure 4.3 4. Second Moments of Lithium Stearate by High Resolution used i n Figure 4.4 - v i -LIST OF ILLUSTRATIONS Figure To Follow Page 2.1 2.2 3.1 3 . 2 3 . 3 4.1 4 . 2 4 . 3 4 . 4 4 . 5 Temperature apparatus Improved temperature apparatus Cryst a l structure of potassium caproate Typical spectra of potassium caprylate V a r i a t i o n of l i n e width and second moment of potassium caprylate with temperature Va r i a t i o n of l i n e width and second moment of lithium stearate with temperature Typical wide-line spectra of lithium stearate Lithium stearate high resolution l i n e widths Lithium stearate high resolution second moments Typical high resolution spectra of lithium stearate 14 14 20 29 29 38 38 39 39 40 -1-INTRODUCTION Nuclear magnetic resonance Nuclear magnetic resonance (nmr) provides a means for studying molecular and crystal structures (1) • The width and shape of the resonance absorption line (the nmr spectrum) depend upon magnetic interactions among neighboring nuclei in a sample. Since the characteristics of the absorption line also depend upon the motion of a nucleus and that of i t s neighbors, nmr has proved to be even more useful in the study of molecular motion i n the sol i d state (3,4). In favorable cases i t ~±s possible to t e l l i f a molecule or a group i s undergoing rotational motion, rotational o s c i l l a t i o n or diffusion. Often one can determine whether the whole molecule reorients or only part of i t , and whether the motion is about one axis or i s more general. The method i s sensitive; a relatively low frequency motion, of the order 1$ kc/s, suffices to narrow an absorption line from the width i t has in the absence of that motion. The above knowledge i s obtained from the nmr spec-* trum. Additional information can be obtained i f we measure a second parameter of the sample, the spin-lattice relaxation time. A f u l l investigation of a sol i d entails measurements -2-of both l i n e shape and s p i n - l a t t i c e relaxation time over as wide a range of temperature as possible. The temperature-dependence of the spectrum frequently s u f f i c e s to es t a b l i s h the existence and nature of the motion; the k i n e t i c s of the motion are determined from the spin l a t t i c e relaxation time (5). When only the magnetic resonance of hydrogen nuclei i s being studied, the method i s c a l l e d proton magnetic res-onance (pmr). Fatty acid s a l t s A l k a l i metal s a l t s of normal long chain f a t t y acids (soaps) pass through several phase t r a n s i t i o n s before melting. Since thermal a c t i v a t i o n of molecular motion occurs at some of these t r a n s i t i o n s , i t i s intere s t i n g to study these substances by proton magnetic resonance. The s a l t s studied by t h i s method i n our laboratory to date are anhy-drous sodium, potassium, rubidium, and caesium stearates, C-^ g (6,7,9), and anhydrous potassium s a l t s from palmitate, C^g, down to caprate, C 1 Q (8). Generally only two t r a n s i t i o n s have been detected by t h i s method. The f i r s t i s a c r y s t a l t r a n s i t i o n which occurs i n the range 50? to 120?C; the second i s a t r a n s i t i o n to a waxy form which takes place at a temperature 15° to -3-235°C above the c r y s t a l t r a n s i t i o n . The work presented here i s a continuation of these e a r l i e r studies. Proton magnetic resonance spectra have been studied i n the temperature range -196° to 295°C for potassium caprylate (KC_), from -196° to 230°C for lithium stearate o ( L i C , 8 ) , and at -196° and 27°C for potassium caproate (KCg). chapter 1 NUCLEAR MAGNETIC RESONANCE Nuclear magnetic resonance has been the subject of a number of books (10,11,12) and reviews (13,14,15). It i s f e l t that there i s no need to reproduce the theory here, instead, a b r i e f review of ideas, d e f i n i t i o n s , and formulae i s given to enable the reader to follow the presentation of th i s thesis without r e f e r r i n g to the o r i g i n a l l i t e r a t u r e . General p r i n c i p l e s The a p p l i c a t i o n of a magnetic f i e l d j-| 6 to a nucleus of spin I removes i t s s p a t i a l degeneracy and establishes 21+1 equally spaced Zeeman energy l e v e l s . The difference i n energy between le v e l s i s g | 3 H 0 where (3 i s the nuclear magneton, 5.049 X 10" 2 4 ergs/gauss and g 3^ I i s the observable nuclear magnetic moment^ M- > 9 being an experimental quantity (5.585 for protons) c a l l e d the nuclear cj factor. Transitions between these l e v e l s may be induced by a weak magnetic f i e l d (generated by a radio frequency o s c i l l a t o r ) applied perpendicularly to M 0 and o s c i l l a t i n g at the resonance frequency l^o - 5 -For protons i n a 10,000 gauss f i e l d , yo = 42.6 mc/s. The p r o b a b i l i t y of the induced t r a n s i t i o n i s the same for a l l the energy l e v e l s . However, when the nuclei in a sample are i n thermal equilibrium with the c r y s t a l l a t t i c e the population of the level 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 from the radio frequency f i e l d . I t i s t h i s e f f e c t which i s measured i n our experiments. Structural investigation Since the configuration of magnetic nuclei i n a sample influences the width and shape of the nmr absorption l i n e , one can in f e r something about the structure of the system being investigated. The width of an nmr absorption l i n e i s defined as the distance between maximum and minimum slope of the absorption curve or as the width at one-half maximum amplitude of the curve. The f i r s t i s used when wide l i n e s are being studied since these l i n e s are weak and only the derivative of the curve can be recorded. The second i s used when the l i n e s are narrow as i n high resolution nmr spectroscopy. Unfortunately t h e o r e t i c a l l i n e shapes cannot be calculated f o r groups containing more than four spins (1,2, 16). However, Van Vleck (17) has shown that the second moment of an nmr l i n e can be rela t e d to a given structure. The second moment i s defined as {(H)(H-Ho)ZJH A . 2 / S -/ f(H) <>H where T(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 units and Ho i s the value of the magnetic f i e l d H at the center of resonance. The t h e o r e t i c a l second moment for a powdered c r y s t a l containing a r i g i d structure i s Z -lo r i f where ^ i s the distance between nu c l e i j and k, and KJ i s the t o t a l number of nu c l e i at resonance i n the unit c e l l considered. Subscripts j and k r e f e r to the nuclear species at resonance and f refers to a l l other species present. When the temperature i s raised, molecules or parts of molecules i n many s o l i d s begin to reorientate about one or more axes. As the reorientation rate approaches the r i g i d - l a t t i c e l i n e width the resonance l i n e narrows. The -7-second moment for a powdered c r y s t a l containing a system of nuclei which rotate about a single axis i s (3) J K , 5" ^ J f where J= ( i Vc) = - U 3 cos __ |} and J K i s the angle between the axis of ro t a t i o n of Vj K and J f T j K i t s e l f . In the sp e c i a l case when a l l a n ( * Jf ^ _ Xj-f = s^Z--' drops to 1/4 of i t s r i g i d value. It should be pointed out here that t h e o r e t i c a l l y the second moment should remain,invariant with motion. I f the r o t a t i o n were uniform, say of angular v e l o c i t y LOr t the resonance l i n e narrows but sidebands of inte n s i t y pro-portional to {y\ u>r) appear at frequencies n tOr , where Y\ i s any integer j on either side of the central l i n e . When these sidebands are Included the second moment does indeed remain invariant ( 5 ) . Actually r o t a t i o n i n a s o l i d i s not uniform but consists of reorientation of the mole-cule or group between a number of equilibrium, positions. This random motion i s expressible as a Fourier d i s t r i b u t i o n of r o t a t i o n a l frequencies up to frequencies of order A / V c where T c i s the c o r r e l a t i o n time of the random motion. Roughly speaking T c i s the average time i t takes for a s i g n i f i c a n t change to occur i n the molecular arrangement. /1.4/ The sidebands are therefore t h i n l y d i s t r i b u t e d over a range of frequencies and are of inte n s i t y comparable to the noise in the spectrum so that they do not contribute much to the observed second moment. When 1 /TT c greatly exceeds the l i n e width the sidebands are unobservably weak. Abrupt changes i n l i n e width and second moment frequently correspond to phase transitions.. In favorable cases a comparison between calculated and experimental second moments provides information concerning the motion responsible for the change i n l i n e shape. I -9-chapter 2 METHOD Preparation of potassium caprylate (KC g) The c a p r y l i c acid used was Eastman Kodak white lable grade, further p u r i f i e d by f r a c t i o n a l d i s t i l l a t i o n under vacuum. A middle f r a c t i o n , which had a freezing point of 16.3°C determined by a cooling curve ( l i t value 16.3°C (35)), was used to prepare the potassium s a l t . A hot satur-ated ethanol s o l u t i o n of potassium hydroxide was t i t r a t e d into the warm p u r i f i e d acid to a phenolphthalein end-point. The p r e c i p i t a t e d soap was recovered, dried under vacuum to remove solvent, powdered, and packed into a sample tube. The f i l l e d sample tube was then evacuated for 22 hours at 115°C and sealed under vacuum. Preparation of potassium caproate (KCg) Fisher " p u r i f i e d grade'* caproic acid was vacuum d i s t i l l e d and a f r a c t i o n used whose freezing point was -3.2°C ( l i t value -3.2?C (35).)* The potassium caproate sample was prepared i n the same way as the potassium caprylate. -10-Preparation of lithium stearate (LiC^g) Eastman Kodak white lable grade s t e a r i c acid was p u r i f i e d by low temperature c r y s t a l l i z a t i o n (36). F i f t e e n gms of s t e a r i c acid were dissolved i n 500 ml of fre s h l y d i s t i l l e d reagent grade acetone. The beaker containing the acid s o l u t i o n Was then placed i n a dry ice - acetone bath at -20°C. The solut i o n was s t i r r e d mechanically for about an hour while the acid c r y s t a l l i z e d out. The solvent was f i l t e r e d o f f and the acid was pressed between f i l t e r papers to remove excess solvent before drying i n a vacuum dessicator over P 2°5* T n e f r e e z i n g point of the r e c r y s t a l l i z e d s t e a r i c acid was 69.6°C ( l i t value 69.69C (35)). The process was repeated but the freezing point did not change. A hot 50% ethanol-water (by volume) solut i o n saturated with lithium hydroxide was t i t r a t e d into a hot ethanol s o l u t i o n of p u r i f i e d s t e a r i c acid to a phenol-phthalein end-point. After cooling, the preci p i t a t e d soap was f i l t e r e d and dried under vacuum over ^2^5* The soap was then fused under vacuum to remove the l a s t traces of water and alcohol (32). The fused soap was ground to a powder, packed into a sample tube, evacuated for 3 hours at about 125°C, and sealed under Vacuum. -11-Spectrometer The nmr spectrometer used was a Varian Associates model V-4200/4300 dual purpose spectrometer with the f i x e d radio frequency unit V-4310 operating at 40Mc/s. The mag-netic f i e l d was supplied by a Varian model V-4012 A 12 inch electromagnet. After work on potassium caprylate and cap-roate was done the spectrometer was converted to the equiv-alent of a DP 60 model (dual purpose with a radio frequency of 60 Mc/s). The magnet was modified to a V-4012 A-SM model and provided a f i e l d of 14,100 gauss. The lithium stearate work was done at 60 Mc/s. The magnetic f i e l d sweep was c a l i b r a t e d against motion of the recorder chart by audio modulating the r - f transmitter then sweeping through a l i q u i d water s i g n a l and the side bands thus generated. The audio frequency was generated by a Hewlett Packard audio o s c i l l a t o r , model 200 CD, and measured with a Hewlett Packard model 522 B e l e c t r o n i c counter. In the high re s o l u t i o n spectra, side bands of the sample s i g n a l were used f o r c a l i b r a t i o n . Since the system of magnetic n u c l e i must be i n thermal equilibrium with the c r y s t a l l a t t i c e at a l l times, we must sweep through the absorption l i n e slowly. During wide-line operation a sweep time of one hour was used. The high re s o l u t i o n sweep time was much less since a s p i n system which gives a narrow l i n e reaches thermal equilibrium much f a s t e r . -12-During wide-line operation the main magnetic f i e l d was modulated at 80 c/s. In a wide-line spectrometer t h i s i s done i n order to use a-c amplifiers i n the output control u n i t . This i s necessary f o r weak wide l i n e s since a-c amplifiers are much more stable than d-c amplifiers and base-line d r i f t i s minimized. The s i g n a l obtained t h i s way i s the derivative of the absorption l i n e . The modulation amplitudes were ca l i b r a t e d by observing the modulation broadening of the s i g n a l from l i q u i d water. The high r e s o l u t i o n spectra for lithium stearate were obtained under moderate res o l u t i o n . The f i e l d homo-geneity c o i l s were not used and the sample could not be spun. Treatment of r e s u l t s The second moment i n terms of the derivative curve which i s obtained under wide-line operation i s (37) c = JL f'CHtH-HoY'JH J / (H)(H-Ha)dH where i s the i n t e n s i t y of the derivative of the absorption curve i n a r b i t r a r y u n i t s . The spectra were /2.1/ -13-integrated numerically by the following expression: S == s c a l e 2 - Y. " 3 '/2.2/ 3 H where i s the value of •f'(H) > H units along from the center of the l i n e , and scale i s the change i n magnetic f i e l d i n gauss per unit length of chart paper. A small broadening of the resonance l i n e i s caused by the modulation f i e l d H (38). When H m i s less than one quarter of the l i n e width, the observed second moment ( SQbs ) c a n be corrected (38). The true second moment i s where HIry, i s the peak to peak modulation amplitude. An SPS computer program f o r an IBM 1620 d i g i t a l computer was written to calculate the second moments from the experi-mental derivative curves. The program used equation /2.2/ and the modulation correction / 2 . 3 / . The high re s o l u t i o n spectra are actual absorption curves so the second moment was calculated using formula /2.4/. o f > n \ K + ± ^ /2.4/ -14-Temperature control The sample was placed into a Dewar which f i t s into the receiver c o i l of the spectrometer. The heating or cooling gas was c a r r i e d to and from the sample by means of "Bewared" leads. The f i r s t apparatus used i s shown i n figure 2.1. An improved version, which was used to obtain the f i n a l r e s u l t s for lithium stearate, i s shown i n figure 2.2. In the apparatus shown i n figure 2.1 only one thermo-couple could be used and t h i s could not be placed i n contact with the sample. Hence a number of temperature c a l i b r a t i o n runs were done i n which a second thermocouple occupied the sample space and i t s reading used to correct the temperature recorded by the f i r s t thermocouple. The advantage of the improved apparatus was that i t used two thermocouples to measure the temperature of the cooling/heating gas stream; one before and one a f t e r the sample. The copper-constantan thermocouples were monitored with a Leeds Northrup 10 mv recorder. Precise temperatures were measured with a Rubicon potentiometer. For temperatures below 0°C the cooling gas was nitrogen vapour which was generated by b o i l i n g l i q u i d nitrogen out of a 25 l i t r e Dewar with an e l e c t r i c heater. For temperatures above room temperature hot a i r was used. For the temperatures of -196°:and -183°C the samples were placed d i r e c t l y i n l i q u i d nitrogen and l i q u i d oxygen respectively. to follow page 14 figure 2.1 - Temperature apparatus to follow page 14 f i g u r e 2*2 - improved temperature apparatus -15-Experimental, potassium caprylate (KC g) The uncertainty i n temperature i s estimated to be f 1° at 50°C and * 3° at 280°C. At most temperatures at which spectra were recorded, the sample was l e f t at the pa r t i c u l a r temperature f o r about 1 1/2 hours before each spectrum was run. At the several -temperatures at which a second spectrum was run a f t e r a further lapse of about 45 minutes, the l i n e widths and second moments of the duplicates agreed very w e l l . This indicated that the sample had reached thermal equilibrium during the 1 1/2 hour wait. At f i v e temperatures, r e s u l t s were obtained i n t r i p l i c a t e . The largest deviation from the mean at a p a r t i c u l a r temperature was 10% i n l i n e width or second moment, and i n no case was greater than 0.5 gauss i n l i n e width or 1.2 gauss 2 i n second moment. Generally the agreement was better than t h i s . The error i n average second moments i s estimated to be about 5%. Experimental, lithium stearate ( L i C 1 8 ) The wide-line spectra above room temperature were taken while using the single thermocouple temperature apparatus (figure 2.1). The uncertainty In temperature i s estimated to be + 1° at 5O0C, + 2° at 150°C and + 3° at 210°C. The high temperature high resolution spectra and the wide-line spectra below room temperature were taken -16-while using the improved temperature apparatus (figure 2.2). The high resolution temperatures are accurate to _+ 1®C. With a thermocouple before and a f t e r the sample we are a c t u a l l y measuring the temperature gradient along the sample. The gradient depends on the flow rate of the cooling gas. At -21°C the temperature gradient along that part of the sample which i s i n the receiver c o i l i s 4°C. Lower temperatures were reached by increasing the flow rate of the nitrogen vapour so the temperature gradient decreases with decreasing o temperature. The gradient i s 1.4 at -1359C. Dry a i r passed through an ice-water bath was used to obtain the spectra at 2°C. The gradient here was Q.5°C. Since i t was anticipated that lithium stearate might be troublesome (no r e s u l t s could be obtained by l i g h t transmission (32)), duplicate spectra were always run. The f i r s t spectrum Was run a f t e r the sample had been at the desired temperature f o r at le a s t one hour. The duplicates agreed quite w e l l , so i t was assumed that thermal equilibrium had been reached within an hour at a l l temperatures. For an addi t i o n a l check the sample was taken quickly through the f i r s t and second t r a n s i t i o n s while the absorption l i n e was observed on the oscilloscope of the spectrometer. With r i s i n g temperature the f i r s t t r a n s i t i o n occurred within 10 minutes. The second was rather d i f f i c u l t to see on the scope but i t seemed to take place within 10 minutes also. With decreasing temperature the t r a n s i t i o n s took about 15 minutes. Five spectra were obtained at 27°C; the largest deviation from the mean second moment was 2.5%. At -196°C four spectra were taken, the largest deviation being 2.3%. Since the c a l i b r a t i o n of the f i e l d sweep indicated that the sweep was not quite l i n e a r , the wide-line second moments are estimated to be accurate only to 5%. Three or four spectra were taken at each temp^ erature during the high r e s o l u t i o n run. The deviations i n second moment are quite large and are shown on the graph i n figure 4.4. This i s a problem inherent i n high r e s o l u -t i o n c i r c u i t r y ; the absorption s i g n a l i s a d-c si g n a l and d-c am p l i f i c a t i o n i s unstable. -18-chapter 3 POTASSIUM SOAPS Powder x-ray d i f f r a c t i o n photographs have been taken for a series of potassium s a l t s of normal f a t t y acids, potassium butyrate (KC^) to stearate (KC l g) by Lomer (18). These s a l t s e x i s t i n three phases. Salts of chain length from 4 to 10 carbon atoms in c l u s i v e c r y s t a l l i z e from alcohol i n a monoclinic phase "A n containing four molecules per unit c e l l , while those from 12 to 18 c r y s t a l l i z e i n a t r i c l i n l c phase "B** containing two molecules per unit c e l l . With the exception of potassium butyrate (KC 4) and caproate (KCg), a l l of the s a l t s transform on heating to a t h i r d d i s t i n c t phase nC" which i s monoclinic and contains four molecules per unit c e l l . KC 4 and KCg show only very s l i g h t changes in pattern on heating and these are due merely to thermal expansion. The change i n pattern on heating potassium caprylate (KCg) i s also s l i g h t , but represents a true phase change from *^ AW to n C H at 55 + 3°C. The c e l l dimensions of the potassium soaps that we are concerned with i n t h i s study are l i s t e d i n table 3.1. The apparent discrepancy between the c e l l dimensions of potassium caprate (KC 1 Q) as determined by powder photograph and singles-crystal measurements i s due merely to a d i f f e r e n t table 3«1. C e l l dimensions of the potassium soaps s a l t temp phase a b c a V density (g ; cm~3 (°c) (kX)/ (kX) (kX) (°) (°) ( ° ) calc. obs. KC 6 25 A 7-98 5-73 18.90 90 91.9 90 1.177 1.185 KCg 25 A 7-90 5.67 22.96 90 92.1 90 1.170 1.171 KC 1 0 25 A 8.06 5.67 27.52 90 93.5 90 1.105 1.125 KC 1 0* 25 A 8.09 5-63 28.81 . 90 108.0 90 1.112 KC 6 75 A 8.05 5-7^  19.10 90 92.8 90 1.15^  1.168 KCg 75 C 8.07 5-72 23.76 90 91.7 90 1.097 1.108 As determined from single c r y s t a l photographs (Vand et a l , 19) / 1 A = 1.00202 kX \ -20-choice of the monoclinic angle; the value of csin(3 i s 27.40 kX f o r both c e l l s . It i s known from s i n g l e - c r y s t a l measurements (19) that phase "A" of potassium caprate (KC 1 0) c r y s t a l l i z e s i n the space group P2 1/a . With the exception of the butyrate (KC 4), the powder photographs indicate that a l l the "A" phase soaps are i n space group P2^/a . The soaps i n the "B" phase are t r i c l i n i c , PI or PI. There i s some evidence that space group P2 1/a applies i n phase "C" as w e l l . POTASSIUM CAPROATE (KCg) Cr y s t a l structure Lomer (20) i n a companion paper to the one mentioned above (18) has determined the complete c r y s t a l structure of potassium caproate (KCg) from powder photo-graphs of the "A" phase at 25°C. Diagrams of the structure are given i n figure 3.1 . A series of powder photographs (18) showed that the c e l l dimensions of KCg varied contin-uously with temperature. The only c e l l dimension to increase s i g n i f i c a n t l y was d , the c o e f f i c i e n t of expansion p a r a l l e l to t h i s axis being 1.75 X 10~ 4 per °C. Lomer found the mean C-C bond length to be 1.53 * to follow page 20 ^ a = 7.96 A Projection along b axis + and — denote adorns above and below "The plane of the paper - 2b = //.44A--Projection along 01 axis molecules represented by full lines are Vi. OB above those represented by broken lines Ionic layer figure 3.1 - Crystal structure of potassium caproate -21-o 0.04 A; the mean distance between alternate carbon atoms 2.45 + 0.03 A; and the bond angle 106° + 2 . 5 ° . He states that these values are almost c e r t a i n l y not s i g n i f i c a n t l y o d i f f e r e n t from those commonly accepted, namely 1.54 A, 2.52 A and 109.5° . The x-ray work gives us the co-ordinates for a l l the carbon atoms and oxygen atoms i n the unit c e l l . However the positions of the hydrogen atoms remain undetermined and some assumptions must be made about carbon hydrogen bond lengths and bond angles i f one i s to determine a t h e o r e t i c a l proton magnetic resonance second moment for the system. Structure of the hydrocarbon chain The commonly accepted parameters for a hydrocar-bon chain are the following (21): a l l bond angles t e t r a -hedral, C-C =1.545 A (as i n diamond), alternate C-C = 2.522 A, and C-H = 1.094 A. In a hydrocarbon chain, the hydrogens occupy a smaller volume than the carbon atoms so that one might expect the angle between the C-C bonds to be strained from i t s tetrahedral value (19). Electron d i f f r a c t i o n studies of n-hydrocarbons, butane to heptane (22,25) have shown the C-H bond to be greater than 1.094 A, C-C less than 1.545 A, and the bond angles nontetrahedral. B a r t e l l (23) -22-says that t h e o r e t i c a l l y C-C i n hydrocarbon chains should be less than 1.545 (the value i n diamond) since i n diamond there are more gauche repulsions. The molecular parameters for n-hexane determined by electron d i f f r a c t i o n , B a r t e l l et a l (22) are: C-C = 1.533 A, a l t C-C = 2.541 A, C-H - 1.118 A angle C-C-C = 111°54», angle H-C-H = 106 o48» The average parameters f o r the hydrocarbons butane to heptane, B a r t e l l et a l (22) are: C-C - 1.532 A, a l t C-C = 2.548 A, C-H = 1.116 A angle C-C-C = 112°27' , angle H-C-H = 103O51' For methane (24) (also by electron d i f f r a c t i o n ) the C-H bond i s 1.107 A. Actually B a r t e l l et a l reported the C-C-H angle ( £ ) so the H-C-H angles ( © ) were calculated using the formula c o s S. — C ° S 2- cos =^ where <x. i s the C-C-C angle. Theoretical second moments For hydrogen nuclei i n a powder sample, second moment equations /1.3/ and /1.4/ become -23-where $ i s i n gauss 2 and r i n Angstroms. The c o n t r i -bution of the potassium nucleus to the second moment of KCg i s i n s i g n i f i c a n t . The c a l c u l a t i o n of the t h e o r e t i c a l second moment i s s p l i t into two parts; the contribution of the interactions of the protons i n the same molecule, c a l l e d the intramolecular contribution, and the contribution of the interactions between protons of d i f f e r e n t molecules, c a l l e d the intermolecular contribution. A number of Fortran pro-grams for an IBM 1620 computer were written to do these c a l c u l a t i o n s . Table 3.2 contains the predicted second moments for KCg at -196°C for a r i g i d structure and for a rot a t i n g end methyl group. The "a" dimension of the unit c e l l was decreased to 7.656 A using the c o e f f i c i e n t of expansion found by Lomer (18). The method used was to take Lomer's posi t i o n for carbon atom 2 (the o£ carbon) and the d i r e c t i o n of the hydrocarbon chain then calculate the hydrogen atom co-ordinates using the following three reasonable sets of assumptions concerning the molecular parameters. The f i r s t table 3'2. Second moment contributions for Potassium Caproate (c6 re-computed f o r Various Molecular Parameters and Lomer's Unit C e l l at -196°C Intramolecular contribution, r < 6k Intermolecular contribution, r < 6A Contribution f o r r ^  6A" Ei g i d l a t t i c e second moment Average CH3 i n t e r n a l contribution, r i g i d CH3 i n t e r n a l contribution, rotating R i g i d CH^ with other protons Rotating CH3 with other protons Second moment with rotating CH3 Average Experimental second moment -196°C Assumption 1 (Tetrahedral Angles) 19.39 gauss* 6.26 0.32 25.97 6.00 1.50 2.38 20.5 Assumption 2 (B a r t e l l f o r h-Cgl!-^) 18.15 gauss^ 6.61 0. 32 25.08 25.5 + 0.5 5.51 1.38 2.49 1. U9 20.0 20.k + O.k 21.3 + 0.8 Assumption 3 B a r t e l l Average Values 19.28 gauss 2 6.31 0.32 25.91 5.51 1.38 2.51 1.51 20.8 1 ro -p-• - 2 5 -set used was the commonly accepted parameters (tetrahedral bond angles e t c ) ; the second used B a r t e l l ' s electron d i f -f r a c t i o n parameters for n-hexane; and the t h i r d , B a r t e l l ' s average parameters for hydrocarbons n-butane to heptane. In the second and t h i r d set the end methyl group co-ordinates are based on a C-H distance of 1.107 A and tetrahedral angles as i n methane. Second moment contributions for inter-proton distances up to 6 A were obtained using the computer. The contribution made by protons at and beyond 6 A separation was obtained by the following i n t e g r a l form of equation /3.1/. /3.3/ where ^ - number of H atoms per A . Experimental r e s u l t s For potassium caproate the observed l i n e was 13.8 +0 . 5 gauss at -196°C and 8.4 gauss at 27°C. The corresponding second moments were 21.3 + 0.8 and 9.9 o gauss respectively. -26-POTASSIUM CAPRATE (KG 1 Q) C r y s t a l structure Vand, Lomer and Lang (19) have done a complete x-ray d i f f r a c t i o n analysis of single c r y s t a l s of potassium caprate i n the "A" phase* The arrangement of the molecules i s s i m i l a r to that i n KCg figure 3.1 . They f i n d that the o average alternate C-C distance i s 2.598 + .007 A and con-si d e r the r e s u l t to be s i g n i f i c a n t since i t i s 0.076 A greater (ten times t h e i r experimental error) than the commonly accepted value of 2.522 A. This leads to a C-C-C angle of 114°30* i f one assumes the accepted value of 1.544 A for the C-C distance. Theoretical second moments Second moments were calculated i n the same manner as i n KCg except that assumption two considered the large alternate C-C distance found by Vand et a l (19). Assumption two used the same parameters as i n set one (accepted values) but with the hydrocarbon chain extended so that the a l t e r -es nate C-C distance i s 2.598 A. The predicted second moments for K C ^ Q are shown in table 3.3 . The c o e f f i c i e n t of expansion used was that table 3.3. Computed f o r Second Moment Contributions f o r Potassium Caprate (Cio) Various Molecular Parameters and Vand's Unit C e l l at -196°C Assumption 1 Assumption 2 Assumption 3 (Tetrahedral Angles) (C-C-C - 2.598 A) (Bartell's parameters) O O O Intramolecular contribution, 19.02 gauss 18.76 gauss 19-15 gauss r < 5A Intermolecular contribution, 6.48 6.V7 6.48 r < 5A Contribution f o r r ^  5A 0.73 0.73 O.73 Rigid l a t t i c e second moment 26.23 25.96 26.36 Average 26.2 + 0.2 CH3 i n t e r n a l contribution, 3-^ 7 3-47 3.19 r i g i d CH3 i n t e r n a l contribution, O.87 O.87 0.80 rotating Rigid CH3 with other protons 1.26 1.59 1.34 Rotating CH3 with other protons O.76 0.95 - 0.80 Second moment with rotating CH3 23.1 22.7 23.43 Average 23.1+0.4 Experimental second moment -196°C 24.0 2 8 -found i n KC^ . The experimental second moment was obtained from curves whose l i n e widths were reported by Grant (8). POTASSIUM CAPRYLATE (KC g) C r y s t a l structure Although complete x-ray analysis of potassium caprylate has not been done, i t seems c e r t a i n that the molecular arrangement w i l l be s i m i l a r to K C ^ Q and KCg. We have assumed then that the positions of the molecules i n the unit c e l l are the same as i n K C 1 Q but with the c e l l shortened along the c-axis so that the long spacing c sin(S o i s equal to 2.156xn + 5.82 A, a formula given by Vand «i a l (19) where n i s the number of carbon atoms i n the s a l t . The co-ordinates of hydrogen atoms and t h e i r Van der Waals r a d i i that resulted from t h i s assumption, and those for K C 1 Q were plotted i n three orthogonal pro-jections* We were p a r t i c u l a r l y interested i n the end methyl groups because the c r i s s cross structure made i t d i f f i c u l t to envisage where they would be. It appeared from these drawings that the above assumption was a reasonable one to make and that the electron cloud interactions between molecules i n KCg would be about the same as i n K C ^ Q . -29-It should be mentioned here also that projections of hydrogen atoms onto the x-y plane were made fo r a l l three soaps i n order to v e r i f y that no interactions were missed i n the moment ca l c u l a t i o n s . Theoretical second moments Second moments were calculated f o r KCg using the above assumption about c r y s t a l structure and the same assump-tions about molecular parameters as i n KC 1 Q. The r e s u l t s are l i s t e d i n table 3.4 * Experimental r e s u l t s Figure 3.2 contains reproductions of representative spectra of KCg .. They are t y p i c a l with respect to both s i g -nal to noise r a t i o and l i n e shape. "A" was obtained at a very low temperature, "B" at a temperature between 20°C and the f i r s t t r a n s i t i o n , "C" at a temperature between the two t r a n s i t i o n s , and "D" at a temperature above the second trans-i t i o n . The v a r i a t i o n of l i n e width and of second moment with temperature i s shown i n figure 3.3 . Two abrupt t r a n s i t i o n s are obvious. The lower temperature t r a n s i t i o n begins at 50° and ends at 53-54°C to follow page 29 I I I I I I I I l I I ' I I I I I I I I I I I I 1 5 10 15 20 GAUSS figure 3.2 - Typical spectra of potassium caprylate Depth of Modulation i s shown by arrow KC8 -200 -160 -120 -80 -40 0 40 80 120 160 200 240 280 TEMPERATURE °C figure 3.3. - •"Variation '^ or'^tie'-vid^h^and1 secottd moment of potassium caprylate with temperature table 3.4. Second Moment Contributions for Potassium Caprylate (Co) Computed for Various Molecular Parameters and Vand's Unit C e l l at -196 C Assumption 1 . Assumption 2 Assumption 3 (Tetrahedral Angles) (C-C-C = 2.598 A) (Barte l l 1 s parameters) 2 o 2 Intramolecular contribution, 19*16 gauss 19 .gauss^ 19.19 gauss r<5A Intermolecular contribution, 6.24 6.19 6.26 r <5A Contribution for r 5A 0.71 0.71 0.71 Rigid la t t i ce second moment 26.11 25.94 26.16 <g Average 26.0 + 0.2 CH3 internal contribution, 4.40 4.40 4.04 r i g i d CH3 internal contribution, 1.10 1.10 1.01 rotating Rigid CH3 with other protons 1.64 1.92 1.69 Rotating CH3 with other protons O.98 1.15 1.01 Second moment with rotating CH3 22.2 21.9 22.5 Average 22.2 + 0.3 Experimental second moment -196°C 22.9+ 0.8 1 -31-f o r l i n e width, and begins at 51° and ends at 55°C for second moment. At the higher temperature t r a n s i t i o n the l i n e width decreases from 4 gauss to a width determined by the depth of modulation between 283° and 288°C. The second moment however remains s i g n i f i c a n t a f t e r the trans-i t i o n because the wings of the absorption si g n a l remain prominent and diminish gradually as the temperature r i s e s . DISCUSSION F i r s t l e t us consider the second moments for r i g i d l a t t i c e s at -196°C i n tables 3.2, 3.3, and 3.4 . The values are s u f f i c i e n t l y a l i k e f o r any one s a l t to show that the second moment has not been influenced much by reas-onable v a r i a t i o n i n the molecular parameters of these soaps and we cannot decide which Of the parameters apply. The the o r e t i c a l second moment i s thus given as the mid value of the range of three computed values together with the l i m i t s of the range. The error i n using the unit c e l l structure of KC 1 Q f o r KCg i s probably small. The t h e o r e t i c a l second moment i s most s e n s i t i v e to change i n the "b" dimension whose value of 5.67 A obtained by Lomer (18) from powder photographs of KCg at 25°C i s only 0.02 A larger than the value for KCio* The "a" parameter assumed i s 0.22 A larger -32-than Lomer 1s value of 7.90 A for KC g . The long spacing 0 c sin@ , i s 0.12 A greater as calculated from Vand's formula than that measured by Lomer. A more serious error may be introduced by the extrapolation involved i n using o Lomer*s c o e f f i c i e n t of expansion down to -196 C. The r i g i d l a t t i c e second moment should be reduced to allow for zero-point v i b r a t i o n a l motion before i t i s compared with experimental values at -196°C. Assess-ment of t h i s e f f e c t i s d i f f i c u l t , but reduction to 0.95 of the r i g i d l a t t i c e value for s t e a r i c acid, Grant (26), seems to be an over-generous estimate. Even i f a 5% reduction were effected, t h i s would be i n s u f f i c i e n t to account for the experimental value of the second moment of any of the o three soaps at -196 C, and one should consider the p o s s i b i l i t y that the end methyl groups rotate i n these compounds. To th i s end, there i s shown i n tables 3.2, 3.3, and 3.4 the contribution to the second moment of a fixed methyl group, rotating methyl group, and fix e d and rotating methyl group with respect to other protons i n the l a t t i c e . From these values one obtains the second moment for end methyl groups rotating i n an otherwise r i g i d l a t t i c e . The d i v i s i o n of the int e r n a l methyl contribution by 4 for ro t a t i o n about i t s 3-fold axis i s a well-known procedure (3). This i s the case when i n second moment equation /3.2/. The second moment of the rotating methyl with respect to other protons has been taken as 0*6 times the contribution for a fixed methyl group (27). The tables show that although -33-the experimental second moments i n KCg and K C ^ Q do not unequivocally correspond to free r o t a t i o n of the end methyl groups at -196°C, the state of motions i s much closer to th i s condition than to the r i g i d l a t t i c e condition. Since the methyl contribution increases as we go to shorter chain length, the s i t u a t i o n i n KCg i s more clea r and we can say that the methyl group i s rotating at -196°C. It i s not cle a r , however, whether or not there i s a progressive increase i n the extent of methyl group ro t a t i o n as one shortens the hydrocarbon chain i n these soaps. The gradual reduction i n second moment and l i n e width i n potassium caprylate (KCg) above -196°C ( f i g 3.3) i s probably due to tors i o n a l o s c i l l a t i o n of the hydrocarbon chain. The sharp decrease i n l i n e width ending at 54 ± 2°C corresponds well to the c r y s t a l phase t r a n s i t i o n observed by Lomer (18) at 55 _+ 3°C. A corresponding c r y s t a l phase t r a n s i t i o n has been observed i n a l l the potassium s a l t s of even numbered f a t t y acids from s t e a r i c (KC^g) to caprate ( K C J Q ) by x-ray d i f f r a c t i o n and microscopy (18), and pmr (7,8). As i n the other potassium soaps that have been studied, the change i n c r y s t a l phase apparently allows a large increase i n molecular motion. This i s indicated by the decrease i n l i n e width from 12 to 5 gauss and i n second moment from 15 to 6 gauss 2 within 5°C. If one assumes that the hydrocarbon chains can rotate about t h e i r long axes, the th e o r e t i c a l second moment -34-2 o would be about 8 gauss which is just 2 gauss 4 more than that observed above the crystal transition. The difference could be explained as the result of independent rotation of the methyl group about i t s C 3 axis and/or vibration of the hydrocarbon chain during rotation. Such a rotation, however, seems to require that one of the oxygen atoms be free to rotate with the chain. But this would probably be prevented by the strongly bonded ionic layer of the salt and the motion be restricted to torsional oscillation near the carboxyl group with the amplitude of oscillation increasing as we go towards the end of the chain. This process might even allow complete rotation of some groups at the end in addition to a rotating methyl group. The expanded crystal lattice pro-bably allows some lateral oscillation also. The higher temperature transition occurring at o 285 + 5 C appears to correspond to onset of motion in the hydrocarbon chain restricted only by continued ordering of the polar end groups in the ionic layer. The situation in which extensive motion occurs, but no diffusion, is a d i f f i -cult one to estimate. Various calculations give values of about 1.0 to 1.5 gauss 2 for the second moment at this con-dition. The second moment observed for this situation then should not f a l l much below 1.0 gauss (28). Our observed decrease to a value of about 0.6 gauss 2 at temperatures above the transition shows that diffusion is s t i l l probably absent. The temperature of this transition f i t s into the progression of higher values for shorter hydrocarbon chains -35-shown by the series 171, 190, 204, 212, and 246°C for the potassium soaps, stearate to caprate (KCjgjKCjg,. . . K C ^ Q ) . This e f f e c t shows the increasing influence of the ionic layers i n re s t r a i n i n g the motion of the hydrocarbon chains as the r a t i o of ionic part to hydrocarbon part increases. -36-chapter 4 LITHIUM STEARATE ( L i C 1 8 ) Introduction Lithium stearate (LiC^g) i s known to pass through two phase tr a n s i t i o n s before melting to an i s o t r o p i c l i q u i d . Void and Void (29) obtained d i f f e r e n t i a l heating curves for a number of f a t t y acid s a l t s . The t r a n s i t i o n temperatures found for L i C l g were 113°, 185°, and 224°C, where 224°C i s the melting point. The t r a n s i t i o n temperatures reported are derived from the experimental curves by backwards extrapolation of the steeply r i s i n g portion of a peak to i t s i n t e r s e c t i o n with the base l i n e . They state that t h i s procedure has been j u s t i f i e d empirically by r e s u l t s obtained on materials of known melting point. The values given are probably correct to within f 2-3°C. They also obtained powder x-ray d i f f r a c t i o n patterns at room temperature. The patterns were almost i d e n t i c a l for lithium palmitate (LiC^g) and stearate (LiC^g). These two soaps also have very s i m i l a r d i f f e r e n t i a l heating curves. Void and Hattiangdi (31) raised the temperature of a sample of L i C 1 8 to 200°C then cooled i t slowly to room temperature. The x-ray d i f -f r a c t i o n patterns at room temperature taken before and a f t e r heating were v i r t u a l l y i d e n t i c a l . They state that t h i s showed -37-that LiCjg i s well c r y s t a l l i z e d and that the phase tr a n s i t i o n s are completely r e v e r s i b l e . D i f f e r e n t i a l heating curves by Void and Void (30) indicate thermal t r a n s i t i o n s i n lithium palmitate (LiCjg) at 103°, 190°, and 223°C, which are quite s i m i l a r to those in LiC-^g. The f i r s t corresponds to a change i n c r y s t a l form ( v e r i f i e d by microscopy), the second to a t r a n s i t i o n to a waxy state, and the t h i r d to a t r a n s i t i o n to a l i q u i d (30). Void and Void state that some measure of three dimensional crys-t a l l i n e r e g u l a r i t y of molecular arrangement probably e x i s t s in the waxy form. This i s indicated by x-ray data on the waxy form of sodium palmitate (34) and the fact that l i q u i d lithium palmitate supercools e a s i l y at the melting point. The heats of t r a n s i t i o n i n lithium palmitate are 3.4, 3.9, and 5.76 kcal/mole and probably w i l l be approximately the same i n lithium stearate. The f i r s t t r a n s i t i o n i n potassium, rubidium and caesium palmitates (30) and stearates (9) has also been shown to be a c r y s t a l phase change. This evidence, together with the evidence that the f i r s t t r a n s i t i o n i n l i t h -ium palmitate i s a c r y s t a l phase change, leads to the conclu-sion that the f i r s t t r a n s i t i o n i n lithium stearate i s also a change i n c r y s t a l l i n e form, e s p e c i a l l y i n view of the s i m i l a r i t y between lithium palmitate and stearate (29). It should be mentioned here that the behaviour of lithium s a l t s of long chain f a t t y acids i s unique among a l k a l i metal soaps i n that other a l k a l i metal soaps pass -38-through more than two phase t r a n s i t i o n s before melting although only two have been observed by wide-line proton magnetic resonance methods. Puddington et a l . have made l i g h t transmission and density studies on a l k a l i metal stearates (32,33). Only the melting point of 229°C could be obtained i n lithium stearate by l i g h t transmission. Below 229°C the photoelectric current was irreproducible. The density studies, however, indicated t r a n s i t i o n s at 115°, 176°, and 229°C. The t r a n s i t i o n temperature i s taken as the temperature at which an abrupt decrease i n density i s complete. Like lithium palmitate, the stearate supercools at the melting point. Experimental r e s u l t s The v a r i a t i o n of proton magnetic resonance l i n e width and second moment with temperature i n lithium stearate i s shown i n figure 4.1. Reproductions of t y p i c a l wide-line spectra are presented i n figure 4.2. Three t r a n s i t i o n s are indicated above room temperature. The f i r s t at 112-116°C i s revealed by both l i n e width and second moment curves. The t r a n s i t i o n temperature i s taken at the positi v e i n f l e c -t i o n i n the curves a f t e r a steep f a l l . In figure 4.2 the spectrum at 49°C shows the derivative of the absorption 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 I I I I M I I I M I • I I I I -ZOO -100 0 100 2.00 T E M P E R A T U R E . ° C k.l - Variation of line width and second moment of lithium stearate with temperature to follow page 38 - 1 o D < •P s CO • p 10 o •H 4H d o 5 • p o cu P4 (0 cu d •rl H I cu H ca o •rl co CO . •H •rl s ! a o - p I P( •a CM -39-l i n e before the t r a n s i t i o n , and the one at 120°C a f t e r the t r a n s i t i o n . The l i n e shape i s about the same i n each case and merely narrows abruptly during the phase t r a n s i t i o n . At the second t r a n s i t i o n , however, there i s a change in l i n e shape. From figure 4.2 we see that the absorption l i n e i n lithium stearate at 49°C and above has a narrow component. In the spectra i n figure 4.2 t h i s narrow l i n e i s modulation broadened. At about 73 C t h i s narrow component begins to grow i n in t e n s i t y u n t i l at 171°C the wide component i s not resolved. Although i t appears to contribute to the t a i l s of the spectrum and probably doesn't vanish for another few degrees. The temp-erature of t r a n s i t i o n i s taken to be that temperature at which the wide component completely disappears. The t r a n s i -t i o n temperature i s therefore denoted as 171 -I- °C. The nature of the change i n l i n e shape i s such that the second moment does not have an abrupt change at t h i s phase t r a n s i -t i o n . In order to see the behaviour of lithium stearate near the melting point more c l e a r l y , high resolution nmr spectra were obtained i n the temperature region 196° to 230°C. Line width at half height versus temperature i s shown in figure 4.3 and second moment in figure 4.4; Reproductions of some of the high resolution spectra are presented in figure 4.5. These spectra were a l l recorded at the same sweep rate, but the l i n e widths and second moments i n T E M P E R A T U R E *C figure k.3 - Lithium stearate high resolution l i n e widths figure k.h - Lithium stearate high resolution second moments -40-figures 4.3 and 4.4 at and above 218 C were taken from spectra recorded at slower sweep rate. The graphs i n figures 4.3 and 4.4 indicate a t h i r d and f i n a l t r a n s i t i o n at 223°-227°C. Second moments obtained from the wide-line spectra are also plotted i n figure 4.4. While they follow the same trend as the high resolution values, they are less accurate than the high resolution second moments because the wide-l i n e spectra of narrow l i n e s are broadened by the modulation amplitude and the modulation frequency. The biggest error i s probably due to the fact that i n most cases the narrow l i n e went o f f the recorder scale and even when i t did not i t was reduced by the noise integrator i n the output c i r c u i t of the spectrometer. The loss of t h i s part of the curve does not make much difference to the numerator of the second moment expression /2.2/ but contributes a s i g n i f i c a n t amount to the area under the curve (the denominator of /2.2/). Therefore the wide-line second moments above about 180°C are too large. The high resolution values are about h a l f the wide-line values. Above 220°C the actual l i n e width i s less than 0.02 gauss and i s broadened by the modulation frequency. to follow page 40 I .... I I I I I 0 / 2 3 4 5 GAUSS figure 4.5 -Typical high resolution spectra of lithium stearate -41-Discussion The c r y s t a l structure of lithium stearate i s o not known except that the long spacing i s 41.8 A (29). This i s nearly the same as that i n potassium stearate which e i s 41.9 A (18). The c r i s s cross chain structure i n the potassium soaps, caprate ( K C J Q ) and caproate (KCg) appears to be the most favourable arrangement. It res u l t s i n the minimum amount of inte r a c t i o n between the hydrocarbon chains and thus the lowest intermolecular second moment (7). The intermolecular second moment for lithium stear-ate at -196°C then would be about the same as i n potassium caprate (KC 1 Q) (6.48 gauss 2, assumption 3 B a r t e l l * s para-meters). The intramolecular contribution can be calculated 2 ° and i s 19.06 gauss . The contribution f o r r > 5 A i s 0.95 o gauss . Thus the r i g i d l a t t i c e second moment would be about 26.5 gauss 2. The average experimental values of 25.8 gauss 2 at -196° and -183°C are only 0.8 gauss 2 less than t h i s r i g i d l a t t i c e value. It would be possible to 2 attri b u t e t h i s difference of 0.8 gauss to zero-point v i b r a t i o n a l motion. Between -183° and -136°C there i s a drop of about 3 gauss 2 i n the second moment. This change i s approximately what would be expected i f the end methyl group were to begin to rotate. The i n f l e c t i o n i n the l i n e width i s not as obvious for the width decreases only about 0.5 gauss. -42-Further decrease i n second moment with increasing temperature to about 90°C can be interpreted as being due to torsi o n a l o s c i l l a t i o n of the chain with gradually increasing amplitude. Between 90° and 120°C there i s a large decrease in l i n e width and second moment, a fact which indicates that there i s a large increase i n motion of the hydrocarbon chain. The t r a n s i t i o n temperature i s taken to be 114°C and corres-ponds to the c r y s t a l phase change. The extent of motion of the hydrocarbon chain above 114°C i s s i m i l a r to that i n potassium caprylate (KCg) just above i t s c r y s t a l t r a n s i t i o n . Thus the second moment i n lithium stearate at 120°C i s approxi-mately equivalent to that estimated for ro t a t i o n of the mole-cule about i t s long axis with independent methyl group reorien-t a t i o n . After t h i s t r a n s i t i o n the second moment and l i n e width f a l l more ra p i d l y i n lithium stearate than i n potassium capry-late (KCg). Also the l i n e width i n lithium stearate s t a r t s to f a l l at about 60°C below the c r y s t a l t r a n s i t i o n whereas o i t only s t a r t s to f a l l about 15 C below t h i s t r a n s i t i o n i n the caprylate (KCg). These e f f e c t s can be attributed to the longer chain length i n lithium stearate and associated increase in f l e x i b i l i t y . The t r a n s i t i o n a few degrees above 171°C corresponds to the change to waxy form. After t h i s t r a n s i t i o n the second o moment of about 1.0 gauss indicates very extensive motion of the chains, which are, however, s t i l l held at one end by the ionic layer i n the soap. This interpretation i s consistent -43-with the x-ray re s u l t s for caesium stearate (9). A number of sharp x-ray r e f l e c t i o n s , thought to be due to d i f f r a c t i o n by well-ordered hydrocarbon chains disappear at the t r a n s i -t i o n to the waxy form. At 213°C the second moment i s 0.43 gauss 2. Above th i s temperature i t drops r a p i d l y to 0.05 gauss 2 at 218°C and 0.0002 gauss 2 at 225°C. These r e s u l t s indicate that the ionic layer s t a r t s to break up and d i f f u s i o n of the molecules begins at about 215°C, the lithium stearate becoming an i s o -tropic l i q u i d at about 225°C. A summary of t r a n s i t i o n temperatures found i n lithium stearate by t h i s study and other methods i s given i n table 4.1. table 4.1 - Transition i n Lithium Stearate Transition Method and Temperature (°C) nmr DTA(29) density(33) light(32) c r y s t a l 114 113 115 waxy form 171+ 185 176 melting 225 224 229 229 point If one takes into account the fact that i n a l l these methods the t r a n s i t i o n temperatures are taken at the change i n curvature of a l i n e , one can see that the nmr t r a n s i t i o n temperatures agree quite well with those found by d i f f e r e n -t i a l thermal analysis (29) and density studies (33). -44-F i n a l l y an attempt should be made to explain the fine structure observed i n the lithium stearate spectrum between room temperature and the waxy t r a n s i t i o n . Although the narrow component i s modulation broadened i n the spectra shown i n figure 4.2 i t s width was measured at 171°C by using modulations of 0.05 and 0.09 gauss and sweeping through just the narrow l i n e . The average l i n e width thus found was 0.34 gauss, a value not much larger than that found at 196°C by high resolution. Previous explanations f o r nar-row components i n s o l i d s have been that they are attributable to a low melting impurity i n the sample or to the onset of l i q u i d - l i k e motion by molecules of the main substance of the sample i n the v i c i n i t y of defects i n the c r y s t a l l a t -t i c e . A l i n e t h i s wide, however, i s not consistent with these explanations. Instead i t i s postulated that there are waxy regions i n the sample at temperatures far below the waxy t r a n s i t i o n . In other words the sample i s not p e r f e c t l y c r y s t a l l i n e . These regions may have been intro^-duced when the sample was fused i n order to make sure that i t was anhydrous. A few preliminary spectra were obtained with an unfused sample and they did not seem to have the narrow component i n them at temperatures up to 92°C. As the sample temperature i s raised these regions increase and the entire sample becomes the waxy form at the second t r a n s i -t i o n . This work,completes the study of a l k a l i metal stearates by proton magnetic resonance begun i n t h i s labora--45-tory. In general the second moment and l i n e width versus temperature graphs for lithium stearate are s i m i l a r to the other a l k a l i metal stearates. In sodium stearate the f i r s t t r a n s i t i o n i s not c l e a r l y indicated by the second moment curve but can be seen by the l i n e width curve. In order to see i f any trend i n the serie s can be found, t r a n s i t i o n temperatures determined by nmr i n the a l k a l i metal stear-ates, lithi u m to caesium are given i n table 4.2. Table 4.3, which l i s t s t r a n s i t i o n s i n a l k a l i metal palmitates, was prepared from the r e s u l t s of a d i f f e r e n t i a l thermal analysis study by Void and Void (30). Only the tr a n s i t i o n s that one would expect to see by nmr are l i s t e d . This table was included so that one might determine whether any trend that might be observed i s c h a r a c t e r i s t i c of the metal seri e s or j u s t the f a t t y a c i d . F i r s t l e t us look at the c r y s t a l t r a n s i t i o n s . No trend can be observed. The t r a n s i t i o n temperature does not change regularly with metal ion s i z e or chain length. The waxy t r a n s i t i o n , however, does exhibit a trend. Except f o r sodium, the temperature of the t r a n s i t i o n to the waxy form i n both seri e s of soaps decreases as one goes from l i t h i u m to caesium. Void and Void (30) suggest that t h i s trend indicates that the int e r a c t i o n between hydrocarbon chains decreases with increasing ionic s i z e of the metal ion, perhaps simply by introducing a somewhat greater average separation between them. Below the waxy -46-table 4.2 - NMR Transitions i n A l k a l i Metal Stearates Tr a n s i t i o n L i # Na (6) K (7) Rb (9) Cs (9) c r y s t a l 114 87 62 77 69 waxy form 171"1" 114 171 143 100 melting 225 283* 353* 357* 351* point # t h i s work * by l i g h t transmission (32) table 4.3 - Transition i n A l k a l i Metal Palmitates Tr a n s i t i o n L i Na K Rb Cs c r y s t a l 101 117 60,66* 67 62 waxy form 191 134 174,190* 126 95 melting 223 297 375 380 375 point * by nmr (8) - 4 7 -t r a n s i t i o n rimr re s u l t s suggest that the hydrocarbon chains are undergoing extensive motion but s t i l l are r e s t r i c t e d mainly to ro t a t i o n a l o s c i l l a t i o n about the long axis of the molecule. At the t r a n s i t i o n the motion becomes quite v i o l e n t , with reorientation of the chains about many axes. It seems ce r t a i n that for t h i s to happen an increase i n the l a t t i c e dimensions (drop i n density) must occur. If the average separation between the chains below t h i s t r a n s i t i o n does indeed increase with the metal ion s i z e , then one might expect the t r a n s i t i o n to be allowed at lower and lower temperatures as the distance i s increased, and r e s u l t i n the trend observed. Accurate x-ray data would be required to confirm t h i s speculation. The anomalous behaviour of sodium stearate i s not understood. Not only i s the nmr t r a n s i t i o n corresponding to the beginning of the waxy phase many degrees too low i n sodium stearate, but i t also f a i l s to show the abrupt decrease i n density that the other a l k a l i metal stearates have at t h e i r waxy t r a n s i t i o n (33). The abrupt decrease i n density i n sodium stearate takes place about 18°C above the waxy t r a n s i t i o n observed at 114°C by nmr (6). As one goes from lithium to rubidium stearate, the melting point increases. Void and Void (30) propose that the strength of the ionic network i n the soap increases with the metal ion s i z e so that higher temperatures are necessary to cause complete mobility of the soap molecules, as i n an isot r o p i c l i q u i d , as one goes to a larger metal ion. Another -48-i n d i c a t i o n of the strength of the ionic layer i s the tempera-ture at which d i f f u s i o n of the molecules occurs. This temperature can be found by nmr methods and i s 225°C i n lithium stearate and 236°C i n sodium stearate, Barr (39). This point has not yet been determined i n the other soaps. These two d i f f u s i o n temperatures are consistent with Voids* proposal but data f o r the other a l k a l i metal soaps are necessary before one can see i f there w i l l be a trend. -49-REFERENCES (1) Pake, J . Chem. Phys. 16, 327 (1948) (2) Gutowsky, Kistiakowsky, Pake, P u r c e l l , J . Chem. Phys. 17, 972 (1949) (3) Gutowsky and Pake, J . Chem. Phys. 18, 162 (1950) (4) Andrew, J . Chem. Phys. 18, 607 (1950) (5) Andrew, J . Phys. Chem. So l i d s . 18, 9 (1961) (6) Grant and Dunell, Can. J . Chem. 38, 2395 (1960) (7) Grant and Dunell, Can. J . Chem. 38, 1951 (1960) (8) Grant and Dunell, Can. J . Chem. 39, 359 (1961) (9) Shaw and Dunell, Trans. Faraday Soc. 58, 132 (1962) (10) Andrew, Nuclear Magnetic Resonance, Cambridge University press, 1958 (11) Saha and Das, Theory and Applications of Nuclear Induction, Saha Inst i t u t e of Nuclear Physics, Calcutta, 1957 (12) S l i c h t e r , P r i n c i p l e s of Magnetic Resonance, Harper and Row, New York, 1963 (13) Smith, Quart. Rev. 7, 279 (1953) (14) Gutowsky, " A n a l y t i c a l Applications of Nuclear Magnetic Resonance", Physical Methods i n Chemical Analysis, v o l . 3, Berl ed., Academic Press, New York, 1956 (15) Pake, "Nuclear Magnetic Resonance" S o l i d State Physics, v o l . 2, Seitz and Turnbull ed., Academic Press, New York, 1956 (16) Bersohn, Gutowsky, Pake, J . Chem. Phys. 22, 643 (1954) (17) Van Vleck, Phys. Rev. 74, 1168 (1948) (18) Lomer, Acta Cryst. 5, 11 (1952) (19) Vand, Lomer and Lang, Acta Cryst. 2, 214 (1949) (20) Lomer, Acta C r y s t . 5, 14 (1952) -50-(21) Pauling, The Nature of the Chemical Bond, Cornell University Press, p 161, 189 (1948) (22) Bonham, B a r t e l l , and Kohl, J . Am. Chem. Soc. 81, 4765 (1959) (23) B a r t e l l , Am. J . Chem. Soc. 81, 3497 (1959) (24) B a r t e l l , Kuchitsu, and DeNeui, J . Chem. Phys. 33, 1254 (1960) (25) Kuchitsu, B u l l . Chem. Soc. Japan, 32, 749 (1959) (26) Grant and Dunell, Can. J . Chem. 38, 359 (1960) (27) Andrew and Eades, Proc. Roy. Soc. A, 216, 398 (1953) (28) Rushworth, J . Phys. Chem. Solids, 18, 77 (1961) (29) Void and Void, J . Am. O i l Chemists Soc. 26, 520 (1949) (30) Void and Void, J . Phys. Chem. 49, 32 (1945) (31) Void and Hattiangdi, Ind. End. Chem. 41, 2311 (1949) (32) Benton, Howe and Puddington, Can. J . Chem. 33, 1384 (1955) (33) Benton, Howe, Farnand, Puddington, Can. J . Chem. 33, 1798 (1955) (34) Bolduan, McBain and Ross, J . Phys. Chem. 47, 528 (1943) (35) Markley, Fatty Acids, Interscience, New York, p. 114 (1947) (36) Brown and Kolb, "Applications of Low Temperature C r y s t a l l i z a t i o n i n the Separation of the Fatty Acids and t h e i r Compounds", Holman et a l , Progress i n the Chemistry of Fats and Other L i p i d s , V o l . 3, p. 57 (1955) (37) Pake and P u r c e l l , Phys. Rev. 74, 1184 (1948) (38) Andrew, Phys. Rev. 91, 425 (1953) (39) Barr, M.Sc.,Thesis i n Chemistry, University of B r i t i s h Columbia, December 1962 -51-APPENDIX 1. Line Widths and Second Moments of Potassium Caprylate Used i n Figure 3.3 Trace Temperature Line Width Second Moment °C gauss gauss 2 24 -196 14.6 23.0 25 -196 14.6 22.9 26 -196 14.7 22.7 33 - 96 13.6 21.7 34 - 96 13.7 21.0 35 16 12.5 20 25 12.4 16.3 23 25 12.2 18.2 A 25 12.3 16.7 B 25 12.2 16.6 47 49 12.1 36 50 11.1 14.4 48 51 12.1 37 51 11.0 15.3 49 52 10.9 45 53 5.2 7.3 51 54 5.0 6.9 38 55 5.0 5.7 39 55 5.0 5.7 40 63 5.0 5.5 -52-1. (continued) Trace Temperature Line Width Second Moment oC gauss gauss 2 41 63 5.0 5.9 42 102 4.5 4.5 70 107 4.4 4.7 43 150 4.4 4.1 72 191 4.2 3.7 74 253 4.7 4.3 75 253 4.5 3.5 76 253 5.2 3.9 58 283 4.2 3.2 59 283 4.3 3.3 62 286 - 1.4 63 286 - 1.3 65 286 - 1-3 64 287 - . 0.85 66 288 - 0*67 67 288 0.66 68 288 - 0;57 55 289 - 0.56 54 295 — 0.67 2. Line Widths and Second Moments of Lithium Stearate Used i n Figure 4.1 Trace Temperature , Line Width Second Moment oc gauss gauss 2 57 49 13.6 18.6 -53-2. (continued) Trace Temperature Line Width Second Moment OC gauss gauss' 58 49 13.7 19.5 60 73 12.0 16.6 61 73 12.1 17.3 63 92 10.6 14.9 64 92 10.6 15.9 65 122 5.7 6.3 66 120 5.8 5.9 67 120 6.2 6.7 68 111 6.9 7.7 69 96 10.6 15.7 70 95 10.0 14.9 72 100 9.2 14.8 73 107 7.3 10.2 74 107 7.3 11.0 75 107 7.2 10.3 76 135 5.3 5.2 77 136 5.1 5.3 78 154 4.4 4.3 79 153 4.5 4.2 81 171 - 2.6 82 171 - 3.2 83 170 - 2.4 84 170 - 3.0 85 170 0.34 — -54-2. (continued) Trace Temperature Line Width Second Moment o c gauss gauss'5 86 171 0.34 87 171 0.36 88 171 0.38 89 171 0.37 90 171 0.39 ' -91 171 0.33 92 171 0.23 93 171 0.39 95 171 0.23 96 171 0.37 98 165 3.7 4.4 99 165 3.75 4.2 100 164 3.85 4.4 101 166 4.2 102 182 - 2.3 103 182 - 1.4 108 189 - 2.0 109 189 - 2.5 111 197 - 2.6 112 207 - 1-1 113 213 - 0.83 114 213 - 0.78 115 217 - 0.85 -55-(continued) Trace Temperature Line Width Second Moment oc gauss gauss 2 116 221 - 0.38 117 221 - 0.21 127 -135 14.8 23.1 128 -136 15.0 22.9 129 -105 14.8 22.9 130 -104 14.6 22.1 131 - 73 14.2 22.2 132 - 21 14.3 22.4 133 - 21 14.4 22.2 134 - 48 14.6 22.6 135 - 50 14.9 23.4 136 - 71 14.9 23*6 137 - 71 14.9 23.7 138 - 71 14.6 23.4 139 2 14.2 23.3 140 2 14.2 21.1 141 -183 15.6 25.8 142 a -183 15.1 24.9 142 b -183 15.4 26.8 155 -196 15.6 26.0 156 -196 15.7 26.4 -56-2. (continued) Trace Temperature Line Width Second Moment °C gauss gauss 2 157 -196 15.6 25.6 158 -196 15.7 25.4 159 27 13.4 20.4 160 27 13.6 20.8 161 27 13.7 20.7 162 27 13.7 20.4 163 27 13^8 20.0 3. Line Widths of Lithium Stearate by High Resolution Used i n Figure 4.3 Trace Temperature Line Width Maximum Number oc gauss Deviation of Traces 143 196 0.32 0.01 4 145 205 0.27 0,05 4 147 218 0.030 0.01 3 148 201 0.28 - 2 149 213 0.15 0.01 3 151 225 0.0126 0.0004 4 153 230 0.0119 0.0001 4 4. Second Moments of Lithium Stearate by High Resolution Used i n Figure 4.4 Trace Temperature Second Moment Maximum Number °C gauss 2 Deviation of Traces 143 196 0.72 0.07 4 -57-4. (continued) Trace Temperature Second Moment Maximum Number oc gauss 2 Deviation of Traces 145 205 0.45 0.10 4 147 218 0.053 0.010 3 149 213 0.43 0.06 3 151 225 1.9 x 1 0 - 4 0.6 x 10~ 4 4 153 230 1.5 x 10~ 4 0.3 x 10" 4 4 

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