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A study of phase transitions in sodium stearate by means of nuclear magnetic resonance Grant, Rowland Frederick 1955

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A STUDY OF PHASE TRANSITIONS IN SODIUM STEARATE BY MEA1TS OF NUCLEAR MAGNETIC RESONANCE BY ROWLAND FREDERICK GRANT A thesis submitted in partial fulfilment of the requirements for the degree of Master of Science in Chemistry. We accept this thesis as conforming to the standard required from candidates for the degree of Master of Science Members of the Department of Chemistry THE UNIVERSITY OF BRITISH COLUMBIA October, 1955. ABSTRACT The mesomorphic phase transitions of sodium stearate occurring "between 23°C. and 200°0. were investigated "by means of the nuclear magnetic resonance of the hydrogen nuclei in sodium stearate. The changes i n the nuclear magnetic resonance line width as the temperature increased revealed three phase transitions. These are the supercurd-*subwaxy transition at llH°C, the subwaxy~waxy at 130°C, and the waxy-auperwaxy transition at approximately l 6 5 ° 0 . . Since the nuclear magnetic resonance line width is reduced as molecular motion increases, a general explanation of the phase transitions has "been attempted. Stearic acid was also investigated "by means of nuclear magnetic resonance at temperatures "between 2h°0. and 90°C.. Only one transition, the melting point at 70°0. could he detected. AOKCTLEDGMENTS I am indebted to Dr. B. A. Dunall for guiding this research and for taking a constant interest i n the work. I am grateful to Dr. G-. M. Volkoff who kindly supplied much of the apparatus used i n this research and who also supplied a place to work among his students i n the Physics building. I would also l i k e to thank Mr. H. A. Buckoiaster and Mr. R. R. Haering for many stimulating discussions. I am particularly indebted to Mr. N. Hedgecock for his aid i n solving technical problems and to my brother Alan for his assistance in drawing some of the diagrams and checking some of the results. The support of the National Research Council in the form of a research grant to Dr. Dunell i s gratefully acknowledged. TABLE OF CONTENTS Page No. CHAPTER I INTRODUCTION A. Fatty Acid Salts Phase Transitions in Sodium Stearate 1 Hydrated Forms of Sodium Stearate 2 Mechanisms of the Phase Transitions 3 B. Nuclear Magnetic Resonance Fundamental Background 4 Relaxation Times 7 Application to Solid State Problems 8 CHAPTER II APPARATUS General Description 10 Arrangement of the Apparatus 11 The Oscillating Detector 12 The Thermostat lk CHAPTER III EXPERIMENTAL A. Methods Preparation of Sodium Stearate l6 Operation of the Thermostat 17 Measurement of Resonance Absorption 18 Sources of Error 18 B. Results Phase Transitions in Sodium Stearate 19 An Investigation of Stearic Acid 21 Line Shapes of Sodium Stearate 21 Pa«s:e Mo. CHAPTER IV DISCUSSION Stearic Acid 22 Sodium Stearate 22 Interpretation of a Line Shape of Sodium Stearate 2h Future Work 25 APPENDIX Line Widths of Sodium Stearate Used i n Figure 9 26 REFERENCES 27** 28 USB, .01!, ILLUSTRATIONS Pacing Page Figure 1 Block Diagram of the Apparatus 11 Figure 2 The Livingston Oscillating Detector and Audio Amplifier 13 Figure 3 Photograph of the Livingston Oscillating Detector and Audio Amplifier 13 Figure k The Regenerative Oscillating Detector and Audio Amplifier lU Figure 5 Photograph of the Regenerative Oscillating Detector and Audio Amplifier ik Figure 6 Modified Regenerative Oscillating Detector ik Figure 7 The Experimental Arrangement 15 Figure 8 Line Width Change i n Sodium Stearate I ^ as the Sample Cools Figure 9 Line Width Change in Sodium Stearate ^ Q as Temperature is Raised Figure 10 Line V/idth Change in Stearic Acid as Temperature i s Raised I Figure 11 Resonance Absorption Line Shapes in Sodium Stearate *l CHAPTER 1 INTRODUCTION A. Patty Acid Salts. Phase Transitions i n Sodium Stearate. Soaps of f a t t y acids containing more than four carbon atoms exhibi t mesomorphismOG). On heating they pass through a series of t r a n s i t i o n s "before melt ing into i s o t r o p i c l i q u i d s . Patty a c i d soaps are geometrical ly anisotropic and have only one strongly po lar group. Such properties general ly favour the formation of mesomotcldc p h a s e s ^ ) . Some of these t r a n s i t i o n s show themselves as sharp changes i n appearance which are most s t r i k i n g when observed between the crossed n i c k o l s of a p o l a r i z -i n g microscope. The temperature of a t r a n s i t i o n i s u s u a l l y determined experimentally by measuring a property such as e l e c t r i c a l c o n d u c t i v i t y ^ ^ ) , dens i ty(3 l ) (27) , thermal c a p a c i t y ^ ) or v i s c o s i t y ^ 2 0 ) ^ ) as the temperature v a r i e s . The t r a n s i t i o n temperature appears as a change of slope when the property observed i s p l o t t e d against temperature. This general procedure has revealed several mesomorphic t r a n s i t i o n s i n sodium stearate. Anhydrous sodium stearate, CjjH-^COONa i s a white opaque s o l i d which becomes suddenly translucent and p l a s t i c above 130°C, p a r t l y t r a n s -parent above 200°C. and completely transparent above 265°C.^). There are other phase t r a n s i t i o n s which are not e a s i l y found v i s u a l l y . The f o l l o w i n g i s a l i s t of a l l the phases so far observed i n anhydrous sodium stearate . The range of temperature given for the beginning of each t r a n s i t i o n indicates the extent of the agreement e x i s t i n g among di f ferent workers us ing d i f ferent methods. Name of Transition Transition Temperature References Genotypical Point 65-70 00. 28,32.26 Curd to Supercurd 89-93 °C 30,33 Supercurd to Subwaxy 110-117°0. 32,26 Subwaxy to Waxy I25-13U0O. 3.32,33 Waxy to Superwaxy i65-i67°0. 3,30,31 Superwaxy to Subneat 19S-209°0. 27.30 .'31.32 Subneat to Neat 226-262°0. 27.30,31.32.35 Mel ting Point 27S-29O°0. 20,31.35 Hydrated Forms of Sodium Stearate. Sodium stearate can exist in several hydrated forms. On crystalli-zation from 95$ ethanol, one molecule of sodium stearate combines with half a molecule of water producing the alpha form. When heated to 52°C. the beta form is obtained which has one eighth of a molecule of water per molecule of sodium stearate. If the alpha or beta forms are heated above 103°0. the gamma or anhydrous form results. These forms differ slightly in crystal structure and can be distinguished from one another best by X-ray analysis'^ v 2 9 ) ( 3 ^ ) . There is at least one more form of sodium stearate in combination with water which is not a stoichiometric hydrate but may instead be a solid solution^ 1*). The anhydrous sodium stearate used for phase transition studies is usually obtained by melting the alpha form under vacuum to remove the water of hydration^ *7)(27). It has been suggested that this treatment may not be drastic enough to remove the last traces of water associated with the sodium iond5), and some of the phase transitions reported might in some manner be due to the water. However, sodium stearate prepared by reacting molten stearic acid with sodium amalgum under vacuum showed the same phases as the sample prepared "by melting the alpha form(27). Therefore, the phase transitions in sodium stearate are not due to the influence of small amounts of water. The explanation now given is that the phase transitions in anhy-drous soaps occur as the intermolecular forces are overcome by molecular motion when the temperature increases(27). Mechanism of the Phase Transitions. X-ray analysis shows that soaps consist of layers of double molecules placed end to end, hydrocarbon to hydrocarbon and carboxyl group to carboxyl group^^). sodi-um carboxylic groups have strong polar bonds between them and the adjacent hydrocarbon chains are held together by weaker van der Waal's forces. In general, low temperature transitions are due to rearrangement of the hydrocarbon chains while at high temperatures there is a rearrangement of the polar ends of the molecules^33). Stearic acid melts at 6S.5°C. It has been suggested that at this temperature the conesionai forces between the hydrocarbon parts of sodium stearate should be overcome. Sodium stearate does not melt at 6g.5°C. however since the forces between the sodium carboxylate groups probably maintain the mean position of the hydrocarbon chains^). The genotypical point at 70°Q. probably indicates that the thermal energy is large enough to loosen the lattice in one dimension^^8). The hydrocarbon chains may now vibrate in one dimension. The amplitude of vibration may increase up to the curd-supercurd transition at 90°0. where vibrations begin in a second dimen-sion, and give rise to a skipping rope type of motion. No simple explanation has been offered for the supercurd-3ubwaisy transition around 1 1 7 ° 0 . , but i t probably represents a suddenly less restricted mode of motion of the hydrocarbon chains. The soap becomes quite plastic at the subwaxy to waxy transition so possibly the hydrocarbon chains have attained maximum freedom of motion i n two dimensions^). The results of X-ray analysis indicate that the sodium stearate chains attain complete freedom of rotation at l65°C.» the waxy-superwaxy t r a n s i t i o n ^ . The superwaxy to subneat transition around 200°C. and the subneat to neat transition around 265°0. are taken to represent two stages of reorientation of the sodium carboxylate groups'^). In the neighbourhood of 300°C. sodium stearate becomes an isotropic l i q u i d indicating that the polar attraction in the molecule has been overcome^). In general, these explanations for the phase transitions in sodium stearate are probably correct. L i t t l e direct physical or chemical evidence, however, exists to support them. An effective method now exists which may show whether or not the explanation involving vibration and rotation i s correct. This method i s the use of nuclear magnetic resonance techniques. B. Nuclear Magnetic Resonance. Fundamental Background. Many atomic nuclei have a magnetic moment due to the spin of the nucleus. A nucleus with a spin I has a magnetic moment yU. of the following magnitude: where yL(0 equals w h i c l x i s t 3 3 e n u°l ear magneton, and g i s the nuclear g factor, which w i l l be defined later. In a manner analogous to atomic spectra i t has "been shown that when the nuclear magnets are placed in an external magnetic field Ho there will "be an interaction and a nucleus of spin I will have 21+1 energy levels accessible to i t . These levels are Zeeman levels with energy values defined by: where /W. s. I , I-l, 1-2. — I and Anm. ss. ±\ (lg) The frequency associated with difference in energy of each level may be expressed as . j i i Vo = 3 Ho % This is called the Larmor frequency and in a field of say 10,000 gauss V* will be in the radio frequency range. The nuclear g factor serves to relate the Larmor frequency and the field Ho for a given nucleus. The expression ^  ^ is called the gyromagnetic ratio. If one subjects a sample containing nuclear magnets to a weak magnetic field placed perpendicular to Ho and oscillating at the Larmor frequency , then a nucleus in a lower Zeeman energy level may absorb a quantum of energy from the radiation field and make a transition to the next higher energy state. If the frequency of the radiation field is not near the Larmor frequency one expects no absorption hence the term resonance phenomenon. There is an equal probability for a nucleus to go to a higher or a lower energy level, so that i f a l l the levels were equally populated no net change should be expected. However, i t can be shown that the thermal energy possessed by a nucleus far exceeds the energy difference between levels. Because of collisions due to thermal agitation the system of nuclear spin states comes into thermal equilibrium with i t s surroundings. The result i s not an equal population in a l l the energy levels, instead there is a Boltzman distribution favouring the lower levels. The difference in population i s very small. For hydrogen nuclei at room temperature, in a f i e l d of 20,000 gauss, there are one million and fourteen nuclei i n the lower states compared to one million in the upper states. This small excess i s responsible for the energy absorption which can be observed at resonance^8*) The excess nuclei i n the lower levels give rise to a nuclear para-magnetic bulk susceptibility: X* =(NAKT) 3V*.* KI+0 Since at resonance the equilibrium distribution of the nuclei i s disturbed, the susceptibility i s altered. This provides the means for measuring the nuclear magnetic resonance'18)m rphe susceptibility i s a complex number with a real component and an imaginary component which is 9 0 ° out of phase hence: It can be shown that the energy absorbed by a nuclear spin system i s propor-tional to , the out of phase component of magnetic susceptibility'* 8'). Now, there w i l l be a net absorption of energy due to the transition between levels as long as there remains a surplus of nuclei in the lower states. To f u l f i l l this latter condition, the net energy gained by the nuclei must be lost to the surrounding environment in some manner. This reduces the l i f e time of the nuclei i n the upper states causing a reduction of A t in the Heisenberg equation: A E - A t The reduction of^"fcincreases the uncertainty of E, the energy of the level and thereby serves to broaden the line width. Line broadening i s usually discussed i n terms of relaxation times rather than the broadening of energy levels (25) . Relaxation Times. The relaxation time i s the time required for the system of nuclear spins to come to equilibrium with the environment and arises from the following interactions. The f i r s t relaxation mechanism arises from interaction of the magnetic moments of the nuclear spins with oscillatory magnetic fields produced by molecular motion of the l a t t i c e . The l a t t i c e refers to a l l the sample except the nuclear spins^ 2 1^. This f i r s t mechanism governs the time required for a l l but %L.o£ the equilibrium excess number to reach the lower energy state and is generally referred to as "Tj", the spin-l a t t i c e relaxation time or the thermal relaxation time' 1 8"). The second relaxation mechanism i s due to interaction with oscillatory and stationary magnetic fi e l d s due to neighbouring nuclei with magnetic moments. There i s one kind of interaction which involves an exchange of energy between neighbouring spins, called spin-spin c o l l i s i o n , with no energy entering or leaving the spin system. This spin-spin c o l l i s i o n limits the lifetime of a spin state and leads through the Heisenberg uncertainty relation to an energy s p r e a d ^ 1 ^ 2 - ^ . A second kind of interaction mechanism involves a local magnetic f i e l d H L superimposed on Ho. This local f i e l d on any given nucleus i s the resultant of the local f i e l d s produced by the static components of neighbour-ing magnetic dipoles. The resonant condition is then: Since H L depends on the orientation of a l l neighbours, the result i s a dispersion of the magnetic fields and hence a spread of values of at different nuclei throughout the sample. The average f i e l d and reson-ance frequency i s s t i l l Ho and\^. Prom the resultant broadening of energy levels A E - 3 ^ Hi a time T g may D e defined! T » - ^ = - $ r . / H i . • This time T^ is called spin-spin relaxation time and the line broadening i t represents i s due to resulting deviations from an average f i e l d Ho due to neighbouring nuclei and also due to spin collisions. It follows then, that inhomogeneities in Ho due to irregularities i n the magnet pole pieces w i l l cause a similar line broadening^^^ 25). Application to Solid State Problems. The internuclear fields are expected to be of the order of a few gauss in magnitude. This gives rise to line broadening i n some solids, and the width of this broadening would also be a few gauss in magnitude. A quantitative relation between sample structure and line width has been developed for a solid having a r i g i d l a t t i c e . This relation involves a quantity called the "second moment of the line shape". If the magnitude of the energy absorption occurring during a sweep through the resonance condition i s plotted against the change in magnetic f i e l d H, or radio-frequency )J , and i f i n such a plot i t has the value P(H) at f i e l d H, then the second moment of the absorption line i s defined as follows: /oO < A H*>AV « / F(H)-(H-/•**/IH S-oQ Where P(H) is the line shape function at any value of the field H, and H* is the value of H at the centre of the absorption line. The second moment can he derived from experimental data by finding the total area under a plot of P(H)•(B-H*)2 against H"( 25). This method has been simplified to some extent and in certain cases the variation of line width due to motion of the lattice can be accounted for, so that i t is possible to predict the second moment for some molecules with reasonable accuracy'1^^'l2^. As lattice motion increases the resonance line width is reduced by averaging out the internuclear fields. In the case of a nucleus resid-ing in a freely rotating molecule, the rotational periods are much smaller than the times associated with the nuclear resonance. If as well, a l l orientations of the molecule are equally probable, the internuclear fields average out to zero so that an extremely narrow line results. In practice, the width of this line is limited by the homogeneity of the field Ho over the sample. Since the reduction of line width due to lattice vibration is much smaller than that caused by rotation of a group, a sudden change in the line width is more likely to be caused by group r o t a t i o n ^ 1 ^ ^ ^ 1 8 ' ^ 2 ^ ) . The measurement of the proton line width of sodium stearate at different temperatures might aid in determining the mechanisms involved in the various mesomorphic phase changes exhibited by sodium stearate. - 10 -CHAPTER II APPARATUS general Description. The apparatus used for this experiment is a standard nuclear magnetic resonance spectrometer. It consists of a large static homogen-eous magnetic f ield Ho in which a solenoidal coil is placed with its axis perpendicular to the large field Ho. The sample under investigation is placed inside this solenoidal co i l . The coil i tself is part of a parallel resonant circuit. Energy is supplied to this circuit from a constant current source which is a weakly oscillating oscillator. The frequency of the oscillator is slowly changed by varying the capacity of the condenser in the resonant circuit. As the frequency passes through the resonant frequency of the nuclei in the sample, radio frequency energy is absorbed from the co i l , thereby decreasing the amplitude of the radio frequency voltage across i t . This decrease in amplitude can, in principle, he observed by amplifying and rectifying the radio frequency voltage and recording the rectified voltage. In order to avoid D.C. amplification which would be necessary in such an arrangement to obtain an observable signal, the large static magnetic field is modulated slightly at a low audio frequency. As a result, the resonance frequency of the nuclei oscillates about the value determined by the large static f ie ld. As the frequency of the oscillator is swept slowly through resonance, the radio frequency voltage across the coil is modulated at this aadio frequency. The modulated radio frequency voltage is amplified and detected in a linear detector giving the audio signal plus noise. This is amplified further and passed through a narrow band amplifier tuned to the modulation frequency which reduces the noise while passing the signal. The signal is passed through a phase BLOCK DIAGRAM OF A P P A R A T U S m o t o r a u d i o o s c i l l a t o r p e r m a n e n t m a g n e t p o w e r a m p l i f i e r > a O O o 2 p r o b e m o d u l a t i o n c o i l s o s c i l l a t i n g ^ d e t e c t o r a u d i o a m p l i f i e r ^1 n a r r o w b a n d a m p l i f i e r p h a s e n e t w o r k s o s c i l l o s c o p e •• r e c o r d i n g m i l l i a m e t e r p h a s e s t n s i t i v e d e t e c t o r FIGURE I TO F A C E PAOC II ~ 11 -sensitive detector and on to a recording milliammeter. To decrease the noise present -with the signal s t i l l further, a long time constant is included after the phase sensitive detector which narrows the hand of the noise recorded. At the same time, the speed with which 4e&ec may he collected is limited by the fact that the time of sweeping through an absorption signal must be several times the time constant used, other-wise the circuit will not be able to follow the signal. If the modula-tion amplitude is less than one-third of the line width the recorded signal closely approximates the derivative of the absorption curve^37). The Arrangement of the Nuclear Magnetic Reymfmce Spectrometer. The arrangement of the nuclear magnetic resonance spectro-meter is outlined by figure 1. The large permanent magnet was supplied by the Department of Physics of the University of British Columbia. The fiel d of this magnet was measured as 7070 gauss at 2U°C. throughout a gap 2.03 inches wide and 7.5 inches, in diameter. Previous measurement has shown a field inhomogeneity of about 0.2 gauss in a volume of one cubic centimeter'37). The large static magnetic field was modulated by two Helmholtz coils wound on ten inch diameter bakelite forms and placed around the magnetic pole tips^37). Some of the recording apparatus was also supplied by the Department of Physics. A Hewlett Packard Model 200B audio oscillator feeds a 30 cycle per second signal into the phase shift networks. The signal is amplified by a Williamson amplifier whose output drives the modulation c o i l s ^ '. Another portion of the signal goes to the horizontal input of an Eico model 400 oscilloscope. A third part of the 30 cycles per - 12 -second signal is changed in phase by the phase shift networks and sent to the phase sensitive detector^2**). The frequency of the oscillating detector is varied "by a Gorrell and Gorrell type M adjustable drive motor. The 30 cycles per second audio component is amplified by a restricted band audio amplifier and is amplified again by a narrow band amplifier tuned to pass thirty cycles. The output of the narrow band amplifier goes to the vertical input of the oscilloscope and to the phase sensitive detector. The deriva-tive of the nuclear magnetic resonance absorption signal is recorded by an Esterline Angus recording milliammeter(37). The frequency of the oscillating detector was measured by mixing radiation from i t with that from a Lampkin Type 105B frequency meter in an Eddystone Model 650 radio receiver. The output of the receiver was displayed on a small oscilloscope and when the beat frequency passed through zero a mane was made on the chart by momentarily shorting the side of the recorder to ground. The frequency at any point on the chart measured by interpolating between two frequency marks, assuming that the frequency varied linearily with distance along the chart(37). The Oscillating Detector. The oscillating detector is a modified Colpitisoscillator followed by an audio amplifier. The sample in the parallel resonance coil of the oscillator absorbs radio frequency energy. This changes the oscillation amplitude which changes the grid voltage of the oscillator tube. The change in grid voltage appears as an audio component at the modulation frequency in the plate voltage of the oscillator tube. The audio component is fed into the audio amplifier after the radio frequency component of the signal is bypassed. This system responds only to the absorptive component of c 9 m to s a m p l e c o i l > o m « CO RFC *3K O0f ,0001 0001 .ooo\ ~ oool ,10 K X HI-8 /0K V7K 6C4 H l -T 7K d r i v e n . b y s y n c h r o n o u s m o t o r | « — p r o b e . . s e p a r a t e b r a s s c h a s s i s + a.37 a u d i o \*7K o . r 0 U f P u t 1 - 0 + 6 V LIVINGSTON OSCILLATING DETECTOR AND AUDIO AMPLIFIER L I V I N G S T O N OSCILLATING D E T E C T O R a AUDIO AMPLIFIER nuclear magnetic resonance*11'. It is essential that the oscillation be extremely weak, a condition not easy to attain. As the strength of the oscillation increases the amplitude of the resonance signal decreases. This decrease appears to be due to satura-tion of the nuclear absorption since the total power that can be absorbed by a small sample is small. For N atoms of spin I at temperature T whose frequency is V and for which the spin—lattice relaxation time is T^  the absorbed power P is : P = a l N (Mi)* <ar*i r, KT For one cubic centimeter of water at room temperature at 30 megacycles per second, P s 1CJ-9 watts( 2 2\ The first oscillating detector constructed involved the Living-ston circuit' 1^). This apparatus is shown in figures 2 and 3. The design is similar to one used by Hopkins for magnetic field control(l^). The amplifier used with the Livingston oscillator was designed to conform to the available recording apparatus. The Livingston oscillating detector gave good absorption signals for protons in liquids such as water or mineral o i l , but very poor signals for protons in solids such as stearic acid. In solids, the optimum oscillation levels are close to the lower limit of stable oscillation. Great difficulty was experienced in lowering the oscillation level of the Livingston oscillator to a point where proton absorption in solids could be properly detected. After several unsuccess-ful modifications of this design such as increasing the range of the grid bias resistance, and changing the plate voltage, i t was decided to build an oscillating detector of different design. C, C3 ZO-tOOf^f IO0K 5AK5 s a m p l e c o i l L /F1 o O O e o\ 9 /OK 403E! 8. .0/ Y7<?K > looK .O0£_ I N 4 0 3 B Aooo< OOl 8 /0 K /O0 K 0 3 B a u d i o o u t p u t .oS 8 82JO< d r i v e n b y s y n c h r o n o u s . m o t o r - 6 v L _ — s e p a r a t e b r a s s c h a s s i s . REGENERATIVE OSCILLATING DETECTOR AND AUDIO AMPLIFIER REGENERATIVE OSCILLATING DETECTOR S AUDIO AMPLIFIER DRIVEN* BY -SYNCHRONOUS [ ' 0 * ^ v MOTOR ' — : ~] MODIFIED REGENERATIVE OSCILLATING DETECTOR F I O U R E 6 TO F A C E P A G E /¥ • ~ Ik -It is usually necessary to have a special feed-back c i r c u i t to stabilize the oscillational level of oscillators operating with variable frequency^?. The Livingston circuit had no such provisions, yet the oscillation level appeared to remain constant over a small frequency range of say 200 kilocycles per second. Since this i s greater than the expected line widths a new design need not have the complications mentioned. A suitable c i r c u i t has been published by Gutowsky, Meyer and McClure (11). A slightly modified version was built and i s shown i n figures k and 5. The frequency control is provided by the variable a i r condenser 0^. The frequency range and the general level of oscillation are both controlled by the variable a i r condensers 0g and 0j . The variable resistor provides a finer control of the o s c i l l a t i o n level. This instrument, called a regen-erative os c i l l a t i n g detector showed proton resonance absorption i n both solids and liquids and also gave a much better signal to noise ratio than the Livingston oscillator. A third oscillating detector was then b u i l t using the same general design as the second, but incorporating certain refinements shown in figure 6. The main alteration was the replacement of the large kOO micro-micro farad variable condensers Cg and C-j with small 35 micro-micro farad ceramic condensers. The apparatus could then be reduced to half i t s former volume, and a desired higher frequency range could be reached. The Thermostat. The arrangement of the thermostat is illustrated i n figure 1. The sample is contained i n a brass case 6 inches long and 1^  inches i n diameter. Prom this case extends a tube 20 inches long and one-half inch in diameter which contains the conductor connecting the sample c o i l to the oscillating detector. This probe was set i n a Dewar. The Dewar was about GENERAL ARRANGEMENT OF APPARATUS mi ^ ° oscillating detector 5T O 1M o thermo — regulator S \ magnet pole pieces / . I audio amplifier -stirring motor probe shaft •stirring shaft -de war -heater fluorothene s p a c e r -probe case resonace coil & sample F I G U R E 7 T O F A C E P A G E l«T - 15 -1 3/8 inches inside diameter and 1 3/^  inches outside diameter for the hottorn 12 inches i n order to f i t conveniently between the pole pieces of the magnet. For the remaining 8 inches of i t s length the Dewar widens out to 3 l/2 inches inside diameter to provide a greater volume for a l i q u i d reservoir. A hath of Nujol mineral o i l i n the Dewar was heated with a Cenco knife type immersion heater. The temperature was controlled with a Cenco De Khotinsky thennoregulator and the l i q u i d was stirred with a crimped aluminum s t i r r i n g shaft which was rotated with a 6 volt D.O. motor. The o s c i l l a t i n g detector and audio amplifier was set on a large brass plate which in turn rested on a wooden platform above the magnet. The Dewar was secured to the brass plate by means of a plexiglass frame, and by the same means i t was held r i g i d i n the magnet, gap, clear of both pole pieces. - l 6 -CHAPTER III EXPERIMENTAL A. Methods. Preparation of Sodium Stearate. The sodium stearate was prepared from Eastman stearic acid which gave a melting point 69-70°C. and a molecular weight of 2S5. The molecular weight was estimated from the neutralization equivalent which in turn was determined by t i t r a t i n g one gram of stearic acid dissolved i n hot alcohol with 0.1 N sodium hydroxide using phenolphthalein as an indicator. Sodium stearate was prepared by two methods. Stearic acid dissolved in hot 95$ ethanol, was titrated with a saturated ethanolic solution of sodium hydroxide to a phenolphthalein end point. Two or three drops extra of the sodium hydroxide solution was added to ensure that a l l the stearic acid was neutralized. It has been shown that a small excess of sodium salt does not interfere with the phase transitions, whereas excess stearic acid w i l l cause serious changes(27). The sodium stearate was f i l t e r e d by suction on a Buchner funnel, washed several times with warm ethanol and allowed to dry i n a i r between several leaves of f i l t e r paper. The second method is essentially the same as the f i r s t except that stearic acid was dissolved in hot absolute ethanol and titrated with a 3$ solution of sodium ethoxide in ethanol to a phenolphthalein end point, i t was slightly overtitrated as before. The f l u f f y sodium stearate crystals contained about 3$ water when dry. This could be removed by heating i n an oven at 110°C. Sodium stearate was sealed in melting point tubes and heated i n a melting point block. The sodium stearate became translucent at about 130°; at 2620 i t became transparent and showed a meniscus* • These two temperatures agree with phase transition temperatures reported i n the literature^O) (32) ^ - 17 -A soft glass tube l / 2 inch i n diameter and 7 inches long was sealed at one end, and then constricted to 3/l6 of an inch in diameter, 1 inch from the sealed end. The result is a bulb 1 inch long and l / 2 in diameter at the bottom of the tube. The open end of the tube was also narrowed sufficiently to f i t on a vacuum l i n e . The tube was f i l l e d with sodium stearate and melted at "}QQ°C. under vacuum. The f l u f f y sodium stearate f i l l i n g the tuhe melted down to an amount just f i l l i n g the bulb. The sodium stearate was kept molten for fifteen minutes to remove any water or ethanol and then i t was allowed to cool to room temperature. The vacuum system was f i l l e d with dry nitrogen and the bulb containing the sample was sealed off. In this manner sodium stearate was made dry and compact, and was protected from oxidation. Operation of the Thermostat. The desired temperature was reached by supplying the required power to the knife heater using a variable voltage A.O. power source. This temperature was maintained within about il°C. by the thermoregulator and the entire system was allowed to remain at the desired temperature for about one half an hour i n order to reach thermal equilibrium. The temperature was measured by mercury-in-glass thermometers which were almost completely immersed in the heating medium. The greater power required to maintain the temperature above say g0°0. also caused some 60 cycle pickup i n the oscillating detector which greatly decreased the signal-to-noise ratio. For this reason, the. heater power was shut off as soon as the resonance absorption was to be measured. At higher temperatures the error i s nearer i 3 ° 0 . . The recorded temperature was taken when the resonance absorption signal passed through the Larmor frequency. - I S -Most of tlie measurements were obtained using Nujol mineral o i l as the heating medium. Nujol tended to smoke at temperatures above 150°0. so Fisher bath wax was used for temperatures between 150°0. and 200°C. Measurement of Resonance Absorption. The Larmor frequency of protons i n a magnetic f i e l d of 7070 gauss was found to be 30«1H8 Mc/sec.. The resonance absorption line spreads out in a symmetrical manner on both sides of this frequency. The frequency of oscillation of the oscillating detector was found by the communications receiver and was adjusted to within about 100 kc/sec. of the Larmor frequency. The frequency of the oscillating detector was then swept at a uniform speed * by a mechanical "drive through the frequency region of resonance absorption. The distance on the recorder trace which corresponds to frequency difference was measured by means of a crystal calibrator i n the manner described. The width of the resonance absorption line was taken to be the difference i n frequency between the peaks on the derivative curve. This frequency d i f f e r -ence was then converted.into terms of magnetic f i e l d by multiplying the frequency by the g factor for protons and . For this case i t was found that; ,-: (line width i n gauss) s O.23U865 in kc/sec. The line widths in gauss have been plotted against temperature. Sources of Error.*/-' • The most serious source of error is that involved i n determining the exact temperature of the sample. There is some assurance, due to the general reproducibility of line widths, that the difference in temperature between the heating bath and the sample was small, but i t could involve a difference of 2~3°C. at higher temperatures. LINE WIDTH IN GAUSS o* >» i — i — m — r r n — m — i i i o Co 'O H © m ? * l * o rn JO > H 6 C 3) < m e e 9 -O o w O o o IS ft > to r H 2 m fl» {A O X m  x w PI o w © O pi o r z - 19 -Since the. actual line width was measured f i r s t i n terms of distance on the recorder graph, small errors could he introduced due to irregularities i n the chart drive. Irregularities i n the mechanical drive of the frequency sweep system also produce errors i n the position of the signal on the chart although this i s minimized to some extent "by the system of frequency measurement. At lower temperatures the derivative lines are broader than at higher temperatures and the exact point of maximum deflec-tion on a trace may be d i f f i c u l t to locate. Sometimes the centre of a peak on the derivative curve must be taken as the point of maximum deflection. As a result, the average uncertainty in the line width i s about £ 0.3 gauss. B. Results. Phase, Transitions, in Sodium Stearate. A preliminary investigation was made on sodium stearate to see 'fri-ll the line width changes in an irregular manner at higher temperatures. One sample was heated .to 130°C. and allowed to cool down to room temperature at a rate of approximately one degree centigrade per minute while line width measurements were made. It was then heated to l67°C. and allowed to cool again. The cooling curveB i n figure g indicate that there are rapid changes ike. i n the line width at vhigher temperatures. The path of the cooling curve depends on the particular temperature to which the sample was originally raised. This hysteresis effect renders the cooling curves of l i t t l e use for line width investigations. Line width measurements were made on the same sample at success-ively higher temperatures in the manner previously described. These measure-ments were then reproduced using a second sample. The f i r s t sample was prepared by ti t r a t i o n with sodium hydroxide and the second was prepared I o S U P E R -WAXY P H A S E 4 0 30 *fo to 6 0 7© 8° °o 100 11a uo is» 1+0 /x© tCo 110 190 Ifo Xoo T E M P E R A T U R E IN by titration with sodium ethoxide. The collected results were plotted against temperature and are shown in figure 9» The resulting curve shows three discontinuities which correspond to phase transitions. These are the supercurd-subwaxy transition at l l h ° 0 . , the subwaxy-waxy at 130°0. and the waxy-sup erwaxy transition at 165PC.. The phase transition temperatures found are in good agreement with some transition temperatures reported in the literature. Transition This Work Vold(33) Benton^) Supercurd-subwaxy llU°C. llU°0. mm Subwaxy-waxy 130°0. 13^ 0C 132°0. Waxy-superwaxy 165°0. - 165°0. Method of Measurement N.M.R. Calorimetric Transmission of Light The curve in figure 9 shows that the line width decreases evenly from 12 to 10 gauss between room temperature and 90°G.. Above 90°C. the line width decreases more rapidly to about 8 gauss at 110°C.. This more rapid:drop might correspond to the supercurd phase reported to begin around 9 0 ° C . ^ < ^ ^ . The supercurd-subwaxy transition at llU°C. is accompanied by a sudden narrowing from 7«5 t o b" gauss. The line width narrows s t i l l further from 6 to 3*5 gauss throughout the subwaxy phase. In the waxy phase between 130°C. and l65°C. the line width remains constant at 3.5 gauss. At 165° there is a sudden decrease in line width from 3*5 *° 1.5 gauss corresponding to the waxy-superwaxy transition. The line width remains constant at 1.5 gauss throughout the superwaxy phase which ends at 200°C. Further investigation at higher temperatures were not considered since the line widths found for water and mineral o i l were about 1.5 gauss. IH •O ' * -/ / -/ • — < © 7 2 6 X 5 L I N E WIDTH C H A N G E IN S T E A R I C A C I D AS T E M P E R A T U R E IS R A I S E D IdB——-EH3 » « » I I I I I L_ To *o £ e s o g o TO gofa T E M P E R A T U R E IN C. F I G U R E 10 IT® . F A C E P A G E X\ RESONANCE ABSORPTION LINE SHAPES SODIUM STEARATE IN DERIVATIVE OF LINE * * 6 f AH LINE 8HAPE AH BELOW 8 0 ° C DERIVATIVE OF LINE i * * AH -4>*-»'o a * • AH I I 4 ° C D E R I V A T I V E 0 F LINE D E R I V A T I V E OF LINE LINE S H A P E I 3 0 ° C 1 6 5 ° C NOT T O S C A L E F I G U R E II T O F A C E P A G E Zl - 21 -An Investigation of Stearic Acid. Stearic acid was melted into a glass tube of the size used for sodium stearate and line width measurements were made at different tempera-tures in the manner already described. The resulting line widths were plotted against temperature and are shown in figure 10. The line width remains constant at 13.5 gauss from 2U°C. to about 70°C.. At this tempera** ture the stearic acid melts and the line width abruptly decreases to l.S gauss. The Line Shanes of Sodium Stearate. The line shapes of sodium stearate are shown in figure 11. From 23°C. to about 100°0. the line remains gaussian in character. Above llU°0. the line has a broad base with a narrower peak. The peak becomes narrower s t i l l above 130°0. and at l6o°0. the line is a narrow spike of liquid line width set on a comparatively broad base. a CHAPTER IV DISCUSSION Stearic Acid. The sharp change in line width from 13*5 to 1*8 gauss when stearic acid is melted illustrates the sensitivity of nuclear magnetic resonance to some phase transitions. The spin-spin relaxation time T 2 is inversely propor-(?) tional to line width i f the resonance line always has the same shape > c / . This is true in the case of stearic acid and is approximately so in the case of sodium stearate. In stearic acid the value of Tg is greatly increased at the melting point, indicating that the effect of the interacting local fields is greatly reduced. It is apparent from this simple illustration that below the melting point the motion of the proton containing groups in stearic acid is greatly hindered by the lattice. There is a laxge line width due to static interacting fields. However, on melting, the line width narrows greatly, a situation which would indicate that the interacting fields cancel one another out. The proton containing groups, that i s , the groups containing hydrogen atoms in the liquid, must therefore be in very rapid motion. The kind of motion that occurs might now be considered. In the case of molten stearic acid, Brownian movement should remove a l l inter-molecular magnetic inter-actions and the intra-molecular interactions should be minimized by free rotation about the carbon-ccarbon bonds. Sodium Stearate. Sodium stearate does not give the sharp change in line width that was found for stearic acid because of the mesomorphic phases through which sodium stearate must pass before melting. However, the line width can s t i l l be interpreted in terms of molecular motion. The cooling curves of sodium stearate show l i t t l e sign of phase transitions. This is probably because - 23 -the sample was cooled too rapidly and several phases were present simultan-eously. The total change in line width will be due to at least two kinds of interactions. As the lattice forms, rotation of bonds in the molecule will be restricted causing intramolecular magnetic interaction. The forma-tion of a more rigid lattice will also pack molecules closer together causing intermolecularmagnetic interaction. It has been shown that the effect of interacting magnetic dipoles varies inversely as the cube of the distance between them^12^. The largest contribution to line width would then be the interaction of the protons attached to adjacent carbon atoms in the aliphatic chain. The contribution of other protons further along the chain or in adjacent molecules would be much smaller in comparison. Since stearic acid melts around 70°0. i t can be said that enough energy has been supplied to cause free rotation of proton containing groups in the aliphatic chain portion of sodium stearate. Although most of the narrowing in line width of sodium stearate would be due to bond rotation, the mechanism governing the details of the line width narrowing is probably a change in the lattice which allows rotation to take place. The line width changes in sodium stearate become, in a qualitative sense, a function of the changes in the lattice parameters. This argument is partly supported by the fact that the change in line width from 2 4 ° 0 . to 1 3 0 ° 0 . follows the dilatometric behaviour of sodium stearate^ 2?). The line width versus temperature curve in figure 9 shows a gradual loosening of the lattice up to about SO°C.. No special change was found in the vicinity of the genotypical point reported at 7O ° 0 . ( 2 S \ This may mean that the genotypical point which was found by calorimetric^ 2) and viscosity measurements^2^) might be a rearrangement of the molecules in the lattice that scarcely affects the hindrance to rotation of the proton groups. -2k-The l a t t i c e loosens much more rapidly throughout the supercurd phase, which begins above 9 0 ° C The more abrupt decrease of about 1 .5 gauss at l l U°C. seems to indicate the end of a trend and perhaps represents the breakdown of the l a t t i c e i n one dimension. The restrictions on rotation diminish rapidly throughout the subwaxy phase as the l a t t i c e continues to loosen. The ends of,the hydrocarbon chains are probably receding from each other i n directions parallel to the molecular axis. The waxy phase which extends from 130°C. to l65°C. maintains an almost constant line width. It cannot be said that the la t t i c e i s not s t i l l loosening or breaking down, however the motion of the proton containing groups must have reached some equilibrium. The l a t t i c e has probably altered considerably i n a second dimension at 1 3 0 ° 0 ., allowing a slightly restricted rotation of groups. There cannot he much restriction since the line width is only about 3 gauss. Whatever the restriction may be i t appears to be completely removed at l 6 5 ° 0 . and the line width becomes 1.6 gauss. This i s the line width obtained for liquids. Interpretation of a Line Shape of Sodium Stearate. When sodium stearate was heated above l65°C., the line became a narrow spike set on a comparatively broad base as shown i n figure 1 1 . It has been postulated that the broad base is due to line width broadening resulting from the spin-spin c o l l i s i o n of a certain proportion of the protons* '. This suggests that an organized structure or l a t t i c e s t i l l exists to some extent above l 6 5 ° 0 . . At this temperature the structure or l a t t i c e i s probably main-tained by the strong attraction between the sodium carboxylate ends of the molecule. Future Work. Two major phase changes occur i n sodium stearate around 200°0. and 2o5°0. which are attributed to the sodium end of the molecule^) (33) # With some modifications the apparatus used for measuring proton line widths could he used to measure the line widths of sodium. The experiment would he more d i f f i c u l t with sodium nuclei than with protons since the concentration of sodium i s relatively small compared to hydrogen, and the sensitivity of sodium nuclei i s much less than that of protons'**). It is not possible to determine the exact mechanism involved i n each phase transition by inspection of the line width versus temperature curve. Only a very qualitative estimation can be given. To obtain a more exact description of the mechanism, i t is necessary to calculate the theore-t i c a l second moment of the line width for sodium stearate under a variety of conditions. For instance, the second moment must f i r s t be calculated for a r i g i d l a t t i c e using the known molecular and unit c e l l parameters'^). This value is compared to the experimental second moment obtained at low tempera-tures. Various different conditions of rotation are then calculated i n the hp) manner described by Gutowsky and Pake ' and compared to the experimental results for the various phase transitions* , x '. Since the spin-lattice relaxation time T-^  may give important contributions to line width change at lower temperatures i t must be determined separately. This requires somewhat different apparatus than was used i n the present investigation* '. In such a manner, i t i s possible to describe the mechanisms of phase transitions with some confidence. APPENDIX LINE WIDTHS OF SODIUM STEARATE USED IN FIGURE 9. 1. Sample prepared by neutralizing stearic acid with, sodium hydroxide.  Temperature Line Width Temoerature Line Width Temperature Line Width in Gauss in Gauss °0. in Gauss 24 12.0 80 10.5 113 7-1 24 11.9 80 10.6 116 5.9 24 12.1 82 10.3 118 5.8 33 12.0 85 9.9 122 5.9 ?3 11.7 88 9.9 124 41 *3 12.0 90 10.1 126 U.s 11.5 92 10.6 130 3.4 50 11.7 92 9.* 130 3.7 \f 10.8 99 9.1 133 3.H 60 11.2 100 8.2 145 3-7" 65 • 11.1 101 9.0 1*5 3.3 65 10.7 io4 9.0 147 3.0 70 11.2 105 8.4 155 3.3 70 11.2 106 8.6 165 1.6 73 11.0 108 9.4 170 1.6 75 10.2 108 8.2 185 75 • 10.6 111 7-7 200 1.4 80 10.6 113 7.4 200 1.3 2. Sample prepared by neutralizing stearic acid with sodium ethoside.  Temperature Line Width Temperature Line Width Temperature Line Width °0. in Gauss 2<L in Gauss °0. in Gauss 23 12.1 122 5.2 151 3-5 44 l l .U 123 5.7 l 6 l 3.1 62 11.0 124 5.2 165 1.7 91 9.9 125 5.2 I65 1.7 108 8.3 126 5.2 166 1.5 112 7.7 130 5.8 178 1.3 114 7.7 130 4.0 180 1.7 115 6.1 148 3.5 180 1.6 121 5.5 149 3.4 REFERENCES 1. Alport. N. Phys. Rev., 25., 398 (19^9). 2. Andrew, E. and R. Eades, Proc. Roy. Soc. A., 2 l 6 . 398 (1953). 3. Benton, D., Howe, P., and I. Puddington, Can. J. Chem., jQ, 138U (1955). k. Bernal, J . and D. Crowfoot, Trans. Paraday Soc, 22., 1032 (1933). 5. Bloemhergen, N., Purcell, E. and R. Pound, Phys. Rev., TJi, 679 (igl+8). 6. Buerger, M., Smith, L., De Bretteville, A. and P. Hyer, P r o c Natl. Acad. Sci. U.S., £8, 526 (19^2). 7. De Bretteville, A., and J. McBain, J. Chem. Phys., 2JL., J+l6 (19^3). 8. Doscher, T., and R. Void, J . Phys. and Colloid Chem*,. 5J>, 97 (19US). 9. Gallay, W., and I. Puddington, Can. J. Research B, 2JL., 202 (19U3). 10. Gutowsky, H., Kistiakowsky, G., Pake, G. and E. Purcell, J. Chem. Phys., 17_, 972 (l9-*9). 11. Gutowsky, H., Meyer, I., and R. McClure, Rev. Sci . Inst., 2j+, (1953). 12. Gutowsky, H., and G. Pake, J. Chem. Phys., 18, 162 (1950). 13. Hedgecock, N., Private Communication. l U . Hopkins, N., Rev. S c i . Inst., ,2j), koi (19^9). 15. Lawrence * A., Trans, Paraday Soc, 3it, 660 (1938). 16. McBain, J., Bolduan, 0 . , and S. Ross, J. Am. Chem. Soc, 65,, 1873 (19U3). 17. McBain, J., Void, R., and M. Prick, J . Phys. Chem., UJ+, lOlk (19H0). IS. Pake, (Sr., Amer. J . Phys., 18, ^38, U73 (1950). 19. Pound, R., and ff. Knight, Rev. Sci. Inst., 21, 219 (1950). 20. Powell, B., and I. Puddington, Can. J. Chem., 31, 828 (1953). 21. Purcell, E., Science ipj., -133 (19^8). 22. Roberts, A., Rev. S c i . Inst., LS., 8U5 (19^7). 23. Rushworth, P., Proc Roy. Soc. A., 222. 526 (195U). - 28 ~ 2k. Schuster, H ., Eev. Sci. Inst., 22, 2$k ( l 9 5 l ) . 25. Smith, J., Quarterly Reviews, J_, 279 (1953). 26. Southern, F., and I. Puddington, Can. J. Research B. 25.. 125 (19^7). 27. Stainshy, Gr., Farnand, R., and I. Puddington, Can. J. Chem., £3., S38 (1951). 28. Thiessen, A., Kleck, J., Gockowinck, H., and J . Stauff, Z. physik. Chem. A., 17JJ-, 335 (1935). 29. Thiessen, P., and J. Stauff, Z. rphysik. Chem. A., 17ji, 397 (1936). 30. Void, M., J. Am. Chem. Soc, 63., l 6 o (19H1). 31. Void, M., Macomber, M., and R. Void, J. Am. Chem. Soc, 63., 168 (19I+I). 32. Void, R., J. Phys. Chem., U&. 315 (19^5). 33. Void, R., J. Am. Chem. Soc, 63., 2915 ( l 9 ^ l ) . 34. Void, R., Grandine, J., and H. Schott, J . Phys. Chem., 56., 128 (1952). 35. Void, R., and M. Heldman, J . Phys. and Colloid Chem., 52,, lUg ( 1 9 ^ ) . 36. Vorlander, D., Berichte. 3x22 (1910). 37. Waterman, H., Ph.D. Thesis, University of B r i t i s h Columbia (195^). 38. Williamson, D., Radiotron Designers Handbook. P. 750 (Radio Corporation of America, Commercial Engineering, Harrison, >T. J., 1951*). 

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