Nov., 1960
FREEZING POINTFOR
THE
SYSTEM ACETAMIDE-PALMITIC ACIDSTEARIC ACID
1613
FREEZING POINT DATA FOR A PORTION OF THE TERNARY SYSTEM: ACETAMIDE-PALMITIC ACID-STEARIC ACID BY ROBERT R. MOD,FRANKC. MAGNEAND EVALD L. SKAU Southern Regional Research Laboratory,l New Orleans, Louisiana Received February 16, 1060
Freezing point data were obtained for stable, metastable and unstable crystalline phases in binary mixtures of the 1 :1 molecular compounds acetamide-palmitic acid (AP) and acetamide-stearic acid (AS) and for a portion of the ternary system: acetamide-palmitic acid-stearic acid. The e uimolar mixture of AP and AS exhibited three freezing points, representing stable equilibrium with the high-melting mo%ification of acetamide, metastable e uilibrium with crystals of AS, and respectively. X-gay long spacing measurements of unstable equilibrium with B crystalline phase of unknown corn?, these solidified 1:1mixtures indicate the presence of the “C” orms of palmitic and stearic acids and the “A” forms of their 1:1 acetamide compounds. The long spacings were essential1 the same whether solidification started from stable or from unstable equilibrium, but the X-ray short spacings and the inJared spectra showed slight characteristic differences.
It has been shown in previous publication^^^^ that acetamide forms 1:1 molecular compounds with long chain saturated fatty acids. X-Ray long spacings of the crystals proved to be equal to the sum of the lengths of two acid and two acetamide molecule^.^ This is similar to the arrangement in crystals of the long chain fatty acids, which are made up of double layers of acid molecules, their carboxyl groups being in juxtaposition with their hydrocarbon chains extending in opposite directions.6 The double moleculee are also present in the liquid state as associated molecules.e It is not surprising therefore that a fused equimolar mixture of palmitic and stearic acids should contain double molecules made up of one molecule of palmitic acid and one molecule of stearic acid and that crystals of this 1 :1 molecular compound can separate on chilling.’ By analogy it might be assumed that there would be a similar 1 : l molecular compound between the l : l acetamide-palmitic acid compound (AP) and the 1 : l acetamide-stearic acid compound (AS). Binary freezing point data were obtained which a t first seemed to confirm this assumption but the supposed molecular compound melted over a tempeIature range, instead of at constant temperature as required. The reason for this apparently anomalous freezing point behavior was revealed by construction of the pertinent part of the freezing point diagram for the ternary system acetamide-palmitic acid-stearic acid.
geneity of the sample. Since nitrogen analysis of the AS indicated an appreciable loss of acetamide by sublimination during the fusion, the required amount of acetamide was added and the process repeated. The final freezing oint for the AP was 59.2”and for the AS, 65.7”. Anal. &lcd. for AP: N, 4.44; neut. equiv., 315.5. Found: N, 4.36; neut. equiv., 314.7. Calcd. for AS: N, 4.09; neut. equiv., 343.2. Found: N, 4.10;neut. equiv., 343.5. The freezing points were determined with an estimated precision of f0.2’ by the thermostatic sealed-tube method previously described,* which involves finding two temperatures a few tenths of a degree apart, one at which the last crystals just disappeared and the other a t which a few crystals remained undissolved after prolonged agitation. The heating curves were obtained by an apparatus and technique previously described.* The X-ray measurements were made by the powder method.‘ The infrared spectra were obtained with a double-beam infrared spectrophotometer with sodium chloride optics employing the technique of O’Connor, et aL8
( 6 ) A. W. Rdston, “Fatty Acida and Their Derivativea,” John Wiley and Bone, New York, N. Y., 1948, p. 287. (7) L. E. 0. de Vimer, Rec. t m v . chim., 17, 182 (1898).
(8) E.L. Skau, Proo. Am. Acad. Arts SCL,67, 551 (1933). (9) R. T. O’Connor, E. F. DuPr6 and E R. McCall, Anal. Chem., 29, 998 (1957).
Results and Discussion
The primary freezing point data for the binary system AS-AP are given in Table I and represented graphically in Fig. 1. All compositions are expressed in mole %. The compositions containing between 12 and 58% of AS exhibited two, and in some instances three freezing points, depending upon the previous treatment of the samples. The solid line in this range represents the temperatures of stable equilibria obtained on samples which had been heated for a few minutes a t about 80” and shock-chilled in an acetone-Dry Ice mixture. The corresponding metastable equilibria, obtained on samples solidified by spontaneous crystallization of the melt, are represented by the broken lines, which are obviously extensions of the AP and AS branches of the diagram. The mixtures from 29 to 50% AS were later shown to exhibit a Experimental still lower freezing point, between about 47 and 50°, The 1:1 compounds, AS and AP, were prepared by fusing equimolar portions of ure acetamide and pure acid, each of involving an unstable crystalline phase which was usually the first to form on spontaneous crystallizawhich had been d r i e f i n a vacuum desiccator over hos phorus pentoxide. The solidified mixture was groundPin tion of the melt. The exact equilibrium temperamortar, remelted, resolidified and reground to ensure homo- ture could not be determined because of a gradual transition to the metastable crystalline phase (1) One of the laboratories of the Southern Utilization Reeearch and before equilibrium could be established. Development Division, Agricultural Research Service, U. 8. DepartOn the basis of this freezing point diagram and ment of Agriculture. (2) F. C. Blagne and E. L. Skau, J . A m . Chsm. Soc., 74, 2628 the precision of the freezing point determinations (1952). it might be assumed that this is a binary system (3) F. C. Magne, R. R. Mod and E. L. Skau, J . A m . Oil Chemists’ in which a congruently melting 1 : l compound, Soc., S4, 127 (1957). AS.AP, forms. However, it was observed that (4) R. T. O’Connor, R. R. Mod, M. D. Murray and E. L. Skau, J . A m . Chem. SOC.,77, 892 (1955). freezing of the 50-50 mixture initiated a t the upper (5) K. 9. Markley, “Fatty Acids,” Interscience Publishers, Ino., (stable) equilibrium temperature took place over :L New York, N. Y., 1947, p. 85.
R. R. MOD,F. C. MAGKEAND E. L. SKAU
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Vol. 64
about 20 and 50% tended to supercool to give an unstable crystalline phase for which the equilibrium temperatures were between about 47 and 50". TABLE I FREEZING POINT DATA~J -F.p., Mole % b
I
MlXTr
MOLE
MIXT s
1
MlXTs
I
501
AP
20
60 MOLE % A S ,
40
so
I O
AS
Fig. 1.-Binary freezing point diagrams for I, the acetamide compounds of palmitic and stearic acids; 11, Mixture r with Mixture s; 111, acetamide nith Mixture a. Broken lines represent metastable equilibria.
" C . 7
Metastable
---F.p.,
Mole
Stable
OC.--
iMetastable
AS-AP system 49.49 58.4 56.5c 53.01 58.6 (58.3)d (58.6)d 55.8 59.71 59.1 54.1c 69.35 60.6 (52.6)d 77.26 61.8 58.1 53.3c 88.52 63.8 55.2e 100.00 65.7 A-Mixture a system' 42.12 54.gC (55.2)d (54.9)d 46.65 55.1 60.94 70.6 60.3 (48.2)d (55.1)d 70.43 76.2 65.7 50.91 60.1 55.2 79.66 79.0 68.7 52.34 61.7 54.9 100.00 79.7 69.5 Mixture sP-Mixture rh System 0.00 59.1 43.ge 55.0E 10.17 57.6 49.64 56.3c 19 21 56.3c 58.77 58.6 28.86 54.OC 69.63 60.6 33.98 52.9" 79.95 62.4 36.32 52.7" 90.78 64.0 (38.0)'' ( 5 2 . 1 ) d 100.00 65.1 40.15 53.2c The values in parentheses were obtained by graphicd extrapolation or interpolation. Mole % of &st-mentioned component. A lower freezing point was observed lying between about 47 and 50°, but could not be accurately determined, because of gradual transition to the next more stable form before equilibrium could be established. "Eutectic" composition and temperature. e Interpolated from A-Mixture a system. f Mixture a = 44.22% S, 55.78% P. Mixture s = 44.69% A, 55.31% S. Mixture r = 43.29% A, 56.71% P. The ternary mixture containing 53.55% $, 27.90% P and 18:55% S gave three freezing points: 63.1 , 53.2', and approxlmately 49", corresponding to stable, metastable and unstable equilibria, respectively. 0.00 11.16 (11.8)d 20.68 29.85 (38.O ) d 39.98 44.28
50
Stable
59.2 57.3 (57 .2)d 57.7 57.9
0
wide temperature range. The same was true of the mixture containing 39.98% AS, supposedly close to a eutectic, when crystallization started at the lower (metastable) equilibrium temperature. Heating curves were run on two completely solidified samples of 1: 1 AS-AP mixture, one prepared by shock-chilling and the other by spontaneous crystallization. Their primary freezing points as determined by the thermostatic sealed-tube method were known to be 58.4 and 56.5", respectively. The first sample started to melt a t about 49", a t which temperature the time-temperature curve showed a typical eutectic halt. The eutectic halt for the secopd sample came a t about 46.5" instead of 52.6" as would be expected from Fig. 1, I. It is obvious, therefore, that the system must be considered as part of the ternary system formed from acetamide (A4), palmitic acid (P) and stearic acid (S). Freezing point measurements were made on pertinent mixtures of acetamide with Mixture a, a mixture consisting of 0.4422 mole of stearic acid and 0.5578 mole of palmitic acid. The results are included in Table I and shown in Fig. 1, 111. Here ce and df represent solid-liquid equilibria for the stable (high-melting) and the metastable (low-melting) modifications of acetamide, respectively. Similar freezing point data obtained for mixtures of Mixture r (43.29% A, 56.71% P) with Mixture s (44.69% A, 55.3101, S) are represented in Fig. 1, 11. Here again the molten mixtures between
On the basis of the data obtained by interpolation in the freezing point diagrams of Fig. 1 and those for the systems acetamide-stearic acid and acetamide-palmitic acid12it is possible t o construct the pertinent part of the primary freezing point diagram for the ternary system acetamide-stearic acidpalmitic acid (A-S-P). Figures 2 and 3 show the primary freezing point behavior for this system when the metastable (low-melting) and stable (high-melting) forms of acetamide are involved, respectively. The broken lines jk Aa and rs represent the compositions in the systems AP-A4S, A-Mixture a, and Mixture rMixture s, respectively. The solid lines are isotherms showing the temperatures a t which crystalline AS, AP or A are in equilibrium with the liquid. The black circles in Fig. 3 represent compositions from which an unstable crystalline phase separated when the melt was allowed to supercool and crystallize spontaneously (see Table I, footnote c). -4lthough the corresponding equilibrium tem-
Kov., 1960
FREEZING POISTFOR THE SYSTEMACETAMIDE-PALMITIC ACIDSTEARIC ACID
peratures could not be determined accurately it was estimated that they all lay between about 47 and 50". The metastable form of acetamide (Fig. 2) or the stable form (Fig. 3) can be caused to crystallize from any molten mixture within area Amno. The curve mn represents the eutectic groove formed by the intersection of the A and AP crystallization surfaces, and no and np represent the corresponding intersections between the A and AS surfaces and between the A P and AS surfaces, respectively. The curves mn and no in Fig. 2, as well as all the isotherms or portions of isotherms on the A, AP and AS surfaces in Fig. 2 lying within the compositional area Amno of Fig. 3 represent metastable equilibria. These ternary diagrams make it possible to identify the solid phase in equilibrium with the various branches of the diagrams in Fig. 1. For compositions along jk (ie., the system AP-AS), it is apparent that the crystals in equilibrium with the liquid along the almost horizontal mid-section of Fig. 1, I are crystals of the stable modification of acetamide and not of a 1:l APeAS molecular compound. Similarly, the ternary diagrams show that the curve bd in Fig. 1, I11 represents temperatures of equilibrium between crystalline AS and the liquid phase. Between c and d this is a metastable equilibrium. At c and d a second crystalline phase, the high-melting or the low-melting modification of acetamide, respectively, is also present in the equilibrium. In the system Mixture rllixture s (Fig. 1, 11) AP and AS are the solid phases in stable equilibrium with the liquid along the left and right branches of the diagram, respectively. While the ternary diagrams are sufficiently complete to explain the primary freezing point behavior observed when stable and metastable equilibria are involved, additional data would be necessary to account for the specific eutectic temperatures found for the equimolar mixture of AP and AS by heating curves. It can be concluded, however, that these "eutectic halts" can be attributed t o eutectic or peritectic points involving one or more unstable crystalline phases of undetermined composition. The marked tendency for supercooling until an unstable crystalline phase appears affords a plausible explanation. Consider for example, the freezing of a melt having the composition a t the mid-point of jk (Fig. 2) in which crystals of AS have started to form. A s the temperature falls, more AS would separate and the composition of the liquid would change along jk toward j until the intersection of the AP and AS crystallization surfaces, np, is reached. At this point the melt would be saturated with respect t o both AP and AS and if crystals of AP formed, complete solidification should take place without further temperature change since a "saddle point" in the diagram is involved. If, however, supercooling with respect to AP took place; i e . , if the AS surface extended into the metastable region below the AP surface, the temperature would continue to fall as more -4s separated. Eventually an unstable crystalline
1615
MOL E '1, S , Fig. 2.--Solid-liquid equilibrium isotherms in the ternary system acetamide-palmitic acid-stearic acid. The 55 and 53" isotherms on the acetamide crystallization surface are not shown. In this diagram the equilibria for all compositions in the area Amno of Fig. 3 are metastable.
Fig. 3.--Stable solid-liquid equilibrium isotherms in the ternary system acetamide-palmitic acid-stearic acid. The 59, 57, 55 and 53' isotherms on the acetamide cryatallization surface are not shown. The black circles represent comDositions showing unstable solid-liquid equilibria.
phase would appear at the intersection of the unstable crystallization surface and the metastable AS surface. The subsequent behavior would depend upon the composition of the unstable crystalline phase. The heating curve of the sample so solidified would be expected to show a halt at a temperature below that which would be predicted from the diagram in Fig. 1, I. Similarly, the apparent anomaly in the heating curve for the 58.4"-melting equimolar mixture of AP and AS can also be attributed to supercooling. In this instance, there is the added possibility that the crystallization surface of the high-melting form of acetamide may extend into a metastable region below the AS surface.
1616
MARJORIE J. VOLD
X-Ray diffraction measurements were made on the completely solidified high-melting (f.p. 58.4’) and low-melting (f.p. 56.5”) equimolar mixtures of AP and AS. Egch had the same two long spacings, 29.1 and 38.8 A. However, they had distinctive short spacings which can be used for identification: for the 58.4” form, 5.80(M), 4.14(S), 3.72(MS), 3.56(MS), 2.20(F) ; and for the 56.5’ form, 7.95(F), 5.29(F), 4.49(S), 4.13(S), 3.72(MS) and 3.51 (M). The 38.8 A. long spacing can be considered as that of a roughly equimolar mixture of the “C” forms of palmitic and stearic acids, of which the long spacings are 36.0 and 40.0 A . 1 0 Piper, et u Z . , ~ ~ showed that an equimolar mixture of two such homologs gives a long spacing considerably higher than the average of their long spacings. Similarly the 29.1 A. spacing can be attributed to the presence of a roughly equimolar mixture of the “A” forms of AP and AS, of which the reported long spacings are 27.6 and 29.9 A., respectively.12 It should be (IO) E. Stenhagen and E. ron Sydow, Arkiu Kemi., 6 , 309 (1953). (11) S. H. Piper, A. C. Chibnall and E. F. Williams, Biochem. J . , 38, 2175 (1934).
(12) R. T. O’Connor, R. R. Mod, M. D. Murray, F. C. Magne and E. L. Skau, J . Am. Chem. Soc., 79, 5129 (1957). More recent X-ray diffraction measurements in this Laboratory ehow that the 27.6 A. long spacing for the “A” form of the acetamidepalmitic acid compound is really a second-order spacing and that the first order and the odd-numbered orders are usually absent.
voi. 64
noted that the long spacings for the “A” forms of AP and AS are usually accompanied by the long spacings of the “C” form of the corresponding acids.4 There was no significant difference between the infrared spectra of the completely solidified 58.4 and 56.5” forms of the 1:l AS-AP mixtures. Except in the region between 7.8 and 8.4 p, where a progression of absorption bands of uniform spacing and intensity characteristic of carbon chain length is observed in the spectra of long-chain fatty acids in the solid state, only minor differences were observed between these spectra and those of the “A” forms of AP and AS ~eparately.~For the 1:l mixture slightly less intense absorption was observed at 6.25, 6.70 and 11.10 p and a considerably less intense band was observed at 7.10 p. The absorption band at about 10.50 p had shifted to 10.75 p . Acknowledgments.-The authors are indebted to Mildred D. Murray for the X-ray diffraction measurements, to Elsie F. DuPr6 for the infrared absorption curves, to Robert T. O’Connor for assistance in interpretation of the X-ray and infrared data, to Lawrence E. Brown for the nitrogen analyses, and to George I. Pittman for drawing the figures.
THE SEDIMENT VOLUME I N DILUTE DISPERSIONS OF SPHERICAL PARTICLES BY MARJORIE J. VOLD’ Department of Chemistry, The University of Southern California, Los Angeles, California Received March XS, 1960
A digital computer has been used to simulate the formation of a sediment by successive deposition of equally sized spherical particles. The sediment density depends critically on the probability that two spheres cohere on contact, provided that the cohesion probability is lower than about 0.35. For higher cohesion probabilities, sediment density is not a sensitive measure of particle interaction. Although the properties of a sediment generated in this way are in good accord with physical model systems such as micron sized glass beads, colloidal systems with at least nearly spherical particles yield sediment densitiea almogt 10 times lower than this model allows. A model is needed which takes both flocculation and sedimentation into account simultaneously.
vides a measure of flexibilityfor interpretation of the results. For spheres with non-homogeneous surfaces containing both cohesive and inert spots it can be looked on as the probability of contact between cohesive sites and hence as the square of the fractional area of the spheres covered by such sites. Alternatively, cohesion requires that the particle resist the continued downward pull of gravity so that the cohesion probability is a measure of the relative magnitudes of the particle interaction and particle weight. The predictions of the model are compared with existing data on the effect of water on the behavior of glass spheres in organic solvents. The Model System.-Particles are chosen with x and y coordinates selected at random from numbers between 0 and 100 (using a random number generator designed by D. Moore and G. Mitchell, Western Data Processing Center. CareRe ful statistical tests of randomness have been carried out).* Each one is given an essentially
The sediment volume of a suspension is an accepted qualitative measure of its caducity (tendency to flocculate in a time comparable to the period of observation) , large volumes corresponding to caducous suspensions and vice versa. In previous work2 it was shown that observed sediment volumes for suspensions of spherical particles in which each particle cohered rigidly to each other sphere that it contacted could be derived from a computer-generated statistical model. The present work extends this model calculation to the case in which two particles have a given probability of rigid cohesion varying between 0 and 1. The model is applicable only to dilute systems since each of the equally sized spheres is allowed to interact only with particles already located in the sediment. The variable cohesion probability pro( 1 ) This work has been supported by the Office of Ordnance searoh, Contract DA-04-495-ORD-1296. (2) M. J. Vold, J . Colloid Sd.,14, 168 (1959).
