Oct., 1963
R~OLECULARASSOCIATION IN PAIRS OF LONG-CHAIN COMPOUNDS
H. M. GHOSE(The GJidden Company).-Ko work was done on counterion influence and lots of work has been done in dissymmetry. Have you done any work on the effect of salts like KI on the coacervation?
1965
A. VEIS.-NO. The simple salts have only a dissociating effect on complex coacervates in contrast t o their role in specifically enhancing phase separation in systems of association colloids.
STUDIES OF n40LECULAR ASSOCIATIOX I N PAIRS OF LOKG-CHAIX CO3lPO’USDS BY DIFFERENTIAL THERMAL AXALYSIS. I . LAURYL AKD JIYRISTYL ALCOHOLS AND SULFATES BY H. C. KUNGAND E. D. GODDARD Research Center, Lever Brothers Company, Edgewater, New Jersey Received March 16, 1963 Studies of molecular interaction between lauryl or myristyl alcohol and sodium lauryl or myristyl sulfate have been undertaken using the technique of differential thermal analysis. Specimens were prepared by heating small amounts of the alcohol and the sulfate, a t varying ratios, to between 110 and 120°, mixing thoroughly for 8 to 10 min., and then cooling. The subsequent melting behavior of such mixtures provides evidence of the existence of association complexes of alcohol and sulfate in (,he mole ratio 1:2. The energy of binding in these complexes apuears to be appreciable. X-Ray and infrared measurements on these systems provide supporting evidence oi t h e existence-oi’ the postulated Eomplexes.
There is much information in the literature concerning the existence and formation of molecular association compounds or complexes between pairs of long-chain polar materials. Much of the early work was carried out by surface chemists with initial impetus being provided by the discovery by Scliulman and Rideall of the monolayer “penetration” phenomenon. While it is not the intention in this report to review this extensive aspect of the field, it can be said that serious difference of opinion exists not only as the composition of the complexes formed and the nature of the binding forces involved but also to the existence of the complexes. Reference is made, however, to various publications in which surface chemical investigations have given evidence of molecular interaction or stoichiometric association in surface Reference also is made to Goodrich,6mho, by measuring excess free energy (AG) of mixing in monolayers, found that some straight chain surface actire agents, including the system myristyl alcohol-sodium myristyl sulfate, combined to form a 1: 1 complex, although the A@ values were small. Interaction between long-chain molecules a t interfaces is of coiisiderablle interest in view of implications in regard to foaming behavior, emulsion stability, etc. The purpose of the present work mas to seek evidence for or against the existence of molecular association compounds between pairs of long-chain molecules using non-surface-chemical techniques, ie., by carrying out investigations in bulk. phase. Some work of this type has been carried out previously. For example, in their work on film drainage and phase relatioils in the system sodium lauryl or myristyl sulfate-lauryl alcohol-water, Epstein, et U Z . , ~ isolated well defined crystalline adducts in which the ratio of (1) J. H.Sohulman and E. K. Ridral, Proc. Roy. SOC.(London), Bl22, 29 1 (1937). ( 2 ) E. D. Goddard and .J. H. Sohulman, J . Collozd Sei., 8, 309, 329 (1953). (3) M.Joly, Nature. 158, 26 (1946). (4) D. G. Derviohian. Contribution in “Surface Phenomena in Chemistry and Biology,” Pergamon, London. 1958, Chapter 2. (5) M. B. Epstein, A. Wilson, C. X. Jakob. I,. E. Conroy, and 3. Ross, J . Phya. Chsm., 68,860 (1954). (6) F. C. Goodrich, Proc. Second Intern. Congr. Surface Acisvzty, 1, 85 (1987).
alcohol t o sulfate was 1: 2. “Acid soap” complexes between stearic acid and sodium stearate were obtained by Ryer7 from alcoholic solutions in the mole ratios 1:1, 3:2, and 2 : 1; from their work on electrical conductivity, John and R/lcBain* concluded that 1:2 acid soap associations also form. Various acid soaps have also been prepared by E k ~ a l l .Furthermore, ~ Schulman and Rideall adduce bulk phase evidence to support their contention of a 1 : l associatioil between cetyl alcohol and cetyl sulfate, and Matalon, et u Z . , ~ O found precipitation of the insoluble Ka lauryl sulfate-cetyltrimethylammonium bromide complex can be inhibited by admixture to the former of equimolar amounts of octyl or nonyl alcohol. This paper reports work on bulk phase studies on long-chain alcohol-sulfate systems. The investigation utilized the technique of differential thermal analysis (DTA), augmented by X-ray diffraction and infrared spectroscopic studies.
Experimental The DTA apparatus and method were very similar to that described by Haighton and Hannewijk.11 However, in the present work the reference thermocouple was placed directly into a small hole in the copper block. Transition temperatures are obtained by subtracting peak heights ( A T ) from the block reference temperature.ll A sample size of about 0.3 g. was used. The heating rate was 1.Boper minute. For lauryl alcohol and its mixtures, a pre-cooling in the DTA cell was necessary; this was done with a gentle current of cold dry air. The temperature of investigation ranged from 0” or room temperature up to slightly above 90’. The lauryl alcohol (LOH), a fractionated sample, and the myristyl alcohol (MOH) from Archer Daniels Midland, were of satisfactory purity as shown by their DTA and/or gas chromatographic patterns. (See Fig. 1, 2 . ) The sodium lauryl sulfate (NaLS) and myristyl sulfate (NaMB) were both prepared by the method of Dreger, et al.,Iz and then recrystallized from ethanol several times and extracted with petroleum ether. Surface tension measurements were carried out on aqueous solutions of the (7) F. V. Ryer, Oil and Soap, 23, 310 (1946). (8)L. M.John and J. W. MoBain, J . Am. 0 2 1 Chem. Sac., 25, 141 (1948). (9) P.Ekwall, Kolloid-Z., 80,77 (1937); P. Ekn-all and G. Lindblad, ibid., 94, 42 (1941). (IO) R. Matdon, M. R. J. Salton, and M. Cohen, Natwe, 167,241 (1951). (11) A. 3 . Haighton and J. Hannewijk, J . Am. 011 Chem. SOC.,35, 344 (195s).
(12) E. E. Dreger, G. I. Keim, G. D. Miles, L. Shedlovsky, and J. Ross, Ind. Eng. Chem., 36, 610 (1944).
H. C. KUNGAND E. D, GODDARD
1966
I
~-~~
1
f I
18 -
3.6
I
1
L LL-i
'J
, , , 50 70 10 30 50 70 10 Reference temp., 'C. -
10
30
1
,
,
30
50
U
70
Fig. I.-DTA curves, lauryl alcohol-sodium lauryl sulfate: (a) LOH; ( b ) 80.0% LOH and 20.0% SaLS; ( c ) 60.0% and 40.0% NaLS; ( d ) 40.0% LOH and 60.0% NaLS; 24.57' LOH and 75.57, KaLS; ( f ) SaLS. 0.
n
l' 2.7' , 20
,
,
40
60
Y .--2-_Li
8 0 2 0 40 60 8 0 2 0 Reference temp., "C.
.
I
40
60
I 80
Fig. 2.-DTA curves, myristyl alcohol-sodium myristyl sulfate: (a) MOH; (b) 80.0% MOH and 20.07, SaRIS; (c) 60.0% MOH and 40.0y0 N a N S ; (d) 40.07, NOH and 60.0% KahIS; (e) 25.3% MOH and 74.770 NaMS; ( f ) SahIS.
"d 7.2 t 0.0
1.8
3.6
\
'u, '
-7
I
,
m,-, d
f I
10
30
50
70 10
30
50
Reference temp.,
70 10
30
50
70
OC.
Fig. 3.-DTA curves, lauryl alcohol-sodium myristyl sulfate: ( a ) LOH; (b) 80.0% LOH and 20.0yc NaRIS; ( e ) 60.07, LQH and 40.0% KaMS; ( d ) 4Q.070 LOH and 60.070 S a k I S ; (e) 22.7% LOH and 77.37, NalCIS; ( f ) KaMS. NaLS and the high purity of the specimen was confirmed.'3 The DTA curve of both specimens showed very small peaks at low temperatures, see (Fig. 1, and 2). The precise reason for these is not clear; they may have been caused by the release of solvent, a transition in the solid, or the melting of a minor amount of parent alcohol,. In order to avoid the effects of solvent inclusion, specimens of mixtures for this work were prepared by a melt, method: weighed amount,s (total weight about 1 g . ) of the two long-chain compounds in a Pyrex test tube a w e mixed thoroughly by stirring with a glass rod betn-een 11Q-12Q0in an oil bath for 8 to 10 min. The mixture then was cooled slon-lj- to room temperature by removing the heat source from the oil bath and allowing to stand overnight. Similar treatment was app!ied t o single components. For the NaLS and NaMS this led t o the disappearance in the (131 G. D. Miles and L. Shedlovslcy, J. Phiis. Chem., 48. 57 (1944).
Yol. 67
DTA patterns of the small low temperature peaks. Heat treatment of the MOH led to the appearance of a very small peak a t 26" followed by the main melting peak at 38". The specimens used for the X-ray and infrared studies were taken from samples prepared as above. They were enclosed in a fine capillary for the former, and gently dispersed as a uniform mull in Nujol and spread thinly on the NaCl plate for the latter. The mulls were all of approximately the same strength. X-Ray exposures were 1.5 hr. in standard Norelco equipment (specimen ~ Scan times for the to film distance 57.3 mm., Cu K o radiation). 2 to 16-p infrared spectrum were set a t 15 min. in the Beckman IR5A instrument. Both of these measurements were run a t room temperature. In addition to the DTA results, cooling curve data on the MOH-NaMS system were obtained for purposes of constructing a partial phase diagram.
Results (1) DTA.-DTA curves of the binary system LOH, NaLS with 0, 24.5, 40.0, 60.0, 80.0, and 100% (by weight) of alcohol are shown in Fig. 1. The LOH alone gave a peak at a sample temperature of 23" due to melting. The addition of sulfate to the alcohol resulted in the appearance of a second endothermic peak near 60'. With increasing amounts of sulfate the high temperature peak grew at the expense of the lorn temperature peak and in the system with 24.5% of alcohol and 75.573 of sulfate, corresponding to a mole ratio of 1:2, only one peak near 60" was present. This constitutes strong indication of an interaction between LOH and XaLS to form an interniolecular compound of mole ratio 1:2. DTA curves for the system MOH-KalVIS are shown in Fig. 2. The results are similar to those of the system described above. The second peak occurred near 65", again a t a molar ratio of alcohol to sulfate of 1:2. The curves of the systenis LOH-SaMS and MOHS a L S are shown in Fig. 3 and 4. The pattern is again similar to the above although some of the curves are not as straightforward as the others. With these two systems, specimens had to be prepared within a specific temperature range and under more restricted conditions ifi order to get reproducible results. This presumably results from the difference in chain length between the alcohol and sulfate, which makes the packing of the molecules more difficult. Although for all systems studied there are slight shifts in the values of the low and high temperature peaks as the alcohol :sulfate ratio is wuied, these effects are more pronounced in the mixed chain length systems. These shifts probably are associated with solid solution phenomena. A partial phase diagram for the NQH-KaMS system has been coiistructed from the DTA results and cooling curve data. Points plotted from the latter data are, for each composition, the temperatures a t which a ehaiige in the cooling rate pattern was observed. Shortly after the observance of the first such change, crystals generally became visible in the cooliiig tubes. We tentatively interpret the phase diagram as iiidicating the existence of a compound with an incongruent melting point and the presence of a eutectic with composition and melting point very close to that of the alcohol. The compound thus "melts" with decomposition a t a relatively lorn temperature (see Fig. 5.) (2) Infrared.-The MOH-NaMS system was chosen for this study and the region around 3 p, which is the hydroxyl band stretching region, turned out to be of interest. TJ'hereas the RlOH alone yielded a broad absorption band around 3 p, the effect of including in-
Oct., 1963
MOLECULaR ASSOCIATION IN PAIRS
creasing amounts of NaMS was to cause the development of a sharp band a t 2.86 p . The latter appears as a shoulder on the broad 3 - p band at the lower NaMS levels (20 and 40%0), and as an auxiliary peak a t the 60% NaMS level; a t the 75% level, Le., corresponding to the 1 MOW :2 NalLlS composition, the sharp 2.86-p band completely replaces the broad band; for pure KaMS (heated) no band is present in this region. The broad absorption band a t 3 p probably is a composite of a number of sharper bands: this suggests that the solid alcohol associates into various polymeric forms. The sharp band of the 1:2 mixture is quite different from that of the alcohol and is characteristic of OH stretching in “single-bridge” hydrogen bonded compound^.'^ Like the DTA, therefore, the infrared spectra suggest the formation of a 1 nlIOH:2 NaMS association. (3) X-Ray.-The report of a more complete X-ray investigation of these systems will be published elsewhere. For present purposes these results are outlined. Single Components.-Comparison of patterns with Lingafelter’s datal6 showed the NaMS to be in the a form HzO) and the NaLS to be composed of both a and o-(anhydrous) phases. After a heat treatment, similar to that given in preparing specimens for DTA, the NaLS was completely in the o-phase and the NaiClS was composed of a- and o-phases. The LOH was of course liquid a t room temperature. The MOH showed a pattern intermediate between that of the a and sub-a forms of Lutton (which forms have a similar long spacingle). It did not seem to be a simple mixture of the two. After heat treatment, the pattern was a better match for the a-phase but with certain lines of the sub-a phase still present. It is possible that the small low-temperature peak observed in the DTA curve a t 26’ of the heated MOH specimen may correspond to a ,8 to a-transition. Mixed Systems.--The pattern of the 1 alcohol: 2 sulfate mixtures was a good match for Lingafelter’s sodium alkyl sulfate monohydrate iota phase1&which is normally unstable. Evidently the long chain alcohol is able to stabilize this structure. I n going through the MOH-XaMS series from 100 to 0% MOH there was a continual change in diffraction pattern, although similarity in the chain-packing structure throughout the series was evident from the primary side spacings pattern. The largest actual change in pattern between neighbors was noted in proceeding from the lillOH-2NaMS to the 100% XaMS composition. Here, too, the only marked change in long spacing value was observed. Although the X-ray data are consistent with the existence of a 1: 2 MOH-SaMS association complex, and superposition of the pattern of the latter upon that of the lOOyoMOH (heated) led to quite good matches for the patterns of intermediate compositions, these matches were not perfect. These intermediate patterns can be explained as being those of a mixture of the alcohol and of the complex slightly modified, possibly by solid solution in it of a small amount of alcohol. For the LOH-KaLS mixtures the data are again (14) L. J . Bellamy, “The Infrared Spectra of Complev Molecules,” 2nd Edition, John Wiley and Sons, Inc., New York, N. Y . , 1958. (15) F. F. Rawlings and E. C . Lingafelter, J . Am. Chem. Soc., 77, 870 (1955): F. F. Rawhngs, Jr., Ph.D. Thesis, University of WashinEton, Seattle, Wash., 1951. (16) D. G . Kolp and E. B. Lutton, J , Am. ChPm. Sac., 78, 6693 (1951).
OF
LOKC-CHAIK COMPOUKDS
1967
1.8
2.7
-
Yb- 3.6 Q
0.0
-
,u,,
2.7
20 40
b
L
, , 60 8020 40 60 80 20 Reference temp., ‘C.
40
60
80
Fig. 4.-DTA curves, myristyl alcohol-sodium lauryl sulfate: (a) MOH; (b) 80.0% MOH and 20.0% NaLS; (e) 60.0% MOH and 40.0% NaLS; ( d ) 42.6% MOH and 57.4% NaLS; (e) 27.1% MOH and 72.9% NaLS; ( f ) NaLS.
u’ O.
80 loo
I\‘ ‘
1 0
NaMS
20
40
60
% by weight of MOH.
80
0
100 MOH
Fig. 5.-Partial phase diagram of myristyl alcohol-sodium myristyl sulfate: X, from DTA; 0, from cooling curves.
consistent with the formation of a 1: 2 complex. For mixtures richer in LON, where the alcohol in excess of that required for formation of the complex is presumably in the liquid state, the patterns matched quite well that of the 1 : 2 mixture. There were again slight modifications, such as changes in line intensities and the appearance of a few additional weak side spacings in intermediate composition patterns. These are due presumably to above-mentioned solid solution phenomena. At the 80% LOH-20% NaLS ratio the 4.68 halo characteristic of liquid paraffinic material was present in the pattern. The long spacing behavior within tliis series was similar to that of the myristyl series. In both series the primary short spacings of the 1 : 2 composition were smaller than those of the 100% alkyl sulfate. This suggests more efficient chain packing in the mixed composition. Discussion The results presented above can be summed up as follows: the thermal investigation has provided evidence of the existence of 1 : 2 association complexes between long-chain alcohols and sulfates. Independent support for this has come from the infrared study. Although the X-ray investigation of the LOH-SaLS and MOH-NaMS system of itself does not constitute absolute evidence of complex formation, the results are consistent with this concept if a small amount of solid solution of alcohol in the complex is assumed. Some evidence of the latter is apparent from the DTA data.
H. C. KUNGAND E. D. GODDARD
1968
Our results are in good agreement with those of Epstein, et al., on alcohol-sulfate adducts isolated from aqueous solution. However, in addition to the three analogs of 1:2 adducts isolated by them we were able to obtain evidence of 1:2 association in the MOW-NaLS system as well. It is quite understaiidable that molecular association of compounds with different chain lengths is more diffirult and likely to take place under more restricted conditions, as we have shown. Although Epstein, et al., state that the X-ray pattern of their ROH-RSO&a adducts differs from that of the starting RS04Na, they did not give any details of this pattern. However, further confirmation of the similarity between the adducts isolated by them and our 1: 2 complex comes from results obtained by X r . Ryerl' of this Laboratory. Working with mixtures of MOH and NahIS in mater or 10% ethanol-9Oy0 water niixtures, he consistently isolated a mixed species which contained approximately 27% of NOH, so confirming the results of Epstein, et al. It is of considerable interest that this species showed the diffraction pattern of Lingafelter's iota phase, exactly as did our 1: 2 specimens prepared from the melt. That the same species can be prepared under such varying conditioiis constitutes strong evidence for the existence of the postulated complex. The binding forces of the complex are evidently van der Waals forces between the hydrocarboii chains and hydrogen bonding between the hydroxyl and sulfate groups. The hydrogen bonding, as discussed above, differs from that in solid alcohols and probably is the chief driving force for the formation of the complex. It is, therefme, desirable to have a knowledge of the energetics of the interaction. Heat data for this purpose are available from the DTA measurements. However, estimates based on the latter information will be a t best approximate: although the area of the DTA4 peaks is primarily controlled by the enthalpy change involved, it is, at constant heating rate and specimen sample size, also a function of the heat capacity and thermal conductivity of the sample. The latter property for solid specimens is affected by the state of packing of the sample and clearly this factor is difficult to control. Mindful of these reservations, me will now estimate the heat effects involved in formation of the complex. As data for heats of fusion ( L )of long-chain alcohols are scanty, long-chain acids were used to calibrate the apparatus. Using stearic acid, L = 47.6 cal./g.,18 the calibration factor for the apparatus 'was calculated to be 1.14 cm.2/cal.;with lauric acid, L = 43.7 cal./g.,'* the ralue 7-'as 0.86 cm.2/cal. For subsequent calculations a mean value of 1.00 cm.2/cal. was taken; however, this discrepancy in calibration values immediately emphasizes the crudeness of the method. Let us consider first the differential thermograms of the MOH-XaMS system. From our earlier analysis, the second peak in the thermogram corresponds to the reaction 65O
RIOH.2VaR!IS(s) +RIOH(1)
+ 2NaMS(s); = 23 kcal./mole
(17) Unpublished work. (18) "International Critioal Tables," Vol. V, New York, K. Y.. p. 134.
Vol. 67
This, of course, neglects heat effects due t o solution of NaAIS in NOH (the solubility of NalCIS in MOH a t this temperature is small, see Fig. 5 ) and also neglects solid solution effects. From the peak area for melting of MOH alone, AHs, the heat of melting can be c+alculated 38'
MOH(s) +MOH(1); AH?8o
=
10 kcal./mole
If we neglect heat, capacity effects, we may put AHi650 = AH1"' and me then have for the reaction 38j
AIOH.2Sal\lS(s) +hIOM(s) A H 3 = AN1
+ 2SaMS(s)
-AH2
=
13 kcal./niole
I n like fashion we have for the reaction 28"
LOH.2NaLS(s) --+
LOH(s)
+ 2NaLS(s) AH3
=
13 kcal./mole
I n the above treatment various lieat effects have been neglected. There is an additional effect. In calculating heat values for the reactions the solid phase assumed is, for the alcohol, that present just prior to melting of the pure species and, for the sulfate, that present just after decomposition of the complex. While the precise phases present are unknown they will clearly affect directly the values of AHa calculated. h t is therefore our intention to obtain diffraction results on these systems a t temperatures equal to those a t which the therinal changes occur. The values of AH3 obtained above seem unreasonably high. This is undoubtedly due in part to the neglect of several heat factors in the calculations. Taken together with the uncertainty of the DTA method for measuring heats, this means that the values of AHo can only be regarded as rough estimates. In spite of the crudeness of the over-all method, it is nonetheless clear that the bonding of the hydroxyl to the sulfate group in the 1: 2 association involves an appreciabk energy change. Support for the correctness of this concept was obtained in the following way. After heating a 1 MOH-2 KaMS mixture in the DTA apparatus beyond the melt-decomposition temperature, it was cooled suddenly to room temperature with cold dry air. On reheating in the apparatus a large exolizeriizic peak was obtained a t a temperature near the melting point of the alcohol. The heat effect in excess of that required for melting the alcohol evidently corresponds to the heat of formation of the complex. On reaching the melt-decomposition temperature a large endothermic heat effect was observed as before. i n conclusion me believe that cogent evidence has been brought forward in support of the existence of a 1: 2 association coniplex between long-chain alcohols and long-chain sulfates. This evidence has come from three different techniques and an estimate of the energy of bonding has shown its magnitude to be appreciable. It is, of course, hazardous to attempt to extrapolate results from bulk phase experiments to surface systems. However, the abox-e results in conjunction xvith evidence which has come from film penetration and film drainage studies indicate that, when considering the properties of mixed films, the existence of interaction between longchain alcohols and sulfates should not be ignored.
CRITICAL OPALESCENCEOF METHANOL-CYCLOHEXAKE
Oct., 1963
cerning the illterpretation of X-ray data and to the c~~~~~~~~ for permissioll to publish this paper.
L~~~~Brothers
~IsCussIox A. W. Ao,4wsos (University of Southern California) -The peak you attribute to decomposition of the association complex appears to go through a maximum with composition in the case of the MOH-SaLS system (Fig. 4). Do you attribute any sig-
1969
E. D. GoDDaRD.-~~e suspect solid solution phenomena are associated with the temperature shifts in the melt-decomposition peaks; these seem to be more pronounced in the mixed chain length systems. F. M. FOWKES (Sprague Electric Company ).-Is the interaction measured in these nonaqueous mixtures attributable to solvation of the fiodiuni ions by the alcohol groups? E. D. G0DDARD.-This is possible, but how would one establish it?
CRITICAL OPALESCENCE OF METHAKOL-CYCLOHEXANE, TRANSIUISSIOK MEASUREMEYTS BY B. CHU Chenaistry Department, University of Kansas, Lawrence, Kansas Received March 16, 1965 For some binary liquid mixtures in the vicinity of their critical solution temperature, the reciprocal of scattered intensity is a linear function of s2 (s = 2 sin (6/2)) and its slope is connected with the range of molecular forceai. The interaction range ( I ) and the critical solution temperature ( T o ) for the system methanol-cyclohexane have been determined by measurements of the wave length dependence of the total turbidity of t h e solution a t its critical solution concentration as a function of the temperature. Results are in reasonable agreement with values calculated from dissymmetry measurements.
The calculation of intermolecular potential energy functions of one component systems in terms of virial coefficients from P--V-T relations lias been a great tradition. Recently, experimental fourth virial coefficients of 1,etrafluoromethane has been compared with a calculation of Boys and Shavitt‘ of the fourth virial coefficient based on the Lennard-Jones potential. Intermolecular forces also determine most of the properties of liquids, such as solubility in other liquids. The mutual solubility curves for binary liquid mixtures reveal intermolecular interactions peculiar to the individual systems. If optical measurements are carried out on binary liquid mixtures a t small temperature distances above the phase separation temperature, the behavior of concentration fluctuations may be observed from either the angular dependence of scattered intensity or tlie Tmve length dependence of total turbidity. In the vicinity of the critical point, the angular dissymmetry of scattering lias been related to the range of molecular forces ( I ) characteristic for the components of the ~ y s t e m . ~The correlation between concentration fluctuations in neighboring points of binary critical mixtures is characterized by a persistence length ( L or the Debye length), defined as the second moment of a correlation function. It also follows that the square of the Debye length is proportional to the rcciprocal of tlie temperature distance from the critical solution temperature.
turbidity of the system polystyrene-cyclohexane a t its critical solution concentration as a function of the temperature has been investigated.8 We must, however, remember that the approximate theory takes into account only the additional average square of the gradient of the concentration fluctuation. Anomalies have been observed6 and attempts have been made to explain the anomalies, especially on the small angle critical scattering. lo On the other hand, several disagreements arise from experimental difficulties and pitfalls, such as trace impurities and multiple scattering. Therefore, it is desirable to perform our experiments from different approaches. The purpose of this paper is to explore the possibility of estimating the range of molecular forces from the ware length dependence of the total turbidity for biliary critical inixturgs where the interaction range is small (say, I = 5-15 A). The turbidity CY of a biliary mixture a t its critical solution concentration can be calculated by integrating the “critical” scattered intensity over all angles.8 For unpolarized light, we get CY CY
= =
K*3TT K * ~ TJOT r
-
T T // To To 8r2I3 1 +-;sin2+-;sin23 x 3 x
1
e
V
X
2
+ cos2 0 X sin B de 2
1 2
=
12
T/T, - 1
in which l 2 is the second moment of tlie interaction energy. Yarious tyxperiments have verified the theory.*--’ The wave length dependence of the total (1) S. F. Boys and I. Shavitt, Proc. Roy. SOC. (London). A254, 487 (1960). (2) D. R. Douslin, R. H. Harrison, R. T. Moore, and J. P. BlcCullough, J . Chem. Phys., 66, 1357 (1961). (3) I?. Debye, ibid., 31, 680 (1959).
(1)
(4) P. Debye, H. COILand D. Woermann, ibid., 33, 1746 (1960). ( 5 ) P. Debye. B. Chu. and D. Woermann, ibid., 36, 1803 (1962).
(6) P. Debye, B. Chu, and H. Kaufmann, ibid., 36, 3373 (1962). (7) P. W. Schmidt and J. Thomas, Physics Department, University of hllssouri, unpublished results on small angle X-ray scattering of argon near the critical point. ( 8 ) P. Debye, D. Woermann, and B. Chu. J . Chem. P h y ~ . ,36, 851 (1962). 19) G. W. Brrsdy and H. L. Frisch. ibid., 35, 2234 (1961). (10) H. L. Frisch and G. W. Brady. ibid., 37, 1514 (1962). (11) W. C. Farrar and H. Brumberger, unpublished results on small angle X-ray scattering of nitrobenzene-n-heptane. (12) D. WcIntyre, A. Wims, and h?. S. Green, J . Chem. Phys., 37,3019 (1962).
