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 a 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 a a = =
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, a n d 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).
