4312
H. BRUMRERGER AND R. PANCIROV
Further Critical Opalescence Measurements on the Nitrobenzene-n-Heptane System’
by H. Brumberger and R. Pancirov Department of Chemistry, Syracuse University, Syracuse, New York
13810
(Received July 19, 1965)
Light scattering measurements on the nitrobenzene+-heptane system near the critical demixing temperature can be represented to a good approximation by the OrnsteinZernike-Debye formalism and yield a Debye 1 value of -9 Small-angle X-ray results yield parameters inconsistent with light scattering; there is a strong suggestion that plots of 1-l vs. sin2 (0/2)/Az are curved over a sufficiently large range of the latter variable, and that an extension of the present theories is required to account for these observations.
Introduction1 The theory of critical phenomena has received considerable attention in recent year^.^^^ I n order to test some of the predictions and to furnish an increasingly reliable body of experimental data, we have undertaken a series of experiments measuring the scattering of electromagnetic radiation from critically opalescent ~ystems.~JThis paper reports light scattering measurements on the nitrobenzene-n-heptane system, and compares them to small-angle X-ray measurement~.~
Experimental Techniques Purification of Materials. Xitrobenzene was purified by triple vacuum fractionation and checked by v.p.c. Only one peak was observed. n-Heptane, used without further purification, was obtained a t a purity of 99.96 mole % from Phillips Petroleum Co. Sample Preparation. All samples were prepared by direct weighing into the light scattering cells inside a drybox under an inert atmosphere. Compositions were known to f0.03 wt. %. No observable difference in the scattering was noticed for filtered and unfiltered samples. Phase Diagram. The phase diagram of the system in the critical region was determined by the method of Rice and Atack.6 The separation temperature a t the critical composition, 49.60 f 0.03 wt. % n-heptane, was found to be 19.03 k 0.005’ for the samples used in this investigation. The Journal of Physical Chemistry
Temperature Measurements. All temperature differences were measured with a Beckmann thermometer which had been calibrated and checked for linearity in the appropriate range against a certified platinum resistance thermometer, using a (3-2 Leeds and Northrup Muller bridge.7 The same thermometer was used to determine the critical temperatures at various compositions and the temperature of the samples in the light scattering cell. Temperature Control. Figure 1 shows the temperature-controlled light scattering cell. Water from a constant-temperature bath was circulated rapidly to the heat exchanger coil, F, through heavily insulated copper tubing; intake and outflow pipes in the bath were located to encourage maximum mixing. The cylindrical cell jacket was constructed of brass, with a (1) This paper represents part of a Ph.D. dissertation submitted to the Department of Chemistry, Syracuse University, by R. Pancirov. Portions of this work were reported a t the IUPAP Conference on Thermodynamics and Statistical Mechanics, Aachen, June 1964. (2) (a) M. Fixman, Advan. Chem. Phys., 6 , 175 (1964); (b) M. E. Fisher, J . Math. Phys., 5 , 944 (1964). ( 3 ) A. MUnster in “Fluctuation Phenomena in Solids,” R. E. Burgess, Ed., Academic Press, New Yorlr, N. y., 1965, p. 180. (4) H. Brumberger and W. C. Farrar, “Proceedings of the Interdisciplinary Conference on Electromagnetic Scattering,” Pergamon Press, London, 1963, p. 403. (5) R. Pancirov and H. Brumberger, J . A m . Chem. Sac., 86, 3562 (1964). (6) 0 . K. Rice and D. Atack, J . Chem. Phys., 22, 382 (1954). (7) The authors are grateful t o the Carrier Corporation Laboratory, Syracuse, N. Y., for its assistance.
4313
LIGHTSCATTERING IN THE NITROBENZENE'~-HEPTANE SYSTEM
rlA
D
were made with vertically polarized incident radiation. Two wave lengths, 4360 and 5460 8. (in vacuo), were used and observations were made at six to eight temperatures near the critical temperature T,, for each of three compositions--42.97, 49.60, and 50.99 wt. % n-heptane. Several cell diameters were used, of which 8 and 6 mm. were found to give the most reproducible data. No qualitative differences in scattering behavior were observed for the 6- and 8-mm. cells. All of the data reported here were obtained with the and have been corrected latter cell diameter at 5460 for changes in scattering volume by multiplication with sin 0. The measurements made at the shorter wave length displayed definite intensity maxima between 60 and 70" 0, probably due to multiple scattering. All cells were tested for symmetry with fluorescein solution. Corrections for internal reflections were found negligible. It was assumed that attenuation corrections are temperature dependent only18and would thus have no effect on the slope-intercept ratios of the Ornstein-Zernike (OZ) plots, which are used to calculate the Debye parameters. No effect of continued irradiation on the light scatteripg behavior of the nitrobenzene-heptane samples was noted; changes in composition due to evaporation in the course of a run were found to be negligible. Runs made at widely different times were reproducible within the experimental error.
w.,
i Figure 1. Temperature-controlled light scattering cell: A, stirrers; B, stirrer bearings; C, centering collar for E; D, cap for E; E, light mattering sample cell; F, heat exchanger coil of copper tubing, soldered to brass wall; G, insulation; H, glass portion of constant-temperature bath; I, centering sleeve for insertion of cell into photometer; J, brass base plate; K, direction of primary light beam; L, well for Beckmann thermometer; M, set screw.
transparent portion, H, cemented to it and to a brass base plate, J. H was a length of precision-bore 5-cm. Pyrex tubing; J and I permitted centering the entire apparatus relative t,o the optical system of the light scattering photometer by means of a sleeve and set screw. The jacket was filled with stirred carbon tetrachloride to minimize interfacial reflections. Turbidity due to the stirring action was found to be negligible. Measured cell temperatures were constant to rt0.005" for several hours, and to j=0.002"during a single run. Temperature gradients were found to be unimportant in determining 4 T values, within these limits. Light Scattering Photometer. A Brice-Phoenix photometer, modified substantially by introducing two 1 X 10-mm. two-slit colliinators (between source and sample, and between sample and photomultiplier) , was used. The light source was monitored and adjusted to maintain constant intensity for all experiments. Light Scattering Measurements. All of the measurements of angular distribution of scattered intensity
Experimental Results Figure 2 shows typical curves of intensity os. scattering angle at various temperature distances 4 T from the critical temperature To,a t three compositions. Table I indicates the compositions and critical temperatures of these mixtures. The maximum observed intensity drops substantially even 1 wt. % away from the critical composition, and the dissymmetry noticeably decreases as well. According to the Debye theorys19in the approximation including the effect of the average square of the Table I Composition, wt. % ' n-heptane 42.97 rt 0.03 49.60 (critical comp. ) 50.99
Demixing temp., OC.
&el at AT = O.O2O, e = 300
18.92 rt 0.005 19.03 18.99
69 179 123
(8) P. Debye, B. Chu, and H. Kaufmann, J. Chem. Phys., 36, 3378 (1962). (9) P. Debye, ibid., 31, 680 (1959).
Volume 69,Number 12' December 1966
H. BRUMBERGER AND R. PANCIROV
4314
where C is a proportionality constant, F(T) is a temperature-dependent attenuation factor, 1 is the Debye “range of intermolecular forces,” and X is the wave length in the medium. For a given composition and wave length
1-l = A(!!’)
+ B ( T ) sin2 (0/2)
(2)
A plot of inverse intensity vs. sin2 (8/2) should therefore be linear at each temperature. A similar result is obtained if the Ornstein-Zernike pair correlation function G(r), where
G(r) = Ar-l exp(-Kr)
(3) in the asymptotic approximation for r -+ m , l o is inserted into the general scattering equation for a fluid medium
sin sr I ( s ) = c 4 n r 2 G ( r ) - sr dr I
I
30
I
I
60
90
8Cdeg )
(4)
where s = 4nX-1 sin (8/2). An OZ plot of the data obtained at the critical composition is shown in Figure 3; one does indeed find
I
/20
Figure 2. Angular distribution of relative intensities as a function of AT = T - T , for three compositions: 0, 50.99 wt. 70 heptane; Ot 49.60 wt. % heptane; (3, 42.97 wt. yoheptane.
1
0
0.5
AT
/O
.sinW/Z)
Figure 3. Typical Omstein-Zernike plot at the critical composition.
concentration fluctuation amplitude and the average square of the fluctuation gradient, the intensity of light scattered a4 an angle 0 from a system near Tc can be represented by The Journal of Physical Chemistry
Figure 4. Plot of extrapolated zero-angle intercepts from Figure 3 vs. AT.
L.S. Ornstein and F. Zernike, Proc. Roy. Acad. Sci. Amsterdam, 17, 793 (1914). (10)
4315
LIGHTSCATTERING IN THE NITROBENZENE+L-HEPTAXE SYSTEM
Figure 6.
*d
O.#
0.20
030
0.40
Plot of
K~
us. AT.
expected, the correlation range increases very rapidly as the critical temperature is approached. From the definition of L
ATPK)
Figure 5. Plot of Debye L parameter us. A T at the critical composition.
reasonably linear behavior except at the smallest and largest scattering angles. A systematic upward deviation at high angles and an upward deviationat small angles which decreases with AT are obtained; such observations seem fairly general, and have also been found for the 2,6-dimethylpyridine-water system5 and for the polystyrene-cyclohexane system.l' Possibly multiple scattering effects are responsible, but this hypothesis has not so far been tested in a clearcut fashion. The temperature dependence of the extrapolated zero-angle intercepts of the OZ plot is predicted to be linear for a model such as Debye's. Figure 4 indicates that an upward deviation from linearity is found, again in agreement with other such observations. There is, of course, a measure of doubt concerning the reliability of the extrapolation, particularly in view of the results of McIntyre, et al.," and of our own lowangle X-ray data for the nitrobenzene-n-heptane system, discussed below. From the QZ plots, the Debye 1 parameter can be calculated using eq. 1 ; a value of 9.3 f 0.94 A. is found and the correlation range, L, determined with this I value from
(where r = T/T,), is plotted us. AT in Figure 5. As is
values for the 02 constant stitution of (3) yielding K
=
K
may be obtained by sub-
(4-w
(7)
values vs. AT are shown in Table 11. Figure 6 shows a plot of K~ us. AT, and indicates a smooth extrapolation through the origin. K
Table I1 AT, OK.
K,
A-1
0.39 0.30 0.19 0.11 0.06 0.04 0.02
x 10'
9.62 8.45 6.72 5.13 3.77 3.07 2.18
Comparison to X-Ray Observations The X-ray data so far available for this system have not as yet been extended to small enough angles to overlap the light scattering curves, and to this extent are still unsatisfactory. There is, however, sufficient evidence to indicate that the OZ plot is inadequate (11) D. McIntyre, A. Wims, and M. S. Green, 3019 (1982).
J. Chem. Phys., 37,
Volume 69, Number id
December 1966
4316
over a large range of sin (t?/2)/X. The most striking facts are these: the OZ plot for the light scattering data shows a series of curves for the dserent temperatures which are nearIy paralIeI over the temperature interval of about 0.4" from T,, which we examined. The corresponding X-ray curves (in the same tempem ture interval from T, for the original X-ray sample) show a change in slope by a factor of nearly five. Further, the Z value calculated from the X-ray data is 3.5 =t0.4 A., about one-third of the light scattering value. The aero-angle extrapolation from the X-ray data is thus almost certainly unreliable. There is, in fact, no assurance that the same may not be true of the light scattering extrapolation; there is some experiment,al evidence that OZ curves may show a downward trend at smallest angles.5~~~ The most reasonable conclusion one may draw from these facts is that the OZ plot is likely to be curved over a sufficiently large range of [sin (t?/2)/XI2. Such observations were also made by Chu12and Debye.13*14 Debye13114has suggested that curvature may be introduced by including higher-order terms in the series expansion for the inverse scattered intensity. I n a recent publication,14 the system perfluorotributylamine-isopentane is indicated to show a curved OZ plot over a large range of s. While the inversion of the intensity curve to obtain information about the interaction potentials remains an unsolved problem for the two-component system, Debye argues by analogy to
The Journal of Physical Chemistrg
H. BRUMBERCER AND R. PANCIROV
the one-component system, for which relatively simple models are available, that only the initial slopes of the OZ curves yield a measure of the range of intermolecular interaction 1, and that the slopes at large values of s have a different (though unknown) physical interpretation. Presumably deviations from linearity will be more easily observed in two-component systems. It appears, from our measurements and those of others, that deviations from the OZD theory are in fact real and not experimental artifacts. The exact nature of these deviations is by no means well known, however, and much more precise experiments very close to T , and over a large range of s will need to be done to ascertain it. Such measurements will require a closer look at the problem of multiple scattering, and are likely to be complicated by new phenomena which will become increasingly important near T,,.l5
Acknowledgment. The authors are grateful to the National Science Foundation for supporting this research under K.S.F. Grant G-19282. (12) (a) B. Chu, J. Chem. Phys., 42, 2293 (1965); (b) B. Chu and W. P. Kao, ibid., 42, 2608 (1965). (13) P.Debye, ref, 4,p. 393. (14) P. Debye, D. Caulfield, and J. Bashaw, J. Chem. Phys., 41, 3051 (1964). (15) D. McIntyre, private communication. Dr. McIntyre observes a change in To when cell thicknesses are made very small (-0.1 mm.).
