VISCOSITY OF THE CYCLOHEXANE-ANILINE BINARY LIQUID SYSTEM
2619
Viscosity of the Cyclohexane-Aniline Binary Liquid System near the Critical Temperature1
by Charles C. Yang and F. R. Meeks* Department of Chemistry, University of Cincinnati, Cincinnati, Ohio 46281
(Received M a y 26, 1970)
Publication costs assisted by the Petroleum Research Fund
The viscosity of the binary liquid system cyclohexane-aniline has been measured in the region just above the coexistence curve for three compositions: 0.430,0.445,and 0.460 mole fraction aniline. The temperature control was better than =kO.OOl"; the data produced a typical branch of a A-shaped curve, and typically, the viscosity is anomalously high as the phase separation temperature is approached. Neither logarithmic nor exponential behavior of the viscosity is followed for the full range of temperatures investigated (0.001-0.3" above phase separations).
I. Introduction Anomalous increase of the viscosity of binary liquid systems near the critical mixing point has long been a matter of record.'t2 For binary liquid mixtures the anomalous increase of the viscosity is of the order of 15-20% at the critical mixing point. I n 1945 Rlondain-Monval and Quiquerez3* investigated the viscosity and opalescence of binary and ternary systems in the critical region. Systems found to possess abnormally high viscosity while still in the "homogeneous" region but near the critical point included water-aniline-ethanol, water-benzene-ethanol, water-toluene-ethanol, aniline-cyclohexane, nitrobenzene-hexane, water-acetone-cyclohexane, and ether-acetone-petroleum ether. The first five systems showed marked opalescence correlated with the viscosity increase, but the last two showed no critical opalescence. The systems showing abnormal viscosity are believed to possess a colloidal structure in the critical region, which becomes visible as opalescence only when the refractive indices of the constituents differ by more than 0.04.3b Reed and Taylor4 have observed an anomalous increase in the viscosity of isooctane-perfluoroheptane mixtures. The viscosity exhibits an anomalous increase up to 25%. The anomalous behavior can be detected as far away as 10" from the critical temperature. However, other investigators found that for some systems the anomaly occurs only a t temperatures much closer to the critical point. Semenchenko and Zorinas investigated the viscosity of nitrobenzene-hexane mixtures. The results showed that the range of temperature and concentration in which the critical phenomena were observed was 1.0 to 1.5" and 10 mol %. The peak of viscosity in that critical region was a t least 20% in excess of the value
that would correspond to a linear increase (from much higher temperatures). Campbell, et ~ l . have , ~ studied the aniline-hexane system. They report that the phenomenon of anomalously high viscosity is observed over a temperature range of 2.4" above the critical solution temperature and over the concentration range of 37-58.5 mol yo hexane. The object of the present work is to establish a precise viscosity curve near the critical temperature. As the temperature approaches the critical point, viscosity readings were made at temperature intervals of the order of 0.001" as compared to 0.01" reported earlier for other system^.^^'*^ It is hoped that these more precise data may be helpful in testing theories of the critical state and, incidentally, in determinihg whether the viscosity is a useful criterion for establishing the correct phase separation temperature (and ultimately, the critical solution temperature) for binary mixtures.
11. Experimental Section A . Reagents. Both the aniline and the cyclohexane (1) Taken in part from the doctoral dissertation of C. Yang, University of Cincinnati, 1970. (2)# (a) M . S. Green and J. V. Sengers, Nat. BUT. Stand. (U.S.) Mzsc. Pub., 273 (1966), see especially, in connection with the present work, pp 9, 21, and 165; (b) D. E. Tsalakatos, BUZZ.Soc. Chim. Fr., 5, 397 (1909). (3) (a) P. Mondain-Monval and J . Quiqueres, BUZZ. SOC.Chim., 12, 380 (1945); (b) ibid., 11, 26 (1944). (4) T . M. Reed and T . E. Taylor, J . Phys. Chem., 63,58 (1959). (5) V. K. Semenohenko and E. L. Zorina, Dokl. Akad. Nauk S S S R , 73,331 (1950); EO, 903 (1951). (6) A. N. Campbell, et al., Can. J. Chem., 46, 2399 (1968). (7) J. Brunet and K. E. Gubbins, Trans. Faraday Sac., 65, 1255 (1969). (8) G. Arcovito, C. Faloci, M . Roberti, and L. Mistura, Phys. Rev. Lett., 22, 1040 (1969).
The JOUTnal of Physical Chemistry, VoZ. 76, N o . 17,1971
2620
were Chromato quality reagents with 99.9 and 99.8% purity, respectively. They were obtained from Matheson Coleman and Bell Go., Norwood, Ohio. Calcium oxide powder was Baker Analyzed reagent obtained from J. T. Baker Chemical Co., Phillipsburg, N. J. A single bottle of each of the above three reagents was used for the preparation of all the samples in this experimentation. Extensive purification and drying of the cyclohexaneaniline mixtures were carried out in an elaborate vacuum system described el~ewhere.~Although high purity is an extremely desirable attribute for reagents used in critical phenomena work, it is well known that reproducibility of the temperature of coalescence, as observed visually, is a suficient guarantee for the cyclohexane-aniline system. (Variations in the absolute value of the temperature of phase separation from laboratory to laboratory are not unknown; indeed the response characteristics of the same apparatus can vary from year to year. It is felt that differences between physical properties of samples from the same bottles, further purified and dried in the same way and measured within a relatively short period of time in the same thermostat, give information relative to one another as valuable as would be that from mixtures of absolutely pure components.) B. The Constant Temperature Bath. The constant temperature bath consisted of a large “fish tank’’ which contained approximately 90 1. of distilled water. It is described elsewhere. C. Temperature Measurements. The temperatures of the water bath were measured by two different, supplementary methods using (1) a Beckmann thermometer and (2) a Wheatstone bridge with a thermistor. The Beckmann thermometer was standardized by using sodium sulfate (Na2S04-10HzO) which has a decomposition temperature of 32.384”. The use of a ‘Gaertner microscope equipped with a movable vernier permitted observation of temperature of the water bath to 0.001”, but the Beckmann thermometer responded to temperature change rather slowly. It was believed that the Beckmann thermometer gave only a “mean” temperature over a small time period, instead of an < linstant” * temperature a t a specific moment. Besides, the readings of the Beckmann thermometer could vary from one observer to the other. Therefore, a thermistor was used to supplement the Beckmann. The Wheatstone bridge consisted of one galvanometer, one thermistor, one carbon-film resistor, two resistance boxes, one switch and two 1.35-V mercury batteries in series. The highly sensitive galvanometer was obtained from the Rubicon Division of Minneapolis, Honeywell Co. Inc. The thermistor was Type GA51P8 obtained from Fenwal Electronics Inc., Framingham, Mass. The resistance of the thermistor was approximately 76,000 The Journal of Physical Chemistry, Vol. 76,No. 17, 1971
CHARLES C. YANG AND F. R.MEEKS
w Figure 1. The modified Cannon-Fenske viscometer.
ohms at 30”. As the temperature of the bath increased, the resistance of the thermistor decreased. The standardized Beckmann thermometer was used to establish the relationship between the temperature of the water bath and the resistance of the thermistor. The plot of temperature vs. resistances showed a straight line in the temperature range of our interest. This standard straight line was then used t o convert the resistance readings of the thermistor back to the actual temperatures. Due to the extremely high sensitivity of the galvonometer and the high resistance of the thermistor, the precision of the temperature measurements was estimated to be approximately i0.0003”. D. The Viscometer. A Cannon-Fensko viscometer, size 100, was obtained from the Cannon Instrument Co., State College, Pa. The viscometer was further modified for measurements of viscosity under vacuum (Figure 1). According to the manufacturer, the radius of the capillary of the viscometer is 0.0315 cm and the volume of the efflux bulb is 3.16 =k 0.15 cm3. The viscometer was attached to a submersible support with a chain which allowed it to rotate 360”. By rotating the viscometer into a downward position, the bulb above “a” in Figure 1 was filled with the sample. The viscometer was allowed to remain in the constant temperature bath for 1 hr. It was then returned to a vertical position by means of a chain control. The sample was allowed to flow freely down past etch mark (9) D. N. Stoneback and F. R. Meeks, J . Phys. Chem., in press.
VISCOSITYOF
THE
CYCLOHEXANE-ANILINE BINARYLIQUIDSYSTEM
“a” and a stopwatch was used to measure the time for the meniscus to pass from mark “a” to mark “b.” I n the design of the viscometer, attention was paid to the capillary diameter in order to avoid shear affects and separation or beating of the sample during the flow time from mark to mark. Radii less than that chosen (0.0315 cm) would of course increase flow times and therefore minimize the percentage of error in them. However, uniformity of bore becomes a problem, as well as uncertainty about the presence of Newtonian flow. Larger capillaries, it was felt, would simply reduce flow time unnecessarily. Repetitive measurements on the three samples gave high reproducibility, so that the limiting factor in error seems to be thermostatic control of the bath. A Swiss-made “Breno” stopwatch was used. It could be read to 0.1 sec and easily estimated to 0.05 sec. A stopwatch holder obtained from the Precision Scientific Co., Chicago, added convenience t o the use of the stopwatch. The viscometer was calibrated with deionized water under vacuum at a constant temperature of 30.0’; the viscometer constant was calculated to be 0.012052 cSt/sec. A legitimate question can be raised as to whether the temperature of the thermostat and that within the sample were the same, to within less than 0.001’. I n the heat capacity work reported in ref 9, the sample was considerably larger, and there was always at least one thermistor inside the sample itself at all times. No discrepancy between bath and sample temperature wa5 observed in that research. E. The Vacuum System. The vacuum system and purification procedure are described elsewhere.
111. Results and Conclusions
2621
-
1.00
0.97-
~
8
z s i!
0.94
-
0.91
-
0.88
T-Tc, “C
Figure 2. Relative viscosity of sample A. I
-
1.00
-
>. 0.97 v) c
0
0
0.94
-
0.91
-
0.88
-
5
r 5
0.85’ I I -0.02 0
1
0.04
I
0.08
I
I
0.12
0.16
T-T,,
I
I
I
1
0.20 0.24 0.28 0
OC
Figure 3. Relative viscosity of sample B. I 1.00
-
>. 0.97-
c
m 0.94
>
-
9 0.91 -
5
W
The viscosities of three samples, A, B, and C, with aniline mole fractions of 0.430, 0.445, and 0.460, respectively, were measured. The results are given in Figures 2-4. A relative viscosity was defined as the ratio of the kinematic viscosity at a temperature T to the maximum kinematic viscosity which occurred a t the phase separation temperature, T,. Therefore, all three samples would have a relative viscosity of 1.000 at To. Thus T , is to be distinguished in this work from the critical consolute temperature, presumed (as seen below) to occur a t a mole fraction of aniline very nearly 0.445. The temperature difference between T and T , is called AT. When T is higher than T,, AT has a positive sign. When AT was 0.3”, all three samples were clear. As AT decreased, the samples became cloudier and the kinematic viscosity increased. At the phase separation temperature, where AT became zero, the samples were opaque and the kinematic viscosity was the highest. When AT became negative, the kinematic viscosity started to decrease. A visible meniscus did not always appear at the same temperature
E
0.88-
0.85’ -0.02
’
o
I 0.04
I
no8
I
I
0.12 0.16
T-T,,
I
0.20
I
I
L
424 0.28 0.:
OC
Figure 4. Relative viscosity of sample C.
as the drop of the kinematic viscosity. Sometimes it appeared at a temperature one or two thousandths of a degree lower. This discrepancy is probably caused by the opalascence of the samples. Figures 2 to 4 show the relative viscosity os. AT curves for the three samples. The slope becomes increasingly negative as the temperature decreases. A distinct discontinuity occurs at the critical solution temperature. The viscosity data were curve-fitted for polynomial equations of degree six using an IBM 360 computer. The program used was R-02-2, University of Cincinnati, March 1969, which was revised form BMD05R, version of the Dec 1965 Health Science Computation Facility, UCLA. The Journal of Physical Chemistry, Vol. 76,No. 17, 1971
2622
CHARLES C. YANGAND F. R. MEEKS
Table I summarizes the experimental data in the form of a sixth-order computer-fitted polynomial in T - T,. From the coefficients given in Table I, the original data can be regenerated to within an error of less than about 1% a t the lower value of T - To (-0.001") and an error of considerably less than 1% for values of T - T,of the order of 0.3".
Xrel
=
c KAT - To)"
Sample A
ko
0.99989
ki kz
-2.05785
ka k4
kg k6
27.5215
-247.730 1251.52 -3194.58 3197.93
Sample B
Sample C
0.99941
0.99992
-2.31437
-2.18194
29.1288
-241.313 1141.26
26.3122
- 207.754
=
- 2201.25
2723.68
2078.23
- A In [(T - T,)/T,I
-
A
3.00
-
2.50
-
C
2.001.50
-
1.00
-
0.50 I
1
I
I
I
2
3
937.610
-02789.58
The curve-fitted equations were used to calculate the slopes of the viscosity curves at any specific temperatures. At a temperature 0.1" above the critical temperature the slopes of all three curves are approximately equal. However, when AT is only 0.001", sample B, which has 0.445 mole fraction of aniline, has the largest slope (Figure 5). The slope of sample C, which has 0.460 mole fraction of aniline, is the second largest and sample C with 0.430 mole fraction of aniline the smallest. It is interesting to see that the maximum slope change occurs at a concentration which is in the middle of a critical concentration range, 0.430-0.465 mole fraction of aniline, as reported by Atack and Rice.loJ1 It can be concluded that if there is only one critical concentration instead of a range of critical concentrations, then this critical concentration is very near, if not at, 0.445 mole fraction of aniline. The results of this work have been compared with two recent publications in this field. Brunet and Gubbins,' in investigating the viscosity of four binary liquid systems near the critical mixing point, have measured the viscosity of a series of aniline-cyclohexane mixtures from 0.4 to 20" above the critical solution temperature. However, they emphasize the approximate location of the viscosity anomaly instead of the exact quantitative aspects of the anomaly. Arcovito, Faloci, Roberti, and Mistmas conclude that the viscosity above the critical solution temperature is quite well fitted over three decades by a logarithmic law A?
4.00
3.50-
I
n=O
B
Table I : Polynomial Coefficients for the Relative Viscosities 8
4.50
+B
where Aq is the excess shear viscosity, A = 0.16, and B = 0.30 cSt. This equation was tested using present The Journal of Physical Chemistry, Vol. 76, No. 17,1971
-log(AT) Figure 5. A comparison of the slopes.
viscosity data; unfortunately, the results were unsatisfactory. A possible discrepancy may be in the fact that the temperature bath which they used was controlled only to *0.01" while in the present work we measured the viscosity of the mixtures at a temperature as close as 0.001" above the critical solution temperature. This temperature range is probably beyond the "three decades of a logarithmic law" as claimed in ref 8. The kinematic viscosity of an aniline-cyclohexane mixture with a composition of 0.440 mole fraction aniline was estimated to be 1.48 cSt near the critical solution temperature, if there were no viscosity anomaly.' I n the present experimentation the kinematic viscosity of a similar mixture is 1.93 cSt at the critical solution temperature and 1.70 at AT = 0.2". These mean a viscosity anomaly of 30 and 15% at the respective temperatures. Fixman12 was the first to treat the viscosity of critical mixtures quantitatively on a theoretical basis. His method involves a calculation of the entropy production through diffusion which results when a mixture in a state of composition fluctuation is caused to have a velocity gradient. The long wavelength part of the spectrum of composition fluctuation is intense and very easily distorted by a velocity gradient in the critical region. The return to uniform composition through diffusion dissipates energy, and the loss is interpreted as an excess viscosity. Botch and Fixman13 investigated the dependence of viscosity on the velocity gradient based on the Fixman's theory. They estimated that (10) D. Atack and 0. K . Rice, Discuss.Faraday Soe., 15,210 (1953). (11) D.Atack and 0. K . Rice, J. Chem. Phys., 22,382 (1954). (12) M.Fixman, {bid., 36, 310 (1962).
(13) W.Botch and M.Fixman, ibid., 36,3100 (1962).
ANOMALOUS FREEXING BEHAVIOROF POLYMER GELSAND SOLUTIONS
T - T,must be 0.2"in order that a 15% decrement be found in the excess viscosity. A cdculation for the present system based On Fixman's theory is not yet feasible due to lack of sufficiently accurate data (partial molar V O ~ U ~ ~etc.) S , for the aniline-cyclohexane system. These should be regarded as necessary parameters to be obtained in order to test the applicability of Fixman's calculation for viscosity in the critical region. Efforts were made, using both the Wang electronic calculator and the IBM 360, to fit the data of the present work to an equation of the form
q =
2623
A ( y ) -
+B
( Y )
+c
with unsatisfactory results. This equation is incapable of giving sufficiently acute variation in ?I in the lower ranges of T - To. However,a plot of In ?I ~ s In . (T T,) gives a moderately good straight line such that
-. [
]
In' = 0.033 In (T - To) Discussion of the physical significance of this result will have to be postponed until comparable data are obtained for other binary systems. lim
T
Tc
Anomalous Freezing Behavior of Polymer Gels and Solutions by D. J. Solms Department of Chemistry, University of Cape Town, Rondebosch C.P., South Africa
and A. M. Rijke* Department of Materials Science, University of Virginia, Charlottesville, Virginia 22901
(Received December 2 , 1970)
Publication costs assisted by the National Science Foundation
An experimental and theoretical study is reported of the anomalous freezing point depression of polymer solutions and gels crosslinked in the presence of large amounts of diluent. It is found that all solutions and gels freeze at temperatures lower than would be predicted on the basis of their known thermodynamic properties. The results for dilute solutions and highly swollen, dilute solution-crosslinked gels can be satisfactorily explained by assuming that rapid annealing accompanies the growth of solvent crystallites that are prevented
from growing larger by the surrounding polymer filaments. These frozen systems are assumed to be crystals in which each individual polymer chain is embedded and immobilized. Annealing is supposed to be slower and less extensive in the more concentrated systems. The freezing-point depressions of swollen natural rubber vulcanizates are larger than predicted by the theory of Kuhn, probably due to extensive interpenetration of network chains, but the presence of diluent at the time of crosslinking reduces this depression well below the theoretical value. The effect of chain interpenetration can also be observed in solution-crosslinked gels if the amount of diluent is sufficiently reduced.
Introduction Gels and solutions of polymers exhibit anomalous freezing behavior in that they freeze a t temperatures lower than would be predicted from conventional thermodynamic considerations. I n crosslinked networks swollen to equilibrium, the chemical potential of the solvent inside the gel must, by definition, be equal to that of the pure solvent and hence no freezing point depression would be expected. I n polymer solutions the effect of the solute on the chemical potential of the solvent is accessible both by theoretical treatments and by direct experimental measurement. The observed freezing points of such solutions are, however, consistently lower than
These observations have failed to attract much attention, mainly because, in most cases of dilute systems, the freezing point lowering is too small to be of use as a method for providing reliable thermodynamic information. The larger freezing point depressions measured for more concentrated systems are obscured by such uncertainties as the inhomogeneity and time(1) J. W. Breitenbach and A. J. Rennix, Monatsh. Chem. 81, 454 (1950). (2) T.Kawai, J. Polym. Sci., 32, 425 (1958). (3) H. Ozssa, Y. Yamamoto, and A. Yamaoka, Himeji Kogyo Daigaku Kenkyu Hbkoku, 10,33 (1958). (4) D.Craig and N. M. Trivisonno, J . Polym. Sci.,Part B , 1, 253 (1963).
The Journal of Phyekal Chemistry, Vol. 76,No. 17, 1971
