from considering the asymmetry of the molecule and the presence of three chiral centers. However, for a particular methylene segment, not all chiral centers are effective to produce inequivalence of the two deuterons. We have found that the molecular packing of AOT in surfactant layers is similar to what is found in phospholipid bilayers-with a preferred bending of one of the chains close to the headgroup - . region. This particular packing of AOT and phospholipids is due to the asymmetry of the molecules. It is interesting to note that, in the case of AOT? this particular packing is found not only in a bilayer (the lamellar phase) but also in a monolayer where the mean curvature of the polar-apolar interface is toward the polar solvent (the reversed hexagonal phase). We note, finally, that the system AOT-H20, strictly speaking, should be recognized as a nine-component system. Stereoisomers
Acknowledgment. We are grateful to HAkan Wennerstrom for clarifying discussions and to Erick J. Duforc for allowing us to use his computer simulation program. T.C.W. thanks the University of Missouri for granting a research leave. This work was supported by the Swedish Natural Science Research Council. Registry No. AOT, 127399-06-8. (35) Stewart, M. V.;Arnett, E. M. In Topics in Stereochemistry; Eliel, N. L., Wilen, S. H., Eds.; Wiley: New York, 1982; Vol. 13, p 195, and references therein. (36) Arnett, E. M.; Gold, J. M. J . Am. Chem. SOC.1982, 104, 636. (37) Wisner, D. A.; Rosario-Jansen, T.; Tsai, M.-D. J . Am. Chem. SOC. 1986, 108, 8064. (38) Sarvis, H. E.; Loffredo, W.; Dluhy, R. A,; Hernqvist, L.; Wisner, D. A.; Tsai, M.-D. Biochemistry 1988, 27, 4625.
Critical Behavior of a Conducting Ionic Solution near Its Consolute Point MaGa L. Japast and J. M. H. Levelt Sengers* Thermophysics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (Received: December 1 , 1989)
Measurements are reported of the coexistence curve and electrical conductivity of the partially miscible aqueous solution of tetra-n-pentylammonium bromide near its consolute point, which was located at T, = 404.90 0.01 K and approximately 0.03 in mole fraction. The compositions of coexisting phases were measured over three decades of temperature, from 21 to 0.01 K from the consolute point. The conductivity was measured in the supercritical regime, from high dilution to compositions exceeding the critical. The degree of dissociation was estimated to be higher than 20% at the critical composition. In the data analysis, attention was given to the assessment of experimental error and proper weight assignment, and also to asymptotic range and choice of order parameter. No evidence of classical behavior was found. This finding is in contrast to several recent reports of effectively classical critical behavior in ionic solutions similar to ours; but it is in accordance with earlier measurements in very weak electrolytes. We present reasons why our conclusion differs from these recent results;an explanation is given why nonclassical behavior might be expected in systems of this type.
*
Introduction Recently, there have been a number of reports of effectively classical critical behavior of coexistence curves of ionic solutions near gas-liquid and liquid-liquid critical points.I4 Classical, mean-field, or van der Waals-like behavior implies that the top of the coexistence curve is parabolic, in terms of suitably chosen variables. For one-component fluids, these are the coexisting densities and temperature; for partially miscible binaries, they are composition and temperature; for binaries near a gas-liquid critical point, several choices are possible, one of them being the isothermal coexisting densities versus pressure. Classical behavior is expected to prevail if the molecular interactions are long-ranged.s The range of intermolecular potentials can be expressed by the value of the exponent n in the 1 / F dependence of the potential on the distance r. Potentials with n smaller than 4.97 lead to critical behavior that begins to depart from the nonclassical behavior associated with short-ranged forces6 Most fluids and fluid mixtures have interactions that are (barely) short-ranged? with an exponent value of n = 6; their critical behavior has been demonstrated to be nonclassical, as exemplified in the shape of their coexistence curves, which are nearly Since Coulombic potentials, with n = 1, are long-ranged, it has been recently suggested by Pitzer and co-w~rkers’-~ that ionic systems might display classical critical behavior. The experiments reported * T o whom correspondence should be addressed. ‘Permanent address: Quimica de Reactores, ComisiBn Nacional de Energla AtBmica, Av. del Libertador 8250, 1429 Buenos Aires, Argentina.
here are meant to test this hypothesis. In this Introduction, we will discuss the experimental evidence in favor of and against the hypothesis that ionic systems have classical critical points. In order to do so, we need to briefly introduce concepts and terminology of the theory of critical phenomena. The concept of universality of critical behavior implies that “near” a fluid-fluid critical point, be it a vapor-liquid critical point in a one-component system or a liquid-liquid consolute point in a binary mixture, the thermodynamic properties scale with critical exponent values that are the same for the large class of threedimensional Ising-like systems; this class includes most fluid critical points. The values of the critical exponents are extremely wellknown from renormalization group theory.I2 As an example, the ( I ) Pitzer, K. S.; Conceicao P. de Lima, M.; Schreiber, D. R. J. Phys. Chem. 1985,89, 1854. (2) Singh, R. R.; Pitzer, K. S.J . Am. Chem. SOC.1988, 110, 8723. (3) Pitzer, K. S.; Bischoff, J. L.; Rosenbauer, R. J. Chem. Phys. Lett. 1987, 134, 60. (4) Glasbrenner, H.; Weingartner, H. J . Phys. Chem. 1989, 93, 3378. (5) Stell, G. Phys. Reo. B 1970, 1, 2265; 1972, 5, 981; 1973, 8. 1271. (6) Kayser, R. F.; Ravechd, H. J. Phys. Reu. A 1984, 29, 1013. (7) Greer, S. C. Phys. Reu. A 1976, 14, 1770. (8) Greer, S. C.; Moldover, M. R. Annu. Reo. Phys. Chem. 1981,32,233. (9) Kumar, A.; Krishnamurthy, H. R.; Gopal, E. S. R. Phys. Rep. 1983, 98. 57. (IO) Sengers. J. V.;Levelt Sengers, J. M. H. Annu. Reu. Phys. Chem. 1986, 37, 189. (11) Levelt Sengers, J. M. H.; Sengers, J. V. In Perspectiues in Statisricul Physics; Ravechd, H. J., Ed.; North Holland: Amsterdam, The Netherlands, 1981; p 239.
This article not subject to U S . Copyright. Published 1990 by the American Chemical Society
5362 The Journal of Physical Chemistry, Vol. 94, No. 13, 1990
Japas and Levelt Sengers
two-term Wegner expansion. Pitzer et al. reported a classical liquid-liquid coexistence curve in the nonaqueous binary tetran-butylammonium picrate- 1-chloroheptane,I and, recently, Singh 1X'- X ' j = BI(T - Tc)/Tcla= B(hT*la (1) and Pitzer found classical behavior in triethyl-n-hexylammonium triethyl-n-hexyl boride in diphenyl ether.2 Also, Glasbrenner and with X', X" the compositions of coexisting phases, T the temWeingartner4 reported a classical critical exponent for the aqueous perature, T , the critical temperature, and AT* a reduced temsolution of tetra-n-butylammonium thiocyanate. In these three perature difference; p is a critical exponent with the theoretical experiments, the temperature accuracy was of the order of 0.1 value of 0.326 f 0.002 for nonclassical and 1 /2 for classical critical K, and only a few points were measured within I K of the critical behavior, and B is a critical amplitude. point. Finally, Bischoff et reported an apparent value of the For many fluid systems, the range of validity of the asymptotic exponent p larger than 0.5 for the isothermal pressuresmq"tion power laws has been found"' to be only of the order of 10-3-10-2 coexistence curves of the system NaCI-H20 near the vapor-liquid in reduced temperature AT*. The first departures from asymptotic critical line and at low concentrations of salt. Harvey and Levelt behavior are described by means of the so-called Wegner corS e n g e r ~however, ,~~ showed that such curves are expected to cross rection The Wegner expansion is poorly converging, over to an exponent value of 1 /3 at the solvent's critical point. and as soon as one correction to scaling is needed, others will have This means that, at temperatures near the solvent's critical temto be added on further expansion of the data range. perature, the value of p cannot be conclusively extracted from Another complexity to be faced, especially when dealing with the pressure-com posi t ion data. fluid mixtures, is proper choice of the order parameter. which is Buback and Franck,17and recently Pitzer et al..'-3 have ascribed the fluid equivalent of the spontaneous magnetization in uniaxial the apparent classical behavior to the existence of long-range ionic magnets or the lsing model. For one-component fluids near the interactions that suppress the fluctuations. The difficulty with gas-liquid critical point, it is believed that the density departure this argument is that the ionic interactions are screened, and from the critical density is a nearly optimal choice. For binary therefore nonclassical behavior should ultimately prevail when liquid-liquid mixtures, the differences of the mole fraction or the critical point is approached. Also, there have been a number volume fraction from their respective critical values are leading of studies of critical behavior of weakly electrolytic systems, such candidates. For lack of theoretical guidance, an operational as isobutyric acid and ~ a t e r , ~triethylamine , ~ ~ , ~ ~ and ~ a t e r , ~ ~ . ~ ~ definition of a proper order parameter might be the one that gives lutidine and and a collection of closed-loop aqueous the largest asymptotic range. Improper choice of the order pabinary coexistence curves reviewed in ref 31; in all cases nonrameter leads to small asymptotic range and additional terms in classical behavior was found. One could, however, argue that these expansions involving the order parameter.'^^," systems were not sufficiently ionized. Far from the critical point, the system is expected to cross over In view of these apparent contradictions, it seemed worthwhile to mean-field or van der Waals-like behavior.I6 One might expect to investigate the critical behavior of a well-dissociated binary. that the crossover from scaling to mean-field behavior would occur Initially, we tried to measure the coexistence curve of tetra-nin a range of the reduced temperature that depends on the range butylammonium picrate in 1 -chloroheptane. We found that we of the intermolecular forces in the system of interest: the system were not equipped to prevent decomposition of our samples; deis expected to cross over to classical behavior sooner. as the range composition proceeded so rapidly that accurate measurements were of the forces becomes larger. impossible. We therefore decided to investigate a member of the Let us now review the experimental evidence in favor of classical class of tetra-n-alkylammonium halides. In mixtures with water, behavior, or quick crossover to classical behavior, for systems with the miscibility decreases with the length of the hydrocarbon chains. Coulombic interactions. In some experiments involving molten Most of the previous experimental work was done at 25 "C and salts such as NH4CI,studied by Buback and Franck,I7 and in liquid properties such as conductivity, viscosity, and partial molar ensodium, measured by Dillon et al..IBa classical critical exponent thalpy of dissociation have been investigated. The separation into 0.5 was found for the coexistence curve.I7 Because of the high two liquid phases was studied at temperatures below 90 "C by temperatures, high pressures, and aggressive nature of the sample Mugnier de Trobriand and L u ~ a s .They ~ ~ found that the lowest fluid, these are very demanding experiments. The temperature alkyl chain length of the tetraalkylammonium bromides that show resolution is no better than 1 K, the approach to the critical point phase separation into two aqueous phases was five. The association no closer than 10 K , and the value of the critical temperature constants of several other tetraalkylammonium bromides in water uncertain to at least 10 K. Indeed, the more recent and far more were studied by Ferndndez Prini33and by from these accurate and detailed measurements of Hensel and c o - ~ o r k e r s ~ ~ , data, ~ ~ we were able to predict, by extrapolation, that the tetraon the vapor-liquid coexistence curves of rubidium and cesium pentylammonium bromide-water solution should produce a large have revealed nonclassical critical behavior for these metallic number of ions. systems. I n the binary mixture Na-NH3, a crossover from the I n this paper we report coexistence curve and electrical connonclassical exponent 0.33 to the classical exponent 0.5 was reductivity measurements in the system tetra-n-pentylammonium ported by Chieux and Sienko.zl This consolute point occurs at bromide (Pe,NBr) and water near its consolute point, which is 231.55 K; the temperature resolution was 10 mK, and the critical at approximately 405 K and 0.03 in mole fraction of Pe4NBr. We point was approached to within 20 mK. Das and Greer,22however, report the compositions of coexisting phases from 383 K to the showed that the same data are quite consistent with a nonclassical critical point near 405 K. The conductivity of the soiution is reported as a function of composition in the supercritical region, power law for the shape of the coexistence curve in a binary liquid mixture is
+
(12) Le Guillou, J . C.; Zinn-Justin, J . J . Phys. 1987, 48, 19.
( 1 3 ) Wegner, F. J. Phys. Reu. B 1972, 5, 4529. (14) Ley-Koo, M.; Green, M. S. Phys. Reu. A 1977, 16, 2483. ( 1 5 ) Scott, R. L. In Chemical Thermodynamics; Specialist Periodical Reports; McGlashan. M. L., Ed.: Chemical Society: London, 1978; Vol. 2.2, Chapter 8, p 238. (16) Chen, Z. Y . :Albright, P. C.; Sengers, J . V. Phys. Reo. A 1990, 41, 3161. ( 1 7) Buback, M.; Franck, E. U . Ber. Bunsen-Ges. Phys. Chem. 1972, 76, 350. (18) Dillon, I . G.; Nelson, P. A,; Swanson, B. S. J. Chem. Phys. 1966.44, 4229. (19) Jiingst, S.; Knuth, B.; Hensel, F. Phys. Rev. Lett. 1985, 55, 2160. (20) Hensel, F.; Jiingst, S.; Knuth, B.; Uchtmann, H.; Yao, M . Physica 1986, 139f140. 90. (21) Chieux, P.; Sienko, M . J. J. Chem. Phys. 1970, 53, 566. (22) Das, B. K.; Greer, S. C. J . Chem. Phys 1981, 7 4 , 3630.
~~
(23) Bischoff, J . L.; Rosenbauer, R. J. Geochim. Cosmochim. Acta 1988, 52. 2121.
(24) Harvey, A. H.; Levelt Sengers, J. M. H. Chem. Phys. Left.1989, 156, 415. ( 2 5 ) Woermann, D.; Sarholtz, W. Ber. Bunsen-Ges. Phys. Chem. 1965,69, 319. ( 2 6 ) Stein, A.; Allen, G . F. J . Phys. Chem. ReJ Data 1974, 2, 443. (27) Thoen, J.; Bloemen, E.; Van Dael, W. J . Chem. f h y s . 1978,68,735. ( 2 8 ) Bloemen, E.; Thoen, J.; Van Dael, W. J. Chem. Phys. 1980, 73,4628. (29) Pusey, P. N.; Goldburg, W. I. Phys. Rev. A 1971, 3, 766. (30) Bak, C. S.; Goldburg, W. I. Phys. Reu. Lett. 1969, 23, 1218. (31) Andersen, G. R.; Wheeler, J. C. J . Chem. Phys. 1978, 69, 3403. (32) Mugnier de Trobriand, A,; Lucas, M . J. Inorg. Nucl. Chem. 1979, 41, 1214. ( 3 3 ) Fernindez Prini, R. Trans. Faraday SOC.1968, 64, 2146. (34) Justice, J.-C.;Justice, M.-C. Pure Appl. Ckem. 1979, 51, 1681.
Critical Behavior of a Conducting Ionic Solution at around 413 K. From the conductivity data we have estimated the dissociation constant, which yields a lower bound to the number of ions present at the critical composition. A careful assessment is made of the sources of error, and of the appropriate assignment of weights to the data. An analysis of our data reveals no evidence of classical behavior over almost three decades in reduced temperature. Range dependence of the asymptotic critical exponent value, and sensitivity of the exponent to error in the critical temperature and to choice of order parameter, are studied. It is proven unlikely that experiments less accurate than ours can reach decisive conclusions about the critical exponent of the coexistence curve.
Sample Commercial 99%+ pure tetra-n-pentylammonium bromide was used. The melting points of the different supplies tried by us were all in the range of 374.05-374.15 K. We first tested the stability of the material by dissolving it in distilled water and observing the transition temperature between the one- and two-phase regions (around 393 K) as a function of time. The transition temperature showed no drift within the precision of our observations (0.1 K). Since some small colored crystals appeared to be mixed in with the clear Pe4NBr crystals, we made some attempts at purification by dissolution in benzene or hexane, and recrystallization. The purified material did not show any change in melting temperature, but a test of the stability of the solution revealed a large drift. For the material that we used in the experiments reported here, we used the original sample but removed the colored crystals by hand-picking. For all coexistence curve measurements, the same stock sample was used. The principal effect of impurities is to shift the critical temperature. This is a systematic effect that should not affect our purpose of determining the critical exponent. A secondary effect of an impurity is, of course, to modify the path of approach to the critical point, moving the critical point away from the top of the coexistence curve in the temperature-composition plane and renormalizing the critical exponent. We have, however, not found such effects in our results. The water used in the experiment was distilled and deionized, with a residual electrolytic conductivity of less than 2 pS cm-I. The Measurement of the Coexistence Curve The method used for determining the coexistence curve is a point-by-point determination of the temperature of transition from a homogeneous to a heterogeneous phase for samples of known composition. The sample holder was a precision-bore glass tube, with a length of 10 cm, inner diameter of 4 mm, and outer diameter of 6.5 mm; the tube was fitted with a glass valve with Teflon stem. The use of a tube with large ratio of outer to inner diameter was dictated by the fact that at the consolute point the vapor pressure of water is about 0.3 MPa. The sample was prepared by weighing in the desired amount of Pe,NBr with a precision of 0.1 mg, after which the cell was carefully evacuated; residual air hastens decomposition. After this, the minimum amount of water required for the particular run was added and the cell weighed again. The total amount of solution was usually of the order of 1 cm3. The absolute accuracy of the solute mole fraction determination was between 2 X and leading to a relative error in solute mole fraction of about 0.2%. The sample was stirred by means of a small Teflon-coated magnet which was moved up and down by means of an external motor-driven moving magnet. The bar dimensions were chosen such as to cause very effective stirring. The sample was immersed in a visual bath filled with silicone oil and stirred thoroughly. The bath was controlled to approximately fO.O1 K over the duration of an experiment. The temperature was measured by means of a commercial platinum thermometer with digital readout to 1 mK and of tested reproducibility on that level of precision; the thermometer was compared with one calibrated on the International Practical Temperature Scale. The departures found did not exceed 0.01 K, the precision
The Journal of Physical Chemistry, Vof.94, No. 13, 1990 5363
of control of the bath, over the entire range of temperatures of the present experiment. We had to develop a method for observing the coexistence curve. The standard procedure is to stir the sample and then let it settle. The position of the meniscus is observed as a function of temperature, and the temperature is noted when the meniscus reached the top or bottom of the liquid sample. This method was not suitable for the sample at hand. First of all, the highly viscous solute-rich phase wets the walls and it takes a very long time for it to drain to the bulk phase. Second, the densities of the coexisting phases are closely matched, there being a density inversion near 373 K; this makes demixing a slow process. At temperatures near the consolute point, the transition temperature drifts at the rate of 10 mK-h-’, so time considerations are crucial in obtaining reliable results. We decided to perform the measurements with continuous stirring. At the transition from the homogeneous to the heterogeneous phase, a change in the transparency of the sample is observed. In the two-phase regions, one phase is dispersed within the other, resulting in opacity of the sample. In the one-phase region the system is transparent. Very close to the critical point, it requires some experience to distinguish between opacity due to heterogeneity and the critical opalescence that also occurs in the homogeneous regime. In view of the fragility of the sample, we had to minimize the time during which it was exposed to high temperature. We did this by first obtaining a preliminary set of data on the coexistence curve location by placing the cell, containing a concentrated sample, in a stirred silicone oil filled beaker on a hot plate, continuously diluting it. This experiment gave us the location of the phase boundary to about 0.5 K. For the real experiment, we set the visual bath at the required temperature for the composition at hand prior to plunging in the cell. The total time span required for equilibrating the solution, finely adjusting, and detecting the transition was of the order of 45 min. Although we had originally planned to follow the coexistence curve from the highest composition downwards by continuous dilution, we had to abandon this idea; for temperatures above 390 K, where the effect of decomposition increases even if the rate remains constant, we could take at most two points with one filling of solute. We therefore carried out the experiment in two cells, filling and preparing one while the transition was being observed in the other.
Results: Coexistence Curve The Data. The results of our measurements are collected in the first two columns of Table I. X’represents the measured mole fraction for which the transition temperature value T i s obtained. The full set has 43 data points, with roughly equal numbers on each side of the critical composition. The data span a range of 21 K below the critical point. Seven points are within the last 0.02 K from the critical temperature; the usefulness of these points is of course marginal, the uncertainty of A T + being of the order of its value. Eight points are between 0.02 and 0.2 K away. Another IO are between 0.2 and 2 K away. The remaining 18 points are between 2 and 21 K away from the critical temperature. The coexistence curve is shown in Figure 1. Since the data below and above the critical composition were not taken at the same temperatures, we performed a graphical interpolation to obtain a set of values X”that are isothermal with the first set X’. These interpolated data are given in column 3 of Table I. A log-log plot of X’-X’’versus AT*, with T, the critical temperature, set equal to the observed value of 404.90 K, is shown in Figure 2. The data are seen to fall on a straight line with slope close to 1 /3. Analysis of the Coexistence Curve Data Weights. In order to obtain a value and reliability estimate of the asymptotic critical exponent from the experimental coexistence curve data, it is necessary to account for the various sources of error. The first one is that of the measured quantities, temperature and mole fraction. The uncertainty of the mole fraction determination was estimated to be bX N and that of the
5364
Japas and Levelt Sengers
The Journal of Physical Chemistry, Vol. 94, No. 13, I990 T/K
TABLE I: Coexisting Mole Fractions X’, X” vs Temperature T, K I 03xf I 03x” est lo’u, 383.25 387.85 390.82 391.92 393.42 396.8 1 399.90 400.98 402.17 402.72 403.38 403.85 404.275 404.66 404.79 404.77 404.85 404.86 404.89 404.89 404.88 404.89 403.90
6.1 1 I 6.195 7.319 7.614 8.072 9.391 1 1.290 12.180 13.540 14.260 15.610 16.750 18.230 20.880 22.350 22.400 24.490 25.080 26.650 28.300 28.920 30.630 30.660
87.800 8 1.600 77.400 75.200 72.620 66.600 60.250 57.250 53.650 51.650 49.150 46.550 43.550 39.500 37. I50 37.550 35.250 34.700 32.600 32.600 33.500 32.600 30.500
404.89 404.88 404.85 404.84 404.80 404.77 404.675 404.60 404.41 404.005 403.545 403.26 401.48 400.27 398.98 397.83 395.08 390.60 387.75 382.45
32.660 32.900 34.900 35.690 36.200 37.680 39.980 40.340 42.440 45.660 48.280 49.690 55.870 59.330 62.500 64.600 69.990 77.370 8 1.850 88.960
27.500 26.350 24.500 24.1 50 22.900 22.350 2 1.050 20.350 19.030 17.200 16.000 15.400 12.700 1 1.600 10.730 10.000 8.700 7.270 6.800 6.000
0
2
4 6 MOLE FRACTION
0.101 0.101 0.101 0.101 0.101 0.102 0.104 0.106 0.109 0.112 0.120 0.131 0.157 0.253 0.416 0.364 0.653 0.728
404 8
400 9
404 5
382.5
10’1
’
X
I
X
I
,I
-
I
I/-
2
