FLUOROCARBON SOLUTIONS AT Low TEMPERATURES
3259
by John B. Gilmour,Judith 0. Zwicker, Jeffrey Katz, and Robert L. Scott Contribution No. 1997 from the Department of Chemistry, University of California,
Los Angeles, California 90064 (Received October 6 , 1966)
Total vapor pressures have been measured for three binary liquid mixtures and from these measurements equations for the molar excess Gibbs free energy have been derived, yielding the following values for dE/cal at z = 0.5: C2H8 C3F8 a t 188"K, 165; c3H8 4-c3F8 at 204"K, 212; a t 214", 204; a t 224"K, 199; and n-C4Hlo C3Fsa t 228"K, 250. Liquid-liquid phase diagrams for 11 systems were determined, with critical solution temperatures as follows: C3Hs C2F6, 190°K; CH, CSFS, 127°K; C2Hs C3F8, 166°K; C ~ H E C~FE, 196°K; n-C4Hlo C3Fs, 226°K; i-C4HIO C3F8, 208°K; C3Hs n-C4F10, 204°K; nC6H14 n-C4FlO, 281°K; n-C,&6 n-C4Flo, 303°K; n-CaHzo n-c4F10, 348°K; nCloHzz n-CqF10,378"K. The critical solution point for the system C2H6 C2F6 is hidden by the melting curve, but is estimated to be 157°K. These results contain and extend fluorocarbon systems, The anomalously large deviations earlier work on hydrocarbon from the predictions of solubility parameter theory are about the same for all systems, and show no significant dependence upon the differences in molar volume (or number of carbon atoms) between hydrocarbon and fluorocarbon. All of the critical solution temperatures fall on a simple grid which permits interpolation and (with caution) extrapolation. The critical composition shows a striking dependence upon the difference in molar volume and gives support to a volume-fraction or surface-fraction formulation of regular solution theory.
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Introduction The work reported in this paper is part of a continuing research program on fluorocarbon solutions; previously we have reported2" low-temperature vapor pressures and phase diagrams for 13 systems involving fluorocarbons and fluorochemicals. I n this paper we report similar measurements6 on 12 more systems, with particular emphasis upon differences in molar volume (and differences in number of carbon atoms). Rowlinson and co-workers6 have shown that large excess free energies persist even when the molar volumes of the pure components in a hydrocarbon fluorocarbon mixture are nearly equal; an increase of 50% in the molar volume of the hydrocarbon had only a small effect
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on the magnitude of the large deviations from ideality. The present research, with hydrocarbons ranging in size from CH, to CloHz2(and those from C3to Clomixed with a single fluorocarbon, n-C4Flo), greatly extends the earlier work and arrives at generally similar conclusions. (1) Based on part of a dissertation by J. B. Gilmour for the Ph.D. degree, University of California, Los Angeles, Calif., June 1965. (2) N. Thorp and R. L. Scott, J . Phys. Chem., 60,670 (1956). (3) N.Thorp and R. L. Scott, ibid., 60, 1441 (1956). (4) I. M. Croll and R. L. Scott, ibid., 62,954 (1958). (5) I. M.Croll and R. L. Scott, ibid., 68,3858 (1964). (6) J. S. Rowlinson, D. E. L. Dyke, and R.Thacker, Trans. Faraday Soc., 55, 903 (1959).
T701ume 71,Number 10 September 1967
J. GILMOUR, J. ZWICKER,J. KATZ,AND R. SCOTT
3260
Experimental Section Materials. The source and purity of the substances are outlined in Table I. Table I : Materials Used
Compound
Source
a
b C
d b
b b b e
f f
Manufacturer’s stated purity, %
99.9 98.0 (min) 99.8 99.5 99.90 99.9+ N99.8 100.00 99.97 99 Bp 173-175”
a Dupont Organic Chemicals Department, Research and Development Division, Jackson Laboratory, Wilmington 99, Del. Matheson Co., Newark, Calif. c Halocarbon Products Corp., Hackensack, N. J. Matheson C P grade purified by Dr. Donald Davis, Chemistry Department, University of California, Los Angeles, Calif. ‘Phillips Petroleum Co., Bartlesville, Okla. Matheson Coleman and Bell, East Rutherford, N. J.
’
All of the materials were degassed by alternate melting and freezing while pumping. With the exception of the C3F8 no further purification was attempted. The C3F8 gas was condensed a t least three times onto a bed of activated charcoal and then allowed to boil off. The charcoal was activated by pumping and heating to 430-480’; it was reactivated between each condensation. Apparatus and Experimental Procedure. Experimental mixtures were prepared by condensing successive measured quantities of gas from a gas buret into the vapor pressure or solubility apparatus at low temperatures. A conventional vacuum manifold arrangement was used to evacuate the apparatus before use and to transfer the gas from the storage bulbs into the gas buret. A liquid Freon low-temperature bath, similar to that described by Croll and Scott15was used for both the solubility and vapor pressure measurements. The bath temperature was measured and controlled using the output from a ten-junction copper-constantan thermopile which was immersed in the Freon. The thermopile was calibrated against the vapor pressures of the pure hydrocarbons as well as against the freezing point of pure xenon (161.3OK). A crushed-ice slush served as the reference temperature. The balancThe Journal of Physical Chemistry
ing and heater control circuit was essentially that of Croll and Scotts except that three times the earlier sensitivity was obtainable with the ten-junction thermopile and a more sensitive recorder. Under control conditions there were sinusoidal oscillations of temperature of * O . 0 Z o about the average temperature. By adjusting the voltage across the heaters, the period of this oscillation could be varied from about 10 to 40 sec. Vapor Pressure Measurement. The “click” gauge (Thorp and Scott2) used to measure vapor pressures is shown in Figure 1 together with the rest of the vapor pressure apparatus. The gauge is essentially a curved glass membrane which changes configuration (with a snap or click) where the difference in pressure between the two sides reaches a reproducible value; measurement of the nitrogen pressure on the far side of the membrane thus serves to determine the pressure inside the bulbs, i.e., the total vapor pressure of the mixture. Random fluctuations in the pressure of the order of 2-4 cm occurred unless the liquid mixture was sealed below the surface of the Freon. At first, the bulb was closed with a solenoid-operated valve which was used for vapor pressure measurements on C2Ha C3Fsand C3Fs. However, this valve proved difficult to operate and had a large vapor space necessitating difficult corrections, so it was later discarded. In all other measurements mercury from the gas buret was allowed to follow the gas into the mixture bulb through a capillary delivery line; the mercury would freeze there and plug the line. After a measurement was made and before more
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V
Figure 1. Schematic diagram of vapor pressure apparatus: A, click gauge; B, mixture bulb; C, stirring bar; D, delivery tube with 12/1 ball joint at end; E, delivery tube heater; F, glass tube to manometer; G, heaters, main and auxiliary; H, thermopile; I, dewar flask.
FLUOROCARBON SOLUTIONS AT Low TEMPERATURES
material was condensed into the vapor pressure bulb, a wire heater around the delivery tube was turned on and the inner dewar lowered so that the liquid Freon was below the frozen mercury. The mercury then melted and the vapor pressure of the mixture forced the mercury out of the delivery tube and into the gas buret which contained the new material to be added. Sometimes when the vapor pressure was low, the mixture had to be heated. This new method of isolating the mixture below the level of the Freon bath proved highly satisfactory; it was simple, reliable, fast, and involved much smaller uncertainties in the liquid composition. Solubility Measurements. Liquid-liquid solubilities and solid-liquid solubilities were measured in an apparatus identical with that of the vapor pressure apparatus (Figure 1) except that a click gauge was not attached to the mixture bulb. A 60-w spotlight was placed behind the dewars, and critical solution temperatures and solid solubilities were directly observed through the two unsilvered dewars. Some observations of the unmixing temperatures T u were made by observing the phase changes when one looked at an angle of 90" to a small focused illuminating beam which could be switched on as an alternative to the regular spot light. The conventional method of determining liquidliquid miscibility is to raise or lower the bath temperature slowly and, when two phases appear (or disappear), the temperature Tu is recorded. However, in the present apparatus one could adjust the dials of the temperature control potentiometer to a point where the bath temperature varied sinusoidally within *0.02" of T , and hold this temperature indefinitely. When the 90" beam was used, the phase change was well defined: as the temperature decreased and increased, passing each time through the unmixing temperature Tu,the mixture went from a transparent white to a very silky composition of two liquid phases which was churned by the smaller stirrer, and back again - to a transparent white. The one-phase mixture was not colorless, but was white owing to critical opalescence. The passage of the system from one phase to two phases and back again occurred four times/min, or less, depending upon the setting of the heaters. At extremes of composition, this procedure was not feasible and the conventional method of varying the temperature had to
Results7 vapor Pressure Measurements. The results of the vapor pressure measurements are shown in Figures 2 4 . The circles are the experimental data and the solid line is a least-squares fit of the data (see below). Only the
3261
total compositions were directly measured; however, since the vapor space is small, application of a small correction to the total composition yields an accurate estimate of the liquid composition (L). The vapor composition curve ( V )is a calculated one. The mole fractions x of the liquid are generally known to h0.01 for C3Hs CaF8 and to iO.005 for n-CaH1, C3F8. The difference in the uncertainties in these two systems arises from the improvement obtained by using the frozen plug of mercury as explained above. The uncertainties in the mole fractions for the system C2He CaFs are comparatively larger than in the other systems because of the large vapor space and the uncertainty in the composition of the vapor in the valve used for the system. Fortunately, the largest uncertainties (*0.035 in the mole fraction) lie in the region z = 0.0-0.5, where the total vapor pressure is least sensitive to the liquid composition. The effect of this uncertainty upon the parameters used in the equation to fit the data was negligible. The liquid compositions for the remainder of the experimental points for this system are usually known to within 0.01 mole fraction. The curve a t T = 2035°K for the system C3Hs C3F8 (Figure 3) is quite flat since the measurements of the vapor pressure were made 7.3"K above the critical solution temperature. Similarly, the vapor pressure CaFR(Figure 4), measured of the system n-C4Hla only 2.2"K above its critical solution temperature, displays the same characteristic flatness. As can be seen from the figures, both systems form azeotropes. These experimental vapor pressure data were processed by the computer program CH08B developed by Myers and Scott.8 This program, a modification of the least-squares procedure proposed by Barker,9 evaluates a set of coefficients (Y in an equation for the molar excess Gibbs free energy
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b E /=~~ ~ ~ + x
+
-~ z2) [
az~ ( ~l
~ xdZl
(1)
Table I1 gives the derived coefficients 010, ( ~ 1 , and W1,W z , and 812 are corrections for nonideality of the vapors and the effect of applied pressure upon the vapor pressure az for eq 1.
(7) All of the experimental results reported here may be found in numerical form in the Ph.D. Dissertation of John B. Gilmour (UCLA, 1965),obtainable from the UCLA Library or from University Microfilms. (8)
D. B. Myers and R. L. Scott, Ind. mg. them., 55,43 (1963).
(9) J. A. Barker, ~ ~ ~ t r aJ.z Chem., i a ~ 6,207 (1953).
Volume 71, Number 10 September 1967
J. GILMOUR, J. ZWICKER,J. KATZ,AND R. SCOTT
3262
1
I
I
I
I
I
I
I
Xb Figure 2. Pressure-composition diagram for the system C2He circles, experimental points; solid lines, computer curves.
0.0
0.1
0.2
0.3
+ CsF8a t 188.3"K:
0.5 x2
0.4
Figure 3. Pressure-composition diagrams for the system CaHs circles, experimental points; solid lines, computer curves.
0.7
0.8
0.9
1.0
+ C3F8 a t 203.5, 213.6, and 223.5"K:
where the subscripts refer to components 1 (hydrocarbon) and 2 (fluorocarbon). The second virial coefficients,BI1and B22,required for the program were obtained from a collection of virial data compiled by Dymond'O or were estimated from the behavior of similar substances with the aid of the Berthelot-type equation proposed by Guggenheim." (5)
The Journal of Physical Chemistry
0.6
v,
where and T , are the molar volume and temperature of the gas-liquid critical point. The parameters a and b and 3/2 in the Guggenheim equation) are not the same for all of the substances and have to be judiciously interpolated. (10) J. A. Dymond, "A Compilation of Second and Third Virid Coefficients," Department of Chemistry, University of Oxford, 1964 (privately circulated). (11) E.A. Guggenheim, J . Imp. CoZZ. Chem. Eng. Soc., 32, 13 (1953); cf. T. B. Tripp and R. D. Dunlap, J . Phys. Chem., 66, 635 (1962).
FLUOROCARBON SOLUTIONS AT Low TEMPERATURES
60
I
1
I
,L
3263
I
1
i
I
-
n
lor-
i
1
Table I1 : Excess Free Energy Coefficients -1-
-11sCsHs CsFs
+
CiHe 4CsFs
T/K" Wl/lO-s torr-' Wz/10-5 torr-' 612/10-s torr-' a0 ff'
ff2
lim In y1
-1IbCiHs CaFe
-110CsHs CsFe
+
+
7-111n-CdHlo CsFa
+
188.3 4.91 18.3 1.4 1.77 f 0.02 0.40 f 0.03 0.13 f 0.06 1.5
203.5 7.74 12.9 0.01 2.08 f 0.04 0.24 f 0.09 0.25 f 0.17 2.1
213.6 6.74 10.7 0.01 1.93 f 0.03 0.28 & 0.06 0.24 f 0.12 1.9
223.5 5.90 9.20 0.01 1.80 f 0.02 0.29 & 0.06 0.28 f 0.11 1.8
227.8 10.8 8.6 0.91 2.21 f 0.01 0.17 =I= 0.02 0.33 & 0.03 2.4
2.3
2.3
2.4
2.4
2.7
11.2 1.3
8.1
9.1 1.9
12.7 1.6
4.3 0.8
Xl+O
lim In y2 zz-0
upltorr 10OUP/PO.6
2.9
The correction 812 (eq 4) involves the cross virial coefficient B12and was estimated by using the law of corresponding states and the Lorentz-Berthelot combining rules for the intermolecular pair potential energy. For the dilute gas, the Scott12 "three-liquid" formulation, combined with eq 2, yields
RT812
=
+
6 . 0 V c [ ( T c / T ) 2 ( 7 2 75 - 0.17f2) - 0.17t2] (6)
+ Tc2)/2,Vc =
where Tc = (TC1
+ vc2)/2,5 =
(VC1
+
+
(V02 - vc1)/(7c2V d , and 7
= (Tc2 - Tc1)/(Tc2 Tcl). The subscripts 1 and 2 again refer to components 1 and 2. This equation and selected values of the critical volumes and temperatures were used to derive the values of 812 tabulated in Table 11. (Actually the Berthelot assumption-geometric mean of the energies-is a poor one for hydrocarbon fluorocarbon mixtures, as these papers have shown. The
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(12) R. L. Scott, J. Chem. Phys., 2 5 , 193 (1953).
Volume 71* Number 10 September 1967
J. GILMOUR, J. ZWICKER, J. KATZ,AND R. SCOTT
3264
parameter 812 is undoubtedly larger than that calculated from eq 6; however, the effect on the thermodynamic properties is entirely trivial.) Also included in Table I1 is the standard deviation u p of the observed pressures from those calculated using eq 1 and the set of coefficients CY. An indication of the relative precision is given by the ratio where is the pressure of the system a t 2 = 0.5. The relative precision is improved for system I11 (and other systems to be reported in a subsequent paper) which were measured on the final version of the vapor pressure apparatus. Some scatter in the vapor pressure may have been caused by condensation of a small amount of liquid in the delivery tube just below the valve on earlier versions of the vapor pressure apparatus. There was no possibility of this occurring with the mercury plug valve since the mercury usually filled the entire length of the delivery tube. An auxiliary computer program was used to calculate vapor pressures for values of x other than these measured; this program also calculated the vapor compositions shown in Figures 2-4. Solubility Measweinents. No liquid-liquid immiscibility was observed for the system C2H6 CzFs shown in Figure 5. However, the slope of the solid solubility dx/dT is so very large that it is obvious that a metastable liquid-liquid miscibility curve lies just below. Such metastable curves have been observed in the systems phosphorus carbon disulfide13and sulfur quinoline. l 4 Figure 6 compares the solubility data for four systems in which the hydrocarbon (CH,, CzHs, C3H8, or nC4HIO)is increased in size while the fluorocarbon, C3F8, remains the same. Also shown in Figure 6 is a branched hydrocarbon, i-C4Hl0, with C3F8. Figure 7 offers a similar comparison of the liquid-liquid phase diagrams for a single hydrocarbon, C3H8, with three fluorocarbons (C2F6, ( 2 8 8 , and n - G F d . Following a suggestion of Munson, l5 we plot these data (and those in Figure 8 as well) in a reduced form as T/Tc zs. @2, where T, is the critical solution tem~ Z ~ P , / ( X ~zzP2) ~ ~ is the volume perature and C ~ J = fraction of fluorocarbon. For convenience and consistency, we define the volume fraction in terms of the molar volumes of each pure liquid at its normal boiling point, a crude approximation t o a corresponding state. No theoretical significance can be attached to any variation of the molar volumes in a volume fraction. Critical opalescence was evident in the systems during solubility measurements. The transparent solutions immediately above Tu had a brown tint when viewed opposite a light which shone through them and,
Tc = (157') x c = (0,371
I65
5
2 160
155
150
I
I
1
I
I
0.2
0.4
0.6
0.8
1.0
x2
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Figure 5. Phase diagram for the system C2He CZF~. An estimated metastable liquid-liquid curve is sketched below the experimental solid-liquid curve.
I
I
I
I
I
1.000.9 8
-
0.96-
+
+
I
0.0
0.94
-
T / T, 0.921-
+
0.84 0.00
I
I
I
0.20
0.40
0.60
0.80
i
1.00
92
Figure 6. Liquid-liquid miscibilities for systems of five hydrocarbons (CHa, GHe, C3H8, n-C4H10, and i-C4H10) with C3Fp. Temperatures are reduced by dividing by the critical solution temperature To. Compositions are volume fractions of fluorocarbon 62 (in terms of molar volumes a t the normal boiling point).
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The Journal of Physical Chemistry
as mentioned earlier, were whitish when viewed 90" from the incident beam. As expected, this phenomenon was most pronounced for composition closest to the critical solution composition xo. Finally, Figure 8 shows miscibility curves for a wide (13) J. H. Hildebrand and T. F. Buehrer, J . A m . Chem. Soc., 42, 2213 (1920). (14) D. L. Hammick and W. E. Holt, J . Chem. Soc., 1995 (1926). (15) hf. S. B. hlunson, J . Phys. Chem., 68, 796 (1964).
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FLUOROCARBON SOLUTIONS AT Low TEMPERATURES
I
I
I
I
Discussion
1.00-
For many nonelectrolyte mixtures, a reasonable zeroth approximation for the molar excess Gibbs free energy is the regular-solution equation’’
-
0.98
-
0.96 0.94
-
I
-
T/ T,
where XI and x2 are the mole fractions of the two comand Pz, ponents; cpl and pzrtheir volume fractions; their molar volumes; and A12is a measure of the interaction energy between unlike molecules relative to that between like molecules. According to solubility parameter theory”
vl
0.90 0.921
0.861
I
0.84 0.00
I
0.20
1
1
0.40
0.60
I
0.80
?
1
1.oo
Figure 7. Liquid-liquid miscibilities in systems of CsHs with three fluorocarbons (C~FE, CSFS, and n-CdFlo. The coordinates and the smoothed curve are the same m in Figure 6.
I
I
I
1
A12
= (61
- 6212
(8)
where ti1 and ti2 are the “solubility parameters” of the components (the square roots of the cohesive energy density or energy of vaporization per unit volume). Table I11 summarizes the physical properties of the pure liquids: the normal boiling point Tb, together with the molar heat of vaporization AH”, the molar volume 9, and the solubility parameter 6 at various relevant temperatures. Table IV compares the values of the excess free
Table 111: Physical Properties of the Pure Liquids
\
5T/
tal-'/*
A?&/
0.00
0.20.
OAO
0.60
0.00
1.00
92
Figure 8. Liquid-liquid miscibilities in systems of five hydrocarbons (C~HS, n-CEHl4, n-C?HlS, n-CgH20, and n-CloHzz) with n-CdFlo. The coordinates and the smoothed curve are the same as in Figure 6.
range of hydrocarbons (Ca&, n-C6H14,n-C,Hls, nC9Hls, and n-C10H2J with the fluorocarbon n-CiFlo. Only the first of these systems could be studied in the low-temperature apparatus; the rest were measured in the conventional way: different amounts of the components were weighed into tubes which were then sealed; then Tuwas determined in an ordinary water or oil bath.16 These mole fractions were usually known to k0.005. In general, these reduced solubilities fall roughly on the same curve. A possible explanation for the success of these Munson plots will be offered a t the end of this paper. Numerical values of T , and xc are found in Table V.
Substance
Tb/OK
T/OI
