J. Phys. Chem. 1881, 85, 1457-1460
On the arbitrary plane section, a liquid on the “phase boundary” curve is in equilibrium with a second liquid which is not on the same section. A liquid a t one of the indentations (a, b, c) is in equilibrium with two other liquids, with compositions not on the section. For compositions in the three-phase region (“inside” the points a, b, c) two of the phases approach identity as they approach the limiting line-equilibrium, E for (12 = 4) + 11, F for (I1 = 12)+ l3 Near E or near F, critical opalescence may be expected. Any opalescence observed in sets of two or three coexisting liquids not near E or F would arise from lack of separation of liquid phases because of similar densities.22 The loci of the four-component critical relations are unclear at present. But it is likely that the course of the consolute curves from the plait point for 11-12 (binodal curve on C4H90Hand H20 edge) on Figure 3c will pass through part I of the S-shaped curve of the hump in Figure 5 (and in Figure 4b), and the course of consolute curve from the plait point for l2-I3 (binodal curve A in Figure 3c) will pass through part I1 of the S-shaped curve. The low interfacial tensions (in the range of 0.01 dyn/cm) in these regions, mentioned before, is one indication of a critical point being approached. Whether opalescence seen at compositions near the asymmetrical boundary curve is due to the approach to critical (consolute) relations or due to lack of separation of liquid phases is not certain at present. The loci of the two consolute curves are also not defined, but the loci of consolute curves will affect the direction of tie lines in three dimensions and eventually will affect the shape of the phase boundary curves on certain plane sections in the tetrahedron. Where we see no opalescence and find no
1457
three-liquid-phase equilibria, i.e., in the aqueous-rich region in systems studied here, the size of the one-phase region increases rapidly with increasing SDPBS (or tert-butylbenzoate) concentration owing to the rapid increase of miscibility of toluene and l-butanol in the sulfonate (or benzoate) solution. It would be of interest to elucidate the tie lines of quaternary systems, the loci of the critical points at a number of aqueous concentrations at fixed temperatures, to measure the interfacial tensions between coexisting phases, and to locate “tricritid points”, (if there are any). For a tricritical point to occur, the two consolute curves must meet, an occurrence which appears improbable. It is possible, however, that at some temperature, in one of the arrays of similar systems having asymmetric boundaries on plane sections containing different alkylbenzenesulfonates or -carboxylates and alcohols (and possibly hydrocarbons), such a point may occur. Much additional work would obviously be necessary to establish it, and the results obtained to date are believed to be of enough interest to report as they stand. Acknowledgment. I am very much indebted to Professor John E. Ricci of New York University for many helpful suggestions and discussions and to Dr. J. S. Johnson, Jr., Dr. K. A. Kraus, and Dr. F. Dowel1 of the Oak Ridge National Laboratory Chemistry Division for suggestions, discussions, and encouragement during the writing of this paper. This research was sponsored by the Division of Chemical Sciences, Basic Energy Sciences, US.Department of Energy, under contract W-7405-eng-26 with the Union Carbide Corp.
Transport through Liquid Membranes Generated by Cholesterol R. C. Srivastava” and R. P. S. Jakhar Chemlstty Department, Blrk Instituie of Technology and Scbnce, H&n/-33303 1, RaJasthan, Indb (Received: September 6, 1980; In Final F m : February 9, 198 1)
The experiments on hydraulic permeability, electroosmoticvelocity, streaming potential, and current reported in this communication demonstrate that cholesterol, which is an effective surfactant when added to water, generates a surfactant-layerliquid membrane at the interface. At or above the critical micelle concentration (cmc) of cholesterol, the interface is completely covered with the liquid membrane, while below the critical micelle concentration it is only partially covered. The interface used in the present study was a cellulose acetate microfiitration membrane/water interface. Experiments have also been designed to demonstrate the formation of cholesterol bilayers.
Kesting’s liquid-membrane which was originally propounded to account for the enhanced salt rejection in reverse osmosis due to the addition of surfactant additives to saline feed, has also been shown4to (1)R. E. Kesting, A. Vincent, and J. Eberlin, OSW R and D Report no. 117,Aug 1964. (2)R. E. Kesting, Reverse-Osmosis Process Using Surfactant Feed Additives, OSW Patent Application SAL 830, Nov 3,1965. (3) R. E. Keating, W. J. Subcasky, and J. D. Paton, J. Colloid Interface Sci., 28, 166 (1968). (4)R. C. Srivastava and Saroj Yadav, J. Non-Equilib. Thermodyn., 4,219 (1979). 0022-3654/81/2085-1457$01.25/0
be of significance in the systems of biophysical interest. Cholesterol,though very slightly soluble in water, has been shown6$to lower considerably the surface tension of water. Cholesterol has a maximum s o l ~ b i l i t y ~of* ~4.7 pM in aqueous solutions, and the measured surface tension6 of its saturated solution in water is -33 dyn/cm. Its cmc (5)N. L.Gershfeld in “Methods in Membrane Biology”,Vol. 1,E. D. Korn, Ed., Plenum Press, New York, 1974,Chapter 2. (6)N. L.W e l d and R. E. Pagano, J. Phys. Chem.,76,1244 (1972). (7)M. E.Haberland and J. A. Reynolde,Roc. Natl. Acad. Sci. U.S.A., 70,2313 (1973). (8)M. K. Jain, Curr. Top. Membr. Tramp., 6,l-67 (1975).
0 1981 American Chemical Society
1458
The Journal of Physlcal Chernlstry, Vol. 85, No. 10, 1981
Srlvastava and Jakhar 6.0 5.0
1:
4.0
YI
E v)
2
3.0
X
h'
2.0 1.o
0 0 E2
HEAD
D
814
MERCURY M
2..;i 2 C
py
4.0
60
80
10.0
120
14.0-16.0
16' Figure 2. Hydraulic-permeability data. Curves I-V are for the case when compartment C was filled wlth cholesterol solutions and compartment D with water. Cholesterol concentratlon: (0)0, Q 9.4, (A) 15.04, (n)28.2, (A)30.08, (0)37.6, and (X) 56.4 nM. Curve V I Is for the case when both compartments were filled wlth cholesterol solution of concentratlon equal to Its cmc. AP X
t
12.0 r
NEEDLE
MAGNETIC STIRRER
2.0
10.0
Figure 1. Transport cell: (M)supporting membrane (cellulose acetate Sartorius mllHpore fitter, Cat. No. 11107); (p) b m t platlnum electrodes; (LlL2)capllaty tube of length 0.17 m and diameter 1.37 X lo3 m; (El, E2) electrode terminals.
is in the range7p8of 25-40 nM. All this indicates that cholesterol is a very effective surfactant and is capable of generating a liquid membrane at the interface. The experiments on electroosmotic transport reported in this communication have been undertaken to demonstrate this. The data on hydraulic permeability, electroosmotic velocity, and streaming current have been utilized to establish the existence of the liquid-membrane phenomena in cholesterol. Experiments have also been designed to demonstrate the formation of cholesterol bilayers. Since cholesterol is an important constituent of biomembranes, the study presented here appears relevant.
Experimental Section Cholesterol (Centron Research Laboratories, Bombay) and distilled water distilled once over potassium permanganate in an all-Pyrex-glass still were used in the present experiments. The critical micelle concentration of aqueous cholesterol was determined from the variation of surface tension with Concentration. The surface tensions were measured by using the method of capillary rise and also a Fisher surface tensiomat Model 21. The cmc value thus determined was found to be 30.08 nM. The aqueous solutions of cholesterolwere prepared by using the method described by Gershfeld and Pagano! The necessary weight of cholesterol to attain the desired concentration dissolved in ethanol was added with constant stirring to the aqueous phase. The stirring was continued for several days-always for more than 120 h. In the aqueous solutions of cholesterol thus prepared, the final concentration of ethanol was never allowed to increase 0.1% by volume. It was experimentally found that a 0.1% solution of ethanol in water did not lower the surface tension of water to any measurable extent. The aqueous solutions of cholesterol were prepared and stored in dark-colored bottles to protect them from exposure to light. The all-glass cell designed for the transport studies is diagrammed in Figure 1, which has been well labeled to make it self-explanatory. A Sartorius cellulose acetate
A @ VOLTS
Figure 3. Electroosmotic veloclty data. Curves I-V are for the case when compartment C was filled with cholesterol solutions and compartment D with water. Cholesterol concentratlon: (0)0, (). 9.4, (A) 15.04, (U) 28.2, (A)30.08, (0)37.6, and (X) 56.4 nM. Curves V I Is for the case when both compartments were filled with cholesterol solutlon of concentratlon equal to Its cmc.
microfiltration membrane (Cat. No. 11107) of thickness 1X m and area 2.55 X m2, which in fact acted as a support for the liquid membrane, divided the transport cell (Figure 1) into two compartments. For the measurements of hydraulic permeability, electroosmotic velocity, streaming potential, and current, the two halves, i.e., the compartment C and the compartment D of the transport cell (Figure l),were filled with the solutions of desired concentrations. Since the cmc of aqueous cholesterol solutions is 30.08 nM, the concentration ranges from 0 to 56.4 nM were chosen for the present experiments in order to obtain data on both the lower and the higher side of the cmc of cholesterol. The procedure followed for the measurements was similar to the one described in an earlier publication! The volume flux was measured by noting the rate of advancement of the liquid meniscus in the capillary LILzwith a cathetometer reading up to 0.001 cm and a stopwatch reading up to 0.1 s. The streaming potentials were measured by using a vacuum tube voltmeter (Phillips Model GM 6020/90) reading up to 0.01 mV. Electrical resistances of the system were measured by using a Toshniwal conductivity meter (Model CL 01/02A). Electrical potential differences needed for the electroosmotic velocity mea(9) R. C. Srivastavaand Saroj Yadav, J. Colloid Znterjoce Sci., 69,280
(1979).
Transport through Llquld Membranes
The Journal of Physical Chemlstry, Vol. 85, No. 10, 1981 ?45@
TABLE I: Values of the Phenomenological Coefficients at Various Concentrations of Cholesterol 106L,,,mA J-I 106L,,,mA J-l lOL,,,a - 1m-a concn of cholesterol, nM 108L,,, m 3 N-'s-' 0.08 0.03 0.02 0.03 0.04 0.03 0.01 0.04
5.36 i 0.12 5.36 i 0.03 4.65 f 0.06 4.67 i 0.03 3.99 i 0.03 3.99 i 0.06 2.83 f 0.02 2.85 i 0.04 2.60 f 0.04 2.62 f 0.04 2.63 t 0.04 2.62 f 0.04 2.61 f 0.02 2.59 i 0.01 a 1.70 i 0.03 1.67 i 0.04 Values for the system when both compartments C and D were filled with cholesterol solution of
0.0 9.4 16.04 28.2 30.08 (cmc) 37.6 56.4
4.17 f 3.43 f 3.14 f 2.22 i 2.11 f 2.13 f 2.14 i 1.34 i
2.62 f 2.31 i 2.07 i 1.78 f 1.63 f 1.57 f 1.51 i 1.26 f
0.17 0.14 0.11 0.08 0.07 0.06 0.06 0.04
concentration equal to
ita cmc. L
10.0,
I
I
32.0
0
I 0
2.0
4.0
6.0
8.0
10.0
AP X
16'
12.0
I 14.0
I 16.0
1 18.0 20.0
Nm'
Flgure 5. Streaming current data. Curves I-V are for the case when compartment C was fllled with cholesterol solutions and compartment D wlth water. Cholesterol concentration: (0)0, (). 9.4, (A) 15.04, (0) 28.2, (A)30.08, (0)37.6, and (X) 56.4 nM. Curve VI Is for the case when both compartments were fllled wlth cholesterol solutlon of concentration equal to its cmc.
A P X 16' Nm'
I
Flgve 4. Streaming potential data. Curves I-V are for the case when compartment C was fllled wlth cholesterol solutions and compartment D with water. Cholesterol concentratlon: (0)0, (m) 9.4, (A) 15.04, (0) 28.2, (A)30.08, (0)37.6, and (X) 56.4 nM. Curve VI Is for the case when both compartments were fllled with cholesterol solutlon of concentration equal to Its cmc.
surements were tapped from an electronically operated, stabilized dc power supply (Systronics Type 612). All measurements were made at constant temperature by placing the transport cell (Figure 1)in a thermostat set a t 40 f 0.01 O C .
Results and Discussion The transport data for various concentrations of cholesterol are plotted in Figures 2-5. The straight-line plots are in accordance with the linear equations for hydraulic permeability, electroosmotic velocity, streaming potential, and current derived from the linear phenomenological equationsgJOfor electroosmotic effects, Le., eq 1 and 2, Jv = LllAP + L12A4 (1) I = L21AP + L22A4 (2) where Jv represents the volume flux, I is the flow of electricity, and AP and A4 are the hydrostatic pressure difference and the electrical potential difference, respectively. Values of the various phenomenological coefficients, viz., L11, L12, L21,and LZ2at various concentrations of cholesterol, estimated from the slopes of the straight-line plots in Figures 2-5, are given in Table I. The validity of Onsager's equality (eq 3) for all of the concentrations L12 = L2l (3) of cholesterol is obvious from the values recorded in Table I. ~~
(10) A. Katchahky and Peter F. Curran, "Non-EquilibriumThermodynamics in Biophysics", Harvard University Press, Cambridge, MA, 1967.
2.2
1
L
.0
o
0
9.4
18.8
28.2
37.6
47.0 56.4 6 1.8
CONCENTRATION OF CHOLESTEROL, nM
Flgure 6. Varlatlon of L 11 with the concentration of cholesterol.
Let us now focus attention on the hydradic-permeability data (Figure 2 and Table I). The variation of the coefficient Lll with the concentration of cholesterol has been shown in Figure 6. From Figure 6 it is obvious that, as the concentration of cholesterol increases, the resistance to volume flow also increases in a progressive manner and it is maximum when the concentration of cholesterolequals its critical micelle concentration. If the concentration of cholesterol is increased further, beyond its cmc, the resistance to volume flow does not register any further increase. Although it is, by the way, the nature of the curve in Figure 6 tempts us to suggest that the variation of the phenomenological coefficient with concentration can be exploited for the cmc determination of surfactants. The trend in Figure 6 is in accordance with Kesting's liquidmembrane hypothesis according to which, when a surfactant is added to a solution flowing through a membrane, a surfactant-layer liquid membrane is generated at the interface. As the concentration of the surfactant is increased, the supporting membrane-the cellulose acetate
1480
Srivastava and Jakhar
The Journal of Physical Chemlstry, Vol. 85, No. 10, 1981
microfiltration membrane in the present case-gets progressively covered with the surfactant-layer liquid membrane. At the cmc the supporting membrane is completely covered with the liquid membrane. When the concentration of the surfactant increases beyond the cmc, almost all of the added surfactant remains in the bulk of the solution in the form of micelles and does not go to the interface. This is why the resistance to flow does not increase beyond the cmc of the surfactant. Analysis of the transport data in the light of the mosaic membrane m~del’l-’~ furnishes further evidence in favor of the liquid-membrane hypothesis. For this let us once again focus attention on the hydraulic-permeability data. Utilizing the analysis for mosaic and following the argument given in earlier publication^^^ one can show that the value of the hydraulic permeability coefficient L,, for half the cmc of cholesterol should be where the superscript c represents equal to (LllC+ Lll8))/2, the supporting membrane and the superscript s represents the composite membrane consisting of the supporting membrane and the liquid membrane in series. Functionally Lllc and Llls respectively represent the values of Lll for 0 and the cmc of cholesterol. The value of the coefficient Lll for half the cmc of cholesterol thus estimated comes out to be (3.14f 0.06) X lo4 m3 N-’ s-l, which matches well the experimental value (Table I). Similar considerations apply to the other phenomenological coefficients as well. The transport data obtained in the case when both compartments C and D of the transport cell (Figure 1)were filled with the cholesterol solution of concentration equal to its cmc can be utilized to demonstrate the formation of bilayers of the cholesterol liquid membrane. Since at the cmc the supporting membrane gets completely covered with the liquid membrane, the supporting membrane in this case would be sandwiched between the two layers of the liquid membrane generated on either side of it. In dealing with a situation like this, it is more convenient to utilize the inverse phenomenological equationslObetween thermodynamic forces X and fluxes J , i.e.
xi = XRikJk k
(4)
(11) K. S. Spielger and 0. Kedem, Desalinution, 1,311 (1966). (12) T. K. Sherwood, P. L. T. Brian, and R. E. Fischer, Ind. Eng. Chern. Fundarn., 6 , 2 (1967). (13) F. L.Harris, G. B. Humphrey, and K. S. Spiegler in “Membrane Separation Proceaaea”, P. Meares, Ed., Elsevier, Amaterdam, 1976, Chapter 4.
TABLE 11: Values of the Resistance Coefficients for the Case When Both Compartments o f the Transport Cell Were Filled with Cholesterol Solution of Concentration Eaual to Its Cmc
R,,* x lo-’, m-3N s -R,,* x m-I A-I J -R,,*x m-l A-l J R,,*, n m a
computed values using eq 9
exptl values
7.10 i 0.16 10.33 * 0.31 10.23 * 0.40 8.41 i 0.26
7.47 * 0.23 9.79 i 0.42 9.62i 0.36 7.92 i 0.25
where the resistance coefficients Rib are related to the coefficients Lik by R11 = L22/ILI R12 = -L12/ILI R2l = -L21/ILl (5) R22 = Lll/lLI with PI = LllL22 - L12L21 (6) Utilizing Kedem and Katchalsky’s theory14J6for permeability of composite membranes, one can write the following relationship among the resistance coefficients Rik* for the series composite membrane-the supporting membrane sandwiched between the two layers of the cholesterolliquid membranes and the corresponding resistance coefficiente for the constituent membrane elements: Rjk* = RikC 4- 2Rii (7) The superscripts 1 stands for the liquid membrane. When eq 8 is used eq 7 can be transformed into eq 9. Values of Rik’
= RikC 4- RjL
(8)
= 2Rik’ - RikC (9) the various resistance coefficients Rik* computed from eq Rjk*
9 by using the values of the various phenomenological coefficients Ljk (Table I) are recorded in Table 11. The computed values of Rik* match with the experimental values (Table 11),lending support to the existence of the liquid membrane bilayer-one layer of the liquid membrane on either side of the supporting membrane.
Acknowledgment. Financial support from the Department of Science and Technology, New Delhi, is thankfully acknowledged. (14) 0.Kedem and A. Katchalsky, Trans. Faraday SOC.,59, 1941 (1963). (115) A. Katchalsky and 0. Kedem, Biophys. J. 2, 53 (1962).
