ANOMALOUS OSMOSISTHROUGH CHARGED MEMBRANES
3181
Anomalous Osmosis through Charged Membranes by Masayasu Tasaka, Department of Industrial Chemistry, Faculty of Engineering, Shinshu University, Wakasato, Nagano, Japan
Yozo Kondo, and Mitsuru Nagasawa Department of Synthetic Chemistry, Faculty of Engineering, Nagoya University, Chikusa-ku, Nagoya, Japan (Received October 88, 1968)
The permeation velocities of water and electrolytes through charged membranes made of collodion and sulfonated polystyrene were simultaneously observed as a function of electrolyte concentration. A remarkable anomalous osmosis was observed when the membrane was fairly porous and had a high charge density. It is pointed out that the presence of charges on the membrane matrix should not affect the ordinary osmotic flow of water through the membrane but should affect the permeation velocity of electrolyte. The anomalous osmosis occurs because the permeation velocity of electrolyte and, consequently, the water transport accompanying the electrolyte is affected by membrane potentials apearing on both sides of membrane. It is shown that this idea can quantitatively explain the experimental results.
Introduction Transport of solvent through a membrane occurs if there is a difference in solvent activity on opposite sides of the membrane. The rate of transport of solvent is, in general, proportional to the difference in the chemical potential of the solvent, ie., to the difference in the total concentration of solutes on both sides of the membrane. If the membrane is a so-called charged membrane and the solutes are ions, however, the rate of water transport is often found not to be proportional to the difference in the chemical potential of water, but appears to be accelerated by the presence of charges.’-4 This phenomenon is called anomalous osmosis and has been discussed by many authors. Jn our opinion, the theories dealing with the phenomenon may be classified into three types. Although there are some differences in their details, all theories6-’ of the first type are based on the idea that the electroosmosis caused by the electrostatic potential difference created on both sides of the membrane is superposed on the pure osmotic flow due to the difference in chemical potential of water, so that the effect of charge is to accelerate solvent flow. However, there seems to be no quantitative theory of this type which can explain such remarkable experimental anomalie~.~ I n the theory of the second t y ~ e ,it~is, assumed ~ that the pressure gradient is set up inside the membrane even though the solutions on both sides of the membrane are maintained a t the same pressure and temperature. I n addition to the electrostatic potential gradient, this pressure gradient is assumed t o cause the movement of the local center of mass, that is, to accelerate the flow of solution through membranes. I n this theory, moreover, the interaction between the migrating ions and solvent is neglected or interpreted in terms of the movement of the local center of mass.
I n the third anomalous osmosis was attributed to cross terms in the phenomenological equations for the fluxes. That is, the solvent flow is caused not only by the chemical potential gradient of solvent but also by the chemical potential gradients of solutes. Thus, the observed flow of solvent relative to ordinary osmotic flow may be changed remarkably with velocity of the flow of solute ions if the friction between solvent and ions is high. I n this paper we employ the concept of the third type. The basic idea employed is entirely the same as in the theory of Kedem and K a t ~ h a l s k y . ~However, considering that the comparison between their theory and experiments was not precise enough to eliminate further discussions on this problem, the experiments were planned so that the idea can be accounted for by experiments with less ambiguity. The flow of water due to the friction between water and ions should not be mistaken as hydration water. If an experiment is carried out in a closed cell, only the hydration water can accompany the migrating ions since counter flow of water must occur in the cell. I n an open system as used here, however, much more water must accompany the ions permeating through the membrane due to the friction between water and ions. If this idea is correct, (1) J. Loeb, J . Gen. Physiol., 1, 717 (1919); 2, 173 (1919). (2) F. E. Bartel and D. C. Carpentev, J . Phys. Chem., 27, 101, 252 (1923). (3) E. Grim and K. Sollner, J . Gen. Physiol., 40, 887 (1957). (4) Y. Toyoshima, Y. Kobatake, and H. Fujita, Trans. Faraday Soc., 63,2828 (1967). (5) J. Loeb, J . Gen. Phusiol., 5 , 8 9 (1922). (6) K. Sollner, 2. Elektrochem., 36,36,234 (1930). (7) Y. Kobatake and H. Fujita, Kolloi&Z., 196, 58 (1964) (8) R. Schlogl, Z . Phys. Chem. (Frankfurt am Main), 3 , 7 3 (1955). (9) 0 . Kedem and A. Katchalsky, J . Gen. Physiol., 45, 143 (1961). (10) W. Dorst, A. J. Staverman, and R. Caramama, Rec. Trav. Chim., 83, 1329 (1964).
Volume 79, Number 10 October 1969
M. TASAKA, Y. KONDO,AND M. NAGASAWA
3182 the observed flow of water is the difference between the ordinary osmotic flow of water and the flow of water caused by its hydrodynamic interaction with moving ions. If the membrane is charged, the permeation velocity is markedly decreased due to the effect of membrane potential appearing on both sides of the membrane, so that the observed flow of water may appear to be accelerated by the presence of charges.
La, and Rap,respectively. lLIae and IRlaa are the appropriate cofactors, and 6 is the thickness of the membrane. Eliminating Ap+ and Ap- from eq 3, eq 3a may be recast into the form
+
Jo = AAMO BJ+
+ CJ-
(5)
where
Theory The system considered is a cell in which a charged membrane separates two aqueous solutions of different concentrations (c1 and c2) of an electrolyte. The solutions on both sides of the membrane are maintained a t the same pressure and temperature. The fluxes of water and ions in a membrane relative to the cell are assumed to be expressed by the following linear equations.
J o = Loograd
po
+ Lo+grad p+ + Lo- grad p-
J + = L+ograd PO
+ L++ grad p+ +
Jo
L.+-.grad pJ - = L-o grad
PO
+ L-+ grad p+ + L--
(lb)
grad p(IC)
where p’s are the chemical potentials including con-, and tribution due to external forces, subscripts 0 refer to cation, anion, and water molecules, respectively, J’s the mass fluxes, and L’s are the phenomenological coefficients. Moreover, p’s may be expressed by
+,
Pc
= pi
+ zip+ + vip +
J+
+ Xo+Ap+ + Xo-ApX+oApo + X++Ap+ + X + - W -
= XooApo =
J - = X-oApo
+ X-+Ap+ + h--Ap-
As is clear from its definition, Loois proportional to the concentration of water which may approximately be treated as a constant independent of electrolyte concentration. Therefore, roo, i.e., A may also be almost independent of concentration and both B and C may be given by
(2)
where xi and vi are the valence and partial molar volume of component i, respectively, the electrical potential, P the pressure, and F is the Faraday constant. By solving eq 1 for the forces and integrating them from one side of the membrane to the other keeping the flux constant, we obtain1’
Jo
dx
(la)
(34
(3b)
if L+- and L-+ are negligible as can be e x p e ~ t e d . ~ Since Lo+/L++(or Lo-/L--) is the ratio of the flux of cation (or anion) to that of water caused by the force exerting on the cation molecules, it is reasonable to assume that the ratio, that is, B and C are almost independent of concentration. In the theory of Kedem Ro+,and Ro- are and K a t ~ h a l s k y the , ~ coefficients ROO, given by (see eq 7-6 of ref 2)
(3~)
where A shows the differences between two fluid phases on both sides of the membrane and hnaisthe permeability coefficient of the membrane of finite thickness. A,, is a matrix which is related to the matrix La, as
where ci and fi0 are the concentrat’ion and frictional coefficient of the ith component in water, respectively, and fom is the frictional coefficient between water and membrane matrix. If the second term is negligible where ILI and IRl are the determinants of the matrix The Journal of Physical C h m i s t r y
(11) J. G. Kirkwood, “Ion Transport across Membranes,” H. T. Clarke, Ed., Academic Press, Inc., New York, N. Y., 1954, p 119.
ANOMALOUS OS~IOSIS THROUGH CHARGED MEMBRANES compared with the first term on the right side of eq 8a, all Roo,Ro+,and Rob, Le., A , B, and C may be assumed to be almost independent of electrolyte concentration. I n electrolyte solution systems with no membrane, the concentration dependence of the frictional coefficients Rapwas well discussed by Miller.1z I n his paper, too, it is pointed out that Rooshould not be concentration dependent and also Ro+ and Ro- would be relatively concentration independent. Although it was found that Roo depends on the concentration, while the others do not, in the system without membrane i t may be reasonable to assume the concentration independence of all these coefficients to be compared with experiments in the membrane-electrolyte system. It will be seen that the assumption causes no contradiction in the comparison between theory and experiments in the membrane-electrolyte system. Here, it is to be noted that all coefficients A , B, and C have positive signs, whereas J+ and J - generally have the opposite signs to Apo and also that J + = J - = J , if there is no externally applied electric field. Therefore, if the coefficients B and C are large, the observed velocity J o may occur in the opposite direction to Apo; in other words, the negative osmosis may occur simply because of the high friction between ions and water. Apo may be transformed into13
(9 ‘> where AT is the osmotic pressure difference, v the number of moles of ions forming 1 mole of the electrolyte, Wothe molecular weight of solvent, the molal osmotic coefficient, and y = cz/cl. The coefficients B and C may be determined from electroosmotic coefficients under an applied electric field as explained below. Thus, if we calculate the following quantity, Joo, from the experimental values of J Oand J,, log J o o must be linear to log c1 with the slope of unity
+
Jo0
Jo - ( B
+ C)J,
(10)
( = A APO)
From the intercept at log c1 = 0, we can calculate the value of A which may roughly be compared with the permeability coefficient of solution through the membrane under applied hydrostatic pressure. Moreover, the intercept must be determined by membrane but independent of ion species used. If the ratio of electrolyte concentration (y = CI/CZ) is changed, the difference in the intercept must be equal to the difference in log (y - 1). Strictly speaking, AT or Apo is not proportional to (cz - cl) but the nonproportionality is minor in a logarithmic plot.
3183 Since the total electric current I is the sum of xlFJ such as I = x+FJ+ x-FJ(11) the value of Jo/(I/F) at Apo = 0 is given by
+
B
C
= - t + + - t -x AP = 0
x+
(12)
Aclo = 0
where tais the transference number of ith ion, i.e.
Aceo = 0
If the membrane is an ideal cation-exchange membrane, that is, if the transference number of anion (i.e., co-ion for the cation exchange membrane) is negligible, the coefficient B can be obtained from electroosmotic experiments carried out in an electrolyte solution without concentration difference.
J- = 0
If the electrolyte used is KCI, it may be reasonable to assume B K C= Ccl- since both ions have the same hydrodynamic radius. It may be further assumed that C a - thus determined for KC1 can be used for other salts, so long as the same membrane is used. Since the membrane-fixed frame of reference is used in the above discussion, the symmetry condition may be one of the disputed points among researchers.‘4-’* However, it may now be concluded that the phenomenological coefficients are practically symmetrical even when the fluxes are written relative to the membrane as in eq 1. At least in the present paper, the symmetry condition need not be used. Experimental Section Membranes. The membranes used in this work were collodion-sulfonated polystyrene interpolymer membranes which were prepared by the same method as N e i h o f ’ ~ , The ~ ~ membrane C-1 was dried for 3 hr (12) D. G. Miller, J . Phys. Chem., 70, 2639 (1966). (13) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” 2nd Ed., Butterworth and Co., Ltd., London, 1959, p 29. (14) R. Schlogl, Discussions Faraday Xoc., 21,46 (1956). (15) J. G. Kirkwood, R. L. Baldwin, P. J. Dunlop, L. G. Gosting, and G. Kegeles, J . Chem. Phys., 33, 1605 (1960). (16) D. D. Fitts, “Nonequilibrium Thermodynamics,” McGraw-Hill Book Co., Inc., New York, N. Y., 1962. (17). S. R. de Groot and P. Maaur, “Non-Equilibrium Thermodynamics,” North-Holland Publishing Co., Amsterdam, 1962. (18) D. C. Mikulecky and S. R. Caplan, J . Phys. Chem., 70, 3049 (1966). (19) R. Neihof, ibid., 58,916 (1954). Volume 73, Number 10 October 1.980
M. TABAKA, Y. KONDO,AND M. NAGASAWA
3184 by evaporating the solvent slowly in a loosely closed box, while the membrane C-2 was dried for 3 days at the same conditions and then dried up for 1 day at 13 mm pressure. An untreated collodion membrane C-3, which was dried a t the same conditions as C-1, was also used for comparison. The characteristics of these membranes are listed in Table I. The changes
I
I
I
Table I : Properties of the Collodion-Base Membranes
Membrane
c-1 c-2 c-3
Wt % of polystyrene sulfonic Time for acid drying, hr
3.8 43.5 0
3 96 3
Thickness, mm
Capacity, Water content mequiv/g g of water/ g of dry of dry membrane membrane
0.4
I ' 10'~
I
10-2
I
10-1
1
Concn, mol/kg of H,O.
0.30 0.15 0.30
0.253 1.24
...
1.96 0.975 1.76
Figure 1. The dependence of t,ransference number on electrolyte concentration for membranes C-1, C-2, and C-3. C-1: A, KCI; B, NaCI; C, LiCl; C-2: D, KC1; C-3: E, KCI.
in transference number of cation t+ in these membranes with salt concentration are shown in Figure 1. They were calculated from membrane potentials A$ using the approximate equation
where ~ ~ ( and 1 ) ~ ~ ( are 2 )the mean activities of salt on both sides of the membrane. The transference number at each concentration was determined by extrapolating the values obtained at various values of a+(2)/ a&) to ak(2)/ak(l) = 1, keeping ~ ~ ( constant.20 2 ) The other characteristics of the membranes as listed in Table I are not used in the present paper and, hence, the methods to determine them will be described in a separate paper. Measurements of Water Transport (Jo). Figure 2 shows a schematic diagram of the apparatus used, which is made of poly(methy1 methacrylate) resin. The membrane was supported by a plastic support. The inner cell was filled with a salt solution of the lower concentration ( c l ) , and immersed in a solution of the higher concentration (cz). A heater and a cooler were inserted in the latter solution to regulate the temperature of the whole apparatus at 25 f 0.05'. A pair of platinized platinum electrodes was inserted into the inner cell in order to measure the change in concentration of electrolyte. To equilibrate the membrane with the electrolyte solutions, fresh electrolyte solution was circulated in the inner cell before starting measurements. The rate of volume flow was determined from movement of the liquid meniscus in the capillary. The rate of water transport, expressed in mol cm-2 min-I, was calculated from the rate of volume flow neglecting the volume of ions contained. Measurements of Permeation Velocity of Electrolyte (J,). The increase of electrolyte concentration in the inner cell was followed by measuring the conductivity The Journal of Physical Chemistry
WMS
Figure 2. The apparatus for measurement of anomalous osmosis: B, bottle for adjusting the head difference; C, cooler; CT, capillary tube; E: electrode; F: feeding bottle; M: membrane; MS: magnetic stirrer; S: stirrer; T: magnetic stirrer tip.
of the solution using a Wagner bridge. The measurements of permeation velocities of both water and electrolyte were carried out simultaneously. It was confirmed that the results of Jo and J , obtained are independent of stirring speeds. Measurement of Electroosmosis. The measurements of electroosmosis were carried out in a cell made of two equal compartments divided by the same membrane, which is similar to the cell used by Mackay and MearesSz1 Each compartment contained a silver-silver chloride electrode and the calibrated capillary which was set horizontally not to cause a head difference between solutions. The electric current density supplied was 0.25 mA cm-2 and the temperature was about 25 f 0.1". The independence of the volume flow per unit current on the current density was roughly confirmed since (20) Y. O d a and T. Y a w a t a y a , Bull. Chern. SOC.Jap., 29,673 (1956). (21) D.Mackay and P. Meares, Trans. Faraday SOC.,55,1221 (1959).
ANOMALOUS OSMOSIS THROUGH
3185
CHARGED MEhlBRANES
the problem was well studied by Carr, et a1.,2* and Kobatake, et aLZ3 Determination of Hydraulic Permeability. In order to cause the flow of solution through the membrane, a constant hydrostatic pressure difference is maintained across the membrane which is set in the same cell as is used for electroosmosis.
60
0
.
.P
- E o -40
- 0
v)
- 3
? !.
E
6
z
20
o
0
10
20
30
Time, min.
Results Velocity of Water Transport (Jo). Examples of the movement of the liquid meniscus in the capillary with time are shown in Figure 3. The velocity of water transport, expressed by mol cm-2 min-’, can easily be calculated from the slope, neglecting the occupied volume of ions. The velocities of water transport thus obtained for membranes C-1 and C-2 in solutions of KCl with various ratios of concentration ( y = CZ/CI) are shown in Figure 4. I n Figure 5 are shown examples of the data for membrane C-1 in solutions of various electrolytes. These experimental data, which are similar to the data for oxidized collodion membranes reported by Sollner, et al.,a and by Toyoshima, et al.,4 clearly show the features of anomalous osmosis, i.e., the N-shape dependence of Jo on the logarithmic concentration of electrolyte. I n solutions of NaCl and LiCI, the so-called negative osmosis is observed. It is observed that the membrane having a higher charge density shows the maximum and minimum at higher salt concentrations than the membrane having a lower charge density. I n Figure 5, the data for C-3 which does not show anomalous osmosis because of the low charge density of the membrane are also shown for comparison with the data for C-1. Permeation Velocity of Electrolyte. Examples of the change in the conductance of solution inside the inner cell with time are shown in Figure 6. The permeation velocity of electrolyte, J,, can be calculated from the slope as mol ern+ min-l. To show the features of electrolyte permeation through charged membranes, the data of J , were converted to the permeation coefficient of electrolyte by the equation Ps = J s / ( c z
- c1)
(16)
The results obtained for membranes C-1, C-2, and C-3 in solutions of KC1, NaCl, and LiCl with various ratios of cz/c1 are summarized in Figures 7 and 8. The features of the graph are also similar to the data of Toyoshima, et alaz4 It is observed that the membrane which has a higher charge density shows a sharp drop in P, a t a higher salt concentration than that having a lower charge density. The drop in Ps is caused by the effect of membrane potential created on both sides of the membrane. Our discussion on the permeation coefficient of electrolyte will be given in a separate paper. It should be noted that the concentration for the sharp drop of P, agrees with the inflection point of J oin Figures 4 and 5 .
Figure 3. Examples of the movement of the liquid meniscus in the capillary, with a concentration difference between the sides of the membrane, with time. The effective area of membrane is 19.63 cm2; the cross section of capillary is 0.0168 cm2; membrane, C-1; electrolyte, KC1; cl/cz: A, 0.0004 m/0.0064 m ; B, 0.0008 m/0.0064 m; C, 0.0016 m / 0.0064 m ; D, 0.0032 m/0.0064 m. 20 I
I
I
I
io+
10-3
I
lo-’
1
KCI concn c,, mol/kg of HZO.
Figure 4. Solvent flow through membranes C-1 and C-2: electrolyte, KCl; C-I: A, y = 2; B, = 4; C, = 8; D, y = 16; (2-2: E, y = 2; F, y 4; G, y = 8.
-5
’ io-4
I
I
I
10-~ IO-* to-’ Concn c,, mol/kg of H20.
1
Figure 5. Examples of solvent flow through membranes in solutions of various electrolytes: y, 8; C-I: A, KCl; B, NaC1; C, LiC1; C-3: D, KC1. Experiments a t y = 2 and 4 are similar.
Electroosmosis. The movement of the liquid meniscus in the capillary with time is quite similar to those (22) C. W.Carr, R. McClintock, and K. Sollner, J . Electrochem. SOC., 109, 251 (1962). (23) Y. Kobatake, M.Yuasa, and H. Fujita, J.Phys. Chem., 72, 1752 (1968). (24) Y. Toyoshima, Y.Kobatake, and H. Fujita, Trans. Faraday SOC., 63,2814(1967).
Volume 73, Number 10 October 1969
R4. TASAKA, Y . KONDO, AND M. NAGASAWA
3186 r
10001
r *
1.17 1.15
5
LL
X
1.13 1.11 C
0"
8
r
C
o
c
m
5
r
-
0 0
Time, min.
,
I
I
I
I
50 0
0.4
Figure 6. Examples of the change in conductance of the solution inside the inner cell with time. The volume of inner cell is 112.0 cm8; the effective area of membrane is 19.63 cmz; membrane, C-1 ; electrolyte, KCl; c1/c2: A, 0.0004 m/0.0064 m ; B, 0.0032 m/0.0064 m.
,
0.5 0.6 0.7 0.8 0.9 1.0 Transference number, t,.
Figure 9. Moles of water transported per Faraday against transference number. Membrane, C-1 ; A, KCl; B, NaCl; C, LiCl.
and C determined for KC1, NaCl, and LiCl are listed in Table 11. It is t o be noted that these values are changed with membrane since the friction between membrane matrix and water is not negligible and the amount of water inside the membrane is limited. Table 11: The Values of B and C for KC1, NaCl, arid LiCl Membrane
C- 1
c-1 c-1 a"*
c-2
KCI concn c,, mol/kg of H20.
t
Figure 7. Permeability coefficient of KC1 for membranes C-1 and C-2. C-1: A, y = 2; B, y = 4; C, y = 8; D, 4; G, y = 8. */ = 16; C-2: E, y = 2; F, y
$.I %
,
I
I
I
B+C
Electrolyte
1.10 x 103 1.30 x 103 1.48 x 103 0.12 x 108
KC1 NaCl LiCl KC1
Permeation Coeflcient of Solution under Applied Hydrostatic Pressure. The movement of the liquid meniscus in the capillary with time is quite similar to that in electroosmosis. If we plot J o (mol min-I) against the applied hydrostatic pressure difference AP (dyn cm-2), we can have Figure 10. From the slope we can calculate the permeation coefficient A' by the equation Jo
=
A'AP
(17)
where A' is nearly equal t o Avo (see eq 5 and 9). The values of permeation coefficients for three membranes in solutions of KC1, A'/vo, are listed in Table 111. 0'
IO-^
, IO-^
I
IO-^
IO-'
1
Concn c,, rnol/kg of HzO. Figure 8. Examples of permeability coefficients of various electrolytes. y, 8; C-1: A, KCl; B, NaCl; C, LiCl; C-3: D, KCl. Experiments a t y = 2 and 4 are similar.
in Figure 3. From the slope and the electric current density used, we can calculate Jo/(I/F) by the unit of mol cm-2 min-l. If we plot J o / ( I / F ) thus obtained against the transference number t+ shown in Figure 1, we can have Figure 9, in which the value of J o / ( I / F ) a t t+ = 1 gives B. For KC1, B = C can safely be assumed since J o / ( I / F ) = 0 a t t+ = 0.5, as was discussed in the theoretical section. The values of B The Journal of Physical Chemistry
Comparison between Theory and Experimental Results From the values of ( B C) listed in Table I1 and the values of J o and P, shown in Figures 4, 5, 7, and 8,
+
Table 111: Permeation Coefficient A' (mol dyn-1 min-l) and Coefficient A (mol2 erg-' om-2 min-l) Membrane
C-1 c-2 C-3 Ratio(C-l/C-3) Ratio(C-l/C-3)
__-A'/vo---0.001 m KC1 1 . 6 x lo-" 1 . 2 x 10-12 2 . 2 x 10-11 12.7 0.7
1 m KC1
A
3 . 1 X lo-" 3 . 5 x 10-12 2.2 X 10-11 8.7 1.4
1.8 X lo-" 2 . 1 x 10-12 2.6 X 8.6 0.7
CHARGEDMEMBRANES
ANOMALOUS OSMOSIBTHROUGH I
I
I
I
3187
I
lo-' r
C ._
,E 10-2 6 g IO-^ \-
g
-
10-~
L
+
5 10-5 v)
I
IO-^
"
0 2 4 6 8 10 Hydrostatic pressure difference AP x dyn cm-2.
Figure 10. Hydraulic permeations through membranes. C-1: A, 0.001 m KCl; B, 1m KCl; C-2: C, 0,001 m KCl; D, 1 m KCI; C-3: E (a), 0.001 m KC1; F ( 0 ) ,1m KC1.
I
10-
I
IO-'
I
1
KCI concn c,, mol/kg o f H,O.
+
Figure 12. The dependence of Jo"(Le., JO - ( B C) J,) on concentration of KC1 for membranes C-2 and C-3. C-2: A, y = 2 ; B, y = 4; C, y = 8; A*, the dependence of Jo on concentration of KCl a t y = 2; C-3: D, = 2; E, y = 4; F, y = 8.
and NaCl solutions occurs because of large values of (B C) for these salts. (2) The difference in the ordinates of the lines in Figures 11 and 12 is found to be equal to the difference in log (y - 1). In practice, the lines in the figures are drawn with the differences in log (y - 1). (3) Since the porosities and thicknesses of membranes C-1 and C-3 are almost equal (though those of C-1 vary with salt concentration), it is expected that J o O for both membranes at the same y must be almost equal, independently of the concentration ratio y. This prediction is well satisfied by the data in Figures 11and 12 for all values of y. Strictly speaking, the ratio is found to be 0.7, which is almost equal to the ratio of the permeation coefficients of both membranes shown in Table 111. (4) One of the most important experimental results reported here is the comparison between the data for membranes of two different charge densities. I n Figure 4,the flow of water through membrane C-1 appears to be more accelerated by the presence of charge than that through membrane C-2, despite the fact that the charge density of membrane C-2 is much higher than the charge density of membrane C-1. This is because the permeation of electrolyte is more effectively slowed by the membrane potential of membrane C-2 than of membrane C-1. The pure osmosis of water, Joe, through membrane C-1 must be much higher than Joothrough membrane C-2 because of the high porosity of C-1. Comparison between the data for C-1 in Figure 11 and the data for C-2 in Figure 12 shows that the ratio of JOo for these membranes is 8.6/1.0 and the ratio is independent of the electrolyte concentration ratio y, as expected. This ratio may be favorably compared with the ratio of the permeation coefficients through the membranes under applied hydrostatic pressure difference which are shown in Table 111. Moreover, not only the ratio
+
10-6
I
I
I
10-~ io+ IO-' Concn cl, rnol/kg o f H,O.
I
+
Figure 11. The dependence of Jo" (Le,, JO - ( B C)J,) on concentration of various electrolytes for membrane C-1. A: y = 2; 6, KCl; 0-, NaCI, -0, LiCl. B: y = 4; d, KC1; 0-, NaC1, -0, LiC1. C: y = 8; d), KC1; O-, NaC1, 4, LiCl. D: y = 16; 0 , KC1. A*, the dependence of JOon concentration of KC1 a t y = 2.
+
we can calculate log [Jo - ( B C ) J , ] , i e . , logJoo to plot against log Apo, L e . , log c1. The caIculated results are shown in Figures 11and 12. All the plots are found to be linear with respect to log CI with a slope of approximately unity, as expected from the theory. Since the osmotic coefficient or the activity coefficient of the electrolyte in solution and the change in swelling of the membrane with electrolyte concentration are neglected, the deviations of the experimental data from the theoretical lines in Figure 11 are insignificant. All other predictions of the theory are well fulfilled by the experimental results. (1) The value of A is independent of the salt species used (see Figure 11). Therefore, it is clear that the negative osmosis in LiCl
Volume 73, Number 10 October 1960
3188 but also the absolute values of A determined from Figures 11 and 12 roughly agree with the values of A’/vo, as shown in Table 111. Since the hydraulic permeation coefficient is affected not only by swelling of the membrane but also by the streaming potential which appears on both sides of the membrane, it is understandable that A’ varies with salt concentration for C-1 and C-2 and, hence, we cannot expect perfect agreement between A and A’/vo.
Discussion In Figure 9, it is observed that J o / ( I / F ) is not linear with respect to t+, in disagreement with eq 12’. This disagreement may arise from the fact that in the theory all diffusible ions are assumed to distribute uniformly in the membrane, whereas in actual membranes the distribution is not uniform except a t low ionic strength. The effects of most cations and anions on the solvent flow must cancel each other in electroosmosis and only the water flow caused by the electric forces acting on the counterions dissociated from the membrane can be observed. These counterions are strongly attracted around fixed charges forming ionic atmospheres at high ionic strength, so that the amount of water accompanying a counterion may decrease as the ionic strength increases. Since the ions which contribute to anomElr lous osmosis must be all ions in the membrane which are believed to distribute almost uniformly in the membrane, the value of B should not be estimated from the
The Journal of Physical Chemistry
M. TASAKA, Y. KONDO, AND M. NAGASAWA dependence of J o / ( I / F ) on t+. However, the conclusion obtained in this paper is not so sensitive to the value of B used. Even if we use the value of B estimated from the dependence of J o / ( I / F ) on t+ in Figure 10, the conclusion need not be changed. I n the present experimental results, it is noticed that the effect of migrating ions on the water flow is really large. Some similar experimental results are found in the l i t e r a t ~ r e . ~It~ ’may ~ ~ be pointed out that the anomalous osmosis is observed for the membranes in which the amount of water accompanying the migrating ions is really large. Thus, in agreement with some previous ~ o r k e r s , ~ ~ ~ ~ we conclude that the so-called anomalous osmosis through charged membranes can be explained by taking into account the cross terms in the phenomenological equations for the fluxes. The charge of a membrane does not affect the velocity of pure osmosis (Le., transport of water due to the difference in chemical potential of water) but simply affects the permeation velocity of electrolyte. If the membrane is charged, the permeation velocity of electrolyte is decreased by the effect of charge so that the flow of water may appear to be accelerated by the charge effect.
Acknowledgment. We wish to thank Professor Y. Kobatake for his helpful discussion and Mr. Y. Koau for his technical assistance in measuring the membrane potential.
