J. H. B. GEORGE AND R. A. COURANT
246
Conductance and Water Transfer in a Leached Cation-Exchange Membrane
by J. H. B. George and R. A. Courant Arthur D. Little, Inc., Cambridge, Massachusetts
(Received March 11, 1966)
Specific conductance and water transfer have been determined for a variety of cations in a polystyrene-sulfonate cation-exchange membrane substantially free of eo-ions. The measurements were made at three temperatures, 10, 25, and 40°,and equivalent conductances and energies of activation for conduction were calculated. Xot surprisingly, it was found that equivalent conductances in the membrane are lower than in free aqueous solution, the difference being much greater for multivalent ions. Among ions of a given class, such as the alkali metals or alkaline earths, the equivalent conductances go through a maximum with increasing atomic number instead of increasing continuously as in free solution. The corresponding activation energies show a minimum. This behavior is interpreted as being due to a balance between increased mobility as the hydration of the cation decreases and an increased degree of ion association with the exchange groups of the membrane. Water transfer per equivalent of charge decreases as the charge on the cation increases although it is nearly constant per mole of ions transferred. It is little affected by temperature but increases markedly at very low current densities. This latter phenomenon may be due to utilization of only the larger pores in the membrane.
Introduction Ion-exchange membranes have some interesting characteristics as electrolytically conductive systems. When they are in equilibrium with sufficiently dilute solutions (generally 0.01 N and lower), virtually all the mobile ions are of one sign, and values for the equivalent conductlance of the counterions can be derived directly from the experimental data. Another feature is the transport of water which accompanies the passage of ions through the membrane, caused partly by ionic hydration and partly by electroosmotic transfer. A comparison of the observed conductances of ions in membranes and in free aqueous solution shows, not surprisingly, that ions are much less conductive in membranes. Part of this is clearly due to the obstructive effect of the polymer chains of the membrane, and Despic and Hills' and Meares2J have employed expressions involving the volume fraction of the resin in the membrane to estimate its magnitude. The most remarkable feature of membrane conductances, however, is the wide differences shown by ions according to their charge type. While the equivalent conductances of the majority of monovalent, divalent, and trivalent cations in free aqueous solution are equal to within The Journal of Physieal Chemietry
l0-20% or so, very large differences are observed in the membrane phase. Thus Rosenberg, George, and Potter4 found values of 12.5, 2.7, and 0.7, respectively, for the equivalent conductances of potassium, barium, and lanthanum in a polystyrene-sulfonate membrane. The objective of the present work was to study the conductance and water transfer accompanying the transport of a wide variety of ion species through a single cation exchange membrane in order to characterize their dependence on ion size and charge type. All measurements were made with the membrane in equilibrium with solutions sufficiently dilute, 0.01 N , so that the counterions were the only conductive species in the membrane and at three temperatures, 10, 25, and 40°, in order that activation energies might be calculated for the conduction processes.
~
~
~~
(1) A. Despic and G . J. Hills, Discussions F a r a d a y Soc., 21, 150 (1956).
(2) J. S. Mackie and P. Meares, Proc. R o y . SOC.(London), A232, 485, 498 (1955). (3).'l Meares, J. Polymer Sei., 20, 507 (1956). (4) N. W. Rosenberg, J. H . B. George, and W.D. Potter, J . Electrochem. Soc., 104, 111 (1957).
CONDUCTANCE AND WATERTRANSFER IN A CATION-EXCHANGE MEMBRANE
Experimental Procedures The cation-exchange membrane selected for the transport measurements was the commercially available Nepton CR-61, Type AZL 183, and was supplied by Ionics, Inc., Watertown, Mass. The CR-61 family of membranes has a polystyrene base and sulfonate exchange groups. Individual members vary in the degree of cross-linking with divinylbenzene. The particular membrane selected had a high divinylbenzene content, approximately 40%, and was prepared by techniques described in the patent literature.6 The membranes are light yellow, approximately 0.07 cm thick, and are supported on an inert backing (in this case a loosely woven Dyne1 cloth). Conversion of the membrane to the various ionic forms was carried out by repeated equilibration with approximately 2 N solutions of the appropriate chloride or nitrate followed by thorough washing with deionized water to remove absorbed electrolyte. For certain costly chemicals, the conversion was carried out electrolytically by containing the solution on one side of the membrane and passing a small current through it. I1 was found that passage of a quantity of electricity equivalent to twice the capacity of the membrane sample was generally sufficient to ensure complete conversion. Before its conductivity and water transfer were measured, the membrane was characterized for capacity, water content, and specific volume by standard methodse6 Conductance Measurements. The conductance measurements were made in a lucite cell consisting of two equivalent electrode sections fitting closely into a cylindrical sleeve. Circular platinized platinum electrodes parallel to the plane of the membrane were embedded in each section and slightly recessed so that neither was in contact with the membrane. The shoulders of the sections fitted closely together, keeping the electrodes at a constant distance from each other (approximately 0.4 cm) when no membrane was present. The diameter of the electrodes and thus of the exposed membrane sample was approximately 1.0 cm. Resistance measurements were made with and without the membrane in a 0.01 N solution of the chloride or nitrate of the ion under investigation. According to the analysis of' Barrer, Barrie, and Rogers,' refraction of the lines of current flow would cause a lowering in the apparent resistance of the order of 4% in a conductance cell with these dimensions. The actual experimental results were not, however, corrected for this effect. The conductance determinations were made with a Campbell-Shackleton bridge which has been described
247
elsewhere.8 Temperature control was attained by use of oil baths, the temperature of which was observed never to deviate from the set value by more than 0.02" at 25" and 0.05" at 10 and 40". A plastic bag was placed around the cell to prevent the cell and its contents from being contaminated by oil from the bath. The effect of frequency on the experimentally determined membrane conductances was investigated. With sodium ions in the membrane the conductance rose gradually by about 7% as the frequency was increased from 60 to 1000 cps. It subsequently remained almost constant as the frequency was further increased to 10,OOO cps and gradually fell by about 2-3010 between 10,OOO and 50,000 cps. Since the effect of frequency thus appeared to be small, 1000 cps was used as the standard for all measurements. The precision of this technique for the measurement of ionic conductivity in the membrane improved with an increase in membrane resistance. For the less conductive multivalent ions the spread in experimental values among half a dozen samples was never greater than about *3%. For the more conductive monovalent ions, the spread was somewhat greater, on the Nonuniformity of the membrane order of *5%. samples is believed to account for the lack of greater precision. Water-TransferMeasurements. Water- transfer measurements were made in a two-compartment Lucite apparatus-the donating chamber, which was stirred vigorously, having a volume of approximately 750 ml, and the receiving chamber, having a volume of approximately 100 ml. A circular sample of membrane, with a diameter of 7 cm, separated the two compartments and WM prevented from buckling by perforated Lucite sheets. The exposed membrane area was 12.5 em2. Volume changes were determined by observing with a cathetometer the liquid level in a glass capillary leading from the smaller chamber. A current of 2.5 ma was passed between large, flat silver-silver chloride electrodes giving a current density of 0.2 ma/cm2 of exposed membrane surface. The correction for change in volume at the electrodes was too small to be significant. All measurements were carried out in constant-temperature oil baths and as an additional check on the constancy of the temperature, a platinumplatinum-rhodium thermocouple was immersed in the (5) J. T. Clarke (Ionics, Inc.), U.8.Patents 2,730,768 and 2,731,411 (1956). (6) F . Helfferioh, "Ion Exchange," McGraw-Hill Book Co., Inc., New York, N. Y., 1962, Chapter 4. (7) R. M. Barrer, J. A. Barrie, and M. G. Rogers, Trans. Faraday Soc., 58, 2473 (1962). (8) R. A. Home and G. R. Frysinger, J. Geophys. Res., 68, 1967 (1963).
Volume 71, Number 8 January 1067
J. H. B. GEORGE AND R. A. COURANT
248
Table I : Membrane Equivalent Conductancea, Activation Energies, and Water Transfer Ionic form of membrane
Li + Na + K+ Rb
cs
+
NH,
+
T1+ Mgz CaZf Sr2+ BaZ + La8
+
+
Am,, cm2 ohm-1 equiv-1
kUl/AP
250
25'
Membrane
2.19 2.82 5.31 3.81 1.86 5.32 3.04 0,689 0.989 0.844 0.749 0.219
0.057 0.058 0.072 0.049 0.019 0.072 0.041 0.013 0.016 0.014 0.012 0.003
5.46 5.39 3.69 4.09 4.15 4.69 4.73 4.87 4.46 4.82 4.80 4.00
E., k c a l / m o l e - - - - - - - - - - , Soln at infinite dilutionD Difference
4.13 3.87 3.47 3.38 3.33 3.86
+1.33 +1.52 +0.22 f0.71 +0.82 +0.83
3.92 3.92 4.04 4.23 4.64
f0.95 +0.54 f O . 78 +0.57 -0.64
...
...
---Water 100
20.6 13.3 10.7 7.9 8.9 14.4 16.4 5.5 7.2 6.3 5.4 3.9
transfer,* mole/faraday--25a 40'
19.6 14.0 10.1 7.7 8.5 12.5 11.5 3.4 6.8 4.8 4.5 2.3
17.1 13.8 9.7 8.1 6.6 14.8 6.4 2.5 6.4 3.2 3.1 2.0
Values for A0 and its temperature coefficient taken from R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd ed, ButterAt 0.2 ma/cmz. worth and Co., Ltd., London, 1959.
'
The capacity of the Nepton CR-61 membrane was found to be2.45 mequiv/g and 1.77 mequiv/ml of surface dried membrane. These figures include the Dyne1 backing mat!erial, reported by the manufacturer to constitute about 36% of the weight of the completely dry membrane. Capacity determinations in various ionic forms differed by less than 2%. Water content data, expressed as a weight percentage of water in the wet membrane (surface dried and including backing), were: Li+, 36.9; Na+, 36.4; K+, 35.7; Rb+, 32.2; CS+, 32.7; NH4+, 36.0; T1+, 37.8; Mg2+, 35.5; Ca2+,35.2; Sr2+,32.8; La3+,32.5. The results of the conductivity measurements, expressed as equivalent conductances X, at 25" and energies of activation E , calculated from the temperature coefficients, are shown in Table I. Over the limited temperature range, 10-40", the Arrhenius plots showed little deviation from linearity. Ratios of Am to XO, the limiting equivalent conductances of the ions in free aqueous solut,ion, and values of Ea calculated from the temperature coefficients of Xo are also included. Table I also contains the results of the water-transfer measurements a t 10, 25, and 40" expressed as mole/ faraday .
For example, the values of A, at 25" for the monovalent ions vary from 1.86 for cesium to 5.32 for ammonium; the values for the bivalent ions, which are much more similar, range from 0.69 for magnesium to 0.99 for calcium while the value for lanthanum, the only trivalent ion studied, is as low as 0.22. Values of Xo for all these ions fall in the range from 38.7 for lithium to 77.8 for rubidium and are not directly related to charge type. It thus appears that Xm/Xo decreases by a factor of about 4 for each unit increase in the charge of the ion. These data are generally similar to earlier results obtained by Manecke and Otto-Laupenmuhleng for a phenol-formaldehyde-based sulfonate membrane. The work of Spiegler and Coryell'O and of Grubb" also showed marked differences in A,, between alkali metal cations and ions of bivalent metals such as zinc, calcium, and copper in membranes of this type. Consideration of the values of X, for the monovalent ions separately leads to some interesting observations. Values increase from lithium through sodium to potassium, but then decrease to rubidium and cesium. This behavior contrasts with that in free aqueous solution where Xo increases monotonically from lithium to cesium. The behavior in solution is interpreted as being due to the decrease in hydration as the crystallographic radius of the cation increases. In the membrane phase, ion hydration is likely to be lower than in solution because of the more limited supply of water.
Discussion The results of the conductance measurements expressed in Table I show very clearly the effect of ionic charge on the mobility of ions in the membrane.
(9) G. Manecke and E. Otto-Laupenmilhlen, 2. Physik. Chem. (Frankfurt), 2, 336 (1954). (10) K. S. Spiegler and C. D. Coryell, J . Phys. Chem., 57, 687 ( 1953). (11) W.T. Grubb, ibid., 6 3 , 5 5 (1959).
receiving chamber. Even so, the precision in the experimental values, some half dozen per ion at each temperature, was only about f 10%.
Results
The Journal of Physical Chemistry
CONDUCTANCE AND WATERTRANSFER IN A CATION-EXCHANGE MEMBRANE
The water content determinations show that only approximately 11 water molecules are present in the solution for every equivalent of exchange capacity. Coulombic forces will be much stronger because of the lower dielectric constant and the high ionic concentration in the membrane. The increase in X, from lithium to potassium may thus be due to decreasing ionic hydration as in free aqueous solution, and the subsequent decrease from potassium to cesium reflects increasing ion association with the exchange groups as a consequence of the diminished hydration cover of the counterions. The same general phenomenon seems to occur also in the bivalent ions in this series although the range
TEMPERATURE = 25'
249
crease for rubidium and cesium, the inverse order of the X, values. It is doubtful whether the water-transfer measurements presented in Table I have much absolute significance although their relative values are believed to be self-consistent. The measurements were carried out at very low current densities (approximately 0.2 ma/cm2) in order to minimize osmotic effects due to concentration polarization in the unstirred receiving solution. However, it became apparent that the water transfer per faraday was in fact a function of the current density, as is demonstrated in Figure 1 for some measurements on the sodium form of the membrane at 25". It can be seen that the water transfer is extremely high at low current densities but falls to a relatively constant value at current densities above about 0.5 ma/cmz. This effect has also been observed in phenolsulfonic membranes by Lakshminarayanaiah, l2 who suggested that transport might be taking place only in the larger pores of the membrane at the lower current densities. The water-transfer coefficient through these large pores is likely to be higher than the average value which obtains when a reasonably high current density is used. The data indicate that water-transfer coefficients generally decrease somewhat with increasing temperature. Water transfer per faraday is about twice as great for monovalent ions as for bivalent ions and four times as great for the trivalent ion lanthanum. The numbers, in fact, suggest that to a first approximation the water transfer is almost the same per mole of ions transferred. Among the monovalent ions, the watertransfer coefficients decrease very substantially from lithium to potassium and are then roughly constant. A great deal of the water transferred with the lithium and sodium ions must be water of hydration. The relatively low values of water transfer for the bivalent and trivalent ions may be some indication that they are less hydrated in the membrane than in free aqueous solution. Thus, while it is not possible to develop any quantitative treatment for the effects of variable hydration and ion association on the conductance and transfer of ions in the membrane, the experimental results do provide broad support for an interpretation in these terms of the gross differences in behavior between ions of different charge types.
' t 0.5
I.o
1.5
0
CURRENT DENSITY ma/cm2 Figure 1. Water transfer in sodium form of Nepton CR-61 as a function of current density.
of values is not so great in this case. At 25", for example, X, values increase from 0.69 for magnesium to a maximum of 0.99 for calcium and then decrease to 0.84 for strontium and 0.75 for barium. Corresponding values for Xo in free aqueous solution show a continuous, if small, increase throughout this series of bivalent ions. Activation energies for the conductance process in the membrane are significantly greater than the values for free solution. The increase in activation energy is undoubtedly related to the interaction of the hydrated ions with the membrane structure and particularly the effect of coulombic interaction with the exchange groups. Among the alkali metal cations, the activation energies for conductance in the membrane appear to decrease from lithium to potassium and then in-
Acknowledgment. This work was supported by Contract No. 14-01-0001-372 with the Office of Saline Water, U. S. Department of the Interior. (12) N. Lakshminarayanaiah, Proc. I n d i a n Acad. Sci., ASS, 200 (1962).
Volume 71, Number 2 January 1967
