BI-IONIC POTENTIALS BY F. BERGSMA AND A. J. STAVERMAN Centraal Laboratorium T.N.O., Delft Received 18th January, 1956 Bi-ionic potentials (BIP) occur between two solutions containing ions of a different nature and separated by a membrane permeable to these ions and impermeable to ions of other sign. The theory of these potentials is reviewed. A large number of measurements is reported of BIP’s from 4 different ion pairs (Ag+ + H+, Na+ + Ag+, Na+ + H+ and Na+ + K+) and compared with transport measurements in mixtures of these ions. It is found that transport ratios in membranes may differ appreciably from those in free solution. Several discrepancies between experiment and theory show that in the simple theory one or more essential factors are omitted. It is well-known that potential differences are found between two solutions separated by a membrane if the two solutions contain the same electrolyte in different concentrations. These potentials are called Nernst potentials.It is equally well-known that potential differences are found if the two solutions contain electrolytes of a different nature. These potentials are of great interest in biology and acquire increasing interest in industrial practice. In this paper we will consider negative membranes of high selectivity and solu- tions of 1 : I-electrolytes differing in the nature of the cation. The potentials arising between these solutions are called bi-ionic potentials (BIP). Summarizing literature about these potentials can be found in a number of papers by Sollner 1 and by Wyllie.2 By “ negative membranes of high selectivity ” we mean membranes showing transport numbers for the cation which are near unity in the concentration range of interest.Such membranes can be prepared in different ways.3 While Nernst potentials are a measure of the selectivity of a membrane between ions of different sign, BIP’s are a measure of its selectivity between ions of equal sign. At present a large variety of membranes has been described showing nearly 100 % selectivity between ions of different sign. Selectivity between ions of equal sign has never been found to such an extent. The purpose of the work reported in this paper was to find out which factors govern the selectivity with respect to ions of equal sign. THEORY The first investigator who derived a relation between BIP and selectivity was Michaelis.4 Considering solutions of equal concentration but different in the nature of the permeating ions he derived the equation RT UI E = -1n- F ~ 2 ’ where E is the bi-ionic potential and u1 and u2 are the mobilities of the different permeating ions.Sollner 1 suggested replacing 4 and 112 the mobilities by tl and t 2 the transference numbers. Marshall 5 replaced the transference numbers by the products of activities and mobilities, whereupon Wyllie 2 remarked that the apparent mobility in a mixture of electrolytes not only depends upon the real mobility as can be cal- culated from conductivity measurements in pure electrolytes but also on the extent 6162 BI-IONIC POTENTIALS to which the membrane prefers one cation to the other i.e.on the ratio KpM of activity coefficients in the membrane. Thus he found for the BIP in which M and P indicate the critical ions, a' the activity in the solutions and u the real mobility. In these theoretical considerations various assumptions had to be made con- cerning the distribution of the ions in the stationary state. It would be much more satisfactory if an expression for the BIP could be derived without any additional assumptions. This has been shown to be possible for Nernst potentials which can be deduced from the transference numbers by general arguments based upon the thermodynamics of irreversible processes.6 However, a serious objection exists against the application of non-equilibrium thermodynamics to BIP's. That is the fact that this branch of thermodynamics deals exclusively with small deviations from equilibrium whereas in BIP measure- ments the thermodynamic potentials of the critical ions show large, theoretically infinite, differences between the two solutions.The most promising way of applying the thermodynamical theory in this case would be to consider layers parallel to the membrane plane and so thin that the change of the thermodynamic potential from one surface of the layer to the other is small. By calculating the potential differences between the surfaces of these layers and integrating from one membrane surface to the other the BIP could be found. However, this procedure implies some assumptions about the distribution of ions in the membranes. In fact it is identical with the careful treatment of Scatchard 7 who also finds the BIP by integration of the diffusion potential in the membrane.Scatchard writes generally for any potential difference between the membrane surfaces a and w : in which ti is the transference number and ai is the activity of ion i. Scatchard gave his final solution as a main term with some correction terms. Considering a negative membrane separating two solutions tc and w, he found that + [I t,dlna,, (4) *w tXZ: uimid In aiax + I , a Z$ujmj * where y = activity coefficient, t, = transference number of the negative ion, t , = transference number of water, s is a standard ion, ,Z+ is a summation of positive ions. The second term is a correction for the variation of the mobilities and activity coefficients in the membrane : the third term accounts for the transport of the nega- tive ion through the membrane : the last term is a correction for the water transport.For a negative membrane and only one kind of univalent cations in solution ct and solution w the main term gives ( & ) E = l n = + l n (ahJ (ws) - , ( 5 ) in which a; and a; are the activities in the solutions w and a respectively. principle this is the same formula as given by Sollner 1 and Wyllie.2 InF. BERGSMA A N D A . J . STAVERMAN 63 CHECKING THE THEORY Eqn. (5) can be checked in a variety of ways. The first check is to measure the BIP between one solution containing ion I and one solution containing the S and to calculate transference numbers tr and ts of these ions by means of (5).These transference numbers can also be measured immediately by passing a known amount of electricity through the membrane with solutions of identical composition con- taining both ions at both sides of the membrane and measuring the contribution of either kind of ions to the current. in the solution and further u for the mobility, c for the concentrations and y for the activity coefficient in the membrane, we have Indeed if we write a, and as for the activities in the membrane a,‘ and t1 UICI UIYS a_I t s uses USYI as a,la, = .,‘I& _ - - - = - By virtue of Donnan’s relation (6) can be written as (7) in which the same quantities appear as in (5). Another check is obtained by measuring the activities in the membrane separa- tely by exchange measurements and the mobilities by measurements of the conduc- tivity in pure electrolytes.Finally a more refined check can be obtained by measuring the transference number of water thus enabling to calculate the last term of the right-hand side in (4). In this paper experiments will be reported directed towards the first check of the theory. Experiments for further checking are in progress in our laboratory but are not reported here, EXPERIMENTAL * BI-IONIC POTENTIALS. The membrane was clamped between the ground-in flanges of two glass cells, containing salt solutions with different cations. These cells formed part of a circuit in which the solutions, volume 60 cm3, were circulated with a velocity of about 2 I/h. The potentials were measured with a lamp voltmeter with compensator (accuracy 0.1 mV).For the chloride solutions, calomel and silver chloride electrodes were used. For the solutions with silver nitrate we used calomel electrodes with a saturated ammonium nitrate bridge to prevent precipitation of Ag. We investigated five types of cation selective membranes, viz., I. 11. 111. IV. A 58, a Cellophane-type membrane with sulphonic acid groups, A 71, a Cellophane-type membrane with phosphonic acid groups, Stamex K, a polythene film with sulphonic acid groups, Dowex 50 + polythene ; a membrane prepared by mixing powdered Dowex 50 and polythene with a weight ratio of 2 to 1 and moulding at about 140” C , V. Amberlite IRC 50 treated with polythene in the same way as Dower 50. Amberlite IRC 50 is a cationic exchanger with carboxylic groups.Some data of the mem- branes are found in table 1. TABLE SO SOME DATA ON THE INVESTIGATED MEMBRANES membrane prepared according to cap. (mequiv./g dry weight) Dowex 50 Br.P. 719.315 2.0 Stamex K Dutch P. 180.986 1-1 Amberlite IRC 50 Br. P. 719.315 3.3 A 58 Br. P.733.100 0.27 A 71 Br. P. 733.100 0.42 * We acknowledge the collaboration in the experimental part of Mr. J. v. Wijngaarden and Mr. H. H. v. d. Berg.64 B I - 10 NI CZ P o TEN TI A L s The following combinations of ions have been studied : H+ and Na+, K+ and Na+, H+ and Ag+, Na+ and Ag+. In the presence of Ag+ ions, nitrate solutions were used, in the absence of Ag+ ions, chloride solutions. All measurements were made at 23 f 0.5" C. TRANSFERENCE NUMBERS. Transference numbers were measured in a multicel1 apparatus as shown in FIG.1 .-Multicell apparatus used for measurements of transference numbers (schema tical 1 y ) . The membrane (3 : 4) was the negative membrane to be tested. Membranes (2 : 3) and (4 : 5) were positive membranes with high selectivity intended to prevent the escape of cations from cells 3 and 4. In the beginning, cells 2, 3, 4 and 5 were filled with solutions of identical composition containing two kinds of cations in equal concentration and a total concentration of 0.1 N. Mean m>!aI a c t i v i ' j c s FIG. 2.-Bi-ionic potentials for HNO3 + AgNO3 solutions + - Stamex K - - - Dowex 50 membranes The cells 3 and 4 each form part of a circuit of 60 cm3 volume in which the solutions are circulated with a velocity of 2 l/h. Cells 2 and 5 are percolated by the same solution as is present in the beginning in cells 3 and 4.The electrode cells are rinsed with 0.1 N NaN03 solution. Membranes (1 : 2) and ( 5 : 6) are negative membranes with the exception of membrane (5 : 6) in Ag" solutions, where it was positive in order t~ prevent precipitation of silver. The area of each membrane was 40 cm2, and current density 0.5 mA/cm2.65 After passage of a known amount of electricity, the contents of cells 3 and 4. were transferred separately and quantitatively into standard flasks. The total amount of either kind of cation was determined. In this way true transference numbers were determined. F . BERGSMA A N D A . J . STAVERMAN Mean ~ o I J I ac;;.iiiies FIG. 3.-Bi-ionic potentials for HN03 + AgN03 solutions - - - - A58 A - - - - - - A 71 - - - - Amberlite IRC 50 membrane biean rnolal a c t i v i t i e s FIG.4.-Bi-ionic potentials for NaN03 + AgN03 solutions A - - - Dowex 50 membrane l a - - - - Amberlite IRC 50 membrane - - - - A 58 - Stamex K A - - - - - - A 71 In order to check the results a balance was made afterwards of the total amount of ions of either kind in cells 3 and 4 together. In this way we found a small loss of cations in the first experiments which disappeared after a number of experiments had been performed. Apparently the membranes absorb a small quantity of ions. C66 BI-IONIC POTENTIALS 0.1 0.01 0.00 I Mean molol a c t i v i t i e s FIG. 5.-Bi-ionic potentials for NaCl + HCl solutions + - Stamex K, measured with calomel electrodes 0 - Stamex K, measured with AgCl electrodes A _ - _ _ _ _ A 71, measured with calomel electrodes - - - A 71, measured with AgCl electrodes > E c a .- - m Mean rnolal a c t i v i t i r s FIG.6.-Bi-ionic potentials for NaCl + HCl solutions ' 9 - - - Dowex 50 membrane, measured with calomel electrodes 7 - - - Dowex 50 membrane, measured with AgCl electrodes I--- Amberlite IRC 50 membrane, measured with calomel electrodes 0 - - - Amberlite IRC 50 membrane, measured with AgCl electrodes 0 _ - _ _ A 58, measured with calomel electrodes 0 - - - - A 58, measured with AgCl electrodesF . BERGSMA AND A . J . STAVERMAN 67 t e j q f i ? ~ ! ~ l C C t ~ v i ~ ~ e F FIG. 7.-Bi-ionic potentials for NaCl + KCI solutions + - Stamex K, measured with calomel electrodes 0 -- Stamex K, measured with AgCl electrodes A - - - - A 71, measured with calomel electrodes i - - - - A 71, measured with AgCl electrodes t 4c + 2c > € 0 - a - m - 2c Meon molal cictiv!tt?q FIG.S.-Bi-ionic potentials for NaCl + KC1 solutions v - - - Dowex 50 membrane, measured with calomel electrodes v - - - Dowex 50 membrane, measured with AgCl electrodes --- Amberlite IRC 50 membrane, measured with calomel electrodes c] - - - Amberlite IRC 50 membrane, measured with AgCl electrodes Q - - - - A 58, measured with calomel electrodes 0 - - - - A 58, measured with AgCl electrodes68 BI-IONIC POTENTIALS In the mixture HN03 + AgN03, the amounts of cations were determined directly. In the mixtures HCI + KCl and AgNO3 + NaNO3, the first cation and the total amount of anion were determined and the second cation was calculated by subtraction.Hf, Ag+ and Cl- were determined by titration, NOT by means of a column of Dowex 50.8 In the mixture KClf NaCl the proportion of K+ and Na+ was determined spectrophotometrically. For checking the sum was compared with total C1-, found by titration. RESULTS The results of the BIP measurement are given in fig. 2-8. The BIP's have been measured as a function of the activity of one of the electrolytes following a procedure of Wyllie.2 From these plots the ratio of transference numbers in the membrane can be calculated. It is easily seen that at the point of intersection of the straight lines with the abscissa, the following relation holds since at that point the BIP vanishes In this way the " transport ratio " ~ ~ y ~ / u ~ y , can be calculated for all the combinations which are investigated.These quantities can be compared with those found from trans- port measurements. The results are given in tables 2-5. TABLE 2 transport ratio Ag+ + H+ ratio of limiting equivalent conductivities is 0-18 membrane transport measurement BIP Dowex 50 0.57 i 0.05 0.50 i 0.01 Stamex K 0.53 & 0.04 0.48 f 0-01 A 58 034 f 0.02 0-24 & 0.02 A 71 0.31 f 0.01 0.22 & 0.02 IRC 50 0.17 f 0.01 0.19 f 0.01 TABLE 3 transport ratio Na+ + Ag+ ratio of limiting equivalent conductivities is 0.8 1 membrane transport measurement BLP Dowex 50 0.62 f 0.02 0.76 5 0.04 Stamex K 0.40 f 0.01 0 5 5 f 0.03 A 58 0.65 f 0.05 0.52 & 0.02 A 71 0.66 f 0.04 0.81 & 0.01 IRC 50 0.53 f 0.04 0.52 & 0.02 TABLE 4 transport ratio Na+ 4- H+ ratio of limiting equivalent conductivities is 0.14 membrane transport measurement BIP Dowex 50 0.36 0.04 0.19 f 0-01 Stamex K 0.25 0.03 0.21 f 0.01 A 58 0.27 & 0.03 0.12 f 0.01 A 71 0-18 0.03 0.14 f 0.02 IRC 50 0.17 5 0.03 0.10 i 0.01 TABLE 5 transport ratio Na+ + K.+ ratio of limiting equivalent conductivities is 0.68 membrane transport measurement BIP Dowex 50 0-73 & 0-04 0.64 i 0.05 Stamex K 0-63 & 0.09 0.65 & 0.04 A 58 0.65 & 0.07 0.56 0.09 A 71 0.72 f 0.08 0.67 i 0.09 IRC 50 048 f 0.07 0.48 & 0.04F .BERGSMA AND A . J . STAVERMAN 69 DISCUSSION From these results the following conclusions can be drawn. (i) Marked differences are found between transport ratios in membranes and in free solutions.However, these differences do not exceed a factor of 2 or 3 and do not reach the high values found by Michaelis 4 in his pioneering work. Presumably Michaelis used membranes of a very low water content or with very narrow pores. (ii) Towards Na+ and K+ ions all membranes behave more or less in the same way. However, with respect to Ag+ and H+ ions the behaviour is different Qualitatively one can say that ions which are more specifically bound by an ion exchanger contribute more to the transport in a membrane made from these exchanges. This would mean, that a decreasing activity of a given ion in a given ion exchanger is not accompanied by a mobillity decreasing to the same extent. However, this point has to be investigated more thoroughly by separate measurements of u and y.In principle this effect can be used to separate ions of the same sign. (iii) Definite discrepancies are found between transport ratios from transport and from BIP measurement. Generally the transport ratios from BIP measurement are the lower but there are a few exceptions to this rule (Na+ + Ag+). These discrepancies indicate that one or more factors of importance are not accounted for in the approximate theoretical expression. One of these factors could be the water transport; experiments to check this assumption are in progress. (iv) An even more serious contradiction with the theory is afforded by the devia- tion of the experimental slopes of the plots for BIP against the logarithm of the activities from the theoretical value of 58 mV. In some instances it is as low as 25 mV. As the membranes are nearly 100 % selective at the concentrations used, it is improbable that this discrepancy results from permeation of anions. The fact that these deviations are particularly strong in hydrophilic membranes would point again to water transport as the cause, Also here measurements of water transport will be needed for a decision. Summarizing, we may say that bi-ionic potentials are neither theoretically nor experimentally sufficiently investigated and that various phenomena cannot be explained satisfactorily at present. 1 Sollner, J . Physic. Chem., 1949, 53, 121 1, 1226. 2 Wyllie, J. Physic. Chem., 1954, 58, 67, 73. 3 Wyllie and Patnode, J . Physic. Chem., 1950, 54, 204. Juda and McRay, J. Amer. 4 Michaelis, Naturwiss., 1926, 14, 33. 5 Marshall, J . Physic. Chem., 1948, 52, 1284. 6 Staverman, Trans. Faraclay SOC., 1952, 48, 176. 7 Scatchard, J. Anwr. Chem. SOC., 1953, 75, 2883. 8 Samuelson, Ion exchangers in analytical Chemistry (John Wiley and Sons, Tnc., New Chem. SOC., 1950, 72, 1044. Kressman, Nature, 1950, 165, 568. York, 1954), chap. 8, p. 117.