J. Chem. SOC., Faraday Trans. 1, 1986,82,2065-2077 Concentration Polarization and Water Dissociation in Ion-exchange Membrane Electrodialysis Mechanism of Water Dissociation Yoshinobu Tanaka" and Manabu Sen6 Central Research Institute, Salt Division, Japan Tobacco Inc., 6-2, Umegaoka, Midori-ku, Yokohama 227, Japan A relationship between the current density i and the current efficiency of H+ and OH- ions generated by dissociation of water above the limiting current density in ion-exchange membrane electrodialysis has been pro- posed. Generation rates of H+ and OH- ions in the dissociation of water, H,O e H+ +OH- are given as the difference between the forward and the reverse reaction rate. The transport of H+ and OH- ions generated is described according to the Nernst-Planck equation.The relationship between i and q is derived by using the conservation law for the generation and the transport of H+ and OH- ions. Comparing the calculated values with experimental ones, it is clear that the water dissociation reaction rate constant increases with increasing i. Such an increase is usually larger for an anion-exchange membrane than for a cation-exchange membrane. An especially remarkable increase is seen for a cation-exchange membrane placed in aqueous MgCl,, NiCl, or CoC1, solution. This is due to violent water dissociation generation by cascade (snow slide) splitting of water molecules in the water dissociation layer. ki kz _ _ _ ~ ~ In the course of demineralization and concentration of ionic solutions by ion-exchange membrane electrodialysis, the concentration of ions in the boundary layer formed on the membrane surface rises at the concentrating side, while it falls at the desalting side owing to concentration polarization.If the product of the concentrations of scale-forming ions in the layer at the concentrating side exceeds the solubility product, the formation of scale becomes feasible. On the other hand, if a depleted layer is formed at the desalting side, not only does the cell voltage rise but also, in extreme cases, water splitting, i.e. water dissociation takes place and results in a decrease in current efficiency and scale formation. It is, therefore, necessary to operate the electrodialytic apparatus at or below a given level of current density to avoid these problems. Concentration polarization has been widely investigated,l-l* and is said to be due to the difference in transport numbers of the counter ions between the membrane and the solution. From a consideration of transport numbers, it is expected that concen- tration polarization would occur more easily on a cation-exchange membrane than on an anion-exchange membrane, and the resultant water dissociation is therefore expected to occur easily on the cation-exchange membrane.However, on the contrary, an inspection of the experimental results of Peers2 and Rosenberg and Ti~-rel,~ shows that water dissociation on a cation-exchange membrane tends to be suppressed. Similar phenomena have been reported in ref. (5) and (11)--(17) and mechanisms have been discussed. Even from these results, however, it cannot be said that the mechanism of water dissociation has been sufficiently clarified.In order to avoid the problems caused by the water dissociation it is necessary to understand the mechanism. This problem will be discussed in this report. 20652066 Ion-exchange Membrane Electrodialysis \ water d i s s o c i a t i o n layer Fig. 1. Water dissociation layer formed on a membrane surface. water dissociation l a y e r ' A I /O X boundary layer -+x a x i s I Fig. 2. Formation and transport of H+ and OH- ions in a water dissociation layer. Theory When an electric current passes across an anion-exchange membrane placed in an ionic solution, a boundary layer is formed on the desalting surface of the membrane (fig. 1). If an electric current larger than the limiting value passes, a salt-depleted layer (water dissociation layer) is formed at the membrane-solution interface as depicted in fig.2. In the water dissociation layer, H+ and OH- ions are generated (generation rates are oH and ooH, respectively), and are transported under the potential difference (transport rates are JH and JOH). Water dissociation is a reversible reaction : kl kz H,O + H+ +OH-. (1) The generation rates of H+ and OH- ions are given by the difference between the forwardY. Tanaka and M. Sen6 2067 where oH is the generation rate of H+ ions at &x; and oOH is the generation rate of OH- ions at x-l; C,, COH and CH20 are the concentrations of H+ ions, OH- ions and H,O respectively, at x; x is the axis drawn in the water dissociation layer; and 1 is the thickness of the water dissociation layer.H+ and OH- ions generated are transported by electromigration and diffusion. The transport rates (fluxes) are obtained from the Nernst-Planck equation as foilows : where JH and JoH are the fluxes of H+ and OH- ions at x, DH and DOH are the diffusion constants of H+ and OH- ions, F is the Faraday constant, zH and zOH are the charges of H+ and OH- ions, R is the gas constant, T is the absolute temperature and # is the electric potential. The following formulae hold between generation and transport from the mass conservation law : (4) f l I T = JH = (i/F)qH OOH = -JOH = (i/F)qOH Current efficiencies are defined as follows: where q,, qoH, qA and q y are the current efficiencies for H+ and OH- ions, cations A and anions Y, respectively. The following equation is obtained from eqn (2)-(4): 1 ( i / F ) q =k,CH201-k,J 0 CHCOHdx --DH---- dCH FDHCHdb dCOH FDOH COH 2 RT d x ' - dx RT dx+Do,-- dx The distributions of C , and CoH in the water dissociation layer in eqn (6) are given by (cf.Appendix): exp (KZ) - 1 exp (Kx) - 1 cH = J( D,, c"~ C G ~ exp ( ~ K z ) exp (- ~ K I ) + [I - exp (- ~ K Z ) ] exp (KZ) - 1 exp [K(l - x)] - 1 DH c,, = J ~ ~ C R C ; , exp(rK~) exp(-rK~)+[l -exp(-rK~)] CH and CgH in eqn (7) are the concentrations of H+ and OH- ions at both ends of the water dissociation layer. K is given by where p is the apparent specific resistance of the water dissociation layer, po is the specific resistance of the water dissociation layer and 4m is the membrane surface potential.2068 Ion-exchange Membrane Electrodialysis 10-‘6t- I I I I I I I 0 0.2 0.4 0.6 0.8 1.0 x / 1 0-4 cm Fig.3. Concentration distributions of H+ and OH- ions in a water dissociation layer. i=0.lAcm~2,l=lO~4cm,p=lO5Rcm.r:(a)0.5,(b)0.3,(c)0.l,(d)O. r i ( I - r ) I I Fig. 4. Concentration distributions of H+ and OH- ions in a water dissociation layer (model).Y. Tanaka and M . Sen6 2069 1 0.2 0.4 0.6 0.8 1.0 x/ 1 o-4 cm Fig. 5. Ionic product distributions of H+ and OH- ions in a water dissociation layer. i = 0.1 A cm-2, I = cm, p = lo5 Q cm. r : (a) 0, (b) 0.1, (c) 0.3, ( d ) 0.5. Taking r from eqn (7), C, and C,, are plotted against x in fig. 3 and illustrated in fig. 4 as a simplified model. Fig. 4 indicates the phenomenological meaning of r as follows : r = (thickness of the region in which the concentrations of H+ and OH- (10) Moreover, it is understandable that r becomes zero at or below the limiting current density and increases with increasing i, but never exceeds 0.5.The ionic product CH C,, is plotted against x in fig. 5 which shows a tendency to have reduced values in the water dissociation layer above the limiting current density. This behaviour is schematically shown in fig. 6. ions change)/(thickness of the water dissociation layer). From eqn (6) and (7), the relationship between i and 1 is obtained as follows: a = k, CHzO [exp (KZ) - 112 exp (rKZ) B = k, c"~ {[exp (KZ) - exp (rKZ)l2 + exp (KZ) [exp (rKZ) - 112 2 +a [exp (KZ) - I] [exp (rKZ) - 11 [exp (KZ) - exp (rKZ)]> y = &'(OH Do, CH COH) [exp (KZ) - 11 exp (rKZ) (exp [(2 - r)KZ/2] -exp (rKZ/2)).(1 5)2070 Ion-exchange Membrane Electrodialysis r l 1 / 2 ( I - r l l I Fig. 6. Ionic product distributions of Hf and OH- ions in a water dissociation layer (model). X Experiment a1 Fig. 7(a) and (b) illustrate the apparatus for measuring water dissociation on a cation-exchange membrane @ and an anion-exchange membrane @ , respectively. The effective areas of membranes @ and @ were reduced to 0.264 cm2 by a gasket in order to generate more easily water dissociation on these membranes rather than on the other membranes used in the apparatus. D and C are the desalting chamber and the concentrating chamber, respectively. Dimensions of D and C are shown in fig. 8. If an electric current passes across @ or @, the ionic concentration changes in D are small, but the ionic concentration in the boundary layer formed on @ or @ decreases owing to concentration polarization and water dissociation takes place at a value of i above the limiting current density.0.1 mol dm-3 NaCl aqueous solution or 0.05 mol dmA3 MgC1, aqueous solution were supplied to D by a pump at a rate of 0.1 cm3 s-l. 1 mol dm-3 aqueous solution of the electrolytes mentioned above were put in D’. 1 eq dm-3 NaCl aqueous solution were put in C and D”, respectively. 1 mol dm-3 NaCl aqueous solution was pumped to the electrode chambers. After these preparations, an electric current was passed for 10 min using AgIAgCl electrodes. When water dissociation takes place on the surface of @ or @ in D, H+ or OH- ions generated are transported into C and accumulated there.Then the electrodialyses were repeated by changing the current densities incrementally. Current efficiencies for H+ or OH- ions were calculated from measurements of pH changes of the solution in C and these were plotted against current densities. At the same time, voltage drops V across the membrane were measured and were plotted against current densities. Results and Discussion i vs. qH plots and I/ vs. i plots are shown in fig. 9 and 10. From the inflection of the curves, the limiting current density ilim is evaluated. i us. rH plots and i vs. qoH plots are shown in fig. 11.Y. Tanaka and M. Sen6 207 1 ( b ) Fig. 7. Electrodialytic apparatus to measure water dissociation : K, cation-exchange membrane; A, anion-exchange membrane; D, desalting chamber; C, concentrating chamber; G, gasket.Fig. 8. Dimensions (mm) of desalting chamber and concentrating chamber. Now, we will make clear theoretically the relationship between i and q by using eqn (1 1)-(15), and compare the result with the observed values. For this purpose, we must know the values of k , and k,. The ratio k,/k,, being the equilibrium constant, must remain constant at a given temperature, so that k, and k, could be expressed using a parameter 2 as follows; k, = 2 x 2 s-l k, = 1.5 x 1014 2 cm3 mot1 s-l. As will be explained, the calculated values of 7 are not consistent with the observed values unless k , and k, increase drastically with increase in i. So, we could tentatively assume that Z is unity below the limiting current density and k , and k, have the values observed2072 Ion-exchange Membrane Electrodialysis 6 5 4 2 1 Fig. 9.Current 0 0.05 0.10 0.15 0.20 ilA cm-2 25 "C. density us. qH plot. Cation membrane Selemion CMV, 0.20 0.1 5 N I 2 0.10 2 0.05 0 0.5 1.0 1.5 2.0 2.5 VlV 0.1 mol dm-3 NaCl, Fig. 10. Current density us. voltage drop plot. Cation membrane Selemion CMV, 0.1 mol dm-3 NaCl, 25 "C. by Eigen,18 and above the limiting current density the values of 2, and therefore, k, and k,, increase with increasing i. Taking 2 and p as variables, the calculated values of q were plotted against i at r = 0.3 and the result gave the curves in fig. 11. By comparing the observed values with the calculated ones, it is clear that 2 (i.e.k, and k2) greatly increases with increasing i. (p seems to increase simultaneously, but it is difficult to identify its changes.) It is recognizable, moreover, that in aqueous NaCl, the increase of Z is more intensely restricted on a cation-exchange membrane than on an anion-exchange membrane. In aqueous MgCl,, however, it was confirmed that Z increases remarkably and violent water dissociation proceeds on the cation-exchange membrane, as indicated by the large increase of qH. In previous reports,lg* 2o it was recognized that water dissociation is generally moreY. Tanaka and M. Sen6 2073 1 6 ~ to2 10’ 1 10 l o 2 i/A cm-2 Fig. 11. Relations between i and qH or qoH. Y = 0.3. solution membrane 0.1 mol dm-3 NaCl 0.05 mol dm-3 MgC1, cationa 0 anionb 0 a A 104 1 O6 1 O8 1 102 1 O6 1 1 o2 104 104 1 O8 1 O8 1 O8 1 O6 1 O6 1 O6 1 os 104 104 104 a ACIPLEX K-102.ACIPLEX A-102. restricted on cation-exchange membranes than on anion-exchange membranes. Such a restriction was proved to be brought about by the acceleration of ionic transport under the high electric potential developed on the desalting surface of cation-exchange membranes. On the other hand, it was recognized that extraordinarily violent water dissociation takes place on cation-exchange membranes placed in aqueous MgCl,, NiC1, or CoC1,. It also became clear that water dissociation is promoted when hydroxides such 69 FAR 12074 Ion-exchange Membrane Electrodialysis + + + + + + + + + cation membrane water dissociation layer Fig. 12. Cascade (snow slide) splitting model of water dissociation. as Mg(OH),, Ni(OH), or Co(OH), are placed under the conditions of low ionic concentration and high electric potential.These conditions were observed to be reproduced easily on the desalting surface of a cation-exchange membrane placed in aqueous MgCl,, NiCl, or CoCl,, so that such circumstances were estimated to cause the extraordinarily violent water dissociation. From the considerations described in this report, it is concluded the reaction rate constants k , and k, increase remarkably in the violent water dissociation. Furthermore, it is clear that the drastic increase in the reaction rate which was observed on the cation-exchange membrane placed in aqueous MgC1, is caused by the precipitation of Mg(OH), on the desalting surface of the membrane.It could be thought that this violent water dissociation is brought about by the accelerated cascade (snow slide) splitting of water molecules as shown schematically in fig. 12. In the cascade water splitting, H+ and OH- ions generated by water dissociation interact with adjacent water molecules on the precipitates of Mg(OH),, with the resultant promotion of water dissociation, accompanied by the generation of majorities of H+ and OH- ions. Appendix Concentration Distribution of H+ and OH - Ions in a Water Dissociation Layer The concentrations of H+ and OH- ions (C, and COH) multiplied by the diffusion constant (DH and DOH), respectively, in a water dissociation layer, and the distributions of these quantities (the converted ionic concentration XH and XOH), are expressed as polynomials of x as follows : n: X,=D,C,= C a n x n n=o cc XOH = DOH CO, = bn(l-x)". n=o From eqn (A 1) and eqn (6) we getY.Tanaka and M. Sen6 2075 Substitution of eqn (A 1) into (A 2) gives eqn (A 3): Eqn (6) indicates that ( i / F ) v should be independent of x. Therefore, with the exception of the first term, all other terms on the right-hand side of eqn (A 3 ) can be regarded as zero and then the relationship of eqn (A 4) is obtained. ... - a, x + b2(l - x) a, x + b,(l-x) = (n+ 1 ) a3 x2 + b,(l- x ) , a, x2 + b , ( l - ~ ) ~ K = 2 = 3 .... an+, xn +bn+l(l-x)n - - an xn + bn(l- x ) ~ Putting x = 1 in eqn (A 4), we get K = 2(a,/a,) = 3(a,/a,) = . . . = (n -/- 1) (an+,/an) = . . . . (A 5 ) From eqn (A 5), the coefficients in the polynomials are obtained as follows: a, = (K/2)a1 = (K/2!)a1 a, = (K/3)a2 = (K2/3!)a1 a, = (K/n) an-, = (Kn-l/n!) a, In the same way, putting x = 0 in eqn (A 4), we get K = 2(b2/b,) = 3(b,/b,) = .. . = (n + 1 ) (b,+,/b,) = . . . (A 7) (A 8) (A 9) 1 b, = (K/2)b, = (K/2!)b1 b, = (K/3) b, = (K2/3!) b, b, = (K/n) b,-, = (Kn-l/n!) b,. Using eqn (A 6) and (A 8), eqn (A 1) can be simplified as: XH = a,+(a,/K) (Kxll ! +K2x2/2! + . . . + Knxn/n! + . . .) = a, + W K ) [exp (Kx) - 11 = bo + (b,/K) (exp [K(l-x)] - 1). X O H = bo+(bl/K) [ K ( l - ~ ) / l ! +K2(1- ~ ) ~ / 2 ! + . . . + Kn(l-x)n/n! + . . .] Further, in order to extinguish the coefficients of the polynomials remaining in eqn (A 9), the distribution of XH and XOH in the water dissociation layer are depicted as the model in fig.13. Xf, and XkH are XH and XOH at x = 0; X,A and XbH are those at x = 1. S is the ionic product of H+ and OH- ions at the end of the water dissociation layer. The following relation exists between these values : x& XLH = XHTAH = s > XHXOH. (A 10) Whereupon, using eqn (A lo), the ratio of the concentrations of H+ and OH- ions at x = 0 and x = 1 is defined as: m = X&/Xf, = XLH/XGH. (A 1 1 ) 69-22076 Ion-exchange Membrane Electrodialysis '0 1 anion exchange water dissociation mern brane layer Fig. 13. Concentration distribution of H+ and OH- ions in the water dissociation layer. Because the quantities of Hf ions generated in the water dissociation layer are equal to those of OH- ions, the following equations are obtained from eqn (A 10) and (A 11).Using eqn in eqn (A the coefficients remaining in eqn (A 9) can be replaced by rn as In eqn (A 13), if i increases above the limiting current density, KZ and rn will also increase. We define the ratio of lnm to KZ by r = lnrn/(KI) (A 14) where r is a parameter concerned with the structure of the water dissociation layer and its meaning is given by eqn (10). Eliminating m by the substitution of eqn (A 14) into (A 13) and putting A', = D , C , and XOH = DOH COH, we get the distribution of C, and C,, in the water dissociation layer described by eqn (7). References 1 T. R. E. Kressman and F. L. Tye, Discuss. Faruduy SOC., 1956, 21, 185. 2 A. M. Peers, Discuss. Faraday SOC., 1956, 21, 124. 3 N. W. Rosenberg and C . E. Tirrel, Znd. h'ng. Chem., 1957, 49, 78. 4 D. A. Cowan and J. H. Brown, Ind. Eng. Chem., 1959,51, 1445. 5 B. A. Cooke, Electrochim. Actu, 1961, 3, 307; 1961, 4, 179. 6 Ch. Forgacs, DECHEMA Monog., 1962 47, 601. 7 Y. Onoue, J. Electrochem. SOC. Jpn, 1962, 30, 415. 8 K. S. Spiegler, Desalination, 1971, 9, 376. 9 N. Takemoto, J. Chem. SOC. Jpn, 1972, 2053; 1973,44. 10 A. J. Makai and J. C. Turner, J . Chem. Soc., Faraduy Trans. I , 1978,14, 2850. 1 I V. J. Frilette, J. Phys. Chem., 1957, 61, 168. 12 T. Uchino, S. Nakaoka, H. Hani and T. Yawataya, J. Electrochem. Soc. Jpn, 1957, 26, 366.Y. Tanaka and M. Sen6 13 M. Sen6, K. Yamagata and T. Yamabe, J. Electrochem. Soc. Jpn, 1966, 34, 770. 14 T. Yamabe and M. Sen& Desalination, 1972, 2, 148. 15 M. Block and J. A. Kitchener, J. Electrochem. SOC., 1966, 113, 947. 16 I. Rubinstein, J . Chem. Soc., Faraday Trans. 2, 1981, 77, 1595. 17 R. Simons, Electrochim. Acta, 1984, 29, 151. 18 M. Eigen, Discuss. Faraday SOC., 1966, 113, 947. 19 Y. Tanaka, S. Matsuda, Y. Sat6 and M. Sen& J, Electrochem. Soc. Jpn, 1982,50, 667. 20 Y. Tanaka and M. Sen6, J. Electrochem. SOC. Jpn, 1983,51, 267; 1983,51,465. 2077 Paper 511019; Received 17th June, 1985