ELECTRODIALYTIC POLARIZATION OF ION-EXCHANGE MEMBRANE SYSTEMS
2201
Electrodialytic Polarization of Ion-Exchange Membrane Systems
by H. P. Gregor and Marvin A. Peterson' Department of Chemistry, Polytechnic Institute of Brooklyn, Brooklyn, N e w Yolk (Received February 89, 1964)
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~~
The extent of electrodialytic polarization a t a cation-exchange membrane in potassium chloride solutions of different concentration (0.0005-0.05 M ) and stirred such that the boundary layer thickness varied from 4 to 30 p was determined by measuring the (equal) rates of production of hydrogen and hydroxide ions as a function of the current density. The hydrogen ion flux across the film rose quite steeply as a critical current density was obtained, above which the transport number of hydrogen ions across the membrane reached 0.4-0.7. At currents below the critical value, the hydrogen ion flux was calculated by assuming that its migration alone was operative, employing its ambient solution concentration (pH 7) and the potential gradient a t the solution-membrane interface, the latter being derived from a solution of the Nernst-Planck equation applied to potassium chloride alone. At currents above the critical value, the hydrogen ion flux and transport number were calculated by assuming that in this region the potassium ion was transported by diffusion alone. Reasonable agreement between theory and experiment was obtained.
During the passage of a direct current across most porous membranes interposed between neutral electrolytic solutions, changes in the pH of these solutions have been observed. Bethe and Toropoff2 noted that during electroosmosis through a collodion parchment or a gelatin membrane the anolyte became alkaline and the catholyte acidic, the reverse of what occurs under ordinary electrolysis of neutral solutions between platinum electrodes. Using material balance considerations, they correlated the transport, numbers of the cation and anion of the salt, and also those of hydrogen and hydroxide ions, postulating that the effect arose because the membrane was more permeable to either cationic or anionic species. With ion-exchange membranes, this pH shift is considerably more marked than is observed with presumably uncharged porous membranes under the same experimental conditions. For example, at low current densities and with neutral salt solutions and cationexchange membranes, the hydrogen ion transport number across the membrane is virtually zero; it rises markedly with increasing current density, and when a critical current density is reached the hydrogen ion flux across the membrane becomes a substantial fraction of the total current. A parallel effect occurs with anion-permeable membranes and hydroxide ion
transport. The effect depends upon the degree of stirring of the ambient solutions, the concentration of salts, the properties of the membrane, and the nature of the electrolyte present. Peers3 measured polarization by exa,mining current-voltage curves, as did Rosenberg and Tirrel14 and Cowan and Brown5; Uchino, et u Z . , ~ measured the extent of the pH disturbance. These polarization effects have been commonly observed in practical electrodialytic processes, as evidenced by an increase in the operating voltage and the formation of acid in compartments being demineralized. This contribution describes polarization phenomena in cation-exchange membrane systems and presents a theoretical interpretation of these effects. (1) Taken in part from the dissertation of Marvin A. Peterson, submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemistry, Polytechnic Institute of Brooklyn, Brooklyn, N. Y . , June, 1960. (2) A. Bethe and T. Toropoff, 2 . physik. Chem., 8 8 , 686 (1914); 8 9 , 597 (1915). (3) A. M.Peers, Discussions Faraday Soc., 21, 124 (1956). (4) N. W. Rosenberg and C. E. Tirrell, I n d . Eng. Chem., 49, 780 (1957).
( 5 ) D. A. Cowan and J. 13. Brown, ihid., 51, 1445 (1959). (6) T. Uchino, 8. Nakaoka, H. Hani, and T. Yawataya, J . Electroc h e n . SOC.J a p a n , 2 6 , 366 (1958).
Volume 68,Number 8
August, 1964
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Experimental Membranes selected for this study were of the homogeneous interpolymer type manufactured by the Nalco Chemical Co. and designated Nalfilm 1. The preparation of similar materials has been described by Gregor, et al.,' while preparation of the same or similar materials is described in two patents.8 The properties of the particular cation-permeable membranes selected were summarized by Peterson and G r e g ~ r . The ~ membranes had a thickness of 96 p and a water content of 23.5% (by weight). Their resistance in 0.1 M potassium chloride solution was 16.5 ohm-cm.2 and 28.0 ohm-cm.2 in 0,001 M solution. The concentration of sulfonic acid groups in the membrane phase was 2.86 m, 8.5 x 10-3 mequiv. (milliequivalents) cm.-2 or 0.88 M . In 0.1 M potassium chloride solution the diffusible electrolyte or co-ion content of the membrane was 0.027 m. In 0.001 M KCI solution the diffusion coefficient of potassium ions was 1.09 X lo-' sec.-l, rising to 1.71 X lo-' cm.2 sec.-l in 0.1 M solution. Other studies by Heymann and O'Donnelll0 and by Jacobsen" have shown that the diffusion coefficients of hydrogen and potassium ions in the membrane phase are approximately proportional to their limiting diffusion coefficients in aqueous solution. The transport number of the potassium ion in the membrane phase in 0.001 M potassium chloride solution was 1,000 and 0.983 in 0.1 M solution, as determined both by diffusion coefficient and by diffusion potential measurements. Drawing an analogy between these membranes and comparable sulfonated ion-exchange resins, the selectivity coefficient for potassium-hydrogen exchange is taken to be approximately 2.0. The experimental determination of the rates of transport across the membrane under the influence of an applied electric field was accomplished in a modified version of the cell used earlier.g The cell was modified by enlarging the opening between the electrode and stirrer compartments to provide for good stirring in the electrode compartments which contained silver-silver chloride electrodes in the form of plated silver screens. Both half-cells were stirred as before in a well-defined manner, and isothermal cooling coils maintained the system at a constant temperature (25.0"). The membrane area common to both sohtions was 3.42 cnx2. With 0.05 M potassium chloride solution in the cell, its resistance was 280 ohms and at the 0.005 M concentration level the resistance was 26 megohms. The boundary layer thickness 8 had been determined previously from exchange-diffusion experiments emT h e Journal of Physical Chemistry
H. P. GRECORA N D MARVINA. PETERSON
ploying potassium and ammonium ions and using Fick's law9; it varied from 1.2 to 30.4 p at different rates of stirring. Since these values were derived from transport experiments, they are functionally correct for the polarization experiments described herein. The performance of a specific experiment was as follows : the membrane specimens were equilibrated in the solution for a t least 24 hr. Then each half-cell compartment (115 ml.) was filled and stirring initiated. Then current was passed for 90 sec. (the duration of each run) during which time the exact setting of the power supply for the desired current density was made. The solutions were replaced and each run repeated until the amount of hydrogen and hydroxide ions found in the ambient solutions was constant. This was necessary because the membrane had to be transformed from its original potassium state into the appropriate potassium-hydrogen state. The duration of each run was 90 sec. with intermittent sampling at 45 sec. The lapsed time was always less than 10% of that required to deplete the left-hand compartment, assuming that only potassium and chloride ions carried the current. At current densities well below the critical current density, the capacity of the membrane was large compared to the amount of acid generated, but at and above the critical current, the membrane capacity was small compared to the acid generated. Typical data are shown in Table I, one set for a dilute solution and a high rate of stirring, and another for a relatively concentrated one a t a lower rate of stirring. The amount of hydrogen and hydroxide ions formed was computed from differences in the initial and final pH values and assuming that the mean activity coefficient of the acid or base was equal to that of the potassium chloride present. Figures 1-4 show plots of a flux for hydrogen ions across the membrane as a function of the current density. The theoretical curves will be discussed in a subsequent section. Also shown is the total current across the membrane. Table I shows that under most conditions the solutions were neutral during only the early part of the process. As will be shown later, it is the total electroly te concentration which is important here; the nature of the ions present plays a secondary role. (7) H. P. Gregor, H. Jacobson, R. C. Shair, and D. M. Wetstone, J. Phys. Chem., 61, 141 (1957); H. P. Gregor and D. M. Wetstone, ibid., 61, 161 (1957); 62, 3, 274 (1968). (8) I T . P. Gregor and H. I. Pazelt, U. S. Patents 3,004,909 (October 17, 19G1), and 3,004,904 (October 17, 19Gl). (9) M.A. Peterson and H. P. Gregor, J . Electrochem. Soc., 106, 1051 (1959). (10) E. Heymann and I. J. O'Donnell, J . Colloid Sci., 4 , 405 (1949). (11) H. Jacobsen, Dissertation, Polytechnic Institute of Brooklyn: 1959.
ELECTRODIALYTIC POLARIZATIOS OF ION-EXCHANGE MENBRASE SYSTEMS
CY
I 7
1”
pi’-
(soln. 1) [
1
2203
I
Y j
E
I (soln. 2)
where a and E are the two stirred regions whose coinposition is known, the 0 and y regions are the two boundary layers of thickness 6 and A, respectively, and the superscript bar refers to the membrane phase of thickness L. The distance x is zero at the CY-@boundary. The membrane-solution interfaces are desig-
0 CT,
;J
II
40
36
44
48
I Figure 1. Flux of hydrogen ions (in equiv. em.-’ set.?) as a function of current (in ma. ern.+) across a cation-permeable membrane in 0.005 M potassium chloride, with the rate of stirring adjusted to give a boundary ) computed from JH+ = layer of 4.3 f i . Curve (e~ taDH +( d@/dz)a’; curve (- - - -) computed from j, + = I - C K A ~ D K +curve / ~ ; (- - -) is the total ionic flux or I .
I
L I
Table I : Measured pH Changes
l20
4
2
Current density, ma. em. - 2
Anolyte or cacholyte
-PH 0 sec.
6
I
45 s e e .
80 aec.
Figure 2.
0.0005 M KC1, 6 = 4 . 3 p 1.46
A C
3.22
A
4.10
A
4.54
A C A
C C
5.85
C
0.05 M KCl, 6 29.2
A C
45.0
A
57.0
A
58.5
A
C C C
6.43 6.04 6.97 6.02 7.87 5.79 9.48 4.49 9.68 4.30
6.04 6.05 6.05 6.05 6.04 6.04 6.05 6.05 6.06 6.05
6.69 6.68 6.67 6.68 6.69 6.67 6.68 6.67
=
6.63 6.03 7.25 6.00 8.17 5.63 9.78 4.20 9.97 4.00
30.4 fi 6.72 6.67 6.81 6.65 7.29 6.45 10.64 3.34
6.76 6.66 6.92 6.61 7.53 6.30 10.83 3.14
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Theoretical For a single membrane interposed between two solutions, the notation employed will designate each region as
nated by the prime and double-prime symbols. Concentrations of the K+, C1-, H+, and OH- ions are designated as el, c2, c3, and c4, all in moles cni. -d. Thus, the designation e l p refers to the potassium ion concentration in the @ region (0 < x < a), c1” is its concentration in p adjacent to the solution-membrane interface, El’ its concentration at the same interface, but in the membrane phase, etc. Consider potassium chloride as being the sole component in the @ region. Then, if I is the current (in equiv. cm. --2 sec. -I)
where D is the diffusion coefficient, 5 the faraday, Z the valence (always positive), J the flux density in moles cm. -2 see. (for univalent species), and $ the potential. Setting CP = Z S $ / R T
Also Volume 68, .Vumber 8
August, 196.4
H. P. GREGORAND MARVIN A. PETERSOX
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d@
Jz - dcz Dz dx
ca-dX
With an ideally selective cation-permeable membrane, J2 = 0 a t x = 6 and in the steady state, : J = 0. D1 can be set equal to D2 because for potassium chloride tl = 0.49 in the solution phase. Also c1 would equal
- Ix/~D)
d@/d= ~ -I/2D(ca
(2)
(d@./dX)”
=
-I/(2Dca - IS)
It is evident that the potential gradient in region p is nonlinear, and that as I -+ 2Dca/6, the field goes to infinity. This is defined as the critical current density I*.
6
7
0.05 M 8 - 30.4~
I
7
0 F
*
I
0 -I
7
9
0 F
I
0
-I I
10
I1
I Figure 3.
12 c2 by the ordinary conditions of electroneutrality. However, since the ficld d@/dx is not uniform in the p region, there is a firiite space charge, proportional to c1 - c2. For the time being, we will neglect this space charge and set c1 = c2. Then
or the concentration gradient is linear and
The Journal of Phyaical Chemietry
50
60
I Figure 4.
As a first approximation it may be assumed that the concentrations of H + and OH- ions are not changed by concentration polarization in the p-region, and that the hydrogen ion flux across the membrane is equal to its concentration at the &membrane boundary times the field at that point, or
J3’ Thc potential gradient is
40
30
=
J3”
=
c~“Da(d@/dx)”= 9,
Figures 1-4 show values of
9, computed on this basis.
ELECTRODIALYTIC POLARIZATION OF ION-EXCHANGE MEMBRANE SYSTEMS
Based on the previous simplifica,tions, 1 3 becomes infinite a t I 2 I*. To compute J , values under these conditions, we assume that the potassium ion is carried by diflusive processes only, and that migration plays no significant part. Then
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generation and also the effect of the solution composition. It was a modification of that of Oda13and consisted of the following chain14 (1) (2) (3) Ag,AgC1/0.2MIAl0.2 MIC10.2 MIA] (4) (5) (6) 0.005 MIAl0.2 MICIO.2 MIAgC1,Ag
and 1 3
=
1 - clUD1/6
These curves were also computed and are shown in Fig. 1-4. It is evidlent that howevler gross these two approximations, the theoretical and experimental curves fit quite well.
Discussion An examination of Fig. 1 4 shows that over a wide range of experimental conditions, the simplified expressions developed here describe the experimental results rather well. Table I shows also that the flux of hydrogen and hydroxide ions was quite constant over the 90-sec. interval, although the pH of solution a was changing from about 7 to 10 or as high as 10.8. Thus, although the composition of the solution phase changed from 5 X l o w 4M potassium chloride to one with the same salt content but 10-4 M in potassium hydroxide, the rate of acid and base production was unchanged. This suggests that the generation process occurs rather independently of the ionic composition of the solution. To fix the site of generation, a cell was constructed wherein the surface of the membrane could be viewed directly. l 2 The large silver-silver chloride anode in 0.5 M potassium chloride was separated from the a-. phase by an anion-permeable membrane. The aregion was unstirred and contained 0.001 IM salt, while the €-region contained 0.5 M salt and the silver-silver chloride cathode. The indicator brom thymol blue was in the a-solution, and on the passage of current it was observed that the membrane surface became strongly alkaline, wit b hydroxide ions migrating away from it into the solution. This result definitely verifies the existence of the generation process and its location a t the solution-membrane interface. Another cell was designed to help clarify the site of
where A and C refer to anion- and cation-permeable membranes, and where the salt was potassium chloride, unless otherwise noted. The solution volumes were small (150 ml.) except in cell 4 through which a large volume was passed to drain (or for analysis). With this cell, it was observed that the flux of hydroxide ions into (3) was equal to the flux of hydrogen ions into (4), with no significant pH change being observed in cell 5 . Further, when the solution in (4) was 0.005 M potassium chloride, 0.004 M salt, and 0.001 M hydrochloric acid or 0.004 M salt and 0.001 M potassium hydroxide, approximately the same generation of acid and base (within a factor of 2) was observed. These observations fix the site of the generation process a t the depleted solution-membrane boundary and verify the assumptions as to the concentration profile, namely that the generation process is influenced primarily by the total electrolyte concentration and only secondarily by its composition. A theoretical treatment of this system, one which does not make the simplifying assumptions described earlier but solves the Nernst-Planck equation for all four species, has been made. It includes terms for the generation process and considers also the change in the rate of the dissociation of water with the electric field (Wien effect), The expressions thus obtained were not susceptible to analysis, but solvable by numerical methods employing a computer.
Acknowledgment. The authors wish to thank the National Science Foundation and the Office of Saline Water for their support of this study. (12) H. P. Gregor and
P. C. Wu, t o be published.
(13) Y . Oda, private communication.
(14) M. Espelosin and H. P. Gregor, to be published. (15) H. P. Gregor and I. F. Miller, to be published.
Volume 68,Number 8 August, 1964
