Electroassisted Transport Phenomenon of Strong and Weak

7892

J. Phys. Chem. B 1997, 101, 7892-7900

Electroassisted Transport Phenomenon of Strong and Weak Electrolytes across Ion-Exchange Membranes: Chronopotentiometric Study on Deactivation of Anion Exchange Membranes by Higher Homologous Monocarboxylates Gadde Ramachandraiah* and Paramita Ray Discipline of ReactiVe Polymers, Central Salt and Marine Chemicals Research Institute, Gijubhai Badheka Marg, BhaVnagar 364 002, India ReceiVed: January 10, 1997; In Final Form: April 28, 1997X

The electrical responses of two interpolymer ion-exchange (anion and cation) membranes have been investigated by chronopotentiometry in dilute solutions of NaCl, KCl, and HCl as strong electrolytes and a 75:25 mixture of (1 mM) RCOOH-RCOONa, where R ) -H, -CH3, -CH2CH3, -CH2CH2CH3, and -CH(CH3)2 as weak electrolytes. The behavior of both of these membranes was nearly ideal in strong electrolytes. The performance of a cation membrane in weak electrolytes R ) -H and -CH3 was as good as in NaCl/KCl and less satisfactory in others. On the other hand, the performance of an anion membrane in electrolytes R ) -H and -CH3 was nearly identical to that in NaCl/KCl, but it steadily decreased as the length and size of the alkyl (-R) chain increased. The poor performance of the anion membrane in higher homologous carboxylates with R ) -CH2CH3, -CH2CH2CH3, and -CH(CH3)2 has been attributed to fouling of the surface by the RCOO- groups next to the membrane in the interfacial zone on the diluate side and/or the choking of ion flow channels by these carboxylate ions on account of a long nonconductive alkyl chain on them. The parameters such as the potential drop across the membrane at the outset of each experiment, Iτ1/2, the permselectivity, and the transference number for both types of membranes in strong as well as in weak electrolytes were measured and compared. The transport across the anion membrane of OH- ions from either water autodissociation or hydrolysis step of RCOO- groups at the anion membrane surface was considered in both strong and weak electrolytes at the above optimum current densities. The fouled anion membrane was regenerated by rinsing with distilled water and equilibrating it with a strong electrolyte solution.

I. Introduction Sand1

The chronopotentiometric method developed by for the variation in concentration of an electroactive species undergoing a change with time in the interfacial zone between solution and electrode has been found useful for many analytical applications including the evaluation of kinetic parameters that are directly or indirectly associated with charge transfer processes.2,3 This technique seems to be similarly applicable to the study of the variation in concentration of a cation/anion being transferred from the interfacial zone on one side of the ion-exchange membrane to the other. The resultant potentialtime data, thus obtained, give more important information regarding polarization phenomena, electrical conductance, ion specificity, surface fouling, heterogeneity, and the values of permselectivity and transference number of the ion-exchange membrane under investigation. Block and Kitchener4 have investigated the polarization phenomena by this method with a number of commercial membranes that are being used in electrodialysis cells for desalting purposes. They successfully proved that the ease of H+ or OH- ion passage through an ionexchange membrane is dependent on the degree of microheterogeneity, which affects the possibility of ion transport by the Grothus mechanism. Brennen and Hills5 have estimated the degree of heterogeneity in commercial ion-exchange membranes by this method. Audinose et al.6,7 have measured6 the transport number of ion-exchange membranes in strong electrolytes of concentration up to 1 M and studied the formation of a deposit on membrane surfaces.7 Recently, Taky et al.8 have used the chronopotentiometric method to study the electrical responses, analytical application, and surface poisoning of a cationX

Abstract published in AdVance ACS Abstracts, August 15, 1997.

S1089-5647(97)00169-7 CCC: $14.00

exchange membrane in the transfer of trivalent chromium. This method is further extended9-11 to examine electrical properties and the electrolyte ion transport across some of the bipolar membranes. The polarization phenomenon in the interface between an ionexchange membrane and a dilute electrolyte solution has been studied previously by several workers.12-14 Methods such as radiotracer autoradiography experiments,15 spectroscopy16,17 (scanning electron, X-ray, small angle X-ray, and neutron scattering, electron spin resonance, Mossbauer, and impedance17), equipotential surface approach,18 and stationary state emf measurement19 have been established to estimate heterogeneity (both micro and macro), conductance, transport number, and other properties of ion-exchange membranes. In the present paper, we studied the electrical responses of two interpolymer (one anion and another cation) ion-exchange membranes that have been developed20 and used in electrodialysis units for versatile applications21-25 by the chronopotentiometric method using dilute solutions of strong and weak electrolytes. From the experimental data, the values of Iτ1/2, permselectivity, and transference number corresponding to each type of membrane at each concentration of the strong/weak electrolyte have been studied. II. Theory II.1. Transport Phenomena in Strong Electrolytes. Consider an ion-exchange membrane placed in aqueous solution (Figure 1) of an electrolyte of concentration C0 possessing a monovalent anion (1) and cation (2) in equilibrium. When an electric current is passed across the membrane by the help of two electrodes, one on each side, the ions in solution move © 1997 American Chemical Society

Deactivation of Anion Exchange Membranes

J. Phys. Chem. B, Vol. 101, No. 40, 1997 7893 forms of the type

dCi I(thi - ti) ) dx ziFDs

(6)

where ti is the solution phase transference number of i. It could be described as eq 7.

dCi IP(1 -ti) ) dx ziFDs

(7)

where P is the permselectivity of the ion-exchange membrane and is defined as Figure 1. View of an ion-exchange membrane separating the current carrying electrodes in a monovalent electrolyte solution.

toward their respective electrodes. In this process, the counterion in one of the membrane-solution interfacial zone moves toward the membrane surface, while away in the other zone. Under steady state conditions and at a constant electric current, the incoming and outgoing flux at both sides of the membrane surfaces are eventually equal as the concentration of the counterion within the membrane phase is constant throughout. According to the Nernst-Plank flux equation,26 the total inward flux (Ji) of the counterion “i”’ (1 or 2) in the interfacial zone is the outcome of chemical and electrical flux. Under ideal conditions this could be given as

[

Ji ) -Di

]

∂Ci ziFCi ∂ψ + ∂x RT ∂x

(1)

where Di ) mean diffusion ionic coefficient, zi ) charge on i, ψ ) electrical potential due to ion mobility, and Ci ) concentration. According to Fick’s second law of linear diffusion and with the help of eq 1, one gets

[

]

∂Ji ∂Ci ∂ ∂Ci ziFCi ∂ψ )) Di + ∂t ∂x ∂x ∂x RT ∂x

(2)

considering that the mean diffusion ionic coefficient (Di) is constant and there are no convection phenomena. Equation 2 results in two forms corresponding to i ) 1 and 2, which after successive mathematical operations conforming to the condition of electroneutrality (z1C1 ) -z2C2) yield two other equations of the form

∂2Ci ∂Ci ) Ds 2 ∂t ∂x

[

(8)

The solution of eqs 3 and 7 under the boundary conditions (Ci ) C0 at x ) 0 and/or t ) 0 or at x ) ∞ and/or any time t at the applied current density I across the membrane; Ci < C0 at 0 < x < ∝; and time, t, at the applied current density, I) could readily be obtained by the help of Laplace transforms, i.e.

Ci ) C0 -

2I(1 - ti)Pt1/2 ziF(ΠDs)1/2

(9)

where C0 is the concentration of the electrolyte in the bulk solution. When time t ) τ (transition time), Ci tends to zero at x ) 0. Equation 9, then, reduces to

Iτ1/2 )

ziF(ΠDs)1/2 C 2(1 - ti)P 0

(10)

which is close to the equation given by Sand1 for the solutionelectrode equilibrium including migration (ti) and membrane phenomenological (P) factors on the right-hand side. II.2. Transport Phenomena in Weak Electrolytes. When the strong electrolyte with which surfaces of the membrane established an equilibrium is replaced by a weak electrolyte such as monocarboxylic acid or a mixture of it with its sodium salt, eq 10 is suitably modified by substituting C0 by (xKaCa + Cs), respectively, where Ca and Cs are the initial concentrations of acid and its salt, and Ka is the acid dissociation constant of the weak acid. III. Experimental Section

ht iI Fzi

(4)

Presumably, in a steady state environment, the contribution of electroosmotic transport of H2O along with “i” to the change in membrane potential is negligible, and we get

-Di

ht i - ti 1 - ti

(3)

where Ds ) [D1D2(z1 - z2)]/(z1D1 - z2D2)], the diffusion coefficient of the electrolyte. The flux (Ji) of “i” in the membrane phase is a function of applied current (I, mA cm-2) and membrane phase transference number (thi) and is given as

Ji )

P)

]

dCi ziFCi dψ ht iI + ) dx RT dx Fzi

(5)

Equation 5 gives two different equations representing the ions 1 and 2, which after successive mathematical operations, in compliance with the condition of electroneutrality, result in two

III.1. Membranes. The cation and anion exchange membrane used in these studies were prepared by the methods developed in our laboratory.20 The membranes were regenerated from 1 M NaCl solution and characterized. Aerial resistance (Ω cm2), moisture content (%), and capacity (mequiv/g) under dry conditions of these membranes were found to be 1.5, 29.8, and 1.80 for the cation and 3.8, 16.35, and 1.69 for the anion, respectively. III.2. Membrane Cell. The experimental cell used for recording the variations in membrane potential under externally applied electrical field was made out of Perspex and is shown in Figure 2. It had two compartments (inner and outer) separated by the circular ion-exchange membrane firmly fitted at the lower end of inner compartment by a threaded cork. Two large surfaced titanium electrodes27 placed one above and the other below the membrane were used to apply a constant current across the membrane. An electrolyte (strong/weak) solution of 100 mL in the inner and 400 mL in the outer compartments of

7894 J. Phys. Chem. B, Vol. 101, No. 40, 1997

Ramachandraiah and Ray

Figure 2. Cell used for recording the chronopotentiograms.

known strength was placed in the cell. The effective membrane area facing the two electrodes was 12.5 cm2. Two saturated calomel electrodes (SCE) were used as probing agents to measure the potential changes across the membrane under static condition. The two probe electrodes were then brought in contact by 1 cm above and below the membrane surfaces through glass tubes filled with saturated KCl solution separated by a G4-glass frit from the contents of the main compartments. A mechanical device in the inner compartment and a magnetic stirring bead operated externally by a magnetic stirrer in the outer compartment were employed to agitate the solutions between two successive measurements to ensure equilibrium conditions in the two solution-membrane interfacial zones. The cell temperature was monitored at 25 °C. III.3. Instrumentation. The constant current applied across the two titanium electrodes was achieved by employing a EG&G PAR Model 174 potentiostat/galvanostat.28 A high-precision EG&G PAR Model 0089 X-Y recorder in conjunction with a PAR Model 174 A was used to record the variations in the potential (Et) across the membrane against time. III.4. Methods. A circularly cut ion-exchange membrane (5.8 cm diameter) was pretreated before use with 0.1 M HCl, thoroughly washed with distilled water and soaked overnight with 1 M strong/weak electrolyte under investigation. The membrane, thus conditioned, was rinsed with distilled water before fitting into the cell containing strong/weak electrolyte solution of known strength, and it was allowed 1 h for equilibrium under constant stirring. The requisite chronopotentiogram (Et-t) plots of the membrane were obtained under static conditions by applying constant current across the titanium electrodes. The direction of the applied current across the membrane was set such that the counterion should move vertically upward from outer to the inner compartment to minimize perturbations caused by natural convection. Care to minimize pH changes caused by the reactions at the electrodes in strong electrolytes was taken by replacing the cell with fresh solution as needed and minimizing the experimental time. IV. Results and Calculations IV.1. Chronopotentiometric Responses of the Cation and Anion Exchange Membranes. (a) In Strong Electrolytes. A solution of 1-100 mM NaCl in double distilled water was used as a strong electrolyte, and the results thus obtained were taken as standard for comparison of succeeding data. The Et-t plots were obtained applying low current density in the range 0.18.0 mA cm-2, depending on NaCl concentration. Typical chronopotentiograms thus obtained for both membranes at four different current densities in 0.05 M NaCl are shown in Figure 3(A and B). These membranes exhibited two potential zones with a well-defined inflection at the transition time (τ). At 3.2 mA cm-2 current density, the anion membrane in 0.05 M NaCl exhibited a less sharp inflection categorically separating the two membrane potential zones at 163 s, as seen in Figure

Figure 3. Chronpotentiometric responses in 0.05 M NaCl of the (A) anion exchange membrane at I ) (a) 3.2, (b) 3.6, (c) 4.0, (d) 4.4 mA cm-2; (B) cation exchange membrane at I ) (a) 2.4, (b) 2.8, (c) 3.2, (d) 3.6 mA cm-2.

3A(a). The inflection, however, was about 0.71 V in height and diffusive in nature by spreading itself over 40 s on the X/time-axis. Moreover, the two potential zones were nearly horizontal. Significantly, the potentials of both zones rose almost equally, while the inflection shifted toward zero with the increase in the immensity of I. Consequently, the values of τ decreased and the broad inflection turned sharp, as seen in Figure 3A(b-d). Potentials of the first zone at the initial stage increased approximately 2 V per 1 mA cm-2. In other concentrations of NaCl studied, the potential zones were nearly horizontal, maintaining the inflection height about 0.16 V at 0.16 mA cm-2 in 1 mM and 0.66 V at 5.6 mA cm-2 in 100 mM NaCl diffusing over for 11.8 and 80 s, respectively. The data further indicated that the potentials of the first zone at the initial stage increased approximately 1 V in 1 mM, 2 V in 50 mM, and 2.3 V in 100 mM NaCl per 1 mA cm-2. As evident in Figure 3B(a-d), the cation membrane, unlike the anion, showed an outright inflection at τ in 0.05 M NaCl at all current densities between 1.25 and 2.3 mA cm-2. Measured data at 3.2 mA cm-2 current density (Figure 3Bc) showed that the inflection in the membrane potential was around 55 s in a span of 14.2 s, which are about 3 times smaller as compared to those in Figure 3A(a) for the anion membrane, despite the fact that the potential separations (about 0.68 V in the case of the cation and 0.71 V in the case of the anion membrane at τ) between the two zones were nearly comparable. The potential jump seen in Figure 3B(c) further shifted with the change in applied current density, i.e. away from the origin when decreased and toward the origin when increased, as shown in Figure 3B(a, b, and d). One of the most striking features noted during the current variations was that the potential of the second buffer zone increased as seen in Figure 3B at about 0.3 V, while that of the first zone increased relatively less at 0.5 V in 50 mM NaCl per 1 mA cm-2. Results in other NaCl concentrations at different applied current densities were found to be comparable to those in Figure 3B except for a proportionate shift in the inflection value at the current density suited to the NaCl concentration. The recorded data showed that the membrane potential grew at τ to a maximum of about 0.37 V in a span of 14.2 s at 0.16 mA cm-2 in 1 mM and 0.76 V in 27.5 s at 5.6 mA cm-2 in 100 mM as compared to 0.68 V in 14.2 s at 3.2 mA cm-2 in 50 mM solution. Further, the potential of the second buffer zone increased about 6 V in 1 mM and 0.25 V in 100 mM against 0.3 V in 50 mM NaCl, while that of the first zone increased 2 V in 1 mM and 0.07 V in 100 mM against


J. Phys. Chem. B, Vol. 101, No. 40, 1997 7895

Figure 5. Chronopotentiometric responses of the anion exchange membrane in a mixture of 75:25 RCOOH-RCOONa (1 mM) at I ) 0.13 mA cm-2, where R ) (a) -H; (b) -CH3; (c) -CH2CH3; (d) -CH2CH2CH3; (e) -CH(CH3)2. Figure 4. Plots of (A) Iτ1/2 Vs I, [NaCl] ) 0.05 M; (B) Iτ1/2 Vs [NaCl] (a) for cation and (b) for anion exchange membranes.

0.5 V in 50 mM NaCl per 1 mA cm-2. Comparison of data in all NaCl concentrations at all current densities selected showed that the first potential zone at all concentrations remained horizontal up to the bottom of inflection at all current densities, while the second one remained horizontal at initial current densities, which gradually rose as shown in Figure 3B(c and d). The τ value, measured in all concentrations of NaCl solutions as the inflection midpoint, was in the range 2-180 s in the case of the anion and 1-155 s in the case of the cation membranes. The value of Iτ1/2 was plotted against I and [NaCl]. The results elucidated that the Iτ1/2 value was fairly constant and independent of I at a given concentration of NaCl, as seen in Figure 4A for 0.05 M NaCl, but linearly increased with the increase in [NaCl], as in Figure 4B, justifying the validity of eq 10. The Iτ1/2 value of these membranes in a given NaCl concentration at low current densities was found to be larger in comparison with other current densities due to delay in the formation of meaningful diffusional layers in the interfacial zones. They were found to be 0.86, 40.3, and 88.6 for the anion exchange membrane and 0.55, 23.6, and 49.4 for the cation exchange membrane in 1, 50, and 100 mM NaCl solutions, respectively. It is evident from this data that the Iτ1/2 values in a given electrolyte concentration are nearly double for the anion than for the cation exchange membrane. A subsequent increase in current density (I > 0.3 in 1 mM, 5 in 50 mM, and 8 mA cm-2 in 100 mM NaCl) dramatically altered the potential at the initial stage across the membrane and shifted the inflection point close to the Y-axis. This resulted in the quick polarization of the membrane at the commencement to an optimum value, which gradually declined and leveled off later. As a result, the measurement of τ was not easy due to constraints in the measuring apparatus. Et-t responses of these membranes, for comparison purposes, were recorded in KCl (1, 10 and 50 mM) and HCl (1 and 10 mM). The data in these solutions were found to be of a nature similar to the data in NaCl described above. (b) Weak Electrolytes. This work was carried out to explore the intricate electrical properties of an ion-exchange membrane in weak electrolytes and the effects of length and size of a nonconductive alkyl substituent (-R) on anion transport phenomenon. The electrolytes selected for this purpose were simple homologous carboxylic acids, RCOOH, with R ) -H, -CH3, -CH2CH3, -CH2CH2CH3, or -CH(CH3)2 having comparable pKa values,29,30 3.53 at 30 °C, 4.42 at 25 °C, 4.52 at 25 °C, 4.63 at 31 °C, and 5.13 at 30 °C, respectively. A mixture of 75:25 RCOOH-RCOONa (1 mM) was used in order

to have sufficient ionic strength on either side of the membrane and to minimize hydrolysis of RCOO- producing OH- ions, near the membrane surface before commencing the experiment and their subsequent involvement in the membrane process. Electrical responses of the anion and cation membranes in the above electrolytes were obtained by varying the current density between 0.03 and 0.19 mA cm-2 and 0.07 and 0.47 mA cm-2, respectively. One inflection and two potential zones identical to those in Figure 3 were observed with each membrane. In all these weak electrolytes, the cation membrane exhibited an excellent inflection and the other one behaved indifferently. The measured τ values were in the range 11-60 for anion and 30-160 s for cation membranes. In all cases, the product Iτ1/2 was fairly constant, proving the validity of eq 10, with the Ka of the weak electrolyte included therein. Figure 5 represents the electrical responses of the anionic membrane in all weak electrolytes at I ) 0.13 mA cm-2. As seen in Figure 5, the inflection in all cases was diffusive. However, it was better in R ) -H and -CH3 and not appreciable in other cases. In these studies, the τ and Iτ1/2 values had decreased as the alkyl chain increased. The data showed a better inflection and larger values for τ and Iτ1/2 in the case of R ) -CH(CH3)2 than those found for R ) -CH2CH2CH3. Et-t responses of these membranes in a HCOOH-HCOONa mixture at three applied current densities are shown in Figure 6(A and B). As in 1 mM NaCl, the anion membrane exhibited a diffusive inflection of 0.13 V height at 0.16 mA cm-2 in a period of 7 s. Potentials of both zones nearly paralleled the X-axis at low current densities, and they rose steadily with an increase in I at about 4.4 V per 1 mA cm-2 coupled with a shift in the inflection toward the origin. From the above data and that of NaCl, it is obvious that the rise in potential of the anion membrane is ∼4.5 times more, while the inflection is found to be twice as long in HCOOH-HCOONa than those in 1 mM NaCl at a given current density I. But, the τ and Iτ1/2 values measured as 17.5 s at 0.16 mA cm-2 and 0.67 were less as compared to 24 s and 0.78, respectively, obtained in 1 mM NaCl under identical conditions. At 0.16 mA cm-2 current density, the sharp inflection in the cation membrane potential in HCOOH-HCOONa, as illustrated in Figure 6B(a-c) continued for about 4.9 s, dichotomizing the two zones by a margin of about 0.6 V. This was about 0.47 V more than that of the anionic membrane in the same solution but 0.24 V more than that found in 1 mM NaCl at 0.16 mA cm-2. The potential of the first zone was nearly constant but increased by about 5 V per 1 mA cm-2. This rise was nearly 3 V larger than that found in 1 mM NaCl but only 0.6 V greater than that of the anion membrane in the same electrolyte. The second potential zone was nearly horizontal at initial current densities, which steadily increased as in Figure 3B(d) at later


Figure 6. Chronpotentiometric responses in a mixture of 75:25 HCOOH-HCOONa (1 mM) of the (A) anion exchange membrane at I ) (a) 0.10, (b) 0.11, (c) 0.13 mA cm-2; (B) cation exchange membrane at I ) (a) 0.11, (b) 0.13, (c) 0.14 mA cm-2.

current densities. Similarly, the rise in potential (5.6 V per 1 mA cm-2 rise in I) measured after 23.6 s from the inflection was comparable to that in 1 mM NaCl, implying that the transport phenomenon across the cation membrane in both HCOOH-HCOONa and NaCl is identical. The Et-t responses in other weak electrolytes were analogous in nature to that shown in Figure 6B, barring a constant reduction in inflection height. The height of the inflection under a set of given experimental conditions was found to be less by about 45% in the case of R ) -CH2CH2CH3 as compared to that of R ) -H. It is obvious that the ion transport phenomenon across the cation membrane in both NaCl and weak electrolytes is nearly identical in nature. Moreover, the measured τ and Iτ1/2 data that lie between 35-48 s and 1.0-1.1 at 0.16 mA cm-2, respectively, showed that they were less influenced by RCOOor the length and size of the alkyl group -R on the coion RCOO-. At high current densities > 1.5 mA cm-2, these selected (anion and cation) membranes behaved similarly in all weak electrolytes. The membrane potential in all these experiments rose rapidly to a maximum value, which decayed later and leveled off subsequently. IV.2. Chronopotentiometric Responses of the Anion Exchange Membrane in the Mixture of Strong and Weak Electrolytes. To ascertain the mechanism of transport of RCOO- ions, the response of the anion exchange membrane was further investigated in a mixture of NaCl (1 mM) and 75: 25 RCOOH-RCOONa (1 or 50 mM). These were performed at low (1 mA cm-2) current densities. Typical electrical responses of the anion exchange membrane in NaCl (1 mM) alone and in the mixture of NaCl and RCOOH-RCOONa (1 mM each) at 0.24 mA cm-2 current density are given in Figure 7A. Like in strong as well as in weak electrolytes (Figures 3A and 6A), two potential zones separated by an inflection at τ, fairly good in R ) -H and -CH3 and feeble in other cases, were observed. The inflection in Figure 7A(b) measuring 0.13 V in height and spanning 8 s was closely comparable in nature to that in Figure 5(a) but found to be less in both height and width as compared to that in Figure


Figure 7. Chronopotentiometric responses of the anion exchange membrane in (A) (a) NaCl (1 mM), b-d a mixture of NaCl (1 mM) and 75:25 RCOOH-RCOONa, (1 mM) where R ) (b) -H; (c) -CH3; (d) -CH2CH2CH3; (e) -CH(CH3)2; I ) 0.24 mA cm-2; (B) a mixture of NaCl (1 mM) and 75:25 CH3CH2CH2COOH-CH3CH2CH2COONa (1 mM) at I ) (a) 0.24; (b) 0.32; (c) 0.40; (d) 0.48; (e) 0.56 (f) 0.64; (g) 0.72; (h) 0.80 mA cm-2; (C) a mixture of NaCl (1 mM) and 75:25 RCOOH-RCOONa (50 mM) at 2.4 mA cm-2, where R ) (a) -H; (b) -CH3; (c) -CH2CH2CH3; (d) -CH(CH3)2.

7A(a). However, the τ and Iτ1/2 values at 0.24 mA cm-2 stayed in between those of Figures 5(a) and 7A(a), reflecting that the membrane process, in the former case probably involves HCOO- ions but not Cl- or both. From Figure 7A(b), it is evident that the potential of the first zone, measured as 0.54 V at initial stages, was about 0.2 V larger than that of Figure 7A(a) but 0.1 V smaller as compared to that of the Et-t plot in HCOOH-HCOONa alone under similar conditions. However, this (0.54 V) value increased, as in 1 mM NaCl, by 1 V per 1 mA cm-2. This was nearly 3.4 V less as compared to that in HCOOH-HCOONa alone. The data in Figure 7A(b-e) further indicate a decrease in height and width of the inflection with the nature of -R from -H to -CH(CH3)2, together with a decrease in τ and Iτ1/2 values and an increase in the initial potential, at the given current density I. The membrane responses in a mixture of NaCl and HCOOHHCOONa in both the compartments at an applied current density between 0.24 and 0.80 mA cm-2 are shown in Figure 7B. These data reveal that, as the current density increases, the inflection separating the two potential zones moves toward zero with simultaneous increase in initial potential near 0 s in such a way that the first zone finally vanished, starting the Et-t plot with the inflection as witnessed in Figure 7B(g and h). Thereafter, the membrane potential instantly grew to a maximum value, which subsequently decayed and leveled off, as seen in Figure 7B(e-h). Some of the chronopotentiometric responses of the anion membrane in a mixture of 1 mM NaCl and 50 mM RCOOHRCOONa at 2.4 mA cm-2 are configured in Figure 7C. A long ill-defined inflection in the case of R ) -H and well-defined in other cases was observed. Conversely, the results in Figure 7A(b-e) indicated an increase in the height of inflection, which turned out to be more sharp as -R changes from -H to -CH(CH3)2, implying a different form of transport mechanism in the present system. The data recorded in the absence of NaCl were closely overlapping with those depicted in Figure 7C.



TABLE 1: Permselectivity, Transport Number, and the Related Chronopotentiometric Data of the Anion and Cation Exchange Membranes in Strong Electrolytes electrolyte NaCl KCl HCl

anion

cation

C0 (mM)

Ds × 105 (cm2 s-1)

ti

Iτ1/2

P

hti

ti

Iτ1/2

P

hti

1 10 50 1 10 50 1 10

1.47 1.40 1.15 1.93 1.78 1.53 3.24 3.02

0.61 0.61 0.63 0.51 0.51 0.51 0.84 0.82

0.86 8.70 40.30 0.82 7.80 36.20 0.63 6.61

0.97 0.94 0.97 0.94 0.93 0.94 0.94 0.86

0.99 0.96 0.94 0.98 0.97 0.92 0.95 0.88

0.39 0.39 0.37 0.49 0.49 0.49 0.16 0.18

0.55 5.40 23.60 0.75 7.50 35.80 2.75 30.45

0.97 0.96 0.95 0.98 0.94 0.92 0.98 0.91

0.98 0.97 0.96 0.99 0.97 0.96 0.99 0.98

TABLE 2: Permselectivity, Transport Number, and the Related Chronopotentiometric Data of the Anion and Cation Exchange Membranes in a 75:25 Mixture of 1 mM RCOOH-RCOONa

a

anionb

cationb

R

Ds × 105 a (cm2 s-1)

ti

Iτ1/2

P

ti

ti

Iτ1/2

P

ti

H CH3 C2H5 n -C3H7 iso -C3H7

2.13 1.66 1.46 1.28 1.28

0.23 0.19 0.17 0.15 0.16

0.70 0.60 0.55 0.49 0.43

0.52 0.32 0.29 0.28 0.28

0.63 0.42 0.41 0.39 0.39

0.77 0.81 0.83 0.85 0.85

1.34 1.01 1.04 0.97 1.04

1.13 0.77 0.74 0.80 0.63

1.04 0.96 0.96 0.97 0.94

Ds ) 0.75Ds(RCOOH) + 0.25Ds(RCOONa). b ti ) 0.75, t1(H+) + 0.25t1(Na+); t2 ) (1 - t1).

IV.3. Calculation of Permselectivity and Transference Numbers. Values of the permselectivity (P) and transference number hti (Table 1) of the membranes studied with respect to Na+, K+, and H+/Cl- in a given strong electrolyte were calculated substituting the Iτ1/2 data in eqs 10 and 8, respectively. Ionic diffusion coefficients D1 and D2 required to calculate Ds at a given electrolyte concentration were obtained from ionic conductance data at infinite dilution31,32 using the DebyeHuckel equation.33 Transference numbers (ti) in a given electrolyte solution were deduced empirically by employing ionic and molecular conductance data. This method was adopted for calculating P and hti values with respect to ions of weak electrolyte mixtures. In these systems, diffusion coefficients of RCOOH and RCOONa and transference numbers of H+ and Na+ were added in a 3:1 ratio, and they were used as values of Ds and ti of the cation, respectively. In turn, the ionic conductances of H+ and Na+ at infinite dilution were added in a 3:1 ratio, and the resultant value was employed for this purpose to obtain the data presented in Table 2. Transference numbers, hti, of these membranes in strong and weak electrolytes were also determined by empirical methods26 after considering suitable modification in theoretical equations for the latter34 using initial membrane potentials obtained under static conditions.19c Measurements were done with differences in the concentrations (0.01 and 0.02 M in the case of strong and 1 mM and 2 mM in the case of weak electrolytes) at both sides of the given membrane. The membrane was first equilibrated at both sides overnight with 0.01 M strong/1 mM weak electrolyte in the membrane cell (Figure 2). The solution in the outer compartment was replaced by 0.02 M strong/2 mM weak electrolyte under static conditions. The potential difference across the membrane noted within 5 min was taken as the initial time potential. V. Discussion and Conclusions When a direct current is applied across two electrodes facing each other in an electrolyte solution, electrolysis occurs instantly. When the current is kept constant, the potential of the cell reaches the value where the most easily electrolyzable species transform to products. The following electrode reactions 11 and/or 12 at the anode and 13 at the cathode occur if the electrolyte is a dilute NaCl solution.

Figure 8. Imaginary Ci-“x” profile for the ion i in the interfacial zone on diluate side.

2H2O f O2 + 4H+ + 4e-

(11)

2NaCl f Cl2 + 2Na+ + 2e-

(12)

2H2O + 2e- f H2 + 2OH-

(13)

The OH-/Cl- and Na+ ions released in reactions 11-13 along with other products at the electrodes have to move in diametrically opposite directions to maintain electroneutrality all over the cell. The rate of formation of products in reactions 11-13 depends exclusively on the mobility of the electrolyte ions carrying current in the solution, which in turn relies on the magnitude of the current applied across the electrodes. When a membrane is placed across the flow, the selective cation or anion (but not both) has to pass through it. In such a scenario, a major portion of the current is carried by the counterion and a negligible amount by the movement of co-ion in opposite direction. This, in other words, implies that the rate of electrolysis at the electrodes now depends on the counterion mobility and permselectivity of the membrane phase also. Consequently, the concentration of electrolyte on the (diluate) side which donates counterion is reduced, affecting an increase on the receiving (concentrate) side as depicted in Figure 8. Diffusion gradients are built up in the vicinity of the two surfaces of the membrane, and this constitutes a type of concentration polarization that is detectable by means of two identical probe electrodes. It varies with the electrical properties of the membrane, applied current density, and physical properties of



the electrolyte ions. Such diffusion layers, in the absence of natural convection, grow in size with time. As a result, the ionic concentration near the membrane surface on the diluate side plummets. Then, resistance of the membrane-solution interfacial zone rises, enhancing the potential across the membrane. A plateau is reached in the growth of this potential drop when the diffusional transport toward and away from the membrane on either side balances the ion transport across the membrane. V.1. Strong Electrolytes. Inflections observed in strong electrolytes, as seen in Figures 3 for NaCl, thus signify the conspicuous rise in resistance across the membrane caused by the growth in the diffusion layers created by the fall and an increase in concentration of counterionsCl- in the case of anion and Na+/K+/H+ in the case of cation membranesswith time in outer and inner electrode chambers, respectively, at the interfacial zone. The difference in diffusional transport of the counterion in solution and membrane phases is instrumental for this kind of polarization. The positions of these inflections drifted with the decrease in current density to higher times, leaving the first potential zone longer. This shows that the electrodes at lower current densities take a long time to set diffusional zones across the membrane as the rate of occurrence of electrolysis producing products and the mobility of counterions in solution and membrane phases decrease. Concurrently, the decrease in height of these inflections which is considered to be a measure of the difference in diffusional rates of flow of counterion in solution and in membrane phases or the thickness of diffusional layers at the interfacial zone is expected. Two types of experiments were performed with each membrane in all strong electrolytes at a given concentration and a current density to ascertain which side (diluate/concentrate) of diffusional layers is more responsible for the prevalent inflection in potential across the membrane. In the first type, the electrolyte in the inner chamber was put under constant stirring to destroy the formation of any kind of diffusional layers near the membrane surface, while in the second, the direction of current density was reversed while maintaining a static condition in both chambers in such a way that the counterion flows down across the membrane, in tandem with the direction of gravitational force. Former experiments showed Et-t responses having inflections similar to those found before stirring. The latter experiments revealed entirely different results exhibiting no inflection, due to natural and forced convection, which was observed before reversal of current. On the basis of these observations it is concluded that the diffusional layer, meaningful and more effective for inflection in membrane potential, is the one that is produced in the diluate side with counterion flowing up. In general, the potential (E0) across an ion-exchange membrane depends on concentrations of electrolyte on both sides, as shown by relation 14.26,34

RT a′ E0 ) (th1 - ht 2) ln F a′′

( )

(14)

where a′ and a′′ are activities of the electrolyte on either side of the membrane. The initial potential rise in Figure 3, whose magnitude increased with an increase in applied current, is referred to as the decline in potential essential for current being kept constant across the membrane against its fixed resistance. This, at a given current density, remained constant for a period of about τ/2 s, which may be considered as the time lapse by the electrodes to reach the potentials of electroactive species to conduct electrolysis apart from the delay in setting up a diffusional layer of considerable thickness in the interfacial arena

in the lower compartment. The diffusional transports of counterion from the interfacial zone to the membrane surface and from the bulk of the solution to the interfacial zone are virtually equal in this (0 < t < τ/2 s) period, implying that the transport of counterion across the membrane is insignificant. The growth in the potential drop (Et) across the membrane in the range τ/2 < t < τ s is then considered for the formation of and growth in diffusion layers, which results in the increase in resistance of the interfacial zone. The transport of counterion toward or across the membrane is obviously more during this time than that of the same from the bulk of the solution to the interfacial zone, and it reaches a maximum value at τ s. The concentration of counterions in the interfacial zone at t ) τ s reaches a minimum value while the transport of ions across or toward the membrane increases. The downward slide in Et at t > τ causes the increase in diffusional transport of counterions from the bulk of the solution into the interfacial zone to compete with that of the ion flow across/toward the membrane. The restricting potential region in the second potential zone is responsible for the saturated state of the membrane process at which the rates of ion flow toward and away from the interfacial zones and the diffusional ion transport across the membrane are equal. The sharp inflection observed in Figure 3B is due to exponential decline in the counterion concentration within the diffusional layers in the interfacial zone. This phenomenon is responsible for the enhanced ionic transport toward or across the membrane, proving that the cation membrane is extremely ionic and is capable of speedy transportation of the counterions across it. The immensity of change in membrane potential at τ reflects the exceptional nature of the ionic (RSO3-) groups present within the cation membrane. On the other hand, the diffusional characteristics of the inflection and the inherent change in the initial potential with applied current density, as evidenced in Figure 3A for anion membrane, signify the low diffusional transport toward/across the membrane as well as the weak ionic character of the quaternary ammonium groups within the membrane. However, the steady increase in the potential across the cation membrane as seen in Figure 3B(c and d) beyond τ at lower applied current densities and fast growth in the potential across both types of membranes at high applied current densities demonstrate the transport of one of the ionic species of water from water autodecomposition (eq 15) following the steep fall in concentration of counterions in the diffusional layers. Apparently, this kind of transport of H+ or OH- across the membranes at high current densities constitutes a distinct change in pH of the solutions. Such pH changes are commonly reported in electrodialysis.4,8,12,35

H2O h H+ + OH-

(15)

The sharp inflection observed in Figure 3B with the cation membrane occurs if the counterion concentration in the diffusional layers in the interfacial zone falls quickly, signifying that the ionic transport toward or across the membrane is massive. This proves that the cation membrane is more ionic in nature and capable of greater ionic transportation than the anion membrane. The data in Table 1 show that in a given electrolyte the observed Iτ1/2 increases linearly for both the membranes with the increase in C0, as seen for NaCl in Figure 4A, as it requires large current density to create diffusion layers at the interfacial zone in concentrated solutions. The Iτ1/2 value, in a given concentration of NaCl or KCl, is greater for the anion exchange membrane as compared to the cation membrane, thus confirming

Deactivation of Anion Exchange Membranes the rapid polarization of the cation membrane, which is due to easy transport and greater mobility of the counterion in the membrane phase. In contrast, the data in HCl indicate a larger Iτ1/2 value for the cation, which is due to low activity of the membrane in H+ ions entailing large current density for polarization. The increase in Iτ1/2 value from NaCl, KCl, to HCl (Table 1) for a given membrane accounts for the dependence of it on electrolyte properties such as diffusion coefficient (Ds) and solution transference number (ti). The permselectivity (P) and transference number (thi) of these membranes are reasonably ideal. The decrease in values of these quantities with the increase in concentration of the electrolyte is expected with the reduction of the Donnan exclusion.26,36 The hti values obtained from membrane potential data for NaCl, KCl, and HCl are 0.95, 0.97, and 0.95 for the anion and 0.97, 0.97, and 0.99 for the cation membrane, respectively, in excellent agreement with the values given in Table 1. V.2. Weak Electrolytes. From the data shown in Figures 6(A and B) and those of in NaCl (1 mM), it is axiomatic that the transport phenomenon across these membranes in HCOOHHCOONa is analogous, which is due to a high degree of dissociation (pKa 3.53) of HCOOH. However, the hike in the potential across membranes and the lowering of the τ value are accounted for the resistance supplemented by the less mobile HCOO- ion and the undissociated HCOOH groups in solution. The steady hike in the potential drop across the anion (Figure 5) and cation membranes in other weak electrolytes from R ) -CH3 to -CH(CH3)2 at a given current density proves that the length and geometrical structure of the nonconductive alkyl (-R) group attached to carboxylate ion profoundly adds to the resistance of the interfacial zone. The proportionate decrease in τ, which was found only in the case of anion transportation as R changes from -H to -CH(CH3)2, is instrumental for the gradual decrease in the degree of dissociation of RCOOH and the mobility of RCOO- ion, whereas the uniform decrease in height of inflection in the anion membrane potential (Figure 5) confirms the snags in transportation of higher homologous carboxylate ions. It is apparent that this kind of membrane deactivation is the direct result of fouling of the membrane surface coupled with the blockage of ion flow channels within the membrane by carboxylate ions possessing long and bulky nonconductive alkyl substituent (-R). Similarly, the decrease in height of the inflection in the cation membrane potential with the increase in alkyl carbon chain is again accounted for by the surface fouling by the RCOO- ions in the interfacial zone and choking of ion flow channels in the membrane with the higher homologous RCOOH groups during its penetration into the membrane along with the solvent molecules. Fouling of ion-exchange membranes by inorganic or organic materials is a common feature.21,37-39 This presumably occurs in the present investigations with the anion membrane, when the carboxylate RCOO- group faces its ionic charge toward the membrane, neutralizing ionic charges on the surface of the latter during operation, and stretches its nonionic alkyl group into the interfacial zone as depicted in Figure 9. Consequently, the resistance of the interfacial zone and mobility of RCOObecome functions of length and size of the alkyl group. Experiments carried out with the fouled anion membrane in 1 mM NaCl after thorough washing with distilled water and 1 h equilibration and with the unfouled membrane were identical, implying that the fouling in the present studies is a physical phenomenon that is easily curable by washing. The Iτ1/2 value obtained with the anion membrane (Table 2) for HCOOH-HCOONa is less and resembles that of 1 mM NaCl/KCl solution. Expectedly, this has further decreased in


Figure 9. Possible arrangement of RCOO- groups on the membrane leading to surface fouling, where R ) (a) -H (b) -CH3; (c) -CH2CH2CH3; (d) -CH(CH3)2.

other weak electrolytes due to a decrease in Ds and ti values on account of an increase in the alkyl chain. Resultantly, the permselectivity (P) and transference number hti of the anion membrane are reduced by about 50% in the case of HCOOHHCOONa and more in other cases as compared to that of the strong electrolyte NaCl/KCl. Conversely, the Iτ1/2 values obtained for cation membrane are nearly equal but twice that of NaCl, as the solution phase transference number (ti) of the cations in weak electrolytes is about two times that in NaCl. Concurrently, the P and hti values that are nearing unity are larger than those of the anion membrane. Values of hti obtained from potential data26,34 are 1.1 for R ) + H and between 1.1 and 2.5 for the rest of R with the anion. They are between 1.7 and 2.1 for all weak electrolytes with the cation membrane. These values are greater than unity for an ideal system which ionizes totally in aqueous solution. This deviation is expected from the restricted mobility of the RCOOion caused by size and complex nature, developing H-bonding with solvent molecules, which in turn raises the resistance and potential across the membrane. V.3. Mixture of Strong and Weak Electrolytes. The chronopotentiograms in Figure 7A(b-e) are similar in nature to those in Figure 5 but are dissimilar to that in Figure 7A(a). It is obvious that the ion-exchange membrane prefers the RCOO- (R ) -H and -CH3) ion to pass through it from a mixture of RCOO- and Cl-, despite that the Ds and ti are small. This happens if RCOO- and/or RCOOH groups in the interfacial zone limits the flow of Cl- ions across the membrane. The rapid rise at high current densities in the initial potential (Et) across the membrane observed in Figure 7B as well as in strong and weak electrolytes alone could be attributed to the transportation of OH- ions from water autodissociation equilibrium (eq 15). Block and Kitchner4 successfully demonstrated the OH- ion transportation across the anion membrane by ascertaining the color change at the membrane surface after adding a few drops of phenolphthalein in the concentrate side. The pH changes in several ion-exchange membrane processes have been extensively studied.4,8,12,35 The trend of the nature of chronopotentiograms shown in Figure 7C, defined with a broad inflection in the case of R ) -H, well-defined in the case of -CH3, and well defined with a relatively sharp and large inflection in other weak electrolyteNaCl mixtures, is contrary to that in Figures 6 and 7A.

7900 J. Phys. Chem. B, Vol. 101, No. 40, 1997 Therefore, the weak inflection found in the case of R ) -CH2CH3, -CH2CH2CH3, and -CH(CH3)2 in Figure 6 could probably be due to transportation of either OH- or RCOO- or both. The source of OH- ions here could be either from eq 15 or by the hydrolysis of RCOO- ions in the interfacial zone. The sharp and intensive inflections reported in Figure 7C(c and d) are solely responsible for the extensive involvement of OH- ions in transportation caused by hydrolysis of higher homologous carboxylate ions at the membrane surface. Acknowledgment. The authors thank Prof. P. Natarajan, Director, CSMCRI, for constant encouragement and constructive suggestions. The authors are also grateful Dr. V. K. Indusekhar and Dr. R. Rangarajan for helpful discussions during the course of this work. References and Notes (1) Sand, H, J. S. Philos. Mag. 1901, 1, 45. (2) Delahay, P. In Treatise on Analytical Chemistry; Kolthoff, I., Elving, P., Eds.; Interscience: New York, 1963; pp 1 and 22. (3) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, Fundamentals and Applications: John Wiley & Sons: New York, 1980; pp 249, 429. (4) Block, M.; Kitchener J. A. J. Electrochem. Soc. 1966, 113, 947, and references therein. (5) Brennen, K. R.; Hills, G. J. See ref 7 in ref 6. (6) Audinose, R.; Pichelin, G. Desalination 1988, 68, 251. (7) Audinose, R.; Jacquet-Battault, F.; Moutounet, M. J. Chim. Phys. Chim. Biol. 1985, 82, 969. (8) Taky, M.; Pourcely, G.; Gavach, C.; Elmidaoui, A. Desalination 1996, 105, 219. (9) Gnusin, N. P.; Zabolotskii, V. I.; Shel’deshov, N. V.; Krikunova, N. D. Electrokhimiya 1980, 21, 152. (10) Gnusin, N. P.; Zabolotskii, V. I.; Shel’deshov, N. V.; Krikunova, N. D. Electrokhimiya 1980, 16, 49. (11) Gaur, P. M.; Prakash, R.; Rangarajan, R.; Ramachandraiah, G.; Indusekhar, V. K.; Adhikary, S. K.; Trivedi, G. S.; Shah, B. G.; Makwana, B. S. Indian J. Chem. 1996, 35A, 796. (12) Gregor, H. P.; Peterson, M. A. J. Phys. Chem. 1964, 68, 2201. (13) Cook, B. A. Electrochim. Acta 1961, 3, 307; 1961, 4, 179. (14) Cook, B. A.; Van Der Walt, S. J. Electrochim. Acta 1961, 5, 216. (15) Wo´dski, R.; Narebska, A.; Ceynova, J. Angew. Makromol. Chem. 1979, 78, 145. (16) Pine´ri, M. In Coulombic Interactions in Macromolecular Systems; Eisemberg, A., Bailey, F. E., Eds.; ACS Symposium Series 302; American Chemical Society: Washington, DC, 1986; p 159.

Ramachandraiah and Ray (17) (a) Malmgrem-Hansen, B.; Sørenson, T. S.; Jensen, B.; Hennenberg, M. J. Colloid Interface Sci. 1989, 130, 359. (b) Plesner, I. W.; MalmgremHansen, B.; Sørenson, T. S. J. Chem. Soc. Faraday Trans. 1994, 90, 2381. (18) (a) Glueckauf, E. Proc. R. Soc. London, Ser. A 1962, 268, 350. (b) Petropoulos, J. H.; Tsimboukis, D. G.; Kouzeli, K. J. Membr. Sci. 1983, 16, 379. (c) Petropoulos, J. H.; Kimura, Y. Iljima, T. J. Membr. Sci. 1988, 38, 39. (d) Petropoulos, J. H. J. Membr. Sci. 1990, 52, 305. (19) (a) Sørenson, T. S.; Jensen, B. J. Non-Equilib. Thermodyn. 1984, 9, 1. (b) Sørenson, T. S.; Jensen, B.; Malmgrem-Hansen, B. J. Non-Equilib. Thermodyn. 1988, 13, 57. (c) Compan, V.; Sørensen, T. S.; Rivera, S. R. J. Phys. Chem. 1995, 99, 12553. (20) Govindan, K. P.; Narayanan, P. K. Indian Patent No. 124573, 1969. (21) Ramachandraiah, G.; Thampy, S. K.; Narayanan, P. K.; Chauhan, D. K.; Rao, N. N.; Indusekhar, V. K. Sep. Sci. Technol. 1996, 31, 523. (22) Thampy, S. K.; Narayanan, P. K.; Chauhan, D. K.; Trivedi, J. J.; Indusekhar, V. K. Sep. Sci. Technol. 1995, 30, 3715. (23) Indusekhar, V. K.; et al. Water Treat. 1992, 7, 291, 439. (24) Indusekhar, V. K.; et al. Desalination 1991, 84, 189, 201, 213. (25) Thampy, S. K.; Narayanan, P. K.; Harkare, W. P.; Govindan, K. P. Indian J. Technol. 1991, 29, 297. (26) Lakshminarayanaiah, N. Transport Phenomena in Membranes; Academic Press: New York, 1969; pp 75, 91, and 199. (27) Both of the electrodes, supplied as titanium anodes by Titanium Tantalum Products Limited (TITAN), Madras, India, were expanded from a 1.5 mm thick sheet. Overall size of each one of these electrodes was 50 mm × 60 mm over which a triple (precious metal) oxide coating of 6 µm thickness was applied. Effective surface area of each electrode was around 24-30 cm2. (28) Ramachandraiah, G. J. Am. Chem. Soc. 1994, 116, 6733. (29) Martell, A. E.; Smith, R. M. Critical Stability Constants, Vol. V; Plenum Press: New York, 1982; p 284. (30) Perrin, D. D. Stability Constants of Metal Ion Complexes, Part B, Organic Ligands; Pergamon Press: New York, 1979. (31) Rabinson R. A.; Stokes, R. H. Electrolyte Solutions, 2nd ed.; Butterworths: London, 1959. (32) Parsons, R. Hand Book of Electrochemical Constants; Butterworths: London, 1959. (33) Glasstone, S. An Introduction to Electrochemistry; Van Nostrand: New York, 1956; p 50. (34) In case of weak electrolytes, the equations were suitably modified by replacing the concentration term of electrolyte by (xKaCa + Cs), where Ca and Cs are the initial concentrations of acid and its salt, and Ka is the acid dissociation constant of the weak acid. (35) Forgacs, C.; Ishibashi, N.; Leibovitz, J.; Sinkovic, J.; Spiegler, K. S. Desalination 1972, 10, 181. (36) Simon, G. Desalination 1986, 59, 61. (37) Korngold, E.; De Korosy, F.; Rahav, R.; Taboch, M. F. Desalination 1970, 8, 195. (38) Grossman, G.; Sonin, A. A. Desalination 1972, 10, 157. (39) Audinose, R. J. Membr. Sci. 1989, 41, 115.

Electroassisted Transport Phenomenon of Strong and Weak

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