Journal of Membrane Science 150 (1998) 43±56
AC impedance spectra of bipolar membranes: an experimental study Antonio Alcaraz1,a, Hans Holdika, Thomas Ruf®nga, Patricio RamõÂrezb, Salvador MafeÂc,* a Institut fuÈr Prozesstechnik, UniversitaÈt des Saarlandes, D-66123 SaarbruÈcken, Germany Departament de CieÁncies Experimentals, Universitat Jaume I, Apdo. 224, E-12080 CastelloÂ, Spain c Departament de TermodinaÁmica, Facultat de FõÂsica, Universitat de ValeÁncia, E-46100 Burjassot, Spain b
Received 30 March 1998; received in revised form 22 June 1998; accepted 24 June 1998
Abstract A bipolar membrane (BM) is composed of one cation and one anion ion-exchange layers joined together in series. In order to obtain the AC electrical impedance of a BM, a small sinusoidal current perturbation was superimposed to the DC current, and the resulting frequency-dependent impedance spectra were recorded under different conditions of electrical polarisation and temperature for ®ve BMs. The experimental spectra were measured in three current ranges: below the limiting current region, at the onset of the overlimiting region and in the electric ®eld enhanced water dissociation region. This allows for a better understanding of the contributions of the salt and water ions to the measured impedance spectra. Measurements of the impedance of the forward biased membrane were also carried out. Although the experimental impedance spectra appear to be in qualitative agreement with previous theoretical models incorporating the effect of the electric ®eld enhanced water dissociation, a quantitative analysis of the results is not still possible due to the high number of parameters involved. # 1998 Elsevier Science B.V. All rights reserved. Keywords: Bipolar ion-exchange membranes; Experimental AC impedance spectra
1. Introduction Bipolar membranes (BMs) consist of a layered structure involving one cation and one anion ionexchange layer joined together in series, and have a series of potential applications in industrial processes [1±7]. Most of these applications are based on the electric ®eld enhanced (EFE) water dissociation phenomenon [8,9]. When high reverse polarisation vol*Corresponding author. Tel.: +34-96-3983119; fax: +34-963983385; e-mail:
[email protected] 1 Permanent address: Departament de CieÁncies Experimentals, Universitat Jaume I, Apdo. 224, E-12080 CastelloÂ, Spain.
tages are applied, a rapid increase of the electric current with the voltage is observed [8±19]. Measurements of the pH of the solutions close to the membrane show the appearance of two new electrical carriers, the water ions H and OHÿ. Ordinary water dissociation cannot explain the magnitude of the measured electric currents [3,9,13,14]. The EFE water dissociation is thus observed only under high enough reverse applied voltages and its magnitude depends critically on the structure and composition of the bipolar junction [8,13,15±19]. It is generally accepted that the large electric ®eld occurring at this region under reverse polarisation increases signi®cantly the generation rate of the water ions produced in protonation±deproton-
0376-7388/98/$ ± see front matter # 1998 Elsevier Science B.V. All rights reserved. PII: S0376-7388(98)00201-4
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ation reactions involving some membrane ionizable groups (e.g. tertiary amino groups) and the water molecules at the bipolar junction [9,20±24]. This phenomenon is known as EFE water dissociation [8], and it is not restricted to some of the usual membrane ®xed charge groups: other ionizable groups such as some metallic hydroxides [21,25±27] and metal complexes [28] may also participate as active sites in the protonation±deprotonation reactions. The current±voltage (I±V) curves under forward and reverse polarisation and the membrane potential measurements give useful but only partial information about the BM properties [15,29,30]. Impedance measurements provide valuable additional information about the functional and structural characteristics of these membranes [27,31±35] and can also contribute to a better understanding of biological membranes [36±38] and liquid electrolytes [39,40]. Unlike other studies that use large amplitude perturbations, impedance techniques are based on the superimposition of a small amplitude alternate signal to the system and the observation of its answer to this perturbation. This procedure presents several advantages. Firstly, the answer to the perturbation is slow enough to make high precision measurements. Secondly, the small value of the perturbation allows a linearised theoretical treatment of the system equations, which simpli®es considerably the study of diffusion and kinetics [41]. We have developed a theoretical model for the AC impedance spectra of a BM [31] based on the Nernst±Planck and Poisson equations and discussed preliminary experimental data [32]. The aim of this paper is to present an exhaustive experimental study of the AC impedance spectra of ®ve modern BMs, which means almost every membrane available for practical purposes. The study covers different conditions of electrical polarisation and temperature. The measurement of impedance curves under simultaneous AC and DC currents is dif®cult and requires a suitable set-up [32]. In reverse polarisation, we have measured the impedance spectra in three current ranges: below the limiting current region, at the onset of the overlimiting region, and ®nally, in the EFE water dissociation range (overlimiting region). This method allows for a better understanding of the different contributions of salt and water ions to the impedance spectra, as well as their dependence on the total current. Measurements of the impedance of the
forward biased membrane are not usual, but have also been presented here because they can provide an additional determination of those membrane transport parameters which appear also in the modelling of the reverse biased membrane [32,42]. Moreover, forward polarisation is sometimes used in electrodialysis units in order to avoid the formation and deposition of impurities on the surface of ion-exchange membranes. (Obviously, it should be checked ®rst if the BM is damaged under these conditions.) Note ®nally that measuring the impedance spectra of ®ve different BMs allows to see how the polymeric material, the reinforcing and the preparation procedures affect the structure and performance of the membrane. From the comparison between the impedance measurements of the empty electrochemical cell and those of the cell with the membrane under forward and reverse bias we can identify the electrical contributions of both the cell and the membrane, and try to eliminate undesirable contributions such as electrode±solution reactions and geometrical effects. 2. Experimental Fig. 1 shows schematically the system considered. The BM separates two solutions of the same univalent electrolyte. Under forward polarisation mobile ions accumulate at the bipolar junction while in reverse bias they are pulled out [15,43]. The H and OHÿ ions are assumed to be generated within the depleted electrical double layer (space charge region extending from xÿN to xP) at the interfacial region between the two ion-exchange layers. Five different BMs were used in this study, two of them (denoted as FTBM-1 and FTBM-2) from FuMATech GmbH (St. Ingbert, Germany), one (denoted as WSI) from WSI Technologies (St. Louis, MO, USA), one Neosepta BP-1 (denoted as BP-1) from Tokuyama (Tokuyama, Japan), and one Aqualytics Bipolar-P6 (denoted as AP6) from Graver-Water (New Jersey, USA). The FTBM-1 membrane (denoted as FhIGB bipolar membrane in previous papers [15,29,30,32]) has a multilayered sandwich structure composed of a cation selective layer (sulphonic acid groups in a cross-linked sulphonated polytherketone), an anion selective layer (quaternary ammonium ions incorporated into a poly-
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Fig. 2. Experimental set-up of the cell employed for the impedance measurements. Two Ag/AgCl plates are used as current electrodes (CEs), and the potential across the bipolar membrane (BM) is measured with two reference electrodes (REs) using Haber±Luggin capillaries (HLCs) as salt bridges. The solution flux (SF) is directed to the membrane and mixed up to keep pH and temperature values constant.
Fig. 1. Sketch of the bipolar membrane (BM) under current flow in forward (a) and reverse polarisation (b). In order to obtain the impedance of the BM, a small sinusoidal perturbation current of amplitude ^i and angular frecuency ! is superimposed to the DC current i.
sulphone matrix) and a very thin intermediate layer (about 10 nm thick) of an insoluble polyelectrolyte complex containing tertiary ammonium groups, that was inserted between the two ion-exchange layers in order to improve the water splitting capability of the BM. The thicknesses of the layers are approximately 40 mm (cation exchange layer) and 20 mm (anion exchange layer) [3,4]. The FTBM-2 membrane has exactly the same structure and composition as FTBM-1, but it is non-reinforced, so it is extremely breakable. The WSI membrane is composed of separate commercial anion and cation-exchange layers, containing strongly basic quaternary ammonium groups and sulphonic acid groups as ®xed charges, respectively. Both layers are Pall Rai ®lms consisting of a ¯uorocarbon polymer matrix in which functional groups have been introduced by radiation grafting. The ®lms were treated previously with solutions containing heavy metals [21]. The thickness of the anion exchange layer is ca.
43 mm, and the thickness of the cation-exchange layer is ca. 73 mm. Neosepta BP-1 is a reinforced single ®lm BM containing the same ®xed charge groups as WSI, but its thickness is 200 mm [19]. The Aqualytics AP6 BM is also a commercial membrane, which has an integrated multilayered structure. It is based on a polystyrene matrix to which quaternary ammonium and sulphonic groups are attached. The measuring technique is based on the wellknown Kelvin four-point method in order to avoid an overlapping of impedance contributions of the current carrying electrodes and the membrane impedance. The experiments were made in a cell specially designed for this purpose composed of two equally sized compartments (see Fig. 2). The special geometry of the cell (conical shape) is intended to make the current through the membrane approximately homogeneous, minimising border effects. The BM was placed separating the two halves of the cell and equilibrated for several hours with the solution used in the experiment before each set of measurements. A thin rubber ring was arranged together with the membrane, preventing the BM from moving during measurements. The AC impedance spectra curves were obtained using a Zahner IM6 (Zahner Elektrik, Kronach, Germany) impedance analyser in galvanostatic mode. Each experimental point is taken as the average of 10 acquired points to minimise noise effects. The potentiostat was controlled by a PC computer. In order to feed the current
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into the cell under forward and reverse polarisation, two Ag/AgCl plates (whose diameter was ca. 3.1 cm) were used, prepared according to a method described in detail elsewhere [44]. The measurements were made alternately under forward and reverse bias so that the electrodes kept in good condition. They were renewed each few measurements. The potential was measured using a pair of commercial available Ag/ AgCl electrodes (Sensortechnik Meinsberg), each connected to Haber±Luggin capillaries (HLCs), ®lled with a 3 mol/l KCl saturated solution as salt bridge. The latter were placed in front of each membrane surface (see Fig. 2). The distance between the membrane (whose diameter was ca. 10 mm) and the tip of the capillaries was approximately 1.5 mm, and the membrane area was A0.79 cm2. The cell was ®lled with 0.5 mol/l KCl solutions. The temperature was controlled by the thermostated coiled glass heat exchanger placed between the solution reservoir and the cell. Temperature measurements were made in the solution reservoir and inside the cell, trying to avoid thermal gradients. The solution was pumped into each half cell, and the solution stream was directed to the membrane surface so that the necessary stirring was provided. After exiting the cell, the solutions were mixed in order to maintain constant their pH values. A ®rst measurement of the cell impedance without membrane was performed to obtain the bulk resistance
of the cell, which was calibrated before measurements were made. 3. Results and discussion 3.1. Impedance spectra at high electric current The results are presented in terms of the electrical impedance (Z), since most of the available experimental data concerning frequency analysis are reported in this way. Fig. 3 shows a logarithmic plot of Im(Z) vs. !/2 for the WSI membrane. The experimental values of Im(Z) are negative in the frequency range considered and present low and high frequency limits close to zero. The curves (parametric in the electric current and taken at 298 K) attain a maximum at max that decreases with the electric current in reverse bias; max shifts to higher values when increasing this current. We have grouped together the impedance curves under forward and reverse bias in order to show that the measured effects come mainly from ion transport and EFE water dissociation in the BM, and they are not due to electrode±solution reactions or geometrical cell effects. The positions of the maxima are in the range 1±10 kHz. The WSI membrane was formed simply by clamping together the two ion-exchange layers, so
Fig. 3. Logarithmic plots of Im(Z) vs. for WSI membrane at 298 K. The symbols denote the experimental data at each electric current under forward and reverse polarisation.
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Fig. 4. Logarithmic plots of Im(Z) vs. for FTBM-1 membrane at 298 K. The symbols denote the experimental data at each electric current under forward and reverse polarisation.
Fig. 5. Logarithmic plots of Im(Z) vs. n for FTBM-2 membrane at 298 K. The symbols denote the experimental data at each electric current under forward and reverse polarisation.
that a very thin layer of water could appear in the junction [32]. The results for the FTBM-1 and FTBM-2 membranes are shown in Figs. 4 and 5, respectively. It is clear that the maxima of Im(Z) correspond to lower frequencies than those of the WSI membrane, as should be the case for a monolayer structure where no water layer is expected to exist between the two
exchange layers [32]. (Note that the existence of this layer should give lower bipolar junction capacitances, and then high values of max [31].) Comparison between membranes FTBM-2 and FTBM-1 in the low frequency range shows the effect of the reinforcing in the transport properties. FTBM-2 membrane shows a considerable scatter in the experimental points. These instabilities might be an indication of
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a decrease in the selectivity of the membrane. As solvated ions permeate into the membrane, polymeric chains become opened, the water content increases, and the membrane swells. Consequently, Donnan exclusion of minority carriers becomes poorer and transport of salt occurs. Then, FTBM-2 membrane shows a resistance smaller than that of FTBM-1. Small positive values of Im(Z) can be observed in the low frequency limit. This effect might be due to the diffusion boundary layers at membrane±solution interfaces. As current ¯ows through these layers concentration gradients appear (the so-called concentration polarisation effect), and a low frequency perturbation induces a phase-shift. (Note that at high frequencies, each cycle is too short in time to build ion concentration pro®les.) If there is a coupling of water ¯ow and ionic ¯uxes (electrophoretic effects), an opposite phase shift is induced, building apparent negative capacitances or ``pseudo''-inductances [36,45,46]. Another point of interest are the high values of Im(Z) found in the high frequency limit of Figs. 4 and 5, although this effect appears also in the other membranes. Measurements without membrane (empty cell) showed noticeable (but not so marked) high frequency dispersions. This effect comes probably from a capacitive coupling between the reference electrodes and the current carrying electrodes. It
can be shown using equivalent circuit arguments that because of the four-point measuring method used this stray capacitances transform into a pseudo-inductance [47]. It is also possible that the presence of the membrane changed signi®cantly the geometry of the cell, and some uncontrolled cell±membrane coupling appeared [48,49]. Therefore, the information contained in the measured impedance spectra cannot be related easily to the particular BM properties for frequencies higher than 105±106 Hz. Figs. 6 and 7 present the impedance curves for BP-1 (Neosepta) and AP6 (Aqualytics) membranes at 298 K, respectively. Extremely low electrical resistances are found in both cases (compare Figs. 3±5 with Figs. 6 and 7). This behaviour appears as a consequence of the large ionic selectivity of those membranes, which produces two main results. Firstly, both membranes show a high coion exclusion, and the undesired salt back diffusion is highly impeded, the limiting current being very low (approximately 6 A/m2 in KCl 0.5 M). Consequently, the contribution of salt diffusion to the total impedance is much lower than in other membranes. Secondly, the EFE water dissociation is particularly effective for those membranes, and determines the impedance even for low currents (note that the admittances of salt diffusion and water splitting are connected in series [32]). For AP6 membrane, we have represented only one value
Fig. 6. Logarithmic plots of Im(Z) vs. for Neosepta BP-1 membrane at 298 K. The symbols denote the experimental data at each electric current under forward and reverse polarisation.
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Fig. 7. Logarithmic plots of Im(Z) vs. for Aqualytics AP6 membrane at 298 K. The symbols denote the experimental data at each electric current under forward and reverse polarisation.
Table 1 Values and position of the maxima of the curves Im(Z) vs. frequency for all membranes under two different reverse currents (I128 A/m2 and I191 A/m2) at 298 K Current (A/m2)
Membrane ÿ128
WSI FTMB-1 FTMB-2 BP-1 AP6
ÿ191
max (Hz)
Im(Z)max ( )
max (Hz)
Im(Z)max ( )
3710 56 22 7595 ±
ÿ30 ÿ15 ÿ10 ÿ0.8 ±
5308 79 32 8307 ±
ÿ27 ÿ10 ÿ8 ÿ0.7 ±
of current, because ion transport and water dissociation are so ef®cient that it is dif®cult to distinguish between forward and reverse bias measurements. Table 1 shows the position of the maxima of the Im(Z) vs. frequency curves for all membranes under two reverse polarisation currents. It is clear that for monolayer membranes (FTBM-1 and FTBM-2) these maxima appear at lower frequencies because these membranes have large capacitances (the thicknesses of their junction equivalent capacitors are relatively small). WSI and BP-1 membranes are bilayer structures, so that they could deviate from the ideal abrupt junction model, specially if a thin water layer appears
at the junction. The AP6 membrane shows no maximum at all, because of the nearly perfect coion exclusion and the high EFE water dissociation. Table 1 shows also that max moves to higher frequencies with increasing the reverse polarisation current for all membranes, since the depletion layer grows and the capacitance of the junction decreases in this case [31]. The logarithmic plot of Re(Z) vs. frequency for FTBM-1 and FTBM-2 membranes are shown, respectively, in Figs. 8 and 9. The experimental data present the same high frequency limit for the three experimental currents used. This limit is approximately equal to the bulk resistance of the cell. The low frequency limits of Re(Z) decrease with the electric current. The experimental curves under reverse bias have an in¯ection point at inf that decreases with the electric current. The frequency inf shifts to higher values when increasing this current. As in Figs. 4 and 5, we can ®nd signi®cant differences in the low frequency behaviour of the membranes. Finally, the Im(Z) vs. Re(Z) plots for the membrane WSI are given in Fig. 10. We have represented only measurements under reverse polarisation, because the forward bias curves are dif®cult to distinguish (they give virtually one unique point) if plotted together. The experimental points have the same high frequency limit.
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Fig. 8. Logarithmic plots of Re(Z) vs. for FTBM-1 membrane at 298 K. The symbols denote the experimental data at each electric current under forward and reverse polarisation.
Fig. 9. Logarithmic plots of Re(Z) vs. for FTBM-2 membrane at 298 K. The symbols denote the experimental data at each electric current under forward and reverse polarisation.
3.2. Impedance spectra at low electrical current Experimental studies on BMs have focused quite frequently only in the current range where EFE water dissociation occurs. The present study will also consider the low current range, where a rich variety of electrochemical phenomena takes place. Figs. 11 and 12 show the impedance curves for FTBM-1 and FTBM-2 membranes before the onset of the water
dissociation phenomenon. Their shape correspond to a linear diffusion phenomenon (the so-called Warburg impedance), as expected from previous theoretical studies [31±33,40]. In this case, the resistance rises with increasing current as the bipolar junction becomes depleted of salt ions. The forward bias curves (not included here) show the same general shape, but now the resistance decreases with increasing current because of the accumulation of salt ions at the bipolar
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Fig. 10. Im(Z) vs. Re(Z) for WSI membrane at 298 K.
Fig. 11. Logarithmic plots of Im(Z) vs. for FTBM-1 membrane at 298 K for currents under the limiting current. The symbols denote the experimental data under reverse polarisation.
junction, as it is seen in the I±V curve [15]. Plots of the curves of Figs. 11 and 12 in the complex plane (Im(Z) vs. Re(Z) curves) show the straight line characteristic of Warburg linear diffusion. Salt diffusion is specially noticeable in the FTBM-1 and FTBM-2 membranes, which agrees with the high limiting currents observed for these membranes (ca. 50 and 140 A/m2 in KCl 0.5 M, respectively). For the other membranes, the salt diffusion effect is not so clear, and its contribution is masked by the EFE water dissociation (note again that the admittances are connected in series, and thus the major admittance dictates the observed behaviour).
When the migration of salt ions out from the bipolar junction can no longer be compensated by the diffusive ¯ux into this region, a limiting current is reached in the I±V curve [15]. Overlimiting currents appear only at high enough voltages, and are due to the EFE water dissociation. Figs. 13 and 14 show the onset of the overlimiting current region for WSI and FTBM-1 membranes. Two main contributions to the impedance appear, one low-frequency region similar to salt diffusion curves (see Figs. 11 and 12), and one higher frequency region related with the presence of water dissociation. Nevertheless, it is not easy to separate the contributions from salt and water ions because the
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Fig. 12. Logarithmic plots of Im (Z) vs. for FTBM-2 membrane at 298 K for currents under the limiting current. The symbols denote the experimental data under reverse polarisation.
Fig. 13. Logarithmic plots of Im(Z) vs. for WSI membrane at 298 K at the onset of the overlimiting current region. The symbols denote the experimental data under reverse polarisation.
onset of water dissociation increases the water ions concentrations at the junction, what changes the boundary conditions under which salt diffusion occurs. Previous theoretical approaches have shown the dependence of the impedance terms on the concentration of salt and water minority carriers [31,32]. Water dissociation can only increase the local concentration of majority carriers of water (decreasing thus the concentration of the minority carriers). There-
fore, it could be not justi®ed to neglect the salt terms in the analysis of the impedance spectra of BMs. 3.3. The effect of temperature on the impedance spectra of BMs Finally, the temperature effects on the impedance spectra under reverse polarisation are shown in Fig. 15 for WSI membrane under the current I101 A/m2. We
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Fig. 14. Logarithmic plots of Im(Z) vs. for FTBM-1 membrane at 298 K at the onset of the overlimiting current region. The symbols denote the experimental data under reverse polarisation.
Fig. 15. Logarithmic plots of Im(Z) vs. for WSI membrane under reverse polarisation and I101 A/m2. The symbols denote the experimental data for three temperatures.
give the impedance curves Im(Z) vs. !/2 for three different temperatures (278, 298 and 308 K). (Note that all curves correspond to the same current.) As can be seen, the position of the maxima depends only slightly on temperature, although the curves are represented in logarithmic axes, and real effects could appear minimised. Table 2 shows the position of the maximum of Im(Z) vs. frequency
for all the membranes at 278 and 308 K. We see that max moves to higher values with increasing temperatures and Im(Z)max decreases signi®cantly with increasing temperature, showing that the EFE water dissociation increases with temperature. Although this appears to be the usual result, some BMs show nearly identical behaviour for different temperatures [14].
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Table 2 Values and position of the maxima of the curves Im(Z) vs. frequency for all membranes under a reverse current of I128 A/m2 at 278 and 308 K Membrane
Temperature (K) 278
WSI FTMB-1 FTMB-2 BP-1 AP6
308
max (Hz)
Im(Z)max ( )
max (Hz)
Im(Z)max ( )
3102 49 19 4479 ±
ÿ80 ÿ18 ÿ11 ÿ1.1 ±
4244 98 32 9501 ±
ÿ23 ÿ12 ÿ8 ÿ0.6 ±
4. Conclusions A complete study of the experimental impedance spectra of ®ve BMs has been presented. It is clear that the polymeric material and the local structure of the bipolar junction exert a marked in¯uence on the experimental curves. Even when two different samples of the same membrane are measured, some differences may still be observed in their impedance curves, which demonstrates that impedance spectroscopy is a very sensitive tool to probe the BM structure [27,31±35]. The differences are not related to the reproducibility of the curves for a given membrane sample, which was checked satisfactorily in previous sets of measurements: each experimental curve reported was measured twice, go and back, and no noticeable hysteresis effects were found. Moreover, different measurements taken from a given membrane sample showed that the only noticeable differences in the AC impedance spectra obtained under identical conditions were those coming from the position of the reference electrodes (note that this position is relevant to the bulk resistance of the cell), while other characteristics like Im(Z)max or max in the Im(Z) vs. plots remained unaltered within the experimental error. We have attempted to compare the survey of experimental curves presented with previous theoretical models [31,32] derived directly from the Nernst± Planck/Poisson equations system without assuming any particular equivalent circuit for the BM. However, the spectra of two BMs (membrane BP-1 and specially, membrane AP6) are different enough when
compared with the other BMs spectra to cast some doubts as to whether some of the assumptions introduced in the theoretical models can be applied to these membranes. For the other BMs, a reasonable qualitative agreement between theory and experiment can be obtained using membrane parameters similar to those found in our previous studies of the I±V curve [15,16,50] and membrane potential [29,30]. Unfortunately, the number of unknown parameters is still too high to attempt a least square ®tting, and unrealistic values for these parameters could be obtained if the model were forced to a quantitative ®tting. It is feasible that a quantitative agreement might be achieved using ad hoc complicated equivalent circuits but due to the complexity of the BM system, it is not trivial to relate any assumed electrical network to the real BM. Also, although we have carried out measurements of the impedance curves of the empty cell and the BM under forward and reverse polarisation in order to check the theory [31,32], we must mention that other effects not included in our model (such as the capacitance of the membrane±solution interfaces and the change in the boundary conditions due to the coupling between ion and water ¯uxes) could also be important, and cannot be discarded at this preliminary stage. Acknowledgements Financial support from the Generalitat Valenciana (Project no. 3242/95), the DGICYT (Project no. PB95-0018) and European Union (Contract no. BRRT-CT97-5038), are gratefully acknowledged. AA wishes to thank the Ministry of Education and Science of Spain for FPU granting, and also the staff of the Institute of Process Technology of SaarbruÈcken for their kind support during his stay there. References [1] I.C. Bassignana, H. Reiss, Ion transport and water dissociation in bipolar ion exchange membranes, J. Membr. Sci. 15 (1983) 27. [2] K.N. Mani, Electrodialysis water splitting technology, J. Membr. Sci. 58 (1991) 117. [3] H. Strathmann, H.-J. Rapp, B. Bauer, C.M. Bell, Theoretical and practical aspects of preparing bipolar membranes, Desalination 90 (1993) 303.
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