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Chronopotentiometry and overlimiting ion transport through monopolar ion exchange membranes
Journal of Membrane Science 162 (1999) 155±164
Chronopotentiometry and overlimiting ion transport through monopolar ion exchange membranes J.J. Krol, M. Wessling, H. Strathmann* University of Twente, Faculty of Chemical Technology, PO Box 217, 7500 AE Enschede, Netherlands Received 28 January 1998; received in revised form 1 April 1999; accepted 8 April 1999
Abstract In this paper chronopotentiometric measurements are described to study the overlimiting ion transport through a Neosepta CMX cation and AMX anion exchange membrane. This technique is used to characterise the ¯uctuations in membrane voltage drop observed in the overlimiting region of current±voltage curves and to investigate the structural inhomogeneity of the aforementioned membranes. Above the limiting current the measurements show large voltage drop ¯uctuations in time indicating hydrodynamic instabilities. The amplitude of these ¯uctuations is increasing with increasing applied current density. The ¯uctuations also occur when a set-up is used where there is no forced convection and the depleted diffusion layer is stabilised by gravitation. Experimental transition times are found to be smaller than calculated for an ideally permselective membrane and indicate a reduced permeable membrane area. The results can be related to the theory of electroconvection due to an inhomogeneous membrane structure. # 1999 Elsevier Science B.V. All rights reserved. Keywords: Ion exchange membranes; Overlimiting current; Membrane inhomogeneity; Electroconvection
1. Introduction In the previous paper [1] concentration polarisation with a Tokuyama Soda Neosepta CMX and AMX cation and anion exchange membrane was studied by measuring current±voltage curves. These curves clearly demonstrated that currents above the limiting current density can be obtained. While the measured curves appear to be smooth at lower current densities, the region of the overlimiting current is characterised by a considerable scatter. This indicates that ¯uctua-
*Corresponding author. Tel.: +31-53-489-2962; fax: +31-53489-4611.
tions in membrane voltage drop occur at a given current density in this region. The occurrence of scattering in the overlimiting current range has been observed by many authors and presumably involves hydrodynamic instabilities [2±11]. It was also established with the abovementioned two membranes that the overlimiting current could not be explained by the occurrence of water dissociation or a loss in permselectivity, i.e. virtually all of the current in this region is still carried by the salt counter ions [1]. Indusekhar and Maeres [12] found a substantial difference between the experimental limiting current density with a cation exchange membrane when it was compared with a reversible electrode under identical
0376-7388/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 6 - 7 3 8 8 ( 9 9 ) 0 0 1 3 4 - 9
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hydrodynamical circumstances. Furthermore, using a special membrane cell, Rubinstein et al. [13] experimentally determined limiting current densities which were up to four times smaller than the theoretical prediction suggesting a reduced permeable membrane area, i.e. the presence of heterogeneities in the membranes. Based on these observations, Rubinstein developed a theory referred to as electroconvection [14±17] to account for the overlimiting current. Electroconvection is a non-gravitational type of convection. The presence of non-conducting parts in the membranes would result in a non-uniform electric ®eld at the membrane surface. Interaction with a weak space charge creates a bulk force which sets the ¯uid in the depleted boundary layer in motion. The formation of turbulences near the membrane surface would not only explain the overlimiting current by salt counter ions but also the instabilities observed in this region. Although electroconvection is possible with a perfectly homogeneous membrane [18,19], the presence of heterogeneities could play an important role in the formation of overlimiting currents [18]. In fact, although many ion exchange membranes are usually denoted as being homogeneous, they very well may have some kind of heterogeneity on the microscale [10,20±23]. A technique which has successfully been applied to determine a reduced permeable area with ion exchange membranes is chronopotentiometry [24]. These measurements are performed in a galvanostatic mode (i.e. a constant current density is applied) in which the voltage drop between the electrode and a reference electrode is measured as a function of time. Originally, this technique has frequently been used to investigate kinetic effects such as adsorption and transport phenomena near electrode surfaces [25±27] but in a limited amount it has also been applied for studying the transport processes near and through ion exchange membranes [28±32]. In this paper chronopotentiometry is used to study ion transport across a Tokuyama Soda CMX cation and an AMX anion exchange membrane. The aim is ®rstly to characterise the ¯uctuations in membrane voltage drop in the overlimiting region as was observed in the current±voltage curves previously recorded [1]. Furthermore, this technique is used to establish the picture of a heterogeneous nature of the two membranes.
2. Mass transport during chronopotentiometric measurements When an electric current is applied to a system containing an ion exchange membrane concentration polarisation phenomena arise, i.e. concentration gradients are developed in the vicinity of the membrane [33]. The transient process occurring near the membrane until a steady state is reached, can be followed by measuring the voltage drop across the membrane as a function of time. To describe the non-steady ion transport, a homogeneous ion selective interface is assumed in contact with a univalent electrolyte solution in the absence of a supporting electrolyte and without any form of convection. The latter indicates an unlimited growth of the diffusion layer adjacent to the membrane. The concentration change of the electrolyte as a function of distance and time can be described by Fick's second law: @C x; t @ 2 C x; t D : @t @x2
(1)
Here C is the electrolyte concentration, x the directional coordinate, t the time and D the electrolyte diffusion coef®cient. At time zero the concentrations throughout the system are equal: C(x,0)C0. Furthermore, since a semi-in®nite diffusion problem is considered, the concentration remains constant at all times for positions suf®ciently far from the membrane: C(x!1, t)C0. The counter ion ¯ux within the membrane, Jim is due to migration and is equal to the counter ion ¯ux in the solution, JiS where both migration and diffusion occurs [30] Jim JiS
iti ; zF
iti @C D : @x x0 zF
(2) (3)
In these equations i is the current density, ti the counter ion transport number in the membrane, ti the counter ion transport number in the solution, z the electrochemical valence and F the Faraday constant. Diffusion coef®cients and transport numbers are assumed independent of concentration. Combining Eqs. (2) and (3) gives a boundary condition for the concentration at the membrane surface
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(x0) at t>0 @C i ti ÿ ti : ÿ @x x0 zFD
(4)
Eq. (1) can now be solved using Laplace transformation [34] " r i ti ÿ ti Dt x2 2 exp ÿ C x; t C0 ÿ 4Dt zFD x (5) ÿx:erfc p : 2 Dt The concentration at the membrane surface as a function of time can thus be expressed as r i Dt ti ÿ ti 2 : (6) C 0; t C0 ÿ zFD From Eq. (6) it is clear that the concentration at the membrane surface decreases with time. At a certain time , called the transition time, this concentration reaches zero. The transition time as a function of applied current density is readily derived from Eq. (6) and is given by D C0 zF 2 1 : (7) 4 ti ÿ ti i2 Eq. (7), which is equivalent to the Sand equation frequently used in studies of electrode systems [35], shows that the transition time is proportional to the inverse of the current density squared. It also shows that the transition time increases when the membrane transport number decreases, i.e. when the membrane is less permselective. 3. Experimental Chronopotentiometric curves were determined with a six-compartment membrane cell and an experimental set-up described elsewhere [1,36]. The voltage drop across the membrane under investigation was measured by means of two Haber±Luggin capillaries connected to calomel reference electrodes (Schott B 2810). At given time a ®xed value of the current density was applied to the membrane cell and the voltage drop across the membrane was measured as a function of time with a sampling rate of 600 times per
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minute. Conductivity and pH of the solutions adjacent to the test membrane were monitored continuously to ensure constant solution composition during a set of experiments. The membranes used in the investigations were the Neosepta AMX anion and CMX cation exchange membrane, supplied by Tokuyama Soda Inc., Japan. The membrane area was 23.8 cm2. All measurements were performed with 0.10 M NaCl solution on either side of the test membrane. The temperature of these solutions was controlled by a thermostat bath and set at 238C. To study the in¯uence of hydrodynamics, chronopotentiometric measurements were performed with two different test con®gurations. The ®rst con®guration equals the set-up which was used in the previous paper to measure current±voltage curves [1]. In this case the membrane cell is placed in such a way that the membranes are in a vertical position. The electrolyte solutions are pumped through the membrane cell with a ¯owrate of 475 ml/min. In the second con®guration the membrane cell is rotated 908. Thus the membranes are placed in a horizontal position. No solution ¯ow (forced convection) is applied during a chronopotentiometric measurement, the solutions in the cell compartments are stagnant. The counter ion ¯ux is directed upwards, i.e. the solution underneath the membrane becomes depleted of ions. With this con®guration the concentration gradients underneath the membrane are stabilised by gravitation and the occurrence of natural convection is minimised (a ``lighter'' salt depleted layer on top of a ``heavier'' solution where no concentration gradients have developed yet) [13,24]. The two con®gurations are shown in Fig. 1. 4. Results and discussion In this section the results of different chronopotentiometric investigations are discussed. The ®rst part deals with the experimental set-up as shown in Fig. 1(A), i.e. test membrane in a vertical position and a solution ¯owing through the membrane cell. The second part is focussed on chronopotentiometric curves obtained with the con®guration as shown in Fig. 1(B) (test membrane in a horizontal position, counter ion ¯ux upwards without solution ¯ow in
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Fig. 1. Schematic drawing of the membrane cell positions used in the chronopotentiometric experiments: (A) test membrane in a vertical position, with solution flow through the membrane cell; (B) test membrane in horizontal position, no solution flow through the membrane cell. Arrow through the membrane indicates the direction of the counter ion flux.
Fig. 2 shows a typical example of a chronopotentiometric curve, measured with a CMX membrane in 0.10 M NaCl when applying a current density above the limiting current density of this system. The curve consists of four parts. At time zero the experiment is started but no current is applied yet and since the solutions on either side of the membrane are equal, the voltage drop remains zero. At point A, a ®xed current density is applied and an instantaneous increase in voltage drop occurs which is part 1 of the curve shown
in Fig. 2. This increase in voltage drop is due to the initial ohmic resistance of the system composed of solution and membrane between the tips of the voltage measuring capillaries. After the increase in voltage due to the ohmic resistance, part 2 commences which is a very slow increase in voltage drop in time. At a certain time this is followed by a strong increase in voltage drop (part 3). The point at which this increase occurs is the transition time which can be determined by the intersection of the tangents to part 2 and 3 of the curve [37]. Finally the fourth part of the curve is reached where the voltage drop levels off. Fig. 3 shows a characteristic set of chronopotentiometric curves measured at different applied current densities with a CMX membrane in 0.10 M NaCl. The limiting current density for this system is 9.50.5 mA/cm2 [1]. It is observed that the curve measured at a current density below the limiting
Fig. 2. Example of a chronopotentiometric curve measured for a CMX membrane in 0.10 M NaCl. Point A denotes the time at which a fixed current density of 15 mA/cm2 is applied, is the transition time. The numbers in the graph refer to the different stages explained in the text.
Fig. 3. Chronopotentiometric curves at different applied current densities measured with a CMX membrane in 0.10 M NaCl (set-up: vertically placed membrane with solution flow). Numbers next to the curves refer to the applied current density.
the membrane cell). In the third part transition times determined from the different chronopotentiometric measurements are compared with those calculated from theory. 4.1. Vertically positioned membrane with solution flow
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current does not show the sharp increase in voltage drop which is measured when applying a current density above the limiting value. This curve is not characterised by a transition time because the concentration near the membrane surface does not reach zero. Furthermore Fig. 3 shows that a more or less steady state voltage drop is reached for the curves measured below the limiting current density. However, this is not the case when current densities larger than the limiting current are applied. For these curves only a quasi-steady state is reached characterised by large ¯uctuations in voltage drop. This is in agreement with the current±voltage curves which showed a smooth pattern below and a considerable scatter near and above the limiting current density [1]. Fig. 3 shows that the amplitude of these ¯uctuations clearly increase with increasing applied current density. Experiments performed with the AMX anion exchange membrane showed similar results [36].
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Fig. 5. The occurrence of fluctuations in voltage drop with the membrane in the horizontally gravitationally stabilised position (CMX membrane, applied current density is 35 mA/cm2).
Fig. 4 shows a set of chronopotentiometric curves measured with zero solution ¯owrate, the membrane placed in a horizontal position and the counter ion ¯ux upwards. Since the solution in this compartment is stagnant, the thickness of the boundary layer increases with time, i.e. no ®xed boundary layer thickness is obtained. This is in agreement with the results shown in Fig. 4: after applying a ®xed current density a similar pattern as shown in Fig. 2 is seen with an
in¯ection at the transition time. However, since there is an unlimited growth of the thickness of the depleted boundary layer, no steady state voltage drop is obtained but the voltage drop remains increasing with time. The curves measured with the depleted membrane boundary layer in the gravitationally stabilised position also show the presence of instabilities; ¯uctuations in voltage drop are evident, the magnitude of which is increasing with time. A clear example of this feature is shown in Fig. 5. Since there is no solution ¯ow through the membrane cell, these measurements demonstrate that the ¯uctuations are not a result of forced convection. The experiments were repeated with the AMX anion exchange membrane using the same set-up con®guration. The results, shown in Fig. 6, are very
Fig. 4. Chronopotentiometric curves at different applied current densities measured with the CMX membrane, horizontally positioned, counter ion flux upwards and without solution flow (gravitationally stabilised position).
Fig. 6. Chronopotentiometric curves at different applied current densities measured with the AMX membrane in the gravitationally stabilised position.
4.2. Horizontally positioned membrane without solution flow
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similar to the results obtained with the CMX membrane. 4.3. Transition times Figs. 3, 4 and 6 show that the transition time decreases with increasing applied current density. Eq. (7) predicts the transition time being proportional to the inverse of the current density squared. Transition times were determined for the CMX membrane as a function of applied current density. This was done for the two set-up con®gurations described earlier. The results, shown in Fig. 7, demonstrate that indeed a linear relationship is observed between the transition time and the inverse current density squared. From Fig. 7 it is clear that the experimentally determined transition times coincide for the two different membrane set-ups although the hydrodynamics are completely different. Eq. (7) was derived for a semi-in®nite diffusion process. This assumes the absence of any forced or natural convection and thus an unlimited growth of the diffusion layer next to the membrane. The chronopotentiometric measurements in Figs. 4 and 6 indicate that these conditions are ful®lled using the system with the horizontally positioned membrane with its depleted boundary layer in the gravitationally stabilised position. This is a priori not the case for the system with the vertically positioned membrane since a (convective) solution ¯ow is forced through the membrane cell thereby creating a laminar ¯ow diffusion layer with ®nite thickness.
Fig. 7. Comparison of transition time as a function of the inverse current density squared between the two different membrane setups, i.e. horizontally positioned membrane, counter ion flux upwards and no solution flow versus vertically placed membrane with solution flow (CMX membrane).
However, a system with forced convection can still resemble the semi-in®nite diffusion problem during a time-scale in which no concentration changes have occurred at a distance from the membrane surface equal to the boundary layer thickness. An in®nite boundary layer concept can thus be used for not too large times, i.e. times p in which the root-mean-square displacement 2Dt is small compared to the thickness of the boundary layer [37,38]. In the previous paper [1] limiting current densities were measured for the CMX and AMX membrane in NaCl solutions of different concentrations. The limiting current density can be calculated according to [33] ilim
FC b D : ti ÿ ti
(8)
Here ilim is the limiting current density, F the Faraday constant, Cb the bulk solution concentration, D the salt diffusion coef®cient, the boundary layer thickness, ti the counter ion transport number in the membrane and ti the transport number in the solution. With Eq. (8) and the experimentally determined limiting current densities, an estimation of the thickness of the boundary layer can be obtained. The boundary layer thickness calculated this way is in the range of 250±300 mm. Using 250 mm for the root-mean-square displacement, an upper limit for the transition time is calculated to be 20 s. Thus as long as transition times smaller than 20 s are determined, a semi-in®nite diffusion process can be assumed, a condition which is ful®lled in Fig. 7. This explains why still a linear relationship is obtained in Fig. 7 for the vertically positioned membrane with solution ¯ow and why in this ®gure the determined transition times coincide with the transition times determined with the horizontally mounted membrane with its depletion layer gravitationally stabilised. The previous discussion has shown that both membrane set-ups can be used to determine the transition time as a function of applied current density. The system with the vertically positioned membrane and solution ¯ow is characterised by a limiting current density. In order to measure a transition time, current densities above the limiting current value have to be applied, otherwise the concentration at the membrane surface will not reach zero. This reduces the range of current densities which can be used to investigate the transition time as a function of applied current density
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Fig. 8. Comparison between experimental (open circles, dashed line) and calculated transition times (solid lines) for the CMX membrane (horizontally, gravitationally stabilised position). The calculated lines refer to an ideally permselective membrane (counter ion transport number in the membrane equals 1) and a membrane with counter ion transport number 0.95.
Fig. 9. Comparison between experimental (open circles, dashed line) and calculated transition times (solid lines) for the AMX membrane (horizontally, gravitationally stabilised position). The calculated lines refer to an ideally permselective membrane (membrane transport number 1) and a membrane with transport number 0.95.
and thus limits a comparison between calculated and experimental transition times. This is not the case with the second membrane set-up where no solution ¯ow is present. Here much lower current densities can be applied while still obtaining a transition time (for a truly in®nite diffusion layer thickness the limiting current density is zero). Fig. 8 shows the transition time as a function of the inverse of the current density squared, determined over a broader range of current densities and transition times. In this ®gure, a comparison is made with the transition time calculated according to Eq. (7). For the calculation, a NaCl diffusion coef®cient of 1.4810ÿ9 m2/s and a Na solution transport number of 0.39 were used for the 0.10 M NaCl solution [39]. It is seen that the experimentally determined transition times are smaller than the transition times calculated for an ideally permselective membrane. The permselectivity of the CMX and the AMX membrane is about 95% [36]. In Fig. 8 also the calculated line is shown using 0.95 as the membrane transport number which demonstrates that a small reduction in membrane permselectivity can signi®cantly increase the transition time. Fig. 9 shows the comparison between calculated and experimentally determined transition times obtained with the AMX membrane, again with the membrane in the horizontal position without solution ¯ow and counter ion ¯ux upwards. The results in Fig. 9 are similar to the ®ndings with the CMX
membrane. Also in this case the experimental transition times are smaller than the values calculated for an ideally permselective membrane. When Figs. 8 and 9 are compared, it is observed that at given applied current density the transition time for the anion exchange membrane is much higher than for the cation exchange membrane. The difference is caused by different counter ions of the two membranes. The Clÿ ion transport number in the solution (0.61) is much larger than that of the Na ion (0.39) and Eq. (7) shows that, given the same membrane transport numbers, this results in higher transition times for the anion exchange membrane. The results in Figs. 8 and 9 show that the experimentally determined transition times are lower than the transition times calculated for an ideally permselective membrane. Any non-ideal behaviour of a real system, such as a reduced permselectivity, consumption of non-Faradaic currents for charging of double layers and the onset of natural convection, would only result in transition times higher than predicted by theory [24,40]. This way it can be argued that transition times lower than the values calculated for an ideally permselective membrane can only be due to a reduction in available membrane area for ion conductance [24]. A reduced permeable membrane area corresponds to a locally higher current density at those points where the membrane is conductive. This causes a faster depletion of salt near the membrane, i.e. a lower transition time is measured compared to the
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situation where the complete membrane area is available for ion conduction. It has to be noted that the difference between the experimental slope and the calculated slope for an ideally permselective membrane in Figs. 8 and 9 is very small, the ratio is about 0.92 for the CMX and 0.95 for the AMX membrane. RoÈsler [24,37] performed experiments with several commercial and lab-made cation and anion exchange membranes and also found experimental transition times lower than predicted by theory. The commercial membranes showed a similar small difference between experimental and calculated transition times measured in CuSO4 and KCl solutions. The difference, however, was much larger when the lab-made cation exchange membranes were studied (the ratio in slopes varied between 0.64 and 0.87 in this case). Sulfonated polysulfone membranes had been prepared with similar permselectivity but differing in ion exchange capacity. A correlation was found between the ion exchange capacity and the transition times. A decrease in ion exchange capacity resulted in a larger difference between the experimental transition times and the ones calculated for an ideally permselective membrane. A membrane with a lower ion exchange capacity can be regarded as being more heterogeneous than a membrane with higher ion exchange capacity. Based on these results the conclusion seems justi®ed that a reduction in transition time compared to theory is due to a reduced permeable membrane area. Mizutani [22] published a review about the structure of Neosepta membranes produced by Tokuyama Soda. Although the Neosepta CMX and AMX membranes are not mentioned, it can be assumed that the results obtained in his paper are applicable to these two membranes as well [41]. The Neosepta membranes are prepared by the paste method. A paste consists of a monomer with a functional group appropriate to introduce an ion exchange group, divinylbenzene as a crosslinking agent, a radical polymerisation initiator and ®nely powdered poly(vinylchloride). The paste is coated onto a PVC cloth as reinforcing material and the monomers are copolymerised and subsequently sulfonated or aminated to produce ion exchange membranes with sulfonic acid or quaternary ammonium groups. The structure of these membranes was studied by removing the ion exchange material using a H2O2 treatment, resulting in
the formation of microporous membranes. Microscopic techniques combined with water permeability measurements revealed that the membranes contain microheterogeneities, i.e. the membranes consist of two continuous phases, a PVC phase and the ion exchange resin, which are closely intertwined. These studies on Neosepta membranes are thus in agreement with the chronopotentiometric results shown here for the CMX and AMX membranes which also indicated the presence of heterogeneities. 5. Conclusions Chronopotentiometric measurements were shown with a CMX cation exchange membrane with the membrane present in a vertical position in the membrane cell while a solution ¯ows through the cell. When a current below the limiting current density was applied the voltage drop increases slowly and a steady state value was reached. If a current larger than the limiting current density was applied, the curves were characterised by a sharp increase in voltage drop at the transition time. After this the voltage drop leveled off and a quasi-steady state was reached showing strong ¯uctuations around an avarage value. This is in agreement with the considerable scatter in data points in the overlimiting region of the current±voltage curve. The amplitude of the ¯uctuations in voltage drop increased with increasing applied current density. The ¯uctuations occurring in the overlimiting current range indicate the presence of hydrodynamic instabilities close to the membrane surface. Chronopotentiometric curves were determined both with the CMX and the AMX membrane using a set-up con®guration without any forced convection in the solution, with the membrane placed horizontally and the counter ion ¯ux upwards. The results for the two types of membranes were very similar. The measurements showed that no steady state voltage drop was reached, but the voltage drop continuously increased with time. This was due to the stabilisation of the concentration gradients in the depleted solution by gravitation. The occurrence of natural convection was minimised allowing for the concentration pro®le to grow into the solution with time. These measurements also showed the presence of ¯uctuations in voltage drop. Since there was no ¯ow through the membrane
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cell, this demonstrates that the ¯uctuations are not a result of a forced convection. Transition times were determined as a function of the applied current density for both the CMX and the AMX membrane. As predicted by theory, a linear relationship was obtained between the transition time and the inverse current density squared. Experimental transition times were found to be smaller than calculated for an ideally permselective membrane, indicating a reduced permeable membrane area for the two investigated membranes. The results obtained can be related to the theory describing electroconvection. Earlier [1], it was found that the overlimiting current for the CMX and AMX membrane could neither be explained by a loss in permselectivity nor by the occurrence of water dissociation. Thus the counter ions remain responsible for carrying the current in the overlimiting region. The chronopotentiometric experiments described in this paper have shown that large ¯uctuations in voltage drop occur even with the set-up where no solution ¯ow is applied and the depleted diffusion layer is stabilised by gravitation. These ¯uctuations indicate that indeed hydrodynamic instabilities occur, i.e. convective phenomena are present close to the membrane surface which destabilise the polarised boundary layer and lead to the overlimiting currents. The chronopotentiometric measurements on the two studied membranes indicated the presence of heterogeneities which are likely to cause the electroconvective phenomena. References [1] J.J. Krol, M. Wessling, H. Strathmann, Concentration polarisation with monopolar ion exchange membranes: current±voltage curves and water dissociation. J. Membrane Sci. 162(1±2) (1999) 145±154. [2] S. Reich, B. Gavish, S. Lifson, Visualization of hydrodynamic phenomena in the vicinity of a semipermeable membrane, Desalination 24 (1978) 295±296. [3] I. Rubinstein, L. Shtilman, Voltage against current curves of cation exchange membranes, J. Chem. Soc., Faraday Trans. II 75 (1979) 231±246. [4] S. Lifson, B. Gavish, S. Reich, Flicker noise of ion-selective membranes and turbulent convection in the depleted layer, Biophys. Struct. Mechanism 4 (1978) 53±65. [5] Y. Fang, Q. Li, M.E. Green, Noise spectra of transport at an anion membrane±solution interface, J. Colloid Interf. Sci. 86 (1982) 185±190.
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potentiometric response of a cation exchange membrane in contact with chromium (III) solutions, Desalination 105 (1996) 219±228. P. Sistat, G. Pourcelly, Chronopotentiometric response of an ion-exchange membrane in the underlimiting current-range. Transport phenomena within the diffusion layers, J. Membr. Sci. 123 (1997) 121±131. K.S. Spiegler, Polarization at ion exchange membrane± solution interfaces, Desalination 9 (1971) 367±385. C.N. Reilly, Fundamentals of electrode processes, in: I.M. Kolthoff, P.J. Elving (Eds.), Treatise on Analytical Chemistry, Wiley, New York, 1963, pp. 2109±2160. H.J.S. Sand, On the concentration at the electrodes in a solution, Phil. Mag. 1 (1901) 45±79. J.J. Krol, Monopolar and bipolar ion exchange membranes ± Mass transport limitations, Ph.D. Thesis, University of Twente, The Netherlands, 1997. H.-W. RoÈsler, Untersuchungen zum uÈberkritischen lonentransport durch Elektrodialyse±membranen mit Hilfe der Chronopotentiometrie, Rausehanalyse und Diffusions±Relaxation, Ph.D. Thesis, University of Essen, Germany, 1991. K.J. Vetter, Elektrochemische Kinetik, Springer, Berlin, 1961. R.A. Robinson, R.H. Stokes, Electrolyte Solutions, Butterworths, London, 1959. A.J. Bard, Effect of electrode configuration and transition time in solid electrode chronopotentiometry, Anal. Chem. 33 (1961) 11±15. Tokuyama Soda Inc., personal communication (1997).
Chronopotentiometry and overlimiting ion transport through monopolar ion exchange membranes J.J. Krol, M. Wessling, H. Strathmann* University of Twente, Faculty of Chemical Technology, PO Box 217, 7500 AE Enschede, Netherlands Received 28 January 1998; received in revised form 1 April 1999; accepted 8 April 1999
Abstract In this paper chronopotentiometric measurements are described to study the overlimiting ion transport through a Neosepta CMX cation and AMX anion exchange membrane. This technique is used to characterise the ¯uctuations in membrane voltage drop observed in the overlimiting region of current±voltage curves and to investigate the structural inhomogeneity of the aforementioned membranes. Above the limiting current the measurements show large voltage drop ¯uctuations in time indicating hydrodynamic instabilities. The amplitude of these ¯uctuations is increasing with increasing applied current density. The ¯uctuations also occur when a set-up is used where there is no forced convection and the depleted diffusion layer is stabilised by gravitation. Experimental transition times are found to be smaller than calculated for an ideally permselective membrane and indicate a reduced permeable membrane area. The results can be related to the theory of electroconvection due to an inhomogeneous membrane structure. # 1999 Elsevier Science B.V. All rights reserved. Keywords: Ion exchange membranes; Overlimiting current; Membrane inhomogeneity; Electroconvection
1. Introduction In the previous paper [1] concentration polarisation with a Tokuyama Soda Neosepta CMX and AMX cation and anion exchange membrane was studied by measuring current±voltage curves. These curves clearly demonstrated that currents above the limiting current density can be obtained. While the measured curves appear to be smooth at lower current densities, the region of the overlimiting current is characterised by a considerable scatter. This indicates that ¯uctua-
*Corresponding author. Tel.: +31-53-489-2962; fax: +31-53489-4611.
tions in membrane voltage drop occur at a given current density in this region. The occurrence of scattering in the overlimiting current range has been observed by many authors and presumably involves hydrodynamic instabilities [2±11]. It was also established with the abovementioned two membranes that the overlimiting current could not be explained by the occurrence of water dissociation or a loss in permselectivity, i.e. virtually all of the current in this region is still carried by the salt counter ions [1]. Indusekhar and Maeres [12] found a substantial difference between the experimental limiting current density with a cation exchange membrane when it was compared with a reversible electrode under identical
0376-7388/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 6 - 7 3 8 8 ( 9 9 ) 0 0 1 3 4 - 9
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hydrodynamical circumstances. Furthermore, using a special membrane cell, Rubinstein et al. [13] experimentally determined limiting current densities which were up to four times smaller than the theoretical prediction suggesting a reduced permeable membrane area, i.e. the presence of heterogeneities in the membranes. Based on these observations, Rubinstein developed a theory referred to as electroconvection [14±17] to account for the overlimiting current. Electroconvection is a non-gravitational type of convection. The presence of non-conducting parts in the membranes would result in a non-uniform electric ®eld at the membrane surface. Interaction with a weak space charge creates a bulk force which sets the ¯uid in the depleted boundary layer in motion. The formation of turbulences near the membrane surface would not only explain the overlimiting current by salt counter ions but also the instabilities observed in this region. Although electroconvection is possible with a perfectly homogeneous membrane [18,19], the presence of heterogeneities could play an important role in the formation of overlimiting currents [18]. In fact, although many ion exchange membranes are usually denoted as being homogeneous, they very well may have some kind of heterogeneity on the microscale [10,20±23]. A technique which has successfully been applied to determine a reduced permeable area with ion exchange membranes is chronopotentiometry [24]. These measurements are performed in a galvanostatic mode (i.e. a constant current density is applied) in which the voltage drop between the electrode and a reference electrode is measured as a function of time. Originally, this technique has frequently been used to investigate kinetic effects such as adsorption and transport phenomena near electrode surfaces [25±27] but in a limited amount it has also been applied for studying the transport processes near and through ion exchange membranes [28±32]. In this paper chronopotentiometry is used to study ion transport across a Tokuyama Soda CMX cation and an AMX anion exchange membrane. The aim is ®rstly to characterise the ¯uctuations in membrane voltage drop in the overlimiting region as was observed in the current±voltage curves previously recorded [1]. Furthermore, this technique is used to establish the picture of a heterogeneous nature of the two membranes.
2. Mass transport during chronopotentiometric measurements When an electric current is applied to a system containing an ion exchange membrane concentration polarisation phenomena arise, i.e. concentration gradients are developed in the vicinity of the membrane [33]. The transient process occurring near the membrane until a steady state is reached, can be followed by measuring the voltage drop across the membrane as a function of time. To describe the non-steady ion transport, a homogeneous ion selective interface is assumed in contact with a univalent electrolyte solution in the absence of a supporting electrolyte and without any form of convection. The latter indicates an unlimited growth of the diffusion layer adjacent to the membrane. The concentration change of the electrolyte as a function of distance and time can be described by Fick's second law: @C x; t @ 2 C x; t D : @t @x2
(1)
Here C is the electrolyte concentration, x the directional coordinate, t the time and D the electrolyte diffusion coef®cient. At time zero the concentrations throughout the system are equal: C(x,0)C0. Furthermore, since a semi-in®nite diffusion problem is considered, the concentration remains constant at all times for positions suf®ciently far from the membrane: C(x!1, t)C0. The counter ion ¯ux within the membrane, Jim is due to migration and is equal to the counter ion ¯ux in the solution, JiS where both migration and diffusion occurs [30] Jim JiS
iti ; zF
iti @C D : @x x0 zF
(2) (3)
In these equations i is the current density, ti the counter ion transport number in the membrane, ti the counter ion transport number in the solution, z the electrochemical valence and F the Faraday constant. Diffusion coef®cients and transport numbers are assumed independent of concentration. Combining Eqs. (2) and (3) gives a boundary condition for the concentration at the membrane surface
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(x0) at t>0 @C i ti ÿ ti : ÿ @x x0 zFD
(4)
Eq. (1) can now be solved using Laplace transformation [34] " r i ti ÿ ti Dt x2 2 exp ÿ C x; t C0 ÿ 4Dt zFD x (5) ÿx:erfc p : 2 Dt The concentration at the membrane surface as a function of time can thus be expressed as r i Dt ti ÿ ti 2 : (6) C 0; t C0 ÿ zFD From Eq. (6) it is clear that the concentration at the membrane surface decreases with time. At a certain time , called the transition time, this concentration reaches zero. The transition time as a function of applied current density is readily derived from Eq. (6) and is given by D C0 zF 2 1 : (7) 4 ti ÿ ti i2 Eq. (7), which is equivalent to the Sand equation frequently used in studies of electrode systems [35], shows that the transition time is proportional to the inverse of the current density squared. It also shows that the transition time increases when the membrane transport number decreases, i.e. when the membrane is less permselective. 3. Experimental Chronopotentiometric curves were determined with a six-compartment membrane cell and an experimental set-up described elsewhere [1,36]. The voltage drop across the membrane under investigation was measured by means of two Haber±Luggin capillaries connected to calomel reference electrodes (Schott B 2810). At given time a ®xed value of the current density was applied to the membrane cell and the voltage drop across the membrane was measured as a function of time with a sampling rate of 600 times per
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minute. Conductivity and pH of the solutions adjacent to the test membrane were monitored continuously to ensure constant solution composition during a set of experiments. The membranes used in the investigations were the Neosepta AMX anion and CMX cation exchange membrane, supplied by Tokuyama Soda Inc., Japan. The membrane area was 23.8 cm2. All measurements were performed with 0.10 M NaCl solution on either side of the test membrane. The temperature of these solutions was controlled by a thermostat bath and set at 238C. To study the in¯uence of hydrodynamics, chronopotentiometric measurements were performed with two different test con®gurations. The ®rst con®guration equals the set-up which was used in the previous paper to measure current±voltage curves [1]. In this case the membrane cell is placed in such a way that the membranes are in a vertical position. The electrolyte solutions are pumped through the membrane cell with a ¯owrate of 475 ml/min. In the second con®guration the membrane cell is rotated 908. Thus the membranes are placed in a horizontal position. No solution ¯ow (forced convection) is applied during a chronopotentiometric measurement, the solutions in the cell compartments are stagnant. The counter ion ¯ux is directed upwards, i.e. the solution underneath the membrane becomes depleted of ions. With this con®guration the concentration gradients underneath the membrane are stabilised by gravitation and the occurrence of natural convection is minimised (a ``lighter'' salt depleted layer on top of a ``heavier'' solution where no concentration gradients have developed yet) [13,24]. The two con®gurations are shown in Fig. 1. 4. Results and discussion In this section the results of different chronopotentiometric investigations are discussed. The ®rst part deals with the experimental set-up as shown in Fig. 1(A), i.e. test membrane in a vertical position and a solution ¯owing through the membrane cell. The second part is focussed on chronopotentiometric curves obtained with the con®guration as shown in Fig. 1(B) (test membrane in a horizontal position, counter ion ¯ux upwards without solution ¯ow in
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Fig. 1. Schematic drawing of the membrane cell positions used in the chronopotentiometric experiments: (A) test membrane in a vertical position, with solution flow through the membrane cell; (B) test membrane in horizontal position, no solution flow through the membrane cell. Arrow through the membrane indicates the direction of the counter ion flux.
Fig. 2 shows a typical example of a chronopotentiometric curve, measured with a CMX membrane in 0.10 M NaCl when applying a current density above the limiting current density of this system. The curve consists of four parts. At time zero the experiment is started but no current is applied yet and since the solutions on either side of the membrane are equal, the voltage drop remains zero. At point A, a ®xed current density is applied and an instantaneous increase in voltage drop occurs which is part 1 of the curve shown
in Fig. 2. This increase in voltage drop is due to the initial ohmic resistance of the system composed of solution and membrane between the tips of the voltage measuring capillaries. After the increase in voltage due to the ohmic resistance, part 2 commences which is a very slow increase in voltage drop in time. At a certain time this is followed by a strong increase in voltage drop (part 3). The point at which this increase occurs is the transition time which can be determined by the intersection of the tangents to part 2 and 3 of the curve [37]. Finally the fourth part of the curve is reached where the voltage drop levels off. Fig. 3 shows a characteristic set of chronopotentiometric curves measured at different applied current densities with a CMX membrane in 0.10 M NaCl. The limiting current density for this system is 9.50.5 mA/cm2 [1]. It is observed that the curve measured at a current density below the limiting
Fig. 2. Example of a chronopotentiometric curve measured for a CMX membrane in 0.10 M NaCl. Point A denotes the time at which a fixed current density of 15 mA/cm2 is applied, is the transition time. The numbers in the graph refer to the different stages explained in the text.
Fig. 3. Chronopotentiometric curves at different applied current densities measured with a CMX membrane in 0.10 M NaCl (set-up: vertically placed membrane with solution flow). Numbers next to the curves refer to the applied current density.
the membrane cell). In the third part transition times determined from the different chronopotentiometric measurements are compared with those calculated from theory. 4.1. Vertically positioned membrane with solution flow
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current does not show the sharp increase in voltage drop which is measured when applying a current density above the limiting value. This curve is not characterised by a transition time because the concentration near the membrane surface does not reach zero. Furthermore Fig. 3 shows that a more or less steady state voltage drop is reached for the curves measured below the limiting current density. However, this is not the case when current densities larger than the limiting current are applied. For these curves only a quasi-steady state is reached characterised by large ¯uctuations in voltage drop. This is in agreement with the current±voltage curves which showed a smooth pattern below and a considerable scatter near and above the limiting current density [1]. Fig. 3 shows that the amplitude of these ¯uctuations clearly increase with increasing applied current density. Experiments performed with the AMX anion exchange membrane showed similar results [36].
159
Fig. 5. The occurrence of fluctuations in voltage drop with the membrane in the horizontally gravitationally stabilised position (CMX membrane, applied current density is 35 mA/cm2).
Fig. 4 shows a set of chronopotentiometric curves measured with zero solution ¯owrate, the membrane placed in a horizontal position and the counter ion ¯ux upwards. Since the solution in this compartment is stagnant, the thickness of the boundary layer increases with time, i.e. no ®xed boundary layer thickness is obtained. This is in agreement with the results shown in Fig. 4: after applying a ®xed current density a similar pattern as shown in Fig. 2 is seen with an
in¯ection at the transition time. However, since there is an unlimited growth of the thickness of the depleted boundary layer, no steady state voltage drop is obtained but the voltage drop remains increasing with time. The curves measured with the depleted membrane boundary layer in the gravitationally stabilised position also show the presence of instabilities; ¯uctuations in voltage drop are evident, the magnitude of which is increasing with time. A clear example of this feature is shown in Fig. 5. Since there is no solution ¯ow through the membrane cell, these measurements demonstrate that the ¯uctuations are not a result of forced convection. The experiments were repeated with the AMX anion exchange membrane using the same set-up con®guration. The results, shown in Fig. 6, are very
Fig. 4. Chronopotentiometric curves at different applied current densities measured with the CMX membrane, horizontally positioned, counter ion flux upwards and without solution flow (gravitationally stabilised position).
Fig. 6. Chronopotentiometric curves at different applied current densities measured with the AMX membrane in the gravitationally stabilised position.
4.2. Horizontally positioned membrane without solution flow
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similar to the results obtained with the CMX membrane. 4.3. Transition times Figs. 3, 4 and 6 show that the transition time decreases with increasing applied current density. Eq. (7) predicts the transition time being proportional to the inverse of the current density squared. Transition times were determined for the CMX membrane as a function of applied current density. This was done for the two set-up con®gurations described earlier. The results, shown in Fig. 7, demonstrate that indeed a linear relationship is observed between the transition time and the inverse current density squared. From Fig. 7 it is clear that the experimentally determined transition times coincide for the two different membrane set-ups although the hydrodynamics are completely different. Eq. (7) was derived for a semi-in®nite diffusion process. This assumes the absence of any forced or natural convection and thus an unlimited growth of the diffusion layer next to the membrane. The chronopotentiometric measurements in Figs. 4 and 6 indicate that these conditions are ful®lled using the system with the horizontally positioned membrane with its depleted boundary layer in the gravitationally stabilised position. This is a priori not the case for the system with the vertically positioned membrane since a (convective) solution ¯ow is forced through the membrane cell thereby creating a laminar ¯ow diffusion layer with ®nite thickness.
Fig. 7. Comparison of transition time as a function of the inverse current density squared between the two different membrane setups, i.e. horizontally positioned membrane, counter ion flux upwards and no solution flow versus vertically placed membrane with solution flow (CMX membrane).
However, a system with forced convection can still resemble the semi-in®nite diffusion problem during a time-scale in which no concentration changes have occurred at a distance from the membrane surface equal to the boundary layer thickness. An in®nite boundary layer concept can thus be used for not too large times, i.e. times p in which the root-mean-square displacement 2Dt is small compared to the thickness of the boundary layer [37,38]. In the previous paper [1] limiting current densities were measured for the CMX and AMX membrane in NaCl solutions of different concentrations. The limiting current density can be calculated according to [33] ilim
FC b D : ti ÿ ti
(8)
Here ilim is the limiting current density, F the Faraday constant, Cb the bulk solution concentration, D the salt diffusion coef®cient, the boundary layer thickness, ti the counter ion transport number in the membrane and ti the transport number in the solution. With Eq. (8) and the experimentally determined limiting current densities, an estimation of the thickness of the boundary layer can be obtained. The boundary layer thickness calculated this way is in the range of 250±300 mm. Using 250 mm for the root-mean-square displacement, an upper limit for the transition time is calculated to be 20 s. Thus as long as transition times smaller than 20 s are determined, a semi-in®nite diffusion process can be assumed, a condition which is ful®lled in Fig. 7. This explains why still a linear relationship is obtained in Fig. 7 for the vertically positioned membrane with solution ¯ow and why in this ®gure the determined transition times coincide with the transition times determined with the horizontally mounted membrane with its depletion layer gravitationally stabilised. The previous discussion has shown that both membrane set-ups can be used to determine the transition time as a function of applied current density. The system with the vertically positioned membrane and solution ¯ow is characterised by a limiting current density. In order to measure a transition time, current densities above the limiting current value have to be applied, otherwise the concentration at the membrane surface will not reach zero. This reduces the range of current densities which can be used to investigate the transition time as a function of applied current density
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161
Fig. 8. Comparison between experimental (open circles, dashed line) and calculated transition times (solid lines) for the CMX membrane (horizontally, gravitationally stabilised position). The calculated lines refer to an ideally permselective membrane (counter ion transport number in the membrane equals 1) and a membrane with counter ion transport number 0.95.
Fig. 9. Comparison between experimental (open circles, dashed line) and calculated transition times (solid lines) for the AMX membrane (horizontally, gravitationally stabilised position). The calculated lines refer to an ideally permselective membrane (membrane transport number 1) and a membrane with transport number 0.95.
and thus limits a comparison between calculated and experimental transition times. This is not the case with the second membrane set-up where no solution ¯ow is present. Here much lower current densities can be applied while still obtaining a transition time (for a truly in®nite diffusion layer thickness the limiting current density is zero). Fig. 8 shows the transition time as a function of the inverse of the current density squared, determined over a broader range of current densities and transition times. In this ®gure, a comparison is made with the transition time calculated according to Eq. (7). For the calculation, a NaCl diffusion coef®cient of 1.4810ÿ9 m2/s and a Na solution transport number of 0.39 were used for the 0.10 M NaCl solution [39]. It is seen that the experimentally determined transition times are smaller than the transition times calculated for an ideally permselective membrane. The permselectivity of the CMX and the AMX membrane is about 95% [36]. In Fig. 8 also the calculated line is shown using 0.95 as the membrane transport number which demonstrates that a small reduction in membrane permselectivity can signi®cantly increase the transition time. Fig. 9 shows the comparison between calculated and experimentally determined transition times obtained with the AMX membrane, again with the membrane in the horizontal position without solution ¯ow and counter ion ¯ux upwards. The results in Fig. 9 are similar to the ®ndings with the CMX
membrane. Also in this case the experimental transition times are smaller than the values calculated for an ideally permselective membrane. When Figs. 8 and 9 are compared, it is observed that at given applied current density the transition time for the anion exchange membrane is much higher than for the cation exchange membrane. The difference is caused by different counter ions of the two membranes. The Clÿ ion transport number in the solution (0.61) is much larger than that of the Na ion (0.39) and Eq. (7) shows that, given the same membrane transport numbers, this results in higher transition times for the anion exchange membrane. The results in Figs. 8 and 9 show that the experimentally determined transition times are lower than the transition times calculated for an ideally permselective membrane. Any non-ideal behaviour of a real system, such as a reduced permselectivity, consumption of non-Faradaic currents for charging of double layers and the onset of natural convection, would only result in transition times higher than predicted by theory [24,40]. This way it can be argued that transition times lower than the values calculated for an ideally permselective membrane can only be due to a reduction in available membrane area for ion conductance [24]. A reduced permeable membrane area corresponds to a locally higher current density at those points where the membrane is conductive. This causes a faster depletion of salt near the membrane, i.e. a lower transition time is measured compared to the
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situation where the complete membrane area is available for ion conduction. It has to be noted that the difference between the experimental slope and the calculated slope for an ideally permselective membrane in Figs. 8 and 9 is very small, the ratio is about 0.92 for the CMX and 0.95 for the AMX membrane. RoÈsler [24,37] performed experiments with several commercial and lab-made cation and anion exchange membranes and also found experimental transition times lower than predicted by theory. The commercial membranes showed a similar small difference between experimental and calculated transition times measured in CuSO4 and KCl solutions. The difference, however, was much larger when the lab-made cation exchange membranes were studied (the ratio in slopes varied between 0.64 and 0.87 in this case). Sulfonated polysulfone membranes had been prepared with similar permselectivity but differing in ion exchange capacity. A correlation was found between the ion exchange capacity and the transition times. A decrease in ion exchange capacity resulted in a larger difference between the experimental transition times and the ones calculated for an ideally permselective membrane. A membrane with a lower ion exchange capacity can be regarded as being more heterogeneous than a membrane with higher ion exchange capacity. Based on these results the conclusion seems justi®ed that a reduction in transition time compared to theory is due to a reduced permeable membrane area. Mizutani [22] published a review about the structure of Neosepta membranes produced by Tokuyama Soda. Although the Neosepta CMX and AMX membranes are not mentioned, it can be assumed that the results obtained in his paper are applicable to these two membranes as well [41]. The Neosepta membranes are prepared by the paste method. A paste consists of a monomer with a functional group appropriate to introduce an ion exchange group, divinylbenzene as a crosslinking agent, a radical polymerisation initiator and ®nely powdered poly(vinylchloride). The paste is coated onto a PVC cloth as reinforcing material and the monomers are copolymerised and subsequently sulfonated or aminated to produce ion exchange membranes with sulfonic acid or quaternary ammonium groups. The structure of these membranes was studied by removing the ion exchange material using a H2O2 treatment, resulting in
the formation of microporous membranes. Microscopic techniques combined with water permeability measurements revealed that the membranes contain microheterogeneities, i.e. the membranes consist of two continuous phases, a PVC phase and the ion exchange resin, which are closely intertwined. These studies on Neosepta membranes are thus in agreement with the chronopotentiometric results shown here for the CMX and AMX membranes which also indicated the presence of heterogeneities. 5. Conclusions Chronopotentiometric measurements were shown with a CMX cation exchange membrane with the membrane present in a vertical position in the membrane cell while a solution ¯ows through the cell. When a current below the limiting current density was applied the voltage drop increases slowly and a steady state value was reached. If a current larger than the limiting current density was applied, the curves were characterised by a sharp increase in voltage drop at the transition time. After this the voltage drop leveled off and a quasi-steady state was reached showing strong ¯uctuations around an avarage value. This is in agreement with the considerable scatter in data points in the overlimiting region of the current±voltage curve. The amplitude of the ¯uctuations in voltage drop increased with increasing applied current density. The ¯uctuations occurring in the overlimiting current range indicate the presence of hydrodynamic instabilities close to the membrane surface. Chronopotentiometric curves were determined both with the CMX and the AMX membrane using a set-up con®guration without any forced convection in the solution, with the membrane placed horizontally and the counter ion ¯ux upwards. The results for the two types of membranes were very similar. The measurements showed that no steady state voltage drop was reached, but the voltage drop continuously increased with time. This was due to the stabilisation of the concentration gradients in the depleted solution by gravitation. The occurrence of natural convection was minimised allowing for the concentration pro®le to grow into the solution with time. These measurements also showed the presence of ¯uctuations in voltage drop. Since there was no ¯ow through the membrane
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cell, this demonstrates that the ¯uctuations are not a result of a forced convection. Transition times were determined as a function of the applied current density for both the CMX and the AMX membrane. As predicted by theory, a linear relationship was obtained between the transition time and the inverse current density squared. Experimental transition times were found to be smaller than calculated for an ideally permselective membrane, indicating a reduced permeable membrane area for the two investigated membranes. The results obtained can be related to the theory describing electroconvection. Earlier [1], it was found that the overlimiting current for the CMX and AMX membrane could neither be explained by a loss in permselectivity nor by the occurrence of water dissociation. Thus the counter ions remain responsible for carrying the current in the overlimiting region. The chronopotentiometric experiments described in this paper have shown that large ¯uctuations in voltage drop occur even with the set-up where no solution ¯ow is applied and the depleted diffusion layer is stabilised by gravitation. These ¯uctuations indicate that indeed hydrodynamic instabilities occur, i.e. convective phenomena are present close to the membrane surface which destabilise the polarised boundary layer and lead to the overlimiting currents. The chronopotentiometric measurements on the two studied membranes indicated the presence of heterogeneities which are likely to cause the electroconvective phenomena. References [1] J.J. Krol, M. Wessling, H. Strathmann, Concentration polarisation with monopolar ion exchange membranes: current±voltage curves and water dissociation. J. Membrane Sci. 162(1±2) (1999) 145±154. [2] S. Reich, B. Gavish, S. Lifson, Visualization of hydrodynamic phenomena in the vicinity of a semipermeable membrane, Desalination 24 (1978) 295±296. [3] I. Rubinstein, L. Shtilman, Voltage against current curves of cation exchange membranes, J. Chem. Soc., Faraday Trans. II 75 (1979) 231±246. [4] S. Lifson, B. Gavish, S. Reich, Flicker noise of ion-selective membranes and turbulent convection in the depleted layer, Biophys. Struct. Mechanism 4 (1978) 53±65. [5] Y. Fang, Q. Li, M.E. Green, Noise spectra of transport at an anion membrane±solution interface, J. Colloid Interf. Sci. 86 (1982) 185±190.
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[6] Y. Fang, Q. Li, M.E. Green, Noise spectra of sodium and hydrogen ion transport at a cation membrane±solution interface, J. Colloid Interf. Sci. 88 (1982) 214±220. [7] Q. Li, Y. Fang, M.E. Green, Turbulent light scattering fluctuation spectra near a cation electrodialysis membrane, J. Colloid Interf. Sci. 91 (1983) 412±417. [8] S.H. Stern, M.E. Green, Noise generated during sodium and hydrogen ion transport across a cation exchange membrane, J. Phys. Chem. 77 (1973) 1567±1572. [9] M. Taky, G. Pourcelly, F. Lebon, C. Gavach, Polarization phenomena at the interfaces between an electrolyte solution and an ion exchange membrane. Part I: Ion transfer with a cation exchange membrane, J. Electroanal. Chem. 336 (1992) 171±194. [10] F. Maletzki, H.-W. RoÈsler, E. Staude, Ion transfer across electrodialysis membranes in the overlimiting current range: stationary voltage current characteristics and current noise spectra under different conditions of free convection, J. Membr. Sci. 71 (1992) 105±115. [11] V.I. Zabolotskii, V.V. Nikonenko, N.D. Pismenskaya, On the role of gravitational convection in the transfer enhancement of salt ions in the course of dilute solution electrodialysis, J. Membr. Sci. 119 (1996) 171±181. [12] V.K. Indusekhar, P. Maeres, The effect of the diffusion layer on the ionic current from a solution into an ion-exchange membrane, in: D.B. Spalding (Ed.), Physicochemical Hydrodynamics II, Advance Publications, London, 1977, pp. 1031± 1043. [13] I. Rubinstein, E. Staude, O. Kedem, Role of the membrane surface in concentration polarization at ion-exchange membrane, Desalination 69 (1988) 101±114. [14] I. Rubinstein, L.A. Segel, Breakdown of a stationary solution to the Nernst-Planck±Poisson equations, J. Chem. Soc., Faraday Trans. II 75 (1979) 936±940. [15] I. Rubinstein, Effects of deviation from local electroneutrality upon electro-diffusional ionic transport across a cation-selective membrane, Reactive Polymers 2 (1984) 117±131. [16] I. Rubinstein, F. Maletzki, Electroconvection at an electrically inhomogeneous permselective membrane surface, J. Chem. Soc., Faraday Trans. 87 (1991) 2079±2087. [17] I. Rubinstein, Electroconvection at an electrically inhomogeneous permselective interface, Phys. Fluids A 3 (1991) 2301± 2309. [18] I. Rubinstein, B. Zaltzman, O. Kedem, Electric field effects in and around ion-exchange membranes, J. Membr. Sci. 125 (1997) 17±21. [19] S.S. Dukhin, N.A. Mishchuk, Intensification of electrodialysis based on electroosmosis of the second kind, J. Membr. Sci. 79 (1993) 199±210. [20] F. de KoÈroÈsy, E. Zeigerson, Investigation by electron microscopy and X-ray diffraction of the microstructure of permselective membranes made from polyethylene, J. Appl. Polym. Sci. 11 (1967) 909±919. [21] N. Sivashinsky, G.B. Tanny, Ionic heterogeneities in sulfonated polysulfone films, J. Appl. Polym. Sci. 28 (1983) 3235± 3245.
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