Role of the membrane surface in concentration polarization at ion-exchange membrane

Desalznatron, 69 (1988) 101-114 Elsevler Science Pubhshers B V , Amsterdam

101 -

Prmted

m The Netherlands

Role of the Membrane Surface in Concentration Polarization at Ion-Exchange Membrane I RUBINSTEIN’,

E STAUDE*’

and 0 KEDEM’

‘Department of Apphed Mathematics and ‘Department of Membrane Research, The Werzmann Znstltute of Scrence, Rehovot (Israel) (Recewed

October 14,1987, m revised form March 21,1988)

SUMMARY

A thm convection-free cell was constructed for the characterlzatlon of cation-exchange membranes, with CuS04 solutions confined between thick copper electrodes. Current-voltage curves were recorded for several homogeneous membranes. The limiting current, 1.e. the flat portion of the curve, was 1.5-4 times lower than the theoretical prediction. At high voltage the current mcreases approximately linearly above its limiting value. Onset of noise and noise frequency were determined. It was suggested that the ion conductance of the membrane surface 1s not uniform. This inhomogeneity decreases the avallable area and, at high voltage, gives rise to local mixing of the unstirred layer by electroconvection. High limiting current was observed with a composite membrane comprlsmg a porous heterogeneous layer and a highly permselectlve dense homogeneous layer (sulfonated polysulfone). This may be due to electroconvectlon in the porous part of the layered structure. The drastic dlfference of polarlzatlon at homogeneous sulfonated polysulfone membranes and at the composite membrane was confirmed m a laboratory electrodialysls stack. Keywords electrodlalyws,

concentration

polarmatlon,

mhomogenelty,

electroconvectlon

INTRODUCTION

Analysis of concentration polarlzatlon (CP) in ellectrodlalysls (ED ) 1s customarily based on the Nernst layer model with some modifications. The central parameter IS thus the thickness of the “unstirred” layer, determined by the flow regime in the experimental cell or the ED stack In the extensive and varied studies devoted to this topic very little emphasis is gven to the direct experimental test of the absolute values of the magnitude of the hmltmg current density through an ion-exchange membrane, as predicted by the Nernst *Permanent

address

OOll-9164/88/$03

Umversltat

50

Gesamthochschule

Essen, F R G

0 1988 Elsevler Science Publishers

BV

102

theory Usually, only the power dependence of the limiting current on &fferent parameters entering the appropriate basic relation is tested. This is due to a virtual impossibility to define a priori the thickness of the unstirred layer in most conventionally employed experimental set ups. The most direct experimental test so far, comparing concentration polarization at a smooth lon-exchange membrane with that at a polished reversible electrode under identical flow conditions, did not show agreement between the two [ 11. In the followmg a thin, convection-free cell for membrane testing is described. With the diffusion layer thickness clearly defined, there is no free parameter in the expression for the limiting current density at a cation-exchange membrane and the former can be tested quantitatively. According to the widely accepted theory, the nature of the membrane mfluences the course of concentration polarization only through permselectlvity, but practical application indicates that different membranes with the same permselectlvity may exhibit a markedly different CP behavlour. This posslbility has not been emphasized sufficiently in the literature. The results of the stationary CP and of the excess electric membrane noise measurements reported here, which were obtained in the convection-free cell and m parallel tests m a laboratory ED stack, show, that polarization depends on the membrane material and may be stronger than pre&cted from the classic CP model. A simple explanation is suggested to account for this hscrepancy as well as for some poorly understood aspects of the “overlimiting” behavlour of the cation-exchange membranes. Recall that current-voltage (I-V) curves for ion-exchange membranes are commonly characterized by three regions: an uutial linear increase (I), saturation tendmg towards a limltmg plateau or inflection (II), and for higher voltage a further increase above the limiting current (III). It was shown conclusively by several authors that the overlimiting current is not due to water splitting or alternative charge-carriers at cation-exchange membranes [ 2-41 This overlimltmg region is characterized by generation of a strong electric lowfrequency excess noise. Moreover, it can be shown in accordance with the existing experimental results [ 5-91, that the overhmltmg current and the excess electric noise associated with it must be due to a sort of chaotic mechanical mixing in the depletion diffusion layer adJacent to the cation-exchange membrane. Mechamsms for this mixing are yet to be identified Thus, mstablhty of a lammar gravitational convection, normally present due to density gradients arising in the course of concentration polarization, cannot be responsible for the above mixmg, since the corresponding Grashoff numbers m most laboratory systems (0.1~ Gr < 10) are much smaller than those required for mstablhty and turbulence of the buoyant convective flow (Gr > 105) [lo] An alternative mechanism for mechanical mixmg in the depleted diffusion layer is suggested below A detailed quantitative analysis of the mechanisms involved will be presented elsewhere [ 111.

103 EXPERIMENTAL

The poluruatlon cell and measurements Thin, unstirred solution layers of stationary composition can be maintained if the current 1s supplied by reversrble electrodes. For cations, this can readily be achieved with a pair of copper electrodes in CuSO, solutions Further, blocks of copper also provide a mechamcally stable structure. The polarization cell consisted of two massive polished copper plates, 4x4~ 0.8 cm, with small solution compartments between them, formed by suitably arranged layers of tape (Fig. 1). To ensure homogeneous and reversible electrode reactions, the working surfaces of the electrodes were pohshed before each run and the cathode surface was amalgamated with Hg(NO,), solutions thus renewing the surface before each experiment. The assembly of the cell consisted of the followmg standard sequence of steps. The freshly treated cathode w&h its workmg side facing upwards was covered with one layer of a 0 018 cm thick electric tape (C-tape) with a 0.8 cm diameter circular workmg aperture The C-tape was followed by the tested membrane, attached to a double layer of the electric tape (A-tape) with a 0.1 cm working aperture The A-tape was followed by the anode plate. The electrode plates were flanked by two rubber gaskets. One drop of the working CuS04 solution was placed mto the large aperture of the C-tape and then sealed by the A-tape with the tested membrane preattached to It The extra solution of the cathode drop was removed and dried up with a filter paper. Another drop

Fig 1 Scheme of the polarlzatlon cell (1) Copper anode, (2) copper cathode, (3) A-tape, (4) Ctape, (5) C-membrane, (6) clamp, (7) rubber gaskets

104

of CuS04 solution was placed into the small aperture of the A-tape. This latter was covered with a freshly treated anode plate. The whole system was next pressed together with a massive clamp. If not stated otherwise, measurements were carried out with the cell fastened horizontally (with N lo accuracy) m a gravitationally stable position (cathode on top), with a degassed 0.01 N solution of CuSO,. The above arrangement (with resistance of the order of 5-100 kS2,depending on the membrane tested and on the stage of CP) was put m series with a known constant 15 M resistor to a batteries current supply. The DC current through the system was controlled with a potentiometer and registered with a standard digital ampermeter. The DC and AC (the excess noise) voltage were measured directly on the cell, respectively with the aid of a standard digital voltmeter and a storage oscilloscope, after a tenfold amphtication. The low-frequency excess noisetime series were recorded with an x-t recorder. The noise measurements were carried out with the polarization cell mounted inside a Faraday cage. The CP measurements on membranes were preceded by recording the I-V curves of a plain 0.1 cm aperture m the A-tape, facing the cathode The corresponding I-V curves were hnear and noiseless m the current range between 1 and 100 A within the accuracy of our mstrumentation. The observation of the amalgamated cathode surface under an optical microscope ( x 75) after a 3000 s long passage of 20 @A DC current did not disclose any noticeable mhomogeneity of copper deposition on the corresponding length scale Every test of a particular membrane specimen (e.g. recordmg an I- V curve) was reproduced repeatedly, each time with a new CuS04 solution drop m the anode compartment. A crude estimate of the expected electroosmotic water transport (5-10 moles of water per Faraday) indicates, that for the currents employed the total electroosmotlc effect could amount to no more than l-4% of the volume of the anode compartment, which could be likely compensated by shght deformation of the membrane Summanzmg, the anode compartment of the polarization cell employed consisted of a 0.036 cm thick, 0.1 cm wide cylindrical hole in the electric tape, confined by a massive anode on one side and by the tested membrane on the other and filled with a CuSO, solution. The Cu2+ ions, dissolved from the anode, were transferred through the membrane into the cathode compartment and were there reduced on the cathode No changes of the ionic composition of the solutions in both compartments were anticipated. The small exposed membrane area, facing the anode, as compared with the working cathode area, guaranteed that the recorded concentration polarization effects were indeed confined to the anode compartment, that is, could be attributed to the tested membrane rather than to the cathode With a horizontal gravitationally stable position of the cell, none or httle of global buoyant convection m the anode compartment is expected. In this case,

105

electrolyte concentration distribution m the anode compartment is linear, assuming an approximately constant diffusion coefficient. For a highly permselective cation-exchange membrane the above concentration profile is nearly antisymmetric with respect to the compartment’s middle-plane, the concentration being maximal at the anode, minimal at the membrane and equal to the average or “bulk” concentration at the middle-plane Thus, the unstirred layer thickness could be defined as one half of that of the anode compartment, that is 0 018 cm for the present set up. Massiveness of the copper electrodes confmmg the thm cell described, makes it likely that the temperature gradients due to the nonuniformity of Joule heatmg within the anode compartment will be mnnmal. Sealed-cell ED-stack In parallel to the measurements m the convection-free cell, overall polarization was estimated m a laboratory ED-stack. The stack, described previously [ 121, consists of sealed brine cells, enabling free circulation of the dialysate, without narrow &stributmg channels From the apparent resistance of the stack during electrodialysis of NaCl solutions the effective thickness of the dialysate compartment is derived. Effectrve thrckness (defl) as a measure for polaruatron The process parameter determining the polarization in ED is the ratio of current density to dialysate concentration, I/cd When a stack is operated at constant voltage, while the dlalysate concentration is decreasing, I/cd changes very little m a wide range of dialysate concentration. When plotting the effective resistance per unit cross-sectional area of a cell pair R, as a function of the specific resistance of the lalysate, straight lines are obtained.

=R,

+R,, +deff.p

where VCP - voltage per cell pair, V potential measured at zero current, V VCI - concentration resistance of membranes, Q cm2 % resistance of brine compartment, Q cm2 & specific resistance of the dialysate, 5-3cm P With the high concentration factor m our system, Rb is always negligible The intercept of the straight line is R,, and its slope is equal to d,, This experimental parameter contains both the slight shadowmg effect of the loose spacer used and the polarization.

106

Membranes and membrane preparation The followmg cation-exchange membranes were tested: (1) Sulfochlorinated polyethylene Neginst C (kindly supplied by Dr. R. Mesalem, R&D Authority, Ben-Gurion University of the Negev, Beer-Sheva, Israel), (2) commercial perfluormated Nation membrane; ( 3 ) homogeneous sulfonated polysulfone membranes ( SPSU ) ; (4) heterogeneous cation-exchange membranes (HC ); (5) a composite membrane, comprismg a layer of SPSU cast on HC (SPSU/ HC). Membranes 3,4, and 5 were prepared m this laboratory A heterogeneous anion-exchange membrane (HA) was used m the sealed-cell stack with HC and SPSU/HC for the determination of d,,. Heat sealable heterogeneous catton-exchange (HC) and anton-exchange (HA) membrane [ 131 The inherent difficulty in the preparation of good heterogeneous membranes is the need for two contmuous phases. effective contact between the ion-exchange particles is necessary in order to create contmuous path-ways for ion transport, and a coherent matrix is necessary to provide mechamcal strength, and prevent the formation of solution channels crossing the matrix. These opposing requirements of contact between the particles and msulation around them dictate a well-defined structure of the elements: m an assembly of closepacked spheres each sphere touches several others, and the mterstlces comprise one contmuous phase. This is m contrast to a packed mass of ground particles with irregular planar edges Further, mcompressible spheres touch each other at pomts only, but if the spheres are shghtly deformable and pressed together, areas of contact will be created. By shght deformation of both matrix and particles upon swellmg, channels can be formed connecting the conducting spheres With these considerations m mmd we chose the following two elements for our membrane* (a) small (@< 70 pm) spherical ion-exchange particles, polystyrene based and moderately cross-lurked with dlvmylbenzene (DVB); (b) for the matrix, polysulfone which is chemically stable and has excellent mechamcal strength and film-forming properties Table I gives the membrane properties (d$ is membrane potential, z, is cation transport number) The performance of the membranes m a stack depends not only on permselectivity and resistance, but also on the surface properties under conditions of polarization With heterogeneous membranes this means that the conducting ion-exchange particles should be readily accessible to the solutions, faclhtatmg ion entrance. In our HC and HA membranes this was achieved by a suitable casting procedure.

107 TABLE I Average characterlstlcs

of the tested C-membranes

4 (mV)

T+

168 178 13 7 156

r+

(mV) (OOl0 02 N CUSOJ

(l-2iVNaCl) Negmst C SPSU HC SPSU/HC

4

097 099 088 093

86 87 84 88

098 099 097 099

R

R

(Qcm2) (0 5 N NaCl)

(Qcm’ ) (0 5 N CuS04)

62 43 71 132

173 308 194 512

Homogeneous sulfonated polysulfone membrane - SPSU Sulfonated polysulfone (SPSU) was described firstly for RO membranes [ 14,15]. Asymmetric microporous SPSU membranes were prepared and suggested for use m ED [ 161. The chemical stability and good conductance of SPSU may also be advantageous for battery separators [17] Indeed solvent cast and fully evaporated SPSU shows excellent permselectivlty and good conductance as shown m Table I. Composite C-membrane (SPSUjHC) SPSU was apphed as a coatmg on an HC membrane. In all measurements this coating faced the brine. Properties of the SPSU/HC membranes are given m Table I. RESULTS

AND DISCUSSION

Fig. 2 shows I-V curves of the three homogeneous cation-exchange membranes tested: Curve 1 - Negmst, Curve 2 - SPSU, Curve 3 - Nafion. These curves were recorded with the membrane m horizontal position, with the cathode on top. In this position the solution layer below the membrane is depleted, the layer above the membrane is concentrated, and thus the concentration gradients are gravitationally stabilized The dashed horizontal line m Fig. 2 marks the theoretical value of the hmsting current through a homogeneous ideally permselectlve membrane. According to the classical theory of polarization [ 18,191 I hm -

d z D

nd2 2 DC,,Fz 4

6

- diameter of the working aperture, cm - valency of the symmetric electrolyte - catron diffusivlty, cm’ s-l

(1)

Fig 2 I- V cures of homogeneous C-membranes Curve 1 Negmst C m a honzontal gravltatlonally stable posltlon Curve 2 SPSU m a honzontal gravltatlonally stable posltlon Curve 3 Nafion m a horizontal gravltatlonally stable posltlon Curve 4 Negmst C m a vertical posltlon Curve 5 Negmst C m horizontal grawtatlonally unstable position Big black dota mark the threshold of the excess noise The dashed honzontal line marks the theoretical value of the hmltmg current

-bulk concentration, mol crnm3 - Faraday constant, coulomb mole1 - thickness of depletion layer, cm (half the hight of the anode compartment ) For the relevant values of parameters (z= 2, Co= 10m5mol cmm3, 6=0.018 cm, D=115~10-~cm~s-‘,d=0.1cm)I~,,=20,~A Note that convection m the anode compartment or deviation from an ideal membrane permselectivity may only lead to an increase of the measured value of Ii,, as compared with that given by Eq. ( 1). The measured values of the hmitmg current presented m Fig. 2 and Table II are from 1.5 to 4 times lower than the theoretical lower boundary. This suggests that not all of the membrane surface is actually permeable for cations Curves 4 and 5 m Fig. 2 give I-V for a Negmst membrane m a vertical and in a horizontal gravitationally unstable position, respectively. As expected, the limiting current is mcreased m these cases. The linear increase in the current at higher voltage, m the overhmitmg range, can be extrapolated back to the lme of the limiting current, giving a critical value for the voltage, V,,, as the start of region III m the I-V curve. As shown m Fig. 2, this critical voltage, determined m the gravitationally unstable position, is only slightly shifted with respect to V,, m the stable position, in contrast to the substantial change of CO

F 6

109 TABLE II Limiting current, cntlcal voltage and threshold voltage All measurements were made m the honzontal gravltatlonally stable posltlon Membrane

I &)

Vtll W)

VC, w

Negmst Negmst Negmst Negmst Negmst Negmst

110 12 0 13 0 13 0 110 75

0 0 0 0 0 0

0 0 0 0 0 0

SPSU SPSU SPSU SPSU SPSU Nafion Naflon Nafion Naflon Nafion

1 2 3 4 5* 6

1 2 3* 4 5

45 45 55 50 65

1 2 3* 4 5

HC l* HC2 SPSU/HC SPSU/HC SPSU/HC

1 2* 3

320 322 362 304 440 402

440 403 500 403 440 440

0411 0 435 0 385 0 592 0 675

0 420 0 480 0 480

90 90 85 10 0 90

0 0 0 0 0

0 0 0 0 0

12 0 12 0

0 410 0 402

26 0 260 240

0 287 0 232 0 244

432 305 435 456 464

480 500 430 470 480

0 430

*I-V curves gwen m Figs 2 and 3

I,,, At some point m region II excess noise appears. The larger black dots denote the threshold, Vth, for the onset of excess noise. Fig. 3 gives the I-Vcurves for the heterogeneous membranes HC and for the composite SPSU/HC. For the latter substantially higher hmltmg currents are obtained, m some cases passing the theoretical convection-free value. In Table II values for Ii,,, V,, and V,, are summarized The typical frequency of the excess noise at the transition points marked by dots was evaluated by counting the average number of zero crossmg of the stationary times series, recorded on the storage oscilloscope or the x-t recorder In Table III are presented the approximate values for these frequencies of the excess noise Usually, as the voltage was mcreased above the critical value, the faster components of the excess noise became more pronounced. The peak to peak amplitude of the excess noise increased with the overlimitmg value of

110

0 200

I

I

I

0 400

0 600

0 600

v (volts)

Fig 3 I-V curves of heterogeneous C-membranes Curve 1 HC Curve 2 SPSU/HC

(honzontal

gravltatlonally stable posltlon)

TABLE III Typical frequency of the excess noise at the threshold

f (Hz)

Negmst

SPSU

Naflon

Heterogeneous HC & MHC

4-5

-2

-2

-4

the current somewhat faster than linearly, from about 0 01 to 1% of the mean value In order to explore the posslbihty that the excess noise and the overhmitmg average behaviour may be caused by microbubbles of air, released during passage of current, measurements were carried out on an open solution drop under a long focus optical microscope (x 75 ) The appropriate experimental set up consisted of the cathode-half of the cell with a Negmst C membrane attached m the usual fashion and placed horizontally, this time in a gravitationally unstable position, on the obJect table of the microscope. The anode was placed vertically next to the working aperture of the C-tape, to enable observation of the membrane surface through the microscope A small drop of the CuSO, solution was placed into the working aperture, so as to wet the anode. The membrane surface and the solution drop were observed contmuously during the consecutive stages of CP at an mcreasmg sequence of DC currents, passed through the membrane. The corresponding hmitmg current was somewhat higher than that with a vertically positioned membrane (Curve 4, Fig. 2)) whereas the critical voltage V,, essentially com-

111

tided with those in the vertical and horizontal gravitationally stable position (0.434 V as compared to 0.422 V and 0.440 V, respectively). No bubbles were observed at any current and no observable difference could be seen in the excess noise characteristics as compared with those for the vertical or horizontal gravitationally stable position of the membrane. A few excess noise power spectra of the Negmst C and SPSU membranes were taken at different values of DC current, but no systematic study of the spectral properties of the excess noise has been undertaken at this prehmmary stage of experiments. Systematic information regardmg the power spectra (although for somewhat different set ups) is given m ref. 10 and references therein. The phenomena observed m the convection-free cell can be summarized as follows: - The three regions in I-V curves are clearly discerned: I - initial lmear increase of current; II - subsequent saturation and flat limitmg current; III - further approximately linear overlimiting increase - The limiting current through the homogeneous membranes tested is from 1.5 to 4 times lower than that predicted theoretically for a membrane surface uniformly permeable for cations. -A low frequency excess noise appears m range II, shghtiy precedmg the mflexion of the I-V curves, at a cell voltage of about 0.4-0.5 V. The typical time scale of this noise at the threshold depends on the type of the membrane and ranges from 0 1 to 0.5 s. - In the same cell with the membrane in vertical or horizontal gravitationally unstable position, the hmitmg current is increased substantially, the noise frequency unchanged, V,,unchanged, and the onset of noise shifted shghtly to lower voltage The increase of the current m region III and the concomitant excess noise reflect some kmd of mixing in the unstirred layer This can hardly be due to global laminar gravitational convection: the noise characteristics are nearly unaffected by changing the orientation of the cell, though the conditions for global convection are quite different in these positions. Further, Grashoff numbers in the conditions of measurement are very low (0.2 < Gr < lo), orders of magnitude lower than values for which m&ability of laminar convection is to be expected. It should be noted here that an increase m the averge stationary value of the current above the hmitmg value requires mixing m the entire region of the Nernst layer. A change of conductance m a very thm layer adJacent to the membrane [ 731, leaving the rest of the layer undisturbed, does not change the maximal diffusional flow through the Nernst layer. A quite different mode of mixing can take place by electroconvection. It was shown previously [ 201 that space charges are formed by high currents in extreme concentration polarization. In a laterally uniform electric field these

112

charges too are laterally uniform, and no spontaneous electroconvectlve mstabihty is to be expected. If, however, the membrane surface comprises patches of varying ion conductance, the electric field lures in the adJacent solution layer are distorted. The mteractlon of space charges with the electric field gives rise to a spatially mhomogeneous bulk force which is bound to set m motion the fluid m the depletion diffusion layer. Electroconvection with a complex circulatory pattern (with a typical vortex size ranging from that of the typical spacing between the conductmg parts at the membrane surface and up) results, causing mlxmg. The overhmiting conductance is observed when electroconvection becomes dominant over molecular diffusion in the depletion unstirred layer of the anode compartment. A simple electrodiffusion calculation for concentration polarization at an mhomogeneous permselective interface [ 111, combmed with the excess noise data reported here, suggests that the typical separation distance between the “conductive spots” varies for different homogeneous membranes in the range of 2-20 pm, whereas the size of the spots themselves is of the order of l-2pm. The dependence of polarization on the nature of the membrane surface for the cation-exchange membranes tested m the convection-free cell was confirmed m the followmg ED experiments Fig. 4 taken from ref. 12 shows an example of effective thickness (apparent resistance per cell pair R,,) measured with heterogeneous membranes m the sealed-cell stack The sealed brine cells consisted of HA and HC membranes For different membrane compositions and conditions of measurement, &rvarles from 0.6 mm to 1 2 mm with this type of membranes, when the geometric thickness of the dialysate compartment is 0.55 mm. These values are m the customary range Curve 1 in Fig. 5 shows the apparent resistance of the laboratory stack contaming sealed cells made of HA and supported SPSU membranes. Clearly polarization 1svery pronounced. Also the concentration dependence of interface behavlour is superimposed on the usual concentration dependence and one does not obtain a straight line with intercept at R,. From a practical pomt of view, stack resrstance is prohibitively high with SPSU membranes, in dilute feed solutions Sealed cells were prepared from the same heterogeneous A-membrane used above, and composite C-membranes: HC coated with a layer of SPSU. As expected, the pair of HA and SPSU/HC membranes give normal polarization, as shown m curve 2 of Fig 5. At the same time, the SPSU coatmg gave high current efficiency. The thm-cell measurements indicated exceptionally low polarization for the SPSU/HC composite membrane. In order to check this in the stack we would need also an exceptionally good A-membrane but tins is not available at present A hypothesis analogous to that stated above may also explain the high hm-

OL--

500 S(ncm)

Fig 4 Remstance per cell pan as a function of the specific resistance of the dlalysate solutions) (HC-HA) Voltagepercellpau (A,o) -lV, (0) -07V, (0) -05V

1000

(NaCl

Fig 5 Effective resistance per cell pan as a function of the specific res&ance of the dlalysate (NaCl) Curve 1 ( A ) HA-SPSU Curve 2 ( 0, A, 0 ) two groups of cell pam, HA-SPSU/HC

ltmg current observed with the heterogeneous membranes. In the pores of such membranes, mobile space-charge regions exist even m the absence of a polarizing current, and the electroosmotic flow in an apphed field may cause local mixing. This effect may be enhanced in the SPSU/HC membrane by the drastically different porosity of the two layers. CONCLUSIONS

Polarization phenomena are substantially different for membranes of different composition, at identical flow conditions. The hmitmg current is lower than expected theoretically for an ideally permselective interface uniformly permeable to cations Overlimiting current carried by the same cations as the lower current, is accompanied by characteristic excess noise. The simple model suggested here agrees with all the observed phenomena if the entrance of cations from the solution mto the membrane is limited to a part of the surface only, the hmitmg current is lower than expected for the total area The conductive inhomogeneity of the membrane surface is expected to yield, at the limitmg current, a strongly nonuniform electric field. The mteractlon of the latter with its own space charge sets m motion the fluid near

114

the membrane. It is speculated that this electroconvection is capable of causing mixmg of the entire diffusion layer in a hydrodynamically free system, yielding the overhmitmg phenomenology of the cation-exchange membrane The measured values of the limiting current density along with the typical frequency of the excess noise, appearing above a certain voltage threshold, suggest that the typical size of a conductive site at the membrane surface is below 2 pm whereas the typical separation distance between such sites varies from 2 to 20 ,um for different types of membranes For use in ED, SPSU membranes have very good permselectivity, but prohibitively high polarization. A composite membrane consisting of a heterogeneous membrane coated on the brine surface by SPSU combines high permselectivity and low polarization. The high limiting current observed with this composite membrane can be explained by local electroconvective mixmg, m analogy to the conductmg patch model for the overhmitmg current in homogeneous membranes

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