Influence of the Membrane Pore Conductance on Tangential

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Influence of the Membrane Pore Conductance on Tangential Streaming Potential M. Sbaı¨,*,† A. Szymczyk,† P. Fievet,† A. Sorin,‡ A. Vidonne,† S. Pellet-Rostaing,‡ A. Favre-Reguillon,‡ and M. Lemaire‡ Laboratoire de Chimie des Mate´ riaux et Interfaces, 16 route de Gray, 25030 Besanc¸ on Cedex, France and Laboratoire de Catalyze et Synthe` se Organique, Universite´ C. Bernard - Lyon 1, CPE Lyon, 43 Bd. du 11 novembre 1918, 69622 Villeurbanne Cedex, France Received June 3, 2003. In Final Form: July 24, 2003 Tangential streaming potential technique is an attractive way to characterize the electrokinetic properties of various kinds of materials such as films or flat membranes with a dense or a porous structure. However, the interpretation of data in terms of zeta potential is usually carried out by doing the implicit assumption of nonconducting substrates. In the present paper, we investigate the electrokinetic properties of a commercial ultrafiltration membrane, the porous structure of which affects the streaming potential because streaming and conduction currents involved in the streaming potential process do not flow through identical paths (the streaming current flows only through the slit channel formed by the two membrane samples facing each other whereas a non-negligible part of the conduction current is likely to flow through the membrane pores filled with electrolyte solution). The correct zeta potential value is determined from an extrapolation method for which a set of measurements with various channel heights is required. A very good agreement is obtained with zeta potential values deduced from consecutive streaming potential and total conductance measurements (referred in the text as the direct method). The ratio of the correct zeta potential to the apparent one (given by Helmholtz-Smoluchowski equation) is dependent on the pH which suggests a non-negligible contribution of surface conductance within the membrane pores.

1. Introduction The selectivity of a porous membrane is usually governed by both steric effects and electrostatic interactions occurring between charged solutes and the charged membrane surface. Indeed, most membranes acquire an electric surface charge when put into contact with an aqueous solution. Hence, the characterization of membrane surface electrical properties appears to be a necessary step to understand and predict their filtration performances. The zeta potential (ζ), defined as the electrostatic potential at the hydrodynamic plane of shear, is a fundamental feature providing useful information about the charge state of a solid surface. This potential cannot be measured directly but can be determined from several experimental methods. Among these ones, streaming potential measurement has become, thanks to its versatility, the most commonly used tool for determining the ζ-potential of macroscopic solid surfaces of various shapes. Streaming potential occurs when there is a relative motion between a fluid containing charged species and a charged surface caused by a hydrostatic pressure gradient. This latter forces the fluid to move tangentially to the charged surface, pulling the ions of the mobile diffuse layer toward the low-pressure side. These moving ions give rise to a streaming current. The resulting charge separation sets up an electric field which drives the counterions to move back in the opposite direction to the pressure-driven flow. This back-flow of counterions therefore generates an electrical conduction current in the opposite direction of the streaming current. When the fluid flow reaches a steady state, the conduction current balances the stream* To whom correspondence should be sent. Fax: +33.3.81.66.20.33; e-mail: [email protected]. † Laboratoire de Chimie des Mate ´ riaux et Interfaces. ‡ Universite ´ C. Bernard - Lyon 1.

ing one and no net electrical current remains. The resulting electrical potential difference that can be measured between high- and low-pressure sides is called streaming potential (∆φs). For flat porous membranes, streaming potential measurement can be carried out by applying a pressure gradient either along the membrane surface (tangential streaming potential, TSP)1-3 or through the membrane pores (transmembrane streaming potential).4-7 The through-pore technique has the advantage of experimental simplicity but interpretation of experimental data may be difficult when measurements are carried out with multilayer membranes or membranes having selective layers.8-10 In such cases, TSP measurement appears as an alternative method providing direct information about the membrane top layer (i.e., active layer). The tangential technique consists of applying a pressure difference across a thin channel formed by clamping two identical membrane samples separated by a spacer. However, conversion of tangential streaming potential data into zeta potential is often made from either the classical Helmholtz(1) Van Wagenen, R. A.; Andrade, J. D. J. Colloid Interface Sci. 1980, 76, 305. (2) Mo¨ckel, D.; Staude, E.; Dal-Cin, M.; Darcovich, K.; Guiver, M. J. Membr. Sci. 1998, 145, 211. (3) Zembala, M.; Adamczyk, Z. Langmuir 2000, 16, 1593. (4) Nystro¨m, M.; Lindstro¨m, M.; Matthiasson, E. J. Colloid Interface Sci. 1989, 36, 297. (5) Staude, E.; Duputell, D.; Malejka, F.; Wyszynski, D. J. Dispersion Science and Technology 1991, 12, 113. (6) Szymczyk, A.; Pierre, A.; Reggiani, J. C.; Pagetti, J. J. Membr. Sci. 1997, 134, 59. (7) Benavente, J.; Jonsson, G. J. Colloid Interface Sci. 1998, 138, 255. (8) Szymczyk, A.; Labbez, C.; Fievet, P.; Aoubiza, B.; Simon, C. AIChE J. 2001, 47, 2349. (9) Can˜as, A.; Ariza, M. J.; Benavente, J. J. Membr. Sci. 2001, 183, 135. (10) Yaroshchuk, A. E.; Boiko, Y. P.; Makovetskiy, A. L. Langmuir 2002, 18, 5154.

10.1021/la034966a CCC: $25.00 © 2003 American Chemical Society Published on Web 09/11/2003

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Sbaı¨ et al. Table 1. Summary of Equations used to Derive Eq 1 Relating the Streaming Potential Coefficient (∆φs/∆P) to the ζ-Potential in the Case of Conducting Wallsa

Is ) 2 L c

∫

h

0

vz(x)‚F(x) dx

∆P 2 (h - x2) 2ηl d2 ψ and F(x) ) -or 2 dx 0rSc ∆P ‚ζ Is ) ηl with vz(x) )

Figure 1. Schematic representation of the rectangular slit channel for tangential streaming potential measurements.

Smoluchowski equation or a version of this equation including surface conductance.2,11,12 Recently, Yaroshchuk and Ribitsch13 have suggested that the membrane pore conductance may play a nonnegligible role in the determination of ζ-potential from TSP measurements. This was demonstrated in a recent paper with a ceramic membrane close to the nanofiltration range by performing TSP and conductance measurements at various channel heights.14 The aim of this work is to investigate the electrokinetic properties of a porous organic membrane from tangential streaming potential by accounting for the membrane pore conductance. The conductive contribution of the substrate (membrane body soaked with the electrolyte solution) is studied over a range of pH to put in evidence the surface conductance phenomenon occurring through the membrane pores. 2. Theory The theoretical principles underlying the measurement of ζ-potential for flat surfaces in a clamping cell can be found in several papers.1-3,12-19 The determination of ζ-potential from tangential streaming potential (TSP) measurements performed in rectangular slit channels made of conducting substrates (such as porous membranes soaked with electrolyte solution) has been presented in detail in a recent paper.14 That is why only a brief theoretical description will be made in this section. The relation between streaming potential measured across channels whose walls are formed by conducting substrates and ζ-potential has been established by Yaroshchuk and Ribitsch.13 In a rectangular slit channel formed by two identical membrane samples (Figure 1) it takes the form:

( )

( )

2ηhmλm 1 ηλ0 ∆P + ) ∆φs I)0 0rζ 0rζ 2h

(1)

Equations used to derive eq 1 are summarized in Table 1 (All symbols are defined in the List of Symbols section). (11) Fairbrother, F.; Mastin, H. J. Chem. Soc. 1924 125, 2319. (12) Lettmann, C.; Mockel, D.; Staude, E. J. Membr. Sci. 1999, 145, 243. (13) Yaroshchuk A. E.; Ribitsch, V. Langmuir 2002, 18, 2036. (14) Fievet, P.; Sbaı¨, M.; Szymczyk, A.; Vidonne, A. J. Membr. Sci. submitted. (15) Werner, C.; Ko¨rber, H.; Zimmermman, R.; Dukhin, S.; Jacobasch, H. J. J. Colloid Interface Sci. 1988, 208, 329. (16) Erickson, D.; Li, D.; Werner, C. J. Colloid Interface Sci. 2000, 232, 186. (17) Werner, C.; Zimmermann, R.; Kratzmu¨ller, T. Colloids Surf., A 2001, 192, 205. (18) Schweiss, R.; Welzel, P. B.; Werner, C.; Knoll, W. Langmuir 2001, 17, 4304. (19) Walker, S. L.; Bhattacharjee, S.; Hoek, E. M. V.; Elimelech, M. Langmuir 2002, 18, 2193.

with Sc ) 2hLc

Ic ) S c λ 0

∆φs ∆φs ∆φs + G s Pw + 2Smλm l l l

with Pw ) 2(Lc+2h) ≈ 2Lc and Sm ) hm Lc

a In systems of interest, the surface conductance in the slit channel (Gs) can be reasonnably neglected (h>>κ-1).

The surface conductivity in the slit channel is neglected in eq 1 which is a reasonable assumption for channel sizes as large as those used in this study (channel heights g100 µm). If the contribution of the membrane pore conductance is not accounted for in the overall conduction phenomenon, then the term (hmλm/h) in eq 1 disappears and eq 1 becomes the classical Helmholtz-Smoluchowski (H-S) relation. According to eq 1, streaming potential measurements carried out at different channel heights allow to determine the true ζ-potential by extrapolating the regressed line ∆P/∆φs ) f(1/2h) at infinitely large channel heights. This procedure of determining the ζ-potential will be referred as “extrapolation method”. Literature shows that the so-called Fairbrother and Mastin (F-M) procedure11 is frequently used to correct the H-S equation. The F-M procedure consists of accounting for the surface conductance in the channel. However, this procedure is ineffective in the case of conducting substrates.13 It does not consider the membrane pore conductance and it has been shown in a recent paper14 that it is likely to lead to substantial error in the determination of the ζ-potential value. An alternative method to determine the true ζ-potential is to perform both streaming potential coefficient (∆φs/ ∆P) and system total conductance (Gt) measurements.13 The ζ-potential can then be determined from the following relation:

( )

0r 2hLc Is ∆φs Gt ) ) ‚ζ ∆P ∆P η l

(2)

The right-hand side of eq 2 contains, apart from the sought for ζ-potential, reasonably known values. To decrease uncertainty on the calculated ζ-potential value, ∆φs/∆P and Gt can be measured at several different channel heights. The parameter (∆φs/∆P) Gt is then plotted as a function of 2h and linear regression is performed. The slope is then related to the ζ-potential according to eq 2. This method of determining the ζ-potential, based on both streaming potential and conductance measurements, will be referred as “direct method”. 3. Experimental Section 3.1 Membrane and Chemicals. The membrane tested in this work, labeled Desal G-10, is a loose thin-film composite membrane (MWCO: 2500 Da) manufactured by Osmonics. It has a multilayer structure with a polyamide filtering layer. Two samples of 75 × 25 mm (corresponding to the measuring cell dimensions) were cut in the sheet membrane. A pore radius of

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Figure 2. (a) Schematic view of the setup used for the tangential streaming potential and conductance measurements of the membrane-channel-membrane system. (b) Detailed cell scheme. 1.3 nm was estimated by Afonso et al.20 using filtration experiments with a set of reference solutes (saccharose and poly(ethylene glycol)s) in the molecular weight range 342-4000 Da. The streaming potential was measured in 10-3 M KCl solutions at different pH values (2 e pH e 6). KCl was of pure analytical grade and all solutions were prepared from milli-Q quality water (conductivity < 1µS cm-1). The pH values were adjusted with ∼0.1 M HCl and ∼0.1 M KOH. 3.2 Tangential Streaming Potential and Conductance Measurements. A ZETACAD (CAD Inst., France) zeta meter was used for TSP measurements. This apparatus measures the electrical potential difference generated by the imposed movement of a electrolyte solution through a thin slit channel formed by a couple of identical membranes. The liquid is forced through the slit channel using the nitrogen gas (Figure 2a). The gas pressure is controlled by means of a pressure sensor. Figure 2b shows a schematic representation of the tangential flow cell used for TSP and conductance measurements. The cell is equipped with two Ag/AgCl wire electrodes, placed on each side from the channel (just at the inlet and outlet of the channel), and linked to a Keithley multimeter (model 2000) to measure the electrical potential difference (∆φs) developed in the solution along the slit. The streaming channel of well-defined dimensions is formed by clamping together two identical flat membranes separated by a spacer, each membrane being inserted in a half cell. The electrical potential difference (∆φs) was measured alternatively in the two flow directions for continuously increasing pressure values (from 0 to 500 mbar). The streaming potential coefficient was determined from the slope of the plot of ∆φs versus ∆P (Figure 3a and 3b). This equipment also measures the temperature and the conductivity of the solution (λ0). Measurements were made at 20 ( 2 °C and for different pressure gradients with flow in the two directions. At least 150 experimental points (∆φs vs ∆P) were collected for each run. The average uncertainty in each experimental run was less than (5%. The cell also includes two other spiral Ag/AgCl electrodes placed on each side from the channel. These spiral electrodes as well as the two wire electrodes were used to measure the total conductance. Conductance measurements were performed using electrochemical impedance spectroscopy. The equipment used was a Solartron 1286 electrochemical interface linked to a Solartron 1255 frequency response analyzer. We used the (20) Afonso, M. D.; Hagmeyer, G.; Gimbel, R. Separation Purif. Technol. 2001, 22-23, 529.

Figure 3. (a and b): Streaming potential (∆φs) vs applied pressure difference (∆P); 1 mM KCl electrolyte support. galvanostatic four-electrode mode. The spiral Ag/AgCl electrodes were used to inject the current whereas the two Ag/AgCl wires permitted to measure the resulting voltage in galvanostatic mode. For each channel height, both TSP and conductance experiments were repeated three times. The conductance was measured under no liquid flow condition. To equilibrate the membranes with the electrolyte solution, the samples were first soaked overnight in the test solution for each new pH value. Next, the test solution was circulated through the membranes during ∼4 h at a transmembrane pressure difference of ∼0.2 bar. The samples were then placed in the TSP and conductance measurement cells. About 30 min of solution circulation through the channel was needed for ∆φs to reach a stable value and thus to start the measurements.

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Figure 5. Product of the total conductance (Gt) by the streaming potential coefficient (∆φs/∆P) as function of the channel height (2h); direct method.

Figure 4. (a and b): Reciprocal streaming potential coefficient (∆P/∆φs) vs reciprocal channel height (1/2h); extrapolation method. TSP and conductance measurements were carried out at various channel heights (by using spacers of 100, 200, 300, 400, and 500 µm in thickness). The measurement of the streaming potential coefficient was always followed by the total conductance measurement of the membrane/channel/membrane system before changing the spacer thickness.

4. Results and Discussion Figure 4a and 4b shows the reciprocal streaming potential coefficient (∆P/∆φs) versus reciprocal channel height (1/2h) at two pH values for which membranes are either positively (pH 2) or negatively (pH 6) charged. The experimental signal appears to be dependent on the channel size for both pH. This first result points out the fact that the widely used Helmholtz-Smoluchowski equation is not suitable here for the interpretation of electrokinetic data since it would lead to a channel size dependent zeta potential. Moreover, as we operated at channel heights of 100 micrometers or more (up to 500 micrometers), the contribution of surface conductance to the overall channel conduction cannot be invoked in any reasonable way (the ratio of the channel half-height to the Debye length, h/κ-1, involved in our experiments ranging from ∼104 to ∼1.7 × 105). The channel size dependence of the streaming potential can then be explained only by the additional conduction through pores of the two membranes facing each other to form the slit channel. The direct consequence of the presence of porous substrates is that neither the Helmholtz-Smoluchowski relationship nor the classical experimental procedure to account for the surface conductivity (first proposed by Fairbrother and Mastin11) is applicable because the hydraulic cross section differs from the electrical cross section. From Figure 4, it is seen that the reciprocal streaming potential coefficient is a linear function of the reciprocal channel height as established in the previous theoretical section. The correct value of the zeta potential can then

Figure 6. pH dependence of ζ-potential determined from both extrapolation (ζextr) and direct (ζdir) methods; 1 mM KCl electrolyte support.

be determined from extrapolation to infinitely large channel according to eq 1. An alternative method is to determine zeta potential from both streaming potential and system conductance measurements. Figure 5 shows the variation of the product of the streaming potential coefficient (∆φs/∆P) by the total conductance (Gt) as a function of channel height (2h) for the same pH values as in Figure 4. According to eq 2, a straight line is obtained, the slope of which is directly related to the zeta potential. The consecutive measurements of streaming potential and total conductance constitutes a direct method to access the zeta potential. As previously mentioned, measurements could be carried out in principle with a single channel height provided the geometric features of the channel are known. The procedure adopted here (i.e., measurements at various channel heights) has the advantage to reduce uncertainty on zeta potential determination. Figure 6 presents the pH dependence of zeta potential determined from both extrapolation (ζextr) and direct (ζdir) methods. Results obtained for both methods are in very good agreement whatever the pH. The zeta potential appears to be sensitive to pH shifting as expected with surfaces for which the charging process involves dissociation of ionizable (acidic or basic) surface groups. The isoelectric point of the Desal G 10 membrane, that is, the pH for which the electrokinetic charge is zero, is close to 3.7. It has been shown above that the presence of membrane pores affects the tangential streaming potential measurement because the porous structure is an additional path through which the conduction current involved in the streaming potential process can flow (whereas the streaming current generated by the pressure gradient applied

Influence of the Membrane Pore Conductance

Figure 7. pH dependence of the ratio of the ζ-potential determined from both extrapolation (ζextr) and direct (ζdir) methods to the apparent one calculated via HelmholtzSmoluchowski equation (ζHS).

along membrane surfaces can flow only through the slit channel, i.e., the hydrodynamically mobile part of the system). The membrane pores can contribute to the conduction process either by a bulk conductivity (in such a case, the conductivity of the solution filling the membrane pores is identical to that of the solution flowing through the slit channel) or by a higher conductivity resulting from a nonnegligible contribution of surface conductance inside membrane pores (this excess conduction, which is not related to any hydrodynamic slipping process, would then enhance the conduction phenomenon through membrane pores). It is possible to get information about conductivity through the membrane pores by investigating the variation of the ratio of correct zeta potential, ζ, to apparent one (i.e., given by Helmholtz-Smoluchowski equation), ζHS, over a range of pH (Figure 7). As can be seen, the ζ/ζHS ratio has a minimum with respect to pH. This minimum is located at the isoelectric point of the membrane. This behavior suggests that the surface conductance (in membrane pores, not in the slit channel) is a non-negligible share of the overall conductivity within membrane pores. Indeed, ζ/ζHS increases as pH moves away from the isoelectric point, which is consistent with the increase in surface conductance as the electrical charge becomes higher (because of exponential rise of counterion concentration within electrical double layer). On the other hand, a porous structure that would act on the tangential streaming potential process only by its bulk conductivity would be characterized by a constant ζ/ζHS ratio, whatever the pH (except for the isoelectric point). According to eq 1, the single value of ζ/ζHS would then be only a function of the system geometry. 5. Conclusion The electrokinetic properties of a porous organic membrane have been investigated from tangential streaming potential measurement. This technique consists of applying an hydrostatic pressure gradient through a slit

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channel formed by two pieces of the material under consideration facing each other and measuring the resulting electrical potential difference. It has been shown that the experimental signal is affected by the membrane pores because this latter constitutes an additional path through which the conduction current involved in the streaming potential process can flow. Consequently, the interpretation of electrokinetic data using the classical Helmholtz-Smoluchowski relationship or the so-called Fairbrother and Mastin correction procedure can give rise to misleading conclusions because the substrate conduction properties are not accounted for. The determination of the correct zeta potential requires to perform tangential streaming potential measurement with various channel heights. The possible contribution of surface conductance in the membrane pores has been investigated by comparing the correct zeta potential with the apparent one (deduced from the Helmholtz-Smoluchowski equation) over a range of pH. 6. List of Symbols Gs Gt h hm I Ic IS l Lc P Pw Sc Sm v x

Surface conductance in the slit channel (Ω-1) total conductance of the membrane/channel/ membrane system (Ω-1) half-height of the slit channel (m) thickness of the membrane layer where the conduction current flows (m) electric current (A) conduction current (A) streaming current (A) length of the slit channel (m) width of the slit channel (m) hydrostatic pressure (N m-2) wetted perimeter of the slit channel (m) cross section of the slit channel (m2) cross-sectional area of the membrane (m2) fluid velocity (m s-1) distance from the center axis of the channel to a plane in the liquid parallel to the solid surfaces (m)

Greek Letters 0 r κ-1 λ0 λm F η φ ψ ζ

Vacuum permittivity (8.854 × 10-12 F m-1) relative dielectric constant of the solvent debye length (m) conductivity of bulk electrolyte (Ω1- m-1) electric conductivity of the membrane (Ω1- m-1) electric charge density (C m-3) viscosity of the electrolyte (kg m-1 s-1) electrical potential (V) electrostatic potential (V) zeta potential (V)

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