Determining the Zeta Potential of Porous Membranes Using Electrolyte Conductivity inside Pores

The zeta potential is an important and reliable indicator of the surface charge of membranes, and knowledge of it is essential for the design and operation of membrane processes. The zeta potential cannot be measured directly, but must be deduced from experiments by means of a model. The possibility of determining the zeta potential of porous membranes from measurements of the electrolyte conductivity inside pores (lambda(pore)) is investigated in the case of a ceramic microfiltration membrane. To this end, experimental measurements of the electrical resistance in pores are performed with the membrane filled with KCl solutions of various pHs and concentrations. lambda(pore) is deduced from these experiments. The farther the pH is from the isoelectric point and/or the lower the salt concentration is, the higher the ratio of the electrolyte conductivity inside pores to the bulk conductivity is, due to a more important contribution of the surface conduction. Zeta potentials are calculated from lambda(pore) values by means of a space charge model and compared to those calculated from streaming potential measurements. It is found that the isoelectric points are very close and that zeta potential values for both methods are in quite good agreement. The differences observed in zeta potentials could be due to the fact that the space charge model does not consider the surface conductivity in the inner part of the double layer. Measurements of the electrolyte conductivity within the membrane pores are proved to be a well-adapted procedure for the determination of the zeta potential in situations where the contribution of the surface conduction is significant, i.e., for small and charged pores. Copyright 2001 Academic Press.     

An improved method for determining zeta potential and pore conductivity of porous materials

An improved method based on streaming potential and streaming current was proposed to determine zeta potential and surface conductance of porous material simultaneously. In the electrokinetic generation mode, a resistor is connected to the generator and by measuring the voltage drop across resistors with different resistance, a true streaming current can be determined. The zeta potential and surface conductivity can be obtained simultaneously from their relation to streaming potential and streaming current. The electrode and ion concentration polarization effects during the measurement were also discussed. The resistance from channel ends to electrodes, which has typically been ignored in the literature, was shown to have a significant influence on the calculated zeta potential and surface conductance. Ignorance of this resistance would lead to underestimation of both zeta potential and surface conductance values.     

Tangential streaming potential as a tool in modeling of ion transport through nanoporous membranes

Tangential streaming potential (TSP) measurements have been carried out so as to assess the electrokinetic properties of the active layer of organic nanofiltration (NF) membranes. Due to the porous structure of NF membranes, cares must be taken to convert the experimental data into zeta potential. Indeed, an assumption that is implicitly made in Smoluchowski's theory (or in related approaches accounting for the surface conduction phenomenon) is that both streaming and conduction currents involved in the streaming potential process flow through an identical path. Such an assumption does not hold with porous membranes since the conduction current is expected to flow wherever the electric conductivity differs from zero. Consequently, a non-negligible share of the conduction current is likely to flow through the membrane body filled with the electrolyte solution. This phenomenon has been taken into account by carrying out a series of TSP measurements at various channel heights. Experiments have been conducted with various electrolyte solutions. The inferred zeta potentials have been further converted into membrane volume charge densities which have been used to predict the membrane performances in terms of rejection rates. The conventional NF theory, i.e. based on a steric/Donnan exclusion mechanism, has been found to be unable to describe the experimental rejection rates. Using the volume charge density of the membrane as an adjustable parameter, it has been shown that the conventional theory even predicts the opposite sign for the membrane charge. On the other hand, the experimental rejection rates have been well described by including dielectric effects in the exclusion mechanism. In this case, a noticeable lowering of the effective dielectric constant of the electrolyte solution inside pores has been predicted (with respect to the bulk value).     

On the use of electrokinetic phenomena of the second kind for probing electrode kinetic properties of modified electron-conducting surfaces

The electrokinetic features of electron-conducting substrates, as measured in a conventional thin-layer electrokinetic cell, strongly depend on the extent of bipolar faradaic depolarisation of the interface formed with the adjacent electrolytic solution. Streaming potential versus applied pressure data obtained for metallic substrates must generally be interpreted on the basis of a modified Helmholtz-Smoluchowski equation corrected by an electronic conduction term-non linear with respect to the lateral potential and applied pressure gradient-that stems from the bipolar electrodic behavior of the metallic surface. In the current study, streaming potential measurements have been performed in KNO(3) solutions on porous plugs made of electron-conducting grains of pyrite (FeS(2)) covered by humic acids. For zero coverage, the extensive bipolar electronic conduction taking place in the plug-depolarized by concomitant and spatially distributed oxidation and reduction reactions of Fe(2+) and Fe(3+) species-leads to the complete extinction of the streaming potential over the entire range of applied pressure examined. For low to intermediate coverage, the local electron-transfer kinetics on the covered regions of the plug becomes more sluggish. The overall bipolar electronic conduction is then diminished which leads to an increase in the streaming potential with a non-linear dependence on the pressure. For significant coverage, a linear response is observed which basically reflects the interfacial double layer properties of the humics surface layer. A tractable, semi-analytical model is presented that reproduces the electrokinetic peculiarities of the complex and composite system FeS(2)/humics investigated. The study demonstrates that the streaming potential technique is a fast and valuable tool for establishing how well the electron transfer kinetics at a partially or completely depolarised bare electron-conducting substrate/electrolyte solution interface is either promoted (catalysis) or blocked (passivation) by the presence of a discontinuous surface layer.     

The electrical conductivity and surface conduction of consolidated rock cores

A fully computerized high-pressure and high-temperature core holder device is simultaneously used to determine the electrical conductivity, zeta potential, and surface conductivity of consolidated rock cores in aqueous and nonaqueous systems. The total electrical conductivity of rock cores was determined by coupling streaming current and potential measurements. This shows that neglecting the surface conductivity Ksigma is crucial to converting the streaming potential into zeta potentials. It is observed that plots of the core total conductivity as a function of the electrolyte conductivity KL exhibit two behaviors. At low ionic strength, the core conductivity clearly depends on the contribution of surface conductivity behind the slip plane, whereas at higher ionic strength, the magnitude of the surface conductivity becomes negligible. The electrical conductivity of rock cores was found to be in good agreement with the O'Brien theory and the Briggs method. The contribution of the stagnant layer to the surface conductivity in nonaqueous systems has been shown to be significant. This shows that the stagnant layer displays significantly different behavior in different nonaqueous systems, depending on the core porosity and the double-layer overlap. The results indicate that the application of electrokinetics in petroleum reservoirs can provide important insights into reservoir fluid flow characterization.     

Streaming potential generated by a long viscous drop in a capillary

The streaming potential generated by motion of a long drop of viscosity mu(d) = lambdamu in a uniform circular capillary filled with fluid of viscosity mu is investigated by means of a model previously used to study electrophoresis of a charged mercury drop in water. The capillary wall is at potential zeta c relative to the bulk fluid within it, and the surface of the drop is at potential zeta(d). Potentials are assumed to be sufficiently small so that the charge cloud is described by the linearized Poisson-Boltzmann equation, and the Debye length characterizing the thickness of the charge cloud is assumed to be thin compared with the gap h(0) between the drop and the capillary wall. Ions in the external fluid are not allowed to discharge at the surface of the drop, and the wall of the capillary has a nonzero surface conductivity sigma c. The drop is assumed to be sufficiently long so that end effects can be neglected. Recirculation of fluid within the drop gives rise to an enhanced streaming current when zeta(d) is nonzero, leading to an anomalously high streaming potential. This vanishes as the drop viscosity becomes large. If V is the velocity of the drop and gamma is the coefficient of interfacial tension between the two fluids, then the capillary number is Ca = mu V/gamma, and the gap varies as h(0)planck'sCa(2/3). When Ca is small, the gap h(0) is small and electrical conduction along the narrow gap is dominated by the surface conductivity sigma(c) of the capillary wall, which is constant. The electrical current convected by flowing fluid is proportional to Ca, as is the change in streaming potential caused by the presence of the drop. If sigma(c) = 0, then the electrical conductance of the gap depends on its width h(0) and on the bulk fluid conductivity sigma and becomes small as h(0) approximately equal to Ca(2/3) --> 0. The streaming potential required to cancel the O(Ca) convection current therefore varies as Ca(1/3). If sigma(c) = 0 and the drop is rigid (lambda --> infinity), then the change in streaming potential over and above that expected due to the change in pressure gradient is proportional to the difference in potentials zeta(c)-zeta(d).     

Influence of roughness and capillary size on the zeta potential values obtained by streaming potential measurements

Streaming potential measurements are performed to determine the zeta potential of flat surfaces, particles, or fibers. Although the zeta potential is a well-defined property of solid surfaces in a liquid, there are indications that the absolute values of the zeta potential calculated using the Helmholtz-Smoluchowski equation are affected by surface roughness and—in case of particle or fiber assemblies—their packing density. The study at hand investigates these influences using flat polymer surfaces with different roughness and topography and assemblies of basalt spheres. It was found that increasing roughness of the flat surface and larger size or smaller number of particles in particle assemblies result in flatter slopes of the streaming potential versus pressure and thus lower apparent absolute values of the zeta potential. The interpretation of streaming potential measurements should therefore not focus on absolute zeta potential values but on trends in pH- and concentration-dependent measurements.     

Zeta potential of ion-conductive membranes by streaming current measurements

Surface charge properties have a significant influence on membrane retention and fouling performance. As a key parameter describing the surface charge of membranes used in aqueous applications, zeta potential measurements on membranes of various types have attracted great attention. During the zeta potential characterization of a series of ion-conductive sulfonated poly(sulfone) membranes, it was found that the measured streaming current varied with the thickness of the sample, which is not predicted by the classical Smoluchowski equation. Moreover, for higher conductivity membranes with an increased concentration of sulfonate groups, the zeta potential tended toward zero. It was determined that the influence of membrane bulk conductance on the measured streaming current must be taken into account in order to correctly interpret the streaming current data for ion-conductive polymers and understand the relationship between membrane chemical composition and zeta potential. Extrapolating the measured streaming current to a membrane thickness of zero has proven to be a feasible method of eliminating the error associated with measuring the zeta potential on ion conductive polymer membranes. A linear resistance model is proposed to account for the observed streaming currents where the electrolyte channel is in parallel with the ion-conductive membranes.     

Surface modification of phenolphthalein poly(ether sulfone) ultrafiltration membranes by blending with acrylonitrile-based copolymer containing ionic groups for imparting surface electrical properties

Asymmetric ultrafiltration membranes were fabricated from the blends of phenolphthalein polyethersulfone (PES-C) and acrylonitrile copolymers containing charged groups, poly(acrylonitrile-co-acrylamido methylpropane sulfonic acid) (PAN-co-AMPS). From the surface analysis by XPS and ATR-FTIR, it was found that the charged groups tend to accumulate onto the membrane surface. This result indicated that membrane surface modification for imparting surface electrical properties could be carried out by blending charged polymer. Furthermore, with the help of a relatively novel method to measure membrane conduction, the true zeta potentials calculated on the basis of the streaming potential measurements were used to reflect the charge state of membrane surface. In addition, it was noteworthy that, from the profiles of zeta potential versus pH curves and the magnitude of zeta potentials, the determination of zeta potential was dependent not only on the electrical properties of membrane surface but also on its hydrophilicity. At last, based on a relatively elaborate study on the electrostatic interaction between the membrane surface and protein, it was found that these charged membranes could meet different demands of membrane applications, such as resisting protein fouling or protein separation, through adjusting solution pH value.     

Measurement of the streaming potential and streaming current near a rotating disk to determine its zeta potential

Methodology for determining the zeta potential of a disk-shaped sample by both streaming potential and streaming current measurements is presented. Integration of Laplace's equation within one radius of the disk surface revealed that the streaming potential decreased strongly in the surface normal direction. With this solution, the zeta potential can be calculated from measurements of the streaming potential near the surface of the disk provided the position of the working electrode near the disk surface is known. Determining the zeta potential of a disk-shaped sample by means of streaming current measurements required determination of a current collection efficiency because not all the streaming current from a disk flows through the auxiliary electronic current path. While the working electrode near the disk should be pointlike, several possible variants on counter electrode shape and size were explored. Although the current collection efficiency was only a few percent in each case, the measured current was of 10 nA order. The current collection efficiency depended only on system geometry and was independent of a disk's zeta potential and solution concentration. Streaming current measurements of zeta potential on silicon wafers in potassium chloride solutions up to 10 mM agreed well with published values.     

Investigation of dynamic streaming potential by dimensional analysis

The theory of streaming potential at sinusoidal flow of liquid in a porous medium is a convenient and fruitful tool for determination of the interface properties of materials and also for construction of apparatus for zeta potential measurements and electrokinetic transducers. An investigation of the dynamic streaming potential by the method of dimensional analysis is presented. This method provides a wider approach to the problem under consideration. As a result, relationships between streaming potential in a porous medium and mechanical quantities are established. These quantities include pressure gradient in a liquid inside pores and capillaries, acceleration of capillaries, and the solid part of a porous medium, and the viscous friction force the liquid exerts on the solid part. The corresponding formulas for streaming potential are presented. The relationship between the streaming potential and viscous friction force does not depend on the frequency of oscillation and pore size. All these formulas in particular cases are transformed to known formulas for the streaming potential.     

Electrochemistry of capillary systems with narrow pores V. Streaming potential: Donnan hindrance of electrolyte transport

The electrochemical theory of capillary systems with narrow pores outlined in Part I of this series is applied to the streaming potential and the electrical hindrance of electrolyte transport across ion selective membranes (Donnan hindrance). Both phenomena are related to the fixed ion concentration. Streaming potentials were measured while using collodion membranes of graded porosity and graded fixed ion concentration. The bulk phases consisted of aqueous KCl solutions with a concentration 2×10⁻⁴ n. The streaming potentials were calculated theoretically by using the electrical conductivity data of the membranes given in Part III of this series. The agreement between the experimental results and the predictions of the theory is good. Theory also predicts that a volume flow across the membrane caused by a hydrostatic pressure difference generates a filtration effect the concentration c_s of the electrolyte in the solution leaving the membrane on the low pressure side is lower than the concentration c on the high pressure side. The concentration ratio (c_s/c) is equal to the ratio (κ/κ_i) of the electrical conductivity of the high pressure phase κ and that of the pore fluid κ_i. The hindrance of the electrolyte transport is a transient phenomenon. It disappears slowly if the experiment is continued over a long period of time. This phenomenon, which is of importance in the understanding of ultrafiltration processes using membranes, is discussed in detail. It is compared with the observed changes in the streaming potential as a function of time. The influence of the electrical convection conductivity (electrical surface conductivity) on the streaming potential can be neglected under the chosen experimental conditions. Its influence will be discussed in Part VI of this series.     

Caractérisation des propriétés électriques des parois de pores d’une membrane

The characterisation of the surface electrical properties of membrane materials is critical for understanding and predicting the filtration performances of membranes. In this paper, four simple experimental methods – streaming potential, electro-osmosis, pore conductivity and membrane potential –, allowing the characterisation of the charge state of membrane pore walls are presented. The four experimental parameters provide information about the sign of the electrical net charge. Examples illustrating the influence of the pH, electrolyte concentration and nature on the four experimental parameters are given. The zeta potential can be then deduced from these measurements by means of a model.     

Influence of the Dukhin and Reynolds numbers on the apparent zeta potential of granular porous media

The Helmholtz-Smoluchowski (HS) equation is widely used to determine the apparent zeta potential of porous materials using the streaming potential method. We present a model able to correct this apparent zeta potential of granular media of the influence of the Dukhin and Reynolds numbers. The Dukhin number represents the ratio between the surface conductivity (mainly occurring in the Stern layer) and the pore water conductivity. The Reynolds number represents the ratio between inertial and viscous forces in the Navier-Stokes equation. We show here that the HS equation can lead to serious errors if it is used to predict the dependence of zeta potential on flow in the inertial laminar flow regime without taking into account these corrections. For indifferent 1:1 electrolytes (such as sodium chloride), we derived two simple scaling laws for the dependence of the streaming potential coupling coefficient (or the apparent zeta potential) on the Dukhin and Reynolds numbers. Our model is compared with a new set of experimental data obtained on glass bead packs saturated with NaCl solutions at different salinities and pH. We find fairly good agreement between the model and these experimental data.     

Electrokinetic coupling in unsaturated porous media

We consider a charged porous material that is saturated by two fluid phases that are immiscible and continuous on the scale of a representative elementary volume. The wetting phase for the grains is water and the nonwetting phase is assumed to be an electrically insulating viscous fluid. We use a volume-averaging approach to derive the linear constitutive equations for the electrical current density as well as the seepage velocities of the wetting and nonwetting phases on the scale of a representative elementary volume. These macroscopic constitutive equations are obtained by volume-averaging Ampère's law together with the Nernst-Planck equation and the Stokes equations. The material properties entering the macroscopic constitutive equations are explicitly described as functions of the saturation of the water phase, the electrical formation factor, and parameters that describe the capillary pressure function, the relative permeability functions, and the variation of electrical conductivity with saturation. New equations are derived for the streaming potential and electro-osmosis coupling coefficients. A primary drainage and imbibition experiment is simulated numerically to demonstrate that the relative streaming potential coupling coefficient depends not only on the water saturation, but also on the material properties of the sample, as well as the saturation history. We also compare the predicted streaming potential coupling coefficients with experimental data from four dolomite core samples. Measurements on these samples include electrical conductivity, capillary pressure, the streaming potential coupling coefficient at various levels of saturation, and the permeability at saturation of the rock samples. We found very good agreement between these experimental data and the model predictions.     

Electrokinetic characterization of poly(acrylic acid) and poly(ethylene oxide) brushes in aqueous electrolyte solutions

Surfaces carrying hydrophilic polymer brushes were prepared from poly(styrene)-poly(acrylic acid) and poly(styrene)-poly(ethylene oxide) diblock copolymers, respectively, using a Langmuir-Blodgett technique and employing poly(styrene)-coated planar glass as substrates. The electrical properties of these surfaces in aqueous electrolyte were analyzed as a function of pH and KCl concentration using streaming potential/streaming current measurements. From these data, both the zeta potential and the surface conductivity could be obtained. The poly(acrylic acid) brushes are charged due to the dissociation of carboxylic acid groups and give theoretical surface potentials of -160 mV at full dissociation in 10(-)(3) M solutions. The surface conductivity of these brushes is enormous under these conditions, accounting for more than 93% of the total measured surface conductivity. However, the mobility of the ions within the brush was estimated from the density of the carboxylic acid groups and the surface conductivity data to be only about 14% of that of free ions. The poly(ethylene oxide) (PEO) brushes effectively screen the charge of the underlying substrate, giving a very low zeta potential except when the ionic strength is very low. From the data, a hydrodynamic layer thickness of the PEO brushes could be estimated which is in good agreement with independent experiments (neutron reflectivity) and theoretical estimates. The surface conductivity in this system was slightly lower than that of the polystyren substrate. This also indicates that no significant amount of preferentially, i.e., nonelectrostatically attracted, ions taken up in the brush.     

Electrochemistry of capillary systems with narrow pores V. Streaming potential: Donnan hindrance of electrolyte transport

The electrochemical theory of capillary systems with narrow pores outlined in Part I of this series is applied to the streaming potential and the electrical hindrance of electrolyte transport across ion selective membranes (Donnan hindrance). Both phenomena are related to the fixed ion concentration. Streaming potentials were measured while using collodion membranes of graded porosity and graded fixed ion concentration. The bulk phases consisted of aqueous KCl solutions with a concentration 2×10⁻⁴ n. The streaming potentials were calculated theoretically by using the electrical conductivity data of the membranes given in Part III of this series. The agreement between the experimental results and the predictions of the theory is good. Theory also predicts that a volume flow across the membrane caused by a hydrostatic pressure difference generates a filtration effect the concentration c_s of the electrolyte in the solution leaving the membrane on the low pressure side is lower than the concentration c on the high pressure side. The concentration ratio (c_s/c) is equal to the ratio (κ/κ_i) of the electrical conductivity of the high pressure phase κ and that of the pore fluid κ_i. The hindrance of the electrolyte transport is a transient phenomenon. It disappears slowly if the experiment is continued over a long period of time. This phenomenon, which is of importance in the understanding of ultrafiltration processes using membranes, is discussed in detail. It is compared with the observed changes in the streaming potential as a function of time. The influence of the electrical convection conductivity (electrical surface conductivity) on the streaming potential can be neglected under the chosen experimental conditions. Its influence will be discussed in Part VI of this series.     

Streaming potentials and conductivities of latex plugs. Influence of the valency of the counterion

Plugs consisting of polystyrene particles with sulphonate surface groups have been investigated in the presence of mono-, di- and trivalent counterions. The streaming potentials and conductivities of the plug and bulk solution have been measured. From the latter, the overall surface conductivity has been estimated. It is shown that for this system, accounting for the surface conductivity in the hydrodynamically stagnant layer is crucial to convert the streaming potentials into zeta potentials. The overall surface conductivity clearly depends on the charge of the counterion, and so do the ionic mobilities in the stagnant layer. The higher the valency of the counterion, the lower is the ionic mobility in the stagnant layer, but for all counterions, the ionic mobility in the stagnant layer is of the same order of magnitude as in the bulk. For the divalent counterions, no indications of specific interactions with the surface groups have been found.     

Streaming potential in open and packed fused-silica capillaries

The surface properties of novel stationary phases in packed and open tubular columns for capillary electrochromatography (CEC) were examined by measuring the streaming potential in a home made apparatus. The surfaces investigated include materials such as porous styrenic sorbents and octadecyl-silica as well as fused-silica tubing, in both raw and surface modified forms. Functionalization of the surface was carried out, for instance, by reductive amination or organosilane grafting on to capillary inner wall. The dependence of the streaming potential on pH was examined with aqueous solutions in the pH range from 2.5 to 9.0. Electrokinetic properties of 50 microm I.D. fused-silica capillaries have been determined by both streaming potential and electrosmotic flow measurements. Both methods gave similar pH profiles of the zeta-potential and the isoelectric points. This confirms the viability of our approach to evaluate the specific charged groups of the packing which is one of the important factors influencing electrosmotic flow (EOF) velocity and protein adsorption during a chromatographic run. In addition to bare silica capillaries, styrenic monolithic columns with different surface functionalities, which have been extensively used in our laboratory for CEC separation of peptides and proteins, were employed for comparison of two methods. Plots of zeta potential as a function of percent ACN show a complex behavior, indicating that zeta potential cannot be predicted simply from binary mixture solvent properties. It is demonstrated that the evaluation of the zeta potential by the streaming potential method is nondestructive, relatively fast, without untoward effects introduced by Joule heating and yet another means for the characterization of the surfaces under conditions employed in CEC.