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.     

The electrical double layer on gold probed by electrokinetic and surface force measurements

Gold surfaces, obtained by vacuum deposition of 15-nm gold films on glass and silica wafers, were studied in aqueous solutions by streaming potential measurements and colloidal-probe AFM force measurements. In the force measurements both a bare and a gold-coated silica particle (6 microm in diameter) have been used as colloidal probes. From the streaming potential measurements we determined the zeta-potential of the gold surface, while from the force measurements the diffuse double-layer potential psi(d) was obtained by fitting the data to the DLVO theory or to the nonlinear Poisson-Boltzmann equation. Measured interactions were found to be entirely due to overlap of electric double layers with no indication of attractive Van der Waals forces. Results of both types of measurements are in good agreement. The double layer potential strongly depends on the pH, probably as a result of the presence of oxide species on the gold surface. Insight in the double layer potential of polarizable interfaces such as the gold/electrolyte solution interface is the first step for understanding the effect of externally applied potentials on the adsorption behavior of charged species.     

Faradaic double layer depolarization in electrokinetics: Onsager relations and substrate limitations

More often than not, the measurement of interfacial potentials by means of electrokinetic techniques is affected by interfering processes that may relax or even annihilate their primary response function. Among these processes are faradaic ones, provided that the substrate is sufficiently conducting and a redox function is available, and non-faradaic ones, if geometrical constraints are in effect. Ample experimental evidence is available, e.g., in the collapse of streaming potentials generated by metal/electrolyte solution interfaces, the bipolar microelectrodic redox processes in fluidized beds of metallic particles, and the "superfast" electrophoresis of dispersed ion exchanger particles and electron-conducting particles. Common feature of these apparently disparate phenomena is that the lateral electric field is affected by coupling with transversal depolarization fields, or by conductance gradients due to Donnan effects. Recent work has rigorously analyzed the deformation of the lateral electric field in a (streaming potential) slit cell by electron transfer reactions at the interface, taking into account both convective diffusion of the electroactive species and kinetics of the interfacial electron transfer reaction. Here a common, generic basis for faradaic and non-faradaic double layer depolarization is formulated along the lines set by Onsager, and methodologies for retrieving the underlying electrokinetic parameters from experimental data are evaluated. Particular attention is paid to the limitations of double layer polarization, as posed by the substrate.     

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.     

Problems and results of zeta-potential measurements on fibers

A survey is given on both theoretical background and methodical details of zeta-potential measurements on fibers. Electro-osmosis and streaming potential/streaming current measurements can be used in order to obtain correct zeta-potentials. Both measuring principles yield the same values for zeta-potential if the errors due to resistance measurements are avoided. This agreement as well as the independence of zeta-potential of applied voltage (in the case of electro-osmosis) and hydrostatic pressure (in the case of streaming potential/streaming current) point out that the Stern-potential at the boundary immobile/diffuse layer can be determined. Electrophoresis and measurement of other electrokinetic phenomena give values related to but not identical with the zeta-potential. Applications of electrokinetic measurements for investigating fiber problems in production, processing and finishing are reviewed. Parameters determining the zeta-potential of fibers are discussed.Dedicated to Prof. Dr. E. R. Schwarzl with congratulations for his 60th birthday.     

Modeling of electrokinetic transport in silica nanofluidic channels

We present a theoretical and numerical modeling study of the multiphysicochemical process in electrokinetic transport in silica nanochannels. The electrochemical boundary condition is solved by considering both the chemical equilibrium on solid-liquid interfaces and the salt concentration enrichment caused by the double layer interaction. The transport behavior is modeled numerically by solving the governing equations using the lattice Poisson-Boltzmann method. The framework is validated by good agreements with the experimental data for all range of ionic concentrations. The modeling results suggest that when the double layers interact, the bulk salt concentration enrichment results in the saturation of conductances for low ionic concentrations. Both the streaming conductance and the electrical conductance are enhanced by the double layer interaction, and such enhancements diminish when the channel size is larger than 10 times of the Debye length. The streaming conductance increases with pH almost linearly when pH < 8, while the electrical conductance increases with pH exponentially.     

Zeta Potential as an Analytical Tool for Graft Copolymers and for Polymer Surfaces

Polymers with electrically charged groups exhibit a zeta potential when in contact with electrolyte solutions in water. This can be measured with solid polymers as fibers, foils, or granulates. The method of streaming potential/streaming current allows the determination of the carboxyl content of cellulose grafted with poly-(acrylic acid). Since zeta-potential measurements concern the surface of the sample, the method yields information on the type of grafting; i.e., whether it takes place mainly on the surface or throughout the bulk. By measuring the pH dependence of the zeta potential it is possible to obtain the pK value of the charged groups. The significance of zeta potential as an analytical tool is emphasized.     

平流式流动电位测试系统的研制

分离膜表面的荷电化显著地影响着膜的分离性能和耐污染能力。因此,定量化表征膜表面电性能具有重要的理论价值和实际意义。作者在前期透过式膜流动电位测试系统研发工作的基础上成功地研制了平流式流动电位测试系统,并且首次将恒电流法测膜体电导引入膜表面ζ(Zeta)电位的确定过程中。以自制不同共混比的合金荷电膜为测试对象,利用该测试系统和经典的Helmholtz-Smoluchowski(H-S)方程及其变体得到了不同pH下的膜表面Zeta电位,从而揭示了膜表面电导、膜体电导对膜表面Zeta电位的贡献,并展示了该流动电位测试系统的有效性。     

Temperature effects on electrical double layer at solid-aqueous solution interface

Despite the significant influence of solution temperature on the structure of electrical double layer, the lack of theoretical model intercepts us to explain and predict the interesting experimental observations. In this work, we study the structure of electrical double layer as a function of thermochemical properties of the solution by proposing a phenomenological temperature dependent surface complexation model. We found that by introducing a buffer layer between the diffuse layer and stern layer, one can explain the sensitivity of zeta potential to temperature for different bulk ion concentrations. Calculation of the electrical conductance as function of thermochemical properties of solution reveals the electrical conductance not only is a function of bulk ion concentration and channel height but also the solution temperature. The present work model can provide deep understanding of micro- and nanofluidic devices functionality at different temperatures.     

Zeta potential determination by streaming current modelization and measurement in electrophoretic microfluidic systems

Electrophoresis in capillary and microfluidic systems, used in analytical chemistry to separate charged species, are quite sensitive to surface phenomena in terms of separation performances. In order to improve theses performances, new surface functionalization techniques are required. There is a need for methods to provide fast and accurate quantification about surface charges at liquid/solid interfaces. We present a fast, simple, and low-cost technique for the measurement of the zeta-potential, via the modelization and the measurement of streaming currents. Due to the small channel cross section in microfluidic devices, the streaming current modelization is easier than the streaming potential measurement. The modelization combines microfluidic simulations based on the Navier-Stokes equation and charge repartition simulations based on the Poisson-Boltzmann equation. This method has been validated with square and circular cross section shape fused-silica capillaries and can be easily transposed to any lab-on-chip microsystems.     

Estimation of zeta potential by electrokinetic analysis of ionic fluid flows through a divergent microchannel

The streaming potential is generated by the electrokinetic flow effect within the electrical double layer of a charged solid surface. Surface charge properties are commonly quantified in terms of the zeta potential obtained by computation with the Helmholtz-Smoluchowski (H-S) equation following experimental measurement of streaming potential. In order to estimate a rigorous zeta potential for cone-shaped microchannel, the correct H-S equation is derived by applying the Debye-Hückel approximation and the fluid velocity of diverging flow on the specified position. The present computation provides a correction ratio relative to the H-S equation for straight cylindrical channel and enables us to interpret the effects of the channel geometry and the electrostatic interaction. The correction ratio decreases with increasing of diverging angle, which implies that smaller zeta potential is generated for larger diverging angle. The increase of Debye length also reduces the correction ratio due to the overlapping of the Debye length inside of the channel. It is evident that as the diverging angle of the channel goes to nearly zero, the correction ratio converges to the previous results for straight cylindrical channel.     

A note on the streaming potential method for measuring surface potentials

Due to the fact that the classical analysis of the streaming potential method for measuring surface potential is somewhat crude, the problem was analyzed by applying the fundamental principles of electrochemistry. It was found that the classical Helmholz-Smoluchowski equation is valid provided that the duct is long and narrow, in which case the potential in the bulk is uniform over the duct's cross-sectional area and varies linearly over its length.In order to follow how the surface potential of a filter varies with time, investigators have measured the streaming potential across the filter's length as well as across segments of the filter. The problem is what do such measurements mean and do the classical equations apply. It was found that the classical result is expressible in differential form from which it followed that the streaming potential over any section of the filter gives a measure of the average surface potential of that section. This is an important result because it shows that the surface potential profile of a filter can be determined from measurements of the streaming potential profile across the filter.     

Streaming potential in cylindrical pores of poly(ethylene terephthalate) track-etched membranes: variation of apparent zeta potential with pore radius

Streaming potential variation with pressure measured through poly(ethylene terephthalate) track-etched membranes of different pore sizes led to the determination of an apparent interfacial potential zetaa in the presence of 10-2 M KCl. The variation of zetaa with the pore radius r0 is interpreted by (i) the electric double layer overlap effect and (ii) the presence of a conductive gel layer. We propose a method which integrates both effects by assuming a simple model for the conductive gel at the pore wall. We observed the following three domains of pore size: (i) r0 > 70 nm, where surface effects are negligible; (ii) approximately 17 nm < r0 < 70 nm, where the pore/solution interface could be described as a conductive gel of thickness around 1 nm; (iii) r0 < approximately 17 nm, which corresponds to the region strongly damaged by the ion beam and is not analyzed here. The first one (zeta = -36.2 mV) corresponds to the raw material when etching has completely removed the ion beam predamaged region, which corresponds to the second intermediate domain (zeta = -47.3 mV). There the conductance of the gel layer deduced from the treatment of streaming potential data was found to be compatible with the number of ionic sites independently determined by the electron spin resonance technique.     

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.     

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).     

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.     

The electrokinetic properties of colloidal magnetic iron oxides

A novel electrokinetic streaming potential technique has been used to determine the ζ potential behavior of three magnetic iron oxides, (Fe(3)O(4), γ-Fe(2)O(3), and CoFe(2)O(4)) as a function of pH and salt concentration. These colloidal materials, (nanosize in one dimension), are held in the form of a plug by means of external magnets. The streaming potential (E) is measured as a function of fluid flow induced by a pressure drop (ΔP) across the plug. The magnetically held plug is found to obey the requirements of the streaming potential technique; in each case an iso-electric point, (iep) independent of salt concentration is observed. However, if one uses the appropriate quantities in the standard formula, the calculated ζ potentials are very much lower than for oxides such as silica, alumina or goethite and other colloidal oxide, latex, etc. particulates in aqueous salt solutions. Furthermore, at a given pH, the measured ζ potentials anomalously increase in magnitude rather than decrease as observed conventionally as the salt concentration is increased. This apparent anomalous behavior could not be eliminated by incorporating surface conductance effects. However by including a conductance pathway, independent of pH or salt concentration, through the magnetic particle network itself, the anomaly was removed. Confirmation of the role of a conductance pathway through the magnetic particle network was obtained by using silica coated magnetic particles which displayed normal electrokinetic behavior. Finally, we have redesigned the plug-electrode assembly to allow measurement of streaming current, a technique know to eliminate contributions from plug network conductances of any kind. The resulting ζ potentials, derived from this streaming current technique are normal.     

Electrokinetics in nanochannels: part I. Electric double layer overlap and channel-to-well equilibrium

In this paper a new model is described for calculating the electric potential field in a long, thin nanochannel with overlapped electric double layers. Electrolyte concentration in the nanochannel is predicted self-consistently via equilibrium between ionic solution in the wells and within the nanochannel. Differently than published models that require detailed iterative numerical solutions of coupled differential equations, the framework presented here is self-consistent and predictions are obtained solving a simple one-dimensional integral. The derivation clearly shows that the electric potential field depends on three new parameters: the ratio of ion density in the channel to ion density in the wells; the ratio of free-charge density to bulk ion density within the channel; and a modified Debye-Hückel thickness, which is the relevant scale for shielding of surface net charge. For completeness, three wall-surface boundary conditions are analyzed: specified zeta-potential; specified surface net charge density; and charge regulation. Predictions of experimentally observable quantities based on the model proposed here, such as depth-averaged electroosmotic flow and net ionic current, are significantly different than results from previous overlapped electric double layer models. In this first paper of a series of two, predictions are presented where channel depth is varied at constant well concentration. Results show that under conditions of electric double layer overlap, electroosmosis contributes only a small fraction of the net ionic current, and that most of the measurable current is due to ionic conduction in conditions of increased counterion density in the nanochannel. In the second of this two-paper series, predictions are presented where well-concentration is varied and the channel depth is held constant, and the model described here is employed to study the dependence of ion mobility on ionic strength, and compare predictions to measurements of ionic current as a function of channel depth and ion density.     

Electrophoresis of a sphere normal to a plane at arbitrary electrical potential and double layer thickness

The electrophoretic movement of a sphere normal to an uncharged, planar surface is analyzed theoretically, taking the effect of double layer polarization into account. Here, both the surface potential of the particle and the thickness of the double layer surrounding it can be arbitrary. We show that if double layer polarization is neglected, the effect of the surface potential of a particle on its electrophoretic velocity is inappreciable. On the contrary, it becomes significant if double layer polarization is present. However, if the distance between the particle and the surface is sufficiently close, since the hydrodynamic effect dominates, the influence of the surface potential and double layer polarization becomes insignificant.     

On the behavior of electrokinetic streaming potential during protein filtration with fully and partially retentive nanopores

An experimental investigation of the electrokinetic streaming potentials of both fully and partially retentive nanopores as compared with the filtration progress of dilute globular protein solution under different surface charge conditions was performed using hollow fibers. The streaming potential is generated by the electrokinetic flow effect within the electric double layer of the charged surface. Depending on the solution pH, both the protein and the pore wall can be either repulsive or attractive due to the long-range electrostatic interaction. The repulsive electrostatic interaction allows the protein particles to stay in a suspended state above the outer surface of hollow fibers instead of being deposited. The apparent streaming potential value at partially retentive pores is larger than that at fully retentive pores for the oppositely charged case; however, the opposite behavior is shown for the same-charged case. The axial-position-dependent streaming potential was also observed in order to explore the development of a concentration polarization layer during the cross-flow filtration. The time evolution of the streaming potential during the filtration of protein particles is related to the filtrate flux, from which it can be found to provide useful real-time information on particle deposition onto the outer surfaces of hollow fibers.