Interfacial biocatalysis on charged and immobilized substrates: the roles of enzyme and substrate surface charge

An enzyme charge ladder was used to examine the role of electrostatic interactions involved in biocatalysis at the solid-liquid interface. The reactive substrate consisted of an immobilized bovine serum albumin (BSA) multilayer prepared using a layer-by-layer technique. The zeta potential of the BSA substrate and each enzyme variant was measured to determine the absolute charge in solution. Enzyme adsorption and the rate of substrate surface hydrolysis were monitored for the enzyme charge ladder series to provide information regarding the strength of the enzyme-substrate interaction and the rate of interfacial biocatalysis. First, each variant of the charge ladder was examined at pH 8 for various solution ionic strengths. We found that for positively charged variants the adsorption increased with the magnitude of the charge until the surface became saturated. For higher ionic strength solutions, a greater positive enzyme charge was required to induce adsorption. Interestingly, the maximum catalytic rate was not achieved at enzyme saturation but at an invariable intermediate level of adsorption for each ionic strength value. Furthermore, the maximum achievable reaction rate for the charge ladder was larger for higher ionic strength values. We propose that diffusion plays an important role in interfacial biocatalysis, and for strong enzyme-substrate interaction, the rate of diffusion is reduced, leading to a decrease in the overall reaction rate. We investigated the effect of substrate charge by varying the solution pH from 6.1 to 8.7 and by examining multiple ionic strength values for each pH. The same intermediate level of adsorption was found to maximize the overall reaction rate. However, the ionic strength response of the maximum achievable rate was clearly dependent on the pH of the experiment. We propose that this observation is not a direct effect of pH but is caused by the change in substrate surface charge induced by changing the pH. To prove this hypothesis, BSA substrates were chemically modified to reduce the magnitude of the negative charge at pH 8. Chemical modification was accomplished by the amidation of aspartic and glutamic acids to asparagine and glutamine. The ionic strength response of the chemically modified substrate was considerably different than that for the native BSA substrate at an identical pH, consistent with the trend based on substrate surface charge. Consequently, for substrates with a low net surface charge, the maximum achievable catalytic rate of the charge ladder was relatively independent of the solution ionic strength over the range examined; however, at high net substrate surface charge, the maximum rate showed a considerable ionic strength dependence.     

Protonation of Lysozymes and Its Consequences for the Adsorption onto a Mica Surface

Several physicochemical properties of chicken egg white lysozyme (LSZ) in electrolyte solutions were determined. The hydrodynamic diameter of LSZ at an ionic strength of 0.15 M was found to be 4.0 nm. Using the determined parameters, the number of uncompensated (electrokinetic) charges, N(c), on the molecule surface was calculated from the electrophoretic mobility data. It was found that the N(c) = 2.8 at pH = 3.0 and an ionic strength of I = 0.15 M. At the lower ionic strength, I = 1 × 10(-3) M, this positive charge increased to N(c) = 5.6 at a pH = 3.0 The physicochemical characteristics were supplemented by the dynamic viscosity measurements. The intrinsic viscosity and the hydrodynamic diameter results were compared with theoretical predictions from Brenner's model. Using this approach, it was found that the effective molecule length of LSZ is equal to L(ef) = 5.6 nm. Additional information on the LSZ adsorbed films was obtained by the contact angle measurements. The notably large contact angles were measured on LSZ films formed under the conditions where both the LSZ and the mica were oppositely charged. The higher the positive zeta potential of LSZ, the greater the contact angle measured, which indicates that LSZ affinity for the adsorption on mica increases with its uncompensated charge. The adsorption dependence on the zeta potential of LSZ was explained, assuming a roughly uniform distribution of the net charge on the molecule surface. This assumption is supported by the results of depositing negatively charged, fluorescent latex particles onto the mica surface, which had been modified by LSZ adsorption. The highest latex coverage was formed on mica surfaces that had first been coated with LSZ solutions of lower pH, as a result of the increasing charge of LSZ monolayers in this condition.     

Polyelectrolyte–particle complex formation. Polyelectrolyte linear charge density and ionic concentration effects. Monte Carlo simulations

The influence of the linear charge density (LCD) of a polyelectrolyte on its adsorption on an oppositely charged colloidal particle is investigated by Monte Carlo simulations. Adsorption characteristics are studied at different linear charge densities and ionic concentrations and for a given polyelectrolyte/particle size ratio so that particle curvature has full effect. The isolated polyelectrolyte goes through a smooth transition from a collapsed structure to an extended rod-like conformation with increasing the linear charge density in the low ionic concentration regime. In the high ionic concentration regime, the polyelectrolyte is less sensitive to the increase in the linear charge density and adopts a coil conformation. We found that complex formation is promoted by decreasing the ionic concentration and increasing the linear charge density and that large changes in the polymer dimensions are observed at the adsorption-desorption limit. By adjusting the linear charge density and ionic strength, we demonstrate that the adsorption-desorption limit corresponds to a sharp transition from non-adsorbed to adsorbed conformations and that the mean adsorption energy per monomer has to be less than -0.4 kT to achieve adsorption. We calculated that the linear charge density at the adsorption-desorption limit is related to the Debye-Hückel length according to LCD^crit ~3². At small values of the linear charge density and low ionic strength (no adsorption is observed at high ionic strength), a large amount of monomers are present in loops and tails. By increasing LCD, the amount of monomers in trains reaches a maximum value and the polyelectrolyte adopt flat conformation at the surface of the particle.     

Fibrinogen adsorption on mica studied by AFM and in situ streaming potential measurements

Adsorption of fibrinogen from aqueous solutions on mica was studied using AFM and in situ streaming potential measurements. In the first stage, bulk physicochemical properties of fibrinogen and the mica substrate were characterized for various ionic strength and pH. The zeta potential and number of uncompensated (electrokinetic) charges on the protein surfaces were determined from microelectrophoretic measurements. Analogously, using streaming potential measurements, the electrokinetic charge density of mica was determined for pH range 3-10 and the NaCl background electrolyte concentration of 10(-3) and 10(-2) M. Next, the kinetics of fibrinogen adsorption at pH 3.5 and 7.4 in the diffusion cell was studied using a direct AFM determination of the number of molecules per unit area of the mica substrate. Then, streaming potential measurements were performed to determine the apparent zeta potential of fibrinogen-covered mica for different pH and ionic strength in terms of its surface concentration. A quantitative interpretation of these streaming potential measurements was achieved in terms of the theoretical model postulating a side-on adsorption of fibrinogen molecules as discrete particles. On the basis of these results, the maximum coverage of fibrinogen Θ close to 0.29 was predicted, in accordance with previous theoretical predictions. It was also suggested that anomalous adsorption for pH 7.4, where fibrinogen and the mica substrate were both negatively charged, can be explained in terms of a heterogeneous charge distribution on fibrinogen molecules. It was estimated that the positive charge was 12 e (for NaCl concentration of 10(-2) M and pH 7.4) compared with the net charge of fibrinogen at this pH, equal to -21 e. Results obtained in this work proved that the coverage of fibrinogen can be quantitatively determined using the streaming potential method, especially for Θ < 0.2, where other experimental methods become less accurate.     

Characterization of a planar poly(acrylic acid) brush as a materials coating for controlled protein immobilization

The adsorption of two different proteins at a planar poly(acrylic acid) (PAA) brush was studied as a function of the ionic strength of the protein solutions applying total internal reflection fluorescence (TIRF) spectroscopy. Planar PAA brushes were prepared with a grafting density of 0.11 nm(-2) and were characterized using X-ray reflectometry. Hen egg-white lysozyme and bovine serum albumin (BSA) were used as model proteins, which have a net positive and negative charge at neutral pH-values, respectively. It has been found that both proteins adsorb strongly at a planar PAA brush at low ionic strength. Whereas lysozyme interacts with a PAA brush under electrostatic attraction at neutral pH-values, BSA binds under electrostatic repulsion at pH > 5. Even at pH = 8, significant amounts of BSA are adsorbed to a planar PAA brush. In addition, the reversibility of BSA adsorption has been characterized. Dilution of a BSA solution leads to an almost complete desorption of BSA from a PAA brush at short contact times. When the ionic strength of the protein solutions is increased to about 100-200 mM, a planar PAA brush appears largely protein-resistant, regardless of the protein net charge. The results of this study indicate that the salt-dependent protein affinity of a PAA brush represents a unique effect that must be explained by a novel protein-binding mechanism. On the basis of a recent model, it is suggested that a release of counterions is the most probable driving force for protein adsorption at a PAA brush. In a general view, this study characterizes a planar PAA brush as a new materials coating for the controlled immobilization of proteins whose use in biotechnological applications appears to be rewarding.     

Adsorption of Cl− ions on bismuth from ethanol

The specific adsorption of Cl^? ions at the bismuth-ethanol interface has been studied both in the solutions of mixed electrolytes with constant ionic strength and in the binary LiCl solutions by the method of measuring the potential dependence of differential capacity of bismuth. The charge due to specifically adsorbed anions was calculated from the experimental capacity data. It was found that in the case of specific adsorption of Cl^? ions at the bismuth—ethanol interface the conditions of undercharged as well as recharded surface of electrode could be observed experimentally. The analysis of the results obtained by fitting the charge of specifically adsorbed ions to the modified virial isotherm including the diffuse layer correction term suggests that in the conditions of recharge of the bismuth surface cations enter the inner part of the double layer and a considerable ionic association occurs in the inner layer. A procedure has been proposed for calculating the charge due to cations in the inner layer, for determining the actual value of the outer Helmholtz plane potential and for evaluating the real parameters of the adsorption isotherm. The reliability of the results of calculations was verified by comparing the data obtained by the method of mixed electrolytes both considering and neglecting the ionic association in the inner layer with the data of the method of binary electrolyte.     

Modeling of protein interactions with surface-grafted charged polymers. Correlations between statistical molecular modeling and a mean field approach

Ion exchange media involving charge groups attached to flexible polymers are widely used for protein purification. Such media often provide enhanced target protein purity and yield. Yet, little is understood about protein interaction with such media at the molecular level, or how different media architectures might affect separation performance. To gain a better understanding of such adsorptive systems, statistical mechanical perturbation calculations, utilizing a Debye-Hückel potential, were performed on surface-grafted charged polymers and their interaction with model proteins. The studied systems were weakly charged, and the polymers were linear and relatively short (degree of polymerization is 30). Segment distributions from the surface were also determined. The interaction of spherical model protein particles of 12-30 A radius were investigated with respect to polymer grafting density, distance from matrix surface, protein charge, and ionic strength. The partitioning coefficient of the model proteins was determined for different distances from the surface. An empirical mean field theory that scales the entropy of the protein with the square of the protein radius correlates well to Monte Carlo statistical modeling results. Upon adsorption to the polymer layers, the model proteins exhibit a critical surface charge density that is proportional to the ionic strength, independent of the grafting density, and appears to be a fundamental determinant of protein adsorption. Partitioning of protein-like nanoparticles to the charged polymer surface is only favored above the particle critical charge density.     

Measurements and theoretical interpretation of points of zero charge/potential of BSA protein

The points of zero charge/potential of proteins depend not only on pH but also on how they are measured. They depend also on background salt solution type and concentration. The protein isoelectric point (IEP) is determined by electrokinetical measurements, whereas the isoionic point (IIP) is determined by potentiometric titrations. Here we use potentiometric titration and zeta potential (ζ) measurements at different NaCl concentrations to study systematically the effect of ionic strength on the IEP and IIP of bovine serum albumin (BSA) aqueous solutions. It is found that high ionic strengths produce a shift of both points toward lower (IEP) and higher (IIP) pH values. This result was already reported more than 60 years ago. At that time, the only available theory was the purely electrostatic Debye-Hu?ckel theory. It was not able to predict the opposite trends of IIP and IEP with ionic strength increase. Here, we extend that theory to admit both electrostatic and nonelectrostatic (NES) dispersion interactions. The use of a modified Poisson-Boltzmann equation for a simple model system (a charge regulated spherical colloidal particle in NaCl salt solutions), that includes these ion specific interactions, allows us to explain the opposite trends observed for isoelectric point (zero zeta potential) and isoionic point (zero protein charge) of BSA. At higher concentrations, an excess of the anion (with stronger NES interactions than the cation) is adsorbed at the surface due to an attractive ionic NES potential. This makes the potential relatively more negative. Consequently, the IEP is pushed toward lower pH. But the charge regulation condition means that the surface charge becomes relatively more positive as the surface potential becomes more negative. Consequently, the IIP (measuring charge) shifts toward higher pH as concentration increases, in the opposite direction from the IEP (measuring potential).     

On the theory of polyelectrolyte adsorption : The effect on adsorption behavior of the electrostatic contribution to the adsorption free energy

A theory has been developed for the adsorption of polyelectrolytes on charged interfaces from an aqueous salt solution. This adsorption is determined by the electrical charge density of the polyelectrolyte, the adsorption energy, the salt concentration, the molecular weight, solubility, flexibility, and concentration of polymer. The theory relates these parameters to the properties of the adsorbed polymer layer, i.e., the amount of polymer adsorbed, the fraction of the adsorbent interface covered, the fraction of the segments actually adsorbed on the interface versus the fraction of the segments in the dangling loops, the final surface charge density, and the thickness of the adsorbed layer. As polyelectrolyte adsorption should resemble nonionic polymer adsorption at high ionic strength of the solution or low charge density on the polymer, this work is an extension of the nonionic polymer adsorption theory to polyelectrolyte adsorption. The following effects are taken into account: (a) the conformational change upon adsorption of a coil in solution into a sequence of adsorbed trains interconnected by loops dangling in solution; (b) the interactions of the adsorbed trains with the interface and with each other; (c) the interaction of the dangling loops with the solvent; (d) the change in surface charge density of the adsorbent due to adsorption of charged trains and the accompanying changes in the electrical double layer which contains “small” ions as well as charged loops; (e) the (induced) dipole interaction of the adsorbed trains with the charged adsorbent interface. The theory is worked out for low potentials (Debye—Hückel approximation); in Appendix B an outline of a more complete treatment is given. The predicted adsorption isotherms have the experimentally observed high-affinity character. A relation between the adsorption energy, the surface charge density on the adsorbent, the degree of dissociation of the polymer, and the salt concentration predicts the conditions under which no adsorption will occur. For adsorbent and polymer carrying the same type of charge (both positive or both negative) the adsorption is predicted to decrease with increased charge density on polymer or adsorbent and to increase with salt concentration. If adsorbent and polymer carry different type charges, the adsorption as a function of the degree of dissociation, α, goes through a maximum at a relatively low value of α and, depending on the adsorption energy, an increase in the salt concentration can then increase or decrease the adsorption. At finite polymer concentration in solution the number of adsorbed segments and the fraction of the interface covered practically do not change with an increase in polymer concentration, whereas the total number of polymer molecules adsorbed increases slightly, as does the average fraction of segments in loops. The experimental results for polyelectrolyte adsorption have been reviewed in general and, as far as data are available, the predictions of the theory seem to follow the experimentally observed trends quite closely, except for the thickness of the adsorbed layer. This thickness is systematically overestimated by the theory and two reasons for this are given. The theoretical model implies a not too low ionic strength of the solution. Extrapolation of results to solutions of very low ionic strength is not warranted.     

Accounting for diffuse layer ions in triple-layer models

The triple-layer model is one of the most widely used surface complexation models for adsorption on mineral surfaces. In current implementations, the accounting of ions in the diffuse layer may be neglected, resulting in a charge imbalance in the modeled solution as well as errors in mass balance, particularly in low ionic strength solutions when mineral-specific surface area is large. This paper introduces an internally consistent scheme for modeling diffuse layer ions in the triple-layer model. Model calculations illustrate the difference between the proposed and previous implementations using an idealized example. The guarantee of charge balance on both sides of the interface assures that pH is accurately modeled. This may be important in reactive transport simulations, such as modeling adsorption in low ionic strength variable charge soil solutions.     

The role of electrostatic interactions in protease surface diffusion and the consequence for interfacial biocatalysis

This study examines the influence of electrostatic interactions on enzyme surface diffusion and the contribution of diffusion to interfacial biocatalysis. Surface diffusion, adsorption, and reaction were investigated on an immobilized bovine serum albumin (BSA) multilayer substrate over a range of solution ionic strength values. Interfacial charge of the enzyme and substrate surface was maintained by performing the measurements at a fixed pH; therefore, electrostatic interactions were manipulated by changing the ionic strength. The interfacial processes were investigated using a combination of techniques: fluorescence recovery after photobleaching, surface plasmon resonance, and surface plasmon fluorescence spectroscopy. We used an enzyme charge ladder with a net charge ranging from -2 to +4 with respect to the parent to systematically probe the contribution of electrostatics in interfacial enzyme biocatalysis on a charged substrate. The correlation between reaction rate and adsorption was determined for each charge variant within the ladder, each of which displayed a maximum rate at an intermediate surface concentration. Both the maximum reaction rate and adsorption value at which this maximum rate occurs increased in magnitude for the more positive variants. In addition, the specific enzyme activity increased as the level of adsorption decreased, and for the lowest adsorption values, the specific enzyme activity was enhanced compared to the trend at higher surface concentrations. At a fixed level of adsorption, the specific enzyme activity increased with positive enzyme charge; however, this effect offers diminishing returns as the enzyme becomes more highly charged. We examined the effect of electrostatic interactions on surface diffusion. As the binding affinity was reduced by increasing the solution ionic strength, thus weakening electrostatic interaction, the rate of surface diffusion increased considerably. The enhancement in specific activity achieved at the lowest adsorption values is explained by the substantial rise in surface diffusion at high ionic strength due to decreased interactions with the surface. Overall, knowledge of the electrostatic interactions can be used to control surface parameters such as surface concentration and surface diffusion, which intimately correlate with surface biocatalysis. We propose that the maximum reaction rate results from a balance between adsorption and surface diffusion. The above finding suggests enzyme engineering and process design strategies for improving interfacial biocatalysis in industrial, pharmaceutical, and food applications.     

Adsorption of polyvinylimidazole onto kaolinite

The adsorption of polyvinylimidazole (PVI) onto kaolinite from aqueous solutions has been investigated systematically as a function of parameters such as calcination temperature of kaolinite, pH, ionic strength, and temperature. According to the experimental results, the adsorption of PVI increases with pH from 8.50 to 11.50, temperature from 25 to 55 degrees C, and ionic strength from 0 to 0.1 mol L(-1). The kaolinite sample calcined at 600 degrees C has a maximum adsorption capacity. Adsorption isotherms of PVI onto kaolinite have been determined and correlated with common isotherm equations such as Langmuir and Freundlich isotherm models. The Langmuir isotherm model appeared to fit the isotherm data better than the Freundlich isotherm model. The physical properties of this adsorbent are consistent with the parameters obtained from the isotherm equations. Furthermore, the zeta potentials of kaolinite suspensions have been measured in aqueous solutions of different PVI concentrations and pH. From the experimental results, (i) pH strongly alters the zeta potential of kaolinite; (ii) kaolinite has an isoelectric point at about pH 2.35 in water and about pH 8.75 in 249.9 ppm PVI concentration; (iii) PVI changes the interface charge from negative to positive for kaolinite. The study of temperature effect has been quantified by calculating various thermodynamic parameters such as Gibbs free energy, enthalpy, and entropy changes. The dimensionless separation factor (RL) has shown that kaolinite can be used for adsorption of PVI from aqueous solutions.     

Adsorption of humic acids onto goethite: effects of molar mass, pH and ionic strength

In this paper, the LCD (ligand charge distribution) model is applied to describe the adsorption of (Tongbersven) humic acid (HA) to goethite. The model considers both electrostatic interactions and chemical binding between HA and goethite. The large size of HA particles limits their close access to the surface. Part of the adsorbed HA particles is located in the compact part at the goethite surface (Stern layers) and the rest in the less structured diffuse double layer (DDL). The model can describe the effects of pH, ionic strength, and loading on the adsorption. Compared to fulvic acid (FA), adsorption of HA is stronger and more pH- and ionic-strength-dependent. The larger number of reactive groups on each HA particle than on a FA particle results in the stronger HA adsorption observed. The stronger pH dependency in HA adsorption is related to the larger number of protons that are coadsorbed with HA due to the higher charge carried by a HA particle than by a FA particle. The positive ionic-strength dependency of HA adsorption can be explained by the conformational change of HA particles with ionic strength. At a higher ionic strength, the decrease of the particle size favors closer contact between the particles and the surface, leading to stronger competition with electrolyte ions for surface charge neutralization and therefore leading to more HA adsorption.     

Adsorption of cationic starch on cellulose studied by QCM-D

The adsorption of cationic starch (CS) from aqueous electrolyte solutions onto model cellulose film has been investigated by the quartz crystal microbalance with dissipation monitoring (QCM-D) and X-ray photoelectron spectroscopy (XPS). The influence of the electrolyte composition and charge density of CS was examined. The adsorption of CS onto cellulose followed the general trends expected for polyelectrolyte adsorption on oppositely charged surfaces, with some exceptions. Thus, as result of the very low surface charge density of the cellulose surface, highly charged CS did not adsorb in a flat conformation even at low ionic strength. The porosity of the film, however, enabled the penetration of coiled CS molecules into the film at high electrolyte concentrations. Differences between the adsorption behavior of CS on cellulose and earlier observations of the adsorption of the same starches on silica could be explained by the different morphologies and acidities of the hydroxyl groups on the two surfaces.     

Polyelectrolyte adsorption on charged surfaces: study by electrokinetic measurements

In order to describe the influence of cationic polyelectrolytes on flocculation of disperse systems the adsorption of poly (diallyldimethylammonium chloride) (PDADMAC) onto silica, mica and acidic polymer latex was investigated. The plateau value of the adsorption isotherms grows with increasing surface charge density of the substrates and electrolyte concentration. The adsorbed layer of the polycation was characterized by zeta potential measurements with KCl solutions of constant ionic strength and varied pH. The zero point of the charge as well as the shape of the zeta potential–pH plot depends on the coverage of the surface with polycations. For fully covered substrates the zero point of the charge as well as the pK_A and pK_B values calculated by a stochastic search programme are independent of the substrate. Maximum flocculation was observed at about 30% of the plateau value of the adsorption isotherms.     

Competitive adsorption of Ca2+ and Zn(II) ions at monodispersed SiO2/electrolyte solution interface

A study of competitive adsorption of Ca(2+) and Zn(II) ions at the monodispersed SiO(2)/electrolyte solution interface is presented. Influence of ionic strength, pH, and presence of other ions on adsorption of Ca(2+) and Zn(II) in the mentioned system are investigated. zeta potential, surface charge density, adsorption density, pH(50%), and DeltapH(10-90%) parameters for different concentrations of carrying electrolyte and adsorbed ions are also presented. A high concentration of zinc ions shifts the adsorption edge of Ca(2+) ions adsorbed from solutions with a low initial concentration at the SiO(2)/NaClO(4) solution interface to the higher pH values. This effect disappears with a concentration increase of calcium ions. The presence of Ca(2+) ions in the system slightly affects the adsorption of zinc ions on SiO(2), shifting the adsorption edge toward lower pH values and thereby increasing the adsorption slope.     

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.     

Electroviscous Effects in Ceramic Nanofiltration Membranes

Membrane permeability and salt rejection of a γ‐alumina nanofiltration membrane were studied and modeled for different salt solutions. Salt rejection was predicted by using the Donnan‐steric pore model, in which the extended Nernst–Planck equation was applied to predict ion transport through the pores. The solvent flux was modeled by using the Hagen–Poiseuille equation by introducing electroviscosity instead of bulk viscosity. γ‐Alumina particles were used for ζ‐potential measurements. The ζ‐potential measurements show that monovalent ions did not adsorb on the γ‐alumina surface, whereas divalent ions were highly adsorbed. Thus, for divalent ions, the model was modified, owing to pore shrinkage caused by ion adsorption. The ζ‐potential lowered the membrane permeability, especially for membranes with a pore radius lower than 3 nm, a ζ‐potential higher than 20 mV, and an ionic strength lower than 0.01 m . The rejection model showed that, for a pore radius lower than 3 nm and for solutions with ionic strengths lower than 0.01 m , there is an optimum ζ‐potential for rejection, because of the concurrent effects of electromigration and convection. Hence, the model can be used as a prediction tool to optimize membrane perm‐selectivity by designing a specific pore size and surface charge for application at specific ionic strengths and pH levels.