Electrostatic interaction of ion-penetrable membranes. Effects of ionic solubility

An analytic, approximate expression for the electrostatic interaction between two membranes immersed in an electrolyte solution is derived on the basis of a simple membrane model. This model assumes that the membrane has a surface layer in which charged groups are uniformly distributed and that electrolyte ions can penetrate into the surface layer. The partition coefficients of cations and anions between the solution and the surface layer, which are related to their solubilities in the surface layer, may be different from unity.The electrostatic interaction depends on the ionic partition coefficients between the solution and the surface layer, and the relative permittivity of the surface layer, as well as on the membrane-fixed charges, the electrolyte concentration in the solution, and the surface layer thickness. It is shown, in particular, that even where the charge layer has no fixed charges, the electrostatic interaction force can be produced if the solubilities of cations and anions are different in the surface layer.     

Dynamics of ion exchange between self-assembled redox polyelectrolyte multilayer modified electrode and liquid electrolyte

A probe beam deflection (PBD) study of ion exchange between an electroactive polymer poly(allylamine)-bipyridyl-pyridine osmium complex film and liquid electrolyte is reported. The PBD measurements were made simultaneously to chronoamperometric oxidation-reduction cycles, to be able to detect kinetic effects in the ion exchange. Layer-by-layer (LbL) self-assembled redox polyelectrolyte films with osmium bipyridyl complex covalently attached to poly(allylamine) (PAH-Os) and poly(styrene sulfonate) (PSS) have been built by alternate electrostatic adsorption from soluble polyelectrolytes. The ionic exchange during initial conditioning of the film ("break-in") undergoing oxidation-reduction cycles and recovery after equilibration in the reduced state have shown an exchange of anions and cations with time lag between them. The effect of the nature of cation on the ionic exchange has been investigated with dilute HCl, LiCl, NaCl, and CsCl electrolytes. The ratio of anion to cation exchanged at the film-electrolyte interface has a strong dependence on the nature of charge in the topmost layer, that is, when negatively charged PSS is the capping layer, a larger proportion of cation exchange is observed. This demonstrates that the electrical potential distribution at the redox polyelectrolyte multilayer (PEM)/electrolyte interface determines the ionic flux in response to charge injection in the film.     

Air-liquid interfaces of imidazolium-based [TF2N-] ionic liquids: insight from molecular dynamics simulations

We present molecular dynamics simulations of the air-liquid interface for three room temperature ionic liquids with a common anion: bis(trifluoromethylsulfonyl) imide ([Tf(2)N]), and imidazolium-based cations that differ in the alkyl tail length: 1-butyl-3-methylimidazolium ([C(4)mim]), 1-hexyl-3-methylimidazolium ([C(6)mim]), and 1-octyl-3-methylimidazolium ([C(8)mim]). The CHARMM type force field is used with the partial charges based on quantum calculations for isolated ion pairs. The total charge on cations and anions is around 0.9e and -0.9e, respectively, which somewhat mimics the anion to cation charge transfer and many-body effects. The surface tension at 300 K is computed using the mechanical route and its value slightly overpredicts experimental values. The air-liquid interface is analyzed using the intrinsic method of Identification of the Truly Interfacial Molecules. Structural and dynamic properties of the interfacial, sub-interfacial and central layers are determined. To describe the structure of the interface, we compute the surface roughness, number density and charge density profiles, and orientation ordering of the ions. We further determine the survival probability, normal and lateral self-diffusion coefficients, and re-orientation correlation functions to characterize the dynamics of the cations and anions in the layers. We found a significant enhancement of the cation density and preferential orientation ordering of both the cations and anions at the interface. Overall, the surface of the interfacial layer is smoother than the surface of the sub-interfacial layer and the roughness of both the interfacial and sub-interfacial layers increases with the increase of the length of the cation alkyl tail. Finally, the ions stay considerably longer in the interfacial layer than in the sub-interfacial layer and dynamics of exchange of the ions between the consecutive layers is related to the distinct diffusion and re-orientation dynamics behavior of the ions within the layers.     

A model for self-diffusion of guanidinium-based ionic liquids: a molecular simulation study

We propose a novel self-diffusion model for ionic liquids on an atomic level of detail. The model is derived from molecular dynamics simulations of guanidinium-based ionic liquids (GILs) as a model case. The simulations are based on an empirical molecular mechanical force field, which has been developed in our preceding work, and it relies on the charge distribution in the actual liquid. The simulated GILs consist of acyclic and cyclic cations that were paired with nitrate and perchlorate anions. Self-diffusion coefficients are calculated at different temperatures from which diffusive activation energies between 32-40 kJ/mol are derived. Vaporization enthalpies between 174-212 kJ/mol are calculated, and their strong connection with diffusive activation energies is demonstrated. An observed formation of cavities in GILs of up to 6.5% of the total volume does not facilitate self-diffusion. Instead, the diffusion of ions is found to be determined primarily by interactions with their immediate environment via electrostatic attraction between cation hydrogen and anion oxygen atoms. The calculated average time between single diffusive transitions varies between 58-107 ps and determines the speed of diffusion, in contrast to diffusive displacement distances, which were found to be similar in all simulated GILs. All simulations indicate that ions diffuse by using a brachiation type of movement: a diffusive transition is initiated by cleaving close contacts to a coordinated counterion, after which the ion diffuses only about 2 A until new close contacts are formed with another counterion in its vicinity. The proposed diffusion model links all calculated energetic and dynamic properties of GILs consistently and explains their molecular origin. The validity of the model is confirmed by providing an explanation for the variation of measured ratios of self-diffusion coefficients of cations and paired anions over a wide range of values, encompassing various ionic liquid classes as well as the simulated GILs. The proposed diffusion model facilitates the qualitative a priori prediction of the impact of ion modifications on the diffusive characteristics of new ionic liquids.     

Theoretical study of interdiffusion of aqueous solutions of 1 : 1 electrolytes having the same anion through a cation-exchange membrane

The interdiffusion of aqueous 1: 1 electrolytes having the same anion through a negatively charged (cation-exchange) membrane has been studied without taking into account the diffusive layers. It has been established that the interdiffusion coefficients of the cations depend (in addition to their own diffusion coefficients in the membrane) on the ratio of the diffusion coefficients of both cations to the diffusion coefficient of the anion and the ratio of the density of charges fixed in the membrane to the equal concentration of the electrolytes on both sides of the membrane, as well as the equilibrium distribution coefficients of cationanion ion pairs in the membrane matrix. The conditions have been found under which the membrane plays the role of a “blocking system” (like a diode) that is impenetrable to cations located on both sides of the membranes in spite of the existence of their concentration gradients. The developed approach can be used to describe the interdiffusion of 1: 1 electrolytes through any uniformly charged membrane.     

Diffusion characteristics of agarose hydrogel used in diffusive gradients in thin films for measurements of cations and anions

The agarose hydrogel has been increasingly used as a diffusive layer in diffusive gradients in thin films (DGT) measurements. However its diffusive characteristics have not been examined in detail. In this study, the performance of agarose gel was tested in DGT measurements of eight cations (Fe(II), Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Pb(II), and Cd(II)) and eight anions (P(V), As(V), Cr(VI), Mo(VI), Sb(V), Se(VI), V(V), and W(VI)). It was found that the thickness of agarose, a key parameter in the calculation of DGT measured concentration, remained unchanged after hydration followed by storage under the following conditions: pH 2–11, ionic strength 0–1.0 M, temperature 4–40 °C, and with the storage time extending to 300 d. Enrichment of cations and repelling of anions were observed in the gel under the ionic strengths of < 2–3 mM and <1 mM (NaNO₃), respectively, which was attributed to the electrostatic interactions of these ions with the fixed negatively charged groups (mainly pyruvate) in the gel. The diffusion coefficients of cations and anions through the agarose gel (plus a PVDF filter membrane) were on average 1.10 ± 0.04 times of the reported diffusion coefficients through the agarose cross-linked polyacrylamide (APA) hydrogel, typically used in DGT technique. The working pH ranges for the agarose gel-assembled DGTs were 4–10 and 5–9 for anions and cations, respectively. The use of agarose gel, either individually or along with different filter membranes, affected the overall diffusion rates of cations and anions. The measured DGT concentrations of cations and anions in filtered natural freshwater and seawater were mostly in line with those measured directly. The results showed that the agarose gel can be used as one of the standard diffusive layers in DGT measurements for a wide range of inorganic and organic analytes.     

Bipolar reverse osmosis membrane for separating mono-and divalent ions

Bipolar reverse osmosis membranes that have both negatively and positively charged layers have been prepared to enhance the selectivity towards mono- and divalent ions in respect of both cations and anions. Positively charged layers are formed on low pressure reverse osmosis membranes having negative charge (NTR-7410 and 7450) by an adsorption method using polyethyleneimine (PEI) or a quaternary ammonium polyelectrolyte (QAP). These layers attach to the membrane's dense layer, which is made of sulfonated polyether sulfone. The selectivity of mono- and divalent ions is proven by experimental results for single electrolytes (NaCl, Na₂SO₄ and MgCl₂). Although negatively charged membranes repulse divalent anions more strongly than cations and monovalent anions, bipolar reverse osmosis membranes reject both divalent cations and divalent anions better than monovalent ions. An optimal preparation method for bipolar membranes showing selectivity towards mono- and divalent ions were developed. The bipolar membranes showed good ion selectivity for artificial sea water.     

Sedimentation of a charged colloidal sphere in a charged cavity

An analytical study is presented for the quasisteady sedimentation of a charged spherical particle located at the center of a charged spherical cavity. The overlap of the electric double layers is allowed, and the polarization (relaxation) effect in the double layers is considered. The electrokinetic equations that govern the ionic concentration distributions, electric potential profile, and fluid flow field in the electrolyte solution are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a symmetric electrolyte with the surface charge densities of the particle and cavity as the small perturbation parameters. An analytical expression for the settling velocity of the charged sphere is obtained from a balance among the gravitational, electrostatic, and hydrodynamic forces acting on it. Our results indicate that the presence of the particle charge reduces the magnitude of the sedimentation velocity of the particle in an uncharged cavity and the presence of the fixed charge at the cavity surface increases the magnitude of the sedimentation velocity of an uncharged particle in a charged cavity. For the case of a charged sphere settling in a charged cavity with equivalent surface charge densities, the net effect of the fixed charges will increase the sedimentation velocity of the particle. For the case of a charged sphere settling in a charged cavity with their surface charge densities in opposite signs, the net effect of the fixed charges in general reduces/increases the sedimentation velocity of the particle if the surface charge density of the particle has a greater/smaller magnitude than that of the cavity. The effect of the surface charge at the cavity wall on the sedimentation of a colloidal particle is found to increase with a decrease in the particle-to-cavity size ratio and can be significant in appropriate situations.     

Controlling the transport of cations through permselective mesoporous alumina layers by manipulation of electric field and ionic strength

The electric field-driven transport of ions through supported mesoporous gamma-alumina membranes was investigated. The influence of ion concentration, ion valency, pH, ionic strength, and electrolyte composition on transport behavior was determined. The permselectivity of the membrane was found to be highly dependent on the ionic strength. When the ionic strength was sufficiently low for electrical double-layer overlap to occur inside the pores, the membrane was found to be cation-permselective and the transport rate of cations could be tuned by variation of the potential difference over the membrane. The cation permselectivity is thought to be due to the adsorption of anions onto the pore walls, causing a net negative immobile surface charge density, and consequently, a positively charged mobile double layer. The transport mechanism of cations was interpreted in terms of a combination of Fick diffusion and ion migration. By variation of the potential difference over the membrane the transport of double-charged cations, Cu2+, could be controlled accurately, effectively resulting in on/off tunable transport. In the absence of double-layer overlap at high ionic strength, the membrane was found to be nonselective.     

Diffusion of electrolytes of different natures through the cation-exchange membrane

Diffusion of different electrolytes through a negatively charged (cation-exchange) membrane into distilled water has been studied. It has been established theoretically (with no regard to the presence of diffusion layers) that the integral diffusion permeability coefficient of an electrolyte depends on the diffusion coefficients and the ratio between the charge numbers of a cation–anion pair, the ratio between the density of charges fixed in the membrane and electrolyte concentration, and the averaged coefficient of equilibrium distribution of cation?anion ion pairs in the membrane matrix. It has been found that, when co-ions have a higher mobility, the dependence of diffusion permeability on electrolyte concentration passes through a maximum. Derived equations have been compared with experimental dependences of the diffusion permeability of an MC-40 membrane with respect to different solutions of inorganic 1: 1 and 2: 1 electrolytes. The developed method has been shown to be applicable for describing diffusion of any electrolytes (including asymmetric ones) through arbitrary uniformly charged membranes.     

On the different roles of anions and cations in the solvation of enzymes in ionic liquids

The solvation of the enzyme Candida antarctica lipase B (CAL-B) was studied in eight different ionic liquids (ILs). The influence of enzyme-ion interactions on the solvation of CAL-B and the structure of the enzyme-IL interface are analyzed. CAL-B and ILs are described with molecular dynamics (MD) simulations in combination with an atomistic empirical force field. The considered cations are based on imidazolium or guanidinium that are paired with nitrate, tetrafluoroborate or hexafluorophosphate anions. The interactions of CAL-B with ILs are dominated by Coulomb interactions with anions, while the second largest contribution stems from van der Waals interactions with cations. The enzyme-ion interaction strength is determined by the ion size and the magnitude of the ion surface charge. The solvation of CAL-B in ILs is unfavorable compared to water because of large formation energies for the CAL-B solute cages in ILs. The internal energy in the IL and of CAL-B increases linearly with the enzyme-ion interaction strength. The average electrostatic potential on the surface of CAL-B is larger in ILs than in water, due to a weaker screening of charged enzyme residues. Ion densities increased moderately in the vicinity of charged residues and decreased close to non-polar residues. An aggregation of long alkyl chains close to non-polar regions and the active site entrance of CAL-B are observed in one IL that involved long non-polar decyl groups. In ILs that contain 1-butyl-3-methylimidazolium cations, the diffusion of one or two cations into the active site of CAL-B occurs during MD simulations. This suggests a possible obstruction of the active site in these ILs. Overall, the results indicate that small ions lead to a stronger electrostatic screening within the solvent and stronger interactions with the enzyme. Also a large ion surface charge, when more hydrophilic ions are used, increases enzyme-IL interactions. An increase of these interactions destabilizes the enzyme and impedes enzyme solvation due to an increase in solute cage formation energies.     

Molecular dynamics simulations of ionic liquid-vapour interfaces: effect of cation symmetry on structure at the interface

The influence of alkyl chain symmetry of the imidazolium cation on the structure and properties of the ionic liquid-vapour interface has been addressed through molecular dynamics simulations. The anion chosen is bis(trifluoromethylsulfonyl)imide (NTf(2)). Profiles of number densities, orientation of cations, charge density, electrostatic potential, and surface tension have been obtained. At the interface, both cations and anions were present, and the alkyl chains of the former preferred to orient out into the vapour phase. A large fraction of cations preferred to be oriented with their ring-normal parallel to the surface and alkyl chains perpendicular to it. These orientational preferences are reduced in ionic liquids with symmetric cations. Although the charge densities at the interface were largely negative, an additional small positive charge density has been observed for systems with longer alkyl chains. The electrostatic potential difference developed between the liquid and the vapour phases were positive and decreased with increasing length of the alkyl group. The calculated surface tension of the liquids also decreased with increasing alkyl chain length, in agreement with experiment. The surface tension of an ionic liquid with symmetric cation was marginally higher than that of one with an asymmetric, isomeric cation.     

Effect of electrolytes on the retention behavior of some benzenesulfonates in electrochemically modulated liquid chromatography

The effects of electrolytes on the retention behavior of some benzenesulfonates in electrochemically modulated liquid chromatography were studied. Both cations and anions were found to have considerable effects on retention. As cation size increases, retention decreases, while anions show more complicated effects were anionic size and charge distribution contribute to the overall behavior of anions. Large anions with a delocalized negative charge on the whole species result in lower retention times, and vice versa. Also, electrolyte concentration plays an important role in the retention behavior observed. Initially, as electrolyte concentration was increased retention increased due to electrostatic interactions of cations with the negatively charged stationary phase. However, retention starts to slightly decrease or increase after some specific electrolyte concentration depending on the nature of the electrolytic species. Finally, an interesting behavior of double peak appearance of a single solute was observed at low electrolyte concentrations and was attributed to the presence of other active sites on the carbon stationary phase.     

Ionic Diffusivity, Electrical Conductivity, Membrane and Thermoelectric Potentials in Colloids and Granular Porous Media: A Unified Model

Ionic diffusivity, electrical conductivity, membrane and thermoelectric potentials in isotropic and homogeneous colloidal suspensions, and granular porous media saturated by a binary symmetric 1:1 electrolyte are four interrelated phenomena. The microstructure and the surface properties of the solid grains-water interface influence directly these properties. The ionic diffusivities (and the electrical conductivity, respectively) in colloids and porous media have contributions from diffusion (and electromigration, respectively) through the bulk solution occupying the pores, together with electromigration occurring at the grains-water interface in the electrical double layer. Surface diffusion in porous materials has no contribution from concentration gradients along the grains-water interface. Instead, surface diffusion is envisioned as a purely electromigration process due to the membrane potential. The tortuosities of the transport of anions and cations are equal to the bulk tortuosity of the pore space only at high ionic strength. As the ionic strength decreases, the dominant paths for transport of the ion corresponding to the counterion of the electrical double layer shift from the pore space to the solid grains-water interface. Because anions and cations do not move independently, the membrane potential created by the charge polarization alters the velocity of the anions and influences the mutual diffusivity coefficient of the salt in the porous material. An electric potential of thermal origin is also produced in nonisothermal conditions. The ionic contributions to the electrical conductivity are based on a differential effective medium approach. These ionic contributions to the electrical conductivity are used to derive the ionic diffusivities and the membrane and thermoelectric potentials. The influence of the temperature and the presence, in the pore space, of a second immiscible and nonwetting phase is also considered in this model. Porosity is shown to affect the membrane potential. Several predictions of the model are checked with success by comparing the model to a set of experimental data previously published. Copyright 1999 Academic Press.     

Electrode screening by ionic liquids

In this work we are concerned with the short-range screening provided by the ionic liquid dimethylimidazolium chloride near a charged wall. We study the free energy profiles (or potentials of mean force) for charged and neutral solutes as a function of distance from a charged wall. Four different wall charge densities are used in addition to a wall with zero charge. The highest magnitude of the charge densities is ±1 e nm(-2) which is close to the maximum limit of charge densities accessible in experiments, while the intermediate charges ±0.5 e nm(-2) are in the range of densities typically used in most of the experimental studies. Positively and negatively charged solutes of approximately the size of a BF ion and a Cl(-) ion are used as probes. We find that the ionic liquid provides excellent electrostatic screening at a distance of 1-2 nm. The free energy profiles show minima which are due to layering in the ionic liquid near the electrodes. This indicates that the solute ions tend to displace ionic liquid ions in the layers when approaching the electrode. The important role of non-electrostatic forces is demonstrated by the oscillations in the free energy profiles of uncharged solutes as a function of distance from the wall.     

Sedimentation velocity and potential in concentrated suspensions of charged porous spheres

The body-force-driven migration in a homogeneous suspension of polyelectrolyte molecules or charged flocs in an electrolyte solution is analyzed. The model used for the particle is a porous sphere in which the density of the hydrodynamic frictional segments, and therefore also that of the fixed charges, is constant. The effects of particle interactions are taken into account by employing a unit cell model. The overlap of the electric double layers of adjacent particles is allowed and the relaxation effect in the double layer surrounding each particle is considered. The electrokinetic equations which govern the electrostatic potential profile, the ionic concentration (or electrochemical potential energy) distributions, and the fluid velocity field inside and outside the porous particle in a unit cell are linearized by assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved for a symmetrically charged electrolyte with the density of the fixed charges as the small perturbation parameter. An analytical expression for the settling velocity of the charged porous sphere is obtained from a balance among its gravitational, electrostatic, and hydrodynamic forces. A closed-form formula for the sedimentation potential in a suspension of identical charged porous spheres is also derived by using the requirement of zero net electric current. The dependence of the sedimentation velocity and potential of the suspension on the particle volume fraction and other properties of the particle-solution system is found to be quite complicated.     

Mechanistic studies on the separation of cations in zwitterionic ion chromatography

Electrostatic ion chromatography, also known as zwitterionic ion chromatography, has been predominantly used for the analysis of anions. Consequently, separation mechanisms proposed for this technique have been based on anion retention data obtained using a sulfobetaine-type surfactant-coated column. A comprehensive cation retention data set has been obtained on a C18 column coated with the zwitterionic surfactant N-tetradecylphosphocholine (which has the negatively and positively charged functional groups reversed in comparison to the sulfobetaine surfactants), with mobile phases being varied systematically in the concentration and species of both the mobile-phase anion and cation. A retention mechanism based on both an ion exclusion effect and a direct (chaotropic) interaction with the inner negative charge on the zwitterion is proposed for the retention of cations. Despite the relatively low chaotropic nature of cations compared with anions, the retention data shows that cations are retained in this system predominantly due to a chaotropic interaction with the inner charge, analogous to anions in a system where the C18 column is coated with a sulfobetaine-type surfactant. The retention of an analyte cation, and the effect of the mobile-phase anion and cation, can be predicted by the relative positions of these species on the Hofmeister (chaotropic) series.     

Effects of ion solvation on phase equilibrium and interfacial tension of liquid mixtures

We study the bulk thermodynamics and interfacial properties of electrolyte solution mixtures by accounting for electrostatic interaction, ion solvation, and inhomogeneity in the dielectric medium in the mean-field framework. Difference in the solvation energy between the cations and anions is shown to give rise to local charge separation near the interface, and a finite Galvani potential between two coexisting solutions. The ion solvation affects the phase equilibrium of the solvent mixture, depending on the dielectric constants of the solvents, reflecting the competition between the solvation energy and translation entropy of the ions. Miscibility is decreased if both solvents have low dielectric constants and is enhanced if both solvents have high dielectric constant. At the mean-field level, the ion distribution near the interface is determined by two competing effects: accumulation in the electrostatic double layer and depletion in a diffuse interface. The interfacial tension shows a nonmonotonic dependence on the salt concentration: it increases linearly with the salt concentration at higher concentrations and decreases approximately as the square root of the salt concentration for dilute solutions, reaching a minimum near 1 mM. We also find that, for a fixed cation type, the interfacial tension decreases as the size of anion increases. These results offer qualitative explanations within one unified framework for the long-known concentration and ion size effects on the interfacial tension of electrolyte solutions.     

A molecular simulation study on the role of ion sizes and dielectric images in near-surface ion distribution far from the strong coupling limit

A series of Monte Carlo simulations of the planar electric double layers are carried out in the primitive model for two electrolyte mixtures next to a smooth and uniformly charged hard wall representing an ideal biological interface with low and moderate surface charge densities. The structural information of the double layers is applied to reveal charge inversion and overcharging through the addition of multivalent electrolyte at a certain physiological concentration. Various values for the radius of the ions are taken into account to capture the impact of short-range correlations. Meanwhile, the influence of image charges on ion distribution is analyzed, which stems from dielectric discontinuity between the interior and exterior of the membrane matrix. It is clearly shown that depending on the amount of foreign salt, the large size of charged species regardless of its polarity plays a positive role in promoting charge inversion. Moreover, our findings indicate that charge inversion do not signify the reversal of the electrophoretic mobility, in consistent with the recent theoretical predictions by Horno and co-workers [J. Colloid Interface Sci. 356, 325 (2011)]. In addition, the depletion effect triggered by repulsive image forces which are intertwined with the excluded volume correlations gives rise to an anomalous overcharging for low surface charged surface in the high concentrations of trivalent salt. Overall, the ion distribution in a double layer is exclusively governed by entropic and electrostatic contributions but with preferentially leading status for different magnitudes of surface charge.     

Diffusiophoretic mobility of charged porous spheres in electrolyte gradients

The diffusiophoretic motion of a polyelectrolyte molecule or charged floc in an unbounded solution of a symmetrically charged electrolyte with a uniform prescribed concentration gradient is analytically studied. The model used for the particle is a porous sphere in which the density of the hydrodynamic frictional segments, and therefore also that of the fixed charges, is constant. The electrokinetic equations which govern the electrostatic potential profile, the ionic concentration distributions (or electrochemical potential energies), and the fluid velocity field inside and outside the porous particle are linearized by assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved for a charged porous sphere with the density of the fixed charges as the small perturbation parameter. An analytical expression for the diffusiophoretic mobility of the charged porous sphere in closed form is obtained from a balance between its electrostatic and hydrodynamic forces. This expression, which is correct to the second order of the fixed charge density of the particle, is valid for arbitrary values of kappaa and lambdaa, where kappa is the reciprocal of the Debye screening length, lambda is the reciprocal of the length characterizing the extent of flow penetration inside the particle, and a is the particle radius. Our result to the first order of the fixed charge density agrees with the corresponding solution for the electrophoretic mobility obtained in the literature. In general, the diffusiophoretic mobility of a porous particle becomes greater as the hindrance to the diffusive transport of the solute species inside the particle is more significant.