Effects of structural properties of the Stern layer on the electrophoretic migration of a highly charged spherical macroion

The electrophoretic migration of a highly charged spherical macroion suspended in an aqueous solution of NaCl is studied using the molecular dynamic method. The objective is to examine the effects of the colloidal surface charge density on the electrophoretic mobility (μ) of the spherical macroion. The bare charge and the size of the macroion are varied separately to induce changes in the colloidal surface charge density. Our results indicate that μ depends on colloidal surface charge density in a nonmonotonic manner, but that this relationship is independent of the way the surface charge density is varied. It is found that an increase in colloidal surface charge density may lead to the formation of new sublayers in the Stern layer. The μ profile is also found to have a local maximum for a bare charge at which a new sublayer is formed in the Stern layer, and a local minimum for a bare charge at which the outer sublayer becomes relatively dense. Finally, the electrophoretic flow caused by the migration of the spherical macroion is studied to find that one decisive factor causing the electrophoretic flow is the ability of the macroion to carry anions in the electrolyte solution.     

Comparing the Predictions of the Nonlinear Poisson-Boltzmann Equation and the Ion Size-Modified Poisson-Boltzmann Equation for a Low-Dielectric Charged Spherical Cavity in an Aqueous Salt Solution

The ion size-modified Poisson Boltzmann equation (SMPBE) is applied to the simple model problem of a low-dielectric spherical cavity containing a central charge, in an aqueous salt solution to investigate the finite ion size effect upon the electrostatic free energy and its sensitivity to changes in salt concentration. The SMPBE is shown to predict a very different electrostatic free energy than the nonlinear Poisson-Boltzmann equation (NLPBE) due to the additional entropic cost of placing ions in solution. Although the energy predictions of the SMPBE can be reproduced by fitting an appropriatelysized Stern layer, or ion-exclusion layer to the NLPBE calculations, the size of the Stern layer is difficult to estimate a priori. The SMPBE also produces a saturation layer when the central charge becomes sufficiently large. Ion-competition effects on various integrated quantities such the total number of ions predicted by the SMPBE are qualitatively similar to those given by the NLPBE and those found in available experimental results.     

On the relationship between charge distribution, surface hydration, and the structure of the interface of metal hydroxides

The double layer structure of metal (hydr)oxides is discussed. Charge separation may exist between the minimum distance of approach of electrolyte ions and the DDL domain. The corresponding capacitance value of the outer Stern layer is similar to the capacitance value of the inner Stern layer. The extended Stern model implicitly supports a hydration structure at the near-surface with some discrete layering of water and electrolyte ions. The significance of dipole orientation is analyzed theoretically. Dipole theory in combination with a calculated ion charge distribution is compared with the experimental overall charge distribution. Ion charge distribution for various oxyanions has been calculated applying the Brown bond valence concept to the geometry of surface complexes that have been optimized with MO/DFT calculations. The comparison is done in detail for silicic acid adsorption on goethite. In addition, results are discussed for arsenite, carbonate, sulfate, and phosphate, using the same approach. The dipole correction depends on the charge introduced in a neutral surface by ion adsorption, which differs for the various ions studied. The fractional correction factor phi derived for the experimental data agrees with the theoretical value phi(m)=0.17+/-0.02. On an absolute scale, the dipole corrections are usually limited to the range about 0-0.15 v.u. The CD values calculated with MO/DFT are not particularly sensitive (approximately 0.03 v.u.) to the precise Fe-octahedral geometry, which suggests that a calculated CD is a reasonable approximation in ion adsorption modeling for ill-defined Fe-oxides like HFO and natural Fe oxide materials of soils.     

Electrokinetic Properties of Fuzzy Colloidal Particles

The presence of a thin polymer layer on the surface of a colloidal particle can have a profound effect on its electrophoretic mobility. The model developed here treats the hydrodynamics of the polymer layer as a distribution of Stokes resistance centers within a thin diffuse layer; fixed charge may reside on the surface of the particle core or throughout the layer. The theory is semianalytical in that asymptotic methods are used to simplify the equations but several integrals must be evaluated numerically. Special attention is paid to the effects of polarization and relaxation. It is shown that distributing immobile charge throughout the layer produces a response where the particle's mobility exceeds that found when the same amount of charge is spread uniformly over the surface of the rigid core. Increasing the drag due to the fuzzy layer always diminishes the mobility. In either case, the hydrodynamic permeability of the layer has a strong influence on particle movement. Results are also given for the dipole coefficient in the expression for the conductivity of a dilute suspension. Copyright 2000 Academic Press.     

Monte Carlo modeling of ion adsorption at the energetically heterogeneous metal oxide/electrolyte interface: Micro- and macroscopic correlations between adsorption energies

Grand canonical Monte Carlo simulations are carried out for the basic Stern model of the electrical double layer formed at the energetically heterogeneous metal oxide/electrolyte interface. The effect of the global (macroscopic) and local (microscopic) adsorption energies correlations as well as the influence of the model parameter on the surface charge density curves were investigated. The linear dependence of point of zero charge (PZC) as a function of H+ ion adsorption energy proves that the acidic/basic properties of the system are mainly governed by proton uptake/release. Two kinds of systems were taken into account: one neglecting lateral interactions and the other one including them. The effect of electrolyte concentrations as well as the surface heterogeneity on the surface charge density curves were shown too. The presented simulation algorithm allows to model two experimentally observed instances of the metal oxide/electrolyte interface: one possessing a common intersection point (CIP) at pH = PZC and the other one with CIP not equal PZC.     

Effect of Electrolyte Concentration on the Stern Layer Thickness at a Charged Interface

The chemistry and physics of charged interfaces is regulated by the structure of the electrical double layer (EDL). Herein we quantify the average thickness of the Stern layer at the silica (SiO₂) nanoparticle/aqueous electrolyte interface as a function of NaCl concentration following direct measurement of the nanoparticles’ surface potential by X‐ray photoelectron spectroscopy (XPS). We find the Stern layer compresses (becomes thinner) as the electrolyte concentration is increased. This finding provides a simple and intuitive picture of the EDL that explains the concurrent increase in surface charge density, but decrease in surface and zeta potentials, as the electrolyte concentration is increased.     

Computer simulation of the structure of the electrochemical double layer

We analyze and compare the structure of the electrochemical double layer obtained from molecular dynamics simulations of concentrated aqueous NaCl and CsF solutions near a model electrode. The electrode is modeled as a corrugated external potential in conjunction with the image charge model. Calculations are performed for uncharged electrodes and for electrodes carrying positive or negative surface charges.     

Molecular dynamics simulations of electrolyte solutions at the (100) goethite surface

Molecular dynamics simulations of electrolyte solutions in contact with a neutral (100) goethite (alpha-FeOOH) surface were used to probe the structure of the mineral-water interface and gain insight into the adsorption properties of monovalent ions. Three electrolyte solutions were considered: NaCl, CsCl, and CsF. The electrolyte ions were chosen to cover a range of ionic sizes and affinities for the aqueous phase. The molecular dynamics simulations indicate the presence of a structured interfacial region resulting from the strong interaction of water with the mineral surface. The specific arrangement and preferred orientation of water that arise from this interaction create adsorption sites in the interfacial region, i.e., as far as 15 A away from the surface, and hence give rise to a strong correlation between the water and ion distributions. The structure of the hydrated ion, its effect on the water arrangement at the interface, and the strength of the ion-water bond are found to be key factors that determine the location and extent of ion adsorption at the interface. Additionally, in all simulations, we find a build up of positive charges near the surface due to cation adsorption, which is compensated by an accumulation of anions in the next few angstr?ms. This creates an excess of negative charges, which is in turn compensated by an excess of positive charges, and so on. As we modeled a neutral surface, the structure of the electrolyte distribution arises from the complex interplay of the interactions between the surface, water, and the electrolyte ions rather than from the need to neutralize a surface charge. In addition, our simulations indicate that the electrolyte distribution does not resemble that of a classical electrical double layer. Indeed, our calculations predict the presence of several condensed layers and oscillations in the net charge away from the surface.     

Solvated calcium ions in charged silica nanopores

Hydroxyl surface density in porous silica drops down to nearly zero when the pH of the confined aqueous solution is greater than 10.5. To study such extreme conditions, we developed a model of slit silica nanopores where all the hydrogen atoms of the hydroxylated surface are removed and the negative charge of the resulting oxygen dangling bonds is compensated by Ca(2+) counterions. We employed grand canonical Monte Carlo and molecular dynamics simulations to address how the Ca(2+) counterions affect the thermodynamics, structure, and dynamics of confined water. While most of the Ca(2+) counterions arrange themselves according to the so-called "Stern layer," no diffuse layer is observed. The presence of Ca(2+) counterions affects the pore filling for strong confinement where the surface effects are large. At full loading, no significant changes are observed in the layering of the first two adsorbed water layers compared to nanopores with fully hydroxylated surfaces. However, the water structure and water orientational ordering with respect to the surface is much more disturbed. Due to the super hydrophilicity of the Ca(2+)-silica nanopores, water dynamics is slowed down and vicinal water molecules stick to the pore surface over longer times than in the case of hydroxylated silica surfaces. These findings, which suggest the breakdown of the linear Poisson-Boltzmann theory, provide important information about the properties of nanoconfined electrolytes upon extreme conditions where the surface charge and ion concentration are large.     

Entropic effects in the electric double layer of model colloids with size-asymmetric monovalent ions

The structure of the electric double layer of charged nanoparticles and colloids in monovalent salts is crucial to determine their thermodynamics, solubility, and polyion adsorption. In this work, we explore the double layer structure and the possibility of charge reversal in relation to the size of both counterions and coions. We examine systems with various size-ratios between counterions and coions (ion size asymmetries) as well as different total ion volume fractions. Using Monte Carlo simulations and integral equations of a primitive-model electric double layer, we determine the highest charge neutralization and electrostatic screening near the electrified surface. Specifically, for two binary monovalent electrolytes with the same counterion properties but differing only in the coion's size surrounding a charged nanoparticle, the one with largest coion size is found to have the largest charge neutralization and screening. That is, in size-asymmetric double layers with a given counterion's size the excluded volume of the coions dictates the adsorption of the ionic charge close to the colloidal surface for monovalent salts. Furthermore, we demonstrate that charge reversal can occur at low surface charge densities, given a large enough total ion concentration, for systems of monovalent salts in a wide range of ion size asymmetries. In addition, we find a non-monotonic behavior for the corresponding maximum charge reversal, as a function of the colloidal bare charge. We also find that the reversal effect disappears for binary salts with large-size counterions and small-size coions at high surface charge densities. Lastly, we observe a good agreement between results from both Monte Carlo simulations and the integral equation theory across different colloidal charge densities and 1:1-electrolytes with different ion sizes.     

Electrophoretic properties of highly charged colloids: a hybrid molecular dynamics/lattice Boltzmann simulation study

Using computer simulations, the electrophoretic motion of a positively charged colloid (macroion) in an electrolyte solution is studied in the framework of the primitive model. In this model, the electrolyte is considered as a system of negatively and positively charged microions (counterions and coions, respectively) that are immersed into a structureless medium. Hydrodynamic interactions are fully taken into account by applying a hybrid simulation scheme, where the charged ions (i.e., macroion and electrolyte), propagated via molecular dynamics, are coupled to a lattice Boltzmann (LB) fluid. In a recent electrophoretic experiment by Martin-Molina et al. [J. Phys. Chem. B 106, 6881 (2002)], it was shown that, for multivalent salt ions, the mobility mu initially increases with charge density sigma, reaches a maximum, and then decreases with further increase of sigma. The aim of the present work is to elucidate the behavior of mu at high values of sigma. Even for the case of monovalent microions, a decrease of mu with sigma is found. A dynamic Stern layer is defined that includes all the counterions that move with the macroion while subjected to an external electrical field. The number of counterions in the Stern layer, q(0), is a crucial parameter for the behavior of mu at high values of sigma. In this case, the mobility mu depends primarily on the ratio q(0)/Q (with Q the valency of the macroion). The previous contention that the increase in the distortion of the electric double layer (EDL) with increasing sigma leads to the lowering of mu does not hold for high sigma. In fact, it is shown that the deformation of the EDL decreases with the increase of sigma. The role of hydrodynamic interactions is inferred from direct comparisons to Langevin simulations where the coupling to the LB fluid is switched off. Moreover, systems with divalent counterions are considered. In this case, at high values of sigma the phenomenon of charge inversion is found.     

Non-equilibrium electric surface phenomena

Non-equilibrium aspects of traditional electrokinetic phenomena (electrophoresis, electroosmosis, streaming potential, sedimentation potential), electrostatic interaction of particles and new electrokinetic phenomena are considered. The significance of non-equilibrium electric surface phenomena for many major areas of modern colloid science (characterization of colloids, membrane science, transport phenomena and separation, particle interaction and coagulation) is established.The study of non-equilibrium electric surface phenomena is connected with the validation of the standard electrokinetic model (SEM), the development of a non-standard model and the development of an extensive programme of disperse system characterization based on integrated electrokinetic investigations. Experimental and theoretical studies of systems with a smooth, non-porous impermeable surface (mica in Anderson's experiments, and quartz microcapillaries with a molecule-smooth surface in Churaev's experiments) have shown that usually there are no significant difficulties in interpreting electrokinetic investigations despite the possible anomaly in the water structure near the surface and the possibility of maximum shear stress (yield stress), i.e. the anomalous viscosity and decreased dissolving power with respect to ions. However, systems which do not satisfy the conditions of the SEM are widely distributed, owing to the porosity, roughness or permeability of the boundary layer of the surface of the solid body which simultaneously belongs to the solid and liquid phases. In this layer, enclosed between the outer Helmholtz plane and the slipping plane, the motion of the liquid strongly slows down and the tangential flow of ions is characterized purely by the mobility which is close to the normal. Thus, a general property of a non-standard electrokinetic model is the presence of an anomalous (additional) surface conductivity in excess of the surface conductivity determined according to Bikerman's equation based on the ζ -potential alone.Confidence in modelling the electrokinetic phenomena has grown with the development of methods for modifying the surface such that its properties approach those of the SEM (Bijsterbosch and co-workers; Saville and co-workers).Extension of the particle characterization concept requires the measurement of both the mobile charge and the electrokinetic charge and from this an estimate of the thickness of the additional conductivity zone can be made. With the additional measurement of a titratable charge, it is possible to estimate the ion distribution between the dense and diffuse parts of the double layer (DL) and to estimate the decreased mobility of ions in the Stern layer or in the immobilized part of the DL.Quantitative laws governing the interaction of particles and corresponding to the non-standard model substantially differ from the traditional laws described by the DVLO theory as applied to the SEM. This is also true for adsorption properties which are characterized without sufficient reason by means of the ζ-potential. Therefore both the development of models of interaction and adsorption of ions, allowing for the non-standard electrokinetic model, and the extension of the particle characterization programme to integrated investigations of electric surface phenomena are required.Further generalization of the theory of electrokinetic phenomena is achieved. In addition to the surface charge another variety of surface force can be the origin of the electrokinetic phenomena.     

Molecular-dynamics simulation of the effect of ions on a liquid-liquid interface for a partially miscible mixture

Molecular-dynamics simulations were performed to model the effect of added salt ions on the liquid-liquid interface in a partially miscible system. Simulations of the interface between saturated phases of a model 1-hexanol+water system show a bilayer structure of 1-hexanol molecules at the interface with -OH heads of the first layer directed into the water phase and the opposite orientation for the second layer. The alignment of the polar -OH groups at the interface stabilizes a charge separation of sodium and chloride ions when salt is introduced into the aqueous phase, producing an electrical double layer. Chloride ions aggregate nearer the interface and sodium ions move toward the bulk water phase, consistent with the explanation that the -OH alignment presents a region of partial positive charges to which the hydrated chloride atoms are attracted. Ions near the interface were found to be less solvated than those in the bulk phase. An electric field was also applied to drive ions through the interface. Ions crossing the interface tended to shed water molecules as they entered the hexanol bilayer, leaving a trail of water molecules. Stabilization and facilitated transport of the ion by interactions with the second layer of hexanol molecules appeared to be an important step in the mechanism of sodium ion transport.     

Secondary Electron Emission from an Organic Layer with a Surface Charge

Using secondary electron emission (SEE) techniques, conditions for the traveling of electrons near a charged surface were studied. A simple analytical expression was found to relate the effective coefficient of secondary electron emission from the charged surface of an organic liquid layer with the primary-electron current. At low currents, the relationship is close to a root law, the pattern of the dependence does not change with the varying conductivity of the liquid, its thickness, and the charge spot area. This finding suggests that the effective secondary electron emission coefficient and, hence, the conditions of electron motion near a surface charge depend on the only parameter, the current density of incident electrons. According to the estimates of the dielectric permittivity of a liquid, its resistivity, and ion mobility, the effective SEE coefficient at low charging currents is formed in the ohmic mode of current flow through the liquid.     

Molecular simulation of electrolytes in nanopores

Behaviour of electrolytes confined in cylindrical and slit pores are studied by computer simulations at the molecular level. Previous equilibrium and structural properties obtained by Monte Carlo techniques using the restrictive primitive model are discussed. Transport properties are calculated by the canonical molecular dynamics technique for ions with Lennard–Jones cores. Assuming an external electric potential, the chemical potential of individual ions can be balanced without the need for a grand canonical procedure. The mobility of the counterion is affected by the surface charge density. At a high surface charge, the mean square axial displacement of the counterion calculated is lower than the bulk value due to its high concentration near the charged wall.     

Solvation of ions in hydrophilic layer of polyoxyethylated nonionic micelle. Cooperative approach by electrophoresis and ion-transfer voltammetry

Electrophoretic measurements of micellar mobility have revealed that polyoxyethylated nonionic surfactant micelles have negative zeta potential in various electrolytes, indicating that the partition of anions into the micelle dominates the entire electrolyte partition and the induced surface potential of the micelle. Although an excess of a negative charge is thus revealed in the micelle, it is uncertain whether anions are preferably solvated in the micelles or cations are expelled from the micelles. To determine the solvation energies of single ions in the hydrophilic layer of the micelle, we have performed ion transfer voltammetric measurements at microinterfaces between nitrobenzene and aqueous tetraethyleneglycol solution, which acts as a model for the palisade layer of the micelles. The cooperative utilization of these different methods has allowed us to determine the Gibbs free energy of transfer of a single ion without an extrathermodynamic assumption. On the basis of the resulting values, the partition of ions and the zeta potential induced by the imbalance of anionic and cationic partition have been quantitatively explained.     

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.     

Hydrolysis versus ion correlation models in electrokinetic charge inversion: establishing application ranges

In this article, we investigate experimentally a wide range of situations where charge inversion (i.e., overcompensation of the surface charge of a colloidal particle by the countercharge) can occur. To that end, the electrophoretic mobility of sodium montmorillonite, silica, and polystyrene latex as functions of pH and concentration of different salts is presented, and conditions are established where charge inversion occurs. The reason for this study is to provide experimental evidence for distinguishing between two existing models for the explanation of charge inversion. One of these is the specific adsorption of ions located in the Stern layer in combination with a Gouy-Chapman diffuse part of the double layer. The other ion-correlation theories explain the phenomenon in terms of purely physical arguments based on Coulombic pair interactions between ions and surface charges and on excluded volume effects. In distinguishing between these two interpretations, the influence of the pH plays a central role because of its effect on the hydrolysis of multivalent cations. In our experiments, it is found that although 1-2 and 2-2 electrolytes provoke a decrease in the absolute values of the electrophoretic mobilities when their concentration in solution is increased, they never lead to charge inversion, whatever the surface charge or the pH. However, in the case of salts of trivalent cations, electrokinetic charge reversal is often observed above a certain critical electrolyte concentration. In addition, the extent of overcharging increases when the concentration is raised above the critical value. This trend occurs for any system in which the surface charge is pH-independent, as in polystyrene latex and montmorillonite. Most of the results presented here are compatible with the specific adsorption of hydrolyzed metal ions as the main driving force for charge inversion. At low pH, when the hydrolysis of trivalent cations is likely to be absent, overcharging can be attributed to ion correlation effects.