Electrokinetics of the amphifunctional metal/electrolyte solution interface in the presence of a redox couple

Double layers (DL) at amphifunctionally electrified interfaces, such as that of an oxidized metal in an aqueous electrolyte solution, arise from coupling between ionic and electronic surface-charging processes. The electronic component enters the double-layer formation in the well-known situation where a potential is externally applied. In that case, the DL is fully or partly polarized depending on the possibility of interfacial electron transfer, that is, a faradaic process. This paper reports on the conjunction of the chemical/electrochemical processes at the interface in the case where the solution contains a redox-active couple. This makes it possible to polarize/depolarize a DL without invoking any external circuit. Streaming potential data obtained for the gold/(Fe(CN)63-/Fe(CN)64-, KNO3) electrolyte interface are analyzed in terms of a recently developed theory which takes into account reversible bipolar faradaic depolarization, the inherent nonlinearity of the lateral field, and the effects of flow on the rate of the faradaic reactions. It appears that the theory largely overestimates the bipolar currents, leading to physically unrealistic ¿-potentials. A careful analysis of monopolar voltammetric data reveals quasi-reversible behavior of the redox couple under the typical convective conditions and electrolyte compositions met in electrokinetic experiments. Inclusion of reduced reversibility (the extent of which is position-dependent under the streaming-potential measurement conditions) leads to a consistent set of ¿-potentials which compare well to the values for the background electrolyte

Electrokinetics of diffuse soft interfaces. 2. Analysis based on the nonlinear Poisson-Boltzmann equation

In a previous study (Langmuir 2004, 20, 10324), the electrokinetic properties of diffuse soft layers were theoretically investigated within the framework of the Debye-H¿ckel approximation valid in the limit of sufficiently low values for the Donnan potential. In the current paper, the electrokinetics is tackled on the basis of the rigorous nonlinearized Poisson-Boltzmann equation, the numerical evaluation of the electroosmotic velocity profile, and the analytically derived hydrodynamic velocity profile. The results are illustrated and discussed for a diffuse soft interface characterized by a linear gradient for the friction coefficient and the density of hydrodynamically immobile ionogenic groups in the transition region separating the bulk soft layer and the bulk electrolyte solution. In particular, it is shown how the strong asymmetry for the potential distribution, as met for high values of the bulk fixed charge density and/or low electrolyte concentrations, is reflected in the electrokinetic features of the diffuse soft layer. The analysis clearly highlights the shortcomings of the discontinuous approximation by Ohshima and others for the modeling of the friction and electrostatic properties of soft layers exhibiting high Donnan potentials. This is in line with reported electrokinetic measurements of various soft particles and permeable gels at low electrolyte concentrations which fail to match predictions based on Ohshima's theory

Faradaic and adsorption-mediated depolarization of electric double layers in colloids

cum laude graduation (with distinction

Electrophoresis of diffuse soft particles

A theory is presented for the electrophoresis of diffuse soft particles in a steady dc electric field. The particles investigated consist of an uncharged impenetrable core and a charged diffuse polyelectrolytic shell, which is to some extent permeable to ions and solvent molecules. The diffuse character of the shell is defined by a gradual distribution of the density of polymer segments in the interspatial region separating the core from the bulk electrolyte solution. The hydrodynamic impact of the polymer chains on the electrophoretic motion of the particle is accounted for by a distribution of Stokes resistance centers. The numerical treatment of the electrostatics includes the possibility of partial dissociation of the hydrodynamically immobile ionogenic groups distributed throughout the shell as well as specific interaction between those sites with ions from the background electrolyte other than charge-determining ions. Electrophoretic mobilities are computed on the basis of an original numerical scheme allowing rigorous evaluation of the governing transport and electrostatic equations derived following the strategy reported by Ohshima, albeit within the restricted context of a discontinuous chain distribution. Attention is particularly paid to the influence of the type of distribution adopted on the electrophoretic mobility of the particle as a function of its size, charge, degree of permeability, and solution composition. The results are systematically compared with those obtained with a discontinuous representation of the interface. The theory constitutes a basis for interpreting electrophoretic mobilities of heterogeneous systems such as environmental or biological colloids or swollen/deswollen microgel particles

Rates of ionic reactions with charged nanoparticles in aqueous media

A theory is developed to evaluate the electrostatic correction for the rate of reaction between a small ion and a charged ligand nanoparticle. The particle is assumed to generally consist of an impermeable core and a shell permeable to water and ions. A derivation is proposed for the ion diffusion flux that includes the impact of the equilibrium electrostatic field distribution within and around the shell of the particle. The contribution of the extra- and intraparticulate field is rationalized in terms of a conductive diffusion factor, fel, that includes the details of the particle geometry (core size and shell thickness), the volume charge density in the shell, and the parameters defining the electrostatic state of the particle core surface. The numerical evaluation of fel, based on the nonlinear Poisson–Boltzmann equation, is successfully complemented with semianalytical expressions valid under the Debye–Hückel condition in the limits of strong and weak electrostatic screening. The latter limit correctly includes the original result obtained by Debye in his 1942 seminal paper about the effect of electrostatics on the rate of collision between two ions. The significant acceleration and/or retardation possibly experienced by a metal ion diffusing across a soft reactive particle/solution interphase is highlighted by exploring the dependence of fel on electrolyte concentration, particle size, particle charge, and particle type (i.e., hard, core/shell, and entirely porous particles)

Electrokinetics of diffuse soft interfaces. I. Limit of low Donnan potentials

The current theoretical approaches to electrokinetics of gels or polyelectrolyte layers are based on the assumption that the position of the very interface between the aqueous medium and the gel phase is well defined. Within this assumption, spatial profiles for the volume fraction of polymer segments (), the density of fixed charges in the porous layer (fix), and the coefficient modeling the friction to hydrodynamic flow (k) follow a step-function. In reality, the "fuzzy" nature of the charged soft layer is intrinsically incompatible with the concept of a sharp interface and therefore necessarily calls for more detailed spatial representations for , fix, and k. In this paper, the notion of diffuse interface is introduced. For the sake of illustration, linear spatial distributions for and fix are considered in the interfacial zone between the bulk of the porous charged layer and the bulk electrolyte solution. The corresponding distribution for k is inferred from the Brinkman equation, which for low reduces to Stokes' equation. Linear electrostatics, hydrodynamics, and electroosmosis issues are analytically solved within the context of streaming current and streaming potential of charged surface layers in a thin-layer cell. The hydrodynamic analysis clearly demonstrates the physical incorrectness of the concept of a discrete slip plane for diffuse interfaces. For moderate to low electrolyte concentrations and nanoscale spatial transition of from zero (bulk electrolyte) to o (bulk gel), the electrokinetic properties of the soft layer as predicted by the theory considerably deviate from those calculated on the basis of the discontinuous approximation by Ohshima

Rates of ionic reactions with charged nanoparticles in aqueous media

A theory is developed to evaluate the electrostatic correction for the rate of reaction between a small ion and a charged ligand nanoparticle. The particle is assumed to generally consist of an impermeable core and a shell permeable to water and ions. A derivation is proposed for the ion diffusion flux that includes the impact of the equilibrium electrostatic field distribution within and around the shell of the particle. The contribution of the extra- and intraparticulate field is rationalized in terms of a conductive diffusion factor, fel, that includes the details of the particle geometry (core size and shell thickness), the volume charge density in the shell, and the parameters defining the electrostatic state of the particle core surface. The numerical evaluation of fel, based on the nonlinear Poisson–Boltzmann equation, is successfully complemented with semianalytical expressions valid under the Debye–Hückel condition in the limits of strong and weak electrostatic screening. The latter limit correctly includes the original result obtained by Debye in his 1942 seminal paper about the effect of electrostatics on the rate of collision between two ions. The significant acceleration and/or retardation possibly experienced by a metal ion diffusing across a soft reactive particle/solution interphase is highlighted by exploring the dependence of fel on electrolyte concentration, particle size, particle charge, and particle type (i.e., hard, core/shell, and entirely porous particles)

Electrophoretic deposition: a quantitative model for particle deposition and binder formation from alcohol-based suspensions

We investigated electrophoretic deposition from a suspension containing positively charged particles, isopropanol, water, and Mg(NO3)2, with the aim of describing the deposition rates of the particles and Mg(OH)2, which is formed due to chemical reactions at the electrode, in terms of quantitative models. LaB6 particles were used as a model system. The particle layer is consolidated by simultaneous precipitation of Mg(OH)2 which acts as a binder to hold the particles together. The Mg(OH)2 content was determined solely by the amount of charge passed through the cell. Quantitative precipitation of all OH¿ formed at the electrode was observed, except at very low current. The occurrence of a minimum current was ascribed to a threshold for Mg(OH)2 deposition. The same minimum current was observed for particle deposition. In combination with results using NaNO3, where no adherent layer was formed, this illustrates that Mg(OH)2 binder is necessary for consolidation. Once the minimum current was exceeded, it was found that all particles that migrate to the electrode under the influence of the electric field contribute to the formation of the layer, i.e., the "sticking coefficient" for the particles equals 1.0. The applicability of the particle and Mg(OH)2 deposition models was tested by variation of the Mg(NO3)2 concentration, pH, and water content

Bipolar electrode behaviour of the aluminium surface in a lateral electric field

This paper reports on the electrochemical processes at the surface of conducting materials such as aluminium in a thin-layer cell usually employed for electrokinetic measurements. The cell contains one or more planar Al wafers in contact with an electrolyte solution, which is subjected to an external electric field parallel to the surfaces of the wafers. Beyond a certain threshold value of the magnitude of the field, the current through the cell increases more than proportionally with the field strength. This is due to faradaic processes occurring at the two ends of the conducting substrates, i.e. reduction at the positive side of the electric field in the solution and oxidation at the negative side. In the case of Al wafers, anodic dissolution of the metal takes place and the progression of the `corroding' edge can be followed visually. The overall electrolytic process, corresponding with the distributed current along the surface of the wafer, could be explained and modeled on the basis of the conventionally measured Butler–Volmer characteristics of the monopolar Al electrod

Bipolar electrode behaviour of the aluminium surface in a lateral electric field

This paper reports on the electrochemical processes at the surface of conducting materials such as aluminium in a thin-layer cell usually employed for electrokinetic measurements. The cell contains one or more planar Al wafers in contact with an electrolyte solution, which is subjected to an external electric field parallel to the surfaces of the wafers. Beyond a certain threshold value of the magnitude of the field, the current through the cell increases more than proportionally with the field strength. This is due to faradaic processes occurring at the two ends of the conducting substrates, i.e. reduction at the positive side of the electric field in the solution and oxidation at the negative side. In the case of Al wafers, anodic dissolution of the metal takes place and the progression of the `corroding' edge can be followed visually. The overall electrolytic process, corresponding with the distributed current along the surface of the wafer, could be explained and modeled on the basis of the conventionally measured Butler–Volmer characteristics of the monopolar Al electrod