Influence of ion sterics on diffusiophoresis and electrophoresis in concentrated electrolytes

We quantify the diffusiophoresis and electrophoresis of a uniformly charged, spherical colloid in a binary electrolyte using modified Poisson-Nernst-Planck equations that account for steric repulsion between finite sized ions. Specifically, we utilize the Bikerman (Bik) lattice gas model and the Carnahan-Starling (CS) and Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equations of state for monodisperse and polydisperse, respectively, hard spheres. We compute the phoretic mobility for weak applied fields using an asymptotic approach for thin diffuse layers, where ion steric effects are expected to be most prevalent. The thin diffuse layer limit requires lambda(D)/R -> 0, where lambda(D) is the Debye screening length and R is the particle radius; this limit is readily attained for micron-sized colloids in concentrated electrolytic solutions. It is well known that the classic Poisson-Boltzmann (PB) model for pointlike, noninteracting ions leads to a prediction of a maximum in both the diffusiophoretic and electrophoretic mobilities with increasing particle zeta potential (at fixed lambda(D)/R). In contrast, we find that ion sterics essentially eliminate thismaximum (for reasonably attainable zeta potentials) and increase the mobility relative to PB. Next, we consider the more experimentally relevant case of a particle with a constant surface charge density and vary the electrolyte concentration, neglecting charge regulation on surface active sites. Rather surprisingly, there is little difference between the predictions of the four models (PB, Bik, CS, and BMCSL) for electrophoretic mobility in concentrated solutions, at reasonable surface charge densities (similar to 1-10 mu C/cm(2)). This is because as the concentration increases, the zeta potential is reduced (to below the thermal voltage for concentrations above about 1 M) and therefore the diffuse layer structure is largely unaffected by ion sterics. For gradients of symmetric electrolytes (equal diffusivities, charge, and size) diffusiophoresis is also essentially unaffected by ion sterics, with a mobility that approaches zero with increasing concentration, just as in electrophoresis. For gradients of asymmetric electrolytes, the difference in diffusivities of the cation and anions leads to an induced electric field that acts on the charged particle. Importantly, we show that ion sterics leads to an excess contribution to the induced electric field, which increases rapidly with concentration. This increase overwhelms the accompanying decrease in zeta potential. The result is the diffusiophoretic mobility increases with concentration, rather than approaching zero. Therefore, diffusiophoresis could be an appealing alternative transport mechanism to electrophoresis in concentrated electrolyte solutions.