The effect of surface charge distribution on hindered diffusion in pores

Abstract

An analytic solution is derived for the hindered diffusion of charged, small solutes in charged, cylindrical pores in which the pore wall potential consists of the sum of an average and an oscillatory component. When the oscillatory contribution is absent, the effect of electrostatic interactions on diffusion is negligible. However, when the wall potential or surface charge density varies axially, electrostatic interactions hinder the rate of diffusion significantly, and can stop it completely if “choke points” develop where the solute concentration becomes zero. The degree of hindrance is generally weaker when the electrostatic charge on the pore wall and the charge on the solute have the same signs, leading to a repulsion, than it is in the presence of an attraction. The electrostatic hindrance is also affected by the length scale of the axial variation along the pore wall, becoming stronger as that length grows, until an asymptotic value is reached. The theory for the effect of variations of the electrostatic potential on rates of diffusion is shown to be in good agreement with experimental data taken from the literature. The results here are obtained by using generalized Taylor dispersion theory, and are therefore rigorous predictions of what occurs over times long enough that the solute diffuses through a tube many times longer than a single periodic cell. The electrostatic interactions are calculated using the linear Poisson–Boltzmann equation.