A modified Poisson–Boltzmann equation: II. Models and solutions Original Research Article

The properties of the charged interface between a dielectric particle and a surrounding aqueous electrolyte solution are calculated numerically over a wide range of surface charge densities for plane, cylindrical and spherical geometries. As a basis for the calculations, we present detailed models for the partial molar volumes, the dielectric permittivity and the activities of the components. These models are combined with a generalized set of local balance thermodynamic and electrostatic differential equations derived in the first part of this series. The influences of volume effects, dielectric saturation, polarization and self-atmosphere potentials on surface potential and electrostatic energy of a charged particle are investigated. Deviations from the ordinary Poisson–Boltzmann theory become very important at surface charge densities above 0.2 C m−2. Quite generally, self-atmosphere potentials are of minor importance. The most important correction of the ordinary Poisson–Boltzmann equation is due to dielectric saturation in combination with the volume effect. It is found that the electrostatic potential, the electric field and the concentration of the counterion near a charged surface strongly depend on the excluded volume of the counterion. This leads to a distinct counterion sensitivity of the Gibbs energy of the system. Assuming a positively charged surface, competition between the counterion pairs Cl−/Br− and Cl−/SO42− is investigated. For sufficiently high surface charge densities it is found that, in the immediate vicinity of the surface, the smaller Br−-ion displaces the larger Cl−-ion and the Cl−-ion, in turn, displaces the larger SO42−-ion, although the latter is divalent.