Polarizable Poisson–Boltzmann equation : the study of polarizability effects on the structure of a double layer

Abstract

We incorporate ion polarizabilities into the Poisson–Boltzmann equation by modifying the effective dielectric constant and the Boltzmann distribution of ions. The extent of the polarizability effects is controlled by two parameters, γ1 and γ2; γ1 determines the polarization effects in a dilute system and γ2 regulates the dependence of the polarizability effects on the concentration of ions. For a polarizable ion in an aqueous solution γ1 ≈ 0.01 and the polarizability effects are negligible. The conditions where γ1 and/or γ2 are large and the polarizability is relevant involve the low dielectric constant media, high surface charge, and/or large ionic concentrations.