Mean-field Theory and Computation of Electrostatics with Ionic Concentration Dependent Dielectrics.
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, γ(1) and γ(2); γ(1) determines the polarization effects in a dilute system and γ(2) regulates the dependence of the polarizability effects on the concentration of ions. For a polarizable ion in an aqueous solution γ(1) ≈ 0.01 and the polarizability effects are negligible. The conditions where γ(1) and/or γ(2) are large and the polarizability is relevant involve the low dielectric constant media, high surface charge, and/or large ionic concentrations.