Abstract

This chapter explores the number of mean field constructions for ions whose structure goes beyond the point charge description, the representation used in the standard Poisson‐Boltzmann (PB) equation. The structural details omitted within a point charge picture can be related to electrostatic structure of an ion, giving rise to polarizability, asymmetric interactions, softening of Coulomb interactions if a distribution of an ion charge is extended in space, or can be related to the Pauli exclusion principle, giving rise to the excluded volume effects or other types of repulsive interactions. The efficient theory for hard‐core interactions, the fundamental measure DFT, shows shortcomings even for the weak‐coupling limit conditions. There is an additional motivation for pursuing various mean field constructions. Simple models such as charged hard spheres are easy to simulate, and for these systems one could simply use simulations to cover the entire range of electrostatics, from weak‐ to strong‐coupling regime.