Mean-field electrostatics beyond the point-charge description

This review explores the number of mean-field constructions for ions whose structure goes beyond the point-charge description, a representation used in the standard Poisson-Boltzmann equation. The exploration is motivated by a body of experimental work which indicates that ion-specific effects play a significant role, where ions of the same valence charge but different size, polarizability, or shape yield quite different, and sometimes surprising results. Furthermore, there are many large ions encountered in soft-matter and biophysics that do not fit into a point-charge description, and their extension in space and shape must be taken into account of any reasonable representation.