Understanding the role of image charges in mean field theories of ionic solutions.

Mean field theories for charged systems such as Poisson-Boltzmann are of great practical importance. Standard applications include the description of molecular and colloidal interactions in an aqueous environment where ions are present. Recent simulations with asymmetric ionic mixtures have shown the existence of non-trivial behavior of ions near interfaces with dielectric contrast. Near these interfaces ion concentrations are increased or depleted in ways not predicted by the Poisson-Boltzmann approach. The origin of this discrepancy can be traced to the omission, in the construction of the mean field theory, of the role of image charges. When these effects are included, a mean field theory can be formulated that addresses the observed phenomena. In this approach, the Poisson-Boltzmann equation acquires an extra term describing the presence of interfaces by means of an effective one-body short range potential.