Analytical form for polarization induced self-energy for ions in solution near rough substrates.

In addition to the direct Coulomb interaction, ions in solution experience polarization mediated interactions. These appear as confining solid walls for an electrolyte typically have a dielectric constant different from that of the solution bulk and therefore exhibit polarization. Electrostatic interaction with the polarization charge induces interactions between pairs of ions as well as an excess self-energy for individual ions. This self-energy has been shown to produce important surface effects. Mean field theories for the solution, such as Poisson-Boltzmann, require modifications to include the self-energy effect. Explicit expressions for the self-energy are therefore necessary. For flat interfaces, these can be calculated using image charges while for more complex geometries only computational methods are available. This presentation considers the effect of roughness in near flat surfaces. The polarization charge and the self-energy of an ion near the surface are calculated using perturbation theory to first order on the amplitude of the roughness. To this order, explicit analytical expressions for the self-energy are obtained. Some consequences of the structure of these solutions are described.