Continuous Self Energy of Ions at the Dielectric Interface

We present a simple, unified theory for the self-energy of an ion near a dielectric interface. Our theory accounts for both the short-range (solvation) and long-range (image force) electrostatic forces, charge polarization induced by these forces, and the cavity energy. In contrast to previous models, our self energy is continuous across the interface and thus applicable to both the water and air (oil) sides of the interface. With no fitting parameters, we predict the specific ion effect on the interfacial affinity of halogen anions at the water/air interface, and the strong adsorption of hydrophobic ions at the water/oil interface, in agreement with experiments and atomistic simulations.