The Electrostatic Interaction between a Dielectric Interface and a Point-Charge-in-Cavity Ion

An interface between a solution and air could attract or dispel ions and thus alter its own thermodynamic properties. One major source of the force is the electrostatic interaction. We solve a different model from previous models on this subject where an ion represented by a point charge at the center of a hollow sphere sits on or close to the dielectric interface. Two numerical methods are developed to solve the corresponding Poisson equations to get the electrostatic self-energy. One is based on expanding the electric potential function by spherical and cylindrical harmonic functions. The other self-consistently calculates the induced charge on the air-solution interface and the shell of the ion. The numerical results support, in certain regions, some simple analytical approximations and some simple physical pictures behind them. The results may help to improve the understanding of complex ion-interface interactions in biological and electrochemical systems.