Ions at the Water−Vapor Interface

We obtain the electrostatic free energy of finite-sized ions near a dielectric interface within the framework of the classical continuum dielectric theory. The ion is modeled as a dielectric sphere with a fixed uniform surface charge density. In order to avoid the generation of additional induced charges on the ionic surface, it is assumed there is no dielectric contrast between the ion core and the external dielectric medium where it is embedded, which allows an exact solution of the electrostatic problem by the image-charge method. It is shown that earlier results reported in the literature, especially when there is partial ionic penetration into the interface, always underestimate the electrostatic free energy associated with nonpolarizable ions. For an ion modeled as a vacuum cavity at the water-vapor interface, it is estimated that the free energy is an order of magnitude larger than prior predictions.