Electrostatic Interaction between a Sphere and a Planar Surface: Generalization of Point-Charge/Surface Image Interaction to Particle/Surface Image Interaction

Abstract

An explicit exact analytic expression for the energy of the electrostatic interaction between a platelike particle 1 and a spherical particle 2 of radiusa2immersed in an electrolyte solution of Debye–Hückel parameter κ is derived on the basis of the linearized Poisson–Boltzmann equation. Both particles may have either constant surface potential or constant surface charge density. In the limit of κa2→ 0, the interaction between a plate with zero surface charge density and a sphere having constant surface charge density becomes identical to the usual image interaction between a point charge and an uncharged plate. The present theory thus leads to a generalization of the usual image interaction of a point charge to cover the case of a charged colloidal particle of finite size.