Approximate Expression for the Double-Layer Interaction Energy between Two Parallel Plates with Constant Surface Charge Density

Abstract

An approximate expression for the potential energy of the double-layer interaction between two parallel similar plates with constant surface charge density is derived via a novel linearization method, in which the Poisson–Boltzmann is linearized with respect to the deviation of the electric potential from the surface potential (which is a function of the interplate separationh). This approximation works quite well for small plate separationshfor all values of the surface charge density (or the unperturbed surface potential) and gives a correct limiting form of the interaction energy (or the interaction force) ash→ 0.