Inhomogeneous Coulomb fluids with image interactions between planar surfaces. I

Abstract

Description of Coulomb particles near a surface is complicated by the effect of the surface on the ion–ion correlations, the electrostatic images (if the surface is a dielectric boundary), and the long range of the correlations in the lateral direction. We formulate the problem of the ion distribution for inhomogeneous Coulomb fluids with an arbitrary core potential and confined between two planar surfaces, with which the particles can interect via any short-ranged potential. All orders of image interactions are included into an effective position-dependent pair potential. The problem is solved by mapping the inhomogeneus three-dimensional system into a homogeneous two-dimensional one. The system is subdivided into M layers, and then shown to be isomorphic to an M-component fluid mixture in two dimensions. The mapping becomes exact as the number of layers (‘‘components’’) M→∞, and is accordingly an excellent approximation for finite, but large M. The correlations and other statistical mechanical functions can now be obtained with any conventional closure scheme. This forms the basis for a numerical method to solve the complete integral equations for the one- and two-particle distribution functions, using, e.g., the hypernetted chain (HNC) closure for the inhomogeneous pair correlations as the sole approximation. The associated numerical procedures are briefly described. The method could also be applied to study various problems for solute particles interacting via other pair potentials.