Effects of surface charge on the two-dimensional one-component plasma: I. Single double layer structure

Abstract

The recent exact analysis of the canonical partition function and one- and two-particle distribution functions for a disc of classical one-component two-dimensional plasma of particle charge -q with a uniform neutralising charged background is extended to consider the effects of surface charge and of having the dielectric constant outside the disc, epsilon 2, different from that inside the disc, epsilon 1. The system is characterised by bulk density rho , the plasma parameter Gamma =q2/ epsilon 1kT, the surface charge density sigma q and the parameter Delta =( epsilon 1- epsilon 2)/( epsilon 1+ epsilon 2). For Gamma =2, Delta =0 or 1 and any value of rho or sigma , the canonical partition function and one and two-particle distribution functions are calculated exactly. The bulk thermodynamic properties are independent of sigma and Delta . The surface properties (surface excess free energy, density profile and two-particle correlation functions) are calculated in the thermodynamic limit and shown to depend strongly on both sigma and Delta .