A simple analysis of the classical hard-sphere one-component plasma. II. Density functional theory

Abstract

The generalized van der Waals free energy density functional formalism of inhomogeneous fluids has been applied to study the thermodynamics and structural properties of a system of identical charged hard spheres neutralized by a uniform penetrating background. Nonlocal entropic effects are included through a simple density independent coarse-graining kernel and the hard-sphere truncation of the Coulomb interaction in the ionic atmosphere is accounted for within a mean-field approximation. In the first instance a parametric charge density of known form is introduced yielding essentially analytic results. Second, the functional is optimized with full variational flexibility to produce a theory directly analogous with the Poisson–Boltzmann approach to Coulomb fluids. A linearized version corresponding to a Debye–Hückel approximation is also discussed. The results compare favorably with Monte Carlo simulation in the regime of low to intermediate bulk density. At high volume fractions (>0.1) the functional becomes ill conditioned as the excluded volume effect is exaggerated and the mean-field hole correction fails to account for the hard-sphere structure.