Structure and thermodynamic properties of simple coulomb systems

Abstract

We have extended a recent perturbation theory [J. Chem. Phys. 82, 414 (1985); 84, 4547 (1986)] for nonionic systems to the one-component plasma (OCP). Characteristic features of the theory are its ability to both fluids and solids and the use of a reference potential whose repulsive range shrinks with density. Based on the computed thermodynamic data, we have developed a simple alternative (optimized hard-sphere) model, whose Helmholtz free energy is a sum of the Helmholtz free energy of the hard-sphere reference system and the Madelung energy of a fcc lattice. Comparison with available Monte Carlo and other theoretical results shows that the optimized hard-sphere model gives reliable solid (fcc) and fluid properties. The theory predicts that the fcc solid will melt at the Coulomb coupling parameter $\Gamma{m}$ =208 versus Helfer et al.``s [J. Stat. Phys. 37, 577 (1984)] Monte Carlo value of 196. This difference is due to a small difference (0.1\%) in the computed excess free energy. The computed internal energy can be accurately fitted by an analytic form. Its two leading terms (for the fluid) are $-0.899488\Gamma + 1.27297\Gamma^{1/4}$, in close agreement with Slattery et al.``s [Phys. Rev. A 21, 2087 (1980); 26, 2255 (1982)] empirical fit to their Monte Carlo data. We conclude that the hard-sphere perturbation theory is applicable to a long-range repulsive system, such as the OCP, so long as the hard-sphere diameter is judiciously chosen by using a density-dependent reference potential. The equilibrium properties of charged hard spheres in a uniform neutralizing background depend on two independent parameters : the Coulomb coupling constant of the one-component plasma and the packing fraction of the hard spheres. The thermodynamic quantities such as excess Helmholtz free energy, excess internal energy, and compressibility factor are calculated from the hard-sphere perturbation theory and the optimized hard-sphere model of charged hard spheres for fluids. The...