Theoretical equations of state for a charged fluid.

Abstract

In this article, we present a molecular thermodynamic study of a system of N particles contained within a volume V and interacting via a hard-core pair potential with an attractive interaction according to the Wolf model for charged systems. This variable-range potential is characterized by three parameters: the repulsive hard-core diameter σ, the energy-well depth ϵ, and the inverse range α; a fourth parameter of the model is a cut-off distance xc that depends on α according to the relation xc = 2/α. Two equations of state (EOSs) are presented and derived from thermodynamic perturbation theory and Monte Carlo (MC) simulation data. The first EOS is given by the standard Zwanzig's high-temperature expansion of the Helmholtz free energy, where the first three perturbation terms a1, a2, and a3 were obtained from MC simulations in the canonical ensemble (NVT) and parameterized as functions of α and the reduced density of particles ρ* = Nσ3/V. The second EOS was obtained from the discrete perturbation theory applied to a discrete representation of the Wolf potential. Results for pressures, internal energies, and isochoric heat capacities are compared to the MC computer simulation data of the Wolf system, including vapor-liquid coexistence curves, for different values of α. Overall, both EOSs give a very good representation of the thermodynamic properties of the Wolf fluid when 0.3 ≤ α ≤ 1.0 and 0.05 ≤ ρ* ≤ 0.8. Since the Yukawa fluid can reproduce information of screened ionic interactions, we discuss the equivalence between the Wolf and Yukawa fluids in the context of equivalent systems in liquid theory.