Thermodynamic perturbation theory of simple liquids: Monte Carlo simulation of a hard sphere system and the Helmholtz free energy of SW fluids

Abstract

The Monte Carlo method is used to simulate similar sized hard sphere systems in a wide range of densities (from η 0.005 to 0.530 with a step of η = 0.005). The models are used to calculate the coefficients of the thermodynamic perturbation theory series for SW fluids up to the fourth order. The width of the attraction zone of the SW potential λ is varied from 1 to 2.5 sphere diameters. The analytical expressions approximating the obtained coefficients by polynomials with respect to the variables η and λ are determined. The absolute accuracy of the approximation is estimated to be better than ±0.001. All the necessary data for the calculation of the Helmholtz free energy of SW fluids up to the fourth-order perturbation theory are given.