Simple analytic equations of state for the generalized hard-core Mie(α, β) and Mie(α, β) fluids from perturbation theory

Abstract

New, simple and analytic perturbation theory equations of state for generalized hard-core Mie HCMie(α, β) and Mie(α, β) fluids are proposed. They are based on the second-order Barker–Henderson perturbation theory in the macroscopic compressibility approximation and the new analytical expression of the radial distribution function of hard spheres, g HS(r), developed by Sun in terms of a polynomial expansion of base functions adapted to the square-well and Sutherland potentials [Can. J. Phys. 83 (2005) 55], the combination of which yields the HCMie(α, β) and Mie(α, β) functions. The compressibility factors, the residual internal energies and the radial distribution function at contact with the hard core are then obtained from this equation of state for the HCLJ(12, 6) potential, which is a particular case of the HCMie(α, β) potentials with α = 12 and β = 6. The results are in good agreement with the existing Monte Carlo (MC) simulation data, and compare favorably with those obtained from five other equations of state, three of which contain numerical coefficients fitted to the Monte Carlo results. For the Mie(α, 6) (α = 8, 10, 12), fluids, the present equation of state is a good representation of recent molecular dynamics (MD) simulations of the pressure and internal energy. It is more accurate than the statistical associating fluid theory of variable range (SAFT-VR Mie(n, 6)) theory for n = 8, and 10, while for n = 12 the SAFT-VR theory is best. For the Mie(14, 7) fluid, which is outside the range of application of the SAFT-VR theory, the results for the pressure are in good agreement with the analytical equation of state obtained from the MC simulation data.