Role of the soft-core repulsion upon density-and temperature-dependent effective diameters from two thermodynamic perturbation theories

Abstract

In this work, density- and temperature-dependent effective diameters from two different thermodynamic perturbation theories (TPTs) are presented. The first theory is well-known Barker and Henderson's TPT, and the second one is based on the pioneering work by Rowlinson but applied to steeply repulsive potentials by Heyes. Three intermolecular potentials- generalized Lennard-Jones (GLJ), inverse power (IP), and square-well square shoulder (SWSS)- were considered to study the steepness effect, n, upon the theoretically deduced effective diameters. As a result, for n ≥ 12, and both TPTs, GLJ, and IP produce numerically equivalent effective diameters for packing fractions (η) less than 0.7. Moreover, for the SWSS potential, Rowlinson's TPT gives a simple cubic polynomial for the effective diameters, in comparison to the sixth- degree polynomial obtained from Barker and Henderson's approach. Both polynomials from these two different TPTs essentially predict the same values of effective diameter for η ≤ 0.7. Thus, the theoretically based cubic polynomial presented in this work could be used into the molecular-based equations of state (EoSs) to perform phase equilibrium calculations at conditions wherein an effective diameter dependent upon both temperature and density is expected to be more relevant (i.e., low temperatures, high pressures, and dense phases).