Monte Carlo and the WCA type perturbation theory for a hard-core with two-Yukawa-tails fluid

Abstract

The ‘exact’ optimized renormalized potential C*(r) is analytically calculated for a fluid with a pair potential by a linear combination of two Yukawa functions plus a hard-core (HCTY). Our method makes use of the mean-spherical-approximation analytic solution of the Ornstein-Zernike equation for the direct correlation function of the three-Yukawa functions form. Two of the functions are related to the interaction potential of the system whereas the other serves to obtain the GMSA solution for the hard-sphere distribution functions c ₀(r) and g ₀(r) which are utilized in the method. C*(r) is then used in various approximated schemes (EXP, LIN, LSQ and QUAD) resulting from the Weeks, Chandler, and Andersen (WCA) preturbation theory to calculate the thermodynamic properties and g(r) for the two-Yukawa fluid and the results are compared with our Monte Carlo data. These results are overall very good for EXP and also for GMSA (thermodynamic properties but not g(r)) and conclusions concur with those by Stell and Weis for a potential consisting of a hard-core with a Lennard-Jones attractive tail (HCLJ). Finally, we calculated the thermodynamic properties of HCLJ fluid using the HCTY fluid as the reference system. The smallness of the first-order term in the perturbation theory and the fact that HCTY system can be mostly treated analytically make this potential an attractive alternative to the hard-sphere system for use in the perturbation theory of fluids.