Non hard sphere thermodynamic perturbation theory over a wide range of temperatures

Abstract

A recently proposed non hard sphere (HS) coupling parameter expansion (CPE)thermodynamic perturbation theory (TPT) is evaluated for its performance over a widerange of temperatures, particularly in tackling a so-called low temperature problem,i.e. the traditional high temperature series expansion TPT performance becomesprogressively less satisfactory as the temperature drops, and finally becomes qualitativelyincorrect. Accordingly, we have performed Monte Carlo simulations in the canonicalensemble for a honeycomb model potential, and the pressure, excess internalenergy, excess Helmholtz free energy, excess chemical potential, and excess enthalpyhave been obtained over wide density and temperature ranges for the fluid phase.These new simulation data, together with published simulation data for an HS + square well fluid at very low temperatures, have been used to test the performanceof the non HS CPE third-order TPT. A general scheme for assimilating partof the tail term of the potential function considered into a reference system isproposed, which ensures running normality of the non HS perturbation codeat subcritical temperatures and smooth transition into a commonly used HSperturbation scheme when the temperatures considered rise infinitely. It is found thatthe non HS CPE third-order TPT is very satisfactory or even very accurate forthese extremely low temperatures for which traditional Zwanzig type TPT isqualitatively incorrect and even an HS CPE third-order TPT also seriously fails insome cases. Among the thermodynamic quantities considered the most difficultone to predict theoretically is the constant volume excess heat capacity, and forthis quantity the non HS CPE third-order TPT is also obviously superior to itscompetitors.