Derivation of a general fluid equation of state based on the quasi-Gaussian entropy theory: application to the Lennard-Jones fluid

Abstract

In this article we present an equation of state for fluids, based on the quasi-Gaussian entropy theory. The temperature dependence along isochores is described by a confined Gamma state, previously introduced, combined with a simple perturbation term. The 11 parameters occurring in the free energy and pressure expressions along the isochores are obtained from molecular dynamics simulation data. The equation of state has been parametrized for the Lennard-Jones fluid in the (reduced) density range 0–1.0 and (reduced) temperature range 1.0–20.0 using (partly new) NVT molecular dynamics simulation data. An excellent agreement for both energy and pressure was obtained. To test the ability to extrapolate to unknown state points, the parametrization was also performed on a smaller set of data in the temperature range 1.0–6.0. The results in the two cases are remarkably close, even in the high temperature range, and are often almost indistinguishable, in contrast to a pure empirical equation of state, like for example the modified Benedict—Webb—Rubin equation. The coexistence line agrees in general very well with Gibbs ensemble and NpT simulation results, and only very close to the critical point there are deviations. Our estimate of the critical point for both parametrizations is somewhat different from the best estimate based on Gibbs ensemble simulations, but is in excellent agreement with other estimates based on NVT simulations and integral equations.