On the thermodynamic properties of the Lennard-Jones fluid

Abstract

An analytical scheme for the evaluation of the compressibility factor of a simple fluid is presented. It is based on the clasical perturbation theory and on a recent (analytical) approximation for the radial distribution function of the hard-sphere fluid. The scheme, which provides, in the case of the Lennard-Jones fluid, explicit expressions for both structural and thermodynamic quantities in a closed form, requires the hard-sphere fluid equation of state as the sole input. Using the Carnahan–Starling equation of state for the hard-sphere reference fluid, the prediction of the critical point as well as the behavior of the pressure of the Lennard-Jones fluid are an improvement in relation to previous work and compare rather well with recent numerical simulations. The same applies to the radial distribution function computed with the present scheme and the Weeks–Chandler–Andersen approach. From a knowledge of the freezing and melting transitions in the hard-sphere system, the liquid and solid branches of the reduced temperature vs. reduced density curve at coexistence for the Lennard-Jones fluid are simply obtained.