Pair Correlation Functions and the Self-Diffusion Coefficient of Lennard-Jones Liquid in the Modified Free Volume Theory of Diffusion

Abstract

In this paper, we apply the Matteoli-Mansoori empirical formula for the pair correlation function of simple fluids obeying the Lennard-Jones potential to calculate reduced self-diffusion coefficients on the basis of the modified free volume theory. The self-diffusion coefficient thus computed as functions of temperature and density is compared with the molecular dynamics simulation data and the self-diffusion coefficient obtained by the modified free volume theory implemented with the Monte Carlo simulation method for the pair correlation function. We show that the Matteoli-Mansoori empirical formula yields sufficiently accurate self-diffusion coefficients in the supercritical regime, provided that the minimum free volume activating diffusion is estimated with the classical turning point of binary collision at the mean relative kinetic energy 3k(B)T/2, where k(B) is the Boltzmann constant and T is the temperature. In the subcritical regime, the empirical formula yields qualitatively correct, but lower values for the self-diffusion coefficients compared with computer simulation values and those from the modified free volume theory implemented with the Monte Carlo simulations for the pair correlation function. However, with a slightly modified critical free volume, the results can be made quite acceptable.