Velocity autocorrelation function of Lennard-Jones fluids

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Abstract
A kinetic equation describing tagged particle motion in a fluid of particles interacting through continuous potentials is used to calculate the velocity autocorrelation function. The kinetic equation takes into account only binary collisions. It is an extension the Lorentz–Boltzmann equation to higher densities, by inserting a factor g(r) in such a way that in the hard sphere limit the Lorentz–Enskog equation is obtained. The velocity autocorrelation function of a fluid consisting of Lennard-Jones particles calculated using this theory compares well with simulation results, even for remarkably high densities. Close to the triple point the theory fails due to the neglect of perturbed binary collisions and correlated collisions. Approximate expressions for the collision operator are given for r−n interactions and a closed expression for the self-diffusion coefficient in terms of the pair distribution function is presented.