The molecular dynamics simulations of the damping matrices in a Lennard-Jones fluid and testing of the two-relaxation time models for the memory function

Abstract

We have carried out the molecular dynamics simulations (MD) for the velocity autocorrelation functions (vacf), the acceleration autocorrelation functions, and the damping matrices in a Lennard-Jones fluid. Seven state conditions, from low densities (ρ*=ρσ3=0.3) to high densities (ρ*=0.85) and from low temperatures (T*=kT/ε=0.73, σ and ε being the Lennard-Jones parameters) to high temperatures (T*=5.2) were investigated. The values of the damping matrices Kn(t=0), n=1,2,3,4, and 5 in the continued fraction representation of the memory kernel, as given by Mori, were obtained directly from the MD via a seventh order backward difference algorithm. These Kn(0) increase rapidly in magnitude as the order increases. They also show strong temperature dependence, but weak density dependence. These damping matrices are used to test the empirical models proposed to represent the memory functions for the velocity autocorrelation. We test some commonly used memory function models with two relaxation times, one representing the short time binary collision effects and the other the long time hydrodynamic effects. It is discovered that in the single dynamic variable autocorrelation approach adopted here none of the empirical models tested perform well in reproducing the MD vacf at intermediate to long times. We attribute this to the lack of mode–mode coupling contributions.