Density expansion of the dynamic structure factor from molecular dynamics simulation

Abstract

Abstract The dynamic structure facto S ( k ,ω) of low-density 36 Ar measured in a recent small-angle inelastic neutron scattering experiment has been analysed for the first time in terms of a virial (density) expansion, and the first (i.e. linear) density correction to the free-gas ( S ( k ,ω) has been compared with the prediction of Enskog kinetic theory for hard spheres. It is demonstrated that the dynamics of density fluctuations is a sensitive probe of the interatomic pair potential, and in order to have a comparison of the experimental results with calculations based on a more realistic potential, we have performed molecular dynamics simulations of a Lennard-Jones system, from which the corresponding time correlation function F(k,t) has been obtained at various densities. The computations are very time-consuming for the following reasons. 1. A large box size is needed to have a range of wavevectors as small as those required for the effect to be detectable. In fact, deviations from free-gas (i.e. single molecule dynamics tend to vanish at k ≈1.5 nm −1 . 2. The free-gas contribution to F(k,t) , which must be subtracted in order to extract the density dependence, accounts for about 90% of the total correlation functions, so that a very accurate simulation is required. 3. The statistical uncertainties must be small enough for a reasonably precise extraction of the linear density dependence and for the determination of the ( k,t )-dependent density range beyond which higher-order deviations begin to be visible. Some preliminary results are presented here where the linear density coefficient is determined and compared with both the experimental results and the hard-sphere theory.