Molecular dynamics study of the dynamical properties of an assembly of infinitely thin hard rods

Abstract

We present molecular dynamics (MD) simulations of a system of N (N=100–500) infinitely thin hard rods of length L (‘hard needles’). An algorithm is described which is reasonably fast and yet is guaranteed not to overlook any collision. Under the assumption that successive binary collisions are uncorrelated (the ‘Enskog’ assumption), we derive expressions for the time correlation functions of linear and angular momentum and rotational energy. We also obtain an exact expression for the collision frequency in a hard needle fluid. The MD results indicate that the Enskog approach works well at reduced densities below ρ*=8. At higher densities (8<ρ*<48) large deviations from the Enskog predictions are observed. However, at these densities the MD data conform to scaling predictions of the kind first put forward by Doi and Edwards. In particular, we find that the rotational diffusion constant D R scales as ρ*-2. One of the surprising consequences of the scaling arguments is that the longitudinal self-diffusion co...