Molecular-dynamics study of the dependence of self-diffusion on system size in a dense binary liquid of hard spheres

The dependence on system size of self-diffusion in a dense binary liquid of hard spheres was studied by molecular dynamics simulation of two systems with 216 and 5832 particles. The ratio of particle radii is α=0.85. The relative difference between the self-diffusion coefficients Ds for both system sizes increases from 11% to 18% as the packing fraction φ is increased from 0.533 to 0.563. The relation between the size dependence of Ds and the underlying size dependence of the velocity-autocorrelation function (VAF) was studied in detail for φ=0.548. For intermediate and long times the difference Δψ(t) of the VAFs for the two sizes is well reproduced by the mode-coupling formula expressing the coupling of self-diffusion to modes of collective flow. However, the short-time part of Δψ(t) is equally important. A simpler relation was found between the size dependence of Ds and that of the memory function M(t) associated with the VAF. M(t) is larger and decays more slowly for the smaller systems, which leads to the observed size dependence of Ds.