The long-time diffusion process of hard disks was compared with that of hard spheres by performing extensive event-driven molecular simulations. The volume fraction dependence of the mean-square displacements, the self-intermediate scattering function, and the non-Gaussian parameter of both systems were fully investigated. The singular function, which was theoretically proposed for three-dimensional systems by Tokuyama (2006), was found to describe the long-time self-diffusion coefficient of both hard disks and hard spheres. The characteristic times of the β relaxation process and the α relaxation process of hard disks were also found to be similar to those of hard spheres when the particles had the same long-time self-diffusion coefficient. The spatial dimension d changes the value of the glass transition point and peak height of the non-Gaussian parameter which were related to the geometric packing characteristics of hard disks and hard spheres.

Spatial Dimensionality Dependence of Long-Time Diffusion on Two- and Three-Dimensional Systems near Glass Transition. Y.Terada, M.Tokuyama: Intermetallics, 2010, 18[10], 1834-6