Universal effects of collective interactions on long-time self-diffusion coefficients in hard-sphere systems

We investigate how universal the collective behavior, due to the many-body interactions in polydisperse hard-sphere systems, is at higher volume fractions. We perform two types of computer simulations, a Brownian-dynamics simulation on colloidal suspensions of hard spheres, where the hydrodynamic interactions between particles are neglected, and a molecular-dynamic simulation on atomic systems of hard spheres. Thus, we show that the long-time self-diffusion coefficients DSL in both systems become singular as DSL(φ) (1−φ/φc)2 because of the collective interactions due to the many-body collision processes, where φ is a particle volume fraction and φc 0.586 for 6% polydispersity. Although DSL exhibits the same singular behavior as that obtained theoretically for the monodisperse suspension with the hydrodynamic interactions, no liquid–glass transition is found because even the polydisperse hard-sphere systems crystallize without the hydrodynamic interactions for all φ above the melting volume fraction, which is lower than φc.