Density-Temperature-Softness Scaling of the Dynamics of Glass-forming Soft-sphere Liquids

Abstract

The principle of dynamic equivalence between soft-sphere and hard-sphere fluids [Phys. Rev. E \textbf{68}, 011405 (2003)] is employed to describe the interplay of the effects of varying the density n, the temperature T, and the softness (characterized by a softness parameter ν^{-1}) on the dynamics of glass-forming soft-sphere liquids in terms of simple scaling rules. The main prediction is that the dynamic parameters of these systems, such as the α-relaxation time and the long-time self-diffusion coefficient, depend on n, T, and ν only through the reduced density n^\ast \equiv nσ^{3}_{HS}(T, ν),where the effective hard-sphere diameter σ_{HS}(T, ν) is determined, for example, by the Andersen-Weeks-Chandler condition for soft-sphere-hard-sphere structural equivalence. A number of scaling properties observed in recent simulations involving glass-forming fluids with repulsive short range interactions are found to be a direct manifestation of this general dynamic equivalence principle. The self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics is shown to accurately capture these scaling rules