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

TL;DR

This paper demonstrates that the dynamics of glass-forming soft-sphere liquids can be universally scaled using a dynamic equivalence principle, linking their behavior to hard-sphere systems through a single reduced density parameter.

Contribution

It introduces a scaling framework based on dynamic equivalence to describe how density, temperature, and softness influence soft-sphere liquid dynamics, validated by simulations and SCGLE theory.

Findings

Dynamic parameters depend only on a reduced density n*

Scaling rules match recent simulation results

SCGLE theory accurately predicts the scaling behavior

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 {\nu}^{-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 {\alpha}-relaxation time and the long-time self-diffusion coefficient, depend on n, T, and {\nu} only through the reduced density n^\ast \equiv n{\sigma}^{3}_{HS}(T, {\nu}),where the effective hard-sphere diameter {\sigma}_{HS}(T, {\nu}) 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