Randium: A minimal model of universal viscous liquid dynamics

Abstract

When liquids are cooled and crystallization is avoided, their dynamics slow dramatically and the material eventually solidifies into an amorphous glass. Experiments show that chemically distinct glass forming liquids share universal features in both the spectral shape and the temperature dependence of the primary structural relaxation. We introduce Randium, a generic, energetically coarse-grained minimal model of viscous liquids. The model, inspired by results from atomistic molecular-dynamics simulations, is implemented on a two-dimensional lattice with Gaussian-distributed nearest-neighbor interactions. Temperature is the only control parameter, and at low temperatures, dynamic facilitation and dynamical heterogeneity emerge from simple nearest-neighbor rearrangements. The relaxation spectra obey time-temperature superposition, and they reproduce shapes observed experimentally for chemically distinct systems. The temperature dependence of the structural-relaxation time follows parabolic scaling, and the relaxation time grows exponentially with the heterogeneity length scale. The mean-squared displacement collapses onto the universal master curve of the random barrier model. The absence of elasticity-induced facilitation in Randium shows that this is not required for universal viscous-liquid dynamics. Other explanations for universal relaxation are discussed in light of Randium.