Origin of the Difference in the Temperature Dependences of Diffusion and Structural Relaxation in a Supercooled Liquid

A supercooled binary mixture of soft disks in 2D, studied using molecular dynamics simulations, exhibits a breakdown of scaling between the self-diffusion constant and a structural relaxation time below a crossover temperature. Evidence is presented that this breakdown arises from two causes. First, the small displacements involved in structural relaxation correspond to the transition between ballistic and diffusive motion. Second, the different physical quantities averaged to obtain transport and relaxation time scales sample different parts of the increasingly heterogeneous distribution of local relaxation times and, hence, exhibit different temperature variation.