Heterogeneous Diffusion in Highly Supercooled Liquids

The diffusivity of tagged particles is demonstrated to be very heterogeneous on time scales comparable to or shorter than the $\alpha$ relaxation time ${\tau }_{\alpha }$ ($\cong$ the stress relaxation time) in a highly supercooled liquid via 3D molecular dynamics simulation. The particle motions in the relatively active regions dominantly contribute to the mean square displacement, giving rise to a diffusion constant systematically larger than the Einstein-Stokes value. The van Hove self-correlation function $G_s(r,t)$ is shown to have a long distance tail which can be scaled in terms of $r\mathrm{/}{t}^{1\mathrm{/}2}$ for $t\text{ls}3{\tau }_{\alpha }$. Its presence indicates heterogeneous diffusion in the active regions. However, the diffusion process eventually becomes homogeneous on time scales longer than the life time of the heterogeneity structure ($\sim 3{\tau }_{\alpha }$).