Heterogeneous Diffusion in Highly Supercooled Liquids

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