Identification of time scales of the violation of the Stokes-Einstein relation in Yukawa liquids

Abstract

We investigate the origin of the violation of the Stokes-Einstein (SE) relation in two-dimensional Yukawa liquids. Using comprehensive molecular dynamics simulations, we identify the time scales supporting the violation of the SE relation $D\propto (\eta /T{)}^{-1}$, where $D$ is the self-diffusion coefficient and $\eta$ is the shear viscosity. We first compute the self-intermediate scattering function $F_s(k,t)$, the non-Gaussian parameter ${\alpha }_2$, and the autocorrelation function of the shear stress $C_{\eta }(t)$. The timescales obtained from these functions are included the structural relaxation time ${\tau }_{\alpha }$, the peak time of the non-Gaussian parameter ${\tau }_{{\alpha }_2}$, and the shear stress relaxation time ${\tau }_{\eta }$. We find that ${\tau }_{\eta }$ is coupled with $D$ for all temperatures indicating the SE preservation, however, ${\tau }_{\alpha }$ and ${\tau }_{{\alpha }_2}$ are decoupled with $D$ at low temperatures indicating the SE violation. Surprisingly, we find that the origins of this violation are related to the non-exponential behavior of the autocorrelation function of the shear stress and non-Gaussian behavior of the distribution function of particle displacements. These results confirm dynamic heterogeneity that occurs in two-dimensional Yukawa liquids that reflects the presence of regions in which dust particles move faster than the rest when the liquid cools to below the phase transition temperature.

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