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

TL;DR

This study uses molecular dynamics simulations to identify specific time scales associated with the violation of the Stokes-Einstein relation in 2D Yukawa liquids, revealing the roles of shear stress relaxation and dynamic heterogeneity.

Contribution

It uncovers the distinct time scales linked to SE violation and demonstrates the connection between non-Gaussian particle displacements, shear stress autocorrelation, and dynamic heterogeneity.

Findings

Shear stress relaxation time remains coupled with diffusion at all temperatures.

Structural relaxation and non-Gaussian times decouple from diffusion at low temperatures.

Dynamic heterogeneity is confirmed in the system below the phase transition temperature.

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.