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∝(η/T)−1, where D is the self-diffusion coefficient and η is the shear viscosity. We first compute the self-intermediate scattering function Fs(k,t), the non-Gaussian parameter α2, and the autocorrelation function of the shear stress Cη(t). The time scales obtained from these functions include the structural relaxation time τα, the peak time of the non-Gaussian parameter τα2, and the shear stress relaxation time τη. We find that τη is coupled with D for all temperatures indicating the SE preservation; however, τα and τα2 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 reflect the presence of regions in which dust particles move faster than the rest when the liquid cools to below the phase transition temperature.