Dynamical Heterogeneity in a Highly Supercooled Liquid under a Sheared Situation

Abstract

In the present study, we performed molecular-dynamics simulations and investigated dynamical heterogeneity in a supercooled liquid under a steady shear flow. Dynamical heterogeneity can be characterized by three quantities: the correlation length ${\xi }_4(t)$, the intensity ${\chi }_4(t)$, and the lifetime ${\tau }_{\text{hetero}}(t)$. We quantified all three quantities by means of the correlation functions of the particle dynamics, i.e., the four-point correlation functions, which are extended to the sheared condition. Here, to define the local dynamics, we used two time intervals $t={\tau }_{\alpha }$ and ${\tau }_{\text{ngp}}$; ${\tau }_{\alpha }$ is the $\alpha$-relaxation time, and ${\tau }_{\text{ngp}}$ is the time at which the non-Gaussian parameter of the Van Hove self-correlation function is maximized. We discovered that all three quantities (${\xi }_4(t)$, ${\chi }_4(t)$, and ${\tau }_{\text{hetero}}(t)$) decrease as the shear rate $\dot{\gamma }$ of the steady shear flow increases. For the time interval $t={\tau }_{\alpha }$, the scalings ${\xi }_4({\tau }_{\alpha })\sim {\dot{\gamma }}^{-0.08}$, ${\chi }_4({\tau }_{\alpha })\sim {\dot{\gamma }}^{-0.26}$, and ${\tau }_{\text{hetero}}({\tau }_{\alpha })\sim {\dot{\gamma }}^{-0.88}$ were obtained. The steady shear flow suppresses the heterogeneous structure as well as the lifetime of the dynamical heterogeneity. In addition, our results demonstrated that the $\alpha$-relaxation time ${\tau }_{\alpha }$ dependences of three quantities coincide with those at equilibrium. This means that all three quantities of the dynamical heterogeneity can be mapped onto those in the equilibrium state through ${\tau }_{\alpha }$.

11 pages, 10 figures

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