Dynamical heterogeneity in a highly supercooled liquid under a sheared situation.

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 ξ(4)(t), the intensity χ(4)(t), and the lifetime τ(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 = τ(α) and τ(ngp); τ(α) is the α-relaxation time, and τ(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 (ξ(4)(t), χ(4)(t), and τ(hetero)(t)) decrease as the shear rate γ of the steady shear flow increases. For the time interval t = τ(α), the scalings ξ(4)(τ(α))~γ(-0.08), χ(4)(τ(α))~γ(-0.26), and τ(hetero)(τ(α))~γ(-0.88) were obtained. The steady shear flow suppresses the heterogeneous structure as well as the lifetime of the dynamical heterogeneity. In addition, we demonstrated that all three quantities in the sheared non-equilibrium state can be mapped onto those in the equilibrium state through the α-relaxation time τ(α). This finding means that the same relation between τ(α) and three quantities holds in both the equilibrium state and the sheared non-equilibrium state and therefore proposes that the dynamical heterogeneity can play a similar role in the drastic change of τ(α) due to not only the temperature but also the shear rate.