Diffusion and viscosity in a supercooled polydisperse system

We have carried out extensive molecular dynamics simulations of a supercooled polydisperse Lennard-Jones liquid with large variations in temperature at a fixed pressure. The particles in the system are considered to be polydisperse in both size and mass. The temperature dependence of dynamical properties such as the viscosity $\left(\eta \right)$ and the self-diffusion coefficients ${(D}_i)$ of different size particles is studied. Both viscosity and diffusion coefficients show super-Arrhenius temperature dependence and fit well to the well-known Vogel-Fulcher-Tammann equation. Within the temperature range investigated, the value of Angell’s fragility parameter $(D\approx 1.4)$ classifies the present system as a very fragile liquid. The critical temperature for diffusion ${(T}_o^{D_i})$ increases with the size of the particles. The critical temperature for viscosity ${(T}_o^{\eta })$ is larger than that for diffusion, and sizable deviations appear for the smaller size particles, implying a decoupling of translational diffusion from viscosity in deeply supercooled liquids. Indeed, the diffusion shows markedly non-Stokesian behavior at low temperatures where a highly nonlinear dependence on size is observed. An inspection of the trajectories of the particles shows that at low temperatures the motions of both the smallest and largest size particles are discontinuous (jump type). However, the crossover from continuous Brownian to large length hopping motion takes place at shorter time scales for the smaller size particles.