The breakdown of the Stokes-Einstein relation in supercooled binary liquids

Using reverse non-equilibrium molecular dynamics simulations, we report the calculation of the shear viscosity and the tracer diffusion coefficient of a binary Lennard-Jones mixture that is known as a model glass-former. Several remarkable temperatures are well reproduced in our calculations, i.e. T-S (the onset of slow dynamics), T-c (the critical temperature predicted by the mode-coupling theory) and T-K (the Kauzmann temperature). A breakdown of the Stokes-Einstein relation is found at temperature T-S. We propose that, at low temperatures below T-S, the size of single-particle positional fluctuations between particle-hopping events corresponds to the length measured by the Stokes-Einstein relation, which is equated to the hydrodynamic radius of particles at high temperatures.