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.