Correlation effects and super-Arrhenius diffusion in binary Lennard-Jones mixtures

An underlying Arrhenius temperature dependence of the diffusion constant can be extracted from the fragile, super-Arrhenius diffusion of a binary Lennard-Jones mixture. The Arrhenius form is found by considering time intervals and temperatures where diffusive motion is present but the system is nonergodic, with averages taken over an ergodic trajectory. The Arrhenius diffusion can be related to the true super-Arrhenius behavior by a factor that depends on the average angle between steps in successive time intervals. This correction factor accounts for the fact that on average, successive displacements are negatively correlated. This negative correlation can be linked directly with the higher apparent activation energy for diffusion in fragile glass formers at lower temperature. Arrhenius dependence of the diffusion constant for nonergodic systems is found over a range of time scales. As time intervals are increased, the time windows become long enough to register negative correlation and the correction decreases. The Arrhenius form changes with time as ergodicity is approached and this change can be characterized by the variation in gradient and intercept with time. We introduce a formalism to describe super-Arrhenius behavior based on Arrhenius and non-Arrhenius contributions to the diffusion constant.