Heterogeneous diffusion, viscosity, and the Stokes-Einstein relation in binary liquids

Abstract

We investigate the origin of the breakdown of the Stokes-Einstein relation (SER) between diffusivity and viscosity in undercooled melts. A binary Lennard-Jones system, as a model for a metallic melt, is studied by molecular dynamics. A weak breakdown at high temperatures can be understood from the collectivization of motion, seen in the isotope effect. The strong breakdown at lower temperatures is connected to an increase in dynamic heterogeneity. On relevant time scales some particles diffuse much faster than the average or than predicted by the SER. The van Hove self-correlation function allows one to unambiguously identify slow particles. Their diffusivity is even less than predicted by the SER. The time span of these particles being slow particles, before their first conversion to be a fast one, is larger than the decay time of the stress correlation. The contribution of the slow particles to the viscosity rises rapidly upon cooling. Not only the diffusion but also the viscosity shows a dynamically heterogeneous scenario. We can define a "slow" viscosity. The SER is recovered as the relation between slow diffusivity and slow viscosity.

Structural relaxation and highly viscous flow

“…But there is no Debye-Stokes-Einstein mechanism, because there is no viscous flow in the small volume of a single molecule. The mechanism might work at higher temperatures [27], but not close to the glass transition.…”

Curled cation structures accelerate the dynamics of ionic liquids

“…This may be interpreted as the absence of pronounced nanostructural or dynamical heterogeneities in the -range and timescale of the diffusion measurements, which agrees with the findings in the experimental SAXS data and MD simulations. The inherent presence of cage structures in ionic liquids, consisting of ions that are surrounded by ions of opposite charge, is reported to lead to timescale-dependent self-diffusion coefficients 101 found by both experiment 19 and simulations. 25 Therefore, the dynamic heterogeneities and breakdown of the Stokes-Einstein behaviour is expected to be observable only at much lower temperatures or much shorter timescales.…”

Viscosity and transport in a model fragile metallic glass

“…Because Eq. ( 8) has no explicit temperature dependence, it is tempting to interpret it as a breakdown of the Stokes-Einstein relation seen both experimentally [44] and computationally [45] for temperatures up to and beyond the liquidus temperature. Such a breakdown is related to a separation of the bulk viscous and bulk diffusion timescales, which is not the case for our values of D and η-instantaneous quantities that here do not capture the long-time collective properties of LSE activity.…”