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Abstract:
We study the Stokes-Einstein SE and the Stokes-Einstein-Debye SED relations, Dt=kBT/6R and Dr=kBT/8R3, where Dt and Dr are the translational and rotational diffusivity, respectively, T is the temperature,
the viscosity, kB the Boltzmann constant, and R the “molecular” radius. Our results are based on
molecular dynamics simulations of the extended simple point charge model of water. We find that both the SE
and SED relations break down at low temperature. To explore the relationship between these breakdowns and
dynamical heterogeneities DHs, we also calculate the SE and SED relations for subsets of the 7% “fastest”
and 7% “slowest” molecules. We find that the SE and SED relations break down in both subsets, and that the
breakdowns occur on all scales of mobility. Thus these breakdowns appear to be generalized phenomena, in
contrast with a view where only the most mobile molecules are the origin of the breakdown of the SE and SED
relations, embedded in an inactive background where these relations hold. At low temperature, the SE and SED
relations in both subsets of molecules are replaced with “fractional” SE and SED relations, Dt /T
−t and
Dr /T
−r, where t0.841 and r0.751. We also find that there is a decoupling between rotational
and translational motion, and that this decoupling occurs in both the fastest and slowest subsets of
molecules. Further, we find that, the decoupling increases upon cooling, but that the probability of a molecule
being classified as both translationally and rotationally fastest also increases. To study the effect of time scale
for SE and SED breakdown and decoupling, we introduce a time-dependent version of the SE and SED
relations, and a time-dependent function that measures the extent of decoupling. Our results suggest that both
the decoupling and SE and SED breakdowns originate at a time scale corresponding to the end of the cage
regime, when diffusion starts. This is also the time scale when the DHs are more relevant. Our work also
demonstrates that selecting DHs on the basis of translational or rotational motion more strongly biases the
calculation of diffusion constants than other dynamical properties such as relaxation times.
