Dynamical heterogeneities and the breakdown of the Stokes-Einstein and Stokes-Einstein-Debye relations in simulated water

We study the Stokes-Einstein (SE) and the Stokes-Einstein-Debye (SED) relations using 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 (DH), 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 the 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, $D_t\sim(\tau/T)^{-\xi_t}$ and $D_r\sim(\tau/T)^{-\xi_r}$ where $\xi_t\approx0.84<1$ and $\xi_r\approx0.75<1$. We also find that there is a decoupling between rotational and translational motion, and that this decoupling occurs in both fastest and slowest subsets of molecules. We also find that when the decoupling increases, upon cooling, 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 are originated at the time scale corresponding to the end of the cage regime, when diffusion starts. This is also the time scale when the DH are more relevant.