Breakdown of the Stokes-Einstein Relation in Supercooled Water

Supercooled water exhibits a breakdown of the Stokes-Einstein relation between the diffusion constant $D$ and the alpha relaxation time $\tau_{\alpha}$. For water simulated with the TIP5P and ST2 potentials, we find that the temperature of the decoupling of diffusion and alpha relaxation correlates with the temperature of the maximum in specific heat that corresponds to crossing the Widom line $T_W(P)$. Specifically, we find that our results for $D\tau_{\alpha}/T$ collapse onto a single master curve if temperature is replaced by $T-T_W(P)$, where $T_W(P)$ is the temperature where the constant-pressure specific heat achieves a maximum. Also, we find agreement between our ST2 simulations and experimental values of $D\tau_{\alpha}/T$. We further find that the size of the mobile molecule clusters (dynamical heterogeneities) increases sharply near $T_W(P)$. Moreover, our calculations of mobile particle cluster size $<n(t^*)>_w$ for different pressures, where $t^*$ is the time for which the mobile particle cluster size is largest, also collapse onto a single master curve if $T$ is replaced by $T-T_W(P)$. The crossover to a more locally structured low density liquid (LDL) environment as $T\to T_W(P)$ appears to be well correlated with both the breakdown of the Stokes-Einstein relation and the growth of dynamic heterogeneities.