Relation between the Widom line and the 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 τα. For water simulated with two different potentials, TIP5P and ST2, 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 Dτα/T collapse onto a single “master curve” if temperature is replaced by T − T W(P). 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) as T → T W(P) appears to be well correlated both with the breakdown of the Stokes–Einstein relation and with the growth of dynamic heterogeneities. Our results are consistent with the possibility that the breakdown of the SE relation in supercooled water at low pressures is associated with the hypothesized liquid–liquid phase transition.