Breakdown of the Stokes-Einstein Relation in Supercooled Water

TL;DR

This study investigates the breakdown of the Stokes-Einstein relation in supercooled water, revealing its correlation with the Widom line, dynamic heterogeneities, and local structural changes near the temperature of maximum specific heat.

Contribution

It demonstrates the collapse of diffusion and relaxation data onto master curves when using the Widom line temperature, linking dynamic heterogeneities and structural transitions in supercooled water.

Findings

Breakdown of the Stokes-Einstein relation correlates with the Widom line.

Mobile molecule clusters grow sharply near the Widom line.

Results for diffusion and relaxation times agree with experimental data.

Abstract

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.