# Identifying time scales for violation/preservation of Stokes-Einstein relation in supercooled water

## TL;DR

This study identifies specific time scales responsible for the violation or preservation of the Stokes-Einstein relation in supercooled water, linking it to structural and stress relaxation dynamics and the emergence of solidity.

## Contribution

The paper provides a comprehensive simulation analysis that classifies time scales affecting the Stokes-Einstein relation, revealing the physical origins of its violation in supercooled water.

## Key findings

- Two classes of time scales determine SE relation behavior.
- SE violation linked to increased plateau modulus and stress relaxation nonexponentiality.
- Mechanism of violation associated with supercooled solidity and dynamic heterogeneity.

## Abstract

The violation of Stokes--Einstein (SE) relation $D\sim (\eta/T)^{-1}$ between the shear viscosity $\eta$ and the translational diffusion constant $D$ at temperature $T$ is of great importance for characterizing anomalous dynamics of supercooled water. Determining which time scales play key roles in the SE violation remains elusive without the measurement of $\eta$. Here we provide comprehensive simulation results of the dynamic properties involving $\eta$ and $D$ in TIP4P/2005 supercooled water. This enabled the thorough identification of the appropriate time scales for SE relation $D\eta/T$. In particular, it is demonstrated that the temperature dependence of various time scales associated with structural relaxation, hydrogen bond breakage, stress relaxation, and dynamic heterogeneities can be definitely classified into only two classes. That is, we propose the generalized SE relations that exhibit "violation" or "preservation". The classification depends on the examined time scales that are coupled or decoupled with the diffusion. On the basis of the classification, we explain the physical origins of the violation in terms of the increase in the plateau modulus and the nonexponentiality of stress relaxation. This implies that the mechanism of SE violation is attributed to the attained solidity upon supercooling, which is in accord with the growth of non-Gaussianity and spatially heterogeneous dynamics.