Conservation of the Stokes-Einstein Relation in Supercooled Water

TL;DR

This study demonstrates through molecular dynamics simulations that the original Stokes-Einstein relation remains valid in supercooled water, challenging previous claims of its breakdown based on variants of the relation.

Contribution

It clarifies that the original SE relation is conserved in supercooled water, attributing previous perceived violations to the use of approximate variants.

Findings

Both Einstein and Stokes relations are conserved in supercooled water.

The apparent breakdown is due to wavevector dependence and decreasing effective radius.

Inconsistencies may also occur in other supercooled liquids.

Abstract

The Stokes-Einstein (SE) relation is commonly regarded as being breakdown in supercooled water. However, this conclusion is drawn upon testing the validities of some variants of the SE relation rather than its original form, and it appears conflicting with the fact that supercooled water is in its local equilibrium. In this work, we show by molecular dynamics simulation that both the Einstein and Stokes relations are indeed conserved in supercooled water. The inconsistency between the original SE relation and its variants comes from two facts: (1) the substitutes of the shear viscosity in the SE variants are wavevector-dependent, so it is only a cursory approximation; (2) the effective hydrodynamic radius actually decreases with decreasing temperature, instead of being a constant as assumed in the SE variants. Besides supercooled water, this inconsistency may also exist in other supercooled liquids.