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Inconsistency between the Stokes-Einstein relation and its variants in supercooled water

The Stokes-Einstein (SE) relation has three commonly used variants: 1 D τ −  , D T τ  and D T η  . In this work, the consistency of the original SE relation and its three variants in supercooled water is examined by molecular dynamics simulation with the TIP5P and Jagla water models, respectively. It is found that the original SE relation remains valid even when the three variants are all invalid in the simulated temperature ranges: 1 D τ −  and D T τ  follow the fractional forms D ξ τ −  and ( ) D T ξ τ −  with a crossover temperature, at which the wavevector-dependent exponent ξ changes its value; D T η  is equivalent to the original SE relation only when the effective hydrodynamic radius a is a constant, which is however found to decrease with decreasing temperature T. Therefore, care should be taken when employing its variants to judge the validity of the original SE relation in supercooled water.