Fractional Stokes–Einstein relation in TIP5P water at high temperatures**Project supported by the National Natural Science Foundation of China (Grant No. 2153200) and the China Postdoctoral Science Foundation (Grant No. 2016M602712).

Abstract

Fractional Stokes–Einstein relation described by D ∼ (τ/T)ξ is observed in supercooled water, where D is the diffusion constant, τ the structural relaxation time, T the temperature, and the exponent ξ ≠ −1. In this work, the Stokes–Einstein relation in TIP5P water is examined at high temperatures within 400 K–800 K. Our results indicate that the fractional Stokes–Einstein relation is explicitly existent in TIP5P water at high temperatures, demonstrated by the two usually adopted variants of the Stokes–Einstein relation, D ∼ τ−1 and D ∼ T/τ, as well as by D ∼ T/η, where η is the shear viscosity. Both D ∼ τ−1 and D ∼ T/τ are crossed at temperature Tx = 510 K. The D ∼ τ−1 is in a fractional form as D ∼ τξ with ξ = −2.09 for T ≤ Tx and otherwise ξ = −1.25. The D ∼ T/τ is valid with ξ = −1.01 for T ≤ Tx but in a fractional form for T > Tx. The Stokes–Einstein relation D ∼ T/η is satisfied below Tx = 620 K but in a fractional form above Tx. We propose that the breakdown of D ∼ T/η may result from the system entering into the super critical region, the fractional forms of D ∼ τ−1 and D ∼ T/τ are due to the disruption of the hydration shell and the local tetrahedral structure as well as the increase of the shear viscosity.