Fractional Stokes–Einstein relation in TIP5P water at high temperatures

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 T_x = 510 K. The D ∼ τ ⁻¹ is in a fractional form as D ∼ τ^ξ with ξ = −2.09 for T ≤ T_x and otherwise ξ = −1.25. The D ∼ T/τ is valid with ξ = −1.01 for T ≤ T_x but in a fractional form for T > T_x. The Stokes–Einstein relation D ∼ T/η is satisfied below T_x = 620 K but in a fractional form above T_x. 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. (paper)