Appearance of a fractional Stokes–Einstein relation in water and a structural interpretation of its onset

Abstract

The Stokes–Einstein equation relates the self-diffusion constant of a liquid with the mobility of its constituents. In water, however, the relation has to be modified for temperatures below ∼290 K. A combined experimental and numerical investigation suggests that this behaviour results from a specific change in the local water structure. The Stokes–Einstein relation has long been regarded as one of the hallmarks of transport in liquids. It predicts that the self-diffusion constant D is proportional to (τ/T)−1, where τ is the structural relaxation time and T is the temperature. Here, we present experimental data on water confirming that, below a crossover temperature T×≈ 290 K, the Stokes–Einstein relation is replaced by a ‘fractional’ Stokes–Einstein relation D∼(τ/T)−ζ with ζ≈3/5 (refs 1, 2, 3 4, 5, 6). We interpret the microscopic origin of this crossover by analysing the OH-stretch region of the Fourier transform infrared spectrum over a temperature range from 350 down to 200 K. Simultaneous with the onset of fractional Stokes–Einstein behaviour, we find that water begins to develop a local structure similar to that of low-density amorphous solid H2O. These data lead to an interpretation that the fractional Stokes–Einstein relation in water arises from a specific change in the local water structure. Computer simulations of two molecular models further support this interpretation.