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The fractional Stokes-Einstein equation: application to Lennard-Jones, molecular, and ionic liquids.

The fractional Stokes-Einstein (FSE) relation, (D/T) proportional to eta(-t), is shown to well correlate the molecular dynamics results of Meier et al. [J. Chem. Phys. 121, 3671 (2004); ibid. 121, 9526 (2004)] for the viscosity (eta) and self-diffusion coefficient (D) of the Lennard-Jones fluid in the liquid and dense supercritical states, with the exponent t = (0.921+/-0.003). The Stokes-Einstein number n is viscosity dependent: ln n = const + (t - 1)ln eta. Molecular and ionic liquids for which high-pressure transport property data are available in the literature are shown to exhibit the same behavior with 0.79 < t < 1. Water is also shown to fit the FSE at atmospheric pressure, with a change in exponent t from 0.94 to 0.67 at about 258 K (265 K for D(2)O), but the FSE holds only approximately at high pressures. It sometimes argued that FSE in supercooled liquids near the glass transition is a diagnostic for dynamic heterogeneity, but this work shows that the FSE holds in normal liquids far from the glass transition. This result may provide a reference for complex liquids such as viscous glass formers that show a transition (dynamic crossover) in the temperature dependence of the viscosity and network-bonded liquids such as water.