Excess entropy determines the applicability of Stokes-Einstein relation in simple fluids

Abstract

The Stokes-Einstein (SE) relation between the self-diffusion and shear viscosity coefficients operates in sufficiently dense liquids not too far from the liquid-solid phase transition. By considering four simple model systems with very different pairwise interaction potentials (Lennard-Jones, Coulomb, Debye-Hückel or screened Coulomb, and the hard sphere limit) we identify where exactly on the respective phase diagrams the SE relation holds. It appears that the reduced excess entropy $s_{\mathrm{ex}}$ can be used as a suitable indicator of the validity of the SE relation. In all cases considered the onset of SE relation validity occurs at approximately $s_{\mathrm{ex}}\lesssim -2$. In addition, we demonstrate that the line separating gas-like and liquid-like fluid behaviours on the phase diagram is roughly characterized by $s_{\mathrm{ex}}\simeq -1$.

12 pages, 5 figures

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