Revisiting the Stokes-Einstein relation without a hydrodynamic diameter

We present diffusion coefficient and shear viscosity data for the Lennard-Jones fluid along nine isochores above the critical density, each involving a temperature variation of roughly two orders of magnitude. The data are analyzed with respect to the Stokes-Einstein (SE) relation, which breaks down gradually at high temperatures. This is rationalized in terms of the fact that the reduced diffusion coefficient D̃ and the reduced viscosity η̃ are both constant along the system’s lines of constant excess entropy (the isomorphs). As a consequence, D̃η̃ is a function of T/TRef(ρ) in which T is the temperature, ρ is the density, and TRef(ρ) is the temperature as a function of the density along a reference isomorph. This allows one to successfully predict the viscosity from the diffusion coefficient in the studied region of the thermodynamic phase diagram.