Relaxation processes in liquids: Variations on a theme by Stokes and Einstein

We investigate numerically the temperature and density dependence of the Stokes-Einstein ratio, Dη/T, and of two commonly-used variants thereof, Dτ and Dτ/T, where D is a diffusivity, η the shear viscosity, and τ a structural relaxation time. We consider a family of atomic binary mixtures with systematically-softened repulsive interactions, and the Lewis-Wahnström model of ortho-terphenyl (OTP). The three quantities grow significantly as the temperature decreases in the supercooled regime, a well-known phenomenon. At higher temperatures, Dτ exhibits negative violations of Stokes-Einstein behavior, i.e., decrease upon cooling, for the atomic systems, though not for OTP. We consider two choices for the relaxation time, one based on the decay of the self-intermediate scattering function, and the other on the integral of the stress autocorrelation function. The instantaneous shear modulus exhibits appreciable temperature dependence for the two classes of systems investigated here. Our results suggest that commonly-invoked assumptions, such as τ ∼ η and τ ∼ η/T, should be critically evaluated across a wide spectrum of systems and thermodynamic conditions. We find the Stokes-Einstein ratio, Dη/T, to be constant across a broad range of temperatures and densities for the two classes of systems investigated here.