Molecular Stokes-Einstein and Stokes-Einstein-Debye relations for water including viscosity-dependent slip and hydrodynamic radius

Abstract

We perform molecular dynamics simulations of liquid water at different temperatures and calculate the water viscosity, the translational and rotational water diffusivities in the laboratory frame as well as in the comoving molecular frame. Instead of interpreting the results as deviations from the Stokes-Einstein and Stokes-Einstein-Debye relations, we describe the translational and rotational diffusivities of water molecules by three models of increasing complexity that take the structural anisotropy of water into account on different levels. We first compare simulation results to analytical predictions for a no-slip sphere and a no-slip ellipsoid. We show that the no-slip sphere can approximate laboratory-frame isotropic translational and rotational diffusivities but fails to describe the anisotropic molecular-frame diffusivities. The no-slip ellipsoid can describe the translational anisotropic molecular-frame diffusivities exactly but fails to describe the translational and rotational anisotropic molecular-frame diffusivities simultaneously. Since an ellipsoidal model with slip boundary conditions is not analytically tractable, we define a heuristic spherical model with tensorial slip lengths and tensorial hydrodynamic radii. We show that this model simultaneously describes the laboratory-frame isotropic translational and rotational diffusivities, as well as, in a restricted viscosity range, the anisotropic molecular-frame diffusivities.