Relation between orientational correlation time and the self-diffusion coefficient of tagged probes in viscous liquids: a density functional theory analysis

Abstract

The usual explanation for the observed inverse relation between the orientational correlation time (τ_R); the self-diffusion (D_S) of a tagged solute probe in a viscous liquid is in terms of the hydrodynamic relations which are known to have dubious conceptual validity for small molecules. Here; we present a microscopic derivation of the relation between τ_R; D_S. This derivation is based on the general ideas of the mode coupling theory; but uses the time-dependent density functional theory to obtain the torque-torque; force-force time correlation functions on the solute probe. Our analysis shows that the orientational correlation time (τ_R) is inversely proportional to the translational diffusion coefficient (D₀) of the solvent molecules. Thus; the viscosity dependence of orientational correlation time enters through the viscosity dependence of the translational diffusion (D₀). The same theoretical analysis also shows that the translational diffusion coefficient of the solute probe (D_S) is also proportional to the translational diffusion coefficient; D₀; of the solvent molecules. This result is in agreement with the recent computer simulation results which show that the product of τ_R; D_S is a weak function of the density (hence of the viscosity) of the liquid. The microscopic expressions provide explanation; in terms of the solute-solvent direct correlation functions; the reason for the sensitivity of orientational diffusion to solute-solvent interaction potential.