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

The usual explanation for the observed inverse relation between the orientational correlation time (tau (R)) and 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 tau (R) and 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 and force-force time correlation functions on the solute probe. Our analysis shows that the orientational correlation time (tau (R)) is inversely proportional to the translational diffusion coefficient (D-0) of the solvent molecules. Thus, the viscosity dependence of orientational correlation time enters through the viscosity dependence of the translational diffusion (D-0). 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, D-0, of the solvent molecules. This result is in agreement with the recent computer simulation results which show that the product of tau (R) and 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. (C) 2001 American Institute of Physics.