Solute rotation in polar liquids: microscopic basis for the Stokes-Einstein-Debye model.

Here, we develop a framework for a molecular level understanding of the celebrated Stokes-Einstein-Debye (SED) formula. In particular, we explore reasons behind the surprising success of the SED model in describing dipolar solute rotation in complex polar media. Relative importance of solvent viscosity and solute-solvent dipolar interaction is quantified via a self-consistent treatment for the total friction on a rotating solute where the hydrodynamic contribution is modified by the friction arising from the longer ranged solute-solvent dipolar interaction. Although the solute-solvent dipolar coupling is obtained via the Mori-Zwanzig formalism, the inclusion of solvent structure via the wave vector dependent viscosity in the hydrodynamic contribution incorporates solvent molecularity in the present theory. This approach satisfactorily describes the experimental rotation times measured using a dipolar solute, coumarin 153 (C153), in protic and aprotic polar liquids, and more importantly, provides microscopic explanation for insignificant contribution of electrical interactions on solute rotation, in contrast to the substantial role played by the translational dielectric friction in the context of ionic mobility. It is also discussed on how the present theory can be suitably extended to study the rotation of a realistic solute in media other than dipolar solvents.