Collective orientational relaxation in a dense liquid of ellipsoidal molecules

Abstract

A molecular theory of collective orientational relaxation in a dense liquid of non-polar ellipsoidal molecules is presented. The theory is based on an extended hydrodynamic equation which is valid both at long and at small, molecular, length scales. The theory takes into account the intermolecular interactions among the liquid molecules through a force term derived from the density functional theory. We calculate the correlation functions C lm ( k, t) = 〈 Y lm (- k) Y lm ( k, t)〉, where Y lm ( k, t) are the Fourier transformed spherical harmonics and l is the rank of the spherical harmonics. Analytic expressions for these correlation functions are obtained for a pure liquid of ellipsoidal molecules. We find that because of the intermolecular orientational correlations among the ellipsoidal molecules, the relaxation of C 2 m ( k, t) is considerably different from its non-interacting limit. The collective orientational relaxation shows down because of the orientational correlations. This slowing down of the collective orientational relaxation increases with increase in the anisotropy of the molecular shape and also with increase in the density of the liquid. The translational modes of the liquid molecules can greatly accelerate the orientational relaxation at intermediate wavevectors.