Bimodal angular hopping model for molecular rotations in liquids

We examine an assortment of properties associated with molecular rotational relaxation in supercooled liquids, in particular relaxation of a spherical harmonic of order l. First, we have fitted the observed phenomena by a procedure employing a two-exponential memory function. We assume strong torques, and we can then obtain semiquantitative descriptions of the librational oscillations, of the low viscosity (αβ) relaxation, and of the high viscosity α and β relaxations; we find the α relaxation to be independent of l, as measured, and we predict the β relaxation to be strongly dependent upon l and to be the dominant (αβ) process at low viscosity. Second, we have associated one of the exponentials in the memory function, the larger more rapidly decaying one, with the relaxation of strong effective torques which are associated with β relaxation and with the librational motions; the other exponential is associated with weak effective torques and is responsible for the α relaxation. In order to gain insight, we have then introduced an ‘‘effective’’ anisotropic potential with two components, one with shallow, angularly closely spaced and narrow wells, which is associated with the strong ‘‘effective’’ torques, and one with deeper, angularly widely spaced and broad wells, which is associated with the weak effective torques.