Generalized M-diffusion model of molecular rotations

Abstract

The widely used M-model of rotational diffusion of molecules in fluid phases is generalized. The ordinary M-model assumes that intermolecular collisions cause instantaneous changes in the orientation of an otherwise free rotor. The present scheme takes cognizance of the ubiquitous intermolecular torques which should make the molecular orientation a continuously variable random function of time. It is assumed here that the component of the angular velocity, which is conjugate to the angle specifying the orientation of the molecule, is a stationary Gaussian-Markov process. The ordinary M-model emerges then as a special case of the more general treatment presented here. The results derived for the dipole correlation function of a linear rotor on the basis of the generalized scheme are applied to a series of infrared data. The observed agreement is highly satisfactory. The present analysis affords a justification for the Gordon scheme which generalizes the M-model by assigning to the mean rate of collision an ad-hoc dependence on the angular speed of the rotor. It is argued also that the model treated here incorporates certain memory effects which are ignored in the ordinary M-model, and may yield, in some cases, results which are similar to those based on certain memory function formalisms.