Molecular Theory of Diffusion Constants in Liquids

Abstract

A molecular theory of diffusion constants in liquids, independent of model, is developed in the language of time-dependent correlation functions and statistical projection operators. Diffusion constants are related to friction constants which in turn depend upon force autocorrelation functions with a time dependence arising from a Liouville operator projected orthogonally to the momentum. The resulting expressions are related to those previously obtained and the ``projected'' friction constants are related to those connected with the dissipation of momentum, i.e., those considered by Kirkwood. The influence of molecular translations on spin relaxation in liquids is analyzed from the same molecular-statistical viewpoint, and the effect of diffusion on both spin-echo experiments and on intermolecular magnetic dipolar relaxation are discussed. The behavior of diffusion phenomena at critical points is also considered, and emphasis is placed on the distinction between particle (self-) and concentration (mutual) diffusion. The theory, it is hoped, represents a simple, coherent molecular-statistical treatment of most of the commonly encountered diffusion phenomena.