Translational and Rotational Diffusion Near the Glass Transition

Abstract

Diffusional transport is involved in most relaxation processes in condensed matter. In one component systems this transport is usually termed “self- diffusion” since the molecules move among themselves. Nevertheless some kind of labeling must be possible in order to observe “tracer” molecules moving relative to their neighbors. The best labels for self diffusion experiments are nuclear spin states used in the NMR methods described below. In all other techniques, the motion of the tracer molecules is somewhat different from that of the environment and should, strictly speaking, be termed “tracer-diffusion”. The corresponding self- or tracer-diffusion coefficients are related to the mean square displacement of the position r(t) by

$$D = \frac{{\lim }}{{t \to \infty }}\,\{ \langle [r(t) - r(0)]^2 \rangle /6t\} \,,$$

(3.1)

where the brackets denote the ensemble average. For rotational diffusion, the position r(i) is replaced by the orientation Q(t) of some molecule fixed with respect to a space fixed coordinate system.