Study of ``Non-Fickian'' Diffusion Anomalies through Time Lags. I. Some Time-Dependent Anomalies

Abstract

The importance of permeation time‐lag measurements for the detection and study of ``anomalous'' diffusion in a simple way is discussed. Measurement of a total of four time‐lag quantities is proposed and their properties investigated for time‐dependent ``non‐Fickian'' behavior, particularly in polymer—penetrant systems near and below the glass‐transition temperature. Detailed calculations were carried out for this case, on the basis of the widely accepted view that the ``non‐Fickian'' anomalies observed are due largely to reversible structural relaxation processes in the substrate. The predicted behavior of the time lag as a function of penetrant concentration exhibits certain general features, which should be of use for the identification of this kind of ``non‐Fickian'' anomaly. Time‐dependent ``non‐Fickian'' anomalies in substrates, where immobilizing chemical reaction or diffusion into sinks can occur independently of a main ``Fickian'' diffusion process, have also been examined. Such anomalies appear to have no effect on any of the time‐lag parameters considered here.