New relation between diffusion and free volume: I. Predicting gas diffusion

Abstract

It has been widely accepted that the gas diffusion through a glassy polymer can be related to the fractional free volume of the polymer through the Doolittle relation D = A exp(−B/f) where f is the fractional free volume and A and B are constants. As the free volume increases and pores become connected and bi-continuous the Doolittle relation does not adequately model the experimental data. By adding newly available high free volume polymers to Park and Paul's large database of 105 polymers, an empirically determined relation of the form D = α exp(βf), with α and β as constants, is shown to model all of the data well. The new relation also agrees with a variety of computer simulations. Plausible reasons for the better fit of this new relation over a wide range of f are postulated. The practical utility of the new relation is that it can be used as an efficient tool for predicting transport properties in the wide range of available polymers based on one readily obtainable material characteristic, namely, fractional free volume. In addition, in Part II of this work the new relation is shown to provide an exact solution to the vacancy diffusion equation allowing thin film physical aging to be accurately and easily modelled.