Correlation between fractional free volume and diffusivity of gas molecules in glassy polymers

Abstract

Despite its oversimplifications, the free-volume approach has proven to provide very useful correlative and even semipredictive capabilities. This article is concerned with the correlation between the diffusivity, D, of gas molecules in glassy polymers and the fractional free volume, FFV, determined by the Bondi method. The diffusivities were taken from a database, generated by the authors in connection with work on the new Landolt Börnstein series “Diffusion in Non-Metallic Solids”, which encompasses a very large variety of glassy polymers. For a given diffusant log D is a linear function of 1/FFV as predicted by the free volume theory. However, the deviations from this relationship are significant and strongly correlated between O2, N2, CO2, and CH4. The systematic deviations are opposite to the predicted effect of the polymer jumping unit size in the free-volume concept of Vrentas and Duda and are interpreted in terms of an increase in the activation energy with increasing chain stiffness. Correlation analysis further suggests that the diffusion mechanisms of H2 and particularly of He differ markedly from that of larger gas molecules. Furthermore the influence of the cohesive energy and the glass-transition temperature of the polymers is investigated. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3344–3358, 1999