Free Volume Concepts Connecting PVT Behavior and Gaseous Diffusion Through Polymers

Abstract

Free volume concepts in polymers, originally suggested by Bueche, have been modified and extended and now generate a good equation of state for polymers above Tg. This paper is concerned with the extension of the concepts to describe gaseous diffusion. In order to do this, the notion of activated diffusion was introduced. A gas molecule in a matrix can jump under three conditions. (1) A hole opens next to it (from segmental oscillations of the polymer) large enough to allow the molecule to jump (passive diffusion). (2) A hole opens which is smaller than the gas molecule, but the kinetic energy of the gas molecule allows it to open the hole and jump by compressing neighboring segments (activation). Once compressed, the segments cannot relax on the segmental oscillation time scale, and thus can assist the gas molecule to jump into other small holes (activated diffusion). The segments at the old site relax, but the segments around the new site are now compressed. This continues until a hole as large or larger than the gas molecule opens. The jump into such a hole allows all segments to relax (deactivation). This approach was successful in correlating diffusivity with activation energy for a wide variety of penetrants in polyethylene and poly(vinyl acetate). It also reproduced the non‐Arrhenius change in diffusivity with temperature for diffusion in rubber using the same constants. This paper gives the initial formulation for diffusion, but much work still needs to be done.