A model for diffusion in a glassy polymer

Abstract

A new technique for estimating diffusion rates in solid materials from transient sorption data was developed and applied to the diffusion of gases in polymer films. Specifically, the analysis developed here applies to solutes which are sorbed according to a particular isotherm: one described by a linear component (Henry's law) and a commonly observed nonlinear component (Langmuir equation). The linear component corresponds physically to gas dissolved in the amorphous regions of the polymer; the nonlinear, to gas trapped in polymer microvoids, analogous to the adherence of gas molecules to sites on the surface of porous adsorbents.

By using this equilibrium isotherm together with the assumptions that the gas trapped in microvoids is immobilized, and that the driving force for diffusion is the concentration gradient of dissolved molecules, a mathematical description of transient sorption was developed; this diffusion model consisted of a nonlinear partial differential equation. With the use of a finite-difference technique, solutions to the equation were obtained; these were next applied to data for the solution of CO₂ in a one mil “Mylar” polyester film at 40°C. The diffusivity was estimated to be 1.74 × 10⁻⁹ cm.²/sec. and the precision of the method was estimated at ±12%.

In summary, the method developed has been successfully applied, and the proposed diffusion mechanism was thereby validated. It is believed that this method has wide potential applicability not only to the study of diffusion in polymers but also to the measurement of effective diffusivities of gases in porous catalysts.