(336c) Thermodynamic Analysis of the Permeability of Gases in Glassy Polymers

 Matteo Minelli, Aweke E. Gemeda, Giulio C. Sarti

Dipartimento di Ingegneria Chimica, Mineraria e delle Tecnologie Ambientali (DICMA)

Alma Mater Studiorum - Università di Bologna, via Terracini 28, 40131, Bologna, Italy.

Permeability and average diffusivity of gases and vapors in glassy membranes are known to vary with upstream pressure. For that dependence the well known Dual Mode Sorption (DMS) model offers valuable and effective expressions which have been successfully used for that purpose over the years. It is known that in several cases the two parameters entering such expressions, i.e. the diffusivities of the dissolved species, D_D, and of the adsorbed species, D_H,  can be retrieved from steady state permeation data and then can be used also for transient transport problems and for time-lag calculations. The DMS expressions, however, are known to hold only in the low pressure range, until the so called plasticization phenomena are not effective; to that aim further parameters would be required to modify the general expressions. In addition, the ability of the DMS model to describe well both steady state and transient behaviors is often not as good as desirable and is sometimes questionable.

Revisiting the permeation behavior of gases and vapors in glassy polymers we have seen that an alternative procedure is possible and preferable, to our opinion. Indeed, by considering another notorious expression of the diffusive flux as the product of the negative mobility (or thermodynamic diffusion coefficient) and chemical potential gradient we obtain a rather simple and general expression containing at most two adjustable parameters: the gas mobility at infinite dilution and the coefficient characterizing the concentration dependence of mobility itself. The two parameters can be retrieved form steady state permeation data at different pressure, as for the DMS model. The new expression with at most two adjustable parameters  allows us to represent rather well both the permeability behavior at all pressures, also in the high pressure range where plasticization is present, as well as the transient behavior.

The effectiveness of the new expression proposed has been checked by using a variety of permeation and sorption data including CO₂ transport in  polycarbonate, in PPO, in PMMA as well as the permeability of different common gases in glassy polymers frequently encountered in different applications.