(130c) Permeability and Solubility of CO2 in Glassy Polymeric Membranes With and Without Plasticization: A Thermodynamic Approach
The description of permeability and diffusivity of gases and vapors in glassy polymeric membranes has been obtained using a simple fundamental approach, which has been tested on a variety of different systems, and proved effective in all cases, with and without plasticization. The model relies on a notorious expression for the diffusive flux as the product of a kinetic factor, mobility, and a thermodynamic factor, associated to the concentration dependence of the chemical potential of the diffusing species. The latter factor can be obtained experimentally from solubility isotherm data, or can be evaluated theoretically by means of the well-known predictive procedures, as for instance the nonequilibrium lattice fluid (NELF) model or other equation-of-state models following the Non Equilibrium Thermodynamics for Glassy Polymers. On the other hand, the mobility factor is endowed with an exponential dependence on penetrant concentration, following the usual trend commonly found experimentally. Consequently, the resulting general permeability model contains only the two adjustable parameters entering the expression for mobility.
The solubility of the penetrant gas in the glassy membrane can be evaluated in a straightforward way through the NELF model, which proved appropriate to describe all the existing experimental sorption data for all the systems considered in this work, also in the presence of important swelling effects.
The final result is a rather simple and general expression for penetrant permeability, which contains at most two adjustable parameters: the gas mobility at infinite dilution and the coefficient characterizing the concentration dependence of mobility itself (plasticization factor). The model describes rather carefully the pressure dependence of permeability of CO2 and other penetrants observed in a variety of different glassy polymers under steady state permeation, even in the presence of the so-called plasticization effects.
Remarkably, the same model parameters not only describe steady state permeation, but also describe the mass uptake versus time resulting from transient diffusivity, in all the cases inspected.
The present model has been tested with success for CO2 permeability in several pure polymers as well as in a variety of complex heterogeneous systems, such as blends, random copolymers, glassy matrices with different degrees of crosslinks, and, further, in matrices additioned with low molecular weight species.
The case of highly plasticizing penetrants, as for instance hydrocarbons, in glassy polymers is also investigated, and the model proved his ability in describing the experimental trends.
Finally, it is also observed that the two parameters of the model follow general trends useful for predictive purposes. In particular, CO2 mobility at infinite dilution correlates very well with the fractional free volume of the glassy matrix, while the plasticization factor correlates very well with the penetrant-induced polymer swelling.