Modeling of gas permeation through polyurethane/polyvinyl acetate/polyethylene oxide–polypropylene oxide blend membranes

The permeability of a two-phase polymer system with weak interactions can be determined with the logarithmic additive model proposed by Min and Paul [1]:LnPblend 1Ln(P1) 2Ln(P2) (1) Where Pblend is the blend gas permeability, 1  and 2  are thevolume fractions of polymer 1 and 2 in the blend, and P1 and P2 are the permeabilities of the pure polymers 1 and 2. A model was adopted which treats the interfacial blockcopolymer regions (Pluronic) as a distinct third phase in the blend. Equation 1 was modified to account for this third phase [2]: LnP blend 1Ln(P1) 2Ln(P2) 3Ln(P3) (2)Where 3  and P3 are the volume fraction and permeability of the interfacial region, related to the block copolymer. If the diffusion process obeys Fick’s law, and the downstream pressure is much less than upstream pressure, the permeability of gas A is given by [3]:PA = SA.DA (3) Where DA is the average effective diffusivity through the film, and SA is the apparent sorption coefficient.Gas transport properties in a semi-crystalline polymer are usually modelled assuming that the crystals act as an impermeable dispersed phase imbedded in an amorphous phase. The gas permeabilityin semi-crystalline blends can be calculated by [3]:    2 . a PA PA , a (4) Where φa is the amorphous phase volume fraction in the blend, and γ is the effective chain immobilization factor. In this study, the experimental gas permeabilities in Polyurethane(PU)/Polyvinyl acetate (PVAc)/Pluronic blends with 15 % (wt) PVAc are predicted with the modified logarithmic additive model