Prediction of gas permeability of block-segregated polymeric membranes by an effective medium model

Abstract

A complete series of aliphatic aromatic copoly(ether-imide)s, based on aromatic dianhydrides (BPDA, BKDA or PMDA) and mixtures of an aromatic diamine (ODA) and an aliphatic diamine terminated poly(ethylene oxide) PEO(2000) (Mw=2000 g/mol) or PEO(6000) (Mw= 6000 g/mol), has been synthesized using different PEO contents. Cast films of these copolymers have been thermally treated to ensure the segregation of the linear PEO chains from the aromatic portion of these copoly(ether-imide)s. Gas permeability (O2, N2, CO2 and CH4) of membranes, made from these copolymers with different proportions of PEO, were compared with the predictions of various electrical or thermal conductivity models adapted to gas permeability. Several of these models, from Maxwell-Garnett to percolation theory, proved to be inaccurate. Nevertheless, the model based on the Effective Medium Approximation (EMA) is proved here to succeed in predicting the main features of the experimental results for all mixture proportions, taking as the starting point the sole input of pure homopolymer permeabilities. Specifically, this later method was able to calculate the volume fraction for the maximum increase of permeability, a common feature for all the studied segregated copolymer membranes. The model was even able to predict the permeabilities of a three phase system consisting in the aromatic (BKDA-ODA) phase plus a mixture of amorphous PEO(6000) and crystalline PEO(6000).