A transport model for sorption and desorption of penetrants in glassy polymer membrane

The transport of penetrants in glassy polymer membranes is assumed to be a process of mixing of penetrant and polymer molecules accompanied by a creep strain of polymer membrane. The stress–strain relation of polymer membrane and its contribution to total Gibbs free energy are calculated by the Voigt creep model of linear viscoelastic solids. The contribution due to mixing of polymer and sorbed penetrant is calculated by Flory–Huggins model. Combining with the mass conservation equation and phenomenological diffusive flux expression, a transport model of penetrant in glassy polymer membrane is then established. The effective diffusion coefficient of penetrants in membrane which is time- and place-dependent is obtained by comparing with Fickian diffusion law. The numerical simulation of integral sorption shows that this model can describe various sorption and desorption curves including sigmoid-type curves. In general case, three adjustable model parameters are used to correlate the sorption curve. Corresponding desorption curve can then be predicted. If the Youngʹs modulus and Flory–Huggins interaction parameter are obtained from other independent experiment, only one adjustable parameter is needed. The correlated and predicted results agree well with the experimental sorption and desorption curves of water and ethanol in polyimide membranes. It is shown that this model is more flexible and require fewer model parameters as comparing with Crank model.