Modeling of gas sorption isotherms and kinetics in penetrant-induced melting polymer: poly(hexadecyl methyl siloxane)/alkane system

For the first time, a model is proposed to describe gas sorption in a penetrant-induced melting polymer, based on an ”anti-Langmuir” isotherm equation and the Michaels–Bixler two-phase framework. The model was successfully validated (R2 > 0.9977) using two semicrystalline polymers (poly(tetradecyl methyl siloxane) (PAMS-14) and poly(hexadecyl methyl siloxane) (PAMS-16)) and alkanes (C2H6, C4H10, and C5H12). In addition to our previously published data, we incorporate new experimental measurements of alkane sorption isotherms and kinetics in PAMS-16 obtained in this work. The temperature range covers both the amorphous (25–45 °C) and semicrystalline (5–20 °C) states of PAMS-16, while the gas pressure reached 20 bar to capture three sorption regimes: semicrystalline polymer, penetrant-induced polymer melting, and amorphous polymer. The proposed model allows for the estimation of polymer crystallinity from equilibrium sorption data at various gas pressures and concentrations. Moreover, the developed approach can be readily adapted to other sorption isotherm equations.A kinetic model is also proposed to describe gas mass uptake in a penetrant-induced melting polymer. The resulting model describes experimental two-stage kinetics of ethane sorption in semicrystalline PAMS-16 (R2 > 0.9955). The presented approach enables the decoupling of total mass uptake into sorption within the polymer amorphous phase and within melted crystallites. For small Damköhler numbers, an analytical expression for initial mass uptake was derived, allowing for straightforward determination of the integral gas diffusion coefficient. The models proposed for equilibrium sorption and sorption kinetics demonstrate high consistency for the PAMS-16–ethane system, confirming the strong interconnection between them.