An equation of state (EoS) based model for the fluid solubility in semicrystalline polymers

It is well known that semicrystalline polymers absorb lower amounts of fluid than the corresponding wholly amorphous polymers. This behavior is due primarily to the fact that the crystalline domains do not absorb fluid molecules but additionally, in some cases, to a reduced sorption capacity of the amorphous phase with respect to the pure amorphous polymer. To represent such behavior, we hypothesize that the amorphous domains of semicrystalline polymers are mechanically constrained by the crystallites, and that such effect can be represented by a constraint pressure, pc, applied on the amorphous phase in addition to the pressure p prevailing in the fluid phase. In this way, any equation of state (EoS) model can be used to evaluate the density, chemical potential, solubility and swelling of the amorphous phase. In particular, we used the Sanchez Lacombe Equation of State (SL EoS), as it describes accurately the behavior of amorphous polymer phases. The binary parameter for the fluid–polymer energetic interactions, kij, and the constraint pressure pc are adjusted on the experimental solubility data above and below the polymer melting point Tm, respectively. For polyolefines, the values of pc lie on a single mastercurve that increases exponentially with the polymer crystalline fraction and decreases exponentially with temperature. The approach describes accurately the experimental solubility behavior of different gases and vapors in conventional semicrystalline polyolefines like polyethylene and polypropylene of different types, as well as in polyethers such as poly(ethylene oxide) (PEO), in wide temperature ranges.