A free-volume hole-filling model for the solubility of liquid molecules in glassy polymers 1: Model derivation

The use of hole-filling models is quite common for the sorption of gases into glassy polymers, but these have yet to be explicitly applied to the case of liquid immersion, where extensive use of Flory-Huggins theory dominates. This paper explores how the models based on the idea of sequential filling of a Gaussian distribution of pre-existing free-volume holes within the structure of the glassy polymer can be modified to allow the prediction of the equilibrium solubility of a liquid penetrant. For liquids, the driving force for sorption is more subtle than for gases, with more emphasis on molecular interactions rather than external pressure. For this reason, terms relating to the molecular interactions of a liquid molecule filling a hole were developed, including the effects of elastic constraint for small holes. Consideration of thermal fluctuations show that configurational entropy provides much of the driving force for sorption. Some comparisons with experimental data show a reasonable agreement, and one which is far better than the Flory-Huggins theory.