Theory for the solubility of gases in polymers: Application to monatomic solutes

The polymer reference interaction site model (PRISM theory) is applied to the problem of calculating the solubility of monatomic gases in amorphous polyethylene. One can consider this system as an approximation to the solubility of gases in ethylene/propylene elastomers. The chemical potential of a solute atom in the polymer is decomposed into two distinct contributions: a positive athermal contribution calculated by growing the solute atom from a point particle and a negative attractive contribution computed from first-order perturbation theory using the athermal system as the reference state. Good agreement is found between the PRISM calculations and available experimental data on solubility of gases in common elastomers with no adjustable parameters. Furthermore, PRISM theory is successful in predicting several interesting trends observed experimentally: (1) solubility increases with the size of the solute atom, (2) solubility is a monotonically increasing function of the critical temperature of the solute species, and (3) the temperature coefficient of solubility crosses over from positive to negative for solutes having critical temperatures of approximately 65 K.