Prediction of gas solubility in binary polymer+solvent mixtures

This paper is devoted to a theory of gas solubility in highly asymmetrical mixed solvents composed of a low molecular weight (such as water, alcohol, etc.) and a high molecular weight (such as polymer, protein, etc.) cosolvents. The experimental solubilities of Ar, CH4, C2H6 and C3H8 in aqueous solutions of polypropylene glycol and polyethylene glycol were selected for comparison with the theory. The approach for predicting these solubilities is based on the Kirkwood–Buff formalism for ternary mixtures, which allowed one to derive a rigorous expression for the Henry constant in mixed solvents. Starting from this expression, the solubilities could be predicted in terms of those in each of the two constituents and the properties of the mixed solvent. This expression combined with the Flory–Huggins equation for the activity coefficient in a binary mixed solvent provided very accurate results, when the Flory–Huggins interaction parameter was used as an adjustable quantity. A simple expression in which the solubility could be predicted in terms of those in each of the two constituents and the molar volumes of the latter was also derived. While less accurate that the previous expression, it provided more than satisfactory results.