Solution Models for Binary Components of Significantly Different Molecular Sizes

Abstract

As a solution theory, Raoult’s law is commonly used to estimate the activities of solutes and solvents of comparable molecular sizes while the Flory–Huggins (F–H) model is used for the activities of small liquids in high polymers. For a great many systems where the solute and solvent differ only moderately in molecular size (e.g., by 4–10 times), there has been no confirmed choice of a preferred model; examples of such systems are those of ordinary organic compounds in liquid triolein (MW = 885.4 g·mol⁻¹) and poly(propylene glycol) (PPG) (MW = ~1,000 g·mol⁻¹). The observed nearly athermal solubilities of many nonpolar organic solids in these solvents provide unique experimental data to examine the merit of a solution model. As found, Raoult’s law underestimates widely, and the F–H model underestimates slightly, the solid solubilities in triolein and PPG because these models underestimate the solution entropy for these solute–solvent pairs. To rectify this problem, the molecular segments of a large sized liquid solvent (e.g., triolein) are assumed to act as independent mixing units to increase the solute–solvent mixing entropy. This adjustment leads to a modified F–H model in which the “ideal” or “athermal” solubility of a solid in volume fraction, at a particular temperature, is equal to the solid’s activity at that temperature. Results from other studies give further support for the modified F–H model to interpret the partition data of compounds with organic solvents.