Solution models for binary components of significantly different molecular sizes

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.