A size-dependent ideal solution model for liquid-solid phase equilibria prediction in aqueous organic solutions

Predictive synthesis of aqueous organic solutions with desired liquid-solid phase equilibria could drive progress in industrial chemistry, cryopreservation, and beyond, but is limited by the predictive power of current solution thermodynamics models. In particular, few analytical models enable accurate liquidus and eutectic prediction based only on bulk thermodynamic properties of the pure components, requiring instead either direct measurement or costly simulation of solution properties. In this work, we demonstrate that a simple modification to the canonical ideal solution theory accounting for the entropic effects of dissimilar molecule sizes can transform its predictive power. Incorporating a Flory-style entropy of mixing term that includes both the mole and volume fractions of each component, we derive size-dependent equations for the ideal chemical potential and liquidus temperature, and use them to predict the binary phase diagrams of water and 10 organic solutes of varying sizes. We show that size-dependent prediction outperforms the ideal model in all cases, reducing average error in the predicted liquidus temperature by 59% (to 5.6 K), eutectic temperature by 45% (to 9.7 K), and eutectic composition by 43% (to 4.7 mol%), as compared to experimental data. Furthermore, by retaining the ideal assumption that the enthalpy of mixing is zero, we demonstrate that, for aqueous organic solutions, much of the deviation from ideality that is typically attributed to molecular interactions may in fact be explained by simple entropic size effects. These results suggest an underappreciated dominance of mixing entropy in these solutions, and provide a simple approach to predicting their phase equilibria.