Predictive Challenges of COSMO-SAC for PEG–Water Liquid–Liquid Equilibria

Liquid liquid equilibrium (LLE) of aqueous polymer solutions remains a thermodynamic challenge for predictive models due to complex interactions and strong size asymmetry. This study evaluates the COSMO-SAC model for predicting the LLE of polyethylene glycol (PEG) and water mixture. Standard computational approaches used for COSMO based models often fail in this polymeric system due to numerical precision limits when handling high molecular weight asymmetry. Additionally, the terminal groups of PEG, frequently omitted in literature, can also influence predicted activity coefficients. Therefore, this study introduces an improved procedure for constructing sigma profiles that incorporates terminal groups, allowing a consistent representation for any molar mass. Furthermore, a global optimization strategy based on the DIRECT method combined with a mass based Rachford Rice flash solver is also presented. This approach successfully solves the LLE without requiring analytical derivatives, overcoming numerical problems where classical algorithms diverge. The methodology allowed qualitative prediction of the closed loop miscibility gap for PEG water systems using only universal parameters. This represents the first instance of COSMO-SAC predicting this diagram format for PEG-water mixture. Also, the inclusion of end groups improves the description of activity coefficient and offers closer approximation to results obtained from full polymer structures. The upper critical solution temperature is well captured, but the lower critical solution temperature (LCST) remains substantially underestimated. Hydrogen bonding contributions prove insufficient to correct these deviations, while the combinatorial term shows dominant influence on inaccurate LCST prediction. These findings suggest that improvements in both enthalpic and entropic terms of COSMO-SAC are required for reliable description of complex polymer solvent systems.