Extension of the NRTL and NRF models to multicomponent polymer solutions: Applications to polymer–polymer aqueous two-phase systems

The modified NRTL (nonrandom two-liquid) model for multisolvent, single polymer solutions proposed by Chen [C.C. Chen, Fluid Phase Equilib. 83 (1993) 301–312] and the modified NRF (nonrandom factor) model for single solvent, single polymer solutions, proposed by Zafarani-Moattar and Sadeghi [M.T. Zafarani-Moattar, R. Sadeghi, Fluid Phase Equilib. 202 (2002) 413–422] have been used for the representation of the excess Gibbs energy of multicomponent polymer solutions. The models represent a synergistic combination of the Flory–Huggins description for the configurational entropy of mixing molecules of different sizes and the NRTL or NRF theory for the local composition contribution from mixing solvents and segments of polymers. These models have been applied for the correlation of the phase behavior of some polymer–polymer aqueous two-phase systems. The results show that the models can accurately correlate a series of the liquid–liquid equilibrium phase diagrams of aqueous two-phase systems at different polymer molecular weights.