Aqueous two-phase systems of poly(vinylpyrrolidone) and potassium citrate at different temperatures—Experimental results and modeling of liquid–liquid equilibrium data

(Liquid+liquid) equilibrium of (NaClO4+PEG 4000+H2O) ternary system at different temperatures

“…Following Zafarani-Moattar and Sadeghi [21] and Sadeghi [22] for the Chen-NRTL and modified Wilson models, the excess Gibbs free energy, G E , is calculated as a sum of three contributions:…”

“…The Flory-Huggins expression [23], the Pitzer-Debye-Hückel equation (PDH) [24] and the Chen-NRTL [21] or modified Wilson [22] models are used to calculate G E,Comb , G E,LR and G E,SR , respectively.…”

“…In the modified Wilson model [22] proposed by Sadeghi, he considered the local composition concept to the individual segments, ion and solvent molecule, rather than polymer, salt and solvent and incorporate the two assumptions of local electro-neutrality and like-ion repulsion proposed by Chen [30] and Chen and Evans [31]. Additionally Sadeghi assumed that the enthalpy of interaction between the cation and segment is different from those between anion and segment.…”

“…On the other hand, the interaction between the cations and ester group is the complexation, these interactions have a salting-in effect, opposite to that noted above. According to these assumptions, the activity coefficient equations for aqueous (polymer + salt) system are presented in reference [22].…”

“…The models based on the lattice theories, the Flory-Huggins theory, and on the local composition concepts and their modifications [17][18][19][20] are among the most familiar among those used to represent the LLE phase diagram of polymer-salts ATPS. In the present work, the Chen-NRTL [21], modified Wilson [22] and extended UNIQUAC [20] models were applied for the correlation of experimental LLE data of the aqueous (NaClO 4 + PEG 4000 + H 2 O) system. The Flory-Huggins expression [23] and the Pitzer-Debye-Hückel equation [24] were used for the entropy of mixing molecules of different sizes and to account for the longrange electrostatic interactions of the ions, respectively.…”