Manije Almaspoor - Department of Textile Engineering, Amirkabir University of Technology, Tehran,Iran.
Mohammad Karimi - Department of Textile Engineering, Amirkabir University of Technology, Tehran,Iran.
Masoud Karimzadeh - Bijar branch, Islamic Azad University

Most commercial products made of polymer are, in fact, a mixture of more than one component and, in many instances, of more than one polymer. Combining the polymers andadditives to reach the properties of a good product is necessary [1]. For example in the presence of Cellulose acetate (CA) asthe fourth component in Polyacrylonitrile (PAN) polymer solution lead to increasing water absorbent property of fibers[2]. In combination, PAN & CA in determined percentages aremiscible, these specified amount must be defined. Then an powerful means for industrial and academic research is tohave capability of predicting the miscibility of mixtures. In this study, phase behavior of quaternary polymer solutionwater (nonsolvent), N-methylpyrrolidone (NMP) and dimethylfomamide (DMF) (first solvent and second solvent, respectively), and Poly (ether imide) (PEI) (polymer) orwater/NMP/DMF/PEI, by using the FH model is predicted. The Gibbs free energy of mixing ΔGmix, in a quaternary system composed of nonsolvent (1), first solvent (2), second solvent (3) and polymer (4) can be formulated based on the extended Flory–Huggins model [3](1) mix 1 1 2 2 3 3 4 4 12 2 1 2 13 3 1 3 14 1 423 3 2 3 24 4 2 4 34 4 3 4ΔG = n lnφ +n lnφ +n lnφ +n lnφRT+χ (u )n φ +χ (ω )n φ +χ n φ+χ (y )n φ +χ (z )n φ +χ (l )n φWhaere R is the gas constant, T the absolute tempreture, niand φi the number of moles and volume fraction of ithcomponent and χ12(u2) ،χ13(w3) ،χ14 ،χ23(y3) ،χ24(z و ( 4 χ34(l4) are the interaction parameters. In eq 1 interaction parameters are considered binary, That are only dependent on the components i and j, and are independent from other components. It is assumed that the interaction parameter between nonsolventand polymer, χ14 is constant, but other interaction parameters are functions of concentration that are defined under pseudobinary condition [3]. These parameters are shown in table 1. Table 1. introduced interaction parameters in equation 1 2 2 1 2 u = φ φ +φ χ12 dependent on u23 3 2 3 y = φ φ +φ χ23 dependent on y3 3 3 1 3 ω = φ φ +φ χ13 dependent on w3 4 4 2 4 z = φ φ +φ χ24 dependent on z44 4 3 4 l = φ φ +φ χ34 dependent on l4