A lattice-fluid model for the determination of the water/polymer interaction parameter from water uptake measurements

The Flory–Huggins (FH) theory is commonly used for a thermodynamic analysis of the phase behavior in ternary nonsolvent/solvent/polymer systems to describe membrane formation, in general. Actually three precisely and independently determined interaction parameters have to be known. Particularly the nonsolvent/polymer interaction parameter is difficult to determine, although it considerably affects the size and location of the miscibility gap in a ternary phase diagram. In a recent publication [M. Karimi, W. Albrecht, M. Heuchel, M.H. Kish, J. Frahn, Th. Weigel, D. Hofmann, H. Modaress, A. Lendlein, Determination of water/polymer interaction parameter for membrane-forming systems by sorption measurements and fitting techniques, J. Membr. Sci. 265 (2005) 1], it was found that the values for the water/polymer interaction parameters obtained by a fit of ternary polymer solution data are significantly smaller than values determined on the basis of the Flory–Huggins model from water vapor sorption on the solid membrane polymer. To resolve the discrepancy, a lattice-fluid model is introduced in which it assumes a state between glass-like and rubber-like (GRP model) for the water-swollen polymer. The contributions of each of the boundary cases to the mixed state depend on the original stiffness of the pure components, indicated by the glass transition temperature of the pure polymer, and the relative amount of penetrant in the polymer matrix, initiating a plasticization of the polymer. The plasticization then causes an increase of chain mobility and, therefore, a continuous transfer from the glass-like to the rubber-like state. Using this approach a Flory water/polymer interaction parameter can be calculated which is in excellent accordance with respective values obtained by the more elaborated fitting technique of experimental cloud points of ternary systems for the investigated systems.