Abstract
A generalized theory has been established for describing the phase equilibrium of multicomponent polymer–single solvent system, by introducing the concept of molecular weight-and concentration-dependence of the polymer–solvent thermodynamical interaction parameter χ to the previous theory. In this theory χ is expressed byχ=χ00(1+k/X)(1+p·vp)where, χ00 is a constant independent of both polymer molecular weight and concentration, X, the molar volume ratio of X-mer to the solvent, vp, the polymer volume fraction, k and p, the molecular weight- and concentration-dependence coefficients, respectively. The mathematical phase separation and fractionation were carried out and the effect of k and p-parameters on the phase separation and fractionation characteristics were studied in detail. The positive molecular weight dependence of χ paramerer (k>0) indices a large polydispersity of the polymers in the polymer-rich and lean-phases, particularly where k>3. In the small ρp (ρp= the relative weight fraction of the polymer in a polymer-rich phase to the total polymer dissolved) region, the ratio of the weight- to number-average X, Xw/Xn of the polymer remaining in a polymer-rich .phase is remarkably influenced by both p and k. In a large ρp region, the polydispersity of the polymer in a polymer-lean phase is predominantly controlled by k. For polystyrene–cyclohexane and polystyrene–methylcyclohexane systems, k, estimated by three methods, was found to lie between 0 and 10. The k values for these systems decrease with increasing temperature.
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Kamide, K., Miyazaki, Y. Effect of Molecular Weight Dependence of the χ-Parameter on Phase Equilibrium of Multicomponent Polymer–Single Solvent System: Comparison of Theory with Experiment. Polym J 13, 325–341 (1981). https://doi.org/10.1295/polymj.13.325
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DOI: https://doi.org/10.1295/polymj.13.325