Concentration Dependence of the Flory Chi Parameter within Two-State Models

The Flory chi parameter is typically assumed to depend only on the temperature, T. Experimental results often require the replacement of this chi(T) by chieff, that depends also on the monomer volume fraction, phi, chieff(phi,T). Such chieff(phi,T) can arise from two state-models, proposed for polyetheleneoxide (PEO) and other neutral water-soluble polymers. The predicted phi dependence of chibar=chieff-(1-phi)\partial \chieff/\partial phi, obtainable from colligative properties, differs qualitatively between the various models: (i) The model of Karlstrom (J. Phys. Chem. 1985, 89, 4962) yields \partial chibar/\partial phi > 0 while the model of Matsuyama and Tanaka (Phys. Rev. Lett. 1990, 65, 341) and of Bekiranov et al (Phys. Rev. E 1997, 55, 577) allows for \partial chibar/\partial phi <0 (ii) chibar(phi) as calculated from the Karlstrom model, utilizing the parameters used to fit the phase diagram of PEO, agrees semiquantitatively with the experimental values. On the other hand, chibar(phi) similarly calculated from the model of Bekiranov et al. differs qualitatively from the measured results. Altogether, chibar(phi) provides useful measure for the performance of a model.