Concentration dependence of the Flory x 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 chi(eff), which depends also on the monomer volume fraction, phi, chi(eff)(phi,T). Such chi(eff)(phi,T) can arise from two-state models, proposed for polyetheleneoxide (PEO) and other neutral water-soluble polymers. The predicted phi dependence of (chi) over bar = chi(eff) - (1 - phi)partial derivativechi(eff)/partial derivativephi, obtainable from colligative properties, differs qualitatively between the various models: (i) The model of Karlstrom (J. Phys. Chem. 1985, 89, 4962) yields partial derivative(chi) over bar/partial derivativephi greater than or equal to 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 derivative(chi) over bar/partial derivativephi < 0. (ii) (chi) over bar(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, (chi) over bar(phi) similarly calculated from the model of Bekiranov et al. differs qualitatively from the measured results. Altogether, (chi) over bar(phi) provides useful measure for the performance of a model.