Concentration dependence of the Flory (X) parameter within two-state models

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V. A. Baulin and A. Halperin

Macromolecules, 35, 6432 – 6438 (2002)

The Flory χ parameter is typically assumed to depend only on the temperature, T. Experimental results often require the replacement of this χ(T) by χ_eff, which depends also on the monomer volume fraction, φ, χ_eff(φ,T). Such χ_eff(φ,T) can arise from two-state models, proposed for polyetheleneoxide (PEO) and other neutral water-soluble polymers. The predicted φ dependence of χ = χ_eff − (1 − φ)∂χ_eff/∂φ, obtainable from colligative properties, differs qualitatively between the various models:  (i) The model of Karlstrom (J. Phys. Chem.1985, 89, 4962) yields ∂χ/∂φ ≥ 0 while the model of Matsuyama and Tanaka (Phys. Rev. Lett.1990, 65, 341) and of Bekiranov et al. (Phys. Rev. E1997, 55, 577) allows for ∂χ/∂φ < 0. (ii) χ(φ) 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, χ(φ) similarly calculated from the model of Bekiranov et al. differs qualitatively from the measured results. Altogether, χ(φ) provides useful measure for the performance of a model.