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

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. E 1997, 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.