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

Abstract

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 ef f , that depends also on the monomer volume fraction, φ, χ ef f (φ, T ). Such χ ef f (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 ef f − (1 − φ)∂χ ef f /∂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.

Poly(N‐isopropylacrylamide) Phase Diagrams: Fifty Years of Research

“…[78] Most of these models were formulated with PEG in mind and their parameters were determined by fitting its phase diagram. Within these "two state" models the monomers are assumed to interconvert between two states:ahydrophilic (P)s tate that is favored at low temperatures and ah ydrophobic (H) state that is preferred at high temperatures.T he chain is modeled as an annealed HP random copolymer.…”

Adhesion of Polymer Vesicles

“…The maximum extension of the polymer above the surface is the height of the completely stretched brush, h 1 . The choice of exponent is a rough treatment of the conformation of PEO, as it is related to the interaction parameter of PEO in water, which changes as a function of temperature and concentration [1,5,6,24]. We treat the correlation exponent only as a description of the overall PEO conformation without reference to solvent quality, as the mean field description is inadequate to describe the interactions of PEO with water.…”

Comparison of aggregation behaviors between branched and linear block polyethers: MesoDyn simulation study

“…Bae et al [49] used an extended Flory-Huggins equation to investigate the relationship between the parameters and concentrations for vapor-liquid or liquid-liquid equilibria at different temperatures through the vapor pressure method and the semi-empirical model. Therefore, the pair-wise interactions in MesoDyn should be considered as the effective Flory-Huggins parameters, like Baulin and Halperin's work [50], # ¼ # eff þ f f ð Þ. From previous successful simulations for poly(ethylene oxideblock-propylene oxide) solutions [30-32, 34, 44, 45, 50-52], χ EW and χ PW were selected as the values from 1.35 to 1.7 at different concentrations from atomic simulations.…”