Signatures of a Concentration‐Dependent Flory χ Parameter: Swelling and Collapse of Coils and Brushes

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Abstract
The quality of solvents of polymers is often described in terms of the Flory χ parameter typically assumed to depend only on the temperature, T. In certain polymer‐solvent systems fitting the experimental data enforces the replacement of (χT) by a concentration‐dependent χeff. In turn, this modifies the swelling and collapse behavior. These effects are studied, in the framework of a mean‐field theory, for isolated coils and for planar brushes. The ϕ dependence of χeff gives rise to three main consequences: (i) shift in the cross‐over between Gaussian and self‐avoidance regimes; (ii) a possibility of first‐order collapse transition for isolated flexible coils; (iii) the possibility of a first‐order phase transition leading to a vertical phase separation within the brush. The discussion relates these effects directly to thermodynamic measurements and does not involve a specific microscopic model. The implementation for the case of poly(N‐isopropylamide) (PNIPAM) brushes is discussed. ϕ vs. z plots, for brushes with N = 300, σ/a2 = 18 (σ/R = 0.019) characterized by different χeff. magnified image ϕ vs. z plots, for brushes with N = 300, σ/a2 = 18 (σ/R = 0.019) characterized by different χeff.
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