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

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 ( χ T ) by a concentration‐dependent χ eff . 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 χ eff 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 / a 2  = 18 ( σ / R   F 2  = 0.019) characterized by different χ eff .