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 chi parameter typically assumed to depend only on the temperature T. In certain polymer-solvent systems fitting the experimental data enforces the replacement of chi(T) by a concentration-dependent chi(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 phi dependence of chi(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.