Polymer Brush in Contact with a Mixture of Solvents

We study a polymer brush, in the strongly-stretched regime, in contact with a binary mixture of low-molecular weight solvents. The height of the polymer brush is found to always scale linearly with polymer chemical length. Depending on the solubility of the monomers in the two solvents, a variety of behaviors are possible as the bulk composition of the mixed solvent is varied. In the case of a mixture of a good and bad solvent, we find that, at intermediate concentrations, a collapse of the brush may occur: the collapsed state is distinguished by a step in monomer density at the brush tip. In a mixture of two good solvents, there may be nonmonotonic dependence of the brush thickness on solvent composition.