Amphiphilic polymer brush in a mixture of incompatible liquids

An analogue of the Alexander-DeGennes box model is used for theoretical inv estigation of polymer brushes in a mixture of two solvents. The basic solve nt A and the admixture B are assumed to be highly incompatible (Flory-Huggi ns parameter chi(AB) = 3.5). Thermodynamics of a polymer in the solvents A and B are described by parameters chi(B) < chi(Lambda) less than or equal t o 1/2. The equilibrium behavior of a brush is investigated in dependence on solvent composition, grafting density. polymer-solvents and solvent-solven t interactions. The possibility of a phase transition related with a strong preferential solvation of a brush by a minor solvent component with higher affinity to polymer is shown and examined. Microphase segregation inside a brush is also demonstrated despite overestimating of the brush homogeneity given by the box model. A further simplification of the model permits to o btain scaling formulas and to investigate main regularities in the brush be havior. This offers a clear physical picture of the phase segregation insid e a brush in correlation with the phase state of a bulk solvent.