SCF theory of a polymer brush immersed into a multi-component solvent

Self-consistent field (SCF) theory is developed for a polymer brush immersed into a multi-component solvent. Thermodynamics of the plane inhomogeneous brush is mainly determined by thermodynamics of the basic system, i.e., a homogeneous solution of a polymer dissolved in a multi-component solvent that is in partial (or membrane) equilibrium with a bulk. Binary solvent with partially miscible components is in the focus of this investigation. The peculiarities of the brush are studied on the basis of the phase diagrams constructed for the basic system. Non-trivial effects are demonstrated: microphase segregation of the brush and collapse of the brush under its filling with a good solvent in a pre-binodal region of the bulk mixed solvent. Mathematical apparatus is developed and allows obtaining phase diagrams, density profiles, and other characteristics of the system under consideration.