Bilayer membrane in copolymer-homopolymer mixtures

The domain morphology in a phase-separated state of diblock copolymer homopolymer mixtures was studied. In the situation that one of the blocks of copolymers is incompatible with homopolymers, formation of a bilayer membrane of block copolymers is shown to be possible in the matrix of homopolymers. Starting with the free-energy functional in terms of the local volume fractions of each monomer, we derive the bending and curvature rigidities in the Helfrich free energy for a membrane. It is found that the curvature modulus is negative only in a limited region of the parameters, where a closed shape of a membrane like a vesicle is possibly formed. We present a method to calculate the rigidities without a molecular picture in a consistent way with the field theoretic model free energy.