Elastic property of bilayer membrane in copolymer-homopolymer mixtures

We study the domain morphology in a phase separated state of diblock copolymer-homopolymer mixtures. 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 establish a method to calculate the rigidities without a molecular picture in a consistent way with the field theoretic model free energy. Stability of a bilayer membrane compared with micelles is also investigated.