Microphase boundaries and chain conformations in multiply branched diblock copolymers

We consider a melt of diblock copolymers consisting of a linear A block connected to a regularly branched B block. A simple `Alexander-de Gennes'-type calculation of the free energy for lamellar, cylindrical, and spherical microphases in strong segregation reveals large shifts in the phase boundaries as a function of the number of generations of the branched block and the functionality of the branch points. Modifying the calculation for the case of just two generations in the branched block, we find that a significant fraction of the second-generation branches fold back to lower the free energy. This is consistent with recent dendrimer theory, which also predicts that branches fold back toward the center. Nevertheless, controlled introduction of branching into copolymer blocks can evidently be quite effective in shifting phase boundaries and thereby influencing mesoscale morphology.