The phase diagram of molten randomly grafted copolymers

We study the microphase segregation of molten randomly grafted copolymers (RGCs) using a Landau field theory. Under one wave number approximation, we find three equilibrium ordered microphases: lamellar phase (LAM), hexagonal cylinder phase (HEX), and bcc sphere phase (BCC). The stability of these phases strongly depends on the architectural parameters describing the RGC chains (e.g., the backbone length, the branch length, and the number of branches). Our calculation reveals that RGCs with high average composition of backbone monomers or with low branching density tend to form LAM microstructures. For a small average composition of backbone monomers, HEX and BCC microphases appear in turn with increasing branching density. Independent of the architectural parameters and composition, the disorder to order transition for molten RGCs is always from the disordered phase to the LAM microphase. The physical reasons underlying this behavior and experimentally testable predictions are discussed.