Influence of Branches on the Phase Behavior of (AB) Starlike Block Copolymer under Cylindrical Confinement

Experimentally, self-assembled morphologies of the (AB) starlike block copolymer are strongly dependent on the number of arms, f. For example, the 2- and 4-arm starlike block copolymers exhibited the morphologies of hexagonally arrayed polystyrene cylinder in the polyisoprene matrix while order-bicontinuous nanostructures were observed in 8-, 12-, and 18-arm stars. Theoretically, we found that the transition sequence for (AB)₃ is C₁^B → Dk^B → P₂^B → L₂^B, which becomes C₁^B → L₁^B when f > 6. To explore the influence of f on the phase behavior of (AB) under cylindrical confinement, we calculated the two-dimensional phase diagram with respect to the volume fraction and the pore diameter. Our conclusions show that the topologies of the phase diagram are independent of the number of arms; however, the number of arms does affect the phase boundary, which inevitably leads to the different phase transition sequences at fixed volume fraction. Therefore, from the calculated phase diagram, the influence of f on the phase behavior of the starlike copolymer is fully understood.