Emergence and Stability of Hierarchical Structures under Cylindrical Confinement

Focusing on the formation of hierarchical structure under cylindrical confinement, the self-assembly of A(BC)₂B multiblock copolymer of chain length N in a nanopore with size R is studied using the self-consistent field theory. The hierarchical concentric ring (HC_k), hierarchical perforated cylinder (HP_k), hierarchical helix (HH_k), and even hierarchical disk (HD_k) is obtained with different number of mid-thin layers k via a proposed design principle. The results show that large pore size and χ_AB favor the hierarchical structure with more k, while χ_BC prefers hierarchical structure with less k, consistent with the results of hierarchical structure in bulk. By investigating the effect of the volume fraction of the tail A block (f_A), the phase transition sequence, HC_k → HP_k → HH_k → HD_k is explored, which shares the same transition of multiblock copolymer in bulk with L_k → G_k → C_k → S_k. Finally, the phase diagram with respect to the f_A and R is explored, where the stability regime of these hierarchical structures is well understood. The results provide a compelling panacea for the fabrication of hierarchical 3D nanostructures under confinement.