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)(2)B multiblock copolymer of chain length N in a nanopore with size R is studied using the self-consistent field theory. The hierarchical concentric ring (HCk), hierarchical perforated cylinder (HPk), hierarchical helix (HHk), and even hierarchical disk (HDk) is obtained with different number of mid-thin layers k via a proposed design principle. The results show that large pore size and chi(AB) favor the hierarchical structure with more k, while chi(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, HCk -> HPk -> HHk -> HDk 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.