Defect Annihilation Mechanisms in Hexagonal Cylinders Formed by Diblock Copolymers under Triangular Confinement

Abstract

The self-assembly of hexagonal cylinder-forming diblock copolymers under laterally triangular confinement provides a useful method for the fabrication of defect-free hexagonal patterns. However, as the triangular confinement size becomes larger, its confinement effect drops down and thus the occurrence of defects is still inevitable. Here, we first use self-consistent field theory (SCFT) to demonstrate that there always exists a thermodynamically stable perfect hexagonal pattern within the triangle of any size by comparing the free energy of the perfect hexagonal morphology with as many defective morphologies as possible. These metastable defects can be categorized into doped- and vacancy-types. Then, we combine SCFT with the string method to determine the minimum free-energy path (MFEP) for defects to evolve into perfect morphologies, focusing on the influence of two key factors on the stability of defects, i.e., the confinement size and the segregation strength χN. The results reveal that the confinement size has an significant effect on the kinetic stability of defects. The defect becomes less stable and easier to annihilate into the perfect equilibrium morphology when the confinement size approaches the most commensurate size. As χN varies, doped-type defects always prefer to annihilate via the evaporation process, while vacancy-type defects tend to annihilate via the fission process at higher χN and the nucleation process at lower χN, respectively. The free-energy barrier of the favorable MFEP for each defect commonly decreases to vanish with decreasing χN, which is consistent with the conclusions in the corresponding bulk system. The dissipative particle dynamics simulations are carried to verify the influence of the triangular size on the stability of defective morphologies.