Defect structures and ordering behaviours of diblock copolymers self-assembling on spherical substrates

One of the main differences of ordered structures constrained on curved surfaces is the nature of topological defects. We here explore the defect structures and ordering behaviours of both lamellar and cylindrical phases of block copolymers confined on spherical substrates by the Landau-Brazovskii theory, which is numerically solved by a highly accurate spectral method with a spherical harmonic basis. For the cylindrical phase, isolated disclinations and scars are generated on the spherical substrates. The number of excess dislocations in a scar depends linearly on the sphere radius. The defect fraction characterizing the ordering dynamics decays exponentially. The scars are formed from the isolated disclinations via mini-scars. For the lamellar phase, three types of defect structures (hedgehog, spiral and quasi-baseball) are identified. The disclination annihilation is the primary ordering mechanism of the lamellar phase.