Direct Observation of Topological Defects in Striped Block Copolymer Discs and Polymersomes

Topology and defects are of fundamental importance for ordered structures on all length scales. Despite extensive research on block copolymer self-assembly in solution, knowledge about topological defects and their effect on nanostructure formation has remained limited. Here, we report on the self-assembly of block copolymer discs and polymersomes with a cylinder line pattern on the surface that develops specific combinations of topological defects to satisfy the Euler characteristics for closed spheres as described by Gauss-Bonnet theorem. The dimension of the line pattern allows the direct visualization of defect emergence, evolution, and annihilation. On discs, cylinders either form end-caps that coincide with λ^+1/2 disclinations or they bend around τ^+1/2 disclinations in 180° turns (hairpin loops). On polymersomes, two λ^+1/2 defects connect into three-dimensional (3D) Archimedean spirals, while two τ^+1/2 defects form 3D Fermat spirals. Electron tomography reveals two complementary line patterns on the inside and outside of the polymersome membrane, where λ^+1/2 and τ^+1/2 disclinations always eclipse on opposing sides ("defect communication"). Attractive defects are able to annihilate with each other into +1 disclinations and stabilize anisotropic polymersomes with sharp tips through screening of high-energy curvature. This study fosters our understanding of the behavior of topological defects in self-assembled polymer materials and aids in the design of polymersomes with preprogrammed shapes governed by synthetic block length and topological rules.