Single gyroid in H-shaped block copolymers

Single gyroid (SG) nanostructured materials, which consist of a single chiral network domain characterized by a triply periodic surface, are promising candidates for next-generation optical applications owing to a complete photonic band gap structure. However, due to thermodynamic metastability, accessing an equilibrium SG nanostructure through block copolymer self-assembly has been difficult to achieve experimentally. In contrast, the double gyroid (DG), consisting of two independent chiral networks, is a well-known stable phase in certain block copolymer systems. In this study, we predict an equilibrium SG phase formed in H-shaped (BA)2A(AB)2 block polymers, where two AB diblock arms are grafted onto each end of an A backbone. Using SCFT calculations, we constructed a phase diagram with respect to an architectural parameter α, defined as the volume fraction of an A backbone block to total A-type blocks, and the overall volume fraction of A blocks fA. The SCFT phase diagram predicts an equilibrium SG stability window at α≈0.7, and we confirm that the stability of SG extends to high segregation strength. Based on an analysis of the thermodynamic factors responsible for the relative stability of SG over DG, including free energy and geometric factors, we propose a molecular packing mechanism where the H-shaped polymers with asymmetric A blocks form a nearly constant mean curvature geometry of SG by localizing A/B junctions on the A/B interfaces and localizing the long A backbones in the majority domain to relieve the packing frustration. In contrast, the competitive DG phase suffers a considerable enthalpic penalty from the diffuse A/B interfaces created by inhomogeneous chain stretching to accommodate its larger mean curvature variation.