Splitting diamonds: a new look at the stability and transformations of bicontinuous phases of block copolymers

Amongst the ordered phases assembled by block copolymers, the triply-periodic, bicontinuous network phases are of particular interest. They are structurally complex, yet assemble in a variety of biological systems, and possess symmetries that are attractive for photonic and phononic applications. Of the cubic symmetry phases, the double gyroid and the double diamond are predominant, with the double diamond often considered to be metastable relative to the double gyroid. However, the transformation pathways between double gyroid and double diamond are not well understood. Taking guidance from existing continuous transformation pathways between gyroid and diamond minimal surfaces, we explore the free energy landscapes between these two structures by using the recently-developed "medial strong-segregation theory." In doing so, we find that cubic double diamond is in fact unstable for neat diblock melts for a large range of molecular parameters. This result is confirmed by standard self-consistent field calculations. Moreover, we find that the double diamond lies at a saddle point that separates the stable double gyroid from a distinct stable tetragonal bicontinuous phase with three-coordinated nodes. In exploring potential transformation landscapes, we have identified surprising new features, highlighting open questions about the assembly of cubic and non-cubic network phases.