Twins in tubular networks: (422) double gyroid twin & (222) double diamond twin

Triply periodic double gyroid (DG) and double diamond (DD) network phases have unique photonic properties as well as superior charge and/or mass transport along with outstanding mechanical properties arising from their 3D continuous morphology. Determination of the nature of defects (e.g. grain boundaries) in these phases is critical for further understanding/improving material performance. Slice-and-view scanning electron microscopy tomography enabled identification of coherent twins in polystyrene-b-polydimethylsiloxane (PS-PDMS) block copolymers. The DG structure was formed from a 43-29.5 kg/mol sample cast from toluene and the DD structure was obtained from a 51-35 kg/mol sample cast from chloroform. In the DG phase, the boundary is a (422) twin while the twin plane in the DD phase is identified as (222). The reconstructions show that the inter-material dividing surface (IMDS) is smooth and continuous across the twin plane with the formation of new types of boundary nodes and loops. The network topology and the IMDS curvature distribution, surface/volume ratio etc. of the twin boundary regions are compared with the corresponding morphological descriptors measured in the adjacent, ordered DG and DD grains and suggest both boundaries are of low energy.