Symmetry and Topology of Twin Boundaries and Five-Fold Twin Boundaries in Soft Crystals

Heteroclusters constructed by tethering dissimilar nanoclusters using organic linkers resemble lipids and self-assemble into cubosomes, namely, microparticles of soft crystals composed of unique nanochannel lattices with a defined symmetry and topology. The internal porous crystal structures can be accurately characterized using transmission electron microscopy. We herein describe twin boundaries and five-fold twin boundaries in cubosomes with a double-diamond Pn3̅m structure. Our analysis indicates a clear distinction in the conformation of the skeletal unit: a centrosymmetric staggered conformation with point group D_3d for the normal skeletal unit and a mirror-symmetric eclipsed one with point group D_3h for the skeletal unit on the twin boundary. This symmetry distinction causes the channels to change direction and elongate slightly as they pass through the twin boundary, but the topology is maintained. For cubosomes containing five-fold twin boundaries, one of the channels is in the center of the particles seamlessly connecting the five blocks. Our conclusion is that the two distinct channel systems are still continuous. This fundamental understanding will contribute to the development of soft crystals with defined shapes and special inner nanostructures for advanced applications.