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 Pn (3) over barm 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.

Automated summary

Heteroclusters formed by tethering dissimilar nanoclusters using organic linkers, resembling lipids and self-assembling into cubosomes, were studied for their unique nanochannel lattice structure and internal crystal porous structure characterized using transmission electron microscopy. Clear distinctions in conformation of skeletal units between normal and twin boundary units were observed, leading to changes in channel direction and slight elongation at the twin boundary while maintaining overall topology. The study concluded that the two distinct channel systems within cubosomes with different twin boundaries remain continuous, indicating potential for the development of soft crystals with defined shapes and special nanostructures for advanced applications.