High-resolution three-dimensional imaging of topological textures in single-diamond networks

Highly periodic structures are often said to convey the beauty of nature. However, most material properties are strongly influenced by the defects they contain. On the mesoscopic scale, molecular self-assembly exemplifies this interplay; thermodynamic principles determine short-range order, but long-range order is mainly impeded by the kinetic history of the material and by thermal fluctuations. For the development of self-assembly technologies, it is imperative to characterise and understand the interplay between self-assembled order and defect-induced disorder. Here we used synchrotron-based hard X-ray nanotomography to reveal a pair of extended topological defects within a self-assembled single-diamond network morphology. These defects are morphologically similar to the comet and trefoil patterns of equal and opposite half-integer topological charges observed in liquid crystals and appear to maintain a constant separation across the thickness of the sample, resembling pairs of full vortices in superconductors and other hard condensed matter systems. These results are expected to open new windows to study defect formation in soft condensed matter, particularly in biological systems where most structures are formed by self-assembly.