School of Chemical Science and Engineering, Tongji University, Shanghai 200092, People's Republic of China
Nobuhisa Fujita
Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan
Hao Chen
Institut für Numerische und Angewandte Mathematik, Georg-August-Universität Göttingen, Lotzestr. 16-18, Göttingen 37083, Germany
Chenyu Jin
Max Planck Institute for Dynamics and Self-Organisation, Am Faßberg 17, Göttingen 37077, Germany
Osamu Terasaki
Centre for High-resolution Electron Microscopy, School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, People's Republic of China
Shunai Che
School of Chemical Science and Engineering, Tongji University, Shanghai 200092, People's Republic of China
Bicontinuous cubic structures in soft matter consist of two intertwining labyrinths separated by a partitioning layer. Combining experiments, numerical modelling and techniques in differential geometry, we investigate twinning defects in bicontinuous cubic structures. We first demonstrate that a twin boundary is most likely to occur at a plane that cuts the partitioning layer almost perpendicularly, so that the perturbation caused by twinning remains minimal. This principle can be used as a criterion to identify potential twin boundaries, as demonstrated through detailed investigations of mesoporous silica crystals characterized by diamond and gyroid surfaces. We then discuss that a twin boundary can result from a stacking fault in the arrangement of inter-lamellar attachments at an early stage of structure formation. It is further shown that enhanced curvature fluctuations near the twin boundary would cost energy because of geometrical frustration, which would be eased by a crystal distortion that is experimentally observed.
