Crystal twinning of bicontinuous cubic structures

Abstract

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.

SPIRE, Surface Projection Image Recognition Environment for bicontinuous phases: application for plastid cubic membranes

“…Although we developed SPIRE to investigate cellular cubic membranes visualized in TEM images, it is also a suitable tool for analyzing microscopy images of any highly symmetric arrangements such as cuboids or polymer assemblies. In the latter, we see similar geometries to those found in the biological cubic membranes (Bates, 2005;Kirkensgaard et al, 2011;Han et al, 2020) or cubic rod packings (O'Keeffe et al, 2001). The latter are used to model the keratin microstructure in skin cells, a geometry that is closely related to-and likely coexistent with-a gyroid surface (Evans and Hyde, 2011;Evans and Roth, 2014;Norlén and Al-Amoudi, 2004).…”

Visualizing the double-gyroid twin

“…This rules out any abrupt, coherent local change of chirality of the PDMS networks within PS matrix at room temperature by mechanical force. Also, SAXS observations following the concentration dependence of structural order in the PS-PDMS toluene solution at room temperature prove no order–order phase transition occurs ( 55 ) [e.g., hexagonally perforated layers to DG transition, which has been suggested to be likely related to the gyroidal TB ( 45 )]. Instead, it is most likely that the (422) BCP DG twin is a growth twin, where nucleation can take place more easily at the concave reentrant grooves formed by low-energy growth faces of a twinned crystal ( 5 ).…”

“…In 2019, Chen ( 44 ) addressed the mathematical existence of twins in TPMSs including Schoen’s G surface, and proposed a near-minimal surface model of the shape of a {211} G-surface twin. In 2020, Han et al ( 45 ) proposed a (211) + 0.5 G TB [which is equivalent to the (422) twin that we study] for a mesoporous silica-air sample based on a single transmission electron microscopy (TEM) image and matching this image to a series projected models of the twin structure (for more discussion see SI Appendix , Previous Studies ). To date, clear 3D visualization of the detailed features of a TB in a chiral DG network structure has yet to be achieved.…”

A unique insight into the defect structures of bicontinuous mesophases in liquid crystals and hybrid materials

“…How stable are the intermediate mesophases that arise as a result? These are the questions that Han et al attempt to answer in this issue of IUCrJ (Han et al, 2020).…”

“…HRTEM image of bincontinous cubic (Ia 3 3d) mesoporous silica crystal showing a {211} twin boundary (left) and 3D reconstructed models of the silica network of the G-twin boundary. Adapted from (Han et al, 2020).…”