The Surface Geometry and Self-Assembly of Bio-Inspired Cholesteric Liquid Crystals

Surface corrugations driven by molecular self-assembly is a ubiquitous pattern observed in nature. Those anisotropic molecules can be found in collagen fibres from human bones, chitin fibres from beetles’ exoskeletons and celluloses in biological plywood. They are responsible for multifunctionalities, for example, the diffraction gratings in tulip petals, and mantis shrimps’ strong endurance to mechanical damage. Closed surface corrugation patterns exhibited in lipid-based droplets have applications in messenger RNA encapsulation, which plays an important role in synthesizing proteins. In this presentation, we study the mechanism and the surface geometry of molecular self-assembly responsible for the self-assembly-driven wrinkling phenomenon in cholesteric liquid crystals. This theoretical study is analyzed under an integrated geometric framework, where the dimensionless shape parameter and the dimensional curvedness are decoupled from the classical curvature tensor. Addressing these complexities will not only enhance our understanding of chiral liquid crystals but also the scientific advancements in various domains.