Biaxial nanowrinkling in cholesteric surfaces: Egg carton surfaces through chiral anchoring

Abstract Periodic micro and nano-structured surfaces in nature are responsible for functionalities including structural colour, superhydrophobicity, where wrinkling plays a significant role. The Bouligand architecture of fibrous composites such as insect exoskeleton and plant cell walls has been shown to generate uniaxial single and multiscale nanowrinkling through the chiral capillarity effect due to anisotropic surface tension and the helical fibre arrangement. The helical arrangement in Bouligand structures is a solid analogue of a cholesteric liquid crystal, which is an intermediate stage in the self-assembly formation process of fibrous composites. We extend uniaxial wrinkling predictions to biaxial wrinkling and show, using the liquid crystal shape equation, how and why egg carton surfaces with orthogonal patterning arise, since a planar helix tangential to a surface is unstable to oblique wrinkling modes. Taken together this work contributes to novel surface pattern formation and engineering principles to study surfaces of biological materials.