Two-wavelength Wrinkling Patterns in Chiral Liquid Crystal Surfaces

We present a model to investigate the formation of two-length scale surface patterns in biological and synthetic anisotropic soft matter through the high order interaction of anisotropic interfacial tension and capillarity at their free surfaces. Focusing on the chiral liquid crystal(CLC) material model, the generalized shape equation for anisotropic interfaces using the quartic anchoring energy is applied to understand the formation of two-length scale patterns, such as those found in floral petals. Analytical and numerical solutions are used to shed light on why and how simple anisotropic anchoring generates two-lengthscale wrinkles whose amplitudes are given in terms of anchoring coefficients. The proposed new nano-wrinkling mechanisms augment previous models dedicated to understand and mimic biological surface pattern formation. Symmetry relations and scaling laws are used to provide the explicit relations between the anchoring constants and surface profile of the two length scale wrinkles. These new findings establish a new paradigm for characterizing surface wrinkling in biological liquid crystals, and inspire the design of novel functional surface structures.