Surface Anchoring Effects on the Formation of Two-Wavelength Surface Patterns in Chiral Liquid Crystals

Abstract

We present a theoretical analysis and linear scaling of two-wavelength surface nanostructures formed at the free surface of cholesteric liquid crystals (CLC). An anchoring model based on the capillary shape equation with the high order interaction of anisotropic interfacial tension is derived to elucidate the formation of the surface wrinkling. We showed that the main pattern-formation mechanism is originated due to the interaction between lower and higher order anchoring modes. A general phase diagram of the surface morphologies is presented in a parametric space of anchoring coefficients, and a set of anchoring modes and critical lines are defined to categorize the different types of surface patterns. To analyze the origin of surface reliefs, the correlation between surface energy and surface nano-wrinkles is investigated, and the symmetry and similarity between the energy and surface profile are identified. It is found that the surface wrinkling is driven by the director pressure and is annihilated by two induced capillary pressures. Linear approximation for the cases with sufficient small values of anchoring coefficients is used to realize the intrinsic properties and relations between the surface curvature and the capillary pressures. The contributions of capillary pressures on surface nano-wrinkling and the relations between the capillary vectors are also systematically investigated. These new findings establish a new approach for characterizing two-length scale surface wrinkling in CLCs, and can inspire the design of novel functional surface structures with the potential optical, friction, and thermal applications.

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

“…For a given direction the amplitude A is linear function of the wrinkling wavelength λ > P 0 , which is larger than the pitch. The former is consistent with our previous results [47,48,49] based on uncoiled helices at the surface. In the material coordinate system (x, y, z) the surface profile (Eqn.…”

“…It is noted that the anchoring mechanism was used to describe the LC Plateau-Rayleigh fibre instability in achiral nematic LCs, which includes surface wrinkling and twisting modes observed experimentally in collagen solutions. Consistency of the anchoring driven surface patterning predictions with experimental observations [50,51,52,53,54] of surface pattern formation include: (1) scaling laws for single wrinkling in cholesteric surfaces [47]; (2) scaling laws for two scale wrinkling in cholesteric surfaces [48,49];…”

“…All these previous predictions [33,47,48,49] and observations focus on uniaxial wrinkling in LCs, with one single wrinkling wave vector and for cases where the helix is uncoiled; in this paper the helix is intact and undeformed.…”

“…The sign of W determines the minimum energy of anchoring: W > 0 is for tangential orientation and W < 0 for perpendicular and only controls the up-down orientation of peaks and valleys; symmetry relations are discussed in [47]. Higher order terms such as (n • k) 4 are important to generate more surface symmetry breaking and secondary surface wrinkling [47,48,49].…”

Rate of Entropy Production in Evolving Interfaces and Membranes under Astigmatic Kinematics: Shape Evolution in Geometric-Dissipation Landscapes

“…Shape and curvedness affect membrane elasticity [ 13 ], the rate of growth of cell tissues [ 14 ] and particle behaviours [ 15 ]. For example, the shape and curvedness of liquid crystals are sensitive to external stimuli such as electromagnetic field [ 16 ], light stimulation [ 17 , 18 ], force field [ 19 ], surface anchoring [ 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ] and surfactants [ 28 , 29 ]. They can be applied in superhydrophobic materials [ 30 ] and optical lenses [ 31 , 32 ].…”