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

Ziheng Wang,Pardis Rofouie,Alejandro Rey

doi:10.3390/cryst9040190

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.

Highlights

A variety of periodic surface structures and wrinkled textures are widely found in the plant and animal kingdoms [1,2,3,4,5,6]
As similar nano/micro scale periodic wrinkles are formed at the free surface of both synthetic and biological cholesteric liquid crystals (CLCs) [12,13], and CLC phases are widely found in Nature and living soft materials both in vivo and vitro [13,14], nematic liquid crystal self-assembly has been proposed as the formation mechanism of helicoidal plywoods and the surface ultrastructures in many fibrous composites ranging from plant cell walls to arthropod cuticles [15,16,17,18,19]
The objective of this paper is to identify the key mechanisms that induce and resist the multiple-length-scale surface wrinkling in CLCs based on a pure higher order anchoring model

Summary

Introduction

A variety of periodic surface structures and wrinkled textures are widely found in the plant and animal kingdoms [1,2,3,4,5,6] Since these surface ultrastructures with micro/nano scale features provide unique optical responses and iridescent colors [7,8,9,10,11], understanding their formation mechanism is crucial in realizing structural color in nature and in biomimetic design of novel photonic systems. If the formation of the Crystals 2019, 9, 190; doi:10.3390/cryst9040190 www.mdpi.com/journal/crystals

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Conclusion