Undulation instabilities in cholesteric liquid crystals induced by anchoring transitions

Maxim O Lavrentovich,Lisa Tran

doi:10.1103/physrevresearch.2.023128

Maxim O Lavrentovich, Lisa Tran

Open Access

https://doi.org/10.1103/physrevresearch.2.023128

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Abstract

Cholesteric liquid crystals (CLCs) have a characteristic length scale given by the pitch of the twisted stacking of their constituent rod-like molecules. Under homeotropic anchoring conditions where the molecules prefer to orient perpendicular to an interface, cholesteric interfaces exhibit striped phases with stripe widths commensurate with the pitch. Conversely, planar anchoring conditions have the molecules remain in the plane of the interface so that the CLC twists perpendicular to it. Recent work [L. Tran et al. Phys. Rev. X 7, 041029 (2017)] shows that varying the anchoring conditions dramatically rearranges the CLC stripe pattern, exchanging defects in the stripe pattern with defects in the molecular orientation of the liquid crystal molecules. We show with experiments and numerical simulations that the CLC stripes also undergo an undulation instability when we transition from homeotropic to planar anchoring conditions and vice versa. The undulation can be interpreted as a transient relaxation of the CLC resulting from a strain in the cholesteric layers due to a tilting pitch axis, with properties analogous to the classic Helfrich-Hurault instability. We focus on CLC shells in particular and show that the spherical topology of the shell also plays an important role in shaping the undulations.

Highlights

Striped patterns abound in nature, with lamellar features observable at the micron scale within the cell walls of fruits [1], the chitinous exoskeleton of beetles [2], and the fruit fly embryo [3], as well as at much larger scales, such as on the skin of zebras, tigers, and certain fish species [4,5]
We examine the undulation instability of Cholesteric liquid crystals (CLCs) stripes on shells for both homeotropic and planar anchoring transitions, using experiments and simulations
When the CLC shell is left to equilibrate for a sufficiently long time, the stripes eventually arrange into lines of latitude on the shell, with stripes terminating at two focal conic domains, as forced in by the spherical topology [8]

Summary

Introduction

Striped patterns abound in nature, with lamellar features observable at the micron scale within the cell walls of fruits [1], the chitinous exoskeleton of beetles [2], and the fruit fly embryo [3], as well as at much larger scales, such as on the skin of zebras, tigers, and certain fish species [4,5]. In the latter examples, the stripes arise from activating and inhibiting dynamics, characteristic of a Turing instability [4,5]. Using varying surfactant concentrations in the ambient aqueous medium, we show that the CLC shell surface develops transient, undulated

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