Twist of cholesteric liquid crystal cell with substrates of different anchoring strengths

TL;DR

This paper analyzes how the twist of cholesteric liquid crystal cells is affected by substrate anchoring strengths, revealing discontinuous behavior, hysteresis, and bistability, with new insights into the effects of anchoring asymmetry.

Contribution

It provides exact solutions for director configurations and explores the impact of substrate anchoring asymmetry on the twist behavior of cholesteric liquid crystals.

Findings

Discontinuous dependence of twist wavenumber on free twisting number with hysteresis.

Finite anchoring asymmetry can lead to continuous twist behavior below a critical value.

Identification of a gap between stable director configurations related to anchoring strengths.

Abstract

We consider director configurations of cholesteric liquid crystal (CLC) cells with two plane confining substrates. Exact solutions of the Euler-Lagrange equations for out-of-plane orientations of the easy axes that correspond to inhomogeneous conical structures of CLC director are derived. We study dependence of the CLC twist wavenumber on the free twisting number assuming that anchoring energies at the substrates are either equal or different. In both cases this dependence is found to be generally discontinuous with hysteresis loops and bistability effects involved. For CLC cells with identical substrates and planar anchoring conditions the jump-like behaviour only disappears in the weak anchoring limit. Contrastingly, when the anchoring strengths are different, there is the finite value of anchoring below which the dependence becomes continuous. Another effect is the appearance of the gap between the adjacent twist wavenumber intervals representing locally stable director configurations. We calculate the critical value of anchoring asymmetry and present the results of numerical calculations.