Static shear layers in nematic liquid crystals
type: Item
instance of: scholarly article
title: Static shear layers in nematic liquid crystals
zbMATH Open document ID: 0597.76002
DOI: 10.1007/BF00251001
author: P. K. Currie
author: F. M. Leslie
published in: Archive for Rational Mechanics and Analysis
publication date: 1984-01-01T00:00:00Z
review text: This paper attempts an explanation of an apparent conflict between continuum theory and an observation by \textit{P. E. Cladis}, and \textit{S. Torza} [(*) Phys. Rev. Lett. 35, 1283 ff. (1975)] of nematic layers sustaining a shear stress without deformation. To describe a possible mechanism for this behaviour, the authors consider the problem of a layer confined between parallel plates situated at \(y=\pm b\). A relaxation in the 'strong anchoring' condition is required as is achieved by introducing line disclinations in the surface of the plates parallel to the z-axis. Seeking two-dimensional static solutions for the director n of the form \(n_ x=\cos \vartheta (x;y),\quad n_ y=\sin \vartheta (x,y),\quad n_ z=0\) and assuming the splay and bend constants are equal, the direction equation becomes \(\nabla^ 2\vartheta =0\). The authors first consider a combination of solutions associated with regularly spaced arrays of line disclinations in the surfaces \(y=\pm b\) given by \[ \vartheta =\vartheta_ 0+N\sum^{\infty}_{n=-\infty}(-1)^ n\{\tan^{- 1}(\frac{y-b}{x-a-nc}\quad)-\tan^{-1}(\frac{y+b}{x+a-nc})\}, \] where \(\vartheta_ 0\), a,b,c are constants and N is an integer representing the disclination index. The shear stress component \(t_{xy}\) is found to be periodic in x and a non-zero average shear stress is obtained. To satisfy the boundary value problem with solid surfaces at \(y=\pm b\) it is necessay to consider the image system which consists of an infinite set of line arrays. The 'strong anchoring' condition is assumed to hold everywhere except at points where there is a disclination line. A non- zero average shear stress is obtained which takes a constant value on all planes parallel to and lying between \(y=\pm b\). Despite several simplifying assumptions in the model and lack of justification for certain steps in the analysis, the authors demonstrate that the continuum equations allow the possibility of layers sustaining shear stress without deforming. Final…
reviewed by: P. J. Barratt
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 82D30
zbMATH DE Number: 3963378
zbMATH Keywords: nematic layers
zbMATH Keywords: strong anchoring
zbMATH Keywords: two-dimensional static solutions
zbMATH Keywords: regularly spaced arrays of line disclinations
zbMATH Keywords: shear stress component
zbMATH Keywords: non-zero average shear stress
zbMATH Keywords: boundary value problem
zbMATH Keywords: infinite set of line arrays
zbMATH Keywords: disclination line
zbMATH Keywords: continuum equations
MaRDI profile type: Publication
cites work: Q4478526
cites work: Hydrostatic theory of liquid crystals
cites work: Some constitutive equations for liquid crystals
cites work: Q3863551
cites work: Q5558293
full work available at URL: https://doi.org/10.1007/bf00251001
OpenAlex ID: W2041545629
description: scientific article; zbMATH DE number 3963378