The electrical untwisting of a homeotropically aligned smectic \(C^*\) liquid crystal
type: Item
instance of: scholarly article
title: The electrical untwisting of a homeotropically aligned smectic \(C^*\) liquid crystal
zbMATH Open document ID: 0836.76005
DOI: 10.1007/BF01176293
author: P. J. Kedney
author: Iain W. Stewart
published in: Continuum Mechanics and Thermodynamics
publication date: 1995-09-20T00:00:00Z
review text: This paper employs the continuum theory of Leslie et al. to examine the effect of a uniform electric field applied parallel to the layers of a sample of ferroelectric smectic \(C^*\) liquid crystal. The sample is homeotropically aligned between two large, horizontal flat plates and strongly anchored at the boundaries. Seeking solutions that depend only upon the spatial Cartesian coordinate \(z\), which denotes distance across the plates, the authors show that the resulting Euler-Lagrange equations yield two distinct types of solution for the \(c\)-director. One represents the more natural helical or twisted \(C^*\) phase given by \(c = (\cos \varphi (z), \sin \varphi (z), 0)\), while the other denotes a constant \(C\)-type phase where \(\varphi (z) = m \pi\) for some integer \(m\). To distinguish between various possibilities the authors make an energy comparison, anticipating that the configuration associated with the least energy is the one that will be observed in practice. It is found that arrangements with 0, 1 or 2 twists can be energetically favourable depending upon the applied field strength, while those with more than 2 twists are never energetically favourable. In particular, they determine a critical field strength \(E_c\) above which it is energetically favourable for the helical structure to unwind. In this event the \(c\)- director becomes aligned perpendicular to the applied field and parallel to the associated spontaneous polarization vector. The authors proceed to examine the effect of sample thickness on \(E_c\) and derive an expression for \(E_c\) in a large sample. Finally, they discuss the effect of director reorientation when the direction of the applied field is reversed.
Mathematics Subject Classification ID: 76A15
Mathematics Subject Classification ID: 82D30
Mathematics Subject Classification ID: 82D45
zbMATH DE Number: 798890
zbMATH Keywords: homeotropic alignment
zbMATH Keywords: strong anchoring
zbMATH Keywords: phase transition
zbMATH Keywords: uniform electric field
zbMATH Keywords: Euler-Lagrange equations
zbMATH Keywords: energy comparison
zbMATH Keywords: critical field strength
zbMATH Keywords: director reorientation
reviewed by: P. J. Barratt
MaRDI profile type: Publication
cites work: The untwisting of a bounded sample of cholesteric liquid crystal
cites work: Q4753681
cites work: Viscous flow in smectic A liquid crystals
cites work: Equivalent smectic C liquid crystal energies
cites work: Q4275389
full work available at URL: https://doi.org/10.1007/bf01176293
OpenAlex ID: W2080004753
description: scientific article; zbMATH DE number 798890