Freedericksz transitions in circular toroidal layers of smectic C liquid crystals

J.E. Kidd, Christian Constanda, Iain W. Stewart

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Abstract

The aim of this paper is to consider theoretically a Freedericksz transition for concentric toroidal layers of smectic C liquid crystal arising from a simple geometric setup, thereby extending the results of Atkin and Stewart [Q. Jl Mech. Appl. Math., 47, 1994] who considered spherical layers of smectic C in the usual cone and plate geometry. Application of smectic continuum theory leads, after suitable approximations are made, to a linear governing equilibrium equation which is satisfied by both the trivial solution and a variable solution involving Bessel functions. We are able to determine the critical magnitude cH of the magnetic field H at which this variable solution exists, and a standard energy comparison reveals that the variable solution is expected to be more energetically favourable than the zero solution provided H > cH. Numerical examples of critical thresholds are given, which are comparable to those in the literature for nematics. The paper ends with a discussion section and some indication of possible future work.
Original languageEnglish
Pages (from-to)387-409
Number of pages22
JournalIMA Journal of Applied Mathematics
Volume66
Issue number4
DOIs
Publication statusPublished - Aug 2001

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Keywords

  • Freedericksz transitions
  • liquid crystals
  • smetic

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