Structure of smectic-A liquid crystals in nonuniform domains: Modeling the impact of imperfect boundaries

Ayad S. al Sallo, Alan J. Walker, and Graeme P. Boswell
Phys. Rev. E 101, 032703 – Published 16 March 2020

Abstract

This paper describes the construction of equilibrium configurations for smectic-A liquid crystals subjected to nonuniform physical boundary conditions, with two-dimensional dependence on the director and layer normal, and a nonlinear layer function. Euler-Lagrange equations are constructed that describe key properties of liquid crystals confined between two boundaries exhibiting spatial imperfections. The results of the model are shown to be consistent with previous published findings in simple domains while results are obtained on how the structure of the liquid crystals changes in response to boundary perturbations. Domain sizes are considered representing those currently used in applications while predictions in smaller domains at the limit of current technologies are also made. In particular, it is shown that the curvature along a boundary impacts on the liquid crystal's structure distant from the boundary feature and therefore previously developed mathematical models, that essentially reduced the problem to a single spatial dimension, cannot be used in such circumstances. Consequences for practical applications are briefly discussed.

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  • Received 15 May 2019
  • Accepted 21 February 2020

DOI:https://doi.org/10.1103/PhysRevE.101.032703

©2020 American Physical Society

Physics Subject Headings (PhySH)

Polymers & Soft MatterNonlinear Dynamics

Authors & Affiliations

Ayad S. al Sallo

  • School of Computing and Mathematics, University of South Wales, Pontypridd CF37 1DL, United Kingdom

Alan J. Walker

  • School of Computing, Engineering and Physical Sciences, University of the West of Scotland, Paisley PA1 2BE, United Kingdom

Graeme P. Boswell*

  • School of Computing and Mathematics, University of South Wales, Pontypridd CF37 1DL, United Kingdom

  • *Corresponding author: graeme.boswell@southwales.ac.uk

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Issue

Vol. 101, Iss. 3 — March 2020

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