Nematic liquid crystal director structures in rectangular regions

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider a shallow rectangular well of nematic liquid crystal subject to weak anchoring on the sides of the well. By considering weak anchoring instead of infinitely strong anchoring, we are able to analyse nematic equilibria in the well without the need to exclude point defects at the corners, as done in previous work in the area. For relatively weak anchoring, we are able to derive analytic expressions for the director alignment angle in terms of an infinite series of modes, involving roots of a transcendental equation. The analytic forms of the director configuration are then used to calculate critical anchoring strengths at which uniform and distorted director structures exchange stability. We also consider the asymptotic behaviour of the director structure and energy for very strong anchoring. We show that in both cases - for the transitions from uniform to distorted states and the limit of infinitely strong anchoring - the approximate analytic expansions agree very well with corresponding numerical calculations of the full model.
LanguageEnglish
Article number022702
Number of pages12
JournalPhysical Review E
Volume97
Issue number2
Early online date16 Feb 2018
DOIs
Publication statusE-pub ahead of print - 16 Feb 2018

Fingerprint

Crystal Structure
Nematic Liquid Crystal
liquid crystals
Point Defects
Transcendental
Infinite series
Numerical Calculation
Alignment
Asymptotic Behavior
Roots
point defects
Angle
Calculate
Configuration
alignment
Energy
expansion
configurations
Model
energy

Keywords

  • nematic liquid crystal
  • liquid crystals
  • weak anchoring

Cite this

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title = "Nematic liquid crystal director structures in rectangular regions",
abstract = "We consider a shallow rectangular well of nematic liquid crystal subject to weak anchoring on the sides of the well. By considering weak anchoring instead of infinitely strong anchoring, we are able to analyse nematic equilibria in the well without the need to exclude point defects at the corners, as done in previous work in the area. For relatively weak anchoring, we are able to derive analytic expressions for the director alignment angle in terms of an infinite series of modes, involving roots of a transcendental equation. The analytic forms of the director configuration are then used to calculate critical anchoring strengths at which uniform and distorted director structures exchange stability. We also consider the asymptotic behaviour of the director structure and energy for very strong anchoring. We show that in both cases - for the transitions from uniform to distorted states and the limit of infinitely strong anchoring - the approximate analytic expansions agree very well with corresponding numerical calculations of the full model.",
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Nematic liquid crystal director structures in rectangular regions. / Walton, J.; Mottram, N.J.; McKay, G.

In: Physical Review E, Vol. 97, No. 2, 022702, 16.02.2018.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Walton, J.

AU - Mottram, N.J.

AU - McKay, G.

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