Uniaxial and biaxial nematic phases of banana-shaped molecules and the effects of an external field

A mean field theory is introduced to describe uniaxial and biaxial nematic phases of banana-shaped liquid crystalline molecules. From a geometric point of view, we derive the tensor order parameter of the banana-shaped molecules as a function of a bend angle and four orientational order parameters....

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Bibliographic Details
Published inLiquid crystals Vol. 46; no. 11; pp. 1672 - 1685
Main Authors Matsuyama, Akihiko, Arikawa, Saki, Wada, Moto, Fukutomi, Nanako
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.09.2019
Taylor & Francis Ltd
Subjects
applied fields
Banana-shaped molecules
bent-core molecules
biaxial nematic
Dependence
Free energy
Landau point
Liquid crystals
Mathematical analysis
Mean field theory
Order parameters
Phase diagrams
Phase transitions
Phases
Temperature
Tensors
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Summary:A mean field theory is introduced to describe uniaxial and biaxial nematic phases of banana-shaped liquid crystalline molecules. From a geometric point of view, we derive the tensor order parameter of the banana-shaped molecules as a function of a bend angle and four orientational order parameters. Using the nematic free energy of the Maier-Saupe type, we calculate the phase diagram on the temperature bend angle ( ) plane and find three uniaxial nematic ( ) and three biaxial nematic ( ) phases, where is the primary axis of the orthogonal molecular axis. We also derive the approximate formulas of a nematic-isotropic phase transition ( ) and a biaxial-uniaxial phase transition ( ) temperature as a function of the bend angle. We also discuss the effects of the external field on the temperature and find the negative dependence of the temperature on the external field.
ISSN:0267-8292
1366-5855
DOI:10.1080/02678292.2019.1595756