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Curvature of the elastic deformations in a nematic sample

  • M. SimõesEmail author
  • W. Bertolino
  • T. Davincy
Regular Article
  • 39 Downloads

Abstract.

In this work we study the geometry of the elastic deformations of the uniaxial nematic liquid crystals at the bulk. We will show that, at this region of the sample, the elastic terms of the free energy can be separated as the sum of two kinds of elastic deformations, the first is proportional to the Gaussian curvature obtained from the director field of a three-dimensional nematic sample and the second is composed by those terms that cannot be expressed as resulting from this curvature. To achieve these results we will construct the metric of an unixial nematic sample using the fact that the director gives the direction of the anisotropy of the system. With this approach we will give analytical and geometrical arguments to show that the elastic terms determined by \(K_{22}\), \(K_{13}\) and \(K_{24}\) are contained in a curvature term, while the terms fixed by the splay elastic term, \(K_{11}\), and the bend elastic term, \(K_{33}\), are not. The novelty here is that while \(K_{13}\) and \(K_{24}\) do not contribute the bulk elastic energy of a nematic sample, they have an important contribution to the curvature of the system.

Graphical abstract

Keywords

Soft Matter: Liquid crystals 

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Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Universidade Estadual de Londrina, Departamento de FısicaLondrina (PR)Brazil

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