Eur. Phys. J. E (2016) 39: 83
https://doi.org/10.1140/epje/i2016-16083-8

Regular Article

Retrieving the saddle-splay elastic constant K₂₄ of nematic liquid crystals from an algebraic approach

¹ Institut Jean Lamour, Université de Lorraine, Boulevard des Aiguillettes, BP 239, 54506, Vandæuvre les Nancy, France
² Laboratoire dÉnergétique et de Mécanique Théorique et Appliquée, CNRS UMR 7563, Nancy Université, 54506, Vandoeuvre Cedex, France
³ Departamento de Física, CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-900, João Pessoa, PB, Brazil
⁴ Departamento de Física, Universidade Federal Rural de Pernambuco, 52171-900, Recife, PE, Brazil
⁵ Escola Politécnica de Pernambuco, Universidade de Pernambuco, Rua Benfíca, 455, Madalena, 50720-001, Recife, PE, Brazil

^* e-mail: erms.pereira@poli.br

Received: 21 March 2016
Accepted: 11 August 2016
Published online: 6 September 2016

Abstract

The physics of light interference experiments is well established for nematic liquid crystals. Using well-known techniques, it is possible to obtain important quantities, such as the differential scattering cross section and the saddl-splay elastic constant K₂₄. However, the usual methods to retrieve the latter involve adjusting of computational parameters through visual comparisons between the experimental light interference pattern or a ² H-NMR spectral pattern produced by an escaped-radial disclination, and their computational simulation counterparts. To avoid such comparisons, we develop an algebraic method for obtaining of saddle-splay elastic constant K₂₄. Considering an escaped-radial disclination inside a capillary tube with radius R₀ of tens of micrometers, we use a metric approach to study the propagation of the light (in the scalar wave approximation), near the surface of the tube and to determine the light interference pattern due to the defect. The latter is responsible for the existence of a well-defined interference peak associated to a unique angle . Since this angle depends on factors such as refractive indexes, curvature elastic constants, anchoring regime, surface anchoring strength and radius R₀, the measurement of from the interference experiments involving two different radii allows us to algebraically retrieve K₂₄. Our method allowed us to give the first reported estimation of K₂₄ for the lyotropic chromonic liquid crystal Sunset Yellow FCF: K ₂₄ = 2.1 pN.