Eur. Phys. J. E (2015) 38: 80
https://doi.org/10.1140/epje/i2015-15080-9

Regular Article

Fredericks transitions in biaxial nematics

¹ Kharkevich Institute for Information Transmission Problems, RAS, 127051, Moscow, Russia
² Department of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
³ Landau Institute for Theoretical Physics, RAS, 142432, Moscow region, Russia
⁴ Moscow Institute of Physics and Technology, 141700, Moscow region, Russia

^* e-mail: blinov.veniamin@gmail.com
^** e-mail: voislav.golo@gmail.com
^*** e-mail: efim.i.kats@gmail.com

Received: 1 May 2015
Revised: 17 June 2015
Accepted: 22 June 2015
Published online: 17 July 2015

Abstract

Much of our understanding (and applications) of biaxial nematic liquid crystals requires the study of the textural transformations in external electric or magnetic fields. To that end, one should employ theoretical approaches which could have bearing on the minimization problem of the multi-parametric free energy. The immediate shortcoming of the direct free-energy minimization (widely used for uniaxial nematics) is the need to resolve several non-linear constraints. To overcome this difficulty, in what follows we shall use the “angular velocity”, which describes space rotations of the order parameter, and is in fact a vector internal curvature of the texture. This method provides a means to resolve the constraints imposed on the order parameter. Thus, we have obtained the set of equations to find all possible one-dimensional textures of biaxial nematics in the external field. To illustrate our method, we calculate the critical fields corresponding to some basic configurations for textural transitions in the biaxial nematics. We feel that this result could be useful to determine the intrinsic degree of biaxiality for liquid crystalline materials.