Eur. Phys. J. E (2010) 31: 37-50
https://doi.org/10.1140/epje/i2010-10547-9

Regular Article

Macroscopic behavior of non-polar tetrahedratic nematic liquid crystals

¹ Max-Planck-Institute for Polymer Research, POBox 3148, 55021, Mainz, Germany
² Cladis Foundation, POB 162, 07902-0162, Summit, NJ, USA
³ Theoretische Physik III, Universität Bayreuth, 95440, Bayreuth, Germany

^* e-mail: brand@uni-bayreuth.de
^** e-mail: pleiner@mpip-mainz.mpg.de

Received: 9 July 2009
Revised: 30 October 2009
Accepted: 20 November 2009
Published online: 27 January 2010

Abstract

We discuss the symmetry properties and the macroscopic behavior of a nematic liquid crystal phase with D_2d symmetry. Such a phase is a prime candidate for nematic phases made from banana-shaped molecules where the usual quadrupolar order coexists with octupolar (tetrahedratic) order. The resulting nematic phase is nonpolar. While this phase could resemble the classic D _∞h nematic in the polarizing microscope, it has many static as well as reversible and irreversible properties unknown to nonpolar nematics without octupolar order. In particular, there is a linear gradient term in the free energy that selects parity leading to ambidextrously helical ground states when the molecules are achiral. In addition, there are static and irreversible coupling terms of a type only met otherwise in macroscopically chiral liquid crystals, e.g. the ambidextrous analogues of Lehmann-type effects known from cholesteric liquid crystals. We also discuss the role of hydrodynamic rotations about the nematic director. For example, we show how strong external fields could alter the D_2d symmetry, and describe the non-hydrodynamic aspects of the dynamics, if the two order structures, the nematic and the tetrahedratic one, rotate relative to each other. Finally, we discuss certain nonlinear aspects of the dynamics related to the non-commutativity of three-dimensional finite rotations as well as other structural nonlinear hydrodynamic effects.