Bulk and surface biaxiality in nematic liquid crystals
Abstract
Nematic liquid crystals possess three different phases: isotropic, uniaxial, and biaxial. The ground state of most nematics is either isotropic or uniaxial, depending on the external temperature. Nevertheless, biaxial domains have been frequently identified, especially close to defects or external surfaces. In this paper we show that any spatially varying director pattern may be a source of biaxiality. We prove that biaxiality arises naturally whenever the symmetric tensor S=(∇n)(∇n)T possesses two distinct nonzero eigenvalues. The eigenvalue difference may be used as a measure of the expected biaxiality. Furthermore, the corresponding eigenvectors indicate the directions in which the order tensor Q is induced to break the uniaxial symmetry about the director n . We apply our general considerations to some examples. In particular we show that, when we enforce homeotropic anchoring on a curved surface, the order tensor becomes biaxial along the principal directions of the surface. The effect is triggered by the difference in surface principal curvatures.
- Publication:
-
Physical Review E
- Pub Date:
- September 2006
- DOI:
- 10.1103/PhysRevE.74.031708
- arXiv:
- arXiv:cond-mat/0605722
- Bibcode:
- 2006PhRvE..74c1708B
- Keywords:
-
- 61.30.Gd;
- 61.30.Hn;
- 61.30.Jf;
- Orientational order of liquid crystals;
- electric and magnetic field effects on order;
- Surface phenomena: alignment anchoring anchoring transitions surface-induced layering surface-induced ordering wetting prewetting transitions and wetting transitions;
- Defects in liquid crystals;
- Condensed Matter - Soft Condensed Matter;
- Condensed Matter - Materials Science