Molecular theoretic study of Freedericksz transition. Symmetry breaking of oblique axial order

Abstract

Freedericksz transition, which is usually analyzed by an elastic theory, is studied on the basis of statistical mechanical ground, where nematics with positive dielectric anisotropy in homogeneous anchoring cell is exposed to an electric field in the direction of wall normal. In low temperature region, an oblique axial symmetry breaking occurs, which is nothing but the Freedericksz transition. In high temperature and high field region, biaxial nematic phase with principal axis parallel to the field direction at interior area of the system is proved to appear. A phase diagram on the field versus temperature plane is obtained and compared with the one at a bulk with common biaxial symmetry, where both of electric and magnetic fields are applied in directions perpendicular to each other. In the latter, no symmetry breaking occurs, in contrast with the former case above-mentioned, and the reason why this difference occurs is elucidated.

Effects of fields and anchoring on biaxial nematic ordering

“…Usually, the Freedericksz transition is ana− lyzed by a uniaxial elastic theory, in which a deformation of director, denoting a direction of uniaxial symmetry axis, is solely taken into account [1]. The symmetry breaking in the Freedericksz transition with biaxial symmetry is quite inter− esting from a microscopic point of view [23].…”

“…We have an− other type of a system with biaxial symmetry in the phenom− ena of Freedericksz transition, where an external field and boundary walls compete with each other [1]. For example, at the field larger than the critical field in a homogeneous sys− tem, a splay deformation occurs, in which the splay direction is degenerate and a symmetry with respect to an oblique order is broken [11,23]. Usually, the Freedericksz transition is ana− lyzed by a uniaxial elastic theory, in which a deformation of director, denoting a direction of uniaxial symmetry axis, is solely taken into account [1].…”

Competition between capillarity, layering and biaxiality in a confined liquid crystal

“…The presmectic film [42] and fully developed confined smectics [43] were also considered. Models dealing only with attractive particle interactions (of the Maier-Saupe type) have also been used for confined nematic liquid crystals [44,45,46,47]. Theories on lattice models [21,48,49] and computer simulations on lattice [50,51,52,53] and continuous [54,55,56,57,58,59,60,61] models are also abundant.…”