The Studyfor Electrohydrodynamic Convection Of Conduction Regime In A Nematic Liquid Crystal

Electrohydrodynamic convection (EHC) of nematic liquid crystals is a well suited system to study pattern formation in anisotropic fluids. It is driven electrically and yields a large variety of spatially extended patterns with different dynamics. EHC in calamitic (rodlike) nematic liquid crystal has been studied experimentally for a long time. Williams domains in nematics represent one of the standard systems for dissipative pattern formation in anisotropic fluids, they have been extensively studied in the past decades. The classical electrohydrodynamic convection (EHC) structures, observed first by Williams and Kapustin, and rolls with a wave vector parallel or slightly oblique to the director easy axis in planar sandwich cells. They destabilize the uniform director ground state in nematics with positive conductivity anisotropyσ_αaand negative or weakly positive dielectric anisotropyε_α.The former may be designated as (-,+),the latter as (+,+) materials, where the first sign refers toε_α,the second toσ_α.The"standard EHC"mechanism has been derived by Carr and Helfrich. Later, a discrimination of the so-called conduction and dielectric regimes under ac excitation has been introduced. In novel liquid crystal materials with unconvectional material parameters, new types of electroconvection patterns have been found .Some of them can be explained by the Carr- Helfrich effect, while other structure require modifications and extensions. The mesogen studied in the present publication is a bent-core compound with positiveε_αaand negativeσ_α,(+,-).In planar alignment it develops unconventional electroconvection patterns above the splay Freedericksz transition , e.g.,longitudinal rolls that are oriented parallel or nearly parallel to the initial direction (n|-)₀(for a description of the Freedericksz transition ).This is in contrast to the classical normal rolls with an orientation perpendicular to (n|-)₀ in the (-,+) case in accordance with the standard model. A mechanism leading to the formation of longitudinal rolls at electric fields above the Freedericksz transition has been introduced and explained within a basic model.We use a set of differential equations which describe the hydrodynamics of a conducting liquid crystal subjected to external electromagnetic fields. We rigorously solve the boundary-value problem associated with the longitudinal rolls in nematic liquids. we quantitatively analyze the period of the longitudinal rolls changes related to increased driving voltage in periodic twist modulation structure of conduction regime by 2-dimensional theoretical numerical simulation..