On electrically driven pattern-forming instabilities in planar nematics

Abstract

The theoretical description of the threshold and near-threshold behavior of electrohydrodynamic convection in nematic liquid crystals in the (low-frequency) conduction regime is reconsidered. We present essentially the full three-dimensional linear stability analysis of the basic state and a major part of the weakly-dependence are treated rigorously but the flexoelectric effect is neglected. Related transitions like the periodic splay-twist instability, which is relevant in polymer materials with positive dielectric anisotropy, are also considered. We give criteria for finding the oblique-roll state and for the competition between different instabilities. Comparison with experiments is made wherever possible. Good qualitative and sometimes quantitative agreement is found Analyse lineaire tridimensionnelle complete de l'etat de base et theorie faiblement non lineaire de l'etat convectif pour decrire le comportement au seuil, et pres du seuil, de la convection electrohydrodynamique de cristaux liquides nematiques dans le regime de conduction (basse frequence). Traitement rigoureux des conditions aux limites aux plaques superieure et inferieure et de la variation temporelle. Extension de l'analyse a diverses transitions, comme l'instabilite de «splay-twist» periodique observee dans des polymeres a anisotropie dielectrique positive. Criteres pour l'observation de l'etat des rouleaux obliques et la competition entre differentes instabilites. Comparaison aux donnees experimentales