Electric field induced static modulated structures in nematics

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Abstract
Linearized continuum theory is used to investigate the possible occurrence of static modulated structures (MS) under the action of an electric field (E) applied parallel to the sample planes with the initial uniform director orientation tilted with respect to the sample boundaries in a plane normal to E. Under the rigid anchoring hypothesis it is shown that the formation of MS with periodicity along E is favoured when a stabilizing magnetic field (H∥) of sufficient strength is impressed along the initial director orientation. When the initial director tilt is sufficiently away from the homeotropic, MS may not occur ; in particular, MS cannot occur in the twist geometry. These results are in qualitative accord with some recent experimental investigations. It appears possible to deter the formation of MS by using high frequency electric fields in materials which have a propensity towards exhibiting strong dielectric relaxation. The facilitating action of H∥ towards MS is rather reminiscent of a hydrodynamical analogue. The effects of weak director anchoring and flexoelectricity are found to be pronounced only when H∥ is small enough. Intriguingly, it appears that an instability mode having periodicity parallel to the sample planes but normal to E may set in at a threshold comparable to that of MS thus indicating a need for more detailed experimental and theoretical investigations taking proper account of the aspect ratio of the sample cell