Generalized Freedericksz Transition in Polymer Nematics

Abstract

Recent theoretical studies on the relative occurrence of field induced static periodic domains (PD) and homogeneous deformation (HD) are reviewed for different sample and field configurations. Apart from energetics the related language of torques can be employed to obtain a qualitative explanation of the destabilizing positive feedback mechanism (PFM) which causes PD to develop in materials having high elastic anisotropy. PD may be suppressed by a proper choice of field direction, initial director orientation or director anchoring strengths at the boundaries; simultaneous application of an orthogonal stabilizing field may also quench PD. In a simple twisted nematic, PD may occur as one of two independent modes associated with orthogonal directions of periodicity. Solutions reminiscent of PD result for biaxial nematics though in this case PD may have a more complex form. When the sample is cylindrical and the field radial PD may result, depending upon the initial director orientation, either as a static Taylor instability or as a distortion whose azimuthal variation is governed by a dimensioniess wavevector taking integral values. Though, in the limit of weak dielectric anisotropy and zero electrical conductivity, analysis for electric field induced PD is similar to that of the magnetic case the importance of flexoeiectricity and non-local interaction of the field cannot be ruled out.