Nonstandard electroconvection and flexoelectricity in nematic liquid crystals

For many years it has been commonly accepted that electroconvection (EC) as primary instability in nematic liquid crystals for the classical planar geometry requires a positive anisotropy of the electric conductivity, sigma(a), and a slightly negative dielectric anisotropy, epsilon(a). This firm belief was supported by many experimental and theoretical studies. Recent experiments, which have surprisingly revealed EC patterns at negative conduction anisotropy as well, have motivated the theoretical studies in this paper. It will be demonstrated that extending the common hydrodynamic description of nematics by the usually neglected flexoelectric effect allows for a simple explanation of EC in the nonstandard case sigma(a)< 0.