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A simple viscoelastic approach is proposed to describe the periodic patterns, characterized by static walls and splay-bend distortion, which appear in samples of nematic liquid crystals having dielectric anisotropy ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{a}}$ dependent on the frequency. The modulated structure, resulting from a steady velocity field v coupled with a steady director field n, is achieved when an electric field is applied normally to the plates of a planar unidirectional nematic cell. Such a kind of quasistatic domain is theoretically investigated not only in the frequency region, where the usual aperiodic Fr\'eedericksz effect becomes unfavorable, Re(${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{a}}$) still being positive, but also where Re(${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{a}}$)0, favoring in principle the initial orientation. Both previous situations are considered in the vicinity of the sign reversal point. The present model describes the dielectric loss near the reversal point in terms of the appearance of the corresponding effective space charge, which interacts with the effective electric field, causing a steady electrohydrodynamic motion of very small amplitude inside the nematic liquid crystal layer. As a result, a quasistatic tilted modulated structure emerges, with wave vector parallel to the initial planar orientation of the nematic cell. \textcopyright{} 1996 The American Physical Society.

Quasistatic domains in planar nematic liquid crystals around the dielectric inversion point