Numerical study of deformations induced by ac electric field in insulating flexoelectric nematic layers

The influence of the frequency f of applied ac electric field on the time dependence of electric field induced deformations of homeotropic nematic layers is studied numerically. Three kinds of nematic liquid crystals were considered: non-flexoelectric nematic with negative dielectric anisotropy, Δε < 0, dielectrically compensated nematic (Δε = 0) possessing flexoelectric properties determined by the positive sum of flexoelectric coefficients e = e¹¹ + e₃₃ > 0, nematic characterised by both Δε < 0 and e > 0. It was found that at sufficiently low frequencies, the deformations varied with time. The deformations of purely dielectric nature had the period 1/(2f). When the frequency was increased, a stationary director distribution was achieved, determined by the rms value of the ac voltage. The time period of purely flexoelectric distortions was equal to 1/f. There was a well defined cut-off frequency above which these deformations vanished. In the case of dielectrically anisotropic and flexoelectric nematic, the flexoelectric contribution vanished above a critical frequency and the deformation of dielectric nature stabilized at high frequencies.