Polar flexoelectric deformations and second order elasticity in nematic liquid crystals

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Abstract
The influence of second order elasticity (K13 ≠ 0) on the flexoelectric polar deformations in a homeotropic (case A) and a homogeneous (case B) nematic layer with negative and positive dielectric anisotropy and an electric field normal to the layer is considered theoretically in this paper. The exact threshold condition is obtained, transcendental equations are solved numerically for different values of the anisotropic interfacial energies Ws1 and Ws2, the total flexoelectric coefficient e1z + e3x and K13. For K13 ≠ 0 and some values of Ws1 or Ws2 (critical values), the deformations start with a jump. The required electric energy for the appearance of the flexoelectric deformations (case A and B) is corrected considerably

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