Strong deformations induced by a DC electric field in homeotropic flexo-electric nematic layers

Elastic deformations of homeotropic nematic liquid crystal layers subjected to a DC electric field were studied numerically in order to determine their development under increasing voltage. Both signs of the dielectric anisotropy, Δ?, and of the sum of flexo-electric coefficients, e ₁₁ + e ₃₃, were considered, as were also low, moderate and high ion concentrations. The electrical properties of the layer are described in terms of a weak electrolyte model. Quasi-blocking electrode contacts and a finite surface anchoring strength were adopted. Director orientation, the electric potential and the ion concentrations were each calculated as a function of the coordinate normal to the layer. The director distributions turned out to depend not only on the sign of Δ? but also on the sign of e ₁₁ + e ₃₃, due to the difference in the mobility of anions and cations. The importance of ion content was also confirmed.