The Flexoelectric Effect And The Non-Symmetric NLC Cell

We study the flexoelectric effect of the non-symmetric liquid crystal cell with the analytical method. We get rigorously Gibbs free energy of the system under electrical field, which involve the Frank free energy, the dielectric free energy, the flexoelectric free energy and the anchoring free energy, where the anchoring free energy is based on the modified formula of Rapini-Papoular. The differential equation and boundary condition of the director tilt angle θ are obtained by applying the proper mathematical method. We have proved that the flexoelectric effect is to produce a new term of surface anchoring energy, which has opposite at upper and lower substrates. The conclusion is the direct result of the flexoelectric effect.Applying the differential equation and boundary condition of the director tilt angle θ, the essential characters are discussed, which include the threshold voltage and the saturation voltage. The essential character of the non-symmetric liquid crystal cell is that the director distribution at the middle layer of the cell is not symmetric, So a new parameter A is introduced to reflect the breaking of symmetry. We also study the symmetry breaking parameter △th at the threshold point and the symmetry breaking parameter △sat at the saturation point. All above physical parameter establish the relation with the parameters in formula of the anchoring energy and the flexoelectric coefficiente1 +e3. The influence of the flexoelectric effect on thethreshold voltage, the saturation voltage and the symmetry breaking parameter is discussed and calculated carefully.With the result of this investigate, a new experimental plan for measurement of the flexoelectric coefficient the non-symmetric liquid crystal cell is proposed. Now we consider a wedge liquid crystal cell.When different voltages U1 U2 U3 are applied to the cell, the value of thickness l1, l2 l3 may be obtained by measurement. We also assume three non-symmetric liquid crystal cells with the same anchoring substrates. But the value of thickness of the three cells are l1 l2 l3, respectively, we can also obtain thethreshold voltage U1 U2 U3 of corresponding to thickness. Using two methods, we can obtain three values group (l1,U1) (l2,U2) (l3,U3), so we get three equations about anchoring substrates A1 A2and flexoelectric coefficient (e1 + e3). The value of e1 + e3 can be determined by resolving the equation group.A new experimental plan for measurement of e is proposed. This plan is a useful innovation in this paper.