The method for determination of flexoelectric coefficients of nematic liquid crystals

A method for determining the flexoelectric coefficients of a nematic liquid crystal (NLC) is proposed. The principle of method suggested is the measurement of characteristics of flexoelectric domains arising in the a polarization- optical microscope (electro-optical method). The digitized images of these domains is used for the optical contrast $K$ determination. Linear fitting of the contrast $K$ depending on the applied voltage $U$ in vicinity of the threshold of flexoelectric domain formation allows rather precisely to determine the critical voltage $U_c$. The spatial period of the observed domains is found by means of a two-dimensional Fourier transformation of digitized images. Using the material parameters of the NLC in the linear analysis of the basic state stability, and the difference between the flexoelectric coefficients ($e_1-e_$) as the fitting parameter, the threshold characteristics (critical voltage and characteristic spatial period) of the flexoelectric domains are calculated so that they were close to experimental ones. The flexocoefficient difference chosen in this way is accepted as the wanted result.