Deformation of nematic-positive liquid crystals by an electric field between two co-axial cylindrical electrodes

The deformation of liquid crystals in an electric field is analyzed theoretically when a nematic-positive liquid crystal is placed between two co-axial cylindrical electrodes. The analysis is made by applying variational calculus to the free energy of the total system. The tilt angle as a function of the distance from the center line of the cylinders is calculated in two cases: 1) where the elastic constants for splay and bend are equal and 2) where they are different values. The results are given as parameters of electric potential and of the ratio of dielectric anisotropy. We show that the co-ordinate r_m, where the tilt angle has the maximum value, is the geometric average of the inner and the outer radius.