On the equation of director motion in ferroelectric liquid crystals

In a one-dimensional situation of a liquid crystal sample between two electrodes perpendicular to thex-axis, it is thex-component of the electrical inductionDx and not the electrical fieldEx which is independent of thex-coordinate. In the present paper the equation of director motion is derived in a more precise way, and some applications for ferroelectric liquid crystals are discussed. WithFd the distortion energy andFs the surface interaction energy it turns out that the expression for the electric Gibbs function can be used in combination with the standard Euler-Lagrange equations provided not only the orientation of the director but also the potential are considered to be independently variable unknown functions. Variation of the orientation leads to its equation of motion and boundary conditions. Variation of the potential under constant electrode voltage leads to Maxwell's equation.