Distribution of Torque in a Dual-Frequency Liquid Crystal

Abstract

We derive the equations that relate the torque distribution to the voltage and configuration when voltages at two or more frequencies are superimposed in a liquid crystal for dual-frequency applications. In such a material, the dielectric anisotropy factor γ changes sign from positive to negative as the frequency is raised through a cross-over frequency f _c. The director torque is proportional to γ, to the square of the electric field E, and to sin(2θ) where θ is the angle between the field and the director. The results are complicated by the fact that E is not constant across the cell, but varies with director orientation. The derived equations apply to the general case of a lossy medium. An example is given in which a high frequency overcomes the orienting effect of a low frequency.