Distribution of torque in a dual-frequency liquid crystal.

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 gamma changes sign from positive to negative as the frequency is raised through a cross-over frequency f (c). The director torque is proportional to gamma, to the square of the electric field E, and to sin (20) where 0 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.