Effect of material constants on the orientation structure of ferroelectric liquid crystal cells

The orientation structure of ferroelectric liquid-crystal cells in layer-normal geometry was studied based on a one-dimensional elastic continuum model which included three nonequal elastic constants. By minimizing the distortion energy and the surface energies, the critical cell thickness for the uniform, splayed, and helical states has been obtained as functions of the cone angle, the helical pitch, the elastic constants, and the surface interaction coefficients. By a proper choice of the handedness of the liquid crystal helicoid and the material constants, the critical cell thickness for the uniform state can be made very large, and the constraint on small polar surface-interaction coefficient for the stabilization of uniform state can be relaxed to a great extent. It is also shown that bistable states can only be stabilized in cells with no polarity difference between the substrate surfaces.