Distorted twisted nematic liquid-crystal structures in zero field

Leslie’s differential equations describing the orientation of the optic axis through a twisted nematic layer are solved for the case where there is a nonzero tilt bias angle. Three classes of solutions are investigated: the simple solution of constant tilt angle through the layer with uniform twist, symmetric solutions where the tilt angle in the middle of the layer has an extreme value, and antisymmetric solutions where the tilt angle in the middle of the layer is identically zero. These solutions and their corresponding elastic deformation energies are compared for typical values of the splay, twist, and bend elastic constants of nematic liquid crystals. For 90° twisted nematic layers the antisymmetric solution always has a higher elastic energy than the symmetric solution. This result explains why regions of reverse twist are suppressed in twisted nematic display devices which have finite tilt bias angles at both boundaries. Reverse-twisted domains can also be avoided by adding chiral dopants to the nematic mixture and by making layers having total twist angles of less than 90°. The effectiveness of these three techniques is discussed in terms of a comparison of the elastic energy difference between the oppositely twisted configurations.