Theory of nonlinear transient patterns in the splay Fréedericksz transition

A nonlinear theory of transient patterns in the electrically induced splay Fréedericksz transition in nematic liquid crystals is presented. Growth conditions for periodic perturbations with a wave vector perpendicular to the initial director alignment, superposed on the homogeneous realignment process, have ben investigated. The decisive effect leading to this type of pattern formation arises from the field distortion resulting from the electric anisotropies. The nonlinear analysis with rigid boundary conditions delivers the onset of the pattern-forming instability at a critical value of the control parameter ${\mathrm{\epsilon }}_{\mathit{c}}$, which appears to be too large.