Freedericksz instability for the twisted nematic device: A three-dimensional analysis

Of interest here is the fully three-dimensional analysis of the Freedericksz transition for the twisted nematic device (TND), which is widely used in liquid-crystal display monitors. Using a coupled electromechanical variational formulation, the problem is treated as a bifurcation instability triggered by an externally applied electric field. More specifically, we study a finite thickness liquid-crystal layer, anchored between two infinite parallel plates relatively rotated with respect to each other by a given twist angle and subjected to a uniform electric field perpendicular to these bounding plates. The novelty of the proposed analysis lies in the fully three-dimensional formulation of the TND problem that considers all possible bounded perturbations about the principal solution. By scanning a wide range of the liquid crystal's material parameter space, we establish whether the Freedericksz transition is global, i.e., has an eigenmode depending solely on the layer thickness coordinate, or local (also termed the periodic Freedericksz transition), i.e., has an eigenmode with finite wavelengths in one or both directions parallel to the plate. It is found that global modes are typical for low values, while local modes appear at large values of the twist angle. Moreover, for certain TND's, the increase in twist angle can lower the critical electric field, findings that could be useful in guiding liquid-crystal selection for applications.