Deformation of nematic liquid crystals in an electric field, Euro

The behaviour of liquid crystal materials used in display devices is discussed. The underlying continuum theory developed by Frank, Ericksen and Leslie for describing this behaviour is reviewed. Particular attention is paid to the approximations and extensions relevant to existing device technology areas where mathematical analysis would aid device development. To illustrate some of the special behaviour of liquid crystals and in order to demonstrate the techniques employed, the specic case of a nematic liquid crystal held between two parallel electrical conductors is considered. It has long been known that there is a critical voltage below which the internal elastic strength of the liquid crystal exceeds the electric forces and hence the system remains undeformed from its base state. This bifurcation behaviour is called the Freedericksz transition. Conventional analytic analysis of this problem normally considers a magnetic, rather than electric, eld or a near-transition voltage since in these cases the electromagnetic eld structure decouples from the rest of the problem. Here we consider more practical situations where the electromagnetic eld interacts with the liquid crystal deformation. Assuming strong anchoring at surfaces and a one dimensional deformation, three nondimensional parameters are identied. These relate to the applied voltage, th