Electro-Hydrodynamic Instabilities in Nematic Liquid Crystals.

We review some of the basic properties of the nematic liquid crystals and re-derive the fundamental quantities necessary for the development of a macroscopic continuum theory. Using this macroscopic theory as a basis, we carry out two separate investigations into the primary transitions of a nematic liquid crystal thin film subjected to an a.c. electric field. We first attempt to establish theoretically the critical behavior of the normal rolls observed slightly above the threshold voltage. A phenomenological free energy description is used and a set of bifurcation diagrams is constructed to illustrate the critical behavior. In our second investigation, we use the method of multi-scale analysis to illustrate the formation of oblique rolls at low frequencies when the director field is given only one rotational degree of freedom. The transformation from the normal to the oblique rolls is shown through the minimization of the neutral surface, thereby establishing the presence of triple point. We furthermore examine the impact of the use of a restrictive director field on the small scale dynamics by deriving an amplitude equation.