A review of mathematical analysis of nematic and smectic-A liquid crystal models

We review the mathematical analysis of some uniaxial, liquid crystal phases. Firstly, we state the models for the two different studied phases: nematic and smectic-A liquid crystals. The spatial and temporal profiles of the liquid crystal configurations will be described by means of strongly nonlinear parabolic partial differential systems, which are presented at the same time. Then we will state some results about existence, regularity, time-periodicity and stability of solutions at infinite time for both models. It is our aim to show that, although nematic and smectic-A phases have different physical properties and are modelled by different nonlinear parabolic problems, there exists a common mathematical machinery to rewrite the models and obtain analytical results.

Molecular Orientation in Uniaxial Liquid Crystal Phases as Studied by Electron Paramagnetic Resonance

The electron paramagnetic resonance spectra of 3/ß-doxyl-5α-cholestane dissolved in five liquid crystals have been recorded as a function of temperature in the isotropic and mesogenic phases. From these spectra the order parameter (P2) has been determined. The results have been com-pared with the data obtained from the optical birefringence measurements and from the polarized absorption spectra of the dichroic dye dissolved in liquid crystal host.