Symmetry Adapted Molecular-field Theory For Thermotropic Biaxial Nematic Liquid Crystals and Its Expansion At Low Temperature

We have analyzed some properties of mean field theories of thermotropic biaxial liquid crystals with (D-2h) symmetry. The study consists of two parts. In the first part we reexamine the standard theory due to Virga and coworkers. We introduce a convenient symmetry-adapted parameterization which allows the phase diagram to be displayed in an explicitly symmetry-preserving triangle. In the second part we use the Laplace approximation to examine the low temperature properties of the liquid crystal order parameters. Two of these (conventionally, D, P) are identically zero at zero temperature in a biaxially ordered phase and nonzero at low temperatures in the liquid crystalline phases but are again zero at higher temperatures in the isotropic phase. We use a low temperature expansion to derive an expression for the dominant terms in the free energy. This functional is minimized to obtain the low temperature properties of the order parameters D, P.