Landau Theory of Biaxial Nematic Liquid Crystals

The orientational order of molecules in a liquid crystal is traditionally described by spatial or temporal averages of functions that are quadratic in the direction cosines of molecular axes with respect to laboratory fixed axes. The free energy describing the nematic phase must be independent of the choice of coordinate systems and therefore rotationally invariant with respect to both laboratory and molecular frames. A Landau theory for biaxial and uniaxial nematics based on six fundamental invariants is developed which is properly rotationally invariant. Four possible nematic phases, two uniaxial and two biaxial, result. NMR experiments should be able to identify which of these actually occur in specific materials.