|An orientational order of anisometric molecules provides a rich variety of phases and phase transitions in liquid crystals, polymers and other soft matter systems. Recently, orientational transitions in materials with molecules of complex non-symmetric shape have attracted the strong interest because of the possibility of biaxial nematic phase. The theoretical studies of the liquid crystal phases are usually performed within three approaches: (1) the microscopic models where the specific intermolecular interaction is averaged over orientations of neighboring molecules to produce the mean potential, (2) the Landau phenomenological power expansion of the free energy in terms of the corresponding order parameters, and (3) computer simulations.|
A new approach for the power expansion of the orientational free energy is proposed. The approach utilizes the specific features of the orientational energy and entropy that reduce the number of terms in the expansion and simplify the analysis of phase diagrams. The expansion is applied to build a phase diagram for uniaxial and biaxial nematic phases in materials with non-polar parallelepiped-type molecules.