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The compatibility of different approximations to the Helmholtz free energy F is analysed in order to provide the consistent definition of the order parameters for liquid crystalline phases. In particular the diagrammatic expansion theory is compared to the weighted, also modified weighted, density approximations. The weight function w is shown to be proportional to the Mayer function. The explicit form of the weight function for the system of non-uniaxial polar molecules is given and the interaction terms of the polar and orientational order parameters in the free energy expansion are discussed. [ABSTRACT FROM AUTHOR]

The nematic-isotropic phase transitions in mixtures of rod-like and disc-like molecules are studied by a mean field theory. We consider both attraction and hard-core repulsion for the model molecules, thermotropic phase transitions are found from the isotropic to one of the two types of uniaxially symmetric nematic phases: optically positive N+ and negative N-. On the other hand, biaxially symmetric nematic phase is shown to be always less stable than the uniaxial phase. We predict that re-entrant phase transition occur for the lyotropic system. [ABSTRACT FROM AUTHOR]