With elastic constants as functions of the order parameters, we have obtained a Landau's elastic free energy expression for biaxial nematic liquid crystals similar to that used by Govers. The relationship between this Govers form and the Saupe form for biaxial nematics is obtained. It shows that simple distortion, splay, twist or bend, may lead to a first order phase transition from isotropic phase to biaxial nematic phase. However, in the case of cholesteric liquid crystal, there exists a critical chirality, above which, instead of first order, the phase transition becomes second order.
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