Molecular foundation of a unified theory for the isotropic and nematic or cholesteric phases of liquid crystals

The thermodynamic functions like the internal energy, the entropy, the pressure and the Gibbs free energy are expanded with respect to scalars constructed from the components of the alignment tensors specifying the orientations of the molecules. Microscopic expressions are derived for the expansion coefficients, which are integrals involving the interaction potential and the pair-correlation function. These quantities are well defined for both the isotropic liquid and the ordered nematic or cholesteric phases. Spatial derivatives of the alignment tensors are also taken into account. This point is of importance for the Frank elasticity coefficients of nematics and the pitch of cholesterics.