A density-functional description of liquid crystals is developed. Formally exact expansions for thermodynamic functions in terms of a direct-correlation function are given. Approximations to the direct-correlation function lead to different versions of the molecular-field theories of liquid crystals. The properties of the uniform nematic phase including the isotropic-nematic phase transition at constant pressure are discussed. Expressions are given for the change in density and order parameters at the transition in terms of the direct-correlation function of the isotropic phase. Methods for calculating the direct-correlation functions of the isotropic phase are also discussed. A formal theory for the statistical mechanics of a nonuniform liquid crystal is developed and used to derive expressions for the Frank elastic constants. This approach provides a starting point for the investigation of the phase transitions in the liquid crystals and the properties of inhomogeneous systems. A microscopic description of the Landau—de Gennes theory is also given.

• Received 5 December 1983

DOI:https://doi.org/10.1103/PhysRevA.30.583