Maier-Saupe and Onsager approaches as limits of the nematic-isotropic phase transition

Through a virial expansion, the long and small range properties of the interaction between ellipsoidal nematic molecules are put together in a unique approach that combines the essentials: of some classical models that describe the nematic-isotropic phase transition. The Lennard-Jones potential that mediates the interaction between the centers of the mass of molecules, the long range Maier-Saupe interaction that favors their alignment and the molecular hard core that hinders their close approximation, as in the Onsager model, are combined in a unique approach that exhibits two phases transitions the gaseous-liquid transition and the nematic-isotropic phase transition. As a conclusion, the Onsager and Maier-Saupe approaches were considered limits of the actual physical situation.