Consistency of Mean Field Theories of Nematic Liquid Crystals

The Maier-Saupe theory of nematic liquid crystals, which uses a one-body mean field potential of the form φ2 nP2(cos θ), where θ is the angle between the molecular long axis and the nematic director and n is the average value of the Legendre polynomial P2(cos θ), is shown to exhibit statistical-thermodynamic self-consistency if and only if φ2 is independent of the temperature and directly proportional to the first power of the density. The significance of this result with respect to a molecular theory of the nematic state is discussed.