Density-functional theory of the nematic phase: Results for a system of hard ellipsoids of revolution

A second-order density-functional theory is used to study the isotropic-nematic transition in a system of hard ellipsoids of revolution. The direct pair-correlation functions of the coexisting isotropic liquid that enter in the theory as input information are obtained from solving the Ornstein-Zernike equation using the Percus-Yevick closure relation. The spherical harmonic expansion coefficients of the correlation functions obtained from this solution are in good agreement with those found from computer simulations. We find that a system spontaneously transforms to a nematic phase when the structural parameter denoted by c^₂₂⁽⁰⁾ attains a value close to 4.40. This value of c^₂₂⁽⁰⁾ depends, although very weakly, on the value of the length-to-width ratio of the molecules. The transition parameters we found are in very good agreement with the results generated by computer simulations. By using the harmonic coefficients of the direct pair-correlation functions, we have calculated the Frank elastic constants of the nematic phase.