Isotropic-Nematic Transition: Landau-de Gennes vs Molecular Theory

Abstract

Landau-de Gennes and molecular mean-field descriptions of the isotropic-nematic transition are compared. We use two methods to calculate the order parameter correlation function and show that corrections due to cubic and quartic terms in the Landau expansion are non-negligible. In the first method we apply lowest order diagrammatic perturbation theory using as perturbation both cubic and quartic terms. The second method essentially treats the cubic term to all orders and the quartic term to leading order. A comparison of the results with experiment indicates only qualitative agreement. It is also found that the supercooling temperature T* is different from Tζ, the temperature at which the correlation length diverges. The fact that the corrections are not small and that the results obtained by the two different methods are inconsistent cast grave doubt on the quantitative validity of the Landau-de Gennes approach in its present form.

We propose a numerical way to establish contact between the meanfield theory and the Landau-de Gennes theory. Our results indicate that the two approaches are irreconcilable.