The Elastic Constants of Maier-Saupe Rodlike Molecule Nematics

Abstract

Abstract The classical Maier-Saupe theory of spatially uniform nernatics is here extended to the case of distorted configurations. Under the assumption that the molecules are rodlike, the mean field potential is here defined as an average over a suitable neighborhood of the test molecule. The energy density thereby calculated automatically accounts for the distortion energy, and properly reduces to the classical expres- sion for the homogeneous situation. In the linear limit, contrary to existing predictions based on Maier- Saupe potential, the three constants of Frank elasticity are found to be different from one another, and ordered as K 1, <K 2, <K 3. The main variables determining the magnitude of the elastic constants are: the order parameter S, the molecular length L, and an interaction distance ℒ A quantitative test of the theory on a standard nematic (PAA) shows good agreement with data for all three constants if ℒ is of the order of 1 nanometer.