Difficulties with the Maier–Saupe theory of liquid crystals

Abstract

The Maier–Saupe anisotropic dispersion energy is estimated and found to be an order of magnitude smaller than the value usually assumed in the liquid crystal theory. The idea behind the estimate is to compare the anisotropic part of the dispersion energy to the average dispersion energy. This is done with the help of the relation R∼ (Δα/3α)², where R is the ratio of the perturbation theory sums involved in the anisotropic and average dispersion energies and Δα, α are the polarizability anisotropy and average polarizability, respectively. It is suggested that the total attractive force contributes to the stability of nematic liquid crystals through both a small change in the radial correlations and any density change at the mesomorphic transition (at constant volume the latter is zero). In the resulting picture of liquid crystals the repulsive forces play the primary role.