Elastic constants in a pseudomolecular approach for a mixed Maier-Saupe and Nehring-Saupe interaction law

Abstract

A pseudomolecular approach is employed to calculate the elastic constants of a nematic liquid crystal by assuming an interaction volume of ellipsoidal shape. We consider a special kind of mixed Maier-Saupe and Nehring-Saupe interaction law characterized by a mixing factor $\ensuremath{\epsilon}$. To $\ensuremath{\epsilon}=0$ corresponds the Maier-Saupe law, whereas to the case $\ensuremath{\epsilon}=1$ corresponds the induced dipole-induced dipole interaction law. The dependence of the elastic constants on the eccentricity of the molecular volume shape and on the mixing factor is investigated by means of a numerical analysis. We show that, for particular values of the eccentricity, the ${K}_{11}$ (splay) and ${K}_{33}$ (bend) elastic constants become negative for some values of the mixing factor. Moreover, the nonmonotonic behavior of the splay-bend elastic constant with respect to the mixing factor, already reported in a spherical approximation for the interaction volume, is also observed. This result reinforces the indication that the subsurface deformations, if any, are not only due to the splay-bend term.