Density functional theory of liquid crystals and surface anchoring: Hard Gaussian overlap-sphere and hard Gaussian overlap-surface potentials

Abstract

This article applies the density functional theory to confined liquid crystals, comprised of ellipsoidal shaped particles interacting through the hard Gaussian overlap (HGO) potential. The extended restricted orientation model proposed by Moradi and co-workers [J. Phys.: Condens. Matter 17, 5625 (2005)] is used to study the surface anchoring. The excess free energy is calculated as a functional expansion of density around a reference homogeneous fluid. The pair direct correlation function (DCF) of a homogeneous HGO fluid is approximated, based on the optimized sum of Percus-Yevick and Roth DCF for hard spheres; the anisotropy introduced by means of the closest approach parameter, the expression proposed by Marko [Physica B 392, 242 (2007)] for DCF of HGO, and hard ellipsoids were used. In this study we extend an our previous work [Phys. Rev. E 72, 061706 (2005)] on the anchoring behavior of hard particle liquid crystal model, by studying the effect of changing the particle-substrate contact function instead of hard needle-wall potentials. We use the two particle-surface potentials: the HGO-sphere and the HGO-surface potentials. The average number density and order parameter profiles of a confined HGO fluid are obtained using the two particle-wall potentials. For bulk isotropic liquid, the results are in agreement with the Monte Carlo simulation of Barmes and Cleaver [Phys. Rev. E 71, 021705 (2005)]. Also, for the bulk nematic phase, the theory gives the correct density profile and order parameter between the walls.