Anisotropic nanoparticles immersed in a nematic liquid crystal: Defect structures and potentials of mean force

We report results for the potential of mean force (PMF) and the defect structures that arise when spherocylindrical nanoparticles are immersed in a nematic liquid crystal. Using a dynamic field theory for the tensor order parameter Q of the liquid crystal, we analyzed configurations, including one, two, and three elongated particles, with strong homeotropic anchoring at their surfaces. For systems with one nanoparticle, the most stable configuration is achieved when the spherocylinder is placed with its long axis perpendicular to the far-field director, for which the defect structure consists of an elongated Saturn ring. For systems with two or three nanoparticles with their long axes placed perpendicular to the far-field director, at small separations the defect structures consist of incomplete Saturn rings fused with new disclination rings orthogonal to the original ones, in analogy to results previously observed for spherical nanoparticles. The shape of these orthogonal rings depends on the nanoparticles' configuration, i.e., triangular, linear, or parallel with respect to their long axis. A comparison of the PMFs indicates that the latter configuration is the most stable. The stability of the different arrays depends on whether orthogonal disclination rings form or not, their size, and the curvature effects in the interparticle regions. Our results suggest that the one-elastic-constant approximation is valid for the considered systems; similar results were obtained when a three-constant expression is used to represent the elastic free energy. The attractive interactions between the elongated particles were compared to those observed for spheres of similar diameters. Similar interparticle energies were observed for linear arrays; in contrast, parallel and triangular arrays of spherocylinders yielded interactions that were up to 3.4 times stronger than those observed for spherical particles.