  A systematic analysis of defect textures in facetted nanoparticles with
polygonal configurations embedded in a nematic matrix is performed using the
Landau-de Gennes model, homeotropic strong anchoring in a square domain with
uniform alignment in the outer boundaries. Defect and textures are analyzed as
functions of temperature T, polygon size R, and polygon number N. For nematic
nanocomposites, the texture satisfies a defect charge balance equation between
bulk and surface (particle corner) charges. Upon decreasing the temperature,
the central bulk defects split and together with other -1/2 bulk defects, are
absorbed by the nanoparticle's corners. Increasing the lattice size decreases
confinement and eliminates bulk defects. Increasing the polygon number
increases the central defect charge at high temperature and the number of
surface defects at lower temperatures. The excess energy per particle is lower
in even than in odd polygons, and it is minimized for a square particle
arrangement. These discrete modeling results show for first time that even
under strong anchoring, defects are attached to particles as corner defects,
leaving behind a low energy homogeneous orientation field that favors
nanoparticle ordering in nematic matrices. These new insights are consistent
with recent thermodynamic approaches to nematic nanocomposites that predict the
existence of novel nematic/crystal phases and can be used to design
nanocomposites with orientational and positional order.
