  A continuum theory is employed to numerically study the equilibrium
orientation and defect structures of a circular cylindrical particle with flat
ends under a homeotropic anchoring condition in a uniform nematic medium.
Different aspect ratios of this colloidal geometry from thin discotic to long
rod-like shapes and several colloidal length scales ranging from mesoscale to
nanoscale are investigated. We show that the equilibrium state of this
colloidal geometry is sensitive to the two geometrical parameters: aspect ratio
and length scale of the particle. For a large enough mesoscopic particle, there
is a specific asymptotic equilibrium angle associated to each aspect ratio.
Upon reducing the particle size to nanoscale, the equilibrium angle follows a
descending or ascending trend in such a way that the equilibrium angle of a
particle with the aspect ratio bigger than 1:1 (a discotic particle) goes to a
parallel alignment with respect to the far field nematic, whereas the
equilibrium angle for a particle with the aspect ratio 1:1 and smaller (a
rod-like particle) tends toward a perpendicular alignment to the uniform
nematic direction. The discrepancy between the equilibrium angles of the
mesoscopic and nanoscopic particles originates from the significant differences
between their defect structures. The possible defect structures related to
mesoscopic and nanoscopic colloidal particles of this geometry are also
introduced.
