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A continuum theory is employed to numerically study the equilibriumorientation and defect structures of a circular cylindrical particle with flatends under a homeotropic anchoring condition in a uniform nematic medium.Different aspect ratios of this colloidal geometry from thin discotic to longrod-like shapes and several colloidal length scales ranging from mesoscale tonanoscale are investigated. We show that the equilibrium state of thiscolloidal geometry is sensitive to the two geometrical parameters: aspect ratioand length scale of the particle. For a large enough mesoscopic particle, thereis a specific asymptotic equilibrium angle associated to each aspect ratio.Upon reducing the particle size to nanoscale, the equilibrium angle follows adescending or ascending trend in such a way that the equilibrium angle of aparticle with the aspect ratio bigger than 1:1 (a discotic particle) goes to aparallel alignment with respect to the far field nematic, whereas theequilibrium angle for a particle with the aspect ratio 1:1 and smaller (arod-like particle) tends toward a perpendicular alignment to the uniformnematic direction. The discrepancy between the equilibrium angles of themesoscopic and nanoscopic particles originates from the significant differencesbetween their defect structures. The possible defect structures related tomesoscopic and nanoscopic colloidal particles of this geometry are alsointroduced.

Equilibrium state of a cylindrical particle with flat ends in nematic liquid crystals