  We use computer simulations and simple theoretical models to analyze the
morphologies that result when rod-like particles end-attach onto a curved
surface, creating a finite-thickness monolayer aligned with the surface normal.
This geometry leads to two forms of frustration, one associated with the
incompatibility of hexagonal order on surfaces with Gaussian curvature, and the
second reflecting the deformation of a layer with finite thickness on a surface
with non-zero mean curvature. We show that the latter effect leads to a
faceting mechanism. Above threshold values of the inter-particle attraction
strength and surface mean curvature, the adsorbed layer undergoes a transition
from orientational disorder to an ordered state that is demarcated by
reproducible patterns of line defects. The number of facets is controlled by
the competition between line defect energy and intra-facet strain. Tuning
control parameters thus leads to a rich variety of morphologies, including
icosahedral particles and irregular polyhedra. In addition to suggesting a new
strategy for the synthesis of aspherical particles with tunable symmetries, our
results may shed light on recent experiments in which rod-like HIV GAG proteins
assemble around nanoscale particles.
