  The structure of the tilted phase of monolayer-protected nanoparticles is
investigated by means of a simple Ginzburg-Landau model. The theory contains
two dimensionless parameters representing the preferential tilt angle and the
ratio epsilon between the energy cost due to spatial variations in the tilt of
the coating molecules and that of the van der Waals interactions which favors
uniform tilt. We analyze the model for both spherical and octahedral particles.
On spherical particles, we find a transition from a tilted phase, at small
epsilon, to a phase where the molecules spontaneously align along the surface
normal and tilt disappears. Octahedral particles have an additional phase at
small epsilon characterized by the presence of six topological defects. These
defective configurations provide preferred sites for the chemical
functionalization of monolayer-protected nanoparticles via place-exchange
reactions and their consequent linking to form molecules and bulk materials.
