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 the preferential 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.