  Nanoparticles are often covered in ligand monolayers, which can undergo a
temperature-dependent order-disorder transition that switches the
particle-particle interaction from repulsive to attractive in solution. In this
work, we examine how changes in the ligand surface coverage and facet
dimensions affect the ordering of ligands, the arrangement of nearby solvent
molecules, and the interaction between ligand monolayers on different
particles. In particular, we consider the case of strongly bound octadecyl
ligands on the (100) facet of CdS in the presence of an explicit n-hexane
solvent. Depending on the facet dimensions and surface coverage, we observe
three distinct ordered states that differ in how the ligands are packed
together, and which affect the thickness of the ligand shell and the structure
of the ligand-solvent interface. The temperature dependence of the
order-disorder transition also broadens and shifts to lower temperature in a
nonlinear manner as the nanoscale is approached from above. We find that
ligands on nanoscale facets can behave very similarly to those on macroscopic
surfaces in solution, and that some facet dimensions affect the ligand
alignment more strongly than others. As the ligands order, the interaction
between opposing monolayers becomes attractive, even well below full surface
coverage. The strength of attraction per unit surface area is strongly affected
by ligand coverage, but only weakly by facet width. Conversely, we find that
bringing two monolayers together just above the order-disorder transition
temperature can induce ordering and attraction.
