Energy vs. Entropy in Superlattices of Ligand-Covered Nanoparticles

Nanoparticles covered with short ligands tend to self-assemble into face-centered cubic (fcc) superlattices, while nanoparticles with longer ligands preferentially form body-centered cubic (bcc) superlattices. The thermodynamic driving forces for these structures are not fully understood and conflicting theories have been proposed. In this paper, we systematically study the thermodynamic stability of fcc and bcc superlattices as a function of ligand length, core size, and ligand coverage with a coarse-grained molecular model. Our simulations reveal that bcc superlattices are stabilized via two fundamentally different mechanisms, depending on ligand length. For shorter ligands, the bcc superlattice has a lower potential energy than fcc, due to additional interactions between ligands on next-nearest neighbors in the superlattice. For longer ligands, the bcc superlattice is stabilized due to a larger configurational entropy of ligands.