Why do cubic nanoparticles favor a square array? Mechanism of shape-dependent arrangement in nanocube self-assemblies

Simple calculations of potential energy were made to account for the preferred appearance of square arrays in cubic nanoparticle self-assemblies, taking into account the van der Waals attractions between the particles. The results showed that the nearest neighbor particles have a dominant contribution to the potential energy, and hence, play a decisive role to determine the lattice symmetry of the resulting arrays. From comparative studies between two close-packed arrangements (a square array and a pseudo-hexagonal array), it was found that the highly coordinated square array is energetically more stable than the lowly coordinated pseudo-hexagonal one.