Free energy calculations on the stability of polymer-grafted nanoparticle superlattices

Deformable soft particles, such as diblock copolymer micelles and polymer-grafted nanoparticles (PGNPs), can self-assemble into various crystalline superlattices with different geometries. The stability of such crystals cannot be understood from a simple packing model of hard spheres because the construction units are no longer isotropic spheres. We apply molecular dynamics simulation to compute the free energy cost of compressing isolated spherical PGNPs into Wigner-Seitz polyhedrons that can tile three-dimensional space. In combination with surface energy calculations, we analyze the stability of simple cubic, body-centered cubic, and face-centered cubic superlattices formed by PGNPs.