Building on a recently introduced inverse strategy, isotropic and convex repulsive pair potentials were designed that favor assembly of particles into kagome and equilateral snub square lattices. The former interactions were obtained by a numerical solution of a variational problem that maximizes the range of density for which the ground state of the potential is the kagome lattice. Similar optimizations targeting the snub square lattice were also carried out, employing a constraint that required a minimum chemical potential advantage of the target over select competing structures. This constraint helped to discover isotropic interactions that meaningfully favored the snub square lattice as the ground state structure despite the asymmetric spatial distribution of particles in its coordination shells and the presence of tightly competing structures. Consistent with earlier published results [W. Piñeros et al., J. Chem. Phys. 144, 084502 (2016)], enforcement of greater chemical potential advantages for the target lattice in the interaction optimization led to assemblies with enhanced thermal stability.

Uniform silicon nanocrystals were synthesized with cuboctahedral shape and passivated with 1-dodecene capping ligands. Transmission electron microscopy, electron diffraction, and grazing incidence wide-angle and small-angle X-ray scattering show that these soft cuboctahedra assemble into face-centered cubic superlattices with orientational order. The preferred nanocrystal orientation was found to depend on the orientation of the superlattices on the substrate, indicating that the interactions with the substrate and assembly kinetics can influence the orientation of faceted nanocrystals in superlattices.

We use inverse methods of statistical mechanics to explore trade-offs associated with designing interactions to stabilize self-assembled structures against changes in density or temperature. Specifically, we find isotropic, convex-repulsive pair potentials that maximize the density range for which a two-dimensional square lattice is the stable ground state subject to a constraint on the chemical potential advantage it exhibits over competing structures (i.e., 'depth' of the associated minimum on the chemical potential hypersurface). We formulate the design problem as a nonlinear program, which we solve numerically. This allows us to efficiently find optimized interactions for a wide range of possible chemical potential constraints. We find that assemblies designed to exhibit a large chemical potential advantage at a specified density have a smaller overall range of densities for which they are stable. This trend can be understood by considering the separation-dependent features of the pair potential and its gradient required to enhance the stability of the target structure relative to competitors. Using molecular dynamics simulations, we further show that potentials designed with larger chemical potential advantages exhibit higher melting temperatures.

We recently observed that a disordered assembly of octadecanethiol-capped gold (Au) nanocrystals can order when heated from room temperature to 60 °C [Yu, Y.; Jain, A.; Guillaussier, A.; Voggu, V. R.; Truskett, T. M.; Smilgies, D.-M.; Korgel, B. A. Faraday Discuss. 2015, 181, 181–192]. This “inverse melting” structural transition was reversible and occurred near the melting-solidification temperature of the capping ligands. To determine the generality of this phenomenon, we studied by in situ grazing incidence small-angle X-ray scattering (GISAXS) the structure of assemblies of Au nanocrystals with shorter C12 and C5 alkanethiol capping ligands that form ordered superlattices at room temperature and have a ligand melting-solidification temperature below room temperature. Superlattices of dodecanethiol-capped Au nanocrystals disorder when cooled below 260 K, which is the melting-solidification temperature for dodecanethiol. Au nanocrystals capped with even shorter pentanethiol ligands that have a melting transition below 100 K (the lowest experimentally accessible temperature) do not undergo the disorder transition.

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