A multiscale approach to uncover the self-assembly of ligand-covered palladium nanocubes

Ligand-mediated superlattice assemblies of metallic nanocrystals represent a new type of mesoscale materials whose structural ordering directly influence emergent collective properties. However, universal control over the spatial and orientational ordering of their constitutive components remains an open challenge. One major barrier contributing to the lack of programmability in these nanoscale building blocks revolves around a gap in fundamental understanding of how ligand-mediated interactions at the particle level propagate to macroscopic and mesoscale behaviors. Here, we employ a combination of scaling theory and coarse-grained simulations to develop a multiscale modeling framework capable of bridging across hierarchical assembly length scales for a model system of ligand-functionalized nanocubes (here, Pd). We first employ atomistic simulations to characterize how specific ligand-ligand interactions influence the local behaviors between neighboring Pd nanocubes. We then utilize a mean-field scaling theory to both rationalize the observed behaviors as well as compute a coarse-grained effective pairwise potential between nanocubes capable of reproducing atomistic behaviors at the mesoscale. Furthermore, our simulations reveal that a complex interplay between ligand-ligand interactions is directly responsible for a shift in macroscopic ordering between neighboring nanocubes. Our results, therefore, provides a critical step forward in establishing a multiscale understanding of ligand-functionalized nanocrystalline assemblies that can be subsequently leveraged to design targeted structures exhibiting novel, emergent collective properties.