The emergence of bulk structure in clusters via isotropic multi-well pair potentials

Materials function is dependent on materials structure. To design materials with greater control over bulk structure and properties, it is essential that we improve our understanding of how structure emerges at small system sizes. Currently, it is not exhaustively understood how interparticle interactions in an N-body system influence resultant structure, and how the structure depends on N. In this study, we investigate this using multi-well isotropic pair potentials to simulate finite cluster formation of four distinct 2D crystal structures. These pair potentials encode multiple preferred length scales into the system, allowing us to extract how anisotropic motifs—as opposed to close-packing—emerges for bulk structures as cluster size N increases. We observe energetic and structural changes in each cluster with increasing system size N. We find a trend towards close-packing at small system sizes irrespective of the bulk structure; however, the system size at which bulk structure emerges is influenced by the coordination number of the bulk and the shape of the pair potential. We discover that multiple preferred bond lengths and relative bond strengths affect the system size at which a secondary bonding length emerges, changing the energetic balance of the structures as N increases. Our findings demonstrate that tuning particle–particle interactions can enable the engineering of nano- or meso-scale soft matter clusters—in applications as diverse as drug delivery and hierarchical materials design.