Kinetic and Thermodynamic Modified Wulff Constructions for Twinned Nanoparticles

Wulff constructions are a powerful tool to predict the shape of nanoparticles, which strongly influences their performance in catalysis, sensing, and surface-enhanced spectroscopies. Previous Wulff models focused on energy minimization and included contributions from the surface energy, interface energy, twin boundaries, and segregation-induced bulk energy changes. However, a large number of shapes cannot be understood by such thermodynamic approaches, in particular many of the twinned late transition metal (Ag, Au, Pt, Pd, etc.) particles of interest in catalysis and plasmonics. A review of the modified Wulff (i.e., twinned) construction is presented here, followed by the development of a modified kinetic Wulff model, which, by including kinetic parameters, explains the emergence of commonly observed shapes such as bitetrahedra, truncated bitetrahedra, thin triangular platelets, perfect decahedra, and decahedral rods.