Surface area limited model for predicting anisotropic coarsening of faceted nanoparticles

The engineering and control of systems of monodispersed polyhedral nanoparticles are important for the development of devices based on size and shape-dependent properties. This includes a detailed understanding of how these designer nanoparticles are formed, and how they evolve and change over time. Although an experimental strategy or atom based theory may be used to observe different stages of this process, it is highly desirable to model the entire process, based on a limited set of physical or chemical parameters. Here we derive a kinetic model of nanoparticle shape evolution as a function of time, using specific concepts relating to surface diffusion, rate of step growth, and particularly surface site availability, referred to as the surface area limited (SAL) theory of growth and nanomorphology. This model is then applied to examples, including the axial growth of an arbitrary nanorod and the anisotropic growth of a nanogold truncated octahedron, restricted to either the 〈111〉 or 〈100〉 direction, each driven by the coarsening mechanism.