Lattice Monte Carlo simulation of cluster coalescence kinetics with application to template-assisted synthesis of quantum dots

A Lattice Monte Carlo (LMC) simulation technique has been developed to describe the synthesis of a single semiconductor nanocrystal inside the droplets of a microemulsion. The LMC simulation can track the diffusion of a precursor, its irreversible reaction with a second precursor to form nuclei, and the diffusion and coalescence of the nuclei into clusters and eventually into a single particle. In this paper we compare two scenarios for forming a single nanocrystal. The first scenario involves very rapid (spontaneous) conversion of a precursor dispersed in the droplet to nuclei that diffuse and coalesce into a single particle. The second scenario involves diffusion of a precursor to the droplet interface where an irreversible reaction with a second precursor forms nuclei that subsequently diffuse into the droplet and coalesce. Simulations were performed describing the synthesis of ZnSe nanocrystals with diameters up to 7 nm, i.e., below the quantum confinement threshold of 9 nm for this material. Comparison of the time required for the formation of a single final particle in each of the two cases reveals that for particles smaller than ∼3.5 nm the formation times are nearly equal. For particles larger than 3.5 nm, the second process is completed faster than the first one. Analysis of intermediate cluster populations indicates that the formation of a larger "sweeper" cluster accelerates the rate of coalescence and is more effective when the nuclei are supplied gradually, as in the second process, compared to spontaneous nucleation throughout the domain. The kinetics of coalescence of an initially monodisperse population of nuclei in spherical domains of finite size were studied and generalized equations were obtained that describe the evolution of the number of different sizes as function of dimensionless time; this constitutes an extension to the classical analysis of coalescence of monodisperse aerosols in an infinite domain.