Lattice Monte Carlo simulation of semiconductor nanocrystal synthesis in microemulsion droplets

A lattice Monte Carlo model has been developed to describe the formation of a single semiconductor nanocrystal (quantum dot) inside a droplet of a microemulsion. The motivation stems from the need to understand the kinetics of quantum dot formation in microemulsion templates with minimal droplet-droplet coalescence. In these systems, a fixed amount of a reactant is dissolved in each droplet, and another reactant is supplied by diffusion through the interface. Nucleation is facilitated by a spontaneous reaction between the precursors at the droplet interface, and the coalescence of nuclei and clusters ultimately leads to the formation of a single particle. The size of the final particle is controlled by the concentration of the first reactant. A hard-sphere potential is used to describe cluster-cluster interactions. The overall particle formation time initially increases with final particle size, quickly passes through a maximum, and subsequently decreases due to the formation of large intermediate clusters apparently acting as effective collision partners to smaller ones. Studies of the evolution of intermediate cluster sizes provided mechanistic details of the final particle formation through cluster-cluster coalescence. A generalized dimensionless equation is obtained that relates the formation time of the final particle to its size for various droplet sizes and diffusivities of the first reactant and clusters. A parametric study reveals that the final particle formation time is more sensitive to changes in the cluster-cluster coalescence probability than in the probability of nucleation.