Mathematical Modelling of Nanocrystal Growth
We will describe a model for the process of synthesizing nanoparticles of a specific size from a liquid solution. Initially, we will consider a single particle model that accounts for monomer diffusion in solution around the particle and kinetic reactions at the particle surface. For the far-field bulk concentration, a mass conservation expression is used. Based on a small dimensionless parameter, we propose a pseudo-steady state approximation to the model. The model is then extended to a system of N particles. Numerical solutions for the time-dependent average particle radius compared against experimental data are shown to have excellent agreement.