Stochastic model analysis of nanoparticle size polydispersity

Nanoparticle synthesis by wet chemical methods is a rather complicated process. Despite the enormous success achieved in the chemical synthesis of a wide range of nanoparticle materials, the understanding of nanoparticles growth in solution at the theoretical level is still very limited. Recently we conducted a study on the reaction kinetics of chemical synthesis of gold nanoparticles based on Brust-Schiffrin reaction. Two models were proposed to compare with the experimental data. One is a simple first-order reaction kinetic as has been used in other reported work and another one is an incremental addition model proposed in our study. While both models gave similar level of curve fitting with experimental data, the two models also showed some clear differences. In this study, we further investigated the polydispersity of nanoparticles by treating particle growth as a Markov process. We defined and solved the stochastic version of both kinetic models. The polydispersity values predicted by these two models are smaller than the experimentally observed data, however, the incremental addition model revealed a significantly larger polydispersity than the first order reaction kinetic model. The difference between modeling and experimental results suggests that other mechanisms such as particle-particle aggregation should exist and have major effect on particles size distribution. This study elucidates quantitatively the contribution of certain reaction pathways towards nanoparticle polydispersity