Modeling the Nucleation and Growth of Colloidal Nanoparticles

Controlling the size and size distribution of colloidal nanoparticles have gained extraordinary attention as their physical and chemical properties are strongly affected by size. Ligands are widely used to control the size and size distribution of nanoparticles; however, their exact roles in controlling the nanoparticle size distribution and the way they affect the nucleation and growth kinetics are poorly understood. Therefore, understanding the nucleation and growth mechanisms and developing theoretical/modeling framework will pave the way towards controlled synthesis of colloidal nanoparticles with desired sizes and polydispersity.

This dissertation focuses on identifying the possible roles of ligands and size on the kinetics of nanoparticle formation and growth using in-situ characterization tools such as small-angle X-ray scattering (SAXS) and kinetic modeling. The presented work further focuses on developing kinetic models to capture the main nucleation and growth reactions and examines how ligand-metal interactions could potentially alter the rate of nucleation and growth rates, and consequently the nanoparticle size distribution. Additionally, this work highlights the importance of using multi-observables including the concentration of nanoparticles, size and/or precursor consumption, and polydispersity to differentiate between different nucleation and growth models and extract accurate information on the rates of nanoparticle nucleation and growth. Specifically, during the formation and growth of colloidal nanoparticles, complex reactions are occurring and as such nucleation and growth can take place through various reaction pathways. Therefore, sensitivity analysis was applied to effectively compare different nucleation and growth models and identify the most important reactions and obtain a reduced model (e.g. a minimalistic model) required for efficient data analysis. In the following chapters, a more sophisticated modeling approach is presented (population balance model) capable of capturing the average-properties of nanoparticle size distribution. PBM allows us to predict the growth rate of nanoparticles of different sizes, the ligand surface coverage for each individual size, and the parameters involved in altering the size distribution. Additionally, thermodynamic calculations of nanoparticle growth and ligand-metal binding as a function of size and ligand surface coverage were conducted to further shed light on the kinetics of nanoparticle formation and growth. The combination of kinetic modeling, in-situ SAXS and thermodynamic calculations can significantly advance the understanding of nucleation and growth mechanisms and guide toward controlling size and polydispersity.