Abstract
Nanoparticle (NP) synthesis has been extensively studied since the mid-1800s and are utilized across numerous fields due to their unique microscopic properties that collectively yield macroscopic benefits. Of particular interest are silver (Ag) NPs, whose controllable size and morphology impart distinct catalytic, electronic, and optical properties advantageous for environmental and energy-related applications. The theoretical understanding of NP nucleation and growth has advanced considerably starting with classical nucleation theory, evolving into the LaMer model centering on burst nucleation and diffusion-limited growth and resulted in near monodispersed hydrosols. Finke and Watzky later introduced the autocatalytic model considering a slow and continuous nucleation and autocatalytic surface growth not limited by monomer diffusion. However, the precise mechanisms remain the subject of active debate for the different homogeneous and heterogenous nucleation systems. In this study, simulation models for NP population balances are developed using both material balanced and constant number Monte Carlo methods to describe NP formation and growth under diffusion-limited and autocatalytic conditions. Perturbative analysis of the model provides insight into whether NP formation is diffusion-limited or autocatalytic and how addition(s) or subtraction(s) of precursor influence the NP growth mechanism. Perturbative analysis reveals the mean particle size and variance can be tuned by adding or removing precursor molecules during the reaction, although the overall size distribution trend remains consistent. The present study together with new experimental capabilities lays the foundation for a model-based design of experiments to explore the nucleation and growth mechanism of metal nanoparticles.