(262a) Prediction of Nanoparticles Size Distribution: The Effects of Ligand Surface Coverage and Nanoparticle Size in Altering the Kinetics of Surface Growth

Controlling nanoparticle size and size distribution is vital for many applications including catalytic reactions, drug delivery and imaging, and surface coating. The process of nanoparticle synthesis often involves using ligands, where they are found to affect not only the size but also the size distribution by binding to the nanoparticle surface and/or metal precursor. In addition to the role of ligands, the nanoparticle size can affect the ligand-nanoparticle binding affinity and the rate of surface growth, and alternatively the size distribution. Despite recent advances in the field, no theoretical approach could yet accurately unravel the roles of ligand surface coverage and nanoparticle size in controlling the evolution of size distribution. This work aims towards investigating the role of size and ligand coverage in controlling the size distribution during the synthesis of colloidal metal nanoparticles. We used in-situ small angle X-ray scattering (SAXS) to measure the evolution of size distribution under different reaction conditions. We further developed a population balance kinetic model (PBM) to understand the effects of ligand coverage, nanoparticle size, and nucleation and growth pathways on the evolution of size distribution. Using palladium (Pd) as a model system, our SAXS results indicate a sharp decrease in nanoparticle polydispersity (or size focusing behavior) despite temporal overlap of nucleation and growth (i.e. increase in concentration of nanoparticles concurrent with nanoparticle growth). Our population balance modeling approach allows us to understand the main factors involved in controlling the size distribution. We show that continuous nucleation (formation of new nuclei and small population) leads to size defocusing. However, continuous nucleation results in different reaction times (or aging time) for the nanoparticle population leading to time and size-dependent ligand coverage. To capture the size focusing trend during the synthesis; we show that the smaller nanoparticles should grow at a much faster rate than the larger size nanoparticles in the population. Our modeling results along with thermodynamic calculations further suggest that the faster growth of smaller nanoparticles (relative to the larger nanoparticles in the population) is due to two factors: lower ligand surface coverage and higher surface reactivity which leads to focusing of the size distribution. Finally, we demonstrate the effects of different nucleation and growth kinetics/mechanisms (e.g. nucleation rate profile, nucleation order, etc.) on the size distribution and how these effects can noticeably impact the shape of distribution during the reaction. The presented methodology allows for the accurate prediction of size distribution and could be potentially applied to other ligated systems to obtain nanoparticles with desired sizes and polydispersity.