Kinetics of the aggregative growth of ligand-capped colloidal nanocrystals

Colloidal nanoparticles’ practical applications (e.g. photovoltaics, catalysis, bio-imaging, sensing, display, and drug delivery) rely substantially on their production. Although significant effort has been devoted to developing synthetic methods in the past few decades, majority of them were developed through time-consuming labor-intensive trial and error, and currently large scale synthesis of high quality (e.g. monodisperse) stable colloidal nanoparticles in a cheap way is very challenging. We believe a better understanding of the growth mechanisms of colloidal nanoparticles would help solve the problem. Recently, non-classical growth pathways (e.g. oriented attachment, step-growth crystallization, and formation of mesocrystals) have been recognized as important mechanisms of crystal growth. Since the pioneering work of Penn and Banfield on oriented attachment, significant progress has been made on the syntheses of new nanostructures (e.g. ultrathin nanowires, nanorods, nanorings, nanosheets) by non-classical growth mechanisms and on understanding and visualizing these processes. However these processes are still poorly understood, especially their kinetics. This work attempts to unravel key parameters that affect the kinetics of aggregative growth of ligand capped colloidal nanocrystals. A model reaction system, in which the colloidal nanocrystals grow by aggregation and the growth by other pathways (e.g. classical growth under supersaturation and Ostwald ripening) is negligible, is needed for the study but was not available. So, we had to first develop a unique sulfur precursor (i.e. oleylammonium hydrosulfide (OLAHS)) that allows us to establish the model reaction system. Its most important trait is that it quickly reacts with lead chloride producing lead sulfide nanoparticles, and the subsequent growth of the nanoparticles by classical growth mechanism under superaturation is finished within a minute. In the meantime, we found that OLAHS can provide a simple solution to a complex and long-standing problem, i.e. sustainable scalable synthesis of metal sulfide nanocrystals at low cost. The synthesis using OLAHS fulfills most of the principles of green chemistry as it (i) can give high reaction yield (e.g. over 70%), (ii) allows recycling of excess precursors, (iii) allows synthesis being conducted under ambient condition, and (iv) allows synthesis under high concentration (e.g. 90 gram of lead sulfide nanocrystals per liter of reaction volume). We collected comprehensive kinetic data (i.e. evolution of particle size, concentration, and polydispersity with time) for the growth of amine-capped lead sulfide colloidal nanoparticles through our model reaction system. Careful data analysis shows that the nanoparticles grow by coalescence (i.e., aggregation followed by reconstruction into a spherical single crystal) and the growth due to classical growth mechanism and Ostwald ripening are negligible. We developed a simple two-parameter mathematical model that fits the comprehensive data well. The model shows that the aggregation rate is dependent on the size of the nanoparticles and the length of the surface capping ligand. The activation energy of coalescence is calculated to be ~67.65 kJ·mol-1 based on the model, and it is composed of two terms of similar magnitude: a term proportional to the contact area between the ligand shells of two colliding particles and a constant term. Our Brownian dynamics simulations show (i) the remarkably large rate constants we observed (10-2 to 101 M-1·s-1) are most likely a side effect of the large difference in size between the particles and their mean free path of diffusion and (ii) the low polydispersity observed in the experiments is the likely result of the suppression of collision rates between rare populations due to crowding. Despite its approximations, we show that the model can successfully predict the growth kinetics of nanoparticles (both particle volume vs. time and concentration vs. time) synthesized with a series of n-alkylamines of different lengths