Persistent nucleation and size dependent attachment kinetics produce monodisperse PbS nanocrystals

Modern syntheses of colloidal nanocrystals yield extraordinarily narrow size distributions that are believed to result from a rapid “burst of nucleation” (La Mer, JACS, 1950, 72(11), 4847–4854) followed by diffusion limited growth and size distribution focusing (Reiss, J. Chem. Phys., 1951, 19, 482). Using a combination of in situ X-ray scattering, optical absorption, and (13)C nuclear magnetic resonance (NMR) spectroscopy, we monitor the kinetics of PbS solute generation, nucleation, and crystal growth from three thiourea precursors whose conversion reactivity spans a 2-fold range. In all three cases, nucleation is found to be slow and continues during >50% of the precipitation. A population balance model based on a size dependent growth law (1/r) fits the data with a single growth rate constant (k(G)) across all three precursors. However, the magnitude of the k(G) and the lack of solvent viscosity dependence indicates that the rate limiting step is not diffusion from solution to the nanoparticle surface. Several surface reaction limited mechanisms and a ligand penetration model that fits data our experiments using a single fit parameter are proposed to explain the results.