Mechanism and modeling of nanorod formation from nanodots

A population balance model based on Smoluchowski aggregation kinetics is developed to explain the formation of nanorods from a colloidal suspension of spherical nanoparticles (nanodots). Our model shows that linear pearl-chain aggregates form by the oriented attachment (OA) of nanodots during the early stages of synthesis, since it occurs with a time scale smaller than the coalescence time scale of nanodots present within an aggregate. The slower coalescence step leads to the transformation of the linear pearl-chain aggregate into a smooth nanorod over a longer time scale of many hours, as observed in experiments. The attachment kinetics is modeled by a modified Brownian collision frequency, with the latter decreasing with nanorod length, leading to the experimentally observed slower growth in nanorod length at longer times. The collision frequency also includes the effects of attractive dipole-dipole and van der Waals interactions between nanodots, which are primarily responsible for OA. Our model predictions are general, and they compare favorably with available experimental data in the literature on the distribution of the aspect ratio (length to diameter) of ZnO and ZnS nanorods over different time scales.