Kinetic Model for Hydrolytic Nucleation and Growth of TiO2 Nanoparticles

A simple kinetic model is derived to describe the formation of TiO2 particles up to the size of a few hundred nanometers in an aqueous suspension. The model system for the kinetic experiments is the hydrolysis and condensation of titanium(IV)-bis(ammonium-lactato)dihydroxide under basic conditions. The formation of nanoparticles was followed by dynamic light scattering (DLS) and UV–vis spectrometric methods. The turbidity (i.e., the apparent absorbance at 500 nm) of a stable TiO2 suspension is shown to be proportional to the TiO2 concentration at a constant particle size and proportional to the size at a constant Ti concentration. The compilation of the DLS and UV–vis data yields characteristic sigmoid-shaped kinetic curves for the evolution of particle size. A kinetic model with three reaction steps is postulated which provides an excellent fit to the experimental data. First, the rapid hydrolysis of the precursor takes place to give primary particles for the subsequent steps. The dimerization of two primary particles is slow and this is followed by the formation of larger particles in the step-by-step addition of subsequent primary units. An integrated rate equation was developed to predict the time-dependent mean particle size as the function of the initial precursor concentration. An important feature of the model is that a simple continuous function describes the temporal evolution of the average particle size up to d = 600 nm. Previously published kinetic data representing various reaction systems were also successfully interpreted by the proposed model