Modeling titanium dioxide (TiO₂) nanoclusters using a 2D sectional method with molecular dynamics (MD) determined coagulation rates

Accurate prediction of the particle size distribution (PSD) evolution of growing nanometer scale particles is important in designing gas-phase synthesis reactors for the production of nanomaterials. Towards improved predictions of growth, we model the evolution of the PSD of 1-4 nm TiO₂ particles from the decomposition of titanium tetraisoproxide (TTIP) using a two-dimensional (2D) sectional method, uniquely with coagulation rates derived from molecular dynamics (MD) trajectory calculations which account for detailed particle–particle interactions. The PSDs predicted by the 2D sectional method are compared to recent experimental measurements of PSDs in the 1-3 nm range in a flow tube reactor. The nucleation of particles is modeled based on prior mobility measurements of ions attributed to TTIP and their decomposition, with the specific nucleation rate here fitted as a fraction of base nucleation rate (k) derived from these prior measurements. In the 2D sectional model, we examine the influence of the initial (nucleated) particle charge distribution on the PSD, with different coagulation rate coefficients for neutral-charged and charged-charged particle collisions. With the MD-derived coagulation rate coefficients, we find that using nucleation rate coefficients between 0.005k and 0.03k leads to strong agreement between modeled PSD and measured PSD for a wide variety of experimental residence times, initial TTIP concentrations and temperatures. Increasing the charge fraction from 0% (uncharged) to 80% (bipolar) does not result in a significant change in the PSD, because the particles rapidly self-neutralize through coagulation based on the simulation results. The results with MD-derived coagulation rate coefficients are compared to those of the sectional method with classical kinetic theory of gases (KTG) rates with a constant enhancement factor to account for potential interactions. Through comparison, we find that the predictions from the classical KTG model consistently exhibit weaker coagulation rates than the MD-derived model during the PSD evolution.