A neural network parametrized coagulation rate model for <3 nm titanium dioxide nanoclusters

Coagulation is a key factor governing the size distribution of nanoclusters during the high temperature synthesis of metal oxide nanomaterials. Population balance models are strongly influenced by the coagulation rate coefficient utilized. Although simplified coagulation models are often invoked, the coagulation process, particularly for nanoscale particles, is complex, affected by the coagulating nanocluster sizes, the surrounding temperature, and potential interactions. Toward developing improved models of nanocluster and nanoparticle growth, we have developed a neural network (NN) model to describe titanium dioxide (TiO₂) nanocluster coagulation rate coefficients, trained with molecular dynamics (MD) trajectory calculations. Specifically, we first calculated TiO₂ nanocluster coagulation probabilities via MD trajectory calculations varying the nanocluster diameters from 0.6 to 3.0 nm, initial relative velocity from 20 to 700 m s^-1, and impact parameter from 0.0 to 8.0 nm. Calculations consider dipole-dipole interactions, dispersion interactions, and short-range repulsive interactions. We trained a NN model to predict whether a given set of nanocluster diameters, impact parameter, and initial velocity would lead to the outcome of coagulation. The accuracy between the predicted outcomes from the NN model and the MD trajectory calculation results is >95%. We subsequently utilized both the NN model and MD trajectory calculations to examine coagulation rate coefficients at 300 and 1000 K. The NN model predictions are largely within the range 0.65-1.54 of MD predictions, and importantly NN predictions capture the local minimum coagulation rate coefficients observed in MD trajectory calculations. The NN model can be directly implemented in population balances of TiO₂ formation.