Generalized Model for Nano- and Submicron Particle Formation in Liquid Phase, Incorporating Reaction Kinetics and Hydrodynamic Interaction: Experiment, Modeling, and Simulation

Abstract

A generalized model of particle formation has been developed, including reaction, nucleation, and simultaneous particle growth by diffusion, coagulation, and Ostwald ripening (OR). This enables a priori prediction of both nano- and submicron size SiO2, from a few nanometers to at least 400 nm. This was possible, on including (i) a finite reaction kinetics, (ii) a hydrodynamic correction in Brownian coagulation, and (iii) the coupled effect of reaction kinetics with OR; the latter two for the first time. We show that the hydrodynamic interaction can reduce the coagulation frequency up to a factor of about 8.5. Consequently, without it, a large prediction error (up to 25% with respect to the experimental particle size) is observed. For the final particle size, synthesis has been conducted up to ∼4 h. This imparts accounting of finite reaction kinetics to be critical, which is substantiated by accurate prediction of temporal particle diameter, throughout the synthesis period. We thus avoid erroneous underprediction or overprediction of size, for moderately fast or slow reaction, respectively, which is true of existing models based on instantaneous reaction kinetics. Our model is further validated by quantitative prediction of SiO2 particle size trends with different reactant concentration and temperature.