Population balance modeling of flame synthesis of titania nanoparticles

The significance of various particle formation pathways during flame synthesis of titania nanoparticles by titanium tetraisopropoxide oxidation in a premixed methane–oxygen flame is investigated by population balance modeling. An efficient moving sectional model is developed accounting for gas phase chemical reactions, coagulation, surface growth and sintering. The model is validated by comparing it against standard sectional solutions and detailed but cumbersome literature models at certain limiting cases (i.e., only coagulation and sintering, only surface growth or only coagulation). The evolution of primary particle size distribution is monitored by rapid thermophoretic sampling and image analysis of transmission electron microscope pictures while the corresponding flame temperature is measured in the presence of particles by Fourier transform infra-red spectroscopy. Excellent agreement is obtained between model predictions and data with respect to the evolution of average primary particle diameter and geometric standard deviation without any adjustable parameters until conditions of pure agglomeration of polydisperse particles are established (here, approximately after the first 9 cm above the burner tip). By comparing detailed measured and calculated size distributions, surface reaction appears to be the dominant route for early particle growth at the conditions studied.