Reduced Chemical Kinetics for the Modeling of TiO₂ Nanoparticle Synthesis in Flame Reactors

Abstract

Flame synthesis represents a viable technique for large-scale production of titanium dioxide (TiO 2 ) nanoparticles.A key ingredient in the modeling of this process is the description of the chemical kinetics, which include Ti oxidation, hydrocarbon fuel combustion, and chlorination. While detailed chemical mechanisms have been developed for predicting TiO 2 nanoparticle properties by West et al. (e.g., Combust. Flame 2009, 156, 1764, their use in turbulent reacting flow simulations is limited to very simple configurations or requires significant modeling assumptions to bring their computational cost down to an acceptable level. In this work, a reduced kinetic scheme describing the oxidation of TiCl 4 in a methane flame is derived from and validated against the predictions of a detailed mechanism from the literature. The reduction procedure uses graph-based methods for unimportant kinetic pathways elimination and quasi-steady-state species selection. Reduction targets are chosen in accordance with previous modeling results that showed the importance of temperature and overall concentration of titanium-containing species in both nucleation and surface growth rates. The resulting reduced scheme is thoroughly evaluated over a wide range of conditions relevant to flame-based synthesis, and the capability of the reduced model to adequately capture the process dynamics at a much lower computational cost is demonstrated. ■ INTRODUCTIONFlame-based synthesis is the preferred method for the industrial level production of commercial grade metal−oxide nanoparticles and, hence, is the chosen technique for production of titania (TiO 2 ) nanoparticles. Titanium dioxide nanoparticles are traditionally used as white pigments but have found use in diverse areas like photocatalysis, 1 reducing nitrogen oxide emissions, 2 catalyst supports, 3 ultraviolet filtering materials, 4 surface treatments like antifog coating, 5 or cosmetics. 6 Despite the industrial importance of titanium dioxide and predicted rise in market revenues, 7 the chemistry and flow dynamics at the core of TiO 2 flame synthesis are not well understood, and process optimization remains mostly empirical. The development of predictive computational models offers an attractive avenue to gain a better insight into the synthesis process and devise strategies to achieve a tighter control over the resulting particle properties.In the flame synthesis of titania nanoparticles, the precursor TiCl 4 is oxidized to form TiO 2 . Typically, a hydrocarbon-based fuel like methane (CH 4 ) is used in the reactor to support the flame and provide the high temperatures needed for titanium (Ti) oxidation. To predict the properties of nanoparticles synthesized in flame-based reactors, computational models have to adequately capture the complexity of the corresponding chemical processes, including the coupling between nanoparticles and hydrocarbon oxidation in the flame, the transition from the gas-phase species to the particulate phase, and the subsequent particle evolution (i.e., nucleat...

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