Toward a Comprehensive Model of the Synthesis of TiO 2 Particles from TiCl 4 Richard H. West, Matthew S. Celnik, Oliver R. Inderwildi, and Markus Kraft* Department of Chemical Engineering, UniVersity of Cambridge, Cambridge CB2 3RA, United Kingdom Gregory J. O. Beran and William H. Green Massachusetts Institute of Technology, 77 Massachusetts AVenue, Cambridge, Massachusetts 02139 The combustion of TiCl 4 to synthesize TiO 2 nanoparticles is a multimillion tonne per year industrial process. The objective of this paper is to further the understanding of this process. Work toward three aspects of this multiscale problem is presented herein: gas-phase chemistry, surface chemistry, and the solution of a multidimensional population balance problem coupled to detailed chemical mechanisms. Presented here is the first thermodynamically consistent mechanism with physically realistic elementary-step rate constants by which TiCl 4 is oxidized to form a stable Ti 2 O x Cl y species that lies on the path to formation of TiO 2 nanoparticles. Second, progress toward a surface chemistry mechanism based on density functional theory (DFT) calculations is described. Third, the extension of a stochastic two-dimensional (surface-volume) population balance solver is presented. For the first time, the number and size of primary particles within each agglomerate particle in the population is tracked. The particle model, which incorporates inception, coagulation, growth, and sintering, is coupled to the new gas-phase kinetic model using operator splitting, and is used to simulate a heated furnace laboratory reactor and an industrial reactor. Using the primary particle information, transmission electron microscopy (TEM)-style images of the particles are generated, demonstrating the potential utility of first-principles modeling for the prediction of particle morphology in complex industrial systems. 1. Introduction Titanium dioxide (TiO 2 ) is widely used as a pigment, a catalyst support, and a photocatalyst. The combustion of titanium tetrachloride (TiCl 4 ) to synthesize TiO 2 nanoparticles is a multimillion tonne per year industrial process. 1 In this “chloride” process, purified TiCl 4 is oxidized at high temperatures (1500- 2000 K) in a pure oxygen plasma or flame to produce TiO 2 particles. 2,3 The size and shape of these particles affects properties that are important to both the industrial processing and the final product, such as ease of milling 2 and opacity of the powder. 3 Furthermore, the ability to control characteristics of specialized functional nanoparticles through flame synthesis would offer considerable financial reward. As such, the ability to simulate a multivariate distribution (for example, mass, surface area, amount of agglomeration) of a population of nanoparticles created in this process would help efforts to improve the final product and save energy. Although it has been used in industry for decades, 4 the process is poorly understood and experimental optimization is incre- mental and costly. It has been demonstrated that the relative rates of gas-phase reactions, leading to particle nucleation, surface growth reactions, and particle agglomeration and sin- tering, are all important in determining the final product properties. 5 It is important that a comprehensive model includes details spanning all relevant length and time scales. Existing models greatly simplify the chemical processes to a single step and are unable to capture the details of temperature and concentration dependencies. For example, the use of additives such as AlCl 3 and KCl to control the crystal structure and primary particle size of the product is common in industry, 6 but current modeling methods can offer no insight into the underlying processes. As well as detailed chemistry on the molecular scale, it is clear that a detailed population balance model of the particles is desirable. Existing models range from simple monodisperse assumptions to two-dimensional (surface-volume) approaches simulating simultaneous nucleation, growth, agglomeration, and sintering. The ability to track primary and agglomerate sizes explicitly will allow the assumptions, such as monodisperse size distributions, that are currently used to model hard- and soft- agglomerate formation 7 to be relaxed. The intention of this work is to create and demonstrate a framework for a comprehensive model that attempts to describe the phenomena at different scales. We present new results in three areas: (1) Ab initio and density functional theory (DFT) investiga- tions of the gas-phase chemistry of the combustion of TiCl 4 lay the foundation for the first detailed kinetic model of seed formation. (2) A DFT study of the surface chemistry of rutile TiO 2 is undertaken as a first attempt to understand the surface growth of TiO 2 nanoparticles. (3) A new population balance model extends existing surface- volume models to track primary particles within each agglomer- ate in the population. This detailed population balance model is coupled to the detailed chemistry with operator splitting and is solved using a stochastic technique. The paper is structured as follows. After this introduction, the background to each of these three areas is described. In the following section, the models developed for the gas-phase chemistry and the detailed population balance are described. The subsequent results and discussion are again divided into the three areas: gas-phase chemistry, surface chemistry, and the detail population balance. These sections are followed by the conclusions. * To whom correspondence should be addressed. Tel.: +44 (0)- 1223 334777. Fax: +44 (0)1223 334796. E-mail address: mk306@ cam.ac.uk. 6147 Ind. Eng. Chem. Res. 2007, 46, 6147-6156 10.1021/ie0706414 CCC: $37.00 © 2007 American Chemical Society Published on Web 08/21/2007 Downloaded by MIT on June 30, 2009 Published on August 21, 2007 on http://pubs.acs.org | doi: 10.1021/ie0706414