Population balance modeling of flame synthesis of titania nanoparticles☆
Introduction
Flame processes are by far the most widely used ones for manufacture of commercial quantities of nanoparticles (such as carbon blacks, fumed silica and pigmentary titania). Typically, in flame reactors, nanostructured powders are produced virtually without control at high temperatures and extremely short process residence times (usually, less than a second). This makes representative particle sampling, model development and process control quite challenging (Pratsinis, 1998). As a result, there is a great interest to better understand the basic phenomena by detailed theoretical and experimental studies so as to optimally design flame reactors by interfacing fluid and particle dynamics (Johannessen, Pratsinis, & Livbjerg, 2000).
Ulrich and Riehl (1982) monitored the evolution of flame-made silica particles by laser scattering. Even though they simulated well particle dynamics by a population balance model that involved an arbitrary shape factor, they were not able to distinguish between aggregate and primary particle sizes. Zachariah and Semerjian (1989) found good agreement with experimental results at high precursor concentrations during the formation of silica particles from silane in an opposed jet reactor but did not distinguish between aggregate and primary particle sizes or gas and surface reactions. Hung and Katz (1992) combined dynamic light scattering and thermophoretic sampling (TS) techniques to determine the effect of process conditions, such as temperature and precursor concentration, on the formation of TiO2–SiO2 mixed powders in a oxy/hydrogen counterflow diffusion flame reactor. Lee, Jeong, Hwang, Choi, and Chung (2001) simulated aggregate particle growth in this reactor by considering the effect of axial particle diffusion and using a two-dimensional sectional model (Xiong & Pratsinis, 1993) for coagulation and sintering along with multi-step hydrogen/oxygen reactions (including both oxidation and hydrolysis of SiCl4) and flame temperature measurements in the absence of particles. Lindackers, Strecker, Roth, Janzen, and Pratsinis (1997) used a particle mass spectrometer (PMS) to monitor the growth of SiO2 particles in a premixed low pressure H2/O2/Ar flame doped with SiH4. A theoretical model including, full homogeneous H2/O2 and SiH4/O2 kinetics, estimated temperatures by a flame model (PREMIX) and sectional calculations for SiO2 homogeneous nucleation and Brownian coagulation, was in good agreement with experimental data. Tsantilis and Pratsinis (2000) described the evolution of both aggregate and primary particle size distributions by incorporating the effect of sintering and mass fractal dimension in the sectional model of Hounslow, Ryall, and Marshall (1988) and achieved good agreement with the experimental aggregate size distributions of Akhtar, Xiong, and Pratsinis (1991). Recently, Jeong and Choi (2001) used a single surface fractal dimension to correlate particle volume and area in a given size interval and thus simplified the detailed two-dimensional sectional model of Xiong and Pratsinis (1993) for coagulation and sintering into a set of two one-dimensional sectional equations for particle volume and area, respectively. In addition, they stated that the above modification could decrease computation time by approximately three orders of magnitude without seriously diminishing the accuracy of their calculations.
Of particular interest is the investigation of the competition between gas phase and surface reaction mechanisms as these could be quite critical for explaining the dominant trends of particle formation and growth (i.e., surface growth dominates carbon black production while gas phase reaction dominates the production of fumed silica). Pratsinis and Spicer (1998) studied the effect of TiCl4 surface reaction (that is oxidation of TiCl4 on the surface of TiO2 particles) on the size of product titania (TiO2) particles over a wide range of process conditions. They developed a monodisperse model and showed that TiCl4 surface oxidation is more important (compared to gas phase oxidation) at high TiCl4 initial concentrations.
In retrospect, there are few studies describing the detailed evolution of aggregate and primary particle characteristics in flames. More specifically, the early stage of particle formation is one of the areas that is ripe for better understanding as instruments that allow for accurate non-intrusive measurements are now available. Fourier transform infra-red (FTIR) spectroscopy is for instance particularly attractive as it concurrently provides information on the flame temperature, gas composition and particle concentration during flame synthesis (Farquharson et al., 1998; Morrison Jr., Raghavan, Timpone, Artelt, & Pratsinis, 1997; Best, Carangelo, Markham, & Solomon, 1986). Likewise, particle sizing at different locations along the flame can be made accurately by TS followed by computer image analysis of transmission electron micrographs (Dobbins & Megaridis, 1987). The insertion of the TEM grid is practically instantaneous, causing minimal disturbance to the upstream motion of the flame gases and particle history (Arabi-Katbi, Pratsinis, Morrison Jr., & Megaridis, 2001).
The present paper relies on those techniques to provide an insight on the full evolution of primary particle size distribution. This provides the opportunity to overcome the limitations of past studies (Okuyama et al., 1986; Xiong, Akhtar, & Pratsinis, 1993; Briesen, Fuhrmann, & Pratsinis, 1998; Johannessen et al., 2000) which typically relied on particle data collected after the process was complete. Therefore, such an investigation could reveal, for instance, the importance of surface growth or other reaction routes, especially at the early stages of particle formation and growth. It should be noted that such an investigation is difficult to carry out by merely analyzing collected powder samples far away from the particle source since for most aerosol processes, coagulation usually obscures the initial steps of particle evolution, leading (given sufficient residence time, typically in the order of 1 s) to the attainment of an asymptotic value (the so-called self-preserving particle size distribution) irrespective of the initial growth mechanisms.
More specifically, the fundamental processes contributing to the observed evolution of titania particle size distribution are investigated by developing a sectional model that describes particle formation by gas phase and surface growth reactions followed by coagulation and sintering, therefore, covering the whole spectrum of particle evolution till the final collection point, typically governed by coagulation and small sintering rates. The significance of gas phase chemical reactions (Okuyama, Ushio, Kousaka, Flagan, & Seinfeld, 1990; Kashima & Sugiyama, 1990; Seto, Shimada, & Okuyama, 1995) and surface growth (Battiston, Gerbasi, Guerra, & Porchia, 1997; Battiston, Gerbasi, Porchia, & Gasparotto, 1999) of titanium tetraisopropoxide (TTIP) on product TiO2 particle size is examined by comparisons between experimental data and model predictions of the evolution of primary particle size distributions along the flame.
Section snippets
Experimental
Titania particles are made from TTIP in a premixed methane–oxygen flat flame (Arabi-Katbi et al., 2001). Fig. 1 shows the experimental setup with the premixed flame aerosol reactor, the thermophoretic sampler and the FTIR spectrometer. The flame reactor consists of three concentric quartz glass tubes. The premixed reactants though are fed through the middle (central) tube with a diameter. The flow rates of methane, oxygen, and nitrogen are , and , respectively. TTIP is
Reaction models
The depletion of TTIP occurs by both homogeneous gas phase reaction and by reaction at the surface of existing TiO2 particles (Pratsinis & Spicer, 1998)where C (molecules/g) is the concentration of TTIP, t (s) is the residence time, A (cm2/g) is the total surface area concentration of TiO2 particles, ρg (g/cm3) is the carrier gas density (based on air), k (1/s) is the overall reaction rate constant, kg (1/s) is the gas phase reaction rate constant and ks (cm/s) is the
Validation
The accuracy of the present (moving) sectional model (, , ) is tested by a series of validation calculations. First, three different cases are considered that do not include surface growth (and consequently, also apply to the fixed sectional model shown in Appendix B). These are namely: pure agglomeration (coagulation of fractal like aggregate particles, consisting of primaries of monomer size), full coalescence (coagulation of spherical particles) and concurrent coagulation and sintering of
Conclusions
The dynamics of titania nanoparticle growth were simulated by an efficient moving sectional aerosol dynamics model accounting for simultaneous gas phase and surface reactions, coagulation and sintering in a premixed TTIP–methane–oxygen flat flame. The model was validated by comparing it against standard sectional solutions and detailed literature models. Three different reaction pathways were investigated, namely, pure gas phase thermal decomposition, gas phase hydrolysis, and gas phase and
Notation
a dummy volume used in Equation B1, A total aggregate area concentration, gas aggregate area concentration in section i, gas C concentration of TTIP, molecules/g gas CARS coherent anti-Stokes Raman spectroscopy collision diameter, cm mass fractal dimension monomer volume equivalent diameter, cm primary particle diameter, cm Sauter mean primary particle diameter, cm ET emission–transmission FTIR Fourier transform infra-red HAB height above burner, cm k TTIP overall thermal
Acknowledgements
This research was supported by the Swiss National Science Foundation, Grant # 2100-055469.98/1. We also wish to acknowledge Dr. Mühlenweg, H., from Degussa, Mr. Olivier Chaoul, Prof. Morrison Jr., P.W., from Case Western Reserve University and Prof. Mountziaris, T.J., from SUNY Buffalo, for their thoughtful comments.
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Presented at the Engineering Foundation Conference on Population Balance Modeling of Particulate Systems, January 2000.