Control of Particle Morphology and Size in Vapor-Phase Synthesis of Titania, Silica and Alumina Nanoparticles

Abstract

Previous studies on vapor-phase synthesis of titania (TiO₂), silica (SiO₂), and alumina (Al₂O₃) nanoparticles were reviewed. Interactions between physicochemical phenomena involved in the particle growth and the operating variables were investigated. Strategies to produce non-aggregated spherical particles of the metal oxides are discussed. Model predictions based on the sintering laws without any adjustments in the sintering parameters rarely agreed with experimental data. There remains more to be understood in reaction and nucleation kinetics, sintering, and fragmentation mechanisms until the technology is developed to the stage of designing reactors for mass production of non-aggregated spherical particles for titania, silica and alumina

1. Introduction

Titania (TiO₂), silica (SiO₂) and alumina (Al₂O₃) nanoparticles have been in commercial production for decades. Titania nanoparticles are used as sun blocking agents and photocatalysts. Silica nanoparticles are used as reinforcing fillers for rubbers and plastics, and ingredients for polishing slurries for semiconductor substrates. Alumina nanoparticles are used as catalyst supports for high-temperature reaction and ingredients for polishing slurries for semiconductor substrates. Theses nanoparticles are largely produced by vapor-phase oxidation of metal chloride vapors in flames, as aggregates composed of primary particles, a few to a few tens of nanometer in diameter. The vapor-phase synthesis is different from the spray pyrolysis: precursors are fed as vapor for the vapor-phase synthesis and as liquid droplets for the spray pyrolysis. The flame oxidation of metal chlorides dates back to 1940 when a fumed silica production was commercialized in Germany. Later in 1951, a plant for producing titania particles for white pigments by flame oxidation of TiCl₄ vapor was come on stream. The pigment-grade titania is larger in size, 0.2–0.3 μm because the hiding power is low if the size is too small. Nano-sized titania particles can be obtained by controlling the operating variables of the flame oxidation of TiCl₄.

It was not until 1980s that control of particle morphology and size for the vapor-phase synthesis of the oxides was studied in a systematic way. Tables 1, 2, and 3 show the selected studies on the investigation of morphology and particle size for titania, silica, and alumina, respectively. Not only metal chlorides but other precursors were used. Fig. 1 shows the pathway from the chemical reaction of a precursor to the formation and growth of particles. The first step is a generation of product clusters by chemical reaction. Then, nuclei are formed from the clusters. The nuclei grow to particles by coagulation, condensation, surface reaction, coalescence between neighboring particles by sintering, and agglomeration. Flame and hot wall reactors were used at various temperatures and precursor concentrations. Fig. 2 shows the types of reactors used in previous studies. In many cases, particles were not dispersed but aggregated or agglomerated. Aggregate is defined as a group of particles joined together strongly with necking between particles, while agglomerate is a group of particles or aggregates joined loosely by van der Walls force.

Table 1 Selected studies on vapor-phase synthesis of titania particles

Precursor	Reactor type	Precursor conc., mol %	Reactor temp., °C	Residence time, s	Particle size		Reference
					Primary, nm	Agglomerate, μm
TiCl4 TTIP	hot wall	0.01–0.11)	860–1000	3.1–10.8	21–41		Yoon et al. (2003)
			350–579		21–50
TTIP	hot wall	1.0–7.0	300–700	1.1–4.4	200–400		Park et al. (2001)
TTIP	hot wall	1.0–7.0	300–700	0.7	25–250		Choi and Park (2006)
TTIP	flame (PM)	0.041)	1200–1500		45		Yang and Biswas (1997)
TiCl4	hot wall	1.61)	1000–1400	1.2	40–50	0.32–0.60	Akhtar et al. (1994)
TiCl4	hot wall	0.05–1.0	900–1100	0.54–0.94	30–70		Jang and Jeong (1995)
TTIP	hot wall	0.01–2.89	300–700	3.8–10.2	20–1200		Kirkbir and Komiyama (1987)
TiCl4	hot wall	1.0–4.1	850–1100		300–700		Suyama and Kato (1976)
TiCl4	flame (PM)	4.18–5.37	900–1400	0.2	450–570		Park et al. (1990)
TTIP	hot wall	1.68–7.84	170–510	2.2	20–140		Kirkbir and Komiyama (1988)
TTIP TiCl4	hot wall	0.00171)	800–1750	< 5	12–17	0.06–0.084	Nakaso et al. (2001)
					4–8	0.041–0.067
TiCl4	hot wall	0.111)	927–1450	0.84–1.87		0.13–0.26	Akhtar et al. (1991)
TiCl4	flame (PM)	0.0045–0.31)	1377	0.05–0.23	41–63		George et al. (1973)
TiCl4	flame (DF)		1427–2727		9.5–145		Formenti et al. (1972)
TTIP	flame (DF)	12.92)	1356–15683)		30–70	0.09–0.15	Akurati et al. (2006)
TTIP	flame (PM)	0.09–0.34	1857–2162	0.2–0.24	26–45		Arabi-Katbi et al. (2001)
TTIP	flame (DF)	0.29–4.62)	900–1650		5–60		Wegner and Pratsinis (2003)
TiCl4	hot wall	1.0–1.4	850–1100	1.8	50–80		Morooka et al. (1989)

DF: diffusion; PM: premixed

1)  Estimated using precursor concentration given in mol/L or precursor flow rate.

2)  Estimated using precursor flow rate in the center tube.

3)  Temperature measured in previous work with similar operating conditions.

Table 2 Selected studies on vapor-phase synthesis of silica particles

Precursor	Reactor type	Precursor conc., mol%	Reactor temp., °C	Residence time, s	Particle size		Reference
					Primary, nm	Agglomerate, μm
SiCl4	hot wall	10.0	150	60	250–300			Park and Park (2008)
HMDS	flame (DF)	1.2–1.32)	1800–2000		18–85			Mueller et al. (2004)
SiCl4	flame (DF)	8.92)	1100–1900		15–110			Zhu and Pratsinis (1997)
SiCl4 HMDS	flame (DF, PM)	0.19–0.87 13.22)	900–1750		11–97			Briesen et al. (1998)
TEOS	hot wall	0.015–0.151)	500	7–26	15–50			Smolik and Moravec (1995)
SiCl4	flame (PM)	0.5–5.0	1527–1827		7–18			Ulrich and Riehl (1984)
SiCl4	flame (DF)	0.28–0.7	1900–2100		20–30	0.05–0.2		Chung et al. (1992)
SiCl4	flame (DF)	0.06–1.2	2000		19–42			Rulison et al. (1996)
SiCl4	flame (PM)	0.8–0.9	1480–1532		7–17			Ulrich et al. (1976)
SiCl4	flame (DM)	0.42–4.31)	794–1901		15–50	0.025–0.14		Cho and Choi (2000)
SiCl4 SiBr4 HMDS	flame (PM)	0.191)	1447		10			Ehrman et al. (1998)
		2.01)			10
		0.211)			10
SiH4	flame (PM)	0.019–0.3653)	1713–2262		20–30	0.05–0.25		Zachariah et al. (1989)

DF: diffusion; PM: premixed

1)  Estimated using precursor concentration given in mol/L or precursor flow rate.

2)  Estimated using precursor flow rate in the center tube.

3)  Silane volume loading

Table 3 Selected studies on vapor-phase synthesis of alumina particles

Precursor	Reactor type	Precursor conc., mol%	Reactor temp., °C	Residence time, s	Particle size		Reference
					Primary, nm	Agglomerate, μm
ATSB	flame (DF)	0.461)	927–1727		16–21	0.1–0.2	Johannessen et al. (2000)
ATSB	hot wall	0.012	500–900	0.14–2.81	15–18		Okuyama et al. (1986)
TMA	flame (DF)	0.1 ppm2)	2000		13–60	0.03–0.09	Xing et al. (1997)
AlCl3	flame (DF)		1427–2727		10–200		Formenti et al. (1972)
AlCl3	flame (DF)	0.21–0.85	1900–2100		20–30	0.05–0.2	Chung et al. (1992)
AlCl3	hot wall	7.0	200	60	70		Yoo et al. (2009)
ATI	hot wall	0.7	200–250	1800	80–100		Nguyen et al. (2011)
TMA	flame (PM)	0.01–0.12)	730–1650		3.0–11.1	Particles per agglomerate: 20–250	Windeler et al. (1997a)

DF: diffusion; PM: premixed

1)  Estimated assuming that the carrier gas was saturated with the precursor.

2)  Particle volume fraction

Fig. 1

Pathways for particle formation and growth in vapor-phase synthesis of metal oxides.

Fig. 2

Schematic drawings of reactors used for vapor-phase synthesis of metal oxides.

A number of review papers have been published. Gurav et al. (1993) reviewed the generation of particles by gas-phase routes for metals, oxides, and non-oxide ceramics. This may be the first comprehensive review on the vapor-phase synthesis of particles for diverse materials, although pioneering articles were published earlier by Ulrich and his coworkers on the growth of silica particles (Ulrich, 1971; Ulrich and Subramanian, 1977; Ulrich and Riehl, 1982; Ulrich, 1984). A few years later, flame synthesis of nanoparticles for ceramic materials including titania, silica, and alumina was reviewed with emphasis on the fundamentals of particle formation and growth. (Pratsinis, 1998) Other reviews followed, most of which deal with synthesis techniques, application fields, and characterization of the particles, with rather shallow discussion on the particle formation and growth (Swihart, 2003; Strobel et al., 2006; Strobel and Pratsinis, 2007; Biskos et al., 2008; Athanassiou et al., 2010). The fundamentals of particle formation for single and mixed oxides were reviewed by Roth (2007) in a way similar to that by Pratsinis (1998) but with a different viewpoint on the importance of the vapor-phase reaction and nucleation kinetics. Recently, the history of the development of commercial aerosol reactors for synthesis of carbon black, titania, silica, zinc oxide, nickel particles and the effects of process variables on particle morphology and size were discussed to conclude that for most of those materials the coagulation washes out the effect of nucleation because precursors are rapidly consumed and product particles attain self-preserving distribution by coagulation. (Pratsinis, 2011)

The present review was confined to the control of particle morphology and size in vapor-phase synthesis of titania, silica and alumina nanoparticles in flame and hot wall reactors. In previous reviews, little attention was paid to the chemical reaction and nucleation kinetics assuming that the reaction occurs rapidly in one step to form nuclei of oxide-monomer size. In reality, the reaction may not occur in one step, but in multiple steps to produce intermediate products significantly different in physical properties from the final oxide products. The chemical reaction and nucleation kinetics were reviewed more extensively than in others. We start by looking at the physicochemical phenomena involved in the particle generation and growth: chemical reaction, nucleation, condensation, coagulation, sintering, restructuring and fragmentation. We then discuss the effects of operating variables on particle morphology and size. Finally, control strategy of particle size and morphology is discussed with future works to be challenged.

2. Physico-chemical phenomena involved in generation and growth of particles

2.1 Chemical reaction

The first step to the particle generation of a metal oxide is the homogeneous reaction of a precursor vapor by oxidation, hydrolysis, or decomposition. The reaction usually occurs in multiple steps. The oxidation of TiCl₄ was reported to occur through step-wise elimination of chlorine and addition of oxygen to form titanium oxy-chlorides, TiO_xCl_y. The oxy-chlorides then collide with each other to form oligomers, (TiO_xCl_y)_n, which are further oxidized toward pure titania. The reaction is homogeneous before particles are generated. In the later stage, a heterogeneous reaction or surface reaction may occur simultaneously on the particles that have been formed. The surface reaction contributes to the growth of particles.

Table 4 shows reaction kinetic parameters reported for vapor-phase synthesis of titania, silica and alumina.

Table 4 Reaction kinetic parameters for vapor-phase synthesis of titania, silica and alumina particles

Oxide	Reaction	Activation energy (kJ/mol)	Pre-exponential factor	Temperature range (K)	Reference
TiO2	TiCl4 + O2→TiO2 + 2Cl2	88.8	8.26 × 104 (s−1)	973 to 1273	Pratsinis et al. (1990)
		102	2.5 × 105 (s−1)	723 to 973	Kobata et al. (1991)
		74.8	4.9 × 103 (cm/s)	673 to 1320	Ghoshtagore (1970)
		60	3.0 × 1013 (cm3/mol s)	500 to 1600	Shirley et al. (2011)
	TTIP→TiO2 + 4C3H6 + 2H2O	70.5	3.96 × 105 (s−1)		Okuyama et al. (1990)
		40	4.0 × 1011 (cm3/mol s)	673 to 873	Zhang and Griffin (1995)
		126	1.0 × 1011 (cm/s)		Tsantilis et al. (2002)
		164		623 to 723	Kanai et al. (1985)
	TTIP + 2H2O→TiO2 + 4C3H7OH	8.43	3.0 × 1015 (s−1)		Kashima and Sugiyama (1990)
SiO2	SiCl4 + O2→SiO2 + 2Cl2	401	8.0 × 1014 (s−1)		French et al. (1978)
	SiCl4 + O2→SiCl3 + 2Cl2	410	1.7 × 1014 (s−1)	1373 to 1573	Powers (1978)
	SiCl4 + 2H2O→SiO2 + 4HCl	121.4	1.0 × 1012.0 (cm3/mol s)	743 to 973	Kochubei (1997)
	SiCl4 + H2O→SiCl3OH + HCl	128	8.2 × 1011 (s−1)	1000 to 2000	Hannebauer and Menzel (2003)
	TEOS→products	176	2.6 × 109 (s−1)	923 to 1023	Satake et al. (1996)
		222	7.4 × 1010 (s−1)	721 to 820	Chu et al. (1991)
	TMOS→products	340	1.4 × 1016 (s−1)	858 to 968	Chu et al. (1991)
	SiBr4 + O2→SiO2 + 2Br2	280	5.0 × 1011 (s−1)		French et al. (1978)
Al2O3	AlCl3 + 3/2H2O→1/2Al2O3 + 3HCl	35.8	1.85 × 109 (L2.27/mol2.27 s)	423 to 483	Park (2014)

TTIP: titanium tetraisopropoxide; HMDS: hexamethyldisiloxane; TEOS:tetraethoxysilane; TMOS: tetramethoxysilane

Power-law type expressions were proposed for the overall reaction of TiCl₄ with oxygen. (Pratsinis et al., 1990; Kobata et al., 1991) In those rate expressions, however, the homogeneous and heterogeneous reactions were not differentiated but combined. The surface reaction rate expression for the TiCl₄ oxidation is available elsewhere. (Ghoshtagore, 1970) In the flame synthesis of titania, not only the oxidation but also the hydrolysis by the water vapor generated from fuel combustion is involved. The competition between oxidation and hydrolysis was studied in a tubular reactor to conclude that the hydrolysis was important, particularly at high H₂O/TiCl₄ ratios. (Akhtar et al., 1994) However, no kinetic data on the sole hydrolysis of TiCl₄ are available, although the rate constants for the initial few steps of the hydrolysis were calculated using the transition-state and RRKM theories (Wang et al, 2010). Titanium tetraisopropoxide (TTIP) was used in some studies in place of TiCl₄. TTIP is thermally decomposed into TiO₂, hydrocarbons and water. As in the oxidation of TiCl₄, the decomposition of TTIP may proceed in multiple steps by successive β-hydride elimination of propene and polymerization (Park et al., 2001). For the overall reaction represented by TTIP = TiO₂ + 4C₃H₆ + H₂O, the reaction rates were determined from measured concentrations of propylene under varying operating condition to obtain a rate equation, 164 kJ/mol in activation energy and a half order with respect to TTIP concentration. (Kanai et al., 1985) A different rate equation was reported later in which the reaction order is one and the activation energy is 70.5 kJ/mol. (Okuyama et al., 1990) The hydrolysis rate of TTIP is known to be faster than that of the thermal decomposition due to the oxidation effect of water that leads to a considerable reduction in activation energy. (Seto et al., 1995) These rate equations for TTIP decomposition do not differentiate between homogeneous and heterogeneous reactions. While, a rate constant assigned to the surface reaction of TTIP was obtained by Tsantilis et al. (2002) by using a reaction model and the experimental data of Battiston et al. (1997). Zhang and Griffin (1995) studied the growth kinetics of a TiO₂ film under the decomposition of TTIP in nitrogen and proposed a rate expression, 4.0 × 10¹¹ exp (−40[kJ mol⁻¹]/RT)[TTIP][N₂].

SiCl₄, SiBr₄, tetraethoxysilane (TEOS), and hexamethyldisiloxane (HMDS) were used as precursor for the vapor-phase synthesis of silica particles. In the oxidation of SiCl₄ vapor with oxygen, pure silica was not formed below 1200 K; instead chlorosiloxanes containing up to 50 Si atoms per molecule were formed. (Giesenberg et al., 2004) This implies that the oxidation of SiCl₄ to silica is a multi-step reaction. The mechanism of the multi-step reaction is not available in the literature, but is presumed to follow the step-wise elimination of chlorine and addition of oxygen to form (SiO_xCl_y)_n, as in the oxidation of TiCl₄ mentioned in the beginning of this section. The oxidation rate of SiCl₄ was studied at 1100–1300 °C. (Powers, 1978) The reaction was first order in SiCl₄ and zero order in oxygen up to a 20-fold excess O₂, and the activation energy was 96 kcal/mol. In an independent study (French et al, 1978), the reaction order was one and the activation energy was 98 kcal/mol. The rate constant of the hydrolysis of SiCl₄ vapor was measured to be 10¹² exp (−121.4/RT) cm³ mol⁻¹ s⁻¹, where the activation energy is expressed in kJ/mol. (Kochubei, 1997) Ignatov et al. (2003) studied the reaction mechanism of the gas-phase hydrolysis of SiCl₄ and calculated the rate constants of the elementary reactions in the early stage using quantum mechanics. A similar kinetic study was carried out by Hannebauer and Menzel (2003). A power-law type expression for the thermal decomposition of TEOS was proposed as 7.4 × 10¹⁰ exp (−49500/RT) s⁻¹. (Chu et al., 1991) The surface reaction rates of TEOS decomposition were measured at temperatures between 923 K and 1023 K, from which a rate constant was obtained with an activation energy of 42 kcal/mol. (Satake et al., 1996) For eighteen elementary reactions composing the decomposition of TEOS, the kinetic parameters were obtained by parameter estimation to fit experimental data. (Shekar et al., 2012a)

AlCl₃, aluminum triisopropoxide (ATI), trimethyaluminum (TMA), and aluminum tri-sec-butoxide (ATSB) were used as precursor for alumina particles. Kinetic data for the alumina precursors are very rare. Recently, a rate expression for the hydrolysis of AlCl₃ vapor was reported. (Park, 2014)

2.2 Nucleation

Nucleation occurs when the supersaturation ratio of a species produced in the reaction system has increased past a critical value. The nucleus size for silica by flame oxidation of SiCl₄ was calculated to be smaller than a SiO₂ monomer using the classical nucleation theory. (Ulrich, 1971) In many studies that follow, the assumption of a product monomer being a nucleus was used in the interpretation of experimental results and in the modeling of particle growth. (Landgrebe and Pratsinis, 1989; Tsantilis and Pratsinis, 2000; Heine and Pratsinis, 2006) The surface tension of the nucleus is required to calculate the nucleus size by the classical theory. However, the surface tension is not well defined for such a small object and the use of the classical nucleation theory does not make sense. The atomistic theory developed by Hoare and Pal (1971) may be better suited for systems with clusters less than 100 molecules. (Kulmala et al., 1987) In some studies, regardless of the nucleus size, the particle size distribution approached the self-preserving size distribution. (Vemury et al., 1994; Spicer et al., 2002) In other studies, however, the nucleus size and the nucleation rate were reported to affect the final particle size distribution. (Suyama and Kato, 1976; Yoon et al., 2003, Park et al., 2014) Using Ti₅O₆C_l8, an intermediate on the transition to TiO₂, as nucleus in place of TiO₂ monomer resulted in a considerably different particle size distribution in a flame synthesis of titania. (Mehta et al., 2013) At present, little data are available on the kinetics of producing the intermediate species and their physical properties including vapor pressure and surface tension that are required for nucleation calculation.

2.3 Condensation and coagulation

Once nuclei or smallest particles are formed, they collide with each other to form larger particles. The clusters condense on the particles while the coagulation between particles proceeds by Brownian motion. In the classical theory of coagulation, coalescence occurs instantaneously after two particles collide, and a new sphere is formed. The instantaneous coalescence may not be valid for metal oxides depending upon operating conditions. If the coalescence is incomplete, particles grow as agglomerates comprised of primary particles. Ulrich and Subramanian (1977) first introduced a time for complete fusion of two SiO₂ particles in contact to calculate the average number of primary particles in an agglomerate. The transition of fully coalesced particles into agglomerated particles was predicted using relative values of the collision and coalescence times. (Windeler et al., 1997b) The collision rates of the agglomerates are faster than those of spherical particles because the collision cross sections are larger. The collision cross section depends on the shapes of the agglomerates. The shape of an agglomerate is defined as a function of the fractal dimension (D_f) which is correlated to the number of primary particles (N_p) in the agglomerate by $N_{\text{p}}=A{\left(\frac{R}{R_0}\right)}^{D_{\text{f}}}$, where A is a constant prefactor, R is the radius of the agglomerate and R₀ is the radius of the primary particle. (Forrest and Witten, 1979) The coagulation rate expressions for spherical particles and agglomerates are available elsewhere. (Friedlander, 2000) The primary particle size increases with increasing condensation and coagulation, but is not affected by agglomeration.

2.4 Sintering, restructuring and fragmentation

If the temperature is high enough, the primary particles composing an agglomerate are sintered to form necks between particles in contact, resulting in a decrease of the surface area. Ulrich and his coworkers (Ulrich and Subramanian, 1977; Ulrich and Riehl, 1982) reported that in the flame synthesis of silica particles the coalescence of primary particles by sintering played a dominant role in determining the primary particle size. Seto et al. (1995) showed that the titania particles obtained from thermal decomposition of TTIP started to change in primary particle and agglomerate sizes by sintering at 1000 K. They showed in a later study (Seto et al., 1997) that the temperatures effective for the coalescence of the particles by sintering were 50–70 % of the bulk melting temperature for titania and 90–100 % for silica. The coalescence of primary particles by sintering was verified in other studies. (Xing et al., 1997; Cho and Choi, 2000) Koch and Friedlander (1990) incorporated into the general dynamics equation a sintering term represented by $\frac{\text{d}a}{\text{d}t}=-\frac{1}{\tau }(a-a_{\text{f}})$ where a is the instantaneous surface area of an agglomerate, a_f is the surface area of the sphere resulted by the full coalescence of the primary particles in that agglomerate, t is the time, and τ is the characteristic time for sintering. The characteristic time is defined as the time necessary to reduce by 63 % the excess surface area. Studies followed to obtain characteristic times for titania and silica, as listed in Table 5. The presence of water vapor in the sintering process was reported to accelerate the kinetics of the coalescence. (Goertz et al., 2011)

Table 5 Expressions for sintering characteristic time

Material	Characteristic time, s	Reference
TiO2	$7.4\times {10}^{8}T{d}_{\text{p}}^4\text{exp}\left(\frac{3.1\times {10}^4}{T}\right)$	Kobata et al. (1991)
TiO2	$1.5\times {10}^{3}T{d}_{\text{p}}^3\text{exp}\left(\frac{3.4\times {10}^4}{T}\right)$	Ehrman et al. (1998)
TiO2	$1.67\times {10}^{16}T{d}_{\text{p}}^4\text{exp}\left(\frac{3.2\times {10}^4}{T}\right)$	Yang and Biswas (1997)
SiO2	$6.3\times {10}^{-10}{d}_{\text{p}}\text{exp}\left(\frac{6.1\times {10}^4}{T}\right)$	Ehrman et al. (1998)
SiO2	$6.5\times {10}^{-15}{d}_{\text{p}}\text{exp}\left[\frac{8.3\times {10}^4}{T}\left(1-\frac{d_{\text{p},\text{min}}}{d_{\text{p}}}\right)\right]$	Tsantilis et al. (2001)
SiO2	$\frac{\left(1-\frac{1}{\text{e}}\right)a_{\text{f}}^2}{2^{2/3}{k}_{\text{s}}}\text{exp}\left(\frac{1.16\times {10}^4}{T}\right)$ ks: 3.5 × 10−4 m2/s af: radius of the completely coalesced sphere, m	Kirchhof et al. (2012)

d_p is the particle diameter in cm, d_p,min is the particle diameter below which the sintering is instantaneous, and T is the temperature in K.

The sizes of the primary particles and the agglomerates exiting the reactor were calculated using the characteristic times, and compared with experimental data. In a heated wall reactor where titania particles were produced by reaction of TiCl₄ vapor with oxygen, the maximum primary particle size was calculated to be 15 nm using the grain boundary diffusion coefficient by Astier and Vergnon (1976), whereas experimentally observed size was 55–65 nm. (Kobata et al., 1991) In a different study by Xiong et al. (1993b), significant deviations were observed for titania and silica between calculated and experimental sizes of primary particles and agglomerates. Wu et al. (1993) produced alumina particles by oxidation of trimethylaluminum (TMA) in flames at 890–1140 K. They compared experimental data with model prediction to show that the primary particle sizes calculated based on either grain boundary diffusion or volume diffusion were smaller by several orders of magnitudes than those experimentally observed. In contrast, Windeler et al. (1997b) reported that good agreement was obtained between experimental and calculated primary particle sizes for titania and silica produced in a premixed flame. In their calculation, the sintering law of Koch and Friedlander (1990) was assumed to hold for groups of primary particles in contact, not the whole agglomerate, as proposed by Lehtinen et al. (1996). Tsantilis et al. (2001) reported that experimental data were better fitted by modifying the sintering time to take into account the particle size dependence of melting temperature. In another study, a melting diameter was introduced, which is defined as half the diameter of particles whose characteristic sintering time is identical to the reactor residence time. Particles smaller than the melting diameter were assumed to coalesce instantaneously upon collision, by which the prediction at low temperatures was improved. (Park and Rogak, 2003)

The agglomerates are restructured by sintering. Not only the primary particle size increases but also the agglomerates shrink to decrease the cross sectional area. Fig. 3 illustrates the restructuring of an agglomerate. (Eggersdorfer and Pratsinis, 2014) The size of an agglomerate decreases by restructuring and fusion until the agglomerate is converted eventually into a sphere. The agglomerate sintering may result in a fragmentation to reduce the agglomerate size. The fragmentation was studied theoretically (Irisawa et al., 1995; Lando et al., 2006; Thouy et al., 1997; Hawa and Zachariah, 2007) and experimentally verified for silver (Bréchignac et al., 2002), but not yet for titania, silica and alumina. The fragmentation may result in producing smaller primary particles.

Fig. 3

Illustration of the evolution of an agglomerate toward a sphere by sintering. D_f represents fractal dimension. The lines showing the variation of r_m and r_va with residence time or temperature were taken from the work of Seto et al. (1997). r_m represents the average of the mobility equivalent diameters of the aggregates and r_va represents the average diameter of the primary particles composing the aggregates. (Adapted from Eggersdorfer and Pratsinis, 2014.)

3. Effects of operating variables on particle morphology and size

3.1 Precursor type and concentration

TiCl₄ and TTIP were used as precursor for titania particles. SiCl₄, SiH₄, TEOS, HMDS, and octamethylcyclotetrasiloxane (OMCTS) were used for silica particles and AlCl₃, ATSB, TMA and ATI for alumina particles. The properties of the precursors are shown in Table 6. Under the same precursor concentration in a hot wall reactor operated at temperatures between 800 °C and 1600 °C, both the primary particles and the agglomerates of titania were larger with thermal decomposition of TTIP in nitrogen than with oxidation of TiCl₄ in a mixture of nitrogen and oxygen. (Nakaso et al., 2001) Titania particles from TTIP decomposition were spherical, while those from TiCl₄ oxidation were faceted. (Yoon et al., 2003) The faceted particles from TiCl₄ turned spherical in the presence of water. (Akhtar et al., 1994) The crystalline structure of the titania from TiCl₄ in oxygen was a mixture of anatase and rutile (Kato and Suyama, 1974); the rutile content was higher in H₂O than in oxygen. While, the crystalline structure of the titania from TTIP was anatase in oxygen and a mixture of anatase and rutile in water vapor. (Choi and Park, 2006) Operating temperature is an important factor in controlling the ratio of anatase to rutile, as discussed in the succeeding section. Three silica precursors, SiCl₄, HMDS, and OMCTS, were compared in a diffusion flame to study the effect of precursor on the primary particle size. (Briesen et al., 1998) At the same precursor concentration, the particle size was the largest with OMCTS and the smallest with SiCl₄. The larger particle sizes with the organometallic precursors were attributed to the higher flame temperatures resulted from the combustion of the organic compounds. Ehrman et al. (1998) reported, for a precursor concentration lower by an order of magnitude, that there was little difference in primary particle size between SiCl₄ and HMDS. No crystalline silica was produced from any precursor. As produced alumina particles by flame oxidation of AlCl₃ vapor were amorphous or contained small amount of δ and θ phases, which are meta-stable. (Pratsinis, 1998)

Table 6 Properties of precursors for vapor-phase synthesis of titania, silica and alumina particles

Oxide	Precursor	Molecular formula (molecular weight)	State	Boiling point, °C	Mass of metal oxide per mass of precursor
TiO2	titanium tetrachloride	TiCl4 (189.7)	liquid	136.4	0.42
	titanium isopropoxide (TTIP)	TiC12H28O4 (284.2)	liquid	232	0.28
SiO2	silicon tetrachloride	SiCl4 (169.9)	liquid	57.65	0.35
	hexamethyldisiloxane (HMDS)	Si2C6H18O (162.4)	liquid	100 to 101	0.74
	tetraethoxysilane (TEOS)	SiC8H20O4 (208.3)	liquid	166 to 169	0.29
	silicon tetrabromide	SiBr4 (347.7)	liquid	153	0.17
	silane	SiH4 (32.1)	gas	−112	1.87
Al2O3	aluminum chloride	AlCl3 (133.3)	solid	178 (sublime)	0.38
	aluminum tri-isopropoxide (ATI)	AlC9H21O3 (204.3)	solid	135 (10 torr)	0.25
	aluminum tri-sec-butoxide (ATSB)	AlO3C12H27 (246.3)	liquid	200 to 206 (30 mmHg)	0.21
	trimethylaluminum (TMA)	Al2C6H18 (144.2)	liquid	125 to 130	0.35

An increase in precursor concentration increases the amount of precursor available for surface reaction, the amount of condensable product clusters, and the number of nuclei. The increases in the amounts of condensable product clusters and the precursor vapors for surface reaction act to increase primary particle size, while the increase in the number of nuclei acts to decrease the size. The opposing effects compete in determining primary particle size. Which effect will dominate depends on the operating condition and the properties of the precursor. In those studies shown in Tables 1 to 3, primary particle sizes increased with increasing precursor concentration, but for a few. The rare events in which primary particle size decreased with increasing precursor concentration are described. In a synthesis of titania particles by thermal decomposition of TTIP in nitrogen at 500 °C, an increase in precursor concentration decreased the primary particle size and increased the number of particles. (Moravec et al., 2001) In a synthesis of silica particles by oxidation of SiCl₄ in oxygen at 1200 °C with precursor concentration varied between 1 % and 8 %, the primary particle size decreased with increasing precursor concentration in the range of 4–8 %. (Suyama and Kato, 1976) In a flame synthesis of alumina with TMA as precursor, the primary particle size was rather insensitive to the precursor concentration. (Windeler et al., 1997a) In contrast with the contradictory effects on primary particle size, aggregate size increased consistently as precursor concentration was increased. (Chung et al., 1992; Windeler et al., 1997a)

3.2 Temperature and residence time

The operating temperature may be the most influential factor in controlling particle morphology and size. An increase in temperature will increase the reaction rate, the nucleation rate, the collision rate and the sintering rate. The temperature profile in a reactor for vapor-phase synthesis of particles could be represented by one of the three types shown in Fig. 4. The figure is more representative of hot wall reactors, but is adaptable in concept to flame reactors in which the temperature gradients are usually stiffer than in hot wall reactors. In Type I the temperature is below the sintering temperature throughout the reactor and the sintering of particles is neglected. If the nucleation is fast enough, the particle sizes for both primary particles and agglomerates are determined by the collision rates to exhibit self-preserving size distributions in the long run (Friedlander and Wang, 1966; Vemury et al., 1994; Spicer et al., 2002). Otherwise, the primary particle size is determined by competition between nucleation and surface growth. Examples of Type I can be found in syntheses with hot wall reactors, in most of which primary particle size decreased with increasing reactor set temperature. (Suyama and Kato, 1976; Kirkbir and Komiyama, 1987; Morooka et al., 1989; Jang and Jeong, 1995; Park et al., 2001; Park et al., 2014) By preheating the reactants before they get in contact or placing the location of reactants mixing at a distance from the inlet toward the center of the reactor, the particle size was decreased. (Jang and Jeong, 1995; Park et al., 2014) In Type II there exists a high-temperature zone in which the temperature exceeds the sintering temperature, but the residence time in the hot-temperature zone is not sufficient, resulting in aggregates in which the boundaries between primary particles are unclear. (Ulrich and Subramanian, 1977; Ulrich and Riehl, 1982; Windeler et al., 1997a; Cho and Choi, 2000) The specific surface area decreased with increasing reactor set temperature. In Type III the residence time in the high temperature zone is long enough for the primary particles in the agglomerates to fully coalesce into larger particles (Xing et al., 1997; Arabi-Katbi et al., 2001; Lee and Choi, 2002; Camenzind et al., 2008). In most studies in Type III, the effects of reaction and nucleation rates in the early stage were washed out by the dominating sintering effect and primary particle size increased with increasing temperature.

Fig. 4

Schematic drawing of axial temperature profiles for producing aggregated particles or loosely agglomerated spherical particles. Three types of temperature profile are shown. Loosely agglomerated particles are produced with types I and III, while aggregated particles are produced with Type II.

In some studies that fall in Type III, primary particle size rather decreased with increasing temperature. In a study on the effect of sintering on the growth of TiO₂ particles in a hot wall reactor, the primary particle size increased with increasing temperature, showed a maximum at 1200 °C, and then decreased as the temperature was further increased to 1600 °C. (Nakaso et al., 2001) In a synthesis of silica particles in a counter-flow diffusion reactor with silane (SiH₄) as precursor, the primary particle size in the hotter flame was smaller than that in the colder flame. (Zachariah et al., 1989) Similar phenomena were observed in other flame syntheses. (Cho and Choi, 2000; Akurati et al., 2006) The decrease of the primary particle size was attributed to an insufficient sintering time (Mueller et al., 2004) or to a lower precursor conversion (Akurati et al., 2006), due to a reduction in flame size. We raise a conjecture that the agglomerates admitted into the sintering-coalescence zone were probably smaller, as reported for a synthesis of iron particles by thermal decomposition of iron pentacarbonyl (Moniruzzaman et al., 2007), or the fragmentation rate of the aggregates was higher. Further studies are necessary to clarify the reason for the decrease of primary particle size under the sintering-coalescence regime.

Aggregate sizes or the number of primary particles composing an aggregate increased with increasing reactor temperature before sintering effects set in, but decreased thereafter due to restructuring. (Camenzind et al., 2008; Chung et al., 1992) In flame reactors, the particles were rapidly cooled to prevent aggregation and growth by sintering. Wegner and Pratsinis (2003) reported that virtually non-aggregated and spherical titania particles as small as 5 nm were produced by placing a quenching nozzle. By comparison, the particle size was 20–60 nm without the nozzle. The particle size increased with increasing the distance of the nozzle from the burner mouth. The nozzle quenching effect was confirmed later in a similar study by Okada et al. (2011) in whose work nearly non-agglomerated titania particles 6.8 nm in diameter were produced by both blowing in a −70 °C argon gas and using a expansion nozzle.

The rutile content of the titania produced by oxidation of TiCl₄ vapor was reported to increase with increasing reaction temperature. (Suyama et al., 1975) In the oxidation of TiCl₄, initially anatase particles are formed and then grow as anatase particles or transformed into rutile particles before they grow. Not only the temperature but also the time that the particles remain small in size is known to be an important factor. Morooka et al. (1989) reported that the rutile content showed a maximum at 1100 °C and then decreased as the temperature was further increased to 1200 °C. This decrease in rutile content with temperature increase was attributed to the faster growth of the anatase particles to the size at which the transformation into rutile is remarkably slowed down. By irradiating titania particles with a CO₂ laser, the rutile content decreased against the expectation that the rutile content would increase because the temperature was increased by the laser irradiation. (Lee and Choi, 2002) The silica particles produced by the vapor-phase synthesis in flame reactors were all amorphous (Formenti et al., 1972; Ehrman et al., 1998), while the alumina particles were amorphous or a mixture of amorphous and metastable crystalline phases. (Pratsinis, 1998) By calcining an amorphous alumina for two hours at 1200 °C, the phase was completely transformed into alpha. (Yoo et al., 2009)

3.3 Reaction medium

The precursors for vapor phase synthesis of the oxides were reacted or decomposed in different media: nitrogen, oxygen, water vapor or a mixture. The morphology and particle size showed differences between reaction media. In a hot wall reactor at 1000–1400 °C, titania particles were synthesized from TiCl₄ with varying ratios of H₂O to O₂ and with five injection points of H₂O located at various distances from the inlet of the reactor. (Akhtar et al., 1994) At a reactor set temperature of 1200 °C, the primary particles obtained with the injection point at 13 cm inward from the inlet were faceted, while those with the injection point at the inlet were spherical. With the injection point at 13 cm, there was no H₂O present in the early stage and the oxygen determined the morphology that is consistent with those faceted shapes observed in earlier studies in pure oxygen. (Suyama and Kato, 1976; Yoon et al., 2003) With the injection point located at the inlet, H₂O was present from the beginning and played to change the particle shape from faceted to round. As the amount of H₂O was increased, the rutile content was invariable up to 1000 °C but decreased at higher temperatures. In a synthesis of titania particles by thermal decomposition of TTIP at 300–700 °C, three different reaction media were used: N₂, O₂, and a mixture of N₂ and H₂O. (Choi and Park, 2006) As shown in Fig. 5, particle morphology and size was significantly different between reaction media. In N₂, agglomerates composed of very small particles whose individual boundaries are not clearly distinguished were produced. In O₂, the primary particles were spherical and larger. As the medium was changed to nitrogen plus water, much larger spherical particles were obtained. The crystalline phases were amorphous in N₂, anatase in O₂, and a mixture of rutile and anatase in N₂ plus water, respectively. A follow-up study may be necessary to understand how the reaction media affect the morphology, size, and crystalline structure.

Fig. 5

Comparison of TEM images of titania particles between reaction media. The particles were synthesized in a tubular reactor by thermal decomposition of TTIP at 700 °C with the precursor concentration at 7 mol % and the residence time at 0.7 s. (Adapted from Choi and Park, 2006.)

In most studies of synthesis of silica particles with SiCl₄ as precursor, the flame reaction was used in which both oxygen and water vapor were present. However, in a synthesis by Park and Park (2008), SiCl₄ was reacted with H₂O only at 150 °C to produce spherical particles, as shown in Fig. 6, which are quite different from those chain-like aggregates resulted by the flame reactions. A similar method was used to produce non-aggregated spherical particles by hydrolysis of AlCl₃ vapor at 300– 700 °C. (Park et al., 2014) Those particles obtained by the low temperature hydrolysis were not pure but contained residual chlorines which were removed downstream in a calciner. The low-temperature hydrolysis of metal chloride vapor appears to be an attractive route to non-aggregated spherical particles of metal oxides when a calcination is necessary as for the transformation of crystalline phase.

Fig. 6

Scanning electron microscopic images of silica particles produced at two different SiCl₄ concentrations: (a) 10 mol % and (b) 20 mol %. The silica particles were produced in a batch reactor at 150 °C by hydrolysis of SiCl₄ vapor. The residence time in the reactor was 60 s and the initial molar ratio of H₂O to SiCl₄ was 2. (Adapted from Park and Park, 2008.)

3.4 Additives and external forces

The presence of additives during vapor-phase synthesis of metal oxides is known to affect the particle morphology and size significantly. (Suyama and Kato, 1985) In the oxidation of TiCl₄ vapor in a hot wall reactor, the titania particles formed in the presence of FeCl₃, AlBr₃, SiCl₄ or ZrCl₄ were 1/2 to 1/5 the size of those without additives. The reduction in particle size was attributed to a retardation of TiO₂ deposition on the particles. An addition of AlCl₃ in the flame oxidation of TiCl₄ increased the rutile content. (Mezey, 1966) While, other additives such as SiCl₄ and POCl₃ decreased the rutile content. (Akhtar et al., 1992) The addition of an alkali salt, sodium or potassium carbonate, to a flame synthesis of silica reduced the primary particle size. (Wu et al., 1993) The alkali salts dissociated into ions, some of which adsorbed on the particle surface to create repulsive forces between particles to retard coagulation. (Xiong et al., 1992) Ferrocene was found to be an effective additive to decrease the primary particle size of silica particles by flame oxidation of SiCl₄. (Fotou et al., 1995) Silica particles by flame synthesis were made smaller by applying electric fields. (Hardesty and Weinberg, 1973) The presence of a gaseous electric discharge (corona) in a flame synthesis of titania particles decreased the primary particle size and the rutile content. (Vemury and Pratsinis, 1995) The corona was applied to a silica flame synthesis; it was as effective as in titania synthesis and negative electric field was more effective in reducing particle growth. (Vemury and Pratsinis, 1996) The control of particle size by external electric field was successfully applied to a scaled up process of flame synthesis of silica particles. (Kammler and Pratsinis, 2000)

In parallel with experimental studies on the effects of the operating variables, numerous modeling studies have been made on the basis of first principles. (Landgrebe and Pratsinis, 1990; Xiong and Pratsinis, 1993b; Pope and Howard, 1997; Lee et al., 2001; Nakaso et al., 2001; Park and Rogak, 2003; Morgan et al., 2006; Moniruzzaman and Park, 2006; Ji et al., 2007; West et al., 2009; Sander et al., 2009; Zaitone et al., 2009; Shekar et al., 2012b; Mehta et al., 2013). However, there remains more to be understood in reaction and nucleation kinetics, sintering, and fragmentation mechanisms until the technology is developed to the stage of designing reactors for mass production of non-aggregated spherical particles for titania, silica, and alumina.

4. Control strategy of particle morphology and size

As discussed in the preceding sections, various physicochemical phenomena are involved in determining particle morphology and size and those phenomena are influenced by temperature and residence time in the reactor, precursor concentration, reaction medium, and additives and external forces. Since the metal oxides in aggregated form have already been in commercial production, the control strategy in this work is focused on the synthesis of non-aggregated spherical particles varying in size.

As shown in Fig. 4, non-aggregated spherical particles can be produced either with temperature and residence time maintained high enough for any aggregates formed earlier to coalesce later by fusion into spheres or with the temperature low enough for any serious necking between particles in contact not to occur. With the low-temperature scheme, the nucleation rate is a key factor in determining primary particle size; the particle size decreases with increasing reactor temperature. Smaller particles can be produced by either preheating the reactants before they get in contact or placing the location of reactants mixing at a distance from the inlet toward the center of the reactor. An additional heat treatment or calcination may be necessary if the conversion of the precursor is incomplete because of the low temperature. With the high-temperature scheme, sintering of particles in agglomerates is a dominant factor. It is a key how to control operating variables to obtain a high-temperature zone for full coalescence of the particles into spheres.

Increasing precursor concentration results in an increase in particle size except for very limited cases. Reaction medium is a factor in controlling particle morphology and size in hot wall reactors. In flame reactors, the control of particle size and morphology by reaction medium is less useful because water vapor is always present in the flame. The particle size and morphology is sensitive to the burner type, premixed or diffusion, and to the configuration of injection nozzles for fuel and oxidizer in diffusion burners. (Akurati et al., 2006) The particle size can also be controlled either by injecting additives into the reactor or by applying electric fields. The use of additives may contaminate the particles, and their uses are limited to the cases where the contamination poses no problem in product specification as in the use of AlCl₃ to control the phase of titania particles. Cooling the particles rapidly before the sintering sets in is a way to obtain small non-agglomerated particles. One needs to be cautious, however, not to freeze the conversion of precursor when using rapid cooling.

The choice of a precursor is based on the volatility, the stoichiometric mass of product per mass of precursor, and the cost of the precursor. Once a precursor is chosen, the next step is to decide reactor type, hot wall or flame reactor. The control of operating variables is simpler with hot wall reactors. In flame reactors, there exist interactions between operating variables to make it difficult to decouple the effect of a variable from those of other variables and to achieve optimal operating conditions. However, there is an advantage with flame reactor that the energy needed for the synthesis of particles is supplied in situ by combustion of fuels.

5. Conclusion

Previous studies on the synthesis of titania, silica, and alumina particles were reviewed with an objective to derive strategies for producing non-aggregated spherical particles in hot wall or flame reactors. Various physico-chemical phenomena are involved in the particle formation and growth: chemical reaction, nucleation, condensation, coagulation, sintering, restructuring, and fragmentation. These phenomena occur in series and parallel as well, and are influenced and controlled by various operating variables: precursor type and concentration, temperature and residence time, reaction medium, and additives and external forces. By investigating the interactions between the physico-chemical phenomena and the operating variables, two approaches were derived to produce non-aggregated spherical particles of the metal oxides. One approach is to have the temperature and residence time high enough for any aggregates formed in the earlier stage to fuse and coalesce into spherical particles before they exit the reactor. The other is to have the temperature low enough for any necking between neighboring particles not to occur. If the conversion is not enough with the low-temperature approach, an increase in residence time or an extra step of calcination may be necessary in order to complete the conversion and to remove any residuals in the particles.

The configuration of reactants mixing is an important factor in controlling the morphology and size. By preheating the reactants before they get in contact or placing the location of reactants mixing at a distance from the inlet toward the center of the reactor, the particle size can be decreased particularly for the low-temperature synthesis. In flame reactors, particle size and morphology are sensitive to the burner type, premixed or diffusion, and to the configuration of injection nozzles for fuel and oxidizer in diffusion burners. The particle size increases with precursor concentration except for limited cases. By using additives, applying electric fields or rapid cooling with a quenching nozzle, both the primary particle size and the degree of aggregation decreased significantly.

It appears that the role of nucleation has been underestimated. The conversion of precursor needs to be checked more carefully in the analysis of early-stage particle growth in flame reactors. Model predictions based on the sintering laws without any adjustments in the sintering parameters rarely agreed with experimental data. There remains more to be understood in reaction and nucleation kinetics, sintering, and fragmentation mechanisms until the technology is developed to the stage of designing reactors for mass production of non-aggregated spherical particles for titania, silica, and alumina.

Author’s short biography

Hoey Kyung Park

Hoey Kyung Park received her B.S. (2005), M.S. (2007), and Ph.D. (2014) degrees in chemical engineering from Kongju National University in Korea. Her main research focus was on gas-phase synthesis of nano-materials (silica and α-alumina etc.). She is currently a post-doctoral researcher at Department of Chemical Engineering, Kongju National University. Her current research interests include gas-phase synthesis and CFD simulation.

Kyun Young Park

Kyun Young Park is Professor of Chemical Engineering at Kongju National University, Korea. He holds a B.S. (1972) from Seoul National University, an M.S. (1982) and a Ph.D. (1984) from the University of Texas at Austin. He was a process engineer at SK Energy from 1975 to 1980 and a researcher at Korea Institute of Geoscience and Mineral Resources from 1985 to 1992 before he joined Kongju National University in 1993. His research interests are in the area of vapor-phase synthesis of particles of metals and metal oxides and gas-solid reactions.

References

•  Akhtar  M.K.,  Xiong  Y.,  Pratsinis  S.E., Vapor synthesis of titania powder by titanium tetrachloride oxidation, AIChE J., 37 (1991) 1561–1570.
•  Akhtar  M.K.,  Pratsinis  S.E.,  Mastrangelo  S.V.R., Dopants in vapor-phase synthesis of titania powders, J. Am. Ceram. Soc., 75 (1992) 3408–3416.
•  Akhtar  M.K.,  Vemury  S.,  Pratsinis  S.E., Competition between TiCl₄ hydrolysis and oxidation and its effect on product TiO₂ powder, AIChE J., 40 (1994) 1183–1192.
•  Akurati  K.K.,  Vital  A.,  Klotz  U.E.,  Bommer  B.,  Graule  T.,  Winterer  M., Synthesis of non-aggregated titania nanoparticles in atmospheric pressure diffusion flames, Powder Technol., 165 (2006) 73–82.
•  Arabi-Katbi  O.I.,  Pratsinis  S.E.,  Morrison Jr  P.W.,  Megaridis  C.M., Monitoring the flame synthesis of TiO₂ particles by in-situ FTIR spectroscopy and thermophoretic sampling, Combust. Flame, 124 (2001) 560–572.
•  Astier  M.,  Vergnon  P., Determination of the diffusion coefficients from sintering data of ultrafine oxide particles, J. Solid State Chem., 19 (1976) 67–73.
•  Athanassiou  E.K.,  Grass  R.N.,  Stark  W.J., Chemical aerosol engineering as a novel tool for material science: from oxides to salt and metal nanoparticles, Aerosol Sci. Technol., 44 (2010) 161–172.
•  Battiston  G.A.,  Gerbasi  R.,  Guerra  M.,  Porchia  M., Gas-phase FT-IR analysis and growth kinetics of TiO₂ in a hot wall LP-MOCVD reactor, Chemical Vapor Deposition, Proceedings of the fourteenth International CVD Conference and EUROCVD-11, in:  Allen-dorf  M.D.,  Bernard  C. (Eds.), Pennington, NJ: Electrochemical Society, 97–25.(1997) 660–667.
•  Biskos  G.,  Vons  V.,  Yurteri  C.U.,  Schmidt-Ott  A., Generation and sizing of particles for aerosol-based nanotechnology, KONA, 26 (2008) 13–35.
•  Bréchignac  C.,  Cahuzac  Ph.,  Carlier  F.,  Colliex  C.,  Leroux  J.,  Masson  A.,  Yoon  B.,  Landman  Uzi, Instability driven fragmentation of nanoscale fractal islands, Phys. Rev., Lett., 88 (2002) 196103-1–196103-4.
•  Briesen  H.,  Fuhrmann  A.,  Pratsinis  S.E., The effect of precursor in flame synthesis of SiO₂, Chem. Eng. Sci., 53 (1998) 4105–4112.
•  Camenzind  A.,  Schulz  H.,  Teleki  A.,  Beaucage  G.,  Narayanan  T.,  Pratsinis  S.E., Nanostructure evolution: from aggregated to spherical SiO₂ particles made in diffusion flames, Eur. J. Inorg. Chem., (2008) 911–918.
•  Cho  J.,  Choi  M., Determination of number density, size and morphology of aggregates in coflow diffusion flames using light scattering and local sampling, J. Aerosol Sci., 31 (2000) 1077–1095.
•  Choi  J.G.,  Park  K.Y., Effect of reaction atmosphere on particle morphology of TiO₂ produced by thermal decomposition of titaniumtetraisopropoxide, J. Nanopart. Res., 8 (2006) 269–278.
•  Chu  J.C.S.,  Breslin  J.,  Wang  N.S.,  Lin  M.C., Relative stabilities of tetramethylorthosilicate and tetraethyl orthosilicate in the gas phase, Mater. Lett. 12 (1991) 179–184.
•  Chung  S-L.,  Sheu  Y-C.,  Tsai  M-S., Formation of SiO₂, Al₂O₃, and 3Al₂O₃·2SiO₂ particles in a counterflow diffusion flame, J. Am. Ceram. Soc., 75 (1992) 117–123.
•  Eggersdorfer  M.L.,  Pratsinis  S.E., Agglomerates and aggregates of nanoparticles made in the gas phase, Adv. Powder Technol. 25 (2014) 71–90.
•  Ehrman  S.H.,  Friedlander  S.K.,  Zachariah  M.R., Characteristics of SiO₂/TiO₂nanocomposite particles formed in a premixed flat flame, J. Aerosol Sci., 29 (1998) 687–706.
•  Formenti  M.,  Juillet  F.,  Meriaudeau  P.,  Teichner  S.J.,  Vergnon  P., Preparation in a hydrogen-oxygen flame of ultrafine metal oxide particles, Journal of Colloid and Interface Science, 39 (1972) 79–89.
•  Forrest  S.R.,  Witten  T.A., Long-range correlations in smoke-particle aggregates, J. Phys. A: Math Gen. 12 (1979) L109–L117.
•  Fotou  G.P.,  Scott  S.J.,  Pratsinis  S.E., The role of ferrocene in flame synthesis of silica, Combust. Flame, 101 (1995) 529–538.
•  French  W.G.,  Pace  L.J.,  Foertmeyer  V.A., Chemical kinetics of the reactions of SiCl₄, SiBr₄, GeCl₄, POCl₃, and BCl₃ with oxygen, J. Phys. Chem., 82 (1978) 2191–2193.
•  Friedlander  S.K, Smoke, Dust and Haze: Fundamentals of aerosol dynamics, Oxford University Press, New York, 2000.
•  Friedlander  S.K.,  Wang  C.S., The self-preserving particle size distribution for coagulation by Brownian motion, Journal of Colloid and Interface Science, 22 (1966) 126–132.
•  George  A.P.,  Murley  R.D.,  Place  E.R., Formation of TiO₂ aerosol from the combustion supported reaction of TiCl₄ and O₂, Faraday Symp. Chem. Soc., 7 (1973) 63–71.
•  Ghoshtagore  R.N., Mechanism of heterogeneous deposition of thin film rutile,J. Electrochem. Soc., 117 (1970) 529–534.
•  Giesenberg  T.,  Hein  S.,  Binnewies  M.,  Kickelbick  G., Synthesis and functionalization of a new kind of silica particle, Angew. Chem. Int. Ed., 43 (2004) 5697–5700.
•  Goertz  V.,  Weis  F.,  Keln  E.,  Nirschl  H.,  Seipenbusch  M., The effect of water vapor on the particle structure and size of silica nanoparticles during sintering, Aerosol Sci. Technol., 45 (2011) 1287–1293.
•  Gurav  A.,  Kodas  T.,  Pluym  T.,  Xiong  Y., Aerosol processing of materials, Aerosol Sci. Technol., 19 (1993) 411–452.
•  Hannebauer  B.,  Menzel  F., The combustion of SiCl₄ in hot O₂/H₂ flames, Z. Anorg. Allg. Chem., 629 (2003) 1485–1490.
•  Hardesty  D.R.,  Weinberg  F.G., Electrical control of particulate pollutants from flames, Fourteenth Symposium (International) on combustion, 14 (1973) 907–918.
•  Hawa  T.,  Zachariah  M.R., Molecular dynamics simulation and continuum modeling of straight-chain aggregate sintering: Development of a phenomenological scaling law, Phys. Rev. B., 76 (2007), 054109-1–9.
•  Heine  M.C.,  Pratsinis  S.E., High-concentration agglomerate dynamics at high temperatures, Langmuir, 22 (2006) 10238–10245.
•  Hoare  M.R.,  Pal  P., Physical cluster mechanics: states and energy surfaces for monatomic systems, Adv. Phys., 20 (1971) 161–196.
•  Ignatov  S.K.,  Sennikov  P.G.,  Razuvaev  A.G.,  Chuprov  L.A.,  Schrems  O.,  Ault  B.S., Theoretical study of the reaction mechanism and role of water clusters in the gas-phase hydrolysis of SiCl₄, J. Phys. Chem. A 107 (2003), 8705–8713.
•  Irisawa  T.,  Uwaha  M.,  Saito  Y., Scaling laws in thermal relaxation of fractal aggregates, Europhy. Lett., 30 (1995) 139–144.
•  Jang  H.D.,  Jeong  J., The effects of temperature on particle size in the gas-phase production of TiO₂, J. Aerosol Sci., 23 (1995) 553–560.
•  Ji  Y.,  Sohn  H.Y.,  Jang  H.D.,  Wan  B.,  Ring  T.A., Computational fluid dynamic modeling of a flame reaction process for silica nanopowder synthesis from tetraethylorthosilicate, J. Am. CeramSoc., 91 (2007) 3838–3845.
•  Johannessen  T.,  Pratsinis  S.E.,  Livbjerg  H., Computational fluid-particle dynamics for the flame synthesis of alumina particles, Chem. Eng Sci., 55 (2000) 177–191.
•  Kanai  T.,  Komiyama  H.,  Inoue  H., TiO₂ particles by chemical vapor deposition–Particle formation mechanism and chemical kinetics, Kagaku Kogaku Ronbunshu, 11 (1985) 317–323.
•  Kashima  K.,  Sugiyama  H., Particle-size control of TiO₂ ultrafine particles by CVD method, Kagaka Kogaku Ronbunsyu 16 (1990) 551–556.
•  Kammler  H.K.,  Pratsinis  S.E., Electrically-assisted flame aerosol synthesis of fumed silica at high production rates, Chem. Eng. Process., 39 (2000) 219–227.
•  Kato  A.,  Suyama  Y., Preparation of rutile powders by vapor phase reaction of TiCl₄-H₂-CO₂ system, Chem. Lett., 6 (1974) 961–962.
•  Kirchhof  M.J.,  Forster  H.,  Schmid  H.-J.,  Peukert  W., Sintering kinetics and mechanism of vitreous nanoparticles, J. Aerosol Sci., 45 (2012) 26–39.
•  Kirkbir  F.,  Komiyama  H., Formation and growth mechanism of porous, amorphous, and fine particles prepared by chemical vapor deposition. Titania from titanium tetraisopropoxide, The Canadian Journal of Chemical Engineering, 65 (1987) 759–766.
•  Kirkbir  F.,  Komiyama  H., Continous production of fine TiO₂ powders by vapor-phase hydrolysis of titanium tetraisopropoxide, Advanced Ceram. Mater., 3 (1988) 511–515.
•  Kobata  A.,  Kusakabe  K.,  Morooka  S., Growth and transformation of TiO₂ crystallites in aerosol reactor, AIChE J., 37 (1991) 347–359.
•  Koch  W.,  Friedlander  S.K., The effect of particle coalescence on the surface area of a coagulating aerosol, J. Colloid Interf Sci., 140 (1990) 419–427.
•  Kochubei  V.F., Kinetics of the gas-phase hydrolysis of silicon tetrachloride, Kinetics and Catalysis, 38 (1997) 212–214.
•  Kulmala  M.,  Olin  M.,  Raunemaa  T., Extension of atomistic nucleation theory for non-ideal vapours, J. Aerosol Sci., 18 (1987) 615–618.
•  Landgrebe  J.D.,  Pratsinis  S.E., Gas-phase manufacture of particulates: Interplay of chemical reaction and aerosol coagulation in the free-molecular regime, Ind. Eng. Chem Res., 28 (1989) 1474–1481.
•  Landgrebe  J.D,  Pratsinis  S.E., A discrete-sectional model for particulate production by gas-phase chemical reaction and aerosol coagulation in the free-molecular regime, J. Colloid Interf Sci., 139 (1990) 63–89.
•  Lando  A.,  Kebaili  N.,  Cahuzac  Ph.,  Masson  A.,  Bréchignac  C., Coarsening and pearling instabilities in silver nanofractal aggregates, Phys. Rev. Lett., 97 (2006) 133402-1–4.
•  Lee  B.W.,  Jeong  J.I.,  Hwang  J.Y.,  Choi  M.,  Chung  S.H., Analysis of growth of non-spherical silica particles in a counterflow diffusion flame considering chemical reactions, coagulation and coalescence, J. Aerosol Sci., 32 (2001) 165–185.
•  Lee  D.,  Choi  M., Coalescence enhanced synthesis of nanoparticles to control size, morphology and crystalline phase at high concentrations, J. Aerosol Sci., 33 (2002) 1–16.
•  Lehtinen  K.E.J.,  Windeler  R.S.,  Friedlamder  S.K., A note on the growth of primary particles in agglomerate structures by coalescence, J. Colloid Interface Sci., 182 (1996) 606–608.
•  Mehta  M.,  Raman  V.,  Fox  R.O., On the role of gas-phase and surface chemistry in the production of titania nanoparticles in turbulent flames, Chem. Eng. Sci., 104 (2013) 1003–1013.
•  Mezey  E.J., Pigments and reinforcing agents, in:  Palmer  C.F.,  Oxley  J.H.,  Blocher  M. (Eds.), Vapor deposition, NY: John Wiley & Sons, New York, 1966.
•  Moniruzzaman  C.G.,  Park  K.Y., A discrete-sectional model for particle growth in aerosol reactor: Application to titania particles, Korean J. Chem. Eng., 23 (2006) 159–166.
•  Moniruzzaman  C.G.,  Park  H.G.,  Park  K.Y., Analysis of iron particle growth in aerosol reactor by a discrete-sectional model, Korean J. Chem. Eng., 24 (2007) 299–304.
•  Moravec  P.,  Smolik  J.,  Levdansky  V.V., Preparation of TiO₂ fine particles by thermal decomposition of titanium tetraisopropoxide vapor, J. Mater. Sci. Lett., 20 (2001) 2033–2037.
•  Morgan  N.M.,  Wells  C.G.,  Goodson  M.J.,  Kraft  M.,  Wagner  W., A new numerical approach for the simulation of the growth of inorganic nanoparticles, J. Comput. Phys., 211 (2006) 638–658.
•  Morooka  S.,  Yasutake  T.,  Kobata  A.,  Ikemizu  K.,  Kato  Y., A mechanism for the production of ultrafine particles of TiO₂ by a gas-phase reaction, Int. Chem. Eng., 29 (1989) 119–126.
•  Mueller  R.,  Kammler  H.K.,  Pratsinis  S.E.,  Vital  A.,  Beaucage  G.,  Burtscher  P., Non-agglomerated dry silica nanoparticles, Powder Technol. 140 (2004) 40–48.
•  Nakaso  K.,  Fujimoto  T.,  Seto  T.,  Shimada  M.,  Okuyama  K.,  Lunden  M.M., Size distribution change of titanianano-particle agglomerates generated by gas phase reaction, agglomeration, and sintering, Aerosol Sci. Tech., 35 (2001) 929–947.
•  Nguyen  T.G.,  Park  K.Y.,  Jung  K.Y.,  Cho  S.B., Vapor-phase synthesis of a solid precursor for α-alumina through a catalytic decomposition of aluminum triisopropoxide, Mater. Res. Bull., 46 (2011) 2199–2203.
•  Okada  Y.,  Kawamura  H.,  Ozaki  H., Formation of non-agglomerated titania nanoparticles in a flame reactor, J. Chem. Eng. Japan, 44 (2011) 7–13.
•  Okuyama  K.,  Kousaka  Y.,  Toghe  N.,  Yamamoto  S.,  Wu  J.J.,  Flagan  R.C.,  Seinfeld  J.H., Production of ultrafine metal oxide aerosol particles by thermal decomposition of metal alkoxide vapors, AIChE J., 32 (1986) 2010–2019.
•  Okuyama  K.,  Ushio  R.,  Kousaka  Y.,  Flagan  R.C.,  Seinfeld  J.H., Particle generation in a chemical vapor deposition process with seed particles, AIChE J., 36 (1990) 409–419.
•  Park  H.K., Preparation and characterization of alumina-precursor powders by gas-phase hydrolysis of AlCl₃, Ph.D. Thesis, Kongju National University, Korea (2014).
•  Park  H.K.,  Park  K.Y., Vapor-phase synthesis of uniform silica spheres through two-stage hydrolysis of SiCl₄, Mate. Res. Bull., 43 (2008) 2833–2839.
•  Park  H.K.,  Park  K.Y.,  Jung  K.Y., Alumina-precursor nanoparticles prepared by partial hydrolysis of AlCl₃ vapor in tubular flow reactor: Effect of hydrolysis conditions on particle size distribution, Ind. Eng. Chem. Res., 53 (2014) 10372–10379.
•  Park  K.Y.,  Lee  I.H.,  Yang  H.S., Pilot scale experiments on the oxidation of TiCl₄, J. Korean Ceram. Soc., 27 (1990) 817–823.
•  Park  K.Y.,  Ullmann  M.,  Suh  Y.J.,  Friedlander  S.K., Nanoparticle microreactor: application to synthesis of titania by thermal decomposition of titanium tetraisopropoxide, J. Nanopart. Res., 3 (2001) 309–319.
•  Park  S.H.,  Rogak  S.N., A one-dimensional model for coagulation, sintering, and surface growth of aerosol agglomerates, Aerosol Sci. Tech., 37 (2003) 947–960.
•  Pope  C.J.,  Howard  J.B., Simultaneous particle and molecule modelling (SPAMM): an approach for combining sectional aerosol equations and elementary gas-phase reactions, Aerosol Sci. Tech., 27 (1997) 73–94.
•  Powers  D.R., Kinetics of SiCl₄ oxidation, J. Am. Ceram. Soc., 61 (1978) 295–297.
•  Pratsinis  S.E., Flame aerosol synthesis of ceramic powders, Prog. Enegy Combust. Sci., 24 (1998) 197–219.
•  Pratsinis  S.E., History of manufacture of fine particles in high-temperature aerosol reactors, in:  Ensor  D.S. (Ed.), Aerosol science and technology: History and reviews, RTI international, USA, 2011, pp. 475–507.
•  Pratsinis  S.E.,  Bai  H.,  Biswas  P.,  Frenklach  M.,  Mastrangelo  S.V.R., Kinetics of titanium (IV) chloride oxidation, J. Am. Ceram. Soc., 73 (1990) 2158–2162.
•  Roth  P., Particle synthesis in flames, Proceed Combust. Inst. 31 (2007) 1773–1788.
•  Rulison  A.J.,  Miquel  P.F.,  Katz  J.L., Titania and silica powders produced in a counterflow diffusion flame, J. Mater. Res., 11 (1996) 3083–3089.
•  Sander  M.,  West  R.H.,  Celnik  M.S.,  Kraft  M., A detailed model for the sintering of polydispersed nanoparticle agglomerates, Aerosol Sci. Tech., 43 (2009) 978–989.
•  Satake  T.,  Sorita  T.,  Adachi  H., Kinetic and theoretical study of the thermal decomposition of tetraethoxysilane in the gas phase, Proc. Electrochem. Soc., 96 (1996) 23–28.
•  Seto  T.,  Shimada  M.,  Okuyama  K., Evaluation of sintering of nanometer-sized titania using aerosol method, Aerosol Sci. Tech., 23 (1995) 183–200.
•  Seto  T.,  Hirota  A.,  Fujimoto  T.,  Shimada  M.,  Okuyama  K., Sintering of polydisperse nanometer-sized agglomerates, Aerosol Sci. Tech., 27 (1997) 422–438.
•  Shekar  S.,  Sander  M.,  Rebecca  C.,  Riehl  R.C.,  Smith  A.J.,  Braumann  A.,  Kraft  M., Modeling the flame synthesis of silica nanoparticles from tetraethoxysilane, Chem. Eng. Sci., 70 (2012a) 54–66.
•  Shekar  S.,  Smith  A.J.,  Menz  W.J.,  Sander  M.,  Kraft  M., A multidimensional population balance model to describe the aerosol synthesis of silica nanoparticles, J. Aerosol Sci., 44 (2012b) 83–98.
•  Shirley  R.,  Akroyd  J.,  Miller  L.A.,  Inderwildi  O.R.,  Riedel  U.,  Kraft  M., Theoretical insights into the surface growth of rutile TiO₂, Combust. Flame, 158 (2011) 1868–1876.
•  Smolik  J.,  Moravec  P., Gas phase synthesis of fine silica particles by oxidation of tetraethylorthosilicate vapour, J. Mater. Sci. Lett., 14 (1995) 387–389.
•  Spicer  P.T.,  Chaoul  O.,  Tsantilis  S.,  Pratsinis  S.E., Titania formation by TiCl₄ gas phase oxidation, surface growth and coagulation, J. Aerosol Sci., 33 (2002) 17–34.
•  Strobel  R.,  Baiker  A.,  Pratsinis  S.E., Aerosol flame synthesis of catalysts, Adv. Powder Technol., 17 (2006) 457–480.
•  Strobel  R.,  Pratsinis  S.E., Flame aerosol synthesis of smart nanostructured materials, J. Mater. Chem., 17 (2007) 4743–4756.
•  Suyama  Y.,  Ito  K.,  Kato  A., Mechanism of rutile formation in vapor phase oxidation of TiCl₄ by oxygen, Journal of Inorganic and Nuclear Chemistry, 37 (1975) 1883–1888.
•  Suyama  Y.,  Kato  A., TiO₂ produced by vapor-phase oxygenolysis of TiCl₄, J. Am. Ceram. Soc., 59 (1976) 146–149.
•  Suyama  Y.,  Kato  A., Effect of additives on the formation of TiO₂ particles by vapor phase reaction, J. Am. Ceram. Soc., 68 (1985) C154–C156.
•  Swihart  M.T., Vapor-phase synthesis of nanoparticles, Curr. Opin. Colloid. In., 8 (2003) 127–133.
•  Thouy  R.,  Olivi-Tran  N.,  Jullien  R., Fragmentation of two-dimensional mass fractals by surface-diffusion sintering, Phys. Rev. B, 56 (1997) 5321–5327.
•  Tsantilis  S.,  Pratsinis  S.E., Evolution of primary and aggregate particle-size distributions by coagulation and sintering, AIChE J., 46 (2000) 407–415.
•  Tsantilis  S.,  Briesen  H.,  Pratsinis  S.E., Sintering time for silica particle growth, J. Aerosol Sci., 34 (2001) 237–246.
•  Tsantilis  S.,  Kammler  H.K.,  Pratsinis  S.E., Population balance modelling of flame synthesis of titania nanoparticles, Chem. Eng. Sci., 57 (2002) 2139–2156.
•  Ulrich  G.D., Theory of particle formation and growth in oxide synthesis flames, Combust. Sci. Technol., 4 (1971) 47–57.
•  Ulrich  G.D.,  Milnes  B.A.,  Subramanian  N.S., Particle growth in flames II: experimental results for silica particles, Combust. Sci. Technol., 14 (1976) 243–249.
•  Ulrich  G.D.,  Subramanian  N.S., Particle growth in flames III. coalescence as a rate-controlling process, Combust. Sci. Technol., 17 (1977) 119–126.
•  Ulrich  G.D.,  Riehl  J.W., Aggregation and growth of submicron oxide particles in flames, J. Colloid. Interf. Sci., 87 (1982) 257–265.
•  Ulrich  G.D., Flame synthesis of fine particles, Chem. Eng. News, 62 (1984) 22–29.
•  Vemury  S.,  Kusters  K.A.,  Pratsinis  S. E., Time-lag for attainment of the self-preserving particle size distribution by coagulation, J. Colloid Interf. Sci., 165 (1994) 53–59.
•  Vemury  S.,  Pratsinis  S.E., Corona-assisted flame synthesis of ultrafine titania particles, Appl. Phys. Lett., 66 (1995) 3275.
•  Vemury  S.,  Pratsinis  S.E., Charging and coagulation during flame synthesis of silica, J. Aerosol Scl., 27 (1996) 951–966.
•  Wang  T.H.,  Navarrete-López  A.M.,  Li  S.,  Dixon  D.A.,  Gole  J.L., Hydrolysis of TiCl₄: initial steps in the production of TiO₂, J. Phys. Chem., A 114 (2010) 7561–7570.
•  Wegner  K.,  Pratsinis  S.E., Nozzle-quenching process for controlled flame synthesis of titania nanoparticles, AIChE J., 49 (2003) 1667–1675.
•  West  R.H.,  Shirley  R.A.,  Kraft  M.,  Goldsmith  C.F.,  Green  W.H., A detailed kinetic model for combustion synthesis of titania from TiCl₄, Combust. Flame, 156 (2009) 1764–1770.
•  Windeler  R.S.,  Friedlander  S.K.,  Kari  E.J., Production of nanometer-sized metal oxide particles by gas-phase reaction in a free jet. I: experimental system and results, Aerosol Sci. Tech., 27 (1997a) 174–190.
•  Windeler  R.S.,  Lehtinen  K.E.J.,  Friedlander  S.K., Production of nanometer-sized metal oxide particles by gas-phase reaction in a free jet. II: Particle size and neck formation-comparison with theory, Aerosol Sci. Tech., 27 (1997b) 191–205.
•  Wu  M.K.,  Windeler  R.S.,  Steiner  C.K.R.,  Börs  T.,  Friedlander  S.K., Controlled synthesis of nanosized particles by aerosol processes, Aerosol Sci. Technol., 19 (1993) 527–548.
•  Xing  Y.,  Rosner  D.E.,  Köylü  Ü.Ö.,  Tandon  P., Morphological evaluation of nanoparticles in diffusion flames: Measurements and modeling, AIChE J., 43 (1997) 2641–2649.
•  Xiong  Y.,  Pratsinis  S.E.,  Mastrangelo  S.V.R., The effect of ionic additives on aerosol coagulation, J. Colloid Interf., 153 (1992) 106–117.
•  Xiong  Y.,  Pratsinis  S.E., Formation of agglomerate particles by coagulation and sintering-Part I. A two-dimensional solution of the population balance equation, J. Aerosol Sci., 24 (1993a) 283–300.
•  Xiong  Y.,  Akhtar  M.K.,  Pratsinis  S.E., Formation of agglomerate particles by coagulation and sintering-part II. The evolution of the morphology of aerosol-made titania, silica and silica-doped titania powders, J. Aerosol Sci., 24 (1993b) 301–313.
•  Yang  G.,  Biswas  P., Study of the sintering of nanosized titania agglomerates in flames using in situ light scattering measurements, Aerosol Sci. Tech., 27 (1997) 507–521.
•  Yoo  Y.S.,  Park  K.Y.,  Jung  K.Y.,  Cho  S.B., Preparation of α-alumina nanoparticles via vapor-phase hydrolysis of AlCl₃, Mater. Lett., 63 (2009) 1844–1846.
•  Yoon  J.D.,  Park  K.Y.,  Jang  H.D., Comparison of titania particles between oxidation of titanium tetrachloride and thermal decomposition of titanium tetraisopropoxide, Aerosol Sci. Technol., 37 (2003) 621–627.
•  Zachariah  M.R.,  Chin  D.,  Semerjian  H.G.,  Katz  J.L., Silica particle synthesis in a counterflow diffusion flame reactor, Combust, Flame, 78 (1989) 287–298.
•  Zaitone  B.A.,  Schmid  H.-J.,  Peukert  W., Simulation of structure and mobility of aggregates formed by simultaneous coagulation, sintering and surface growth, J. Aerosol Sci., 40 (2009) 950–964.
•  Zhang  Q.,  Griffin  G.L., Gas-phase kinetics for TiO₂ CVD: hot-wall reactor results, Thin Solid Films, 263 (1995) 65–71.
•  Zhu  W.,  Pratsinis  S.E., Synthesis of SiO₂ and SnO₂ particles in diffusion flame reactors, AIChE J., 43 (1997) 2657–2664.