日本燃焼学会誌 第 50 巻 151 号（2008 年）8-18 Journal of the Combustion Society of Japan Vol.50 No.151 (2008) 8-18

■FEATURE■

― Recent and Future Progress in Combustion Chemistry ―

Chemical Kinetic Mechanism of Polycyclic Aromatic Hydrocarbon Growth and Soot Formation

SHUKLA, Bikau, MIYOSHI, Akira, and KOSHI, Mitsuo*

Department of Chemical System Engineering, The University of Tokyo, 7-3-1 Hongo, Bnkyo-ku, Tokyo 113-8656, Japan

Abstract : This review is subjected to impart light on the formation schemes of one ring aromatic compound to the polycyclic aromatic hydrocarbons (PAHs) and their further sequential growth into the first soot particle, i.e. soot nucleation. It mainly includes the role of stable and radical species in the formation of PAHs and soot. With some focus on limitations of previous results, new experimental investigations and related mechanisms are discussed in detail. A new and efficient kinetic mechanism for the formation of large PAHs via the active role of a phenyl radical, i.e. phenyl addition /cyclization (PAC), is proposed. An alternative mechanism, methyl addition/cyclization (MAC), is also proposed. This mechanism is especially applicable to the pyrolysis of aliphatics and alkylated aromatic hydrocarbons which produces methyl sufficient radicals. These new mechanisms are expected to be helpful especially for kinetic modeling in many theoretical works on hydrocarbons combustion. Recent progress in kinetic simulations of soot particle growth is also reviewed briefly.

Key Words : PAHs, Soot, Chemical Kinetic Mechanism, PAC, MAC, HACA

many studies have forwarded pyrene as final aromatic precursor 1. Introduction [18-21]. On the other hand Bockhorn et al. [22] proposed Being a very fast process, soot formation is not perfectly coronene instead of pyrene. Recently, it again becomes a subject understood yet due to its high complexity. Better understanding of discussion among the combustion scientists that “Is coronene of this process needs resolution of its complexities, which is only (mass 300 amu) sufficient for coagulation into very high mass possible by the systematic kinetic study about its precursors. of first soot particle (~2000 amu)?”, because some previous and The study of soot precursors, carbonaceous nanoparticles (NP) recent studies [23-26] have detected many PAHs greater than and polycyclic aromatic hydrocarbons (PAHs, precursor of NP), coronene. Thus, the formation mechanism of PAHs and soot produced from many practical combustion systems such as a still remains unclear in the area of oxidation and pyrolysis of diesel engine and a spark ignition engine, is a hot and interesting hydrocarbon fuels. In spite of the similar activation energies for research topics in combustion, environment and health research soot formation, the beginning of soot formation in aliphatic and [1-9]. aromatic hydrocarbons is different [27]. The kinetic mechanism Though more than a century of continuous research in of aromatic hydrocarbons (i.e. BTX = Benzene, Toluene and combustion chemistry [10], Wen et al. [11] proposed that both Xylene) combustion and pyrolysis is poorly understood. PAHs and polyynes are soot precursors. It has been widely There are several comprehensive reviews on the formation of accepted that gaseous PAHs are precursors of soot particles PAHs. In the reviews of Harvey et al. [28] and Bockhorn et al. [12-17] because: (i) it bridges the mass gap between hydrocarbon [15], the formation of seven aromatic rings PAHs (m/z = 378) fuel and soot , (ii) the chemical structure of soot is similar to were discussed. Kennedy et al. [29] has especially focused PAH on an atomic level, i.e. honeycomb like network of sp2 on numerical simulation of soot formation and oxidation. carbons. However, until now, no attempt has been successful Very recent review on this complex subject has been reported to clarify the size of PAHs at which their rate of coalescence by Richter et al. [30]. They have successfully presented the exceeds the rate of growth. Although reaction pathways and soot detail discussion about the formation of benzene to coronene precursors differ with a fuel type (aliphatic or aromatic) and in different conditions including the formation of fullerene process parameters (pressure, temperature and equivalence ratio), precursor corannulene with main focus on the HACA (Hydrogen

Abstraction/ acetylene(C2H2) Addition, see sec. 3.) mechanism * Corresponding author. E-mail: [email protected] although it is well known that it is slow to compete with fast

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process of soot formation. They also fail to explain about the flight mass spectrometer (TOFMS) proved to be powerful and formation of PAHs larger than coronene. useful technique for online detection of gas phase species if the Since several excellent reviews on the soot formation VUV wave length is shorter enough to ionize all of them. A already exist, the aim of the present review is not to give the typical photon energy of laser based SPI (118 nm) is 10.5 eV comprehensive perspective on this subject. Rather, we focus on which is sufficient enough to ionize almost all the aliphatic and previous works regarding the formation mechanism of benzene aromatic products except for small molecules such as CH4 and to PAHs including soot growth. The major objective is to impart C2H2. Many research groups [33-48] have successfully detected light on the recent improvement in those mechanisms on the gas phase products in combustion by the VUV-SPI-TOFMS basis of kinetic analysis of formation pathways of large PAHs. technique. In addition, recent progresses in kinetic simulation of soot We also used this technique with a flow tube reactor to detect nucleation, coagulation and oxidation are described. large PAHs. Detail of the experimental set up has been explained At first, we briefly summarize the experimental technique elsewhere [49]. Since new kinetic mechanisms for large PAHs for the detection of large PAHs. Next we discuss the chemical growth will be discussed on the basis of those results, those kinetics of the ring formation in the pyrolysis of simple aliphatic experiments are briefly summarized here. The gas phase reaction hydrocarbons. Detailed discussion of formation mechanisms products from methyl radical (m/z = 15) to large PAHs up to from benzene to large PAHs is followed. Finally kinetic C42H18 (m/z =522) have been detected as pyrolysis products of modeling of soot growth is reviewed. aromatic and aliphatic hydrocarbons at temperature 1136- 1507 K, pressure ~10 Torr with constant residence time of ~0.6 s. For an example a typical mass spectra of toluene and toluene 2. Experimental techniques for the detection of + benzene mixture at different temperatures with assigned large PAHs species is shown in Fig. 1. Dominant outputs of our study are the direct detection of large PAHs and findings of new reaction Until now, most attempts were made for this very complex pathways for the formation of those large PAHs with major issue by using shock tubes and products detection by indirect roles of cyclopenta fused, benzyl, phenyl and methyl radicals. methods i.e. gas chromatography (GC), liquid chromatography At low temperatures (<1300 K), the products mainly produced (LC) or high pressure liquid chromatography (HPLC) with mass from benzyl radicals were detected in toluene pyrolysis while spectrometer (MS). Mathieu et al. [23] has used Laser desorption phenyl-PAHs and their corresponding condensed PAHs were ionization (LDI) TOFMS and Dobbins et al. [24,25] used found abundantly in the pyrolysis of benzene. At moderate laser microprobe mass spectrometer (LMMS). These detection temperature (~1300-1400 K) where maximum number of methods are classified to the “Pre-concentration method”, in products could be detected, products were found mainly which the exhaust molecules are trapped on suitable adsorbent contributed by cyclopentafused, phenyl and methyl radicals which are further separated by pretreatment (i.e. extraction). together with some HACA (Hydrogen abstraction and acetylene Those methods are time consuming and exclude direct real time addition, see next section) were detected in the toluene pyrolysis in-situ analysis [31]. It is only suitable for stable species and do while condensed PAHs produced from phenyl-PAHs and some not provide any information about radicals which are key species products of HACA were detected in benzene pyrolysis. On the for developing the mechanism. other hand, at high temperatures (>1400 K) in both cases mainly In-situ detection of soot precursor in hydrocarbon combustion products contributed by the HACA and some polyynes could and pyrolysis needs a selective and sensitive analytical method. be detected due to self decomposition of active species such as The most promising one for instrumental analytical purpose is benzyl, phenyl, cyclopentadienyl radicals and benzene itself. the TOF-MS with a selective and soft (fragment free) ionization Due to these reasons the formation routes of large PAHs were techniques like Chemical Ionization (CI), Photo Ionization decelerated and resulted in the inhibition of large PAHs at high [i.e. single photon ionization (SPI) or multi photon ionization temperatures. (MPI)] and Electron Impact ionization (EI). The CI method is highly sensitive to matrix effect. The Resonantly Enhanced 3. Production and growth of PAHs Multi-photon Ionization (REMPI) is highly sensitive only for aromatic products and the Electron impact ionization (EI) The construction of perfect soot formation mechanism for causes massive fragmentation. Lukky et al. [32] concluded that fuel oxidation and pyrolysis is still a challenging problem of the vacuum ultraviolet (VUV) photon can ionize most of the continuing interest for combustion researchers. First difficulty aliphatic and aromatic species. Thus, the production of VUV is the reactions which are responsible for the soot nucleation. radiation to achieve single photon ionization (SPI) and time of It involves the discrimination between a “molecule” and a

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Fig.1 Mass spectra of toluene and toluene+benzene mixture at different temperatures and at constant pressure of 10 Torr with residence time of 0.56 s.

“particle”. Second is the involvement of a large number of of PAHs which was further modified and named the HACA elementary reactions most of which are still unknown. Third is mechanism by Frenklach et al. [51]. It was further supported the existence of a large number of isomers especially of PAHs by many other studies [23,53-59]. An example of the HACA and fourth is the unavailability of thermodynamic and kinetic mechanism for the formation of naphthalene from benzene is parameter for large number of species and involved reactions. shown in Fig.2. Although there are many disagreements about the mechanism The HACA mechanism had also been considered for based on fuel types and experimental conditions, some general large PAHs growth. However, in recent days many groups agreement on the mechanism can be found. Mainly for aliphatic [20,21,53,60-64] believe that increase in mass of PAHs by fuels, the first aromatic ring (benzene) is produced through HACA is not sufficient to fit with very fast formation of soot a large number of elementary reactions involving C2, C3 and in combustion processes. Homann and Wagner [65] proposed

C4 species. On the other hand, in case of aromatic fuels, the the mechanism for the formation of soot precursor by aromatic mechanism starts from the first aromatic ring i.e. benzene or radical-radical recombination and radical-molecule reactions. An phenyl. Until now four different reaction mechanisms have been example of fluorene and biphenyl formation by the reactions R1 proposed from different research groups. (1) Hydrogen abstraction and acetylene addition (HACA) (2) Aromatic radical-radical and radical-molecule reactions (3) Polyyne reactions (4) Ion-molecule reactions Among them the well known mechanism for the growth of PAHs under pyrolytic conditions is the HACA mechanism [22,50-52]. Bockhorn et al. [22] proposed first time the hydrogen Fig.2 Formation of naphthalene by the HACA mechanism abstraction and acetylene addition mechanism for the formation

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and R2 can be represented as follows. aromatic ring. Besides those pathways, formation of benzene from methylcyclopentadiene via fulvene is also proposed in some studies [87-90]. The cyclopentadiene is converted into methylcyclopentadiene and further into benzene by ring expansion through fulvene (R3-R7).

CH3 + c - C5H6= C5H5CH3 + H R3

Later Bohm et al. [66,67] and McKinnon et al. [68] also C5H5CH3 + H = C5H5CH2 + H2 R4 proposed that the HACA mechanism is too slow as it only C5H5CH3 + CH3 = C5H5CH2 + CH4 R5 increases the mass of product species by 24 amu. C5H5CH2 = C6H6 (fulvene) + H R6

Calcote et al. [69,70] pointed out that free radical mechanisms C6H6 (fulvene) = C6H6 (Benzene) R7 are too slow for the fast soot formation processes. They proposed the role of ionic species in soot formation rather than PAHs Those reactions can be presented in the schematic form as with an experimental evidence that the concentration of PAH following. under some conditions continues to increase after the rate of soot formation has gone to zero. They concluded that reaction of ion and molecule is faster than radical reactions. It was further supported by some other studies [71-74]. Homann et al. [75] and Crittenden et al. [76] have forwarded the role of polyacetylenes Melius et al. [91] computed the rate of isomerization of fulvene in soot formation under certain conditions of aliphatic species in to benzene. Melius et al. [92] and Moskaleva et al. [93] found the form of polyyne mechanism. In favor of polyyne mechanism activation energy barrier of 30 kJ/mole between reactants and any Krestinin et al. [77] discussed that thermodynamic stability of one of above products. polyacetylenes increases with temperature while the stability of In our recent studies, significantly high concentration of C4H4/ other hydrocarbon decreases. This mechanism is also found to C4H3 species was observed in the pyrolysis of acetylene, ethylene be applicable only at high temperatures since acetylene, the key and acetone. This observation fairly supports the formation of species for this model, is only produced from other hydrocarbons benzene or phenyl by the active role of those species with C2H2/ at high temperatures. C2H3. On the other hand propyne (source of propargyl radical) After all, particularly the chemical identity of the soot nuclei was detected significantly in acetone pyrolysis, indicating that is not defined and elementary reaction steps involved in their the dimerization reaction of propargyl (C3H3) has a role for the formations are not perfectly explored until now. In the next formation of first aromatic ring. Methylcyclopentadiene clearly two sections, we discuss more details of the chemical kinetic detected only in acetone pyrolysis, indicating the formation of mechanism for the formation of the first aromatic ring from benzene or phenyl via reactions R1-R5. It can be concluded that aliphatic fuels, and details of the growth mechanism of larger aliphatic species which can produce methyl radical contribute PAHs. to the formation of first aromatic ring through propargyl, vinylacetylene and methyl- cyclopentadiene routes, while smaller 3.1. Chemical Kinetics of the First Aromatic Ring aliphatics such as acetylene and ethylene dominantly contribute

Formation to the formation of first aromatic ring via the reaction of C4H4/

After the early work of Berthelot et al. [78], who suggested the C4H3 with C2H3/C2H2. formation of benzene via direct polymerization of acetylene, various pathways have been reported [79-85] for the formation 3.2. Formation Mechanisms of Large PAHs of the first aromatic ring (benzene or phenyl radical) under In spite of the well established kinetic mechanism for the pyrolytic conditions. Detailed reaction flow scheme reported by formation of first aromatic ring, formation mechanisms of Skjoth-Rasmussen et al. [86] shows that the propargyl radical large PAHs are unclear. At first the HACA mechanism was

(CH2CCH) is the dominant precursor for the formation of proposed for the formation of large PAHs [22,51]. But later benzene or phenyl radical. Detailed explanation of the formation it was found that it is too slow to compete with fast process mechanism for one aromatic ring compound can be found in of soot formation, because HACA needs six steps with a recent review of Richter et al. [30]. These theoretical and involvement of two molecules of acetylene for growth of one experimental studies focused on the reactions of C2 species (C2H, more aromatic ring in the primary linear PAHs (see Fig. 2).

C2H2 and C2H3), C3 species (C3H4 and C3H3), and C4 species Later vinyl radical (C2H3) was found to be important for the

(C4H2, C4H3, C4H4, C4H5 and C4H6), in the formation of first further PAHs growth at short reaction time [62]. Proposals of

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direct formation of phenylacetylene [94] or styrene [95] from observed mass spectra, the PAC (phenyl addition/ cyclization) unsaturated aliphatic radicals by the cyclization processes have mechanism is proposed for the growth of large PAHs. This PAC been made. Formation of naphthalene by the dimerization of mechanism is found highly efficient for the ring growth of PAHs cyclopenta- dienyl radicals was also proposed by Dean et al. having triple fusing sites. The reason of this high efficiency is [96] and Melius et al. [92]. Phananthrene production from indene caused by following reasons. (a) It increases the size by two and cyclopentadienyl radical was reported by many studies aromatic rings in each step which is three times of the HACA. [55,56,97]. Bittner and Howard proposed free radical addition (b) It always produces only benzenoid PAHs. (c) All products schemes for PAHs and soot involving acetylene, phenyl, benzyl PAHs contain one more active site (triple fusing site) than that and methyl radicals reactions [98]. The role of benzene or phenyl of reactant PAH. An example is the formation of benzo[e]pyrene as a growth species is also reported to produce non-benzenoid from phenanthrene. PAHs such as fluoranthene [55,99], benzo[b]fluoranthene and indeno[1,2,3-cd]pyrene from naphthalene, phenanthrene and pyrene respectively. Those previous studies indicate that some specific products especially small PAHs is possibly produced by different routes than HACA but there is a lack of study about the formation mechanism of large PAHs through an alternative PAC mechanism is also found efficient for the growth of mechanism to the HACA. PAHs having double fusing site into cyclopentafused PAHs In our recent studies on pyrolysis of aromatic hydrocarbons and (CP-PAHs) having internally fused 5 membered ring. The growth their mixtures [49,100], many large PAHs and their derivatives of naphthalene into fluoranthene is an exmple. In this case, the could be detected. Kinetic analysis of formation mechanism HACA step is completely inefficient. of those products indicates the active role of benzyl, phenyl, cyclopentadienyl and methyl radicals. For the understanding of formation mechanisms of large PAHs, some terminologies have been defined as follows.

Products of those reactions increase triple fusing sites (indicated by dotted arrows) from which further efficient ring growth by PAC as well as HACA will occur. It is noted that this process never stops the further growth. On addition of acetylene or (a) Site of PAH having no bay like structure and can be fused at high temperatures due to formation of acetylene from the with another aromatic ring from only one side is assigned as a decomposition of active radicals, the products formation single fusing site. (b) A bay structure of three carbon atoms is was dominated by the HACA. The role of the HACA is only named as a double fusing site. (c) A bay structure of four carbon important for the formation of stable condensed PAHs from atoms is named as a triple fusing site. unstable primary PAHs with zig-zag structure (having triple To our knowledge, there is no theoretical calculation on the fusing sites), such as the growth of pyrene from phenanthrene by energy barrier for the hydrogen abstraction from different fusing the following reaction. sites of a PAH. Based on the discussion of the HACA mechanism in previous studies, the reactivity of those sites for hydrogen abstraction and acetylene addition is expected to be in the order of triple fusing site > double fusing site > single fusing site. For example, almost all studies have considered the effective growth of phenanthrene into pyrene by the HACA mechanism rather Similarly it is found efficient for the formation of externally than the formation of acephenanthrenyl or ethynylphenanthrene. fused cyclopentafused PAHs (CP-PAHs) by the addition of acetylene to a double fusing site of a PAH in one step by ring growth with two carbon atoms. An example is the growth of acenaphthylene and pyracylene by the following reaction.

Considering this different reactivity of different fusing sites and

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Main drawback of the HACA seems the closing of further growth Table 1 Comparison of HACA and PAC mechanism sites by forming externally fused 5 membered rings. Another noticeable point of PAC mechanism is the formation of corannulene, a sub unit of all fullerenes at high temperatures with the help of the HACA steps after the formation of fluoranthene.

Comparison of the HACA with the proposed mechanism of PAC is summarized in table 1. The PAC mechanism is important especially for soot growth from aromatic hydrocarbons. However, without help of HACA reactions, a symmetric PAH (soot precursor) can not be produced. Thus PAC with HACA mechanism is necessary to explain the soot process in greater extent. The detailed reaction flow of PAH growth by the PAC with HACA is shown in Fig. 3. It shows that the phenyl-PAHs sequences started from benzene and phenylacetylene produce only benzenoid PAHs while the sequences started with toluene and naphthalene produce only non-benzenoid PAHs having an internally fused 5-membered ring. On the other hand HACA3 routes are active for filling

Fig. 3 A schematic representation of products formation by the PAC and HACA mechanism. (Ref.100)

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the triple fusing sites and ends in symmetrical PAHs such as coronene and corannulene. HACA2 routes ends in a CP-PAHs like pyracylene. At temperatures higher than 1400 K, it is found that the formation of large PAHs was suppressed. As a new species, polyacetylenes, such as diacetylene and triacetylene, and CP-PAHs having externally attached 5 membered ring resulted from acetylene addition were detected abundantly. Those new products favor the production of acetylene in significant concentration from the decomposition of chain carrier radicals such as benzyl, phenyl and cyclopnetadienyl. Because of this, the formation routes of large PAHs might be decelerated. In the pyrolysis of acetone and its mixtures, methyl- PAHs, CP-PAHs, methyl-CP-PAHs, and primary PAHs were detected in our recent study. The kinetic analysis of those products showed Fig.4 A schematic representation of the MAC mechanism the conversion of methyl-PAHs into CP-PAHs and their further growth into closest primary PAHs through ring expansion. These reaction paths are termed as MAC (methyl addition/cyclization). The MAC mechanism has been found to be only efficient for the growth of the externally fused 5 membered ring CP-PAH which is produced by the methyl addition into the closest primary PAHs through ring expansion. Transformations of cyclopentadiene, indene, fluorene and 4H-cyclopenta[def] phenanthrene into benzene, naphthalene, phenanthrene and pyrene are examples of MAC mechanism. The MAC mechanism is not efficient as HACA and PAC for the growth of large PAHs because of mass growth by only 14 amu. MAC mechanism is shown in detail in Fig. 4. In the pyrolysis of aliphatic hydrocarbons (acetylene, ethylene and acetone), various products were detected. Products are ranging from C2H4 (m/z = 28) to C24H12 (m/z = 300) including polyacetylenes, PAHs and ethynyl-PAHs or CP-PAHs. Mass Fig.5 PAH formation in the pyrolysis of C2H2, C2H4, CH3COCH3 spectra showed the dominant species at interval of mass of 24 amu which corresponds to HACA mechanism. On the other hand, detection of vinylacetylene and its corresponding radicals C4H4/ particle formation, the physical processes of particle inception,

C4H3, in significantly high concentrations indicates that these coagulation, aggregation and condensation have to be considered species are actively participating in the ring growth. From kinetic in addition to the gas-phase chemistry. At the current stage, analysis it is found that the products formation mechanism is three parallel processes, particle inception, surface growth, and dominated by the aliphatic radical-molecule reactions in addition coagulation, are widely accepted for the soot particle formation to the HACA. As HACA mechanism needs two steps while and growth. Each process is discussed below. vinylacetylene needs only one step for ring growth, latter is (1) Particle inception (nucleation): Large PAHs are dominantly expected to be the most probable route. Pyrolysis mechanism of formed by sequences of chemical reactions of radicals of smaller aliphatic is summarized in Fig. 5. PAH with C2H2 (by HACA), PAH or PAH radicals (by PAC). At certain size, PAH species react with each other to form condensed particles (soot), i.e. particle inception (nucleation) 4. Soot growth occurs. Until now, it is not clear what size of PAH will generate Numerous theoretical and experimental studies have been a first particle. In other word, we do not know which PAH the performed on the soot particle growth during the hydrocarbon precursor of the soot formation is. As already mentioned in pyrolysis and combustion and reviews on this topic are available introduction, pyrene is most frequently assumed to be a precursor [29,30]. For the understanding of the mechanism of soot [18-21]. However, coronene is also thought to be a precursor

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[22]. Most PAHs assumed in the formation of soot nuclei have the bin for the particle class is increased, larger particles can be molecular masses of not more than 300 amu [101-103]. On the described at the expense of computational cost. other hand, many PAH having molecular weight lager than 300 Frenklach et al. [105-107,113,114] applied the method of amu are detected in many recent works as mentioned in the moments, which is based of the fact that the solution of an previous section. Those recent experimental results suggested infinite set of equations for the moments of the size distribution that the precursor for formation of soot nuclei is the PAH with is equivalent to the solution of the master equation. This method molecular weight larger than 300 amu. Identification of the is computationally very efficient and it provides integral precursor PAH is still open for the future study. quantities such as total number density and volume fraction. (2) Surface growth: Reactions at the surface of growing particles However, the size distribution function (SDF) of soot particle considerably contribute to the soot growth. Although details is not obtained directly. Also, approximations (interpolation of those reactions on the soot surface are not known, similar schemes) are required to close the system of equations for reactions to those of PAH are often assumed [14,17]. Reactive moments. The knowledge of the shape of the SDF is important sites on the surface are activated by the hydrogen abstraction for the prediction of ultra-fine particles. (reaction S1), and soot is growing by the addition of acetylene Recently, Kraft et al. [115-119] indicated that the stochastic (reaction S4) and PAHs. Those growth processes compete with approach is very powerful for solving the Smoluchowski the oxidation by O2, OH, (reactions S5 and S6) and O atom (burn equation. In this stochastic method, the ensemble of soot particles out). The surface reaction mechanism proposed by Frenklach and is approximated by a stochastic particle system. The calculation co-workers is successfully used in the numerical simulation of of SDF by this method is straight forward, and the sizes and soot growth [104-107]. the time history of particles are known explicitly. All processes of soot formation (inception, surface growth, and coagulation)

Csoot - H +H => Csoot. + H2 S1 are treated probabilistically using Monte-Carlo techniques. The

Csoot. + H2 => Csoot - H +H S2 method successfully applied to the soot formation in laminar

Csoot. + H => Csoot - H S3 flames [115-118] and in the turbulent diffusion flame [119].

Csoot. + C2H2 => Csoot - H + H S4 According to the Smoluchowski equation, size of soot particle

Csoot. + O2 => products S5 is growing up continuously and number density decreases

Csoot - H +OH => products S6 monotonically. However, it is experimentally known that the number density of soot particles remains almost constant in More detailed discussion of the surface reaction is beyond the the post-flame zone, and therefore, the size of the particle also scope of this review. remains constant. This ‘stopped coagulation’ cannot be explained (3) Particle coagulation: Sizes of soot increase further by the master equation [120]. It is experimentally observed that, by collision of growing soot particles. Initially, colliding after the initial coagulation period, soot particles are aggregated particles coalesce completely yielding a new spherical particle with nearly mono-dispersed primary particles, and growth of the [17]. Particle coagulation process can be described by the primary particle seems to be stopped at certain size. Frenklach Smoluchowski’s master equations of Brownian coagulaton [108]. et al. [120-122] attributed this “stopped coagulation” to the onset of aggregation. A dynamic Monte Carlo (DMC) simulation [122] of the particle aggregation has also been performed with simultaneous surface growth. Combining the information obtained by the DMC, Balthasar and Frenklach [121] could explain nearly constant primary particle size.

Here, Ni is the number density of particles of size i, bi,j is the Recently, effect of the aggregation on the shape of soot particle collision frequency between particles i and j. It is noted that this is also investigated by the stochastic method [123]. Nevertheless, master equation does not include the reverse collision. there remain many unknown factors for the prediction of soot Several approaches have been developed to find a solution to particle size distribution. Those problems are open for near future this master equation. In the discrete sectional method [109-112], research. the particle ensemble is divided into classes of particle size. Properties such as mass, the numbers of carbon and hydrogen 5. Concluding remarks atoms are averaged within each section. An advantage of this method is the similarity of the description of the gas phase and An overview on the formation mechanism of one aromatic aerosol chemistry, and therefore, it is easy to implement. A ring to large PAHs has been discussed. Significant recent drawback is the limitation on the particle size. If the number of improvements in the formation mechanism of large PAHs have

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