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Formation of polycyclic aromatic hydrocarbons and their growth to soot—a review of chemical reaction pathways H. Richter, J.B. Howard * Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Masssachusetts Avenue, Cambridge, MA 02139-4307, USA Received 7 February 2000; revised 28 February 2000; accepted 28 February 2000 Abstract The generation by combustion processes of airborne species of current health concern such as polycyclic aromatic hydro- carbons (PAH) and soot particles necessitates a detailed understanding of chemical reaction pathways responsible for their formation. The present review discusses a general scheme of PAH formation and sequential growth of PAH by reactions with stable and radical species, including single-ring aromatics, other PAH and acetylene, followed by the nucleation or inception of small soot particles, soot growth by coagulation and mass addition from gas phase species, and carbonization of the particulate material. Experimental and theoretical tools which have allowed the achievement of deeper insight into the corresponding chemical processes are presented. The significant roles of propargyl (C 3 H 3 ) and cyclopentadienyl (C 5 H 5 ) radicals in the formation of first aromatic rings in combustion of aliphatic fuels are discussed. Detailed kinetic modeling of well-defined combustion systems, such as premixed flames, for which sufficient experimental data for a quantitative understanding are available, is of increasing importance. Reliable thermodynamic and kinetic property data are also required for meaningful conclusions, and computational techniques for their determination are presented. Routes of ongoing and future research leading to more detailed experimental data as well as computational approaches for the exploration of elementary reaction steps and the description of systems of increasing complexity are discussed. q 2000 Elsevier Science Ltd. All rights reserved. Keywords: Polycyclic aromatic hydrocarbons; Combustion processes; Chemical reaction pathways; Fullerenes Contents 1. Introduction .................................................................. 566 2. The first reaction steps ........................................................... 568 3. Formation of the first aromatic ring ................................................. 571 3.1. Contribution of C 3 -hydrocarbons ............................................... 578 3.2. Formation of other first aromatic rings ........................................... 584 4. Further growth process .......................................................... 585 5. Roles of acetylene and PAH in the growth process ...................................... 591 6. Formation of fullerenes and their relation to PAH and soot formation ........................ 594 7. Other soot nucleation models ...................................................... 596 8. Impact of thermodynamics ........................................................ 597 9. Future routes of research ......................................................... 599 10. Conclusions .................................................................. 600 Acknowledgements ................................................................ 601 References ...................................................................... 601 Progress in Energy and Combustion Science 26 (2000) 565–608 PERGAMON www.elsevier.com/locate/pecs 0360-1285/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved. PII: S0360-1285(00)00009-5 * Corresponding author. Tel.: 11-617-253-4574; fax: 11-617-258-5042. E-mail address: [email protected] (J.B. Howard).
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Formation of polycyclic aromatic hydrocarbons and their growth tosoot—a review of chemical reaction pathways

H. Richter, J.B. Howard*

Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Masssachusetts Avenue, Cambridge, MA 02139-4307, USA

Received 7 February 2000; revised 28 February 2000; accepted 28 February 2000


The generation by combustion processes of airborne species of current health concern such as polycyclic aromatic hydro-carbons (PAH) and soot particles necessitates a detailed understanding of chemical reaction pathways responsible for theirformation. The present review discusses a general scheme of PAH formation and sequential growth of PAH by reactions withstable and radical species, including single-ring aromatics, other PAH and acetylene, followed by the nucleation or inception ofsmall soot particles, soot growth by coagulation and mass addition from gas phase species, and carbonization of the particulatematerial. Experimental and theoretical tools which have allowed the achievement of deeper insight into the correspondingchemical processes are presented. The significant roles of propargyl (C3H3) and cyclopentadienyl (C5H5) radicals in theformation of first aromatic rings in combustion of aliphatic fuels are discussed. Detailed kinetic modeling of well-definedcombustion systems, such as premixed flames, for which sufficient experimental data for a quantitative understanding areavailable, is of increasing importance. Reliable thermodynamic and kinetic property data are also required for meaningfulconclusions, and computational techniques for their determination are presented. Routes of ongoing and future research leadingto more detailed experimental data as well as computational approaches for the exploration of elementary reaction steps and thedescription of systems of increasing complexity are discussed.q 2000 Elsevier Science Ltd. All rights reserved.

Keywords: Polycyclic aromatic hydrocarbons; Combustion processes; Chemical reaction pathways; Fullerenes


1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5662. The first reaction steps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5683. Formation of the first aromatic ring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571

3.1. Contribution of C3-hydrocarbons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5783.2. Formation of other first aromatic rings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584

4. Further growth process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5855. Roles of acetylene and PAH in the growth process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5916. Formation of fullerenes and their relation to PAH and soot formation. . . . . . . . . . . . . . . . . . . . . . . . 5947. Other soot nucleation models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5968. Impact of thermodynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5979. Future routes of research. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59910. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601

Progress in Energy and Combustion Science 26 (2000) 565–608PERGAMONwww.elsevier.com/locate/pecs

0360-1285/00/$ - see front matterq 2000 Elsevier Science Ltd. All rights reserved.PII: S0360-1285(00)00009-5

* Corresponding author. Tel.:11-617-253-4574; fax:11-617-258-5042.E-mail address:[email protected] (J.B. Howard).

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1. Introduction

Combustion processes used in transportation, manufac-turing, and power generation are major sources of airbornespecies of current health concern. In epidemiological studies[1,2], air pollution was positively associated with death fromlung cancer and cardiopulmonary disease. Fine particles—defined by a diameter equal to or below 2.5mm—arethought to pose a particularly great risk to health becausethey are more likely to be toxic than larger particles and canbe breathed more deeply into the lungs [3]. A possibleexplanation of the hazardous health effects of atmosphericaerosols is their association with polycyclic aromatic hydro-carbons (PAH). The amounts of different PAH associatedwith different aerosol size fractions were measured in orderto obtain a better understanding of their fate and humanexposure [4]. Many PAHs present in aerosols have beenfound to be mutagenic or tumorigenic [5–10] and a mol-ecular biological pathway linking one of them—benzo[a]-pyrene—to human lung cancer has been establishedrecently [11].

The need to control the emission of combustion productsof environmental and health concern while also promotingmore efficient utilization of fossil energy resources requiresthe development of cleaner and more economic combustionequipment which in turn requires a better physical andchemical understanding of combustion processes. A

significant research effort on PAH and soot has been under-taken during recent years [12–15]. Although many impor-tant details of PAH and soot formation remain poorlyunderstood, there is considerable agreement on the generalfeatures of the processes involved, which are summarizedbelow as introductory overview and shown schematically inFig. 1.

(a) Formation of molecular precursors of soot:The mol-ecular precursors of soot particles are thought to be heavyPAHs of molecular weight 500–1000 amu. The growthprocess from small molecules such as benzene to largerand larger PAH appears to involve both the addition ofC2, C3 or other small units, among which acetylene hasreceived much attention, to PAH radicals, and reactionsamong the growing aromatic species, such as PAH–PAHradical recombination and addition reactions. The relativecontribution of the different types of growth reactions seemsto depend on the fuel. In the case of aromatic fuels such asbenzene, acetylene and other active reactants for aromaticsformation are formed in relatively large concentrations inthe breakdown of the fuel, whereas in the case of aliphaticfuels such as acetylene, ethylene or methane, the firstaromatic ring must be formed from fuel decompositionproducts by a sequence of elementary reactions in whichthe active ring formation reactants are in lower concentra-tions than in the aromatics flames. This picture is consistentwith a trend of increasing ease of soot formation from

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608566

Fig. 1. A rough picture for soot formation in homogeneous mixtures (premixed flames) (Bockhorn [15]).

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paraffin to mono- and di-olefins, benzenes and naphthalenes[16–18]. Much progress toward a better understanding ofthe chemistry of PAH formation has been made in the recentyears.

(b) Nucleation or inception of particles from heavy PAHmolecules:In this process mass is converted from molecularto particulate systems, i.e. heavy PAH molecules formnascent soot particles with a molecular mass of approxi-mately 2000 amu and an effective diameter of about1.5 nm. Chemical details of the formation of nascent sootparticles are relatively poorly understood, mostly because ofexperimental difficulties. Efficient identification of speciesproduced at different stages of the growth process is limitedto molecular masses less than about 300 amu using gaschromatography while the observation and counting ofsoot particles by high resolution electron microscopy hasbeen limited to particle diameters of larger than about1.5 nm. The analysis of larger PAH by means of liquidchromatography and mass spectrometry as well as theincrease of the resolution of electron microscopic tech-niques are objectives of ongoing research. Additionalinformation has been obtained using optical techniquesand contributes to an increasing body of experimental data.

(c) Mass growth of particles by addition of gas phasemolecules:After the formation of the nascent soot particlestheir mass is increased via the addition of gas phase speciessuch as acetylene and PAH, including PAH radicals. Thesereactions are believed to involve radical sites on the sootparticles in the case of stable reactants such as acetylene andstable PAH but not necessarily so in the case of PAH radi-cals. This process of course does not affect the number ofsoot particles. The relative contributions of acetylene andPAH is the subject of current discussions in the combustioncommunity.

(d) Coagulation via reactive particle–particle collisions:Sticking collisions between particles during the massgrowth process significantly increases particles size anddecreases particle number without changing the total massof soot present. The continuation of substantial molecularaddition of gas phase species after the early formation ofcomposite particles via sticking particle–particle collisions,partly hides the identity of primary particulate units in elec-tron microscopy images of soot particles.

(e) Carbonization of particulate material:At higher resi-dence times under pyrolytic conditions in the postflamezone, the polyaromatic material comprising the yet formedparticles undergoes functional group elimination, cycliza-tion, ring condensation and ring fusion attended by dehy-drogenation and growth and alignment of polyaromaticlayers. This process converts the initially amorphous sootmaterial to a progressively more graphitic carbon material,with some decrease in particle mass but no change in parti-cle number. Recently, additional interest in this process hasbeen motivated by the observation of soot containing curvedor fullerenic layers.

(f) Oxidation: Oxidation of PAH and soot particles is a

process competing with the formation of these species. Itdecreases the mass of PAH and soot material through theformation of CO and CO2. Depending upon flame type,oxidation may occur simultaneously with formation as inpremixed aromatics flames and well-mixed combustors, orit may occur subsequent to formation as in diffusion flamesor staged combustors. The main oxidation reactants are OH,O and O2, the largest contributor in general being OH underfuel-rich conditions and O2 under fuel-lean conditions.

Since the early work of Street and Thomas [19] a moreand more detailed characterization of soot formation beha-vior, including the effects of parameters like fuel type,global and local equivalence ratio, temperature, pressureand the presence of additives has been attained. Assistedby the availability of more and more sophisticated exper-imental techniques, this evolution facilitated improvedinsight into the mechanistic processes involved in soot andPAH formation, which is described in excellent review arti-cles [18,20–25]. Due to the tremendous body of availabledata no systematic attempt is undertaken here to retrace thehistory leading to the present state of the knowledge. Inaddition to the experimental work, the increase of computa-tional power has allowed the critical testing of chemicalreaction networks, in particular for premixed flames, wellstirred, plug flow reactors and shock tubes. Suitable andeasy to use software [26–33] has been developed andapplied to more and more complex combustion systems[28,34–36]. Many thermodynamic and kinetic propertyvalues have been determined by means of increasinglysophisticated molecular-mechanical and in particular quan-tum-mechanical techniques. The discovery of fullerenes[37,38] and fullerenic nanostructures [39] in fuel-richhydrocarbon flames presents an additional challenge to themechanistic understanding to PAH and particle formation.

The present review focuses on the chemical understand-ing of the formation of PAH and soot. The elucidation ofreaction networks requires the investigation of well-definedand physically easy to describe experimental systems.Therefore mainly results from easy to model combustionsystems such as premixed flames, well-stirred and plug-flow reactors are discussed here. In particular the followingaspects are covered:

1. The first sequences of the growth process beginning withdifferent compounds are described. Pathways leading tothe first aromatic rings are discussed. Different reactionsequences forming benzene from compounds containingbetween one and four carbon atoms are described. Thedecay of small aromatic fuel components such asbenzene, which is an important source of growth reac-tants such as acetylene, and the role of C5-moities in thegrowth process is addressed.

2. The pre-particle or molecular chemistry leading to sootprecursors, i.e., species forming nascent soot particles intheir subsequent reaction step, is discussed. Differentforms of the hydrogen-abstraction/acetylene-addition

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mechanism are described. The roles of small PAH asreactants in the formation of larger PAH and soot areassessed.

3. The formation of fullerenes and of fullerenic nanostruc-tures, especially in connection—or in competition—with soot formation is addressed. The recent observationof fullerenes appearing to behave as soot growthreactants is discussed.

4. In a brief review of soot formation mechanisms alterna-tive to the above described—and today widelyaccepted—route, the possible roles of ionic species andpolyacetylenes are discussed.

5. Methods for the determination of thermodynamic proper-ties are discussed, and evidence for thermodynamiceffects on the concentrations of PAH at different resi-dence times are summarized.

6. Possible future directions for PAH and soot formationresearch, such as experimental and computationalapproaches which could provide deeper insight into keyelementary reaction steps are discussed. Currently usedtheoretical techniques for the determination of pressure-dependent rate constants, and limitations of thesemethods, are discussed.

2. The first reaction steps

Even in the very early stages of combustion research,hypotheses have been advanced [40–42] regarding potentialreaction pathways for the growth of the initial fuel to“carbon”, nowadays in general called soot. Correlationsbetween soot formation tendency and fuel structure havebeen established and qualitative conclusions have beensuggested about possible chemical reaction sequences lead-ing to soot. As summarized by Palmer and Cullis [20],sooting tendencies were shown to decrease in the order:naphthalenes. benzenes. diolefins . monoolefins.paraffins. Different theories have been presented duringthe last two centuries [20] and many of them are today ratherof historical interest. The foundations of the evolution to amore realistic understanding of soot formation were laid inthe so-called “Hydrocarbon Polymerisation Theory” whichhas been stated by Gaydon [43] as follows: “In the presenceof an excess of fuel molecules, free radicals initiate chainpolymerisation processes which lead to the formation ofhigher hydrocarbons which decompose thermally to solidcarbon and hydrogen. In the presence of sufficient oxygenthe radicals are removed by reaction with this and do notcause so much polymerisation.” Different versions of thistheory were associated with liquid polymers or polymers ofhigh molecular weight, while in 1941, Rummel and Veh[44] were the first to advocate strongly a version of thetheory based on polycyclics and polyaromatics.

The use of more and more sophisticated equipment gavedeeper insight into species occurring as intermediates in thegrowth process and therefore conclusions about chemicalmechanisms. Bradley and Kistiakowsky [45] coupled a

time-of-flight mass spectrometer to a shock tube and studiedpyrolysis and oxidation of acetylene. They identified masspeaks corresponding to polymeric C4, C6 and C8 species anda sharp drop in the concentration of these polymers wascorrelated with the formation of carbon. They suggestedthe radical reaction C2H 1 C2H2!C4H2 1 H as beingresponsible for diacetylene formation in the presence ofoxygen.

A breakthrough in the systematic investigation of sootgrowth processes in flames was achieved with the use ofmass spectrometric analysis coupled to a molecular beamsampling technique. Homann and Wagner [46,47] studiedpremixed flat flames at reduced pressure using mixtures ofthe following fuels with oxygen: C2H2, C2H4, C3H8, C6H6

and C2H5OH. They measured stable as well as radicalspecies and, using the same molecular beam samplingsystem, they collected particles which were analyzed byelectron microscopy. They determined particle concentra-tions and size distributions. Additionally, optical measure-ments by Bonne and Wagner [47,48] gave OHconcentration, emission profiles, the concentration ofcarbon, average particle size and number concentration ofcarbon particles, and temperature. Polyacetylenes up toC12H2 formed in the oxidation zone by a radical mechanismwere detected, and the intermediate radicals C2H and C4H3

were identified. The production and the disappearance ofacetylene and especially its homologues was interpretatedto be strongly related to the process of carbon formationconfined to a relatively narrow zone near to the oxidationzone. The authors suggest that in a later stage of the poly-merization process large radicals can react with each otheror mainly with higher polyacetylenes, forming a variety of“aggregates” of C atoms which are no longer straight andplanar and may contain ring closures.

Shortly thereafter, in 1967, Homann and Wagner [49]used the same but improved equipment for a detailedcomparison of fuel rich acetylene and benzene combustion.Acetylene was chosen as a model substance for aliphaticfuels since acetylene was observed to be formed in consid-erable amounts prior to solid carbon in flames of ethylene,methane and propane. In addition to the molecular beamsampling and mass spectrometric results described in thiswork, mass spectra of the volatile components of sootsampled in the flame were measured. The authors reportedthe following results concerning the presence of high-molecular-weight hydrocarbons.

(a) In acetylene flames:Acetylene and polyacetyleneswere shown to be by far the greatest part of the hydro-carbons in the burned gas but could not be detectedamong the compounds evaporated from the soot samples.They were believed not to condense on carbon particles or toreact irreversibly with them. All major peaks of the volatilesmatched with those of polycyclic aromatic hydrocarbons offive- and six-membered rings: e.g. naphthalene (128 amu),acenaphthalene (152 amu), phenanthrene (178 amu), pyrene(202 amu), and coronene (300 amu). The same species

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could be identified by direct sampling in the gas phasewith the molecular beam system and it was shownthat—in contrast to polyacetylenes—their concentrationincreases steadily behind the oxidation zone withoutgoing through a maximum. Compared to polyacetylenestheir individual concentrations are relatively small and liebetween that of C10H2 and C12H2. Based on these results,Homann and Wagner [49] interpreted these results to be inconflict with the hypothesis that polycyclic aromatics areimportant intermediates or “nuclei” for carbon formationin acetylene flames, since its rate was observed to go downto zero while the concentrations of these compounds arestill increasing. Besides the cited “normal” polycyclicaromatics Homann and Wagner [49] observed also manyother hydrocarbons, mainly with molecular masses greaterthan about 250 amu, which do not survive in the hot gasbehind the oxidation zone. They supposed that thesesubstances also contain carbon rings but that they probablyhave side chains. Groups of mass peaks up to 550 amuwere found to appear closely behind the oxidation zone,which ends about 10 mm above the burner and to reachtheir maximum intensity at about 14 mm before disappear-ing at about 35 mm. Homann and Wagner [49] consideredthese, not unambiguously identified species with mole

fractions of about 1027 to be intermediates or “nuclei”for carbon particles.

(b) In benzene flames:Although both polyacetylenes (andacetylene) and polycyclic aromatic hydrocarbons are alsoformed in benzene flames, features substantially differentfrom those in acetylene flames were observed [49]. Therate of carbon formation is higher, but the process seemsto be finished earlier than in acetylene flames. Benzene–oxygen flames start to form carbon at a C/O ratio of about0.75 while for acetylene flame the threshold is at a C/O ratioof about 0.95. Polycyclic aromatic compounds are formed inconcentrations about 100 times larger than from aliphaticfuel for the same C/O ratio. Their maximum concentrationsoccur within the oxidation zone and decrease at the end of itwhere most of the carbon is formed. Polyacetylenes arise inthe oxidation zone but—in comparison with the behavior inacetylene flames—their concentration does not decrease asrapidly in the region where molecular oxygen has beenconsumed. Similar to acetylene flames, hydrocarbons ofmolecular masses higher than 250 amu were observed insoot samples and also in the flame gases.

Based on their very detailed and careful experimentalstudy Homann and Wagner [49] suggested pathways leadingto carbon formation. They considered that in flames of both

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608 569

Fig. 2. Reaction scheme suggested to account for the formation of polyacetylenes and PAH in rich premixed flames (Crittenden and Long [50]).

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aliphatic and aromatic fuels mainly three groups take anactive part in the formation process:

1. Acetylene and polyacetylenes (mass range 26–146 amu)2. Polycyclic aromatic hydrocarbons (from 78 to about

300 amu)3. Reactive polycyclic hydrocarbons, probably with side

chains (from about 150 to.550 amu)

The authors point out that carbon particles are not giantchain molecules and they state that in the case of a radical,e.g. C2H, attack on a polyacetylene molecule, the probabil-ity that it occurs at one end decreases with increasing chainlength. A reaction at any other carbon atom without

breaking a carbon–carbon bond leads to a branched radicalwhich can add further polyacetylenes or other hydrocarbonswithout losing its radical character. Finally, ring closureswill yield the above discussed reactive hydrocarbons(group 3). In view of their high reactivity these species areprobably radicals which can add further polyacetylenes andform small carbon particles. On the other hand, those reac-tive intermediate hydrocarbons may form relatively inactivepolycyclic aromatics by intramolecular rearrangements orby splitting off parts in which the aromatic structure isalready formed. Based on the differences between acetyleneand benzene flames, Homann and Wagner [49] concludethat an additional pathway should contribute significantlyin the latter case. A striking difference consists in main

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608570

Fig. 3. Reaction scheme for the formation of aromatic hydrocarbons (Bockhorn et al. [59]).

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unsaturated hydrocarbons present in the oxidation zonewhich are C2H2 and C4H2 and to a minor extent higherpolyacetylenes in acetylene flames, and benzene and poly-cyclic aromatics in benzene flames. The suggestion of poly-cyclic aromatics as “building bricks” of carbon in benzeneflames was supported by the decrease of their concentrationin the flame region where carbon is formed, a behaviorsimilar to that of polyacetylenes in acetylene flames. Inaddition, in benzene flames polycyclic aromatics are presentin substantial concentrations in the oxidation zone, wherehydrocarbon radicals, in much larger concentrations than inthe burned gas, are available for addition to polycyclicaromatics. In benzene flames, the addition of polycyclicaromatics together with other hydrocarbons to hydrocarbonradicals forms small soot particles. Polyacetylenes containfewer carbon atoms than polycyclic aromatics on the aver-age and therefore require more steps than polycyclicaromatics for a given amount of mass growth. Taking intoaccount the appearance of soot earlier in benzene flamesthan in acetylene flames, Homann and Wagner [49]connected the formation of greater amounts of carbon inbenzene flames to the fact that more efficient hydrocarbon“building bricks” for soot particles are available in the zoneof maximum hydrocarbon radical concentration.

Some years later, in 1973, Crittenden and Long [50]studied the formation of polycyclic aromatics in fuel-richpremixed low pressure acetylene and ethylene low-pressureflames using microprobe sampling followed by high resolu-tion mass spectrometry and chromatographic analysis. Theysuggest that polycyclic aromatic hydrocarbons are possibleprecursors of some “carbon” in aliphatic fuels. While thisview differs from that of Homann and Wagner [49], thegeneral picture of the growth process drawn by Crittendenand Long and summarized in Fig. 2 is relatively similar tothe ideas of Homann and Wagner, in particular the potentialrole of cyclic structures with side-chains. Crittenden andLong believe thatchain lengthening of acetylene leads tothe formation of unsaturated C4, C6, C8, etc. radical specieswhich can either stabilize as polyacetylenes, or in somecases, either by formation of a branched radical withring-closure or by cyclization, form an aromatic ring witha 2-carbon side-chain (i.e. C6–C2). This is considered to bea most important step; radical species of this type might wellbe stabilized on sampling in the form of phenylacetylene andstyrene (found in the products). Further step-wise synthesisinvolving these C6–C2 radical species probably then leadsto the wide variety of polycyclic aromatic hydrocarbonsidentified in the products. Crittenden and Long cite theexperimental findings of Stehling et al. [51] and of Berthelot[52] as additional evidence of the contribution of these C6–C2 species. Berthelot described the synthesis of anthracenefrom benzene and styrene, and Stehling et al. showed aslight increase of naphthalene formation in acetylenepyrolysis after addition of styrene.

The importance of cyclization reactions and the remark-able ease of carbon formation in benzene flames [53]

prompted Palmer and Cullis [20] to suggest that, at leastunder certain conditions, benzene formed either bypolymerization of acetylene or in some other way may bean important intermediate in soot formation. Whereas theassessment of such suggested reaction pathways was ratherqualitative in former times, the increasing use of detailedkinetic modeling in recent years has necessitated, andprovided a means to achieve, a better and quantitativeunderstanding of reaction mechanisms if possible includingelementary reaction steps. Therefore, different pathwaysleading to benzene in aliphatic fuel flames and possiblepathways to larger PAH without passing through benzeneare discussed below.

3. Formation of the first aromatic ring

After the early work of Berthelot [54] who suggested theformation of benzene via direct polymerization of acetyleneand Bone and Coward [55] hypothesized a potential role forCH2 and CH fragments [55], a great number of differentchemical pathways have been critically discussed. Reactionsequences involving stable species as in the case of Diels–Alder addition of 1,3-butadiene to ethylene [56,57] or thealkene trimerization into rings [58], and pathways involvingat least one radical have been assessed. An increasing bodyof experimental data pertinent to combustion reactions andnumerical modeling have now made it possible to criticallytest suggested mechanisms so as to determine the majorpathways and the dependence on conditions such as fueltype and temperature. Radical pathways have been shownclearly to be more important and are discussed in moredetail below.

Similar to the general scheme suggested by Homann andWagner [49] and Crittenden and Long [50], Bockhorn et al.[59] suggested a reaction sequence beginning with diacety-lene and C2H forming a branched hydrocarbon radicalfollowed by acetylene attack and ring closure leading to aphenylacetylene radical. A scheme of the chemical path-ways suggested by Bockhorn et al., including the formationof larger polycyclic aromatics which is discussed later, isshown in Fig. 3. They studied flat premixed low pressureflames of propane, acetylene or benzene using a quartzsampling probe, a soot filter, and gas analysis by on-linemass spectrometry for species with mole fractions of 1024

or larger and by means of gas chromatography after collec-tion in a cold trap for species of lower concentration. Acet-ylene and diacetylene were found to be major species inboth acetylene and propane flames, as is represented bythe suggested mechanism.

The work of Cole et al. [60] represents a first attempt at amore quantitative assessment of the formation of aromaticcompounds in flames of aliphatic fuels. The authors testedpossible mechanisms by comparing predicted formationrates against values calculated from mole fraction profilesmeasured by means of molecular beam sampling coupled to

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mass spectrometry in a near-sooting premixed low pressure1,3-butadiene flame. Using kinetic data taken from theliterature or from thermochemical estimations, Cole et al.found Diels–Alder additions to butadiene to be much slowerthan the experimental formation rate of aromatics. Anotherinvestigated pathway was the following reaction sequencestarting with the attack of vinyl-radical on 1,3-butadiene andfollowed by cyclization and hydrogen elimination reactions:

C2H3 1 1; 3-C4H6 $ C6H9

C6H9 $ c-C6H9

c-C6H9 $ c-C6H8 1 H

c-C6H8 ! C6H6 1 H2

The analysis showed the first three reactions to be suffi-ciently fast but the high activation energy of H2 eliminationwould require a cyclohexadiene (c-C6H8) partial pressurenearly 10 times the total system pressure in order to producethe observed rate of benzene formation. Also the possibilityof hydrogen abstraction from c-C6H8 by a free radicalfollowed by spontaneous H loss cannot explain benzeneformation starting with vinyl radicals and 1,3-butadiene

because the necessary c-C6H8 mole fraction is much largerthan the measurements [60]. A similar mechanism wastested by Ebert et al. [61] in a modeling study of then-hexane pyrolysis at 819 K. Benzene and toluene formationswere predicted by means of a kinetic model consisting of661 elementary reactions and 180 species. In contrast toCole et al. [60], these authors suggested that hydrogen-abstraction from c-C6H8 by H or alkyl radicals followedby spontaneous hydrogen loss is a suitable explanation forbenzene formation. However, no experimental informationabout radical intermediates was available and the exper-imental conditions differ significantly from those ofcombustion, so this work is not necessarily in conflict withthat of Cole et al. [60].

Finally, based on their flame study, Cole et al. [60]suggested the 1,3-butadienyl radical as key intermediatefor the formation of benzene via the following free-radicalmechanism involving ring closure and hydrogen loss:

1; 3-C4H5 1 C2H2 ! C6H7

C6H7 ! c-C6H7

c-C6H7 ! C6H6 1 H

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608572

Fig. 4. Net rates of first-ring cyclization reactions in a sooting low-pressure acetylene flame (Frenklach and Warnatz [63]).

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Benzene formation through this reaction pathway was foundto be governed by acetylene attack on 1,3-butadienyl radicals.Potentially competitive side reactions of the intermediatespecies, hexatrienyl (C6H7) and cyclohexadienyl (c-C6H7),neither of which was detected, were found to be insignificantin the region of benzene formation. Cole et al. [60] showedalso that H-abstraction from the fuel by hydrogen radicals isthe main source of 1,3-C4H5 in a 1,3-butadiene flame. Theobserved tendency of the C4H4 concentration profile inaliphatic flames to mimic the concentration profiles ofaromatics was interpreted as evidence that C4H4 is mainlyformed via hydrogen abstraction from butadienyl-radicalswhich were suggested to be precursors of both benzeneand C4H4. For other fuels than butadiene, Cole et al. suggestvinyl-addition to acetylene, i.e. the reactionC2H2 1 C2H3$ 1,3-C4H5, as the principal route to butadie-nyl and, in the next step, to benzene. Cole et al. alsosuggested also pathways similar to that of benzene forma-tion leading to toluene, styrene and polyacetylene withoutpassing through benzene as intermediate. Thus they suggestthat C4H5 reacts with C3H4 in toluene formation, with C4H2

in phenylacetylene formation and with C4H4 in styreneformation, the initial step in each case being followed bycyclization and hydrogen loss. The comparison of experi-mentally derived formation rates showed encouragingagreement in trends and magnitude, in particular for styreneand polyacetylene. The larger deviation in the case oftoluene was attributed to possibly competing reactionssuch as C7H8 1 R!C7H7 1 RH. Concurrent with thework of Cole et al. [60], Weissman and Benson [62] inves-tigated the pyrolysis of methyl chloride at 1260 and 1310 Kand analyzed the products by means of gas chromatographycoupled to mass spectrometry. A sequence of elementaryreactions explaining the formation of major products andrate constants were derived based on the experimentallymeasured reaction rates and thermochemical property esti-mations. Benzene formation pathways starting withC2H3 1 1,3-C4H6$ C6H9 and 1,3-C4H5 1 C2H2! C6H7

were suggested but the absence of data concerning inter-mediate species did not allow assessment of their relativecontributions. The rate constant assigned to the H2 elimina-tion reaction c-C6H8! C6H6 1 H2 is similar to the valueused in the analysis of Cole et al. [60], thus supportingtheir conclusion to rule out C6H8 as intermediate for benzeneformation in premixed low pressure butadiene flames.

Numerical modeling using reaction mechanisms andkinetics and taking into account transport phenomena allowsthe determination of contributions of different reactionsequences in a complex flame environment consisting of alarge number of stable and radical species. Different exper-imental conditions, e.g. different fuels, feed gas mixturecompositions, temperatures and pressures can be analyzedby means of this approach. Frenklach and Warnatz [63]made a decisive step towards a quantitative understandingof benzene formation by comparing concentration profilespredicted with a detailed kinetic model against experimental

profiles of Bockhorn et al. [59] measured in a low pressuresooting acetylene flame mentioned above. The determina-tion of net rates allowed assessment of the contribution ofdifferent benzene formation pathways included in themodel. Conclusions from net rate analysis are of coursedependent on the kinetics property information used, andsubsequent revisions of poorly known rate constants mayhave a significant impact on the computed contributions ofthe affected reaction pathways. Frenklach and Warnatzincluded four pathways leading to the first aromatic ring,all of them based on the cyclization of unsaturated aliphaticradicals:

n-C6H5 ! phenyl

i-C8H5 ! C6H4C2H

n-C8H5 ! C6H4C2H

n-C6H7 ! benzene1 H

The first and fourth cyclization reactions in the above listwere previously found by Frenklach et al. [64] to be im-portant at shock tube oxidation conditions while the secondwas suggested by Bockhorn et al. [59] as shown in Fig. 3.The net reaction rates, given in Fig. 4, show the reactionsequence

C2H3 1 C2H2 ! n-C4H5

n-C4H5 1 C2H2 ! n-C6H7

n-C6H7 ! benzene1 H

to be dominant in the first part of the main oxidation zone.Although the nomenclature is slightly different, this path-way is similar to the benzene formation route suggested byCole et al. [60] for aliphatic fuels other than 1,3-butadiene,the only difference being the simultaneous cyclization andhydrogen loss used by Frenklach and Warnatz [63]. Further-more, the net reaction rate analysis [63] shows an increase ofradical decomposition with increasing temperature in themain reaction zone and the domination of the formation ofthe first aromatic ring by the cyclization ofn-C6H5, theproduct of the reaction of acetylene withn-C4H3. Two path-ways can lead ton-C4H3, hydrogen abstraction from viny-lacetylene or—emerging in the post-flame zone—thereaction C2H 1 C2H2. The cyclization ofn-C8H5 to phenyl-acetylene radical, C6H4C2H, precedes the correspondingreaction of i-C8H5 and peaks at the same location in theflame as the cyclization ofn-C6H5 to phenyl. As can beseen in Fig. 4, the rate of formation of C6C2 species issignificantly smaller than that of an unsubstituted firstaromatic ring.

Similar conclusions were reached by Colket [65] in theshock tube pyrolysis of acetylene and vinylacetylene.Experiments were conducted in a temperature range from1100 to 2400 K. The concentrations of stable species such as

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C2H2, C4H2, C6H2, vinylacetylene (C4H4), benzene andphenylacetylene were determined by gas chromatography.Numerical modeling predictions using a reaction networkand kinetics were compared to the experimental data, andthe contributions of different pathways were assessed usingcalculated net formation rates. Colket [65] concluded in thecase of acetylene pyrolysis that benzene formation attemperatures below 1500 K is principally via the pathwaysuggested by Cole et al. [60], i.e. from acetylene addition ton-butadienyl, followed by cyclization and hydrogen loss.The linear C6H7 species is defined to be the 1,3,5-hexa-trien-1-yl radical. For temperatures above 1500 K, Colketsuggested, in agreement with Frenklach et al. [63,66], thatacetylene addition ton-C4H3 is the major pathway leading tocyclic compounds.n-C4H3 is formed by the reactionC2H2 1 C2H which is consistent with the analysis of Frenk-lach and Warnatz [63] for the post-flame zone, where thevery low oxygen concentrations are similar to pyrolyticconditions.

The investigation of vinylacetylene pyrolysis [65]revealed again for temperatures above 1600 K that phenylformation fromn-C4H3 1 C2H2 recombination is the domi-nant pathway. At lower temperatures, the predominateformation routes of aromatics were found to be

C4H4 1 C2H3 ! C6H7

C6H7 ! c-C6H7

c-C6H7 ! C6H6 1 H

for benzene formation, and

C4H41n-C4H5 ! C8H9

C8H9 ! c-C8H9

c-C8H9 ! C8H8 1 H

for styrene formation. Phenylacetylene is produced princi-pally by

C8H8 1 H! C8H7 1 H2

C8H7 ! C8H6 1 H

near 1500 K and below, but at higher temperatures, acety-lene addition to phenyl also occurs. Colket points out in thecase of vinylacetylene pyrolysis that C6H7 represents the1,3,5-hexatrien-3-yl and which requires a 1,3 or 1,4 H-atom shift prior to cyclization. Therefore, C4H5 1 C2H2

should be a preferred route for cyclization, but the rateconstant required by the acetylene pyrolysis modeling issignificantly too low to match also experimental data ofvinylacetylene pyrolysis. In view of this and other unsettlingfeatures, Colket [65] mentions the possibility that reactionsnot considered in the kinetic model may contribute toaromatics production or significantly enhance the concen-tration ofn-C4H5.

Using a similar approach as the previous authors, Harriset al. [67] modeled the formation of small aromatic mol-ecules in sooting atmospheric pressure premixed ethyleneflames. Gases were withdrawn from the flame with a quartzmicroprobe and analyzed by means of on-line mass spectro-metry. Radiation corrected temperatures were measuredusing coated thermocouples. No measurements could betaken beyond about 3.3 mm above the burner because sootwould clog the probe. The work of Harris et al. has the meritof providing data on heavily sooting flames, at higherequivalence ratios than the investigations discussed above.In addition, ethylene is an important component for kineticmodels to be applied to practical fuels which containcompounds such as octane that are converted largely toethylene on their way to being oxidized [68]. The benzeneformation rate determined by Harris et al. for a flame with C/O� 0.92 peaks at a height above the burner between 1.6 and2.2 mm (1450–1600 K), and was comparable to peakformation rates of the C3 and C4 species between 1 and1.6 mm. In agreement with the results of Frenklach andWarnatz [63] for a fuel-rich premixed acetylene flame aswell as with the pyrolytic study of Colket [65], Harris etal. [67] deduced that acetylene addition ton-C4H3 followedby cyclization and recombination with atomic hydrogendominates benzene formation in this region. The modelpredictions show a higher concentration of C4H5 comparedto n-C4H3 for the pre-reaction zone with temperatures below1000 K, which is reflected by the domination of benzeneformation through the reaction C4H5 1 C2H2! benzene1H, similar to reaction sequences suggested by Cole et al.[60] and used by Frenklach and Warnatz [63]. Similar tothe previous authors, Harris et al. [67] included also theformation of phenylacetylene and styrene in their kineticmodel. Most of the phenylacetylene comes from the directreaction between phenyl and acetylene but also the reactionof diacetylene withn-C4H3 leading to C8H5 and followed bycyclization contributes substantially. The comparison of themodel prediction with an experimental phenylacetyleneprofile shows an underprediction of a factor up to 7, adisagreement which could not be explained after sensitivityanalysis. No new reaction pathway could be found whichgave a sufficiently large increase in the phenylacetyleneconcentration. Nevertheless a much better overall agree-ment could be achieved by lowering the heat of formationof phenylacetylene by 5 kcal mol21. Therefore, uncertaintyin the thermodynamics of critical species could be an expla-nation for the discrepancy between model and experiment.Phenyl addition to ethylene is the major pathway for styreneformation identified by Harris et al. [67] while the decay tobenzene and vinyl (C2H3) radicals after attack of hydrogenatoms represents the principal destruction reaction. Beyond1.8 mm above the burner (1550 K) the rate of this consump-tion exceeds the rate of formation through the reactionbetween phenyl and ethylene which causes the styrenemole fraction to fall. The very rapid decrease of the styrenemole fraction is not in agreement with the experimental

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data. Harris et al. point out that the styrene profile is verysensitive to the thermodynamic assumptions made for thevinyl radical, a 2 kcal mol21 change in the radical’s assumedheat of formation having a factor of 2 effect on the calcu-lated styrene profile. Finally, Harris et al. completed theiranalysis by the modeling of a low pressure benzene flame[69] and shock tube benzene pyrolysis [70,71] experimentsand concluded that their model is able to predict benzene

profiles in a variety of systems despite the great uncertaintyin many of the rate constants.

A systematic screening of benzene formation pathwaysfollowed by the determination of the corresponding rateconstants was performed by Westmoreland et al. [72]based on the concept of chemical activation and using aQuantum Rice–Ramsperger–Kassel (QRRK) approach.Chemical activation allows the formation of benzene to be

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608 575

Fig. 5. Energy diagram for product channels of 1-C4H5 1 C2H2 association (Westmoreland et al. [72]).

Fig. 6. Screening comparisons of possible benzene formation pathways in a slightly sooting premixed acetylene/oxygen/argon low pressure flame:measured net rate of benzene formation, -B-; CH3 1 1,3-C4H6, N; C2H3 1 n-C4H5, M; C2H3 1 C4H6, S; C3H3 1 C3H3, ×; C3H3 1 C3H4, K; n-C4H3 1 C2H2, L; n-C4H5 1 C2H2, W; n-C4H5 1 C2H4, p ; 1,3-C4H6 1 C2H2, A (Westmoreland et al. [72]).

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explained without the assumption of stabilized intermedi-ates which could be destroyed by bimolecular reactions.Chemically activated intermediates can form aromaticrings faster than bimolecular collisions, stabilizing orreactive, can take place. In effect, aromatics are formed“directly” from the reactants without observable inter-mediates. The initially formed adduct contains energyreleased by chemical bond formation plus thermal energyfrom the reactants. Excess energy relative to the therma-lized, ground state can be dissipated by energy-removingcollisions or used in opening “new” channels with, e.g.,an isomerization reaction as the first step. Westmorelandet al. illustrated the concept of chemical activation usingthe above discussed reaction of the butadienyl radicalwith acetylene as an example (Fig. 5). Initially, the asso-ciation reaction forms a chemically activated 1,3,5-hexa-trienyl or n-C6H7

p. This energized adduct may becollisionally stabilized to thermaln-C6H7, it may decom-pose to reactants, it may decompose to 3,5-hexadien-7-yne plus H, or it may isomerize. Total energy isconserved in isomerization, so the species formed is ahot cyclohexadienyl, c-C6H7

p, with the same energycontent as the initial adduct but with much more excessenergy relative to its ground state. The chemically acti-vated cyclohexadienyl can itself isomerize backwards ton-C6H7, it can be collisionally stabilized, or it candecompose to benzene and H. Thus, four different reac-tion channels can be observed and “apparent” rateconstants describing the formation of the products can

be determined:


n-C4H5 1 C2H2 ! n-C6Hp7 ! n-C6H7


n-C4H5 1 C2H2 ! n-C6Hp7 ! 3; 5-hexadien-7-yne1 H


n-C4H5 1 C2H2 ! n-C6Hp7 ! c-C6Hp

7 ! c-C6H7


n-C4H5 1 C2H2 ! n-C6Hp7 ! c-C6Hp

7 ! benzene1 H

In order to assess potential benzene formation pathways,Westmoreland et al. [72] screened pathways suggestedpreviously in the literature for a lightly sooting, laminar,premixed acetylene low pressure flame [73]. For thispurpose, they used experimental concentration profiles ofstable and radical species being reactants of consideredbenzene formation pathways and which had been measuredby molecular beam sampling followed by mass spectrom-etry (MBMS). Upper limits of benzene formation rates weredetermined based on high pressure rate constants andcompared to experimental benzene formation rates. Thesame procedure was applied to the 1,3-butadiene flameinvestigated with the same equipment by Cole et al. [60]and discussed above. As shown in Fig. 6, in the lightlysooting acetylene flame, only additions ofn-C4H3 and n-C4H5 to C2H2 and C3H3 1 C3H3 combination would be fasterthan the measured net benzene formation rate. Next fastestare C3H3 1 C3H4 and C2H3 1 C4H5, slower than themeasured rate but within the feasibility limits based onuncertainties in measured and predicted benzene formationrates. For the butadiene flame screening implies thatn-C4H5 1 C2H2 and C2H3 1 1,3-C4H6 were the most feasibleassociation reactions in the high pressure limit.C2H3 1 C4H5 was shown to be a factor of 10 slower thanthe measured rate and therefore was considered as margin-ally feasible. The fastest alternative considered as infeasiblewas C3H3 1 C3H3 while n-C4H3 1 C2H2 could not be testedbecause no C4H3 data had been reported for the 1,3-C4H6

flame.The determination of the “apparent” rate constants for the

formation of benzene or alternative products by means ofthe bimolecular quantum-RRK approach [74] confirmed theprior results reported above. In agreement with the conclu-sions of Cole et al. [60], the addition/stabilization reaction of1,3-C4H6 with vinyl (C2H3) to n-C6H9 is shown to be negli-gible and addition/decomposition to 1,3,5-hexatriene1 H ispredicted to dominate. The QRRK approach also allowedthe combination of vinyl withn-C4H5 to be excluded. Under

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608576

Fig. 7. Test of product-specific rate constants deduced by means ofQRRK computations in a slightly sooting premixed acetylene/oxygen/argon low pressure flame for reactions that could lead tobenzene; measured (net) rate, -B-; n-C4H3 1 C2H2! phenyl,L;n-C4H5 1 C2H2! benzene1 H, W; C2H3 1 n-C4H5! 1,3,5-C6H8,M; sum of predictedks, - - - (Westmoreland et al. [72]).

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low pressure conditions, the rate constant corresponding tothe formation of benzene1 H2 reaches a maximum contri-bution of only 5% relative to the high pressure limit.

Westmoreland et al. [72] identified the reactions ofn-C4H5 andn-C4H3 with C2H2 as major pathway for benzeneformation. The sum of the predicted formation rates usingthe two product-specific rate constants is sufficient toaccount for the measured net benzene formation rate inthe investigated acetylene flame (Fig. 7). In the butadieneflame, the contribution ofn-C4H5 1 C2H2 is not sufficient toexplain all the benzene formation, in particular close to theburner. Beyond about 6 mm the discrepancy can be consid-ered to be within the uncertainty of experimental and kineticdata. Nevertheless, this lack of agreement must be seen inthe light of the fact that the contribution ofn-C4H3 is missingfrom this analysis because experimental data were unavail-able for this species in the butadiene flame.

The reactions between two C3H3 radicals as well as theaddition of C3H3 to propadiene (C3H4) were shown to bepromising in the initial screening [72] (Fig. 6) based onhigh pressure rate constants. However, they were notanalyzed further because of the necessity of hydrogen shifts[72]. Possible reaction pathways involving C3 species willbe discussed in more details below.

The work of Westmoreland et al. [72] has the merit ofsignificantly improving the knowledge of benzene forma-tion by providing rate constants of “apparent” reactionswhich describe the direct formation of benzene from thereactants at different pressures and temperatures. Rateconstants determined by means of systematic approaches

and therefore closer to chemical reality are valuable forthe quantitative description of benzene formation incombustion or pyrolytic processes. Agreements—ordisagreements—between model predictions, obtained withcarefully chosen kinetics properties values, andexperimental results are meaningful and allow mechanisticconclusions.

In a combined experimental and modeling study Bastin etal. [75] tested the formation of the first aromatic ring in asooting acetylene–O2–Ar premixed low-pressure flamethrough the reactions C4H5 1 C2H2! benzene1 H andC4H3 1 C2H2! phenyl. Model predictions were comparedagainst experimental mole fraction profiles of stable andradical species measured by molecular beam samplingcoupled to mass spectrometry. At least satisfactory resultswere obtained for benzene and the species involved in itsformation. Nevertheless, certain characteristics of thechemical reaction network used by Bastin et al. [75] raisedsome doubts as to whether benzene formation can be unam-biguously explained by the above mentioned reactions ofC4H5 and C4H3.

First, both of these reactions are treated as irreversible inthe mechanism used by Bastin et al. [75], thus neglecting thecontributions of the reverse reactions which could be signif-icant, in particular at higher temperature.

Second, Bastin et al. used higher values for the rateconstants than those deduced by Westmoreland et al.[72], but it is difficult to know which of the valuesare more accurate considering the uncertainty of therate constant determinations. Still another concern is

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608 577

Fig. 8. Comparison of model predictions for different benzene formation pathways with the experimental data of Bastin et al. [75]: (a) model ofTable 1 in [77]; (b) model of Table 1 in [77] with the addition of C3H3 1 C3H3 X C6H5 1 H (k � 1 × 1013cm3mol21s21); (c) model of Table 1in [77] with the addition of C3H3 1 C3H2 X C6H5 �k � 5 × 1013cm3mol21s21; (d) model of Table 1 in [77] with the addition ofi-C4H3 1

C2H2 X C6H5 andi-C4H5 1 C2H2 X C6H6 1 H (same rate coefficients as for the analogousn-C4H3 andn-C4H5 reactions); (e) model of Table 1in [77] with rate coefficients ofn-C4H3 1 C2H2 X C6H5 andn-C4H5 1 C2H2 X C6H6 1 H increased by a factor of 10; (f) model of Table 1 in[77] with the heat of formation ofi-C4H3 increased from 111.3 kcal mol21 to 121.7 kcal mol21. In cases d, e, and f, the predictions are for thesum of C6H6 and C6H5O (Miller and Melius [77]).

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the necessity to consider two isomers for both C4H3 andC4H5 species [76].

3.1. Contribution of C3-hydrocarbons

In the light of persisting uncertainties in kinetic and ther-modynamic data, the formation mechanism of the firstaromatic ring in the fuel-rich premixed acetylene flamesstudied by Bastin et al. [75] was later re-examined by Millerand Melius [77]. The kinetic model was the same as thatused by Miller et al. [78] for three rich, non-sooting, low-pressure premixed flames. Experimental flames structureshad been obtained by mass spectrometry after microprobesampling, optical measurements allowed the determinationof CH, OH and hydrogen-atom concentration. Temperatureprofiles were determined from thermocouple measurementsnear the burner surface and the rotational temperature of theOH radical for positions higher in the flame. Miller et al.paid particular attention to the quality of the thermodynamicdata. For some key C3 and C4 species they supplemented the

commonly used CHEMKIN data base [79] by quantum-mechanical ab initio computational results. In particular,Miller et al. [77,78] distinguished between different isomerssuch asi-C4H3 andn-C4H3, i-C4H5 andn-C4H5, or allene andmehtylacetylene in the case of C3H4. The structural identityand sound thermodynamic data on these species are essen-tial for the assessment of their contributions to the formationof aromatic rings. Therefore the more detailed approachused by Miller et al. [77,78] as compared to prior modelsallows meaningful assessment of the significance of differ-ent pathways, as is confirmed by the generally good agree-ment between model predictions and experimental data forstable and radical species.

Based on their carefully tested kinetic model, Miller andMelius [77] evaluated different pathways leading to theformation of the first aromatic ring in the sooting C2H2–O2–Ar flame studied by Bastin et al. [75]. The comparisonof different model prediction with the experimental benzeneprofile is shown in Fig. 8. It is obvious that contributions ofthe reactions n-C4H3 1 C2H2 O C6H5 and n-C4H5 1

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Fig. 9. Pathway from 1,5-hexadiyne to 3,4-bismethylenecyclobutene, fulvene and benzene (Henry and Bergman [84]).

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C2H2 O C6H6 1 H are not sufficient to explain the formationof benzene, even in the case of an unrealistic increase of thecorresponding rate constants by a factor of 10. Then-C4H3

andn-C4H5 species are thermodynamically less stable thanthe corresponding isomers and reactions allowing isomer-ization for both C4H3 and C4H5 are included in the model.The effect of possible uncertainties in the heats of formationaffecting the equilibria was tested by increasing theDHf

0 ofi-C4H3 by about 10 kcal mol21, favorable for the relativeconcentration ofn-C4H3. Only a slight, clearly insufficient,increase of benzene formation was observed. Thereforethermodynamic uncertainties seem unlikely to be the reasonfor the under-prediction of benzene. Miller and Melius [77]discuss also the work of Bastin et al. [75] and point out thatthese authors did not distinguish between the isomers ofC4H3 and C4H5 and therefore they would implicitly includethe reactionsi-C4H3 1 C2H2 O C6H5 andi-C4H5 1 C2H2 O

C6H6 1 H in their mechanism. Effectively, the inclusion ofthese two reactions leads to a predicted benzene concentra-tion profile with a peak value and location close to theexperimental profile measured by Bastin et al. [75]. Never-theless, this agreement can be considered as artificialbecause, as discussed by Miller and Melius,i-C4H3 and i-C4H5 are stabilized by delocalization of the free electron andtherefore form only very weak bonds with stable moleculessuch as acetylene. The necessity of rearrangements includ-ing hydrogen shifts seems to be consistent with cyclizationof i-C4H3 and i-C4H5 addition complexes either not occur-ring or having much lower rate constants than do similarreactions involvingn-C4H3 and n-C4H5 which have a freeelectron at a terminal carbon atom without the possibility ofdelocalization.

Miller and Melius [77] also comment on the Frenklachand Warnatz [63] modeling of the sooting low-pressure

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Fig. 10. Reaction mechanism of the formation of benzene and 1,3-hexadien-5-yne from the chemically activated recombination products of 2-propynyl (Alkemade and Homann [86]).

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acetylene flame investigated by Bockhorn and co-workers[59], discussed above. They attribute the agreement betweenpredicted and experimental benzene profile to the absence ofsuitable isomerization reactions between the C4H3 and C4H5

isomers and to the use unreasonably high rate constants.The overall conclusion from the structural and thermo-

dynamic considerations of Miller and Melius [77] is that oneor more additional pathways are necessary in order toexplain the formation of the first aromatic ring. Miller andMelius [77] discuss in some detail the possible contributionof the reactions C3H3 1 C3H3 O C6H5 1 H and C3H3 1C3H2 O C6H5 as reflected in Fig. 8. The comparison ofmodel predictions for C3H3 and C3H2 with experimentaldata shows very good agreement for C3H3 but a significantover-prediction for C3H2. Therefore, based on this findingand the results shown in Fig. 8, Miller and Melius concludethat the recombination of two C3H3 molecules represents amore attractive source of benzene in acetylene flames.

The role of C3H3 has been initially suggested by Hurd etal. [80] in a survey of principles of the formation of aromaticspecies from aliphatics under pyrolytic conditions. Hurd etal. proposed a mechanism beginning with an 1,2-hydrogenshift from the C3H3 ground state, CHCCH2, to trimethine,

CHCHCH. Trimethine is both a radical and carbene and indimerization should readily form benzene. The formation oftrimethine has been ruled out by Westmoreland et al. [72]because of its thermodynamic disadvantage, estimated to beof about 70 kcal mol21 relative to its CHCCH2 isomer.Referring to the work of Hurd et al. [80] and consideringtheir own shock-tube and kinetic-modeling study of allene(H2CCH2) pyrolysis, Wu and Kern [81] suggested therecombination of C3H3 and the reaction of C3H3 with alleneas the main routes of benzene formation. In an independentshock-tube and kinetic-modeling study of propyne andallene pyrolysis Hidaka et al. [82] confirmed the role ofC3H3 for benzene formation.

Wu and Kern [81] also mention the possibility of theformation of linear C6H6 species. In order to substantiatethese finding, Kern et al. [83] subsequently investigatedthe thermal decomposition of 1,2-butadiene in a temperaturerange from 1300 to 2000 K and obtained good agreementsfor benzene formation with experimental data using a reac-tion mechanism which includes the recombination of twoC3H3 molecules. In addition to the dimerization oftrimethine after 1,2-hydrogen shift, discussed above, Kernet al. [83] refer to a sequence of rearrangements suggested

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608580

Fig. 11. Reaction coordinate diagram for head-to-head and tail-to-tail recombination of propargyl (C3H3) radicals (Miller and Melius [77]).

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by Henry and Bergman [84]. Based on the thermolysis of1,5-hexadiyne (HCCCH2CH2CCCH), its deuterated equiv-alent (DCCCH2CH2CCCD) and compounds identified in theproduct mixture such as bismethylenecyclobutene orfulvene, Henry and Bergman [84] suggested the reactionmechanism shown in Fig. 9 for deuterated 1,5-hexadiyne.1,5-hexadiyne (1b) is proposed to rearrange first to diallene(2b) which reacts to bismethylenecyclobutene (3b) andfulvene (7b). This mechanism seems to be appealingbecause 1,5-hexadiyne can be formed by self-recombinationof C3H3 and is the only such species which has been reportedso far [85]. However, this mechanism is exclusively basedon indirect evidence; high energy barriers could be presentand make it unlikely.

Despite the above shock-tube and kinetic-modelingevidence for benzene formation from C3H3 reactions, nodirect measurements of the rate constants or the relativeabundances of the different C6H6 species are available.Using the in situ generation of 2-proynyl radicals (C3H3)from the respective chloride or bromide, Alkemade andHomann [86] measured product distribution and the overallrecombination rate constant in a temperature range from 623to 673 K in a flow reactor operating at pressure between 300and 600 Pa. Analyses were performed by nozzle beam/massspectrometry and by gas chromatography coupled to massspectrometry. Consistent with the two possible resonancestructures of C3H3, i.e. the free electron being located atthe carbon-1 or and at the carbon-2 position, the directrecombination products 1,5-hexadiyne, 1,2-hexadiene-5-yne and 1,2,4,5-hexatetraene were identified. Benzene and1,3-hexadien-5-yne were detected in significant yieldswhich decreased with increasing pressure. The relativeproduct yield of benzene was 30% and Alkemade andHomann concluded that it should be close to 100% in acombustion environment. The authors showed also thatthe addition of stable unsaturated hydrocarbons such as acet-ylene, ethylene or butadiene did not have any impact on thecomposition of the product mixture. Therefore C3H3 recom-bination can be considered as being faster than possiblycompeting reactions with stable molecules present in acombustion mixture. Alkemade and Homann [86] deducedan overall recombination rate constant for 2-propynyl of3.4× 1013 cm3 mol21 s21 in the investigated temperaturerange and suggested a reaction mechanism explaining theformation of benzene and 1,3-hexadien-5-yne from thechemically activated recombination of 2-propynyl (Fig. 10).

In agreement with the increasing evidence of the role ofC3H3 radicals for the formation benzene, Miller and Melius[77] explored possible reaction paths using ab initio quan-tum-mechanical computations (BAC-MP4). They consid-ered possible initial recombinations, i.e. “head-to-head”,“tail-to-tail” and “head-to-tail”, where the CH2 end of theHCCCH2 molecule is the head and the CH end is the tail.The potential energy surface beginning with the “head-to-head” and “tail to tail” recombination is shown in Fig. 11.Miller and Melius [77] conclude that the recombination of

C3H3 radicals is the most likely reaction producing the firstaromatic ring. They emphasized the potential importance ofresonantly stabilized free radicals in forming aromaticsand PAH in flames. In addition, Melius et al. [87]investigated unimolecular reaction mechanisms involvingC3H4 and C4H4 such as the allene–cyclopropene–propyneisomerization.

Miller et al. [77,78] discussed the formation pathwayleading to C3H3 in fuel-rich acetylene flames and suggestedthe reaction CH2 1 C2H2 O C3H3 1 H. More recently, thecontribution of the reaction CH3 1 C2H2 O CH3C2H 1 H,the product being a likely source of C3H3, has been investi-gated theoretically at different pressures and temperaturesby Diau et al. [88]. In order to assess in more detail thechemistry of C3 species involving competing oxidationand decay pathways, Miller et al. analyzed experimentallyand by means of kinetic modeling the oxidation of allene inan H2/O2/Ar flame [89] as well as the effect of allene addi-tion on the structure of a rich C2H2/O2/Ar flame [90].

Independently from Miller and Melius, Stein et al. [91]investigated different unimolecular steps leading from C3H3

radicals to benzene. Their experiments have been conductedin atmospheric and very low pressure flow reactors. Atatmospheric pressure and low temperature (250–4008C),1,2-dimethylenecyclobutene was the sole product butisomerized to benzene and fulvene above 4608C. Undervery low pressure conditions all three C6H6 products,namely, 1,2-dimethylenecyclobutene, fulvene and benzenewere formed in parallel even at the lowest reaction tempera-tures. Benzene was clearly the principal product approach-ing the highest investigated temperatures of about 8008C.Stein et al. attributed this pronounced pressure dependenceto chemical activation and could fit rates of 1,5-hexadiyneobtained at very low pressure with those at atmosphericpressure after fall-off correction using a conventionalRRKM calculation.

Stein et al. predicted also the benzene formation rate inthe lightly sooting premixed low pressure acetylene flamestudied by Westmoreland et al. [72] using the measuredC3H3 concentration and a conservative estimate of the effec-tive C3H3 recombination rate constant. Based on theseresults and also comparing with benzene formation throughthe reactions ofn-C4H3 andn-C4H5 with acetylene computedby Westmoreland et al. [72], Stein et al. [91] conclude thatonly the C3H3 route correctly describes the onset of exper-imentally observed benzene formation and that the maxi-mum rate for this pathway is significantly greater than forthe others.

Despite the extensive work on the elementary reactionsleading to the first aromatic ring in a combustion environ-ment, a generally accepted consensus about “the” dominantbenzene formation pathway does not seem to have beenreached. In a recent modeling study of atmospheric pressurepremixed methane and ethane flames, Marinov et al. [92]concluded that C4H3 and C4H5 species were not a factor in abenzene formation while C3H3 must be attributed a key role.

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In another recent modeling study, Wang and Frenklach [93]revisited the premixed low pressure acetylene flames inves-tigated by Bockhorn et al. [59] and Westmoreland et al.[72,73] as well as the atmospheric pressure premixed eth-ylene flames of Harris et al. [67]. They concluded thatn-C4H3

andn-C4H5 make a significant contribution, particularly in thelow-temperature preheat zone of the flames and suggested theuse of significantly lower values for benzene formationthrough C3H3 recombination than the rate constant of 1×1013 cm3 mol21 s21 assigned by Miller and Melius [77].

Dagaut and Cathonnet [94] recently assessed the relativecontributions of the different benzene formation pathways ina jet-stirred reactor operated at atmospheric pressure withdifferent fuels and temperatures. The tendency towardbenzene formation was investigated for the oxidation ofacetylene, allene, propyne, propene and 1,3-butadiene. Allexperiments were conducted at an equivalence ratio off � 2.0 and a temperature in the range 900–1200 K.Comparison of the measured benzene mole fractions as afunction of fuel conversion for the different fuels shows that,under the studied conditions, acetylene has clearly thelowest tendency to produce benzene. For all fuels butpropene, the yield of benzene increased almost exponen-tially with increasing fuel conversion up to a conversionof 70%, with the same slope for acetylene, propyne andallene. It was shown that at low fuel conversions, 1,3-buta-diene produces more benzene than does propene, propyne

and allene but at fuel conversions larger than 60% thereverse is observed. Based on these results but also takeninto account previous modeling studies such as the work ofMiller and Melius [77], Dagaut and Cathonnet [94]conclude that in the oxidation of acetylene, propyne andallene, benzene is formed by the recombination of propargyl(C3H3) radicals, and they explain the smaller benzene yieldin the case of acetylene oxidation by differences in the easeof propargyl formation from the fuel. The early formation ofbenzene and its decrease at high fuel conversions areexplained as being the consequence of the participation ofthe fuel itself—or of its radical—in benzene formation. Inthis context the authors refer to the modeling work of Lind-stedt and Skevis [95] who investigated premixed low pres-sure 1,3-butadiene flames [60] and found a competitionbetween the C2 1 C4 and the C3 1 C3 benzene formationroutes. Interestingly, and in contradiction with the conclu-sions of Cole et al. [60], Lindstedt and Skevis attribute asignificant fraction of the benzene formation to the reactionof 1,3-butadiene with vinyl radicals (1,3-C4H6 1 C2H3! c-C6H8 1 H) followed by the elimination of H2 (c-C6H8!benzene1 H2). Kinetic models represent an extremelyuseful tool for the assessment of the relative contributionof formation pathways, but the significant uncertainty stillpresent in rate constants of key reactions prevents definitiveelucidation of the role of 1,3-C4H6, in particular in compar-ison to then-C4H5 radical.

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608582

Fig. 12. Reaction pathway diagram for the reaction of fulvene with H atom. BAC-MP4 energies (in kJ mol21) are given for stable intermediatesand transition-state structures (Melius et al. [98]).

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A potential role of C5 species in benzene formation hasbeen discussed. They were included in the unimolecularrearrangements of linear C6 species discussed by Millerand Melius [77,87] and Henry and Bergmann [84]. Thecontribution of C5 species as reactants in the formation ofbenzene and its derivative was suggested in 1979 by Denteet al. [96] in a kinetic modeling study of hydrocarbon py-rolysis. The reaction of cyclopentadiene or of its methyl-derivatives with C2 or C3 species such as acetylene, vinyl ormethylacetylene to form toluene or different xylene isomersis discussed. The mechanism of Dente et al. takes intoaccount benzene formation by ethylene attack on cyclopen-tadiene followed by hydrogen and methyl loss, passingthrough norbonene, a CH2-bridged cyclohexene:

C2H4 1 c-C5H6 ! benzene1 H 1 CH3

Based on the comparison of model predictions to exper-imental data, this pathway has been suggested recently tocontribute significantly to benzene formation in ethylenecombustion and pyrolysis [97]. Despite the interest inthese results, no direct evidence of this benzene formationpathway based on kinetic studies or theoretical investigationof the potential energy surface is available. Therefore,further work is necessary in order to confirm or rule outthis pathway.

A detailed investigation of the role of substituted five-

membered ring species in benzene formation has beenconducted by Melius et al. [98]. In continuation of thework of Miller and Melius [77] in which fulvene figuredas intermediate on the potential energy surface betweenthe initial C3H3 recombination product and benzene, adetailed reaction pathway diagram for the reaction offulvene with H atom, including stable intermediates andtransition-state structures (Fig. 12), is computed. Compari-son with the energy diagram of the unimolecular reactionsequence (Fig. 11) shows a significant catalytic effect of thecontribution of hydrogen radicals in the isomerizationprocess. Finally, Moskaleva et al. [99] computed thepotential energy surface for the CH3 1 C5H5 reactionand showed fulvene to be a possible product and there-fore C5H5 a potential benzene precursor. The concept ofthe contribution of resonantly stabilized free radicals toPAH growth has been extended by Miller [100] pointingout that reactions of propargyl-derivatives, R-CCCH2,where R is a large PAH radical, could play a role inPAH growth.

As a conclusion regarding the current knowledge of theformation of the first aromatic ring in combustion environ-ments, important pathways involving C4H3, C4H5 and C3H3

species have been identified and their relative contributionsvery likely depend on experimental conditions, in particulartemperature and pressure. The knowledge of rate constants

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608 583

Fig. 13. Reaction pathway diagram for the rearrangement of the C5H5–C5H4 radical to form naphthalene. BAC-MP2 energies (in kJ mol21) aregiven for stable intermediates and transition-state structures (Melius et al. [98]).

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is limited and additional work is necessary to determine therate constant describing the formation of benzene (orphenyl) after C3H3 recombination at different pressuresand temperatures. A high pressure limit value of 2.6×1013 cm3 mol21 s21 for the recombination reaction, recentlymeasured at room temperature by Atkinson and Hudgens[101] using ultraviolet cavity ring-down spectroscopy is inreasonably good agreement with the rate constants deter-mined by Alkemade and Homann [86] and Morter et al.[102].

3.2. Formation of other first aromatic rings

Besides the formation of benzene, the first species of thehomologous series of polycyclic aromatic hydrocarbons,other compounds may play a role as precursor in the growthprocess to larger and larger PAH without passing throughbenzene as intermediate. One example, already mentionedabove, is the direct formation of phenylacetylene [63] orstyrene [65] via the cyclization of unsaturated aliphatic radi-cals.

The formation of naphthalene, i.e. a compound with twoaromatic rings, via the reaction of two cyclopentadienylradicals was included by Dean [103] in a kinetic modeldescribing the methane pyrolysis. The key role of cyclopen-tadiene in an autocatalytic effect was identified. The surpris-ingly rapid formation of cyclopentadiene could be explainedby means of the concept of chemical activation [72,74]; theaddition of allyl radical to acetylene yields a chemicallyactivated linear adduct which undergoes cyclization priorto collisional stabilization. Once formed, cyclopentadienedissociates unimolecularly to cyclopentadienyl radical(c-C5H6 O c-C5H5 1 H). Cyclopentadiene is regenerated inthe next step by hydrogen abstraction from methane(c-C5H5 1 CH4 O c-C5H6 1 CH3). The resulting net reactionof this reaction chain—CH4 O CH3 1 H—explains thecatalytic effect of the formation of cyclopentadiene. Deandeserves much credit for pointing out the potential role ofC5-moities. He treated naphthalene formation as a chemicallyactivated process and suggested the rate constantk � 4:30×1036T26:268 exp�245;671 cal=RT� cm3 mol21 s21 for thereaction c-C5H5 1 c-C5H5$ naphthalene1 H2.

Based on combined experimental and kinetic modelingstudies of PAH formation in methane and ethylene flames,Marinov et al. [92] and Castaldi et al. [104] jointlyconcluded that acetylene addition processes cannot accountfor the PAH levels observed in experimental flames. As aresult of this work, they proposed that in aliphatic hydro-carbon flames, the larger aromatics originate from resonancestabilized cyclopentadienyl radicals. In particular, theysuggested that two cyclopentadienyl radicals combine andrearrange to form naphthalene:

This reaction differs from the one proposed by Dean [103] in

that two hydrogen atoms are formed instead of one hydro-gen molecule.

Motivated by the potential importance of the cyclopenta-dienyl radical, Melius et al. [98] conducted a detailed quan-tum chemical analysis of the elementary reaction stepswhich participate in the conversion of two cyclopentadienylradicals to naphthalene. In the first step, two cyclopentadi-enyl moities react with loss of an hydrogen atom in a slightlyendothermic reaction forming a resonance-stabilized C5H5–C5H4 radical. The subsequent rearrangement reactionsfollowed by loss of a hydrogen atom and naphthaleneformation are shown in Fig. 13. Based on the work ofMelius et al. [98] the rate constantk � 2:00×1013 exp�28000 cal=RT� cm3 mol21 s21 for the formationof naphthalene from cyclopentadienyl has been suggestedrecently [105].

The authors conclude that these results support the im-portant role of the cyclopentadienyl moiety in aromatic ringformation. They also point out that the resonance-stabilizedmoiety may also be formed from oxidation of largeraromatic rings, e.g. indenyl may be formed from naphtha-lene. Therefore, similar to the naphthalene formationprocess, a phenanthrene formation pathway based on thecombination of cylcopentadienyl with indenyl followed byrearrangement has been suggested [92,104,105]:

Pathways leading to cyclopentadienyl formation havebeen the object of a substantial research effort. Cyclopenta-dienyl is generally formed via the oxidation of benzene andit is therefore not surprising that the reaction between twocyclopentadienyl units is found to be by far the most im-portant naphthalene formation pathway in benzene flames[106]. Thermal decomposition of phenoxy radicals has beenconfirmed to be a possible pathway [107–109] and phenyldecay via the reaction C6H5 1 O! c-C5H5 1 CO has beendiscussed [109]. Phenoxy-decay via a bimolecular reactionwith oxygen atom to form c-C5H5 and CO2 has been shownto be a minor pathway in a flow reactor study at roomtemperature [110]. High-temperature shock-tube pyrolysisof phenol has shown its decay to cyclopentadiene and CO tobe the dominating initiation step [111]. Benzoquinone(C6H4O2) is another potential oxidation product of phenylor phenoxy, yielding in subsequent reaction steps first cyclicC5 species [109,110] and ultimately smaller molecules suchas acetylene or CO. A systematic study ofpara-benzo-quinone pyrolysis and oxidation has been conducted in aflow reactor by Alzueta et al. [112]. The unimoleculardecomposition of cylcopentadiene under high-temperaturepyrolytic conditions behind reflected shock waves has beenstudied by Roy et al. [113], who deduced experimentallythat hydrogen loss to form cyclopentadienyl is the maincyclopentadiene decomposition channel and suggested a

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corresponding rate expression. In the same work the analy-sis of measured C2H2- and H-absorption profiles assisted byab initio computations allowed also the determination of arate constant for unimolecular decomposition of cyclo-pentadienyl radicals to acetylene and C3H3.

4. Further growth process

Without excluding the possibility of other “buildingbricks” such polyacetylene or ionic species, the importanceof polycyclic aromatic hydrocarbons (PAH) in the growthprocess leading to soot particles has received more and moreattention in the combustion community [114,115]. Quanti-tative testing of the possible contribution of the differentreaction pathways has become possible with the increasingcomputational power which allows more and detailedkinetic modeling of combustion processes [28,34]. Simulta-neously, an increasing body of thermodynamic and kinetic

data describing elementary reactions has led to a betterunderstanding and more reliable description of combustionchemistry. The first published attempt to make numericpredictions about soot formation chemistry by means of afundamental model was that of Jensen [116] in 1974. Fiveprocesses controlling the production of soot from gaseoushydrocarbons were distinguished: gas reactions producingradicals which serve as precursors of soot nuclei; coagula-tion; growth; and oxidation. The model of Jensen included asequence of reversible gas phase reactions forming theinitial nucleus, taken as C2 or C2H. The following irrever-sible reactions with the growth species C2, C2H or C2H2 gaverise to the first particle containing four carbon atoms. Par-ticle coagulation and growth were considered to appearsimultaneously and irreversibly. All particles except thelargest were permitted to coagulate with all others via inclu-sion of rate terms for processes of the type Ci 1 Cj ! Cj11:

Similar to the nucleation steps in the gas phase chemistry,C2, C2H and C2H2 were taken into account as growth species

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608 585

Fig. 14. Possible free radical addition schemes for PAH and soot formation (Bittner and Howard [69]).

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and particle growth terms such as Ci 1 C2H2 ! Ci11 1 H2;

in the case of acetylene, were included in the model. Finally,oxidation of particles was treated in an analogous mannerand terms for conversions of the type Ci 1 OH! Ci21 1CO1 �1=2�H2 were written. The model was applied to thenon-equilibrium conditions of a practical rocket engine andan agreement with experimental results was reached. Modelcalculation were carried out with different combinations ofnucleation and growth species, and Jensen [116] concludedthat among the compounds considered, namely, C2, C2H,C2H2, only acetylene yielded model predictions consistentwith the experimental data.

Although this early modeling work included in some formall the key features of later, more detailed models, i.e. gasphase chemistry and particle nucleation, coagulation,growth and oxidation, the lumping of individual chemicalcompounds with particles beginning with species as small asfour carbon atoms limits the meaning of the chemical

identities of the intermediates in the growth process.Being aware of this limitation, Jensen [116] points outthat the coagulation-growth treatment implicitly allowsreactions among molecules containing four or more carbonatoms to be accounted for, i.e. as coagulation. Jensen refersto the necessity of reliable kinetic and thermochemical datafor such larger molecules in order to allow for their reactionsand to gain the consequent physical insight into the earlystages of particle formation. Therefore, the identification ofacetylene as the key reactant in Jensen’s study [116] of thegrowth process leading ultimately to soot grow species doesnot imply any conclusion concerning the relative contribu-tions of acetylene and other species, such as PAH whichwere not included in the modeling calculations and whichis a question of considerable recent interest [117,118].

The identification of chemical processes responsible forthe pre-particle molecular weight growth and the massgrowth of particle systems requires the development of

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608586

Fig. 15. Principal reaction pathways for formation of two-ring aromatics. For a given reaction step, the difference in the lengths of the arrowsrepresents the difference in forward and reverse reaction rates as computed for the test case atT� 1700 K and a reaction time of 0.5 ms(Frenklach et al. [66]).

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possible reaction networks and the availability of thecorresponding thermodynamic and kinetic data followedby model calculations. The degree of agreement betweenmodel predictions and experimental data indicates the feasi-bility of the mechanisms included in the model. The re-liability of this approach depends strongly on the qualityof the thermodynamic and kinetic data used to describethe elementary reactions involved in the process.

Based on the detailed measurement of the compositionprofiles of stable and intermediate species in a near-sootingpremixed benzene/oxygen/argon by means of a molecularbeam sampling system coupled to mass spectrometry,

Bittner and Howard [69] suggested possible free radicaladdition schemes for PAH and soot formation shown inFig. 14. Acetylene or vinylacetylene contribute in all threereaction sequences as growth species reacting with eitherphenyl or benzyl in the first growth step. Thermodynamicconsiderations showed that additions to phenyl are morefavorable than to benzyl and that decompositions back tothe reactants are slower for vinylacetylene (C4H4) additionsdue to the resonance stabilization of the adduct. Qualita-tively, reactions of phenyl- or benzyl-type species withacetylene or vinylacetylene (Fig. 14: Mechanisms I–IV)can explain the formation of many of the PAH observed

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608 587

Fig. 16. Principal reaction pathways for formation of fused polycyclic aromatics. For a given reaction step, the difference in the lengths of thearrows represents the difference in forward and reverse reaction rates as computed for the test case atT� 1700 K and a reaction time of 0.5 ms(Frenklach et al. [66]).

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experimentally. Nevertheless, motivated by the observationof other authors of a soot formation onset at a lower equiva-lence ratio in toluene flames than in benzene flames [19],Bittner and Howard also suggested a reaction scheme basedon two methyl-substitution/acetylene-addition pathwaysresulting in ortho- and peri-fused ring systems such aspyrene (Fig. 14: Mechanism V). The authors point out thatthis pathway would have the advantage of methyl being themost abundant hydrocarbon radical in their near-sootingbenzene flame and would agree with the observation byLevy and Szwarc [119] that the reactivity of aromatic hydro-carbons for methyl substitution increases with molecularweight.

Bockhorn et al. [59], using the flame sampling andspecies analysis techniques described above, obtained valu-able information about the identity of compounds includingisomers which cannot be separated by mass spectrometryalone. This approach allowed the investigation of flame

structure under sooting conditions which would haveprohibited the use of molecular beam sampling necessaryfor the on-line detection of radical species. In a very detailedstudy the authors identified nearly 100 PAHs up to a mass of300 amu and a significant number of aliphatic hydrocar-bons, mostly polyacetylenes with the general formulaC2nH2 with n� 1; 2; 3;… (up to 10). The reaction schemefor the first aromatic ring suggested by Bockhorn et al. [59]is discussed above, the formation of molecules with two ormore aromatic rings is shown in the lower part of Fig. 3.Acetylene attack to aromatic radicals of arylacetylene-typespecies, e.g. the arylacetylene radical3 of Fig. 3, is followedby ring closure and leads to another PAH. The possibleformation of species containing five-membered rings, suchas acenaphthalene, is suggested as well. The growth reactionpathway to larger and larger PAH advanced by Bockhorn etal. [59] appears to be the first explicit representation of thehydrogen-abstraction/acetylene-addition mechanism.

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608588

Fig. 17. Principal reaction pathways for formation of two-ring aromatics in pyrolysis of 1,3-butadiene (Frenklach et al. [125]).

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Independently of Bockhorn et al., Frenklach et al. [66]used a similar growth sequence in an investigation of themain chemical reaction pathways to soot under the condi-tions used in shock-tube pyrolysis of acetylene. Theapproach taken was to develop a mechanism composed ofconventional elementary reactions and to compare itspredicted time scale of soot formation and soot yieldsagainst the experimental measurements. The model allowedquantitative assessment of the relative contribution of differ-ent pathways considered in the model. Since, the formationof the first aromatic ring is discussed above, the discussionhere is limited to the formation of two-ring aromatics andthe further growth of fused polycyclic aromatics. Frenklachet al. considered about 10 essentially different pathways.The route via phenylacetylene, shown in the upper part ofFig. 15 and similar to the reaction sequence suggested byBockhorn et al. [59], was found to be dominant by at leastthree orders of magnitude under the investigated conditions.Based on the computational results, the next fastest reactionsequence leading to two-ring aromatics was the two-stepacetylene addition route suggested by Bittner and Howard[69] (Fig. 14: Mechanism I) and shown in the lower part ofFig. 15. According to Frenklach et al. [66] the reason for thedominance of the hydrogen-abstraction/acetylene additionis mainly related to the instability of the first intermediateadduct of the two-step acetylene addition route, i.e.C6H5CHCH, resulting in stabilization to phenylacetylenebeing much faster than the next addition reaction.

After the formation of the two-ring aromatic naphthalene,the kinetic model [66] described further growth to speciesup to benzo[ghi]perylene (C22H12) based on the hydrogen-abstraction/acetylene-addition mechanism. Two routes wereconsidered and are shown in Fig. 16. Route 1 starts with theformation of a five-membered ring species, acenaphthalene,and continues with subsequent hydrogen-abstraction/acety-lene-addition steps to acephenanthrylene, cyclopenta[cd]-pyrene, etc. The authors consider the cyclopenta-group asrelatively unstable, and therefore partially lost, as indicatedin Fig. 16, along the reaction pathway to larger and larger

species. Route 2 is also based on a sequence of hydrogen-abstraction/acetylene-addition steps, the only differencerelative to Route 1 being the absence of the formation offive-membered rings. Route 1 generally dominated thecarbon mass flow, although both routes proceeded withapproximately equal rates at the lowest temperature tested(1500 K). Taking into account long-standing evidence[50,120], which is strongly supported and extended bymore recent experimental observations [121–123], of asignificant number of five-membered ring containingspecies of different size, ring closure reactions similar tothe formation of acenaphthalene in Route 1 are likely tobe possible at any stage of the growth process.

Finally, to compute soot yields an infinitely long reactionsequence of Route 1 (Fig. 16) was assumed and all species

beginning with coronene considered as

soot. The resulting soot yields were believed to be lowerlimits, arguing that somewhere in the growth process, othermechanisms such as physical condensation, particle coagu-lation and surface reactions become more efficient and takeover in the soot formation process. Although this modelinvestigation was conducted under pyrolytic conditions, anexperimental shock-tube study of the oxidation of differentfuels such as acetylene, allene, 1,3-butadiene, toluene,benzene or chlorobenzene was conducted at temperaturesfrom 1430 to 3490 K and pressures from 0.20 to 3.14 barand led to the conclusion that soot formation mechanismsunder pyrolytic and oxidative conditions are similar [124].

The early modeling work of Frenklach et al. [66] is thedecisive step toward the use of detailed kinetic model as toolfor the development of a realistic understanding of PAH andsoot formation. At the time of the work much of the thermo-dynamic and kinetic data for the calculations had to beestimated. The resulting uncertainties were sufficientlylarge as to preclude definitive conclusions regarding thequantitative contributions of different growth pathways atthe time of the study. This difficulty does not diminish theimportance of this pioneering modeling work.

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608 589

Fig. 18. Dominant reaction pathway for formation of small polycyclic aromatics in pyrolysis of benzene (Frenklach et al. [125]).

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Frenklach and co-workers extended and refined theirpicture of PAH and soot formation in the subsequentyears. The influence of fuel structure on reaction pathwaysleading to soot was investigated using detailed kineticmodeling of shock-tube pyrolysis of 1,3-butadiene, benzeneand ethylene [125]. The comparison of the reaction path-ways for shock-tube pyrolysis of 1,3-butadiene with theacetylene case discussed above (Fig. 15) led to the conclu-sion that vinyl-radicals, a main decomposition product of1,3-butadiene, and to a smaller extend vinylacetylene,replace acetylene as the dominant growth species for theformation of two-ring aromatics, i.e. naphthalene (Fig.17). Besides its high concentration in 1,3-butadiene pyroly-sis, the role of vinyl as growth species has the added advan-tage of a more favorable equilibrium than that of phenyladdition to acetylene. Another interesting result of thisstudy is the significant sensitivity of the resulting sootformation to thermodynamic data. The sensitivity decreasesin the order ethylene, acetylene, 1,3-butadiene and benzene,which reflects the relative importance of cyclization reac-tions necessary for the formation of the first aromatic ring.Also, for the conditions of 1,3-butadiene pyrolysis studiedby Frenklach et al. [125], the main fragmentation pathway isthe reverse reaction of acetylene addition to phenyl, thedominant naphthalene formation route for acetylene py-rolysis. For the further PAH growth, vinyl is shown to bean important growth species only at short reaction times,within the induction period. At longer reaction times theconcentration of acetylene is high and that of vinyl hasdecayed, and the hydrogen-abstraction/acetylene-additionroute is, similar to acetylene pyrolysis, the fastest one. Inthe case of ethylene pyrolysis the formation and furthergrowth of polycyclic aromatics follows a course similar tothat observed for 1,3-butadiene pyrolysis. Nevertheless, thevinyl-addition route and pathways involving C4 species asshown in Fig. 17 are less important for ethylene than forbutadiene.

For benzene pyrolysis the initial fuel does not disappearquickly, in contrast to the pyrolysis of butadiene or ethylene.During the benzene decomposition period, a pathway begin-ning with the formation of biphenyl and followed by thesequential addition of acetylene, first to phenanthrene and

then to pyrene (Fig. 18) is shown to be the dominant path-way. At longer reaction times, i.e. at a very advanced degreeof benzene consumption, the hydrogen-abstraction/acety-lene-addition pathway takes over. For the growth to largerand larger polycyclic aromatic hydrocarbons, a reactionpattern based on alternating additions of benzene and acet-ylene (Fig. 18) was included in the model but the mass fluxwas found to be at least three times smaller than that throughsequential additions of acetylene. Finally, in this compara-tive study of the pyrolysis of different fuels, Frenklach et al.[125] reached the conclusion that the pathways leading tosoot in the pyrolysis of every fuel considered always relax tothe acetylene-addition mechanism and that fuel structureinfluences the process only at an early stage.

In subsequent studies, Frenklach and co-workersextended and refined their model description of soot nuclea-tion and growth and applied it to laminar premixed acety-lene and ethylene flames under different pressures [126,127]for which experimental data where available. The computa-tional model used for the prediction of soot formation inlow-pressure acetylene–oxygen [59,72,73] as well as atmo-spheric [67] and high pressure [128] ethylene/air flamesconsisted of three logical parts: (I) initial PAH formation,which includes a detailed chemical description of fuel py-rolysis and oxidation, formation of the first aromatic ring,and its subsequent growth to a prescribed size; (II) planarPAH growth, comprised of replicating-type growth of PAHbeyond the prescribed size; and (III) spherical particleformation and growth of the resulting particles. In step(III), PAH formed in (II) coagulate, followed by continuedgrowth of the resulting particles by their coagulation tolarger ones and surface reactions. The computation of parti-cle number density, its surface area and average diameter atdifferent heights above the burner was performed using atwo-stage approach. The Sandia burner code [30] was usedfor the modeling of PAH formation and growth up to coro-nene (C24H12). The computed profiles of H, H2, C2H2, O2,OH, H2O and of a prescribed-size PAH, Ai, served then asinput for another kinetic code which simulates particlenucleation and growth based on a method of moments.Nucleation describes the growth of planar PAH via the H-abstraction/C2H2-addition sequence beginning with one-ring

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608590

Fig. 19. Formation of larger polycyclic aromatic hydrocarbons (PAH) from phenyl-substituted propargyl radicals (Stein et al. [91]).

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species and preceding up to an infinite size using the tech-nique of chemical lumping. The PAH Ai, containingi fusedrings, formed in the nucleation process are then allowed tocoagulate, that is, all the Ai �i � 1; 1 1 1;…;∞� collide witheach other forming dimers; the dimers in turn, collide withA i forming trimers or with other dimers forming tetramers;and so on. PAH beginning with the dimers were assumed tobe soot particles and it was allowed to add and lose mass bysurface reactions. The chemical mechanism adopted for thisheterogeneous process is based on the H-abstraction/C2H2-addition reaction sequence and rate constants were esti-mated based on analogous gas phase reactions of one-ringaromatics: benzene and phenyl. The comparison of themodel predictions of soot volume fraction, particle numberdensity, and particle radius or diameter with experimentaldata from different flames is encouraging.

Although the work of Frenklach et al. represents a signif-icant step towards the modeling of the entire course of sootformation based on a fundamental description of theprocesses involved, several questions remained to beaddressed. For instance, the description of surface growthincludes a factora , defined as the fraction of surface sitesavailable for a given reaction. However, the value ofa wasobtained empirically and depended significantly on theflame being modeled. This observation led to the conclusionthat a represents a steric phenomenon [126]. Anotherconcern [129] has been the treatment of coagulation as irre-versible by Frenklach and co-workers [126,127]. Appar-ently their model requires that the reactions of PAH ortheir dimers are irreversible in order to explain the role ofPAH as precursors or building blocks in soot formation.According to Miller et al. [130], a treatment of coagulationas reversible homogeneous gas phase reactions would leadto concentrations far below the number densities observedfor small soot particles.

The decoupling of PAH and soot formation in modeling,i.e. the use of an independent flame code computation ofPAH concentrations as input parameters for the particlenucleation and growth simulation, is a source of error.Also the strong impact of the choice of the prescribed sizeof PAH at the start of the nucleation process, on the nuclea-tion rate [126] shows some weakness of the approach.Recently, this limitation was overcome for well-stirred reac-tor conditions by means of the incorporation of the abovementioned method of moments in an existing computationalcode [131]. Under the investigated conditions, the couplingof gas phase and surface chemistry was shown to be signifi-cant and to increase with increasing pressure.

Another approach called Simultaneous Particle and Mole-cule Modeling (SPAMM) has been developed by Pope andHoward [132]. Sectional equations are applied beyond acertain mass for the description of soot formation andconverted into equivalent elementary-step reactions. Thesereactions can be incorporated into a gas-phase reactionmechanism, allowing the simultaneous modeling of gasphase chemistry and soot formation.

5. Roles of acetylene and PAH in the growth process

The formation of larger and larger PAH and the nuclea-tion and growth of soot particles has been described mainlyusing different variations of H-abstraction/C2H2-additionsequences. After the qualitative assessment of the contribu-tion of this pathway [59,66,69] the increasing use of kineticmodeling required reliable rate constants for the elementaryreactions. Kinetic data of key reactions involving specieswith one aromatic ring have been deduced but only fewstudies have investigated the impact of increasing moleculesize which is essential for reliable modeling of the formationof larger and larger PAH and soot particles. A rate constantfor H-abstraction by hydrogen-radicals from benzene hasbeen suggested by Kiefer et al. [133] based on a pyrolyticshock tube study for a temperature range from 1900 to2200 K. Nicovich and Ravishankara [134] studied the reac-tion H 1 C6H6! products in the temperature range of 298–1000 K using the pulsed photolysis–resonance fluorescencetechnique. On the basis of the obtained kinetic information,it was shown that even at sub-atmospheric pressure (10–200 Torr) the primary path of this reaction is addition ofthe hydrogen atom to the benzene ring to form cyclohexa-dienyl radical. The reverse reaction was concluded to bevery fast for temperatures above 600 K while H-abstractionwas deduced to be negligible at any temperature of theconsidered range, i.e. less than 1000 K. In addition, themeasurement of H1 C6H6 at 12, 30, and 100 torr at 298 Kshowed no pressure dependence, so was concluded that thehigh pressure limit is reached even at 12 torr at roomtemperature. A quantum-mechanical ab initio study byMebel et al. [135] of the potential energy surface for thereactions C6H5 1 H2 and C6H6 1 H allowed the determina-tion of the corresponding rate constants by means of tunnel-ing corrected transition-state theory. The predicted rateconstant for H-abstraction is in good agreement with theexpression suggested by Kiefer et al. [133] while RRKMtreatment revealed a strong pressure dependence of theH 1 C6H6 addition reaction above room temperature. Thecomparison of the computational results using Nicovich andRavishankar’s conditions [134] led to good agreement withthe experimental data.

Unfortunately, no data for the assessment of the effect mole-cule size on H-abstraction from aromatic species are available.Low temperature measurements (25–1258C) of the gas phasereactions of hydrogen atoms with benzene and naphthalene ledto a significantlyhigher rateconstant in the caseof naphthalene[136] but—as discussed above [134,135]—refer to hydrogenaddition and not to hydrogen abstraction. Nevertheless, a rela-tive importance of hydrogenaddition,which increases with thesize of the molecule, may be expected due to the increasingnumber of vibrational degrees of freedom which leads to amore efficient stabilization of the initial adduct. However, noconclusion about the impact of PAH size on H-abstractionunder conditions relevant for combustion processes is possi-ble based on the currently available data.

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Electronic structure calculations were used for the predic-tion of C–H dissociation energies of PAH containing up tofour six-membered rings [137]. The analysis of homolyticC–H bond cleavage at different carbon sites showed thecorresponding energies to be governed almost entirely bysteric factors and not by molecule size, the hydrogens fromcongested regions being removed preferentially. The reac-tion of hydrogen radicals with PAH shows pronouncedsensitivity of reaction products and rate constants totemperature, pressure and location in a specific moleculefor many reactions relevant for combustion chemistry.Therefore, a careful analysis of all reaction steps includedin kinetic models is necessary and the development of tech-niques—or general rules—for the prediction of rateconstants covering a large number of different moleculesand radical sites will have to be addressed. Also, other radi-cals besides hydrogen atoms may contribute significantly toH-abstraction. In this category are O and OH as well asmethyl, cyclopentadienyl and phenyl which can be presentin significant concentrations in the reaction zone. Exper-imental data are only available for the first aromatic ring[138–140] and a complex competition between differentreaction pathways including addition and oxidation reac-tions depending on pressure, temperature and carbon sitecan be expected.

Experimental kinetics data are also only available for thefirst aromatic ring for reactions of PAH radicals with acet-ylene. The reaction of phenyl with acetylene has beenstudied by Fahr and Stein [141] at very low pressure (1–10 mtorr) over the temperature range 1000–1330 K using aKnudsen cell flow reactor. The deduced rate constants areconsistent with data obtained in a shock tube of Heckmannet al. [142] covering temperatures from 1050 to 1450 K. Adetailed analysis of the potential energy surface of thereaction C6H5 1 C2H2 has been performed by Yu et al.[143]. They combined an experimental approach measuringabsolute rate constants in the temperature range 297–523 Kwith thermochemical and molecular structure datacomputed on an ab initio level. Pressure dependence wasanalyzed in terms of the RRKM theory and the resultingkinetic data were correlated with the low-pressure/high-temperature results of Fahr and Stein [141]. The calculatedresults show the rate constant for the total C6H5 1 C2H2

reaction to be pressure-independent, whereas those for theformation of C6H5C2H 1 H and the C6H5C2H2 adduct arestrongly pressure-dependent. To summarize, phenylacety-lene (C6H5C2H) is the dominant product under low pressureas well as high temperature conditions while the stabiliza-tion of the C6H5C2H2 adduct is favored by decreasingtemperature and increasing pressure. In view of these kineticdata, PAH growth via the addition of acetylene to the initialadduct as suggested by Bittner and Howard [69] (Fig. 14,Mechanism I) and identified as “minor route” by Frenklachet al. [66] (Fig. 15) may play a significant role in the forma-tion of larger and larger PAH, especially at high pressureand relatively low temperature. In addition, increasing

molecule size may favor the stabilization of the initialPAH–C2H2 adducts and therefore their contribution to thegrowth process. A systematic study of rate constants forchemically activated reactions of acetylene with vinylicand aromatic radicals has been conducted by Wang andFrenklach [144] using semi-empirical quantum-mechanicalAM1 calculations. RRKM treatment allowed the suggestionof corresponding rate constants for different pressures whichhave been used for the modeling of different acetylene andethylene flames at atmospheric as well as at reducedpressure [93]. Wang and Frenklach [144] addressed notonly the issue of acetylene addition to PAH radicals contain-ing up to three aromatic rings but also the formation ofacenaphthalene in competition with the formationof 1-naphthylacetylene or the corresponding 1-C10H7C2H2

adduct. Another key reaction investigated by Wang andFrenklach [144] was the second step of the H-abstraction/C2H2-addition sequence which leads from the first to thesecond aromatic ring, i.e. the reaction of the 2-phenylacety-lene radical followed by cyclization. Potential energybarriers of the last reaction were estimated on the basis ofanalogous reactions. Molecular parameters used in thisstudy were corrected to reproduce available experimentaldata. The results obtained by Wang and Frenklach [144]support the hypothesis that reactions of multi-ring aromaticspecies are in principle similar to those of benzene andphenyl. Nevertheless, due to the limited reliability ofsemi-empirical quantum mechanical techniques, additionalwork, e.g. using higher-level computational methods, isnecessary in order to obtain kinetic property values of asufficient level of confidence.

In addition to PAH growth via H-abstraction/C2H2-addition sequences, other pathways may be important forthe growth to larger and larger PAH. The potential role ofcyclopentadienyl has been studied [98], discussed aboveand, similar to benzene formation via propargyl (C3H3)units, the contribution of phenyl-substituted propargylmolecules to the formation of larger polycyclic aromaticspecies (Fig. 19) has been suggested by Stein et al. [91].Formation of biphenyl via the two subsequent reactions ofphenyl with propargyl (Fig. 19) as well as naphthaleneformation via the reaction of benzyl with propargyl hasbeen included in the kinetic model developed by D’Annaand Violi [145] and tested against experimental datameasured at atmospheric pressure in slightly sooting lami-nar premixed ethylene–oxygen flames. The model takesinto account PAH containing up to three rings and threedifferent sub-mechanisms are tested: (a) reactions involvingH-abstraction/C2H2-addition to aromatic radicals; (b) thereaction of species containing five-membered rings leadingto naphthalene and phenanthrene, i.e. the cyclopentadienylpathway; and (c) the propargyl pathway. Comparison of thenet formation rates shows a dominant role of the cylcopenta-dienyl and, in particular, the propargyl pathway. The authorsconclude that H-abstraction/C2H2-addition sequences are notsufficient to account for PAH concentrations observed

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experimentally. Braun-Unkhoff et al. [146] studied sootformation in laminar premixed ethylene/air high-pressureflames and in comparisons of model predictions with experi-mental data they also found some evidence of the contributionof additional reaction routes, besides the H-abstraction/C2H2-addition mechanism, in the early stage of soot formation.Bohm et al. [147] modeled the growth of high-molecular-weight PAH at high pressure under pyrolytic shock tube condi-tions and compared the predictions to experimental data. Themodel includedmainly two PAHgrowth pathways, i.e. succes-sive H-abstraction/C2H2-addition and ring–ring condensationreactions of aromatics. Reaction flux analysis indicated amajor role of the latter pathway, especially at early reactiontimes, for both acetylene and benzene pyrolysis. Soot massgrowth rates and the calculated formation rates of PAHshow the same dependence on temperature, an observationwhich confirmed the strong relation of soot mass growth toPAH and soot precursor formation.

One possible set of additional reactions consists in thecontribution of small PAH to the formation of larger andlarger ones. For instance, the dominant contribution ofbiphenyl, the product of the reaction between phenyl andbenzene, for the formation of phenanthrene was shown byFrenklach et al. [125] for the case of shock tube pyrolysis ofbenzene (Fig. 18). Kinetic property values includingpressure dependence for this reaction but also biphenylformation by phenyl recombination have been deducedrecently [148,149]. Other authors included benzene or

phenyl as growth species for fluoranthene

[92,106] and benzo[b]fluoranthene and

indeno[1,2,3-cd]pyrene [106]. Naphthalene and

naphthyl radicals have been considered as growth

species for the formation of benzo[k]fluoranthene

[106]. The contribution of small and medium

PAH to the formation of larger ones has been confirmedexperimentally by means of the pyrolysis of naphthalene[150–152], phenanthrene [153], anthracene [151,152,154,155], pyrene [151,156] and anthracene–naphthalenemixtures [152]. The experimental identification of differentbiaryl isomers and of condensed PAH containing a five-membered ring was explained by all authors in terms of atwo-step mechanism of biaryl formation followed bycyclodehydrogenation. Biaryls and the corresponding cyclo-dehydrogenation products were also identified in premixedlow-pressure naphthalene flames [157]. They are suggestedto be important intermediates in the growth to larger highlycondensed PAH, as shown in Fig. 20 for the case of coro-nene formation. The contribution of PAH to the growth tolarger and larger PAH was also concluded to be importantby Siegmann et al. [158,159] who investigated PAH forma-tion in a laminar diffusion flame of methane using time-of-flight mass spectroscopy. While larger PAH were generallyfound higher in the flame than smaller ones, some PAHhowever deviate from this trend as for example C20H12

which the authors suggest to be formed by reactive dimer-ization of two naphthalene units.

A detailed computational analysis of the potential energysurface of cyclodehydrogenation after biaryl formation hasbeen conducted by Cioslowski et al. [160] choosing 1-phenylnapthalene as reactant. Different competing pathwayscould be identified for the formation of fluoranthene as wellas rearrangements leading to isomers. The relative im-portance of the different pathways depends on conditionssuch as temperature or radical concentrations. Based thestudy of Cioslowski et al. [160], a direct radical mechanismbeginning with hydrogen-loss (or abstraction) then followedby ring closure with hydrogen-loss to fluoranthene is domi-nant at low temperatures. At higher temperatures thesubsequent loss of two hydrogen-atoms yielding toarynes and followed by isomerization through inter-mediates containing carbene-like structures gains

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608 593

Fig. 20. Mole fraction profiles of 1,10-binaphthyl and its consecutive products towards coronene (Griesheimer and Homann [157]).

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increasing importance. Indeed, isomerization reactionshave been reported under pyrolytic conditions[151,153,161–164] and have been included in kineticmodels [92,104–106,165]. Evidence for the thermo-dynamic and kinetic feasibility of the formation poten-tially mutagenic PAH such as cyclopenta[cd]pyrene

by isomerization reactions in a combustion

environment has been shown [166].

6. Formation of fullerenes and their relation to PAH andsoot formation

Fullerenes, a class of all-carbon, polyhedral, closed shellswere identified as ionic species in fuel-rich flat premixedacetylene- and benzene–oxygen low-pressure flames usingmolecular beam sampling coupled to on-line mass spec-trometry [167,168]. Later, the solvent extraction of sootgenerated in premixed laminar low-pressure benzene flamesallowed the identification of macroscopic amounts of differ-ent fullerenes such as C60 and C70 [169–173] but also oflarger ones up to C116 [174]. The yield of C60 plus C70, themost abundant fullerenes, was as much as 20% of the sootand up to 0.5% of the carbon fed under certain conditions[172]. A connection between fullerenes and soot formationwas postulated [175] shortly after their discovery in laservaporization experiments of graphite [176]. The reactionsforming fullerene and soot in carbon vapor may have muchin common with reactions occurring in fuel rich combustion.In fact, onion-like fullerenic nanostructures which areformed along with fullerenes and soot in the graphite vapor-ization method of fullerene production have also beenidentified in soots produced in premixed benzene and acet-ylene by means of high-resolution transmission electronmicroscopy (HRTEM) [177,178].

Recently, the structure of a fullerene-forming premixedbenzene/oxygen low pressure flame has been measured.High resolution electron microscopy [179] and chromato-graphic techniques (GC-MS, HPLC) [180] were used toinvestigate the formation of PAH, soot and fullerenes aswell as the carbon morphology. In the reaction zone of theflame the number of closed-shell structures in the soot aswell as the concentration of fullerene molecules in the gasphase were found to increase with increasing residence time.Beyond a height above the burner of 70 mm, fullereneconcentrations decreased as well as, within the scatter ofthe data, the percentage of the closed-shell structuresobserved between 60 and 120 mm. The transition fromamorphous to fullerenic carbon can be explained by thedeposition of gas phase species, like PAH, on soot particlesfollowed by internal rearrangement of the solid phasecarbon, and by reaction of gas-phase fullerenes with grow-ing soot particles which is consistent with the fullereneconsumption beyond 70 mm above the burner. Highlyordered nanostructures, such as nanotubes and fullerene

onions, appeared to be limited to samples collected asbulk solids from the walls and top flange of the combustionchamber, which indicates that they are formed by internalrearrangement processes occurring in the solid phase carbonon time scales that are much longer than 100 ms. Thisconclusion is in agreement with the formation of closed-shell particles by intense heat treatment of the initially disor-dered insoluble part of fullerene containing soot generatedby electric arc discharge [181].

In contrast to the suggested role of fullerenic structures assoot precursors [175], the results of Grieco et al. [179,180]indicate parallel gas phase growth of fullerene molecules asdetected along vertical trajectories in the flame and thenucleation of young soot particles followed by reactivedeposit of fullerenes on the growing soot particles.

Mainly two pathways explaining fullerene formation inflames have been discussed. In a comment on the proposedrole of spheroidal carbon clusters in soot formation, Frenk-lach and Ebert [182] argue based on kinetic and structuralconsiderations that there is no need to invoke spherical clus-ters to account for soot formation in flames and suggest asequential buildup of “bent”, i.e. curved, PAH containingfive- and six-membered rings leading finally to fullerenes.They argue that “bent” PAH should be less prevalent thanplanar PAH in flames, which is consistent with measure-ments of concentrations of PAH, including corannulene, acurved molecule, in fullerene-forming flames [183,184].

Corannulene represents a substructure of almost

all fullerenes and is therefore of particular interest as a full-erene precursor. Although corannulene is present in detect-able concentrations in atmospheric pressure ethylene–aircombustion in which fullerenes have not been detected, itis found in larger concentrations in low-pressure fullerene-producing benzene flames [183]. The presence of corannu-lene in fullerene-deficient flames was explained by thedominance of oxidative or pyrolytic destruction reactionsthat consume fullerene precursors [183,184]. Consistingwith the picture of competing reactions forming curved orplanar PAH, dicyclopentapyrenes, isomers of corannulene,were only found to be present in fullerene-deficient flames[184].

The kinetic plausibility of fullerene formation by sequen-tial homogeneous gas-phase reaction steps has been shownby Pope et al. [185,186] using a plug-flow reactor computa-tion and experimental species concentrations as input. Theydescribed the formation of C60 and C70 fullerenes startingwith fluoranthene, with growth proceeding by successive H-abstraction/C2H2-addition steps and with corannulene asintermediate. Additional reactions necessary for hydrogenelimination and ring closure, such as unimolecular hydrogenloss or intramolecular rearrangement to ensure proper place-ment of five- and six-membered rings are included in themodel. The investigation of thermodynamic driving forcesfor fullerene formation [187] showed no insuperable ther-modynamic barriers for any of the included reactions. In

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agreement with the experimental findings [170–172], globalequilibrium considerations showed an increase of the peakamount of fullerenes possible at lower pressures. Formationof C60 and C70 fullerenes is thermodynamically favorableonly in a temperature window which is consistent withexperimental temperatures measured in fuel-rich hydrocar-bon flames [69,188] and which is broader at lower pressures.The competition between the formation of curved andplanar PAH was addressed by comparison of the thermody-namic stability of the C30H10 bowl-shaped, “half-bucky”,PAH with that of the corresponding C30Hx planar PAH,where x necessarily exceeds 10. It was found that theC30H10 bowl is favored by high temperatures and low partialpressures of H2 [187].

Formation of C60 and C70 fullerenes via H-abstraction/C2H2-addition sequences was also tested by the modelingof a fullerene-forming laminar premixed benzene–oxygen–argon low-pressure flame at equivalence ratio 2.4. The peakconcentrations compared to experimental measurementswere under-predicted by a factor of 50–100 [106]. Whilethis under-prediction may be explained by the sensitivity ofC60 and C70 yields to kinetic property values [186] which aresignificantly uncertain, the shapes of the predicted C60 andC70 concentration profiles also differed significantly fromthe data and this discrepancy was attributed to the presenceof at least one additional reaction pathway besides sequen-tial H-abstraction/C2H2-addition. For instance, the fuller-enes concentration profiles [180,189] exhibit two localmaxima, the first of which is minor compared to the secondone with regard to the corresponding net amounts of full-erenes formation, and not reproduced by the model. Basedon the evolution of fullerenes, PAH and soot concentrationswith increasing height above the burner, Grieco et al. [180]conclude that the first maximum may involve reactivecoagulation of PAH followed by intramolecular condensa-tion including dehydrogenation, cross-linking, rearrange-ment, and ring formation. In this first region, the measuredtotal rate of consumption of PAH was shown to be morethan large enough to account for the rate of formation offullerenes. Most of the PAH consumption apparently goes to

soot formation and a much smaller fraction goes to fuller-enes formation. Conversely, Grieco et al. [180] concludedthat the second, and much larger concentration maximum,corresponding to a region of much more extensive fullerenesformation, cannot be explained by a pathway involving onlyPAH, whose concentrations in that region are at or below thedetection limit of the analytical equipment, but can beexplained by stepwise acetylene addition to PAH.

Detailed investigations in order to elucidate fullereneformation pathways in flames have been conducted by theHomann group measuring flame structures mostly by meansof online mass spectrometry of ionic [189–193] and neutral[191,194] species. They studied low-pressure premixedflames of acetylene [189,191], benzene [189,191–193],butadiene [191] and naphthalene [190,191] with oxygenusing molecular beam sampling coupled to mass spec-trometry. They attributed an important role in fullerenegrowth to bimolecular reactions between two PAH withconcerted hydrogen elimination, the so-called “zipper”mechanism [189,191,192]. The pathway starts with a sand-wich-like arrangement of twoperi-condensed PAH (Fig. 21)and has the appealing feature forming exactly 12 pentagonsindependently of the size of the PAH provided they are

larger than or equal to coronene . It is well

known that, independently of the size of the fullerenecontaining only pentagons and hexagones, the number ofpentagons is always 12. Simultaneously to the zippermechanism, the pentagons must be brought into the mostenergetically favorable positions [191,192], e.g. via Stone–Wales pyracyclene rearrangement [195]. Some experimen-tal evidence for the zipper mechanism has been observed.Thus, hydrogenated species, such as C60Hx �1 , x , 6�have been identified [190–192], and the shape and locationof their number density profiles are consistent with theirbeing precursors of the corresponding fullerenes. In addi-tion, a new class of molecules, so-called aromers, has beenidentified as negative ions which are suggested as beingproducts of the reactions between two PAH. Aromers arehydrogen-rich PAH species with a relatively low degree ofstructural condensation and direct precursors of fullerenes[192].

The measurement of lateral as well as vertical numberdensity profiles [192,193] in low-pressure premixedbenzene/oxygen flames at equivalence ratio 2.0 revealedadditional information for the assessment and understandingof the competition between fullerene and soot formation.For the equivalence ratio studied, fullerenes are mainlygenerated along a trajectory close to the center-line withno or only very little soot formation while close to the rimof the burner fullerenes concentrations decrease drasticallyand significant amounts of PAH and soot are formed. Thisobservation is attributed to the radial distribution of the flametemperature, being considerably higher close to the center-line [192]. Fullerenes formation necessitates a number ofunimolecular reaction steps, such as cage closure reactions,

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608 595

Fig. 21. Model of the formation of five- and six-membered ringsthrough the connection of two PAH by the zipper mechanism(Ahrens et al. [191]).

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breaking of C–H bonds, intramolecular rearrangements, andis therefore favored at higher temperatures. On the otherhand, if the zipper mechanism stops because of geometricincompatibilites [191], oxidation reactions are fast enoughto prevent these PAH from continuing the growth process tosoot. Conversely, at the rim of the burner, lower tempera-tures favor further growth of PAH, aromers and sootcompared to fullerene formation and prevent PAH andsoot from complete oxidation. The limiting equivalenceratio, and extent of fullerenes formation, above which theformation of fullerenes could occur with no or little sootalong the center-line would be interesting to know.

Different of the MIT group [180,185,186], Homann et al.exclude the formation of fullerenes via a step by step H-abstraction/C2H2-addition pathway due to kinetic considera-tions [189,191] and the absence of experimental evidencefor corresponding intermediate species [191]. Nevertheless,as mentioned above, nearly no PAH could be detected in theflame region leading to the maximum of the fullerenesconcentration profiles [180], observation which led to theconclusion that acetylene may contribute to the fullereneformation process. Fullerene fragments, i.e. bowl-shapedPAH which could be possible intermediates in a sequentialgrowth process have been synthesized by means of high-temperature gas-phase cyclization reactions [196]. Inaddition, concentrations of intermediate bowl-shaped PAHlarger than corannulene may be below the detection limitand therefore not observed experimentally [180].

In conclusion, a combined fullerene formation mechan-ism may be envisioned. Considering the geometric incom-patibility for fullerene growth of most aromers, i.e. productsof reactions between different PAH, reactions with acety-lene may lead to further growth to a molecule with ageometry suitable for cage closure. Also a role for solid-phase reactions has been proposed by Baum et al. [189] whosuggest that young soot particles may be reactors for full-erenes production based on a strong increase of fullerenes

formation at C/O larger than the soot threshold while only asmall gradual increase of the gas-phase concentration ofPAH could be observed. This pathway is in agreementwith the observation of fullerenic structures in soot particlesby high-resolution electron microscopy [179]. In addition,flames suitable for the synthesis of macroscopic amounts offullerenes [169–174] operate at higher C/O ratios thanflames allowing molecular-beam sampling [167,168,189–194]. The formation of soot as well as fullerenes along thecenter-line of flames at higher C/O ratios that producesubstantial yields of fullerenes seems to be likely and there-fore the contribution of condensed phase fullerene forma-tion pathways cannot be excluded.

7. Other soot nucleation models

Although there is considerable evidence that PAH are keyreactants in soot formation and that PAH growth is throughfree radical intermediates, historically other species havealso been considered key soot formation reactants andsome of these are still of interest. Calcote and Gill[197,198] advocate the role of ionic species and point outexperimental evidence that the concentration of PAH undersome conditions continues to increase after the rate of sootformation has gone to zero [197]. They consider free radicalmechanisms to be too slow to account for the rapid sootformation rates in flames and cite the necessity of cyclizationreactions with extensive molecular rearrangements and largeentropy changes as possible explanations. The alternative theysuggest is an ionic mechanism, shown schematically in Fig.22. It is generally accepted that ion-molecule reactions arefaster than similar reactions involving radical species. Somequantitative testing of the ionic mechanism has been done[198] but definitive conclusions may be limited by the currentknowledge of thermodynamic and kinetic data for ionicspecies. Also, some of the steps of possible ionic pathwaysleading to aromatic species (Fig. 22) do not appear to havebeen discussed in sufficient detail for quantitative testing.Recent free radical mechanisms reflecting the current knowl-edge of PAH growth have not been used in the assessment ofpossible contributions of ions [198]. Ionic species have beenfound to be absent in soot-forming but oxygen-free shock-tube pyrolysis of hydrocarbons [199].

However, this finding does not exclude the possibility thationic pathways to soot formation might be important underother conditions. The further development of a detailedkinetic modeling including ionic species will be necessaryin order to assess quantitatively their role.

The role, at least under certain conditions, of aliphaticspecies in the soot nucleation process has been discussed[49,50] and reaction pathways involving polyacetylenes(polyynes) have been suggested (Figs. 2 and 3) Recently,a kinetic model based on polyynes as growth reactants hasbeen developed and tested against experimental data fromthe pyrolysis of a set of hydrocarbons including methane,

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608596

Fig. 22. Ionic mechanism of incipient soot formation (Calcote[197]).

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acetylene, ethane, and benzene [129]. Krestinin [129] pointsout that the thermodynamic stability of acetylene and poly-ynes C2nH2 �n� 2; 3;…� grows as the temperature increaseswhereas the stability of all other hydrocarbons decreases.The model starts with the fast polymerization of “super-saturated polyyne vapor” and continues with polymericgrowth and, finally, pyrolytic carbon formation. Polymericgrowth consists of polyyene addition to radical sites and theformation of aromatic structures seems to be assumed.Based on the high concentrations of polyynes, observedexperimentally [47,69], the assessment of their contributionto soot formation is appealing, but the currently suggestedmodel [129] does not include sufficiently detailed chemicalreaction pathways to allow thorough assessment of itsconsistency with experimental observations. In particular,the chemical identity of the soot nuclei is not defined andelementary reaction steps involved in their formation are notdiscussed. Nevertheless, the possible contribution of ali-phatic species to soot formation deserves further attention.

The possible role of aliphatic molecules or of aliphaticside-chains attached to aromatic species in the soot nuclea-tion step has been investigated by McKinnon et al. [200].The ratio of the aromatic to aliphatic C–H stretch infraredabsorption peak heights was measured in soot samplescollected from a premixed benzene/oxygen flame at differ-ent heights above the burner and extracted with dichloro-methane. A growing aromatic character was observed withincreasing height above the burner followed by a dropbeginning at the soot inception zone, similar to the profileof total PAH measured by optical absorption. The increasingaliphatic character of the samples after the beginning of sootinception was interpreted as being related to the cleavage ofaliphatic side chains forming reactive PAH radicals whichcombine rapidly to form soot nuclei, thereby becoming partof the dichloromethane insoluble material.

8. Impact of thermodynamics

Detailed kinetic modeling requires the use of reversibleelementary reaction steps with the ratio of the rate constantsof forward and reverse reaction determined by the equi-librium constant, i.e. by the thermochemical properties ofthe species involved.

Forward and reverse reaction fluxes of elementary reac-tions contributing to aromatics mass growth are often tightlybalanced [93] and it has been shown by Frenklach andWarnatz [63] that uncertainties in the thermochemical datacan affect significantly PAH concentration profiles in thepost-flame region. The calculation of equilibrium concen-trations of flame species in general and of PAH in particularand their comparison with experimentally measured concen-trations allows assessment of the degree to which thermo-dynamic equilibration is reached in flames at specifictemperatures, residence times or other conditions. Thermo-dynamic considerations allow the potential feasibility of

reaction pathways to be determined before the use ofcomplex kinetic models and can guide the experimentalsearch for yet unidentified species. The investigation of ther-modynamic driving forces for fullerene formation [187],discussed above, is an example of this approach.

An essential condition for a correct assessment of ther-modynamic factors is the availability of sufficient thermo-dynamic data. The estimation of thermodynamic propertiesby means of additivity rules [201–204] is an appealing tech-nique because of its ease of application. Groups are definedand characterized by their inner-molecular chemical envir-onments such as connected bond types, and the thermody-namic property values they contribute are assigned based oninformation on molecules for which reliable data are avail-able. Thermodynamic property values of another moleculecan be determined by composing its structure using thepredefined groups. The implementation of this approach incomputer codes [205] allows the straightforward predictionof heats of formation, entropies and heat capacities at differ-ent temperatures as well as the generation of data basescompatible with chemical kinetics simulation softwaresuch as CHEMKIN [29]. Essential to the quality of thethermodynamic property values derived by group additivityis of course the availability of accurate data on which to basegroup values. Groups for PAH were first defined for speciescontaining only six-membered rings [202–204] and werethen extended to species containing also five-memberedrings [206,207].

The development of suitable theoretical tools togetherwith the evolution of computational power led in recentyears to an increasing use of direct calculation of thermo-dynamic properties. Two types of approaches commonlyused are: molecular mechanics [208,209] and quantum-mechanical techniques, the latter ones including semi-empirical [210–213] and ab initio [214] ones. Herndon etal. [215] compared heats of formation of a large number ofcondensed PAH obtained with different group additivity,molecular mechanical and semi-empirical approaches,and, where available, experimental data. They concludedthat molecular mechanics offers a reasonable predictivecapability for the relative stabilities and heats of formationof both planar and non-planar polycyclic benzenoidaromatic hydrocarbons. In comparisons using experimentalmeasurements, Herndon et al. [215] showed the semi-empirical technique they used to be unreliable for precisepredictions ofDHf

0. They also showed for the investigatedclass of species, applicability of group additivity using aparameterization based on molecular mechanics calcula-tions including resonance energy. In agreement with thefindings of Herndon et al. [215], Pope and Howard [216]found a molecular mechanics technique, compared to othermethods, to most accurately predict heats of formation ofC60 and C70 fullerenes as known from experimental data.They deduced new groups for fullerenes and their precursorsbut found limitations of their group additivity approach intrying to account for curvature-induced ring strain and H–H

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repulsion which become noticeable in the nearly-completedcage structures. In the same work [216], relative results ofsemi-empirical techniques were shown to be consistentcompared to molecular mechanics, and therefore theviability of group-corrected semi-empirical techniques asdeveloped by Wang and Frenklach [217] was supported.The need for reliable thermodynamic property data for radi-cal species, essential for the description of the PAH growthprocess, also requires the use of other techniques in additionto the molecular mechanics approach which is not suitablefor the treatment of radicals.

Using ab initio quantum-mechanical computations, Pecket al. [218] determined heats of formation by a least-squaresfit of experimental heats of formation to the ab initio ener-gies. The root-mean-square error inDHf

0 for the training setwas only 0.7 kcal mol21, indicating the potential forextrapolation to other, mostly larger, PAH for which noexperimental heats of formation are available. A significantadvantage of this approach compared to group additivity isthe use of ab initio energies which are computed for themolecules of interest and therefore account for their specifi-cities. Ab initio quantum-mechanical techniques are usedmore and more extensively for the determination of mole-cular properties [77,87,88,98,107,108,135,137,143,148,149,160] including those of transition states, necessary forkinetic calculations. These techniques seem to be becomingthe method of choice, although the computation timerequired for the large PAH of interest as soot precursors isas yet prohibitive.

Stein [219] investigated the high temperature chemicalequilibria of PAH with acetylene and H2 over a temperaturerange from 1400 to 3000 K. In addition, equilibriumconstants for benzene polymerization, i.e. for global reac-tions from benzene to PAH1 nH2 were deduced in hisstudy. A chemical thermodynamic analysis of hydrocarbon

molecules from 1500 to 3000 K is presented by Stein andFahr [220] for species C2nH2m, n� 1–21,m� 1–8. Groupadditivity was used as the primary estimation method for theidentification of the molecular structure and chemical ther-modynamic properties of the most stable isomers, the “stabi-lomers” [221]. Stein and Fahr [220] discussed stabilities ofC2nH2m in terms of their hypothetical equilibrium concentra-tions in the reactionnC2H2 Y C2nH2m 1 �n 2 m�H2: Rela-tive concentrations were shown to depend significantly onthe partial pressure of acetylene and H2. At higher H2/C2H2

ratios (< $ 1) most species are PAH and a free energybarrier appears in the range 1400–1800 K which increasessharply with increasing temperature. At lower H2/C2H2

ratios, many smaller species are acyclic, and as this ratiobecomes smaller the barrier declines and becomes lesssensitive to temperature.

Lam et al. [222] applied the Stein and Fahr [220] stabi-lomers concept for the comparison of predicted C2nH2m/C2H2 ratios with experimental ones measured in anatmospheric pressure jet-stirred/plug-flow reactor. Thechemical structures identified by Lam et al. [222] usinggas chromatography are shown in Fig. 23 and, except forethynylacetylene (C14H8), they are the stabilomers predictedby Stein and Fahr [220]. The comparison of experimentalwith predicted C2nH2m/C2H2 ratios showed that equilibriumis attained or close to being attained for all measured poly-acetylenes, benzene and phenylacetylene. PAH concentra-tions are significantly below the equilibrium values, andmore so with increasing molecular weight, but rapidlyincreasing toward the equilibrium values with increasingtime in the plug-flow reactor.

The importance of thermodynamic considerations as wellas the applicability of the stabilomer concept of Steinand Fahr [220] has been confirmed by the analysis ofsamples from laminar ethylene diffusion flames using laser

H. Richter, J.B. Howard / Progress in Energy and Combustion Science 26 (2000) 565–608598

Fig. 23. Chemical structures of the most abundant PAH species observed experimentally which are the stabilomers as predicted by Stein andFahr [220], with the exception of ethynylacenaphthalene, C14H18 (Lam et al. [222]).

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microprobe mass spectrometry (LMMS) [223,224]. Thecomparison of the mass spectra of identical ethylene andC2D4 flames allowed the unambiguous identification of therelative amounts of carbon and hydrogen (CxHy) [223]. Themajor species identified are treated in the thermodynami-cally allowed space of the stabilomer grid as predicted byStein and Fahr.

Alberty [225,226] investigated equilibrium distributionsof PAH in the benzene flame studied experimentally byBittner and Howard [69]. Using analytical expressionsrepresenting thermodynamic equilibrium, Alberty showedthere to be a correlation between equilibrium predictionsand the experimentally measured concentration profiles.For instance, the experimental concentration profiles ofthe PAH C10H8, C14H10 and C16H10 exhibit maxima atabout 8 mm above the burner. Alberty showed that theconcentrations of these species that would be in equilibriumwith benzene, acetylene and H2 decrease sharply withincreasing height above the burner, passing almost exactlythrough the peak values of the experimental profiles. Thusthe equilibration of these PAH with benzene, acetylene andhydrogen is being approached both by the rising PAHconcentrations prior to the maxima and by the fallingPAH concentrations after the maxima, and the equilibrationis achieved at the maxima. The rapid fall in the equilibriumconcentrations with increasing height above the burner isdriven by the profiles of temperature and benzene, acetyleneand hydrogen concentrations. The apparent response of theexperimental concentrations to the equilibrium conditions isindicative of the thermodynamic influence on the chemistryof PAH formation and consumption.

Thermodynamic calculations have been applied to theinvestigation of carbon condensation process in the coolenvelopes of carbon rich supergiant stars [227]. Equilibriumconcentrations of PAH including radicals, which would alsobe of interest for combustion and pyrolytic processes, weredetermined.

9. Future routes of research

The development in the recent years of increasinglysophisticated kinetic models has stimulated significantqualitative and quantitative advances in the understandingof flame chemistry in general and of PAH and soot growthprocesses in particular. Simultaneously, new experimentalmeasures in different combustion environments such aspremixed and diffusion flames, shock tubes, well-stirredand plug-flow reactors have enlarged the data base availablefor the testing and improvement of kinetic models. In addi-tion, kinetic modeling is being extended to high pressuressuch as those in diesel engines, and to extremely highpressures such as those of interest in the oxidation ofwaste materials in supercritical water ($250 bar) [228,229].

As suggested by Westbrook and Dryer [34], the develop-ment of chemical reaction mechanisms describing the

oxidation or pyrolysis of fuels of increasing complexitycan be considered as a hierarchical process. The reactionnetworks developed for simple fuels, i.e. consisting ofsmall molecules, are sub-mechanisms of the reaction setsnecessary for more complex ones. Thus, the CO–H2–O2

reaction mechanism is part of the formaldehyde oxidationmechanism, and the CH2O mechanism is in turn part of themethane oxidation mechanism. This process can be contin-ued through C2 and C3 species and so on, building eachmechanism on a foundation of reaction mechanisms forsimpler molecules [34].

Nevertheless, the development of kinetic models cannotbe limited to the addition of more and more species andreactions. Assumptions and conclusions reported in theliterature based on the knowledge at the time of the publica-tion must be continuously checked against new data as theybecome available. An example of the necessity of this care-ful approach is the possible role of vinyl radicals (C2H3) inthe growth process of PAH as initially suggested by Frenk-lach et al. [125]. An uncertainty of about5 kcal mol21 forthe heat of formation of C2H3 persisted for a long time, butnew experimental data were eventually obtained [230] and arecent compilation [231] suggestsDHf

0� 71.5^ 1.2kcal mol21. In addition, recent experimental and theoreticalwork has improved significantly the knowledge of thekinetic properties of elementary reactions involving thisspecies. For instance, the temperature and pressure depen-dence of the reaction C2H3 1 H was studied theoretically[232], allowing the assessment of the competition betweenthe formation of C2H2 1 H2 and C2H4. Also the kinetics ofunimolecular decomposition of vinyl has been studied indetail [233] and will contribute to a more accurateassessment of the role of vinyl in PAH growth at differenttemperatures and pressures.

Ethylene and methane are important components of manypractical gaseous fuels as well as important intermediates inthe breakdown of higher molecular weight fuels. Newkinetic property data describing these species, e.g. theirreactions with hydrogen-radicals [234], should be consid-ered as they become available and existing kinetic modelsshould be checked for consistency with new data. Anotherclass of reactions is radical–radical reactions, for whichkinetic measurements are difficult and kinetic propertydata are rather scarce. An example of such reactions isCH3 1 C2H3 [235], in which both reactants are abundantunder many conditions.

Another important issue is the pressure dependence ofunimolecular and many bimolecular reactions. Differenttheoretical treatments [236–238], all based on the pioneer-ing work of Rice and Ramsperger [239,240] and Kassel[241], or RRK theory, allow the calculation of rate constantsof chemically activated reactions at different pressures. Twoof the methods in particular, described below, are used forthe treatment of the pressure dependence of rate constants.

The quantum Rice–Ramsperger–Kassel approach(QRRK) [72,74,242–244] employs the assumption of

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random energy distribution between the different, mainlyvibrational, degrees of freedom and is characterized solelyin terms of incremental energy levels, i.e. in the case ofvibrations, multiples of hn where h is Planck’s constantandn is the characteristic vibrational frequency. Reactionto products, dissociation back to reactants, or isomerizationoccurs when a specific reaction coordinate contains suffi-cient energy, i.e.$Ea where Ea is the activation energy,and with a rate depending on the corresponding energydistributions. QRRK analysis has been used successfullyfor the prediction of rate constants of reactions relevant tocombustion and pyrolysis such as radical addition andrecombination reactions [74] or benzene formation path-ways [72]. Recently, the QRRK approach has beenimproved significantly [245]. Multiple wells are includedwhich allows the investigation of complex isomerizationsequences. For each well, the distribution of vibrationalenergy can be approximated by three frequencies. TheenergyEi of one vibrationn i is expressed byEi � kihni

whereki is the quantum number. All combinations ofk1,k2 andk3 that give the total energyE are taken into account,as well as the degeneracies of the three frequencies. In addi-tion, the use of a higher-order approximation for the effi-ciency of collisional deactivation allows uncertainties to bereduced, in particular for larger molecules.

The RRKM theory [236–238,246] is a refinement devel-oped by Marcus of the initial RRK model. A main feature ofthe RRKM approach is the inclusion of an activatedcomplex (transition state) between the energized moleculeand the products of the reaction instead of allowing directreaction of the energized molecule, depending on the avail-able energy, as in the RRK model. In the recent years, theuse of the RRKM technique for rate constants relevant tocombustion and pyrolytic processes has been largely for thedetermination of the pressure-dependence of reactions suchas phenyl radicals with acetylene [143], ethylene [247], O2

[248], or benzene [148], or the recombination of two phenylradicals [149]. A systematic RRKM treatment has beenperformed by Wang and Frenklach for reactions involvedin the growth process of PAH [144] and implemented intheir kinetic model [93].

More sophisticated treatments of the pressure dependenceof kinetic properties are based on master-equationapproaches, i.e., the description of the evolution with timeof a physical system consisting ofN discrete energy levelsby means of a set of complex integro-differential equations[236]. In recent master equation analyses of isomerizationand decomposition reactions, Tsang et al. [249–252] haveshown that some unimolecular and chemically activatedreactions, in particular at high temperatures or low pressuresand in the case of low reactions thresholds, are characterizedby non-steady-state behavior. Thus the characteristic time ofreaction becomes comparable with or shorter than the timerequired for the population energy distribution to achieve itssteady state. In such cases the notion of time-independentrate constants becomes invalid and the division of the over-

all population of the affected species into virtual compo-nents has been suggested in order to take into account thisbehavior in complex kinetic schemes [252].

An increasing amount of experimental data on PAH hasbecome available over the last four or so decades withincreasingly detailed information. An important recent addi-tion to the data are concentration profiles of aryl radicalsmeasured by Hausmann et al. [253] using nozzle-beamsampling with radical scavenging. This type of data willallow assessment of the contributions of different PAH radi-cals in growth reactions.

The increasing availability of experimental speciesconcentration measurements and kinetic property datawill allow PAH and soot formation to be described ona more and more elementary reaction level. The sizeand complexity of such reaction networks make theidentification of all significant reactions difficult.Improved systematic and efficient methods are needed.Encouraging progress has been made recently in thedevelopment of algorithms for the computer generationof reaction schemes [254]. In order to include in anappropriate manner in complex reaction schemes thekinetic property data of increased accuracy, moreprecise fits than the currently used Arrhenius or three-parameter expression may become necessary. A possibleway to overcome the deficiencies of conventional fits isto approximate rate constants using Chebyshev expan-sions. Over a specific interval of temperature andpressure the rate constants is approximated as a finitesum of global basis functions, namely Chebyshev poly-nomials [255,256]. An interface which allows the incor-poration of this technique in CHEMKIN [29] andtherefore its use for chemical-kinetics simulations ofsystems such as premixed flames [30], well-stirred[31] and plug-flow [32] reactors and shock waves [33]has been developed [256]. This approach has the signif-icant advantage that a kinetic model can be used forapplications at any pressure in the range for which theChebyshev approximation has been performed. A relatedtechnique based on damped pseudo-spectral functionalforms that with the same number of parameters leadsto approximations as, but of higher accuracy than, apure Chebyshev expansion has been suggested recently[257].

10. Conclusions

Considerable progress in the qualitative as well as quan-titative understanding of the growth steps occurring incombustion processes and leading finally to the formationof soot particles has been made during recent decades. Anincreasing body of experimental data has become availableand the use of kinetic modeling has allowed the quantitativetesting of the role of suggested reaction pathways. Thus, theimportance of propargyl (C3H3) for benzene formation and

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of cyclopentadienyl (C5H5) for naphthalene formation undercertain conditions has been shown. The continuing investi-gation of elementary reactions using experimental andtheoretical techniques has helped to increase the reliabilityof the kinetic data included in reaction networks. An essen-tial task for further work will be the construction of consis-tent thermodynamic data bases using computational andexperimental methods. Elementary reaction steps contribut-ing to the formation of larger and larger polycyclic aromatichydrocarbons (PAH) are often thermodynamically limitedand therefore even small uncertainties in thermodynamicdata can preclude the accurate assessment of the feasibilityof a suggested reaction pathway. Additional experimentaltechniques, such as the Homann method of nozzle-beamsampling with on-line radical scavenging [253], are neededto distinguish between different radical sites so as to be ableto test more and more refined kinetic models against exper-imental data. The further improvement of the predictivecapability of kinetic models under different experimentalconditions such as different fuel compositions, temperaturesor pressures will also allow the application of kinetic model-ing to combustion or pyrolytic processes of industrial rele-vance. Given the enormous complexity and size of thereaction networks involved in these processes and the everincreasing demand for more refined predictive capability, asfor example in the control of PAH and soot emissions fromengines, an ever increasing number of reactions will have tobe considered and more efficient systematic methods foridentifying the most significant reactions will be required.In response to this need, encouraging progress has beenmade recently in the development of algorithms for thecomputer generation of reaction schemes.


We are grateful for financial support from the ChemicalSciences Division, Office of Basic Energy Sciences, Officeof Energy Research, US Department of Energy under grantDE-FG02-84ER13282, and from the National Institute ofEnvironmental Health Sciences, MIT Center for Environ-mental Health Sciences and the US Environmental Protec-tion Agency, MIT Center on Airborne Organics.


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