Proceedings

Proceedings of the Combustion Institute 30 (2005) 1397–1405

www.elsevier.com/locate/proci

of the

CombustionInstitute

Detailed modeling of PAH and soot formationin a laminar premixed benzene/oxygen/argon

low-pressure flame

Henning Richtera,b,*, Silvia Granataa,c, William H. Greena,Jack B. Howarda,b

a Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USAb Nano-C, Inc., Westwood, MA 02090, USA

c CMIC Department, Politecnico di Milano, 20133 Milan, Italy

Abstract

Combustion-generated polycyclic aromatic hydrocarbons (PAH) and soot particles are of significantenvironmental concern whereas controlled combustion is of increasing interest for the synthesis of carbo-naceous nanostructures such as fullerenic material. Improved understanding of chemical and physical pro-cesses involved in PAH and soot formation is required to correlate operating conditions with emissioncharacteristics. A detailed kinetic model describing the formation and consumption of PAH and soot infuel-rich hydrocarbon combustion has been developed. Using a sectional approach, large PAH and carbo-naceous particles with diameters of up to �70 nm are defined as classes (BINs) covering given mass ranges.Numbers of carbon and hydrogen atoms corresponding to their average masses are assigned to each BIN,accounting for a decrease in H/C ratios with increasing particle size. The model has been successfully testedfor a rich premixed benzene/oxygen/argon flame (/ = 2.4, 10% argon, v = 25 cm s�1, 5.33 kPa). Modelpredictions are compared with published experimental data including mole fraction profiles of individualPAH and concentration as well as number density profiles of soot. Reactions of PAH radicals with PAHand between PAH radicals were found to be the dominant pathway to soot nuclei. Surface growth contrib-utes �75% to the final particle mass, and reaction of acetylene with particle radicals is the major growthpathway. Surface growth reactions are involved in PAH depletion in the postflame zone. Particle coagu-lation involving BINs and BIN radicals significantly contributes to the formation of progressively largerparticles whereas oxidation by OH plays a non-negligible role in their depletion.� 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Soot; PAH; Modeling; Benzene; Combustion

1540-7489/$ - see front matter � 2004 The Combustion Institdoi:10.1016/j.proci.2004.08.088

* Corresponding author. Fax: +1 781 407 9419.E-mail address: richter@mit.edu (H. Richter).

1. Introduction

Many large-scale uses of combustion includingtransportation, power generation, and wasteincineration are major sources of airborne speciesof significant health concerns such as sootparticles and polycyclic aromatic hydrocarbons

ute. Published by Elsevier Inc. All rights reserved.

1398 H. Richter et al. / Proceedings of the Combustion Institute 30 (2005) 1397–1405

(PAH) [1,2]. Fuel-rich combustion is widely usedfor the synthesis of carbonaceous material suchas carbon black [3], and under certain conditions,such as in fuel-rich premixed low-pressure ben-zene flames, fullerenes have been identified in thecondensed material [4,5]. Efficient operation ofcombustion equipment, i.e., minimization of pol-lution, optimization of energy conversion and, insome cases, reproducible synthesis of carbona-ceous material of given characteristics, requireswell-controlled operating conditions. Identifica-tion of such conditions necessitates qualitativeand quantitative understanding of the chemicalprocesses involved in hydrocarbon oxidation, for-mation, and depletion of PAH and soot.

PAH are thought to be key intermediates insoot formation [6–8]. To assess formation path-ways leading to carbon structures of increasingsize, many experimental studies using on-line ana-lytical techniques such as mass spectrometry [9–11], optical methods [11–13] or probe samplingfollowed by chemical or optical analysis [5,12,14]have been conducted. The internal structure ofgrowing soot particles, correlated to macroscopicproperties of the resulting material [3], has beeninvestigated by means of transmission electronmicroscopy [15,16]. At the current stage, the pic-ture of soot formation, consisting in the following,partially parallel processes, is widely accepted: (a)Particle nucleation. PAH of increasing size aremainly formed by sequences of chemical reactionsof radicals of smaller PAH with acetylene, PAHor PAH radicals. At some size, PAH species reactwith each other while individual PAH keep ongrowing; particle inception (nucleation) occurs.(b) Surface growth. Reactions at the surface ofgrowing particles significantly contribute to theaccumulated carbon mass. Such reactions are as-sumed to be similar to those of PAH [7,8], reactivesites are activated by hydrogen abstraction whilegrowth competes with oxidation by O2, OH, andO. Acetylene and PAH are possible growth spe-cies, their relative contributions are likely to de-pend on conditions [11,17–19]. The decline ofthe surface growth rate with increasing particlesize is consistent with the decrease in experimen-tally observed H/C ratios [14,20]. (c) Particlecoagulation. Particle sizes increase further by colli-sion of growing soot particles. Initially, collidingparticles coalesce completely yielding new spheri-cal structures while later they agglomerate intofractal units, i.e., chainlike structures [8].

To gain more quantitative insight, detailedreaction networks describing the formation anddepletion of PAH [21–24] have been extended toparticle formation [25–30]. Most mechanisms arebased on the above outlined scheme, i.e., they as-sume PAH of a certain size to be soot nuclei.However, also rapid polymerization of acetylenewas advocated as route leading to carbon struc-tures of increasing size [30]. Two major concepts

have been applied: the method of moments [25]and the sectional approach [26,27]. In the discretesectional technique, the particle ensemble is di-vided into classes (BINs), properties such as mass,the numbers of carbon and hydrogen atoms areaveraged within each section. An appealing fea-ture of the sectional approach is the similarity ofthe description of gas phase and aerosol chemis-try, they are directly coupled and are both writtenin the common form A + B fi C + D.

2. Objectives and approach

The major objective of the present study was toprovide a reliable predictive tool for PAH andsoot based on a realistic understanding of the for-mation process, using the sectional approach. Dif-ferent from previous work, details of sootinception have been described, and no steady-state assumptions have been made. The currentknowledge on soot formation has been tran-scribed into a reaction network that has beenadded to a detailed kinetic model describing theformation of PAH up to C30H10 and exhaustivelytested in benzene, acetylene, ethylene, and meth-ane flames [22,24,31,32]. The extended modelhas been applied to a fuel-rich premixed low-pres-sure benzene flame (equivalence ratio / = 2.4,10% argon, gas velocity at burner at 298 Kv = 25 cm s�1, and pressure = 5.33 kPa) for whicha large set of experimental data is available. Num-ber density profiles as well as average particlediameters of soot particles have been measuredusing on-line techniques [12] while probe samplingallowed for the subsequent determination of PAHand fullerene concentration profiles [5]. Soot con-centration profiles, connected to number densitiesvia density and size of soot particles, have beenobtained gravimetrically after sampling [5,33].The evolution of the degree of curvature of carbo-naceous material collected in this flame has beeninvestigated using high-resolution electronmicroscopy [15]. Reaction pathway analysis al-lowed for the identification of major soot forma-tion routes under the investigated conditions.

3. Kinetic model

Formation of PAH and soot has been describedin the form of usual gas phase kinetics with main-tenance of mass and elemental balances of all indi-vidual reactions. All model computations wereconducted with the Premix code of the Chemkinsoftware package [34] using the experimental tem-perature profile measured by means of the bright-ness-emissivity method [12] (Fig. 1). A modifiedversion of the gas phase Interpreter [35] allowedfor the handling of molecules with number ofcarbon and hydrogen atoms sufficiently large to

Fig. 1. Temperature profile ([12], right scale): d, mea-sured using the brightness-emissivity method; –––, fit.Ratios between concentrations of radical BINs andcorresponding parent molecules (left scale) in a premixedbenzene/oxygen/argon flame (/ = 2.4, 10% argon,v = 25 cm s�1, 5.33 kPa).

H. Richter et al. / Proceedings of the Combustion Institute 30 (2005) 1397–1405 1399

correspond to soot particles of increasing size. Thereaction mechanism developed in the present workconsists of 295 species, 1102 conventional gasphase, and 5552 reactions describing particlegrowth. It is, together with the corresponding ther-modynamic and transport property data[22,24,31], available on-line [36] and as electronicsupplementary material. At the current stage, noeffort has been made to determine thermodynamicproperties of aerosol species, forward and reversereactions are independently described or reversereactions are neglected.

The number of species of similar mass and thenumber of structural isomers increase quicklywith molecular mass. Therefore, classes (BINs)of very large PAH and of particles covering cer-tain mass ranges have been defined. The averagemolecular mass and the number of carbon andhydrogen atoms are assigned to each BIN. Char-

Table 1Definition of classes of molecules (BINs) describing large PAH

BIN Mass (amu) Cx

1 201–400 C2

2 401–800 C4

3 801–1600 C9

4 1601–3200 C1

5 3201–6400 C3

6 6401–12,800 C7

7 12,801–25,600 C1

8 25,601–51,200 C3

9 51,201–102,400 C6

10 102,401–204,800 C1

11 204,801–409,600 C2

12 409,601–819,200 C5

13 819,201–1,638,400 C1

14 1,638,401–3,276,800 C2

15 3,276,801–6,553,600 C4

16 6,553,601–13,107,200 C8

17 13,107,201–26,214,400 C1

18 26,214,401–52,428,800 C3

19 52,428,801–104,857,600 C6

20 104,857,601–209,715,200 C1

acteristics of the BINs are given in Table 1. Diam-eters, r, have been determined based on theassumption of spherical structures and a densityof 1.8 g cm�3 [3]. Transition from gaseous speciesto particles is expected to depend on conditionslike temperature and pressure. Based on the detec-tion of compounds containing up to �160 carbonatoms in solvent extracts of flame-generated con-densed material [37], BINs 5 and larger are con-sidered as ‘‘particles’’ while BINs 1 to 4 areconceptually treated as ‘‘large PAH.’’ Thisdescription is consistent with the definition of spe-cies with a molecular mass of �2000 amu and adiameter of �1.5 nm as nascent soot particles[11,12] and the definition of soot as ‘‘unextracta-bles’’ in the case of gravimetric determination ofits concentration [5]. Decreasing H/C ratios andthe resulting increase in curvature are inducedby the presence of five-membered ring structuralunits and were found to correlate in many caseswith the formation of fullerenic structures[15,38]. In the present work, maxima of experi-mental particle diameter distributions measuredin one-dimensional premixed low-pressure acety-lene flames [39,40] have been correlated with H/C ratios determined under similar conditions[20]. BINs have been correspondingly defined.

3.1. Particle nucleation

Fast depletion of PAH at the onset of soot for-mation has provided evidence that these two pro-cesses are correlated [5,9,10,12,14]. Exclusiveformation of nascent soot particles by hydrogen-abstraction/acetylene-addition sequences from aninitial seed PAH has been found to be too slow[12], and experimental evidence for the associationof PAH to larger structures has been found using

and soot particles

Hy r (nm) H/C

4H12 0.85 0.500

8H24 1.07 0.500

6H48 1.34 0.500

93H84 1.69 0.435

88H144 2.13 0.371

78H264 2.68 0.339

560H480 3.37 0.308

124H912 4.24 0.292

256H1728 5.35 0.276

2528H3264 6.73 0.261

5088H6144 8.48 0.245

0240H11520 10.69 0.229

00608H21504 13.46 0.214

01472H39936 16.96 0.198

03456H73728 21.36 0.183

07936H135168 26.91 0.167

617920H245760 33.91 0.152

239936H442368 42.72 0.137

483968H835584 53.83 0.129

2972032H1622016 67.82 0.125

1400 H. Richter et al. / Proceedings of the Combustion Institute 30 (2005) 1397–1405

optical techniques [13] and mass spectrometry[10]. Reactive coagulation of stable PAH has beeninvestigated [41] while other authors emphasizedthe role of activation by hydrogen abstraction[7,42]. Most PAH thought to be involved in theformation of soot nuclei have molecular massesof not more than 300 amu [5,12,14]. Such speciesare assumed to react similar to other gas phasespecies [42]. Corresponding to this concept andillustrated in the example of Eq. (1), BIN1 andBIN2 are described to be formed via a total of609 reactions between PAH and their radicals,and between PAH radicals.

ð1Þ

Such reactions do not represent a single step but asequence of elementary steps. H/C ratios decreas-ing with size can be explained by hydrogen losseither via unimolecular reaction or abstractionby other radicals such as H. Reactions betweenPAH units are consistent with the observationin PAH pyrolysis of cyclodehydrogenation, i.e.,formation of PAH dimers followed by ringclosure [43]. At the current stage, these reactionsare treated as irreversible. Based on the structuralsimilarity, rate constants determined forphenyl + benzene [44] and phenyl + phenyl [45]have been used as reference for the correspondingPAH radical–PAH and radical–radical reactions.While activation energies were kept constant forboth types of reactions, pre-exponential factorshave been scaled based on the change in collisionfrequencies (kf, Eq. (2)) relative to those of ben-zene/phenyl + phenyl to take account for the in-crease in reactive sites.

kf ¼ NAd2

ffiffiffiffiffiffiffiffiffiffiffiffi8pRTl

s; ð2Þ

where NA is the Avogadro�s constant, d is the sumof radii, and l is the reduced mass. In addition,BIN1, identical to coronene, is also formed viaacetylene addition to benzo[ghi]perylenyl radicalsfollowed by ring closure and hydrogen loss:

ð3Þ

Confirming the importance of PAH associationfor soot inception, omission of correspondingreactions in the kinetic model developed in thepresent work yielded to underpredictions by twoto three orders of magnitude for particle concen-trations and number densities compared to exper-imental data [5,33]. Reactions of radical BINswith acetylene and PAH as well of stable BINswith PAH radicals are included in the modeland will be discussed below.

3.2. Formation of radicals

All BINs are activated by hydrogen abstractionwith H and OH radicals as well as unimolecularhydrogen loss. Both forward and reverse reactionsare given explicitly in the model. Available kineticdata for benzene and phenyl have been used asstarting point for the determination of rate con-stants of reactions involving BINs of increasingsize. The rate constant determined by Mebel etal. [46] for phenyl + H2 has been used for BIN rad-ical (BINJ) + H2 reactions, assuming similarity ofradical sites in an aromatic environment. Rateconstants, k, for the reverse reactions, i.e.,BIN + H fi BINJ + H2, have been deduced byscaling k of benzene + H corresponding to thenumber of hydrogen atoms. Absence of changesin symmetry has been assumed for all BIN + Hreactions. Based on the expression measured byMadronich and Felder [47] for benzene + OH, rateconstants describing hydrogen abstraction by OHhave been obtained using a similar scaling proce-dure. Finally, the recommendation of Baulchet al. [48] has been used for all BINJ + H reactionswhereas for the reverse reactions, i.e, unimolecularhydrogen loss, rate constants have been adjustedcorresponding to the number of hydrogen atoms.All scaled rate constants are smaller than corre-sponding collision frequencies. Ratios betweenconcentrations of BIN radicals and the corre-sponding parent BINs, computed in the premixedbenzene/oxygen/argon flame investigated here[5,12,15,22,33], are shown in Fig. 1. Consistentwith the shift of the corresponding equilibria, rad-ical BIN/parent BIN ratios increase with size. Be-yond BIN13, BIN radical concentrations in theregion of maximum temperature were even higherthan those of the corresponding parent BINs. BINradical abundances drastically decreased in thepostflame zone due to lower temperatures as wellas H and OH concentrations.

3.3. Growth to particles of increasing size

Parallel to the formation of BINs 1 and 2, di-rect particle precursors, reactions of all parentBINs with PAH radicals and of all radical BINswith acetylene, PAH, and PAH radicals are in-cluded in the model. Acetylene addition to BINradicals (BINJ) forms fractions of the parentBIN, the next larger BIN and of hydrogen,accounting for the definition of BINs as a groupof molecules covering a given mass range, e.g.:

BIN10Jþ C2H2 ! 0:9998408 BIN10

þ 0:0001592 BIN11

þ 0:5414 H: ð4Þ

Stoichiometric coefficients are calculated from theH and C atom balances. Rate constants for this

H. Richter et al. / Proceedings of the Combustion Institute 30 (2005) 1397–1405 1401

type of reactions have been scaled correspondingto the increase of collision efficiencies, based onthe high-pressure limit for 1-naphthyl + acetylene,calculated by means of transition state theoryusing density functional theory [49]. Resultingrate constants for BINJ + C2H2 reactions areequivalent to collision efficiencies of �5 · 10�2

(at 1800 K). Accounting for the fact that the rad-ical–parent ratio for BIN10 at 1800 K has beenfound to be between 1.9 · 10�2 and 5 · 10�2

(Fig. 1), and that these ratios multiplied by5 · 10�2 give 9.5 · 10�4 to 2.5 · 10�3, rate con-stants used for reaction of acetylene with BIN rad-icals are consistent with experimentallydetermined global collision efficiencies for acety-lene-soot reaction of �3–6 · 10�4 between 1580and 1800 K [12,18,50] not distinguishing particlesand radicals. This observation indicates that, in-deed, mainly radicals and not parent soot precur-sors and particulates are involved in surfacegrowth reactions with acetylene. The number ofradical sites per molecule is thought to increasewith its size [7], resulting in faster rate constants,as implemented in the present model. Also, reac-tions of PAH, which are—as acetylene—gaseousin a combustion environment, are assumed to re-quire radical sites. Therefore, only reactions ofBIN radicals with PAH and PAH radicals(BINJ—PAH/PAH–radical) as well as of stableBINs with PAH radicals (BIN–PAH–radical) areincluded in the mechanism. The assumption ofnegligibly slow BIN–PAH reactions is consistentwith the determination of a collision efficiency of�10�8 for fullerene C60-soot reactions under rad-ical poor conditions [51], i.e., relatively low tem-peratures (1023–1273 K) and the absence on theC60 structure of hydrogen or other substitutinggroups allowing for the formation of r-radicals,i.e., localized radicals in opposition to p-radicalsthat are part of a resonance structure. Taking intoaccount previous findings indicating a likely roleof particles in the depletion of PAH in the post-flame zone [22], collision efficiencies, c, forBINJ–PAH/PAH–radical and BIN–PAH–radicalreactions have been estimated to be 0.1 for allBINs larger than BIN2. BINs 1 and 2 are thoughtto have characteristics very similar to those ofPAH, therefore the above-described scaling proce-dure for PAH–PAH radical and radical–radicalreactions has been used. BINJ–BIN and BINJ–BINJ reactions are included in the model, andc = 0.1 was used up to BIN4.

The increase in particle size diameters and thepronounced decrease in number densities in thepostflame zone [12] indicate the importance ofparticle coagulation processes. In course of thedevelopment of the present model, it was foundthat only fast reactions between particles could ex-plain the experimental findings. Accounting for asudden change in properties at the transition fromlarge PAH to first solid particles (BIN5), reactions

between parent BINs have been included in themodel beginning with BIN5. Collision efficienciesfor all BIN–BIN reactions beyond BIN4, includ-ing those involving radicals, have been set tounity. This approach is consistent with the fast in-crease in molecular mass of polarizabilities andtherefore van der Waals attraction forces [52].

3.4. Oxidation

Species concentrations in a combustion envi-ronment are the result of the competition be-tween formation and depletion pathways, andoften there are only small differences betweenboth contributions [21,24,53]. Soot oxidation isthought to be a complex process consisting of asequence of elementary reactions. Oxidation ratesof carbonaceous material were found to signifi-cantly depend on the internal structure, particu-larly curvature [54]. OH was identified to bethe dominant soot-oxidizing species in flames,and collision efficiencies ranging from 0.13 to0.27 were determined for the global reaction[55]. Recently, collision efficiencies were mea-sured for soot oxidation by O radicals and foundto be similar to those of OH [56]. In the presentwork, oxidation by OH and O of all BINsdescribing solid particles, i.e., all BINs largerthan BIN4, has been included in the model usingc = 0.2. Soot oxidation involves loss of CO, anda fraction of the next smaller BIN is formed asshown in the following example:

BIN11þOH ! 0:9999204 BIN11

þ 0:0000796 BIN10þ CO

þ 1:229 H: ð5Þ

This description is consistent with the reportedabsence of particle breakup in the case of oxida-tion by OH [57]. Analysis of the model predictionsof the present work showed the contribution ofoxidation by O to be negligible, consistent withsmall O concentrations in comparison to OH. To-tal omission of oxidation in the model yielded anincrease in final soot concentration, as representedby BINs5 to 20, by more than 25%.

4. Results

The predictive capability of the model ex-tended in the present work has been successfullytested in rich premixed flames for all key speciesinvolved in the particle growth process, i.e., radi-cals such as H and OH, acetylene, H2, and majorPAH [22,24,31]. In the present work, addition ofparticle formation yielded only insignificantchanges in computed concentration profiles inthe reaction zone, not affecting previous modelvalidations. For instance, maxima of PAH molefractions profiles are only reduced by �10% due

1402 H. Richter et al. / Proceedings of the Combustion Institute 30 (2005) 1397–1405

to their role in particle formation. However, pre-dictions show more pronounced depletion in thepostflame zone, confirming the previously postu-lated consumption of PAH by reaction with sootparticles. Less than two-fold discrepancies be-tween computed and experimental peak were ob-served for nearly all PAH, confirming the goodpredictive capability of the model. Comparisonsof model predictions of fluoranthene and ben-zo[a]pyrene in the premixed low-pressure benzeneflame (/ = 2.4, 10% argon, v298 K = 25 cm s�1,pressure = 5.33 kPa) [5] are shown in Fig. 2. Flu-oranthene has been considered as fullerene precur-sor [22] whereas a pronounced mutagenic effect ofbenzo[a]pyrene has been reported [2]. Compari-sons of computed soot concentrations, definedas the sum of the concentrations of BIN5 andall larger BINs including the corresponding radi-cals, with experimental soot concentrations areencouraging (Fig. 3) and should account for dis-crepancies between both available data sets

Fig. 2. Mole fraction profiles in a premixed benzene/oxygen/argon flame (/ = 2.4, 10% argon, v = 25 cm s�1,5.33 kPa). Fluoranthene: d, experimental [5]; –––, modelprediction; benzo[a]pyrene: �, experimental 5· [5]; - - - -,model prediction 5·.

Fig. 3. Concentration profiles in a premixed benzene/oxygen/argon flame (/ = 2.4, 10% argon, v = 25 cm s�1,5.33 kPa). d, experimental, unextracted condensedmaterial [33]; �, experimental, condensed materialinsoluble in dichloromethane [5]; –––, model prediction,sum of BINs5–20 including radicals; and - - - -, modelprediction, sum of major PAH.

[5,33]. The use of identical experimental condi-tions and the use of similar gravimetrical tech-niques by both authors illustrate the range ofpossible experimental uncertainties. A major dif-ference between both investigations is the extrac-tion with dichloromethane of the collectedcondensed material prior to weighing by Griecoet al. [5]. While virtually no extractable materialwas identified beyond 2 cm from the burner [5],some losses during handling and particularly dry-ing might have occurred. The possibility of sucherrors has been minimized in the work of Goel[33] by avoiding extraction but the presence ofsome moisture cannot be entirely excluded. Thesurprisingly high concentrations of condensedmaterial close to the burner measured by Goel[33] can be—at least partially—attributed to unex-tracted PAH. The concentration profile represent-ing the computed sum of 16 most abundant PAH,accounting for nearly all the mass of the PAH in-cluded in the model, is shown in Fig. 3. Formationof gas phase fullerenes [22] is not included in thepresent model but their contribution to the totalmass of condensed material is small in comparisonto the uncertainty of currently available experi-mental data [5,33].

Under the investigated conditions and with themodel developed in the present work, surfacegrowth has been found to contribute �75% tothe final mass of carbonaceous material presentat the end of the postflame zone. For this purpose,computations totally omitting surface growth inthe model have been conducted. Acetylene wasidentified as major surface growth species, con-tributing �90%, the rest of the mass was providedby PAH. However, such conclusions are limitedby the precision of available kinetic data and de-pend significantly on conditions such as PAHand acetylene concentrations.

As shown in Fig. 4 and similar to experimentalparticle size distributions determined in low-pres-sure acetylene flames [39,40], with increasingmolecular mass, maxima of concentration profiles

Fig. 4. Concentration profiles computed for a premixedbenzene/oxygen/argon flame (/ = 2.4, 10% argon,v = 25 cm s�1, 5.33 kPa): BIN5, BIN10, BIN13,BIN16, BIN19, and BIN20.

H. Richter et al. / Proceedings of the Combustion Institute 30 (2005) 1397–1405 1403

of BINs are located further and further from theburner. Depletion after the maximum is more pro-nounced for smaller BINs, no local maximum ispresent beyond BIN17. As shown by reactionpathway analysis, conversion to larger BINs bysurface growth, reactions between BINs or BINradicals, and oxidation by OH contribute to theconsumption of particles. In addition to soot con-centration profiles, also experimental particlenumber densities and average sizes are availablein the premixed benzene flame investigated inthe present work [12]. While the use of in situ opti-cal techniques avoids perturbation of the flame,contributions of gas phase species includingPAH to absorption and scattering as well as theneed to estimate optical properties of particles[12] makes such measurements particularly chal-lenging. In agreement with data [12], model pre-dictions taking into account BINs 5 to 20 and 7to 20, both including radicals, show a continuousdecrease in number densities due to particle coag-ulation (Fig. 5). Underpredictions close to theburner are possibly attributable to experimentaluncertainties due to absorption of smaller parti-cles. Experimental uncertainties are difficult toquantify and not quoted in the original work[12]. The increase in predicted average particlesizes along the flame axis is significantly slowerthan experimentally while improved agreementscould be reached taking into account only BINs7 to 20 (Fig. 5). The d6 (d: diameter) dependenceof scattering might lead to underestimation ofsmall particles in the experimental data but alsoinadequate description of particle coagulation inthe model cannot be excluded. Enhancement ofcollision efficiencies by van der Waals forces tovalues larger than unity has been reported [58],and its effect on number densities and particlesizes will be investigated in future work.

Fig. 5. Number densities and average particle sizes in apremixed benzene/oxygen/argon flame (/ = 2.4, 10%argon, v = 25 cm s�1, 5.33 kPa). Number densities (leftscale): d, experimental [12]; –––, prediction based onBINs 5 to 20 including radicals; and � � �� � �, predictionbased on BINs 7 to 20 including radicals. Averageparticle sizes (right scale): �, experimental [12]; - - - -,prediction based on BINs 5 to 20; and Æ-Æ-Æ-Æ-Æ: predictionbased on BINs 7 to 20.

5. Conclusions

A kinetic model describing formation and con-sumption of PAH and soot has been successfullytested in a premixed low-pressure benzene flame(/ = 2.4, 10% argon, v298 K = 25 cm s�1, pressur-e = 5.33 kPa). The sectional method, i.e., the defi-nition of classes (BINs) of molecules coveringcertain mass ranges to which given numbers of car-bon and hydrogen atoms have been assigned, hasbeen shown to be suitable for the description ofthe growth of carbonaceous material. Reactionsof PAH radicals with PAH and with PAH radicalswere found to be dominant pathways to soot nu-clei. Under the investigated conditions and basedon the developed reaction mechanism, surfacegrowth contributes�75% to the final particlemass,and reaction of acetylene with particle radicals isthe major growth pathway. Particle coagulationinvolving BINs and BIN radicals significantly con-tributes to the formation of progressively largerparticles whereas oxidation by OH plays a non-negligible role in their depletion. However, averageparticle diameters reported in the literature growsignificantly faster than computed ones indicatingthe need for further elucidation. Future work willcomprise the definition of carbonaceous materialwith different H/C ratios (i.e., degrees of curvature)of similar molecular mass and the description inthe model of their formation based on thermody-namic and kinetic driving forces.

Acknowledgments

The authors are grateful to the National Sci-ence Foundation for the financial support underGrant CTS-0123345. One of the authors (S.G.)thanks the Italian Ministry of Education, Univer-sity and Research (MIUR) for financial assis-tance. Professors Ranzi and Faravelli areacknowledged for helpful discussions.

Appendix A. Supplementary data

Supplementary data associated with this articlecan be found, in the online version, atdoi:10.1016/j.proci.2004.08.088.

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Comment

Vadim D. Knyazev, The Catholic University of Amer-

ica, USA. You scaled the rate constants of recombina-tion of PAH radicals according to the collisionfrequency values. Did you also scale the correspondingsteric factors? The probability of recombination uponcollision is likely to decrease with the increasing size ofthe PAH radicals.

Reply. With size decreasing reactivity of large PAHand young soot particles is taken into account by

means of decreasing H/C ratios. Consistent withexperimental findings ([14,20] in paper), H/C ratiosof large PAH and young soot particles are definedto decrease (Table 1) whereas collision frequencies in-crease with size, reflecting the number of radical sitesper molecule ([7] in paper). Steric factors are not nec-essary in such approach.