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Proceedings of the Combustion Institute, Volume 29, 2002/pp. 23072314

NUCLEATION OF SOOT: MOLECULAR DYNAMICS SIMULATIONS OFPYRENE DIMERIZATION

CHARLES A. SCHUETZ1 andMICHAEL FRENKLACH2

1Department of Mechanical EngineeringUniversity of California, USA

2Environmental Energy Technologies DivisionLawrence Berkeley National Laboratory

Berkeley, CA 94720, USA

Experimental and numerical studies indicate that particle coagulation plays an important role in sootformation. However, to date, neither method has been able to conclusively determine the stage at whichchemical precursors begin to coalesce. In the present study, molecular dynamics (MD) with on-the-fly

quantum forces was used to investigate binary collisions between pyrene molecules. The molecular struc-ture and internal motion were treated explicitly. Most of the runs were performed at 1600 K, within thetemperature window of soot nucleation in flames. The MD simulations were successful in producing dimers

with substantial collisional frequency and lifetimes far exceeding the equilibrium-based predictions, dem-onstrating that pyrene dimerization is physically realistic in flame environments. The principal finding ofthe present study is the development of internal rotors by colliding pyrene molecules, the phenomenonresponsible for stabilization of the forming dimer. Analysis of the MD results shows that the mechanismof stabilization is rooted in the pattern of energy transfer. The translational energy of the individual collidingmolecules is trapped in internal rotors that emerge upon collision and in the vibrational modes of thedimer, including the van der Waals bond established between the pyrene molecules. This model extendsthe view of stabilization of aromatic species dimerization, with the implication that aromatic dimers ofspecies as small as pyrene can survive long enough to evolve into soot nuclei.

Introduction

Particle inception is the least understood processof soot formation in hydrocarbon combustion. It is

widely accepted that gaseous precursors to solid sootparticles are polycyclic aromatic hydrocarbons(PAH) [16]. However, the understanding of thistransformation in mechanistic terms is far from com-plete.

One may consider the initial phase of the nuclei

formation aspurely chemicalgrowth: aromatic pre-cursors grow in size due to chemical reactions, and,by the virtue of the increasing size, the species ac-quire the property of a condensed phase. This pointof view has received support in several recent studies[713]. A purely chemical growth model, tested innumerical simulations, was shown to be able to pre-dict the correct order of magnitude of the incipientsoot particle concentration [9,14], but was found in-sufficient to reproduce the particle size [15]. De-tailed modeling demonstrated that the correct mag-nitude of the particle size requires introduction ofparticle coagulation, beginning with coalescence of

aromatic species [15].From experimental observations, it is well estab-

lished that particle coagulation plays an important

role in soot formation [1,4,16]. It is thus obvious thatregardless of the origin of chemical precursors,sooner or later they begin to coalesce. The questionis, at what stage does the coagulation commence,and what form does it take? The majority of numer-ical studies performed with detailed models of sootformation (see Refs. [1724] and referencestherein)invoked irreversible dimerization of pyrene mole-cules as the initial nucleation step for the condensedphase (although smaller [2527] and larger [28] ar-

omatic species were also employed). From theagreement attained between modeling [6] and ex-perimentspanning over various properties of sootappearance in laminar premixed [18,29,30], laminardiffusion [21,22,26], and turbulent [19] flames along

with stirred-jet [31] and diesel-engine [23,32] com-bustionone can conclude that physical coales-cence of PAH starting at the size of four rings seemsto be adequate to explain soot inception in quanti-tative terms. But is pyrene dimerization at flameconditions physically realistic? Investigation into thisquestion constitutes the subject of the present study.

The choice of pyrene dimerization for initiating

particle nucleation was motivated by the exceptionalthermodynamic and kinetic stability of this mole-cule: in a long chain of tightly balanced reversible

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2308 FORMATION AND DESTRUCTION OF POLLUTANTSAromatics and Particulates

reactions building aromatic species, pyrene is thefirst major island of stability [14]. However, theassumption of irreversible dimerization of pyrene isin conflict with the results of Miller et al. [33]. Theseauthors calculated equilibrium concentrations of

benzene, coronene, and circumcoronene dimers andfound that the estimated values are significantly be-low the number densities observed for small sootparticles in flames. Based on this analysis, they ruledout the possibility that soot nucleation can begin

with PAH dimerization. In a follow-up study, Miller[34] calculated size-dependent lifetimes of PAH di-mers and found that they approach chemical-reac-tion times of aromatic growth at a PAH monomermass 4 times that of pyrene. In his analysis, Miller[34] relied on the equilibrium results of the priorstudy [33], but derived PAH collision rates using tra-

jectory calculations. He found that when the relative

kinetic energy of the colliding molecules is of thesame order as the potential energy well, the mole-cules can orbit one another for more than 75 ps.However, Millers findings precluded PAH dimers

with mass of less than 800 amu from having lifetimeslong enough to contribute to soot nucleation.

In the trajectory calculations of Miller [34], thePAH molecules were assumed to be structurelessballs, attracted to each other through the Lennard-Jones potential. In the present study, we investigatebinary collisions between pyrene molecules, consid-ering the molecular structure and internal molecularmotions, using a technique of molecular dynamics(MD) with quantum forces that are computed on-the-fly [35]. This method allows us to examine, in amore physically realistic way, the dynamics of energytransfer between external and internal degrees offreedom. We chose to focus first on pyrene becauseof its presumed role in kinetic simulations and theoverlap with the work of Miller and coworkers[33,34]. The principal finding of the performed nu-merical simulations is that the constituent PAHmonomers of the dimer develop internal free rotors,and this phenomenon translates into substantially in-creased dimer lifetimes.

Theoretical Approach and ComputationalProcedures

Molecular Dynamics with On-the-Fly QuantumForces

MD is the technique of modeling the behavior ofmolecules as a classical system of particles, wherethe particles are the constituent atoms. A potentialfunction is used to determine the interatomic forcesat an instant in time. The motion of the atoms is then

determined by numerically integrating differentialequations expressing Newtons second law. The nu-merical integration is repeated over a large number

of time steps, resulting in the evolution of the systemover a period of time.

In the present study, the semiempiricalparametricmethod 3 (PM3) Hamiltonian [36] was used as theinteratomic multibody potential. PM3 is a member

of the modified neglect of diatomic overlap(MNDO) family of semiempirical quantum mechan-ical methods. Semiempirical methods are quantummechanical in nature, yet they differ fromab initiotechniques in that some of the computationally in-tensive terms of the Hamiltonian are replaced withparameters fitted to reproduce experimental data.Semiempirical potentials are thus computationallymuch faster than ab initio ones and hence suitablefor use in MD. Additionally, semiempirical poten-tials are preferable to empirical potentials becausethey are quantum mechanical modelchemistries andas such should represent atomic interactions more

realistically than empirical force fields.The PM3 Hamiltonian does not explicitly include

dispersion, yet it is parameterized to predict the ex-istence of van der Waals forces. For instance, Stewart[37] showed that PM3 predicts the heat of associationfor the benzene dimer to be 3.8 kcal/mol. This isin good agreement with the ab initio work of Jaffeand Smith [38], who computed a 3.33 kcal/mol bind-ing energy at the MP2/6-311G(2d,2p) level of quan-tum theory, corrected for basis set superposition errorusing the counterpoise method. In the present study,the binding energy of the pyrene dimer was found tobe 4.69 kcal/mol, as obtained in static calculations

with the PM3 Hamiltonian. To our knowledge, noquantumab initiostudy has been carried out on thisdimer, and it is unlikely, even nowadays, to do so at areliable level of theory. From general considerations,the PM3 prediction appears reasonable because thebinding is greater than that of the benzene dimer,showing a moderate increase in binding with themonomer size.

At each time step of MD simulation, self-consis-tent-field convergence of the PM3 wave function

was achieved, providing the potential energy and theinteratomic forces of the system. The numerical in-

tegration was performed using the predictor of Bee-mans predictor-corrector method [39]. By using asimulation time step of 0.5 fs, the total energy of thesystem was maintained constant to within 1 kcal/mol per 10 ps of simulation time. Further details ofthis MD technique can be found in Ref. [35].

Collisions of Aromatic Molecules

Prior to the simulation of a collision, the pyrenemolecules were vibrationally equilibrated at thesimulation temperature. The molecules were

brought to vibrational equilibrium with a 5 ps MDrun, during which the atomic velocities were re-scaled while the angular and linear momenta of the

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MOLECULAR DYNAMICS SIMULATIONS OF PYRENE DIMERIZATION 2309

Fig. 1. The relative angular momenta of the two pyrenemolecules in simulation 1, about thex(crosses),y(circles),andz(diamonds) axes as indicated. The initial translational

velocities of the molecules were along the x axis.

molecules were held to zero. The velocities were re-scaled using the method of Berendsen et al. [40],

which couples the MD system to a heat bath. Afterthe vibrational equilibration, the molecules were re-laxed with a 1 ps simulation, during which there wasno manipulation of the atomic velocities. This phase

allowed the perturbative effects of velocity rescalingand momenta control to damp out.

Simulation of a collision was initiated by position-ing two vibrationally equilibrated, but rotationallycold, molecules 1517 Aapart and giving them op-posite translational velocities that would result in acollision. The molecules were prepared rotationallycold in order to emphasize the development of in-ternal rotations. The observation of internal rota-tions is a critical aspect of the present study. A col-lection of obvious collision geometries wasinvestigated, including T-shaped, edge-to-edge, and

face-to-face (sandwich). For each of the general ge-ometries, several series of runs were made. The im-pact parameters were varied from zero to greaterthan the collision diameter, in increments of1 A.Additionally, the initial orientations of the monomers

were iterated with rotations of 30 about all threeaxes. The initial translational velocities of each mol-ecule were varied from the most probable velocity,

vmp, assuming a Maxwell-Boltzmann distribution, toas little as 5% ofvmp.

In our study, the instant of collision was definedas the point when the derivative of the intermolec-ular separation with time changed sign from negative

to positive. This marked the instant at which themolecules stopped approaching one another and be-gan to rebound.

Results and Discussion

The technique of MD with quantum forces yieldsmore physically realistic simulations, yet it has amuch higher computation cost than simulationswithempirical potentials. Consequently, this technique

cannot be carried out for long reaction times or fora large number of runs. At present, these limitationsprohibit this technique from being used to establishthe statistics of collisions, which are required to de-termine the steric collision factor. In light of this, theobjective of the present study was to explore the fea-sibility of colliding pyrene molecules sticking, andhence we only focused on some selected collisiongeometries that were most favorable to forming di-mers. The majority of the runs were conducted at1600 K, the temperature of soot nucleation in flames[32]. As a very rough measure, out of about 200 runsat 1600 K, approximately 15% resulted in dimers,

with the majority lasting 28 ps and a substantialfraction lasting longer. Below, we examine two ofthese runs to illustrate the general characteristicsob-served in our study.

Simulation 1

This run began with two pyrene molecules thatwere vibrationally equilibrated at 1600 K, with zeroangular momenta and positioned 17 A apart. Theinitial translational velocity was supplied at 49% of

vmp. The molecules then collided at a simulationtime of 3 ps and remained bound by van der Waalsforces for 17 ps.

When the molecules collided, the relative angularmomenta of the individual molecules, about theirrespective mass centers, increased rapidly. This isdepicted in Fig. 1, which shows that at 3 ps bothmolecules abruptly began to rotate about they axisand more gradually began to rotate about the xand

zaxes. It is also apparent that the molecules exertedtorques on one another, as evidenced by the way therelative angular momentum of each moleculechanged in a discontinuous manner with time.

In terms of energy, the two molecules initially had

a total of 1.71 kcal/mol of translational kinetic energyand zero rotational kinetic energy, as shown in Fig.2. There was a peak in the translational energy,around 3 ps in the simulation time, as attractiveforces accelerated the molecules toward one anotherimmediately before the collision. When the mole-cules collided and become bound, the translationalenergy decreased, and there was a corresponding in-crease in the rotational kinetic energy. This indicatesthat translational energy was transferred to internalrotations on a sub-picosecond timescale. A portionof the translational energy was also transferred to the

vibrational mode between the pyrene molecules, as

evidenced by an oscillation in their intermolecularseparation. As the simulation progressed, the rota-tional kinetic energy increased. Around 17 ps, the

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Fig. 2. The translational and rotational kinetic energy ofboth pyrene molecules in simulation 1.

Fig. 3. A series of snapshots from simulation 2 showinghow the monomers develop internal rotations during theformation of a dimer. Shading of the atoms indicates dis-tance from the observer, and arrows indicate the develop-ing rotations.

Fig. 4. The translational (dashed line) and rotational(solid line) kinetic energy of both pyrene molecules insimulation 2.

rotational kinetic energy reached 6 kcal/mol, ex-ceeding the static binding energy of the pyrene di-mer predicted by PM3. This is a significant amount

of rotational energy; for comparison, the equilibriumenergy of a single free rotor is 1.6 kcal/mol. Shortlyafter that, at 19.4 ps, there was a sharp decrease in

rotational energy and a corresponding increase inthe translational energy. From the center of massseparation, it is clear that at this moment the bindingbetween the molecules was broken.

Simulation 2

In this run, also at 1600 K, the molecules wereinitially separated by 17 Aand each was given aninitial translational velocity of 15% ofvmp. After thecollision, the molecules stayed bound for the re-maining 17.5 ps of the simulation, and there was noindication of the dimer breaking. A sequence ofsnapshots from this simulation is depicted in Fig. 3.The first two snapshots show the initial configurationof the simulation and the onset of rotations as themolecules collided. The progression of snapshotsfrom 10 ps onward depicts how the molecules con-tinued to rotate after the dimer was formed. Thecorresponding translational and rotational energies

of the two molecules are shown in Fig. 4. As in simu-lation 1, there was an increase in translational energyas the molecules accelerated toward one another im-mediately before the collision, at 7.5 ps. Also, in asimilar manner to simulation 1, the collision was fol-lowed by a notable increase in the rotational energyof the system.

Throughout the simulation, there were closelypaired spikes in the translational and rotational en-ergies, as can be seen in Fig. 4. These pairs of spikesindicate that the intermolecular vibrational modeand the internal rotors are coupled to each other.For instance, at 10 ps, immediately after a spike in

the rotational energy, there was a spike in the trans-lational energy, indicating the transfer of energy be-tween the two modes. Similarly, around 18 ps there

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TABLE 1The dimer lifetimes, calculated according to equation 2,for a range of numbers of internal rotational degrees of

freedom (IRDF)

IRDF Lifetime (s)

0 1.2 1014

1 1.3 1012

2 5.5 1010

3 3.0 107

4 7.6 105

5 4.1 102

was a spike in the translational energy immediatelyfollowed by a spike in the rotational energy. These

two examples, of pairs of spikes, seem to indicatethat there is no preferred direction in the energytransfer: energy can be transferred from translationto rotation or vise versa. It is also interesting to notethat while the total energy of the simulation is con-stant, the sum of the energy in the translational androtational modes changes rapidly. This indicates thatthere exists coupling between the A4-A4 bond, theinternal rotors, and the interatomic oscillators. Inother words, it appears that all of the internal modesof the dimer are coupled to one another, thus en-abling rapid accommodation of energy released dur-ing the collision.

Simulations at 1200 K

A series of additional MD simulations was per-formed at 1200 K, with the expectation that the colli-sions would be stickier. However, out of approxi-mately 100 runs carried outat this temperature, neitherthe sticking frequency of colliding pyrene moleculesnor the lifetime of the forming dimers was noticeablydifferent from that observed at 1600 K. The longestobserved dimer at 1200 K was only 12 ps, as comparedto over 17 ps at 1600 K. On the basis of these results,

we conjecture that the probability of dimer formationis not nearly as sensitive to vibrational temperature asit is to initial translational velocity or the collision ge-ometry. In fact, at both temperatures, variations of just1% in the initial translation velocity or 0.5 A in theinitial geometry changed the resulting dimer lifetimeby as much as 10 ps. Thus, while vibrational modes aidin energy redistribution during the collision, the prob-ability of sticking is only a weak function of vibrationaltemperature.

Dimer Lifetimes

As mentioned above, the computational cost of theMD simulations prohibits one from obtaining reac-tion statistics or carrying the calculations long

enough to observe when the dimers fall apart. None-theless, rough estimates of dimer lifetimes can bemade in the following manner.

For a dimer that does not fall apart within thesimulation time, we assume that its internal energy

distribution has equilibrated to the extent that thelaws of statistical mechanics are applicable. In otherwords, we consider the reaction

A A s (A ) (1)4 4 4 2

obeying detailed balance. True thermal equilibriumcan only be attained after multiple collisions with thebath gas. However, we rationalize the present work-ing assumption by the large number of internal de-grees of freedom and the shallow (5 kcal/mol) po-tential well of the dimer. The equilibrium constantfor this reaction can then be expressed as the ratioof partition functions,K1 The par-

2q /q .dimer pyrenetition function of the dimer,qdimer, and therefore theequilibrium constant, increases with the number ofactive internal rotational degrees of freedom. TheMD simulations indicate that rotations of the indi-

vidual pyrene molecules within the forming dimerare activated in all three dimensions. However, thesame numerical results show that not all of theseinternal rotors are activated to the same extent, andone would anticipate that some of these internal ro-tors would be hindered because of the geometry ofthe dimer. In light of this, calculations were per-formed for a range of internal rotational degrees of

freedom. The active rotational modes were treatedas free rotors, and the remaining degrees of freedomwere treated as harmonic oscillators.

WithK1evaluated in this manner, the approximatedimer lifetime was determined as the inverse of thereverse rate of reaction 1,

1 K1s (2)

k k1 1

where k1 and k1 are the rate coefficients of theforward and reverse directions, respectively, of re-action 1. Since it is not currently feasible to find the

rate of dimerization from the statistical sampling ofMD simulations, the forward rate was assigned to bethe gas-kinetic rate. With the assumptions made,equation 2 gives an upper bound for the dimer life-time.

The results of these calculations are summarizedin Table 1. They show that every additional internalrotational mode increases the dimer lifetime byroughly 2 orders of magnitude. The predicted life-time of a dimer with only external rotations is ex-tremely short, just 12 fs. However, the MD simula-tions produced many dimers that survived for amuch longer time, more than 10 ps. Even consid-

ering that the steric factor would likely reduce thecollision frequency,k1, by 1 or possibly 2 orders ofmagnitude, the dimer lifetimes observed in the MD

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simulations are much longer than the ones predictedby a thermodynamic model without internal rotors.This strongly suggests the appearance of internal ro-tations in PAH dimers.

To serve as a soot nucleus, a pyrene dimer must

survive until collisions with surrounding gases en-sue. The collision rate of a single dimer with thebath gas molecules, like N2, at 1600 K is on theorder of 1 1010Ps1, wherePis the gas pressurein atmospheres. Thus, a dimer must survive forabout 1 1010/Ps before the onset of collisions.At 10 atm, a midrange pressure of diesel combus-tion, this amounts to 10 ps, definitely shorter thanthe duration of the dimers we observed in the MDsimulations. Furthermore, according to the resultspresented in Table 1, the 10 ps lifetime can beattained with two free internal rotors. Based on theMD simulations, such an expectation is quite rea-

sonable. For instance, the results depicted in Fig. 1show that each molecule has significant angularmomentum about at least one axis. It is conceivablethat the dimer could have up to five internal rota-tional modes, and having at least two is extremelylikely. With three internal rotors activated, which isstill a distinct possibility, the dimer lifetime ap-proaches the chemical reaction times of aromaticsgrowth [15]. These observations suggest that py-rene dimers can survive long enough to participatein the soot nucleation process.

ConclusionsThe results of the MD simulations demonstrate

that pyrene dimerization is physically realistic inflame environments. The MD simulations were suc-cessful in producing dimers with substantial colli-sional frequency and lifetimes far exceeding theequilibrium-based predictions, sufficient to surviveuntil collisions with the surrounding gas ensue. Theprincipal finding of the present study is the devel-opment of internal rotors by colliding pyrene mol-ecules, the phenomenon responsible for stabilizationof the forming dimer. Analysis of the MD results

shows that the mechanism of stabilization is rootedin the pattern of energy transfer. The translationalenergy of individual colliding molecules is trappedin internal rotors emerging upon collision and in the

vibrational modes of the dimer, including the van derWaals bond established between the pyrene mole-cules. The present model extends that of Miller [34],

who proposed an increased stability of aromatic spe-cies dimerization due to the development of an or-biting rotation of one incoming molecule around an-other. However, considering explicitly the molecularstructure and internal motion, with the use of a morerealistic, quantum-mechanical potential, the present

study, while supporting the general notion of rota-tional stabilization, revealed the development of in-ternal rotations. As many of the internal rotors are

seen to be activated, emergence of internal rotationrepresents a further increase in stabilization as com-pared to a single orbiting rotation. The implicationof the increased stability is that aromatic dimers ofspecies as small as pyrene can survive long enough

to evolve into soot nuclei. The effects of varying spe-cies size is the subject of future investigation.

Acknowledgments

This research was supported by the Director, Office ofEnergy Research, Office of Basic Energy Sciences, Chem-ical Sciences Division of the U.S. Department of Energyunder contract no. DE-AC03-76SF00098.

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COMMENTS

J. Troe, University of Gottingen, Germany.There havebeen recent measurements by the CRESU technique,done by Hamon et al. (see Ref. [1] below) on benzenedimerization rates. These have been interpreted by statis-

tical unimolecular rate theory by I. W. M. Smith. It wouldbe useful to compare studies of your type with these in-vestigations, which, at the same time, are realistic, and in-ternally convenient.

Authors Reply.A direct comparison between the workof Hamon et al. [1] and our MD technique would be dif-ficult because our approach is too computationally costlyto allow the calculation of rates, especially at low tempera-tures. In this study, we investigated the feasibility of PAHdimerization at the temperature of soot nucleation inflames. The low temperature dimerization of benzene [2,3]and other aromatics [4,5] is an interesting problem, and wehope it will be explored further in the future.

REFERENCES

1. Hamon, S., Picard, D., Canosa, A., Rowe, B., and Smith,I.,J. Chem Phys. 112:10 (2000).

2. Spirkoo, V., Engkvist, O., Soldan, et al.,J. Chem Phys.111:2 (1999).

3. Hirata, T., Ikeda, H., and Saigusa, H.,J. Phys. Chem. A103:1014 (1999).

4. Gonzales, C., and Lim, E., J. Phys. Chem. A 104:2953

(2000).5. Joireman, P., Ohline, S., and Felker, P.,J. Phys. Chem.

A102:4481 (1998).

John C. Mackie, University of Sydney, Australia.Arethere low-frequency ring puckering modes with which the

internal rotor can exchange energy? How is vibration-vibration transfer handled?

Authors Reply.In our MD simulations, atomic motionis entirely due to the interatomic forces computed by themultibody potential energy function. This means that all ofthe normal mode vibrations are included. In this way, en-ergy exchange between low-frequency vibrational modesand rotational modes and between distinct vibrationalmodes is automatically included in MD simulation.

Frank Behrendt, Technical University of Berlin, Ger-many.Does the potential you used allow for collisions ofthe dimers with a molecule of the bath gas?

Authors Reply.The PM3 potential has parameter setsfor 29 chemical elements, including N. In fact, this is oneof the advantages of our techniqueMD simulations caninclude a wide range of chemical species without the needfor additional parameterization. While outside of the scopeof the present study, it is entirely possible to use this MDtechnique to simulate a collision between a pyrene dimerand a bath gas molecule like N2.

Albert Wagner, Argonne National Laboratory, USA.Why did all your trajectory runs have a rotationally cold

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initial distribution? If they were rotationally hot, wouldthatinfluence dimer formation?

Authors Reply.Our simulations were initialized with themolecules rotationally cold to better illustrate the devel-opment of internal rotors. Based on the results of HoustonMiller [1], we expected to see rotations as the moleculescollide. The emergence of molecular rotations could bebest observed if the molecules were not rotating prior tothe collision. It is possible that this affects dimerizationbecause the rotational modes of a rotationally cold mole-cule may be able to absorb more collisional energy thanthose of a rotationally hot one. However, according to ourresults, the main effects on dimerization are geometry andtranslational velocity. At equilibrium, pyrene molecules at1600 K rotate roughly 50 degrees per picosecond. In oursimulations, the molecules only translated 23 ps beforethey began to interact. Thus, rotationally hot molecules

would make about half a rotation before the collision.Based on this, we believe that starting the simulations ro-tationally hot should be similar to changing the initial ge-ometry of the molecules. Still, we intend to test the effectof this in future work.

REFERENCE

1. Miller, J. H.,Proc. Combust Inst. 23:91 (1990).

Phillip Westmoreland, University of Massachusetts Am-herst, USA. Previous studies have shown the presence ofgraphitic stacks of several layers within soot particles [1].Those layers are rather larger than pyrene. Is not dimeri-zation (and trimerization and so on) of larger PAH more

consistent with the data?

REFERENCE

1. Wagners, H. Gg.,Proc. Combust. Inst. 17:3 (1978).

Authors Reply.Our study explored the feasibility of py-rene dimerization leading to soot nucleation. Pyrene wasselected for reasons that are discussed at length in the pa-per, and we do not imply that larger PAH play no role innucleation. It should be noted, however, that analysis on

mature soot particles may be misleading. As the particlesevolve, they undergo significant surface growth, a processthat increases the molecular size of the PAH moieties.Thus, even if a soot particle were to nucleate with a pyrenecluster, the particle would ultimately consist of larger PAHspecies [1].

REFERENCE

1. Frenklach, M.,Phys. Chem. Chem. Phys. 4 (2002).

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