Chemistry of fullerenes C60 and C70 formation in flames - The Journal

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J. Phys. Chem. 1993,97, 11001-11013

11001

Chemistry of Fullerenes Cm and C ~ Formation O in Flames Christopher J. Pope,Joseph A. Marr, and Jack B. Howard' Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 021 39 Received: July 21, 1993'

A kinetic mechanism is constructed for the formation of fullerenes C60 and C70 in flames, based on types of reactions used in describing growth of polycyclicaromatic hydrocarbons (PAH) and including additional chemical processes needed to describe evolution of the unique structural features of fullerenes. The mechanism consists of types of reactions, each characterized by an approximate rate coefficient, including processes for ring formation (via H atom abstraction, C2H2 addition, and cyclization leading to ring closing), reactive coagulation of aromatic molecules, and cage closing via H2 elimination and ring closing but also allowing for additional processes such as intramolecular rearrangements. Curved PAH, including benzo[ghi]fluoranthene ( C ~ S H I Oand ) dibenzo[ghi,mno]fluoranthene (corannulene, CzoHlo), are likely fullerene precursors. Corannulene is considered a key intermediate in the fullerene formation mechanism. Although alternatives to corannulene as an intermediate are mentioned, the proposed mechanism is based on corannulene and other related PAH of C5, symmetry. Trivial nomenclature for the C5"intermediates is also introduced. Preliminary kinetic testing of the mechanism, using approximate rate coefficients based on analogous flat P A H reactions, shows the mechanism to be plausible within the uncertainties of the rate coefficients and the experimental data on fullerenes formation rates. The predicted fullerene formation times extend over a range that includes the experimentally observed times, and the predicted c70/c60 ratio agrees well with flame data. Predicted fullerene formation rates are increased strongly by increased C2H2 and decreased H2 concentrations and moderately by increased H atom concentrations. Similarities between growth species in flames and carbon vapor systems imply that much of the mechanism may be pertinent to fullerene formation in carbon vapor systems.

Introduction Fullerenes,pure carbon molecules with closed-cagestructures consisting of five- and six-membered rings, have been intensely studied both experimentallyand theoretically since their discovery in 1985.' Fullerenes are formed in vaporization of graphite or diamond (by laser, electric arc discharge, or plasma)2 and in low-pressureflames. Flame-produced fullerenes were observed first in ionic form within the flame3 and later as neutral species recovered in macroscopic quantities4.5 in low-pressure benzene flames. The fullerenes most prevalent in flames are Cm and C70 (Figure l), which are the focus of the present work though the concepts discussed are pertinent to other fullerenes. Previous discussions of chemical mechanisms of fullerene formation have described general features of the proce~s,2.6.~but detailed mechanisms have not been proposed. Fullerene formation in flames is a molecular weight growth process, analogous to polycyclic aromatic hydrocarbons (PAH) and soot formation, which has been extensively studied.*-'' The molecular weight growth reactions are thought to include addition of small molecules such as CzHz to larger aromatic structures, as in PAH growth and soot surface growth. Also included are addition of larger PAH to other such molecules, as in soot particle inception, and to soot, as in another mode of surface growth. Important differences exist between the mechanism of flat PAH formation and that of fullerene formation. To produce fullerenes, curvature is introduced by the inclusion of fivemembered rings (5-rings) in the growing PAH, thereby straining the structure and affecting the energetics. All fullerenescontain, in addition to six-membered rings (6-rings), exactly 12 5-rings. Published analyses of PAH growth sequences are largely concerned with PAH containing only 6-rings (PAH6). However, the existence in flames of PAH-containing 5-rings is well-kna~n12-~~ (Figure 2). Such molecules are already known to account for more than half of the PAH inventory in flames,l6 *Abstract published in Advance ACS Abstracts, September 15, 1993.

b) Go Figure 1. Modified Schlegel projections of (a) Cm and (b) C70. (Many diagrams of the three-dimensional structures have been published, e.g., ref 2. Subsequent figures depicting fullerene precursors are based on these projections.)

and the fraction continues t o increase as more of the PAH in flames are identified by extendingthe analyses to larger molecular ~eights.1~ The 5-rings in flame-generated PAH reported in publications to date are located in the periphery of molecules, as dicyclopenta[cdfg] pyrene, or in partially internal locations not completely surrounded by 6-rings, as in benzo[ghi]fluoranthene. Such molecules do not have the extent of curvature seen in fullerenes but could be converted to strongly curved species by completely surrounding a 5-ring with 6-rings through either ring rearrangements (e.g., dicyclopenta[cdfg]pyrene + corannulene) or the formation of new 6-rings by carbon addition (e.g., benzo[ghi]-

0022-3654/93/2091- 11001%04.00/0 0 1993 American Chemical Society

Pope et al.

11002 The Journal of Physical Chemistry, Vol. 97,No. 42, 1993 I_\

c> C14H8

e> C16H10

d) CisHio

000 Figure 2. Selected five-membered-ring-containing flame PAHI2-l4of possible relevance to fullerene formation: (a) acenaphthalene(CIZHIO); (b) fluorene (C13Hlo);(c) cyclopentIfg]acenaphthalene or pyracyclene (C14HS);(d) 4H-cyclopenta[deflphenanthrene(C15Hlo);(e) fluoranthene (ClsHlo);(f) benzo [ghi]fluoranthene(ClgHlo);(8)cyclopenta [cd pyrene (ClgHlo). (The existence of pyracyclene in flames is not confirmed.) fluoranthene to corannulene by C2H2 addition (see below)). Intramolecular shifting of 5- to 6-rings in PAH has been observed under conditionspertinent to combustion,'*and the formation of new 6-rings which increase the degree of containment of a 5-ring within the molecule would be consistent with the observation of benzo[ghi]fluoranthene along with fluoranthene in flames.19 The curvature of fullerenesis achieved with specific structures within which ring locations are not random. The required arrangement of rings can be achieved by the exact placement of 5- and 6-rings during cage formation, by ring rearrangement during or after cage formation, or by both processes. Another differencebetween fullerene formation and flat PAH growth is the hydrogen content of the final structure being approached; i.e., only the fullerenes are free of hydrogen. The introduction of 5-rings into a PAH structure provides more elements of unsaturation per molecule than is possible for even the most peri-condensed (having the mostly tightly-packed ring structure) PAH6. Among PAH6, the most peri-condensed compounds have the smallest possible number of hydrogen atoms for a given carbon number,20and the number of hydrogen atoms in the molecule increases monotonically with increasing carbon number. In fullerene formation, the number of hydrogen atoms becomes zero as the final structure is attained. A chemical mechanism for the formation of fullerenesCa and C70 is constructedby combining the chemistryof flat PAH growth with the chemistry of the origin of the additionalstructural features of fullerenes. The reactions are characterized using rate coefficients from analogous reactions of flat PAH. For ring-forming reactions that introduce strain into the molecule, use of flat PAH rate coefficients is an approximation. The purpose here is to perform a kinetic test of plausibility of the fullerene formation mechanism.

j>G 2 H l z k) G4Hiz Figure 3. Selected neutral flame PAH6:I2-l4(a) naphthalene (Clds); (b) biphenyl (C12H10);(c) phenanthrene (ClrHlo); (d) anthracene (CMHIO); (e) pyrene (CMHIO); ( f ) benzo[4pyrene (CWH12); (g) t w o [elpyrene (Cd12); (h) pcrylene (CmH12); (i) benzo[ghi]perylene (C22H12); (j) anthanthracene (Cz~Hl2);(k) coronene ( C ~ I Z )(Most . of these compounds have the most peri-condensed structures possible.)

Overview of Molecular Weight Growth Chemistry in Flames and Experimental System Free radical reactions predominate in combustion systems, including those in which fullerenes form, which have temperatures in the fullerene-producing regions of roughly 1800-2300 K. In hydrocarbon combustion, the main process is stepwise (one C atom at a time) oxidation of the fuel to products.2* Premixed flames are described in terms of the equivalenceratio, 4, defined as the actual fuel-to-oxidantratio divided by the theoretical fuelto-oxidant ratio required for complete oxidation of the fuel to, in the case of hydrocarbons, COZand H2O (e.g., for benzene oxygen flames, 4 = 2.5 X atomic C/O ratio). Flames with 4 < 1 are called fuel-lean, and those with 4 > 1 are fuel-rich. The major products are C02 and H20 for 4 < 1 and CO, H2, C2H2, C02, and H20 for 4 > 1. Molecular weight growth appears as a minor pathway in fuelrich flames, leading to the formation of PAH and, if 4 is large enough, soot. After formationof the first aromatic ring, molecular weight growth is believed to occur by successive C2H2 addition to an aryl radical, followed by ring closing to form the next larger PAH. The aryl radicals can be formed by H-abstraction from the parent PAH. Peri-condensedPAH6, and similar structures with one or more 6-rings replaced by 5-rings, are preferentially formed. Figure 3 shows several important PAH6 observed. The critical value of 4 for the onset of sooting for the types of benzene-oxygen flames considered here is 1.9. Large PAH are considered to be intermediates in the formation of soot. The growth of soot particles in flames involves particleparticle coagulation as well as carbon addition to the particles by reaction with molecular ~pecies.22.~3The reactants include small hydrocarbons such as C2H2Z4as well as PAH having from 1 to 10 or

-

Cm and

c70

Formation in Flames

more rings (Le., up to molecular weight >300).*5-27 The PAH are grown by additions from the same small hydrocarbons that also add directly to the soot.28 The inception of soot particles appears to involve the reactive coagulation of large (>300 amu) PAH,26929-33 to form soot nuclei which in turn grow by additions from small hydrocarbons and PAH. The resulting soot structure is not well-defined on an atomic level, but general features are known. Small (-1-3 nm) graphite-like regions of stacked large PAH exist within the soot particle, surrounded by regions of more random ~tructure.~’36 Parallels can be drawn between the molecular weight growth processes that form PAH and soot in flames and those that form fullerenes in flames. The only flames in which fullerenes have been observed are sooting or nearly-sooting, and large yields of fullerenes have only been observed in sooting flames (e.g., the largest published fraction of fuel carbon converted to Ca and C70 fullerenesis 5 X 10-3, observed in sooting benzene/oxygen flames at 4 = 2.5;37the fraction drops by a factor of 2500 when r$ is lowered by 28%,38to a value of 1.8,which is just below the sooting limit of 1.9 and hence in the nearly-sooting regime). The high molecular weight PAH that form soot in sooting flames are also present in nearly sootingflames, but at concentrations below that required for the onset of soot particle formation. Therefore, the molecular weight growth processes that form fullerenesin flames are accompanied by the molecular weight growth processes that form flat PAH and soot. Fullerenes can be considered a novel type of PAH in which, unlike the planar PAH6 and approximately planar PAH containing 5-rings in the periphery of the molecule (which are collectively called “flat” in the present work, because even the nearly planar PAH are indeed flat relative to fullerenes and their curved precursors), curvature is introduced by the incorporation of 5-rings at internal locations in the molecule and from which hydrogen is eliminated to form the closed-cage structure. The present work develops a detailed chemical mechanism for the formation of fullerenes in flames by considering the fullerene formation route to be a subset of the molecular weight growth processes occurring in fuel-rich flames. The fullerene formation pathway is known to be open only under certain conditions, in that not all sooting flames produce f~llerenes.3~ Theoretical studies of flame chemistry can be supported by detailed kinetic modeling of the complete flame chemistry when the reactions being studied are sufficiently well known.40 This approach was deemed unsuitable for the present preliminary test of kinetic plausibility. The composition profiles resulting from coupled convection, diffusion, and reaction of all flame species are computed in such simulations, so the chemical mechanism used as input must be sufficiently detailed to include all the important types of reactions. While approximate mechanisms exist for the formation of small PAH in combustion,”ll formation of the initial fullerene precursors is not included. Also, due to limited understanding of aromatics’ oxidation and growth chemistry, predictions of concentrations of smaller species important to fullerene formation (e.g., C2H2 and H atom (see below)) are sufficiently inaccurate to obscure testing of the fullerene formation mechanism. Therefore, the present kinetic testing is focused on only the fullerene formation mechanism. To that end, input conditions and concentrations of the reactants supporting the fullereneforming chemistry are taken from experimental measurements in a fullerene-producing flame, thereby avoiding the need to compute them as part of the modeling. When the necessary supportingchemistry is sufficiently completeand reliable, testing the fullereneformation mechanismvia simulationof the complete flame chemistry will be desirable.

Review of Mechanistic Concepts of Fullerene Formation Early speculationson fullereneformation routes appear to have been influenced by the fact that fullerenes were formed, then

The Journal of Physical Chemistry, Vol. 97,No. 42, 1993 11003 exclusively, by graphite vaporization. Ablation of single sheets from bulk graphite followed by ring rearrangement leading to cage closure was proposed.’ The only detail mentioned regarding the locations of rings was the “isolated pentagon rule” (IPR), which states that adjoining 5-rings are to be avoided, due to their higher strain energy.4I Sequential addition of smaller (CZ, C3) units to a curved fullerene precursor was then proposed,2 with growth along the edges, similar to PAH growth, proceeding directly to closed-cage structures. These ideas were first presented in the context of soot formation in flames. Kroto et a1.1,4Z.43suggestedthat imperfectly formed fullerenes might be soot nuclei, with a corannulene-like seed molecule. Frenklach and EbertMargued against fullerenes as soot nuclei but considered fullerene formation in flames, proposing benzo[ghi]fluoranthane(Cl8Hlo) formationas the point of divergence from flat PAH. Homann’ suggested soot particles may be supports for fullerene growth-a precursor like corannulene attaches to the soot surface, grows by acetylene addition, and detaches upon cage closure. The corannulene structure is also a proposed fullerene precursor in carbon vapor systems.45 Recent work on carbon arc systems2has shown an abundance of C2 and C3 radicals, leading current thought toward fullerene growth in these systems proceeding via stepwise addition of small carbon units. Homann et aLMrecentlyproposed that largeribbonshaped PAH containing k i n g s , such as C48H18. may serve as fullerene precursors, by curling and reacting at the sides with two benzene molecules to form Cm. Their current fullereneformation ideas include condensed-phase formation of fullerenes inside of young soot parti~les.4~ Thus, in flames, formation of fullerene precursors, first identifiable by the onset of curvature, is a subset of the PAH growth reactions. Since PAH6 are flat and acenaphtha rings do not greatly bend the molecule, the Curved PAH may contain a 5-ring in which each atom is part of an adjacent 6-ring, such as in benzo[ghi]fluoranthene and corannulene. Fluoranthene, though flat, has such a 5-ring and may be a precursor of curved species. Other curved PAH includethose with methylenebridges, of thecyclopentaphenanthrenetype,12J3in bay regions of otherwise 6-ring PAH, e.g., coronene with one or more, but not adjacent, outer 6-ringsreplaced by k i n g s , as in tricyclopenta[defjkl,pqr] triphenylene. Smalley’s well-known “pentagon road” concept holds that fullereneformation occurs through a series of polycyclic aromatic intermediatesconsisting of 5-ringsand 6-ringspositioned, through facile intramolecular rearrangements, so as to maximize the number of nonadjacent 5-rings while minimizing the number of dangling bonds.@ Goeres and Sedlmayflgalso consider polycyclic aromatic precursors and describe Ca and C70 formation via polymerization of naphthalene-like Clo and subsequent rearrangement. Kerner et al.50 employ statistical, thermodynamic, and kinetic arguments to analyze intermediate structures in the formation of Ca and C70. They consider successive 5-ring and 6-ring additions starting from hydrogen-less indene and naphthalene units and predict a yield of 10% CSO, a C ~ O / Cratio ~ O of -0.3, a c84/c70 ratio of -0.2, and an optimal temperature of -2500 K for fullerene formation in carbon vapor systems. Most of the intermediates in the mechanism are not described, and the characteristic time for fullerene formation is not computed. Other published mechanistic concepts of fullerene formation inclde reactions of planar carbon rings to form fullerenes. Wakabyashi and Achibasl propose stacking of even-numbered carbon rings (e.g., CIO,CIZ,CIS)onto a growing curved polycyclic aromatic base. Other mechanismss2-54consider large carbon rings collapsing to form fullerenes. The proposed intermediates are bi- or tricyclic rings, which are considered to form fullerenes without passing through an open curved polycyclic aromatic intermediate,with the required multiplerearrangementspresumed

-

11004 The Journal of Physical Chemistry, Val. 97, No. 42, 1993

Pope et al.

C30H1 0

4 C&M

-- FB

C40H1 0

-- XB

e) CsoHID

Figure 4. Fullerene precursors of Cs symmetry and “cup”or “bowl” shape: (a) corannulene= COR (dibenzo[ghi,mno]fluoranthene,C~&O); (b) llz-bucky = HB (pentacyclopcnta[bc,ef,hi,kl~lcorannulcne,C d I 3 ; (c) 2/a-bucky= TB (pentabenzo[b~dSghj&l,nop,rsr]~/2-bucky, CaHlo); (d) 5/6-bucky = FB (pentabenzo[bcd~ghj&kl,nop,rsrJ~/~-bucky, C&~O); (e) expanded-bucky = XB (pcntabenz~[bcdJghjkl,nop,rst]~/~-bucky, CaHio). to be facile and concurrent. When the resulting fullerenes are smaller than (260, growth is proposed by incorporation of smaller (e.g., Cz) units, as in Heath’s “fullereneroad” mechanism:52when the fullerene is larger than Cm, C2 elimination is presumed to shrink the fullerene to the more stable Cm.53

Fullerene Formation Mechanism Overview of Mechanism. The proposed chemistry of fullerene formation provides the basis of a reaction mechanism, described below with a specific example for the formation of fullerenes Cm and C70, each by two overall pathways. The first is called the direct pathway, in which all carbon is added by C2H2 addition to the growing molecule. Intermediatesrepresentativeof different growth stages in the mechanism are PAH of C5, symmetry. Such intermediates in Cm and C70 formation are shown in Figure 4. In the absence of standard nomenclature, except for corannulene (dibenzo[ghi,mno]fluoranthene,COR, C ~ O H ~these O ) , intermediates are referred to below as half-bucky (HB, C~oHlo),twothirds-bucky (TB, CmHlo), five-sixths-bucky (FB, CSoHlo), and expanded-bucky (XB, CmH10). FB proceeds directly to form C60 or to XB, which proceeds to form C70. An outline of the direct formation pathways for Cm and C ~isOshown in Figure 5. Extending the sequence of C5, PAH beyond XB could be seen as a pathway for the constructionof a cylindrical carbon structure, possibly leading to formation of a buckytube. The second pathway for Cm and C70 formation is called the coagulation pathway, since it involves reactive coagulation or C-C bonding between two Csuintermediates. For Cm formation, two HB molecules, at least one of which is a radical, react to form CsoHls,which then undergoes successive dehydrogenation steps to form the completed C ~ cage. O One HB and one TB molecule, again at least one of which is a radical, dimerize to form C70H18, which dehydrogenates to form C70. The coagulation pathway branches off the direct fullerene formation pathway: these additional reactions are outlined in Figure 6. Reaction Types. The proposed mechanism consists of six general types of reactions, all of which are known in PAH chemistry and represented by model reactions in Figure 7: (1) H-abstraction to form an aryl radical; (2) CzH2 addition to an aryl radical to form a vinylic adduct: (3) cyclization of a five- or six-membered adduct, leading to 5- or 6-ring closure and H-elimination; (4) reactive coaguIation26328-coupling of an aryl radical and a PAH or aryl radical; (5) dehydrogenation and ring closure; and (6) intramolecular rearrangements. Reaction type

Figure 5. Outline of the direct pathway for Ca and

c70

formation.

a)

.

C30H10+C40H9 ‘30H9

C40H10

7 fl

‘70H18

c70

&H

Figure 6. Outline of the coagulation pathway for (a) C a and (b) C70 formation. 5 can be considered to be a concert4 reaction (Figure 7, part Sa) or a sequence of two reactions (Figure 7,part 5b). The sequence is a type 1, H-abstraction (called type 5-1, to signify a type 1 reaction that is part of an overall type 5 reaction) followed by a type 3, cyclization (called type 5-3). The same types of reactions are expected to describe the formation of other fullerenes. For simplicity, H-abstraction is assumed to form only monoradicals, However, PAH with multiple radical sites, Le., biradicals, triradicals, etc., are expected to be present, even to the extent of including the most prevalent radical of a given PAH under some conditions in fullerene-forming benzene-oxygen flames. PAH with multiple radical sites or dangling bonds would be expected to lead to faster rates of fullerene formation, not only becausetheir presence would increase the concentrationof radical

The Journal of Physical Chemistry, Vol. 97,No. 42, 1993 11005

Cm and C70 Formation in Flames

The reaction sequence from HB through TB, FB, and XB consists of sequential 6-ring formation in the bay regions of the growing structure and as such will not lead to 5-ring formation or dehydrogenation, both of which are needed for fullerene formation. The cage closure reaction sequence, which produces Cm from FB and C70 from XB, therefore diverges from the Cso species formation chemistry and is more complicated (Figure 9). The reaction sequence is the same for both cage-closing sequences, so the following discussion is based on the FB c 6 0 chemistry. FB1, formed by net C2 addition to FB, has a 6-ring in a location wherea 5-ring wouldneed tobeforCmformation. In theproposed chemistry leading to c 6 0 formation, the next net C2 addition forms a species with a 5-ring adjoining the "out-of-place" 6-ring. The compound is called FBZQ, the Q indicating a divergence from the preceding 6-ring addition sequence. (A C2 unit could conceivably add to FB to yield a fulvene-like 5-ring moiety. Species containing fulvene moieties are not included in the fullerene formation mechanism for reasons outlined below.) The two rings added to FB then undergo an intramolecular rearrangement (type 6), forming FB2QR-R for rearranged compound. (See Figure 7, part 6 for the prototype reaction.) The remaining steps leading to c 6 0 are three repetitions of reaction types 5, 1, 2, and 3 and two of type 5 to close the cage. The formation of completed fullerenes c60 and c 7 0 from the CS,precursors therefore proceeds in a conceptually straightforward way, with all rings ending up in their proper locations. Details of Cm and C70 Formation via Reactive Coagulation. Reactive coagulation of large flat PAH does occur in flames and is believed to be a step in soot particle in~eption.'9,26,*~,30.32,55,56 At least one of the reacting species is assumed to be a radical (reaction type 4). The proposed fullerene precursors are also expected to be able to undergo such reactions. Thus, dimerization of two C30H9 species (called H E , the - signifying a a-radical) yields C6oHls (called HBHBDl-two HB moieties joined by a C-C bond, the D1 signifying dehydrogenation to an extent leaving one fewer pair of H atoms than the 10 pairs contained in two HB molecules). Reactive coagulation of HB and HB-similarly yields HBHBDl H. (See Figure 7, part 4, for the prototype reaction and Figure 6a for the overall reaction sequence.) Nine additional dehydrogenation/ring-closingsteps (type 5) zip together theedges of the dimer and complete the c 6 0 cage (Figure 10). The band of 10 6-rings, correctly arranged to close the c 6 0 cage, develops as a direct consequence of the structures of the combining species. In the reactive coagulation sequence for C70 formation, HBand T E react to form a C70H18compound consisting of one TB and one HB moiety joined by a single C-C bond. Analogously to HBHBD1, this C7oHls species is called TBHBDI. Reactive coagulation of HB TB-, or H E TB, yields TBHBDl + H. (See Figure 6b for pairs of reactants leading to TBHBDl formation.) Formation of C70 from TBHBDl follows the same reaction sequence as c 6 0 formation from HBHBDl (cf. Figure 10). Complete Reaction Mechanism, Nomenclature, Rate Coefficients, and Thermodynamic Properties. The complete fullerene formation mechanism, containing 125species and 124elementary reactions, is shown in Table I. The complete list of species, with their empirical formulas and molecular weights, is given in Table 11. Rationale for the naming of stable species and a-radicals is given above. Cb0and CT0are both given A and B forms to denote which pathway is forming each fullerene. Thus, C& and formvia the direct pathway; CmB and C70B are produced through reactive coagulation of Cs, species. Reaction types referred to in Table I are the same as types described above or combinations or subdivisions of them as defined below. Reactions of type 1 (H-abstraction) and type 6 (intramolecular rearrangement) are used as defined above. Sequences of reaction type 2 (CzHz addition) followed by type 3 (ring closing) have been replaced by single reactions called type

-

pg+. 00

Figure 7. Model PAH reactionsrepresentativeof the reaction types used in the fullerene formation mechanism. (1) H-abstraction: CloHs + H C10H7 Hz; (2) CzHz addition: C10H7 CzHz C12H9; (3) ring

-

+

-

+

--

closure: C12H9 ClzHs + H; (4) reactive coagulation: CloHs + CloH7 C20H14 + H; ( 5 ) H- or H2-elimination and ring formation: (a) concerted, CmHlr C20H12+ Hz; (b) H-abstraction followed by ring closure, CZOHI~ + H CZOH13 + Hz, C2oH13 CZOHIZ + H; (6) intramolecular rearrangement: acephenanthrylene fluoranthene.

--

reactants but also because the rate coefficients for acetylene addition and reactive coagulation would increase with increasing number of radical sites in the PAH reactants. Therefore, neglecting the presence of multiple-site radicals leads to some underestimation of fullerene formation rates. Although the concentrations of the multiple-site radicals could be estimated,2s the required level of detail would be inconsistent with the rest of this study. Details of Direct Ca and C70 Formation. This portion of the mechanism is a molecular weight growth sequence starting from either fluoranthene (FLTHN, C16HlO)r benzo[ghi] fluoranthene (BGHIF, ClsHlo), or corannulene (COR, C20Hlo). Starting with fluoranthene, growth leading to fullerene precursors up to FB proceeds via repetition of reaction of types 1, 2, and 3 (Figure 8). Formation of XB from FB is an extension of the sequence leading to the other Cs, intermediates. Formation of the next larger ring occurs by net C2 addition. Five repetitions of the reactions of types 1,2, and 3 transform one Cs, species to the next larger one (e.g., HB TB). In the ring-formation sequence between FLTHN and FB, the correct placement of 5-rings and 6-rings required for C6o formation occurs as a direct consequence of the growth reactions. Notation for species larger than corannuleneis basedon that for the Cs, intermediates. The names of the stable species are based on the parent CsDcompound. For example, COR2 is COR with two additional rings.

-

+

+

+

11006 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993

FLTHN

BGHIF

COR3

Pope et al.

COR

COR4

COR 1

COR2

HBl

HB

V

HB3

HB2

@-

TB

Figure

HB4

-.

TB1

TB2

TB3 TB4 FB Reaction sequence for the direct pathway of the fullerene formation mechanism, for species bctwcen

6HlO

+ HB-

HBHBD 1

HBHBD2

FB3Q

HBHBD3

HBHBD4

HBHBDS

FB4QD

HBHBD6

HBHBD7

HBHBDS

FB

FB 1

FB2Q

FB2QR

FB2QRD

FB3QD

FB4Q

FB5Q

FB5QD

-

+

+

-+

C&

Ngure 9. Reaction squence for cage closing in the direct pathway of

the fullerene formation mechanism, case of FB

(FLTHN) and CSOHIO (FB).

C&.

23. The type 23 reaction corresponding to the prototypical reactions in Figure 7 would then be 1-naphthalenyl + C2H2 8

HB

HBHBD9

C&

-

Figure 10. Reaction sequencefor cage closing in the coagulation pathway

of the fullerene formation mechanism, case of HB + HB-

CaB.

acenaphthalene + H. Reactions of type 2 and type 3 were combined because the rate coefficient used in modeling was for

The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 11007

Cm and C ~ Formation O in Flames

TABLE I: List of Detailed Reactions (with Reaction Type) in the Fderene Formation Mechanism' reaction

+ +

+

1, FLTHN H FLTHN- H2 2. FLTHN- C2H2 BGHIF H 3. BGHIF + H BGHIF- + H2 4. BGHIF- + C2H2 COR + H 5 . COR + H COR- H2 6. COR- + C2H2 CORl + H 7. CORl H = COR1- H2 8. COR1- C2H2 COR2 H 9. COR2 + H COR2- + H2 10. COR2- C2H2 = COR3 H 11. COR3 + H COR3- H2 12. COR3- C2H2 COR4 H 13. COR4 H = COR4- H2 14. COR4- + C2H2 = HB + H 15. HB H = H E + H2 16. H E + C2H2 = HBl + H 17. HB1 H HB1- H2

+

+

+ + + + + + + + + + + + + + 35. FB + H = F B - + H2 36. FB- + C2H2 = FB1+ H 37. FB1 + H FB1- + H2 38. FBI- + C2H2 = FB2Q + H 39. FB2Q = FB2QR 40. FB2QR + H = FB2QR- + H2 41. FB2QR- = FB2QRD + H 42. FB2QRD + H = FB2QRD- + H2 43. FB2QRD- + C2H2 = FB3Q + H 44. FB3Q + H = FB3Q- + H2 45. FB3Q- = FB3QD + H 56.2HB- = HBHBDl 57. H E + HB = HBHBDl H 58. HBHBDl + H = HBHBDl- + H2 59. HBHBDl- = HBHBD2 H 60. HBHBD2 + H HBHBD2- H2 61. HBHBD2- = HBHBD3 H 62. HBHBD3 + H HBHBD3- H2 63. HBHBD3- = HBHBD4 H 64. HBHBD4 + H = HBHBD4- + H2 65. HBHBD4- = HBHBD5 H

+ + + + + + +

+ + +

+ +

76. FB1- C2H2 FB2 H 77. FB2 H = FB2- H2 78. FB2- C2H2 = FB3 H 79. FB3 + H FB3- + H2

+

+ + + +

+

+

+

+ +

104. H E TB- = TBHBDl 105. H E TB = TBHBDl + H 106. HB + TB- = TBHBDl + H 107. TBHBDl + H = TBHBDl- H2 108. TBHBDl- = TBHBD2 H 109. TBHBD2 + H TBHBD2- + H2 110. TBHBD2- TBHBD3 + H 111. TBHBD3 + H TBHBD3- + H2 112. TBHBD3- = TBHBD4 + H 113. TBHBD4 + H = TBHBD4- + H2 114. TBHBD4- = TBHBD5 + H

+

a

+ + + + + + +

+

+ +

+

tvw 23 1 23 1 23 1 23 1 23 1 23 1 23 1 23 1 23

+

+

+ +

+

FB (CsoHio) to Cso 1 46. FB3QD + H = FB3QD- H2 23 47. FB3QD- + C2H2 = FB4Q H 48. FB4Q H = FB4Q- H2 1 49. FB4Q- = FB4QD H 23 50. FB4QD H = FB4QD- H2 6 5- 1 51. FB4QD- + C2H2 = FB5Q H 5-3 52. FB5Q + H = FB5Q- H2 1 53. FB5Q- = FB5QD H 23 54. FB5QD H = FBSQD- H2 5- 1 5 5 . FBSQD- = C60A + H 5-3 Coagulation Pathway to Cso 4-A 66. HBHBD5 + H = HBHBD5- H2 4-B 67. HBHBD5- HBHBD6 H 5-1 68. HBHBD6 H HBHBD6- H2 5-3(rot) 69. HBHBD6- = HBHBD7 + H 5-1 70. HBHBD7 + H = HBHBD7- H2 7 1. HBHBD7- = HBHBD8 + H 5-3 5- 1 72. HBHBD8 + H = HBHBDI- H2 5-3 73. HBHBD8- HBHBD9 + H 5- 1 74. HBHBD9 H = HBHBD9- + H2 75. HBHBD9- C60B H 5-3 Formation of XB (CaHlo) 23 80. FB3- + C2H2 = FB4 + H 1 81. FB4 + H = FB4- + H2 23 82. FB4- C2H2 = XB H 1

+

+ +

+

+

+

+

+

+

+

+ + + +

+

+

+

1 23 5-1 5-3 1 23 5-1 5-3 5-1 5-3

+

+

5-1 5-3 5-1 5-3 5-1 5-3 5-1 5-3 5-1 5-3

+

+

83. XB H = X B - + H2 84. XB- C2H2 = XB1+ H 85. XB1 H = XBl- H2 86. XBl- C2H2 = XB2Q + H 87. XB2Q = XB2QR 88. XB2QR H = XB2QR- + H2 89. XB2QR- XB2QRD H 90. XB2QRD + H = XB2QRD- + H2 91. XB2QRD- + C2H2 = XB3Q + H 92. XB3Q + H = XB3Q- + H2 93. XB3Q- = XB3QD H

+

tYDe reaction Fluoranthene (C16HIO) to FB (C3oHlo) 1 18. HBl- C2H2 HB2 + H 23 19. HB2 + H HB2- + H2 1 20. HB2- C2H2 = HB3 + H 23 21. HB3 H HB3- + H2 1 22. HB3- C2H2 HB4 + H 23 23. HB4 H = HB4- H2 1 24. HB4- C2H2 = TB H 23 25. TB H = T B - + H2 1 26. TB- + C2H2 = TB1+ H 23 27. T B 1 + H = TB1- + H2 1 28. TB1- C2H2 = TB2 + H 23 29. TB2 H = TB2- H2 1 30. TB2- + C2H2 = TB3 + H 23 31.TB3+H=TB3-+H2 32. TB3- + C2H2 = TB4 + H 1 23 33. TB4 H = TB4- + H2 1 34. TB4- C2H2 = FB H

23 1 23

+

XB (CsoHio) to G o 1 94. XB3QD + H = XB3QD- + H2 23 95. XB3QD- + C2H2 = XB4Q H 1 96. XB4Q + H = XB4Q- + H2 23 97. XB4Q- = XB4QD H 6 98. XB4QD H = XB4QD- H2 99. XB4QD- C2H2 = XB5Q + H 5-1 100. XB5Q H = XB5Q- H2 5-3 101. XB5Q- = XB5QD H 1 102. XB5QD H = XBSQD- H2 23 103. XBSQD- = C70A + H 5- 1 5-3 Coagulation Pathway to c 7 0 115. TBHBD5 + H = TBHBD5- H2 4-c 4-D 116. TBHBD5- TBHBD6 + H 4-D 117. TBHBD6 + H = TBHBD6- + H2 5-1 118. TBHBDC = TBHBD7 + H 5-3(rot) 119. TBHBD7 H TBHBD7- H2 5-1 120. TBHBD7- TBHBDI + H 5-3 121. TBHBDI + H = TBHBD8- + H2 5-1 122. TBHBD8- TBHBD9 H 5-3 123. TBHBD9 H = TBHBD9- + H2 5-1 124. TBHBD9- C70B + H 5-3

+

+ + + +

+

+

+

+

+

+

+

+

+

+

1 23 5-1 5-3 1 23 5-1 5-3 5-1 5-3

5-1 5-3 5-1 5-3 5-1 5-3 5-1 5-3 5-1 5-3

See text for definitions of types of reactions and Table I1 for specics identifications.

the combined C2H2 addition/ring-closing reaction. The type 4 reactions (reactive coagulation) are split into four subtypes (4-A, 4-B, 4-C, and 4-D), since each subtype is characterized by a

different rate coefficient: 2HB- e HBHBDl is the reaction of type 4-A, HB HB- s HBHBDl H is type. 4-B, H E TBe TBHBDl is type 4-C, and both HB TB- e TBHBDl

+

+

+

+

+

Pope et al.

11008 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993

TABLE Ik Species Included in the Fullerene Formation Mechanism (Shorthand Name, Molecular Weight, and Empirical Formula)' species mol weight no. of C no. of H species mol weight no. of C no. of H species mol weight no. of C no. of H H FLTHN FLTHNBGHIF BGHIFCOR CORCORl CORlCOR2 COR2COR3 COR3COR4 COR4HB H E HB 1 HBlHB2 HBHBDl HBHBDlHBHBD2 HBHBD2HBHBD3 HBHBD3HBHBD4 FB2 FB2FB3 FB3FB4 FB4XB XBXB 1 XB1TBHBDl TBHBDlTBHBD2 TBHBD2TBHBD3 TBHBD3TBHBD4 a

1.007 202.258 201.250 226.280 225.272 250.302 249.294 274.325 273.317 298.347 297.339 322.369 321.361 346.391 345.383 370.414 369.406 394.4 36 393.428 418.458 738.812 737.804 736.796 735.788 734.780 733.772 732.764 658.681 657.673 682.704 68 1.696 706.726 705.718 730.748 729.740 754.771 153.763 858.923 857.915 856.908 855.900 854.892 853.884 852.876

1 10 9 10 9 10 9 10 9 10 9 10 9 10 9 10 9 10 9 10 18 17 16 15 14 13 12 10 9 10 9 10 9 10 9 10 9 18 17 16 15 14 13 12

0 16 16 18 18 20 20 22 22 24 24 26 26 28 28 30 30 32 32 34 60 60 60 60 60 60 60 54 54 56 56 58 58 60 60 62 62 70 70 70 IO 70 70 70

H2 HB2HB3 HB3HB4 HB4TB TBTB 1 TB1TB2 TB2TB3 TB3TB4 TB4FB FBFB 1 FB1HBHBD4HBHBD5 HBHBD5HBHBD6 HBHBDb HBHBD7

2.015 417.450 442.48 1 441.473 466.503 465.495 490.525 489.517 514.548 513.540 538.570 537.562 562.592 561.584 586.614 585.606 610.637 609.629 634.659 633.651 731.756 730.748 129.740 728.732 727.724 726.716

0 34 36 36 38 38 40 40 42 42 44 44 46 46 48 48 50 50 52 52 60 60 60 60 60 60

XB2Q XB2QR XB2QRXB2QRD XB2QRDXB3Q XB3QXB3QD XB3QD-

778.793 778.793 777.785 776.777 775.769 800.799 799.791 798.783 191.175

64 64 64 64 64 66 66 66 66

TBHBD4TBHBD5 TBHBD5TBHBD6 TBHBD6TBHBD7

851.868 850.860 849.852 848.844 847.836 846.828

70 70 70 70 70 70

C2H2 FB2Q FB2QR FB2QRFB2QRD FB2QRDFB3Q FB3QFB3QD FB3QDFB4Q FB4QFB4QD FB4QDFB5Q FB5Q FB5QD FB5QDC60A

26.038 658.681 658.681 657.673 656.665 655.651 680.688 679.680 678.672 677.664 702.694 701.686 700.678 699.610 724.700 123.692 722.684 721.616 720.669

2 54 54 54 54 54 56 56 56 56 58 58 58 58 60 60 60 60 60

2 10 10 9 8 7 8 7 6 5 6 5 4 3 4 3 2 1 0

HBHBD7HBHBD8 HBHBDIHBHBD9 HBHBD9C60B

725.708 724.700 723.692 122.684 121.676 720.669

60 60 60 60 60 60

5 4 3 2 1 0

10 10 9 8 I 8 I 6 5

XB4Q XB4QXB4QD XB4QDXB5Q XB5QXB5QD XBSQDC70A

822.806 821.798 820.790 819.782 844.812 843.804 842.796 841.788 840.780

68 68 68 68 70 70 70 70 70

6 5 4 3 4 3 2 1 0

11 10 9 8 7 6

TBHBD7TBHBD8 TBHBDITBHBD9 TBHBD9C70B

845.820 844.812 843.804 842.796 841.788 840.780

70 70 70 70 70 70

5 4 3 2 1 0

2 9 10 9 10 9

10 9 10 9 10 9 10 9 10 9 10 9 10 9 11 10 9 8 7 6

See text for definitions of nomenclature and Figures 4 and 8-10 for structures of most of the stable species.

+

+

H and HBTB 8 TBHBDl H are type 4-D. Type 5 reactions (dehydrogenation/ring closing) have been modeled as consecutive H-abstractions (type 5-1) and ring closings (type 5-3) (Figure 7, part 5b). The alternative Hz elimination channel (Figure 7, part 5a) was not included for lack of a sufficiently reliable rate coefficient. The type 5-3 reactions involving HBHBDl- and TBHBDl- are a separate subtype 5-3(rot), because the ring closing involves rotation along a C-C singlebond rotor. Though reaction type 5-3 and 5-3(rot) are tentatively modeled using the same rate coefficient, this distinction may be important when more detailed rate information becomes available. Forward rate coefficients used in the kinetic testing are given in Table 111. Thermodynamic properties for the fullerenes and the proposed precursors are necessary to determine reverse rate coefficients for reversible reactions. Due to the paucity of thermodynamic data for many PAH, group additivity methods are commonly employed.59 For modeling of PAH6, the groups of Stein et aL60fj1 are commonly used. Moiseeva and Dorofeeva62have developed groups for properties of flat PAH containing 5-rings, including fluoranthene. Nevertheless, the existing groups are insufficient for estimation of properties of curved PAH such as all of the proposed fullerene precursors beyond FLTHN. (Any PAH containing a 5-ring such as that in fluoranthene or even an ace-

TABLE IIk Rate Coefficients for Types of Reactions Used in the Fullerene Formation Mechanism' reaction type A b E lb 23b 4-A' 4-Bd 4-C' 4-Dd 5-1' 5-3f

5-3(rot)c 6h

2.50E+14' 4.00E+ 13 7.15E+ 12 2.86E+12 1.44E+ 13 2.88E+12 2.50E+14 1.00E+13 1.00E+13 8.5 1E+ 12

0 0 0.5 0.5 0.5 0.5

0 0 0 0

15.99 10.1 1 0 0 0 0 15.99 0

0 62.86

a See text for definitionsof reaction types. Rate coefficient k = ATb exp(-E/RT); A has units of cm3/(mol s), except for reaction types 5-3, 5-3(rot), and 6, for which the units are s-l; b is dimensionless; and E is in kcal/mol. Reference 57. Collision frequency. d0.2 X collision frequency (ref 19). *Sameas type 1. /Reference 8. 8 Same as type 5-3. * Reference 58. ' Read as 2.50 X 10". group is not exactly planar, but the distortion from planarity is minimal, especially compared to the fullerenes and the proposed precursors.) Details of the thermodynamic property calculations will be published separately. Briefly, a new group accounting for the curvature-induced ring strain and for resonance stabilization has

C ~ and O

c70

Formation in Flames

been derived from the properties of Cm. The W d g ) of C a is obtained from the experimental AHor(crystal)63and the experimental AHsub64 values. A S O f and C, values are taken from McKinnon's statistical mechanics calculation^^^ based on calculated vibrational frequencies of Stanton and Newton.66 (A recent determination of W d ~ r y s t a l yields ) ~ ~ a value for A H o f (8) approximately 8% larger than that used in the present work.) This new group, combined with the groups of Stein and of Moiseeva and Dorofeeva, completes a set of group sufficient to estimate the needed thermodynamic properties. In summary, the properties are reliably pinned down at the end points of the fullerene formation sequence (fluoranthene and C,) and exhibit reasonable trends in the in-between region.

The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 11009 10

/ /

' 6

..

A C

/

I

/

Preliminary Kinetic Test of Mechanism 0

Approach. The fullerene formation mechanism was tested against experimentalmeasurementsin a fullerene-producingflame to determine whether the mechanism predicts that Cm and C70 fullerenes should form in flames under conditions known to produce them and whether the predicted times for their formation are consistent with experimental observations. Since only fullerene formation chemistry is included, the simulations,which yield concentration profiles of all species in the mechanism as functions of time, predict 100% conversion of precursor to Cm and C70 at infinite reaction time. The criterion of kinetic plausibility was taken to be substantial (>50%) conversion of precursorto fullerenesin the time observed for fullerenesformation in the flame ( - 5 ms). The flames considered are premixed, laminar, and onedimensional, with axial diff~sion.~,3~J8,68 All these properties except axial diffusion were included in the present study. Fullerenes and their precursors are high-molecular-weight compounds relative to the bulk gas, therefore having lower diffusion coefficientsthan thegreat majorityof the flamespecies. Although diffusion has been found to affect the concentration profiles of high-molecular-weight compounds in flames,69the effect is small enough to be neglected here, given the preliminary nature of the test being performed. The profiles for the contributing lighter species (H, H2, and C2H2) are approximated as a constant-valued input at the beginning of the region of the flame being simulated, with their resulting concentration profiles being nearly flat (see below). This approximation is reasonable because the zone in which much of the fullerene formation occurs is downstream of the zone of the most intense species concentration gradients.13 Simulations were done using the CHEMKIN-I1 subroutine packages7O and a plug-flow simulator (SENKIN71). Each calculation tookapproximately 30 CPU seconds on the MIT Cray X-MP. Input conditions for testing are for an experimentally studied19937.68 premixed benzene/oxygen/ 10% argon fullerene-producing flame: combustion chamber pressure, 40 Torr (5.34 P a ) ; 4,2.2; inlet gas velocity (298 K, 40 Torr), 25 cm/s. Mole fraction profiles for Cm and c7037968 and major stable flame species19 in this flame have been reported. Peak fullerene mole fractions are approximately 4 X 1 V for Cm and 6 X 1 V for C70. Species whose concentrations are needed as inputs are H, H2, C2H2, and the initial fullerene precursor (chosen to be FLTHN). Basecasevalues for temperature (2050 K) and the mole fractions of Hz(0.12) and C2H2 (0.06) are representative of flame values in the region of interest. The base case H atom mole fraction is 0.025-5 times the global equilibrium value (obtained via the CHEMKIN-I1compatibleversionof STANJAN72)for the flame conditions (4, pressure) at 2050 K. A factor of 5 is representative of the ratios of measured H atom concentrations to global equilibrium predictions for a near-sooting (4 = 1.8) benzene flame.13 Since the results of the simulation give fractional conversion of fullerene precursor with time, the input mole fraction of

0

2

6

4

time (milliseconds)

8

IO

+

Figure 11. Predicted mole fractions of Ca, c70, and Cm c70 vs time for conditions of 4 = 2.2 fullerene-producing benzene flame.

precursor is only important to the extent to which increased precursor concentration increases the amount of intermediates which can dimerize in the coagulation pathway. To get an approximate upper limit on the importance of the coagulation pathway, a high value (1 X 10-5) for the base case FLTHN mole fraction was chosen. The input mole fraction of argon was taken to be unity minus the input mole fractions of H, H2, C2H2, and FLTHN. Model hedictions. Predicted mole fractions of C, and C70 as a function of time are shown in Figure 11. As expected from the neglect of competing pathways including destruction via oxidation, complete conversion to C, C70isobtained. Virtually all of the fullerenes are formed via the direct pathway (Figure 5 ) ; less than 3 X l e 7of the Cm + C70 comes from the coagulation pathway (Figure 6). The final C7o/C@ ratio predicted is 1.5, comparable to the average of observed values for theseconditions.37 The predicted time required for fullerene formation is of the correct order of magnitude of that seen in the flame (-5 ms). The results for the entire 124-reaction mechanism can be shown to be approximately consistent with a global first-order reaction preceded by an induction time. Plotting In( 1/( 1 - x)), where x is the fractional yield of Cm and/or C70 from fullerene percursor, gives straight line for a reaction which is first-order in fullerene precursor, with the slope being equal to the overall rate coefficient k* and the time axis intercept being the induction time T * (Figure 12). Except for low conversions, the results fit the form

+

x, = [x,]

f-m

[ 1 - e-'f('+)]

+ +

where f is either C, c70, or (C, c70). For f = (C, + c70), these parameters are [x& = 1, kf* = 363 s-l, and T/" 2.26 ms. (Henceforth, f denotes (C, C70), and the subscripts on k* and T* are dropped.) Sensitivity to Input Concentrations. In order to assess the impact of specifying only inlet concentrations of H, H2, CzH2, and FLTHN and not the concentration profiles, these inputs were varied so as to determine first-order sensitivity coefficients for k* and T* for overall CW+ c70 formation with respect to [HI, [H2], and [C~HZ]. The computed sensitivity coefficients are shown in Table IV. The results indicate that fullerene formation is accelerated dramatically by increased C2H2 and decreased H2concentrations and to a lesser extent by increased H atom concentrations. This behavior reflects the role these species play in the mechanism, C2H2 appearing only as a reactant in reaction type 23 and H2 appearing only as a product of reaction type 1. The H atom is a reactant in reaction type 1 and a product in types 23,4-B, 4-D, 5-3, and 5-3(rot), so its effect on the overall mechanism is mixed but generally promoting fullerene formation.

Pope et al.

11010 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 , 3

1 ,

0 0

2

4

6

time (milliaeconds)

a

IO

Figure 12. Predicted fractional conversion of (C, + c70) vs time for conditions of 9 = 2.2 fullerene-producingbenzene flame: linear plot on left ordinate,replotted to show global firsborder kineticson right ordinate. (See text for discussion.)

TABLE IV First-Order Sensitivity Coefficients for CO and C70 Formation Parameters k* and 7* (See Text for Definitions) with Respect to Input Concentrations for H, H2, and C2H2 species d (In k*)/d (In [species]) d (in 7*)/d (ln[species]) H +0.67 -0.62 Hz -2.79 +OS1 CzHz +3.48 -0.85 Sensitivity to Rate Coefficients. Published values of the rate coefficients for the PAH reaction types used in constructing the mechanism vary widely, by as much as 3 orders of magnitude. Exploration of the specific effects of each rate coefficient used on fullerene formation predictions is in progress. An overall measure of the variation was found by predictionsusing collective sets of all the fastest published rates and all the slowest rates. The results in both cases were fit to the global first-order form. The values ranged from k* = 2400 s-’ and T * = 0.42 ms (fastest) to k* = 19 s-l and T* = 34 ms (slowest). The values quoted above (k* = 363 s-1 and T* = 2.26 ms) for what were considered the best values of rate coefficients are near the middle of the extremes. Obviously, more confident values for the rate coefficients would be desirable. Nevertheless, sincethe experimentaltime is midway within the predicted range, the mechanism as presented has not been disproved and appears to be kinetically plausible. Additional Results. The concentrations of the fullerene precursors are much less than those of H, Hz, and C2H2. Therefore, the fullerene formation chemistry perturbs these supporting species’s concentrations very little (at most 1%), leaving the mole fractionsof H, Hz, and C2H2 effectivelyconstant. All of the reactions in the mechanism (except those of type 4, which have been shown to be negligible) therefore become pseudofirst-order in both directions. This result is suspected to account for the global first-order behavior of the entire mechanism and aids in the determination of rate-limiting steps in the fullerene formation mechanism.73 Calculations reveal two rate-limiting portions of the mechanism: (1) ring formation up to and including C3,)HlOywhich is thermodynamically uphill, and (2)the intramolecular rearrangements which, while having faster rates than all reactions of types 1 and 23, are the least thermodynamically favored, having reverse rates -8 times faster than their forward rates. All of the type 1 reactions also have sufficiently strong back-reactionsto influencethe overall rate of fullerene formation throughout the entire process. A kinetically-basedexplanation for the C70/Cm ratio was also found by considering the reaction rates at the branching of the direct formation pathways for c 6 0 and C70a73The strong reverse

-

reaction of the intramolecular rearrangement at the beginning of the cage-closing sequence for Cm (reaction 39,Table I) slows Cm formation relative to C70 formation; in the absence of reverse reactions, the mechanism predicts a C70/Cm ratio of unity. This feature of the mechanism may be indicative of a more general competitionbetween cage-closing and continued tubelike growth toward larger fullerenes. The ability of the fullerene formation mechanism to predict observed trends with respect to t e m p e r a t ~ r e ~ .and ’ ~ , ~pressure4s7 ~ has also been te~ted.~3 The mechanism predicts a maximum in fullereneformationrate with increasingtemperature, qualitatively agreeing with flame data.47 The mechanism by itself predicts fullerene formation to increase linearly with pressure; the mechanism does not includethe effect of pressureon flame species (e.g., H atom) or other molecular-weightgrowth pathways which lead to soot formation. The features of the mechanism which account for the apparent enhancement of fullerene formation with increasing pressure would similarly affect flat PAH formation. The extent of soot formation in fullerene-formingflames is known to increase stronglywith increasing probably reflecting soot growth by reactive coagulation processes which are second-order in pressure.Z6s2* Therefore, as pressure is increased, the competition between fullerene formation and flat PAH and soot formationwould be assumed toshift strongly toward soot formation, consistent with observations that fullerene formation decreases as pressure is increased toward atmospheric. Discussion and Conclusions Relevance to Carbon Vapor Systems. Carbon vapor systems used to generate fullerenes differ from flames by including only carbon and an inert gas (often helium). The chemistry therefore differs from the present hydrocarbon-based mechanisms. No hydrogen is present to satisfy valences of edge carbons, and hydrogen removal is not needed in cage-closing steps. The presence of an extremely high-energy plasma region is also a feature of carbon vapor systems not found in flames, which have maximum temperatures of roughly 1500-2300 K. While the temperatures of the carbon vapor systems are not well-known, the species created may be sufficiently energetic to undergo strained ring formationand intramolecularrearrangements.Some speciesmay be so energized by (exothermic) C-C bond formation as to require a sufficiently high bath-gas pressure to keep the transition state from decomposing back to reactants. The combination of very high temperature and lack of hydrogen may be necessary for the formation of planar carbon rings. Such structures have not been detected in combustion environments, although linear carbon chains, in the form of polyacetylenes, are present in Therefore, planar carbon rings are not considered here to be important for fullerene formation in flames. In the absence of hydrogen the more prevalent structures for certain carbon numbers may be closed-cage clusters instead of the incompletely formed cages proposed as intermediates in the present mechanism. The incorporation of CZand C3 units into such clusters would require a different mechanism, perhaps attachment of the smaller species to the cage followed by cage rearrangement to accept the new carbon atoms. Again, such a growth mechanism could more readily occur with the highly excited species existing in carbon vapor systems than in a flame around 2000 K. Some features of the chemistryof fullerenes formationin flames may be pertinent to carbon vapor systems. Small (CZand C3) carbon molecules exist in carbon vapor systems, and the chemistry of their reactions would have features similar to molecularweight growth processes in flames. Also, thermodynamic equilibrium calculations show the hydrogen-less corannulene structure to be a significant fraction of the C20 present under conditions of interesL45 The presence of the main types of growth species used in the present mechanism, both cup-shaped fullerene precursors

CWand

c 7 0

Formation in Flames

and small C2 growth species, suggests that parts of this mechanism would be of interest in carbon vapor systems. Conversely,fullerene precursors in flames may be similar to those in carbon vapor systems, since the fraction of radical sites (dangling bonds) on the edges of PAH in combustion environments may be as high as 20-40%,28 corresponding,for example, to 2-4 dangling bonds per corannulenespecies (i.e., CzoHlo, c20H9, C20H8, c20H7, cZ0H6, etc.). Recent work on c a r b e n e ~(hydrocarbons ~~,~~ with two dangling bonds) shows that, for certainstructuressuchaso-benzyne(C6H4), the ground state is a singlet which is -38 kcal/mol more stable than thecorresponding triplet biradicalstate. Effectively, a weak triple bond is formed. Extensionof the concept to other aromatic structures for which adjoining dangling bonds can pair to form singlet triple bonds on the edges of the molecule suggests that these structures may be more stable than previously thought. Structures in which all dangling bonds can be so paired (such as the hydrogen-less analogues to naphthalene and to the Csv precursors) might then be favored energetically. Corannulene, for example,could conceivably be 190kcal/mol lower in energy in such a singlet state than in the 10-dangling-bond (1 1-plet) state. Relevance to Soot Formation. The proposed mechanism does not rely on the presence of soot for fullerene formation, consistent with the detection of fullerenes in a non- (but near-) sooting benzene flame as mentioned above. The mechanism also does not suggest that fullerenes, or their precursors, contribute to soot formation to any greater degree than do other PAH species. In flames producing both fullerenes and soot, the main formation of fullerenes lags significantly the formation of In contrast to soot, fullerenes have specific, well-defined molecular structures. Exactly formingthese carbon cagesrequires specific types of reaction sequences, any appreciable deviation from which would preclude fullerene formation. Evidence for the special nature of the fullerene formation process is seen in the narrow range of combustionconditionsfavoring fullerene growth (high temperatures and below-atmosphericpressure). Allowing for intramolecular rearrangements would increase the number of fullerene precursors allowed, but given the relatively slow rate of rearrangements below -2000 K, the residence time of flames would not normally permit multiple rearrangements. This places severe restrictions on the types of structures which can lead to fullerenes. The placement of 5- and 6-rings must be such that the structure is, or can readily rearrange to, that of a portion of a fullerene. Any reaction which removes a molecule from the group of suitable structures (e.g., reactive coagulation of HB and coronene) must be excluded from the fullereneformationsequence. These constraints are clearly dependent upon reaction conditions, and their existence for fullerenes is in stark constrast to soot particle inception and growth. Consideration of differences between fullerenes formationand soot formationthereforerequires discussion of the special nature of fullerene-forming intermediates. Any reactive coagulation of PAH can be seen as part of the soot formation process except for a small subset of these reactions which result in molecules with structures permitting further growth toward fullerenes. Accordingly, proposed mechanisms of fullerene formation should therefore be specific in the description of intermediates. This requirement can create a combinatorial problem in the case of PAH coagulation unless simplifying assumptions are made. For example, in the present work, only reactive coagulation of C,, precursors is considered. Similarly, Goeres and Sedlmayf19 consider only coagulation of naphthalenoctyl (hydrogen-lessnaphthalene), and Wakabyashi and Achibas' propose stacking of even-numbered carbon rings (e.g.,Clo,C12,Cle).Although theworkat presentdoesnot present all coagulation sequences which can contribute to fullerene formation in combustion sequences which can contribute to fullerene formationin combustion, it does for the first timedescribe

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The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 11011 a set of feasible reaction pathways in sufficient detail to permit critical testing. Several of the 3-5-ring PAH observed in flames (cf. Figures 2d-g and 3c,e) were observed by Chang et ~ 1in a. carbon ~ ~ arc fullerenereactor to which hydrogen donor compounds were added. They outline a mechanism for c 6 0 and C70 formation which contains several of the features of the present fullerene formation mechanism. A linear c16 is proposed to isomerize to a hydrogenless fluoranthene structure, which then undergoes successive C2 addition to yield the hydrogen-less analogues to benzo[ghi]fluoranthene, corannulene, and the other C5, intermediates (HB, TB, FB, XB), paralleling earlier versions of the present mecha n i ~ m . The ~ ~ proposed . ~ ~ mechanismof cage closing is formation, by either addition or isomerization, of a CS,structure with five fulvene-like moieties, which then cyclizes to form the completed cage. The role of fulvene-likestructural features in cage closing was also considered in the present work but was rejected based on the endothermicity of rearrangement of a 6-ring to a fulvenelike 5-ring and the absence of a clear mechanism for their formation by direct addition to the growing structure. Just as with the coagulation portion of the present mechanism, the direct formation chemistry presented for Cm and C70 cannot be considered to be complete, since other intermediates besides the ones proposed can be envisioned. Among the other fullerenes observed in flames, e.g., c76, (284, 0 , and C94,79the formation of c 7 6 , cs4, and c 9 4 would require different intermediate compounds than the C5, precursors larger than corannulene. For IPR fullerenes containing only 5- and 6-rings, it is a tautology that each 5-ring is part of a corannulenemoiety. It further follows that any IPR fullerene structure containing the HB moiety contains the FB moiety. However, the HB structure is not part of any IPR fullerene structure for (276, C B ~and , (294, and we conjecture that only Cion fullerenes (n 1 6) with 5-fold axes of symmetry (point groups D5d, D5h, 1,) can contain the HB moiety within an IPR structure. Therefore, formation of fullerenes besides Cion compounds requires eitherpultiple rearrangements or, more likely, divergencefrom the corannulene HB reaction pathway. However, the mechanism as described can be seen as at least a good approximation to the most likely route to direct Cm and C70 formation. Fullerene formation can then be seen as branching from the soot/flat PAH molecular weight growth sequence at the point where significant curvature is introduced into the molecule via internal 5-rings. Corannulene can therefore be seen as the prototypical fullerene precursor, although it is not the molecule having a suitable structure. Continuedgrowth along the fullerene sequence is contingentupon proper location of 5-ringswith respect to 6-rings or facility in ring rearrangement leading to such structures. As mentioned above, reactions causing significant deviations from the ideal structure prevent the molecule from forming a fullerene. Therefore,fullereneformationin combustion is an uphill battle, in terms of both thermodynamic barriers73 and structural considerations. Certain trends in soot formation are also followed in fullerene formation in flames. Thus, fewer fullerenes are produced in acetylene flames than in benzene and the peak values of PAH6 and soot in acetylene flamesare lower than in comparable benzene flames. Models for PAH and soot formation as well as the present model of fullereneformation rely on CzH2 as a primary growth species. The rate of formation of these molecular weight growth products therefore depends on C2H2 concentration to a high power (cf. Table IV). Since C2H2 concentrations are higher when C2H2is the fuel than for flames in which C6H6 is the fuel, these results appear inconsistent. The differencelies in the orders of magnitude increase in PAH concentration in the benzene flames, making more aromatic "seed" molecules available for continued molecular weight growth. The mechanism presented for fullerene formation is consistent with this behavior.

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11012 The Journal of Physical Chemistry, Vol. 97, No. 42, 1993

Not only the fullerene ions been 0bserved3.6.~~ but also PAH ions have long been observed in flames.*143 Among the ions observed, few correspond to the fullerene precursors presented here. Most of the neutral PAH observed have an even number of carbon atoms. Ionic PAH6 observed predominantly have odd numbers of carbon atoms, i.e., PAH6 with a phenalene ( C I ~ H ~ + ) core structure. For PAH6, the ionic species track a different, but analogous,sequenceof growth as compared to the neutrals. Also, PAH ion concentrations are generally orders of magnitude lower than those of comparable neutral species. Since the fullerene formation mechanism is based on curved PAH precursors with even numbers of carbon atoms, it is not surprising that ionic forms of them have not been observed. Furthermore, that ionic forms of these precursors have not been observed does not in any way preclude the existence of the proposed precursors. The observed ions show the beginning of a sequence of odd-numbered curved PAH containing 5- and 6-ring~.~,*!Such a growth sequence, analogous to the observed (phenalene) sequence of PAH6 would be a reasonable consequenceof extending the chemistry of PAH6 growth to the chemistry of 5- and 6-ring containing PAH (PAH5/6). However, like the phenalene sequence, such ionic forms of PAH5/6 would be expected to be present in concentrations orders of magnitude lower than comparably sized neutral PAH5/6. There is an additional complication in using such a sequence of PAH5/6 with odd numbers of carbon atoms to explain fullerene formation. Stable fullerenes, both neutrals and ions, have even numbers of carbon atoms. An explanation of the cage closing steps for odd-numbered cages would need to be developed. Proposed mechanisms for removal of carbon atoms from fullerenes are based on their ejection in multiples of CZ.*~ In short,observations of ionic species relevant to fullerene formation do not cast doubt upon the mechanism’s validity.

Conclusion The detailed chemical mechanism presented here predicts formation times for fullerenes C ~ and O C70 which agree with experimentallyobserved times to within the range of uncertainty associated with the reaction rate coefficients. Therefore, the mechanism is kinetically plausible. Consideration of the elementary reactions in the mechanism facilitated the consideration of rate-limiting processes and of a kinetically-basedexplanation for the C ~ O / C ~ ratioa73 O Application of the mechanism to prediction of known trends in fullerene formation with respect to temperature and pressure yielded results showing encouraging consistency with data, though limited by the inability of the simplified modeling approach to account for the chemistry of the entire flamea73These results will be published separately. An equivalent mechanism for carbon vapor systems is expected to be relevant to fullerene formation in the graphite vaporization process. The mechanism is based on known PAH reaction types and does not depend on the presence of soot for fullerene formation.

Acknowledgment. We are grateful to the Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research, US.Department of Energy, under Grant DE-FGO284ER13282 for financial support of the research. References and Notes (1) Kroto, H. W.; Heath, J. R.; OBrien, S. C.; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162. (2) Kroto, H. W.; Allaf, A. W.; Balm, S . P. Chem. Reu. 1991,91, 1213. (3) Gerhardt, Ph.; LBffler, S.;Homann, K. H. Chem. Phys. Lett. 1987, 137, 306; Twenty-Second Symposium (Internutionul) on Combustion; The Combustion Institute: Pittsburgh, 1989;p 395. (4) Howard, J. B.; McKinnon, J. T.; Mahrovsky, Y.;Lafleur, A,; Johnson, M. E.Nature 1991, 352, 139. (5) McKinnon, J. T.; Bell, W. L.; Barkley, R. B. Combust. Flume 1992, 88, 102.

Pope et al. (6) Haufler, R. E.;Chai, Y.; Chibante, L. P. F.; Conceicao, J.; Jin, C.; Wang, LA.; Maruyama, S.;Smalley, R. E. Mater. Res. Soc. Symp. Proc. 1991, 206, 627. (7) Curl, R. F. Nature 1993, 363, 14. (8) Frenklach, M.; Clary, D. W.; Gardiner, W. C., Jr.; Stein, S. E. Twentieth Symposium (Internutionul) on Combustion; The Combustion Institute: Pittsburgh, 1984; p 887. (9) Frenklach, M.; Warnatz, J. Combust. Sci. Technol. 1987,51, 265. (10)Bauer, S. H.; Jeffers, P. M. Energy Fuels 1988, 2, 446. (1 1) Harris, S.J.; Weiner, A. M.; Blint, R. J. Combust. Flame 1988, 72, 91. (12) Prado, G. F.; Lee, M. L.; Hites, R. A.; Hoult, D. P.; Howard, J. B. Sixteenth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, 1976;p 649. (13) Bittner, J. D.; Howard, J. B. Eighteenth Symposium (Internutionul) on Combustion; The Combustion Institute: Pittsburgh, 1981;p 1105. (14) Bockhorn, H.; Fetting, F.; Wenz, H. W. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 1067. (15) Homann, K. H. Twentieth Symposium (Inlernutional) on Combustion; The Combustion Institute: Pittsburgh, 1984; p 857. (16) Lam, F. W.; Longwell, J. P.; Howard, J. B. Twenty-ThirdSymposium (Internutionul) on Combustion; The Combustion Institute: Pittsburgh, 1991; p 1477. (17) Lafleur, A. Personal communication. (18) Scott, L. T.; Roelofs, N. H. J. Am. Chem. Soc. 1987, 109, 5461. (19) McKinnon,J.T. Ph.D. Thesis,Massachusetts Instituteof Technology, Cambridge, MA, 1989. (20) Dias, J. R. J. Chem. Inf. Comput. Sci. 1984, 24, 124. (21) Warnatz, J. RateCoefficientsin theC/H/OSystem. In Combustion Chemistry, Gardiner, W. C., Jr., Ed.; Springer-Verlag: New York, 1984; Chapter 5. (22) Howard, J. B.; Wersborg, B. L.; Williams, G. C. Furaday Symp. Chem. SOC.1973, 7, 109. (23) Wersborg, B. L.; Howard, J. B.; Williams, G. C. Fourteenth Symposium (Internutionul) on Combustion; The Combustion Institute: Pittsburgh, 1973;p 929. (24) Harris, S.J.; Weiner, A. M. Combust. Sci. Technol. 1983,31, 155. (25) Lam, F. W.; Howard, J. B.; Longwell, J. P. Twentysecond Symposium (Internutionul) on Combustion; The Combustion Institute: Pittsburgh, 1989;p 323. (26) McKinnon, J. T.; Howard, J. B. Combust. Sci. Technol. 1990,74, 175. (27) Dobbins, R. A,; Subramaniasivam, H. In Mechanisms and Models of Soot Formation-Lecture Notes in Physics; Bockhorn, H., Ed.; SpringerVerlag, in press. (28) Howard, J. B. Twenty-Third Symposium (Internutionul) on Combustion; The Combustion Institute: Pittsburgh, 1990; p 1107. (29) Wersborg, B. L.; Yeung, A. C.; Howard, J. B. Fifteenth Symposium (Internutionul) on Combustion;The Combustion Institute: Pittsburgh, 1975; p 1439. (30) Harris, S.J.; Weiner, A. M. Twenty-Second Symposium (Internutionul) on Combustion; The Combustion Institute: Pittsburgh, 1988;p 333. (31) Colket, M. B.; Hall, R. J.; Sangiovanni, J. J.; Seery, D. J. The Determinution of Rate-Limiting Steps during Soot Formation, Report No. UTRC89-13;UnitcdTechnologiesResearchcenter: East Hartford, CT, 1989. (32) Frenklach, M.; Wang, H. Twenty-ThirdSymposium (Internutionul) on Combustion; The Combustion Institute: Pittsburgh, 1990;p 1559. (33) McKinnon, J. T.; Howard, J. B. Twenty-Fourth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, 1992;p 965. (34) Street, J. C.; Thomas, A. Fuel 1955, 34, 4. (35) Heckman, F. A.; Harling, D. E. Rubber Chem. Technol. 1966, 39, 1. (36) Ebert, L. B.; Scanlon, J. C.; Clausen, C. A. Energy Fuels 1988, 2, 438. (37) Howard, J. B.; Lafleur, A. L.; Makarovsky, Y.; Mitra, S.; Pope, C. J.; Yadav, T. K. Carbon 1992, 30, 1183. (38) Howard, J. B.; McKinnon, J. T.; Johnson, M. E.;Mahrovsky, Y.; Lafleur, A. J. Phys. Chem. 1992,96, 6657. (39) Malhotra, R.; R w ,D. S. J. Phys. Chem. 1991, 95,4599. (40) Warnatz, J. Twenty-Fourth Symposium (Internutionul) on Combustion; The Combustion Institute: Pittsburgh, 1992; p 553. (41) Schmalz, T. G.;Seitz, W. A,; Klein, D. J.; Hite, G. E.J. Am. Chem. Soc. 1988, 110, 1113. (42) Kroto, H. W. Nature 1987, 329, 529. (43) Kroto, H. W.; McKay, K. Nature 1988, 331, 328. (44) Frenklach, M.; Ebert, L. B. J. Phys. Chem. 1988, 92, 561. (45) Brabec, C. J.; Anderson, E. B.; Davidson, B. N.; Kajihara, S. A.; Zhang, Q.-M.; Bernholc, J.; Todnek, D. Phys. Reu. B 1992.46, 7326. (46) Baum, Th.; Mffler, S.;Weilmiinster, P.; Homann, K. H. ACS Diu. Fuel Chem. Prepr. 1991,36, 1533. (47) Baum, Th.;Mffler, S.;LBffler, Ph.; Weilmlinster, P.;Homann, K.H.Ber. Bunsen-Ges. Phys. Chem. 1992, 96, 841. (48) Smalley, R.E. Acc. Chem. Res. 1992, 25, 92. (49) Goeres, A.;Sedlmayr, E. Chem. Phys. Lett. 1991,184, 310. (50) Kerner, R.; Penson, K. A.; Bennemann, K. H. Europhys. Lett. 1992, 19, 363. (51) Wakabayshi, T.;Achiba, Y. Chem. Phys. Lett. 1992, 190, 465.

C a and C ~ Formation O in Flames (52) Heath, J. R. In Fullerenes-Synthesis, Properties, and Chemistry

ofLargeCarbonclucters;Hammond,G. S.,Kuck,V. J.,Eds.;ACSSymposium

Series 481; American Chemical Society: Washington, DC, 1992;Chapter 1, pp 1-21. (53) von Helden, G.;Gotts, N. G.; Bowers, M. T. Nature 1993,363,60. (54) Hunter, J.; Fye, J.; Jarrold, M. F. Science 1993, 260,784; J. Phys. Chem. 1993, 97, 3460. (55) Miller, J. H.; Smyth, K. C.; Mallard, W. G. Twentieth Symposium (International)on Combustion; The Combustion Institute: Pittsburgh, 1984; p 1139. (56) Miller, J. H. Twenty-Third Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, 1990; p 91. (57) Frenklach, M.; Wang, H. Mechanisms and Models of Soot FormatiorrLecture Notes in Physics; Bockhorn, H., Ed.; Springer-Verlag, in press. (58) Brouwer, L.; Trce, J. In?. J . Chem. Kine?. 1988, 20, 379. (59) Benson, S. W. Thermochemical Kinetics, 2nd ed.; John Wiley & Sons: New York, 1976. (60) Stein, S. E.; Golden, D. M.; Benson, S . W. J. Phys. Chem. 1977,81, 3 14. (61) Stein, S. E.; Fahr, A. J . Phys. Chem. 1985,89, 3714. (62) Moiseeva, N. F.; Dorofeeva, 0. V. Thermochim. Acta 1990, 168, 179. (63) Beckhaus, V. H.-D.;RiIchardt, M. K.; Diederich, F.; Kao, M.; Foote, C. S . Angew. Chem. 1992, 104,69. (64) Pan, C.; Sampson, M. P.; Chai, Y.; Hauge, R. H.; Margrave, J. L. J. Phys. Chem. 1991, 95, 2944. (65) McKinnon, J. T. J. Phys. Chem. 1991, 95, 8941. (66) Stanton, M. D.; Newton, R. E. J. Phys. Chem. 1988, 92, 2141. (67) Steele, W. V.; Chirico, R. D.; Smith, N. K.; Billups, W. E.; Elmore, P. R.; Wheeler, A. E. J. Phys. Chem. 1992,96,4731. (68) Mitra, S.; Pope, C. J.; Gleason, K. K.; Makarovsky, Y.;Lafleur, A. L.; Howard, J. B. Mater. Res. SOC.Symp. Proc. 1992, 270, 149.

The Journal of Physical Chemistry, Vol. 97, No. 42, 1993 11013 (69) Pope, C. J. M.S. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1988. (70) Kee, R. J.; Rupley, F. M.; Miller, J. A. Chemkin-II: A Fortran Chemical Kinetics Packagefor the Analysis of Gas-Phase Chemical Kinetics, Report SAND89-8009; Sandia National Laboratory: Livermore, CA, 1989. (71) Lutz, A. E.; Kee, R. J.; Miller, J. A. SENKIN: A Fortran Program for Predicting Homogeneous Gas Phase Chemical Kinetics with Sensitivity Analysis, Report SAND87-8248; Sandia National Laboratory: Livermore, CA, 1988. (72) Reynolds, W. C. STANJAN Multicomponent Equilibrium Program v.3.60, available on disk, 1986. (73) Pope, C. J. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1993. (74) Westmoreland, P. R. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1986. (75) Blush, J. A.; Clauberg, J.; Kohn, D. W.; Minsek, D. W.; Zhang, X.; Chen, P. Acc. Chem. Res. 1992, 25, 385. (76) Zhang, X . ; Chen, P. J. Am. Chem. SOC.1992, 114, 3147. (77) Howard, J. B. Twenty-Fourth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, 1992; P 933. (78) Chang, T.-M.; Naim, A.; Ahmed, S . k ;Goodl&, G.; Shevlin, P. B. J. Am. Chem. Soc. 1992, I 14,7603. (79) Anacleto, J. F.; Boyd, R. K.; Pleasance, S.; Quilliam, M. A.; Howard, J. B.: Lafleur, A. L.: Makarovskv. Y. Can. J. Chem. 1992, 70.2558. (80) Unpublished results. (81) Olson, D. B.; Calcote, H. F. Eighteenth Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, 1981; p 453. (82) Calcote, H. F.; Keil, D. G. Combust. Flame 1988, 74, 131. (83) LBMer,S.; Homann, K. H. Twenty-ThirdSymposium(International) on Combustion; The Combustion Institute: Pittsburgh, 1990; p 355. (84) OBrien, S. C.; Heath, J. R.; Curl, R. F.; Smalley, R. E. J. Chem. Phys. 1988,88, 220.