Reaction Mechanisms Governing the Formation of Polycyclic Aromatic

Nov 21, 2006 - as 700 °C.1 Furthermore, to sustain flow in these fuel systems .... a flow rate of 50 mL/h to the reactor coil (Restek Silcosteel- ... ...
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J. Phys. Chem. C 2007, 111, 86-95

Reaction Mechanisms Governing the Formation of Polycyclic Aromatic Hydrocarbons in the Supercritical Pyrolysis of Toluene: C28H14 Isomers Jennifer W. McClaine and Mary J. Wornat* Department of Chemical Engineering, Louisiana State UniVersity, Baton Rouge, Louisiana 70803 ReceiVed: June 6, 2006; In Final Form: September 25, 2006

Reaction pathways for the formation of C28H14 polycyclic aromatic hydrocarbons (PAH)sof which there are eight benzenoid isomerssduring the supercritical pyrolysis of toluene are described in detail. These reaction mechanisms involve the addition of benzyl, methyl, and/or phenyl radicals to smaller PAH products in three specific reactions: (A) addition of methyl and benzyl, usually to a position adjacent to a bay region; (B) addition of phenyl to a bay region; and (C) addition of two methyls to a bay region. Using these three types of reactions, we are able to explain why the five identified C28H14 PAH-benzo[a]coronene, phenanthro[5,4,3,2-efghi]perylene, benzo[cd]naphtho[3,2,1,8-pqra]perylene, benzo[ghi]naphtho[8,1,2-bcd]perylene, and benzo[pqr]naphtho[8,1,2-bcd]perylene-are present in our product mixture and why bisanthene, a C28H14 isomer that we know is not present from UV spectral data, is not formed. We then determine reaction pathways for the remaining two C28H14 benzenoid isomers, naphthaceno[3,4,5,6,7-defghij]naphthacene and tribenzo[cd,ghi,lm]perylene, to deduce that the sixth C28H14 PAH detected in our product mixture by HPLC/MS is most likely tribenzo[cd,ghi,lm]perylene.

Introduction In addition to providing power through combustion, fuel in future hypersonic aircraft will be used as a coolant to absorb heat from the engine. It is estimated that the required cooling demands could cause the jet fuel to reach temperatures as high as 700 °C.1 Furthermore, to sustain flow in these fuel systems and prevent boiling, the pressure is maintained well above the critical pressure of the jet fuel.1-3 This combination of high temperature and high pressure causes the fuel to become supercritical, and thus to have unique properties characteristic of both gas and liquid states (e.g., diffusion is more gaslike, yet solvation properties are more similar to those of a liquid). A supercritical environment not only changes the physical properties of the fuel, but can also lead to thermal decomposition. On one hand, this can be advantageous because pyrolytic reactions in which hydrocarbons are “cracked” are endothermic, thus providing an additional heat sink;1 however, these same conditions also encourage the formation of carbonaceous solids. In fact, one of the main problems in using jet fuel as a coolant in these aircraft engines is that accumulation of solid deposits on the surfaces of the fuel system components leads to fouling2-4sand in an extreme case, could cause complete plugging of fuel lines, which would be disastrous for an aircraft during flight. To prevent the formation of carbonaceous deposits from supercritical fuel pyrolysis, it is first necessary to understand the chemical reactions responsible for the formation of deposit precursors under pyrolytic conditions. The development of reaction pathways, however, first requires the identification of product components; in particular, it is necessary to identify * Corresponding author. Mailing address: Department of Chemical Engineering, Chemical Engineering Building, South Stadium Drive, Louisiana State University, Baton Rouge, LA 70803. E-mail: [email protected]. Telephone: (225) 578-7509. Fax: (225) 578-1476.

all polycyclic aromatic hydrocarbons (PAH), compounds that are precursors to carbonaceous solids, for systematic development of reaction mechanisms that can describe both the formation of all identified PAH as well as aid in the identification of unknown PAH by reducing the number of possible product structures. Specifically, reaction pathways can be developed using (1) bond energies of the fuel molecules, to determine which radicals are present in a given system and which radicals are most likely to be in greater abundance; (2) general information regarding bond energies [for example, an alkyl carbon-hydrogen (C-H) bond is usually of lower energy than an aryl C-H bond5], for the case of larger molecules in which published bond energies are not available; (3) an analysis of a radical’s resonance structures, which can be used to explain why particular locations on a radical might be more favored for reaction; and (4) steric hindrance considerations, which can reveal why certain reactions might be preferred over others. Use of these four types of data allows consistent reaction mechanisms to be developed for PAH observed as products of supercritical pyrolysis. These models can then be extended to predict the formation of even larger PAHscompounds whose decreased solubility might cause them to fall out of solution and form the first solid deposits. For this effort, use of a model fuel (such as a single component of jet fuel) allows reaction mechanisms to be more easily determined; these reaction pathways can then be extended for multicomponent systems. Supercritical pyrolysis experiments with methylcyclohexane,6 toluene,7,8 and 1-methylnaphthalene9 have led to the identification of more than 35 2- to 10-ring PAH products for each individual fuel. Many of the PAH identified as products of these model fuels have also been found in the supercritical pyrolysis products of jet fuel.1 Therefore, reaction mechanisms developed to describe PAH formation in the supercritical pyrolysis of an individual component of jet fuel will also be applicable to jet fuel itself.

10.1021/jp063507q CCC: $37.00 © 2007 American Chemical Society Published on Web 11/21/2006

Reaction Mechanisms of PAH Formation: C28H14 Isomers Most research reported in the literature involving toluene pyrolysis has been performed at or below atmospheric pressure,10-21 at temperatures between 600 and 1300 °C; under these conditions, toluene is clearly in the gas phase. Gas-phase reaction mechanisms governing PAH formation under conditions that favor cleavage of toluene’s aromatic ring (T > 800 °C) have been investigated by a number of authors.14,19,22-24 It is generally accepted that the hydrogen-abstraction/C2-addition (HACA) reaction sequence25 governs PAH formation at temperatures high enough to facilitate breaking of aromatic carboncarbon (C-C) bonds. In the HACA reaction mechanism, repeated addition of two-carbon hydrocarbons to various fuels yields small PAH; further reaction of the small PAH with C2 hydrocarbons leads to the formation of larger PAH. Experiments discussed in this article, using toluene as a model fuel, have been performed at 100 atm and 535 °Csconditions well above toluene’s critical pressure and temperature (Pc ) 41 bar, Tc ) 320 °C). Under these conditions, we have found no evidence that toluene’s aromatic ring ruptures: acetylene is not produced,7 nor are any cyclopenta-fused PAH or ethynylsubstituted PAH, products frequently found26-29 in combustion or high-temperature pyrolysis systems that signify the participation of acetylene in PAH formation reactions. Gaseous products formed in our experiments are predominantly methane, with a small amount of ethane-both of which are made from toluene’s methyl group. (Breaking of the alkyl-aryl carbon-carbon bond is observed in this system.) In the absence of aromatic ring cleavage (as observed in our system), we are limited to reaction pathways involving toluene and radicals generated from the thermal decomposition of toluene. In addition, the high-pressure, supercritical environment forces molecules to be in close quarters, constraining the radicals to react with species that are nearby (generally, these are molecules that are in greatest abundance) and also possibly affecting reaction specificity. We therefore expect the reaction mechanisms governing PAH formation under supercritical conditions to be markedly different from those observed for high-temperature, low-pressure systems in which the aromatic ring ruptures. Figure 1 shows an HPLC/UV chromatogram of the products of supercritical toluene pyrolysis7 at 535 °C, 100 atm, and a residence time of 140 s-conditions representative of those predicted for fuel lines of hypersonic aircraft. Depicted in Figure 1 are the structures of over 40 2- to 10-ring PAH that have been identified8,30 in this product mixture by high-pressure liquid chromatography (HPLC) coupled with ultraviolet-visible (UV) diode-array detection and mass spectrometry (MS). There are three features of the HPLC/UV chromatogram shown in Figure 1 that characterize the supercritical pyrolysis of toluene: (1) 3 times as many benzenoid PAH (PAH composed of only sixcarbon rings) have been identified in this product mixture relative to PAH containing a five-membered ring; (2) all benzenoid PAH products are fully aromatic; and (3) none of the PAH identified have a cove or fjord region (concave faces of five or six carbons, respectively31). (For all three cases, an extensive search through UV spectra of compounds that were not fully aromatic,32,33 contained a cove or fjord region,32-37 and/or contained a five-membered ring33,38 did not yield any matches with the products of supercritical toluene pyrolysis.) In this article, we focus on reaction mechanisms to describe the formation of the six eight-ring C28H14 PAH identified as products in the supercritical pyrolysis of toluene (compounds eluting between 55 and 65 min in Figure 1), using the unique set of PAH identified in the product mixture (and shown in Figure 1). The C28H14 compounds are representative of the large

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Figure 1. HPLC chromatogram of products of supercritical toluene pyrolysis at 535 °C, 100 atm, and 140-s residence time. The rise in the baseline at ∼43 min is due to a change in the mobile phase to the UV-absorbing dichloromethane. Identified components, in order of elution, from left to right, are: toluene, indene, naphthalene, 1-methylnaphthalene, biphenyl, 2-methylnaphthalene, fluorene, phenanthrene, anthracene, fluoranthene, pyrene, 2-methylanthracene, benzo[a]fluorene, 1-methylpyrene, 1-phenylpyrene, benz[a]anthracene, chrysene, benzo[a]fluoranthene, benzo[e]pyrene, benzo[b]fluoranthene coeluting with perylene, benzo[k]fluoranthene, benzo[a]pyrene, pentaphene, benzo[ghi]perylene, indeno[1,2,3-cd]pyrene, methylated benzo[ghi]perylene, anthanthrene, methylated benzo[ghi]perylene, coronene, naphtho[2,1a]pyrene, methylated anthanthrene, dibenzo[b,ghi]perylene, 1-methylcoronene, benzo[a]coronene, phenanthro[5,4,3,2-efghi]perylene, benzo[cd]naphtho[3,2,1,8-pqra]perylene, benzo[ghi]naphtho[8,1,2-bcd]perylene, benzo[pqr]naphtho[8,1,2-bcd]perylene, naphtho[8,1,2-abc]coronene, methylated naphtho[8,1,2-abc]coronene, ovalene, and methylated ovalene.

PAH that are thought to precede solids formation. In developing a set of reaction mechanisms to describe how C28H14 PAH are formed in this environment, we first determine which radicals are more dominant in our system (based on toluene’s bond energies), show how smaller PAH (naphthalene, phenanthrene) are formed through reaction of these radicals with toluene molecules, and discuss the three types of reactions found to govern growth of large PAH in our system. We then use these three types of reactions to show how each of the five identified C28H14 PAH are formed, as well as deduce the structure of the sixth unknown C28H14 isomer. Experimental Methods Supercritical pyrolysis experiments were performed using a reactor designed by Davis39 and following the procedure described by Ledesma et al.7 A schematic of the apparatus is shown in Ledesma et al.7 After liquid toluene (HPLC grade, 99.8% purity) had been sparged with nitrogen for several hours at room temperature, 200 mL of fuel was loaded into a highpressure nonreciprocating pump. Toluene was then pumped at a flow rate of 50 mL/h to the reactor coil (Restek Silcosteelcoated stainless steel tubing; i.d. 1.016 mm, o.d. 1.59 mm, length 2.44 m); a silica-lined reactor was chosen to prevent wallcatalyzed reactions.39 The temperature of the reactor coil was maintained at 535 °C using a fluidized-alumina bath and was monitored with three thermocouples spaced evenly around the external wall of the reactor coil. Once toluene was flowing through the system, the pressure was increased to 100 atm and held constant by a back-pressure regulator. Reactions were quenched as the reaction mixture exited the reactor by passing the products through a water-cooled heat exchanger, maintained at 25 °C. The products then flowed through a 10-µm filter and

88 J. Phys. Chem. C, Vol. 111, No. 1, 2007 on to a high-pressure sample loop from which liquid products were collected. A gas bag was attached to the apparatus after the sample loop to collect noncondensable products for analysis by gas chromatography. Prior to an experiment, dichloromethane was used to clean the pump, pressure transducer housings, and back-pressure regulator. The pressure transducer housings and pressure regulator were then placed under a fume hood to evaporate any remaining dichloromethane, and the pump was purged with nitrogen several times. The apparatus was then reassembled and pressure-tested with toluene to ensure that there were no leaks in the system. All tubing and fittings were made of stainless steel (except for the reactor, which was made of silica-lined stainless steel) and were changed before each experiment. Condensed products were analyzed by gas chromatography (GC) coupled with mass spectrometry (MS) to identify and quantify smaller aromatic products (up to approximately four rings). High-pressure liquid chromatography (HPLC) with ultraviolet-visible (UV) diode-array detection and mass spectrometry (MS) was used to identify larger aromatic compounds. Specific details regarding the GC/MS and HPLC/UV/MS systems (e.g., equipment description and operation) are given in Ledesma et al.7 and McClaine et al.30 A 2-mL aliquot of product mixture was concentrated and dissolved into 100 µL of dimethyl sulfoxide (DMSO). A 25µL aliquot of the resulting product mixture was injected into a Hewlett-Packard model 1050 HPLC instrument, coupled to a UV diode-array detector that monitors UV absorbance from 190 to 520 nm. Product components were separated with a reversephase Vydac 201-TP C18 column (250 mm × 4.6 mm; particle size, 5 µm) using a water/acetonitrile, acetonitrile, and dichloromethane sequence of solvents (0-40 min, linear gradient from 60:40 water/acetonitrile to pure acetonitrile; 40-80 min, linear gradient from acetonitrile to dichloromethane). The HPLC/UV chromatogram of Figure 1, which shows the products of supercritical toluene pyrolysis, was generated using this method. A 20-µL aliquot of the product mixture (2 mL of product concentrated in 100 µL of DMSO) was also injected into an Agilent Technologies 1100 Series LC/MSD SL instrument (MSD model G1956B). The mass spectrometer used an atmospheric-pressure photoionization (APPI) source to acquire two signals: the first signal was optimized for smaller PAH (up to five or six rings), and the second signal was optimized for large PAH (six or more rings, up to mass/charge ratios of 700). Compounds in the product mixture were separated with a reverse-phase Pinnacle II PAH C18 column (250 mm × 4.6 mm; particle size, 5 µm; pore size, 110 Å) using a water/ methanol, methanol, and dichloromethane sequence of solvents (0-40 min, linear gradient from 50:50 water/methanol to pure methanol; 40-100 min, hold in methanol; 100-140 min, linear gradient from methanol to dichloromethane; 140-180 min, hold in dichloromethane). After separation, components in the product mixture passed through an ultraviolet-visible diode-array spectrophotometer, which was set to monitor UV absorbance from 190 to 520 nm with a resolution of 1 nm, and a mass spectrometer. UV and mass spectra of the separated components were recorded every 0.4 and 1 s, respectively, as the components exited the column. For more details regarding the HPLC/MS system, the reader is referred to McClaine et al.30 For each peak in the HPLC/UV chromatogram, product UV spectra were compared to those in our comprehensive PAH reference library, as well as those published in the literature. A product was identified when the UV spectrum, which alone is sufficient to establish the identity of an unsubstituted PAH,

McClaine and Wornat matched that of a reference standard. Mass spectra were useful in substantiating the identities of compounds for which we had UV spectra; for compounds for which a UV spectrum was not available, the MS data significantly reduced the number of possible PAH product structures. The MS results can also aid in the identification of substituted PAH; for the case of an alkylated PAH (where, for this research, the alkyl group is mainly a methyl group), the UV spectrum looks almost identical to that of the parent PAH, but is shifted a few nanometers to higher wavelengths.40,41 Although MS and UV spectra cannot always give the exact position on a PAH to which a substituent group is attached, knowledge of the extent to which PAH are methylated aids in the development of reaction pathways. Six of the eight C28H14 PAH discussed in this article have available reference standards or published UV spectra: phenanthro[5,4,3,2-efghi]perylene,37 benzo[pqr]naphtho[8,1,2-bcd]perylene,42,43 benzo[a]coronene,44,45 benzo[cd]naphtho[3,2,1,8pqra]perylene,46,47 benzo[ghi]naphtho[8,1,2-bcd]perylene,30 and bisanthene.32 The remaining two, tribenzo[cd,ghi,lm]perylene and naphthaceno[3,4,5,6,7-defghij]naphthacene, do not have published UV spectra, although certain features of their UV spectra have been deduced using annellation theory.30 Results and Discussion There has been a fair amount of research concerning the formation of radicals during toluene pyrolysis at moderate temperatures in which the aromatic ring remains intact.11,21,48-50 The possible radicals generated at these temperatures are benzyl, phenyl, methyl, tolyl, and atomic hydrogen. Recombination of these radicals primarily yields benzene, xylenes (three isomers), ethylbenzene, and 17 C14H14 compoundssdiphenylethanes (bibenzyl and 1,1-diphenylethane), benzyltoluenes (three isomers), and dimethyldiphenyls (12 isomers). An explanation as to how these nonfused two-ring aromatic products form from the recombination of two radicals is relatively straightforward and has been discussed by others.13,48,51-53 However, at the conditions studied in this article, larger compounds are formed (PAH) that cannot be explained by simple two-radical recombination reactions. Thus, it is the purpose of this article to explain how these PAH are formed from the successive addition of radicals. Specifically, we focus on the C28H14 PAH, eight-ring compounds of which there are eight benzenoid isomers. Using HPLC/UV/MS data, we have been able to identify8,30 five of these isomers in our supercritical toluene pyrolysis product mixture: benzo[a]coronene, phenanthro[5,4,3,2-efghi]perylene, benzo[cd]naphtho[3,2,1,8-pqra]perylene, benzo[ghi]naphtho[8,1,2-bcd]perylene, and benzo[pqr]naphtho[8,1,2-bcd]perylene. A sixth C28H14 isomer has been detected, and its UV spectrum is inconsistent with the one published32 for bisanthene. This sixth C28H14 PAH product of toluene pyrolysis is thus either tribenzo[cd,ghi,lm]perylene or naphthaceno[3,4,5,6,7-defghij]naphthacene, neither of whose UV spectrum is published. Through the development of reaction pathways, we are able to show why the five observed C28H14 isomers are present in the toluene product mixture and why bisanthene is not. We then compare reaction mechanisms for naphthaceno[3,4,5,6,7-defghij]naphthacene and tribenzo[cd,ghi,lm]perylene to suggest which of these two isomers is the sixth C28H14 product. This is the first time a mechanism has been developed to describe the formation of C28H14 PAH, or any large PAH, from radicals generated during toluene pyrolysis. Before we show the pathways through which large PAH (in particular, the eight benzenoid C28H14 isomers) are formed, we

Reaction Mechanisms of PAH Formation: C28H14 Isomers first briefly establish which radicals are formed from toluene decomposition and determine those likely to be more dominant in our system, based on observations of major products as well as bond dissociation energies for the various carbon-carbon (C-C) and carbon-hydrogen (C-H) bonds of toluene. Radicals Generated in Supercritical Toluene Pyrolysis. Hein and Mesee54 and Szwarc21 were among the first to study the initial decomposition of toluene into radicals, which can be summarized in the following three initiation reactions:

As is shown, toluene can decompose into phenyl and methyl (reaction 1), benzyl and atomic hydrogen (reaction 2), or tolyl (shown here as o-tolyl, but could also form m- or p-tolyl) and atomic hydrogen (reaction 3). Thus, the radicals available as building blocks for PAH in our system are benzyl, phenyl, tolyl, and methyl. Although atomic hydrogen does not facilitate PAH growth directly, it can form other radicals through abstraction of a hydrogen or methyl from a neighboring toluene molecule, to form hydrogen gas and tolyl/benzyl or methane and phenyl, respectively. It is also possible for phenyl to abstract a hydrogen atom from toluene to form benzene and, depending on where the hydrogen was abstracted, tolyl or benzyl:

Similar reactions could be written for other radicals reacting with toluene; these propagation reactions yield smaller products and additional radicals. We could also show the products of phenyl and toluene to be diphenylmethane and atomic hydrogen:

In reaction 5, toluene’s methyl C-H bond decomposes to yield atomic hydrogen and benzyl (reaction 2), which then reacts with phenyl to form diphenylmethane. Reactions 4 and 5 are consistent with products reported for methyl addition to toluene under pyrolytic conditions;11,13,21,52,55-59 we expect that these results can be extended for different types of radicals reacting with toluene. The major findings of the research involving methyl addition to toluene can be summarized as follows: (1) methyl radicals both abstract and displace hydrogen on the toluene molecule, (2) hydrogen abstraction occurs primarily on the methyl carbon, (3) methyl adds preferentially to the methyl carbon in gas-phase experiments, and (4) methyl adds to both methyl and aryl carbons of toluene in liquid-phase pyrolysis

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Figure 2. Bond energies for the aryl-methyl C-C bond,5 aryl C-H bond,5 methyl C-H5 bond, and aromatic C-C bond72 in toluene.

experiments (with yields of o- and m-xylene greater than that of p-xylene).15,52,60 In addition to the initiation (reactions 1-3) and propagation (reactions 4 and 5) reactions, termination reactions also exist and involve the reaction of two radicals. For example, atomic hydrogen and phenyl react to yield benzene, and reaction of benzyl and phenyl yields diphenylmethane. Figure 2 shows the bond dissociation energies for all C-C and C-H bonds in the toluene molecule.5 As can be seen, the bond with the lowest bond dissociation energy is the methyl C-H bond, followed by the methyl-aryl C-C bond, the aryl C-H bond, and finally the aryl C-C bond (which is not broken under our conditions). Thus, we expect that the bonds primarily broken in our system are the methyl C-H bond and methylaryl C-C bond, forming benzyl, methyl, and phenyl, and that tolyl, which requires breaking of an aryl C-H bond, is a relatively minor player in reaction mechanisms. Results of our supercritical pyrolysis studies show the major products to be benzene, the three xylene isomers and ethylbenzene, as well as the 17 C14H14 isomers (bibenzyl, 1,1diphenylethane, 3 benzyltoluenes, and 12 dimethyldiphenyls). Ethylbenzene can be formed through the reaction of benzyl and methyl; the xylenes form from displacement of an aryl hydrogen on toluene by methyl, not requiring tolyl. Kershaw53 explained in detail how reactions of benzyl with o-, m-, and p-tolyl could result in the 17 C14H14 isomers. However, he considered the C14H14 isomers to be formed from two radicals in termination reactions and did not consider propagation reactions, in which benzyl reacts with toluene to displace hydrogen. Because the conversion of toluene is approximately 3% under our conditions, it makes sense that toluene would be an important reactant with which radicals can react. In addition, bibenzyl has a yield almost as high as the combined yield of all other C14H14 isomers found in our product mixture, demonstrating that benzyl is indeed the dominant radical in our system. Thus, although it is possible that tolyl is formed under our conditions, based on bond energies, we believe that the dominant radicals in our system are benzyl, methyl, and phenyl. They, along with toluene, are therefore the principal reactants in our supercritical toluene reaction environment. The structures of our PAH products in Figure 1 indicate that several PAH would be difficult to make from benzyl, methyl, phenyl, and toluene alonesand that naphthalene (I) must be required for their formation. In fact, we believe that naphthalene, the highest-yield fused-ring PAH product in our experiments,7 is required to form two of the observed C28H14 isomers. Therefore, although the focus of this article is to discuss the C28H14 isomers (eight-ring PAH), we briefly discuss the formation of naphthalene in our system. Formation of Naphthalene. In the combustion and pyrolysis literature, the two mechanisms that are generally accepted for the formation of naphthalene are the reaction of two cyclopentadiene molecules61,62 and the reaction of benzene with two acetylene molecules,63-65 although the reaction of benzene with 1,3-butadiene has also been suggested.66 We have already established that acetylene is not present in our system. Formation

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SCHEME 2

of cyclopentadiene (a cyclic five-carbon molecule) or 1,3butadiene (a four-carbon alkene) would require either rupture of toluene’s aromatic ring, which we have shown does not occur under our experimental conditions, or sequential reaction of methyls and subsequent dehydrogenation. Because we do not observe any 1,3-butadiene or cyclopentadiene in our product mixturesnor any four- or five-carbon compounds that could potentially be precursors to 1,3-butadiene or cyclopentadiene, respectivelysit is unlikely that naphthalene is formed by either of these two pathways. In our system, in which the aromatic C-C bond is not broken and the building blocks are benzyl, phenyl, and methyl, the only reaction pathway in which naphthalene could be formed is through successive addition of methyl to toluene, followed by cyclization to form tetralin and dehydrogenation to form naphthalene (I), shown in Scheme 1. In reaction 1-a, methyl displaces hydrogen at the ortho position to yield o-xylene. Hydrogen abstraction (by a radical, R) gives the o-xylyl radical (reaction 1-b), which then reacts with methyl to form 2-ethyltoluene (reaction 1-c). Abstraction of hydrogen from toluene’s methyl group in reaction 1-d (a position allowing for resonance stabilization) yields a radical that can then react with methyl to form 1,2-diethylbenzene (reaction 1-e). Ring closure (1-f) and further dehydrogenation (1-g) yield naphthalene (I). (We note that, although we have shown hydrogen abstraction by a radical in reactions 1-b and 1-d, it is also possible that the C-H bonds dissociate to produce a radical and atomic hydrogen.) Although Scheme 1 shows naphthalene formation from 1,2-diethylbenzene, naphthalene could also be formed from butylbenzene or 2-propyltoluene (C10H14 compounds with a molecular weight of 134). Our GC/MS results show at least a dozen peaks with a molecular weight of 134, which could correspond to one or more of the compounds that we believe are precursors to naphthalene under supercritical conditions. Now that we have shown how we believe naphthalene is formed in our system, we extend our discussion of reaction pathways to include larger PAH. Before focusing on the C28H14 isomers, we first discuss the set of reaction pathways that describe the formation of almost all PAH found in our products. Reaction Pathways for PAH Formation from Supercritical Toluene Pyrolysis. The reaction model in which large (>5ring) PAH are formed in our system is based on the idea that large PAH are formed from small PAH, analogous to the HACA pathway that describes PAH growth in systems in which smaller C2 compounds are in abundance. However, because we do not have reactive C2 species in our system, addition of methyl, benzyl, and phenyl to smaller PAH must yield the large PAH observed in our product mixture. An alternative to this scheme would be the idea that large PAH are formed from the combination of two smaller PAH. Although this is certainly possible in systems that have very high yields of PAH, in our system, the conversion of toluene is approximately 3%, and the concentration of individual large PAH is roughly between 1

and 10 µg of PAH per gram of toluene fed.7 Using benzo[ghi]perylene as an example (a six-ring PAH found in this product mixture), a 1-10 µg/g concentration would correspond to 1-10 benzo[ghi]perylene molecules for every three million toluene molecules. Clearly, the probability that two PAH molecules encounter each other under our conditions is rare, and PAH are much more likely to react with radicals generated from the millions of toluene molecules that surround them. Before attempting to develop reaction mechanisms to describe the formation of large PAH, we first had to establish whether the small PAH observed in our product mixture can be formed through reactions of toluene with methyl, benzyl, phenyl, and to a lesser extent naphthalenesand, indeed, we found this to be the case. For example, phenanthrene (II) forms from benzyl addition to toluene, shown in Scheme 2. In reaction 2-a, loss of a methyl hydrogen, either through decomposition or through abstraction by a radical, gives benzyl. Reaction with an additional benzyl yields bibenzyl (reaction 2-b). Loss of an aliphatic hydrogen in reaction 2-c, either by abstraction by another radical or by decomposition, yields a bibenzyl radical, which, through loss of a second hydrogen (shown in reaction 2-d), becomes stilbene (one of our observed products). Further dehydrogenation of stilbene yields phenanthrene (II) in reaction 2-e. The formation of phenanthrene from cis-stilbene has also been demonstrated by others.67,68 As depicted in Figure 3a and 3b, addition of methyl, benzyl, and phenyl to these smaller PAH products such as naphthalene and phenanthrene leads to the formation of larger PAH identified in our product mixture. As Figure 3 reveals, we have determined that three types of reactions dominate: (A) addition of methyl, followed by addition of benzyl to the methyl carbon (for large PAH this usually occurs at a site adjacent to a bay region); (B) addition of phenyl (for the formation of benzenoid PAH, this addition occurs at a bay region); and (C) addition of two methyls to a bay region, the second methyl adding to the methyl carbon of the first. All three of these reactions are then followed by subsequent dehydrogenation to produce a larger PAH. Although it is possible that reactions other than those of types A-C could lead to formation of the large PAH in our system, the fact that just three specific types of reactions can explain the formation of almost all of the observed PAH in our product mixture lends credence to our methodology. The details of reactions of type A are shown in Scheme 3 for the example of phenanthrene (II) f benzo[ghi]perylene (III). In reaction 3-a, methyl attacks phenanthrene at the 3 position, a location adjacent to a bay region, to yield 3-methylphenanthrene. Loss of a methyl hydrogen, either by abstraction or by decomposition, yields a 3-methylphenanthrene radical (reaction 3-b). Benzyl then attacks the methyl carbon of the 3-methylphenanthrene radical to yield 3-(2-phenylethyl)phenanthrene in reaction 3-c. Loss of an aliphatic hydrogen in reaction 3-d by either abstraction by another radical or dissociation (an

Reaction Mechanisms of PAH Formation: C28H14 Isomers

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Figure 3. Reaction mechanisms to describe the formation of C28H14 products formed during the supercritical pyrolysis of toluene: (a) phenanthro[5,4,3,2-efghi]perylene (XI), benzo[pqr]naphtho[8,1,2-bcd]perylene (XII), and benzo[a]coronene (IV); (b) benzo[cd]naphtho[3,2,1,8-pqra]perylene (VIII) and benzo[ghi]naphtho[8,1,2-bcd]perylene (IX). The formation of large PAH is shown through addition of methyl (dashed arrow), benzyl (solid arrow), and phenyl (dashed-dotted arrow) radicals. Dehydrogenation is shown as the double-lined arrow. In general, the three types of reactions are (A) addition of methyl followed by benzyl, (B) addition of phenyl, and (C) addition of two methyls. Structures shown in bold print are PAH that have been identified, by their UV spectra, as products of the supercritical pyrolysis of toluene.

SCHEME 3

SCHEME 4

aliphatic position would have a lower C-H bond dissociation energy than an aryl C-H) yields a 3-(2-phenylethyl)phenanthrene radical, which then becomes 3-(2-phenylethenyl)phenanthrene through further loss of a hydrogen atom, shown in reaction 3-e. Subsequent dehydrogenation in reaction 3-f yields benzo[ghi]perylene (III); this is consistent with the findings of Tinnemans and Laarhoven,70 who used irradiation to show that stilbene-like compounds, in the presence of iodine, form polycyclic aromatic compounds. Reactions of type B, shown for benzo[ghi]perylene (III) f benzo[a]coronene (IV) in Scheme 4, are those in which phenyl adds to a bay region of a PAH molecule. In reaction 4-a, phenyl attacks benzo[ghi]perylene (III) at the 7 position to yield

7-phenylbenzo[ghi]perylene, which then becomes benzo[a]coronene (IV) through dehydrogenation (reaction 4-b). Dehydrogenation of PAH containing a phenyl substituent has been documented by others.69,70 In reactions of type C, shown in Figure 3b for benz[a]anthracene (V) or chrysene (VI) f benzo[a]pyrene (VII), two methyls add to a bay region to create an additional ring. Scheme 5 shows the details of this type of reaction for benz[a]anthracene (V) f benzo[a]pyrene (VII). In reaction 5-a, methyl attacks benz[a]anthracene at the 1 position to yield 1-methylbenz[a]anthracene. Loss of an aliphatic hydrogen, either by abstraction by another radical or by decomposition (a methyl C-H bond is easier to break than an aryl C-H bond) gives a 1-methylbenz[a]anthracene radical (reaction 5-b). The 1-methylbenz[a]anthracene radical reacts with methyl to form 1-ethyl-benz[a]anthracene in reaction (5-c). Loss of hydrogen on the aliphatic portion of 1-ethyl-benz[a]anthracene (through either decomposition or abstraction) yields a radical that can then convert to a resonance structure in which the radical is on an aryl carbon, shown in reaction 5-d. Reaction between the resulting radical and the terminal aliphatic carbon in reaction 5-e leads to cyclization, and further dehydrogenation yields benzo[a]pyrene (VII), shown in reaction 5-f. In this section, we have established the types of reactions that we believe occur in our system and have given details regarding how radicals react with small PAH to yield larger PAH. We now apply reaction types A-C to the set of C28H14 PAH, of which there are only eight benzenoid isomers,40 to explain why the five observed C28H14 PAH are produced in the supercritical toluene pyrolysis environment and why others are not. From this analysis, we are able to speculate on the identity of the sixth C28H14 product. Formation of C28H14 PAH. Figure 3a,b shows the formation of the five C28H14 PAH identified8,30 in our product mixture: phenanthro[5,4,3,2-efghi]perylene (XI), benzo[pqr]naphtho[8,1,2-bcd]perylene (XII), benzo[a]coronene (IV), benzo[cd]naphtho[3,2,1,8-pqra]perylene (VIII), and benzo[ghi]naphtho[8,1,2-bcd]perylene (IX). Phenanthrene (II) is formed through dehydrogenation of bibenzyl, the details of which are shown in Scheme 2. As illustrated in Figure 3a, addition of phenyl to the bay region of phenanthrene, a reaction of type B, yields 4-phenyl-phenanthrene; further dehydrogenation leads to benzo[e]pyrene (X). Addition of methyl and benzyl in reactions of type A to the 2 or 11 carbon of benzo[e]pyrene, followed by dehydrogenation, yields phenanthro[5,4,3,2-efghi]perylene (XI) or benzo[pqr]naphtho[8,1,2-bcd]perylene (XII), respectively. Alternatively, Figure 3a shows that methyl and benzyl addition to the 3 position of phenanthrene (II), a reaction of type A, and subsequent dehydrogenation give benzo[ghi]perylene (III). Addition of phenyl in a reaction of type B to the 7 position of benzo[ghi]perylene forms benzo[a]coronene (IV), as shown in Scheme 4. Last, Figure 3b shows that methyl and benzyl

92 J. Phys. Chem. C, Vol. 111, No. 1, 2007

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SCHEME 6

SCHEME 7

addition (type A reaction) to the 1 or 2 position of naphthalene (I), followed by dehydrogenation, yields chrysene (VI) or benz[a]anthracene (V), respectively. Addition of two methyls to the bay region of chrysene or benz[a]anthracene and subsequent dehydrogenation yields benzo[a]pyrene (VII)-a reaction of type C. Addition of a methyl and benzyl (in a reaction of type A) to the 9 or 12 position of benzo[a]pyrene yields benzo[ghi]naphtho[8,1,2-bcd]perylene (IX) or benzo[cd]naphtho[3,2,1,8-pqra]perylene (VIII), respectively, after dehydrogenation. Using the three types of reactions discussed in this article, we are able to explain how the five identified C28H14 isomers found in our products can be formed from methyl, benzyl, and phenyl addition to smaller PAH, such as naphthalene and phenanthrene. We note that the four-, five-, and six-ring PAH that are intermediates in the pathways leading to the C28H14 products in Figure 3 are themselves all components of our product mixture; all of them are also fully aromatic. We next consider the reaction pathways for the remaining three C28H14 isomers, bisanthene, naphthaceno[3,4,5,6,7-defghij]naphthacene, and tribenzo[cd,ghi,lm]perylene. In developing possible reaction mechanisms for bisanthene, naphthaceno[3,4,5,6,7-defghij]naphthacene, and tribenzo[cd,ghi,lm]perylene, we apply the same rules that we have used for the five identified C28H14 isomers: radical addition to small PAH to form large PAH, using reactions of types A-C whenever possible. The first compound we consider is bisanthene (XIV), a PAH that we know from UV spectral data is not present in our product mixture. Benzyl addition to phenanthrene (II), which we believe forms from the dehydrogenation of cis-stilbene (Scheme 2), yields 8H-dibenzo[a,de]anthracene (XIII), as illustrated in Scheme 6. 8H-Dibenzo[a,de]anthracene (XIII) is a C21H14 polycyclic compound (molecular weight of 266) that is not fully aromatic. Use of mass spectral data to isolate peaks corresponding to compounds with a molecular weight of 266 in our product mixture and comparison of the UV spectra of these compounds with the UV spectrum published32 for 8H-dibenzo[a,de]anthracene show that 8H-dibenzo[a,de]anthracene is not produced under our conditions. (Compounds with a molecular weight of 266 that we have identified are methylbenzo[e]pyrene and methylbenzo[a]pyrene.) Further, addition of benzyl to a small PAH without prior addition of methyl is not a reaction pathway that is consistent with the three reaction types devised for other large PAH. To complete the reaction mechanism, additional reaction of benzyl with 8H-dibenzo[a,de]anthracenesagain not preceded by methyl additionsand subsequent dehydrogenation would yield bisanthene (XIV). Thus, not only are the reactions required to make bisanthene not consistent with reactions of types A-C, but the intermediate compound is not fully aromatic and is not observed in our product mixture. It therefore makes sense that bisanthene is not a component of our product mixture.

We next consider naphthaceno[3,4,5,6,7-defghij]naphthacene (XVIII), for which no UV spectrum has been published. As illustrated in Scheme 7, benzyl addition to naphthalene (I) yields 7H-benz[de]anthracene (XV) upon dehydrogenation. By comparing the UV spectra of compounds identified with a molecular weight of 216 (the molecular weight of 7H-benz[de]anthracene) to UV spectra published for 7H-benz[de]anthracene as well as other benz[de]anthracene isomers,32 we are able to determine that 7H-benz[de]anthracene and benz[de]anthracene isomers are not present in our product mixture. (It is likely that benzyl addition to naphthalene would take the less sterically hindered route to form benzo[a]fluorene (XVI), a compound that we have identified in our products.) Nevertheless, methyl and benzyl addition to 7H-benz[de]anthracene (XV) in a reaction of type A would yield 9-(2-phenylethyl)-7H-benz[de]anthracene, which, through dehydrogenation, would become 7H-dibenzo[a,mn]naphthacene (XVII)sanother PAH that is not fully aromatic. Addition of three methyls, in a reaction that is unlike others observed for the large PAH, would form naphthaceno[3,4,5,6,7defghij]naphthacene (XVIII) after dehydrogenation. As was the case for bisanthene, formation of naphthaceno[3,4,5,6,7-defghij]naphthacene requires intermediate PAH that are not fully aromatic and are not observed in the product mixture. In addition, the reaction of three methyls required for the synthesis of naphthaceno[3,4,5,6,7-defghij]naphthacene is not consistent with reactions of types A-C. The predicted UV spectral characteristics of naphthaceno[3,4,5,6,7-defghij]naphthacene30 also do not agree with the UV spectra of any of our C28H14 products. Thus, it is unlikely that naphthaceno[3,4,5,6,7-defghij]naphthacene is a product of supercritical toluene pyrolysis. The remaining compound, tribenzo[cd,ghi,lm]perylene (XXI), has the reaction scheme shown in Scheme 8. Addition of two methyls to the bay region of phenanthrene (II), in a reaction of type C, yields 4-ethylphenanthrene, which then becomes pyrene (XVIII) upon dehydrogenation. Addition of methyl and benzyl to pyrene at the 1 position, in a reaction of type A, yields 1-(2phenylethyl)pyrene. Dehydrogenation of 1-(2-phenylethyl)pyrene gives naphtho[2,1-a]pyrene (XIX). Addition of two methyls to a bay region (reaction type C) of naphtho[2,1-a]pyrene yields 7-ethylnaphtho[2,1-a]pyrene, which then becomes dibenzo[cd,lm]perylene (XX) through dehydrogenation. Further addition of two methyls to a bay region of dibenzo[cd,lm]perylene would yield 5-ethyldibenzo[cd,lm]perylene, and ultimately tribenzo[cd,ghi,lm]perylene (XXI) after dehydrogenation. Both pyrene (XVIII) and naphtho[2,1-a]pyrene (XIX) are fully aromatic benzenoid PAH that have been unequivocally

Reaction Mechanisms of PAH Formation: C28H14 Isomers SCHEME 8

identified8 as products of supercritical toluene pyrolysis (Figure 1), by matching their UV spectra with those of reference standards. Our HPLC/MS data indicate that we have a toluene product component of molecular weight 326 [the molecular weight of dibenzo[cd,lm]perylene (XX)] at the correct elution time (we have identified6,9,27 the elution time for dibenzo[cd,lm]perylene in product mixtures of other fuels), but because the yield is so small and the compound is coeluting, we are unable to distinguish this component’s UV spectrum (to unequivocally establish the component’s identity). Nevertheless, the mechanism shown for tribenzo[cd,ghi,lm]perylene in Scheme 8 is consistent with the reaction pathways devised for the other C28H14 isomers present in our product mixture. Therefore, tribenzo[cd,ghi,lm]perylene is most likely the sixth C28H14 isomer detected by HPLC/MS in our product mixture. Although no UV spectrum is available for tribenzo[cd,ghi,lm]perylene, preliminary inspection of the product component’s UV spectrum and comparison to UV spectra of PAH differing by a single aromatic ring30 lead us to the same conclusion. In this section, we have established the reaction pathways through which we believe the five observed C28H14 isomers can be formed through addition of methyl, phenyl, and benzyl to small PAHspathways that are consistent with reactions of types A-C. We have also explained why bisanthene, a compound that we know from UV spectral data is not in our products, is not found. We have then devised pathways for the remaining two C28H14 isomers and speculated that tribenzo[cd,ghi,lm]perylene is our unknown C28H14 compound because its reaction pathway is consistent with reaction types A-C and naphthaceno[3,4,5,6,7-defghij]naphthacene’s pathway is not. We now briefly discuss the relative yields of the C28H14 isomers (and other PAH in general) and show how they relate to our reaction schemes. Relationship between Reaction Pathways and Component Yields. Although it is difficult to quantify the yields of the C28H14 isomers as a result of coelution, the areas of the peaks in Figure 1 can be used to estimate the relative yields of the various components.71 (We note that this is not the case for PAH with fewer than four rings, as the procedure by which our sample was concentrated for HPLC analysis can cause smaller compounds to evaporate.) The first C28H14 peak in Figure 1 (at 57.5 min) contains three compounds: benzo[a]coronene, phenanthro[5,4,3,2-efghi]perylene, and benzo[cd]naphtho[3,2,1,8-pqra]perylene; the second peak (58.3 min) is benzo[ghi]naphtho[8,1,2-bcd]perylene;thethird(61.2min)isbenzo[pqr]naphtho[8,1,2bcd]perylene; and the fourth (63 min) is the unknown C28H14 isomer that we believe is tribenzo[cd,ghi,lm]perylene, coeluting with other PAH. As can be seen from Figure 1, benzo[ghi]naphtho[8,1,2-bcd]perylene has, by far, a much larger yield than any other of the C28H14 isomers. We believe the reason for this is that the other four identified C28H14 isomers all contain bay regions that, through addition of methyl and benzyl or phenyl (in reactions of type A or B, respectively), would yield larger

J. Phys. Chem. C, Vol. 111, No. 1, 2007 93 PAH that do not contain any cove or fjord regions, which introduce molecular strain and lead to nonplanar structures. (Of the 40 PAH that we have identified8,30 so far in the products of supercritical toluene pyrolysis, none contains a cove or fjord region.) For benzo[ghi]naphtho[8,1,2-bcd]perylene, on the other hand, addition of methyl and benzyl or phenyl would yield compounds with a cove region, and the associated molecular strain would cause such products to be disfavored. Benzo[ghi]naphtho[8,1,2-bcd]perylene therefore accumulates, as further molecular growth by reactions of type A or B is discouraged. Finally, the unknown C28H14, which we believe is tribenzo[cd,ghi,lm]perylene, has the lowest yield of all six C28H14 isomers contained in the product mixture. This is consistent with the fact that its two postulated precursors in Scheme 8, naphtho[2,1-a]pyrene and the compound of molecular weight 326 that we believe is dibenzo[cd,lm]perylene, both have low yields. The yields of all PAH are, of course, proportional to (1) the yields of the smaller PAHs from which they come, (2) the relative abundance of the radicals from which they are formed, (3) the number of possible pathways through which they can be made, and (4) the number of pathways in which they are involved in forming larger PAH, which can be related to the number of bay regions contained in their structure, as the bay region appears to be the location at which radicals react in this system. Although it is difficult to separate the effects of these four criteria for some PAH, in some cases, we can use one or more of these criteria to explain why certain PAH have lower or higher yields than might have been expected. As shown in Figure 1, benzo[a]pyrene has a much larger yield than benzo[e]pyrene; thus, it makes sense that benzo[ghi]naphtho[8,1,2-bcd]perylene (which comes from benzo[a]pyrene) has a larger yield than benzo[pqr]naphtho[8,1,2-bcd]perylene or phenanthro[5,4,3,2-efghi]perylene, both of which come from benzo[e]pyrene. Because the bond energy of the methyl C-H bond is the lowest, PAH that are formed through addition of benzyl radicals can have larger yields in comparison to those requiring the less stable phenyl radical, which we know also reacts with atomic hydrogen to yield benzene, the largest-yield product of supercritical toluene pyrolysis. We note that it is likely that activation energies and/or preexponential factors for radical addition reactions should also be considered. However, because kinetic data are not available for these addition reactions, we are unable to speculate on their role in the relative yields of product PAH. Nevertheless, the more likely abundance of benzyl relative to phenyl from bond energy considerations also lends support to the fact that benzo[e]pyrene (which requires phenyl) has a lower yield than benzo[a]pyrene, even though phenanthrene (benzo[e]pyrene’s precursor) is present in larger yield than both benz[a]anthracene and chrysene (benzo[a]pyrene’s precursors).

Naphtho[8,1,2-abc]coronene (XXII), a nine-ring C30H14 PAH, has a surprisingly high yield for such a large PAH; yet, if we consider the pathways through which naphtho[8,1,2-abc]coronene can be made, we see that this result makes sense. The addition of two methyls to the bay regions of benzo[a]coronene, phenanthro[5,4,3,2-efghi]perylene, benzo[cd]naphtho[3,2,1,8pqra]perylene, benzo[ghi]naphtho[8,1,2-bcd]perylene, or benzo[pqr]naphtho[8,1,2-bcd]perylene-all yield naphtho[8,1,2-abc] coronene.

94 J. Phys. Chem. C, Vol. 111, No. 1, 2007 Pyrene (XVIII), anthanthrene (XXIII), coronene (XXIV), and ovalene (XXV)sPAH that lack bay, fjord, and cove regionss also have larger yields than might have been expected. This is most likely because further reactions of types A-C would not yield benzenoid PAH that are fully aromatic, but rather would yield PAH with a single five-membered ring. Although compounds with a single five-membered ring are found in this product mixture, there are roughly 3 times as many identified benzenoid PAH, all of which are fully aromatic. The largest PAH that we have been able to identify so far8 is ovalene, a 10-ring C32H14 PAH that elutes at 74 min. Several other PAH with slightly longer retention times and unique UV spectra have also been detected, but because of a lack of reference standards, we have thus far been unable to identify these compounds. Because we expect reaction types A-C to apply to the larger unidentified PAH eluting after ovalene, we can narrow the field of possible structures by applying these reaction pathways to the PAH thought to be precursors to their formationsin this case, most likely the C28H14 isomers. Identification of the g10-ring PAH that elute after ovalene will aid in our understanding of the types of PAH structures that directly precede solids formation. Conclusions Reaction pathways for the formation of large PAH, in particular, the C28H14 isomers, from the supercritical pyrolysis of toluene have been described in detail. These mechanisms are markedly different from those described for systems in which the aromatic ring of toluene is ruptured. The pathways that describe PAH formation in a supercritical environment, with toluene as the fuel, involve addition of benzyl, methyl, and/or phenyl radicals to smaller PAH products in a set of specific reactions: (A) addition of methyl and benzyl, usually to a position adjacent to a bay region; (B) addition of phenyl to a bay region; and (C) addition of two methyls to a bay region. Using this method, we are able to explain why the five observed C28H14 PAHs-benzo[a]coronene, phenanthro[5,4,3,2-efghi]perylene, benzo[cd]naphtho[3,2,1,8-pqra]perylene, benzo[ghi]naphtho[8,1,2-bcd]perylene, and benzo[pqr]naphtho[8,1,2-bcd]perylene-are present in our product mixture and why bisanthene, which we know is not present based on UV spectral data, is not formed. Finally, by determining reaction pathways for the remaining two C28H14 benzenoid isomers, naphthaceno[3,4,5,6,7defghij]naphthacene and tribenzo[cd,ghi,lm]perylene, and comparing speculated UV characteristics30 of both compounds, we are able to deduce that the sixth C28H14 PAH detected in our product mixture by HPLC/MS is most likely tribenzo[cd,ghi,lm]perylene. Although shown in this article for C28H14 benzenoid PAH, we believe that the three types of reactions discussed are also applicable to the many other PAH identified as products of supercritical toluene pyrolysis, and we expect them to be able to explain the formation of even larger PAH that form under more extreme conditions. Acknowledgment. This work was supported by the United States Air Force Office of Scientific Research, Grants FA955004-1-0005 and FA9550-05-1-0253. The authors appreciate the experimental contributions made by Dr. Elmer Ledesma and the technical assistance of Dr. Xia Zhang in use of the HPLC/ MS. The authors also thank Dr. Arthur Lafleur and Ms. Elaine Plummer, Massachusetts Institute of Technology; Dr. John Fetzer, Chevron Research and Fetzpahs Consulting; and Professor Maximilian Zander, Ru¨tgerswerke, for PAH reference standards and UV spectra.

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