Formation Mechanism of Polycyclic Aromatic Hydrocarbons beyond

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Formation Mechanism of Polycyclic Aromatic Hydrocarbons Beyond The Second Aromatic Ring Vadim V. Kislov, Alexander I. Sadovnikov, and Alexander Moiseevich Mebel J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp402481y • Publication Date (Web): 14 May 2013 Downloaded from http://pubs.acs.org on May 23, 2013

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The Journal of Physical Chemistry

Formation Mechanism of Polycyclic Aromatic Hydrocarbons Beyond The Second Aromatic Ring V.V. Kislova, A.I. Sadovnikovb, A.M. Mebela a

Department of Chemistry and Biochemistry, Florida International University, Miami, FL 33199, USA

b

Department of Chemistry and Biology, Ivanovo State University, 153025, Ivanovo, Russia

Abstract. The formation mechanism of polycyclic aromatic hydrocarbons (PAH) with three fused aromatic rings starting from naphthalene has been studied using accurate ab initio G3(MP2,CC)//B3LYP/6-311G** calculations followed by the kinetic analysis of various reaction pathways and computations of relative product yields. The results reveal new insights into the classical Hydrogen Abstraction-C2H2 Addition (HACA) scheme of PAH growth. The HACA mechanism has been shown to produce mostly cyclopentafused PAHs instead of PAHs with six-member rings only, in contrast to the generally accepted view on this mechanism. Considering naphthalene as the initial reactant, the HACA-type synthesis of higher PAHs with all six-member rings, anthracene and phenanthrene, accounts only for 3-6% of the total product yield at temperatures relevant to combustion (1000-2000 K), whereas cyclopentafused PAHs, including acenaphthalene (41-48%), 4-ethynylacenaphthalene (~14%), 3-ethynylacenaphthalene (~7.5%),

1-methylene-1H-cyclopenta[b]naphthalene

(~6%),

and

3-methylene-3H-

cyclopenta[a]naphthalene (~5%) account for another ~75%. It has been shown that acetylene addition to the radical site adjacent to the bay region in naphthalene (as in 1-naphthyl radical) or other similar PAH with a bay region is highly unlikely to be followed by the addition of a second acetylene molecule; alternatively, the bay region closure with a build-up of a new five-member ring occurs. Acetylene addition to a non-bay carbon atom (as in 2-naphthyl radical) can be followed by the second acetylene addition only at T < 1000 K producing anthracene and phenanthrene. However, at temperatures relevant to combustion such pathways give negligible contributions to the total product yield, whereas the dominant reaction product, 2ethynylnaphthalene, is formed by simple hydrogen atom elimination from the attached ethenyl group. An additional six-member ring build-up may occur only after intermolecular hydrogen abstraction from ethynyl-substituted PAH (2-ethynylnaphthalene), in particular, from the carbon 1 ACS Paragon Plus Environment


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atoms adjacent to the existing ethynyl (C2H) fragment, followed by C2H2 addition producing adducts with two ethynyl C2H and ethenyl C2H2 groups next to each other, which then undergo a fast six-member ring closure. Nevertheless, this process has been shown to be relatively minor (~25%), whereas the major process is a five-member ring closure involving the same C2H and C2H2 groups and leading to a cyclopentafused PAH molecule. Although the computed product yields show a good agreement with experimentally observed concentrations of acenaphthalene and anthracene in various aliphatic and aromatic flames, the yield of phenanthrene, which exhibits an order of magnitude higher concentrations than anthracene both in combustion flames and environmental mixtures, via the considered pathways is significantly underpredicted. This result points at possible existence of another mechanism responsible for the formation of phenanthrene and other all-six-member-ring PAHs. The overall kinetic scheme for the HACA build-up process leading to various three-ring PAHs (both with six-member rings only and cyclopentafused) from naphthalene, which can be included in flame kinetic models, has been constructed, with rate constants for all individual reaction steps provided.

1. Introduction The formation mechanism of polycyclic aromatic hydrocarbons (PAH) has been a fundamental research subject for the combustion community due to the great impact these compounds exert on our environment and health. The simple gaseous PAH molecules, such as naphthalene, indene, phenanthrene, pyrene, etc. can be involved in the sequential build-up process in combustion flame environments eventually leading to larger PAH, fullerenes, bowlshaped nanostructures and solid-phase species including carbonaceous dust, graphene particles and soot.1 Such particles then appear in the ambient air and soil, and can be inhaled by humans or consumed with food leading to major health problems, such as tumors, birth defects, and a variety of pulmonary diseases.

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Figure 1. Most abundant PAHs found in flames and various environmental mixtures and food products (abbreviations used in main text are shown). Numbers represent carcinogenic potency factors relative to benzo[a]pyrene, according to the U.S. EPA 19935 (in parentheses), and Clement et al.6 (in brackets).



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It has been firmly established that many PAH species possess strong carcinogenic and mutagenic properties.2-18 The most potent of them5,6,8 are shown in Figure 1. According to various epidemiological studies, some PAHs are proven to cause skin cancer in mice even after a single dose.5,7 In humans, prolonged contacts with smoke and aerosols produced in combustion, as well as with coal dust in mining facilities or with used motor oil showed much higher occurrence of various types of cancer than in other groups.9-12 Numerous studies showed that emissions from coke and aluminum production, coal gasification, iron and steel founding, coal tars, coal tar pitches, and soot have produced lung cancer in humans.9 Skin and scrotal cancers have resulted from exposure to coal tar, coal tar pitches, nonrefined mineral oils, shale oils, and soot.9,11,13 In total, 15 PAH species (Fig. 1) have been tested on laboratory animals and proven for their tumorogenic activity or considered as potentially carcinogenic for humans.5,8 For instance, benzo[a]pyrene (B[a]P), a well-studied carcinogen with high potency, is prevalent in many complex environmental mixtures. For that reason B[a]P has been considered as an index compound and a “gold standard” for its carcinogenic activity defined as 1.0 according to the U.S. EPA.5,8 As illustrated in Fig. 1, the majority of other PAHs possess substantially lower potency factors than B[a]P. According to the U.S. EPA, B[a]P along with six other PAHs, benz[a]anthracene,

benzo[b]fluoranthene,

benzo[k]fluoranthene,

chrysene,

dibenz[a,h]anthracene, and indeno[1,2,3-c,d]pyrene are classified as Group B2 carcinogens (probable human carcinogen, based on sufficient evidence of carcinogenicity in animals). It is worth mentioning that cancer caused about 13% of all human deaths worldwide (7.9 million) in 2007 and this rate continues to rise.19 Because of serious health concerns, the formation of PAHs and soot in combustion processes attracts considerable attention and knowledge of reaction mechanisms leading to the formation of these species is a particularly important step in the construction of the cleaner combustion equipment and in reducing pollutions to our environment. Although some PAH species like B[a]P or dibenz[a,h]anthracene exhibit a strong carcinogenic activity, many others, such as naphthalene, anthracene, phenanthrene, fluoranthene, pyrene, either are not carcinogenic or possess low relative potency factors,8 which allows us to classify them as less harmful as compared to strong carcinogenic PAHs. Also, we should keep in mind that the most carcinogenic PAHs are built from five-six fused rings, whereas smaller or larger PAH usually do not possess a strong carcinogenic activity. This is an indication that carcinogenic PAH are likely formed within the same time scale and possibly from the same 4 ACS Paragon Plus Environment

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precursors. From this standpoint, we would like to comprehend which chemical routes in combustion processes lead to the formation of the most hazardous, carcinogenic PAHs with fivesix rings and which routes are responsible for the synthesis of relatively safer, from the environmental point of view, polycyclic aromatic species. If the routes leading to different PAH species can be established, the combustion conditions, such as the temperature, pressure, fuel/oxygen ratio, the use of additives or catalysts, can be altered to shift the overall reaction sequence towards the formation of less hazardous PAHs. The Hydrogen Abstraction-C2H2 Addition (HACA) mechanism is now commonly accepted as the major reaction route leading to the formation of PAHs and soot in combustion flames.1,2029

The importance of this mechanism is based on its intrinsic features, such as low reaction

barriers and high exothermicities of the steps involved, which was originally stated by Frenklach21 and later corroborated by various computational studies.26-28 For acetylene additions to PAH radicals, the predicted barriers are usually within 2-6 kcal/mol and the exothermicities are ~30-40 kcal/mol, whereas the subsequent ring closure steps normally exhibit ~2-5 kcal/mol barriers and are ~30-50 kcal/mol exothermic. Another reason for HACA to be the prevalent PAH formation mechanism is a high abundance of acetylene and benzene/phenyl in combustion flames30-43 in a broad range of distances from the burner surface and in various types of aliphatic and aromatic flames including those of methane,30 ethane,31-33 ethylene,33-35 butadiene,36 butane,37 heptane,38 benzene,39,40 toluene,41 gasoline mixtures,42 and even polymers (polyethylene, polystyrene, and polyvinyl chloride).43 Experimental concentration profiles of C2H2, C6H6, and several major PAHs for ethane, n-butane and benzene flames are illustrated in Figure 2 as examples. Usually, maximal concentrations of most PAH species are observed within the same, relatively narrow interval of distances from the burner surface and this interval normally corresponds to the maximal flame temperature.



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Figure 2. Experimental concentration profiles for the most abundant hydrocarbons and PAHs in aliphatic ethane,31 n-butane,37 and aromatic benzene39 flames. 6 ACS Paragon Plus Environment

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Theoretically, the potential energy surface (PES) for the formation of the second aromatic ring via the HACA sequence has been thoroughly studied by Kislov et al.26 by applying a chemically accurate G3(MP2,CC) approach. Two energetically favorable mechanisms suggested before were mapped out. The first one involves a single-activation-repetitive-acetylene-addition pathway proposed by Bittner and Howard,25 in which the second acetylene unit adds to the first one, i.e., to the ethenyl C2H2 side chain of the C6H5C2H2 radical produced as a result of the first acetylene addition to phenyl. The computed barriers for the addition of the first and second C2H2 units are 3.5 and 4.8 kcal/mol, respectively. The second addition is followed by a closure of a second six-member ring with a barrier of only 3.6 kcal/mol and the product of this reaction – the simplest PAH naphthalene C10H8 – is formed after H atom elimination from 9-H-hydronaphthyl radical with a barrier of 14.8 kcal/mol. The second mechanism considered is a repetitiveactivation-acetylene-addition sequence introduced by Frenklach.20-23 In contrast to the mechanism proposed by Bittner and Howard, in Frenklach’s pathway the addition of second acetylene occurs after the adduct resulting from the first acetylene addition event loses a hydrogen atom producing an ethynyl side chain in the phenylacetylene product. This product is re-activated by another H-abstraction and then acetylene adds to the aromatic ring and an extra six-member ring is subsequently formed after a ring closure involving the adjacent ethynyl and ethenyl side chains via a low barrier of 5.4 kcal/mol and producing 1-naphthyl radical. In Frenklach’s early publications,20,21,24 only the latter mechanism was called HACA, but since then a broader concept was adopted by the combustion community for the HACA mechanism,1 including various repetitive sequences initiated by H-abstraction and followed by a mass growth step via acetylene addition. Due to feasible energetics of the steps involved, both mechanisms may compete in the overall PAH build-up process, however, further accurate kinetic modeling is required to reveal their relative importance. The goal of the present study is to investigate PESs and product distribution beyond the formation of the second aromatic ring. Here we consider the formation of tricyclic aromatic molecules including acenaphthalene (ACN), anthracene (ANT), phenanthrene (PTR), as well as other possible products, starting from the bicyclic PAH naphthalene as the initial reactant via HACA mechanism. Obviously, ACN, ANT and PTR can play an important role as precursors to higher PAHs, such as B[a]P, dibenz[a,h]anthracene, and other carcinogens. The formation mechanism of those larger molecules will be discussed in our subsequent publications. 7 ACS Paragon Plus Environment


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Numerous experimental studies of PAH abundances, including the tricyclic ACN, ANT and PTR molecules, in various environmental mixtures and food products, such as ambient air and dust,44,45 soil,46,47 water48-50 and sediments,49,50 live fish,50 plants,51 cigarette smoke,52,53 processed (smoked, grilled, roasted) foods,54-62 and combustion flames,30-43 have been reported. For illustration, the measured concentrations of various PAHs including those considered in the present study are shown in Table S1 (Supporting Information) for different environments and products. The amount of available data is much larger than that presented in Table S1, but all of them demonstrate similar trends. Among the tricyclic PAHs, in all studied mixtures and products PTR shows significantly higher levels as compared to ANT. Typically, PTR concentrations are a factor of 3-10 higher than the respective levels of ANT. A similar behavior is observed for the ANT and PTR concentrations in combustion flames; as seen in Fig. 2, in ethane, n-butane, and benzene flames PTR usually exhibits about an order of magnitude higher peak mole fractions than those of its isomer ANT. Experimental peak mole fractions of ACN in flames are found to be close or even higher than those for naphthalene and significantly higher than the respective mole fractions for both PTR and ANT, which is in contrast to the tendency observed in environmental mixtures and foods where PTR concentrations are much higher than those for ACN. These observations set another goal of our study, to find out whether the HACA mechanism can correctly describe the observed relative abundances of ACN, ANT, and PTR in combustion flames and environmental mixtures.

2. Computational Methods To optimize geometries of all local minima structures and transition states we used the hybrid DFT B3LYP63-66 method with the 6-311G** basis set and the same method was applied to calculate vibrational frequencies, zero-point energy (ZPE) corrections, and other molecular structural parameters of the stationary points required for further statistical theory calculations of rate constants. All transition states were tested by animating the motions corresponding to imaginary modes, and in cases where the connectivity of a transition state was not obvious, intrinsic reaction coordinate (IRC) calculations were performed. To refine the final energies we applied a modified G3(MP2,CC)//B3LYP67,68 composite scheme with single-point energies computed at the G3(MP2,CC) level using B3LYP optimized structures, according to the following formula 8 ACS Paragon Plus Environment

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E0[G3(MP2,CC)] = E[RCCSD(T)/6-31G*] + ∆EMP2 + ∆E(HLC) + E(ZPE),

(1)

where ∆EMP2 = E[MP2/G3large] – E[MP2/6-31G*] is a basis set correction, ∆E(HLC) is a higher level correction, and E(ZPE) is the zero-point energy. ∆E(HLC) was omitted in our calculations because in most cases isomerizations of radical species considered here proceed without a spin change resulting in HLC cancellation. Otherwise, a neglect of HLC may introduce an error of about 2-3 kcal/mol. T1 diagnostics were checked during coupled cluster calculations to ensure that wave functions do not possess any multireference character. The described calculation scheme represents a modification and reduction of the original G369 method to lower the cost of calculations, hereafter we denote this approach as G3 for brevity. All calculations were performed using GAUSSIAN 9870 and MOLPRO 200271 program packages. In the discussion of the reaction mechanisms to follow, we use the notation for intermediates based on the carbon atom number in the initial PAH molecule (e.g. naphthalene), which is subjected to hydrogen abstraction followed by C2H2 addition, the letter abbreviation of the initial PAH reactant, and the intermediate number within the network. For example, the notation 1-N2 means that this intermediate belongs to the reaction network which starts from Habstraction/C2H2 addition to the C1 carbon in naphthalene (“1-N”) and it is a second intermediate within this network. The optimized structures of all stationary points as well as B3LYP and G3 energies and other molecular structure parameters are collected in Table S2 of Supporting Information. Calculations of PES were followed by statistical calculations of reaction rate constants for all elementary reactions involved at the high-pressure limit. We did not perform master equation simulations to take into account pressure effects because, as has been shown in our previous publications,72,73 at temperatures relevant to combustion collisional stabilization of reaction intermediates normally does not play a significant role, especially at the atmospheric pressure. The system we consider here includes both unimolecular isomerizations and bimolecular additions of acetylene, which significantly complicates master equation calculations. Nevertheless, possible effects of pressure will be investigated in the future and will be reported in a separate study. For bimolecular reactions, including hydrogen abstractions and acetylene 9 ACS Paragon Plus Environment


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additions we applied conventional transition state theory (TST)74 with Wigner’s correction for tunneling75 to obtain thermal rate constants, whereas for unimolecular steps we used canonical Rice-Ramsperger-Kassel-Marcus (RRKM) theory.75-77 In both TST and RRKM calculations, to compute partition functions for species with internal rotations (i.e. having rotational barriers close to RT/2 and lowest vibrational modes of less than 100 cm-1), we applied the hindered rotor approximation.75,78 In this case, rotational potentials were calculated using the B3LYP/6-311G** level of theory and respective rotational barriers were then refined at the G3 level. Lowfrequency vibrational modes corresponding to internal rotors were excluded during the calculation of vibrational partition functions and hindered rotor partition functions were included instead. Calculations of rate constants for all elementary reaction steps were performed within the 300-3000 K temperature range and all calculated rate constants are collected in Table S3 of Supporting Information. Computed thermodynamic properties of all species are reported in Table S7 of Supporting Information. To compute product distributions we used TST/RRKM computed thermal rate constants for all elementary steps involved to solve the system of kinetic equations in the steady-state regime. Such calculations were performed separately for the reaction Networks I and II, i.e. considering 1-naphtalenyl-2-ethenyl radical (1-N2) and 2-naphtalenyl-2-ethenyl radical (2-N2) as the initial reactants. The relative yields of the 1-N2 and 2-N2 adducts produced via H abstractions from naphthalene followed by subsequent addition of acetylene to 1-naphthyl (1-N1) and 2-naphthyl (2-N1) radicals, respectively, were simply evaluated as the ratios k(1-N1)/ktot, and k(2-N1)/ktot, where ktot = k(1-N1) + k(2-N1) is a sum of bimolecular rate constants for the abstraction reactions producing 1-N1 and 2-N1 radicals from naphthalene (the calculated NP + H → 1-N1 + H2 and NP + H → 2-N1 + H2 rate constants are collected in Table S3 of Supporting Information and relative product yields of 1-N1 and 2-N1 are shown in Table 1). For a wide range of temperatures (T = 300-3000 K), additions of the second acetylene unit, 1-N2 + C2H2 → 1-N3, 2-N2 + C2H2 → 2N3, etc., were included in the kinetic calculations considering them as pseudo first-order reactions. This assumption is reasonable because it is based on the fact that acetylene mole fractions in various combustion flames30-32,34-37,39,40 are at least two orders of magnitude higher than that of naphthalene and, subsequently, even higher than those of 1-N2, 2-N2, and other adducts formed from naphthalene in a wide range of distances from the burner surface. This means that the acetylene concentration can be considered constant (time-independent) when 10 ACS Paragon Plus Environment

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solving kinetic equations. For example, in the case of a nearly sooting low-pressure benzene/oxygen flame,39 experimental concentration profiles show acetylene mole fractions of about 0.05 within 0.5-3 cm from the burner, whereas the naphthalene mole fraction reaches its peak value of 1x10-4 at 0.75 cm and then rapidly decreases to less than 10-5 at distances larger than 1 cm from the burner. Similar differences between the mole fractions of naphthalene and C2H2 were observed for the atmospheric pressure aliphatic n-butane/oxygen flame37 (Fig. 2). If we take the concentration of acetylene as a constant, then the pseudo first-order reaction rate constant for acetylene addition (keff, s-1) at a given temperature T can be expressed as keff = k * XC2H2 * P / RT,

(2)

where k is the bimolecular (cm3 s-1 mol-1) rate constant for acetylene addition, XC2H2 is the acetylene mole fraction (we used the value near the peak of the acetylene concentration profile), P is the system pressure, and R is the gas constant. Here, two important issues should be noted. First, keff values computed using equation (2) represent their upper limit since XC2H2 is chosen at its maximum (near the peak, see Fig. 2). Second, the actual mole fractions of the adducts involved in the reaction with a second acetylene unit, 1-N2, 2-N2, 1-N7, 2-N8, etc., are expected to be lower than those of naphthalene shown on its concentration profiles meaning even higher [C2H2]/[adduct] ratios. Table 1. Computed branching ratios for the formation of 1-naphthyl and 2-naphthyl radicals by hydrogen atom abstractions from C1 and C2 carbons of naphthalene. T, K

300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500

Branching ratios, % 1-N1

2-N1

43.1 44.8 45.8 46.5 47.0 47.4 47.7 47.9 48.1 48.2 48.4 48.5 48.6

56.9 55.2 54.2 53.5 53.0 52.6 52.3 52.1 51.9 51.8 51.6 51.5 51.4



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1600 1700 1800 1900 2000 2200 2400 2600 2800 3000

48.7 48.8 48.8 48.9 48.9 49.0 49.1 49.2 49.2 49.3

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51.3 51.2 51.2 51.1 51.1 51.0 50.9 50.8 50.8 50.7

In calculations of keff, we chose reaction conditions corresponding to two different combustion flames. The first is an atmospheric pressure laminar premixed sooting nbutane/oxygen flame (P = 760 Torr, XC2H2 = 0.04, XNP = 4.0x10-5)37 and the second is a lowpressure nearly sooting benzene/oxygen flame (P = 20 Torr, XC2H2 = 0.04, XNP = 1.0x10-4).39 Experimental temperature profiles for both flames show maximal flame temperatures of ~1600 and ~1900 K for the n-butane and benzene flames, respectively, and maximal concentrations of acetylene and PAHs are observed near the peak temperatures, as follows from the respective concentration profiles.37,39 To give an example of keff calculations, taking the n-butane flame at 1500 K, the TST calculated rate constant for the 1-N2 + C2H2 → 1-N3 reaction k = 3.2x1011 cm3 s-1 mol-1, the acetylene concentration [C2H2] of 3.3x10-7 mol cm-3, the concentration of the 1-N2 reactant of 3.3x10-10 mol cm-3 ([1-N2] ≈ [NP]), we obtain keff = 1.0x105 s-1. Using the calculated pseudo first-order rate constants keff for all acetylene addition steps considered for the reaction Networks I and II we were able to perform calculations of product yields in the steady-state regime. In addition, to ensure the accuracy of our simplified pseudo first-order approach, for a selected set of temperatures (800, 1000, 1500, and 2000 K) we solved kinetic equations numerically considering acetylene addition reactions as bimolecular, i.e. including the actual C2H2 + adduct bimolecular rate constants and acetylene/naphthalene concentrations taken from the experimental concentration profiles. To do so, we included only the most important channels from Networks I and II to the kinetic scheme and applied the Adams-Moulton and Rosenbrock methods for stiff differential equations79,80 to solve the corresponding systems of kinetic equations. Since such calculations are relatively expensive, they were performed only at several temperatures relevant to combustion, in the 1000-2000 K range corresponding to maximal concentrations of acetylene and the considered PAHs. The computed concentrations of 12 ACS Paragon Plus Environment

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intermediates and products versus time were then compared with the corresponding product yields obtained using the simplified pseudo first-order treatment. Hereafter, we for brevity denote our results as for the n-butane and benzene flames, even though our approach does not represent modeling of overall chemical processes in actual flames. In fact, we deal with so-called “isolated” mechanisms with the main goal to reveal major and minor reaction products within reaction networks considered and reaction pathways leading to those products, and to evaluate relative product distributions. These “isolated” mechanisms can be further included in more complex combustion models involving other chemical reactions in combustion flames.

3. Results and Discussion 3.1. Potential energy surface The formation of the second aromatic ring via the HACA sequence26 can be followed by activation of naphthalene via abstraction of a hydrogen atom from this molecule by H, OH, CH3 or other abundant small radicals. Typically, H radicals exhibit much higher concentrations and are easily available in flames. Such activation produces either 1- or 2-naphthyl radicals (1-N1 and 2-N1, respectively) as illustrated in Fig. 3. Both 1-N1 and 2-N1 can then react with acetylene as the most abundant hydrocarbon molecule in combustion flames leading to either 1naphtalenyl-2-ethenyl (1-N2) or 2-naphtalenyl-2-ethenyl (2-N2) adducts, respectively, which participate in the further growth processes as described by Networks I and II shown in Figs. 4 and 5, respectively. Eventually, the HACA sequences lead to a variety of products including tricyclic PAHs ACN, ANT, and PTR. The analysis of experimental concentration profiles for various combustion flames (see refs. 30-43 and Fig. 2) shows that acetylene possess much higher concentrations than other small hydrocarbons and PAHs in a wide range of distances from the burner, whereas peak concentrations for variety of PAHs are usually observed within a narrow interval of distances from the burner surface, typically at maximal flame temperatures and peak acetylene concentration. Acetylene mole fractions are about an order of magnitude higher than respective mole fractions of H radicals, which indicates that PAH formation via acetylene addition reactions should be the major buildup process.



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Figure 3. Two possible activations of naphthalene molecule by intermolecular hydrogen abstraction followed by the addition of the first acetylene. Numbers show G3 computed barrier heights and reaction energies in kcal/mol.


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Figure 4. Reaction Network I for the HACA growth starting from 1-naphtalenyl-2-ethenyl radical (1-N2). Numbers show G3 computed barrier heights and reaction energies for both forward and reverse reactions in kcal/mol. 15 ACS Paragon Plus Environment


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Figure 5. Reaction Network II for the HACA growth starting from 2-naphtalenyl-2-ethenyl radical (2-N2). Numbers show G3 computed barrier heights and reaction energies for both forward and reverse reactions in kcal/mol. 16 ACS Paragon Plus Environment

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Both hydrogen abstractions from naphthalene, NP + H → 1-N1/2-N1 + H2, exhibit very similar barrier heights and reaction energies (Fig. 3), which differ only by 0.2 and 0.4 kcal/mol, respectively, indicating that both abstractions should equally contribute to the reaction kinetics. Similarly, further acetylene additions to 1-N1 and 2-N1 radicals are alike; the reaction barriers and energies differ by 0.3 and 0.5 kcal/mol, respectively. Additions of the first acetylene unit produce 1-N2 and 2-N2 radical adducts via low barriers of only 2.3 and 2.6 kcal/mol and with exothermicities of 39.5 and 40.0 kcal/mol, respectively. At this point, the major difference in the reaction mechanisms involving 1-N2 and 2-N2 (see Figs. 4 and 5) is related to the structural feature of 1-N2, which has the ethenyl fragment (C2H2) in a close vicinity to the bay region of naphthalene. This feature makes a cyclopenta ring closure in 1-N2 possible, producing an acenaphthalene core in the AN1 intermediate via a relatively low barrier of 16.6 kcal/mol and exothermicity of ~20.0 kcal/mol. The AN1 radical further eliminates an “extra” hydrogen atom overcoming a 26.4 kcal/mol barrier and producing the ACN product with endothermicity of 19.3 kcal/mol. We also considered an alternative two-step mechanism involving prior H-migration in AN1 to the central carbon, AN1 → AN2, followed by H-elimination, AN2 → ACN + H. The two-step process is expected to be less favorable than the direct one-step H elimination due to a relatively high barrier for the AN1 → AN2 hydrogen shift (23.4 kcal/mol) and high entropy of the transition state typical for H atom migration processes. Besides the five-member ring closure in 1-N2, both 1-N2 and 2-N2 may further be involved in similar reaction scenarios. The simplest one is the direct H atom elimination from the ethenyl group yielding either 1-ethynylnaphthalene (1-ETN) or 2-ethynylnaphthalene (2-ETN) products; these processes are characterized by relatively high barriers of 36.7 and 36.6 kcal/mol for Heliminations from 1-N2 and 2-N2, respectively. Another possibility is the addition of a second acetylene molecule to the first one (ethenyl group) of 1-N2 and 2-N2 leading to structures 1-N3 and 2-N3 via barriers of 3.6 and 4.5 kcal/mol with reaction exothermicities of 35.8 and 34.1 kcal/mol, respectively; the energetics of the second acetylene addition is very similar to that for the additions of the first acetylene unit. Obviously, the 1-N3 and 2-N3 adducts exhibit structures suitable for an immediate closure of a third six-member ring: 1-N3 → 1-N4, 2-N3 → 2-N4, and 2-N3 → 2-N5, whereas for 1-N3 a seven-member ring closure 1-N3 → 1-N5 is also possible.



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A third route involves a four-member ring closure leading to the structure 1-N6 from 1-N2 and to 2-N6 and 2-N7 from 2-N2. The structures formed possess two six- and one four-member rings fused together and the respective cyclization barriers are similar, 32.0, 31.2, and 33.6 kcal/mol to form 1-N6, 2-N6, and 2-N7, respectively, whereas all the cyclization reactions are 816 kcal/mol endothermic. The subsequent H-loss from 1-N6 and 2-N6 yields the same product, cyclobuta[a]naphthalene CB[a]N, while the H-loss from 2-N7 produces cyclobuta[b]naphthalene CB[b]N. Interestingly, the barrier heights for H eliminations from 1-N6 and 2-N6 to form CB[a]N (~50 kcal/mol) are considerably higher than the 35.2 kcal/mol barrier for the H elimination from 2-N7 which leads to CB[b]N. The fourth and final pathway considered from the 1-N2 and 2-N2 adducts is internal hydrogen abstraction via migration of a hydrogen atom from the aromatic ring in naphthalene to the terminal carbon of the ethenyl fragment producing a vinyl side-chain group and the activated aromatic ring. Because such H-migrations involve only hydrogen atoms adjacent to the ethenyl group, four different products can be formed, 1-N7 and 1-N11 from 1-N2 and 2-N8 and 2-N11 from 2-N2. Among these H-migrations, the 1-N2 → 1-N7 step exhibits the lowest barrier of 12.3 kcal/mol, whereas the others feature much higher barriers of 24-28 kcal/mol. The products of Hmigrations possess vinyl fragments attached either to C1 or C2 carbons of the naphthalene core and have a radical site on the aromatic ring, making possible the addition of a second acetylene unit to the aromatic ring rather than to the first acetylene. The similar H atom migration from the phenyl ring to the ethenyl group of phenylethen-2yl radical C6H5-C2H2 was thoroughly studied by Moriarty et al.29 using various ab initio methods followed by RRKM calculations of the reaction rate constants. Their calculated energetics for this reaction agrees well with our G3 predictions; at their best G2MP2 level the barrier height and reaction energy predicted by Moriarty et al. are 28.4 and 5.6 kcal/mol, respectively, in close agreement with our G3 prediction of 28.2 and 3.0 kcal/mol (28.2 and 2.1 kcal/mol), respectively, for the similar 1-N2 → 1-N11 (2N2 → 2-N8) isomerizations. A slightly lower barrier of 24.7 kcal/mol and the reaction energy of 0.5 kcal/mol are predicted for the 1-N2 → 1-N11 hydrogen migration, whereas the migration from the bay carbon C8, 1-N2 → 1-N7, is calculated to proceed via a considerably lower barrier of 12.3 kcal/mol. Subsequent pathways involving the 1-N7, 1-N11, 2-N8, and 2-N11 intermediates are discussed below.


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The most probable scenario for the 1-N3 and 2-N3 adducts formed after two sequential additions of acetylene molecules to 1-N1 and 2-N1 is a closure of an additional six- or sevenmember ring. For 1-N3, a six-member ring closure 1-N3 → 1-N4 produces a phenanthrene core, whereas the alternative seven-member ring closure over the bay region of naphthalene, 1-N3 → 1-N5, leads to a cycloheptanaphthalene core. In 2-N3, only two six-member ring closures are possible producing either phenanthrene or anthracene precursors 2-N4 and 2-N5, respectively. All described cyclizations are highly exothermic in the range of 30-40 kcal/mol and possess low barriers of 1.4-4.6 kcal/mol, with the 1-N3 → 1-N5 seven-member ring closure step having the lowest barrier of 1.4 kcal/mol. Further eliminations of an “extra” H-atom produce the ANT, PTR, or cycloheptanaphthalene (CHN) products via barriers of 16-36 kcal/mol. From the energetic point of view, the ring closure to form the phenanthrene core structure 2-N4 appears to be more favorable than the isomerization to the anthracene core structure 2-N5 because the former process exhibits more than a factor of 2 lower barrier of 2.1 kcal/mol as compared to the 4.6 kcal/mol barrier for the latter. The same is true for the reaction energies; the 2-N3 → 2-N4 ring closure is 10 kcal/mol more exothermic (by 40 kcal/mol) as compared to the 2-N3 → 2-N5 cyclization

leading

to

ANT,

exothermic

by

29.1

kcal/mol.

The

formation

of

cycloheptanaphthalene CHN appears to be the most energetically favorable process among all cyclizations involving the 1-N3 and 2-N3 radicals. The final part of the considered mechanism includes pathways starting from the structures 1N7, 1-N11, 2-N8, and 2-N11 formed by H atom migrations from the aromatic ring to the ethenyl units of 1-N2 and 2-N2, i.e., internal hydrogen abstractions. Due to its structural features, the 1N7 intermediate is able to undergo cyclization over the bay region of naphthalene yielding the acenaphthalene precursor 1-N8, which produces ACN after subsequent hydrogen atom elimination. The barrier for the 1-N7 → 1-N8 ring closure is only 10.5 kcal/mol, which is ~6 kcal/mol lower than the similar closure of the cyclopenta ring 1-N2 → AN1. Also, the reaction is highly exothermic by 40 kcal/mol. In contrast, the 1-N11, 2-N8, and 2-N11 structures are unable to undergo ring closures and can only be involved in further addition of a second acetylene unit to the aromatic ring. Note that 1-N7 may also add a second acetylene molecule, 1-N7 + C2H2 → 1-N9, alternatively to the cyclopenta ring closure described above. The energetics of acetylene additions to 1-N7, 1-N11, 2-N8, and 2-N11 is rather similar to that observed for the acetylene addition steps discussed earlier; the barrier heights range within 2.4-4.2 kcal/mol and reaction 19 ACS Paragon Plus Environment


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exothermicities are about 35-40 kcal/mol. Subsequent rearrangements of all four C2H2 adducts 1N9, 1-N12, 2-N9, and 2-N12 are alike. First, they can lose a hydrogen atom from the ethenyl fragment producing branched products 2-ethynyl-1-vinylnaphthalene (2E1VN), 1-ethynyl-8vinylnaphthalene

(1E8VN),

1-ethynyl-2-vinylnaphthalene

(1E2VN),

and

2-ethynyl-3-

vinylnaphthalene (2E3VN), where all these H-loss reactions exhibit barriers in the range of 3436 kcal/mol and endothermicities of 27-28 kcal/mol. The second option encompasses cyclization involving the adjacent ethynyl and ethenyl fragments producing the anthracene (from 2-N13), phenanthrene (from 1-N13 and 2-N10) or cycloheptanaphthalene (from 1-N10) core structures eventually leading to the ANT, PTR and CHN products after subsequent hydrogen atom eliminations. All described cyclization steps have low barriers within 2-6 kcal/mol indicating that the formation of an extra ring is the most probable scenario if addition of second acetylene to 1-N7, 1-N11, 2-N8 and 2-N11 adducts may occur. Considering only the computed energetics for the described HACA networks, we can see that the acetylene addition sequences represent the most energetically favorable scenarios and ACN, PTR and ANT should be anticipated as major reaction products. Indeed, the acetylene addition reactions 1-N2 + C2H2 and 2-N2 + C2H2 possess considerably lower barriers (of 3.6 and 4.5 kcal/mol, respectively) than the unimolecular four-member ring closures 1-N2 → 1-N6, 2-N2 → 2-N6, 2-N2 → 2-N7, the H atom eliminations 1-N2 → 1-ETN + H, and 2-N2 → 2-ETN + H, and all possible H-migrations from the aromatic ring to the ethenyl group. However, the real product distribution is determined by the reaction kinetics, which takes into account actual concentrations of the participating species, especially acetylene as the main reactant. As will be shown in the following section, the kinetics of the considered HACA mechanism is more complicated than it follows from the pure energetic consideration.

3.2. Reaction kinetics and product yields Relative yields of the reaction products ACN, ANT, PTR, 1-ETN, CHN, CB[a]N, CB[b]N, 2E1VN, 1E8VN, 2-ETN, 1E2VN, and 2E3VN shown on Figs. 4 and 5 were calculated as described in Computational Methods, separately for the reaction Networks I and II. For all acetylene additions rate constants keff were computed using equation (2) to match the reaction conditions of two model combustion flames, n-butane and benzene. The computed relative product yields for both networks are shown in Tables 2 and 3. 20 ACS Paragon Plus Environment

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Table 2. Calculated relative product yields (%) for Network I for the conditions corresponding to n-butane/benzene flames. T, K

300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000

Contributions from different routes

Combined product yields

ACN from AN1

ACN from AN2

ACN from 1-N8

CHN from 1-N5

CHN from 1-N10

PTR from 1-N13

PTR from 1-N4

ACN

PTR

1-ETN

CHN

CB[a]N

0.1 / 0.1 0.7 / 0.7 2.1 / 2.1 4.2 / 4.2 6.8 / 6.8 9.8 / 9.8 12.6 / 12.6 15.4 / 15.4 17.9 / 17.9 20.2 / 20.2 22.3 / 22.3 24.1 / 24.1 25.6 / 25.6 26.7 / 26.7 27.3 / 27.3 27.8 / 27.8 27.8 / 27.8 27.3 / 27.3 25.6 / 25.6 22.9 / 22.9 19.9 / 19.9 17.0 /17.0 14.4 / 14.4

0/0 0/0 0.1 / 0.1 0.2 / 0.2 0.4 / 0.4 0.7 / 0.7 1.1 / 1.1 1.4 / 1.4 1.8 / 1.8 2.1 / 2.1 2.4 / 2.4 2.6 / 2.6 2.8 / 2.8 3.0 / 3.0 3.1 / 3.1 3.2 / 3.2 3.2 / 3.2 3.1 / 3.1 2.9 / 2.9 2.6 / 2.6 2.3 / 2.3 1.9 / 1.9 1.6 / 1.6

83.2 / 99.4 98.6 / 99.3 97.8 / 97.8 95.5 / 95.6 92.7 / 92.7 89.5 / 89.5 86.3 / 86.3 83.2 / 83.2 80.2 / 80.2 77.5 / 77.5 74.8 / 74.8 72.2 / 72.2 69.6 / 69.6 66.9 / 66.9 64.2 / 64.2 60.8 / 60.8 57.4 / 57.4 53.9 / 53.9 46.2 / 46.2 38.6 / 38.6 31.5 / 31.5 25.6 / 25.6 20.8 / 20.8

15.5 / 0.5 0.6 / 0 0.1 / 0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0

0.1 / 0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0

0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0

1.1 / 0 0.1 / 0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0

83.3 / 99.5 99.3 / 99.9 99.9 / 99.9 99.9 / 99.9 99.9 / 99.9 99.9 / 99.9 99.9 / 99.9 99.9 / 99.9 99.9 / 99.9 99.8 / 99.8 99.5 / 99.5 98.9 / 98.9 98.0 / 98.0 96.6 / 96.6 94.6 / 94.6 91.8 / 91.8 88.4 / 88.4 84.3 / 84.3 74.7 / 74.7 64.1 / 64.1 53.7 / 53.7 44.5 / 44.5 36.8 / 36.8

1.1/0 0.1/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0

0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0.1 / 0.1 0.2 / 0.2 0.5 / 0.5 1.1 / 1.1 2.0 / 2.0 3.4 / 3.4 5.5 / 5.5 8.2 / 8.2 11.6 / 11.6 15.6 / 15.6 25.3 / 25.3 35.8 / 35.8 46.2 / 46.2 55.2 / 55.2 62.7 / 62.7

15.6/0.5 0.6/0 0.1/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0

0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0.1 / 0.1 0.1 / 0.1 0.2 / 0.2 0.3 / 0.3 0.4 / 0.4



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Table 3. Calculated relative product yields (%) for Network II for the conditions corresponding to n-butane/benzene flames. T, K

300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000

Contributions from different pathways

Combined product yields

PTR from 2-N4

PTR from 2-N10

ANT from 2-N5

ANT from 2-N13

2-ETN

PTR

ANT

CB[a]N

CB[b]N

1E2VN

2E3VN

98.6 / 98.6 96.0 / 94.4 88.5 / 56.3 58.8 / 44.6 45.2 / 32.3 36.3 / 5.6 15.2 / 0.6 3.4 / 0.1 0.8 / 0 0.2 / 0 0.1 / 0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0

0/0 0/0 0.2 / 3.0 3.5/ 10.0 9.9 / 8.8 10.7 / 1.7 5.0 / 0.2 1.2 / 0.0 0.3 / 0.0 0.1 / 0.0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0

1.4 / 1.4 3.9 / 3.9 6.9 / 4.4 7.0 / 5.3 7.2 / 5.2 7.3 / 1.1 3.6 / 0.1 0.9 / 0 0.2 / 0 0.1 / 0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0

0/0 0 / 1.7 4.5 / 36.3 30.7 / 39.4 36.7 / 28.1 30.8 / 4.8 12.9 / 0.5 2.9 / 0.1 0.7 / 0 0.2 / 0 0.1 / 0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0

0/0 0/0 0/0 0.0 / 0.7 0.9 / 25.6 14.9 / 86.8 63.3 / 98.5 91.5 / 99.7 97.9 / 99.9 99.4 / 99.9 99.7 / 99.9 99.8 / 99.9 99.8 / 99.9 99.8 / 99.8 99.7 / 99.8 99.7 / 99.7 99.6 / 99.6 99.5 / 99.5 99.4 / 99.4 99.2 / 99.2 99.0 / 99.0 98.7 / 98.7 98.5 / 98.5

98.6 / 98.6 96.0 / 94.4 88.7 / 59.3 62.3 / 54.6 55.1 / 41.1 47.0 / 7.3 20.2 / 0.8 4.6 / 0.1 1.1 / 0 0.3 / 0 0.1 / 0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0

1.4 / 1.4 3.9 / 5.6 11.4 / 40.7 37.7 / 44.7 43.9 / 33.3 38.1 / 5.9 16.5 / 0.6 3.8 / 0.1 0.9 / 0 0.3 / 0 0.1 / 0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0

0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0.1 / 0.1 0.1 / 0.1 0.1 / 0.1 0.2 / 0.2 0.3 / 0.3 0.4 / 0.4 0.5 / 0.5 0.7 / 0.7

0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0.1 / 0.1 0.1 / 0.1 0.1 / 0.1 0.2 / 0.2 0.2 / 0.2 0.2 / 0.2 0.3 / 0.3 0.3 / 0.3 0.4 / 0.4 0.5 / 0.5 0.6 / 0.6 0.7 / 0.7 0.8 / 0.8

0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0

0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0


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In the reaction Network I, the major predicted product is ACN (Table 2) with relative yields of above 90% at temperatures up to 1800 K for both flames. With a further temperature increase which is beyond the normal temperature regime for both flames, the production of ACN rapidly decreases yielding to the formation of 1-ethynylnaphthalene 1-ETN. The formation of the other considered products, PTR, CHN, and CB[a]N, practically is not observed at all temperatures; these products appear as very minor only within the 300-400 K temperature interval not relevant to combustion. The computed product yields can be understood by analyzing the critical rate constants for the reaction steps involving the 1-N2 adduct, i.e. at the point where the reaction mechanism branches into six different routes (see Table S4 in Supporting Information). Here, the five-member ring closure 1-N2 → AN1 and the internal H-abstraction 1-N2 → 1-N7 (which is then followed by the cyclopenta ring closure, 1-N7 → 1-N8) exhibit at least an order of magnitude higher rate constants than the other competing steps, including keff for the acetylene addition 1-N2 + C2H2 → 1-N3 as well as the rate constants for the four-member ring closure 1N2 → 1-N6 and hydrogen atom migration 1-N2 → 1-N11, which also acts as internal Habstraction. Hence, 1-N2 almost completely undergoes either direct closure of a cyclopenta ring 1-N2 → AN1 or, after fast internal H-abstraction 1-N2 → 1-N7, produces an acenaphthalene precursor 1-N8 by a five-member ring closure. At the temperatures relevant to combustion the latter pathway contributes about 60-80% to the ACN product formation, with 15-30% coming from the former pathway; relative contributions to the product yields are shown in Table 2. The contribution of the AN1 → AN2 → ACN + H pathway to the ACN production does not exceed 3.2% at all studied temperatures. Here we see that although acetylene addition to 1-N2 proceeds via a very low barrier, and, as a result, exhibits high absolute values of bimolecular rate constants, the keff value for this process appears to be low as compared to the rate constants for the competing steps (Table S4). This result stems from relatively low absolute acetylene concentrations serving as a multiplying factor in equation (2) and also, a low barrier for the acetylene addition leading to a slow growth of both k and keff with the temperature increase. In the benzene flame, keff is even an order of magnitude lower than the respective value for the nbutane flame at the same temperatures because the reaction pressure of 20 Torr for the former is more than an order of magnitude lower than that for the latter (760 Torr) and the pressure P is present in the numerator of Eq. (2). A similar behavior is observed for acetylene addition to the 1-N7 adduct; keff for this process is significantly lower than the rate constant for the competing 23 ACS Paragon Plus Environment


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cyclopenta ring closure 1-N7 → 1-N8. As a result, the 1-N7 → 1-N8 → ACN + H sequence is preferable, predominantly leading to the ACN product. One may expect some contribution from the 1-N2 + C2H2 → 1-N3 acetylene addition channel if the acetylene concentration is significantly higher than that considered here or for much higher pressures, or both. However, this is not a realistic picture for the considered flames and the kinetic analysis given below shows that this hypothesis is not the case even at those extreme conditions. So far, the formation of ACN is shown to be the major reaction route for Network I. The production of 1ethynylnaphthalene (1-ETN) becomes important only at T > 1800 K, i.e. above the normal temperature regime. Therefore, this product can be considered as very minor at typical combustion temperatures relevant to the considered flames. The increased contribution of the 1N2 → 1-ETN + H channel at high temperatures originates from its relatively high barrier (36.7 kcal/mol) resulting in a rapid growth of the respective rate constant with temperature as compared to the other competing reactions. A critical mechanistic feature of the reaction mechanism in Network I is the role of the 1-N2 → 1-N7 and 1-N2 → 1-N11 internal H-abstractions. Due to the higher barrier of 28.2 kcal/mol, the latter process is not competitive with the former, as well as with the 1-N2 → AN1 fivemember ring closure, as obvious from the comparison of the respective rate constants in Table S4 and the calculated contributions to PTR from the 1-N13 adduct shown in Table 2. In contrast, the 1-N2 → 1-N7 hydrogen atom migration possesses almost a factor of 3 lower barrier (12.3 kcal/mol) and, as a result, exhibits considerably faster rate constant than its competitors resulting in a higher contribution of the 1-N2 → 1-N7 → 1-N8 → ACN + H sequence to the ACN production. This observation leads us to conclude that in similar mechanisms involving PAH molecules with bay regions (e.g. ANT, pyrene, etc.), internal H-abstractions over the bay to the adjacent ethenyl fragment should play a crucial role. Such abstraction preferably leads to a closure of the bay region and the formation of a new five-member ring instead of the second acetylene addition and an additional six-member ring closure. In contrast, H-migrations from non-bay carbons to the ethenyl group attached to the bay carbon (C1 carbon in the case of naphthalene) are not among competitive pathways and their contributions are expected to be negligible; here, we calculated zero contributions from both 1-N2 → 1-N11 → 1-N12 → 2E1VN + H and 1-N2 → 1-N11 → 1-N12 → 1-N13 → PTR + H channels. One may argue that the 1-N2 adduct has two conformations with the ethenyl group oriented towards or against the bay region 24 ACS Paragon Plus Environment

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and in the latter case the H-migration will require prior rotation (isomerization) of the ethenyl unit to form the 1-N2 conformation shown on Fig. 4, with the C2H2 unit oriented towards the bay region. However, as follows from our G3 calculations of the rotational potential for the ethenyl group in 1-N2, the rotational barrier is only 1.1 kcal/mol and therefore the rearrangement between the two conformations should be very fast and should not affect the overall reaction kinetics. The importance of the internal hydrogen abstraction mechanism in PAH formation was postulated more than a decade ago by Frenklach’s group (see, for example, ref. 29 by Moriarty et al.) on the basis of ab initio/RRKM calculations of hydrogen migration in the phenylethen-2-yl radical. This process was proposed to play an important role in the chemistry of polycyclic aromatic ring growth and in the formation of the second aromatic ring (naphthalene) in particular, which can be produced after addition of the second acetylene unit to the phenyl ring of the ortho-styrenyl radical, followed by a six-member ring closure and H atom elimination. However, according to the present study, while internal H-abstraction is shown to be important in the overall mechanism, as in the case of acetylene addition to 1-naphthyl, it mostly results in the formation of cyclopentafused PAHs, regardless of where the ethenyl group is attached, either to a bay or non-bay carbon. To ensure the accuracy of our pseudo first-order/steady-state approach we also performed direct numerical integration of differential equations for the suggested mechanism at three temperatures of 1000, 1500, and 2000 K. For the reaction Network I we included the following reactions to the simplified kinetic scheme utilized for numerical integration:

1-N2 + C2H2 1-N3 1-N4 → PTR + H 1-N3 1-N5 → CHN + H 1-N2 → 1-ETN + H 1-N2 1-N7 1-N8 → ACN + H 1-N2 AN1 → ACN + H Here, we excluded those channels from the overall Network I, which obviously cannot compete. The initial concentrations of acetylene and 1-N2 were chosen as those in the n-butane flame at the atmospheric pressure. The calculated concentrations of all species relative to the initial reactant 1-N2 versus time (concentration profiles) are plotted in Figure 6. The results 25 ACS Paragon Plus Environment


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demonstrate practically the same equilibrium concentrations (product yields) for the reaction products as those obtained using the steady-state approach and keff for acetylene addition. The analysis of computed concentration profiles reveals two competing reaction sequences, 1-N2 → AN1 → ACN + H and 1-N2 → 1-N7 → 1-N8 → ACN + H. The initial adduct 1-N2 quickly disappears producing tri-cyclic intermediates AN1 and 1-N8 via fast 1-N2 → AN1 and 1-N2 → 1-N7 → 1-N8 isomerizations and at a certain point both AN1 and 1-N8 reach their maximum concentrations, with maximum for 1-N8 considerably shifted towards longer reaction times as compared with the respective maximum for AN1. Then, AN1 and 1-N8 lose an H-atom through the AN1 → ACN + H and 1-N8 → ACN + H reactions yielding the ACN product, with the former being considerably faster due to its lower barrier of 26.4 kcal/mol as compared to 40.6 kcal/mol for the latter. This explains why the AN1 intermediate disappears much faster and the equilibrium concentration of ACN from AN1 is reached considerably sooner than from 1-N8. In contrast, 1-N8 requires a significantly longer time to convert to the final product, which is reflected by the concentration profiles showing a maximum for the 1-N8 intermediate at longer reaction times. Noteworthy, the reverse isomerization 1-N8 → 1-N7 does not play any role in the reaction kinetics owing to its very high barrier of 50.7 kcal/mol. The overall equilibrium concentration of ACN varies within 85-98% relative to the initial 1-N2 reactant depending on temperature, whereas the highest yield of 1-ETN, 15.6%, is observed at 2000 K, i.e. above the maximum flame temperatures for both flames. This result is in close agreement with those of the pseudo first-order/steady-state calculations described above and summarized in Table 2.


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100

Relative concentrations, %

Relative concentrations, %

80

1-N8

60 40

1-N7 20

ACNtot

AN1

0

1-N8 80

ACN

Formation Mechanism of Polycyclic Aromatic Hydrocarbons beyond

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