PAH Growth Initiated by Propargyl Addition: Mechanism Development

Article pubs.acs.org/JPCA

PAH Growth Initiated by Propargyl Addition: Mechanism Development and Computational Kinetics Abhijeet Raj,† Mariam J. Al Rashidi,*,‡ Suk Ho Chung,‡ and S. Mani Sarathy‡ †

Department of Chemical Engineering, The Petroleum Institute, Abu Dhabi, United Arab Emirates Clean Combustion Research Center, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

‡

S Supporting Information *

ABSTRACT: Polycyclic aromatic hydrocarbon (PAH) growth is known to be the principal pathway to soot formation during fuel combustion, as such, a physical understanding of the PAH growth mechanism is needed to effectively assess, predict, and control soot formation in flames. Although the hydrogen abstraction C2H2 addition (HACA) mechanism is believed to be the main contributor to PAH growth, it has been shown to under-predict some of the experimental data on PAHs and soot concentrations in flames. This article presents a submechanism of PAH growth that is initiated by propargyl (C3H3) addition onto naphthalene (A2) and the naphthyl radical. C3H3 has been chosen since it is known to be a precursor of benzene in combustion and has appreciable concentrations in flames. This mechanism has been developed up to the formation of pyrene (A4), and the temperature-dependent kinetics of each elementary reaction has been determined using density functional theory (DFT) computations at the B3LYP/6-311++G(d,p) level of theory and transition state theory (TST). H-abstraction, H-addition, H-migration, β-scission, and intramolecular addition reactions have been taken into account. The energy barriers of the two main pathways (H-abstraction and H-addition) were found to be relatively small if not negative, whereas the energy barriers of the other pathways were in the range of (6−89 kcal·mol−1). The rates reported in this study may be extrapolated to larger PAH molecules that have a zigzag site similar to that in naphthalene, and the mechanism presented herein may be used as a complement to the HACA mechanism to improve prediction of PAH and soot formation.

1. INTRODUCTION The adverse health and environmental impacts of soot particles have motivated efforts toward reducing combustion generated soot emissions. However, the physical and chemical mechanisms of soot formation are still not fully characterized. These mechanisms comprise fuel decomposition, polycyclic aromatic hydrocarbon (PAH) formation, particle inception, coagulation, coalescence and surface growth processes.1−3 Considering that the organic carbon fraction of soot consists almost exclusively of PAHs4 and that soot formation is initiated by PAH inception and growth reactions,5−8 a thorough understanding of these reactions is required to establish soot formation models capable of predicting soot emissions under diverse combustion conditions. The hydrogen abstraction C2H2 addition (HACA) mechanism constitutes a crucial route for the formation of aromatic species. Most of the earlier studies available in the literature regarding PAH growth mechanisms and kinetics rely heavily on the HACA mechanism.9−14 However, it has been since shown that the HACA mechanism alone is incapable of adequately assessing soot emission profiles. In their study on the effect of C/O ratio, temperature, and pressure on the formation of aromatic species, Violi et al.15 have observed that the rates and concentrations determined using the HACA mechanism are under-predicted by 1 order of magnitude at lean conditions. Similar results have been reported by ref 16 whereby it was shown that the HACA © 2014 American Chemical Society

mechanism is not fast enough to explain the experimentally observed PAH formation rates. Furthermore, this mechanism cannot predict some phenomena associated with combustion, namely, the synergistic effect of fuel mixing on soot formation, unless it is coupled to other mechanisms.17−20 In an attempt to assess the effect of fuel structure on soot formation, Hwang et al.21 conducted a study measuring the influence of mixing small amounts of propane with ethylene diffusion flames on PAH concentrations and soot volume fractions. Such studies were further developed in ref 17 and extended to include ethylene mixing with benzene,18 methane, ethane, and propene.20 The experimental results showed that fuel mixing synergistically enhances PAH and soot formation. These observations could be reproduced through modeling only if the odd-carbon chemistry, mainly C3 and C5, involved in incipient ring formation and subsequent PAH growth is accounted for in the kinetic mechanism.17−21 Finally, a study published recently by Kislov et al.22 shows that, contrary to the generally accepted view, acetylene addition to naphthalene produces cyclopentafused PAHs rather than six-membered ring species. In fact, within temperature ranges relevant to combustion (1000−2000 K), the yields of 6-membered ring species anthracene and Received: October 30, 2013 Revised: March 19, 2014 Published: March 20, 2014 2865

dx.doi.org/10.1021/jp410704b | J. Phys. Chem. A 2014, 118, 2865−2885

The Journal of Physical Chemistry A

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followed by H-abstraction, H-addition, intramolecular addition (ring closure), H-migration, and β-scission reactions. H-radicals are the only H-abstracting species that have been taken into account since they are the most abundant abstracting species under sooting flame conditions (i.e., high temperature fuel rich environments).33 2.2. Quantum Calculations. The temperature-dependent kinetic rate constants of all mechanistic pathways were determined using quantum mechanics and transition state theory software, namely, Gaussian 0934 and ChemRate.35 Ab initio quantum mechanical methods would have been ideal for energy calculation since they are usually more accurate than other methods. However, considering the large number of heavy atoms in the studied PAH species and transition states (C10−C16), and the current efficiency of computing resources, the use of the computationally demanding ab initio methods is infeasible. Therefore, the less computationally expensive density functional theory (DFT) methods were adopted instead, as is usually the case for large molecules.36−38 Although these methods are less accurate than ab initio methods, they provide fairly good results within reasonable time. In this study, the geometries, energies, and frequencies of all chemical species and transition states were optimized and calculated using the hybrid DFT B3LYP method coupled to the 6-311++G(d,p) basis set. This method has been previously validated against some well-characterized reactions and has been shown to give values that agree reasonably well with experimental results.37 The vibrational modes of all transition states were animated to ensure that there exists only one negative vibrational frequency corresponding to the implicated transition. Isodesmic and isogyric reactions were employed to improve accuracy in the determination of the activation energy, which is expressed as the difference between the enthalpy of formation of the transition state and the sum of formation enthalpies of the reactants. Two isodesmic reactions were elaborated for each chemical species and transition state. The enthalpy value used in ChemRate is the average of the two values. In some cases, it was not possible to establish isodesmic reactions due to the limited experimental thermodynamic databases available in the literature, and thus, isogyric reactions were used instead. Formation enthalpies (ΔHf) are often expressed in terms of atomization energies as shown below.

phenanthrene is only 3−6%, which is less than that observed experimentally. These results have motivated numerous investigations into alternative routes of PAH growth. Among the different chemical species that can contribute to PAH growth in combustion, resonantly stabilized radicals are of particular importance since they can attain high concentrations due to their relatively stable nature.15 Their importance has been demonstrated experimentally23 as well as theoretically,24 particularly when it comes to benzene and naphthalene formation.25 In fact, recombination of propargyl, a resonantly stabilized radical, is considered to be a key reaction in benzene formation.25 Similarly, the recombination of cyclopentadienyl radicals contributes significantly to naphthalene formation.26,27 Propargyl radical has also been shown to play an important role in PAH growth mechanisms.6,28−30 However, although PAH growth predictions improve considerably when the contributions of resonantly stabilized species such as propargyl and cyclopentadienyl are accounted for, certain discrepancies between modeling and experimental data persist.6,28,30 This indicates that the available mechanisms are incomplete and need to be improved. In particular, the mechanisms should be extended to include PAH growth reactions initiated by propargyl, propenyl, and cyclopentadienyl addition to benzene and larger PAHs, among others. Moreover, the rates adopted for these reactions should be revised and more accurate values provided. Many studies rely on estimation in determining the rates of particular reactions. Usually, rates determined for benzene are extrapolated to larger PAH molecules. However, such methods might lead to invalid rates since, unlike benzene (A1), reaction sites in larger PAHs are not necessarily equivalent. Depending on their structure, PAHs larger than A1 may have zigzag, armchair, or bay sites in addition to the free-edge sites characteristic of benzene.31 The rates of addition or abstraction from these different sites are probably different and thus should not be used interchangeably. In this study, the mechanism of propargyl addition to naphthalene (A2) and the naphthyl radical is developed up to pyrene (A4). The temperature-dependent kinetics of the implicated elementary reactions is computationally assessed using density functional (DFT) and transition state theories (TST). Considering that the two resonance structures of propargyl, C3H3(1) (alkynyl radical, one triple and one single bond) and C3H3(2) (dienyl radical, two double bonds), yield different intermediates, mechanisms were developed separately for C3H3(1) and C3H3(2) addition to A2 and A2-radical. Although computational rates of the A1 + C3H3 reaction are available in the literature,32 to the best of our knowledge no information exists concerning the kinetics of A2 + C3H3. The kinetic mechanism developed herein may be added to some of the PAH growth mechanisms to improve soot formation predictions.

xC + y H → Cx Hy

(1)

ΔHf (Cx Hy) = ECx Hy − (xEC + yE H) + (xΔHf (C) + yΔHf (H))

(2)

where EC, EH, and ECxHy represent the energies of C, H, and CxHy, respectively, determined computationally using the same level of theory. Meanwhile, ΔHf (C) and ΔHf (H) constitute the experimental values of the enthalpies of formation of C and H as reported in the literature, respectively. Although these experimental values are highly accurate, there is still some error associated with them (ΔHf (H) = 217.998 ± 0.006 and ΔHf (C) = 716.68 ± 0.45 kJ·mol−1.39 Thus, for molecules with a large number of C and H atoms, such as PAH molecules, the use of atomization reactions in the determination of ΔHf (CxHy) implicates relatively large error margins. This error may be reduced significantly if isodesmic or isogyric reactions are used instead. This hypothesis has been validated for naphthalene (A2), pyrene (A4), and C3H3. As shown in Table

2. MECHANISM DEVELOPMENT AND CALCULATION DETAILS 2.1. Mechanism Development. The developed mechanism consists of two parts, (i) the addition of propagyl radical onto naphthalene (A2) and naphthyl radical leading to the formation of phenalene (CS9) and (ii) the addition of propargyl onto the phenalenyl radical (CS14) leading to the formation of pyrene (A4). Two mechanisms were developed, one for each resonance structure of propargyl (C3H3(1) and C3H3(2)). Only reactions leading to the desired products have been considered. These reactions include C3H3-addition 2866



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Although the Eckart model is better suited for the estimation of tunneling corrections, it has been shown that at combustion relevant temperatures (>500 K), both methods give similar results.43,44

1, isodesmic/isogyric (ISO) reactions reduce the difference between experimental and computational enthalpy values by Table 1. Comparison of Computational Enthalpy Values Determined Using B3LYP (Atomization), B3LYP (Isodesmic/Isogyric), and CBS-QB3 (Atomization) with the Experimental Values Reported in the Literature for A2, A4, and C3H3 in Units of kcal·mol−1

3. RESULTS AND DISCUSSION The mechanism developed in this study is depicted in Figures 1−6. Figures 1−3 show the mechanistic pathways of addition of C3H3(1) and C3H3(2) leading to the formation of phenalene and the phenalenyl radical, whereas Figures 4−6 illustrate the routes of propargyl addition to the phenalenyl radical resulting in pyrene (A4). In this work, we have only considered H-mediated activation of closed shell species. The closed shell isomerization reactions could be of relevance for species such as CS3, CS6, and CS18. Some isomerization reactions leading to 5- and 6-membered ring formation were tested on CS3. The one-step ring formation reaction in this molecular system requires loss of aromaticity (in the naphthalene part) and diradical formation, which makes isomerization unfavorable (energy barrier of 47 kcal compared to 3 kcal for the reverse reaction). H transfer reactions also lead to diradical formation and thus are expected to be unfavorable as well. 3.1. Potential Energy Diagrams. The mechanistic pathways implicated in this study are depicted in Figures 7−17. Pathways 1.1−1.5 describe the mechanism of A2 + C3H3; whereas pathways 2.1−2.6 describe that of phenalenyl radical (CS14) + C3H3. Both mechanisms are initiated by C3H3-addition onto A2 or CS14 followed by H-abstraction and H-addition reactions. The subsequent radicals undergo Hmigration, β-scission, and intramolecular addition reactions, ultimately leading to the formation of the desired product, pyrene (A4). Separate mechanisms have been developed for each resonance structure of C3H3 since they yield different intermediates, products, and mechanistic pathways. Further

ΔHf (298 K) A2 A4 C3H3

B3LYP

CBS-QB3

ISO

exptl

66.9 109.4 86.8

38.1 56.0 85.2

38.7 58.5 84.1

36.0 ± 0.441 53.2 ± 0.641 81.0 ± 1.042

78, 96, and 3% for A2, A4, and C3H3, respectively. In fact, the ISO enthalpy values are within 1−2% difference of those calculated using the more accurate CBS-QB3 level of theory.40 The calculated energies and frequencies were used to evaluate the kinetic rate constants in ChemRate. The obtained constants were fitted to the modified Arrhenius expression, k(T) = ATn exp(−Ea/RT), in the temperature range 300−3000 K in order to determine the pre-exponential frequency factor, the temperature exponent, and the activation energy, A, n, and Ea, respectively. Wigner correction of the rate constants was applied to account for tunneling using the expressions: k = WCk′

(3)

and WC = 1 +

1 hν 24 kT

2

(4)

where k and k′ are the temperature-dependent rate constants with and without tunneling, respectively, h is Plank’s constant, ν is the imaginary frequency, and k is Boltzmann constant.

Figure 1. Mechanism of C3H3(1) addition to A2 to form CS6 and CS14. 2867



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Figure 2. Mechanism of C3H3(2) addition to A2 to form CS6 and CS9.

Figure 3. Mechanism of the conversion of CS6 to CS9 and CS1.

difference is probably due to the difference in the level of theory used for energy calculation. The kinetics of propargyl addition to benzene and phenyl radical was studied at the G3(MP2,CC)//B3LYP level of theory, whereas that used in this study is B3LYP/6-311++G(d,p). The energy barrier of CS2 + C3H3(1) is considerably higher than that expected for radical−radical association reactions, which are commonly barrierless. However, computations at the M062X/6-311+ +G(d,p) level of theory also predict a positive barrier that is only 10% lower than that calculated with B3LYP. This ensures

details and discussion concerning the sequence and energetics of each pathway are given below. 3.1.1. Pathway 1.1. Figure 7 presents the potential energy diagram of Pathway 1.1 describing the addition of C3H3(1) onto naphthalene and the naphthyl radical, followed by Haddition on CS3 and subsequent reactions. In Figure 7, ΔHf of A2 + C3H3 is set as zero and all other enthalpy values are reported accordingly. The activation energy of the initiation step is 6 and 12 kcal for the naphthyl radical and naphthalene, respectively, compared to 0 and 16 kcal for the addition of C3H3(1) on the phenyl radical and benzene.32 The observed 2868



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Figure 4. Mechanism of C3H3(1) addition to CS14 to form A4, H-abstraction pathways.

Figure 5. Mechanism of C3H3(1) addition to CS14 to form A4, H-addition pathways.

energies (2 and 4 kcal), which makes them both, thermodynamically and kinetically favorable. The radicals formed upon H-addition (CS4 and CS7) undergo intramolecular addition reactions followed by C−H scission, resulting in the formation of 5- and 6-memebered ring species CS6 and CS9 (phenalene), respectively. The routes of formation of CS6 from CS4 and CS9 from CS7 are highly

the validity of the positive energy barrier calculated for CS2 + C3H3(1). As shown in Figure 7, CS3 is more readily formed from the naphthyl radical (one-step reaction) than from A2 (two-step reaction). Once formed, CS3 undergoes H-addition reactions to carbon #1 or #2. In addition to being highly exothermic (ΔHR = −34 and −38 kcal), these reactions have low activation 2869



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Figure 6. Mechanism of C3H3(2) addition to CS14 to form A4.

Figure 7. Pathway 1.1, A2 + C3H3(1) H-addition reactions.

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Figure 8. Pathway 1.2, A2 + C3H3(1) H-abstraction reactions.

degeneracy effects (nondynamical electron correlation) such as those involved in radical−radical association reactions.45 Therefore, the transition states of the H-addition reactions to radical species CS15 and CS13 (TS16 and TS24, respectively) have not been determined and thus are not presented in the potential energy diagram of Figure 8. However, such radical− radical association reactions are expected to be very fast and to have negative activation energies. The rates of these reactions were estimated by analogy as explained in section 3.2. Alternatively, CS13 and CS15 may undergo 1−2 and 1−3 Hmigration reactions, respectively. Other H-migration reactions may also occur; however, they were not studied as they do not eventually lead to the formation of the desired product phenalene (CS9). H-migration pathways for CS13 and CS15 are much slower than the H-addition pathways with activation energies in the order of 37−48 kcal. As shown in Figure 8, the H-abstraction pathways of CS3 lead to the formation of CS6 and CS9 just like the H-addition pathways (Figure 7). 3.1.3. Pathway 1.3. The second resonance structure of propargyl (C3H3(2)) has 2 double bonds instead of one single and one triple bond. Therefore, the products and mechanism of C3H3(2) addition to A2 are different from those of C3H3(1). Figure 9 depicts the potential energy diagram of the Habstraction pathways of the A2 + C3H3(2) mechanism. The enthalpy values in Figure 9 are relative to that of A2 + C3H3. A2

competitive with the activation barriers of the intramolecular addition and β-scission reactions being comparable. 3.1.2. Pathway 1.2. In addition to H-addition, CS3 may undergo H-abstraction reactions. H-abstraction pathways of CS3 are presented in Figure 8 where all enthalpy values are reported relative to CS3 + H. In this study, only H-radicals have been considered as H-abstracting species due to their high concentrations under sooting flame conditions. There are three possible sites of abstraction that eventually lead to the formation of the desired products. Those are carbon #1, #3, and #4, yielding CS11, CS12, and CS10, respectively. Intramolecular addition of CS11 is not possible since a linear structure is dictated by the sp hybridization of carbon #2. Therefore, the only mechanistic pathway open for CS11 is Hmigration from carbon #1 to carbon #4, leading to the formation of CS10. Similarly, intramolecular addition of CS12 is expected to have a high activation energy barrier since the transition state of this reaction involves the formation of a highly strained 4-membered ring. Thus, this reaction has been neglected in favor of the H-migration reaction to CS10, which implicates a less-strained 5-membered ring transition state. CS10 then undergoes 5- or 6-membered ring intramolecular reactions to sp2 radical species CS15 and CS13, respectively. Single-reference computational methods including DFT fail to compute the energies of systems that exhibit important near2871



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Figure 9. Pathway 1.3, A2 + C3H3(2) H-abstraction reactions.

Figure 10. Pathway 1.4, A2 + C3H3(2) H-addition reactions.

addition followed by C−H bond scission, whereas CS2 → CS18 occurs in one step. However, unlike CS2 → CS3 of

and CS2 react with C3H3(2) to give CS18. As in the case of C3H3(1), A2 → CS18 is a two-step reaction consisting of C3H32872



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Figure 11. Pathway 1.5, ring interconversion reactions (CS6 to CS9 and CS14).

pathway 1.1, which has an activation energy of 7 kcal, CS2 → CS18 was found to have no activation barrier. Once formed, CS18 may undergo H-abstraction from carbon #1, #3, and #4 leading to the formation of CS12, CS33, and CS32, respectively. The energy barrier for the formation of CS32 is 13 kcal, whereas the formation of CS33 and CS12 is practically barrierless (2 kcal). However, in the developed mechanistic scheme, CS33 and CS12 isomerize to CS32. The isomerization reactions involve 5- and 7-membered ring transition states and have activation barriers in the order of 44−53 kcal. CS32 undergoes intramolecular addition to carbon #1 or #2, which leads to the formation of CS13 and CS16, respectively. The energy barriers of these reactions are low (2 and 7 kcal), which means that they occur readily. Addition to carbon #3 is also possible, but is expected to have high activation energy associated with the formation of a strained 4-membered ring structure. Moreover, it does not lead to the formation of the desired product. Therefore, this mechanistic pathway was not investigated. 3.1.4. Pathway 1.4. In addition to H-abstraction, CS18 undergoes H-addition via three mechanistic routes involving the addition to carbon #1 (TS32), #2 (TS29), and #3 (TS28) (Figure 10). All three routes have comparable activation energies (0−2 kcal), rendering them highly competitive. The radicals formed upon H-addition are CS4, CS19, and CS24. Reactions of CS4 have been discussed earlier in section 3.1. As for CS19 and CS24, they undergo H-migration or intramolecular addition reactions. One to two and 1−4 H-migration reactions of CS19 yield CS24 and CS21, respectively, whereas intramolecular addition of CS19 ultimately gives CS9. A comparison of the energy barriers of these reactions shows that the intramolecular addition route is much more favorable with a barrier of 16 kcal compared to 41 and 60 kcal for the 1−4 and 1−2 H-migration reactions, respectively. Although 1−4 Hmigration is less favorable than intramolecular addition, it is still a very important reaction since it leads to the formation of a highly reactive species (CS21) that readily gives CS23 via TS35, a reaction that has no activation barrier. As discussed in section 3.1.5, dissociation of CS23 yields CS9. Unlike CS19, the 1−5 H-migration route of CS24 has very low activation energy (4 kcal) and is slightly more favorable than the intramolecular addition route (10 kcal) at low temperatures. This can be explained by the higher reactivity of CS24 compared to CS19 as well as the relative stability of the 6-membered ring transition

state involved in the formation of CS25 (TS37). Both reaction routes of CS24 (intramolecular addition and H-migration) eventually lead to the formation of CS27 through C−H bond scission in CS26 and intramolecular addition of CS25 followed by C−H bond scission in CS28. Alternative reactions of CS28 include 1−3 H-migration to CS22, 1−2 H-migration to CS30, and C−C bond scission to CS29. The energy barriers of these mechanistic routes do not exhibit great variations (42, 30, and 36 kcal, respectively), and thus, they are competitive. Species CS22 and CS30 are interchangeable via 1−2 H-migration with the reaction being more thermodynamically and kinetically favorable in the direction of CS30 formation, which in turn dissociates to give CS6 + H. As expected, the C−C bond scission barrier of CS28 (36 kcal) is lower than the C−H scission barrier (45 kcal). However, C−C bond scission does not lead to the formation of the desired product and so was not investigated further. Finally, CS27 undergoes H-abstraction from the CH3 or the sp2 CH moieties to give CS16 and CS31, respectively. The formation of CS16 is highly favorable with an activation barrier that is practically zero. The energy barrier of CS31 formation is also small (6 kcal). However, the formation of CS16 from CS31 via 1−3 H-migration requires substantial activation energy (47 kcal). As shown in Figure 8, CS16 is also a product of the H-abstraction of CS6. 3.1.5. Pathway 1.5. As per sections 3.1.1−3.1.4 and Figures 7−10, the different mechanistic pathways of C3H3(1) and C3H3(2) addition to A2 and A2 radical (CS2) yield CS9 and CS6. Reactions of the CS9 radical (CS14) with C3H3(1) and C3H3(2) to form pyrene (A4) will be discussed in sections 3.1.6−3.1.9. Meanwhile, this section discusses the ring interconversion reactions from CS6 to CS9 and its radical CS14. The reaction routes of this submechanism are presented in Figure 11 where all energy values are reported relative to that of CS6 + H. Ring interconversion reactions are initiated by H-abstraction from CS6 to form either CS15 or CS16. The pathway leading to the formation of CS16 is not presented in Figure 11 as it has already been shown in Figure 8 (TS23). The formation of CS15 requires a bit more energy; however, both routes are favorable at low temperature with activation barriers in the order of 0−10 kcal. Once formed, CS15 undergoes intramolecular addition onto an sp2 or sp3 hybridized carbon followed by β-scission to give CS13 and CS38, respectively. Although we were able to computationally identify an addition 2873



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Figure 12. Pathway 2.1, CS14+C3H3(1) H-abstraction reactions.

Figure 13. Pathway 2.1, CS14 + C3H3(1) H-abstraction reactions continued.

intermediate (CS37) in the case of radical addition to the sp2 hybridized carbon, we were unable to assess the energy of an analogous species resulting from addition to the sp3 carbon. The addition C−C bond scission sequence occurs in a concerted manner with slightly higher energy barrier in the second case. The activation energy of the H-addition reaction to the sp2 hybridized carbon in CS38 was found to be negative, just like that of CS13 + H. The rate of this reaction was similarly estimated by analogy as discussed in section 3.2. Both H-addition reactions produce phenalene (CS9), and there exists an equilibrium between the two species (CS13 and

CS38), maintained by a 1−2 H-migration reaction whose barrier is just over 50 kcal in both directions. However, only one intramolecular addition route exists for CS16. This route produces a computationally discernible, highly reactive intermediate consisting of a strained 3membered ring structure (CS34) that undergoes C−C bond scission to give CS14 via CS36. CS34 may also exhibit 1−2 Hmigration leading to the formation of CS35, which in turn produces CS14 as well. However, the energy barrier for the Hmigration route is approximately 22 kcal greater than that of the dissociation route, which makes the former less favorable. 2874



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Figure 14. Pathway 2.2, CS14 + C3H3(2) H-addition reactions.

initiated by an H atom has a negative energy barrier, showing that this reaction would be very fast. Sections 3.1.6−3.1.10 provide an overview of the mechanistic routes initiated by C3H3-addition to phenalenyl radical and leading to the formation of pyrene (A4). Similar to A2 + C3H3, two separate mechanisms were developed for each resonance structure of propargyl. In this section we discuss the energetics of CS14 + C3H3(1). H-abstraction pathways are presented in Figures 12 and 13, wherein all the energies are reported relative to that of CS43. Propargyl addition to CS6 is not investigated since it does not lead to the formation of A4, and it can readily get converted to a more stable species, CS9 (or its radicals), through H-addition reaction, as discussed in section 3.1.5. C3H3(1) addition to CS14 seems to be less favorable than addition to CS2 with the energy barrier being approximately 19 kcal. However, the exothermicity of this reaction (ΔHR = 35 kcal) drives it forward especially at the high temperatures relevant to combustion. The species produced (CS41) has 4 abstraction sites that are relevant to the formation of A4 (carbon #1, #3, #4, and #5). The energy barriers are 29, 3, 14, and 2 kcal for abstraction from 1, 3, 4, and 5, respectively. To simplify the potential energy diagram, H-abstraction reactions of CS41 are shown on the right side of the figure, as pointed out by arrows. As expected, H-abstraction from the tertiary sp3 carbon (#4) is most favorable. Intramolecular addition reactions of CS53 and CS54 are structurally and energetically restricted since they lead to the formation of highly strained products. Thus, only H-migration reactions of these species have been investigated. In the case of CS53, 1−6 and 1−4 H-

In addition to the H-abstraction pathways discussed above, 5to 6-membered ring interconversion may also occur via Haddition pathways. H-addition to carbon #1 in CS6 produces CS30. The energies of this reaction and subsequent mechanistic routes have been discussed in section 3.1.4. Meanwhile, Haddition to carbon #2 in CS6 produces C22. The exothermicity (ΔHR = −29 kcal) and low activation barrier (3 kcal) favor this reaction relative to the H-abstraction pathways. Once formed, CS22 undergoes intramolecular addition to an sp3 or sp2 hybridized carbon followed by C−C bond scission and ringopening in a concerted or nonconcerted sequence to give CS39 and CS23, respectively. As shown in Figure 11, the energy barrier of the concerted mechanistic pathway leading to the formation of CS39 is 37 kcal greater than that leading to CS23. However, both species, CS39 and CS23, undergo C−H scission reactions to form CS9. An overview of the different mechanistic routes involved in the 5- to 6-membered ring interconversion submechanism shows that although the energy barriers of the H-addition and H-abstraction reactions of CS6 are relatively similar (within 0− 10 kcal), the subsequent reaction pathways of the species generated via H-abstraction seem to require greater energy than the H-addition counterparts. This indicates that the interconversion routes initiated by H-addition are more favorable. 3.1.6. Pathway 2.1. We have shown in sections 3.1.1−3.1.5 that C3H3-addition to naphthalene and the naphthyl radical leads to the formation of phenalene (CS9) and the phenalenyl radical (CS14). Note that CS14 is a resonantly stabilized radical. The conversion of CS9 to CS14 through H-abstraction 2875



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Figure 15. Pathway 2.3, CS14 + C3H3(2) H-abstraction reactions.

different products (CS58, CS60, CS48, and CS50). The transition states of H-addition reactions to CS47 and CS57 to form CS48 and CS58, respectively, could not be found with DFT. The rates of these reactions were estimated. C−H bond scissions of CS48 and CS58 lead to the formation of CS49 and CS59, respectively, the reactions of which are discussed in section 3.1.9. Meanwhile, CS50 and CS60 undergo intramolecular addition reactions. CS50 may undergo addition to a secondary or tertiary sp3 hybridized carbon producing CS51 and CS52, respectively. The route leading to the formation of CS52 has an energy barrier of 7 kcal compared to 54 kcal for the CS51 formation reaction, meaning that addition to the tertiary carbon site is more favorable. However, the radical in CS60 may add to a secondary sp3 hybridized carbon or to a tertiary sp2 carbon site resulting in the formation of CS62 and CS61, respectively. Addition to the unsaturated bond is more favorable than the alternative addition to the saturated bond by 36 kcal. Once formed, CS61 readily undergoes C−C bond scission to form CS52 (energy barrier of 2 kcal), whereas CS62 exhibits C−H bond scission to form CS63 with an activation barrier of 45 kcal. Reactions of CS51, CS52, and CS63 will be discussed in the next section. 3.1.7. Pathway 2.2. Besides H-abstraction reactions, CS41, the product of propargyl addition to CS14, may exhibit Haddition reactions to carbon #1 or #2. These pathways are portrayed in Figure 14 where all energy values are given relative to that of CS67 + H. Intramolecular addition reactions of the products of H-addition to CS41, CS65, and CS70 give 6- and 5membered ring tertiary radical structures, CS66 and CS71, respectively. Two possible C−H bond scission routes of comparable energy barriers (27−32 kcal) exist for each intramolecular addition product. These routes lead to the formation of CS63 and CS67 from CS66, and to CS57 and CS47 from CS71. The reactions of CS47 and CS57 have

migration reactions lead to the formation of CS55 and CS42, respectively; whereas CS54 undergoes 1−4 and 1−2 Hmigration reactions to give CS55 and CS42, respectively. Hmigration to CS42 (25 kcal) seems to be more energetically favorable than H-migration to CS55 (41 kcal) for CS54. However, in the case of CS53, the energy barriers for both Hmigration reactions are comparable. Still, the formation of CS42 is more favored due to its higher stability compared to CS55 (52 kcal difference in energy). Intramolecular addition reactions of CS55 are fairly quick with energy barriers in the order of 5−6 kcal and lead to the formation of CS56 and CS64. Meanwhile, intramolecular addition reactions of CS42 have higher energy barriers, 33−38 kcal, and produce CS46 and CS43. The subsequent reactions of the 6-membered ring products CS64 and CS43 include 1−2 and 1−3 H-migration reactions leading to CSS44 and CS45, followed by C−H bond scission to form A4. Considering the high energy barriers (32−62 kcal) associated with the aforementioned H-migration reactions, H-addition to the sp2 hybridized radical sites in CS64 and CS43 constitutes a more energetically viable reaction pathway. As we were unable to acquire appropriate transition state geometries using DFT computations, we used the CASPT2/cc-pvdz computational results reported by Harding et al.46 for the C6H5 + H reaction to estimate the rates of CS64 + H and CS43 + H. The expected products of these reactions are CS63 and CS67 whose consequent reactions are displayed in Figure 14 and discussed in section 3.1.7. Similarly, and for the same reason, the rates of CS46 + H and CS56 + H were estimated by analogy to the C2H3 + H reaction.46 The expected products are CS47 and CS57, the reactions of which are depicted in Figures 13 and 14. There are two nonaromatic H-addition sites on each one of these species. The implicated H-addition pathways have low energy barriers (4−6 kcal) and lead to the formation of four 2876



Article

Figure 16. Pathway 2.4, CS14 + C3H3(2) H-addition reactions.

thermodynamically favorable pathway. Subsequent intramolecular addition reactions of CS76 and CS77 are prohibited by the high strain evoked on the product of the former, and the linearity of the (C1−C2−C3) moiety of the latter. Only Hmigration routes have been considered for these species. One to two and 1−4 H-migration in CS76 lead to the formation of CS73 and CS78, respectively. The same species are produced via 1−4 and 1−6 H-migration of CS77. The energy barriers of these migration reactions are relatively high, particularly those of CS77 (47−56 kcal). This can be explained by the strain involved in breaking the linearity imposed by the sp hybridization of carbon #2 in CS77 while forming the implicated transition states. Intramolecular addition reactions of CS78 yield 5- and 6memebered ring structures CS79 and CS64, respectively. Reactions of CS64 have been discussed earlier in section 3.1.6. Meanwhile CS79 undergoes H-addition to give CS57. This reaction was found to have negative activation energy, and its rate is estimated by analogy (section 3.2). Meanwhile, intramolecular addition of CS73 gives CS74 and CS75 with energy barriers in the range of 33−36 kcal. H-addition to CS74 occurs relatively quickly (Ea = 11 kcal) and yields CS47; whereas CS75 undergoes 1−3 and 1−2 H-migration to give CS44 and CS45, respectively. Also included in the PED presented in Figure 15 is the pathway of H-addition to CS73 leading to CS72 with an energy barrier of 8 kcal. 3.1.9. Pathway 2.4. Figure 16 depicts the potential energy diagram of the different reaction pathways instigated by Haddition to CS72, relative to the energy of CS82. The addition pathways have low energy barriers (3−5 kcal) and are highly exothermic, leading to the formation of sp3 and sp2 radicals CS80 and CS81, respectively. Intramolecular addition of CS80 has activation energy of approximately 24 kcal and yields CS66, a product whose reaction pathways have been discussed in the preceding sections. Meanwhile, intramolecular addition of CS81 has an energy barrier of 4 kcal and gives a 5-membered ring tertiary radical species CS82. This latter species may undergo C−H scission reactions giving CS49 and CS59 or 1−2 H-migration reactions giving CS48 and CS91. All four mechanistic routes have comparable energy barriers (28−32 kcal) and thus are competitive. CS49 and CS59 exhibit H-

already been discussed in the previous section. Meanwhile, CS63 and CS67 undergo H-abstraction via two possible routes (abstraction from secondary or tertiary carbon atoms) resulting in the formation of CS44 and CS45. These H-abstraction reactions are rather fast, and the energy barriers do not exceed 3 kcal. Just as seen previously in section 3.6, abstraction from the tertiary carbon is more favorable than abstraction from the secondary carbon for both species, with the activation barrier of the former being negative. The kinetic parameters of these reactions were estimated by analogy as detailed in section 3.2. Once formed, CS44 and CS45 may produce A4 via β-scission, as shown earlier in section 3.1.6, or they may add an H-radical to give CS63 and CS67. A comparison of the energy barriers of both pathways shows that H-addition is more favorable. Alternatively, CS63 and CS67 may undergo H-addition reactions resulting in the formation of CS51, CS52, and CS62. The route leading to the formation of CS62 is not presented in Figure 14 since the reverse reaction has been discussed and presented previously (Figure 13 and section 3.1.6). The energy barriers of the other three reactions (TS115, TS116, and TS117) do not exceed 3 kcal. β-scission reactions of CS52 lead back to CS63 and CS67; however, C−H scission in CS51 may lead to a new species CS68 if the energy barrier of 26 kcal is overcome. The energetically favorable H-abstraction reactions of CS68 produce CS44 and CS69, both of which yield A4 upon β-scission. 3.1.8. Pathway 2.3. Now that we have discussed the mechanistic pathways of CS14 + C3H3(1) leading to A4, we move on to the mechanistic pathways initiated by the addition of the other resonance structure of propargyl (C3H3(2)) onto CS14. These pathways are split into three Figures based on the type of reactions (H-addition, H-abstraction, and ring interconversion). In this section we discuss the H-abstraction pathways of Figure 15 in which the energies are reported relative to CS73. CS72, the product of C3H3(2) addition to the phenalenyl radical CS14 readily undergoes H-abstraction from 4 available sites, carbon #1, #3, #4, and #5 (Figure 6). As shown in Figure 15, although all of these abstraction reactions have low energy barriers (1−13 kcal), abstraction from the tertiary site leading to the formation of CS73 is the most kinetically and 2877



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Figure 17. Pathway 2.5, ring interconversion reactions (CS88 to CS46).

As shown in Figure 17, the energy barriers of all the mechanistic routes depicted in the PED of pathway 2.5 are rather large (36−88 kcal) except for that of the CS86 → CS45 reaction. However, all of the discussed pathways lead to CS45, which readily decomposes to A4 + H. 3.2. Elementary Reaction Rate Constants and Thermodynamic Data. In total, 173 reactions were studied in this work. The high pressure limit temperature-dependent rate constants of the elementary reactions depicted in Figures 1−6 are listed in Table 2 in terms of the pre-exponential factor A, the activation energy Ea and n, in units of kcal, cm3, molecule, and s. These rates are valid within the temperature range 300− 2500 K. Master equation analysis and pressure-dependent rate parameters may be determined in the future to further enhance the predictive capabilities of the developed model. The rates of 14 reactions (19, 27, 36, 123, 126, 16, 24, 69, 85, 86, 99, 100, 150, and 164) in the developed mechanism could not be determined, either because the reactions are barrierless or because their transition states could not be found using the DFT methods employed herein. The rates of the barrierless reactions (19, 27, 36, 123, and 126) have been estimated by analogy to similar reactions. Reaction 19 represents an Habstraction reaction from an allylic position, and thus, its rate was estimated by analogy to reaction 120. Meanwhile, the rate of 36 was estimated by analogy to 57 since both reactions describe an intramolecular addition reaction of an sp 2 hybridized radical site to an unsaturated bond, leading to the formation of a 5-membered ring structure with an sp 3 hybridized radical site. In the case of reactions 123 and 126, analogies were made with 114 since all three reactions describe H-abstraction from an sp3 hybridized carbon site. For lack a better analogy, the rate parameters of reaction 27 were estimated by analogy to those of C3H3 + C3H3 radical−radical addition.47 Analogies were also used to estimate the rates of reactions 16, 24, 69, 85, 86, 99, 100, 150, and 164, whose

addition and H-abstraction reactions, whereas CS48 and CS91 undergo β-scission reactions. As discussed earlier, C−H scission in CS48 gives CS49. The PED of this reaction is presented in Figure 13. As for CS91, C−C and C−H bond scissions may occur leading to the formation of CS92 and CS59, respectively. The energy barriers of the two scission routes are similar (29 and 34 kcal) with the C−C scission being slightly more favorable. The H-addition reaction of CS49 is basically the reverse of the C−H scission of CS48 discussed in section 3.1.6. Meanwhile, H-abstraction of CS49 yields the primary radical CS83 whose reactivity is examined in the next section. Finally, H-addition to CS59 is the reverse of the C−H scission of CS91, and the H-abstraction pathway, which has an energy barrier of 5 kcal, yields CS87. 3.1.10. Pathway 2.5. Species CS83 and CS87, produced via the C3H3(2) addition to CS14 (section 3.1.9), undergo ringinterconversion reactions which ultimately lead to the formation of A4. These reactions are presented in Figure 17 and the energy values are reported relative to CS82. The ring interconversion reactions are initiated by intramolecular addition of the primary radical of CS83 onto the sp2 or tertiary sp3 carbon atoms, leading to the formation of CS85 and CS84, respectively. 1−2 H-migration of CS84 gives CS45, which has been shown to produce A4. CS85, however, undergoes 1−2 Hmigration to CS86 and CS90, respectively. Moreover, Hmigration from CS86 to CS90 can take place. Both structures comprise 3-membered rings and are highly strained, which makes them highly reactive. C−C scission of CS90 gives CS87, while the C−C scission of CS86 gives CS45. The energy barrier of the latter reaction was found to be negative. Therefore, the rate of this reaction was estimated by analogy to that of CS35 → CS14 as discussed in section 3.2. Finally, intramolecular addition onto the tertiary sp2 carbon leads to the formation of CS88 which in turn undergoes a bond breaking reaction leading to CS89. One to two H-migration of CS89 then gives CS45. 2878


2879

CS24 = CS26 CS26 = CS27 + H CS27 + H = CS28 CS27 + H = CS30 CS30 = CS28 CS30 = CS6 + H C30 = C22 CS27 + H = CS31 CS27 + H = CS16 CS31 = CS16 CS18 + H = CS32 CS18 + H = CS33 CS18 + H = CS12 CS33 = CS32 CS12 = CS32 CS32 = CS13 CS32 = CS16 CS16 = CS34 CS34 = CS35 CS35 = CS14

41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

+ H2 + H2 + H2

+ H2 + H2

A2 + C3H3 = CS1 CS2 + C3H3 = CS3 CS1 = CS3 + H CS3 + H = CS4 CS4 = CS5 CS5 = CS6 + H CS3 + H = CS7 CS7 = CS8 CS8 = CS9 + H CS3 + H = CS10 + H2 CS3 + H = CS11 + H2 CS3 + H = CS12 + H2 CS11 = CS10 CS12 = CS10 CS10 = CS13 CS13 + H = CS9 CS13 = CS14 CS14 + H = CS9 CS9 + H = CS14 + H2 CS10 = CS15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

−20.2 25.4 −44.2 −48.1 3.9 50.8 21.5 8.3 −22.7 −31.0 6.7 −22.7 −19.8 29.5 26.5 −35.6 −63.1 40.2 1.5 −65.9

−1.4 −87.6 28.8 −38.6 −21.9 24.0 −34.4 −32.4 23.6 9.6 30.2 −25.3 −20.6 34.9 −44.0 −113.0 −50.8 −62.2 −42.0 −36.3 ΔHR (kcal ·mol−1)

ΔHR (kcal ·mol−1)

A (s−1 3.2 2.9 6.6 3.0 4.7 5.6 2.3 8.0 6.5 7.2 6.5 1.1 5.8 1.9 8.8 8.7 1.5 3.8 7.9 8.9

× × × × × × × × × × × × × × × × × × × × 10 1011 10−16 10−15 1011 1010 1011 10−16 10−17 1011 10−17 10−16 10−17 1011 1010 1011 1012 1012 1011 1012

11

2.4 × 10 5.8 × 10−23 8.5 × 1010 6.3 × 10−15 2.8 × 1011 2.0 × 1011 1.4 × 10−15 2.4 × 1011 2.0 × 1011 1.9 × 10−16 1.2 × 10−14 7.9 × 10−17 1.3 × 1011 4.0 × 1011 1.2 × 1012 6.9 × 10−11 2.3 × 1011 7.4 × 10−16 2.2 × 10−16 1.3 × 1012 or cm3·molec−1·s−1)

−23

A (s−1 or cm3·molec−1·s−1)

0.2 0.7 1.5 1.5 0.4 1.0 0.5 1.7 1.8 0.7 1.8 1.9 1.9 0.5 0.4 0.0 0.1 0.1 0.5 0.1

2.9 3.0 0.8 1.5 0.2 0.8 1.5 0.1 0.7 1.8 1.7 1.8 0.6 0.4 0.1 0.2 0.5 1.4 1.7 0.1 n

n

10.3 28.7 0.9 −0.6 34.4 50.9 43.1 5.9 −0.2 46.6 13.7 2.5 2.3 44.2 53.0 8.0 2.9 48.7 49.2 8.8

10.9 5.0 34.7 2.3 9.1 28.0 3.8 1.4 27.7 13.3 29.5 2.0 16.5 47.8 8.4 0.0 31.9 4.9 0.9 4.7 Ea (kcal·mol−1)

Ea (kcal·mol−1)

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 CS34 = CS36 CS36 = CS14 CS16 = CS13 CS6 + H = CS15 + H2 CS15 = CS37 CS37 = CS13 CS15 = CS38 CS38 = CS13 CS38 + H = CS9 CS6 + H = CS22 CS22 = CS39 CS39 = CS9 + H CS22 = CS40 CS40 = CS23 CS23 = CS9 + H CS14 + C3H3 = CS40 CS41 = CS42 + H CS41 + H = CS42 + H2 CS43 = CS44 CS43 = CS44

CS15 = CS16 CS16 + H = CS6 CS6 + HCS16 + H2 CS15 + H = CS6 A2 + C3H3 = CS17 CS17 = CS18 + H CS2 + C3H3 = CS18 CS18 + H = CS4 CS18 + H = CS19 CS19 = CS20 CS20 = CS9 + H CS18 + H = CS24 CS24 = CS19 CS19 = CS21 CS21 = CS23 CS21 = CS22 CS24 = CS25 CS25 = CS28 CS28 = CS22 CS28 = CS29 + CH3 19.4 −83.8 27.0 9.8 −41.5 −49.2 −7.1 0.6 −113.6 −29.3 −22.4 44.9 7.8 −15.6 30.4 −34.6 61.0 −43.2 12.7 −60.2

−34.7 −79.3 −24.9 −114.0 −7.0 −23.4 −93.2 −33.0 −58.0 −7.9 28.3 −38.9 −19.1 22.0 −32.0 −24.2 −2.9 −36.0 17.7 32.1 ΔHR (kcal·mol−1)

ΔHR (kcal·mol−1)

A (s−1

6.6 1.3 3.1 3.1 8.7 7.5 2.8 1.1 6.9 5.2 2.8 5.3 4.3 1.0 1.3 1.9 3.8 4.6 3.1 8.7

× × × × × × × × × × × × × × × × × × × ×

1012 1012 1012 1012 1011 1012 1012 1012 10−11 10−16 1011 1011 1011 1013 1011 10−23 1010 10−16 1011 1010

1.6 × 10 9.5 × 10−16 1.2 × 10−16 6.5 × 10−11 3.4 × 10−23 7.0 × 1010 6.4 × 10−12 5.0 × 10−16 1.1 × 10−15 3.5 × 1011 2.1 × 1011 2.0 × 10−15 2.1 × 1011 6.6 × 1011 2.5 × 1011 1.5 × 1012 6.1 × 1010 5.2 × 1011 1.7 × 1011 1.1 × 1013 or cm3·molec−1·s−1) 11


Table 2. Reaction Enthalpies and Rate Constants of Elementary Reactions in the Modified Arrhenius Equation Form k(T) = ATn exp(−Ea/RT)

0.2 0.1 0.2 1.8 0.3 0.0 0.2 0.5 0.2 1.4 0.3 0.9 0.1 0.1 0.8 2.9 1.2 1.7 0.0 0.7

0.6 1.5 1.8 0.2 2.9 0.8 0.2 1.5 1.5 0.1 0.8 1.5 0.5 0.4 0.1 0.1 0.5 0.1 0.6 0.6 n

n

26.9 2.4 73.7 9.9 42.6 4.1 51.9 51.8 0.0 3.4 49.7 44.8 13.2 6.4 32.0 18.5 58.3 2.2 33.9 62.2

48.4 9.6 −0.5 0.0 10.2 32.4 −2.8 2.5 1.8 17.0 31.0 0.7 41.8 41.8 0.3 2.9 4.5 4.8 42.4 37.3 Ea (kcal·mol−1)

Ea (kcal·mol−1)

The Journal of Physical Chemistry A Article


CS43 CS44 CS45 CS42 CS46 CS47 CS48 CS47 CS50 CS50 CS41 CS41 CS41 CS53 CS54 CS53 CS54 CS55 CS56 CS57

CS69 CS67 CS67 CS66 CS63 CS63 CS63 CS63 CS41 CS70 CS71 CS71 CS14 CS72 CS72 CS73 CS74 CS73 CS75 CS75

81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140

2880

= = + = = + = + + = = = + = + = + = = =

= = = = + + = + = = + + + = = = = = + +

A4 + H CS44 + H H = CS44 + H2 CS63 + H CS44 + H H = CS44 + H2 CS45 + H H = CS45 + H2 H = CS70 CS71 CS47 + H CS57 + H C3H3 = CS72 CS73 + H H = CS73 + H2 CS74 H = CS47 CS75 CS44 CS45

CS45 A4 + H A4 + H CS46 H = CS47 H = CS48 CS49 + H H = CS50 CS51 CS52 H = CS53 + H2 H = CS54 + H2 H = CS55 + H2 CS42 CS42 CS55 CS55 CS56 H = CS57 H = CS58

Table 2. continued

22.0 51.6 −52.6 21.6 56.5 −47.7 79.3 −24.9 −37.2 −20.3 27.0 22.4 −40.0 59.3 −44.9 −7.4 −77.1 15.0 −55.5 −32.6

2.1 2.4 4.8 1.2 2.5 4.8 1.8 6.4 6.0 3.5 1.1 1.0 2.3 2.8 5.5 2.9 6.6 3.5 2.4 3.7

× × × × × × × × × × × × × × × × × × × × 10 1010 10−16 1011 1010 10−16 1010 10−17 10−15 1011 1011 1011 10−23 1010 10−16 1011 10−16 1011 1011 1011

11

0.7 1.1 1.6 0.8 1.2 1.6 1.3 1.9 1.5 0.1 0.8 0.8 2.9 1.2 1.6 0.2 1.5 0.0 0.5 0.6

0.5 0.8 0.7 0.2 0.2 1.5 0.9 1.4 0.3 0.0 1.7 1.9 1.8 0.4 0.4 0.4 0.4 0.1 0.2 1.5 n

2.6 × 10 1.2 × 1011 1.9 × 1011 4.1 × 1011 6.5 × 10−11 1.4 × 10−15 1.1 × 1011 5.4 × 10−16 3.8 × 1011 1.8 × 1012 6.5 × 10−15 6.0 × 10−17 1.7 × 10−16 2.8 × 1011 2.1 × 1011 6.3 × 1010 6.2 × 1010 6.4 × 1011 6.5 × 10−11 1.2 × 10−15 or cm3·molec−1·s−1)

−37.4 34.9 12.0 20.9 −112.5 −38.1 34.0 −33.3 −8.8 −9.6 29.2 −18.1 8.9 −72.5 −25.1 −20.3 27.0 −35.1 −113.1 −46.7 ΔHR (kcal ·mol−1) A (s−1

n

11


ΔHR (kcal ·mol−1)

25.0 62.6 1.2 26.9 63.4 1.2 84.8 3.3 3.4 10.5 31.5 28.0 16.0 67.6 0.9 33.9 11.2 36.6 31.8 38.5

42.7 36.1 18.7 38.1 0.0 1.7 35.9 4.7 55.2 7.4 29.5 3.0 13.4 16.7 25.5 14.6 41.4 5.9 0.0 1.5 Ea (kcal·mol−1)

Ea (kcal·mol−1)

141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160

101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 CS72 CS72 CS72 CS76 CS76 CS77 CS77 CS78 CS78 CS79 CS72 CS80 CS72 CS81 CS82 CS82 CS49 CS83 CS84 CS83

CS58 CS57 CS60 CS61 CS60 CS62 CS55 CS64 CS64 CS41 CS65 CS66 CS67 CS67 CS67 CS52 CS67 CS51 CS68 CS68 + + + = = = = = = + + = + = = = + = = =

= + = = = = = = = + = = = + + = + = + + H = CS76 H = CS77 H = CS78 CS73 CS78 CS73 CS78 CS64 CS79 H = CS57 H = CS80 CS66 H = CS81 CS82 CS48 CS49 + H H = CS83 CS84 CS45 CS85

+ H2

+ H2 + H2 + H2

CS59 + H H = CS60 CS61 CS52 CS62 CS63 + H CS64 CS44 CS45 H = CS65 CS66 CS67 + H CS45 + H H = CS45 + H2 H = CS52 CS63 + H H = CS51 CS68 + H H = CS44 + H2 H = CS69 + H2 −12.8 −11.7 10.3 −32.1 23.1 −33.1 22.0 −35.4 −55.9 −36.2 −55.7 −3.6 −35.5 −17.5 −10.3 23.7 −23.0 22.4 −32.6 1.7

47.2 −24.0 6.2 −17.5 −25.0 44.2 −44.2 −55.5 −32.6 −31.6 −33.0 26.5 74.5 −29.7 −35.3 30.4 −34.4 21.1 −39.3 −26.4 ΔHR (kcal·mol−1)

ΔHR (kcal·mol−1)

A (s−1

1.9 1.9 1.8 0.5 0.5 0.6 0.4 0.1 0.2 0.2 1.4 0.0 1.5 0.2 0.6 0.8 1.8 0.1 0.6 0.2

× × × × × × × × × × × × × × × × × × × ×

10−17 10−17 10−16 1010 1009 1010 1010 1011 1011 10−10 10−15 1011 10−15 1013 1011 1011 10−17 1012 1011 1012 7.5 7.1 2.0 3.3 9.3 1.8 1.8 3.0 3.2 2.6 1.7 1.4 1.8 1.8 2.3 1.5 6.8 9.1 4.5 3.0

0.9 1.4 0.0 0.0 0.2 0.9 0.1 0.5 0.6 1.5 0.0 0.8 1.3 1.6 1.5 0.8 1.5 0.7 1.6 1.7 n

n

8.6 × 10 5.5 × 10−16 8.9 × 1011 1.0 × 1013 5.7 × 1011 9.4 × 1010 5.4 × 1011 2.4 × 1011 4.5 × 1011 9.9 × 10−16 3.1 × 1011 2.1 × 1011 9.7 × 1009 4.8 × 10−16 1.1 × 10−15 9.1 × 1010 9.0 × 10−16 7.6 × 1010 1.8 × 10−15 2.2 × 10−16 or cm3·molec−1·s−1) 10


3.5 3.7 13.0 28.2 40.8 56.1 47.1 9.7 6.6 −0.5 4.7 23.8 2.9 5.1 31.7 28.3 4.4 37.0 42.2 60.2

48.9 6.1 13.4 2.4 49.4 44.7 6.7 32.1 42.2 5.1 5.6 31.6 87.2 1.2 2.1 33.1 2.3 26.6 1.2 0.9 Ea (kcal·mol−1)

Ea (kcal·mol−1)

The Journal of Physical Chemistry A Article


Article

0.8 1.9 0.2 0.1 0.6 0.1 × × × × × ×

34.1 5.2 81.2 77.7 43.2 52.2

transition states could not be found using DFT. The rates of reactions 16 and 69 were estimated by analogy to that reported by Harding et al.46 for the C6H5 + H reaction; whereas the rate of C2H3 + H was used to asses those of reactions 24, 85, and 99.46 The aforementioned reactions all describe the addition of an H-radical to an sp2 hybridized primary or secondary alkyl radical site. The association reactions of H-radical with alkyl radicals are known to be barrierless. Harding et al.46 report the temperature-dependent rates of some H-atom association reactions with hydrocarbon radicals, determined using corrected CASPT2/cc-pvdz computational energy values and variable reaction coordinate transition state theory. Their results show that the high pressure limit of the H-phenyl and H−C2H3 association reactions are given by k = 6.92 × 10−11T0.15 and k = 6.45 × 10−11T0.2, respectively, in the temperature range 200−2000 K. The rates of H-addition to unsaturated bonds leading to the formation of tertiary alkyl radicals in reactions 86 and 100 have been estimated by analogy with the reverse rates of reactions 87 and 101, respectively. These estimates are very rough since the addition sites for these reactions are not the same; addition to primary carbon in 86 and 100 versus addition to secondary carbon in reverse 87 and 101 reactions. However, we were unable to identify rates that better fit these reactions in the literature. Finally, the rate of H-addition to the resonantly stabilized sp3 alkyl radical in 150 was estimated by analogy to that of the allylic radical in C3H5,48 whereas the rate of intramolecular C−C scission in 164 was estimated by analogy to 60. The transition states of reactions 46 and 106 could not be optimized with DFT. However, good transition states of these reactions were determined using HF. Single-point DFT energy calculations on the HF optimized structures were used to estimate the rates of reactions 46 and 106. The thermodynamic data of the species involved in the developed mechanism are listed in Table 3 in terms of ΔHf, ΔS, and Cp. The enthalpies of formation were calculated using isodesmic/isogyric reactions (section 2.2), whereas the entropies and heat capacities were calculated using the computational frequency values and partition functions. 3.3. Comparison. The rate of propargyl addition to naphthalene is compared to that of C3H3-addition to benzene (A1) in order to assess the influence of the nature of addition site (zigzag or free-edge) on the reaction kinetics. Kislov and Mebel32 previously studied the kinetics of C3H3-addition to benzene at the G3 level of theory, as it is an important source pathway in the eventual formation of indene. They noted that this reaction yields two different products, one for each resonance structure of the reactant C3H3. Similarly, our study considers both resonance structures, C3H3(1) and C3H3(2), in the assessment of C3H3 + A2 kinetics. The results reported by Kislov and Mebel show that both reactions of C3H3 + A1 have similar barriers, in the range of 15−18 kcal·mol−1. Meanwhile, the energy barriers of C3H3 + A2 vary within the range of 11− 12 kcal·mol−1, notably lower than those of C3H3 + A1. In order to discern the reason behind this discrepancy, the computational method used herein was employed in the rate parameter determination of the C3H3 + A1 reactions. The use of the B3LYP/6-311++G(d,p) level of theory yields energy barriers of 13 to 14 kcal·mol−1, thus reducing the difference in the Ea values of C3H3 + A1 and C3H3 + A2 from approximately 30% to 15%. The 15% difference is probably due to the chemical nature of the addition sites (free-edge for A1 and zigzag for

88.5 88.4 48.8 8.8 28.1 32.5 29.2 0.4 0.3 0.5 0.1 0.8 0.6 0.5 10 1012 1011 1012 1011 1011 1012

× × × × × × × 6.2 1.1 8.3 8.9 1.4 2.0 4.6 41.6 41.4 0.3 −53.6 23.8 −6.5 22.1 CS86 CS90 CS86 CS45 CS59 + H CS91 CS92 + CH3 = = = = = = = CS85 CS85 CS90 CS86 CS82 CS82 CS91 161 162 163 164 165 166 167

n A (s−1 or cm3·molec−1·s−1) ΔHR (kcal ·mol−1)

Table 2. continued

11

Ea (kcal·mol−1)

168 169 170 171 172 173

CS91 CS59 CS87 CS88 CS89 CS87

= + = = = =

CS59 + H H = CS87 + H2 CS88 CS89 CS45 CS90

30.3 −16.5 0.8 19.8 −17.6 36.5

1.2 4.7 5.4 4.3 2.4 3.8

11

10 10−17 1012 1012 1011 1012

n ΔHR (kcal·mol−1)


Ea (kcal·mol−1)


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Table 3. Thermodynamic Properties of Chemical Species Involved in the Mechanism species

ΔHf (298 K)

ΔS (298 K)

CP100

CP200

CP300

CP400

CP600

CP800

CP1000

CP1200

CP1500

CP2000

CP2500

CP3000

H C3H3 CH3 A2 A4 CS1 CS2 CS3 CS4 CS5 CS6 CS7 CS8 CS9 CS10 CS11 CS12 CS13 CS14 CS15 CS16 CS17 CS18 CS19 CS20 CS21 CS22 CS23 CS24 CS25 CS26 CS27 CS28 CS29 CS30 CS31 CS32 CS33 CS34 CS35 CS36 CS37 CS38 CS39 CS40 CS41 CS42 CS43 CS44 CS45 CS46 CS47 CS48 CS49 CS50 CS51 CS52 CS53 CS54 CS55 CS56

52.1 84.1 35.1 38.7 58.5 121.3 101.5 98.0 111.5 89.6 61.5 115.7 83.3 54.8 159.7 180.3 124.7 115.7 64.9 123.4 88.7 115.8 92.4 86.5 78.6 108.5 84.3 76.5 105.6 102.7 85.4 58.8 66.7 60.9 62.8 119.2 151.3 121.8 128.9 130.3 148.2 164.9 116.3 62.0 92.1 114.4 123.3 136.0 75.7 98.6 144.2 83.8 97.8 79.7 102.7 93.9 93.1 195.7 148.4 175.4 140.3

26.0 60.9 48.7 82.9 99.0 103.6 82.8 101.1 103.7 96.1 94.8 102.9 95.5 93.8 102.7 101.9 100.3 93.7 91.3 94.8 93.4 104.8 101.9 100.9 94.4 104.2 99.6 96.6 104.1 103.6 97.0 95.7 96.3 87.4 98.3 95.9 101.1 101.4 91.6 91.6 95.5 93.8 94.0 94.3 93.2 110.9 109.8 102.9 102.1 101.4 103.7 103.6 107.7 104.5 108.2 105.7 105.9 111.5 113.3 111.5 103.2

5.0 8.7 8.0 11.4 15.1 18.1 11.4 17.2 18.4 15.2 14.8 18.0 14.9 14.3 17.5 17.9 16.7 14.4 13.3 14.8 14.2 18.2 17.2 17.4 14.6 18.4 16.8 15.6 19.1 18.8 16.0 15.6 15.6 12.2 16.7 15.9 17.5 17.4 13.6 13.5 15.3 14.4 14.5 14.6 14.0 19.7 19.2 16.7 16.4 16.0 17.1 17.0 19.3 17.8 19.0 18.0 18.1 20.5 19.9 19.9 17.0

5.0 12.0 8.7 20.4 30.6 31.7 20.5 30.4 31.4 28.6 27.5 31.0 28.0 26.8 30.5 30.2 30.4 26.8 25.9 27.7 27.3 31.6 30.3 30.7 27.8 31.0 30.0 28.7 32.0 31.8 29.5 28.4 29.0 23.3 29.7 28.4 30.5 31.1 25.9 26.0 27.9 28.0 26.9 27.8 27.4 36.2 35.9 32.6 32.2 32.1 33.4 33.2 35.6 34.1 35.8 34.6 34.6 36.2 36.8 36.3 33.3

5.0 15.1 9.4 32.3 48.9 47.5 31.9 45.5 46.7 44.8 43.0 46.5 44.0 42.1 45.2 44.2 45.5 41.7 41.2 42.9 42.7 47.2 45.3 46.4 43.8 46.2 45.7 44.3 46.8 46.6 45.2 43.3 44.8 37.2 45.0 42.7 45.0 45.6 41.3 41.7 43.0 43.6 41.8 43.6 43.9 55.0 54.4 51.2 50.9 51.1 52.3 52.3 54.4 52.7 55.1 53.8 53.8 54.0 55.3 54.6 52.1

5.0 17.4 10.2 43.7 65.9 62.0 42.6 59.5 61.1 59.9 57.5 61.2 59.2 56.6 58.5 57.5 58.9 55.6 55.5 56.8 56.9 61.9 59.3 61.1 59.0 60.7 60.5 59.2 61.0 60.9 60.1 57.5 59.7 50.2 59.7 56.2 58.4 58.8 55.7 56.2 57.0 57.7 55.7 58.8 59.4 72.3 71.2 68.5 68.3 68.7 69.6 70.2 72.4 70.3 73.2 72.1 72.0 70.7 72.0 71.2 69.4

5.0 20.6 11.6 60.7 91.0 83.5 58.5 80.1 82.8 82.5 79.1 83.0 82.0 78.5 78.0 77.4 78.4 76.4 76.5 77.2 77.4 83.5 80.0 83.0 81.8 82.6 82.6 81.8 82.6 82.6 82.4 78.9 82.2 69.2 82.0 76.5 78.0 78.2 76.8 77.2 77.6 78.0 76.4 81.6 82.3 97.9 95.9 94.3 94.2 94.6 95.1 96.9 99.8 96.9 100.4 99.7 99.7 95.6 96.4 95.8 94.9

5.0 22.9 13.0 71.5 106.9 97.4 68.6 93.4 97.0 96.9 92.9 97.1 96.6 92.6 90.5 90.3 90.7 89.6 89.7 90.2 90.3 97.4 93.5 97.1 96.5 96.8 96.9 96.5 96.9 96.8 96.9 92.8 96.7 81.3 96.6 89.7 90.6 90.6 90.0 90.3 90.6 90.8 89.7 96.3 96.9 114.5 111.6 110.8 110.7 111.0 111.3 114.0 117.7 114.0 118.0 117.6 117.6 111.5 111.9 111.5 111.2

5.0 24.6 14.2 78.9 117.5 106.9 75.4 102.5 106.8 106.8 102.4 106.8 106.6 102.1 99.0 99.0 99.2 98.6 98.6 98.9 99.0 107.0 102.6 106.8 106.5 106.6 106.7 106.5 106.7 106.6 106.7 102.3 106.6 89.4 106.5 98.6 99.2 99.1 98.8 99.0 99.3 99.4 98.6 106.3 106.7 125.7 122.2 121.8 121.8 122.0 122.2 125.6 129.8 125.6 129.9 129.7 129.7 122.3 122.4 122.2 122.1

5.0 26.0 15.2 84.2 124.9 113.7 80.2 109.1 113.7 113.8 109.1 113.7 113.7 108.9 105.1 105.1 105.2 104.9 104.8 105.1 105.1 113.9 109.2 113.7 113.6 113.6 113.7 113.6 113.7 113.6 113.8 109.0 113.6 95.0 113.6 104.8 105.2 105.2 105.0 105.2 105.5 105.5 104.9 113.5 113.7 133.8 129.7 129.6 129.6 129.7 129.8 133.8 138.4 133.8 138.4 138.3 138.3 129.9 129.9 129.7 129.7

5.0 27.5 16.3 89.6 132.4 120.8 85.0 115.8 120.9 120.9 115.9 120.8 120.8 115.8 111.3 111.4 111.3 111.2 111.2 111.3 111.3 120.9 115.9 120.8 120.8 120.8 120.8 120.8 120.8 120.8 120.9 115.8 120.8 100.8 120.8 111.2 111.4 111.4 111.3 111.4 111.6 111.6 111.2 120.7 120.8 142.0 137.4 137.4 137.4 137.5 137.6 142.1 147.1 142.1 147.0 147.0 147.0 137.6 137.5 137.4 137.5

5.0 29.0 17.6 94.7 139.4 127.6 89.7 122.3 127.7 127.8 122.4 127.7 127.7 122.3 117.3 117.3 117.3 117.3 117.2 117.3 117.3 127.7 122.4 127.6 127.7 127.7 127.7 127.7 127.7 127.7 127.8 122.4 127.7 106.2 127.7 117.2 117.4 117.3 117.3 117.4 117.5 117.5 117.3 127.7 127.7 149.9 144.8 144.9 144.8 144.9 144.9 150.0 155.4 150.0 155.3 155.3 155.3 144.9 144.8 144.8 144.9

5.0 29.9 18.3 97.5 143.2 131.4 92.2 125.8 131.4 131.5 125.9 131.4 131.4 125.9 120.5 120.5 120.5 120.5 120.5 120.5 120.5 131.4 125.9 131.4 131.4 131.4 131.4 131.4 131.4 131.4 131.5 125.9 131.4 109.2 131.4 120.5 120.6 120.5 120.5 120.6 120.7 120.6 120.5 131.4 131.4 154.1 148.7 148.8 148.8 148.8 148.9 154.2 159.8 154.2 159.7 159.8 159.8 148.9 148.8 148.8 148.8

5.0 30.4 18.7 99.2 145.5 133.6 93.7 127.9 133.6 133.6 127.9 133.6 133.6 127.9 122.4 122.4 122.4 122.4 122.4 122.4 122.4 133.6 127.9 133.6 133.6 133.6 133.6 133.6 133.6 133.6 133.6 127.9 133.6 110.9 133.6 122.4 122.4 122.4 122.4 122.4 122.5 122.5 122.4 133.6 133.6 156.6 151.1 151.2 151.1 151.2 151.2 156.7 162.4 156.7 162.3 162.4 162.4 151.2 151.1 151.1 151.2

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Table 3. continued species

ΔHf (298 K)

ΔS (298 K)

CP100

CP200

CP300

CP400

CP600

CP800

CP1000

CP1200

CP1500

CP2000

CP2500

CP3000

CS57 CS58 CS59 CS60 CS61 CS62 CS63 CS64 CS65 CS66 CS67 CS68 CS69 CS70 CS71 CS72 CS73 CS74 CS75 CS76 CS77 CS78 CS79 CS80 CS81 CS82 CS83 CS84 CS85 CS86 CS87 CS88 CS89 CS90 CS91 CS92

79.3 84.7 79.8 104.3 110.5 79.3 71.4 131.2 134.9 101.8 76.2 63.0 88.6 129.3 109.0 109.0 116.2 108.8 131.2 148.3 149.3 171.4 115.4 105.4 125.6 108.1 108.8 131.2 110.6 152.2 115.4 116.2 136.0 152.0 101.6 88.6

103.2 107.2 104.4 107.3 102.2 103.5 101.9 101.8 113.7 104.3 103.0 102.1 101.9 113.7 106.3 112.2 109.8 102.5 101.8 116.5 113.2 112.4 102.7 113.5 106.2 106.2 102.5 101.8 102.5 100.9 102.7 102.7 102.9 100.6 106.4 96.4

17.0 18.9 17.8 18.9 16.2 16.9 16.3 16.3 20.7 17.1 16.6 16.5 16.3 21.0 17.7 19.9 19.3 16.6 16.3 21.4 19.9 20.0 16.6 20.1 18.3 18.3 16.6 16.3 16.6 15.9 16.6 16.6 16.7 15.9 18.3 14.5

33.1 35.3 34.1 35.6 33.0 33.5 32.3 32.4 36.8 33.5 32.6 32.6 32.5 37.2 34.2 36.1 35.8 33.0 32.4 37.6 36.8 36.1 33.3 36.5 35.1 35.1 33.0 32.4 33.0 31.9 33.3 33.3 32.6 31.5 35.3 29.0

52.2 54.2 52.8 54.9 53.1 52.9 51.3 50.9 56.0 53.0 51.5 51.5 51.4 56.1 53.9 54.8 54.2 52.1 50.9 55.4 55.3 54.3 52.5 55.9 54.4 54.4 52.1 50.9 52.1 51.2 52.5 52.5 51.2 50.4 54.6 46.6

70.1 72.3 70.4 73.2 72.0 71.4 69.3 68.3 74.0 71.6 69.5 69.3 68.8 73.9 72.5 72.1 71.0 69.6 68.3 71.8 72.0 71.1 70.0 74.0 72.7 72.7 69.6 68.3 69.6 69.0 70.0 70.0 68.5 68.3 72.8 63.1

96.8 99.7 96.9 100.4 100.0 99.3 96.3 94.2 100.9 99.5 96.4 96.2 94.6 100.7 100.1 97.9 95.8 95.2 94.2 96.1 96.4 95.8 95.5 100.9 100.1 100.1 95.2 94.2 95.2 95.0 95.5 95.5 94.3 94.5 100.2 87.2

113.9 117.6 114.0 118.0 117.8 117.3 113.6 110.7 118.2 117.5 113.7 113.5 111.0 118.1 117.9 114.6 111.6 111.4 110.7 111.7 111.9 111.6 111.5 118.2 117.9 117.9 111.4 110.7 111.4 111.4 111.5 111.5 110.8 111.0 117.9 102.5

125.5 129.7 125.6 129.9 129.8 129.5 125.3 121.8 130.0 129.7 125.4 125.3 122.0 130.0 129.9 125.9 122.3 122.2 121.8 122.3 122.4 122.3 122.3 130.0 129.9 129.9 122.2 121.8 122.2 122.2 122.3 122.3 121.8 122.0 129.9 112.7

133.7 138.3 133.8 138.4 138.3 138.1 133.6 129.6 138.5 138.3 133.7 133.5 129.7 138.4 138.4 133.9 129.8 129.8 129.6 129.8 129.9 129.9 129.9 138.4 138.4 138.4 129.8 129.6 129.8 129.9 129.9 129.9 129.6 129.7 138.4 119.8

142.0 147.0 142.1 147.0 147.0 146.9 142.0 137.4 147.1 147.0 142.0 141.9 137.5 147.0 147.1 142.1 137.5 137.5 137.4 137.5 137.5 137.5 137.6 146.9 147.1 147.1 137.5 137.4 137.5 137.6 137.6 137.6 137.4 137.5 147.1 127.0

149.9 155.3 150.0 155.3 155.3 155.2 149.9 144.8 155.3 155.3 149.9 149.9 144.9 155.3 155.3 150.0 144.9 144.9 144.8 144.9 144.8 144.9 144.9 155.2 155.4 155.4 144.9 144.8 144.9 144.9 144.9 144.9 144.9 144.9 155.3 133.9

154.2 159.7 154.2 159.7 159.7 159.7 154.2 148.8 159.7 159.7 154.2 154.2 148.9 159.7 159.8 154.2 148.8 148.8 148.8 148.8 148.8 148.8 148.9 159.7 159.8 159.8 148.8 148.8 148.8 148.9 148.9 148.9 148.8 148.8 159.8 137.5

156.7 162.4 156.7 162.3 162.3 162.3 156.7 151.1 162.3 162.4 156.7 156.7 151.2 162.3 162.4 156.7 151.1 151.2 151.1 151.1 151.1 151.2 151.2 162.3 162.4 162.4 151.2 151.1 151.2 151.2 151.2 151.2 151.2 151.2 162.4 139.7

A2). Figure18 compares the temperature-dependent rate constants of the propargyl addition reactions to A1 and A2,

for both resonance structures, calculated at the same level of theory. At temperatures higher than 450 K, the difference in the rate constant values of A1 and A2 (Figure 18) is less than 1 order of magnitude, with higher values for the addition at the zigzag site of A2. Both, A1 and A2 exhibit faster addition to C3H3(2), the resonance structure comprising two double bonds. On the basis of a recent study published by Kislov et al.,22 the energy barrier of acetylene addition to the naphthyl radical, computed at the G3 level of theory, is 2.6 kcal·mol−1. This value lies between the energy barrier values of the addition of the two resonance structures of propargyl to the naphthyl radical (zero and 5 kcal·mol−1). This means that propargyl addition reactions are highly competitive with acetylene reactions, especially under conditions where the concentration of the propargyl radical is high. Therefore, reactions initiated by propargyl addition to naphthalene and the naphthyl radical have to be included in PAH mechanisms for them to be sufficiently valid.

4. CONCLUSIONS Recent studies have shown that PAH growth mechanisms currently available in the literature are incapable of reproducing

Figure 18. Comparison of the rates of C3H3-addition to A1 and A2, calculated at the B3LYP/6-311++G(d,p) level of theory. 2883



Article

experimental results under particular conditions.15−22 Therefore, further development of the available mechanisms is needed to improve their predictive capabilities, particularly when it comes to the chemistry of resonantly stabilized radicals such as propargyl and cyclopentadienyl radicals. The propargyl radical is especially important since it is known to play a crucial role in the inception of the first aromatic ring25 and has been shown to promote PAH growth reactions.6,28−30 In this study, we investigate the kinetics of the PAH growth mechanism initiated by propargyl addition to naphthalene and the naphthyl radical using DFT computations coupled to TST. The mechanism has been developed up to the formation of pyrene. The results show that although propargyl addition to A2 is not particularly fast, with energy barriers of 10 to 11 kcal· mol−1, the addition to the naphthyl radical is much quicker (Ea = 0−5 kcal·mol−1). This means that, depending on the concentrations of the C3H3 radicals in combustion environments, propargyl addition pathways of PAH growth may be competitive with other pathways, such as those implicated by the HACA mechanism. Therefore, the chemistry of propargyl addition to PAHs needs to be accounted for in order to enhance the efficiency and predictive capability of PAH growth mechanisms. The results reported herein may also be used to estimate the reactivity of C3H3-addition to zigzag sites in PAHs larger than A2. Further kinetic and mechanistic studies are needed to evaluate the contribution of propargyl addition onto armchair and bay sites to the overall PAH growth rate. Future work will focus on the reduction and validation of the developed mechanism under a wide range of conditions.

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(5) Appel, J.; Bockhorn, H.; Frenklach, M. Kinetic Modeling of Soot Formation with Detailed Chemistry and Physics: Laminar Premixed Flames of C2 and Hydrocarbons. Combust. Flame 2000, 121, 122−136. (6) D’Anna, A.; Violi, A.; D’Alessio, A.; Sarofim, A. F. A Reaction Pathway for Nanoparticle Formation in Rich Premixed Flames. Combust. Flame 2001, 127, 1995−2003. (7) Violi, A. Modeling of Soot Particle Inception in Aromatic and Aliphatic Premixed Flames. Combust. Flame 2004, 139, 279−287. (8) Violi, A.; Sarofim, A. F.; Voth, G. A. Kinetic Monte CarloMolecular Dynamis Approach to Model Soot Inception. Combust. Sci. Technol. 2004, 176, 991−1005. (9) Cole, J. A.; Bittner, J. D.; Longwell, J. P.; Howard, J. B. Formation Mechanisms of Aromatic Compounds in Aliphatic Flames. Combust. Flame 1984, 56, 51−70. (10) Frenklach, M. On the Driving Force of PAH Production. Symp. Combust. 1988, 22, 1075−1082. (11) Frenklach, M.; Clary, D. W.; Gardiner, W. C.; Stein, S. E. Detailed Kinetic Modeling of Soot Formation in Shock-Tube Pyrolysis of Acetylene. Symp. Combust. 1984, 887−901. (12) Richter, H.; Benish, T. G.; Mazyar, O. A.; Green, W. H.; Howard, J. B. Formation of Polycyclic Aromatic Hydrocarbons and Their Radicals in a Nearly Sooting Premixed Benzene Flame. Proc. Combust. Inst. 2000, 28, 2609−2618. (13) Vlasov, P. A.; Warnatz, J. Detailed Kinetic Modeling of Soot Formation in Hydrocarbon Pyrolysis Behind Shock Waves. Proc. Combust. Inst. 2002, 29, 2335−2341. (14) Wang, H.; Frenklach, M. A Detailed Kinetic Modeling Study of Aromatics Formation in Laminar Premixed Acetylene and Ethylene Flames. Combust. Flame 1997, 110, 173−221. (15) Violi, A.; D’Anna, A.; D’Alessio, A. Modeling of Particulate Formation in Combustion and Pyrolysis. Chem. Eng. Sci. 1999, 54, 3433−3442. (16) D’Anna, A.; Violi, A. A Kinetic Model for the Formation of Aromatic Hydrocarbons in Premixed Laminar Flames. Symp. Combust. 1998, 425−433. (17) Lee, S. Y.; Yoon, S. S.; Chung, S. H. Synergistic Effect on Soot Formation in Counterflow Dissusion Flames of Ethylene−Propane Mixtures with Benzene Addition. Combust. Flame 2004, 136, 493−500. (18) Wang, Y.; Raj, A.; Chung, S. H. A PAH Growth Mechanism and Synergistic Effect on PAH Formation in Counterflow Diffusion Flames. Combust. Flame 2013, 160, 1667−1676. (19) Yoon, S. S.; Ahn, D. H.; Chung, S. H. Synergistic Effect of Mixing Dimethylether with Methane, Ethane, Propane, and Ethylene Fuels on Polycyclic Aromatic Hydrocarbon and Soot Formation. Combust. Flame 2008, 154, 368−377. (20) Yoon, S. S.; Lee, S. Y.; Chung, S. H. Effect of Mixing Methane, Ethane, Propane, and Propene on the Synergistic Effect of Pah and Soot Formation in Ethylene-Base Counterflow Diffusion Flames. Proc. Combust. Inst. 2005, 30, 1417−1424. (21) Hwang, J. Y.; Lee, W.; Kang, H. G.; Chung, S. H. Synergistic Effect of Ethylene-Propane Mixture on Soot Formation in Laminar Diffusion Flames. Combust. Flame 1998, 114, 370−380. (22) Kislov, V. V.; Sadovnikov, A. I.; Mebel, A. M. Formation Mechanism of Polycyclic Aromatic Hydrocarbons Beyond the Second Aromatic Ring. J. Phys. Chem. A 2013, 117, 4794−4816. (23) Alkemade, U.; Homann, K. H. Formation of C6H6 Isomers by Recombination of Propynyl in the System Sodium Vapour/Propynyl Halide. Z. Phys. Chem. 1989, 161, 19−34. (24) Stein, S. E.; Walker, J. A.; Suryan, M. M.; Fahr, A. A New Path to Benzene in Flames. Proc. Combust. Inst. 1990, 23, 85−90. (25) Miller, J. A.; Melius, C. F. Kinetic and Thermodynamic Issues in the Formation of Aromatic Compounds in Flames of Aliphatic Fuels. Combust. Flame 1992, 91, 21−39. (26) D’Anna, A.; A’Alessio, A.; Kent, J. A Computational Study of Hydrocarbon Growth and the Formation of Aromatics in Coflowing Laminar Diffusion Flames of Ethylene. Combust. Flame 2001, 125, 1196−1206. (27) D’Anna, A.; Kent, J. Aromatic Formation Pathways in NonPremixed Methane Flames. Combust. Flame 2003, 132, 715−722.

ASSOCIATED CONTENT

S Supporting Information *

Thermodynamic data of the chemical species in NASA polynomial format and the detailed mechanism in Chemkin format are supplied. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*(M.J.A.R.) Tel: 966544700179. E-mail: mariam.elrachidi@ kaust.edu.sa. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS KAUST CCRC is grateful to Saudi Aramco for sponsoring this research.

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REFERENCES

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