Article pubs.acs.org/JPCA
Role of Carbon-Addition and Hydrogen-Migration Reactions in Soot Surface Growth Hong-Bo Zhang,†,‡ Dingyu Hou,†,‡ Chung K. Law,†,§ and Xiaoqing You*,†,‡ †
Center for Combustion Energy, Tsinghua University, Beijing 100084, China Key Laboratory for Thermal Science and Power Engineering of the Ministry of Education, Tsinghua University, Beijing 100084, China § Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, United States ‡
S Supporting Information *
ABSTRACT: Using density functional theory and master equation modeling, we have studied the kinetics of small unsaturated aliphatic molecules reacting with polycyclic aromatic hydrocarbon (PAH) molecules having a diradical character. We have found that these reactions follow the mechanism of carbon addition and hydrogen migration (CAHM) on both spin-triplet and open-shell singlet potential energy surfaces at a rate that is about ten times those of the hydrogenabstraction-carbon-addition (HACA) reactions at 1500 K in the fuel-rich postflame region. The results also show that the most active reaction sites are in the center of the zigzag edges of the PAHs. Furthermore, the reaction products are more likely to form straight rather than branched aliphatic side chains in the case of reacting with diacetylene. The computed rate constants are also found to be independent of pressure at conditions of interest in soot formation, and the activation barriers of the CAHM reactions are linearly correlated with the diradical characters.
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INTRODUCTION Substantial understanding has been gained in the soot formation mechanism in the past several decades.1 It is widely accepted that the soot mass growth rate is essentially determined by the process of soot surface growth,2−4 which is controlled by the surface hydrogen-abstraction-carbonaddition (HACA) mechanism,5,6 in which hydrogen abstraction takes place first to form an aryl radical site, and is followed by acetylene addition to accomplish mass growth. Hence, the surface HACA mechanism requires that the hydrogen atoms are sufficiently abundant to form active sites. It is also believed that soot mass growth is not likely to occur at temperatures below 1500 K in the postflame region because of the correspondingly low concentration of hydrogen atoms.1 However, recent experiments, including morphological observations, chemical composition analysis, soot particle size statistics, and soot volume observations,7−13 have all shown that in a laminar premixed ethylene-oxygen−argon flame (equivalence ratio φ = 2.5) at 1450 K, the soot volume fraction increases with the height above the burner and the nascent soot is wax-like and rich in aliphatics with unity C/H ratio.1,10 These experimental observations indicate that the formation of nascent soot in the premixed flames has the structure consisting of an aromatic core with an aliphatic shell. Mechanistically, the aromatic core is first formed in the hightemperature region of the premixed flame, followed by the formation of the aliphatic shell over the aromatic core when temperature decreases.1 Furthermore, Raman spectroscopic © XXXX American Chemical Society
experiments show that the composition of the aliphatic groups in the nascent soot is alkyl or alkenyl functionalities.10 In addition to these premixed flame observations, similar phenomena, being rich in aliphatics and having the liquid-like appearance of nascent soot, are generally observed in other flames, for example in the central region of coflow diffusion flames.14−18 None of this experimental evidence can be explained by the surface HACA mechanism that requires enough H atoms to initiate the reaction sequence, implying that a new mechanism of soot mass growth without hydrogen atoms needs to be formulated. To identify a viable mechanism, let us consider the following. When a gas-phase unsaturated aliphatic molecule is attached to the soot particle surface, a carbon−carbon bond is formed to generate an adduct. Since no free radical is involved, both the π bonds originating from the gas-phase unsaturated aliphatic molecule and the soot particle surface should be broken in the process of forming the linkage. Hence, it is natural to generate two unpaired electrons (diradical) in the adduct of the gasphase aliphatic molecule and the soot particle. Meanwhile, due to delocalized π electrons, some polycyclic aromatic hydrocarbons (PAHs) have diradical properties, which can be described by the radical character y0 having twice the weight of a doubly excited configuration in the multiconfiguration selfReceived: October 21, 2015 Revised: January 16, 2016
A
DOI: 10.1021/acs.jpca.5b10306 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A consistent field theory, ranging from 0 to 1. From the above definition, PAHs are closed-shell if y0 = 0, and they are pure diradicals if y0 = 1.19 It can be easily concluded that both the spin-triplet and the open-shell spin-singlet PAH molecules with a large diradical character should be involved. Consequently, Zhang et al.20 recently proposed a new soot surface growth pathway, namely the spin-triplet carbon-addition-hydrogenmigration (CAHM) pathway. As shown schematically in Figure 1, the reaction path begins with the addition of an unsaturated aliphatic (i.e., acetylene) to
functional and the Lee−Yang−Parr correlation functional (B3LYP) with the 6-311+G(d,p) basis set.22,23 The density functional method used in this study has been validated in Zhang et al.20 by comparing their results with those at the CBSQB3 level. The zero-point energy and vibrational frequencies were scaled by a factor of 0.968.24 The connection of each saddle point to its local minima was confirmed by using the intrinsic reaction path analysis. All the quantum chemistry calculations were carried out using the Gaussian 09 program.25 In addition, all degrees of freedom were approximated as rigid-rotor harmonic-oscillator (RRHO) in obtaining the equilibrium constants, the canonical and the microcanonical rate constants. High-pressure-limit rate constants were obtained from canonical transition state theory (CTST), and the microcanonical rate constants were obtained from RiceRamsperger-Kassel-Marcus theory (RRKM). One-dimensional tunnelling corrections based on asymmetric Eckart potentials were included. The equilibrium constants and high-pressurelimit rate constants were calculated using the Thermo program in Multiwell package suite.26 The pressure-dependent reaction rate constants were calculated by solving the master equations using MESMER27 and fitting the species profiles with a phenomenological model for temperatures ranging from 1000 to 2000 K and pressures from 0.1 to 10 atm. The collisional energy transfer probability was approximated by an exponential-down model with an average downward energy transfer ⟨ΔEdown⟩ = 260 cm−1, the same as in Zhang et al.20 The Lennard-Jones parameters for the relevant molecules were estimated from an empirical correlation,28 taking σ = 3.47 Å and ε = 114 K for the bath gas collider, argon.
Figure 1. Reaction path of the spin-triplet CAHM reactions.
a triplet PAH, followed by hydrogen migration to form a product with an aliphatic side chain. As can be seen, the acetylene molecule loses one unsaturated C−C bond and adds to the soot surface as a vinyl group. Consequently, the soot mass increases without hydrogen atoms, and this CAHM pathway could be used to explain the observed aromatic-corealiphatic-shell structure of nascent soot at low temperatures. Detailed studies have shown that the surface mass growth rate is an order of magnitude larger than that of HACA at low temperatures in the postflame region. Furthermore, the fact that the unsaturated aliphatic loses one unsaturated C−C bond in CAHM also explains the experimental Raman spectroscopic observation that the aliphatic groups in the nascent soot are alkyl or alkenyl functionalities.11 Zhang et al.20 studied the CAHM on the spin-triplet potential energy surface (PES) and suggested that no spinsinglet CAHM was found. However, large PAH molecules mostly exist in the open-shell singlet ground state.21 Consequently, identification of the CAHM with open-shell singlet PAHs compels a re-examination of the PESs and the associated reaction rate constants and the reactivity of different PAH reaction sites in the open-shell singlet CAHM. In addition, we need to discuss other aspects, including the possibility of subsequent CAHM, the results of different unsaturated aliphatics, and the characteristics of the aliphatic side chains of the products. Finally the open-shell singlet CAHM and the triplet CAHM will be compared with HACA, leading to further understanding of the CAHM soot surface growth mechanism.
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RESULTS AND DISCUSSION Potential energy surface of CAHM. Figure 2 shows the spin-triplet and open-shell spin-singlet PESs of pentacene
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THEORETICAL METHODS Similar to the previous study of Zhang et al.,20 the hypothesis of chemical similarity6 between the reactions taking place on the surface of a soot particle and those of large PAHs is invoked to define both the physical nature of the reaction sites and the electronic structures of the local soot particle surface. Considering the relatively large diradical character20 and the relative small molecular size to reduce computational cost, we have selected pentacene as a prototype of large PAHs to approximate the soot particle surface. Moreover, the optimized molecular structures, the single-point energies and the vibrational frequencies for all stationary points on the relevant PESs of both spin-singlet and triplet CAHM were obtained via density functional theory employing the Becke three-parameter
Figure 2. Spin-triplet and open-shell spin-singlet PESs of pentacene reacting with C2H2.
reacting with C2H2. The triplet surface is plotted in dashed lines and the open-shell singlet surface in solid lines. Clearly, there seems to be no obvious crossing between the singlet and triplet PESs. Both PESs begin with acetylene addition to singlet pentacene (Rsin) and triplet pentacene (Rtri) to form adducts IM1 and IM3, respectively, followed by cis−trans transition to form IM2 and IM4, and finally H atom migration reactions to generate the products singlet and triplet vinyl pentacene (Psin and Ptri) separately. The transition state connecting Rsin+C2H2 and IM2, and that between Rtri+C2H2 and IM4 have not been found. In addition, intrinsic reaction path analysis of the B
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most by a factor of 3 from its high-pressure-limit value at 2000 K and only about 0.8% at 1500 K. Similar to the triplet CAHM reaction, IM1 and IM2 satisfy the quasi-steady state approximation and do not accumulate. Consequently, the rate constants can be assumed to be at the high-pressure limit and analyzed by the canonical transition state theory (CTST), and the overall forward reaction rate constant is determined by the forward reaction rate constant of IM2-TS3-Psin and the equilibrium constant of Rsin+C2H2 → IM2. For comparison, the three-parameter fittings of the forward and backward reaction rate constants of the open-shell singlet CAHM as well as the triplet CAHM at different pressures are listed in Table 1. It is seen that, at 1500 K and 1 atm, the rate constants of the open-shell singlet and triplet CAHM are 5.5 × 104 and 1.2 × 106 cm3/mol/s, respectively. Thus, the reaction rate constant of the triplet CAHM is 21.8 times of that of the open-shell singlet CAHM. Our thermodynamic analysis shows that the equilibrium concentration ratio of vinyl pentacene (Psin) to pentacene (Rsin) is 10−4 at 1500 K, 1 atm with 2% mole fraction of acetylene. Although the equilibrium ratio is low, the master equation analysis indicates the reaction system will reach its equilibrium in 10 ms, which is longer than the typical time scale of nascent soot formation. Therefore, the open-shell singlet CAHM will not reach its equilibrium throughout the process of soot formation. Growth site. In addition to the path of acetylene reacting with the center site of pentacene in the open-shell singlet CAHM, paths involving other growth sites are also studied and mapped in Figure 4.
hydrogen migration channel shows that TS3 indeed connects the products with IM2, rather than IM1, so is the triplet path. All the geometric configurations of the conformers on the open-shell singlet PES are similar to their triplet counterparts, and are given in the Supporting Information. The geometric configurations of IM1 and singlet vinyl pentacene Psin are also plotted in Figure 2, which shows that the energies of IM1, IM2, and TS2 are similar to those of IM3, IM4, and TS5, respectively. However, the energies of singlet pentacene Rsin and singlet vinyl pentacene Psin, together with transition states TS1 and TS3, are different from those of triplet pentacene Rtri, triplet vinyl pentacene Ptri, TS4, and TS6, respectively. In particular, the forward energy barrier of IM2-TS3-Psin is 5.2 kcal/mol smaller than that of IM4-TS6-Ptri, leading to a larger forward reaction rate constant kf of IM2 → Psin than that of IM4 → Ptri; and the reaction enthalpy at 0 K of Rsin+C2H2 → IM2 is 16.1 kcal/mol larger than that of Rtri+C2H2 → IM4, which contributes to a much smaller equilibrium constant Kc for Rsin+C2H2 → IM2. Their impact on the overall reaction rate constants will be given in the following section. Reaction rate constants. Based on the molecular properties from quantum chemistry calculations, the reaction rate constants of the open-shell singlet pentacene reacting with C2H2 were computed from master equation analysis and the results are presented in Figure 3. It shows that in the pressure
Figure 3. Reaction rate constants of open-shell singlet pentacene reacting with C2H2.. Figure 4. PESs of open-shell singlet pentacene reacting with acetylene at different growth sites in the open-shell singlet CAHM.
and temperature ranges of interest to combustion and soot formation, the pressure dependence of the rate constants of the open-shell singlet CAHM reaction is very weak, differing at
Table 1. Computed Rate Constants of Reaction between Pentacene and C2H2, Fitting into a Three-Parameter Form A × Tne−Ea/T for Temperatures Ranging from 1000 to 2000 K Pentacene + C2H2 → Vinyl Pentacene forward rate constant (cc/mol/s) A
pressure (atm) Triplet
Open-shell Singlet
0.1 1.0 10.0 ∞ 0.1 1.0 10.0 ∞
5.09 1.39 1.66 8.16 3.36 4.96 1.27 6.18
× 1036 × 1024 × 108 × 1034 × 1013 × 103
n
backward rate constant (1/s) A
Ea (K)
−7.19 −3.56 0.97 3.05 −6.40 −0.48 2.52 3.18 C
2.72 2.34 1.80 1.55 3.28 2.57 2.21 2.13
× × × × × × × ×
104 104 104 104 104 104 104 104
2.47 9.25 2.11 2.65 2.24 3.79 3.66 4.29
× × × × × × × ×
n 1046 1033 1018 1011 1044 1023 1013 1011
−9.48 −5.89 −1.44 0.53 −8.75 −2.84 −0.00 0.56
Ea (K) 4.47 4.09 3.57 3.34 4.98 4.28 3.93 3.87
× × × × × × × ×
104 104 104 104 104 104 104 104
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of bisanthrene is lower than that in the case of pentacene by 1.7 cal/mol/K. However, the dependence of the rate coefficient on the diradical character of PAHs is very weak such that the rate coefficients are basically of the same order. Subsequent CAHM. The PESs of the reactions between open-shell singlet vinyl pentacene and C2H2 in the subsequent CAHM are shown in Figure 5. The vinyl pentacene produced from pentacene reacting with C2H2 may further react with another C2H2 on the active site of the vinyl group to form butadiene pentacene.
It is noted that there are two significant differences among the PESs of the different growth sites. One is the lower enthalpy of reaction at 0 K for growth sites farther from the center, which results in a larger overall equilibrium constant. The other is the higher forward and lower backward energy barriers of R1-TS1-IM1 for growth sites farther from the center, which results in a smaller equilibrium constant between R1 and IM1. Therefore, the overall reaction rate coefficient is lower for the growth sites farther from the center. Indeed, master equation analysis shows that the rate constant for site B in Figure 4 is slightly smaller than that for site A, being 2.8 × 104 versus 5.5 × 104 cm3/mol/s. And the rate constant for site C, being 3.4 × 103 cm3/mol/s at 1500 K and 1 atm, is much smaller than those for sites A and B, all due to the differences in the energy barrier heights for different growth sites. Consequently, it can be concluded that the growth at the center site or the sites next to it are the most reactive, which is the same with the triplet CAHM.20 Diradical character effect. Having demonstrated that the most reactive reaction site is located in the center of a PAH edge, we next study the PESs of the reactions between acetylene and four different PAHs, namely pentacene, hexacene, heptacene, and bisanthrene, at the center growth sites in the open-shell singlet CAHM. These PESs are shown in the Supporting Information, in Figure S1. It is seen that each PES in Figure S1 is similar to the PES in Figure 2, initiated with acetylene addition and followed by tran-cis transition and hydrogen migration. Furthermore, the energy barriers in each PES are also similar to the other PESs. Consequently as in the case of pentacene, the rate-limiting reaction is the hydrogen migration reaction IM2-TS3-Psin in the cases of hexacene, heptacene, and bisanthrene. The energy barrier of hydrogen migration TS3 on each PES, together with the diradical character of their reactant PAH molecules, are listed in Table 2.
Figure 5. PESs of open-shell singlet vinyl pentacene reacting with acetylene.
The pressure dependence of its reaction rate constants is also very weak in the temperature and pressure ranges interested, and the rate constant at 1500 K is 2.6 × 104 cm3/mol/s, which is comparable to the first CAHM in Figure 2. However, the reaction rate in producing butadiene pentacene is much smaller than that of producing vinyl pentacene, since the concentration of vinyl pentacene is much smaller than that of pentacene, as shown in section 3.2. Therefore, further addition of acetylene on the product of the first addition is not likely to take place, and the aliphatic side chains will not grow into long chains. Other aliphatics. Regarding the difficulty to grow into long side chains via subsequent adding C2H2, other unsaturated aliphatic molecules reacting with the open-shell singlet PAH have also been studied to explain the experimental observation of aliphatic shell with side chain longer than two carbon atoms. In principle, an open-shell singlet PAH can react with any unsaturated aliphatic molecule such as ethylene (C2H4), diacetylene (C4H2), 1,3,5-hexatriyne (C6H2) and so on. Considering that diacetylene (C4H2) is relatively abundant in fuel-rich flames,29 we selected C4H2 as the unsaturated aliphatic molecule to study. As shown in Figure 6, there are two nonequivalent carbon atoms, C1 and C2 in C4H2 due to its symmetry. Either carbon atom can be a reactive site, and the PESs of reactions between pentacene and C4H2 at sites C1 and C2 are displayed in Figure 6. Product P2 from reaction at site C1 has a straight side chain, while product P4 from reaction at site C2 has a branched one. The energy barrier of adding C4H2 at site C2, being 48.8 kcal/ mol (TS8), is much higher than that at site C1, being 40.8 kcal/ mol (TS3), thus we can conclude that site C1 is much more reactive than site C2, and that in the case of diacetylene addition the formed aliphatic side chains should be straight instead of branched chains. Consequently, the PES of the reaction at site C1 is studied in more details. As shown in Figure 6, C4H2 first reacts with open-shell singlet pentacene to
Table 2. Potential Energy of TS3 Relative to the Reactants and the Diradical Characters of Various PAHs y0a ΔE(TS3) (kcal/mol) a
pentacene
bisanthrene
hexacene
heptacene
0.42 46.0
0.51 44.8
0.56 43.4
0.70 41.8
Taken from ref 19.
Obviously, the potential energy of TS3 relative to the reactants ΔE(TS3) in each reaction decreases as the diradical character y0 of PAH increases. Further fitting shows a linear relation as eq 1. ΔE(TS3) = 52.4 − 15.3y0
(1)
Hence, the PAH is more reactive with a larger diradical character, resulting a lower energy barrier. On the other hand, the entropy change of TS3 relative to the reactants varies nonmonotonically with the diradical character, therefore the reaction rate constants do not vary monotonically with the diradical character due to the direct contribution from the entropy. In fact, the detailed master equation analysis shows that at 1 atm and 1500 K, the reaction rate constants of acetylene reacting with pentacene, bisanthrene, hexacene and heptacene are 5.5 × 104, 3.7 × 104, 1.1 × 105, and 1.8 × 105 cm3/mol/s, respectively. Despite the fact that the diradical character of bisanthrene is larger than that of pentacene, suggesting a lower barrier height of TS3, the reaction rate constant of bisanthrene is smaller than that of pentacene. This is because the entropy of TS3 relative to its reactants in the case D
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equilibrium between singlet and triplet pentacene is assumed.20 Consequently, the overall reaction rate of the open-shell singlet CAHM is of the same order as that of the triplet CAHM path. In fact this characteristic can be generalized to other PAHs examined in this study, which can be demonstrated as follows. The reaction rates ω of the open-shell singlet and triplet CAHM paths are given by eqs 2 and (3), respectively, ωsin = ksin[PAH ]sin [C2H2]
(2)
ωtri = ktri[PAH ]tri [C2H2]
(3)
where ksin and ktri are the reaction rate constants of open-shell singlet and triplet CAHM paths respectively, and [PAH] represents the concentration of PAH. Due to the weak pressure dependence, the rate constants may be computed using the canonical transition state theory. And because the intermediate species on the PES in Figure 2 are in quasi-steady state, ksin and ktri may be derived as ksin = Kc , sin(R sin + C2H2 → IM 2) ⎛ GTS3 − G R sin+ C2H2 ⎞ k f , sin(IM 2 → Psi n) ∝ exp⎜ − ⎟ RT ⎝ ⎠
(4)
ktri = Kc , tri(R tri + C2H2 → IM 4) ⎛ GTS6 − G R tri + C2H2 ⎞ k f , tri(IM 4 → Psi n) ∝ exp⎜ − ⎟ RT ⎠ ⎝
(5)
where G is the Gibbs free energy, R is the universal gas constant, and T is the temperature. Assuming the singlet and triplet PAHs are in thermal equilibrium,20 the concentration ratio of the singlet to triplet PAHs is
Figure 6. PESs of open-shell singlet pentacene reacting with diacetylene on C1 site (top) and C2 site (bottom).
form IM1, followed by hydrogen migration to form P1, P3 (dashed lines) and P2 (solid lines). Since the hydrogen atom on the pentacene group can be transferred to carbon atoms C2, C1′ or C2′ in the C4H2 group in IM1 via a 4-, 6- or 5membered ring transition state, respectively, the corresponding hydrogen migration products are P2, P1 or P3. However, product P3 has two unpaired electrons on carbon atom C1′, which leads to a much larger potential energy of P3 compared to that of P2. Moreover, in the 6-membered ring structure of TS2, atoms C1′, C2′ and C2 are linked to the adjacent carbon atoms by double bonds. Consequently, three double bonds stand in a row in the 6-membered ring and their bond angles deviate from 180 deg by a large mount to enclose the ring, resulting in a high energy barrier of producing P1 (TS2), being 12 kcal/mol larger than that of producing P2 (TS3). Consequently, the reaction path of producing P2 is favored and the rate constant at 1500 K and 1 atm of producing P2 is 3.9 × 105 cm3/mol/s, which is eight times higher than that of the case of C2H2. However, similar to the case of acetylene addition, the equilibrium concentration of butadiene pentacene is much smaller than that of pentacene at combustion temperatures due to the larger Gibbs free energy increase. Therefore, the side chain is also not likely to grow longer with repetitive CAHM pathways for C4H2. Comparison of open-shell singlet CAHM, triplet CAHM, and HACA. As shown in section 3.2, at 1500 K and 1 atm, the reaction rate constant of the triplet CAHM path is 21.8 times of that of the open-shell singlet CAHM path in the case of pentacene. The concentration of singlet pentacene, however, is about 12.4 times of triplet pentacene if the thermal
[PAH ]sin 1 ⎛ G R − G R tri ⎞ = exp⎜ − sin ⎟ [PAH ]tri 3 ⎝ RT ⎠
(6)
where the pre-exponential factor 1/3 is due to the electronic degeneracy. From eqs 2−6, we may derive the reaction rate ratio of the singlet and triplet CAHM paths as eq 7, ωsin k [PAH ]sin 1 ⎛ G − GTS6 ⎞ ⎟ = sin = exp⎜ − TS3 ⎠ ωtri ktri[PAH ]tri 3 ⎝ RT 1 ⎛ H − HTS6 ⎞ ⎛ STS3 − STS6 ⎞ ⎟exp⎜ ⎟ = exp⎜ − TS3 ⎠ ⎝ ⎠ 3 ⎝ RT R
(7)
Both entropy and enthalpy differences between TS3 and TS6 contribute to the reaction rate ratio of the singlet and triplet CAHM paths (Table 3), which is about 0.27−0.56 at 1500 K, indicating both the singlet and triplet CAHM paths should be considered. In order to compare the product formation rates of HACA and CAHM mechanisms, we took heptacene as an example of the soot surface and built a kinetic model including both HACA Table 3. Comparison of Open-Shell Singlet with Triplet CAHMs at 1500 K STS3 − STS6 (cal/mol/K) HTS3 − HTS6(kcal/mol) ωsin/ωsin E
pentacene
bisanthrene
hexacene
heptacene
−2.77 −5.68 0.56
−2.65 −3.63 0.30
−2.46 −3.93 0.36
−2.28 −2.8 0.27
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a
Rate constants at 1500 K, 1 atm
HACA
S−H + H ↔ S + H2
Singlet CAHM
S + H → S−H S + C2H2 → S−C2H + H S−H(sin) + C2H2 ↔ S−C2H3(sin)
Triplet CAHM
S−H(tri) + C2H2 ↔ S−C2H3(tri)
kf: 1.17 × 1012 cc/mol/s30 kb: 7.03 × 1013 cc/mol/s1,30 1.00 × 1014 cc/mol/s30 1.33 × 1011 cc/mol/s31 kf: 1.80 × 105 cc/mol/sa kb: 4.83 × 102 /sa kf: 5.30 × 105 cc/mol/s20 kb: 1.50 × 103 /s20
This work.
CAHM, it is unlikely to take place so that the aliphatic side chains will not grow into long chains. Furthermore, the side chains in the aliphatic shell are straight chains rather than branched chains in the case of adding diacetylene C4H2. The reaction rate constants are not pressure-dependent at the temperature and pressure ranges interested in soot formation, and the activation barriers of the CAHM reactions are linearly correlated with the diradical characters. The effect of CAHM on soot surface growth has been studied in detail by using the hypothesis of chemical similarity between the soot particle and large PAHs. A large diradical character of PAH is the key feature in the CAHM pathway. Therefore, in terms of PAH chemistry, for PAHs with a large diradical character, CAHM reactions will be the additional reaction paths, while for PAHs with a small diradical character, CAHM reactions will not take place and as such will not modify the existing PAH chemistry mechanism. In the simulation of soot formation, the results of the CAHM surface growth pathway can be implemented without difficulty into the widely used models, for example, the method-ofmoments models or the sectional models. Specifically, in the method-of-moments models, the mass growth rate per unit area ks33 should be modified by adding a term to include the CAHM pathway at low temperatures. And in the sectional-method models the surface growth rate of each soot section RG,i34 will need to include a new term to present the CAHM pathway. The new term should be proportional to the soot surface area of the section, the concentration of typical unsaturated aliphatics such as acetylene, the forward reaction rate constant of the CAHM reaction, and a term representing the available surface sites for the CAHM reactions and the effect of other surface chemistry. Detailed investigation along these directions merits further study. Furthermore, after the alkenylation or alkylation via the CAHM pathway, these nascent soots will become mature soot by the subsequent carbonization. Obviously, the processes of carbonization of the alkenyl/alkyl PAH in soot formation also call for further study.
and CAHM reactions (as listed in Table 4). The initial mole fraction of heptacene was set to be 10−6, and those of the gasphase species H2, H, and C2H2 were set to be 0.1, 10−6, and 0.02, respectively, based on the simulation results of a laminar premixed ethylene-oxygen−argon flame with equivalence ratio 2.5 from Ö ktem et al.10 The predicted product profiles of the HACA and CAHM reactions at constant temperature 1500 K and pressure 1 atm are shown in Figure 7. The product
Figure 7. Product profiles of HACA and CAHM reactions at 1500 K and 1 atm.
concentrations of both the singlet and the triplet CAHMs are larger than that of the HACA. At 1 ms, the product concentration ratio of singlet CAHM to HACA is about 3.9, and that of triplet CAHM to HACA is about 5.8. Consequently, the ratio of the overall CAHM to HACA is 9.7. Note that this is a simplified kinetic model, and a better comparison would require kinetic Monte Carlo simulations with a detailed surface growth reaction model.32 Detailed investigation along this direction is in progress and will be reported later.
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SUMMARY The present study on the CAHM reaction paths with openshell singlet PAHs has shown that the open-shell singlet CAHM satisfactorily explains the aromatic-core-aliphatic-shell structure of the nascent soot, the increase of soot volume, and the chemical composition of aliphatics in the postflame region of premixed flames or in the central region of coflow diffusion flames at temperatures below 1500 K, which are aspects of the soot formation processes that cannot be explained by the surface HACA mechanism. These findings complement those from past studies on the triplet CAHM, particularly demonstrating that the most active reaction sites are in the center of the zigzag edge of each PAH. As to the subsequent
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b10306. All the data in this work, including the geometry configurations, the frequencies and rotational constants of the molecules on relevant PESs, and the additional PESs presenting diradical character effects (PDF) F
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (91541122), and Tsinghua National Laboratory for Information Science and Technology.
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REFERENCES
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DOI: 10.1021/acs.jpca.5b10306 J. Phys. Chem. A XXXX, XXX, XXX−XXX
