Role of Spin-Triplet Polycyclic Aromatic Hydrocarbons in Soot Surface

Jan 15, 2015 - Department of Mechanical and Aerospace Engineering, Princeton University, Olden Street, Princeton, New Jersey 08544,. United States...
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Role of Spin-Triplet Polycyclic Aromatic Hydrocarbons in Soot Surface Growth Hong-Bo Zhang,†,‡ Xiaoqing You,*,†,‡ and Chung K. Law†,§ †

Center for Combustion Energy, Tsinghua University, Meng Minwei Science Technology Building, Zhishan Road, Beijing 100084, China Key Laboratory for Thermal Science and Power Engineering of the Ministry of Education, Tsinghua University, Mechanical Engineering Building, Tsinghua Road, Beijing 100084, China § Department of Mechanical and Aerospace Engineering, Princeton University, Olden Street, Princeton, New Jersey 08544, United States ‡

S Supporting Information *

ABSTRACT: Using density functional theory, a possible pathway of soot surface growth is studied in the low-temperature, postflame region in which spin-triplet polycyclic aromatic hydrocarbon (PAH) molecules with a small singlet−triplet energy gap react with unsaturated aliphatics such as acetylene via the carbon-addition-hydrogen-migration (CAHM) reaction. Results show that a PAH-core-aliphatic-shell structure is formed and the mass growth rate of this triplet soot surface growth reaction is one order of magnitude larger than that of the surface hydrogen-abstraction-carbon-addition (HACA) reaction at temperatures below 1500 K.

T

with unity C/H ratio.1,10 This result indicates that the nascent soot formed in laminar premixed flames has an aromatic-corealiphatic-shell structure, in which the aromatic core is first formed in the early stages of the flame when the temperature is high, followed by the formation of the aliphatic shell over the aromatic core when the gas temperature becomes lower.1 Furthermore, Raman spectroscopic evidence suggests that the aliphatic groups in the nascent soot are alkyl or alkenyl functionalities.11 All of this experimental evidence cannot be explained by the surface HACA mechanism. Consequently, as a supplementary mechanism to surface HACA, a new mechanism of soot mass growth without hydrogen atoms1 needs to be identified to explain the aromatic-core-aliphatic-shell structure and the increase in the soot volume fraction. In this regard we note that many recent studies in theoretical material science, nonlinear optics, and soot formation have shown that due to localized π electrons some spin-singlet PAHs have diradical properties,1,14 which can be described by the radical character y0, defined as twice the weight of a doubly excited configuration in multiconfiguration self-consistent field theory,15 ranging from 0 to 1. From the above definition, PAHs are closed-shell if y0 = 0 and are pure diradicals if y0 = 1.15 As y0 increases, PAHs behave more like diradicals and hence are more reactive. With y0 = 0, the triplet−singlet energy gap of

he formation of condensed-phase carbon materials from reacting gases is of interest to a wide range of scientific, technological, and societal problems.1 In the past several decades, substantial understanding has been gained on the mechanism of soot formation, showing that starting from gasphase molecules with the size of a few angstroms, polycyclic aromatic hydrocarbon (PAH) molecules are first formed, followed by nucleation, coagulation, surface growth and oxidization, and finally aggregation into mature soot with the size of a few microns.1 Among the above steps, surface growth is the key step in controlling the soot mass growth rate2−4 and is usually described by the surface hydrogen-abstraction-carbonaddition (HACA) mechanism at the molecular level,5,6 in which hydrogen atoms should be sufficiently abundant because it requires H-abstraction to form an aryl radical site, followed by acetylene addition. Consequently, soot mass growth is not likely to occur at temperatures below 1500 K in the postflame region based on the surface HACA mechanism because of the low concentration of hydrogen atoms.1 However, recent experiments, including observations using transmission electron microscopy (TEM), atomic force microscopy (AFM), helium-ion microscopy (HIM), mobility sizing, photoionization aerosol mass spectrometry (PIAMS), small angle neutron scattering (SANS), thermocouple particle densitometry (TPD), and Fourier transform infrared spectroscopy (FTIR),7−13 unexpectedly showed that in an ethylene− oxygen−argon laminar premixed flame (φ = 2.5) at 1450 K, soot volume fraction increases without gas-phase hydrogen atoms and the nascent soot is liquid-like and rich of aliphatics © 2015 American Chemical Society

Received: December 13, 2014 Accepted: January 15, 2015 Published: January 15, 2015 477

DOI: 10.1021/jz502635t J. Phys. Chem. Lett. 2015, 6, 477−481

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The Journal of Physical Chemistry Letters

Figure 1. Dependence of triplet-singlet energy gap and mole fraction ratio on the radical character y0 for large PAHs at the level of B3LYP/ 6-311+g(d,p). Assuming the triplet PAH is in thermal equilibrium with its singlet, the mole fraction ratio of the triplet and the singlet PAH xtri/xsin is related to the energy gap between the triplet and the singlet PAH through the equation xtri/xsin = gtri/gsin exp(−(Etri − Esin)/kBT), where g is the spin multiplicity, kB is the Boltzmann constant, and T is the temperature. The radical characters are taken from Nagai et al.15

oscillator (RRHO) approximation except for the torsional degrees of freedom, which were treated as hindered rotors with torsional potentials obtained by relaxed scan of the corresponding dihedral angles. The equilibrium constants were obtained by MESMER,20 and the reaction rate coefficients were obtained by solving the master equations using MESMER20 and fitting the species profiles with a phenomenological model for temperatures ranging from 1000 to 2000 K and pressures from 10−3 to 103 atm. The collisional energy transfer probability was approximated by an exponential-down model with an average downward energy transfer ⟨ΔEdown⟩ = 260 cm−1. Other values of the average downward energy transfer, such as ⟨ΔEdown⟩ = 500 cm−1, were also examined, with the identical rate coefficients obtained in the temperature and pressure ranges studied herein. The Lennard-Jones parameters for the relevant molecules and radicals were estimated from an empirical correlation,21 and σ = 3.47 Å and ϵ = 114 K for the bath gas collider, argon. Onedimensional tunneling corrections based on asymmetric Eckart potentials were included for reactions involving the transfer of H atoms. To demonstrate the triplet reaction pathway in which the triplet PAH reacts with an unsaturated aliphatic molecule, we show a scheme of the reaction path in Scheme 1. The reaction path is constituted by a series of repetitive steps. Each step begins with carbon (i.e., acetylene in Scheme 1) addition to a triplet PAH, followed by hydrogen migration. After each step, an acetylene molecule is added to the soot surface as a vinyl group, leading to a longer side chain. As an example we chose acetylene as the unsaturated aliphatic molecules for its large concentration in the postflame region and heptacene as the PAH for its large y0, respectively. The PES of the reaction between triplet heptacene and acetylene together with all of the geometry configurations of the local minima on this PES are presented in Figure 2, in which R2, IM1, IM2, IM3, and P1 lie on the triplet PES while R1 and P2 lie on the singlet one. IM1 and IM3 are cis and trans conformers, respectively. All structures, frequencies, and rotational constants of the molecules in Figure 2 are reported in the Supporting Information. Because the singlet heptacene is 4.4 kcal/mol lower in energy than the triplet heptacene and the singlet product is also 4 kcal/mol

benzene is quite large, being 84 kcal/mol at the B3LYP/ 6-311+g(d,p) level. However, as shown in Figure 1, for those PAHs with larger y0, the energy gap becomes smaller and decreases with y0 linearly. If the triplet and singlet PAHs are assumed to be in thermal equilibrium, the mole fraction ratio of triplet to singlet decreases with the triplet-singlet energy gap exponentially and thus increases with y0 exponentially. Therefore, the concentration of spin-triplet PAHs cannot be neglected for those PAHs with large y0. However, in conventional studies of soot surface growth, only spin-singlet PAHs are considered and the non-negligible spin-triplet PAHs with large y0 have not been sufficiently studied. In light of these considerations, we have studied the reaction mechanism involving spin-triplet PAHs in soot surface growth and will show in due course that this new mechanism could explain the experimental observations of the core−shell structure and hence the increase in soot volume fraction without hydrogen atoms. Assuming that chemical reactions taking place on the surface of a soot particle are similar to those of large PAHs,6 we selected four rectangular PAHs, namely, pentacene, hexacene, heptacene, and bisanthrene, as prototypical large PAHs in this study. The optimized molecular structures, single-point energies, and vibrational frequencies for all stationary points on the relevant potential energy surfaces (PESs) of both the spinsinglet and triplet PAHs were obtained via density functional theory employing the Becke three-parameter functional and the Lee−Yang−Parr correlation functional (B3LYP) with the 6-311+G(d,p) basis set.16,17 Zero-point energy (ZPE) and vibrational frequencies were scaled by a factor of 0.968.18 The connections of each saddle point to its local minima were confirmed by using the intrinsic reaction path analysis. All of the ab initio calculations were carried out using the Gaussian 09 program.19 To validate the density functional method used, a much smaller system, that is, the reaction between triplet benzene and singlet acetylene, has been studied both at the level of CBS-QB3 and B3LYP/6-311+g(d,p) (see Supporting Information); the differences in energy barriers computed by the two methods are ∼2 kcal/mol. Therefore, the density functional method is expected to be adequate. Furthermore, the microcanonical rate coefficients were obtained from RRKM theory employing the rigid-rotor harmonic478

DOI: 10.1021/jz502635t J. Phys. Chem. Lett. 2015, 6, 477−481

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The Journal of Physical Chemistry Letters Scheme 1. Reaction Path of Carbon Addition and Hydrogen Migration (CAHM) Reactionsa

a

The path is constituted by a series of repetitive steps. Only the first two of the successive steps are shown in this scheme.

Figure 2. PES of the reaction between triplet heptacene and acetylene.

lower than the triplet product, it is necessary to assess if the singlet pathway affects the reaction and if it has the lower barrier. Our results show that no stationary points can be found for IM1, IM2, and IM3 on the singlet surface, and single-point energy calculations of singlet R2, TS1, IM1, IM2, and IM3 with the optimized triplet structures show that the single-point energy of singlet R2 is 2 kcal/mol lower than that of triplet R2, while singlet TS1 lies 2 kcal/mol above triplet TS1 and the single-point energy of IM1 is 26 kcal/mol larger than that of triplet IM1; thus the crossing between singlet and triplet PESs takes place somewhere before the nonrecrossed configuration TS1. Therefore, this crossing is merely the conversion between R1 and R2 nonadiabatically, being one way of attaining thermal equilibrium between R1 and R2, and does not affect the triplet reaction pathway. As shown in Figure 2, assuming the triplet and singlet heptacene molecules are in thermal equilibrium, the PES of the reaction pathway begins with the singlet acetylene addition to the triplet heptacene molecule to form IM1, followed by H-atom migration reactions to form IM2 and IM3, and finally leading to the triplet product vinyl heptacene. These processes constitute the first CAHM step. Subsequently, the system would go through the second CAHM step repeatedly, in which the vinyl heptacene molecule produced will further react with acetylene, followed by hydrogen migrations. Obviously, the pathway shown in the dashed line is energetically unfavorable and the dominant path is the one shown in the solid line. Hence, we neglect the dashed-line path in the following analysis.

Among all reaction steps on the triplet PES the key step is R2-TS1-IM1 because there is no counterpart on the relevant singlet PES for both close-shell and open-shell calculations, while the rate-limiting step is IM3-TS5-P1 due to the high reaction barrier and the decrease in entropy. Furthermore, it is interesting to note that one unsaturated C−C bond in acetylene disappears after the reaction, which may explain the Raman spectroscopic result that the aliphatic groups in the nascent soot are alkyl or alkenyl functionalities.11 We further noted that the backward reaction barrier of IM3-TS5-P1 in Figure 2 is 40 kcal/mol larger than that of the forward reaction and suspected that the backward reaction might be negligible. To test our hypothesis, we solved the master equations by treating IM3-TS5-P1 as both reversible and irreversible. The two treatments indeed gave identical reaction rate coefficients in the temperature and pressure range studied. Using the solution of the master equations, we found IM1 and IM3 are quasi-steady and in partial equilibrium with each other due to the shallow barrier. From the species profiles of R2, the rate coefficients were computed for temperatures ranging from 1000 to 2000 K and pressures ranging from 10−3 to 103 atm. No pressure dependence was found for the rate coefficient in these temperature and pressure ranges. The logarithm of the rate coefficient and the inverse of temperature are in a strong linear relationship and can be expressed as 4

k = 60.1 × T 2.82 e−1.71 × 10 / T cm 3/mol/s 479

DOI: 10.1021/jz502635t J. Phys. Chem. Lett. 2015, 6, 477−481

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Figure 3. PESs of triplet heptacene reacting with acetylene at different growth sites.

At 1500 K, the forward and backward rate coefficients are 6.1 × 105 cm3/mol/s and 1.5 × 103/s, respectively. As a result, P1 reacting with 2% mole fraction of acetylene will reach its half equilibrium value around 1 ms, implying that the forward reaction rate is much larger than the reverse rate on the typical time scale of the soot formation process. Compared with the first CAHM, the second CAHM has a similar PES, as shown in Figure S1 in the Supporting Information. At 1500 K and 1 atm, the rate coefficient of the second CAHM is 2.6 × 105 cm3/mol/s, which is comparable to that of the first CAHM. Besides the path of acetylene reacting with the center growth site of the heptacene, we also studied the paths involving other growth sites, as shown in Figure 3. There are two significant differences among the PESs of the different growth sites. One is the lower enthalpy of the products 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 step 1 for growth sites farther from the center, which results in a smaller equilibrium constant for step 1. Considering that the energy barrier of step 2 and the forward energy barrier of step 3 are independent of the growth sites and the backward reaction rate coefficient of step 3 is negligible, the overall reaction rate coefficient is lower for the growth sites farther from the center. Indeed, master equation analysis shows that the rate coefficient for the red-line path in Figure 3 is 7.0 × 104 cm3/mol/s and that for the blue-line path is 2.9 × 103 cm3/mol/s, both of which are much smaller than the rate for the black-line path, 6.1 × 105 cm3/mol/s at 1500 K and 1 atm due to the large difference of energy barrier heights among different growth sites. Therefore, the growth at the center site is the most active. Recognizing this point, the PESs of the reactions between acetylene and four different PAHs at the center growth site are also studied. A master equation analysis shows that at 1500 K and 1 atm the rate coefficients of pentacene, hexacene, heptacene, and bisanthrene reacting with acetylene are 1.2 × 106, 6.9 × 105, 6.1 × 105, and 5.3 × 105 cm3/mol/s, respectively. Therefore, the dependence of the rate coefficient on the size and shape of PAHs is very weak such that the rate coefficients are basically on the same order.

Table 1. Mechanism and Carbon-Atom Addition Rate of the Surface HACA and the Triplet Reaction Mechanism, Where the Unit of ω is (mol C-atom/cm3 s) surface HACA

1

triplet reaction mechanism (CAHM)

Si − H + H· ↔ Si + H2 Si· + H· → Si − H Si· + C2H2 → Si+2 − H + H· 1 ωH = 2k 3Keq

[H] [Si − H][C2H 2] [H 2]

Si − Htri + C2H2 → Si − C2H3

ωT = 2k[Si − H]tri[C2H2]

In Table 1, the surface HACA and the triplet reaction mechanisms and the associated carbon-atom addition rates are listed, with the ratio of the carbon-atom addition rate given by ωT k [H 2] [Si − H]tri = 1 ωH [H] [Si − H] k 3Keq

where K1eq and k3 are, respectively, the equilibrium constant of (1) and reaction rate coefficient of (3) in the surface HACA reaction and k is the rate coefficient of the triplet reaction. As an estimate, taking the typical value of K1eq ≈ 1/60 from Wang,1 k3 ≈ 1010 to 1011 cm3/mol/s from Wang22 and You et al.,23 [Si − H]tri/[Si − H] ≈ 10−1 for large PAHs such as hexacene and heptacene from Figure 1, and [H2]/[H] ≈ 10−1/ 10−6 = 105 in the postflame region from a simulation of the laminar premixed ethylene−oxygen−argon flame with equivalence ratio ϕ = 2.5 and with the temperature profile taken from Ö ktem et al.10 using the Premix code24 and the reaction mechanism USC-Mech II in ref 25, we have ωT k ≈ 4 ωH 10 ∼ 105

where k is in the unit of cm3/mol/s. As previously discussed, k is on the order 105 ∼ 106 cm3/mol/s. If we conservatively take k as the rate coefficient of the reaction between heptacene and acetylene, 6.1 × 105 cm3/mol/s, then the rate of the triplet reaction is roughly one order larger than that of the surface HACA. This is because although the rate coefficient of the triplet reaction is small compared with that of the surface HACA, the triplet reaction mechanism is free of H atoms such 480

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(9) Cain, J. P.; Camacho, J.; Phares, D. J.; Wang, H.; Laskin, A. Evidence of Aliphatics in Nascent Soot Particles in Premixed Ethylene Flames. Proc. Combust. Inst. 2011, 33, 533−540. (10) Ö ktem, B.; Tolocka, M. P.; Zhao, B.; Wang, H.; Johnston, M. V. Chemical Species Associated with the Early Stage of Soot Growth in a Laminar Premixed Ethylene−Oxygen−Argon Flame. Combust. Flame 2005, 142, 364−373. (11) Santamaría, A.; Mondragón, F.; Molina, A.; Marsh, N. D.; Eddings, E. G.; Sarofim, A. F. FT-IR and 1H NMR Characterization of the Products of an Ethylene Inverse Diffusion Flame. Combust. Flame 2006, 146, 52−62. (12) Wang, H.; Zhao, B.; Wyslouzil, B.; Streletzky, K. Small-Angle Neutron Scattering of Soot Formed in Laminar Premixed Ethylene Flames. Proc. Combust. Inst. 2002, 29, 2749−2757. (13) Zhao, B.; Uchikawa, K.; Wang, H. A Comparative Study of Nanoparticles in Premixed Flames by Scanning Mobility Particle Sizer, Small Angle Neutron Scattering, and Transmission Electron Microscopy. Proc. Combust. Inst. 2007, 31, 851−860. (14) Zhang, H. B.; You, X.; Wang, H.; Law, C. K. Dimerization of Polycyclic Aromatic Hydrocarbons in Soot Nucleation. J. Phys. Chem. A 2014, 118, 1287−1292. (15) Nagai, H.; Nakano, M.; Yoneda, K.; Kishi, R.; Takahashi, H.; Shimizu, A.; Kubo, T.; Kamada, K.; Ohta, K.; Botek, E.; et al. Signature of Multiradical Character in Second Hyperpolarizabilities of Rectangular Graphene Nanoflakes. Chem. Phys. Lett. 2010, 489, 212−218. (16) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (17) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. SelfConsistent Molecular-Orbital methods. XX. Basis Set for Correlated Wave Functions. J. Chem. Phys. 1980, 72, 650−654. (18) Andersson, M. P.; Uvdal, P. New Scale Factors for Harmonic Vibrational Frequencies Using the B3LYP Density Functional Method with the Triple-ζ Basis Set 6-311+G(d,p). J. Phys. Chem. A 2005, 109, 2937−2941. (19) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, revision B.01; Gaussian, Inc.: Wallingford, CT, 2009. (20) Glowacki, D. R.; Liang, C.-H.; Morley, C.; Pilling, M. J.; Robertson, S. H. MESMER: An Open-Source Master Equation Solver for Multi-Energy Well Reactions. J. Phys. Chem. A 2012, 116, 9545− 9560. (21) Wang, H.; Frenklach, M. Transport Properties of Polycyclic Aromatic Hydrocarbons for Flame Modeling. Combust. Flame 1994, 96, 163−170. (22) Wang, H.; Frenklach, M. Calculations of Rate Coefficients for the Chemically Activated Reactions of Acetylene with Vinylic and Aromatic Radical. J. Phys. Chem. 1994, 98, 11465−11489. (23) You, X. Q.; Whitesides, R.; Zubarev, D.; Lester, W. A.; Frenklach, M. Bay-Capping Reactions: Kinetics and Influence on Graphene-Edge Growth. Proc. Combust. Inst. 2011, 33, 685−692. (24) Kee, R. J.; Grcar, J. F.; Smooke, M. D.; Miller, J. A. PREMIX: A Fortran Program for Modeling Steady Laminar One-Dimensional Premixed Flames; Report No. SAND85-8240; Sandia National Laboratories: Livermore, CA, 1985. (25) You, X. Q.; Egolfopoulos, F. N.; Wang, H. Detailed and Simplified Kinetic Models of n-Dodecane Oxidation: The Role of Fuel Cracking in Aliphatic Hydrocarbon Combustion. Proc. Combust. Inst. 2009, 32, 403−410.

that its rate is enhanced by a factor of [H2]/[H], which is very large in the postflame region where the triplet reaction mechanism dominates. So far, acetylene is chosen as an example of the unsaturated aliphatic molecules that can be attached to the triplet PAHs. In principle, any unsaturated aliphatic molecule can react with the triplet PAHs. To demonstrate this point, we take as an example the reaction between the triplet pentacene and ethylene to produce ethyl pentacene, noting that the PES of this reaction is similar to the reaction with acetylene. In this case, after the first CAHM step, ethylene becomes an ethyl group. Because there is no unsaturated C−C bond, the second CAHM will not occur. Moreover, the computed rate coefficient is 2.4 × 105cm3/mol/s at 1500 K and 1 atm, which is smaller than the reaction with acetylene. Together with the fact that the mole fraction of acetylene is larger than ethylene in the postflame region, we conclude that the addition of acetylene to the triplet PAHs is much more important.

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ASSOCIATED CONTENT

S Supporting Information *

Reaction between triplet benzene and acetylene at the level of CBS-QB3 and B3LYP/6-311+g(d,p). Structures, frequencies, and rotational constants in this work. The spin triplet PES of the second CAHM. This material is available free of charge via the Internet at http://pubs.acs.org.

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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 Science Foundation of China (51206090), the National Basic Research Program (2013CB228502), and Tsinghua National Laboratory for Information Science and Technology.

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REFERENCES

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DOI: 10.1021/jz502635t J. Phys. Chem. Lett. 2015, 6, 477−481