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Theoretical Prediction of Rate Constants for Hydrogen Abstraction by OH, H, O, CH3, and HO2 Radicals from Toluene Shu-Hao Li,† Jun-Jiang Guo,‡ Rui Li,† Fan Wang,*,§ and Xiang-Yuan Li*,‡ †

School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, China School of Chemical Engineering, Sichuan University, Chengdu 610065, China § Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China ‡

S Supporting Information *

ABSTRACT: Hydrogen abstraction from toluene by OH, H, O, CH3, and HO2 radicals are important reactions in oxidation process of toluene. Geometries and corresponding harmonic frequencies of the reactants, transition states as well as products involved in these reactions are determined at the B3LYP/6-31G(2df,p) level. To achieve highly accurate thermochemical data for these stationary points on the potential energy surfaces, the Gaussian-4(G4) composite method was employed. Torsional motions are treated either as free rotors or hindered rotors in calculating partion functions to determine thermodynamic properties. The obtained standard enthalpies of formation for reactants and some prodcuts are shown to be in excellent agreement with experimental data with the largest error of 0.5 kcal mol−1. The conventional transition state theory (TST) with tunneling effects was adopted to determine rate constants of these hydrogen abstraction reactions based on results from quantum chemistry calculations. To faciliate its application in kinetic modeling, the obtained rate constants are given in Arrhenius expression: k(T) = ATn exp(−EaR/T). The obtained reaction rate constants also agree reasonably well with available expermiental data and previous theoretical values. Branching ratios of these reactions have been determined. The present reaction rates for these reactions have been used in a toluene combustion mechanism, and their effects on some combustion properties are demonstrated.

1. INTRODUCTION Aromatic hydrocarbons are important components of practical fossil fuels, and toluene is one of the most important aromatic hydrocarbons.1−4 The comprehensive oxidation mechanism of toluene is thus important in developing the combustion mechanism and understanding combustion processes of fossil fuels.1−7 Reasonable rate constants for reactions involved in the combustion process of toluene are critical to achieve a reliable combustion mechanism. Hydrogen abstraction (H-abstraction) reactions by hydroxide radical (OH), hydrogen atom (H), oxygen atom (O), methyl radical (CH3) and hydroperoxyl radical (HO2) from toluene (C6H5CH3) are main chain propagation steps to produce alkyl radicals in combustion process of toluene. Toluene are consumed mainly through these H-abstraction reactions and they play an important role in combustion characteristics of toluene.1,2 It has been shown that C6H5CH3 + OH → C6H5CH2 + H2O, C6H5CH3 + OH → C6H4CH3 + H2O, and C6H5CH3 + H → C6H5CH2 + H2 are among the most important reactions that affect ignition delay times of toluene.1 Therefore, accurate knowledge of rate constants for these reactions is needed to improve models for toluene combustion. These hydrogen abstraction reactions are cleavage of a C−H bond by hydrogen transfer from toluene to the abstracting reactants. Reaction rate constant of H-abstraction depends on © 2016 American Chemical Society

the type of H atom being abstracted (a: methyl, b: ortho-, metaand parapositions of toluene) as well as on the abstracting reactant. Abstracting reactants are mainly small active radicals such as H, O, OH, CH3 and HO2 and the resultant radicals are benzyl (C6H5CH2) or methylphenyl (ortho-, meta-, paraC6H4CH3). In this paper we investigate the following 20 Habstraction reactions of toluene by OH, H, O, CH3, and HO2 radicals: C6H5CH3 + OH → C6H5CH 2 + H 2O

(R1-1)

C6H5CH3 + OH → o‐C6H4CH3 + H 2O

(R1-2)

C6H5CH3 + OH → p‐C6H4CH3 + H 2O

(R1-3)

C6H5CH3 + OH → m‐C6H4CH3 + H 2O

(R1-4)

C6H5CH3 + H → C6H5CH 2 + H 2

(R2-1)

C6H5CH3 + H → o‐C6H4CH3 + H 2

(R2-2)

C6H5CH3 + H → p‐C6H4CH3 + H 2

(R2-3)

Received: March 24, 2016 Revised: April 22, 2016 Published: May 10, 2016 3424

DOI: 10.1021/acs.jpca.6b03049 J. Phys. Chem. A 2016, 120, 3424−3432

Article

The Journal of Physical Chemistry A C6H5CH3 + H → m‐C6H4CH3 + H 2

(R2-4)

C6H5CH3 + O → C6H5CH 2 + OH

(R3-1)

C6H5CH3 + O → o‐C6H4CH3 + OH

(R3-2)

C6H5CH3 + O → p‐C6H4CH3 + OH

(R3-3)

C6H5CH3 + O → m‐C6H4CH3 + OH

(R3-4)

C6H5CH3 + CH3 → C6H5CH 2 + CH4

(R4-1)

C6H5CH3 + CH3 → o‐C6H4CH3 + CH4

(R4-2)

C6H5CH3 + CH3 → p‐C6H4CH3 + CH4

(R4-3)

C6H5CH3 + CH3 → m‐C6H4CH3 + CH4

(R4-4)

C6H5CH3 + HO2 → C6H5CH 2 + H 2O2

(R5-1)

C6H5CH3 + HO2 → o‐C6H4CH3 + H 2O2

(R5-2)

C6H5CH3 + HO2 → p‐C6H4CH3 + H 2O2

(R5-3)

C6H5CH3 + HO2 → m‐C6H4CH3 + H 2O2

(R5-4)

Metcalfe et al.,2 Andrae,6 and Yuan et al.7 Rate constants for these H-abstraction reactions in the above toluene mechanisms are taken either from estimated values or from available experimental values. However, most of experimental reaction constants for these H-abstraction reactions are only applicable to rather narrow conditions. Furthermore, only a few of these reactions are investigated theoretically and different computational methods have been employed in these calculations. This makes it difficult to choose consistent and reliable reaction constants of these reactions in reaction mechanism for toluene. Accurate rate constants for these H-abstraction reactions are necessary to improve compressive kinetic mechanisms for combustion of toluene. In this work, the G4 composite method is employed to determine energies, structures and harmonic frequencies of reactants, products, as well as transition states for these Habstraction reactions of toluene. It has been shown to provide barrier heights with an average error of less than 1 kcal mol−1.36 Rate constants for these reactions over a wide temperature range will be reported using transition state theory based on G4 results. These rate constants can be adopted in developing reaction mechanisms of toluene oxidation. Some combustion properties of tolune using the obtained reaction rate constants will also be reported.

Several experimental investigations for reaction R1-1 have been carried out previously,8−13 and the rate constant for R1-1 was measured experimentally at a single temperature or in a narrow temperature range. These experimental data for R1-1 are thus insufficient to be adopted in comprehensive kinetics mechanism of toluene that can be applied to a wide range of conditions. Uc et al. investigated R1-1 by quantum chemical calculation at the BHandHLYP/6-311++G(d,p) level, followed by CCSD(T) on energies of the optimized structures, but only reaction rates under low temperaturs are given in their work.14 Seta et al. investigated R1-1 by a combination of experimental measures and quantum chemical calculation at G3(MP2)// B3LYP and CBS-QB3 levels. Barrier height used in their calculations is estimated based on experimental rate constants.15 For R2-1, a variety of experimental techniques have been employed to investigate this reaction before 1990.16−20 Recently, Oehlschlaeger et al. investigated this reaction using UV laser absorption of benzyl radicals at 266 nm in shock tube experiments and gave the best-fit rate coefficient for this reaction.21 This reaction has also been studied theoretically by Kislov et al. with the G3 method22 and by Tian et al. at the CBS-QB3 level.23 Experimental study on R3-1 was reported by Hoffmann;24 and there is no theoretical investigation reported. As for R4-1, previous theoretical and experimental investigations only applies to temperature below 1000 K and these values may be limited in practical application,25−32 except for the theoretical work by Tian et al.23 at the CBS-QB3 level. R5-1 has been studied experimentally using a variety of techniques by Eng et al. and Scott et al., respectively.33,34 Potential energy surface for this reaction was studied theoretically by Luzhkov et al.,35 but no rate constants were given. On the other hand, theoretical and experimental investigations for the Habstraction reaction to produce methylphenyl radical are rare, and most of the rate constants for this type of H-abstraction reaction were estimated from those of similar reactions. Only Seta et al. and Tian et al. investigated reactions R1-2, R1-3, and R1-4 with the G3/CBS-QB3 method and R2-2, R2-3, and R2-4 at the CBS-QB3 level, respectively.15,23 Due to their importance, these reactions are included in the detailed chemical combustion mechanisms for toluene such as those developed by Bounaceur et al.,1 Narayanaswamy et al.,5

2. COMPUTATIONAL METHODS Energies of stationary points on potential energy surfaces of the involved reactions as well as their geometries and harmonic frequencies are calculated with the G4 composite method using the Gaussian 09 program package37 on computers of the National Supercomputing Center of Shenzhen. Geometries and harmonic frequencies (scaled by a factor 0.9845)36 for reactants, products and transition states involved in the reaction schemes were determined at the B3LYP/6-31G(2df,p) level as implemented in G4 except for the transition structure of R1-1. Transition state for reaction R1-1: C6H5CH3 + OH → C6H5CH2 + H2O cannot be located using B3LYP with the 631G(2df,p) basis set as well as even larger basis set. Reaction R1-1 is exothermic, and experimental results show that rate constant increases with temperature, which implies than an energy barrier exists in this reaction. Transition state for R1-1 has been locate with BHandHLYP/6-311G(d,p) method in ref 14 and B3LYP/6-31G(d) in ref 15. To be more consistent with calculation protocol in G4, we choose to calculate transition structure for this reaction with B3LYP/6-31G(d). Energies of the achieved stationary points were obtained from results of a series of methods with high accuracy in the G4 composite method. The G4 method has been shown to be able to precisely predict thermochemical data and barrier heights with an average error of less than 1 kcal mol−1.36 All the transition-state structures were confirmed by only one imaginary frequency and intrinsic reaction coordinate (IRC)38 calculations with B3LYP/6-31G(2df,p) were also carried out to verify that the transition state connects the corresponding reactants and products. Internal rotations were considered in these reaction systems in calculating partition functions. The internal rotation potentials were calculated by relaxed scans of the dihedral angle with an interval of 5° at the B3LYP/631G(2df,p) level and the barrier height of rotation, number of rotational minima, and symmetry number can be obtained from the obtained potential curve. For internal rotations with torsional energy barriers much less than 1 kcal mol−1, torsional energy curves are irregular due to numerical errors in 3425


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The Journal of Physical Chemistry A Table 1. Standard Enthalpies of Formation (Δf Hθ(298 K), kcal mol−1) for Reactants and Products species

calculated

experimental47

species

calculated

experimental47

H O OH H2 HO2 H2O2 H2O

52.10 59.43 8.64 −0.34 2.99 −31.68 −57.38

52.10 59.57 8.93 0.00 2.94 −32.45 −57.79

CH3 CH4 C6H5CH3 C6H5CH2 o-C6H4CH3 m-C6H4CH3 p-C6H4CH3

34.52 −17.87 11.99 49.71 72.11 72.15 72.69

35.06 −17.83 11.95 49.71 -------

Table 2. Relative Energies of Transtion States and Products Systems transition-state (kcal mol−1)

reactants C6H5CH3+OH

C6H5CH3+H

C6H5CH3+O

C6H5CH3+CH3

reactants C6H5CH3+HO2

TSOH−CH3 TSOH‑o TSOH‑m TSOH‑p TSH−CH3 TSH‑o TSH‑m TSH‑p TSO‑CH3 TSO‑o TSO‑m TSO‑p TSCH3‑CH3 TSCH3‑o TSCH3‑m TSCH3‑p transition states (kcal mol−1) TSHO2‑CH3 TSHO2‑o TSHO2‑m TSHO2‑p

products (kcal mol−1) 1.2 3.2 3.5 3.6 5.9 15.2 15.3 15.6 4.2 9.6 9.7 10.0 10.2 16.3 16.6 16.8 complexes (kcal mol−1)

13.5 22.7 23.3 23.7

--CPHO2‑o CPHO2‑m CPHO2‑p

--21.3 21.4 22.1

−28.5 −6.2 −6.1 −5.6 −15.2 7.1 7.2 7.7 −13.6 8.7 8.8 9.3 −14.2 7.8 7.9 8.5 products (kcal mol−1)

C6H5CH2+H2O2 o-C6H4CH3+H2O2 m-C6H4CH3+H2O2 p-C6H4CH3+H2O2

2.8 25.1 25.2 25.7

kB is the Boltzmann constant, h is the Planck constant. Q‡, QX, and QY in eq 1 are the partition functions of the transition state and the reactants, respectively; R is the gas constant, ΔEB,0 in is the electronic barrier height with zero-point vibrational energy (ZPVE) correction. Several formulas exist in calculating the tunneling coefficient such as the Eckart function45 and the Wigner formular.46 However, tunneling effect is generally less important at high temperatures, which are a main concern of the present work for combustion of toluene. Due to simplicity of Wigner tunneling correction, we choose the Wigner’s formular in the present work for the tunneling coefficient κ as the following:46

calculations and they are treated as free rotors. The other internal rotation modes are treated as hindered rotors, and the one-dimensional hindered internal rotor method39 was applied to obtain contributions of low-frequency torsional motions in calculation of partition functions. Standard enthalpies of formation (Δf Hθ(298 K), kcal mol−1) were determined with the G4 method using the atomization method,40 where experimental values of Δf Hθ(0 K) for C (169.98 kcal mol−1), H (51.63 kcal mol−1) and O (58.99 kcal mol−1) for the calculation of Δf Hθ(0 K) are adopted. Enthalpies of formation (Δf Hθ), entropies (Δf Sθ), and heat capacities of species (Cp) at different temperature for reactants, products, and transition states were obtained by employing the ChemRate program41 using standard enthalpies of formation, vibrational frequencies, and moments of inertia as well as hindered rotator or free rotator treatment on internal rotations based on statistical mechanical principles. Rate constants for these reactions are predictable from transition state theory (TST).42 This theory is one of the best available method to calculate rate constants of gas phase bimolecular reactions.43 According to TST, reaction rate constant k for a bimolecular reaction X + Y = XY‡ reads:44 k T Q‡ k = κVm B exp( −ΔE B,0 /RT ) h Q XQ Y

C6H5CH2+H2O o-C6H4CH3+H2O m-C6H4CH3+H2O p-C6H4CH3+H2O C6H5CH2+H2 o-C6H4CH3+H2 m-C6H4CH3+H2 p-C6H4CH3+H2 C6H5CH2+OH o-C6H4CH3+OH m-C6H4CH3+OH p-C6H4CH3+OH C6H5CH2+CH4 o-C6H4CH3+CH4 m-C6H4CH3+CH4 p-C6H4CH3+CH4

κ=1−

2 1 ⎛ hν ⎞ ⎛ RT ⎞ ⎟⎟ ⎜ ⎟ ⎜⎜1 + 24 ⎝ kBT ⎠ ⎝ ΔE B,0 ⎠

(2)

where ν is the imaginary frequency associated with the reaction coordinate. Rate constants from 300 to 2000 K are fitted with a three-parameter form of the Arrhenius equation: k = AT n( −Ea /RT )

(3)

This three-parameter form for reaction rate constants is used extensively in combustion mechanisms.

(1)

3. RESULTS AND DISCUSSION 3.1. Geometry and Thermochemical Properties. In calculating thermochemical properties, torsional rotation

where κ is the tunneling coefficient accounting for tunneling effects, Vm is the molar volume of an ideal gas at temperature T, 3426


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The Journal of Physical Chemistry A

Table 3. Modified Arrhenius Parameters for H-Abstraction Reactions of Toluene Fitted in the temperature of 300−2000 K (unit: A(cm3 mol−1 s−1), Ea(cal)) reactions

A

n

Ea

reactions

A

n

Ea

kOH−CH3 kOH‑o kOH‑m kOH‑p kOH‑ring kO−CH3 kO‑o kO‑m kO‑p kO‑ring kHO2‑CH3 kHO2‑o kHO2‑m kHO2‑p kHO2‑ring

130169.1 277.7315 819.6653 763.895 1747.54 75372.24 281049.1 1.16 × 1006 1.57 × 1006 2.57 × 1006 0.00788 1.71418 3.02029 3.79741 7.60247

2.28048 2.99789 3.09594 3.10443 3.09666 2.57378 2.41207 2.44202 2.40693 2.44074 4.29278 3.64569 3.64209 3.6191 3.64626

−572.972 1245.721 1507.708 1688.651 1548.924 3145.746 8837.35 9052.875 9440.521 9143.372 11250.72 21743.27 22208.17 22697.45 22222.04

kH−CH3 kH‑o kH‑m kH‑p kH‑ring kCH3‑CH3 kCH3‑o kCH3‑m kCH3‑p kCH3‑ring

1.07 × 1006 3.21 × 1007 1.11 × 1008 1.05 × 1008 2.00 × 1008 2.55836 91.44079 197.2672 204.9017 537.7265

2.26764 1.81483 1.80464 1.81188 1.83443 3.80712 3.28308 3.28482 3.30806 3.28445

4392.371 14155.56 14389.02 14672.52 14381.82 7395.743 14233.33 14542.45 14723.92 14601.08

On the other hand, barrier height of hydrogen abstraction from the methyl group is about 10 kcal mol−1 lower than those from the phenyl ring for H and HO2. One would thus expect that difference between rate constants of H-abstraction by H and HO2 from the methyl group and those from the phenyl ring will be more pronounced. It should be noted that products are even higher in energy than the corresponding transition states for hydrogen abstraction reactions from the phenyl ring for HO2. Detailed IRC calculations reveal that three product-like van der Waals complexes exist and they are 1.4, 1.9, and 1.6 kcal mol−1 lower in energy than the corresponding transition states, respectively. These product-like complexes dissociate into the corresponding products via endothermic reactions of 3.8, 3.8, and 3.6 kcal mol−1, respectively. 3.3. Reaction Rate Constants. The modified arrhenius parameters for these reactions are obtained by fitting reaction rate constants in the temperature range of 300−2000 K and they are given in Table 3. All pre-exponential terms (ATn) quoted are in units of cm3 mol−1 s−1, with temperatures in K. In all toluene kinetics mechanism, rate constants for the three aromatic-ring H-abstraction channels were summed to one channel and three methyl phenyl radicals (o-C6H4CH3, mC6H4CH3, and p-C6H4CH3) are lumped to a methylphenyl radical (C6H4CH3). Rate constant for the lumped reaction is equal to the sum of rate constants for these three channels and it is also represented with the modified Arrhenius equation. The modified Arrhenius parameters for the lumped reactions are also listed in this table. These reaction rate constants can be readily compared with those in the existing toluene mechanism and the other calculated and experimental values. These rate constants proposed in the Supporting Information are provided for use in kinetic models of toluene. For the four channels of H-abstraction by OH from C6H5CH3, the transition states resides above the reactants by 1.2 kcal mol−1, 3.2 kcal mol−1, 3.5 kcal mol−1, and 3.6 kcal mol−1 for abstraction of H atom from methyl, ortho-position, meta-position, and para-position on the phenyl ring, respectively. Rotations of CH3 in toluene, TSOH‑m and TSOH‑p, were treated as free rotors, while they are taken as hindered rotors in TSOH‑o and TSOH−CH3. Our rate constants for R1-1 are about 2−3 times smaller than the experimentally recommended values48 and other calculated or estimated

around the C−C bond between the phenyl and the methyl groups are treated with special care. From the results of relaxed scan, rotation of methyl in toluene is treated as a free rotor, since this torsional energy barrier is only 0.028 kcal mol−1 and the energy curves are irregular. Similarly, rotation of the methyl group in transition states of hydrogen abstraction at meta- and parapositions were also treated as free rotors. On the other hand, rotation of the methyl group in transition states of hydrogen abstraction at methyl and ortho- positions are treated as hindered rotors. The standard enthalpies of formation of all reactants and products at G4 level are listed in Table 1 together with available experimental data.47 Equilibrium geometries, harmonic vibrational frequencies and potential curves of the involved hindered rotors for all the reactants, products and the involved transition states, which are required to obtain the standard enthalpies of formation, are provided in te Supporting Information. One can see from this table that the obtained results are in excellent agreement with experimental values and the largest difference is less than 1 kcal mol−1. These results demonstrate reliability of the employed G4 method in calculating thermodynamic properties of these molecules. The entropies and heat capacities at different temperatures for all the reactants, products, and transition states are provided in the Supporting Information. 3.2. Barrier Heights and Reaction Rate Constants. Barrier heights as well as energy of the products with respect to the reactants from G4 theory with ZPVE correction are listed in Table 2. It can see from this table that the barrier heights for abstraction of hydrogen atom from the methyl group of toluene is lower than those on the phenyl ring, as one would expect since the resulting radical C6H5CH2 is about 22 kcal mol−1 more stable than C6H4CH3 radicals. Furthermore, differences between barrier heights for hydrogen abstraction at o-, m-, ppositions are less than 0.5 kcal mol−1 except for HO2, where their differences are within 1 kcal mol−1. According to the obtained barrier heights, we would expect that reactivity of OH is the highest among all the abstracting reactants, followed by O, H and CH3, while reactivity of HO2 is the lowest. Furthermore, barrier height of hydrogen abstraction from the methyl group is only about 2 kcal mol−1 smaller than those from the phenyl ring for OH. This indicates that the difference in reaction rate constants of H-abstraction by OH from the methyl group and those from the phenyl ring will be modest. 3427


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Figure 1. Branching ratios for H-abstraction form toluene by OH, H, O, CH3, and HO2 in Ar.

H-abstraction by O from methane by Yuan et al.7 The present results are in better agreement with experimental values than those estimated by Yuan et al. data of Hoffmann than that of Yuan. There is no previous experimental or computational study on H-abstraction by O from phenyl ring of toulene. On the other hand, our calculated values kO‑ring are larger than that of H-abstraction by O from benzene given by Bounaceur et al.1 This may be related to the fact that the bond energy of C−H in benzene is 112.9 kcal mol−1, while they are 79.9, 95.3, and 110.6 kcal mol−1 for C−H bond at ortho-, meta- and parapositions in toluene, respectively.49 Reaction R4-1: C6H5CH3 + CH3 → R• + CH4 is the important consumption channel in both combustion and pyrolysis processes of C6H5CH3. There are many experimental studies25−32 of this reaction. The present rate constants agree well with available experimental values and theoretical results

values. As for rate constant of abstraction from phenyl ring, the present rate constants are lower than those given by Seta et al.15 at low temperatures, while they are larger at higher temperatures. Over all, the present reaction rate constants for R1-1 to R1-4 are consistent with those previous experimental and theoretical results. H-abstraction reactions by H atom, i.e., R2-1 to R2-4 are important consumption channels for C6H5CH3. Our calculated values of kH−CH3 agree well with experimental values of Ellis et al.16 and are in good agreement with theoretical values by Tian et al.23 at low temperatures, while their differences increase at higher temperatures. Furthermore, the present rate constants for H-abstraction from the phenyl ring by H atom are also in good agreement with the results of Tian et al. Hoffmann et al.24 reported experimental rate constants of R3-1, while reaction rate for this reaction is estimated based on 3428


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reactor (JSR) model and laminar flame speed in combustion of toluene have been simulated with CHEMKIN 2.051 with the original Andrae’s mechanism6 and the revised mechanism. Simulation results are presented in Figures 2−6.

given by Tian et al. based on CBS-QB3.23 As for kCH3‑ring, our results are slightly larger than those estimated by Pamidimukkala et al. and Bounaceur et al. based on similar reaction of benzene.1,47 H-abstraction reactions of C6H5CH3 + HO2 → R• + H2O2 are important consumption channels for C6H5CH3, particularily in low temperature combustion process, when the concentration of OH, H, O and CH3 radicals is lower than that of HO2. In H-abstraction from phenyl ring, postreaction van der Waals complexes exist. We assume that these postreaction van der Waals complexes will dissociate to o-, m- and p- C6H4CH3 + H2O2 rapidly once formed, and we thus treat this reactions as proceeding directly from C6H5CH3 + HO2 to C6H4CH3 + H2O2, via the homologous transition structures. This treatment has also been adopted by Silva et al. in a similar situation.50 The present values of kHO2‑CH3 are a little bit smaller than experimental values by Scott et al.34 and Eng et al.33 As for kHO2‑ring, our calculated values are larger than the estimated data by Bounaceur et al.,1 while similar to recommended values given by Baulch et al.48 3.4. Branching Ratios. Branching ratios are important to understand details of combustion chemistry. They have been determined in the temperature range of 300−2000 K for all possible product channels and demonstrated in Figure 1. Bond energy C−H in methyl group is smaller than that on the phenyl ring of toluene and the channel to produce C6H5CH2 is thus always more important than those to produce C6H4CH3 at low temperature. However, at high temperatures, the channel of Habstraction from the phenyl ring becomes more important for OH and O, while the channel of H-abstraction from the methyl group is always more important for the other abstracting reactant in this temperature range. This is because the reaction barriers of H-abstraction from the phenyl ring by OH and O and smaller than those by the other abstracting reactant. Rate constants of H-abstraction from the phenyl ring by OH and O becomes larger than those from the methyl group at high temperautres. As for H-abstraction from the phenyl ring, Habstraction from the ortho-site is always the least important channel. Furthermore, differences in braching ratios between H-abstrion from ortho-, meta- and parapositions are the most significant for OH and O, while their differences are not as pronounced for the other abstracting reactants, although the reaction barriers for these three channels are rather similar. 3.5. Kinetic Modeling. In order to investigate effects of rate constants of these reactions on combustion properties of toluene, rate constants for these reactions in oxidation mechanisms of toluene provided by Andrae6 are replaced by the present values. Reaction rate constants of R1-1 and C6H5CH3 + OH → C6H4CH3 + H2O in Andrae’s mechanism are taken from Seta’s data.15 Rate constants of R1-1 in Andrae’s mechanism are about 3 times larger than our calculated values. For C6H5CH3 + OH → C6H4CH3 + H2O, the present rate constants are lower than those given by Seta et al. at low temperatures, while they are larger at higher temperatures.15 Experimental rate constants provided by Oehlschlaeger et al.21 and Hoffmann et al.24 for R2-1 and R3-1 are employed in Andrae’s mechanism. The present rate constants for R2-1 and R3-1 are in reasonable agreement with those used Andrae’s mechanism. Rate constants of the other H-abstraction reactions in Andrae’s mechanism are mostly estimated from similar reactions.48 Ignition delay time in a rapid compression machine(RCM) as well as in a shock tube, mole fraction of toluene in variable pressure flow reactor (VPFR) and Jet-stirred

Figure 2. Ignition delay for toluene/O2/N2/Ar mixtures in a rapid compression machine at p = 45 atm and mole fraction toluene = 0.00962. Symbols = experimental data by Mittal and Sung.52 Solid lines and dashed lines are model predictions.

One can see from Figures 2 and 3 that ignition times with revised mechanism are always larger than those using the

Figure 3. Shock tube ignition delay for toluene/air at 12 atm, equivalence ratio equal of 1.0. Symbols = experiment by Shen et al.;53 solid line and dashed line are model predictions.

original mechanism. Revised mechanism provide ignition delay times in RCM that are in better agreement with experimental data52 at low temperatures, while the original mechanism affords better ignition delay times at high temperatures. On the other hand, experimental ignition delay times mostly lie between the predicted values with these two mechanisms in shock tube.53 Brute-force sensitivity analysis is carried out to understand effects of these H-abstraction reactions on ignition delay of toluene based on the original mechanism under the condition of equivalence ratio equal of 1.0, initial temperature at 1000 K, and pressure at 45 atm. The most two important reactions that promote ignition of toluene at 1000 K are C6H5CH2 + HO2 = C6H5CH2O + OH, H + O2 + N2 = HO2 + N2. This indicates that C6H5CH2 is rather important on ignition delay time for toluene. C6H5CH2 is produced mainly through H-abstraction reactions R1-1 and R2-1. Rate constants of R1-1 in the original mechanism are larger than the present 3429


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The Journal of Physical Chemistry A values. It is thus understandable that predicted ignition delay times with the present rate constants will be larger than those with the original mechanism. As for mole fraction of toluene in VPFR and JSR demonstrated in Figures 4 and 5, one can see that consumption

Figure 6. Laminar burning velocities of the C6H5CH3/air mixture as a function of the equivalence ratio at 3 atm, 450 K; symbols are experimental data;55 solid line and dashed line are model predictions.

Figure 4. Oxidation of toluene in variable pressure flow reactor. 0.14% C6H5CH3 in N2, ϕ = 0.977, T = 920 K, p = 12.5 atm. Symbols = experiments by Metcalfe et al.;2 solid line and dashed line are model predictions.

abstraction reactions, many other reactions also play important roles in combustion properties of toluene, such as sub mechanism of benzyl or methylphenyl, and C0−C4 core mechanism. Furthermore, effect of rate constants of these Habstraction reactions on combustion properties also depends on rate constants of other reactions. This means using the present rate constants in other toluene combustion mechanisms may result in different effects from what has been shown with Andrae’s mechanism. To achieve reasonable description on combustion properties of toluene, reliable reaction constants for all the important reactions are required.

4. CONCLUSIONS Rate constants of H-abstraction reaction from toluene by OH, H, O, CH3, and HO2 radicals have been investigated in this work. G4 theory is employed to locate stationary points on potential surfaces of the involved reactions and to calculate vibrational frequencies as well as thermodynamic properties. The obtained enthalpies of formation of components agree well with available experiment data. Rate constants are obtained using the TST theory with the tunneling effect taken into consideration. Rate constants obtained in this work are in reasonable agreement with available previous experimental and theoretical results. The three-parameter modified Arrhenius expression is employed to express the obtained reaction rate constants in the temperature range of 300−2000 K, which facilitate their application in combustion mechanisms. Branching ratios for these reactions are determined based on the obtained reaction rate constants. Relative importance between H-abstraction from the methyl group and that from the phenyl ring at different temperature by different H-abstracting reactant are clarified. The obtained reaction rate constants are employed in the combustion mechanism of toluene developed by Andrae. Ignition delay times in RCM and shock tube, mole fraction on toluene in VPFR and JSR, as well as laminar flame speeds are simulated with the revised mechanism. The results show that with the new reaction rate constants, the obtained combustion properties of toluene are improved to some extent. It should be noted that the investigated combustion properties also depend critically on other reactions, and using these reaction rates together with the other combustion mechanism of toluene may not necessarily improve performance of the combustion mechanism.

Figure 5. Jet-stirred reactor species concentration profiles of 0.15% C6H5CH3, in N2, ϕ = 1.0, p = 1.0 atm, and residence time (τ) = 0.1 s. Symbols are experimental data;54 solid line and dashed line are model predictions.

of toluene is much slower with the revised mechanism that that with the original mechanism. Furthermore, mole fractions of toluene with the revised mechanism provided are in better agreement with experimental data.2,54 This is consistent with the fact that rate constant R1-1, which is one of the most important reaction in consumption of toluene, in the original mechanism is larger than the present value. Laminar burning velocities with the original and revised mechanisms as well as experimental data55 are illustrated in Figure 6. One can see from this figure that reaction rate constants of these Habstraction reactions do not affect Laminar burning velocities much. Sensitivity analysis of Laminar burning velocities was carried out based on original mechanism, H + O2 = O + OH and CO + OH = CO2 + H are the most important two reactions that promote flame speed increase. These Habstraction reactions thus have limited effect on Laminar burning velocities of toluene. It should be noted that reaction mechanism of toluene combustion is highly complicated. Besides these key H3430


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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.6b03049. Predicted thermochemical properties of stable species and rate constants expressions in CHEMKIN format (TXT) All of the geometries of reactants, transition states, and products used in calculating rate constants (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*(F.W.) E-mail: [email protected]; Phone: +8615828332921. *(X.-Y.L.) E-mail: [email protected]; Phone: +86-28-85405233. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (No. 91441132). We acknowledge the National Supercomputing Center in Shenzhen for providing the computational resources and Gaussian software.

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REFERENCES

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