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Article

Theoretical Prediction of Rate Constants for Hydrogen Abstraction by OH, H, O, CH and HO Radicals from Toluene 3

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Shu-Hao Li, Junjiang Guo, Rui Li, Fan Wang, and Xiang-Yuan Li J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b03049 • Publication Date (Web): 10 May 2016 Downloaded from http://pubs.acs.org on May 14, 2016

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The Journal of Physical Chemistry

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Theoretical Prediction of Rate Constants for Hydrogen Abstraction by OH, H, O, CH3 and HO2 Radicals from Toluene

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Shu-Hao Li,1 Jun-Jiang Guo,2 Rui Li,1 Fan Wang,3,* Xiang-Yuan Li2,*

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1. School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065 , China；

1 2

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2. School of Chemical Engineering, Sichuan University, Chengdu 610065, China; 3. Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China.

*Corresponding authors. Fan Wang, E-mail: [email protected], Phone: +86-15828332921; Xiang-Yuan Li, E-mail: [email protected], Phone: +86-28-85405233.

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Abstract: Hydrogen abstraction from toluene by OH, H, O, CH3 and HO2 radicals are

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important reactions in oxidation process of toluene. Geometries and corresponding

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harmonic frequencies of the reactants, transition states as well as products involved in

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these reactions are determined at the B3LYP/6-31G(2df,p) level. To achieve highly

15

accurate thermochemical data for these stationary points on the potential energy

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surfaces, the Gaussian-4(G4) composite method was employed. Torsional motions are

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treated either as free rotors or hindered rotors in calculating partion functions to

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determine thermodynamic properties. The obtained standard enthalpies of formation

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for reactants and some prodcuts are shown to be in excellent agreement with

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experimental data with the largest error of 0.5 kcal mol-1. The conventional transition

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state theory (TST) with tunneling effects was adopted to determine rate constants of

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these hydrogen abstraction reactions based on results from quantum chemistry

23

calculations. To faciliate its application in kinetic modelling, the obtained rate

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constants are given in Arrhenius expression: k(T) = ATn Exp(−EaR/T). The obtained

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reaction rate constants also agree reasonably well with available expermiental data

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and previous theoretical values. Branching ratios of these reactions have been

27

determined. The present reaction rates for these reactions have been used in a toluene

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ACS Paragon Plus Environment


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combustion mechanism and their effects on some combustion properties are

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demonstrated.

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1. Introduction

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Aromatic hydrocarbons are important components of practical fossil fuels and toluene

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is one of the most important aromatic hydrocarbons.1-4 Comprehensive oxidation

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mechanism of toluene is thus important in developing combustion mechanism and

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understanding combustion processes of fossil fuels.1-7 Reasonable rate constants for

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reactions involved in combustion process of toluene are critical to achieve a reliable

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combustion mechanism. Hydrogen abstraction (H-abstraction) reactions by hydroxide

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radical (OH), hydrogen atom (H), oxygen atom (O), methyl radical (CH3) and

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hydroperoxyl radical (HO2) from toluene (C6H5CH3) are main chain propagation steps

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to produce alkyl radicals in combustion process of toluene. Toluene are consumed

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mainly through these H-abstraction reactions and they play an important role in

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combustion characteristics of toluene.1,2 It has been shown that C6H5CH3 + OH →

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C6H5CH2 + H2O, C6H5CH3 + OH → C6H4CH3 + H2O and C6H5CH3 + H →

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C6H5CH2 + H2 are among the most important reactions that affect ignition delay times

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of toluene.1 Therefore, accurate knowledge of rate constants for these reactions is

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needed to improve models for toluene combustion.

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These hydrogen abstraction reactions are cleavage of a C-H bond by hydrogen

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transfer from toluene to the abstracting reactants. Reaction rate constant of

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H-abstraction depends on the type of H atom being abstracted (a: methyl, b: ortho-,

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meta- and para- positions of toluene) as well as on the abstracting reactant.

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Abstracting reactants are mainly small active radicals such as H, O, OH, CH3 and HO2

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and the resultant radicals are benzyl (C6H5CH2) or methylphenyl (ortho-, meta-,

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para-C6H4CH3). In this paper we investigate the following twenty H-abstraction

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reactions of toluene by OH, H, O, CH3 and HO2 radicals:

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C6H5CH3 + OH → C6H5CH2 + H2O,

(R1-1)

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C6H5CH3 + OH → o-C6H4CH3 + H2O,

(R1-2)

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C6H5CH3 + OH → p-C6H4CH3 + H2O,

(R1-3)

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C6H5CH3 + OH → m-C6H4CH3 + H2O,

(R1-4)

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C6H5CH3 + H →C6H5CH2 + H2,

(R2-1)

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C6H5CH3 + H → o-C6H4CH3 + H2,

(R2-2)

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C6H5CH3 + H → p-C6H4CH3 + H2,

(R2-3)

C6H5CH3 + H → m-C6H4CH3 + H2,

(R2-4)

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C6H5CH3 + O →C6H5CH2 + OH,

(R3-1)

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C6H5CH3 + O → o-C6H4CH3 + OH,

(R3-2)

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C6H5CH3 + O → p-C6H4CH3 + OH,

(R3-3)

C6H5CH3 + O → m-C6H4CH3 + OH,

(R3-4)

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C6H5CH3 + CH3 →C6H5CH2 + CH4,

(R4-1)

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C6H5CH3 + CH3 → o-C6H4CH3 + CH4,

(R4-2)

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C6H5CH3 + CH3 → p-C6H4CH3 + CH4, C6H5CH3 + CH3 → m-C6H4CH3 + CH4,

(R4-3) (R4-4)

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C6H5CH3 + HO2 → C6H5CH2 + H2O2,

(R5-1)

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C6H5CH3 + HO2 → o-C6H4CH3 + H2O2,

(R5-2)

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C6H5CH3 + HO2 → p-C6H4CH3 + H2O2,

(R5-3)

C6H5CH3 + HO2 → m-C6H4CH3 + H2O2.

(R5-4)

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Several experimental investigations for reaction R1-1 have been carried out

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previously, 8-13 and rate constant for R1-1 was measured experimentally at a single

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temperature or in a narrow temperature range. These experimental data for R1-1 are

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thus insufficient to be adopted in comprehensive kinetics mechanism of toluene that

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can be applied to a wide range of conditions. Víctor H. Uc et al. investigated R1-1 by

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quantum chemical calculation at the BHandHLYP/6-311++G(d,p) level, followed by

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CCSD(T) on energies of the optimized structures, but only reaction rates under low

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temperaturs are given in their work14. Seta et al. investigated R1-1 by a combination

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of experimental measures and quantum chemical calculation at G3(MP2)//B3LYP and

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CBS-QB3 levels. Barrier height used in their calculations is estimated based on

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experimental rate constants15. For R2-1, a variety of experimental techniques have

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been employed to investigate this reaction before 1990.16-20 Recently, Oehlschlaeger

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et al. investigated this reaction using UV laser absorption of benzyl radicals at 266 nm

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in shock tube experiments and gave the best-fit rate coefficient for this reaction. 21

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This reaction has also been studied theoretically by Kislov et al. with the G3 method22

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and by Tian et al. at the CBS-QB3 level23. Experimental study on R3-1 was reported

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by Hoffmann;24 and there is no theoretical investigation reported. As for R4-1,

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previous theoretical and experimental investigations only applies to temperature

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below 1000 K and these values may be limited in practical application,25-32 except for

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the theoretical work by Tian et al.23 at the CBS-QB3 level. R5-1 has been studied

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experimentally using a variety of techniques by R.A. Eng et al. and M. Scott et al.,

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respectively.33,34 Potential energy surface for this reaction was studied theoretically by

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Luzhkov et al.,35 but no rate constants were given. On the other hand, theoretical and

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experimental investigations for the H-abstraction reaction to produce methylphenyl

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radical are rare, and most of the rate constants for this type of H-abstraction reaction

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were estimated from those of similar reactions. Only Seta et al. and Tian et al.

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investigated reactions R1-2,3,4 with G3/CBS-QB3 method and R2-2,3,4 at CBS-QB3

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level respectively.15,23

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Due to their importance, these reactions are included in the detailed chemical

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combustion mechanisms for toluene such as those developed by Bounaceur et al.,1

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Narayanaswamy et al.,5 Metcalfe et al.,2 J.C.G. Andrae.6 and Yuan et al..7 Rate

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constants for these H-abstraction reactions in the above toluene mechanisms are taken

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either from estimated values or from available experimental values. However, most of

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experimental reaction constants for these H-abstraction reactions are only applicable

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to rather narrow conditions. Furthermore, only a few of these reactions are

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investigated theoretically and different computational methods have been employed in

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these calculations. This makes it difficult to choose consistent and reliable reaction

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constants of these reactions in reaction mechanism for toluene. Accurate rate

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constants for these H-abstraction reactions are necessary to improve compressive

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kinetic mechanisms for combustion of toluene.

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In this work, the G4 composite method is employed to determine energies,

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structures and harmonic frequencies of reactants, products as well as transition states

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for these H-abstraction reactions of toluene. It has been shown to provide barrier

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heights with an average error of less than 1kcal mol-1.36 Rate constants for these

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reactions over a wide temperature range will be reported using transition state theory

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based on G4 results. These rate constants can be adopted in developing reaction

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mechanisms of toluene oxidation. Some combustion properties of tolune using the

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obtained reaction rate constants will also be reported.

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2 Computational methods

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Energies of stationary points on potential energy surfaces of the involved reactions

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as well as their geometries and harmonic frequencies are calculated with the G4

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composite method using the Gaussian 09 program package37 on computers of

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National Supercomputing Center of Shenzhen. Geometries and harmonic frequencies

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(scaled by a factor 0.9845)36 for reactants, products and transition states involved in

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the reaction schemes were determined at the B3LYP/6-31G(2df,p) level as

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implemented in G4 except for the transition structure of R1-1. Transition state for

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reaction R1-1: C6H5CH3 + OH → C6H5CH2 + H2O cannot be located using B3LYP

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with the 6-31G(2df,p) basis set as well as even larger basis set. Reaction R1-1 is

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exothermic, and experimental results show that rate constant increases with

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temperature, which implies than an energy barrier exists in this reaction. Transition

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state for R1-1 has been locate with BHandHLYP/6-311G(d,p) method in Ref. 14 and

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B3LYP/6-31G(d) in Ref. 15. To be more consistent with calculation protocol in G4,

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we choose to calculate transition structure for this reaction with B3LYP/6-31G(d).

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Energies of the achieved stationary points were obtained from results of a series of

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methods with high accuracy in the G4 composite method. The G4 method has been

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shown to be able to precisely predict thermochemical data and barrier heights with an

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average error of less than 1 kcal mol-1.36

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All the transition-state structures were confirmed by only one imaginary frequency

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and intrinsic reaction coordinate (IRC)38 calculations with B3LYP/6-31G(2df,p) were

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also carried out to verify that the transition state connects the corresponding reactants

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and products. Internal rotations were considered in these reaction systems in

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calculating partition functions. The internal rotation potentials were calculated by 6


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relaxed scans of the dihedral angle with an interval of 5° at the B3LYP/6-31G(2df,p)

2

level and the barrier height of rotation, number of rotational minima, and symmetry

3

number can be obtained from the obtained potential curve. For internal rotations with

4

torsional energy barriers much less than 1 kcal mol-1, torsional energy curves are

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irregular due to numerical errors in calculations and they are treated as free rotors.

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The other internal rotation modes are treated as hindered rotors and the

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one-dimensional hindered internal rotor method39 was applied to obtain contributions

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of low-frequency torsional motions in calculation of partition functions.

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θ Standard enthalpies of formation ( ∆ f H (298K) , kcal mol-1) are determined with

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the G4 method using the atomization method,40 where experimental values of

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∆ f H θ (0K) for C (169.98 kcal mol−1), H (51.63 kcal mol−1) and O (58.99 kcal mol−1)

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for the calculation of ∆ f H θ (0K) are adopted. Enthalpies of formation ( ∆ f H θ ),

13

entropies ( ∆ f S θ ) and heat capacities of species (Cp) at different temperature for

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reactants, products and transition states are obtained by employing the ChemRate

15

program41 using standard enthalpies of formation, vibrational frequencies, and

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moments of inertia as well as hindered rotator or free rotator treatment on internal

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rotations based on statistical mechanical principles.

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Rate constants for these reactions are predictable from transition state theory

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(TST).42 This theory is one of the best available method to calculate rate constants of

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gas phase bimolecular reactions.43 According to TST, reaction rate constant k for a

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bimolecular reaction X +Y = XY≠ reads:44

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k BT Q ≠ k = κVm exp ( -∆ EB,0 RT ) h QX QY

(1)

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where κ is the tunneling coefficient accounting for tunneling effects, Vm is the molar

24

volume of an ideal gas at temperature T, kB is the Boltzmann constant, h is the Planck

25

constant. Q≠, QX, and QY in Eq. (1) are the partition functions of the transition state

26

and the reactants, respectively; R is the gas constant, ∆EB,0 in is the electronic barrier

27

height with zero-point vibrational energy (ZPVE) correction. Several formulas exist

7



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Page 8 of 30

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in calculating the tunneling coefficient such as the Eckart function45 and the Wigner

2

formular46. However, tunneling effect is generally less important at high temperatures,

3

which are main concern of the present work for combustion of toluene. Due to

4

simplicity of Wigner tunneling correction, we choose the Wigner’s formular in the

5

present work for the tunneling coefficient κ as the following:46

κ = 1-

6

1 hν 2 RT ( ) (1 + ) 24 k BT ∆EB,0

(2)

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where ν is the imaginary frequency associated with the reaction coordinate. Rate

8

constants from 300 to 2000 K are fitted with a three-parameter form of the Arrhenius

9

equation:

k = AT n ( − Ea /RT) .

10

(3)

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

12

combustion mechanisms.

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3. RESULTS AND DISCUSSION

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3.1 Geometry and Thermochemical Properties

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In calculating thermochemical properties, torsional rotation around the C-C bond

16

between the phenyl and the methyl groups are treated with special care. From the

17

results of relaxed scan, rotation of methyl in toluene is treated as free rotor, since this

18

torsional energy barrier is only 0.028 kcal mol-1 and the energy curves are irregular.

19

Similarly, rotation of the methyl group in transition states of hydrogen abstraction at

20

meta- and para- positions were also treated as free rotors. On the other hand, rotation

21

of the methyl group in transition states of hydrogen abstraction at methyl and ortho-

22

positions are treated as hindered rotors.

23

The standard enthalpies of formation of all reactants and products at G4 level are

24

listed in Table 1 together with available experimental data47. Equilibrium geometries,

25

harmonic vibrational frequencies and potential curves of the involved hindered rotors

26

for all the reactants, products and the involved transition states, which are required to

27

obtain the standard enthalpies of formation, are provided in Supporting Information.

8


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One can see from this table that the obtained results are in excellent agreement with

2

experimental values and the largest difference is less than 1kcal mol-1. These results

3

demonstrate reliability of the employed G4 method in calculating thermodynamic

4

properties of these molecules. The entropies and heat capacities at different

5

temperatures for all the reactants, products and transition states are provided in

6

Supporting Information .

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3.2 Barrier heights and reaction rate constants

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Barrier heights as well as energy of the products with respect to the reactants from

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G4 theory with ZPVE correction are listed in Table 2. It can see from this table that

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the barrier heights for abstraction of hydrogen atom from the methyl group of toluene

11

is lower than those on the phenyl ring, as one would expected since the resulting

12

radical C6H5CH2 is about 22 kcal mol-1 more stable than C6H4CH3 radicals.

13

Furthermore, differences between barrier heights for hydrogen abstraction at o-, m-, p-

14

positions are less than 0.5 kcal mol-1 except for HO2, where their differences are

15

within 1 kcal mol-1. According to the obtained barrier heights, we would expect that

16

reactivity of OH is the highest among all the abstracting reactants, followed by O, H

17

and CH3, while reactivity of HO2 is the lowest. Furthermore, barrier height of

18

hydrogen abstraction from the methyl group is only about 2 kcal mol-1 smaller than

19

those from the phenyl ring for OH. This indicates that difference in reaction rate

20

constants of H-abstraction by OH from the methyl group and those from the phenyl

21

ring will be modest. On the other hand, barrier height of hydrogen abstraction from

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the methyl group is about 10 kcal mol-1 lower than those from the phenyl ring for H

23

and HO2. One would thus expect that difference between rate constants of

24

H-abstraction by H and HO2 from the methyl group and those from the phenyl ring

25

will be more pronounced.

26

It should be noted that products are even higher in energy than the corresponding

27

transition states for hydrogen abstraction reactions from the phenyl ring for HO2.

28

Detailed IRC calculations reveal that three product-like van der Waals complexes

29

exist and they are 1.4, 1.9 and 1.6 kcal mol-1 lower in energy than the corresponding

30

transition states, respectively. These product-like complexes dissociate into the 9



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1

corresponding products via endothermic reactions of 3.8, 3.8 and 3.6 kcal mol-1,

2

respectively.

3

3.3 Reaction rate constants

4

The modified arrhenius parameters for these reactions are obtained by fitting

5

reaction rate constants in the temperature range of 300-2000 K and they are given in

6

Table 3. All pre-exponential terms ( AT n ) quoted are in units of cm3mol-1s-1, with

7

temperatures in K. In all toluene kinetics mechanism, rate constants for the three

8

aromatic-ring H-abstraction channels were summed to one channel and three methyl

9

phenyl radicals (o-C6H4CH3, m-C6H4CH3 and p-C6H4CH3) are lumped to a

10

methylphenyl radical (C6H4CH3). Rate constant for the lumped reaction is equal to the

11

sum of rate constants for these three channels and it is also represented with the

12

modified Arrenius equation. The modified Arrenius parameters for the lumped

13

reactions are also listed in this table. These reaction rate constants can be readily

14

compared with those in the existing toluene mechanism and the other calculated and

15

experimental values. These rate constants proposed in the Supporting Information are

16

provided for use in kinetic models of toluene.

17

For the four channels of H-abstraction by OH from C6H5CH3, the transition states

18

resides above the reactants by 1.2 kcal mol-1, 3.2 kcal mol-1, 3.5 kcal mol-1 and 3.6

19

kcal mol-1 for abstraction of H-atom from methyl, ortho--position, meta-position and

20

para-position on the phenyl ring, respectively. Rotations of CH3 in toluene, TSOH-m

21

and TSOH-p were treated as free rotors, while they are taken as hindered rotors in

22

TSOH-o and TSOH-CH3. Our rate constant for R1-1 are about 2-3 times smaller than the

23

experimentally recommended values48 and other calculated or estimated values. As

24

for rate constant of abstraction from phenyl ring, the present rate constants are lower

25

than those given by Seta et al.15 at low temperatures, while they are larger at higher

26

tempertures. Over all, the present reaction rate constants for R1-1 to R1-4 are

27

consistent with those previous experimental and theoretical results.

28

H-abstraction reactions by H atom, i.e. R2-1 to R2-4 are important consumption

29

channels for C6H5CH3. Our calculated values of kH-CH3 agree well with experimental

30

values of Ellis et al.16 and are in good agreement with theoretical values by Tian et 10


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1

al.23 at low temperatures, while their differences increase at higher temperatures.

2

Furthermore, the present rate constants for H-abstraction from the phenyl ring by H

3

atom are also in good agreement with the results of Tian et al.

4

Hoffmann et al.24 reported experimental rate constants of R3-1, while reaction rate

5

for this reaction is estimated based on H-abstraction by O from methane by Yuan et.

6

al.7 The present results are in better agreement with experimental values than those

7

estimated by Yuan et. al. data of Hoffmann than that of Yuan. There is no previous

8

experimental or computational study on H-abstraction by O from phenyl ring of

9

toulene. On the other hand, our calculated values ko-ring are larger than that of

10

H-abstraction by O from benzene given by Bounaceur et al.1 This may be related to

11

the fact that the bond energy of C–H in benzene is 112.9 kcal mol-1, while they are

12

79.9, 95.3 and kcal mol-1 for C–H bond at ortho-, meta- and para- position in toluene

13

respectively.49

14

Reaction R4-1: C6H5CH3 + CH3 → R• + CH4 are the important consumption

15

channel in both combustion and pyrolysis processes of C6H5CH3. There are many

16

experimental studies25-32 of this reaction. The present rate constants agree well with

17

available experimental values and theoretical results given by Tian et al. based on

18

CBS-QB3.23 As for kCH3-ring, our results are slightly larger than those estimated by

19

Pamidimukkala et al. and Bounaceur et al. based on similar reaction of benzene.1,47

20

H-abstraction reactions of C6H5CH3 + HO2 → R • + H2O2 are important

21

consumption channels for C6H5CH3, particularily in low temperature combustion

22

process, when the concentration of OH, H, O and CH3 radicals is lower than that of

23

HO2. In H-abstraction from phenyl ring, postreaction van der Waals complexes exist.

24

We assume that these postreaction van der Waals complexes will dissociate to o-, m-

25

and p- C6H4CH3 + H2O2 rapidly, once formed and we thus treat this reactions as

26

proceeding directly from C6H5CH3 + HO2 to C6H4CH3 + H2O2, via the homologous

27

transition structures. This treatment has also been adopted by Silva et al. in a similar

28

situation.50 The present values of kHO2-CH3 are a little bit smaller than experimental

29

values by Scott et al.34 and Eng et al.33 As for kHO2-ring, our calculated values are larger

30

than the estimated data by Bounaceur et al.,1 while similar to recommended values 11



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

given by Baulch et al.48

2

3.3 Branching Ratios

3

Branching ratios are important to understand details of combustion chemistry. They

4

have been determined in temperature range of 300-2000 K for all possible product

5

channels and demonstrated in Figure 1. Bond energy C-H in methyl group is smaller

6

than that on the phenyl ring of toluene and the channel to produce C6H5CH2 is thus

7

always more important than those to produce C6H4CH3 at low temperature. However,

8

at high temperatures, the channel of H-abstraction from the phenyl ring becomes more

9

important for OH and O, while the channel of H-abstraction from the methyl group is

10

always more important for the other abstracting reactant in this temperature range.

11

This is because the reaction barriers of H-abstraction from the phenyl ring by OH and

12

O and smaller than those by the other abstracting reactant. Rate constants of

13

H-abstraction from the phenyl ring by OH and O becomes larger than those from the

14

methyl group at high temperautres. As for H-abstraction from the phenyl ring,

15

H-abstraction from the ortho-site is always the least important channel. Furthermore,

16

differences in braching ratios between H-abstrion from ortho-, meta- and para-

17

positions are the most significant for OH and O, while their differences are not as

18

pronounced for the other abstracting reactants, although reaction barrier for these

19

three channels are rather similar.

20

3.4 Kinetic Modeling

21

In order to investigate effects of rate constants of these reactions on combustion

22

properties of toluene, rate constants for these reactions in oxidation mechanisms of

23

toluene provided by Andrae6 are replaced by the present values. Reaction rate

24

constants of R1-1 and C6H5CH3 + OH → C6H4CH3 + H2O in Andrae’s mechanism are

25

taken from Seta’s data.15 Rate constants of R1-1 in Andrae’s mechanism are about 3

26

times larger than our calculated values. For C6H5CH3 + OH → C6H4CH3 + H2O, the

27

present rate constants are lower than those given by Seta et al. at low temperatures,

28

while they are larger at higher tempertures.15 Experimental rate constants provided by

29

Oehlschlaeger et al.21 and Hoffmann et al.24 for R2-1 and R3-1 are employed in

30

Andrae’s mechanism. The present rate constants for R2-1 and R3-1 are in reasonable 12


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1

agreement with those used Andrae’s mechanism. Rate constants of the other

2

H-abstraction reactions in Andrae’s mechanism are mostly estimated from similar

3

reactions48. Ignition delay time in a rapid compression machine(RCM) as well as in a

4

shock tube, mole fraction of toluene in variable pressure flow reactor (VPFR) and

5

Jet-stirred reactor (JSR) model and laminar flame speed in combustion of toluene

6

have been simulated with CHEMKIN 2.051 with the original Andrae’s mechanism6

7

and the revised mechanism. Simulation results are presented in Figs. 2-6.

8

One can see from Figs 2 and 3 that ignition times with revised mechanism are

9

always larger than those using the original mechanism. Revised mechanism provide

10

ignition delay times in RCM that are in better agreement with experimental data52 at

11

low temperatures, while the original mechanism affords better ignition delay times at

12

high temperatures. On the other hand, experimental ignition delay times mostly lie

13

between the predicted values with these two mechanisms in shock tube53. Brute-force

14

sensitivity analysis is carried out to understand effects of these H-abstraction reactions

15

on ignition delay of toluene based on the original mechanism under the condition of

16

equivalence ratio equal of 1.0, initial temperature at 1000 K, pressure at 45 atm. The

17

most two important reactions that promote ignition of toluene at 1000 K are C6H5CH2

18

+ HO2 = C6H5CH2O + OH, H + O2 + N2 = HO2 + N2. This indicates that C6H5CH2 is

19

rather important on ignition delay time for toluene. C6H5CH2 is produced mainly

20

through H-abstraction reactions R1-1 and R2-1. Rate constants of R1-1 in the original

21

mechanism are larger than the present values. It is thus understandable that predicted

22

ignition delay times with the present rate constants will be larger than those with the

23

original mechanism.

24

As for mole fraction of toluene in VPFR and JSR demonstrated in Figs. 4-5, one

25

can see that consumption of toluene is much slower with the revised mechanism that

26

that with the original mechanism. Furthermore, mole fractions of toluene with the

27

revised mechanism provide are in better agreement with experimental data2,54. This is

28

consistent with the fact that rate constant R1-1, which is one of the most important

29

reaction in consumption of toluene, in the original mechanism is larger than the

30

present value. Laminar burning velocities with the original and revised mechanisms as 13



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

well as experimental data55 are illustrated in Figure 6. One can see from this figure

2

that reaction rate constants of these H-abstraction reactions do not affect Laminar

3

burning velocities much. Sensitivity analysis of Laminar burning velocities was

4

carried out based on original mechanism, H + O2 = O + OH and CO + OH = CO2 + H

5

are the most important two reactions that promote flame speed increase. These

6

H-abstraction reactions thus have limited effect on Laminar burning velocities of

7

toluene.

8

It should be noted that reaction mechanism of toluene combustion is highly

9

complicated. Besides these key H-abstraction reactions, may other reactions also play

10

important roles in combustion properties of toluene, such as sub mechanism of benzyl

11

or methylphenyl, C0-C4 core mechanism. Furthermore, effect of rate constants of

12

these H-abstraction reactions on combustion properties also depends on rate constants

13

of other reactions. This means using the present rate constants in other toluene

14

combustion mechanisms may result in different effects from what has been shown

15

with Andrae’s mechanism. To achieve reasonable description on combustion

16

properties of toluene, reliable reaction constants for all the important reactions are

17

required.

18

4 Conclusions

19

Rate constants of H-abstraction reaction from toluene by OH, H, O, CH3 and HO2

20

radicals have been investigated in this work. G4 theory is employed to locate

21

stationary points on potential surfaces of the involved reactions and to calculate

22

vibrational frequencies as well as thermodynamic properties. The obtained enthalpies

23

of formation of components agree well with available experiment data. Rate constants

24

are obtained using the TST theory with the tunneling effect taken into considered.

25

Rate constants obtained in this work are in reasonable agreement with available

26

previous experimental and theoretical results. The three-parameter modified Arrhenius

27

expression is employed to express the obtained reaction rate constants in the

28

temperature range of 300-2000 K, which facilitate their application in combustion

29

mechanisms. Branching ratios for these reactions are determined based on the

14


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1

obtained reaction rate constants. Relative importance between H-abstraction from the

2

methyl group and that from the phenyl ring at different temperature by different

3

H-abstracting reactant are clarified. The obtained reaction rate constants are employed

4

in the combustion mechanism of toluene developed by Andrae. Ignition delay times in

5

RCM and shock tube, mole fraction on toluene in VPSR and JSR as well as laminar

6

flame speeds are simulated with the revised mechanism. The results show that with

7

the new reaction rate constants, the obtained combustion properties of toluene are

8

improved to some extent. It should be noted that the investigated combustion

9

properties also depend critically on other reactions and using these reaction rates

10

together with the other combustion mechanism of toluene may not necessarily

11

improve performance of the combustion mechanism.

12

ACKNOWLEDGMENT

13

This work is supported by the National Natural Science Foundation of China (No.

14

91441132). We acknowledge National Supercomputing Center in Shenzhen for

15

providing the computational resources and Gaussian software.

16

Supporting Information Available

17

All of the geometries of reactants, transition states and products used in calculating

18

rate constants have been included. Predicted thermochemical properties of stable

19

species and rate constants expressions in CHEMKIN format are given in supporting

20

information.

21

REFERENCES

22

(1) Bounaceur, R.; Da Costa, I.; Fournet, R.; Billaud, F.; Battin-Leclerc F. Experimental and modeling

23 24 25

study of the oxidation of toluene. Int. J. Chem. Kinet. 2005, 37, 25˗49. (2) Metcalfe W. K.; Dooley S.; Dryer F. L. Comprehensive detailed chemical kinetic modeling study of toluene oxidation. Energy Fuels 2011, 25, 4915˗4936.

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(5) Narayanaswamy, K., Blanquart, G., Pitsch, H. A consistent chemical mechanism for oxidation of substituted aromatic species. Combust. Flame, 2010, 157, 1879˗1898. (6) Andrae J.C.G. Comprehensive chemical kinetic modeling of toluene reference fuels oxidation, Fuel 2013, 107,740˗748.

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(7) Yuan, W.; Li, Y.; Dagaut, P.; Yang, J.; Qi, F. Investigation on the pyrolysis and oxidation of

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hydroxyl radicals with aromatic hydrocarbons over the temperature range 296-473 K. J. Phys.

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Chem. 1977, 81, 296˗304.

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(9) Kenley, R. A.; Davenport, J. E.; Hendry, D. G. Gas-phase hydroxyl radical reactions. Products and

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Wine, P. H. Kinetics of the reactions of hydroxyl radical with benzene and toluene. J. Phys. Chem.

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(13) Markert, F.; Pagsberg, P. UV spectra and kinetics of radicals produced in the gas phase reactions of Cl, F and OH with toluene. Chem. Phys. Lett. 1993, 209, 445˗454.

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other elementary reactions involved. Combust. Flame 2003, 132, 291˗304.

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(17) Rao, V. S.; Skinner, G. B. Formation of hydrogen and deuterium atoms in the pyrolysis of

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toluene-d8 and toluene-. alpha.,. alpha.,. alpha.-d3 behind shock waves. J. Phys. Chem., 1989, 93,

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Elsevier, 1989, 22, 1053˗1061.

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(19) Robaugh, D.; Tsang, W. Mechanism and rate of hydrogen atom attack on toluene at high temperatures. J. Phys. Chem. 1986,90, 4159˗4163. (20) Hippler, H.; Reihs, C.; Troe, J. Elementary steps in the pyrolysis of toluene and benzyl radicals. Zeitschrift für Physikalische Chemie 1990, 167, 1˗16. (21) Oehlschlaeger, M. A.; Davidson, D. F.; Hanson, R. K. Experimental investigation of toluene+ H→ benzyl+ H2 at high temperatures. J. Phys. Chem. A 2006, 110, 9867˗9873.

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compounds in the gaseous phase. I. Kinetics of the reaction of methyl radicals with toluene. Aust.

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radicals and the pressure dependence of the recombination of methyl radicals. Can. J. Chem. 1970,

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48, 1269˗1272.

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benzene, toluene, and cyclopentane by methyl and ethyl radicals over the temperature range

8

650-770 K. Can. J. Chem. 1989, 67, 1541˗1549.

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(31) Szwarc, M.; Roberts, J. S. The activation energy and the steric factor of the reaction between methyl radicals and toluene. Transactions of the Faraday Society, 1950, 46, 625˗629.

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atmosphere. The effect of added toluene. Recueil des Travaux Chimiques des Pays-Bas 1984, 103,

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and 1400 K. Symposium (International) on Combustion, Elsevier. 1998, 27, 211˗218.

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Internal Rotation I. Rigid Frams with Attached Tops. J. Chem. Phys. 1942, 10, 428˗440.

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(40) J. W. Ochterski, Thermochenistry in Gaussian, Gaussian, Inc. 2000.

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Hall: New York, 1999. (47) NIST. Computational Chemistry Comparison and Benchmark Database; NIST Standard Reference Database Number 101, 2013,available at http://webbook.nist.gov/.

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M. J.; Troe J.; Walker R.W.; Warnatz J. Summary table of evaluated kinetic data for combustion

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modeling: Supplement 1. Combust. Flame 1994, 98, 59˗79.

18

(49) Luo, Y. R. Handbook of bond dissociation energies in organic compounds. CRC press. 2002.

19

(50) da Silva, G.; Bozzelli, J. W. Kinetic Modeling of the Benzyl +HO2 Reaction. Proc. Combust. Inst

20

2009, 32, 287˗294.

21

(51) Kee R. J. , Rupley F. M. , Miller J. A. , Chemkin-II: A FORTRAN Chemical Kinetics Package for

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the Analysis of Gas-Phase Chemical Kinetics, Sandia Report, SAND89-8009, Sandia National

23

Laboratories, 1989.

24 25 26 27 28 29 30

(52) Mittal G.; Sung C. J. Autoignition of toluene and benzene at elevated pressures in a rapid compression machine. Combust Flame 2007, 150, 355˗68. (53) Shen, H. P. S.; Vanderover, J.; Oehlschlaeger, M. A. A shock tube study of the autoignition of toluene/air mixtures at high pressures. Proc. Combust. Inst. 2009, 32, 165˗72. (54) Dagaut, P.; Pengloan, G.; Ristori, A. Oxidation, ignition and combustion of toluene: Experimental and detailed chemical kinetic modeling. Phys. Chem. Chem. Phys. 2002, 4, 1846˗1854. (55) Johnston, R. J.; Farrell, J. T. Laminar burning velocities and Markstein lengths of aromatics at 19



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1

elevated temperature and pressure. Proc. Combust. Inst. 2005, 30, 217˗24.

2

20


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1 2

TABLE Table 1. Standard enthalpies of formation ( ∆ f H

θ

(298K) , kcal mol-1) for reactants and products

Species

Calculated

Experimental47

Species

Calculated

Experimental47

H

52.10

52.10

CH3

34.52

35.06

O

59.43

59.57

CH4

-17.87

-17.83

OH

8.64

8.93

C6H5CH3

11.99

11.95

H2

-0.34

0.00

C6H5CH2

49.71

49.71

HO2

2.99

2.94

o-C6H4CH3

72.11

---

H2O2

-31.68

-32.45

m-C6H4CH3

72.15

---

H2O

-57.38

-57.79

p-C6H4CH3

72.69

---

3 4

21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

Page 22 of 30

Table 2. Relative energies of transtion states and products systems Reactants

Transition-state

Products

(kcal mol-1) C6H5CH3+OH

C6H5CH3+H

C6H5CH3+O

C6H5CH3+CH3

Reactants

C6H5CH3+HO2

(kcal mol-1)

TSOH-CH3

1.2

C6H5CH2+H2O

-28.5

TSOH-o

3.2

o-C6H4CH3+H2O

-6.2

TSOH-m

3.5

m-C6H4CH3+H2O

-6.1

TSOH-p

3.6

p-C6H4CH3+H2O

-5.6

TSH-CH3

5.9

C6H5CH2+H2

-15.2

TSH-o

15.2

o-C6H4CH3+H2

7.1

TSH-m

15.3

m-C6H4CH3+H2

7.2

TSH-p

15.6

p-C6H4CH3+H2

7.7

TSO-CH3

4.2

C6H5CH2+OH

-13.6

TSO-o

9.6

o-C6H4CH3+OH

8.7

TSO-m

9.7

m-C6H4CH3+OH

8.8

TSO-p

10.0

p-C6H4CH3+OH

9.3

TSCH3-CH3

10.2

C6H5CH2+CH4

-14.2

TSCH3-o

16.3

o-C6H4CH3+CH4

7.8

TSCH3-m

16.6

m-C6H4CH3+CH4

7.9

TSCH3-p

16.8

p-C6H4CH3+CH4

8.5

Transition states

Complexes

Products

(kcal mol-1)

(kcal mol-1)

(kcal mol-1)

TSHO2-CH3

13.5

---

---

C6H5CH2+H2O2

2.8

TSHO2-o

22.7

CPHO2-o

21.3

o-C6H4CH3+H2O2

25.1

TSHO2-m

23.3

CPHO2-m

21.4

m-C6H4CH3+H2O2

25.2

TSHO2-p

23.7

CPHO2-p

22.1

p-C6H4CH3+H2O2

25.7

2 3

22


Page 23 of 30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

Table 3. Modified Arrhenius parameters for H-Abstraction reactions of toluene fitted in the

2

temperature of 300-2000 K(unit: A(cm3 molecule-1 s-1), Ea(cal)). Reactions

A

n

Ea

Reactions

A

n

Ea

kOH-CH3

130169.1

2.28048

-572.972

kH-CH3

1.07E+06

2.26764

4392.371

kOH-o

277.7315

2.99789

1245.721

kH-o

3.21E+07

1.81483

14155.56

kOH-m

819.6653

3.09594

1507.708

kH-m

1.11E+08

1.80464

14389.02

kOH-p

763.895

3.10443

1688.651

kH-p

1.05E+08

1.81188

14672.52

kOH-ring

1747.54

3.09666

1548.924

kH-ring

2.00E+08

1.83443

14381.82

kO-CH3

75372.24

2.57378

3145.746

kCH3-CH3

2.55836

3.80712

7395.743

kO-o

281049.1

2.41207

8837.35

kCH3-o

91.44079

3.28308

14233.33

kO-m

1.16E+06

2.44202

9052.875

kCH3-m

197.2672

3.28482

14542.45

kO-p

1.57E+06

2.40693

9440.521

kCH3-p

204.9017

3.30806

14723.92

kO-ring

2.57E+06

2.44074

9143.372

kCH3-ring

537.7265

3.28445

14601.08

kHO2-CH3

0.00788

4.29278

11250.72

k HO2-o

1.71418

3.64569

21743.27

k HO2-m

3.02029

3.64209

22208.17

k HO2-p

3.79741

3.6191

22697.45

k HO2-ring

7.60247

3.64626

22222.04

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

23



1

FIGURE

2 1.2

C6H5CH2+H2O

1.0

m-C6H4CH3+H2O

(b) C6H5CH3+H

0.8

p-C6H4CH3+H2O

0.8

Branching Ratios

Branching Ratios

(a) C6H5CH3+OH

o-C6H4CH3+H2O

1.0

C6H4CH3+H2O

0.6 0.4

C6H5CH2+H2 o-C6H4CH3+H2

0.6

m-C6H4CH3+H2 p-C6H4CH3+H2

0.4

C6H4CH3+H2

0.2

0.2 0.0

0.0 400

600

800

1000

3

1200

1400

1600

1800

2000

400

800

1000

1200

1400

1600

1800

(d) C6H5CH3+CH3

1.0

(c) C6H5CH3 + O

0.8

0.8

0.6

Branching Ratios

C6H5CH2+OH o-C6H4CH3+OH m-C6H4CH3+OH p-C6H4CH3+OH

0.4

C6H4CH3+OH

C6H5CH2+CH4 o-C6H4CH3+CH4

0.6

m-C6H4CH3+CH4 p-C6H4CH3+CH4

0.4

C6H4CH3+CH4 0.2

0.2

0.0

0.0 400

600

800

1000

1200

1400

1600

1800

2000

400

600

800

1000

T (K)

1400

1600

1800

(e) C6H5CH3+HO2


1200 T (K)

1.0 C6H5CH2+H2O2 o-C6H4CH3+H2O2 0.6

m-C6H4CH3+H2O2 p-C6H4CH3+H2O2

0.4

C6H4CH3+H2O2

0.2 0.0 400

5 6

2000

T (K)

1.0

4

600

T (K)

Branching Ratios

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 30

600

800

1000

1200

1400

1600

1800

2000

T (K)

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

7 8 9 10

24


2000

Page 25 of 30

1

-1

10 Ignition Delay Time, sec

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-2

10

-3

10

φ = 1.0 φ = 0.5

Εxp Εxp

Andrae's mechanism Andrae's mechanism

revised mechanism revised mechanism

-4

10 0.90

0.95

1.00

1.05

1.10

1000/T (1/K)

2 3

Figure 2. Ignition delay for toluene/O2/N2/Ar mixtures in a rapid compression machine at p = 45 atm

4

and mole fraction toluene = 0.00962. Symbols – experimental data by Mittal and Sung.52 line and

5

dashed line are model predictions.

6

25



1 2

-2

10 Ignition delay time (sec)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 30

-3

10

Exp Andrae's mechanism revised mechanism

-4

10

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1000/T (1/K)

3 4

Figure 3. Shock tube ignition delay for toluene/air at 12 atm, equivalence ratio equal of 1.0. Symbols –

5

experiment by Shen et al.53 line and dashed line are model predictions.

6

26


Page 27 of 30

1

0.0016 C6H5CH3

0.0014 0.0012 Mole fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.0010 0.0008 0.0006 0.0004 0.0002 0.0000 0.0

Exp Andrae's mechanism revised mechanism 0.5

1.0

1.5

2.0

2.5

Time (sec)

2 3

Figure 4. Oxidation of toluene in variable pressure flow reactor. 0.14% C6H5CH3 in N2, ϕ = 0.977, T =

4

920 K, p = 12.5 atm. Symbols – experiments by Metcalfe et al..2 line and dashed line are model

5

predictions.

6

27



1

0.0016

Experiment revised mechanism Andrae's mechanism

0.0014 0.0012

Mole fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 30

0.0010 0.0008 0.0006 0.0004 0.0002 0.0000 1100

1150

1200

1250

1300

1350

1400

T (K) 2 3

Figure 5. Jet-stirred reactor species concentration profiles of 0.15% C6H5CH3, in N2, ϕ = 1.0, p = 1.0

4

atm, and residence time (τ) = 0.1 s. Symbols are experimental data,54 line and dashed line are model

5

predictions.

6

28


Page 29 of 30

1

60 Laminar burning velocity (cm/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


50 40 30 20

Exp Andrae's mechanism revised mechanism

10 0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

Equivalence ratio

2 3

Figure 6. Laminar burning velocities of the C6H5CH3/air mixture as a function of the equivalence ratio

4

at 3 atm, 450 K, symbols are experimental data;55 line and dashed line are model predictions.

5

29



TOC Graphic

1 1.2

C6H5CH2+H2O

C6H5CH3+OH

o-C6H4CH3+H2O


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 30

m-C6H4CH3+H2O p-C6H4CH3+H2O

0.8

C6H4CH3+H2O

0.6 0.4 0.2 0.0 400

600

800

1000

2

1200 T (K)

1400

1600

3

30


1800

2000

Theoretical Prediction of Rate Constants for ... - ACS Publications

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