Article pubs.acs.org/JPCA

Temperature and Pressure Dependent Rate Coefficients for the Reaction of C2H4 + HO2 on the C2H4O2H Potential Energy Surface JunJiang Guo,† JiaQi Xu,‡ ZeRong Li,‡ NingXin Tan,*,† and XiangYuan Li*,† †

College of Chemical Engineering, Sichuan University, Chengdu 610065, P.R. China College of Chemistry, Sichuan University, Chengdu 610064, P.R. China

‡

S Supporting Information *

ABSTRACT: The potential energy surface (PES) for reaction C2H4 + HO2 was examined by using the quantum chemical methods. All rates were determined computationally using the CBS-QB3 composite method combined with conventional transition state theory(TST), variational transition-state theory (VTST) and Rice−Ramsberger−Kassel−Marcus/ master-equation (RRKM/ME) theory. The geometries optimization and the vibrational frequency analysis of reactants, transition states, and products were performed at the B3LYP/CBSB7 level. The composite CBS-QB3 method was applied for energy calculations. The major product channel of reaction C2H4 + HO2 is the formation C2H4O2H via an OH···π complex with 3.7 kcal/mol binding energy which exhibits negativetemperature dependence. We further investigated the reactions related to this complex, which were ignored in previous studies. Thermochemical properties of the species involved in the reactions were determined using the CBS-QB3 method, and enthalpies of formation of species were compared with literature values. The calculated rate constants are in good agreement with those available from literature and given in modified Arrhenius equation form, which are serviceable in combustion modeling of hydrocarbons. Finally, in order to illustrate the effect for low-temperature ignition of our new rate constants, we have implemented them into the existing mechanisms, which can predict ethylene ignition in a shock tube with better performance.

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shock tubes10−12 and premixed laminar flames3 covering a wide range of temperatures and pressures. Meanwhile, many theoretical researches have been paid on C2H4 with OH13−16 and O2.17−21 But there still have few studies focused on the reaction of C2H4 with HO2. It is well know that reactions involved in HO2 radical are typically slow due to its low activity. However, because of its high concentration in the lowtemperature preignition regime, even relatively slow reactions involving HO2 can have significant effect in combustion process especially in low-temperature combustion chemistry.3,22 Furthermore, C2H4 + HO2 reaction is important at high pressure and an accurate determination of the rate constant and branching fraction is desirable.9 Skancke and co-worker23 investigated the parts of the potential surface for the system of C2H4 + HO2 based on ab initio studies, which optimized geometries at the UHF/6-31G* level and followed by UMP2 and UMP4/6-31G* energy calculations. They found that the products oxirane and OH would be obtained with a two-step pathway going through an intermediate C2H4O2H. Chen and Bozzelli24 calculated rate constants, varying with both temperature and pressure calculated by QRRK/master equation

INTRODUCTION Combustion is common in the world and plays a critical role in power source and engineering science. Great efforts have been invested to explore combustion processes of practical fuels for clean energy and engine design. Hydrocarbons, being the critical source of energy, are by far and away the best studied class of compounds for which reliable and detailed chemical kinetic models for combustion exist.1,2 Ethylene is one of the preferred products resulting from thermal cracking of higher hydrocarbons under certain conditions.3,4 And it is one of the key intermediates in combustion of hydrocarbon fuels5 and has been received a wide research interest. Because of its high reactivity, it usually has been used to simulate cracked hydrocarbon fuels to test combustors for hypersonic propulsion systems.6 In addition to supplying propulsive power, hydrocarbon fuels must precede thermal cracking and catalytic cracking to generate a larger heat sink before going into the combustion chamber.7 Moreover, since ethylene is identified as an important precursor of soot,8 it is necessary to study the ethylene chemistry to reduce pollutant emission in combustion process. Ethylene has received increasing attention in recent years because of its importance in combustion of hydrocarbon fuels. A considerable amount of experiments have been conducted for C2H4 oxidation in flow reactors,9 rapid compression machine,3 © 2015 American Chemical Society

Received: December 1, 2014 Revised: March 15, 2015 Published: March 16, 2015 3161

DOI: 10.1021/jp511991n J. Phys. Chem. A 2015, 119, 3161−3170

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The Journal of Physical Chemistry A

O, respectively. Thermochemical properties (Δf Hθ, Δf Sθ, and Cp) are evaluated from standard enthalpies of formation, vibrational frequencies, and moments of inertia, according to statistical mechanical principles employing the ChemRate program.35 Usually, low-frequency internal rotations treated by the harmonic oscillator (HO) approximation can lead to significant errors in the partition function. Vansteenkiste et al.36 found that treating hindered internal rotations is crucial to get accurate entropies and heat capacities. Therefore, the onedimensional (1-D) hindered internal rotor method37 was applied to estimate the contributions of low-frequency torsional motions in the partition functions calculation. Internal rotor potentials were calculated by relaxed scans of the dihedral angle with an interval of 5° at the B3LYP/CBSB7 level, to determine the barrier height of rotation, number of rotational minima, and symmetry number. In this study, the low-frequency vibrational modes corresponding to internal rotation around the breaking bonds for barrierless reactions were assumed as free rotors. The method proposed by Pitzer and Gwinn37 in ChemRate was applied to compute reduced moments of inertia rotations for each species using the geometries calculated at the B3LYP/ CBSB7 level. Rate Constant Calculations. The high-pressure-limit(HPL) rate constants for reactions with pronounced barriers were calculated according to canonical transition state theory(TST), and HPL rate constants for barrierless reactions were treated using variational transition state theory(VTST). The pressure-dependent rate constants were computed with the time-dependent RRKM/ME method at the pressures varying from 0.01 to 100 atm. All elementary reactions were calculated in ChemRate program.35 In the present work, the VTST computation method proposed by da Silva et al.38 was employed to deal with the reaction channels without apparent transition state. In the VTST approach, the rate constants was obtained by constructing minimum energy points(MEP) along the assigned reaction coordinate. Thermochemical parameters were obtained at each point along the MEP for all barrierless reactions in ChemRate. In the VTST formalism, the reaction rate constants were minimized as a function of reaction coordinate (s) and temperature (T):

analysis, of several important reactions for alkene + HO2 system at the CBS-q//MP2(full)/6-31G(d) level. Furthermore, Zádor et al.22 reported pressure- and temperature-dependent alkene + HO2 rate constants basing on QCISD(T) calculations with slightly adjusted to better reproduce the experimental data of Taatjes and co-workers.25,26 These results indicate that the relative importance of these reaction channels relies heavily on the structure of the olefin. Villano et al.27 proposed rate rules and branching ratios for the concerted addition and radical addition pathways that result from the reaction of olefins with HO2. It is found that the resulting coefficients for the various channels of the radical addition reaction were quite sensitive to pressure, and falloff effects were predicted over an extended range of pressures that are relevant to most combustion applications.27 These theoretical studies all just give several reaction channels for C2H4 + HO2 system which are incomplete to describe C2H4 oxidation in low temperature. Though those reactions containing HO2 radicals are critical to predict the ignition behavior for ethylene combustion in the low-temperature chemistry,3 only a few of them appeared in popular combustion mechanisms. Moreover, a detailed kinetic model is a valuable design tool to describe the low-temperature oxidation of hydrocarbon fuels, which can be used to improve the efficiency and emissions of internal combustion engines. Therefore, it is necessary to make a detailed investigation for C2H4 + HO2 system. The objective of the present work is to investigate the mechanism and kinetics of reactions C2H4 + HO2 on the C2H4O2H potential energy surface by means of quantum chemical calculations and to obtain accurate rate constants for these reactions at different temperatures and pressures, which are useful in the chemical kinetic modeling of hydrocarbons combustion process. To explicitly test the effect of our calculated rate coefficients, we compared the ignition delay times for ethylene combustion in Ar mixture between the experimental data and simulation results of several ethylene mechanisms.

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COMPUTATIONAL DETAILS Potential Energy Surface Calculations. The potential energy surface and molecular properties of stationary points were performed by the Gaussian 03 quantum chemistry package.28 In all case, the geometries, frequencies(scaled by a factor 0.99), and hindering potentials involved in the reaction schemes were calculated at the B3LYP/CBSB7 level, while the single point energy were corrected by a series of high accuracy methods including a complete basis set extrapolation in the CBS-QB329 composite method. This composite method is able to precisely predict thermochemical and kinetic data for hydrocarbon fuels combustion.30−33 All the transition-state structures were confirmed with one and only one single imaginary frequency. Moreover, intrinsic reaction coordinate(IRC)34 calculations were carried out in all case to verify that the transition-state structure connected with the corresponding reactant and product. Calculated molecular geometries (in Cartesian coordinates), and vibrational frequencies are provided in Supporting Information for all stationary points. Thermochemical Properties. Standard enthalpies of formation (Δf Hθ(298 K),kcal/mol) have been calculated for all minima and transition states in this paper. The values of Δf Hθ(298 K) are determined at the CBS-QB3 level using atomization method. The experimental values of Δf Hθ(0K) are 169.98, 51.63, and 58.99 kcal/mol for the elements C, H, and

VTST

TST

k(T ) = min k(T , s)

(1)

TST

where k denotes the reaction rate constant from the TST. All the transition-state structures used in the VTST calculations have only one imaginary frequency with the mode of vibration corresponding to C−C, C−O, O−O or C−H bond scission. Basing on RRKM theory implemented in ChemRate program, the pressure-dependent reaction rate constants were calculated by ⎛ G+(E) ⎞ k(E) = l +⎜ ⎟ ⎝ hN (E + E0) ⎠

(2)

+

where G (E) is the total number of states of the transition state, up to and including E, l+ is the reaction path degeneracy, N(E +E0) and h denote, respectively, the density of states of the reactant at energy E+E0 and the Planck constant. In the RRKM calculations the density and sum of states were got by the direct count algorithm of Beyer and Swinehart.39 The one-dimensional Eckart transmission coefficients have been calculated for those reactions involved in H atom transfer 3162

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Figure 1. Schematic energy profile for C2H4 + HO2 reaction system. Relative energies are those at the CBS-QB3 level and the energy scale is kcal/ mol.

Information, Table S1. As in the present calculation reported above, internal rotations in all species were treated as hindered rotors rather than harmonic oscillators in the calculations of standard entropies and heat capacities. Enthalpies of formation of species in this work show good agreement with literature values.46,52 Reaction Mechanisms. As shown in Figure 1, The main reaction path takes place without a barrier to produce a van der Waals complex (C1) with exothermicity of 3.7 kcal/mol as calculated at the CBS-QB3 level in good agreement with those from Ignatyev et al.48 (2.8 kcal/mol at the B3LYP/TZ2PF level) and Miller et al.49 (3.9 kcal/mol at the G2-like//B3LYP/ 6-311++G(d,p) level), respectively. That is similar to C2H4 + OH system, which will also form a van der Waals complex(HO···C 2H4) with a binding energies of 1.9 kcal/mol investigated by Zhu et al.14 at the PMP2/aug-cc-PVQZ// MP2/cc-PVTZ level and Senosiain et al.15 at the RQCIT/QCI level. However, most of researches have ignored this van der Waals complex especially in kinetic calculation,24,27,46,50,51 which has an effect on the total rate constants.14 In the present work, a range of isomerization and decomposition routes are available from this van der Waals complex. C1 mainly proceed along two distinct pathways: through the concerted addition reaction to form an ethylperoxy radical (C2H5O2) and through the radical addition channel to form ethylhydroperoxy radical (C2H4O2H). These two reactions have 14.2 and 16.2 kcal/mol barrier height, respectively. The most difficult step for C1 channels is H abstraction reaction to produce C2H5 + O2, because the calculated barrier (32.3 kcal/mol) is much higher than that of the other two reactions. The most energetic reaction channel for C2H4O2H is broken down into OH + CH2OCH2 with a barrier of 13.9 kcal/mol, which have some difference of that from Miller et al. (16.4 kcal/mol at the G2like//B3LYP/6-311++G(d,p) level). The main reason is that some of the structures in Figure 1 have more than one conformation. In this case we have adopted the energy of the most stable conformation, with the implicit assumption that

by using ChemRate program to estimate quantum mechanical tunneling corrections. The characteristic length of the Eckart function was obtained using the equations reported by Johnston and Heicklen40 with the parameters such as the imaginary frequency of the transition state and barrier height. Lennard-Jones parameters σ and ε are used to estimate the collision frequency between reactant and bath gas, which are taken from the JetSurF version 1.1 transport database41 and literature data reported by Hippler et al.42 Argon is used as a bath gas collider with values of σ = 3.47 Å, and ε = 114 K. The collision energy transfer is applied using a single-parameter exponential down model43 with ⟨ΔEdown⟩=200 cm−1 for all the calculations. This function form is reasonable, and similar form has been used in previous study of Zhu et al.,14 Zádor et al.,22 Silva et al.,44 Ding et al.,45 and Sheng et al.46 All calculations were carried out with a series of energy grain sizes and variations in the maximum system energy to ensure that the results have converged. Rate constants from 300 to 2000 K were fit to an modified empirical three-parameters form of the Arrhenius equation (eq 3) to obtain the elementary rate parameters A, n, and Ea k = AT n( −Ea /RT )

(3) n

All pre-exponential terms (AT ) quoted in this study are in units of s−1 (first order) or cm3 mol−1 s−1 (second order), with all temperatures in K.

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RESULTS AND DISCUSSION C2H4O2H Potential Energy Surface. The C2H4O2H potential energy surface(PES) for C2H4 + HO2 reactions at the CBS-QB3 level is presented in Figure 1. It is found that some channels marked in blue are also very important in lowtemperature oxidation in C2H5 + O2 reaction system taking place on C2H5O2 potential energy surface.46−51 For practical applications in hydrocarbon combustion, the enthalpies of formation, entropies and heat capacities of species involved in C2H4 + HO2 reaction are presented in the Supporting 3163

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The Journal of Physical Chemistry A conformational rearrangements are rapid compared with chemical reactions and are thus treated as internal rotations calculated in this work. Another dissociation channel, produced OH + CH3CHO products, is quite important for ignition with a barrier calculated to be 31.0 kcal/mol. C2H4O2H can also isomerize to C2H5O2 and CH2OCH2OH, respectively. The conversion of C2H4O2H to C2H5O2 occurs via a 5-member ring transition state(TS5) with a barrier of 19.1 kcal/mol. And the new reaction intermediate CH2OCH2OH is produced by the terminal OH group rotation and transfer to the second C atom with a barrier of 30.7 kcal/mol at the CBS-QB3 level. As an important intermediate in the C2H5 + O2 system, C2H5O2 has a big effect on low-temperature chemistry for hydrocarbon fuels. It can break C−C and O−O bond to form CH3 + CH2O2 and C2H5O + O. These two decomposition reactions have 64.4 and 61.4 kcal/mol barrier heights, respectively. C2H5O2, similar to C2H4O2H, can also produce OH + CH3CHO via a 4-member ring transition state(TS8) with a barrier 41.2 kcal/mol, which is also important for ignition because of the formation of OH. CH2OCH2OH is a new intermediate found in the C2H4 + HO2 system. There are three different pathways relevant to CH2OCH2OH, which include the −H2O elimination, −OH elimination and isomerization through 1,3 H-shift followed by −H elimination, which produce several stable species. For example, it can decompose to give CH2CHO + H2O through a 4-member ring transition state (TS11) with a barrier 38.0 kcal/ mol. It also can directly break C···O−H bond to produce OH + CH2OCH2 to contribute to ignition. And the favorable consecutive two steps for CH2OCH2OH reaction, first to isomerize and then decompose, have a lower activation of 26.5 kcal/mol compared to another two channels. Comparison of previous studies and current work about the heat of reaction, reaction heights and wells for the elementary reactions of C2H4 + HO2 system is available in Table S2 in the Supporting Information. Rate Constants for Barrierless Reactions. The main barrierless reactions for the C2H4 + HO2 reaction mechanism are listed in as follows: C1 → C2H4 + HO2

(4)

C2H5O2 → C2H5 + O2

(5)

C2H5O2 → C2H5O + O

(6)

C2H5O2 → CH3 + CH 2O2

(7)

CH 2OHCHOH → CHOHCHOH + H

(8)

Figure 2. Relaxed potential energy surface scan for C−O bond cleavage of C1 at the B3LYP/CBSB7 level.

of C1 along the reaction coordinate as an example of VTST calculation. For the C1 dissociation reaction, we found that the transition occurs at the 6.738 Å at pressures from 0.01 atm to HPL. Figure 3 displays the calculated rate constants in the temperature range from 300 to 2000 K, and the pressure varying from 0.01 atm to HPL.

Figure 3. Calculated rate constants at different pressures for reaction C1 → C2H4 + HO2 in this work.

Employing the VTST calculation method, rate constants for reactions that C2H5O2 dissociate to form C2H5 + O2, C2H5O + O and CH3 + CH2O2 have also been calculated. Similar to reaction 4, reaction 7, C2H5O2 → CH3 + CH2O2, is found to have a transition occur at the 2.516 Å at HPL. For reaction 5, C2H5O2 → C2H5 + O2, the location of the variational transition state is at a C−O bond length of 2.660 Å at 300−400 K and 2.691 Å at 500−2000K at HPL. And for reaction 6, C2H5O2 → C2H5O + O, we find that the transition state occurs at O−O bond of 2.510 Å at 300−1200K and 2.210 Å at 1300−2000K at HPL. Figure 4 displays the calculated rate constants in the temperature range 300−2000 K and with the pressure varying from 0.01 atm to HPL for reactions 5 and 6. These reactions correspond to decomposition are all pressure-dependent as shown in Figures 3 and 4. There is no theoretical calculation or experimental data available for reaction C1 → C2H4 + HO2. The results show this reaction seems extremely sensitive to pressures. And the rate constants nearly remain unchanged at pressures from 0.01 to 100 atm in the temperature regime above 600 K. A greater pressure effect is found on reaction C2H5O2 → C2H5 + O2 than others, e.g., C2H5O2 → C2H5O + O. Moreover, we find that the pressure effect becomes much more significant as the temperature increases for all these decomposition reactions. This implies that the pressure effect should not be neglected especially for

Because each of these reactions 4−8 does not have a welldefined transition state, the VTST calculation were used to calculate these barrierless reactions and the pressure-dependent rate constants were computed with the RRKM/ME method. The calculated rate constants of these decomposition reactions were compared with those available from literature. Similar to the C2H4 + OH reaction, the main reaction pathway for C2H4 + HO2 is first to form a prereaction van der Waals complex (C1). As shown in Figure 2, the dissociation potential function was calculated, which covered the range of C−O separations varying from 3.425 to 9.225 Å at the B3LYP/CBSB7 level. During this calculation, relaxed potential energy scan was performed. The resultant B3LYP/CBSB7 PES was then scaled to provide a more accurate single energy at the CBS-QB3 level. Table S3 lists calculated reaction rate constants in the temperature range of 300−2000K at the HPL of C−O scission 3164

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Figure 4. Calculated rate constants at different pressures for reaction(a) C2H5O2 → C2H5 + O2 and (b) C2H5O2 → C2H5O + O in this work.

CH2OCH2 + OH derived from Baulch et al.55 The rate constants about this reaction of Konnov et al.56 was estimated based on k for C2H6 + HO2C2H5 + H2O2 and made a correction for A and Ea to represent the difference between vinylic and primary C−H bond strengths.57 And the rate constants of this reaction contained in Dagaut’s mechanism58 were predicted on the basis of general rules.59 Comparison with kinetic data from Li et al.,54 Konnov et al.56(data from mechanism), and Dagaut et al.58(data from mechanism), it can be seen that the data in this work are consistent with those from Dagaut et al.58 in low-temperature range and much more closer to those from Li et al.54 in high-temperature range. As this bimolecular reaction ignored the pressure-dependent effect, the only HPL rate constants are calculated in this work and represented by the following expression:

high temperatures in combustion chemistry. Thus, pressure effects must be taken into account and the rate constants proposed in the Supporting Information are provided for use in kinetic models. It can be noted that a rather good agreement exists between our values and those from the literature46 at HPL as presented in Figure 4. As the computational accuracy is much higher, the rate constants calculated in this work should be regarded much more accurate. All the reaction rate constants for the barrierless reactions in the temperature range 300−2000 K at variable pressure were given in Supporting Information Table S4. Rate Constants for Reactions with Tight Transition States. Transition states have been located for remaining reactions in the C2H4 + HO2 system. Reaction rate constants at a variable pressure in the temperature range of 300−2000 K were put into the Supporting Information, Table S5. We find that it will produce a postreaction van der Waals complex(C2) before the HO2 abstract a H atom from C2H4 to form C2H3 + H2O2 products. And the IRC calculation indicates that TS1 connects the reactants and the postreaction van der Waals complex. We assume that, once formed, the postreaction van der Waals complex(C2) will dissociate to C2H3 + H2O2 rapidly, and we treat this reaction as proceeding directly from C2H4 + HO2 to C2H3 + H2O2, via TS1. This approximate method was reported by Silva et al.53 who adopted it to deal with the benzyl + HO2 reaction. The HPL rate constant for this bimolecular reaction is shown in Figure 5. The reaction C2H4 + HO2C2H3 + H2O2, for ethylene combustion, is very important which can shorten ignition time at lower temperature.54 There are some other iterations and mechanisms involved in this reaction. Li et al.54 estimated the rate constants corresponding to that of addition reaction C2H4 + HO2

k∞(T ) = 1.0 × 10−22.77 × T 3.79 × exp(− 21588/RT ) cm 3 molecule−1 s−1 (R = 1.987 cal mol−1K−1)

The elementary reactions with pressure-dependent rate constants for van der Waals complex (C1) are depicted in Figure 6. To the best of our knowledge, there is no theoretical calculation or experimental data available for comparison of these three reactions as mentioned above, which have been neglected in kinetic calculation for this van der Waals complex by many researches. These reactions show significant pressuredependent impact, especially for the concerted addition reaction shown in Figure6c. And the pressure effect becomes significant as the temperature increases. The reactions involved in new intermediate CH2OCH2OH, delineated in Figure 7−9, are the first time to be found in the C 2 H 4 + HO 2 system. These two kinds of reactions corresponding to isomerization and decomposition reactions are both pressure-dependent. Because it is known that the falloff behavior of the rate is influenced by the collision energy transfer. In this paper, the collision energy transfer was kept at ⟨ΔEdown⟩ = 200 cm−1. And the ⟨ΔEdown⟩ was also taken to be proportional to the temperature with the proportionality coefficient of 0.8 cm-1/K for comprising. The results show that both the isomerization reaction pictured in Figure 7a and the decomposition reactions pictured in Figures 8a−9a become much more sensitive to the pressure when using ⟨ΔEdown⟩ = 200 cm−1. The deviation gets quite large especially for reaction in low pressure at high temperature. It should be mentioned that the values of ⟨ΔEdown⟩ can be modified for practical kinetic model application in order to get a good fit. Branching Ratios. Branching ratios for formation of the different products sets in the C2H4 + HO2 reaction at pressures

Figure 5. High-pressure limit rate constants of reaction C2H4 + HO2 → C2H3 + H2O2 calculated in current work, Li et al.,54 Konnov et al.,56 and Dagaut et al.58 3165

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Figure 6. Comparison calculated rate constants at different pressures for C1 reactions (a) C1 → C2H4O2H, (b) C1 → C2H5 + O2, and (c) C1 → C2H5O2 in this work.

Figure 7. Comparison calculated rate constants with different ⟨ΔEdown⟩: (a) 200 cm−1 and (b) 0.8T cm−1 K−1 at varying pressures for reaction C2H4O2H → CH2OCH2OH.

Figure 8. Comparison calculated rate constants with different ⟨ΔEdown⟩: (a) 200 cm−1 and (b) 0.8T cm−1 K−1 at varying pressures for reaction CH2OCH2OH → CH2CHO + H2O.

of 1 and 100 atm are shown in parts a and b of Figure 10, respectively. Additional plots for pressures of 0.01, 0.1, and 10 atm are given in Supporting Information Figure S1. At 1 atm, the most competitive products are C2H5 + O2 in the whole temperature range of 300−2000 K, the branching ratio gets smaller with increasing temperature. The formation of

CH2OCH2 + OH becomes quite important at intermediate temperature. The contribution of this reaction arrives at the highest value at 1000 K. The third competitive reaction channel is CH3CHO + OH formation when temperature above 900 K and its contribution almost linearly increase along temperature. Comparison with these three channels, the others product 3166

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Figure 9. Comparison calculated rate constants with different ⟨ΔEdown⟩: (a) 200 cm−1 and (b) 0.8T cm−1K−1 at varying pressures for reaction CH2OCH2OH → CH2OCH2 + OH.

Figure 10. Plot of the temperature dependent branching ratios for C2H4 + HO2 reactions at pressure of (a) 1 atm and (b) 100 atm in Ar.

Figure 11. Comparison of experimental data of ignition delay time and calculated results using different mechanisms under 7 × 105 Pa and (a) Φ = 0.5 and (b) Φ = 1.0 (symbols are experimental data; lines are the simulation results of different mechanisms).

Figure 12. Comparison of experimental data of ignition delay time and calculated results using different mechanisms under 1.2 × 106 Pa and (a) Φ = 0.5 and (b) Φ = 1.0 (symbols are experimental data; lines are the simulation results of different mechanisms).

of CH2OCH2 + OH products is dominant at 1100−1300 K, the branching ratio of which at 100 atm larger than that at 1 atm as a whole. But comparison with the braching ratio at 1 atm, the

branching ratios can be neglected because of their low rate constants. At 100 atm, the channel of C2H5 + O2 formation is not dominant in the whole temperature range. The formation 3167

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combustion environment. Finally, the revised mechanisms by adding the kinetic calculation proposed in this paper can have a good performance in modeling ethylene combustion characteristics especially in low-temperature ignition chemistry.

formation of CH3CHO + OH gets smaller at high temperatures. Notably, the formation of CH3 + CH2O2, C2H5O + O, CH2CHO + H2O, and CHOHCHOH + H shows little pressure dependence. Kinetic Modeling. At present, main core mechanisms for C2H4 combustion are well validated in high-temperature ignition such as USC-Mech II,60 the USCD model,61 and AramcoMech 1.3.62 To illustrate the effect for low-temperature ignition of our new rate constants, we have implemented them into the existing mechanisms mentioned above named USC-2st and USCD-2st, respectively. Because the AramcoMech 1.3 model contains a lot of low-temperature combustion reactions, we do not develop it using our new rate constants in the presented work. The simulations for ignition delay in shock tube were carried out by using the CHEMKIN-2.0 software package.63,64 All simulations presented in this section were performed under the assumption of constant-volume, homogeneous and adiabatic conditions. The ignition delay of ethylene/O2/Ar was measured in a shock tube by Liang et al.65 covering a temperature range of 800−1650 K and with equivalence ratios of 0.5, 1.0, and 2.0. The comparison of ignition delay time calculated using the original and revised mechanisms mentioned above and the experimental data from Liang et al.65 are presented in Figures 11 and 12. As can be seen from the results, the original mechanisms could not reproduce the C2H4 ignition in low temperature, the revised mechanisms which add the new rate constants could significantly have a better performance on ignition in low temperature especially for USCD-2st model. Even though the new rate constants can observably improve the ignition characteristic for ethylene combustion, there are still obvious deviation between calculated and experimental results for ignition delay time under the condition of pressure at 7 × 105 Pa and Φ = 0.5 as shown in Figure 12(a). Furthermore, a detailed mechanism usually consists of hundreds of species and thousands of reactions. The revised mechanism cannot obtain very good performance for predicting the fuel combustion characteristics by adding several reactions. Thus, in order to improve the prediction of ignition under a wide range conditions, the development of detailed mechanisms that are comprehensive is without a question an important and challenging component.

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ASSOCIATED CONTENT

S Supporting Information *

All of the geometries of reactants, transition states, and products used in calculating rate constants have been included, predicted thermochemical properties of stable species (Table S1), comparison of previous studies and current work about the heat of reaction, reaction heights and wells for the elementary reactions of C2H4 + HO2 system (Table S2), HPL rate constants as a function of temperature and position for reaction C1 → C2H4 + HO2 (Table S3),expressions of fitted rate constants of barrierless reactions and reactions with tight transition states (Tables S4 and S5) and rate constants expressions in chemkin format, and calculated product branching ratios for the C2H4 + HO2 reaction at pressures of (a) 0.01, (b) 0.1, and (c) 10 atm in Ar (Figure S1). This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (N.X.Tan). *E-mail: [email protected] (X.Y.Li). 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 (Nos.91441132, 91441114). REFERENCES

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CONCLUSIONS In this paper, the mechanism and kinetics of bimolecular association reaction C2H4 + HO2 and the further decomposition and isomerization reactions by quantum chemical calculations have been investigated. The reaction of C2H4 + HO2 is initiated by forming a prereaction van der Waals complex (C1) without an entrance barrier. Thermochemical properties of the species involved in the reactions are determined using the CBS-QB3 method and enthalpies of formation of species in the present work agree well with literature values. The rate constants obtained by using the TST are expected to be of high accuracy, in which the tunneling effect has been taken into account. The barrier heights, heat of reaction and rate constants are compared with those available from literature, and good agreement is achieved. The VTST calculations on barrierless associations are carried out to obtain rate constants. Furthermore, rate constants of pressuredependent reactions in the three-parameter modified Arrhenius expression are derived in the temperature range of 300−2000 K which can be used to simulate conditions encountered in a real 3168

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