Reaction Kinetics of Hydrogen Atom Abstraction from C4-C6 Alkenes

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Reaction Kinetics of Hydrogen Atom Abstraction from C4C6 Alkenes by the Hydrogen Atom and Methyl Radical Quan-De Wang, and Zi-Wu Liu J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b03659 • Publication Date (Web): 23 May 2018 Downloaded from http://pubs.acs.org on May 24, 2018

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The Journal of Physical Chemistry

Reaction Kinetics of Hydrogen Atom Abstraction from C4-C6 Alkenes by the Hydrogen Atom and Methyl Radical Quan-De Wanga,*, Ziwu Liua a

Low Carbon Energy Institute and School of Chemical Engineering, China University of Mining and

Technology, Xuzhou 221008, Jiangsu, People’s Republic of China *Corresponding author. Email address: [email protected] (Q.-D. Wang)

Abstract: Alkenes are important ingredients of realistic fuels and are also critical intermediates during the combustion of a series of other fuels including alkanes, cycloalkanes and biofules. To provide insights into the combustion behavior of alkenes, detailed quantum chemical studies for crucial reactions are desired. Hydrogen abstractions of alkenes play a very important role in determining the reactivity of fuel molecules. This work is motivated by previous experimental and modeling evidences that current literature rate coefficients for the abstraction reactions of alkenes are still in need of refinement and/or re-determination. In light of this, this work reports a theoretical and kinetic study of hydrogen atom abstraction reactions from C4-C6 alkenes by the hydrogen (H) atom and methyl (CH3) radical. A series of C4-C6 alkene molecules with enough structural diversity are taken into consideration. Geometry and vibrational properties are determined at the B3LYP/6-31G(2df, p) level implemented in the G4 composite method. The G4 level of theory is used to calculate the electronic single point energies for all species to determine the energy barriers. Conventional transition state theory with Eckart tunnelling corrections is used to determine the high-pressure limit rate constants for 47 elementary reaction rate coefficients. To faciliate their applications in kinetic modeling, the obtained rate constants are given in Arrhenius expression and rate coefficients for typical reaction classes are recommended. The overall rate coefficients for the reaction of H atom and CH3 radical with all the studied alkenes are also compared. Branching ratios of these reaction channels for certain alkenes have also been analyzed.

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1. Introduction Alkenes are important constituents of realistic fuels.1 They are also critical intermediates during the combustion of a series of other fuels including alkanes, cycloalkanes and biofules,2-3 and their production during fuel oxidation process represents the first step towards soot formation.4-5 Due to the importance of alkenes in combustion systems, extensive work has been conducted to study their chemistry. Butene is usually selected as the first typical alkene molecule toward to large fuel molecules. Recently, Li et al. performed systematical experimental and modeling study of combustion chemistry of 1-butene, 2-butene and isobutene.6-8 Battin-Leclerc conducted a detailed study of the formation and decomposition of unsaturated hydrocarbons at high temperatures.9 Mehl et al. developed a wide-range kinetic model for the oxidation of C5-C6 linear alkenes and investigated the auto-ignition behavior of C5-C6 linear alkenes in the low and high temperature regimes via numerical and experimental techniques.10 Cheng et al. performed experimental and kinetic study of pentene isomers in laminar flames.11 Vanhove et al. studied the influence of the position of the double bond on the low-temperature combustion chemistry of hexenes.12 Yang et al. carried out comparative study on ignition characteristics of 1-hexene and 2-hexene behind reflected shock waves.13 Sensitivity and reaction path analysis from these experimental and modeling studies reveals that abstraction reactions from alkenes are key initiation steps and are crucial in prediction combustion properties. Thus, elementary abstraction reactions have been one of the research focuses of recent chemical kinetics at combustion relevant conditions. Vasu et al. studied the reaction of OH with three butene isomers in a shock tube facility, and they also performed theoretical study on the hydrogen abstraction channels of the reaction of OH with 1-butene.14 Sun et al. conducted a theoretical study of OH with butene isomers using transition state theory.15 Direct experimental or theoretical studies of longer chain alkenes (C5 and higher) are scarce in literature, though a series of theoretical studies have been performed on small alkenes and biofuels.16-20 Recently, Khaled et al. measured and fitted the overall rate coefficients for the reaction of C4-C6 straight chain alkenes with OH by using shock tube experiment.21 Despite these researches, it has been highlighted that further refinement of some important kinetic parameters is still necessary. Particularly, fewer studies have been performed on the abstraction reactions of alkenes with H radical, which plays a significant role in the prediction of combustion properties of alkenes, especially for flame simulations. To provide insights into the combustion behavior of alkenes, detailed quantum chemical studies for hydrogen abstractions of alkenes with H and CH3 radicals are presented in this work. The main objective 2


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of this study is to provide high-fidelity rate coefficients for the titled reactions through utilisation of high-level quantum chemical methods with kinetic theory. A comprehensive set of reactions of different structural C4-C6 alkene molecules with H and CH3 radicals are considered in order to allow application of the values derived in this work to similar reaction classes occurring in larger molecules. 2. Computational details All quantum chemical calculations have been performed using Gaussian 09 software.22 Geometry optimizations and analytical harmonic frequency calculations are carried out at the B3LYP/6-31G(2df, p) level of theory. Relaxed potential energy scans are employed to account for the presence of hindered rotors at the same level. Specifically, the potentials of each internal rotation of all alkenes are calculated at the B3LYP/6-31G(2df, p) level of theory using a relaxed energy scan of the corresponding dihedral over 360° with an interval of 10°. For the transition states, the potentials of hindered internal rotations closest to the reaction centers are also computed at the same level of theory using a relaxed energy scan but with the bond lengths at the critical geometries frozen, while the properties for the other hindered internal rotations employ the scan results for the corresponding alkenes. The intrinsic reaction coordinate (IRC) calculations23 are performed to verify that the transition states are the right minima connecting the reactants and the products. The composite G4 method24 is then applied to compute the zero-point corrected electronic energies of all species including reactants, transition states, and products. It has been shown to provide barrier heights with an average error of less than 1 kcal mol−1.24 High-pressure limit rate constants as a function of temperature from conventional transition state theory (TST) are computed via KiSThelP software.25 Quantum mechanical tunnelling has been accounted for via inclusion of 1-D tunnelling through an unsymmetrical Eckart energy barrier.26 The rate constants are calculated at temperatures from 500 to 2500 K in increments of 100 K, and the data are fitted to the modified Arrhenius expression, = exp− /, in which A is the Arrhenius prefactor, T is the temperature, Ea is the barrier height, and n is the temperature exponent indicating the deviation from the standard Arrhenius equation. 3. Results and discussion 3.1. Reaction barriers and enthalpies

In this work, a total number of 12 C4-C6 alkenes molecules with various structural diversity are taken into considerations. These alkenes molecules include butene isomers (1-butene, 2-butene, isobutene),

pentene

isomers

(1-pentene,

2-pentene,

2-methyl-1-butene,

3


2-methyl-2-butene,


2-methyl-3-butene), hexene isomers (1-hexene, 2-hexene, 3-hexene) and 1-4-pentadiene. Due to the location of the C=C bond, there are cis and trans isomers of 2-butene, 2-pentene, 2-hexene and 3-hexene. The G4 results indicate that the trans structures have lower energy that of the corresponding cis structures, revealing that the trans structures are more stable and thus is considered in this work, while the cis structures are treated as the hindered rotations in order to implicitly include their contributions. Considering all the abstraction reaction sites on the studied alkenes, there are a total number of 47 elementary abstraction reactions, corresponding to 8 types of hydrogen atoms, namely, primary vinylic hydrogen, secondary vinylic hydrogen, secondary allylic hydrogen, primary hydrogen, primary allylic hydrogen, secondary hydrogen, tertiary allylic hydrogen, and super secondary allylic hydrogen. Further, it is noted that both the calculated energy barriers and rate constants between the two primary vinylic hydrogen atoms are negligible.

Figure 1. Optimized geometries of the reactant alkene molecules.

Except for the abstraction reactions at the vinylic reaction sites, different TS configurations can be formed due to the different positions of the H atom connecting to the same carbon atom for the other abstraction reactions. In the present work, we only consider the lowest energy transition states and the other modes are treated as hindered rotors. Figure 2 shows two typical hindrance potential of reaction R3 and R4 along the corresponding torsional angle illustrating the local minima corresponding to transition 4


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states at different hydrogen atoms. For the secondary allylic abstraction reaction as shown in figure 2 for R3, the two hydrogen atoms, defined as in-plane and out-plane hydrogen atoms relative to the C=C double bond can lead to the in-plane and out-of plane transition states alone the torsional angle. The in-plane transition state has two local minima structures with higher energies of 13.86 and 20.73 kJ mol-1 compared with the lowest out-of plane transition state, respectively. Similar trend is observed for primary allylic abstraction reactions but with a higher relative potential of 23.91 kJ mol-1 compared with the hindered rotor of the secondary allylic abstraction reaction. For the primary hydrogen atom abstraction of R4, the lowest energy transition state tend to extend the length of the reactant molecule as illustrated in figure 2. The abstraction reactions of alkene with the CH3 radical exhibit the similar hindrance potential.

Figure 2. Hindrance potential analysis of R3 and R4 at the B3LYP6-31G(2df, p) level.

The reaction barriers (∆E) and enthalpies (Δ H ) involved for all the H-atom abstraction reactions

by H atom and CH3 radical are listed in Table 1. ∆E is calculated from the difference in the computed G4 energies between the TS and the reactants, while the reaction enthalpies Δ H is defined as the G4

energy difference between the products and reactants, which helps in identifying the nature of the reaction as either exothermic or endothermic. It is obvious that the abstraction reactions by the H atom and CH3 radical are all found to be exothermic with negative Δ H values except that the ones at the primary and

secondary vinylic reaction sites are endothermic as shown in table 1. Further, compared to all the abstraction reactions, the abstraction reactions by the H atom demonstrate higher reactivity than that by the CH3 radical due to the lower reaction barriers. The differences of the reaction enthalpies for all the abstraction reactions by the H atom and CH3 radical are small compared with the larger differences of the 5



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reaction barriers. Table 2 summarizes the calculated energies of all the studied reactions belonging to different reaction classes. It can be seen that both the reaction barriers and enthalpies for the abstraction reactions by the H atom and CH3 radical reveal the same tendencies of the reactivity for the eight abstraction reaction classes: super secondary allylic hydrogen > tertiary allylic hydrogen > secondary allylic hydrogen > primary allylic hydrogen > secondary hydrogen > primary hydrogen > secondary vinylic hydrogen > primary vinylic hydrogen. Although extensive work has been done on abstraction reactions of various fuels, a systematical and consistent study on abstraction reactions on alkenes are scarce. Wang et al.27 reported a systematic theoretical and chemical kinetic study of the hydrogen abstraction reactions by the H atom on a series of saturated and unsaturated C6 methyl esters at the CBS-QB3 level of theory, in which they found that the reaction barriers for primary and secondary hydrogen atom abstraction reactions are from 10.1 to 10.4 kcal mol-1 and from 6.8 to 7.6 kcal mol-1, respectively. This is a little higher than the reported values in this work, but the deviations are within 1 kcal mol-1 for most similar reactions. Zhou et al.28 reported a theoretical study on hydrogen atom abstraction from allylic C-H bonds by molecular oxygen, and they found that the reaction barriers also show the general trend from primary through secondary to tertiary with the super secondary allylic hydrogen atom being the lowest. Based on the computed reaction barriers and enthalpies, it is anticipated that dominant abstraction channels for certain alkenes would be the allylic hydrogen abstraction reactions.

Table 1 Theoretical predicted reaction barriers and reaction enthalpies for all the reactions in kcal mol-1. +H 1-butene

2-butene isobutene 1-pentene

2-pentene

+ CH3

Reaction

H atom

∆E

∆E

R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16 R17

CH2=CHCH2CH3 → •HC=CHCH2CH3 CH2=CHCH2CH3 → CH2=C•CH2CH3 CH2=CHCH2CH3 → CH2=CHCH•CH3 CH2=CHCH2CH3 → CH2=CHCH2CH2• CH3CH=CHCH3 → CH3CH=CHCH2• CH3CH=CHCH3 → CH3C=C•CH3 H2C=C(CH3)2 → •HC=C(CH3)2 H2C=C(CH3)2 → H2C=C(•CH2)CH3 CH2=CHCH2CH2CH3 → •CH=CHCH2CH2CH3 CH2=CHCH2CH2CH3 → CH2=C•CH2CH2CH3 CH2=CHCH2CH2CH3 → CH2=CHCH•CH2CH3 CH2=CHCH2CH2CH3 → CH=CHCH2CH•CH3 CH2=CHCH2CH2CH3 → CH=CHCH2CH2CH2• CH3CH=CHCH2CH3 → •CH2CH=CHCH2CH3 CH3CH=CHCH2CH3 → CH3C•=CHCH2CH3 CH3CH=CHCH2CH3 → CH3CH=C•CH2CH3 CH3CH=CHCH2CH3 → CH3CH=CHCH•CH3

14.43 11.33 3.81 9.41 5.75 11.85 14.92 5.99 14.04 10.90 3.59 6.57 9.44 5.42 11.43 11.37 3.25

4.71 1.29 -21.27 -5.10 -18.51 1.80 5.75 -16.77 4.36 0.95 -21.09 -8.13 -5.19 -18.73 1.42 1.63 -21.46

16.50 14.05 8.41 13.47 10.47 14.55 16.91 10.34 16.07 13.59 8.04 10.97 13.68 10.05 14.02 13.90 8.10

5.50 2.07 -20.48 -4.32 -17.73 2.59 6.54 -15.98 5.15 1.74 -20.30 -7.34 -4.41 -17.95 2.21 2.42 -20.68

6


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2-methyl-1-butene

2-methyl-2-butene

2-methyl-3-butene

1-hexene

2-hexene

3-hexene

1-4-pentadiene

R18 R19 R20 R21 R22 R23 R24 R25 R26 R27 R28 R29 R30 R31 R32 R33 R34 R35 R36 R37 R38 R39 R40 R41 R42 R43 R44 R45 R46 R47

CH3CH=CHCH2CH3 → CH3CH=CHCH2CH2• H2C=C(CH3)CH2CH3 → •HC=C(CH3)CH2CH3 H2C=C(CH3)–CH2–CH3 → H2C=C(CH2•)CH2CH3 H2C=C(CH3)CH2CH3 → H2C=C(CH3)CH•CH3 H2C=C(CH3)CH2CH3 → H2C=C(CH3)CH2CH2• HC(CH3)=C(CH3)2 → •C(CH3)=C(CH3)2 HC(CH3)=C(CH3)2 → HC(CH2•)=C(CH3)2 HC(CH3)=C(CH3)2 → HC(CH3)=C(CH2•)CH3 H2C=CHCH(CH3)2 → •HC=CHCH(CH3)2 H2C=CHCH(CH3)2 → H2C=C•CH(CH3)2 H2C=CHCH(CH3)2 → H2C=CHC•(CH3)2 H2C=CHCH(CH3)2 → H2C=CHCH(CH2•)(CH3) CH2=CHCH2CH2CH2CH3 → •CH=CHCH2CH2CH2CH3 CH2=CHCH2CH2CH2CH3 → CH2=C•CH2CH2CH2CH3 CH2=CHCH2CH2CH2CH3 → CH2=CHCH•CH2CH2CH3 CH2=CHCH2CH2CH2CH3 → CH2=CHCH2CH•CH2CH3 CH2=CHCH2CH2CH2CH3 → CH2=CHCH2CH2CH•CH3 CH2=CHCH2CH2CH2CH3 → CH2=CHCH2CH2CH2CH• CH3CH=CHCH2CH2CH3 → •CH2CH=CHCH2CH2CH3 CH3CH=CHCH2CH2CH3 → CH3C•=CHCH2CH2CH3 CH3CH=CHCH2CH2CH3 → CH3CH=C•CH2CH2CH3 CH3CH=CHCH2CH2CH3 → CH3CH=CHCH•CH2CH3 CH3CH=CHCH2CH2CH3 → CH3CH=CHCH2CH•CH3 CH3CH=CHCH2CH2CH3 → CH3CH=CHCH2CH2CH2• CH3CH2CH=CHCH2CH3 → •CH2CH2CH=CHCH2CH3 CH3CH2CH=CHCH2CH3 → CH3CH•CH=CHCH2CH3 CH3CH2CH=CHCH2CH3 → CH3CH2C•=CHCH2CH3 CH2=CHCH2CH=CH2 → •CH=CHCH2CH=CH2 CH2=CHCH2CH=CH2 → CH2=C•CH2CH=CH2 CH2=CHCH2CH=CH2 → CH2=CHCH•CH=CH2

9.10 15.51 5.60 3.27 9.68 11.08 4.66 5.15 13.93 10.95 2.17 8.91 13.70 10.56 3.21 6.43 6.38 9.18 5.05 11.07 11.02 3.06 6.42 9.34 8.81 2.92 10.90 14.29 11.28 1.81

-5.34 4.98 -16.52 -19.60 -4.97 1.42 -19.93 -18.14 4.33 1.22 -23.02 -5.14 4.09 0.68 -20.79 -8.02 -8.11 -5.51 -19.08 1.11 1.33 -21.32 -8.31 -5.32 -5.63 -21.73 1.20 4.59 1.16 -27.70

13.17 17.76 9.90 7.65 13.63 14.04 9.49 9.62 15.98 13.49 6.45 12.82 15.77 13.25 7.66 10.46 10.78 13.21 9.73 13.69 13.53 7.68 10.66 13.36 12.81 7.68 13.44 16.27 13.69 5.12

-4.55 5.76 -15.73 -18.81 -4.18 2.20 -19.14 -17.35 5.12 2.01 -22.24 -4.36 4.87 1.47 -20.00 -7.24 -7.32 -4.72 -18.29 1.90 2.12 -20.54 -7.53 -4.53 -4.84 -20.94 1.98 5.38 1.95 -26.92

Table 2 Summary of the reaction barriers and enthalpies belonging to different reaction classes. +H Hydrogen atom type

primary vinylic hydrogen secondary vinylic hydrogen secondary allylic hydrogen primary carbon hydrogen primary allylic hydrogen secondary carbon hydrogen tertiary allylic hydrogen super secondary allylic hydrogen

+ CH3

Reactions

∆E

R1, R7, R9, R19, R26, R30, R45

13.70 ~ 15.51

4.09 ~ 5.75

15.77 ~ 17.76

4.87 ~ 6.54

10.56 ~ 11.85

0.68 ~ 1.80

13.25 ~ 14.55

1.47 ~ 2.59

2.92 ~ 3.81

-21.73 ~ -19.60

7.65 ~ 8.41

-20.94 ~ -18.81

8.81 ~ 9.68

-5.63 ~ -4.97

12.81 ~ 13.68

-4.84 ~ -4.18

R5, R8, R14, R20, R24, R25, R36

4.66 ~ 5.99

-19.93 ~ -16.52

9.49 ~ 10.47

-19.14 ~ -15.73

R12, R33, R34, R40

6.38 ~ 6.57

-8.31 ~ -8.02

10.46 ~ 10.97

-7.53 ~ -7.24

R28

2.17

-23.02

6.45

-22.24

R47

1.81

-27.70

5.12

-26.92

R2, R6, R10, R15, R16, R23, R27, R31, R37, R38, R44, R46 R3, R11, R17, R21, R32, R39, R43 R4, R13, R18, R22, R29, R35, R41, R42

7


∆E


3.2. High-Pressure limit rate constants

The main objective of this study aims to determine of the high-pressure limit rate constants of the hydrogen abstraction reactions on the above alkenes and to analyze the rate constants within the same reaction class in order to extend their applicability to large alkenes. The high-pressure limit rate constants for the studied reactions are calculated via TST with 1-D hindered rotor approximation. Quantum tunneling effect is taken into account by the Eckart method because it is computationally inexpensive yet accurate enough for the temperatures of interest.27, 29 A full list of the calculated rate coefficients for the studied abstraction reactions of alkenes with the H atom and CH3 radical are provided in the supporting information. Table 3 lists the recommended rate coefficients for the eight reaction classes via detailed comparisons of the reactions within the same reaction class. Figure 3 compares the rate constants of some reactions studied in this work with the previous rate constants used in typical detailed combustion reaction mechanisms for 1-butene, 2-butene, and 1-pentene, respectively. For 1-butene, both the calculated rate constants in this work and that used in detailed mechanism developed by Li et al6-8 reveal the same reactivity of the four abstraction reaction site that abstraction from the allylic site is the fastest followed by primary carbon site, secondary vinylic site, and primary vinylic site being the slowest, corresponding to the calculated reaction barriers. However, the reported rate constants are larger than that used in detailed mechanism for 1-butene, especially for R3. However, the rate constants of primary allylic site of R5 used by Li et al6-8 are slightly higher than the reported rate constants in this work. Figure 3 also compares the computed rate constants for reactions R11, R12, and R13 of 1-pentene with H atom in this work with that used in the JetSurF model30 developed for jet surrogate fuel. The rate constants used in JetSurF model was adopted from Touchard et al31 for R11, while the rate constants for R12 and R13 were obtained through analogy with similar reactions of 1-butene and propane with H. Obviously, there still exists deviations between the computed rate constants in this work and those adopted in JetSurF model. Further, we also note that the study on the abstraction reactions of large alkene with the CH3 radical are very scarce. The rate constants used in the development of combustion mechanisms for butene were analogy with propene with CH3, which even cannot describe the correct reactivity of different abstraction reaction site as shown in the supporting information, indicating the necessity to refine and/or re-determine accurate rate constants for these reactions with high-level quantum chemical calculations.

8


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14

14

10

10 14

13

10

12

10

10

13

10

12

-1

-1

k (cm mol s )

-1

10

9

10

8

10

7

10

R1 R2 R3 R4 Solid: this work 6-7 Dash: Detailed mechanism 0.4

0.6

0.8

1.0 1.2-1 1000/T (K )

11

10

3

10

+H

+H 10

10

9

10

R5 R6 Solid: this work 6-7 Dash: Detailed mechanism

1.6

1.8

2.0

10

11

10

10

10

R11 R12 R13 Solid: this work 30 Dashed: JetSurF mechanism

9

8

1.4

12

10

-1

-1

10

3

-1 3

11

10

k (cm mol s )

13

10 k (cm mol 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


0.4

0.6

0.8

1.0 1.2 -1 1.4 1000/T (K )

1.6

1.8

2.0

10

0.4

0.6

0.8

1.0 1.2-1 1000/T (K )

1.4

1.6

1.8

2.0

Figure 3. Comparisons of the calculated rate constants of some reactions.

As shown previously, the studied 47 elementary reactions can be classified into 8 reaction classes. Through a detailed comparisons of the rate constants within the same reaction classes, it is found that the rate constants for abstraction reactions by the H atom and CH3 radical exhibit small deviations compared with each other except for the abstraction reactions by the H atom at the secondary allylic sites, which shows a little larger deviations at low temperature as displayed in figure 4. It can be seen that the length of alkenes and location of C=C double bond can affect the rate constants of this reaction class. The reactivity at this site increases as the length of alkenes increase, and the rate constants decrease from 3-hexene through 2-hexene to 1-hexene. Further, the reactivity at this site of branched alkenes is higher than straight chain alkenes. However, the deviations are not large and decrease quickly as the temperature increases. The rate constant of reaction R43 is a factor of 2.4 faster than that of reaction R3 at 500 K, while only a variation by a factor of 1.6 is depicted at 1000 K. Then, rate constants of the two reactions tend to approach the same values at higher temperature. For this abstraction reaction class by the CH3 radical, the rate constants for the reactions within this reaction class are nearly identical. Therefore, only one specific rate coefficients of this reaction class is recommended for simplicity, which will be shown to be effective to describe the overall reactivity of the studied alkenes.

9



14

10

-1

k (cm mol s )

-1

+H R3 R11 R17 R21 R32 R39 R43

13

10

3

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

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12

10

0.4

0.6

0.8

1.0 1.2 -1 1000/T (K )

1.4

1.6

1.8

2.0

Figure 4. Comparisons of the H-abstraction rate constants at the secondary allylic sites.

The recommended high-pressure limit rate constants for the 8 abstraction reaction classes with H atom and the CH3 radical as a function of temperature are highlighted in figure 5 and 6 respectively. As shown in figure 5 and 6, the rate constants of the 8 reaction classes exhibit the following tendency over the whole temperature range of interest: super secondary allylic site > tertiary allylic site > secondary allylic site > primary allylic site > secondary carbon site > primary carbon site > secondary vinylic site > primary vinylic site, corresponding to the computed reaction barriers. The deviations among different reaction classes become large as the temperature decreases. For abstraction reactions at the super secondary allylic, tertiary allylic and secondary allylic sites, it can be seen that the rate constants for abstraction reactions by H atom exhibit smaller deviations and changes more gently as a function of temperature compared with the abstraction reactions by the CH3 radical. The abstraction reactions by H atom and the CH3 radical at the primary allylic and secondary carbon sites can be competitive with each other due to the small differences of the rate constants over the studied temperature ranges.

Table 3 Recommended rate coefficients for the 8 abstraction reaction classes +H

+ CH3

Hydrogen atom type

A

n

Ea

A

n

Ea

primary vinylic hydrogen

3.55×107

1.95

11583

4.31×100

3.33

11356

secondary vinylic hydrogen

1.39×107

2.03

7810

2.08×107

1.98

7764

10


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secondary allylic hydrogen

4.87×106

2.10

304

2.25×100

3.34

3491

primary carbon hydrogen

3.20×106

2.18

5335

4.11×100

3.38

8278

primary allylic hydrogen

4.74×105

2.40

1516

6.46×10-1

3.54

5514

secondary carbon hydrogen

3.20×107

1.85

2829

8.15×100

3.16

6267

tertiary allylic hydrogen

2.69×107

1.86

-65

1.18×101

3.17

2611

super secondary allylic hydrogen

7.16×106

2.05

-638

7.96×100

3.29

1490

14

10

13

10 10

-1

-1

k (cm mol s )

12

11

10

3

primary vinylic H secondary vinylic H secondary allylic H tertiary allylic H super secondary allylic H primary carbon H primary allylic H secondary carbon H

10

10

9

10

8

10

0.4

0.6

0.8

1.0 1.2-1 1000/T (K )

1.4

1.6

1.8

2.0

Figure 5. Recommended rate coefficients for typical abstraction reaction classes by H atom

12

10

11

10

10

10 -1

9

10

3

-1

k (cm mol 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


10

8

primary vinylic H secondary vinylic H secondary allylic H tertiary allylic H super secondary allylic H primary carbon H primary allylic H secondary carbon H

7

10

6

10

5

10

0.4

0.6

0.8

1.0

1.2 -1 1.4 1000/T (K ) 11


1.6

1.8

2.0


Figure 6. Recommended rate coefficients for typical reaction classes by the CH3 radical

For the investigated hydrogen atom abstraction reactions, the uncertainty of the calculated rate constants is mainly caused by the uncertainties in the reaction barriers, quantum tunneling effects, and the treatment of some critical internal rotation modes. The adopted Eckart method can give accurate results compared with multidimensional tunneling method,29 and the uncertainty induced via tunneling effect can be less than a factor of 1 for the studied temperature range. Although the treatment of internal rotations in this work is approximated, the effect is small and such approximation may only yield an error of about 5-15% in the final rate constants based on previous studies for similar reaction systems.19, 27, 32 The accuracy of reaction barriers are still the decisive factor. The average deviation of the reaction barriers obtained via G4 method can be less than 1 kcal mol-1, and the resulting uncertainty of the rate constants can be controlled within a factor of 2.33 By taking the effects from different reactions within the same reaction classes to derive the recommended rate constants, the overall uncertainty of the recommended rate constants can be well controlled within the factor of 3. 3.3. Overall reactivity of the studied alkenes

The overall reactivity of the studied alkenes are compared with each other by summing contributions from all abstraction reaction sites, assuming that neither mixing nor crossover between different abstraction channels pathways occurs. Figure 7 and 8 displays the overall rate coefficients for the reactions of the H atom and CH3 radical with the investigated alkenes, respectively. As mentioned earlier, there are no direct experimental or theoretical calculations available in the literature for the systematic comparisons of the reactivity of alkenes with the H atom and CH3 radical. However, a series of similar research has been performed on the global combustion properties of alkenes. For the three butene isomers, Li et al.7 studied the effect of isomeric structure on ignition delay times and compared the reactivity of the butene isomers. They concluded that 1-butene is the fastest to ignite, followed by 2-butene, and isobutene is the slowest. As shown in figure 7 and 8, the total rate coefficients reveal the same reactivity for the three butene isomers. Based on the computed high-pressure limit rate constants for the abstraction reactions, it is obvious that the total rate constants for 1-butene with the H atom and CH3 radical is the largest due to the abstraction reaction at the secondary allylic C-H site, and the differences between 2-butene and isobutene are smaller since it is mainly caused by the abstraction reactions at the vinylic sites. 12


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For straight C5 and C6 alkenes, it can be seen that 2-alkenes are more reactive that 1-alkenes because the position change of the C=C double bond equivalently introduces additional primary allylic H atom and secondary vinylic H atom in 2-alkenes both showing higher reactivity compared with the secondary carbon H atom and primary vinylic H atom in 1-alkenes. The reactivity of 3-hexene with H is the highest among the studied straight alkenes due to the existence of two secondary allylic C-H sites induced by the position of the C=C double bond. The overall reactivity of the studied C4-C6 straight chain alkenes is in good accordance with the results for the reaction of the alkenes with OH radical from shock tube experiments at the temperature range that the abstraction reaction channels dominant the overall reactivity of alkene with OH radical.21 The overall reactivity of the studied C4-C6 straight chain alkenes with the CH3 radical also reveals the same tendency as that with H atom, although the differences in the total rate constants are smaller compared to that with H atom since the rate constants with the CH3 radical at different reaction sites involved is not larger than that with H atom. For the reactions of three C5 branched alkenes with H atom and CH3 radical, the rate constant of 2-methyl-3-butene with tertiary allylic C-H site is the largest, followed by 2-methyl-1-butene with secondary allylic C-H site, and 2-methyl-2-butene with primary allylic C-H site is the lowest, which again reveals that the overall reactivity is mainly due to the reactivity of the allylic C-H sites. As shown in figure 7 and 8, the total rate constant of the reaction of 1-4-pentadiene with H atom is smaller compared with the reaction of 3-hexene with H atom, while the total rate constant of the reaction of 1-4-pentadiene with CH3 radical is larger than that of the reaction of 3-hexene with CH3 radical. The difference are mainly induced by the abstraction reaction at the secondary allylic C-H site as shown in figure 5 and 6 that the rate constant of the reaction of super secondary allylic C-H site with H atom is less than that of the secondary allylic C-H site with H atom by a factor of 2, while the rate constant of the reaction of super secondary allylic C-H site with CH3 radical is larger than that of the secondary allylic C-H site with CH3 radical by a factor of 4.

13



14

13

10

3

-1

-1

k (cm mol s )

10

1-butene 2-butene isobutene 1-pentene 2-pentene 2 methyl-1-butene 2 methyl-2-butene 2 methyl-3-butene 1-hexene 2-hexene 3-hexene 1-4-pentadiene

12

10

0.4

0.6

0.8

1.0 1.2 1.4 -1 1000/T (K )

1.6

1.8

2.0

Figure 7. The overall rate coefficients for the reactions of the H atom with the investigated alkenes.

12

10

11

10

10

10

3

-1

-1

k (cm mol 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

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9

10

1-butene 2-butene isobutene 1-pentene 2-pentene 2 methyl-1-butene 2 methyl-2-butene 2 methyl-3-butene 1-hexene 2-hexene 3-hexene 1-4-pentadiene

8

10

7

10

0.4

0.6

0.8

1.0 1.2 -1 1.4 1000/T (K )

1.6

1.8

2.0

Figure 8. The overall rate coefficients for the reactions of the CH3 radical with the investigated alkenes.

3.4. Branching ratio analysis of typical alkenes

The different trends of the rate constants as a function of temperature at different reaction sites for alkenes would directly affect the results of combustion chemical kinetic modeling due to the resulting products from the abstraction reactions. In order to further understand the chemical kinetics, a branching ratio analysis for 1-butene, 2-methyl-3-butene, 2-hexene, and 1-4-pentadiene with H atom representing the studied reaction classes in this work has been carried out in the temperature range 500-2500 K, as 14


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shown in figure 9. As shown in figure 9, it is obvious that the abstraction reactions at the allylic C-H site completely dominates the branching ratios at temperature below 1500 K for 1-butene, 2-methyl-3-butene, and 1-4-pentadiene. The branching ratios at the other reaction sites gradually increase as temperature rises, but the ratios are all less than that at the allylic site. It should be mentioned that two primary carbon C-H sites exist for 2-methyl-3-butene, while two symmetrical primary and secondary vinylic C-H sites exist for 1-4-pentadiene. Thus, branching ratio of reaction R29, R45 and R46 is multiplied by a factor of 2. However, it can be seen that branching ratios of R28 and R47 are still large than that of the other sites since the rate constants for the two reactions is greatly larger than the other reactions. For 2-hexene, branching ratio of reaction R39 at the secondary allylic C-H site is dominant at temperature below 1000 K, while the abstraction reactions at the primary allylic C-H site (R36) and secondary carbon C-H site (R40) can be competitive with reaction R39 above 1000 K. However, the branching ratios of R26 and R40 hardly change as a function of temperature above 1000 K and the value is around 0.25. Contributions from the primary carbon C-H site and the vinylic sites are less than 0.1 over the whole temperature range of interest.

1.0

1.0 1-butene R1 R2 R3 R4

0.6

0.4

0.2

0.6

0.4

0.2

0.0 500

2-methyl-3-butene R26 R27 R28 R29

0.8 Branching ratio

Branching ratio

0.8

0.0 1000

1500 T (K)

2000

2500

500

0.8

1000

1500 T (K)

2000

2500

1.0 2-hexene R36 R37 R38 R39 R40 R41

0.6 0.5 0.4

1-4-pentadiene R45 R46 R47

0.8 Branching ratio

0.7

Branching ratio

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


0.3 0.2

0.6

0.4 0.2

0.1 0.0 500

0.0 1000

1500 T (K)

2000

2500

500

1000

15


1500 T (K)

2000

2500


Figure 9. Predicted branching ratio for different abstraction sites of 1-butene, 2-methyl-3-butene, 2-hexene, and 1-4-pentadiene between 500 and 2500 K.

4. Conclusions Recent years, kinetic modeling based on detailed chemical kinetic mechanisms has proven to be an effective way to understand fuel combustion behaviors. As an effort to continuously improve the accuracy of detailed chemical kinetic mechanisms, systematic studies of important reaction classes are crucial. This work reports a systematic and comprehensive study of the rate constants for hydrogen atom abstraction reactions by H atom and CH3 radical on a series of C4-C6 alkenes. Altogether, 47 elementary abstraction reactions belonging to 8 different reaction classes with enough structural diversity are considered. The reaction barriers and energies are computed for the titled reactions at the G4 level of theory. Both the computed reaction barriers and energies reveal that abstraction by the H atom is more favorable over the CH3 radical. Combined with conventional transition state theory, high-pressure limit rate coefficients have been determined. General trends for the reactivity of the 8 abstraction reaction classes from the computed reaction barriers and rate constants have been found as follows: super secondary allylic site > tertiary allylic site > secondary allylic site > primary allylic site > secondary carbon site > primary carbon site > secondary vinylic site > primary vinylic site. To faciliate applications of the calculated results in kinetic modeling, rate coefficients for the 8 reaction classes are recommended via a detailed comparisons of the reaction rate constants within the same reaction classes. The overall reactivity for the abstraction reactions of H atom and CH3 radical with all the studied alkenes are also compared. It is shown that longer chain alkenes have higher overall reaction rate coefficients with H atom and CH3 radical, although the increase in rate coefficients with increasing chain length is not monotonic. The overall reactivity of alkenes with the H atom and CH3 radical is greatly affected by the position of C=C double bond and the extent of the impact of the position of double bond depends on the type of the allylic C-H site in the alkene molecule. Specifically, for straight C5 and C6 chain alkenes, 3-alkenes are more reactive than 2-alkenes, with 1-alkenes being the least active. However, 1-butene is more reactive than 2-butene since secondary allylic C-H site does not exist in 2-butene due to the short chain length. To the best of our knowledge, this work provides the first systematic study on the key initiation abstraction reaction classes for alkenes with the H atom and CH3 radical.

16


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ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Full list of the computed high-pressure limit rate constants and summary of G4 single point energies for all species.

AUTHOR INFORMATION

Corresponding Author *(Q.-D. Wang) E-mail: [email protected] ORCID Quan-De Wang: 0000-0002-3941-0192 Ziwu Liu: 0000-0003-1275-1381

Notes The authors declare no competing financial interest.

Acknowledgments This work is supported by the Fundamental Research Funds for the Central Universities of China (No. 2017XKQY064). We also thank National Supercomputing Center in Shenzhen for providing the computational resources and Gaussian 09 suite of programs (Revision D.01).

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TOC

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Reaction Kinetics of Hydrogen Atom Abstraction from C4-C6 Alkenes

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