Kinetics of Decomposition and Isomerization of Methylcyclohexane

Article pubs.acs.org/EF

Kinetics of Decomposition and Isomerization of Methylcyclohexane: Starting Point for Studying Monoalkylated Cyclohexanes Combustion Feng Zhang,*,† Zhandong Wang,† Zhaohui Wang,† Lidong Zhang,† Yuyang Li,‡ and Fei Qi†,‡ †

National Synchrotron Radiation Laboratory and ‡State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui 230029, People’s Republic of China S Supporting Information *

ABSTRACT: Monoalkylated cyclohexanes are one of the typical constituents existing in practical fuels, especially in jet fuel. As the first step to study the combustion chemistry of monoalkylated cyclohexanes, the unimolecular reactions of methylcyclohexane (MCH) were investigated by combined theoretical calculations and experimental measurements for MCH pyrolysis and flames in the present work. The temperature- and pressure-dependent kinetics of unimolecular reactions of MCH including its dissociation and isomerization channels were computed by high-level quantum chemical calculations and Rice− Ramsperger−Kassel−Marcus/master equation simulations, which also reveal the competition relationship between the two channels. The theoretical predictions were examined by the experimental observations including species identification measured by photoionization efficiency spectra. The presented unimolecular reaction mechanism and corresponding temperature- and pressure-dependent rate constants provide a useful reference for further exploring combustion chemistry of cyclohexanes by kinetic modeling.

1. INTRODUCTION Monoalkylated cyclohexanes are typical components of practical fuels such as diesel and jet fuel.1 For instance, typical North American diesel fuel consists of up to 40% cyclohexanes and its derivatives by volume, which is comparable to the concentration of n-alkanes plus branched alkanes.2 The reaction mechanism and rate rules of straight- or branched-chain alkanes involved in the combustion system have been greatly developed by extensive effort of experimentalists, theoreticians, and kinetic modelers in combustion community.3−14 Compared to the comprehensive studies on chain alkanes, available knowledge on cycloalkanes combustion chemistry appears limited although the community has been aware of its importance.8,15−28 Methylcyclohexane (MCH, C7H14) is the smallest alkylated cyclohexane, which is also a significant component of practical fuels (e.g., diesel, Jet A, and JP-8).25,28 The detailed reaction mechanism of the MCH reaction and its kinetics is the foundation of building a universal mechanism for monoalkylated cyclohexanes combustion. MCH may decompose by losing a hydrogen or methyl radical at high temperature, or it may isomerize into various alkene isomers via ring-opening, as shown in Scheme 1. These decomposition and isomerization channels are initial reactions in the MCH combustion process. Therefore, investigating the kinetics of these channels is the starting point to study MCH combustion and larger alkylated cyclohexanes combustion as well. Pioneering studies on cyclohexane have shown that the hydrogen loss is completely negligible compared with the efficient isomerization reaction due to the high dissociation threshold of hydrogen dissociation and high entropy of its variational transition state.16,18,21,22 Recently, Skeen et al. analyzed MCH decomposition in low-pressure premixed flames.20 With the help of theoretical calculations, the authors © 2013 American Chemical Society

Scheme 1. Decomposition and Isomerization of MCH

estimated that the amount of six possible isomerization products (two heptenes and four methyl-hexenes, see Scheme 1) are comparable and the overall rate for isomerization is likely similar to that for −CH3 loss.20 However, these statements are quite different from the previous prediction, which suggested that the −CH3 loss channel might be negligible and the two heptenes are dominant isomerization products.27,29 The ambiguous and insufficient knowledge on unimolecular reactions of MCH especially under combustion condition Received: December 17, 2012 Revised: February 18, 2013 Published: February 19, 2013 1679

dx.doi.org/10.1021/ef302097s | Energy Fuels 2013, 27, 1679−1687

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Figure 1. Molecular orbitals in the active space chosen for an isomerization channel of MCH (only bonding orbitals are shown). dissociation reaction require multireference calculations. Therefore, all stationary points (including reactants, transition states, and products) of the isomerization channels were optimized by the complete active space self-consistent field method (CASSCF)32 with the basis set 6-31+g(d,p). The active space was chosen as six electrons occupying six orbitals for diradical intermediates involved in channels 4 and 5 in Scheme 1, while the six molecular orbitals are four σC−H and corresponding σ*C−H and two singly occupied molecular orbitals. For channel 3, an additional σC−H orbital and its antibonding orbital were used, since the diradical intermediates present three possible Hmigration channels. Thus, CAS(8e, 8o) was used for channel 3, and CAS(6e, 6o) was used for channels 4 and 5. Minimum active space (i.e., CAS(2e, 2o)) was applied for the −CH3 loss reaction. Then, single point energies (SPEs) were corrected by the multireference configuration interaction (MRCI) method including the Davidson correction with the 1s and 2s orbitals of carbon atoms frozen.33,34 The zero-point energies (ZPEs) computed by the CASSCF method were scaled by a factor of 0.93, which is determined by comparison of the calculated ZPE at CASSCF/6-31+g(d,p) and B3LYP/CBSB7 for the MCH molecule. The ZPE scaled factor of CBS-QB3 (B3LYP/6311G(2d, d, p) for geometry optimization and Hessian calculation) is well recognized as 0.99.35 The products were not optimized by the CASSCF method, since multireference calculations are not necessary for them, and moreover, the reaction energies have no impact on rate constant calculations without considering the tunneling effect. Instead, the reaction energies at CBS-QB335 were shown in this work. All multireference calculations were performed by the Molpro package,36 while the CBS-QB3 calculations were done by the Gaussian 09 program.37

urges further study to examine the competition between the decomposition and various isomerization channels and to reveal the temperature and pressure dependence of these reactions. A detailed description on these initial reactions including their temperature and pressure dependence will undoubtedly help to analyze the soot formation tendency and the macroscopic properties (such as flame velocity, ignition delay time, etc.) of monoalkylated cyclohaxanes combustion. In the present work, dissociation (losing −CH3 group) and isomerization channels of MCH were described in detail with high-level ab initio calculations. On the basis of the computed potential energy surfaces, the rate coefficients of these reactions among the temperature range 800−2000 K at various pressures (from 7.6 to 76 000 Torr) were calculated with the Rice− Ramsperger−Kassel−Marcus(RRKM)/master equation method.30 The theoretical predictions were examined by experimental observations for MCH pyrolysis and flame experiments at low pressure. The initial pyrolysis/flame products, particularly the C7H14 isomers, were identified by the technique of synchrotron vacuum ultraviolet photoionization mass spectrometry (SVUV-PIMS).9,31

2. THEORETICAL AND EXPERIMENTAL METHODS 2.1. Ab Initio Methods and Rate Constant Calculations. As shown in Scheme 1, not only the unstable diradical intermediates involved in the open-ring isomerization reactions but also the configurations with long C−C bond length during the bond 1680


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Each isomerization channel of MCH experiences multiple steps, that is, H migration from a diradical intermediate following an openring reaction. Considering the complexity of accurate RRKM treatment for this type of reaction, the rate coefficients were estimated by a simple one transition-state model with treating the ring-opening step as the rate-controlling step, while the branching fraction of subsequent multiple isomerized products were estimated by the computed partition functions of the corresponding transition states. The rate-limiting estimation was also suggested by Kiefer et al. when studying cyclohexane isomerization, giving reasonable high-pressure limit (HPL) isomerization rate constants within the uncertainty less than 3.18 The −CH3 loss channel is barrierless requiring variational treatment. Thus, the position of the transition state varying with temperature was determined variationally in the studied temperature range.38,39 The Lennard−Jones parameters for MCH and the bath gas−Ar used in the falloff calculations were defined as σMCH = 5.982 Å, εMCH = 477 K, σAr = 3.542 Å, and εAr = 114 K, which were deduced empirically.40 The collision energy transfer was treated using a singleparameter exponential down model, that is, down = 0.4 T. This choice was made referred to down used for cyclohexane previously, which is 600 cm−1 among the temperature range 1300− 2000 K.18 The pressure- and temperature-dependent rate constants (with the temperature varying from 800 to 2000 K, and the pressure varying from 7.6 to 76 000 Torr) were computed with the RRKM/ME method using the ChemRate program.41 2.2. Experimental Method. The pyrolysis and flames of MCH were investigated by SVUV-PIMS combined with molecular-beam sampling at the National Synchrotron Radiation Laboratory (NSRL) in Hefei, China. A detailed description of the experimental apparatus can be found in the literature;9,22,31 only a brief description is given here. The pyrolysis of MCH was studied in an alumina flow tube with an inner diameter of 6.8 mm and a heated length of 150 mm, which was mounted in a high-temperature furnace in the pyrolysis chamber. The pressure of the pyrolysis chamber was kept as 30 Torr. The pyrolysis species were sampled by a quartz nozzle with an orifice of ∼500 μm at the tip. The formed molecular beam was crossed by the synchrotron VUV light, and then, photoions were collected and analyzed by reflectron time-of-flight mass spectrometry (RTOF-MS). The total flow rate of the mixture (2% MCH and 98% Ar) is 1.0 standard liter per minute (SLM). The low-pressure flame apparatus includes a flame chamber with a moveable 6.0 cm diameter McKenna burner, a differentially pumped chamber with a molecular beam sampling system, and a photoionization chamber combined with a RTOF-MS. The combustion species were sampled by a quartz cone with a ∼500 μm orifice at the tip. The formed molecular beam passed through a nickel skimmer into the photoionization chamber, where it was crossed by the synchrotron VUV light, and then, the photoions were collected and analyzed by RTOF-MS. The experimental conditions are shown in Table S1 in the Supporting Information. Two experiment modes were used in the experiment. First, a series of mass spectra were measured by changing the heating temperature in the pyrolysis experiment or the burner position in the flame experiment at chosen photon energies. Then, the signal profiles of species with the temperature or burner position can be obtained. Second, the photoionization efficiency (PIE) spectra of species for example m/z = 98 were measured by scanning the photon energies at a fixed temperature or burner position, helping to identify isomers by comparing the onsets of PIE spectra with ionization energies of various isomers.

active space of all stationary points was kept consistent for each isomerization channel, as described in Section 2. Figure 1 illustrates an example for the active space selected for the following reaction channel, where only bonding orbitals are shown:

The other three unshown molecular orbitals are the corresponding antibonding ones. MCH has 28 doubly occupied molecular orbitals; thus, the active orbitals in CAS(6e, 6o) are from orbital numbers 26−31. Clearly, the characteristics of the illustrated molecular orbitals in Figure 1 are R: 26 #σC2−C3; 27 #σC4−H9 ; 28# σC1−H15 TS5: 26 #σC1−H15; 27 #σC4−H9 ; 28# n C2 , n C3 INT2: 26 #σC4−H9 ; 27 #σC1−H15; 28# nC2 , nC3 TS6: 26 #σC4−H9; 27 #σC1−H15; 28# n C2 , n C3

The other isomerization channels were also computed following the same rule. The complete and consistent active space along each reaction channel confirms the reliability of the consequent SPE correction by MRCI at each optimized configuration. Figure 2 shows the calculated potential energy profiles of above reaction channel at MRCI+Q//CAS(6,6)/6-31+g(d,p).

Figure 2. Potential energy profiles for the isomerization of MCH with breaking the C2−C3 bond at MRCI/6-31+g(d,p)//CAS(6,6)/631+g(d,p). (energy unit: kcal/mol.)

The transition states of hydrogen migration from the diradical intermediate, that is, TS6 and TS7, have lower energies than INT2. However, the CASPT2/cc-pVDZ optimizations with minimum active spaces provide 2−3 kcal/mol barrier heights for TS6 and TS7, as listed in Table 1.20 Yang et al. investigated the open-ring pathways of dioxane by using multiple multireference methods with large basis set.42 The results suggest that MRCI+Q with the small (2e, 2o) active space gives unreliable barrier height for the ring-opening reaction of dioxane.42 Nevertheless, similar tendency is not observed in our calculations, as shown in Table 1. In addition, the computational error of the high-level multireference calculations used for the bond breaking/H-transfer events of dioxane was assigned as several kilocalories per mole.42 The energy differences between our MRCI+Q and Skeen’s CASPT2 calculations are well within the computational uncertainties of

3. RESULTS AND DISCUSSIONS 3.1. Potential Energy Profiles. Our calculations start from the lowest energy conformer of MCH based on the CBS-QB3 calculations for four possible conformers, whose optimized structures and energies are shown in Table S2 in the Supporting Information. Skeen et al. have investigated the ring-opening isomerization of MCH by the CASPT2/cc-pVDZ method with the minimum active space.20 Considering that the choice of active space may affect the calculated energies, the 1681


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assuming that the location of the methyl group has only a minor effect on the threshold energies for ring-opening. Although the −CH3 loss is the energetically most favored channel according to theoretical calculations, Skeen et al. estimated that the total rate for ring-opening isomerization is likely similar to that of −CH3 loss considering that there are multiple ring-opening pathways.20 In contrast, the −CH3 loss channel was predicted to be negligible by Brown et al.29 Figure 4 illustrates the step-wisely optimized potential energy curve of the −CH3 loss channel of MCH at MRCI/6-

Table 1. Relative Energies of Stationary Points in the MCH Isomerization with Breaking the C2−C3 Bond by Various Methods MRCI(+Q)/ CAS(6,6)a

INT2 TS5 TS6 TS7

MRCI(+Q)/ CAS(2,2)a

CASPT2/ CAS(6,6)a

CASPT 2(2,2)/ccpVDZb

C 1s frozen

C 1s and C 2s frozen

C 1s frozen

C 1s and C 2s frozen

C 1s frozen

83.4 (85.3) 87.1 (89.0) 81.8 (82.3) 83.5 (83.6)

83.7 (85.5)

81.2 (85.4)

84.5

85

87.3 (89.1)

87.0 (89.0)

88.0

86

81.3 (81.6)

−

78.6

87

82.8 (82.6)

−

79.5

88

a

Computed in this work with 6-31+g(d,p) basis set; values in brackets are relative MRCI energies including Davidson correction. bCited from ref 20.

both methods. As described in Section 2, the 1s and 2s orbitals of carbon atoms were frozen during the MRCI calculations, while only inner orbitals (e.g., C 1s) are frozen by the default procedure in Molpro. In order to confirm the feasibility of this choice, the computed results for the reaction channel R→→P6 with and without freezing C 2s orbitals are displayed in Table 1. Clearly, freezing the C 2s orbital does not introduce significant error. In the rate constant calculations, only the ring-opening transition states were considered, with estimating the consequent isomerization products by the partition functions of corresponding H-migration transition states. The potential energy model used for the RRKM/ME calculation is shown in Figure 3, where the energies shown in brackets are previous

Figure 4. Step-wisely optimized potential energy curve of the −CH3 loss channel at MRCI(+Q)/6-31+g(d,p)//CAS(2,2)/6-31+g(d,p).

31+g(d,p)//CAS(2e,2o)/6-31+g(d,p). The transition states were located variationally with varying temperature from 800 to 2000 K, while the methodology has been reported elsewhere.38,39 As shown in Figure 4, the “barrier height” of the variational transition state varies from 74 to 78 kcal/mol among the studied temperature range with C−C bond stretching from 2.9 to 3.2 Å. Comparing the energies of the variational transition states for the −CH3 loss channel with those for ring-opening transition states shown in Figure 3, one at least should not neglect the −CH3 loss channel. The competition between the −CH3 loss and ring-opening reactions and its temperature and pressure dependence will be further examined by rate constant calculations. 3.2. Rate Constants. In order to validate the ratecontrolling assumption, we first computed the HPL rate constants of the two-step isomerization reaction R→→P6. As a result, that of R→INT2 varies from 10−9 to 106 s−1 in the temperature range 800−2000 K, while that of INT2→P6 is around 1011 s−1 in the temperature range (the energy of TS6 was artificially increased to 87 kcal/mol). Undoubtedly, it is reliable to compute temperature- and pressure-dependent rate constants by RRKM/ME methods based on the potential energy profiles shown in Figure 3. As shown in Figure 3 and Figure S1 (Supporting Information), there are two possible pathways leading to 1-heptene:

Figure 3. Potential energy model used for RRKM/ME simulation (the results shown are at MRCI+Q/6-31+g(d,p); values in brackets are CASPT2/cc-pVDZ results cited from ref 20).

CASPT2 results.20 The dash lines indicate that the diradical intermediates and H-migration transition states were neglected. The red dash line indicates that two possible H-migration channels exist that can generate 1-heptene (see details in Figure S1 in the Supporting Information). It is noticeable that the calculated barrier height of TS1 (corresponding to C1−C2 or C1−C6 bond breaking) in this work is 4 kcal/mol lower than TS5 and TS8, while the three saddle points have equivalent energies in the study of Skeen et al..20 Our results support earlier work26,29 that suggest that the C−C bonds adjacent to the side chain break most readily among all of the C−C bonds in the MCH ring, in contrast to the recent ab initio result20 1682

MCH → CH3 + C6H11

(R1)

→1‐heptene

(R2)

→2‐heptene

(R3)

→5‐methyl‐1‐hexene

(R4)


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(R5)


(R6)


(R7)

cyclohexane being reduced from 88.7 to 86.0 kcal/mol to fit the experimental data in Kiefer’s study.18 Figure 6a,b shows the pressure dependence of rate constants of MCH dissociation R1 and the overall isomerization channels

Figure 5 displays the HPL rate constants of above reaction channels with omitting those of R5 and R7, since the computed

Figure 5. High-pressure limit rate constants of dissociation and isomerization of MCH. (The results of cyclohexane isomerization were cited from ref 18.)

HPL rate constants of R4−R7 are quite close to each other. The results of cyclohexane isomerization by Kiefer et al.18 are also shown. First of all, R3 has comparable higher rate constant than R2 due to the lower energy of the saddle point connecting INT1 and 2-heptene, although two channels lead to 1-heptene. Second, the rate constants of R2 and R3 are distinguishable from those of the other four isomerization channels, which may be caused by the lower barrier of the transition state corresponding to break the C−C bonds adjacent to the methyl group, as seen from Figure 3. However, it is noticeable that the HPL rate constant of R3 is 4.3 times higher than that of R4 even at 2000 K, which probably cannot be explained by the difference of barrier height. Instead, it indicates high entropy of TS1, which is related to the more flexible structure of TS1 than those of TS5 and TS8. Therefore, our rate constant calculations indicate that MCH pyrolysis at high pressure will yield few amount of methyl-substituted hexene isomers. Third, the −CH3 loss channel dominates the unimolecular reactions of MCH at low temperature; however, its significance changes dramatically with increasing temperature due to the high A factor of isomerization reaction. As mentioned above, pioneering studies assumed that the −CH3 loss was negligible during MCH pyrolysis,29 while Skeen et al. estimated that the dissociation and isomerization channels have comparable rate constants according to their quantum chemical calculations.20 Our rate constant calculations quantitatively validate the Skeen et al. predication that the −CH3 loss channel is extremely needed in the MCH pyrolysis mechanism. Besides, we compare our calculated HPL rate constants for MCH with that for cyclohexane calculated by Kiefer et al.,18 which is shown in Figure 5 by a dash line. The value deduced from the given Arrhenius equation in ref 18 is divided by six considering the degeneracy. The rate constant of cyclohexane is much closer to that of R3 rather than those of other channels, which might be due to the barrier height of the ring-opening reaction of

Figure 6. Pressure dependence of rate constants of MCH dissociation and isomerization at (a) 1000 K and (b) 1500 K. (The vertical coordinate in (a) on the left side corresponds to the dissociation channel, while that on the right side corresponds to the isomerization channel.)

(i.e., the sum of rate constants for R2−R7) at 1000 and 1500 K, respectively. In Figure 6a, the vertical coordinate on the left side corresponds to the dissociation channel, while that on the right side corresponds to the isomerization channel. The rate constants of both two channels have more significant pressure dependence at high temperature than those at low temperature accordingly, which is easily understood by the strong collision model.43,44 More importantly, the rate constant of the isomerization channel always exhibits stronger pressure dependence than the dissociation pathway. For instance, at 1500 K, the rate constant of the dissociation channel at 7.6 Torr is 6.5 times lower than that at 76 000 Torr, while this ratio is 22.5 for the rate constant of total isomerization pathways. As a result, the branching ratio of the −CH3 loss channel decreases with increasing temperature at any pressures, as shown in Figure 7. The branching ratio reaches around 97% at the highpressure limit with 800 K. At a specific temperature, the branching ratio drops down with increasing pressure, since the rate constant of the dissociation channel rises with pressure more slowly than that of the isomerization channel. The calculated rate constants at various pressures and at the highpressure limit were fitted into the modified Arrhenius equation, which were given in Table 2. As mentioned above, the rate constant of the −CH3 loss channel was estimated by the canonical variational TST; a rough rigid rotor harmonic oscillator (RRHO) assumption combined with a quite simple 1683


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Figure 7. Temperature and pressure dependence of the branching ratio of the −CH3 loss channel.

Figure 8. Normalized signals of MCH, CH3, and overall isomerization products (m/z 98) along with temperature.

energy transfer model was used to compute the temperatureand pressure-dependent rate constants. The overall methodology could introduce large uncertainty; the rate constants provided in the present work are probably correct within an order of magnitude and should be only considered as a reference to estimate kinetic data for cycloalkanes combustion models especially to estimate the competition between various channels. 3.3. Experimental Observation. Figure 8 shows the normalized signals of CH3 and overall isomerization products (m/z 98) along with the decay curve of MCH in the pyrolysis experiment at 30 Torr. The production of CH3 and m/z 98 were detected at the very early stage of MCH decay, when the temperature rose to around 1100 K. The signal of the cyclohexyl radical (m/z 83) was not detected in this work due to its instability. This experimental observation confirms the importance of the −CH3 loss channel among the MCH unimolecular decay, which is exactly in accordance with our quantum chemical calculations shown in Figure 3 and the low

barrier heights of the varitional transition states of the −CH3 loss channel displayed in Figure 4. The relative yield of various isomerization products is a big issue in previous studies20,27,29 and our theoretical prediction. Without kinetic calculations, the six possible C7H14 isomers were estimated to be generated evenly by Skeen et al.20 However, our rate constant calculations indicate that most of isomerized products are 1-heptene and 2-heptene, while the methyl-substituted hexene isomers have small fractions. Figure 9 shows the PIE of m/z 98 in the pyrolysis of MCH at 30 Torr with a temperature of 1345 K, where the solid symbols represent the measured PIE signals. The ionization energies of MCH and its isomers referred to the NIST Chemistry WebBook45 and previous calculations.20 As shown in Figure 9, the onsets at 9.64 and 8.84 eV are quite distinguishable, which correspond to the IE of MCH and 2-heptene, respectively. According to the NIST Chemistry WebBook and high level calculations by Skeen et al., 1-heptene, 3-methyl1-hexene, 4-methyl-1-hexene, and 5-methyl-1-hexene have very close ionization energies (∼ 9.34 eV). However, the onset at

Table 2. Arrhenius Parameters of the Calculated Rate Constants for the −CH3 Loss and Isomerization Pathways of MCH at Various Pressuresa 7.6 Torr A k1 k2 k3 k4 k5 k6 k7

1.85 5.49 9.52 1.99 2.25 1.87 1.70

× × × × × × ×

k1 k2 k3 k4 k5 k6 k7

5.93 5.57 9.66 2.89 3.27 4.07 3.71

× × × × × × ×

Ea

10105 10115 10114 10132 10132 10119 10119

−26.15 −29.26 −28.98 −34.11 −34.10 −30.34 −30.34 760 Torr

129 214 143 180 140 737 154 207 155 250 146 825 147 025

n

Ea

1064 1069 1068 1074 1074 1073 1073

−14.15 −15.49 −15.21 −16.83 −16.83 −16.58 −16.58

108 486 121 178 118 735 126 667 127 710 125 964 126 164

A

a

30 Torr

n

A 1.19 1.03 1.74 1.28 1.46 1.95 1.77

× × × × × × ×

1092 10104 10103 10109 10109 10108 10108

A 3.59 4.90 8.51 2.73 3.09 5.59 5.09

× × × × × × ×

1045 1044 1043 1047 1047 1046 1046

150 Torr

n

Ea

−22.23 −25.68 −25.40 −27.20 −27.20 −26.95 −26.94 7600 Torr

122 595 138 280 135 829 143 306 144 350 142 703 142 902

n

Ea

−8.56 −8.17 −7.89 −8.93 −8.92 −8.72 −8.72

97 430 107 073 104 630 111 662 112 705 111 019 111 220

A 1.50 1.92 3.34 3.61 4.09 5.13 4.67

× × × × × × ×

1080 1088 1087 1093 1093 1092 1092

A 1.66 7.98 1.38 1.93 2.18 7.33 6.68

× × × × × × ×

1033 1026 1026 1027 1027 1026 1026

300 Torr

n

Ea

−18.67 −20.96 −20.68 −22.49 −22.49 −22.24 −22.23 76000 Torr

116 938 130 954 128 511 136 462 137 505 135 803 136 004

n

Ea

−4.99 −3.02 −2.74 −3.08 −3.08 −2.95 −2.95

90 100 96 627 94 184 99 905 100 948 99 418 99 619

A 8.65 3.07 5.32 4.30 4.87 4.47 4.07

× × × × × × ×

n

A 1.10 1.09 1.90 5.34 6.04 2.78 2.53

Ea

1063 −13.89 108 211 1080 −18.65 126 930 1079 −18.37 124 487 1085 −20.13 132 511 1085 −20.13 133 555 10107 −26.52 143 045 10107 −26.52 143 245 high-pressure limit × × × × × × ×

1027 1017 1016 1015 1015 1015 1015

n

Ea

−3.20 −0.16 0.12 0.27 0.27 0.35 0.36

86 385 90 732 88 289 93 008 94 051 92 602 92 802

Units: s−1 for A; cal/mol for Ea. 1684


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by breaking the C−C bond at different positions, while each one is regarded as double degenerated approximately. The chainlike isomerized products are generated efficiently via multiple steps. The potential energy surfaces of these isomerization pathways and the −CH3 loss reaction of MCH were computed by the multireference method (MRCI// CASSCF) in detail. On the basis of the quantum chemical calculations, the temperature-dependent (800−2000 K) and pressure-dependent (7.6−76 000 Torr) rate constants of the unimolecular reactions were computed. Our calculations suggest that the competition between dissociation (i.e., −CH3 loss) and isomerization channels has significant temperature and pressure dependence. Experiments of MCH pyrolysis at low pressure and flames at various stoichiometric ratios were performed to examine our theoretical predictions on MCH unimolecular reactions. The production of CH3 and m/z 98 isomers besides MCH were detected at the very early stage of MCH decay, which gives evidence of the important role of the −CH3 loss channel. The calculated branching ratio of various isomerization channels were used to fit the measured PIE profiles of m/z 98; as a result, the fitted PIE curves agree with the experimental measurements under pyrolysis and flame conditions. The detailed studies on unimolecular reactions of MCH involved in its combustion process is valuable to estimate the kinetic data required by kinetic models and further to analyze the soot formation tendency, flame velocity, ignition delay time, and so forth of MCH and monoalkylated cyclohexanes combustion.

Figure 9. PIE of m/z 98 in the pyrolysis of MCH at 30 Torr with a temperature of 1345 K. Solid symbol are experimental measurement. Red solid line is the simulated PIE curve for a mixture of 0.072% 1heptene, 0.222% 2-heptene, 0.020% 2-methyl-1-hexene, 0.025% 3methyl-1-hexene, 0.029% 4-methyl-1-hexene, 0.025% 5-methyl-1hexene, and 99.607% MCH. The accepted ionization thresholds of 2-heptene and MCH are assigned by arrows.

9.34 eV is not very clear in Figure 9 due to the scatter of the signal. Another isomer is 2-methyl-1-hexene with an IE of 9.04 eV. The line in Figure 9 illustrates the fitted PIE curve using a photoionization cross section (PICS) of various C7H14 species, while the proportion of each isomer was predicted by our calculated branching ratio of various isomerization channels at 30 Torr and 1500 K. The basic idea of this method is that the PIE spectra correspond to the isomers composition after considering the PICS of each isomer. In this work, The PICS of MCH was taken from the measurement of Zhou et al.46 The PICSs of C7H14 alkenes referred to molecules with similar structure.47,48 Details about the PIE fitting method and reference of PICSs for the C7H14 alkenes can be found in the Supporting Information. The PIE fitting was done based on a primary best fitting of 2-hepene signal, since 2-heptene has the lowest IE (8.84 eV). Then, the fractions of the other five C7H14 isomers relative to that of 2-heptene were estimated by the calculated branching ratio of each isomerization reaction. The inset in Figure 9 shows the PIE curve along a wider energy range including the MCH signal. The composition of the overall C7H14 species under this condition was given by the following: 99.607% MCH, 0.072% 1-heptene, 0.222% 2heptene, 0.020% 2-methyl-1-hexene, 0.025% 3-methyl-1-hexene, 0.029% 4-methyl-1-hexene, and 0.025% 5-methyl-1hexene. We also measured the PIE curves of m/z 98 in lean and rich MCH flames. The comparison between experimental and fitted PIE curves for each experiment was shown in Figures S4 and S5 in the Supporting Information, which also supports our theoretical prediction on the branching ratio of the isomerized reactions accompanying with the pyrolysis experiment shown in Figure 9.

■

ASSOCIATED CONTENT

S Supporting Information *

Method for PIE fitting of m/z 98 in the pyrolysis and flames of MCH; experimental conditions for the present flame studies; Cartesian coordinates (in Å) and energies (in hartree) of four conformers of MCH at CBS-QB3; Cartesian coordinates of all optimized stationary points at the level of CAS(6,6)/631+g(d,p); potential energy profiles for the isomerization of MCH with breaking the C1−C2 bond and that with breaking the C3−C4 bond; comparison of PICS for 1-hexene and 1butene and trans-2-hexene and trans-2-butene; measured and fitted PIE of m/z = 98 in the lean and rich flames of MCH at 30 Torr. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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4. CONCLUSIONS In the present work, the kinetics of unimolecular reactions of MCH was investigated by quantum chemical calculations and RRKM/ME simulations. This work is a start point for studying kinetics of MCH and monoalkylated cyclohexanes combustion, which are typical components of practical fuels such as diesel and jet fuel. MCH has three open-ring isomerization pathways

ACKNOWLEDGMENTS

We greatly appreciate many useful discussions with Dr. Donald G. Truhlar’s group. This research was supported by National Key Scientific Instruments and Equipment Development Program of China (2012YQ22011305), Natural Science Foundation of China (U1232127), Chinese Academy of Sciences and China Postdoctoral Science Foundation (2011M501049). 1685


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Kinetics of Decomposition and Isomerization of Methylcyclohexane

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