Article pubs.acs.org/EF
Theoretical Kinetic Study of Thermal Decomposition of Cyclohexane Chun-Ming Gong,† Ze-Rong Li,*,‡ and Xiang-Yuan Li*,† †
College of Chemical Engineering, and ‡College of Chemistry, Sichuan University, Chengdu 610065, People’s Republic of China S Supporting Information *
ABSTRACT: In the present work, the reaction mechanisms for thermal decomposition of cyclohexane in the gas phase have been investigated using quantum chemical calculations and transition-state theory. Three series of reaction schemes containing 38 elementary reactions are proposed. The geometry optimization and vibrational frequencies of reactants, transition states, and products are determined at the BH&HLYP/cc-pVDZ level, while energies are calculated at the CCSD(T)/cc-pVDZ level. The rate constants for the reactions without transition states, including the initial steps of cyclohexane decomposition (C−C bond scission or C−H bond scission), are obtained by the canonical variational transition-state theory (CVT), while the rate constants for the other reactions with saddle-point transition states are obtained by the conventional transition-state theory (TST) in the temperature range of 300−3000 K. The rate constants are in good agreement with data available from the literature. The kinetic parameters in the modified Arrhenius equation form for all of the reactions studied are given and can be used in chemical kinetic modeling studies.
1. INTRODUCTION Cycloalkanes play an important role in practical fuel chemistry because of their significant presence in diesel fuels, jet fuels, and oil-sand-derived fuels.1 Cyclohexane (c-C6H12) is one of the prominent representatives among cycloalkanes and a common component of surrogate for fuels.2 However, during the cyclohexane decomposition and oxidation processes, a number of radicals are formed, and it is difficult to obtain the rate constants of these elementary reactions to different specific channels involving radicals experimentally. There have already been many experimental studies on the pyrolysis and oxidation of cyclohexane because of the importance of this compound in combustion chemistry. In 1978, Tsang3 studied the decomposition of cyclohexane in the temperature range of 970−1210 K, using a single-pulse shock tube. The major products were found to be 1,3-butadiene, ethylene, and 1-hexene. It was concluded that the main initial reaction channel was the isomerization of cyclohexane to 1-hexene, and the rate constant for cyclohexane to 1-hexene was fitted as k = 1016.7 exp(−44400/T) s−1. Brown and co-workers4 studied the thermal decomposition of cyclohexane at temperatures in the range of 900−1223 K, with very low pressure pyrolysis (VLPP). The results showed that ring-opening isomerization to open-chain alkenes was the major process. From the study of the “addition of cyclohexane to slowly reacting H2−O2 mixtures at 480 °C”, Walker et al.5 suggested a reaction pathway of the formation of benzene in the following sequence: cyclohexane → cyclohexene → 1,3-cyclohexadiene → benzene. Minetti et al.6 studied the oxidation of cyclohexane, cyclohexene, and cyclohexa-1,3-diene in an environment similar to an engine between 600 and 900 K and between 0.7 and 1.4 MPa. They proposed the low-temperature pathways leading to benzene. Steil et al.7 carried out an experimental study on the pyrolysis of cyclohexane using two different shock-tube techniques to study the initial reaction steps of cyclohexane decomposition, and the rate constants of cyclohexane decomposition leading from H elimination to cyclohexyl radical © 2012 American Chemical Society
were obtained. They also showed the rate constants of dominant reaction routes of cyclohexane decomposition to ethylene, ethyne, and butadiene. An experimental study dealing with the thermal decomposition of cyclohexane was carried out by Kiefer et al.2 in a shock tube by the laser-schlieren technique over the temperature range of 1300−2000 K and for 25−200 Torr. High-pressure limit rate constants for some important reaction channels were obtained by performing Rice−Ramsperger−Kassel−Marcus (RRKM) calculations, but rate constants for elementary steps are still lacking. There are also several theoretical studies on cyclohexane oxidation and pyrolysis, with detailed chemical kinetic mechanisms developed. However, in the modeling study of cyclohexane decomposition, most of the rate constants were estimated using generic rates, and rate constants for these reactions calculated of high accuracy are still lacking. Voision et al.8 studied cyclohexane oxidation in the temperature range of 750−1100 K at 10 atm and performed kinetic modeling on cyclohexane oxidation using estimated rate constants. El-Bakali et al.9 presented a detailed reaction mechanism for cyclohexane oxidation with comparisons of computed and experimental mole fraction profiles and concluded that the dehydrogenation of the cyclohexyl radical dominated over ring-opening decomposition. Granata et al.10 presented a semi-detailed kinetic model for the pyrolysis and oxidation of cyclohexane using a lumped approach. The kinetic parameters of the elementary reactions in the mechanism were directly evaluated from the primary pyrolysis and oxidation reactions of linear and branched alkanes. The Utah surrogate mechanism was extended to include a detailed description of the cyclohexane flame by Zhang et al.11 Generic rates basing on reaction class rules were used extensively in the extended mechanism. Cavallotti et al.12 investigated the kinetics on pyrolysis and oxidation of cyclohexane through detailed kinetic modeling. Received: January 2, 2012 Revised: April 5, 2012 Published: April 8, 2012 2811
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The vibrational frequencies for all of the stationary points are obtained at the same level of theory of geometry optimizations, and they are scaled by a scaling factor of 0.97 recommended by Huynh et al.20 The single-point energies are calculated at the CCSD(T)21/ccpVDZ level with zero-point energy (ZPE) corrections obtained at the BH&HLYP/cc-pVDZ level. The structures of the intermediates and transition states have been confirmed by vibrational analysis. Moreover, intrinsic reaction coordinate (IRC)22 calculations at the BH&HLYP/cc-pVDZ level are carried out to confirm that the transition states connect the right reactants and products. Cyclohexane has two stable conformations: boat conformation and chair conformation. According to the study by Sirjean et al.,14 the distinction between chair and boat conformations is not fundamental to derive accurate thermodynamic properties. Therefore, in this work, only the chair conformation has been taken into account. Singlet and triplet states are considered for the biradicals in the present work. Although it might be questionable for describing open-shell singlet biradicals at the density functional theory (DFT) level, Sirjean et al.14 proposed that it was proper for geometry optimization of the biradicals using the DFT. Therefore, geometry optimization of the biradicals is performed at the UBH&HLYP/cc-pVDZ level. However, spin contamination is pronounced for the wave function obtained from the unrestricted single-reference approach because of a significant mixing between singlet and triplet states. The energy of the singlet biradical is calculated on the basis of the method proposed by Ziegler et al.23 as follows:
They performed ab initio calculations to calculate the kinetic parameters of some primary reactions following the oxygen attack to the cyclohexyl radical, and used these calculated parameters and other estimated parameters in further kinetic modeling. Westbrook et al.13 developed a detailed kinetic mechanism to study the oxidation of cyclohexane in the temperature range of 650−1150 K. Moreover, rules for reaction constants were also developed for the low-temperature combustion of cyclohexane, which could be used for chemical kinetic mechanisms of other cycloalkanes. Sirjean et al.14 performed a kinetic study of the ring opening of cyclohexane and obtained the rate constants at the CBS-QB3 level for reactions involving C−C bond scission in the ring opening of cyclohexane at 1 atm and temperatures ranging from 600 to 2000 K. The accurate rate constants of cyclohexane decomposition involving C−H bond scission are still lacking. The objective of the present work is to investigate the thermal decomposition of cyclohexane by means of high-level quantum chemical calculations and to obtain accurate rate constants for a series of elementary reactions that are important in chemical kinetic modeling of cyclohexane decomposition and oxidation.
2. COMPUTATIONAL METHODS
Es = 2Emix − Et
2.1. Potential Energy Surface Calculations. All of the electronic structure calculations are performed using the Gaussian 03 program.15 It has been found earlier that the combination of the hybrid Becke half and half nonlocal exchange16 with Lee−Yang−Parr17 correlation functionals (BH&HLYP) can give quite accurate geometries and frequencies at a low computational cost and can yield comparable accuracy for large systems;18 therefore, in this work, BH&HLYP with Dunning’s correlation-consistent basis set cc-pVDZ19 is employed to optimize the geometries of the reactants, transition states, and products.
(1)
where Es and Et are the energy of singlet and triplet biradicals, respectively, and Emix is the energy from unrestricted calculation using the GUESS=MIX option of Gaussian 03. 2.2. Reactions of Cyclohexane Decomposition. In this study, three reaction schemes are considered to describe the major reaction pathways for thermal decomposition of cyclohexane, which are mainly integrated from the mechanisms proposed by Granata et al.,10 Zhang et al.,11 and Sirjean et al.14 (Schemes 1−3). In these schemes, 38 elementary reactions are involved, among which two reactions, C−H and C−C bond scissions of cyclohexane, are barrierless.
Scheme 1. C−H Bond Scission of Cyclohexane and Subsequent Steps of Cyclohexyl by β-Scission and Isomerization
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further refined by single-point calculation at the CCSD(T)/cc-pVDZ level. Then, the energies at the CCSD(T)/cc-pVDZ level together with geometries and frequencies at the BH&HLYP/cc-pVDZ level are used for rate constant calculations. For reactions from R1 to R32, the rate constants are calculated using the TST/Eckart method, i.e. k T q≠ k(T ) = κ(T )σ B exp(−ΔE0 /RT ) h ∏ qR (2)
Scheme 2. C−H Bond Scission of Cyclohexane and Subsequent Steps of Benzene Formation and Other β-Scission Reactions
where κ(T), σ, kB, and h are Eckart’s tunneling factor, the reaction symmetry number,18 Boltzmann’s constant, and Planck’s constant, respectively. T is the temperature ranging from 300 to 3000 K, and qR represents the total molar partition consisting of the function translation, vibration, rotation, and hindered rotation. The partition function of the activated complex is q≠. ΔE0 is the electronic activation barrier including ZPE. For the intermediates and transition states with low-frequency torsional motions, the one-dimensional (1D) hindered internal rotor approximation24 is applied to estimate their contributions to the partition functions. For the practical use in chemical kinetic modeling, three kinetic parameters A, n, and Ea for each reaction are obtained by fitting the calculated rate constants over the temperature range of 300−3000 K to a modified Arrhenius expression. k(T ) = AT n exp(− Ea /RT ) a Dehydrogenation means β-scission of the C−H bond. bH abstraction means that the H radical abstracts the H atom to form H2.
(3)
3. RESULTS AND DISCUSSION 3.1. Geometries of Stationary Points. All of the optimized geometries of the reactants, products, and transition states at the BH&HLYP/cc-pVDZ level can be found in the Supporting Information. Figure 1 shows the geometries of some reactants and products whose experimental geometric data are available from the literature (shown in parentheses). In comparison to the experimental data, the deviations of bond lengths are within 0.02 Å and the maximum deviation of the calculated bond angle is 1.2°. The results indicate that geometry optimization at the BH&HLYP/cc-pVDZ level is in good agreement with the experiment. 3.2. PES and Reaction Mechanism Analysis. As mentioned above, the initial steps of cyclohexane decomposition (C−H bond scission and C−C bond scission) are barrierless, and they are not shown in the potential energy profiles. For C−H bond scission of cyclohexane, the bond dissociation energy (BDE) is larger than that for C−C bond scission. Thus, the initial step of C−C bond scission is easier to take place than C−H bond scission. Nevertheless, the decomposition of cyclohexyl is still taken into account to perform the chemical kinetic study in the present work. On the basis of the above considerations, the discussion below contains two parts. The first part is the decomposition of cyclohexyl formed by C−H bond scission of cyclohexane, and the other part is the decomposition of biradical 1,6-C6H12 formed by C−C bond scission of cyclohexane. For the convenience of analysis, the potential energy profiles of cyclohexyl decomposition are shown in Figures 2−4, while the potential energy profile of the decomposition of the biradical 1,6-C6H12 is shown in Figure 5. 3.2.1. Cyclohexyl Decomposition. From Figures 2−4, one can see that there are three initial steps of cyclohexyl decomposition. The pathway to the linear intermediate 1-hexen6-yl (1-C6H11-6) by β-scission appears to be the most competitive step, as shown in Figure 2, and then the unimolecular dehydrogenation, as shown in Figure 4. The most difficult step is the direct isomerization to the intermediate cyclopentylmethyl (1-CH2−c-C5H9) (Figure 3) because the calculated barrier (64.4 kcal/mol) is much higher than those for R1 and R18. Thus, this
Scheme 3. C−C Bond Scission of Cyclohexane and Subsequent Steps
The barrierless reactions are labeled Ra and Rb, and the other reactions are marked Rn, with n being the number of the reaction. All of the reactions investigated in this work are listed in Table 1. 2.3. Rate Constant Calculations. The rate constants for reactions Ra and Rb are calculated with the canonical variational transition-state theory (CVT). The rate constants for the others are calculated with conventional transition-state theory (TST), and the Eckart method is adopted to correct the quantum mechanical tunneling effect. All of the rate constant calculations are performed using the TheRate18 program. For reactions Ra and Rb, a potential energy surface (PES) scan is performed. Force constants at 20 selected points along the minimum energy path (MEP) are determined to obtain the necessary potential energy surface information for CVT calculations. These points are chosen based on the focusing technique,18 which are sufficient to show all major features of the two reactions. The energies along the MEP are 2813
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Table 1. High-Pressure Limit Rate Parameters of Cyclohexane Decomposition Reactionsa reactions Ra
c-C6H12 → c-C6H11 + H
Rb
c-C6H12 → 1,6- C6H12
R1
c-C6H11 → 1-C6H11-6
R2
1-C6H11-6 → 1-C6H11-3
R3
1-C6H11-6 → 1-C4H7-4 + C2H4
R4
1-C4H7-4 → 1-C4H7-3
R5
1-C4H7-4 → 1,3-C4H6 + H
R6 R7 R8
1-C4H7-4 → C2H4 + C2H3 1-C6H11-6 → 1-C6H11-5 1-C6H11-5 → 1-C3H5-3 + C3H6
R9
1-C6H11-3 → 2-C6H11-4
R10
1-C6H11-3 → 1,3-C4H6 + C2H5
R11
2-C6H11-4 → 2,3-C5H8 + CH3
R12 R13
1-C6H11-6 → 1-CH2−c-C5H9 1-CH2−c-C5H9 → 1-CH2−C5H8 + H
R14
1-CH2−c-C5H9 → 1-CH3−C5H8-3
R15
1-CH3−C5H8-3 → 2-CH3-4-C5H8-1
R16
2-CH3-4-C5H8-1 → C3H6 + 1-C3H5-3
R17
1-CH3−C5H8-3 → 1-CH3-4-C5H8-1
R18
c-C6H11 → c-C6H10 + H
R19
c-C6H10 → 1,3-C4H6 + C2H4
R20
c-C6H10 + H → c-1-C6H9-4 + H2
R21 R22 R23
c-1-C6H9-4 → 1,4-C6H9-6 1,4-C6H9-6 → 1,3-C4H6 + C2H3 c-C6H10 + H → c-1-C6H9-3 + H2
R24
c-1-C6H9-3 → c-1,3-C6H8 + H
R25
c-1,3-C6H8 + H → c-1,4-C6H7-3 + H2
R26
c-1,4-C6H7-3 → c- C6H6 + H
R27 R28 R29 R30
c-1-C6H9-3 → 1,3-C6H9-6 1,3-C6H9-6 → 1,3-C4H5-4 + C2H4 1,3-C6H9-6 → 1,3,5-C6H8 + H 1,6-C6H12(s) → 1-C6H12
R31
1,6-C6H12(s) → 1,4-C4H8(s) + C2H4
R32
1,4-C4H8(s) → C2H4 + C2H4
R33
1,6-C6H12(t) → 1-C6H11-6 + H
log A
n
Ea/R
ravg
rmin
rmax
T (K)
reference
11.00 17.36 15.32 21.32 12.11 13.20 2.40 11.30 12.80 13.51 −2.48 8.37 10.48 13.51 13.10 −4.38 11.83 12.66 −3.69 3.97 12.73 11.53 11.74 13.69 10.60 9.81 8.89 −1.02 1.82 11.81 12.55 12.31 12.73 12.43 12.88 10.74 11.52 12.06 15.18 −17.69 6.41 12.04 13.00 −17.45 6.41 11.33 12.50 −16.54 6.89 10.50 11.90 12.28 13.78 9.96 10.92 2.46 12.83 10.40 12.63 7.32 10.39
1.08 0.00 0.21 −0.97 0.55 0.00 2.67 0.00 0.43 0.00 4.36 0.88 0.84 0.00 0.40 4.76 0.49 0.13 4.49 2.38 0.56 0.66 0.70 −0.21 0.02 0.83 1.11 3.40 2.85 0.45 0.15 0.38 0.12 0.36 0.15 0.88 0.69 0.93 0.00 2.38 2.40 0.53 0.47 2.28 2.40 0.92 0.00 2.05 2.40 0.83 0.00 0.57 0.35 0.88 0.19 2.57 0.12 0.99 −0.01 1.52 0.85
43655 47806 45285 46613 16573 14240 5527 7095 15968 14291 11981 14895 17245 17512 19568 14202 12043 12273 12257 11143 19802 16237 20085 16782 3857 17610 17421 7734 10610 18638 16308 12428 13876 18216 16308 17932 17085 33813 33212 1631 2250 16166 24912 1815 2250 23549 18599 1764 1510 13992 14301 22768 20887 17433 1486 715 15955 12958 2056 1042 18475
57.70
44.42
70.17
65.96
59.96
72.69
2.17
1.15
5.84
1.48
1.05
1.96
1.59
1.06
2.38
6.85
5.71
9.53
2.13
1.65
2.86
2.41
2.08
2.66
300−3000 1400−1900 300−3000 600−2000 300−3000 800−1800 300−3000 800−1800 300−3000 800−1800 300−3000 1400−3000 300−3000 800−1800 300−3000 300−3000 300−3000 600−1900 300−3000 600−1900 300−3000 600−1900 300−3000 600−1900 300−3000 300−3000 600−1900 300−3000 600−1900 300−3000 600−1900 300−3000 600−1900 300−3000 600−1900 300−3000 600−1900 300−3000 800−900 300−3000 800−1800 300−3000 300−3000 300−3000 800−1800 300−3000 800−1800 300−3000 800−1800 300−3000 1000−2000 300−3000 300−3000 300−3000 300−3000 600−2000 300−3000 600−2000 300−3000 600−2000 300−3000
this work 7 this work 14 this work 11 this work 11 this work 11 this work 29 this work 11 this work this work this work 30b this work 30 this work 30 this work 30c this work this work 30d this work 30 this work 30 this work 30 this work 30 this work 30 this work 31e this work 11 this work this work this work 11 this work 11 this work 11 this work 32 this work this work this work this work 14 this work 14 this work 14 this work
2814
115.0
7.60
890.7
7.53
1.19
48.40
10.03
1.00
72.16
1.02
1.00
1.05
1.68
1.06
3.20
8.80
1.90
41.80
9.95
6.12
21.93
4.78
1.51
18.29
3.58
2.15
7.72
4.61
4.97
4.24
5.54
4.15
8.59
1.96
1.60
2.27
4.12
1.16
15.51
1.31
1.17
1.39
1.85
1.51
2.36
7.92
2.72
19.62
36.7 1.63
13.4 1.10
153.9 2.11
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Table 1. continued reactions R34 R35 R36 a
1,6-C6H12(t) → 1,2-C6H12(t) 1,6-C6H12(t) → 1,4-C4H8(t) + C2H4 1,4-C4H8(t) → C2H4(t) + C2H4
log A 4.01 12.48 12.66
n
Ea/R
1.92 0.46 0.38
5212 15784 15858
ravg
rmin
rmax
T (K)
reference
300−3000 300−3000 300−3000
this work this work this work
For H abstraction reactions, the abstractor is the H radical. bFrom allyl + ethylene and detailed balance. cFrom H + butadiene and detailed balance. From non-terminal H + isobutene and detailed balance. eDerived from the rate expression extrapolated from the experimental value.
d
Figure 1. Optimized geometries at the BH&HLYP/cc-pVDZ level for species with available experimental geometries (shown in parentheses). The bond lengths are in angstroms, and the angles are in degrees.
Figure 2. Potential energy profile for cyclohexyl (c-C6H11) decomposition by β-scission and H-transfer isomerization. Energy is in kcal/mol.
For the initial step of cyclohexyl decomposition by β-scission to form the linear intermediate 1-C6H11-6, it occurs with a
step is not considered in the reaction scheme for rate constant calculations. 2815
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Figure 3. Potential energy profile for cyclohexyl (c-C6H11) decomposition by β-scission and H-transfer isomerization. Energy is in kcal/mol.
Figure 4. Potential energy profile for cyclohexyl (c-C6H11) decomposition to form benzene. Energy is in kcal/mol. For H abstraction reactions, the abstractor is the H radical.
further decompose to propylene. The second step is the product pentadiene (1,3-C5H8) formed in the channel R1 → R2 → R9 → R11 and 1,3-butadiene formed in the channel R1 → R2 → R10, as shown in Figure 2. First, the intermediate 1-C6H11-3 can decompose to ethyl and the product 1,3butadiene via a barrier of 38.3 kcal/mol or isomerize to the intermediate 2-C6H11-4 with a barrier of 36.1 kcal/mol. The barriers of these two reactions are close to each other, which makes the two steps competitive. Then, the intermediate 2-C6H11-4 can split a CH3 group (barrier height of 38.7 kcal/mol) and lead to the product of 1,3-pentadiene. Another less competitive channel is
barrier of 32.3 kcal/mol, as shown in Figure 2, which agrees well with that obtained by Knepp et al.25 (31 kcal/mol) using the G2(MP2) theory. As shown in Figures 2 and 3, the linear intermediate 1-C 6 H 11 -6 can then decompose to four intermediates, among which the barrier of R12 with a barrier of 8.7 kcal/mol is the lowest. Thus, as seen from Figure 3, the formation of propylene through the channel R1 → R12 → R14 → R17 → R8 is the most competitive. In this channel, the intermediate 1-CH2−c-C5H9 first isomerizes to the intermediate 1-CH3−C5H8-3 via a barrier of 25.4 kcal/mol. Then, the intermediate 1-C6H11-5 is formed by a β-scission step, which can 2816
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Figure 5. Potential energy (kcal/mol) diagram for dissociation of singlet and triplet states of the biradical 1,6-C6H12. Energy is in kcal/mol.
the production of ethylene and 1,3-butadiene formed via the channel R1 → R3 → R5. The intermediate 1-C6H11-6 first decomposes to the intermediate 1-C4H7-4 and ethylene by β-scission. The 1-C4H7-4 intermediate can then undergo an isomerization step to form the intermediate 1-buten-3-yl (1-C4H7-3), decompose by splitting a hydrogen atom to the product 1,3-butadiene, or decompose to the product ethylene. The barriers of the three reactions are 35.0, 34.4, and 38.0 kcal/mol, respectively. Obviously, the path to form 1,3-butadiene is the easiest reaction pathway. Figure 4 describes benzene formation by dehydrogenation. First, cyclohexene is formed by dehydrogenation of cyclohexyl with a barrier of 35.2 kcal/mol, which agrees very well with that obtained by Knepp et al.25 (35 kcal/mol) with the G2(MP2) theory, and then two cyclohexenyl isomers (c-1-C6H9-3 and c-1-C6H9-4) are produced through H abstractions from cyclohexene by the H radical. Moreover, cyclohexene decomposes to 1,3-butadiene and ethylene; however, the barrier is too high, and this step is less competitive than c-1-C6H9-3 and c-1-C6H94 formation. From the comparison of the two barriers of c-1C6H9-3 and c-1-C6H9-4 formation, we predict that the formation of benzene is mainly from c-1-C6H9-3. In the subsequent reactions, β-scission and dehydrogenation turn out to be competitive. Although the barrier height of reaction 24 is slightly higher than reaction 27, the barrier of reaction 29 is 7.0 kcal/mol higher than that of reaction 26; hence, the channel to benzene formation is more competitive.
It should be noted that the formation of benzene strongly depends upon the reaction conditions. Aribike et al.26 studied the thermal decomposition of cyclohexane in an annular flow reactor at atmospheric pressure with nitrogen dilution, and traces of benzene were found in the product. From the simulation of cyclohexane oxidation, it was suggested that benzene formation was from the cascading dehydrogenation of the cyclohexyl radical and H, OH, and O radicals were the most powerful abstractors of H atoms.11 Stein et al.27 found that the proportion of benzene is up to 30% of the products in the system with the ethyl radical. Therefore, it seems that the ethyl radical is a major factor in the production of benzene. From the above discussions, we can find that traces of benzene are produced in the thermal decomposition of cyclohexane. However, in the case of oxidation or in the presence of other reactants, a lot of benzene can be found in the products. Despite the traces of benzene formation in thermal decomposition of cyclohexane, the reactions are also taken into account, which might be important in the mechanism of cyclohexane oxidation. 3.2.2. Biradical 1,6-C6H12 Decomposition. In Figure 5, dissociations of the singlet and triplet biradicals, 1,6-C6H12(s) and 1,6-C6H12(t), are shown in parts I and II, respectively. As shown in part I, the singlet biradical can undergo a rearrangement reaction through 1,5-H shift to produce 1-hexene (1-C6H12). The calculated barrier for this process is 3.7 kcal/mol, which 2817
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agrees well with that obtained by Herbinet et al.28 (3.9 kcal/mol) using the CBS-QB3 method. Another channel of this biradical decomposition is to form ethylene ultimately by β-scission, and the barriers of the two steps (R31 and R32) in this pathway are 31.5 and 3.9 kcal/mol, respectively. The barrier of R32 agrees well with that by Herbinet et al. (2.8 kcal/mol), but the barrier of R31 is slightly higher than that by Herbinet et al. (27.8 kcal/mol). The energy profile (Figure 5) suggests that the preferred way of decomposition for the singlet biradical 1,6-C6H12(s) is the formation of 1-hexene, which was also proposed by Tsang.3 For the triplet biradical, 1,6-C6H12(t), three channels are considered. As shown in part II in Figure 5, the preferred pathway is the triplet biradical 1-C6H12(t) formation, the barrier of which is 16.6 kcal/mol. Another two channels are not competitive as a result of their high barriers. Moreover, the elementary steps in part II are energetically unfavorable compared to those in part I. 3.3. Rate Constant. To facilitate the use of the reaction rate constants for chemical kinetics modeling, the rate constants are calculated in this work at the temperature range from 300 to 3000 K at high pressures. The kinetic parameters A, n, and Ea of all of the 38 elementary steps obtained in the present work are shown in Table 1. The kinetic parameters available from the literature are also listed for comparison. To compare our rate constants to those from the literature, we define a ratio r as
r = k max /k min
Figure 6. Comparison of calculated rate constants of Ra in this work and the literature.
814 to 902 K and obtained the rate constant for the reaction of cyclohexene decomposition to ethylene and 1,3-butadiene. They assigned values of the A factor and activation energy to be 1.5 × 1015 s−1 and 66 kcal/mol. As shown in Figure 7, the rate
(4)
where kmax is the larger rate constant between k1 and k2, i.e., kmax = max(k1, k2) and kmin is the smaller rate constant between k1 and k2, i.e., kmin = min(k1, k2). k1 and k2 are the rate constants of this work and the literature at the same temperature, respectively. From the definition, we see that kmax ≥ kmin, and hence, r ≥ 1.0. Further, we define ravg, rmax, and rmin as the average, maximum, and minimum of the ratios over the temperature range, respectively. In the discussion below, the analysis on the accuracy of the rate constants calculated in this work is performed in three parts. The first analysis is the comparison between the rate constants in this work and those available from the experiment for Ra and R19. The second analysis is the comparison between the rate constants in this work and those calculated by other authors. The final analysis is the rate constants first reported in this work. Generally, when the data of ravg, rmin, and rmax listed in Table 1 are less than 10.0, we believe that our calculated rate constants are in good agreement with the rate constants suggested by experiments. As seen from Table 1, the rate constant of reaction Ra in this work does not agree well with that from the literature. The rate of C−H bond scission calculated in the present work is smaller (ravg = 57.7) than that by Steil et al.,7 who studied the pyrolysis of cyclohexane using a high-purity shock tube with atomic resonance absorption spectroscopy (ARAS) in the temperature range of 1335−1895 K. Steil et al. obtained the rate constants from those by Voisin et al.8 by increasing by a factor of 7.5. It should be noted that the temperature range in the work by Voision et al. (750−1100 K) and Steil et al. (1400− 1900 K) is different, which may cause the value obtained by Steil et al. to be larger than ours. In Figure 6, we can also find that the values given by Steil et al. are larger than ours. Whereas, the rate constants used by Voision et al. in the modeling of cyclohexane oxidation agree well with ours. Uchiyama et al.31 studied thermal decomposition of cyclohexene in a flow system with temperatures ranging from
Figure 7. Comparison of calculated rate constants of R19 in this work and the literature.
constants calculated in the present work agree well with those from Uchiyama et al. It should be mentioned that an advantage of our work over the experiment is the wider temperature range, as shown in Figure 7. Because CVT is a powerful tool for dealing with reactions without a transition state, as discussed above, the result of reaction Rb (C−C bond scission of cyclohexane) is also believable, although the rate constant by us is smaller than that by Sirjean et al.,14 who gave the transition states of reaction Rb and calculated the rate constants with TST. This may be caused using the different computational methods, i.e., TST by Sirjean et al. and CVT by us, leading to the variation of the rate constants. Sirjean et al. calculated the energy using the CBS-QB3 method and fitted the activation energy to a value of 92.6 kcal/mol. In this work, the fitted activation energy was 90.0 kcal/mol at the CCSD(T)/cc-PVDZ level. Generally speaking, the CBS-QB3 results should be more reliable than those by CCSD(T). We further consider the rate constants by the TST method. The literature data of reactions R1, R2, R3, R5, R20, R23, R24, and R25 listed in Table 1 are from ref 11, which are used as kinetic parameters in the detailed mechanism for kinetics modeling. Besides, the data of reactions R8, R9, R10, R11, R13, R14, R15, R16, R17, and R18 from ref 29 are also used for the same purpose. Many rate constants of those reactions were estimated using a generic method, which are in fact not accurate enough. For example, the rate constant of R8 was obtained 2818
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experiment or high-accuracy calculations, and good agreement is achieved. Finally, reaction rate constants for all 38 elementary reactions in the three-parameter modified Arrhenius expression have been derived in the temperature range of 300−3000 K, which can be used in kinetic modeling studies of pyrolysis and combustion of cyclohexane.
from allyl + ethylene and detailed balance. Consequently, for those reactions mentioned above, the rate constants calculated in this work should be regarded more accurately. As seen from Table 1, some rate constants of those reactions from the literature are quite different from the rate constants given in this work. Therefore, to improve the complicated reaction mechanism for kinetics modeling, continuous effort should be made to provide more accurate kinetic parameters. The calculated rate constants for reactions R4, R26, and R32 are in good agreement with the reported values by other authors over the whole temperature range, because ravg, rmin, and rmax are less than 10.0. However, the discrepancies between the rate constants for reactions R30 and R31 by us and those by Sirjean et al.14 become larger, with rmax being greater than 10.0. As seen from Figure 8, our calculated data are in good agreement
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ASSOCIATED CONTENT
S Supporting Information *
All of the geometries of reactants and products involved in the pyrolysis of cyclohexane at the BH&HLYP/cc-pVDZ level. This material is available free of charge via the Internet at http://pubs.acs.org.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] (Z.-R.L.);
[email protected] (X.-Y.L.). Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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REFERENCES
This work is supported by the National Natural Science Foundation of China (91016002 and 20973118).
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Figure 8. Comparison of calculated rate constants of R30 in this work and the literature.
with those by Sirjean et al. at a temperature beyond 1000 K. A large discrepancy is observed, especially at the temperature range of 600−1000 K. The reason for this deviation in the lowtemperature range is possibly induced by the different methods used to account for the tunneling effect. In this work, Eckart tunneling correction is applied, while Sirjean et al. used the method provided by Skodje and Truhlar.33 For reaction 31, the reason for the large discrepancy is the slight difference between the barrier calculated in this work and that by Sirjean et al. More reliable and accurate theoretical methods should be developed and applied to such reactions involving biradicals to minimize the uncertainties of the reaction barriers.34 To the best of our knowledge, there is no theoretical calculation or experimental data available for comparison for these reactions R6, R7, R12, R21, R22, R27, R28, R29, R33, R34, R35, and R36.
4. CONCLUSION In the present work, we have calculated the rate constants of cyclohexane decomposition at the temperature range from 300 to 3000 K using the CVT and TST methods combined with quantum chemical calculations, and the detailed reaction mechanism has been analyzed. All of the important elementary reactions have been investigated. The channels to the formations of 1,3-butadiene, ethylene, propylene, and 1-hexene identified from experiments are also discussed. Moreover, 38 elementary steps in the pyrolysis of cyclohexane have been considered to make a detailed investigation. The computed rate constants for these steps are expected to be of high accuracy, in which the tunneling effect has been taken into account. These values have been compared to those available from the 2819
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