Experimental and Theoretical Study on the Thermal Decomposition of

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Experimental and Theoretical Study on the Thermal Decomposition of C3H6 (Propene) Wei-Chung Hung,† Chieh-Ying Tsai,† Hiroyuki Matsui,*,† Niann-Shiah Wang,*,† and Akira Miyoshi*,‡ †

Department of Applied Chemistry, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 30010, Taiwan Department of Chemical System Engineering, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo, Japan

‡

S Supporting Information *

ABSTRACT: The mechanism of the thermal unimolecular decomposition of C3H6 (propene) is studied both theoretically and experimentally. The potential energy surfaces for possible reaction pathways are investigated by CBS-QB3 level of quantum chemical calculations, and RRKM/master-equation calculation is performed for the main channels. The time evolutions of H atoms are observed experimentally by using a highly sensitive detection technique (ARAS, detection limit ≈ 1011 atoms cm−3) behind reflected shock waves (0.5−1.0 ppm C3H6 diluted in Ar, 1450−1710 K at 2.0 atm). The objective of this study is to examine the main product channels by combining the experimental and theoretical investigations on the yield and the rates of H atom production. Present quantum chemical calculations identify reactions (1a−1d) as the candidates of product channels: C3H6 → aC3H5 (allyl radical) + H (1a), C3H6 → CH3 + C2H3 (vinyl radical) (1b), C3H6 → CH4 + :CCH2 (singlet vinyldene radical) (1c), and C3H6 → C3H4 (allene) + H2 (1d). The RRKM calculations reveal the branching fractions for (1a), (1b), and (1c) to be approximately 0.8, 0.2, and 0.01, respectively. Reaction (1d) and other product channels are negligible (< 0.1 %), and the pressure dependence of the branching fraction is small under the present experimental conditions. The experimental yield of H atoms (1.7−2.0) is consistent with the theoretical branching fractions considering the Hatom production from the rapid subsequent thermal decomposition of a C3H5 and C2H3. From the observed time profiles of H atoms, the rate of overall thermal decomposition of C3H6 can be evaluated as Ln(k1/s−1) = (38.05 ± 1.18) − (48.91 ± 1.85) × 103 K/T, which is in excellent agreement with the theoretical prediction.

1. INTRODUCTION C3H6 (propene) is one of the most important petrochemical feedstock for a variety of chemical products. It is also formed as an intermediate in the pyrolysis and oxidation of C4 and larger alkanes, which are the major constituents of practical fuels. For example, C3H6 is the dominant product of the thermal decomposition of i-C3H7, s-C4H9, and i-C4H9 radicals and their analogues1 formed by the thermal decomposition of alkanes and larger alkyl radicals produced by the H atom abstraction reactions from alkanes. Elucidation of the mechanisms of pyrolysis and oxidation of C3H6 at high temperatures is still a challenge in the chemistry of alkane combustion. This study focuses on the thermal decomposition of C3H6 (reaction 1). C3H6 → products

is presumed to be the main channel rather than the C−C bond fission (1b). C3H6 → aC3H5 (allyl radical) + H ΔH °298 = 368.7 kJ mol−1 C3H6 → CH3 + C2H3 (vinyl radical) ΔH °298 = 426.1 kJ mol−1

(1b)

The bond dissociation energy (BDE) of C−H in CH3 group (that is, the reaction enthalpy of 1a) is smaller than that of propane (423.2 kJ mol−1) by 54.5 kJ mol−1, while the C−C BDE is larger than that of propane (372.0 kJ mol−1) by 54.1 kJ mol−1. Here, BDEs were calculated from the evaluated standard enthalpy of formation.11 However, the insignificance of 1b is still not conclusive at elevated temperatures. Substantial contribution from 1b has been suggested at high temperatures (1100−1700 K) in

(1)

Reaction 1 has been examined experimentally in the past several decades but not so abundantly compared to the saturated hydrocarbons of similar size.2−10 It is well-known that the decomposition mechanism of C3H6 is different from those of alkanes. Mostly due to the resonance stabilization of the product aC3H5 (allyl radical), C−H bond rupture reaction (1a) © XXXX American Chemical Society

(1a)

Received: October 9, 2014 Revised: January 27, 2015

A

DOI: 10.1021/jp5102169 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Figure 1. Zero-point energy corrected energy diagram for possible decomposition channels of propene (C3H6). The indicated numbers are the results of CBS-QB3 calculations except for those indicated with the ∼ symbol, which are estimated from the triplet CBS-QB3 calculations with the singlet−triplet energy difference calculated by UB3LYP/6-311G(d,p). Broken lines denote triplet states and channels, while solid lines indicate singlet ones. Thick lines indicate the channels 1a−1d that are included in the RRKM/master-equation calculation. The blue lines indicate the channels that contribute to the H/D isotope scrambling during decomposition (see text for details).

calculation is another objective. Quantum chemical calculations on the potential energies of the possible pathways are conducted. Then, the rates for the main channels (1a) and (1b) are calculated by using RRKM/master-equation approach. The rates of the reactions (1c) and (1d) are also evaluated for comparison, although later they will be shown to be minor.

previous studies with a single-pulse shock tube technique based on the yields of the stable products (C2H2, C2H4, CH4, allene, propyne, etc.).2,3 Rao and Skinner employed a noble technique to examine the relative contributions of 1a and 1b by using an atomic resonance absorption spectrometry (ARAS). They monitored H and D atoms in the pyrolysis of partially deuterated propenes (CD 2 CHCH 3 , CH 2 CDCH 3 , and CH2CHCD3) in the temperature range of 1500−1800 K at 0.42 and 2.8 atm.7 From the correlations of the yields of H and D atoms against the difference of the deuterated sites, they derived a relatively large branching fraction for 1b as 0.3−0.37 (0.28 atm) and 0.39 (2.8 atm). Since many of the previous experimental studies employed relatively high concentrations of C3H6, the information on reaction 1 was obscured by the secondary kinetics (i.e., the consumption of propene was rather dominated by the chain reactions of C3H6 with radicals), where the kinetic analysis strongly depends on the uncertain rate coefficients of many elementary processes. Although a sensitive detection method (ARAS) was employed by Rao and Skinner,7 the concentration of propenes (5−10 ppm) was not low enough to eliminate the influence of the side reactions for the whole observation time. In the present study, highly diluted C3H6 sample gases (0.5− 1.0 ppm in Ar) are used to study reaction 1, and H atoms are detected by using the ARAS technique. Interferences of the side reactions of C3H6 with reactive products can be ignored in such low concentration, and therefore, the observed evolutions of H atoms directly represent the decomposition reaction 1 and the consecutive prompt decomposition of radicals. Examination of the mechanism of the thermal decomposition of C3H6 (1) from the yield and the rate of H atoms production is the main objective of this study, since the branching fractions of main channels are sensitive to the evolutions of H atoms. Examination of the mechanism of 1 by the theoretical

C3H6 → : CCH 2 (singlet vinylidene) + CH4

C3H6 → C3H4 (allene) + H 2

(1c)

ΔH °298 = 170.5 kJ mol−1 (1d)

Theoretical branching fractions are compared with the observed time history of H atoms, and the reaction mechanism of 1 is examined by combining these results and presented in the subsequent sections.

2. THEORETICAL CALCULATIONS 2.1. Quantum Chemical Calculations. Quantum chemical calculations have been performed with Gaussian 0912 and MOLPRO 2012.113,14 program packages. Geometries of stationary points were optimized by B3LYP/6-311G(d,p) method and vibrational frequencies were calculated with the same method. Spin-unrestricted wave functions were used for the calculations of open-singlet biradicals and reaction coordinates of bond fission reactions. The energies of the stationary points were calculated by the CBS-QB3 method,15,16 except for the open-singlet biradicals, for which the energies were estimated based on the CBS-QB3 energies of corresponding triplet biradicals and UB3LYP energy differences between singlets and triplets. Calculated reaction enthalpies and entropies of relevant chemical species are compared with literature values11 in Tables S1 and S2 of the Supporting Information, respectively. The agreement in enthalpies was satisfactory considering the possible errors in the calculation B

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The Journal of Physical Chemistry A method16 (≈4.6 kJ mol−1) and typical uncertainty of the experimental heat of formation (up to ≈4 kJ mol−1). Also, the entropies were found to be in excellent agreement. Figure 1 shows the result of the comprehensive search for possible decomposition channels. The dominant dissociation route is expected to be the barrierless C−H bond fission (eq 1a) leading to allyl radical + H located at the lowest energy of 359 kJ mol−1. Three other channels with lowest threshold energies, namely, the C−C bond fission (1b) to vinyl radical + CH3 (416 kJ mol−1), decomposition to singlet vinylidene (H2CC:) + CH4 (1c) with a barrier of 379 kJ mol−1, and H2elimination channel (1d) to form allene (420 kJ mol−1), were included in the RRKM calculations described below. It should be noted that present system (C3H6) is isoelectronic to acetaldehyde (CH3CHO). When the CH2 moiety of propene was replaced by O (oxygen), the major product channels described above correspond to the major decomposition channels of acetaldehyde,17 that is, CH2CHO (vinoxy) + H, HCO + CH3, CO + CH4, and ketene (H2CCO) + H2. This also invokes the potential energy surface of acetaldehyde is a part of the complex reaction system of O(3P) + C2H4,18 in which the ethylene oxide (oxirane) and biradicals play important roles. The corresponding cyclic species, cyclopropane (c-C3H6), biradicals, and potential energy surfaces connected to them were also investigated in the present study as shown in Figure 1. However, as a result, their contributions to the decomposition of propene were concluded to be negligible. That is, none of them are connected to the dissociation products by a route without a high barrier. More specifically, the lowest “tight” transition state was found at 446 kJ mol−1, but this is higher than the similarly tight transition for channel 1d (420 kJ mol−1) which will be shown to be negligible later by RRKM calculations. Also, the lowest “loose” channel to C2H4 + 1CH2 is higher than the energy of channel 1b by 36 kJ mol−1. The calculated equilibrium constant indicated that, even the lowest C3H6 isomer, c-C3H6, exists only 0.2% relative to propene in the equilibrium state at around 1600 K. This indicates that the existence of c-C3H6 and more unstable C3H6 species including biradicals can be neglected. The energies of open-singlet biradicals shown in Figure 1 may not be accurate enough since they are based on the UB3LYP calculations. However, no further attempt for higher-level calculations was made because they were concluded to be unimportant. Calculated molecular parameters of stationary points are listed in Table S3 of the Supporting Information. Since the two major bond-fission channels 1a and 1b do not have pronounced barriers along the reaction coordinate, variational transition state theory (VTST) treatments were necessary for the evaluation of the rate constants. Geometries and vibrational frequencies along the reaction coordinates were optimized and calculated at the B3LYP/6-311G(d,p) level of theory using spin-unrestricted wave functions. Since the reaction coordinates for these reactions can be wellapproximated by varying the C−H and C−C bond lengths, geometry optimizations were performed by restricting the bond lengths, and all the other geometric parameters were relaxed. Energies along the reaction coordinates were evaluated by CASPT2 and MRSDCI+Q single-point calculations with ccpVDZ, cc-pVTZ, and cc-pVQZ basis sets. The wave functions were optimized by the CASSCF calculations with 4-electron/4orbital (4e/4o) active space, which was used as the reference space for further CASPT2 and MRCI calculations. The calculated potential energy curves are shown in Figure 2. The

Figure 2. Potential energy, Vpot, along the reaction coordinates of C− H bond fission (1a) and C−C bond fission (1b) channels calculated by UB3LYP/6-311G(d,p) [ub3lyp], MRSDCI+Q/cc-pVDZ [mrci/ vdz], MRSDCI+Q/cc-pVTZ [mrci/vtz], and MRSDCI+Q/cc-pVQZ [mrci/vqz]. The upper traces show the examples of canonical VTST procedures for rate constants at 1600 K, k1600. At this temperature, the locations of the bottleneck are rC−H ≈ 2.67 Å for C−H fission and rC−C ≈ 2.97 Å for C−C fission.

MRSDCI+Q calculations showed well-converged results with respect to the size of the basis set. Though not shown, the CASPT2 method gave nearly the same results as MRSDCI+Q. It should be noted that the choice of the minimal, 2e/2o, active space gave almost identical results as those with 4e/4o active space for C−C bond fission channel, while use of 2e/2o active space significantly deteriorated the energy profile of the C−H bond fission channel. Including the π-orbitals in active space is inevitable for the C−H fission channel since they significantly interact with the σ-orbitals of the breaking bond and finally form the conjugated π-orbitals of the allyl radical product. On the other hand, for the C−C fission channel, the π-orbital is perpendicular to the CCC plane where the σ-orbitals of the breaking bond reside, and the interaction is symmetrically restricted. In this study, the energies obtained by MRSDCI+Q/ cc-pVQZ with 4e/4o reference space were used for further calculations. Examples of the variational minimization of the canonical rate constants for dissociation at 1600 K are also shown in the upper traces in Figure 2. The location of the canonical bottleneck changed from rC−H = 2.86 (1000 K) to 2.58 Å (2000 K) for C−H bond fission channel, while it is found at rC−C = 3.25 (1000 K) to 2.88 Å (2000 K) for C−C bond fission. 2.2. RRKM Calculations. The high-pressure limiting rate constants were calculated by TST and canonical VTST using GPOP.19 Density of states and microscopic rate constants were calculated by the modified version of UNIMOL program suit.20 Microcanonical VTST was performed by processing the calculated microscopic rate constants manually. The steadystate solutions to the master equation were calculated by using the SSUMES program.21 As described above, four channels, 1a through 1d, were included in the RRKM/master-equation calculations. The vibrational frequencies calculated by B3LYP/ 6-311G(d,p) were scaled by 0.99 for zero-point energy correction as defined in the CBS-QB3 protocol, while they were scaled by 0.97 for the calculation of partition functions and density of states. The torsion motions of the CH3-group along the C−C bond fission reaction coordinate were treated as C

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The Journal of Physical Chemistry A free rotors at rC−C = 3.8 Å and above, and as hindered rotors at rC−C less than 3.8 Å by using the Pitzer-Gwinn approximation22 and corresponding density-of-state formula by Knyazev.23 The torsion barrier height, V0, was estimated from the vibrational frequency, ν, assuming the sinusoidal potential, that is n2BV0 = (hν)2, where n is the rotational symmetry number (3 for CH3), B is the rotational constant for internal rotation calculated from the geometry, and h is the Planck constant. Tunneling corrections were made for channels 1c and 1d by using the analytical transmission coefficients24 for the asymmetric Eckart potential. The grain size for the master-equation calculation was 100 cm−1. Lennard-Jones collision frequencies were calculated by using the collision diameter, σ, and well depth, ε, for Ar (σ = 3.542 Å, and ε/kB = 93.3 K) and propene (4.678 Å and 298.9 K).25 The collisional energy transfer parameter, α, or ⟨ΔEdown⟩, was assumed to be, α = 400(T/1000)0.7 cm−1 based on the previous studies.26,27 Calculated rate constants at a temperature range of 1000− 2000 K are shown in Figure 3. The rate constants under

4. The rate constants in low-pressure range did not show straight lines, and the slope is far from unity (1) except for the

Figure 4. Fall-off behavior of the calculated rate constants in wide pressure range (Ar buffer). Two filled circles indicate the present experimental values 1a (red) and 1b (blue) [1602 K, 2 atm, 1.0 ppm].

main channel (1a). This is partly because of the interference of the internal populations in multiple channel reactions,30 which makes the slopes in the low-pressure region significantly larger than unity for minor channels. Another cause of the unusual pressure dependence at low-pressures is the effect of the tunneling,31 which makes the low-pressure part strongly curved and makes slopes significantly smaller than unity at very low pressures. The calculated branching fractions in the present experimental temperature range are summarized in Figure 5 for Ar

Figure 3. RRKM rate constants in the temperature range 1000−2000 K and at pressures of 0.1, 1, and 10 atm (Ar buffer). The high-pressure limiting rate constants, k∞, are also shown for comparison. For the right figure, different colors are used to distinguish the rate constants for different channels 1a (red), 1b (blue), 1c (orange), and 1d (green), and the different styles of lines are used for the pressures, infinite (HPL), 10, 1, and 0.1 atm, as shown in the left figure.

pressures 0.1−10 are in the falloff region. Similar to many other decomposition reactions of relatively small molecules,11 the pressure dependence becomes significant at higher temperatures, and the falloff expression is necessary for the kinetic modeling. The C−H fission channel 1a is the main product channel in this temperature and pressure range. However, the C−C fission channel 1b also contributes significantly, depending on the temperature and pressure, and, at 2000 K, the highpressure limiting rate constant becomes nearly equal to that of channel 1a. Although minor, the CH4-elimination channel 1c showed the branching fraction of approximately 1%. The H2elimination channel 1d seems to be unimportant as its contribution was always less than 0.1%. It should be noted that the singlet vinylidene (H2CC:) produced by channel 1c is known to be unstable,28,29 even at room temperature and is expected to isomerize promptly to acetylene (HCCH). The lifetime of the singlet vinylidene was estimated to be 0.60 and 0.11 ps at 298 and 1000 K, respectively, from the present TST rate constant, and the equilibrium constant, [H2CC:]e/ [HCCH]e, was estimated to be 1.1 × 10−31 and 3.54 × 10−9 at 298 and 1000 K, respectively. The pressure dependence of the rate constants cannot be expressed by Lindemann or Troe’s formula as shown in Figure

Figure 5. Temperature and pressure dependence of the branching fractions predicted in the present theoretical study for the Ar buffer.

buffer. The averaged branching fractions at present experimental pressure (2 atm) are ≈80% for C−H fission (1a), ≈19% for C−C fission (1b), and ≈1% for CH4 elimination (1c). Because the main channel has the lowest threshold energy (359 kJ mol−1) as shown in Figure 1, the population at the high-energy region is significantly dissipated at lower pressures, and the branching fractions for higher energy channels (1b) at 416 kJ mol−1 and (1c) at 379 kJ mol−1 significantly fall off. The effects of the collisional energy transfer parameters on the calculated rate constants and branching fractions under the present experimental condition are shown in Figure S1 of the Supporting Information. Since the rate constants are close to the high-pressure limit, the results were found to be insensitive to these parameters. D

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The Journal of Physical Chemistry A 3. Experimental Section. The present experiment is conducted behind reflected shock waves in a diaphragmless shock tube at NCTU (length 5.9 m and i.d. 76 mm). The details of the apparatus are described previously.32−34 The diaphragmless shock tube has several advantages over the widely used equipment with diaphragms. First, the test section is maintained under very clean conditions (such as those required for the microelectronic fabrications!), since the exposure to ambient air during the diaphragm replacement can be avoided. Second, the remarkable reproducibility of the shock speeds enables us signal averaging for typically 2−3 shots under the same condition and comparative measurements with reference samples; for example, C2H5I/Ar is used in the present study for the H-ARAS reference. These have become a standard protocol in our group and are proven to be powerful in improving the quality of experimental data.32−34 H atoms are detected by using an atomic resonance absorption spectrometry (ARAS) technique behind reflected shock waves. Light of the atomic transition [2P−2S1/2(2p−1s)] of H at 121.6 nm from a microwave discharge lamp (using a flowing gas mixture of 1% H2/He) is filtered with a monochromator and detected by a solar-blind photomultiplier tube. Calibration curve for H atoms is constructed by the measurements with the mixtures of (0.2−1.0 ppm of C2H5I in Ar) in the temperature range of 1500−1900 K utilizing the well-known reactions,

C2H5I → C2H5 + I

(2a)

C2H5I → C2H4 + HI

(2b)

C3H6 (99.5%, Chiao-Tai Gas Co., Reagent Plus grade) and C2H5I (99%, Sigma-Aldrich, Reagent Plus grade) are purified by repetitive degassing by successive freezing and pumping cycles.

4. EXPERIMENTAL RESULTS AND DISCUSSIONS The total reaction rate for eq 1, k1, and the branching fractions for eqs 1a and 1b are evaluated by monitoring evolutions of H atoms in the 0.5−1.0 ppm of C3H6 diluted in Ar over 1450− 1710 K at a fixed pressure P = 2.0 ± 0.05 atm. In the present experimental condition, the decomposition reactions C3H6 → aC3H5 + H (1a) and C3H6 → CH3 + C2H3 (1b) are followed by the successive production of H by eqs 5 and 6, respectively. (5)

C2H3 → C2H 2 (acetylene) + H

(6)

Reaction 5 is relatively slow compared to reaction 6 or the decomposition of alkyl radicals (except for CH3) due to the resonance stabilization of the allyl radical. However, it is still sufficiently faster than reaction 1. Direct measurement of allyl radical decomposition indicates k5 = 2.3 × 104 s−1 at the lowest temperature of this study (1450 K) at 1 atm,38 and also, the contributions of the isomerization of allyl radical and successive reactions have been indicated to be unimportant. The final yields of H atoms should be, thus, 2 and 1 for reactions 1a and 1b, respectively. The product channels other than 1a and 1b are ignored here based on the result of the theoretical calculation. Examples of temporal profile of H atoms observed in a mixture of 0.5 ppm of C3H6 in Ar are demonstrated in Figure 6. As clearly shown, [H]/[C3H6]0 at 1714 K approaches to the terminal value of about 2.0. This strongly implies the dominance of channel 1a over 1b.

followed by, C2H5 → C2H4 + H

aC3H5 → C3H4 (allene) + H

(3)

Cross-calibration experiments are also performed under the same conditions by measuring O atoms at 130.5 nm in the reaction,

H + O2 → OH + O

(4)

by using the mixtures of 0.2−0.5 ppm of C2H5I and 100−300 ppm of O2 diluted in Ar. The calibration curve for O-ARAS is constructed by using the thermal decomposition of N2O at higher temperatures of 2800−3300 K. As shown in Figure S2 of the Supporting Information, the observed time history of the O atom concentration agree excellently with the kinetic simulations, in which the rate constant for reaction 4 recommended in the latest publications is used.35−37 The branching fraction of 2a is given by ϕ2a = 0.90 ± 0.05. The error limit of the concentration of H is estimated to be within ±10% for [H] < 1013 atom cm−3, considering the uncertainty of the branching fraction of 2a as well as the scatter of the signal intensity of H atoms. In order to avoid the saturation of absorption, the H atom concentration is designed to be less than ≈2 × 1013 atom cm−3. Each time, the signal of H atoms resulting from the impurities or contamination is confirmed to be below the detection limit (1011 atom cm−3) in the blank test using pure Ar. H-ARAS measurements are repeated 2−3 times at the same conditions and the absorption signals are averaged so as to reduce the noise and the shot-by-shot fluctuations. A reference H atom measurement with 0.2−1.0 ppm of C2H5I/Ar accompanies each set of measurements to increase the accuracy of the absolute concentration. Ar (99.9995%, AGA Specialty Gases) and O2 (99.995%, Scott Specialty Gases) are used without further purification.

Figure 6. Examples of the observed evolutions of [H] produced in the 0.5 ppm of C3H6 + Ar mixture (P = 2.0 atm). Black solid line: observed evolution of [H], where experimental condition is shown by the inset. Red solid curve: profiles of [H] obtained by the analytical solution of (I) by optimizing the rate parameters with using nonlinear least-squares analysis. Red dotted curve: optimized analytical solution assuming ϕ1a = 0.85. The right-hand side ordinate ([H]/[C3H6]0) applies only to the 1714 K data.

The concentration of C3H6 in this study is low enough to suppress the secondary reactions. In this case, the evolutions of H can be analytically given by [H]/[C3H6]0 = (1 + ϕ1a)[1 − exp( −k1t )] E

(I)

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The Journal of Physical Chemistry A where, k1 (total rate) = k1a + k1b, ϕ1a = k1a/k1, and [C3H6]0 is the initial concentration of C3H6. Numerical simulation of the H atom profile has been also conducted by using the extended reaction mechanism shown in Table 1. Excellent agreement is found between the simulated

and [H]/[C3H6]0 ≪ 1. Then the normalized profile is analyzed by a linear function of the form [H]/[C3H6]0 = (1 + φ1a)k1t

In this case, k1 is evaluated by assuming ϕ1a = 0.85 (average of the measurements for T > 1600 K). All the experimental results are summarized in Table 2. The experimental result on ϕ1a for T > 1600 K is compared with the

Table 1. Reaction Mechanism Used for Numerical Simulations of C3H6 Decomposition reaction

Aa

na

Eaa

reference

C3H6 → aC3H5 + H C3H6 → C2H3 + CH3 C3H6 + H → aC3H5 + H2 C3H6 + CH3 → aC3H5 + CH4 aC3H5 → C3H4 + H C2H3 → C2H2 + H 2 CH3 (+ M) → C2H6 (+ M) CH3 + CH3 → C2H4 + 2 H CH3 + H2 → CH4 + H N2O + M → N2 + O + M H + O2 → OH + O

2.85 × 1016 5.03 × 1015 5.00 × 1012

0 0 0

97135 97135 1100

this studyb this studyb estimated

1.40 × 1011

0

8800

estimated

1.30 × 1067 2.00 × 1014 6.77 × 1016c

−15.6 0 −1.2c

88168 39653 654c

38 39 39

3.17 × 1013

0

14680.5

40

5.49 × 10

2.7

9414

41

3.98 × 1014

0

556613

42

−0.59

16191

37

03

1.15 × 10

16

(II)

Table 2. Summary of the Branching Fraction of (1a) and the Total Rate k1 Measured in 0.5 and 1.0 ppm of C3H6 + Ar Mixtures (P = 2.0 ± 0.05 atm) [C3H6]/[Ar] 0.5 ppm

1.0 ppm

a

k = ATn exp(−Ea/RT); in the unit of mol, s, cal, cm3, and K. b Determined in the present experimental study. The branching fractions are assumed to be constants (ϕ1a = 0.85 and ϕ1b = 0.15). c Parameters are listed only for the high pressure limit.

a b

T (K)a 1450 1507 1558 1605 1647 1714 1447 1509 1550 1602 1659 1712

± ± ± ± ± ± ± ± ± ± ± ±

3 5 5 6 3 4 2 3 5 5 5 3

k1 (s−1)

ϕ1a

0.71 ± 0.08 0.84 ± 0.08 1.00 ± 0.10

0.84 ± 0.09 0.88 ± 0.08 0.90 ± 0.10

(0.73 (2.30 (7.30 (2.74 (5.65 (1.03 (0.71 (2.08 (8.45 (2.13 (5.31 (1.05

± ± ± ± ± ± ± ± ± ± ± ±

0.03) 0.02) 0.03) 0.05) 0.06) 0.01) 0.02) 0.03) 0.05) 0.05) 0.06) 0.02)

× × × × × × × × × × × ×

102b 102b 102b 103 103 104 102b 102b 102b 103 103 104

The error represents the scatter of the shock wave conditions. Evaluated by assuming ϕ1a = 0.85.

profiles and those of eq (I). An example of the sensitivity analysis is also shown in Figure 7, which assures the validity of

Figure 8. Comparison of the branching fraction obtained in the present experimental and theoretical results (P = 2.0 atm). Black and red ○ present experimental results on ϕ1a in the 0.5 and 1.0 ppm of C3H6 in Ar, respectively. Black, red, and blue curves present theoretical calculations for ϕ1a, ϕ1b, and ϕ1c., respectively.

Figure 7. An example of the sensitivity analysis. The sensitivity coefficient for H atom; 0.5 ppm of C3H6 + Ar mixture, T = 1714 K, P = 2.0 atm. The reaction numbers correspond to those in the text. Except for reactions 1a, 1b, and 5, all other reactions in Table 1 showed negligible sensitivity.

present theoretical calculation in Figure 8. It is shown that the experimental result of the branching fraction ϕ1a is consistent with theoretical conclusion, ϕ1a > 0.8 over T = 1450−1700 K at 2.0 atm. Present study implies that the contribution of 1b is much less than those reported in the previous studies with the single-pulse shock tube2,3 or the shock tube/ARAS techniques.7 In the latter, Rao and Skinner7 reported an interesting study by using partially deuterated propenes, (i) CD2CHCH3, (ii) CH2CDCH3, and (iii) CH2CHCD3, and by observing the time evolutions of H- and D atom concentrations. Since the concentrations of propenes were low (5−20 ppm), initial rates of production of H and D atoms were not seriously affected by the secondary reactions. In order to assess the cause of this disagreement, the H/D branching ratios by Rao and Skinner are compared with those estimated from the present branching fractions (ϕ1a = 0.85 and ϕ1b = 0.15) in Table 3. One clear fact

the simplified analysis. The deviation of the analytical solution (I) from the numerical simulation with full kinetics was found to be smaller than the fluctuation of experimental data. For example, the deviation in the scale of [H]/[C3H6]0 was less than 0.03 at t > 200 μs for 0.5 ppm of C3H6 decomposition at 1650 K and 2.0 atm. For the high temperature data (ca. T > 1600 K), the branching fraction of 1a ϕ1a and the total rate k1 have been evaluated by fitting the observed profiles to eq (I) by using nonlinear least-squares analysis. For the low temperature data (T < 1600 K), however, the total rate and the branching fraction cannot be determined independently because k1t ≪ 1 F

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decomposition may be ascribed to much faster motion of the roaming H atom than that of the roaming CH3 radical in acetaldehyde decomposition. In Figure 9, the experimental result on k1 is compared with the present theoretical calculation and the previous exper-

Table 3. Estimated H/D Production Ratio (kH/kD) from Partially Deuterated Propenes kH/kD Rao and Skinnera

present estimate

compound

2.8 atm

0.42 atm

(frozen isom.b )

(i)

CD2CH−CH3

1.36

3.07

(ii) (iii)

CH2CD−CH3 CH2CH−CD3

1.34 0.67

2.44 1.30

11.3 (2ϕ1a/ ϕ1b) 1.18 (1/ϕ1a) 1.18 (1/ϕ1a)

statisticalc

2 (d2) 5 (d1) 1 (d3)

a

Experimental results from ref 7. bEstimated by assuming the H/D exchange isomerization reactions are frozen. cCalculated assuming the statistical compositions of propane-d2, -d1, and -d3, which correspond to the limiting case that the H/D scrambling reactions are infinitely fast.

is that their H/D ratios for (ii) and (iii) are mutually inconsistent since they should be equal (= 1/ϕ1a). The discrepancy from the present estimate is especially large for (i); it is 1.36 and 3.07 (at 2.8 and 0.42 atm) by Rao and Skinner but is 11.3 in the present estimate. One possible cause of this discrepancy is the H/D isotope scrambling reactions. As shown in Figure 1 (in which the relevant part is indicated by blue), the barrier heights for 3,1-hydrogen shift reaction 7, 2,1-H shift reaction 8 to 2-propylidene CH3C(:)CH3, and 1,2-shift and 2,1back shift reaction 9 via 1-propylidene [:CHCH2CH3]‡, which does not have a minimum on the potential energy surface are 321, 310, and 322 kJ mol−1, respectively, which are sufficiently lower than the threshold energy for the dominant C−H dissociation channel (359 kJ mol−1). CH 2CHCH3 ⇄ CH3CHCH 2

(7)

CH 2CHCH3 ⇄ CH3C(:)CH3( ⇄ CH3CHCH 2)

(8)

CH 2CHCH3 ⇄ [:CHCH 2CH3]‡ ⇄ CH 2CHCH3

(9)

Figure 9. Comparison of the total rate constant k1 derived in this study with the previous works. ● present experiment (0.5 and 1.0 ppm of C3H6 in Ar, P = 2.0 atm). Black broken, solid, and dotted curves present theoretical calculation for P = 10, 1.0, and 0.1 atm, respectively. The results of previous studies are assigned by the ref number in the figure: green dashed curve, ref 3; blue solid curve, ref 4; green solid curve, ref 5 (P = 0.1−0.4 atm); blue dashed curve, ref 6 (HPL); red dashed curve, ref 7 (P = 2.8 atm); red solid curve, ref 8 (P = 1.5−3.0 atm).

imental results. A linear-least-squares analysis gives the following expression for the present experimental result on k1 over the temperature range of 1450−1710 K at P = 2 atm. ln(k1/s−1) = (38.05 ± 1.18) − (48.91 ± 1.85) × 103 K /T

These reactions scramble H/D atoms in partially deuterated propenes. As shown in Figure S3 of the Supporting Information, from (i) CD2CH−CH3, all the possible other propene-d2 isomers (CHDCD−CH3, CHDCH−CH2D, CH2CD−CH2D, and CH2CH−CHD2) are accessible via reactions 7−9. Similarly, all the d1 and d3 isomers are accessible from (ii) CH 2 CD−CH 3 and (iii) CH 2 CH−CD 3 , respectively. The estimated rate constants for eqs 7−9 in the relevant temperature range are compared with those for dissociation in Figure S4 of the Supporting Information. The rate constants for isotope scrambling reactions are comparable to, or even larger than, those for dissociation reactions. As the limiting case, the expected H/D ratio from the statistical mixture of propene-d2, d1, and -d3 are also shown in Table 3. The experimental results are rather close to these “statistical” values. The contribution of the reaction via a roaming transition state (RTS) C3H6 → RTS‡ → C3H4 + H 2

Although the experimental result agrees very well with the theoretical calculation, the observed temperature dependence is slightly larger than the theoretical prediction. The above empirical Arrhenius expression includes some uncertainty due to the assumption of the branching fraction ϕ1a employed in the low temperature region; however, it is not likely the main cause of this disagreement. Substantial disagreement exists among the previous experimental results on k1. Pressure dependence of k1 indicated in the present theoretical calculation is not large and cannot explain such disagreement. The present experimental result is substantially smaller than the recommended rate coefficients4,5 but consistent with the study by Rao and Skinner (P = 2.8 atm),7 as well as that of Hidaka (P = 1.5−3.0 atm).8 It may be worthwhile to note that the present data is the first direct measurement on k1 without being influenced by the secondary reactions.

5. CONCLUSIONS Main conclusions of this study are summarized as follows. (i) The reaction channel 1a is concluded to be dominant in the decomposition of C3H6 in both theoretical and experimental examinations, that is, ϕ1a = 0.8−1.0 in the temperature range of this study. Numerical simulations for the pyrolysis of C3H6 for the enriched concentrations of C3H6 suggest that the product branching fractions ϕ1a and ϕ1b are very sensitive to the

(1d′)

is not evidenced in the present experimental observation. It is concluded that the branching fraction of 1d′ is less than 0.1 even if taking the upper limit of the uncertainty of [H] into consideration. Relatively large contribution of roaming radical channel (20−30%) has been indicated in the thermal decomposition of acetaldehyde.43,44 The difference of C3H6 G

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(3) Burcat, A. Cracking of Propylene in a Shock Tube. Fuel 1975, 54, 87−93. (4) Tsang, W. Chemical Kinetic Data Base for Combustion Chemistry. Part V. Propene. J. Phys. Chem. Ref. Data 1991, 20, 221−273. (5) Kiefer, J. H.; Al-Alami, M. Z.; Budach, K. A. A Shock Tube, LaserSchlieren Study of Propene Pyrolysis at High Temperatures. J. Phys. Chem. 1982, 86, 808−813. (6) Dean, A. M. Predictions of Pressure and Temperature Effects upon Radical Addition and Recombination Reactions. J. Phys. Chem. 1985, 89, 4600−4608. (7) Rao, V. S.; Skinner, G. B. Study of the High-Temperature Pyrolysis of Propene by Determination of H and D Atoms Fromed from Partially Deuterated Propenes Heated Behind Shock Waves. J. Phys. Chem. 1989, 93, 1869−1881. (8) Hidaka, Y.; Nakamura, T.; Tanaka, H.; Jinno, A.; Kawano, H. Shock Tube and Modeling Study of Propene Pyrolysis. Int. J. Chem. Kinet. 1992, 24, 761−780. (9) Yano, T. Shock-Tube Study of Thermal Decomposition of Propene in the Presence of Deuterium. Int. J. Chem. Kinet. 1977, 9, 725−741. (10) Barbe, P.; Martin, R.; Perrin, D.; Scacchi, G. Kinetics and Modeling of the Thermal Reaction of Propene at 800 K. Part I. Pure Propene. Int. J. Chem. Kinet. 1996, 28, 829−847. (11) Baulch, D. L.; Bowman, C. T.; Cobos, C. J.; Cox, R. A.; Just, Th.; Kerr, J. A.; Pilling, M. J.; Stocker, D.; Troe, J.; Tsang, W.; et al. Evaluated Kinetic Data for Combustion Modeling: Supplement II. J. Phys. Chem. Ref. Data 2005, 34, 757−1397. (12) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09, revision D.01; Gaussian, Inc.: Wallingford, CT, 2009. (13) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M. Molpro: A General-Purpose Quantum Chemistry Program Package. WIREs Comput. Mol. Sci. 2012, 2, 242−253. (14) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M.; Celani, P.; Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G. et al. MOLPRO, version 2012.1, A Package of Ab Initio Programs, MOLPRO Home Page. http://www.molpro.net (accessed Aug 31, 2014). (15) Montgomery, J. A., Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. VI. Use of Density Functional Geometries and Frequencies. J. Chem. Phys. 1999, 110, 2822−2827. (16) Montgomery, J. A., Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. A Complete Basis Set Model Chemistry. VII. Use of the Minimum Population Localization Method. J. Chem. Phys. 2000, 112, 6532−6542. (17) Smith, B. J.; Nguyen, M. T.; Bouma, W. J.; Radom, L. Unimolecular Rearrangements Connecting Hydroxyethylidene (CH3− C−OH), Acetaldehyde (CH3−CHO), and Vinyl Alcohol (CH2 CH−OH). J. Am. Chem. Soc. 1991, 113, 6452−6458. (18) Nguyen, T. L.; Vereecken, L.; Hou, X. J.; Nguyen, M. T.; Peeters, J. Potential Energy Surfaces, Product Distributions and Thermal Rate Coefficients of the Reaction of O(3P) with C2H4(X1Ag): A Comprehensive Theoretical Study. J. Phys. Chem. A 2005, 109, 7489−7499. (19) Miyoshi, A. GPOP software, rev. 2013.07.15m4, GPOP Home Page. http://www.frad.t.u-tokyo.ac.jp/~miyoshi/gpop/ (accessed Aug 31, 2014). (20) Gilbert, R. G.; Smith, S. C.; Jordan, M. J. T. UNIMOL Program Suite, Computational Chemistry List Home Page. http://www.ccl.net/ cca/software/SOURCES/FORTRAN/unimol/index.shtml (accessed Aug 31, 2014). (21) Miyoshi, A. SSUMES software, rev. 2010.5.23m4, SSUMES Home Page. http://www.frad.t.u-tokyo.ac.jp/~miyoshi/ssumes/ (accessed Aug 31, 2014).

production rates of stable end products, CH4, C2H2, and C2H6; for example, the production rates of these products increase by a factor of about five if ϕ1a = ϕ1b = 0.5 is assumed for the 0.1− 5.0% C3H6 at 1450 K and 2.0 atm. The results in this study may be meaningful not only in the fundamental kinetics but also in the practical applications. (ii) The total first-order decomposition rate k1 for C3H6 → products (eq 1) is expressed as Ln(k1/s−1) = (38.05 ± 1.18) − (48.91 ± 1.85) × 103 K/T in the temperature range 1450−1710 K and at a pressure of 2.0 atm (Ar buffer). This agrees very well with the present theoretical calculation although the experimental temperature dependence is slightly larger than that of theoretical calculation. The decomposition of C3H6 is concluded to be substantially slower than alkanes of similar size. Nevertheless, contribution of C3H6 cannot be neglected in thermal decomposition of alkanes if C3H6 is a main reaction intermediate. For example, thermal decomposition of i-C4H10 has been studied by the measurement of the yield of H atom where the result of this study is directly applied in order to examine the contribution of the roaming radical/atom mechanisms. (iii) Further examination of the secondary reactions is desirable to improve the kinetic model of the C3H6 pyrolysis at higher concentrations. Understanding the detailed kinetics of unsaturated hydrocarbon radicals is still a challenging and interesting subject.

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ASSOCIATED CONTENT

S Supporting Information *

Comparison of theoretical reaction enthalpies with literature values, comparison of theoretical entropies with literature values, effects of collisional energy transfer parameters on rate constants and branching fractions, an example of the analysis of [O] produced in the C2H5I + O2 mixture, possible H/D isotope scrambling reactions of CD2CH−CH3, CH2CD− CH3, and CH2CH−CD3, estimated high-pressure limiting rate constants for H-shift isomerization reactions of propene in comparison with the experimental and theoretical rate constants for overall dissociations, and calculated molecular properties of stationary points. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by the National Science Council of Taiwan under Grant NSC 101-2113-M-009-020. H.M. deeply acknowledges the support by the National Science Council of Taiwan and National Chiao Tung University. A.M. thanks the support from CSTI-SIP “Innovative Combustion Technology” funded by JST, Japan.

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