Direct Measurements of Rate Constants for the Reactions of CH

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Direct Measurements of Rate Constants for CH Radicals with CH, CH, and CH at High Temperatures 2

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Sebastian L. Peukert , Nicole J. Labbe, Raghu Sivaramakrishnan, and Joe V Michael J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp4073153 • Publication Date (Web): 22 Aug 2013 Downloaded from http://pubs.acs.org on August 28, 2013

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The Journal of Physical Chemistry

Direct Measurements of Rate Constants for CH3 Radicals with C2H6, C2H4, and C2H2 at High Temperatures

by

S. L. Peukert, N. J. Labbe, R. Sivaramakrishnan*, and J.V. Michael* Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, IL 60439, USA

Corresponding Authors:

Dr. J. V. Michael D-183, Bldg. 200 Argonne National Laboratory Argonne, IL 60439, USA Phone: (630) 252-3171, Fax: (630) 252-9570 E-mail: [email protected] Dr. R. Sivaramakrishnan L-117, Bldg. 200 Argonne National Laboratory Argonne, IL 60439, USA Phone: (630) 252-3712, Fax: (630) 252-9292 E-mail: [email protected]

The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357. The U.S. Government retains for itself, and others acting on its behalf, a paid-up nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government.

This work was supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, under Contract No. DE-AC0206CH11357.

ACS Paragon Plus Environment

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ABSTRACT The shock tube technique has been used to study the reactions,

CH3 + C2H6 → C2H4 + CH4 + H

(1)

CH3 + C2H4 → Products + H

(2)


(3)

Biacetyl, (CH3CO)2, was used as a clean high temperature thermal source for CH3radicals for all the three reactions studied in this work. For reaction (1), the experiments span a T-range of 1153 K ≤ T ≤ 1297 K, at P ~ 0.4 bar. The experiments on reaction (2) cover a T-range of 1176 K ≤ T ≤ 1366 K, at P ~ 1.0 bar, and those on reaction (3) a T-range of 1127 K ≤ T ≤ 1346 K, at P ~ 1.0 bar. Reflected shock tube experiments performed on reactions (1) – (3), monitored the formation of H-atoms with H-atom Atomic Resonance Absorption Spectrometric (ARAS). Fits to the H-atom temporal profiles using an assembled kinetics model were used to make determinations for k1, k2, and k3. In the case of C2H6, the measurements of [H]-atoms were used to derive direct hightemperature rate constants, k1, that can be represented by the Arrhenius equation,

k1(T) = 5.41 × 10-12 exp(-6043 K/T) cm3 molecules-1 s-1


(1153 K ≤ T ≤ 1297 K)

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for the only bimolecular process that occurs, H-atom abstraction. TST calculations based on abinitio properties calculated at the CCSD(T)/CBS//M06-2X/cc-pVTZ level of theory show excellent agreement, within ± 20%, of the measured rate constants. For the reaction of CH3 with C2H4, the present rate constant results, k2’, refers to the sum of rate constants, k2b + k2c, from two competing processes, addition-elimination, and the direct abstraction,

CH3 + C2H4 → C3H6 + H

(2b)

CH3 + C2H4 → C2H2 + H + CH4

(2c)

Experimental rate constants for k2’ can be represented by the Arrhenius equation,

k2’(T) = 2.18 × 10-10 exp(-11830 K/T) cm3 molecules-1 s-1

(1176 K ≤ T ≤ 1366 K)

The present results are in excellent agreement with recent theoretical predictions. The present study provides the only direct measurement for the high-temperature rate constants for these channels. Lastly, measurements of H-atoms from the reaction of CH3 with C2H2 provided direct unambiguous determinations of the rate constant for the dominant process under the present experimental conditions, the addition-elimination,

CH3 + C2H2 → p-C3H4 + H


(3b)

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Experimental rate constants for k3b can be represented by the Arrhenius equation,

k3b(T) = 5.16 × 10-13 exp(-3852 K/T) cm3 molecules-1 s-1

(1127 K ≤ T ≤ 1346 K)

The present determinations for k3b represent the only direct measurements for this reaction and are also in good agreement with recent theoretical predictions. The present experimental k3b values were also used to derive rate constants, k-3b, for the more extensively studied backprocess, the reaction of H-atoms with propyne. The best fit Arrhenius equation, combining the presently derived k-3b values with a recent experimental determination for k-3b, can be represented by,

k-3b(T) = 3.87 × 10-11 exp(-1313 K/T) cm3 molecules-1 s-1

(870 K ≤ T ≤ 1346 K)

The present studies represent a novel implementation of the sensitive H-ARAS technique to measure rate constants for poorly characterized and difficult to isolate “slow” CH3-radical reactions with stable C2 hydrocarbons.

Keywords: Kinetics, H-ARAS, Transition State Theory, Bimolecular Reactions, Shock Tubes, Soot Precursor


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INTRODUCTION The intention of this paper is to experimentally determine accurate rate constants for reactions between CH3-radicals and three important C2-hydrocarbon compounds: ethane (C2H6), ethylene (C2H4), and acetylene (C2H2) using H-atom Atomic Resonance Absorption Spectroscopy (ARAS) as the diagnostic. Even though these reactions play important roles in the chemistry of fuel rich flames leading to the formation of polycyclic aromatic compounds, (PAH), and soot,1,2 direct rate constant measurements are scarce at combustion temperatures. In the present study, rate constants were obtained for the reactions,

CH3 + C2H6 → C2H4 + CH4 + H

(1)


(2)


(3)

Reaction (1) proceeds by H-atom abstraction with C2H5 and CH4 being the products. Under the conditions of the present shock tube experiments, C2H5 dissociation to C2H4 + H proceeds at a faster rate than CH3-radical induced H-abstraction. Hence, the rate of formation of [H]t (the absolute H-atom concentration as a function of time) refers only to the abstraction process. Reactions (2) and (3) however have more than one product channel. Reaction (2) can proceed through,

CH3 + C2H4 → n-C3H7

(2a)

→ C3H6 + H

(2b)

→ C2H2 + H + CH4

(2c)


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addition (2a), addition-elimination (2b), and direct abstraction (2c). The non-H forming addition process (2a) is negligible, particularly at high temperature and low pressure. The present HARAS diagnostic is sensitive enough to make observations of [H]t due to the processes (2b) and (2c). Hence, the present measurements represent determinations for k2b + k2c. A similar scenario exists in the case of reaction (3) that can also proceed through

CH3 + C2H2 → CH3CHCH

(3a)

→ pC3H4 + H

(3b)

→ aC3H4 + H

(3c)

→ C2H + CH4

(3d)

addition (3a), addition-eliminations leading to propyne and allene, respectively, (3b and 3c) through C3H5 adducts that originate from the entrance channel (3a), and lastly through direct abstraction (3d). Again, in this case, addition is a minor process at high temperatures and low pressures. Hence, the present observations of H-atoms using the high sensitivity H-ARAS diagnostic are a probe for only channels (3b) and (3c) (that lead to H-atoms) and provide unambiguous determinations for k3b + k3c with reaction (3b) being the dominant additionelimination channel between the two. The abstraction channel (3d) does not form H-atoms and is also expected to be energetically inaccessible (∆HR298K = 28.4 kcal/mol) for making any significant contributions to k3, particularly under the present experimental conditions. The most direct attempt to measure rate constants for reaction (1), k1, has been reported by Möller et al.3 In their work, gas mixtures of azomethane (CH3N)2 and C2H6 in Ar were prepared, and CH3-radical depletion was measured behind incident shock waves using UV


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absorption at λ = 216.5 nm to probe [CH3]. Additional high temperature rate constants for reaction (1) have been reported,4 - 10 but none of these experimental studies were designed to 567

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measure k1. Instead, the observations of CH3-radical depletion in some of these studies were most likely complicated by contributions from the CH3-CH3 self-reaction and potentially other unimolecular and bimolecular processes. The remaining studies used measured product yields from flow systems and shock tubes coupled with modeling to derive estimates for k1. There are limited experimental studies in the literature on reaction (2). Holt and Kerr11 reviewed much of the earlier classical reactor studies on this reaction, and their low temperature measurements in the 350-500 K temperature range are possibly unambiguous measurements for the high-pressure limit for reaction 2a because under these conditions k2a ≈ k2. At higher temperatures (750-2000K), k2b and k2c become competitive with k2a as suggested in the most recent theoretical study on the C3H7 Potential Energy Surface by Miller and Klippenstein.12 Measurements of C3H6 in the pyrolysis of C2H4 were attributed to reaction (2b) and, using a relative rate technique, Mackenzie et al.13 obtained k2b/k2c = 1.7 (896 K). At high temperatures in shock tube studies, Tabayashi and Bauer14 determined that reaction (2c) was the dominant channel and suggested rate constants over the 2000-2700 K temperature range. In a series of studies, Back and co-workers,8,15-17 determined values for k2c by a relative rate technique using observations of CH4 formed during the pyrolysis of C2H4. Note that the majority of these experimental studies used relative rate methods and are indirect estimates for k2b and k2c. As with reaction (2), there are very limited experimental studies on reaction (3). The low temperature studies of Holt and Kerr11 concluded that their measurements were in reasonable agreement with the earliest studies on this reaction by Mandelcorn and Steacie,18 but then postulated that the later measurements of Garcia-Dominguez and Trotman-Dickenson19


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underestimated k3. It is very likely that at the low temperature conditions of these classical reactor studies, the measurements refer to only the addition channel k3a. Modeling studies by Diau and Lin20 concluded that even the Holt and Kerr11 experiments were indirect estimates for k3. The NIST chemical kinetics database21 also reports estimates for k3a and k3b at high temperatures by Hidaka et al.22 The lack of direct studies on this reaction motivated the laserphotolysis photo-ionization mass spectrometry study by Kislytsin et al.23 CH3-radical depletion and pC3H4 formation were monitored over the T-range 750 – 1000 K at pressures ranging from ~ 16 – 30 Torr using helium as the bath gas in a heated tubular quartz reactor. Kislytsin et al.23 suggested that under their experimental conditions, the measurements referred primarily to k3b. A recent theoretical study on reactions pertinent to the C3H5 surface by Miller et al.24 shows excellent agreement with the k3a predictions by Holt and Kerr11 for the stabilization channel at low temperatures (albeit with a barrier height adjustment by 2.34 kcal/mol). However, Miller et al.24 suggest that the measurements of Kislytsin et al.23 probably reflect the sum of contributions from k3a and k3b. It still appears that there are limited experimental studies at high temperatures on this potentially important reaction of relevance to PAH and soot precursor formation. In the present work, reflected shock tube experiments have been coupled with the sensitive H-ARAS method for monitoring [H]t. Experiments were performed to measure rate constants for the three title reactions in the temperature and pressure regimes: (a) reaction (1) 1153 K ≤ T ≤ 1297 K and P ~ 0.4 bar: (b) reaction (2) - 1176 K ≤ T ≤ 1366 K and P ~ 0.8 bar: (c) reaction (3) - 1127 K ≤ T ≤ 1346 K and P ~ 0.8 bar. Biacetyl ((CH3CO)2) was used as a source of CH3-radicals. Its thermal dissociation has been characterized in a recent study by Yang et al.25 behind incident shock waves with laser schlieren densitometry. An ab initio based Master Equation analysis of this dissociation provided a fall-off model that agreed well with experiment.


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The present study is a novel implementation of the H-ARAS diagnostic method for measuring “slow” (k ~ 10-15 - 10-14 cm3 molecules-1 s-1) rate constants. This study reports the first experimental determinations of high-temperature rate constants for k2b + k2c, unambiguous hightemperature measurements for k1, and the first direct measurements for k3b at T > 1000 K.

EXPERIMENTAL The present experiments, in Kr diluent, were performed with the reflected shock tube technique using H-atom ARAS detection. The methods and the apparatus currently being used have been previously described. 26,27 The shock-tube was constructed entirely from a 7-m (10.2 cm o.d.) 304 stainless steel tube with the cylindrical section being separated from the He driver chamber by a 4 mil unscored 1100-H18 aluminum diaphragm. The tube was routinely pumped between experiments to less than 1.3 x 10-11 bar by an Edwards Vacuum Products Model CR100P packaged pumping system. Shock-wave velocities were measured with eight equally spaced pressure transducers (PCB Piezotronics, Inc., Model 113A21) mounted along the downstream part of the test section and recorded with the LeCroy model LC334A oscilloscope. Since there is no appreciable attenuation of the incident shock waves in this shock tube, the velocity of the incident wave is calculated as the average over 7 time intervals with standard deviations of about ± 0.3 to 0.7%. In order to calculate temperature and density in the reflected shock-wave regime, the preshock-conditions (T and p) as well as the speed of the incident shock wave are required. This procedure has been given previously, and corrections for boundary layer perturbations have been applied.28–30


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The oscilloscope was triggered by a pulse derived from the last velocity gauge signal. The photometer system was radially located at 6 cm from the endplate.

H-Atom ARAS Detection H-atom ARAS detection was used to quantitatively follow [H]t, the absolute H-atom concentration as a function of time. The optical components (windows and lenses) were crystalline MgF2, and the resonance lamp beam intensity (filtered through 4 cm of air (21% O2) at 1 atm to isolate the Lyman-αH (LyαH) wavelength at 121.6 nm) was measured by a Hamamatsu R8487 solar blind photomultiplier tube, as described previously.31-34 The atmospheric air filter serves as a monochromator since there is a narrow region of high transmittance in the O2 absorption spectrum at 121.6 nm. Signals were recorded with the LeCroy model LC334A oscilloscope. For H-atom detection, the microwave driven resonance lamp was operated at 35 watts and 1.5 Torr of research grade He (99.9999%) (effective Doppler temperature: 470 K).35 Due to lamp gas hydrogeneous impurities in research grade He, LyαH radiation is emitted from the lamp along with a low percent of radiation that is extraneous (nonresonant). In order to measure the fraction of non-resonant radiation present in the lamp, a room temperature H2 discharge flow system, an atom filter, is used to create large [H] (~1 × 1014 atoms cm-3) between the lamp and shock tube window31,35 - 37 thereby removing all of the LyαΗ from the 36

emission lamp. The path length of the atomic filter section is 3 cm. It can be shown using line absorption theory31,35,38 that 3 cm of [H] = 1 × 1014 atoms cm-3 at room temperature will remove 99.6% of LyαH. The fraction of non-resonant emission is ~ 10-15%. This fraction is subtracted from the measured photomultiplier-signal, meaning that 85-90% of the measured signal-intensity is LyαH radiation.


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GASES High purity He (99.995%), used as the driver gas, was from AGA Gases. The lamp gas was He research grade (99.9999%) also from AGA Gases. Research grade Kr (99.999%), the diluent gas in reactant mixtures, was from Praxair, Inc. The ~10 ppm impurities (N2 < 5 ppm, O2 < 2 ppm, Ar < 1 ppm, CO2 < 0.5 ppm, H2 < 1 ppm, H2O < 3 ppm, Xe < 2 ppm, and THC < 0.2 ppm) are all either inert or in sufficiently low concentration so as to not perturb H-atom profiles. H2 (Research grade) was obtained from Airgas. The following compounds were used in this study: C2H6 (Purity: ≥ 99.0%, Sigma Aldrich), C2H4 (Chemically pure, 99.5%, AGA), C2H2 (dissolved, AA Grade, Airgas), and biacetyl (CH3CO)2, 97% Purity; Sigma-Aldrich). All compounds were further purified by bulbto-bulb distillation, retaining only middle thirds for mixture preparation. Gas mixtures of C2H6/(CH3CO)2/Kr, C2H4/(CH3CO)2/Kr, and C2H2/(CH3CO)2/Kr were accurately prepared from pressure measurements using a Baratron capacitance manometer in an all glass high-purity vacuum line.

THEORY The rovibrational properties of the reactants, saddle points for the transition states, and products for the H-abstraction reaction (1) were determined at the M06-2X/cc-pVTZ level of theory. The M06-2X method was used because it has been shown to be an excellent functional for use in thermochemical kinetics39 and is also computationally inexpensive. Higher level energy estimates for the stationary points were obtained using the CCSD(T)/cc-pV∞Z method, where the infinite basis set limits are estimated from an extrapolation of results obtained from sequences of cc-pVnZ where n = (T,Q) basis sets.40,41 The T1 diagnostic,42 which is a measure of


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the multi-reference character, was 0; N* = 2 × [1-0.15log(1.5x)] for log(1.5x) < 0. (+M)

[33] [56]

Best fit H-atom profiles were obtained by adjusting only the rate constant k1 for each experiment with all other rate constants taken as known. Figure 2 shows the local H-atom sensitivity analysis for the 1220 K profile.

1.0

C 2H6 + CH 3 → C 2H 5 + CH 4 CH3 + CH 3 → 2 H + C 2H4

0.8

C 2H6(+M) = CH3 + CH 3(+M) CH4 = CH 3 + H

H sensitivity

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(CH3CO)2 (+M) →

0.6

CH 3CO + CH 3CO(+M)

0.4 0.2 0.0 -0.2 0

500

1000

1500

2000

t / µs Figure 2. Local H-atom sensitivity analysis for the experiment using the Table 2 reaction model and the modeled rate constant for k1. The normalized H-atom-sensitivity is defined as S = (dXH/dki)×(ki/XH,local).


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By measuring H-atom formation, the influence of CH3-CH3 self-reactions is suppressed. The only reaction substantially contributing to [H]t is the H-abstraction (1). Therefore Fig. 2 is a demonstration that k1 can be successfully chemically isolated. The experimental conditions and the best fit rate constants k1 are summarized in Table 3.

Table 3: Summary of experimental conditions for CH3 + C2H6 experiments. P1 / Torra)

Ms

b)

ρ5 / (1018 cm-3)

T5 / K

k1 / cm3molecule-1 s-1 c)

16 Torr experiments 15.9 15.66 15.97 15.86 15.87 15.98 15.81 15.84 15.78

X(C2H6) = 1.92 × 10-4 / X(CH3CO2)2 = 3.78 × 10-6 2.170 2.612 1220 3.82 × 10-14 2.241 2.657 1295 6.31 × 10-14 2.101 2.517 1156 2.74 × 10-14 2.098 2.495 1153 3.24 × 10-14 2.153 2.574 1207 3.69 × 10-14 2.195 2.649 1248 3.70 × 10-14 2.124 2.525 1179 3.07 × 10-14 2.219 2.658 1272 4.57 × 10-14 2.243 2.680 1297 4.65 × 10-14

a)

1 Torr corresponds to 133.32 Pascal Quantities with the subscript 5 refer to the thermodynamic state of the gas in the reflected shock wave region. c) The average uncertainty of k1 is estimated to be ± 10%.

b)

The present experimental values for k1, as well as rate constant evaluations from Baulch et al.,57,58 and Tsang and Hampson,59 and experimentally derived rate constants from Möller et al.3 are shown in Fig. 3.


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T/K 1400 1300 1200

1100

1000

Baulch et al. 1992 Baulch et al. 2005

k1 / cm3s-1

öööö

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M ller et al.

10-13

Tsang/ Hampson

Theory: This work

10-14

7.0 7.5 8.0 8.5 9.0 9.5 10.0

10000 K / T Figure 3. Comparison between experimentally based, recommended, and theoretical rate constants k1: [■] Experiments: This work; [▬▬] 2-parameter Arrhenius fit: This work, (E1); [▬ ▪ ▪ ▬] TST calculations: This work, (E2); [▬ ▪ ▬] Möller et al.3; [▬ ▪ ▪ ▬] Baulch et al.58 2005; [▪ ▪ ▪] Baulch et al.57 1992; [▬ ▬ ▬] Tsang, Hampson 1986.59

Over the T-range 1153 – 1297 K, the temperature dependence of the experimental rate constants in Table 3 can be described by the following expression

k1(T) = 5.41 × 10-12 exp(-6043 K/T) cm3 molecules-1 s-1

(E1)

The values from Table 3 are within ± 10%, at the one standard deviation level of those calculated from Equation (E1). Inspection of Fig. 3 shows that the values reported by Möller et al.3 are a factor of ~ 4 higher than the present study. CH3-radical depletion was monitored by measuring absorption in


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the UV between λ = 192.0 and 216.5 nm. Figure 4a shows two simulated [CH3]-profiles (using the mechanism in Table 2 with a more extensive set of reactions to account for larger C2H6 concentrations used by Möller et al.3) for an experiment at T = 1160 K reported in Figure 4 from the article by Moller et al.3

14

0.5

5x10

T = 1160 K, P = 0.49 bar -5 [(CH3)2N2]0 = 9.9 x 10 [C2H6]0 = 0.013

3x10

14

2x10

Panel (a)

14

0.3

CH3 sensitivity

CH3+CH3 → C2H6

14

1x10

0.5 N2(CH3)2 → N2+CH3+CH3

0.4

CH 3 sensitivity

4x1014

[CH3] / cm-3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


C2H6+CH3 → C2H5+CH4 CH4 = CH3+H

0.2 0.1

Panel (b)

0.0 -0.1

0.4

N2(CH3)2 → N2+CH3+CH3

0.3

C2H6+CH3 → C2H5+CH4

CH3+CH3 → C2H6 C2H6 → CH3 + CH3

0.2 0.1

Panel (c)

0.0 -0.1 -0.2

-0.2

0 0

50

100

150

t / µs

200

250

0

50

100

150

200

250

-0.3

0

t / µs

50

100

150

200

250

t / µs

Figure 4. Panel (a): Symbols: Experimental data extracted from Fig. 4 in ref. 3. [▪ ▪ ▪]-Simulated CH3-profile using k1 from Möller et al.3 The experimental conditions and the rate constant used for this simulation were taken from Fig. 2 and Table 2 in Ref. 3. [▬▬]-Simulated CH3-profile using k1 calculated by Equation (E1). Panel (b): Local CH3-radical sensitivity analysis for this particular experiment using k1 from Möller et al. The normalized CH3-radical sensitivity is defined as S = (dXCH3/dki)×(ki/XCH3,local). Panel (c): Local CH3-radical sensitivity analysis using k1 calculated by (E1).

The symbols are measured from the data shown in Fig. 4, Ref. 3. The only difference between simulations is the choice of k1 values, with the solid line being the simulation using k1 from Eqn. (E1), and the dotted line being the result using the k1 value reported for Fig. 4 by Moller et al.3 For this particular experiment at 1160 K, Möller et al.3 derive a rate constant that is a factor of 2.6 higher than the k1 value from Eqn. (E1). While the simulated profiles using the


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value for k1 from Möller et al.3 is in slightly better agreement with the experimental profile than when using the present k1 value, it should also be noted here that the results of either of these simulations are probably within the noise-level of the observed signal for the [CH3]t profile.3 These simulations also present a contradictory observation. Using the larger k1 value from Möller et al.3, a slower CH3 decay results than when the present slower k1 values from Eqn. (E1) are used. The local [CH3]-sensitivity analysis for either of these simulations shown in Figs. 4b (k1 from Moller et al.3) and Fig. 4c (k1 from Eqn. E1), demonstrates that [CH3]t is much more sensitive to CH3-radical recombination than reaction (1). Consequently, given the relative insensitivity of k1 to the CH3 decay profile (for this particular experiment in Fig. 4a), any choice of k1 within a factor of 2 may reproduce the experimental profile adequately. These simulations lend further credence to the present arguments that the [CH3]t decay profiles from Möller et al.3 cannot be used to derive unambiguous values for k1. In 1992, Baulch et al.57 evaluated existing data for k1. Their values are plotted in Fig. 3 and differ from the present work by a factor of ~ 1.4 - 1.7. The same is true for the Tsang and Hampson59 evaluation. It is interesting to note that a newer evaluation (2005) of k1 by Baulch et al.58 shows greater disagreement with the present experimentally derived rate constants. Baulch et al.58 explained that the new evaluation gave more statistical weight to the data from Möller et al.3 resulting in a large deviation compared to the evaluation from 1992.57 The present conventional transition state theory (TST) calculations, using ab initio properties at the CCSD(T)/CBS//M06-2X/cc-pVTZ level of theory, agree well with the present experimental results. The theoretical predictions for k1 are within ± 20% of the measured rate constants. The present CCSD(T)/CBS//M06-2X/cc-pVTZ based TST predictions for k1 are described to within ± 7 % over the 500-2000 K T-range by


20

Page 21 of 42

k1(T) = 5.73 × 10-23 T 3.44 exp(-5229 K/T) cm3 molecules-1 s-1 (500 – 2000 K)

(E2)

Equation (E2) is also plotted in Fig. 3 as the lowest dash-dot-dotted curve. The present analyses having confirmed the insensitivity of the Möller et al.3 results for k1, then suggest that the present experiments provide the first high-temperature direct measurements for k1. The novel implementation of the H-ARAS technique has also allowed probing reactions of CH3 with the C2 unsaturated hydrocarbons.

CH3 + C2H4 A photomultiplier-signal from the absorption of LyαH in a CH3 + C2H4 experiment at T = 1193 K is shown in Fig. 5a. The initial reactant concentrations are [(CH3CO)2]0 = 2.48 × 1013 cm-3 and [C2H4]0 = 1.30 × 1014 cm-3.

18 16 14.76 mV 14 12 I0 = 11.63 mV 10 8 6 Panel (a) 4 2 0 -0.5 0.0 0.5 1.0 1.5

1.2x1012 CH + C H 3 2 4

[H] / cm-3

Photomultiplier signal / mV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.0x1012 8.0x1011

T5 = 1193 K, P5 = 0.81 bar 13

-3

[(CH3CO)2]0 = 2.48 x 10 cm [C2H4] 0 = 1.29 x 1015 cm-3

6.0x1011 4.0x1011

Panel (b)

2.0x1011 0.0 2.0

0

500

1000

1500

2000

t / µs

t / ms

Figure 5. Panel (a): Measured photomultiplier signal for a CH3 + C2H4 experiment at T5 = 1193 K, P5 = 0.81 bar, [C2H4]0 = 1.29 × 1015 cm-3 and [(CH3CO)2]0 = 2.48 × 1013 cm-3. Panel (b): Measured and simulated best fit profile by using the Table 2 reaction mechanism.


21


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Page 22 of 42

Figure 5a is corrected for the fraction of non-resonant light. As described for Fig. 1a, stepwise changes in signal-intensity are caused by the arrival of the incident and reflected shock wave at the photometer position. The solid line indicates the signal-intensity caused by reactant absorption in the reflected shock wave regime, giving I0 = 11.63 mV for this experiment. The level of signal resulting from the arrival of the incident shock wave is shown as the dashed line in Fig. 5a. The signal intensity of the first step is 14.76 mV. Figure 5b shows the H-atom profile as described above for this experiment. The solid curve is the simulated H-profile using the Table 2 reaction mechanism. Reactions (1), as well as reactions (3b) and (3c) were not included in the modeling of the C2H4 + CH3 experiments. Best fit H-atom profiles were obtained by adjusting the rate constant, k2’, for only the H-atom producing processes, where k2’ = k2b + k2c. Note that k2a gives no H-atoms and is not included. The simulated rate constants are not dependent on the branching ratio between k2b and k2c. Hence, fits only depend on k2’ as long as k2b + k2c sum to k2’. The present experiments therefore cannot be used to determine branching ratios. The theoretical rate constants from Klippenstein and Miller12 suggest that at 1 atm, k2b/k2c ~ 2 to 3 over the temperature range of the present experiments, with slightly lower values at higher temperatures. Figure 6a shows a brute force sensitivity check, varying k2’ by ±25%.


22

Page 23 of 42

0.8 1.2x10

(C3H6+ H and C2H2 + H + CH4 )

0.6

Panel (a)

1.0x10 12 8.0x10

CH3 + C2 H4 → Products + H

12

11

6.0x10 11 4.0x10 11

0.0

0.0

-0.4 1000

1500

2000

(CH3 CO)2 (+M) → CH3CO + CH3 CO(+M)

0.2

-0.2 500

CH3 + CH3 → 2H + C2H4

0.4

2.0x10 11 0

C2 H6 (+M) = CH3 + CH3(+M) CH4 = CH3 +H

H sensitivity

[H] / cm-3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Panel (b) 0

500

t / µs

1000

1500

2000

t / µs

Figure 6. Panel (a): Brute force sensitivity analysis for reaction (2) for the experiment shown in Fig. 5. [▬] Best fit profile; [▬ ▬ ▬] k2’ × 1.25; [▪▪▪▪] k2’ × 0.75. Panel (b): Local H-atom sensitivity analysis for this experiment.

The local H-atom sensitivity shown in Fig. 6b confirms that H-atom formation strongly depends on k2’. CH3-radical self-reactions and the recombination reaction H + CH3 = CH4 show H-atom sensitivity. However, the sum of the H-atom forming channels, (2b) and (2c), have the largest sensitivity over the whole observation period of 2 ms. The experimental conditions and the best fit rate constants k2’ are summarized in Table 4, and the present experimental values for k2’ are plotted in Fig. 7 together with the theoretical prediction for k2’ from Miller and Klippenstein.12 Over the T-range 1176 – 1366 K, the temperature dependence of the experimental rate constants in Table 4 can be described by the following Arrhenius expression

k2’(T) = 2.18 × 10-10 exp(-11830 K/T) cm3 molecules-1 s-1


(E3)

23


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 42

The data presented in Table 4 are within ± 25%, at the one standard deviation level, of those calculated from equation (E3).


Ms

b)

ρ5 / (1018 cm-3)

T5 / K

k2’ / cm3molecule-1 s-1 c)

30 Torr experiments 30.68 30.41 30.6 30.56 30.82 30.79 30.59 30.75 30.81 30.56 30.85 30.27 30.83

X(C2H4) = 1.92 × 10-4 / X(CH3CO)2 = 3.78 × 10-6 2.160 4.888 1193 1.23 × 10-14 2.142 4.795 1176 1.15 × 10-14 2.322 5.287 1358 2.66 × 10-14 2.215 5.030 1244 1.45 × 10-14 2.234 5.104 1267 2.49 × 10-14 2.225 5.076 1258 1.99 × 10-14 2.173 4.910 1207 8.30 × 10-15 2.181 4.95 1214 8.30 × 10-15 2.240 5.12 1273 3.24 × 10-14 X(C2H4) = 2.20 × 10-4 / X(CH3CO)2 = 4.21 × 10-6 2.238 5.071 1271 2.08 × 10-14 2.320 5.323 1355 2.16 × 10-14 2.330 5.247 1366 4.40 × 10-14 2.301 5.273 1335 2.16 × 10-14

a)

1 Torr corresponds to 133.32 Pascal Quantities with the subscript 5 refer to the thermodynamic state of the gas in the reflected shock wave region. c) The average uncertainty of k2’ is estimated to be ± 25%. k2’ = k2b + k2c (see text).

b)

Since no other experimental and theoretical rate constants are available for k2’ at T > 1000 K, the present data have been compared to the most recent theoretical predictions.12 In the theory paper, pressure dependent rate constants were calculated for the reverse process, (-2b), C3H6 + H = CH3 + C2H4. Using thermochemical data for the reactants and products taken from the database from Goos, Burcat, and Ruscic,60 rate constants for the forward reaction, (2b), were


24

Page 25 of 42

then derived for P = 1 atm. The summation of this theoretically derived k2b at 1 atm with the theoretical abstraction rate constant k2c is plotted as the dotted line in Figure 7.

T/K 10 -13

1400 1300 1200

1100

1000

10 -14

'

k2 / cm 3s-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10 -15 7.0 7.5 8.0 8.5 9.0 9.5 10.0

10000 K / T Figure 7. Comparison between present experimental results [○] and ab initio/master equation based prediction for k2’, [▪ ▪ ▪] - k2’ = k2b + k2c, from Miller and Klippenstein12; [▬] - 2-parameter Arrhenius fit of experimental data: This work, (E3).

The remarkable agreement between experiment and theory12 for k2’ is gratifying.

CH3 + C2H2 Figure 8a shows the photomultiplier-signal from the absorption of LyαH in a CH3 + C2H2 experiment at T = 1188 K. The initial reactant concentrations are [(CH3CO)2]0 = 1.69 × 1013 cm-3 and [C2H2]0 = 1.53 × 1015 cm-3.


25

CH3 + C2H2

14 12

12.26 mV

12 10

I0 = 9.76 mV

8 6 4 2 0 -0.5

Page 26 of 42

2.0x1012

16

[H] / cm-3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Photomultiplier signal / mV


1.5x10

T5 = 1188 K, P5 = 0.79 bar [(CH3CO)2]0 = 1.69 x 1013 cm-3

12

1.0x10

[C2H2]0 = 1.53 x 1015 cm-3

5.0x1011

Panel (a)

Panel (b) 0.0

0.0

0.5

1.0

1.5

2.0

0

500

1000

1500

2000

t / µs

t / ms

Figure 8. Panel (a): Measured photomultiplier signal for a CH3 + C2H2 experiment at T5 = 1188 K, P5 = 0.79 bar, [C2H2]0 = 1.53 × 1015 cm-3 and [(CH3CO)2]0 = 1.69 × 1013 cm-3. Panel (b): Measured and simulated best fit profile for this experiment.

Figure 8a is corrected for the fraction of non-resonant light. I0 for this particular experiment is 9.76 mV and the signal intensity arising from the arrival of the incident shock wave is 12.26 mV. The corresponding [H]t-profile is shown in Fig. 8b. Best fit H-atom profiles were obtained by adjusting total rate constants k3’, k3’ = k3b + k3c. Reactions (1), (2b), and (2c) were not relevant for modeling of the CH3 + C2H2 experiments. As before, simulations were performed using the Table 2 reaction mechanism. Both reactions (3b) and (3c) can potentially contribute to [H]t and therefore discerning the contributions of any one of these channels individually is experimentally infeasible. In order to further analyze the data from this complex system we have relied on recent theoretical predictions from Miller et al.24 who have analyzed the thermal kinetics pertinent to the C3H5 potential energy surface. In that study24, rate constants were calculated applying variational transition state theory for dissociations and recombinations, and conventional transition state theory for H-abstraction reactions. The theoretical rate constants


26

Page 27 of 42

for the reverse reactions (-3b), pC3H4 + H = C2H2 + CH3, and (-3c), aC3H4 + H = C2H2 + CH3, were transformed by utilizing thermochemistry from Goos, Burcat, and Ruscic.60 Over the Trange of the present experiments, the theoretical predictions indicate that contributions from channel (3c) are negligible with k3c ~ 0.02 × k3b. Therefore, H-atom formation in the present experiments is predominantly due to only channel (3b). By varying k3b by ± 25%, the brute force sensitivity analysis shown in Fig. 9a demonstrates the sensitivity of the simulated [H]t profiles.

2.0x10 12 1.5x10

0.8

12

1.0x10

12

5.0x10

11

C 2H 2 + CH3 → pC3 H4 + H C 2H 6(+M) = CH 3 + CH 3(+M) CH4 → CH 3 + H

0.6

Panel (a)

H sensitivity

[H] / cm-3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


CH3 + CH 3 → 2H + C 2H 4 (CH 3CO) 2 (+M ) →

0.4

CH3 CO +CH 3 CO(+M)

0.2 0.0 -0.2

0.0 0

500

1000

1500

2000

-0.4

Panel (b) 0

500

t / µs

1000

1500

2000

t / µs

Figure 9. Panel (a): Brute force sensitivity analysis for reaction (3) for the T5 = 1188 K experiment. [▬] Best fit profile; [▬ ▬ ▬] k3b × 1.25; [▪▪▪▪] k3b × 0.75. Panel (b): Local H-atom sensitivity analysis for this experiment.

The local sensitivity analysis in Fig. 9b confirms that reaction (3b) has the largest impact on the measured H-atom formation. The experimental conditions and the best fit rate constants k3b are summarized in Table 5 and plotted in Fig. 10 together with the experimentally determined


27


k3 values from Kislytsin et al.,23 and the theoretical predictions for k3b from Miller et al.24 transformed from the reverse values of k-3b.

T/K 10 -13

k3b / cm 3s-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 42

1400 1200

1000

800

Exp. results (This work) 2-parameter fit, This work, (E4) Calculation for 760 To rr; Miller et al. 24 2008

10

-14

Kislitsyn et al.2 3 2002 Calculation for 30 Torr; Miller et al.24 2008

10 -15 7

8

9

10

11

12

13

10000 K / T Figure 10. Comparison between experimentally obtained and theoretical rate constants calculated by Miller et al.24

Over the T-range 1127 – 1346 K, the temperature dependence of the experimental rate constants in Table 5 can be described by the Arrhenius equation

k3b(T) = 5.16 × 10-13 exp(-3852 K/T) cm3 molecules-1 s-1

(E4)

The values shown in Table 5 are within ± 25%, at the one standard deviation level, of those calculated from Equation (E4).


28

Page 29 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



30.32 30.67 30.86 30.34 30.81 30.49 30.86 30.75 30.7 30.73 30.48 30.72 30.44

k3b / cm3molecule-1 s-1 c) ρ5 / (1018 cm-3) T5 / K 30 Torr experiments X(C2H2) = 2.21 × 10-4 / X(CH3CO)2 = 5.19 × 10-6 2.157 4.822 1191 2.24 × 10-14 2.091 4.696 1127 1.46 × 10-14 2.101 4.755 1137 1.93 × 10-14 2.236 5.028 1269 2.16 × 10-14 X(C2H2) = 3.15 × 10-4 / X(CH3CO)2 = 3.47 × 10-6 2.157 4.915 1186 1.74 × 10-14 2.158 4.868 1188 2.03 × 10-14 2.098 4.763 1130 2.08 × 10-14 2.240 5.130 1269 2.16 × 10-14 2.119 4.795 1150 1.83 × 10-14 2.308 5.292 1339 2.57 × 10-14 2.293 5.230 1319 3.24 × 10-14 2.316 5.309 1346 3.40 × 10-14 2.198 4.965 1227 1.79 × 10-14 Ms

b)

a)

1 Torr corresponds to 133.32 Pascal Quantities with the subscript 5 refer to the thermodynamic state of the gas in the reflected shock wave region. c) The average uncertainty of k3’ is estimated to be ± 25%. k3’ = k3b + k3c (see text).

b)

The theoretical predictions for k3b are in good agreement with the experimentally determined rate constants; i.e., the theoretical rate constants are within ± 40% of the experimental data. While the theoretical predictions24 for k3b also appear to be in good agreement with the data from Kislytsin et al.23 at pressures of ~ 30 Torr, Miller et al.24 suggest that these experiments may be complicated by interference from the addition channel. This is an argument also suggested in the experimental work23 since at T < 1000 K, k3a is competitive with k3b even at 30 torr and the loss of [CH3], (the diagnostic used in Ref. 23), may also be due to other secondary reactions involving the stabilized adduct (CH3CHCH). Consequently, the present experimental data are the most direct determinations for the addition-elimination channel (3b).


29


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Page 30 of 42

Of particular relevance to the present measurements on (3b) are the studies of Bentz et al.61 and Rosado-Reyes et al.62 on the reaction, pC3H4 + H = Products, reaction (6). This reaction involves multiple channels,

pC3H4 + H → CH3CCH2

(6a)

pC3H4 + H → CH3CHCH

(6b)

pC3H4 + H → aC3H4 + H

(6c)

pC3H4 + H → C2H2 + CH3

(-3b)

pC3H4 + H → C3H3 + H2

(6d)

The processes involved include additions, (6a) and (6b), dominant addition-eliminations from the primary adducts formed in (6a) and (6b), (6c) and (-3b), respectively, and finally direct abstraction, (6d). Bentz et al.61 studied reaction (6) by measuring [H]t behind reflected shock waves over the T-range 1200 – 1400 K and pressures between 1.3 and 4.0 bar. The addition channels are minor processes at high temperatures and (6c) does not contribute to the H-atom decay profile under their experimental conditions.61 Therefore, over their T-range, rate constants derived from H-atom depletion refer to the sum from the addition elimination channel, (-3b), and the abstraction channel, (6d), kH = k-3b + k6d. The recent single pulse shock-tube study on reaction (6) by Rosado-Reyes et al.62 at temperatures 870 – 1200 K, and pressures of 1.6 – 7.6 bar involved measurements of stable reaction products. The observations of C2H2 in their study62 were used to determine k-3b. Using the thermochemical data from ref. 60, the present experimentally determined rate constants k3b were transformed to k-3b and compared with the Rosado-Reyes et al. high-temperature measurements for k-3b. Combining the 2-parameter fit to


30

Page 31 of 42

the present data over the T-range 1127 K ≤ T ≤ 1346 K, with the two-parameter fit reported by Rosado-Reyes et al.62 gives the Arrhenius equation over the 870-1346 K T-range,

k-3b(T) = 3.87 × 10-11 exp(-1313 K/T) cm3 molecules-1 s-1

(E5)

T/K 1400

k-3b / cm3s-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1200

1000

-11

10

10-12

7

8

9

10

11

12

10000 K / T Figure 11. Comparison between experimentally based and theoretical rate constants for the reverse reaction of (3b): H + pC3H4 = CH3 + C2H2 (-3b); [∆] k-3b based on k3b-data from this work (P5 ~ 760 Torr); [▬] - 2-parameter fit, equation (E5) (870 K – 1346 K); [▬ ▪ ▬] - kH = k-3b + k6d (see text) measured by Bentz et al.61; [▪ ▪ ▪] - k-3b measured by Rosado-Reyes et al.62 (870 K – 1145 K); [▬ ▬ ▬] - Calculation by Miller et al.24 for P = 760 Torr.

Fig. 11 is the Arrhenius plot for reaction (-3b) with the symbols representing k-3b from this work. Also shown in this plot are the 1 atm theoretical predictions from Miller et al.24 It is quite evident that the present transformed k-3b values are in good agreement, within ± 25% of the theoretical


31


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 42

predictions. The data from Rosado-Reyes et al.62 are also in good agreement, ± 40%, with theory. The predictions from Bentz et al.61 appear to be slightly higher than the theoretical predictions, simply because these measurements also reflect contributions from the abstraction channel (6d). In summary, the present H-ARAS data have provided the first unambiguous measurements for the dominant process in reaction (3) at high temperatures, the addition-elimination channel (3b).

CONCLUSIONS The reflected shock tube technique was used to measure total rate constants for three CH3-radical reactions with simple C2 hydrocarbons, C2H6, C2H4, and C2H2. Experiments were performed over the T-range, 1127-1366 K, at pressures of 0.4-1.0 bars. Biacetyl was used as a thermal source for CH3 radicals in the present experiments. The high sensitivity H-atom ARAS diagnostic was used to probe the kinetics for the three title reactions. In the case of C2H6, the measurements of [H]-atoms were used to derive direct high-temperature rate constants, k1, for the only bimolecular process that occurs, H-atom abstraction,

CH3 + C2H6 → C2H4 + H + CH4

(1)

TST calculations based on ab-initio properties calculated at the CCSD(T)/CBS//M062X/cc-pVTZ level of theory show excellent agreement, within ± 20%, of the measured rate constants. The present measurements and theory suggest a downward revision for this abstraction rate constant from recent Baulch et al.58 estimates to values closer to the older Tsang and Hampson59 and Baulch estimates.57


32

Page 33 of 42

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


For the reaction of CH3 with C2H4, the present rate constant results, k2’, refers to the sum of rate constants, k2b + k2c, from two competing processes, addition-elimination, and the direct abstraction,

CH3 + C2H4 → C3H6 + H

(2b)

CH3 + C2H4 → C2H2 + H + CH4

(2c)

The present results are in excellent agreement with the recent theoretical predictions from Miller and Klippenstein.12 The present study provides the only direct measurement for the hightemperature rate constants for these channels. Lastly, measurements of H-atoms from the reaction of CH3 with C2H2 provided direct unambiguous determinations of the rate constant for the dominant process under the present experimental conditions, the addition-elimination, to form,

CH3 + C2H2 → p-C3H4 + H

(3b)

The present determinations for k3b represent the only direct measurements for this reaction and are in good agreement with the recent theoretical predictions from Miller et al.24 The present experimental k3b values were also used to derive rate constants, k-3b, for the more extensively studied back-process, the reaction of H-atoms with propyne. The present studies represent a novel implementation of the sensitive H-ARAS technique to measure rate constants for poorly characterized and difficult to isolate “slow” CH3-radical reactions with stable C2 hydrocarbons.


33


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Page 34 of 42

ACKNOWLEDGEMENTS This work was supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, under Contract No. DE-AC0206CH11357. Support for R. S. and partial support for J. V. M. was provided as part of the Argonne-Sandia Consortium on High-Pressure Combustion Chemistry, FWP# 2009 ANL 59044.

References 1

Miller, J. A.; Melius, C. F. Kinetic and Thermodynamic Issues in the Formation of Aromatic Compounds in Flames of Aliphatic Fuels Combust. Flame 1992, 91, 21-39.

2

Richter, H.; Howard, J. B. Formation of Polycyclic Aromatic Hydrocarbons and their Growth to Soot—A Review of Chemical Reaction Pathways Prog. Energy Combust. Sci. 2000, 26, 565-608.

3

Möller, W.; Mozzhukin, E.; Wagner, H. Gg. High Temperature Reactions of CH3 2. H-Abstraction from Alkanes Ber. Bunsenges. Phys. Chem. 1987, 91, 660-666.

4

Clarke, T. C.; Izod, T. P. J.; Kistiakowsky, G. B. Reactions of Methyl Radicals Produced by the Pyrolysis of Azomethane or Ethane in Reflected Shock Waves J. Chem. Phys. 1971, 54, 1295-1303.

5

Pacey, P. D.; Purnell, J. H. Arrhenius Parameters of the Reaction CH3 + C2H6 → CH4 + C2H5 J. Chem. Soc. Faraday Trans.1 1972, 68, 1462-1473.

6

Yampolskii, Y. P.; Rybin, V. M. Arrhenius Parameters of the Reaction CH3 + C2H6 → CH4 + C2H5 React. Kinet. Catal. Lett 1974, 1, 321-325.

7

Bradley, J. N.; West, K. P. Single-Pulse Shock Tube Studies of Hydrocarbon Pyrolysis


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Part 6.-The Pyrolysis of Isobutene J. Chem. Soc. Faraday Trans. 1 1976, 72, 558 – 567. 8

Chen, C. J.; Back, M. H.; Back, R. A. The Thermal Decomposition of Methane. II. Secondary Reactions, Autocatalysis and Carbon Formation; Non-Arrhenius Behaviour in the Reaction of CH3 with Ethane Can. J. Chem. 1976, 54, 3175-3184.

9

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TABLE OF CONTENTS GRAPHIC


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Direct Measurements of Rate Constants for the Reactions of CH

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