Direct Observation of Roaming Radicals in the Thermal

J. Phys. Chem. A 2010, 114, 755–764

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Direct Observation of Roaming Radicals in the Thermal Decomposition of Acetaldehyde R. Sivaramakrishnan, J. V. Michael,* and S. J. Klippenstein* Chemical Sciences and Engineering DiVision, Argonne National Laboratory, Argonne, Illinois 60439 ReceiVed: July 21, 2009; ReVised Manuscript ReceiVed: August 28, 2009

The thermal dissociation of acetaldehyde has been studied with the reflected shock tube technique using H(D)-atom atomic resonance absorption spectrometry detection. The use of an unreversed light source yields extraordinarily sensitive H atom detection. As a result, we are able to measure both the total decomposition rate and the branching to radical versus molecular channels. This branching provides a direct measure of the contribution from the roaming radical mechanism since the contributions from the usual tight transition states are predicted by theory to be negligible. The experimental observations also provide a measure of the rate coefficient for H + CH3CHO. Another set of experiments employing C2H5I as an H-atom source provides additional data for this rate coefficient that extends to lower temperature. An evaluation of the available experimental results for H + CH3CHO can be expressed by a three-parameter Arrhenius expression as k ) 7.66 × 10-20T 2.75 exp((-486 K)/T) cm3 molecule-1 s-1 (298-1415 K). Analogous experiments employing C2D5I as a D-atom source allow for the study of the isotopically substituted reaction. The present experiments are the only direct measure for this reaction rate constant, and the results can be expressed by an Arrhenius expression as k ) 5.20 × 10-10 exp((-4430 K)/T) cm3 molecule-1 s-1 (1151-1354 K). The H/D + CH3CHO reactions are also studied with ab initio transition-state theory, and the results are in remarkably good agreement with the current experimental data. Introduction The photochemical and thermal decompositions of acetaldehyde, CH3CHO, have been of interest in chemical kinetics for over 70 years1 since these topics represent prototypical linear radical chain reactions. Acetaldehye can be used as a source of CH3 radicals in classical photochemical experiments, and these results along with atom and/or radical abstraction rate constants have relevance to interstellar cloud chemistry, where acetaldehyde has been identified to be an important polyatomic species.2 Acetaldehyde is also an intermediate in oxygenated fuel combustion, and, therefore, knowledge of its decomposition reactions is important for describing fuel oxidation.3 This ongoing interest has prompted three new thermal dissociation studies within the past 3 years.4-6 The new studies employed analytical techniques that required the use of large initial concentrations of acetaldehyde. Therefore, all modern studies are complicated by secondary reaction perturbations that may interfere with precise measurements of decomposition rate constants. In contrast, the present work uses high-sensitivity atomic resonance absorption spectrometry (ARAS) for H-atom detection. The resonance light source used in this laboratory is unreversed, allowing for an increase of ∼5 in sensitivity over that used by Bentz et al.,6 who also use the ARAS technique, but with a substantially reversed resonance light source.7 As in earlier work,8 we show that this unreversed source allows experiments to be performed under pseudo-firstorder conditions, i.e., with no secondary reaction interferences. In contrast, the Bentz et al.6 use of the ARAS technique required a substantially larger initial concentration of acetaldehyde, and, therefore, one secondary reaction, namely, H + CH3CHO f products, had a major effect on the long time values of [H]. * Corresponding authors. Tel.: (630) 252-3171 (J.V.M.); (630) 252-3596 (S.J.K.). Fax: (630) 252-9570 (J.V.M.); (630) 252-9292 (S.J.K.). E-mail: [email protected] (J.V.M.); [email protected] (S.J.K.).

These authors were then able to specify rate constants for this reaction as well as those for decomposition. In the present work, we also did experiments with roughly the same [CH3CHO]0 as Bentz et al.6 and determined both rate constants in the same way. Furthermore, we measured rate constants for D + CH3CHO directly in order to extend the T-range of the measurements and to compare with this, other earlier work, and our own theoretical estimates. In all previous experimental studies (see refs 4-6 and references cited therein) the thermal decomposition of CH3CHO is presumed to yield CH3 + CHO via C-C bond scission.

CH3CHO f CH3 + CHO

(R1)

9-14

Theoretical analyses indicate the presence of tight transition states for molecular elimination leading to CH4 + CO and CH2CO + H2

CH3CHO f CH4 + CO

(R2)

CH3CHO f CH2CO + H2

(R3)

that are actually lower in energy than the channel R1 threshold. However, channel R1 is strongly favored entropically over both reactions R2 and R3, with transition-state theory predicting negligible contributions from the tight transition states for these channels for temperatures at which the decomposition is accessible experimentally.4,15 These transition state theory calculations also indicate that the higher lying radical channels, CH3CO + H and CH2CHO + H, are not important for the temperatures and pressures of the present study. However, recent experimental and theoretical work suggests the possibility for new routes to forming reaction R2 and R3 products. In formaldehyde, it was shown that during the process of CH bond fission some of the departing H-atoms can roam around the HCO moiety at long range and subsequently abstract a hydrogen atom to produce H2 + CO.16 Subsequent experi-

10.1021/jp906918z  2010 American Chemical Society Published on Web 12/17/2009

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Sivaramakrishnan et al.

TABLE 1: Stationary Point Properties for the Reaction of CH3CHO with H or D Atoms E/(kcal/mol) stationary point

CASPT2a

QCISD(T)b

CH3CHO

vibrational frequenciesc/cm-1

rotational constantsd/cm-1

158, 509, 779, 910, 1131, 1147, 1393, 1419, 1485, 1497, 1780, 2908, 3077, 3157, 3207

0.304, 0.339, 1.90

CH3CHO + H f CH3CO + H2

5.5

4.6

1696i, 133, 274, 320, 498, 873, 901, 1059, 1139, 1259, 1341, 1379, 1451, 1458, 1816, 3073, 3168, 3202

0.265, 0.334, 1.04

CH3CHO + D f CH3CO + HD

5.0

4.0

1573i, 129, 203, 288, 497, 873, 886, 938, 1143, 1158, 1336, 1389, 1482, 1489, 1840, 3080, 3169, 3203

0.240, 0.334, 0.732

CH3CHO + H f CH2CHO + H2

9.3

9.5

1711i, 152, 315, 489, 590, 843, 941, 1076, 1139, 1251, 1261, 1357, 1427, 1470, 1733, 2999, 3148, 3251

0.284, 0.293, 1.26

CH3CHO + D f CH2CHO + HD

8.6

8.8

1645i, 132, 253, 479, 555, 823, 925, 1011, 1109, 1138, 1246, 1264, 1426, 1470, 1733, 2999, 3147, 3251

0.257, 0.266, 1.02

CH3CHO + H f CH3CH2O

8.7

9.4

1057i, 169, 455, 500, 555, 853, 942, 1110, 1142, 1393, 1425, 1494, 1499, 1629, 2963, 3080, 3169, 3201

0.291, 0.324, 1.30

CH3CHO + D f CH3CHDO

8.3

9.0

798i, 166, 385, 410, 491, 842, 934, 1086, 1133, 1393, 1425, 1493, 1499, 1620, 2963, 3080, 3169, 3201

0.277, 0.319, 1.01

CH3CHO + H f CH3CHOH

10.3

11.1

1646i, 113, 233, 499, 603, 773, 928, 1097, 1146, 1390, 1411, 1478, 1495, 1616, 3051, 3061, 3146, 3200

0.284, 0.311, 1.49

CH3CHO + D f CH3CHOD

9.9

10.7

1230i, 110, 179, 463, 513, 766, 925, 1093, 1146, 1385, 1408, 1476, 1495, 1584, 3051, 3061, 3145, 3200

0.267, 0.291, 1.28

a CASPT2/CBS//CASPT2/aug-cc-pvtz zero point corrected energy relative to CH3CHO + H. b QCISD(T)/CBS//CASPT2/aug-cc-pvtz zero point corrected energy relative to CH3CHO + H. c CASPT2/aug-cc-pvtz harmonic oscillator vibrational frequencies. Numbers in italics are imaginary. d CASPT2/aug-cc-pvtz rotational constants.

Figure 1. [H] profile at 1601 K. The solid line is a fit over the entire time range using the mechanism in Table 2 with k1 + k2 + k3 ) 3700 s-1 and BR1 ) 0.8. The dashed lines represent changes in k1 + k2 + k3 by (25% with BR1 ) 0.8. The dotted lines represent changes in BR1 by (0.08 with k1 + k2 + k3 fixed at 3700 s-1. The conditions for the experiment at T5 ) 1601 K are P1 ) 5.92 Torr, Ms ) 2.522, F5 ) 1.136 × 1018 molecules cm-3, and [CH3CHO]0 ) 8.339 × 1011 molecules cm-3.

mental and theoretical studies of acetaldehyde photodissociation demonstrated the presence of the analogous process with a roaming CH3 radical to give CH4 + CO.15,17-19 The corresponding H-atom roaming in acetaldehyde decomposition would yield H2 + CH2CO, but the higher energy of the corresponding CH3CO + H radical channel implies that this roaming channel is insignificant.4

The experimental study of Heazlewood et al.18 demonstrates that the roaming pathway provides the dominant route to the formation of the molecular products R2 in the photodissociation of acetaldehyde. However, this experiment does not provide any guidance on the magnitude of the roaming branching relative to the radical channel R1. But, the theoretical analysis of Shepler et al.19 suggests that the branching via roaming to the molecular products R2 should be even greater than the branching to radical products R1. To date, there has been no direct experimental observation of the branching between roaming and radical channels in a thermal dissociation. The primary motivation for the present experimental effort is to measure this branching for the thermal decomposition of acetaldehyde. As discussed below, the actual measurements provide the branching between the radical channel R1 and the molecular channels R2 and R3. However, the theoretical analysis in the companion paper15 indicates that this branching is essentially the branching between the radical channel R1 and the roaming contribution from channel R2. As part of this experimental effort, we also determine both experimentally and theoretically the rate constants for the H + CH3CHO and D + CH3CHO reactions. Experiment The present experiments were performed with the reflected shock tube technique using H(D)-atom ARAS detection. The methods and the apparatus currently being used have been described previously,20,21 and only a brief description of the experiment will be presented here.

Thermal Decomposition of Acetaldehyde

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TABLE 2: Mechanism for CH3CHO Decomposition and H/D + CH3CHOa rate constant

ref

1

CH3CHO f CH3 + HCO

k1 ) to be fitted

present work

2

CH3CHO f CH4 + CO

k2 ) to be fitted

present work

3

CH3CHO f CH2CO + H2

k3 ) see text

present work

4

CH3CHO + H f CH3 + H2 + CO

k4 ) to be fitted

present work

5

CH3CHO + D f CH3 + HD + CO

k5 ) to be fitted

present work

6

HCO + Kr f H + CO + Kr

k6 ) 6.00 × 10-11 exp((-7722 K)/T)

37

7

CH3 + CH3 f C2H6

k7 ) k7(F,T)

38

8

CH3 + CH3 f C2H4 + 2H

k8 ) 5.26 × 10-11 exp((-7392 K)/T)

25

9

C2H5I f C2H4 + H + I

k9 ) 6.34 × 109 exp((-15894 K)/T)

44

10

C2H5I f C2H4 + HI

k10 ) 0.15k9

44

11

C2D5I f C2D4 + D + I

k11 ) 2.49 × 1010 exp((-17729 K)/T)(0.3037 + (2.744 × 10-4)T)

39

12

C2D5I f C2D4 + DI

k12 ) 2.49 × 1010 exp((-17729 K)/T)(0.6963 - (2.744 × 10-4)T)

39

13

H + C2D4 f C2D3H + D

k13 ) 3.48 × 10-10 exp ((-2784 K)/T)

40, 41

14

D + CH3 f CH2D + H

k14 ) 2.20 × 10-10

39

a

All unimolecular rate constants are in s-1, and bimolecular rate constants are in cm3 molecule-1 s-1.

The shock tube was constructed entirely from a 7 m (10.2 cm o.d.) 304 stainless steel tube with the 10.2 cm o.d. 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 10-8 Torr 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 a 4094C Nicolet digital oscilloscope. Temperature and density in the reflected shock wave regime were calculated from this velocity. This procedure has been given previously, and corrections for boundary layer perturbations have been applied.22-24 The oscilloscope was triggered by the pulse derived from the last velocity gauge signal on the end plate. The photometer system was radially located at 6 cm from the end plate. For H(D)-atom detection, the lenses were crystalline MgF2, and the resonance lamp beam intensity (filtered through 6 cm

Figure 2. H-atom sensitivity analysis for the 1601 K profile shown in Figure 1 using the full reaction mechanism scheme. The three most sensitive reactions are shown in the inset.

758



TABLE 3: High-T Rate Data [CH3CHO f CH3 + HCO, CH3CHO f CH4 + CO, and CH3CHO f CH2CO + H2] F5b/(1018 cm-3) T5b/K

Msa

5.89 5.92 5.94 5.93 5.96 5.93 5.95 5.96

2.679 2.522 2.534 2.611 2.544 2.417 2.446 2.482

XCH3CHO ) 7.340 × 1.196 1790 1.136 1601 1.145 1616 1.176 1708 1.154 1628 1.090 1481 1.111 1509 1.126 1555

10-7 8740 2960 2212 6187.5 1840 864 840 1575

10.93 10.95 10.94 10.92

2.391 2.540 2.557 2.632

XCH3CHO ) 4.730 × 1.994 1448 2.116 1623 2.128 1643 2.182 1732

10-7 308.75 16.25 1820 780 3187.5 1062.5 6900 2300

0.95 0.70 0.75 0.75

10.93 10.90 10.97 10.90 10.99 10.90

2.686 2.563 2.463 2.412 2.514 2.569

XCH3CHO ) 7.340 × 2.224 1799 2.132 1644 2.057 1534 2.000 1476 2.103 1593 2.129 1656

10-7 11100 3479 1050 280 2040 4140

0.74 0.71 0.70 0.80 0.68 0.69

10.93 10.91

2.507 2.476

XCH3CHO ) 5.418 × 10-7 2.086 1584 2555 2.056 1549 1066.5

945 283.5

0.73 0.79

15.93 15.96 15.94 15.96 15.92 15.90 15.87 15.94

2.665 2.662 2.609 2.480 2.402 2.517 2.572 2.519

XCH3CHO ) 5.418× 10-7 3.203 1757 12000 3.206 1754 13600 3.148 1691 5616 3.012 1545 1742 2.915 1459 422.5 3.041 1585 1815 3.095 1648 4284 3.051 1587 3015

3000 3400 2184 858 227.5 935 2016 1485

0.8 0.8 0.72 0.67 0.65 0.66 0.68 0.67

2.558 2.591 2.512 2.405 2.370 2.673 2.470

XCH3CHO ) 2.722 × 10-7 5.894 1606 3740 5.979 1645 6560 5.793 1554 3420 5.571 1437 873 5.449 1405 696 6.078 1746 13340 5.699 1513 1920

1760 1440 180 27 104 1160 480

0.68 0.82 0.95 0.97 0.87 0.92 0.80

30.84 30.92 30.83 30.92 30.80 30.70 30.92

k1c

k2 + k3c BR1d

P1/Torr

2760 740 588 2062.5 460 336 160 525

3900 1421 450 70 960 1860

0.76 0.80 0.79 0.75 0.80 0.72 0.84 0.75

a The error in measuring the Mach number, Ms, is typically 0.5-1.0% at the one standard deviation level. b Quantities with the subscript 5 refer to the thermodynamic state of the gas in the reflected shock region. c Rate constants: First order in s-1. d BR1 ) k1/(k1 + k2 + k3).

of dry air (21% O2) to isolate the Lyman-RH or Lyman-RD wavelengths at 121.6 nm) was measured by an EMR G14 solar blind photomultiplier tube, as described previously,7,8,25,26 and was recorded with a LeCroy Model LC334A oscilloscope. To measure the fraction of non-Lyman-RΗ present in the resonance absorption emission lamp, an H2 discharge flow system was used to create large [H] between the lamp and shock tube lens,25 thereby removing all of the Lyman-RΗ lamp emission. The H-atom experiments were then performed with the discharge system turned off. However, the D-atom experiments required metering very small amounts of D2 into the resonance lamp such that the lamp intensity was similar to that for H-atoms. This ensures that the D-atom lamp will then be effectively unreversed, i.e., a Gaussian distribution.7 In this case, D-atoms in the presence of H-atoms can be directly detected by carrying out the experiment with the H2 discharge flow system turned on (i.e., removing Lyman-RH) during the D-atom experiment.

Gases High-purity He (99.995%), used as the driver gas, was 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 total hydrocarbon content (THC) < 0.2 ppm) are all either inert or in sufficiently low concentration so as to not perturb H-atom profiles. For H(D)-atom detection, the microwave driven resonance lamp operated at 35 W and 1.9 Torr of ultrahighpurity He (99.999%). This grade of He contains a trace of hydrogenous impurities that are sufficient to give measurable Lyman-RH radiation. For the H + CH3CHO experiments, C2H5I was the source of H-atoms and was supplied by Aldrich Chemical Inc. (reagent grade, g99%). For the D + CH3CHO experiments, C2D5I was the source of D-atoms and was supplied by Aldrich (reagent grade, g99.5%). Acetaldehyde (ACS reagent grade, g99.5%) was obtained from Sigma Aldrich Inc. All three compounds were further purified by bulb-to-bulb distillation, retaining only middle thirds for mixture preparation. Gas mixtures were accurately prepared from pressure measurements using a Baratron capacitance manometer in an all-glass high-purity vacuum line. Theory The reaction of H with CH3CHO (R4) involves either the abstraction of one of the H atoms (R4a and R4b) or addition across either side of the CO π bond (R4c and R4d).

H + CH3CHO f products

(R4)

f CH3CO + H2

(R4a)

f CH2CHO + H2

(R4b)

f CH3CH2O

(R4c)

f CH3CHOH

(R4d)

The rovibrational properties of the reactants and the saddle points for the transition states for each of these channels were studied with multireference second-order perturbation theory employing a complete active space reference wave function (CASPT2).27,28 The calculations for the addition reactions, R4c and R4d, employed a three-electron, three-orbital active space consisting of the CO π and π* orbitals, and the H radical orbital. For the abstraction reactions, R4a and R4b, the active space also included the σ and σ* orbitals for the CH bond being broken to yield a five-electron, five-orbital active space. The correlation consistent augmented polarized valence triple-ζ (aug-cc-pvtz) basis of Dunning and co-workers was employed in these rovibrational analyses.29,30 Higher level energy estimates for these stationary points were obtained via QCISD(T) (quadratic configuration interaction with perturbative inclusion of triples)31 calculations employing the correlation consistent polarized valence triple- and quadruple-ζ basis sets of Dunning and co-workers.29,30 These QCISD(T)/ cc-pvtz and QCISD(T)/cc-pvqz energies employed the spinrestricted QCISD(T) formalism and were extrapolated to the complete basis set (CBS) limit.32 The QCISD(T)/CBS//CASPT2/ aug-cc-pvtz and corresponding CASPT2/CBS//CASPT2/augcc-pvtz energies are summarized in Table 1 together with the CASPT2/aug-cc-pvtz rovibrational properties. The T1 diagnostic33 was less than 0.03 for each of these stationary points, which is low enough to suggest that there is no need to consider multireference effects. These electronic structure calculations were performed with the MOLPRO software package.34



Figure 3. Bimolecular rate constants for CH3CHO + Kr f CH3 + HCO + Kr (where, for example, 1E-13 represents 1 × 10-13). The four panels represent data obtained at four different reflected shock densities from 1 × 1018 to 6 × 1018 molecules cm-3. Symbols are experiments, and lines are theoretical predictions.15

The rate coefficients for reactions R4a-R4d were estimated with conventional transition-state theory (TST).35 Tunneling corrections were obtained from one-dimensional asymmetric Eckart barriers while low-frequency torsional modes were treated as hindered rotors.36 Sample evaluations of variational corrections for the dominant channel, R4a, indicated that they were of negligible significance, as is typical for reactions with significant barriers. Results and Discussion In the present experiments, we measured H-atoms from the subsequent instantaneous HCO-radical decomposition from channel R1 to H + CO. In the absence of reactions that deplete [H], the results will then be a direct measure of reaction R1. Figure 1 shows a typical H-atom profile at T ) 1601 K using [CH3HCO]0 ) 8.339 × 1011 molecules cm-3, yielding [H]∞ ) 6.620 × 1011 atoms cm-3. The line shown in the figure is determined from the mechanism shown in Table 2, where rate constants for reactions R1, R2, and R3 are varied until agreement is obtained. The simulations were performed using the SENKIN42 suite of programs in the CHEMKIN package. The corresponding sensitivity plot is shown in Figure 2, where it is seen that the profile depends only on k1 and k2; i.e., secondary reactions involving H are completely unimportant since the detectability for [H] is so low, indicating that first-order analysis is appropriate. The normalized sensitivity coefficients are defined as S ) ∂ ln [H]/∂ ln ki, where [H] is the H-atom concentration and ki the rate constant for reaction i. Hence, the present results are a direct measure of dissociation. Also, note that the sensitivity to reaction R3 is low because of the theoretically based presumption of a low rate constant for this channel.4,15 First-order analysis gives the simple closed form result

[H]t ) {k1[CH3HCO]0/(k1 + k2 + k3)} {1 - exp(-(k1 + k2 + k3)t)} (E1) where [H]∞ ) k1[CH3HCO]0/(k1 + k2 + k3), BR1 ) k1/(k1 + k2 + k3), and BR2,3 ) 1 - BR1. In the illustration shown in Figure 1, inspection shows that BR1 ) 6.62 × 1011/8.33 × 1011 ) 0.80. We have determined the total decomposition rate constant,

kt ) k1 + k2 + k3, from temporal profiles such as that shown in Figure 1. Subsequently, we determine k1 and k2 + k3 from the measured BR1 for the same experiment. The results are given in Table 3 along with the measured BR1. The decomposition rate constants at various densities are shown in Figures 3 and 4 as Arrhenius plots. The major decomposition pathway is reaction R1, as assumed in all previous work. However, we find significance to reaction R2 that can be either due to concerted and/or roaming mechanisms. This point has been addressed theoretically in the companion paper to follow in this issue,15 and the lines shown in Figures 3 and 4 are the predicted theoretical values from that work. The theoretical calculations15 predict that the concerted processes for reactions R2 and R3 contribute less than 1% to the total rate at the pressure and temperature ranges of the present experiment. Therefore BR1 in these experiments refers to the branching ratio between the radical channel R1 and the sum of R1 and the roaming mechanism in R2. The temperature and density dependences of BR1 are shown in Figure 5. Within experimental error, there is really no clear indication that BR1 varies substantially with either T or F. Over the range of conditions used in the present work, this is confirmed by theory,15 where very slight dependence due to both quantities is predicted. Overall, for the full temperature and pressure range of the experiments, the branching ratio BR1 is measured to be 0.77 ( 0.09. The results for ktotal ) k1 + k2 + k3 from Table 3 are compared in Figure 6 to earlier decomposition studies4,6 and the theoretical predictions from the following paper in this issue.15 The overall agreement among the three data sets is satisfactory over the Tand P-ranges of overlap. The theoretical predictions are in excellent agreement with the present data represented by black symbols. At the highest temperatures and pressures the theoretical predictions are lower than the studies of Gupte et al.4 (blue symbols) and Bentz et al.6 (red symbols). The theoretical predictions can be represented with the following Troe fit: k0 ) 1.90 × 1035T-11.3 exp (-48270/T) cm3 molecule-1 s-1, k∞ ) 2.72 × 1022T-1.74 exp(-43460/T) s-1, and Fcent ) 0.138 exp(670/ T), where T is in K. This fit is valid over the temperature range

760



Figure 4. Bimolecular rate constants for CH3CHO + Kr f CH4 + CO + Kr and H2 + CH2CO + Kr (where, for example, 1E-14 represents 1 × 10-14). The four panels represent data obtained at four different reflected shock densities from 1 × 1018 to 6 × 1018 molecules cm-3. Symbols are experiments, and lines are theoretical predictions.15

Figure 5. Branching ratios for reaction R1 in the thermal decomposition of CH3CHO. The four panels represent data obtained at four different reflected shock densities from 1 × 1018 to 6 × 1018 molecules cm-3. Symbols are experiments, and lines are theoretical predictions.15

from 600 to 2500 K and for pressures ranging from 1 to 1 × 105 Torr. These expressions should replace those given in ref 4, which had a number of errors, although the underlying calculations themselves were correct. As pointed out in the Introduction in connection with the data of Bentz et al.,6 their successful derivation of values for k1 required simultaneous fits for k1 and k4. Their experiments were carried out with much larger concentrations of CH3CHO in which case reaction R4 becomes an important H-atom removal reaction. Note that for the temperatures of their experiments CH3CO and CH2CHO, formed by the abstraction channels R4a and R4b, decompose rapidly to CH3 + CO.43 Furthermore, at high-T (>1000 K) the addition channels are minor (cf. the theoretical predictions given below), and for the purpose of modeling the present experiments, the two abstraction channels can be written as one channel (reaction 4 in Table 2).

We also carried out experiments with roughly the same [CH3CHO]0 as Bentz et al.6 in order to extend the temperature range of our measurements for k1 to lower values. A typical profile is shown in Figure 7, and the solid line is a fit with the Table 2 mechanism. Initial values of k1, k2, and k3 for simulating the profile in Figure 7 are obtained by extrapolation of the results in Table 3 to lower temperatures by means of an Arrhenius expression for each particular reflected shock density range. The corresponding sensitivity analysis, Figure 8, clearly shows that the two reactions that determine the profile in Figure 7 are indeed k1 and k4. This strong sensitivity is also shown in Figure 7, where the dashed and dotted lines are simulations with (30% changes in k1 and k4, respectively. Table 4 lists the conditions for these lower-T experiments and the derived values for both k1 and k4 obtained from simulating the experimental data.


J. Phys. Chem. A, Vol. 114, No. 2, 2010 761 TABLE 4: Intermediate-T Rate Data [CH3CHO f CH3 + HCO, H + CH3CHO f Products]

Figure 6. First-order rate constants for CH3CHO + Kr f products. Blue symbols: (9) P ∼ 50 Torr, (×) P ∼ 200 Torr, (O) P ∼ 350 Torr, (∆) P ∼ 500 Torr. Black symbols: (×) P ∼ 200 Torr, (O) P ∼ 350 Torr, (∆) P ∼ 500 Torr, ([) P ∼ 1000 Torr. Red symbols: ([) P ∼ 1000 Torr, (0) P ∼ 2200 Torr, (+) P ∼ 3500 Torr. Black lines: ( · · · ) P ∼ 50 Torr, (--) P ∼ 100 Torr, (- · -) P ∼ 350 Torr, I- · · -) P ∼ 1000 Torr, [---] - P ∼ 3200 Torr, [-] - P ∼ infinity. Blue symbols represent the data of Gupte et al.,4 black symbols represent the present data, red symbols represent the data of Bentz et al.,6 and black lines are the results of the theoretical calculations.15

Figure 7. [H] profile at 1314 K. The solid line is a fit over the entire time range using the mechanism in Table 2 with the fitted values for k1 and k4 given in Table 4. The dashed lines represent changes in k1 by (30%. The dotted lines represent changes in k4 by (30%. The conditions for the experiment at T5 ) 1314 K are P1 ) 15.92 Torr, Ms ) 2.256, F5 ) 2.713 × 1018 molecules cm-3, and [CH3CHO]0 ) 3.218 × 1013 molecules cm-3.

Figure 8. H-atom sensitivity analysis for the 1314 K profile shown in Figure 7 using the full reaction mechanism scheme in Table 2. The two most sensitive reactions are shown in the inset.

To extend the T-range of validity for k4 to even lower T, we have also performed experiments over the T-range of 1085-1195 K using C2H5I as a thermal source for H-atoms.44 The present experiments are over an order of magnitude more sensitive than the experiments of Bentz et al.6 with peak [H] levels ∼1 ×

P1/Torr

Msa

15.98 15.90 15.92 15.99 15.92 15.89

2.280 2.177 2.226 2.353 2.256 2.352

30.74 30.82 30.88 30.99

2.294 2.224 2.162 2.288

F5b/(1018 cm-3)

T5b/K

k1c

k4d

XCH3CHO. ) 1.186 × 2.755 2.614 2.684 2.858 2.713 2.830

10-5 1339 1230 1279 1411 1314 1415

31 8 5 120 22 110

2.00(-11) 1.10(-11) 1.25(-11) 4.00(-11) 2.50(-11) 4.00(-11)

XCH3CHO. ) 1.186 × 5.221 5.074 4.905 5.264

10-5 1334 1258 1201 1323

35 5 3 43

2.50(-11) 2.00(-11) 1.50(-11) 2.25(-11)

a

The error in measuring the Mach number, Ms, is typically 0.5-1.0% at the one standard deviation level. b Quantities with the subscript 5 refer to the thermodynamic state of the gas in the reflected shock region. c Rate constants: First order in s-1. d Rate constants: Bimolecular in cm3 molecule-1 s-1.

Figure 9. [H] profile at 1085 K. The solid line is a fit over the entire time range using the mechanism in Table 2 with the fitted values for k4 given in Table 5. The dashed lines represent changes in k4 by (30%. The conditions for the experiment at T5 ) 1085 K are P1 ) 15.92 Torr, Ms ) 2.022, F5 ) 2.387 × 1018 molecules cm-3, [CH3CHO]0 ) 2.838 × 1014 molecules cm-3, and [C2H5I] ) 2.533 × 1012 molecules cm-3.

Figure 10. H-atom sensitivity analysis for the 1085 K profile shown in Figure 9 using the full reaction mechanism scheme in Table 2. The four most sensitive reactions are shown in the inset.

1012 atoms cm-3 with S/N ratios at ∼1 × 1011 atoms cm-3. Consequently, an added complication in the present experiments is H-atom formation from the thermal decomposition of CH3CHO, and therefore, we have utilized the model in Table 2

762



TABLE 5: Low-T Rate Data [H + CH3CHO f Products] P1/Torr

F5b/(1018 cm-3)

Msa

T5b/K

k4c

-4

-6

XCH3CHO ) 1.189 × 10 10.89 2.143 10.90 2.100 10.97 2.043

XC2H5I ) 1.061 × 10 1.743 1195 1.35(-11) 1.701 1153 1.20(-11) 1.652 1098 1.04(-11)

XCH3CHO ) 1.189 × 10-4 15.92 2.022 15.92 2.079

XC2H5I ) 1.061 × 10-6 2.387 1085 9.99(-12) 2.479 1134 1.10(-11)

a The error in measuring the Mach number, Ms, is typically 0.5-1.0% at the one standard deviation level. b Quantities with the subscript 5 refer to the thermodynamic state of the gas in the reflected shock region. c Rate constants from modeling H profiles using scheme in Table 2 in units of cm3 molecule-1 s-1.

Figure 12. Plot of the temperature dependence of the theoretically predicted branching between channels R4a, R4b, R4c, and R4d.

TABLE 6: Modified Arrhenius Parameters for the Rate Coefficients for Reactions R4a-R4d reaction

Figure 11. Arrhenius plot of the H + CH3CHO rate constants. Black symbols and lines: (-) theory, present work, 298-2000 K; (--) threeparameter evaluation, present work, eq E2, 298-2000 K; ( · · · ) threeparameter evaluation, Bentz et al.,6 298-2000 K; (/) Michael and Lee,46 298 K; (O) Whytock et al.,45 298-500 K; (+) Ohmori et al.,47 299 K; (0) Bentz et al.;6 (b) present work, C2H5I/CH3CHO mixtures (Table 5), 1085-1195 K. Red symbol: (b) present work, large concentration CH3CHO mixtures (Table 4), 1201-1415 K. Blue symbol and line: (∆) present work, C2D5I/CH3CHO mixtures (Table 7), 1151-1354 K; (-) theory, present work, D + CH3CHO, 298-2000 K. Inset depicts an expanded version of the Arrhenius plot over the T-range of 1000-2000 K for clarity.

to derive k4. This complication is the limiting factor in extending the use of this source to higher T. Figure 9 shows the H-atom profile for an experiment at 1085 K. The solid line represents the fit to the profile using the mechanism in Table 2. Changes by (30% degrade the quality of the fit essentially highlighting the strong sensitivity of k4 in these experiments. This is also highlighted in Figure 10, which depicts the corresponding linear sensitivity analysis for the H-atom profile in Figure 9. Table 5 provides a listing of the experimental conditions and the derived values for k4. Combining the present sets of data (Tables 4 and 5) for reaction 4, the data of Bentz et al.,6 and the lower-T results of Whytock et al.,45 Michael and Lee,46 and Ohmori et al.,47 rate constants have been evaluated over the temperature range of 298-1415 K to give k4 ) 7.66 × 10-20T2.75 exp((-486 K)/T) cm3 molecule-1 s-1

(E2) A plot of eq E2 and the data from which it was derived is shown in Figure 11. As discussed by Whytock et al.45 uncertainties in the T-dependent stoichiometric corrections applied by Aders and Wagner48 is the most probable cause for their rate constants being a factor of 2 lower than that of

A

n

E

CH3CHO + H f CH3CO + H2

2.18 × 10-19

2.58

614

CH3CHO + D f CH3CO + HD

1.85 × 10-19

2.58

555

CH3CHO + H f CH2CHO + H2

4.52 × 10-21

3.10

2620

CH3CHO + D f CH2CHO + HD

2.59 × 10-21

3.16

2470

CH3CHO + H f CH3CH2O

7.66 × 10-17

1.71

3570

CH3CHO + D f CH3CHDO

1.14 × 10-16

1.63

3720

CH3CHO + H f CH3CHOH

2.89 × 10-18

2.20

3780

CH3CHO + D f CH3CHOD

2.92 × 10-17

1.89

4320

a k ) AT n exp(-E/T) cm3 molecule-1 s-1, where A is in cm3 molecule-1 s-1 and T is in K. Valid for T ) 200-2500 K.

Whytock et al.45 We have consequently ignored the Aders and Wagner48 measurements when making the experimental evaluation. The present theoretical predictions for the branching between channels R4a, R4b, R4c, and R4d are illustrated in Figure 12. For the two addition channels the predictions correspond to the high-pressure limit. Clearly, the two abstraction channels dominate the kinetics, with (R4a) contributing more than 80% for temperatures up to 1000 K. At even higher temperatures, the contribution from (R4b) can become significant. Modified Arrhenius fits of the individual channel rate coefficients for (R4) are reported in Table 6. The theoretical calculations, with no scaling of the ab initio potential energy surface or force fields, predict the k4 values



Figure 13. [D] profile at 1190 K. The solid line is a fit over the entire time range using the mechanism in Table 2 with the fitted values for k5 given in Table 5. The dashed lines represent changes in k5 by (30%. The conditions for the experiment at T5 ) 1190 K are P1 ) 15.92 Torr, Ms ) 2.133, F5 ) 2.548 × 1018 molecules cm-3, [CH3CHO]0 ) 2.104 × 1014 molecules cm-3, and [C2D5I] ) 4.388 × 1012 molecules cm-3.

shown in Figure 11 as the solid line. It is clear that the theory is in excellent agreement being within (15% of the present experimental evaluation in the higher-T regime (>1000 K). The theoretical predictions show increasing deviations from the evaluation of Bentz et al.6 at high-T (>1500 K) with theory predicting a total abstraction rate constant that is 33% higher at 2000 K. The lower-T data45-47 are higher than the unscaled theory by 15-30%. It is evident that theory is in excellent agreement with the available literature data, especially at high-T (>1000 K). A very small change in the imaginary frequency (well within the uncertainties of the theoretical methods) yields excellent agreement with the lower-T results without degrading the fit to the high-T data. We have also carried out experiments on the isotopically substituted reaction

D + CH3CHO f products

(R5)

as a further test of the theoretical predictions. A typical profile is shown in Figure 13. With all rate constants set to the values measured in this work and laboratory, simulation was successful using the Table 2 mechanism but with only variations in k5. Figure 14 shows the accompanying sensitivity analysis. Clearly, at long times k5 values show substantial sensitivity, and this point is additionally illustrated in Figure 13 where the dashed lines are obtained with (30% changes in k5. The values obtained are listed in Table 7, where the details of the experiments are also given.

Figure 14. D-atom sensitivity analysis for the 1190 K profile shown in Figure 13 using the full reaction mechanism scheme in Table 2. The four most sensitive reactions are shown in the inset.

The data can be represented by means of an Arrhenius expression over the T-range, 1151-1354 K, giving

k5 ) 5.20 × 10-10 exp((-4430 K)/T) cm3 molecule-1 s-1 (E3) Equation E3 is an excellent representation and lies within (6% of the data. These results are plotted in Figure 11 where the agreement with the corresponding theory predictions is excellent, being within (12% of one another. The isotope effect, k4/k5, over the limited temperature range of the present study is computed from theory to be 1.09, and the data given in Tables 4, 5, and 7 yield a ratio of 1.14 ( 0.03 in excellent agreement with the theoretical predictions. Conclusion The contribution of the roaming channel to the total thermal dissociation rate in acetaldehyde is measured to be 0.23 ( 0.09 for temperatures in the range from 1346 to 1888 K and pressures of a few hundred Torr. The combination of these measurements with the theoretical analysis of ref 15 provides definitive evidence for a significant contribution from roaming radicals in a thermal decomposition. In the studied range there is little dependence of this branching on temperature and/or pressure. The rate coefficient for the CH3CHO + H/D reaction was also measured in the present experimental work using a variety of techniques to obtain accurate values over the range from 1085 to 1415 K. The corresponding predictions from the present ab initio TST analysis are in good agreement with these measured rate coefficients. An evaluation of the data from 298 to 1415 K yields the expression given in eq E2.

TABLE 7: Low-T Rate Data [D + CH3CHO f Products] P1/Torr

Msa

F5b/(1018 cm-3)

-5

XCH3CHO. ) 8.256 × 10 15.92 2.133 15.86 2.217 15.84 2.299 15.89 2.255 15.90 2.097 15.90 2.112

T5b/K

k5c

k5d

-6

2.548 2.662 2.765 2.717 2.501 2.515

XC2D5I ) 1.722 × 10 1190 1.14(-11) 1270 1.47(-11) 1354 2.05(-11) 1308 1.75(-11) 1151 1.13(-11) 1170 1.42(-11)

1.20(-11) 1.49(-11) 2.08(-11) 1.74(-11) 1.12(-11) 1.25(-11)

a The error in measuring the Mach number, Ms, is typically 0.5-1.0% at the one standard deviation level. b Quantities with the subscript 5 refer to the thermodynamic state of the gas in the reflected shock region. c Rate constants: pseudo-first-order in units of cm3 molecule-1 s-1. d Rate constants from modeling D profiles using scheme in Table 2 in units of cm3 molecule-1 s-1.

764


Acknowledgment. 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-AC02-06CH11357. Drs. Lawrence B. Harding and Yuri Georgievskii are acknowledged for helpful discussions. References and Notes (1) Benson, S. W. The Foundations of Chemical Kinetics; McGrawHill: New York, 1960. (2) Gilmore, W.; Morris, M.; Johnson, D. R.; Lovas, F. J.; Zuckerman, B.; Turner, B. E.; Palmer, P. Astrophys. J. 1976, 204, 43. (3) Zhang, Y.; Yang, Y.; Boehman, A. L. Combust. Flame 2009, 156, 1202. (4) Gupte, K. S.; Kiefer, J. H.; Tranter, R. S.; Klippenstein, S. J.; Harding, L. B. Proc. Combust. Inst. 2007, 31, 167. (5) Yasunaga, K.; Kubo, S.; Hoshikawa, H.; Kamesawa, T.; Hidaka, Y. Int. J. Chem. Kinet. 2008, 40, 73. (6) Bentz, T.; Striebel, F.; Olzmann, M. J. Phys. Chem. A 2008, 112, 6120. (7) Michael, J. V.; Lifshitz, A. In Handbook of Shock WaVes, Vol. 3; Ben-Dor, G., Igra, O., Elperin, T., Lifshitz, A., Eds.; Academic Press: New York, 2001; pp 77-105. (8) Kumaran, S. S.; Carroll, J. J.; Michael, J. V. Proc. Combust. Inst. 1998, 27, 125. (9) Yadav, J. S.; Goddard, J. D. J. Chem. Phys. 1986, 84, 2682. Martell, J. M.; Yu, H.; Goddard, J. D. Mol. Phys. 1997, 92, 497. (10) Smith, B. J.; Nguyen, M. T.; Bouma, W. J.; Radom, L. J. Am. Chem. Soc. 1991, 113, 6452. (11) Joshi, A.; You, X.; Barckholtz, T. A.; Wang, H. J. Phys. Chem. A 2005, 109, 8016. (12) Nguyen, T. L.; Vereecken, L.; Hou, X. J.; Nguyen, M. T.; Peeters, J. J. Phys. Chem. A 2005, 109, 7489. (13) Shepler, B. S.; Braams, B. J.; Bowman, J. M. J. Phys. Chem. A 2007, 111, 8282. (14) Harding, L. B.; Klippenstein, S. J.; Jasper, A. W. Phys. Chem. Chem. Phys. 2007, 9, 4055. (15) Harding, L. B.; Georgievskii, Y.; Klippenstein, S. J. J. Phys. Chem. A, the following paper in this issue, DOI: 10.1021/jp906919w. (16) Townsend, D.; Lahankar, S. A.; Lee, S. K.; Chambreau, S. D.; Suits, A. G.; Zhang, X.; Rheinecker, J. L.; Harding, L. B.; Bowman, J. M. Science 2004, 306, 1158. (17) Houston, P. L.; Kable, S. H. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 16079. (18) Heazlewood, B. R.; Jordan, M. J. T.; Kable, S. H.; Selby, T. M.; Osborn, D. L.; Shepler, B. C.; Braams, B. J.; Bowman, J. M. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 12719. (19) Shepler, B. S.; Braams, B. J.; Bowman, J. M. J. Phys. Chem. A 2008, 112, 9344. (20) Michael, J. V. Prog. Energy Combust. Sci. 1992, 18, 327.

Sivaramakrishnan et al. (21) Michael, J. V. In AdVances in Chemical Kinetics and Dynamics Barker, J. R., Ed.; JAI: Greenwich, 1992; Vol. I, pp 47-112 (for original references). (22) Michael, J. V.; Sutherland, J. W. Int. J. Chem. Kinet. 1986, 18, 409. (23) Michael, J. V. J. Chem. Phys. 1989, 90, 189. (24) Michael, J. V.; Fisher, J. R. In 17th International Symposium on ShockWaVes and Shock Tubes; Kim, Y. W., Ed.; AIP Conference Proceedings 208; American Institute of Physics: New York, 1990; pp 210-215. (25) Lim, K. P.; Michael, J. V. Proc. Combust. Inst. 1994, 25, 713, and references therin. (26) Kumaran, S. S.; Su, M.-C.; Lim, K. P.; Michael, J. V. Proc. Combust. Inst. 1996, 26, 605. (27) Werner, H.-J. Mol. Phys. 1996, 89, 645. (28) Celani, P.; Werner, H.-J. J. Chem. Phys. 2000, 112, 5546. (29) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007. (30) Kendall, R. A.; Dunning, T. H., Jr.; Harrison, R. J. J. Chem. Phys. 1992, 96, 6796. (31) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 1987, 87, 5968. (32) Martin, J. M. L.; Uzan, O. Chem. Phys. Lett. 1998, 282, 16. (33) Lee, T. J.; Taylor, P. R. Int. J. Quantum Chem. 1989, 23, 199. (34) Werner, H.-J.; Knowles, P. J. MOLPRO, a package of ab initio programs (contributions from: Almlof, J.; Amos, R. D.; Berning, A.; Cooper, D. L.; Deegan, M. J. O.; Dobbyn, A. J.; Eckert, F.; Elbert, S. T.; Hampel, C.; Lindh, R.; Lloyd, A. W.; Meyer, W.; Nicklass, A.; Peterson, K.; Pitzer, R.; Stone, A. J.; Taylor, P. R.; Mura, M. E.; Pulay, P.; Schutz, M.; Stoll, H.; Thorsteinsson, T. The majority of calculations reported here were done with Version 2006.1. (35) Truhlar, D. G.; Garrett, B. C.; Klippenstein, S. J. J. Phys. Chem. 1996, 100, 12771. (36) Miller, J. A.; Klippenstein, S. J. J. Phys. Chem. A 2000, 104, 2061. (37) Krasnoperov, L. N.; Chesnokov, E. N.; Stark, H.; Ravishankara, A. R. J. Phys. Chem. A 2004, 108, 11526. (38) Srinivasan, N. K.; Su, M.-C.; Sutherland, J. W.; Michael, J. V. J. Phys. Chem. A 2005, 109, 7902. (39) Su, M.-C.; Michael, J. V. Proc. Combust. Inst. 2002, 29, 1219. (40) Michael, J. V.; Su, M.-C.; Sutherland, J. W.; Harding, L. B.; Wagner, A. F. Proc. Combust. Inst. 2005, 30, 965. (41) Sugawara, K.; Okazaki, K.; Sato, S. Bull. Chem. Soc. Jpn. 1981, 54, 2872. (42) Lutz, A. E.; Kee, R. J.; Miller, J. A. SAND87-8248 Revised, Sandia National Laboratory, November 1997. (43) Senosiain, J. P.; Klippenstein, S. J.; Miller, J. A. J. Phys. Chem. A 2006, 110, 5772. (44) Kumaran, S. S.; Su, M.-C.; Lim, K. P.; Michael, J. V. Proc. Combust. Inst. 1996, 26, 605. (45) Whytock, D. A.; Michael, J. V.; Payne, W. A.; Stief, L. J. J. Chem. Phys. 1976, 65, 4871. (46) Michael, J. V.; Lee, J. H. Chem. Phys. Lett. 1977, 51, 303. (47) Ohmori, K.; Miyoshi, A.; Matsui, H.; Washida, N. J. Phys. Chem. 1990, 94, 3253. (48) Aders, W.-K.; Wagner, H. Gg. Ber. Bunsen-Ges. Phys. Chem. 1973, 77, 332.

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Direct Observation of Roaming Radicals in the Thermal

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