Proceedings

Proceedings of the Combustion Institute 30 (2005) 1119–1127

www.elsevier.com/locate/proci

of the

CombustionInstitute

High-temperature ethane and propane decomposition

Matthew A. Oehlschlaeger*, David F. Davidson, Ronald K. Hanson

Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-3032, USA

Abstract

The decomposition rates of ethane and propane in the falloff regime at high temperatures were studied in ashock tube usingUV narrow-line laser absorption of CH3 at 216.6 nm. Experimental conditions ranged from1343 to 2034 K and 0.13 to 8.4 atm with mixtures varying in concentration from 100 to 402 ppm of ethane orpropane diluted in argon. Decomposition rate coefficients were determined bymonitoring the formation rateof CH3 immediately behind shock waves andmodeling the CH3 formation with a detailed kinetic model. Cal-culations were performed using RRKM/master equation analysis with a restricted (hindered) Gorin modelfor the transition state and fit to the current high-temperature dissociation data as well as previous low-tem-perature recombination measurements. The decomposition rate coefficient for ethane decomposition from700 to 1924 K can be described, using the Troe pressure broadening formulation, by k1, 1 (T) = 1.88 · 1050

T�9.72 exp(�54,020 K/T) s�1, k0,1 (T) = 3.72 · 1065T�13.14 exp(�51,120 K/T) cm3 mol�1 s�1, andFcent, 1 (T) =0.61 exp(�T/100 K) + 0.39 exp(�T/1900 K) + exp(�6000 K/T). The decomposition rate coefficient for pro-pane decomposition from 600 to 1653 K can be described by k1, 2 (T) = 1.29 · 1037T�5.84 exp(�49,010K/T) s�1, k0, 2 (T) = 5.64 · 1074 T�15.74 exp(�49,680 K/T) cm3 mol�1 s�1, and Fcent, 2 (T) = 0.69 exp(�T/50 K) + 0.31 exp(�T/3000 K) + exp(�9000 K/T).� 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Shock tube; Ethane; Propane; Decomposition; Pyrolysis

1. Introduction

The alkane decomposition reactions are impor-tant initiation steps in the detailed reaction mech-anisms describing alkane oxidation and indescribing global combustion phenomena suchas ignition times. With the development of aCH3 laser absorption diagnostic at 216.6 nm, de-tailed measurements of the following reactionsare possible at high temperatures:

C2H6 ! CH3 þ CH3 ð1Þ

1540-7489/$ - see front matter � 2004 The Combustion Institdoi:10.1016/j.proci.2004.07.032

* Corresponding author. Fax: +1 650 723 1748.E-mail address: moehlsch@stanford.edu (M.A.

Oehlschlaeger).

C3H8 ! CH3 þ C2H5 ð2ÞReaction (1) has been extensively studied in

both the dissociation and recombination direc-tions across a broad range of temperatures. Previ-ous high-temperature shock tube measurementshave utilized different techniques: gas chromatog-raphy in a single-pulse shock tube [1], H-atomatomic resonance absorption spectroscopy(ARAS) [2,3], IR absorption of ethane at3.39 lm [4], xenon lamp absorption of CH3 [5], la-ser-schlieren [6,7], and laser absorption of CH3 [8–11]. Reaction (1) has also been the subject ofmany theoretical studies of varying levels of com-plexity [12–20]. At low temperatures (<1000 K)the theoretical studies agree with each otherand with the experimental data quite well,due in a large part to the excellent low-scatter

ute. Published by Elsevier Inc. All rights reserved.

1120 M.A. Oehlschlaeger et al. / Proceedings of the Combustion Institute 30 (2005) 1119–1127

recombination data of Slagle et al. [21] (296–906 K), but at higher temperatures the theoreticalhigh-pressure rate coefficients show some dis-agreement with each other and with the experi-mental data. High-temperature data with verylow scatter are thus needed to resolve thesedisagreements.

Reaction (2) has been studied much less thanreaction (1), with previous high-temperature stud-ies including single-pulse shock tube studies[22,23], and several studies utilizing time-resolvedtechniques: H-atom ARAS [24], laser-schlieren[25], and 3.39 lm absorption of propane [26–28];additionally, a recent recombination study of reac-tion (2) has been performed by Knyazev and Sla-gle [30] over the temperature range 301–800 K.Reaction (2) has also been examined using variouslevels of unimolecular theory [12,15,29–31].

In this work, we present measurements of k1and k2 using a narrow-linewidth laser absorptionmethod for ppm-sensitive CH3 detection. Theexperiments utilized low concentration mixturesto maintain excellent sensitivity to k1 and k2, butwith sufficient concentration (100–402 ppm C2H6

or C3H8) to be insensitive to impurities. The anal-ysis only focused on the early-time behavior of theCH3 profiles to maintain isolation of the decom-position reactions and to avoid interfering absorp-tion from other product species that are formed atlonger times.

In addition to the experiments presented here,calculations based on a RRKM/1-D master equa-tion approach have been performed using a re-stricted Gorin model for the transition states[14,32]. These calculations were fit to the currentdecomposition rate coefficient measurements aswell as the low-temperature methyl recombinationmeasurements of Slagle et al. [21] and the low-temperature methyl/ethyl recombination measure-ments of Knyazev and Slagle [30]. The data andfits provide strong evidence for a positive temper-ature dependence of ÆDEædown (collisional energytransfer parameter). Additionally, the data andRRKM results point to a more severe falloff inthe high-pressure rate coefficients at high temper-ature than the current theoretical models predict.Analytic expressions for k1, k0, and Fcent weredetermined for reactions (1) and (2).

2. Experiment

2.1. Apparatus

The experiments reported here were performedbehind both incident and reflected shock waves ina pressure-driven stainless-steel shock tube. Thedriven section is 8.54 m long and the driver is3.35 m long; both sections are 14.13 cm in innerdiameter. The driven section vacuum system con-sists of a zeolite-trapped mechanical pump and a

Varian V-250 turbomolecular pump, providingultimate pressures of 10�7 torr with a typical leakrate of 10�6 torr/min. Shock velocities wereextrapolated to the endwall from four incidentshock wave velocity measurements made withpiezo pressure transducers over the last 1.5 m ofthe shock tube. The pre-shock initial mixture pres-sure was measured using a high-accuracy Bara-tron pressure transducer. The incident andreflected shock conditions were calculated usingthe normal shock equations; uncertainties in theexperimental pressure and temperature are 1.1%and 0.6%, respectively, with the primary contribu-tion being the uncertainty in the measured shockvelocity. Mixtures were made in a turbo-pumpedstainless-steel mixing chamber with an internalstirring system. Research grade argon (99.999%)was used as the driven carrier gas, and heliumwas used as the driver gas. Ethane and propanewere provided by Praxair in purities of 99.5%and 99%, respectively.

2.2. CH3 diagnostic

Methyl radicals (CH3) were monitored duringthese experiments using laser absorption at216.6 nm. Laser light at 433.2 nm was created bypumping a Coherent 699 ring dye laser, operatingon stilbene 420 dye, with 7 W (all-lines UV) froma Coherent Innova 25/7 Ar+ laser. The output ofthe dye laser was then frequency-doubled in aSpectra-Physics Wavetrain external doubling cav-ity using an angle-tuned BBO crystal. The wave-length was monitored by passing a portion ofthe dye laser output (undoubled) into a waveme-ter; mode quality was monitored by passing a por-tion through a scanning interferometer.

The doubled UV beam (2–3 mW at 216.6 nm)was passed to the shock tube where it was split intotwo components: one passing through the shocktube to be absorbed by CH3 (I), the other was de-tected prior to absorption as a reference (I0). Thesetwo beams were detected using amplified S1722-02Hamamatsu silicon photodiodes (risetime <0.5 ls)and recorded on a digital oscilloscope.

The CH3 Bð2A01Þ Xð2A002Þ transition has anabsorption maximum at 216.6 nm [33]. Theabsorption coefficient at this wavelength has beenpreviously measured by Davidson et al. [34].Prior to performing the current experiments thetemperature dependence of the absorption coeffi-cient was investigated once again. Dilute mixtures(200 ppm) of azomethane, methyl iodide, and eth-ane were shock heated to produce known, instan-taneous post-shock CH3 yields. The absorptioncoefficient was determined by measuring thetime-zero absorption of the immediate CH3 yield.These most recent measurements differ by nomore than 10% with those of Davidson et al.[34] and have about a factor of two less experi-mental scatter. A least-squares fit to the absorp-

Fig. 1. Example ethane data, modeling, and sensitivity.Reflected shock conditions: 1589 K, 1.664 atm, 202 ppmC2H6. Top graph: solid line, fit to data using GRI-Mech3.0 [35] and adjusting k1; dashed lines, variation of k1±50%. The spike at 0 ls is caused by deflection of thediagnostic beam by the reflected shock wave.S = (dXCH3

/dki) (ki/XCH3,local), where ki is the rate con-

stant for reaction i, and XCH3,localis the local CH3 mole

fraction.

Fig. 2. Example propane data, modeling, and sensitivity.Reflected shock conditions: 1433 K, 4.535 atm, 201 ppmC3H8. Top graph: solid line, fit to data using GRI-Mech3.0 [35] and adjusting k2; dashed lines, variation ofk2 ± 50%; dotted lines, variation of rate coefficient forH + C3H8 fi C3H7 + H2 by ±50%. S = (dXCH3

/dki) (ki/XCH3,local

), where ki is the rate constant for reaction i, andXCH3,local

is the local CH3 mole fraction.

M.A. Oehlschlaeger et al. / Proceedings of the Combustion Institute 30 (2004) 1119–1127 1121

tion coefficient data over the range 1200–2500 K isgiven by

kk;CH3¼ 1:475� 104 T�1:004

� expð2109K=T Þatm�1 cm�1

with a 2r least-squares deviation of ±5% in thedata. The absorption coefficient shows no pressuredependence across the range of pressures presentedin this study.

The CH3 mole fraction in a given experimentcan be determined using Beer�s law: I/I0 =exp(�kkPXCH3

L), where I is the intensity of theabsorbed UV beam, I0 is the intensity of the refer-ence beam, kk is the absorption coefficient(atm�1 cm�1) at the wavelength k, P is the totalpressure (atm), XCH3

is the mole fraction of theabsorbing species, CH3, and L is the shock tubediameter (14.13 cm). The CH3 diagnostic providesa minimum detectivity of 0.1% absorbance (ln (I0/I) = 0.001), and thus is capable of ppm CH3

detection.

2.3. Method for determination of rate coefficients

To determine rate coefficients for reactions (1)and (2), the measured CH3 mole fractions were fitusing a detailed kinetic model, GRI-Mech 3.0[35]. Fortunately, the low initial fuel concentrationsused in these experiments allowed fits that are quiteinsensitive to the choice of the other rate coeffi-cients. The only rate coefficients changed in themechanism, for the purpose of fitting these data,are those of reactions (1) and (2). Computationswere done using CHEMKIN 2.0 and SENKIN[36,37].

The kinetic modeling is quite simple, the initialrise of CH3 provides a direct fit to reaction (1) or(2), as there is only one decomposition route forthe fuel at the conditions of these experiments.Additionally, during the early rise, interferingabsorption due to C2H4 and C2H2 is negligible;the absorption coefficients for these two specieshave been measured by several groups [33,38,39]and were verified with good agreement prior tothe current experiments. An example data traceand sensitivity plot for ethane decomposition isshown in Fig. 1. Notice that interfering reactionshave essentially no effect on the fit of reaction(1). An example of propane decomposition exper-iment and sensitivity is shown in Fig. 2. Here, theprimary interfering reaction is C3H8 + H and, be-cause of the low initial propane concentration, ithas little effect on the fit of reaction (2).

The present rate coefficient determinations aretabulated in Table 1 and shown in Figs. 3 and 4on Arrhenius plots along with least-squares fits;the experimental scatter is very small (<15%). Theprimary contributions to uncertainties in the ratecoefficients are: temperature (±10%), CH3 absorp-tion coefficient (±5%), fitting the data to computed

profiles (±5%), and uncertainties resulting frominterfering chemistry (±0% in k1 and ±5% in k2).These uncertainties give overall uncertainties in k1and k2 of ±20% and ±25%, respectively.

3. RRKM calculations

Single-channel RRKM calculations withnumerical solution to the 1-D (internal energy)

Table 1Summary of experimental results

T (K) P (atm) k1 (1/s)

Initial XC2H6: 398 ppm

a

1503 0.219 4.2E+021566 0.207 8.2E+021623 0.196 1.6E+031720 0.181 4.3E+031795 0.167 7.5E+031924 0.148 1.8E+042034 0.126 2.7E+04

Initial XC2H6: 202 ppm

1862 1.511 5.2E+041716 1.576 1.4E+041589 1.664 3.7E+031488 1.730 7.7E+02

Initial XC2H6: 100 ppm

1891 1.432 7.0E+04

Initial XC2H6: 402 ppm

1421 1.859 2.8E+021435 1.600 3.9E+02

Initial XC2H6: 200 ppm

1624 4.190 8.3E+031537 4.326 2.8E+031453 4.434 7.5E+021676 4.204 1.5E+041753 3.847 4.2E+04

Initial XC2H6: 101 ppm

1419 4.493 4.2E+021489 4.391 1.7E+03

Initial XC2H6: 402 ppm

1859 3.885 9.5E+04

Initial XC2H6: 100 ppm

1710 7.068 3.5E+041598 7.620 9.0E+031494 7.983 1.7E+031771 6.942 5.7E+04

Initial XC2H6: 402 ppm

1504 8.059 2.0E+03

T (K) P (atm) k2 (1/s)

Initial XC3H8: 399 ppm

a

1435 0.244 1.3E+031365 0.228 4.5E+021572 0.206 7.5E+031653 0.187 1.65E+04

Initial XC3H8: 201 ppm

1662 1.561 6.5E+041553 1.616 1.9E+041448 1.683 3.9E+031379 1.759 1.2E+03

Initial XC3H8: 402 ppm

1375 1.772 1.2E+03

Initial XC3H8: 201 ppm

1554 4.378 2.5E+041433 4.535 3.6E+041538 3.715 2.1E+041658 3.529 8.9E+041550 4.387 2.3E+04

Fig. 4. Experimental data and least-squares fits forC3H8 fi CH3 + C2H5. Filled squares, 1.7 atm data,k2 = 1.97 · 1013 exp(�32,400 K/T); filled triangles,4.3 atm data, k2 = 5.10 · 1013 exp(�33,400 K/T); filledstars, 7.9 atm data, k2 = 4.97 · 1013 exp(�33,100 K/T);and open squares, 0.19–0.23 atm data.

Fig. 3. Experimental data and least-squares fits forC2H6 fi CH3 + CH3. Filled squares, 1.6 atm data,k1 = 1.08 · 1012 exp(�31,200 K/T); filled triangles,4.2 atm data, k1 = 4.01 · 1012 exp(�32,400 K/T); filledstars, 7.5 atm data, k1 = 1.55 · 1013 exp(�34,200 K/T);and open squares, 0.13–0.22 atm data.

Table 1 (continued)

T (K) P (atm) k1 (1/s)

Initial XC3H8 402 ppm

1426 4.514 3.1E+031343 4.712 9.0E+02

Initial XC3H8: 101 ppm

1490 7.928 1.0E+041414 8.092 3.3E+031562 7.757 3.2E+041607 7.548 5.6E+04

Initial XC3H8: 200 ppm

1387 8.393 2.2E+03

a Incident shock experiments.

1122 M.A. Oehlschlaeger et al. / Proceedings of the Combustion Institute 30 (2005) 1119–1127

master equation, to account for weak collision ef-fects, were carried out using a restricted (hin-dered) Gorin model for the transition states of

M.A. Oehlschlaeger et al. / Proceedings of the Combustion Institute 30 (2004) 1119–1127 1123

reactions (1) and (2). These calculations were fit tothe current dissociation data, the methyl/methylrecombination data of Slagle et al [21] (296–906 K), and the methyl/ethyl recombination dataof Knyazev and Slagle [30] (301–800 K).

The model locates the transition state at themaximum of an effective potential, using the Len-

nard-Jones form of the potential: r�/r = (6D0/

Fig. 5. Hindrance parameter temperature dependence.Filled squares, RRKM fit to k1 data of current study;filled circles, RRKM fit to k2 data of current study; opensquares, RRKM fit to k1 data of Slagle et al. [21]; andopen circles, RRKM fit to k2 data of Knyazev and Slagle[30].

Table 2Data used for RRKM calculations

C2H6

Heat of formation (0 K) �16.34 kcal/mMoments of inertia (amu A2) 25.3 (inactiveFrequencies (cm�1) 2977(4), 2954

CH3 � � � CH3

Frequencies (cm�1) 3184(4), 3002Active 1-D external rotor (amu A2) 6.3, r = 3Active 1-D internal torsion (amu A2) 1.777, r = 3Active 2-D internal rotor (amu A2) 1.760, r = 2;Active 2-D internal rotor (amu A2) 1.760, r = 2;Barrier at 0 K 87.6 kcal/mo

C3H8

Heat of formation (0 K) �19.69 kcal/mMoments of inertia (amu A2) 67.75 (inactivFrequencies (cm�1) 2977, 2973, 2

1462, 1451, 1869, 748, 369

CH3 � � � C2H5

Frequencies (cm�1) 3184(2), 30021175(2), 1138

Active 1-D external rotor (amu A2) 17.3, r = 1Active 1-D internal torsion (amu A2) 3.1, r = 3Active 2-D internal rotor (amu A2) 1.76, r = 2; gActive 1-D internal rotor (amu A2)Active 1-D internal rotor (amu A2) 22.3, r = 1; gBarrier at 0 K 87.9 kcal/mo

RT)1/6. The restricted Gorin transition state issimilar to its product fragments. The transitionstate frequencies of vibration are assumed to bethose of the product fragments, and internal rota-tions are represented by the moments of inertia ofthe product fragments with hindrance, g. The hin-drance parameters, g, were chosen to reproducethe current data and the recombination data. Pre-vious studies [14,32,40] have shown that the hin-drance parameter follows the functional form,g = a + bT�1/6. The current RRKM fits suggestthat although this may be true over a small tem-perature range, in fact the hindrance parameterasymptotes from high temperature to a constantvalue at lower temperatures; see Fig. 5. Len-nard-Jones parameters for ethane, propane, andargon were taken from [41]; the molecular fre-quencies [42,43], moments of inertia [14,31,44,45], heats of formation [46,47], and barrier heights[48,49] were taken from various references and arelisted in Table 2.

The exponential-down collision energy transfermodel was used with a temperature-dependent col-lisional energy transfer parameter which was fit tothe current experiments and low-temperaturerecombination data. The resulting expressions forthe energy collisional transfer parameter for argoncollisions with ethane and propane, respectively,are: ÆDEædown = 0.8 · (T [K]) cm�1 (ethane) andÆDEædown = 1.2 · (T [K]) cm�1 (propane). The fall-off behavior of the current experiments could not

ol); 25.3 (inactive); 6.3 (active), r = 3, 2896, 1469(4), 1382(2), 1190(2), 995, 822(2), 260

(2), 1384(4), 580(2)

g (see Fig. 5)g (see Fig. 5)l

ole); 59.84 (inactive); 17.3 (active), r = 1968(2), 2967, 2962, 2887(2), 1476, 1472, 1464,392, 1378, 1338, 1278, 1192, 1158, 1054, 940, 922,, 268, 216

, 1384(2), 580, 3112, 3033, 2987(2), 2942, 1440(3), 1366,, 528(3)

(see Fig. 5)

(see Fig. 5)l

Fig. 6. Falloff plot for C2H6 fi CH3 + CH3. Solid sym-bols, current study; open symbols, Davidson et al. [9];open symbols with ·, Du et al. [11]; half filled symbols,Hwang et al. [10]; solid lines, RRKM/master equationresults with ÆDEædown = 0.8 · (T [K]) cm�1; dashed lines,ÆDEædown = 1.2 · (T [K]) cm�1; and dot-dashed lines,ÆDEædown = 0.4 · (T [K]) cm�1.

Fig. 7. Falloff plot for C3H8 fi CH3 + C2H5. Solid sym-bols, current study; open symbols, Al-Alami and Kiefer[25]; half filled symbols, Simmie et al. [27]; open symbolswith line, Hidaka et al. [28]; open symbols with ·, Chiangand Skinner [24]; solid lines, RRKM/master equationresults with ÆDEædown = 1.2 · (T [K]) cm�1; dashed lines,ÆDEædown = 1.8 · (T [K]) cm�1; and dot-dashed lines,ÆDEædown = 0.8 · (T [K]) cm1.

1124 M.A. Oehlschlaeger et al. / Proceedings of the Combustion Institute 30 (2005) 1119–1127

be accurately fit without a temperature-dependentÆDEædown; similar results have been given by Klip-penstein and Harding [19], Knyazev and Slagle[30,50], and Knyazev and Tsang [51]. TheRRKM/1-D master equation calculations wereperformed with the Multiwell code of Barker [52].

The RRKM/master equation calculations pro-vided rate coefficients in both the high-pressureand low-pressure limits for reaction (1) (296–1924 K) and for reaction (2) (301–1653 K). Accu-rate three-parameter analytic expressions(ATnexp(�E/T)) for k1 and k0 over large temper-ature ranges are difficult to develop due in part tothe simplicity of the pre-exponential temperaturedependence term, which is a function of thechange in specific heat from the reactant to thetransition state ðhDCzpiÞ. One coefficient to repre-sent the heat capacity term over a large range oftemperatures is simply not enough (most polyno-mial expressions for heat capacitance contain fiveterms). Therefore, analytic expressions for reac-tions (1) and (2), in the Troe formulation, are gi-ven over a smaller temperature range thanRRKM calculations were carried out for, andthe resulting pre-exponential temperature depen-dences are large. The reaction (1) rate expressionsfor 700–1924 K are:

k1;1ðT Þ¼ 1:88�1050T�9:72

� expð�54;020K=T Þ ½s�1�;k0;1ðT Þ¼ 3:72�1065T�13:14

� expð�51;120K=T Þ ½cm3 mol�1 s�1�;F cent;1ðT Þ¼ 0:61expð�T=100KÞ

þ0:39expð�T=1900KÞþexpð�6000K=T Þ:

The reaction (2) rate expressions for 600–1653 K are:

k1;2ðT Þ¼ 1:29�1037T�5:84

�expð�49;010K=T Þ ½s�1�;k0;2ðT Þ¼ 5:64�1074T�15:74

�expð�49;680K=T Þ ½cm3 mol�1 s�1�;F cent;2ðT Þ¼ 0:69expð�T=50KÞ

þ0:31expð�T=3000KÞþexpð�9000K=T Þ:

Figures 6 and 7 show the current data, RRKMcalculations, and selected previous experimentalstudies on falloff plots; Figs. 8 and 9 show the cur-rent high-pressure-limit rate coefficients with com-parison to selected theoretical studies.

4. Discussion

The current experimental findings for reactions(1) and (2) can be compared with the experimental

results of previous studies; see Figs. 6 and 7. Thecurrent findings for reaction (1) are in good agree-ment with the dissociation data of Davidson et al.[9], although the current experimental scatter ismuch improved. The low-pressure (�1 atm)recombination data of Du et al. [11] and thehigh-pressure (�50–100 atm) recombination dataof Hwang et al. [10] show fair agreement withthe current study, although their results are bothslightly lower than our data and RRKM fits.

Fig. 8. High-pressure rate coefficient for C2H6 fi CH3

+ CH3 (700–1924 K). Symbols, current RRKM results(listed on figure); solid line, fit to current RRKM results;dashed line, Klippenstein and Harding [19]; dotted line,Hessler and Ogren [17]; and dot-dashed line, Wagnerand Wardlaw [13].

Fig. 9. High-pressure rate coefficient for C3H8 fi CH3

+ C2H5 (600–1653 K). Symbols, current RRKM results(listed on figure); solid line, fit to current RRKM results;dashed line, Mousavipour and Homayoon [31]; dottedline, Knyazev and Slagle [30]; dot-dashed line, Tsang[15]; and dot-dot-dashed, Dean [12].

M.A. Oehlschlaeger et al. / Proceedings of the Combustion Institute 30 (2004) 1119–1127 1125

The current findings for reaction (2) are ingood agreement with the work of Al-Alami andKiefer [25]. At low temperatures, our findingsare in good agreement with the work of Simmieet al. [27] but at higher temperatures their resultsare significantly lower and their scatter increased.Both the measurements of Hidaka et al. [28] andChiang and Skinner [24] are significantly lowerthan the current findings. Of concern are the highactivation energies reported by Hidaka et al. andChiang and Skinner for their 2 atm (falloff) exper-iments. Their data cannot be reconciled with thepresent findings or other theoretical results.

As stated above, the current data for bothreactions (1) and (2) were fit with RRKM/masterequation calculations by adjusting two parame-ters: the collisional energy transfer parameter,ÆDEædown (influences falloff), and the hindranceparameter for the internal rotors, g, in the transi-tion state (influences k1). The current data andRRKM analysis suggest an increase in ÆDEædownwith temperature and a stronger falloff in k1 (in-creased hindrance) at higher temperatures thanthe current theoretical studies predict for bothreactions (1) and (2), see Figs. 8 and 9. The cur-rent theoretical models do an excellent job of pre-dicting the low-scatter data of Slagle et al. [21] andKnyazev and Slagle [30], but previous high-tem-perature experimental data had excessive scatterwhich made accurate theoretical fitting difficult;in fact, many theoretical studies predict high tem-perature rates that were simply extrapolated fromthe low temperature results.

5. Conclusions

Laser absorption of methyl radicals at216.6 nm offers a sensitive, high-accuracy methodto determine the decomposition rates for ethaneand propane. Using this technique measurementsof k1 and k2 have been made in the falloff regimewith experimental conditions ranging from 1343to 2034 K and 0.13 to 8.4 atm. Calculations basedon RRKM theory and the 1-D (internal energy)master equation were performed and fit to the cur-rent data set and previous low-temperaturerecombination data. Expressions are given forthe high- and low-pressure limit rate coefficientsas well as Troe-formulated falloff parameters.

Acknowledgments

The present work was supported by the Chem-ical Sciences Division, Office of Basic Energy Sci-ences, U.S. Department of Energy. The authorsthank David M. Golden of Stanford Universityfor helpful discussions.

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Comments

Wing Tsang, NIST, USA. The step size down seems

very large; could this be due to the use of theGorinmodel?

Reply. Values for the step size down, <DE>down,

have large uncertainties. While the step size down values

used in the current work are higher than those of Kiefer

et al. given in these proceedings, the current values for

<DE>down are similar to the values given for small alk-

anes by Knyazev and Slagle [1] and for dichloroketene

given by Shestov et al. also in these proceedings. All of

these studies use more advanced treatments of the tran-

sition state than the Gorin model. A better understand-

ing of collisional energy transfer is needed before these

values can be evaluated further.

M.A. Oehlschlaeger et al. / Proceedings of the Combustion Institute 30 (2004) 1119–1127 1127

Reference

[1] V.D. Knyazev, I.R. Slagle, J. Phys. Chem. A 105

(2001) 6490–6498.

d

Horst Hippler, University of Karlsruhe, Germany. The

mechanism for ethane decomposition contains the reac-

tion CH3 + CH3 fi C2H5 + H. What is the reason that

in the mechanism only one decomposition pathway

C2H6 fi CH3 + CH3 is given and the competing channel

C2H6 fi C2H5 + H is neglected? Since the reaction is

close to the high-pressure limit, the second channel must

compete when CH3 + CH3 fi C2H5 + H plays an impor-

tant role.

Reply. The competing channel C2H6 fi C2H5 + H

was included in the mechanism, but for the experimental

conditions of this study plays a minimal role in the con-

sumption of ethane. At the highest temperatures

(�2000 K) the C2H5 + H channel is responsible for less

than 1% of the consumption of ethane.

d

J. Troe, University of Gottingen, Germany. I always

recommend not presenting the <DE>-fitting results in

the form of <DE>down but of <DE>total for a number of

fundamental reasons. For an exponential collisionmodel,

the two quantities are linked by < DE>total � �< DE>2

down=ð< DE>down þ F EkT Þ. We generally have ob-

served a temperature independent <DE>total which would

suggest <DE>down�T0.5. Could you also live with this

weaker T-dependence?

Reply. Falloff calculations with <DE>down�T0.5 pro-

vide a much poorer fit to the current data set than the

<DE>down � T calculation, although reasonable agree-

ment is achieved with <DE>down � T0.75.