Detailed Kinetic Modeling of 1,3-Butadiene Oxidation at High Temperatures

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ALEXANDER LASKIN,1,* HAI WANG,1 CHUNG K. LAW2 1Department of Mechanical Engineering,University of Delaware, Newark, DE 19716-3140 2Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544-5263 Received 31 October 1999; accepted 16 May 2000

ABSTRACT: The high-temperature kinetics of 1,3-butadiene oxidation was examined with detailed kinetic modeling. To facilitate model validation, ﬂow reactor experiments were carried out for 1,3-butadiene pyrolysis and oxidation over the temperature range 1035–1185 K and at atmospheric pressure, extending similar experiments found in the literature to a wider range of equivalence ratio and temperature. The kinetic model was compiled on the basis of an extensive review of literature data and thermochemical considerations. The model was critically validated against a range of experimental data. It is shown that the kinetic model compiled in this study is capable of closely predicting a wide range of high-temperature oxidation and combustion responses. Based on this model, three separate pathways were identiﬁed for 1,3-butadiene oxidation, with the chemically activated reaction of Hи and 1,3-butadiene to produce ethylene and the vinyl radical being the most important channel over all experimental conditions. The remaining uncertainty in the butadiene chemistry is also discussed. ᭧ 2000 John Wiley & Sons, Inc. Int J Chem Kinet 32: 589–614, 2000

INTRODUCTION Brezinsky et al. [7] examined 1,3-butadiene oxidation in an atmospheric ﬂow reactor at temperature

The oxidation kinetics of 1,3-butadiene (1,3-C4H6)is of ϳ1100 K and equivalence ratios (␾) of 0.55, 1.18, considerably important to the hierarchical develop- and 1.65. Their analysis revealed that the concentra- 9 " 9 ment of the kinetic mechanisms of hydrocarbon com- tion of crotonaldehyde (CH3 CH CH CHO) bustion. In several publications [1–3], we reported a peaked at an early reaction time. It was concluded comprehensive kinetic model of allene, propyne, pro- that crotonaldehyde was formed from 3-butenal " 9 9 pene, and propane combustion. This model uses GRI- (CH2 CH CH2 CHO) as a result of rapid isom- Mech 1.2 [4] as the C1-C2 kinetic subset, with the re- erization during passage through the GC injector sys- actions relevant to ethylene and acetylene combustion tem. Following this analysis, Brezinsky et al. [7] pro- carefully reexamined recently [5,6]. In the present posed that the oxidation of 1,3-butadiene starts mainly work, we report an experimental and kinetic modeling through O atom addition to the double bond to form study of 1,3-butadiene oxidation, a recent step in the 3-butenal. This is followed by its decomposition to direction towards a comprehensive and self-consistent allyl and CO: kinetic model of liquid hydrocarbon fuel combustion. ϩ !: 1,3-C46 H O " 9ии9 9 !: CH22CH CH CH O Correspondence to: H. Wang ([email protected]) " 9 9 !: CH22CH CH CHO *Current address: William R. Wiley Environmental Molecular " 9 9ииϩ Sciences Laboratory, Paciﬁc Northwest National Lab., P.O. Box CH22CH CH CO H 999, MSIN K8-88, Richland, WA 99352. short ᭧ " 9 9ии!: ϩ 2000 John Wiley & Sons, Inc. CH22CH CH CO aCH 35CO standard long JCK(Wiley) LEFT INTERACTIVE

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It was also found that the H abstraction of 1,3-buta- relevant to 1,3-butadiene oxidation. These studies in- и и " diene by H and OH radicals to yield the CH2 clude rate-constant measurements for the reactions of CH9иC"CH (i-C H ) and CH "CH9CH" OOHؒؒand with 1,3-butadiene [32–34] and of и 2 4 5 2 CH (n-C4H5) isomers may also play a significant role ؒCH45radicals with O2 [35]. The thermochemical in butadiene oxidation. stability of the C4H5 radicals was also examined [36]. Reaction intermediates and products in two 1,3-bu- Finally, additional combustion data of 1,3-butadiene tadiene flames were determined by Cole et al. [8] using such as the ignition delay time [10] and the flame Molecular Beam Mass Spectrometry. These were lam- speed [37] were reported recently. inar, burner-stabilized flames, burning mixtures of 1,3- In this article, we present a detailed kinetic model butadiene, oxygen, and argon with equivalence ratios of 1,3-butadiene oxidation. The kinetic model was equal to 1.0 and 2.4. The emphasis of that work, as compiled by incorporating mechanistic and rate-con- well as the later kinetic modeling of these flames [9– stant information of C4HxOy species into the C3Hx 11], was the mechanism of aromatics formation. The mechanism published previously [1–3]. A large num- oxidation pathway, especially the mechanism of O- ber of the rate constants were estimated based on ther- atom addition to 1,3-butadiene, was left beyond the mochemical considerations and Rice-Ramsperger- focus of these studies. Kassel-Marcus (RRKM) [38,39] calculations using Recently, Dagaut and Cathonnet [12] published ex- potential energies and vibrational frequencies obtained perimental and modeling results of their study on the from molecular orbital calculations. For a critical val- oxidation of 1,3-butadiene in a jet-stirred reactor. Vi- idation of the model, we extended the flow reactor nyloxirane was observed in the postreaction mixtures. study of Brezinsky et al. [7] to a wider range of equiv- This finding prompted the authors to propose that the alence ratios and temperatures, using the same Prince- attack of the O atom on 1,3-butadiene leads primarily ton Turbulent Flow Reactor. The proposed model was to the formation of vinyloxirane, that is, validated against the experimental data of 1,3-butadiene oxidation in the flow reactor, shock tube, and ϩ и !: 1,3-C46 H O vinyloxirane flames. For all experimental conditions considered here, the The disappearance of vinyloxirane was assumed to oxidation of 1,3-butadiene was found to be controlled ϩ : ϩ proceed via unimolecular channels, mostly by Hؒ 1,3-C4H6 C2H4 ؒC2H3, followed

-by the consumption of ؒC2H3 by O2. The O-atom at !: ϩ Vinyloxirane CH36 CO tack on 1,3-C4H6 also influences the overall oxidation !: ϩ CH24CH 2 CO process, but this influence is not as significant as the preceding reaction. The addition of the butadiene or through H abstraction by the radical pool. chemistry did not affect the predictive capability of

The reaction pathway mentioned above is signifi- the C2-C3 model. cantly different from that of Brezinsky et al. [7], as the Dagaut-Cathonnet pathway leads to effective radical-chain termination, whereas the pathway of Bre- EXPERIMENTAL DATA FOR MODEL zinsky et al. leads to effective chain branching. Despite VALIDATION this difference, both studies emphasized the dominant role of the reaction between 1,3-butadiene and the O Experimental data used for model verification are atom. For this reason, we conducted a critical review summarized in Table I. The data consist a total of 15 of the studies on the thermal reaction of various C4H6O cases, which range from pyrolysis and oxidation of isomers [13–20]. Our analyses led us to adopt and 1,3-butadiene in a flow reactor, to shock-tube pyrol- propose a viewpoint quite different from the previous ysis and ignition, and finally to laminar flames. The work. burner-stabilized flame of Cole et al. [8] was not in- A large volume of the fundamental kinetic data of cluded because the temperature profile of the flame is 1,3-butadiene oxidation has been accumulated over not known [9,11]. Below, we shall discuss the present the last decade. Significant progress was made in the flow-reactor experiments. Other experiments given in pyrolysis kinetics. Hidaka et al. [21] reviewed studies Table I are also briefly described. on the pyrolysis of 1,3-butadiene [22–27], 1,2-butadiene [28,29], 1-butyne [30], and 2-butyne [31]. A ki- Flow Reactor Data netic model was proposed [21] which was capable of reconciling a wide spectrum of experimental data. In- The Princeton Turbulent Flow Reactor (PTFR), its short vestigations were also made on the elementary kinetics mode of operation, and the sampling system are de- standard long JCK(Wiley) RIGHT INTERACTIVE

DETAILED KINETIC MODELING OF 1,3-BUTADIENE OXIDATION AT HIGH TEMPERATURES 591

Table I List of Experimental Data of 1,3-Butadiene High-Temperature Oxidation Used in Model Validation Reactant Composition, % Initial Conditions Case References/ ␾ a No. Experiment Type 1,3-C4H6 O2 Diluent T (K) p (atm) Comments 1a Flow reactor ϱ 0.3 — 99.7 1100 1 This work 1b 1150 1c 1185 2 Single-pulse shock tube ϱ 0.175 — 99.825(Ar) 1200–1800 6.5 Colket [27] 3 Single-pulse shock tube ϱ 0.5 — 99.5(Ar) 1200–1800 1.4–2.2 Hidaka et al. [21] 4 Flow reactor 1.63 0.142 0.48 99.378 1035 1 This work 5 Flow reactor 0.55 0.14 1.4 98.46 1035 1 This work 6 Flow reactor 4.7 0.14 0.12 99.74 1120 1 This work 7 Flow reactor 1.62 0.144 0.488 99.368 1110 1 This work 8 Flow reactor 1 0.14 0.78 99.368 1120 1 This work 9 Flow reactor 0.55 0.14 1.4 98.46 1120 1 This work 10 Flow reactor 1.65 0.143 0.477 99.38 1125 1 Brezinsky et al. [7] 11 Flow reactor 1.18 0.143 0.626 99.231 1125 1 Brezinsky et al. [7] 12 Shock-tube ignition 0.69 1 8 91(Ar) 1300–1500 8.5–10 Fournet et al. [10] 13 Shock-tube ignition 1.38 1 4 95(Ar) 1300–1700 8.5–10 Fournet et al. [10] 14 Shock-tube ignition 1.38 3 12 85(Ar) 1200–1500 8.5–10 Fournet et al. [10] 15 Flame speed 0.7–1.7 — — — — 1 Davis and Law [37]

a Unless otherwise indicated, the diluent in all experiments is nitrogen (N2). scribed elsewhere [40,41]. The reactor is a near-adia- results of Brezinsky et al. [9]. The concentrations of batic, continuous-flow device with nitrogen as the car- reaction products were calculated from their GC peak rier gas. The reactor operates at the atmospheric areas using calibration factors obtained from the anal- pressure. The mixture was sampled at distinct loca- ysis of a certified standard gas mixture. Carbon bal- tions along the centerline of the reactor. The distances ance was checked and was found to be within ϳ5% between the locations were transformed into reaction of the total carbon value. time by knowledge of the temperature and flow veloc- ity. Reaction products were quenched in a water- cooled sampling probe and analyzed using gas chro- Ignition Delay Times matography. Temperature was measured by a type-B Ignition delay times of 1,3-butadiene were reported by thermocouple (Pt-Pt/13% Rh). Fournet et al. [10] (Nos. 12–14 in Table I). In that The reactor conditions are specified in Table I work, mixtures of 1,3-butadiene, oxygen, and argon (Cases 1a–1c and 4–9). These conditions were de- were heated behind reflected shock waves to temper- signed to overlap with those of Brezinsky et al. [9] atures between 1200 and 1700 K and pressures be- (Cases 10 and 11) and to extend the flow-reactor data tween 8.5–10 atm. Ignition delay times were deter- to wider ranges of temperature and equivalence ratio. mined for two equivalence ratios (␾ ϭ 0.69 and 1.38) 1,3-Butadiene, listed as 99% pure, was supplied by by monitoring the intensity of light emission from OH Matheson. The impurity contains mainly p-tert-butyl- radicals at 306 nm. The ignition delay time was de- catechol, which serves as an inhibitor against 1,3-bu- fined as the elapsed time between the reflected shock tadiene dimerization. Oxygen was supplied by Airco arrival and the instant when the emission signal with purity Ն99.993%. The nitrogen carrier gas was reached 10% of its maximum value. taken from a liquid reserve, supplied by Liquid Car- bonic and was found to contain 25–30 ppm of oxygen. All gases were used without further purification. Flame Speed GC analysis was performed on the PlotQ and DB- 5 columns, each equipped with a flame-ionization de- Laminar flame speeds of 1,3 butadiene/air mixtures tector. For detection of CO and CO2, the PlotQ column were reported recently by Davis and Law [37] over was also equipped with a nickel catalyst methanizer. the equivalence ratio range of 0.7 to 1.7 and at atmo- Identification of reaction products was based on their spheric pressure (No. 15 in Table I). The laminar flame short retention time and assisted by comparison with the speed was determined using the counterflow twin- standard long JCK(Wiley) LEFT INTERACTIVE

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flame technique, employing linear and nonlinear ex- ical simulation, Held and Dryer [54] showed that this trapolations [42–44] to eliminate the flame-stretch ef- nonideality just shifts the experimental concentration fect. and temperature profiles along the time axis, and it does not affect the shape of the profiles. Consequently, the experimentally observed reaction time is only rel- Additional Data ative time, and a proper comparison between experi- In addition to 1,3-butadiene pyrolysis in PTFR, the mental data and computational results can be made by shock-tube data reported by Colket [27] and Hidaka time shifting the experimental data to longer times. For et al. [21] were also included for model validation the same reason, however, the species profiles do not (Nos. 2, 3 in Table 1). Colket [27] studied the thermal yield information on initiation reactions. In this work, decomposition of 1,3-butadiene behind reflected the experimental profiles from the flow-reactor studies shock waves for a 0.175% 1,3-butadiene–argon mix- were artificially time shifted. The magnitude of the ϭ ture over the temperature range T5 1200–1900 K time shift ranges from 5 to 70 ms and is within 30% ϭ and pressure p5 6.5 atm. A similar experimental of the full observation time in each experiment. In all technique was also used in the work of Hidaka et al. cases, the amount of the time shift is given in the re- ϭ [21], who conducted experiments at T5 1200–1700 spective figure captions. ϭ K and p5 1.4–2.2 atm with a 0.5% 1,3-butadiene– Laminar flame speeds were calculated using the argon mixture. Sandia Chemkin II [45] and Premix [55] codes, employing windward differencing for the convective terms, multicomponent transport formula, and includ-

COMPUTATIONAL DETAILS ing the thermal diffusion of H and H2. A large number of mesh points were used in the simulation to ensure The kinetic model contains 92 species and 613 ele- proper convergence. Further reduction in gradient and mentary reactions. The reactions, their associated rate curvature results in less than ϳ1 cm/s difference in the constants, and thermochemical data are not presented computed flame speed. here because of excessive space requirement. Instead, they are provided at the World Wide-Web address: http://ignis.me.udel.edu/13-butadiene. The reaction REACTION MECHANISM scheme is presented there in the Sandia Chemkin [45] format. References and notes for the individual reac- In this section, we shall discuss the key elements of tions are given at the end of the file. The thermody- the kinetic model. Although emphasis will be given to namic properties of the species were taken mostly the reactions of 1,3-butadiene, the combustion chem- from previous compilations [4,46–48] and in part istry of C1-C3 hydrocarbons will be discussed briefly. from individual works [2,31,36,49]. The heats of formation of several species were estimated using the C -C Chemistry NIST Structures and Properties code [50]. 1 2

Simulation of the flow-reactor and shock-tube ex- The C1-C2 subset of the reaction mechanism is based periments was carried out using the Sandia Chemkin on GRI-Mech 1.2 [4]. This model was expanded to II [45] and the Senkin codes [51]. Computations were describe acetylene and ethylene oxidation in burner- performed with a constant-pressure model for flow re- stabilized fuel-rich flames and in counterflow diffusion actor and with a constant-density model for reflected flames [49,56], and subsequently in the prediction shock waves [52]. Computational ignition delay times [5,6] of acetylene and ethylene flame speeds and ig- were determined following the same fashion as that in nition delay times. The more recent work on propyne, the experimental study. propene, and propane combustion [1–3] also used the

Simulation of flow-reactor experiments was carried same C1-C2 subset. Several changes were made here out using an adiabatic, zero-dimension, constant-pres- to include more recent literature results crucial to the sure, and homogeneous-mixture model. In practice, oxidation of 1,3-butadiene and its major reaction in- this model cannot adequately treat the mixing region termediates, including acetylene, vinyl, and ethylene. и ϩ и : (upstream part) of the reactor. Nonideality in the mix- Specifically, the rate expressions for HO2 H и ϩ и и ϩ и : ϩ ing region and its influence on the experimental results OH OH and HO2 H H2 O2 were up- were studied and discussed in great detail in the lit- dated by those reported by Mueller et al. [57]. The erature [53,54]. In general, this nonideality tends to reaction of triplet methylene with O produces both и 2 accelerate initial fuel consumption. Based on numer- HCO and CO2, short standard long JCK(Wiley) RIGHT INTERACTIVE

DETAILED KINETIC MODELING OF 1,3-BUTADIENE OXIDATION AT HIGH TEMPERATURES 593

3 ϩ !: ииϩ и CH22O HCO OH With this assignment the channel to HCO and CH2O has the largest rate constant at T Ͻ 900 K and p ϭ 1 3 ϩ !: ϩ ииϩ CH22O CO 2H H atm, while at temperatures most relevant to combus- Ͼ и ϩ и tion (T 900 K) CH2CHO O becomes the major The total rate constant was set equal to that used in channel. и The rates of vinoxy (CH2CHO ) decomposition GRI-Mech, but the branching ratio kCH22ϩO :HCOϩOH/ were taken from our recent quantum mechanical and ktotal was assigned with a value of 0.8, based on the RRKM calculations [68]. It was found that the disso- CO/CO2 ratio reported in [58] and [59]. This change was necessary to properly predict the ignition delay ciation of vinoxy is mainly times of acetylene [5]. The reactions ии!: ϩ CH23 CHO CH CO ϩ иии!: ϩ CH22 O HCCO H via 1,2-H shift followed by the rupture of the C9C ϩ ии!: 3 ϩ CH22O CH 2 CO 9 bond in CH3CO. The C H bond breaking, and ии!: ϩ CH22 CHO CH CO H ииϩ !: ϩ и CH23O CH 2 CO H is competitive only at temperatures Ͼ1600 K. иииCH ϩ O !: CH ϩ CO At relatively low temperatures, the oxidation of al- 23 3 и kenes is strongly inﬂuenced by the addition of HO2 ␲ и were assigned, respectively, with the branching ratios radicals to the -bond, which produces the OH rad- reported by Michael et al. [60] and Donaldson et al. ical and the highly reactive alkene oxides (oxiranes) [61]. The expressions of the total rate constants were [69]. The formation of ethylene oxide from the reaction of HO и with ethylene was included in the model taken from GRI-Mech [4] and Tsang’s compilation 2 [62], respectively. with the rate expression taken from the compilation of Preferred initiation pathway for acetylene oxidation Baulch et al. [70]. The reactions of ethylene oxide and was found to proceed via the formation of vinylidene their rate expressions were assigned on the basis of the as the ﬁrst step, followed by the reaction of vinylidene experimental studies of Wu¨rmel et al. [71] and Lifshitz C and Ben-Hamou [72]. (H2CC ) with O2 [5],

ϩ !: C ϩ CH22M HCC 2 M C3 Chemistry C ϩ !: HCC22O products The details of model development and veriﬁcation

against experimental data of C3 hydrocarbons are Based on energy considerations, the addition of vi- found elsewhere [1–3]. Briefly, the rates of the mutual nylidene to O2 leads to the production of a variety of isomerization of propyne and allene and of the rele- radical products. In the present work the formation of vant reactions on the C H potential energy surface и 3 5 two HCO radicals was assumed.и were obtained from molecular orbital and RRKM cal- The reaction between C2H3 and O2 influences culations [2]. The reaction kinetics of allyl and pro- markedly the combustion characteristics of ethylene pene was compiled largely based on the review of and 1,3-butadiene. The reaction products and branch- Tsang [73]. The rate expressions for the reaction of ing ratios have been examined by theoretical methods и allyl with O2 and with HO2 were taken respectively in recent years [63–67]. We adopted the rate coeffi- from Bozzelli and Dean [64] and Baulch et al. [70]. cients of Mebel et al. [67] and assigned three relevant Combined with the C1-C2 subset, the C3 model was reaction channels, shown to predict a wide range of combustion data. The data included product distribution in the pyrolysis and ииϩ !: ϩ CH23O 2CH 22HO 2 oxidation of propyne and propene in a flow reactor under fuel-lean, stoichiometric, and fuel-rich condi- иииϩ !: ϩ CH23O 2CH 2 CHO O tions; the shock-tube ignition delay times of propyne, allene, and propene; and the laminar flame speeds of ииϩ !: ϩ CH23O 2CH 2 O HCO propyne, propene, and propane. short standard long JCK(Wiley) LEFT INTERACTIVE

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C4 Chemistry 1. The mutual isomerization of 1,3-butadiene, 1,2- butadiene, 1-butyne, and 2-butyne are described The reaction subset was constructed based on a critical by the reactions, review of the literature. The emphasis was placed on the C4H6 species. The C4H2 and C4H4 reaction mech- !: 1,3-C46 H 1,2-C 46 H anisms were established as a logical part of the C4H6 mechanism. The present model also includes the 1- 1,3-C H !: 2-C H butene chemistry. 46 46 !: 2-C46 H 1,2-C 46 H C4H6 Pyrolysis. A detailed description of the pyrolysis kinetics of 1,3-butadiene and its isomers is beyond 1,2-C H !: 1-CH, the primary scope of the present study. However, to 46 46 ensure that artifacts in the pyrolytic part of the model where 1,2-C H , 1-C H , and 2-C H are, re- do not inﬂuence the oxidative kinetics of 1,3-butadi- 4 6 4 6 4 6 spectively, 1,2-butadiene, 1-butyne, and 2-bu- ene, we examined closely the literature on the thermal tyne. These reactions are not elementary steps reactions of C H and incorporated the relevant kinetic 4 6 [21,29–31,74]. Figure 1 shows a schematic en- features into the model. ergy diagram for C H mutual isomerization, The mechanisms of the thermal decomposition of 4 6 where the energy barriers represent the effective 1,3-butadiene have been discussed extensively in the activation energies obtained from experiments literature [21–27]. The initial step was thought to be: [21,29–30]. It is seen that the energy barrier of (a) C9C bond rupture to form two vinyl radicals 1,3-C H isomerization to 1,2-C H and 2-C H [23,25,26] 4 6 4 6 4 6 are about 85 kcal/mol or about 17 kcal/mol lower than that of C9H ﬁssion in 1,3-C H and !: ииϩ 4 6 1,3-C46 H CH 23CH 23 about 33 kcal/mol lower than the C9C bond

strength in 1,3-C4H6. On the other hand, the and/or (b) the formation of ethylene and acetylene isomerization of 1,3-C4H6 does not yield the iso- [22,24,25]. The second pathway, originally proposed mers in signiﬁcant concentrations. Computer [22,24] to occur as a concerted unimolecular process, simulations showed that the equilibrium concen- was lately considered [25] to proceed in two steps via tration of 1-butyne never exceeds 0.5% (mol) of the formation of vinylidene. 1,3-butadiene at 1000 K. For this reason, we in-

cluded 1,2-C4H6 and 2-C4H6 in the model, but 1,3-C H !: CH ϩ HCCC 46 24 2 excluded 1-C4H6. The combined uncertainty in the chemistry of 1-C H and 2-C H decompo- C ϩ !: ϩ 4 6 4 6 HCC222M CH M sition renders an inclusion of the 1-C4H6 chemistry not worthwhile at this time. Studies on 1,2-butadiene [28,29] and 2-butyne [31] demonstrated relatively low-energy barriers for their mutual isomerization, and particularly for their isomerization to 1,3-butadiene. Based on these results Hi- daka et al. [21] proposed a reaction mechanism that was shown to reconcile a large amount of experimental data for 1,3-butadiene [22–27] and its isomers [28– 31]. Hidaka and coworkers showed that the isomerization of 1,3-butadiene to 1,2-butadiene and 2-butyne is much faster than its fragmentation. The decomposition of the isomers plays an important role in the overall pyrolysis mechanism of 1,3-butadiene. Fur- thermore, the formation of CH4, allyl (a-C3H5), propyne (p-C3H4), C2H6, and propene (C3H6) could not be systematically predicted without considering C9C bond rupture in 1,2-butadiene.

We introduced the following set of the reactions in Figure 1 Energy diagram of the C4H6 mutual isomeriza- the present kinetic model: tions. The energy levels are in kcal/mol. short standard long JCK(Wiley) RIGHT INTERACTIVE

DETAILED KINETIC MODELING OF 1,3-BUTADIENE OXIDATION AT HIGH TEMPERATURES 595 и 2. The formation of the C4H5 radicals—namely, 3. Additional fragmentation reactions of 1,3-buta- и" 9 " и HC CH CH CH2 (n- C4H5), diene and 1,2-butadiene were also considered. " и9 " и H2C C CH CH2 (i- C4H5), and They are " " и9 CH2 C C CH3, are described by the re- !: ϩ actions of H ejection and abstraction from C4H6: 1,3-C46 H CH 44H 2 !: HCCC ϩ CH !: ииϩ 224 1,3-C46 H n-CH 45 H !: ииCH ϩ CH !: ииϩ 23 23 i-CH45 H 1,2-C H !: ииCH ϩ CH !: ииϩ 46 33 3 1,2-C46 H i-CH 45 H 4. The H-atom attack on the ␲-bonds in 1,3-buta- 2-C H !: CH "C"Cии9CH ϩ H 46 2 3 diene, 1,2-butadiene, and 2-butyne leads to the ϩ ии!: ϩ и 1,3-C46 H R n-CH 45 HR formation of ﬁve rovibrationally excited C4H7 adducts, which may mutually isomerize. The !: i-CHи ϩ HR и 45 C4H7 potential energy surface is quite complex, as demonstrated in Figure 2, where only 1,2-H 1,2-C H ϩ Rии!: i-CHϩ HR 46 45 shift was considered. The energy barrier of this 2-C H ϩ Rии!: CH "C"C 9CH ϩ HR process was estimated to be 40 kcal/mol on the 46 2 3 и и basis of previous studies of C3H5 [2], C4H3 [75], and иC H [76]. It can be inferred from и ϭ и и и и 4 5 where R H , CH3, C2H3, and C3H3. Both Figure 2 that a variety of C ϩ C and C ϩ C и " " и9 2 2 3 1 i- C4H5 and CH2 C C CH3 are reso- products can form as a result of chemically nantlyи stabilized and are thus more stable than activated reactions. These products include n- C4H5. In the present model, the mutual isom- ϩ и ϩ и ϩ и C2H4 C2H3, p-C3H4 CH3, and C2H2 erization of C4H5 is described by 1,2-H shift: и C2H5. To obtain the pressure-dependent rate coefﬁcients for all reaction channels is beyond ии;: ;: " " и9 n-CH45i-CH 45CH 2C C CH 3 the scope of the present study. Here we included

Figure 2 Energy diagram of the reactions occurring on the C4H7 potential energy surface. The relative energy levels of the radical adducts were obtained from quantum chemical calculation at the G2(B3LYP) level of theory [2]. The energy barriers of all isomerization steps were estimated. All other energy values (kcal/mol) were determined from thermochemical data. short standard long JCK(Wiley) LEFT INTERACTIVE

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the following six chemically activated reactions:

ϩ ии!: ϩ 1,3-C46 H H CH 24CH 23 !: ϩ и p-C34 H CH 3 !: ϩ и a-C34 H CH 3 ϩ ии!: ϩ 1,2-C46 H H p-C 34 H CH 3 !: ϩ и a-C34 H CH 3 ϩ ии!: ϩ 2-C46 H H p-C 34 H CH 3

Among these reactions, the channel leading to the formation of vinyl and ethylene is the most critical to the oxidation kinetics of 1,3-butadiene. Our initial simulation tests showed that the overall oxidation rate of 1,3-butadiene is highly ϩ sensitive to the rate parameter of 1,3-C4H6 и : ϩ и H C2H4 C2H3. For this reason, we justify below our rate-constant choice.

: ؉ RRKM Analysis of Reaction 1,3-C4H6 H ؉ C2H4 C2H3. To simplify the analysis, only the part Figure 3 Comparison of the experimental (symbols) and ϩ : of the potential energy surface involving the formation computed (lines) rate coefficients of 1,3-C4H6 H prod- " 9 9и ϩ : ϩ of the CH2 CH CH2 CH2 adduct followed by ucts (top panel) and C2H3 C2H4 1,3-C4H6 H (bottom ϩ и ϩ : its dissociation to C2H4 C2H3 was included in the panel). In the top panel, the values for 1,3-C4H6 H ϩ analysis (see Fig. 2). Based on a previous study [76] n-C4H7 and C2H4 C2H3 were obtained at 100 Torr, which ϩ и : ϩ и is equal to the pressure under which the rate coefficients are of C2H2 C2H3 C4H4 H, we do not expect that this simplification yields significant errors in the reported [84,85]. The rate coefficients for the production of p-C H and a-C H ϩ CH and the two H-abstraction reac- predicted rate coefficients. The most favorable out- 3 4 3 4 3 tions were estimated from previous studies [2,49]. k is the come of the hot CH "CH9иCH9CH isomer is tot 2 3 total rate of the 1,3-C H ϩ H reactions considered in the ϩ и 4 6 for it to dissociate back to 1,3-C4H6 H . present model (see text). RRKM parameters are given in [49]. The energy barrier of H-atom addition to 1,3-C4H6 was lowered by 0.6 kcal/mol from that used in [49] to fit the room temperature data [77–83], as seen in Figure 3a. These data were collected under a wide range of pressures (0.38 to 760 Torr), but our analysis shows that all of ϩ ии!: ϩ them are at the high-pressure limit. Figure 3a shows 1,3-C46 H H n-CH 45H 2 also the RRKM rates for ϩ ии!: ϩ 1,3-C46 H H i-CH 45H, 2 ϩ ии!: ϩ 1,3-C46 H H CH 24CH 23 ϩ и : and the total rate constant, ktot, for 1,3-C4H6 H ϩ ии!: " 9 9 products. It is seen that ktot is in close agreement with 1,3-C46 H H CH 2CH CH 2CH 2 the available data at ϳ1100 K [84,85]. at 100 Torr, the sum of the rate coefficients previously Figure 3b presents a comparison between experi- ϩ estimated [2] for mental and computed rate coefficients for C2H4 и : ϩ и C2H3 1,3-C4H6 H at 1 mTorr of pressure. It is ϩ ии!: ϩ seen that the computed rate constant is slightly larger 1,3-C46 H H p-C 34 H CH 3 than the experimental data [86]. This is reasonable ϩ ии!: ϩ 1,3-C46 H H a-C 34 H CH 3 , considering that the experimental rates were obtained relative to that of vinyl recombination with an as- the rate coefficients previously estimated [49] for re- sumed rate constant of 2 ϫ 1013 cm3 molϪ1 sϪ1. Recent short actions studies [87,88] showed that the vinyl-recombination standard long JCK(Wiley) RIGHT INTERACTIVE

DETAILED KINETIC MODELING OF 1,3-BUTADIENE OXIDATION AT HIGH TEMPERATURES 597 rate constant is a few factors larger than 2 ϫ 1013 cm3 2. Reactions of 2,5-dihydrofuran and vinyloxirane molϪ1 sϪ1. have been studied in great detail [15–20,89– 91] and are illustrated in Figures 4 and 5, re- 1,3-Butadiene Oxidation. It was concluded [7,12] spectively. that the initial step during the oxidation of 1,3-buta- It is known [17,18] that 2,5-dihydrofuran un- diene involves mainly the addition of the O atom to dergoes H2 elimination to produce furan, the double bond. Two different mechanisms were proposed, as discussed in the Introduction section. Here we propose a pathway entirely different from the pre- H ϩ vious suggestions and show that the formation of cro- 2 O O tonaldehyde [7] and vinyloxirane [12] are accounted for by the mechanism proposed here. Furan dissociates in nearly the same rate [89– и и 91] to, 1. Reactions of 1,3-butadiene with O and HO2 . As a result of O-atom addition to the ␲ bond in 1,3-butadiene, two possible biradical isomers ϩ can be formed, that is, C2H2 CH2CO O Oи p-C H ϩ CO и 3 4 H C"CH9CH9CH (A) or 2 2 It is seen in Figure 4 that the energy level of 1,3- Oи ϩ и ϩ C4H6 O is high enough to yield furan H2, и ϩ ϩ ϩ ϩ H C"CH9CH9CH (B) C2H2 CH2CO H2, and p-C3H4 CO H2 2 2 in one step through chemically activated pro- cesses. Because of resonant stabilization, isomer A is The reaction path via vinyloxirane is more more stable than B and is thus favored over B. complex than that via 2,5-dihydrofuran. It is Based on energy considerations, we believe that known that vinyloxirane undergoes rapid ring the favorable reaction of A is for it to isomerize expansion to 2,3-dihydrofuran at relatively low to 2,5-dihydrofuran or vinyloxirane, temperatures [13,14]

и9 " 9 9 и H2C CH CH CH2 O O O O O " 9и 9 9 и H2C CH CH CH2 O The reactions of 2,3-dihydrofuran were reported

Figure 4 Energy diagram of the reactions of 1,3-butadiene with O and HO2 radicals, via the formation 2,5-dihydrofuran. The short energy values are in kcal/mol. standard long JCK(Wiley) LEFT INTERACTIVE

598 LASKIN ET AL

Figure 5 Energy diagram of the reactions of 1,3-butadiene with O and HO2 radicals, via the formation vinyloxirane. The energy values are in kcal/mol.

[15] to be unimolecular isomerizations to cro- The thermal decomposition of crotonalde- tonaldehyde and cyclopropanecarboxaldelde- hyde produces propene and carbon monoxide hyde. [20] or radical products [19],

9 " 9 CH3 CH CH CHO 9 " 9 !: ϩ CH3 CH CH CHO CH36 CO O !: 9 " 9ииϩ CH3 CH CH CO H O !: ии9 " 9 ϩ CH2 CH CH CHO H

In the work of Lifshitz et al. [15] on the thermal Figure 5 shows the energy of the entrance chan- decomposition of 2,3-dihydrofuran, these two nel is high enough to allow many products to isomers were not fully separated by GC analy- form through chemically activated process. In sis. As a result, the reaction sequence was not summary, the reaction channels of potential sig- clearly identiﬁed. However, the formation of niﬁcance are crotonaldehyde can be inferred based on a later ϩ !: ϩ ϩ work [92] on the thermal reactions of 2-methyl- 1,3-C46 H O H 2CH 22CH 2 CO 4,5-dihydrofuran, which showed that 2,3-dihy- !: ϩ ϩ H234p-C H CO drofuran can isomerize either directly to a non- !: ϩ ϩ cyclic aldehyde or via the cyclopropane to form CH24CH 2 CO CO !: ϩ the noncyclic aldehyde. In addition, the uni- CH22 oxirane molecular fragmentation of 2,3-dihydrofuran, !: 9 " 9ииϩ CH3 CH CH CO H 9 " и ϩ (CH3 CH CH CO) O ϩ !: ииCH 9CH"CH9CHO ϩ H C2H2 2 O и ϩ (aCH35 CO) ϩ C2H4 CH2CO In the present study, the total rate constant of ϩ и was also reported, but both reactions are ex- 1,3-C4H6 O reported [32,33] for the tem- short pected to be slow [15]. perature range of 280–1016 K was used as is standard long JCK(Wiley) RIGHT INTERACTIVE

DETAILED KINETIC MODELING OF 1,3-BUTADIENE OXIDATION AT HIGH TEMPERATURES 599

without modification. The largest uncertainty is tion reactions are included in the model, the branching ratio of various product channels. ϩ ии!: ϩ In particular, the choice of radical versus mo- 1,3-C46 H OH i-CH 45HO 2 lecular products has a significant influence on !: n-CHи ϩ HO the overall reaction rate of 1,3-butadiene oxi- 45 2 dation. Our initial computer simulation shows The rate constant reported in [34] was adopted that the fuel-disappearance rates can be pre- and split into two parts. We assumed that the A- dicted only if the reaction products are radical " factor for H-abstraction from the CH2 group species. Therefore, we assumed that the reaction is twice that of the 9CH" group. The tem- ϩ и 9 " of 1,3-C4H6 O produces CH3 CH perature exponent was assumed to be equal to 9и ϩ и и 9 " 9 CH CO H and CH2 CH CH 2. The activation energy to i-иC H was as- ϩ и 4 5 CHO H with a natural branching ratio of sumed to be 3 kcal/mol lower than that to 9 " 9 1:3. Dissociation of the CH3 CH CH n-иC H because of the difference in reaction и и 9 " 9 4 5 CO and CH2 CH CH CHO radicals enthalpy. The resulting rate expressions are k ϩ 9 " и и yields CO CH3 CH CH and a- C3H5, (cm3 molϪ1 sϪ1) ϭ 6.2 ϫ 106 T2 exp(Ϫ1730/T) respectively. for n-C H and 3.1 ϫ 106 T2 exp(Ϫ220/T) for Our model differ principally from the previ- 4 5 i-C4H5. ous proposals [7,12], in that we assume that the 4. Reactions of иC H with O . We took the rate ϩ D 4 5 2 reaction between 1,3-C4H6 O is chemically expression of Slagle et al. [35] and assigned the activated, whereas previous studies assumed ϩ и reaction products to be CH2CO CH2CHO , that the major products of the reaction come и ϩ based on a similar channel for the C2H3 O2 from the collisional stabilization of the adduct. reaction. Based on the energy levels shown in Figures 4 The reaction of O with n-иC H is expected and 5, it is questionable whether the stabilization 2 и 4 5 to be faster than with i- C4H5. We assumed that of adducts can be of any significance. the rate constant was equal to that of the anal- Also shown in Figures 4 and 5 are the reac- и ϩ и ogous C2H3 O2 reaction but found that the tions between 1,3-butadiene and the HO2 и ϩ n- C4H5 O2 reaction has little or no influence radical. Here we assume that in addition to on model predictions under all tested conditions. D H-abstraction of 1,3-C4H6 by HO2 , the reaction also leads to the formation of vinyloxirane and 2,5-dihydrofuran, RESULTS

ϩ ии!: ϩ Figure 6 presents selected experimental and computed 1,3-C46 H HO 2 vinyloxirane OH species and temperature profiles during 0.3% 1,3-bu- !: 2,5-dihydrofuran ϩ иOH tadiene pyrolysis in the flow reactor. The experimental data were collected at three initial temperatures The trace amounts of crotonaldehyde [7] and ϳ1100–1200 K. GC analyses identified ethylene and vinyloxirane [12] can be well accounted for by acetylene to be the dominant products at all tempera- a single mechanism. Simulation of the flow re- tures. The concentrations of methane, allene, propyne, actor experiment [7] showed that while vinylox- propene, 1,2-butadiene, 2-butyne, cyclopentadiene, irane and crotonaldehyde are formed in detect- benzene, toluene, styrene, and naphthalene were also able amounts (ϳ10 ppm), the computed notable. The concentration profiles of ethylene and concentrations of furan, 2,3- and 2,5-dihydro- acetylene are nearly identical for each temperature. furans are less than 1 ppm. The source of cro- The concentration of propyne is about a factor of 2 tonaldehyde is vinyloxirane, which is produced larger than that of allene, because of rapid attainment

from the reaction of 1,3-butadiene with HO2, of partial equilibrium at these temperatures [2]. The and not with O atom, as originally proposed. concentration of methane reaches ϳ240 ppm for T ϭ 3. Reactions of 1,3-butadiene with иOH. Liu et al. 1200 K, but it is still much smaller than those of eth- [34] reported the overall rate constant in the ylene and acetylene. The sharp rise of the 1,2-butadi- temperature range of 305–1173 K. Based on ene concentration to its equilibrium value at early re- their analysis, the major reaction channel is иOH action times is certainly indicative of rapid addition at temperatures Ͻ1000 K, while the H- isomerization of 1,3-butadiene and of partial equilib- abstraction by DOH is the major channel at rium of the isomerization products thereafter. The short higher temperatures. Here only the H-abstrac- model predicts quite well the proﬁles of 1,2-butadiene standard long JCK(Wiley) LEFT INTERACTIVE

600 LASKIN ET AL

qualitative feature of the reactant, intermediate, and product concentrations as a function of temperature. In particular, the rise and fall in the concentrations of intermediate species, including ethylene, vinylacetylene, benzene, and propyne, are all well reproduced by the model. The model also predicts quantitatively the concentrations of all species over a wide temperature range. We conducted seven experiments for 1,3-butadiene oxidation in the ﬂow reactor. GC measurements were focused largely on the species relevant to the major oxidative pathway of 1,3-butadiene, as will be discussed in further detail. We lowered the reaction temperature from that used in [7] to about 1035 K and performed experiments at two equivalence ratios of 1.63 and 0.55. These are Cases 4 and 5, respectively. In Cases 6–9, we conducted the experiments at the similar temperature as those in Cases 10 and 11 [7], but the range of the equivalence ratio was extended,

Figure 6 Experimental (symbols) and computed (lines) concentration and temperature proﬁles during the pyrolysis of 0.3% 1,3-butadiene–N2 in a ﬂow reactor at initial temperatures of 1110, 1150, and 1185 K. The data were taken in the present work (Cases 1a, b, and c, see Table I) and were time shifted by 55, 45, and 20 ms, respectively.

and other species. This includes both the absolute concentration levels, as well as the temporal shapes of the concentration profiles. The effect of oxygen contamination was examined numerically. It was found that the addition of 25–30 ppm of oxygen in nitrogen affects only the initial period of reaction. It does not affect the concentration profiles after a small reaction time. Thus, the effect of oxygen contamination is partly reflected by time-shifting the experimental profiles. To examine the capability of the kinetic model for predicting the pyrolysis of 1,3-butadiene at higher temperatures, we performed simulation for the shock- Figure 7 Experimental [27] (symbols, Case 2) and com- tube experiments of Colket [27] (Case 2) and Hidaka puted (lines) concentration profiles for species formed dur- et al. [21] (Case 3). Figures 7 and 8 present the com- ing the pyrolysis of 0.175% 1,3-butadiene in argon in a sin- parison of model and experiment. It is seen that for gle pulse shock tube. The experimental and computational short both cases the model predicts very well the dwell time is 0.7 ms. standard long JCK(Wiley) RIGHT INTERACTIVE

DETAILED KINETIC MODELING OF 1,3-BUTADIENE OXIDATION AT HIGH TEMPERATURES 601

the fuel-rich condition. This is expected considering that the variation of the equivalence ratio is mainly caused by a large initial oxygen concentration in the fuel-lean case. It is seen in Figures 9 and 10 that the model cap- tures quite well the major species profiles. The concentration profiles of propyne and allene are also rea- sonably well predicted. The temperature computed at long reaction times is seen to be higher than the experimental counterpart. This discrepancy is certainly caused by the adiabatic assumption employed in the simulation. The large rates computed for 1,3-butadiene disappearance and CO production may be a direct con- sequence of the temperature difference between simulation and experiment. Comparisons of the experimental and computed species profiles at the initial temperature of ϳ1120 K are presented in Figures 11–14, varying the equivalence ratio from 4.7 (Fig. 11), 1.6 (Fig. 12), 1.0 (Fig. 13), to 0.55 (Fig. 14). Again, a comparison of the 1,3- butadiene and CO profiles in these figures show that an increase in the initial oxygen concentration facili- tates faster reactions. It is seen that the model predicts very well the major and minor species profiles for all

four mixtures. In particular, the sharp rise in the CO2 profiles and the rise–then fall of the CO concentrations for the stoichiometric (Fig. 13) and fuel-lean Figure 8 Experimental [21] (symbols, Case 3) and com- (Fig. 14) cases are well captured by the model, sug- puted (lines) concentration profiles for species formed dur- gesting that the radical pool concentrations in these ing the pyrolysis of 0.5% 1,3-butadiene in argon in a single- experiments are well reproduced. pulse shock tube. The experimental and computational dwell Comparisons between experimental data and model time is between 1.3 and 2.4 ms. predictions were also made for the original flow reactor data of Brezinsky et al. [7]. Figures 15 and 16 plot the experimental and computed concentration profiles for Cases 10 and 11, respectively. It is seen

that the concentrations of the C3 and C4 aldehydes are from the ultra fuel-rich condition of ␾ ϭ 4.7 (Case 6) well reproduced by the current model. to the fuel-lean condition of ␾ ϭ 0.55 (Case 9). In Having veriﬁed the model against the detailed addition, Case 7 from the present study was designed structure of 1,3-butadiene oxidation, we turned our at- to overlap with Case 10 from [7]. tention to global combustion properties. Figure 17 The experimental results of Brezinsky et al. [7] and compares experimental [10] and computed ignition those of the present work showed that under all con- delay times for three 1,3-butadiene–oxygen–argon ditions only ethylene, acetylene, and carbon monoxide mixtures. In general, the predicted ignition-delay times were formed in large amounts. Other products, like are smaller than the experimental data at low temper- methane, ethane, allene, propyne, propene, vinylacet- atures, while they are large than the experimental val- ylene, benzene, other C4 and C5 species, and some ues at high temperatures. The predictions are in close oxygenated compounds, were also detected in the agreement in the mid-temperature range for each data post reaction mixtures, but they are formed in rela- set. The discrepancy in the activation energies between tively small concentrations or even trace quantities model and experiment is certainly discomforting. (Ͻ10 ppm). Fournet et al. [10] also reported the experimental data Figures 9 and 10 present data at the equivalence of acetylene, propyne, and allene. In each case, the ratios of 1.63 and 0.55, respectively, at the identical activation energy was larger, by a factor of 2 or more, initial temperature of 1035 K. The overall reaction in than previously measured values. For example, the short the fuel-lean case is seen to be faster than that under activation energy of acetylene ignition obtained by standard long JCK(Wiley) LEFT INTERACTIVE

602 LASKIN ET AL

Figure 9 Experimental (symbols) and computed (lines) concentration and temperature proﬁles during the oxidation of 0.142%

1,3-butadiene–0.48% O2-N2 in a ﬂow reactor at the initial temperature of 1035 K. The data were taken in the present work (Case 4, see Table I) and were time shifted by 18 ms.

Figure 10 Experimental (symbols) and computed (lines) concentration and temperature proﬁles during the oxidation of 0.14%

1,3-butadiene–1.4% O2-N2 in a ﬂow reactor at the initial temperature of 1035 K. The data were taken in the present work short (Case 5, see Table I) and were time shifted by 25 ms. standard long JCK(Wiley) RIGHT INTERACTIVE

DETAILED KINETIC MODELING OF 1,3-BUTADIENE OXIDATION AT HIGH TEMPERATURES 603

Figure 11 Experimental (symbols) and computed (lines) concentration and temperature proﬁles during the oxidation of 0.14%

1,3-butadiene–0.12% O2-N2 in a ﬂow reactor at the initial temperature of 1120 K. The data were taken in the present work (Case 6, see Table I) and were time shifted by 12 ms.

Figure 12 Experimental (symbols) and computed (lines) concentration and temperature proﬁles during the oxidation of

0.144% 1,3-butadiene–0.488% O2-N2 in a ﬂow reactor at the initial temperature of 1110 K. The data were taken in the present short work (Case 7, see Table I) and were time shifted by 12 ms. standard long JCK(Wiley) LEFT INTERACTIVE

604 LASKIN ET AL

Figure 13 Experimental (symbols) and computed (lines) concentration and temperature proﬁles during the oxidation of 0.14%

1,3-butadiene–0.78% O2-N2 in a ﬂow reactor at the initial temperature of 1120 K. The data were taken in the present work (Case 8, see Table I) and were time shifted by 20 ms. The dashed lines in the top panels are the model calculations ϩ : ϩ for the 1,3-butadiene and CO concentrations assuming the reaction channel of 1,2-C4H6 O C2H2 oxirane, instead of ϩ : ϩ ϩ 1,2-C4H6 O CH3 · CHCHCO H and CH2CH · CHCHO H (see text).

fitting previous data [93–99] was 20 kcal/mol. In speeds are slightly lower than the experimental coun- comparison, the data reported in [10] give an activa- terpart from the stoichiometric to fuel-rich condition energy of ϳ60 kcal/mol. Similarly, the activation tions. energy of propyne ignition was reported by Curran et In addition to the results shown in Figures 6–18, al. [100] to be 33 kcal/mol, whereas the data reported we also repeated simulations for experiments previ- in [10] yield an activation energy value of 64 kcal/ ously reported for C3 fuels [2,3]. In all cases, the ad- mol. In each case the experimental activation energy dition of the butadiene chemistry did not affect the for the 1,3-butadiene data as seen in Figure 17 is also predictive capability for C3 fuels. large than that predicted by the current model by about a factor of 2. Based on these comparisons, we con- clude that the discrepancy may well originate from the accuracy of the data; and a rigorous validation of the DISCUSSION current model against ignition delay of 1,3-butadiene cannot be made without having the experimental data Based on the current model, the radical chain process validated first. in the early period of 1,3-butadiene pyrolysis (Cases Figure 18 shows the variation of experimental and 1a–c) is initiated via the isomerization of 1,3-butadi- computed flame speeds as a function of equivalence ene to 1,2-butadiene and 2-butyne. This is followed ratio. The data for the fuel-lean mixtures are well pre- by the dissociation of these isomers and the further short dicted by the model, whereas the computed flame reactions of the dissociation products: standard long JCK(Wiley) RIGHT INTERACTIVE

DETAILED KINETIC MODELING OF 1,3-BUTADIENE OXIDATION AT HIGH TEMPERATURES 605

Figure 14 Experimental (symbols) and computed (lines) concentration and temperature proﬁles during the oxidation of

0.144% 1,3-butadiene–1.4% O2-N2 in a ﬂow reactor at the initial temperature of 1120 K. The data were taken in the present work (Case 9, see Table I) and were time shifted by 18 ms.

!: 1,3-C46 H 2-C 46 H trolled by the following two reactions: !: 1,3-C46 H 1,2-C 46 H ϩ ии!: ϩ 1,3-C46 H H CH 23CH 24 !: ииϩ 2-C46 H CH 2 CCCH 3 H ии!: ϩ CH23CH 22 H ииCH CCCH !: i-CH 23 45 The H abstraction of 1,3-butadiene by the H atom !: ииϩ 1,2-C46 H CH 33CH 3 1,3-C H ϩ Hии!: i-CHϩ H ϩ иии!: 46 45 2 1,3-C46 H CH 3i- C 45 H and n-CH 45 ϩ CH4 proceeds at a rate that is an order of magnitude slower than the иC H ϩ C H channel. Very little ethylene ии!: ϩ и 2 3 2 4 i- C45 H and n-CH 45CH 44 H is consumed via the H abstraction by the H atom. This explains the nearly equal concentrations of acetylene We found that under the ﬂow reactor condition the rate and ethylene for all cases shown in Figure 6. of unimolecular decomposition of 1,3-butadiene to Propyne and allene are also produced by the chem- ϩ C form C2H4 H2CC was comparable with those of ically activated reactions of 1,3-butadiene with the H the isomerization reactions. Vinylidene isomerizes atom, rapidly to acetylene, thus provides little to no contribution to the radical pool. ϩ ии!: ϩ 1,3-C46 H H p-C 34 H CH 3 The radical-chain reaction process becomes domi- short ϩ ии!: ϩ nant in just a few microseconds. This chain is con- 1,3-C46 H H a-C 34 H CH 3 standard long JCK(Wiley) LEFT INTERACTIVE

606 LASKIN ET AL

Figure 15 Experimental [7] (symbols, Case 10, see Table I) and computed (lines) concentration and temperature proﬁles during the oxidation of 0.143% 1,3-butadiene–0.477% O2-N2 in a ﬂow reactor at the initial temperature of 1110 K. The data is time shifted by 10 ms.

Figure 16 Experimental [7] (symbols, Case 11, see Table I) and computed (lines) concentration and temperature proﬁles during the oxidation of 0.143% 1,3-butadiene–0.626% O2-N2 in a ﬂow reactor at the initial temperature of 1110 K. The data short is time shifted by 10 ms. standard long JCK(Wiley) RIGHT INTERACTIVE

DETAILED KINETIC MODELING OF 1,3-BUTADIENE OXIDATION AT HIGH TEMPERATURES 607

Methane is produced mainly as a result of H abstraction from 1,3-butadiene by the methyl radicals. For 1,3-butadiene pyrolysis in shock tubes (Cases 2 and 3), the overall reaction sequence is similar to those found in the ﬂow-reactor experiment. At temperatures higher than 1400 K, however, additional reactions become important. In particular, the unimole- ϩ C cular dissociation of 1,3-butadiene to C2H4 H2CC ϩ and C4H4 H2 is increasingly important. The H abstraction of 1,3-butadiene by the H atom begins to compete effectively withи the chemicallyи activated reactions. The resulting i- C4H5 and n- C4H5 isomers dissociate rapidly to form vinylacetylene, which is consumed by

ϩ ии!: ϩ CH44H CH 22CH 23

In addition, intermediates such as ethylene, propyne, and allene begin to decompose via the following channels:

ϩ ии!: ϩ CH24H CH 23H 2 ϩ ии!: ϩ p-C34 H H CH 22CH 3 !: и ϩ p-C34 H CH 33 H !: и ϩ a-C34 H CH 33 H

Figure 17 Experimental [10] (symbols) and computed (lines) ignition-delay times of 1,3-butadiene–oxygen–argon mixtures behind reﬂected shock waves. I: Case 12 (1% 1,3-

C4H6–8%O2–91% Ar); II: Case 13 (1% 1,3-C4H6–4%O2–

95% Ar); III: Case 14 (3% 1,3-C4H6–12% O2–85% Ar). The dashed lines are the calculated ignition-delay times as- ϩ : ϩ suming the reaction channel 1,2-C4H6 O C2H2 ox- ϩ : B ϩ irane, instead of 1,2-C4H6 O CH3CHCHCO H and ϩ CH2CH · CHCHO H (see text).

In the present model, we assume the rate constants of these reactions to be equal. This is not crucial to the prediction of the relative concentrations of propyne and allene, since they rapidly convert to each other via unimolecular isomerization as well as H-atom cata- lyzed isomerization [2]. Figure 18 Experimental [37] (symbols) and computed (line) laminar ﬂame speeds of 1,3-butadiene–air mixtures at !: p-C34 H a-C 34 H atmospheric pressures. The ﬁlled symbols represent data de- rived from linear extrapolation; open symbols are nonlinear short ϩ ии!: ϩ p-C34 H H a-C 34 H H extrapolation. standard long JCK(Wiley) LEFT INTERACTIVE

608 LASKIN ET AL

!: ϩ C Diacetylene in these single-pulse shock-tube ex- 1,3-C46 H CH 24HCC 2 periments is produced from vinylacetylene: Although vinylidene radicals isomerize rapidly to ϩ ии!: иϩ acetylene, some of them react with O to produce the CH44H n-CHor 43i-CH 43H 2 2 initial radical species, that is, ии!: ϩ и n-CHor43i-CH 43CH 42 H C !: HCC222CH where n-иC H and i-иC H are the HC#C9 4 3 4 3 C ϩ !: ииϩ "и # 9и " HCC22O HCO HCO CH CH and HC C C CH2 radicals, respectively. Under all conditions, the recombination of ииHCO !: H ϩ CO the propargyl radicals, along with the reaction pres- ently postulated, The isomerization of 1,3-butadiene to 2-butyne followed by the C9H bond ﬁssion of 2-butyne also con- ииϩ !: ϩ CH232266 CCCH CH CH H tributes to the initial radical pool. After the radical pool is established, there are three is the leading source of benzene in these shock tube separate pathways contributing to the overall reac- experiments. tions. These three pathways are described in Figure 19 For 1,3-butadiene oxidation in the ﬂow reactor and are seen as a result of the different starting reac- (Cases 1 and 4–11), the radical-chain process is ini- tions of 1,3-butadiene, that is, with H, O, and OH. The tiated through the formation of vinylidene, relative contribution of each pathway does not vary

short Figure 19 Oxidative reaction pathways of 1,3-butadiene. standard long JCK(Wiley) RIGHT INTERACTIVE

DETAILED KINETIC MODELING OF 1,3-BUTADIENE OXIDATION AT HIGH TEMPERATURES 609 и drastically as a function of equivalence ratio. The rates CH3, forming propene and 1-butene, respectively. of these pathways range from being nearly equal in Propene and 1-butene are subsequentlyи consumedи by fuel-lean cases to being different by just a few factors the chemically activated reaction of H (or CH3) ad- : и и under the fuel-rich condition. Pathway I is the fastest dition CH3 (or H ) elimination to yield ethylene. under all flow-reactor conditions. Similar to the py- The allyl pathway has a net effect of reducing the rad- rolysis case, this pathway starts with the chemically ical pool concentrations, because each reaction step activated reaction of 1,3-butadiene with the H atom to following allyl formation involves either radical–rad- yield vinyl and ethylene. Ethylene is consumed either ical combination or the exchange of the H atom for a by its reaction with the Oи atom to yield the methyl lesser reactive methyl radical. and formyl radicals, or through H abstraction by Hи In all flow-reactor experiments, the propene con- and иOH radicals to produce the vinyl radical. Thus, centrations in the oxidation butadiene are larger than Pathway I can be viewed as that of ethylene oxidation those in pyrolysis. For a limited range of equivalence with the addition of the initial, chemically activated ratio, the propene concentration increases with a de- H-atom attack on 1,3-butadiene. crease in the equivalence ratio (cf. Figs. 9 and 10). Pathway II starts from the reactions of 1,3-butadi- This trend is clearly caused by an increase in the con- ene with the O atom, with the subsequent reactions tribution of Pathway II with a decrease in the equiv- и 9 involving mostly the C3H5 radicals. The CH3 alence ratio. CH"иCH radical undergoes rapid ␤-scission, lead- In general, Pathway III proceeds at a slower rate ing to acetylene and the methyl radical. The allyl rad- than the first two pathways. This route starts with H ical, on the other hand, tends to combine with Hи and abstraction of 1,3-butadiene by иOH and under fuel-

Figure 20 First-order sensitivity coefﬁcients computed at 25 ms of the reaction time for 1,3-butadiene oxidation in the ﬂow short reactor. standard long JCK(Wiley) LEFT INTERACTIVE

610 LASKIN ET AL rich conditions, also by the H atom.и Diacetylene is This finding extends the critical role of vinylidene produced from the decomposition of C4H5 via C4H4 identified [5] in the initiation reaction of acetylene ox- and C4H3 and is oxidized through its reactions with idation to the present case of 1,3-butadiene oxidation. Oи and иOH. There is little difference in the major pathways of Sensitivity analyses reveal essentially the same fea- 1,3-butadiene oxidation between flow reactor, shock ture as the reaction pathway analysis. Figure 20 pre- tube, and flame. Prior to ignition, three separate path- sents the ranked first-order sensitivity coefficients ways proceed at the rates that are within a few factors computed for 1,3-butadiene concentration at a reaction of each other. In shock tubes toward high tempera- time of 25 ms in Cases 7 (␾ ϭ 1.62), 8 (␾ ϭ 1), and tures, the isomerization of 1,3-butadiene to 2-butyne, 9(␾ ϭ 0.55). No major change in the ranking of sen- followed by the C-H fission of 2-butyne, also proceeds sitivity coefficients was observed. The reactions per- very rapidly. The ranked sensitivity coefficients are tinent to each pathway exhibit large influences on fuel- shown in Figures 21 and 22 for ignition delay times disappearance rates. The dominant influence comes (Cases 12 and 13). Figure 23 presents the sensitivity ϩ и ϭ ϩ и from 1,3-C4H6 H C2H4 C2H3. coefficients for flame speeds computed at three equiv- For the oxidation of 1,3-butadiene in shock tubes alence ratios. It is seen that the reactions between 1,3- (Cases 12–14), it was found that the initiation reaction butadiene and the H atom to yield ethylene and the sequence is the same as that in the flow-reactor case. vinyl radical, as well as the subsequent oxidation of

The radical-chain reaction prior to ignition is largely the vinyl radical by O2 to form vinoxy radical, are one initiated by 1,3-butadiene decomposition to vinyli- of the major driving forces for the radical chain pro- dene, followed by the reaction of vinylidene with O2. cess. In addition, there is no speciﬁc kinetic reason to

Figure 21 First-order sensitivity coefﬁcients computed for the ignition-delay time of Case 12. short standard long JCK(Wiley) RIGHT INTERACTIVE

DETAILED KINETIC MODELING OF 1,3-BUTADIENE OXIDATION AT HIGH TEMPERATURES 611

Figure 22 First-order sensitivity coefﬁcients computed for the ignition-delay time of Case 13.

explain the difference in the experimental and com- acetylene ϩ oxirane as the only reaction channel. puted activation energies of ignition delay shown in While the product assignment has little effects on Figure 17. flame-speed prediction, it markedly affects the igni- Through the present analysis, we identified the tion-delay time. The dashed lines in Figure 17 were greatest uncertainty in the oxidation kinetics of 1,3- obtained with acetylene ϩ oxirane as the only reaction butadiene to be the branching ratio of the reaction products and show that the ignition-delay times were over-predicted. Lastly, we note that although our anal- ϩ !: 1,3-C46 H O products ysis suggests that the formation of molecular species from the reaction cannot be very significant, this sug- From energy considerations (Figs. 4 and 5), a substan- gestion remains to be verified. tial amount of the products are molecular species. In the present model, however, we assumed that the above reaction leads entirely to the production of rad- SUMMARY ical species. This assumption was critically needed in order to predict the flow-reactor data. Having assumed The oxidation kinetics of 1,3-butadiene was examined ϩ that the entire reaction of 1,3-C4H6 O leads to mo- by detailed kinetic modeling. A comprehensive mech- lecular species, we would have the rates of fuel dis- anism is proposed and shown to predict well a variety appearance and CO production seriously underpre- of combustion responses including the detailed species dicted. This is seen by the dashed lines in Figure 13, profiles during the oxidation of 1,3-butadiene in a flow which were obtained by assuming the production of reactor, the shock-tube ignition-delay time, and lami- short standard long JCK(Wiley) LEFT INTERACTIVE

612 LASKIN ET AL

Figure 23 First-order sensitivity coefﬁcients computed for the laminar ﬂame speed of 1,3-butadiene–air mixtures.

nar flame speed. The present study advances the un- The authors thank Mr. Joe Sivo and Mr. Delin Zhu for their derstanding of 1,3-butadiene oxidation by identifying generous help in the PTFR experiment, and Professors Irvin the multiplicity of major oxidative pathways. These Glassman and Fredrick Dryer for making the PTFR facility pathways are initiated by the reactions of 1,3-butadi- accessible to us. This work was supported by the Air Force ene with the Hи,Oи, and иOH radicals, featuring, re- Office of Scientific Research under the technical monitoring of Dr. Julian M. Tishkoff. The work at the University of spectively, the C ,C, and C intermediates, until they 2 3 4 Delaware was also partially supported by the NSF CAREER converge to small C1 and C2 intermediates. Unlike pre- program (CTS-9874768) under the technical monitoring of vious findings, we found that the path following the Dr. Farley Fisher. A part of the computation was performed chemically activated reaction of H and 1,3-butadiene at the Facility for Computational Chemistry at the University to produce ethylene and the vinyl radical is the most of Delaware, which is funded by NSF (CTS-9724404). important in the overall oxidation mechanism. The initiation of the radical-chain process was identified to involve the production of vinylidene, followed by the reaction of vinylidene with molecular oxygen. The un- BIBLIOGRAPHY certainty in the oxidation kinetics of 1,3-butadiene oxidation is discussed with specific emphasis on the re- 1. Davis, S. G.; Law, C. K.; Wang, H. Twenty-Seventh action between 1,3-butadiene and the O atom. In Symposium (International) on Combustion; The Com- particular, the branching ratio of the product channels bustion Institute: Pittsburgh, PA, 1998; pp 305–312. was found to be critical in order to achieve a better 2. Davis, S. G.; Law, C. K.; Wang, H. J Phys Chem A short description of 1,3-butadiene oxidation. 1999, 103, 5889. standard long JCK(Wiley) RIGHT INTERACTIVE

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