High-Temperature Measurements of the Reactions of OH with Small

Article pubs.acs.org/JPCA

High-Temperature Measurements of the Reactions of OH with Small Methyl Esters: Methyl Formate, Methyl Acetate, Methyl Propanoate, and Methyl Butanoate King-Yiu Lam,* David F. Davidson, and Ronald K. Hanson Department of Mechanical Engineering, Stanford University, Stanford, California 94305, United States ABSTRACT: The overall rate constants for the reactions of hydroxyl radicals (OH) with four small methyl esters, namely methyl formate (CH3OCHO), methyl acetate (CH3OC(O)CH3), methyl propanoate (CH3OC(O)C2H5), and methyl butanoate (CH3OC(O)C3H7), were investigated behind reflected shock waves using UV laser absorption of OH radicals near 306.69 nm. Test gas mixtures of individual methyl esters and tert-butyl hydroperoxide (TBHP), a fast source of OH at elevated temperatures, diluted in argon were shock-heated to temperatures spanning from 876 to 1371 K at pressures near 1.5 atm. The overall rate constants were determined by matching the measured OH time-histories with the computed profiles from the comprehensive chemical kinetic mechanisms of Dooley et al. (2010) and Dooley et al. (2008), which were originally developed for the oxidation of methyl formate and methyl butanoate, respectively. These measured values can be expressed in Arrhenius form as kCH3OCHO+OH = 2.56 × 1013 exp(−2026/T) cm3 mol−1 s−1, kCH3OC(O)CH3+OH = 3.59 × 1013 exp(−2438/T) cm3 mol−1 s−1, kCH3OC(O)C2H5+OH = 6.65 × 1013 exp(−2539/T) cm3 mol−1 s−1, and kCH3OC(O)C3H7+OH = 1.13 × 1014 exp(−2515/T) cm3 mol−1 s−1 over the temperature ranges studied. Detailed error analyses were performed to estimate the overall uncertainties of these reactions, and the estimated (2σ) uncertainties were found to be ±29% at 913 K and ±18% at 1289 K for kCH3OCHO+OH, ± 29% at 930 K and ±17% at 1299 K for kCH3OC(O)CH3+OH, ± 25% at 909 K and ±17% at 1341 K for kCH3OC(O)C2H5+OH, and ±24% at 925 K and ±16% at 1320 K for kCH3OC(O)C3H7+OH. We believe these are the first direct high-temperature rate constant measurements for the reactions of OH with these small methyl esters. These measured rate constants were also compared with the estimated values employed in different comprehensive kinetic mechanisms. Additionally, the structure−activity relationship from Kwok and Atkinson (1995) was used to estimate these four rate constants, and the estimations from this group-additivity model are in good agreement with the measurements (within ∼25%) at the present experimental conditions.

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the first comprehensive chemical kinetic mechanisms for the oxidation of methyl formate and methyl butanoate. However, the mechanisms were validated against only a limited set of low-temperature experimental data. Recently, Dooley et al.11 have compiled a detailed mechanism for methyl formate oxidation, and the mechanism has been validated against a wide variety of experimental data, including shock tube ignition delay times, speciation data from a variable-pressure flow reactor, and laminar burning velocities of outwardly propagating spherical flames. Similarly, Ren et al.12 conducted direct rate constant measurements of the initial dissociation pathways of methyl formate over 1202−1607 K at pressures near 1.6 atm using shock tube/laser absorption techniques, and their measurements are in close accord with the estimated values adopted in the Dooley et al. mechanism.11 Concurrently, Peukert et al.13,14 investigated the high-temperature thermal decomposition and

INTRODUCTION Biodiesel is a promising alternative fuel because it has physical properties similar to conventional crude-oil-derived fossil fuels, and it provides the opportunity to reduce overall emissions of atmospheric pollutants.1 Biodiesel is generally comprised of a mixture of extended alkyl chain methyl esters 16−18 carbon atoms long,2 that are typically derived from soybean oil in U.S. or rapeseed oil in Europe. Despite the complexity of these molecules, there has been a growing effort to develop comprehensive reaction mechanisms that can be used to describe the combustion of these large methyl esters.3−6 In these detailed mechanisms, the reaction rate constants for large methyl esters are primarily based on the kinetic parameters of smaller methyl esters (e.g., methyl formate and methyl butanoate).3,4,7−9 Thus, accurate knowledge of the kinetic parameters for smaller methyl esters is crucial to the development of the detailed mechanism for practical biodiesel fuels. The combustion chemistry of small methyl esters has been a subject of interest for the past decade. Fisher et al.10 developed © 2012 American Chemical Society

Received: October 16, 2012 Revised: November 28, 2012 Published: November 29, 2012 12229

dx.doi.org/10.1021/jp310256j | J. Phys. Chem. A 2012, 116, 12229−12241

The Journal of Physical Chemistry A

Article

ensure purity of the test mixtures. Test mixtures were prepared manometrically in a 40 L stainless-steel tank heated uniformly to 50 °C and mixed with a magnetically driven stirring vane. A double-dilution process was employed to allow for more accurate pressure measurements in the manometrical preparation of a highly dilute mixture. A more concentrated mixture was first prepared and mixed for at least 2 h to ensure homogeneity and consistency, and the mixture was then further diluted with argon and mixed for additional 2 h prior to the experiments. The gas utilized in this study was argon (Research grade) 99.999%, which was supplied by Praxair and used without further purification. The liquid chemicals were commercially available 70% tert-butyl hydroperoxide (TBHP) in water, methyl formate (≥99%), methyl acetate (≥99%), methyl propanoate (≥99%), and methyl butanoate (≥99%) from Sigma-Aldrich, and were purified using a freeze−pump− thaw procedure to remove dissolved volatiles and air prior to mixture preparation. The mixture composition was confirmed by sampling a portion of the mixture (from near the endwall) into an external multipass absorption cell with a path length of 29.9 m and monitoring the fuel concentration in the cell with a Jodon Helium−Neon laser at 3.39 μm. The details of the laser diagnostic setup are discussed elsewhere.22 Beer’s law was used to convert the measured absorption data into the fuel mole fraction. The absorption cross sections of methyl esters for Beer’s law were directly obtained from the PNNL database,23 and the measured fuel concentrations were consistent with the values expected from the manometrical preparation within ±5%. OH radical concentration was measured using the frequencydoubled output of a narrow-line width ring dye laser near 306.69 nm. The laser wavelength was tuned to the peak of the well-characterized R1(5) absorption line in the OH A−X (0, 0) band. Visible light near 613.4 nm was generated by pumping Rhodamine 6G dye in a Spectra Physics 380A laser cavity with the 5 W, cw output of a Coherent Verdi laser at 532 nm. The visible light was then intracavity frequency-doubled using an angle-tuned LBO nonlinear crystal to generate ∼1 mW of light near 306.69 nm. Using a common-mode-rejection detection scheme, a minimum absorbance of 0.1% could be detected, which resulted in a minimum detection sensitivity of ∼0.2 ppm at 1400 K and 1.5 atm. Further details of the OH laser diagnostic setup are discussed elsewhere.24,25 OH species concentration can be calculated from Beer’s law: I/Io = exp(−kOHXOHPL), where I and Io are the transmitted and incident laser intensities, kOH is the OH absorption coefficient, XOH is the OH mole fraction, P is the total pressure, and L is the path length (15.24 cm). The overall estimated uncertainty in the measured OH mole fraction (XOH) is approximately ±3%, mainly due to the uncertainty in temperature (±0.7%). Measurements were also conducted with the laser tuned away from the absorption line to verify that there was no significant interference absorption. Lack of emission in the measurement channel was also verified. All data were recorded at 2 MHz using a high-resolution (14 bit) data acquisition system.

the H atom abstraction reactions by H atoms for methyl formate and methyl acetate over 1194−1371 K at pressures around 0.5 atm using shock tube/atomic resonance absorption spectrometry technique. In addition, Westbrook et al.15 developed a detailed mechanism for a group of four small alkyl esters, including methyl formate, methyl acetate, ethyl formate, and ethyl acetate. The mechanism was validated against the speciation data from fuel-rich, low-pressure, premixed laminar flames. Similarly, Dooley et al.16 and Hakka et al.17 developed two separate detailed mechanisms for methyl butanoate oxidation, and the mechanisms were tested against different sets of experimental data, including shock tube and rapid compression machine ignition delay times and speciation data from a flow reactor, a jet-stirred reactor, and an opposedflow diffusion flame. Moreover, numerous experimental studies18−21 for methyl butanoate pyrolysis and oxidation were performed in order to improve the global performance of the existing detailed mechanisms. However, among most of these studies, little attention has been given to a better understanding of the elementary kinetics of these methyl esters. In particular, the H atom abstraction reactions by OH radicals for methyl esters, which are one of the major fuel consumption pathways during oxidation, are not well understood at combustion-relevant conditions. In the present study, the overall rate constants for the reactions of OH with four small methyl esters, namely methyl formate (CH3OCHO), methyl acetate (CH3OC(O)CH3), methyl propanoate (CH3OC(O)C2H5), and methyl butanoate (CH3OC(O)C3H7), were determined behind reflected shock waves over the temperature range of 876−1371 K at pressures near 1.5 atm: CH3OCHO + OH → products

(1)

CH3OC(O)CH3 + OH → products

(2)

CH3OC(O)C2H5 + OH → products

(3)

CH3OC(O)C3H 7 + OH → products

(4)

We believe these are the first direct high-temperature measurements of the overall rate constants for reactions 1−4. These high-temperature kinetic data were compared with the values adopted in several detailed kinetic mechanisms and the estimates using a group-additivity model.

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EXPERIMENTAL SETUP Experiments were performed in a stainless-steel, high-purity, low-pressure shock tube at Stanford. The shock tube is comprised of a 3.7-m driver section and a 10-m driven section, with an inner diameter of 15.24 cm. Reflected shock temperatures and pressures were determined from the incident shock speed at the endwall using standard normal shock relations, with uncertainties of approximately ±0.7% and ±1%, respectively, mainly due to the uncertainty in the measured shock velocity (±0.2%). The endwall incident shock speed was measured using a series of five piezoelectric pressure transducers over the last 1.5 m of the shock tube and linearly extrapolated to the endwall. The OH laser diagnostic, along with a Kistler piezoelectric pressure transducer for pressure measurements, was located at a test section 2 cm from the driven section endwall. Between experiments, the shock tube and mixing assembly were routinely turbomolecular pumped down to ∼6 μtorr to

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KINETIC MEASUREMENTS A total of 52 reflected shock wave experiments were performed to determine the overall rate constants for the reactions of OH with four methyl esters (methyl formate, methyl acetate, methyl propanoate, and methyl butanoate) over 876−1371 K at pressures near 1.5 atm. Experiments were carried out using 12230



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Table 1. Reactions Describing Methyl Ester + OH Experiments at P = 1.5 atm rate constant [cm3 mol‑1 s‑1] reaction CH3OCHO + OH → products CH3OC(O)CH3 + OH → products CH3OC(O)C2H5 + OH → products CH3OC(O)C3H7 + OH → products TBHP → (CH3)3CO + OH (CH3)3CO → CH3COCH3 + CH3 TBHP + OH → H2O + O2 + tert-C4H9 TBHP + OH → H2O + HO2 + iso-C4H8 CH3 + OH → CH2(s) + H2O C2H6 (+ M) → CH3 + CH3 (+ M) low-pressure limit Troe centering: 0.39 CH2O + OH → HCO + H2O CH3OH + M → CH3 + OH + M CH3COCH3 + OH → CH3COCH2 + H2O

A

b

number

reference

1 2 3 4 5 6 7 8 9 10

this work this work this work this work 28 29 28 28 28 34

11 12 13

36 31 24

see see see see 3.57 1.26 2.30 2.49 1.65 1.88 3.72 100 7.82 5.62 3.30

× × × × × × ×

text text text text 0 0 0 0 0 −9.72 −13.14 1900 1.63 0 0

E [cal/mol]

1013 1014 1013 1013 1013 1050 1065

× 1007 × 1015 × 1013

3.575 1.530 5.223 2.655 0 1.073 1.015 6000 −1.055 6.128 4.840

× × × ×

1004 1004 1003 1003

× 1005 × 1005 × 1003 × 1004 × 1003

TBHP reacts with the OH radicals to form other products, and the TBHP chemistry set can be described as follows:

different initial fuel concentrations: methyl formate (322 ppm, 404 ppm), methyl acetate (323 ppm, 384 ppm), methyl propanoate (∼281 ppm), and methyl butanoate (241 ppm, 270 ppm). Test mixtures with individual methyl esters and 80−102 ppm TBHP (and water) diluted in argon were utilized in the present study. Note that dilute mixtures were preferred in order to minimize the temperature change resulted from the chemistry effects, and the temperature profile behind the reflected shock wave (from the present study) was nearly constant (less than 1 K change based on the calculation from CHEMKIN PRO26) over the time frame of the experiment (the first 100 μs). The CHEMKIN PRO package26 was used to simulate the OH time-histories under the standard constant energy and volume assumption. A comprehensive chemical kinetic mechanism of Dooley et al.11 was chosen as the base mechanism for methyl formate and methyl acetate. This mechanism can successfully simulate shock tube ignition delay times, laminar burning velocities of outwardly propagating spherical flames, and speciation data from a shock tube and a variable-pressure flow reactor11,12 during methyl formate pyrolysis and oxidation. Additionally, this kinetic mechanism incorporates the submechanism for methyl acetate, which was previously developed by Westbrook et al.15 The submechanism for methyl acetate consists of the unimolecular decomposition pathways and the H atom abstraction reactions by H, OH, and CH3 radicals, and was validated against speciation data from fuel-rich, low-pressure, premixed laminar flames. A detailed kinetic mechanism of Dooley et al.16 was also selected as the base mechanism for methyl propanoate and methyl butanoate. This mechanism was originally developed to predict the autoignition of methyl butanoate in a shock tube and a rapid compression machine over a wide range of experimental conditions, and was further validated against speciation data available in the literature from a flow reactor, a jet-stirred reactor, and an opposed-flow diffusion flame. Tert-butyl hydroperoxide (TBHP or (CH3)3−CO−OH) was used as an OH radical precursor at the present experimental conditions. It dissociates near-instantaneously to form an OH radical and a tert-butoxy radical, (CH3)3CO, at temperatures greater than 1000 K.27 The tert-butoxy radical further dissociates to form acetone and a methyl radical. Concurrently,

(CH3)3 −CO−OH → (CH3)3 CO + OH

(5)

(CH3)3 CO → CH3COCH3 + CH3

(6)

(CH3)3 −CO−OH + OH → H 2O + O2 + tert‐C4 H 9 (7)

(CH3)3 −CO−OH + OH → H 2O + HO2 + iso‐C4 H8 (8)

In the present analysis, the above TBHP chemistry set was also implemented into the base mechanisms, and the rate constants for reactions 5−8 are provided in Table 1. The rate constants for reactions 5, 7, and 8 were adopted from Pang et al.,28 and the rate constant for reaction 6 was obtained from Choo and Benson.29 In addition, the thermodynamic parameters for TBHP and tert-butoxy radical were taken from the thermodynamic database from Goos et al.,30 and the standard enthalpy of formation for OH radical was updated with the measured value from Herbon et al.25 Methyl Formate (MF) + OH Kinetics. The reaction of OH with methyl formate consists of 2 different channels: CH3OCHO + OH → CH3OCO + H 2O

(1a)

CH3OCHO + OH → CH 2OCHO + H 2O

(1b)

The branching ratios of channels 1a and 1b are 0.32 and 0.68, respectively, at 1168 K, based on the Dooley et al. mechanism.11 In their analysis, the estimated rate constant for channel 1a was assumed to be an intermediate value between typical primary and secondary C−H bonds (as in propane) due to the weaker bond strength of the CH3OCO−H position (100.1 kcal/mol at 298 K). Similarly, the estimated rate constant for channel 1b (per H atom) was assumed to be 5% faster than the value for a typical primary C−H bond, and the corresponding bond strength was estimated to be 100.9 kcal/ mol at 298 K. An OH radical sensitivity analysis for the mixture of 322 ppm methyl formate with 26 ppm TBHP (and 70 ppm H2O) in Ar at 1168 K and 1.40 atm is shown in Figure 1. The OH sensitivity is calculated as SOH = (∂XOH/∂ki) × (ki/XOH), where XOH is the local OH mole fraction and ki is the rate constant for 12231



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Figure 2. Sample methyl formate + OH rate constant measurement using the mixture of 322 ppm methyl formate with ∼26 ppm TBHP (and 70 ppm water) in Ar at 1168 K and 1.40 atm. Simulation from the Dooley et al. mechanism11 for the best-fit rate constant, along with perturbations of ±50%, is also shown.

Figure 1. OH sensitivity plot for the rate constant measurement of methyl formate + OH at 1168 K and 1.40 atm.

reaction i. More importantly, the analysis reveals that the reaction of OH with methyl formate (reaction 1) is the dominant reaction over the time frame of the experiment, with some minor interference from the secondary reactions: CH3 + OH → CH 2(s) + H 2O

expected to be less than the maximum value and was assumed to be the same as the measured peak OH mole fraction due to the fact that the OH radical was formed almost nearinstantaneously after the thermal decomposition of TBHP behind the reflected shock wave at T > 1000 K. According to the measured peak OH yields, the mixtures with 96 ppm TBHP/water are comprised of ∼25−28 ppm TBHP in the present study. It should also be noted that the presence of H2O in the test mixture does not have any significant influence on the computed OH profiles. As shown in Figure 2, a best-fit overall rate constant for reaction 1 of 4.26 × 1012 cm3 mol−1 s−1 was obtained between the experimental data and the simulation at 1168 K and 1.40 atm. The simulations for the perturbations of ±50% in the inferred rate constant are also shown in Figure 2. Additionally, the effect of the branching ratios for reaction 1 on the overall rate constant determination was tested at 1168 K by interchanging the branching ratios of channels 1a and 1b while maintaining the overall value, and no discernible effect could be observed from the simulated OH profiles. Hence, the original branching ratios proposed by Dooley et al.11 were kept in our simulations. In addition, Table 2 summarizes the overall rate constant measurements (k1 = k1a + k1b) of reaction 1 at T = 880−1344 K and P = 1.24−1.63 atm. A detailed error analysis was conducted to estimate the overall uncertainty of the measured rate constant for reaction 1 at 1168 K. The primary contributions to the overall uncertainty in the measured rate constant were considered: (a) temperature (±1%), (b) mixture composition (±5%), (c) OH absorption coefficient (±3%), (d) wavemeter reading in the UV (±0.01 cm−1), (e) fitting the data to the simulated profiles (±5%), (f) locating time-zero (±0.5 μs), (g) the rate constant for CH3 + OH → CH2(s) + H2O (uncert. factor =2), (h) the rate constant for CH2O + OH → HCO + H2O (uncertainty factor =2), and (i) the rate constant for C2H6 (+ M) → CH3 + CH3 (+ M) (uncertainty factor =2). As demonstrated in Figure 3, the individual error sources were introduced separately (within the positive and negative bounds of their 2σ uncertainties) and their effects on the overall rate constant for reaction 1 were studied. These uncertainties were combined in a root-sumsquared method to give an overall (2σ) uncertainty of ±24% at 1168 K. Similar error analyses were performed for k1 at 913 and

(9)

C2H6( +M) → CH3 + CH3( +M)

(10)

CH 2O + OH → HCO + H 2O

(11)

The rate constant for reaction 9 was updated with the value of 1.65 × 1013 cm3 mol−1 s−1 measured by Pang et al.28 This measured value is in good agreement with the measurements from Srinivasan et al.31 and Vasudevan et al.32 and the calculated values from Jasper et al.33 (within ±35%). The rate constant for reaction 10 was updated with the measured values from Oehlschlaeger et al.,34 and the measurements from Oehlschlaeger et al. are in close accord with another experimental study from Kiefer et al.35 The rate constant for reaction 11 was also measured directly using UV laser absorption of OH near 307 nm behind reflected shock waves over 934−1670 K at pressures near 1.6 atm by Vasudevan et al.,36 and their measured rate constant was adopted in the present study. Additionally, the rate constant for CH3OH + M → CH3 + OH + M

(12)

reaction 12) was updated with the measurements from Srinivasan et al.31 at ∼0.3−1.1 atm, and their values agree well with the calculated values from Jasper et al.33 and the measured values from Vasudevan et al.32 at 1.3 atm. Meanwhile, the rate constant for CH3COCH3 + OH → CH3COCH 2 + H 2O

(13)

reaction 13 was updated with the recent direct rate constant measurements from Lam et al.24 The rate constants for reactions 9−13 are also provided in Table 1. Figure 2 illustrates a sample measured OH concentration time-history for the mixture of 322 ppm methyl formate in Ar at 1168 K and 1.40 atm, and the measured peak OH concentration is approximately 26 ppm. Raoult’s law suggests that a 70%, by weight, solution of TBHP in water in the liquid phase corresponds to 69% water and 31% TBHP in the vapor phase initially.36 Hence, a 96 ppm TBHP/water mixture should have 29.8 ppm TBHP. Because of wall adsorption and condensation of TBHP, the initial TBHP mole fraction is 12232



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Table 2. CH3OCHO + OH → Products: Rate Constant Data T5 [K]

P5 [atm]

k1 [cm3 mol−1 s−1]

96 ppm TBHP (and water), 322 ppm CH3OCHO, Ar 1337 1.36 5.87 × 1012 1315 1.25 5.60 × 1012 1264 1.28 4.98 × 1012 1229 1.37 4.81 × 1012 1168 1.40 4.26 × 1012 1114 1.39 3.99 × 1012 1024 1.51 3.50 × 1012 965 1.55 3.10 × 1012 913 1.63 2.81 × 1012 904 1.55 2.91 × 1012 101 ppm TBHP (and water), 404 ppm CH3OCHO, Ar 1344 1.27 5.85 × 1012 1289 1.24 5.62 × 1012 1124 1.37 4.04 × 1012 1060 1.44 3.66 × 1012 880 1.62 2.57 × 1012

Figure 4. Arrhenius plot for methyl formate + OH (k1) at temperatures above 833 K.

Recently, Tan et al.37 performed a systematic ab initio quantum mechanical investigation of the H atom abstraction reactions for methyl formate by five radicals: H, CH3, O, HO2, and OH. They employed a multireference correlated wave function method (the CBS-MRSDCI composite scheme) including size-extensivity corrections to calculate the barrier heights and reaction enthalpies of these H atom abstraction reactions. The rate constants for these H atom abstraction reactions were computed using transition state theory within the separable-hindered-rotor approximation for torsions and the harmonic oscillator approximation for other vibrational modes.37 As illustrated in Figure 4, the calculated overall rate constant for reaction 1 from Tan et al.37 is substantially lower than the present measurements and the estimated values from Fisher et al.10 and Dooley et al.11 (by a factor of 2.2 at 1250 K and a factor of 4.8 at 850 K). To investigate this large discrepancy between the present measurements and the theoretical calculation, the rate constants for the reactions of H, CH3, O, and HO2 with methyl formate in the Dooley et al. mechanism11 were first updated with the expressions provided by Tan et al.37 The overall rate constant for reaction 1 was then reexamined by matching the measured OH time-histories with the simulated profiles from the detailed mechanism, and the same measured rate constant expression (as the one provided previously) was obtained. This indicates that our rate constant measurements are insensitive to the H atom abstraction reactions for methyl formate by other species (i.e., H, CH3, O, and HO2), and also that the theoretical calculations for these H atom abstraction reactions may require further review. Methyl Acetate (MA) + OH Kinetics. The reaction of OH with methyl acetate consists of two different channels:

Figure 3. Uncertainty analysis for the rate constant of methyl formate + OH → products at 1168 K and 1.40 atm.

1289 K, and the overall uncertainties were estimated to be ±29% and ±18%, respectively. Figure 4 presents the Arrhenius plot for the overall rate constant measurements of reaction 1 at T = 880−1344 K, along with the estimated values proposed by Fisher et al.10 and Dooley et al.11 Note that two different mixture compositions (322 and 404 ppm methyl formate) were used to confirm that the current measurements are weakly dependent on the secondary chemistry effects from the model, and the measured values from these two mixtures are consistent with each other. The measured values can be expressed in Arrhenius form as k1 = 2.56 × 1013 exp(−2026/T) cm3 mol−1 s−1 over 880−1344 K. As is evident in Figure 4, the present measurements are in good agreement with the estimated values from Fisher et al. and Dooley et al. within 10%, and the activation energy from the present measurements seems to be slightly higher. Interestingly, the estimated values from Fisher et al. and Dooley et al. are nearly identical over 833−1150 K and start to deviate at higher temperatures (T > 1150 K). It also appears that the estimated overall rate constant from Fisher et al. is in better agreement with the present measurements at T > 1150 K.

CH3OC(O)CH3 + OH → CH3OC(O)CH 2 + H 2O (2a)

CH3OC(O)CH3 + OH → CH 2OC(O)CH3 + H 2O (2b)

The branching ratios of channels 2a and 2b are 0.14 and 0.86, respectively, at 1091 K, based on the estimated values from the Dooley et al. mechanism.11 Note that the submechanism for methyl acetate adopted in the Dooley et al. mechanism was previously developed by Westbrook et al.15 In the development of the methyl acetate submechanism from Westbrook et al., the rate constant for channel 2b (the H atom abstraction from the 12233



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methyl group bound to the O atom in the ester group) was taken directly from that of the structurally similar methyl group in methyl butanoate (developed by Fisher et al.10). In addition, the bond strength of the C−H bond adjacent to the carbonyl group is 97.7 kcal/mol (at 298 K), which is similar to that of a tertiary C−H bond in methylcyclohexane. Thus, the rate constant for channel 2a (per H atom) was first assumed to be the same as the rate constant for the tertiary C−H bond in methylcyclohexane. Channel 2a produces the CH3OC(O)CH2 radical, followed by the formation of ketene (CH2CO) and methoxy radical (CH3O) via β-scission. Concurrently, the methoxy radical can react with CH3 to form dimethyl ether. When compared with their flame measurements,15 the model predicted excessively high levels of ketene and dimethyl ether, which suggested the need to reduce the rate constant for channel 2a. Consequently, the rate constant for channel 2a was reduced by a factor of 10 to match their experimental data. The OH sensitivity analysis was performed for the overall rate constant determination (k2 = k2a + k2b) of reaction 2 using the mixture of 384 ppm methyl acetate with 28.5 ppm TBHP (and 73.5 ppm water) diluted in argon at 1091 K and 1.37 atm. As illustrated in Figure 5, the analysis shows that reaction 2 is

Figure 6. Sample methyl acetate + OH rate constant measurement using the mixture of 384 ppm methyl acetate with ∼28.5 ppm TBHP (and 73.5 ppm water) in Ar at 1091 K and 1.37 atm. Simulation from the Dooley et al. mechanism11 for the best-fit rate constant, along with perturbations of ±50%, is also shown.

Table 3. CH3OC(O)CH3 + OH → Products: Rate Constant Data T5 [K]

P5 [atm]

k2 [cm3 mol−1 s−1]

Figure 5. OH sensitivity plot for the rate constant measurement of methyl acetate + OH at 1091 K and 1.37 atm.

100 ppm TBHP (and water), 323 ppm CH3OC(O)CH3, Ar 1371 1.25 5.88 × 1012 1258 1.29 5.09 × 1012 1160 1.36 4.33 × 1012 1078 1.44 3.74 × 1012 1028 1.50 3.41 × 1012 102 ppm TBHP (and water), 384 ppm CH3OC(O)CH3, Ar 1299 1.27 5.39 × 1012 1215 1.34 4.91 × 1012 1126 1.36 4.40 × 1012 1091 1.37 3.93 × 1012 1017 1.43 3.29 × 1012 961 1.54 2.82 × 1012 930 1.58 2.63 × 1012 907 1.59 2.38 × 1012 876 1.60 2.18 × 1012

the dominant reaction over the time frame of the experiment, with some minor interference from reactions 5 and 9−11. Note that the TBHP decomposition reaction (reaction 5) becomes more important at the early times as temperature decreases. Figure 6 shows a sample OH time-history measurement for the mixture of 384 ppm methyl acetate in argon at 1091 K and 1.37 atm, and the measured peak OH mole fraction is ∼28.5 ppm. Thus, we inferred that the initial TBHP mole fraction was around 28.5 ppm, and there was approximately 73.5 ppm H2O. As illustrated in Figure 6, a best-fit overall rate constant for reaction 2 of 3.93 × 1012 cm3 mol−1 s−1 was obtained between the experiment and the simulation using the Dooley et al. mechanism.11 In addition, the simulations with the variations of ±50% in the inferred rate constant are shown in Figure 6. The same test (as the test for methyl formate) was performed at 1091 K to confirm that the branching ratios have negligible influence on the overall rate constant determination of reaction 2. Thus, the original branching ratios from Westbrook et al.15 were maintained in our simulations. Table 3 summarizes the present overall rate constant measurements of reaction 2 at T = 876−1371 K and P = 1.25−1.60 atm.

Figure 7 presents the Arrhenius plot for the current overall rate constant measurements of reaction 2 over the temperature range of 876−1371 K, along with the estimated values proposed by Westbrook et al.15 Note that the measured values from two different mixture compositions (323 and 384 ppm methyl acetate) were compared and were found to be consistent with each other. These measured values can be expressed in Arrhenius form as k2 = 3.59 × 1013 exp(−2438/T) cm3 mol−1 s−1 over 876−1371 K. Detailed error analyses were carried out with the consideration of experimental and mechanism-induced contributions, and the overall (2σ) uncertainties in k2 were estimated to be ±29% at 930 K, ± 23% at 1091 K, and ±17% at 1299 K. As illustrated in Figure 7, the activation energy of reaction 2 inferred from the present measurements is higher than that of Westbrook et al.15 The estimated value from Westbrook et al. is approximately 30% lower than the current data at 1371 K, while the estimated values are in good agreement with the current data (within 8%) over a limited temperature range of 876−960 K. Moreover, theoretical studies of the reactions of OH with ethers (dimethyl, ethylmethyl, and isopropylmethyl ethers) and 12234



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stable products through β-scission. For instance, channel 3a forms a CH3OC(O)CH2CH2 radical and a H2O molecule, and the CH3OC(O)CH2CH2 radical is rather short-lived and will further decompose to form C2H4 and CH3OCO through βscission. Similar treatments were applied to channels 3b and 3c. Because of the structure similarity between methyl propanoate and ethyl propanoate, the rate constants for channels 3a and 3b were first assumed to be the same as the rate constants for the reactions of OH with ethyl propanoate at the β and α sites, respectively, which were taken from the Metcalfe et al. mechanism of NUI Galway.40 In addition, the rate constant for channel 3c was first assumed to be the same as the rate constant for the reaction of OH with methyl butanoate at the methyl group bound to the O atom in the ester group, which was taken directly from the Dooley et al. mechanism.16 The resulting branching ratios of channels 3a-3c at 1208 K are 0.20, 0.31, and 0.49, respectively. These 3 channels, along with their corresponding rate constants, were then incorporated into the Dooley et al. mechanism.16 The reaction of H atom with methyl propanoate was also considered in the present study. Similar to the reaction of OH with methyl propanoate, it consists of three different channels:

Figure 7. Arrhenius plot for methyl acetate + OH (k2) at temperatures above 833 K.

ketones (dimethyl, ethylmethyl, and isopropylmethyl ketones) were performed by Zhou et al.38,39 using the computationally less-expensive methods of G3 and G3MP2BH&H to calculate the energy barriers and using the Variflex code including Eckart tunneling corrections to compute the total rate constants over 500−2000 K. They also provided the expressions of the group rate constants (per H atom) for three different carbon sites (primary, secondary, and tertiary carbon atoms) adjacent to the ether group (−O−) and the carbonyl group (−C(O)−). In the present analysis, we can estimate the overall rate constant for reaction 2 using the group rate constants provided by Zhou et al.,38,39 and the estimated overall rate constant is k2 = 3 × k(CH 3O) + 3 × k(CH3 C(O)), where k(CH3O) and k(CH3C(O)) are the group rate constants (per H atom) for primary carbon sites adjacent to the ether group and the carbonyl group, respectively. As illustrated in Figure 7, the estimated values are at least 60% higher than the present measurements, but the estimation seems to capture the temperature dependence of reaction 2 reasonably well. Methyl Propanoate (MP) + OH Kinetics. The reaction of OH with methyl propanoate is comprised of three different channels:

CH3OC(O)C2H5 + H → C2H4 + CH3OCO + H 2 (14a)

CH3OC(O)C2H5 + H → CH3CHCO + CH3O + H 2 (14b)

CH3OC(O)C2H5 + H → C2H5CO + CH 2O + H 2 (14c)

Channel 14a describes the H atom abstraction at the β position, and channel 14b describes the H atom abstraction at the α position. In addition, channel 14c describes the H atom abstraction at the methyl group bound to the O atom in the ester group. Similarly, the rate constants for channels 14a and 14b were assumed to be the same as the rate constants for the reactions of H with ethyl propanoate at the β and α sites, respectively, which were also taken from Metcalfe et al.40 Additionally, the rate constant for channel 14c was assumed to be the same as the rate constant for the reaction of H with methyl butanoate at the methyl group bound to the O atom in the ester group, which was also taken from Dooley et al.16 It is important to note that the simulated OH profiles of the present study are effectively insensitive to channels 14a-14c; hence, the computed OH profiles are nearly identical with and without the addition of these 3 channels. This conclusion is expected as there are very few H atoms available in the initial test mixtures. Nevertheless, channels 14a−14c were included in the Dooley et al. mechanism16 for completeness. The OH sensitivity analysis was performed for the overall rate constant determination (k3 = k3a + k3b + k3c) of reaction 3 using the mixture of 281 ppm methyl propanoate with 22 ppm TBHP (and 68 ppm H2O) in Ar at 1208 K and 1.33 atm. As demonstrated in Figure 8, the analysis reveals that the OH time-history is predominantly sensitive to reaction 3 over the time frame of the experiment. There is also some minor interference from the secondary reactions (reactions 9, 11, and (12)). Figure 9 shows a representative OH time-history measurement for the mixture of 281 ppm methyl propanoate in Ar at 1208 K and 1.33 atm, and the measured peak OH mole fraction is ∼22 ppm. Thus, this inferred that the initial TBHP mole fraction was approximately 22 ppm and the initial water mole

CH3OC(O)C2H5 + OH → C2H4 + CH3OCO + H 2O (3a)

CH3OC(O)C2H5 + OH → CH3CHCO + CH3O + H 2O (3b)

CH3OC(O)C2H5 + OH → C2H5CO + CH 2O + H 2O (3c)

Channel 3a is the H atom abstraction reaction from methyl propanoate at the β position (on the same side of the carbonyl group), and channel 3b is the H atom abstraction reaction from methyl propanoate at the α position. In addition, channel 3c is the H atom abstraction reaction from methyl propanoate at the methyl group bound to the O atom in the ester group. Note that the Dooley et al. mechanism of NUI Galway,16 which was originally developed for methyl butanoate oxidation, was used to model the OH consumption from methyl propanoate. Unfortunately, the mechanism does not contain a submechanism for methyl propanoate. In the present analysis, we assumed that the fuel radicals formed right after the H atom abstraction reactions would decompose immediately into the (relatively) 12235



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reaction 3 over the temperature range of 909−1341 K at pressures of 1.23−1.58 atm. Table 4. CH3OC(O)C2H5 + OH → Products: Rate Constant Data T5 [K]

P5 [atm]

k3 [cm3 mol−1 s−1]

90 ppm TBHP (and water), 281 ppm CH3OC(O)C2H5, Ar 1341 1.26 1.01 × 1013 1208 1.33 8.01 × 1012 1124 1.39 6.70 × 1012 1049 1.36 5.81 × 1012 954 1.58 4.76 × 1012 91 ppm TBHP (and water), 283 ppm CH3OC(O)C2H5, Ar 1289 1.26 9.58 × 1012 1252 1.27 8.67 × 1012 1200 1.23 8.08 × 1012 1181 1.30 7.79 × 1012 1016 1.44 5.37 × 1012 909 1.52 4.11 × 1012

Figure 8. OH sensitivity plot for the rate constant measurement of methyl propanoate + OH at 1208 K and 1.33 atm.

Figure 10 presents the Arrhenius plot for the present overall rate constant measurements of reaction 3 over the temperature

Figure 9. Sample methyl propanoate + OH rate constant measurement using the mixture of 281 ppm methyl propanoate with ∼22 ppm TBHP (and 68 ppm water) in Ar at 1208 K and 1.33 atm. Simulation from the Dooley et al. mechanism16 for the best-fit rate constant, along with variations of ±50%, is also shown. Figure 10. Arrhenius plot for methyl propanoate + OH (k3) at temperatures above 870 K.

fraction was around 68 ppm. As is evident in Figure 9, a best-fit overall rate constant for reaction 3 of 8.01 × 1012 cm3 mol−1 s−1 was used to match the experimental data with the computed profile, and the simulations for the variations of ±50% in the inferred rate constant are also shown. Concurrently, the effect of the branching ratios on k3 was found to be negligible at 1208 K (by interchanging the branching ratios of channels 3b and 3c while maintaining the total value). Thus, the original branching ratios based on the structure similarity were kept in our simulations. Moreover, Diévart et al.8 have recently developed a methyl propanoate submechanism, which includes the unimolecular decomposition reactions and the H atom abstraction reactions for methyl propanoate. This submechanism was also implemented into the Dooley et al. mechanism,16 and the thermodynamic parameters for the fuel radicals from methyl propanoate (provided by Diévart et al.) were also added to the thermo database of Dooley et al. Interestingly, nearidentical results were found with and without the use of the detailed submechanism for methyl propanoate. Hence, the present measurements are insensitive to the secondary chemistry effects strictly from methyl propanoate. In addition, Table 4 summarizes the overall rate constant measurements of

range of 909−1341 K, along with the estimated values used by Diévart et al.8 The measured values can be expressed in Arrhenius form as k3 = 6.65 × 1013 exp(−2539/T) cm3 mol−1 s−1 over 909−1341 K. Detailed error analyses were conducted with the consideration of experimental and mechanism-induced contributions, and the overall (2σ) uncertainties in k3 were estimated to be ±25% at 909 K, ± 21% at 1208 K, and ±17% at 1341 K. It is also interesting to note that the estimated rate constants for channels 3a−3c provided by Diévart et al. are exactly identical to our initial approximations for these three rate constants. Thus, Diévart et al. employed the same type of approximation to estimate the rate constants for the H atom abstraction reactions based on the structure similarity between methyl propanoate and ethyl propanoate. However, the estimated value is ∼53% higher than the measured value at 1341 K, and is higher than the data by at least a factor of 2 at 909 K. Additionally, the activation energy of reaction 3 inferred from the present measurements is higher than that of the estimation from Diévart et al. This demonstrates the importance of direct rate constant measurements in validating 12236



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Figure 12 shows the OH sensitivity analysis for the mixture of 241 ppm methyl butanoate with 20 ppm TBHP (and 60

the current estimation methods in the literature. Moreover, Figure 10 presents the estimated overall rate constant for reaction 3 using the group rate constants for the reactions of OH with ethers and ketones provided by Zhou et al.38,39 Interestingly, the estimated values are at least 65% higher than the current data, but the estimation appears to capture the temperature dependence of reaction 3 reasonably well. Methyl Butanoate (MB) + OH Kinetics. The reaction of OH with methyl butanoate consists of 4 different channels, which are: CH3OC(O)C3H 7 + OH → CH3OC(O)CH 2CH 2CH 2 + H 2O

(4a)

CH3OC(O)C3H 7 + OH → CH3OC(O)CH 2CHCH3 + H 2O

(4b)

CH3OC(O)C3H 7 + OH → CH3OC(O)CHCH 2CH3 + H 2O

Figure 12. OH sensitivity plot for the rate constant measurement of methyl butanoate + OH at 1133 K and 1.37 atm.

(4c)

CH3OC(O)C3H 7 + OH → CH 2OC(O)C3H 7 + H 2O

ppm H2O) in argon at 1133 K and 1.37 atm. Similarly, the analysis reveals that reaction 4 is the dominant reaction pathway over the time frame of the experiment, with some minor interference from the secondary reactions (reactions 9, 10, and 12). Figure 13 shows a sample OH time-history measurement for the mixture of 241 ppm methyl butanoate in Ar at 1133 K and

(4d)

Channels 4a−4c describe the H atom abstraction from methyl butanoate at the γ, β, and α positions, respectively. In addition, channel 4d describes the H atom abstraction from methyl butanoate at the methyl group bound to the O atom in the ester group. On the basis of the Dooley et al. mechanism,16 the resulting branching ratios of channels 4a−4d are 0.15, 0.24, 0.25, and 0.36, respectively, at 1133 K. In their analysis, the rate constants for channels 4a−4d were estimated based on the nature of the C−H bonds (primary, secondary, or tertiary carbon atoms), and were strictly based on a study of methylcyclohexane (MCH) oxidation from Orme et al.41 The rate constant for channel 4a was assumed to be the same as the rate constant for the reaction of MCH + OH → CYCHEXCH2 + H2O, and the rate constant for channel 4b was assumed to be the same as the rate constant for the reaction of MCH + OH → MCH−R4 + H2O. The chemical notations for the fuel radicals formed from the reactions of OH with MCH are taken directly from Orme et al.,41 as illustrated in Figure 11. In addition, due

Figure 13. Sample methyl butanoate + OH rate constant measurement using the mixture of 241 ppm methyl butanoate with ∼20 ppm TBHP (and 60 ppm water) in Ar at 1133 K and 1.37 atm. Simulation from the Dooley et al. mechanism16 for the best-fit rate constant, along with variations of ±50%, is also shown. Figure 11. Chemical notations for fuel radicals from MCH + OH reactions used by Orme et al.41

1.37 atm, and the measured peak OH mole fraction is ∼20 ppm. On the basis of the measured peak OH yield, the initial TBHP mole fraction was ∼20 ppm and the initial H2O mole fraction was around 60 ppm. As illustrated in Figure 13, a bestfit overall rate constant (k4 = k4a + k4b + k4c + k4d) of 1.17 × 1013 cm3 mol−1 s−1 was used to match the experimental data with the simulated profile from the Dooley et al. mechanism.16 Additionally, the simulations for the variations of ±50% in the inferred rate constant are also shown. Similar to the previous methyl esters, the branching ratios of reaction 4 have negligible influence on the overall rate constant determination at the present experimental conditions. This was also confirmed by

to the weaker C−H bond enthalpy, the carbon atom attached to the carbonyl group (at the α position) was treated as a tertiary carbon atom, and the corresponding rate constant for channel 4c (per H atom) was taken from the rate constant for the reaction of MCH + OH → MCH−R1 + H2O. Similarly, the carbon atom at the methyl group bound to the O atom in the ester group was treated as a secondary carbon atom, and the corresponding rate constant for channel 4d (per H atom) was taken from the rate constant for the reaction of MCH + OH → MCH−R4 + H2O (per H atom). 12237



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and Hakka et al.17 by approximately 40% and 83%, respectively, at 1133 K. Interestingly, the temperature dependence of these rate constants seems to be consistent with each other. Table 6 shows a comparison of the rate constants for channels 4a−4d employed in these three mechanisms at 1133 and 1300 K. The rate constants for channels 4a−4c proposed by Fisher et al. and Dooley et al. are nearly identical, but the rate constant for channel 4d from Fisher et al. is lower than that of Dooley et al. by a factor of 2.48 at 1133 K. Fisher et al. treated the rate constant for channel 4d the same as the rate constant for channel 4a. On the other hand, Dooley et al. proposed that channel 4d should be more reactive than channel 4a due to the weaker C−H bond enthalpy at the methyl group bound to the O atom. Interestingly, the rate constants for channels 4a−4d proposed by Hakka et al. are consistently higher than those of Fisher et al. As illustrated in Figure 14, the present measurements display somewhat higher activation energy than the previous estimations. Of all three estimations, the values from Fisher et al. seem to be in closer agreement with the present measurements. The measured rate constant is ∼17% higher than the value from Fisher et al. at 1355 K, and is ∼35% lower at 897 K. Furthermore, Figure 14 presents the estimated overall rate constant for reaction 4 using the group rate constants for the reactions of OH with ethers and ketones developed by Zhou et al.,38,39 as was done for reactions 2 and 3. The estimated values are at least 27% higher than the current data, but it appears that the estimation captures the temperature dependence of reaction 4 very well. Comparison with Low Temperature Data. Figure 15 presents the current high-temperature data for the reactions of OH with four small methyl esters, along with some earlier experimental work42−46 at low temperatures (250−440 K). At a first glance, these kinetic data cannot be described accurately by a simple Arrhenius expression over a wide range of temperatures. Le Calvé et al.42 measured the rate constants for the reactions of OH with a series of formate (including methyl formate) under pseudofirst-order kinetic conditions using the pulsed laser photolysis−laser-induced fluorescence technique in a reaction cell over 233−372 K, as illustrated in Figure 15a. Surprisingly, they suggested that the H atom abstraction from the −OC(O)H group (channel 1a) is negligible over their temperature range studied, and their suggestion is very different from the observation based on the high-temperature measurements. Similarly, Wallington et al.43 measured the rate constant for reaction 1 at room temperature (296 K) under pseudofirstorder kinetic conditions using the flash photolysis−resonance fluorescence technique in a reaction cell, and their room temperature rate constant is ∼24% higher than that of Le Calvé et al.42 As mentioned previously, the estimated rate constants for reaction 1 from Fisher et al.10 and Dooley et al.11 are in good agreement with the present high-temperature data. However, neither of them can predict those low-temperature data from Le Calvé et al. and Wallington et al. For instance, the value from Fisher et al. is higher than the measured room temperature data by a factor of 2.8, and the value from Dooley et al. is lower than the data by a factor of 2.2. Additionally, the estimated rate constant from Fisher et al. seems to exhibit more non-Arrhenius curvature than that of Dooley et al., as illustrated in Figure 15a. As shown in Figure 15b, Wallington et al.43 studied reaction 2 under pseudofirst-order kinetic conditions over the temperature range of 240−440 K. El Boudali et al.44 measured the absolute rate constants for the reactions of OH with a series of

interchanging the branching ratios of channels 4a and 4d while maintaining the total value at 1133 K. Moreover, Table 5 summarizes the present overall rate constant measurements of reaction 4 over the temperature range of 897−1355 K at pressures of 1.23−1.59 atm. Table 5. CH3OC(O)C3H7 + OH → Products: Rate Constant Data T5 [K]

P5 [atm]

k4 [cm3 mol−1 s−1]

80 ppm TBHP (and water), 241 ppm CH3OC(O)C3H7, Ar 1303 1.27 1.65 × 1013 1225 1.30 1.40 × 1013 1181 1.32 1.30 × 1013 1133 1.37 1.17 × 1013 1016 1.48 9.38 × 1012 897 1.59 6.85 × 1012 85 ppm TBHP (and water), 270 ppm CH3OC(O)C3H7, Ar 1355 1.23 1.87 × 1013 1320 1.23 1.71 × 1013 1262 1.27 1.56 × 1013 1062 1.44 1.02 × 1013 961 1.53 8.50 × 1012 925 1.57 7.74 × 1012

Figure 14 shows the Arrhenius plot for the present overall rate constant measurements of reaction 4 over the temperature

Figure 14. Arrhenius plot for methyl butanoate + OH (k4) at temperatures above 870 K.

range of 897−1355 K, along with the estimated values from Fisher et al.,10 Dooley et al.,16 and Hakka et al.17 Note that two different mixture compositions were employed to verify that the current rate constant evaluations are weakly dependent on the secondary chemistry effects, and the measured values from these two mixtures agree well with each other. These measured values can be expressed in Arrhenius form as k4 = 1.13 × 1014 exp(−2515/T) cm3 mol−1 s−1 over 897−1355 K. Similar detailed error analyses were also carried out with the consideration of experimental and mechanism-induced contributions, and the overall (2σ) uncertainties in k4 were estimated to be ±24% at 925 K, ± 20% at 1133 K, and ±16% at 1320 K. As is evident in Figure 14, the estimated rate constants adopted in three different detailed mechanisms are quite different from each other. In particular, the estimated value from Fisher et al.10 is lower than the values from Dooley et al.16 12238



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Table 6. Comparison of the Rate Constants for Channels 4a−4d from Fisher et al.,10 Dooley et al.,16 and Hakka et al.17 at 1133 and 1300 K authors

A [cm3 mol‑1 s‑1]

Fisher et al. Dooley et al. Hakka et al.

5.250 × 1009 5.280 × 1009 2.700 × 1006


4.680 × 1007 4.680 × 1007 2.600 × 1006


1.146 × 1011 1.146 × 1011 2.400 × 1006


5.250 × 1009 7.020 × 1007 3.600 × 1006

b

EA [cal/mol]

1133 K rate

1300 K rate

CH3OC(O)C3H7 + OH → CH3OC(O)CH2CH2CH2 + H2O 0.97 1590 2.376 × 1012 2.973 0.97 1586 2.394 × 1012 2.995 2.00 450 2.838 × 1012 3.833 CH3OC(O)C3H7 + OH → CH3OC(O)CH2CHCH3 + H2O 1.61 −35 3.929 × 1012 4.893 1.61 −35 3.929 × 1012 4.893 2.00 −765 4.689 × 1012 5.909 CH3OC(O)C3H7 + OH → CH3OC(O)CHCH2CH3 + H2O 0.51 63 4.024 × 1012 4.332 0.51 63 4.024 × 1012 4.332 2.00 −2450 9.153 × 1012 1.048 CH3OC(O)C3H7 + OH → CH2OC(O)C3H7 + H2O 0.97 1590 2.376 × 1012 2.973 1.61 −35 5.894 × 1012 7.340 2.00 −100 4.831 × 1012 6.324

ratio (1133 K) to Fisher et al.

× 1012 × 1012 × 1012

1.00 1.01 1.19

× 1012 × 1012 × 1012

1.00 1.00 1.19

× 1012 × 1012 × 1013

1.00 1.00 2.27

× 1012 × 1012 × 1012

1.00 2.48 2.03

Figure 15. Arrhenius plots for methyl ester + OH reactions at temperatures above 250 K.

acetates (including methyl acetate) using the pulsed laser photolysis−laser-induced fluorescence technique in the cell over 243−372 K, and their measurements are consistent with the data from Wallington et al.43 Similarly, the estimated rate constant for reaction 2 from Westbrook et al.15 cannot accurately predict the present high-temperature data and the previous low-temperature data. The value from Westbrook et al. is ∼30% lower than the present data at 1371 K, and is ∼77% higher than the previous data at 333 K. Parts c and d of Figure 15 present the experimental results for the rate constant measurements of reactions 3 and 4, respectively, at temperatures above 250 K. Le Calvé et al.46

measured the absolute rate constants for the reactions of OH with methyl propanoate, methyl butanoate, methyl valerate, and methyl caproate using the pulsed laser photolysis−laserinduced fluorescence technique in the cell over 253−372 K. They concluded that the reaction of OH with methyl caproate was the most reactive one among those 4 methyl esters due to more −CH2− groups available in the molecule. In addition, their rate constant measurements exhibited slight negative temperature dependence, except for methyl propanoate. Wallington et al.43 also measured the room temperature rate constants for reactions 3 and 4, and their results agree well with the data from Le Calvé et al.46 at 296 K. Furthermore, the 12239



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16. Note that the measured rate constants for reactions 1 and 2 are nearly identical at T > 1000 K, but they start to deviate at

estimated rate constants for reactions 3 and 4 from several detailed kinetic mechanisms8,10,16,17 are rather different from the measurements over the temperature range of 250−1355 K. Comparison with Structure−Activity Relationship (SAR). The present high-temperature overall rate constant measurements for reactions 1−4 can be compared with the estimations using the structure−activity relationship (SAR) developed by Atkinson and co-workers.47−49 Their estimation is strictly based on the group rate constants for the H atom abstraction from primary (−CH3), secondary (−CH2−), and tertiary (>CH−) groups, and these group rate constants also depend on the nature of the neighboring atoms (substituents bound to the groups). As discussed by Kwok and Atkinson,49 the group rate constants are expressed as k(CH3−X) = kprimF(X), k(X−CH2−Y) = ksecF(X)F(Y), and k((X)(Y)CH(Z)) = ktertF(X)F(Y)F(Z), where kprim, ksec, and ktert are the standard group rate constants for the H atom abstraction from primary, secondary, and tertiary groups, and F(X), F(Y), and F(Z) are the substituent factors for the substituent groups (X, Y, and Z). For instance, the estimated rate constant for the reaction of OH with methyl propanoate using SAR can be expressed as k3 = kprimF(−OC(O)R) + ksecF(−C(O)OR) F(−CH3) + kprimF(−CH2−), where R is defined as the alkyl group. In addition, Kwok and Atkinson49 updated the parameters for the standard group rate constants and the substituent factors to improve their estimation technique. Consequently, the structure−activity relationship from Kwok and Atkinson49 can accurately predict the recent rate constant measurements for the reactions of OH with n-pentane, nheptane, and n-nonane from Pang et al.28 over the temperature range of 869−1364 K. As demonstrated in Figure 15, the SAR estimations for reactions 1-4 cannot accurately predict the present hightemperature measurements. More importantly, the SAR estimation for the reaction of OH with methyl formate requires some additional attention. Le Calvé et al.42 suggested that the H atom abstraction from the −OC(O)H group (channel 1a) is negligible for the methyl formate + OH reaction over 233−372 K. The SAR estimation without the consideration of channel 1a seems to agree well with the room temperature measurements from Le Calvé et al.42 and Wallington et al.,43 but the estimated values are ∼40% lower than the present high-temperature data. Hence, there is a need to consider the effect of channel 1a in the SAR estimation at high temperatures. In the present analysis, we could treat the C−H bond in the −OC(O)H group as a tertiary site, and the estimated rate constant for reaction 1 can be expressed as k1 = ktertF(=O)F(−OR) + kprimF(−OC(O)H), where R is the alkyl group. The present SAR estimation with the consideration of channel 1a is ∼25% higher than the current high-temperature data, but the estimated values are quite different from the previous low-temperature measurements.42,43 Similarly, the SAR estimations show good agreement with the kinetic measurements of reactions 2−4 at 298 K, but the estimated values are higher than the measured values over 333−1371 K. In particular, the estimated values are ∼25% faster than the current rate constant measurements of reactions 2-4 over 876−1371 K. Interestingly, the SAR estimations seem to capture the temperature dependence of reactions 1-4 reasonably well, implying that the pre-exponential factors for the group rate constants kprim, ksec, and ktert should be reduced by 25%, particularly for these methyl ester + OH reactions. The modified SAR estimations are in excellent agreement with the present high-temperature measurements, as shown in Figure

Figure 16. Comparison of the present rate constant measurements with the modified SAR estimations.

lower temperatures. The data for reaction 1 is ∼16% higher than the data for reaction 2 at T = 880 K. This trend is also well-captured by the modified SAR estimations, as demonstrated in Figure 16.

■

CONCLUSIONS The overall rate constants for the reactions of OH with methyl formate (k1), methyl acetate (k2), methyl propanoate (k3), and methyl butanoate (k4) were measured using OH laser absorption near 306.69 nm behind reflected shock waves over 876−1371 K at pressures near 1.5 atm. These measured rate constants can be expressed in Arrhenius form as k1 = 2.56 × 10 13 exp(−2026/T) cm 3 mol −1 s −1 , k 2 = 3.59 × 10 13 exp(−2438/T) cm3 mol−1 s−1, k3 = 6.65 × 1013 exp(−2539/ T) cm3 mol−1 s−1, and k4 = 1.13 × 1014 exp(−2515/T) cm3 mol−1 s−1 over the temperature ranges studied. Detailed error analyses were conducted with the consideration of both experimental and secondary chemistry contributions, and the overall (2σ) uncertainties were estimated to be ±29% at 913 K and ±18% at 1289 K for k1, ± 29% at 930 K and ±17% at 1299 K for k2, ± 25% at 909 K and ±17% at 1341 K for k3, and ±24% at 925 K, and ±16% at 1320 K for k4. Additionally, the structure−activity relationship (SAR) developed by Atkinson and co-workers47−49 was employed to estimate the overall rate constants for reactions 1−4, and the estimated values are in good agreement with the present measurements (within ∼25%).

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy, Basic Energy Sciences (DE-FG02-88ER13857) with Dr. Wade Sisk as program manager.

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REFERENCES

(1) Agarwal, A. K. Prog. Energy Combust. Sci. 2007, 33, 233−271.

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High-Temperature Measurements of the Reactions of OH with Small

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