Shock Tube Measurements of the tert-Butanol + OH Reaction Rate

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Shock Tube Measurements of the tert-Butanol + OH Reaction Rate and the tert-C4H8OH Radical β‑Scission Branching Ratio Using Isotopic Labeling Ivo Stranic,* Genny A. Pang, Ronald K. Hanson, David M. Golden, and Craig T. Bowman Department of Mechanical Engineering, Stanford University, Stanford, California 94305, United States S Supporting Information *

ABSTRACT: The overall rate constant for the reaction tert-butanol + OH → products was determined experimentally behind reflected shock waves by using 18O-substituted tert-butanol (tert-butan18ol) and tert-butyl hydroperoxide (TBHP) as a fast source of 16 OH. The data were acquired from 900 to 1200 K near 1.1 atm and are best fit by the Arrhenius expression 1.24 × 10−10 exp(−2501/T [K]) cm3 molecule−1 s−1. The products of the title reaction include the tert-C4H8OH radical that is known to have two major βscission decomposition channels, one of which produces OH radicals. Experiments with the isotopically labeled tert-butan18ol also lead to an experimental determination of the branching ratio for the β-scission pathways of the tert-C4H8OH radical by comparing the measured pseudo-first-order decay rate of 16OH in the presence of excess tert-butan16ol with the respective decay rate of 16OH in the presence of excess tert-butan18ol. The two decay rates of 16OH as a result of reactions with the two forms of tert-butanol differ by approximately a factor of 5 due to the absence of 16OH-producing pathways in experiments with tert-butan18ol. This indicates that 80% of the 16OH molecules that react with tert-butan16ol will reproduce another 16OH molecule through β-scission of the resulting tert-C4H816OH radical. 16OH mole fraction time histories were measured using narrow-line-width laser absorption near 307 nm. Measurements were performed at the line center of the R22(5.5) transition in the A−X(0,0) band of 16OH, a transition that does not overlap with any absorption features of 18OH, hence yielding a measurement of 16OH mole fraction that is insensitive to any production of 18OH.

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INTRODUCTION Accurate knowledge of the rate constants for reactions of alcohol fuels with OH radicals is critical for developing hightemperature kinetic models for the combustion of alcohol fuels. In this study, the high-temperature rate constant for the overall reaction tert-butanol + OH → products was determined using isotopic labeling of 18O in the alcohol group of tert-butanol as a key tool. The isotopic labeling eliminated the interference of OH-producing secondary reactions typical of rate constant measurements for reactions of OH with alcohols. This phenomenon is explained in detail in the Reaction Pathways section. In addition, isotopic labeling enabled a determination of the relative reaction rate constant for the two β-scission pathways of the tert-C4H8OH radical, a product of the tertbutanol + OH reaction. These rate constant parameters significantly affect the combustion properties of tert-butanol at high temperatures because they strongly influence the size of the OH radical pool. tert-Butanol is a common fuel additive used as an octane booster to prevent knock in spark-ignition engines. Several experimental studies,1−9 many of which were performed in the past decade, have explored the combustion kinetics of tertbutanol. In addition, several detailed kinetic mechanisms have been developed1,10−13 with varying success in matching the kinetic targets produced in these experimental studies. Discrepancies in mechanism performance are ultimately © XXXX American Chemical Society

explained by order-of-magnitude differences in rate constants for several reactions important to combustion, including for those of the H-atom abstraction of tert-butanol by OH and the β-scission decomposition of the tert-C4H8OH radical.

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REACTION PATHWAYS The reaction tert-butanol + OH proceeds via H-atom abstraction from the methyl (CH3) and alcohol (OH) groups in tert-butanol, as specified by reactions 1a and 1b, respectively. Figure 1 illustrates the network of chemical reactions relevant to the production and consumption of OH as a result of these reactions, as well as the structural formulas of relevant chemical species. tert ‐C4 H 9OH + OH → tert ‐C4 H8OH + H 2O (1a) tert ‐C4 H 9OH + OH → tert ‐C4 H 9O + H 2O

(1b)

The overall rate constant for the reaction tert-butanol + OH, defined as k1 = k1a + k1b

was previously measured using relative rate methods by Cox and Goldstone14 and Wu et al.15 and absolute measurement Received: March 3, 2013 Revised: May 16, 2013

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producing pathways exist can be performed by designing experiments where consumed OH radicals are distinguishable from those produced. This can be achieved by isotopic labeling of the OH radical either in the alcohol or in the OH precursor. Hess and Tully20 and Dunlop and Tully26 have demonstrated this method in measuring the overall reaction rate constant for ethanol + OH and propanol + OH using laser photolysis of H218O as a OH precursor. Isotopic substitution of 18O is preferred to isotopic substitution of deuterium due to the lower expected kinetic isotope effect (KIE). Furthermore, Carr et al.27 have demonstrated that in alcohols with a deuterium-labeled alcohol group, proton exchange may occur with trace amounts of water present in the experiments, thus reducing the deuterium enrichment of the alcohol mixture.

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Figure 1. Dominant reaction pathways related to tert-butanol + OH reactions.

EXPERIMENTAL METHODS The title reaction rate constants were inferred by fitting the measured pseudo-first-order decay rate of 16OH following the shock heating of tert-butanol/TBHP/water/argon mixtures using kinetic simulations (see the Kinetic Modeling section for details). TBHP (tert-butyl hydroperoxide) was used as a fast source of 16OH, and a tert-butanol/TBHP ratio of at least 15 ensured that the tert-butanol concentration remained approximately constant throughout the measurement time, resulting in pseudo-first-order OH decay. Experiments were performed behind reflected shock waves in the Stanford Kinetics Shock Tube with a 14.13 cm inner diameter. Further details on this facility are provided elsewhere.2,28,29 The initial temperature and pressure in the reflected shock region are known to within ±0.3 and 0.6%, respectively. tert-Butan16ol (anhydrous, >99.5%) and TBHP (70 wt % in H2O solution) were obtained from Sigma Aldrich. The molar water/TBHP ratio in the reacting mixtures was approximately 3:1, though the presence of water does not affect measurements or simulations of 16OH time histories. tert-Butan18ol (>99.8% chemical purity, >97.9% isotropic enrichment) was obtained from Cambridge Isotope Laboratories. Because the room-temperature melting point of tert-butanol is 25.1 °C, mixtures were prepared manometrically inside of a stainless steel mixing tank heated to 40 °C, and the room temperature of the laboratory was kept above 25.3 °C. Direct laser absorption at 3.39 μm using a similar procedure as that described in a previous work2 confirmed that the tertbutanol concentration inside of the shock tube was equal to the manometric calculations. 16 OH species time histories were measured using direct absorption of light near 307 nm. This wavelength was generated by frequency doubling the visible output of a narrow-line-width ring dye laser, resulting in approximately 1 mW of UV light. Visible light near 614 nm was produced by pumping rhodamine 6G dye in a Spectra Physics 380A laser cavity using a Coherent Verdi 5W continuous wave laser at 532 nm. A temperature-tuned AD*A nonlinear crystal was used for intracavity frequency doubling. A common mode rejection scheme was used in order to significantly improve the sensitivity of the detection system. Further details on the 16 OH detection system as well as the OH spectrum can be found elsewhere.30,31 Because 16OH mole fractions were measured in the presence of 18OH in this study, measurements were performed on an R22(5.5) transition in the A−X(0,0) band that has negligible spectral overlap with 18OH. Transition selection was performed by comparing the well-characterized30 UV spectrum of 16OH with measured transition line centers32 of 18OH. Though

methods by Wallington et al.,16 Teton et al.,17 Saunders et al.,18 and McGillen at al.,19 all near room temperature. However, these measured values cannot be accurately extrapolated to combustion temperatures. Measurements of the overall rate constant for the reaction tert-butanol + OH at high temperatures are complicated by the existence of an OH-producing pathway that effectively reduces the apparent OH consumption rate. As discussed by Hess and Tully,20 H-atom abstraction of alcohols by OH radicals from β-sites produces hydroxyalkyl intermediates that may rapidly dissociate to OH + alkenes at elevated temperatures (above approximately 500 K). For tertbutanol, this OH regeneration from β-sites occurs via the tertC4H8OH radical produced by reaction 1a, which as described by reaction 2a and depicted in Figure 1, can undergo β-scission to produce OH radicals. It can also undergo β-scission via an alternative major pathway that does not produce OH, described by reaction 2b. tert ‐C4 H8OH → OH + iso‐C4 H8

(2a)

tert ‐C4 H8OH → CH3 + iso‐C3H5OH

(2b)

It follows that consecutive reaction of OH with tert-butanol via reactions 1a and 2a leads to the production of OH, and the relative production of the different products via reactions 1a/1b and 2a/2b, which can be defined through the branching ratios BR1 =

k1a (k1a + k1b)

BR 2 =

k 2a (k 2a + k 2b)

are critical kinetic parameters that significantly affect simulations of tert-butanol oxidation. It is noted that reaction 3, which represents the decomposition of the tert-C4H9O radical (produced by reaction 1b), is not expected to form OH. Therefore, this reaction channel does not significantly affect the OH concentration in this study. tert ‐C4 H 9O → C3H6O + CH3

(3)

OH-producing pathways such as reaction 2a complicate measurements of the overall rate constant for the reactions of alcohols with OH radicals using traditional methods of solely monitoring the pseudo-first-order decay of OH in the presence of excess alcohol.21−25 However, measurements of rate constants for alcohol + OH reactions where secondary OHB

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spectral parameters of 18OH transitions such as line broadening and line strength have not been measured, it was assumed that for a given transition, the line strength and line width of the 18 OH transitions were equal to those of 16OH. Thus, as demonstrated in Figure 2, there is negligible spectral overlap for

of 16OH is not affected by the existence of OH-regenerating pathways discussed in the Reaction Pathways section. The overall rate constant for the reaction tert-butanol + OH needed to best fit the measured data is independent of BR1 for experiments with tert-butan18ol. The high sensitivity of this measurement of k1 is demonstrated by the OH sensitivity analysis shown in Figure 3, which reveals that the 16OH

Figure 2. 16OH and 18OH spectra of the R22(5.5) transition in the A− X(0,0) band at 1000 K and 1 atm. The 18OH line shape is assumed to be the same as that of 16OH as determined by Herbon et al.30 The 18 OH line center was taken from Cheung et al.32.

the R22(5.5) transition between the peak of the 16OH transition and the 18OH spectrum. This was verified experimentally by studying 16OH and 18OH in the shock tube using the detailed procedure provided in the Supporting Information. In addition to verifying the lack of spectral interference between 16OH and 18OH for the R22(5.5) transition, the accuracy of the absorption coefficient for 16OH at the line center of the R22(5.5) transition (32558.72 cm−1) was verified. This was necessary because spectral parameters for the R22(5.5) transition have not been determined with the same accuracy in the literature as that for the R11(5.5) transition that is typically used to make OH measurements in this laboratory.30 The details of this procedure are also provided in the Supporting Information.

Figure 3. Sensitivity analysis of 16OH for representative tert-butan18ol data shown in Figure 6, performed using the Sarathy et al.10,11 mechanism with modifications described in the text. The sensitivity of 16 OH concentration to reaction i is defined as Si(t) = {∂[16OH](t)/ ∂ki}/{[16OH](t)/ki}.

concentration is overwhelmingly sensitive to the tert-butanol + OH reaction rate constant. Secondary reactions that consume OH exist and appear in the OH sensitivity analysis shown in Figure 3, though the rate constants for these reactions are wellcharacterized, and the kinetic model was modified to account for secondary OH-consuming reactions, as discussed later in this section. The experiments are pseudo-first-order; therefore, the first-order decay constant due to reactions of 16OH with tert-butan18ol can be defined by

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KINETIC MODELING Experiments were simulated assuming a constant volume, constant internal energy model, using a modified version of the tert-butanol mechanism proposed by Sarathy et al.10,11 The modifications made to the mechanism include updates to the critical secondary reaction rate constants, the addition of reactions for TBHP decomposition, and the addition of duplicate reactions for reactions of tert-butan18ol and its fragments that are assumed to have equal reaction rate constants and thermodynamic data as their 16O-containing counterparts. Further details on the mechanism modifications are discussed at the end of this section. Simulations using this mechanism were performed in order to account for secondary chemistry while fitting the measured pseudo-first-order decay rates of OH. Simulations were executed using the CHEMKINPRO kinetics solver designed by Reaction Design. The overall rate constant for the reaction tert-butanol + OH (k1) can be determined from experiments with tert-butan18ol by fitting the simulated 16OH time history from the kinetic mechanism to the experimental data using the overall rate constant as the free parameter. Because there are no secondary 16 OH generation pathways in these experiments, the decay rate

18

k′ = k1 = (k1a + k1b)

This value can be combined with the experimental data with tert-butan16ol to provide information about the branching ratio BR2. The measured 16OH removal rate in experiments with tertbutan16ol also demonstrates a pseudo-first-order decay. However, as shown in Figure 4, sensitivity analysis for a representative experiment in tert-butan16ol shows that after initial TBHP decomposition, 16OH time histories are most sensitive to multiple rate constants including k1a, k1b, k2a, and k2b. This is expected considering that in experiments containing tert-butan16ol, 16OH is consumed by reactions 1a and 1b and is produced by reaction 2a. This complex OH sensitivity behavior makes it difficult to measure any single rate constant from these experiments. However, because the tert-C4H8OH radical decomposes rapidly, a quasi-steady-state assumption can be invoked (d[tert-C4H8OH]/dt = 0), and the rate law describing the disappearance of 16OH due to the reaction with tertbutan16ol simplifies to C

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and secondary OH-consuming chemistry from Pang et al.29 are appended to the Sarathy et al.10,11 mechanism in order to accurately account for secondary reactions that may affect the inferred values of 16k′ and 18k′. The accuracy in the rate constants for critical secondary reactions was verified by confirming that simulations of OH time histories during neat TBHP pyrolysis agree with measurements acquired in this study and in the study by Pang et al.29 Kinetic simulations were also used to verify that conversion of 18OH to 16OH through the reaction 18OH + H216O ↔ 16OH + H218O does not perturb the inferred values of 18k′ or 16k′. The rate constant for this reaction was computed using the “Thermo” code in the MultiWell33 software suite with structures, frequencies, and energies from theoretical calculations by Uchimaru et al.34 Tunneling corrections were included, and the estimated rate constant from this study is in good agreement with theoretical calculations by Masgrau et al.35

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UNCERTAINTY ANALYSIS The total uncertainty in the measurements was calculated by adding the root-mean square sum of the random errors to the linear sum of systematic errors. The propagated uncertainty in a representative measurement of 18k′ due to all considered uncertainty factors is shown in Figure 5 for a temperature of

Figure 4. Sensitivity analysis of 16OH for representative tert-butan18ol data shown in Figure 6, performed using the Sarathy et al.10,11 mechanism with modifications described in the text. The sensitivity of 16 OH concentration to reaction i is defined as Si(t) = {∂[16OH](t)/ ∂ki}/{[16OH](t)/ki}.

⎛ d[16OH] ⎞ ⎜ ⎟ ⎝ dt ⎠tert −butan16ol = − (k1a + k1b)(1 − BR1BR 2)[tert −butan16ol][16OH]

The component of the first-order decay rate due to reactions with tert-butan16ol is thus 16

k′ = (k1a + k1b)(1 − BR1BR 2) = 18k′(1 − BR1BR 2)

While the first-order rate constant is a function of more than one kinetic parameter, the overall value of 16k′ needed to simulate the experimental data is unique. Therefore, 16k′ was inferred by best-fitting kinetic simulations of OH time histories to the experimental measurements of 16OH decay in the experiments with excess tert-butan16ol. Given the measured 18k′, it was verified the value of 16k′ required to best fit the experimental data is independent of the value of the free parameters BR1 and BR2. It is observed that measurements cannot be fit using kinetic simulations if either BR1 or BR2 are below 0.72. A brute force analysis indicates that within the span of BR1:BR2 combinations examined, using possible values of BR1 and BR2 ranging from 0.72 to 1.0, the value of 16k′ that fits the experimental data can be determined to within 3%. It is noted that the inferred values of 16k′ are independent of the chosen value for k1, though the measured value of k1 = 18k′ is preferred. After determining 18k′ and 16k′ from the experimental data, the ratio of these two values leads to the value of the product BR1BR2. As discussed in the Results and Discussion section, estimates of BR1 can then be used to infer BR2. Rate of production analyses indicate that 75−90% of the 16 OH consumption results from reactions with tert-butanol at the conditions in the current experiments, though secondary reactions that consume OH exist and the Sarathy et al.10,11 mechanism was modified with well-characterized rate constants for these reactions. Both the TBHP decomposition chemistry

Figure 5. Magnitude of the uncertainty in the measured 18k′ associated with each factor considered in the uncertainty analysis. All uncertainties are ± , unless otherwise specified; 500 ppm tertbutan18ol, 28 ppm TBHP, 81 ppm H2O, diluted in argon, T = 1167 K, P = 1.20 atm.

1167 K. It is noted that the uncertainty in 16k′ and 18k′ caused by some of the uncertainty factors shown in Figure 5 are dependent on temperature. These uncertainties are propagated into the overall uncertainties of the inferred values for BR1BR2, BR1, and BR2. Because measurements with tert-butan18ol were used to infer the rate constant for the overall tert-butanol + OH reaction, it must be confirmed that KIEs do not cause variations in the reaction rates of H-atom abstraction by OH radicals in tertbutan16ol and tert-butan18ol. Primary KIEs are those that involve the breaking of a bond at the site of kinetic substitution, which in this study occurs at the alcohol group that reacts with OH through reaction 1b. Due to small changes in both the overall molecular weight of tert-butanol and the vibrational frequency of the OH bond in the alcohol group, transition-state theory predicts that KIEs will have a negligible effect on the rate of reaction 1b. Previous studies have shown that KIEs involving D

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breaking of bonds at molecular sites away from the site of isotopic substitution do not significantly affect reaction rate constants.36,37 Therefore, given that KIEs are negligible for reaction 1b, they are assumed to be nearly zero for reaction 1a. Because reaction 1a accounts for over 90% of the overall tertbutanol + OH reaction (see the Results and Discussion section), KIEs do not affect the extrapolation of the measurements of the title parameters involving tert-butan18ol to the respective kinetic parameters involving tert-butan16ol.

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RESULTS AND DISCUSSION Measurements of 18k′ were acquired from 896 to 1208 K for a variety of mixtures, with tert-butan18ol concentrations near 500 ppm and TBHP concentrations varying from 14 ppm to 29 ppm. Measurements of 16k′ were performed from 896 to 1204 K for a variety of mixtures, with tert-butan16ol concentrations varying from 307 to 2080 ppm and TBHP concentrations varying from 9 ppm to 26 ppm. Two sets of 16k′ data were acquired independently by the first two authors of this work. Measurements of 18k′ were generally performed at lower tertbutanol concentrations compared to measurements of 16k′ because, as the data will demonstrate, the decay rate of 16OH in tert-butan18ol is much faster compared to that in equal amounts of tert-butan16ol. All experiments were performed near 1.1 atm. Figure 6 shows representative measurements and kinetic simulations of 16OH time histories in the presence of excess

Figure 7. Arrhenius plot of measured 16k′ and 18k′. Solid lines show Arrhenius fits; 18k′ = (k1a + k1b) = 1.24 × 10−10 exp(−2501/T [K]) cm3 molecule−1 s−1; 16k′ = (k1a + k1b)(1 − BR1BR2) = 3.87 × 10−11 exp(−2935/T [K]) cm3 molecule−1 s−1. 16

k′ = (k1a + k1b)(1 − BR1BR 2) = 3.87 × 10−11 exp( −2935/ T [K ]) cm 3 molecule−1 s−1

As demonstrated in Figure 8, kinetic mechanisms offer a wide variety of values for the overall rate constant for the reaction

Figure 8. Comparison of the measured overall tert-butanol + OH reaction rate constant (k1 = 18k′) with values used in mechanisms from the literature.

tert-butanol + OH. Notably, good agreement is shown with the Moss et al.1 mechanism, which agrees with the current measurements within the estimated uncertainties. The Moss et al.1 mechanism estimates the rate of reaction 1a using an Evans−Polanyi type correlations based on H-atom abstraction rates from ethane.38 The mechanism also assumes that the rate of reaction 1a is greater than that of reaction 1b by exactly a factor of 9, which is a reasonable estimate that is discussed in detail later in this section. The rate constant estimate for the overall reaction tert-butanol + OH in the Sarathy et al.10,11 mechanism, obtained from a combination of theory and experimental data, is 50% lower than the current measurement. The Grana et al.13 mechanism suggests a rate constant for the overall reaction tert-butanol + OH, which is also 50% lower than the current measurement; their rate constants were derived from previous work on predicting kinetic parameters for H-atom abstraction reactions, validated against a wide array of experimental data.39 The Grana et al.13 mechanism also assumes that the rate of reaction 1a is greater than that of reaction 1b by exactly a factor of 9. The Van Geem et al.12

Figure 6. Representative 16OH time histories for tert-butanol/TBHP/ argon mixtures (k′ in units of cm3 molecule−1 s−1). Initial postreflected shock conditions: T = 1020 K and P = 1.2 atm.

tert-butan18ol and tert-butan16ol. Measured 16OH time histories exhibit low noise, and kinetic simulations of the pseudo-firstorder decay rate of 16OH demonstrate excellent sensitivity to 18 k′ and 16k′, as shown in Figure 6 by simulations with 18k′ and 16 k′ adjusted by ±20%. It is estimated that the fitting uncertainty of 18k′ and 16k′ is ±3%. Measurements of 18k′ and 16k′ exhibit Arrhenius behavior with low scatter and uncertainty over the temperature range studied, as shown in Figure 7 (tabulated data are presented in the Supporting Information). Arrhenius fits for these parameters are 18

k′ = (k1a + k1b) = 1.24 × 10−10 exp( − 2501/T [K]) cm3 molecule−1 s−1 E

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mechanism estimates the rates for reactions 1a and 1b using the open source software package Reaction Mechanism Generator (RMG),40 and these rate constants yield a value for the rate constant for the reaction tert-butanol + OH, which is 80% slower than the current measurement. The ratio of 18k′ and 16k′ enables an experimentally determined value for BR1BR2 approximately equal to 0.8 over the entire temperature range studied, as shown in Figure 9.

Figure 10. Comparison of the estimated branching ratio BR1 with values used in mechanisms from the literature.

O−H bond dissociation energies in the alcohol group41 for methanol, ethanol, and n-butanol lead to calculated rate constants for the H-atom abstraction in the alcohol group by OH in these alcohols that agree within 40% of one another.42,43 Because the O−H bond dissociation energy in tert-butanol is also expected to be similar, quantum calculations for the rate of H-atom abstraction by OH from the alcohol group of n-butanol provide a reasonable estimate for the rate constant of reaction 1b. Using this estimate for reaction 1b, the rate constant for reaction 1a was calculated under the constraint that the sum of the two reaction rates, the overall tert-butanol + OH reaction rate, must lie within the uncertainty of the measurement in this study. Using this method, an estimate of BR1 equal to 0.96 is calculated with an overall uncertainty (peak-to-peak) of 6%, as shown in Figure 10. Despite an uncertainty estimate of a factor of 4 on in the rate of reaction 1b, BR1 is calculated accurately because the relatively large measured value of the overall tertbutanol + OH reaction rate requires that the vast majority of Hatom abstraction by OH in tert-butanol proceeds via reaction 1a. Using the above estimate of BR1, BR2 is calculated from the measurement of BR1BR2 with overall uncertainties (peak-topeak) of approximately 17 and 12% near 900 and 1200 K, respectively. As shown in Figure 11, the probability of the tertC4H8OH radical undergoing β-scission through reaction 2a is greater than 80% at the conditions studied. These results are significant because high-accuracy measurements of the branching of radicals produced during decomposition of organic compounds are rare, though accurate knowledge of

Figure 9. Comparison of the measured branching ratio product BR1BR2 near 1.1 atm with values used in mechanisms from the literature.

This indicates that for every OH molecule that reacts with tertbutanol, there is an 80% probability that another OH molecule will be produced through the β-scission of the resulting tertC4H8OH radical. This provides further evidence that a rate constant measurement for the reaction tert-butanol + OH is difficult without the use of isotopic substitution because the net OH decay rate in a mixture of tert-butan16ol is strongly reduced by the regeneration of OH radicals. Because neither BR1 nor BR2 can be greater than unity, the measurement of BR1BR2 places an upper limit on both BR1 and BR2. The comparison of the measured BR1BR2 product with the values of BR1BR2 obtained using the rate constants in the different mechanisms studied is shown in Figure 9. An estimation of BR1 can be used to infer BR2. To first-order, BR1 can be estimated to be between 0.9 and 1.0 based on the number of H atoms that are available for abstraction at the methyl and alcohol sites (i.e., reaction 1a can proceed via nine different H atoms in the methyl groups of tert-butanol, whereas reaction 1b can only proceed via a single H atom in the alcohol group) and with the assumption that C−H bonds are generally weaker than O−H bonds. As shown in Figure 10, the Sarathy et al.,10,11 Grana et al.,13 and Moss et al.1 mechanisms indicate that BR1 lies within this range, though the Van Geem et al.12 mechanism does not. The Sarathy et al.10,11 mechanism value of BR1 is a consequence of separate reaction rate estimates of reactions 1a and 1b described previously, whereas the Grana et al.13 and Moss et al.1 mechanism values of BR1 are equal to 0.9 based solely on the degeneracy of reaction sites. The Van Geem et al.12 mechanism, which uses RMG to estimate the rate constants for reactions 1a and 1b, does not provide a reasonable estimate for BR1. In the current analysis, BR1 will be estimated more accurately than in the mechanisms discussed previously through the use of quantum calculations for H-atom abstraction reactions by OH radicals from the alcohol group and the measurements of the overall tert-butanol + OH reaction rate from this study. Similar

Figure 11. Comparison of the inferred branching ratio BR2 near 1.1 atm with values used in mechanisms from the literature. F

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these kinetic parameters can be important in developing kinetic mechanisms. Because of the previous lack of knowledge surrounding these kinetic parameters, kinetic mechanisms provide a wide range of estimates for BR2 ranging from 0.09 to 0.98, as shown in Figure 11. The Moss et al.1 and Sarathy et al.10,11 mechanisms provide reasonable estimates of BR2, compared to the inferred value. It should be noted that these mechanisms present rate constant expressions for reactions 2a and 2b that were estimated at the high-pressure limit, and depending on the relative falloff behavior of these reactions, BR2 may exhibit some pressure dependence. Rate constants for reactions 2a and 2b in the Moss et al.1 mechanism were derived from estimates of β-scission reaction rate constants in alkanes and ethers. Evans−Polanyi type correlations using enthalpies obtained from THERGAS44 software are used to adjust the rate constant for reaction 2b due to the effect of the alcohol group on the strength of the C−C bond. The rates of reactions 2a and 2b in the Sarathy et al.10,11 mechanism were determined from rate constants for similar reverse reactions. Because the estimated rate constants from the Sarathy et al.10,11 mechanism for the β-scission directions of these reactions are sensitive to thermodynamic properties used in the estimation process, the uncertainty limits of the BR2 suggested by the Satathy et al.10,11 mechanism are likely to overlap with the inferred value of BR2 from the current experimental data. As shown in Figure 11, calculations of BR2 using the Van Geem et al.40 mechanism, which are based on RMG estimates, predict a value of BR2 that is significantly below the lower bound imposed by measurements of BR1BR2. Calculations of BR2 using the Grana et al.13 mechanism exhibit the same problem. It is noted that the products of reaction 2b in the Grana et al.13 mechanism are CH3 and (CH3)2CO (acetone), instead of CH3 and CH3CH2COH. However, the rate constant for this reaction as it is written in their mechanism provides a similar value of the rate constant for the β-scission to CH3 and CH3CH2COH as written in the Sarathy et al.10,11 mechanism.

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ASSOCIATED CONTENT

S Supporting Information *

Tabulated data, including a summary of measured 16k′ and 18k′, as well as procedures used to characterize spectral interference between 16OH and 18OH and verify the accuracy of the absorption coefficients of 16OH. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, with Dr. Wade Sisk as contract monitor. The authors would like to thank Prof. Mani Sarathy and Dr. David Davidson for valuable insights and advice provided throughout the study.

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REFERENCES

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CONCLUSIONS The overall rate constant for the reaction tert-butanol + OH → products, as well as the branching ratio for the β-scission pathways of the tert-C4H8OH radical, was measured behind reflected shock waves in a shock tube. The overall rate constant measurement demonstrates the utility of using isotopic labeling of 18O in the alcohol group to eliminate secondary reaction interference in the rate constant measurement for reactions of OH with alcohols. By spectrally separating the measured OH radicals that are consumed and the OH radicals that are produced using isotopic labeling, measurements of the pseudofirst-order decay rate of 16OH radicals that react with tertbutan18ol are largely sensitive to the overall tert-butanol + OH rate constant. The branching ratio measurement for the tertC4H8OH radical represents a unique measurement of the decomposition of organic radicals at high temperatures using a novel method exploiting isotopic labeling of 18O in the alcohol group of tert-butanol. Comparisons of the measured pseudofirst-order decay rates of 16OH in the presence of tert-butan16ol with those in the presence of tert-butan18ol are used to calculate the branching ratio for the β-scission pathways of the tertC4H8OH radical. To the authors’ knowledge, this is the first instance in which isotopic substitution and narrow-line-width laser absorption have been used for high-temperature reaction rate constant measurements behind reflected shock waves. G

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