Shock tube measurements of the tert-butanol + OH reaction rate and the tert-c 4 H 8 OH radical β-scission branching ratio using isotopic labeling

Transcription

1 8 th U. S. National Combustion Meeting Organized by the Western States Section of the Combustion Institute and hosted by the University of Utah May 19-22, 2013 Shock tube measurements of the tert-butanol + OH reaction rate and the tert-c 4 H 8 OH radical β-scission branching ratio using isotopic labeling Ivo Stranic,* Genny A. Pang, David F. Davidson, Ronald K. Hanson, David M. Golden, Craig T. Bowman Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA The overall rate constant for the reaction tert-butanol + OH products was determined experimentally behind reflected shock waves by using 18 O-substituted tert-butanol (tert-butan 18 ol) 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 x exp(-2501/t [K]) cm 3 molecule -1 s -1. The products of the title reaction include the tert-c 4 H 8 OH radical which is known to have two major β-scission decomposition channels, one of which produces OH radicals. Experiments with the isotopically-labeled tert-butan 18 ol also lead to an experimental determination of the branching ratio for the primary β-scission pathways of the tert-c 4 H 8 OH radical by comparing the measured pseudo-first-order decay rate of 16 OH in the presence of excess tert-butan 16 ol, with the respective decay rate of 16 OH in the presence of excess tert-butan 18 ol. The two decay rates of 16 OH as a result of reactions with the two forms of tert-butanol differ by approximately a factor of five, due to the absence of 16 OH-producing pathways in experiments with tert-butan 18 ol. This indicates that 80% of the 16 OH molecules that react with tert-butan 16 ol will reproduce another 16 OH molecule through β-scission of the resulting tert-c 4 H 8 16 OH radical. 16 OH mole fraction time-histories were measured using narrow-linewidth laser absorption near 307 nm. Measurements were performed at the linecenter of the R 22 (5.5) transition in the A-X(0,0) band of 16 OH, a transition that does not overlap with any absorption features of 18 OH, hence yielding a measurement of 16 OH mole fraction that is insensitive to any production of 18 OH. 1. Introduction Accurate knowledge of the rate constants for reactions of alcohol fuels with OH radicals is critical for developing high-temperature 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 18 O 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 primary β-scission pathways of the tert-c 4 H 8 OH radical, a product of the tert-butanol + 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 last decade, have explored the combustion kinetics of tert-butanol. In addition, several detailed kinetic mechanisms have been developed 1,10 13 with varying success in matching the kinetic targets produced in these experimental studies. Discrepancies in mechanism performance are ultimately 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- C 4 H 8 OH radical. 1

2 2. Reaction Pathways The reaction tert-butanol + OH proceeds via H-atom abstraction from the methyl (CH 3 ) 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-c 4 H 9 OH + OH tert-c 4 H 8 OH + H 2 O tert-c 4 H 9 OH + OH tert-c 4 H 9 O + H 2 O Reaction (1a) Reaction (1b) The overall rate constant for the reaction tert-butanol + OH, defined as k 1 = k 1a +k 1b was previously measured using relative rate methods by Cox and Goldstone 14, and Wu et al. 15, and absolute measurement methods by Wallington et al 16, Teton et al. 17, and Saunders et al. 18, all near room temperature. However, these measured values cannot be accurately extrapolated to combustion temperatures. Furthermore, measurements of the overall rate constant for the reaction tert-butanol + OH at high temperatures are complicated by the existence of an OHproducing pathway that effectively reduces the apparent OH consumption rate. As discussed by Hess and Tully 19, 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 tert-butanol, this OH regeneration from β-sites occurs via the tert-c 4 H 8 OH 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-c 4 H 8 OH OH + iso-c 4 H 8 tert-c 4 H 8 OH CH 3 + iso-c 3 H 5 OH Reaction (2a) Reaction (2b) It follows that consecutive reaction of OH with tert-butanol via Reactions (1a) and (2a) leads to the production of OH. Therefore, the relative production of the different products via Reactions (1a/b) and (2a/b), which can be defined through the branching ratios: BR 1 = k 1a /(k 1a +k 1b ) BR 2 = k 2a /(k 2a +k 2b ) are critical kinetic parameters which significantly affect simulations of tert-butanol oxidation. It is noted that Reaction (3), which represents the decomposition of the tert-c 4 H 9 O 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-c 4 H 9 O C 3 H 6 O + CH 3 Reaction (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 However, measurements of rate constants for alcohol + OH reactions where secondary OH-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 Tully 19 and Dunlop and Tully 25 have demonstrated this method in measuring the overall reaction rate constant for ethanol + OH and propanol + OH using laser photolysis of H 2 18 O as an OH precursor. Isotopic substitution of 18 O is preferred to isotopic substitution of deuterium due to the lower expected kinetic isotope effect. Furthermore, Carr et al. 26 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. 2

3 Figure 1: Dominant reaction pathways related to tert-butanol + OH reactions. 3. Experimental Methods The title reaction rate constants were inferred by fitting the measured pseudo-first-order decay rate of 16 OH following the shock heating of tert-butanol/tbhp/water/argon mixtures using kinetic simulations (see Kinetic Modeling section for details). TBHP (tert-butyl hydroperoxide) was used as a fast source of 16 OH, and a tert-butanol/tbhp ratio of at least 15 ensured that the tert-butanol concentration remains 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 cm inner diameter. Further details on this facility are provided elsewhere 2,27,28. The initial temperature and pressure in the reflected shock region are known to within ± 0.3% and 0.6%, respectively. tert- Butan 16 ol (anhydrous >99.5%) and TBHP (70% wt. in H 2 O solution) were obtained from Sigma Aldrich. The water:tbhp ratio in the reacting mixtures was approximately 3:1, though the presence of water does not affect measurements or simulations of 16 OH time-histories. tert-butan 18 ol (>99.8% chemical purity, >97.9% isotropic enrichment) was obtained from Cambridge Isotope Laboratories. Since the room temperature melting point of tertbutanol is 25.1 C, mixtures were prepared manometrically inside 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 described in a previous work 2 confirmed that the tert-butanol concentration inside 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-linewidth 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 non-linear 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 29,30. Since 16 OH mole fractions were measured in the presence of 18 OH in this study, measurements were performed on a R 22 (5.5) transition in the A-X(0,0) band that has negligible spectral overlap with 18 OH. Transition selection was performed by comparing the well-characterized 29 UV spectrum of 16 OH, with measured transition linecenters 31 of 18 OH. Though spectral parameters of 18 OH transitions such as line broadening and line strength have not been measured, it was assumed that for a given transition, the line strength and linewidth of the 18 OH transitions were equal to those of 16 OH. Thus, as demonstrated in Figure 2, there is negligible spectral overlap for the R 22 (5.5) transition between the peak of the 16 OH transition and the 18 OH spectrum. This was verified experimentally by studying 16 OH and 18 OH in the shock tube generated by the pyrolysis of tert-butan 16 ol and tert-butan 18 ol, respectively In addition to verifying the lack of spectral interference between 16 OH and 18 OH for the R 22 (5.5) transition, the accuracy of the absorption coefficient for 16 OH at the linecenter of the R 22 (5.5) transition ( cm -1 ) was verified experimentally. This was necessary because spectral parameters for the R 22 (5.5) transition have not been determined with the same accuracy in the literature as for the R 11 (5.5) transition that is typically used to make OH measurements in this laboratory 29. 3

4 Absorption Coefficient [cm -1 atm -1 ] Paper # OH 18 OH R 22 (5.5) Wavenumber [cm -1 ] Figure 2: 16 OH and 18 OH spectra of the R 22 (5.5) transition in the A-X(0,0) band at 1000 K, 1 atm. 18 OH lineshape assumed to be the same as that of 16 OH as determined by Herbon et al OH linecenter taken from Cheung et al 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. Several modifications were made to the mechanism including 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-butan 18 ol and its fragments that are assumed to have equal reaction rate constant as their 16 O-containing counterparts. More details on the mechanism modifications are discussed later in this section. Simulations were executed using the CHEMKIN-PRO kinetics solver designed by Reaction Design. To infer the overall tert-butanol + OH reaction rate as well as the branching ratio for the β-scission pathways of the tert-c 4 H 8 OH radical, the measured 16 OH removal rates for reactions of 16 OH with tert-butan 16 ol or tert-butan 18 ol in excess were determined from the experimental data using the detailed kinetic model. OH rate-of-production calculations using the kinetic model illustrate that 16 OH is primarily produced by the decomposition of TBHP and the tert-c 4 H 8 16 OH radical, and removed primarily by reactions with tert-butanol and methyl radicals. The latter is produced from the TBHP decomposition secondary chemistry. The measured 16 OH removal rate was determined by fitting the simulated OH time history from the kinetic mechanism to the experimental data using the free parameters that affect the theoretical firstorder decay rate due to reactions with tert-butanol. The theoretical first-order decay rate is determined using the following rate law analyses. During reactions of 16 OH in the presence of tert-butan 18 ol, there are no expected secondary 16 OH production pathways, and the rate law for 16 OH due to the reaction with tert-butan 18 ol is equal to: ( [ ] ) ( )[ ][ ] Since the tert-butan 18 ol is in excess in these experiments, its concentration is approximately constant and the 16 OH concentration is expected to exhibit a pseudo-first-order decay with a decay constant of 18 k [tert-butan 18 ol] due to reactions with tert-butan 18 ol, where 18 k = k 1 = (k 1a + k 1b ) Therefore, 18 k, which represents the net 16 OH removal rate due to reactions with tert-butan 18 ol, is determined by best fitting kinetic simulations of measurements of 16 OH decay in experiments of 16 OH in the presence of excess tertbutan 18 ol using k 1 as a free parameter. The overall k 1 needed to best fit the measured data is independent of BR 1 for experiments with tert-butano 18 ol. The high sensitivity of this measurement of k 1 is demonstrated by the OH sensitivity analysis shown in Figure 3, which demonstrates that the OH concentration is overwhelmingly sensitive to the tertbutanol + OH reaction rate constant. Secondary reactions that consume OH exist and appear in the OH sensitivity 4

5 analysis shown in Figure 3, though the rate constants for these reactions are well-characterized, and the kinetic model was modified to account for secondary OH-consuming reactions as discussed later in this section. Sensitivity analysis in tert-butan 16 ol shows that after initial TBHP decomposition, 16 OH time histories are most sensitive to multiple rate constants including k 1a, k 1b, k 2a, and k 2b. This is expected considering that in experiments containing tert-butan 16 ol, 16 OH is expected to be 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, since the tert-c 4 H 8 OH radical decomposes rapidly, a quasi-steady state assumption can be invoked (d[tert-c 4 H 8 OH]/dt = 0), and the rate law describing the disappearance of 16 OH due to the reaction with tertbutan 16 ol simplifies to: ( [ ] ) ( )( )[ ][ ] Since the tert-butan 16 ol is in excess, its concentration can be modeled as approximately constant and the 16 OH concentration is expected to exhibit a pseudo-first-order decay with a decay constant of 16 k [tert-butan 16 ol] due to reaction with tert-butan 16 ol, where 16 k = (k 1a + k 1b ) (1 - BR 1 BR 2 ) = 18 k (1 - BR 1 BR 2 ) Therefore, 16 k is inferred by best-fitting kinetic simulations of OH time histories to the experimental measurements of 16 OH decay in experiments of 16 OH in the presence of a known excess concentration of tert-butan 16 ol, using 16 k as the free parameter. Simulations with different combinations of k 1, BR 1, and BR 2 confirm that 16 k is indeed the critical fitting parameter for the decay of 16 OH, and that the value of 16 k needed to best fit the data is roughly independent of the relative values of its component parameters. Given that the overall rate constant for the reaction tert-butanol + OH products must lie within the measurement uncertainty of 18 k, it is observed that measurements cannot be fit using kinetic simulations if either BR 1 or BR 2 are below A brute force analysis indicates that within the span of BR 1 :BR 2 combinations examined (using possible values of BR 1 and BR 2 ranging from 0.72 to 1.0), the value of 16 k that fits the experimental data can be determined to within 3%. After determining 18 k and 16 k from the experimental data, the ratio of these two values leads to the value of the product BR 1 BR 2, and as discussed in the Results section, estimates of BR 1 can be used to infer BR 2. It was previously mentioned that secondary OH-consuming reactions exist, and that the rate constants for these reactions are well-characterized. A kinetic model can be modified to correctly account for these reactions and this model can be used to infer 16 k and 18 k. 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. Both the TBHP decomposition chemistry and secondary OH-consuming chemistry from Pang et al. 28 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 16 k and 18 k. 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. 28 5

6 Normalized 16 OH Sensitivity Paper # time [ s] Primary Reactions tert-c 4 H 9 OH + OH tert-c 4 H 8 OH + H 2 O - [Reaction (1a)] tert-c 4 H 9 OH + OH tert-c 4 H 9 O + H 2 O - [Reaction (1b)] Secondary Reactions CH 3 + OH + M CH 3 OH + M - [Reaction (4)] CH 3 + OH 1 CH 2 + H 2 O - [Reaction (5)] iso-c 4 H 8 + OH iso-c 4 H 7 + H 2 O tert-c 4 H 9 OOH tert-c 4 H 9 O + OH Figure 3: Sensitivity analysis of 16 OH for representative tert-butan 18 ol data shown in Figure 4, performed using the Sarathy et al. 10,11 mechanism with modifications described in the text. Sensitivity of 16 OH concentration to reaction i is defined as S i (t) = { [ 16 OH](t)/ k i }/{[ 16 OH](t)/k i } 5. Results and Discussion Measurements of 18 k were acquired from 896 to 1208 K for a variety of mixtures, with tert-butan 18 ol concentrations near 500 ppm, and TBHP concentrations varying from 14 ppm to 29 ppm. Measurements of 16 k were performed from 896 to 1204 K for a variety of mixtures, with tert-butan 16 ol concentrations varying from 307 to 2080 ppm, and TBHP concentrations varying from 9 ppm to 26 ppm. Two sets of 16 k data were acquired independently by the first two authors of this work. Measurements of 18 k were generally performed at lower tert-butanol concentrations compared to measurements of 16 k, because, as the data will demonstrate, the decay rate of 16 OH in tert-butan 18 ol is much faster compared to that in equal amounts of tert-butan 16 ol. All experiments were performed near 1.1 atm. Figure 4 shows representative measurements and kinetic simulations of 16 OH time histories in the presence of excess tert-butan 18 ol and tert-butan 16 ol. Measured 16 OH time histories exhibit low noise, and kinetic simulations of the pseudo-first-order decay rate of 16 OH demonstrate excellent sensitivity to 18 k and 16 k. It is estimated that the fitting uncertainty of 18 k and 16 k is ± 3%. 6

7 Net OH decay rate due to reaction with tert-butanol [cm 3 molecule -1 s -1 ] 16 OH Mole Fraction [ppm] ppm t-butan 18 ol 29 ppm tbhp Measurement 18 k' = 1.06x k' 0.818k' 500 ppm t-butan 16 ol 17 ppm tbhp Measurement 16 k' = 2.12x k' k' time [ s] Figure 4: Representative 16 OH time histories for tert-butanol/tbhp/argon mixtures (k in units of cm 3 molecule -1 s -1 ). Post-reflected shock conditions: T = 1020 K, P = 1.2 atm. Measurements of 18 k and 16 k exhibit Arrhenius behavior with low scatter and uncertainty over the temperature range studied, as shown in Figure 5. Arrhenius fits for these parameters are: 18 k = (k 1a + k 1b ) = 1.24 x exp(-2501/t [K]) cm 3 molecule -1 s k = (k 1a + k 1b ) (1-BR 1 BR 2 ) = 3.87 x exp(-2935/t [K]) cm 3 molecule -1 s K 1111 K 1000 K 909 K k ' = k 1a +k 1b 16 k ' = (k 1a +k 1b ) (1-BR 1 BR 2 ) /T [K -1 ] Figure 5: Arrhenius plot of measured 16 k and 18 k. Solid lines show Arrhenius fits. As demonstrated in Figure 6, kinetic mechanisms offer a wide variety of values for the overall rate constant for the reaction 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) by performing Evans-Polanyi type correlations based on H-atom abstraction rates from ethane 32. The mechanism also assumes that since the bond energy of the O-H bond in alcohols is similar to that of the C-H bond of an alkylic primary H atom 33, the rate of Reaction (1a) is greater than that of Reaction (1b) by exactly a factor of nine. Rate constant 7

8 Net OH decay rate due to reaction with tert-butanol [cm 3 molecule -1 s -1 ] Paper # 0014 estimates for the overall reaction tert-butanol + OH in the Sarathy et al. 10,11 mechanism are 50% lower than the current measurement. The rate constant estimate for Reaction (1a) in the Sarathy et al. 10,11 mechanism was generated by performing Evans-Polanyi type correlations with site-specific quantum calculations of the reaction rate of n-butanol + OH 34. The rate for Reaction (1b) was assumed to be equal to abstraction from the alcohol group by OH in n-butanol. The Grana et al. 13 mechanism contains a rate constant for the overall reaction tert-butanol+oh which is also 50% lower than the current measurement. This mechanism derives estimates for the rates of Reactions (1a) and (1b) from previous work on predicting kinetic parameters for H-atom abstraction reactions, validated against a wide array of experimental data 35. The Grana et al. 13 mechanism also assumes that the rate of H-atom abstraction from the alcohol group is equal to the rate of primary H-atom abstraction from the methyl group. The Van Geem et al. 12 mechanism estimates the rates for Reactions (1a) and (1b) using the open source software package Reaction Mechanism Generator (RMG) 36, 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 K 1111 K 1000 K 909 K k ' = k 1a +k 1b Measurement Sarathy et al. (2012) Grana et al. (2010) Van Geem et al. (2010) Moss et al. (2008) /T [K -1 ] Figure 6: Comparison of the measured overall tert-butanol + OH reaction rate constant ( 18 k ) with values used in mechanisms from the literature. The ratio of 18 k and 16 k enables an experimentally-determined value for BR 1 BR 2 approximately equal to 0.8 over the entire temperature range studied, as shown in Figure 7. This indicates that for every OH molecule that reacts with tert-butanol, there is an 80% probability that another OH molecule will be produced through the β-scission of the resulting tert-c 4 H 8 OH radical. This provides further evidence that a rate constant measurement for the reaction tertbutanol + OH is difficult without the use of isotopic substitution, because the net OH decay rate in a mixture of tertbutan 16 ol is strongly reduced by the regeneration of OH radicals. Since neither BR 1 nor BR 2 can be greater than unity, the measurement of BR 1 BR 2 places an upper limit on both BR 1 and BR 2. The comparison of the measured BR 1 BR 2 product with the values of BR 1 BR 2 obtained using the rate constants in the different mechanisms studied is shown in Figure 7, and the reasons for the discrepancies will be made apparent in the following individual analyses of BR 1 and BR 2. 8

9 K 1000 K 909 K 0.8 BR 1 BR Measurement Sarathy et al. (2012) Grana et al. (2010) Van Geem et al. (2010) Moss et al. (2008) /T [K -1 ] Figure 7: Comparison of the measured branching ratio product BR 1 BR 2 near 1.1 atm with values used in mechanisms from the literature. An estimation of BR 1 can be used to infer BR 2. To first order, BR 1 can be estimated by examining the number of H atoms in tert-butanol that are available for abstraction by OH through Reactions (1a) and (1b). As shown in Figure 1, Reaction (1a) can proceed via nine separate H atoms in the methyl group of tert-butanol, whereas Reaction (1b) can only proceed via a single H atom in the alcohol group. Furthermore, C-H bonds in methyl groups are generally weaker than O-H bonds in the alcohol group. Therefore, degeneracy arguments and bond-strength comparisons suggest that BR 1 is between 0.9 and 1.0. As shown in Figure 8, the Sarathy et al. 10,11, Grana et al. 13, and Moss et al. 1 mechanisms indicate that BR 1 lies within this range, though the Van Geem et al. 12 mechanism does not. The Sarathy et al. 10,11 mechanism value of BR 1 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 BR 1 are equal to 0.90 based solely on the degeneracy of reaction sites. The value of BR 1 indicated by the Van Geem et al. 12 mechanism cannot be used with any value of BR 2 to match the experimentally determined product of BR 1 BR 2, which may indicate a problem in the RMG method for calculating the rate constant for Reactions (1a) and (1b). In the current analysis, BR 1 will be estimated more accurately by examining calculated rates of H-atom abstraction reactions by OH radicals from the alcohol group in various alcohols and measurements of the overall tertbutanol + OH reaction rate from this study. Due to similar O-H bond dissociation energies in the alcohol group 37 for methanol, ethanol, and n-butanol, quantum calculations of the abovementioned reaction rates in these alcohols agree within 40% of one another 34,38. 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 good estimate for the rate of Reaction (1b). Using this rate 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 BR 1 equal to 0.96 is calculated with an uncertainty of ± 3%, as shown in Figure 8. Despite an uncertainty estimate of a factor of four on in the rate of Reaction (1b); BR 1 can be calculated accurately because the relatively large measured value of the overall tert-butanol + OH reaction rate combined with slow rate estimate of Reaction (1b) requires that the vast majority of H-atom abstraction by OH in tert-butanol proceeds via Reaction (1a). 9

10 K 1000 K 909 K 0.9 BR Measurement Sarathy et al. (2012) Grana et al. (2010) Van Geem et al. (2010) Moss et al. (2008) /T [K -1 ] Figure 8: Comparison of the estimated branching ratio BR 1 with values used in mechanisms from the literature. Using the above estimate of BR 1, BR 2 is calculated from the measurement of BR 1 BR 2. As shown in Figure 9, the probability of the tert-c 4 H 8 OH radical undergoing β-scission through Reaction (1a) 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 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 BR 2 ranging from 0.09 to 0.98, as shown in Figure K 1000 K 909 K 0.8 BR Measurement Sarathy et al. (2012) Grana et al. (2010) Van Geem et al. (2010) Moss et al. (2008) /T [K -1 ] Figure 9: Comparison of the inferred branching ratio BR 2 near 1.1 atm with values used in mechanisms from the literature. The Moss et al. 1 and Sarathy et al. 10,11 mechanisms provide reasonable estimates of BR 2, compared to the inferred value. However, it must be noted that these mechanisms present rate constant expressions for Reactions (2a) and (2b) that were estimated at the high-pressure-limit. At the conditions studied, depending on the relative falloff behavior of these reactions, BR 2 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 reactions in alkanes and ethers. Evans-Polanyi type correlations using enthalpies obtained from THERGAS 39 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 are written in the exothermic addition direction, which is the reverse of how these reactions proceed and are written in this study. In the Sarathy et al. 10,11 mechanism the rate constant for the reverse of Reaction (2a) is assumed to be equal to the high-pressure-limit of the addition of OH to n-butene 40. The reverse rate constant for Reaction (2b) is assumed to be equal to that of the addition of CH 3 to iso-butene

11 As shown in Figure 9, calculations of BR 2 using the Van Geem et al. 36 mechanism, which are based on RMG estimates, predict a value of BR 2 which is significantly below the lower bound imposed by measurements of BR 1 BR 2. Calculations of BR 2 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 CH 3 and (CH 3 ) 2 CO (acetone), instead of CH 3 and CH 3 CH 2 COH. However, since CH 3 CH 2 COH is expected to isomerize rapidly to (CH 3 ) 2 CO, the non-oh-producing β-scission pathway of the tert-c 4 H 8 OH radical in this mechanism is expected to be an accurate representation of Reaction (2b). 6. 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-c 4 H 8 OH radical, were measured behind reflected shock waves in a shock tube. The overall rate constant measurement demonstrates the utility of using isotopic labeling of 18 O 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 pseudo-first-order decay rate of 16 OH radicals that react with tert-butan 18 ol are largely sensitive to the overall tert-butanol + OH rate constant. The branching ratio measurement for the tert-c 4 H 8 OH radical represents a unique measurement of the decomposition of organic radicals at high temperatures using a novel method exploiting isotopic labeling of 18 O in the alcohol group of tert-butanol. Comparisons of the measured pseudo-first-order decay rates of 16 OH in the presence of tert-butan 16 ol with those in the presence of tert-butan 18 ol are used to calculate the branching ratio for the β-scission pathways of the tert-c 4 H 8 OH radical. To the authors knowledge, this is the first instance that isotopic substitution and narrow-linewidth laser absorption have been used for high-temperature reaction rate constant measurements behind reflected shock waves. 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. 11

12 References (1) Moss, J. T.; Berkowitz, A. M.; Oehlschlaeger, M. A.; Biet, J.; Warth, V.; Glaude, P.-A.; Battin-Leclerc, F. J. Phys. Chem. A 2008, 112, (2) Stranic, I.; Chase, D. P.; Harmon, J. T.; Yang, S.; Davidson, D. F.; Hanson, R. K. Combust. Flame 2012, 159, (3) Choudhury, T. K.; Lin, C.; Lin, C. Y.; Sanders, W. A. Comb. Sci. Tech. 1990, 71, (4) Tsang, W. J. Chem. Phys 1964, 40, (5) Lewis, D.; Keil, M.; Sarr, M. J. Am. Chem. Soc. 1974, 94, (6) Dorko, E. A.; Mcghee, D. B.; Painter, C. E.; Caponecchi, A. J.; Crossley, R. W. J. Phys. Chem. 1971, 75, (7) Cai, J.; Zhang, L.; Yang, J.; Li, Y.; Zhao, L.; Qi, F. Energy 2012, 43, (8) Gu, X.; Li, Q.; Huang, Z.; Zhang, N. Energy Conv. Manag. 2011, 52, (9) Lefkowitz, J. K.; Heyne, J. S.; Won, S. H.; Dooley, S.; Kim, H. H.; Haas, F. M.; Jahangirian, S.; Dryer, F. L.; Ju, Y. Combust. Flame 2012, 159, (10) Sarathy, S. M.; Vranckx, S.; Yasunaga, K.; Mehl, M.; Oßwald, P.; Metcalfe, W. K.; Westbrook, C. K.; Pitz, W. J.; Kohse-Höinghaus, K.; Fernandes, R. X.; Curran, H. J. Combust. Flame 2012, 159, (11) Yasunaga, K.; Mikajiri, T.; Sarathy, S. M.; Koike, T.; Gillespie, F.; Nagy, T.; Simmie, J. M.; Curran, H. J. Combust. Flame 2012, 159, (12) Van Geem, K. M.; Pyl, S. P.; Marin, G. B.; Harper, M. R.; Green, W. H. Ind. Eng. Chem. Res. 2010, 49, (13) Grana, R.; Frassoldati, A.; Faravelli, T.; Niemann, U.; Ranzi, E.; Seiser, R.; Cattolica, R.; Seshadri, K. Combust. Flame 2010, 157, (14) Cox, R. A.; Goldstone, A. Physico-chemical behaviour of atmospheric pollutants: proceedings of the fourth European symposium 1982, 2, (15) Wu, H.; Mu, Y.; Zhang, X.; Jiang, G. Int. J. Chem. Kinet. 2003, 35, (16) Wallington, T. J.; Dagaut, P.; Liu, R.; Kurylo, M. J. Env. Sci. Tech. 1988, 22, (17) Teton, S.; Mellouki, A.; Le Bras, G. Int. J. Chem. Kinet. 1996, 28, (18) Saunders, S. M.; Baulch, D. L.; Cooke, K. M.; Pilling, M. J.; Smurthwaite, P. I. Int. J. Chem. Kinet. 1994, 26, (19) Hess, W. P.; Tully, F. P. Chem. Phys. Let. 1988, 152, (20) Vasu, S. S.; Davidson, D. F.; Hanson, R. K.; Golden, D. M. Chem. Phys. Let. 2010, 497,

13 (21) Pang, G. A.; Hanson, R. K.; Golden, D. M.; Bowman, C. T. J. Phys. Chem. A 2012, 116, (22) Pang, G. A.; Hanson, R. K.; Golden, D. M.; Bowman, C. T. J. Phys. Chem. A 2012, 116, (23) Pang, G. A.; Hanson, R. K.; Golden, D. M.; Bowman, C. T. J. Phys. Chem. A 2012, 116, (24) Sivaramakrishnan, R.; Su, M.-C.; Michael, J. V; Klippenstein, S. J.; Harding, L. B.; Ruscic, B. J. Phys. Chem. A 2010, 114, (25) Dunlop, J. R.; Tully, F. P. J. Phys. Chem. 1993, 97, (26) Carr, S. A.; Blitz, M. A.; Seakins, P. W. J. Phys. Chem. A 2011, 115, (27) Oehlschlaeger, M. A.; Davidson, D. F.; Hanson, R. K. J. Phys. Chem. A 2004, 108, (28) Pang, G. A.; Hanson, R. K.; Golden, D. M.; Bowman, C. T. Z. Phys. Chem. 2011, 225, (29) Herbon, J. T.; Hanson, R. K.; Golden, D. M.; Bowman, C. T. Proc. Comb. Inst. 2002, 29, (30) Herbon, J. T. Shock Tube Measurement of CH3+O2 Kinetics and the Heat of Formation of the OH Radical, Stanford University, 2004, pp (31) Cheung, A. S.-C.; Chan, C. M.-T.; Sze, N. S.-K. J. Molec. Spec. 1995, 174, (32) Buda, F.; Bounaceur, R.; Warth, V.; Glaude, P. A.; Fournet, R.; Battin-Leclerc, F. Combust. Flame 2005, 142, (33) Luo, Y.-R. Comprehensive Handbook of Chemical Bond Energies; 1st ed.; CRC Press: Boca Raton, FL, 2007; p (34) Zhou, C.-W.; Simmie, J. M.; Curran, H. J. Combust. Flame 2011, 158, (35) Ranzi, E.; Dente, M.; Faravelli, T.; Pennati, G. Comb. Sci. Tech. 1993, 95, (36) Green, W. G.; Allen, J. W.; Ashcraft, R. M.; Beran, G. J.; Goldsmith, C. F.; Harper, M. R.; Jalan, A.; Magoon, G. R.; Matheu, D. M.; Petway, S.; Raman, S.; Sharma, S.; Van Geem, K. M.; Song, J.; Wen, J.; West, R. G.; Wong, A.; Wong, H.-W.; Yelvington, P. E.; Yu, J. RMG - Reaction Mechanism Generator (37) DeTuri, V. F.; Ervin, K. M. J. Phys. Chem. A 1999, 103, (38) Xu, S.; Lin, M. C. Proc. Comb. Inst. 2007, 31, (39) Muller, C.; Michel, V.; Scacchi, G.; M., C. G. J. Chim. Phys. 1995, 92, (40) Black, G.; Curran, H. J.; Pichon, S.; Simmie, J. M.; Zhukov, V. Combust. Flame 2010, 157, (41) Curran, H. J. Int. J. Chem. Kinet. 2006, 38,