Experimental Determination of the High-Temperature Rate Constant

Article pubs.acs.org/JPCA

Experimental Determination of the High-Temperature Rate Constant for the Reaction of OH with sec-Butanol Genny A. Pang,* Ronald K. Hanson, David M. Golden, and Craig T. Bowman Department of Mechanical Engineering, Stanford University, Stanford, California 94305, United States ABSTRACT: The overall rate constant for the reaction of OH with secbutanol [CH3CH(OH)CH2CH3] was determined from measurements of the near-first-order OH decay in shock-heated mixtures of tert-butylhydroperoxide (as a fast source of OH) with sec-butanol in excess. Three kinetic mechanisms from the literature describing sec-butanol combustion were used to examine the sensitivity of the rate constant determination to secondary kinetics. The overall rate constant determined can be described by the Arrhenius expression 6.97 × 10−11 exp(−1550/T[K]) cm3 molecule−1 s−1, valid over the temperature range of 888−1178 K. Uncertainty bounds of ±30% were found to adequately account for the uncertainty in secondary kinetics. To our knowledge, the current data represent the first efforts toward an experimentally determined rate constant for the overall reaction of OH with secbutanol at combustion-relevant temperatures. A rate constant predicted using a structure−activity relationship from the literature was compared to the current data and previous rate constant measurements for the title reaction at atmosphericrelevant temperatures. The structure−activity relationship was found to be unable to correctly predict the measured rate constant at all temperatures where experimental data exist. We found that the three-parameter fit of 4.95 × 10−20T2.66 exp(+1123/T[K]) cm3 molecule−1 s−1 better describes the overall rate constant for the reaction of OH with sec-butanol from 263 to 1178 K.

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INTRODUCTION

The overall rate constant for reaction 1 can be experimentally determined from measurements of OH time histories in shock-heated mixtures of a OH precursor with sec-butanol in excess; this procedure is equivalent to the procedure used in our previous works on the rate constants for reactions of OH with n-butanol and iso-butanol.2,3 Similar to the reaction pathways possible in the subsequent kinetics following reactions of OH with n-butanol and iso-butanol, the five isomers of the C4H9O radical produced from reaction 1 will react via β-scission reactions and isomerization reactions, and several of these pathways can lead to secondary OH-forming reactions. Therefore, kinetic modeling is required in the determination of the overall rate constant for reaction 1 from the experimental data. Cleavage at C−C and C−O bonds are the dominant channels for the β-scission reactions (cleavage at C−H bonds will occur to a lesser extent), and the dominant isomerization reactions are the ones proceeding through a five-membered-ring transition state. Figure 1 illustrates the dominant reactions occurring subsequent to reaction 1. Reactions 2a and 3a are secondary OH-generating reactions that will occur, and thus, the determination of the rate constant for reaction 1 from a measured pseudo-first-order OH decay will be complicated by these reactions and any non-OHproducing competing reaction channels, such as reactions 2b, 2c, and 3b.

The sec-butanol isomer of butanol (also known as 2-butanol) can be produced from glucose through a process involving fermentation and other chemical processes.1 Thus, sec-butanol has the potential to become an important component of commercially produced biobutanol, and the kinetics of the hightemperature oxidation of sec-butanol is of interest for developing kinetic models of biobutanol combustion. The reaction of OH with sec-butanol is an important reaction pathway in a kinetic mechanism for sec-butanol combustion. This reaction can occur through five different reaction channels. CH3CH(OH)CH 2CH3 + OH → CH 2CH(OH)CH 2CH3 + H 2O

(1a)

→ CH3C(OH)CH 2CH3 + H 2O

(1b)

→ CH3CH(OH)CHCH3 + H 2O

(1c)

→ CH3CH(OH)CH 2CH 2 + H 2O

(1d)

→ CH3CH(O)CH 2CH3 + H 2O

(1e)

We will refer to the overall reaction of OH with sec-butanol, including all product channels, as reaction 1; the individual reaction channels will be referred to as reactions 1a−1e. Similar nomenclature will be used to discuss other overall reactions and individual reaction channels. © 2012 American Chemical Society

Received: July 13, 2012 Revised: August 31, 2012 Published: September 4, 2012 9607

dx.doi.org/10.1021/jp306977e | J. Phys. Chem. A 2012, 116, 9607−9613

The Journal of Physical Chemistry A

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Figure 1. Dominant reaction pathways of sec-butanol after reaction with OH. OH-consuming reactions are shown with red arrows, and OH-producing reactions are shown with green arrows.

CH 2CH(OH)CH 2CH3 → 1‐C4H8 + OH → CH 2CHOH + C2H5

(2b)

→ CH3CH(OH)CH 2CH 2

(2c)

CH3CH(OH)CHCH3 → 2‐C4H8 + OH

This paper presents the results of OH time history measurements in shock tube experiments of mixtures of tertbutylhydroperoxide (TBHP), as a fast source of OH, with secbutanol in excess. Three kinetic mechanisms from the literature are used to analyze the OH time history measurements, and an overall rate constant for reaction 1 is determined. The sensitivity of the rate constant determination to secondary chemistry is also discussed.

(2a)

(3a)

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→ CH3CHCHOH + CH3 (3b)

The experimental details are identical to those described in our previous works;2,3,8 thus, only a brief description will be given. All experiments were performed in the Stanford Kinetics Shock Tube facility. The test mixtures were prepared manometrically in a 12 L stainless steel mixing tank using anhydrous 99.5% sec-butanol (2-butanol) and tert-butylhydroperoxide solution 70% by weight in water, each from Sigma Aldrich, and 99.998% purity argon gas from Praxair as the mixture diluent. Two test mixtures were prepared, with mixture compositions of 151 ppm sec-butanol with nominally 14 ppm TBHP and 214 ppm sec-butanol with nominally 14 ppm TBHP. Temperatures of 888−1178 K at pressures near 1 atm were generated behind reflected shock waves in the shock tube facility. The OH time history was monitored in the reflected shock experiments using a laser system that output ultraviolet laser light at 306.7 nm, specifically tuned to the peak of the R1(5) absorption line in the OH A-X(0,0) band. This laser system consisted of a Coherent Verdi 532 nm solid-state laser used to pump a Spectra Physics 380 ring dye cavity with a temperaturetuned intracavity frequency-doubling crystal. The continuouswave laser light at 306.7 nm was passed through the shock tube, and incident and transmitted laser intensities were monitored at a sample rate of 1 MHz. Common-mode rejection was employed, and time-resolved OH time history measurements could be determined using the Beer−Lambert Law with an estimated measurement accuracy of ±3% in OH mole fraction. The absorption coefficient for OH was taken from the work of Herbon et al.9

Formation of the CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals that can lead to secondary OH-producing reactions can also occur through hydrogen abstraction from secbutanol by hydrogen radicals that are eventually produced from subsequent decomposition of the isomers of the C4H9O radicals. The hydrogen abstraction from sec-butanol by hydrogen radicals can occur through five different pathways, as described by reactions 4a−4e. CH3CH(OH)CH 2CH3 + H → CH 2CH(OH)CH 2CH3 + H 2

(4a)

→ CH3C(OH)CH 2CH3 + H 2

(4b)

→ CH3CH(OH)CHCH3 + H 2

(4c)

→ CH3CH(OH)CH 2CH 2 + H 2

(4d)

→ CH3CH(O)CH 2CH3 + H 2

(4e)

EXPERIMENTAL SECTION

Detailed kinetic mechanisms containing reactions describing the global oxidation of sec-butanol have been developed by several research groups; these include the mechanisms described in the works of Moss et al.,4 Frassoldati et al.,5 Hansen et al.,6 and Sarathy et al.7 These mechanisms contain rate constants for secondary reactions occurring subsequent to reaction 1 and can be used in the analysis to determine the rate constant for reaction 1 from measured OH time histories in shock-heated mixtures of a OH precursor with sec-butanol in excess. 9608



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Table 1. Reactions Added and Rate Constants Determined in Our Previous Work8 Used in the “TBHP-Modified” Kinetic Mechanisms of sec-Butanol to Correctly Describe the OH Behavior in Experiments with TBHPa no.

reaction

A[b]

m

E [K]

ref

5 6 7a 7b 8 9

(CH3)3COOH → (CH3)3CO + OH (CH3)3CO → CH3 + CH3COCH3 (CH3)3COOH + OH → (CH3)3C + H2O + O2 (CH3)3COOH + OH → (CH3)2CCH2 + H2O + HO2 CH3 + OH → CH2(s) + H2O CH3COCH3 + OH → CH2COCH3 + H2O

3.57 × 10+13 1.26 × 10+14 3.82 × 10−11 4.13 × 10−11 2.74 × 10−11 4.90 × 10−11

0.0 0.0 0.0 0.0 0.0 0.0

1.80 × 104 7.70 × 103 2.63 × 103 1.37 × 103 0.00 2.31 × 103

Pang et al.8 Choo and Benson10 Hong et al.12 Sivaramakrishnan and Michael11 Pang et al.8 Vasudevan et al.13

a

Rate constants are given in the form k = A·Tm exp(−E/T). bThe units of A are cm3 molecule−1 s−1 for bimolecular reactions and s−1 for unimolecular reactions.

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SECONDARY REACTION PATHWAY MODELING As shown in Figure 1, reactions 2a and 3a are secondary OH-generating reactions that will occur subsequent to reactions 1a and 1c, respectively. Therefore, simulated OH time histories using a sec-butanol detailed kinetic mechanism are expected to be sensitive to the fractional amount of reaction 1 that proceeds via reactions 1a and 1c; this can be described by the branching ratios k1a/k1 and k1c/k1, where ki is the rate constant for reaction i (therefore, k1 is the total sum of k1a through k1e). Furthermore, reactions 2b and 2c are non-OH-producing reactions competing with reaction 2a as a decomposition pathway for the CH2CH(OH)CH2CH3 radical, and reaction 3b is a non-OH-producing reaction competing with reaction 3a as a decomposition pathway for the CH3CH(OH)CHCH3 radical. Thus, simulated OH time histories are also expected to be sensitive to the branching ratios k2a/k2 and k3a/k3. Values for these branching ratios are necessary to determine the rate constant for reaction 1 from the experimental data presented in this paper. Detailed kinetic mechanisms describing sec-butanol combustion, such as those by Frassoldati et al.,5 Hansen et al.,6 and Sarathy et al.,7 can be used to account for secondary reaction pathways. Each of these mechanisms can be modified to include tert-butylhydroperoxide (TBHP) chemistry by adding reactions 5−7 using the rate constants determined in our previous work.8 (CH3)3 COOH → (CH3)3 CO + OH

(5)

(CH3)3 CO → CH3 + CH3COCH3

(6)

(CH3)3 COOH + OH → (CH3)3 C + H 2O + O2

(7a)

→ (CH3)2 CCH 2 + H 2O + HO2

Figure 2. OH sensitivity analysis of the 214 ppm sec-butanol and 14 ppm TBHP mixture at 969 K and 1.15 atm using the TBHP-modified Sarathy et al.7 mechanism.

literature with the additions and modifications of the reactions and rate constants in Table 1. Figure 2 presents the results of a OH sensitivity analysis of the TBHP-modified Sarathy et al.7 mechanism under typical experimental conditions. OH sensitivity is defined by SOH, i =

where SOH,i is the time-dependent OH sensitivity to the rate constant for reaction i, xOH is the local time OH mole fraction, and ki is the rate constant for reaction i. Except for at very short times, the rate constant for reaction 1 dominates the OH sensitivity; however, reactions 3a, 3b, 4c, and 8, among others, are shown to influence the simulated OH time history, as would be expected from examination of the reaction pathways in Figure 1. The secondary reactions appearing in the OH sensitivity analysis support conclusions suggesting the importance of the branching ratios k1a/k1, k1c/k1, k2a/k2, and k3a/k3 in the simulated OH time history. Similar OH sensitivity analysis results are generated with the TBHP-modified Frassoldati et al.5 and Hansen et al.6 mechanisms. To our knowledge, no studies have focused directly on any of the branching ratios important in simulating the OH time history under the current experimental conditions. However, each detailed mechanism contains estimated rate constants for the reactions needed to calculate the branching ratios. Figure 3 illustrates the branching ratios k1a/k1 and k1c/k1 at 969 K as described by the mechanisms of Frassoldati et al.,5 Hansen et al.,6 and Sarathy et al.7 These three mechanisms show reasonable agreement on the branching ratios for k1a/k1 and k1c/k1. The branching ratios k2a/k2 and k3a/k3 calculated at 969 K from the

(7b)

Furthermore, if the rate constants for reactions 8 and 9 in each of the mechanisms are updated with the respective values from our previous work,8 the mechanisms correctly predict the OH time history behavior associated with the decomposition of TBHP. CH3 + OH → CH 2(s) + H 2O

(8)

CH3COCH3 + OH → CH 2COCH3 + H 2O

(9)

∂xOH ki · ∂ki xOH

Table 1 lists the reactions that are important in correctly simulating the OH behavior due to the presence of TBHP. Also listed are the rate constants for these reactions that were needed to accurately simulate the OH time histories of the TBHP decomposition data in our previous work;8 these rate constants were measured in our previous work8 or taken from other literature sources.10−13 In this paper, we will use the term “TBHP-modified” to describe a sec-butanol mechanism from the 9609



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TBHP and water, where only the liquid composition of the solution was known. At temperatures below 1000 K, the initial TBHP mole fraction was assumed to be equivalent to the inferred initial TBHP mole fraction from an experiment above 1000 K using the same mixture. In the model simulations, an initial water mole fraction was prescribed to be the difference between the initial TBHP mole fraction and the mole fraction of TBHP/water solution vapor originally introduced into the mixture; model simulations show that the presence of water has a negligible effect on the results; thus, this was included in the simulations solely for completeness. Further discussion of the procedure used for determining the initial mole fraction of TBHP for similar types of experiments is presented in a previous work.8

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OH TIME HISTORIES AND RATE CONSTANT DETERMINATION A representative measured OH time history at 969 K is shown in Figure 5 with the simulated OH time history from the TBHPmodified mechanism of Sarathy et al.7 with the value of the rate constant for reaction 1 that leads to the best fit to the measured trace (k1 = 1.25 × 10−11 cm3 molecule−1 s−1). Also shown are simulations using perturbations of the best-fit rate constant for reaction 1 by ±30%, illustrating the sensitivity of the simulated OH decay rate to the rate constant. While a rate constant of k1 = 1.25 × 10−11 cm3 molecule−1 s−1 in the TBHP-modified Sarathy et al.7 mechanism leads to a simulated OH time history that shows an excellent fit to the data at 969 K, a value of k1 = 1.88 × 10−11 cm3 molecule−1 s−1 is needed in the TBHP-modified Hansen et al.6 mechanism to generate a simulated OH time history that matches the experimental data. Thus, the determination of the rate constant for reaction 1 from the experimental data is mechanismdependent, indicating differences in the modeling of secondary reactions. Figure 6 presents an Arrhenius plot of the mechanismdependent rate constant determined for reaction 1 from the experimental data; the figure illustrates the sensitivity of the inferred value of the rate constant for reaction 1 to the kinetic mechanism used for analysis. Table 2 presents a list of the inferred rate constants for each experimental data point from all three mechanisms. The peak-to-peak discrepancy of the inferred value of k1 using the different mechanisms is approximately a factor of 0.5, with the rate constant inferred using the TBHPmodified Frassoldati et al.5 mechanism as the slowest and the rate constant inferred using the TBHP-modified Hansen et al.6 mechanism as the fastest. The analysis using the TBHP-modified Sarathy et al.7 mechanism results in rate constant determinations that are very similar to those determined using the TBHPmodified Frassoldati et al.5 mechanism. The rate constant determination dependence on the mechanism is not surprising given that the mechanisms predict different branching pathways for the CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals, as illustrated by Figure 4. The mechanisms of Frassoldati et al.5 and Sarathy et al.7 both ascribe rate constants for the channels of reactions 2 and 3 that predict the non-OH-forming decomposition/isomerization reaction channels of the CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals to be dominant. Therefore, the majority of the decay in simulated OH time histories using the TBHP-modified mechanisms of Frassoldati et al. and Sarathy et al. is caused by reaction 1. In the Hansen et al.6 mechanism, however, the rate constants for the channels of reactions 2 and 3 describe reaction pathways indicating that the CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals will react primarily through

Figure 3. Branching ratios for reactions 1a−1e as suggested by the detailed mechanisms of Frassoldati et al.,5 Hansen et al.,6 and Sarathy et al.7 The thickness of each arrow illustrates the relative rates of each reaction channel.

three mechanisms are shown in Figure 4. The relative amounts of OH regeneration subsequent to the formation of the CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals do not reach agreed-upon values when comparing the predicted branching ratios from the three mechanisms. TBHP-modified versions of the Frassoldati et al.,5 Hansen et al.,6 and Sarathy et al.7 mechanisms are used for the analysis of the measured OH time histories reported in this paper. These three mechanisms will each be used to determine the rate constant for reaction 1 from the experimental data, and from the results, we will explore the sensitivity of the determination of the rate constant for reaction 1 to secondary chemistry. The rate constant for reaction 1 is inferred at the conditions of each measured data trace using a kinetic mechanism by adjusting the rate constant for reaction 1 in the mechanism to generate a simulated OH time history that fits the experimental data. In the analyses, the branching ratios for reactions 1a−1e (i.e., k1a/k1, etc.) suggested by each mechanism are preserved, as well as the rate constants for all secondary reactions. In this study, all simulations and analyses of the TBHPmodified mechanisms were performed using the CHEMKINPRO suite of programs by Reaction Design, and constant internal energy and constant volume constraints were assumed. The initial TBHP mole fraction used in the model simulations was inferred directly from the initial OH mole fraction measured in experiments for temperatures greater than 1000 K; this was done because the mixture was prepared from a vapor of a solution of 9610



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Figure 4. Branching ratios for the consumption of the CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals as suggested by the detailed mechanisms of Frassoldati et al.,5 Hansen et al.,6 and Sarathy et al.7 The thickness of each arrow illustrates the relative rates of each reaction channel.

Figure 6. Arrhenius plot of k1 determined using three different TBHPmodified kinetic mechanisms for sec-butanol from the literature.5−7 Individual points (squares) are shown for the rate constant determination for each individual data point using the TBHP-modified Sarathy et al.7 mechanism, along with a fit to the data points. For clarity, only the fits to the rate constant determinations using the TBHP-modified Frassoldati et al.5 and Hansen et al.6 mechanisms are shown. The average value of the rate constant determinations at the high- and low-temperature point are shown (stars) with ±30% uncertainty bounds (the fit of the average is shown in Figure 7). Also shown (dotted lines) are the original values for k1 in the Frassoldati et al. and Sarathy et al. mechanisms (the original k1 from the Hansen et al. mechanism does not fit on the scale of this figure).

Figure 5. Measured OH time history for the experiment at 969 K and 1.15 atm with 214 ppm sec-butanol and 14 ppm TBHP. Also shown are simulated OH time histories using the TBHP-modified mechanism of Sarathy et al.7 with the best-fit value of k1 and perturbations of ±30% on the best-fit value of k1.

OH-producing channels. This leads to simulated OH regeneration, and thus, a faster value for k1 is needed to simulate a OH time history to match the same measured OH data trace. Reactions 2a, 2b, 2c, 3a, and 3b are obviously important secondary reactions in the analysis of the current data. However, to our knowledge, neither the rate constants for these reactions nor the branching ratios of interest have been critically studied under the current experimental conditions. Therefore, the secondary chemistry described by these reactions from the different mechanisms will be assumed to represent the approximate bounds of uncertainty in the rate constant determination.

The overall rate constant for reaction 1 can be described by the Arrhenius expression ⎛ 1550 ⎞ 3 −1 −1 k1av. = 6.97 × 10−11 exp⎜ − ⎟ cm molecule s ⎝ T[K] ⎠ 9611



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Table 2. Values for k1 Determined for Each Experimental Data Point Using the TBHP-Modified Mechanisms of Frassoldati et al.,5 Hansen et al.,6 and Sarathy et al.7 a mixture 151 ppm sec-butanol, 15 ppm TBHP

214 ppm sec-butanol, 14 ppm TBHP

T [K] 1112 1032 977 1178 1144 1118 969 939 888

P [atm] 1.03 1.09 1.10 0.95 0.99 1.00 1.15 1.15 1.24

k1 Frassoldati et al. −11

1.41 × 10 1.33 × 10−11 1.28 × 10−11 1.58 × 10−11 1.54 × 10−11 1.41 × 10−11 1.25 × 10−11 1.13 × 10−11 1.08 × 10−11

k1 Hansen et al. −11

2.24 × 10 1.99 × 10−11 1.91 × 10−11 2.50 × 10−11 2.41 × 10−11 2.24 × 10−11 1.88 × 10−11 1.74 × 10−11 1.58 × 10−11

k1 Sarathy et al. −11

1.58 × 10 1.33 × 10−11 1.28 × 10−11 1.74 × 10−11 1.66 × 10−11 1.58 × 10−11 1.25 × 10−11 1.16 × 10−11 1.08 × 10−11

kav. 1 1.71 × 10−11 1.52 × 10−11 1.46 × 10−11 1.90 × 10−11 1.83 × 10−11 1.71 × 10−11 1.43 × 10−11 1.32 × 10−11 1.22 × 10−11

a av. Also listed is kav. 1 , where ln(k1 ) was taken to be the average of the three ln(k1) values determined from each mechanism determination at each temperature point. All rate constants are in units of cm3 molecule−1 s−1.

with uncertainty limits of ±30%, valid from 888 to 1178 K. This Arrhenius expression was determined using a linear least-squares av. fit to ln(kav. 1 ) versus 1/T, where ln(k1 ) at each temperature was taken to be the average of the three ln(k1) values determined from each mechanism for each data point. The uncertainty limit of ±30% accounts for the uncertainty in the secondary chemistry within the analysis; this uncertainty is larger than the experimental errors (by a factor of 3) and thus approximately represents the overall uncertainty of k 1 , including all experimental and modeling errors. This averaged value for k1 is listed in Table 2 for each data point and shown in Figure 7.

Sarathy et al. mechanism is within 10% of their original rate constant value; therefore, the Sarathy et al. mechanism best simulates the current measured OH time histories. The Frassoldati et al.5 mechanism also appears to be capable of simulating OH time histories in reasonable agreement with the current data as their original rate constant for reaction 1 is within 25% of the experimentally determined rate constant using the secondary chemistry from their mechanism. The Hansen et al.6 mechanism uses a value for k1 that is an order of magnitude slower than all of the experimentally determined rate constant values. Therefore, OH time histories simulated using the Hansen et al. mechanism will provide poor agreement with the current data, and the simulated OH time histories using that mechanism will predict OH decays much slower than the presented measurement traces. While the value of k1 in the Hansen et al. mechanism appears to be incorrect, we cannot find any compelling evidence to suspect that the rate constants for reactions 2a, 2b, 2c, 3a, and 3b (important secondary reactions in the analysis of the current data) in their mechanism are subject to the same degree of inaccuracy. Therefore, the value for k1 determined from the current data using the secondary chemistry in the Hansen et al. mechanism could be a reasonably accurate evaluation of the actual rate constant, and using this rate constant determination in the Hansen et al. mechanism would significantly improve the accuracy of their kinetic mechanism. While comparison of the original k1 value used in a mechanism with the experimentally determined rate constant using the same mechanism can illustrate the performance of a mechanism, no insight can be gained on the accuracy of any specific rate constants. This is because of the number of important secondary reactions involved in the simulation of the OH time history, as illustrated by the OH sensitivity analysis shown in Figure 2. Excellent performance of a mechanism could indicate the use of accurate rate constants for all reactions appearing in the OH sensitivity analysis; however, such performance could also be due to errors in rate constants fortuitously canceling out. Therefore, further studies into the important branching ratios discussed in this paper are necessary to develop detailed sec-butanol kinetic mechanisms that are accurate over a wide range of conditions and experimental validation targets. Low-Temperature Rate Constants. The current determination of k1 can be compared with data presented in the literature14−16 for atmospheric-relevant temperatures (near 298 K). Figure 7 presents an Arrhenius plot of the current data (the current data represents the average of the rate constant for reaction 1 determined using the three mechanisms, where ln(kav. 1 ) was taken to be the average of the three ln(k1) values determined from each

Figure 7. Arrhenius plot of k1. The data from the current work is the average of the rate constants determined using the three mechanisms discussed in this work, and the uncertainty limits of ±30% encompass the mechanism dependence of the rate constant determination. Also shown are data at atmospheric-relevant temperatures14−16 and the rate constant estimated using the structure−activity relationship (SAR) of Atkinson and co-workers17−20 extrapolated to high temperatures.

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DISCUSSION Mechanism Performances. The performance of a reaction mechanism can be evaluated by how well the experimentally determined k1 using a given mechanism matches the original rate constant used in that mechanism. Figure 6 shows the original k1 used in the Frassoldati et al.5 and Sarathy et al.7 mechanisms. The rate constant k1 from the Hansen et al.6 mechanism is not shown because it is over an order of magnitude slower than the data shown in Figure 6. The rate constant k1 determined from the experimental data using the secondary chemistry of the 9612



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in sec-butanol kinetics are recommended to develop a more accurate sec-butanol kinetic mechanism. The SAR of Atkinson and co-workers17−20 overpredicts both previously reported lowtemperature (near 298 K) measured rate constants for the reaction of OH with sec-butanol and also the current hightemperature rate constant determination. A three-parameter modified Arrhenius expression is presented that replicates both the current high-temperature rate constant data and the lowtemperature data from the literature.

mechanism determination at each temperature point) compared with recommendations for the overall rate constant from the literature from atmospheric-relevant studies. An empirical threeparameter fit of ⎛ 1123 ⎞ 3 −1 −1 k1 = 4.95 × 10−20T 2.66 exp⎜ + ⎟ cm molecule s ⎝ T[K] ⎠

best describes the data for the rate constant for reaction 1 over the temperature range of 263−1178 K. The low-temperature data exhibit a negative temperature dependence, similar to the temperature dependence observed in the data of the rate constant for the reaction of OH with iso-butanol.3 Therefore, the rate constant at low temperatures may be pressure- and bath-gas-dependent, and caution must be taken when applying the current expression for k1 at pressures outside of the range of the data presented in the literature14−16 for temperatures under ∼400 K. A temperature-dependent expression for k1 can also be estimated using the structure−activity relationship (SAR) of Atkinson and coworkers.17−20 This SAR was empirically developed for rate constants for similar reactions at atmospheric-relevant temperatures, and the SAR-predicted rate constant is also shown in Figure 7 for comparison with the data. Though the SAR was only developed using empirical data at atmospheric-relevant temperatures, we have found that the SAR-estimated rate constant for reactions of OH with alkanes and iso-butanol can be extrapolated accurately to temperatures up to near 1300 K.3,8 For the reaction of OH with sec-butanol, the rate constant predicted using the SAR method is ∼20% higher than the low-temperature data and also fails to predict the current determination of the high-temperature rate constant within the ∼30% uncertainty limit. Discrepancies of this sort between experimentally measured and SAR-estimated rate constants have been previously discovered in the literature for reactions of OH with alcohols.20,21 The most likely explanation is attributed to longrange effects with respect to hydrogen atom abstraction at sites remote from the substituent group due to the formation of a hydrogen-bonded complex;21 the SAR method considers only effects of the alcohol group on the alpha and beta carbon sites. Therefore, the three-parameter expression given above is recommended for a more accurate description for the rate constant for reaction 1.

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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 The authors gratefully acknowledge insightful conversations and experimental support from D. F. Davidson and I. Stranic from Stanford University. Helpful discussions regarding sec-butanol mechanisms with W. H. Green and S. S. Merchant from MIT are also acknowledged. This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, with Dr. Wade Sisk as contract monitor.

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REFERENCES

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CONCLUSIONS OH time histories were measured in shock-heated mixtures of tert-butylhydroperoxide (TBHP) with sec-butanol in excess, diluted in argon. A value for k1, the rate constant for the overall reaction of OH with sec-butanol, was determined by fitting simulated OH time histories from modified detailed mechanisms of sec-butanol combustion from the literature to the measured data, using the overall rate constant of interest as the free parameter. The k1 determination from the measured OH time histories was found to be mechanism-dependent, and analysis of the differences in three different mechanisms indicates that the reaction pathways of the CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals need to be better understood. An Arrhenius expression for k1 is suggested based on the current measurements, and a ±30% uncertainty is ascribed to account for the mechanism dependence of the rate constant determination. The measured OH time histories are best simulated using the mechanism of Sarathy et al.7 While this agreement could indicate the use of accurate rate constants for key reactions in this mechanism, the agreement could also be attributed to errors in rate constants canceling out in the simulation; therefore, further studies on the rate constants of important secondary reactions 9613


Experimental Determination of the High-Temperature Rate Constant

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