Rate coefficients for the reactions of OH with butanols from 298 K to temperatures relevant for low-temperature combustion

Rate coefficients for the reactions of OH with n, s, and iso-butanol have been measured over the temperature range 298 to ∼ 650 K. The rate coefficients display significant curvature over this temperature range and bridge the gap between previous low-temperature measurements with a negative temperature dependence and higher temperature shock tube measurements that have a positive temperature dependence. In combination with literature data, the following parameterizations are recommended: suggests that at temperatures of ∼ 1000 K, the OH yields, primarily from decomposition of β -hydroxyperoxy radicals, are ∼ 0.3 ( n -butanol), ∼ 0.3 ( s -butanol) and ∼ 0.2 (iso-butanol) with β -hydroxyperoxy decompositions generating OH, and a butene as the main products. The data suggest that decomposition of β hydroxyperoxy radicals predominantly occurs via OH elimination.


INTRODUCTION
The high-energy densities of liquid fuels is attractive, and in some cases essential, for transport and other applications. With careful production, liquid biofuels have the potential to reduce net CO 2 emissions 1-3 and oxygenated biofuels, such as ethanol, have additional benefits in reduced soot and NOx emissions. 4 Currently, primarily due to ease of manufacture, the major alcohol biofuel is ethanol, but butanols have advantages in terms of higher energy densities, better miscibility with fossil fuels in blends, and reduced corrosivity. 1,[5][6][7] Recent developments in engine technology such as homogeneous charge compression ignition (HCCI) and reaction-controlled compression ignition (RCCI) 8 have enhanced the focus on low-temperature combustion chemistry. [9][10][11] In HCCI and RCCI, auto-oxidation controls the ignition process and full optimization requires a detailed knowledge of the chemistry including the reaction kinetics of initiation processes, primarily reaction of the OH radical with the fuel.
There have been a number of studies of the reactions of OH with the butanols between 250 and 400 K (with a focus on atmospheric chemistry) and several shock tube studies, primarily by the Stanford group, at temperatures of 900-1200 K. [12][13][14][15] OH + CH 3 However, there are no experimental measurements in between these temperature regimes in the region most relevant for low-temperature combustion, as exemplified in Figure 1, that shows literature data on the reaction of OH with n-butanol (R1). Data from the low-temperature studies 16,17 seem to demonstrate some slight curvature and while curvature has been predicted by several theoretical calculations, [21][22][23][24][25] to link the low-and high-temperature data, 12 the agreement with experiment can be poor.
OH can abstract H atoms from various positions in the butanols, including from the O−H bond; the possibilities for n-butanol are as follows: OH + CH 3 There have been a few direct studies [26][27][28] on the branching ratios of (R1) that confirm (R1a) as the dominant product between 300 and 600 K. McGillen et al 16 combined literature end-product analysis and structure activity relationships (SAR) to estimate site-specific rate coefficients. Limited site-specific data exist for other alcohols, that also suggest that abstraction at the α position dominates at room temperature, but that the reactions become less specific as temperature increases. 29,30 While the focus of this work is on the determination of the overall rate coefficients, our data do give some insights into branching ratios. At high temperatures, there is potential for OH regeneration following abstraction at the β-position, for example, for n-butanol, (R1b) produces CH 3 CH 2 CHCH 2 OH that can decompose via two pathways: The shock-tube studies of Pang et al [12][13][14] and Stranic et al 15 were aware of this possibility, that is that measurements simply following the OH decay would be measuring the net rate of OH consumption. In the Pang et al studies, predictions of branching ratios and models of secondary chemistry were used to extract the total rate coefficient and in the study of Stranic et al isotopic labeling of the OH was used to ensure that the total rate coefficient was being measured. We will report on direct studies of OH regeneration in subsequent publications. Extending the direct McGillen et al. 16 Mu et al. 17 Pang et al. 12 Sarathy et al. 18 Atkinson SAR 19 Bethel etal. SAR 20 F I G U R E 1 Temperature dependence of k 1 (OH + n-butanol) prior to this work. The temperature parameterizations of both experimental data 12,16,17 and SAR [18][19][20] have been extended over the full range of temperature to emphasize the discrepancy between low and high-temperature data [Color figure can be viewed at wileyonlinelibrary.com] measurements of the rate coefficients allows some estimation of the validity of the indirect approach of Pang et al.
To summarize, the main objectives of this study are as follows: • to obtain rate coefficients on the reaction of OH with the four butanol isomers at temperatures relevant for lowtemperature combustion. This paper focuses primarily on n-, s-, and iso-butanol. Results on t-butanol will be presented, but a detailed consideration of the t-butanol system will be presented elsewhere. • to demonstrate that the low-and high-temperature rate coefficient data that have different temperature dependencies in some cases can be bridged, and • to provide more comprehensive datasets against which the demanding theoretical calculations can be tested. With only limited experimental data, such calculations are likely to be the main source of data on branching ratios.

EXPERIMENTAL
The reaction of the butanols with OH was studied as a function of temperature using the laser flash photolysislaser induced fluorescence method across the temperature range 298-715 K. The apparatus has been described in greater detail in previous studies. [31][32][33] The butanol reactants (all from Sigma-Aldrich), n-butanol, (≥99.4%), sbutanol (≥99.5%), i-butanol (≥99.0%) were made up into 10 L glass bulbs of alcohol diluted in nitrogen (N 2 , BOC, oxygen free, 99.99%). For experiments requiring higher concentrations of butanol, the reagent was introduced via a bubbler. A reservoir of liquid reagent was placed in the bubbler, pressurized with a backing pressure of nitrogen to roughly 2 bar, and a flow of nitrogen over the top of the liquid was used to introduce butanol to the reaction cell. The vapor pressure of the butanol reservoir within the delivery bubbler was calculated based on the temperature of the room (measured via thermocouple prior to each trace being taken), and the concentration of reagent within the bubbler was then calculated as a percentage of the measured total pressure of the bubbler. Conducting experiments at 298 K using both bubbler and bulb methods of each butanol delivery consecutively allowed for corrections to be made on the bubbler delivery concentration. This correction introduces an additional uncertainty (<5%) in the rate coefficients measured using this method of butanol delivery. The OH precursor (H 2 O 2, Sigma-Aldrich, 50% w/w in H 2 O), nitrogen bath gas, and butanol in nitrogen were flowed through calibrated mass flow controllers into a mixing manifold, before flowing into the six-way stainless steel reaction cell. When hydrogen peroxide makes contact with the metal inside of the mass flow controller, subsequent decomposition results in the delivery of some oxygen into the system. This is expected to be around 2.5 × 10 14 molecule cm −3 based on experiments conducted using the method described by Potter et al, 34 in which the residual oxygen present in the system is estimated based on the amount of OH recycled via O 2 -dependent low pressure well-skipping. However, experiments in which larger concentrations of oxygen (>10 16 molecule cm −3 ) were added showed no variation in rate coefficient in agreement with the work of McGillen et al. 16 The total gas flow was typically maintained around 1 or 2 L min −1 , for pressures of 30-40 or 85-90 Torr, respectively, to ensure a fresh sample of gas was used for each photolysis pulse. The pressure inside the reaction cell was maintained by a rotary pump throttled by a needle valve and monitored by a capacitance manometer. The reaction cell was heated by a series of cartridge heaters surrounding the cell, with the reaction cell temperature monitored by calibrated K-type thermocouples located near the reaction zone. Errors in the temperature, estimated by comparing the thermocouple readings around the reaction zone, were ±5 K at the lower end of the temperature range, rising to ±15 K at the highest temperatures.
OH radicals were generated by pulsed laser photolysis of hydrogen peroxide precursor (R6) in nitrogen buffer gas (N 2, BOC) at 248 nm using an excimer laser (KrF, Lambda Physik LPX 200), and monitored as a function of time by off-resonance laser-induced fluorescence. The photolysis laser fluence was measured prior to entrance into the reaction cell and was used to estimate the starting concentration of OH radicals produced during experiments. The laser repetition rate was typically 10 Hz (but was varied, between 2 and 10 Hz, with no impact on the measured rate coefficient), with a fluence of approximately 60-90 mJ cm −2 pulse −1 . This produces an approximate photon density of 1.1 × 10 17 photons cm −2 , generating an initial [OH] of ∼1 × 10 12 molecule cm −3 from an initial H 2 O 2 concentration of approximately 7 × 10 13 molecule cm -3 .
The probe laser was a frequency-doubled Nd: YAG (Continuum Powerlite 8010) pumped dye laser (Spectra Physics PDL-3), operating on Rhodamine-6-G dye. The transition A 2 Σ (v′ = 1) ← X 2 Π (v″ = 0) was probed at 282 nm, and fluorescence was detected at 308 nm using a photomultiplier tube (CPM, Perkin-Elmer, C1943P) with a 308 nm filter (308 ± 5 nm, Barr Associates), and was detected perpendicular to the intersection of the photolysis and probe laser beams. A digital oscilloscope collected and integrated the fluorescence signal, before being transferred to a personal computer for analysis.
A time-dependent profile of OH fluorescence was built up by varying the time between the photolysis pulse and the probe pulse using a delay generator. Each experimental trace generated typically contained 200 time points, with 20 prezero time points to allow for averaging of a pretrigger background signal to subsequently be removed from the experimental trace. Kinetic traces were averaged for between 5 and 12 traces depending on signal quality. Reactions were carried out under pseudo-first-order conditions in which [butanol] >> [OH] 0 . Under these conditions, the signal intensity S t at time t is proportional to the OH concentration [OH] t , and the time dependence of S t is given by where S 0 represents signal intensity at time zero when the photolysis pulse occurs and k′ is the pseudo-first-order rate coefficient related to the bimolecular rate coefficient, k bi , via Equation (2), where k bi represents the total bimolecular rate coefficient for the reaction of butanol with OH and k d represents other first-order loss processes for OH such as reaction with precursor and diffusive losses out of the observation region. Kinetic traces were fit using a nonlinear least squares fit to Equation (1) (Figure 2A). Bimolecular rate coefficients are calculated from the slope of a plot of these pseudo-first-order rate constants ′ 1 against varying concentration of butanol (E2), an example of which can be seen in Figure 2B. The intercept of the bimolecular reaction plot represents the k d parameter, that is measured experimentally via a kinetic trace in the absence of any butanol.

RESULTS AND DISCUSSION
Results and discussion are presented for each of the n-, s-, i-butanols followed by a brief intercomparison of all the butanols and how their rate coefficients and properties compare to other alcohols.

n-Butanol
Results for the reaction of OH with n-butanol are presented in Table 1 and Figure 3. The measured bimolecular rate coefficients were independent of OH precursor (most experiments were carried out with H 2 O 2 , but a few used a urea/H 2 O 2 , although this was found to deliver   16 where n-butanol deliver to the reaction chamber was monitored by both UV and IR spectroscopy, is likely to provide the most reliable comparison. Relative rate measurements should not be susceptible to the same uncertainties, but there will be a spread in values caused by uncertainties in the rate This Work 18 OH McGillen et al. 16 16 OH McGillen et al. 16 Mu et al. 17 Pang et al. 12 Sarathy et al. 18 Zhou et al. G3 22 Zhou et al. CCSD 22 Atkinson SAR 19 Bethel et al. SAR 20 Seal et al. 23 McGillen et al 16 reported a small isotope enhancement (∼10%) when they used 18 OH, suggesting that for n-butanol, there is a mechanism to recycle 16 OH. For alcohols, abstraction at the β-position followed by elimination of the hydroxyl group to form an alkene is the most obvious explanation; however, the effect persisted in the McGillen et al study even with the addition of large concentrations of O 2 that might be expected to intercept the β-hydroxyalkyl radical before OH elimination. Additionally, the effect appears to decrease with temperature in the McGillen et al study that seems to be incompatible with (R5a) as the source of the OH. No significant isotope effect was noted in our experiments when OD was used instead of OH. Figure 3 shows that our measurements show an upturn in k 1 linking the lower temperature values of Mu and Mellouki, 17 and McGillen et al 16 (negative temperature dependence) with the high-temperature, positive temperature dependence results of Pang et al. 12 Curvature of k 1 had been predicted by theoretical calculations, but quantitative agreement with experimental values has been mixed. The calculations of Zhou et al 22 are strongly dependent on the ab initio method used and limited to temperatures above 500 K. At 500 K, they overestimate our measured value and extrapolation below 500 K (that may not be valid) is in poor agreement with experimental data. The more recent calcu-lations of Seal et al 23 are in better agreement with experiment across the whole temperature range.
SARs are another way of predicting both total and site-selective rate coefficients. The original OH SAR of Atkinson 19 were known to perform badly for oxygenated species and were revised by Bethel et al. 20 The SAR of Bethel et al leads to an improved agreement at room temperature, but these relatively simple SAR are unable to capture the complex temperature dependence of the butanol systems. The branching ratios predicted by theoretical calculations and SAR differ significantly, and we return to this topic later in the discussion.
Combining the data of McGillen et al 16

s-Butanol
Temperature-dependent rate coefficients for the reaction of OH with s-butanol (k 2 ) are shown in Table 3 and Figure 4. Our values show a clear decrease in k 2 between 300 and 370 K, beyond this minimum in k 2 around 370-420 K, k 2 gradually increases with temperature.   This Work McGillen et al. 16 Jimenez et al. 41 Pang et al. 13 Sarathy et al. 18 Atkinson SAR 19 Bethel et al. SAR 20 Zheng et al. 24 Modified Pang et al. 13 Recommended fit   This Work McGillen et al. 16 Mellouki et al. 42 Pang et al. 14 Sarathy et al. 18 Atkinson SAR 19 Bethel et al. SAR 20 Zheng et al. 25

i-Butanol
Temperature-dependent rate coefficients for the reaction of OH with i-butanol (k 3 ) are shown in Table 5 and Figure 5.
Our values show a decrease in k 3 between 300 and 370 K, beyond this minimum in k 3 around 370-420 K, k 3 gradually increases with temperature. For i-butanol, both the negative and positive temperature dependencies are less pronounced than for s-butanol. Although there are slightly fewer studies for comparison, as detailed in Table 6, the agreement of the current work with the room temperature values, 38  The reaction has been studied theoretically most recently by Zheng et al 25 using ab initio calculations and transition state theory. As with the other calculations on reactions (1) and (2), the Truhlar group has demonstrated the impor-tance of a careful consideration of anharmonic factors in calculating site-specific rate coefficients with low or negative barriers. These calculations successfully predict the change from negative to positive temperature dependence for R1-R3.

t-Butanol
Details on the reaction of OH with t-butanol are in Sime 43 and will be presented in a subsequent paper that includes direct measurements of the β-hydroxyperoxy decomposition to regenerate OH. To allow comparisons on OH reactivity with other butanols, we summarize the temperature dependence of reaction 4 in Figure 6. In contrast to the other butanols, the room temperature rate coefficient is approximately an order of magnitude smaller and the temperature dependence above 300 K is entirely positive and there appears to be good agreement with the direct measurements on R4, obtained via isotope studies, by Stranic et al. 15 The above data on k 4 can be parameterized to give: This Work McGillen et al. 16 Stranic et al. 15 Wallington et al. 43 Sarathy et al. 18 Atkinson SAR 19 Kwok and Atkinson SAR 44 Bethel SAR 20

Comparison of rate coefficients, implications on branching ratios and the fate of β-hydroxyperoxy radicals
The most obvious difference between the overall rate coefficients of the butanols is that R4, the reaction of OH and t-butanol, is significantly smaller at room temperature, shows only a positive temperature dependence and that the positive temperature dependence is stronger than for the other butanols. This is entirely consistent with OH having to abstract from the relatively strong primary β C−H bonds or from the O−H bond. In contrast to most of the abstractions in the other butanols, these processes are predicted to have positive barriers.
Despite, having different numbers and types of α, β, γ, and δ C−H bonds, the room temperature rate coefficients of n, s, and i-butanol are remarkably similar. The limited product studies, predominantly at room temperature, suggest that abstraction at the α position dominates at 298 K, but the studies of Truhlar and coworkers [23][24][25] have emphasized that the way that barrier heights and anharmonicity effects combine to determine branching ratios is complex and branching ratios will change as a function of temperature. Further product studies are required, particularly at lower temperatures (∼200 to 300 K) where the studies of Truhlar and coworkers suggest that branching ratios should change substantially with α abstractions no longer dominating.
Although this work only determines total removal rate coefficients, comparison with the studies of Pang et al [12][13][14] do allow us to draw conclusions on β abstraction pathways and the fate of the resultant β-hydroxyperoxy radicals. As discussed in the Introduction, decomposition of the βhydroxyperoxy radical will be very rapid under shock tube conditions with a fraction of the decompositions regenerating OH. Pang et al were aware that they were only measuring the net OH removal rate and made use of modeling studies and calculations from other groups to generate the total removal rate coefficients.
Let us start by looking at the reaction of OH with i-butanol (R3). Here there is only a single β channel (abstraction at the tertiary C−H bond) and experimental, SAR, 20 evaluations, 16  Pang et al 14 were therefore able to accurately convert their net measurements of R3 into overall rate coefficients, and these values are in excellent agreement with the extrapolations of this work (where there is no significant β decomposition) as can be seen in Figure 5. This good agreement confirms the accuracy of the β branching ratio for the shock tube region.
The situation is quite different for s-butanol (R2). Examination of Figure 4 shows that our measured value of k 2 at ∼600 K is already equal to the proposed value of k 2 at ∼900 K. For the β-hydroxyperoxy arising from i-butanol OH regenerating was in competition with C−H bond cleavage that has a significantly higher barrier. However for the β-hydroxyperoxy arising from s-butanol, OH regeneration is in competition with C−C bond cleavage that has a lower barrier than C−H cleavage. Pang et al 13 modeled their overall k 2 based on modified models from Frassoldati et al, 46 Hansen et al, 47 and Sarathy et al. 18 Each of these models has a different branching ratio for β abstraction and deals differently with the decomposition of the resulting β-hydroxyperoxy radicals: There are several differences between the mechanisms. The Hansen et al mechanism uses a value for k 2 that is almost an order of magnitude too slow; however, the main differences refer to the fraction of k 2 leading to β abstraction and then, more significantly, the fate of the βhydroxyperoxy radicals with the Sarathy et al and Frassoldati et al mechanisms favoring the elimination of the methyl radical. Pang et al 13 tabulated the values of k 2 for each mechanism and as shown in Figure 4, the mechanism of Hansen et al 47 (∼38% production of β-hydroxyperoxy radicals with ∼80% OH regeneration) is in good agreement with the extrapolation of the current measurements. This OH yield of ∼30% could of course be made up of a variety of combinations of branching ratios. However, the high yield of OH regeneration from the β-hydroxyperoxy is consistent with measurements from the β-hydroxyperoxy radical produced from reaction 4. Zheng et al 24 calculate a total branching ratio to β-hydroxyperoxy of 47% in reasonable agreement with our observations. We recommend the following parameterization based on the current work, the low-temperature studies of McGillen et al and the data of Pang et al 13  For the β-hydroxyperoxy radical produced from R1b, again two channels are possible: CH 3 CH 2 CHCH 2 OH → OH + 1−butene (R5a) → CH 3 + CH 2 = CHCH 2 OH.
However, there is also an additional source of OH from the δ abstraction: CH 2 CH 2 CH 2 CH 2 OH → OH + 2C 2 H 4 .
Pang et al 12 modeled their shock tube data based around the calculated branching ratios of Zhou et al 22 (8% for β abstraction and 34% for δ abstraction) with OH regeneration from the δ hydroxyperoxy radical at 85% and at 17% for the β-hydroxyperoxy radical giving an overall OH generation of 30%. Figure 3 shows the overall rate coefficients from Pang et al are in good agreement with the extrapolation of our current work suggesting that the overall OH regeneration yield is correct, but the mechanism for β-hydroxyperoxy radical decomposition is different. The high yield of the δ-hydroxyperoxy radical is surprising and does not match either the evaluation of McGillen et al 16 (β = 19%, δ = 14%) or the more recent calculations of Seal et al 23 (β = 18%, δ = 8%) for the shock tube temperature regime. However, if OH regeneration is the dominant process from both β and δ-hydroxyperoxy radicals, then the OH yield should be somewhere between 0.25 and 0.33, in good agreement with the observations.

CONCLUSIONS
The rate coefficients for the reactions of OH with n, s, and i-butanol have been measured over temperature ranges relevant to the onset of low-temperature combustion. The values measured provide a clear link between the negative temperature dependence of lower temperature measurements (∼250 to 350 K) 16,42 and the positive temperature dependence of the rate coefficients determined from shock tube measurements (∼900 to 1200 K). [12][13][14][15] Data from 250 to 1200 K have been combined and fit with modified Arrhenius parameters to provide accurate and precise data for modeling studies. The lowtemperature combustion behavior of butanols is strongly dependent on the branching ratios of the initial abstractions from butanol 48,49 and calculations are likely to provide the best information on these, particularly at higher temperatures. The current data provide a good test of ab initio and transition state calculations for systems with low or negative barriers. Although only the total rate coefficient has been measured in this study, comparison of this work with the shock tube measurements of Pang et al [12][13][14] are able to shed light on the degree of OH regeneration, which primarily occurs from abstraction at the β position. Our analysis is broadly consistent with the branching ratio evaluations of McGillen et al 16 and the theoretical calculations of Truhlar and coworkers. [23][24][25] The analysis also suggests that OH is the major product from the decomposition of β-hydroxperoxy radicals (with alkene coproduct), whereas the mechanisms of Sarathy et al 18 and Frassoldati et al 46 have alkyl radical elimination (mainly CH 3 ) with enol as the coproduct.

A C K N O W L E D G M E N T S
SLS is grateful for a studentship from the EPSRC doctoral training programme in Bioenergy.