A Combined Experimental and Theoretical Study of the Reaction OH +

Article pubs.acs.org/JPCA

A Combined Experimental and Theoretical Study of the Reaction OH + 2‑Butene in the 400−800 K Temperature Range Ivan O. Antonov, Justin Kwok,† Judit Zádor, and Leonid Sheps* Combustion Research Facility, Mail Stop 9055, Sandia National Laboratories, Livermore, California 94551-0969, United States S Supporting Information *

ABSTRACT: We report a combined experimental and theoretical study of the OH + cis-2-butene and OH + trans-2-butene reactions at combustionrelevant conditions: pressures of 1−20 bar and temperatures of 400−800 K. We probe the OH radical time histories by laser-induced fluorescence and analyze these experimental measurements with aid from time-dependent master-equation calculations. Importantly, our investigation covers a temperature range where experimental data on OH + alkene chemistry in general are lacking, and interpretation of such data is challenging due to the complexity of the competing reaction pathways. Guided by theory, we unravel this complex behavior and determine the temperature- and pressuredependent rate coefficients for the three most important OH + 2-butene reaction channels at our conditions: H abstraction, OH addition to the double bond, and back-dissociation of the OH−butene adduct.

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role in the kinetics under practically relevant conditions).13,14 As a result, the reaction rate coefficients and product branching ratios show complex T- and P-dependence, and OH time profiles in OH + alkene experiments contain multiple decay time scales in certain T, P, and concentration regimes. For reactions at or near the high-pressure limit, this complex behavior is most apparent for temperatures between 500 and 700 K, where all channels in Scheme 1 contribute comparably. In the following, we refer to this approximate temperature range as intermediate. Previous reports, e.g., by Tully and Goldsmith,12 presented the OH decays in reactions with alkenes for the intermediate T range without full analysis. The only exception is the work by Kappler et al.,15 who studied competing channels in the reaction of OH + propene over a range of T = 200−950 K and P = 1−95 bar using OH detection by laser-induced fluorescence (LIF). Their experimental results, including OH time histories at intermediate temperatures, were combined with calculated high-pressure limit rate coefficients of Zádor et al.14 to yield Arrhenius expressions for the channels in Scheme 1 over the whole experimental T range. Theory was used to extend the rate coefficients to temperatures outside this range and to calculate rate coefficients at finite pressures. In the present paper we investigate the OH + trans-2-butene and OH + cis-2-butene reactions at pressures 1−20 bar and

INTRODUCTION Reactions of the OH radical with alkenes play an important role in combustion1,2 and atmospheric chemistry.3 In the troposphere, alkenes make up a substantial fraction of the total volatile organic compound emissions from both natural and anthropogenic sources,3,4 and during daylight hours their primary removal mechanism is by reactions with OH.5,6 Consequently, OH + alkene reactions have long been of interest in atmospheric chemistry, albeit typically over limited temperature ranges near 300 K. From a combustion chemistry perspective, OH is the most important radical chain carrier at temperatures up to ∼1000 K;7 it is also used extensively as a probe of fundamental reaction kinetics (e.g., ref 8) and as an experimental marker for ignition (e.g., ref 9). Meanwhile, alkenes are common additives to commercial gasoline and are also formed during oxidation and pyrolysis of hydrocarbon fuels. Therefore, a comprehensive understanding of combustion chemistry includes detailed knowledge of the OH + alkene reactivity over a wide range of pressures (P) and temperatures (T). A simplified scheme for alkene + OH reactions was proposed by Tully et al.:10−12 According to Scheme 1, H atom abstraction channels compete with OH addition to the double bond, which forms β-hydroxyalkyl radicals. The β-hydroxyalkyl radicals may dissociate back to the reactants; alternatively, they can isomerize or decompose to bimolecular products other than OH and alkene. The OH-alkene adducts are relatively stable with substantial (∼30 kcal mol−1) potential energy wells, but require collisions to be stabilized. In contrast, H abstraction is essentially a direct bimolecular reaction (the OH−alkene prereactive complex, if present, is too shallow to play a direct © 2015 American Chemical Society

Special Issue: 100 Years of Combustion Kinetics at Argonne: A Festschrift for Lawrence B. Harding, Joe V. Michael, and Albert F. Wagner Received: January 31, 2015 Revised: April 5, 2015 Published: April 10, 2015 7742

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of the equilibrium constant, which can be compared to the values derived from thermodynamic tables.

Scheme 1

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EXPERIMENTAL METHODS The experimental measurements were carried out at T = 400− 800 K and P = 1−20 bar in a heatable high-pressure reactor with optical access, described in detail previously.25 We produced OH radicals by laser flash photolysis of acetylacetone in the presence of cis- or trans-2-butene in a He bath, and followed the evolution of the transient OH population by LIF. Acetylacetone and 2-butene were mixed on the fly with He bath gas (99.9999% purity) at subatmospheric pressure using precision-metered mass flow controllers, and the sample was compressed prior to entering the LIF cell in a high-purity diaphragm compressor (Pressure Products Industries, Inc.). The temperature and pressure in the LIF cell were controlled by active feedback loops. We generated OH radicals using the fourth harmonic of an Nd:YAG laser at 266 nm by photolysis of acetylacetone, which occurs predominantly in its H-bond-stabilized enol form in the gas phase:26

temperatures 400−800 K. We determine the rate coefficients of addition, H abstraction, and back-dissociation reactions separately in both chemical systems, and interpret the results with the aid of time-dependent master-equation calculations based on the potential energy surface (PES) for OH + 2butene. Compared to propene, the reactions of OH with 2butene are a step up in chemical complexity. The increased system size, greater number of potential reaction channels, and the presence of multiple conformers are a challenge to both experiment and theory. Nonetheless, 2-butene is sufficiently small to be tractable with high-level ab initio calculations, and therefore serves as a useful rigorous benchmark for OH + alkene reactions. Because of their status as prototype systems as well as their practical importance, OH + butene reactions have been studied previously. However, existing work on these reactions has been limited to either low or high temperatures, where the addition or abstraction channels, respectively, dominate the experimentally observed OH decays. Rate coefficients of OH addition to butene isomers were measured in several studies at temperatures below 425 K, summarized in a review by Atkinson.16 Several groups studied H atom abstraction by OH radicals at high temperatures. Tully10 studied abstraction of hydrogen from 1-butene over the temperature range 650−900 K. Smith17 measured rate coefficients of hydrogen abstraction from 1butene, trans-2-butene, and isobutene at temperatures between 1225 and 1260 K. Most recently, Vasu et al.18 investigated H abstraction in all four butene isomers above 1000 K. Vasu et al.,18 Sun and Law,19 and Hyunh et al.20 also used high-level ab initio methods to study abstraction reactions from various butene isomers by OH. The results of their calculations suggest that H abstraction mostly occurs on the allylic carbon, with the vinylic and alkylic (in 1-butene) channels being less important. We note that Sun and Law explicitly call for more experimental and theoretical work on 2-butenes. By contrast, no experimental results are available at intermediate T, where OH−butene adduct dissociation competes effectively with the other available pathways; consequently, there have been no experimental measurements of the adduct dissociation rate coefficient. This pathway is of special interest in our study, because the OH + 2-butene adduct is the 3-hydroxy-2-butyl radical (CH3CH(OH)CHCH3, 3H2B)a representative β-hydroxybutyl radical and a key intermediate21 in the oxidation of 2-butanol, an important potential biofuel.22 Welz et al.23 showed that the dissociation of 2-hydroxy-1-butyl radical to OH + 1-butene was one of the main kinetic pathways in the low-temperature oxidation of 1butanol above 700 K. This finding is in agreement with recent theoretical results by Zhang et al.,24 who explored the decomposition and isomerization pathways for 1-hydroxybutyl and 1-butoxy radicals. Therefore, direct measurements of 3H2B decomposition rates in the reactions of OH with 2-butene have implications not only for the OH + 2-butene system itself, but also for modeling of the combustion of alcohol-containing biofuels.23 Moreover, obtaining the forward and reverse rate coefficients in this system gives an experimental determination

Scheme 2

The concentration of acetylacetone was chosen to give initial OH number density of (1−3) × 1012 cm−3, based on its absorption cross-section26 at 266 nm (3.8 × 10−17 cm2), the photolysis laser fluence (∼55 mJ cm−2), and assuming a photolysis yield of unity for the enol form and zero for the keto form. Increased acetylacetone flows were used during higher temperature experiments, because the keto−enol equilibrium shifts toward the keto form.26 The 2-butene concentrations were at least 2 orders of magnitude higher than the initial [OH] to ensure pseudo-first-order conditions for the OH + 2-butene reaction; radical coproducts27 of acetylacetone photolysis at the ∼1012 cm−3 concentration levels had negligible effect on the fate of the OH radicals. The time dependence of OH concentration was probed by LIF on the (0,1) band of A2Σ+ ←X2Π transition of OH using a frequency-doubled output of a Nd:YAG-pumped dye laser at 281.9 nm. The LIF signal was recorded as a function of pump− probe delay time in the presence of varying 2-butene concentrations, and also without 2-butene to determine the OH removal due to wall loss and to reactions with acetylacetone or with impurities. To ensure that probe laser photolysis of acetylacetone or OH−2-butene adduct does not perturb our results, the probe power was lowered until no OH fluorescence was observed at time delays >20 ms, even at room T, where we expect significant adduct concentration to be present on such long time scales. We also tested the possibility that O2 (a contaminant in the He bath gas) interfered with our measurements by reacting with the radical products of acetylacetone photolysis and creating additional OH radicals. At our experimental conditions, we estimate a maximum O2 contamination of ∼1012 cm−3; however, adding up to 1016 cm−3 of O2 to the acetylacetone/He mixture produced no evidence of secondary OH formation or any detectable changes in the OH time profiles. 7743

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of theory, and the chemical network was only explored up to the initial adduct’s first neighbors (wells or bimolecular products). As we discuss later, none of the other wells play a role under our experimental conditions; therefore, using this trimmed PES does not introduce significant errors in the analysis. KinBot also searches for the lowest energy conformers of the structures it finds, scans the dihedral angles associated with hindered rotors, and constructs the chemical connectivity matrix of the explored species in a format, which can be readily used in the PAPER code31 that solves the corresponding timedependent master equation. The version of KinBot used could not automatically explore direct bimolecular reactions, such as abstraction; therefore, these channels were explored manually in this work. Accurate energies for all stationary points were calculated at the CCSD(T)-F12a/cc-pVTZ-F12//M06-2X/6311++G(d,p) level of theory using the Molpro 2010 suite of programs.32 The OH + 2-butene entrance channels are dynamically complex pathways featuring a barrierless entrance (outer transition state) into a van der Waals well followed by a submerged barrier (inner transition state). The presence of these features is typical of OH + alkene reactions.14,15,33−35 To calculate the sum of states for the transitional modes along the barrierless part of the potential the variable-reaction coordinate transition state theory (VRC-TST)36,37 was used, in analogy to our work on propene + OH.14 Namely, we evaluated the longrange potential between OH and 2-butene using the stateaveraged CASPT2(5e,4o)/aug-cc-pVDZ multireference method. The active space consisted of the bonding and antibonding π orbitals of 2-butene (2 electrons), the π orbital (2 electrons) and the radical orbital (1 electron) of OH. Neither geometry relaxation, nor basis set extrapolation was necessary, as described, e.g., in ref 13. The conserved modes for the barrierless channel, including the hindered rotor sum of states, as well as the sum of states corrected with tunneling corresponding to the submerged (tight inner) barrier, were convolved with the transitional mode sum of states within the PAPER code in the framework of a two-transition-state model.14,33−35,38 The spin−orbit coupling of the OH radical (139.7 cm−1) needs to be considered in the state counts of the reactant and also at the region of the outer transition state, where it is assumed that the conserved and transitional degrees of freedoms are separable and the interaction between the fragments is still small. At the inner (tight) transition state, the spin−orbit coupling changes the number of states only negligibly, and has an effect on the barrier only: it increases its height by 0.2 kcal mol−1. Instead of a canonical correction factor,14,34 which we used previously, in this work we corrected the partition functions of the reactant OH and of the outer transition state directly, also at the canonical level. This treatment is not only free of an ad hoc interpolation scheme, but also automatically preserves the correct value of the equilibrium constant, which in turn influences the backdissociation rate coefficient. Using the values from ref 14, we calculated the T-dependent correction factor Qcoup e,r /(QeQr), where Qcoup e,r is the true, coupled partition function of OH, while Qe and Qr are the uncoupled electronic and rotational partition functions, respectively. The correction factor is less than 17% at any T and can be found in the Supporting Information. For the abstraction channels, we did not use the above twotransition-state model. Although some abstraction channels might be connected directly to the van der Waals well,13,14 the dynamical consequences of this topology are negligible, because

In order to facilitate the interpretation of experimental data and comparison with theoretical predictions, we focused on the temperature dependence of the OH + 2-butene reaction in the high-pressure limit. At each T, we performed survey measurements at increasing P; detailed measurements of second-order reaction rate coefficients were then done at conditions where OH signal decays showed no further pressure-dependence. A complete list of all experimental conditions is presented in Table 1. Table 1. Experimental Conditions for the OH + trans-2Butene and OH + cis-2-Butene Reactions concentration (1012 cm−3) T (K) P (bar)

[2-butene]

400 450 500 550 575 600 625 650 675 700 725 750 775 800

2 2 2a 2 1, 3 2a 2a 1, 3a 2, 4a 2, 4a 4 4 4 4a

0−8300 0−4200 0−2100 0−430 0−3500 0−5900 0−3100 0−2600 1400−8000 0−14000 720−4100 720−4000 720−2100 0−2200

500 600 650 750

1a 2 2a 2

0−8800 0−3700 0−11000 0−1900

[acetylacetone] trans-2-butene 12 12 12 12 7 9−12 13 2−6 18−27 5−27 13 13 13 6−13 cis-2-butene 8−10 10 10 12−18

[OH]b at t = 0

# traces

8.9 7.6 6.3 5.2 2.8 3.2−4.3 4.3 0.6−1.8 5−7.5 1.3−6.9 3.1 2.9 2.7 1.2−2.5

37 44 35 19 35 31 30 56 22 47 11 12 12 18

5.2 3.6 3.0 2.6−4

24 10 31 15

a

To ensure that the experiments were done at the high-P limit, survey measurements were performed at certain temperatures. For OH + trans-2-butene, we surveyed pressures 2−10 bar (500 K), 2−20 bar (600−625 K), 1−20 bar (650 K), 2−16 bar (675 K), 2−4 bar (700 K), and 2−8 bar (800 K). For OH + cis-2-butene, we surveyed pressures 1−3 bar (500 and 650 K). bThe initial OH concentration was calculated assuming OH yields of 0 and 1 for the photolysis of ketoand enol- forms of acetylacetone, respectively, and using extrapolated values of the keto/enol equilibrium constant by Nakanishi et al.26

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THEORETICAL METHODS The stationary points on the PES for the isomerization and unimolecular dissociation of the initial OH−2-butene adduct, 3H2B, was explored by KinBot software.28,29 KinBot is an expert system enabling the automatic and systematic exploration of PESs relevant in gas-phase kinetics of C, H, and O atom-containing species using generic rules for possible reaction pathways. KinBot constructs good initial guesses for the 3-D structures of wells, bimolecular products, and transition states in a reaction network happening on a single PES, and uses Gaussian 09 software30 to optimize the geometries to the true stationary point locations at the prescribed level of theory. KinBot systematically explores the interconnected species and stops the search when all pathways are explored within the user-defined energy range and network size. To focus on the relevant pathways, the exploration was limited to 15 kcal mol−1 above the reactant energy at the M06-2X/6-311++G(d,p) level 7744

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chemically activated OH−butene complex).31,41 Yet another possibility is H abstraction by OH to form one of two possible C4H7 products (3-methylallyl and 1,3-dimethylvinyl radicals) and a water molecule (R4). Finally, reactions R5 and R6 need to be included to account for all possible losses of the OH radical or 3H2B due to reactions with impurities or diffusion out of the probe volume; we assume that these losses are firstorder processes or are well approximated by such a process within the time window of our experiments. Channels R1, R-1, and R2 in the OH + 2-butene reaction scheme outlined above depend on the collisional stabilization or activation of the 3H2B adduct. Therefore, the overall reaction shows T- and P-dependent competition between the available pathways, and the observed OH time-histories exhibit three distinct qualitative regimes under pseudo-first-order conditions ([OH] ≪ [C4H8]). At sufficiently high pressures, the contribution from formally direct reaction R3 is negligible, and transient OH signals below T ∼500 K show singleexponential decays, dominated by OH addition to the C−C double bond (reaction R1). At T above ∼500 K, OH addition and adduct dissociation (R-1) become increasingly more rapid, and equilibrium between the initial OH radicals and 3H2B is established on time scales shorter than the experimental time window. At the same time, reactions R2−R6 act as irreversible sinks of the total radical reservoir, leading to biexponential OH decays. Finally, at T above ∼700 K the equilibrium in reactions R1 and R-1 is reached very rapidly and strongly favors the reactants ([3H2B] ≪ [OH]), because the near-barrierless association rate coefficient has inherently weak T-dependence, whereas the back-dissociation rate coefficient has strong positive T-dependence. Meanwhile, the H abstraction rate coefficient increases with increasing T. As a result, single exponential OH decays are observed again, dominated by reaction R4. Figure 1 shows typical OH time traces for a range of cis-2butene concentrations at T = 600 K and P = 2 bar. The interpretation of the results in the context of the full kinetic

the abstraction barriers are not submerged. On the other hand, based on our previous findings,15 we expect variational effects to be significant for the allylic abstraction channel. To this end, we calculated projected vibrational frequencies in a curvilinear coordinate system and the resulting zero-point energy (ZPE) correction along the electronic minimum-energy path using Polyrate39 at the M06-2X/6-311++G(d,p) level of theory, and applied microcanonical variational transition state theory within the PAPER code. For the vinylic abstraction channels, we used nonvariational transition state theory, as the transition state is significantly tighter. The effect of spin−orbit coupling was also taken into account for the state counts of the reacting OH fragment. To account for some of the vibrational anharmonicity of all species, the 1-D separable hindered rotor approximation was used. Bends were treated as harmonic oscillators. In the case of the near-linear C−H−O substructure in the direct (intermolecular) H abstraction hindered rotor scans were done along the C−O “bond,” and not along the breaking C−H and forming H−O bonds separately. In several cases, when the initial adduct isomerizes or dissociates, we identified transition states that had two distinct geometries (cis- and transconformers, but not rotamers) connecting the same stationary points on the PES. The state counts were simply added up for these transition states. Tunneling corrections were taken into account with an asymmetric Eckart barrier. In the case of the entrance channel, the height of the Eckart barrier on the reactant side is calculated from the van der Waals well. Although there is no tunneling through a submerged barrier, tunneling still increases the number of states at any given energy level, i.e., in this case starting from the energy of the reactants. Note, however, that there is no tunneling through the barrierless outer region, because there is no barrier. A simple temperature-dependent exponential model was used for the downward energy transfer, with ⟨ΔEdown⟩ = 250 × (T/300)0.85 cm−1. The Lennard-Jones parameters for the C4H9O isomers were taken as 324 cm−1 and 5.27 Å, based on the values determined for butanol.40

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EXPERIMENTAL AND MODELING RESULTS When modeling the OH time histories in the reaction of OH with 2-butene, the following channels need to be taken into account: CH3−CHCH−CH3 + OH ⇄ CH3•CH−CH(OH)−CH3

(R1,R-1)

CH3•CH−CH(OH)−CH3 → products

(R2)

CH3−CHCH−CH3 + OH → products

(R3)

CH3−CHCH−CH3 + OH → C4 H 7 + H 2O

(R4)

OH → loss

(R5)

CH3•CH−CH(OH)−CH3 → loss

(R6)

The addition reaction (R1) proceeds via a near-barrierless region of the PES and forms the initial adduct (3H2B), which may dissociate back to the reactants (R-1). Alternatively, 3H2B can isomerize or decompose to bimolecular products other than OH and alkene, as summarized by the reaction R2. These products may also be formed in a formally direct reaction R3 (i.e., well-skipping, without collisional stabilization of the

Figure 1. Representative experimental OH decays in the OH + cis-2butene reaction, taken at T = 600 K and P = 2 bar with varying cis-2butene concentrations, [C4H8] = 0−3.7 × 1015 cm−3. The symbols are measured LIF signals as a function of time, and the lines are fits to eqs 1−5 7745

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T but at various P and [C4H8] were fit simultaneously to eqs 1−5. The rate parameters k1, k−1, k4, k5, and k3H2B were linked for all experimental traces taken at the same temperature. Whenever the fits included OH decays taken at multiple pressures, the P-dependence of k1 and k−1 was also linked through the equilibrium constant K. The fits were further simplified by fixing some of the rate parameters in eqs 1−5 at calculated or extrapolated values, as described below; a full account of the fitting algorithm can be found in the Supporting Information. At T < 550 K, the OH signals exhibit single-exponential decays. Our theoretical calculations indicate that OH addition is considerably faster than other competing channels at these conditions. Therefore, when fitting the data below 550 K, k−1and k4 were fixed at values extrapolated from their fitted values at higher temperatures using an Arrhenius expression, an approach that is justified by the close agreement of the extrapolated values with theoretical results (see below). The extrapolated values of k−1 and k4 were small and did not affect the fits greatly. Because there is no appreciable backdissociation of 3H2B at these conditions, potential adduct losses do not affect the OH decays either; therefore, k3H2B was set to 0 and only k1 and k5 were allowed to vary. At temperatures 550 K < T ≤ 700 K, the OH concentration decays show clear biexponential character. Fitting of the OH time traces at these conditions allows for unambiguous determination of k′1 and k−1, while k′OH and k3H2B are strongly correlated and could not be determined independently. Our calculations suggest that the main mechanism of unimolecular 3H2B decomposition in this temperature range is dissociation back to OH and 2-butene, meaning that the contribution from reaction R2 is negligible (see Supporting Information). However, k3H2B may still be nonzero because of potential radical−radical reactions or wall losses of the OH−2-butene adduct (R6). To account for the latter possibility, we numerically simulated the removal of 3H2B in our experiments due to diffusion-limited wall loss and to radical−radical reactions, using the COMSOL 4.3a software package.39 The simulation details, including the choice of diffusion parameters and bimolecular reaction coefficients, are given in the Supporting Information. Simulated time profiles of the OH concentrations were fit with exponential decay functions, and the resulting effective first-order loss rate coefficients at P = 2 bar and T = 550−700 K varied from ∼90 to ∼130 s−1. Consequently, we fixed k3H2B at the simulated values for each experimental temperature with uncertainties of ±100%; k1, k−1, k4, and k5 were optimized. Varying k3H2B within its conservative error bars affects the fitted values of k′1 and k−1 by at most a few percent; the determination of k4 changes by ∼25% at 500 K (where H abstraction is still slow), ∼10% at 600 K, and even less at higher T. Above ∼700 K, the OH traces were again single exponential, because H abstraction from 2-butene is fast, whereas the addition reaction is not observable experimentally due to the rapid back-dissociation of the complex. Direct determination of k′1 and k−1 at these conditions is not possible from the fits; however, the equilibrium in the OH addition and dissociation reactions still affects the apparent OH decay rate coefficient: keff ′ /(1 + k1 · [C4H8]/k−1). To account for this, we fixed OH ∼ kOH k1′ and k−1 at the values extrapolated using Arrhenius expressions from experimental values at lower T. As a result of including the contribution from OH addition and back′ differs from dissociation, the OH addition rate coefficient kOH

Figure 2. (A) OH + 2-butene submechanism based on the reactions R1−R6. (B) Simplified kinetic scheme for data analysis in this study.

model that incorporates reactions R1−R6 (see also Figure 2A) is quite challenging. However, our choice of experimental conditions enables two simplifying assumptions. First, because [OH] ≪ [C4H8] except in zero-butene experiments, all reactions can be treated as first-order processes, and the system of coupled kinetic equations in the model can be solved analytically. Second, reactions R1−R6 can be grouped in terms of their dependence on T, P, and 2-butene concentration. Specifically, the pseudo-first-order rate coefficient of reaction R1 (k′1 = k1 · [C4H8]) depends on T, P, and [C4H8]. The rate coefficient of the reverse reaction R-1 depends only on T and P; furthermore, k1′ and k−1 are linked through K, the pressureindependent equilibrium constant between the reactants and the 3H2B adduct. Aside from addition to the double bond, OH decays mainly by the H abstraction reaction R4, which depends only on T and [C4H8]. The formally direct reaction R3 depends on P, T, and [C4H8]; however, our master equation calculations (see below) show that, at the elevated P used in this study, R3 is negligible compared to the addition and abstraction channels. Based on the above, OH losses other than by reaction R1 can be represented at any given temperature by a pressureindependent rate coefficient, kOH ′ = k5 + k4 · [C4H8]. Similarly, all removal pathways of the 3H2B adduct other than backdissociation (R-1) can be grouped into a single first-order loss term, k3H2B = k2 + k6, which does not depend on [C4H8], but may depend on T and P. The simplified kinetic scheme is summarized in Figure 2B. The solution to the simplified kinetic scheme takes the form of a biexponential decay (see also Kappler et al.):15 (γ − λ1) exp( −λ1t ) − (γ − λ 2) exp( −λ 2t ) I (t ) = I0 λ 2 − λ1

(1)

where I(t) is the experimental OH signal as a function of time, I0 is the signal at time t = 0, and γ = k −1 + k 3H2B λ1,2 =

a±

a 2 − 4c 2

(2)

(3)

′ + k −1 + k 3H2B a = k1′ + k OH

(4)

′ + k OH ′ ·k 3H2B c = k1′·k 3H2B + k −1·k OH

(5)

We employed a global nonlinear least-squares fitting procedure, in which all OH time histories taken at the same 7746

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parameter k3H2B was fixed at zero, although its value does not affect the fit at all, because at all T above 700 K, the equilibrium is strongly shifted to the reactants, so the total radical pool is depleted by H abstraction much faster than by irreversible loss of the adduct. The values of the key rate coefficients, determined in the analysis of the experimental data, are shown in Table 2. Uncertainties in k1, k−1, and k4 were computed by Gaussian error propagation and are listed at the 1σ level. The main uncertainty sources were statistical fitting errors, the uncertainty in the 2-butene/He gas mixture concentration, and the uncertainty in the fixed parameter k3H2B. The aggregate contribution of all other experimental uncertainties, such as flow rates, pressure, and temperature, was at least 1 order of magnitude smaller. The Supporting Information provides the full details of our fitting procedure, as well as the values of the loss parameters k5 and k3H2B, which are characteristic of our experimental apparatus rather than the OH + 2-butene reaction system.

Table 2. Fitted Rate Coefficients of Addition (k1), BackDissociation (k−1), and Abstraction (k4) for the Reactions OH + trans-2-Butene and OH + cis-2-Butene fitted rate coefficients T (K)

P (bar)

400 450 500 550 575 600 625 650

725 750 775 800

2 2 2 2 1−3 2 2 1 3 2 4 2 4 4 4 4 4

500 600 650 750

1 2 2 2

675 700

k1 (10−12 cm3 s−1)

k−1 (1000 s−1)

trans-2-butene 33.3 ± 2.9 (2 ± 1) × 10−4a 30.2 ± 2.9 (6 ± 2.5)× 10−3a 26.1 ± 4.5 0.10 ± 0.03a 18.7 ± 2.0 1.15 ± 0.2 19.3 ± 2.3 4.0 ± 1.0 18.3 ± 1.5 5.7 ± 0.6 17.9 ± 2.3 14.5 ± 2.4 9.8 ± 1.6 16.3 ± 3.0 21.6 ± 4.0 37.1 ± 7.3 9.3 ± 4.6 36.7 ± 18.7 16.4 ± 3.5 65 ± 16.1 8.7+5.2 85+50 −7.6 −70 21.9 ± 5.9 190 ± 60 15.7 ± 1.4a 230 ± 40a a 15.2 ± 1.4 410 ± 90a a 14.7 ± 1.3 700 ± 180a 14.3 ± 1.3a 1150 ± 320a cis-2-butene 17.2 ± 3.6 0.10 ± 0.03a 12.9 ± 1.7 5.5 ± 1.0 12.5 ± 1.7 31.1 ± 5.1 11.0 ± 1.7a 410 ± 90a

k4 (10−12 cm3 s−1) 0.16 ± 0.04a 0.40 ± 0.08a 0.8 ± 0.15a 3.1 ± 1.5 2.2+1.2 −1.3 3.6 ± 0.5 3.5 ± 0.5 3.2 ± 0.4 3.5 ± 0.5

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4.2 ± 0.4 4.7 6.6 8.5 9.1

± ± ± ±

THEORETICAL RESULTS AND DISCUSSION The relevant stationary point energies of the lowest energy conformers for the OH + 2-butene system are shown in Figure 3. The lowest-energy barrier of all the decomposition pathways of the OH−2-butene adduct leads to the formation of propen1-ol + CH3. Other possible β-scission channels, leading to bimolecular product pairs but-2-en-2-ol + H and but-3-en-2-ol + H, have higher barriers and are also entropically less favored than the methyl loss. In addition, 3H2B can also isomerize into four different radicals, accessible within the energy threshold set for our exploration of the PES. Of these, the lowest-energy barrier leads to the alkoxy radical, which is the highest-energy isomer of 3H2B on this PES; the tertiary 2-hydroxy-2-butyl radical is the lowest-energy isomerization product. The abstraction channels have a relatively low barrier, and are very similar for the cis and trans isomers. We also find that the vinylic abstraction has a higher barrier than the allylic one. The

1.8 1.5 1.3 1.0

0.6 ± 0.2a 2.4 ± 0.5 2.9 ± 0.3 3.9 ± 0.6

During the fitting of data at T ≤ 500 K, the rate coefficients k−1 and k4 at were fixed at values extrapolated from higher temperatures. At T ≥ 725 K, k1 and k−1 were fixed at values extrapolated from lower temperatures. a

the apparent single-exponential decay rate by ∼21% at 725 K and at the highest 2-butene concentration (4 × 1015 cm−3) used at this temperature, and even less at higher temperatures. The

Figure 3. Calculated energies of the reactants, wells, and bimolecular products on the C4H9O PES relevant for the OH + 2-butene reactions in this work. ZPE-inclusive stationary point energies are calculated at the CCSD(T)-F12a/cc-pVTZ-F12//M06-2X/6-311++G(d,p) level. For clarity, only the trans-isomers of the abstraction products are shown. Some energies are adjusted in the master-equation calculations to the values (in kcal mole−1) of (a) −2.19; (b) −2.92; (c) 2.89, (the variational barrier is 2.08); (d) 5.00 (the variational barrier is 3.20); (e) −29.45. 7747

DOI: 10.1021/acs.jpca.5b01012 J. Phys. Chem. A 2015, 119, 7742−7752

Article

The Journal of Physical Chemistry A

obtained previously.42 When extrapolated to higher T (450− 650 K), the value of Atkinson et al. is higher than our measurements by 20−60% for trans-2-butene and 65−85% for cis-2-butene. This agreement is quite good, considering the limited temperature range on which the original extrapolation was based. The present measurements extend the experimental determination of the OH addition rate coefficient to T = 700 K for trans-2-butene and 650 K for cis-2-butene. A fit of our experimentally derived k1(T) values, combined with the results of Atkinson et al.,16,42 allows an updated parametrization of the OH addition rate coefficient:

PES in Figure 3 forms the basis of our chemical kinetics calculations, and their results are discussed in detail along with the experimental findings in the following sections. OH Addition. Figures 4A and 4B compare measured and calculated rate coefficients of OH addition to the C−C double

⎡ (704 ± 27)K ⎤ 3 −1 k1,trans = (5.93 ± 0.50) × 10−12 × exp⎢ ⎥ cm s ⎣ ⎦ T (6)

⎡ (785 ± 44)K ⎤ 3 −1 k1,cis = (3.93 ± 0.57) × 10−12 × exp⎢ ⎥ cm s ⎣ ⎦ T (7)

Figure 4 also includes the theoretical T- and P-dependent values of k1, obtained with the energy of the inner barrier for OH addition lowered from the ab initio calculated value of −2.52 to an adjusted value of −2.92 kcal mol−1 in the trans, and from −2.64 to −3.34 kcal mol−1 in the cis case (energies are relative to the respective OH + 2-butene asymptotes). The discrepancy between the original calculations and the experimental values of k1 is