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Chain Reaction Mechanism in Hydrogen/Fluorine Combustion Akira Matsugi,*,† Hiroumi Shiina,† Kentaro Tsuchiya,‡ and Akira Miyoshi§ †

Research Institute of Science for Safety and Sustainability and ‡Energy Technology Research Institute, National Institute of Advanced Industrial Science and Technology, 16-1 Onogawa, Tsukuba, Ibaraki 305-8569, Japan § Department of Chemical System Engineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan S Supporting Information *

ABSTRACT: Vibrationally excited species have been considered to play significant roles in H2/F2 reaction systems. In the present study, in order to obtain further understanding of the chain reaction mechanism in the combustion of mixtures containing H2 and F2, burning velocities for H2/F2/O2/N2 flames were measured and compared to that obtained from kinetic simulations using a detailed kinetic model, which involves the vibrationally excited species, HF(ν) and H2(ν), and the chain-branching reactions, HF(ν > 2) + F2 = HF + F + F (R1) and H2(ν = 1) + F2 = HF + H + F (R2). The results indicated that reaction R1 is not responsible for chain branching, whereas reaction R2 plays a dominant role in the chain reaction mechanism. The kinetic model reproduced the experimental burning velocities with the presumed rate constant of k2 = 6.6 × 10−10 exp(−59 kJ mol−1/RT) cm3 s−1 for R2. The suggested chain-branching reaction was also investigated by quantum chemical calculations at the MRCI-F12+CV+Q/cc-pCVQZ-F12 level of theory.

1. INTRODUCTION The strong oxidizing ability of F2 can potentially be utilized for many industrial processes that require high reaction energies. The application of F2 has also been proposed for propulsion systems and high-intensity HF chemical lasers. However, the mechanism of combustion involving F2 is only partly understood, even for the simplest H2/F2 systems. Although a number of studies have been conducted on the combustion of the H2/F2 mixtures, the reaction mechanism, especially for the chain-branching steps, remains unclear. This motivated the present study to investigate the chain reaction mechanism in the H2/F2 combustion The mixtures of H2 and F2 are known to explode spontaneously, and their explosion limits have been studied in the 1960−70s.1−7 The kinetic behavior of H2/F2 mixtures has also been examined in flow reactors.8−14 These studies indicated rapid reactions of H2/F2 mixtures even at room temperature due to the chain reaction mechanism outlined below. They also suggested inhibition of the reactions and explosions upon addition of a small amount of O2. This can be explained by the chain-inhibition reaction of H + O2 + M = HO2 + M. The reaction mechanisms of the H2/F2 system and the elementary reactions involving H and F have also been extensively studied, motivated by the fundamental interest in chemical dynamics involving vibrationally excited species and their importance in the HF chemical lasers.15,16 The explosion limits of the H2/F2 mixtures could be interpreted with a kinetic mechanism involving vibrationally excited HF and H2 molecules;5 the former is generated from H + F2 and F + H2 reactions, and the latter is produced by the intermolecular energy transfer from the vibrationally excited HF. The kinetic modeling study of Sullivan et al.5 indicated that © 2013 American Chemical Society

two chain-branching reactions were responsible for reproducing the observed second explosion limits in the H2/F2 mixtures2 HF(ν > 2) + F2 = HF + F + F

(R1)

H 2(ν = 1) + F2 = HF + H + F

(R2)

where ν denotes the vibrational quantum numbers for HF and H2. They suggested the rate constants of (3−12) × 10−18 and (1−3) × 10−19 cm3 s−1 for reactions R1 and R2 at 350 K, respectively. The rate constant for reaction R2 was also estimated by a thermometric technique to be (7.5 ± 1.5) × 10−20 cm3 s−1 at 310 K.17 A classical trajectory study of Thompson and McLaughlin18 on a semiempirical potential energy surface revealed the qualitative features of reaction R2. The significance of the chain-branching steps was also indicated by Warnatz et al.19,20 They suggested a significantly large rate constant of ∼10−11 cm3 s−1 for reaction R1 in order to reproduce the structure of the H2/F2/Ar flame. The objective of the present study is to obtain further understanding of the chain-branching reactions and elucidate the reaction mechanism of H2/F2 combustion based on the measurements of burning velocities. The burning velocity is one of the fundamental combustion properties of gases and can be used to investigate the reaction mechanisms of combustion. In this study, the burning velocities for H2/F2/O2/N2 flames were measured and compared to the data from kinetic simulations, which were performed with a detailed kinetic model that involves vibrationally excited species and chainReceived: October 27, 2013 Revised: November 27, 2013 Published: December 2, 2013 14042

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branching reactions. The suggested chain-branching reaction was also investigated by quantum chemical calculations.

F + H 2 = HF(ν = 1−3) + H

Energy transfer:

2. EXPERIMENTAL METHOD The experiment was performed using a spherical closed vessel, as described elsewhere.21 Briefly, a sample mixture of known composition was introduced into a spherical vessel with an inner volume of 15 L and was ignited by an electric discharge between electrodes placed at the center of the vessel. The pressure profile after ignition was measured by a pressure transducer located at the vessel wall. The burning velocity, Su0, of the flame was obtained by the pressure profile method22,23 following the procedure described in ref 21. The sample mixtures used were composed of H2, F2, O2, and N2. In order to avoid spontaneous ignition caused by the mixing of H2 and F2, the mixtures were prepared to contain 5− 10% of O2. The burning velocities for the H2/F2/O2/N2 flame were measured at various equivalence ratios, ϕ, and mole fractions of N2 and O2. The equivalence ratio is defined as ϕ = X(H2)/X(F2), where X denotes the mole fraction of the species in the sample. The initial temperature and pressure were 298 ± 5 K and 101.3 kPa, respectively.

(R7)

HF(ν) + HF(ν′) = HF(ν + 1) + HF(ν′ − 1)

(R8)

HF(ν = 1) + H 2 = HF + H 2(ν = 1)

(R9) (R10)

HF(ν > 2) + F2 = HF + F + F

(R1)

H 2(ν = 1) + F2 = HF + H + F

(R2)

The rate constants for reactions R3 and R4 were taken from the recommendation of Baulch et al.28 They were parametrized based on a number of shock tube studies. Reactions of H + F2 (reaction R5) and F + H2 (reaction R6) have been extensively studied as prototypes for fundamental reaction dynamics. These reactions are known to generate the vibrationally excited HF molecules. The rate constant for H + F2 was taken from Baulch et al.,28 as recently recommended,29 while that for F + H2 was taken from the data sheet of ref 30. The nascent vibrational distributions of HF from reactions R5 and R6 were adopted from the review of Manke and Hager,15 who have summarized the extensive studies conducted for these reactions in the 1970−80s. The parameters for the energy-transfer reactions of HF, reactions R7 and R8, were incorporated into the model from Manke and Hager15 and Cohen and Bott.16 They determined the parameters from a number of experimental measurements and extrapolations. The V−V energy-transfer reaction between HF(1) and H2 (reaction R9) is one of the important reaction steps in the present model because the vibrationally excited H2 works as a chain carrier, leading to the chain-branching reaction R2. Due to the small energy change in this V−V exchange reaction, the deactivation of HF(1) by H2 is expected to predominantly occur through the V−V exchange process, as indicated by Bott and Cohen.16,31 A rate constant of 5.2 × 10−13 cm3 s−1 was reported for this process.31 The rate constant for the relaxation of H2(1) was taken from a shock tube study by Dove and Teitelbaum.32 The reactions R1 and R2 have been proposed as the chainbranching steps, but their rate constants, k1 and k2, are highly uncertain. Therefore, the rate constants for these reactions were parametrically varied in the simulation of the burning velocity to determine the most probable values. In this procedure, the rate constant for reaction R1 was assumed to be temperatureindependent, and the A factor was used as a parameter, whereas the activation energy, Ea2, was varied for reaction R2, assuming an Arrhenius temperature dependence, k = A exp(−Ea/RT), where R is the universal gas constant. The A factor for reaction R2 was determined from the presumed activation energy (Ea2) and the rate constant at 310 K, k2(310 K) = (7.5 ± 1.5) × 10−20 cm3 s−1, as estimated in the thermometric study by Orkin and Chaikin.17

4. RESULTS AND DISCUSSION 4.1. Experimental Results. Figure 1 shows the burning velocities for the H2/F2/O2/N2 flame obtained in the present study as a function of ϕ. The measurements were performed under three different experimental conditions with respect to the mole fractions of N2 and O2 with X(N2)/X(O2) ratios of

(R4)

Chain propagation: H + F2 = HF(ν = 0−8) + F

HF(ν) + M = HF(ν − 1) + M

H 2(ν = 1) + M = H 2 + M

3. KINETIC MODELING 3.1. Simulation Method. The kinetic simulations were performed to calculate the burning velocities of the H2/F2/O2/ N2 flame and investigate the reaction mechanisms. The burning velocities were computed using the Cantera program24 as laminar flame speeds of one-dimensional freely propagating flames. A detailed kinetic model constructed in the present study was employed in the simulations. The flame computations were performed at an initial temperature of 298 K and an initial pressure of 101.3 kPa with adaptive meshes specified by the maximum relative gradient and curvature between two adjacent points of 0.1. A sensitivity analysis was performed to identify the important reaction steps. The sensitivity coefficients for the burning velocities were computed by finite central differences with displacements of the rate constant by ±3%. 3.2. Kinetic Model. A detailed kinetic model for H2/F2/ O2/N2 combustion was constructed, which consists of H/O, H/F, and H/F/O subsets. The reactions and the thermochemical data of the H/O subset were taken from the mechanism proposed by Leeds.25 The kinetic data for the H/F/O reactions were adopted from the NIST kinetic database26 or estimated from analogous reactions. The reaction mechanism for the H/F subset was constructed mostly based on the HF chemical laser mechanism of Manke and Hager,15 as described below. The thermochemical data for the species containing fluorine were taken from a database of CEA2,27 and those for the vibrationally excited species were calculated by simply adding the vibrational energies to the enthalpies of formation of the corresponding molecules. The kinetic model constructed in this study is available as Supporting Information. The dominant reaction steps are described as follows: Dissociation/recombination: F2 + M = F + F + M (R3) HF + M = H + F + M

(R6)

(R5) 14043

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4.2. Kinetic Simulation. The laminar burning velocities were calculated using the present kinetic model employing various values of the rate constants for the presumed chain branching reactions, k1 and k2. Figures 3 and 4 show a

Figure 1. Burning velocities for the H2/F2/O2/N2 flame with X(N2)/ X(O2) of 0.84/0.05 (circles), 0.82/0.05 (squares), and 0.79/0.10 (diamonds) as a function of the equivalence ratio. Lines represent the results of the kinetic simulation using the model including reaction R2 with Ea2 = 59 kJ mol−1. Figure 3. Comparison of the experimental (symbols) and simulated (lines) burning velocities for the H2/F2/O2/N2 flames at X(N2) = 0.84 and X(O2) = 0.05. The lines denote the simulation results with k1 = 0 (solid), 1 × 10−14 (dotted), 5 × 10−14 (dashed), and 1 × 10−13 (dashed−dotted) cm3 s−1. The reaction R2 was not included in these simulations.

0.84/0.05, 0.82/0.05, and 0.79/0.10. The symbols represent the experimental results, and the lines are the results of the kinetic simulation described later. The burning velocities had their peaks at ϕ = 1.2; the peak value at X(N2) = 0.84 and X(O2) = 0.05 was 165 cm s−1. A reduction of only 2% of the N2 mole fraction resulted in a significant increase of the burning velocity, indicating the strong oxidizing ability of F2. On the other hand, increase of the mole fraction of O2 to X(O2) = 0.10 while keeping the sum of X(N2) and X(O2) constant at X(N2) + X(O2) = 0.84 + 0.05 = 0.89 caused a slight decrease in the peak burning velocity to 124 cm s−1. This behavior can be explained by the inhibition of the H2/F2 chain reactions by the H + O2 + M = HO2 + M reaction, as suggested previously.11 The dependence of the burning velocity on the mole fraction of N2 at ϕ = 1.0 and X(O2) = 0.05 is plotted in Figure 2. The burning velocity exhibited a monotonic decrease with an increase in X(N2).

Figure 4. Comparison of the experimental (symbols) and simulated (lines) burning velocities for the H2/F2/O2/N2 flames at X(N2) = 0.84 and X(O2) = 0.05. The lines denote the simulation results excluding reaction R2 (solid) and including reaction R2 with Ea2 = 50 (dotted), 55 (dashed), 59 (dashed−dotted), and 60 (dashed−dotted−dotted) kJ mol−1. The reaction R1 was not included in these simulations.

comparison of the burning velocities calculated by varying the rate parameters for reactions R1 and R2, respectively, at X(N2) = 0.84 and X(O2) = 0.05. The experimental burning velocities are also plotted as symbols. In Figure 3, the burning velocities were computed with k1 = 0, 1 × 10−14, 5 × 10−14, and 1 × 10−13 cm3 s−1 and without including reaction R2. The simulation performed without considering both of the chain-branching reactions, which is represented by the solid line, underestimated the experimental velocities by a factor of ∼2. Including reaction R1 with k1 less

Figure 2. Burning velocities for the H2/F2/O2/N2 flame at ϕ = 1.0 and X(O2) = 0.05 as a function of X(N2). Lines represent the results of the kinetic simulation using the model including reaction R2 with Ea2 = 59 kJ mol−1. 14044

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than 10−14 cm3 s−1 had almost no effect on the calculated burning velocity. The velocity was increased slightly and significantly with k1 = 5 × 10−14 and 1 × 10−13 cm3 s−1, respectively, but only at the low ϕ condition. The reaction R1 is the collision-induced dissociation of F2 by the vibrationally excited HF; this reaction should be increasingly effective as the equivalence ratio is lowered where the mixture contains excess F2 compared to H2. Therefore, the reaction R1 is not responsible for the chain-branching step in the H2/F2/O2/N2 flame, and the upper bound of its rate constant was determined to be ∼10−13 cm3 s−1. This upper bound is smaller by a factor of ∼102 than the value of the rate constant employed by Warnatz et al.19,20 in their kinetic modeling studies of the H2/F2/Ar flame; however, the value is consistent with those obtained in the studies of Sullivan et al.5 and Seeger et al.,12 who suggested the values of k1 = (3−12) × 10−18 cm3 s−1 at 350 K and k1 < 1.7 × 10−13 cm3 s−1 at ∼400 K, respectively. The burning velocities calculated including the reaction R2 and excluding reaction R1 are plotted in Figure 4. The rate constant for reaction R2 was assumed to be 7.5 × 10−20 cm3 s−1 at 310 K,17 and its activation energy, Ea2, was varied between 50 and 60 kJ mol−1. The corresponding A factor can be calculated as A = 7.5 × 10−20/exp(−Ea2/310R) cm3 s−1. No significant change in the burning velocity was observed at Ea2 < 50 kJ mol−1. On the other hand, the burning velocity was sensitive to the value of Ea2 at Ea2 > 55 kJ mol−1, and the experimental results were accurately reproduced with an Ea2 of 59 kJ mol−1. The corresponding A factor was 6.6 × 10−10 cm3 s−1. The simulation results obtained with this rate constant under other conditions are also plotted in Figures 1 and 2. The sensitivity analysis was performed at ϕ = 0.8, 1.0, and 1.4, X(N2) = 0.84, and X(O2) = 0.05 using the model including reaction R2 with k2 = 6.6 × 10−10 exp(−59 kJ mol−1/RT) cm3 s−1. The reaction R1 was not included in this calculation. The reactions with the 10 largest sensitivity coefficients for the burning velocity are shown in Figure 5. The presumed chainbranching reaction has the largest positive sensitivities, suggesting the significant role of this reaction in H2/F2 combustion systems. The large negative sensitivities of the H

+ O2 + M = HO2 + M reaction are due to the inhibition of the chain reactions by trapping H atoms, which are important chain carriers. The positive sensitivities of the reactions of F + H2 and H + F2, producing the vibrationally excited HF radicals, demonstrate the importance of the vibrationally excited species in the chain reaction mechanism. The V−V exchange reaction between HF and H2, HF(1) + H2 = HF + H2(1) (reaction R9), also exhibits a positive sensitivity because H2(1) contributes to the chain branching. 4.3. Quantum Chemical Calculation on the H2 + F2 Reaction. The present modeling study suggested that the reaction R2, H2(1) + F2 = HF + H + F, plays a dominant role as a chain-branching step in the combustion of H2/F2 systems, with an estimated rate constant of k2 = 6.6 × 10−10 exp(−59 kJ mol−1/RT) cm3 s−1. Here, a quantum chemical calculation was performed in order to examine the transition state and barrier height of this reaction. The calculation was performed using Molpro 2012.1 software.33,34 The geometry, vibrational harmonic frequencies, and energy of the transition state were calculated by an explicitly correlated internally contracted multireference configuration interaction (MRCI-F12) method.35−37 The reference wave functions were obtained from a full-valence multiconfiguration self-consistent field (MCSCF) calculation. The inner-shell correlation (+CV) and Davidson’s quadruples correction (+Q) were included in the MRCI calculation. A correlation-consistent quadruple-ζ basis set that was optimized for describing core−valence correlation effects with explicitly correlated methods, cc-pCVQZ-F12,38 was used throughout the study. The geometries and vibrational frequencies for H2, F2, and HF were obtained from the database.39 The energies of the reactants and the products were calculated at sufficiently large separations using the same level of theory as that used for the transition state. The MRCI-F12+CV+Q/cc-pCVQZ-F12 calculation identified a linear HHFF transition state for the H2 + F2 = HF + H + F reaction with an imaginary frequency of 1620i cm−1, which was directly correlated to the H2 + F2 reactants and the HF + H + F products. The H−H, H−F, and F−F bond lengths of the transition state were 0.865, 1.159, and 1.727 Å, respectively. The previously reported trapezoidal transition state on the empirical potential energy surface18 could not be located at the MRCI-F12+CV+Q/cc-pCVQZ-F12 level. The zero-point energy corrected energies of the linear transition state and the products were 113.0 and 24.8 kJ mol−1, respectively, relative to the reactants. The barrier height can be reduced to 63.2 kJ mol−1 by artificially lifting the energy of the reactants by the energy gap between H2(1) and H2, 4161 cm−1.39 This artificial barrier height agrees well with the activation energy of reaction R2 determined in the modeling study, 59 kJ mol−1. On the other hand, the vibrationally adiabatic energy of the transition state was 87.4 kJ mol−1 relative to the H2(1) + F2 reactants, considering the harmonic frequency of 2020 cm−1 for the H−H stretching mode of the transition state. However, the use of this value for Ea2 in the Arrhenius expression of k2 results in unphysically large A factor, 4 × 10−5 cm3 s−1 if k2 is assumed to be 7.5 × 10−20 cm3 s−1 at 310 K.17 Because rate constants for reactions involving vibrationally excited species depend largely on the configurations of the potential energy surfaces, a detailed dynamics study on a precise potential energy surface of this reaction is needed for further discussion.

Figure 5. Sensitivity coefficients for the burning velocity of the H2/F2/ O2/N2 flame at ϕ = 0.8, 1.0, and 1.4, X(N2) = 0.84, and X(O2) = 0.05. Calculations were performed using the model including reaction R2 with Ea2 = 59 kJ mol−1. 14045

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(10) Levy, J. B.; Copeland, B. K. W. Kinetics of the Hydrogen− Fluorine Reaction. III. The Photochemical Reaction. J. Phys. Chem. 1968, 72, 3168−3177. (11) Taylor, R. L.; Lewis, P. F.; Cronin, J. A Mechanism for the Photochemical Induced Combustion of H2/F2 Mixtures Inhibited by O2. J. Chem. Phys. 1980, 73, 2218−2223. (12) Seeger, C.; Rotzoll, G.; Lubbert, A.; Schugerl, K. A Study of the Reactions of Fluorine with Hydrogen and Methane in the Initiation Phase Using a Miniature Tubular Reactor. Int. J. Chem. Kinet. 1981, 13, 39−58. (13) Tiwari, A. K.; Patkar, V. C.; Yadav, C.; Ahamed, R.; Fani, H. Z.; Patwardhan, A. W.; Prasad, C. S. R.; Singhal, A. K.; Gantayet, L. M. Experimental and Numerical Investigation of the Subatmospheric H2− F2 Reaction. Combust. Sci. Technol. 2011, 183, 303−320. (14) Tiwari, A. K.; Prasad, C. S. R.; Patkar, V. C.; Patwardhan, A. W.; Gantayet, L. M. Influence of Excess Hydrogen and Nitrogen on Temperature Distribution of a Hydrogen−Fluorine Flame Reactor. Combust. Sci. Technol. 2011, 183, 883−896. (15) Manke, G. C.; Hager, G. D. A Review of Recent Experiments and Calculations Relevant to the Kinetics of the HF Laser. J. Phys. Chem. Ref. Data 2001, 30, 713−733. (16) Cohen, N.; Bott, J. F. Review of Rate Data for Reactions of Interest in HF and DF Lasers, Report No. SD-TR-82-86; Aerospace Corp.: El Segundo, CA, 1982. (17) Orkin, V. L.; Chaikin, A. M. Thermometric Determination of the Rate-Constant for the Reaction of Vibrationally Excited Hydrogen with Molecular Fluorine. Kinet. Catal. 1979, 20, 1129−1135. (18) Thompson, D. L.; McLaughlin, D. R. A Quasiclassical Trajectory Study of the H2 + F2 Reactions. J. Chem. Phys. 1975, 62, 4284−4299. (19) Warnatz, J. Calculation of the Structure of Laminar Flat Flames III: Structure of Burner-Stabilized Hydrogen−Oxygen and Hydrogen− Fluorine Flames. Ber. Bunsen-Ges. Phys. Chem. 1978, 82, 834−841. (20) Homann, K. H.; Schwanebeck, W.; Warnatz, J. Formation and Relaxation of Vibrationally Excited HF in H2−F2−Ar Flames. Ber. Bunsen-Ges. Phys. Chem. 1979, 83, 943−949. (21) Matsugi, A.; Shiina, H.; Takahashi, A.; Tsuchiya, K.; Miyoshi, A. Burning Velocities and Kinetics of H2/NF3/N2, CH4/NF3/N2, and C3H8/NF3/N2 Flames. Combust. Flame 2013, DOI: 10.1016/ j.combustflame.2013.12.001. (22) Metghalchi, M.; Keck, J. C. Laminar Burning Velocity of Propane−Air Mixtures at High Temperature and Pressure. Combust. Flame 1980, 38, 143−154. (23) Hill, P. G.; Hung, J. Laminar Burning Velocities of Stoichiometric Mixtures of Methane with Propane and Ethane Additives. Combust. Sci. Technol. 1988, 60, 7−30. (24) Goodwin, D. G. Cantera program, version 2.0.2; Caltech: Pasadena, CA, 2013; available at http://code.google.com/p/cantera (accessed Oct 10, 2013). (25) Hughes, K. J.; Turanyi, T.; Clague, A. R.; Pilling, M. J. Development and Testing of a Comprehensive Chemical Mechanism for the Oxidation of Methane. Int. J. Chem. Kinet. 2001, 33, 513−538. (26) Manion, J. A.; Huie, R. E.; Levin, R. D.; Burgess, D. R., Jr.; Orkin, V. L.; Tsang, W.; McGivern, W. S.; Hudgens, J. W.; Knyazev, V. D.; Atkinson, D. B.; et al. NIST Chemical Kinetics Database, NIST Standard Reference Database 17, version 7.0, release 1.6.7, Data version 2013.03; National Institute of Standards and Technology: Gaithersburg, MD, 2013. (27) Gordon, S.; McBride, B. J. Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications, NASA Reference Publication 1311; National Aeronautics and Space Administration: Cleveland, OH, 1996. (28) Baulch, D. L.; Duxbury, J.; Grant, S. J.; Montague, D. Evaluated Kinetic Data for High Temperature Reactions. Volume 4. Homogeneous Gas Phase Reactions of Halogen- and Cyanide-Containing Species. J. Phys. Chem. Ref. Data 1981, 10, 1−721. (29) Han, J.; Heaven, M. C.; Manke, G. C. Hydrogen Atom Reactions with Molecular Halogens: The Rate Constants for H + F2 and H + Cl2 at 298 K. J. Phys. Chem. A 2002, 106, 8417−8421.

5. CONCLUSION The burning velocities for the H2/F2/O2/N2 flames were measured at various equivalence ratios and mole fractions of N2 and O2. The results were compared to that obtained by a kinetic simulation with a detailed kinetic model involving vibrationally excited species, HF(ν) and H2(ν), and chainbranching reactions, HF(ν > 2) + F2 = HF + F + F (reaction R1) and H2(1) + F2 = HF + H + F (reaction R2). The present study indicated that the reaction R1 is not responsible for the chain-branching step, while the reaction R2 plays a dominant role in the chain reaction mechanism. With a rate constant of k2 = 6.6 × 10−10 exp(−59 kJ mol−1/RT) cm3 s−1 for reaction R2, the kinetic model reproduced the experimental burning velocities. A linear transition state with a barrier height of 113.0 kJ mol−1 was identified for the H2 + F2 = HF + H + F reaction by quantum chemical calculations at the MRCIF12+CV+Q/cc-pCVQZ-F12 level of theory, which reproduced the activation energy for reaction R2 determined from the modeling study if the energy of the reactants was artificially lifted by the energy gap between H2(1) and H2.

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ASSOCIATED CONTENT

* Supporting Information S

Kinetic model for H2/F2/O2/N2 combustion. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by the Ministry of Economy, Trade and Industry (METI). REFERENCES

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The Journal of Physical Chemistry A

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dx.doi.org/10.1021/jp410597n | J. Phys. Chem. A 2013, 117, 14042−14047