On the role of excited species in hydrogen combustion

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On the role of excited species in hydrogen combustion Alexander A. Konnov∗ Division of Combustion Physics, Lund University, Lund, Sweden

a r t i c l e

i n f o

Article history: Received 25 May 2015 Revised 8 July 2015 Accepted 9 July 2015 Available online xxx Keywords: Hydrogen Ozone Singlet oxygen Kinetic mechanism Ignition Oxidation Flame

a b s t r a c t Recently updated hydrogen combustion mechanism was combined with ozone decomposition reactions and extended by reactions of excited species: O(1 D), OH(2  + ), and O2 (a¹g). The reliability and the accuracy of the rate constants pertinent to these excited species were evaluated. Many reactions proposed in the literature and implemented in other kinetic schemes were found irrelevant or insignificant. The new mechanism for hydrogen combustion was then validated against commonly accepted sets of laboratory experiments. It was expected that new reactions incorporated into the model should not affect its predicting ability for “thermal” combustion of H2 , i.e. in the absence of excited species in the initial mixtures. The model validation showed that predictions of ignition, oxidation, flame burning velocities and flame structure of hydrogen– oxygen–inert mixtures are indistinguishable or very close to those of the basic mechanism at all condition, except for hydrogen oxidation in a flow reactor close to explosion limit. It was further demonstrated that singlet oxygen formed in reaction H2 + O2 (1) = H + HO2 at ppm levels may notably accelerate the process. Kinetic role of O(1 D) and OH(2  + ) in the “thermal” combustion of H2 was found negligible. In addition, hydrogen + air flame enhancement by singlet oxygen was modeled. It was demonstrated that the burning velocity increase with 1% of O2 (a¹g) seeded into the air is rather modest. Moreover, purely thermal effect due to additional enthalpy brought to the mixture exceeds chemical flame enhancement by the singlet oxygen. © 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction Macroscopic characteristics of fuel + oxidizer mixtures, such as ignition delays, flammability limits or laminar burning velocity, often impose constraints on efficiency and safety of practical combustion appliances. Enhancement and control of combustion processes is therefore highly important, especially if it can be achieved by modification of the mixture reactivity without changing the equivalence ratio or mass flow into a combustion device. Different scenarios, combined in a concept of plasma-assisted combustion, have been proposed, such as electrical discharge through the reacting mixtures or generation of active species, ozone, singlet oxygen, etc., upstream the oxidizer flow [1]. For the simplest hydrogen + air system it was demonstrated that ignition delays can be significantly shortened under the action of a high-voltage nanosecond discharge that was also successfully reproduced by the detailed kinetic model including electronically excited species [2]. Furthermore, direct current low pressure glow discharge was shown to substantially reduce induction length of the H2 + O2 mixture ignition in a flow reactor [3]. This experiment was simulated using one-dimensional [4] and 2D models [5] with the

∗

Corresponding author. E-mail address: [email protected]

emphasis on the relative role of singlet states of oxygen and odd oxygen (O + O3 ). Indeed, the discharge generates not only excited singlet states of oxygen, O2 (a¹g) and O2 (b¹ g+), but also ozone and excited atomic oxygen O(1 D). Depending on the distance from the generator to combustion zone, pressure, gas composition, and treatment of the surfaces, excited species may survive or not [5–7]. The only demonstration of the hydrogen flame acceleration caused by generation of active species in the low-pressure glow discharge was realized in the pioneering experiment of Basevich and Kogarko [8]. This effect was attributed to the enhanced chain branching in the reaction H + O2 (a¹g) [8, 9]. Owing to very limited experimental evidences, the individual effects of exited species on hydrogen combustion were often analyzed numerically. Starik and co-authors extensively investigated different types of excitation, such as vibrational [10–13], electronic, caused by discharge [4, 13–18], resonant laser radiation [19–21], or laserinduced decomposition of ozone [22]. The effects of excited species were modeled at the conditions of ignition, detonation, and flame propagation. In all cases it was claimed that excited species may effectively shorten ignition delays [4, 13, 14, 22], accelerate burning velocities [16, 17], and improve stabilization of detonation waves in supersonic flows [11–15, 18–20]. Other relevant studies of hydrogen combustion affected by excited species are not so numerous, yet tackle photochemical ignition of premixed H2 + air by excimer lasers [23], acceleration of detonation

http://dx.doi.org/10.1016/j.combustflame.2015.07.014 0010-2180/© 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Please cite this article as: A.A. Konnov, On the role of excited species in hydrogen combustion, Combustion and Flame (2015), http://dx.doi.org/10.1016/j.combustflame.2015.07.014

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development by addition of ozone [24], decrease of ignition delays [25–29], and increase of the burning velocities in hydrogen + air mixtures [26]. The detailed kinetic models developed and implemented in these numerical works are fundamentally diverse both in the ground-state (thermal) hydrogen chemistry and in the reactions of excited species. Chukalovsky et al. [5] compared the MSU (Moscow State University) mechanism [25, 30], the mechanisms developed by Starik and Titova in 2003 [19], by Starik et al. in 2010 [13], and updated mechanism based on the works of Popov [27–29]. They found that at the conditions of experimental study of Smirnov et al. [3], the most important initiation reaction is

H2 + O2 = OH + OH

(X1)

in the MSU mechanism, in the earlier model of Starik and Titova [19], and in their own model [5]. Admitted that this reaction is an artificial “brutto process” they argued that its inclusion is required for proper description of the thermal self-ignition of hydrogen. This and other reactions to be excluded from the hydrogen kinetic mechanism are discussed in the present work. Most recent models of Starik et al. [13, 18, 31, 32] seem to properly incorporate reaction

H2 + O2 = H + HO2

(14)

as initiation step in the absence of excited species. However, overall performance of these mechanisms in hydrogen combustion modeling was shown to be unsatisfactory. Olm et al. [33] presented extensive analysis of the performance of 19 recent hydrogen combustion models in comparison with ignition measurements in shock tubes and rapid compression machines, burning velocity measurements and concentration–time profiles in jet-stirred and flow reactors, covering wide ranges of temperature, pressure and equivalence ratio. The analysis indicates that the performance of the mechanism of Starik et al. [31] is far from being satisfactory and cannot be recommended for the modeling of hydrogen combustion. Reactions pertinent to excited singlet states of oxygen and ozone implemented in the most recent models of Starik et al. [13, 32], of Popov [5, 29], and in the MSU mechanism [25, 30] are most often inconsistent and largely different in rate constants as well. The inconsistency is manifested in the irreversibility of many reactions with excited species. It was demonstrated [34] that due to the incompleteness of the MSU mechanism (absence of many reverse reactions) it predicts an incorrect balance between O atoms, excited and ground state oxygen in ozone flames. It should be noted, however, that ozone reactions from the MSU mechanism [25, 30] excluding excited oxygen species are mostly balanced, and their implementation in the recent studies of combustion enhancement by ozone [6, 35–39] is justified. Yet, conclusions based on the complete set of reactions taken from the MSU mechanism by Ombrello et al. [7], and by Bourig et al. [26], should be treated cautiously. In the present study recently updated hydrogen combustion mechanism [40] is combined with ozone decomposition reactions [34] and extended by reactions of excited species: O(1 D), OH(2  + ), O2 (a¹g). The goal of the present work was to evaluate the reliability and the accuracy of the rate constants pertinent to these excited species, and to validate and analyze kinetic mechanism predictions at high temperatures. A possible role of excited species in hydrogen combustion is evaluated and analyzed.

combustion chemistry [19, 20, 41]. However, the O2 (b¹ g+)-state is very short lived and due to physical quenching relaxes quickly to the lowest lying excited state, O2 (a¹g). Collisional deactivation prevails at temperatures relevant to atmospheric chemistry (up to 370 K) [42– 44] with negligible importance of chemical reactions. Kozlov et al. [45] demonstrated that the physical deactivation dominates in the collision of O2 (a¹g) and O2 (b¹ g+) with H2 up to temperatures of 780–790 K. One may conclude that in the modeling of any technological combustion concept with upstream generation of O2 (b¹ g+)state, such as premixed flames, it can be represented by O2 (a¹g)state. Thus in the present mechanism only the O2 (a¹g)-state is included and in the following referred to as singlet oxygen. The triplet ground state of oxygen, O2 (X³ g−), is always termed O2 . Likewise vibrationally excited species are not considered in the model. Hydrogen polyoxides, HOOOH, HOOOOH and radical HO3 are not included as well. Although these species have recently received some attention as possible temporary reservoir of OH in atmosphere [46, 47], they were never considered in combustion models, except in [48]. Thermodynamic data were taken from the recent database of Goos et al. [49]. All reactions in the mechanism are reversible. Rate constants of the reverse reactions are calculated from the forward rate constants and thermodynamic data. The choice of the transport parameters implemented in the Chemkin package [50] for flame modeling was discussed by Alekseev et al. [40]. Following recommendations of Brown et al. [51] recently measured diffusion coefficients for OH, HO2 , and ozone [52] are adopted in the present model. Transport properties of excited species were assumed equal to those of corresponding ground-state species. 2.2. Reactions The detailed reaction mechanism developed in this study is listed in Table 1. The rate coefficients in the present work are given in cm3 mol s units, while activation energies are in cal/mole. In the following, the sources of the rate constants are outlined and particular choices are discussed. Also temperature ranges over which the rate constants were determined and associated uncertainties are presented. An estimated uncertainty factor, UF, implies that the rate constant is expected to be in the range k/UF < k < k∗ UF. Reactions comprising updated hydrogen combustion mechanism as well as ozone decomposition reactions and associated rate constants have been discussed recently [34, 40], therefore they are only mentioned here if alternative product channels were proposed in in the most recent models of Starik et al. [13, 32], of Popov [5, 29], and in the MSU mechanism [25, 30]. The numbering of the reactions included in the present mechanism corresponds to Table 1, while reactions excluded from the model are listed in Table 2 with numbers (X1), (X2), etc. 2.2.1. Reactions of initiation Reaction

H2 + O2 = H + HO2

(14)

is adopted as the main initiation step of hydrogen oxidation in all contemporary models including those of Hong et al. [53], Burke et al. [54] and Keromnes et al. [55]. The second channel of initiation in hydrogen–oxygen mixtures

2. Reaction mechanism

H2 + O2 = OH + OH

2.1. Species, thermodynamic and transport parameters

is of negligible importance as discussed elsewhere, e.g., [54, 56], and can be excluded from the model. Chukalovsky et al. [5] had to implement reaction (X1) with unrealistically high rate constant to increase reactivity of their model at the conditions of experiments of

Coherent laser radiation may excite molecular oxygen to O2 (a¹g) or O2 (b¹ g+) singlet states of oxygen that could individually affect

(X1)

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3

Table 1 Extended H/O kinetic mechanism, units are cm3 mol s cal K, k = ATn exp(−Ea /RT). UF—uncertainty factor. No 1a

1b 1c 1d 2

3

4a

4b 5a

5b

5c

5d

6

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21a 21b

22a 22b 23

24a

Reaction

A

n

H + H+M = H2 +M a 7.00E+17 −1.0 Enhanced third-body efficiencies (relative to Ar): H2 = 0, N2 = 0, H = 0, H2 O = 14.3 1.00E+17 −0.6 H + H + H 2 = H2 + H2 5.40E+18 −1.3 H + H+N2 = H2 +N2 3.20E+15 0 H + H + H = H2 + H 1.00E+17 −1.0 O+O+M = O2 +M a Enhanced third-body efficiencies (relative to Ar): O = 28.8, O2 = 8, NO = 2, N = 2, N2 = 2, H2 O = 5, O3 = 8 6.75E+18 −1.0 O + H+M = OH+M a Enhanced third-body efficiency: H2 O = 5 6.06E+27 −3.312 H2 O+M = H+OH+M a Enhanced third-body efficiencies (relative to Ar): H2 O = 0, H2 = 3, N2 = 2, O2 = 1.5, He = 1.1 1.00E+26 −2.44 H2 O + H2 O = H+OH + H2 O 4.66E+12 0.44 H+O2 (+M) = HO2 (+M) a , b Low pressure limit: 1.74E+19 −1.232 Fcent = 0.67 Enhanced third-body efficiencies (relative to N2 ): Ar = 0, H2 O = 0, O2 = 0, H2 = 1.5, He = 0.57 4.66E+12 0.44 H+O2 (+Ar) = HO2 (+Ar) b Low pressure limit: 4.57E+18 −1.12 Fcent = 0.5 4.66E+12 0.44 H+O2 (+O2 ) = HO2 (+O2 ) b Low pressure limit: 5.69E+18 −1.094 Fcent = 0.5 4.66E+12 0.44 H+O2 (+H2 O) = HO2 (+H2 O) b Low pressure limit: 3.67E+19 −1.0 Fcent = 0.8 2.00E+12 0.9 H2 O2 (+M) = OH+OH(+M) Low pressure limit: 2.49E+24 −2.3 Fcent = 0.42 Enhanced third-body efficiencies (relative to Ar): H2 O = 7.5, H2 O2 = 7.7, CO2 = 1.6, O2 = 1.2, N2 = 1.5, He = 0.65, H2 = 3.7, CO = 2.8 5.08E+04 2.67 O + H2 = OH + H 1.04E+14 0 H + O2 = OH+O 2.14E+08 1.52 H2 + OH = H2 O + H 3.34E+04 2.42 OH + OH = H2 O + O 2.85E+10 1 HO2 + O = OH + O2 7.08E+13 0 H + HO2 = OH + OH 2.20E+08 2.0 H2 O + O = HO2 + H 7.40E+05 2.43 H2 + O2 = H + HO2 7.0E+12 0 HO2 + OH = H2 O + O2 c + 4.5E+14 0 c 1.03E+14 0 HO2 + HO2 = H2 O2 + O2 + 1.94E+11 0 5.02E+06 2.07 H2 O2 + H = HO2 + H2 2.03E+07 2.02 H2 O2 + H = H2 O+OH 9.55E+6 2 H2 O2 + O = HO2 + OH 1.74E+12 0 H2 O2 + OH = HO2 + H2 O c + 7.59E+13 0 4.29E+17 −1.5 O2 + O + Ar = O3 + Ar + 5.10E+21 −3.2 6.53E+17 −1.5 O2 + O + M = O3 + M Enhanced third-body efficiencies (relative to N2 ): Ar = 0, O2 = 0.95, O3 = 2.5, O = 4 + 1.33E+22 −3.3 Enhanced third-body efficiencies (relative to N2 ): Ar = 0, O2 = 1.07, O3 = 2.5, O = 4 4.82E+12 0 O3 + O = O2 + O2 1.44E+11 0 O3 + O = O2 (1) + O2 7.00E+15 −1.0 O + O + M = O2 (1) + M Enhanced third-body efficiencies (relative to Ar): O = 28.8, O2 = 8, NO = 2, N = 2, N2 = 2, H2 O = 5, O3 = 8 1.80E+06 0 O2 (1) + M = O2 + M Enhanced third-body efficiencies (relative to O2 ): O = 0, H = 0, Ar = 0.005, He = 0.005, N2 = 0.002, CO2 = 0.01, H2 O = 3.3, H2 = 2.5, CO = 5.6

Ea

T range (K)

UF

Source

0

77–5000

2

[175]

0 0 0 0

300–2000 50–5000 77–2000 50–5000 300–5000

5 2.5 3.2 3.2 2

[175] [175] [175] [175] [115] [176, 177] [178] [179] [180]

0

2950–3700

2 3 2 3

120770

300–3400

2

[181] [182] [182]

120160 0 0

300–3400 300–2000 300–700

2 1.2 1.3

[182] [183] [184]

0 0

300–2000 300–700

1.2 1.3

[184] [183] [184]

0 0

300–2000 300–700

1.2 1.3

[183] [184]

0 0

300–2000 1050–1250

1.2

[183] [185]

48750 48750

500–1500 500–1500

1.5 2.5

[186] [186] [186]

6292 15286 3450 −1930 −723.9 300 61600 53500 −1093 10930 11040 −1409 4300 2620 3970 318 7269 0 0 0

297–2495 1100–3370 300–2500 250–2400 150–1600 300–1000 1500–4000 400–2300 300–2200

1.3 1.1 1.5 1.5 2 2 5 1.5 2

300–1250

80–1500

2.5 1.4 3 3 3 1.5 1.5 1.2

[187] [160] [188] [188] [54] [172] [189] [82] [67] [67] [66] [66] [151] [151] [190] [159] [159] [191]

100–1000

1.2

[191]

1.1 2

[192] [193] [191] [65] [193] [65] [116] See text [34]

300–2400 300–2400 300–2500 280–1640

0

4094 4094 0

200–400 200–400 300

1.1 2 1.15 3 2

400

100–450

1.5

[65]

2 1.2

[88] [89, 90] [194] (continued on next page)

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Table 1 (continued) No

Reaction

24b 24c 25

O2 (1) + O = O2 + O 7.80E+07 4.00E+13 O2 (1) + H= O2 + H 3.60E+15 O2 (1) + O + M = O + O2 + M Enhanced third-body efficiencies (relative to O2 ): Ar = 0.63 3.13E+13 O2 (1) + O3 = O2 + O2 + O 6.03E+12 O(1D) + O2 (1) = O + O2 1.59E+13 O(1D) + O2 = O + O2 (1) 2.81E+12 O(1D) + O2 = O + O2 O(1D) + M = O + M 4.80E+11 Enhanced third-body efficiencies (relative to Ar): O2 = 0, N2 = 0, O = 10, H2 O = 3 1.26E+13 O(1D) + N2 = O + N2 7.23E+13 O(1D) + O3 = O2 + O + O 7.23E+13 O(1D) + O3 = O2 + O2 6.16E+05 H2 + O2 (1) = H + HO2 3.50E+08 H + O2 (1) = OH + O 9.89E+09 H + O2 (1) + M = HO2 + M 1.093E+05 HO2 + OH = H2 O+O2 (1) 1.30E+13 OH + O2 (1) = O + HO2 8.43E+13 O3 + H = OH + O2 1.00E+12 O3 + OH = HO2 + O2 5.85E−04 O3 + HO2 = OH + O2 + O2 2.50E+12 H + HO2 = H2 O + O(1D) 8.10E+13 O(1D) + H2 = OH + H 1.00E+14 O(1D) + H2 O = OH + OH ∗ 1.50E+13 O + H + M = OH + M Enhanced third-body efficiencies (relative to H2 ): Ar = 0.35, H2 O = 6.5, O2 = 0.4, N2 = 0.4 8.40E+11 OH∗ + O2 = OH + O2 1.08E+11 OH∗ + N2 = OH + N2 2.96E+12 OH∗ + H2 O = OH + H2 O ∗ 3.54E+11 OH + H2 = OH + H2 1.50E+12 OH∗ + OH = OH + OH 1.50E+12 OH∗ + H = OH + H 1.50E+12 OH∗ + O = OH + O 2.17E+10 OH∗ + Ar = OH + Ar 2.60E+12 OH∗ + H2 = H2 O + H 2.52E+11 OH∗ + O2 = O3 + H ∗ 1.008E+12 OH + O2 = HO2 + O ∗ 2.96E+12 OH + H2 O = H2 O2 + H 1.40E+06 OH∗ = OH + hν

26 27 28a 28b 29a

29b 30a 30b 31 32 33 34 35 36 37 38 39 40 41 42

43a 43b 43c 43d 43e 43f 43g 43h 44 45 46 47 48 a b c

A

n

Ea

T range (K)

UF

Source

3 3 10

[99] [27] [195]

300

1.2 10 1.2 5 1.2

[116] [65] [196] [65] [34] [197] [116] [144] [198] [65] [65] This work [112] [73] [124] [14] [134] [65] [65] See text [144] [144] [149] [149] See text [154] See text See text [150] [150] [150] [146, 155] See text See text See text See text [158]

0 0 0

0 5030 0

300 300–1000 300

0 0 0 0 0

5644 0 −139 −139 0

280–360 300 200–350

0 0 0 2.335 1.45 2.03 1.707 0 0 0 4.57 0 0 0 0

−230 0 0 31080 4508 3360 12535 34000 934 1870 −1377 300 0 −71 5970

210–370 100–400 100–400 300–2300 300–2000 200–1100 200–2000 300–2000 200–430 220–450 250–340 300–2500 227–453 227–453 1400–3300

2 2 1.2 1.1 1.1 3 3 10 3 10 2 1.5 1.6 3 1.1 1.1 1.5

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0

−482 −1238 −861 −444 0 0 0 2060 −444 −482 −482 −861 0

300–2000 300–2000 300–2000 300–2000 1200–3200 1200–3200 1200–3200 1900–2300 300–2000 300–2000 300–2000 300–2000 300

1.5 1.5 3 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 3 1.1

All other species have efficiencies equal to unity. The fall-off behavior of this reaction is expressed in the form as used by Baulch et al. [188] and others. Rate constant is the sum of two expressions.

Table 2 Reactions not included in the present mechanism.

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22

Reaction

A

n

Ea

Ref.

Included in

H2 + O2 = OH + OH H2 + O2 => O + H2 O H2 + O2 + O2 => HO2 + HO2 HO2 + HO2 = H2 O + O3 HO2 + HO2 = H2 O2 + O2 (1) HO2 + HO2 + M = H2 O2 + O2 + M H2 + O2 (1) => H2 O + O(1D) H2 + O2 (1) => OH + OH O2 (1) + O + M = O3 + M HO2 + O2 (1) = O2 + HO2 ∗ O2 (1) + HO2 ∗ = H + O2 + O2 HO2 ∗ + O2 = HO2 + O2 O + OH + M = HO2 + M O3 + H = OH + O2 (1) O3 + H = O + HO2 O3 + OH = HO2 + O2 (1) O3 + HO2 = OH + O2 + O2 (1) O3 + H2 = OH + HO2 H + OH + OH = OH∗ + H2 O O(1D) + H + M = OH∗ + M H2 + HO2 = H2 O + OH∗ H2 O + OH = H2 + HO2

2.04E+12 3.0E+13 2.0E+17

0.44 0 0

69,155 69,545 25,830

[62] [61] [61]

[5, 25] [25] [25]

9.0E+12 6.84E+14 3.5E+13 1.7E+15 6.9E+12 1.0E+13

0 0 0 0 0 0

1000 −1950 39,750 33,780 −2090 0

[14] [65] [62] [14] [14] [107]

[25] [56] [25] [25] [25] [5]

3.6E+12 1.0E+15

0 0

0 0

[102] [114]

[5] [25] [25]

2000 2000 20,000 0 0 38,000 71,700

[14] [14] [13] [150] [25] [61] [174]

[25] [25] [32]

4.8E+11 1.0E+10 6.0E+10 1.1E+16 1.5E+18 4.8E+19 7.9E+09

0 0 0 0 −1 −1.7 0.43

[25] [25] [25]

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Smirnov et al. [3]. This motivation, however, is clearly misleading since the problem of the disagreement between experimental measurements of hydrogen self-ignition and model predictions at lower temperatures (below around 1000 K) is well recognized and does not relate to the gas-phase chemistry. This disagreement has been observed in different types of equipment, such as shock tubes, flow reactors and rapid compression machines, and has generally been attributed to perturbations [57, 58], for example variations in equivalence ratio due to gradual mixing, pressure and temperature rise caused by isentropic compression, or catalytic effects from reactor vessel walls or particles. Dryer and Chaos [58, 59] indicated that catalytic reactions on surfaces of the experimental apparatus responsible for significantly reducing autoignition times can be accounted for in the modeling by accelerating reactions H2 + HO2 = H2 O2 + H, and H2 O2 + M = OH + OH, and thus artificially increasing production of hydroxyl radicals. In the models of Popov et al. [5, 29], in the earlier model of Starik and Titova [19], and in the MSU mechanism [25] the same increase is achieved by reaction (X1). The disagreement was again observed in recent flow-reactor experiments by Schonborn et al. [60]. When the kinetic model of Keromnes et al. [55] was extended to explicitly include surface reactions on the reactor walls, the calculations could be reconciled with the experimental data, suggesting that wall reactions had a significant influence on autoignition delays at lower temperatures [60]. The MSU mechanism [30, 25] incorporates two more irreversible initiation reactions

H2 + O2 => H2 O + O

(X2)

H2 + O2 + O2 => HO2 + HO2

(X3)

Smekhov et al. [25] implemented the rate constant of reaction (X2) shown in Table 2, while referring on the work of Skrebkov et al. [61] as the origin of it. In any case, the rate constants of reaction (X2) are much smaller than that calculated for reaction (X1) [62], and therefore it cannot be kinetically important. Note that Skrebkov et al. [61] also found reactions (X1) and (X2) unimportant in their analysis of hydrogen self-ignition from 1000 to 2500 K. Reaction (X3) is essentially a reverse process of reaction between hydroperoxyl radicals which may lead to different products [63, 64]:

HO2 + HO2 = H2 O2 + O2 HO2 + HO2 = H2 + O2 + O2

(16) (-X3)

HO2 + HO2 = H2 O + O3

(X4)

HO2 + HO2 = H2 O2 + O2 (1)

(X5)

At lower temperatures typical for atmospheric chemistry the rate constant of this reaction is known to be pressure-dependent and represented as

HO2 + HO2 + M = H2 O2 + O2 + M

(X6)

Moreover, reaction (X6) is enhanced in the presence of water or methanol molecules, yet this effect is confined to low temperatures only [64, 65]. The rate expression for reaction (16) proposed by Kappel et al. [66] and recently reconfirmed by Hong et al. [67] was adopted by Konnov [56], Alekseev et al. [40], and kept in the present work. Yield of hydrogen in reaction (-X3) was experimentally found negligible and below 1E−4 [68], while the branching ratio of the reaction path (X4) forming O3 was determined to be less than 1E−3 [69] thus both channels can be safely ignored. Recent ab initio calculations of reaction between hydroperoxyl radicals [63, 70, 71] equally

5

confirmed that the most favored product channel is formation of hydrogen peroxide and oxygen. At the G2M level of theory [63] the transition states associated with formation of singlet oxygen were found 2.8–5.6 kcal/mol above the reactants, that is already higher than the activation energy of 1 kcal/mol implemented in the MSU mechanism [25]. Anglada et al. [71] questioned these calculations and identified the lowest transition state for reaction (X5) 8.4 kcal/mol above the reactants. Formation of O2 (1) has never been observed experimentally [72] and therefore this channel is excluded from the present model. Reaction (X6) was included in the mechanism of Konnov [56] with the rate constant suggested in the review of the IUPAC [65] to investigate a possible role of the pressure dependence of the HO2 self-reaction. Zhou et al. [70] later found that the effect of pressure is negligible at all pressures below 10 atm and above 700 K. Therefore this reaction was not included in the updated model of Alekseev et al. [40], and in the present mechanism. In the presence of singlet oxygen, initiation will be enhanced in reaction

H2 + O2 (1) = H + HO2

(31)

Starik and Sharipov [73] recently reviewed existing theoretical calculations and estimations of the rate constant of this reaction and recommended to use expression recalculated from the reverse reaction rate constant obtained by ab initio calculations at the G3 level of theory [74]. Yet, in the latest modification of the mechanism by Sharipov and Starik [32] they implemented the rate constant suggested by Basevich and Belyaev [9]. This rate constant, in turn, was an upper limit estimation [9] not supported by experimental data. The rate constant evaluated using bond-energy–bond-order method [75] was found approximately 10 times smaller. Ab initio analyses of the potential energy surface [73, 74, 76] indicated significantly different activation barriers depending on the level of theory employed. Hence, to derive the rate constant in the present study, existing measurements of the reverse reaction (-31) were analyzed. Reaction between hydroperoxyl radicals and atomic hydrogen forming singlet oxygen has been studied only at room temperature [72, 77–79]. Formation of O2 (b¹ g+) has been detected by Hislop and Wayne [77], Keyser et al. [78], and Michelangeli et al. [79] with the branching ratios relative to all products found to be 2.8E−4, <8E−3, and ≤2.1E−2, respectively. Washida et al. [72] used photoionization mass-spectrometer to detect singlet oxygen and determined the yield of 0.015 ± 0.003. Arguing that only O2 (a¹g) and O2 (b¹ g+) could be ionized and that formation of O2 (b¹ g+) is negligible [77], this branching ratio was attributed to O2 (a¹g) assuming the ionization cross section for singlet oxygen states are equal. This photoionization technique has been developed by Clark and Wayne [80] to study reactions involving O2 (a¹g). Later McLaren and co-authors [81] realized that this method is not really state-specific and contribution from small amount of other excited oxygen states may significantly affect concentrations and branching ratios deduced from it. For this reason the measurements of Washida et al. [72] could be considered only as an upper limit and they were not included in the evaluation of the IUPAC [65]. Michelangeli et al. [79] attempted to reconcile available experimental data [72, 77–79] using detailed kinetic model with reactions of both O2 (a¹g) and O2 (b¹ g+) states. Remarkably, they found the best agreement with the branching ratio of O2 (a¹g) formation of 0.017, in good agreement with the value obtained by Washida et al. [72]. Accepting the recommended overall rate constant of H + HO2 = Products [65], the rate constant of reaction (-31) at room temperature is then 7.2 E+11 cm3 /mol s. Comparing this value with the rate constant of reaction

H + HO2 = H2 + O2

(-14)

shows that 27% of oxygen formed in reaction between hydroperoxyl radicals and atomic hydrogen is in O2 (a¹g) state. Hence, in the

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present mechanism the expression for the rate constant of reaction (-14) based on the results of Michael et al. [82] was multiplied by a factor of 0.27 and recalculated back using thermodynamic data for singlet oxygen to obtain the rate constant of reaction (31) listed in Table 1. Owing to the uncertainty of the rate constant of reaction (14) and assumptions discussed above the uncertainty of this expression is evaluated to be of a factor of 3. Effective activation energy of this rate constant is somewhat lower than the earlier estimations [9, 75], yet the difference between this expression and the rate recalculated from the reverse reaction rate constant [74] by Starik and Sharipov [73] does not exceed a factor of 3. Note that in the most recent models of Starik et al. [13, 32] reaction (31) is considered irreversible, thus no singlet oxygen could be formed from H and HO2 . On the contrary, in the MSU mechanism [25, 30] this reaction is written in the reverse direction only. The MSU mechanism contains two more irreversible reactions of initiation:

H2 + O2 (1) => H2 O + O(1D)

(X7)

H2 + O2 (1) => OH + OH

(X8)

The rate constant of reaction (X7) originates from the calculations of Karkach and Osherov [62] and is significantly smaller than that of reaction (31). The existence of the reverse reaction has not been completely ruled out [83, 84], yet there is no data to substantiate the significance of it. The rate constant of reaction (X8) was estimated by Starik and Titova [14], however it was excluded from the recent models of the same co-authors. Both reactions are ignored in the present mechanism as well. 2.2.2. Reactions of singlet oxygen Collisional quenching of singlet oxygen

O2 (1) + M = O2 + M

(24)

is important process since it competes with enhanced initiation and chain branching caused by O2 (1). Rate constants for interaction with O2 , O, O3 , N2 and Ar have been discussed previously [34], in the present work some collisional efficiencies are updated and the mechanism is extended by hydrogen-containing collisional partners. IUPAC recommendations [65] were adopted for quenching by O2 with the activation energy obtained by Billington and Borrell [85]. Their measurements are in a very good agreement with the results of Chatelet et al. [86] and with the rate obtained later by Furui et al. [87]. Findlay and Snelling [88] summarized earlier measurements of collisional deactivation of singlet oxygen and concluded that hydrogen-containing species possess efficiencies close to molecular oxygen, which was recently confirmed for hydrogen [89], water [90], and a range of hydrocarbons [91]. This was attributed to weak chemical interaction otherwise manifested in reaction (31) or reaction between O2 (1) and H2 O discussed in the following. The measurements of deactivation rate constants for H2 and H2 O at room temperature show good consistency and recent accurate results [89, 90] are adopted in the present work. Since deactivation of O2 (1) is a spin forbidden process, the rates of quenching by non-reacting species, Ar, He, N2 and CO2 , are very small compared to O2 and hydrogen-containing collision partners. For consistency, all these rates were taken from the work of Findlay and Snelling [88]. The values for N2 and Ar used in our previous work [34] and based on the measurements of Clark and Wayne [80, 92] were apparently overestimated due to experimental problems [81] discussed above in relation to reaction (31). The temperature dependence obtained for O2 between 100 and 450 K [85] was assumed for other colliders with exception of atomic oxygen and hydrogen. In fact, the Arrhenius behavior of collisional quenching should not necessarily be expected; predictions of different models

of E–V energy transfer [85, 93, 94] can be better presented as powerlaw temperature dependences. Findlay and Snelling [88] approximated their measurements with the rate proportional to T0.78 ± 0.32 , while Popov [28] adopted T0.5 dependence based on theoretical calculations. One should note that description of the rate constant by T0.5 dependence does not deviate more than by a factor of 2 from the Arrhenius expression with activation energy of 400 cal/mol [85] over the entire temperature range from room to combustion temperatures. Much higher activation energy was found by Borrell and Richards in their experiments with H2 [95] and other collisional partners, SO2 and HCl [96]. The origin of this significant deviation is not clear, yet one can assume an impact of other participating species, such as atomic oxygen or other radicals and impurities. This is also indicated by the collisional quenching rate obtained at room temperature for H2 [95], which is 10 times higher than the commonly adopted value [89]. The expression obtained by Borrell and Richards [95] and similar one proposed by Popov [27] were implemented by Ombrello et al. [7] in attempt to explain rather low ethylene flame propagation enhancement by singlet oxygen observed experimentally. Both expressions exceed the rate of initiation reaction (31) by orders of magnitude up to temperatures around 2000 K as discussed by Popov [29], who then preferred the power-law dependence [5, 28]. Collisional quenching by O was also expected to be comparatively fast since it relates to chemical interaction and energy transfer in reactions

O2 + O + M = O3 + M

(21)

O2 (1) + O + M = O + O2 + M

(25)

O(1D) + O2 (1) = O + O2

(27)

O(1D) + O2 = O + O2 (1)

(28a)

O(1D) + O2 = O + O2

(28b)

The rate constants of these reactions were discussed previously [34]. Note that Starik and Titova [14] suggested the reversible reaction

O2 (1) + O + M = O3 + M

(X9)

with the estimated rate constant close to that of the ground-state oxygen recombination with O atoms. Since formation of significant amounts of singlet oxygen during ozone decomposition has no experimental evidence, this reaction was excluded from the ozone mechanism [34] and from the recent models of Starik and co-authors [18, 32], though it is present in the MSU mechanism [25, 30]. In the previous work [34] the rate of collisional quenching of singlet oxygen by O was taken from Cupitt et al. [97]. They, in turn, accepted an upper limit suggested by Evans et al. [98] from the analysis of atmospheric oxygen emissions. Clark and Wayne [92, 99] directly measured the rate of quenching by O using photoionization technique and found much smaller value. Although McLaren and co-authors [81] questioned this method themselves, the concentrations and branching ratios deduced from it can still be considered as upper limit values. For instance, the rate of collisional deactivation of O2 (1) by O2 found in these experiments [100] is only 40% higher than currently accepted value [65]. Thus the rate of Clark and Wayne [92, 99] is attributed here to individual reaction channel

O2 (1) + O = O2 + O

(24b)

Collisional quenching by H

O2 (1) + H = O2 + H

(24c)

is in direct competition with enhanced chain branching

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H + O2 (1) = OH + O

(32)

and relates to chemical interaction in reactions

H + O2 = OH + O

(8)

H + O2 (+ M) = HO2 (+ M)

(5)

H + O2 (1) (+ M) = HO2 (+ M)

(33)

All available experiments, except the study of Basevich and Vedeneev [101], of the rate constants of reactions (24c) and (32) have been summarized and analyzed by Hack and Kurzke [102]. They emphasized that Schmidt and Schiff [103] and Cupitt et al. [97] have measured the sum of the rate constants of quenching (24c) and chain branching (32). The same is applicable to the upper limit estimation of Schofield [104] based on atmospheric observations of singlet oxygen and to the measurements of Basevich and Vedeneev [101] in a flow reactor with detection of O2 (1) using ESR technique similar to other studies, e.g., [97]. Only Brown [105] analyzed his experiments [106] to provide separate upper limits for these rates. Hack and Kurzke [102] measured concentrations of H and O atoms and OH radicals and interpreted their temporal profiles using detailed kinetic scheme. They derived the rate constant of reaction (32) mostly from the profiles of O atoms in assumption that significant fraction (70%) of O2 (1) is consumed in reaction with HO2 forming excited HO2 radicals:

HO2 + O2 (1) = O2 + HO2 ∗

(X10)

This process is quite efficient due to resonant energy transfer [107]. Excited HO2 ∗ may further react with O2 (1) with very high rate constant [108]

O2 (1) + HO2 ∗ = H + O2 + O2

(X11)

or quench in

HO2 ∗ + O2 = HO2 + O2

(X12)

In this model (hereafter Model HK) enhanced chain branching due to the presence of O2 (1) occurs both in reactions (32) and (X11). Additional branching may occur due to decomposition of HO2 ∗ into O + OH. Since reaction (24c) does not consume H atoms and does not affect the profiles of O atoms, Hack and Kurzke [102] did not include it in the reaction scheme; they only estimated the pre-exponential factor of the rate constant of reaction (24c) to be of the order of 1E+12 cm3 /mol s that is about a factor of 10 faster than the rate constant derived for reaction (32). Quenching reaction (24c) was not a competing process for the chain branching (32) producing O atoms since the major sink of singlet oxygen was in reaction with HO2 radicals (X10). Contrary to the Model HK, in the original consideration of Basevich and Kogarko [8] (hereafter Model BK) and in other studies [9, 97, 101, 103–105] the role of hydroperoxyl radicals leading to the energy branching (the participation of excited intermediates in chain branching) was not considered. The Model HK is probably correct and has been substantiated in other studies, e.g., [79]; yet it requires consideration of the ground-state, vibrationally and electronically excited HO2 radicals. However, the Model BK is also suitable for description of the consumption of H atoms and singlet oxygen in reactions (24c) and (32) leading to physical quenching or chain branching. Hack and Kurzke [102] noted that additional chain branching in reactions with excited HO2 ∗ radicals is essentially included in the observable rate constant of reaction (32) obtained, for instance, by Cupitt et al. [97]. Moreover, dedicated experiments showed that the overall rates

7

observed are first-order with respect to H and O2 (a¹g) concentrations [103]. Thus both Models are appropriate for the modeling of enhanced chain branching by singlet oxygen. All available rate constant measurements for reactions (24c) and (32) are shown in Fig. 1. Raw data of Basevich and Vedeneev [101] are shown to illustrate pertinent experimental uncertainty. Chukalovsky et al. [5] employed simplified Model HK and suggested rather low rate constant of reaction (32) at the conditions of experimental study of Smirnov et al. [3]. Note that the rate constants interpreted in the Model HK [5, 102] are essentially the lower limit for the rate constant deduced in the Model BK [9, 97, 101, 103–105]. Sharipov and Starik [18, 109] recommended the rate constant of reaction (32) nicely crossing experimental points of Cupitt et al. [97] and Basevich and Vedeneev [101]. They also concluded that reaction (24c) contributes less than 10% to the total rate of reaction following suggestions that reactive channel (32) is faster than physical quenching [97, 101]. Since reactions of vibrationally excited species (essential in the complete Model HK) are beyond the scope of the present study, the Model BK is adopted here. To be consistent with this model rather high rate constant of O2 (a¹g) deactivation by HO2 in reaction (24) implemented in the models of Starik et al. [13, 32] is not considered as it would mimic reaction (X10) efficiently removing singlet oxygen especially at lower temperatures, yet without energy branching. Independent experiments or quantum calculations could be most helpful in elucidating the real elementary rate constants. The calculations, however, are very sensitive to the selection of potential energy surface that dramatically affects the calculated rate constants, as demonstrated by Sharipov and Starik [109]. Particularly, employment of the energy barriers taken from the ab initio calculations of Li et al. [110], Klos et al. [111], or their own [73], generates significantly different rate constants diverging by two orders of magnitude at room temperature. In the present work the rate constant of reaction (32) recently calculated with the potential energy surface [110] by Szabo and Lendvay [112] is adopted. The authors found that the rate of enhanced chain branching (32) is many orders of magnitude higher than the thermal reaction (8), yet it is several times lower than collisional quenching (24c). Arguing that experiments of Cupitt et al. [97] and of Basevich and Vedeneev [101] yield overall rate of the process, Szabo and Lendvay [112] suggested to use the expression of Popov [27] for the quenching rate; this recommendation is also adopted in the present work. Due to significant data scattering (Fig. 1) and remaining deviation of the theoretical calculations from the experiments, both rates are probably accurate to within a factor of 3. At practical atmospheric and higher pressures the role of recombination of H and O2 (a¹g) forming HO2 in reaction (33) is of increasing importance. In the absence of any experimental data the rate constant of reaction (33) calculated by Starik and Sharipov [73] is adopted in the present model. Only low-pressure term of this rate is implemented since the “fall-off” region for this reaction is expected at very high pressures. Hydroperoxyl radicals can be also formed in termolecular recombination of O atoms and hydroxyl radicals [113]:

O + OH + M = HO2 + M

(X13)

From the models considered in the present work this reaction is included only in the MSU mechanism [25, 30]. Burke et al. [54] demonstrated that with the currently adopted rate constant based on the theoretical study of Germann and Miller [114], inclusion of reaction (X13) has no effect on any of the model predictions. Besides of quenching, additional loss of singlet oxygen may occur in the reaction of its decomposition at high temperatures. In the previous work [34] the rate constant of reverse recombination

O + O + M = O2 (1) + M

(23)

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Fig. 1. Rate constants of reactions of H atoms with O2 (a¹g). Solid line: reaction (32) [112], dashed line: reaction (24c) [27]. Experiments: diamonds [97], dots [101], triangles [102], star [5].

was derived based on the total rate of reaction

O + O + M = O2 + M

deviate from the calculations of Gonzalez et al. [123]. In the absence of experimental data for reaction channel forming singlet oxygen (2)

taken from Warnatz [115], and suggestion of Vasiljeva et al. [116] that 10% of oxygen formed is in singlet state. This suggestion is correct, yet it comprises both excited states, O2 (a¹g) and O2 (b¹ g+). The statespecific fraction for reaction (23) is 7% [117], which is implemented in the present work. The uncertainty of this rate constant is then similar to that of the rate of reaction (2). Reacting with water singlet oxygen may produce two radicals, OH and HO2 . This process is essentially the reverse minor channel of reaction

HO2 + OH = H2 O + O2

(15)

Until recent studies of Hong et al. [67, 118] and of Burke et al. [119] there was a controversy between the rate constant of reaction (15) measured within 250–400 K [120] and anomalous deep and unusually narrow rate constant minimum observed around 1250 K [66, 121]. Srinivasan et al. [122] found no evidence for temperature dependence of the rate constant from 1237 to 1554 K. Hong et al. [118] measured this rate constant in the range 1600–2200 K and concluded that the expression of Keyser [120] can be extended from room up to these high temperatures. Ab initio calculations of Gonzalez et al. [123] also indicated small negative apparent activation energy supporting this rate constant. Most recently Burke et al. [119] re-interpreted experimental measurements for the H2 O2 decomposition including those indicating deep rate constant minimum [66, 121]. Their analysis guided by ab initio calculations showed that the rate constant of reaction (15) does exhibit weak temperature dependence with a shallow minimum around 1000 K. Simultaneously Hong et al. [67] performed dedicated experiments between 1070 and 1280 K and came to the same conclusion. The expression of Hong et al. [67] is adopted in the model of Alekseev et al. [40] and in the present work. This rate constant of reaction (15) is shown in Fig. 2 and does not significantly

HO2 + OH = H2 O + O2 (1)

(34)

one has to rely on theoretical rates. Reaction (34) was studied by Gonzalez et al. [124], by Xu et al. [125], and by Starik and Sharipov [73]. The rate constants calculated in these works and derived from discrete values [124] or from the reverse rate [73] are also shown in Fig. 2. Implementation of the rate constant recommended by Starik and Sharipov [73] in the models for hydrogen or syngas [32, 18] results in formation rate of singlet oxygen exceeding the rate of formation of the ground state oxygen at typical combustion temperatures that has no experimental evidence. Predictions of Gonzalez et al. [124], accepted in the present work, are based on potential energy surface which is in good agreement with that of Xu et al. [125]. Comparing rate constants of reaction (-31) between H atoms and HO2 radicals and reaction (34), one may conclude that formation of singlet oxygen in the last reaction has negligible impact on hydrogen combustion. Indeed, the rate constant of reaction (34) is at least four orders of magnitude smaller than that of reaction (-31) and thus requires unlikely [OH]/[H] ratio above 103 to be of any influence. Reaction (34), however, is kept in the model since its reverse may have important initiation role in the presence of singlet oxygen. The MSU mechanism [25, 30] and the models of Starik and coworkers since 2001 [14, 32] incorporate reaction

OH + O2 (1) = O + HO2

(35)

with the rate constant estimated in [14] without any explanation. It is tentatively retained in the present mechanism with high uncertainty factor since the calculated reverse rate constant of reaction (35) is 1–2 orders of magnitude smaller than the rate constant of reaction

HO2 + O = OH + O2 ,

(11)

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9

Fig. 2. Rate constants of reactions of OH radicals with HO2 . Dash-dot line: reaction (15) [67], dashed line: reaction (15) [123], solid line: reaction (34) [124], dash-double dot line: reaction (34) [73].

which, in its turn, is adopted from the model of Burke et al. [54]. Formation of O2 (1) in reaction between hydroperoxyl radicals and oxygen atoms has never been observed. Keyser et al. [78] determined an upper limit of O2 (b¹ g+) formation below 0.01. Kaye [126] and Lunt et al. [127] concluded that the energy released in this reaction is mostly converted into vibrational excitation of OH radicals. A possible role of reaction (35) will be further analyzed in the following. 2.2.3. Reactions of ozone Reactions of radicals with ozone may energetically produce singlet oxygen as discussed in atmospheric chemistry studies, e.g., [128, 129]. These channels, however, are always minor and may hardly influence combustion processes. For instance, the rate constant of reaction

O3 + O = O2 (1) + O2

(22)

(36)

These OH radicals could be vibrationally excited [130], which is not considered in the present work. The rate constant was measured mostly at low temperatures with consistent activation energies around 900 cal/mol [132, 133], though with notable scattering indicating an uncertainty of a factor of 2. In the present mechanism the evaluation of DeMore et al. [134] is adopted over extended temperature range reflecting good agreement with the experiments of Keyser [133] within 196–424 K. Formation of the singlet oxygen in reaction

O3 + H = OH + O2 (1)

(X15)

is not considered since it accounts for less than 0.02 of the total rate [137]. Its minor role was supported by theoretical calculations, e.g., [138]. Reaction

O3 + OH = HO2 + O2

Major channel of the ozone reaction with H atoms leads to formation of hydroxyl radicals:

O3 + H = OH + O2

O3 + H = O + HO2

(22b)

adopted in the ozone decomposition mechanism [34] is only a small fraction (<0.03) [130, 131] of the major channel

O3 + O = O2 + O2

was not detected [135, 136] and Washida et al. [136] determined an upper limit of the branching ratio as 0.001, therefore it is not considered in the present model. This reaction is included as irreversible in the MSU mechanism [25, 30] in its reverse direction (-X14) with the rate constant suggested by Starik and Titova [14]; yet, this rate is several orders of magnitude smaller than collisional quenching (24a), and thus kinetically unimportant in both directions. Similarly, reaction

(X14)

(37)

is important for ozone balance in atmospheric chemistry, therefore it was studied experimentally [65] and theoretically. Theoretical studies [139, 140] did not indicate a possibility of singlet oxygen formation

O3 + OH = HO2 + O2 (1)

(X16)

considered in the MSU mechanism [25], therefore reaction (X16) is not included in the present model. The rate constant of reaction (37) based on experimental studies [65] and supported theoretically [139, 140] is adopted. Note that reaction (X16) is included in the MSU mechanism with very high rate constant (half of the rate of reaction (37)) suggested by Starik and Titova [14]. Another sink of atmospheric ozone is via reaction with HO2 radicals

O3 + HO2 = OH + O2 + O2

(38)

Similarly to the previous reaction (37) of ozone with hydroxyl radical, formation of singlet oxygen in

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O3 + HO2 = OH + O2 + O2 (1)

(X17)

was not invoked in the theoretical study [141], and simple mechanism of H atom transfer is generally accepted [65]. The recommended rate constant of reaction (38) [65] is adopted here. Reaction (X17) with the rate constant inherited from Starik and Titova [14] is implemented in the MSU mechanism. Other processes with ozone participation were examined in the literature, such as O3 –H2 O complex formation [142], yet direct reaction of ozone with hydrogen was only considered by Sharipov and Starik [32]. Reaction

O3 + H2 = OH + HO2

(X18)

is essentially the reverse of reactions (15) and (34) discussed above. However, formation of ozone and hydrogen was not observed in reaction between hydroxyl and hydroperoxyl radicals either on singlet [124] or triplet [123] potential energy surfaces and therefore ignored in the present mechanism. 2.2.4. Reactions of O(1 D) Excited atomic oxygen O(1 D) can be generated in a discharge together with excited singlet states of oxygen and ozone. It will hardly survive between ozone generator and combustion zone, yet pertinent reactions are included in the model for completeness since it can also be formed in reactions of non-excited radicals. Specifically, reaction between hydrogen atoms and hydroperoxyl radicals has several channels

H + HO2 = OH + OH

(12)

H + HO2 = H2 + O2

(-14)

H + HO2 = H2 + O2 (1)

(-31)

H + HO2 = H2 O + O

(-13)

H + HO2 = H2 O + O(1D)

(39)

Theoretical studies of Karkach and Osherov [62], of Mousavipour and Saheb [74] and of Burke et al. [54] revealed that atomic oxygen can be formed in a ground state (reaction (-13)) or in excited state via reaction (39). These channels, however, are minor and their role is still disputable. Reaction (39) was only considered in the MSU mechanism [25] with the rate constant suggested by Skrebkov et al. [61]. Reaction (-13) was not included in the models of Burke et al. [54] and Keromnes et al. [55] arguing that it is kinetically similar to the channel (12) forming OH + OH. Yet, it was implemented in the mechanism of Hong et al. [53], and in the previous [56] and current [40] hydrogen combustion models of the author. Burke et al. [54] performed extensive analysis of possible reaction channels with high level ab initio TST calculations. It was found that formation of H2 O + O (1D) constitutes less than 4% of the total H + HO2 flux at temperatures from 300 to 2500 K. This is consistent with the analysis of Keyser [143] who summarized available measurements of the branching ratio and from his measurements found that the fraction of H2 O + O formation in reaction between H atoms and HO2 radicals is 0.02 ± 0.02. In the present work the rate constant of reaction (39) is estimated as 4% of the rate of reaction (12), which is the main product channel, with an uncertainty of a factor of 3. A possible role of reaction (39) will be analyzed in the following. In the presence of H2 excited atomic oxygen O(1 D) can react

O(1D) + H2 = OH + H with high temperature-independent rate [65] or quench in

(40)

O(1D) + M = O + M

(29a)

The rate constant of reaction (40) measured by Vranckx et al. [144] is adopted in the present work. The rate of quenching is still highly uncertain. The branching ratio for reaction (29a) with H2 as a partner was found to be 0.007 ± 0.007 [144], and thus it is consistent with the rate expression used for other species discussed earlier [34] (see Table 1). Similarly, for reaction

O(1D) + H2 O = OH + OH

(41)

the latest available measurements of Vranckx et al. [144] are accepted both for reaction and quenching. Approximately 1% of O(1D) will quench in collision with water, thus the enhanced third body efficiency relative to Ar in reaction (29a) is evaluated to be around 3 with remaining uncertainty [65] of a factor of 2. 2.2.5. Reactions of OH(2  + ) Reactions of OH(2  + ), hereafter OH∗ , have been extensively investigated in relation to chemiluminescence diagnostics of combustion processes. Majority of contemporary combustion submechanisms for OH∗ in hydrogen + oxygen systems [145–148] share the same reactions: formation in recombination of O and H atoms, and radiative and collisional quenching. Major reaction forming OH∗ in hydrogen combustion is commonly accepted to be

O + H + M = OH∗ + M

(42)

The rate constant from the recent study of Kathrotia et al. [149] is in agreement with the measurements of Hidaka et al. [150] and is adopted in the present work. Other possible formation reactions, e.g.

H + OH + OH = OH∗ + H2 O

(X19)

were discussed as well, yet, eventually ruled out [146, 150]. The MSU mechanism incorporates two more reactions of OH∗ formation

O(1D) + H + M = OH∗ + M

(X20)

H2 + HO2 = H2 O + OH∗

(X21)

Reaction (X20) was not considered here since concentration of excited atomic oxygen is much lower compared to the ground state O atoms due to very high reactivity of the first, as discussed above. Reaction (X21) relates to H3 O2 potential energy surface and to reactions

H2 O2 + H = HO2 + H2

(17)

H2 O2 + H = H2 O + OH

(18)

H2 O + OH = H2 + HO2

(X22)

In the present mechanism, as well as in the model of Keromnes et al. [55] the rate constant derived by Ellingson et al. [151] was adopted for reaction (17). Several theoretical works [151–153] investigated reactions (17) and (18), yet never indicated any importance of the channels (X21) or (X22); therefore they were ignored here. Collisional quenching of OH∗ implemented in recent models [145– 148] is consistently described by individual reactions for different colliders originated from the measurements of Hidaka et al. [150], Tamura et al. [154] and Paul et al. [155]. In all mechanisms (with exception of the MSU model) only non-reactive quenching was considered as

OH∗ + M = OH + M.

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However, it is well established, e.g., [156, 157], that reactive quenching substantially contributes to the overall collisional quenching of OH∗ . In the present mechanism the overall collisional quenching rates by H2 , O2 and H2 O suggested by Tamura et al. [154] were adopted and recalculated using branching ratios derived by Lehman et al. [157] for reactions

is presented, with a particular attention to those illustrating different behavior of the current mechanism. A complete set of validation runs can be found in the Supplemental Material.

OH∗ + O2 = OH + O2

The basic mechanism [40] was validated against experimental speciation profiles obtained in shock tubes [118, 151, 159, 160]. These works were essentially kinetic studies designed for determination of the rate constants of reactions (6), (15) and (20). It was proven [40] that implementation of the updated rate constants of hydrogen peroxide decomposition (reaction (6)) and its reaction with hydroxyl (reaction (20)) brings excellent agreement of the modeling with H2 O profiles in decomposition of H2 O2 measured by Hong et al. [159] and with other experiments. The current model predictions were found indistinguishable from those of the basic mechanism of Alekseev et al. [40] (see Fig. S12 in the Supplemental Material). Although additional product channel of reaction between hydroperoxyl and hydroxyl radicals was included in the present mechanism (reaction (34)), it is kinetically negligible compared to reaction (15) as discussed above and illustrated in Fig. 2. Ignition delays measured behind shock waves is a classical type of experimental data explored for model validation. Fair comparison with the modeling requires implementation of the same criteria for the calculated ignition delay as those used experimentally. This is, however, not always possible, e.g. when OH∗ emission was recorded, while kinetic scheme does not include excited OH∗ . Therefore, Alekseev et al. [40] compared ignition delay times in H2 + O2 + Ar mixtures [55] assuming that maximum rise of the ground state OH, d[OH]/dtmax is close to the maximum of OH∗ emission. This assumption can be validated with the present mechanism as well as with the model of Keromnes et al. [55], as shown in Fig. 3. Indeed, the difference between both criteria is not significant and close to the scattering of the experimental data. One should note that substantial deviation of the modeling from ignition delays longer than 1 ms is due to neglecting facility-related effects of pressure and temperature rise not accounted for in the present work. To allow for direct comparison of the current mechanism and of the basic mechanism of Alekseev et al. [40], the modeling was also performed with the same criteria of ignition delay, the maximum rise of the ground state OH, d[OH]/dtmax (see Fig. S14 in the Supplemental Material). No difference in the predictions of these two models was observed.

(43a)

OH∗ + O2 = O3 + H

(45)

OH∗ + O2 = HO2 + O

(46)

and

OH∗ + H2 = OH + H2

(43d)

OH∗ + H2 = H2 O + H

(44)

with an uncertainty of a factor of 1.5. In the absence of experimental data for reactive quenching of OH∗ by water, a branching ratio of 50%:50% is estimated with possible uncertainty of a factor of 3.

OH∗ + H2 O = OH + H2 O

(43c)

OH∗ + H2 O = H2 O2 + H

(47)

The radiative quenching rate obtained by German [158] is also adopted in the present model. 3. Modeling details The modeling was performed using Chemkin-Pro Release 15101 [50]. For simulations of jet-stirred reactor studies, the Perfectly Stirred Reactor Model was used. The Closed Homogeneous Reactor Model was used for the simulations of flow reactor, rapid compression machine (RCM) and shock tube data. For the flow reactor simulations, constant pressure and enthalpy were assumed, while the calculated species profiles were time-shifted to match the position where the mole fraction of H2 is half of the initial value from the corresponding experimental study. For the simulations of species profiles recorded in shock tubes and ignition delay times, constant volume and internal energy were assumed. Ignition delay times in the RCM were calculated applying the experimental volume histories. Premix code was used for the simulation of the burning velocity and flame structure. The modeling was performed with multicomponent transport coefficients and thermal diffusion option. Adaptive mesh parameters were GRAD = 0.005 and CURV = 0.1 for the Freely Propagating Flame Model, resulting in a typical number of grid points around 1500. The simulations of the flame structure were performed with experimental temperature profiles approximated by a spline function. Adaptive mesh parameters were GRAD = 0.005 and CURV = 0.5, resulting in a typical number of grid points above 1000. 4. Mechanism validation No attempt to adjust the reaction rate coefficients was made in the present work. In the following figures, the present model is referred to as “current mechanism” and plotted in dashed lines. New reactions incorporated into the model should normally not affect its predicting ability for “thermal” combustion of H2 , i.e. in the absence of excited species in the initial mixtures. The primary goal of the mechanism validation was, therefore, direct comparison of the performance of the current mechanism and of the basic mechanism of Alekseev et al. [40], plotted hereafter in solid lines. Predictions of the recent model of Keromnes et al. [55] are shown for ancillary comparison and plotted in dash-dotted lines. A selected set of validation cases

4.1. Shock tube experiments

4.2. Ignition in a rapid compression machine Ignition delay times of stoichiometric H2 mixtures in a rapid compression machine at compression pressures 15–50 bar [161] were also modeled. The reactant concentrations were H2 = 12.5%, O2 = 6.25%, N2 = 18.125%, Ar = 63.125%. The ignition delay times were defined as an interval from the end of compression cycle to the moment of maximum pressure gradient. The current model predictions were found indistinguishable from those of the basic mechanism of Alekseev et al. [40] (see Fig. S13 in the Supplemental Material). 4.3. Laminar premixed flames Among reactions pertinent to ozone decomposition, only two rate constants were modified in the present work as compared to the previous study [34]: for reactions (23) and (24b). To ensure that these modifications do not affect the model performance, laminar burning velocities of ozone + oxygen flames at atmospheric pressure as a function of ozone concentration in the mixture were calculated. As expected, the current model predictions were found indistinguishable from those of the previous ozone mechanism [34].

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Fig. 3. Ignition delay times for lean (ɸ = 0.1) 0.81% H2 + 4.03% O2 + Ar mixtures at different pressures [55].

Fig. 4. Laminar burning velocity of lean H2 + air flames at standard conditions (Tg = 298 K, P = 1 atm). Symbols: experiments, lines: modeling. Experimental: black: Alekseev et al. [162]; blue (spherical flame, NLM): Dayma et al. [163], Varea et al. [164]; orange (counterflow, NLM): Das et al. [165, 166], Park et al. [167]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Laminar burning velocities of H2 + air flames at atmospheric pressure both at room and at elevated temperatures were modeled. The current model predictions were found only slightly lower than those of the basic mechanism of Alekseev et al. [40] (see Figs. S17 and S19 in the Supplemental Material). To illustrate the difference, Fig. 4 presents selected experimental data for lean flames. Only burning velocities derived using non-linear models for stretch correction

in spherical and counterflow flames, together with recent measurements in non-stretched flat flames [162] are shown. For lean hydrogen flames the current model coincides with the predictions of the mechanism of Keromnes et al. [55]. Profiles of major and minor species in rich (ɸ = 1.93) 39.7% H2 + 10.3% O2 + Ar flame [168] at low pressure (4.75 kPa) and initial mixture temperature of 576 K were modeled as well. The current

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Fig. 5. Profiles of major species for a stoichiometric mixture (1.01% H2 + 0.52% O2 + N2 ) at 3.44 atm and initial temperature of 934 K [172].

Fig. 6. Profiles of major species and temperature for a stoichiometric mixture (0.95% H2 + 0.49% O2 + N2 ) at 3.02 atm and initial temperature of 934 K [172].

model predictions were found indistinguishable from those of the basic mechanism [40] (see Figs. S20 and S21 in the Supplemental Material). 4.4. H2 oxidation in a JSR Oxidation products of the H2 + O2 + N2 mixture in a jet-stirred reactor [169] measured at P = 10 atm; ɸ ∼ 0.1, and residence time of 1 s, have been modeled using three kinetic models (see Fig. S1 in the Supplemental Material). Although initial mixture composition was stated as dry with 1% of H2 , real initial reactant concentrations were taken from the corresponding figure in [169] at temperatures where no reaction occurs and assuming correct equivalence ratio, following recommendations of the authors. Similar problem was observed for other experimental conditions [169, 170] that makes model validation using JSR data rather ambiguous. The current model predictions were found indistinguishable from those of the basic mechanism of Alekseev et al. [40].

hydrogen oxidation in flow reactors. Hence all test cases from the studies of Yetter et al. [171] and of Mueller et al. [172] were modeled and analyzed. It was found that in lean mixtures the current model predictions are almost indistinguishable from those of the basic mechanism [40] at all pressures from low (0.3–0.6 atm) to high (up to 15.7 atm), see Figs. S2–S7 in the Supplemental Material. One may note that performance of the mechanism of Keromnes et al. [55] is also very similar at these conditions. However, in the mixtures close to stoichiometric (Figs. S6 and S7) three models diverge. The current mechanism indicates earlier reactivity as compared to the basic one. Two examples of the model behavior at stoichiometric conditions are shown in Figs. 5 and 6. At the conditions depicted in Fig. 6 the process exhibits particularly rich pattern: reaction begins slowly but accelerates, and at some critical state quickly consumes the remaining reactants in explosion-type mode, as discussed by Mueller et al. [172]. It is therefore instructive to analyze the behavior of the current mechanism at this sensitive situation. 4.6. The role of excited species

4.5. H2 oxidation in a flow reactor The only type of experiments for which significant difference between predictions of the current and basic models was found is

Rate-of-production and sensitivity analyses have been performed at the conditions of the experiment depicted in Fig. 6. In the following, specific outcome is given for the time of 0.23 s

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Fig. 7. Normalized sensitivity of H2 concentration at 0.23 s at the conditions of Fig. 6.

Fig. 8. Absolute rate of production of O2 (1) in mole/cm3 s at 0.23 s at the conditions of Fig. 6.

corresponding to the temperature of 950 K calculated using the current model. It should be noted that at other times of the process before the explosion-type mode, the chemistry is essentially the same differing only in absolute numbers of the rates and normalized sensitivities. The rate of production analysis shows that hydrogen at this point is consumed mostly in reactions

H2 + OH = H2 O + H

(9)

H2 + O = OH + H

(7)

with specific rates of −5.1E−7 and −7.1E−8 mole/cm3 s, respectively. H2 is also formed, yet to much lesser extent, in reactions

H2 + O2 = H + HO2

(14)

H2 + O2 (1) = H + HO2

(31)

with specific rates of 3.1E−8 and 8.5E−9 mole/cm3 s, respectively. Significant contribution of reaction (31) into formation of H2 is not totally unexpected. As it is discussed above, the rate constant of this reaction was evaluated in the present work assuming that 27% of oxygen formed in reaction between hydroperoxyl radicals and atomic hydrogen at room temperature is in O2 (a¹g) state. Singlet oxygen then participates in hydrogen oxidation accelerating the overall process. Critical role of reaction (31) is further confirmed by the sensitivity spectrum of hydrogen concentration shown in Fig. 7. From reactions of excited species only reaction (31) is found sensitive, other disputable reactions, such as

H + HO2 = H2 O + O(1D)

(39)

do not appear to be important at these conditions. Although reaction (39) is the main source of O(1D), excited atomic oxygen instantly quenches in reaction

O(1D) + N2 = O + N2

(29b)

and has no kinetic influence on hydrogen oxidation. Kinetic role of OH∗ was also found negligible. Singlet oxygen is formed mostly in reaction (31) as confirmed by the rate-of-production data presented in Fig. 8. Reaction

OH + O2 (1) = O + HO2

(35)

Fig. 9. Normalized sensitivity of O2 (1) concentration at 0.23 s at the conditions of Fig. 6.

tentatively retained in the current mechanism, barely contributes to its formation. Major sink of O2 (1) is via reactions

O2 (1) + H = O2 + H

(24c)

H + O2 (1) = OH + O

(32)

A quasi-steady state concentration of singlet oxygen, equal to 4.5 ppm at 0.23 s, is established due to these competing reactions. The net rate of O2 (1) formation is about 0.3% of its rates of production or consumption. If reactions of excited species are excluded, the thermal population of singlet oxygen would be only 5.8 ppb. The spectrum of O2 (1) sensitivity shown in Fig. 9 further corroborates important role of only a limited number of reactions; other reactions of excited species (often with uncertain rate constants) possess minor impact on the concentration of the singlet oxygen and on the acceleration of hydrogen oxidation. One may conclude that at specific conditions of hydrogen oxidation in a flow reactor incorporation of new reactions for excited species does affect performance of the model as compared to the “thermal” kinetic scheme. The key contribution is due to reaction (31) forming singlet oxygen when hydroperoxyl radicals and hydrogen atoms are available. It was also found that physical quenching of

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Fig. 10. Laminar burning velocity of H2 + oxidizer flames at atmospheric pressure. Symbols: experiments [173], lines: modeling.

Fig. 11. Normalized sensitivities of the burning velocity of stoichiometric hydrogen flame in the presence of O2 (1).

O2 (1) by atomic hydrogen (reaction (24c)) is more important than corresponding chain branching in reaction (32). 5. Flame enhancement by O2 (1) Since the first and the only demonstration of hydrogen flame acceleration caused by active species generated in the low-pressure glow discharge, the effect was attributed to the enhanced chain branching in the reaction H + O2 (1) [8, 9]. Subsequent modeling studies [16, 17, 26] supported this point of view and discussed other reactions of excited species, often from Table 2, as well. It was stated that singlet oxygen may effectively accelerate burning velocities. Since the current mechanism is largely different from the MSU model and from the models of Starik and colleagues implemented there, it was interesting to analyze its predictions for the flame enhancement too. Both Bourig et al. [26] and Kozlov et al. [16] claimed that more than 5% of O2 can be converted into O2 (1) in electric discharge at atmospheric pressure, referring, however, on experimental studies performed at subatmospheric pressures in O2 + He mixtures. Nevertheless, this upper limit was also considered in the present work. The laminar burning velocities of hydrogen flames at atmospheric pressure were compared for two oxidizers: air and 20% O2 + 1% O2 (1) + 79% N2 . Corresponding calculations are shown in Fig. 10 as

dashed and dash-dotted lines, respectively. The effect is clearly visible over entire range of equivalence ratios. On the other hand, the difference between calculated burning velocities for two oxidizers is not higher than typical experimental uncertainty in, e.g., [173] that indicates potential difficulties in experiments attempting to validate relevant kinetic schemes at atmospheric pressure. Figure 11 shows normalized sensitivities of the burning velocity of stoichiometric H2 + (20% O2 + 1% O2 (1) + 79% N2 ) flame. In addition to reactions of the “thermal” hydrogen combustion governing the burning velocity, only three reactions of singlet oxygen appear in the spectrum: (31), (24c) and (32). Reaction of physical quenching of O2 (1) by atomic hydrogen (24c) competes with chain branching in the reaction of H + O2 (1). Somewhat surprisingly, reaction (31) has higher normalized sensitivity (by absolute value) and inhibits flame propagation. It acts as additional to reaction (14) channel for recombination of hydroperoxyl radicals and hydrogen atoms forming fuel and singlet oxygen. Even though O2 (1) is more reactive than O2 , the chemical role of the first is suppressed by physical quenching. Feeding singlet oxygen into a fresh mixture brings additional enthalpy that is eventually converted into higher adiabatic flame temperature, as noted by Kozlov et al. [16]. To elucidate the role of this additional enthalpy the following calculations have been performed: Firstly, fresh mixtures of H2 + (20% O2 + 1% O2 (1) + 79% N2 ) with initial temperature of 298 K were kept adiabatic for a few seconds

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with all chemical reactions frozen. Due to rapid collisional quenching of the singlet oxygen, the temperature of the mixture increases; depending on the mixture composition, and thus the overall heat capacity, the temperature rise varied from 26.7 K at equivalence ratio of 0.5 down to 10.4 K at ɸ = 5. Then flame burning velocities of these mixtures of H2 + air having higher initial temperature were calculated. Hence, the thermal (not chemical) effect of the singlet oxygen is isolated. The resulting calculated burning velocities are shown in Fig. 10 as solid line. Remarkably, purely thermal effect exceeds flame enhancement by the singlet oxygen. In other words, if the energy required for production of O2 (1) is directly used for the mixture preheating, the effect of the burning velocity increase would be higher. Similar observation on the inefficiency of the singlet oxygen for improving performance of HCCI engines was made by Flowers et al. [41], who concluded that major effect on ignition is primarily thermal, not chemical. 6. Conclusions In the present study recently updated hydrogen combustion mechanism [40] was combined with ozone decomposition reactions [34] and extended by reactions of excited species: O(1 D), OH(2  + ), and O2 (a¹g). The reliability and the accuracy of the rate constants pertinent to these excited species were evaluated. Many reactions proposed in the literature and implemented in other kinetic schemes were found irrelevant or insignificant; they are compiled in Table 2. The new mechanism for hydrogen combustion, Table 1, was then validated in comparison with commonly accepted sets of laboratory experiments. It was naturally expected that new reactions incorporated into the model should normally not affect its predicting ability for “thermal” combustion of H2 , i.e. in the absence of excited species in the initial mixtures. Contemporary detailed kinetic schemes silently ignore reactions of ozone and of excited species. For instance, reactions of ozone are not included since Dougherty and Rabitz [174] demonstrated that pertinent chemistry is not important over all conditions of hydrogen oxidation covering three explosion limits. Although possible channels of excited atomic oxygen formation were considered [54], their role remained uncertain. The model validation showed that predictions of ignition, oxidation, flame burning velocities and flame structure of hydrogen– oxygen–inert mixtures are indistinguishable or very close to those of the basic mechanism [40] at all condition, except for hydrogen oxidation in a flow reactor close to explosion limit. It was further demonstrated that singlet oxygen formed in reaction (31) H2 + O2 (1) = H + HO2 at ppm levels may notably accelerate the process. This finding certainly calls for revisiting reaction (31) both experimentally and with theoretical calculations. Kinetic role of O(1 D) and OH(2  + ) in the “thermal” combustion of H2 was found negligible. In addition, hydrogen + air flame enhancement by singlet oxygen was modeled. It was demonstrated that the burning velocity increase with 1% of O2 (a¹g) seeded into the air is rather modest. Moreover, purely thermal effect due to additional enthalpy brought to the mixture exceeds chemical flame enhancement by the singlet oxygen. Thus, if the energy required for production of O2 (1) is directly used for the mixture preheating, the flame acceleration would be more efficient. Model analysis, therefore, clearly demonstrates that some concepts of plasma-assisted combustion by O2 (1) based on the predictions of earlier kinetic mechanisms could be over-optimistic. Acknowledgments Financial support of the Centre for Combustion Science and Technology (CECOST) is gratefully acknowledged. V.A. Alekseev kindly helped with the modeling and numerous plots.

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