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Gas-Phase Reaction of Hydroxyl Radical with Hexamethylbenzene Jean-Christophe Loison,†,‡,* Marie-Thérèse Rayez,†,‡ Jean-Claude Rayez,†,‡ Aline Gratien,†,‡ Pranay Morajkar,†,‡,§,⊥ Christa Fittschen,§,⊥ and Eric Villenave†,‡ †

Universite Bordeaux, ISM, UMR 5255, F-33400 Talence, France CNRS, ISM, UMR 5255, F-33400 Talence, France § Universite Lille, PC2A, UMR 8522, F-59655 Villeneuve d’Ascq, France ⊥ CNRS, PC2A, UMR 8522, F-59655 Villeneuve d’Ascq, France ‡

S Supporting Information *

ABSTRACT: Aromatic hydrocarbons are important components of polluted ambient air. The reaction of OH radicals with hexamethylbenzene (HMB) is a prototype system to study ipso addition leading eventually to dealkylation. We have investigated the OH + HMB and OD + HMB reactions between 323 and 433 K using a discharge fastflow reactor coupled to a time-of-flight mass spectrometer with singlephoton VUV photoionization (10.54 eV). The H atom abstraction channel has been found to be equal to (13.7 ± 4.4) % at 330 K leading to (11.1 ± 3.6) % at 298 K, higher than predicted by commonly used structure−reactivity relationships. The back dissociation rate constant has also been measured and has been found to be smaller than the rate of other aromatic hydrocarbons, in good agreement with density functional theoretical calculations. The dealkylation channel, leading to pentamethylphenol (PMP) + CH3, is always found to be the minor channel, estimated inferior to 2% at 298 K.

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INTRODUCTION Aromatic hydrocarbons are a major class of anthropogenic compounds emitted into the troposphere with major sources being automobile emissions, petroleum refining processes and industrial solvent evaporation.1 Monocyclic aromatic compounds (i.e., mainly benzene, toluene, dimethylbenzenes, and trimethylbenzenes) may account for up to 20% of the total nonmethane hydrocarbon content of the atmosphere especially in urban areas.1 This individual class of compounds may reside in the atmosphere at low ppb levels. However, their high reactivity toward OH radicals makes them some of the major contributors to photochemical smog and ozone formation. The dominant loss processes of monocyclic aromatics in the troposphere are their gas-phase reactions with OH radicals. Depending on their degree of alkylation, such processes can proceed either by OH addition to the aromatic ring or by H atom abstraction from a side group, the H atom abstraction accounting at room temperature for less than 10% of the overall OH radical reactions in the case of toluene, xylenes, and trimethylbenzenes.2 The main first-step oxidation product is the hydroxycyclohexadienyl radical or its alkylated derivatives formed by addition of the OH radical on the aromatic ring, at the ortho, meta, or para positions. In addition to these pathways, there is another possibility that has been less considered up to now: the ipso addition, followed by dealkylation. The importance of ipso addition has already been discussed in the literature for methylated benzenes3 in the © 2012 American Chemical Society

context of combined density functional theory (DFT) and statistical calculations for toluene, leading to a prediction of 3% of ipso addition. The ipso addition has also been suggested to explain the biexponential decay of OH radical in the OH + HMB reaction in presence of O2 and NO.4 An ipso addition to p-cresol (OH addition to the carbon atom carrying the methyl group) was found to occur in the liquid phase with a 12% probability, forming 4-hydroxy-4-methyl-2,5-cyclohexadiene-1one as the final product.5 Recently, Noda et al.6 used chemical ionization mass spectrometry to study dealkylation from the reaction of OH radicals with toluene and o-, m-, and p-xylenes, conducted at (154 ± 4) Torr total pressure, with dealkylation accounting for (5.4 ± 1.2) % of the toluene reaction and (4.5 ± 3.2) %, (11.2 ± 3.8) % and (4.3 ± 3.1) % of the o-, m-, and p-xylene reactions, respectively. These last results are in contradiction with the new measurements of Aschmann et al7 which indicate less than 1% of dealkylation in the case of (OH + m-xylene) reaction. Very recently, a study of OH + trimethylbenzenes has also reported evidence for ipso-adduct formation, but this channel was in any case a minor process.8 Among the various oxidation products arising from the OHinitiated oxidation of monocyclic aromatic compounds, ringretaining species such as benzaldehyde, cresols, as well as highly Received: July 31, 2012 Revised: November 29, 2012 Published: November 30, 2012 12189

dx.doi.org/10.1021/jp307568c | J. Phys. Chem. A 2012, 116, 12189−12197

The Journal of Physical Chemistry A

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photoionization cross sections of the different products as they have not been experimentally or theoretically determined before. In this way, we used the model of Koizumi,17,20 neglecting autoionization and using the excitation cross section of the hydrogen atom to the continuum (6.3 × exp(−0.148 × (hν-IE)) Mb)21,22 to estimate the photoionization cross section, IE (in eV) being the ionization energy. The calculated photoionization cross section is the sum of the contribution of each electron participating in the ionization process at 10.54 eV. This model works well for ionization involving bonding or nonbonding electrons for which the corresponding excited Rydberg states lead mainly to dissociation. This is the case for alkanes, alkenes, and alcohols,20 but also for radicals for which the absolute ionization cross section is known: methyl,15,23,24 vinyl,25 propargyl,25 allyl,26 2-propenyl,26 phenyl,27 and formyl.28 Photoionization cross sections are definitively the most sensitive parameters of our study, their determination presenting a relative global uncertainty estimated to be 30%. The fast flow reactor consists of a main tube and a movable injector. The main tube is a 24 mm internal diameter/65 cm long quartz tube, inside which is mounted a pyrex sliding injector which has a 6 mm internal diameter and is 90 cm long with a showerhead mixer. The reactor was coupled to a twostage Edwards primary pump (300 m3 h−1) and the pressure was measured using an Edwards capacitance gauge 600AB TRANS 10Mb (0−10 Mbar). Typical flow velocities ranged from 7 to 31 m s−1. OH and OD radicals were produced by the well-known F + H2O (D2O) → OH (OD) + HF reaction.29 Fluorine atoms were produced in a microwave discharge at 2450 MHz (Sairem GMP 03 KSM) in a mixture of 1% F2 in He (Linde), introduced into the main reactor 50 cm before the reaction zone. The interface between the reactor and the mass spectrometer consisted of a differentially pumped orifice-skimmer combination. The reacting gases at 0.8−3.0 Torr total pressure were expanded through a 1.0 mm diameter homemade Kel-F skimmer (a 2 cm high cone with a base diameter of 2 cm, with a sampling orifice of 1 mm at the end of the cone) into a region where the background pressure is maintained at 1 × 10−3 Torr, using an Alcatel T550 turbomolecular pump (450 L s−1 for He). The central portion of the expanded jet passed through a 2.1 mm skimmer (Beam Dynamics) aperture into the ionization chamber, which was maintained at less than 10−5 Torr by a turbomolecular pump (Varian 550 L s−1 for He). Typically, the initial OH concentration ranged from 1 to 4 × 1012 molecules cm−3. The HMB concentration ranged from 2 to 8 × 1013 molecules cm−3, with a ratio [HMB]/[OH] always greater than 10. The OH concentration has been estimated by electron-impact beam ionization, comparing the OH signal with a signal obtained from a known NO concentration, both having well-known electron-impact ionization cross sections.30−32 A flux of HMB in the vapor phase was generated by passing helium (Linde, purity >99.996%) through a heated cell containing solid HMB.

oxidized species resulting from bicyclic peroxy radicals leading to scission of the aromatic ring to form glyoxal and methyl glyoxal, have been detected to date.9 However, to the best of our knowledge, the master chemical mechanism (MCM) still overpredicts the ozone and OH productions in environmental simulation chamber studies.10,11 Such a disagreement may highlight the fact that fairly important channels in the initial steps of the oxidation mechanisms of volatile organic compounds (VOCs) are still missing or not properly accounted for. Hence, our incomplete knowledge of the oxidation pathways of aromatics may lead to uncertain predictions of ozone and secondary organic aerosol (SOA) formation, and the oxidative capacity in urban air. In order to clarify the importance of the dealkylation channel, this work reinvestigates the reaction of hexamethylbenzene (HMB) with OH radicals which only leads, in the case of addition, to the formation of HMB−OH ipso-adduct radicals, as each position on the ring is equivalent. The ipso type addition and its reversibility for the HMB + OH reaction have been discussed in detail by Koch et al4 and its rate constant has been determined at 295 K by Berndt and Böge12 leading to k(295 K) = (1.13 ± 0.11) × 10−10 cm3 molecule−1 s−1. More recently, Zetzsch and co-workers13 measured the rate between 300 and 370 K, leading to k(295 K) = 1.5 × 10−10 cm3 molecule−1 s−1. In this study, we present both theoretical and experimental approaches to the (HMB + OH) reaction. Experiments were performed in a discharge fast-flow reactor, coupled to a time-offlight mass spectrometer, at total pressures between 0.8 and 3.0 Torr and as a function of temperature. The final aim was to focus on the existence of the HMB−OH ipso-adduct and the subsequent dealkylation channel by measuring the various reaction product branching ratios. A theoretical approach was used to interpret the experimental results by presenting a comprehensive investigation of OH attack on the different sites of HMB, including both abstraction and addition reaction channels. No similar theoretical investigation has been reported so far for this system.

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EXPERIMENTAL SECTION The experimental setup used in this study has already been detailed elsewhere.14−17 Briefly, it consists of a fast-flow reactor coupled to a time-of-flight mass spectrometer from R. M Jordan Co. (USA), equipped with a D850 Reflectron. Molecules and radicals were detected through vacuum ultraviolet (VUV) single photon ionization (SPI) mass spectra after ionization with photons at 117.6 nm (i.e., 10.54 eV) generated by tripling a UV laser beam in a rare gas (35 Torr of Xe). Ionized particles were extracted and sent to the detector through a 820 mm reflectron, maintained at the pressure of 1 × 10−7 Torr, by a turbomolecular pump (Varian 150 L s−1 for He). Ions were detected through a microchannel plate detector (MCP: C-726; 40 mm active area). A mass resolution R50% of m/z = 1300 (measured at m/z = 30) was achieved. Electrical signals produced by ion detection were acquired by a digital oscilloscope (TDS 3000 from Tektronix) coupled to a micro computer. The HMB concentration in the reactor was determined by ionization at 117.6 nm (i.e., 10.54 eV) relative to a known propene concentration, using σ(C3H6, 10.54 eV) = (11.0 ± 1.0) × 10−18 cm2,18 and σ(HMB, 10.54 eV) = σ(benzene, toluene, o,m,p-xylenes, 10.54 eV) = (30.0 ± 5.0) × 10−18 cm2.19 To estimate the branching ratios leading to the different reaction channels, we had to evaluate the relative

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THEORETICAL APPROACHES All calculations were performed using the GAUSSIAN 09 package.33 The geometries and energies were optimized using DFT with the hybrid meta exchange-correlation functional M06-2X, coupled either to the split valence double-ζ and double polarization basis set 6-31+G(d,p) or to the Dunning’s correlation consistent polarized valence double-ζ basis set ccpVDZ. This highly nonlocal M06-2X functional developed by 12190



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Table 1. Experimental and Theoretical Adiabatic Ionization Energies (IEad) and Vertical Ionization Energies (IEvert) for Ground and Excited Ionic States Accessible at 10.54 eVa IEexp (eV) HMB → HMB PMB• → 1PMB+ → 3PMB+ 2 HMB−OH• → 1HMB−OH + → 3HMB−OH 1 PMB−NO2 → 2PMB−NO2+ 1 HMB−OH−NO2 → 2HMB−OH−NO2+ 1

2

+

7.85

2

a

+

IEvert (eV), EPT/VDZ state1/state2/state3/state4 7.56(4) 6.59(1), 6.17(1), 7.95(2), 7.60(2),

σion,calc (Mb = 10−18 cm2) 16 22 23 17 18

7.94(1), 9.32(1) 7.71(1), 8.41(1) 8.21(1), 10.12(1) 7.78(1), 9.72(1) 8.09(2) 9.87(2)

The number in brackets is the number of electrons involved in each ionization step.

Truhlar et al.34 is well suited for structures and energetics of the transition states. The unrestricted Hartree−Fock (UHF) formulation has been used since it is a convenient way to describe open-shell and bond-breaking processes. Its use is justified in our study by the fact that we did not observe any significant spin contamination for all the stationary points explored, the quantum average value ⟨S2⟩ of the square of the total spin operator remaining close to 0.75, i.e., the characteristic value for a doublet state. Full geometry optimization has been performed throughout. We have checked carefully that all the saddle points found are correctly connected to two minima and are characterized by the existence of only one negative eigenvalue of the Hessian matrix corresponding to an imaginary frequency in the normal-mode analysis. The vertical IEs were calculated with the electron propagator theory (EPT), using a cc-pVDZ basis set at the geometry obtained at the M06-2X/cc-pVDZ. The calculated IEs and the estimated photoionization cross sections at 10.54 eV of the various radicals studied in this work are presented in Table 1. The relative uncertainty in photoionization cross sections for hydroxyl and benzyl radicals is estimated to be equal to 30%.

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Figure 2. M06-2X/6-31+G(d,p) optimized structures for HMB and transition state structures.

25 kJ/mol below the energy of the separated reactants. In the PRC structure, the C--O distance is around 2.5 Å. On the way from the PRC to the addition transition state TSadd, the C--O distance decreases from 2.5 to ∼2.0 Å. The ZPE for the PRC: ΔE0,PRC, the energy barrier ΔE#0, and the reaction energy ΔE0 for HMB−OH adduct formation with respect to the ZPE of the reactants HMB + OH are given in Table 2. The overall

RESULTS AND DISCUSSION

Theoretical calculations. The energy diagram calculated for the HMB + OH reaction at the M06/6-31+G level including zero-point energies (ZPE) is presented in Figure 1

Table 2. M06-2X/6-31+G(d,p) Zero-Point Corrected Energies: Pre-Reactive Complex, ΔE0(PRC); Barriers, ΔE#0; Reaction Energy ΔE0 Values and Free Energy Barriers, ΔG#298 at 298 K Relative to the Reactants HMB + OHa reactants addition abstraction a

ΔE0(PRC)

ΔE0#

ΔG#298

ΔE0

0.00 −27.1

0.00 −12.5 − 4.6

0.00 21.3 28.8

0.00 −102.0 −81.1

Energies are given in kJ mol−1.

addition reaction energy ΔE0 is highly exothermic with a value of −100 kJ/mol. ΔE#0 is negative by 13 kJ/mol with respect to the reactant energy, a situation which leads to a small barrier of 14 kJ/mol with respect to the PRC energy. The presence of a submerged barrier relative to the reactants is fully compatible with the large value of the rate constant.35,36 The calculated Gibbs free energy values ΔG#298 are also given in Table 2. The HMB−OH → PMP + CH3 Reaction. The adduct HMB−OH can decompose by the loss of a methyl radical CH3 from the carbon where OH is attached to give pentamethylphenol (PMP) through another transition state TSdealkyl which is at approximately the same energy level as the reactants.

Figure 1. Energy diagram for the HMB + OH reaction calculated at the M06/6-31+G level including ZPE, energy in kJ mol−1.

with the corresponding M06-2X/6-31+G(d,p) optimized structures for HMB and the transition states depicted in Figure 2. Addition Reaction: HMB + OH → HMB−OH. Because of the symmetry of the molecule, six equivalent addition carbon sites lead to the formation of only one isomer of the HMB− OH adduct. The reaction pathway is initiated by the formation of a pre-reactive complex (PRC) corresponding to a long-range interaction between HMB and the OH radical lying roughly 12191



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This reaction is exothermic by 42 kJ/mol with respect to the reactants. Abstraction Reaction: HMB + OH → PMB + H2O. Each abstraction pathway results in an H atom abstraction from one of the six CH 3 alkyl groups of HMB leading to pentamethylbenzyl radical (PMB) + H2O formation. On the way to the products, a transition state (TSabs) has been located energetically −4.6 kJ/mol below the reactants. An intrinsic reaction coordinate (IRC) calculation has shown that this abstraction pathway correlates directly the transition state to the free reactants. The results displayed in Figure 1 and Table 2 show that the transition state (TSabs) as well as the free energy barrier (ΔG#298) for abstraction are energetically above the corresponding ones for addition. These results agree with the experimental findings showing that abstraction is a minor pathway compared to addition. It should be noted that we did not find a path corresponding to the dissociation of the HMBOH adduct into PMB + H2O. It is worth noting that the large exothermicity of the reaction (−81 kJ/mol) can be explained by the fact that the loss of the H atom from CH3 leads to a resonant allylic structure of the C6(CH3)5CH2 radical.

Figure 3. Typical high sensitivity VUV (10.54 eV) single photon ionization difference mass spectra of the HMB + OD reaction at 344 K (top), 379 K (middle), and 433 K (bottom). The initial concentration of OD radicals was equal to 2 × 1012 molecules cm−3 and the HMB concentration was equal to 3 × 1013 molecules cm−3.

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product formation using OH and OD radicals. Typical traces of the variations of HMB−OD and PMB concentrations, recorded in the case of the HMB + OD reaction performed at 379 K, are presented as a function of the distance d between the injector and the skimmer in Figure 4. The dot and open circles are the

EXPERIMENTAL PART The product distributions from the reaction of OH (or OD) radicals with HMB were studied by adding HMB together with the main He flow containing OH (or OD) radicals. The total pressure in the reactor was between 0.8 and 3 Torr. The termolecular adduct stabilization efficiency depends on the number of vibrators as well as on the exothermicity of adduct formation. Compared to smaller systems,36−38 there is no doubt that the OH + HMB reaction is already in the high pressure regime at 0.8 Torr, considering the size of the system and the large exothermicity of HMB−OH adduct formation. To follow the progression of the reactions, product concentrations were monitored by their mass spectra, using the ionization cross sections given in Table 1. In this study, we used both OH and OD radicals, as the use of isotopologues allows us to clarify some fragmentation patterns, thereby allowing us to distinguish the PMBOD+ ion arising from the minor OD + PMB secondary reaction from the fragment HMB−OD+ - H, both having the same mass. Because of experimental difficulties to obtain large concentrations of HMB in the gas-phase (its vapor pressure at 298 K being equal to 12 mTorr),39 HMB was introduced in excess by only a factor of 10 to 30 with respect to the initial OH concentration. Therefore, the (HMB + OH ⇆ HMB−OH) equilibrium, established quickly, was not always fully shifted toward the adduct and the stationary OH concentration was not always negligible, particularly at high temperatures, leading to potential OH induced secondary reactions. For example, for a usual [HMB] concentration of 3.0 × 1013 molecules cm−3 and using the equilibriuim constant Keq = 2.0 × 10−25exp (11407 K/T) cm3 molecule−1 reported by Zetzsch and co-workers,13 the ratio [HMBOH]/[OH] at equilibrium is equal to 65 at 380 K but falls to only 4 at 420 K. Typical VUV-SPI (10.54 eV) mass spectra, recorded for the HMB + OD reaction at T = 344, 379, and 433 K are presented in Figure 3 (as a difference between the HMB + OD system and HMB alone). The main peaks are PMB+ and HMB−OD+ which partly fragment into HMBO+ (loss of a D atom) and HMB−OD+ − H (loss of an H atom). In order to estimate the back dissociation and the effect of secondary reactions, we performed kinetic studies focusing on

Figure 4. Relative traces of the ion signal as a function of the distance d in the reactor for the HMB + OD reaction at 379 K: (●) m/z = 180 (HMB−OD+); (○) m/z = 161 (PMB+). The initial concentration of OD radicals was equal to 1.6 × 1012 molecules cm−3 and the HMB concentration was equal to 3.0 × 1013 molecules cm−3. Solid curves correspond to the best simulation, the dashed line corresponds to the simulation considering (kabst + 2σ), (kback + 2σ) and (kHMBOH,PMB+OH + 2σ) and the dashed-dotted line corresponds to the simulation including (kabst − 2σ), (kback − 2σ) and (kHMBOH,PMB+OH − 2σ).

experimental data converted into concentration−time profiles, using the calculated ionization cross sections reported in Table 1. The various lines correspond to different simulations taking into account the back dissociation and the secondary PMB + OD and HMB−OH + OD reactions, which play only minor roles in this case. Simulations were performed by numerical integration of the full kinetic system using fourth order Runge−Kutta 12192



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method, the step size of the integration being equal to 1 × 10−8 s. The kinetic system used to simulate the HMBOD and PMB concentrations is presented below:

222 kJ/mol and PMB−ONO being stabilized by 213 kJ/mol, stabilization relative to PMB + NO2 energy. The relatively high stabilization energy ensures that negligible back dissociation occurs for these reactions between 300 and 450 K. Considering that HMB−OH−NO2 and HMB−OH−ONO, as well as PMB−NO2 and PMB−ONO, have very similar properties, we have decided in each case to consider both isomers together. The global scheme becomes:

kabst

HMB + OD ⎯⎯⎯→ HDO + PMB kadd

HMB + OD ⎯⎯→ HMB−OD k back

HMB−OD ⎯⎯⎯→ OHD + HMB

kabst

HMB + OH ⎯⎯⎯→ H 2O + PMB

k dealk

HMB−OD ⎯⎯⎯⎯→ CH3 + PMP(D)

kadd

HMB + OH ⎯⎯→ HMB−OH

kHMBOD + OD

HMB−OD + OD ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ cyclohexadienyl‐1,2‐diol

k back

HMB−OH ⎯⎯⎯→ OH + HMB

kPMB + OD

PMB + OD ⎯⎯⎯⎯⎯⎯⎯⎯→ pentamethylbenzyl alcohol

kdealk

HMB−OH ⎯⎯⎯⎯→ CH3 + PMP

Values for ktotal and kback are from Zetzsch and co-workers.13 ktotal was maintained constant but kback was adjusted to (185 ± 90) s−1 (the value of 93 s−1 from Zetzsch13 can be used considering a photoionization cross section for PMB equal to 29 Mb instead of 22 Mb). kabst was also adjusted to (1.8 ± 0.4) × 10−11 cm3 molecule−1 s−1 and the value for kdealk was set to zero as this channel is negligible at this temperature, as shown by the mass signal at M/z = 165. Rate constants for the HMBOD + OD and PMB + OD reactions were estimated using capture rate theory,40 as they are very likely to occur without a barrier in the entrance valley for the singlet surface (doublet radical + doublet radical reaction).41 Taking into account the electronic degeneracy factor leads to rate constant values equal to (1 ± 0.6) × 10−10 cm3 molecule−1 s−1 in both cases. At 379 K, and in the case of the conditions corresponding to Figure 4, the secondary OD reactions play a very minor role. A sensitivity analysis was performed by varying rate constant by two standard deviation ((kabst ± 2σ), (kback ± 2σ) and (kHMBOH,PMB+OH ± 2σ)). The resulting simulation is shown in Figure 4 (dashed and dash-dot lines). The large uncertainties on experimental data are mainly due to uncertainties in the photoionization cross sections, as discussed earlier. However, both uncertainties are correlated, as the sum of the branching ratios must equal 100%. At 330 K, the accuracy is much better as HMB−OH and HMB−OD adduct back dissociation is very slow. As a result, it was possible to measure the direct H atom abstraction branching ratio at this temperature, using the HMB−OH+/HMB−OD+ and PMB+ ions, leading to a final value of (14 ± 5) % for the direct abstraction. Another convenient way to measure the product distribution and to properly evaluate the back dissociation following the HMB + OH reaction was proposed in this work. It consisted of adding NO2 to the reaction system assuming that, in the present experimental conditions, the reactions of NO2 with PMB and HMB−OH lead only to adduct formation.42,43 When NO2 was added in great excess to the reactor, it induced competitive addition reaction processes allowing us to better separate the HMB−OH back dissociation, the dealkylation channel (CH3 + PMP) and its reaction with NO2. Indeed, NO2 reacts quickly with alkyl and hydroxy radicals leading to very stable adducts.4,44 The HMB−OH + NO2 reaction can lead to HMB−OH−NO2 and HMB−OH−ONO adducts, HMB− OH−NO2 being stabilized by 171 kJ/mol and HMB−OH− ONO being stabilized by 176 kJ/mol at the M06-2X/cc-pVDZ level, stabilization relative to HMB−OH + NO2 energy. Similarly, the PMB + NO2 reaction can lead to PMB−NO2 and PMB−ONO adducts, PMB−NO2 being stabilized by

kHMBOHOH + NO2

HMB−OH + NO2 ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ HMB−OH−NO2 kPMB + NO2

PMB + NO2 ⎯⎯⎯⎯⎯⎯⎯⎯⎯→ PMB−NO2

(1) (2) (3) (4) (5) (6)

The rate constants of the HMB−OH + NO2 and PMB + NO2 reactions have never been reported in the literature. As all similar aromatic−OH + NO24 and alkyl + NO2 reactions44 present high rate constant values, close to 3 × 10−11 cm3 molecule−1 s−1 and independent of temperature (as barrierless reactions), it was reasonably decided to use this value in the case of the HMB−OH + NO2 and PMB + NO2 reactions, the uncertainty taken to be equal to 40%. Typical VUV (10.54 eV) SPI difference mass spectra recorded for the HMB + OD + NO 2 system, performed at 340 and 410 K, are presented in Figure 5. As it can be

Figure 5. Typical high sensitivity VUV (10.54 eV) Single Photon Ionization difference mass spectra of the HMB + OD + NO2 reaction at 340 K (top) and 410 K (bottom). The initial concentration of OD radicals was equal to 2 × 1012 molecules cm−3, the HMB concentration was equal to 3 × 1013 molecules cm−3, the NO2 concentration was equal to 1.2 × 1014 molecules cm−3 and the reaction time was set to 6 ms.

seen, products undergo substantial fragmentation. In order to identify the origin of the main peaks, the intensity of each peak was recorded by varying the temperature in the reactor. As for the OH + HMB reaction, the contribution of 12193



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(there is much less ambiguity in ion fragmentation pathway with NO2 than without NO 2, we performed then the same number of experiments with OH radicals as with OD radicals):

the addition channel decreases with increasing temperature and the abstraction channel strongly increases with increasing temperature. It was therefore obtained, without any ambiguity, the following peak distribution and attribution

HMB−OD−NO2 + hν (10.54 eV) → HMB−OD−NO2+

(m /z = 226) (2 ± 0.4)%

+

HMB−OD−NO2 −CH3 (m /z = 211) (6 ± 1)% HMB−OD−NO+

(m /z = 210) (4 ± 0.5)%

HMB−OD+

(m /z = 180) (44 ± 4)%

+

HMB−OD −H

(m /z = 179) (20 ± 3)%

HMBO+

(m /z = 178) (12 ± 4)%

C10H15

+

(m /z = 135) (12 ± 2)%

PMB−NO2 + hν (10.54 eV) → PMB−NO2 PMBO+

+

(m /z = 207) (28 ± 2)% (m /z = 177) (14 ± 4)%

+

(m /z = 161) (58 ± 4)%

+

(m /z = 165) (100 ± 0)%

PMB PMP + hν (10.54 eV) → PMP

As the (HMB−OD)-(NO2)+ bond strength is weak and as the ionization potential of HMB−OD is low, the HMB−OD− NO2+ ion should easily fragment when ionized at 10.54 eV, leading to HMB−OD+ and NO2. The main fragments correspond to the loss of the NO2 radical for the HMB− OD−NO2+ ion and also for the PMB−NO2+ ion. The specific C10H15+ fragment comes from the HMB−OD−NO2+ ion, the origin being well identified by the temperature dependency of the recorded signal. It can be seen that the PMB−NO2+ ion leads to less dissociation. The temperature dependency of both addition and abstraction channels allowed us to determine that HMB−OD−NO2+ (addition channel) did not fragment into the same masses as the PMB−NO2+ ion (abstraction channel). The signal recorded at m/z = 165, corresponding to deuterated PMP, is always very low. As a stable molecule, its photoionization at 10.54 eV leads to very low fragmentation. We consider that the PMP+ ions stem only from PMP photoionization as the PMP+ ion signal increases with temperature. Therefore, PMP+ is not formed from HMB−OH−NO2+ ion fragmentation, and it seems difficult that PMB−NO 2 + (C6(CH3)5CH2NO2+) ions may fragment into the same masses as C6(CH3)5OD+. We finally consider that the signal at the PMP+ mass obtained at high temperature arises from ionization of PMP only. Our results on PMP production correspond anyway to an upper limit. To measure the kinetics of product formation, the mechanism described by the eqs 1−6 for HMB−OH−NO2, PMB−NO2, and PMP production was used. A simulation using numerical integration of the global kinetic system, first without NO2 then with NO2 in great excess, is presented in Figure 6, at a temperature of 400 K. Without the presence of NO2 (solid lines) the equilibrium leads to nonstationary HMB−OH, PMB, and PMP concentrations, as the HMB−OH adduct is slowly transformed into PMB and PMP. In the presence of NO2 ([NO2] equal to 8 × 1013 molecules cm−3), the equilibrium cannot be established and OH radicals follow almost a single exponential decay (represented by dashed and dashed-dot lines).

Figure 6. Kinetic simulation at 410 K, performed with and without NO2. The black solid line corresponds to OH without NO2, the black dashed solid line corresponds to OH with NO2. The red solid line corresponds to the HMB−OH adduct without NO2, the red dashed solid line corresponds to the HMB−OH adduct with NO2, and the red dashed-dotted line corresponds to HMB−OH−NO2. The green solid line corresponds to PMB without NO2, the green dashed solid line corresponds to PMB with NO2, and the green dashed-dotted line corresponds to PMB−NO2. The purple solid line corresponds to PMP without NO2, the purple dashed solid line corresponds to PMP with NO2. [OH] radicals was set equal to 2 × 1012 molecules cm−3, [HMB] was set equal to 3 × 1013 molecules cm−3, and [NO2] was set equal to 1.2 × 1014 molecules cm−3.

The HMB−OH adduct reacts rapidly with NO2, leading to small fraction dissociating into HMB + OH and PMP + CH3, only occurring during the first two milliseconds. Then, HMB− OH−NO2, PMB−NO2, and PMP reach their final concentration levels. To estimate the PMB−NO2 and PMP branching ratios, we have integrated the kinetic system described by eqs 1-6, 12194



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PMP. Moreover, as we neglect the PMB reaction with OH radicals, we have [PMBNO2] (t = ∞) = [PMB] (t = ∞) as all PMB radicals react only with NO2. Finally:

considering expressions of [OH] and [HMB−OH] from Wahner and Zetzsch.45 We have considered HMB and NO2 concentrations in great excess and kHMBOH+NO2 = kPMB+NO2 = kNO2. Using the following abbreviation: a = (kabst + k add) × [HMB], c = kadd × [HMB],

τ1−1 =

I01 =

d = k back + k pmp + k NO2

bc +

2

− d)

(τ1−1

2

− d)

I02 =

,

I01 × c τ1−1 − d

[−τ1 + τ2]

[PMP] = kPMP × [OH]0 ×

(a − d)2 + bc 4

a+d − 2 (τ1−1

×

(a − d)2 + bc , 4

a+d + 2

τ2−1 =

[HMB−OH−NO2 ] = k NO2 × NO2 × [OH]0

b = k back ,

(7)

I01 × c τ1−1 − d

[−τ1 + τ2]

(8)

[PMB−NO2 ] = kabst × [HMB] × [OH]0 × [τ1 × I01 + τ2 × I02]

bc bc + (τ1−1 − d)2

(9)

Expressions 7−9 lead to PMB−NO2 and the PMP branching ratio values presented in Figure 7. Above 380 K, the

The OH and HMB−OH concentrations are given by: ⎡ ⎛ t⎞ [OH] = [OH]0 × ⎢I01 × exp⎜ − ⎟ ⎢⎣ τ1 ⎠ ⎝ ⎛ t ⎞⎤ + I02 × exp⎜ − ⎟⎥ τ2 ⎠⎥⎦ ⎝

[HMB−OH] = [OH]0 ×

⎛ t⎞ I01 × c ⎡ ⎢ −exp⎜ − ⎟ −1 τ1 − d ⎣⎢ ⎝ τ1 ⎠

⎛ t ⎞⎤ + exp⎜ − ⎟⎥ ⎝ τ2 ⎠⎥⎦

Then as d[HMB−OH−NO2 ]/dt = k NO2 × NO2 × [HMB−OH] d[PMP]/dt = kPMP × [HMB−OH] and d[PMB]/dt = kabst × [OH] × [HMB]

Figure 7. Arrhenius diagram of the PMB−NO2 (●) experimental branching ratios (with [NO2] equal to 1.2 × 1014 molecules cm−3 and the reaction time equal to 6 ms). The solid black curves correspond to the best simulation and the dashed-dotted line corresponds to the simulation including (kabst ± 2σ), (kback ± 2σ), and (kHMBOH,PMB+NO2 ± 2σ). The red dots correspond to PMB−NO2 branching ratios, multiplying the photoionization cross section of PMB−NO2 by a factor of 1.43, and the red curve is the best simulation corresponding (kabst is multiplied by 0.70 and kback is multiplied by 0.78).

The integration as a function of time leads to [HMB−OH−NO2 ] = k NO2 × NO2 × [OH]0 × ⎤ ⎡ ⎛ t ⎞ ⎛ t⎞ × ⎢τ1 exp⎜ − ⎟ − τ2 exp⎜ − ⎟ − τ1 + τ2 ⎥ ⎥⎦ ⎢⎣ ⎝ τ2 ⎠ ⎝ τ1 ⎠ [PMP] = kPMP × [OH]0 ×

I01 × c τ1−1 − d

I01 × c

τ1−1 − d ⎤ ⎡ ⎛ t ⎞ ⎛ t⎞ × ⎢τ1 exp⎜ − ⎟ −τ2 exp⎜ − ⎟ − τ1 + τ2 ⎥ ⎥⎦ ⎢⎣ ⎝ τ2 ⎠ ⎝ τ1 ⎠

HMB−OH + NO2 reaction is not fast enough to completely avoid back dissociation, leading to an increase in PMB−NO2 production. Considering the values used in the simulation, PMP production is always low, in good agreement with experimental determinations. The curves show one simulation in the complete temperature range using expressions 7−9. kback was then further optimized alone using full numerical integration of the kinetic system to consider the influence of secondary OH radical reactions, which lead to a very minor correction. Uncertainties on experimental data do not include those on photoionization cross section values, but these last uncertainties were taken into account to estimate final rate constant uncertainties. The continuous lines correspond to the best fit of the simulations using the following set of rate constants for the production of HMB−OH, PMB, and PMP.

[PMB] = kabst × [HMB] × [OH]0 ⎡ ⎛ t ⎞ ⎛ t⎞ × ⎢ −τ1 × I01 × exp⎜ − ⎟ − τ2 × I02 × exp⎜ − ⎟ ⎢⎣ ⎝ τ2 ⎠ ⎝ τ1 ⎠ ⎤ + τ1 × I01 + τ2 × I02 ⎥ ⎥⎦

In our experiment, the reaction time was fixed to 6 ms, ensuring that all OH radicals, as well as HMB−OH and PMB radicals, were transformed into HMB−OH−NO2, PMB−NO2, and 12195



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k total = 2.8 × 10−11 × exp(500/T ) cm3 molecule−1 s−1

used structure−reactivity relationships (SARs) of Kwok and Atkinson.47 The addition rate constant is estimated using the electrophilic substituent constants of Brown and Okamoto48 as discussed by Zetzsch.49 The electrophilic substituent constant Σσ+ is calculated assuming that (a) steric hindrance can be neglected (b) Σσ+ is the sum of all of the substituent constants of the substituent groups attached to the aromatic ring, (c) the OH radical adds to the position yielding the most negative value of Σσ+, and (d) if all positions on the ring are occupied, the ipso position can be treated as a meta position). The HMB + OH addition rate constant obtained from the SAR is equal to 6.6 × 10−11 cm3 molecule−1 s−1, a value close to a half of the experimental one. Note that this k(SAR)/k(experimental) ratio close to 0.5 is very similar for all the poly methylbenzenes (xylenes and trimethylbenzenes).46 The H atom abstraction rate constant is calculated using a SAR based on the additivity of group of rate constants for H atom abstractions.47 The room temperature abstraction rate constant obtained is then equal to 8.1 × 10−13 cm3 molecule−1 s−1, corresponding to a branching ratio equal to 1.2%, which can be compared to our experimental H atom abstraction branching ratio equal to (11.1 ± 3.6) % at the same temperature. Therefore, the SAR obviously underestimates the abstraction channel, as it underestimates the H atom abstraction branching ratio for all reactions between OH and aromatics at room temperature, compared to experimental values from Perry and co-workers.46 This large discrepancy, already noted by Kwok and Atkinson,47 is due to the use of a substituent group factor F(−C6H5) equal to 1 in the SAR, instead of a higher value, as a phenyl group is stabilizing a radical in the α position (the benzyl radical for example). Indeed, due to the much higher reactivity for addition than for abstraction, particularly at room temperature, there is a lack of data for abstraction, leading to the fact that F(−C6H5) is not well-defined. From kinetic measurements, a reasonable value for F(−C 6 H 5 ) of around 5 can be estimated from experimentally reported data from the OH + toluene, OH + toluene-d5, and OH + xylenes reactions.2 Our result on H atom abstraction for the OH + HMB reaction rather implies a factor F(−C6H5) equal to 9. Further experimental measurements of H abstraction branching ratios are necessary to get a better description of the general reaction pattern of OH radicals with aromatics. The dealkylation channel (HMB + OH → CH3 + PMP) is always very low and is negligible below 370 K for total pressures above 1 Torr and is estimated to be below 2% at room temperature. This result strongly suggests that the transition state for dealkylation, calculated to be −1.3 kJ/mol below the reactant energy, may indeed be higher in energy. The precision of ab initio calculations is always a delicate discussion. However, considering the small size of the basis used in this work, imposed by the large number of atoms in the HMB + OH system, an uncertainty of few kilojoules/mole for the various transition states is reasonable. Considering such uncertainty, the transition state for delakylation may be above the reactants which may explain the low rate constant for this channel, lower than 2% at room temperature.

(10)

kabst = (3.2 ± 1.0) × 10−11 × exp(− 200/T ) cm 3 molecule−1 s−1

(11)

kadd = k total − kabst

(12)

k back = (2.7 ± 1.1) × 1014 × exp( −10500/T ) s−1

(13)

kdealk = (2.4 ± 1.4) × 1012 × exp( −10200/T) s−1

(14)

The expression for ktotal was taken from Zetzsch and coworkers,13 and it is in good agreement with ktotal(295 K) from Berndt and Böge.12 The expressions for kabst and kdealk were obtained in this study. In the case of the back dissociation rate constant, as the temperature range (390−430 K) was quite narrow in this study, results were not very sensitive to the temperature dependency. We preferred to choose the temperature dependency reported by Zetzsch and co-workers,13 adjusting only the pre-exponential factor. The main source of uncertainty is again the uncertainty of photoionization cross section values. A minor one is the uncertainty of the HMB− OH + NO2 reaction rate constant as this value plays a role in the competition between the HMB−OH + NO2 reaction and HMB−OH back dissociation. Taking into account all uncertainties, the value for kback determined in this work is in reasonably good agreement with the experimental determination reported by Zetzsch and co-workers,13 i.e., kback = 1.0 × 1014 × exp(−10500/T) s−1. A simplified sensitivity analysis, performed by varying rate constant by two standard deviation ((kabst ± 2σ), (kback ± 2σ), (kdealk ± 2σ), and (kHMBOH,PMB+NO2 ± 2σ)), is shown in Figure 7, indicated by dashed-dot lines. The resulting PMB branching ratio, obtained by varying the ratio of the photoionization cross sections of HMB−OH−NO2 and PMB−NO2 by a factor of 0.70, is presented in red in the Figure 7. To fit properly the data, the abstraction rate constant values have to be multiplied by a factor of 0.70 and the back dissociation rate constant by a factor of 0.78, showing that both rate constants are correlated (as expected). Using the calculated ionization cross section values presented in Table 1 leads to an abstraction branching ratio equal to (13.7 ± 4.4) % at 330 K, a value in very good agreement with that obtained through direct measurements (presented above). The abstraction branching ratio calculated using expressions 10 and 11 is equal to (11.1 ± 3.6)% at 300 K. The relatively large variation between 300 and 330 K is due to the fact that the addition rate constant has a positive temperature dependency in contrast to the abstraction rate constant which presents a negative one. The value of the back dissociation rate constant for the HMB−OH adduct is notably smaller than for other aromatics,46 clearly showing the strength of the HMB−OH bond. This result is confirmed by the theoretical calculations performed in this work. Calculations lead to a submerged barrier for addition and abstraction channels, in agreement with high rate constants for both addition and abstraction. The theoretical difference between the energy of the two barriers is equal to 8 kJ/mol, corresponding to 950 K, close to the experimental value of 700 K (i.e., 500 K to −200 K). It is always interesting to compare the rate constants for the OH + HMB reaction determined experimentally for addition and abstraction channels to those estimated using the widely

■

CONCLUSION The HMB + OH reaction is a prototype of ipso addition on aromatic rings. The high value of the rate constant at room temperature shows that ipso addition occurs readily in this case and may play a role for the reaction of OH radicals with various aromatics. In this work, it has been shown that the dealkylation 12196



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process, calculated with an exit barrier close to the entrance level, is indeed negligible below 370 K. It has also been shown that the H-abstraction reaction pathway is equal to 11% at room temperature and may play a non negligible role in the first steps of the OH-initiated-oxidation of aromatics, in contrast to some current global oxidation mechanisms for aromatics. Our results show a disagreement with the Habstraction rate constant proposed by the structure−reactivity relationship from Kwok and Atkinson,47 a disagreement already noted by Kwok and Atkinson themselves for the OH + toluene, toluene-d5, and xylenes reactions,2 clearly indicating the need for new measurements on H atom abstraction branching ratios for OH reactions with aromatics.

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ASSOCIATED CONTENT

S Supporting Information *

Tabulated data corresponding to Figures 4 and 7. 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]. Telephone: +33 5 4000 6346. Fax: +33 5 4000 6994. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the CNRS-INSU/DFG bilateral project “Novel Approaches in the Understanding of Aromatic Compound Degradation in the Atmosphere: From Theoretical Studies to Simulation Chamber Experiments”.

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REFERENCES

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