Experimental Study of the Reactions of Limonene with OH and OD

Article pubs.acs.org/JPCA

Experimental Study of the Reactions of Limonene with OH and OD Radicals: Kinetics and Products Tristan Braure,† Yuri Bedjanian,*,‡ Manolis N. Romanias,‡ Julien Morin,‡ Véronique Riffault,† Alexandre Tomas,† and Patrice Coddeville† †

Département Sciences de l’Atmosphère et Génie de l’Environnement (SAGE), Ecole Nationale Supérieure des Mines de Douai, Douai 59508, France ‡ Institut de Combustion, Aérothermique, Réactivité et Environnement (ICARE), CNRS, Orléans Cedex 2 45071, France S Supporting Information *

ABSTRACT: The kinetics of the reactions of limonene with OH and OD radicals has been studied using a low-pressure flow tube reactor coupled with a quadrupole mass spectrometer: OH + C10H16 → products (1), OD + C10H16 → products (2). The rate constants of the title reactions were determined using four different approaches: either monitoring the kinetics of OH (OD) radicals or limonene consumption in excess of limonene or of the radicals, respectively (absolute method), and by the relative rate method using either the reaction OH (OD) + Br2 or OH (OD) + DMDS (dimethyl disulfide) as the reference one and following HOBr (DOBr) formation or DMDS and limonene consumption, respectively. As a result of the absolute and relative measurements, the overall rate coefficients, k1 = (3.0 ± 0.5) × 10−11 exp((515 ± 50)/ T) and k2 = (2.5 ± 0.6) × 10−11 exp((575 ± 60)/T) cm3 molecule−1 s−1, were determined at a pressure of 1 Torr of helium over the temperature ranges 220−360 and 233−353 K, respectively. k1 was found to be pressure independent over the range 0.5−5 Torr. There are two possible pathways for the reaction between OH (OD) and limonene: addition of the radical to one of the limonene double bonds (reactions 1a and 2a) and abstraction of a hydrogen atom (reactions 1b and 2b), resulting in the formation of H2O (HOD). Measurements of the HOD yield as a function of temperature led to the following branching ratio of the H atom abstraction channel: k2b/k2 = (0.07 ± 0.03) × exp((460 ± 140)/T) for T = (253−355) K.

1. INTRODUCTION The organic compounds emitted from vegetation and plants are classified as biogenic volatile organic compounds (BVOCs). Global BVOC emissions are roughly estimated to be 1150 Tg C year−1,1 exceeding by 1 order of magnitude the emissions of VOCs due to anthropogenic activities.2−5 The contribution of BVOCs to air quality and climate change is significant, since they act as precursor molecules for photochemical smog6 and secondary organic aerosol (SOA) formation.7 Isoprene is the most abundant biogenic compound released in the troposphere representing around 50% of the total BVOC emissions. Monoterpenes also represent a class of compounds with a biogenic source accounting for ∼11% of the total BVOC atmospheric budget.8 Their concentrations in air vary considerably depending on the environmental conditions (light, temperature, time of day/year) and the type of vegetation.9,10 Limonene (C10H16, structure with labeling of the different carbons is given below) is a representative of monoterpenes that appears to have significant atmospheric interest. It is mainly released from several trees and bushes. Upon its emission to the atmosphere, limonene is oxidized in reactions with atmospheric detergents (OH, NO3, O3, Cl) forming lower volatility compounds leading to SOA formation.11 Furthermore, the presence of the cyclohexene ring and ethylene tailing © 2014 American Chemical Society

group renders limonene as one of the most effective SOA precursor molecules (presence of two double bonds) that can contribute disproportionally to SOA formation compared to other terpenoid compounds.11,12 Received: July 18, 2014 Revised: September 9, 2014 Published: September 11, 2014 9482

dx.doi.org/10.1021/jp507180g | J. Phys. Chem. A 2014, 118, 9482−9490

The Journal of Physical Chemistry A

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Figure 1. Diagram of the flow reactor.

halocarbon wax in order to minimize the heterogeneous loss of active species. The fast reaction of hydrogen atoms with NO2 was used as the source of OH radicals, H atoms being produced in a microwave discharge of a H2/He mixture:

The understanding and description of the degradation mechanism of an organic compound in the atmosphere requires first and foremost the information on kinetics and primary products of its reactions with atmospheric oxidants. The present study reports the results of the experimental investigation of the reaction of limonene with OH radicals. This reaction is of special kinetic and mechanistic interest, since it proceeds through both OH addition and H atom abstraction channels: OH + C10H16 (+ M) → C10H16OH (+ M)

(1a)

→C10H15 + H 2O

(1b)

H + NO2 → OH + NO

Similarly, the reaction of D atoms with NO2 was used to produce OD radicals: D + NO2 → OD + NO

(2a)

→C10H15 + HOD

(2b)

(4)

NO2 was always used in excess over H and D atoms. OH and OD radicals were detected as HOBr+ (m/z = 96/98) and DOBr+ (m/z = 97/99), respectively, after scavenging by an excess of Br2 ([Br2] = (5−10) × 1013 molecules cm−3, added at the end of the reactor, 5 cm upstream of the sampling cone) via the following reactions:

The precise knowledge of the kinetics and mechanism of both channels requires a detailed study of the overall reaction as a function of temperature and pressure. Three relative rate kinetic studies of reaction 1 at 760 Torr total pressure have been published so far, where the overall rate constant at room temperature13,14 and in the temperature range 298−362 K was measured.15 The branching ratio of the abstraction channel (1b) at T = 298 K has also been reported.16 In the present paper, we report complementary results on reaction 1, including pressure and temperature dependence of k1, in extended temperature range T = 220−360 K, and branching ratio of the H atom abstraction channel (1b) (measured via direct detection of the reaction product, H2O) as a function of temperature. To study the temperature dependence of the abstraction channel, we have chosen the reaction of OD radicals with limonene essentially for practical reasons: the residual concentration of HOD in the flow reactor was much lower than that of H2O. In this respect, the kinetics of the reaction of OD radicals with limonene was also investigated as a part of this study: OD + C10H16 (+ M) → C10H16OD (+ M)

(3)

OH + Br2 → HOBr + Br

(5)

OD + Br2 → DOBr + Br

(6)

This method for OH and OD detection was preferred to the direct detection of these radicals at m/z = 17 (OH+) and m/z = 18 (OD+), respectively, due to significant contributions of water vapor traces at these peaks. The same procedure of OH (OD) chemical conversion to HOBr (DOBr) was used for the measurements of the absolute concentrations: [OH] = [HOBr] = Δ[Br2] (or [OD] = [DOBr] = Δ[Br2]). Thus, OH (OD) concentrations were determined from the consumed fraction of Br2 concentration. The Br2 concentration was determined from the measured flow rate of known Br2/He mixtures. The possible influence of secondary chemistry on this method of HOBr (DOBr) detection and their absolute calibration procedure was discussed in details in previous papers from this group.17,18 The limonene vapor was introduced into the flow reactor by passing helium through a thermostated glass bubbler containing liquid limonene. The absolute calibration of the mass spectrometer for limonene was performed by injecting known amounts (a few μL) of liquid limonene inside the flow tube and recording the parent mass peak intensity of C10H16 at m/z = 136. The integrated area of the mass spectrometric signals corresponding to a known total number of limonene molecules injected into the reactor allowed the determination of the calibration factor. Similar (within 10%) results were obtained when limonene was introduced into the reactor from the flask

2. EXPERIMENTAL SECTION Experiments were carried out in a discharge flow reactor using a modulated molecular beam mass spectrometer as the detection method.17−21 The main reactor, shown in Figure 1 along with the movable injector for the reactants, consisted of a Pyrex tube (45 cm length and 2.4 cm i.d.) with a jacket for the thermostated liquid circulation (water or ethanol). The walls of the reactor as well as of the injector were coated with 9483



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with a known C10H16/He mixture, and its concentration was calculated from the measured flow rate. All species were detected by mass spectrometry at their parent peaks (except OH and OD as discussed above): m/z = 136 (C10H16+), 94 (CH3SSCH3+), 86 (C6H14+), 160 (Br2+), 46 (NO2+), 30 (NO+), 19 (HOD+), and 18 (H2O+). The concentrations of the stable species in the reactor were calculated from their flow rates obtained from the measurements of the pressure drop of mixtures of the species with helium in calibrated volume flasks.

3. RESULTS 3.1. Rate Constants of Reactions 1 and 2. 3.1.1. Absolute Rate Constants. Two types of experiments were carried out to measure the rate constants of the OH and OD reactions with limonene, either by monitoring the OH (OD) consumption kinetics in an excess of limonene or by monitoring the limonene decay kinetics in an excess of OH (OD) radicals. In experiments carried out in excess of limonene, the initial concentration of OH (OD) radicals was (0.3−0.6) × 1012 molecules cm−3, and the initial concentration of limonene, [C10H16]0, was varied in the range (0.4−4.5) × 1012 molecules cm−3. The flow velocity in the reactor was (2800−3100) cm s−1. The concentrations of OH (OD) radicals and limonene were simultaneously measured as a function of reaction time. Examples of the exponential decay kinetics of OH in reaction 1 are shown in Figure 2.

Figure 3. Example of a pseudo-first-order plot obtained from OH decay kinetics in excess of limonene (T = 360 K).

first-order rate constant, k1′ = k1[C10H16] + kw, as a function of the limonene concentration. kw represents the rate of OH decay in the absence of limonene in the reactor and was measured in separate experiments. All the measured values of k1′ were corrected for axial and radial diffusion22 of OH. The diffusion coefficient of OH in He was calculated using the following expression: D0 = 640 × (T/298)1.85 Torr cm2 s−1.23−25 Corrections were less than 12%. The slope of the straight line in Figure 3 gives the value of k1 at T = 360 K. The intercept in Figure 3, 45 ± 10 (1σ) s−1, is in fair agreement with the OH-loss rate of 35 s−1 measured in the absence of limonene in the reactor. All the results obtained for k1 and k2 within the described approach and at different temperatures are shown in Tables 1 and 2, respectively. Limonene is a sticky molecule, which could lead to heterogeneous complications in the study of its reactions in a flow reactor, particularly at low temperatures. Indeed, in the present study, we have observed an abnormal increase of the reaction rate constant below room temperature, which was attributed to the heterogeneous reaction of OH(OD) with surface-adsorbed limonene. For this reason, the absolute measurements of the rate constants were carried out at relatively high temperatures (Tables 1 and 2). As noted above, OH (OD) radicals were scavenged by Br2 at the end of the reactor to be detected as HOBr (DOBr) molecules (reactions 5 and 6). This led to the simultaneous production of Br atoms, which could react with limonene. However, the important point is that the Br atom reactions could not affect the concentration of HOBr through its formation or consumption reactions, and therefore, they had no impact on the observed kinetics of OH. In addition, the Br + limonene reaction had a negligible impact on limonene: it was observed that the concentration of limonene did not change (within a few percents) upon addition of Br2 at the end of the reactor. Secondary reactions of OH radicals with primary products of reaction 1, C10H15 and C10H16OH, could also be considered as negligible, taking into account the very high value of the rate constant of the primary reaction, k1, and the sufficient excess of limonene over OH radicals in most of the experiments.

Figure 2. Examples of the exponential decay kinetics of OH in reaction 1 (T = 360 K).

A consumption of C10H16 was also observed as a result of the use of insufficient excess of limonene over OH (OD). In most cases, this consumption was less than 15%; however, in a few kinetic runs, it was much higher (up to 50%). The use of the insufficient excess of limonene over the radicals in some experiments was due to an extremely high rate constant and limited sensitivity of OH (OD) detection. For the rate constant calculations, we therefore used the mean values of C10H16 concentration over the reaction time of the OH (OD) kinetics. A numerical simulation of the OH (OD) decay kinetics, using the observed temporal profiles of limonene, gave the same (within 5%) values for k1 and k2. Figure 3 shows the pseudo9484



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mainly due to the heterogeneous loss of the radicals and to their reactions with limonene and products of the primary reaction. The values of the rate constant k1 (k2) were derived from the numerical simulation of the limonene decays (k1 (k2) being the only varied parameter), using the observed OH (OD) concentration temporal profiles. A summary of the experimental conditions and results obtained for k1 and k2 is presented in Tables S1 and S2 (Supporting Information). 3.1.2. Relative Rate Measurements. The rate constants of reactions 1 and 2 were measured using two reference reactions of OH (OD), with Br2 and DMDS. In the relative study with reference reaction

Table 1. Summary of the Measurements of the Rate Constant of the Reaction OH + Limonene T (K)

k1a (10−10 cm3 molecule−1 s−1)

methodb

220 230 240 253 263 266 278 278 293 295 300 303 308 313 315 325 336 342 348 355 360

3.23 3.13 2.58 2.15 1.96 1.97 1.85 1.85 1.65 1.72 1.65 1.61 1.62 1.41 1.58 1.49 1.46 1.33 1.36 1.22 1.37

RM/DMDS RM/DMDS RM/DMDS RM/DMDS RM/DMDS RM/DMDS RM/Br2 RM/DMDS RM/DMDS RM/Br2 AM/excess OH RM/DMDS RM/Br2 RM/DMDS RM/Br2 AM/excess C10H16 AM/excess C10H16 AM/excess OH AM/excess C10H16 RM/Br2 AM/excess C10H16

OH + Br2 → HOBr + Br

the fast titration of the initial concentration of OH radicals, [OH]0, by a mixture of excess limonene and Br2 was performed, and the yield of HOBr as a function of the [C10H16]/[Br2] ratio was measured. The concentration of HOBr formed was defined by the fraction of [OH]0 reacting with Br2: [HOBr] =

[OH]0 k [C H ] − 1 = 1 10 16 [HOBr] k5[Br2]

Typical uncertainty on k1 is nearly 15%. bRM/DMDS and RM/Br2: relative rate method with OH + DMDS and OH + Br2 as reference reactions, respectively; AM/excess C10H16 and AM/excess OH: absolute rate measurements from OH and C10H16 decays in excess of limonene and OH, respectively.

methodb

233 243 253 258 258 263 273 283 293 300 300 320 323 330 338 348 353

3.21 2.58 2.36 2.17 2.16 2.26 2.23 2.01 1.76 1.69 1.50 1.48 1.43 1.54 1.33 1.29 1.32

RM/DMDS RM/DMDS AM/excess OD RM/Br2 RM/DMDS AM/excess OD RM/DMDS RM/Br2 AM/excess OD RM/DMDS RM/DMDS RM/DMDS RM/Br2 AM/excess C10H16 RM/DMDS RM/DMDS AM/excess C10H16

(I)

k1/k5, and hence k1, could be obtained by plotting ([OH]0/ [HOBr] − 1) as a function of the [C10H16]/[Br2] ratio. It can be noted that this method did not need absolute calibration of the mass spectrometric signals for OH radicals and HOBr because the initial concentration of OH could be expressed as HOBr signal in the absence of limonene, when OH is titrated with an excess of Br2. Thus, in the experiments, only the HOBr signal was detected, first in the limonene-free system, corresponding to [OH]0, and then in the Br2 and C10H16containing system, corresponding to the fraction of [OH]0 reacted with Br2. A similar procedure was applied to measure the rate constant of reaction 2 using the reference reaction

Table 2. Summary of the Measurements of the Rate Constant of the Reaction OD + Limonene k2a (10−10 cm3 molecule−1 s−1)

k5[Br2] × [OH]0 k5[Br2] + k1[C10H16]

Considering the derived expression,

a

T (K)

(5)

OD + Br2 → DOBr + Br

(6)

The initial concentrations of OH (OD) radicals were in the range (2−5) × 1012 molecules cm−3. The concentration ranges of limonene and Br2 used in these experiments are shown in Tables 3S and 4S (Supporting Information). The reaction time was typically 5 × 10−3 s. An example of the experimental data obtained at T = 308 K for different pressures in the reactor is presented in Figure 4. According to eq I, the slope of the linear dependence in Figure 4 gives the k1/k5 ratio. The data presented in Figure 4 indicate that the rate constant of reaction 1 is independent of pressure in the range (0.5−5) Torr, considering that the rate constant of the bimolecular reference reaction OH + Br2 does not depend on pressure. Figure 5 shows similar data observed at different temperatures and 1 Torr total pressure in the reactor. All the results obtained in this way for k1/k5 and k2/k6 as well as the final results obtained for k1 and k2 are presented in Tables S3 and S4 (Supporting Information), respectively. The values of k5 used in the calculations of k1 were determined from the Arrhenius expression k5 = 1.9 × 10−11 exp(235/T) cm3 molecule−1 s−1. This last expression is based on two previous studies of reaction 3,18,26 where similar values were measured for the activation factor, E/R = 235 K18 and 238

a Typical uncertainty on k2 is nearly 15%. bRM/DMDS and RM/Br2: relative rate method with OD + DMDS and OD + Br2 as reference reactions, respectively; AM/excess C10H16 and AM/excess OD: absolute rate measurements from OD and C10H16 decays in excess of limonene and OD, respectively.

In a few experiments, the rate constants of reactions 1 and 2 were extracted from the kinetics of limonene consumption in excess of OH and OD radicals, respectively. Temporal profiles of OH (OD) were monitored simultaneously with the decay kinetics of limonene. Significant consumption, up to 70%, of OH (OD) was observed. The consumption of OH (OD) was 9485



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limonene and reference compound, DMDS, are defined by the rate constants of their reactions with OH: ln

[DMDS]0 [C10H16]0 k = 1 × ln [C10H16] k7 [DMDS]

(II)

where the expressions under the logarithm are the ratios of the compound concentration in the absence of to that in the presence of OH radicals for a given reaction time. Experiments were carried out at a total pressure of 1 Torr. Initial concentrations of limonene and DMDS were in the range (3.8−9.4) × 1011 and (0.14−2.1) × 1013 molecules cm−3, respectively, and that of OH (OD) radicals was varied between 4 × 1011 and 6 × 1012 molecules cm−3. Reaction time was also varied, being in the range (0.004−0.016) s. Examples of the dependence of ln([C10H16]0/[C10H16]) on ln([DMDS]0/ [DMDS]), observed with OD and OH radicals, are shown in Figures 6 and S1 (Supporting Information), respectively.

Figure 4. HOBr yield from OH titration with Br2 + limonene mixtures at T = 308 K and different pressures in the reactor (see eq I in the text). Vertical and horizontal error bars correspond to (9−28)% and nearly 20% uncertainties, respectively.

Figure 6. Example of ln([C10H16]0/[C10H16]) vs ln([DMDS]0/ [DMDS]) dependence for the reaction OD + limonene.

According to eq II, the slopes of the straight lines in these figures represent the k1/k7 and k2/k8 ratios. It can be noted that variations of the initial concentrations of limonene and DMDS and of the reaction time had no impact on the results obtained for k1/k7 (k2/k8). This indicates the negligible role of the possible secondary reactions that could lead to additional consumption of limonene and DMDS. For the rate constant of the reference reaction 5, we have used the Arrhenius expression, k7 = 5.9 × 10−11 exp(380/T) cm3 molecule−1 s−1, from a unique previous temperature-dependent study of the reaction.27 No data are available for the rate constant of reaction 6. In calculations of k2, we have considered that k8 = k7. This assumption seems to be reasonable, considering that (i) secondary isotopic effect is generally observed to be negligible and (ii) the values of k2 calculated with k8 = k7 are in good agreement with those obtained above by other methods (Tables 1 and 2). 3.1.3. Temperature Dependence of k1 and k2. All the results obtained for k1 and k2 in the present study are shown in Tables 1 and 2 and Figures 7 and 8. The combined uncertainty on the measurements of the rate constants was estimated to be

Figure 5. HOBr yield from OH titration with Br2 + limonene mixtures at P = 1 Torr and different temperatures (see eq I in the text).

K,26 and the difference between the reported preexponential factors was around 10%. For the rate constant of the reference reaction 4, the expression k6 = 1.9 × 10−11 exp(220/T) cm3 molecule−1 s−1, determined earlier in our group,18 was used. In another series of experiments, the rate constants of reactions 1 and 2 were measured using reference reactions of OH (OD) with DMDS: OH + DMDS → products

(7)

OD + DMDS → products

(8)

In this case, the “classical” relative rate method was employed that consisted of the monitoring of the consumption of limonene and DMDS, simultaneously present in the reactor, in reactions with OH (OD). The relative consumptions of 9486



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dotted line in Figure 8, shown for comparison, corresponds to the Arrhenius equation obtained for k1. The rate constant measurements at lower temperatures were performed with the relative rate method in order to avoid the possible impact of the reactions on the wall of the reactor. In the first relative method, with monitoring HOBr formation, the potential heterogeneous complications are limited due to rapid consumption of OH radicals in the gas phase when sufficiently high concentrations of Br2 and limonene are used. In the second method, using the DMDS reaction with OH as the reference one, the heterogeneous loss of OH radicals has no impact on the measurements of the limonene loss relative to that of DMDS. In addition, we have not observed any loss of limonene and DMDS on the wall of the reactor. Good agreement between the values of the rate constants obtained with different methods seems to indicate that the possible impact of the heterogeneous chemistry on the results of the measurements was insignificant. 3.2. Determination of k1b/k1 and k2b/k2. There are two possible pathways for the reaction between OH (OD) and limonene: addition of the radical to one of the double bonds of limonene (reactions 1a and 2a) and abstraction of a hydrogen atom (reactions 1b and 2b), resulting in the formation of H2O (HOD). In this series of experiments, we have measured the branching ratio for the H atom abstraction channel of reactions 1 and 2. Experiments consisted in the titration of the initial concentration of OH (OD in most experiments) with an excess limonene and the direct detection of the reaction product, H2O (HOD). The yield of H2O in the reaction of OH with limonene was measured relatively to that in the reaction of OH with hexane, where the yield of H2O is 100%. Accordingly, in the experiments, the same concentration of OH was successively consumed with limonene and hexane, and the concentration of H2O formed was monitored. The advantage of this approach is that it does not require any knowledge of the absolute concentrations of H2O (HOD) and OH (OD) radicals. An example of the data observed at T = 300 K is shown in Figure 9.

Figure 7. Summary of the measurements of the rate constant of the reaction OH + limonene: this work and literature data.

Figure 8. Temperature dependence of the rate constant of the reaction OD + limonene.

in the range 15−20%, including statistical error and those on the measurements of the flows, pressure, temperature, and the absolute concentrations of the relevant species. The lines in Figures 7 and 8 represent an unweighted exponential fit to all the data obtained, respectively, for k1 and k2, yielding the following Arrhenius expressions: k1 = (3.0 ± 0.5) × 10−11 exp((515 ± 50)/T ) cm 3 molecule−1 s−1 k 2 = (2.5 ± 0.6) × 10−11 exp((575 ± 60)/T ) cm 3 molecule−1 s−1

Figure 9. H2O (filled symbols) and HOD (open symbols) formed in the reactions of OH and OD with limonene (circles) and hexane (squares) as a function of the consumed concentration of OH (OD). Error bars correspond to a maximum uncertainty of 10% on the determination of the relative concentrations.

where the cited uncertainties are 2σ statistical ones. Although the two equations are somewhat different, the rate constants for the reactions of OH and OD with limonene can be considered as identical in the temperature range of the present study: the 9487



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relative rate method and at 760 Torr total pressure.13−15 Winer et al.13 and Atkinson et al.14 have reported near room temperature values of k1 = (1.45 ± 0.23) × 10−10 at T = 305 K and (1.69 ± 0.50) × 10−10 cm3 molecule−1 s−1 at T = 294 K, respectively. Gill and Hites15 reported the only, to date, measurement of the temperature dependence of the rate constant: k1 = (4.2 ± 0.5) × 10−11 exp(401 ± 43)/T) over the temperature range 295−364 K. All these results are shown in Figure 7 together with the data from the present study. One can note an excellent agreement between all the studies: the maximum deviation of the previous data from the current Arrhenius expression (solid line in Figure 7) is nearly 12%. It should be noted that previous studies were carried out at total pressure of 1 atm, while the data from the present study were obtained at nearly 1 Torr pressure. The good agreement between the results obtained at different pressures as well as the pressure independence of k1 in the range (0.5−5.0) Torr observed in the present study, clearly indicate that the highpressure regime of reaction 1 extends at least to P = 0.5 Torr. Correct modeling of the OH-initiated atmospheric oxidation of the unsaturated VOCs, including final product distribution, requires the knowledge of all site-specific rate constants for OH ́ ́ addition and H atom abstraction pathways. Ramirez-Rami rez and Nebot-Gil28 by means of ab initio calculations have investigated the OH addition to the endocyclic and exocyclic double bonds of d-limonene. These authors reported that, although both addition pathways are significant, there is one preferred orientation for the OH addition, corresponding to an endocyclic addition of OH to the H-substituted carbon atom (carbon “c”) on the syn side to the isopropenyl group. Peeters et al.29 have developed a structure−activity relationship (SAR) for the site-specific addition of OH radicals to (poly)alkenes at 298 K. Within this SAR, the total rate constant for the addition reaction is approximated by a sum of individual site-specific contributions for addition to the double bonds. The total rate constant for OH addition to limonene, calculated in the frame of the SAR (T = 298 K), is k1a = 1.45 × 10−10 cm3 molecule−1 s−1, with the major contribution of the addition paths leading to the formation of tertiary hydroxy-adduct radicals, that is, endocyclic addition of OH to the H-substituted carbon (carbon “c”) and to the external carbon atom (carbon “i”) of the exocyclic double bond. The predicted value of k1a is in fair agreement with the experimental one from the present study, k1a = 1.14 × 10−10 cm3 molecule−1 s−1, calculated as k1 − k2b, using Arrhenius expressions for k1 and k2b/k2. Although it is generally believed that the reaction of OH with alkenes proceeds mainly via radical addition to the double bond, the hydrogen atom abstraction was shown to be an important pathway of the OH reactions with some cyclic biogenic compounds. Peeters et al.30 by directly measuring the amount of H2O formed in the reactions of α-terpinene and αphellandrene with OH, determined branching ratios for the H atom abstraction channel of (30 ± 7)% and (27 ± 10)%, respectively. It was speculated that, in these particular cases, the hydrogen abstraction is facilitated by stabilization of the organic product radical due to a strong delocalization of the unpaired electron throughout the ring (over three C atoms). More recently, Rio et al.16 have shown that the contributions of the H atom abstraction channel in reactions of OH radicals with γterpinene and d-limonene were, respectively, (31 ± 9)% and (34 ± 8)% at atmospheric pressure and (28 ± 6)% and (28 ± 8)% at (0.5−2.8) Torr total pressure. The branching ratio for H

The ratio of the slope of the line corresponding to limonene to that of the line observed with hexane provides the branching ratio for the H atom abstraction channel of reactions 1 and 2: 0.39 and 0.37, respectively. As one can see from Figure 9, the measured branching ratio is independent of the initial concentration of radicals, which was varied by an order of magnitude. This seems to indicate on the negligible role of the possible formation of water in secondary reactions. As it was already noted, the temperature dependence of the abstraction channel was studied for reaction of OD radicals with limonene essentially for practical reasons: the residual concentration of HOD in the flow reactor was much lower than that of H2O. All the results obtained for k2b/k2 are shown in Table S5 (Supporting Information) and Figure 10. In the range

Figure 10. Temperature dependence of the branching ratio for the H atom abstraction channel (2b) of reaction 2: open symbols, this work; filled symbols, data from Rio et al.16 Error bars correspond to a nearly 15% estimated uncertainty on the measurements of k2b/k2.

of experimental uncertainty, all the data can be adequately represented with a slight negative temperature dependence for T = 253−355 K (straight line in Figure 10): k 2b/k 2 = (0.07 ± 0.03) × exp((460 ± 140)/T )

Although the temperature dependence of the H atom abstraction channel was measured for reaction of OD radicals with limonene, we believe that similar results can be expected for the OH radicals. Indeed, we have observed a negligible isotopic effect, as one could expect for reaction proceeding without isotopically substituted atom bond breaking (secondary isotopic effect). First, the total rate constants (addition + abstraction) for reactions of OH and OD radicals with limonene were found to be identical in the temperature range of the study (Figure 8). Second, similar branching ratios were determined for H atom abstraction by OH and OD at room temperature (Figure 9). These observations seem to show that mechanistic data obtained with OD can be quantitatively applied to OH radicals.

4. DISCUSSION To our knowledge, the rate constant for the reaction of OH with limonene was measured in three previous studies, using a 9488



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Fund (ERDF), and in the CaPPA (Chemical and Physical Properties of the Atmosphere) project (ANR-10-LABX-005) funded by the French National Research Agency (ANR) through the PIA (Programme d’Investissement d’Avenir). T.B. is grateful for a PhD grant from Armines.

atom abstraction in the OH + limonene reaction is in excellent agreement with the data of the present study (Figure 10). SARs,31 which quite well describe H atom abstraction from alkanes, largely underestimate this channel in reactions of OH with complex (poly)alkenes.16 Vereecken and Peeters32,33 attempted to qualitatively relate the rates of H atom abstraction by OH radicals with the C−H bond strengths and effect of the delocalization−resonance stabilization of the product radical and proposed predictive correlations for the abstraction rate constant with C−H bond strength.33 However, it was noted that, for allyl and superallyl resonance stabilization (the case of biogenic cyclic (poly)alkenes), insufficient data were available to model the curvature of the correlation.33 Clearly, systematic studies of the H atom abstraction channel in reactions of OH with (poly)alkenes of different structures are needed to develop a SAR for the site-specific H atom abstraction. Concerning the OH + limonene reaction, the abstraction of hydrogen atoms on carbons “d” and “g” and of the tertiary hydrogen (carbon “e”) enhanced via allyl-resonance stabilization of the product radicals can be expected to be the major abstraction pathways. Combining the Arrhenius expressions obtained in the present study for k2 (or k1) and k2b/k2 results in a rather high negative activation energy (≈ −2 kcal mol−1) for the H atom abstraction channel. This somewhat unexpected result might be an indication that this reaction proceeds mainly through an addition−elimination mechanism and not through direct H atom abstraction. In this respect, in order to establish the detailed mechanism and to better understand the dynamics of this reaction, additional theoretical as well as experimental studies in an extended (to higher and lower temperatures) temperature range would be very beneficial.

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ASSOCIATED CONTENT

S Supporting Information *

Experimental conditions and results of the absolute measurements of k1 in excess of OH radicals over limonene (Table S1); experimental conditions and results of the absolute measurements of k2 in excess of OD radicals over limonene (Table S2); experimental conditions and results of the relative measurements of k1 using OH + Br2 (k5) as the reference reaction (Table S3); experimental conditions and results of the relative measurements of k2 using OD + Br2 (k6) as the reference reaction (Table S4); summary of the measurements of the branching ratio for the HOD forming channel of the reaction OD + limonene (Table S5); example of the ln([C10H16]0/ [C10H16]) versus ln([DMDS]0/[DMDS]) dependence for the reaction OH + limonene (Figure S1). This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*Phone: +33 238255474; fax: +33 238696004; e-mail: yuri. [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Mines Douai participates in the Institut de Recherche en Environnement Industriel (IRENI), which is financed by the Communauté Urbaine de Dunkerque, the Nord-Pas de Calais Regional Council, the French Ministry of Higher Education and Research, the CNRS, and the European Regional Development 9489



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Experimental Study of the Reactions of Limonene with OH and OD

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