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Atmospheric Environment 90 (2014) 133e145

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Atmospheric Environment

journal homepage: www.elsevier .com/locate/atmosenv

Estimation of gas-phase rate coefficients for the reactions of a series ofa,b-unsaturated esters with OH, NO3, O3 and Cl

Ma Paz Gallego-Iniesta a, Beatriz Cabañas a,b, Sagrario Salgado b, Ernesto Martínez a,b,Pilar Martín a,b,*

aDepartamento de Química Física, Facultad de Ciencias y Tecnologías Químicas, Universidad de Castilla La Mancha, Avda. Camilo José Cela S/N,13071 Ciudad Real, Spainb Instituto de Combustión y Contaminación Atmosférica (ICCA), Universidad de Castilla La Mancha, Camino Moledores S/N, 13071 Ciudad Real, Spain

h i g h l i g h t s

* Corresponding author. Departamento de QuímicaTecnologías Químicas, Universidad de Castilla La MaS/N, 13071 Ciudad Real, Spain.

E-mail address: mariapilar.martin@uclm.es (P. Ma

http://dx.doi.org/10.1016/j.atmosenv.2014.03.0361352-2310/� 2014 Elsevier Ltd. All rights reserved.

g r a p h i c a l a b s t r a c t

� Rate coefficients for reactions of at-mospheric oxidants and a�b unsat-urated esters were estimated.

� Physico-chemical correlations andSAR methods have been used to es-timate rate coefficients.

� New correlations to estimating ratecoefficients have been proposed.

� Group reactivity factors f(eC(O)OR)have been calculated.

a r t i c l e i n f o

Article history:Received 29 October 2013Received in revised form24 February 2014Accepted 19 March 2014Available online 20 March 2014

Keywords:Atmospheric oxidantsRate coefficientsa,b-Unsaturated estersEstimation methodsSAR methodGroup-reactivity factors

a b s t r a c t

Rate coefficients for reactions of a series of a,b-unsaturated esters with OH and NO3 radicals, O3 andCl atoms have been estimated using different methods: i.e., physico-chemical correlations andStructure Activity Relationships (SARs). In this study new correlations to estimate rate coefficientshave been proposed (only for a,b-unsaturated esters): log kNO3

� � ¼ (13.9 � 2.8) þ (2.75 � 0.26) � log(kOH); log (kOH) ¼ (4.93 � 1.14) þ (1.60 � 0.12) � log (kCl); ln(kOH/cm

3 molecule�1 s�1) ¼(1.71 � 0.21) � EHOMO/eV � (6.25 � 2.24); ln(kNO3

/cm3 molecule�1 s�1) ¼(5.94 � 0.35) � EHOMO/eV þ (27.87 � 3.65); ln(kO3

/cm3 molecule�1 s�1) ¼ (2.20 � 0.63) � EHOMO/eV � (16.75 � 6.65) andln(kCl/cm

3 molecule�1 s�1) ¼ (0.21 � 0.23) � (EHOMO)/eV � (19.8 � 2.4). The group reactivity factorsnecessary to estimate the rate coefficients by SAR methods have also been calculated for a series ofa,b-unsaturated esters for the first time: f(eC(O)O(CH2)3CH3), f(eC(O)O(CH2)5CH3), f(eC(O)OCH2CH(CH2CH3)CH2CH2CH2CH3) for reactions with the NO3 radical, OH radical and O3. Furthermore,f(eC(O)OCH3), f(eC(O)OCH2CH3), f(eC(O)O(CH2)3CH3), f(eC(O)OCH2CH2CH2CH2CH2CH3), f(eC(O)OCH2CH(CH2CH3)CH2CH2CH2CH3) for reactions with chlorine atoms have been estimated.

The results show that for NO3 and OH radicals these methods are generally satisfactory. In the case ofCl atoms, all methods used in this study reproduce the rate coefficient within a factor of 1.5. In generalthe best method for estimating the rate coefficient of a,b-unsaturated esters with the main atmosphericoxidants is the correlation of ln k versus EHOMO.

� 2014 Elsevier Ltd. All rights reserved.

Física, Facultad de Ciencias yncha, Avda. Camilo José Cela

rtín).

MaP. Gallego-Iniesta et al. / Atmospheric Environment 90 (2014) 133e145134

1. Introduction

a,b-Unsaturated esters are volatile oxygenated organic com-pounds that are emitted into the atmosphere by several sources asprimary pollutants (Graedel, 1978; Japar et al., 1990; Blanco et al.,2006) or as secondary pollutants (Smith et al., 1991; Nouaimeet al., 1998; Riemer et al., 1998; Stroud et al., 2001; Roberts et al.,2003). In recent years several studies have been carried out in or-der to obtain information about the reactivity of this kind of com-pounds (Canosa et al., 1999, 2005; Teruel et al., 2006; Blanco et al.,2009a,b, 2010; Martín et al., 2010; Salgado et al., 2011; Gaona-Colmán et al., 2013). In some cases a kinetic study is difficult tocarry out, especially for the reactions of NO3. In these reactions theuse of estimation methods may represent a good approach toobtain information about their reactivity.

Some estimation methods have been developed in recent yearsin order to obtain information about the reactivity of the main at-mospheric oxidants. There are numerous methods to estimate ratecoefficients and these include (1) methods based on correlationswith measured or calculated physical and chemical parameters(Grosjean et al., 1992; Güsten, 1999; Klamt, 1996; King et al., 1999)and (2) methods based on structureeactivity relationships or SARmethods.

The first SAR method was developed by Atkinson (1986) for OHradicals and it can reproduce rate coefficients with a good degree ofagreement with respect to the experimental values. Subsequentlyother SAR methods have also been developed, for example, Pfranget al. (2006a, 2006b, 2007, 2008) developed a SAR method thatallows the quantification of the effect of functional groups on thereactivity of OH and NO3 radicals and the ozone molecule. Kerdouciet al. (2010) analyzed the results of the estimation methods pro-posed to date and developed a SAR method to estimate rate co-efficients for the reactions of the nitrate radical with alkanes,alkenes and saturated and unsaturated oxygenated compounds.The major advantage of this method is that the group rate co-efficients (ki) and the group reactivity factors are calculatedempirically from the kinetic database for the reaction of the NO3radical with different types of organic compounds, such as satu-rated and unsaturated oxygenated species. Recently, an update andextension to aldehydes of this SAR has beenmade by Kerdouci et al.(2014). In this new version, the SAR method predicts rate co-efficients within a factor of two of the measured values for 90% ofthe compounds considered.

In this sense, and taking into account new experimental ratecoefficient data for reactions of a,b-unsaturated esters with NO3(Wang et al., 2010; Salgado et al., 2011), OH (Teruel et al., 2006;Blanco and Teruel, 2008; Teruel et al., 2012; Colomer et al., 2013)and Cl (Teruel et al., 2009; Martín et al., 2010; Teruel et al., 2012) inthe work reported here these data have been included in the cor-relations proposed by Pfrang et al. (2007). As a result, new correla-tions are proposed for use in conjunction with SAR methods toestimate the rate coefficients for a,b-unsaturated esters (methylacrylate, methyl methacrylate, ethyl acrylate, ethyl methacrylate,butyl acrylate, butyl methacrylate, methyl crotonate, ethyl crotonate,methyl-3-methyl-2-butenoate, methyl-E-2-methyl-2-butenoate,(E)-ethyltiglate, hexyl acrylate and 2-ethylhexyl acrylate) in the re-action with OH, NO3, O3 and Cl.

In this study the following areas have been addressed:

- Correlations between log kx and log ky (x or y¼ OH, NO3, O3 andCl) were used in order to estimate rate coefficients or proposenew correlations.

- The HOMO energies (EHOMO) for a series of a,b-unsaturated es-ters were calculated and their rate coefficients were estimatedusing the correlation ln(k) versus eEHOMO.

- New group-reactivity factors, f(Ri), were calculated.- The rate coefficients for a,b-unsaturated esters in reactions withOH and NO3 radicals and Cl atomswere calculated using the SARmethods developed by Kwok and Atkinson (1995), Kerdouciet al. (2010) and Teruel et al. (2009), respectively.

2. Methodology

2.1. Correlations

- Correlation between the rate coefficients.

Kinetic data are available for the gas-phase reactions of the NO3radical and OH radical with a wide variety of organic compounds.These data allow possible rate coefficient trends to be examined.

The general form of these correlations is a linear relationship be-tween the logarithms of the rate coefficients for the reactions of NO3and those for the reactionsofOHwithaparticular seriesof substrates:

log�kNO3

� ¼ cþ d logðkOHÞ (I)

Several correlations between log kNO3

� �and log(kOH) have been

reported. For alkenes, a linear free energy relationship correlationof rate coefficients for reactions with NO3 and OH radicals is ob-tained (Wayne et al., 1991).

log kNO3

� � ¼ 21� 2ð Þ þ 3:3� 0:2ð Þlog kOHð Þ (II)

In order to confirm that the reactions of NO3 and OH radicalswith a,b-unsaturated esters follow a similar mechanism to that ofalkenes, in this study we used experimental rate coefficients andplotted the pairs log kNO3

� �� log kOHð Þ. Furthermore, equation (II)was used to estimate the rate coefficients for the reactions of a,b-unsaturated esters with NO3, once the OH rate coefficients wereknown, in order to compare the results with the experimental ratecoefficients or vice versa.

Similarly, a correlation is proposed for the reactions with Clatoms and OH radicals and with OH radicals and O3 molecules forthese compounds by plotting log (kOH) versus log (kCl) and log (kOH)versus log kO3

� �.

- Correlation between the rate coefficients and energy of the HighestOccupied Molecular Orbital, HOMO.

In the reactions between atmospheric oxidants and unsaturatedorganic compounds the dependency of rate coefficients with theenergy HOMO has been well established (King, 1998; King et al.,1999; Marston et al., 1999). The results of several studies(Martínez et al., 1996a,b, 1997; Marston et al., 1999; Pfrang et al.,2006a) have shown that the rate coefficients, k, for the reactionsof the main atmospheric oxidants can be predicted from thecalculated energies of the highest occupied molecular orbital(HOMO) of the unsaturated compound. This prediction was ach-ieved using a correlation such as the following:

ln�k.cm3 moleculee1 se1

�¼ mEHOMOðeVÞ þ c (III)

where m and c are constants.In the work described here, the correlations between ln k and

EHOMO for reactions of alkenes with NO3 and OH radicals and withthe O3 molecule proposed by Pfrang et al. (2006a):

ln�kNO3

.cm3 moleculee1 se1

�¼ 6:40 EHOMO=eVþ 31:69

(IV)

MaP. Gallego-Iniesta et al. / Atmospheric Environment 90 (2014) 133e145 135

ln�kOH

.cm3 moleculee1 se1

�¼ 1:21 EHOMO=eVe12:34 (V)

ln�kO3

.cm3 moleculee1 se1

�¼ 3:28 EHOMO=eVe6:8 (VI)

were used to estimate the rate coefficients for the reactions of a setof a,b-unsaturated esters with NO3, OH and O3, respectively.

In the case of the reaction with Cl atoms the correlation pro-posed by Blanco et al. (2009a) was used:

ln�kCl

.cm3 moleculee1 se1

�¼ 0:1 ðEHOMOÞ=eVe21:2 (VII)

In this study the HOMO energies were calculated in the mannerdescribed by Pfrang et al. (2006a,b, 2007, 2008) using theGaussian09 package (Frisch et al., 2003). The geometry optimisa-tions and initial values of the energies were obtained at the Har-treeeFock (HF) level and using an ab initio Hamiltonian with a 6e31G(d,p) basis set. The energies were then calculated by MøllerePlesset perturbation theory (MP2-SCF) using an ab initio Hamilto-nian with a 6e311 þ G(d,p) basis set.

- SAR formulation

SAR formulation (Kwok and Atkinson, 1995) assumes that thereactivity of an oxidant can be estimated by an additive group-contribution approach and that the overall reaction rate coeffi-cient for the oxidant is the sum of all possible individual reactionrates. Thus, the overall rate coefficient is given by equation (VIII):

kSAR ¼X

kðaddition C]CÞþX

kðH abstraction from CeH and OeHÞ (VIII)

There are different groups of rate coefficients, ki, for bothpathways (addition and H-abstraction), kprim, ksec, ktert, kOH,kC]C(3H), kC]C(2H) and kC]C (Kwok and Atkinson, 1995). Thedifferent groups present in the organic compound in the a- or b-positions have an effect on the rate coefficients. This effect can betaken into account using the substituent factors, F(X), for theabstraction and G(X) for the addition process.

kSAR ¼X

kðaddition C]CÞY

GðxÞþX

ðH abstraction from CeH and OeHÞY

FðxÞ(IX)

Only in the case of the reactions with OH and NO3 radicals theserate coefficients, ki, and substituent factors, F(X) and G(X) (calcu-lated empirically) are available in the literature (Kwok andAtkinson, 1995; Kerdouci et al., 2010, 2014).

There is another SAR method (Pfrang et al., 2006a) in which theabstraction pathways are not taken into account and, as a result, itcan only be applied to the reactions of unsaturated compounds.

kSAR ¼ kbasicY4

i¼1

f ðRiÞ (X)

where kbasic is the rate coefficient for a basic structure (i.e., a doublebond) and f(Ri) are the group-reactivity factors that reflect the typeof substituent attached to the double bond.

Pfrang et al. (2006a,b, 2007, 2008) developed a method tocalculate the group-reactivity factors f(Ri) and to estimate the ratecoefficients of reactions between unsaturated compounds and OH,NO3, O3 and O(3P). In this case the rate coefficients predicted fromthe alkene correlations (equations IV, V and VI) were used to derive

the group-reactivity factors. The correlation-derived rate co-efficients, kCorr, for the reaction with the target molecule wereplotted as a function of the estimated rate coefficients obtained forthe basic structure, kbasic, where the functional groups are replacedby corresponding hydrogen atoms or carbon chains. The group-reactivity factor, f(Ri), corresponds to the gradient of these plots.

kCorr ¼ f ðRiÞ � kbasic (XI)

For further details see the publications by Pfrang et al. (2007,2008).

According to this approach, the rate coefficients for the reactionsof a series of a,b-unsaturated esters with OH, NO3 and O3 wereestimated in our study using equation (X) and the group-reactivityfactors calculated by Pfrang et al. (2007). However, it should benoted that only the group-reactivity factors eC(O)OCH3 and eC(O)OCH2CH3 are available in the literature. Thus, the group-reactivityfactors for eC(O)OCH2CH2CH2CH3, eC(O)OCH2CH2CH2CH2CH2CH3andeC(O)OCH2CH(CH2CH3)CH2CH2CH2CH3 were calculated for OHand NO3 radicals and O3 molecules using the procedure describedby Pfrang et al. (2007, 2008). For Cl atoms all factors were calculatedfor the first time in this study.

Finally, Teruel et al. (2009) used equation (X) to estimate the ratecoefficients for a series of oxygenated compounds in their reactionswith Cl atoms, but in this case the group-reactivity factors werecalculated empirically from the existing kinetic database, C(xi).

kSAR ¼ kbasicY4

i¼1

CðxiÞ (XII)

The C(xi) data tabulated for the groups eC(O)OCH3, eC(O)OCH2CH3 and eC(O)OCH2CH2CH2CH2CH3 are 0.74, 0.84 and 0.87,respectively (Teruel et al., 2009; Blanco et al., 2010).

The following terminology is used for the rate coefficientscalculated by the different methods: kPCP1 (rate coefficient calcu-lated using the correlation log kx versus log ky where x is the OH,NO3 radical, Cl atoms or O3 and y is Cl, OH); kPCP2 (rate coefficientcalculated using the correlation ln kx versus EHOMO where x is theatmospheric oxidant); kSAR1 (rate coefficient calculated using theSARs method of Kwok and Atkinson for OH reactions and Kerdoucifor NO3 reaction); kSAR2 (rate coefficient calculated using equation(X) for OH and NO3 radicals, O3 and Cl atoms where f(Ri) weredetermined using equation (XI) or from the study of Pfrang et al.(2007)); kSAR3 (rate coefficient for Cl atoms calculated using equa-tion (XII) and C(xi) from the study of Teruel et al. (2009)).

In order to provide a clear overview of the methodology used inour study, the process that was carried out is represented in Fig. 1.

3. Results and discussion

3.1. Correlations

- Correlation between the rate coefficients

The pairs of logarithms for the experimental rate coefficientsfor the reactions of NO3 are shown in Fig. 2 along with the loga-rithms of the experimental rate coefficients for the reaction of OHfor methyl acrylate, methyl methacrylate, ethyl acrylate, ethylmethacrylate, butyl acrylate, butyl methacrylate, methyl crotonate,together with equation (II) (line a). It can be seen that the pairslog kNO3

� �� log kOHð Þ do not correlate with equation (II) and theestimated rate coefficients kNO3

are very different from thoseexperimentally obtained (see Table 1). As a result, a new correla-tion (r2 ¼ 0.95, Eq. XIII) is proposed for these a,b-unsaturatedesters:

Fig. 1. Scheme used to estimate rate coefficients.

MaP. Gallego-Iniesta et al. / Atmospheric Environment 90 (2014) 133e145136

log kNO3

� � ¼ 13:9� 2:8ð Þ þ 2:75� 0:26ð Þ � log kOHð Þ (XIII)

In this correlation the pair data log kNO3

� �� log kOHð Þ for methyl-3-methyl-2-butenoate is not included because do not correlate.Equation (XIII) could also be used to estimate the rate coefficientskNO3

for ethyl crotonate, (E)-ethyltiglate and the rate coefficient kOHfor methyl-E-2-methyl-2-butenoate for which experimental dataare not available. All of the rate coefficients (experimental andestimated) are summarized in Table 1.

A plot of log (kOH)elog(kCl) is shown in Fig. 3 for a series of al-kenes, terpenes, unsaturated aldehydes, furans and furanaldehydes(Data are shown in Table A1 supplementary information). It can beseen that the data show an acceptable correlation (r2 ¼ 0.89) andthe following equation is proposed:

log kOHð Þ ¼ 4:93� 1:14ð Þ þ 1:6� 0:1ð Þ � log kClð Þ (XIV)

A similar correlation was proposed by Blanco et al. (2009a).The pairs of data log (kOH)elog(kCl) are also plotted in Fig. 3 for

methyl acrylate, methyl methacrylate, ethyl acrylate, ethyl

Fig. 2. Plot of log kNO3

� �as a function of log (kOH ) with the same substrates. - Data

pairs for a,b-unsaturated esters compounds: [1] Methyl acrylate, [2] Methyl methac-rylate, [3] Ethyl acrylate; [4] Ethyl methacrylate, [5] Butyl acrylate, [6] Butyl methac-rylate, [7] Methyl crotonate. Reference data for kNO3

, Canosa-Mas et al., 1999; Salgadoet al., 2011; Wang et al., 2010; Canosa-Mas et al., 2005. Reference data for kOH Teruelet al., 2006; Blanco et al., 2006; Blanco and Teruel, 2008; Teruel et al., 2012. e (a) Plotof equation (II) for alkenes, Wayne et al., 1991.

methacrylate, butyl acrylate, butyl methacrylate, methyl crotonate,ethyl crotonate, methyl 3-methyl-2-butenoate and (E)-ethyltiglate.The data for all of these compounds present a relative good cor-relation with equation (XIV) (except butyl acrylate and (E)-ethyl-tiglate) indicating that the reactions of a,b-unsaturated esters withCl atoms and OH radicals proceed by a reaction mechanism similarto alkenes.

It can be seen from the data in Table 1 that the rate coefficientsestimated for the reactions of NO3 using equation (II) do notreproduce the experimental rate coefficients, with kexp/kest ratiosin the range 0.024e0.083, i.e., far from unity, the number thatrepresents the best agreement. This discrepancy could indicatethat the reaction of NO3 with a,b-unsaturated esters does notproceed by the same reaction mechanism as the reaction of NO3with alkenes. Moreover, the acceptable correlation obtainedfor log kNO3

� �� log kOHð Þ, on considering only a,b-unsaturated es-ters (equation XIII), indicates that the reactions of these com-pounds with NO3 and OH follow the same reaction mechanism.Once again, when equation (XIII) is used to estimate the rate co-efficient for the reactions of NO3, the values obtained are betterthan those obtained with equation (II) with ratios of kexp/kest z 1for methyl acrylate, methyl methacrylate, ethyl acrylate, ethylmethacrylate, butyl acrylate, butyl methacrylate, kexp/kest ¼ 0.6 formethyl crotonate and kexp/kest ¼ 5 for methyl 3-methyl-2-butenoate. This last discrepancy between experimental and esti-mated rate coefficient could be due that the experimental ratecoefficient is not well established.

For OH radicals, the rate coefficients estimated with equationXIII show good agreement with the respective experimental data,with ratios of kexp/kest z 1 except for methyl 3-methyl-2-butenoate. The equation XIV predicts rate coefficients with valuesof kexp/kest in the range of 0.4 (for butyl acrylate) and 2 (for (E)-ethyltiglate).

Recently Gaona-Colman et al. (2013) have been proposed forfirst time a correlation between kOH and kO3

(equation XV) for al-kenes and unsaturated volatile organic compounds:

log kOHð Þ ¼ � 3:7� 1:3ð Þ þ 0:39� 0:08ð Þ � log kO3

� �(XV)

This equation has been used to estimate the rate coefficients forthe ozone reaction. The data have been showed in Table 1. It can beseen that the estimated rate coefficients using the equation XV arein disagreement with respect the experimental data except to

Table 1Summary of estimated (using PCP1) and experimental rate coefficients for the reactions of a,b-unsaturated esters with NO3 and OH radicals, O3 molecules and Cl atoms, k inunits of cm3 molecule�1 s�1.

a,b-unsaturated ester akOH/10�11 akNO3=10�15 akO3

=10�18 akCl/10�10 OH tkNO3=10�15 uNO3

vO3

kOH/10�11 kexp/kest kNO3=10�15 kexp/kest kO3

=10�18 kexp/kest

CH2]CHeC(O)OCH3

methyl acrylate1.30f 0.10b 1.05k 1.71i 1.27r

2.00s1.020.65

1.19 0.09 1.11 0.37 2.83

CH2]C(CH3)C(O)OCH3

methyl methacrylate4.15g 3.60c 7.5l 2.30i 4.70r

3.22s0.881.28

54.9 2.24 1.60 7.35 1.02

CH2]CHC(O)OCH2CH3

ethyl acrylate1.70f 0.18d 5.71m 1.82i 1.57r

2.21s1.080.77

2.88 0.19 0.95 0.74 7.71

CH2]C(CH3)C(O)OCH2CH3

ethyl methacrylate4.58g 5.40c 7.68n 2.71i 5.43r

4.19s0.841.09

76 2.93 1.84 9.47 0.81

CH2]CHeC(O)O(CH2)3CH3

butyl acrylate1.80h 0.21d 2.40n 2.94i 1.66r

4.77s1.080.37

3.48 0.22 0.95 0.86 2.79

CH2]C(CH3)C(O)O(CH2)3CH3

butyl methacrylate7.08g 7.90c 10o 3.83i 6.24r

7.29s1.130.97

319 9.72 0.81 28.9 0.34

CH3CH]CHC(O)OCH3

Methyl crotonate4.65p 1.85e 4.38o 2.21i

2.20p3.68r

3.03s1.261.53

79.9 3.06 0.60 9.85 0.44

CH3CH]CHC(O)OCH2CH3

ethyl crotonate4.96p e 8.0o 2.52p 3.73s 1.33 98 3.65 e 11.6 0.68

(CH3)2C]CHC(O)OCH3

Methyl-3-methyl-2-butenoate4.46q 14.1e e 3.58i

2.78q7.70r

6.54s0.580.68

69.6 2.73 5.16 8.85 e

(CH3)CH]C(CH3)C(O)OCH3

Methyl-E�2-methyl-2-butenoatee 49.1e e e 12.7r e e e e e e

(CH3)CH]C(CH3)C(O)OCH2CH3

(E)-ethyltiglate8.32q e e 2.53q 3.75s 2.21 545 15.1 e 4.37 e

CH2]CHC(O)O(CH2)5(CH3)hexyl acrylate

e e e 3.32j 5.80s e e e e e e

CH2]CHC(O)OCH(CH2CH3)(CH2)3CH3

2-ethylhexyl acrylatee e e 3.50j 6.30s e e e e e e

a Experimental Rate coefficients.b Canosa-Mas et al., 1999.c Salgado et al., 2011.d Wang et al., 2010.e Canosa-Mas et al., 2005.f Teruel et al., 2006.g Blanco et al., 2006.h Blanco and Teruel, 2008.i Martín et al., 2010.j Gallego-Iniesta PhD Thesis, 2012.k Grosjean and Grosjean, 1998.l Grosjean et al., 1993.

m Munshi et al., 1989.n Yanbo et al., 2009.o Gaona-Colman et al., 2013.p Teruel et al., 2012.q Colomer et al., 2013.r Data estimated using equation (XIII) and the experimental kNO3

.s Data estimated using equation (XIV) and the experimental kCl.t Data estimated using equation (II) and the experimental kOH.u Data estimated using equation (XIII) and the experimental kOH.v Data estimated using equation (XV) and the experimental kOH.

MaP. Gallego-Iniesta et al. / Atmospheric Environment 90 (2014) 133e145 137

methyl methacrylate and ethyl methacrylate. The ratios, kexp/kest,calculated are: 0.37, 0.98, 0.13, 1.23, 0.36, 2.89, 2.25, and 0.45 formethyl acrylate, methyl methacrylate, ethyl acrylate, ethyl meth-acrylate, butyl acrylate, butyl methacrylate, methyl crotonate andethyl crotonate respectively.

It can therefore be concluded that in general the equations XIIIand XIV can be used to estimate the rate coefficients for the re-actions of a,b-unsaturated esters presented in this work with OHand NO3 radicals (equation XIII) and Cl atoms (equation XIV) whenone of them is known. In this sense, the NO3 rate coefficient forethyl crotonate and (E)-ethyltiglate, and OH rate coefficients formethyl-E-2-methyl-2-butenoate, hexyl acrylate and 2-ethylhexylacrylate which are not experimentally available, were estimatedand the values are given in Table 1.

- Correlation between the rate coefficients and energy of the HighestOccupied Molecular Orbital, HOMO. ln kxeEHOMO

The natural logarithms of the experimental rate coefficients forreactions of Cl atoms, OH and NO3 radicals and O3 with the series ofa,b-unsaturated esters studied here as a function of the calculatedHOMO energies (data summarized in Table 2) are shown in Fig. 4along with the plots of equations IV, V, VI and VII (correlation forsimple alkenes), i.e., lines c, b, d and a, respectively. The same plotwas published by Pfrang et al. (2007) for OH, NO3 and O3 and byBlanco et al. (2009a) for Cl atoms. In the work presents here newexperimental rate coefficients have been included for NO3 (Wanget al., 2010; Salgado et al., 2011), OH (Teruel et al., 2006; Blancoand Teruel, 2008; Teruel et al., 2012; Colomer et al., 2013), O3(Yanbo et al., 2009; Gaona-Colman et al., 2013) and Cl atoms(Martín et al., 2010; Teruel et al., 2012). It can be seen that in thecase of the reaction with NO3 radicals the data for a,b-unsaturatedesters (triangles) show good linearity and a good correlation withline c, while for OH reactions some data deviate from line b (cor-relation for simple alkenes). This deviation is more significant for

Fig. 3. Plot of log (kOH) as a function of log (kCl) with the same substrates Data pairsfor alkenes and terpenes, unsaturated aldehydes, furans and furanaldehydes (DataTable A1); Data pairs of a,b-unsaturated esters compounds. [1] Methyl acrylate, [2]Methyl methacrylate, [3] Ethyl acrylate; [4] Ethyl methacrylate, [5] Butyl acrylate, [6]Butyl methacrylate, [7] Methyl crotonate, [8] Ethyl crotonate, [9] Methyl-3-methyl-2-butenoate, [10] E-ethyltiglate. Reference data for kOH; Teruel et al., 2006; Blancoet al., 2006; Blanco and Teruel, 2008; Reference data for kCl; Martín et al., 2010;Gallego-Iniesta PhD Thesis 2012. Colomer et al., 2013. Teruel et al., 2012.

MaP. Gallego-Iniesta et al. / Atmospheric Environment 90 (2014) 133e145138

the reactions of ozone and chlorine, for which significant scatter isobserved if the scale is amplified. The same behaviour for OH, NO3and O3 was observed by Pfrang et al. (2007, 2008) in the study ofa,b-unsaturated esters and ketones but using a lower number ofcompounds. In this work Pfrang et al. (2007) justified thedisagreement for O3 base on the orbital asymmetry in the HOMOenergy of an alkene that may have an effect on the reactivity of thealkene towards ozone (Johnson et al., 2000). The equations IV, V, VIand VII predict rate coefficients for a,b-unsaturated esters withratios of kexp/kest in the range 1.5e4 for the case of OH and NO3reactions, 1e6 for Ozone reactions and 0.8e2 for Cl reactions.

Table 2EHOMO data calculated at the MP2/6e311 þ G(d,p)//HF/6e31G(d,p) level of theory using

a,b-unsaturated ester eEHOMO (eV) k(OH)/10�11 kexp/kest k(NO3)/

Exp Estq Exp

Methyl acrylate 10.865 1.3 � 0.2g 1.6 0.79 0.10 � 0Methyl methacrylate 10.337 4.15 � 0.32f 4.06 1.02 3.6 � 0Ethyl acrylate 10.766 1.7 � 0.4g 1.9 0.9 0.18 � 0Ethyl methacrylate 10.303 4.58 � 0.59f 4.30 1.06 5.4 � 1Butyl acrylate 10.802 1.80 � 0.26h 1.83 0.98 0.21 � 0Butyl methacrylate 10.160 7.08 � 0.75f 5.50 1.28 7.9 � 3Methyl crotonate 10.310 4.65 � 0.65o 4.25 1.09 1.85 � 0Ethyl crotonate 10.283 4.96 � 0.61o 4.45 1.11 e

Methyl-3-methyl-2-butenoate 9.993 4.46 � 1.05n 7.31 0.60 14.1 � 2Methyl-E�2-methyl-2-butenoate 9.877 e 8.92 e 49.1 � 1(E)-Ethyltiglate 9.847 8.32 � 1.95n 9.39 0.88 e

Hexyl acrylate 10.745 e 2.02 e e

2-Ethylhexyl acrylate 10.745 e 2.02 e e

a Munshi et al., 1989.b Grosjean et al., 1993.c Grosjean and Grosjean, 1998.d Canosa-Mas et al., 1999.e Canosa-Mas et al., 2005.f Blanco et al., 2006.g Teruel et al., 2006.h Blanco and Teruel, 2008.i Yanbo et al., 2009.j Wang et al., 2010.k Martín et al., 2010.l Salgado et al., 2011.

m Gallego-Iniesta PhD Thesis 2012.n Colomer et al., 2013.o Teruel et al., 2012.p Gaona-Colman et al., 2013.q Using equation XVI.r Using equation XVII.s Using equation XVIII.t Using equation XIX.

On the other hand, using only the data of a,b-unsaturated esters,new correlations can be proposed (instead of Equations for alkenes,IV, V, VI and VII) to predict the rate coefficients with a knowledge ofEHOMO.

ln�kOH

.cm3 moleculee1 se1

�¼ð1:71� 0:21Þ � EHOMO=eV

eð6:25� 2:24Þ; �r2 ¼ 0:88�

ðXVIÞ

ln�kNO3

.cm3 moleculee1 se1

�¼ð5:94� 0:35Þ � EHOMO=eV

þ ð27:87� 3:65Þ; �r2 ¼ 0:95�

ðXVIIÞ

ln�kO3

.cm3 moleculee1 se1

�¼ð2:20� 0:63Þ � ðEHOMOÞ=eVeð16:7� 6:6Þ; �r2 ¼ 0:66

�

ðXVIIIÞ

ln�kCl

.cm3 moleculee1 se1

�¼ð0:21� 0:23Þ � ðEHOMOÞ=eVeð19:8� 2:4Þ; �r2 ¼ 0:07

�

ðXIXÞThe rate coefficients predicted with these equations are also

shown in Table 2. It can be seen that the rate coefficients for re-actions of acrylates with OH and nitrate radicals and chlorine atomsare similar to their experimental values, with kexp/kest z 1 except

Gaussian09 and estimated rate coefficients (k in units of cm3 molecule�1 s�1).

10�15 kexp/kest k(O3)/10�18 kexp/kest k(Cl)/10�10 kexp/kest

Estr Exp Ests kExp Estt

.06d 0.12 0.84 1.05 � 0.15c 2.21 0.47 1.71 � 0.13 2.37 0.72

.6l 2.7 1.3 7.5 � 0.9b 7.1 1.1 2.30 � 0.18 2.65 0.86

.02j 0.21 0.84 5.71a 2.74 2.08 1.82 � 0.13 2.42 0.75

.9l 3.3 1.6 7.68 � 0.88i 7.61 1.01 2.71 � 0.21 2.67 1.01

.03j 0.17 1.21 2.40 � 0.29i 2.53 0.94 2.94 � 0.23 2.40 1.22

.9l 7.8 1.0 10 � 3.0p 10.4 0.95 3.83 � 0.30 2.75 1.39

.56e 3.21 0.57 4.38b 7.49 0.58 2.21 � 0.16 2.66 0.833.77 e 8.0 � 1.8p 7.95 1.01 2.52 � 0.62o 2.68 0.94

.30e 21.10 0.67 - 15.0 e 3.58 � 0.30 2.85 1.261.5e 42.0 1.17 - 19.4 e e 2.92 e

50.2 e - 20.7 e 2.53 � 0.35n 2.93 0.860.24 e - 2.89 e 3.32 � 0.30m 2.43 1.360.24 e - 2.87 e 3.50 � 0.29m 2.43 1.44

Fig. 4. Logarithm of the rate coefficients for the reaction of OH ( ), NO3 ( ), O3 ( ) andCl ( ) as function of HOMO energy of a,b-unsaturated esters: [1] Methyl acrylate, [2]Methyl methacrylate, [3] Ethyl acrylate; [4] Ethyl methacrylate, [5] Butyl acrylate, [6]Butyl methacrylate, [7] Methyl crotonate, [8] Ethyl crotonate, [9] Methyl-3-methyl-2-butenoate, [10] E-ethyltiglate. e (a) Plot of equation (VII), for Cl atom reaction(Blanco et al., 2009a, 2010). (b) - Plot of equation (V) for OH radical reaction; (c) - Plotof equation (IV) for NO3 radical reaction; (d) - Plot of equation (VI) for O3 reaction.Pfrang et al., 2006a. Reference data for kOH; Teruel et al., 2006; Blanco et al., 2006a;Blanco and Teruel, 2008; Teruel et al., 2012, Colomer et al., 2013. Reference data forkNO3

; Canosa-Mas et al., 1999; Canosa-Mas et al., 2005; Wang et al., 2010; Salgadoet al., 2011; Reference data for kCl; Martín et al., 2010; Gallego-Iniesta PhD Thesis 2012.Reference data for kO3

; Yanbo et al., 2009, Gaona-Colman et al., 2013.

MaP. Gallego-Iniesta et al. / Atmospheric Environment 90 (2014) 133e145 139

for reactions of methyl-3-methyl-2-butenoate, with OH and NO3and methyl crotonate with NO3 and O3 for which the estimatedvalues are twice those obtained experimentally. So it can beconcluded that in general the equations XVI, XVII, XVIII and XIXpredict better rate coefficients for the reaction of a,b-unsaturatedesters with atmospheric oxidants than equations IV, V, VI and VII.

3.2. SAR methods

- SARs to predict rate coefficients for the reactions with OH and NO3.kSAR1

In the case of the OH reaction the rate coefficients were esti-mated using the AOPWIN 4.0 program (Environmental ProtectionAgency, 2000 U.S. V. 1,92). This program based on SAR methods(Equation VIII) and development by Kwok and Atkinson (1995),allows the molecular structure of a,b-unsaturated esters to bedrawn and the overall rate coefficient is automatically calculated.The overall rate coefficient (kov) is the sum of two contributions,one for the addition processes (kadd) and the other for theabstraction of hydrogen (kab). An example of the calculations car-ried out with this program is described in Annex 1 (supplementaryinformation).

For the reaction with NO3, the rate coefficients were estimatedusing the method developed by Kerdouci et al. (2010, 2014). In thiscase, the rate coefficients were calculated using equation (IX),where kprim, ksec, ktert, kOH, kC]C(3H), kC]C(2H), kC]C(1H), kC]C andgroup reactivity factors G(x) and F(x) are tabulated in Tables A2eA5(See supplementary information) together with all calculations(Annex 2, in supplementary information) in the supplementaryinformation. As a representative example the calculation formethyl acrylate is given here:

O

OCH3CH2

koverall ¼ kC]Cð3HÞ � Gð � CðOÞORÞ ¼ 6:70� 10�15 � 0:014

¼ 9:38� 10�17 cm3 molecule�1 s�1

All rate coefficients (kSAR1) obtained for OH and NO3 are sum-marized in Table 3.

It can be seen that in the case of OH all of the rate co-efficients (kSAR1) obtained are lower than those obtainedexperimentally. When the abstraction rate coefficients (kab) andaddition rate coefficients (kadd) were analyzed it was found thatkab increases with the chain length of R, although this increaseis not sufficient to explain the discrepancy in the experimentalvalues. In the case of the addition process, the rate coefficientsare the same in all cases for alkyl acrylates, because in this SARmethod the group reactivity factor is not dependent on thechain R (f(eC(O)eOR) ¼ 0.35). Therefore, and in contrast to theoutput from the AOPWIN program, the contribution of thegroup reactivity factors of eC(O)OCH3, eC(O)OCH2CH3, eC(O)OCH2CH2CH2CH3, eC(O)OCH2CH2CH2CH2CH2CH3 and eC(O)OCH2CH(CH2CH3)CH2CH2CH2CH3 must be different in order toobtain good agreement between the rate coefficients estimatedby this SAR method and the experimental data. The kSAR1 valuesthat show the highest deviation are those corresponding tomethyl, ethyl, butyl methacrylate esters and (E)-ethyltiglate.This fact could be due to the presence of the methyl group in thea-position which has a greater influence on the reactivity thanthat predicted in the estimation method (a value of unity). Inthe case of methacrylate esters it was found experimentally thatthe eCH3 group in the a-position promotes addition to thedouble bond due to its positive inductive effect (þI) (Blanco etal., 2006; Martín et al., 2010; Salgado et al., 2011).

In the case of the NO3 reaction, the agreement between calcu-lated and experimental values is reasonably good, with the ratiokexp/kest x 1 for methyl acrylate, methyl methacrylate, ethyl acry-late, ethyl methacrylate, butyl acrylate, butyl methacrylate, and0.48, 0.2 and 0.66 for methyl crotonate, methyl-3-methyl-2-butenoate and methyl-E-2-methyl-2-butenoate, respectively. Inlast cases the disagreement could be due to the same reason as forthe OH reaction described above (not include the effect of CH3e in aposition). The rate coefficients for ethyl crotonate, (E)-ethyltiglate,hexyl acrylate and 2-ethylhexyl acrylate, for which experimentalrate coefficients are not available, were also estimated.

- SARs to predict rate coefficients in the reaction with OH, NO3, Clatoms and O3. kSAR2

According to equation (X),

kSAR ¼ kbasicY4

i¼1

f ðRiÞ (X)

in order to estimate the rate coefficients by this method (kSAR2) it isnecessary to calculate the rate coefficients of the acrylate basicstructures, kbasic, for each oxidant. The basic structure of an acrylateis the one that results from replacing the eC(O)OR group by a eCH3group, for which the reactivity factor is considered unity. Forexample, for methyl, ethyl and butyl methacrylate esters the basicstructures correspond to isobutene:

O

ORCH2

CH3

CH3CH2

CH3

Table 3Rate coefficient data for OH and NO3 radicals estimated by SAR methods (kSAR1). k in units of cm3 molecule�1 s�1

a,b-unsaturated ester kOH/10�12 kNO3=10�15

kadd kab akov kexp kexp/kest bkest kexp kexp/kest

Methyl acrylate 9.20 0.217 9.4 13.0 � 2.0g 1.4 0.1 0.10 � 0.06c 1.1Methyl methacrylate 17.9 0.35 18.3 41.5 � 3.2h 2.3 3.8 3.6 � 0.6d 0.9Ethyl acrylate 9.20 1.66 10.8 17.0 � 4.0g 1.6 0.16 0.18 � 0.02e 1.12Ethyl methacrylate 17.9 1.79 19.7 45.8 � 5.9h 2.3 4.3 5.4 � 1.9d 1.2Butyl acrylate 9.20 4.56 13.7 18.0 � 2.6i 1.3 0.28 0.21 � 0.03e 0.75Butyl methacrylate 17.9 4.70 22.6 70.8 � 7.5h 3.1 4.9 7.9 � 3.9d 1.6Methyl crotonate 19.7l

22.4m0.36 20l

22.7m46.5 � 0.6j 2.3 3.79 1.85 � 0.56f 0.48

Ethyl crotonate 19.7l

22.441.79 21.5l

24.2m49.6 � 0.6j 2.3 4.28 e e

Methyl-3-methyl-2-butenoate 30.4 0.48 30.9 44.6 � 10.5k 1.4 73.50 14.10 � 2.30f 0.19Methyl-E�2-methyl-2-butenoate 30.4 0.48 30.9 e e 73.5 49.1 � 11.5f 0.66(E)-Ethyltiglate 30.4 1.93 32.3 83.2 � 19.5k 2.6 73.5 e e

Hexyl acrylate 9.20 7.39 16.5 e e 0.36 e e

2-Ethylhexyl acrylate 9.20 10.9 20.1 e e 0.53 e e

a Rate coefficients estimated using the AOPWIN program.b Rate coefficients estimated using equation (IX) by Kerdouci et al., 2010.c Canosa-Mas et al., 1999.d Salgado et al., 2011.e Wang et al., 2010.f Canosa-Mas et al., 2005.g Teruel et al., 2006.h Blanco et al., 2006.i Blanco and Teruel, 2008.j Teruel et al., 2012.k Colomer et al., 2013.l Cis-isomer.

m Trans-isomer.

MaP. Gallego-Iniesta et al. / Atmospheric Environment 90 (2014) 133e145140

According to this criterion, all the basic structures of thea,b-unsaturated esters studied here are shown in Table A6(supplementary information).

Substituting the values of EHOMO calculated for each of the basicstructures into equations IV, V, VI and VII allows the rate co-efficients for NO3 and OH radicals, O3 and Cl atoms, respectively, to

Table 4HOMO energies in units of eV, and the predicted kbasic values for a,b-unsaturated esters

Basic structure R]CH3 eEHOMO kbasic/cm3 molecule�1

kbasic,OH

CH2

R9.855 2.89 � 10�11

CH2

R

CH3

9.508 4.40 � 10�11

R CH3 9.392 5.07 � 10�11

R

CH3

9.394 5.06 � 10�11

RCH3

CH3

9.077 7.42 � 10�11

R CH3

CH3CH3

8.802 1.03 � 10�10

EHOMO calculated at the MP2/6e311 þ G(d,p)//HF/6e31G(d,p) level of theory using Gaus

be predicted. These kbasic values are listed in Table 4 together withthe EHOMO values.

In order to estimate the rate coefficients for a,b-unsatu-rated esters it is also necessary to know the group-reactivityfactors (f(Ri)) of the Ri group present in the structure of theester.

using equation IV, V, VI and VII. SAR2.

s�1

kbaisc;NO3kbaisc;O3

kbasic,Cl

2.34 � 10�14 1.04 � 10�17 2.31 � 10�10

2.16 � 10�13 3.24 � 10�17 2.39 � 10�10

4.54 � 10�13 4.75 � 10�17 2.42 � 10�10

4.49 � 10�13 4.71 � 10�17 2.42 � 10�10

3.41 � 10�12 1.33 � 10�16 2.50 � 10�10

1.98 � 10�11 3.28 � 10�16 2.57 � 10�10

sian09.

MaP. Gallego-Iniesta et al. / Atmospheric Environment 90 (2014) 133e145 141

3.2.1. Calculation of group-reactivity factors; f(Ri)The HOMO orbital energies (EHOMO) of structures resulting from

the substitution of the R group (ester group) in the seven basicstructures were calculated. These EHOMO values can be used inconjunction with equations (IVeVII) to estimate the rate co-efficients (kcorr) for all atmospheric oxidants. These rate coefficientsand EHOMO values are shown in Table 5.

For each oxidant, the rate coefficients (kcorr) are plotted as afunction of kbasic. According to equation (XI), the plot should be alinear plot and the slope corresponds to the group-reactivity factorf(Ri). Examples of the linear relationships for kcorr and kbasic areshown in Fig. 5(a)e(d) for the calculation of f(C(O)OCH2CH2CH2CH3).The calculated group-reactivity factors are presented in Table 6together with those calculated by Pfrang et al. (2007).

These group-reactivity factors can be used to estimate the ratecoefficients for the reactions of butyl acrylate, butyl methacrylate,hexyl acrylate and 2-ethylhexyl acrylate with OH, NO3 and O3 and

Table 5Structures, HOMO Energies (EHOMO) in eV and estimated rate coefficients (kcor) in units ofO3 and Cl.

R] eC(O)OCH3 eC(O)OCH2CH3 eC(O)O(

CH2

R eEHOMO ¼ 10.865 eEHOMO ¼ 10.766 eEHOMO

kCl ¼ 2.09 � 10�10 kCl ¼ 2.11 � 10�10 kOH ¼ 9kNO3

¼ 5kO3

¼ 4.kCl ¼ 2.1

CH2

R

CH3

eEHOMO ¼ 10.337 eEHOMO ¼ 10.303 eEHOMO

kCl ¼ 2.20 � 10�10 kCl ¼ 2.21 � 10�10 kOH ¼ 2kNO3

¼ 3kO3

¼ 3.kCl ¼ 2.2

R CH3eEHOMO ¼ 10.299 eEHOMO ¼ 10.262 eEHOMO

kCl ¼ 2.21 � 10�10 kCl ¼ 2.22 � 10�10 kOH ¼ 1kNO3

¼ 1kO3

¼ 2.kCl ¼ 2.2

R

CH3

eEHOMO ¼ 10.310 eEHOMO ¼ 10.274 eEHOMO

kCl ¼ 2.21 � 10�10 kCl ¼ 2.22 � 10�10 kOH ¼ 1kNO3

¼ 1kO3

¼ 2.kCl ¼ 2.2

RCH3

CH3

eEHOMO ¼ 9.932 eEHOMO ¼ 9.890 eEHOMO

kCl ¼ 2.29 � 10�10 kCl ¼ 2.30 � 10�10 kOH ¼ 3kNO3

¼ 4kO3

¼ 1.kCl ¼ 2.3

RCH3

CH3

eEHOMO ¼ 9.861 eEHOMO ¼ 9.784 eEHOMO

kCl ¼ 2.31 � 10�10 kCl ¼ 2.33 � 10�10 kOH ¼ 3kNO3

¼ 3kO3

¼ 1.kCl ¼ 2.3

H3C CH3

R eEHOMO ¼ 9.877 eEHOMO ¼ 9.847 eEHOMO

kCl ¼ 2.31 � 10�10 kCl ¼ 2.02 � 10�10 kOH ¼ 2kNO3

¼ 2kO3

¼ 1.kCl ¼ 2.3

RCH3

CH3 CH3

eEHOMO ¼ 9.480 eEHOMO ¼ 9.349 eEHOMO

kCl ¼ 2.40 � 10�10 kCl ¼ 2.43 � 10�10 kOH ¼ 4kNO3

¼ 3kO3

¼ 4.kCl ¼ 2.4

EHOMO calculated at the MP2/6e311 þ G(d,p)//HF/6e31G(d,p) level of theory using Gaus

for the reactions methyl acrylate, methyl methacrylate, ethylacrylate, ethyl methacrylate, butyl acrylate, butyl methacrylate,methyl crotonate, ethyl crotonate, methyl 3-methyl-2-butenoate,methyl E-2-methyl-2-butenoate, (E)-ethyltiglate, hexyl acrylate, 2-ethylhexyl acrylate with Cl atoms. All rate coefficients are shown inTable 7.

In general, the rate coefficients obtained with this method ofestimation show a reasonable degree of reproducibility for re-actions of these compounds with OH and NO3 radicals (kexp/kSARsvalues in the range of 0.5e3). These results are acceptable whenone considers that in other previous studies (Pfrang et al., 2006b,2007, 2008) the experimental values differed by around a factorof 3 from the estimated data for oxygenated compounds. The kSAR2values that show the highest deviation are those corresponding tomethyl, ethyl, butyl methacrylate esters. Again, this fact could bedue to the presence of the methyl group in the a-position of theacrylate esters, which has a greater influence on the reactivity than

cm3 molecule�1 s�1 using equations (IV, V, VI and VII) for the reactions with OH, NO3,

CH2)3CH3 eC(O)O(CH2)5CH3 eC(O)OCH2CH(CH2CH3)(CH2)3CH3

¼ 10.802 eEHOMO ¼ 10.743 eEHOMO ¼ 10.745.21 � 10�12 kOH ¼ 9.89 � 10�12 kOH ¼ 9.87 � 10�12

.48 � 10�17 kNO3¼ 7.99 � 10�17 kNO3

¼ 7.89 � 10�17

65 � 10�19 kO3¼ 5.65 � 10�19 kO3

¼ 5.61 � 10�19

0 � 10�10 kCl ¼ 2.12 � 10�10 kCl ¼ 2.12 � 10�10

¼ 10.160 eEHOMO ¼ 10.298 eEHOMO ¼ 10.204.00 � 10�11 kOH ¼ 1.69 � 10�11 kOH ¼ 1.89 � 10�11

.33 � 10�15 kNO3¼ 1.37 � 10�15 kNO3

¼ 2.51 � 10�15

82 � 10�18 kO3¼ 2.43 � 10�18 kO3

¼ 3.31 � 10�18

4 � 10�10 kCl ¼ 2.21 � 10�10 kCl ¼ 2.23 � 10�10

¼ 10.280 eEHOMO ¼ 10.275 eEHOMO ¼ 10.281.73 � 10�11 kOH ¼ 1.74 � 10�11 kOH ¼ 1.73 � 10�11

.54 � 10�15 kNO3¼ 1.59 � 10�15 kNO3

¼ 1.53 � 10�15

58 � 10�18 kO3¼ 2.62 � 10�18 kO3

¼ 2.57 � 10�18

2 � 10�10 kCl ¼ 2.22 � 10�10 kCl ¼ 2.22 � 10�10

¼ 10.269 eEHOMO ¼ 10.329 eEHOMO ¼ 10.187.75 � 10�11 kOH ¼ 1.63 � 10�11 kOH ¼ 1.93 � 10�11

.66 � 10�14 kNO3¼ 1.13 � 10�15 kNO3

¼ 2.80 � 10�15

67 � 10�18 kO3¼ 2.19 � 10�18 kO3

¼ 3.50 � 10�18

2 � 10�10 kCl ¼ 2.20 � 10�10 kCl ¼ 2.24 � 10�10

¼ 9.766 eEHOMO ¼ 9.843 eEHOMO ¼ 9.756.22 � 10�11 kOH ¼ 2.93 � 10�11 kOH ¼ 3.26 � 10�11

.15 � 10�14 kNO3¼ 2.53 � 10�14 kNO3

¼ 4.42 � 10�14

39 � 10�17 kO3¼ 1.08 � 10�17 kO3

¼ 1.43 � 10�17

3 � 10�10 kCl ¼ 2.31 � 10�10 kCl ¼ 2.34 � 10�10

¼ 9.779 eEHOMO ¼ 9.776 eEHOMO ¼ 9.768.17 � 10�11 kOH ¼ 3.18 � 10�11 kOH ¼ 3.21 � 10�11

.82 � 10�14 kNO3¼ 3.89 � 10�14 kNO3

¼ 4.10 � 10�14

33 � 10�17 kO3¼ 1.34 � 10�17 kO3

¼ 1.38 � 10�17

3 � 10�10 kCl ¼ 2.33 � 10�10 kCl ¼ 2.33 � 10�10

¼ 9.834 eEHOMO ¼ 9.793 eEHOMO ¼ 9.840.97 � 10�11 kOH ¼ 3.12 � 10�11 kOH ¼ 2.94 � 10�11

.19 � 10�14 kNO3¼ 2.85 � 10�14 kNO3

¼ 2.11 � 10�14

09 � 10�17 kO3¼ 1.24 � 10�17 kO3

¼ 1.07 � 10�17

2 � 10�10 kCl ¼ 2.33 � 10�10 kCl ¼ 2.32 � 10�10

¼ 9.438 eEHOMO ¼ 9.447 eEHOMO ¼ 9.442.79 � 10�11 kOH ¼ 4.74 � 10�11 kOH ¼ 4.77 � 10�11

.38 � 10�13 kNO3¼ 3.19 � 10�13 kNO3

¼ 3.30 � 10�13

08 � 10�17 kO3¼ 3.96 � 10�17 kO3

¼ 4.03 � 10�17

1 � 10�10 kCl ¼ 2.41 � 10�10 kCl ¼ 2.41 � 10�10

sian09.

Fig. 5. Plots of kCorr as function of kbasic for the reaction of OH (a), NO3 (b), O3 (c) and Cl (d). The slope corresponds to value of f(C(O)OCH2CH2CH2CH3).

MaP. Gallego-Iniesta et al. / Atmospheric Environment 90 (2014) 133e145142

that predicted in the estimation method (a value of unity).Regarding the rate coefficients estimated for O3, the ratios are be-tween 1 and 3 except for ethyl acrylate.

Best agreement has been found in the case of Cl atoms reactions,with ratios, kexp/kSARs in the range of 0.8e1.7. The rate coefficientsestimated for the reactions of Cl atoms indicate that the functionalgroup is not a determining factor in the reactivity, because theestimated coefficients are all very close to that for the basic struc-ture, inwhich the functional groupeC(O)OR is replaced by amethylgroup (eCH3). It is known that reactions with chlorine atoms arevery fast (with k in the order of 10�10 cm3 molecule�1 s�1 near tocollision limit), indicating that the reactivity depends more on theeffectiveness of collisions between the reagents than on the func-tional groups to which the double bond is attached.

- SARs to predict rate coefficients in the reaction with Cl atoms. kSAR3

The kbasic data tabulated in Table A6 (supplementaryinformation) can be used in conjunction with the group-reactivityfactors C(xi) of 0.74, 0.84 and 0.87 for eC(O)OCH3, eC(O)OCH2CH3and C(O)OCH2CH2CH2CH3, respectively, in equation (XII) (Teruelet al., 2009; Blanco et al., 2010) to estimate the rate coefficientsfor the reactions of a,b-unsaturated esters with Cl atoms (kSAR3).

Table 6Group-reactivity factors R (eC(O)OR), for the different atmospheric oxidants OH, NO3, O

R] fOH(R) fNO

C(O)OCH3 (0.394 � 0.027)a (0.C(O)CH2CH3 (0.397 � 0.021)a (0.C(O)O(CH2)3CH3 0.468 � 0.032 0.0C(O)O(CH2)5CH3 0.458 � 0.032 0.0C(O)OCH2CH(CH2CH3)(CH2)3CH3 0.567 � 0.027 0.0

a Pfrang et al. (2007); Quoted errors correspond to 95% confidence limit.

The results are summarized in Table 8. Almost all kexp/kSAR3 ratiosobtained are between 0.7 and 1.6, except for butyl acrylate with aratio of 2.41. Similar results were obtained by Blanco et al. (2010),where the rate coefficients for methyl methacrylate, ethyl acrylate,ethyl methacrylate, butyl acrylate, butyl methacrylate, methylcrotonate, and methyl 3-methyl-2-butenoate where estimated bySAR3 method. Regarding hexyl acrylate and 2-ethylhexyl acrylate,the lack of rate coefficient data precluded the estimation of thefactors corresponding to the functional groups eC(O)O(CH2)5CH3and eC(O)OCH2CH(CH2CH3)CH2CH2CH2CH3, and therefore the ratecoefficients could not be estimated. In this method of estimation, asin the method described above, the reactivity factors approachunity, thus demonstrating once again that the reactions involvingchlorine atoms are very fast and therefore the functional group e

C(O)OR does not have a determining effect on the reactivity.In order to evaluate which estimation methods is the best, all

the rate coefficients for the a,b-unsaturated esters studied with themain atmospheric oxidants are listed in Tables A7eA10. Thesevalues include both the experimental data available in the literatureand estimated values obtained in this study. The ratios of kexp/kest ofeach compound-oxidant and estimation method have beenplotted; (Figs.1A and 2A, supplementary information). We considerthat this study represents a significant step towards the completion

3 and Cl.

3ðRÞ fO3

ðRÞ fCl(R)

0073 � 0.0015)a (0.081 � 0.011)a 0.919 � 0.0210082 � 0.0025)a (0.084 � 0.013)a 0.925 � 0.024173 � 0.0005 0.125 � 0.005 0.928 � 0.012162 � 0.0006 0.121 � 0.007 0.925 � 0.010167 � 0.0004 0.124 � 0.004 0.929 � 0.010

Table 7Rate coefficient data for OH and NO3 radicals, Cl atoms and O3 estimated by SAR methods (kSAR2); (k in units of cm3 molecule�1 s�1).

a,b-unsaturated ester kOH/10�11 kNO3=10�15 kO3

=10�18 kCl/10�10

kexp kest kexp/kest kexp kest kexp/kest kexp kest kexp/kest jkexp kest kexp/kest

Methyl acrylate 1.3 � 0.2g 1.1a 1.1 0.10 � 0.06c 0.17a 0.58 1.05 � 0.15m 0.84a 1.25 1.71 � 0.13 2.12b 0.80Methyl methacrylate 4.15 � 0.32h 1.73a 2.40 3.6 � 0.6d 1.6a 2.3 7.5 � 0.9l 2.6a 2.86 2.30 � 0.18 2.19b 1.05Ethyl acrylate 1.7 � 0.4g 1.1a 1.5 0.18 � 0.02e 0.19a 0.95 5.71k 0.87a 6.56 1.82 � 0.13 2.13b 0.85Ethyl methacrylate 4.58 � 0.59h 1.75a 2.61 5.4 � 1.9d 1.8a 3.1 7.68 � 0.88n 2.72a 2.82 2.71 � 0.21 2.21b 1.22Butyl acrylate 1.80 � 0.26i 1.35b 1.33 0.21 � 0.03e 0.40b 0.52 2.40 � 0.29n 1.30b 1.84 2.94 � 0.23 2.14b 1.37Butyl methacrylate 7.08 � 0.75h 2.06b 3.43 7.9 � 3.9d 3.7b 2.1 10 � 3.0r 4.0b 2.4 3.83 � 0.30 2.21b 1.73Methyl crotonate 4.65 � 0.65q 1.99a 2.33 1.85 � 0.56f 3.28a 0.56 4.38l 3.82a 1.14 2.21 � 0.16 2.22b 0.98Ethyl crotonate 4.96 � 0.61q 2.01a 2.46 e 3.68a e 8.0 � 1.8r 3.9a 2.0 2.52 � 0.62q 2.24 1.12Methyl-3-methyl-2-butenoate 4.46 � 1.05o 2.92a 1.52 14.10 � 2.30f 24.90a 0.56 e 10.5a e 3.58 � 0.30 2.29b 1.56Methyl-E-2 methyl-2-butenoate e 2.92a e 49.1 � 11.5f 24.9a 2.0 e 10.5a e e 2.29b e

(E)-Ethyltiglate 8.32 � 1.95o 2.95a 2.82 e 28.0a e e 10.9a e 2.53 � 0.35o 2.31b 1.09Hexyl acrylate e 1.33b e e 0.38b e e 1.26b e 3.32 � 0.30p 2.13b 1.552-Ethylhexyl acrylate e 1.64b e e 0.39b e e 1.29b e 3.50 � 0.29p 2.14b 1.63

a Rate coefficients estimated using equation (X) and group-reactivity factors from the literature (Pfrang et al., 2007).b Rate coefficients estimated using equation (X) and group-reactivity factors calculated in this study.c Canosa-Mas et al., 1999.d Salgado et al., 2011.e Wang et al., 2010.f Canosa-Mas et al., 2005.g Teruel et al., 2006.h Blanco et al., 2006.i Blanco and Teruel, 2008.j Martín et al., 2010.k Munshi et al., 1989.l Grosjean et al., 1993.

m Grosjean and Grosjean, 1998.n Yanbo et al., 2009.o Colomer et al., 2013.p Gallego-Iniesta PhD Thesis, 2012.q Teruel et al., 2012.r Gaona-Colman et al., 2013.

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of our understanding of the tropospheric reactivity of a,b-unsatu-rated esters as it allows the calculation of rate coefficients that arenot experimentally available; e.g. for methyl-E-2-methyl-2-butenoate, hexyl acrylate and 2-ethylhexyl acrylate with the OHradical; ethyl crotonate, (E)-ethyltiglate, hexyl acrylate and 2-ethylhexyl acrylate with NO3, methyl-3-methyl-2-butenoate,methyl-E-2-methyl-2-butenoate, (E)-ethyltiglate, hexyl acrylateand 2-ethylhexyl acrylate with O3 and methyl-E-2-methyl-2-butenoate with Cl atoms.

Table 8Rate coefficient data for Cl atoms estimated by SAR methods (kSAR3); (k in units ofcm3 molecule�1 s�1).

a,b-unsaturated ester kCl/10�10

bkexp akest kexp/kest

Methyl acrylate 1.71 � 0.13 1.04 1.65Methyl methacrylate 2.30 � 0.18 2.50 0.92Ethyl acrylate 1.82 � 0.13 1.17 1.55Ethyl methacrylate 2.71 � 0.21 2.83 0.95Butyl acrylate 2.94 � 0.23 1.21 2.41Butyl methacrylate 3.83 � 0.30 2.94 1.30Methyl crotonate 2.21 � 0.16 2.96 0.74Ethyl crotonate 2.52 � 0.62d 3.36 0.75Methyl-3-methyl-2-butenoate 3.58 � 0.30 2.92 1.22Methyl-E-2-methyl-2-butenoate e 2.92 e

(E)-Ethyltiglate 2.53 � 0.35e 3.32 0.76Hexyl acrylate 3.32 � 0.30c e e

2-Ethylhexyl acrylate 3.50 � 0.29c e e

a Rate coefficients estimated using equation (XII) and reactivity factors from theliterature (Teruel et al., 2009).

b Martín et al., 2010.c Gallego-Iniesta PhD Thesis, 2012.d Teruel et al., 2012.e Colomer et al., 2013.

4. Conclusions

Different methods for the estimation of rate coefficients for thereactions of a,b-unsaturated esters have been applied, fromphysico-chemical parameters and SAR methods. The reactivityfactors (f(eC(O)O(CH2)3CH3), f(eC(O)O(CH2)5CH3), f(eC(O)OCH2CH(CH2CH3)CH2CH2CH2CH3) for reactions with OH, NO3 and O3, andf(eC(O)OCH3), f(eC(O)OCH2CH3), f(eC(O)O(CH2)3CH3), f(eC(O)OCH2CH2CH2CH2CH2CH3), f(eC(O)OCH2CH(CH2CH3)CH2CH2CH2CH3)) for reactions with chlorine atoms have been calculated forthe first time. These factors will be useful for the prediction of ratecoefficients for similar compounds with a eC(O)OR group in theirstructure.

In summary, the following conclusions can be drawn for thea,b-unsaturated compounds presented here:

- For the reactions with OH and NO3 radicals, the estimationmethods obtained from correlations of the physico-chemicalparameters kPCP1 (log kOHð Þ versus log kNO3

� �; and log(kCl)

versus log(kOH); or log(kOH) versus log(kCl)) reproduce the ratecoefficients with good agreement, but in general, the bestmethod is PCP2 (ln(k) versus EHOMO) where the HOMO energieswere calculated in the manner describes by Pfrang et al. (2006a,b, 2007, 2008).

In this sense, the equations IV, V, VI and VII proposed initially foralkenes could be extended to the unsaturated esters present in thiswork, but the new equations proposed only for unsaturated esters(XVI, XVII, XVIII and XIX) give better rate coefficients with ratioskexp/kest near to unity.

- The StructureeActivity Relationships (SARs) methods reproducerate coefficients with larger discrepancies than physico-

MaP. Gallego-Iniesta et al. / Atmospheric Environment 90 (2014) 133e145144

chemical methods, except SAR1 for NO3 radical. The discrepancycould be due to the fact that SAR methods do not consider theeffect of alkyl chain in the eC(O)OR group and consider thatmethyl group contributes with the unity in the addition processwhen this group is bonded directly to the double bond C]C.

- In the case of Cl atoms, all estimation methods are good,indicating that the group attached to the double bond has littleor no influence on the reactivity.

In order to improve these methods, in especial for SARsmethods, to establish the reactivity factors in those cases wherethey have not been established to date and to evaluate the effect ofthe methyl group in the a-position of acrylate esters, more kineticstudies are required to increase the kinetic database for reactions ofVOCs.

Acknowledgements

The authors wish to thank the Spanish Ministerio de Ciencia eInnovación for supporting this research through project ENE2007-67529CO2-02.

Appendix A. Supplementary data

Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.atmosenv.2014.03.036

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