Rate constants for the atmospheric reactions of alkoxy radicals: An updated estimation method

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Atmospheric Environment 41 (2007) 8468–8485 www.elsevier.com/locate/atmosenv

Rate constants for the atmospheric reactions of alkoxy radicals: An updated estimation method Roger Atkinson,1 Air Pollution Research Center, University of California, Riverside, CA 92521, USA Received 11 March 2007; received in revised form 3 July 2007; accepted 4 July 2007

Abstract Alkoxy radicals are key intermediates in the atmospheric degradations of volatile organic compounds, and can typically undergo reaction with O2, unimolecular decomposition or unimolecular isomerization. Previous structure–reactivity relationships for the estimation of rate constants for these processes for alkoxy radicals [Atkinson, R., 1997. Atmospheric reactions of alkoxy and b-hydroxyalkoxy radicals. International Journal of Chemical Kinetics, 29, 99–111; Aschmann, S.M., Atkinson, R., 1999. Products of the gas-phase reactions of the OH radical with n-butyl methyl ether and 2-isopropoxyethanol: reactions of ROC(Od)o radicals. International Journal of Chemical Kinetics, 31, 501–513] have been updated to incorporate recent kinetic data from absolute and relative rate studies. Temperature-dependent rate expressions are derived allowing rate constants for all three of these alkoxy radical reaction pathways to be calculated at atmospherically relevant temperatures. r 2007 Elsevier Ltd. All rights reserved. Keywords: Alkoxy radical; Decomposition reaction; Reaction with O2; Isomerization reaction; Volatile organic compounds; Atmospheric chemistry

1. Introduction Volatile organic compounds (VOCs) emitted into the atmosphere can generally undergo photolysis and/or chemical reaction with OH radicals, NO3 radicals, Cl atoms, and O3 (Atkinson and Arey, 2003), with the dominant reaction occurring depending on the specific VOC. However, in most cases the reaction involves formation, at least in part, of an alkyl- or substituted alkyl radical Tel.: +1 951 827 4191.

E-mail address: [email protected] Also at: Department of Environmental Sciences and Department of Chemistry, University of California, Riverside, CA 92521, USA. 1

1352-2310/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2007.07.002

(Atkinson and Arey, 2003). In general, these alkyl or substituted alkyl radicals react in the troposphere as shown schematically in Fig. 1, with the key intermediates being organic peroxy (ROd2 ) and alkoxy (ROd) radicals. Organic peroxy radicals react with NO, NO2, NO3 radicals, HO2 radicals and organic peroxy radicals in the atmosphere (Atkinson and Arey, 2003; Collins et al., 2005; Atkinson et al., 2006; IUPAC, 2007), with their reactions with NO, organic peroxy radicals and NO3 radicals leading in part to the formation of alkoxy radicals. In the presence of sufficient NO that ROd2 +NO reactions dominate, the key intermediate species are alkoxy radicals (Fig. 1) and their atmospheric reactions then determine the majority of first-generation products (Devolder,

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2003; Atkinson and Arey, 2003; Orlando et al., 2003; Mellouki et al., 2003; Atkinson et al., 2006; IUPAC, 2007). R O2 HO2

ROOH

NO2

RO2

ROONO2

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Under tropospheric conditions, most alkoxy radicals potentially undergo reaction with O2, unimolecular decomposition, and unimolecular isomerization (Devolder, 2003; Atkinson and Arey, 2003), as shown in Fig. 2 for the 2-pentoxy radical. Alkoxy radicals of structure RC(O)OCH(Od)R0 formed from esters can also undergo isomerization proceeding through a 5-membered transition state (Tuazon et al., 1998; Christensen et al., 2000). RCðOÞOCHðOd ÞR0 ! RCðOÞOH þ R0 Cd O:

RO2

NO NO3

carbonyl + alcohol

RONO2

RO

products Fig. 1. Schematic of reactions of alkyl radicals in the atmosphere.

The database concerning the atmospherically relevant reactions of alkoxy radicals is still rather limited, especially if only absolute rate data are considered. In the sections below the literature data on alkoxy radical reactions with O2, isomerization, and decomposition are summarized, and recommendations made for estimation of rate constants of these reactions. Atkinson (1997) proposed a structure–reactivity relationship (SAR) for estimating the importance of the various alkoxy radical reaction pathways at room temperature, and

CH3CH(O)CH2CH2CH3 isomerization

CH3

O2

CH3C(O)CH 2CH2CH3

decomposition

CH3CHO + CH3CH2CH2

O HC

O2

H

H2C

CH2

NO

NO2

CH2 CH3CH2CH2O O2 CH3CH(OH)CH2CH2CH2

CH3CH2CHO

O2 NO

(1)

NO2

CH3CH(OH)CH2CH2CH2O isomerization CH3C(OH)CH2CH2CH2OH O2 CH3C(O)CH 2CH2CH2OH Fig. 2. Atmospheric reactions of the 2-pentoxy radical in the presence of NO.

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R. Atkinson / Atmospheric Environment 41 (2007) 8468–8485

temperature-dependent expressions were proposed for alkoxy radical decompositions and for reactions with O2, but not for the isomerizations. This SAR has been used in the formulation of the University of Leeds Master Chemical Mechanism, version 3 (Saunders et al., 2003). The original estimation scheme of Atkinson (1997) was slightly revised by Aschmann and Atkinson (1999) to take into account product data from the OH radical-initiated reactions of ethers, and this version was also summarized in the Supporting Information to Aschmann et al. (2001). There is a continuing need for an estimation method allowing the relative importance of the various alkoxy radical reactions to be reliably calculated for the very large number of larger alkoxy radicals formed during the atmospheric degradations of VOCs, so that these reactions can be included in atmospheric chemistry computer models. At the time of the Atkinson (1997) article, absolute rate constants for XC2 alkoxy radicals were only available for the reactions of ethoxy and 2-propoxy radicals with O2 (Gutman et al., 1982; Balla et al., 1985; Hartmann et al., 1990), and few useful (for development of SARs) relative rate studies had been carried out at room temperature and atmospheric pressure (Carter et al., 1979; Cox et al., 1981; Niki et al., 1981; Atkinson et al., 1995a). Since 1997 a significant number of absolute and relative rate studies of alkoxy radical reactions have been reported, and an update of the Atkinson (1997) estimation method is warranted. However, rate data for alkoxy radicals are still only available for a handful of simple alkoxy radicals, generally the smaller, pC6, alkoxy radicals formed during alkane photooxidations. Unfortunately, these are precisely those alkoxy radicals for which fall-off effects in the decomposition and isomerization reactions are most evident and this leads to added difficulties in deriving estimation methods for the rates of these reaction pathways for the larger alkoxy radicals, which are expected to be at the high-pressure limit under atmospheric conditions. 2. Reaction with O2 A number of relative rate studies have measured rate constants for alkoxy radical decomposition (kdecomp) or isomerization (kisom) relative to the rate constant for the corresponding O2 reaction (kO2 ) at atmospherically relevant temperatures (Carter et al., 1979; Cox et al., 1981; Niki et al., 1981; Lightfoot

et al., 1990; Wallington et al., 1992; Atkinson et al., 1992, 1995a; Aschmann et al., 1997; Platz et al., 1999; Orlando et al., 2000a; Libuda et al., 2002; Geiger et al., 2002; Meunier et al., 2003; Johnson et al., 2004; Cassanelli et al., 2005, 2006). However, since the decomposition and isomerization rate constants are less well known than the O2 reaction rate constants, data from these studies are most useful for deriving rate constants for the decomposition and isomerization pathways, using rate constants for the O2 reactions obtained from absolute rate studies. Absolute rate constants for XC2 alkoxy radical reactions with O2 are available from the studies of Gutman et al. (1982), Balla et al. (1985), Hartmann et al. (1990), Mund et al. (1998, 1999), Hein et al. (1998, 1999, 2000), Fittschen et al. (1999), Deng et al. (2000, 2001), Dusanter et al. (2003), Falgayrac et al. (2004) and Zhang et al. (2004, 2005). However, only a very limited number of XC2 alkoxy radicals (ethoxy, 1- and 2-propoxy, 1- and 2-butoxy, 3pentoxy, cyclohexoxy and trans-4-methylcyclohexoxy) have been studied to date using absolute rate methods (Table 1). While the studies of Hein et al. (1998, 1999, 2000) are somewhat indirect in that alkoxy radical reaction rate constants were obtained from fitting the OH radical and NO2 time–concentration profiles observed after pulsed formation of the parent alkyl radical to an assumed mechanism, they are viewed as absolute rate studies in this study. Rate constants at room temperature have been measured by more than one group for the reactions of O2 with the ethoxy, 1- and 2-propoxy, 2-butoxy and 3-pentoxy radicals (Table 1), with agreement within the sometimes large stated error limits (which range up to 750%). Moreover, for the ethoxy and 1- and 2-propoxy radical reactions the measured temperature dependencies are in good agreement, noting that the Deng et al. (2000) study in which rate constants for the 2-propoxy radical reaction were measured as a check on the experimental system was carried out over the very restricted range of 296–330 K (Table 1). In particular, the studies of Mund et al. (1998, 1999) and Fittschen et al. (1999) for the 1- and 2-propoxy radical reactions are in excellent agreement (although the temperature ranges studied overlap only slightly) and for 2-propoxy these studies (Mund et al., 1998, 1999; Fittschen et al., 1999) are also in excellent agreement with the data of Balla et al. (1985). Based on the temperature-dependent data for ethoxy and

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Table 1 Absolute rate data, k ¼ A eB/T, for the reactions of XC2 alkoxy radicals with O2 (k and A in cm3 molecule1 s1 units) Alkoxy radical

1014  A

B (K)

Temp. range (K)

1015  k (298 K)

Reference

Ethoxy

2.86 7.1 2.4 4.85

378 552764 3257120 529

296–353 295–411 286–390 245–395

8.0 11.1 8.1 8.2

Gutman et al. (1982) Hartmann et al. (1990) Fittschen et al. (1999) Dusanter et al. (2003)

1-Propoxy

1.4 2.5 2.6

108760 241760 253760

223–303 289–381 223–381

9.7 11.1 11.1

Mund et al. (1998) Fittschen et al. (1999) Fittschen et al. (1999)a

2-Propoxy

1.51 1.4 1.6 1.9 0.76

1967141 217748 265724 310724 0

294–384 218–311 288–364 218–364 296–330

7.8 6.8 6.6 6.9 7.6

Balla et al. (1985) Mund et al. (1998,1999) Fittschen et al. (1999) Fittschen et al. (1999)a Deng et al. (2000)b

29373

1477

Hein et al. (1999)

293 223–311 221–266 291–295

6.572 1274 7.7c 972

Hein et al. (1998) Deng et al. (2000) Deng et al. (2001) Falgayrac et al. (2004)

1-Pentoxy

29373

p100

Hein et al. (1999)

2-Pentoxy

29373

p65

Geiger et al. (2002)

1-Butoxy 2-Butoxy 0.133 0.12

659783 5537192

3-Pentoxy Cyclohexoxy Cyclohexoxy-d11 trans-4-Methyl-cyclohexoxy

0.410

319776

29373 220–285

7.273.5 1276c

Hein et al. (2000) Deng et al. (2001)

580

1720796

225–302

18

Zhang et al. (2004)

3.7 14

7607400

228–267

8107400

228–292

c

Zhang et al. (2005)

c

Zhang et al. (2005)

2.9 9.2

a

Combined data of Mund et al. (1998, 1999) and Fittschen et al. (1999). The measured rate constants of (8.7372.46)  1015 cm3 molecule1 s1 at 296 K, (6.7371.92)  1015 cm3 molecule1 s1 at 314 K and (7.4570.96)  1015 cm3 molecule1 s1 at 330 K show no obvious temperature dependence, and a temperature-independent average is listed here. c Calculated from extrapolation of the Arrhenius expression to 298 K. b

1- and 2-propoxy and the room temperature rate constants for 1- and 2-butoxy and 3-propoxy, then kO2 ¼ 2:5  1014 e300=T cm3 molecule1 s1

(I)

with kO2 ¼ 9  1015 cm3 molecule1 s1 at 298 K, is recommended for both primary (RCH2Od) and secondary (RCH(Od)R0 ) alkoxy radicals. While this 298 K rate constant kO2 is also consistent with that for the trans-4-methylcyclohexoxy radical reaction (Zhang et al., 2005), it is a factor of 2 lower than the room temperature rate constant for the cyclohexoxy radical reaction (Zhang et al., 2004). Furthermore, the temperature dependence in Eq (I) is not consistent with the data of Dibble and coworkers for the 2-butoxy (Deng et al., 2000, 2001), 3-pentoxy (Deng et al., 2001), cyclohexoxy (Zhang et al., 2004) and trans-4-

methylcyclohexoxy (Zhang et al., 2005) radical reactions, although the Zhang et al. (2005) temperature dependence for the trans-4-methylcyclohexoxy reaction almost overlaps with the above recommendation. For the 2-butoxy and 3-pentoxy radicals, Deng et al. (2000, 2001) obtained negative temperature dependencies, in contrast to the small positive temperature dependencies for the ethoxy (Gutman et al., 1982; Hartmann et al., 1990; Fittschen et al., 1999; Dusanter et al., 2003), 1propoxy (Mund et al., 1998; Fittschen et al., 1999) and 2-propoxy (Balla et al., 1985; Mund et al., 1998, 1999; Fittschen et al., 1999) radical reactions, despite the general similarity in the room temperature rate constants (Table 1). The data presented in Table 1, and those for the ethoxy, 1- and 2-propoxy, 1- and 2-butoxy and 3-pentoxy radical reactions

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plotted in Arrhenius form in Fig. 3, show that either the room temperature rate constants, and especially the temperature dependencies, for the XC4 alkoxy radicals depend on the specific alkoxy radical or that the rate constants measured by Dibble and coworkers were subject to as yet not understood interfering effects. If the former is correct, than development of a SAR for alkoxy+O2 reaction rate constants is going to be difficult; in any case additional absolute data are obviously needed for this class of reactions. The differences in ring-strain between the cycloalkoxy radical and the cycloketone product may have some effect on the room temperature rate constants and the temperature dependence for the reactions of O2 with cycloalkoxy radicals; for example, the difference in ring-strain between cyclohexoxy and cyclohexanone is 2.5 kcal mol1 and that between cyclopentoxy and cyclopentanone is 1 kcal mol1 (NIST, 1994). Further useful information on the cyclohexoxy+O2 reaction is available from the Orlando et al. (2000a) study. Combination of the 100

1015 x k (cm3 molecule-1 s-1)

50

20 10 5

rate constant ratio of kO2 /kdecomp(cyclohexoxy) ¼ 1.3  1027 e5550/T cm3molecule1 reported by Orlando et al. (2000a) with the above recommendation for kO2 results in kdecomp(cyclohexoxy) ¼ 1.9 1013 e5850/T s1, which fits in well with other acyclic alkoxy radical decompositions (see below). In contrast, combination of the Orlando et al. (2000a) rate constant ratio with the Zhang et al. (2004) expression for kO2 (cyclohexoxy) leads to kdecomp(cyclohexoxy) ¼ 4.5  1015 e7270/T s1, with a very high A-factor and correspondingly high activation energy. While circumstantial, this does suggest that the above recommendation [Eq (I)] for kO2 is applicable to most alkoxy radicals, including the cyclohexoxy radical. The above recommended rate constant kO2 corresponds to a pseudo-first-order alkoxy radical loss rate of 4.7  104 s1 at 298 K and 760 Torr of air. For alkoxy radicals of structure ROC(Od)o formed from ethers, the heat of reaction, DH O2 [calculated using compilations of heats of formation (IUPAC, 2007; Kerr and Stocker, 1999–2000) and/or use of the NIST (1994) program] are all DH O2 49 kcal mol1, significantly more exothermic than for other alkoxy radical+O2 reactions, with DH O2 32.4 kcal mol1 for primary ROd radicals and 35.9 kcal mol1 for secondary ROd radicals. Accordingly, a value of kO2 ¼ 1.5  1014 cm3 molecule1 s1, independent of temperature (i.e., close to the pre-exponential factors A for the ROd+O2 reactions for alkoxy radicals formed from alkanes), may be reasonable for the reactions of O2 with alkoxy radicals of structure ROC(Od)o (Aschmann and Atkinson, 1999). Hence at 298 K and 760 Torr of air, kO2 [O2] ¼ 8  104 s1 for ROC(Od)o radicals.

2

3. Isomerization 1 2.0

2.5

3.0

3.5

4.0

4.5

5.0

1000 /T (K)

Fig. 3. Arrhenius plot of absolute rate constants for the reactions of alkoxy radicals with O2. J, ethoxy data of Gutman et al. (1982), Hartmann et al. (1990) and Fittschen et al. (1999); J–J, Dusanter et al. (2003) expression for ethoxy; ,–,, Mund et al. (1998) expression for 1-propoxy; ,, 1-propoxy data of Fittschen et al. (1999); n–n, Mund et al. (1999) expressions for 2-propoxy; n, 2-propoxy data of Balla et al. (1985), Fittschen et al. (1999) and Deng et al. (2000); ., 1-butoxy data of Hein et al. (1999); K, 2-butoxy data of Hein et al. (1998) and Falgayrac et al. (2004); dashed lines, Deng et al. (2000, 2001) expressions for 2-butoxy; m, 3-pentoxy data of Hein et al. (2000); dash-dot-dot line, Deng et al. (2001) expression for 3-pentoxy; solid line, present recommendation for alkoxy+O2 reaction.

As shown in Fig. 2, if an abstractable hydrogen is available on the 4th carbon atom from that to which the alkoxy ‘‘O’’ is attached the alkoxy radical can undergo isomerization through a 6-member transition state to form a 4-hydroxyalkyl radical. To date, few useful rate data are available concerning the rates of these alkoxy radical isomerizations (Carter et al., 1979; Cox et al., 1981; Niki et al., 1981; Atkinson et al., 1995a; Hein et al., 1999; Geiger et al., 2002; Johnson et al., 2004, 2005; Cassanelli et al., 2005, 2006). Absolute rate constants (or lower limits thereof) for the isomerization of 1-butoxy, 1-pentoxy and 2-pentoxy of (3.572)  104 s1,

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X1  105 s1 and (1.871)  105 s1, respectively, at 29373 K and 50 mbar (37.5 Torr) pressure have been reported by Hein et al. (1999) and Geiger et al. (2002). These isomerization rate constants are in the fall-off region at atmospheric pressure and below (Somnitz and Zellner, 2000a) and are hence not directly applicable to atmospheric conditions, but are consistent with the relative rate data obtained at atmospheric pressure of air. The calculations of Somnitz and Zellner (2000a) also indicate that at 298 K and 760 Torr of air the isomerization rate constants for 1-butoxy and 1- and 2-pentoxy radicals are within 20% of the high-pressure limit. Isomerization rate constants for 1-butoxy, 1- and 2-pentoxy and 5-methyl-2-hexoxy radicals have been measured at atmospheric pressure relative to the corresponding O2 reaction rate constant (Carter et al., 1979; Cox et al., 1981; Niki et al., 1981; Atkinson et al., 1995a; Geiger et al., 2002; Johnson et al., 2004; Cassanelli et al., 2005, 2006), with the recent studies of Johnson et al. (2004) and Cassanelli et al. (2005, 2006) being carried out over significant temperature ranges. Fig. 4 shows Arrhenius plots of the measured rate constant ratios for these four alkoxy radicals, which are really (kisom+kdecomp)/kO2 but which to a good approximation can be equated to kisom/kO2 . As evident 200

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from Fig. 4, for the 1-butoxy radical the rate data of Carter et al. (1979), Cox et al. (1981), Niki et al. (1981), Geiger et al. (2002) and Cassanelli et al. (2005, 2006) are in excellent agreement. For the 2-pentoxy radical, the 296 K rate constant ratio of Atkinson et al. (1995a) is in agreement with the data of Johnson et al. (2004) within the experimental uncertainties, which were cited as a factor of 2 in the Atkinson et al. (1995a) study and shown by the error bars in Fig. 4 for the Johnson et al. (2004) study. For 1-pentoxy and 5-methyl-2-hexoxy, only a single study of each has been carried out relative to the corresponding O2 reaction (Johnson et al., 2004). In Fig. 5, the relative rate constant ratios plotted in Fig. 4 data are plotted on an absolute basis, using the value of kO2 ¼ 2.5  1014 e300/T cm3 molecule1 s1 derived above. Least-squares analyses of the rate constants for the four alkoxy radicals studied lead to the Arrhenius parameters given in Table 2. Clearly, the isomerization rate increases as the reaction proceeds from H-atom abstraction from a primary CH3 group to a secondary CH2 group to a tertiary CH group (Figs. 4 and 5). However, while the isomerization of 1-butoxy and 2-pentoxy radicals both involve an H-atom abstraction by the alkoxy ‘‘O’’ from a CH3 group bonded to a CH2 group, the 2-pentoxy radical isomerization is a factor of 2.5 faster than that of the 1-butoxy radical. As noted above, the calculations of Somnitz

5-Methyl-2-hexoxy

100

1e+7

1- Pentoxy

20

5e+6

10

2e+6

(k isom + k decomp ) s-1

10-19 x (k isom + k decomp) /kO2)

2e+7 50

5 2 2-Pentoxy

1 1-Butoxy

0.5

-CH2CH(CH3)2

1e+6 5e+5 2e+5

-CH2CH2CH3

1e+5 5e+4

0.2 3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

1000 /T (K)

-CH2CH3

2e+4 1e+4 3.0

Fig. 4. Arrhenius plots of the rate constant ratio (kisomerization+ kdecomposition)/kO2 for 1-butoxy: J, Carter et al. (1979); &, Cox et al. (1981); n, Niki et al. (1981) and Geiger et al. (2002); }, Cassanelli et al. (2005); ,, Cassanelli et al. (2006), 2-pentoxy: K, Atkinson et al., 1995a; m, Johnson et al. (2004), 1-pentoxy: &, Johnson et al. (2004), and 5-methyl-2-hexoxy: ., Johnson et al. (2004). The solid lines are the least-squares fits to the data for each alkoxy radical.

3.2

3.4

3.6 3.8 1000 /T (K)

4.0

4.2

4.4

Fig. 5. Arrhenius plots of the rate constants kisomerization for 1-butoxy, 2-pentoxy, 1-pentoxy and 5-methyl-2-hexoxy radicals. The solid lines are the recommended Arrhenius expressions for abstraction from the underlined CH3, CH2 and CH groups (see text). Symbols for experimental data are as in Fig. 4.

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Table 2 Temperature-dependent parameters, k ¼ A eB/T, for the isomerizations of alkoxy radicalsa Alkoxy radical

A (s1)

B (K)

k at 298 K (s1)

1-Butoxy 2-Pentoxy 1-Pentoxy 5-Methyl-2-hexoxy

3.06  109 1.23  1011 5.62  1010 4.05  1010

2909 3723 2899 2443

1.76  105 4.61  105 3.35  106 1.11  107

a From least-squares analyses of the data shown in Fig. 4, placed on an absolute basis using kO2 ¼ 2.5  1014 e300/T cm3 molecule1 s1.

and Zellner (2000a) suggest that at atmospheric pressure of air only a small fraction of this difference is due to enhanced fall-off behavior of the 1-butoxy radical compared to the 2-pentoxy radical. The difference between these two isomerization rate constants is, however, relatively small compared to the change in rate constant in going from abstracting from a primary CH3 group to a secondary CH2 group to a tertiary CH group (Figs. 4 and 5). For the 2-pentoxy, 1-pentoxy and 5-methyl-2-hexoxy radical isomerizations, the preexponential factors, A, show a trend with the number of abstractable H-atoms, n (Table 2). Accordingly, an A factor of 4  1010 n s1 is used, and this leads to the following Arrhenius expressions for isomerization involving H-atom abstraction from the underlined group kisom involving CH2 CH3 ¼ 1:2  1011 e3825=T s1 ¼ 3:2  105 s1 at 298 K,

kisom involving CH2 CH2 CH3 ¼ 8:0  1010 e3010=T s1 ¼ 3:3  106 s1 at 298 K

and kisom involving CH2 CHðCH3 Þ2 ¼ 4:0  1010 e2440=T s1 ¼ 1:1  107 s1 at 298 K.

These expressions are shown as the solid lines in Fig. 5. While, as noted above, the 1-butoxy radical rate data were not used for the derivation of the A-factors for these isomerizations, the temperature dependence for isomerization involving H-atom abstraction from a CH3 group was derived from the room temperature rate constants of both the 1-butoxy and 2-pentoxy radicals. This results in a 298 K rate constant for isomerization from a CH3

group bonded to a CH2 group (i.e., 1-butoxy and 2-pentoxy) of 3.2  105 s1; use of the 2-pentoxy data alone would result in a 298 K rate constant of 4.6  105 s1, a relatively small difference. These rate constants are for isomerizations involving abstraction of an H-atom on CH, CH2 and CH3 groups attached to other alkyl groups. In an attempt to estimate rate constants for isomerization involving H-atom abstraction from –CH2OH and –CH(OH)– groups and from CH, CH2 and CH3 groups attached to hetero-atom containing groups or to ether linkages, an approach analogous to the OH radical rate constant estimation method of Atkinson (1986, 1987) is used. In this approach, the rate of reaction (with OH radicals or isomerization) depends on the group to which the H-atom is attached (for example, a CH, CH2 and CH3 group) and the neighboring group(s). Thus, for H-atom abstraction from CH3–X, k ¼ kprimF(X); for H-atom abstraction from X–CH2–Y, k ¼ ksec F(X)F(Y); and for H-atom abstraction from X–CH(–Y)–Z, k ¼ ktertF(X)F(Y)F(Z), where kprim, ksec and ktert are the rate constants for H-atom abstraction from CH3, CH2 and CH groups respectively, and F(X), F(Y) and F(Z) are substituent factors for neighboring groups X, Y and Z. Note that, by definition, F(CH3) ¼ 1.00. Isomerization involving H-atom abstraction from CH3, CH2 and CH groups, each with one neighboring CH2 group, have 298 K rate constants in the ratio 1: 10: 34, and this can be compared to the corresponding ratios of 1:6.9:14 for the corresponding OH radical reactions (Kwok and Atkinson, 1995). One may then estimate that at 298 K, F(X)isom[F(X)OH]1.3 and hence that F(–CH2–)isom ¼ F(4CH–)isom ¼ F(4Co)isom ¼ 1.3 (as noted above, F(–CH3)isom ¼ 1.00). Taking into account the substituent effect of the neighboring CH2 group on the derived rate constants given above, at 298 K the isomerization rate constants are therefore kprim ¼ 2.5  105 s1, ksec ¼ 2.5  106 s1, and ktert ¼ 8.5  106 s1. Additional substituent factors F(–OH)isom ¼ 4.0, F(–CH2OH)isom ¼ isom F(4CHOH) ¼ 3.5 [based on the substituent factors for OH radical reactions of Bethel et al. (2001)] and F(–OR)isom ¼ 16 (where R ¼ alkyl) can be derived from the corresponding factors for H-atom abstraction by OH radicals (Kwok and Atkinson, 1995). Additional substituent factors can be determined from the corresponding factors for OH radical reactions (Kwok and Atkinson, 1995; Atkinson, 2000). Assuming that the substituent

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groups have no effect on the pre-exponential factor, then F(X) ¼ eE/T and the values of kprim, ksec and ktert are

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and

in formation of a 1,4-hydroxyalkoxy radical. If this radical has an available H-atom at the carbon to which the OH group is attached, then a second isomerization can occur. If it can occur, this second isomerization, involving an H-atom abstraction from a C–H bond in a –CH2OH or –CH(OH)– group, is predicted to be as, or more, rapid than the initial isomerization.

ktert ¼ 4:0  1010 e2520=T s1 ,

4. Decomposition

with F(–CH2–)isom ¼ F(4CH–)isom ¼ F(4Co)isom ¼ e80/T. The rate of isomerization at 298 K for an isomerization occurring across an ether –O– linkage is estimated to be decreased by a factor of 30 (Aschmann and Atkinson, 1999) because of additional ring strain. While isomerization occurring across a 4C ¼ O group may also be expected to be affected by the presence of the 4C ¼ O group in the 6-membered transition state (see Ferenac et al., 2003), the product data of Atkinson and Aschmann (1995) for the OH radical-initiated reactions of 4-methyl-2-pentanone and 2,6-dimethyl-4-heptanone suggest that any effect of the 4C ¼ O group is relatively small and probably within the uncertainties of the data and/or estimation method. Hence isomerization across a 4C ¼ O group is assumed to be unaffected by the presence of the 4C ¼ O group. Additional product and/or theoretical studies (see, for example, Me´reau et al., 2000a) are clearly needed to establish the rates of isomerization across various functional groups. The A-factors for these isomerization reactions are significantly lower (by an order of magnitude or more) than those calculated by Somnitz and Zellner (2000a) and Me´reau et al. (2003), but are similar to those predicted by Baldwin et al. (1977) [8  1010 s1 per abstractable H-atom]. Note that fall-off effects for the isomerizations of XC5 alkoxy radicals are expected to be minor (Somnitz and Zellner, 2000a) and hence fall-off effects cannot account for the significantly lower A-factors than recent theoretical calculations (Somnitz and Zellner, 2000a; Me´reau et al., 2003) predict. Since all of the presently available isomerization rate data at atmospherically relevant conditions are relative to the rate constant for the ROd+O2 reaction, absolute rate measurements at atmospheric pressure (or over a range of pressure allowing reliable extrapolation to atmospheric pressure) are clearly needed. As shown in Fig. 2, the initial isomerization leads to a 1,4-hydroxyalkyl radical which, after addition of O2 and reaction with NO, results at least in part

Absolute rate constants for the decomposition of alkoxy radicals, kdecomp, are available only for ethoxy (Caralp et al., 1999; Fittschen et al., 2000), 2-propoxy (Balla et al., 1985; Devolder et al., 1999; Fittschen et al., 2000), 2-butoxy (Hein et al., 1998; Falgayrac et al., 2004), tert-butoxy (Blitz et al., 1999; Fittschen et al., 2000) and 3-pentoxy (Hein et al., 2000) radicals. These reactions are all in the fall-off region at atmospheric pressure and below at the temperatures studied, and the studies of Caralp et al. (1999), Devolder et al. (1999), Blitz et al. (1999), Fittschen et al. (2000) and Falgayrac et al. (2004) were conducted as a function of both temperature and pressure and limiting high-pressure Arrhenius parameters were derived (Table 3). In the studies of Hein et al. (1998, 2000), rate constants were obtained at 37.5 Torr total pressure and 293 K (Table 3), and theoretical calculations (Somnitz and Zellner, 2000a) indicate that the measured rate constants are lower than those at 760 Torr of air by a factor of 5. Note that none of these studies provided direct experimental evidence for the assumed reaction. Under atmospheric conditions, decompositions of the ethoxy and 2-propoxy radicals are of no importance, because the O2 reactions dominate. Batt and co-workers (Batt, 1979 and references therein) studied the thermal decomposition of a series of alkyl nitrites at elevated temperatures and derived rate constants for the alkoxy radical decompositions relative to those for the ROd+NO reaction. Data were obtained (Batt, 1979) for 2-propoxy (433–473 K), 2-butoxy (440–473 K), 2-methyl-2-propoxy (tert-butoxy) (395–435 K) and 2-methyl-2-butoxy (433–463 K) radicals. Because of uncertainties in extrapolating the derived rate constant ratios, obtained over small temperature ranges, to room temperature and in the rate constants for the ROd+NO reference reactions, the rate expressions which can be derived are judged to be of only semi-quantitative use for atmospheric

kprim ¼ 1:2  1011 e3905=T s1 , ksec ¼ 8:0  1010 e3090=T s1

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8476

Table 3 Absolute rate data, k ¼ A eB/T, for alkoxy radical decompositions (at the high-pressure limit unless noted otherwise) Alkoxy radical

kN (s1) at 298 K

A

Ethoxy

5 2

1.1  1013 1.0  1014

2-Propoxy

8.2  102 8.7  102

2-Butoxy

B (K)

Temperature range (K)

Reference

8456 9406

391–471 391–471

Caralp et al. (1999) Fittschen et al. (2000)a

1.2  1014 1.0  1014

7662 7590

330–408 330–408

Devolder et al. (1999) Fittschen et al. (2000)a

(3.572)  103b 4.4  104 2.9  104c

1.1  1014 6.7  1012c

6447 5737c

293 291–348 291–348

Hein et al. (1998) Falgayrac et al. (2004) Falgayrac et al. (2004)

tert-Butoxy

1.4  103 2.5  103

1.4  1013 1.0  1014

6856 7277

303–393 323–383

Blitz et al. (1999) Fittschen et al. (2000)

3-Pentoxy

(5.072.5)  103b

293

Hein et al. (2000)

a

Re-evaluation of the Arrhenius parameters reported by Caralp et al. (1999) and Devolder et al. (1999). At 37.5 Torr (50 mbar) pressure. c At 750 Torr (1 bar) pressure of N2. b

conditions and are not used here [see also Johnson et al. (2005)]. Batt and Robinson (1982, 1987) and Batt et al. (1989) also investigated the decomposition of the tert-butoxy radical using the thermal decomposition of di-t-butyl peroxide at 402–443 K in the presence of NO (Batt and Robinson, 1982, 1987) and the photolysis of t-butyl nitrite at 303–393 K (Batt et al., 1989). Using a highpressure rate constant for the ROd+NO reaction of 8.6  1012 e400/T cm3 molecule1 s1, based on an average of absolute rate data for the 1- and 2-propoxy, 2-butoxy, tert-butoxy and 3-pentoxy radical reactions (Balla et al., 1985; Fittschen et al., 1999; Blitz et al., 1999; Deng et al., 2000, 2001; Lotz and Zellner, 2000, 2001; Falgayrac et al., 2004), re-evaluation of the rate expression of Batt et al. (1989) leads to a rate constant for the decomposition of t-butoxy of kN ¼ 2.3  1013 e7119/T s1 (303–443 K), with kN ¼ 960 s1 at 298 K. This is in reasonable agreement with the absolute rate data of Blitz et al. (1999) and Fittschen et al. (2000) listed in Table 3. The bulk of the present database concerning alkoxy radical decompositions at around room temperature arises from product studies conducted at atmospheric pressure, from which rate constant ratios of kdecomp/kO2 or kdecomp/kisom have been derived. One complication which arises concerns decomposition rate constants being in the fall-off regime at atmospheric pressure and below (this also applies to absolute studies, except that rate constants have generally been measured as a function of both temperature and pressure in the absolute rate

studies conducted to date and cited in Table 3; see also above). While experimental data are available mostly for the smaller alkoxy radicals which are more prone to have decomposition rate constants in the fall-off regime at atmospheric pressure and room temperature, the need is for decomposition rate constants for larger alkoxy radicals for which no experimental data exist, and these rate constants are more likely to be at the high-pressure limit under atmospheric conditions. Hence the need is to be able to estimate the high-pressure limiting rate constants. The approach here is to use the limiting highpressure rate expressions obtained from absolute rate studies (Table 3) together with rate expressions derived from relative rate data, often available at effectively only a single temperature. Based on the absolute rate studies (Table 3) and theoretical calculations (Somnitz and Zellner, 2000a; Me´reau et al., 2000b; Peeters et al., 2004; Falgayrac et al., 2004), a pre-exponential factor A in the expression kdecomp ¼ A eB/T is assumed to be 5  1013 s1 per reaction path degeneracy (although Falgayrac et al. (2004) argue in favor of A ¼ 1  1014 s1, independent of the reaction path degeneracy). Hence it is assumed that kdecomp ¼ A n eB/T, where n is the reaction path degeneracy. 4.1. Alkoxy radicals formed from alkanes For simple alkoxy radicals other than ethoxy, 2-propoxy and t-butoxy, for which absolute rate data are available (Table 3), rate constant ratios kdecomp/kO2 are available for the 2-butoxy (Carter et al., 1979; Cox

ARTICLE IN PRESS R. Atkinson / Atmospheric Environment 41 (2007) 8468–8485

CH3 CHðOd ÞCH2 CH3 ! CH3 CHO þ CH3 Cd H2 (2) are plotted in Arrhenius form in Fig. 6. The rate constant ratios kdecomp/kO2 determined by Carter et al. (1979), Cox et al. (1981), Libuda et al. (2002), Meunier et al. (2003) and Cassanelli et al. (2005) are placed on an absolute basis using kO2 ¼ 2.5  1014 e300/T cm3 molecule1 s1. The rate expressions reported by Falgayrac et al. (2004) for the high-pressure limit and for 1 bar N2 are also plotted in Fig. 6. The relative rate data are in excellent agreement and lead to an Arrhenius expression of kdecomp ¼ 9.9  1012 e5932/T s1 (256–313 K) at atmospheric pressure. Based on the theoretical calculations of Somnitz and Zellner (2000a) and Falgayrac et al. (2004), the value of kdecomp at atmospheric pressure and 298 K is 0.65 kN, and hence kN ¼ 3.6  104 s1 at 298 K. Combined with an A-factor of 5  1013 s1, this leads to the recommended value of kN(2-butoxy) ¼ 5  1013 e6273/T s1, which is shown as the thick solid line in Fig. 6. Clearly, the relative rate and absolute rate measurements are in excellent agreement (within 25% for atmospherically relevant temperatures). Using a generally similar approach, Arrhenius expressions for several other simple alkoxy radical decompositions have been derived from relative rate data (in most cases at room temperature), and these are listed in Table 4 together with reference to the relative and/or absolute rate studies on which they

1e+7

1e+6

k decomp (s-1)

et al., 1981; Libuda et al., 2002; Meunier et al., 2003; Cassanelli et al., 2005), 2-methyl-1-propoxy (isobutoxy) (Geiger et al., 2002); 3-pentoxy (Atkinson et al., 1995a; Geiger et al., 2002; Meunier et al., 2003), 2,2-dimethyl-1-propoxy (neopentoxy) (Lightfoot et al., 1990; Wallington et al., 1992) and cyclohexoxy (Atkinson et al., 1992; Aschmann et al., 1997; Platz et al., 1999; Orlando et al. 2000a) radicals, and also for the CH3CH(Od)OC(CH3)3 radical formed from ethyl t-butyl ether (Wallington and Japar, 1991; Smith et al., 1992; Aschmann and Atkinson, 1999). Data are also available for the relative importance of the two decomposition pathways of the 2-methyl-2-butoxy radicals, and for the rates of the two decomposition pathways of the 2-methyl-3-pentoxy radical relative to the rate constant for the isomerization (Johnson et al., 2005). The most studied decomposition reaction is that for the 2-butoxy radical, and the decomposition rate constants for the process

8477

Falgayrac et al.

k∞ k1atm

Recommended k ∞

1e+5

1e+4

1e+3

1e+2 2.8

3.0

3.2 3.4 3.6 1000 /T (K)

3.8

4.0

Fig. 6. Arrhenius plots of rate constants for the decomposition of the 2-butoxy radical to CH3CHO+dC2H5. K, Carter et al. (1979); m, Cox et al. (1981); n, Libuda et al. (2002); ,, Meunier et al. (2003); J, Cassanelli et al. (2005). The thin solid line is the least-squares fit to the experimental data at atmospheric pressure; the dashed lines are from the absolute rate expressions of Falgayrac et al. (2004) at 1 atmosphere N2 and at the highpressure limit; and the thick solid line is the present recommendation (see text).

are based. Consistent with previous observations (Choo and Benson, 1981; Atkinson, 1997), Table 4 and Fig. 7 show that the Arrhenius activation energy Ed in the expression kdecomp ¼ A n eE d =RT depends on the leaving radical. Sufficient data are available for alkoxy radical decompositions with a methyl radical as the leaving radical (Fig. 7) to establish a relationship between Ed and DH for the decomposition reaction of the form Ed ¼ a+b(DH), where DH is the heat of reaction (Atkinson, 1997). The values of DH were calculated using the thermochemical data from NIST (1994), Kerr and Stocker (1999–2000) and IUPAC (2007) and/or the NIST (1994) estimation method, and a O–H bond dissociation energy of 104 kcal mol1 was always used. As noted by Somnitz and Zellner (2000b), the use of a term dependent on DH in the estimation of alkoxy radical decomposition rates is not optimum because of the inherent uncertainties in the estimation of heats of reaction. However, there is a need to estimate decomposition rate constants for more complex alkoxy radicals, including branched alkoxy radicals, 1,2-hydroxyalkoxy and 1,2-oxo-alkoxy radicals, and to date there do not appear to be reliable methods other than, possibly, that presented

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R. Atkinson / Atmospheric Environment 41 (2007) 8468–8485

Table 4 Arrhenius parameters for decompositions of selected alkoxy radicals Reaction

DH (kcal mol1)

n

Ed (kcal mol1)

Note

CH3CH2Od-HCHO+dCH3 (CH3)2CHOd-CH3CHO+dCH3 (CH3)3COd-CH3C(O)CH3+dCH3 CH3CH(Od)CH2CH3-CH3CHO+dC2H5 (CH3)2CHCH2Od-(CH3)2CdH+HCHO CH3CH2CH(Od)CH2CH3-CH3CH2CHO+dC2H5 Cyclohexoxy-dCH2(CH2)4CHO (CH3)3CCH2Od-HCHO+(CH3)3Cd (CH3)2C(Od)CH2CH2CH3-CH3C(O)CH3+CH3CH2CdH2 (CH3)2C(Od)CH2CH2CH3-CH3C(O)CH2CH2CH3+dCH3 (CH3)2C(Od)CH2CH3-CH3C(O)CH3+dC2H5 (CH3)2C(Od)CH2CH3-CH3C(O)CH2CH3+dCH3 CH3CH(Od)OC(CH3)3-(CH3)3COCHO+dCH3 CH3CH(Od)OC(CH3)3-CH3CHO+(CH3)3COd

12.7 7.9 4.8 5.9 10.6 7.6 7.3 10.6 4.4 5.3 4.2 4.7 4.5 10.2

1 2 3 1 1 2 2 1 1 2 1 2 1 1

18.1 15.1 14.7 12.5 12.2 12.9 12.5 10.570.4 13.0 15.2 (13.1) (15.8) 11.0 11.9

a b c d e f g h i i j k l l

a

From Fittschen et al. (2000), fit with an A-factor of 5  1013 s1. From Fittschen et al. (2000). c From Fittschen et al. (2000), fit with an A-factor of 1.5  1014 s1. d From the relative rate data of Carter et al. (1979), Cox et al. (1981), Libuda et al. (2002), Meunier et al. (2003) and Cassanelli et al. (2005) and the absolute rate data of Falgayrac et al. (2004) (see text). e From Geiger et al. (2002). f From the relative rate data of Atkinson et al. (1995a), Geiger et al. (2002) and Meunier et al. (2003). g From the relative rate data of Atkinson et al. (1992), Aschmann et al. (1997), Platz et al. (1999) and Orlando et al. (2000a). h From the data of Lightfoot et al. (1990) and Wallington et al. (1992). i From Johnson et al. (2005), relative to the isomerization reaction. Placed on an absolute basis using kisom ¼ 1.2  1011 e3825/T s1 (see text). j The relative rate study of Batt et al. (1978) leads to the activation energy given in parentheses, which appears too high by 1.4 kcal mol1. k The data of Johnson et al. (2005) show that formation of CH3C(O)CH2CH3+dCH3 (n ¼ 2) is 2.75 kcal mol1 more endothermic than formation of CH3C(O)CH3+dC2H5 (n ¼ 1). l From the product studies of Wallington and Japar (1991) and Smith et al. (1992); see also Atkinson (1994) and Aschmann and Atkinson (1999). b

here and the theoretically based approach of Peeters et al. (2004). It can be noted (see also Somnitz and Zellner, 2000b) that within a homologous group of alkoxy radicals (examples of such homologous groups being RCH2CH2Od, RCH2CH(Od)CH2R, RCH(OH)CH2Od, and RCH2CH(Od)CH2OH, where R ¼ H or alkyl), the estimated values of DH (and hence Ed) for the alkoxy radicals in each homologous series are essentially identical. Least-squares analysis of the data in Fig. 7 and Table 4 for the methyl radical as the leaving radical results in Ed (kcal mol1) ¼ (12.770.65)+ (0.4070.09)DH, where DH is in kcal mol1 and the cited errors are two standard deviations. Assuming that b is constant (b ¼ 0.40), then for each of the decomposition reactions a value of a for that leaving radical (methyl, ethyl, 1-propyl, ‘‘general’’ RCdH2, 2-propyl and t-butyl) can be calculated. It has previously been proposed that a is related to the ionization potential (IP) of the leaving radical

(Choo and Benson, 1981; Atkinson, 1997), and a least-squares analysis of these values of a against the corresponding values of IP leads to a ¼ 1.81(IP)4.92 kcal mol1, where IP is in eV. The resulting values of a and b for alkoxy radicals of structure RR0 R00 COd (R, R0 and R00 ¼ H or alkyl) are listed in Table 5 together with the ionization potentials (in eV) used. While the values of a and b differ from the values given by Aschmann and Atkinson (1999) by up to 1.7 kcal mol1 in a and 0.09 in b, apart from methyl as a leaving radical the presently calculated decomposition rate constants are quite similar to the earlier values (within a factor of 5 for DH in the range 5 to +20 kcal mol1). Fig. 8 shows the calculated decomposition rates for selected alkyl radical leaving groups as a function of DH from both the Atkinson (1997) [as revised by Aschmann and Atkinson, 1999) for methyl as the leaving radical] and the present work. Also shown in Fig. 8 are the

ARTICLE IN PRESS 20

1e+9

18

1e+8

ethyl

12

2-propyl

t - butyl

1e+7

16 14

8479

ethyl

methyl

2-propyl

1-propyl RCH2

t-butyl

10

k decomp (s-1) at 298 K

Arrhenius activation energy Ed, kcal mol-1

R. Atkinson / Atmospheric Environment 41 (2007) 8468–8485

1e+6 1e+5 1e+4

methyl kO2[O2] in air

1e+3

8 1e+2

6

1e+1

-5

0

5

10

15

ΔH (reaction), kcal mol-1 Fig. 7. Plot of the derived Arrhenius activation energies Ed for alkoxy radical decompositions against the heats of reaction, DH listed in Table 4. J, methyl as the leaving radical; m, ethyl as the leaving radical; ’, 1-propyl as the leaving radical; ., general RCdH2 as the leaving radical (from decomposition of the cyclohexoxy radical); &, 2-propyl as the leaving radical; ,, t-butyl as the leaving radical. The line is a least-squares fit to the data with methyl as the leaving radical.

Table 5 Parameters a and b for estimating activation energies Ed for alkoxy radical decompositions Leaving radical

a (kcal mol1)

b

IP (eV)

Methyl Ethyl 1-Propyl General RCdH2 2-Propyl General R2CdH t-Butyl General R3Cd d CH2OH RCdHOH R2CdOH CH3Od RCH2Od R2CHOd R3COd HCdO CH3CdO

12.9 9.8 9.6 9.5 8.4 8.2 7.2 7.1 6.8a 5.2a 4.8a 7.5 7.5 7.5 7.5 E10 5

0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40

9.84 8.12 8.02 7.98 7.37 7.24 6.70 6.65 7.56 6.7 6.5

a Reduced by 2.0 kcal mol1 from the value predicted using the ionization potential; see text.

decomposition rates for 2-butoxy (kN) and 3pentoxy radicals and the reaction rate of alkoxy radicals of structure RR0 CHOd (R ¼ alkyl and

-10

-5

0

5

10

15

20

ΔH (kcal mol-1) Fig. 8. Plots of calculated alkoxy radical decomposition rates at 298 K for methyl, ethyl, 2-propyl and t-butyl as the leaving radicals. Dashed lines are using the Atkinson (1997) [as revised for methyl as the leaving radical by Aschmann and Atkinson, 1999)] method, and the solid lines are using the present method with A ¼ 5  1013 n s1. The reaction rate with O2 (if feasible) is shown as the dash-dot-dot line (see text) for 760 Torr of air and 298 K, and the experimental 298 K decomposition rates for 2-butoxy (kN) and 3-pentoxy radicals (ethyl as the leaving radical) are shown as the solid circles (K).

R0 ¼ H or alkyl) with O2 at 298 K and 760 Torr of air (for alkoxy radicals of structure ROC(Od)o, the predicted reaction rates with O2 are 70% higher; see above). For the 2-butoxy and 3-pentoxy radicals the presently predicted decomposition rates (with ethyl as the leaving radical) are in better agreement with experimental data that were the previous Atkinson (1997) predictions. 4.2. 1,2-Hydroxyalkoxy radicals The above derived relationship between a and the IP of the leaving radical leads to predicted values of a for a-hydroxy leaving radicals of: dCH2OH, 8.8 kcal mol1; RCdHOH, 7.2 kcal mol1; and R2CdOH, 6.8 kcal mol1. Use of these values of a leads to decomposition rates of 1,2-hydroxyalkoxy radicals which are within a factor of 5 of the Atkinson (1997) predictions over the range of DH ¼ 5 to +20 kcal mol1. However, Orlando et al. (1998) and Vereecken et al. (1999) showed from theoretical and experimental studies of the OH radical-initiated reactions of ethene and propene, respectively, at atmospheric pressure that the

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Arrhenius activation energies (at the high-pressure limit) for decomposition of the 1,2-hydroxyalkoxy radicals HOCH2CH2Od and CH3CH(Od)CH2OH (both with dCH2OH as the leaving radical) are lower by 2–3 kcal mol1 than predicted using the above relationship between a and the IP of the leaving group. Accordingly, the predicted values of a for the 1,2-hydroxyalkoxy radicals dCH2OH, RCdHOH and R2CdOH have been decreased by 2.0 kcal mol1 and are listed in Table 5. Note that the decompositions of thermalized HOCH2CH2Od and CH3CH(Od)CH2OH radicals are in the falloff region at atmospheric pressure and below at around room temperature (Orlando et al., 1998; Vereecken et al., 1999). The presently predicted high-pressure decomposition rates for 1,2-hydroxyalkoxy radicals are therefore higher than the previously predicted values (Atkinson, 1997) by factors of 6–60, depending on the leaving group (dCH2OH, RCdHOH or R2CdOH) and the value of DH (within the range 5 to +20 kcal mol1). However, the present predictions lead to better agreement with the kdecomp/kO2 ratios derived by Aschmann et al. (2000) for the CH3CH2CH(Od)CH2OH, d CH3CH(OH)CH(O )CH3 and CH3CH2CH(OH)CH(Od)CH2CH3 radicals. Thus, the presently predicted value of kdecomp for the CH3CH2CH(Od) CH2OH radical of 1.4  107 s1 at 296 K is a factor of 4 higher than that derived by Aschmann et al. (2000), while the predicted decomposition rates of the CH3CH(OH)CH(Od)CH3 and CH3CH2CH (OH)CH(Od)CH2CH3 radicals at 296 K are higher by factors of 1.3 and 1.9, respectively, than the lower limits derived by Aschmann et al. (2000). Moreover, the presently predicted 298 K decomposition rate constants for 1,2-hydroxyalkoxy radicals which can undergo isomerization, such as the CH3CH2CH2CH2CH(OH)CH2Od and CH3CH2CH2CH2CH(Od)CH2OH radicals formed after OH radical addition to 1-hexene, are of a similar magnitude to the predicted isomerization rate constants for these radicals (with predicted ratios of kisom/kdecomp ¼ 1.0 and 0.15, respectively, for the above radicals), consistent with experimental observations which show that decomposition and isomerization of these 1,2-hydroxyalkoxy radicals in the proportion formed from the OH+1-hexene reaction are roughly equivalent at room temperature and atmospheric pressure of air (Atkinson et al., 1995b; Aschmann et al., 2002) [but see the section below on chemically-activated alkoxy radicals].

4.3. Alkoxy radicals of structure R2C(Od)OCR3 (R ¼ alkyl or H) These alkoxy radicals are formed from the reactions of OH radicals with ethers and glycol ethers, and can potentially decompose by two pathways, in addition to reaction with O2 and isomerization. Reaction pathway (3a) has been dealt with above. R2 CðOd ÞOCR3 ! Rd þ RCðOÞOCR3 ;

(3a)

R2 CðOd ÞOCR3 ! RCðOÞR þ R3 COd :

(3b)

Only a limited amount of data exist concerning the elimination of an alkoxy radical, R3COd (Aschmann and Atkinson, 1999), with the most definitive evidence for the occurrence of this decomposition channel arising from the observation of acetaldehyde from ethyl tert-butyl ether (Smith et al., 1992; Atkinson, 1994), with the t-butoxy leaving radical reacting mainly with NO to form tbutyl nitrite in the Smith et al. (1992) study, allowing this channel to be differentiated from decomposition of the CH3CH2OC(CH3)2Od radical to acetone plus ethoxy. This reaction is included in Table 4, and the value of a for t-butoxy derived from the data in Table 4 is given in Table 5. Based on product studies of the photooxidations of methyl tert-butyl ether (Japar et al., 1990; Smith et al., 1991; Tuazon et al., 1991) and diethyl ether (Eberhard et al., 1993), values of a for methoxy and ethoxy as the leaving radicals appear to be similar to that for t-butoxy (Table 5). However, significant uncertainties in the estimation of the rate constants for this reaction channel remain. 4.4. Alkoxy radicals of structure RC(O)C(Od)R2 These alkoxy radicals are formed in the atmospheric degradations of carbonyl compounds, including of a,b-unsaturated carbonyls. The available data for the reactions of CH3C(O)CH(Od)CH3 (Cox et al., 1981) and CH3C(O)CH2Od (Orlando et al., 2000b) radicals show that kdecomp/kO2 4100 at room temperature and atmospheric pressure of air. The value of a in Table 5 for CH3CdO as a leaving radical is based on the experimental and theoretical study of the CH3C(O)CH2Od radical of Orlando et al. (2000b), and is consistent with the nonobservation of 2,3-butanedione from the CH3C(O) CH(Od)CH3 reaction with O2 at 296 K and atmospheric pressure of air in the Cox et al. (1981) study

ARTICLE IN PRESS R. Atkinson / Atmospheric Environment 41 (2007) 8468–8485

and with the product data of Tuazon and Atkinson (1989) for the OH radical-initiated reaction of methyl vinyl ketone. The value of a derived for HCdO as a leaving radical is very approximate, being consistent from the product data of Tuazon and Atkinson (1990) and Tuazon et al. (2005) for the OH radical-initiated reactions of methacrolein and 3-methyl-2-butenal. 4.5. Chemically activated alkoxy radicals An additional degree of complexity for alkoxy radical decompositions (and potentially isomerizations) arises from observations that a fraction of certain alkoxy radicals [for example, CF3CHFOd (Wallington et al., 1996), HOCH2CH2Od (Orlando et al., 1998) and CH3CH(Od)CH2OH (Vereecken et al., 1999)] formed from ROd2 +NO reactions, which are exothermic by 10–11 kcal mol1 (IUPAC, 2007), are chemically activated and undergo ‘‘prompt’’ decomposition (Wallington et al., 1996; Orlando et al., 1998; Vereecken et al., 1999). In contrast, alkoxy radicals formed from the self- or cross-reactions of ROd2 radicals, which are slightly endothermic for simple ROd2 +ROd2 -ROd+ ROd+O2 reactions (IUPAC, 2007), are thermalized. As an example of this chemical activation, 25% of the HOCH2CH2Od radicals formed from the OH radical-initiated reaction of ethene in the presence of NO undergo ‘‘prompt’’ decomposition, independent of temperature (Orlando et al., 1998). This ‘‘prompt’’ decomposition of alkoxy radicals formed from the exothermic ROd2 +NO reaction appears to be important for alkoxy radicals with a barrier to decomposition of approximately 9 kcal mol1 or less (Orlando et al., 2000a,b), with prompt decomposition being unimportant for alkoxy radicals with higher barriers to decomposition [such as the cyclohexoxy radical with a barrier to decomposition of 11.572.2 kcal mol1 (Orlando et al., 2000a)]. For the 2-butoxy radical, with a measured barrier to decomposition of 11.3 kcal mol1 (Libuda et al., 2002; see also Table 3), Libuda et al. (2002) and Cassanelli et al. (2005) observed 8–9% of the 2-butoxy radicals formed from the ROd2 +NO reaction to undergo ‘‘prompt’’ decomposition at 298 K, with a trend to a lower fraction of ‘‘prompt’’ decomposition at lower temperatures and vice-versa (Libuda et al., 2002; Cassanelli et al., 2005). ‘‘Prompt’’ decomposition would have also occurred in the Carter et al. (1979), Cox et al. (1981) and Hein et al. (1998, 2000) studies, and this could be the

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reason for the slightly higher rate constant ratios of kdecomp./kO2 obtained in the studies of Carter et al. (1979) and Cox et al. (1981) compared to that of Libuda et al. (2002) in which the ‘‘prompt’’ decomposition was taken into account. However, the effect in the case of the 2-butoxy radical is relatively small and has not been corrected for in this evaluation, for example, in Fig. 6. It is also possible that a similar ‘‘prompt’’ isomerization of chemically activated alkoxy radicals may occur for alkoxy radicals formed from the ROd2 +NO reaction (Lendvay and Viskolcz, 1998; Dibble, 2002; Cassanelli et al., 2005). 5. Conclusions and atmospheric implications Despite the significantly more extensive database presently available for alkoxy radical reactions from both absolute and relative rate studies used in this updated estimation method, the changes in alkoxy radical reaction rates compared to the earlier predictions (Atkinson, 1997; Aschmann and Atkinson, 1999) are, for the most part, fairly minor. Although the temperature dependence of the O2 reaction rate constants is slightly changed, the 298 K rate constants are unchanged. The 298 K rate constants for alkoxy radical isomerizations are a factor of 1.5–2.1 higher than previously proposed, and the decomposition rate constants are generally somewhat higher than previously proposed, especially for 1,2-hydroxyalkoxy radicals, which now appear to be in better agreement with experimental data than were the previously predicted (Atkinson, 1997) decomposition rates. Recognizing that the likely uncertainties in the calculated values of DH and the Arrhenius activation energies Ed for alkoxy radical decompositions are at least 71 kcal mol1, which corresponds to an uncertainty in the decomposition rate constant of a factor of 5.4 at 298 K, within this level of uncertainty there are unlikely to be any major changes in most of the predicted dominant alkoxy reaction pathways. One area of uncertainty concerns the reactions of R2C(Od) OCR3 radicals formed from ethers, where the decomposition pathway to form Rd+RC(O)OCR3 is exothermic by 3–5 kcal mol1 and is hence predicted to be rapid; the present method may possibly overestimate the rate of this decomposition pathway for leaving radicals other than methyl. For thermalized alkoxy radicals, the rates of decomposition and isomerization are significantly temperature dependent, and hence the dominant

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atmospheric reaction pathway (decomposition, isomerization and/or reaction with O2) can change with increasing altitude (or decreasing temperature), as observed for the cyclohexoxy radical (Orlando et al., 2000a). For example, at 298 K and atmospheric pressure of air the reaction rates of the 2-pentoxy radical are estimated to be: reaction with O2, 4.7  104 s1, decomposition, 2.7  104 s1, and isomerization, 3.2  105 s1, while at 220 K and 100 Torr total pressure, the rates are estimated to be: reaction with O2, 5.9  103 s1, decomposition, 14 s1, and isomerization, 3.4  103 s1. This results in a predicted changeover from dominantly (80%) isomerization in the lower troposphere to mainly (60–65%) reaction with O2 in the upper troposphere. However, the occurrence of a significant fraction of a given alkoxy radical undergoing ‘‘prompt’’ decomposition or isomerization could change this picture. For 1,2-hydroxyalkoxy radicals and RC(O)C(Od)o radicals, decomposition and/or isomerization is predicted to dominate over reaction with O2 at room temperature and atmospheric pressure of air, and hence for these particular alkoxy radicals the O2 reaction can be neglected under these conditions. Ackowledgements The author thanks the National Science Foundation (Grant nos. ATM-0234586 and ATM-0650061) for supporting this research. While this research has been supported by the NSF, it has not been reviewed by the NSF and no official endorsement should be inferred. The author also thanks the University of California Agricultural Experiment Station for partial salary support and the two anonymous reviewers for their helpful comments.

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