Under tropospheric conditions, the major alkoxy radi-cal removal processes involve reaction with O2, uni-molecular decomposition, and isomerization [1–4].The alkoxy radical isomerizations proceed by a cyclictransition state [5,6] and, because of the ring straininvolved, the 1,4-H shift isomerizations proceedingthrough a 5-member ring transition state are calcu-lated to be much less important (by a factor of ca. 53 103 at 298 K [6]) than the 1,5-H shift isomeriza-tions proceeding through a 6-member, essentiallystrain-free, transition state [1,6]. Eberhard et al. [7]observed no evidence for the 1,4-H shift isomeriza-tions for the 2- and 3-hexoxy radicals, in agreementwith predictions [1,6], and the 1,4-H shift isomeriza-tion reactions of alkoxy radicals are therefore ne-glected in the following discussion. For the 2-pentoxyradical, the decomposition and isomerization reac-tions and the reaction with O2 are shown in Scheme I.

INTRODUCTION

Alkoxy radicals are key intermediates in the tropo-spheric degradation of volatile organic compounds[1–4]. For example, the reactions of alkanes andalkenes (RH) with the OH radical leads to the forma-tion of alkoxy and b-hydroxyalkoxy (RO) radicals[4].

OH 1 RH 9: R (1)

R1 O2 RO2 (2)9:M

Atmospheric Reactions of Alkoxy and b-Hydroxyalkoxy RadicalsROGER ATKINSON

Statewide Air Pollution Research Center and Department of Soil and Environmental Sciences, University of California,Riverside, California 92521

ABSTRACT

Alkoxy and b-hydroxyalkoxy radicals are key intermediates formed in the atmospheric degra-dations of alkanes and alkenes, respectively. In the troposphere, these alkoxy radicals can de-compose, isomerize, and react with O2 . The literature data concerning the rates of these reac-tions are evaluated, and predictive schemes allowing the calculation of rate constants forthese alkoxy radical reactions for atmospheric purposes are proposed. Good agreement be-tween calculated reaction rates and experimental data concerning the absolute and relativeimportance of these reaction pathways is obtained, and alkoxy and b-hydroxyalkoxy radicalreaction rates for radicals for which experimental data are not presently available can now becalculated for use in atmospheric modeling. © 1997 John Wiley & Sons, Inc.

RO2 1 NO (3)RONO2

M

RO 1 NO2?

?

Received April 11, 1996; accepted June 6, 1996International Journal of Chemical Kinetics, Vol. 29, 99–111 (1997)

© 1997 John Wiley & Sons, Inc. CCC 0538-8066/97/020099-13

RO 1 RO 1 O2

R21CHO 1 (1 2 )ROH

1 RO2 products 1 O2

RO2 1 RO2

(4)

a a

???

?

?

100 ATKINSON

Reactions of the alkoxy radicals with NO and NO2,though generally of no importance under tropo-spheric conditions, must also be considered for labo-ratory conditions [4].

Despite over two decades of research into the at-mospherically-important reactions of alkoxy radicals(see, for example, refs. [1,3,4,6, and 8–12]), the rateconstants for the decomposition, isomerization, andreaction with O2 of most of the alkoxy radicals of im-portance in the troposphere are neither quantitativelyknown nor can they be reliably estimated [4]. This isparticularly the case for the b-hydroxyalkoxy radicalsformed after OH radical addition to alkenes, whichhave been experimentally shown to dominantly de-compose rather than react with O2 under troposphericconditions [13–17] but which are calculated to reactalmost exclusively with O2 [8,18]. During the pasttwo years, important results concerning the isomer-ization reactions of alkoxy radicals formed as inter-mediates in the tropospheric degradations of alkanes[7,19,20], alkenes [16,17], alcohols [21], and ketones[22] have become available, allowing more reliableassessments of the importance of alkoxy radical iso-merization to be made. In this work, the status ofalkoxy radical reactions is discussed and estimationmethods for the reliable calculation of the tropo-

spheric reaction rates of alkoxy and b-hydroxyalkoxyradicals are proposed.

Reaction with O2

Absolute rate constants for the reactions of alkoxyradicals with O2 have been determined for the CH3O [23–26], C2H5O [24,27], and (CH3)2CHO[28] radicals over the temperature ranges 298–973 K,295–411 K, and 295–384 K, respectively, and theArrhenius plot for the reaction of the CH3O radicalwith O2 shows pronounced upward curvature aboveca. 600 K [26]. The IUPAC recommendations [29]for the rate constants for these reactions are given inTable I, with the recommendation for the CH3O radi-cal reaction being restricted to temperatures # 608 K.In addition to these absolute rate constants, Zellnerand co-workers [30] have reported, using an indirectmethod, rate constants at 298 K for the reactions of O2 with propoxy, 1-butoxy, 2-methyl-1-propoxy,pentoxy, hexoxy, heptoxy, and octoxy radicals of(7.3–8)3 10215 cm3 molecule21 s21, very similar tothose for the ethoxy and 2-propoxy radicals (Table I).Based on the recommended rate constants given inTable I for the reactions of the C2H5O and(CH3)2CHO radicals with O2, it is recommended [4]

CH3CH(O)CH2CH2CH3

CH3CH(OH)CH2CH2CH2

HO2 1 CH3C(O)CH2CH2CH3

decomposition isomerization

O2

CH3 1 CH3CH2CH2CHO

or

CH3CHO 1 CH3CH3CH2

OCH9CH3

CH2

CH2

H

CH2

?

?

?

?

Scheme I

Table I Recommended 298 K Rate Constants and Temperature Dependent Expressions, kO2

5 A e2B/ T, for the Reactions of O2 with Alkoxy (RO ) Radicalsa

A kO2(298 K)

RO (cm3 molecule21 s21) B(K) (cm3 molecule21 s21)

CH3O 7.2 3 10214 1080 1.93 10215

CH3CH2O 6.0 3 10214 550 9.53 10215

(CH3)2CHO 1.5 3 10214 200 83 10215

a From Atkinson et al. [29]; these Arrhenius expressions are only appropriate for temperatures & 600 K.

ALKOXY AND b-HYDROXYALKOXY RADICALS 101

that for primary (RCH2O) and secondary (R1R2CHO)alkoxy radicals at temperatures & 600 K,

k(RCH2O 1 O2) 5 6.0 3 10214 e2550/T

cm3 molecule21 s21

5 9.5 3 10215 cm3 molecule21 s21

at 298 K, (I)

and

k(R1R2CHO1 O2) 5 1.5 3 10214 e2200/T

cm3 molecule21 s21

5 8 3 10215 cm3

molecule21 s21 at 298 K. (II)

For the reaction of the C2H5O radical with O2, Hart-mann et al. [27] measured the formation yield of theHO2 radical after conversion to OH radicals and LIFdetection of OH radicals, and obtained a formationyield of HO2 radicals of 0.8910.22

20.12, showing thatwithin the experimental uncertainties the reactionproceeds, as expected, by

CH3CH2O 1 O2 9: CH3CHO 1 HO2 (5)

Relationships between the rate constants for the reac-tions of alkoxy radicals with O2 and the exothermici-ties of these reactions have previously been derived[4,6,28] and, based on the three reactions for whichrecommendations [29] are given (Table I) and usingthe heats of formation given in the IUPAC evaluation[29], a least-squares analysis leads to (DHO2 in kcalmol21)

k(RO1 O2) 5 kO25 4.0 3 10219

n e2(0.28DHO2) cm3 molecule21 s21 (III)

at 298 K, where n is the number of abstractable Hatoms in the alkoxy radical. This expression fits the298 K rate constants given in Table I to within 35%,and differs somewhat from the expression recom-mended by Atkinson [4], of k(RO1 O2) 5 1.3 310219 n e2(0.32DHO2) cm3 molecule21 s21, because ofdifferent values for the heat of formation of the 2-propoxy radical. At 760 torr total pressure of air and298 K, eq. (III) leads to

kO2[O2] 5 2.1 n e2(0.28DHO2) s21 (IV)

Equations (III) and (IV) can be used to estimate therate constants and reaction rates, respectively, for thereactions of substituted alkoxy radicals with O2 for

which experimental measurements are not available.For the alkoxy and b-hydroxyalkoxy radicals dealtwith here, the rate constants kO2

calculated from eq.(III) are generally within a factor of 2 of those rec-ommended in eq. (I) and (II) for primary or sec-ondary alkoxy radicals, respectively, with the excep-tion of the neopentyloxy radical for which the rateconstant calculated from eq. (III) is up to a factor ofca. 4 lower than the recommendation for primaryalkoxy radicals [eq. (I)].

Alkoxy Radical Decompositions

The gas-phase decompositions of alkoxy radicalsformed from the OH radical-initiated reactions ofalkanes have been the subject of several previous re-views and discussions [1–4,6,8–12]. These previousarticles have derived relationships between the mea-sured Arrhenius activation energies for the alkoxyradical decompositions (Ed) and the heats of the de-composition reaction (DHd), with the Arrhenius pre-exponential factors for these decomposition reactionsall being of a similar magnitude. Most of these rela-tionships have assumed, or shown, that a single rela-tionship between Ed and DHd exists, with

Ed 5 a 1 bDHd (V)

irrespective of the structure of the alkoxy radical orthe leaving alkyl group [1–4,6,9,10]. Choo and Ben-son [11], however, presented data indicating that theparameter a in the above relationship depends on thealkyl leaving-group, with the parameter a decreas-ing monotonically along the alkyl leaving-group series CH3, C2H5, (CH3)2CH, and (CH3)3C and de-pending on the ionization potential of the alkyl leav-ing-group.

Batt and co-workers [31–38] and Dóbé et al. [39]have measured the rate constants for the decomposi-tion of the ethoxy [34], 2-propoxy [33], 2-butoxy[32], tert-butoxy [31,36–38], 2-pentoxy [39], and 2-methyl-2-butoxy [35] radicals relative to the alkoxyradical combination reaction with NO.

RO 1 NO RONO (6)

Additional alkoxy radical decomposition rate con-stants are available from the studies of Carter et al.[40], Cox et al. [41] and Drew et al. [42] for the 2-bu-toxy radical, Lightfoot et al. [43] and Wallington etal. [44] for the 2,2-dimethyl-1-propoxy (neopenty-loxy) radical, and Atkinson et al. [19] for the 3-pen-toxy radical, relative to the alkoxy radical reactionswith O2 [19,40,41,43,44] or relative to other decom-

9:M

102 ATKINSON

position pathways [42]. One immediate conclusionfrom the studies of the decomposition reactions of the2-butoxy [42] and 2-methyl-2-butoxy [35] radicals isthat of the two decomposition channels for thesealkoxy radicals,

stants for the alkoxy radical reactions with O2. Forthe 2-butoxy radical, the 298 K decomposition rateconstant obtained by extrapolation of the rate con-stants measured relative to the alkoxy radical reactionwith NO at 440–470 K [32] is within a factor of 4 ofthose measured relative to the O2 reaction at roomtemperature [40,41]. Given the uncertainties in therate constants for the alkoxy radical reactions withNO and O2 and the extrapolation of the decomposi-tion rate constant from 440 K to 298 K, this is reasonable agreement and within the likely uncertain-ties.

The data given in Table II show that the rate con-stants for alkoxy radical decomposition at 298 K arenot inversely proportional to the values of DHd andthat there is no linear relationship between Ed andDHd. These data are consistent with the conclusionsof Choo and Benson [11] that Ed depends on theidentity of the alkyl leaving-group. The approach ofChoo and Benson [11] has therefore been used, and aleast-squares analysis of the Arrhenius activation en-ergies Ed and heats of decomposition,DHd, for thedecompositions with a methyl leaving-group lead toEd 5 (15.11 0.36DHd), where the energies are inkcal mol21 and the values of a and b have significantuncertainties. Using the value of b 5 0.36 leads tovalues of a 5 12.2 kcal mol21 for the ethyl radical asthe leaving group and a 5 7.5 kcal mol21 for the tert-butyl radical as the leaving-group. Using an analo-gous equation to that proposed by Choo and Benson[11] to relate Ed and a, the data are reasonably well fit by

Ed 5 (2.4(IP)2 8.1) 1 0.36DHd (VI)

where IP is the ionization potential (in eV) of thealkyl radical leaving-group [46] and Ed and DHd arein kcal mol21. This leads to values of a (kcal mol21)of: methyl, 15.5; primary alkyl, RC˙ H2, 11.1 (includ-ing ethyl, 11.4 and 1-propyl, 11.3); secondary alkyl,R1R2CH, 9.3 (including 2-propyl, 9.6); and tertiaryalkyl, R1R2R3C , 7.9 (including tert-butyl, 8.0). TheArrhenius activation energies Ed calculated from eq.(VI) agree with the values of Ed given in Table II towithin ca. 61 kcal mol21.

This approach to alkoxy radical decompositionscan be extended to the b-hydroxyalkoxy radicalsformed after OH radical addition to alkenes, using theionization potentials for the a-hydroxyalkyl radicalleaving-groups. For example, for the two b-hydrox-yalkoxy radicals formed after OH radical addition topropene.

CH3CH(OH)CH2O 9: HCHO 1 CH3CHOH (9)

those leading to ethyl radicals [reactions (7a) and(8a)] dominate by a factor of . 150 at 298 K [35,42],despite the endothermicities of the two reaction chan-nels (7a) and (7b), and (8a) and (8b), for each ofthese alkoxy radicals being similar (within 1 kcalmol21). Furthermore, decomposition of the 2,2-di-methyl-1-propoxy radical [43,44] is much more rapid(by a factor of 105 to 106) than anticipated on the ba-sis of a linear relationship between Ed and DHd inde-pendent of the reaction products [4]. As previouslyproposed by Choo and Benson [11], these observa-tions imply that the alkyl leaving-group influences theenergetics of the alkoxy radical decompositions.

The literature alkoxy radical decomposition rateconstants have been reevaluated to be relative to therecommendation of Atkinson [4] for the combinationreaction of alkoxy radicals with NO, of k

`(RO 1

NO) 5 2.3 3 10211 e150/T cm3 molecule21 s21 (whichremains unchanged using the most recent IUPACevaluation [29]). The preexponential factors, Ad, werethen set at Ad 5 2 3 1014 d s21 [the mean of the vari-ous values of Ad after reevaluation to the commonvalue of k

`(RO 1 NO)], where d is the reaction path

degeneracy and the Arrhenius activation energies Edwere adjusted to yield the same decomposition rateconstant at the mid-point of the temperature rangeemployed in the experimental studies of Batt and co-workers [32–35,38], Dóbé et al. [39], and Drew et al.[42]. Table II gives the resulting Arrhenius parame-ters together with the heats of decomposition,DHd,and the calculated 298 K decomposition rate con-stants kd. Also given in Table II are the 298 K decom-position rate constants calculated from the studies ofCarter et al. [40], Cox et al. [41], Lightfoot et al. [43],and Atkinson et al. [19] in which the decompositionrate constants were measured relative to the rate con-

CH3CH(O)CH2CH3(7a)

(7b)

CH3CHO

1 C2H5

CH3CH2CHO

1 CH3

CH3CH2C(CH3)2O(8a)

(8b)

CH3C(O)CH3

1 C2H5

CH3C(O)CH2CH3

1 CH3

? ?

?

?

?

?

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S103

Table II Temperature-Dependent Parameters, kd 5 Ad e2Ed /RT, and 298 K Rate Constants, kd , for the Gas-Phase Decompositions of Alkoxy Radicals (at or Close to theHigh-Pressure Limit), Relative to k

`(RO 1 NO) 5 2.3 3 10211 e150/T cm3 molecule21 s21

DHda Ed kd (s21)

RO (kcal mol21) Ad (s21) (kcal mol21) (298 K) Reference

CH3CH2O : CH3 1 HCHO 13.0 23 1014 20.2 0.31 Batt and Milne [34](CH3)2CHO: CH3 1 CH3CHO 7.8 43 1014 17.6 49 Batt and Milne [33]CH3CH(O)CH2CH3 : C2H5 1 CH3CHO 6.0 23 1014 14.3 6.53 103 Batt and McCulloch [32]

2.5 3 104 b Carter et al. [40]2.1 3 104 b Cox et al. [41]

CH3CH(O)CH2CH3 : CH3 1 C2H5CHO 6.7 23 1014 16.6 1.33 102 Drew et al. [42](CH3)3CO : CH3 1 CH3C(O)CH3 4.7 63 1014 16.2 7.93 102 Batt et al. [38]CH3CH(O)CH2CH2CH3 : CH3CH2CH2 1 CH3CHO 6.8 23 1014 14.1 9.13 103 Dóbé et al. [39]CH3CH2C(CH3)2O : C2H5 1 CH3C(O)CH3 4.3 23 1014 13.9 1.33 104 Batt et al. [35]CH3CH2C(CH3)2O : CH3 1 CH3C(O)CH2CH3 4.6 43 1014 18.3 15 Batt et al. [35]CH3CH2CH(O)CH2CH3 : C2H5 1 C2H5CHO 7.7 2.63 104 b Atkinson et al. [19](CH3)3CCH2O : (CH3)3C 1 HCHO 11.5 1.93 106 b Lightfoot et al. [43]

a Thermochemistry quantities were calculated using the thermochemical data given in refs. [29,45, and 46]. When alkoxy radical heats of formations or O!H bond dissociation energies were notavailable from refs. [29 and 45], the alkoxy radical heats of formation were calculated from the measured or estimated alcohol heats of formation [46] using an O!H bond dissociation energy of 104kcal mol21.

b Relative to the rate constants for reaction of the alkoxy radical with O2, using rate constants at 298 K of k(RCH2O 1 O2) 5 9.5 3 10215 cm3 molecule21 s21 and k(R1R2CHO 1 O2) 5 8 3

10215 cm3 molecule21 s21 as recommended here [eqs. (I) and (II)].

104 ATKINSON

CH3CH(O)CH2OH 9: CH3CHO 1 CH2OH (10)

With ionization potentials of a-hydroxyalkyl radicalsof 7.56 eV for the C˙H2OH radical [46], 6.7 eV for the CH3CHOH radical [46], 6.74 eV for theCH3CH2CHOH radical [47] and 6.48 eV for the(CH3)2COH radical [47], then the values of a (kcalmol21) in eq. (VI) are: CH2OH, 10.0; R1CHOH, 8.0;and R1R2C OH, 7.5. These values of a are used be-low to calculate the relative importance of decompo-sition, isomerization, and reaction with O2 of the b-hydroxyalkoxy radicals formed after OH radi-cal addition to a series of alkenes.

Certain of the alkoxy radical decomposition reac-tions are in the fall-off region between first-order andsecond-order kinetics at around room temperatureand atmospheric pressure [6,9,10,12,28,36–38,48].For the two alkoxy radicals for which pressure depen-dent decomposition rate constants have been ob-served (2-propoxy [28,48] and 2-methyl-2-propoxy(tert-butoxy) [36–38]), the rate constants at roomtemperature and atmospheric pressure are reasonablyclose to the limiting high pressure values [28,36,37](see also Table II in Baldwin et al. [6], which predictsthat the corrections for fall-off behavior are small forC3 and higher alkoxy radicals, being less than a factorof 2 at room temperature and atmospheric pressure).For example, at 298 K and 760 torr of N2, the decom-position rate constant for the 2-methyl-2-propoxyradical is calculated to be a factor of ca. 1.3 below thehigh-pressure limit [37], and Balla et al. [28] mea-sured absolute decomposition rate constants for the 2-propoxy radical at 378 K and 300 torr total pressureof N2 which are a factor of ca. 2.2–2.3 below thehigh-pressure limit [28,33]. However, at temperaturesmuch above room temperature, fall-off effects for thealkoxy radical decompositions may become impor-tant, and the rate constants for the decomposition re-actions given here should only be used for tropo-spheric conditions.

Alkoxy Radical Isomerizations

Apart from the radical-trapping study of Dóbé et al.[39], only recently has direct evidence for the occur-rence of alkoxy and b-hydroxyalkoxy radical isomer-ization been reported [7,17,19,20]. Previously, the oc-currence of alkoxy radical isomerization reactions in the alkane photooxidations was inferred by the absence of the products expected from the alkoxyradical decomposition and/or reaction with O2[5,40,41,49], and until the recent studies of Atkinsonet al. [16] and Kwok et al. [17] there was no evidence

for the occurrence of b-hydroxyalkoxy radical iso-merization. No absolute rate constants for the isomer-ization reactions are available, but isomerization rateconstants have been estimated [1,4–6], initially byCarter et al. [5] and subsequently and in more detailby Baldwin et al. [6] and with further minor adjust-ments being carried out recently [1,2,4]. For thealkoxy radicals formed from the alkanes, the experi-mental data available concern measurements of therate constant ratios for the isomerization reactions ofthe 1-butoxy [40,41,49], 2-pentoxy [19] and the 2-and 3-hexoxy [7] radicals relative to their reactionswith O2. No quantitative data are available for the b-hydroxyalkoxy radicals formed from the alkenes. Themeasured rate constant ratios kisom/kO2

are given inTable III, and the three measurements for the 1-bu-toxy radical [40,41,49] are in good agreement. Rateconstants kisom can be obtained from these rate con-stant ratios kisom/kO2

using the rate constants kO2rec-

ommended above [eqs. (I) and (II)], and the resultingisomerization rate constants are also given in TableIII. The rate constant for isomerization of the 2-pen-toxy radical obtained by Dóbé et al. [39] relative tothe 2-pentoxy radical decomposition rate using a rad-ical trapping method is a factor of ca. 20 lower thanthe other values of kisom reported for isomerization viaH-atom abstraction from 9CH3 groups, and isclearly in error (probably due to difficulties in quanti-tatively trapping the 4-hydroxy-1-pentyl radicalsformed after the isomerization). Also given in TableIII are the rate constants for isomerization ofRCH2C(CH3)(OH)CH2C(O)(CH3)2 radicals (R5 Hand CH3) obtained relative to the decomposition rateconstants of these g-hydroxyalkoxy radicals [21].

The data presented in Table III show that alkoxyradical isomerization proceeding by H-atom abstrac-tion from a !CH3 group has a rate constant of ca. 2 3 105 s21 at room temperature, and that this is alsothe case for the g-hydroxyalkoxy radical studied byAtkinson and Aschmann [21]. Based on the rather un-certain data of Eberhard et al. [7] for the 2-hexoxyradical and the data of Atkinson and Aschmann [21]for a g-hydroxyalkoxy radical (Table III), the rateconstant at room temperature for isomerization pro-ceeding by H-atom abstraction from a 9CH29group is kisom ca. 23 106 s21. The rate constant forisomerization via H-atom abstraction from a 9CH3group at 298 K is a factor of 3 higher than the mostrecent estimate of Atkinson [4] (which was based onthe experimental data for the 1-butoxy radical[40,41,49]), and is a factor of ca. 3 lower than theoriginal estimate by Baldwin et al. [6]. However, therate constant for isomerization by H-atom abstractionfrom a 9CH29 group at 298 K is significantly

AL

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Table III Room Temperature Rate Constant Ratios kisom/kO2and Rate Constants kisom for the Reactions of Alkoxy Radicals formed from Alkanes and Alcohols

kisom/kO2at T kisomer

a

RO (molecule cm23) (K) Reference (s21)

Abstraction from a !CH3 group (per !CH3 group)1-Butoxy 1.63 1019 303 Carter et al. [40]

(1.5 6 0.5) 3 1019 2956 2 Cox et al. [41] 1.63 105

(1.9 6 0.2) 3 1019 2986 2 Niki et al. [49]2-Pentoxy 3.13 1019 2966 2 Atkinson et al. [19] 2.53 105

301 Dóbé et al. [39] ca. 63 103 b

3-Hexoxy (2.3–5.4)3 1019 2976 3 Eberhard et al. [7] (1.8–4.3)3 105

(CH3)2C(OH)CH2C(O)(CH3)2 2966 2 Atkinson and Aschmann [21] 1.33 105 c

Abstraction from a !CH2! group (per !CH2! group)2-Hexoxy (1.7–5.9)3 1020 2976 3 Eberhard et al. [7] (1.4–4.7)3 106

CH3CH2C(CH3)(OH)CH2C(O)(CH3)2 2966 2 Atkinson and Aschmann [21] 1.63 106 c

a Using rate constants at 298 K recommended in eqs. (I) and (II) for the reaction of the 1-butoxy radical with O2 of 9.53 10215 cm3 molecule21 s21 and for the reactions of the 2-pentoxy and 2- and3-hexoxy radicals with O2 of 8 3 10215 cm3 molecule21 s21, unless noted otherwise.

b The isomerization rate constant is relative to the decomposition rate constant measured in the same study [39] and given in Table II.c The isomerization rate constants are relative to the decomposition rate constants and placed on an absolute basis using calculated decomposition rate constants of ca. 83 105 s21 at 296 K, assum-

ing that the RCH2C(CH3)(OH)CH2 leaving radical behaves as an average primary alkyl radical with a 5 11.1 kcal mol21. These decomposition rate constants calculated using the methods describedhere are identical to those calculated by Atkinson and Aschmann [21].

6

106 ATKINSON

lower than previous estimates [1,2,4,6], and the ex-perimental data (Table III) showing that H-atom ab-straction from a 9CH29 group is a factor of 10faster than from a 9CH3 group differ significantlyfrom the estimate [6] of a factor of 100 for this ratio.

The room temperature rate constants of 23 105

s21 for isomerization involving H-atom abstractionfrom a 9CH3 group and 23 106 s21 for isomeriza-tion involving H-atom abstraction from a 9CH29group can be combined with the estimated preexpo-nential factors of Baldwin et al. [6] to arrive at

kisom(H-atom abstraction from a 9CH3 group)5 2.4 3 1011 e24170/T s21 (VII)

and

kisom(H-atom abstraction from a !CH2! group)5 1.6 3 1011 e23360/T s21 (VIII)

Baldwin et al. [6] estimated that the rate constant forisomerization by H-atom abstraction from a . CH!group should be a factor of 2 lower than that for iso-merization by H-atom abstraction from a 9CH2!group, independent of temperature (and therefore 13105 s21 at 298 K using the present values of kisom).However, by analogy with H-atom abstraction by OHradicals from !CH3, !CH2! , and . CH!groups [50], isomerization involving H-atom abstrac-tion from a . CH! group should be more rapid thanisomerization involving H-atom abstraction from a9CH29 group. Assuming that alkoxy radical iso-merization and H-atom abstraction by the OH radicalare analogous reaction systems, then for H-abstrac-tion from two differing C!H bonds, i and j,kisom

j/kisomi 5 (kOH

j/kOHi )a [this is equivalent to the

Arrhenius activation energies depending linearly onthe C9H bond dissociation energies]. Furthermore,using the approach used to estimate the rate constantsfor the H-atom abstraction reactions of the OH radi-cal [50], group isomerization rate constants kprim,ksec, and ktert at 298 K of 1.63 105 s21, 1.63 106

s21, and 43 106 s21, respectively, are derived. TheArrhenius parameters are given in Table IV, and therelevant substituent factors Fisom(X) for substituent

group X [Fisom(X) 5 {FOH(X)} 1.16] are given in TableV, with Fisom(X) 5 eBx / T. As an example, the rateconstant for isomerization of the CH3CH2CH2CH2Oradical is kisom 5 kprim Fisom(9CH29) 5 1.6 3 105

3 1.27 s21 5 2.0 3 105 s21, identical to the value of kisom derived from the experimental data (as it should be).

For the cyclohexyloxy (cyclo-C6H11O) radical thereaction with O2

cyclo-C6H11O 1 O2 9:cyclohexanone1 HO2 (11)

accounts for 426 5% of the overall reaction path-ways at 2966 2 K and atmospheric pressure of air[51] (consistent with the product data of Rowley et al.[52]). This relative importance of the O2 reaction sug-gests that the isomerization reaction is not importantfor the cyclo-C6H11O radical, and that the competingpathway is the alkoxy radical decomposition reaction[52]. Indeed, the conformation of the cyclohexanering prohibits isomerization of the cyclohexyloxyradical, and this expectation has been confirmed bythe absence of the isomerization product using at-mospheric pressure ionization tandem mass spec-trometry (API-MS) [53]. The alkoxy radical O˙CH2(CH2)4CHO formed subsequent to decomposition ofthe cyclohexyloxy radical appears to undergo mainlyisomerization [53], as predicted from the above dis-cussion.

The hydroxyalkyl radicals formed from the iso-merization of the initial alkoxy or b-hydroxyalkoxy

Table IV Arrhenius Parameters, kisom 5 Aisom e2Bisom /T, for the Isomerization of AlkoxyRadicals

H-atom Abstraction From Aisom (s21) Bisom (K) kisom (s21) at 298 K

!CH3 (kprim) 2.4 3 1011 4240 1.63 105

!CH2! (ksec) 1.6 3 1011 3430 1.63 106

. CH! (ktert) 8 3 1010 2745 43 106

Table V Group Substituent Factors Fisom(X) for AlkoxyRadical Isomerizations

Substituent Group X Fisom(X) at 298 Ka

!CH3 1.00b

!CH2!. CH! 1.27. C,!OH 4.3

a Fisom(X) 5 eBx /T.b By definition [50].

6

ALKOXY AND b-HYDROXYALKOXY RADICALS 107

Scheme II

radicals (a d-hydroxyalkyl radical from the alkoxyradical and g,d- and d,e-dihydroxyalkyl radicals fromb-hydroxyalkoxy radicals) then add O2 to produce ad-hydroxyalkyl peroxy or g,d- or d,e-dihydroxyalkylperoxy radical [4], which then undergoes a sequenceof reactions similar to those of alkyl peroxy radicals[4]. In the presence of NO, the d-hydroxyalkyl per-oxy radical produced after isomerization of thealkoxy radical in the alkane degradation sequenceforms the d-hydroxyalkyl nitrate or the d-hydrox-yalkoxy radical plus NO2, and similarly for the dihy-droxyalkoxy radicals produced after isomerization ofthe b-hydroxyalkoxy radicals in the OH1 alkenedegradation sequence. The formation yields of thehydroxyalkyl nitrates and dihydroxyalkyl nitratesfrom the d-hydroxyalkyl and dihydroxyalkyl peroxyradical reactions with NO are not known, althoughEberhard et al. [7] have reported the formation of 2-hydroxy-5-hexyl nitrate as a product following theisomerization of the 2-hexoxy radical.

The hydroxyalkoxy and dihydroxyalkoxy radicalsformed from the hydroxyalkyl peroxy and dihydrox-yalkyl peroxy radical plus NO reactions are expectedto undergo a second isomerization if an abstractableH-atom is present. For example, the expected reac-tions of the 2-pentoxy (R5 CH3) and 1-hydroxy-2-pentoxy (R5 CH2OH) radicals formed from the OHradical-initiated reactions of n-pentane and 1-pentene,respectively, in the presence of NO and omitting or-ganic nitrate formation are shown in Scheme II.

The a-hydroxy radicals expected to be formedsubsequent to the second isomerization reaction, suchas the RC(OH)CH2CH2CH2OH radical formed inScheme II, are expected to react solely with O2 undertropospheric conditions to form the HO2 radical and acarbonyl [4]. For example, for the a-hydroxy radicalformed in Scheme II,

isomerization

O2

RCH(O)CH2CH2CH3 RCH(OH)CH2CH2CH2

RCH(OH)CH2CH2CH2O2

NO2NO

RCH(OH)CH2CH2CH2O

isomer

RC(OH)CH2CH2CH2OH

? ?

?

?

?

RC(OH)CH2CH2CH2OH 1 O2 9:RC(O)CH2CH2CH2OH 1 HO2 (12)

(R 5 CH3 and CH2OH), leading to the formation ofd-hydroxycarbonyls (in this case, 5-hydroxy-2-pen-tanone from the 2-pentoxy radical and 1,5-dihydroxy-2-pentanone from the 1-hydroxy-2-pentoxy radical).

The second isomerization is estimated to be gener-ally significantly more rapid than the first isomeriza-tion, and for the 2-pentoxy radical reactions shown inScheme II (R5 CH3) the first isomerization (of theCH3CH(O)CH2CH2CH3 radical) is calculated tohave a rate constant of kisom 5 2 3 105 s21 at 298 K,and the second isomerization (of the CH3CH(OH)CH2CH2CH2O radical) is calculated to have a rateconstant of ca. 23 107 s21 at 298 K, using the rateconstants and group substituent factors given in Ta-bles IV and V. The second isomerization then domi-nates over decomposition or reaction with O2. The re-sulting d-hydroxycarbonyls have recently beenobserved from the OH radical-initiated reactions ofthe n-alkanes n-butane through n-octane and n-pen-tane-d12 through n-octane-d18 using derivatization [7]and API-MS analyses [19,20], and dihydroxycar-bonyls have been observed from the OH radical-initi-ated reactions of 1-butene through 1-octene usingAPI-MS analyses [17].

Relative Importance of Alkoxy and b-Hydroxyalkoxy Radical Reactions underTropospheric Conditions

Rate constants for the decomposition, isomerization,and reaction with O2 of alkoxy and b-hydroxyalkoxyradicals at 298 K and in the presence of 760 torr totalpressure of air, calculated as described above, aregiven in Tables VI and VII for a series of alkoxy radi-

108 ATKINSON

cals and b-hydroxyalkoxy radicals, respectively, forwhich experimental data are available concerning therelative importance of the three reaction processesunder tropospheric conditions. For the alkoxy radi-cals for which data are available and given in TableVI, the dominant alkoxy radical reaction pathwaysare predicted correctly, and are well predicted quanti-tatively. Similarly, the dominant reaction pathwaysfor the b-hydroxyalkoxy radicals formed after OHradical addition to a series of alkenes are correctlypredicted (Table VII), although there are some quan-titative differences between the calculated rates andthe experimental data for the HOCH2CH2O radicalformed from ethene and the b-hydroxyalkoxy radi-cals formed from 1-pentene.

Considering that an uncertainty of 6 1 kcal mol21

in the Arrhenius activation energies for decomposi-tion or isomerization corresponds to an uncertainty inthe 298 K rate constant of a factor of 5, the agreementbetween the calculated rates of reaction and the (gen-erally qualitative or semi-quantitative) experimentaldata is good. This good agreement between predictedand experimental data for the tropospheric reactionsof the b-hydroxyalkoxy radicals formed from the OHradical reactions with alkenes appears to resolve alongtime problem for these particular alkoxy radicals[8,9]. Furthermore, extension of this approach to the OH radical-initiated reaction of isoprene in the presence of NO leads to predictions that the b-hydroxyalkoxy radicals (for example, HOCH2C(O)(CH3)CH"CH2) react by decomposition to givemethacrolein plus HCHO or methyl vinyl ketone plus

HCHO, and that the d-hydroxyalkoxy radicals (forexample, HOCH2C(CH3)"CHCH2O) react by iso-merization to yield unsaturated d-hydroxyaldehydes.These predictions are in agreement with experimentaldata [4,55] and with a recent detailed chemical mech-anism [56] for isoprene photooxidation.

Rate constants for the decomposition, isomeriza-tion, and O2 reactions can now be calculated as afunction of temperature, and hence the reaction ratesof the alkoxy and b-hydroxyalkoxy radicals can bepredicted for higher altitude conditions in the tropo-sphere. Because of the higher Arrhenius activationenergies for the decomposition and isomerization re-actions than for the reactions with O2, even allowingfor the reduced O2 concentrations at higher altitudesthe O2 reactions will become more dominant athigher altitudes in the troposphere. In particular, thedecomposition rate constants will decrease rapidlywith increasing altitude, by at least a factor of 100from 298 K to 220 K. Therefore, the dominant reac-tions of alkoxy and b-hydroxyalkoxy radicals canswitch from decomposition or isomerization beingdominant in the lower troposphere to the O2 reactionsdominating in the upper troposphere. For example,the rates of the O2 reactions with primary and sec-ondary alkoxy radicals are (4.1–4.9)3 104 s21 at298 K and 760 torr air and (4.5–5.5)3 103 s21 at220 K and 100 torr air, while isomerization involvingH-atom abstraction from a !CH3 group has a rateconstant of 2.03 105 s21 at 298 K and 1.43 103 s21

at 220 K. However, isomerizations involving H-atomabstraction from !CH2! and . CH! groups are

Table VI Calculated Reaction Rates of Alkoxy Radicals at 298 K and 760 Torr Total Pressure of Air, and Comparisonwith Experimental Observations

Experimental Calculated Reaction Rates (s21) (calculated ratio in parentheses)

RO kO2 [O2] kd kisom kd/kO2

[O2] kisom/kO2 [O2] Reference

Ethoxy 4.93 104 0.3 a ,, 1 [9]1-Propoxy 4.93 104 3.4 3 102 a ,, 1 [12]2-Propoxy 4.13 104 15 a ,, 1 [9]1-Butoxy 4.93 104 5.8 3 102 2.0 3 105 3.3 (4) [40,41,49]2-Butoxy 4.13 104 2.3 3 104 a 0.55 (0.6) [40,41]Neopentyloxy 4.93 104 2.5 3 105 a 39 (5) [43]

2.0 3 104 b 7.0 3 105 b (35)2-Pentoxy 4.13 104 1.7 3 104 2.0 3 105 6 (5) [19]3-Pentoxy 4.13 104 1.6 3 104 a 0.6 (0.4) [19]2-Hexoxy 4.13 104 2.8 3 104 2.0 3 106 0.7–6 (0.7) 33–114 (50) [7]3-Hexoxy 4.13 104 3.4 3 104 2.0 3 105 1.0–2.1 (0.8) 4–10 (5) [7]

a Isomerization via a 6-member transition state not possible.b Values of kO2

[O2] and kd are from eq. (IV) and eq. (V), respectively, using an O!H bond dissociation energy of 104 kcal mol21 to de-rive DHf (neopentyloxy).

AL

KO

XY

AN

Db

-HY

DR

OX

YAL

KO

XY

RA

DIC

AL

S109

Table VII Calculated Reaction Rates of b-Hydroxyalkoxy Radicals Formed from OH 1 Alkenes at 298 K and 760 Torr Total Pressure of Air, and Comparison withExperimental Observations

Experimental Calculated Reaction Rates (s21) (calculated ratio in parentheses)

Alkene RO kO2 [O2] kd kisom kd/kO2

[O2] kisom/kd Reference

Ethene HOCH2CH2O 4.9 3 104 4.6 3 103 a 3.6 (0.1) [14]

PropeneCH3CH(OH)CH2O 4.9 3 104 1.9 3 106 a

. 6 [13]CH3CH(O)CH2OH 4.13 104 9.1 3 104 a

1-ButeneCH3CH2CH(OH)CH2O 4.9 3 104 1.7 3 106 2.0 3 105

* 5 ca. 0.04 (0–0.1)d [15,17]CH3CH2CH(O)CH2OH 4.13 104 1.1 3 105 a

2-Butene CH3CH(OH)CH(O)CH3 4.1 3 104 2.7 3 107 a * 10 (73 102) [13]

1-PenteneCH3CH2CH2CH(OH)CH2O 4.9 3 104 1.6 3 106 2.0 3 106

* 3 ca. 0.2 (1.2–2)d [16,17]CH3CH2CH2CH(O)CH2OH 4.13 104 1.0 3 105 2.0 3 105

1-HexeneCH3CH2CH2CH2CH(OH)CH2O 4.9 3 104 2.0 3 106 2.0 3 106

c ca. 1 (1–13)d [16,17]CH3CH2CH2CH2CH(O)CH2OH 4.13 104 1.5 3 105 2.0 3 106

2-Methylpropene(CH3)2C(O)CH2OH b 5.0 3 105 a

* 4c [54](CH3)2C(OH)CH2O 4.9 3 104 1.4 3 107 a

a Isomerization via a 6-member transition state impossible.b No a-H present and hence no O2 reaction possible.c No evidence for the O2 reaction observed from API-MS analysis [17,54].d The calculated ratio depends on the relative fractions of the two b-hydroxyalkoxy formed from the OH radical reaction with the alkene.

656

66

6

5

555

110 ATKINSON

predicted to dominate over reaction with O2 through-out the troposphere.

The estimation methods proposed here for the cal-culation of rate constants for the decomposition, iso-merization, and reaction with O2 of the alkoxy radi-cals formed from alkanes and b-hydroxyalkoxyradicals formed from alkenes can be extended to b-nitrooxyalkoxy radicals formed from the NO3 radicalreactions with alkenes and to alkoxy radicals formedfrom oxygenates such as alcohols [21] and ketones[22]. However, extension of the present methods tothe alkoxy radicals involved in the atmosphericdegradations of ethers [3] and esters, especially forthe calculation of decomposition rate constants forthese types of alkoxy radicals, remains to be ex-plored. As noted above, the estimation methods pro-posed here are only applicable to tropospheric condi-tions and should not be used for combustion systems.

This work was carried out under Contract ARA-1995-01 toAtmospheric Research Associates, Inc. (M. W. Gery) insupport of the U.S. Environmental Protection AgencyPrime Contract 68D50129 to H. E. Jeffries at the Universityof North Carolina (D. J. Leucken, Project Officer). Al-though the research described in this article has beenfunded by the U.S. Environmental Protection Agency, it hasnot been subjected to Agency review and therefore does notnecessarily reflect the views of the Agency and no officialendorsement should be inferred.

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