Temperature dependence of the rate coefficients for β-hydroxyperoxy radical self reactions

Article abstract of DOI:10.1002/(SICI)1097-4601(1997)29:5<323::AID-KIN2>3.0.CO;2-W

A laser flash photolysis/UV absorption technique was used to study the temperature dependence of the self-reaction kinetics of representative primary, secondary, and tertiary β-hydroxyperoxy radicals. Arrhenius expressions were derived for the rate coefficient of reactions and for the product branching ratios of reaction as a function of temperature. The product branching ratios and the Arrhenius parameters were compared with those for other substituted and unsubstituted peroxy radical self reactions.

Full text of DOI:10.1002/(SICI)1097-4601(1997)29:5<323::AID-KIN2>3.0.CO;2-W

The Temperature
Dependence of the Rate
Coefficients for
␤-Hydroxyperoxy
Radical Self Reactions
ANDREW A. BOYD, ROBERT LESCLAUX
Laboratoire de Photophysique et Photochimie Moléculaire, Université Bordeaux I, 33405 Talence Cedex, France
Received 28 May 1996; accepted 12 September 1996
ABSTRACT: A laser-flash photolysis/UV absorption technique has been used to study the tem-
perature dependence (from T ϭ 300–470 K) of the self-reaction kinetics of representative pri-
mary, secondary, and tertiary ␤-hydroxyperoxy radicals:
2 HOCH2CH2O2 9: 2 HOCH2CH2O ϩ O2
9: HOCH2CH2OH ϩ HOCH2CHO ϩ O2
(1a)
(1b)
(2a)
2 HOCH(CH3)CH(CH3)O2 9: 2 HOCH(CH3)CH(CH3)O ϩ O2
9: HOCH(CH3)CH(CH3)OH
ϩ HOCH(CH3)C(CH3)O ϩ O2
(2b)
(3)
2 HOC(CH3)2C(CH3)2O2 9: 2 HOC(CH3)2C(CH3)2O ϩ O2
The following Arrhenius expressions were derived for the rate coefficients of reactions (1)–(3)
(in cm3moleculeϪ sϪ ) and for the product branching ratios of reactions (1) and (2) as a func-
1
1
tion of temperature (all errors 1␴):
k1 ϭ (6.9ϩ 1.5) ϫ 10Ϫ14 exp[(1040 Ϯ 100)/T]
Ϫ
2.1
1700) exp[(Ϫ2400 Ϯ 280)/T] (where ␤1 ϭ k1a/k1b)
Ϫ
␤1 ϭ (3100ϩ
k2 ϭ (7.7ϩ
3700
4.8) ϫ 10Ϫ15 exp[(1330 Ϯ 350)/T]
Ϫ
12.8
␤2 ϭ (4.0ϩ 0.1) ϫ 104 exp[(Ϫ3600 Ϯ 100)/T]
Ϫ
0.2
k3 ϭ (4.7ϩ 2.7) ϫ 10Ϫ13 exp[(Ϫ1420 Ϯ 320)/T]
Ϫ
6.5
The calculated rate coefficients for reactions (1)–(3) at 298 K are therefore (in 10Ϫ13 cm3mole-
1
1
culeϪ sϪ ) 23 Ϯ 2, 6.7 Ϯ 1.3, and 0.040 Ϯ 0.012, respectively, which compare well with the
values measured elsewhere at this temperature using a similar technique. The product
branching ratios and the Arrhenius parameters are compared with those for other substituted
and unsubstituted peroxy radical self reactions. © 1997 John Wiley & Sons, Inc. Int J Chem Kinet
29: 323–331, 1997.
Correspondence to: R. Lesclaux
© 1997 John Wiley & Sons, Inc.
CCC 0538-8066/97/050323-09

324
BOYD AND LESCLAUX
tion for this ␤-hydroxyperoxy self reaction (␣1 ϭ
k1a/k1 ϭ 0.5 [7]). A study of reaction (1) has also
been reported by Anastasi et al. [8], who found a
INTRODUCTION
The addition of the hydroxy radical to alkenes leads,
under tropospheric conditions, to the formation of
peroxy radicals with an OH group in the ␤ position to
the carbon possessing the peroxy functionality [1].
Kinetic studies of such reaction systems containing
␤-hydroxyperoxy radicals are thus important in un-
derstanding the atmospheric oxidation of alkenes,
which are an important class of volatile organic com-
pound (VOC). In the absence of NOx , reactions of
such radicals with HO2 , with themselves (self reac-
tions), and with other peroxy radicals (cross reac-
tions) may be in competition [2]. While the cross re-
12
1
1
value for k1 of 7.7 ϫ 10Ϫ cm3moleculeϪ sϪ , the
difference between their value and the preferred value
of Jenkin and Hayman having been previously ex-
plained [9]. For reaction (2), no branching ratio mea-
surement had been carried out and this is reflected in
the large uncertainty range for k2 at room temperature
(corresponding to the branching ratio extremes of 0
and 1 and hence a k2 range given by kobs/(1 ϩ ␣2)
where kobs is the measured global second-order rate
coefficient for HOCH2CH2O2 loss).
In this article we have used a laser-flash photolysis
technique to extend measurements of the self-reaction
rate coefficients to elevated temperatures, allowing
the Arrhenius parameters for reactions (1)–(3) and
also the branching ratios for reactions (1) and (2) to
be derived where possible. Possible trends are high-
lighted for these parameters and comparisons are
made with corresponding data available for the self
reactions of other classes and sizes of peroxy radical.
actions of
a peroxy radical with CH3O2 or
CH3C(O)O2 are generally more important than its
self reaction from an atmospheric point of view, in-
vestigations of self-reaction kinetics nevertheless re-
main essential in laboratory studies used to determine
cross-reaction rate coefficients. Furthermore, the re-
sults are of use in improving the validity of tropos-
pheric degradation models both for these simple
alkenes and for more complex unsaturated VOCs,
since such models rely on the extrapolation of struc-
ture-reactivity relationships based on the kinetics of
various types of RO2 radical [2–5].
EXPERIMENTAL
Jenkin and Hayman recently reported [6] revised
room temperature measurements of the UV absorp-
tion spectra of three simple primary, secondary, and
tertiary ␤-hydroxyperoxy radicals and the following
rate coefficients for their self reactions (1)–(3) at
298 K.
The laser-flash photolysis technique and radical-gen-
eration method used have both recently been de-
scribed in detail [4,6,10]. In summary, hydroxy radi-
cals are generated by the longitudinal laser-flash
photolysis (at ␭ ϭ 248 nm) of H2O2 flowing slowly
through a heatable cell (70 cm long, 1.5 or 2.3 cm
i.d.) at atmospheric pressure. This leads, in the pres-
ence of excess O2 and the appropriate alkene, to the
formation of the ␤-hydroxyperoxy radical of interest
on a near instantaneous timescale compared to that
for its subsequent decay, the decay being monitored
by UV absorption spectrometry. For example, with
ethylene:
2 HOCH2CH2O2 9: 2 HOCH2CH2O ϩ O2
(1a)
(1b)
9: HOCH2CH2OH
ϩ HOCH2CHO ϩ O2
k1 ϭ 2.1 ϫ 10Ϫ cm3moleculeϪ sϪ
12
1
1
2 HOCH(CH3)CH(CH3)O2 9:
2 HOCH(CH3)CH(CH3)O ϩ O2 (2a)
H2O2 ϩ h␯ 9: 2 OH
(4)
9: HOCH(CH3)CH(CH3)OH
9
2 9
HO ϩ CH
CH ϩ M 9: HOCH CH ϩ M
2 2 2
ϩ HOCH(CH3)C(CH3)O ϩ O2 (2b)
(5)
13
1
1
k2 ϭ (4.2 Ϫ 8.4) ϫ 10Ϫ cm3moleculeϪ sϪ
12
1
k5 (298 K) ϭ 9 ϫ 10Ϫ cm3moleculeϪ sϪ1 in 1 atm
of air [11]
2 HOC(CH3)2C(CH3)2O2 9:
2 HOC(CH3)2C(CH3)2O ϩ O2 (3)
HOCH2CH2 ϩ O2 ϩ M 9: HOCH2CH2O2 ϩ M
(6)
15
1
1
k3 ϭ 5.7 ϫ 10Ϫ cm3moleculeϪ sϪ
k6 (298 K) ϭ 3 ϫ 10Ϫ cm3moleculeϪ sϪ1 in 1 atm
12
1
For reaction (1), Jenkin and Hayman derived their
rate coefficient using the only previous reported study
of the branching ratio towards alkoxy radical forma-
of air [1]
Similar reaction schemes with excess trans-2-

TEMPERATURE DEPENDENCE OF RATE COEFFICIENTS
325
butene and 2,3-dimethyl-2-butene (tetramethyl-
2 HOC(R’)(R”)C(R’)(R”)O2 9:
2 HOC(R’)(R”)C(R’)(R”)O ϩ O2
ethylene, TME) lead to the stoichiometric con-
version of OH into HOCH(CH3)CH(CH3)O2 and
HOC(CH3)2C(CH3)2O2 radicals [1,6,11]. The purities
of the gases and precursor alkenes used were as fol-
lows: N2 (AGA Gaz Spéciaux, Ͼ99.995%), O2
(AGA, Ͼ 99.995%), C2H4 (AGA, 99%), C4H8
(Aldrich, Ͼ 99%), and C6H12 (Aldrich, Ͼ 99%). The
low vapor pressure of hydrogen peroxide required the
passage of most of the nitrogen or synthetic air car-
rier gas through a bubbler containing a concentrated
solution of H2O2 (85%, Air Liquide). Resulting gas-
phase hydrogen peroxide concentrations were in the
␣
3 ϫ k1 3 (see text)
1
Ϫ
Ϫ
HOC(R’)(R”)C(R’)(R”)O ϩ M 9:
HOCR’R” ϩ R’C(O)R” ϩ M (fast) [Ref. [1]]
HOC(R’)(R”) ϩ O2 9:
R’C(O)R” ϩ HO2 (fast) [Ref. [1]]
HOC(R’)(R”)C(R’)(R”)O2 ϩ HO2 9:
HOC(R’)(R”)C(R’)(R”)OOH ϩ O2 k8 (see text)
HO2 ϩ HO2 9:
H2O2 k9 [Ref. [12]]
3
range 0.9–2.8 ϫ 1016 molecule cmϪ , as measured
by absorption at 220 nm (where ␴ (H2O2) ϭ 2.6 ϫ
The molecular channel of the generalized self-reac-
tion is not included because the products of this chan-
nel neither absorb significantly nor react with any
other absorbing species during the subsequent sec-
ondary chemistry and thus are not required in the
mechanism used to analyze decay curves. The kinetic
model does however still contain a term for the total
loss of peroxy radicals by both channels. None of the
carbonyl compounds resulting from either alkoxy
radical decomposition or subsequent reaction of the
hydroxyalkyl radical produced with O2 are likely to
contribute significantly to the total absorbance at the
UV analysis wavelengths of interest. Hence, only
HO2 , H2O2 , and the corresponding alkyl hydroperox-
ide (taken equivalent to CH3OOH) had to be taken
into account as products in the kinetic simulations at
220 nm (with inclusion of their known absorption
cross sections [12]).
19
1
10Ϫ cm2moleculeϪ ) and yielding initial OH con-
3
centrations of 2.5–8.5 ϫ 1013 molecule cmϪ . The
determination of OH radical concentrations was
through simulation of the initial HO2 absorbance sig-
nal obtained in the absence of alkene (using the
known HO2 cross section at 220 nm). The OH radical
was rapidly converted to HO2 in the absence of
alkene by the reaction:
HO ϩ H2O2 9: H2O ϩ HO2
(7)
12
1
k7 (298 K) ϭ 1.7 ϫ 10Ϫ cm3moleculeϪ sϪ1 [12]
Allowances were also made in the kinetic model for
minor signal contributions from H2O2 photolysis and
the reactions of HO2 with OH and with itself.
Dichroic mirrors allowed only light in the wave-
length range 235–265 nm to be reflected through the
cell (including the photolyzing laser radiation at 248
nm) and hence restricted the transmitted analysis
wavelengths provided by a deuterium lamp source to
those regions where the peroxy radicals absorb on ei-
ther side of this range. Radical decays were therefore
generally monitored at 220 and 270 or 280 nm for a
given set of experimental conditions, with the signal-
to-noise ratio being improved by the averaging of
several tens of such decays.
Kinetics and Branching Ratio of Reaction 1
Kinetic decays corresponding to the self reaction of
the HOCH2CH2O2 radical and associated secondary
chemistry were recorded at analysis wavelengths of
220, 270, and 280 nm. Figure 1 shows typical decay
traces obtained at T ϭ (400 Ϯ 2) K. Extrapolation to
t ϭ 0 for decays recorded over shorter timescales
both in the presence and absence of ethylene allowed
the absorption cross section of the radical of interest
to be measured relative to that known for HO2 at a
given wavelength, as described by Jenkin and Hay-
man [6]. Use of the same HOCH2CH2O2 cross sec-
tions determined by Jenkin and Hayman indicated the
correct starting point for the simulation if the previ-
ously estimated initial concentration of HO2 was
used, confirming their cross sections at these wave-
lengths [6] and allowing accurate initial radical con-
centrations to be employed in the kinetic simula-
tions.
RESULTS AND DISCUSSION
Reaction Mechanism used for Kinetic
Simulations
The following general mechanism was used in kinetic
simulations and was valid for all three reaction sys-
tems (comprising reactions (1), (2), or (3) and their
associated secondary chemistry, where R’, R” ϭ H or
CH3):

326
BOYD AND LESCLAUX
Figure 2 Arrhenius plots for the self reactions of
the ␤-hydroxyperoxy radicals: (᭹)–HOCH2CH2O2 ;
(᭝)–HOCH(CH3)CH(CH3)O2 ; and (᭜)–HOC(CH3)2C-
(CH3)2O2 . Filled symbols, this work; open symbols, room
temperature data of Jenkin and Hayman [6] for comparison.
under identical experimental conditions but at differ-
ent analysis wavelengths [10]. At elevated tempera-
tures, the rate coefficient for the secondary reaction
with HO2 (k8) was estimated by calculating the pre-
exponential factor A using the literature value at
Figure 1 Typical decay traces obtained over 60 ms reac-
tion time for the HOCH2CH2O2 self reaction at T ϭ 400 K
and analysis wavelengths of (a) 270 nm and (b) 220 nm.
The simulated lines used to extract k1 and ␣1 show the con-
tributions of various absorbing species to the total ab-
sorbance profile, the best-fit simulations for both traces be-
ing obtained iteratively using [HOCH2CH2O2]0 ϭ 2.5 ϫ
11
1
1
room temperature (1.5 ϫ 10Ϫ cm3moleculeϪ sϪ
[16]) and a temperature dependence similar to that
recently measured for HOC(CH3)2CH2O2 ϩ HO2
(E/R ϭ Ϫ1650 K) [13], and then extrapolating to
the temperature of interest. The derived values of k1
and ␣1 at each of the temperatures studied are given
in Table I. The Arrhenius plot for k1 is shown in
Figure 2 along with the room temperature value
of Jenkin and Hayman for comparison [6], while
Figure 3 includes the temperature dependence of ␣1
in the form ␤1 ϭ ␣1/(␣1 Ϫ 1) vs. 1/T for T ϭ
303–470 K. The best fits shown correspond to the
linear regressions (errors 1␴):
1013 molecule cmϪ and the optimized parameters ␣1 ϭ
3
0.90 Ϯ 0.06, k1 ϭ (9.6 Ϯ 0.5) ϫ 10Ϫ cm3moleculeϪ sϪ
.
13
1
1
The errors quoted for the optimized parameters result from
the nonlinear least-squares fitting procedure.
In particular, the different contributions of HO2
(formed from the alkoxy-radical-forming channel 1a)
to the total absorption at 220 nm and 270/280 nm
allowed the value of the branching ratio ␣1 to be
estimated, as described previously using an iterative
procedure performed for a pair of decays recorded
k1 ϭ (6.9ϩ 1.5) ϫ 10Ϫ14 exp[(1040 Ϯ 100)/T ]
Ϫ
2.1
1
1
cm3moleculeϪ sϪ
␤1 ϭ (3100ϩ
1700) exp[(Ϫ2400 Ϯ 280)/T ]
Ϫ
3700
Table I Rate Coefficients and Branching Ratios Derived for the HOCH2CH2O2 Radical Self
Reaction (1) as a Function of Temperature
a
12
1
1
b
T/K
k1 /10Ϫ cm3moleculeϪ sϪ
No. of Meas.
␣
1
303
352
400
422
470
2.35 Ϯ 0.21
1.20 Ϯ 0.12
0.98 Ϯ 0.12
0.84 Ϯ 0.14
0.66 Ϯ 0.03
5
5
3
2
3
0.55 Ϯ 0.04
0.73 Ϯ 0.08
0.90 Ϯ 0.06
0.91 Ϯ 0.08
Ϸ1
a Errors 1␴ for number of measurements indicated.
b Errors based on best fit to two pairs of decays recorded at 220 and 270 (or 280) nm.

TEMPERATURE DEPENDENCE OF RATE COEFFICIENTS
327
ing the common chemical mechanism shown above,
the known room temperature value for k8 of 1.5 ϫ
11
1
1
10Ϫ cm3moleculeϪ sϪ , and an assumed tempera-
ture dependence for reaction (8) of Ϫ1300 K, i.e.,
similar to that measured for other secondary peroxy
radical reactions with HO2 [12]). This room tempera-
ture branching ratio could also be estimated to lie in
the range 0.1–0.3 by using the k2 values measured
here at 351 and 421 K and an assumed temperature
dependence of 1750 K (the average of the E/R values
measured for two other secondary peroxy radicals
[14]). The results are summarized in Table II, with
Figure 2 showing the Arrhenius plot for reaction (2)
for T ϭ 303–421 K (with the value of Jenkin and
Hayman measured at 298 K for comparison), and
corresponding to:
Figure 3 Plots of ln ␤ vs. 1/T for the HOCH2CH2O2 (᭹)
and HOCH(CH3)CH(CH3)O2 (ᮀ) self reactions (␤ ϭ ␣/
(1 Ϫ ␣), ␣1 ϭ k1a/k1 and ␣2 ϭ k2a/k2).
Kinetics and Branching Ratio of Reaction 2
k2 ϭ (7.7ϩ
4.8) ϫ 10Ϫ15 exp[(1330 Ϯ 350)/T]
Ϫ
12.8
1
1
cm3moleculeϪ sϪ
As with reaction 1, absorption cross sections of the
HOCH(CH3)CH(CH3)O2 radical from the previously
measured spectrum of Jenkin and Hayman [6] were
used to estimate the initial concentration at the wave-
lengths of interest. Such concentrations again agreed
with the initial concentration of HO2 radicals mea-
sured in the absence of trans-2-butene (allowing for
an error of around 5% in extrapolating the signals
to t ϭ 0), confirming their absorption cross sections.
A typical decay recorded at 270 nm is shown in Fig-
ure 4. At room temperature, very little deviation from
second order behavior was detected at 220 nm, with
␣2 requiring a value of Յ 0.3 in the model to repro-
duce well the shape of the experimental decays
recorded at this wavelength. In contrast, at higher
temperatures, a good fit to decays at both 220 and
270 nm could only be obtained for iterated values of
k2 and a significantly greater branching ratio for the
reaction channel towards alkoxy radical products (us-
Although ␣2 was only accurately derived at two tem-
peratures, fixing ␣2 a reasonable room temperature
value of 0.2 allowed an approximate representation of
␤2 as a function of temperature to be derived (Fig. 3):
␤2 ϭ (4.0ϩ 0.1) ϫ 104 exp[Ϫ(3600 Ϯ 100)/T ]
Ϫ
0.2
(errors 1␴, precision only)
Furthermore, this expression could be used to esti-
mate ␣2 at 393 K and thus to derive k2 at this tem-
perature where, for technical reasons, no direct
branching ratio measurement had been performed
(see Table II).
Kinetics of Reaction 3
A typical decay recorded at 270 nm for self reaction
(3) is shown in Figure 5. Again, measured initial radi-
cal concentrations and those estimated using the
spectrum of Jenkin and Hayman [6] for this radical
were in good agreement. The tetramethylethylene
precursor absorbed a large fraction of the incident
light intensity of the deuterium lamp at 220 nm and
hence no decays with a reasonable signal-to-noise ra-
tio could be recorded at this wavelength. The lack of
an abstractable hydrogen atom on the peroxy carbon
in the radical concerned means that the branching ra-
tio, by definition, is unity and the reaction proceeds
completely via t-alkoxy radical formation, followed
by its rapid decomposition and the subsequent sec-
ondary chemistry included in the general mechanism
Figure
4
Typical decay trace obtained for the
HOCH(CH3)CH(CH3)O2 self reaction at T ϭ 392 K and
270 nm. The best-fit simulation shown was obtained using
[HOC(CH3)C(CH3)O2]0 ϭ 6.9 ϫ 1013 molecule cmϪ , ␣2
estimated at 0.8 (see text), and with the optimized parame-
ter k2 ϭ (1.97 Ϯ 0.02) ϫ 10Ϫ cm3moleculeϪ sϪ
3
11
given above (with k8 taken as 1.5 ϫ 10Ϫ cm3mole-
1
1
13
1
1
.
culeϪ sϪ at room temperature [6]). At higher tem-

328
BOYD AND LESCLAUX
Table II Rate Coefficients and Branching Ratios Derived for the HOCH(CH3)CH(CH3)O2
Radical Self Reaction (2) as a Function of Temperature
a
13
1
1
T/K
k2 /10Ϫ cm3moleculeϪ sϪ
No. of Meas.
␣
2
303
351
392
421
6.79 Ϯ 0.41
2.81 Ϯ 0.24
1.88 Ϯ 0.09
0.84 Ϯ 0.14
5
5
4
4
0.2b
0.56 Ϯ 0.05c
0.8d
0.88 Ϯ 0.10c
a Errors 1␴.
b Fixed at this value in simulations used to derive k2 at 303 K (see text).
c Errors based on best fit to two pairs of decays recorded at 220 and 270 (or 280) nm.
d Estimated using the expression derived for ␤2 as a function of temperature and then fixed at this value in
simulations used to derive k2 at 393 K (see text).
peratures, the rate coefficient for the secondary reac-
tion (8) was again estimated using a similar tempera-
ture dependence to that for the reaction
HOC(CH3)2CH2O2 ϩ HO2 [13]. Figure 2 shows the
Arrhenius plot for reaction (3) using the results from
Table III for T ϭ 307–448 K and again with the
room temperature measurement of Jenkin and Hay-
man for comparison. The best-fit linear regression
corresponds to:
of a different alkoxy radical decomposition mecha-
nism at such elevated temperatures [11].
Structure-Reactivity Trends
It is of interest to compare the kinetic and product
yield data of the peroxy radical self reactions studied
here with those of other related substituted and un-
substituted peroxy radicals of various sizes. Table IV
shows these collected data, grouping peroxy radicals
as primary, secondary, and tertiary according to their
previously recognized general reactivities (kprim Ͼ
ks Ͼ ktert) [15], but with the recently recommended
parameters of Lesclaux [16].
Product Branching Ratios. From Table IV, the
striking feature of the room temperature product
branching ratios (␣298) for the self reactions of the
eight primary peroxy radicals of size ՆC2 , is that,
whether unsubstituted or ␤-substituted, all such reac-
tions have a value for this parameter in the range
0.4–0.65, irrespective of the size of the radical or the
nature of the ␤ substituent. Thus, it would appear that
a reasonable recommended mean value for this class
of peroxy radical self reaction would be ␣ ϭ 0.55 Ϯ
0.10 at 298 K. For secondary radical self reactions,
the branching ratio is generally slightly lower than for
k3 ϭ (4.7ϩ 2.7) ϫ 10Ϫ13 exp[(Ϫ1420 Ϯ 320)/T ]
Ϫ
6.5
1
1
cm3moleculeϪ sϪ
with the errors again representing 1␴.
Some rate coefficient measurements were also at-
tempted at more elevated temperatures (up to 540 K)
but did not fit well to the above Arrhenius relation-
ship, the deviation suggesting a change in the mecha-
nism used in the simulations. The discrepancy may
be at least in part explained by increasing competition
between H-atom abstraction by OH and its addition
to the double bond, combined perhaps with the onset
Table III Rate Coefficients Derived for the
HOC(CH3)2C(CH3)2O2 Radical Self Reaction (3) as a
Function of Temperature
a,b
14
1
1
T/K
k3 /10Ϫ cm3moleculeϪ sϪ
No. of Meas.
307
357
395
409
448
0.55 Ϯ 0.08
0.66 Ϯ 0.15
1.30 Ϯ 0.12
1.19 Ϯ 0.16
2.58 Ϯ 0.20
2
3
3
3
5
Figure
5
Typical decay trace obtained for HOC-
(CH3)2C(CH3)2O2 self reaction at T ϭ 409 K and 270 nm.
The best-fit simulation shown over 250 ms was obtained
using [HOC(CH3)C(CH3)O2]0 ϭ 4.8 ϫ 1013 molecule
3
cmϪ and with the optimized parameter k3 ϭ (1.13 Ϯ
a ␣3 ϭ 1.
b Errors 1␴.
0.02) ϫ 10Ϫ cm3moleculeϪ sϪ
.
14
1
1

TEMPERATURE DEPENDENCE OF RATE COEFFICIENTS
329
Table IV Arrhenius Parameters for the Self Reactions of ␤-Hydroxyperoxy Radicals and
some Related Alkylperoxy Self Reactions
Radical
k(298 K)a
Aa
E/Rb
␣
Ref.
298
primary
HOCH2CH2O2
12
12
12
12
12
12
12
13
12
14
14
2.3 ϫ 10Ϫ
2.1 ϫ 10Ϫ
7.7 ϫ 10Ϫ
5.6 ϫ 10Ϫ
3.3 ϫ 10Ϫ
4.6 ϫ 10Ϫ
7.7 ϫ 10Ϫ
6.8 ϫ 10Ϫ
1.2 ϫ 10Ϫ
6.8 ϫ 10Ϫ
6.9 ϫ 10Ϫ
Ϫ1040
0.50c
0.50
This work
[6,7]
[8]
[17,18]
[16]
[12]
[19]
[5,10]
[16]
[16]
14
13
14
14
14
15
14
BrCH2CH2O2
ClCH2CH2O2
HOC(CH3)2CH2O2
C6H5CH2O2
9
5.4 ϫ 10Ϫ
1.1 ϫ 10Ϫ
1.4 ϫ 10Ϫ
2.7 ϫ 10Ϫ
5.4 ϫ 10Ϫ
1.7 ϫ 10Ϫ
6.8 ϫ 10Ϫ
Ϫ1390
Ϫ1020
Ϫ1740
Ϫ1680
Ϫ760
Ϫ1961
0
0.57
0.69
0.60
0.40
0.61
0.41
0.63
CH
CHCH O
2 9
2
2
neo-C5H11O2
C2H5O2
secondary
HOCH(CH3)CH(CH3)O2
13
13
13
15
14
14
15
6.7 ϫ 10Ϫ
7 ϫ 10Ϫ
6.8 ϫ 10Ϫ
1.1 ϫ 10Ϫ
4.5 ϫ 10Ϫ
4.2 ϫ 10Ϫ
7.7 ϫ 10Ϫ
Ϫ1330
Ϸ0.2c
This work
[6]d
[17,18]
[12]
[14]
[14]
Ϸ0.5c
0.56
–
14
12
13
14
BrCH(CH3)CH(CH3)O2
i-C3H7O2
c-C5H9O2
1.3 ϫ 10Ϫ
1.7 ϫ 10Ϫ
2.9 ϫ 10Ϫ
7.7 ϫ 10Ϫ
Ϫ1185
2188
555
c-C6H11O2
184
0.30
tertiary
HOC(CH3)2C(CH3)2O2
15
15
14
17
13
4.0 ϫ 10Ϫ
5.7 ϫ 10Ϫ
2.5 ϫ 10Ϫ
3.0 ϫ 10Ϫ
4.7 ϫ 10Ϫ
1420
1.00e
This work
[6]
[17]
BrC(CH3)2C(CH3)2O2
t-C4H9O2
–
–
4200
1.00e
1.00e
11
4.0 ϫ 10Ϫ
[15]
a Units cm3moleculeϪ sϪ , calculated using the Arrhenius parameters shown.
b Units, K.
1
1
c Calculated using the appropriate expression for ␤ as a function of temperature.
d Calculated using the kobs value of Jenkin and Hayman and ␣ ϭ 0.2 as estimated here (kobs ϭ k2(1 ϩ ␣2)).
e By definition for a tertiary peroxy radical self reaction assuming no adduct formation under these
conditions.
primary radicals, an effect which might be related to
the fact that the C9H bond dissociation energy is
lower in the case of the secondary radical, thus favor-
ing the internal H-atom transfer in the intermediate
RO4R complex which leads molecular products
(channel b). The variations of ␤1 and ␤2 with temper-
ature are the first to be investigated for ␤-substituted
peroxy radicals and show positive ‘activation ener-
gies’ which are larger than those reported for other
peroxy radical self reactions [15]. However, a limited
database and large total uncertainty in these expres-
sions (particularly in the measured preexponential
factors), preclude the drawing of more detailed con-
clusions between the temperature dependence of ␤
and the structure of the peroxy radical.
(HOCH2CH2O2 , BrCH2CH2O2 , ClCH2CH2O2) have
all, within a factor of two, the same preexponential
13
1
1
factors (A ϭ (0.5–1) ϫ 10Ϫ
cm3moleculeϪ sϪ )
and similar, fairly large, ‘negative’ activation energies
(E/R ϭ Ϫ(1000–1400) K). The ethylperoxy self re-
action also has a preexponential factor in this range
but shows practically no variation with temperature
so that the difference in activation energy alone ap-
pears to explain why the rate coefficient at room tem-
perature is some 30–50 times smaller for C2H5O2
than for the substituted radicals.
A similar enhancement of the self-reaction rate
constant has also been observed for several types of
␣-substituted peroxy radicals [13], suggesting that
this large substituent effect is independent of whether
the substituent is in the ␣ or ␤ position. It would be
worthwhile assessing up to which distance this sub-
stituent effect is significant. In particular, any effect
induced by the presence of a ␦-OH group could be
important for peroxy radicals formed from the 1,5
isomerization of alkoxy radicals formed during the
oxidation of ՆC5 alkanes and during the OH-initi-
Arrhenius Parameters. Some general comments
can be made concerning apparent trends in the Arrhe-
nius parameters measured for the self reactions of
substituted primary, secondary, and tertiary peroxy
radicals (see Table IV).
For primary radical reactions, the three C2 radicals
which have been studied possessing a ␤-substituent

330
BOYD AND LESCLAUX
ated oxidation of dienes such as isoprene [1,6]. Un-
fortunately, to date, there is no known method for the
clean generation of ␦-hydroxyperoxy radicals under
conditions which would allow us to study their self-
reaction kinetics. Upon passing to larger primary per-
oxy radicals, the rate constant enhancement induced
by the presence of the hydroxyl group seems lower
than for C1 or C2 radicals. For example, the room
temperature rate constant is only four times larger for
the self reaction of (CH3)2C(OH)CH2O2 than for
(CH3)3CCH2O2 . It must be pointed out, however, that
the rate constant for the neopentylperoxy radical self
reaction is already significantly enhanced compared
to that for C2H5O2 (Table IV), probably as a result of
the larger number of carbon atoms, as suggested re-
cently [16]. It should be noted that this enhancement
in reactivity for such large radicals is accompanied by
a significantly larger negative temperature depen-
dence (ER ϭ Ϫ(1700–2000) K).
It would also appear that the enhancement of reac-
tivity for self reactions appears to be independent of
whether the peroxy radical substituent is an electron-
withdrawing group (such as a halogen atom) or an
electron-donating group (such as CH3O). All such
substituents result in similar enhancements of the rate
constant [15]. In contrast, the double bond in the al-
lylperoxy radical has only a minor effect when com-
pared with the n-propylperoxy radical, whereas the
aromatic group in benzylperoxy induces a large en-
hancement, mainly resulting from a large increase in
the negative temperature dependence [12]. Unfortu-
nately, there is no current way of rationalizing these
observations in terms of potential energy barriers on
the reaction coordinate or of transition-state struc-
tures since no determinations of the molecular prop-
erties of such complex systems have as yet been re-
ported.
As far as secondary radicals are concerned, the
striking feature is the inversion of the temperature de-
pendence resulting from ␤-substitution involving OH
or Br [17] compared to unsubstituted secondary alkyl
or cycloalkylperoxy radicals (Table IV). This differ-
ence is principally responsible for an enhancement of
the room temperature rate constant by up to two or-
ders of magnitude where ␤ substitution is present.
However, values remain a factor of 3 to 10 smaller
than the rate constants for substituted primary radi-
cals, a difference which would appear to be essen-
tially determined by a smaller preexponential factor
for substituted secondary radical reactions. Thus, as
previously pointed out [6], a higher reactivity is ob-
served for ␤-substituted primary radicals than for sec-
ondary radicals, but the difference is much smaller
than that between unsubstituted primary and sec-
ondary alkylperoxy radicals (Table IV).
In the case of tertiary peroxy radicals, the activa-
tion energy is positive for the OH-substituted peroxy
radical, but much smaller than for the tert-butylper-
oxy radical self reaction, resulting in a two orders of
magnitude increase of the room temperature rate con-
stant upon substitution. However, general trends can-
not be given for this type of reaction as this is only
the second reported measurement of the temperature
dependence of a tertiary peroxy radical self reaction.
The predicted positive temperature dependence was
impossible to confirm for the ␤-brominated tertiary
radical owing to mechanistic complications at higher
temperatures [17]. Nevertheless, at room temperature,
the rate constant enhancement is even larger than for
the OH-substituted radical (see Table IV).
CONCLUSIONS AND
RECOMMENDATIONS
Lesclaux has recently summarized the available data
on peroxy radical self reactions, making some tenta-
tive recommendations concerning individual rate pa-
rameters and structure-reactivity trends [16]. Our val-
ues presented therein for the Arrhenius parameters of
reactions (1)–(3) differ slightly from those presented
herein since we have decided here not to include the
room temperature data of Jenkin and Hayman [6],
which were taken into account in our original Arrhe-
nius plots [20].
The data presented in this article on the branching
ratios and Arrhenius parameters of primary ␤-hydrox-
yperoxy radicals have been used in part to form the
rate coefficient recommendations of Lesclaux [16]
and may even allow some predictions for primary and
secondary peroxy radicals to be made with slightly
more confidence. We now suggest that for all primary
peroxy radical self reactions for radicals of size
Ն C2 , the branching ratio towards alkoxy radical for-
mation, ␣, at room temperature can be taken as
0.55 Ϯ 0.10. Also, for ␤-substituted primary radi-
cals of size Ն C2 (where the substituent is OH, a
halogen atom, or an aryl group) we recommend that
the self reaction rate constant at room temperature
12
1
1
be taken as (5 Ϯ 2) ϫ 10Ϫ cm3moleculeϪ sϪ with
14
1
1
A ϭ (6 Ϯ 4) ϫ 10Ϫ cm3moleculeϪ sϪ and Ea/R ϭ
Ϫ(1400 Ϯ 300) K (averages for the five such peroxy
radicals studied to date).
There remains, as of yet, very limited temperature
dependent kinetic data available for tertiary peroxy
radicals and no trends in reactivity with radical size
or type can be suggested with any confidence. How-
ever, for ␤-substituted secondary radicals, a large and
negative temperature dependence similar in magni-

TEMPERATURE DEPENDENCE OF RATE COEFFICIENTS
331
Hayman, J. Chem. Soc. Faraday Trans., 87, 2351
(1991).
10. A. A. Boyd, B. Nozière, and R. Lesclaux, J. Chem.
Soc. Faraday Trans., 92, 201 (1996).
11. R. Atkinson, J. Phys. Chem. Ref. Data Monograph 1,
1989.
12. W. B. DeMore, M. J. Molina, S. P. Sander, D. M.
Golden, R. F. Hampson, M. J. Kurylo, C. J. Howard, C.
E. Kolb, and A. R. Ravishankara, Chemical Kinetics
and Photochemical Data for Use in Stratospheric
Modelling, NASA-JPL Publication 94-26, Pasadena,
1994.
tude to that for the primary analogues may be applic-
able in all cases but needs to be confirmed, as does
the apparent inverse variation of both A-factor and
activation energy with carbon number for unsubsti-
tuted secondary radicals (see Table IV). Measure-
ments of the Arrhenius parameters for the linear sec-
ondary radicals n-C12H25O2 and n-C5H11O2 are
planned with this confirmation in mind.
BIBLIOGRAPHY
13. A. A. Boyd, R. Lesclaux, M. E. Jenkin, and T. J.
Wallington, J. Phys. Chem., 100, 6594 (1996).
14. D. M. Rowley, R. Lesclaux, P. D. Lightfoot, K.
Hughes, M. D. Hurley, S. Rudy, and T. J. Wallington, J.
Phys. Chem., 96, 7043 (1992).
1. R. Atkinson, J. Phys. Chem. Ref. Data Monograph 2,
1994.
2. S. Madronich and J. G. Calvert, J. Geophys. Res., 95,
5696 (1990).
3. S. Madronich, R. B. Chatfield, J. G. Calvert, G. K.
Moortgat, B. Veyret, and R. Lesclaux, Geophys. Res.
Lett., 17, 2361 (1990).
15. P. D. Lightfoot, R. A. Cox, J. N. Crowley, M. Destriau,
G. D. Hayman, M. E. Jenkin, G. K. Moortgat, and F.
Zabel, Atmos. Environ., 24, 1805 (1992).
4. M. E. Jenkin, T. P. Murrells, S. J. Shalliker, and G. D.
Hayman, J. Chem. Soc. Faraday Trans., 89, 433
(1993).
5. F. Kirchner and W. R. Stockwell, J. Geophys. Res.,
submitted.
16. R. Lesclaux, in Peroxy Radicals, Z. B. Alfassi, Ed.,
Wiley, New York, 1996, in press.
17. E. Villenave and R. Lesclaux, Proceedings of
EUROTRAC/HALIPP/LACTOZ Workshop, Strasbourg,
25–27 Sept. 1995.
6. M. E. Jenkin and G. D. Hayman, J. Chem. Soc. Fara-
day Trans., 91, 1911 (1995).
18. J. N. Crowley and G. K. Moortgat, J. Chem. Soc. Fara-
day Trans., 88, 2437 (1992).
7. I. Barnes, K. H. Becker, and L. Ruppert, Chem. Phys.
Lett., 203, 295 (1992).
8. C. Anastasi, D. J. Muir, V. J. Simpson, and P. Pagsberg,
J. Phys. Chem., 95, 5791 (1991).
19. B. Nozière, R. Lesclaux, M. D. Hurley, M. A. Dearth,
and T. J. Wallington, J. Phys. Chem., 98, 2864 (1994).
20. A. A. Boyd and R. Lesclaux, Proceedings of
EUROTRAC/HALIPP/LACTOZ Workshop, Strasbourg,
25–27 Sept. 1995.
9. T. P. Murrells, M. E. Jenkin, S. J. Shalliker, and G. D.

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