Kinetic study of the self-reactions of the BrCH2CH2O2 and BrCH(CH3CH(CH3O2 radicals between 275 and 373 K

Article abstract of DOI:10.1021/jp0258558

A conventional flash photolysis technique was used to measure the self-reaction rate constants of the primary BrCH₂CH₂O₂ (2-bromoethylperoxy) and secondary BrCH(CH₃)CH(CH₃)O₂ (2-bromo-l-methylpropylperoxy) β-brominated peroxy radicals, at temperatures in the range of 275-373 K. The absolute UV absorption spectra of BrCH₂CH₂O₂ and BrCH(CH₃)CH(CH₃)O₂ were also measured and compared to those obtained previously for these radicals. The temperature dependence of the self-reaction rate constants provided the following Arrhenius expressions: k(BrCH₂CH₂O₂ + BrCH₂CH₂O₂) = (6.15^+5.15_2.99) × 10^-14 exp{(1247 ± 203) K/T} cm³ molecule^-1 s^-1 and k(BrCH(CH₃)CH(CH₃)O₂ + BrCH(CH₃)CH(CH₃)O₂) = (7.60^+22.05_-5.65) × 10^-15 exp{(1305 ± 428) K/T} cm³ molecule^-1 s^-1, where the uncertainties represent 95% confidence limits associated with the statistical fitting procedure and include the contribution for the expanded uncertainties in the individual rate constant. These results confirm the enhancement of the peroxy radical self-reaction reactivity upon β-substitution, which is similar for Br, Cl, or OH substituents. Structure-activity relationships are proposed for self-reactions of β-substituted peroxy radicals.

Full text of DOI:10.1021/jp0258558

2470
J. Phys. Chem. A 2003, 107, 2470-2477
Kinetic Study of the Self-Reactions of the BrCH2CH2O2 and BrCH(CH3)CH(CH3)O2
Radicals between 275 and 373 K
Eric Villenave,* Sandy Moisan, and Robert Lesclaux
Laboratoire de Physico-Chimie Mole´culaire, UniVersite´ Bordeaux I, UMR 5803 CNRS,
33405 Talence Cedex, France
ReceiVed: March 29, 2002; In Final Form: September 21, 2002
A conventional flash photolysis technique was used to measure the self-reaction rate constants of the primary
BrCH2CH2O2 (2-bromoethylperoxy) and secondary BrCH(CH3)CH(CH3)O2 (2-bromo-1-methylpropylperoxy)
â-brominated peroxy radicals, at temperatures in the range of 275-373 K. The absolute UV absorption spectra
of BrCH2CH2O2 and BrCH(CH3)CH(CH3)O2 were also measured and compared to those obtained previously
for these radicals. The temperature dependence of the self-reaction rate constants provided the following
Arrhenius expressions: k(BrCH2CH2O2 + BrCH2CH2O2) ) (6.15+5.51
-2.91) × 10-14 exp{(1247 ( 203) K/T} cm3
+22.05
-5.65
molecule-1 s-1 and k(BrCH(CH3)CH(CH3)O2 + BrCH(CH3)CH(CH3)O2) ) (7.60
) × 10-15 exp{(1305
( 428) K/T} cm3 molecule-1 s-1, where the uncertainties represent 95% confidence limits associated with
the statistical fitting procedure and include the contribution for the expanded uncertainties in the individual
rate constant. These results confirm the enhancement of the peroxy radical self-reaction reactivity upon
â-substitution, which is similar for Br, Cl, or OH substituents. Structure-activity relationships are proposed
for self-reactions of â-substituted peroxy radicals.
Introduction
K. Kinetics of tertiary â-brominated radical reactions have
already been investigated in a previous work by our group.11
Peroxy radicals RO2 play an important role in atmospheric
oxidation processes and in the low-temperature oxidation of
hydrocarbons.1,2 Studies of peroxy radical self-reactions are of
interest as a necessary step for studying their reactions with
NOx, HO2, or other RO2 compounds. Self-reactions are well-
known to present rate constants varying over several orders of
magnitude, depending principally on the structure of the radical
or on the presence of functional groups.3-5 It has been shown
that substitution of alkylperoxy radicals with hydroxy, carbonyl,
or halogen groups, either in the R-position or in the â-position
to the peroxy group, significantly increases the self-reaction rate
constants.3,6-10 Although very significant progress has been
made in defining structure-reactivity relationships for kinetics
of peroxy radical reactions, only a few works have been reported
to study the influence of the temperature on the kinetics of
substituted peroxy radical reactions.3 For instance, in the case
of the methylperoxy self-reactions, the presence of substituents
(F or Cl, whatever their number) results in variations in
activation energies of approximately a factor of 2 (with Ea/R
values between -400 and -800 K) and variations of a factor
of 4 in pre-exponential factors (from 1 × 10-13 to 4 × 10-13
cm3 molecule-1 s-1). When substituents are in the â-position,
rate constants of substituted-peroxy self-reactions mainly depend
on the class of the radical: for primary and secondary peroxy
radicals, â-substitution always yields a negative temperature
dependence (with Ea/R values between -700 and -1400 K),
whereas, for substituted tertiary radicals, Ea is positive.3 Hence,
the objectives of the present work were to provide further
information on the effects of â-substitution on primary and
secondary peroxy radicals, by investigating the case of bromine
â-substitution at various temperatures in the range of 275-373
Trends for rate constants and Arrhenius parameters are proposed
on the basis of the data available for the self-reactions of various
â-substituted peroxy radicals.
A conventional flash photolysis technique was used to
determine the rate constant of the following reactions:
2BrCH2CH2O2 f 2BrCH2CH2O + O2
(1a)
f BrCH2CH2OH + BrCH2CHO + O2 (1b)
2BrCH(CH3)CH(CH3)O2 f 2BrCH(CH3)CH(CH3)O + O2
(2a)
f BrCH(CH3)CH(CH3)OH +
BrCH(CH3)C(O)CH3 + O2 (2b)
Experimental Section
Kinetic studies were performed at atmospheric pressure, using
the conventional flash photolysis technique, coupled with UV
absorption spectrometry as real-time monitoring of radical
concentrations. This technique has already been described in
detail12 and is addressed only briefly here.
The setup consisted of a 70-cm-long Pyrex reaction cell, fitted
with a water-filled thermostat jacket. Flashes were generated
by discharging two capacitors through external argon flash
lamps. The UV analysis beam from a deuterium lamp was
directed along the length of the cell and focused onto the slit
of a monochromator. The light intensity at the selected wave-
length (λ ) 200-300 nm) was monitored by a photomultiplier
tube, and the signal was stored in a digital oscilloscope and
transferred to a microcomputer for signal averaging and further
data analysis.
To whom correspondence should be addressed. E-mail address:
e.villenave@lpcm.u-bordeaux1.fr.
10.1021/jp0258558 CCC: $25.00 © 2003 American Chemical Society
Published on Web 03/12/2003

Self-Reactions of BrCH2CH2O2 and BrCH(CH3)CH(CH3)O2
J. Phys. Chem. A, Vol. 107, No. 14, 2003 2471
Brominated peroxy radicals BrCH2CH2O2 (2-bromoethyl-
peroxy) and BrCH(CH3)CH(CH3)O2 (2-bromo-1-methylpropyl-
peroxy) were generated using the UV-visible photolysis of
molecular bromine (Br2), producing Br atoms that added to the
double bond of either ethene (C2H4) or (E)-but-2-ene (C4H8),
respectively, in the presence of oxygen and nitrogen:
was completely replenished between each flash, thus preventing
complications arising from the reaction products.
Oxygen, nitrogen (AGA Gaz Spe´ciaux, >99.995%), acetal-
dehyde (Aldrich, 99%), (E)-but-2-ene (Aldrich, >99%), ethene
(AGA Gas Spe´ciaux, 99.8%), bromine (Aldrich, 99.5%),
2-bromoethanol (Aldrich, 95%), and 3-bromo-2-butanone (Lan-
caster, >97%) were all used without further purification. Liquid
compounds (bromine and acetaldehyde) were introduced into
the gas mixture by passing a slow flow of nitrogen (or oxygen)
through a bubbler cooled in a water-ice bath.
Br2 + hν (λ > 280 nm) f 2Br
(3)
Br + CH2dCH2 + M h BrCH2CH2 + M (4,-4)
Experimental decay traces (absorbance versus time) were
analyzed by numerical integration of a set of differential
equations that took into account the complete reaction mech-
anisms. Resulting simulations were fitted by adjusting selected
parameters (i.e., self-reaction rate constants), using nonlinear
least-squares fitting.
where k4(298 K) ) 1.23 × 10-13 cm3 molecule-1 s-1 in 700
Torr of air,13 or
Br + (CH3)CHdCH(CH3) + M f
BrCH(CH3)CH(CH3) + M (5)
where k5(298 K) ) 8.5 × 10-12 cm3 molecule-1 s-1 in 750
Results
Torr of molecular nitrogen (N2),14,15
The kinetic studies of the self-reactions of the BrCH2CH2O2
and BrCH(CH3)CH(CH3)O2 radicals are reported below. The
self-reaction of the 2-bromoethylperoxy radical (BrCH2CH2O2)
has been selected as a typical case for a detailed presentation
of the results. The results for the 2-bromo-1-methylpropylperoxy
radical (BrCH(CH3)CH(CH3)O2) are reported only briefly,
because experiments and data analyses were conducted in a
similar way. Therefore, only the particular features specific to
this study are noted.
BrCH2CH2 + O2 + M f BrCH2CH2O2 + M
(6)
where k6 was estimated to be similar to k(C2H4Cl + O2) (1 ×
10-11 cm3 molecule-1 s-1) at 298 K,16 or
BrCH(CH3)CH(CH3) + O2 + M f
BrCH(CH3)CH(CH3)O2 + M (7)
where k7 was estimated to be larger than k(s-C4H9 + O2) (1.67
× 10-11 cm3 molecule-1 s-1) at 298 K (in 4 Torr of helium).17
The concentration of Br2 was measured by its absorption at
BrCH2CH2O2 and BrCH(CH3)CH(CH3)O2 Ultraviolet
Absorption Spectra. Absolute UV absorption cross sections
were required to quantify the radical concentrations of interest
in the present work. The UV spectra were obtained by measuring
the initial absorption of the decay traces at different wavelengths
in the range of 210-290 nm. The presence of a short postflash
dead time meant that the decay traces had to be extrapolated to
time zero by modeling the decay profile, using the complete
reaction mechanisms, as described in the next section. Absolute
cross-section values were obtained by calibrating the photolysis
yield of Br2, from which the initial radical concentrations were
deduced, as detailed previously.
Spectra of BrCH2CH2O2 and BrCH(CH3)CH(CH3)O2 radicals
are respectively presented in Figures 1 and 2, and the corre-
sponding cross sections are given in Table 1. The UV spectra
resemble those of most alkyl peroxy radicals, appearing as a
broad band in the range of 200-300 nm, without any vibrational
structure and with maxima at 240 nm (σ(BrCH2CH2O2) ) (4.77
( 0.09) × 10-18 cm2 molecule-1 and σ(BrCH(CH3)CH(CH3)-
O2) ) (4.27 ( 0.16) × 10-18 cm2 molecule-1).
415 nm (σ ) 6.45 × 10-19 cm2 molecule-1 18
) and maintained
in the concentration range of 1 × 1015-5 × 1015 molecules
cm-3. The photolysis yield of Br2 in our system was calibrated
against the acetylperoxy radical absorption formed by replacing
ethene (or (E)-but-2-ene) by acetaldehyde (which reacts ef-
ficiently with Br atoms) before and after each set of experiments,
keeping all other experimental conditions identical. Absorption
cross sections of CH3C(O)O2 are well established: σ(207 nm)
) 6.75 × 10-18 cm2 molecule-1 and σ(250 nm) ) 3.22 × 10-18
cm2 molecule-1.2 Under the experimental conditions, initial Br
atom concentrations were usually in the range of 2 × 1013-1
× 1014 molecules cm-3
.
Concentrations of ethene (and (E)-but-2-ene) were chosen
such that the conversion of Br atoms to radicals was almost
instantaneous, compared to the time scale of the reactions of
interest, and dominated all other possible loss processes of Br
atoms, in particular, reaction 8:
Also shown in Figures 1 and 2 are the spectra measured
previously by Crowley and Moortgat10 for the same radicals,
using the molecular modulation technique. Although the shapes
of the spectra are similar in both studies, note the discrepancy
in the absolute cross-section values at short wavelengths. Cross
sections reported by Crowley and Moortgat10 are 5%-15%
lower for BrCH2CH2O2 and are quasi-identical for BrCH(CH3)-
CH(CH3)O2 to those determined in this work in the range of
250-290 nm. However, the discrepancies increase at <240 nm,
up to 70% at 210 nm. In the molecular modulation experiments,
the absolute spectra were calibrated by scaling the UV cross
sections to the values obtained at 270 nm for both radicals.
Reported spectra were obtained using a deconvolution procedure
to take into account the absorption of HO2 radicals, which absorb
significantly at <240 nm and are expected to be produced in
the secondary chemistry following the RO2 self-reaction. This
deconvolution procedure, which was performed without con-
Br + BrCH2CH2O2 (or BrCH(CH3)CH(CH3)O2) + M f
BrCH2CH2OOBr (or BrCH(CH3)CH(CH3)OOBr) + M (8)
where k8 was estimated to be similar to k(C2H5O2 + Br) (∼1
× 10-10 cm3 molecule-1 s-1) at 298 K and in 1 atm of air.19
Concentrations of ethene were typically set in the range of 1
× 1017-4 × 1018 molecule cm-3, and those of (E)-but-2-ene
were always in the range of 3.5 × 1016-1 × 1017 molecule
cm-3. The oxygen partial pressure was varied in the range of
10-730 Torr; however, most experiments were performed under
a large excess of molecular oxygen (O2), to scavenge BrCH2-
CH2 radicals rapidly and avoid reaction -4 (k-4(298 K) ) 1.16
× 106 s-1 in air).20
In experiments where the oxygen concentration was varied,
nitrogen was used as the diluent gas. The total flow rate in the
cell was sufficiently high to ensure that the reaction mixture

2472 J. Phys. Chem. A, Vol. 107, No. 14, 2003
Villenave et al.
TABLE 1: UV Absorption Cross Sections for BrCH2CH2O2, BrCH(CH3)CH(CH3)O2, BrCH2CH2OH, and BrCH(CH3)C(O)CH3
at 298 K
wavelength (nm)
σ(BrCH2CH2O2)a,b
σ(BrCH(CH3)CH(CH3)O2)a,b
σ(BrCH2CH2OH)a,c
σ(BrCH(CH3)C(O)CH3)a,c
210
220
230
240
250
260
270
280
290
3.05 ( 0.19
3.77 ( 0.07
4.48 ( 0.17
4.77 ( 0.09
4.55 ( 0.17
3.62 ( 0.11
2.29 ( 0.30
1.36 ( 0.15
0.68 ( 0.04
2.87 ( 0.17
3.31 ( 0.20
3.98 ( 0.17
4.27 ( 0.16
4.22 ( 0.33
3.70 ( 0.10
2.88 ( 0.19
1.66 ( 0.03
0.90 ( 0.03
0.41
0.23
0.08
0.81
0.69
0.44
0.27
0.17
0.14
0.17
0.22
0.27
a Given in units of 10-18 cm2 molecule-1
are ∼15%.
.
b Uncertainties are the 95% confidence level components due to random effects only. c Uncertainties
traces and their best-fit simulations are presented in Figure 3.
By analogy with previous studies of alkylperoxy radical self-
reactions, the reaction mechanism for the BrCH2CH2O2 self-
reaction is as follows:
BrCH2CH2O2 + BrCH2CH2O2 f 2BrCH2CH2O + O2 (1a)
f BrCH2CH2OH +
BrCH2CHO + O2 (1b)
BrCH2CH2O + O2 f HO2 + BrCH2CHO
(9)
where k9 was estimated to be similar to k(CH3CH2O + O2) (1.0
× 10-14 cm3 molecule-1 s-1) at 298 K.21
BrCH2CH2O2 + HO2 f products
(10)
where k10 was estimated to be similar to k(CH3CH2O2 + HO2)
(7.8 × 10-12 cm3 molecule-1 s-1) at 298 K.2
Figure 1. UV absorption spectrum measured in this work (circles)
for the BrCH2CH2O2 radical, compared to that previously reported by
Crowley and Moortgat10 (dotted line) using the molecular modulation
technique.
HO2 + HO2 f H2O2 + O2
(11)
with k11 ) 3.0 × 10-12 cm3 molecule-1 s-1 at 298 K and in 1
atm of air.22
This reaction mechanism is consistent with Fourier transform
infrared product studies of the Br-atom-initiated oxidation of
ethene,14,23 which showed that 2-bromoethanol (BrCH2CH2OH),
bromoacetaldehyde (BrCH2CHO), and 2-bromohydroethylper-
oxide (BrCH2CH2OOH) are the major reaction products. The
branching ratio R ) k1a/k1 for the nonterminating channel of
reaction 1 was taken to be equal to 0.57.23 This value is
confirmed by the present study, because experimental traces
could never be satisfactorily simulated using R values of <0.4
or >0.7. It was assumed that the BrCH2CH2O radicals formed
via reaction 1a only react with O2 (under high oxygen
concentration) to form HO2 in the temperature range of interest,
because no change was observed in the shape of experimental
traces when the temperature was varied.
As shown in Figure 3, the shape of experimental decays
depends on the analysis wavelength. At λ > 240 nm, traces
display essentially simple second-order kinetics. At λ values
between 210 and 230 nm, the distortion of the decays was
characteristic of the formation of significant quantities of HO2
through reaction 9. In addition, a non-negligible residual
absorption was observed at λ < 240 nm and was attributed
mainly to the formation of BrCH2CH2OH and BrCH2CHO, in
agreement with the end-product studies.10,14,23 Therefore, UV
absorption cross sections of BrCH2CH2OH and BrCH(CH3)C-
(O)CH3 (which are supposed to be similar to those of BrCH2-
CHO, which is commercially unavailable) were measured in
the range of 210-290 nm using a Hewlett-Packard model
8452A spectrophotometer. They are reported in Table 1. By
Figure 2. UV absorption spectrum of BrCH(CH3)CH(CH3)O2 deter-
mined in this work (circles). Dotted line represents that previously
reported by Crowley and Moortgat10 using the molecular modulation
technique.
sidering the entire complete mechanism (in particular, the
brominated products formed by the peroxy self-reaction), may
explain the observed discrepancies at short wavelengths. At
longer wavelengths, the differences observed between the two
studies are within the uncertainties.
Kinetics of the BrCH2CH2O2 Self-Reaction. The kinetic
measurements of k1 were performed at temperatures in the range
of 275-373 K, at monitoring wavelengths that were systemati-
cally varied over a range of 210-290 nm, and decay traces
were recorded over various time scales. Typical experimental

Self-Reactions of BrCH2CH2O2 and BrCH(CH3)CH(CH3)O2
J. Phys. Chem. A, Vol. 107, No. 14, 2003 2473
Figure 3. Typical experimental traces recorded at (a) 210 and (b) 240 nm and best-fit simulations for the determination of k1(BrCH2CH2O2 +
BrCH2CH2O2) at 298 K.
TABLE 2: Experimental Values of the Rate Constant for
the BrCH2CH2O2 Self-Reaction
Thus, to avoid such complications, kinetic experiments were
always performed under high oxygen concentration (700 Torr).
The results of our experiments on the BrCH2CH2O2 self-
reaction are summarized in Table 2. A weighted least-squares
fit of all the data yields the following Arrhenius expression for
k1 in the temperature range of 275-371 K:
a
temp
(K)
k1
number of
determinations
(× 10-12 cm3 molecule-1 s-1
)
275
298
318
348
371
5.51 ( 0.26
4.49 ( 0.22
3.00 ( 0.11
2.11 ( 0.23
1.80 ( 0.04
12
14
7
6
8
k1 ) (6.15
) × 10-14 × exp{(1247 ( 203) K/T}
+5.51
-2.91
cm3 molecule-1 s-1
a Errors are the 95% confidence level components due to random
effects only.
The corresponding Arrhenius plot is shown in Figure 4. The
quoted uncertainties represent 95% confidence limits associated
with the statistical fitting procedure and include the contribution
for the expanded uncertainties in the individual rate constant.
To quantify the sensitivity of the rate constant k1 toward the
parameters used for analysis, a systematic analysis of error
propagation was performed, as described previously.12 It appears
that the rate constant k1 is mainly sensitive to the variations of
σ(BrCH2CH2O2), to the branching ratio R, and to the rate
constant k10 for the (BrCH2CH2O2 + HO2) reaction. This is
particularly true when k1 is extracted from experimental traces
recorded at short wavelengths (λ < 240 nm), where the
absorptions of HO2, BrCH2CHO, and BrCH2CH2OH directly
influence the decay shapes. Thus, most measurements were
performed at wavelengths of >240 nm, where residual absorp-
tions are negligible and the signal-to-noise ratio was its
maximum value. Measurements performed at shorter wave-
lengths allowed us to validate the chemical mechanism. Al-
lowing for errors of ∼20% in σ(BrCH2CH2O2) resulted in a
introducing BrCH2CH2OH and BrCH(CH3)C(O)CH3 cross sec-
tions into our model, the residual absorption was fairly well
reproduced in the simulations, and the measured rate constants
did not vary with the analysis wavelength, which allowed us to
validate the mechanism presented earlier.
The dependence of the formation rate of the 2-bromoethyl-
peroxy radical (BrCH2CH2O2) on oxygen concentration was
investigated at two different analysis wavelengths (210 and 250
nm), by decreasing the oxygen partial pressure regularly from
700 Torr to 10 Torr. If no significant change in the shape of
experimental traces was noted at 250 nm, the rates of decay
traces obtained at 210 nm were clearly slower for low oxygen
concentrations (<150 Torr) than those recorded in 700 Torr of
O2 at the same wavelength. These observations are consistent
with those of Barnes et al.,14 who indicated that the apparent rate
constant for the reaction of bromine with C2H4 increases as the
oxygen partial pressure increases, suggesting the existence of an
equilibrium between bromine, ethene (C2H4), and BrCH2CH2.

2474 J. Phys. Chem. A, Vol. 107, No. 14, 2003
Villenave et al.
200 ms). A typical decay recorded at 250 nm is shown in Figure
5. No data for product yields of the BrCH(CH3)CH(CH3)O2
self-reaction were available; thus, the reaction mechanism used
in the simulations was similar to that of the BrCH2CH2O2 radical
self-reaction. All experiments were performed under high
oxygen partial pressure (730 Torr), to prevent further complica-
tions resulting, on one hand, from a potential equilibrium
between Br atoms, C4H8, and BrCH(CH3)CH(CH3) (as discussed
previously for C2H4), and, on the other hand, from the possible
decomposition of the alkoxy radical BrCH(CH3)CH(CH3)O
formed via reaction 2a.
BrCH(CH3)CH(CH3)O + O2 f
HO2 + BrCH(CH3)C(O)CH3 (12)
Note that the unsubstituted 2-butoxy radical is mainly reacting
with O2 (>90% in 730 Torr of O2) rather than decomposing
(<10%).24 Decomposition of the BrCH(CH3)CH(CH3)O radical
would lead to the formation of a new peroxy radical, according
to reactions 13 and 14:
Figure 4. Arrhenius plot for the self-reaction of BrCH2CH2O2 (circles).
The room-temperature measurement of the overall rate constant k1obs
,
by Crowley and Moortgat,10 is represented by the triangle. The quoted
uncertainties represent 95% confidence limits associated with the
statistical fitting procedure and include the contribution for the expanded
uncertainties in the individual rate constant.
BrCH(CH3)CH(CH3)O + M f
BrCH(CH3) + CH3CHO + M (13)
variation of 18% in k1. A variation of 30% in R results in a
variation of only 5% at 250 nm but a variation of 27% at 210
nm. Reasonably varying the value of k10 by a factor of 2 (from
5 × 10-12 to 1 × 10-11 cm3 molecule-1 s-1) results in a change
in k1 of 6% at 250 nm and 21% at 210 nm. The sensitivity of
the fit to the variations of σ(HO2), σ(BrCH2CHO), and σ(BrCH2-
CH2OH) was negligible at 250 nm. However, variations of 10%
in σ(HO2) and 15% in σ(BrCH2CHO) and σ(BrCH2CH2OH)
respectively result in variations of 15%, 30%, and 10% in the
self-reaction rate constant k1 at 210 nm. All the above-described
uncertainties are combined with the statistical errors in an overall
uncertainty of ∼30% in k1.
BrCH(CH3) + O2 + M f BrCH(CH3)O2 + M (14)
No information on both the kinetics and the product yield of
BrCH(CH3)O2 reactions was available; therefore, we proceeded
again by analogy to propose a kinetic model that accounts, at
best, for the experimental observations. The BrCH(CH3)O2
radical is the R-brominated analogue of the ethylperoxy radical
C2H5O2, which presents a well-known self-reaction rate constant,
i.e., k ) 6.8 × 10-14 cm3 molecule-1 s-1 at 298 K.22 As a
primary brominated peroxy radical, we can expect that BrCH-
(CH3)O2 presents a higher reactivity than the nonsubstituted
ethylperoxy radical.7 However, the enhancement of the reactivity
observed upon â-substitution appears to be less important for
R-substituted radicals (see discussion); thus, BrCH(CH3)O2
should be less reactive than the primary â-brominated BrCH2-
CH2O2 radical studied in this work. Therefore, we have
estimated that the rate constant for the BrCH(CH3)O2 self-
reaction was intermediate between those of the C2H5O2 and
BrCH2CH2O2 radicals and set its value at ∼2 × 10-13 cm3
molecule-1 s-1 in simulations. By considering 100% of BrCH-
(CH3)CH(CH3)O decomposition and introducing the BrCH-
(CH3)O2 radical chemistry in the simulations, the value of the
rate constant k2 did not vary by >35%. Therefore, considering
Kinetics of the BrCH(CH3)CH(CH3)O2 Self-Reaction. The
self-reaction of the 2-bromo-1-methylpropylperoxy radical,
2BrCH(CH3)CH(CH3)O2 f 2BrCH(CH3)CH(CH3)O + O2
(2a)
f BrCH(CH3)CH(CH3)OH +
BrCH(CH3)C(O)CH3 + O2 (2b)
was investigated at different temperatures (275-371 K), dif-
ferent wavelengths (210-290 nm), and various time scales (40-
Figure 5. Typical decay trace obtained at 250 nm for the BrCH(CH3)CH(CH3)O2 self-reaction at T ) 293 K.

Self-Reactions of BrCH2CH2O2 and BrCH(CH3)CH(CH3)O2
J. Phys. Chem. A, Vol. 107, No. 14, 2003 2475
TABLE 4: Rate Constants for Self-Reactions of
TABLE 3: Experimental Values of the Rate Constant for
the BrCH(CH3)CH(CH3)O2 Self-Reaction
â-Substituted Ethylperoxy Radicals
a
a
b
temp
(K)
k2
number of
determinations
radical
C2H5O2
k298K
R298K
Aa,c
Ea/Rd
-60 26
ref
(× 10-13 cm3 molecule-1 s-1
)
8.2 × 10-14 0.76 6.7 × 10-14
ClCH2CH2O2 3.3 × 10-12 0.63e 1.1 × 10-13 -1020 27
275
293
318
343
371
8.0 ( 0.3
6.4 ( 0.4
5.6 ( 0.5
3.7 ( 0.5
2.2 ( 0.3
6
15
6
6
7
BrCH2CH2O2 4.0 × 10-12f 0.57 6.15 × 10-14 -1247 this work
HOCH2CH2O2 2.3 × 10-12 0.50 6.9 × 10-14 -1040 10
a Given in units of cm3 molecule-1 s-1 b Branching ratio for the
.
nonterminating channel. c A denotes the pre-exponential factor. d Given
in kelvin. e Arithmetic mean of the value reported by Wallington et
al.28 (R ) 0.69) and that reported by Yarwood et al.23 (R ) 0.57).
f Recalculated from the Arrhenius expression.
a Errors are the 95% confidence level components due to random
effects only.
ated with the statistical fitting procedure and include the
contribution for the expanded uncertainties in the individual rate
constant.
As was done for the previous case, a study of error
propagation has been conducted. The formations of HO2, BrCH-
(CH3)CH(CH3)OH, and BrCH(CH3)C(O)CH3 particularly influ-
ence the shape of the experimental traces recorded at wave-
lengths of <240 nm; therefore, most kinetic measurements were
performed at higher wavelengths, where the contributions of
the quoted compounds to the total absorption were negligible.
Thus, a variation of 30% in the value of R results in a variation
of 34% in k2 at λ ) 210 nm, but a variation of only 10% at λ
> 240 nm. In simulations, the rate constant for the reaction of
BrCH(CH3)CH(CH3)O2 with HO2 was estimated to be k(HOCH-
(CH3)CH(CH3)O2 + HO2) ) 1.5 × 10-11 cm3 molecule-1 s-1
at 298 K.8,9 Reasonably varying this value by a factor of 2 results
in a change in the self-reaction rate constant k2 of 37% at λ )
210 nm and only 5% at λ ) 240 nm. The total systematic error
was finally estimated to be ∼23%, yielding an overall propa-
gated error of ∼55%.
Figure 6. Arrhenius plot for the self-reaction of BrCH(CH3)CH(CH3)-
O2 (circles). The room-temperature measurement of the overall rate
constant k2obs, by Crowley and Moortgat,10 is represented by the triangle.
The quoted uncertainties represent 95% confidence limits associated
with the statistical fitting procedure and include the contribution for
the expanded uncertainties in the individual rate constant.
Discussion and Conclusion
this additional uncertainty and the recent work of Zabel’s group
on the unsubstituted 2-butoxy radical,24 it was finally decided
to simplify the mechanism and simulate all experimental traces,
accounting only for the reaction of BrCH(CH3)CH(CH3)O with
O2, neglecting its decomposition and the BrCH(CH3)O2 forma-
tion under our experimental conditions. The effect of this final
assumption is included in the total uncertainties of the rate
constant.
At shorter wavelengths, slower experimental decays were
observed and interpreted by the presence of HO2 formed by
reaction 12. As in the case of BrCH2CH2O2, the residual
absorption observed at long time scales and short wavelengths
for the BrCH(CH3)CH(CH3)O2 self-reaction was attributed to
the formation of the corresponding ketone (BrCH(CH3)C(O)-
CH3) and alcohol (BrCH(CH3)CH(CH3)OH).
At all temperatures and wavelengths, very good fits of kinetic
traces were obtained using an R value that was similar to those
measured for the BrCH2CH2O2 (R ) 0.57 at 298 K)23 and CH3-
CH(CH3)O2 (R ) 0.56 at 298 K)3 self-reactions, i.e., R ≈ 0.5
at 298 K. The systematic uncertainties introduced by this
assumption are discussed below.
The averages of optimized values of k2 are presented as a
function of temperature in Table 3. Figure 6 shows the variation
of k2 with temperature in Arrhenius form, yielding the following
rate expression:
The rate constants of the BrCH2CH2O2 and BrCH(CH3)CH-
(CH3)O2 self-reactions have been determined for the first time
as a function of temperature. A previous measurement was
already reported in the literature by Crowley and Moortgat;10
however, it was performed at room temperature only, and they
only proposed an overall (observed) rate constant of disappear-
ance of the peroxy radicals, without accounting for the complete
reaction mechanism. By employing the relation kreal ) kobs/(1
+ R)4 to recalculate the true rate constants kreal from the observed
rate constant (kobs) data of Crowley and Moortgat,10 the
agreement becomes excellent, despite the discrepancies between
the two works observed via UV absorption spectra at short
wavelengths. However, this recalculation can be done only when
the rate constants for the peroxy self-reaction and its reaction
with HO2 are separated by at least 1 order of magnitude, which
is the case for the BrCH(CH3)CH(CH3)O2 radical but not that
for BrCH2CH2O2. In this last case, the complete reaction
mechanism must be taken into account to extract kreal from
experimental data.
A comparison with other rate-constant values for â-mono-
substituted ethylperoxy self-reactions is proposed in Table 4.
At room temperature, it clearly appears that self-reactions of
C2H5O2, ClCH2CH2O2, BrCH2CH2O2, and HOCH2CH2O2 all
present two channels (see reactions 1a and 1b), with the R values
being similar (within uncertainties) for all radicals. In addition,
the â-substitution by Cl, Br, or OH results in a large increase
in the self-reaction rate constant, by a factor of ∼30-50 at 298
K, compared to that of the C2H5O2 radical. This may suggest
that â-substitution leads to decreased energies of the transition
state for decomposition of the stable intermediate of both
+22.05
k2 ) (7.60
) × 10-15 × exp{(1305 ( 428) K/T}
-5.65
cm3 molecule-1 s-1
(T ) 275-371 K)
where the uncertainties represent 95% confidence limits associ-

2476 J. Phys. Chem. A, Vol. 107, No. 14, 2003
Villenave et al.
ref
TABLE 5: Rate Constants for Self-Reactions of Secondary Peroxy Radicals
radical
k298K
R298K
Aa,c
Ea/Rd
a
b
CH3CH(CH3)O2
BrCH(CH3)CH(CH3)O2
HOCH(CH3)CH(CH3)O2
1.1 × 10-15
6.1 × 10-13e
6.7 × 10-13
0.56
∼0.50f
0.20
1.7 × 10-12
7.6 × 10-15
7.7 × 10-15
+2188
-1305
-1330
4
this work
9
a Given in units of cm3 molecule-1 s-1 b Branching ratio for the nonterminating channel. c A denotes the pre-exponential factor. d Given in
.
kelvin. e Recalculated from the Arrhenius expression. f See text.
TABLE 6: Recommended Structure-Activity Relationships
for â-Substituted Peroxy Radical Self-Reaction Rate
Constants (with Substituent Cl, Br, or OH) as a Function of
Temperature
terminating and nonterminating channels in the same way. It
may also strengthen the belief that both transition states are
identical, as already suggested by Lesclaux.3 These observations
are confirmed when examining the Arrhenius expressions of
the self-reaction rate constants in Table 4. The pre-exponential
factors are the same (within a factor of <2) and the rate
expressions corresponding to ClCH2CH2O2, BrCH2CH2O2, and
HOCH2CH2O2 all present a negative temperature coefficient
(approximately -1000 K), whereas the C2H5O2 self-reaction
rate is temperature-independent. Therefore, all the differences
observed in the reaction rate constants between unsubstituted
and substituted ethylperoxy radicals result more in a change in
activation energies (for decomposition of the intermediate
complex) than a change in chemical reaction mechanism. The
same observations were made, to a lesser extent, for R-substi-
tuted methylperoxy radicals.3
The self-reaction rate constant of BrCH(CH3)CH(CH3)O2 is
compared to those of other secondary peroxy radicals in Table
5. It appears that both BrCH(CH3)CH(CH3)O2 and HOCH-
(CH3)CH(CH3)O2 present self-reaction rate constants that are a
factor of ∼600 higher than that of CH3CH(CH3)O2, which, until
now, has been considered to be a model for the small secondary
peroxy radical reactivity.25 Note the change of the temperature
dependence, which becomes negative with the substitution. The
rate-constant change from unsubstituted to substituted radicals
is not directly a consequence of the temperature dependence;
rather, the temperature dependence indicates a drastic change
of the reaction mechanism. The presence of a potential barrier
indicates a tight transition state and a elementary bimolecular
reaction whereas the negative temperature dependence shows
the presence of an intermediate potential well and a complex
nonelementary reaction mechanism. This also corresponds to
very different pre-exponential factors. It should be noted that
Arrhenius parameters are remarkably identical for BrCH(CH3)-
CH(CH3)O2 and HOCH(CH3)CH(CH3)O2, and that activation
energies are also fairly similar to those of primary â-substituted
peroxy self-reactions (see Table 4). However, the rate constants
for secondary radicals are still a factor of 3-8 smaller than
those of their primary homologues. This difference may be
explained from pre-exponential factors, which are systematically
smaller for secondary substituted peroxy radical reactions.
Similar observations were already reported in previous works
by our group on tertiary â-substituted peroxy radicals:9,11
Tertiary peroxy radical self-reactions present a large activation
energy, varying from Ea/R ) 4200 K for t-C4H9O2 to Ea/R )
1420 K for the HOC(CH3)2C(CH3)2O2 radical. No measurement
of the variation of the BrC(CH3)2C(CH3)2O2 self-reaction rate
constant, relative to temperature, was possible, because of a
change that was occurring in the mechanism at high temperature
and was difficult to account for.11
a
peroxy radical
k298K
uncertainty factorb
Ea/Rc
primary
secondary
tertiary
4 × 10-12
5 × 10-13
1 × 10-14
1.5
2
2.5
-1200
-1200
+1400
a Given in units of cm3 molecule-1 s-1
.
b The uncertainty factor is
defined as a multiplicative factor reflecting the overall confidence in
the rate constant at 298 K, as proposed by the JPL evaluation.22 c Given
in kelvin.
recommended values are given in Table 6 for Cl, Br, and OH
substituents. Similar trends were observed for multiple fluorine-
substituted radicals; however, until now, no data have been
available for mono-fluorine-atom substitution. Unfortunately,
no data are available for other substituents such as NO3 and
OCH3. We can probably expect similar enhancements of rate
constants compared to unsubstituted radicals.
Acknowledgment. The authors wish to thank the European
Commission for financial support within the Environment and
Climate Program.
References and Notes
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