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Rate constant and branching ratio of the reaction

of ethyl peroxy radicals with methyl
Cite this: Phys. Chem. Chem. Phys.,
peroxy radicals
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2023, 25, 17840

Cuihong Zhang,abc Chuanliang Li,cd Weijun Zhang,a Xiaofeng Tang, a

Laure Pillier,c Coralie Schoemaecker c and Christa Fittschen *c

The cross-reaction of ethyl peroxy radicals (C2H5O2) with methyl peroxy radicals (CH3O2) (R1) has been
studied using laser photolysis coupled to time resolved detection of the two different peroxy radicals by
continuous wave cavity ring down spectroscopy (cw-CRDS) in their AÖX̃ electronic transition in the
near-infrared region, C2H5O2 at 7602.25 cm1, and CH3O2 at 7488.13 cm1. This detection scheme is
not completely selective for both radicals, but it is demonstrated that it has great advantages compared
to the widely used, but unselective UV absorption spectroscopy. Peroxy radicals were generated from
the reaction of Cl-atoms with the appropriate hydrocarbon (CH4 and C2H6) in the presence of O2,
Received 13th March 2023, whereby Cl-atoms were generated by 351 nm photolysis of Cl2. For different reasons detailed in the
Accepted 22nd June 2023 manuscript, all experiments were carried out under excess of C2H5O2 over CH3O2. The experimental
DOI: 10.1039/d3cp01141k results were best reproduced by an appropriate chemical model with a rate constant for the cross-
reaction of k = (3.8  1.0)  1013 cm3 s1 and a yield for the radical channel, leading to CH3O and
rsc.li/pccp C2H5O, of (f1a = 0.40  0.20).

Introduction ozone (O3) and is the only relevant formation path of tropo-
spheric ozone. In clean environments with low NOx (NOx = NO +
The oxidation of volatile organic compounds (VOCs) in the NO2) concentrations, the fate of RO2 change and their domi-
troposphere is mainly driven by hydroxyl radicals (OH) and nant loss becomes the reaction with HO2 forming hydro-
leads, after addition of O2, to the formation of organic peroxy peroxides ROOH and terminating the radical reaction chain.
radicals (RO2). The fate of these RO2 radicals depends on Other reaction pathways under low NOx conditions for RO2
the chemical composition of the environment and a detailed radicals are either self-reaction (RO2 + RO2) or cross-reaction
review on their chemistry has been given by G. Tyndall and with other RO2 (RO2 + R 0 O2)1 or with OH radicals (RO2 + OH).3
collegues.1,2 Briefly, in a polluted atmosphere they mainly react Methane and ethane are amongst the most abundant hydro-
with nitric oxide (NO) to form alkoxy radicals or react with carbons, and their atmospheric oxidation leads to the formation
nitrogen dioxide (NO2) to form peroxynitrates (RO2NO2). Sub- of methyl peroxy (CH3O2) and ethyl peroxy (C2H5O2) radicals. For
sequent to the reaction with NO, alkoxy radicals can react with both radicals, the kinetic and product distribution for the self-
O2 to form hydroperoxy radicals (HO2) together with carbonyl reaction has been studied numerous times (for CH3O24–12 and for
compounds. HO2 further oxidises NO into NO2 and thus C2H5O213–26), the same is true for their reaction with HO2 (for
regenerates OH, closing the quasi-catalytic cycle. The photolysis CH3O25,9,27–32 and for C2H5O213,14,20,26,30,33–35). Their reaction with
of the produced NO2 leads subsequently to the formation of OH radicals has been the subject of a few studies (for CH3O23,36–41
and for C2H5O242–44). The cross-reaction between both peroxy
a
radicals has only been measured once using UV absorption
Anhui Institute of Optics and Fine Mechanics, Hefei Institutes of Physical Science,
Chinese Academy of Sciences, Hefei 230031, Anhui, China
spectroscopy45 whereby the experimental details given in that
b
Science Island Branch, Graduate School, University of Science and Technology of paper are sparse and it is not clear how the rate constant was
China, Hefei 230026, Anhui, China extracted from the absorption time profiles measured at only
c
Université Lille, CNRS, UMR 8522-PC2A-Physicochimie des Processus de one wavelength where the cross sections of both radicals are very
Combustion et de l’Atmosphère, F-59000 Lille, France.
similar. As for the product distribution of this cross reaction,
E-mail: christa.fittschen@univ-lille.fr
d
Shanxi Engineering Research Center of Precision Measurement and Online
three pathways can be expected:
Detection Equipment and School of Applied Science, Taiyuan University of Science
and Technology, Taiyuan 030024, China C2H5O2 + CH3O2 - C2H5O + CH3O + O2 (R1a)

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-C2H5OH/CH3OH + CH2O/CH3CHO + O2 (R1b) in the reactor. A small helium purge flow prevented the mirrors
from being contaminated. Three different DFB lasers are used
-C2H5O2CH3 + O2 (R1c) for the detection of the three species: HO2: NEL NLK1E5GAAA,
whereby currently no information is available on the branching 6629  17 cm1, on CRDS path 1, CH3O2: NEL NLK1B5EAAA,
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ratio between these pathways. 7480  20 cm1 on CRDS path 2, C2H5O2: AOI-1312-BF-20-CW-
The investigation of this reaction is not straightforward, F1-H2-N127, 7622  15 cm1 on CRDS path 2. They are coupled
because secondary chemistry cannot be avoided. Both radicals into one of the cavities by systems of lenses and mirrors.
will react in self-reactions, leading to analogous reaction pro- Each probe beam passed an acousto-optic modulator (AOM,
ducts. The measurements are complicated, because the pro- AAoptoelectronic) to rapidly turn off the 1st order beam once a
duct of the reaction path (R1a) leads, after rapid reaction with threshold for light intensity at the exit of the cavity was reached,
O2, to the formation of HO2 radicals in order to measure the ring-down event. Then, the decay of
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light intensity was recorded and an exponential fit is applied to

CH3O + O2- CH2O + HO2 (R2) retrieve the ring-down time. The absorption coefficient a is
derived from eqn (1).
C2H5O + O2- CH3CHO + HO2 (R3)
 
RL 1 1
with the HO2 radicals reacting subsequently with both peroxy a ¼ ½A  sA ¼  (1)
c t t0
radicals:
where t is the ring-down time with an absorber present
CH3O2 + HO2- CH3O2H + O2 (R4)
(i.e. after the photolysis pulse); t0 is the ring-down time with
C2H5O2 + HO2 - C2H5O2H + O2 (R5) no absorber present (i.e. before the photolysis pulse); sA is the
absorption cross section of the absorbing species A; RL is the
The rate constants of (R4) and (R5) are faster than the rate ratio between cavity length (79 cm) and effective absorption
constant of (R1), and thus the CH3O2 and C2H5O2 decays are path (28.8 cm); c is the speed of light.
accelerated. Therefore, determining the rate constant k1 from Ethyl- and methylperoxy radicals were generated by pulsed
observed CH3O2 and C2H5O2 decays depends also on the 351 nm photolysis of C2H6/CH4/Cl2/O2 mixtures inducing the
branching ratio k1a/k1 as well as the branching ratios for the following reactions:
two self-reactions used in the data treatment: for a given
experimental C2H5O2 or CH3O2 decay the retrieved rate con- Cl2 + hn351 nm - 2 Cl (R7)
stant k1 will decrease with increasing branching ratio.
CH4 + Cl - CH3 + HCl (R8)
In this work we present a more direct measurement of the
rate constant of (R1). Measurements have been carried out C2H6 + Cl - C2H5 + HCl (R9)
under an excess of C2H5O2 radicals over CH3O2, and both
CH3 + O2 (+ M) - CH3O2 (+ M) (R10)
radicals have been followed in their ÖX̃ electronic transition
using two different wavelengths. HO2 concentration time pro- C2H5 + O2 (+ M) - C2H5O2 (+ M) (R11a)
files have been measured simultaneously in a highly selective
C2H5 + O2 - C2H4 + HO2 (R11b)
way in the 2n1 vibrational overtone at 6638.21 cm1.
In order to rapidly convert the different radicals (C2H5, CH3,
C2H5O and CH3O) into peroxy or HO2 radicals ((R2), (R3), (R10)
Experimental and (R11)), all experiments have been carried out in 100 Torr O2
Experimental setup (Air Liquide, Alpha Gaz 2).
The setup has been described in detail before46–49 and is only C2H6 (Air Liquide, N35), CH4 (Air Liquide, N45) and Cl2 (Air
briefly discussed here. The setup mainly consists of a 0.79 m Liquide, 5% in Helium) were used directly from the cylinder:
long flow reactor made of stainless steel. The beam of a pulsed a small flow was added to the mixture through a calibrated flow
excimer laser (Lambda Physik LPX 202i), running at 351 nm, meter (Bronkhorst, Tylan). All experiments were carried out
passed the reactor longitudinally. The flow reactor contained at 298 K.
two identical continuous wave cavity ring-down spectroscopy
(cw-CRDS) absorption paths, which were installed in a small Results and discussion
angle with respect to the photolysis path. An overlap of the near
IR-path with the photolysis beam of 0.288 m is achieved with an Determination of the absorption cross sections
excimer beam width delimited to 2 cm. Both beam paths were Detecting peroxy radicals in the ÖX̃ electronic transition in the
tested for a uniform overlap with the photolysis beam before near IR region has the potential of a more selective detection
experiments. For this purpose, both cw-CRDS instruments were for peroxy radicals compared to UV absorption spectroscopy. In
operated to simultaneously measure HO2 concentrations. order to demonstrate this, we have carried out measurements
Deviations between HO2 concentrations were less than 5%, for the determination of the rate constant of the cross reaction
demonstrating that the photolysis laser was well aligned, between CH3O2 and C2H5O2 radicals. The rate constant of
i.e. both light paths probed a very similar photolysed volume this reaction was measured only once using UV absorption

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spectroscopy45 whereby the experimental details given in that Table 1 Ratio and absorption cross sections for CH3O2, C2H5O2 and CH4
paper were sparse. It is not clear how the rate constant was at three wavelengths
extracted from the absorption time profiles measured only at s (M1)/cm2 s (E1)/cm2 s (E2)/cm2
one wavelength where the cross sections of both radicals are Ratio
(speak/soff) 7488.13 cm1 7596.47 cm1 7602.25 cm1
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very similar.
The ÖX̃ transitions of peroxy radicals consist generally of CH3O2 4.0 2.2  1020 5.5  1021 5.5  1021
C2H5O2 6.6/5.0 1.5  1021 1.0  1020 7.6  1021
peaks with a few cm1 FWHM on a rather broad background.50 CH4 53
1.2  1024 1.1  1023 5.0  1025
To check for the mutual selectivity of the detection for both Ratio 14.6 0.55 (= 1/1.81) 0.72 (= 1/1.38)
radicals, the absorption cross sections for both radicals have sðCH3 O2 Þ
sðC2 H5 O2 Þ
been measured at three different wavelengths: at one ‘‘peak’’ of
the ÖX̃ transitions of the CH3O2 radical at 7488.14 cm1
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(named in the following M1, green symbols in Fig. 1), at the have been carried out). The results are summarized in Table 1
maximum of the transition of C2H5O2 at 7596.47 cm1 (named and illustrated in the lower graph of Fig. 1.
E1, red symbols in Fig. 1) and at a ‘‘plateau’’ at 7602.25 cm1 It can be seen that the absorption cross sections for both
(named E2, blue symbols in Fig. 1). radicals at the ‘‘counterpart wavelengths’’ (in italic in Table 1)
The upper graphs of Fig. 1 show for one Cl-concentration are small (1.5 and 5.5  1021 cm2), but not zero, and thus
the absorption time profiles for both radicals (left: CH3O2, complete selectivity cannot be obtained.
right: C2H5O2) at all three wavelengths. It can be seen that
both radicals still absorb at the wavelength corresponding to
the transition of the counterpart radical: for both radicals Determination of the rate constant
the absorption at its peak is around 4 times larger than at the To get best selectivity for investigating the cross reaction
peak of the counterpart radical (second column Table 1). The between both radicals, C2H5O2 was used for all experiments
absorption cross sections at the peak wavelengths are known in excess over CH3O2 for different reasons:
from earlier works3,51,52 and have been used here to obtain  To limit the reaction of Cl-atoms with peroxy radicals: the
the absorption cross sections at the peak wavelength of the reaction of Cl-atoms with CH4 is much slower than the reaction
counterpart radical from the relative intensities in Fig. 1 type of Cl-atoms with C2H6 (0.01 and 5.9  1011 cm3 s1 for CH4
experiments (experiments using 3 different Cl-atom concentrations and C2H6, respectively).54 Therefore, to even obtain identical

Fig. 1 CH3O2 (upper left graph, [Cl]0 = 4.2  1013 cm3, [CH4] = 1.9  1017 cm3) and C2H5O2 (upper right graph: [Cl]0 = 1.0  1014 cm3, [C2H6] = 4.4 
1016 cm3) profiles obtained at the three different wavelengths represented by colored vertical lines in the lower graph. Lower graph shows spectrum for
both species (CH3O2 as circles, adapted from Farago et al.51 and C2H5O2 as square adapted from Zhang et al.52), main graph shows zoom on both
sections with x-axis interrupted, insert shows continuous wavelength scale. Magenta lines in insert represent CH4 spectrum from HITRAN database.53

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CH3O2 and C2H5O2 concentrations, already 580 times more carried out at (M1) and (E2) due to the much lower CH4
CH4 than C2H6 is needed. And because CH4 is absorbing in the absorption cross sections at (E2) compared to (E1): even though
near IR region (the absorption cross sections for CH4 at the C2H5O2 is used in excess, high CH4 concentrations (up to
three wavelengths are given in Table 1 and is shown as magenta 3  1017 cm3) were still added and absorbed too much light
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stick spectrum53 in Fig. 1), the amount of CH4 that can be at (E1).
added in our experiments is limited to a few 1017 cm3. If an Three series of experiments have been carried out, and the
excess of CH3O2 would have been chosen, only a few 1013 cm3 experimental conditions are summarized in Table 2. The initial
C2H6 would need to be added to obtain comparable C2H5O2 Cl-atom concentrations (column 1) have been measured before
concentrations. Such low hydrocarbon concentrations would each experiment through measuring and fitting HO2 decays
lead to Cl-atom decays too slow to avoid major complications from the reaction of Cl-atoms with excess CH3OH. C2H6 and
due to the reaction of Cl-atoms with CH3O2 or C2H5O2. CH4 concentrations (column 2 and 3) have been obtained from
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 To limit absorption of the ‘‘counterpart’’ radical and thus flow and pressure measurements, and the initial peroxy radical
increase selectivity: the ratio of the absorption cross sections concentrations (column 4 and 5) and their ratio (column 6)
between both radicals at a given wavelength (last row of have then been calculated using the literature values of the rate
Table 1) is higher at the methyl peroxy transition: s(CH3O2) is constants for (R8) and (R9), as given in Table 3. To demonstrate
14.6 times higher compared to s(C2H5O2) at (M1), while the the relatively good selectivity towards both radicals, the percen-
inverse ratio is only 1.81 and 1.38 at (E1) and (E2), respectively. tage of the absorbances at M1 and E2, that are due to the
Therefore, in the example of a 10-fold (5-fold) excess of CH3O2 searched-after radical, have then been calculated using the
over C2H5O2, the absorbance at (M1) would be more than 99% radical concentrations and the absorption cross sections from
(98%) due to CH3O2 (i.e. excellent selectivity), but at (E1) only Table 1 (column 7 and 8).
15% (27%) and at (E2) only 12% (22%) of the absorbance would Fig. 2 shows the experimental absorption time-profiles
be due to C2H5O2, respectively. In the example of a 10-fold obtained at M1 and E2 for the 3 series (highest C2H5O2 excess
(5-fold) excess of C2H5O2 over CH3O2, the absorbance at (E1) upper graph, note the different y-axis for both wavelengths, and
would be around 95% (90%) and at (E2) 93% (87%) due to lowest C2H5O2 excess bottom graphs) as colored dots: the absorp-
C2H5O2 (i.e. still good selectivity), but now at (M1) around 59% tion time-profiles obtained at M1, the wavelength mostly selective
(75%) of the signal is due to CH3O2 absorption. to CH3O2, are shown in the left column, the profiles obtained at
 To maximize the importance of the cross-reaction: the self- E2, mostly selective to C2H5O2, are shown in the right column.
reaction of C2H5O2 is 3.5 times slower than that of CH3O2 (or 2 The profiles at both wavelengths have been simulated
times, taking the very recent determination of the CH3O2 self- simultaneously using the model from Table 3, by best reprodu-
reaction rate constant by Onel et al.12), making the loss through cing the signals at M1 as
self-reaction less important in a reaction system with excess
C2H5O2 compared to excess CH3O2. aM1 = sCH3O2,M1  [CH3O2] + sC2H5O2,M1  [C2H5O2] (2)
Therefore, experiments with a 5- to 10-fold excess of C2H5O2
and the signals at E2 as:
over CH3O2 should lead to a good sensitivity towards the rate
constant of the cross-reaction: decays at (E1) or (E2) represent aE2 = sCH3O2,E2  [CH3O2] + sC2H5O2,E2  [C2H5O2] (3)
nearly pure C2H5O2 decays mostly governed by the self-reaction, the
correction of these profiles due to CH3O2 absorption is very minor. using the corresponding absorption cross sections such as
Simultaneously measured profiles obtained at (M1) can now be given in Table 1. These simulations are shown as full lines.
corrected for C2H5O2 absorption, and the remaining CH3O2 decay The dotted lines in each graph represent the part of the
is mostly due to the cross reaction with C2H5O2: the rate constant of absorption that is due to the ‘‘major’’ radical, i.e. CH3O2 in
the cross reaction can be extracted with good sensitivity. the left column and C2H5O2 in the right column.
Even though the absorption cross section for C2H5O2 is The model contains, next to peroxy self-and cross reactions,
higher on (E1) compared to (E2), all experiments have been also some secondary chemistry of Cl-atoms: these reactions

Table 2 Experimental conditions used for measuring the rate constant of the cross reaction between CH3O2 and C2H5O2

aC2H5O2 aCH3O2
[Cl]/1013 cm3 [C2H6]/1015 cm3 [CH4]/1017 cm3 [C2H5O2]0/1013 cm3 [CH3O2]0/1013 cm3 [C2H5O2]0/[CH3O2]0 at E2 (%) at M1 (%)
8.1 2.90 2.00 7.25 0.85 8.56 92.2 63.2
11.0 9.85 1.15
13.8 12.4 1.44
7.4 2.08 2.98 5.95 1.45 4.12 85.1 78.1
10.4 8.37 2.03
12.5 10.1 2.44
7.1 1.25 2.98 5.05 2.05 2.46 77.3 85.6
9.2 6.54 2.66
11.8 8.39 3.41

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Table 3 Reaction mechanism used to fit all experiments in this work

Reaction k cm3 s1 Ref.

Initiation reactions
Cl + CH4 - CH3 + HCl  1013
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8 1.0 54
9 Cl + C2H6 - C2H5 + HCl 5.9  1011 54
10 CH3 + O2 + M - CH3O2 + M 1.4  1013 55
11a C2H5 + O2 + M - C2H5O2 + M 4.8  1012 56
11b C2H5 + O2 - C2H4 + HO2 3.5  1014 This work
Peroxy radical self- and cross-reactions
1a C2H5O2 + CH3O2 - C2H5O + CH3O + O2 1.5  1013 This work
1b C2H5O2 + CH3O2 - stable products 2.3  1013 This work
2 CH3O + O2 - CH2O + HO2 1.92  1015 54
3 C2H5O + O2 - CH3CHO + HO2 8  1015 57
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4 CH3O2 + HO2 - CH3OOH + O2 5.2  1012 52

5 C2H5O2 + HO2 - C2H5OOH + O2 6.2  1012 52
12a 2 C2H5O2 - 2 C2H5O + O2 3.2  1014 24
12b 2 C2H5O2 - stable products 7.0  1014 24
13a 2 CH3O2 - 2 CH3O + O2 1.3 1013 54
13b 2 CH3O2 - stable products 2.2  1013 54
14 CH3O + HO2 - products 1.1  1010 58
15 2 HO2 - H2O2 + O2 1.7  1012 59
Secondary Cl-atom reactions
6a Cl + C2H5O2 - ClO + C2H5O 5–8  1011 See text
6b Cl + C2H5O2 - Products 5–8  1011 See text
16 Cl + CH3O2 - ClO + CH3O 7.5  1011 60
17 Cl + CH3O2 - Products 7.5  1011 60
18 Cl + CH2O + O2 - HCl + HO2 + CO 7.32  1011 61
19 C2H5O2/CH3O2 + ClO - C2H5O/CH3O + ClOO 1.6  1012 54
20 HO2 + ClO - O2 + HOCl 6.9  1012 62
21 ClOO (+ M) - Cl + O2 (+ M) 6.2  1013 62
22 Cl + O2 (+ M) - ClO2 (+ M) 1.6  1033 62
Other secondary chemistry
23 C2H5O + C2H5O2 - products 7  1012 This work
24 C2H5O + HO2 - products 1  1010 63
25 C2H5O2/CH3O2 - diffusion 2 s1 This work
26 HO2 - diffusion 3 s1 This work

could not completely be avoided, even though their impact is These two pathways are very minor for CH3O2. For both radicals,
minor. Preliminary results in our laboratory indicate that the the fraction having reacted with Cl-atoms (green symbols), is
reaction of Cl-atoms with C2H5O2 leads with a rate constant of small, up to 5% for CH3O2 in the worst case of high initial radical
around 1  1010 cm3 s1 and a yield of 50% to formation of concentration.
C2H5O and ClO, while no clear statement can currently be
made for the fate of the other 50%. The rate constant of Determination of branching ratio
this reaction has also been determined by Maricq et al.64 to Simultaneously measured HO2 profiles allow in principle the
be 1.6  1010 cm3 s1, and therefore this reaction has been estimation of the branching ratio for the radical and molecular
included into the mechanism (see Table 3) and tests have been path of the cross reaction. The right graph of Fig. 4 shows the
run with the rate constant being varied between 1.0–1.6  HO2 profiles obtained for the series with the highest C2H5O2/
1010 cm3 s1, but the impact on simulated profiles and thus CH3O2 ratio. The initial fast rise of HO2 has two origins: it is
on the sought-after rate constant was within the noise of the partially due to the reaction of Cl-atoms with the peroxy
experimental profiles. radicals (R6) and partially due to the small fraction of C2H5
Fig. 3 shows for the example of the highest C2H5O2 excess radicals that form HO2 in reaction with O2 (R11b) rather than
(upper graphs of Fig. 2) the breakdown of the fate of the 2 the C2H5O2 radical. The first process is taken into account in
peroxy radicals into the different possible reaction paths: the the chemical model by adding a simplified reaction schema
left graphs represent CH3O2, the right graphs C2H5O2. The red (see Table 3), the second process has been implemented to best
symbols represent the fraction of the peroxy radical, which has represent the initial HO2 concentration and represents less
reacted in the cross reaction (R1): it can be seen that for CH3O2, than 1% of the initial C2H5 concentration. This observation is
this reaction is the major fate for all initial radical concentra- in excellent agreement with earlier works.24,52,65,66 These two
tions (upper graph represent blue symbols from Fig. 2, lower processes are finished within a few hundred ms, and the
graph represent green symbols from Fig. 2), while for C2H5O2 branching ratio of the cross reaction then influences the HO2
this reaction is a minor loss. The major reaction path for concentration at longer reaction time. This is conceivable,
C2H5O2 is its self-reaction (black symbols), with the cross- because the HO2 concentration at longer reaction times repre-
reaction with HO2 being the secondary contributor (blue symbols). sents the steady-state concentration between production from

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Fig. 2 Absorption-time profiles at M1 (left graphs) and E2 (right graphs) for all three series with conditions such as given in Table 2. Full lines present the
simulated absorption-time profiles using the model from Table 3 and are presented as sum of absorbance due to CH3O2 and C2H5O2, dotted lines
represent the part of the absorbance due to major radical: CH3O2 in the left column, C2H5O2 in the right column.

peroxy self-and cross reactions and the consumption through the simplest peroxy radicals CH3O2 and C2H5O2 there are
cross reaction of HO2 with the peroxy radicals. Best results are still large uncertainty in rate constant and branching ratio.
obtained with a branching ratio towards the radical channel of For CH3O2 the IUPAC recommendation54 since many years was
f1a = 0.40, i.e. very similar to the branching fraction of the k13 = 3.5  1014 cm3 s1 with a branching ratio of 0.37 for the
two self-reactions, f12a = 0.32 and f13a = 0.37 for C2H5O2 and radical channel. In a very recent work, Onel et al.12 have
CH3O2, respectively. To demonstrate the influence of the cross re-determined the rate constant and found only k13 = (2.0  0.9) 
reaction on the HO2 profiles, the full black lines in the right 1014 cm3 s1, nearly 2 times slower, but they confirmed the radical
graph represent for the highest radical concentration the yield as recommended by IUPAC. They convincingly argue that
simulation with the best rate constant and a branching ratio earlier experiments suffered from interferences of the fast reac-
varied by 0.2. It can be seen that such variation of the tion of Cl-atoms with CH3O2 and this would have increased the
branching ratio makes the model clearly deviating from the apparent rate constant. The rate constant for the self-reaction of
experimental results and therefore we estimate the uncertainty C2H5O2 radicals was also recommended by IUPAC for many
of the branching fraction from the comparison between model years at k12 = 7.6  1014 cm3 s1 with a radical yield of 0.63,
and experiment to be better than 0.2. based on the measurement of stable end products. Recently,
However, a major problem for estimating the branching Noell et al.14 and Shamas et al.24 obtained through direct radical
ratio in these experiments is, that even for the self-reactions of measurements a much lower yield for the radical path and a

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Fig. 3 Modeling results for conditions from first raw of Fig. 2 (highest excess of C2H5O2). Left graph CH3O2, right graph C2H5O2. Upper graphs are results
for lowest Cl-concentration (blue symbols in Fig. 2), lower graph are results for highest Cl-concentration (green symbols in Fig. 2). Open black circles are
CH3O2/C2H5O2 concentration, blue symbols represent CH3O2/C2H5O2 concentration having reacted through cross reaction with HO2, black symbol
represent CH3O2/C2H5O2 concentration having reacted through self-reaction, green symbols represent CH3O2/C2H5O2 concentration having reacted
with Cl-atoms, red symbols represent CH3O2/C2H5O2 concentration having reacted through cross reaction with C2H5O2/CH3O2.

Fig. 4 Left graph: CH3O2 profiles for highest C2H5O2 excess: full lines represent best simulation with rate constants from Table 3 (k1 = 3.8  1013 cm3 s1),
dashed lines represent a variation of k1 of 1.5  1013 cm3 s1. Right graph: HO2 profiles for the same experiment. Full coloured line represents best model with a
radical yield of 0.4, dashed lines in the right graph show the model with k1 varied as shown in left graph, but the branching ratio varied to best reproduce experiment
(see text). The black lines show a variation of 0.2 for the branching ratio for the highest radical concentration.

subsequently higher rate constant (0.32 radical yield leading to self-reaction of HOC2H4O2 radicals and has been proven to
k12 = (1.0  0.2)  1013 cm3 s1). A possible explanation for decompose easily on quartz or metal surfaces.67 But even though
this disagreement could be a non-negligible yield of dimer- the cross reaction (R1) is the major HO2 production path in the
formation, ROOR, in the self-reaction of peroxy radicals. The current experiments and the two self-reactions are only minor
decomposition of such dimer on reactor walls could lead to contributors, the above described uncertainties increase of
formation of aldehydes and thus appear as additional radical course directly the uncertainty of the deduced yield in this work.
formation when measuring stable end products. The dimeric Also, the HO2 signal quality is poor in these experiments due to
product has very recently been detected in the self-reaction of the absorption of high CH4 and C2H6 concentrations, therefore
C2H5O225 using advanced vacuum ultraviolet (VUV) photoioniza- we estimate the final uncertainty of the radical yield to be f1a =
tion mass spectrometry with a yield of 10  5%. The dimer has 0.40  0.20. It should be noted that the uncertainty in the
also been directly detected by CIMS with a yield of 23% in the branching ratio has negligible influence on the determination

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Fig. 5 Series of lowest C2H5O2/CH3O2 ratio (lower raw in Fig. 3) with simulations using a rate constant for the cross reaction such as predicted by the
geometric mean rule, if using data from Table 3 (full lines) and when using the recently determined rate constant for the CH3O2 self-reaction12 (dashed
lines).

of the rate constant: a change in radical yield for (R1) from 0.2 to reaction of CH3O2 and C2H5O2 and using the values for the self-
0.6 is barely visible in the modelled absorption-time profiles at reactions from Table 3, one obtains an excellent agreement
both wavelengths. (k1,geometric rule = 3.74  1013 cm3 s1) with the rate constant
To demonstrate the sensitivity of the observed absorption- obtained in this work. However, when using the value for the
time profiles to the rate constant of the cross reaction, the left CH3O2 self-reaction recently obtained by Onel et al.,12 the
graph of Fig. 4 shows the CH3O2 profiles of the same experi- geometric mean rule predicts a rate constant for the cross
ments, i.e. high excess of C2H5O2. The full lines show again the reaction of only k1 = 2.9  1013 cm3 s1. In Fig. 5 are shown
model from Table 3, while the dashed lines represent a varia- the results for both wavelength for the experiments with the
tion of k1 = (3.8  1.5)  1013 cm3 s1. Such variation brings lowest C2H5O2 excess, using this rate constant for the cross
the simulated profiles outside the experimental data. In these reaction.
simulations, the branching ratio f1a has been adapted to best It can be seen that this rate constant does not allow to
reproduce the HO2 profiles (dashed coloured lines on the right reproduce the observed absorption-time profiles, as the decays
graph): for the upper and lower limit of k1, f1a was changed to at both wavelengths are clearly too slow. However, it has not
0.31 (for k1 = 4.8  1013 cm3 s1) and 0.54 (for k1 = 2.8  been demonstrated that in the case of cross-reactions of peroxy
1013 cm3 s1) to best reproduce HO2. However, this variation radicals the geometric mean rule is a good approximation, in
has no influence on the CH3O2 profiles as can be seen in Fig. 3 particular because there are no reliable determinations of the
the cross reaction with HO2 is only a minor path for CH3O2 and rate constants for self- and cross-reactions of peroxy radicals to
therefore a change in the branching ratio has a negligible effect validate the approach. Therefore, from the current experiments
on the CH3O2 profile. From these simulations we estimate one cannot infer about the rate constant of the CH3O2 self-
the uncertainty of the rate constant of the cross reaction to reaction. But it is clear that recent research using more selective
be k1 = (3.8  1.0)  1013 cm3 s1. detection methods for peroxy radicals, compared to UV absorp-
The simulation corresponding to the lower limit of the rate tion, have challenged long-standing results on even the sim-
constant (upper curves in Fig. 4) is close to the only published plest peroxy radicals, and more research is necessary to better
value for the cross reaction rate constant45 (k1 = 2.0  1013 cm3 s1), understand their reactivity under low NOx conditions.
and is can be seen that the observed absorption time profiles
are poorly reproduced by such a model. In the work of Villenave
et al.45 no details are given on how the rate constant was Conclusion
obtained by solely measuring UV absorption profiles, The rate constant for the cross reaction of the two most simple
and therefore no speculation about possible reasons for the and abundant peroxy radicals, CH3O2 and C2H5O2, has been
disagreement can be proposed. determined by following their concentration-time profiles in
The geometric mean value rule is an empirical approach their respective ÖX̃ electronic transition. A good selectivity has
that allows for the estimation of cross-reaction rate coefficients been obtained by working under excess of C2H5O2 and by
from the self-recombination rate constants of the reacting monitoring CH3O2 radical at 7488.13 cm1 and C2H5O2 radicals
partners68 at 7602.25 cm1. A rate constant for the cross reaction of
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k1 = (3.8  1.0)  1013 cm3 s1 and a yield for the radical
kAþB ¼ 2  kAþA  kBþB
channel of f1a = 0.40  0.20 have been obtained. The present
It has shown to work to better than 20% in the prediction of rate constant is nearly two times faster than the only earlier
radical–radical rate coefficients for a series of hydrocarbon value, but in excellent agreement with an estimation based on
radicals69 and has proven to be valid also for the cross reaction the mean geometric rule. This work shows again, that the
of HO2 and DO2 radicals.70 When applying this rule to the cross chemistry of peroxy radicals under low NO conditions is still

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not well understood and more work is needed to improve the 16 C. Anastasi, D. J. Waddington and A. Woolley, J. Chem. Soc.,
knowledge. Faraday trans. I, 1983, 79, 505–516.
17 J. Munk, P. Pagsberg, E. Ratajczak and A. Sillesen, J. Phys.
Chem., 1986, 90, 2752–2757.
Conflicts of interest
This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.

18 T. J. Wallington, P. Dagaut and M. J. Kurylo, J. Photochem.

There are no conflicts to declare. Photobiol., A, 1988, 42, 173–185.
19 D. Bauer, J. N. Crowley and G. K. Moortgat, J. Photochem.
Photobiol., A, 1992, 65, 329–344.
Acknowledgements 20 F. F. Fenter, V. Catoire, R. Lesclaux and P. D. Lightfoot,
J. Phys. Chem., 1993, 97, 3530–3538.
This work is a contribution to the LabEx CaPPA project funded 21 D. B. Atkinson and J. W. Hudgens, J. Phys. Chem. A, 1997,
Open Access Article. Published on 23 June 2023. Downloaded on 8/29/2025 5:51:07 AM.

by the French National Research Agency under contract ANR- 101, 3901–3909.
11-LABX-0005-01 and to the CPER research project ECRIN 22 H. Niki, P. D. Maker, C. M. Savage and L. P. Breitenbach,
funded by the French Ministère de l’Enseignement Supérieur J. Phys. Chem., 1982, 86, 3825–3829.
et de la Recherche. The authors thank the Regional Council 23 T. J. Wallington, C. A. Gierczak, J. C. Ball and S. M. Japar,
‘‘Hauts-de-France’’ and the ‘‘European Regional Development Int. J. Chem. Kinet., 1989, 21, 1077–1089.
Fund’’ for their financial support to these projects. The authors 24 M. Shamas, M. Assali, C. Zhang, X. Tang, W. Zhang,
thank Mohamed Assali and Mirna Shamas for assistance with L. Pillier, C. Schoemaecker and C. Fittschen, ACS Earth
initial experiments. C. Z. and C. L. thanks the Chinese Scholar- Space Chem., 2022, 6, 181–188.
ship Council for financial support (no. 202006340125 (C. Z.) 25 H. Yue, C. Zhang, X. Lin, Z. Wen, W. Zhang, S. Mostafa, P.-
and no. 201908140178 (C. L.)). C. F. thanks the CAS for funding L. Luo, Z. Zhang, P. Hemberger, C. Fittschen and X. Tang,
through PIFI no. 2018VMA0055. Int. J. Mol. Sci., 2023, 24, 3731.
26 Z. Wen, H. Yue, Y. Zhang, X. Lin, Z. Ma, W. Zhang, Z. Wang,
References C. Zhang, C. Fittschen and X. Tang, Chem. Phys. Lett., 2022,
806, 140034.
1 J. J. Orlando and G. S. Tyndall, Chem. Soc. Rev., 2012, 41, 27 P. Dagaut, T. J. Wallington and M. J. Kurylo, J. Phys. Chem.,
6294–6317. 1988, 92, 3833–3836.
2 G. S. Tyndall, R. A. Cox, C. Granier, R. Lesclaux, G. K. 28 G. K. Moortgat, R. A. Cox, G. Schuster, J. P. Burrows and G. S.
Moortgat, M. J. Pilling, A. R. Ravishankara and T. J. Tyndall, J. Chem. Soc., Faraday Trans., 1989, 85, 809–829.
Wallington, J. Geophys. Res., 2001, 106, 12157–12182. 29 P. D. Lightfoot, B. Veyret and R. Lesclaux, J. Phys. Chem.,
3 C. Fittschen, Chem. Phys. Lett., 2019, 725, 102–108. 1990, 94, 708–714.
4 B. Veyret, J. C. Rayez and R. Lesclaux, J. Phys. Chem., 1982, 30 A. A. Boyd, P.-M. Flaud, N. Daugey and R. Lesclaux, J. Phys.
86, 3424–3430. Chem. A, 2003, 107, 818–821.
5 R. A. Cox and G. S. Tyndall, J. Chem. Soc., Faraday Trans., 31 M. T. Raventós-Duran, M. McGillen, C. J. Percival, P. D.
1980, 76, 153–163. Hamer and D. E. Shallcross, Int. J. Chem. Kinet., 2007, 39,
6 S. P. Sander and R. T. Watson, J. Phys. Chem., 1981, 85, 571–579.
2960–2964. 32 P. D. Lightfoot, P. Roussel, F. Caralp and R. Lesclaux,
7 K. McAdam, B. Veyret and R. Lesclaux, Chem. Phys. Lett., J. Chem. Soc., Faraday Trans., 1991, 87, 3213–3220.
1987, 133, 39–44. 33 P. Dagaut, T. J. Wallington and M. J. Kurylo, J. Phys. Chem.,
8 M. J. Kurylo and T. J. Wallington, Chem. Phys. Lett., 1987, 1988, 92, 3836–3839.
138, 543–547. 34 M. M. Maricq and J. J. Szente, J. Phys. Chem., 1994, 98,
9 M. E. Jenkin, R. A. Cox, G. D. Hayman and L. J. Whyte, 2078–2082.
J. Chem. Soc., Faraday Trans., 1988, 84, 913–930. 35 M. T. Raventós-Duran, C. J. Percival, M. R. McGillen, P. D.
10 F. G. Simon, W. Schneider and G. K. Moortgat, Int. J. Chem. Hamer and D. E. Shallcross, Phys. Chem. Chem. Phys., 2007,
Kinet., 1990, 22, 791–812. 9, 4338–4348.
11 P. D. Lightfoot, R. Lesclaux and B. Veyret, J. Phys. Chem., 36 A. Bossolasco, E. P. Faragó, C. Schoemaecker and
1990, 94, 700–707. C. Fittschen, Chem. Phys. Lett., 2014, 593, 7–13.
12 L. Onel, A. Brennan, F. F. Østerstrom, E. Cooke, L. Whalley, 37 C. Fittschen, L. K. Whalley and D. E. Heard, Environ. Sci.
P. W. Seakins and D. E. Heard, J. Phys. Chem. A, 2022, 126, Technol., 2014, 118, 7700–7701.
7639–7649. 38 C. Yan, S. Kocevska and L. N. Krasnoperov, J. Phys. Chem. A,
13 F. C. Cattell, J. Cavanagh, R. A. Cox and M. E. Jenkin, 2016, 120, 6111–6121.
J. Chem. Soc., Faraday trans. II, 1986, 82, 1999–2018. 39 E. Assaf, B. Song, A. Tomas, C. Schoemaecker and C.
14 A. C. Noell, L. S. Alconcel, D. J. Robichaud, M. Okumura and Fittschen, J. Phys. Chem. A, 2016, 120, 8923–8932.
S. P. Sander, J. Phys. Chem. A, 2010, 114, 6983–6995. 40 C. Fittschen, M. Al Ajami, S. Batut, V. Ferracci, S. Archer-
15 H. Adachi, N. Basco and D. G. L. James, Int. J. Chem. Kinet., Nicholls, A. T. Archibald and C. Schoemaecker, Atmos. Chem.
1979, 11, 1211–1229. Phys., 2019, 19, 349–362.

17848 | Phys. Chem. Chem. Phys., 2023, 25, 17840–17849 This journal is © the Owner Societies 2023
 View Article Online

Paper PCCP

41 R. L. Caravan, M. A. H. Khan, J. Zádor, L. Sheps, I. O. 54 R. Atkinson, D. L. Baulch, R. A. Cox, J. N. Crowley, R. F.

Antonov, B. Rotavera, K. Ramasesha, K. Au, M.-W. Chen, Hampson, R. G. Hynes, M. E. Jenkin, M. J. Rossi and J. Troe,
D. Rösch, D. L. Osborn, C. Fittschen, C. Schoemaecker, Atmos. Chem. Phys., 2006, 6, 3625–4055.
M. Duncianu, A. Grira, S. Dusanter, A. Tomas, C. J. Percival, 55 R. X. Fernandes, K. Luther and J. Troe, J. Phys. Chem. A,
This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.

D. E. Shallcross and C. A. Taatjes, Nat. Commun., 2018, 9, 4343. 2006, 110, 4442–4449.
42 E. P. Faragó, C. Schoemaecker, B. Viskolcz and C. Fittschen, 56 R. X. Fernandes, K. Luther, G. Marowsky, M. P. Rissanen,
Chem. Phys. Lett., 2015, 619, 196–200. R. Timonen and J. Troe, J. Phys. Chem. A, 2015, 119,
43 E. Assaf, C. Schoemaecker, L. Vereecken and C. Fittschen, 7263–7269.
Int. J. Chem. Kinet., 2018, 50, 670–680. 57 C. Fittschen, A. Frenzel, K. Imrik and P. Devolder, Int.
44 E. Assaf, S. Tanaka, Y. Kajii, C. Schoemaecker and J. Chem. Kinet., 1999, 31, 860–866.
C. Fittschen, Chem. Phys. Lett., 2017, 684, 245–249. 58 E. Assaf, C. Schoemaecker, L. Vereecken and C. Fittschen,
Open Access Article. Published on 23 June 2023. Downloaded on 8/29/2025 5:51:07 AM.

45 E. Villenave and R. Lesclaux, J. Phys. Chem., 1996, 100, Phys. Chem. Chem. Phys., 2018, 20, 8707.
14372–14382. 59 R. Atkinson, D. L. Baulch, R. A. Cox, J. N. Crowley, R. F.
46 J. Thiebaud and C. Fittschen, Appl. Phys. B, 2006, 85, Hampson, R. G. Hynes, M. E. Jenkin, M. J. Rossi and J. Troe,
383–389. Atmos. Chem. Phys., 2004, 4, 1461–1738.
47 A. E. Parker, C. Jain, C. Schoemaecker, P. Szriftgiser, O. 60 V. Daele and G. Poulet, J. de Chimie Physique, 1996, 93,
Votava and C. Fittschen, Appl. Phys. B., 2011, 103, 725–733. 1081–1099.
48 O. Votava, M. Mašát, A. E. Parker, C. Jain and C. Fittschen, 61 R. Atkinson, D. L. Baulch, R. A. Cox, J. N. Crowley,
Rev. Sci. Instrum., 2012, 83, 043110. R. F. Hampson, R. G. Hynes, M. E. Jenkin, M. J. Rossi,
49 E. Assaf, O. Asvany, O. Votava, S. Batut, C. Schoemaecker J. Troe and T. J. Wallington, Atmos. Chem. Phys., 2008, 8,
and C. Fittschen, J. Quant. Spectrosc. Radiat. Transfer, 2017, 4141–4496.
201, 161–170. 62 R. Atkinson, D. L. Baulch, R. A. Cox, J. N. Crowley,
50 E. N. Sharp, P. Rupper and T. A. Miller, Phys. Chem. Chem. R. F. Hampson, R. G. Hynes, M. E. Jenkin, M. J. Rossi and
Phys., 2008, 10, 3955–3981. J. Troe, Atmos. Chem. Phys. Discuss, 2007, 7, 981–1191.
51 E. P. Faragó, B. Viskolcz, C. Schoemaecker and C. Fittschen, 63 E. Delbos, C. Fittschen, H. Hippler, N. Krasteva, M.
J. Phys. Chem. A, 2013, 117, 12802–12811. Olzmann and B. Viskolcz, J. Phys. Chem. A, 2006, 110,
52 C. Zhang, M. Shamas, M. Assali, X. Tang, W. Zhang, 3238–3245.
L. Pillier, C. Schoemaecker and C. Fittschen, Photonics, 64 M. M. Maricq, J. J. Szente, E. W. Kaiser and J. Shi, J. Phys.
2021, 8, 296. Chem., 1994, 98, 2083–2089.
53 L. S. Rothman, I. E. Gordon, Y. Babikov, A. Barbe, D. Chris 65 E. P. Clifford, J. T. Farrell, J. D. DeSain and C. A. Taatjes,
Benner, P. F. Bernath, M. Birk, L. Bizzocchi, V. Boudon, J. Phys. Chem. A, 2000, 104, 11549–11560.
L. R. Brown, A. Campargue, K. Chance, E. A. Cohen, L. H. 66 J. D. DeSain, S. J. Klippenstein, J. A. Miller and C. A. Taatjes,
Coudert, V. M. Devi, B. J. Drouin, A. Fayt, J. M. Flaud, J. Phys. Chem. A, 2003, 107, 4415–4427.
R. R. Gamache, J. J. Harrison, J. M. Hartmann, C. Hill, 67 S. E. Murphy, J. D. Crounse, K. H. Møller, S. P. Rezgui,
J. T. Hodges, D. Jacquemart, A. Jolly, J. Lamouroux, R. J. Le N. J. Hafeman, J. Park, H. G. Kjaergaard, B. M. Stoltz and
Roy, G. Li, D. A. Long, O. M. Lyulin, C. J. Mackie, S. T. P. O. Wennberg, Environ. Sci.: Atmos., 2023, 3, 882–893.
Massie, S. Mikhailenko, H. S. P. Müller, O. V. Naumenko, 68 A. W. Jasper, S. J. Klippenstein and L. B. Harding, J. Phys.
A. V. Nikitin, J. Orphal, V. Perevalov, A. Perrin, E. R. Chem. A, 2007, 111, 8699–8707.
Polovtseva, C. Richard, M. A. H. Smith, E. Starikova, 69 S. J. Klippenstein, Y. Georgievskii and L. B. Harding, Phys.
K. Sung, S. Tashkun, J. Tennyson, G. C. Toon, V. G. Tyuterev Chem. Chem. Phys., 2006, 8, 1133–1147.
and G. Wagner, J. Quant. Spectrosc. Radiat. Transfer, 2013, 130, 70 M. Assali, J. Rakovsky, O. Votava and C. Fittschen, Int.
4–50. J. Chem. Kinet., 2020, 52, 197–206.

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