Measurements and modeling of HO2 formation in the reactions of n-C3H7 and i-C3H7 radicals with O2

Article abstract of DOI:10.1021/jp046514s

The formation of HO₂ in the reactions of C₂H ₅, n-C₃H₇, and i-C₃H₇ radicals with O₂ is investigated using the technique of laser photolysis/long-path frequency-modulation spectroscopy. The alkyl radicals are formed by 266 nm photolysis of alkyl iodides. The formation of HO₂ from the subsequent reaction of the alkyl radicals with O₂ is followed by infrared frequency-modulation spectroscopy. The concentration of I atoms is simultaneously monitored by direct absorption of a second laser probe on the spin-orbit transition. The measured profiles are compared to a kinetic model taken from time-resolved master-equation results based on previously published ab initio characterizations of the relevant stationary points on the potential-energy surface. The ab initio energies are adjusted to produce agreement with the present experimental data and with available literature studies. The isomer specificity of the present results enables refinement of the model for i-C₃H₇ + O₂ and improved agreement with experimental measurements of HO₂ production in propane oxidation. ? 2005 American Chemical Society.

Full text of DOI:10.1021/jp046514s

8374
J. Phys. Chem. B 2005, 109, 8374-8387
Measurements and Modeling of HO2 Formation in the Reactions of n-C3H7 and i-C3H7
Radicals with O2†
Edgar G. Estupi n˜ a´ n, Stephen J. Klippenstein, and Craig A. Taatjes*
Combustion Research Facility, Mail Stop 9055, Sandia National Laboratories,
LiVermore, California 94551-0969
ReceiVed: August 3, 2004; In Final Form: NoVember 6, 2004
The formation of HO
technique of laser photolysis/long-path frequency-modulation spectroscopy. The alkyl radicals are formed by
66 nm photolysis of alkyl iodides. The formation of HO from the subsequent reaction of the alkyl radicals
with O is followed by infrared frequency-modulation spectroscopy. The concentration of I atoms is
2 2 5 3 7 3 7 2
in the reactions of C H , n-C H , and i-C H radicals with O is investigated using the
2
2
2
simultaneously monitored by direct absorption of a second laser probe on the spin-orbit transition. The
measured profiles are compared to a kinetic model taken from time-resolved master-equation results based
on previously published ab initio characterizations of the relevant stationary points on the potential-energy
surface. The ab initio energies are adjusted to produce agreement with the present experimental data and with
available literature studies. The isomer specificity of the present results enables refinement of the model for
i-C H
3 7
2 2
+ O and improved agreement with experimental measurements of HO production in propane oxidation.
Introduction
Branching between OH and HO2 via reactions 1d and 1d is
important for chain propagation because of the different
reactivities of the two radicals. In addition, the reactions of
QOOH with O2 are thought to be responsible for chain branching
The reaction between alkyl radicals, R, and molecular oxygen
plays a pivotal role in the oxidation mechanism of alkanes at
low temperatures. Complete understanding of the R + O2
mechanism has implications in diverse areas such as combustion
chemistry (including autoignition and engine knock), atmo-
spheric chemistry, and radical reaction chemistry. The properties
of these reactions cause a change in the mechanism of alkane
oxidation between approximately 500 and 800 K, which results
in the “negative temperature coefficient” behavior in hydrocar-
bon oxidation. The precise mechanism of the R + O2 reactions
has attracted much interest and has been a source of confusion
and controversy. Nevertheless, a fairly detailed model of the
mechanism has recently emerged thanks to the large number
of experimental and theoretical studies that have been conducted.
The initial step in R + O2 reactions involves the formation of
an alkylperoxy complex, RO2, that can subsequently dissociate
or isomerize:
7
,8
at low temperatures (∼600-800 K). The complexity of
possible isomerization pathways in higher-hydrocarbon-radical
reactions leads naturally to an effort to build general models
on the basis of simpler, more easily characterized systems. The
ethyl (C2H5) + O2 system is the most extensively studied of
2
,6,9-20
the alkyl + O2 reactions both experimentally
and
1
,3,5,19-27
theoretically.
The reaction of the ethyl radical with O2
is considered the “prototype” alkyl + O2 reaction because it is
the smallest system where alkene formation and isomerization
to QOOH are possible.
Recently, the time-dependent production of HO and OH has
2
been measured for several photolytically initiated alkane oxida-
2
,20,28-31
tion systems.
The experimental results have been
compared to detailed master-equation calculations based on ab
initio characterizations of the potential-energy surfaces for the
reactions combined with integrated rate equation models that
R + O T RO2
(1a)
2
include both radical formation and radical destruction reactions
Direct elimination of HO2 from the RO2 radical is the principal
3,5,20,31
that occur among species present in the experiment.
The
mechanism for alkene + HO2 formation:1
-6
models accurately describe the time behavior and amplitude of
HO2 from Cl-initiated oxidation of both C2H6 and C3H8.2
However, the models underpredict the amount of OH observed
at high temperatures (>600 K) and overpredict the amount of
OH observed at lower temperatures (although uncertainties in
the rate coefficients of some key reactions involving OH affect
0,31
RO f alkene + HO2
(1b)
2
Alternatively, the RO2 radical can isomerize via intramolecular
hydrogen transfer to form a variety of different hydroperoxyalkyl
radicals, usually denoted as QOOH:
20
the model results). The results of these comparisons emphasize
several important aspects of R + O2 systems. First, it is essential
to include formally direct pathways for chemically activated
reactions. In other words, one must include reactions from the
reactants to each of the unimolecular and bimolecular products,
from each of the unimolecular species to every other one, and
from each of the unimolecular species to the bimolecular
products. For example, direct HO2 production from R + O2
must be included. This reaction does not represent a separate
abstraction mechanism but an immediate production of HO2 via
RO f QOOH
(1c)
2
Decomposition of the QOOH species via O-O bond fission
provides the primary route of OH formation:
QOOH f O-heterocycle + OH
(1d)
†
Part of the special issue “George W. Flynn Festschrift”.
Corresponding author. E-mail: cataatj@sandia.gov.
*
1
0.1021/jp046514s CCC: $30.25 © 2005 American Chemical Society
Published on Web 02/09/2005

HO2 Formation in the Reactions of Radicals with O2
J. Phys. Chem. B, Vol. 109, No. 17, 2005 8375
rapid dissociation of a chemically activated RO2* prior to
collisional stabilization. The master-equation results also em-
phasize the rapid reversibility of the RO2 T QOOH isomer-
izations under most experimental conditions. Finally, experi-
the signal-to-noise ratio, the probe beam is split into signal and
reference beams. The reference beam impinges on a low-noise
detector (I0), after traveling an equal path length as the signal
beam, through an analogous modified Herriott-type multipass
arrangement open to atmospheric pressure. The signal beam is
directed through the multipass flow cell and onto a second
low-noise detector (I). The time-resolved FM signal is mon-
itored as the demodulated difference between balanced signal
(I) and reference (I0), permitting the subtraction of common
noise. Approximately 50 µW of infrared power is incident on
each detector. A commercial traveling-interferometer wavemeter
is used to monitor the frequency of the diode laser beam.
The I-atom concentration is probed by a second external-
cavity diode laser tuned to the P1/2 r P3/2 transition at ∼1315
nm. The transient I-atom absorption is monitored by subtracting
the output of balanced signal (I) and reference (I0) detectors.
To stabilize the frequency output of the diode laser, a fraction
of the laser beam is phase-modulated, directed through a high-
temperature cell (∼1100 K), in which I2 is thermally dissociated
to generate I atoms, and imaged on a fast infrared detector. The
resulting single-tone FM signal (after subsequent demodulation)
is used as the “error signal” for a proportional-integral-
derivative controller to automatically correct any frequency
deviations away from line center.
31
mental and theoretical studies on the butyl + O2 and neopentyl
29
+
O2 systems have suggested that master-equation solutions
for a smaller system can be extended to effectively model
analogous, larger R + O2 systems.
In the present work, time-resolved production of HO2 from
the reactions of ethyl, n-propyl, and i-propyl radicals with O2
is measured as a function of temperature and pressure in the
“
transition region” between 623 and 703 K. The present
investigation uses photolysis of alkyl iodides to initiate the
reactions and extends the scope of earlier work in one very
important aspect: direct photolysis studies allow independent
determinations of HO2 production in the reactions of the two
propyl isomers (n-propyl and i-propyl) with O2 in the “transition
region”. Experimental measurements, both pulsed-photolytic Cl-
2
2
20,28,31
initiated oxidation experiments conducted previously
and
the present results using direct photolysis of ethyl, n-propyl,
and i-propyl iodides, are compared to kinetic models based on
the results of time-dependent master-equation calculations with
ab initio characterization of stationary points. In the course of
these experiments, the branching fraction of spin-orbit-excited
2
iodine atoms, I( P1/2) (denoted I*), following the photodisso-
Gas flows are controlled by calibrated mass flowmeters, and
the total pressure is maintained by a butterfly valve at the exit
of the cell, which operates under feedback from a capacitance
manometer. The quartz flow cell is heated by three resistive
elements, each under microprocessor control, with feedback
from a separate K-type thermocouple.
ciation of ethyl, n-propyl, and i-propyl iodides at 266 nm is
measured by using time-resolved laser gain versus absorption
spectroscopy.
Methods
Typical gas concentrations in the alkyl + O2 study are [O2]
Experiment. The reactions of ethyl (C2H5) and propyl (C3H7)
radicals with O2 are investigated using a modification of the
laser photolysis-continuous-wave infrared two-tone frequency-
1
7
-3
15
-3
)
1.5 × 10 cm and [alkyl iodide] ) (1-2) × 10 cm .
Approximately 3% of the alkyl iodide molecules are photolyzed
in the beam path volume. Helium is added to a total density of
modulation (FM) method employed previously for other R +
17
-3
17
-3
3
.65 × 10 cm (8.45 × 10 cm in some ethyl experiments).
Experiments are carried out at four different temperatures (623,
48, 673, and 703 K). At the relatively high levels of O2 in
these experiments, I* atoms are quenched to the ground state
O2 reactions.2
,20,28-32
Ethyl, n-propyl, and i-propyl radicals are
generated by 266 nm photolysis of ethyl, 1-propyl, and 2-propyl
iodides:
6
35-38
very rapidly (on the order of a few microseconds)
and, thus,
2
2
RI + hν (266 nm) f I( P , P ) + R
(2)
1/2
3/2
I-atom concentrations can be easily derived from the probe-
laser path length (defined as the interaction path length between
the photolysis laser and the 1315 nm probe) and the absolute
absorption cross section of I atoms for the F* ) 3 r F ) 4
The HO2 radical is monitored by laser probing in the 000-000
2
2
33
band of the A˜ A′ f X˜ A′′ electronic transition near 1.4 µm.
3
9,40
The concentration of I atoms is deduced from a simultaneous
measurement of the absorption on the spin-orbit transition of
the I-atom photolysis coproduct, permitting transient HO2 FM
signals to be scaled to the initial I-atom absorption in order to
compare results among different experiments. However, because
the HO2 line strength is not known, the yield of the HO2 radical
cannot be directly derived from the present data as it was in
previous Cl-initiated alkyl + O2 reactions.
hyperfine transition at 1315.246 nm.
I* relative quantum-
yield determination studies are performed at 673 K and a total
1
7
-3
density of 3.65 × 10 cm . Oxygen concentrations in the I*
14
branching-fraction measurements range from 5.0 × 10 to 6.0
1
5
-3
× 10 cm , and initial alkyl iodide concentrations are again
1
5
-3
kept in the range of (1-2) × 10 cm .
Theory of Alkyl + O2 Reactions. The master-equation
simulations have been performed as described in previous work
on ethyl + O2 and propyl + O2, using the stationary-point
energies calculated in previous works.
potential-energy surface has been described in detail else-
The detection sensitivity of the infrared absorption technique
is enhanced by employing a modified Herriott-type multipass
flow cell.34 The tunable infrared power is passed multiple times
3
,5,20,31
The ethyl + O2
3
,5,20
(17 or 21 passes) through the multipass flow cell. The flow
where,
and no further details are presented here. The
cell is about 1.3 m long with CaF2 windows and is surrounded
by a commercial ceramic-fiber heater capable of reaching
temperatures in excess of 1200 K. This arrangement allows the
infrared probe to overlap the UV photolysis beam only in the
center of the flow cell, where the temperature is more readily
controlled. The effective path length (i.e., overlapping path of
photolysis and probe beams) is between 9 and 11 m, depending
on the number of passes through the flow cell.
n-propyl + O2 and i-propyl + O2 potential-energy surfaces have
also been described extensively in previous publications.2
However, because one focus of the present work is to refine
the model of the propyl + O2 reactions, key earlier results are
summarized below.
0,31
The primary pathway to HO2 formation in the n-propyl and
i-propyl + O2 reactions is concerted elimination of HO2 from
3
1,41,42
C3H7O2.
The elimination transition state is calculated to
-
1
An external-cavity tunable diode laser is employed to probe
the time-resolved absorption profile of HO2. To further improve
lie 5.2 kcal mol below the energy of the reactants for n-C3H7
and 7.0 kcal mol below the energy of the reactants for
-
1

8376 J. Phys. Chem. B, Vol. 109, No. 17, 2005
Estupi n˜ a´ n et al.
TABLE 1: Rate Coefficients for the i-C
of 3.65 × 10 cm
reaction
3
H
7
+ O
2
System Generated from Solutions to the Master Equation at a Total Density
17
-3
a
a
a
a
k
623
k
648
k
673
k
703
-
-
-
-
-
12
16
13
14
16
-12
-16
-13
-14
-16
-12
-16
-13
-14
-15
3
-12
-16
-13
-14
-15
3
i-C
i-C
i-C
i-C
i-C
i-C
i-C
i-C
i-C
i-C
i-C
i-C
i-C
i-C
i-C
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
7
7
7
7
7
7
7
7
7
7
6
6
6
6
6
+ O
+ O
+ O
+ O
+ O
2
2
2
2
2
f i-C
f i-C
3
3
H
H
H
7
O
2
3.25 × 10
5.96 × 10
5.51 × 10
1.87 × 10
8.15 × 10
272
2.65 × 10
5.11 × 10
5.41 × 10
1.85 × 10
9.22 × 10
665
2.14 × 10
4.39 × 10
5.30 × 10
1.83 × 10
1.04 × 10
1.48 × 10
3.09
1.63 × 10
3.67 × 10
5.16 × 10
1.79 × 10
1.19 × 10
3.46 × 10
7.55
6
OOH
f C
3
6
+ HO
2
f methyloxirane + OH
f acetone + OH
O
O
O
O
O
2
2
2
2
2
f i-C
f i-C
3
H
H
7
+ O
OOH
2
3
H
6
0.607
1.40
f C
3
6
+ HO
2
31.4
0.601
71.2
1.30
149
326
f methyloxirane + OH
2.52
4.65
-
3
3
2
-3
3
-2
3
-2
3
f acetone + OH
3.01 × 10
1.50 × 10
1.29 × 10
5.50 × 10
9.93 × 10
2.45 × 10
6.73 × 10
2.38 × 10
1.61 × 10
7.85 × 10
1.33 × 10
3.89 × 10
1.37 × 10
3.66 × 10
1.95 × 10
1.09 × 10
1.74 × 10
5.98 × 10
2.74 × 10
5.90 × 10
2.37 × 10
1.52 × 10
2.31 × 10
9.56 × 10
OOH f i-C
OOH f i-C
OOH f C
3
3
H
H
7
+ O
2
4
4
4
4
7
O
2
4
4
5
5
3
H
6
+ HO
2
5
6
6
6
OOH f methyloxirane + OH
OOH f acetone + OH
-
-2
-2
-2
a
Units of cm molecule s-1 for second-order reactions and s for first-order reactions.
3
-1
-1
i-C3H7.31 The 1,4 hydrogen shift to form QOOH is calculated
For channels with a well-defined saddlepoint, the microca-
nonical rate coefficients have been evaluated on the basis of
conventional transition-state theory. For the barrierless entrance
channel, variable reaction-coordinate transition-state theory is
employed. For propyl + O2, the requisite transitional-mode
potential is based on ab initio quantum evaluations at the
B3LYP/6-31G* level of the energies along the minimum energy
at -2.6 kcal mol- for n-C3H7 + O2 and -1.4 kcal mol for
i-C3H7 + O2, again relative to the energies of the reactants.
The transition state for the formation of OH from CH3CHCH2-
1
-1
-
1
OOH is 6.5 kcal mol below the energy of n-C3H7 + O2, and
-
1
the transition state for HO2 formation is 3.4 kcal mol below
the energy of the reactants. From i-C3H6OOH, the transition
31
-
1
path. An exponential down model is employed for the energy-
states for OH and HO2 formation lie 4.9 and 1.9 kcal mol ,
respectively, below the energy of the reactants. The n-C3H7O2
radical has another possible isomerization, the 1,5 hydrogen shift
to form CH2CH2CH2OOH. This isomerization has a much lower
transfer process. For ethyl + O2, a temperature-independent
-
1
3,5,20
value of ∆Edown ) 200 cm is employed, as in prior work.
-
1
For propyl + O2, a value of 350 cm is instead employed,
again independent of temperature.
2
0,31
-
1
The one-dimensional
barrier, 11.2 kcal mol below the energy of the reactants, but
CH2CH2CH2OOH has a sizable barrier to the formation of either
time-dependent master equation is solved via diagonalization
of the transition matrix. The time-dependent populations of
reactants, and unimolecular and bimolecular products, are
determined directly from the eigenvalues and eigenvectors. The
31
OH or HO2. The barriers to formation of CH3CHCH2 via direct
-1
abstraction are 16.1 kcal mol for n-propyl + O2 and 13.0 kcal
-
1
mol for i-propyl + O2.
4
3
VARIFLEX software is used in the master-equation simula-
tions.
For n-propyl + O2, the barrier heights, and indeed the full
31
model, are precisely as described in an earlier work, including
the minor adjustment of the energies made in order to reproduce
the available experimental data.20 In these revisions, the
transition state for the elimination of HO2 from CH3CH2CH2-
The results of the time-dependent master-equation analysis
of ethyl + O2 and propyl + O2 reactions have been reduced to
a set of elementary reactions and phenomenological rate
coefficients that include pathways for HO2 and OH formation.
Phenomenological rate coefficients are obtained from solutions
to the master equations using the methodology described by
-
1
OO is raised by 1.4 kcal mol from the ab initio value and the
transition state for isomerization from CH3CH2CH2OO to CH3-
-
1
CHCH2OOH is also raised by 0.5 kcal mol . For i-propyl +
O2, minor adjustments of the calculated potential energies also
allow the time-resolved master-equation calculations to fit the
available experimental data, including the present experimental
data (as is described in the Results and Discussion section).
These adjustments differ somewhat from those given in an
44
Klippenstein and Miller. Table 1 shows the set of elementary
reactions and phenomenological rate coefficients that are used
to model the reaction of i-propyl + O2 at 623, 648, 673, and
17
-3
7
03 K, and a total density of 3.65 × 10 cm , using the
modified stationary-point energies described above. Rate coef-
ficients and equilibrium constants for ethyl + O2 and n-propyl
20
earlier work for a variety of reasons. In a previous computation
5,20
+
O2 are available from previous works,
changes are performed here.
as no further
20
of the rate coefficients for the i-propyl + O2 reaction, incorrect
rotational constants were inadvertently used for some of the
master-equation calculations. As a result, the adjustments to the
stationary-point energies used to produce agreement with the
available body of experimental work were somewhat in error,
and they are corrected here. The (CH3)2CHOO well depth is
Comprehensive Kinetic Model. The calculated phenom-
enological rate coefficients for ethyl + O2, n-propyl + O2, and
i-propyl + O2 derived from the time-dependent master equations
allow a model of the reaction systems to be constructed by using
the elementary reactions involved in the three reaction systems.
The experimentally observed HO2 time traces can then be
compared to predictions of this model. For these calculated
phenomenological rate coefficients to reproduce the observed
experimental data, rate coefficients must be added to the model
that describe the loss and formation of all other radicals involved
-1
increased from the ab initio value by 1.3 kcal mol and is now
-
1
set at 38.1 kcal mol below the energy of the reactants, and
-
1
the transition state for HO2 elimination is raised by 2 kcal mol
from the ab initio value of -7 kcal mol-1 to 5 kcal mol below
the energy of the reactants. In addition, the transition state for
isomerization from (CH3)2CHOO to CH3CH(CH2)OOH is raised
by 2.3 kcal mol , as described previously. Except for these
changes, all of the barrier heights and other stationary points
for both n-propyl + O2 and i-propyl + O2 are left as calculated
from ab initio simulations.
-1
2
0
in the experiment, as performed previously. Literature rate
coefficients associated with these reactions are combined with
the rate coefficients derived from the solutions to the master
equations to form an integrated rate equation model that
describes HO2 formation and removal mechanisms important
-
1
20

HO2 Formation in the Reactions of Radicals with O2
J. Phys. Chem. B, Vol. 109, No. 17, 2005 8377
TABLE 2: Reactions and Rate Coefficients Used To Model the HO
2
and I Signals from the Cl-Initiated Oxidation of Ethane
and the Photodissociation of Ethyl Iodidea
reaction
Ab
n
E
a
/R (K)
reference
C
C
HO
2
H
H
5
+ O
+ Cl f HCl + C
f O
2
system
MEc
69
-
11
2
6
2
H
O
5
3.4 × 10
0.7
-150
-600
125
125
-702
-
13
2
+ HO
2
2
+ H
2
2
2.2 ×10
φ × 8.5 × 10
(1 - φ) × 8.5 × 10
64
-
14
d
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
C
2
H
5
H
5
H
5
H
5
H
5
H
5
H
5
H
5
H
5
H
5
H
5
H
5
H
5
H
5
H
5
H
5
O
O
O
+ C
+ C
2
2
2
+ C
+ C
2
H
H
5
2
f 2C
f C
2
H
5
O + O
OH + CH
H + O
2
70
-
14
d
2
5
2
H
5
3
CHO + O
2
70
-
13
+ HO
2
f C
f products
f 2C
f OH + C
f O + C
O f (C
H
2 5
O
2
2
6.9 × 10
71
72
-
11
2
H
H
5
1.99 × 10
-
11
11
12
12
14
13
13
11
e
2
O
5 2
2
H
2
5
O
4.0 × 10
73
73
-
e
+ HO
+ HO
2
H
5
O
3.3 × 10
-
e
2
2
2
H
6
6.0 × 10
73
-
+ C
2
H
5
2
H
5
)
2
O
H
2.0 × 10
74
75
73
-
O + O
2
f HO
f H
2
+ C
2
2
4
O
2.4 × 10
325
-
e
O + HO
2
2
O
+ C
2
H
4
O
5.0 × 10
-
e
O + C
O + C
2
H
H
5
O
5
f C
O f C
+ CH
2
H
5
OOH + C
2
4
H O
5.0 × 10
73
-
2
2
H
5
OH + CH
3
CHO
6.0 × 10
f
1
1
1
1
3
O f CH
3
2
O
7.9 × 10
6.3 × 10
5.0 × 10
7.9 × 10
11060
12100
13580
14830
76
76
76
76
g
70
h
3
2 4
O f H + C H O
O f CH
O f CH
3
2
3
CHOH
CH OH
2
2
CH
CH
CH
CH
3
3
3
3
+ O
2
2
+ M f CH
+ CH f 2CH
+ C f CH
f CH O + HO
+ M f HO + M
3
O
2
+ M
-
-
-
14
13
14
O
O
O + O
3
O
2
3
O + O
2
9.2 × 10
1.4 × 10
7.2 × 10
-390
1080
290
2
2
5
H O
2
3
+ C
2
H
5
O + O
2
2
2
2
77
i
H + O
2
2
-
10
Cl + C
Cl + C
Cl + C
2
H
2
H
2
H
5
5
5
f HCl + C
2
H
4
2
2
7.57 × 10
78
79
79
64
64
e
80
80
81
82
68
83
84
see text
see text
75
85
75
86
87
87
-
11
11
11
11
11
11
12
11
34
O
O
2
f ClO + C
f HCl + C
H
5
O
O
7.7 × 10
-
2
H
4
7.3 × 10
-
Cl + HO
2
f ClO + OH
f HCl + O
O f C O + HCl
f C Cl + Cl
f Cl + CH Cl
+ H f Cl + HCl
+ M
f HI + O
I f I + C
f HI + C
f HOI + CH
4.1 × 10
450
-170
-
Cl + HO
2
2
1.8 × 10
-
Cl + C
2
H
5
2
H
4
1.9 × 10
-
Cl
Cl
Cl
2
2
2
+ C
+ CH
2
H
5
2
H
5
1.3 × 10
-120
240
209
-575
1090
8600
-
3
3
4.8 × 10
-
8.0 × 10
-
I + I + M f I
I + HO
2
5.5 × 10
-
-
-
11
2
2
1.47 × 10
1.69 × 10
1.16 × 10
10
11
I + C
I + C
I + C
H
2 5
H
2 5
H
2 5
2
2 5
H I
2
H
4
-
12
11
10
11
11
O
2
3
CHO
2.0 × 10
-
I + X f products
1.0 × 10
-
I
I
2
+ OH f HOI + I
+ C f I + C
O + I
f I + C
+ I
I f HI + C
2.1 × 10
-
2
H
2 5
H
2 5
I
5.0 × 10
-
HI + OH f H
2
1.6 × 10
-
12
HI + C
2
H
I f C
5
2
H
6
4.57 × 10
-384
25201
26602
1
3
C
C
2
H
H
5
2
H
5
4.5 × 10
1
4
2
5
H
2 4
1.27 × 10
a
n
-E /RT
unless otherwise noted. Units of s-1 for first-order reactions, cm molecule s-1 for
b
3
-1
Rate coefficients are written in the form A(T/298) e
a
6
-2 -1
for third-order reactions. c Rate coefficients are generated from solutions to the master equation
second-order reactions, and cm molecule
s
5
,20
d
70
e
73
f
(
ME).
The branching fraction is fit to the function φ ) 1.33 exp(-209/T).
Estimated on the basis of the CH
3
/O
2
system.
Calculated
7
3,88,89 g
based on an average of three literature studies.
Effective second-order rate coefficient is calculated from the expression given by DeMore
9
0
300
) 4.5 × 10 cm molecule s-1, k
-31
6
-2
300
-12
3
-1 -1
, n ) 3.0, m ) 1.7, and Fcent ) 0.6. h Calculated based
et al. where k
0
∞
) 1.8 × 10 cm molecule
s
on an average of the rate coefficients of reaction C
estimated by Kaiser ). Effective second-order rate coefficient is calculated from the expression given by DeMore et al. where k
cm molecule
2
H
5
O
2
+ C and reaction CH
2 5
H
O
2
O
3 2
+ CH , assuming no temperature dependence (as
3 2
O
6
i
90
300
-32
0
) 5.7 × 10
6
-2 -1
300
-11
3
-1 -1
s
, k
∞
) 7.5 × 10 cm molecule
s , n ) 1.6, m ) 0, and Fcent ) 0.6.
in the time domain of the experiment. The reactions and rate
coefficients used in the model are listed in Table 2 for ethyl +
O2 and in Table 3 for propyl + O2. Chlorine and iodine reactions
are included jointly in the two master kinetic models. The
experiments are initiated by either the photolysis of Cl2 or the
photolysis of alkyl iodides, and the model is adapted by setting
the initial Cl- or I-atom concentration accordingly.
Several reactions appear in the model that have not been
experimentally studied. The rate coefficients for these reactions
are estimated by using rate coefficients for similar reactions.
Estimates of several of these rate coefficients are based on
similar reactions in the more thoroughly studied CH3/O2 system.
In other cases, rate coefficients that have not been determined
experimentally for the C3H7/O2 systems are assumed to be
identical to the analogous rate constants in the C2H5/O2 system.
One important reaction that has not been experimentally studied
is the reaction of RO2 radicals with I atoms. However, the
reaction
CF O + I f IO + CF O
(3)
3
2
3
has been experimentally studied at room temperature by Wayne
4
5
and co-workers and is found to have a rate coefficient of 3.7
-
11
3
-1 -1
× 10 cm molecule s . Some Br + alkyl radical reactions
have also been measured experimentally to have smaller rate
coefficients. Specifically, the rate coefficient for the reaction
-
13
3
of Br + CH3O2 has been measured to be 4.4 × 10
cm
-
1
-1 46
molecule s , and the rate coefficient for the reaction of
-
12
3
3
CCl3O2 + Br has been measured to be 5.99 × 10
molecule
A rate coefficient of 2 × 10
cm
cm
-
1
-1 47
-12
s
.

8378 J. Phys. Chem. B, Vol. 109, No. 17, 2005
Estupi n˜ a´ n et al.
TABLE 3: Reactions and Rate Coefficients Used To Model the HO
2
and I Signals from the Cl-Initiated Oxidation of Propane
and the Photodissociation of n-Propyl Iodide and i-Propyl Iodidea
reaction
Ab
n
E
a
/R (K)
reference
c
i-C
n-C
3
H
7
+ O
+ O
2
system
system
ME
ME
c
3
H
7
2
-
10
11
C
C
C
C
3
3
3
3
H
H
H
H
8
8
8
8
+ Cl f HCl + n-C
+ Cl f HCl + i-C
+ OH f n-C + H
+ OH f i-C + H
+ HO f O + H
OH + HO f H O + O
OH + OH f O + H
OH + OH + M f H
3
H
H
7
7
1.12 × 10
8.13 × 10
212
86
145
145
-600
-250
-945
55
55
91
-
3
-
12
d
3
H
7
2
O
φ × 1.87 × 10
1.72
1.72
-
12
d
3
H
7
2
O
(1 - φ) × 1.87 × 10
91
-
13
HO
2
2
2
2
O
2
2.2 ×10
64
64
75
64
64
64
-
11
14
2
2
2
4.8 × 10
6.2 × 10
-
2
O
2.6
-0.80
-
31
2
O
2
+ M
f 2 n-C
f n-C
6.89 × 10
-
13
e
n-C
n-C
3
H
H
7
O
O
2
+ n-C
+ n-C
3
H
H
7
O
O
2
3
H
7
7
O + O
OH + C
O + O
OH + CH
2
φ × 3.0 × 10
(1 - φ) × 3.0 × 10
φ × 1.6 × 10
(1 - φ) × 1.6 × 10
-
-
13
12
e
3
7
2
3
7
2
3
H
H
2
H
5
CHO + O
2
2
-
12
e
i-C
i-C
3
H
7
O
2
+ i-C
3 7
H O
2
f 2i-C
f i-C
f n-C
f products
H + O
H + O
+ n-C
+ i-C
f HOOC
f C OOH + O
3
7
2
2200
2200
64
64
e
3
H
7
O
2
+ i-C
+ i-C
+ i-C
3
H
7
O
2
3
H
3
7
3
COCH
3
+ O
2
n-C
n-C
n-C
3
H
7
O
O
O
2
2
2
3
H
7
O
2
H
7
O + i-C
3
H
7
O + O
e, f
e, f
g
g
h
h
i
i
i
3
H
H
7
3
H
7
O
2
-
-
-
-
13
13
11
11
3
7
+ HO
+ HO
+ OH f HO
+ OH f HO
OOH + O
2
f n-C
3
H
7
O
2
2
6.9 × 10
6.9 × 10
4.0 × 10
4.0 × 10
-702
-702
i-C
3
H
7
O
2
2
f i-C
3
H
7
O
2
2
n-C
3
H
7
O
2
2
3
H
7
O
i-C
3
H
7
O
2
2
3
7
H O
-
12
3
C H
6
2
3
H
6
O
2
3.98 × 10
7.11 × 10
1.98 × 10
1.37 × 10
-0.44
-2.45
3.27
1
1
1
6
HOOC
HOOC
HOOC
HOOC
HOOC
H
3 6
H
3 6
H
3 6
H
3 6
H
3 6
O
O
O
O
O
2
2
2
2
2
3
H
6
2
17665
13954
19588
21905
14331
0
1
f OH + HOOC
f OH + HOOC
3
H
H
5
O
O
3
5
3.19
i
i
i
1
5
f OH + OOC
f HO + C
+ H
+ H
f n-C
f C
f i-C
f C
3
H
O
6
O
3.0 × 10
10
2
3
H
6
2
4.17 × 10
3.51
-
11
11
11
12
11
12
n-C
3
H
7
+ OH f C
+ OH f C
+ n-C
+ n-C
+ i-C
+ i-C
+ n-C
+ n-C
+ i-C
+ n-C
+ n-C
3
H
6
2
O
4.0 × 10
92
92
92
92
92
92
92
92
93
j
j
j
k
k
k
k
l
l
l
l
k
k
94
94
k
k
k
k
k
k
m
m
m
95
95
96
n
-
i-C
3
H
7
3
H
6
2
O
4.0 × 10
-
n-C
n-C
3
H
H
7
7
3
H
7
6
H
14
1.7 × 10
-
3
H
3 7
3
H
H
6
+ C
3
H
8
2.8 × 10
-
i-C
i-C
i-C
i-C
i-C
i-C
3
H
7
3
H
H
7
6
14
1.0 × 10
-0.7
-0.7
-0.35
-0.35
-
3
3
3
3
3
H
7
H
7
H
7
H
7
H
7
3
7
3
H
6
+ C
14
3
H
8
6.5 × 10
-
-
-
-
-
-
11
3
H
7
f C
f C
6
H
H
2.91 × 10
1.16 × 10
1.66 × 10
1.66 × 10
1.66 × 10
1.66 × 10
11
11
11
11
11
H
3 7
3
6
3 8
+ C H
H O
3 7
3
H O
7 2
f 2i-C
f i-C
f 2n-C
f i-C
f OH + n-C
f OH + i-C
f O + C
f O + C
O f n-(C
O f i-(C
3
H
7
O
2
3
H
7
O + n-C
O
O + n-C
O
3
H
7
7
O
O
n-C
n-C
n-C
3
H
7
7
7
3
H
7
O
2
3
H
7
3
H
3
H
+ i-C
+ HO
+ HO
+ HO
+ HO
+ n-C
+ i-C
+ i-C
+ n-C
H
3 7
O
2
3
H
7
3
H
-
11
11
12
12
12
12
12
12
11
11
14
2
3
H
7
7
3.3 × 10
-
i-C
3
H
7
2
3
H
8
O
3.3 × 10
-
n-C
3
H
7
2
2
3
H
6.0 × 10
-
i-C
3
H
7
2
2
3
H
8
6.0 × 10
-
n-C
3
H
7
3
H
7
3
H
7
7
)
2
O
2.0 × 10
-
i-C
3
H
7
3
H
7
3
H
)
2
2
O
2.0 × 10
-
n-C
3
H
7
3
H
7
O f (C
O f (C
3
H
H
7
)
)
O
O
2.0 × 10
-
i-C
3
H
7
H
3 7
3
7
2
2.0 × 10
-
n-C
3
H
7
O + OH f C
3
H
H
6
O + H
O + H
+ C
+ C
+ C
+ C
f n-C
f i-C
2
O
O
3.0 × 10
-
i-C
i-C
3
H
7
O + OH f C
O + O f HO
f HO
O + HO f H
f H
3
6
2
3.0 × 10
-
3
H
7
2
2
3
H
6
O
O
1.6 × 10
264.6
240.6
-
14
n-C
n-C
3
H
7
O + O
2
2
2
3
H
6
2.5× 10
-
-
-
-
-
-
-
-
-
13
13
13
13
13
13
11
11
11
3
H
7
2
O
2
2
3
6
H O
5.0 × 10
5.0 × 10
5.0 × 10
5.0 × 10
5.0 × 10
5.0 × 10
6.0 × 10
6.0 × 10
6.0 × 10
2.0 × 10
i-C
3
H
7
O + HO
O + n-C
O + i-C
O + i-C
O + n-C
O + n-C
O + i-C
O + i-C
O f H + CO(CH
O f CH + CH CHO
O f C + CH
+ O + M f CH
+ CH f 2CH
O + O f CH
2
2
O
3
H
6
O
n-C
3
H
7
3
7
H O
2
3
H
7
OOH + C
OOH + C
OOH + C
OOH + C
3
H
6
O
i-C
3
H
7
3
H
7
O
2
3
H
3
7
3
H
6
O
O
n-C
3
H
7
3 7
H O
2
f i-C
f n-C
H
7
3
H
3
6
i-C
3
H
7
3 7
H O
2
3
H
H
7
H
6
O
n-C
3
H
7
3
H
7
O f n-C
O f i-C
O f C
3
7
OH + C
3
H
6
O
i-C
3
H
7
3
H
7
3
H
7
OH + C
3
H O
6
n-C
3
H
7
3
H
7
3
H
7
OH + C
3
6
H O
1
4
i-C
i-C
3
H
7
3
)
2
10800
8660
7850
1
1
4
3
3
H
7
3
3
3.98 × 10
5.01 × 10
n-C
3
H
7
H
2 5
2
O
+ M
O + O
CH
CH
CH
3
2
3
O
2
-
14
14
3
O
2
O
3 2
3
2
9.2 × 10
-390
1080
70
77
72
73
73
-
3
2
2
O + HO
2
7.2 × 10
-
11
2
C H
2
C H
2
C H
5
5
5
+ C
+ HO
+ HO
2
H
5
f products
f OH + C
f O + C
1.99 × 10
-
11
12
k
2
2
H
5
O
3.3 × 10
-
k
2
2
2
H
6
6.0 × 10

HO2 Formation in the Reactions of Radicals with O2
J. Phys. Chem. B, Vol. 109, No. 17, 2005 8379
TABLE 3: Continued
reaction
Ab
n
E
a
/R (K)
reference
-
12
C
2
H
5
+ C
2
2
H
5
O f (C
2
H
5
)
2
O
2.0 × 10
74
ï
97
98
99
100
p
p
q
q
q
q
64
64
101
101
80
r
80
81
82
68
102
s
t
t
see text
see text
see text
75
85
u
75
V
86
H + O + M f HO + M
n-C
n-C
i-C
i-C
Cl + n-C
2
1
1
1
1
3
2
2
0
3
H
H
7
f C
f C
3
H
H
6
+ H
3.98 × 10
6.95 × 10
2.19 × 10
3.98 × 10
7.57 × 10
7.57 × 10
17608
15211
17819
14816
290
3
7
2
4
+ CH
3
-0.1
3
H
7
f C
f C
3
H
6
+ H
1.83
3
H
7
2
H
4
+ CH
f HCl + C
f HCl + C
3
-
-
10
10
3
H
7
3 6
H
3
Cl + i-C
Cl + n-C
Cl + n-C
3
H
7
H
6
290
-
11
11
11
11
11
11
11
11
3
H
7
O
2
f ClO + n-C
f HCl + C
f ClO + i-C
f HCl + C
f ClO + OH
f HCl + O
O f C
O f C
f Cl + i-C
f Cl + n-C
f Cl + CH Cl
+ H f Cl + HCl
+ M
f HI + O
I f I + n-C
I f I + i-C
f HI + C
f HI + C
f HOI + C
f HOI + CH
I + X f products
3
H
7
O
2
7.7 × 10
-
3
H
7
O
2
3
H
6
O
7.3 × 10
-
Cl + i-C
Cl + i-C
3
H
7
O
2
3
H
7
O
7.7 × 10
-
3
H
7
O
2
3
H
6
O
2
7.3 × 10
-
Cl + HO
Cl + HO
2
4.1 × 10
450
-170
-
2
2
1.8 × 10
-
k
Cl + n-C
Cl + i-C
3
H
7
3
H
6
O + HCl
O + HCl
Cl
Cl
1.9 × 10
-
k
3
H
7
3
H
6
1.9 × 10
-
-
11
Cl
Cl
Cl
Cl
2
2
2
2
+ i-C
+ n-C
+ CH
3
H
7
3
H
7
2.51 × 10
2.51 × 10
-240
-240
240
11
3
H
7
3
H
7
-
12
11
34
3
3
4.8 × 10
-
8.0 × 10
209
-
I + I + M f I
I + HO
I + n-C
2
5.5 × 10
-575
1090
9301
9301
-
-
-
-
-
11
2
2
1.47 × 10
2.09 × 10
2.09 × 10
1.16 × 10
1.16 × 10
10
10
11
11
3
H
7
2
3
H
7
I + i-C
I + n-C
H
3 7
2
3
H
6
7
3
H
7
3
H
I + i-C
I + n-C
I + i-C
H
3 7
3
H
6
-
12
12
11
10
11
11
11
3
H
7
O
2
2
H
5
CHO
COCH
2.0 × 10
-
H
3 7
O
2
3
3
2.0 × 10
-
1.0 × 10
-
I
2
I
2
I
2
+ OH f HOI + I
+ n-C f n-C
+ i-C f i-C
O + I
f I + C
f I + C
I f n-C + I
I f HI + C
2.1 × 10
-
3
H
7
3
H
7
I + I
5.0 × 10
-
3
H
7
3
H
7
I + I
5.0 × 10
-
HI + OH f H
HI + n-C
HI + i-C
n-C
n-C
2
1.6 × 10
-
-
12
3
H
7
3
H
8
3.95 × 10
3.95 × 10
-613
-613
25201
25201
22701
12
3
H
7
3
H
8
1
1
3
3
H
H
7
H
3 7
1.0 × 10
1.0 × 10
103
103
104
3
3
7
3 6
H
1
3
i-C
3
H
7
I f HI + C
H
3 6
4.68 × 10
a
n
-E /RT
unless otherwise noted. b Units of s-1 for first-order reactions, cm molecule s-1 for
3
-1
Rate coefficients are written in the form A(T/298) e
second-order reactions, and cm molecule
a
6
-2 -1
c
s
for third-order reactions. Rate coefficients generated from solutions to the master equation (ME).
d
91
-6
2
The branching fraction determined by Droege and Tully has been fit to the function φ ) -0.293 + 0.00286T - 3.47 × 10
T
+ 1.51 ×
and
Estimated on the
Estimated on the basis
-
9
3
e
70 f
1
0
T . Branching ratio to form C
3
H
7
O estimated on the basis of the C
2
H
5
/O
2
2
system.
3 7 2
Estimated on the basis of the mean of the i-C H O
g
71
h
n-C
3
H
7
O
2
self-reaction rate coefficients. Literature value of C
2
5
H O
2
+ HO
is used as an estimate of the rate coefficient.
1
05
i
l
26
j
93 k
basis of CF
of the CH /O
3
O
2
2
+ OH.
system.
Estimated on the basis of C
Estimated on the basis of C
2
H
2
5
OOH + O
2
.
Estimated on the basis of i-C
3
H
7
3 7 2
+ i-C H O .
7
3
.74 Calculated on the basis of an average of three literature studies.
m
73,88,89
3
H
5
O + C H
2 5
n
90
300
) 4.5 × 10 cm molecule s-1
-31
6
-2
Effective second-order rate coefficient is calculated from the expression given by DeMore et al. where k
0
,
300
-12
3
-1 -1
o
k
∞
) 1.8 × 10 cm molecule
s
, n ) 3.0, m ) 1.7, and Fcent ) 0.6. Effective second-order rate coefficient is calculated from the expression
9
0
300
-32
6
-2 -1
300
-11
3
-1 -1
given by DeMore et al. where k
0
) 5.7 × 10 cm molecule
s
, k
H
∞
) 7.5 × 10 cm molecule
s
, n ) 1.6, m ) 0, and Fcent ) 0.6.
80 s
p
78
q
79
r
Estimated on the basis of C
2
t
H
5
+ Cl.
Estimated on the basis of C
2
5
O
2
+ Cl.
Estimated on the basis of Cl
2
+ i-C
3
H
7
.
Estimated on
1
02
84
u
85
V
the basis of I + n-C
3 7
H I.
Estimated on the basis of I + C
H
2 5
.
Estimated on the basis of I
2
+ n-C
3
H
7
.
Estimated on the basis of HI +
8
6
3 7
i-C H .
molecule- s-1 is used in the present kinetic model for all three
1
electronic ground state and the spin-orbit-excited state, I*. The
I + RO2 reactions independent of temperature.
I atoms are produced with statistically populated hyperfine
48-50
It is further necessary to include an additional loss of I atoms,
namely, I + X, in the kinetic models in order to suitably simulate
the I-atom profiles resulting from the photolysis of ethyl,
levels.
If a suitable concentration of quencher is introduced,
ensuring a complete transfer of the initial I* population to
ground-state I but still permitting resolution of the quenching
time scale, the yield of I* can be accurately derived using gain
-11
n-propyl, and i-propyl iodides. A rate coefficient of 1.0 × 10
3
-1 -1
cm molecule
s
is employed in the simulations. All of the
48-50
versus absorption spectroscopy on the spin-orbit transition.
experimental I-atom decays exhibit second-order behavior, and,
thus, good agreement between the models and the experimental
data is found by setting the initial X-species concentration
between the values of 0.5 and 0.85 of the initial I-atom
concentration, depending on the experiment.
The technique of laser gain versus absorption spectroscopy
involves monitoring of the time-resolved gain or absorption
immediately after dissociation (initial signal amplitude ≡ Si,
positive for gain and negative for absorption), and the total
absorption after quenching of I* to I is completed (final signal
amplitude ≡ Sf, always positive). The ratio of the initial and
final amplitudes (extrapolated to t ) 0, which is the time when
the laser fires) is directly related to the relative yield of the two
states. Because of the finite time for the translational relaxation
Results and Discussion
I* Yields. The I-atom photofragment resulting from the
photodissociation of alkyl iodides is produced in both the

8380 J. Phys. Chem. B, Vol. 109, No. 17, 2005
Estupi n˜ a´ n et al.
Figure 2. Experimental HO
2
time traces obtained by infrared FM
spectroscopy taken in the photolysis experiments of n-propyl io-
dide (solid circles) and i-propyl iodide (open circles) at 648 K and a
17
-3
total density of 3.65 × 10 cm . Only every 20th point is shown for
clarity.
and n-propyl iodide, indicating that the yield of I* is greater
1
than /3 for both molecules. In i-propyl iodide photolysis, a
prompt absorption signal is visible, implying that the yield of
I* is smaller than /3. Subsequently, collisions with O2 quench
1
Figure 1. Transient absorption signals for (a) ethyl iodide, (b) n-propyl
iodide, and (c) i-propyl iodide at 266 nm and 673 K. Only every 100th
experimental point is shown for clarity. The technique of time-resolved
laser gain vs absorption spectroscopy is employed in the determination
of φ*. This method involves the determination of the back-extrapolated
all of the I* atoms generated in the photodissociation, yielding
ground-state I atoms (as observed by the increasing absorption
signal). At longer times, ground-state atoms are removed from
the probe volume by reaction with other species present in the
photolysis mixture such as HO2 and RO2, leading to a decrease
in the absorption signal.
time-zero amplitude (S
weighted population difference of the I* and I atoms initially produced,
and the long-time asymptotic amplitude (S ), which is proportional to
i
), which is proportional to the degeneracy-
f
the total I-atom population generated by the photolysis pulse. These
amplitudes are illustrated in parts a and c.
The I* branching fractions, φ*, are determined to be 0.68 (
0
(
.07 for ethyl iodide, 0.68 ( 0.07 for n-propyl iodide, and 0.25
0.03 for i-propyl iodide. The spread among individual
of I atoms, the initial amplitude is most reliably obtained from
the extrapolation to t ) 0 of an exponential fit to the quenching
decay. Similarly, because of the reactive removal of I atoms at
longer times, the final amplitude is derived from an exponential
fit to the long-time decay.
determinations is only a few percent; the uncertainty bounds
include an estimate of possible systematic uncertainties such
5
1
as errors in extrapolation. Uma and Das have previously
measured φ* for ethyl iodide and i-propyl iodide at 266 nm
using a two-photon laser-induced fluorescence scheme to probe
the photofragments I and I*. They report yields of 0.72 ( 0.02
for ethyl iodide and 0.44 ( 0.03 for i-propyl iodide. The I*
quantum yield for ethyl iodide reported from the present work
is in good agreement with the yield determined by Uma and
Figure 1 displays typical I-atom transient absorption signals
for ethyl, n-propyl, and i-propyl iodides obtained at 266 nm
and at a temperature of 673 K. An illustration of the extrapola-
tion used to derive amplitudes Si and Sf is given by the solid
lines. Only relative signal levels are required for the φ*
51
48-50
Das, although they derive a higher I* yield for i-propyl iodide
than what is obtained here. At least two measurements of φ*
for i-propyl iodide have been carried out at 248 nm, resulting
measurement. As developed by Leone and co-workers,
the
relative I* quantum yield, φ* {φ* ≡ [I*]/([I*] + [I])}, can be
obtained from the following expression:
5
2,53
in values between 0.23 and 0.26.
No measurements of φ*
Si
Sf
have been reported at 266 nm for n-propyl iodide, although
previously measured values for φ* at 248 nm range from 0.56
to 0.60.
1
φ* ) 1 +
(4)
(
)
3
5
2,53
where Si, the initial back-extrapolated time-zero amplitude, is
proportional to the population difference of the I and I* atoms
initially produced (weighted by the state degeneracies) and Sf,
the asymptotic long-time amplitude, is proportional to the total
I-atom density generated by the photolysis pulse. Because of
the state degeneracies, an initial gain is observed if the number
of excited-state I* atoms exceeds half the number of ground-
state I atoms (φ* > /3); if φ* < /3, initial absorption is seen.
Very accurate quantum yields can be derived from laser gain
versus absorption spectroscopy because of the independence of
the measurement on parameters such as the concentrations of
the precursor and the quenching gas, precise tuning of the probe
laser, photolysis laser power, precursor absorption cross sections,
and probe laser power.4
Measurements and Modeling of HO2 Production in Alkyl
+ O2 Reactions. Figure 2 shows experimental HO2 time traces
obtained by infrared FM spectroscopy taken in the photolysis
experiments of n-propyl iodide and i-propyl iodide at 648 K.
The results depicted in this figure show clearly the differences
between HO2 formation in i-propyl and n-propyl oxidation and
confirm that current experiments are sensitive probes of the
reaction of both isomers with O2. Similarly to other alkyl + O2
1
1
2
,20,28-32
reactions,
HO2 formation is observed to occur on two
different time scales: a prompt HO2 signal, which is observed
immediately following the UV flash and which cannot be
temporally resolved under the current experimental conditions,
and a second, slower delayed rise that becomes faster as the
temperature is raised between 623 and 703 K (reflecting the
reduced thermal stability of the alkylperoxy radical). The prompt
HO2 production is governed by the competition between
8-50
As seen in Figure 1, prompt gain is observed immediately
after the photolysis pulse in the photodissociation of ethyl iodide

HO2 Formation in the Reactions of Radicals with O2
J. Phys. Chem. B, Vol. 109, No. 17, 2005 8381
Figure 4. Comparison of the predicted (solid curve) and observed
Figure 3. Comparison of the predicted (solid curve) and observed
(
2
circles) HO produced in the photodissociation of n-propyl iodide at
(
circles) HO
2
produced in the photodissociation of ethyl iodide at 648
17
-3
several temperatures and a total density of 3.65 × 10 cm obtained
1
7
-3
17
-3
K and total densities of (a) 3.65 × 10 cm and (b) 8.45 × 10 cm
by infrared FM spectroscopy. Only every 50th point is shown for clarity.
obtained by infrared FM spectroscopy. Only every 20th point is shown
for clarity.
collisional stabilization and direct reaction (concerted elimination
of HO2 from the chemically activated RO2*). The longer-time-
scale production of HO2 arises from dissociation of the
thermalized RO2 species. HO2 formation from the reaction of
i-propyl + O2 displays a bigger prompt yield and a faster
secondary delayed production rate than those of the HO2 formed
from the n-propyl + O2 reaction. Naturally, the next goal is
to simulate both profiles with the integrated rate equation
models.
A first test is to see whether the HO2 production in the present
ethyl iodide photolysis experiments is reproduced by the
integrated rate equation model. The same parametrized master-
equation rate coefficients that successfully modeled previous
work20 are used here, so this comparison tests the agreement of
the present experiments with the Cl-initiated ethane oxidation
studies. As can be observed in Figure 3, the kinetic model
accurately reproduces the time behavior and amplitude of the
HO2 observed at the two different densities investigated.
The next step is to simulate the present isomeric propyl +
O2 experiments. Figures 4 and 5 show a comparison of the
predicted and observed HO2 and I signals at several temperatures
in the n-propyl + O2 experiments. The agreement between the
experimental data and the model is very good for both HO2
and I atoms for these experimental conditions. Figures 6 and 7
depict the same comparisons using similar experimental condi-
tions, but this time for the i-propyl + O2 experiments. The model
underestimates the prompt HO2 production, especially as the
temperature increases, and displays slower secondary production
rates than those observed experimentally. Even though the
agreement between the experimental and modeled I-atom
profiles in the i-propyl oxidation experiments is, in general, fairly
good, the model does not capture the extra delayed rise in the
I-atom concentration, which reduces the agreement between the
model and the experimental data for approximately the first 4
ms after the flash.
Figure 5. Comparison of the predicted (solid curve) and observed
(circles) I-atom profiles produced in the photodissociation of n-propyl
1
7
-3
iodide at several temperatures and a total density of 3.65 × 10 cm
obtained by infrared absorption spectroscopy. Observed I-atom con-
centrations are derived by using the absolute absorption cross section
for the F* ) 3 r F ) 4 hyperfine transition of iodine atoms at 1.315
µm.3 Only every 100th point is shown for clarity.
9,40
formation of the n-propyl radical ∼53% of the time and to the
5
4-56
i-propyl radical ∼47% of the time.
Figure 8 shows a
comparison between two experimental HO2 traces obtained at
a temperature of 645 K, and at two different total densities,
and the present and previously employed kinetic models. The
most significant difference between the two kinetic models is
the somewhat different values for the rate coefficients for the
elementary reaction steps involved in the i-propyl + O2 reaction
(as derived from solutions to master equations using the present
stationary-point energies). The present model reproduces the
experimental traces very well and, in fact, does a better job of
simulating the delayed HO2 formation than the model used
2
0
2
0
To check consistency, the new integrated rate equation model
has been employed to predict the HO2 profiles obtained in
previously.
Specific trends in the experimental and modeling results offer
insight into the reaction mechanism. Figure 3 shows the HO2
generated in the photodissociation of ethyl iodide at two different
total densities but otherwise very similar experimental condi-
2
8
previous Cl-initiated propane oxidation experiments. The
reaction of Cl atoms with propane forms both isomers of C3H7.
For example, at 645 K, the Cl + propane reaction leads to the

8382 J. Phys. Chem. B, Vol. 109, No. 17, 2005
Estupi n˜ a´ n et al.
Figure 6. Comparison of the predicted (solid line) and observed
circles) HO produced in the photodissociation of i-propyl iodide at
(
2
1
7
-3
several temperatures and a total density of 3.65 × 10 cm obtained
by infrared FM spectroscopy. Only every 50th point is shown for clarity.
Figure 8. Comparison of the predicted (solid line) and observed
(
2
circles) HO produced in the Cl-initiated oxidation of propane at 645
17
-3
17
-3
K and total densities of (a) 3.65 × 10 cm and (b) 8.45 × 10 cm
obtained by infrared FM spectroscopy.2
0,28
Also shown as a dashed
generated by the previously
curve for comparison is the predicted HO
2
employed kinetic model.20 The experimental concentration is determined
relative to the initial Cl-atom concentration using the reference Cl/
3 2
CH OH/O system. There is no arbitrary scaling of the amplitudes. Only
every 10th experimental point is shown for clarity.
more reactive flux through the stabilized RO2 species. If the
temperature is high enough that RO2 dissociates on the time
scale of the experiment, delayed HO2 is observed from these
stabilized RO2 radicals.
Figures 4 and 6 show how the time behavior of the HO2
concentrations produced in the photodissociation of propyl
iodides changes as a function of temperature at a constant
density. Both the prompt and delayed productions of HO2
increase as a function of temperature, as has been described
Figure 7. Comparison of the predicted (solid curve) and observed
(
circles) I-atom profiles produced in the photodissociation of i-propyl
17
-3
iodide at several temperatures and a total density of 3.65 × 10 cm
28
previously. As the temperature is raised, collisional stabiliza-
tion of the propylperoxy radical becomes less effective as its
thermal dissociation becomes faster. Concomitantly, the fraction
of HO2 molecules that are generated by direct reaction of R +
O2, whether in the initial reactive encounter or after dissociation
of a propylperoxy radical, increases as the temperature is raised
throughout the “transition regime” (∼580-750 K). As Miller
obtained by infrared absorption spectroscopy. Observed I-atom con-
centrations are derived by using the absolute absorption cross section
for the F* ) 3 r F ) 4 hyperfine transition of iodine atoms at 1.315
3
9,40
µm.
Only every 100th point is shown for clarity.
tions. The relative prompt HO2 production is a factor of 2 higher
in the lower-density experiment, and only the higher-density
experiment exhibits an evident secondary delayed production
of HO2. The decrease in prompt HO2 with increasing pressure
observed in Figure 3 reflects more efficient stabilization of the
ethylperoxy radical, leading to a smaller initial yield of HO2
5
and Klippenstein have thoroughly discussed, as the transition
regime is traversed from low to high temperatures (∼750 K), a
“stabilization limit” is eventually reached, a temperature above
which no collisional stabilization products can be formed, no
matter how high the pressure. Therefore, in the high-temperature
regime, HO2 is formed purely by the direct reaction pathway
and the prompt appearance of HO2 is observed with no
secondary production.
The prompt and delayed productions of HO2 are both higher
at each temperature in the i-propyl + O2 reaction than they are
in the n-propyl + O2 reaction. Two major factors may contribute
to the difference: the energy of the transition state for HO2
elimination is lower with respect to the reactants in the i-propyl
+ O2 reaction, and, entropically, the elimination transition state
of the i-propylperoxy radical is favored because there are six
2
,6,16,17
molecules.
The secondary HO2 production reflects the escape of mol-
ecules from the R + O2 T RO2 system via the concerted
elimination transition state. This can be accomplished either by
dissociation of RO2 to R + O2 followed by direct reaction or
by thermal elimination of HO2 from the stabilized RO2 radical.
For example, about 66% of the HO2 yield in the lower-density
measurement of Figure 3 is from this “delayed” production,
whereas about 85% of the HO2 in the higher-density experiment
is formed by this mechanism. More efficient stabilization of
the alkylperoxy radical at higher pressures naturally leads to

HO2 Formation in the Reactions of Radicals with O2
J. Phys. Chem. B, Vol. 109, No. 17, 2005 8383
available H atoms in the two adjacent methyl groups in the
i-propylperoxy radical versus two adjacent H atoms in the case
of the n-propylperoxy radical. The overall effect is larger direct
HO2 production at each temperature in the i-propyl + O2
reaction, which increases both prompt and delayed HO2.
Before more fully discussing the possible impact of iodine
chemistry and the photolysis of alkyl iodides on the experimental
results, the results of the master-equation calculations are
compared to other experiments in the literature. Theoretical
results of the ethyl + O2 reaction have been satisfactorily
compared with measurements of total rate coefficients, HO2
3,5
production rate coefficients, and HO2 branching fractions, and
some of the experimental data have been used to successfully
constrain key stationary-point energies on the ethyl + O2
potential-energy surface. As an additional point of comparison,
the ethyl kinetic model has been employed to reproduce the
6
ethene percentage yields obtained by Kaiser at three temper-
atures in his study of the mechanism of the ethyl + O2 reaction.
Kaiser’s experiments involved the steady-state photolysis of
mixtures containing Cl2, C2H6, and O2 over a wide temperature
Figure 9. Comparison of the predicted (open circles) and measured
(filled circles) equilibrium constants for the reaction of i-propyl + O
to form i-propylperoxy. The predicted equilibrium constants are derived
from solutions to master equations, and the measured equilibrium
2
1
8
-3
range (298-680 K) and a constant density of 6.8 × 10 cm .
After a period of UV irradiation, the resulting mixtures are
analyzed by gas chromatography/mass spectrometry to deter-
mine product yields. The present kinetic model predicts the
following ethene yields under Kaiser’s experimental condi-
tions: 1.4% at 450 K, 31% at 550 K, and 87% at 650 K. These
results are in good agreement with the experimental values
9
constants are taken from the work of Knyazev and Slagle.
of their determination. There is generally good agreement
between the theoretical results reported here for ethyl, n-propyl,
and i-propyl + O2 reactions and the wide range of experimental
results reported in the literature.
6
obtained by Kaiser: 1.3% at 450 K, 39% at 550 K, and 92% at
Iodine Chemistry. As depicted in Figure 7, the integrated
rate equation model does not capture the delayed rise in the
I-atom concentration observed in the i-propyl oxidation experi-
ments (seen in the overshoot of the experiment at early time).
Understanding this effect might provide clues as to the possible
reasons for the systematic differences between the modeled and
experimental HO2 profiles in the i-propyl + O2 experiments
and to the identity of species X that has been introduced to
model the I-atom decay. At least three possible explanations
can be considered. The first possibility is that the I-atom
absorption cross section might be changing over this initial time
period as a result of velocity relaxation of I atoms as they collide
with helium molecules (which leads to a change in Doppler
6
50 K.
The theoretical results of the n-propyl + O2 reaction have
been satisfactorily compared31 to the measured total rate
coefficients for n-propyl + O2 from Slagle et al. and Ruiz
and Bayes. In the present work, the propene yields obtained
57
5
8
5
9
by Kaiser are compared with the yields obtained by the propyl
integrated rate equation model developed here using Kaiser’s
experimental conditions. Kaiser59 investigated the generation
of propene from the reaction of propyl + O2 as a function of
temperature (450-550 K) and at a constant density of 5.5 ×
18
-3
1
0
cm by irradiating mixtures of propane, Cl2, and O2.
59
Because Kaiser generates propyl radicals by the reaction of
Cl with propane, both n-propyl and i-propyl radicals are formed
in his experiments. The present propyl kinetic model results in
the following propene yields under Kaiser’s conditions: 0.5%
at 450 K, 4% at 500 K, and 26% at 550 K. The calculated yields
are in reasonable agreement with the values measured by Kaiser:
62
shift). Cline et al. have studied this effect by direct laser
probing of I* Doppler profiles in the photodissociation of
n-C3F7I at 266 nm. However, their experimental results indicate
that velocity relaxation of I* atoms by He, which is expected
to be very similar to relaxation of ground-state I atoms, occurs
in approximately 50 collisions. This corresponds to a time of
less than 1 µs, under the present experimental conditions, making
this explanation unlikely. A second possibility involves the
excited oxygen molecules produced in the quenching of I*:
5
9
0
.7% at 450 K, 7% at 500 K, and 33% at 550 K.
Slagle and co-workers9,60 have studied the equilibration of
the reaction of i-propyl radicals + O2 to form i-propylperoxy
radicals over a range of temperatures (592-692 K) by monitor-
ing the decay of i-propyl radicals with photoionization mass
spectrometry. Figure 9 compares the results of the equilibrium
constant derived by the master-equation calculations to the
experimental values obtained by Slagle and co-workers. The
plot shows excellent agreement between the theory and the
experiments. Gulati and Walker61 have measured propene and
propane yields, by gas chromatography, formed in the oxidation
of isobutyraldehyde (over the temperature range of 653-773
K and a pressure of 50 Torr), and those results have been used
to obtain rate coefficients for the reaction of i-propyl + O2 to
form propene. Master-equation calculations performed at 648,
1
I* + O f I + O ( ∆)
(5)
2
2
9
,60
If the concentration of O is not in large excess, then a significant
2
equilibrium concentration of I* may be present at long times,
leading to a competition between the re-emergence of I atoms
and losses due to reactions with other species present in the
oxidation system (which would manifest itself as a delayed rise
in the I absorption profile). However, the equilibrium concentra-
tion of I* is negligible at the O concentrations used in the
2
present experiments. The third argument involves the effect of
1
7
03, 733, and 773 K and a total pressure of 50 Torr have been
O2( ∆) reactions on the overall chemistry. Because of the long
61
1
63
compared with the results obtained by Gulati and Walker, and
it is found that the simulated rate coefficients are within a factor
of 2 of Gulati and Walker’s values, within probable uncertainties
radiative lifetime of O2( ∆) and its slow quenching by bath
6
4
1
gases, including He, it is possible that O2( ∆) may alter the
chemistry of the experiments. However, a review of the

8384 J. Phys. Chem. B, Vol. 109, No. 17, 2005
Estupi n˜ a´ n et al.
1
1
52
chemistry of O2( ∆) reveals that O2( ∆) reacts fairly slowly with
mental energy-partitioning results of Godwin et al. and Kang
65
66
most species of interest here, including alkenes. Another piece
of information that points away from O2( ∆), or a product of
it, as species X is that it appears necessary to set the initial
concentration of species X to values higher than the measured
yield of I* atoms resulting from the photodissociation of i-propyl
iodide (i.e., φ* ) 0.25).
et al. and the φ* measurements obtained from the present work
indicates that the ethyl, n-propyl, and i-propyl radicals have,
1
-
1
on average, approximately 12.5, 22, and 30.6 kcal mol of
internal energy, respectively, following the 266 nm photolysis
pulse. Collisional deactivation of the alkyl radical is expected
to take on the order of tens of microseconds, which is adequate
to thermalize the radicals before significant reaction with O2
but perhaps not fast enough to prevent dissociation of the most
highly excited alkyl radicals.
67
Transient HO2 FM signals are scaled on the basis of the initial
I-atom absorption in order to compare results among different
experiments because no internal calibration is available, as it
was in previous Cl-initiated experiments. The key assumption
in this comparison is that the initial I-atom concentration is equal
to the initial alkyl-radical concentration. The simulated HO2
profile is expressed as [HO2]t/[R]0, but the experimental HO2
signal is merely proportional to [HO2]t, with an unknown
proportionality constant R that relates the HO2 concentration
to the FM signal amplitude. When the HO2 signals are compared
to those of the simulations, this detectivity constant (on the order
Although there is generally good agreement between the
theoretical results reported in this work for the i-propyl + O2
reaction and the wide range of experimental results reported in
the literature, the present kinetic model does not completely
accurately reproduce the experimental prompt HO2 production
and the secondary delayed HO2 production, as described above.
A number of possible sources exist for the discrepancy,
including deficiencies in the experimental evidence and in the
theoretical treatment. However, it must be recognized that the
comparison of the master-equation calculations to the experi-
mental results depends on the kinetics of a number of reactions
beyond the R + O2 system, including several reactions that have
either never been studied or not been thoroughly studied. One
such reaction is the reaction of I atoms with HO2. This reaction
of R ) 1016 cm V ) can be taken as an arbitrary scaling
factor. However, although this constant is not precisely known,
it should depend significantly, but predictably, only on tem-
perature T and pressure p for identical probe-laser conditions.
That is, the same concentration of HO2 should give the same
signal regardless of the photolysis source. The relative HO2
signal does not depend on the initial alkyl iodide concentration,
suggesting that pressure broadening by alkyl iodide is negligible
under the present conditions. If [R]0 is assumed to equal the
measured initial I-atom concentration [I]0, the experimental HO2
yield [HO2]t/[R]0 can be written in terms of the measured HO2
signal FM(t) and the measured initial I-atom concentration:
-3
-1
has been experimentally studied over the temperature range of
83-353 K, temperatures much lower than those employed
in the present experimental studies. The Arrhenius expression
68
2
68
provided by Jenkin et al. has been used to extrapolate rate
coefficients to the temperatures of this study. Another important
reaction that has not been experimentally studied is the reaction
of RO2 radicals with I atoms, for which a rate coefficient of 2
[
HO2]
R(p,T) FM(t) R(p,T) FM(t)
-12
3
-1 -1
t
× 10
cm molecule
s
has been used to model all three
)
≈
(6)
[
]
I + RO2 reactions independent of temperature. The integrated
rate equation model predicts that these two reactions have a
noticeable effect on both the observed HO2 formation and the
I-atom profile. The I + RO2 reaction has a relatively bigger
impact at the lower temperatures of the present experimental
studies because RO2 lives longer at these temperatures. The
iodine decay cannot be even qualitatively modeled without a
significant rate coefficient for the RO2 + I reaction. Although
it does not appear feasible to derive precise values for these
rate coefficients from the present data, the combined experi-
mental HO2 and I profiles do constrain the values of certain
critical rate coefficients, including I + RO2 and I + HO2.
[R]0
[R]0
[I]0
exp
The proportionality constant R can be estimated by scaling the
modeled [HO2]/[R]0 to the experimental ratio. However, match-
ing the overall amplitudes of the model to the experimental HO2
signals yields different values of the detectivity constant R for
different alkyl radicals. Therefore, either R depends on the
identity of the alkyl iodide in addition to its pressure and
temperature dependence or the initial alkyl-radical concentration
differs from the initial I-atom concentration. In the present
simulations, the latter is assumed. Taking the minimum derived
R to correspond to the case [R]0 ) [I]0, the initial alkyl-radical
concentration (compared to the initial I-atom concentration) is
then reduced in the integrated rate equation model at the two
highest temperatures investigated in the photolysis of n-propyl
iodide and i-propyl iodide (depicted in Figures 4 and 6) and at
all temperatures and pressures investigated in the photolysis of
ethyl iodide (depicted in Figure 3). A reduction of the assumed
initial alkyl-radical concentration, more pronounced at the
highest temperature, is employed in the n-propyl and i-propyl
oxidation models ([R]0/[I]0 factors ranging from 0.33 to 0.87),
whereas a temperature-independent factor of [R]0/[I]0 ) 0.5 is
employed in the simulations of the ethyl oxidation system.
Following the other possible assumption, a changing detectivity
constant (or treating R as an arbitrary scaling constant) gives
similar agreement between models and experimental traces. The
reason for this scaling change is not completely clear.
Figure 10 shows a comparison of the predicted and observed
HO2 and I concentrations in the study of i-propyl + O2 at 673
K. Both the experimental data and the simulated solid curves
are the same as the ones shown in Figures 6 and 7, which
employed the rate coefficients given in Table 3 for the
simulations. The dashed curves employ the same model except
that the rate coefficient for I + RO2 has been increased by a
-
11
3
-1 -1
factor of 10, to 2 × 10
to the room-temperature rate coefficient of 3.7 × 10
molecule determined by Wayne and co-workers in their
cm molecule
s
(a value closer
-
11
3
cm
-
1
-1
s
4
5
study of the CF3O2 + I reaction ), and the rate coefficient for
I + HO2 has been increased by a factor of 3. Interestingly, the
revised kinetic model accurately reproduces the experimental
HO2, but it does not, however, simulate the I trace as well as
the previous model. A similar model can be employed to
simulate the HO2 and I experimental traces resulting from the
photodissociation of n-propyl iodide. Figure 11 shows the
comparison at 648 K, where, once again, the solid curves
represent the same simulations as those displayed in Figures 4
and 5 and the dashed curves represent the revised model, where
It can be assumed that, for every I atom formed, one alkyl
radical is initially formed. Nevertheless, it is conceivable that
the excess energy of the photodissociation at 266 nm leads to
the dissociation of some of the alkyl radicals before they are
collisionally stabilized. A simple calculation using the experi-

HO2 Formation in the Reactions of Radicals with O2
J. Phys. Chem. B, Vol. 109, No. 17, 2005 8385
Figure 11. Comparison of the predicted (solid and dashed curves)
2
and observed (circles) (a) HO (every 50th point shown for clarity)
Figure 10. Comparison of the predicted (solid and dashed curves)
and observed (circles) (a) HO (every 50th point shown for clarity)
2
and (b) I (every 100th point shown) produced in the photodissociation
of i-propyl iodide at 673 K obtained by infrared FM spectroscopy. The
solid curve is obtained by using the present kinetic model (as depicted
in Figures 7 and 8), and the dashed curve is obtained by increasing the
and (b) I (every 100th point shown) produced in the photodissociation
of n-propyl iodide at 648 K obtained by infrared FM spectroscopy.
The solid curve is obtained by using the present kinetic model (as
depicted in Figures 4 and 5), and the dashed curve is obtained by
increasing the rate coefficients for I + RO
2
2
and I + HO by factors of
1
0 and 3, respectively. Observed I-atom concentrations are derived by
rate coefficients for I + RO
2
2
and I + HO by factors of 10 and 3,
using the absolute absorption cross section for the F* ) 3 r F ) 4
respectively. Observed I-atom concentrations are derived by using the
hyperfine transition of iodine atoms at 1.315 µm.3
9,40
absolute absorption cross section for the F* ) 3 r F ) 4 hyperfine
3
9,40
transition of iodine atoms at 1.315 µm.
energies used to generate the phenomenological rate coefficients
presented here). These changes lead to a higher prompt HO2
production and a faster delayed HO2 production, which fairly
accurately reproduces the present experimental profiles (after
the reduction of the i-propyl radical concentration with respect
to the initial I concentration, as performed previously). However,
the calculated rate coefficient for i-propyl + O2 to form propene
is then about a factor of 9 higher than the value derived in the
it is now not necessary to include an additional loss of I atoms
by reaction with species X. However, in this case, neither the
HO2 nor I experimental profile is modeled correctly, suggesting
that the altered I + HO2 and I + RO2 rate coefficients employed
in the revised simulations are not consistent with the wide range
of experimental data obtained here. The change in the assumed
HO2 + I rate coefficient required to give significant improve-
ment in modeling the experimental HO2 production in the
i-propyl + O2 reaction cannot be reconciled with the ethyl +
O2 and n-propyl + O2 data. Additionally, it is probably
reasonable to assume that the reactions of I atoms with
ethylperoxy, n-propylperoxy, and i-propylperoxy have similar
rate coefficients, making a sizable increase in the assumed
i-propyl-O2 + I reaction unlikely. This comparison highlights
the advantages of simultaneously probing two species, HO2 and
I, over a wide range of temperatures to demand consistency
with theoretical simulations that partially depend on the kinetics
of a number of reactions beyond the R + O2 system but also
points out the remaining uncertainties in the iodine chemistry.
Reliability of Adjusted Stationary-Point Energies. Other
possible adjustments of theoretical parameters in the study of
the i-propyl + O2 reaction, such as the energies of stationary
points along the calculated potential surface, energy-transfer
constants, and collision cross sections, are less successful in
accurately simulating the HO2 profiles while maintaining
consistency with the available literature data. For example, the
elimination transition state of HO2 from i-C3H7O2 can be
6
1
experimental work of Gulati and Walker, which is beyond
the reasonable uncertainties for this value, and the agreement
9
with experimental equilibrium constants is diminished, incon-
sistencies that seem to invalidate this revision.
It is common in the study of complex reaction systems to
derive experimental rate coefficients on the basis of an assumed
kinetic mechanism. It may thus be tempting to simply extract
rate coefficients for key elementary reactions in the alkyl + O2
system using an optimization of the developed kinetic model.
However, even if the set of elementary reactions that ultimately
lead to HO2 formation in the alkyl + O2 system are reduced to
four reactions (namely, reactions 1a, -1a, and 1b and the direct
reaction of R + O2 to form alkene + HO2), additional
experimental data (e.g., the RO2 time profile) are necessary in
order to have as many measured species as unknown rate
coefficients in the system. Second, and more importantly, even
if the assumed mechanism is complete and correct, the predicted
rate coefficients depend on the kinetics of a number of reactions
beyond the R + O2 system, some of which have been discussed
here. These facts lead to the present strategies of employing
high-level computational kinetic methods for the prediction of
rate coefficients in these systems and of restricting the optimiza-
-
1
lowered by 1 kcal mol and the i-C3H7O2 well depth reduced
-
1
by 1.3 kcal mol (with respect to the adjusted stationary-point

8386 J. Phys. Chem. B, Vol. 109, No. 17, 2005
Estupi n˜ a´ n et al.
tion of the resulting mechanism to minor adjustments of
stationary-point energies within the estimated uncertainty of the
quantum chemical method. The rate coefficients presented here
reasonably reproduce the available kinetic data on alkyl + O2
reactions while maintaining consistency with quantum chemical
calculations.
(19) Wagner, A. F.; Slagle, I. R.; Sarzynski, D.; Gutman, D. J. Phys.
Chem. 1990, 94, 1853.
(20) DeSain, J. D.; Klippenstein, S. J.; Miller, J. A.; Taatjes, C. A. J.
Phys. Chem. A 2003, 107, 4415.
(21) Stark, M. S. J. Am. Chem. Soc. 2000, 122, 4162.
(
22) Quelch, G. E.; Gallo, M. M.; Schaefer, H. F., III. J. Am. Chem.
Soc. 1992, 114, 8239.
23) Quelch, G. E.; Gallo, M. M.; Shen, M.; Xie, Y.; Schaefer, H. F.,
(
III; Moncrief, D. J. Am. Chem. Soc. 1994, 116, 4953.
(24) Chen, C. J.; Bozzelli, J. W. J. Phys. Chem. A 2000, 104, 9715.
Conclusions
(
(
25) Bozzelli, J. W.; Dean, A. M. J. Phys. Chem. 1990, 94, 3313.
26) Bozzelli, J. W.; Sheng, C. J. Phys. Chem. A 2002, 106, 1113.
New experimental measurements of HO2 production resulting
from the photolysis of ethyl iodide, n-propyl iodide, and i propyl
iodide have been compared to integrated rate equation models
based on the results of time-dependent master-equation calcula-
tions with ab initio characterization of stationary points. The
production of HO2 from the reaction of the two propyl isomers
(27) Sheng, C. Y.; Bozzelli, J. W.; Dean, A. M.; Chang, A. Y. J. Phys.
Chem. A 2002, 106, 7276.
(
28) DeSain, J. D.; Clifford, E. P.; Taatjes, C. A. J. Phys. Chem. A 2001,
05, 3205.
29) DeSain, J. D.; Klippenstein, S. J.; Taatjes, C. A. Phys. Chem. Chem.
Phys. 2003, 5, 1584.
1
(
(
30) DeSain, J. D.; Taatjes, C. A. J. Phys. Chem. A 2001, 105, 6646.
(n-propyl and i-propyl) with O2 has been studied directly in
(31) DeSain, J. D.; Taatjes, C. A.; Miller, J. A.; Klippenstein, S. J.;
the transition region. The current experiments unambiguously
probe the reaction of each isomer with O2 and permit isolation
and refinement of the i-propyl + O2 reaction model. The
previous model accurately describes the time scale and ampli-
tude of the HO2 formation from both C2H5 + O2 and n-C3H7
Hahn, D. K. Faraday Discuss. 2001, 119, 101.
(32) DeSain, J. D.; Klippenstein, S. J.; Taatjes, C. A.; Hurley, M. D.;
Wallington, T. J. J. Phys. Chem. A 2003, 107, 1992.
(
(
33) Fink, E. H.; Ramsay, D. A. J. Mol. Spectrosc. 1997, 185, 304.
34) Pilgrim, J. S.; Jennings, R. T.; Taatjes, C. A. ReV. Sci. Instrum.
1
997, 68, 1875.
+
O2. However, the present revised model slightly underesti-
(35) Burde, D.; McFarlane, R. J. Chem. Phys. 1976, 64, 1850.
(
(
(
36) Burrows, M. J. Chem. Phys. 1984, 81, 3546.
37) Donovan, R. J.; Husain, D. Chem. ReV. 1970, 70, 489.
38) Young, A.; Houston, P. J. Chem. Phys. 1983, 78, 2317.
mates the prompt HO2 production and the slower, secondary
production rate for i-propyl + O2, although prediction of HO2
formation in Cl-initiated propane oxidation has been improved.
Measured I profiles have been employed to scale experimental
HO2 FM signals in order to compare results among different
experiments and to place additional demands on the kinetic
models. Although uncertainty remains concerning some of the
iodine chemistry, the experimental results suggest significant
rate coefficients for the I-atom reaction with alkylperoxy
radicals.
(39) Ha, T.-K.; He, Y.; Pochert, J.; Quack, M.; Ranz, R.; Seyfang, G.;
Thanopoulos, I. Ber. Bunsen-Ges. Phys. Chem. 1995, 99, 384.
40) Davis, S.; Mulhall, P.; Bachman, M.; Kessler, W.; Keating, P. J.
Phys. Chem. A 2002, 106, 8323.
41) Chen, C.-J.; Bozzelli, J. W. J. Phys. Chem. A 2000, 104, 4997.
(42) Lay, T. H.; Bozzelli, J. W. J. Phys. Chem. A 1997, 101, 9505.
43) Klippenstein, S. J.; Wagner, A. F.; Dunbar, R. C.; Wardlaw, D.
(
(
(
M.; Robertson, S. H.; Miller, J. A. VARIFLEX, 1.12m ed.; Argonne National
Laboratory: Argonne, IL, 2002.
(44) Klippenstein, S. J.; Miller, J. A. J. Phys. Chem A 2002, 106, 9267.
(
45) Canosa-Mas, C. E.; Vipond, A.; Wayne, R. P. Phys. Chem. Chem.
Phys. 1999, 1, 761.
46) Aranda, A.; Laverdet, G.; Le Bras, G.; Poulet, G. J. Chim. Phys.
Phys.-Chim. Biol. 1998, 95, 963.
47) Fenter, F. F.; Lightfoot, P. D.; Niiranen, J. T.; Gutman, D. J. Phys.
Chem. 1993, 97, 5313.
48) Hess, W. P.; Kohler, S. J.; Haugen, H. K.; Leone, S. R. J. Chem.
Phys. 1986, 84, 2143.
49) Hess, W. P.; Leone, S. R. J. Chem. Phys. 1986, 86, 3773.
(50) Haugen, H. K.; Weitz, E.; Leone, S. R. J. Chem. Phys. 1985, 83,
402.
51) Uma, S.; Das, P. K. J. Chem. Phys. 1996, 104, 4470.
52) Godwin, F. G.; Paterson, C.; Gorry, P. A. Mol. Phys. 1987, 61,
27.
Acknowledgment. The experiments reported here were
facilitated by the outstanding technical support of Leonard E.
Jusinski. This work is supported by the Division of Chemical
Sciences, Geosciences, and Biosciences, Office of Basic Energy
Sciences, U.S. Department of Energy. Sandia is a multiprogram
laboratory operated by Sandia Corporation, a Lockheed Martin
Company, for the National Nuclear Security Administration
under Contract DE-AC04-94-AL85000.
(
(
(
(
3
(
(
References and Notes
8
(
53) Brewer, P.; Das, P.; Ondrey, G.; Bersohn, R. J. Chem. Phys. 1983,
(
1) Ignatyev, I. S.; Xie, Y.; Allen, W. D.; Schaefer, H. F., III. J. Chem.
Phys. 1997, 107, 141.
2) Clifford, E. P.; Farrell, J. T.; DeSain, J. D.; Taatjes, C. A. J. Phys.
Chem. A 2000, 104, 11549.
3) Miller, J. A.; Klippenstein, S. J.; Robertson, S. H. Proc. Combust.
Inst. 2000, 28, 1479.
4) Rienstra-Kiracofe, J. C.; Allen, W. D.; Schaefer, H. F., III. J. Phys.
Chem A 2000, 104, 9823.
7
9, 720.
(54) Taatjes, C. A. Unpublished results. Measurements of rate coef-
(
ficients and HCl yields from reactions of Cl with partially deuterated
propanes suggest an n-propyl branching fraction of 0.53 ( 0.16 at 575 K.
(
(55) Tschuikow-Roux, E.; Niedzielski, J.; Faraji, F. Can. J. Chem. 1985,
6
2
3, 1093.
(
(
(
56) Sarzynski, D.; Sztuba, B. Int. J. Chem. Kinet. 2002, 34, 651.
57) Slagle, I. R.; Park, J.-Y.; Gutman, D. Proc. Combust. Inst. 1984,
(
(
(
(
(
5) Miller, J. A.; Klippenstein, S. J. Int. J. Chem. Kinet. 2001, 33, 654.
6) Kaiser, E. W. J. Phys. Chem. A 2002, 106, 1256.
7) Pitz, W. J.; Westbrook, C. K. Combust. Flame 1986, 63, 113.
8) Westbrook, C. K. Proc. Combust. Inst. 2000, 28, 1563.
9) Knyazev, V. D.; Slagle, I. R. J. Phys. Chem. A 1998, 102, 1770.
0, 733.
(58) Ruiz, R. P.; Bayes, K. D. J. Phys. Chem. 1984, 88, 2592.
(59) Kaiser, E. W. J. Phys. Chem. A 1998, 102, 5903.
(60) Slagle, I. R.; Ratajczak, E.; Heaven, M. C.; Gutman, D.; Wagner,
A. F. J. Am. Chem. Soc. 1985, 107, 1838.
(61) Gulati, S. K.; Walker, R. W. J. Chem. Soc., Faraday Trans. 2 1988,
84, 401.
(62) Cline, J. I.; Taatjes, C. A.; Leone, S. R. J. Chem. Phys. 1990, 93,
6543.
(63) Fisk, G. A.; Hays, G. N. J. Chem. Phys. 1982, 77, 4965.
(64) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampson, R. F., Jr.; Kerr,
J. A.; Rossi, M. J.; Troe, J. J. Phys. Chem. Ref. Data 1997, 26, 521.
(65) Ashford, R. D.; Ogryzlo, E. A. J. Am. Chem. Soc. 1975, 97, 3604.
(66) Kang, W. K.; Jung, K. W.; Kim, D. C.; Jung, K.-H.; Im, H.-S.
Chem. Phys. 1995, 196, 363.
(67) Donaldson, D. J.; Leone, S. R. J. Phys. Chem. 1987, 91, 3128.
(68) Jenkin, M. E.; Cox, R. A.; Mellouki, A.; LeBras, G.; Poulet, G. J.
Phys. Chem. 1990, 94, 2927.
(
10) Slagle, I. R.; Ratajczak, E.; Gutman, D. J. Phys. Chem. 1986, 90,
02.
11) Slagle, I. R.; Feng, Q.; Gutman, D. J. Phys. Chem. 1984, 88, 3648.
12) Baldwin, R. R.; Pickering, I. A.; Walker, R. W. J. Chem. Soc.,
Faraday Trans. 1 1980, 76, 2374.
13) McAdam, K. G.; Walker, R. W. J. Chem. Soc., Faraday Trans. 2
987, 83, 1509.
14) Walker, R. W.; Morley, C. Basic Chemistry of Combustion. In Low-
4
(
(
(
1
(
Temperature Combustion and Autoignition; Pilling, M. J., Ed.; Elsevier:
Amsterdam, 1997; p 1.
(
(
(
15) Dobis, O.; Benson, S. W. J. Am. Chem. Soc. 1993, 115, 8798.
16) Kaiser, E. W. J. Phys. Chem. 1995, 99, 707.
17) Kaiser, E. W.; Lorkovic, I. M.; Wallington, T. J. J. Phys. Chem.
990, 94, 3352.
18) Kaiser, E. W.; Rimai, L.; Wallington, T. J. J. Phys. Chem. 1989,
3, 4094.
1
(
(69) Pilgrim, J. S.; McIlroy, A.; Taatjes, C. A. J. Phys. Chem. A 1997,
101, 1873.
9

HO2 Formation in the Reactions of Radicals with O2
J. Phys. Chem. B, Vol. 109, No. 17, 2005 8387
(
67.
70) Wallington, T. J.; Dagaut, P.; Kurylo, M. J. Chem. ReV. 1992, 92,
(89) Yee Quee, M. J.; Thynne, J. C. J. Ber. Bunsen-Ges. Phys. Chem.
1968, 72, 211.
6
(
(
(
71) Maricq, M. M.; Szente, J. J. J. Phys. Chem. 1994, 98, 2078.
72) Atkinson, D. B.; Hudgens, J. W. J. Phys. Chem. A 1997, 101, 3901.
73) Tsang, W.; Hampson, R. F. J. Phys. Chem. Ref. Data 1986, 15,
(
90) DeMore, W. B.; Sander, S. P.; Golden, D. M.; Hampson, R. F.;
Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R.; Kolb, C. E.; Molina,
M. J. Chemical Kinetics and Photochemical Data for Use in Stratospheric
Modeling; Jet Propulsion Laboratory: Pasadena, CA, 1997.
1
087.
(74) Foucaut, J.-F.; Martin, R. J. Chim. Phys. Phys.-Chim. Biol. 1978,
(91) Tully, F. P.; Droege, A. T.; Koszykowski, M. L.; Melius, C. F. J.
7
5, 132.
Phys. Chem. 1986, 90, 691.
(75) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Crowley, J. N.; Hampson,
(92) Tsang, W. J. Phys. Chem. Ref. Data 1988, 17, 887.
R. F., Jr.; Kerr, J. A.; Rossi, M. J.; Troe, J. Summary of EValuated Kinetic
and Photochemical Data for Atmospheric Chemistry: IUPAC Subcommittee
on Gas Kinetic Data EValuation for Atmospheric Chemistry. http://
www.iupac-kinetic.ch.cam.ac.uk (Nov 2003).
(93) Munk, J.; Pagsberg, P.; Ratajczak, E.; Sillesen, A. Chem. Phys.
Lett. 1986, 132, 417.
(94) Fittschen, C.; Frenzel, A.; Imrik, K.; Devolder, P. Int. J. Chem.
Kinet. 1999, 31, 860.
(76) Hoyermann, K. O. M.; Seeba, J.; Viskolcz, B. J. Phys. Chem. A
1
999, 103, 5692.
(95) Batt, L. Int. J. Chem. Kinet. 1979, 11, 977.
(
77) Atkinson, R. Int. J. Chem. Kinet. 1997, 29, 99.
(96) Choo, K. Y.; Benson, S. W. Int. J. Chem. Kinet. 1981, 13, 833.
(78) Maricq, M. M.; Szente, J. J.; Kaiser, E. W. J. Phys. Chem. 1993,
(97) Kerr, J. A.; Trotman-Dickenson, A. F. Trans. Faraday Soc. 1959,
9
7, 7970.
5
5, 572.
(79) Maricq, M. M.; Szente, J. J.; Kaiser, E. W.; Shi, J. J. Phys. Chem.
(
98) Bencsura, AÄ .; Knyazev, V. D.; Xing, S.-B.; Slagle, I. R.; Gutman,
1
994, 98, 2083.
D. Proc. Combust. Inst. 1992, 24, 629.
(
80) Timonen, R. Ann. Acad. Sci. Fenn., Ser. A2 1988, 218, 5.
(81) Berho, F.; Rayez, M.; Lesclaux, R. J. Phys. Chem. A 1999, 103,
(99) Seakins, P. W.; Robertson, S. H.; Pilling, M. J.; Slagle, I. R.;
Gmurczyk, G. W.; Bencsura, A.; Gutman, D.; Tsang, W. J. Phys. Chem.
1993, 97, 4450.
(100) Kerr, J. A.; Trotman-Dickenson, A. F. Trans. Faraday Soc. 1959,
55, 921.
5
501.
82) Baulch, D. L.; Duxbury, J.; Grant, S. J.; Montague, D. C. J. Phys.
Chem. Ref. Data 1981, 10 (Suppl. 1).
(
(
(
83) Hartley, D. B.; Benson, S. W. J. Phys. Chem. 1963, 39, 132.
84) Hunter, T. F.; Kristjansson, K. S. J. Chem. Soc., Faraday Trans. 2
(101) Daele, V.; Laverdet, G.; Poulet, G. Int. J. Chem. Kinet. 1996, 28,
1
1
6
982, 78, 2067.
5
89.
(
(
85) Hayes, D. M.; Strong, R. L. J. Phys. Chem. 1986, 90, 6305.
86) Seetula, J. A.; Russell, J. J.; Gutman, D. J. Am. Chem. Soc. 1990,
(
(
(
102) Sullivan, J. H. J. Phys. Chem. 1961, 65, 722.
103) Butler, E. T.; Polanyi, M. Trans. Faraday Soc. 1943, 39, 19.
104) Tsang, W. J. Phys. Chem. 1964, 41, 2487.
12, 1347
(
(
87) Yang, J. H.; Conway, D. C. J. Chem. Phys. 1965, 43, 1296.
88) Hassinen, E.; Koskikallio, J. Acta Chem. Scand., Ser. A 1979, 33,
(105) Biggs, P.; Canosa-Mas, C. E.; Shallcross, D. E.; Vipond, A.;
Wayne, R. P. J. Chem. Soc., Faraday Trans. 1997, 93, 2701.
25.