Infrared frequency-modulation probing of product formation in alkyl + O2 reactions: III. The reaction of cyclopentyl radical (c-C5H9) with O2 between 296 and 723 K

Article abstract of DOI:10.1021/jp010364t

The production of HO₂ from the reaction of c-C₅H₉ + O₂ has been investigated as a function of temperature (296-723 K) by using laser photolysis/CW infrared frequency modulation spectroscopy. The HO₂ yield is derived by comparison with the Cl₂/CH₃OH/O₂ system and is corrected to account for HO₂ signal loss due to competing reactions involving HO₂ radical and the adduct c-C₅H₉O₂. The time behavior of the HO₂ signal following cyclopentyl radical formation displays two separate components. The first component is a prompt production of HO₂, which increases with temperature and is the only component observed between 296 and 500 K. The yield from the prompt production rises from less than 1% at 296 K to ～23% at 693 K. At temperatures above 500 K a second slower rise in the HO₂ signal is also observed. The production of HO₂ on a slower time scale is attributable to cyclopentylperoxy radical decomposition. The total HO₂ yield, including the contribution from the slower rise, increases dramatically with temperature from ～2% at 500 K to ～100% at 683 K. From 683 to 723 K the total HO₂ yield remains constant. The second slower rise accounts for a majority of the product formation at these higher temperatures. The biexponential time behavior of the HO₂ production from c-C₅H₉ + O₂ is similar to that previously observed in studies of C₂H₅ + O₂ and C₃H₇ + O₂ reactions. The rate of formation for delayed HO₂ production from c-C₅H₉ + O₂ is larger than the rate of formation from either C₂H₅ + O₂ or C₃H₇ + O₂ at each temperature. However, apparent activation energies, obtained by an Arrhenius plot of the rates of formation for delayed HO₂ formation, are very similar for the three systems (C₂H₅ + O₂, C₃H₇ + O₂, and c-C₅H₉ + O₂). The results suggest a similar coupled mechanism for HO₂ production in the C₂H₅ + O₂, C₃H₇ + O₂, and c-C₅H₉ + O₂ reactions, with concerted elimination of HO₂ from the RO₂ radical responsible for HO₂ + alkene production.

Full text of DOI:10.1021/jp010364t

6646
J. Phys. Chem. A 2001, 105, 6646-6654
Infrared Frequency-Modulation Probing of Product Formation in Alkyl + O2 Reactions:
III. The Reaction of Cyclopentyl Radical (c-C5H9) with O2 between 296 and 723 K
John D. DeSain and Craig A. Taatjes*
Combustion Research Facility, Mail Stop 9055, Sandia National Laboratories,
LiVermore, California 94551-0969
ReceiVed: January 29, 2001; In Final Form: April 12, 2001
The production of HO
296-723 K) by using laser photolysis/CW infrared frequency modulation spectroscopy. The HO
derived by comparison with the Cl /CH OH/O system and is corrected to account for HO signal loss due
to competing reactions involving HO radical and the adduct c-C . The time behavior of the HO signal
following cyclopentyl radical formation displays two separate components. The first component is a prompt
production of HO , which increases with temperature and is the only component observed between 296 and
00 K. The yield from the prompt production rises from less than 1% at 296 K to ∼23% at 693 K. At
temperatures above 500 K a second slower rise in the HO signal is also observed. The production of HO
on a slower time scale is attributable to cyclopentylperoxy radical decomposition. The total HO yield, including
the contribution from the slower rise, increases dramatically with temperature from ∼2% at 500 K to ∼100%
at 683 K. From 683 to 723 K the total HO yield remains constant. The second slower rise accounts for a
majority of the product formation at these higher temperatures. The biexponential time behavior of the HO
production from c-C + O is similar to that previously observed in studies of C + O and C + O
reactions. The rate of formation for delayed HO production from c-C + O
formation from either C + O or C + O at each temperature. However, apparent activation energies,
obtained by an Arrhenius plot of the rates of formation for delayed HO formation, are very similar for the
three systems (C + O , C + O , and c-C + O ). The results suggest a similar coupled mechanism
for HO production in the C + O , C + O , and c-C + O reactions, with concerted elimination of
HO from the RO radical responsible for HO + alkene production.
2
from the reaction of c-C
5
H
9
+ O
2
has been investigated as a function of temperature
(
2
yield is
2
3
2
2
2
H O
5 9 2
2
2
5
2
2
2
2
2
2
H
5 9
2
2
H
5
2
3 7
H
2
H
5 9
2
is larger than the rate of
H
2 5
2
3
H
7
2
2
H
2 5
2
H
3 7
2
5
H
9
2
2
H
2 5
2
H
3 7
2
5
H
9
2
2
2
2
Introduction
vessel by using gas chromatography. They observed products
from reaction pathway 1b (c-C5H8), but do not report any
products from pathway 1c. They postulate that the other products
Alkyl radical (R) reactions with oxygen are critical in
understanding many combustion systems. Studies of R + O2
have focused mainly on understanding the complex mechanisms
involved in smaller straight-chained alkyl radical (ethyl and
propyl) reactions with O2. Recently more focus has been placed
on studying the oxidation of larger cyclic alkanes. The oxidation
of cyclopentane has been studied by two separate groups. If
the reaction of the cyclopentyl radical (c-C5H9) with O2 is similar
to other R + O2 reactions, then the major product channels
should be
(H2, CH4, C2H4, C3H6, 1,3-C4H6) observed are principally
produced by decomposition of the cyclopentyl radical (c-C5H9):
1
,2
They propose that cyclopentene is produced via the following
mechanism:
M
c-C H + O 7
9
8 c-C H O
(1a)
(1b)
(1c)
5
9
2
5
9
2
[M]
c-C H + O 7 8 c-C H O f c-C H OOH f
f c-C H + HO
2
5
9
2
5
9
2
5
8
5
8
c-C H + HO (3)
5
8
2
f c-C H O(1,2-epoxycyclopentane) + OH
5
8
1
Simon et al. used Schemes 2 and 3 together to fit the formation
of four experimentally observed products (H2O, C2H4, c-C5H6,
and c-C5H8).
where reactions 1b and 1c include possible formation from a
c-C5H9O2 intermediate. Reaction 1b appears to be favored at
temperatures between 673 and 873 K as the two previous
2
Handford-Styring and Walker also used gas-phase chroma-
studies1,2 agree that the major product of this reaction is
tography/mass spectrometry to observe product formation from
cyclopentane oxidation. Once again c-C5H8 was observed as a
cyclopentene (c-C5H8).
Simon et al. studied the oxidation of cyclopentane at 873 K
and observed product formation in a jet-stirred flow reaction
1
primary product, along with smaller amounts of acrolein (CH2-
CHCHO), 1,2-epoxycyclopentane (c-C5H8O), ethylene (C2H4),
cyclopenta-1,3-diene (c-C5H6), carbon monoxide (CO), and trace
*
Author to whom correspondence should be addressed
amounts of propene (C3H6) and buta-1,3-diene (C4H6). Cyclo-
1
0.1021/jp010364t CCC: $20.00 © 2001 American Chemical Society
Published on Web 06/19/2001

Reaction of Cyclopentyl Radical (c-C5H9) with O2
J. Phys. Chem. A, Vol. 105, No. 27, 2001 6647
pentene is found to be the dominant initial product at O2
pressures greater than 1 Torr. Handford-Styring and Walker used
a formally direct step (i.e., without intervening isomerization
to C5H8OOH) for the formation of the cyclopentene to model
their results:
to c-C5H9O2 dissociation. The rate of formation for the delayed
formation of HO2 is similar to that observed in C2H5 + O2 and
C3H7 + O2, which suggests that the three reactions have a
similar reaction mechanism for HO2 + alkene formation.
Experiment
The reaction of c-C5H9 + O2 is investigated by using a
modification of the laser photolysis/CW infrared long path
absorption (LP/CWIRLPA) method employed in previous
c-C H + O f c-C H + HO
2
(4)
5
9
2
5
8
At low oxygen pressures (<1 Torr O2) C2H4 formation became
significant, indicating that C2H4 is formed from the competing
reaction of c-C5H9 decomposition. Also, Handford-Styring and
Walker observed an additional source of C2H4 formation, which
they attributed to adduct decomposition, similar to the HO2
formation scheme above. This additional reaction channel
3
,4,24-28
experiments.
at 355 nm, and the c-C5H9 is generated by subsequent Cl
abstraction from cyclopentane. The c-C H radical then reacts
The Cl is generated by photolysis of Cl2
2
5
9
with O2 to produce the HO2 radical.
hν (355 nm)
Cl2
82Cl•
(6a)
(6b)
(1)
Cl• + c-C H f c-C H • + HCl
5
10
5
9
c-C H • + O f products
5
9
2
explains the appearance of acrolein and 1,2-epoxycyclopentane
as well as other minor products.
The O2 concentration is kept at least 30 times greater than the
Cl2 concentration in order to minimize the effects of the
competing chain reaction of Cl2 with c-C5H9.
3
We have recently investigated the reactions of ethyl (C2H5)
4
4-10
and propyl (C3H7), with O2. The propyl + O2
and ethyl +
3
,11-23
O2
reactions have been much more extensively studied
The progress of reaction 1b is monitored by two-tone
frequency modulation (FM) spectroscopy on the overtone of
the O-H stretch in HO2 near 1.5 µm by using a tunable diode
laser. The detection sensitivity decreases at higher temperatures
because of increases in the vibrational and rotational partition
functions, and the concomitant quantum state dilution. The diode
laser output is passed multiple times (17 passes) through a
than reactions involving larger alkyl radicals. The HO2 formation
from C2H5 + O2 and C3H7 + O2 reactions are very similar.
The HO2 + alkene channel is the dominant bimolecular product
channel observed at temperatures between 296 and 683 K for
both C2H5 + O2 and C3H7 + O2. For both reactions, the HO2
yield exhibits a biexponential time behavior with both a very
fast direct component and a much slower delayed component.
The prompt component of the yield increases with temperature,
while the delayed component of the yield increases sharply from
2
9,30
Herriott-type flow cell.
The flow cell is 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.
550 to 683 K. The prompt HO2 yield is slightly larger for C2H5
+
O2 than C3H7 + O2 in the temperature region studied. Both
The gold-coated spherical mirrors that comprise the Herriott
cell are located outside the flow cell and are separated by a
distance of approximately 1.5 m. The photolysis beam, a 5 ns
pulse from a Nd:YAG laser at 355 nm, passes through the center
of the front Herriott mirror. It travels on axis through the quartz
flow cell and then passes through the center of the back Herriott
mirror. The IR probe beam enters off axis through a notch in
the back Herriott mirror and is multipassed through the flow
cell. The beam traverses a circular pattern around the outer edge
of the Herriott mirrors, while mapping out a smaller circle in
the center of the cell. Finally, the probe exits from a notch in
the front Herriott mirror. After exiting, the probe beam is
focused onto a detector. This arrangement allows the IR probe
to overlap the UV photolysis beam only in the center of the
flow cell, where the temperature is more readily controlled. By
using this multipass arrangement the effective path length
(i.e., overlapping path of the photolysis and probe) is about 9
m.
reactions show a similar increase in total yield with temperature,
changing from ∼5% at 500 K to nearly 100% at 683 K. The
delayed component makes a large contribution to the total yield
at these higher temperature, while having no significant
contribution at temperatures below 550 K. The rate of formation
for delayed HO2 production from C3H7 + O2 is slightly larger
than for C2H5 + O2 at each temperature. Apparent activation
energies, obtained by an Arrhenius plot of the rates of formation
of the delayed HO2 yield, are very similar for the two systems,
-
1
-1
∼
+
+
25 kcal mol and ∼26 kcal mol for C2H5 + O2 and C3H7
O2, respectively. The HO2 yield and time behavior for C2H5
O2 derived from recent master equation calculations by Miller,
20
Klippenstein, and Robertson, based on quantum calculations
of the transition state for the concerted HO2 elimination from
the ethylperoxy radical,23 also showed excellent agreement with
the experimental results.3
This study investigates the yield and time behavior of the
HO2 formation from the c-C5H9 + O2 reaction at elevated
temperatures. Both Handford-Styring and Walker and Simon
The relative yield of the HO2 radical produced by the reaction
is monitored by comparison with the corresponding HO2 yield
from the reaction of CH2OH + O2. This reaction produces a
100% yield of HO2 as a product over the temperature range of
2
1
et al. used gas chromatography to measure stable products of
the cyclopentane oxidation. Using this method they were able
to measure stable product yields, but not the time dependence
of the product formation. In these studies the time behavior of
HO2 formation from the reaction of c-C5H9 + O2 is directly
observed by using infrared frequency modulation spectroscopy.
The time profile of the HO2 formation permits separation of
initially formed “prompt” HO2 from the product of redissociation
of the cyclopentylperoxy adduct. In this way the increase in
HO2 + c-C5H8 yield above 500 K is unambiguously assigned
3
1
concern. The CH2OH is produced by Cl abstraction of
hydrogen from methanol.
hν (355 nm)
Cl2
82Cl•
(7a)
(7b)
(7c)
CH OH + Cl• f CH OH• + HCl 100%
3
2
CH OH• + O f CH O + HO • 100%
2
2
2
2

6648 J. Phys. Chem. A, Vol. 105, No. 27, 2001
DeSain and Taatjes
Figure 2. Time-resolved infrared FM signals for HO
and 56.2 Torr. The larger amplitude (blue) trace is the HO
the reference reaction of CH OH + O ; the smaller amplitude (red)
trace is the HO signal from c-C + O
2
taken at 638 K
Figure 1. Time-resolved infrared FM signals for HO
and 40.0 Torr. The larger amplitude (blue) trace is the HO
the reference reaction of CH OH + O ; the smaller amplitude (red)
trace is the HO signal from c-C + O
2
taken at 453 K
signal from
2
signal from
2
2
2
2
2
H
5 9
2
.
2
H
5 9
2
.
2
R[HO2]0
1 + 2k t[HO ]
2 0
The experiments are conducted by first observing the HO2 signal
produced from the CH2OH + O2 reaction. Then the methanol
is replaced with a nearly equal concentration of cyclopentane
and the HO2 signal from the c-C5H9 + O2 reaction is observed.
The yield is then obtained by comparison of the intensities of
the two resulting HO2 signals. To relate the observed quantities
to characteristics of the reaction, corrections must be made for
the removal reactions of HO2, as well as for certain side
reactions, as discussed below. Typical gas concentrations are
I (t) ) R[HO ] )
(9)
ref
2 t
8
where R is a constant relating the observed FM signal to HO2
concentration. A plot of the inverse of the reference HO2 signal
vs time gives a line with slope 2k8/R. Since the temperature-
dependent line-strength of the probe transition is unknown, the
absolute value of k8 remains undetermined in these experiments;
however, the analysis requires only the phenomenological rate
coefficient 2k8/R. The differential equation governing the HO2
1
6
-3
15
-3
[
1
O2] ) 6.6 × 10 cm , [Cl2] ) 2.1 × 10 cm , and 8.0 ×
15
-3
concentration in the cyclopentyl + O reaction can be written
0
cm of either cyclopentane or methanol. Helium is added
2
17
-3
as
to a total gas density of 8.5 × 10 cm .
d
dt
2
[
HO ] ) R
- 2k [HO ] - R
removal
(10)
Analysis
2
production
8
2
The HO2 signal from c-C5H9 + O2 is similar to the signal
observed from the C2H5 + O2 and C3H7 + O2 studies. At low
temperatures, <500 K, very little HO2 is observed. The HO2
observed below 500 K appears rapidly after the photolysis pulse
where Rproduction is the effective time-dependent rate of HO2
production and Rremoval is the effective time-dependent rate for
removal of HO2 by processes besides self-reaction. Determining
the time-resolved production of HO2 from reaction 1, denoted
Rproduction, is the aim of the measurement. Equation 10 has the
formal solution
(see Figure 1), with a rise time faster than the experimental
resolution of ∼10 µs, (limited by the low-pass filter used in
the two-tone FM method). Above 500 K a second slower HO2
signal is observed. Figure 2 shows the HO2 signal from c-C5H9
t
t
2
[
HO ] )
∫
Rproduction(x) dx - 2k8
∫
[HO ] dx -
2
t
2 x
+
O2 and CH2OH + O2 at 638 K. In Figure 2 the HO2 signal
0
0
t
shows two components: an initial sharp rise that is not resolved
and a second much slower rise. Determining the fraction of HO2
that appears via this delayed mechanism requires correction for
the ongoing removal of HO2 by self-reaction and by reactions
with other radical species.
∫
Rremoval(x) dx (11)
0
The time-dependent FM signal, I(t), from HO2 produced in
reaction 1 is related by the detection constant R to the HO2
concentration:
As in previous studies,3,4 an iterative integration technique
is employed to correct the signal for the loss of HO2. Correction
for the self-reaction uses only information inherent to the HO2
signals from CH2OH + O2 and c-C5H9 + O2, and requires
no assumed rate coefficients. The HO2 signal generated from
the CH2OH + O2 reaction decays by a second-order kinetic
process dominated by the HO2 + HO2 recombination reac-
tion,
t
t
2
I(t) ) R
∫
Rproduction(x) dx - 2Rk8
∫
[HO ] dx -
2 x
0
0
t
R
∫
Rremoval(x) dx (12)
0
The integrated profiles method32-34 uses this formal solution
along with the measured time-resolved relative concentrations
to correct for known rate processes. The quantity 2k8/R is known
from the reference reaction, and the time profile of the HO2
FM signal from reaction 1 has been measured: I(t) ) R[HO2]t.
The self-reaction term in the expression for the FM signal
amplitude, the second term on the right in eq 12, can be replaced
by a time integral of the observed signal:
HO + HO f products
(8)
2
2
The time profile of the HO2 signal from the reference reaction
is given by

Reaction of Cyclopentyl Radical (c-C5H9) with O2
J. Phys. Chem. A, Vol. 105, No. 27, 2001 6649
2
k8
TABLE 1: Rate Coefficients Used to Obtain the Relative
t
t
2
R
∫
Rproduction(x) dx ) I(t) +
∫
I(x) dx +
Rates Used to Correct for HO
2
Loss from the c-C
5
H
9
O
2
+
0
0
R
Reactiona
2
HO
t
rate constant (cm molecule s-1
3
-1
)
R
∫
Rremoval(x) dx (14)
reaction
0
1
4
-32
-13 (599 K/T)
HO
c-C
c-C
2
5
5
+ HO
2
k
k
k
8
) 4.5 × 10 [M] + 2.2 10
e
3
6
-13 (1150 (200 K/T)
H
H
9
O
O
2
+ HO
+ c-C
2
15 ) 3.2[ +1.5-1.1] × 10
e
If HO2 recombination were the only loss mechanism of
significance, then Rremoval would be equal to zero and all
parameters in eq 14 are measured directly by the experiment.
This assumption produces a lower bound to the actual HO2
production rate, since additional corrections for HO2 signal lost
by other mechanisms (Rremoval) will increase the amplitude of
the final “corrected” time profile. The yields obtained by this
assumption thus produce a lower limit to the true yields, but
have the advantage of being dependent only on data acquired
in this experiment.
Whereas the data necessary for removing the contributions
of HO2 self-reaction are inherent in the measurements them-
selves, relating the phenomenological yields to the time-
dependent HO2 production rate requires additional modeling to
account for the Rremoval processes. Under the conditions of the
present experiments, Rremoval reflects principally the reaction of
HO2 with c-C5H9O2 radicals,
37
-14 (188 (83 K/T)
9
2
5
H
O
9 2
17 ) 1.3 ( 0.4 × 10
e
a
The evaluated rate coefficient for the HO self-reaction is used to
2
scale the value for c-C
H
5 9
O
2
+ HO
2
and c-C
5
H
9
O
2
5 9 2
+ c-C H O .
experimental conditions are nearer the lower limit, and that value
has been chosen for k17.
By using reactions 1,8,15, and 17, a formal solution to the
kinetic equations can be constructed that allows recursive
extraction of a corrected HO2 profile. The equation for the
observed HO2 FM signal is modified to reflect that Rremoval is
dominated by reaction with cyclopentylperoxy radicals, and the
kinetic equations are recast as equations by using the observed
signals (i.e., effectively using signal amplitude as a concentration
unit):
t
A ≡ R[c-C H O ] ) I (0) - R
∫
Rproduction(x) dx -
5
9
2 t
ref
0
2
k
k
1
7
t
2
15
t
HO + c-C H O f products
(15)
∫
(R[c-C H O ] ) dx -
∫
R[c-C H O ]I(x) dx (18)
5 9 2
2
5
9
2
0
5
9
2 x
0
R
R
so that Rremoval ≈ k15[c-C5H9O2]t[HO2]t. The c-C5H9O2 + HO2
2k
t
8
t
2
B ≡ R
∫
Rproduction(x) dx ) I(t) +
∫
I(x) dx +
reaction has been studied previously, and k15 can be estimated
0
0
R
from literature expressions.3
5,36
Since the actual correction
k15
t
method uses the observed signals, not absolute concentrations,
the value for the relevant rate coefficients must be scaled by
the (unknown) factor R. The values for the rate coefficients
∫
R[c-C H O ] I(x) dx (19)
5 9 2 x
0
R
We initially assume A(0) ) 0, and then calculate successive
approximations to the quantities A and B by using the following
equations:
(
listed in Table 1) are therefore scaled to the literature value of
the HO2 recombination rate coefficient (whose phenomenologi-
cal rate coefficient, 2k8/R, is measured in the CH2OH + O2
reference reaction), e.g.,
2
k8
k15
t
t
2
B (t) ) I(t) +
∫
I(x) dx +
∫
A(n-1)I(x) dx
(
n)
0
0
R
R
k15
2k8 k15
1
(20)
)
(16)
(
) ( )( )
R
R
k 2
8
2
k17
t
2
A (t) ) (I (0) - B ) -
∫
(I (0) - B ) dx -
(n)
ref
(n)
ref
(n)
0
R
Information on the concentration of c-C5H9O2 is needed as well.
Unfortunately there is no direct measure of the time behavior
of the cyclopentylperoxy radical concentration. An estimate can
be obtained assuming that all cyclopentyl radicals react to
produce either HO2 or c-C5H9O2. This assumption is good if
k
15
t
∫
(Iref(0) - B(n))I(x) dx (21)
0
R
Iteration of these equations converges to a solution for B that
2
represents the production of HO from reaction 1 that gives rise
reaction 1c is small, and if the steady-state for reaction 1a favors
2
to the observed signal under the conditions of the model. The
yields extracted from this procedure are necessarily larger than
or equal to the raw yields taken directly from the data (corrected
the products, which should be the case under the high-[O2]
conditions of the present experiments, if the c-C5H9 + O2 T
c-C5H9O2 equilibrium is similar to that of other alkyl radicals
C2H5, i-C3H7, or t-C4H9 + O2 (∆H ∼ 36 kcal mol and ∆S ∼
7 cal mol K ). Then immediately after the fast establish-
ment of the steady-state concentration [c-C5H9O2] ≈ [c-C5H9]0
[HO2]. Note that above 668 K the raw yield obtained by
-
1
only for HO self-reaction).
2
-1
-1 16
3
Results
-
HO Yields. Figure 3 shows the HO signals from both the
2
2
correcting for only HO2 + HO2 already produces a nearly 100%
yield and this correction becomes insignificant.
The self-reaction of the cyclopentylperoxy is another removal
mechanism for c-C5H9O2:
CH OH + O and c-C H + O reactions at 638 K with the
2
2
5
9
2
loss of signal due to reactions 8 and 15 removed. The HO signal
2
from the CH OH + O reaction now displays a nearly
2
2
instantaneous increase in HO after the UV pulse with no
2
observable decrease in the signal over the 30 ms time window.
c-C H O + c-C H O f products
(17)
5
9
2
5
9
2
The HO2 production from the c-C5H9 + O2 reaction also appears
different from the signal shown in Figure 2. At the end of the
second rise the amplitude approaches a plateau. The total yield
can now be obtained by a comparison of final amplitude of the
two signals. In practice the final HO2 signal amplitude from
the c-C5H9 + O2 is obtained by a fit of the delayed HO2 rise to
an exponential.
The c-C5H9O2 recombination rate constant (k17) has been found
to be dependent on O2 concentration. Rowley et al. report a
3
7
-
14
low O2 concentration limit (<1 Torr O2) of 1.3 ( 0.4 × 10
(
188 ( 83 K/T)
e
, whereas the high O2 limit (>50 Torr O2) was
-
13 [-(555 ( 77 K)/T]
found to be 2.9 ( 0.8 × 10
e
. The present

6650 J. Phys. Chem. A, Vol. 105, No. 27, 2001
DeSain and Taatjes
TABLE 2: Yields and Rates of Production for HO
2
Production from c-C
5
H
9
+ O
2
at a Constant Density of 8.5
1
7
-3a
×
10 cm
Temperature
K)
-
1
τ
(
(s-1)
Φ
prompt
Φ
total
Φ
raw
2
3
3
4
5
5
5
5
5
6
6
6
6
6
96
38
93
53
13
43
58
73
88
03
23
38
53
68
<0.01
<0.01
<0.01
0.02
0.02
0.04
0.04
0.06
0.06
0.06
0.07
0.09
0.11
0.15
0.16
0b.23
<0.01
<0.01
<0.01
0.02
<0.01
<0.01
<0.01
0.02
0.05
0.06
0.13
0.25
0.31
0.50
0.74
0.83
0.87
0.95
1.00
0.97
0.97
0.99
0.14 ( 0.08
0.41 ( 0.15
0.51 ( 0.14
0.60 ( 0.07
0.63 ( 0.08
0.73 ( 0.06
0.84 ( 0.04
0.88 ( 0.03
0.92 ( 0.05
0.96 ( 0.03
1.00 ( 0.02
0.97 ( 0.03
0.98 ( 0.04
1.00 ( 0.03
40 ( 35
60 ( 35
100 ( 35
150 ( 50
240 ( 50
540 ( 60
700 ( 60
1080 ( 60
1720 ( 80
2840 ( 80
Figure 3. Correction of HO
method at 638 K and 56.2 Torr. The largest amplitude trace (blue) is
the HO signal from the reference reaction of CH OH + O after
correction for HO self-reaction, the dominant removal process for HO
in this system. The middle (red) trace is the HO
after correction accounting for both the HO
the reaction with c-C radicals as described in the text. This trace
represents the time-resolved production of HO corresponding to the
observed time-resolved FM signal. The lowest (green) trace is the HO
signal from the c-C + O after correction accounting for only the
HO self-reaction. The biexponential time behavior of the HO
formation from c-C + O is more clearly shown by the inner graph,
which is an expansion of the first 5 ms of the middle (red) trace.
2
FM signal by using the integrated profiles
683
693
708
723
3540 ( 140
5570 ( 140
6600 ( 140
2
2
2
2
2
9
2
signal from the c-C
5
H
a
Numbers are an average of 2 measurements for temperatures below
68 K and an average of 4 for temperatures above 668 K. The stated
error bars for τ and Φtotal represent propagated uncertainties introduced
in the modeling, as described in the text. The estimated accuracy of
the prompt yield is (40% and is dominated by possible systematic
error in the extrapolation to t ) 0. The HO
to systematic uncertainties of ∼ (10%. See text for details. Above
93 K the rapid rate of formation of the delayed HO makes it too
difficult to separate the delayed and prompt yield.
+
O
2
2
self-reaction and
6
5
H
9
O
2
-1
2
2
5
H
9
2
2
yields are further subject
2
2
b
5
H
9
2
6
2
(corrected only for HO2 self-reaction, and by using Rremoval )
k15[c-C5H9O2]t[HO2]t) are given in Table 2 as Φraw and Φtotal,
respectively. The total yield of HO2 is relatively small at
temperatures below 500 K. Above 500 K, a sharp increase in
the total yield is observed in conjunction with a change in the
time profile of the HO2 signal. At these higher temperatures
the HO2 signal has two risessan instantaneous rise after the
laser pulse followed by a slower secondary rise. The total yield
reaches ∼100% by about 683 K.
The HO2 yield below 450 K is below the ∼1% detection
limit of these experiments. Above 450 K an HO2 signal is
observed. At 453 K the HO2 signal appears to be produced
nearly instantaneously as shown in Figure 1. Plotted in Figure
5
is the prompt yield of HO2 measured from the amplitude of
the initial rapid rise of the HO2 signal. The prompt yield
increases slightly with increasing temperature. At higher tem-
peratures, it is sometimes hard to discern by eye the prompt
yield from the initial slow HO2. At these temperatures the
intercept of an exponential fit to the slow HO2 production is
used to obtain the prompt yield. At temperatures above 693 K
the prompt and delayed production become indistinguishable.
The prompt yield (Φprompt) at several temperatures is also listed
in Table 2.
Figure 4. The measured total yield of HO
2 5 9
from the reaction of c-C H
+
O
2
as a function of temperature at a constant total density of 8.5 ×
1
7
-3
1
0
molecule cm . The filled squares 9 represent the total yield
assuming only HO self-reaction, which is a lower bound to the true
yield. The triangles 3 represent the yield accounting for both the
self-reaction and the reaction with c-C radicals as described
yield observed.
2
HO
HO
2
2
5 9 2
H O
in the text. The filled circles b represent the prompt HO
2
Uncertainty estimates represent a combination of statistical and possible
systematic errors.
The time-resolved FM signal shown in Figure 3, after the
correction for HO2 self-reaction and c-C5H9O2 + HO2 reactions,
is related to the production of HO2 in reaction 1:
1
7
-3
The HO2 yield at a constant total density (8.5 × 10 cm )
and a constant partial density of O2, Cl2, and methanol/
cyclopentane for several different temperatures is shown in
Figure 4. Each point in Figure 4 represents an average of two
separate measurements, except at temperatures above 668 K,
which are an average of 4 measurements. The total HO2 yield
obtained by the two different correction methods is shown. The
first method considers the total yield obtained by correcting only
HO2 loss due to the HO2 self-reaction, i.e., by using only data
inherent in the raw measurements themselves. This yield is a
lower limit to the HO2 yield. The second yield is obtained by
correcting the HO2 signal by considering all the reactions
discussed above. The yield estimates based on both methods
t
Ieff(t) ≈ R
∫
Rproduction(x) dx
(22)
0
The present experiments require relatively large concentrations
of O2, since the signal size is determined by the initial Cl
concentration (and hence the Cl2 concentration), and [O2] is
maintained at 30 × [Cl2]. As a result, the initial rise of HO2
from the reaction of cyclopentyl radical with O2 is rapid and
unresolved. However, the rate constant of formation, the inverse
-
1
of the time constant, τ , in the production of HO2 can be

Reaction of Cyclopentyl Radical (c-C5H9) with O2
J. Phys. Chem. A, Vol. 105, No. 27, 2001 6651
on the data measured in this experiment and thus not subject to
these modeling uncertainties. At higher temperatures (g668 K),
where replacing only the loss of signal due to HO2 recombina-
tion already produces a nearly 100% yield, modeling of the more
poorly known secondary reactions has very little effect on the
corrected HO2 signal. At lower temperatures, where the slow
secondary rise of the HO2 signal is not observed, these reactions
also have very little effect on the yield. From Figure 4 one can
see that the raw and total yields are very similar at the extremes
of the temperature range.
Uncertainties in the total yields and rates arising from
uncertainty in k8, k15, and k17 are obtained by modeling with k8,
k15, and k17 values that were either double or half those listed
in Table 1. Since the modeling depends on rate constants relative
to k8, the maximum deviation is usually obtained when k8 and
k15 are changed in the opposite direction (i.e., if k15 is doubled
then k8 is halved). The rates show little dependence on k17. The
uncertainties obtained by this method are listed in Table 2 next
to the total yield and rates. The lower temperature corrected
yields and rates show the largest uncertainties, since they are
most affected by the correction for reactions 15 and 17. The
higher temperature yields show little added uncertainty from
the modeling. Systematic uncertainties add an estimated (10%
relative uncertainty to the yields. The possible role of channel
Figure 5. The temperature dependence of the “prompt” yield of HO
2
from the reactions c-C
5
H
9
+ O
2
, C
3
H
7
+ O
2
, and C
2
H
5
2
+ O at constant
1
7
-3
17
-3
densities of 8.5 × 10 molecule cm , 8.45 × 10 molecule cm
,
1
7
-3
and 7.7 × 10 molecule cm , respectively. The c-C
5
H
9
+ O
2
yields
+ O
2
yields (from
from this work are represented by the filled circles b, the C
H
2 5
2
yields (from ref 3) by the squares 0, and the C
ref 4) by the open circles O.
3
H
7
+ O
1
c could be systematically underestimated by these measure-
ments, since the OH product will regenerate c-C5H9, as discussed
below. An overall accuracy of (40% in the prompt yield
determination is estimated based on possible systematic errors
in describing the HO2 production as two separable steps as well
as the statistical uncertainty in the extrapolation back to t ) 0.
Another possible concern at the highest temperatures of this
study is the effect of cyclopentyl thermal decomposition.
2
Handford-Styring and Walker have measured this decomposi-
1
3
-1 2
tion rate to be 1.38 × 10 exp(-17260 K/T) s . At 723 K
-
1
this corresponds to a rate of ∼600 s which is still an order of
magnitude smaller than the observed HO2 formation rate
constant. The major products of the decomposition reaction are
the allyl radical (CH2CHCH2) and C2H4. At the temperatures
of interest the allyl + O2 reaction should form negligible HO2
Figure 6. Arrhenius plot of the apparent rate constants of formation
-
19
3
-1
38
-
1
(k ) 4.15 × 10
cm s at 753 K) on these time scales,
(
C
τ
) for delayed production of HO
+ O , and C + O
at constant densities of 8.5 × 10 molecule
cm , 8.45 × 10 molecule cm , and 7.7 × 10 molecule cm
respectively. The c-C + O rate constants represented by the open
triangles 3 are from this work. The squares 0 represent the C
rates of formation from ref 3 and the open circles O represent the
rates of formation from ref 4. The experimental determina-
2
from the reactions c-C
5
H
9
+ O
2
,
17
and any cyclopentyl radical lost to dissociation will not result
in formation of HO2. Given that the raw HO2 yields are
approximately 100% at these higher temperatures, cyclopentyl
radical decomposition does not appear to be significant under
the present conditions.
3
H
7
2
2
H
5
2
-
3
17
-3
17
-3
,
5
H
9
2
2 5
H +
O
C
2
3
H
7
+ O
2
tions are subject to larger uncertainty at lower rate coefficient values.
Discussion
The filled triangles 2 represent the rate constants of formation predicted
by the master equation calculations for C
2
H
5
2
+ O (ref 20).
The present results can be compared to previous investigations
of C2H5 + O2 and C3H7 + O2. The total yields of HO2 produced
from C2H5 + O2, C3H7 + O2, and c-C5H9 + O2 are shown in
Figure 7. The HO2 yields produced by C2H5 + O2 and C3H7 +
O2 were previously seen to have nearly identical temperature
dependence. The HO2 yield from c-C5H9 + O2 shows a slightly
different temperature dependence. The onset of the increased
production of HO2 occurs at a lower temperature (∼500 K
compared to 550 K). The rise in HO2 yield at these higher
temperatures for C2H5 + O2 has been previously modeled very
measured by using an exponential fit. The rate constants are
listed in Table 2. Figure 6 shows an Arrhenius plot for the rates
of formation of the delayed HO2, extracted from the effective
signals after correction for self-reaction and the HO2 +
c-C5H9O2 reaction (reaction 15), as a function of inverse
temperature. The rate of formation displays a rapid increase from
approximately 40 s-1 at 543 K to several thousand per second
at 723 K. The lowest temperature production rates are strongly
affected by the correction for reaction 15, but at higher
temperatures this correction is less important and the rates of
formation are independent of the details of the HO2 removal
mechanism.
3
,18
successfully by a coupled reaction scheme,
The uncertainties associated with the rate coefficients used
in the model to correct for the adduct + HO2 reaction place
limits on the precision of the total yields and rates obtained in
this experiment. However, the raw yields are dependent only

6652 J. Phys. Chem. A, Vol. 105, No. 27, 2001
DeSain and Taatjes
1
Figure 7. The open triangles 3 represent the measured total yield of
HO from the reaction of c-C + O as a function of temperature at
a constant total density of 8.5 × 10 molecule cm . The squares 0
represent the measured total yield of HO from the reaction of C
as a function of temperature at a constant total density of 7.7 ×
Figure 8. Pressure dependence of the rate constant of formation τ-
2
5
H
9
2
for delayed production of HO
638 K and at a constant O
2
from the reaction of c-C
5
H
9
2
+ O at
1
7
-3
16
-3
2
density of 6.6 × 10 molecule cm . Each
2
H
2 5
+
point represents an average of 4 separate measurements.
O
1
2
01 molecule cm (ref 3). The open circles O represent the measured
total yield of HO from the reaction of C + O as a function of
temperature at a constant total density of 8.45 × 10 molecule cm
ref 4).
7
-3
Scheme 23 can be sufficiently described by an energetic
model with one well on the potential energy surface. The R +
O2 reaction proceeds over a barrierless transition state to form
the adduct (RO2). There is a second transition state for the
formation of HO2 + alkene with a barrier slightly below the
reactants’ energy. Even in this simple formulation the observed
delayed rate of formation cannot be described as an elementary
rate constant in the reaction, but will depend on all of the rate
coefficients. Thus the measured activation energy is a phenom-
enological activation energy for the whole mechanism leading
to delayed product formation. The apparent activation energies
of the three reactions, as seen in an Arrhenius plot (Figure 6),
2
3
H
7
2
1
7
-3
(
where ke represents concerted elimination from C2H5O2 and ka
represents a direct production of HO2 and ethylene from the
reactants. This direct production is not strictly speaking a distinct
process, but is best described as concerted elimination of the
HO2 from the excited ethylperoxy adduct prior to stabiliza-
tion.2
0,23
In general, the kinetics of Scheme 23 give a biexpo-
nential production of HO2 products, where the rates of formation
and amplitudes depend on all the rate coefficients of the system.
This phenomenological scheme reproduces the biexponential
behavior of the HO2 yields from C2H5 + O2. The first
exponential is not resolved in these experiments and results in
the appearance of prompt HO2 formation, while the second
exponential is resolved and can be fit by an exponential to obtain
-
1
-1
are very similar, 25 kcal mol , 26 kcal mol , and 23 kcal
-
1
mol
for C H + O , C H + O , and c-C H + O2,
respectively. (Because of the large uncertainty in the lowest
temperature HO2 formation rate coefficients, the estimated
uncertainty in the activation energies is (5 kcal mol .) The
fit to the rate of formation predicted by master equation
calculations for C H + O yields a slightly larger apparent
activation energy (29.5 kcal mol ). These rates of formation
in the master equation calculations display a strong dependence
on the energy of the second transition state between C H O
2
2
5
2
3
7
2
5
9
-
1
-
1
a rate constant of formation for the delayed HO2, τ . The
2
5
2
1
-1 20
mechanism is similar to the one used by Simon et al. to describe
HO2 production from c-C5H9 + O2, except that the reaction
does not proceed through a QOOH intermediate.2
2
5
-
1
As shown in Figure 6 the rate constant of formation for the
and C2H4 + HO2 (-3.0 kcal mol as measured from the
reactants). Assuming similar R-O2 bond energies (∼32-37
-
1
20
delayed HO2, τ , is larger at each temperature for c-C5H9 +
O2 than for C2H5 + O2 or C3H7 + O2. The larger rate of HO2
formation for c-C5H9 + O2 could in principle reflect different
falloff behavior for the three reactions. However, the previous
-
1 16
kcal mol ), the fact that these three reactions have similar
experimentally observed temperature dependences strongly
suggests similar energetics for the transition state for HO2
elimination in these R + O2 reactions. This transition state in
C2H5O2 is the concerted elimination of HO2 from a five-
membered (CH-OOC) ring structure. However, larger alkyl
radicals also have the possibility of forming larger ring
structured transition states after O2 addition that cannot occur
in the ethyl + O2 system. Recent quantum chemistry calculations
on C2H5 + O2, C3H7 + O2, and C4H9 + O2 suggest that the
HO2 elimination channel from the five-membered ring transition
state is indeed similar for those three reaction systems (with a
3
,4
experiments on C2H5 + O2 and C3H7 + O2 show that their
rates of HO2 formation are already pressure independent under
the conditions of these experiments. The rate constant of form-
ation with c-C5H9 + O2 is also pressure independent at 638 K
(see Figure 8), which precludes falloff effects as the source of
the difference among these R + O2 reactions. The difference
may arise from a difference in the Arrhenius A factor for the
HO2 elimination channels. Thermochemically the A factor is
related to the entropy difference between the reactant RO2
adduct and the transition state. The adducts formed by acyclic
radicals such as ethyl and propyl lose internal methyl rotation
on the carbon atom in forming the five-membered (CH-OOC)
ring in the transition state. In the cyclopentyl adduct these
hydrogen atoms are already relatively fixed as the neighboring
carbon atoms are not free to rotate. The loss of the internal
rotation in the elimination from acyclic radical adducts implies
a greater reduction in entropy when forming this five-membered
ring than for the cyclopentyl adduct, thus giving a lower A factor.
-
1
barrier to HO2 formation of ∼30 kcal mol as measured from
3
9
the RO2 well). The present results suggest that a similar
concerted elimination dominates HO2 formation in c-C5H8 +
O2.
The overall temperature dependence of the prompt yield for
cyclopentyl + O2 (seen in Figure 5) is similar to other R + O2
reactions. The prompt HO2 yield at lower temperatures appears
to decrease with increasing size of the alkyl radical. This trend
8
was previously noted by Kaiser and Wallington for alkene

Reaction of Cyclopentyl Radical (c-C5H9) with O2
J. Phys. Chem. A, Vol. 105, No. 27, 2001 6653
small amount of OH formation, in the range of what is expected
from the experiments of Handford-Styring and Walker (i.e.
e10%). The OH formed can react with the cyclopentane (k )
-
11
3
-1 -1
2
1
.84 × 10
cm molecule
s
at 753 K) or with radical
species (i.e., OH, HO2, c-C5H9O2, with rate constants ranging
-
11
-13
3
-1 -1 14,36
from 6 × 10 to 10 cm molecule s ).
The reaction
with cyclopentane forms another cyclopentyl, which then reacts
with O2 to form OH and HO2. This cycling should continue
until all OH is depleted by forming the end product HO2 or
removed from the system by radical-radical reactions. With
the initial radical density and cyclopentane concentrations used
in this study, simulations show that a 10% contribution of the
OH-producing channel could still produce a nearly 100% yield
1
of HO2. It is interesting to note that Simon et al. do not report
any observation of 1,2-epoxycyclopentane formation at the
higher temperature of 873 K and explain acrolein formation by
secondary reactions without any direct formation from the
cyclopentylperoxy. Further studies focused on sensitive real time
measurements of OH formation from this reaction are underway
and may clarify the role of the adduct in acrolein and
2
Figure 9. The pressure dependence of the prompt yield of HO from
the reaction of c-C
6
5
H
9
+ O
2
at 638 K and at a constant O
.6 × 10 molecule cm . The mean values are shown as the open
circles O and the individual determinations as the filled circles b. The
2
density of
1
6
-3
-
n
dash-dotted line is the best fit to a P dependence, shown for
1
,2-epoxycyclopentane formation.
reference.
Conclusion
formation from C3H7 + O2 compared to C2H5 + O2. They
postulated that the smaller alkene yield for C3H7 + O2 is due
to more efficient stabilization of the propylperoxy radical relative
to ethylperoxy due to the additional vibrational degrees of
freedom in the propylperoxy radical. Since the cyclopentylp-
eroxy radical is still larger than propylperoxy, it would be
expected to give still lower prompt HO2 yields at low temper-
ature, although the present experimental precision is insufficient
to distinguish the difference.
The reaction of cyclopentyl radicals with O2 has been
investigated as a function of temperature between 296 and 723
K by using laser photolysis/CW frequency modulation spec-
troscopy. The overall yield of HO2 from the cyclopentyl radical
+ O2 has been observed as a function of temperature. The HO2
occurs on two different time scales; a prompt HO2 signal is
observed immediately following the UV flash, and a second
slower delayed rise is also observed at higher temperatures. The
results from the c-C5H9 + O2 reaction are similar to the previous
The prompt HO2 yield produced by the coupled kinetic
mechanism is anticipated to be pressure dependent. The
decomposition pathway of the adduct to HO2 and cyclopentene
competes with the adduct stabilization pathway. The adduct is
stabilized by collisional relaxation with the background gas. An
increase in the pressure should increase in the stabilization rate
and thus a decrease in the observed prompt yield. Kaiser et
3,4
results obtained from the C2H5 + O2 and C3H7 + O2 reactions.
Previous work demonstrated that product formation from C2H5
+
O2 had excellent agreement with the predictions from a
coupled kinetics model, where the formation of an ethylperoxy
3
radical is the antecedent to the ethylene + HO2 formation. The
present paper shows a strong similarity of the HO2 product
formation from the reactions of C H + O and c-C H + O .
8,11-13
al.
have previously established such a pressure dependence
2
5
2
5
9
2
This similarity suggests that c-C5H9 + O2 undergoes a very
similar coupled kinetics scheme, where cyclopentylperoxy
radical is the antecedent to cyclopentene + HO2 formation. The
apparent activation energies of the three reactions are also very
similar, and suggest that the relative energies of the transition
states for the concerted HO2 elimination in the three reactions
are similar as well.
for both C3H7 + O2 and C2H5 + O2. The HO2 prompt yield
from c-C5H9 + O2 also shows an inverse pressure dependence
as seen in Figure 9.
The initial product yields in the experiments of Handford-
Styring and Walker show 9.4% total for acrolein and 1,2-
epoxycyclopentane and 87.8% total for cyclopentene and
cyclopenta-1,3-diene (from column 1 and 5 of Table 4 in ref 2,
with 70 Torr O2 at 753 K). The cyclopenta-1,3-diene observed
is likely formed by further oxidation of cyclopentene, and the
total of the two is a measure of the branching ratio of reaction
Acknowledgment. These experiments described here were
made possible by the able technical support of Leonard E.
Jusinski. We thank Dr. James A. Miller and Dr. Stephen J.
Klippenstein for communicating results prior to publication. This
work is supported by the Division of Chemical Sciences,
Geosciences, and Biosciences, the Office of Basic Energy
Sciences, the U.S. Department of Energy.
1
b. The total amount of acrolein and 1,2-epoxycyclopentane is
an estimate of the branching ratio of the OH producing pathway-
s) (represented by reaction 1c). The review of Walker and
Morley gives the total initial yield of conjugate alkene to be
(
9
4
0% at 753 K with an initial yield of 87% cyclopentene and
% cyclopentadiene.40 These totals imply that ∼10% OH is
References and Notes
formed in reaction 1 at 753 K.
In the present study at 723 K the HO2 yield is still ∼100%,
remaining relatively constant after reaching 100% at 683 K.
The HO2 yields corrected only for self-reaction are also near
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(
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1
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(

6654 J. Phys. Chem. A, Vol. 105, No. 27, 2001
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