Reaction OH + OH studied over the 298-834 K temperature and 1 - 100 bar pressure ranges

Article abstract of DOI:10.1021/jp211805v

Self-reaction of hydroxyl radicals, OH + OH → H₂O + O (1a) and OH + OH → H₂O₂ (1b), was studied using pulsed laser photolysis coupled to transient UV-vis absorption spectroscopy over the 298-834 K temperature and 1-100 bar pressure ranges (bath gas He). A heatable high-pressure flow reactor was employed. Hydroxyl radicals were prepared using reaction of electronically excited oxygen atoms, O(¹D), produced in photolysis of N₂O at 193 nm, with H₂O. The temporal behavior of OH radicals was monitored via transient absorption of light from a dc discharge in H₂O/Ar low-pressure resonance lamp at ca. 308 nm. The absolute intensity of the photolysis light was determined by accurate in situ actinometry based on the ozone formation in the presence of molecular oxygen. The results of this study combined with the literature data indicate that the rate constant of reaction 1a, associated with the pressure independent component, decreases with temperature within the temperature range 298-414 K and increases above 555 K. The pressure dependent rate constant for (1b) was parametrized using the Troe expression as k_1b,inf = (2.4 ± 0.6) × 10^-11(T/300)^-0.5 cm³ molecule ^-1 s^-1, k_1b,0 = [He] (9.0 ± 2.2) × 10^-31(T/300)^-3.5±0.5 cm³ molecule ^-1 s^-1, F_c = 0.37.

Full text of DOI:10.1021/jp211805v

Article
pubs.acs.org/JPCA
Reaction OH + OH Studied over the 298−834 K Temperature and
- 100 bar Pressure Ranges
1
†
‡
,†
Manuvesh Sangwan, Evgeni N. Chesnokov, and Lev N. Krasnoperov*
†Department of Chemistry and Environmental Science, New Jersey Institute of Technology, University Heights, Newark,
New Jersey 07102, United States
‡
Institute of Chemical Kinetics and Combustion, Novosibirsk, 630090, Russia
*
S Supporting Information
ABSTRACT: Self-reaction of hydroxyl radicals, OH + OH → H O + O (1a) and OH + OH
2
→
H O (1b), was studied using pulsed laser photolysis coupled to transient UV−vis
2
2
absorption spectroscopy over the 298−834 K temperature and 1−100 bar pressure ranges
(
bath gas He). A heatable high-pressure flow reactor was employed. Hydroxyl radicals were
1
prepared using reaction of electronically excited oxygen atoms, O( D), produced in photolysis
of N O at 193 nm, with H O. The temporal behavior of OH radicals was monitored via
2
2
transient absorption of light from a dc discharge in H O/Ar low-pressure resonance lamp at
2
ca. 308 nm. The absolute intensity of the photolysis light was determined by accurate in situ
actinometry based on the ozone formation in the presence of molecular oxygen. The results of
this study combined with the literature data indicate that the rate constant of reaction 1a, associated with the pressure independent
component, decreases with temperature within the temperature range 298−414 K and increases above 555 K. The pressure
= (2.4 ± 0.6) × 10− (T/300)
11
−0.5
cm
3
dependent rate constant for (1b) was parametrized using the Troe expression as k
1
b,inf
molecule− s , k = [He] (9.0 ± 2.2) × 10 (T/300)
1
−1
−31
−3.5±0.5
cm molecule s , F = 0.37.
3
−1 −1
1
b,0
c
INTRODUCTION
through the singlet state and is pressure dependent, as other
■
22,24
1
−7
barrierless recombination reactions.
It should be noted that
Hydroxyl radical plays a central role both in atmospheric
8
,910−14
the two major interfering reactions, (2) and (3), also have
pressure independent and pressure dependent components,
which further complicates experimental studies of the kinetics
of hydroxyl radical reactions.
and in combustion
chemistry. This is one of the reasons
for numerous studies of the kinetics and mechanisms of gas
phase reactions of this radical.
of the radical, its concentrations in typical practically important
systems are low, and the self-reaction 1 plays only a minor role:
15−17
Due to the high reactivity
There have been numerous experimental studies of reaction
1
. Kaufman and Del Greco used fast discharge flow system with
OH + OH → H O + O
(1a)
(1b)
27,28
2
OH detection using absorption spectroscopy.
An additional
stoichiometric factor of 3/2 was involved in the data inter-
pretation, due to the subsequent fast reaction of the reaction
product, oxygen atom, with hydroxyl radical (reaction 2). The
→
H O
2 2
However, this reaction is very important in the laboratory
kinetic studies of hydroxyl radicals, where the concentrations
should be sufficiently high to provide accurate monitoring of
the radical decay. This reaction not only provides an additional
sink for the radical but also initiates a sequence of secondary,
highly undesirable reactions of oxygen and hydrogen atoms,
formed in channel 1a and subsequent reactions 2 and 3:
derived rate constant at 300 K is 1.3 × 10− cm molecule
12
3
−1 −1
s
−12
3
−1
(
actually, the reported value was 2.5 × 10 cm molecule
−1
s , the value was recalculated with the correct account of
the stoichiometric number). The reaction was studied at
29
low pressures (2−3 Torr), and no hydrogen peroxide
(
the product of reaction 1b) was detected by freezing the
30
reaction products with liquid nitrogen. Caldwell and Back
O + OH → O + H
(2a)
(2b)
2
evaluated the relative importance of channels 1a and 1b on the
basis of the measured yields of H and O from flash photolysis
→
HO
2
2
2
of H O vapor over a range of energy, water vapor pressure, and
2
H + OH → H + O
(3a)
(3b)
2
pressure of added inert gases (He, Ar, Xe, N ). Dixon-Lewis
2
et al. used quantitative ESR spectroscopy in combination with a
→
H O
2
In addition, reaction 1 is one of the simplest radical−radical
Special Issue: A. R. Ravishankara Festschrift
reactions, where both the singlet and triplet states play
18−24
comparable roles.
It is generally accepted that reaction
Received: December 7, 2011
Revised: March 6, 2012
Published: March 7, 2012
1
a proceeds via the triplet state and is buffer gas pressure
1
8,19,25,26
independent.
Reaction 1b is assumed to proceed
©
2012 American Chemical Society
6282
dx.doi.org/10.1021/jp211805v | J. Phys. Chem. A 2012, 116, 6282−6294

The Journal of Physical Chemistry A
Article
31
−1
fast flow system to study reaction 1 at ca. 1 Torr. NO was
used as a paramagnetic calibration gas. As in the previous
study, fast reaction 4
of −3.7 kJ mol . Most recently, Bahng and Macdonald
remeasured the rate constant of reaction 1 using laser
photolysis−transient IR absorption in the temperature range at
2
7
43
low bath gas pressures in the range 293−373 K. They confirmed
the negative temperature dependence of k ; however, their room
H + NO → OH + NO
(4)
2
1a
temperature rate constant is on the high side of the previous
was used to produce OH radicals. The rate constant at 300 K is
2
mass-spectrometry in combination with the fast discharge flow
measurements, 2.7 × 10− cm molecule s .
12
3
−1 −1
.6 × 10− cm molecule s . Wilson and O’Donovan used
12
3
−1 −1
There have been studies of reaction 1 over extended pressure
3
2
−12
3
−1 −1
44,45
44
tube. The rate constant obtained, 2.1 × 10 cm molecule s ,
ranges.
Forster et al. used laser photolysis combined with
32
is somewhat lower than that obtained in the previous study.
Breen and Glass reported 0.84 × 10
using ESR detection, significantly lower than in all previous
measurements. The discrepancy is assigned to the noninclusion
of the hydroxyl wall loss reaction in the reaction mechanism in
saturated laser induced fluorescence of OH. Experiments
performed between 1 and 150 bar of the bath gas He allowed
for falloff extrapolations to the high-pressure limit of the
recombination reaction 1b. The high-pressure limit rate constant
at ambient temperature for reaction 1b was evaluated as 2.2 ×
−
12
cm molecule s−1
3
−1
33
−1
−11
the previous studies, which in this study was too high (124 s ).
10 . The low-pressure extrapolation of the falloff curve
34
Mulcahy and Smith performed mass-spectrometric study
of the products of the primary and secondary reactions of
the species generated in reaction 4, and relative determination
of the rate constant of reaction 1 at pressures below 1 Torr.
The rate constant is 1.83 × 10
McKenzie et al. reported 2.2 × 10
(combined with the previous literature data) resulted in k =
1a
1.9 × 10− cm molecule s . In a subsequent study the
measurements were extended to the 200−700 K temperature
range. In this study, at four elevated temperatures the rate
constants of reaction 1 were measured in single pressure points
of ca. 85−90 bar.
12
3
−1 −1
45
−
12
12
3
−1
−1
cm molecule s .
−
3
−1 −1 35
cm molecule s ,
ESR was used as a detection technique. Another ESR study
at room temperature by Westenberg and DeHaas with careful
Reaction 1a has been studied at high temperatures using
36
46
shock tubes. Ernst et al. used thermal decomposition of HNO
3
−
12
3
accounting of the wall loss resulted in 2.3 × 10
cm
as a source of OH radicals, and resonance UV absorption to
molecule− s . Clyne and Down used resonance fluorescence
1
−1
monitor the radical decay over the temperature range 1200−
37
for OH detection. The room temperature rate constant was
1
800 K. Wooldridge et al. also used thermal decomposition of
1
.7 × 10− cm molecule s . Farquharson and Smith used
12
3
−1 −1
HNO as a source of OH, but narrow laser line absorption to
3
−
12 3
discharge flow-resonance fluorescence, to yield 1.7 × 10 cm
47
monitor OH at 306.7 nm. The experiments were conducted
molecule− s . All fast flow tube studies were performed at
low (Torr range) pressures combined with different OH
detection techniques, and all relied upon the same source of
hydroxyl radicals, reaction 4.
1
−1 38
over the temperature range 1050−2380 K and the pressure
range 0.18−0.60 atm. Both these studies resulted in positive
temperature dependence with the apparent activation energy of
−1
2
0−22 kJ mol . Sutherland et al. derived the rate constant of
Trainor and Von Rosenberg employed flash photolysis of
water vapor to generate OH radical, with time-resolved
reaction 1 on the basis of the directly measured rate constant
of the reverse reaction, O( P) + H O, and the reaction
thermochemistry. The value of the rate constant determined
3
39
2
monitoring by UV absorption. The reported value is 2.1 ×
48
−12
3
−1 −1
10
cm molecule
s
at room temperature. All single room
in this way absolute is in good agreement with the data of
Wooldridge et al., with a less positive temperature dependence
temperature low-pressure measurements resulted in the rate
constant of reaction 1 (channel 1a) within the range (0.84−
−
1
(
ca. 9 kJ mol ).
12
3
−1 −1
2
.6) × 10− cm molecule s .
18−26
Reaction 1 was extensively studied theoretically.
Temperature dependence in the low-temperature range of
reaction 1a was a subject of some controversy. Wagner and
18
Harding and Wagner performed calculations using variational
transition-state theory on ab initio MCSCF electronic potential
energy surfaces that correlate reactants with products. After the
barrier scaling to match the experiment at room temperature,
agreement with the experiment was obtained over the full
temperature range, including a sharp upward curvature above
1000 K. The excited-state surface is shown to be important in
this curvature, contributing over 35% of the rate constant at
higher temperatures. For the reverse direction, it is argued that
Zellner used flash photolysis of H O combined with resonance
2
absorption of OH to measure rate constant of reaction 1 in the
40
range 250−580 K. They found a weak positive temperature
−1
dependence with the activation energy of ca. 2 kJ mol .
−
12
3
The room temperature rate constant was 1.42 × 10
cm
molecule−1 s . Subsequently, Zellner et al. extended the
−1
41
study to measure pressure falloff in reaction 1 over the sub-
atmospheric pressure range (26−1100 mbar) at 253, 298, and
the H O + O measured rates are about a factor of 2 too large,
3
53 K. On the other hand, Bedjanian et al., using discharge flow
2
although this difference could be largely accounted for by
uncertainty in the equilibrium constant.
combined with mass-spectrometric detection obtained a slightly
negative temperature dependence in the range 233−360 K
2
9
The long-range interaction potentials between two OH
radicals were characterized using ab initio multireference CI
at 1 Torr of He. The apparent activation energy obtained was
−
1
−
1.7 kJ mol , the room temperature rate constant 1.44 ×
25
−12 3
−1 −1
calculations. There are four singlet surfaces correlating with
ground-state OH radicals. These states strongly interact, which
results in a complex reaction path for addition. At very long
separations (rO−O > 0.8 nm) where the four states are nearly
degenerate, the electrostatic dipole−dipole interaction domi-
nates. At intermediate distances (rO−O of 0.3−0.6 nm)
hydrogen bond provides the major attractive force. At short
distances (rO−O < 0.25 nm) covalent bonding is important. In
this region only one singlet surface remains attractive.
1
0
cm molecule s . Both the room temperature value
and the negative temperature dependence of Bedjanian et al.
15
are currently accepted in the IUPAC recommendation. Sun
and Li, using the discharge flow coupled with mass spectro-
metry and resonance fluorescence method measured the rate
constant of reaction 1 in the temperature range 220−320 K
4
2
at 1 Torr. The rate constant for the reaction at 298 K is
−
12
3
−1 −1
determined to be 1.20 × 10 cm molecule s , negatively
dependent on temperature with the apparent activation energy
6
283
dx.doi.org/10.1021/jp211805v | J. Phys. Chem. A 2012, 116, 6282−6294

The Journal of Physical Chemistry A
Article
19
Karkach and Osherov investigated stationary points on the
H O triplet potential energy surface. The transition states and
2
2
minimum energy structures on the lowest triplet H O2
2
potential surface were analyzed. Several energetically possible
reaction channels were evaluated using the transition-state
20
theory. Kuhn et al. performed calculations of the electronic
ground-state potential energy surface of hydrogen peroxide by
two different ab initio techniques.
23
Braunstein et al. calculated the global potential energy
surfaces for the three lowest triplet states in O + H O collisions
2
and performed classical trajectory calculations for the reverse
3
1
2
2
reaction 1a (O( P) + H O(X A ) → OH(X Π) + OH(X Π)).
2
1
Figure 1. Experimental setup schematics. ArF Excimer laser (EX100
GAM Laser Inc., 193.3 nm, 40 mJ); E, beam expander, consists of a
spherical lens f = 30 cm and cylindrical lens f = 30 cm cylindrical lens
f = 30 cm; M and M , dielectric mirrors; M and M , dielectric mirrors
Computed rate constants are in accord with the measurements
49
in the 1000−2400 K temperature range.
2
1
Brouwer et al. applied simplified statistical adiabatic
channel theory to calculate specific rate constants, product
quantum state distributions, and the rate constant for the
5
3
5
3
with high reflectivity at 193 nm at 45°; M
reflectivity at 308 nm and 45°; L , L , and L
3
, dielectric mirror with high
3
, fused silica lenses; D1
1
2
24
and D2, diaphragms forming monitoring beam (1/4 in. each). Several
sources of monitoring light are used: Xe arc lamp (75 W, Oriel
Instruments), radio frequency discharge low-pressure mercury lamp,
and dc discharge OH lamp (see text). M and M , dielectric mirrors
with high reflectivity at 193 nm normal incident light. These mirrors
were installed at 19° incident angle, which leads to the shift of the
high-reflectivity range originally centered at 193 nm to 200−230 nm.
This combination of mirrors works as a bandpass filter for the 200−
230 nm region, attenuating the visible light from the arc lamp by a
factor of ca. 200.
reaction HOOH → 2 OH. Troe and Ushakov used statistical
adiabatic channel model combined with classical trajectory
calculations for the dissociation/recombination dynamics of
hydrogen peroxide. Specific rate constants k(E,J), thermal rate
constants k in the high-pressure limit, as well as the lifetime
distributions were determined. The calculated thermal high-
pressure rate constants for HO recombination is in reasonable
1
2
44
agreement with the experimental data and was represented by
0
.47
0.74
−10
3
k1b,inf = (0.376 (298 K/T) + 0.013 (T/298 K) ) 10 cm
molecule−
1
s
−1
over the range 60−1500 K.
et al. investigated the ground-state potential
26
Sellevag
̊
Some details of the experimental arrangements and the signal
energy hypersurface of the reaction by means of high-level ab
initio methods. Variable reaction coordinate transition-state
theory, classical trajectory simulations, and a two-transition-
state model have been used to calculate the rate constant in the
high-pressure limit. A two-dimensional master equation was
used to characterize the pressure falloff of reaction 1 and to
calculate the low-pressure limiting rate coefficient. The results
51−53
accumulation are described elsewhere.
Helium was used as
the buffer gas in all measurements. The measurements were
performed over the 1−100 bar pressure and 25−561 °C
temperature range. A heatable high-pressure flow reactor of a
52,53
novel design
was employed (Figure 2). The reactor was
24
are in good agreement with the study of Troe and Ushakov.
Despite the large number of experimental and theoretical
studies of reaction 1, there are still remaining issues that require
attention. Recently, Troe presented an extended analysis of the
5
0
dissociation−recombination kinetics of H O . The analysis of
2
2
the pressure falloff was consistent with the accepted value of the
rate constant k = 1.45 × 10 at 298 K. However, the most
recent direct measurements of Bahng and Macdonald are in
−12
1a
43
significant, almost a factor of 2, disagreement with this value
2.7 × 10− ). The experimental high-pressure data that were
12
(
used to create the pressure falloff curves for k at elevated
1
b
45
45
temperatures are sparse. In this study, at four elevated
temperatures the rate constants of reaction 1 were measured in
single pressure points of ca. 85−90 bar.
In addition, the turning point in the temperature dependence
of the disproportionation channel 1a, which is expected from
the combination of the low-temperature and high-temperature
shock tube studies was never observed in a single experimental
study. In our current study of the reaction of methyl radicals
with hydroxyl over extended temperature and pressure ranges,
kinetic data on an extended temperature and pressure grid were
required. These reasons were the motivation for the current
study.
Figure 2. Detailed sketch of the high-pressure flow reactor (A) and the
flow pattern around internal windows (B).
made of 12.7 mm o.d. (1/2 in.) stainless steel tubing. The
central part of the tube (20 cm) was inserted into an aluminum
cylindrical block, which serves as a heat distributor. Two
electrical resistance heaters were located within the aluminum
block parallel to the reactor. A thermocouple (K-type, Omega)
was located in the middle of the block. The reagents were
supplied through a 3.175 mm o.d. (1/8 in.) stainless steel tube
that was passed seven times (total length 140 cm) through the
EXPERIMENTAL SECTION
■
Experimental Setup. The experimental approach is based
on excimer laser photolysis coupled to UV−vis transient absorp-
tion spectroscopy and a high-pressure flow system (Figure 1).
6
284
dx.doi.org/10.1021/jp211805v | J. Phys. Chem. A 2012, 116, 6282−6294

The Journal of Physical Chemistry A
Article
aluminum block for preheating. Such an arrangement ensured
complete preheating of the reactant mixture to the reactor
temperature without using additional ovens and temperature
controllers. Calculations based on the Graetz formula for gas
heating in a Poiseuille’s flow show guaranteed preheating of
the gas flow well within 0.001 K for the experimental conditions
used in the current work.
OH Radical Generation and Monitoring. Hydroxyl
radicals were generated in pulsed photolysis of N O in the
2
presence of water at 193.3 nm (ArF excimer laser):
1
54
N O + hv(193 nm) → O( D) + N
(5a)
(5b)
2
2
4
2
→
N( S) + NO( Π)
Two UV-grade quartz windows (12.7 in diameter, 9.5 mm
thick) were sealed at the end of the reactor at ambient
temperature outside the high-temperature zone using Viton
O-rings. The preheated reactant mixture entered the reactor
tube in the center and left through two outlets located on two
sides 5 cm away from the center but within the uniform temp-
erature zone. Additional buffer gas flows entered the reactor
near the windows to flush gas from the windows toward the
outlets. Two additional thick (9.5 mm) quartz windows,
separated by a stainless steel insert, were placed without sealing
inside the reactor near the reactor outlets. The length of the
insert determined the optical path in the zone of reactants of
1
O( D) + H O → 2OH(v=0,1)
(6a)
2
3
→
→
O( P) + H O
(6b)
(6c)
2
H2 + O2
The quantum yield of the major channel 5a is unity within 1%;
the minor channel 5b is less than 0.8%.
The fraction of vibrationally excited hydroxyl radicals OH(v=1)
55
1
formed in the reaction of O( D) + H O (reaction 6a) is 22−
2
5
6−59
56−58
30%.
According to more recent data the yield is 22−24%.
1
Fraction of O( D) formed in photolysis of N O reacts with
2
1
0.13 cm. The reactant mixture flowed toward the inside
N O:
2
windows, leaving through three small grooves in the insert
toward the reaction wall, where it was mixed with the external
windows flush flow penetrating through the narrow gap
between the inside window and the reaction wall, and left the
reactor through the exhaust outlets (see inset in Figure 2). In
this way, the two flows (reactant and flush) never met within
the observation zone. This “four windows” configuration
prevented penetration of the reactants out of the observation
zone, provided precise definition of the observation zone within
the uniform temperature region, and did not require sealing of
the windows at elevated temperatures.
The axial temperature profiles were measured in 1 cm steps
along the reactor length for each set of the experimental condi-
tions (the temperature set points, total flows and pressures)
used in the kinetic measurements. One of the windows was
replaced by a movable coaxial 1.6 mm o.d. K-type thermo-
couple (1/16 in.) sealed using a commercial adapter. One of
the internal windows was replaced with a ceramic cylinder with
a hole in the center for the thermocouple. The temperature
profiles were uniform within ±5 K in the reactant zone.
The average temperature in the reactant zone was taken as the
reactor temperature.
1
O( D) + N O → NO + NO
(7a)
(7b)
2
→
→
O + N2
2
3
O( P) + N O
(7c)
2
The kinetics of hydroxyl radical decay was monitored by
absorption in the UV (multiline at ca. 308 nm). A low-pressure
resonance hydroxyl lamp was employed. Because the
absorption cross sections of hydroxyl depend upon the lamp
parameters, mainly due to the gas temperature in the lamp,
a detailed description is given below. The lamp was made of
glass tubing 4.0 mm i.d., 6.0 mm o.d., 10.0 cm long, equipped
with two fused silica windows. Argon flow was saturated with
water vapor at ambient temperature (296 ± 3 K) and 1.28 atm
(4.0 psig) pressure. The H O/Ar gas mixture entered near
2
the output window and pumped through the discharge tube
with the flow rate of 137 sccm at pressure 40 Torr. The lamp
was powered from a stabilized high-voltage dc power supply
(2900 V via a ballast resistor of 66 kΩ). The electrode near the
light exit window was the anode (positive). The discharge
current was 37 mA, the discharge length 10.0 cm. The discharge
tube was vigorously cooled by a strong stream of compressed air.
The linear power density dissipated in the discharge was 1.94 W/
cm. The output light from the lamp was focused inside the cell
using a fused silica lens, and after the cell onto the entrance slit of
an imaging spectrograph.
The imaging spectrograph (Acton 300i) was equipped with a
PMT (Hamamatsu R106) with a preamplifier (EMI) and a gated
intensified CCD (ICCD) camera (ICCD Max, Roper Scientific).
The residual light from the excimer laser pulse was removed
using a liquid filter (4.3 × 10− M solution NaCl in water, 1 cm).
The liquid filter provides virtually complete depression of
193 nm light. A photomultiplier tube (Hamamatsu R106)
mounted on the exit slit operates on a reduced number of
dynodes (6) with a high-voltage divider current (maximum
2.7 mA), which ensures good linearity and lower noise at
high photon fluxes. A typical anode current was 10−20 μA. The
PMT signal was preamplified (EMI preamplifier), digitized, and
stored using a digital storage oscilloscope (LeCroy 9310A, Dual
channel, 400 MHz, 100 Msamples/s, 50 Kpts/ch). The time
resolution is determined by the preamplifier setting and can be
0.03, 0.3, 3, or 30 μs. Typically, 0.3 μs time constant was used
The gas flow rates were controlled by high-pressure mass
flow controllers (Brooks, model 5850). The total flow rates of
the reactant mixtures with helium were in the range 6−75 sccs.
Additional flush flows to the cold reactor windows were in the
range 4.5−10 sccs. Liquid H O was injected into the high-
2
pressure system using a precision syringe pump (Harvard
Apparatus, Model PHD 4400). The flow of liquid H O in the
2
range 0.5−10 μL/min flowed from the syringe pump through a
capillary tube to an evaporator kept at 90 °C. This approach
2
produced steady and stable flow of H O over the pressure
2
range 1−100 bar.
1
7
Concentrations of the precursors used were (0.3−1.7) × 10
molecules cm− (N O) and (1.3−7.0) × 10 (H O). The
3
17
2
2
photolysis laser photon fluence inside the reactor was varied
1
5
−2
in the range (2.4−9.7) × 10 photons cm . The initial
1
2
concentrations of hydroxyl radicals were in the range (4−25) × 10
−3
molecules cm . The pressure range of the current study is
1−100 bar (He). The temperature range was 295−834 K.
The repetition rate of the laser was set to ensure complete
replacement of the gas mixture in the reactor between the
pulses (0.1−4 Hz depending on pressure).
6
285
dx.doi.org/10.1021/jp211805v | J. Phys. Chem. A 2012, 116, 6282−6294

The Journal of Physical Chemistry A
Article
Table 1. Reaction Mechanism Used for Fitting of the Experimental Profiles
relative
maximum
rate
a
b
reaction
reactants
products
rate constant
reference
comments
13
29
1
a
OH + OH
H + H
2
O
7.1 × 10− exp(210 K/T)
29
16
lit. for T < 415 K, Troe fit
0.11
above 414 K (see text)
1b
2a
2b
3a
3b
6a
6b
6c
7a
H O
2
fitted, this work
fitting parameter
0.89
2
11
−3
OH + O
O + H
2
2.4 × 10− exp(110/T)
9.0 × 10
9.4 × 10
1.8 × 10
6.2 × 10
−31
−2.6
−2
−9
−3
HO2
[M] 1.6 × 10 (T/298)
as for reaction 3b
14
2.8
OH + H
H + O
2
6.86 × 10− (T/298) exp(−1950/T)
[M] 1.6 × 10− (T/298)−2.6
1.7 × 10−10 exp(36/T)
<0.003k6a
73
74
60
75
16
31
H O
2
1
O( D) + H O
OH + OH
2
3
O( P) + H O
neglected
7
total rate constant k =
10
2
12
H
2
+ O
2
2.2 × 10−
1
8.37 × 10−11
O( D) + N
2
O
NO + NO
branching ratio
of 0.62 based
on ref 16
−
(1.37 ± 0.11) × 10 is the
76−78
average of three studies,
discussed in ref 43
as
11
7b
O + N
2
5.13 × 10−
branching ratio
of 0.38 based
on ref 16
2
3
1.3 × 10−12
8,0 = 6.0 × 10−31(T/300)−2.5
8,inf = 3.3 × 10−11(T/300)−0.3
60
k7c/k
7
< 0.01, set to 1.3 × 10−12
7c
8
O( P) + N
HONO
2
O
60
79
OH + NO
k
k
F
8,c: fit of the data from ref 79
0.28
F
8,c= 0.60 exp(91/T)
9
1
1
1
1
1
1
1
1
OH + HO
2
2 2
H O + O
4.8 × 10− exp(250/T)
11
80
81
82
16
16
83
83
83
84
4.5 × 10
4.5 × 10
1.3 × 10
9.4 × 10
4.7 × 10
1.2 × 10
1.1 × 10
4.9 × 10
7.5 × 10
−2
−4
−2
−5
−8
−6
−5
−7
−7
12
0
HO + NO
OH + NO2
4.0 × 10− exp(223/T)
2
12
1
OH + H O
H O + HO
2
2.9 × 10− exp(−109/T)
2.70 × 10− exp(224/T)
1.40 × 10− exp(−2000/T)
7.11 × 10− exp(−710/T)
2.81 × 10− exp(−440/T)
5.00 × 10− exp(−866/T)
3.29 × 10−12(T/298) exp(81/T)
2
2
2
11
2
O + HO2
O + H O
O + OH
2
12
3
OH + HO2
H +O
2
2
11
4a
4b
4c
4d
H + HO2
2
2
10
2OH
11
H O + O
2
1
1.55
O( D) + H O
2
a
3
b
Rate constants and concentrations units based on molecule, cm and s. Maximum reaction rate relative to the maximum (initial) total rate of
14
−3
reaction 1, for the experimental conditions at 301 K, 100 bar, [OH] = 1.50 × 10 molecules cm (other relevant concentrations are listed in Table 2).
0
60
(the measured actual rise time t0.1−0.9 was 0.46 μs). The traces
assuming the accuracy of k and k of ±8% ). The absorption
6a 7
were accumulated (500−5000 pulses) and transferred to a PC
for processing. The ICCD camera installed on the second outlet
of the spectrograph was used to record transient as well as
continuous spectra.
The photolysis laser beam was merged before the cell with
and separated after the cell from the monitoring beam using two
cross-section of N O is accurately known at 298 and 1 bar. At
2
other conditions, the cross sections of N O were measured in this
2
work (Supporting Information). The major source of errors is the
determination of the laser light intensity inside the reactor. The
outside laser energy meters require calibrations, in addition,
windows transmittance drift due to film deposition caused by
contaminations introduces additional errors. In this work, we
used in situ laser light actinometry based on the stable molecule
formation with very well characterized cross-section at the
monitoring wavelength. Specifically, ozone formation, monitored at
4
5° multilayer dielectric mirrors (CVI). While the photolysis
beam was filling homogeneously the whole cross-section of the
reactor (see below), the monitoring beam was formed by two
1
/4 in. diaphragms before and after the reactor (Figure 1).
Before entering the reactor, the laser beam was formed (to
provide uniformity) with spherical (f = 30 cm, the distance from
the reactor 70 cm) and cylindrical (f = 30 cm, the distance from
the reactor 23 cm) lenses. The beam profile was measured by
scanning with a small hole diaphragm (ca. 0.5 mm) combined
with an energy meter. The beam uniformity across the reactor
cross-section was ±7.3% from the mean value.
In Situ Actinometry. There are several difficulties in
measuring rate constants of radical−radical reactions. The most
critical one is the necessity of knowing the absolute radical
concentrations. In this work, the absolute concentrations of
OH radicals were determined on the basis of the photon
2
53.7 nm, in the photolysis of N O/O /N mixtures at 1 bar and
2 2 2
298 K was used. Essentially, this is a modification of the technique
where ozone depletion in photolysis at 248 nm was (Ravishankara
et al.) used to determine in situ photon flux from a KrF laser.
61
In these measurements, N O diluted with 5.0% O in N
2
2
2
mixture was pumped through the reactor at ambient
measured) pressure and photolyzed at 193.3 nm. Formation
(
of O was monitored using a low-pressure radio frequency
discharge mercury lamp at 253.7 nm. After formation in the
photolysis, excited oxygen atoms O( D) undergo relaxation in
3
1
= 2.6 × 10−
11
)
17
and oxygen
collisions with nitrogen (k
q,N
2
kq,O2 = 4.0 × 10−11) or react with N O (k = 1.35 × 10−10,
17
(
flux inside the reactor, the absorption cross-section of N O at
2
2
1
193.3 nm, and the efficiency of conversion of O( D) atoms
Table 1). The concentration of oxygen−nitrogen mixture
19
−3
produced in the photolysis of N O to OH radicals. The latter
(2.43 × 10 molecules cm ) is much higher than the con-
2
1
6
was typically about (0.84 ± 0.02) × 2 and was accurately
evaluated using a reaction mechanism (Table 1, reactions 6 and 7,
centration of N O used in this experiments (7.4 × 10
molecules cm ), which provided almost complete (98.5%)
2
−3
6
286
dx.doi.org/10.1021/jp211805v | J. Phys. Chem. A 2012, 116, 6282−6294

The Journal of Physical Chemistry A
Article
1
3
relaxation of O( D) to the ground-state oxygen atoms O( P)
then to introduce proper corrections for the drift of the laser
energy during the series of experiments.
and subsequent conversion to ozone in fast (ca. 56 μs) reaction
with molecular oxygen, O( P) + O + M → O + M.
Sample ozone formation traces are shown in Figure 3. Trace
A is the absorbance profile with the mixture N O/O /N
2
3
Reagents. In the initial experiments UHP helium 99.9995%
purity from Airgas passed through an in-line oxygen trap
(R&D Separations, Model OT2-SS, manufacturer stated
oxygen content reduction to 15 ppb) was used. Later, it was
replaced with BIPHelium from Airgas with 99.9999% purity
with reduced oxygen content (<10 ppb). Pure nitrous oxide
was obtained from Scott Specialty Gases (purity 99.9995%).
2
3
2
2
In the high-pressure experiments certified mixture of N O in
2
He (2.50%, accuracy ±2%) obtained from Matheson Tri-Gas.
was used. Purified water (Milli-Q) with TOC less than 5 ppb
was degassed by freeze−pump−thaw cycles and used as a
reactant supplied by a syringe pump (Harvard Apparatus
PHD4400) as well as in the low-pressure H O/Ar discharge
2
hydroxyl monitoring lamp. UHP Ar obtained from Matheson
TriGas (99.999% purity) was used in the H O/Ar lamp.
2
RESULTS AND DISCUSSION
■
Transient absorption profiles of OH were measured at 41 com-
binations of temperature and pressure. Examples of measured
temporal profiles of absorption at 308 nm are shown in
Figure 4. To determine the rate constant of reaction 1, a
reaction mechanism described below was used to model and
fit the experimental profiles. Absorption profiles were fitted by
a numerical solution of a system of differential equations
corresponding to the reaction mechanism using SCIENTST
Figure 3. In situ actinometry based on the ozone formation. Trace A:
absorbance profile with the mixture N O/O /N (N O = 2.28 Torr,
2
2
2
2
5
.0% O /N mixture, total pressure 1 bar) in the reactor (between the
2 2
two internal windows). Trace B: “blank” experiment, the flow of N O
2
is turned off, only the O /N mixture is pumped through the reactor.
2
2
The residual absorbance is due to the photolysis of molecular oxygen
inside the reactor and between the external and internal windows
flushed with the O /N mixture, as well as in the air outside the reactor
2
2
63
software. The reaction mechanism used in the fits included
where the photolysis beam and the monitoring beam overlap. The
difference in the absorbances is used to calculate the concentration of
ozone formed. (Only the initial parts of the traces are shown to resolve
the buildup stage. In the measurements, a longer time domain (ca. 10 ms)
was used).
reactions 1−7 and additional reactions (Table 1). Reactions
1
involving excited O( D) atoms are completed within 50 ns and
were treated separately. The products of these reactions served as
the initial reactants for the residual reactions in the mechanism
occurring on a much longer (0.1−100 ms) time scale.
The UV absorption cross sections and the rate constants,
used in the fits, were either measured in the current work (e.g.,
(
N O = 2.28 Torr, 5.0% O /N mixture, total pressure 1 bar)
2
2
2
in the reactor (between the two internal windows). Trace B is
the “blank” experiment, the flow of N O is turned off, and only
absorption of N O, absorption cross-section of OH) or were
2
2
O /N mixture is pumped through the reactor. The residual
taken from the literature. The reaction mechanism as well as
the kinetic parameters used in the model are listed in Table 1.
The decay of hydroxyl radicals is almost entirely controlled
by reactions 1 and subsequent fast reaction of oxygen atoms
with hydroxyl radicals, reaction 2. Several other reactions also
contribute into the decay rate. The rest of the reactions were
considered to elucidate their potential role. Several of them play
only a marginal role (if any) under the conditions of the current
study. In addition to hydroxyl production in reaction 6a,
formation of OH radicals and H atoms in direct photolysis of
2
2
absorbance is due to the photolysis of molecular oxygen inside
the reactor and between the external and internal windows
flushed with the O /N mixture, as well as in the air outside the
2
2
reactor where the photolysis beam and the monitoring beam
overlap. The difference in the absorbances, ΔA, is used to
calculate the concentration of ozone formed due to the
−2
photolysis of N O. The photon fluence F (photons cm ) is
2
then calculated as
ΔA
−21
F =
water at 193.3 nm with the cross-section (1.51 ± 0.15) × 10
σO3·l·0.985·σ
[N O]
2
−1
N O
2
(E1)
cm molecule (measured in this work) was also taken into
account. Correction for the diffusion controlled wall loss of the
hydroxyl radical was performed by introducing the first-order
2
where σO3 = (1.148 ± 0.034) × 10− cm molecule is the
17
2
−1
62
2
ozone absorption cross section at 253.7 nm; l = 10.13 cm is
rate constant kw,OH = 5.784DOH‑He/R , where the diffusion
1
.6
the length of the reactor (the distance between the two internal
coefficient was expressed as DOH‑He = DOH‑He,296(T/296 K) .
−
20
2
−1
2
−1
windows), and σN2O = (8.77 ± 0.44) × 10 cm molecule is
The room temperature value of D
= 662 Torr cm s
=
OH‑He,296
6
2
2
−1
64
the N O absorption cross section at 193.3 nm (all at 298 K
0.883 bar cm s was taken from the literature. With the
reactor insert internal radius of 0.38 cm, at the highest
temperature 834 K this results in kw,OH = 183, 61, and 18 s− for
1, 3, and 10 bar, respectively. The largest contribution of the
wall loss to the decay rate of ca. 25% was at the highest
temperature, 834 K, and the lowest pressure, 1 bar. At ambient
temperature and 1 bar pressure the contribution was ca. 5%.
At higher pressures the contribution is inversely proportionally
smaller, and is completely negligible above 10 bar.
2
and 1 bar). All actinometry measurements were performed at
pressure 1 bar and ambient temperature, where all required
cross sections are accurately known.
Usually, two such determinations were performed, before
and after a series of measurements. Simultaneously, the readout
of the pyroelectric detector measuring laser pulse energy after
passing the reactor (Figure 1) was recorded. The readout of the
pyroelectric detector in the kinetic measurements was used
1
6
287
dx.doi.org/10.1021/jp211805v | J. Phys. Chem. A 2012, 116, 6282−6294

The Journal of Physical Chemistry A
Article
Table 2. Experimental Conditions and the Rate Constants for Reaction 1 (k = k1a + k )
1
1b
photon fluence/
k1/10− cm
12
3
1
6
a
17
3
11
12
no. density/1020 10 photon cm
15
−2
13
−1 −1
p/bar (He) T/K [N O] /10
[H O] /10
[O( P)] /10
[NO] /10
[OH] /10
molecule
6.17
s
2
0
2
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
9
9
9
9
9
9
9
9
9
9
9
.16
.16
.16
.16
.16
.16
.16
.16
.16
.16
.16
.11
.11
.01
.01
.01
.91
.91
.91
.91
.91
.91
.91
.91
.91
.91
.84
.84
.84
.84
.84
.84
.84
.84
.84
.84
.84
296
298
354
354
414
414
555
555
626
714
714
769
834
834
834
834
298
354
414
555
626
714
769
834
834
834
297
354
414
555
626
714
769
834
834
834
834
294
354
414
555
626
714
769
301
414
555
626
714
9.49
3.87
4.47
3.21
3.74
2.75
3.19
2.05
2.39
1.81
1.59
1.86
1.69
1.56
1.43
1.43
1.41
7.05
5.89
5.05
3.77
3.34
2.93
2.72
2.51
2.32
2.32
3.61
3.00
2.57
1.92
1.71
1.49
1.41
1.30
1.29
1.29
1.30
6.76
5.58
4.79
3.59
3.18
2.79
4.27
3.88
3.12
2.34
2.09
1.84
2.21
1.63
2.21
1.58
2.13
1.57
2.22
1.62
2.18
2.22
1.59
2.77
4.40
2.87
2.78
3.40
2.55
2.05
2.13
2.06
2.06
3.03
6.28
5.52
4.01
4.07
3.14
3.18
3.14
3.29
3.26
3.29
5.64
5.08
3.5
5.40
3.97
5.41
3.87
5.20
3.85
5.43
3.97
5.32
5.44
3.89
7.99
12.67
8.23
7.98
9.77
5.76
5.08
6.14
5.94
5.92
8.19
18.0
15.9
11.5
11.7
9.36
9.64
9.37
9.82
9.70
9.81
20.0
18.2
12.6
12.9
15.2
5.76
5.85
5.54
5.47
5.49
5.86
14.4
19.0
26.1
27.9
28.5
28.9
0.243
0.281
0.202
0.235
0.173
0.201
0.129
0.150
0.114
0.100
0.117
0.103
0.096
0.087
0.087
0.087
0.706
0.589
0.505
0.377
0.335
0.293
0.272
0.251
0.253
0.253
2.40
4.75
3.11
4.76
3.04
4.63
3.03
5.00
3.13
4.78
4.86
3.08
6.07
9.64
6.93
6.73
8.33
3.08
3.08
2.68
2.65
2.61
2.47
8.33
7.33
5.78
5.87
6.86
6.86
6.73
6.99
6.89
6.94
9.11
8.19
5.74
5.90
6.83
2.64
2.69
2.55
2.53
2.54
2.71
8.19
4.54
3.03
2.84
2.83
2.83
6.74
4.95
6.74
4.83
6.49
4.8
11.0
6.24
3.45
4.15
2.59
2.72
1.75
1.73
1.56
1.48
1.73
2.18
1.77
1.98
1.98
2.01
8.79
6.51
5.79
2.48
2.32
2.72
2.18
1.87
1.90
1.90
7.87
9.17
6.73
7.85
5.03
5.87
4.46
3.91
4.56
3.62
3.34
3.04
3.04
3.01
6.77
4.95
6.64
6.78
4.86
8.45
13.4
8.73
8.47
10.4
6.87
5.36
6.06
6.10
6.10
6.12
19.1
16.8
12.24
12.39
9.14
9.25
9.15
9.59
9.48
9.59
15.45
13.9
9.59
9.85
11.5
5.91
5.97
5.63
5.53
5.53
5.90
25.3
15.0
16.4
17.6
17.9
18.2
15.1
1.16
9.92
7.41
6.58
5.76
5.82
5.37
4.96
4.96
11.3
12.6
9.40
8.05
6.01
5.34
4.67
4.15
3.83
3.78
3.78
3.83
1.99
8.52
6.41
3.71
3.30
3.12
3.27
2.72
2.32
2.42
2.81
1.71
1.27
1.13
0.990
0.922
0.850
0.858
0.858
0.858
7.29
3.6
4.22
1.95
1.99
1.88
1.87
1.87
2.00
7.29
5.40
6.29
6.73
6.87
6.96
2
2
2
2
2
2
2
9.9
9.9
9.9
9.9
9.9
9.9
9.9
14.7
18.7
12.3
10.5
5.99
12.9
10.1
5.14
7.89
3.85
4.89
6.99
6.12
5.64
3.42
5.25
5.70
4.44
2.99
2.80
1
1
1
1
1
01
01
01
01
01
16.6
22.9
18.2
16.2
9.54
15.2
11.4
10.1
16.8
12.6
11.26
9.89
6.60
5.96
8.92
a
All concentrations in molecules cm−3.
The results are listed in Table 2 and shown in Figure 5. The
mechanism. It is quite clear that at elevated pressures a number
of recombination type reactions (such as 7b, 8, 10) cannot be
discarded, whereas they are negligible at low pressures. A
completely negligible at 300 K reaction of hydrogen atoms with
hydroxyl radicals (reaction 3a) might play a minor role at the
highest temperatures of this study. Another feature should be
stressed; at high pressures, the reaction of recombination of
hydroxyls with NO (reaction 8) plays significant role and
cannot be discarded. For the reaction of recombination of OH
reaction mechanism used to fit experimental profiles is shown
in Table 1. In the last column of the table, the maximum
reaction rate relative to the initial total rate of reaction 1 is
given for a specific set of experimental conditions (low
temperature 301 K and high pressure 100 bar). The relative
importance of the reactions depends on temperature and
pressure. However, the relative rates listed in the table provide
some insight on the importance of specific reactions for the
6
288
dx.doi.org/10.1021/jp211805v | J. Phys. Chem. A 2012, 116, 6282−6294

The Journal of Physical Chemistry A
Article
larger, and maximal at 100 bar, where the rate constant of this
study is ca. 18% smaller than the mean value from the previous
4
4,45
works.
However, this is still within the combined
uncertainty of the two studies.
50
As pointed out by Troe, irrespective of the impressive
efforts and the temperature and pressure ranges covered in the
experimental studies of reaction 1, the experimental data alone
still are not sufficient to derive the reaction parameters, such
as the low-pressure limit and the high-pressure limit rate constants,
the falloff broadening, etc. The case is further complicated by the
presence of the pressure independent channel 1a as well as the
controversial data on the kinetic parameters of this channel.
Therefore, the following strategy in the data processing was
chosen. At the lowest temperature of this study (ambient), the
pressure falloff curve approaches the high-pressure limit, and it
was used as a fitting parameter. However, at higher temper-
atures no reliable determination of the high-pressure limit is
possible, and the theoretically derived temperature dependence
Figure 4. Sample temporal profiles of OH decay. Pressure = 100 bar
(
He). Temperatures = 714, 555, and 301 K, from upper to lower
curves. Solid lines: fits by the reaction mechanism (see text). The
of k1b,inf as well as the value of the temperature independent
1
6
16
residual is shown for 555 K. [N O] = 8.93 × 10 , 11.4 × 10 , and
26,50
2
broadening factor
were accepted:
16
−3
1
6.6 × 10 molecules cm for 714, 555, and 301 K, respectively.
−
0.5
k
b,inf(T) = k
1b,inf,298K
(T/298)
1
(E2)
(E3)
with O forming HO (reaction 2b) no kinetic data are available.
2
If the rate constant of this reaction is set as the rate constant of
reaction 3b, then the simulations show a significant role of this
reaction at elevated pressures.
The impact of the reaction mechanism on the fitted rate
constant was evaluated at 1 bar and 298 K, 100 bar and 301 K,
and 100 bar and 714 K. The profiles were fitted with the
complete mechanism listed in Table 1, the reduced mechanism
of reactions 1a, 1b, 2a, and 8, and the limiting mechanism of
reactions 1a, 1b, and 2a only. The maximum impact was found
for 100 bar and 714 K. Using the reduced mechanism leads to
Fc = 0.37
The situation is further complicated by the ambiguity of the
literature data on the pressure independent channel 1a.
15
The value recommended by IUPAC (based on the discharge
29
flow study of Bedjanian et al. ) is ca. a factor of 2 lower than
43
the most recent value of Bahng and Macdonald by laser
photolysis−time-resolved IR absorption. Except for one study
all other temperature studies agree on the negative temperature
dependence of reaction 1a near the ambient temperature,
although in a pretty narrow temperature range.
the increase of k by 17%, and additional removal of reaction
1
8
1
lead to additional increase of the rate constant by 17%. At
00 bar and 301 K, the increments were 7% and 12%, res-
Therefore, for the data processing over the temperature
range 295−414 K we accepted the room temperature value as
well as the negative temperature dependence for k from
pectively. Finally, at 1 bar and 298 K, the increments were 7%
and 6%, respectively.
1a
IUPAC recommendation and used the values of the rate
constant as fixed parameters. At higher temperatures, however,
the information on k1a is completely unavailable. Fortunately,
at higher temperatures the pressure falloff is strongly shifted
toward high pressures, and the low-pressure extrapolation
becomes reliable. Therefore, at temperatures above 414 K the
At high temperatures, the reverse reaction −1b1b of dis-
sociation of hydrogen peroxide, might become important.
Estimates based on the equilibrium constant for reaction 1b
50
show, however, that the rate constant of this reaction at the
highest temperature of this study does not exceed 14 s−1 and
rate constant k was used as a fitting parameter.
can be neglected.
There are two major sources of errors in the measured rate
constants. The first one is the uncertainty of the absolute
concentrations of hydroxyl radicals. The accuracy of the N O
cross sections (ca. ±6%), the O determination (ca. ±4%), and
1a
65,66
The data were fitted using Troe expression:
⎛
⎜
⎞
⎟
[
M]/[M]
c
k1 = k1a + k
1b,∞
2
⎝
1 + [M]/[M] ⎠
c
3
the uncertainties introduced by the ozone formation model
2
log(F )/[1+([log([M]/[M] )]/N) ]
c
c
(E4)
E5)
(E6)
×
10
(
ca. ±3%) contribute to the accuracy of the determination of
the absolute concentrations of OH radical. The second source
is the statistical error in the decay parameters of OH radicals
[
M] = pN /(ZRT)
(
A
(±12% in the worst cases at 100 bar, negligible at 1 bar) and
N = 0.75 − 1.27 log(Fc)
the uncertainties associated with the reaction model (estimated
as ±15%). Assuming that all these sources are independent, an
overall estimate of the accuracy of the rate constants is ±21%.
The rate constants measured in this work are in good
where k1b,inf is the rate constant of reaction 1b in the high-
pressure limit, [M] is the number density of the gas, [M] is
c
the density in the “center” of the pressure falloff curve. The
4
4,45
agreement with the previous study at elevated pressures.
temperature independent broadening factor (F = 0.37) was
c
Direct comparison of the data from refs 44 and 45 with the
results of this study in a figure is not possible, because neither
the temperature nor pressure grids coincide. The deviation at
the lowest temperature of this study, 298 K, is ca. 8−16% at low
pressures (1−3 bar), where the rate constants of this study are
accepted according to ref 50. The small nonideality of helium
(
4.7% at 298 K and 100 bar) was taken into account via the
67
compression factor Z(T,p):
Z = 1 + 0.00047(p/bar)(298 K/T)
(E7)
6
289
dx.doi.org/10.1021/jp211805v | J. Phys. Chem. A 2012, 116, 6282−6294

The Journal of Physical Chemistry A
Article
The fits are shown in Figure 5 as solid lines. The center
pressure of the falloff curves p (defined as the pressure of ideal
c
Figure 7. Rate constant of the pressure independent channel 1a (OH
+
OH → H O + O). Low-temperature data (dotted squares) are taken
2
29
from the literature. Filled squares are obtained by short extrapolation
n
of the data obtained in this work under the assumption k1b,inf ∼ T , n =
Figure 5. Pressure dependence of the rate constant of reaction 1 at
different temperatures. Solid lines: fits using the Troe expression (see
text): open squares, 299 K; solid circles, 354 K; open triangles up, 414
K; solid triangles down, 555 K; open diamonds, 626 K; solid triangles
left, 714 K; open triangles right, 769 K; solid stars, 834 K (see also
inset in the figure).
−
0.5, F = 0.37. Error bars are the standard deviations of the fits.
c
Model variation: open triangles tip down, n = −0.75, F = 0.37; open
c
triangles tip up, k
is temperature independent (n = 0, F = 0.37);
1b,inf
c
filled stars, n = −0.5, F = 0.74; open star, n = −0.5, F = 0.19. Crosses
c
c
43
are the extrapolated k based on the Bahng and Macdonald data
1a
using the same approach (n = −0.5, F = 0.37).
c
gas at the center number density [M] ) as a function of
temperature is shown in Figure 6.
c
Table 3. Rate Constant of Reaction 1a in the Temperature
Range 555 K ≤ T ≤ 773 K
p = ([M] /N )RT
k1a/1 × 10−12 cm molecule s−1
3
−1
c
A
(E8)
temperature/K
c
a
555
626
714
769
834
1.0 ± 0.6
1.5 ± 0.5
1.6 ± 0.5
1.7 ± 0.5
1.76 ± 0.40
a
Indicated uncertainty is the combined standard error of the fits and
the scatter due to the model variations.
n
dependence k1b,inf ∼ T and F ) as well as to the low-
c
temperature data (where a significant discrepancy exists) was
verified. The theoretically derived n = −0.5 and F = 0.37 were
c
chosen as the base parameters. First, it was determined that the
derived values of k at T ≥ 555 K are almost independent of the
1a
accepted low-temperature data. Using Bahng and Macdonald
43
29
data instead of the Bedjanian et al. data (which differ by a
factor of 1.8) results in almost indistinguishable results (the
difference is ca. 2%). Then at fixed F = 0.37 the parameter n in
c
Figure 6. Fitting parameter p (the center of the falloff curves) plotted
the temperature dependence was varied as n = 0, −0.5, and
c
vs temperature in the log−log coordinates. Filled squares are obtained
−0.75. In addition, at n = −0.5, F was varied by a factor of 2, F
c
c
n
with the recommended values: k1
b,inf
∼ T , n = −0.5, F = 0.37. The
c
= 0.19 and 0.74. All results are shown in Figure 7. The results
4.0
resulting power dependence is p /bar = 1.12 (T/300 K) The error
c
indicate that the extrapolated k is quite stable with respect to
1a
bars are the standard deviations of the fits. Impact of the falloff
the parameters variation. The most unstable value is at 555 K,
where the center of the pressure falloff curve is only ca. 13 bar.
At higher temperatures the pressure falloff shifts toward higher
pressures (reaching ca. 70 bar at 834 K), making the low-
pressure data of this work much closer to the low-pressure
limit, and hence, the extrapolation much more reliable. At the
highest temperature of this study, 834 K, the extracted rate
constant k is almost independent of the variations of the falloff
parameters variation: open triangles tip down, n = −0.75, F = 0.37;
c
open triangles tip up, n = 0, F = 0.37; filled stars, n = −0.5, F = 0.74;
c
c
open stars: n = −0.5, F = 0.19. Crosses are from the fits based on the
c
43
Bahng and Macdonald data using n = −0.5, F = 0.37.
c
Figure 7 shows the rate constant of the pressure independent
channel 1a obtained from the fits at higher temperatures
29
combined with the literature data at low temperatures. The
rate constants are also summarized in Table 3. The stability of
the extrapolated rate constant of channel 1a to the parameters
of the theoretical falloff curve (parameter n in the temperature
1a
curve parameters outlined above (<±6%). It should be stressed
that the positive temperature dependence above 555 K is
confirmed for all evaluated combination of the falloff
6
290
dx.doi.org/10.1021/jp211805v | J. Phys. Chem. A 2012, 116, 6282−6294

The Journal of Physical Chemistry A
Article
parameters. Moreover, the positive temperature dependence is
already apparent from the data at 1 bar: the rate constant at
Combination of (E10) with (E11) leads to the low-pressure
limit rate constant k1b,0
:
8
34 K is ca. 25−30% larger than at 626 and 714 K (Table 2).
−
31
−3.5±0.5
k
= (9.0 ± 2.2) × 10 (T/300)
[He]
Together with the literature data, the results of this study
indicate a turning point in the temperature dependence of k in
1b,0
3
−1 −1
1a
×
cm molecule
s
(E12)
the range of 400−550 K. The positive temperature dependence
At 300 K, eq E12 gives factor of 2.2 higher value compared to
that recommended by Troe and slightly stronger negative
temperature dependence (the recommended low-pressure limit
of k measured in this work in the 555−834 K temperature
1a
range correlates well with the shock tube studies of Sutherland
4
8
47
et al. and Wooldridge et al. (Figure 8).
−
31
rate constant with He as the bath gas is 4 × 10 (T/
−
3.2 50
3
3
00)
). The theoretical work of Sellevag et al. predicts
.22 × 10− cm molecule
31
3
−1 −1
s
for k1b,0 at 300 K, which is
factor of 2.8 lower. Predicted temperature dependence over the
temperature range of 300−800 K is k1 ∼ T
agreement with our results E12.
−3.56
, in excellent
b,0
The results also indicate the existence of the turning point in
the temperature dependence for the disproportionation
channel 1a (Figure 7). The data suggest that the negative
temperature dependence of the rate constant k1a at low
temperatures should switch to a positive temperature depend-
ence somewhere between 400 and 550 K. Such a behavior is
actually expected on the basis of the comparison of low-
temperature low-pressure data with the shock tube results,
where the positive temperature dependence of k was observed
1a
(
Figure 8). In the shock tube studies, due to much higher
temperatures, the pressure falloff region is shifted to much
higher pressures, so that any observed rate constant must be
assigned to channel 1a. Besides, the equilibrium in reaction 1b
is shifted toward the reactants at T > 1000 K at realistic initial
concentrations of OH, and hydrogen peroxide cannot be
formed. Figure 8 shows that the temperature dependence of k1a
obtained in this study is consistent with other low- and high-
Figure 8. Rate constant of the disproportionation channel 1a
compared to data from other experimental studies: filled circle,
4
3
29
48
38
39
Bahng and Macdonald; open triangle up, Bedjanian et al.;
47
horizontal bar, Wooldridge et al.; vertical bar, Sutherland et al.;
cross, Wagner and Zellner; crossed circle, Farquharson and Smith;
double cross, Ernst and Wagner; star, Trainor and Von Rosenberg;
filled pentagon, Del Greko and Kaufman; filled triangles, Sun and
4
0
46
temperature data.
28
A negative temperature dependence that switches to positive
at ca. 500 K is quite typical for reactions with “negative
barriers”, i.e., reactions with the bottleneck on the potential
energy surface having the “ground-state” energy below the
42
Li; open dotted circles, this work.
6
8,69
reactants ground-state energy.
In reaction 1a in favorable
The center pressure p as a function of temperature is shown
c
18,25,26
orientations a hydrogen bond is formed.
Formation of a
in Figure 6 in the log−log coordinates. The temperature
dependence determined from the linear regression is
relatively long-range and relatively strong attractive interaction
results in a “negative barrier” condition by bringing the barrier
26
below the reactants level.
p /bar = (1.12 ± 0.40)(T/300)4
.0±0.4
c
(E9)
CONCLUSIONS
■
Therefore, for the low-pressure limit rate constant k1b,0
Experimental data on the rate constant of reaction 1 measured
over extended temperature (295−834 K) and pressure (1−100
bar) ranges were used to parametrize the pressure falloff in the
recombination channel 1b as well as to obtain independent data
on the pressure independent disproportionation channel 1a at
T > 450 K. The minor deviation in the high-pressure rate
constant for reaction 1b (−37%) and a substantial (factor of
k
= ([He]/[M] )k
1b,inf
1
b,0
c
=
=
[He]k
RT/(p N )
A
c
1
b,inf
−
20
−3.0
(T/300)
[He]k b,inf3.70 × 10
1
(E10)
2
.2) deviation of the low-pressure limit rate constant from the
The expression for the high-pressure rate constant k1b,inf with
recommended values are reported. The low-pressure extrap-
the 298 K value obtained from the fit and presumed
olations of the rate constant k suggest the existence of the
1
−0.5
temperature dependence of T
is
turning point in the temperature dependence of reaction 1a in
the 400−550 K range.
−
11
k
= (2.4 ± 0.6) × 10
b,inf
1
APPENDIX
−
0.5
3
−1 −1
■
(
T/300)
cm molecule
s
(E11)
OH Apparent Absorption Cross sections and the
Spectroscopic Model
At 300 K, this is 37% lower than that recommended by Troe,
and 28% lower than that calculated
by Sellevag et al., 3.34 × 10
Determination of a rate constant of a second-order reaction
requires accurate determination of the absolute concentrations
of free radicals. A multiline light source (a dc powered H O/Ar
11
−0.5 50
3
.8 × 10− (T/300)
,
−
11
3
−1
−1
cm molecule
s .
2
6
291
dx.doi.org/10.1021/jp211805v | J. Phys. Chem. A 2012, 116, 6282−6294

The Journal of Physical Chemistry A
Article
discharge lamp) was used to record the hydroxyl temporal
profiles. The apparent cross sections of hydroxyl radical at
different temperatures and pressures were determined as
follows. Mixtures of N O/H O/He were photolyzed at 193.3
2
2
nm using a uniform beam. The transient intensity profiles were
recorded and processed according to the reaction mechanism.
The initial concentrations of OH radicals were determined
via the photon fluence, the absorption cross sections of N O
2
1
(
measured separately), and the fraction of O( D) atoms
converted to hydroxyl radical. The conversion efficiency
1
(
(1/2)[OH] /[O( D)] ) was calculated on the basis of a
0 0
1
small mechanism of reactions involving O( D) atoms and was
always close to unity (ca. 84%), which ensures reliable
determination of this parameter. The photon fluences were
determined in additional in situ actinometry experiments via
the ozone yield in the N O/N /O + 193.3 nm system at 1 bar
2
2
2
and 298 K. In all experiments the relative laser beam intensity
was recorded with high accuracy using a pyroelectric sensor,
and corrections for the laser power drift were introduced, when
needed.
The emission spectrum of the hydroxyl lamp as well as the
absorption spectrum of the OH radical consists of a large
number of narrow rotational lines grouped around 308 nm.
The relative intensity as well as the widths of the absorption
lines depend on the reactor temperature and pressure.
Consequently, the apparent absorption cross-section of
hydroxyl is also temperature and pressure dependent.
The relative intensities of the different rotational lines in the
hydroxyl lamp as well as their shapes and widths depend upon
the conditions inside the lamp discharge (gas temperature,
pressure, composition, etc.). Therefore, care was taken to
characterize and specify the lamp construction and operational
parameter, and to keep them constant. It should be stressed
that for the current results on the apparent cross-section of
hydroxyl to be transferrable to other studies, the lamp
parameters should be closely followed.
The apparent cross sections of the hydroxyl radical are
shown in Figure A1 at different temperatures and pressures
relevant to the current study. The experimental cross sections
were directly used in the data processing and the rate constant
determinations. For the purposes of the data interpolation and
the evaluation of the “curves of growth”, a spectroscopic model
was built. The solid lines in Figure A1 represent the model fit to
the experimental data.
Figure A1. Apparent absorption cross-section of hydroxyl radical as a
function of temperature at different pressures. Solid lines represent the
fits by a spectroscopic model. The model: rotational temperature in
the lamp 1300 K, 187 lines, emission lines Doppler broadened with
́
translational temperature equal to the rotational temperature, fwhm/Å =
0
.01957 (at T = 1300 K), absorption lines with Voigt profile, collision
́
0.3
broadening fwhm/Å = 0.0045(298 K/T) (p /bar).
He
calculations require hydroxyl rotational temperature. To
determine the rotational temperature of hydroxyl in the lamp,
the lamp emission spectra were recorded (with low resolution
of 0.18 nm) and compared with the spectra simulated using
LIFEBASE. The temperature determined in this way was 1300
K. Furthermore, the translational temperature (which enters in
the Doppler line width) of hydroxyl radicals in the lamp was
assumed to be equal to the rotational, 1300 K.
The absorption spectrum of hydroxyl radicals was con-
structed in a similar manner:
I (λ) = ∑ B ·f (λ−λ ,T,p)
A
i
i
V
i
(A3)
The spectroscopic model was built as follows. The emission
spectrum of the hydroxyl lamp is a superposition of narrow
lines:
where B
are the relative intensities of the absorption lines in
(λ−λ ,T,p) is the Voigt line
shape function, which depends on the temperature and
pressure in the reactor. The relative line intensities B were
i
the OH absorption spectrum and f
V
i
I (λ) = ∑ A ·f (λ − λ )
E
i
i
i
D
(A1)
calculated for different temperatures using LIFBASE. The
collision broadening parameter was assumed to be the same for
all lines. The following temperature and pressure of the
collision broadening parameter was assumed:
i
where λ and A are the line positions and the relative intensities
i
i
in the OH emission spectrum and f (λ − λ ) are the line shape
D
0
function (assumed to be Gaussian with Doppler broadening
only because of the low pressure in the hydroxyl lamp, 40
Torr). In the calculations, the 187 strongest lines were taken
into account. The set of the line intensities and the line shape
function are defined to be normalized:
ΔλFWHM = a·p·(300 K/T)b
(A4)
where Δλ
is the full width at half maximum of the Lorentz
shaped line and a and b are the empirical parameters.
FWHM
The apparent cross section is then calculated as
∑i Ai =
f (λ − λ ) dλ = 1
i
D
∫
(A2)
σOH(T,P) = SF· I (λ) I (λ) dλ
∫
E
A
(A5)
The line positions λ and the relative line intensities A were
calculated using the LIFBASE software, available online. The
i
i
7
0
where SF is a scaling factor.
6
292
dx.doi.org/10.1021/jp211805v | J. Phys. Chem. A 2012, 116, 6282−6294

The Journal of Physical Chemistry A
Article
The spectroscopic model has three fitting parameters: the
scaling factor SF, the collision broadening constant a and the
parameter b that determines the temperature dependence of
the collision broadening according to eq A4. The results of the
temperature ranges. This information is available free of charge
via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION
■
́
model fits (with a = 0.0045 Å/bar and b = 0.3) are shown in
Corresponding Author
Figure A1. The agreement of the model with the experimental
data and the model is quite good, in particular taking into
account the simplifying assumptions and the few fitting
parameters of the model. The model reproduces perfectly the
temperature dependences of the cross sections. The absolute
values deviate at elevated pressures about 7−9%, however, not
in a systematic manner. Most probably these deviations reflect
the experimental accuracy. It should be stressed that the
hydroxyl lamp emission spectrum in this model is characterized
by only one parameter, the rotation temperature, which is
obtained from an independent measurement. The spectro-
scopic model was used only in the curves of growth
calculations, direct experimental data were used in the kinetic
data processing.
*
Fax: (973)-596-8436. E-mail: krasnoperov@adm.njit.edu.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
This material is based upon work supported by the National
Science Foundation under Grant No. CBET-0827398.
REFERENCES
■
(
(1) Atkinson, R. Chem. Rev. 1986, 86, 69−201.
2) Lelieveld, J.; Dentener, F. J.; Peters, W.; Krol, M. C. Atmos. Chem.
Phys. 2004, 4, 2337−2344.
(
(4) Calvert, J. G.; Derwent, R. J.; Orlando, J. J.; Tyndall, J. S.;
Wallington, T. J. Mechanisms of Atmospheric Oxidation of the Alkanes;
Oxford University Press: New York, 2008.
(
(
3) Finlayson-Pitts, B. J.; Pitts, J. N. Science 1997, 276, 1045−1051.
The empirical fitting parameter a is in good agreement with
2
+
the average collisional line broadening for the A Σ (υ=0) ←
2
́
71
X Π(υ=0) transition at 293 K of 0.0047 Å/bar. Also, it could
be compared with the collisional pressure broadening in He of
four absorption lines of OH near 308 nm ranging from 0.0053
5) Ravishankara, A. R. Annu. Rev. Phys. Chem. 1988, 39, 367−394.
6) Montzka, S. A.; Krol, M.; Dlugokencky, E.; Hall, B.; Jockel, P.;
̈
́
72
to 0.0082 Å/bar.
Lelieveld, J. Science 2011, 331, 67−69.
Due to the comparable widths of the absorption and
emission lines as well as to the multitude of lines with different
oscillator strengths the Beer-Lambert law is, in general, not
applicable, and the apparent cross sections can be used only for
small absorptions that do not exceed about 1%. To evaluate the
deviations from the Beer−Lambert law at larger absorptions,
the model described above was used to calculate the reduced
(7) Smith, I. W. M.; Ravishankara, A. R. J. Phys. Chem. A 2002, 106,
4798−4807.
(
(
(
8) Smith, R. H. Coal Res. CSIRO 1967, 32, 9−18.
9) Westbrook, C. K. Proc. Combust. Inst. 2000, 28, 1563−1577.
10) Miller, J. A.; Pilling, M. J.; Troe, J. Proc. Combust. Inst. 2005, 30,
4
(
3−88.
11) Warnatz, J. Combust. Sci. Technol. 1983, 34, 177−200.
(
(
(
12) Haber, F. Angew. Chem. 1929, 42, 745−751.
“
curves of growth” (see Supporting Information). The
13) Kondrat’ev, V. N. Usp. Khim. 1939, 8, 195−240.
14) Tsang, W. Chem. Phys. Processes Combust. 2009, 1−9.
deviations from the Beer−Lambert law are linear with respect
to the apparent absorbance with high accuracy when the
apparent absorbance does not exceed 15%, and can be
expressed as
(15) Website: http://www.iupac-kinetic.ch.cam.ac.uk 2001, IUPAC
Subcommittee on Gas Kinetic Data Evaluation.
(16) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Crowley, J. N.;
Hampson, R. F.; Hynes, R. G.; Jenkin, M. E.; Rossi, M. J.; Troe, J.
Atmos. Chem. Phys. 2004, 4, 1461−1738.
A
/A
= sapp/sapp,0 = 1 − SAapp
app app,0
(A6)
(
17) Manion, J. A.; Huie, R. E.; Levin, R. D.; Jr., D., R. B.; Orkin, V.
where S is the slope of the ratio σ /σapp,0 plotted vs A . This
L.; Tsang, W.; McGivern, W. S.; Hudgens, J. W.; Knyazev, V. D.;
Atkinson, D. B.;et al. NIST Chemical Kinetics Database; NIST Standard
Reference Database 17, Version 7.0 (Web Version), Release 1.4.3,
Data version 2008.12; National Institute of Standards and
Technology: Gaithersburg, MD; http://kinetics.nist.gov/, 2008.
app
app
slope depends on temperature and pressure, the deviations are
larger at low pressures (Supporting Information). The analysis
shows that for apparent absorbances <0.5% the correction does
not exceed 1% at any pressure, and was neglected in the data
processing. For maximum absorbances encountered in this
work (< 6%), linear representation eq A6 is accurate (and can
be used for absorbances up to 15%), and was used to correct
the data:
(
18) Harding, L. B.; Wagner, A. F. Symp. (Int.) Combust., [Proc.]
989, 22nd, 983−989.
19) Karkach, S. P.; Osherov, V. I. J. Chem. Phys. 1999, 110, 11918−
1927.
20) Kuhn, B.; Rizzo, T. R.; Luckhaus, D.; Quack, M.; Suhm, M. A.
J. Chem. Phys. 1999, 111, 2565−2587.
21) Brouwer, L.; Cobos, C. J.; Troe, J.; Duebal, H. R.; Crim, F. F.
J. Chem. Phys. 1987, 86, 6171−6182.
22) Maergoiz, A. I.; Nikitin, E. E.; Troe, J. J. Chem. Phys. 1995, 103,
083−2091.
23) Braunstein, M.; Panfili, R.; Shroll, R.; Bernstein, L. J. Chem. Phys.
005, 122, 184307.
1
(
1
(
A
= [OH]sapp,0l = Aapp/(1 − SAapp
)
app,0
(A7)
(
From these simulations, it was also apparent that for
absorbances of 30−50% the deviations from the Beer−Lambert
law are large, about a factor of 2 or higher. Without proper
corrections, it leads to apparently longer decay profiles that can
lead to gross underestimation of the rate constants (factor or
two or even higher, especially at low pressures).
(
2
(
2
(24) Troe, J.; Ushakov, V. G. Phys. Chem. Chem. Phys. 2008, 10,
3915−3924.
(
(
25) Harding, L. B. J. Phys. Chem. 1991, 95, 8653−8660.
26) Sellevag, S. R.; Georgievskii, Y.; Miller, J. A. J. Phys. Chem. A
ASSOCIATED CONTENT
Supporting Information
■
2
(
009, 113, 4457−4467.
*
S
27) Kaufman, F.; Del Greco, F. P. Symp. (Int.) Combust., [Proc.]
Absorption cross-section of N O and the curves of growth for
2
1962, 659−666; discussion 666−668.
(28) Del Greco, F. P.; Kaufman, F. Discuss. Faraday Soc. 1962, 33,
128−138.
hydroxyl radical absorption as well as their linear approx-
imations over the 1−100 bar and 298−834 K pressure and
6
293
dx.doi.org/10.1021/jp211805v | J. Phys. Chem. A 2012, 116, 6282−6294

The Journal of Physical Chemistry A
Article
(
7
(
1
29) Bedjanian, Y.; Le Bras, G.; Poulet, G. J. Phys. Chem. A 1999, 103,
017−7025.
30) Caldwell, J.; Back, R. A. Trans. Faraday Soc. 1965, 61, 1939−
945.
31) Dixon-Lewis, G.; Wilson, W. E.; Westenberg, A. A. J. Chem.
Phys. 1966, 44, 2877−2884.
32) Wilson, W. E. Jr.; O’Donovan, J. T. J. Chem. Phys. 1967, 47,
(65) Gilbert, R. G.; Luther, K.; Troe, J. Ber. Bunsen-Ges. Phys. Chem.
1983, 87, 169−177.
(66) Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 161−169.
(67) International Thermodynamic Tables of the Fluid State.
Helium-4. In IUPAC Division of Physical Chemistry Commission on
Thermodynamics and Thermochemistry Thermodynamic Tables Project;
Angus, S., de Reuck, K. M., McCarty, R. D., Eds.; Pergamon Press:
New York, 1977.
(
(
5
(
(
455−5457.
33) Breen, J. E.; Glass, G. P. J. Chem. Phys. 1970, 52, 1082−1086.
34) Mulcahy, M. F. R.; Smith, R. H. J. Chem. Phys. 1971, 54, 5215−
(68) Krasnoperov Lev, N.; Peng, J.; Marshall, P. J. Phys. Chem. A
2006, 110, 3110−3120.
(69) Gao, Y.; Alecu, I. M.; Hsieh, P. C.; Morgan, B. P.; Marshall, P.;
Krasnoperov, L. N. J. Phys. Chem. A 2006, 110, 6844−6850.
(70) Luque, J.; Crosley, D. R. SRI International Report MP 99-009,
1999.
(71) Engleman, R. J. Quantum Spectrosc. Radiat. Transfer 1969, 9,
391.
(72) Kasyutich, V. L. Eur. Phys. J. D 2005, 33, 29−33.
(73) Tsang, W.; Hampson, R. F. J. Phys. Chem. Ref. Data 1986, 15,
5221.
(
1
(
4
(
7
(
1
(
6
(
1
35) McKenzie, A.; Mulcahy, M. F. R.; Steven, J. R. J. Chem. Phys.
973, 59, 3244−3254.
36) Westenberg, A. A.; DeHaas, N. J. Chem. Phys. 1973, 58, 4066−
071.
37) Clyne, M. A. A.; Down, S. J. Chem. Soc., Faraday Trans. 2 1974,
0, 253−266.
38) Farquharson, G. K.; Smith, R. H. Aust. J. Chem. 1980, 33, 1425−
435.
39) Trainor, D. W.; Von Rosenberg, C. W. Jr. J. Chem. Phys. 1974,
1, 1010−1015.
40) Wagner, G.; Zellner, R. Ber. Bunsen-Ges. Phys. Chem. 1981, 85,
122−1128.
41) Zellner, R.; Ewig, F.; Paschke, R.; Wagner, G. J. Phys. Chem.
1
(
087−1279.
74) Zellner, R.; Erler, K.; Field, D. Symp. (Int.) Combust., [Proc.]
1
(
(
977, 16, 939−948.
75) Carl, S. A. Phys. Chem. Chem. Phys. 2005, 7, 4051−4053.
76) Takahashi, K.; Takeuchi, Y.; Matsumi, Y. Chem. Phys. Lett. 2005,
4
(
(
10, 196−200.
(
77) Carl Shaun, A. Phys. Chem. Chem. Phys. 2005, 7, 4051−4053.
1
(
988, 92, 4184−4190.
78) Dunlea, E. J.; Ravishankara, A. R. Phys. Chem. Chem. Phys. 2004,
42) Sun, H.; Li, Z. Chem. Phys. Lett. 2004, 399, 33−38.
43) Bahng, M.-K.; Macdonald, R. G. J. Phys. Chem. A 2007, 111,
6
(
, 2152−2161.
(
79) Fulle, D.; Hamann, H. F.; Hippler, H.; Troe, J. J. Chem. Phys.
3
(
850−3861.
44) Forster, R.; Frost, M.; Fulle, D.; Hamann, H. F.; Hippler, H.;
Schlepegrell, A.; Troe, J. J. Chem. Phys. 1995, 103, 2949−2958.
45) Fulle, D.; Hamann, H. F.; Hippler, H.; Troe, J. J. Chem. Phys.
996, 105, 1001−1006.
46) Ernst, J.; Wagner, H. G.; Zellner, R. Ber. Bunsen-Ges. Phys. Chem.
977, 81, 1270−1275.
47) Wooldridge, M. S.; Hanson, R. K.; Bowman, C. T. Int. J. Chem.
Kinet. 1994, 26, 389−401.
48) Sutherland, J. W.; Patterson, P. M.; Klemm, R. B. Symp. (Int.)
Combust., [Proc.] 1991, 23rd, 51−57.
49) Lifshitz, A.; Michael, J. V. Symp. (Int.) Combust., [Proc.] 1991,
1
(
(
998, 108, 5391−5397.
80) Keyser, L. F. J. Phys. Chem. 1988, 92, 1193−1200.
81) Bardwell, M. W.; Bacak, A.; Teresa Raventos, M.; Percival, C. J.;
(
1
(
1
Sanchez-Reyna, G.; Shallcross, D. E. Phys. Chem. Chem. Phys. 2003, 5,
381−2385.
82) Jimenez, E.; Gierczak, T.; Stark, H.; Burkholder, J. B.;
Ravishankara, A. R. J. Phys. Chem. A 2004, 108, 1139−1149.
83) Baulch, D. L.; Cobos, C. J.; Cox, R. A.; Esser, C.; Frank, P.; Just,
T.; Kerr, J. A.; Pilling, M. J.; Troe, J.; et al. J. Phys. Chem. Ref. Data
992, 21, 411−734.
84) Mousavipour, S. H.; Saheb, V. Bull. Chem. Soc. Jpn. 2007, 80,
901−1913.
2
(
(
(
(
1
(
1
(
2
(
3rd, 59−67.
50) Troe, J. Combust. Flame 2011, 158, 594−601.
51) Grebenkin, S. Y.; Krasnoperov, L. N. J. Phys. Chem. A 2004, 108,
(
1
953−1963.
52) Krasnoperov, L. N.; Chesnokov, E. N.; Stark, H.; Ravishankara,
A. R. J. Phys. Chem. A 2004, 108, 11526−11536.
53) Krasnoperov, L. N.; Chesnokov, E. N.; Stark, H.; Ravishankara,
A. R. Proc. Combust. Inst. 2005, 30, 935−943.
54) Mulcahy, M. F. R.; Pethard, M. R. Aust. J. Chem. 1963, 16, 526−
43.
55) Greenblatt, G. D.; Ravishankara, A. R. J. Geophys. Res. 1990, 95,
539−3547.
56) Sauder, D. G.; Stephenson, J. C.; King, D. S.; Casassa, M. P.
J. Chem. Phys. 1992, 97, 952−961.
57) Tanaka, N.; Takayanagi, M.; Hanazaki, I. Chem. Phys. Lett. 1996,
54, 40−46.
58) Butler, J. E.; Talley, L. D.; Smith, G. K.; Lin, M. C. J. Chem. Phys.
981, 74, 4501−4508.
59) Cleveland, C. B.; Wiesenfeld, J. R. J. Chem. Phys. 1992, 96, 248−
55.
60) Vranckx, S.; Peeters, J.; Carl, S. Phys. Chem. Chem. Phys. 2010,
2, 9213−9221.
61) Ravishankara, A. R.; Wine, P. H.; Nicovich, J. M. J. Chem. Phys.
983, 78, 6629−6639.
62) Sander, S. P.; Friedl, R. R.; Barker, J. R.; Golden, D. M.; Kurylo,
(
(
(
5
(
3
(
(
2
(
1
(
2
(
1
(
1
(
M. J.; Wine, P. H.; Abbatt, J. P. D.; Burkholder, J. B.; Kolb, C. E.;
Moortgat, G. K.;et al. JPL Publication 10-6, 2011.
(
(
63) SCIENTIST; Micromath Scientific Software: Saint Louis, MO.
64) Ivanov, A. V.; Trakhtenberg, S.; Bertram, A. K.; Gershenzon, Y.
M.; Molina, M. J. J. Phys. Chem. A 2007, 111, 1632−1637.
6
294
dx.doi.org/10.1021/jp211805v | J. Phys. Chem. A 2012, 116, 6282−6294