O(1D) branching fraction from the reaction N(2D) + O2 → NO(2II,v,J) + O(3P,1D)

Article abstract of DOI:10.1021/jp031340k

The reaction N(²D) + O₂ → NO(²II,v,J) + O(³P,¹D) has been considered for many years as a possible source of O(¹D) in the thermosphere. We have used the Cold Chemical Infrared Simulation Experiment (COCHISE) facility to determine an upper limit to the O(¹D) branching fraction of this reaction by observing the absence of the radiative decay of O(¹D) and O₂(b ¹σ) produced by efficient energy exchange with O₂. By carefully modeling the kinetic and fluid dynamics of the experiment, an upper limit of 0.02 ± 0.02 was found for the branching fraction into the O(¹D) product channel.

Full text of DOI:10.1021/jp031340k

5588
J. Phys. Chem. A 2004, 108, 5588-5599
O(1D) Branching Fraction from the Reaction N(2D) + O2 f NO(2Π,v,J) + O(3P,1D)
Steven M. Miller* and Martin Hunter†
Space Vehicles Directorate, Air Force Research Laboratory, AFRL/VSBYM, Hanscom Air Force Base,
29 Randolph Road, Bedford, Massachusetts 01731-3010
ReceiVed: December 16, 2003; In Final Form: April 5, 2004
The reaction N(2D) + O2 f NO(2Π,v,J) + O(3P,1D) has been considered for many years as a possible source
of O(1D) in the thermosphere. We have used the Cold Chemical Infrared Simulation Experiment (COCHISE)
facility to determine an upper limit to the O(1D) branching fraction of this reaction by observing the absence
of the radiative decay of O(1D) and O2(b1Σ) produced by efficient energy exchange with O2. By carefully
modeling the kinetic and fluid dynamics of the experiment, an upper limit of 0.02 ( 0.02 was found for the
branching fraction into the O(1D) product channel.
I. Introduction
distribution at V ) 8, that the branching ratio for producing
O(1D)/O(3P) from reaction 2 was ∼70%. This result was then
used by the aeronomers whose models required additional O(1D)
as evidence of a second source of O(1D).
We have modified the Cold Chemical Infrared Simulation
Experiment, or COCHISE, which is the same apparatus that
Kennealy and Rawlins used, to extend its spectral range from
the infrared into the visible and near-ultraviolet. We then
carefully measured emission at 630.0 nm for evidence of O(1D)
product of reaction 2. Because O(1D) possesses a very long
radiative lifetime (148 s) and, therefore, is difficult to detect,
we also used the 0-0 band emission at 760-765 nm from the
O2(b1Σ) product of the additional energy transfer mechanism
O(1D) is a long-lived radiator (τ ) 148 s at 630 nm) in the
thermosphere. This long radiative lifetime allows most of the
O(1D) electronic energy to be transferred to other thermospheric
species, such as N2 and O2, to create N2(v), which does not
radiate, and O2(b1Σ) which possesses a shorter lifetime (τ ) 12
s) and radiates in the near-infrared region at 760-765 nm.
Observations of O(1D) radiance have been used extensively to
measure both the temperature of the thermosphere and thermo-
spheric wind velocities. There has been an ongoing controversy
during the past 20 years, in regard to the source of this important
thermospheric species. The original source, which was suggested
in 1979 by Sharp et al.,1 is the dissociative recombination of
+
O2
:
O(1D) + O2 f O(3P) + O2(b1Σ)
(3)
O2+ + e- f O(1D) + O
(1)
as a tracer.
A model of the COCHISE flow and reaction kinetics was
developed and is presented in the appendix of this paper. Using
this model and the calibration results, the upper limit detection
thresholds for O(1D) and O2(b1Σ) signals were calculated and
the best-fit upper limit branching ratio for reaction 2 is found.
This reaction is well-accepted as the main source of thermo-
spheric O(1D). Several aeronomers2,3 have claimed that this
dissociative recombination source cannot account for all of the
630.0 nm radiation observed. This conclusion was based on the
analysis of rocket and satellite data. However, others4 have
interpreted that same rocket data, and data from similar
campaigns, in such a way that all of the 630.0 nm radiance can
be accounted for by the aforementioned reaction. Those whose
analysis has implied a missing source of O(1D) have relied on
the reaction
II. Experimental Section
The COCHISE facility is well-described by the 1984 article
by Rawlins et al.7 Only the modifications relevant to this work
will be described here. A fiber-optic bundle was designed with
cryogenic feed-throughs so that both infrared (IR) and visible
(vis) emission could be detected simultaneously (see Figure 1).
Fused silica fiber was chosen, because of its low loss in the
visible range and its lack of transmission in the IR range. This
ensured that no room-temperature IR background would leak
into the chamber through the fiber-optic material. The fiber
bundle is comprised of 80 100-µm-diameter fibers, each with a
numerical aperture of 0.22. The internal end of the bundle is a
close-packed cylinder that collects light focused from the
reaction chamber by a 2.54-cm-diameter spherical fused silica
lens. At the external end, the fibers are all placed in a line, 100
µm in diameter by 1 cm in length. This provides particularly
efficient coupling into a 0.5-m CVI model 480 monochromator
N(2D) + O2 f NO(2Π,v,J) + O(3P,1D)
(2)
to produce the additional O(1D). Support for this second source
came from papers by Kennealy et al.5 in 1979 and Rawlins et
al.6 in 1989, which described laboratory studies of reaction 2
and the resulting product distribution of NO(v,J). Those
laboratory studies concluded, using the indirect evidence of a
break in the nitric oxide product ground-state vibrational
* Author to whom correspondence should be addressed. Telephone:
(781)-377-2807. Fax: (781)-377-8900. E-mail address: steven.miller@
hanscom.af.mil.
† Now with G. R. Harrison Spectroscopy Laboratory, Massachusetts
Institute of Technology, Cambridge, MA 02139.
10.1021/jp031340k CCC: $27.50 © 2004 American Chemical Society
Published on Web 06/04/2004

O(1D) from N(2D) + O2 f NO(2Π,v,J) + O(3P,1D)
J. Phys. Chem. A, Vol. 108, No. 26, 2004 5589
Figure 1. Schematic diagram of the Cold Chemical Infrared Simulation Experiment (COCHISE). Facility shown with added fiber optics for
visible spectroscopy.
via a simple two-lens system. One lens is matched to the
numerical aperture of the fiber bundle, and one is matched to
the numerical aperture of the monochromator, 0.064. The lenses
magnify the 100-µm-wide fiber bundle by 2.5 to produce an
image of the bundle 2.5 cm by 250 µm on the entrance slit of
the monochromator. This matches well to the entrance slit
dimensions of 2.5 cm × 250 µm, which provides a spectral
resolution of 0.4 nm. The light exiting the monochromator is
collected by an additional lens and focused onto a Hamamatsu
model R943-2 photomultiplier tube encased in a Products-for-
Research model TE182TSRF housing cooled to -23 °C. The
signal is then amplified by an SRS model SR445 fast pream-
plifier and connected to an SR430 multichannel averager. A
LabVIEW 5.1 program running under Windows NT 4.0 on a
Pentium-based personal computer (PC) collects the output of
the averager. At the same time, the IR emission is collected
through a cryogenic IR monochromator onto a Si:As detector.
The detector signal is fed into a cold preamplifier and onto an
SRS model SR530 lock-in amplifier. A LabVIEW program
running on a second PC collects the output of the lock-in
amplifier.
ments to measure the pressure in this region. These included
Granville Phillips model 275 mini-convectron gauges, an MKS
Instruments model 120AA-000 RAJ Baratron gauge, and a
Varian model 580 nude Bayard-Alpert type ionization gauge
tube. The convectron gauge is the least accurate and is used to
monitor the pressure in the inlet ports as well as major
fluctuations in the reaction cell pressure. The ionization gauge
is significantly more accurate but cannot be used during data
collection, because of its bright visible emission during opera-
tion. Thus, the Baratron monitored the pressure during data
collection and direct comparisons were made to the nude
ionization gauge before and after each run. The disparity
between the readings of these gauges was never greater than
30% for experiments contributing to these results.
The study was comprised of three parts. First, the visible
optical path and detection systemsboth via fiber and direct
detectionswere calibrated. Second, the sensitivity with which
O(1D) and O2(b1Σ) can be detected in COCHISE was deter-
mined. And, finally, the visible signal from O(1D) and O2(b1Σ)
from the reaction of N(2D) with O2 in the COCHISE reaction
chamber was measured.
To gain additional sensitivity to the visible chemilumines-
cence of O(1D) and O2(b1Σ), a series of experiments were
performed by providing a window and lens directly into the
reaction chamber (Figure 2). Although this precludes the use
of IR spectroscopy during these runs, the IR chemiluminescence
has been well-characterized from many previous experiments
under the same conditions.
Sensitivity analysis of the COCHISE kinetic modeling
(Section V) demonstrates that the concentration of O(1D) and
O2(b1Σ) in the center of the reaction chamber is highly sensitive
to the total pressure there. Therefore, we used several instru-
The calibration of the optical systems was performed before
and after each experimental run. An Optronics Laboratory model
220IR standard spectral NIST traceable reference lamp and
power supply were used for all calibrations. To reduce the
intensity of the lamp sufficiently to fall within the dynamic range
of the photomultiplier tube, two reflective Melles Griot neutral
density filters with known calibration curves were used. Care
was taken to remove all scattering surfaces during calibration.
The geometry and gas flows of the COCHISE reaction cell, as
shown in Figure 1, create a stagnation zone such that all product
species are made within a 50-cm-long cylinder with a radius of

5590 J. Phys. Chem. A, Vol. 108, No. 26, 2004
Miller and Hunter
Figure 2. COCHISE adapted for the detection of direct visible emission from the reaction zone. Under these conditions, the 300 K blackbody light
leaking in through the coupling window prohibits the infrared detection of gas-phase products.
TABLE 1: COCHISE Optical Collection Efficiencies
The third experimental portion of this study involved the
measurement of the O(1D)/O2(b1Σ) concentrations produced by
reaction 2. The experimental conditions in the reaction zone
are similar to those used in previous measurements of the NO
vibrational distribution from this reaction:6,9 a 10% mole fraction
of nitrogen in an argon discharge opposed to a pure oxygen
counterflow. In the present study, only a 1% mole fraction of
nitrogen was used to limit O(1D) quenching by N2. A total of
700 µmol/s of argon was flowed through each of the four
discharges and a momentum balance of 560 µmoles of oxygen
was flowed through each of the counterflow inlets. It was found
previously6 that under these conditions, NO is produced from
this reaction at a concentration level of 3 × 109 cm-3 in the
field of view. Spectra were taken at both the 630 nm wavelength
region of O(1D) emission and at the 765 nm wavelength region
of O2(b1Σ) emission. This experiment was performed using both
fiber-optic collection conditions (Figure 1) and direct lens
collection conditions (Figure 2).
fiber-optic direct optical collection
collection
via 5 in. lens
a
solid angle efficiency, ꢀΩ
1.5 × 10-4
6.3 cm3
6.7 × 10-4
1.42 × 10-1
7.7 cm3
light collection efficiency, ꢀ0 1.9 × 10-3
b
collection volume, V
a ꢀΩ represents the efficiency as a result of the effective solid angle
of light collection. b ꢀ0 represents the efficiency of light collected by
the optical path.
9 cm. The solid angle and imaging of the optical system collects
light from a cone-shaped volume within the reaction zone
of 6.3 cm3 for the fiber-optic collection and 7.7 cm3 for the
direct collection configuration. All calibrations were performed
using the same optical path as the experimental observations.
Systematic errors in the calibration (e.g., alignment, aging of
the lamp filament, and photomultiplier tube temperature) are
estimated to be ∼30%. The calibrations gave the collection
efficiencies shown in Table 1, where ꢀΩ represents the solid
angle over which light is collected and ꢀ0 represents the
efficiency of the optical collection system from the first
collection lens to the output of the discriminator.
III. Experimental Results
1. O2(b1Σ) Detection Sensitivity. After thorough intensity
calibration of the collection optics, measurement of the O2(b1Σ)
detection sensitivity was performed as described in Section II.
The O(1D) made in the high-pressure (1 Torr) sidearm from a
discharge of an oxygen and argon mixture is rapidly quenched
by O2 to O2(b1Σ). O2(b1Σ,v > 0) is quenched further as it flows
to the center of the reaction cell. Here, emission from the
O2(b1Σ) is monitored. With a high mole fraction (33%) of
oxygen in an argon buffer, in the discharge, emission from the
O2(b1Σ) electronic state to the O2(X,3Σ) ground state can clearly
be observed in Figure 3.
Along with the O2(b1Σ) emission, this spectral band contains
line emission from Ar and O atoms. The NIST Atomic Spectra
Database10 was used to identify these atomic lines and these
line positions were, in turn, used to calibrate the experimental
data spectrally. Many metastable levels of argon are directly
The long fluorescence lifetime (148 s), low nascent densities,
and fast quenching by O2 in this set of experiments combine to
make it very difficult to observe O(1D) directly at 630.0 nm.
The fast and efficient8 quenching of O(1D) by O2 (4.0 × 10-11
cm2 molecule-1 s-1 at room temperature) to produce O2(b1Σ)
provides an excellent tracer of the O(1D), because O2 is a factor
of 100 more abundant than its next-fastest quencher, N2 (2.6 ×
10-11 cm2 molecule-1 s-1), in our experiments. We calibrated
the sensitivity of COCHISE to O2(b1Σ) by performing a separate
experiment, which consisted of an argon microwave discharge
with varying mole fractions of oxygen while counterflowing
pure argon. Although there are potentially several mechanisms
for the production of O2(b1Σ) from a discharge, the main one
follows from the dissociative recombination of ionized oxygen
molecules, which produces O(1D) that is subsequently quenched
by O2.

O(1D) from N(2D) + O2 f NO(2Π,v,J) + O(3P,1D)
J. Phys. Chem. A, Vol. 108, No. 26, 2004 5591
Figure 3. Emission in the COCHISE reaction chamber from products originating in a 33% O2/Ar discharge in the sidearm. The thin gray line is
the experimental data and the dark thick line represents a two-temperature (100 and 200 K) fit to the O2(b1Σ) emission. The fit contains a 70%
relative contribution from the O2(b1Σ) (0,0) band at 100 K, a 30% relative contribution from the O2(b1Σ,0,0) band at 200 K, a 12% relative contribution
from the O2(b1Σ,1,1) band at 100 K and a 5% relative contribution from the O2(b1Σ,1,1) band at 200 K. The Ar lines observed were used to
spectrally calibrate the emission. These data were taken using the fiber-optic optical path.
TABLE 2: COCHISE Detection Thresholds of [O(1D)] and
excited by the microwave discharge. As these atoms relax, the
[O2(b1Σ)] for Both Fiber-Optic and Direct Optic Collection,
resulting cascade, through the atomic levels, results in line
emission at various wavelengths from the ultraviolet (UV) region
through the IR region. The O atom lines are emission from the
35P state to the 35S of neutral oxygen. The microwave discharge
Assuming a Signal-to-Noise Ratio of 2
[O(1D)]
[O2(b1Σ)]
Ffiber
Fdirect
2.8 × 109 cm-3
1.9 × 108 cm-3
3.3 × 108 cm-3
2.2 × 107 cm-3
+
ionizes oxygen molecules to produce O2+. The O2 then
O2(b1Σ+g ,v ) 0) f O2(b3Σ-g ,v ) 0) emission is 6:1. Thus, this
signal is approximately a factor of 6 above the threshold of
detection.
The number density of the emitting molecules in the field of
view can be calculated using the efficiencies from Table 1 and
the integrated count rate as follows:
undergoes dissociative recombination to produce O atoms. Some
of these O atoms are excited to high-lying Rydberg states via
collisional energy exchange with metastable Ar atoms. These
long-lived Rydberg atoms are then transported to the reaction
5
cell, by which time they have relaxed to the triplet P state of
oxygen from which they promptly radiate at 777.5 nm. Note
that, although ions are precursors to the production of these O
atoms, the higher pressures (1-2 Torr) in the sidearms cause
recombination of the ions before they enter the reaction cell.
DIATOM,11 which is a diatomic modeling program that
handles non-allowed transitions well, was used to model the
O2(b1Σ) spectral data. The results of this modeling were fit to
the data. This is shown as the bold lines in Figures 3 and 4.
The fitting parameters were the intensity of each band
O2(b1Σ+g ,v ) 0) f O2(X3Σg-,v ) 0) and O2(b1Σ+g ,v ) 1) f
O2(X3Σ-g ,v ) 1) and the rotational temperature. The best fit to
the data shown in Figure 3 requires two rotational tempera-
tures: 100 and 200 K. The O2(b1Σ) state molecules are formed
in the discharge sidearm at a higher temperature and are cooled
during the supersonic expansion into the reaction cell (see Figure
A1 in the Appendix) and then begin an equilibration process in
the stagnation region. The two-temperature fit represents an
ensemble of molecules that have been thermalized together
with a component that has yet to be fully equilibrated. The
mole fraction of O2 in the discharge was then reduced to
3%, to determine the detection threshold for O2(b1Σ), and the
results are shown in Figure 4. The signal-to-noise ratio of the
Iτ
F )
(4)
∆λꢀ0ꢀΩV
where F is the number density of emitting molecules in the field
of view, I the integrated count rate, τ the fluorescence lifetime
of O2(b1Σ) (12 s), ∆λ the resolution of the monochromator (250
µm slits, 0.4 nm) used, and V the reaction zone volume sampled
by the collection optics from Table 1. For these conditions, the
detection thresholds are shown in Table 2.
Results from N(2D) + O2 Experiments. No O(1D) signal
was ever observed using either fiber-optic or direct optical
collection. This is not at all surprising, because of both the long
radiative lifetime of O(1D) and the relatively high detection
thresholds of Table 2. Upper limits on the production of O2(b1Σ)
in the reaction volume from reaction 1 can be determined using
the spectral scans of both the fiber-optic collection and the direct
lens collection optical paths (Figures 5 and 6). Clearly, there is
no detectable signal using the fiber-optic collection method,
Figure 5. There is no clear evidence for O2(b1Σ) emission in
the direct lens collection experiments either, although if one

5592 J. Phys. Chem. A, Vol. 108, No. 26, 2004
Miller and Hunter
Figure 4. Emission in the COCHISE reaction chamber from products originating in a 3% O2/Ar discharge in the sidearm. The thin gray line is the
experimental data and the dark thick line represents a fit to the O2(b1Σ) emission using DIATOM. These data were taken using the fiber-optic
optical path.
TABLE 3: Parameters for Chemical Dynamics Model Fit to
COCHISE Dataa
Fitting the model to the data produces an upper limit on
the branching fraction of reaction 2 to O(1D) of 0.02, which
is significantly below the previously reported value of 0.76.
To determine the potential error in this result, an analysis of
the sensitivity of the model to the major parameters was
performed.
parameter
value
pressure
temperature
4 mTorr
100 K
N(2D) + O2 reaction rate
O(1D) + O2 quenching rate
diffusion coefficients
4 × 10-12 cm3 molecule-1 s-1
2.5 × 10-11 cm3 molecule-1 s-1
see Table A2 in the Appendix
mole fraction of N(2D) in discharge 4 × 10-5
V. Sensitivity Analysis
branching fraction to O(1D) product floating variable
Because of the complexity of the fluid/kinetic model de-
scribed in the appendix, it is prudent to characterize which small
changes in parameters cause the greatest changes in [O2(b1Σ)]
and [O(1D)].
a Values reflect the COCHISE experimental conditions.
uses the differential signals of Figures 5 and 6 at 762.3 nm as
a possible indication of O2(b1Σ) emission, then an upper limit
on the O2(b1Σ) concentration can be calculated using eq 4. The
mean differential signals3000 counts/s at a signal-to-noise ratio
of 2sindicates a [O2(b1Σ)] of <5 × 107 cm-3 in the reaction
zone. The modeling results of the next two sections will
determine the best-fit upper limit branching ratio and its error.
The first test for the model’s accuracy in representing the
dynamics in the COCHISE reaction zone is to determine
whether it can reproduce the measured steady-state pressure (P)
under typical experimental conditions (T ) 100 K and M )
0.027 g Ar/s). The measured pressure (P ) 4 mTorr) is used to
define the reaction zone cylindrical radius (rRZ) via eq 5. After
the reaction zone geometry is established, a simplified master
equation is constructed that involves only the formation and
loss processes of the argon carrier gas, as described in the
appendix. The equation is solved numerically for the steady-
state argon density, which can then be compared to the
experimentally measured value.
IV. Fit to Chemical Dynamics Model
The chemical dynamics model, which is described in the
appendix, was run with all inputs fixed except for the branching
fraction of reaction 2. The most significant parameters are shown
in Table 3.
The pressure and temperature were those measured experi-
mentally. The rate coefficient used for N(2D) + O2 was a taken
from the experimentally determined temperature-dependent
coefficients of Slanger et al.12 evaluated at 100 K (4.0 × 10-12
cm3 molecule-1 s-1). The room-temperature rate coefficient for
the quenching of O(1D) by O2 is k ) 4.0 × 10-11 cm3
The result of this test indicates that our model slightly
underestimates the steady-state pressures in COCHISE experi-
ments (by ∼20%). The good agreement is notable, considering
that the test does not involve optimization of any adjustable
parameters. To correct for the slight density underestimation,
however, we decided to treat the carrier gas source term as an
adjustable parameter (see Appendix).
molecule-1 s-1 8
. The reaction has a very weak negative
temperature dependence, and its expected value at COCHISE
An important consideration is the concentration of N(2D) and
N(2P) made in the discharge and transported to the reaction cell.
Inputs to the model include a mole fraction of 3 × 10-5 of
N(2D) and a mole fraction of N(2P) that is a factor of 4 less
than this value,6 both consistent with the [NO] observed in the
operating temperatures lies in the range of k(100 K) ) 0.2 ×
10-10-1.8 × 10-10 cm3 molecule-1 s-1 13
reaction, to avoid overpredicting the [O2(b1Σ)] that is expected.
.
Our models use a
lower-end value of 2.5 × 10-11 cm3 molecule-1 s-1 for this

O(1D) from N(2D) + O2 f NO(2Π,v,J) + O(3P,1D)
J. Phys. Chem. A, Vol. 108, No. 26, 2004 5593
Figure 5. O2(b1Σ,v ) 0) spectral region using fiber-optic collection. The experimental data curve is the difference between an averaged co-added
set of monochromator scans with a pure O2 counterflow and a scan with a pure argon counterflow (no in situ production of O(1D)/O2(b1Σ) possible).
The calculated model spectrum of O2(b1Σ,v ) 0) is shown for spectral reference. The larger noise at wavelengths >762.5 nm is due to the differential
nature of the experimental curve (the difference of large numbers under the Ar line).
Figure 6. O2(b1Σ,0,0) band spectral region via direct optical collection by lens. The experimental data curve is the difference between a spectrum
taken with a pure O2 counterflow and a scan taken with a pure Ar counterflow (no in situ production of O(1D)/O2(b1Σ) possible). The calculated
model spectrum of O2(b1Σ,0,0) band is shown for spectral reference. The larger noise and negative signal at wavelengths >762.5 nm is due to the
differential nature of the experimental curve (the difference of large numbers under the Ar line).
reaction cell and literature values. Although there are no
published articles demonstrating the production of NO + O from
the reaction of N(2P) + O2, one can use the published quenching
rate of N(2P) by O2,14 1.8 × 10-12, together with the concentra-
tions used previously to determine that any production of O(1D)
by N(2P) + O2 will be at least an order of magnitude lower
than that produced by reaction 2.
The results of the kinetic model sensitivity testing show strong
changes to the O(1D) and O2(b1Σ) densities as a function of
pressure, temperature, mole fraction of N(2D), and the O2
quenching rate of O(1D). As can be seen in Figures 7 and 8,
both [O(1D)] and [O2(b1Σ)] are very sensitive to the pressure
in the center of the reaction cell. Within our measured operating
range of P ) 4 ( 0.2 mTorr in COCHISE experiments,

5594 J. Phys. Chem. A, Vol. 108, No. 26, 2004
Miller and Hunter
Figure 7. Pressure dependence of [O(1D)]. Conditions for this model
run were as follows: a reaction zone temperature of 100 K, an N(2D)
mole fraction of 4 × 10-5, and a quenching rate coefficient of 2.5 ×
10-11 cm3 molecule-1 s-1 for the quenching of O(1D) by O2.
Figure 9. Temperature dependence of [O(1D)]. Conditions for this
model run were as follows: a reaction zone pressure of 4 mTorr, an
N(2D) mole fraction of 4 × 10-5, and a quenching rate coefficient of
2.5 × 10-10 cm3 molecule-1 s-1 for the quenching of O(1D) by O2.
Figure 8. Pressure dependence of [O2(b1Σ)]. Conditions for this model
run were as follows: a reaction zone temperature of 100 K, an N(2D)
mole fraction of 4 × 10-5, and a quenching rate coefficient of 2.5 ×
10-11 cm3 molecule-1 s-1 for the quenching of O(1D) by O2.
Figure 10. Temperature dependence of [O2(b1Σ)]. Conditions for this
model run were as follows: a reaction zone pressure of 4 mTorr, an
N(2D) mole fraction of 4 × 10-5, and a quenching rate coefficient of
2.5 × 10-11 cm3 molecule-1 s-1 for the quenching of O(1D) by O2.
however, the corresponding uncertainties in [O(1D)] and [O2(b1Σ)]
are expected to be only 5% and 10%, respectively. Figures 9
and 10 shows that [O2(b1Σ)] decreases as a function of
temperature, whereas [O(1D)] is insensitive to temperature for
this range of temperature values. As the temperature increases,
O(1D) is quenched more slowly because [O2] is lower. At the
same time, the combined diffusion and convection rate increases
for O(1D). These offsetting effects result in an apparent
insensitivity to temperature in Figure 9. For the same conditions,
[O2(b1Σ)] decreases because of both lower [O2] and increased
diffusion and convection rates. Thus, Figure 10 displays a
decrease as a function of temperature. Experimentally, the lower
temperature limit is determined by the ability to flow N2 through
the gas lines. Heating the gas lines to a temperature of <100 K
allows solid plugs to develop at cold spots in the lines. The
temperature in the reaction zone is accurately monitored by
determining the best nonlinear least-squares fit to the NO(v,J)
infrared spectra. The measured temperature is typically T ) 100
( 5 °C, corresponding to an uncertainty in predicted [O(1D)]
and [O2(b1Σ)] of 2% and 10%, respectively. Although the
quenching rate of O(1D) quenched by O2 is well-established at
room temperature, it is likely to be larger at 100 K.13 The
sensitivity test shows the expected result of a reduced [O(1D)]
and an enhanced [O2(b1Σ)] (Figures 11 and 12). Because the
[O(1D)] is too low to be observed directly under any conditions
in COCHISE (see detection limits in Table 2), any increase in
quenching rate increases our ability to observe the [O2(b1Σ)].
This is limited, of course, by the depletion of the [O(1D)], which
appears as a saturation of the [O2(b1Σ)] in Figure 12.
The mole fraction of N(2D) from the discharge is linearly
related to the production of O(1D) and O2(b1Σ). Both [O(1D)]
and [O2(b1Σ)] vary by a factor of 4, because the mole fraction
N(2D) is varied over a factor of 4 in the discharge by varying
the mole fraction of N2 (Figures 13 and 14). Although these
figures could be interpreted to imply a large potential variance
in the concentrations of O(1D) and O2(b1Σ), experimentally, we
obtained an indirect measurement of [N(2D)] separately by
monitoring the corresponding [NO] produced from reaction 2.
Finally, Figures 15 and 16 show the sensitivity for the
production of [O(1D)] and [O2(b1Σ)] on the diffusion rates of
excited atomic species. As described in the Appendix, it is
possible that, at high [O2], the diffusion rates of excited atoms

O(1D) from N(2D) + O2 f NO(2Π,v,J) + O(3P,1D)
J. Phys. Chem. A, Vol. 108, No. 26, 2004 5595
Figure 13. [O(1D)] dependence on [N(2D)]. Conditions for this model
run were as follows: a reaction zone pressure of 4 mTorr, a temperature
of 100 K, and a quenching rate coefficient of 2.5 × 10-11 cm3
molecule-1 s-1 for the quenching of O(1D) by O2.
Figure 11. O2 quenching rate dependence of [O(1D)]. Conditions for
this model run were as follows: a reaction zone pressure of 4 mTorr,
a temperature of 100 K, and an N(2D) mole fraction of 4 × 10-5
.
Figure 14. [O2(b1Σ)] dependence on [N(2D)]. Conditions for this model
run were as follows: a reaction zone pressure of 4 mTorr, a temperature
of 100 K, and a quenching rate coefficient of 2.5 × 10-11 cm3
molecule-1 s-1 for the quenching of O(1D) by O2.
Figure 12. O2 quenching rate dependence of [O2(b1Σ)]. Conditions
for this model run were as follows: a reaction zone pressure of 4 mTorr,
a temperature of 100 K, and an N(2D) mole fraction of 4 × 10-5
.
may be reduced. These figures show that any reduced diffusion
rates increase the concentrations of O(1D) and O2(b), thus
making them more easily detected. In the unlikely event that
the diffusion rates for these excited atomic species were to be
larger than those used in our model, these figures show that it
requires an increase of more than a factor of 3 in diffusion rate
to half the [O2(b1Σ)].
Table 4 summarizes the sensitivity of the most important
parameters in the model. The first column contains the
uncertainty to which the parameters were either measured or
are known from the literature. The second column contains the
resulting uncertainty in the [O2(b1Σ)] from the corresponding
input from column 1. Clearly, the pressure, temperature, and
mole fraction of N(2D) in the discharge are the most sensitive
parameters. A conservative error estimate is made by running
the model with each parameter of Table 4 set at its extreme
uncertainty to produce either the least or the greatest [O2(b1Σ)]
and, therefore, the smallest and largest values of the branching
fraction of reaction 2. The error using this methodology is
(0.02. Although this method probably overstates the error by
assuming all variables are at their maximum error in either
direction, it is reasonable when considering the 30% error in
calibration and difficulty in determining precise systematic errors.
TABLE 4: Uncertainties in [O2(b1Σ)] as a Result of Sensitivity Studies Performed on the Listed Parameters in the Kinetic
Model
uncertainty in
parameter(%)
uncertainty
range of
parameter
range of parameter values
in [O2(b1Σ)] (%)
[O2(b1Σ)] values
pressure
(15
(10
(12
(100
(20
(25
3.4-4.6 mTorr
(37
(26
(6
3.0 × 107-6.5 × 107
6.1 × 107-3.6 × 107
4.4 × 107-5.0 × 107
3.9 × 107-5.0 × 107
4.33 × 107-5.19 × 107
3.5 × 107-5.9 × 107
temperature
90-110 K
N(2D)+ O2 reaction rate
3.5 × 10-12-4.5 × 10-12 cm3 molecule-1 s-1
O(1D) + O2 quenching rate
1.0 × 10-11-4.0 × 10-11 cm3 molecule-1 s-1
(13
(9
diffusion coefficient of exited atom
mole fraction of N(2D) in discharge
3.0 × 10-5-5.0 × 10-5
(25

5596 J. Phys. Chem. A, Vol. 108, No. 26, 2004
Miller and Hunter
Office of Scientific Research for funding this research, under
Task No. 2303ES/92VS04COR.
Appendix. Kinetic/Fluid Dynamical Model Used in
COCHISE
A kinetic model was developed to simulate the rate of
chemical reactions observed in the COCHISE reactor/spectrom-
eter. The model incorporates a fluid dynamical analysis of the
gas flow in the reaction chamber, which predicts the pressure
(P) and temperature (T) of the gas on the tank centerline, based
on the mass flow per inlet tube (M) and inlet tube pressure (Pi)
and temperature (Ti).17
A schematic diagram of the flow field during COCHISE
experiments is shown in Figure A1. The gas stream from each
inlet tube undergoes a supersonic expansion upon entering the
reaction chamber (region 1). The collision of opposing jets
creates an axisymmetric stagnation zone around the tank
centerline (region 2), from which the gas is then cryogenically
pumped onto the chamber walls (region 3). In passing from
region 1 to region 2, the gas flowing along a jet centerline
traverses a plane normal shock wave (Mach disk). Therefore,
the gas flow in the stagnation zone is subsonic and it may be
treated as incompressible. Under these conditions, the pressure
(P) at the axisymmetric stagnation point, on the tank centerline,
is given by18
Figure 15. [O(1D)] dependence on diffusion rates. Diffusion rates from
this figure were changed fractionally from the following values: O(1D),
442 s-1; N(2D), 570 s-1; and N(2P), 487 s-1. Other conditions included
a pressure of 4 mTorr, a temperature of 100 K, an N(2D) mole fraction
of 4 × 10-5, and a quench rate for O(1D) by O2 of 2.5 × 10-11 cm3
molecule-1 s-1
.
(γ + 1)πMVt
P )
(A-1)
8(γ - 1)θ∞ (r - rM)2
2
where γ is the specific heat capacity ratio of the gas, r the tank
cylinder radius, rM the distance of the Mach disk from tank
centerline, θ∞ the Prandtl-Meyer maximum turning angle for
the expansion of an isentropic gas into a vacuum, and Vt the
terminal velocity of the supersonic jet in region 1, given by
x
2γRTi
Vt )
(A-2)
(γ - 1)m
where m is the molecular weight of the gas and R is the gas
constant. Because the gas flow in the inlet tubes is maintained
in a laminar flow regime (Reynolds number of Re < 2300),
one may neglect the effect of viscous heating in the inlet tubes
and assume that the gas temperature in the stagnation zone
(region 2) is equivalent to the temperature of the gas entering
the inlet tubes (Ti):
Figure 16. [O2(b1Σ)] dependence on diffusion rates. Diffusion rates
from this figure were changed fractionally from the following values:
O(1D), 442 s-1; N(2D), 570 s-1; and N(2P), 487 s-1. Other conditions
included a pressure of 4 mTorr, a temperature of 100 K, an N(2D)
mole fraction of 4 × 10-5, and a quench rate for O(1D) by O2 of 2.5
× 10-11 cm3 molecule-1 s-1
.
VI. Conclusion
T ) Ti
(A-3)
This work places an upper limit of 0.02 ( 0.02 on the
branching fraction for the production of O(1D) from the reaction
of N(2D) with O2. This value is in good agreement with both
the field analysis of Link4 and the theoretical calculations of
both Gonza´lez15and Braunstein.16 The original interpretation6
that a break in the vibrational distribution of the NO product at
v ) 8 inferred a channel to the production of O(1D) is not
feasible, considering the results of this paper. An alternative
explanation for the vibrational distribution will be explained in
a forthcoming paper on the rotational and vibrational quenching
of the NO product by O2.
Under typical COCHISE operating conditions (P g 4 mTorr),
the Mach disk location on the jet centerline is rM g 9 cm. This
is considerably greater than the radius of the cylindrical field
of view sampled by the infrared monochromator (rIR ) 1.75
cm). Therefore, the IR chemiluminescence measured in our
COCHISE experiments samples a region of bulk, thermalized
gas (region 2) whose temperature and pressure (T and P) are
given by eqs A-1 and A-3.
The variation in P along the tank centerline is insignificant
(∼1% deviation from the value of P along the jet centerlines).7
Therefore, in developing our kinetic/fluid dynamical model for
chemical reactions in COCHISE, we define a cylindrical reaction
zone whose radius rRZ is equivalent to rM, and whose total
volume VRZ is given by
Acknowledgment. The authors would like to acknowledge
the essential support of Vincent Kennedy and John Cappelli in
operating and maintaining the COCHISE facility during these
experiments and Ramesh Sharma for valuable theoretical
consultations. We would also like to thank the U.S. Air Force
2
VRZ ) 4πdrRZ
(A-4)

O(1D) from N(2D) + O2 f NO(2Π,v,J) + O(3P,1D)
J. Phys. Chem. A, Vol. 108, No. 26, 2004 5597
Figure A1. Schematic diagram of the COCHISE flow field.
TABLE A1: Estimated Mole Fractions of N-Atom Species in
the Exit Plane of the Gas Inlet Tubes for 1% N2/Ar
Dischargesa
where d is the distance between two adjacent gas inlet tubes. It
is possible to calculate rRZ from first principles; however, this
requires exact knowledge of the cryopumping conditions in the
chamber and characterization of the fluid dynamical constraints
in region 3. A model to predict the sticking coefficient of gases
onto cryogenically cooled surfaces has been developed by
Dawson.18 However, this model applies to the cryopumping of
a stationary Maxwellian gas, a condition which is not satisfied
in COCHISE experiments.7 In the present model, therefore, rRZ
is determined empirically from the reaction zone pressure (PRZ),
which is measured 5 cm vertically above the tank centerline, in
the central region of the tank (region 2). The parameter rRZ is
then calculated by rearranging eq A-2 and setting P ) PRZ and
rM ) rRZ. After a reaction zone is defined via eq A-4, our
kinetic/fluid dynamical model calculates the temporal evolution
of a given gas species j within the reaction zone, according to
the master equation:
species
mole fraction at inlet tube exit
N(4S)
N(2D)
N(2P)
2.1 × 10-3
1 × 10-5-4 × 10-5
2 × 10-6-5 × 10-6
a From ref 11.
The flux of carrier gas from the COCHISE inlet jets into the
reaction zone can be calculated by evaluating the surface integral
of the flux distributions (eqs A-6 and A-7) over the bounding
surface of the reaction zone defined previously (eqs 1-4). It
may then be shown that, under typical COCHISE operating
conditions (T ) 100 K, P ) 4 mTorr), 57% of the argon carrier
gas from the inlet jets enters directly into the reaction zone.
This corresponds to an argon carrier gas source term in the
reaction zone of kf(Ar) ) 3.2 mTorr/ms.The source terms for
all other species in the COCHISE reaction zone are evaluated
according to their expected mole fraction upon exiting the gas
inlet tubes. The values used for N atoms (ground state and
electronically excited) are based on direct observations of
discharge effluents in a flow reactor at the same flow rate and
discharge pressure conditions as these COCHISE experiments,
but at room temperature (Table A1).2,20
∂[j]
) k (j) - k (j)[j] - k [j] + k [R ][â ] -
∑
f
d
c
m
m
m
∂t
m
k [R ][j] - k [j] (A-5)
∑
∑
n
n
o
n
o
where [j] is the concentration of species j in the reaction zone;
kf(j) is the zeroth-order rate of formation of species j within the
reaction zone, corresponding to a constant input from the inlet
tubes into the reaction zone; kd(j) and kc are the diffusive and
convective loss coefficients, respectively, for species j out of
the reaction zone; km and kn correspond to second-order chemical
formation and destruction processes, respectively, for species j
in the reaction zone; and ko correspond to first-order loss
processes of species j in the reaction zone, other than diffusion
and convection (e.g., radiative quenching). The master equation
is solved numerically using the Acuchem algorithm.19 A detailed
description of the individual terms contributing to this master
equation is presented below.
(B) Diffusive Losses. The diffusive loss rate constants, kd(j),
are calculated by assuming irreversible loss of diffusing species
upon reaching the bounding surface of the reaction zone (i.e.,
no “re-crossing” of species back into the reaction zone after
they exit it). In this case, kd(j) is given by21
2
π
4d
5.81
kd(j) ) DjR
+
(A-8)
(
)
2
[
]
rRZ
where DjR is the binary diffusion coefficient for species j in a
bath of gas R, diffusing irreversibly out from a cylindrical
volume of length 4d and a cross-sectional area of πrR2 Z
.
Because of the lack of experimental characterizations of
diffusion parameters for chemical species and conditions
relevant to COCHISE experiments, our kinetic model relied on
calculation of most of these parameters from first principles
and/or extrapolation of values measured at room temperature
to the cryogenic conditions present in the COCHISE reactor.
For the simple case of hard-sphere collisions, the binary
diffusion coefficient, DjR, may be calculated from the rigorous
kinetic theory of gases, as14
(A) Rate of Direct Gas Input into the Reaction Zone. The
density of carrier gas in a jet’s free expansion region is given
approximately by7
Af(θ)M
Vtr2i
F )
(A-6)
where ri is the spherical radius from the exit plane of the inlet
tube; A is a normalization factor; M ) 0.027 g/s, which
corresponds to 1 slpm of argon flow per inlet tube; and f(θ) is
the polar angular dependence of the jet density, given by7
3
2RT
DjR )
(A-9)
2
πµ
(
)
x
16FdjR
jR
2/(γ-1)
πθ
2θ∞
where F is the number density of the bath gas, µjR is the reduced
mass of species j and R, and djR is the average atomic or
f(θ) ) cos
(A-7)
(
)
[
]

5598 J. Phys. Chem. A, Vol. 108, No. 26, 2004
Miller and Hunter
TABLE A2: Diffusion Coefficients at T ) 100 K in an Argon Bath Gas
diffusing
species
diffusion coefficient at
T ) 100 K (cm2 mTorr s-1
)
reference
Ar
17 500
19 200
44 200
Hirschfelder et al.16 (Table 1.2-2)
O2, O2(b1Σ)
our estimate, based on Lennard-Jones interaction parameters from Maitland et al.17
our estimate, based on N(2D) value scaled by relative diffusion coefficients of
N(4S) and N(2D) in N2 bath gas11
N(4S)
N(2D)
36 000
30 700
27 900
27 900 (upper limit)
21 200
Lin and Kaufman26
N(2P)
Ianuzzi and Kaufman27
O(3P)
Morgan and Schiff28
O(1D)
no experimental data available; value arbitrarily set equal to the O(3P) diffusion coefficient
Our estimate, based on Ar diffusion coefficient scaled by NO/Ar reduced mass and collision
cross section21
NO(Π,v,J)
molecular diameter of the colliding species j and R. Equation
A-9 may also be used to calculate self-diffusion coefficients
(DR) by simply substituting the molecular weight (mR) and
diameter (dR) for µjR and djR, respectively.
The chemical species of interest in our COCHISE experiments
are Ar, O2, O2(b1Σ), N(4S), N(2D), N(2P), NO(Ω,v,J), O(3P),
and O(1D). Table A2 lists the diffusion coefficients of these
species under COCHISE reaction conditions, based on an
extrapolation of measured room-temperature values via a T11/6
dependence (with the exception of Ar, for which DAr(100 K)
has been experimentally determined).
However, a more sophisticated approach is required to
calculate diffusion coefficients at cryogenic temperatures,
because of the significant role played by intermolecular attractive
forces under those conditions. Numerous theories have been
developed to account for this effect.22,23 A common method,
known as the Chapman-Enskog formalism, enables precise
calculation of transport properties of gases, provided that the
intermolecular pair potential between the colliding atoms or
molecules is known. If a Lennard-Jones 6-12 interaction
potential is assumed, the binary diffusion coefficient for species
j diffusing through a bath gas R is given by14
The Lennard-Jones collision diameters of Ar and O2 are
almost identical (σAr ) 3.35 Å; σO ) 3.38 Å). However, the
2
attractive potential well depth is slightly larger for Ar/Ar
interactions (ꢀAr,Ar ) 12.15 meV) than for O2/Ar and O2/O2
collisions (ꢀO ,Ar ) 11.5 meV and ꢀO ,O ) 10.8 meV).5
2
2
2
According to the Chapman-Enskog formalism, this should
result in a 10% higher diffusion coefficient for O2/Ar than for
Ar/Ar at T ) 100 K (see Table A2). This is consistent with the
experimentally determined value of the self-diffusion coefficient
of O2 at T ) 100 K, which is 15% larger than DAr(100 K).13,24,25
The diffusion coefficients listed in Table A2 correspond to
the case of a pure argon bath gas at T ) 100 K. In the present
COCHISE experiments, the O2:Ar mixing ratio in the reaction
zone is close to 1:1. Because of the similarity in interaction
potentials between Ar and O2 species, this change in bath gas
composition does not significantly affect the diffusion of inert
species through this medium (e.g., the diffusion coefficients of
O2 and Ar themselves will change by <5%).13 However, atomic
species that interact strongly with O2 (e.g., electronically excited
N and O atoms) may have substantially lower diffusion rates
under high O2 mole fraction conditions. It is beyond the scope
of this paper to estimate these effects accurately. A sensitivity
analysis is therefore presented, to ascertain the range of
variability introduced into our kinetic model by the added
uncertainty in diffusion parameters under high O2 mole fraction
conditions.
The diffusion properties of metastable N atoms in Ar at T )
300 K are fairly well-established experimentally.8,15,16 However,
to our knowledge, no such information is available for meta-
stable O atoms. Therefore, our kinetic model utilizes the
experimentally determined diffusion coefficient of ground-state
O atoms as an upper limit for the diffusion coefficients of O(1D).
The actual values are expected to be 10%-30% lower than this;6
we explore the effect of this uncertainty in the sensitivity
analysis section below.
3
1
2RT
DjR )
(A-10)
2
/
πµ
(
)(
)
x
16FσjR ΩjR
jR
where σjR is the Lennard-Jones collision diameter. Ω/ , which
jR
is the reduced collision integral, incorporates the effect of
intermolecular forces and is dependent on temperature and on
the Lennard-Jones interaction energy, or well depth (ꢀjR),
between species j and R. At T ) 300 K, Ω/jR is normally very
close to unity (within 5%) and eq A-10 reduces to the simple
hard-sphere collision expression given in eq A-9.13 However,
at cryogenic temperatures, Ω/jR > 1 and the diffusion coef-
ficient DjR becomes significantly smaller than that predicted by
the hard-sphere model. For nonpolar gases interacting via an
attractive U(r) ) -C6/r6 potential (Lennard-Jones 6-12), DjR
can be shown to exhibit a T11/6 temperature dependence (as
opposed to the slower T3/2 dependence predicted by eq A-8).14
In this particular case, diffusion coefficients calculated using
eq A-10 for typical COCHISE reaction zone conditions (T )
100 K) would be 30% lower than that predicted via a simple
hard-sphere model (eq A-9).
The self-diffusivity of argon at cryogenic temperatures has
been determined empirically and, thus, serves to illustrate the
validity of the Chapman-Enskog formalism described previ-
ously. At T ) 100 K, the experimentally measured value of
DAr ) 17 500 mTorr cm2 s-1 13
This agrees well with an
.
extrapolation of the experimentally determined DAr(300 K) via
a T11/6 dependence, which yields DAr(100 K) ) 18 900 mTorr
cm2 s-1. Thus, the self-diffusivity of argon at cryogenic
temperatures is well-described (within an accuracy of 10%) by
the Chapman-Enskog model for nonpolar gases interacting via
a Lennard-Jones 6-12 potential. By contrast, a hard-sphere
collision model calculation based on dAr ) σAr ) 3.35 Å (ref
5) predicts DAr(100 K) ) 28 300 mTorr cm2 s-1. This large
discrepancy illustrates the tendency for significant reduction in
diffusion coefficients at low temperatures due to the intermo-
lecular force effect.
On the basis of these parameters, the argon carrier gas
diffusion rate coefficient under typical COCHISE operating
conditions (T ) 100 K, P ) 4 mTorr) can be shown to be kd(Ar)
) 340 s-1. This value corresponds to a diffusion half-life of
τd(Ar) ) 2.0 ms out of the reaction zone.
(C) Convective Losses. The rate of convective loss of gases
from the COCHISE reaction zone is calculated by considering
the conservation of linear momentum of the jet gas plumes along
a plane perpendicular to the jet directions. The mass flow rates
in opposing jets in COCHISE experiments are set to achieve

O(1D) from N(2D) + O2 f NO(2Π,v,J) + O(3P,1D)
J. Phys. Chem. A, Vol. 108, No. 26, 2004 5599
momentum balance along the jet centerlines. However, any
momentum component perpendicular to a jet centerline will be
imparted onto the thermalized reaction zone, thereby displacing
it vertically toward the top (and bottom) walls of the COCHISE
reaction chamber. It may then be shown, by a simple Newtonian
balance of forces argument, that the convective loss coefficient
(kc) for all species in the reaction zone is given by
10-11 cm3 molecule-1 s-1 for this reaction, to avoid overpre-
dicting the expected [O2(b1Σ)] value.
References and Notes
(1) Sharp, W. E.; Rees, M. H.; Stewart, A. I. J. Geophys. Res. 1979,
84 (A5), 1977.
(2) Rusch, D. W.; Gerard, J.-C.; Sharp, W. E. Geophys. Res. Lett. 1978,
5, 1043.
(3) Torr, D. G.; Richards, P. G.; Torr, M. R. Geophys. Res. Lett. 1980,
7 (5), 410-412.
Vi
kc )
(A-11)
(4) Link, R.; Swaminathan, P. K. Planet. Space Sci. 1992, 40, 699-
r2
705.
x
RZ
(5) Kennealy, J. P.; DelGreco, F. P.; Caledonia, G. E.; Green, B. D. J.
Chem. Phys. 1979, 69, 1574.
(6) Rawlins, W. T.; Fraser, M. E.; Miller, S. M. J. Phys. Chem. 1989,
93, 1097-1107.
(7) Rawlins, W. T.; Murphy, H. C.; Caledonia, G. E.; Kennealy, J. P.;
Robert, F. X.; Corman, A.; Armstrong, R. A. Appl. Opt. 1984, 23, 3316-
3324.
(8) Lee, L. C.; Slanger, T. G. J. Chem. Phys. 1978, 69, 4053-4060.
(9) Rawlins, W. T.; Fraser, M. E.; Miller, S. M.; Blumberg, W. A. M.
J. Chem. Phys. 1992, 96, 7555.
(10) NIST Atomic Spectra Database, http://ww.physics.nist.gov/cgi-bin/
Atdaa/main-asd.
where Vi is the component of gas jet velocity perpendicular
to the jet centerline, averaged over all polar angles -θmax < θ
< θmax for which the expanding gas jet traverses the COCHISE
reaction zone defined previously (eq A-3). θmax is defined as
rRZ
tan θmax
)
(A-12)
z0
(11) Huestis, D. L. Radiative Transition Probabilities. In Atomic,
Molecular, and Optical Physics Handbook; Drake, G. W. F., Ed.; AIP
Press: Woodbury, NY, 1996.
(12) Slanger, T. G.; Wood, B. J.; Black, G. J. Geophys. Res. 1971, 76
(34), 8430-8433.
(13) DeMore, W. B.; Sander, S. P.; Howard, C. J.; Ravishankara, A.
R.; Golden, D. M.; Kolb, C. E.; Hampson, R. F.; Kurylo, M. J.; Molina,
M. J. Chemical Kinetics and Photochemical Data for Use in Stratospheric
Modeling, Evaluation Number 12. JPL Publ. 1997, 97-4.
(14) Phillips, C. M.; Steinfeld, J. I.; Miller, S. M. J. Phys. Chem. 1987,
91, 5001.
where z0 ) 20.5 cm is the distance between the inlet tube gas
source and the COCHISE reaction cell centerline. The parameter
Vi may be calculated from the angular dependence of the gas
flow in an isentropic, supersonic expansion of a gas into
vacuum; it is given by the relation
Vi ) (1 - cos θmax)Vt
(A-13)
(15) Gonza´lez, M.; Miquel, I.; Sanyos, R. Chem. Phys. Lett. 2001, 335,
339-247.
The convective loss coefficient, kc, is independent of the
chemical identity of species j in the reaction zone. At T ) 100
(16) Braunstein, M.; Duff, J. W. J. Chem. Phys. 2000, 113 (17), 7406-
7413.
K and P ) 4 mTorr, it may be shown that kc ) 175 s-1
rendering a convective loss half-life of τc ) 4.0 ms.
,
(17) Caledonia, G. E.; Green, B. D.; Simmons, G. A.; Kennealy, J. P.;
Robert, F. X. Corman, A.; Delgreco, F. P. AFGL-TR-77-0281, 1977,
Environmental Research Papers, No. 619.
(18) Dawson, J. P. J. Spacecr. Rockets 1966, 3, 218.
(19) Braun, W.; Herron, J. T.; Kahaner, D. K. Int. J. Chem. Kinet. 1988,
20, 51.
(20) Rawlins, W. T.; Piper, L. G.; Fraser, M. E.; Murphy, H. C.; Tucker,
T. R.; Gelb, A. USAF Report No. PSI-9032/TR-901, 1989.
(21) Cunningham, R. E.; Williams, R. J. J. Diffusion in Gases and
Porous Media; Plenum Press: New York, 1980.
(22) Hirschfelder, J. O.; Curtiss, C. F.; Byrd, R. B. Molecular Theory
of Gases and Liquids, 3rd ed.; Wiley: New York, 1966.
(23) Maitland, G. C.; Rigby, M.; Smith, E. B.; Wakeham, W. A.
Intermolecular Forces: Their Origin and Determination, 2nd ed.; Oxford
University Press: Cambridge, U.K., 1987.
(D) Quenching Rates (Radiative and Collisional). The
radiative lifetimes of O(1D) metastables are well-established.
O(1D) may decay via 630-nm emission with a radiative lifetime
of 148 s.29
For collisional quenching of atomic metastable species to be
of significant magnitude, a resonant or complex-forming mech-
anism is required. Collisions with the Ar bath gas (k < 5 ×
10-13 cm3 molecule-1 s-1 30
) can therefore be ignored, because
the interaction of this inert gas with atomic metastables is purely
physical. Collisions of O(1D) with O2, on the other hand, proceed
via an excited O3 intermediate and are thus highly efficient
channels for electronic quenching of these electronically excited
species. The room-temperature rate coefficient for the quenching
of O(1D) by O2 is k ) 4.0 × 10-11 cm3 molecule-1 s-1. The
reaction has a very weak negative temperature dependence, and
its expected value at COCHISE operating temperatures lies in
the range of k(100 K) ) 0.2 × 10-10-1.8 × 10-10 cm3
(24) Winn, E. B. Phys. ReV. 1950, 80, 1024.
(25) Winter, E. R. S. Trans. Faraday Soc. 1951, 47, 342.
(26) Lin, C.-L.; Kaufman, F. J. Chem. Phys. 1971, 55 (8), 3760.
(27) Ianuzzi, M. P.; Kaufman, F. J. Chem. Phys. 1980, 73 (9),
4701.
(28) Morgan, J. E.; Schiff, H. I. Can. J. Chem. 1964, 42, 2300.
(29) Wiese, W. L.; Smith, M.; Glennon, B. M. Atomic Transition
Probabilities, Vol. I; National Standard Reference Data System Report
NRRDS-NBS-4, 1966.
molecule-1 s-1 13
.
Our models use a lower-end value of 2.5 ×
(30) Shi, J.; Barker, J. R. Int. J. Chem. Kinet. 1990, 22, 1283.