Chemical kinetics of the NaO (A2∑+) + O(3P) reaction

Article abstract of DOI:10.1021/jp002641m

Recent evidence has shown that the mesospheric sodium nightglow, a chemiluminescent process which produces atomic sodium D-line radiation in the Earth's upper atmosphere, proceeds through the first excited (A ²∑⁺) electronic state of NaO. The rate of D-line radiation production is proportional to the rate constant for the reaction of NaO(A ²∑⁺) + O(³P) and its branching ratio to produce excited Na(²P) rather than ground-state Na(²S). The only previously published measurement of the NaO + O(³P) reaction rate and branching ratio was performed under slow flow conditions and almost certainly primarily represents the reaction of groundstate NaO (X ²∏). We present low-pressure measurements of the NaO + O reaction kinetics using an NaO source reaction known to produce NaO in the (A ²∑⁺) state and determine the 290 K reaction rate constant to be (5.1 ± 1.8) × 10^-10 cm³ s^-1 and the branching ratio to produce Na(²P) to be 0.14 0.04. New data on the termolecular rate coefficient for the reaction Na + O₂ + He → NaO₂ + He at 290 K are also presented.

Full text of DOI:10.1021/jp002641m

J. Phys. Chem. A 2001, 105, 1643-1648
1643
2
Chemical Kinetics of the NaO (A Σ+) + O(3P) Reaction†
J. Griffin,‡ D. R. Worsnop,*,§ R. C. Brown,§ C. E. Kolb,*,§ and D. R. Herschbach*,‡
Department of Chemistry and Chemical Biology, HarVard UniVersity, Cambridge, Massachusetts 02138, and
Center for Cloud and Aerosol Chemistry, Aerodyne Research, Inc., Billerica, Massachusetts 01821-3976
ReceiVed: July 25, 2000; In Final Form: October 17, 2000
Recent evidence has shown that the mesospheric sodium nightglow, a chemiluminescent process which produces
2
atomic sodium D-line radiation in the Earth’s upper atmosphere, proceeds through the first excited (A Σ+)
electronic state of NaO. The rate of D-line radiation production is proportional to the rate constant for the
2
reaction of NaO(A Σ+) + O(3P) and its branching ratio to produce excited Na(2P) rather than ground-state
Na(2S). The only previously published measurement of the NaO + O(3P) reaction rate and branching ratio
was performed under slow flow conditions and almost certainly primarily represents the reaction of ground-
2
state NaO (X Π). We present low-pressure measurements of the NaO + O reaction kinetics using an NaO
2
source reaction known to produce NaO in the (A Σ+) state and determine the 290 K reaction rate constant
to be (5.1 ( 1.8) × 10-10 cm3 s-1 and the branching ratio to produce Na(2P) to be 0.14 ( 0.04. New data on
the termolecular rate coefficient for the reaction Na + O2 + He f NaO2 + He at 290 K are also presented.
Introduction
able to reproduce the approximate magnitude of both the normal
sodium nightglow and long-lived “meteor trails”.1,6,7 Laboratory
experiments eventually confirmed the magnitude of rate con-
stants predicted by Kolb and Elgin for both reaction 18,9 and
reaction 2.9,10
Atomic sodium ablated from meteorites entering the Earth’s
atmosphere forms the mesospheric sodium layer. This layer
typically extends from ∼80 to 100-110 km in altitude and peaks
at concentrations of several thousand Na cm-3 near 90 km.1 At
night the layer can be observed to emit visible Na D-line
radiation known as the sodium nightglow.1,2 The accepted
explanation for chemiluminescent production of the mesospheric
sodium nightglow (reactions 1-3) was first published by Sydney
Chapman in 1939:3
In 1980, on the basis of what was known about mesospheric
levels of O3 and typical sodium nightglow emission rates, Bates
and Ojha7 estimated that the product of the rate constant, k1,
for reaction 1 (which is rate controlling in the Chapman
mechanism since upper mesospheric [O] .[O3]), and the
branching ratio, f2, for reaction 2 to produce electronically
excited Na(2P) would need to be k1f2 > 1 × 10-10 cm3 s-1
.
Na + O3 f NaO + O2
NaO + O f Na(2P) + O2
f Na (2S) + O2
(1)
(2a)
(2b)
(3)
Bates and Ojha7 also presented a symmetry correlation analysis
of reaction 2 for ground-state NaO(X 2Π) reacting with O(3P),
which they claimed supported an f2 as large as 0.33. In 1986,
Swider11 used somewhat updated atmospheric and kinetic data
to determine that k1f2 > 2.1 × 10-10 cm3 s-1 was required. Using
our measured k1 of (6.9 (1.5) × 10-10 cm3 s-1 at 216 K,8
Swider’s analysis requires an f2 > 0.3. More recent analyses
based on atmospheric kinetic models plus measured Na layer
intensities and Na D-line emissions by Plane and co-workers
suggest that an f2 ∼ 0.1 is sufficient.12,13
Na(2P) f Na(2S) + hν
The Chapman mechanism allows the potential chemical
energy produced by solar induced photodissociation of upper
atmospheric molecular oxygen, which is stored in the form of
upper atmospheric O and O3, to drive the chemiluminescent
production of Na D-line radiation. Chapman later suggested that
this mechanism could also account for the long-lived visible
glow produced by the atmospheric entry of some larger
meteors.4 However, quantitative atmospheric models of this
latter phenomenon failed to reproduce the magnitude of the
radiation observed from large “meteor trails”5 until Kolb and
Elgin6 pointed out that reactions 1 and 2 could be expected to
proceed by electron jump mechanisms and would have rate
constants near the gas kinetic limit, even at the very low
temperatures (∼200 K) of the upper mesosphere. Using rate
constants estimated by Kolb and Elgin, atmospheric models were
Unfortunately, the only laboratory measurement of f2, deter-
mined by Plane and Husain10 in a relatively high pressure, slow
flow heat pipe experiment, indicated that f2 e 0.01. Since Plane
and Husain used a slow flow reactor, with estimated NaO
residence times before reaction of order 1 s, it is certain that
they were predominantly studying NaO in its ground X 2Π state.
While the interpretation of this experiment has been criticized
by Schofield,14,15 it is very unlikely that its estimate of f2 is in
error by an order of magnitude. However, in 1993 we reported
a crossed molecular beam study of reaction 1 that showed its
NaO product was produced predominantly, and quite possibly
exclusively, in the low-lying A 2Σ+ state.16 This conclusion was
reinforced by photoelectron studies of the product of reaction
1 by Wright et al.17 A symmetry correlation analysis of the
NaO(A 2Σ+) + O(3P) reaction indicated that f2 for this reaction
along energetically assessable doublet surfaces could be as large
† Part of the special issue “Harold Johnston Festschrift”.
* Corresponding authors: worsnop@aerodyne.com, kolb@aerodyne.com,
fax: 978-663-4918; hbach@chemistry.harvard.edu, fax: 617-495-4723.
‡ Harvard University.
§ Aerodyne Research, Inc.
10.1021/jp002641m CCC: $20.00 © 2001 American Chemical Society
Published on Web 12/21/2000

1644 J. Phys. Chem. A, Vol. 105, No. 9, 2001
Griffin et al.
with Na vapor pressures of 10-5 to 10-3 Torr, producing initial
[Na] in the flow reactor on the order of 1012 to 1013 cm-3. The
Na vapor was entrained in a small He flow and introduced into
the main (usually He) carrier gas flow. The main, 70 cm long,
reaction section of the flow reactor can be uniformly cooled to
215 K, but was operated at ∼290 K for the studies reported
here. Gas volumetric flows were monitored with a calibrated
thermal conductivity mass flow meter, and pressures were
determined with a MKS Baratron (Model 122A) capacitance
manometer. Total flow reactor pressure varied from 1.4 to 4.3
Torr for the results reported below.
Two 0.6 cm o.d. glass tubes served as movable injectors for
introducing O3 and atomic O flows into the reactor. A hexagonal
Teflon cap with holes through each of its six radial faces was
fitted to the atomic O injector to speed mixing with the main
flow. Commercial chemicals including 99.95% sodium metal
(Alfa), 99.995% gaseous He, 99% gaseous N2O, 99.993%
gaseous O2, and 99.999% gaseous Ar were used without further
purification. The method of O3 generation, introduction, and
quantification has been described previously.8,21 Atomic O was
generated in an Evenson cavity microwave discharge through
a He/O2 mixture. The discharge tube was fused into the inlet
of the second injector and the discharge cavity translated with
the injector along a guide rail parallel to the flow reactor. A
combination of two three-way solenoid valves created a
computer controlled four-way valve which allowed rapid
switching of carefully matched gas flows between the injectors
and the main flow reactor. This allowed the rapid on/off
switching of gaseous reactants on time scales that are short
compared with output drifts in atomic Na from the oven.
Figure 1. Schematic of the fast-flow reactor for Na/O3/O kinetics.
as 0.67,18 while any correlation to excited Na(2P) from the
2
NaO(X Π) ground state is through energetically forbidden
quartet states. Given this latter fact, the symmetry analysis
presented by Bates and Ojha for the ground-state reaction7 is
not actually in conflict with the low value of f2 measured for
the NaO ground-state reaction.10 Thus, our recent work,16,18
supported by work in other laboratories,10,17 strongly indicates
that Chapman’s simple mechanism expressed by reactions 1-3
must be amended so that it proceeds though the excited NaO(A
2Σ+) state:
k1
9
Na + O3
8 NaO(A 2Σ+) + O2
(1′)
(2′a)
(2′b)
(3)
k2′a
NaO(A 2Σ+) + O 8 Na(2P) + O2
The reaction section of the flow reactor projects into a 10
cm diameter six-way cross whose four sidearms perpendicular
to the flow reactor permit optical detection of reactant and
product species. Ground-state atomic Na(2S) was detected via
an Na hollow cathode lamp resonance fluorescence, while
excited-state Na(2P) was detected using the same photomultiplier
tube (PMT) detector by monitoring lamp-shuttered chemilumi-
nescent emission. A computer controlled spring-loaded solenoid
shutter masked the Na lamp during the chemiluminescence
measurements. Atomic oxygen was monitored via resonance
absorption with a PMT detector using the O (3S-3P) triplet at
130.22, 130.49, and 130.60 nm following the method of
Anderson.22 The atomic O discharge lamp was operated to
produce optically thin emissions. It consisted of a 1.2 cm He
filled (to ∼5 Torr) glass tube with a MgF2 window fused to
one end. The lamp was excited with ∼30 W from an Evenson
microwave discharge cavity. Powered metallic Ba in one
sidearm served as an internal getter for the lamp assembly, while
KMnO4 in a second sidearm served as an oxygen source. Atomic
O(3P) levels of (2-9) × 1012 were measured in the flow reactor,
dependent on discharge conditions, injector position, and sodium
oxide levels.
k2′b
8 Na(2S) + O2
k3
9
Na(2P)
8 Na(2S) + hν
Further, since our symmetry/reaction energy analysis18 sug-
2
gests that f2 ∼ 0 for the NaO(X Π) ground state, any loss of
the NaO(A 2Σ+) produced by reaction 1′ by either radiative or
collisional quenching before it can react with O will be
manifested by an apparent reduction in f2.
Until recently, the NaO(A 2Σ+) state had not been observed
experimentally but had been widely investigated theoretically.19
2
2
We recently observed over 150 lines of the A Σ+ r X π
infrared transition and determined that T0-0 ) 1992.905 cm-1
for this transition.20 In this paper we report on experiments to
investigate the room temperature kinetics of reaction 2 under
low-pressure conditions using reaction 1 as the source of NaO.
The goal of this work was to assess the overall rate constant,
k2′, and the branching ratio, f2′ ) k2′a/(k2′a + k2′b), for reaction
2 with NaO(A 2Σ+) as the predominant reactant under conditions
where radiative and/or collisional quenching losses of NaO(A
2Σ+) are minimized.
A DT2805 Data Translation board allowed personal computer
control of reactant line solenoid valves and the Na lamp shutter
and also collected data from the Baratron and the Na and O
phtomultiplier tube detectors. Typical experimental runs yielded
data from a range of predetermined conditions for each injector
position. Selected conditions included O discharge source flow,
O3 flow, main carrier flow, and Na lamp shutter position.
Solenoid mechanical lags and flow times to clear injectors set
minimum times required to reach steady-state conditions and
allow transient free data collection. In general time the times
required to reach stable flow conditions and acquire sufficient
data ranged from 5 to 30 s.
Experimental Design and Procedures
The apparatus used for this study is a 3.8 cm diameter fast-
flow reactor designed for alkali atom and molecule kinetics
studies, as shown schematically in Figure 1. Its basic features
have been described previously8 and will only be summarized
here. The first 20 cm section of the flow reactor contained a
monel sodium oven and was water cooled. Na atoms were
generated by heating ∼1 g samples of metallic sodium in a silver
“boat” placed in the 2.5 cm oven to temperatures commensurate

2
Chemical Kinetics of NaO (A Σ+) + O(3P)
J. Phys. Chem. A, Vol. 105, No. 9, 2001 1645
Typical kinetic runs were made under a range of variable
flows through the first and second injectors, using the resonance
fluorescence determination of ground-state [Na] as a function
of the second injector position as the common observable. Four
of the most important flow conditions are described here. First,
[Na] without the O2/He discharge on and with He/Ar rather than
He/O3 flowing through the first injector was determined. Here
Na loss is due only to the relatively slow Na + O2 + M f
NaO2 + M reaction and Na loss to the flow reactor walls.
Second, the O2/He discharge was ignited, producing atomic O
and a small, but significant, amount of O3 from O + O2 + M.
Atomic O levels were monitored by resonance absorption. Here,
Na loss is dominated by NaO formation from reaction 1′ and
by termolecular recombination of Na with O to form NaO. NaO
formation is not completely balanced by Na re-formation via
reaction 2/2′ and can be followed by secondary reaction 4a
between NaO + O3:
Figure 2. Experimental plots of [Na] decays and kinetic model fits
for a 290 K, 4.3 Torr case. Reaction conditions corresponding to each
data curve are explained in the text.
collisional quenching by the He carrier flow is not a significant
loss process under the low-pressure, fast-flow conditions
employed for the kinetic measurements described below.
NaO + O3 f NaO2 + O2
f Na + 2O2
(4a)
(4b)
Representative experimental data taken at a flow reactor total
pressure of 4.26 Torr and temperature of 290 K are shown in
Figure 2. The top data points (open circles) are for experimental
condition 1 and represent the Na decay as a function of second
injector position with only Ar from the first injector and a He/
O2 mixture entrained from the second injector. The second
highest data set (condition 2, filled circles) represent Ar flow
through the first injector and an He/O2 discharge on flow through
the second injector, which provides a modest amount of O3 from
O + O2 combination plus a high level of O. The third data set
(condition 3, bowties) represents O2 flow through the first
injector and the same He/O2 discharge on through the second
injector as condition 2. The lowest data set (triangles) represents
condition 4, with [O3] ) 1.5 × 1012 cm-3 added through the
first injector and the He/O2 discharge on with its O/O2/O3
mixture added though the second injector.
The data in Figure 2 have been simulated using a kinetic
model based on the CHEMKIN code23 and the reaction set
shown in Table 1. Reaction rate coefficients for most sodium,
sodium oxide, and oxygen species were adopted from the
DeMore et al. evaluation of atmospheric reaction kinetic
parameters,24 although reaction rates for several termolecular
(He third body) oxygen atom reactions were selected from the
National Institute of Standards and Technology (NIST) kinetic
data compilation.25 A room temperature Na + O + He
termolecular rate constant of 2.0 × 10-30 cm6 s-1 was estimated
from the Na + O2 + He rate coefficient. These reactions proceed
by an electron jump from the Na to the electrophilic reactant,
followed by a Columbic attraction between the resulting Na+
and O- or O2-. Since the electron affinity of O (1.46 eV) is
higher than that of O2 (0.45 eV), the initial electron jump will
occur at longer range, but the nascent NaO will also have a
shorter lifetime against dissociation than the nascent NaO2 while
waiting for a third body collision to stabilize the reaction
product. Our estimate that the Na + O + He reaction should
be modestly faster than the Na + O2 + He reaction is supported
by a reported estimate of a 290 K rate for the Na + OH + He
rate constant of (4.1 ( 0.9) × 10-30 cm6 s-1 (OH has an electron
affinity of 1.83 eV), based on a measured value at 635 K
extrapolated with a Tro¨e unimolecular reaction formulation to
lower temperatures.26 The estimate for the reaction rate coef-
ficient for the NaO3 + O reaction was taken from ref 12.
The third experimental condition is similar to the second; O2
is introduced through the first injector, enhancing [Na] loss due
to the Na + O2 + He reaction. In condition 4, O3 in an He
carrier is introduced though the first injector, converting most
of the Na to NaO(A 2Σ+) via reaction 1′, while the products O
+ O3 of the O2/He discharge continue to be added through the
second injector. In this case, reactions 2′ and 4b continue to
regenerate Na, but reaction 1′ also continues to consume it.
Under this condition chemiluminescence from Na(2P), created
by reaction 2′a, is monitored via its emission, as well as the
Na(2S) from reactions 2′b, 3, and 4b.
In all four cases, there will be loss of sodium species,
including Na, NaO, and NaO2, on the flow reactor walls. Our
previous work has shown that the loss of all Na species occurs
at essentially unit probability with each wall collision and the
rate of wall collisions can be well-estimated from calculated
diffusion coefficients.8,21 Experimental data on relative ground-
state Na concentrations, for reaction conditions 1-4, atomic O
concentrations, for reaction conditions 2 and 3, and Na
chemiluminescent D-line emission levels, for reaction condition
3, were taken for a range of flow tube pressures between 1.4
and 4.3 Torr under room temperature conditions, 290 ( 2 K.
In some runs N2O, expected to be an effective quenchant for
2
NaO(A Σ+), since its ν3 vibrational band is nearly coincident
with T0-0 for the NaO ArX transition,20 was added to the
carrier flow, with little effect.
Results
The goal of this study was to investigate the magnitude of
the overall rate coefficient for reaction 2′, k2′ ) k2′a + k2′b, and
the branching ratio for excited-state Na(2P) production, f2′
)
k2′a/(k2′a + k2′b), under conditions where NaO is produced by
2
reaction 1, and is predominantly NaO(A Σ+). Since the data
reported here were taken at flow reactor pressure below 5 Torr
2
to minimize collisional quenching of NaO(A Σ+), and since
our spectroscopic measurements and available theoretical
calculations indicate that the radiative lifetime of NaO(A 2Σ+),
1-100 ms,19,20 will be much longer than the chemical lifetime
of NaO via reaction 2 of ∼0.25 ms under our experimental
conditions, we believe that the k2′ and f2′ values reported below
are representative of NaO in the A 2Σ+ state. The fact that even
moderate amounts of added N2O did not significantly diminish
the observed Na(2P) emission is taken as evidence that its
To ensure the current fast-flow reactor yielded reliable
reaction rates, we fitted the measured [Na] decay rates for six
290 K experimental runs where O2 was added through either

1646 J. Phys. Chem. A, Vol. 105, No. 9, 2001
Griffin et al.
TABLE 1: Kinetic Mechanism Used in Fitting the NaO + O Reaction Rate Data
reaction
rate constant
source
Wall-Loss Reactions
Na f Na(s)
83.7 s-1
modeled from diffusion coefficients
modeled from diffusion coefficients
modeled from diffusion coefficients
modeled from diffusion coefficients
modeled from diffusion coefficients
NaO f NaO(s)
NaO2 f NaO2(s)
NaO3 f NaO3(s)
O f O(s)
139.3 s-1
69.7 s-1
63.5 s-1
2.7 s-1
Reactions from Chapman’s Mechanism
1.0 × 10-9 e-95/T cm3 s-1
Na+O3 ) NaO + O2
NaO + O ) Na + O2
ref 24
see text
(5.1 ( 1.8) × 10-10 cm3 s-1
Significant Secondary Reactions
7.5 × 10-29 cm6 s-1
Na + O + He ) NaO + He
Na + O2 + He ) NaO2 + He
NaO2 + O ) NaO + O2
NaO + O3 ) Na + O2 + O2
NaO + O3 ) NaO2 + O2
NaO3 + O ) NaO2 + O 2
NaO + O2 + He ) NaO3 + He
O + O3 ) O2 + O2
estdssee text
see text
ref 24
ref 24
ref 24
ref 12
ref 25
ref 24
ref 25
(1.49 ( 0.3) × 10-30 cm6 s-1
2.2 × 10-11 cm3 s-1
6.0 × 10-11 cm3 s-1
1.1 × 10-9 e-570/T cm3 s-1
1.8 × 10-11 T0.5 cm3 s-1
1.3 × 10-30 cm3 s-1
8.0 × 10-12 e-2060.0/T cm3 s-1
3.5 × 10-34 cm6 s-1
O2 + O + He ) O3 + He
O + O + He ) O2 + He
1.3 × 10-33 cm6 s-1
ref 25
TABLE 2: Na + O2 + He f NaO2 + He Kinetics Results
(290 K)
TABLE 3: NaO + O f Na + O2 Kinetics Results and
Measured f2′
run no.
k5 (cm6 s-1
)
NaO + O f Na + O2 Kinetics Results (290 K)
1
2
3
4
5
6
1.53 × 10-30
1.34 × 10-30
1.87 × 10-30
1.53 × 10-30
1.25 × 10-30
1.43 × 10-30
run no.
k2′ (cm3 s-1
)
run no.
k2′ (cm3 s-1
)
1
2
3
5.71 × 10-10
5.98 × 10-10
5.81 × 10-10
4
5
6
5.15 × 10-10
3.82 × 10-10
3.99 × 10-10
av
5.08 × 10-10
std dev
0.80 × 10-10
av
1.49 × 10-30
0.30 × 10-30
Measured 290 K f2′ Valuesa
std dev
for given P (Torr)
reac distance (cm)
4.3
4.3
3.2
1.4
the first or second injector (condition 1). These decays are
dominated by the termolecular reaction:
10
15
20
25
0.149
0.137
0.123
0.083
0.142
0.139
0.124
0.092
0.137
0.125
0.112
0.080
0.122
0.131
0.106
0.077
k5
Na + O2 + He
98 NaO2 + He
(5)
a 16 pt av ) 0.12; 16 pt std dev ) 0.02; 8 initial pt av ) 0.14; 8
initial point std dev ) 0.01.
Including computed diffusional wall loss for Na and NaO2,
the linear least-squares fits for k5 from these six decays are
tabulated in Table 2. The average of these data yields k5(290
K) ) (1.49 ( 0.30) × 10-30 cm6 s-1, where the stated error is
one standard deviation about the mean. This result is in excellent
agreement with the value of (1.44 ( 0.20) × 10-30 cm6 s-1 for
290 K previously measured in our laboratory,27 and in reason-
able agreement with higher temperature values reported by
Husain and Plane28 ((0.6 ( 0.1) × 10-30 cm6 s-1 for 724-844
K) and Vinckler et al.29 ((0.89 ( 0.07) × 10-30 cm6 s-1 for
290 K via a Tro¨e extrapolation of data taken between 392 and
777 K) and a single lower temperature point of (1.2 ( 0.2) ×
10-30 cm6 s-1 at 250 K reported by Plane and Rajeskhar.30 We
used the k5 measured in this study in the CHEMKIN model.
Linear least-squares model fits to two condition 2 decays
(filled circles), two condition three decays (bowties), and two
condition 3 decays (triangles) with k2′ as a free parameter yielded
measurement, a prudent estimate of the additional uncertainty
due to systematic error is (20% of the measured value, leading
to a final value of k2′ ) (5.1 ( 1.8) × 10-10 cm3 s-1 at 290 K.
The solid lines plotted on the representative decay data shown
in Figure 2 are simulations based on the average values derived
for k5 and k2′. Fits to decays where these parameters were
variables reproduced the decay curves more closely and yielded
the individual run values tabulated in Tables 2 and 3.
A study state analysis for Na(2P) from reaction 2′ and 3 yields
f2′k2′[NaO][O] ) k3[Na(2P)]
which can be rearranged to
f2′ ) k3[Na(2P)]/k2′[NaO][O]
(6)
(7)
2
values of this rate coefficient where the A Σ+ state is the
where k3 is the inverse of the [Na(2P)] radiative lifetime, (16.40
( 0.03) × 10-9 s.31 In principle, we can determine [Na(2P)]
from its observed chemiluminescent signal (CL) in the reaction
region in front of the Na PMT:
predominant form of NaO. These individual fitted values of k2′
are tabulated in Table 3. The mean value for the six fits of k2′
at 290 K is (5.1 ( 0.8) × 10-10 cm3 s-1, where the stated error
is one standard deviation about the mean. In addition to the
random measurement error expressed as the single standard
deviation about the mean, it is prudent to add an estimate of
the probable systematic errors involved in both measuring
experimental variables and modeling the flow reactor kinetics
to derive k2′ Given the moderately indirect nature of the
CL ) (CV)(DE)k3[Na(2P)]
(8)
where CV is the chemiluminescent photon optical collection
volume for the Na PMT and DE is its detection efficiency. In

2
Chemical Kinetics of NaO (A Σ+) + O(3P)
J. Phys. Chem. A, Vol. 105, No. 9, 2001 1647
measured f2′ values are noticeably smaller for the two longer
reaction distances. This is likely due to the influence of
secondary chemistry, which is not completely accounted for by
the reaction set in Table 1. The average and standard deviation
of all tabulated 16 points are 0.12 ( 0.02, while the average
and standard deviation for the two shortest reaction distance
points are 0.14 ( 0.01. The average of the first two points is
recommended as a more reliable value for f2′. However, a
significant allowance for systematic error must be added to the
statistical error represented by the single standard deviation
about this mean. Systematic uncertainties include the effect any
NaO produced which is not in the A Σ+ state (particularly from
the Na + O + M and NaO2 + O reactions), any loss of Na A
state due to radiative, reactive (other than reaction 2′), or
physical quenching, and systematic errors in the measured
experimental and modeled parameters in eq 11, including
uncertainty in the estimate of the spectral line shape overlap
integral, R, and in the measurement of [O]. We estimate that
these systematic errors combined with the computed statistical
error result in a recommended value of f2′ ) 0.14 ( 0.04.
Figure 3. Plots of components of eq 11 and the resultant value of f2′
as a function of reaction distance for a 290 K, 4.3 Torr case.
practice, it is more accurate to ratio out the optical collection
and PMT efficiency factors by stimulating the ground-state
Na(2S) to fluorescence using the Na resonance lamp. Since the
Na PMT optics were arranged so that the resonance lamp output
fills the Na PMT field of view, with the lamp on the Na PMT
records a signal which is the sum of CL plus a fluorescence
signal equal to
Discussion
The value of k2′ (290 K) reported here, for conditions where
2
the A Σ+ state is designed to be nearly the exclusive form of
NaO, can be compared with the value of (3.7 ( 0.9) × 10-10
cm3 s-1 at 573 K obtained by Plane and Husain under conditions
where NaO(X 2Π) predominated,10 and the value of 1.6 × 10-10
FL ) (CV)(DE)khν[Na]
(9)
2
cm3 s-1 predicted for ground-state NaO(X Π) by a simple
where khν) σF/(1 + R2)1/2, σ is the Na(2Sf2P) absorption cross-
section of 1.85 × 10-11 cm2 derived from the excited-state
radiative lifetime,31 F is the measured resonance lamp photon
flux though the PMT observation volume, and R is the overlap
integral between the room temperature ground-state Na absorp-
tion line and the lamp output spectra.2 The value of R can be
obtained from the ratio of the Doppler broadened half-width of
the lamp Na emission line and the room temperature Doppler
broadened absorption width of the Na in the low-pressure flow
reactor, which can be approximated by the square root of the
ratio of the lamp operating temperature (600 K) divided by the
flow tube gas temperature (290 K), to give R ) 1.44.
Combing eqs 8 and 9 yields
electron jump mechanism at mesospheric temperatures.6 Obvi-
ously the two experimental values agree within their experi-
mental errors. The reaction rate of O(3P) with the ground state
of NaO is ∼3.8 eV exothermic, based on recently published ab
initio calculations of Do(NaO X) ) 2.43 eV.33 It seems
reasonable to assume that the additional 0.16 eV of exothemicity
2
for the A Σ+ state will not greatly influence the kinetics. We
might expect a slightly longer range electron jump given the
2
slightly lower ionization potential of NaO(A Σ+). The evalu-
ation of DeMore et al.23 recommends a temperature independent
value for k2 of 3.7 × 10-10 cm3 s-1, while a temperature
dependent rate coefficient which corresponds to a 300 K value
of 2.7 × 10-10 cm3 s-1 has been adopted by Plane and co-
workers for atmospheric modeling.12,13 Under conditions where
[Na(2P)] ) (CL/FL)khν[Na]/k3
(10)
2
NaO(A Σ+) dominates, these values should be increased in
future models.
Substituting eq 10 into eq 7, the branching ratio, f2′, to produce
The measured value of f2′ ) 0.14 ( 0.04 far exceeds the
value of ∼0.01 for the slow flow study of Plane and Husain,10
which is presumably representative of the f2 for NaO(X 2P). Ιt
is reasonably close to the value of ∼0.1 derived by Plane and
co-workers from model analyses of Na nightglow and associated
atmospheric measurements12,13 and is also comfortably below
the upper limit of 0.67 we deduced from an analysis of
symmetry correlations.18
Na(2P) can be derived from the expression
f2′ ) (CL/FL)(khν/k2′[O])([Na]/[NaO])
(11)
where CL is the chemiluminescent signal from Na(2P) and FL
is the fluorescence signal in the same reaction volume from
Na(2S) (obtained by subtracting the chemiluminescence signal
with the resonance lamp off from the total fluorescence plus
chemiluminescence signal obtained with the Na lamp on). The
ratio [Na]/[NaO] is taken from the kinetic model, and [O] is
derived from the resonance absorption measurement.
Figure 3 shows the three terms in parentheses on the right-
hand side of eq 5 for the data presented in Figure 2, as well as
the resulting values of f2′, all plotted as a function of the second
injector’s distance from the detection region. Table 3 displays
the f2′ values measured for four cases, with the total flow tube
pressures on 4.2 (two cases) 3.2, and 1.4 Torr, respectively.
For each case an f2′ is determined for four reaction distances
varying between 10 and 24 cm. Clearly, while the two shortest
reaction distances in each case produce similar values, the
Atmospheric Implications
It is critical that the excited-state kinetics (reactions 1′ and
2′) be considered in nightglow analyses similar to those of Plane
and collaborators.12,13 A recent publication by Hecht et al.33
which used measured Na layer parameters from the Coqui Dos
campaign to estimate f2 is almost certainly in serious error
because it was performed under very cold mesospheric condi-
tions where the average O density was about 2 × 1011 cm3.
2
This means that the mean chemical lifetime of NaO(A Σ+)
created in reaction 1′ was 1/(k2′[O]) ∼ 10 ms. Langhoff19 has
2
calculated that the NaO(A Σ+,ν′)0) radiative lifetime is 14.5

1648 J. Phys. Chem. A, Vol. 105, No. 9, 2001
Griffin et al.
ms and the calculated radiative lifetimes for higher upper
vibrational states, which are surely populated given the exo-
thermicity of reaction 2′, decrease rapidly and monotonically,
e.g. 7.9 ms for V′ ) 1, 5.3 ms for V′ ) 2, 3.9 ms for V′ ) 3, to
1.4 ms for V′ ) 9. Therefore, if these calculated radiative
lifetimes are at all accurate, it is very likely that the radiative
loss of NaO(A 2Σ+) exceeded its loss via reaction 2′. Since we
gratefully acknowledge the financial support of the Atmospheric
Sciences Division of the National Science Foundation under
Grant No. 9304528.
References and Notes
(1) Plane, J. M. C. Intl. ReV. Phys. Chem. 1991, 10, 55.
(2) Kolb, C. E.; Worsnop, D. R.; Zahniser, M. S.; Robinson, G. N.;
Shi, X.; Herschbach, D. R. In Gas-Phase Metal Reactions; Fontijn, A., Ed.;
Elsevier Science: Amsterdam, 1992; p 15.
2
know that ground-state NaO(X Π) + O does not produce
Na(2P) at significant levels,10,16 radiative decay of NaO(A 2Σ+)
almost certainly helped produce the low estimate of f2 (<0.05)
Hecht et al. reported. Also at low rates of reaction 2′, NaO(A
2Σ+) may be lost to physical quenching via collisions with N2
and O2 and by reactive collisions with H2 and H2O, all processes
which Hecht et al. failed to consider. It is interesting to note
that the similar analysis by Clemesha et al.13 measured their
highest Na levels near 98 km, where O atom densities were
derived to be ∼8 × 1011, allowing reaction 2′ to process a much
higher fraction of the NaO(A 2Σ+) produced by reaction 1′ and
leading to a significantly higher estimate for f2.
(3) Chapman, S. Astrophys. J. 1939, 90, 309.
(4) Chapman, S. In The Airglow and Aurorae; Armstrong, E. B.,
Delgarno, A., Eds.; Pergammon Press: London, 1956; p 204.
(5) Baggaley, W. J. Nature 1975, 257, 567.
(6) Kolb, C. E.; Elgin, J. B. Nature 1976, 263, 488.
(7) Bates, D. R.; Ojha, P. C. Nature 1980, 286, 790.
(8) Worsnop, D. R.; Zahniser, M. S.; Kolb, C. E. J. Phys. Chem. 1991,
95, 3691 (errata, J. Phys. Chem. 1992, 96, 9088) and references cited therein.
(9) Plane, J. M. C.; Helmer, H. In Research in Chemical Kinetics;
Compton, R. G., Hancock, G., Eds.; Elsevier Science: Amsterdam, 1994;
Vol. 2, p 313.
(10) Plane, J. M. C.; Husain, D. J. Chem. Soc., Faraday Trans. 2 1986,
82, 2047.
(11) Swider, W. J. Geophys. Res. 1986, 91, 4067.
To perform the analyses presented in refs 13, 33, and 34
(where f2 was varied over a large range) correctly, our value of
f2′ should be redetermined at typical mesospheric temperatures
(180-220 K), although we do not expect the branching ratio
for this exothermic reaction to depend strongly on temperature.
(12) Helmer, M.; Plane, J. M. C. J. Geophys. Res. 1993, 98, 23207.
(13) Clemesha, B. R.; Simonich, D. M.; Takahashi, H.; Melo, S. M. L.;
Plane, J. M. C. J. Geophys. Res. 1995, 100, 18909.
(14) Schofield, K. Geophys. Res. Lett. 1993, 20, 2837.
(15) Schofield, K. Int. J. Chem. Kinet. 1993, 25, 719.
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Chem. 1993, 97, 2113.
(17) Wright, T. G.; Ellis, A. M.; Dyke, J. M. J. Chem. Phys. 1993, 98,
2891.
(18) Herschbach, D. R.; Kolb, C. E.; Worsnop; Shi, X. Nature 1992,
356, 414.
(19) Langhoff, S. R.; Partridge, H.; Bauschlicher, C. W., Jr. Chem. Phys.
1991, 153, 1, and references cited therein. Calculated NaO (A 2Σ+) radiative
lifetimes for various vibrational levels were supplied by: Langhoff, S. R.
Private communication, 1992.
(20) Joo, S.; Worsnop, D. R.; Kolb, C. E.; Kim, S. K.; Herschbach, D.
R. J. Phys. Chem. A. 1999, 103, 3193.
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(22) Anderson, J. G. Geophys. Res. Lett. 1975, 2, 231.
(23) Kee, R. J.; Miller, J. H.; Jefferson, T. H. CHEMKIN: A Chemical
Kinetics Code Package; Sandia Laboratories: Albuquerque, NM, 1989.
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Kurylo; M. J.; Howard, C. J.; Ravishankara, A. R.; Kolb, C. E.; Molina,
M. J. Chemical Kinetics and Photochemical Data for Use in Stratospheric
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(25) Mallard, W. G.; Westley, F.; Herron, J. J.; Hampson, R. F. NIST
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(26) Husain, D.; Plane, J. M. C.; Xiang, C. C. J. Chem. Soc., Faraday
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2
In addition, rate coefficients for the reaction of NaO(A Σ+)
with H2, H2O, and O and its physical quenching rate constants
by N2 and O2 should be measured over a significant temperature
range extending down to mesospheric temperatures. Finally,
2
2
accurate measurement of the NaO(A ΣS+fX P) radiative
lifetime as a function of V′ as well as the nascent NaO(A Σ+)
2
vibrational distribution from reaction 1 also need to be made.
We believe the value of f2′ for the NaO(A Σ+) might be
2
more precisely determined at various temperatures by exploiting
our recent measurement of precise line positions for NaO(A
2Σ+rX 2P) transition,20 which should allow easier preparation
2
of NaO(A Σ+) using pulsed infrared laser techniques. More
definitive values of k2′, f2′, and the rate coefficients for NaO(A
2Σ+) physical, reactive, and radiative quenching at mesospheric
temperatures should also be accessible using this technique.
These parameters would then allow accurate nighttime upper
mesospheric ozone profiles to be derived from the measurement
of altitude resolved resonant fluorescent measurement of Na
concentration profiles and Na D-line nightglow levels.13,33,34
(27) Silver, J. A.; Zahniser, M. S.; Stanton, A. C.; Kolb, C. E.
Proceedings of the Twentieth Symposium (International) on Combustion;
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(33) Hecht, J. H.; Collins, S.; Kruschwitz, C.; Kelly, M. C.; Roble, R.
G.; Walterscheid, R. L. Geophys. Res. Lett. 2000, 27, 453.
(34) Takahashi, H.; Melo, S. M. L.; Clemesha, B. R.; Simonich, D. M.;
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Acknowledgment. We dedicate this paper to Professor
Harold S. Johnston in celebration of his 80th birthday. In richly
fulfilling his roles of mentor, teacher, textbook author, re-
searcher, environmental leader, and gentleman, Hal Jonhston
has inspired us. His life and work stand as an outstanding
example of the power and purpose of physical chemistry in the
twentieth century. We also thank Aerodyne colleagues M. S.
Zahniser, D. D. Nelson, J. T. Jayne, S. Kallelis, and J. T.
Mulholland for technical assistance and R. Heroux, E. Wein-
stock, and J. G. Anderson of Harvard for providing atomic
oxygen resonance absorption equipment and advice. We also