A shock tube study of the product branching ratio for the reaction NH2 + NO using frequency-modulation detection of NH2

Article abstract of DOI:10.1021/jp983613v

The product branching ratio of (NH₂ + NO → N₂H + OH]:[NH₂ + NO → N₂ + H₂O] has been determined in the temperature range of 1340-1670 K in a shock tube study with laser photolytic generation of the NH₂ radicals. Sensitive frequency-modulation detection of the NH₂ radical enables experiments with very low initial radical concentrations and, hence, virtually no interference from secondary reactions or dependence on the overall rate coefficient of the reaction. The branching ratio, a, defined as α = k_1a/(k_1a+k_1b), increases from 0.42 at 1340 K to 0.53 at 1670 K. Over this temperature range our results can be expressed as α = 0.5 + (3.36 × 10^-4)(T/K - 1600). A detailed error analysis yields an uncertainty in the values of a of ±0.02 near 1500 K, increasing to ±0.05 at the temperature extremes.

Full text of DOI:10.1021/jp983613v

1566
J. Phys. Chem. A 1999, 103, 1566-1571
A Shock Tube Study of the Product Branching Ratio for the Reaction NH2 + NO Using
Frequency-Modulation Detection of NH2
M. Votsmeier, S. Song, R. K. Hanson, and C. T. Bowman*
High-Temperature Gasdynamics Laboratory, Department of Mechanical Engineering,
Stanford UniVersity, Stanford, California 94305
ReceiVed: September 3, 1998; In Final Form: January 13, 1999
The product branching ratio of [NH2 + NO f N2H + OH]:[NH2 + NO f N2 + H2O] has been determined
in the temperature range of 1340-1670 K in a shock tube study with laser photolytic generation of the NH2
radicals. Sensitive frequency-modulation detection of the NH2 radical enables experiments with very low
initial radical concentrations and, hence, virtually no interference from secondary reactions or dependence on
the overall rate coefficient of the reaction. The branching ratio, R, defined as R ) k1a/(k1a+k1b), increases
from 0.42 at 1340 K to 0.53 at 1670 K. Over this temperature range our results can be expressed as R ) 0.5
+ (3.36 × 10-4)(T/K - 1600). A detailed error analysis yields an uncertainty in the values of R of (0.02
near 1500 K, increasing to (0.05 at the temperature extremes.
1. Introduction
produces four chain carriers, while reaction 1b consumes one
radical, it is apparent that the branching ratio, R, defined as R
) k1a/(k1a + k1b) must be at least 0.25 in order to ensure a self-
sustained chain reaction. Owing to the critical role of R in
determining the chain-branching character of the overall process,
detailed modeling of the thermal De-NOx process shows
considerable sensitivity to this parameter.
In the Thermal De-NOx process invented by Lyon,1,2 NH3 is
added to high-temperature exhaust gases in order to reduce NOx
emissions. The dominant pathway for NO reduction in this
process is the reaction of NO with the NH2 radical, which
proceeds through the two product channels:3-5
NH2 + NO f N2H + OH
NH2 + NO f N2 + H2O
(1a)
(1b)
Due to its importance for De-NOx modeling, a relatively large
body of experimental data on the NH2 + NO reaction has been
reported in the literature. The overall rate coefficient seems to
be well established, at least for temperatures below 1400 K.5
There also is good agreement on the branching ratio R at
temperatures up to about 700 K. At higher temperatures, in the
range most relevant for the De-NOx process (1000-1400 K),
there still is considerable uncertainty in the branching ratio. A
number of low-temperature direct flash photolysis studies yield
a relatively small increase of R with temperature and, when
extrapolated to De-NOx temperatures, give values of R well
below 0.25.6-9 As discussed above, such low R values are
inconsistent with the De-NOx process being a self-sustaining
radical chain process. On the other hand, an early combustion-
driven flow reactor study10 yielded a sharp increase of the
branching ratio, R, at temperatures above 1000 K, leading to a
value of R ) 0.6 at 1300 K. Lin and co-workers11,12 confirmed
the sharp increase of R at temperatures above 1000 K. However,
a recent reinterpretation of the experimental data in refs 11 and
12 by Park and Lin13 has resulted in a reduction in the R values
at elevated temperatures. Glarborg et al.14 recently determined
the branching ratio, R, in the temperature range of 1211-1370
K from De-NOx flow reactor experiments and found that R
increases from about 0.35 at 1211 K to about 0.45 at 1370 K.
This result is in agreement with earlier flame speed modeling
studies by Vandooren et al.15 and Brown and Smith.16
The NH2 radicals are formed through a radical chain mechanism,
mainly by the following reactions:
H + NH3 f H2 + NH2
(2)
(3)
OH + NH3 f H2O + NH2
Reaction 1a serves not only as a major NO-removal reaction
but also as a branching step that produces two chain carriers.
The N2H formed in reaction 1a either dissociates directly
N2H f N2 + H
(4)
or in the presence of oxygen forms an OH radical through the
following sequence:
N2H + O2 f HO2 + N2
HO2 + NO f OH + NO2
(5)
(6)
In the presence of oxygen, three additional chain carriers are
produced from each H atom formed in reaction 4 by the
following sequence:
H + O2 f OH + O
(7)
(8)
The objective of this study is to use our newly developed
shock tube/frequency-modulation detection scheme in conjunc-
tion with laser flash photolytic generation of NH2 to measure
directly the branching ratio, R, at high temperatures in order to
resolve the existing disparate results.
O + NH3 f OH + NH2
Reaction 1a, followed by reactions 4, 7, and 8, is the major
chain-branching step in the mechanism. As this sequence
10.1021/jp983613v CCC: $18.00 © 1999 American Chemical Society
Published on Web 03/02/1999

Shock Tube Study of Product Branching Ratio
J. Phys. Chem. A, Vol. 103, No. 11, 1999 1567
2. Outline of the Experiments
The high sensitivity of the De-NOx process to the branching
ratio, R, makes it difficult to quantitatively predict De-NOx
efficiencies and to validate the De-NOx reaction mechanism
without using the branching ratio as a fitting parameter in the
modeling process. Our approach is to find experimental condi-
tions where we can directly observe the temporal evolution of
a process with a chain-branching behavior similar to the full
De-NOx process, but with a sufficiently simplified chemistry
to allow a determination of R with little sensitivity to secondary
reactions. To achieve this we use the following three experi-
mental techniques: (1) a traditional shock-tube technique to
produce controlled and uniform high-temperature conditions;
(2) laser photolysis to initiate the chain process by instanta-
neously producing controlled concentrations of chain-branching
radicals; (3) frequency-modulation (FM) detection of the NH2
radical to allow sensitive measurement of the chain carrier
radical concentration.
Figure 1. Solid lines: CHEMKIN simulations of NH2 mole fraction
time profiles for three different values of the branching ratio, R, and
typical experimental conditions of this study: [NH3] ) 1%, [NO] )
0.2%, [H]0 ) [NH2]0 ) 5 ppm, T ) 1500 K, p ) 1.3 atm. Dashed
line: eq 10 for the same conditions.
In the experiments, an initial NH2 radical population is
generated by laser flash photolysis of a mixture containing NH3
and NO diluted in argon:
tion with an effective rate coefficient kobsd
NH3 + hν f NH2 + H
(9)
kobsd ) koverall(2R - 1)
where koverall ) k1a + k1b.
(10)
The NH3 concentration is chosen to be sufficiently high so that
the H atoms formed during NH3 photolysis quickly react with
excess NH3 to form NH2:
In the special case where R ) 0.5, kobsd is independent of
koverall, and the NH2 concentration will remain at a constant level.
H + NH3 f H2 + NH2
(2)
Hence, it should be possible to determine R for a small
temperature range, where R is close to 0.5, nearly independent
of assumptions for koverall. For temperatures where R differs from
R ) 0.5, the determination of R will of course begin to show
After a few microseconds, an NH2 concentration of approxi-
mately twice the initial NH2 concentration is established.
Under the present experimental conditions, NH2 reacts mainly
with NO via the two reaction channels 1a and 1b:
some sensitivity to koverall
.
The simple kinetic scheme consisting of reactions 1-4 and
resulting in eq 10 is useful as it provides intuitive insight into
the sensitivity of the measurements to the branching ratio, R,
and the overall rate coefficient koverall. However, the actual data
analysis was carried out using CHEMKIN simulations with the
full 129-reaction De-NOx mechanism of Miller and Glarborg5
with R as a single adjustable parameter to fit the simulations to
the experimental NH2 concentration time profiles. Sensitivity
and reaction path analyses for the conditions of the present study
show that only a small subset of the complete mechanism
contributes to formation and removal of NH2. Figure 1 shows
simulations using the full mechanism for three values of R near
0.5. The simulations clearly demonstrate the high sensitivity of
the measurements to the branching ratio. Also shown in Figure
1 is the constant NH2 concentration profile predicted by the
simple kinetic scheme and eq 10 for R ) 0.5. For the conditions
of Figure 1, secondary reactions are responsible for only a small
change after the peak in the NH2 time history. The most
important secondary reactions are relatively well-known so that
if the measurements are modeled by the full mechanism, the
relative error in R caused by uncertainty in the secondary rate
parameters for the conditions of Figure 1 can be estimated to
be less than 1%.
NH2 + NO f N2H + OH
NH2 + NO f N2 + H2O
(1a)
(1b)
Since, in contrast to the normal De-NOx process, the mixture
does not contain O2, the N2H formed in reaction 1a quantita-
tively decomposes into N2 and H:
N2H f N2 + H
(4)
At the high NH3 concentrations in our experiments, the two
reactive radicals resulting from reaction 1a, H and OH, react
quickly with excess NH3 to reform NH2:
H + NH3 f H2 + NH2
(2)
(3)
OH + NH3 f H2O + NH2
Consequently, each NH2 radical reacting via the channel 1a
leads to the formation of two new NH2 radicals, while chan-
nel 1b is chain terminating and leads to the loss of one NH2
radical. In this way a chain process is initiated with a branching
behavior that is almost entirely controlled by reactions 1a
and 1b.
Figure 2 shows a sensitivity plot for the conditions of Figure
1 with the normalized sensitivity to the branching ratio, R,
defined as SR ) (d[NH2]/dR)(R/[NH2]max), the normalized
sensitivity to the overall rate coefficient for reaction 1, koverall
,
In a simplified treatment, assuming that the rates of reaction
3 and the sequence 4 plus 2 are instantaneous compared to
reactions 1a and 1b (due to the high NH3 concentration), we
expect an exponential increase/decrease of the NH2 concentra-
and the normalized sensitivities for the most important secondary
reactions. The sensitivity plot confirms that the experiments are
highly sensitive to the branching ratio and are virtually free of
interference from secondary reactions and the overall rate

1568 J. Phys. Chem. A, Vol. 103, No. 11, 1999
Votsmeier et al.
was used. The exiting laser beam had a height of ∼2 cm and
was expanded in the horizontal plane by a 50-mm focal width
cylindrical lens to a width of more than 60 cm. The central
part of the expanded beam entered the shock tube, parallel to
the shock tube axis through a 14-cm wide and 2-cm high
Suprasil window in the end wall. Due to the expansion of the
excimer beam and the use of only the central part of the beam
for the photolysis experiment the effect of excimer laser beam
nonuniformity is greatly reduced. For this setup the beam
nonuniformity across the shock tube diameter was less than 3%.
The excimer photolysis beam and the frequency-modulated laser
beam are carefully aligned to ensure full overlap in the shock
tube. The excimer laser was triggered by the last pressure gauge
of the shock velocity measurement system and was appropriately
delayed so that the heated mixture is photolyzed approximately
30 µs after passage of the reflected shock wave.
3.2. Frequency-Modulation Detection. The development of
more sensitive diagnostic techniques for shock tubes enables
experiments at lower initial concentrations and, hence, reduced
sensitivity to secondary reactions. The introduction of narrow
line width laser absorption measurements has allowed consider-
able progress in this direction.19 However, even if state-of-the-
art laser noise cancellation techniques are applied, classical laser
absorption measurements are still subject to the noise caused
by the passage of the laser beam through the shock tube itself,
such as scattering and beam steering. Frequency-modulation
detection, as a differential absorption scheme, is insensitive to
these effects and thus potentially allows a considerable improve-
ment in detection sensitivity.
The frequency-modulation (FM) technique in the form applied
in this work was first introduced by Bjorklund20 for the detection
of stable molecules. The detection of transient species via FM
spectroscopy, in combination with photochemical modulation,
has been utilized by Whittaker et al.21 to obtain spectra of HCO
and ND4. Recently North et al.22 demonstrated the usefulness
of FM detection for time-resolved chemical kinetic measure-
ments. A detailed introduction to the principles of FM spectros-
copy and the relation between absorption line shapes and the
corresponding FM signals has been given by Bjorklund et al.23
Passing a narrow line width laser beam with an optical
frequency (ωL) through an electrooptical crystal and modulating
Figure 2. Normalized relative sensitivities SR ) (d[NH2]/dR)(R/
[NH2]max), Sk ) (d[NH2]/dk)(k/[NH2]max), respectively, to the branching
ratio R, the overall rate constant koverall, and the most important
secondary reactions for the experimental conditions of Figure 1.
coefficient. It must be emphasized that these insensitivities result
from the low radical concentrations for our experimental con-
ditions, which are made possible by the high sensitivity of the
FM detection scheme.
3. Experimental Setup
The experimental setup consists of a conventional shock tube,
a photolysis laser, and the FM system for sensitive quantitative
detection of NH2.
3.1. Shock Tube and Photolysis System. The shock tube
facility and the laser photolysis setup have been described
previously,17 and only a brief description is presented here.
Experiments were carried out behind reflected shock waves
in a stainless steel shock tube with a 6-m long driven section
and an internal diameter of 15 cm. Incident-shock velocities
were determined using a series of five PCB model 11A36
piezoelectric pressure gauges. Reflected-shock pressure and
temperatures were calculated from these velocities using frozen
chemistry one-dimensional shock wave theory. An earlier study
at similar conditions has shown that, over the reflected shock
test time of approximately 1 ms, temperature and pressure vary
no more than the experimental uncertainty of 1.5%.18
the refractive index of the crystal with an RF frequency (ωRF
)
results in a phase-modulated laser beam with a central frequency
To reduce the uncertainty in the initial NH3 concentration
due to wall adsorption effects, mixtures were prepared continu-
ously by a flow controller system (Hastings 0-3 slpm and Sierra
Flow 0-2 slpm) from two commercial gas mixtures containing
nominally 1% NH3 (Praxair) and 2% NO (Praxair), respectively.
The NO mixture was analyzed by the manufacturer upon
completion of the experiments and was found to contain 86 ppm
of NO2, corresponding to 8.6 ppm of NO2 in the final mixture.
CHEMKIN calculations with the mechanism of Miller and
Glarborg revealed that the effect of the NO2 impurity on the
determined branching ratio varies from less than 0.005 at lower
temperatures to about 0.02 at higher temperatures. The influence
of the small NO2 impurity was taken into account in the data
analysis and for the estimation of the measurement uncertainties.
The uncertainty in the reactant mixture composition due to
uncertainties in the base mixtures and the mixing process is
less than 1%. Before each shock, the shock tube was flushed
for at least 10 min with the mixture at the initial pressure of
the experiment and the shock was performed with a delay of
less than 30 s after the flow was stopped.
(ωL) and sidebands with the frequencies ωL + ωRF and ωL -
ωRF. In the absence of any absorber, each of the two sidebands
forms a beat signal with the central band and the two beat signals
are displaced in phase by 180° and equal in amplitude, so that
they completely cancel and, ideally, no RF amplitude modulation
is observed. When the phase-modulated beam propagates
through an absorbing medium, differential absorption or phase
shift between the two sidebands leads to imperfect cancellation
of the two beat signals and, hence, to an amplitude modulation
of the laser beam. Shock tube related distortions such as
scattering and beam steering influence both sidebands equally
and accordingly do not set the limit on the minimum detectable
fractional absorption of the experiment.
In the limit of small absorption, dispersion and modulation
index the signal detected at the modulation frequency is given
by20
IFM ) MI0[(δ+ - δ-) cos θ + (φ- - 2φc + φ+) sin θ] (11)
where M is the sideband modulation index, I0 is the intensity
of the carrier beam, δ+ and δ- are the amplitude attenuations
For the laser flash photolysis, a Lambda-Physik (Compex
102) ArF excimer laser producing ∼60-mJ pulses at 193 nm
at the higher and lower sideband frequencies, respectively, φ ,
-

Shock Tube Study of Product Branching Ratio
J. Phys. Chem. A, Vol. 103, No. 11, 1999 1569
φc, φ are the optical phase shifts at the sideband and carrier
+
frequencies, respectively, and θ is the absolute phase between
the reference and the beat signal at the mixer. Due to careful
alignment of the phase θ to 0° the signal becomes proportional
to the differential absorption between the two sidebands only.
Absolute concentrations of the detected species can be calculated
from the measured signal IFM if the response characteristic of
the electronic setup has been calibrated and if the absorption
spectrum of the detected transition is known.
We have used the A˜ 2A1fX2B1(090f000)ΣPQ1,N7 doublet
lines for the detection of the NH2 radical. This feature has been
previously used for the detection of the NH2 radical by con-
ventional narrow-bandwidth laser absorption. Its absorption line
shape has been measured by rapid scanning laser absorption,
and we have recently redetermined its average line strength.17,24
Furthermore, we have recently measured the FM spectrum of
this feature in shock tube experiments and have shown that the
measured FM line shape is well reproduced by the line shape
calculated from the measured absorption line shape and line-
strength.25 The FM spectrum of the A˜ 2A1fX2B1(090f000)-
ΣPQ1,N7 overlapping doublet shows two extrema at 16739.79
and 16740.00 cm-1. A carrier wavelength of 16739.79 cm-1
was used throughout this work. Details of the calibration
procedure for quantitative FM measurements in shock tubes are
given in ref 25.
Figure 3. Thin lines: normalized NH2 concentration time profiles for
three different temperatures. Experimental conditions: [NH3] ) 1%,
[NO] ) 0.2%, p = 1.3 atm. One arbitrary concentration unit corresponds
to NH2 mole fractions of 5.5, 7.3, and 4.8 ppm at 1351, 1524, and
1652 K, respectively. Bold lines: CHEMKIN fits with R as a single
fit parameter.
magnitude lower than the minimum detectivities achieved with
the classical narrow line width absorption method19 (0.1%
absorption). Furthermore, in the case of the FM measurements
the noise shows a nearly statistical frequency characteristic. This
means that even lower minimum detectivities than stated above
can be achieved if, as in the current study, the signals vary on
a sufficiently long time scale to allow a reduction of the
measurement bandwidth. In contrast, the shock tube related noise
in classical narrow line width laser absorption measurements
has a characteristic low-frequency component that interferes with
the time scale of the measurement so that reducing the
bandwidth does not improve the signal-to-noise ratio (S/N) as
much as expected with purely statistical noise. For this reason
FM detection becomes even more favorable compared to
classical laser absorption detection if the observed concentration
changes take place on a long time scale relative to the detection
bandwidth.
In the experimental setup, a Spectra-Physics model 380 ring
dye laser operated with rhodamine 6G dye and pumped with
the 4 W all-lines output of a Spectra-Physics model 164 Ar+
laser was used as the narrow line width laser source. The output
wavelength was monitored with a Burleigh WA-10 wavemeter.
The probe beam was phase modulated at a frequency of 600
MHz by a Quantum Technology model TWAP-10 nonresonant
modulator. Residual amplitude modulation (RAM) in the
electrooptic modulator was minimized by careful adjustment
of the input polarization of the laser beam and the modulator
alignment and was found to form a constant background on
the differential output on the time scale of the experiments. The
relative intensity of the sidebands as well as the single-mode
nature of the carrier beam were monitored with a Spectra Physics
model 470 8-GHz scanning interferometer in the transmissive
mode. The same interferometer in the reflective mode was used
to calibrate the response of the electronic setup by simulta-
neously measuring the FM and absorption signal of the reflective
etalon. Radio frequency power into the phase modulator was
adjusted to give first-order sidebands with typically 10-15%,
each, of the carrier frequency intensity.
4. Results and Discussion
Figure 3 shows normalized NH2 concentration time profiles
for three different temperatures. As expected from the simula-
tions described in section 2, a qualitative change in the overall
chain-branching behavior from carrier decay at lower temper-
atures to carrier growth at higher temperatures is observed. The
temperature where the NH2 concentration change switches from
negative to positive and where the branching ratio reaches R )
0.5 can be determined with very high accuracy to be close to
1600 K. In the temperature range from 1340 to 1670 K,
branching ratios were determined by fitting NH2 profiles using
CHEMKIN simulations with R as a single fit parameter. Such
simulations are shown along with the corresponding measured
concentration traces in Figure 3. Table 1 and Figure 4 present
results for the branching ratio as a function of temperature. An
increase in R from 0.42 at 1340 K to 0.53 at 1670 K is observed.
Over the limited temperature range of the measurements, the
branching ratio is well fit by the following linear expression:
The modulated beam was slightly focused through the shock
tube 2 cm from the end-wall, and the transmitted beam with an
intensity of 2 mW was focused on a New Focus model 1601
detector with a bandwidth of 1 GHz. The ac signal from the
photodetector was filtered by a band-pass filter combination,
amplified (Minicircuits ZFL-1000LN) with gain of 24 dB, and
demodulated by a double balanced mixer (Minicircuits ZFM-
2000). The local oscillator was driven at ωRF with a cable of
adjustable length in order to match the phase so that only the
absorption part of the FM signal was detected. The output signal
was amplified by a factor of 10 by a low-noise amplifier with
a bandwidth of 1 MHz (Stanford Research Systems model
SR560) and was stored in a laboratory computer for subsequent
data analysis.
R ) 0.5 + (3.36 × 10-4)(T/K - 1600)
(12)
With our current FM setup a detection limit of 0.5 ppm NH2
at 1500 K with a bandwidth of 1 MHz (S/N ) 1) can be
routinely achieved. This corresponds to a minimum detectable
absorption of less than 0.01% and is more than 1 order of
As pointed out in section 2, in a temperature range where R
is approximately 0.5 we expect the determination of the
branching ratio to be insensitive both to secondary reactions

1570 J. Phys. Chem. A, Vol. 103, No. 11, 1999
Votsmeier et al.
Figure 4. Determined branching ratio, R, as a function of temperature.
Thin error bars: estimated uncertainty including measurement errors,
uncertainty of secondary reactions, and the effect of the overall rate
coefficient koverall. Bold error bars: estimated uncertainty not including
Figure 5. The sensitivity of the determined values for the branching
ratio, R, to the overall rate coefficient koverall
.
rate coefficient become available. Furthermore, as pointed out
in sections 1 and 2, the simplified chain process used to deter-
mine R is very similar to the chain process of the actual De-
NOx process. Therefore, for consistent De-NOx modeling the
present values for R are most advantageously used in combina-
tion with the Miller-Glarborg values of koverall that were used
to determine the branching ratio from the NH2 profiles.
the effect of uncertainty in koverall
.
TABLE 1: Measured Branching Ratios as a Function of
Temperature
temp (K)
R
temp (K)
R
1338
1351
1355
1356
1359
1366
1371
1423
1436
1448
1453
1459
0.415
0.420
0.420
0.420
0.420
0.425
0.425
0.430
0.440
0.445
0.450
0.450
1480
1484
1524
1539
1550
1552
1559
1570
1572
1611
1652
1674
0.460
0.460
0.475
0.475
0.490
0.485
0.480
0.485
0.495
0.510
0.515
0.530
Sensitivity calculations indicate that for the temperature range
of this study, apart from the overall rate coefficient koverall, the
only secondary reaction rate coefficient that, when varied within
its uncertainty range, significantly affects the determination of
R is the rate of the unimolecular decomposition of the NNH
radical. This sensitivity is due not so much to a particularly
high sensitivity to the lifetime τNNH of the NNH radical, but
rather to the current large uncertainty in τNNH. While theoretical
studies predict a lifetime ranging from 10-10 to 10-8 s, Miller
and Glarborg5 have pointed out that a lifetime on the order of
10-7 s is required in order to consistently model De-NOx
behavior. For our data analysis we adopted the value of τNNH
) 10-7 s from Miller and Glarborg, which can be viewed as an
upper limit of the possible values for τNNH. Decreasing the value
used for τNNH in the data analysis to 10-8 s leads to slight
decrease in the values obtained for R by about 4% at the lower
end and by less than 1% at the higher end of our temperature
range. For lifetimes below 10-8 s, NNH completely dissociates
unimolecularly and no further sensitivity to τNNH is observed.
The influence of changing the value of τNNH used for the data
analysis from τNNH ) 10-7 s to a value below 10-8 s for the
temperature range of our measurements can be represented by
and to the overall rate coefficient of reaction 1. For temperatures
further removed from this point, some sensitivity to the overall
rate coefficient koverall is expected. For the data analysis, the
overall rate coefficient kov,M+G from Miller and Glarborg 5 was
used:
kov,M+G ) (1.3 × 1016)(T/K)-1.25 × mol-1 cm3 s-1 (13)
The dependence of the determined R values on the assumed
overall rate coefficient koverall is shown for different temperatures
in Figure 5. If one assumes an uncertainty range for koverall of
0.7kov,M+G < koverall < 1.5kov,M+G, a relative uncertainty in R,
induced by the uncertainty of koverall, of about 9% at the lower
end and of about 7% at the higher end of our temperature range
is observed.
Since the uncertainty induced by the overall rate coefficient
is relatively large compared to other error sources in the
determination of R, we have chosen to fully parametrize the
dependence of the determined values R on the assumed overall
rate coefficient. Over the temperature range of the measurements
and the uncertainty range of koverall specified above, the
dependence of the determined R values on the assumed overall
rate coefficient koverall is well represented by
R(τNNH<10-8 s) ) R(τNNH)10-7 s)[0.993-0.0323/(1 +
(T/1471.5 K)44.22)] (15)
This equation can be used to correct the present results for R if
more accurate information on τNNH becomes available.
In Figure 4 two different sets of error bars are shown. The
bold error bars show the estimated uncertainty that includes the
statistical error due to measurement uncertainties, the systematic
error due to the uncertainty in τNNH, and the uncertainties
involved in taking into account the NO2 impurity. It does not
include any uncertainty resulting from errors in the overall rate
coefficient koverall. The rationale for displaying these error bars
is to show the uncertainty in R when the overall rate coefficient
is determined with high enough accuracy so that the error
induced in the determination of R becomes insignificant. The
R ) Req12[1 + (1.169 - (7.168 × 10-4)T/K)y +
(-0.931 + (5.723 × 10-4)T/K)y2] (14)
where y ) (koverall/kov,M+G - 1). Equation 14 allows adjustment
of the present results, when more precise data on the overall

Shock Tube Study of Product Branching Ratio
J. Phys. Chem. A, Vol. 103, No. 11, 1999 1571
allow a precise determination of this branching ratio R ) k1a/
(k1a + k1b). Sensitive frequency-modulation detection of the
chain carrier, NH2, enables experiments with very low initial
radical concentrations and, hence, virtually no dependence on
secondary reactions and the overall rate coefficient of reaction
1. The branching ratio is found to increase from 0.42 at 1340
K to 0.53 at 1670 K, in good agreement with a recent De-NOx
modeling study by Glarborg et al.,14 with lower temperature
measurements by Park and Lin9,11 and by Bulatov et al.,7 and
with a recent reinterpretation of the higher temperature data in
refs 11 and 12.13
Acknowledgment. This work was supported by the Depart-
ment of Energy, Office of Basic Energy Sciences, Division of
Chemical Sciences. M.V. thanks the Deutsche Forschungs-
gemeinschaft for a research fellowship. We are thankful to
Trevor Sears and co-workers at Brookhaven National Laboratory
for sharing their experience with frequency-modulation kinetics
experiments. Discussions with Prof. H. Gg. Wagner and co-
workers about the application of FM spectroscopy for shock
tube measurements and the helpful assistance of Dr. David
Davidson at Stanford are acknowledged.
Figure 6. Summary of results for the branching ratio, R, as a function
of temperature.
fine error bars in Figure 4 display the error including the
uncertainty resulting from koverall if one assumes as an uncertainty
range for the overall rate coefficient: 0.7kov,M+G < koverall
1.5kov,M+G
<
.
References and Notes
Figure 6 shows a summary of the reported data for the
branching fraction of the NH2 + NO reaction. The present values
for R are consistent with the results of the recent De-NOx
modeling study by Glarborg et al.14 and the lower temperature
data of Park and Lin9,11 and of Bulatov et al.7 There is also
good agreement with the higher temperature data obtained in a
NH3/NO flame velocity modeling study by Vandooren et al.15
and Brown and Smith16 and with the results of a recent shock
tube study by Deppe et al.,26 who determined the branching
ratio in the temperature range from 1500 to 2000 K directly
from product measurements. A combined fit to these data sets
and our data gives the following fit expression for R as function
of temperature:
(1) Lyon, R. K. U.S. Pat. 3,900,554, 1975.
(2) Lyon, R. K. Int. J. Chem. Kinet. 1976, 8, 315.
(3) Miller, J. A.; Bowman, C. T. Prog. Energy Combust. Sci. 1989,
15, 287.
(4) Glarborg, P.; Dam-Johansen, K.; Miller, J. A.; Kee, R. J.; Coltrin,
M. E. Int. J. Chem. Kinet. 1994, 26, 421.
(5) Miller, J. A.; Glarborg, P. Springer Ser. Chem. Phys. 1996, 61,
318.
(6) Atakan, B,; Jacobs, A.; Wahl, M.; Weller, R.; Wolfrum, J. Chem.
Phys. Lett. 1989, 155, 609.
(7) Bulatov, V. P.; Ioffe, A. A.; Lozovsky, V. A.; Sarkisov, O. M.
Chem. Phys. Lett. 1989, 161, 141.
(8) Stephens, J. W.; Morter, C. L.; Farhat, S. K.; Glass, G. P.; Curl, R.
F. J. Phys. Chem. 1993, 97, 8944.
(9) Park, J.; Lin, M. C. J. Phys. Chem. 1996, 100, 3317.
(10) Kimball-Linne, M. A.; Hanson, R. K. Combust. Flame 1986, 64,
337.
(11) Park, J.; Lin, M. C. J. Phys. Chem. 1997, 101, 5.
(12) Halbgewachs, M. J.; Diau, M. J.; Mebel, A. M.; Lin, M. C; Melius,
C. F. 26th Symposium (Int.) Combustion; The Combustion Institute:
Pittsburgh, PA, 1996; p 2106.
(13) Park, J.; Lin, M. C. J. Phys. Chem. Submitted for publication.
(14) Glarborg, P.; Kristensen, P. G.; Dam-Johansen, K.; Miller, J. A. J.
Phys. Chem. A 1997, 101, 3741.
(15) Vandooren, J.; Bian, J.; van Tiggelen, P. J. Combust. Flame 1994,
98, 402.
(16) Brown, M. J.; Smith, D. B. 25th Symposium (Int.) Combustion;
The Combustion Institute: Pittsburgh, PA, 1994; p 1011.
(17) Kohse-Ho¨inghaus, K.; Davidson, D. F.; Chang, A. Y.; Hanson, R.
K. J. Quant. Spectrosc. Radiat. Transfer 1989, 42, 1.
(18) Chang, A. Y.; Rea, E., Jr.; Hanson, R. K. Appl. Optics 1987, 26,
885.
R ) 0.057 + (7.01 × 10-6)(T/K)1.503
(16)
There are obvious discrepancies between this best fit expres-
sion and the sharp increase in the branching fraction between
950 and 1200 K reported by Kimball-Linne et al.,10 Halbgew-
achs et al.,12 and Park and Lin.11 A recent reinterpretation of
the higher temperature experimental data of refs 11 and 12 by
Park and Lin13 yield values of R that are in agreement with the
present results. Comparison with our results further indicates
that the earlier lower temperature studies by Atakan et al.6 and
Stephens et al.8 seem to have underestimated the increase of R
with temperature.
(19) Hanson, R. K. In Proceedings of the 19th Shock Tube Symposium;
Marseille, 1993; p 7.
(20) Bjorklund, G. C. Opt. Lett. 1980, 5, 15.
(21) Whittaker, E. A.; Wendt, H. R.; Hunziker, H. E.; Bjorglund, G. C.
Appl. Phys. B 1984, 35, 105.
(22) North, S. W.; Ruian, F.; Sears, T. J.; Hall, G. E. Int. J. Chem. Kinet.
1997, 29, 127.
5. Conclusion
A photolytically initiated radical chain process in NH3/NO/
Ar mixtures with an overall branching behavior that is nearly
exclusively controlled by the branching ratio of the two reactions
(23) Bjorklund, G. C.; Levenson, M. D.; Lenth, W.; Ortiz, C. Appl. Phys.
B 1983, 32, 145
(24) Votsmeier, M.; Song, S.; Davidson, D. F.; Hanson, R. K. Submitted
for publication.
(25) Votsmeier, M.; Song, S.; Hanson, R. K submitted for publication.
(26) Deppe, J.; Fiederichs, G.; Ibrahim, A.; Romming, H.-J.; Wagner,
H. Gg. Phys. Chem. Chem. Phys. 1999, 1, 427.
NH2 + NO f N2H + OH
NH2 + NO f N2 + H2O
(1a)
(1b)
is described. Shock tube measurements of this chain process