Kinetics of atomic nitrogen photofragment produced by laser photodissociation of N2O

Article abstract of DOI:10.1021/jp0039058

The kinetics of ground-state atomic nitrogen photofragments produced by laser photodissociation of nitrous oxide have been investigated using two-photon LIF. A single 207 nm laser pulse was used for both N₂O photolysis and N atom two-photon LIF. The dependency of the LIF signal with laser power indicated that the observed N atom fragment was produced by N₂O dissociation via single-photon absorption. Effects of translational energy of the N atom fragment were detected in collisional quenching rates of the two-photon excited N atom (3p)⁴S state as observed in the decay lifetime of the induced fluorescence. The mean translational kinetic energy of the N atom fragment was determined to be 0.6 ± 0.2 eV from the quenching data. An analysis of the Doppler broadened absorption line shape of the recoiling atomic nitrogen confirmed the mean kinetic energy and further presented a model speed distribution and anisotropy parameter that was consistent with the line shape data. The NO translational and internal energies of 0.3 ± 0.1 eV and 0.2 ± 0.1 eV, respectively, were also assigned by momentum and energy conservation.

Full text of DOI:10.1021/jp0039058

J. Phys. Chem. A 2001, 105, 5977-5983
5977
Kinetics of Atomic Nitrogen Photofragment Produced by Laser Photodissociation of N2O
Steven F. Adams* and Charles A. DeJoseph, Jr.
Air Force Research Laboratory, Wright Patterson Air Force Base, Ohio 45433
Christopher C. Carter and Terry A. Miller
Laser Spectroscopy Facility, Department of Chemistry, The Ohio State UniVersity, Columbus, Ohio 43210
James M. Williamson
InnoVatiVe Scientific Solutions Inc., Dayton, Ohio 45440
ReceiVed: October 23, 2000; In Final Form: March 15, 2001
The kinetics of ground-state atomic nitrogen photofragments produced by laser photodissociation of nitrous
oxide have been investigated using two-photon LIF. A single 207 nm laser pulse was used for both N
photolysis and N atom two-photon LIF. The dependency of the LIF signal with laser power indicated that the
observed N atom fragment was produced by N O dissociation via single-photon absorption. Effects of
2
O
2
translational energy of the N atom fragment were detected in collisional quenching rates of the two-photon
4
excited N atom (3p) S state as observed in the decay lifetime of the induced fluorescence. The mean translational
kinetic energy of the N atom fragment was determined to be 0.6 ( 0.2 eV from the quenching data. An
analysis of the Doppler broadened absorption line shape of the recoiling atomic nitrogen confirmed the mean
kinetic energy and further presented a model speed distribution and anisotropy parameter that was consistent
with the line shape data. The NO translational and internal energies of 0.3 ( 0.1 eV and 0.2 ( 0.1 eV,
respectively, were also assigned by momentum and energy conservation.
Introduction
Atomic nitrogen is commonly produced for laboratory or
industrial applications by dissociation of N2 in a glow discharge.
A glow discharge source is a relatively efficient method of N
atom production, but the various radical species produced in
the discharge source as well as the excessive background
radiation can be prohibitive for some laboratory measurements.
Laser photolysis of a nitrogen containing molecule can also be
considered for atomic nitrogen production, with the advantage
of eliminating the radical species and background radiation
concerns of a discharge source. The photolysis technique would
be especially useful if a molecule is used with a dissociation
energy that matches the photon energy for the N atom two-
photon absorption laser-induced fluorescence (TALIF) detection
technique. The molecule can thereby be photodissociated and
the atomic photofragment detected by TALIF within the same
laser pulse. Both H atoms and O atoms have previously been
produced and probed by TALIF in this manner. The H and O
Figure 1. Energy level diagram of N O, including dissociative
2
2
pathways from N O excited states obtainable by absorption of 207 nm
radiation with resulting N
along with a superposition of the N atom TALIF process.
2
-O and N-NO photofragment pairs shown
1
2
atoms were produced from the photolysis of C2H2 and NO2
can be used to determine the cell view factor for use with other
atomic sources, such as a discharge.
with laser wavelengths of 205 and 226 nm, respectively, and
probed by TALIF with the same laser pulse. Such photodisso-
ciation/TALIF techniques have been used to calibrate the TALIF
signal collection view factor in a reactor cell that has spatial
regions of restricted view. The reactor cell can be uniformly
filled with the precursor molecule, which results in a spatially
uniform atomic density and corresponding TALIF intensity,
except where the view is restricted. The data from a spatial scan
of the photodissociation induced TALIF signal in a reactor cell
Nitrous oxide is investigated here as a suitable precursor for
producing ground-state N atoms by photodissociation with
4
subsequent TALIF via the (3p) S° state using 207 nm laser
3/2
light. An energy level diagram for N O is presented in Figure
2
1 and shows the dissociative pathways from N O excited states
2
3
below 6 eV, which is the photon energy of 207 nm radiation.
The resulting photofragment pairs of N2-O and N-NO are both
included in Figure 1, along with a superposition of the N atom
energy levels involved in the subsequent TALIF process.
*
Corresponding author.
1
0.1021/jp0039058 CCC: $20.00 © 2001 American Chemical Society
Published on Web 06/05/2001

5978 J. Phys. Chem. A, Vol. 105, No. 25, 2001
Adams et al.
1
Since the photodissociation channel resulting in N2 and O( D)
nitrogen. The Doppler analysis provided results consistent with
the quenching analysis.
involves spin-allowed transitions, this combination of photo-
fragments is the predominate photolysis pathway compared to
the path producing NO and N( S), which involves spin forbidden
4
Experiment
transitions. The kinetics of the predominate N2-O photofrag-
ment pair have been studied extensively,4-7 while no detailed
investigation of the NO-N photofragment kinetics has been
A. Two-Photon LIF Detection of Atomic Nitrogen. A single
ultraviolet laser pulse was used to both photodissociate N2O
and detect atomic nitrogen by the TALIF technique. Laser
excitation for the photodissociation and TALIF technique was
at 207 nm with the fluorescence detected at 747 nm.10 The
energy level diagram of the N atom TALIF scheme is included
in Figure 1, with the upper state of the scheme being the (3p)
4
reported. Suzuki et al. reported laser photodissociation of N2O
at 205 nm, where the percent branching ratios of the primary
paths were measured to be
hν
1
1
N O
9
8 N (X Σ) + O( D)
(∼90%)
(∼5%)
(∼2%)
2
2
4
S°3/2 state. For convenience, two different laser configurations
hν
were used in separate experiments to generate the 207 nm laser
pulse. A Nd:YAG pumped dye laser system including two
nonlinear optic crystal frequency conversions was used for the
collisional quenching and laser power dependency analyses. The
second harmonic output of the Nd:YAG pumped DCM dye to
produce a 620 nm beam, which was then frequency doubled
with a KDP crystal to generate 310 nm radiation. The doubled
dye was then mixed with the residual dye fundamental in a BBO
crystal to produce 0.2 mJ of 207 nm radiation. The temporal
profile of the 207 nm laser pulse, which was needed for the
TALIF quenching analysis, was determined with a photodiode
to be roughly Gaussian with a width of 6.0 ns (fwhm). A high-
energy ultraviolet variable attenuator was used for the laser
power dependency analysis, with the laser pulse energy
determined with a pyroelectric joulemeter. A second dye laser,
operating with Fluoroscene 2 dye and pumped by a XeCl
excimer laser, was employed for the Doppler broadening
measurements. The 414 nm dye laser output was frequency-
doubled with a BBO to generate 0.2 mJ of 207 nm laser pulse.
In both configurations, the atomic nitrogen fluorescence from
the 207 nm laser pulse was collected with a single 7.5 cm focal
length f/1 lens. The fluorescence was passed through a 10 nm
bandwidth interference filter centered at 747 nm and imaged
onto a Hamamatsu R928 photomultiplier tube. The temporal
response function of the detection system was found to have a
time constant of 6.4 ns, which was used in the TALIF quenching
analysis. The time-resolved TALIF signal was recorded with a
digitizing oscilloscope.
1
1
N O
98 N (X Σ) + O( S)
2
2
hν
9
1
3
N O
8 N (X Σ) + O( P)
(1)
2
2
The secondary dissociative branch that produces the NO-N
photofragment pair is
hν
2
4
N O
9
8 NO(X Π) + N( S)
(2)
2
which has been shown to exist4,8 but with an upper bound of
2
% of the primary process.
Despite the seemingly low yield of N atoms, the photolysis
of N2O is a more efficient source of atomic nitrogen than the
photolysis of NO2 or NO with λ > 200 nm. Bengtsson and
co-workers reported N2O photolysis and two-photon absorption
as the first step in a process that further excited the N atoms
from the (3p) S°3/2 state to a series of Rydberg states by single-
photon absorption using a secondary dye laser beam. They
produced ground state N atoms in a few hundred milliTorr of
N2O and detected N atoms via TALIF. However, the published
8
9
4
4
data indicated that the upper (3p) S°3/2 state of the TALIF
scheme was severely quenched as the N2O pressure neared 0.5
Torr. The authors claimed that a lack of a well-defined collision
partner in the interaction region prevented any analysis of the
quenching. The quenching rate was not stated but, by inspection,
can be seen to be much greater than the quenching rate due to
N2 measured at 300 K.10 This severe quenching could limit the
usefulness of the technique, since a higher pressure nitrous oxide
environment would be necessary to produce more N atoms.
Bengtsson also did not investigate the energetics of the N2O
photodissociation process that produced the N atom fragment,
which left in question whether the dissociation was prompted
via single- or multiphoton absorption.
In this work, nitrous oxide photodissociation and atomic
nitrogen TALIF detection were both accomplished with a single
pulse of 207 nm laser radiation. The N2O photodissociation
event that produced the observed N atom fragments was
experimentally determined to be a single-photon process. The
B. N Atom Detection Cell. Photodissociation of N2O and
laser detection of atomic nitrogen were conducted in a quartz
cell with Suprasil laser entry and exit windows which had a
third window (quartz) perpendicular to the entry and exit
windows for monitoring the fluorescence. Gas flow to the cell
was from a 2.5 cm diameter quartz tube, through which either
a slow flow of N2O or the products of an N2 microwave
discharge, including atomic nitrogen, were carried to the laser
interaction region. A diagram of the laser photodissociation and
detection cell is shown in Figure 2. For the photolysis experi-
ments, the N2O would flow from a sidearm gas inlet directly to
the laser interaction cell where photodissociation and TALIF
detection would occur. The experimental conditions included a
5 sccm slow flow of pure nitrous oxide with no active discharge.
For experiments requiring production of atomic nitrogen in a
discharge, N2 flowed through a sidearm gas inlet within an
Opthos 2.45 GHz microwave discharge cavity before entering
the laser interaction cell (shown as an option in Figure 2). The
sidearm gas inlets were positioned so that N2O could be added
downstream of the discharge but before the laser probe region
to test the collisional quenching effect of N2O on the excited
4
quenching rate of the N atom (3p) S°3/2 TALIF upper state was
experimentally determined within the laser photolysis region.
The N atom (3p) 4S°3/2 state quenching by N2O was then
independently investigated using a microwave discharge N atom
source and mixing N2O in the flowing afterglow region.
4
Quenching of the N atom (3p) S°3/2 state in the photolysis
environment was found to have a much higher rate than the N
atom (3p) 4S°3/2 quenching by N2O alone in the flowing
afterglow, which was attributed to the excessive kinetic energy
imparted to the atomic nitrogen photofragment during N2O
photodissociation. The Doppler broadened two-photon absorp-
tion line shape of the recoiling atomic nitrogen photofragment
was fit with a model kinetic energy distribution of atomic
4
atomic N (3p) S°3/2 state. When the N2O was added to the
flowing afterglow region of the microwave discharge, the N2
partial pressure was maintained at 2 Torr. With the TALIF signal

Kinetics of Atomic Nitrogen Photofragment
J. Phys. Chem. A, Vol. 105, No. 25, 2001 5979
Figure 2. Diagram of the laser photodissociation and detection cell
including the sidearm that provides option of N
discharge.
2
flowing microwave
Figure 3. Laser pulse energy dependency plot of the two-photon LIF
signal of the atomic nitrogen photofragment produced from photodis-
2
sociation of N O.
quenching effects of N2 well established,10 the quenching effect
of the added N2O was extracted from an analysis of the
fluorescence decay lifetime. Gas flow and pressure in the
microwave discharge system were governed by a mass flow
controller/downstream throttle value combination which was
controlled by an MKS-146 control unit. A diaphragm pump
backed oil free molecular drag pump evacuated the discharge
cell.
C. Fraction of Photolyzed N2O in TALIF Region. In this
work, quenching rates of the laser excited state of N atom
photogragments have been quantified and attributed to collisions
with ground state N2O. This relies on the assumption that the
number density of background N2O greatly exceeds any other
species generated during the photolysis of N2O. A rough
estimate of the number density of photofragments compared to
the N2O background gas supports this assumption. The estimated
number density of excited-state nitrous oxide, [N2O]*, produced
by 207 nm absorption can be used to gauge the number density
of photofragments in the photolysis region since most of the
excited N2O states below 6 eV are pre-dissociative. The number
density, [N2O]*, within the laser focal region can then be given
as
produced in fast secondary reactions, are not likely to be major
contributors to the N atom (3p) S°3/2 state quenching in this
experiment.
4
Results and Discussion
A. Photodissociation Energy Analysis. The 207 nm laser
power dependency of the TALIF signal was analyzed to
experimentally determine whether the N2O photodissociation
was single- or multiphoton induced. These data provided the
first experimental verification that this secondary photodis-
sociation process of N2O, producing the observed atomic
nitrogen fragment, was indeed a single-photon event, as
9
suggested in previous work. The results of the analysis are
shown in Figure 3 for a slow flow of N2O with no discharge.
Since the TALIF signal scales, within uncertainty, with the cube
of the laser pulse energy, the absorption was determined to be
a three-photon process, including a single-photon dissociation
plus the two-photon detection. The laser power dependency of
the two-photon LIF signal alone was calibrated with an N2
discharge source, which confirmed that laser saturation effects
were not a factor in the TALIF detection under the conditions
of interest.
µ
Al Io
Ia
[
N O]* ≈
(3)
B. Collisional Quenching Results. Analysis of the fluores-
cence decay from the (3p) S°3/2 state of the N atom photofrag-
2
4
ment in the presence of photolyzed N2O was done for a slow
flow of N2O at a cell pressure of 0.05 Torr to 0.8 Torr. The
decay constant determined in the analysis is equal to 1/τd, which
is defined as
where Ia/Io is the fraction of laser light absorbed within the focal
region, µ is the number of incident photons, A is the cross
sectional area of the beam focus, and l is the length of the focal
region. If the Beer-Lambert law is assumed to be valid in the
laser focal region, the laser light absorption may then be
1
1
8
expressed as
)
k [M] +
(6)
∑i qi
i
τd
τr
-kpl
I /I ) (1 - e
)
(4)
a
o
where τr is the radiative decay lifetime and the sum is over
all the species present after the N2O photolysis, with [M] being
the number density and kq the quenching rate of each species.
To determine the decay constant, 1/τd, from experimental data,
we deconvolved the temporally resolved TALIF signal from
the pulse laser temporal profile and photomultiplier temporal
response function, both of which are described in section IIA.
An example of the collisional quenching effect on the decay of
the fluorescence signal is shown in Figure 4 for background
N2O pressures of 0.2 and 0.8 Torr of N2O. The decay constant,
1/τd, is found from the deconvolved fluorescence signal to be
where k is the absorption coefficient of N2O in Torr cm-1
-
1
-
3
-1
-1
and p is the N2O pressure. With k ) 10 Torr cm for 207
1
1
nm light, p < 1 Torr, and l < 1 mm; therefore, kpl , 1 so
that
µkp
[
N O]* ≈ A
(5)
2
Thus, a nitrous oxide pressure of 0.5 Torr and a laser pulse
energy of 0.2 mJ with a beam diameter of 200 µm results in
1
4
-3
-1
-1
[
N2O]* ) 2 × 10 cm , which is approximately 1% of the
0.047 ns for 0.2 Torr and 0.080 ns for 0.8 Torr. Since the
density of each of the collision partners in the photolysis
interaction region is not known, an effective quenching rate,
[
N2O] in the region. This small [N2O]*/[N2O] fraction indicates
that the N2, O, and NO photofragments, as well as any molecules

5980 J. Phys. Chem. A, Vol. 105, No. 25, 2001
Adams et al.
4
6
-1
S3°/2 by N2 at 300 K to be kq(N ,300K) ) (2.1 ( 0.3) × 10 Torr
2
3
-
1
-11
s
or (6.7 ( 0.9) × 10 cm /s. These results are also shown
in Figure 5 for comparison with the N2O quench.
C. Discussion of TALIF Quenching by N2O. Quenching
4
of the N atom (3p) S°3/2 state by nitrous oxide at 300 K was
-
10
3
found be 4.2 × 10 cm /s, which is a factor of 6 greater than
the rate of quenching by molecular nitrogen. The measured rate,
though, is still a factor of 4 smaller than the effective quenching
rate measured in the photolysis experiments. The difference in
the quench rates between the two experiments can be shown to
be a direct result of excess kinetic energy imparted to the atomic
nitrogen during photodissociation.
To deduce kinetic information for the recoiling N atom from
the quenching data, it is necessary to determine the major
collision partners of the N atom in the photolysis region. The
molecules N2 and NO are both present in the photolysis region
as products of N2O photodissociation, but their contribution to
Figure 4. Temporally resolved experimental fluorescence signals at
.2 Torr (circles) and 0.8 Torr (triangles) of N O demonstrate the
reduction in excited-state lifetime with increased N O background
pressure due to collisional quenching. Solid lines represent the fit of
the signal decay.
0
2
2
4
the N (3p) S3°/2 quenching was calculated to be negligible during
the short lifetime of the TALIF signal. The density ratio of
photolytically produced N2 to N2O was estimated to be 1% from
the calculations in section IIC, and the [NO]-to-[N2O] ratio can
be estimated to be <0.02% when considering the branching ratio
of the secondary photodissociation path. The corresponding [N2]
and [NO] densities were determined to be too small to
substantially contribute to the observed quenching in the
photolysis region, even when assuming gas kinetic reaction rates
between the recoiling molecule and the excited N atom. Thus,
kinetic information for the recoiling N atom may be derived
4
from the effective quenching rate of N (3p) S3°/2 in the photolysis
region by assuming the quenching is due only to collisions with
N2O.
The collisional quenching rate can be expressed as
k ) 〈σ (V)V〉
(9)
4
q
q
Figure 5. Stern-Volmer plot of atomic nitrogen (3p) S
3
/2 state decay
2 2 2
with quenching by photolyzed N O products, N O, and N .
where V is the mean relative speed of collision and σq(V) is the
2
k′q, due to the collective quenching of all species is introduced
quenching cross section in cm . Over a small spread of
as
velocities, σq(V) can be assumed to be constant, given as 〈σq〉,
and can be determined by
k′[N O] ) kqi[M]i
(7)
q
2
∑i
kq
〈
σq〉 )
(10)
〈
V〉
where k′q is coupled with the number density of nitrous oxide
in the cell prior to photolysis. The results in Figure 5 show that
the species in the N2O photolysis region quench the N atom
upper state very rapidly, with an effective quenching rate of k′q
In the experiment where N2O was added to the discharge
afterglow, the excited N atoms and N2O reacting in the afterglow
were assumed to be in thermal equilibrium at T ) 300 K. The
mean relative speed between two colliding particles, each with
a Maxwellian velocity distribution, can be found by12
7
-1 -1
-9
3
)
(5.2 ( 0.9) × 10 Torr
s
or (1.6 ( 0.3) × 10 cm /s.
To isolate the quenching effects of N2O as a collision partner
4
with the N atom (3p) S3°/2 state, we introduced N2O downstream
of a 2 Torr of N2 microwave discharge. On the basis of TALIF
signal strengths, the discharge was found to produce 2 orders
of magnitude more of atomic nitrogen than photodissociation
of N2O alone. The discharge source was far enough from the
N2O interaction region that the N atoms should be thermalized
to ∼300 K. The decay constant of the TALIF upper state in
this case behaves as
8
kT
〈
V〉 )
(11)
x
πm1,2
where m1,2 ) m1m2/(m1+m2) is the reduced mass of the colliding
particles. For the case of excited N atoms and N2O colliding at
300 K, the mean relative speed is found to be 〈V〉 ) 77 300
4
cm/s, and a quenching rate for N(3p) S3°/2 by N2O of kq(N O,300K)
2
-
10
3
1
τd
1
) 4.2 × 10
cm /s with equation 10 yields 〈σq(300K)〉 ) (54
)
k
[N O] + k
[N ] +
(8)
q(N O,300K)
2
q(N ,300K)
2
-16
2
2
2
τr
( 13) × 10
cm .
Now, when the photolysis experiment is considered, the 4-fold
increase in quenching of N atom photofragments by N2O
indicates a significant N atom recoil velocity. When the
quenching rate measured in the photolysis experiment and the
quenching cross section at 300 K are used, with the assumption
that the cross section does not vary with mean relative speed,
The quenching rate, kq(N ,300K), is found by varying only the
2
partial pressure of nitrous oxide in the post-discharge mix. The
result, determined from the plot in Figure 5, is that kq(N ,300K) )
2
7
-1 -1
-10
3
(
1.3 ( 0.3) × 10 Torr
s
or (4.2 ( 1.0) × 10 cm /s. In
1
0
previous work, we determined the quenching of N atom (3p)

Kinetics of Atomic Nitrogen Photofragment
J. Phys. Chem. A, Vol. 105, No. 25, 2001 5981
the average N atom recoil velocity after photolysis is
-
9
3
k′
q
1.6 × 10 cm /s
) 296 000 ( 87 000 cm/s
-16 2
〈
V〉 )
)
〈
σ 〉
q
54 × 10 cm
(12)
The average kinetic energy of the atomic nitrogen photofrag-
ment, given by
1
2
2
〈
ꢀ 〉 ) m〈V〉
(13)
N
is then 0.6 ( 0.2 eV, or ∼16 times the kinetic energy of atomic
nitrogen at 300 K.
This value of 〈ꢀN〉 can be checked against the theoretically
maximum N atom recoil energy, which is determined from the
laser photolysis photon energy (5.99 eV for 207 nm) and the
Figure 6. Two-photon absorption line shape spectrum data (circles)
for thermalized atomic nitrogen at 300 K in the afterglow produced by
a N microwave discharge where ∆νD was calculated from Doppler
2
3
N-NO bond energy (4.93 eV ). The difference in the photon
L
broadening theory and ∆ν was determined from fit (solid line).
energy and bond energy of ꢀ(N+NO) ) 1.06 eV is the energy
available for photofragment kinetic energy as well as internal
excitation of the photofragments. The maximum possible N atom
recoil kinetic energy would occur with no internal energy
excitation of the NO fragment. By conservation of momentum,
the N atom fragment would have a maximum kinetic energy of
contribution to the broadening of the two-photon absorption line
shape. Figure 6 shows the N atom absorption line shape
spectrum in the afterglow, along with a least-squares fit of eq
-
1
1
5 to the data. With ∆νD set to 0.32 cm and ∆νN negligible,
-
1
the ∆νL, the laser line width at 207 nm, is 0.63 cm . Since
this 207 nm laser line width was a system constant, a Gaussian
-
1
mNO
laser line shape component with ∆νL ) 0.63 cm was used in
the subsequent Doppler broadening analysis for the photolysis
experiment.
ꢀN(max)
)
ꢀ
(N+NO)
) 0.72 eV
(14)
mNO + mN
E. Doppler Broadening of N atom Photofragment Ab-
sorption Line. The TALIF quenching data presented in section
IIIC suggests that atomic nitrogen produced by photodissociation
of N2O recoils with an average speed that greatly exceeds the
average speed of thermalized N atoms at 300 K in the afterglow.
This increase in average speed of the atomic nitrogen photo-
fragments gives rise to an increased Doppler broadening of the
two-photon absorption line shape. In contrast to the line shape
analysis in section IIID for thermalized N atoms, the photodis-
sociation process produces a recoil velocity distribution which
This shows that the average recoil kinetic energy of 0.6 eV
found in the quenching analysis is within the upper kinetic
energy limit of 0.72 eV for the atomic nitrogen photofragment
from N2O photodissociation with 207 nm radiation.
D. Doppler Broadening of N atom Absorption Line in
Discharge. A direct method of determining the velocity of the
N atom photofragments is to analyze the Doppler broadening
of the two-photon absorption line. The experimental absorption
line shape spectrum was first studied in the afterglow of the
microwave discharge where the atomic nitrogen was, to a good
approximation, in thermal equilibrium at 300 K. For the thermal
equilibrium condition, a Maxwell-Boltzmann velocity distribu-
tion can be assumed for which a normalized two-photon
absorption line shape is
1
3
is in general nonisotropic and non-Boltzmann. Since we used
a single linearly polarized laser as the dissociation and probe
source, the velocity distribution of N atom photofragments is
1
3
of the form
1
4π
â(V)
2
2
x
ln(2)
2
W(V,θ) ) W(V) 1 -
P2(cos θ)
(17)
[
]
g(ν) )
×
2
L
2 1/2
N
x
π(2∆ν + ∆ν + 2∆ν )
D
2
where θ is the angle between the laser propagation vector and
the recoil direction, W(V) is the normalized N atom speed
distribution averaged over all angles, P2 is the second Legendre
4
ln(2)(2ν - νo)
exp -
(15)
(
2
2
2
)
(
2∆ν + ∆ν + 2∆ν )
L D N
3
2
1
polynomial where P2(x) ) ( /2)x - /2, and â is the anisotropy
parameter, with limiting values of 2 and -1 representing
fragment recoil parallel and perpendicular to the laser polariza-
tion, respectively.
where ∆νL is the fwhm frequency spread of the laser radiation,
νN is the natural line width of the two-photon transition, which
is usually comparatively small, and ∆νD is the fwhm of the
Doppler broadening of the line. The fwhm of the Doppler
broadened line is given by the formula8
∆
The parameter V can be defined for convenience as the
velocity component of a recoiling N atom in the direction of
k
laser beam propagation, so that cos θ ) Vk/V. The Doppler
profile can then be determined as a function of Vk corresponding
to the directional distribution in eq 17. The normalized Doppler
profile, g(Vk), for a single fragment recoil speed, V, is14
2
x
2 ln(2)
c
kT
∆
νD )
νo
(16)
x
M
where νo is the peak absorption frequency, M is the atomic mass,
k is the Boltzmann constant, T is the temperature of the
absorbing species, and c is the speed of light.
The Doppler broadening of the thermalized N atoms at 300
K in the afterglow can be calculated from eq 16 to be 0.32
-1
1
2
g(V ) ) (2cν ) 1 - â(V)P (V /V) ; for V e V
k
o
[
2
k
]
k
(18)
g(V ) ) 0;
for V > V
k
k
-
1
cm . Assigning this value to the Doppler width created the
opportunity to experimentally determine the laser line width
where the latter condition gives a zero result since the velocity
component, Vk, may not exceed the recoil speed, V. The Doppler

5982 J. Phys. Chem. A, Vol. 105, No. 25, 2001
Adams et al.
profile corresponding to the entire speed distribution of recoiling
N atoms can now be determined by integrating eq 18 as
W(V)
Vνo
â(V)
2
V
k
∞
G(V ) ) ∫|Vk|2
[1 -
P2
( )] dV
(19)
k
V
For the purpose of analyzing the two-photon absorption
spectrum of the recoiling atomic nitrogen, the Doppler profile
in eq 19 can be rewritten in terms of laser frequency, ν, using
the Doppler relation ν ) νo(1 - Vk/c) so that
W(V)
â
1 - P
2
(
ν - ν )c
o
∞
G(ν) )
∫
dV (20)
2
(
)
c|ν-νo|/νo
[
]
2Vνo
Vνo
Figure 7. Normalized kinetic energy model distribution of atomic
nitrogen fragments recoiling from N O photodissociation.
2
The velocity dependence of the anisotropy parameter, â(V), was
neglected in this analysis since the precision of this measurement
did not allow for such a determination. Instead, an effective â
was determined which represented the entire speed distribution.
The convolution of the expression in eq 20 with the laser line
shape and the parent molecule Doppler distribution produces a
line shape that may be used to fit the experimental N atom
absorption spectrum.
A unique determination of both the speed distribution, W(V),
and the anisotropy parameter, â, is generally not possible when
analyzing only a single Doppler profile, such as when employing
a single laser for dissociation and probing.1 A determination
of both W(V) and â is achieved in this work by including the
additional information on the average recoil velocity of the N
atom fragments obtained through the quenching analysis in
section IIIC. The process of fitting the absorption spectrum data
included introducing various select functions of W(V) to eq 20
and varying â to find the least-squares fit to the Doppler profile
data. The W(V) functions selected for fitting included speed
distributions calculated from simple N atom kinetic energy
distributions, F(ꢀN). The velocity and kinetic energy of the
3
Figure 8. Two-photon absorption line shape spectrum data (circles)
for atomic nitrogen photofragments produced by photodissociation of
N
2
O with 207 nm laser radiation. Solid line represents best fit with eq
2
0 using the 〈ꢀ 〉 ) 0.6 eV energy distribution in Figure 7.
N
expressed in terms of the known mean kinetic energy and the
maximum kinetic energy as
1
2
atomic photofragment are related by ꢀN ) /2 mV , with their
respective normalized distributions related by
-1
F(ꢀ ) ) (ꢀ
- 〈ꢀ 〉)
×
for ꢀ e ꢀN(max)
N
N
N(max)
N
exp[(ꢀ - ꢀN(max))/ꢀ
- 〈ꢀ 〉];
N
W(V(ꢀ )) ) F(ꢀ )mV(ꢀ )
(21)
N
N(max)
N
N
N
F(ꢀ ) ) 0;
for ꢀ > ꢀ
N(max)
(24)
N
N
Kinetic energy distributions of delta functions, Gaussian func-
tions, and exponential increasing functions were introduced to
the problem with the constraints that 〈ꢀN〉 ) 0.6 ( 0.2 eV, as
determined in the quenching analysis and that F(ꢀN) ) 0 for ꢀN
The normalized kinetic energy distribution corresponding to the
energy constraints 〈ꢀN〉 ) 0.6 eV and ꢀN(max) ) 0.72 eV is shown
in Figure 7. The normalized speed distribution corresponding
to this kinetic energy distribution is
>
ꢀN(max) ) 0.72 eV, in accordance with the energy limitation
of the two-photon absorption, as discussed in section IIIC.
The absorption line shape data in this experiment were best
fit using an exponentially increasing atomic nitrogen kinetic
energy distribution, which had a normalized form of
2
2 -1
W(V) ) 2V(V
- 〈V〉 )
×
for V e V(max)
for V e V(max)
(max)
2
2
(
2
2
exp[(V - V max))/(V
- 〈V〉 )];
(25)
(max)
W(V) ) 0;
F(ꢀ ) ) 1/b exp[(ꢀ - ꢀ
)/b]; for ꢀ e ꢀ
N
N
N(max)
N
N(max)
N(max)
(22)
The expression in eq 25 is the N atom photofragment speed
distribution that was used, along with eq 20 and convolved with
eq 15, to determine the anisotropy parameter â by least-squares
fit to the measured line shape data. For the line shape function
F(ꢀ ) ) 0;
for ꢀ > ꢀ
N
N
where 1/b determines the exponential rise of the function. The
mean kinetic energy of this distribution is
-1
in eq 15, we set ∆νL ) 0.63 cm and assumed ∆νN to be
negligible, as found in section IIID, and the fwhm of the Doppler
broadening due to the parent N2O speed at 300 K from eq 16
to be ∆νD ) 0.18 cm .
The result of the fitting process is shown in Figure 8, in which
the data was best fit using an N atom distribution with 〈ꢀN〉 )
0.6 eV and a â value of 1.4 ( 0.2. To determine the uncertainty
in â across the range of 〈ꢀN〉 ) 0.6 ( 0.2 eV, we also fit the
data with N atom distributions corresponding to the upper and
-
(
ꢀN(max)
〈
ꢀN〉 ) ꢀ
- b 1 - exp
(23)
N(max)
[
)
]
-1
b
which can be approximated by 〈ꢀN〉 ) ꢀN(max) - b since ꢀN(max)
is sufficiently large compared to b for this set of data. The
constant b can then be given as b ) ꢀN(max) - 〈ꢀN〉, which allows
the atomic nitrogen kinetic energy distribution function to be

Kinetics of Atomic Nitrogen Photofragment
J. Phys. Chem. A, Vol. 105, No. 25, 2001 5983
4
lower limits of uncertainty for 〈ꢀN〉. The resulting best fits were
with â ) 1.9 ( 0.2 and â ) 0.4 ( 0.2 for the upper and lower
limits of 〈ꢀN〉, respectively. Since values of â > 2 are beyond
the physical limits of -1 â < 2, the result can be interpreted
that â in this experiment is within the range of 0.2-2. An
anisotropy parameter value of less than 2 suggests that N atom
recoil is not exclusively parallel to the laser polarization. The
assumption of photodissociation from a bent N2O state is
consistent with this reduced value of â.
separate measurement of N atom (3p) S°3/2 state quenching by
isolated N2O in the flowing afterglow of a microwave discharge,
where the atomic nitrogen was assumed to be thermalized at
300 K, produced a lower quenching rate of kq(N O) ) (4.2 (
2
-
10
3
1.0) ×
cm /s. The difference in the quenching rates was
attributed to a much higher mean speed of the recoiling atomic
nitrogen photofragments compared to that of the thermalized
atomic nitrogen. Analysis of the quenching data resulted in the
assignment of the mean kinetic energy of the N atom photo-
fragments as 0.6 ( 0.2 eV, with quenching almost entirely from
collisions with background N2O. According to energy and
momentum conservation for the photodissociation event, the
maximum recoil kinetic energy of the atomic nitrogen was 0.72
eV.
The Doppler broadening of the two-photon absorption
spectrum of the recoiling atomic nitrogen was also examined.
A model kinetic energy distribution of the N atom photofrag-
ments was generated which met the constraints of mean and
maximum kinetic energy values determined in the quenching
analysis. An exponentially increasing model energy distribution
produced good fits of the N atom two-photon absorption line
data. Effective anisotropy parameters from the analysis ranged
from â ) 0.2 to 2 over the average energy range of 〈ꢀN〉 ) 0.6
F. N and NO Photofragment Kinetic Energy Distribution.
In section IIIC, the total kinetic energy distributed among the
N and NO fragments after absorption of two 207 nm photons
was calculated to be ꢀ(N
+
NO) ) 1.06 eV. TALIF data has
indicated that the atomic nitrogen fragments recoil from the 207
nm photodissociation of N2O with a distribution that has a mean
N atom kinetic energy of
〈
ꢀ 〉
) 0.6 ( 0.2 eV
(26)
N trans
The partitioning of kinetic energy into the translational and
internal energy of the NO fragment can therefore be determined
by conservation of energy and momentum. By conservation of
momentum, the mean translational energy of the NO fragment
is found to be
(
0.2 eV.
Assignments were also made for the translational and internal
mN
2
energy of the NO(X Π) photofragment based on the mean
kinetic energy of the recoiling atomic nitrogen. The mean NO
translational kinetic energy was found to be 0.3 ( 0.1 eV. The
mean internal energy of the NO molecule was found to be 0.2
〈
ꢀ
〉
)
〈ꢀ 〉
) 0.3 ( 0.1 eV
(27)
NO trans
N trans
mNO
which corresponds to a mean speed of 140 000 ( 40 000 cm/s.
The remaining energy must reside as internal energy within the
NO photofragment with a mean value of
(
NO.
0.1 eV, indicative of mostly rotational excitation within the
〈
ꢀ
〉
) ꢀ(N + NO) - 〈ꢀ 〉
- 〈ꢀ 〉
NO trans
)
NO int
N trans
References and Notes
0
.2 ( 0.1 eV (28)
(
1) Tserepi, A. D.; Dunlop, J. R.; Preppernau, B. L.; Miller, T. A. J.
Appl. Phys. 1992, 72, 2638-2643.
2) Tserepi, A. D. Laser Diagnostics for Bulk and Near-Surface
Since the energy required to excite the V ) 1 state of NO from
(
15
the ground vibrational state is 0.23 eV, there is some possibility
of vibrational excitation, but the internal energy of NO is most
probably rotational in nature. The rotational excitation of the
NO photofragment is not unexpected since the N2O photodis-
sociative processes from 207 nm absorption all involve N2O
excited states that have Cs, or bent, symmetry as is shown in
Figure 1.
Detection of Atomic Hydrogen and Oxygen in Plasma Environments. PhD
thesis, The Ohio State University, Columbus, OH, 1994.
(
3) Hopper, D. G. J. Chem. Phys. 1984, 80 (9), 4290-4316.
(4) Suzuki, T.; Katayanagi, H.; Mo, Y.; Tonokura, K. Chem. Phys.
Lett. 1996, 256, 90-95.
(5) Hanisco, T. F.; Kummel, A. C. J. Phys. Chem. 1993, 97, 7242-
7
1
77-182.
(7) Shafer, N.; Tonokura, K.; Matsumi, Y.; Tasaki, S. J. Chem. Phys.
Conclusion
1991, 95, 6218-6223.
8) Okabe, H. Photochemistry of Small Molecules; Wiley: New York,
1978.
(
Photodissociation of nitrous oxide with subsequent TALIF
detection of atomic nitrogen, both using 207 nm laser radiation,
was accomplished in a low-pressure N2O cell, where the ground
(9) Bengtsson, G. J.; Larsson, J.; Svanberg, S.; Wang, D. D. Phys.
ReV. A 1992, 45, 2712-2715.
(
10) Adams, S. F.; Miller, T. A. Chem. Phys. Lett. 1998, 295, 305-
4
2
state N( S) and NO(X Π) fragments were secondary products
of this photodissociative process. Analysis of the N atom TALIF
signal as a function of laser power provided experimental
verification that the secondary photodissociation process of N2O
producing the observed atomic nitrogen fragment was a single-
311.
(
11) Zelikoff, M.; Watanabe, K.; Inn, E. C. J. Chem. Phys. 1953, 21,
1
643.
(12) Mitchner, M.; Kruger, C. H. Partially Ionized Gases; Wiley: New
York, 1973.
(13) Dubs, M.; Bruhlmann, U.; Huber, J. R. J. Chem. Phys. 1986, 84,
3106-3119.
4
photon process. The N atom (3p) S°3/2 state, excited by two-
photon absorption, was determined to be quenched by N2O in
the photolysis region at a rate of (1.6 ( 0.3) × 10 cm /s. A
(
14) Zare, R. N.; Herschbach, D. R. Proc. IEEE 1963, 51, 173.
(15) Huber, K.-P.; Herzberg, G. Constants of Diatomic Molecules; Van
-
9
3
Nostrand Reinhold: New York, 1979.