Diagnostics and kinetic modeling of the ignition and the extinction transients of a Hollow Cathode N2O discharge

Article abstract of DOI:10.1021/jp993958t

The present work describes the first experimental study of the transients involved in the turn on and off of a N₂O hollow cathode discharge until the attainment of the respective stationary states. Time-resolved Fourier transform infrared spectroscopy and quadrupole mass spectrometry with ionization by electronic impact have been used to measure the temporal evolution of the concentrations of the stable species present in the discharge N₂O, Na, O₂, NO, and NO₂. A model based on a reduced set of kinetic equations gives a global account of the measured data; this model takes into account all the mechanisms considered in a former work (Arcos, T. et al. J. Phys. Chem. A 1998, 102, 6282) to explain the steady state of a continuous N₂O discharge but includes also additional mechanisms to which transient phenomena have proven to be much more sensitive than the stationary results. In particular, excitation of some vibrational levels of N₂O and homogeneous reactions of vibrationally excited species, as well as electron impact dissociation of the stable products of the discharge are considered. On the other hand, the partial formation of NO₂ by an heterogeneous reaction previously proposed seems to be confirmed.

Full text of DOI:10.1021/jp993958t

3974
J. Phys. Chem. A 2000, 104, 3974-3983
Diagnostics and Kinetic Modeling of the Ignition and the Extinction Transients of a Hollow
Cathode N2O Discharge
T. de los Arcos, C. Domingo, V. J. Herrero, M. M. Sanz,† and I. Tanarro*
Instituto de Estructura de la Materia (CSIC), Serrano 123, 28006 Madrid, Spain
ReceiVed: NoVember 8, 1999; In Final Form: January 20, 2000
The present work describes the first experimental study of the transients involved in the turn on and off of
a N2O hollow cathode discharge until the attainment of the respective stationary states. Time-resolved Fourier
transform infrared spectroscopy and quadrupole mass spectrometry with ionization by electronic impact have
been used to measure the temporal evolution of the concentrations of the stable species present in the discharge
N2O, N2, O2, NO, and NO2. A model based on a reduced set of kinetic equations gives a global account of
the measured data; this model takes into account all the mechanisms considered in a former work (Arcos, T.
et al. J. Phys. Chem. A 1998, 102, 6282) to explain the steady state of a continuous N2O discharge but
includes also additional mechanisms to which transient phenomena have proven to be much more sensitive
than the stationary results. In particular, excitation of some vibrational levels of N2O and homogeneous reactions
of vibrationally excited species, as well as electron impact dissociation of the stable products of the discharge
are considered. On the other hand, the partial formation of NO2 by an heterogeneous reaction previously
proposed seems to be confirmed.
1. Introduction
All the studies commented on until now are restricted to the
stationary state of the various glow discharges considered;
however, the steady state condition is ultimately determined by
a competition between processes having very different rates like
electron dissociation and excitation, homogeneous, and hetero-
geneous reactions, convection, and diffusion. To investigate
more accurately the kinetics of the plasma one should perform
temporally resolved measurements with different time scales.
In this respect, the study of transients associated with the ignition
and the extinction of the discharge is a very useful tool to assess
the actual contribution of the various kind of processes to the
overall kinetics.
N2O is used in various types of glow discharges that find
widespread application in many scientific and technological
fields, including spectroscopy, kinetics, and plasma-enhanced
chemical vapor deposition (PECVD) (see references in ref 1).
Despite the undoubted interest of the cold plasmas generated
in glow discharges, the detailed kinetic modeling of these
plasmas is still a major challenge, given the high number of
interrelated concurrent processes and the lack of basic data about
many of them. Radiofrequency (RF) discharges of N2O were
systematically studied by Cleland and Hess2 and by Kline et
al.3 The two groups developed global kinetic models that were
checked by monitoring some of the species present in the
stationary discharge. Cleland and Hess2 used Fourier transform
infrared (FTIR) measurements of N2O and NO, and Kline et
al.3 employed downstream mass spectrometric measurements
of N2O, NO, N2, and O2. These models include a large set of
basic kinetic processes for the N2O plasma and the mentioned
authors discuss their relative relevance. Less exhaustive studies
have also been published for microwave discharges of mixtures
of N2O with inert gases.4,5
In a previous work of our group, the stationary state of a DC
hollow cathode N2O discharge was experimentally characterized,
and a kinetic model was proposed in order to explain the
different concentrations of the involved molecular species found
for different physical conditions.1 This model took into account
the kinetic mechanisms considered in the previous works on
RF and MW, N2O discharges, found in the literature,2-5 and
incorporated also some new heterogeneous reactions, mainly
in order to explain the relatively high NO2 concentration found
in the DC hollow cathode discharge, and not observed in
previous N2O discharges.
In the present work, “slow” transients are studied in the
system. To that end, the hollow cathode discharge is turned on
and off within a time interval of several seconds, long enough
to guarantee that the respective stationary states are reached for
all the chemical species involved in the process. As we shall
see, this time scale will be of great help to clarify the relative
influence of many of the relevant processes such as electron
impact dissociation and homogeneous and heterogeneous reac-
tions. Additional information can be obtained from the study
of “faster” transients, as it will be demonstrated in a future
paper,6 where a 45 Hz square wave modulated N2O discharge
will be studied. With this modulation, time scales of a few ms
can be reached and one can have access to the competition
between processes of excitation, deexcitation and diffusion.
To achieve a characterization as complete as possible of the
nitrous oxide plasma, FTIR absorption spectroscopy has been
used for monitoring the temporal evolution of the concentration
of the NO and NO2 produced in the discharge, whereas the
infrared inactive homonuclear products, N2 and O2, have been
detected by mass spectrometry. The N2O concentration has been
determined also with both methods. To elucidate the most
significant processes leading to the observed results, a simplified
kinetic model is proposed, based on the numerical solution of
* Corresponding author. Fax: +34.91.5855184. E-mail: itanarro@
iem.cfmac.csic.es.
† Universidad Alfonso X el Sabio, Villanueva de la Can˜ada, 28691
Madrid, Spain.
10.1021/jp993958t CCC: $19.00 © 2000 American Chemical Society
Published on Web 04/27/2000

Hollow Cathode N2O Discharge
J. Phys. Chem. A, Vol. 104, No. 17, 2000 3975
the time-dependent differential equations for the relevant species
involved in the discharge.
2. Experimental Measurements
The detailed description of the hollow cathode discharge cell
used in this work and of the method employed with the FTIR
and the quadrupole mass spectrometers to characterize the
discharge, when operated in the DC mode, is given elsewhere.1,7
Briefly, the discharge cell was designed in our laboratory, easy
to disassemble and with a symmetrical geometry of the
electrodes, to be used for both mass spectrometry and FTIR
emission and absorption spectroscopy. It consists of a cilindrical
hollow cathode made of stainless steel, 90 mm long and with a
16 mm inner diameter, and two circular anodes of copper, each
one of them placed at each end of the cathode at a distance of
25 mm and supported by an anode holder made of Pyrex and
stainless steel. The discharge is fed by a 2000 V, 150 mA,
square-wave modulated source, operative between 0 and 200
Hz. The electrodes are refrigerated by water. The discharge is
sustained in a continuous and regulable flow of N2O, evacuated
by a rotary pump, and can be maintained stable approximately
between 0.01 and 3 mbar. The cell was disassembled and
cleaned carefully, including polishing of the electrodes, periodi-
cally, and no diferences were noticed in the experimental results
obtained before and after each cleaning process. For absorption
and emission measurements, a FTIR Bruker IFS66 spectrometer
with both rapid-scan and step-scan options for the movable
mirror was used. The detection of infrared inactive homonuclear
species such as N2 and O2 generated in the discharge was done
by means of a quadrupole mass spectrometer Balzers QMG112
working as a partial pressure detector, with electron impact
ionization and a Faraday cup as the charge collector.
In the present work, the rapid-scan option of the FTIR
spectrometer was used with a deuterated triglycine sulfate
(DTGS) infrared detector to study, by time-resolved absorption
spectroscopy, a single cycle of turning on and off the discharge.
With a spectral resolution of 40 cm-1 and a mirror speed of
0.3 cm.s-1, the minimum time required to perform a complete
interferogram is ∼42 ms, and taking into account the time
interval between the end of a scan and the beginning of the
following one, a temporal resolution of 100 ms was achieved.
This resolution is enough to measure the transient phenomena
of interest in the present work with a suitable level of detail.
Two very different gas flow rates, 3 and 108 sccm, were
characterized for an initial N2O pressure of 2 mbar. The
electrical power was 45 W. Each measurement was repeated
two times and the agreement between them was very satisfac-
tory. In this kind of experiments the interferograms were not
averaged and thus, the noise level of the spectra was substantial;
therefore, the relatively weak (ν1 + 2ν2) N2O band, which was
used in the DC discharge1 to calibrate the absolute concentration
values of N2O, could not be used here for the 3 sccm gas flow
rate, where the N2O absorption signals are too small; instead,
the absorption intensity of the more intense ν3 band was
employed. The intensity of this band versus the N2O pressure
without discharge was experimentally calibrated. The NO and
NO2 concentrations were calibrated as in the previous work,1
by comparing the experimental data treated to simulate a
transmittance spectra, with the simulated data obtained from
the HITRAN database.8
Figure 1. Time dependence of the absolute concentration of N2O, NO,
and NO2, during the turn on and off of the discharge. The experimental
data obtained by rapid-scan FTIR absorption spectroscopy are compared
with the predictions of the present kinetic model. N2O starting pressure,
2 mbar; electrical power, 45 W. (a) N2O flow rate: 3 sccm. (b) N2O
flow rate: 108 sccm.
temporal evolution of the N2 and O2 relative densities was
measured with the quadrupole mass spectrometer synchronized
to the m/q ratio of the respective parent ions, and collected by
means of a digital oscilloscope working in the averaging mode.
In the case of N2, it was necessary the subtraction of a portion
of the signal corresponding to a fragment of the parent ion, N2O,
at m/q ) 28, which was a time dependent function. At the
highest gas flow rates, the mass spectrometric signals of N2
and O2 were buried in noise. The NO signals could not be
recovered suitably by mass spectrometry, due to the high
contribution of the m/q ) 30 peak from the fragmentation of
N2O. The FTIR and mass spectrometric results are shown in
Figures 1 and 2, respectively. Electron densities and mean
electron energies were taken from double Langmuir probe
measurements of the continuous N2O discharge1 and were
assumed to reach the stationary state almost instantaneously,
in comparison with the time scales of the present work.9
3. Chemical Kinetics Model
In our previous article1 a kinetic model accounting basically
for the stationary concentrations of the stable species appearing
in a DC hollow cathode N2O discharge was reported. In the
present work, this model has been improved in an attempt to
describe the transient effects observed when turning on and off
the N2O discharge, with a frequency of modulation low enough
to allow for the establishment of the respective stationary states.
The inadequacy of the previous kinetic model derived from
steady state data for the description of the transients investigated
in the present work is clearly exemplified in Figure 3, where
the measured time evolution of the concentration of nitrogen
oxides after switching on and off the discharge is shown together
with the model predictions for a slow (3 sccm) N2O flow. As
can be seen, only the evolution of the N2O precursor is
reproduced satisfactorily, but neither the initial rise nor the
subsequent decay of the NO and NO2 concentrations can be
accounted for by the model.
The time resolution of the quadrupole mass spectrometer is
determined by the gas residence time in the quadrupole vacuum
chamber, which depends on its volume (3.5 L) and the pumping
speed (300 L/s). In the present case this value is 12 ms. The

3976 J. Phys. Chem. A, Vol. 104, No. 17, 2000
de los Arcos et al.
Figure 2. Temporal evolution of the concentration of N2 and O2 during
the turn on and off of the hollow cathode N2O discharge, obtained by
mass spectrometry. The intensities of the experimental signals have
been scaled to the predictions of the present kinetic model. N2O starting
pressure, 2 mbar; electrical power, 45 W. N2O flow rate: 3 sccm.
Figure 4. Theoretical predictions of the temporal evolution of the
concentrations of all the species involved in the chemical kinetics model
for the ignition and extinction of a N2O hollow cathode discharge
operating at 2 mbar, 45 W, and 3 sccm. The stable species are
considered to be homogeneously distributed along the whole cell,
concentrations of transient species are considered to be significant only
in the plasma volume (see text).
N2 is incorporated to the model. On the other hand, the relative
importance of some heterogeneous reactions is modified after
an inspection of the time evolution of the relevant concentrations
when the discharge is turned off.
In a way similar to that in ref 1 and in previous works dealing
with the stationary state of N2O glow discharges,2-5 diffusion
effects have not been considered here because the transients of
interest in the present work are still slow enough to justify the
assumption of stable species being well mixed and occupying
all the reactor volume. Short lived species, however, are actually
considered to be confined to the plasma region.
The results of the application of the present model to the
conditions of our discharges and its comparison to the time-
resolved measurements of this work is shown in Figures 1, 2,
and 4. The predictions of the model for steady-state conditions
are compared in Figure 5 to the experimental data. In the
following, we comment on the various types of dynamic
processes that have been considered.
Dissociation Processes. Electron impact dissociation of N2O
in the plasma volume is the key process in the chemical kinetics
of the discharge and the main cause of the decrease of N2O
concentration when the discharge is turned on. As can be seen
in Table 1, three N2O electron dissociation channels have been
considered, two of them producing N2 + O, but with the oxygen
atoms in its fundamental, 3P, or in the excited, 1D state (reactions
D1 and D2), and the last one producing NO + N (reaction D3).
This latest reaction was not included in the previous work1
because NO and N are known to react very quickly through
the homogeneous reaction NO + N f N2 + O(3P), which now
is also included in the model (reaction G7), and could be
considered as intermediate stages of the first dissociation
channel. In the steady-state model, the inclusion of the two
reactions did not lead to appreciable differences; nevertheless,
both of them are taken into account in the present work, due to
their possible influence on transient effects. The respective rate
Figure 3. Temporal variation of the absolute concentrations of the
nitrogen oxides N2O, NO and NO2 during the turn on and off of the
hollow cathode N2O discharge, compared with the predictions of the
kinetic model of ref 1, based on steady-state data. N2O starting pressure,
2 mbar; electrical power, 45 W. N2O flow rate: 3 sccm.
The new model contains all the chemical reactions considered
in the former one, although some of the rate coefficients have
been revised. In addition, some physicochemical processes,
which have been revealed to be crucial for the satisfactory
reproduction of transient effects, have been included. The
previous steady state data are nearly insensitive to the inclusion
of these new processes in the model over the range of physical
conditions where the discharge has been characterized. These
results stress the importance of time-resolved measurements for
the elucidation of the contribution of particular mechanisms to
the kinetics of this kind of systems.
The kinetic model finally presented here describes not only
the present experimental measurements, but also the steady-
state DC discharge1 and is compatible too with the faster
transient data obtained with a higher modulation frequency of
the discharge which will be described in a forthcoming paper,6
although in that case diffusion effects should be taken into
account in detail.
The main modifications of the present work are now advanced
briefly: the electron impact excitation of some vibrational N2O
stretching modes and some of their deexcitation pathways are
included, and at the same time the reactivity of N2O homoge-
neous reactions is considered to be increased when some of
these excited levels are involved. Besides, the electron impact
dissociation of all the stable molecules of the discharge except

Hollow Cathode N2O Discharge
J. Phys. Chem. A, Vol. 104, No. 17, 2000 3977
TABLE 1: Reactions Included in the Kinetics Model of the
N2O Hollow Cathode Dischargea
reaction
rate constant
ref
Disocciation by Electronic Impact
D1
D1
D1
D2
D2
D2
D3
D3
D3
D4
D5
D6
D7
N2O + e- f N2 + O(3P) + e-
8.0 × 10-10
b
N2O(001) + e- f N2 + O(3P) + e-
N2O(100) + e- f N2 + O(3P) + e-
N2O + e- f N2 + O(1D) + e-
N2O(001) + e- f N2 + O(1D) + e-
N2O(100) + e- f N2 + O(1D) + e-
N2O + e- f NO + N + e-
3.7 × 10-10
1.2 × 10-10
b
b
N2O(001) + e- f NO + N + e-
N2O(100) + e- f NO + N + e-
NO + e- f N + O(3P)
8.5 × 10-10
8.5 × 10-10
4.8 × 10-11
7.2 × 10-11
b
b
b
b
NO2 + e-f NO + O(3P) + e-
O2 + e- f 2 O(3P) + e-
O2 + e- f O(3P) + O(1D)+ e-
Electronic Impact Excitation
N2O + e- f N2O(001) + e-
E1
E2
1.4 × 10-8
c
c
N2O + e- f N2O(100) + e-
1.4 × 10-8
Figure 5. Comparison between the measured concentrations of the
species involved in a (symbols) N2O continuous discharge operating
at different gas flow rates1 and the theoretical results obtained with the
(lines) present kinetic model. The discharge was maintained at a
pressure of 2 mbar, with an electrical power of 15 W.
Quenching of Excited States
N2O(001) + N2O f 2 N2O
Q1
Q2
Q3
Q4
2.44 × 10-14
5.26 × 10-13
2.6 × 10-11
1.5 × 10-10
7
14
16
17
N2O(100) + N2O f 2 N2O
O(1D) + N2 f O(3P) + N2
O(1D) + NO f O(3P) + NO
constants for the three N2O dissociation reactions by electronic
impact have been assumed to be 8 × 10-10, 3.7 × 10-10, and
1.2 × 10-10 cm3 molecule-1 s-1. Since rate constants for
electron impact dissociation at low energies are not available
in general, the former ones have been calculated in this work
using a method similar to that described in ref 1 for a continuous
discharge. The sum of the three rate constants is chosen in order
to reproduce the experimental ground-state N2O concentration
when the discharge is on, and the values of the individual rate
constants are adjusted to account appropriately for the N2 and
NO stationary concentrations.
Homogeneous Reactions
N2O + O(1D) f 2 NO
G1
G1
G1
G2
G2
G2
G3
G4
G5
G6
G7
G8
7.2 × 10-11
16
16
N2O(001) + O(1D) f 2 NO
N2O(100) + O(1D) f 2 NO
N2O + O(1D) f N2 + O2
4.4 × 10-11
N2O(001) + O(1D) f N2 + O2
N2O(100) + O(1D) f N2 + O2
N2O(001) + O(1D) f NO2 + N
NO + O(3P) + Mf NO2 + M
NO2 + O(1D) f NO + O2
NO2 + O(3P) f NO + O2
NO + N f N2 + O(3P)
1.0 × 10-10
10-31
b
16
b
16
34
34
3.0 × 10-10
9.7 × 10-12
3.0 × 10-11
8.5 × 10-11
NO + O(1D) f O2 + N
In the present work, the excitation of some N2O vibrational
levels by electronic impact has been taken into account. They
were not included in our previous work on DC N2O discharges
but have been included here, mainly because a high population
(∼9%) of N2O in the weakly collisionally coupled (001)
asymmetric stretching mode was observed by emission mea-
surements.7 Similar percentages of (001) population were
obtained by other authors in previous spectroscopic studies of
N2O glow discharges.10,11 Since the incorporation of N2O
excitation rate constants originates a slight depletion of the N2O
molecules remaining in the fundamental state and since a third
dissociation channel has been included here, the revised values
of the N2O dissociation rate constants are slightly different than
those assumed in ref 1. Nevertheless, these rate constants agree
quite well with those proposed by Cleland and Hess2 and are
slightly smaller than the estimates of Kline et al.3 for N2O
dissociation rate constants in a glow discharge plasma with a
higher mean electron energy. On the other hand, the same rate
constant values are assumed for dissociation processes of excited
N2O molecules, since the energies required to dissociate the
vibrationally excited N2O molecules are only 7-15% smaller
than that required from the N2O ground state.
Heterogeneous Reactions
O(1D) + wall f O(3P)
O(3P) + wall f O(S)
W1
W2
W3
W4
W5
W6
W7
2200
2200
180
16.1
222
d
d
2
d
d
d
b
O(3P) + O(S) f O2
N + wall f (1/2) N2
N2O(001) + wall f N2O
N2O(100) + wall f N2O
NO + O(S) f NO2
222
2.75 × 10-3
Radiative Deexcitation
N2O(001) f N2O (τ1 ∼ 4 ms)
N2O(100)f N2O (τ2 ∼ 83 ms)
R1
R2
258
12
7
22
a Rate Coefficients are in units of cm3 molecule-1 s-1 for dissociation
by electronic impact and bimolecular reactions. cm6 molecule-2 s-1
for trimolecular reactions and s-1 for heterogeneous Reactions b Esti-
mated in this work. c Calculated from ref 15. d Calculated for our cell
geometry assuming γ ) 1 (see text).
stationary state of the discharge on is reached and the resulting
value is very similar to that assumed by Kline et al.3 The NO2
dissociation rate constant has been assumed to be similar to
that of NO and its inclusion leads to a better agreement with
the observed evolution of the NO2 concentration at the beginning
of the discharge.
Dissociation by electronic impact of NO and NO2, appearing
as stable products in the N2O discharge, has been included in
the present model with the rate constants shown in Table 1
(reactions D4 and D5). The bond strengths of these molecules
are 6.5 and 3.1 eV, respectively.12 The inclusion of a NO
dissociation term is crucial in order to account for the time
evolution of the NO concentration during the beginning of the
discharge, as it will be shown later. Its rate constant has been
estimated in order to fit the NO concentration when the
The dissociation of molecular oxygen, with a bond energy
of 5.11 eV,12 is assumed to happen through two possible
channels, one of them (reaction D6) giving rise to two oxygen
atoms in their fundamental state, and the other one (reaction
D7) producing one of the oxygen atoms in its electronically
1
excited D level, as shown in Table 1. The ratio between the
respective rate constants agrees with that found in the litera-
ture.3,12 In any case, the sum of the two dissociation rates
assumed in the present model is smaller than the assumed values

3978 J. Phys. Chem. A, Vol. 104, No. 17, 2000
de los Arcos et al.
for NO and NO2. No theoretical or experimental absolute values
have been found for these rate constants at low electron energies
but in some tests performed in our laboratory with pure O2
discharges, a very low dissociation efficiency, lower than 1%,
was found for physical conditions analogous to those of the
N2O discharges. Similarly, a very small amount of N2 dissocia-
tion was experimentally obtained with a N2 hollow cathode
discharge, and N2 dissociation has not been included in the
model because its bond strength is 9.76 eV, notably higher than
the mean electron energy measured in the plasma (∼3 eV) and
its relative dissociation rate constant is known to be much lower
than that of O2 for low electron energies.13 Ionization processes
by electronic impact are not included in the present model, in
a way similar to refs 1 and 2, since reactions including ions
were shown not to affect significantly the concentrations of the
precursor and products in other N2O discharges,3 when they
were included in the corresponding kinetic model.
the present work, and because the broadening of the infrared
bands during the discharge has been observed to be in fact small.
Deexcitation. The most significant excited species involved
in the kinetics of the N2O discharge is the metastable O(1D). It
is produced in the electron impact dissociation of N2O and,
besides its active participation in the chemical kinetics of the
plasma, it is known to be efficiently quenched through inelastic
collisions with the N2 and NO molecules appearing as products
of the N2O discharge. Rate coefficients for these O(1D)
quenching processes included in the model (reactions Q3 and
Q4) and shown in Table 1 have been obtained from refs 16 and
17, respectively. These coefficients, as well as those of
homogeneous reactions where O(1D) is involved, are high
enough to make diffusion of the excited atoms outside the
plasma volume negligible.
To explain the deexcitation of the vibrational excited levels
(001) and (100) of N2O, three kind of processes have been
considered: spontaneous emission, quenching with N2O in its
ground state, and diffusion outward the plasma volume with
possible deexcitation by collision on the wall. Self-absorption
effects, which would populate secondarily these vibrational
levels and extend their effective lifetimes, are not included, since
changes in the ratios of the intensities of the more intense
spectral lines were not observed when emission was detected
through an optical path length twice the original one, with a
mirror placed behind the rear window of the hollow cathode
discharge cell.
Excitation Processes. In the present model, vibrational
excitation of the weakly collisionally coupled (001) asymmetric
stretching mode of N2O by electron impact has been included
(reaction E1), to explain the high population in excited levels
of this mode observed by emission measurements in the hollow
cathode discharge, equivalent to a (001) vibrational temperature
of ∼1300 K. This fact originates a slight but noticeable depletion
in the population of N2O in its ground state which is observed
by absorption spectroscopy. In the same way, excitation of the
(100) symmetric stretching has been included too (E2), since
its excitation rate constant is quite similar to that of the (001)
mode for the electron energy distribution considered in the
present work; however, the (100) mode is known to relax by
collision impact much faster than the (001) one.11,14 The rate
constant for N2O excitation to the vibrational mode (001) is
assumed to be 1.4 × 10-8 cm3 molecule-1 s-1. This rate constant
has been calculated from the work of Hayashi et al.,15 where
the cross sections for the different processes originated by
electron impact on N2O are reported as a function of electron
energy. Following Hayashi et al., the cross section for the
excitation of the (001) mode has a maximum of 1.5 × 10-16
cm-2 at 2.5 eV. The electron energy distribution inside the
cathode of our discharge is assumed to be of the Maxwell type,
its mean energy, measured with a double Langmuir probe,1 is
2.8 ( 0.5 eV and is thus close to that of the maximum in the
excitation cross section. An upper limit for the rate constant
reported here has been estimated roughly by assuming that all
the electrons have a uniform kinetic energy close to 2.5 eV,
and a cross section equal to the above-mentioned maximum
value.
The lifetime for spontaneous emission of the ν3 band (R1)
starting from the (001) vibrational level was measured to be 4
ms,7 in good agreement with other values found in the
literature.18 The quenching rate constant of this stretching mode
by collision with N2O in its ground state (reaction Q1) has been
taken from the Stern-Volmer plot of the (001) emission decay,
obtained by emission measurements in a 45 Hz N2O discharge
at different N2O flow rates (and consequently, different N2O
concentrations), made in our laboratory.7 The resulting value,
2.44 × 10-14 cm3 molecule-1 s-1, is in approximate good
agreement with Bates et al.,10 who measured it by means of
laser-induced fluorescence, and with previous works,19,20 and
it corresponds to a large mean collision number (∼8000) which
implies that the asymmetric stretching mode is only weakly
collisionally coupled to other levels in this molecule, although
several overtone and combination states of the symmetric stretch
and bend lie close in energy to the 00°1 state. In this way,
molecules excited within this manifold survive for a time interval
comparable to the lifetime for spontaneous emission, which is
long enough to diffuse from the plasma volume to the walls of
the cathode (diffusion time ∼1 ms) and even to be promoted to
successively higher levels, hence the high (001) vibrational
temperatures found in the present work (1300 K) and in refs
11 and 21. Diffusion effects will be considered in more detail
in the section of heterogeneous reactions.
The rate constant assumed for N2O excitation to the sym-
metric stretching mode, (100), has been estimated in a way
similar to that of (001) and has the same value. The cross section
for the excitation of this mode has also a peak at 2.5 eV, with
a broader distribution, but a very similar maximum value (1.4
× 10-16 cm-2) than that of (100).15
The N2O symmetric stretching mode (100) has a lifetime for
spontaneous emission, corresponding to the ν1 band,22 of 83
ms (reaction R2), markedly larger than that of (001), so
apparently this level should persist longer than the latest one;
nevertheless, its quenching rate constant, 5.26 × 10-13 cm3
molecule-1 s-1 (ref 14), implies a mean collision number of
only ∼300 collisions (reaction Q2) and it relaxes much faster
than the (001) mode at the pressures of the present experiments
(relaxation time ∼70 µs with 1 mbar of N2O). Therefore, (100)
vibrational temperatures not higher than 300-350 K are usually
observed.10,21 On the other hand, no diffusion to the surroundings
Other vibrational or electronic excitation paths have not been
considered here because their excitation cross sections by
electron impact within the interval of electron energies involved
in the present work are much smaller than those of (100) or
(001).15 Furthermore, deexcitation by emission or quenching
from these levels are very fast, so their populations are very
small and do not contribute significantly to the depletion of the
ground state of N2O during the discharge. Rotational excitation
has not been included because its relaxation can be assumed to
happen instantaneously in comparison with the time scale of

Hollow Cathode N2O Discharge
J. Phys. Chem. A, Vol. 104, No. 17, 2000 3979
need to be considered for this level, since it deexcites fast
enough to be present only in the plasma volume.
shown to play an important role in the kinetics of the N2O
plasma.5 In the present case, an upper limit of ∼ 10-12 cm3
molecule-1 s-1 was estimated by Davison et al.26 for the room-
temperature rate constant of the reaction with ground-state
molecules, O(1D) + N2O f N + NO2. The rate constant
proposed in the present model for the N2O(001) reaction is about
2 orders of magnitude higher. This is not unreasonable. The
beneficial effect of vibrational excitation for reactions with
suitable barriers on their potential surfaces is well-known (see
refs 27-29 and references therein). In fact, enhancements of
more than 2 orders of magnitude in the comparative effect of
reagent vibrational energy versus relative translational energy
upon the reaction cross sections are well documented for some
of the most prototypic A + BC reactions,30,31 and the effect of
vibrational excitation could be even more important for reactions
with polyatomic molecules, where lower vibrational modes are
accessible.32 Unfortunately, the potential surface for this reaction
pathway is largely unknown and one can only speculate with
the existence of a suitable barrier. In the absence of more direct
evidence, the incorporation of this process as source of NO2 to
the kinetic model is thus only a tentative hypothesis mainly
justified by the better accordance with the data and should be
taken with caution. On the other hand, the present results invite
further theoretical and experimental investigation about the role
of vibrational excitation on the O(1D) + N2O reaction.
In general, throughout this work, the ground-state N2O and
the vibrationally excited stretching modes N2O(100) and N2O-
(001) will be treated as separate species.
Homogeneous Reactions. In the comparatively low-pressure
plasma of the hollow cathode discharge, atom-molecule
bimolecular reactions with significant participation of excited-
state species are predominant. The set of homogeneous reactions
considered here includes all those from the previous model1
and incorporates a few new ones. In both models just one three
body gas-phase reaction has been included. In addition, slight
modifications of the former rate coefficients, in agreement with
more recent data found in the literature, have been taken into
account. The whole set of rate constants used can be found in
Table 1 and the original bibliographic sources are cited in the
fourth column of this table. Room-temperature rate coefficients
have been considered, in accordance with the “cold” character
of the hollow cathode glow discharge. All the homogeneous
reactions are assumed to be irreversible, this assumption being
justified by comparison of the reverse and forward rate
constants.17,23
Because of its large activation energy,24 the reaction of
ground-state oxygen atoms O(3P) with N2O plays no significant
role in the plasma kinetics and has been consequently ignored.
However, the reactions of nitrous oxide with O(1D) are certainly
relevant. The two major exit channels of the O(1D) + N2O
reaction lead to 2NO and N2 + O2 respectively (reactions G1,
G2). As indicated above, the evolution of ground-state N2O and
that of the vibrationally excited (100) and (001) modes are
considered separately and, for each channel, the rate coefficient
has been assumed to be the same for the three cases. Although
no specific rate constants have been found in the literature for
these reactive channels with vibrationally excited N2O, this
assumption is reasonable since the two exit channels considered
have no barrier or a very small one25 and vibrational excitation
of N2O is not expected to increase their reactivity.
The rest of the possible exit channels of O(1D) with ground-
state N2O should play a very minor role; in fact an upper limit
of a few percent, as compared with the two major channels just
commented on, has been estimated for the global reactivity of
all of them.26 However, in an attempt to explain the NO2
concentration experimentally found in our hollow cathode
discharge, too high in comparison with other N2O discharges2,3
where it was not detectable at all, we have assumed that the
vibrational excitation of N2O can enhance markedly the reactiv-
ity of the exit channel leading to the formation of NO2. In our
former work,1 a possible heterogeneous reaction was invoked
as the main source of the observed NO2, but the evolution of
the NO2 concentration predicted with this hypothesis is clearly
at variance with the present time-resolved experiments (see
Figure 3 and the discussion on heterogeneous reactions below).
In the present study we have included the reaction G3 between
the N2O molecules excited to the long-lived, highly populated,
(001) vibrational mode and the O(1D) atoms: N2O(001) +
O(1D) f N + NO2. No direct information is available for this
reaction and we have assumed a high rate constant for it in
order to account better for the measured data. The effect on the
kinetic model has been a considerable increase in the calculated
NO2 concentrations, approximating it more satisfactorily to the
stationary values and to the temporal behavior of the experi-
mental data, without further appreciable influences on the rest
of the stable species appearing in the discharge. This channel
is spin forbidden, but other spin forbidden processes have been
In comparison with the former process, reaction G4 between
NO and O(3P) in the presence of a third body represents a minor
contribution to NO2 production, but it has been included here,
in the same way as it was included in the modeling of the DC
discharge1 and in previous works on N2O microwave and RF
discharges.2,3 Its three-body rate coefficient has been considered
at each moment of the theoretical simulation to depend on the
relative concentration of the predominant species N2O, N2 and
O2, and their partial contribution as a third body.
The reaction G6 between NO2 and oxygen atoms in their
fundamental state represents a well-known,16 very fast channel
of NO2 disappearance in the kinetics of the N2O discharge, and
is mainly responsible for the low NO2 concentration. In the
present model, the NO2 reaction with oxygen in the metastable
state (reaction G5) has been also included, for the sake of
coherence. The rate constant for the reaction33 is markedly larger
than that for the reaction with O(3P), but given the very small
O(1D) concentration predicted with the model, its contribution
to the depletion of NO2 in the discharge is a very minor one.
Finally, reactions labeled G7 and G8 in Table 1, and not
considered in ref 1 have been included here: the first one as a
very efficient channel of recombination of the NO and N species
produced from dissociation processes of N2O by electronic
2,4
impact through reaction D3 and the second one because of
its relatively high rate coefficient in comparison with other
processes where NO or O(1D) are involved, too.
Some attempts have been made to include other chemical
reactions in the gas phase, mostly intended to explain the
experimental values of the NO2 concentration. The very
encouraging agreement between calculated and measured con-
centrations for the other stable species found in this work, and
their temporal dependencies, are practically insensitive to these
minor corrections. In particular, the inclusion of a chain of
reactions related with molecular oxygen in the excited state,
O2 (1∆), was essayed. In fact, metastable O2(1∆) is known to
be the primary product of the N2O + O(1D) f N2 + O2
reaction,25 since the exit channel producing O2 in its fundamental
state is spin forbidden. On the other hand the rate coefficient
of 4.88 × 10-18 cm-3 molecule-2 s-1 at 300 K reported35 for

3980 J. Phys. Chem. A, Vol. 104, No. 17, 2000
de los Arcos et al.
the reaction O2 (1∆) + NO f NO2 + O(3P) is large enough to
lead to a significant formation of NO2 molecules if high
concentrations of O2 (1∆) are present. Nevertheless, the O2 (1∆)
concentration has been found to decay too quickly by quenching
with ground state36 O2 or through heterogeneous reactions,37,38
when included in the model, and the O2(1∆) chemistry has been
disregarded.
wall collisions on stainless steel leading to recombination44 is
markedly smaller than that of the former processes, γ ) 4.2 ×
10-3 at 300 K, and a similar behavior is observed for the fraction
of N atoms which collide with the wall to generate N2 molecules,
γ ) 3.5 × 10-4; therefore, the rate coefficients for reactions
W3 and W4 are some orders of magnitude smaller than those
corresponding to the diffusion limit and are estimated with the
following expression:45
Homogeneous reactions among two or three of the stable
species involved in the discharge, for example, the well-known
reaction39,40 2NO + O2 f 2NO2 have not been considered in
the model, since their reported rate coefficients are many orders
of magnitude lower than those of reactions involving atoms and
become only important at much larger pressures than those of
this work. Other reactions as NO + NO2 f N2 + NO2 have
been studied only at high temperatures,41,42 but their rate
coefficients in the reported interval are too small. Reaction
chains involving radicals41 such as NO3 or N2O5 to produce
NO2 have been also disregarded, since the presence of a
significant concentration of these radicals in the hollow cathode
N2O discharge was not observed by infrared spectroscopy in a
conclusive way.
kx,wall [X]Vx ) [X] ωjx γx A/4
where A is the reactive wall area, ωjx the mean molecular
velocity, and Vx the volume occupied by the X species.
At this point, some remarks should be made about the spatial
distribution of the species in the hollow cathode discharge. In
the present model, the reaction volume for all the stable
molecular species involved in the process has been assumed to
be the whole cell volume, so the assumption that the reagents
are well mixed is included implicitly. To evaluate this assump-
tion, the characteristic diffusion time τd ) kd-1 of each species
in N2O was estimated.1,43 In our case, with 2 mbar of N2O in
the hollow cathode discharge cell, one gets τd ≈ 2 ms for the
diffusion of N2O and NO2 and even smaller values for the lighter
diatomic products. This characteristic τd is much shorter than
the duration of the transient effects to be studied, and smaller
than the residence times (τp ≈ 47 ms to 4.7 s) for all the gas
flow rates considered (φ ) 3-300 sccm), so diffusive transport
dominates over convection by pumping and the reactor can be
considered effectively well mixed. Nevertheless, the O(1D)
atoms deexcite or react in a very fast way by collisions with
N2O and other stable species, with typical deexcitation times
of some microseconds; during this time interval, O(1D) diffuses
on average less than 1 mm, a distance considerably smaller than
the characteristic diffusion length; therefore, the reaction volume
for this species has been assumed to be that of the plasma, and
the diffusion term involving O(1D) turns out to be of minor
significance. A similar behavior is found for atomic nitrogen
and vibrationally exited N2O; all of them quench or react too
fast to diffuse effectively outside the plasma volume, and the
effect of their heterogeneous reactions is actually unimportant.
The disappearance of O(3P) atoms by homogeneous reactions
is not so fast as that of O(1D), but has characteristic times in
the millisecond range, similar to the time employed by this
species to diffuse up to the cathode wall, and an effective O(3P)
volume similar to that of the cathode could be considered in
principle. Nevertheless, the disappearance of O(3P) by adsorption
at the cathode wall and subsequent chemical reaction with new
colliders is known to be very efficient, so that the effective O(3P)
concentration is close to zero near the cathode surface43 and a
significant gradient of O(3P) density should be assumed from
the plasma volume to the cathode wall; however, for the sake
of simplicity, the reaction volume for this species has been
assumed to be that of the plasma too, although the diffusion
term has more importance in this case.
Heterogeneous Reactions. Among the heterogeneous reac-
tions considered in the present work, the reactions termed W1,
W5, and W6 in Table 1 describe the contribution of the reactor
walls to the depletion of the electronically or vibrationally
excited levels of oxygen atoms and N2O molecules appearing
explicitly in the model. On the other hand, the reactions labeled
W2, W3, and W4 represent the wall recombination of oxygen
and nitrogen atoms to form O2 and N2, and W7 contributes to
NO2 generation through the reaction of NO with oxygen atoms
adsorbed in the cathode wall. This last reaction was already
considered in ref 1 to account approximately for the observed
concentration of NO2 and has been included here, but with a
smaller rate constant. At this point, it should be noted that a
wrong value of this rate constant (9 × 10-4 cm3 molecule-1
s-1) was listed by mistake in Table 1 of ref 1. The actual rate
constant used for that simulations was 6.2 × 10-3 cm3
molecule-1 s-1. When this rate constant is used to simulate the
present experimental conditions, a large increase in the NO2
concentration is predicted after the switching off of the discharge
(see Figure 3), which is not observed in the measurements. A
reduction of this rate constant to a value of 2.75 × 10-3 cm3
molecule-1 s-1 was thus necessary in order to account better
for the observations. In any case this is now a minor source of
NO2. As indicated above, in the present model, it is the
homogeneous reaction G3 the one assumed to be responsible
for most of the NO2 concentration.
The reaction W4 involving nitrogen atoms has been added
here as alternative decay channel to the disappearance of this
atomic species. The rate coefficients for the reactions involving
oxygen atoms W1 and W2 are slightly larger when considering
the probability per individual collision2,3 of deexcitation or
sticking, γ ) 1, wall recombination and geometrical consider-
ations,1 than when considering the diffusion-limited case,43 kd
) D/Λ2, with D the diffusion coefficient and Λ the characteristic
diffusion length of the cell, which is essentially dependent on
the cathode radius. This fact indicates that O atoms diffuse
slightly slower than they recombine in the walls, so these
reactions have been considered diffusion limited. Deexcitation
of N2O molecules by wall collision has been assumed also to
happen with a high probability, next to one, but these processes
(reactions W5 and W6) are diffusion-limited too, since being a
heavier species, the N2O diffusion coefficient is even smaller
than that of oxygen atoms. In contrast, the fraction of O(3P)
Differential Equations. The set of coupled differential
equations obtained from the reactions included in Table 1 has
been numerically solved by means of a fourth-order Runge-
Kutta method. The solution of this set of equations yields the
time evolution of the concentrations of each species from the
beginning of the discharge to the attainment of the stationary
state and from the following extinction of the discharge until
the recovery of the original conditions.
For the sake of simplicity, the electron density is assumed to
be homogeneous in the plasma volume and negligible outside
this region; this plasma volume displays a cylindrical geometry

Hollow Cathode N2O Discharge
J. Phys. Chem. A, Vol. 104, No. 17, 2000 3981
and is located fundamentally in the middle of the cathode, as
experimentally demonstrated in ref 1 for the continuous
discharge. In comparison with the time scales relevant for this
work, the electron density and energy distributions are assumed
to appear and disappear instantaneously upon turning on and
off the discharge, in agreement with some literature measure-
ments,9 where transients of some tens of microseconds are
reported for the establishment of the stationary state of the
electronic distributions in hollow cathode discharges.
both species decrease slowly. Nevertheless, this sudden peak
at the ignition of the discharge is not observed in the time
evolution of the concentration of the other two stable products,
O2 and N2, as it is shown in Figure 2. In Figure 1b it can be
seen that the former behavior with a sudden maximum is also
not observed for the nitrogen oxides when the gas flow rate is
considerably higher than that employed in Figure 1a; on the
contrary, the two respective stationary states, discharge on/off,
are reached very quickly.
Besides the five stable molecular species N2O, N2, O2, NO,
and NO2, and the transient species O(1D), O(3P), N, N2O(001),
N2O(100), appearing in the gas phase or adsorbed on the cathode
wall, the model takes into account the overall mass balance,
M, in such a way that the sum of concentrations of all the species
equals that predicted by the ideal gas law and allows the
estimation of the total pressure in the reactor at each moment.
The pressure variation in the discharge cell determines the
variation in the output conductances of the experimental system,
which were previously calibrated with pure N2O for different
pressures and flow rates. As it was indicated in ref 1, this
dependence had to be incorporated into the model for the precise
estimation of the temporal dependence of residence times (τp),
because it influences very remarkably the process of removal
by pumping of each stable species, especially at low flow rates.
On the contrary, since the rates at which the transient species
disappear by gas-phase reactions and heterogeneous recombina-
tion are many times larger than the rate at which they are
pumped, the inclusion of a pumping term in the respective
differential equations has been verified to be irrelevant.
To reproduce theoretically such features, the inclusion of
electron impact dissociation terms for both nitrogen oxides in
the kinetic model, which were not considered in the previous
study of the DC discharge,1 turns out to be crucial, specially
regarding the NO behavior, since without it, a much smoother
evolution would be obtained. However, the NO stationary
concentrations obtained in the N2O discharge are not so sensitive
to these dissociation terms. Analogously, the smoother temporal
behavior of O2 and N2 observed in Figure 2 may be attributed
to the fact that, once generated, they do not react with the
transient species, as the nitrogen oxides do, and hardly dissoci-
ate, since their dissociation coefficients by electronic impact
should be either very small or negligible under the present
conditions. On the other hand, the inclusion of the third N2O
dissociation channel D3 to give NO + N, followed by the fast
reaction G7 between both species to give N2 + O(3P), turns out
not to be significant for the sudden increase and depletion of
NO observed at the beginning of the discharge, since it has been
demonstrated by simulation that both terms equilibrate in less
than 1 ms.
The NO2 generation is dominated by the homogeneous
reaction, G3, and therefore, its time evolution (see Figure 1a)
depends on the evolution of the N2O(001) and O(1D) concentra-
tions involved in that reaction, which are larger at the beginning
of the discharge, as it is shown in Figure 4, where the time
dependence of all the species considered in the model are drawn.
On the other hand, once the discharge is turned off, a slight but
noticeable increase in the experimental NO2 concentration can
be observed, so that NO2 depletion begins in fact two or three
seconds after the discharge has been extinguished and not just
in the turn off instant, in contrast with NO, O2 and N2 (Figures
1a and 2), which begin to disappear immediately by the action
of the exit gas flow. This effect can be traced back to the
heterogeneous recombination of NO with oxygen atoms ad-
sorbed in the wall, W7, which is responsible for the delayed
generation of NO2. As mentioned above, this source of NO2
was already assumed in the previous model developed for the
steady-state discharge but as shown in Figure 3 the value of
the rate constant (6.2 × 10-3) used in ref 1 is too large and
gives rise to an exaggerated growth of NO2 after the discharge
has been switched off. In the present model, the contribution
of this reaction to the stationary concentration of NO2 has been
relatively diminished by using a smaller rate constant. The other
source of NO2 contemplated in ref 1 is the three body reaction:
O(3P) + NO + M, with a well-known rate constant2,3 and also
included in the present model as reaction G4.This and the
heterogeneous reaction alone lead to a too slow rise in the
concentration of NO2 at the beginning of the discharge, and a
faster process like the homogeneous reaction G3, not included
in the previous model, becomes necessary in order to approach
better the experimental observations. It should be pointed out
here that rejecting contributions of the most dubious reactions
(i.e., those for which no direct information is available in the
literature) G3 and W4 to the kinetics and leaving only the
contribution of the best established reaction G4 as the only NO2
4. Results and Discussion
In Figures 1 and 2 the results of the present chemical kinetics
model are compared with the experimental measurements
obtained in this work with FTIR and mass spectrometric
techniques for the switching on and off of the discharge.
Figure 1a,b shows the experimental absolute concentrations
of N2O in its ground state and NO and NO2 products obtained
by time-resolved rapid scan FTIR absorption spectroscopy, in
addition to the model predictions for the modulated discharge,
at two, very different gas flow rates: 3 and 108 sccm,
respectively. Figure 2 shows the time-resolved mass spectro-
metric results of N2 and O2 for a 3 sccm N2O flow rate,
normalized to the absolute concentrations predicted by the
model. In the results for the slower flow (Figures 1a and 2),
the concentrations of all the species produced in the discharge
show a steep increase after switching on, and a slow decrease
when the discharge is turned off. In the case of the faster flow
(Figure 1b) the time evolution of the concentrations resembles
more closely the square shape of the electrical discharge. As
can be seen from Figure 1a,b, the agreement between experi-
mental and calculated data is very good for the precursor, N2O,
and for the NO product, both in the absolute values and in the
temporal behavior; and it is qualitatively encouraging for the
minor NO2 product although in this last case the absolute
concentration values predicted by the model are smaller than
the measured ones. The agreement shown in Figure 2 for the
measured and predicted temporal evolution of the homonuclear
species is also quite satisfactory.
Concerning Figure 1a, some interesting facts should be noted.
At the beginning of the discharge, the concentrations of NO
and NO2 increase suddenly until a maximum value and then
decrease rapidly, reaching a plateau ∼500 ms after the peak,
corresponding to the stationary state with discharge on, and
when the discharge is switched off the concentration values of

3982 J. Phys. Chem. A, Vol. 104, No. 17, 2000
de los Arcos et al.
source2,3 results in NO2 concentrations some 3 orders of
magnitude lower than the data experimentally obtained in this
work.
oxygen, generated at the discharge. To rationalize the collected
set of data, a relatively simple chemical kinetics model including
a reduced number of reactions is proposed. The corresponding
set of coupled, time dependent, differential equations has been
numerically solved and the time-resolved solutions compared
with the measurements. This model has been also compared
with the steady-state experimental results obtained with a DC
hollow cathode discharge. The fitting of the simulated transient
phenomena to the measured ones has proven to be much more
sensitive to the suitable choice of the particular kinetic processes
than the stationary studies performed on DC discharges, or based
on RF or microwave discharges applied in a continuous way.
The present work demonstrates thus the great usefulness of time-
resolved studies on low-frequency modulated discharges for the
elucidation of the influence of relevant kinetic mechanisms in
the plasma chemistry.
Besides the agreement of the present kinetic model with the
experimental results of the modulated N2O hollow cathode
discharge, the validation of the present model would require a
good agreement between the calculations and the stationary data
from the continuous discharge. Figure 5 shows the experimental
data obtained for the stationary concentrations of the stable
compounds involved in a 2 mbar continuous N2O discharge,
and the predictions of the present model. This figure may be
compared with Figure 5 of ref 1, where the results of the former
simplified model were displayed. Although the agreement
between calculated and experimental concentrations of the major
species of the discharge, N2O, N2, O2, and NO was encouraging
in ref 1, it can be observed that this agreement is even better
with the present theoretical data. Particularly, NO concentrations
fit the experimental results in a more accurate way at low flow
rates than they did in the former article, and the homonuclear
molecules fit it slightly better at the highest flow rates. On the
other hand, the predicted NO2 concentration dependence on flow
rate agrees much better than before with the DC experimental
results. All these facts lead us to the conclusion that the present
model is more suitable to reproduce the N2O hollow cathode
discharge.
Together with the stable species, Figure 5 shows the stationary
concentrations calculated for the transient species appearing
explicitly in the current model, such as the atoms and the excited
N2O molecules. It was not possible to detect these species
experimentally either by absorption spectroscopy or mass
spectrometry under the present conditions. Nevertheless, the
FTIR emission spectra of a 45 Hz modulated, N2O discharge,
obtained by phase-sensitive detection techniques at intermediate
gas flow rates (36 sccm)7 and spectrally calibrated with a
blackbody source, allowed an estimate of the intensity of the
ν3 vibrorotational band, and the temperature of the (001)
vibrational level, which turned out to be ∼1300 K. This fact
implied a N2O population of this level ∼9%, which is in very
satisfactory agreement with the predictions of the present model.
Similarly, N2O excited to the (100) vibrational level is predicted
by the model to be populated between 2 and 3 orders of
magnitude less than the N2O ground state, depending of the
gas flow rate, as shown in Figure 5. As it was formerly
explained, the (100) state of N2O is known to quench and
depopulate much more efficiently than the (001) state, and hence
vibrational temperatures only slightly higher than the ambient
value are experimentally found in the literature for (100).11 For
a 300 K temperature, a ∼0.2% population of the (100) level
can be estimated in relation with the fundamental state, assuming
a Boltzman distribution, while a 400 K temperature implies a
(100) population of ∼1%. These values agree quantitatively in
a very encouraging way with those estimated by the present
model.
A considerable effort has been devoted to the identification
of the possible reactions generating NO2 in the discharge cell,
because the rate coefficients of the reactions available in the
kinetic databases and in the literature could not justify the
relatively high concentration of this species found in the N2O
hollow cathode discharge. In this way, the delayed depletion
of NO2 concentration once the discharge has been extinguished,
a feature that has not been observed for the other stable products
of the discharge, seems to confirm the occurrence of a
heterogeneous reaction generating NO2 molecules, which was
proposed by Arcos et al.;1 nevertheless, to reproduce more
suitably the temporal evolution of NO2 at the beginning of the
discharge and the general behavior of the DC discharges for
different physical conditions, a large enhancement of the rate
constant of the bimolecular reaction O(1D) + N2O f NO2 +
N by the long-lived vibrationally excited N2O(ν3) molecules
has been proposed for the first time. This reaction decreases
the relative significance of NO2 generation by wall reaction.
To justify the temporal behavior of the rest of the stable
products at the beginning of the discharge, dissociation processes
by electron impact have been incorporated into the model, this
fact being specially decisive for NO, which seems to dissociate
in a much more efficient way than N2 and O2.
The inclusion of vibrational N2O excitation processes and
relaxation channels in the kinetics model, specially for the (001)
state, justify the fact that the N2O signals obtained by FTIR
absorption spectroscopy are not exactly due to the total N2O
concentration, but to ground-state N2O molecules, which under
the present experimental conditions may differ by some ten
percent from the total density of N2O molecules.
The agreement between the model predictions and the
experimental data for the N2O, N2, O2, and NO is good. The
calculations can also reproduce satisfactorily the qualitative
behavior of the minor NO2 product and, although the values
obtained are still low, the predictions of the model are closer,
by several orders of magnitude, to the absolute concentrations
observed for this molecule than those of other models described
in the literature. This general agreement between calculations
and experiment, both time-resolved and in the steady state,
suggests that the model provides a reasonable global description
of the processes performed on the hollow cathode N2O
discharge.
5. Summary and Conclusions
In this work the transient processes which happen around
the ignition and extinction of a low frequency, square wave
modulated, hollow cathode discharge of N2O until the attainment
of the respective stationary states have been studied for the first
time. To follow the evolution of the absolute concentrations of
the stable nitrogen oxides, time-resolved rapid-scan FTIR
absorption spectroscopy has been employed; complementarily,
time-resolved mass spectrometry has allowed to know the
evolution of the homonuclear molecular species, nitrogen and
Acknowledgment. We are indebted to J. L. Domenech, who
wrote the program for the simulation of the spectra. The
technical advice and support of J. M. Castillo, M. A. Moreno,
and J. Rodr´ıguez have been most valuable for the achievement
of the present experiments. The SEUID of Spain (Projects PB95-

Hollow Cathode N2O Discharge
J. Phys. Chem. A, Vol. 104, No. 17, 2000 3983
(22) Yardley, J. T. Introduction to Molecular Energy Transfer; Academic
Press: London, 1980.
0918-C03-02 and PB96-0881) is gratefully acknowledged for
financial support.
(23) Chase, M. W., Davies, C. A., Downey, J. R., Frurip, D. J.,
McDonaald, R. A., Syverud, A. N., Eds. JANAF Thermochem Tables, 3rd
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