22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
A parametric Boltzmann equation analysis of CO 2 dissociation in cold plasmas
and afterglows
L.D. Pietanza, M. Capitelli, G. Colonna, G. D’Ammando and A. Laricchiuta
CNR-IMIP, via Orabona 4, 70126 Bari, Italy
Abstract: CO 2 dissociation has been studied in discharge and post discharge conditions by
comparing direct electron impact dissociation rates with those rates obtained by considering
a pure vibrational dissociation mechanism in which excitation of vibrational modes of CO 2
is taken into account. Results have been obtained by solving a Boltzmann equation
including elastic, inelastic, superelastic and electron electron collisions.
Keywords: CO 2 , dissociation, superelastic collisions, vibrational mode excitation
Plasma processing of CO 2 under non-equilibrium
conditions is nowadays considered a promising substitute
to conventional routes to specifically tackle the ratelimiting dissociation into CO [1-4]. The idea to use cold,
i.e. non-equilibrium plasma, for the CO 2 dissociation has
a long history started with the works of Russian [5, 6] and
Italian groups [7, 8], at the beginning of plasma-chemistry
activities. The basic idea was the impossibility to
rationalize experimental dissociation rates of CO 2 by
using the direct electron impact dissociation process. On
the contrary, especially at low electron temperature
(𝑇𝑇~1𝑒𝑒), the input of electrical energy goes through the
excitation of vibrational modes of CO 2 (in particular the
asymmetric one), followed by VV energy exchange
processes able to spread the low lying vibrational quanta
over the whole vibrational ladder of CO 2 , ending in the
dissociation process. The upper limit to the dissociation
rate of this mechanism, called pure vibrational
mechanisms, can be obtained by the simplified equation
𝐾𝑑𝑢𝑢𝑢𝑢𝑢 =
1
𝑣𝑚𝑚𝑚
𝐾𝑒𝑒 (000 → 001)
(1)
where 𝐾𝑒𝑒 (000 → 001) is the rate of the resonant
vibrational excitation process and 𝑣𝑚𝑚𝑚 the number of
vibrational quanta contained in the vibrational ladder of
CO 2 (to a first approximation we can imagine to pump
vibrational energy selectively on the asymmetric mode of
CO 2 ). This rate can be several orders of magnitude
higher than the corresponding dissociation process
induced by electron impact. These simple considerations
are at the basis of the numerous experimental attempts to
use vibrational energy in the dissociation process rather
than the direct electronic process with the belief that the
activation energy of the vibrational excitation process is
much less than the corresponding electron impact process.
Unfortunately, the situation is much more complicated
than that given by Eq. (1), which completely disregards
the relaxation of the vibrational energy by VT energy
exchange processes. Moreover, the possible enhancement
of the direct electron impact dissociation process due to
the presence of vibrationally excited molecules should be
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taken into account. The last has a twofold effect on the
direct dissociation process: 1) it enlarges the electron
energy distribution function (eedf) through the effect of
superelastic vibrational and electronically excited state
collisions, increasing at the same time the direct
dissociation rate; and 2) it increases the dissociation rate
due to the lowering of the energy threshold of
dissociation, decreasing with vibrational quantum
number. The first point has been considered in the past to
understand the dissociation of CO 2 in laser mixtures [9],
this aspect being reiterated more recently for the same
aim [10].
The second point has been recently
reinvestigated in the case of nitrogen plasmas [11].
To better understand these points, we report in Fig. 1
the dissociation rate of CO 2 as a function of vibrational
temperature of CO 2 at E/N 30 Td calculated in different
approximations: 1) according to Eq. (1); 2) considering
only the direct electronic excitation-dissociation from the
CO 2 ground state, 𝑘𝑑 (000); and 3) including the effect of
vibrational levels in direct dissociation according
𝜀00𝑣
𝑣
𝐾𝑑 (𝑎𝑎𝑎) = ∑𝑣𝑚𝑚𝑚 𝑒𝑒𝑒 �
𝑘𝐵
1
1
� − �� 𝑘𝑑 (000)
𝑇𝑒
𝑇𝑣
(2)
𝑣𝑚𝑚𝑚 being the maximum value of vibrational levels in
the asymmetric stretching ladder, i.e., 21 according to [3].
This equation results from the crude assumption of a shift
of cross-section threshold for excited vibrational levels,
and Boltzmann distribution function of VDF and EEDF at
𝑇𝑣 and 𝑇𝑒 temperatures, respectively, reducing to
𝐾𝑑 (𝑎𝑎𝑎) = 𝑣𝑚𝑚𝑚 𝑘𝑑 (000) for the case 𝑇𝑣 = 𝑇𝑒 as reported
by [12]; 4) including the effect of vibrational levels in the
pure vibrational mechanism
(𝑢𝑢𝑢𝑢𝑢)
𝐾𝑑
(𝑎𝑎𝑎) =
1
𝑣𝑚𝑚𝑚
∑8𝑛=1
𝜀𝑣𝑛
𝜀𝑣8
𝑘𝑒𝑒 (0 → 𝑣𝑛 )
(3)
where 𝑣𝑛 are the excited vibrational levels belonging to
different normal CO 2 modes, as reported in Table 1.
𝑘𝑑 (000) and 𝑘𝑒𝑒 (0 → 𝑣𝑛 ) rate coefficients have been
calculated from the solution of the Boltzmann equation
including vibrational and electronic superelastic
collisions, considering a parametric change of the
1
Fig. 1. Rate coefficients for dissociation channels in CO 2
plasma, as a function of vibrational temperature of
asymmetric mode (on the upper axis the corresponding
values of characteristic energy E c are reported), at
E/N = 30 Td.
Table 1. Channels in CO 2 kinetics.
Notation
State
CO 2 (v 0 )
CO 2 (v 1 )
CO 2 (v 2 )
CO 2 (v 3 )
CO 2 (v 4 )
CO 2 (v 5 )
CO 2 (v 6 )
CO 2 (v 7 )
CO 2 (v 8 )
CO 2 (e 1 )
(000)
(010)
(020)+(100)
(030)+(110)
(0n0)+(n00)
(0n0)+(n00)
(0n0)+(n00)
(0n0)+(n00)
(001)
Energy
[eV]
0.000
0.083
0.167
0.252
0.339
0.442
0.505
2.500
0.291
7.000
CO 2 (e 2 )
10.500
CO 2 +
13.300
Channel
vib-excitation
vib-excitation
vib-excitation
vib-excitation
vib-excitation
vib-excitation
vib-excitation
vib-excitation
direct
dissociation
electronic
excitation
ionization
temperatures associated to the different vibrational normal
modes, 𝑇𝑣 for the asymmetric stretching and 𝑇𝑣′ for the
symmetric and bending modes, imposing 𝑇𝑣 > 𝑇𝑣′
following what observed in CO 2 laser physics. Moreover,
the concentration of the CO 2 (e 2 ) electronically excited
state has been set at equilibrium with the symmetric and
2
bending modes (𝑇𝑣′ ), while, only in the post discharge
regime, a fixed concentration of 10-5 has been imposed.
Finally, the electron-electron Coulomb collisions have
been inserted with different electron ionization degrees.
All the cross-section data entering the Boltzmann
equation have been taken from [13], while superelastic
cross sections have been derived by detailed balance
principle. Note that in the corresponding database [13],
the 7 eV threshold process is considered as a dissociative
channel, while the electronic excitation is limited to a
process with energy threshold of 10.5 eV. The addition of
further excitation levels [3, 5] can improve the accuracy
of the present results, without altering their qualitative
validity.
Inspection of Fig. 1 shows that the pure vibrational
mechanisms including all vibrational channels are
dominant at lower T v vibrational temperature, while
direct dissociation channels become competitive at higher
vibrational temperatures. In any case, at E/N = 30 Td,
direct dissociation strongly increases with T v as a result
of the corresponding behaviour of the eedf (see Fig. 2).
At the same time, the pure vibrational mechanisms
become more and more important as the reduced field
decreases (E/N < 30 Td), the reverse being true for E/N >
30 Td. These points nowadays are practically forgotten
when trying to rationalize the experimental results of CO 2
dissociation. Attempt in this direction should take into
account the strong coupling between eedf and nonequilibrium vibrational kinetics, including electronic
(dissociative and excitation) transitions involving
vibrational excited states as shown in Fig. 1. The above
reported scenario applies mainly in the low-electron
temperature plasmas dominated by the excitation of
vibrational modes, a situation that can occur in
microwave (Mw) discharges operating at moderate
pressures. Microwave (Mw) driven CO 2 plasma at
sub-atmospheric pressures can reach energy efficiencies
as high as 60% at low specific injected energies (around
1 eV/molecule CO 2 ) thus confirming the importance of
vibrational excitation in the dissociation process [4]. The
use of atmospheric DBD pulsed discharges revealed an
energy efficiency of about 10% [3, 4].
Another interesting case could be the use of nanosecond
high-voltage discharges operating at atmospheric
pressure. The situation in this case is completely different
from the Mw case because during the pulse one creates
very elevate electron temperatures, able to excite
electronic states of CO 2 rather than vibrational states.
However, in the post-discharge following the pulse, the
electronically excited states can create structures in the
eedf due to superelastic collisions between cold electrons
and electronically excited states, increasing the
dissociation rate of CO 2 also in the post-discharge regime
[14]. In Fig. 3 we report the electron energy distribution
function at different vibrational temperatures in the postdischarge regime (E/N = 0 Td).
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by elastic and inelastic relevant collisions, including
electron-electron collisions not considered by [14]. The
plateau length strongly decreases with the increase of
vibrational temperatures. It should be pointed out that in
ns pulsed discharges the realistic values of vibrational
temperatures do not exceed 3000 K, while the selected
values of the electronic state and electron concentrations
are typical of ns pulsed discharges. In Fig. 4, the rate
coefficients for the dissociative channels are reported in
the post-discharge regime (E/N = 0 Td). In this case, the
pure vibrational mechanisms dominate the direct
dissociation channels in the whole T v vibrational
temperature range. In any case, the direct dissociation
channels cannot be neglected and should be included in
the description of post-discharge regime.
Fig. 2.
Electron energy distribution function at
E/N = 30 Td, including electron-electron collisions, with
electron molar fraction 𝜒𝑒 = 10−5 for different selected
values of the temperatures of the symmetric/bending
modes and CO 2 (e 2 ) electronically excited state (𝑇𝑣′ ) and
of the asymmetric mode (𝑇𝑣 ).
Fig. 4. Rate coefficients for dissociative channels in CO 2
plasma, as a function of vibrational temperature of
asymmetric mode (on the upper axis the corresponding
values of characteristic energy E c are reported), in the
post-discharge regime (E/N = 0 Td).
Fig. 3. Electron energy distribution function in the postdischarge regime (E/N = 0 Td), including electronelectron collisions, with electron molar fraction
𝜒𝑒 = 10−5 and 𝜒𝐶𝐶2 (𝑒2 ) = 10−5 , for different selected
values of the temperatures of symmetric/bending (𝑇𝑣′ ) and
asymmetric (𝑇𝑣 ) normal modes.
We can see that superelastic electronic collision from
the excited electronic level CO 2 (e 2 ) forms a source of
electrons at the threshold energy for the excitation
process, i.e., 10.5 eV, which is transformed in a plateau
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The results reported in this abstract should be taken in
the present case from a qualitative point of view.
Improvements of the vibrational ladder as well as of the
dynamical information for the corresponding inelastic
channels should require a not trivial effort. On the other
hand, a state-to-state vibrationally and electronically
excited state kinetics coupled to a self-consistent
Boltzmann equation should be developed. Particular care
should be devoted to the VV and VT processes involving
a realistic vibrational CO 2 ladder [15]. Moreover we
should insert these modules in a more complex one
describing the plasma chemistry occurring in the
discharge [3]. Dedicated experiments are then expected
3
to validate the theoretical model to transform it in a
predictive tool.
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4
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