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# Investigation of Filamentary and Diffuse DBD in CO2 by Means of InSitu FTIR Absorption Spectroscopy

Corentin Bajon, Edmond Baratte, Dihya Sadi, O. Guaitella, A. Belinger,

Simon Dap, T. Hoder, N. Naudé

► To cite this version:

Corentin Bajon, Edmond Baratte, Dihya Sadi, O. Guaitella, A. Belinger, et al. Investigation of Filamentary and Diffuse DBD in CO2 by Means of InSitu FTIR Absorption Spectroscopy. Journal of Physical Chemistry C, 2025, 129 (38), pp.16967-16976. 10.1021/acs.jpcc.5c02224. [DOI] [Full Text]

HAL Id: hal-05338187

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Submitted on 19 Nov 2025

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# Investigation of filamentary and diffuse DBD in CO₂ by means of *in-situ* FTIR absorption spectroscopy

C Bajon<fnref n="1" />, E Baratte<fnref n="2" />, D Sadi<fnref n="2" />, O Guaitella<fnref n="2" />, A Belinger<fnref n="1" />, S Dap<fnref n="1" />, T Hoder<fnref n="3" />, N Naudé<fnref n="1" />*

*corresponding author : nicolas.naude@laplace.univ-tlse.fr

## Abstract

This work investigates CO₂ dielectric barrier discharges at atmospheric pressure in the filamentary and diffuse regimes for the first time using *in situ* FTIR absorption measurements. The conversion factor of CO₂ is determined and is consistent with the results obtained for DBDs in the literature, following a power law with respect to the specific energy input in both regimes. Vibrational temperatures for CO₂ and CO molecules as well as rotational temperature are also determined within the discharge. A noticeably high vibrational temperature of CO is observed for low specific energy input (SEI). It drops abruptly when increasing the SEI which is attributed to strong vibrational to translational energy transfers by O atoms coming from CO₂ dissociation. Except that, the ordering of the different temperatures is similar to the results reported for other CO₂ discharges generated at lower pressures: the vibrational temperature of CO is higher than those of the different vibrational modes of CO₂. The latter are slightly higher than the rotational temperature of the gas for the diffuse mode, whereas they are almost the same for the filamentary mode. The evolution of the measured parameters as a function of the specific energy input is then discussed and a detailed comparison of the two different regimes is carried out. These data together with the knowledge of the reduced electric field in the diffuse regime, which is included in the range 120-140 Td for all conditions, can be of significant importance for further studies exploring the fundamentals of CO₂ plasma chemistry at atmospheric pressure, serving as reference for kinetic models.

## Introduction

Interest in CO₂ plasmas started from the studies of CO₂ lasers in the 60's <fnref n="1" />. Further studies were dedicated to astrophysical observations <fnref n="2" />,<fnref n="3" /> or to spacecraft shield design for atmosphere re-entry ⁴⁻⁶. In the 70's, Fridman ⁷ and Capezzuto ⁸ were among the first to take advantage of the capability of non-equilibrium plasmas to induce chemistry in gases and to study the dissociation of CO₂ molecules. Non-equilibrium plasma discharges are an excellent way to produce oxygen from CO₂ during space missions ⁹⁻¹¹, especially on Mars, where the atmosphere is composed of 95 % of CO₂. In addition, the current context, where global warming is a significant concern, motivates studies on CO₂ conversion into value-added products, for example, the production of methane from CO₂ and H₂ ¹², or energy storage by the production of CO-H₂ "syngas" from CO₂ and CH₄, to reform hydrocarbons later ¹³,¹⁴.

<footnote n="1">¹ Université de Toulouse, Toulouse INP, CNRS, LAPLACE, 118 route de Narbonne, 31062, Toulouse, France</footnote>

<footnote n="2">²Laboratoire de Physique des Plasmas, Ecole Polytechnique, Route de Saclay, F-91128, Palaiseau Cedex, France</footnote>

<footnote n="3">³Department of Plasma Physics and Technology, Faculty of Science, Masaryk University, Kotlářská 2, 61137 Brno,
Czech Republic</footnote>
Dielectric barrier discharges (DBDs) are interesting because they work at atmospheric pressure, are easy to set up, scalable and can be coupled with catalytic materials to improve CO₂ conversion. At this pressure, barrier discharges generally work in the well-known filamentary regime. However, we have demonstrated in a previous contribution that obtaining a diffuse discharge in CO₂ at atmospheric pressure is possible as well¹⁵. This diffuse type of discharge works in the well-known atmospheric pressure Townsend regime (APTD), as it was initially reported in N₂ and later also in air¹⁶⁻¹⁸.

In short, a Townsend discharge results from a Townsend breakdown. It can be obtained when two conditions are met¹⁹: a sufficient number of seed electrons are present before the breakdown and the applied voltage increases sufficiently slowly (i.e. low amplitude and frequency for sine wave excitation). The higher the amount of seed electrons, the higher is the maximum variation rate of the applied voltage allowing a Townsend breakdown to occur. Seed electrons are generated by various mechanisms whose occurrence is linked to the previous discharges. The nature and strength of these mechanisms are strongly related to the operating conditions. For example in N₂ with admixtures of tens of ppm of O₂, NO or N₂O, a significant amount of seed electrons can be generated in between two discharges by associative ionization reactions triggered by the long lived metastable specie N₂(A³Σ⁺u) remaining from the previous discharge¹⁸,²⁰,²¹. In this case, the memory effect thus arises in the discharge volume and is strongly influenced by the gas flow rate. On the contrary in air or in CO₂ where the lifetime of metastable species is very low, the memory effect is almost independent of the gas flow but strongly dependent on the nature of the dielectric materials¹⁵,¹⁹. Thus, even if it has not yet been fully elucidated, the memory effect in these conditions is much more related to a mechanism arising at the dielectric surfaces and able to release trapped electrons¹⁹. When the two aforementioned requirements for a Townsend breakdown to occur are not fulfilled (low amount of seed electrons, fast increase of the voltage), streamer breakdowns occur leading to filamentary discharges. Contrary to the filamentary regime where the electric field strongly varies in time and space and generally requires strong effort to be determined, in the Townsend regime, the electric field is almost constant along the gas gap²²,²³. It can be easily determined from the knowledge of the gas gap voltage, which can be determined by electrical measurements. This regime constitutes an exciting way to study the discharge mechanisms involved in CO₂ discharges because of the easy determination of the reduced electric field. In such APTD regime barrier discharge, it changes on relatively slow microsecond scales and peaks at low fields of approximately 120-140 Td, which represents another uniqueness in discharge conditions for CO₂ plasma study.

Infrared absorption spectroscopy (FTIR) was used in low-pressure glow discharge²⁴⁻²⁷, DBD²⁸ and recently in atmospheric pressure RF jets²⁹,³⁰ to determine the dissociation rate of CO₂, and measure the energy distribution in the CO₂ and CO vibrational levels associated with their own temperature. The conversion rate of the CO₂ molecule into CO appears to be a function of the energy dissipated within the discharge. A non-equilibrium between the temperatures of the different vibrational modes of CO₂ was observed in the different discharge configurations, and a higher vibrational temperature of CO compared to vibrational temperatures of CO₂ was reported. In addition, the works of Morillo-Candas et al.²⁶,²⁷ highlighted the importance of the CO(a³Π) metastable and oxygen species, such as O₂ and atomic oxygen in the discharge kinetic.

Despite the numerous efforts that have already been paid to study the chemistry and energy exchanges in pure CO₂ low pressure plasmas, there is still a need for experimental data obtained at atmospheric pressure where the dominant mechanisms can strongly differ and where the determination of the reduced electric field is often complicated. In this work, in-situ FTIR absorption spectroscopy was used for the first time in CO₂ DBDs at atmospheric pressure in both diffuse (also referred as Townsend) and filamentary regimes, providing important set of parameters such as the
dissociation degree and the rotational and vibrational temperatures of CO₂ and CO molecules together
with the reduced electric field value (in the diffuse regime).

# 1. Experimental setup

The experimental setup used for this work is similar to the one used in ¹⁵. The DBD cell, shown schematically in Figure 1a, was composed of two alumina plates 115x50 mm with a squared electrode of 3x3 cm painted on the outer side using a silver-based conductor painting (ESL 9916-G). The gas gap *d*=2 mm was set using four printed pieces, which maintain a glass plate to ensure a laminar gas flow. The glass plates were cut 5 mm before the electrode output allowing the IR beam to pass through the discharge.

<figure><img src="image_3.png" /><figcaption>b)</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 1: a) Diagram of the discharge cell (Top, Front and side views), on the top view the upper alumina plate is not represented to show the interior of the discharge cell and b) picture of the experimental setup.</figcaption></figure>

Before each experiment, the primary pump allows to reach a pressure of 10⁻³ mbar within the vessel. The vessel was filled with pure CO₂ Alphagaz 1 from Air Liquide®, with a purity of 99.999 %, for the experiments. During operation, the CO₂ gas flow was set using mass flow controllers. Flow rates ranging from 7.4 to 740 sccm were used. An electronically controlled valve associated with a diaphragm pump was used to maintain a constant pressure of 1015 mbar during the experiments. The discharge cell was supplied by a low-frequency generator Keysight 33210A coupled to an audio amplifier connected to a high-voltage transformer. The applied voltage was measured using a Tektronix P6015A probe, and the current was measured through a shunt resistor of 1 kΩ placed in series with the discharge cell using a Rohde & Schwarz RT-ZP03 probe. Electrical characteristics were acquired using an oscilloscope Rohde & Schwarz RTB2004 with a bandwidth of 300 MHz. The discharge power was calculated by integrating the product of the measured voltage and current over one period. In a DBD, part of the applied voltage is reported across the dielectrics due to their charging by plasma electrons and ions. Consequently, only part of the applied voltage is indeed applied over the gas gap. The latter, called gas voltage (sometimes also referred to as gap voltage), was determined from electrical measurements using an equivalent electrical circuit as detailed in ³¹. An example of the application of the equivalent circuit method to APTD generated in CO₂ is provided in ¹⁵. As the electric field is almost constant along the gas gap for a Townsend discharge, the time dependent electric field *E*(*t*) can be easily determined by
dividing the gas voltage $V_g(t)$ by the gas gap $d$. Finally, the reduced electric field $E/N$ is obtained by dividing the electric field by the gas density $N$ provided by the ideal gas law, see equation (1).

$$ \frac{E}{N}(t) = \frac{V_g(t)}{d \times N} \qquad (1) $$

As an example, for the experiment performed with a sine applied voltage of 17 kVpp / 1 kHz and a gas flow of 7.4 sccm, which is the most powerful condition explored in the Townsend regime, the applied voltage amplitude is 8.5 kV, whereas the gas gap voltage value at the Townsend plateau¹⁵ is 5.91 kV. The corresponding gas temperature determined from FTIR measurements (see below for the determination method) being 347 K, the resulting reduced electric field is thus $1.39 \times 10^{-19} \text{ V.m}^2 \text{ i.e. } 139 \text{ Td.}$

The FTIR measurement setup was composed of a FTIR spectrometer Bruker V70 coupled with a MCT sensor cooled with liquid nitrogen. The IR beam of the spectrometer was guided through the discharge cell by a set of mirrors and collected on the other side by the MCT sensor. The FTIR beam was collimated to pass through the gas gap. However, due to the large section of the IR beam, a part of it is cut, and only a fraction of the incident beam is collected by the MCT sensor. The absorption signal therefore corresponds to an average over the inter-dielectric space (gas gap 2mm). Measurements were done at the end of the plasma region i.e. at the exit side of the gas flow. At atmospheric pressure, the large amount of CO₂ molecules can be responsible for a total extinction of the IR beam in given spectral regions. To limit this saturation effect, the length of the optical path containing CO₂ was reduced using dedicated CaF₂ windows disposed as close as possible to the discharge cell (Figure 1a). In addition, the optical path from the FTIR spectrometer to the MCT sensor was purged with nitrogen circulation (see Figure 1b). Only the volume between the windows and the discharge area, called dead volume, contains pure CO₂ unexposed to the discharge. It must, therefore, be considered during the analysis of the absorption spectra. IR measurements were repeated for each condition until a steady state was reached.

Using the method described in ²⁴, the IR spectra (Figure 2) were fitted to determine the vibrational temperatures of CO ($T_{CO}$) and CO₂ ($T_{12}$ and $T_3$, see explanations below), the rotational temperature ($T_{rot}$) and the conversion factor $\alpha$ given in equation (2):

$$ \alpha = \frac{[CO]}{[CO] + [CO_2]} \qquad (2) $$

where $[CO]$ and $[CO_2]$ are the CO and CO₂ densities, respectively. For that purpose, the absorption band of the asymmetric stretching mode of CO₂ between 2200 and 2400 cm⁻¹ (fully absorbed above 2300 cm⁻¹) and the ro-vibrational band of CO between 2000 and 2250 cm⁻¹ were used.

The vibrational kinetic of the CO₂ molecule is described in ⁷. The CO₂ molecule has three vibrational modes: a symmetric stretching mode $v_1$, a double degenerate bending mode $v_2$ and an asymmetric stretching mode $v_3$ associated with the vibrational temperatures $T_1$, $T_2$ and $T_3$, respectively. The temperatures of the symmetric and bending modes of CO₂ are considered in Fermi equilibrium ($\hbar v_1 = 2\hbar v_2$), and consequently, a single temperature $T_{12}$ is used to describe them. The temperature of the asymmetric mode $T_3$ is considered independently. A Treanor distribution is assumed for the population densities of the vibrational levels. The rotational temperature ($T_{rot}$) is assumed to be the same for all vibrational modes of CO₂ and CO. In the dead volumes, unlike in the plasma volume, the gas is assumed to be thermalised i.e. vibrational and rotational temperatures are equal to an equilibrium temperature $T_{th}$, which is not fixed but assumed to range between 273 K and $T_{rot}$. A similar gas composition is considered in both plasma volume and dead volume. The densities of gas molecules in the discharge
and dead volumes are obtained from the ideal gas law considering the pressure *p* and temperatures *T*<sub>rot</sub> and *T*<sub>th</sub> respectively.

Basically, the fitting algorithm calculates synthetic spectra for different values of the fitting parameters, namely *T*₁, *T*₂, *T*₃, *T*CO, *T*rot, *α*, the pressure *p* and *T*th. The fitting procedure follows successive steps: calculation of the thermal and non-thermal rovibrational state distributions, calculation of the line strengths, application of temperature and pressure broadening considering Voigt profiles, computation of the transmittance using the Beer-Lambert law and finally, convolution of the transmittance with the instrument line shape (approximated as Gaussian).

The temperatures are determined with an error estimated to 30 K for CO₂ and around 100 K for CO using a sensitivity analysis by varying *T*<sub>rot</sub>, *T*<sub>12</sub>, *T*<sub>3</sub> and *T*CO individually, as described in <sup>24</sup>.

<figure><img src="image_5.png" /><figcaption>Figure 2: Example of a fitted IR spectrum. The IR spectrum is represented in black and the calculated spectrum in red ($f = 2$ kHz, $V = 17$ kVpp, gas gap = 2 mm, gas flow = 200 sccm). The absorption band of the asymmetric stretching mode of CO₂ is located between 2200 and 2400 cm⁻¹ (fully absorbed above 2300 cm⁻¹) and the ro-vibrational band of CO between 2000 and 2250 cm⁻¹.</figcaption></figure>

## 2. Results and discussion

### 2.1. Specific energy input

This study investigates and compares the diffuse regime with a classical filamentary discharge regime. The frequency of the sine voltage is chosen as a parameter to switch from one discharge regime to the other. Indeed, for an amplitude of the applied voltage lower than 17 kVpp, the discharge is systematically diffuse for a frequency of 1 kHz. At higher frequencies (2 kHz and 3 kHz), the applied voltage increases too fast to allow a Townsend breakdown to occur and the discharge works in the filamentary regime. The influence of the amplitude of the applied voltage and the gas flow will be
discussed later. The effect of all these parameters can considered using the specific energy input (SEI), which represents the amount of energy dissipated within a defined volume of gas during its interaction with the discharge. Then, many authors use SEI as a scaling parameter for CO conversion to compare discharges with different geometry, pressure, and electrical excitation 28,32–34. The SEI is calculated using equation (3).

$$SEI = \frac{P}{\Phi} \cdot \frac{p_0 T_g}{p T_0} = \frac{\tau \times P}{V} \qquad (3)$$

with P the discharge power, Φ the gas flow injected through the discharge, p₀ and T₀ the standard conditions of pressure and temperature, T_g the gas temperature and p the experimental pressure.

$\tau = \frac{V}{\Phi}$ is the residence time of the gas and V the volume of the discharge obtained by multiplying the area of the electrodes by the gas gap value. It is worthwhile to mention that during the experiments, a careful attention was paid to ensure that no micro discharges were observed when the discharge was running in the diffuse mode at 1 kHz.

To check the possible influence of the gas flow parameter on the dissipated plasma power in the discharge, we have conducted the following analysis. Figure 3a shows the discharge power as a function of the gas flow. For each excitation condition (frequency and amplitude of the applied voltage), the discharge power is almost independent of the gas flow in the explored range. It is worth mentioning that, as mentioned in the introduction, for an APTD generated in N₂ with small admixtures of oxidising gases such as O₂ (tens of ppm), some processes in the gas phase, such as associative ionisation reactions, occur 20. Then, in N₂, a change in the gas flow rate while keeping the electrical parameters unchanged, induces a change in the discharge power. Whereas, in CO₂ APTD, the gas chemistry seems to have almost no influence. This is in good agreement with previous results provided in 15, where the memory effect was found to be independent of the species in the volume.

<figure><img src="image_6.png" /><figcaption>Figure 3: a) Discharge power and b) specific energy input (SEI) as a function of the gas flow for both diffuse regime (Townsend): black shapes (◆: 1 kHz 14 kVpp, □: 1 kHz 15 kVpp, ◊: 1 kHz 16 kVpp, ■: 1 kHz 17 kVpp) and filamentary regime: red shapes (●: 2 kHz 17 kVpp and ○: 3 kHz 17 kVpp).</figcaption></figure>

The specific energy as a function of the gas flow for the different conditions of electrical excitation is represented in Figure 3b. SEI falls rapidly by two orders of magnitude when the gas flow increases from 7.4 sccm to 740 sccm, or residence time decreases from 14.6 s to 146 ms. The higher the gas flow, the lower the residence time of the gas and the lower the SEI for a similar electrical excitation condition. The moderate increase of the gas temperature with SEI (see section 2.3), as well as the independence
of the discharge power regarding the gas flow, makes the SEI just inversely proportional to the gas flow.
The SEI can thus be modified by changing the discharge power for a given gas flow, or by changing the
gas flow for a given power, or by combining both approaches.

<figure><img src="image_7.png" /></figure>

Figure 4: Conversion ratio α as a function of specific energy input (SEI). Our results were added to the figure reproduced from ³². The dashed lines correspond to the fit of the experimental results obtained in the present work by imposing a slope of 0.75 for the diffuse regime (Townsend): black shapes (●: 1 kHz 14 kVpp, □: 1 kHz 15 kVpp, ◇: 1 kHz 16 kVpp) and filamentary regime: red shapes (●: 2 kHz 17 kVpp and ◇: 3 kHz 17 kVpp). Our results were added to the figure reproduced from ³², available under a CC-BY 4.0 license. Copyright © 2023 by the authors. Licensee MDPI, Basel, Switzerland.

<figure><img src="image_8.png" /></figure>

Figure 5: EEDF computed using Bolsig+ ³⁵ and the cross sections from IST Lisbon database ³⁶⁻³⁸ for different reduced electric fields and gas compositions.

2.2. CO₂ conversion factor

Figure 4 is reproduced from an article by Brandenburg et al. ³² and summarises the results obtained by different groups in CO₂ DBDs together with the results of this work. The conversion factor is shown as a function of the SEI. Red circles correspond to conditions for which the discharge works in the filamentary regime, whereas black squares are related to the diffuse discharge regime. The conversion ratio does not exceed a few percents, as it is reported in the literature for different barrier discharge configurations ³⁹. It is important to note that the discharge did not cover the whole electrode surface for the diffuse conditions at 14 kVpp and 15 kVpp. Then, the spreading of the discharge along the gas flow was estimated from the electrical measurements and imaging performed during additional dedicated measurements (see e.g. ¹⁹,⁴⁰). According to the obtained results, measurements at 15 kVpp
were still done within the discharge zone, whereas for the condition at 14 kVpp, the measurements
were done at the boundary between the discharge and the very beginning of the post-discharge. In
the following, the SEI and residence time calculations were done considering the real discharge volume
i.e. considering the spreading of the discharge. The values of α for the filamentary regime are in good
agreement with the ex-situ measurements results obtained by Brehmer et al. ²⁸ in atmospheric
pressure DBD with quartz dielectrics and a gas gap of 1 mm (half of the gap used in this work). For a
given SEI, the α factor is always higher for the filamentary regime than for the diffuse one. Indeed, it is
now well accepted that in DBDs the CO₂ dissociation mainly occurs through direct electron impact with
a low contribution of the vibrational ladder climbing ⁴¹. Then, electrons with high energy in the tail of
the energy distribution function play a significant role. To illustrate this, the electron energy distribution
function (EEDF) was computed using Bolsig+ ³⁵ and the cross sections of the IST Lisbon database ³⁶,
based on the work of ³⁷,³⁸ for reduced electric fields in the range of the diffuse (120–140 Td) and the
filamentary regime (400 to 1000 Td), without CO and with 5 % of CO. The corresponding results are
presented Figure 5. One can see that the presence of CO has almost no consequences on the EEDF due
to the low dissociation fraction. In addition, the total cross section for CO₂ dissociation from Polak and
Slovetsky ⁴² is also presented. The dissociation fraction results from a balance between the production
and destruction of CO molecules. Considering that both regimes share rather similar conditions
(pressure, nature of the surface, gas composition...) and assuming that the dominant production and
destruction mechanisms are the same in both regimes (see discussion further), the lower dissociation
degree observed in the diffuse regime could be explained by the lower reduced electric field values in
this regime, which in turn is responsible for a lower population of energetic electrons. Indeed, E/N
calculated in the diffuse mode remains in the range 120-140 Td for all the conditions presented in this
study, compared to the filamentary regime where typical E/N values within the micro-discharges can
reach around 500 Td in the gas bulk according to the literature ⁴³,⁴⁴. Note that increasing the applied
voltage in the Townsend regime (i.e. at a frequency of 1 kHz), does not result in an increase of the gas
gap voltage, which remains close to the breakdown voltage, keeping unchanged the E/N value. Instead,
it causes the discharge current and, thus, the electron density to increase, resulting in a slight increase
of the discharge power (Figure 3) and thus of the dissociation fraction α (Figure 4). Conversion factor
α grows when SEI increases. Both diffuse and filamentary results can be fitted by a straight line in log-
log scale (which is similar to a power law in linear scale) i.e. α = k × SEIⁿ. A corresponding slope of
n = 0.67 is found for both the filamentary and the diffuse regimes with R-squared values R² = 0.99 and
R² = 0.94 respectively. Aerts et al. ⁴⁵ have already shown using their numerical model that the
conversion factor α in DBDs follows such a power law as a function of the SEI. In their review article,
Brandenburg et al. ³² observed the same behaviour for SEI lower than 10 eV per particle by comparing
the results of several works for different dielectric barrier discharge configurations. In his article
Brehmer et al. reported a slope of n = 0.75 and developed a simple model considering the dissociation
of CO₂ by collisions with electrons as a source term for CO production, and surface and volume
recombination of CO as a loss term. If there are no losses, then n = 1, whereas including recombination
losses leads to a lower value of the exponent. More recently, Douat et al. ³³ reported a similar power
law dependence with n = 0.75 for a discharge in pin-to-pin configuration at lower SEI. They attributed
the power-law dependence to the fact that the number of filaments in filamentary DBDs also follows a
power law. Nevertheless, the fact that this behaviour is also observed in purely diffuse DBD challenges
this hypothesis and suggests that it is probably much more the result of a balance between gain and
loss processes. Our value of the exponent n = 0.67 would thus suggest slightly higher CO losses than
those of Brehmer and Douat, as discussed later. However, fitting our data by imposing n = 0.75 results
in a good agreement for filamentary (R² = 0.98) and diffuse (R² = 0.91) regimes (see dashed lines on
Figure 4). This shows that our results and the previously published ones remain close to each other.
One of the possible explanations for this slight difference might be related to the lower number of measurements in our study.

The three-body recombination, see equation (4), is efficient only at high temperature or at the wall<sup>41,46</sup>, equation (5) (in this case, M represents the wall itself).

$$CO + O + M \rightarrow CO_2 + M \quad (4)$$

$$CO + O + wall \rightarrow CO_2 + wall \quad (5)$$

In our conditions, the gas temperature remains moderate (see<sup>31</sup> and next part), thus if this reaction plays a role, it will likely occur at the surface. The rate of wall recombination is difficult to assess but one can estimate the characteristic diffusion time $\tau_{diff}$ of O and CO to the walls and the associated frequency. Due to the small gas gap compared to the dimension of the system, $\tau_{diff}$ can be approximated to $\tau_{diff} = \frac{d^2}{\pi^2 D}$ where $d = 2mm$ is the gap length and $D$ the diffusion coefficient of the species of interest. Morillo-Candas et al.<sup>47</sup> reported two different diffusion coefficients for atomic oxygen, coming from Cenian et al.<sup>48</sup> and Klarenaar et al.<sup>25</sup>. Under our conditions, $\tau_{diff}$ for O atoms is in the range of 9 – 15 ms using the diffusion coefficient from Cenian, and 2 times larger according to Klarenaar. For CO, estimated $\tau_{diff}$ ranges between 18 and 28 ms where the diffusion coefficient of CO was calculated according to<sup>49</sup>. These values are well below the lower value of the residence time $\tau$ in our conditions which is about 140 ms. It means that particles have enough time to reach the surface by diffusion during their stay within the gas flow. Brehmer et al. used coefficient rates from<sup>48</sup> to study the backreaction mechanisms in gas phase, see equation (4), and at the surfaces, eq. (5), and reported a similar rate coefficient $k \approx 1.5 \times 10^{-15} \text{ cm}^3 \text{ s}^{-1}$. Our results are comparable to<sup>28</sup> in terms of $\alpha$, gap length and gas temperature (see next section). Therefore, we assume a similar coefficient rate for both reaction mechanisms. Considering only these backreaction mechanisms as CO loss channels is consistent with behaviour similar to that observed by Brehmer et al.. Note that also other mechanisms are suspected to be of major importance in the backreactions mechanisms in CO₂ plasmas, such as the metastable species O(¹D) or CO(a³Π), which could react with CO and/or O₂ to form CO₂ again, or O₂(a¹Δg) and O₂(b¹Σ⁺g)<sup>41</sup>. Despite an impossible estimation of their contribution with the available data, the fact that the slope of the $\alpha = f(SEI)$ curve is the same for both discharge regimes suggests that the dominant mechanisms are the same whether they are gain or loss processes, and that their relative importance does not strongly vary with the E/N value in the range covered by the present study.
<figure><img src="image_9.png" /><figcaption>Figure 6: Rotational temperature ($T_{rot}$: ■) and vibrational temperature of CO₂ and CO ($T_{12}$: ▲, $T_3$: ● and $T_{CO}$: ▲) as a function of the SEI in a) Diffuse regime (Townsend) and b) filamentary regime.</figcaption></figure>

## 2.3. Vibrational kinetic

As explained in section 1, due to the Fermi resonance between $v_1$ and $v_2$, important energy transfers occur between these two modes, which are thus strongly coupled and can be considered as a triple degenerate mode associated with a single vibrational temperature denoted hereafter as $T_{12}$. The CO molecule has only one vibration mode associated with temperature $T_{CO}$. Figure 6 shows the rotational temperature $T_{rot}$, the vibrational temperature of the symmetric-bending mode of CO₂ ($T_{12}$), the vibrational temperature of the asymmetric mode of CO₂ ($T_3$) and the vibrational temperature of CO ($T_{CO}$) obtained for both studied discharge regimes. Let us first discuss the results obtained for the diffuse regime (Figure 6a), whereas the results obtained for the filamentary regime (Figure 6b) will be discussed at the end of this section.

The general ordering of the different temperatures: $T_{CO} > T_3 > T_{12} \approx T_{rot}$ is consistent with the results reported in several works<sup>41,50</sup> except that under our conditions, the difference between $T_{CO}$ and $T_3$ is very large, with $T_{CO}$ being at least 500 K higher. Due to the short energy gap between the vibrational levels of symmetric stretching and bending modes of CO₂, the V-T relaxation mechanisms are efficient. The energy of the vibrational levels $v_1$ and $v_2$ is thus easily lost in gas heating, and consequently, $T_{12}$ remains close to $T_{rot}$. On the contrary, the energy gap between the vibrational levels of the asymmetric mode is larger, and thus, the V-T relaxation mechanisms are less efficient. This difference results in a non-equilibrium between symmetric-bending mode ($T_{12}$) and asymmetric stretching mode ($T_3$). This non-equilibrium is generally favoured by the resonance between the vibrational level of CO and the asymmetric stretching mode of CO₂, which can result in vibrational energy transfer from CO to the $v_3$ mode of CO₂. Nevertheless, in our conditions, the dissociation fraction is too low for these energy transfers to significantly contribute to a rise of $T_3$. This is especially true for low SEI for which $T_{CO}$ exceeds $T_3$ by more than 2000 K in the diffuse regime and can at least partly explain why $T_{CO} \gg T_3$. Energy stored in the different vibrational modes can be estimated by the product $\epsilon = nk_B T$, where $n$ is the density of CO₂ or CO, $k_B$ the Boltzmann constant and $T$ the temperature associated to the vibrational mode under study. Corresponding results are represented in Figure 7 for diffuse and filamentary regimes. Note that here $\epsilon_{12} = 2 \times n_{CO_2} k_B T_{12}$. It is clearly visible that the energy of the CO vibrations is very low regarding to the CO₂ vibrational modes. Indeed, $\epsilon_{CO}$ represents less than 1 % of the total vibrational energy. It confirms that even if there is a resonance
between CO and the asymmetric mode of CO₂, the amount of energy stored in the vibrational modes of CO is too low to significantly impact T₃. Other phenomena can also be responsible for this large difference between T₃ and TCO. Vibrational intermodal exchanges occur between the asymmetric mode of CO₂ and the symmetric stretching and bending modes (V-V' exchanges), while these V-V' exchanges do not exist for the CO molecule. Also, according to²⁶, the V-T relaxation processes are slightly more efficient for the v₃ mode of CO₂ compared to CO, whereas vibrational excitation by collision with electronically excited species as CO(a³Π) and O(¹D), which are products of the CO₂ dissociation by direct electron impact, could be more efficient for CO. Fromentin et al.⁵⁰ also reported an unusually large cross section for the excitation of the vibrational levels of CO which is related to a resonance effect with short-lived negative ions CO⁻⁵¹. In conclusion, the higher value of TCO compared to T₃ probably results from a combination of several mechanisms, including: 1) limited vibrational energy transfer from CO to CO₂, 2) V-V' transfers and higher V-T relaxation for v₃ compared to CO and 3) higher energy transfers towards the vibrational levels of CO.

<figure><img src="image_10.png" /><figcaption>Figure 7: Energies associated to the vibrational temperatures *T*<sub>rot</sub>, *T*<sub>12</sub>, *T*<sub>3</sub> and *T*<sub>CO</sub> as a function of the SEI for diffuse regime (filled shapes) and filamentary regime (empty shapes).</figcaption></figure>

Another interesting phenomenon is the evolution of the temperatures with the SEI, and especially TCO.
The trends are similar for both regimes. As SEI increases, TCO rapidly decreases. In the diffuse regime,
it drops from 2073 K at 73 J/l to 986 K at 3058 J/l. The decrease is less pronounced for T<sub>3</sub>. Indeed, on
the same range of SEI, it only decreases from 520 K to 413 K. Whereas T<sub>12</sub> only slightly increases from
room temperature (300 K) for the lower SEI to 348 K for 13877 J/l. Having in mind that the dissociation
fraction α in both regimes is different, it is interesting to have a look at the evolution of the
temperatures as a function of α. Figure 8 shows the evolution of TCO with α. All the experimental data
for both regimes are aligned on the same curve, indicating that α is a relevant parameter and
suggesting that the dissociation products O and/or CO can play a role in this evolution. Atomic oxygen
is known to be a good quencher of vibrational levels and the V-T relaxations of CO₂ and CO molecules
by collision with O atoms are dominant²⁶. Figure 9 shows the quenching frequencies of the vibrational
levels of CO and CO₂ (ν₂ and ν₃) by O atoms as a function of α. These frequencies were determined by
multiplying the quenching rate coefficient *k* taken from the literature ²⁶,⁵⁰ by the density of O atoms,
which is estimated from the dissociation fraction using the ideal gas law and the measured rotational
temperature. The O atoms density was considered equal to the CO density, thus neglecting
recombination. In this way, atomic oxygen density is overestimated, and the computation provides an
upper limit of the quenching rate. V-T relaxation rate by CO₂, which is the dominant species within the discharge, is added for direct comparison. The quenching rate coefficient of CO₂ symmetric and asymmetric stretching modes were found in ²⁶,⁵⁰ from the work of ⁵²⁻⁵⁴. The rate coefficient for the quenching of CO(ν = 1) by collision with O atoms came from ⁵⁵ and the rate coefficient for V-T relaxation of CO(ν) through collisions with CO₂ was obtained using the same method as described in ⁵⁰. Due to the large number of CO₂ molecules in our conditions (low dissociation rate), deexcitation frequencies of CO₂ by collision with another CO₂ molecule are almost constant independently of the conversion factor. The calculated quenching frequencies by O atoms increase rapidly for low values of α with the apparition of CO and O. The results clearly show that V-T processes of CO are dominated by collisions with O atoms. The deexcitation frequency is thus directly related to the O atom density. It is thus reasonable to assume that for very low SEI, the appearance of O atoms in the discharge is responsible for a significant increase of the V-T processes of CO, leading to the observed drop of T<sub>CO</sub> in the diffuse and filamentary regimes. In addition, due to the large amount of CO₂, V-T relaxations of CO₂ vibrations by collision with another CO₂ molecule are efficient, which could explain why T<sub>3</sub> and T<sub>12</sub> remain low whatever the dissociation degree. A large difference between the vibrational temperatures of CO and the asymmetric mode of CO₂ was also observed in noble gases with an admixture of CO₂ ²⁹,³⁰. In these works, the dilution of CO₂ into noble gas limits the transfer between T<sub>CO</sub> and T<sub>3</sub> as it is in our conditions due to the low amount of CO. It also reduces the quenching rate of CO vibrations by atomic oxygen.

<figure><img src="image_11.png" /><figcaption>Figure 8: Vibrational temperature of CO as a function of α. Diffuse regime (Townsend): black shapes (◆: 1 kHz 14 kV<sub>pp</sub>, □: 1 kHz 15 kV<sub>pp</sub>, ◦: 1 kHz 16 kV<sub>pp</sub>, ■: 1 kHz 17 kV<sub>pp</sub>) and filamentary regime: red shapes (●: 2 kHz 17 kV<sub>pp</sub> and ○: 3 kHz 17 kV<sub>pp</sub>).</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Figure 9: V-T relaxation frequencies of the vibrational levels of CO₂($v_2$ and $v_3$) and CO($v$) by collision with O and CO₂ as a function of $\alpha$. Diffuse regime (Townsend) corresponds to filled shapes and filamentary regime is associated to empty shapes. The reactions involving atomic oxygen are represented in red and those involving CO₂ molecule as collision partner are in blue. Two different reaction rates, coming from 26 (■) and 50 (★), were used for the calculation of the V-T frequencies by collision with O for the symmetric bending mode ($v_2$).</figcaption></figure>

In the filamentary regime (Figure 6b), the main difference with the results obtained in the diffuse regime concerns $T_3$ which is equal to $T_{12}$ and $T_{rot}$. The general ordering becomes $T_{CO} > T_3 \approx T_{12} \approx T_{rot}$. Note that in addition for a given SEI, $T_{CO}$ is systematically lower compared to the diffuse regime (from 300 K at lower SEI to 150 K i.e. above the error bar). One of the possible explanations is related to the measurement technique itself. Indeed, FTIR absorption measurements are integrated over space (along the beam path and the width of the beam) and over time. The filamentary discharge being made of numerous plasma filaments randomly distributed in time and space, an average is done during the measurements between the gas contained within the filaments and the cold gas located around. Another hypothesis is that in the filamentary regime, the dissociation of CO₂ molecules occurs within the volume of a plasma filament, which means that the local density of the dissociation products can reach high values during the filament lifetime. The aforementioned V-T processes related e.g. to oxygen atoms can thus be significantly higher compared to the diffuse discharge, explaining both the lower $T_{CO}$ and $T_3$ even for very small SEI. This V-T processes probably also plays a role in the diffuse regime but to a lower extent: $T_3$ continuously decreases when increasing the SEI and approaches the value of $T_{12}$ only for the largest SEI investigated. As a conclusion, the observed equilibrium between $T_3$, $T_{12}$ and $T_{rot}$ in the filamentary regime probably results both from an averaging effect during the measurement and from strong V-T energy transfers due to a high O atoms density within the plasma filaments.

To go further in this discussion, an accurate determination of the O atom density is thus necessary as well as the use of a detailed modelling of the vibrational kinetics.

### 3. Conclusions

In-situ FTIR measurements were performed in pure CO₂ DBD at atmospheric pressure in the diffuse and filamentary regimes. The results were analysed to get the dissociation fraction and the vibrational
excitation of CO₂ and CO through the determination of the vibrational temperatures *T*₃, *T*₁₂ and *T*CO of the CO₂ and CO molecules, respectively.

The dissociation fraction follows a power law with respect to the specific energy input (SEI) with an exponent of 0.67 for both the diffuse and the filamentary regimes. It is close to value of 0.75 already published in the literature²⁸,³³. This power law is probably the result of the complex chemistry taking place in CO₂ discharges. The maximum conversion rate in the investigated range of specific energy input (SEI) was about 4% at 46 000 J/l (≈10 eV/particle). For a given SEI, the dissociation was found to be more efficient in the filamentary regime, probably due to higher values of the reduced electric field.

In the diffuse regime, the ordering of the different temperatures is similar to what has already been reported in the literature: *T*<sub>CO</sub> > *T*<sub>3</sub> > *T*<sub>12</sub> ≈ *T*<sub>rot</sub>. Nevertheless, we observed an unexpectedly significant difference between *T*<sub>3</sub> and the temperature *T*<sub>CO</sub>. Part of the explanation probably relies on the low density of CO molecules limiting the transfer between vibrations of CO and the asymmetric mode of CO<sub>2</sub>. In addition, a significant drop of *T*<sub>CO</sub> with SEI was observed for low SEI values in both discharge regimes, which was attributed to V-T transfers with oxygen atoms. Surprisingly in the filamentary regime, *T*<sub>3</sub> is found to be equal to *T*<sub>12</sub> over the whole range of SEI investigated. It can result from an averaging effect between the excited gas within the plasma filaments and the surrounding cold gas during the absorption measurements and to strong V-T transfers in the filaments due to the higher density of O atoms. To go further, the possible role played by ground state and excited species, such as CO(a<sup>3</sup>P) or metastable states of molecular oxygen, would require a numerical model to be investigated. In addition, the determination of the O atoms density would be beneficial to definitely validate the aforementioned hypothesis, which will be the topic of future work.

## Acknowledgments

This work has been supported by the Hubert Curien Partnerships Barrande program funded jointly by the Ministry of Education, Youth and Sports of the Czech Republic and the French Ministry for Europe and Foreign Affairs (project 8J23FR008) and Campus France, by the French network on cold plasmas from the CNRS (Réseau des Plasmas Froids) and the GDR EMILI. Part of the work was carried out with the support of CEPLANT Research Infrastructure (LM2023039) funded by the Ministry of Education, Youth and Sports of the Czech Republic.

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<figure><img src="image_13.png" /><figcaption>TOC Graphic</figcaption></figure>