Time-Resolved CO₂ Dissociation in a Nanosecond Pulsed Discharge

Abstract

Electrical discharges are increasingly used to dissociate CO₂ in CO and O₂. This reaction is the first step in the way for the synthesis of value-added compounds from CO₂ by using renewable electricity. If efficient, this technology might allow at the same time recycling CO₂ and storing renewable energy in chemical form. At present, while the dissociation degree is measured in the reactor exhaust, little is experimentally known about the dissociation kinetics in the discharge and post-discharge. This knowledge is however critical to increasing the overall efficiency of the plasma process. To estimate the time dependence of the CO₂ dissociation following a discharge event, we have coupled a LIF diagnostics to a nanosecond repetitively pulsed discharge in a mixture of CO₂ and H₂O. This paper discusses a procedure to obtain data on the time evolution of the CO₂ dissociation, its limits and future perspectives. In addition, the local gas temperature is measured as well. We find that a few microseconds after the discharge pulse, CO₂ is highly dissociated with a temperature around 2500 K. In about 100 µs, the temperature decreases at about 1500 K while the dissociation is reduced by about a factor of three.

Introduction

If driven by renewable energy, the efficient conversion of CO₂ into fuels and value-added products would be a tremendous step forward towards a sustainable energy scenario and an economy less dependent on fossil fuels [1]. In fact, besides recycling CO₂, the simultaneous efficient storage of renewable electricity in the chemical form would open the way for both an increasing share of intermittent energy sources and the electrification of the chemical industry.

Among the novel technologies proposed for the CO₂ conversion, the only one that currently parallels in performance a more mature technology as the water electrolysis is the plasma-chemical conversion, whose record solar-to-fuel efficiency, 23%, compares favourably with the 19% value of the water electrolysis [2].

Recently, and with increasing evidence, it has become clear that the key to the success of the plasma-chemical conversion of CO₂ lies in the non-equilibrium feature of cold plasmas [2, 3]. Although the dielectric barrier discharge is at the moment the most popular discharge for the plasma conversion of CO₂ [4,5,6,7,8,9], we decided to exploit a plasma characterised by a higher degree of non-equilibrium, namely a Nanosecond Repetitively Pulsed discharge (NRP). Understanding the promising results achieved by using the NRP [10] requires a thorough study of the microscopic processes occurring in the plasma. For this purpose, we have investigated the time evolution of CO₂ dissociation in the post-discharge by time-resolved Laser Induced Fluorescence (LIF) diagnostics. In such an approach, the discharge is no longer a “black box”, since we can investigate what happens in the time interval between each pair of pulses.

In this paper, we show results on the fragmentation kinetics of CO₂ on the μs scale in the post-discharge by performing Collisional Energy Transfer LIF, CET-LIF, [11] on the OH radical, which is used as a probe molecule. The OH radical is produced in the discharge by adding trace H₂O to CO₂. Our data indicate that the final CO₂ dissociation, i.e. the one observed in the exhaust of the reactor, is much lower than that found immediately after a single discharge event. As a consequence, much room exists for improvements in the process performance.

Experimental

Discharge Apparatus

The plasma driven CO₂ conversion was carried out in a pin-to-sphere configuration, see Fig. 1. It is worth to note that we have chosen this electrode arrangement because it is suitable to be coupled with the LIF diagnostic, and not to get the maximum conversion value.

Fig. 1

Schematic representation of the experimental setup. FC1, FC2 and FC3: mass flow controllers (1179, MKS) with 500, 200 and 1000 sccm full scale, respectively; WFG waveform generator, NPG nanosecond power supply, HV probe high voltage probe, I.S. internal standard IS

The high voltage (HV) electrode was a stainless steel tube (internal diameter 1.2 mm, external diameter 1.65 mm), which also acted as inlet gas line. The grounded electrode was a stainless steel sphere (8 mm in diameter) placed in front of the needle. The inter-electrode gap was set at 5 mm.

NRP discharges were produced by an NPG 18/3500 power supply,(Megaipulse Ltd.), triggered by a wave-form generator (33220A, Agilent). In this work, the pulse repetition rate $f_{p}$ ranged from 900 to 3000 Hz. The applied voltage $V\left( t \right)$ and the current $I\left( t \right)$ flowing in the discharge were measured by a high voltage probe (P6015A, Tektroniks) and an I/V converter (CT-D1.0, Magnelab), respectively. A digital oscilloscope (WaveSurfer 104MXs-A, LeCroy) was used to record $I\left( t \right)$ and $V\left( t \right)$. The energy delivered by each pulse $Ep$ was calculated as the time integral of the product of the measured voltage $V\left( t \right)$ and current $I\left( t \right)$. The spurious time delay between $I\left( t \right)$ and $V\left( t \right)$ was measured when no breakdown occurred and appropriately taken into account [10].

Two mass flow controllers set the CO₂ input flow. A CO₂ stream flowed through a water vessel kept at 15 °C, then was furtherly diluted by a dry CO₂ stream. The total CO₂ flow through the HV needle was 100 sccm. The water vapour content in the inlet gas was 1.35%, partial pressure 10 Torr, for a total pressure of 735 Torr.

Effluent Gas Analysis

A two channels gas chromatograph (GC) equipped with a thermal conductivity detector (3000 Micro GC, Agilent) is placed in the exhaust gas line for in-line analysis. N₂ (9%) was added to the exhaust gas as an internal standard (IS) to take into account the mole variation due to the CO₂ dissociation. After external standard calibration, nitrogen, carbon monoxide and hydrogen were quantified by a Molsieve 5A column with back-flush, whereas carbon dioxide was quantified by a PLOT U column. Argon was used as a gas carrier. GC analysis was run before and during each plasma process. The CO₂ conversion ($C_{{CO_{2} }}$) is calculated as:

$$C_{CO2} ( {\text{\% )}} = \frac{{n_{CO2}^{in} \left( {mol} \right) - n_{CO2}^{out} \left( {mol} \right)}}{{n_{CO2}^{in} \left( {mol} \right)}} \cdot 100$$

(1)

where $n_{CO2}^{in}$ and $n_{CO2}^{out}$ are the measured input and output CO₂ mol.

Laser Induced Fluorescence Apparatus and Method

We already presented the LIF setup in [12], and the reader can refer to that paper. For the time-resolved LIF measurements, we used a discharge pattern made of pulse bursts repeated at a frequency of 300 Hz, corresponding to a burst period of $T_{b}$ = 3.33 ms. Each burst was composed of 4 pulses, each other separated by $T_{p}$ = 333 μs, corresponding to a pulse frequency inside the burst of 3 kHz. A digital delay generator synchronised the laser firing with the discharge pattern. LIF measurements on the OH radical were carried out at 10 Hz as a function of the time delay $t_{d}$ from the last pulse of the corresponding burst, see Fig. 2.

Fig. 2

Temporal pattern of the discharge (upper graph) and laser firing trigger (lower graph). The discharge operated in burst mode (burst period $T_{b}$ = 3.33 ms; pulse to pulse period $T_{p}$ = 333 μs), the LIF measurement was carried out at a variable delay $t_{d}$ respect to the last pulse of the burst every 100 ms

By LIF spectroscopy we can obtain information on both temperature and composition of the gas. For OH, we used the classical LIF scheme [12]

$$\begin{array}{*{20}c} & OH\left( {X,0,N^{\prime\prime}} \right) + hv_{L} & \to & OH\left( {A,1,N^{\prime}} \right) & \to & OH\left( {X,1} \right) + hv_{1,1} & \\ & & & \downarrow VET & & \\ & & & OH \left( {A,0} \right) & \to & OH\left( {X,0} \right) + hv_{0,0} \\ \end{array}$$

(2)

The gas temperature T can be measured by recording the excitation spectrum of ${\text{OH}}$, i.e. the spectrum obtained by scanning the laser frequency and recording the fluorescence with a fixed spectral window including, in our case, the entire (0, 0) and (1, 1) bands. In such a way the different rotational levels $N^{\prime\prime}$ of ${\text{OH}}\left( X \right)$ are probed, whose population is determined by the gas temperature (given the equality T_rot = T for ${\text{OH}}\left( X \right)$). We used the transitions R₂(9) at 2817.32 Å, R₁(11) at 2817.38 Å, R₂(4) at 2817.57 Å, and R₂₁(11) at 2817.59 Å and we fitted the experimental spectrum with a synthetic spectrum with T as a free parameter. The present choice of transitions includes quite high rotational numbers, and is more suitable for temperatures higher than 1000 K than the set of transitions used in [12] that were chosen for temperature measurement in a cold plasma jet.

Due to the collisions with the surrounding molecules M, the fluorescence photons are emitted from levels other than the single state ${\text{OH}}\left( {A,1,N^{\prime}} \right)$ populated by the laser. In particular, the rotational energy transfer process, RET, populates rotational levels other than $N^{\prime}$ in ${\text{OH}}\left( {A,1} \right)$ and eventually generates the fluorescence $hv_{1,1}$, while the vibrational energy transfer process, VET, ${\text{OH}}\left( {A,1} \right) + M \to {\text{OH}}\left( {A,0} \right) + M$ populates the ${\text{OH}}\left( {A,0} \right)$ that produces the fluorescence $hv_{0,0}$. The gas composition affects the LIF spectrum because the single state initially excited by the laser is depopulated non-radiatively by collisions with the background gas. Since the frequency of the energy transfer processes strongly depends on the collision partner [13], different gas mixtures give rise to distinct fluorescence spectra. Thus in principle, one can infer the gas composition if the relevant rate coefficients are known. Such a procedure has been described in [11]. The ratio between the (1, 1) and (0, 0) bands depends on the CO₂ dissociation. The conversion of CO₂ to CO and O₂ lowers the VET effectiveness since both CO and O₂ are collisional partners M less efficient than CO₂ for the vibrational energy transfer process ${\text{OH}}\left( {A,1} \right) + M \to {\text{OH}}\left( {A,0} \right) + M$. In particular, the band ratio depends only on the rate coefficient ratio k_VET/k_Q0 [11], where k_VET is the effective (dependent on the gas composition) VET rate coefficient, and k_Q0 is the effective rate coefficient for the quenching of the ${\text{OH}}\left( {A,0} \right)$ state. By fitting the LIF spectrum using the 5-level model described in [12], the ratio k_VET/k_Q0 can be inferred and eventually the gas composition can be calculated once the collisional rate coefficients are known. This is the CET-LIF procedure we have presented in [11].

It is worth to underline that the sole dependence on the k_VET/k_Q0 ratio makes the procedure independent of the absolute concentration of the gas components. This fact is crucial in our specific case, in which the discharge channel has an explosive behaviour, i.e. a fast gas heating, in the first few ns, up to 2000–2500 K temperatures, followed by gas expansion and cooling in the tens of μs timescale.

There are two points to address before CET-LIF can give fully quantitative outcomes. Both points arise from the fact that reliable collisional data are available mainly at room temperature and for thermalised rotational distributions of ${\text{OH}}\left( {A,0 - 1} \right)$ [13].

The first point is due to the rate coefficient dependence on the rotational levels. Rotational thermalisation requires a sufficient number of RET collisions within the lifetime of the vibro-electronic state. In a mixture of CO₂, CO and O₂ as main components, this is not achieved, since the rapid collision quenching shortens too much the lifetime. Both ${\text{OH}}\left( {A,1} \right)$ and ${\text{OH}}\left( {A,0} \right)$ present a non-Boltzmann rotational distribution, since: ${\text{OH}}\left( {A,1} \right)$ starts from a nascent distribution in which only one rotational level is populated by laser light absorption; ${\text{OH}}\left( {A,0} \right)$ starts from a highly supra-thermal distribution generated by the VET population process [11, 14]. A detailed knowledge of the the actual rotational distribution of the ${\text{OH}}\left( A \right)$ state and of specific rate coefficients related to those rotational distributions is then required. From now on we call these specific rate coefficients with the adjective “non-thermal”. Such a measurement campaign is in due course.

The second point is the temperature dependence of the rate coefficients, that might induce a temperature dependence of the k_VET/k_Q0 ratio, or of the cross sections, given that k_VET/k_Q0 = σ_VET/σ_Q0. Here we deal only with “temperature averaged” cross sections. This issue is critical in our case since in the discharge pulse, as we shall see, the temperature rises to about 2500 K and then decreases to about 1000 K in the after-pulse. The temperature dependence is determined by the interaction between ${\text{OH}}\left( A \right)$ and the collider. The latter, being governed by attractive forces, gives rise to the following law for the temperature averaged cross section as a function of T [15,16,17]:

$$\sigma = \sigma_{\infty } { \exp }\left( {{\raise0.7ex\hbox{$\epsilon $} \!\mathord{\left/ {\vphantom {\epsilon {kT}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${kT}$}}} \right) .$$

(3)

where $\epsilon$ is related to the well depth of the attractive potential and $\sigma_{\infty }$ is the value at very high T. The $\epsilon /k$ value, determined in [16] for the quenching of (A, v = 0), is equal to 488, 397 and 243 K for CO₂, CO and O₂ respectively. As a consequence, in the range 1400–2500 K (that is the temperature variation of our measurements), the temperature dependence of the cross section is rather smooth and small (see also the collection of measurements reported in [15]). Should this law be strictly true, both VET and quenching would have the same dependence on T, since the well depth for low v is negligibly affected by the vibrational state, such that the ratio σ_VET/σ_Q0 is independent on T. Actually, although this conclusion appears reasonable and the law (3) has been found to provide a good fit to the available data at different temperatures for the (A, v = 0) quenching [16], it has no true experimental demonstration. VET cross sections measurements exist at ambient temperature (see [11] and references therein), including a data set at 195–294 K [17], and for high temperatures in a shock tube at 1900 and 2300 K [18]. A larger data set exists for quenching cross sections, for which law (3) has been tested [16]. In [18] it was noted that the cross sections do not change appreciably from 1900 to 2300 K and that, for CO₂ collider, the ratio σ_VET/σ_Q0 at high temperature is substantially the same as that at 300 K.

It is clear that this issue requires further investigation. At the present status of the knowledge, and for the present purposes, we conclude that the ratio σ_VET/σ_Q0 is independent of T and equal to the value at T = 300 K in the best case, while in the worst case it is reasonably independent of T, in the temperature range 1400–2500 K of our concern, and with a value that can be slightly different from that at T = 300 K.

Waiting for fully clarifying these issues, it is nevertheless possible to establish a procedure based on the current knowledge to estimate the gas composition. The method is based on the following assumptions: a) the k_VET/k_Q0 ratio is independent on T; b) the non-thermal k_VET/k_Q0 ratio can be determined by measuring spectra of pure gases in a cell at T = 300 K; c) the differences between thermal and non-thermal k_VET/k_Q0 ratios are due mainly to variations of k_Q0.

Assumption (a) has been already justified, while points (b) and (c) are discussed in the following.

The starting point is that fluorescence spectra recorded from a gas cell at room temperature with pure gases [11] can be used to estimate the non-thermal k_VET/k_Q0 ratios, once the rotational distributions of both ${\text{OH}}\left( {A,1} \right)$ and ${\text{OH}}\left( {A,0} \right)$ are guessed, as in [11]. Two spectra are shown in Fig. 4b, for comparison with spectra measured in the discharge. They refer to the cases of pure CO₂ and pure CO. As a rough guess of the rotational distribution of ${\text{OH}}\left( {A,0} \right)$, we have used a Boltzmann one at T_rot = 1500 K. Such a guess, at the present spectral resolution, appears to be equally good for both CO₂ and CO. The case of pure O₂ is almost identical to that of CO, so that it is not reported in the figure to avoid confusion (note that, from the data of [13], the thermal k_VET/k_Q0 ratio is practically the same for CO and O₂). Then, the CO case spectrum of Fig. 4b is, with very good approximation, what is expected in the case of full CO₂ dissociation into CO and O₂. We underline that the estimate of the non-thermal k_VET/k_Q0 ratio depends on the rotational distribution guess for ${\text{OH}}\left( {A,0} \right)$ state. Having chosen the same guess for the three pure gases can be a source of error in the estimation of the gas composition, i.e. the absolute CO₂ dissociation. Nevertheless, the, relative time evolution of the band ratio after the discharge pulse should not be affected, since no significant change in the rotational distributions is observed along the time.

Finally, we point out that differences between thermal and non-thermal k_VET/k_Q0 ratios must very likely be attributed mainly to variations of k_Q0 only. As reported in [11], both k_VET and the rotational distribution of ${\text{OH}}\left( {A,0} \right)$ do not depend appreciably on the rotational level excited by the laser, i.e. they appear to be independent on the rotational distribution of ${\text{OH}}\left( {A,1} \right)$. On the other hand, as pointed out in [13], the thermal quenching, due to fast RET transfers, is dominated by the faster quenching rates of low J-levels. In the present non-thermal case, in which RET rates are slower than the quenching, the quenching rate corresponds to an average of individual J-levels quenching rates, such that slowly quenched J-levels contribute much to the value averaged over the rotational distribution. Although this hypothesis is reasonable, it can be another source of error, We return on this point later, showing how much it can affect the gas composition estimation.

In summary, the use of the empirical non-thermal k_VET/k_Q0 ratios at T = 300 K to analyse the band ratio values and obtain the gas composition does not affect the temporal behaviour of the gas mixture in the after-pulse, while it may affect its absolute value by an amount that we shall try to estimate. The mixture composition found in the effluent gas by GC measurements is a reference to compare with CET-LIF estimations.

Results and Discussion

Effluent Products and Final CO₂ Conversion

The main products of discharge treatment were CO and O₂. A negligible amount of H₂ was detected (< 0.05%). Although powders were found in the reactor, the carbon balance is always higher than 98%. We report in Fig. 3 the CO₂ conversion as a function of the specific energy input (SEI) calculated as:

Fig. 3

Conversion of CO₂ in dry and humid condition (upper graph), energy conversion efficiency $\eta$ and energy cost $EC$ (lower graph) as a function of SEI. Measurement in the effluent gas by gas chromatography (GC)

$$SEI \left( {{\text{kJ}} \;{\text{dm}}^{ - 3} } \right) = \frac{{P_{d} \left( {\text{W}} \right) }}{{\phi_{r} \left( {{\text{cm}}^{3} \;{\text{s}}^{ - 1} } \right)}} = \frac{{\widetilde{{E_{p} }}\left( {\text{J}} \right) f_{p} \left( {\text{Hz}} \right) }}{{\phi_{r} \left( {{\text{cm}}^{3} \;{\text{s}}^{ - 1} } \right)}} ,$$

(4)

$$SEI \left( {{\text{kJ}}\;{\text{mol}}^{ - 1} } \right) = \frac{{P_{d} \left( {\text{W}} \right) }}{{\phi_{r} \left( {{\text{cm}}^{ 3} \;{\text{s}}^{ - 1} } \right) 22.4 \left( {{\text{dm}}^{ 3} \;{\text{mol}}^{ - 1} } \right)}} = \frac{{\widetilde{{E_{p} }} \left( {\text{J}} \right) f_{p} \left( {\text{Hz}} \right) }}{{\phi_{r} \left( {{\text{cm}}^{ 3} \;{\text{s}}^{ - 1} } \right) 22.4 \left( {{\text{dm}}^{ 3} \;{\text{mol}}^{ - 1} } \right)}}$$

(5)

where $P_{d}$ is the discharge power, $\widetilde{{E_{p} }}$ is the mean discharge pulse energy calculated averaging 500 $E_{p}$, $\phi_{r}$ is the standard flux of reactant gases. The SEI value is varied by acting both on the discharge voltage, i.e. on the pulse energy, and on the frequency. The conversion comes out to be dependent on the SEI value only. In the same figure the energy conversion efficiency $\eta$ and the energy cost $EC$ are shown:

$$\eta = \frac{{C_{{CO_{2} }} \Delta H_{{300\;{\text{K}}}}^{0} \left( {{\text{kJ}}\;{\text{mol}}^{ - 1} } \right)}}{{SEI \left( {{\text{kJ}}\;{\text{mol}}^{ - 1} } \right)}}$$

(6)

$$EC\;({\text{eV}}\;{\text{molecule}}^{ - 1} ) = \frac{{SEI \left( {{\text{kJ }}\;{\text{mol}}^{ - 1} } \right) 6.24 \cdot 10^{21} \left( {{\text{eV }}\;{\text{kJ}}^{ - 1} } \right)}}{{C_{{CO_{2} }} 6.022 \cdot 10^{23} \left( {{\text{molecule }}\;{\text{mol}}^{ - 1} } \right)}}$$

(7)

where $\Delta H_{{300\;{\text{K}}}}^{0}$ = 283 kJ mol⁻¹ is the reaction entalpy for pure CO₂ splitting [2].

In Fig. 3, data are reported for dry CO₂ and for humid CO₂ with the addition of 1.35% of H₂O. The primary purpose of water addition is to compare effluent gas conversion to CET-LIF outcomes. Interestingly we note that water addition lowers CO₂ conversion and anticipates its saturation behaviour on increasing SEI. In [10] we argued a role of water formation as a limiting factor for the conversion. Specific studies are needed to clarify this issue.

LIF Results: CO₂ Conversion

First, we point out that all LIF measurements start at a delay of 4 µs after the discharge pulse. Earlier delays cannot at present be reached due to the overwhelming light emission generated by the discharge itself that blinds the detectors. Measurements are reported until a useful LIF signal could be recovered. Due to OH concentration decrease, after 150 μs the signal drops too much for reliable signal analysis.

The CET-LIF procedure shows a significant variation of the gas composition as a function of the time after a discharge pulse. An example of the fluorescence spectra at two different time-delays is shown in Fig. 4. It is evident that the ratio between the (0, 0) and (1, 1) bands increases as a function of time, indicating an increasing efficiency of the VET processes. The post-discharge spectra in comparison with the pure gases spectra measured in a cell, appear to be intermediate between the two pure gases one, or, in other words, between the full and null CO₂ dissociation. The k_VET/k_Q0 ratio time evolution, deduced from the LIF spectra, after the last discharge pulse in the burst is reported in Fig. 5. According to the discussion of par. 2.3 we are allowed to explain it as mostly due to a change in the gas composition, i.e. to the conversion of CO₂ into CO and O₂.

Fig. 4

a Fluorescence spectra in the CO₂ + 1.35% H₂O NRP discharge at two delays from the last pulse of the burst. SEI = 7.2 kJ dm⁻³. b Spectra measured in a cell at room temperature filled with CO₂ (red) and CO (black), and with a very small addition of H₂O₂ + H₂O. The laser is tuned to the P₁(3) line

Fig. 5

Temperature, k_Q0/k_VET and $C_{{CO_{2} }}$ as a function of the delay after the last pulse of the burst. Gas composition CO₂ + 1.35% H₂O, SEI = 7.2 kJ dm⁻³. CO₂ splitting causes a decrease of the k_VET/k_Q0 ratio. The 12% CO₂ dissociation in the effluent gas measured by GC is reported as a red horizontal line

LIF Results: Gas Temperature

Examples of experimental excitation spectra fitted by synthetic ones at the appropriate temperature are plotted in Fig. 6 at increasing time-delays from the discharge. The change of lines ratio corresponding to the temperature range is evident. The evolution of T in the post-pulse is reported in Fig. 5. Error bars are calculated by the fitting algorithm. T varies in the range from around 2500 K at 5 μs after the discharge down to around 1400 K after around 150 μs. Again, at higher delays, the LIF signal decreases too much for a reliable measurement. The timescale of gas cooling is comparable to that of gas expansion after its fast heating in the discharge [19]. The expansion is followed by recirculation of cold surrounding gas, that might be one of the possible causes for the decrease of the “local” dissociation degree in the region sampled by the laser.

Fig. 6

Excitation spectra of OH at different delays with respect to the last discharge of a burst. Gas composition CO₂ + 1.35% H₂O, SEI = 7.2 kJ dm⁻³

LIF Results: Discussion

The most important finding is the substantial variation of the gas composition in the post-discharge. In addition, we have tried to quantify the CO₂ dissociation according to the procedure detailed in Sect. 2.3, to get a reasonable idea of the quantities involved. The k_VET/k_Q0 ratio, in the hypothesis of its temperature independence in the high-temperature range of the measurements, correctly represents the relative time evolution of the gas composition, while the absolute CO₂ dissociation value is somewhat influenced by the choices made in the analysis of the spectra in the cell filled with pure gases. In Fig. 5 we report the dissociation values calculated with the procedure of “Laser Induced Fluorescence Apparatus and Method” section, The red points are those calculated assuming that the whole difference between the thermal and the non-thermal k_VET/k_Q0 ratios is due to a variation of k_Q0 only. Although very reasonable, can be somewhat incorrect. To look for the effect of a different choice, we have calculated the dissociation values in the cases: (a) the difference is equally shared between k_VET and k_Q0 (dark shadow); (b) the difference is attributed to k_VET only (light shadow). In Fig. 5, it is also reported the dissociation value of about 12% found in the effluent gas at the same SEI of = 7.2 kJ dm⁻³ by GC measurements. There are many reasons for which this value can be lower than it is at 150 μs in the after-pulse: a further decrease in the post-pulse due to still evolving chemical kinetics; the further cooling of the gas; the fact that the discharge pulses sequence in the burst may not fill the entire gas volume, such that a lower dissociation value in GC measurements gas can be due to the presence of an “untreated” part of gas. Certainly, the C_CO2 value of the effluent gas cannot be larger than the value at 150 μs in the post-discharge. It then represents a lower limit for the CO₂ dissociation estimated by CET-LIF.

Finally, and thanks to this lower limit, if we put into question the main hypothesis of temperature independence of the k_VET/k_Q0 ratio, and attribute the k_VET/k_Q0 variation in the post discharge to the temperature change, we are led to rather odd conclusions: most (about a factor of 2) of the k_VET/k_Q0 change with temperature must occur in the temperature range 1400–2500 K, while a minimal change should occur in the range 300–1400 K. This is exactly the opposite of the temperature dependence of law (3). Reminding that law (3) is experimentally verified for the cross sections of the quenching of (A, v = 0), we should conclude that the VET cross section must have quite an exotic dependence on T, with a monotonic decrease at least up to 2500 K.

It is important to correlate the results obtained for the temperature and the dissociation. Allowing for data scattering, temperature measurement errors and the fact that our measurements start 4 µs after the discharge, we can set a maximum value of the temperature at about 2800 K. In a thermal process, the dissociation value at 2800 K is about 31%, and even at 3000 K it raises to 46% (see Fig. 2 in [2]). A few μs after the pulse, the CO₂ dissociation estimated by CET-LIF analysis is about 60% at 2500 K, see Fig. 5, or even larger if we move into the shadowed area. With all the caution related to the uncertainty of the CET-LIF analysis, and given that equilibrium concentrations in a thermal process may not be valid in this fast transient system, we feel encouraged to think that important non-equilibrium mechanisms are at work in the ns discharge.

Conclusions

The main result of the present paper is the disclosure of time evolution of the CO₂ dissociation after a discharge pulse. In comparison to the dissociation degree measured in the effluent gas at the exit of the reactor, we observe in the near post-pulse a much higher value that successively decreases by about a factor of three. Of course, this finding indicates room for improvements that relies on understanding the causes of such a decrease: (a) fluid-dynamic—remixing with “untreated” gas after fast expansion of the discharged volume; (b) chemical back-reactions; (c) still too slow cooling of the gas.

Insights into these issues can be achieved thanks to time-resolved, local diagnostics again. The precious help of LIF has been shown here, as a tool that opens a window in the “black box” of a plasma gas treatment, but also how much this technique is complicated and even now in need of fundamental data. So much so that the full quantitative application of CET-LIF still requires investigations on the non-thermal collision rate coefficients and their temperature dependence. We indeed believe that efforts are worth in this direction, and in general, in the development of diagnostic techniques in such a harsh environment.

A final consideration concerns the non-equilibrium contribution to the conversion. Though at present we cannot quantify the latter, as we still are not able to extract accurate absolute values of the dissociation from CET-LIF outcomes, there are some hints that non-equilibrium dissociation can be significant.