Vibrational quenching by water in a CO₂ glow discharge measured using quantum cascade laser absorption spectroscopy

A CO₂ flow was controlled by mass flow controller MFC1 (Bronkhorst F-201CV, 750 sccm N₂ calibrated), which was combined with a controlled flow of water from a He-pressurised vessel containing distilled water using MFC2 (Bronkhorst μ-Flow L01, 0.25 g h⁻¹) by a controlled evaporative mixer (CEM) at 120 °C. This gas stream then went through a 250 mL buffer volume, where a reduced pressure below 200 mbar was maintained and monitored by pressure gauge P1, to allow water up to 10% to be added without water condensation within the gas feed system. A flow of 7.4 sccm of this gas stream was sampled using MFC3 (Bronkhorst F-201CV, 100 sccm N₂ calibrated), with the remainder leaving the system through pump 1. Using this configuration, relatively large CO₂ and H₂O flows could be used to help maintain a good gas feed stability, while a low flow and pressure could be maintained in the plasma reactor.

The sampled gas stream flowed from MFC3 through a Bruker multipass cell with a length of 25 cm, which was placed in the sample compartment of a Bruker Vertex 80v Fourier-transform infrared (FTIR) spectrometer, to allow the molar fraction of the dosed water to be monitored. The internals of the FTIR spectrometer were pumped down to 2 mbar, while a small N₂ flow was supplied to purge as much water from the FTIR spectrometer as possible. The pressure in the multipass cell was monitored using a Pfeiffer CMR 263 pressure gauge (P2). The gas stream subsequently travelled to the plasma reactor through a gas line of a few meters. This gas line prevents products created in the plasma reactor to diffuse into the FTIR multipass cell. The pressure inside the reactor is maintained at 6.7 mbar. A current of 50 mA is supplied during the plasma on-time of a sequence of pulses with a 5 ms–10 ms on–off cycle [26].

The time evolution of the current and applied voltage over the reactor, as well as the instantaneous power are measured for all water admixtures and can be found in supplementary figure S1 (https://stacks.iop.org/PSST/29/095017/mmedia). Supplementary table S1 lists the energy input per cycle, derived from the instantaneous power, for all water admixtures.

A set of three colinear distributed feedback quantum cascade lasers (QCLs) were used to measure the transmittance of the plasma over three different frequency intervals. QCL 1 was used to measure the ${\mathrm{C}\mathrm{O}}_{2}\enspace \left({v}_{1},{v}_{2}^{{l}_{2}},{v}_{3}\right)\to \left({v}_{1},{v}_{2}^{{l}_{2}},{v}_{3}+1\right)$ band between 2252.30 and 2253.51 cm⁻¹. QCL 2 and QCL 3 were used to measure the CO (v_CO) → (v_CO + 1) band in the 2211.64–2212.85 cm⁻¹ and 2179.20–2180.11 cm⁻¹ intervals. These lasers were current-driven in the intermittent scanning mode [36], allowing the scan rate of the QCLs to be sufficiently slow to avoid rapid passage effects [37–40]. A fraction of the laser emission was split off using a 95/5 beamsplitter to allow for frequency calibration using an etalon (free spectral range 0.01617 cm⁻¹).

The master clock for the experiment was generated by the QCL controller (Neoplas Q-MACS Basic MC) at an interval of 1.5 ms, with the plasma clock phase shifted by a time t_d by a set of two pulse delay generators (Stanford Research Systems DG535). An additional time shift with respect to the master clock of 0 μs, 40 μs and 75 μs was introduced for QCL 1, 2 and 3, respectively, to prevent time overlap in their emission. Hence, for each plasma cycle, spectra are collected at 10 time points t = 1.5 ⋅ i + t_d (in ms), with 0 < i < 10, significantly reducing the acquisition time with respect to previous work [26]. By adjusting t_d stepwise from t_d = 0 ms up to 1.4 ms, a time resolution of 100 μs is achieved within a single period of an infinite sequence of plasma pulses. A schematic representation of the timing scheme is depicted in figure 2.

Zoom In Zoom Out Reset image size

An example of the measured transmittance, 500 μs after starting the plasma, is shown in figure 3 for water admixtures ranging from 0% to 10%. Figure 3(a) includes only CO₂ transitions, while figure 3(b) only includes CO transitions. The absorption spectra of all three QCLs were analysed using a single custom least-squares fitting algorithm. This algorithm is based on data from the HITEMP database [41, 42] for CO₂ and a HITRAN-like dataset by Li et al for CO [43]. 1393 CO₂ transitions and 29 CO transitions are used to perform a least-squares fit of the transmittance of the measured spectral regions.

Zoom In Zoom Out Reset image size

The fit algorithm calculates the transmittance for a dual slab system, with one 18.5 cm long slab representing the non-equilibrium plasma column and a second 5.2 cm long slab representing the regions between the plasma column and the reactor windows. For the latter, a constant time-invariant temperature of 400 K is assumed, which can affect the measured temperatures. However, transitions with high rotational and/or vibrational quanta are mainly measured, which are relatively weak at 400 K. The effect of this assumption on measured temperatures is thus only small and is included in the statistical errors of the respective parameters. The fitting algorithm was validated against a previously published non-equilibrium spectrum measured by Dang et al using tunable diode laser absorption spectroscopy [29] and time evolutions of vibrational temperatures measured by Klarenaar et al using Fourier-transform infrared spectroscopy [32], showing excellent agreement with previous work [26].

The measured spectra contain contributions from transitions up to v₃ = 4 → 5 and v_CO = 1 → 2 for CO₂ and CO, respectively. T_gas represents the gas temperature and was extracted from the Doppler line broadening, assuming a constant pressure broadening contribution at 6.7 mbar during the plasma cycle. T_rot describes the rotational state distribution, while T₁₂ describes the combined temperature of the symmetric stretch and bending vibrational modes of CO₂, both assuming a Boltzmann distribution. The CO₂ asymmetric stretch vibrational temperature T₃ and the CO vibrational temperature T_CO were used to calculate vibrational populations using a Treanor distribution, due to fast vibration–vibration (V–V) interactions in these respective modes [29, 44]. While the Treanor temperatures T₃ and T_CO are expressed in K, they are strictly apparent vibrational temperatures [45, 46]. However, it has become common to refer to these parameters as vibrational temperatures and we will follow this convention [29, 32, 47–49]. It is also important to note that the Treanor and Boltzmann distributions produce almost identical absorption strengths for the measured CO₂ and CO transitions within the range of temperatures measured. Despite some of the saturated CO transitions in figure 3(b), the fit algorithm can still accurately determine T_CO, since the line strength of these saturated transitions is related to the width of the line. This does require an accurate measurement of Doppler and pressure line broadening however, which can be done thanks to the narrow bandwidth of the QCLs and the non-saturated transitions in figure 3. The typical statistical error for T_CO is 12% (determined using a reduced chi-squared analysis), despite the presence of some saturated transitions [26].

The absolute number densities ${n}_{{\text{CO}}_{2}}$ and n_CO for CO₂ and CO were determined from their respective contributions to the measured spectra. The initial values of the fit were set to 600 K for T_gas, T_rot, T₁₂, T₃ and T_CO, while the initial conditions for ${n}_{{\text{CO}}_{2}}$ and n_CO were set to 4 × 10²² m⁻³.

Time-resolved absorption spectra were taken according to the following procedure. Every measurement series was started with the reactor pumped down to below at least 1 × 10⁻¹ mbar. All three QCLs were subsequently configured and their emission was started. A background measurement was taken to obtain the QCL emission without any absorption by the plasma. The CO₂ flow was started by setting MFC1 to the appropriate setpoint, which varied between 50 and 100 sccm depending on the desired water vapour admixture. The pressure P1 was then increased to the desired value, followed by setting the flow of MFC2 to admix the desired water vapour. The pressure setpoint in the reactor (P3) was subsequently increased to 6.7 mbar. Once the pressure inside the reactor (measured by P3) reached the pressure setpoint, the system was given an additional 10 min to fully stabilise. Hereafter, 4 FTIR absorption spectra were acquired within 10 min, at 4 different times, to check the dosed water content and its stability.

An absorption spectrum was collected for the given CO₂/H₂O mix, initially without starting the plasma to check the CO₂ content in the reactor. The plasma was subsequently started and the current during the plasma on-time was set to 50 mA. The plasma was given a few minutes to stabilise, after which the (automatic) acquisition of the QCL absorption spectra was started using custom software, collecting 150 absorption spectra during both the plasma on-time and off-time over about 6 min. Once the QCL acquisition finished, the scope traces for the applied voltage and current were acquired as well on the oscilloscope. Once this was completed, the plasma was turned off and the QCL emission was stopped. The system was now purged for 5 min with pure CO₂ at 6.7 mbar, followed by pumping down the system to at least below 1 × 10⁻¹ mbar, to remove as much water as possible, before starting the next acquisition series.

Care has been taken to prevent water to accumulate inside the system over time. This was checked by repeating the measurements without water admixed after all other measurements were completed. The results were almost identical to the pure CO₂ measurements before the water admixing experiments.

In addition to absorption spectroscopy, rotational Raman scattering was used to perform spatially resolved measurements. These measurements were performed using the same gas feed system and plasma setup described above, although 23 cm long extensions were attached to either end of the reactor to reduce the laser energy density at the windows. Since the laser scattering setup is described in detail in previous work [33], this section only provides a brief overview of this setup. Rotational Raman spectroscopy serves as a validation for the line-integrated absorption spectroscopy measurements. While spatially resolved measurements in a pulsed CO₂ glow discharge have already shown the uniformity of the plasma [27], it should be validated that this also holds for a CO₂ plasma with water admixed. Measurements were performed in the centre of the plasma at 11 strategically determined time points during the plasma cycle and were limited to 0% and 5% water admixture. This is due to acquisition times of up to 45 min per time point for rotational Raman scattering, in contrast to about 2 s for a QCL absorption spectrum.

A frequency-doubled Nd:YAG laser at 532 nm was focused into the centre of the plasma reactor by a set of lenses. Hence, it should be mentioned that the reactor configuration differed from the one depicted in figure 1. Scattered light was collected at 90°, focused into a glass fibre and subsequently collimated. This light passed through a volume Bragg grating, which allowed the strong Rayleigh scattering to be filtered [50]. The collimated beam was then focused onto the 100 μm wide entrance slit of a spectrometer and was spectrally resolved by a 2400 lines/mm grating. It was then detected by a custom intensified camera, for which the spectral sensitivity was determined from the black-body radiation of a W-ribbon lamp.

Both the Stokes and anti-Stokes branches were recorded up to a positive and negative Raman shift of 96 cm⁻¹ and analysed using a custom fitting algorithm. The rotational temperature T_rot describes the rotational state distribution, assuming a Boltzmann distribution. The number densities ${n}_{{\text{CO}}_{2}}$, n_CO and ${n}_{{\mathrm{O}}_{2}}$, for CO₂, CO and O₂, respectively, were determined from the contributions of the respective species to the total spectrum. The initial values of the fit were set to T_rot = 600 K and ${n}_{{\text{CO}}_{2}}={n}_{\text{CO}}={n}_{{\mathrm{O}}_{2}}=4{\times}1{0}^{22}$ m⁻³. The scattering intensity and instrumental broadening (assuming equal Gaussian and Lorentzian contributions) were both calibrated using a rotational Raman spectrum for pure CO₂ at room temperature and a pressure of 6.7 mbar.

In the vibrational ground state of CO₂, only even rotational levels contribute to the rotational Raman spectrum, whereas odd rotational levels have a degeneracy of zero. If higher vibrational levels are populated however, odd rotational levels can have a non-zero degeneracy [35, 51]. Hence, the rotational Raman spectrum of CO₂ is affected by the vibrational temperatures T₁₂ and T₃ through the apparent degeneracy of even and odd rotational levels ⟨g_J,e/o⟩ [35]:

$$\begin{equation}\langle {g}_{J,\mathrm{e}/\mathrm{o}}\rangle =\frac{1}{2}{\pm}\frac{1}{2}\left(\frac{1-{z}_{2}}{1+{z}_{2}}\right)\left(\frac{1-{z}_{3}}{1+{z}_{3}}\right),\end{equation} \tag{ 1 }$$

with the plus sign corresponding to the degeneracy of even rotational levels and the minus sign corresponding to the degeneracy of odd rotational levels. Furthermore, ⟨g_J,e⟩ + ⟨g_J,o⟩ always equals unity for CO₂. The factor z_i is related to the vibrational temperature T_i through

$$\begin{equation}{z}_{i}=\mathrm{exp}\left(-\frac{hc{G}_{1,i}}{{k}_{\mathrm{B}}{T}_{i}}\right),\end{equation} \tag{ 2 }$$

with h the Planck constant, c the speed of light and k_B the Boltzmann constant. G_1,i is the energy spacing between the vibrational ground state and the first vibrationally excited state for vibrational mode i, which is equal to 667.47 cm⁻¹ for the bending mode of CO₂ and 2349.16 cm⁻¹ for the asymmetric stretch mode of CO₂ [32]. Due to the strong Fermi-resonance between the symmetric stretch and bending modes of CO₂, a shared temperature T₁₂ is used, which substitutes the vibrational temperature T₂ in the equation above.

By including ⟨g_J,o⟩ as a fitting parameter (with an initial value of 0.25), it is possible to characterise vibrational excitation locally. Since ⟨g_J,o⟩ measures the combined effect of changes in T₁₂ and T₃, it is not possible to find values for T₁₂ and T₃ independently, but it can be used verify measured vibrational temperatures using line-integrated absorption spectroscopy with a spatially resolved technique. This allows verification of the assumption that the plasma is uniform.

The measured time evolutions of the rotational temperatures are shown in figure 4. Solid lines represent absorption spectroscopy measurements, with the lines colour coded based on the water admixture, ranging from blue for 0% water admixture to yellow for 10% water admixture. Rotational temperatures measured using rotational Raman scattering at 0% and 5% water admixture are included as scatter points (including a 2σ fitting error) at a few time points, using the same colour coding of the corresponding solid lines. The grey shaded time interval represents the on-time of the plasma, between t = 0 ms and t = 5 ms.

Zoom In Zoom Out Reset image size

The measured rotational temperature T_rot starts at 370 ± 19 K for a pure CO₂ plasma at t = 0 ms. This is due to the residual heat that is left over from previous pulses. The rotational temperature then increases during the on-time of a pure CO₂ plasma to T_rot = 840 ± 42 K at t = 5 ms, followed by an exponential decrease before starting the next plasma cycle. This measured evolution of the rotational temperature corresponds well with previous measurements on the same discharge [26, 27, 32]. A similar increase in the measured rotational temperatures is observed upon admixing water, reaching a maximum temperature of 810 ± 41 K, which is well within the statistical error of results for pure CO₂. Despite differences in reactor design for rotational Raman spectroscopy with respect to absorption spectroscopy measurements (due to the extensions mounted to either end of the reactor for rotational Raman scattering), the rotational temperatures measured using rotational Raman spectroscopy and QCL absorption spectroscopy agree well when taking into account their statistical (fitting) error.

For the absorption spectroscopy results, some small sawtooth features are visible with a period of 1.5 ms, especially near the end of the plasma off-time. These features are related to long-term drift of either the plasma or QCL in combination with the triggering scheme (see also figure 2). The effect of these features on the measured rotational temperature is included in the statistical error estimation of 5%.

The gas temperature T_gas is generally assumed equal to the rotational temperature T_rot due to the high translation–rotation (T–R) interaction rates [52, 53]. To verify this assumption, the gas temperature T_gas can be determined from the Doppler broadening width of the absorption line. The absorption cross section is a convolution of the Gaussian-shaped Doppler broadening contribution and the Lorentzian-shaped pressure broadening contribution. Hence, if the pressure broadening is known, the gas temperature T_gas can be extracted from the absorption line profile. To determine the spectral profile of the absorption profile though, the instrumental broadening needs to be sufficiently small. It was verified experimentally that the instrumental broadening of each QCL is negligible by measuring the gas temperature T_gas from a pure CO₂ absorption spectrum at room temperature.

At the conditions presented in this work, the typical Doppler broadening full-width at half-maximum (FWHM) is around 0.004 cm⁻¹ for CO₂ at T_gas = 600 K and exceeds the pressure broadening FWHM by about one order of magnitude. However, the tail of the Lorentzian pressure broadening contribution can become significant, especially for highly saturated lines (such as those of CO). Hence, the error in the measured gas temperature T_gas depends for a significant part on the error in pressure broadening constants. Only a few pressure broadening constants are available, such as the self broadening coefficients for CO₂ and CO [41, 42] and for broadening of CO by CO₂ [43]. To our knowledge though, no database is available that includes broadening of CO₂ and CO by water. Hence, we estimated the statistical error for T_gas to be 10% as a result of experimental uncertainties and the uncertainties in the pressure broadening component.

Figure 5 shows the time evolution of the measured gas temperature T_gas. Generally, T_gas is slightly elevated with respect to T_rot, with T_gas = 410 ± 41 K just before turning on the plasma and T_gas = 845 ± 85 K at t = 5 ms without water admixture. Measurements on T_gas and T_rot show good agreement when considering their related errors. Similarly to the time evolution of T_rot, no significant changes in T_gas were observed due to the addition of water.

Zoom In Zoom Out Reset image size

Figure 6 shows the time evolution of the vibrational temperatures of CO₂ and CO, during the plasma on-time and the cooldown phase, for water admixtures from 0% (blue lines) up to 10% (yellow lines). The related statistical error for vibrational temperature T₁₂ is determined to be 9% on average from a reduced chi-squared analysis. Figure 6(a) shows the time evolution of T₁₂, where the admixture of water vapour causes a slight reduction in T₁₂, especially towards the end of the plasma on-time. To visualise the degree of non-equilibrium, the elevation of T₁₂ above T_rot is included in figure 6(d). This shows that the elevation of T₁₂ during the plasma on-time almost completely disappears upon admixing 10% water vapour. This is in line with high rate constants reported for vibrational relaxation of the bending mode upon admixture of water, which exceeds those of a pure CO₂ mixture by over three orders of magnitude [18, 54]. It should be noted though that these changes in elevation of T₁₂ are only just above the statistical error for T₁₂ − T_rot of 40 K at the beginning of the plasma on-time, while the statistical error increases to 100 K towards the end of the plasma on-time. Hence, it is difficult to differentiate between subsequent water admixture conditions. In the cooldown phase, T₁₂ − T_rot initially goes to zero, before increasing again towards the end of the cooldown phase. This is attributed to the fact that T₁₂ is determined from transitions with high rotational quantum number J and thus the sensitivity for T₁₂ is reduced significantly at low rotational temperature. Furthermore, the regions outside the positive column are assumed to have a constant temperature in the fit algorithm. While this assumption affects T_rot and T₁₂ only very marginally, its effect becomes more significant at lower (rotational) temperatures and thus mainly affects T_rot and T₁₂ at the beginning of the plasma on-time and the end of the cooldown phase.

Zoom In Zoom Out Reset image size

The time evolution of the asymmetric stretch vibrational temperature T₃ of CO₂ is depicted in figure 6(b), with the statistical error for T₃ being 8% on average. Here, a fast increase of T₃ is visible upon starting the plasma, with a maximum of 1060 ± 85 K being reached at t = 700 μs. T₃ subsequently decreases slightly, followed by a relatively constant temperature at the end of the plasma on-time. When admixing water, T₃ is mainly affected in the first few milliseconds after turning on the plasma, while the temperature near the end of the plasma on-time is only slightly affected. After the plasma is turned off, a similar exponential temperature decrease is observed for all water admixtures. Towards the end of the cooldown phase, the statistical error of measured T₃ values increases due to a lower population of v₃ > 0 levels, with almost all of the sensitivity being lost below T₃ = 500 K with only very minor changes to the measured CO₂ spectrum as a function of T₃. Hence, this method does not produce reliable results for T₃ < 500 K, which is demonstrated by the time evolution of T₃ in figure 6(b), which shows occasional underestimations of T₃ near the (low temperature) end of the cooldown phase.

The relatively constant T₃ in the last 3 ms of the plasma on-time suggests that excited asymmetric stretch levels show only a minor effective relaxation. However, the relatively high T₃ towards the end of the plasma on-time is mainly caused by the simultaneous increase in T_rot. Hence, it is more illustrative to visualise the non-equilibrium with respect to T_rot, as depicted in figure 6(e). Here, a fast increase in T₃ − T_rot in the first few hundred μs is observed, with a slope that does not change upon admixing water. Since this initial slope is mostly affected by e–V and V–V interaction rates, this seems to imply that the electron density does not change significantly during this part of the plasma on-time, despite the electronegativity of water (vapour) which is generally considered to reduce electron density [1, 25]. Alternatively, changes in e–V and V–V interaction rates could be compensated by a simultaneous change in both electron density and temperature. Upon admixing water, the maximum value for T₃ − T_rot is reached much sooner with respect to pure CO₂ and the maximum vibrational non-equilibrium T₃ − T_rot is much lower. For pure CO₂, T₃ − T_rot reaches a maximum of 580 ± 86 K at t = 500 μs, while the maximum of 230 ± 63 K is reached at t = 200 μs for an admixture of 10% water vapour. This change is indicative of a significant increase in vibrational relaxation rates upon admixing water, which has been linked to fast V–V relaxation towards the bending mode of CO₂ via the bending mode of H₂O, with a typical quenching rate of around 1 × 10⁻¹² cm³ molecule⁻¹ s⁻¹ at T = 300 K. This exceeds quenching due to CO₂ molecules by about two orders of magnitude [17–19]. Additionally, atomic oxygen and molecular hydrogen can contribute to efficient quenching of the CO₂ asymmetric stretch, due to their relatively high typical quenching rates of about 2 × 10⁻¹³ cm³ molecule⁻¹ s⁻¹ and 4 × 10⁻¹² cm³ molecule⁻¹ s⁻¹ at T = 300 K, respectively [55, 56]. However, the molar fraction of atomic oxygen is not expected to increase upon admixing water since it is typically consumed in the formation of hydrogen containing reactive oxygen species [57], while typical yields for the formation of molecular hydrogen from admixed water are only around a few percent [12, 24]. Hence, the quenching of the asymmetric stretch mode of CO₂ by atomic oxygen and molecular hydrogen with respect to the quenching by water vapour is expected to be only marginal. Furthermore, since V–T relaxation also increases significantly with increasing rotational temperature [32], the non-equilibrium decreases further towards the end of the plasma on-time, with T₃ − T_rot showing only very minor changes towards t = 5 ms for each individual water admixture. Once the plasma is turned off, equilibrium conditions are reached within about 200 μs.

Finally, figure 6(c) shows the time evolution of the CO vibrational temperature T_CO, with its relative elevation above T_rot in figure 6(f). The statistical error for T_CO is determined to be 12% on average. The measured trends of T_CO are very similar to those of T₃, with an initial fast rise of T_CO in the first few hundred μs. Due to the increase in V–T relaxation rates as a result of the increase in T_rot during the plasma on-time, a maximum is reached for T_CO, followed by a slight decrease towards a steady-state temperature. Once the plasma is turned off, T_CO goes down exponentially and quickly equilibrates with the rotational temperature. Similar to T₃, the sensitivity to T_CO is lost at temperatures below 400 K due to the low contribution of transitions from excited CO vibrational levels in the measured spectral regions. Upon addition of water, the initial fast rise of T_CO − T_rot does not change, again indicative of a relatively constant excitation of the vibrational mode through e–V and V–V excitation. However, an increase in vibrational relaxation due to the presence of water results in reaching a lower maximum for T_CO − T_rot and sooner after starting the plasma, suggesting efficient vibrational quenching of CO by water. Indeed, the vibrational bending mode (ν₂) of water is suggested as a possible loss channel for this CO vibrational excitation [54, 58]. Since energy exchange between the asymmetric stretch vibrational mode of CO₂ and CO is relatively easy [26, 54, 59], this quenching of the CO vibrational mode can indirectly also affect the asymmetric stretch vibrational excitation of CO₂.

In addition to the vibrational temperatures measured using line-of-sight QCL absorption spectroscopy, a few spatially resolved rotational Raman spectroscopy measurements in the centre of the reactor were performed at 0% and 5% water admixture, respectively, to verify the spatial uniformity of the plasma. While the measured rotational temperatures using rotational Raman scattering were already presented in figure 4, these measurements also yield information on vibrational excitation through the apparent odd fraction ⟨g_J,o⟩ (equation (1)).

Figure 7(a) shows the measured apparent odd fraction ⟨g_J,o⟩ at a few times during the plasma cycle, which increases both due to vibrational non-equilibrium and due to overall heating of the plasma. This figure shows that the measured apparent odd fractions for 0% water admixture exceed those for 5% water admixture during the plasma on-time, which subsequently equalise in the cooldown phase.

Zoom In Zoom Out Reset image size

To distinguish between vibrational non-equilibrium and heating of the plasma, figure 7(b) shows the difference between the measured odd fraction ⟨g_J,o⟩ and the calculated odd fraction at thermal conditions ${\langle {g}_{J,\mathrm{o}}\rangle }_{\text{th}}$, assuming T₁₂ and T₃ equal T_rot. Here, a value for $\langle {g}_{J,\mathrm{o}}\rangle -{\langle {g}_{J,\mathrm{o}}\rangle }_{\text{th}}$ above zero indicates that T₁₂ and/or T₃ are elevated above T_rot, while this equals zero for thermal equilibrium conditions. Additionally, the time evolution of the apparent odd fraction from line-of-sight absorption spectroscopy measurements is included as solid lines for 0% and 5% water admixture, respectively.

The data presented in figure 7(b) shows a good agreement between line-of-sight QCL measurements and spatially resolved rotational Raman spectroscopy measurements in the centre of the reactor. A slight disagreement is observed in the cooldown phase, where $\langle {g}_{J,\mathrm{o}}\rangle -{\langle {g}_{J,\mathrm{o}}\rangle }_{\text{th}}$ from absorption spectroscopy is above zero. This corresponds to the measured elevation of T₁₂ above T_rot (as depicted in figure 6(d)) and is caused by the assumed time invariant temperature in the cold regions outside the plasma column. This leads to a slight underestimation of T_rot, especially when T_rot in the plasma column is relatively low. Since ⟨g_J,o⟩ is quite sensitive to changes in especially T_rot and T₁₂, this slight underestimation of T_rot can manifests itself as an overestimation of ⟨g_J,o⟩. It should be stressed though that this does not affect the measured apparent odd fractions during the relatively hot plasma on-time, where the effect of the assumed time invariant temperature in the regions outside the plasma column is negligible.

The good agreement between the measured apparent odd fractions and the rotational temperature evolution presented in figure 4 with a spatially resolved and line-of-sight technique confirms the absence of large spatial temperature gradients within the positive column of the plasma.

In addition to rotational and vibrational temperatures from relative differences in transition line strengths, the number densities ${n}_{{\text{CO}}_{2}}$ and n_CO of CO₂ and CO, respectively, can be determined from the absolute line strengths obtained using absorption spectroscopy. The fraction of converted CO₂ molecules α_abs can be expressed as:

$$\begin{equation}{\alpha }_{\text{abs}}=\frac{{\left[\mathrm{C}\mathrm{O}\right]}_{\mathrm{f}}}{{\left[{\mathrm{C}\mathrm{O}}_{2}\right]}_{\mathrm{i}}}=\frac{{\left[\mathrm{C}\mathrm{O}\right]}_{\mathrm{f}}}{{\left[\mathrm{C}\mathrm{O}\right]}_{\mathrm{f}}+{\left[{\mathrm{C}\mathrm{O}}_{2}\right]}_{\mathrm{f}}}\end{equation} \tag{ 3 }$$

where [CO] and [CO₂] express the amount of moles of CO and CO₂, respectively. The indexes i and f refer to the initial (before the plasma) and final (after the plasma) number densities, such that ${\left[\mathrm{C}\mathrm{O}\right]}_{\mathrm{f}}={\left[{\mathrm{C}\mathrm{O}}_{2}\right]}_{\mathrm{i}}-{\left[{\mathrm{C}\mathrm{O}}_{2}\right]}_{\mathrm{f}}$. We assume here that there is no significant loss of carbon by carbon deposition on surfaces or through formation of hydrocarbons. Under the additional assumption that the dissociation reaction stoichiometry is fixed (e.g. 2CO₂ → 2CO + O₂), equation (3) can be expressed in terms of the measured number densities n_CO and ${n}_{{\text{CO}}_{2}}$, such that ${\alpha }_{\text{abs}}={n}_{\text{CO}}/\left({n}_{{\text{CO}}_{2}}+{n}_{\text{CO}}\right)$, taking into account the expansion as a result of the dissociation reaction. The effective conversion α_eff expresses the fraction of the total gas that is converted to CO and is related to the absolute conversion through

$$\begin{equation}{\alpha }_{\text{eff}}={\alpha }_{\text{abs}}\cdot {f}_{{\text{CO}}_{2}},\end{equation} \tag{ 4 }$$

where ${f}_{{\text{CO}}_{2}}$ is the initial molar fraction of CO₂. The energy efficiency η is now related to the effective conversion α_eff by

$$\begin{equation}\eta ={\alpha }_{\text{eff}}\cdot \frac{{\Delta}{H}_{\mathrm{R}}}{{E}_{\text{molec}}}\end{equation} \tag{ 5 }$$

with ΔH_R the reaction enthalpy for CO₂ dissociation of 2.9 eV per molecule. E_molec is the average energy input per molecule and is calculated from the average energy input P in W and the flow rate of the gas mixture through the reactor F in slm and can be expressed as

$$\begin{equation}{E}_{\text{molec}}\left(\mathrm{e}\mathrm{V}\right)=1.39{\times}1{0}^{-2}\frac{P\left(\mathrm{W}\right)}{F\left(\mathrm{s}\mathrm{l}\mathrm{m}\right)}.\end{equation} \tag{ 6 }$$

The change in absolute conversion α_abs as a function of the water admixture is depicted in figure 8, including results from both QCL absorption measurements in black and rotational Raman spectroscopy in red. A good agreement is found between the absorption spectroscopy measurements and rotational Raman scattering measurements, although the statistical errors associated to the conversion α_abs for rotational Raman spectroscopy measurements are high due to the low CO scattering cross section.

Zoom In Zoom Out Reset image size

Without admixing any water vapour, the conversion α_abs measured using absorption spectroscopy is 23 ± 2%, while the conversion does not change significantly upon admixing up to 0.5% of water vapour, with the conversion α_abs = 21 ± 2%. However, when increasing the water vapour admixture above 1%, the conversion quickly decreases by almost a factor of 4 to α_abs = 6.2 ± 0.7% upon admixing 10% water. The related energy efficiencies range from 1.3 ± 0.1% without water to 0.33 ± 0.04% for a 10% water admixture and show a very similar trend as the conversion α_abs due to the relatively small changes in ${f}_{{\text{CO}}_{2}}$. For completeness, a plot of the energy efficiency as a function of the water vapour content is included in supplementary figure S2.

The decrease of the conversion could be partially related to the reduction in vibrational excitation depicted in figure 6. Morillo-Candas et al [60] have recently shown however that most of the conversion occurs through direct electron impact (up to 80%) in a very similar reactor (although their discharge current was 40 mA instead of 50 mA). This does not strictly exclude the vibrational excitation from affecting the direct electron impact dissociation rate though, since a higher vibrational excitation can lead to a reduction in the energy barrier to overcome for CO₂ dissociation, allowing a larger fraction of the electrons to have sufficient energy available for dissociation [61]. The large reduction in conversion upon water admixing can also be related to other effects, which can include a reduction in electron density by electron attachment to atomic oxygen [1, 21] or by OH and CO reacting to form CO₂ [1, 25]. However, the initial slope in the measured vibrational temperatures (figure 6) does not change when admixing water, which seems to suggest that the (initial) e–V and V–V interaction rates do not change significantly. This can be either due to a constant electron density, or due to a simultaneous increase in the electron temperature that compensates the suggested decrease in electron density. Further measurements on electron density and temperature are required to attribute the drop in conversion due to water to the electron density and temperature and/or reactions involving OH.