CO2 Reduction by Nanosecond-Plasma Discharges: Revealing the Dissociation’s Time Scale and the Importance of Pulse Sequence

Power-to-chemical technologies with CO2 as feedstock recycle CO2 and store energy into value-added compounds. Plasma discharges fed by renewable electricity are a promising approach to CO2 conversion. However, controlling the mechanisms of plasma dissociation is crucial to improving the efficiency of the technology. We have investigated pulsed nanosecond discharges, showing that while most of the energy is deposited in the breakdown phase, CO2 dissociation only occurs after an order of microsecond delay, leaving the system in a quasi-metastable condition in the intervening time. These findings indicate the presence of delayed dissociation mechanisms mediated by CO2 excited states rather than direct electron impact. This “metastable” condition, favorable for an efficient CO2 dissociation, can be prolonged by depositing more energy in the form of additional pulses and critically depends on a sufficiently short interpulse time.


Experimental set-up
The scheme of the experimental set-up is reported in Fig. S1, detailing the spectroscopic apparatus, as well as the gas system. Light detection The detection system adopted for the optical emission spectroscopy and the collisional energy transfer laser-induced fluorescence (CET-LIF) consisted of a spectrograph equipped with a 300 mm focal length monochromator (SR303i-B, Shamrock, 2400, and 1200 grooves/mm gratings) and a gated ICCD (intensified charge-coupled device) camera (DH334T-18U-03, Andor iStar).
The light was collected by a lens L4 of focal length f L4 =200 mm placed at f L4 from the centre of the gap. A lens L3 with f L3 =75 mm served to focus the image on the entrance slit of the spectrograph.

Electrical characterization
The pulsing scheme adopted in the present work is presented in Fig. S2. A continuous pulse sequence with inter-pulse time t c =5 ms was superimposed to a burst sequence characterized by an inter-burst time t b =50 ms. The temporal separation of the nanosecond pulses inside the burst is indicated as t p , the inter-pulse time t p . The burst sequences employed in the present work consisted of five pulses and were characterized by t p =100 µs and t p =33 µs.
The adoption of this modulated pulsing pattern reduced the total power delivered by the NPG18/100k compared to the burst sequences commonly used in plasma-mediated processes, also providing a better stability of the whole control system of the apparatus. The pulsing pattern composed of: a continuous pulse sequence with inter-pulse time t c =5 ms, a superimposed burst sequence with inter-burst time t b =50 ms. t p is the inter-pulse time inside the burst. In this work, measurements were only performed in or after the burst.

Data analysis
The energy of the pulses was calculated by integrating the product V(t) x I(t) over the pulse duration, where V(t) and I(t) are the voltage and current signals, respectively. V(t) and I(t) were affected by a spurious delay introduced in the acquisition system for several reasons: length of the cables, separation of the probes, and the matching box of the high voltage probe. The delay was measured by preventing the discharge ignition and overlapping V(t) x I(t) so that the integral of the reactive power was zero. An example of voltage and current S4 signals is reported in Fig. S4. Instantaneous power P(t) and cumulative energy E(t) are shown in the panel Fig. S5. In both Fig. S4 and Fig. S5 a re-ignition of the discharge at around 400 ns can be observed in the 1 st pulse (re-trigger of the NPG18/100k).
The profile of the 1 st pulse of the burst depends on the temporal separation from the preceding pulse. As observed in, 1 provided that the discharge event that preceded the burst is distant enough -5 ms in the case under study -the electrical characteristics of the 1 st pulse are the same for the two sequences (t p =100 µs and t p =33 µs). Despite the presence of a reignition, about 85% of the total energy of the pulse is dissipated by the first discharge event, as shown in Fig. S3. The total energy deposited by the two burst sequences is presented in  around 20% to 35%. Additionally, the burst sequences also differed by the profiles of voltage and current, as reported in the section "Additional voltage, current, power and energy profiles": Fig. S12-S13-S14-S15. This behaviour is consistent with what was observed in 1-3

S5
and with the so-called memory-dominated regime that appears by shortening t p .   Burst with t p =33 µs. In blue is a pictorial representation of the nanosecond discharge pulses.

S7
Spectroscopic gas temperature The gas temperature can be estimated from optical emission spectra, specifically using the emission of the second positive system (SPS) of nitrogen, 4,5 in an atmospheric nanosecond pulsed discharge. 3 In this work, the N 2 C 3 Π u , υ ′ = 0 state was produced by the discharge itself and the signal was collected in the first 20 ns of the discharge pulse.
ns pulse aux. ns pulse ns pulse ns pulse Intensity [a.u.]

Wavelength [nm]
data best fit Fig. S8: Second positive system emission spectra representative of T g =400 K (a) and T g =2600 K (b). The synthetic spectra were simulated using the software DIATOMIC 6 To span the post-discharge of each pulse of the burst sequence, an auxiliary nanosecond S8 (aux. ns. pulse) pulse was used to produce the state N 2 C 3 Π u , υ ′ = 0 , see Fig. S7. The aux. ns. pulse was progressively delayed (τ oes 0 , τ oes 1 , τ oes 2 , ...) with respect to the ns. pulse to be probed by using the DDG. The auxiliary pulse cannot be closer than 10 µs with respect to the pulse of interest since it is the minimum achievable inter-pulse time for the NPG18/100k power supply. The sketch of the timing of the experiment is shown in Fig. S7.

Data analysis
Two examples of emission spectra produced by the second positive system of nitrogen Fig. S8. To find the best fit of the data, a set of synthetic spectra was produced by using the software DIATOMIC 6 in a temperature range of [280 K-4000 K], with a temperature step of dT=50 K. Each data-set was fitted on each synthetic spectrum, the best fit corresponds to the minimum value of the χ 2 red .

S9
The uncertainty was derived by using the χ 2 red procedure, as presented in. 7 The data are fitted on a much more granular set of synthetic spectra (dT=5 K); the resulting dependence of the χ 2 red with respect to T [K] is a parabola with half width χ 2 red,min + 0.5, representing the uncertainty; it is 130 K for the measurements presented in this work.
Additionally, if a fit is performed on the post-discharge evolution of the gas temperature, all the uncertainties on the fit parameters must be considered in the extrapolation of the temperature values. An example of the extrapolation in the non-accessible region by the auxiliary pulse is presented in Fig. S9. The experimental point at 40 ns and 80 ns were collected because the discharge was ignited by the first reflection travelling back and fourth in the cable, see Fig. S3. S10

CET-LIF
Collisional energy transfer -laser induced fluorescence (CET-LIF) was introduced in 8 to derive the gas composition in a highly collisional environment, e.g. atmospheric pressure discharges. The collisional processes undergone by the probe molecule -OH in the specific case -affect its fluorescence spectrum. Despite that operation in a highly collisional environment is detrimental for the LIF quantum yield, 9 if the species-dependent rate coefficients of those processes are known, the information on the gas composition can be inferred by the fluorescence spectrum of OH. The set of non-thermal rate coefficient k(T) Q1 , k(T) Q0 , a for several collider partners of OH (CO 2 , CO, O 2 , H 2 , CH 4 ) was measured in. 10 The temperature dependence of the k(T) was also highlighted.
The spectroscopic scheme used in this work corresponds to the one adopted in. 11,12 The notation is the following: the vibrational (υ) and rotational (N) quantum numbers of the states OH X 2 Π, υ, N ′ and OH A 2 Σ + , υ ′ , N ′′ will be indicated with their integer values. If the rotational quantum number is omitted, the state represents the rotational manifold. The spectroscopic scheme was as follows: The P 1 (3) transition at 283.009 nm was chosen to excite the OH A 2 Σ + , υ ′ = 1 state. The laser-populated state could undergo different energy transfer processes: i) rotational energytransfer (RET) in which the energy is redistributed in the rotational manifold; ii) vibrational energy-transfer in which OH A 2 Σ + , υ ′ = 1 is depopulated in favour of OH A 2 Σ + , υ ′ = 0 ; iii) electronic quenching: non-radiative decay of the OH A 2 Σ + , υ ′ = 1 state. The timea k(T) Q1 , k(T) Q0 , k(T) 1→0 are the rate coefficients corresponding to the quenching of OH A 2 Σ + , υ ′ = 1 , OH A 2 Σ + , υ ′ = 0 and the vibrational energy-transfer OH A 2 Σ + , υ ′ = 1 →OH A 2 Σ + , υ ′ = 0 S11 integrated fluorescence spectrum I (λ) LIF was acquired by the intensified CCD. I (λ) LIF can be expressed as the sum of the contributions coming from the two emitting bands (0,0) and (1,1) (see the spectroscopic scheme of Eq. S1): ψ(λ) (0,0) and ψ(λ) (1,1) are the normalized emission spectra of the band (0,0) and (1,1) for a given rotational population distribution, respectively. t G is the gate-time of the ICCD, fixed to 20 ns to be larger than the lifetime of the laser-populated state. P 0 (t) and P 1 (t) are the time-dependent vibrational populations. The ratio (R p ) between the time-integrated vibrational populations can be expressed as the ratio between the effective rate coefficients of VET (k eff VET ) and quenching (k eff Q0 ) of the state OH A 2 Σ + , υ ′ = 1 : 13 ns pulse laser pulse ns pulse ns pulse Fig. S10: Timing of the discharge pulses in a CET-LIF experiment for the determination of the CO 2 conversion at microsecond timescales. The label 'ns pulse' represents the discharge event to be probed; the label 'laser pulse' represents the probing laser pulse that produces the excited state OH A 2 Σ + , υ ′ = 1 at a given delay τ lif by the ns pulse.

Data analysis
The spectral fitting routine used in 10 was adopted to extract the rotational population distributions of OH A 2 Σ + , υ ′ = 0 and OH A 2 Σ + , υ ′ = 1 , together with the ratio described in Eq. S3. If the rotational population distributions of the investigated state of OH are known, the fitting routine can be simplified by reducing the number of fitting parameters.
In this framework, the number of rotational levels of the manifolds υ = 1 and υ = 0 was fixed and the fitting function for I (λ) LIF that can be parameterized as a linear combination of the normalized emission spectra, see Eq. S4: where a and b are the fitting parameters. To validate this approach, the rotational population distributions were probed at different τ lif rot and the data-sets collected at τ lif ̸ = τ lif rot were fitted using the simplified fitting function of Eq. S4 b . An example of the procedure is provided in Fig. S11. The first two rows show three different fits for a fluorescence spectrum acquired at a b the fitting routing mentioned above was used to fit resolved spectra acquired at specific τ lif .

S13
given τ lif (30 µs and 5 µs). Each fit is performed by using a rotational population distribution measured at τ lif rot =1, 5, 30 µs, respectively. The values of the ratios are compatible for the different τ lif rot , implying that the rotational population distributions do not vary in a sensitive way to affect R p . The rotational population distributions are presented in the third row.  Fig. S15: Instantaneous power P and energy E profiles for the five pulses of the burst with t p =100 µs. Subfigures (a) to (e) correspond to pulse indices 1 to 5 respectively, as can also be seen from the blue highlighted pulse in the pictrographic burst representation in each graph.