Ammonia decomposition in a dielectric barrier discharge plasma: Insights from experiments and kinetic modeling

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Introduction
A global energy transition from fossil hydrocarbon-based energy sources to renewable energy sources such as wind and solar is currently underway.However, these renewable sources are highly weather-dependent, and efficient energy storage methods and energy carriers are therefore necessary (Hasan et al., 2021).Hydrogen (H 2 ) is considered a possible energy carrier as it is a clean and carbon-free energy source.However, delivery and storage issues for H 2 obstruct its implementation (Edwards et al., 2007).Other indirect storage media are therefore of interest for distribution.Ammonia (NH 3 ) is currently investigated as a storage medium for H 2 due to its ability to condense at 25 °C and ca. 10 atm, which makes storage and distribution easier (Lamb et al., 2019;Salmon and Bañares-Alcántara, 2021;Schüth et al., 2012;Wan et al., 2021).Recently, Iriawan et al. (2021) reviewed existing and novel methods for producing ammonia by either reduction or oxidation.However, effective conversion processes must be developed for NH 3 to be utilized as a H 2 carrier.
Thermal NH 3 decomposition (see Reaction 1) has been an ongoing research area where reaction temperatures above 500 °C and a catalyst are used to achieve sufficient conversion.Different metals have been studied for the reaction, such as Fe, Ni, Mo, Co, Pt, Pd, and Rh, as well as different two-component combinations of these metals (Silva et al., 2015;Klerke et al., 2009;Lendzion-Bielun et al., 2013;Lucentini et al., 2021;Simonsen et al., 2012;Zheng et al., 2008).
An alternative to thermal activation could be electrical activation by plasma, which further promotes the green energy transition, as renewable energy sources can be used to power the plasma (Bogaerts and Neyts, 2018;Conrads and Schmidt, 2000).Various plasma types can be used, but dielectric barrier discharges (DBDs) in combination with different packing materials have received significant attention lately for the conversion/synthesis of various chemicals such as methane, carbon dioxide, and ammonia (Bogaerts, 2019;Bogaerts et al., 2020;Snoeckx and Bogaerts, 2017;Whitehead, 2016).Recently, an enhanced ability for NH 3 decomposition (Reaction 1) was reported (Akiyama et al., 2018;Andersen et al., 2022;El-Shafie et al., 2021, 2020;Hayakawa et al., 2020;Wang et al., 2019Wang et al., , 2017Wang et al., ,2015;;Yi et al., 2019).Akiyama et al. (2018) proposed that the NH 3 decomposition only proceeds in the plasma atmosphere, as a common linear correlation between power and conversion was found when different wool-like, metallic (Ag, Al, Cu, Fe, and Ti) inner electrodes were utilized.Our recent work (Andersen et al., 2022) showed a linear correlation between the number of micro-discharges and the conversion, independent of packing material (except for a fully metallic Fe-based packing), indicating that the decomposition primarily proceeds in the gas phase through collisions with highenergy electrons.Wang et al. (2015) reported that the ratelimiting step in plasma-catalytic decomposition of NH 3 over metals (Fe, Co, Ni, and Cu) is the recombinative desorption of adsorbed N atoms.In another study, Wang et al. (2017) suggested that the plasma pre-activates the NH 3 by forming an electronically excited state (NH 3 *) which accelerates the adsorption and improves the conversion.Yi et al. (2019) similarly argued that pre-activation of NH 3 and formation of radicals (NH 2 and NH) by the plasma plays a crucial role for increasing the activity, as well as the catalyst capability to adsorb these species.Hayakawa et al. (2020) showed that by removing the produced H 2 , an increased NH 3 conversion occurred.This indicates that the reverse reaction of Reaction 1 limits the NH 3 conversion in a plasma environment.This is not surprising since studies have shown that NH 3 can be synthesized from H 2 and N 2 in a plasma (Bai et al., 2003;Engelmann et al., 2021;Hong et al., 2018;van 't Veer et al., 2020a).
As discussed above, it is clear that different processes for NH 3 decomposition in a plasma are claimed to be vital, however, only little is known about the underlying reactions that drive the NH 3 decomposition.Hence, there is a clear need for a more detailed understanding.The cited studies investigating NH 3 decomposition are all experimental, and only in some of these papers, attempts were made to interpret the data based on simple chemical reactions assumed from the literature to occur in the DBD reactor.
In this work, we present a combined experimental study, utilizing a DBD reactor, and a plasma kinetic model, to improve the understanding of the reaction mechanism of NH 3 decomposition in such a DBD plasma.In the experimental part, the influence of plasma power, frequency, feed flow rate, residence time, and the presence of packing material in the discharge zone were examined for a diluted NH 3 feed stream.The plasma characteristics, recorded in the experiments, were used as input to the zero-dimensional (0D) plasma kinetic model, where special attention was paid on separating the effects of the micro-discharges and their afterglows in the assessment of the reaction mechanisms.

Experimental
Experiments were performed in a coaxial quartz DBD reactor setup described in detail elsewhere (Andersen et al., 2022).A stainless steel rod (ø: 10 mm) was utilized as the inner electrode, while a stainless steel mesh wrapped around the reactor worked as the outer electrode.This steel mesh had a varying length of 1-15 cm, to evaluate the effect of the size of the plasma volume (defining the residence time).The quartz tube reactor had an outer and inner diameter of 22 and 19 mm, respectively.The discharge gap between the inner electrode and the reactor wall was 4.5 mm.A TREK high voltage amplifier (model 20/20C-HS), controlled by a Tektronix function generator (AFG1022), was used to power the outer electrode.A Tektronix high voltage probe (P6015A), a Pearson Rogowski coil (4100), and an external capacitor (10 nF) with a Picotech low voltage probe (TA150) were used to measure the applied voltage, current, and generated charges, respectively.The voltage, current, charge, and calculated plasma power were continuously recorded by a Picotech digital oscilloscope (Picoscope 6402C).
Mass flow controllers (Bronkhorst) were used to pass a N 2 flow through the reactor for 10 min to remove any oxygen prior to each experiment.A feed mixture of 2.02 mol% NH 3 in N 2 at a flow rate of 50-125 Nml/min was then fed to the reactor.After 20 min of feeding the mixture, the plasma was ignited.The effluent was diluted in N 2 to a total flow rate of 1 Nl/min to comply with the flow requirement of the analyzer.The diluted flow was then analyzed using an online NH 3 -analyser (ABB, AO2000-Limas 11 HW gas analyzer) to determine the concentration of the remaining NH 3 .The decomposition was carried out at different plasma power values of 10-25 W, at a constant frequency of 3.0 kHz, and at different frequencies in the range of 1.0-3.5 kHz, at a constant plasma power of 15 W.
For experiments with packing material, MgAl 2 O 4 pellets were crushed and sieved to a particle size of 0.85-1.4mm and an outer electrode length of 5 cm, corresponding to a discharge volume of ca. 10 cm 3 , was used.The physicochemical properties of MgAl 2 O 4 were reported in our previous work (Andersen et al., 2022).The plasma zone was fully packed for the packed-bed experiments, corresponding to ca. 10 g of material.Glass wool was placed on each side of the bed to hold the material in place.All experiments were conducted at atmospheric pressure without external heating, with a plasma power stabilization period of 1 h after plasma ignition.
The conversion (X) of NH 3 was calculated according to Eq. ( 1) and the specific energy input (SEI) is defined as the plasma power over the total volumetric flow rate measured at nominal conditions (Eq. ( 2)).The NH 3 concentration in the reactor effluent was determined when the online analyzer showed a stable signal by taking an average over a 15-minute period.The average value was then used to calculate the conversion by Eq. (1).
3. Computational method The 0D plasma kinetics solver ZDPlasKin (Pancheshnyi et al., 2008) was used in this study.The solver is coupled to BOLSIG+ (Hagelaar and Pitchford, 2005), which is a numerical solver for the steady state Boltzmann equation for electrons.BOLSIG + uses the collision cross sections, the ratio of the electric field (E) to the total number density of gas phase species (N) (i.e., reduced electric field (E/N)), and the gas temperature as inputs.The reduced electric field and the gas temperature were determined from experimental measurements, with N determined from the ideal gas law (pressure and temperature) and E from power density and electron conductivity (see equations Eq.S1-Eq.S6 in the Supporting Information, section S.2).The parameters used to determine the power density and electron conductivity are the charge transfer (Q 0 ), burning voltage (DU), capacitance of the cell (C cell ), effective capacitance (f diel ), and dielectric capacitance (C diel ), which are determined from the voltage and charge measurements (see Supporting Information, section S.2).The gas temperature was determined with a thermocouple placed on the outside of the reactor wall as described in Andersen et al. (2022), and was measured to be ca.100 °C, independent of the length of the outer electrode.The gas mixture ratio of 98/2 N 2 /NH 3 used in our experiments was also used as input.The plasma kinetic model was previously used to investigate plasma-based NH 3 synthesis (van 't Veer et al., 2020b't Veer et al., , 2020a)), but in this study, the model was used for plasma-based NH 3 decomposition, where the same plasma chemistry is expected to occur.
Collisions between electrons, so-called heavy particles (i.e., molecules, atoms, radicals, excited species and ions), and surfaces are considered to take place in the plasma.The plasma chemistry included in the model therefore considers the corresponding atoms, radicals, ions, and vibrationally and electronically excited states, which could appear during the decomposition, Reaction 1, along with empty surface sites and surface-adsorbed species, as listed in Table 1.Rate coefficients taken from the literature are used in the kinetic model to calculate the time-dependent density development of the gas and surface species.In the recent work by van 't Veer et al. (2020a) it was specifically noted that the surface kinetics is associated with uncertainty, that is, the exact properties of the surface.It was further discussed that assumptions were made for the Eley-Rideal (ER) sticking coefficients, due to the lack of reliable kinetic data, hence the surface described in the model was iron, simply for reference (van 't Veer et al., 2020a).In the present work, MgAl 2 O 4 is used as the packing material due to its high synergy for plasma-catalytic NH 3 decomposition reported in our previous work (Andersen et al., 2022).Here, it was also reported that the surface reactions might not have a significant impact on the decomposition.The acquired results from the plasma kinetic model when including packing material are therefore primarily used to understand the effect of the surface reactions, and how the plasma characteristics, which are different in the presence of packing material, affect the decomposition in the gas phase.A full list of the gas phase and surface kinetics was reported by van 't Veer et al. (2020avan 't Veer et al. ( , 2020b)).
A surface site density of 10 15 cm À2 is assumed in the model, to represent a generic surface (Cortright and Dumesic, 2001).Furthermore, an experimental reactor-specific volume-to-surface area ratio is used to convert the rate coefficients of the surface reactions from s À1 to cm 3 s À1 or cm 6 s À1 .Here, the surface area is the sum of the outer surface of the particles, reactor wall, and inner electrode surface area.Note that only the outer surface area of the particles is used to determine this factor, since the plasma is not expected to propagate into the pores of the material (Zhang and Bogaerts, 2018).The outer surface area of the particles is calculated by assuming the shape of the particles to be an equal mixture of spheres and cylinders with radius and height determined from the specified particle size.This assumption was made based on visual inspection of the particles.A specific reactor volume-tosurface area ratio of 0.225 cm and 0.0143 cm was determined for the unpacked and packed setup, respectively.
A unique feature of the model is the inclusion of the spatial and temporal nature of micro-discharges developed by van 't Veer et al. (2020b).In the model, the power distribution factor ðcÞ is used to define the power density distribution between micro-discharges and a uniform plasma, with c ¼ 1 yielding a fully uniform plasma.
Compared to the micro-discharges, the uniform plasma is a weaker plasma that is continuously present throughout the whole reactor.
c is determined based on the appearance of the experimental power profile (see Fig. 1), such that the power of the microdischarges and of the uniform plasma in the model is in agreement with the experiments.However, as seen in Fig. 1, not all the microdischarges have the same maximum power and the power of the uniform plasma is also not constant.Therefore, it is not possible to obtain an exact agreement between the ratio of power transferred to the micro-discharges and to the uniform plasma; hence several values of c could be considered to characterize the plasma, as illustrated in Fig. 1.
The different discharge lengths tested and their corresponding residence times are shown in Table 2. Here, the number of micro-discharges per half cycle (N MD ) is also shown, along with the lifetime of a single micro-discharge (s MD ).These values were experimentally determined by analyzing the current characteristics obtained from the digital oscilloscope.
A triangular power density pulse with the experimentally determined lifetime is used to model the micro-discharges.The power profiles used as input in the model, for different values of c, are shown in Fig. 1 for the case of a discharge length of 5 cm over two half cycles.Here, it is observed that c = 0.05 yields a better fit for the higher energy micro-discharges, as expected.Yet, this value overshoots the power for a significant part of the micro-discharges, where c = 0.1 and 0.2 show a better fit.Additionally, c = 0.1 and 0.2 show a better fit for the uniform plasma in the time period where micro-discharges occur (difficult to see on Fig. 1 due to the scale).
The plasma kinetic model assumes that the micro-discharges are uniformly distributed in time and in the plasma.A single molecule therefore cannot be affected by all the micro-discharges.Hence, a factor that determines how many micro-discharges a

Table 1
Overview of the species used in the model, with surface-adsorbed species indicated by (s).

Ground state molecules
Vibrationally excited states Electronically excited states Ions Surface-adsorbed species molecule is exposed to is therefore introduced, as the time of a full discharge period divided by the residence time of the gas (van 't Veer et al., 2020b).Furthermore, the volume of a micro-discharge when no packing is present is modelled as a cylinder, as described by Equation 3, where h is the gap size (4.5 mm) and r is the radius of the micro-discharge, which has been reported to be in the order of 0.1 mm (Bogaerts et al., 2016).
When packing material is included, the volume of a microdischarge is modelled as a spherical volume between solid particles (van 't Veer et al., 2020b).For this calculation, a packing factor of 0.68 is used to define the gas volume available in the reactor.This factor was determined experimentally by finding the displaced volume of water by the MgAl 2 O 4 packing, after the pores of the material were first saturated with water.

Results and discussion
4.1.NH 3 conversion as function of flow rate, power, and frequency Fig. 2 shows the results obtained from varying the plasma power and feed flow rate when conducting the decomposition in plasma-only.It is clear that when the SEI increases, hence more energy per molecule is applied, the conversion of NH 3 increases, which is similar to the results observed by Akiyama et al. (2018) and El-Shafie et al. ( 2021).The highest conversion achieved was 82 % at a SEI of 18 kJ/Nl.Both curves show a decreasing slope with increasing SEI, which corresponds to a decreasing energy efficiency.Interestingly, the two conversion curves, obtained by either changing the power or the feed flow rate, show similar results for the majority of the SEI values tested, even though the change in feed flow rate causes a change in residence time, which the power alteration does not.The effect of changing the residence time is discussed further in Section 4.2.A lower power yields a lower conversion.The lower power is the result of a lower applied voltage that will give a weaker electric field and therefore a lower acceleration of the electrons.The electron/molecule collisions will thereby transfer less energy and generally lead to fewer collisions giving rise to less decomposition.
The effect of altering the frequency is shown in Fig. 3. Here, a nearly linear increase in conversion with increasing frequency is observed, hence weaker, but more frequent energy pulses favor NH 3 decomposition.Increasing the frequency reduces the number of micro-discharges per half cycle (see Table S1), but on a time basis the number is higher.This indicates that collisions with the high-energy electrons initiate the decomposition, as the higher frequency leads to a larger number of micro-discharges for the full residence time.Therefore, a larger number of molecules can potentially interact with the micro-discharges and dissociate.This correlates with the observation in our recent work (Andersen et al., 2022), where the number of micro-discharges was found to be a determining factor for the conversion of NH 3 .

NH 3 conversion as function of residence time
The effect of the gas residence time was investigated by altering the length of the outer electrode, hence the length of the discharge zone.In contrast to changing the residence time by changing the flow rate, this method does not alter the SEI for a fixed power input.
The experimentally determined NH 3 conversion as function of the gas residence time for a power input of 15 W is shown in Fig. 4 (black curve).A maximum conversion of 54 % is observed  at a residence time of 6 s.For residence times between 12.5 and 25 s the conversion only changes slightly, indicating that a balance between the decomposition and re-formation of NH 3 could have been established at a conversion around 47 %.It must be mentioned, that DU decreases as the residence time (length of the outer electrode) is increased, see Table S2.A lower DU, results in a weaker electric field, and therefore a lower average energy of the electrons, which could be the reason for the decrease in conversion between the residence times of 6 and 12.5 s.Additionally, Fig. 4 shows calculated NH 3 conversions using different values of the power density distribution factor.Using a value of c equal to 0.2 predicts clearly lower conversion in the residence time range from 1 to 10 s than observed experimentally.However, at residence times of 12.5 and 18.8 s, the predicted conversions are very close to the experimental values.Lowering the value of the power density distribution factor to 0.15 and 0.1 increases the conversion for all investigated residence times, and with c equal to 0.1, the model predicts the experimental conversions at residence times up to 6 s reasonably well.Nevertheless, for the shorter residence times (1 and 2.5 s), the modelled conversions remain lower than the experimental values, indicating that even less power is admitted to the uniform plasma.The model therefore predicts a change in the plasma distribution behavior (between microdischarges and more uniform plasma) when the discharge volume is altered, and that having a more non-uniform plasma, i.e. lower c, characterized by more intense micro-discharges (see Fig. 1 above), promotes the decomposition.This observation is consistent with the high-energy electrons initiating the decomposition, as a lower

Introduction of packing material
Packing the discharge zone with a material with a dielectric constant below 26 has previously been shown to improve the decomposition of NH 3 when treating a pure NH 3 feed (Andersen et al., 2022;Wang et al., 2015).In the present study, where a gas feed with 2 mol% NH 3 was examined, the introduction of the MgAl 2 O 4 packing (dielectric constant of 8.3 (Shannon and Rossman, 1991)) was found to decrease the NH 3 conversion (X NH 3 = 37 %) compared to the empty reactor (X NH 3 = 51 %) at a comparable residence time (2.5 s in the empty reactor versus 2.0 s with packing) and identical power of 15 W as shown in Fig. 5.It must be noted that the reduction in residence time below 2.5 s could have an impact on the NH 3 conversion, as observed in Fig. 4.However, the empty reactor still shows a slightly higher conversion at a residence time of 1.25 s (X NH 3 = 39 %), hence another Fig. 3. NH 3 conversion as function of frequency obtained after 1 h, at a plasma power of 15 W and flow rate of 100 Nml/min (corresponding to an SEI of 9 kJ/Nl) and a discharge volume of 10 cm 3 .Fig. 4. NH 3 conversion as function of residence time obtained by changing the outer electrode length.Experimental data obtained after 1 h at a plasma power of 15 W and frequency of 3 kHz, flow rate of 100 Nml/min (corresponding to SEI of 9 kJ/Nl), and discharge gap of 4.5 mm.Results determined from the kinetic model were calculated for the case-specific parameters listed in Table 2 and Table S2 for various values of c. parameter must also affect the conversion.It must further be noted that on Fig. 5, the outer electrode length for the empty reactor corresponding to the residence time of 2.5 s is 2 cm, but for the packed reactor, an electrode length of 5 cm was used to yield a (comparable) residence time of 2.0 s.
A larger number of micro-discharges per half cycle was present when packing material was introduced in the discharge zone, as indicated in Table 2. Here, the electron energy is significantly higher compared to the afterglows (see Figure S2).However, this was not found to have a positive effect, even though it was observed for the empty reactor that the high-energy electrons from the micro-discharges were mainly contributing to the decomposition.Interestingly, the average electron energy during the afterglows was predicted by the model to be slightly lower for the packed setup than for the unpacked.Additionally, the total number of electrons was predicted by the model to be higher for the packed setup over the full course of the gas residence time (see Figure S3), even though c was found to increase to 0.35, meaning that a more uniform plasma was promoted by the MgAl 2 O 4 packing (see Figure S4 for I-V measurements for the plasma-only and packed with MgAl 2 O 4 ).Moreover, the increased N MD was found to lower the duration of the afterglows, which in turn affects the reactions occurring in this period.This could mean that the enhanced electric field and the larger number of micro-discharges are not the only two factors dominating the conversion when introducing packing material.Plasma reactions with and without packing material will be discussed further below.

Plasma species densities and surface coverage
The transient behavior of the densities of selected gas phase species, as predicted from the model, is shown in Fig. 6, for the unpacked and packed reactor, with residence time of 2.5 s (c = 0.08) and 2.0 s (c = 0.35), respectively.Fig. 6a and 6c depict the neutral and vibrationally excited species during two microdischarges and their afterglows, while Fig. 6b and 6d displays the radicals and charged species.
For the unpacked reactor, it is seen that the afterglow of a micro-discharge lasts approximately 120 ms, which is 6 orders of magnitude longer than the lifetime of the micro-discharges (ca.200 ns).The time in plasma shown in Fig. 6a and 6b corresponds to the seventh and eighth micro-discharge encountered by a molecule.After this, only small variations in the concentrations are observed between micro-discharges for the species plotted in Fig. 6b, while for the neutral species, the NH 3 concentration slowly decreases, and as a result the N 2 and H 2 concentrations increase.The full transient density development for the unpacked and packed setup is shown in the Supporting Information (Figures S5  and S6).
The high density of N 2 observed in Fig. 6a is due to the feed composition used, and as a result, the density of vibrationally excited N 2 (N 2 (v)) species is predicted to be in the order of 2x10 18 to 7x10 18 molecules/cm 3 , since the main consumption of N 2 in micro-discharges (indicated by md) is by vibrational excitation (Reaction 2).In the afterglow (indicated by ag), N 2 is primarily predicted to collide with N 2 (v) of a higher vibrational state, resulting in the formation of two N 2 (v) of a lower vibrational state (Reaction 3).Simultaneously with Reaction 3, the N 2 (v) species decay to N 2 at a slow rate, explaining the long falloff and slow rise of N 2 (v) and N 2 , respectively, in Fig. 6a.Furthermore, the density of NH 3 is decreasing slowly (barely visible on Fig. 6a), while H 2 has a net drop in the micro-discharges and a net rise in the afterglows.
From Fig. 6b it is clear that H atoms have the highest density of the radicals, which increases during a micro-discharge to a value of ca.5x10 16 molecules/cm 3 and then slowly decreases in the afterglow to a value of ca.4x10 15 molecules/cm 3 .The H atoms are predicted to have a density approximately 600 times higher than the N atoms during the afterglow and 5 times higher during a microdischarge, even though the N 2 density is approximately-two orders of magnitude higher than that of H 2 .This is attributed to the higher bond strength of N 2 (9.8 eV) compared to H 2 (4.5 eV) (Hong et al., 2018).The high difference in density between N and N 2 (v) is also a result of the large difference between the formation energy of the species (9.8 eV for N and 0.29 eV for N 2 (v = 1) and 0.57 eV for N 2 (v = 2)).Interestingly, the formation of H atoms during a micro-discharge is mainly a result of collisions between electronically excited N 2 and H 2 (Reaction 4) and not from direct splitting of NH 3 .However, obviously, H 2 is first produced from NH 3 , as it is not introduced as feed gas.Furthermore, during the afterglow, the splitting of NH 3 (Reaction 5) and NH 2 (Reaction 6) contribute equally to the H formation as the previous collision reaction (Reaction 4).
The increase in the N atom density during the micro-discharges comes from the dissociation of N 2 (Reaction 7), which is in high concentration in the feed.During the afterglow, the N atoms almost solely come from collisions between H and NH (Reaction 8).
The high electron density in the micro-discharges is a result of ionization of the feed gas (NH 3 + N 2 ) (Reaction 9 and 10), where the NH 3 + density (not shown on Fig. 6) increases from 10 2 to 10 12 molecules/cm 3 .As the N 2 concentration is roughly 49 times higher than the NH 3 concentration, Reaction 10 contributes to a larger extent to the formation of electrons.However, it only contributes ca. 10 times more, which is attributed to the higher ionization potential of N 2 (15.6 eV (''IST-Lisbon database www.lxcat.net"2022)) vs NH 3 (10.2eV (''Hayashi database www.lxcat.net"2022)).
Interestingly, the formed NH 3 + reacts with NH 3 to form NH 4 + and NH 2 (Reaction 11), thereby contributing to the decomposition.However, the main NH 4 + destruction reaction is by recombination with an electron (Reaction 12) to form again a stable NH 3 molecule; hence, the formation of NH 3 + also has a negative effect on the NH 3 decomposition, due to the loss of electron energy in this cycle of electron impact ionization (Reaction 9) and recombination (Reaction 12).
Fig. 6c shows the densities of the neutral and vibrationally excited species during two micro-discharges and their afterglows, and Fig. 6d for the radicals and charged species, for the packed reactor.Here, the time in plasma corresponds to the 23rd and 24th micro-discharge encountered by a molecule, as a larger number of micro-discharges occurs per half period compared to the unpacked setup.Furthermore, the lifetime of the afterglows is reduced from 120 ms for the unpacked reactor to 30 ms for the packed bed.
The previously discussed reactions (Reaction 2-12) remain dominant for the packed bed, but some of them become more prominent for the formation or consumption of a given species.Fig. 6c shows that the density of N 2 (v) between micro-discharges increases from 1.9 Â 10 18 (in the unpacked setup, cf.Fig. 6a) to 3.8 Â 10 18 molecules/cm 3 in the packed setup, but the peak density in the micro-discharges is lower (6.0 Â 10 18 compared to 7.0 Â 10 18 molecules/cm 3 ).This is due to a lower rate of Reaction 2 (by a factor of ca. 2), while the rate of Reaction 3 is increased by a factor of 2.5.Furthermore, only small changes are seen for the N 2 and H 2 densities during a micro-discharge, meaning that the formation rate of N and H is lower for the packed setup compared to the unpacked (Fig. 6).Similar to the unpacked setup, the density of NH 3 is decreasing slowly for the packed setup (barely visible on Fig. 6c).The rate of density change (source term) will be discussed further below.
The plateau concentrations in the afterglows for radicals and charged species seen in Fig. 6 are a result of the non-zero power density distribution.This means that the electrons are continuously heated by a small power deposition, which allows for electron collision reactions, however, at a lower reaction rate compared to during the micro-discharges.
Additionally, the introduction of MgAl 2 O 4 packing increases the contribution of surface reactions.Indeed, for the unpacked setup, surface reactions can only occur at the reactor wall and inner electrode surface, while in the packed setup, the packing greatly enhances the available surface area.Fig. 7 shows the surface coverage during the 23rd and 24th micro-discharge, similar to Fig. 6c  and d.Here, H(s) is determined to be the main adsorbate, which correlates with the adsorption energies at the reaction tempera-Fig.7. Calculated surface coverage and fraction of empty sites as a function of time when operating in a packed reactor with an outer electrode length of 5 cm andc = 0.35.ture, and shows a small increase in coverage during the microdischarges that stays constant during the afterglows.However, during the first few micro-discharges, the H(s) coverage is increasing rapidly due to the formation of H and H 2 from the NH 3 decomposition (see Figure S7).A somewhat similar tendency is observed for N(s) on Fig. 7, with an almost constant coverage during the afterglows.However, in contrast to H(s), the N(s) coverage is slowly decreasing during the micro-discharges and during the first few micro-discharges it is the main adsorbed species on the surface, because of the high N 2 concentration present in the feed gas.A plot of the surface coverage during the complete residence time is shown in the Supporting Information (Figure S7).
In contrast to H(s) and N(s), the NH(s) and NH 2 (s) coverage is clearly observed to increase during the micro-discharges with up to two orders of magnitude.For NH 2 (s) this is partly due to the fast increase in density of NH 2 in the gas phase that adsorbs on empty surface sites (see Reaction 13) and due to an ER reaction between NH and H(s) (see Reaction 14).For NH(s), the increased coverage is almost solely a result of an ER reaction between N and H(s) (see Reaction 15).During the afterglow, the coverage of both species slowly decreases to a value slightly below the previous afterglow, hence leading to an overall drop in surface coverage of both species over a longer time scale.
The decrease in surface coverage of NH(s) during the afterglow is due to its consumption in the formation of NH 2 (s), which subsequently forms NH 3 causing a negative effect of the packing material on the NH 3 decomposition.The model thereby predicts that the NH 3 decomposition is taking place in the gas phase and is initiated by electron collisions, mainly during the micro-discharges, but is counteracted by NH 3 formation from NH 2 (s) due to the packing during the afterglows.The NH 3 decomposition reaction pathway to H 2 and N 2 will be discussed in further detail in section 4.6.
The current model describes the formation of NH 3 from surfaceadsorbed species by desorbing NH 3 as it is formed, and the surface coverage of NH 3 is therefore not determined.Furthermore, the model does not include electronically/vibrationally excited NH 3 , and their surface adsorption contribution is therefore also not included.

Change of species in the micro-discharges and afterglows
The time-averaged net source terms for the various gas phase species, in a single micro-discharge and the following afterglow, are shown in Fig. 8, to identify whether species are produced or removed.The data shown in Fig. 8 is taken from the second to last micro-discharge, since the system has reached a state where the previous cycle (micro-discharge and afterglow) resembles the next cycle.As also observed in Fig. 6, NH 2 , NH, H, N, and the electrons are net produced during the micro-discharges for both the unpacked and packed setup (non-patterned compared to patterned bars in Fig. 8) and consumed in the afterglows.For the molecules, NH 3 , H 2 , and N 2 , a net consumption is predicted by the model during the micro-discharges, which for NH 3 also is the case during the afterglows; however, the source term is 6 orders of magnitude smaller in the afterglows (red bar compared to grey bar).Generally, the source term of the species during the afterglows (typically in the order of 10 16 to 10 19 cm À3 s À1 ) is found to be smaller than during the micro-discharges (in the order of 10 21 to 10 25 cm À3 s À1 ), meaning that the reaction rates are higher in the microdischarges.Interestingly, H 2 and N 2 are the only two species in Fig. 8 that are produced during the afterglows, indicating that a relaxation period is important for the formation of the desired decomposition products.However, it is during the microdischarges that the main destruction of NH 3 occurs.Moreover, during the afterglows a net consumption of electrons is found, which is attributed to the lack of ionization collisions.It is therefore likely that there is an optimal discharge frequency for the NH 3 decomposition, which is outside of the range tested in Fig. 3.
Comparing the difference between the unpacked and packed setup in Fig. 8, a generally slightly higher source term during the micro-discharges is predicted for the unpacked setup.This aligns well with the higher density of electrons during micro-discharges for the unpacked setup, as electron-molecule collisions are the dominant reactions in this phase.During the afterglows, the source terms for NH 3 , H 2 , H, N, and N 2 are almost equal, and for NH 2 , NH, and electrons the consumption is slightly higher for the packed setup.The higher consumption of NH comes from adsorption on the surface and from the formation of NH 2 (s) via Reaction 14. Similarly for NH 2 , adsorption on the surface as well as formation of NH 3 causes the higher consumption.

NH 3 reaction pathways in micro-discharges and their afterglows
Based on the preceding sections, the reaction pathways for the NH 3 decomposition in a micro-discharge and its afterglow for plasma alone are summarized in Fig. 9.The %-values given within the parentheses in Fig. 9 are normalized with the NH 3 consumption in the specific plasma phenomena, which is also the case for the %values given in the text of this section.The main reaction for NH 3 is dissociation by collision with an electron, which can yield either NH 2 or NH (Reaction 5 and 16) both in the micro-discharges and afterglows.However, the dissociation to NH 2 occur ca. 3 times faster compared to NH in a micro-discharge, and ca. 5 faster in the afterglow.Additionally, in a micro-discharge a small fraction of NH 3 (2.6 %) is ionized to NH 3 + (Reaction 9).
The formed NH 3 + then almost solely react with NH 3 to form NH 4 + and NH 2 (Reaction 11).The NH 4 + then collide with an electron to either re-form NH 3 or form NH 2 (Reaction 12 and 17).
Subsequently, the formed NH 2 from Reaction 5, 11, and 17 collide with N to form N 2 and two H or H 2 (Reaction 6 and 18), which in a micro-discharge occurs equally (35 %).As explained earlier, the dissociation of N 2 forms N (Reaction 7), hence the N 2 content in the plasma thereby impacts the decomposition of NH 3 due to the use of N in the conversion of NH 2 .
In the afterglows two additional reactions (Reaction 19 and 20) contribute significantly to the consumption of NH 2 .In Reaction 19, NH 2 reacts with H to form NH 3 and in Reaction 20, NH 2 reacts with H to form H 2 and NH.This yields a contribution of 25 % for Reaction 6 and 18, 18 % for Reaction 19, and 10 % for Reaction 20 in the NH 3 consumption in the afterglows.
The remaining 22 % of the NH 3 consumption is through NH reactions.Indeed, the formed NH reacts with H or N to yield H 2 and N (Reaction 8) or H and N 2 (Reaction 21), respectively.Both of these reactions occur in the micro-discharges and afterglows.However, the relative contribution of Reaction 8, compared to 21, is ca. 2 times higher during a micro-discharge, which increases to ca. 9 times in the afterglow.Additionally, Reaction 8 is the main reaction path for H atoms in a micro-discharge, but during the afterglows, the H atoms are mainly consumed in the formation of H 2 by recombination with a second H atom.
A small amount of NH also reacts with another NH molecule and yields two H and N 2 (Reaction 22).The relative contribution of Reaction 22 during a micro-discharge (2.4 %) is a result of the high density of NH momentarily present (see Fig. 6).The density then quickly drops in the afterglow, resulting in a lower contribution of Reaction 22 (0.4 %).
The model predicts a similar reaction pathway for NH 3 decomposition when packing material is introduced in the plasma (see Figure S8).As can be seen, the same reactions described for the plasma alone (Reaction 5,6,8,9,11,12,and 16 to 22) also dominate for the NH 3 decomposition reaction pathway for the packed setup.However, due to the introduction of a surface, additional reactions occur, such as Reactions 13 to 15.The formed NH(s) from reaction 15 stepwise reacts with H(s), formed from Reaction 23, to produce NH 2 (s) (Reaction 24) and finally NH 3 (Reaction 25) both in the micro-discharges and afterglows.However, the combined contribution of these reactions towards the NH 3 conversion are small.During micro-discharges less than 0.1 % and during afterglows ca.1.6 %.Moreover, in the afterglows, an ER reaction between NH 2 and H(s) contributes to the removal of NH 2 , but the product of this reaction is NH 3 (Reaction 26) with a relative negative contribution of 4.9 % in the NH 3 decomposition reaction pathway (see Figure S8).Hence, these surface reactions re-form NH 3 , thereby lowering the overall NH 3 decomposition.
From the reactions presented in this section, it is evident that the high energy electrons play a crucial role in the conversion of NH 3 by initiating its decomposition.Furthermore, the electrons also form key reactants (N and H) through dissociation in the micro-discharges, which are used in the intermediate steps to decompose NH x .This importance of high energy electrons correlates well with the experimental observations made from Fig. 2 and Fig. 3 where increased power and frequency lead to an increased conversion.However, in the presence of a surface, the N and H atoms also react with each other or NH x radicals, through Eley-Rideal and Langmuir-Hinshelwood reactions, to form again NH 3 , partially explaining the lower NH 3 decomposition in the packed reactor.
These results are in agreement with the findings of Akiyama et al. ( 2018) and our previous work on NH 3 decomposition (Andersen et al., 2022), where the decomposition also was concluded to occur mainly in the gas phase by interaction with the high energy electrons.Moreover, in our previous work (Andersen et al., 2022) we observed a linear correlation between the number of micro-discharges and the conversion, which is not the case in this study.This is likely due to the different feed composition used in the two studies, as the collision with N atoms was found to influence the NH 2 conversion greatly in current work (Reaction 6 and 18).These N atoms were not formed in high concentrations with a pure NH 3 feed and could only be formed by converting the feed NH 3 .Hence, the rate of the NH 3 decomposition will initially be slower in the absence of N or N 2 because the rate of NH 3 reformation from NH 2 will be approximately equal to the further dissociation by electron collision in the micro-discharges without N atoms.In the afterglow, with N 2 in the feed, the rate of NH 3 dissociation by electron collision drops below the rate of re-formation of NH 3 , and the consumption of the formed H atoms is (in relation to Fig. 8. Time-averaged net source terms (S i ) (cm À3 s À1 ) in the second to last micro-discharge and its subsequent afterglow for the various molecules, radicals, and electrons in the gas phase, for both the packed and unpacked setup (see legend).
NH 2 ) predicted to be mainly for re-formation of NH 3 and not dissociative collisions under the experimental conditions.Removing this produced H/H 2 could improve the conversion of NH 3 by limiting the re-formation, as shown by Hayakawa et al. (2020) with a plasma membrane reactor.
As mentioned previously, the model predicts a negative effect of the packing material due to the re-formation of NH 3 from H 2 (s), NH (s), and NH 2 (s).The adsorption of NH and NH 2 are therefore not expected to increase the N 2 and H 2 formation, as indicated experimentally by Yi et al. (2019), because the surface is mainly covered by H(s) that reacts with the radicals and re-form NH 3 .As mentioned earlier, the current model does not include electronically excited NH 3 molecules and how the adsorption of these affects the conversion.Since this was proposed by Wang et al. (2017) and Yi et al. (2019) to be a crucial part of the decomposition, this could be included in future work to yield a more detailed kinetic model, if reliable data are available.

Conclusion
A combination of experiments and kinetic modelling were used to study the NH 3 decomposition in an unpacked and packed DBD plasma reactor.The experiments showed that increasing the SEI (higher plasma power or lower flow rate) resulted in a higher NH 3 conversion, and that the same conversion was achieved independent of changes to the flow rate or the plasma power when the SEI was the same.At the highest SEI value (18 kJ/Nl) tested in this study, a conversion of 82 % was achieved.Additionally, the NH 3 conversion was found to increase from 44 to 57 % upon rising the frequency from 1.0 to 3.5 kHz.
Furthermore, a change in the plasma distribution, i.e. the fraction of plasma power transferred through micro-discharges or as a uniform plasma, was observed when the electrode length (discharge volume) was altered at a constant plasma power.Here, smaller volume were found to result in a more non-uniform plasma with a larger number of micro-discharges per volume.This makes it difficult to investigate the pure effect of the gas residence time in the plasma, as the plasma behavior also changes if the residence time is altered through flow rate or electrode length changes.However, it was discovered that a more non-uniform plasma, characterized by more intense micro-discharges, promotes the NH 3 decomposition, which indicates that it is collisions with the high-energy electrons that initiate the decomposition of NH 3 .This observation was confirmed by analyzing the contributions of the different reactions in the NH 3 decomposition reaction network predicted by the kinetic model.Here, it was identified that the main conversion of NH 3 occurs due to collision with electrons in the micro-discharges and their afterglows.Overall, a good agreement between the experimental and model-predicted NH 3 conversion could be obtained, when using an appropriate value of the power distribution factor ðcÞ.For the studied conditions, c was found to change from 0.2 to 0.1 as the plasma volume was changed from 31 to 10 cm 3 .
The introduction of packing material resulted in a lower conversion (X NH 3 = 37 % at 2.0 s) when compared at a comparable residence time and identical power as for the plasma alone (X NH 3 = 51 % at 2.5 s).Yet, the seemingly small reduction in residence time with packing material was observed to be part of the reason for the lower NH 3 conversion.Furthermore, a more uniform plasma was formed by the packing material, with a lower electron density during micro-discharges and a lower average electron energy during the afterglows, which also was found to reduce the NH 3 conversion.
Moreover, the net rate of NH 3 destruction was found to be 5 to 6 orders of magnitude higher during a micro-discharge than during the afterglow for both the unpacked and packed setup.Indeed, a considerable re-formation of NH 3 was found to take place during the afterglow, leading to a stable conversion of NH 3 after a residence time of 13 s (47 % at the conditions of 15 W plasma power, 3 kHz frequency, and 100 Nml/min feed flow rate).The model further identified that N and H radicals are key reactants in the intermediate steps of the decomposition for converting NH 2 and NH.Furthermore, the packing material was found to introduce high concentrations of H(s), which led to significant re-formation of NH 3 through an Eley-Rideal reaction with NH 2 causing a negative effect of the packing on NH 3 conversion.

Fig. 1 .
Fig. 1.Experimental plasma power as a function of time, and the model interpretation using different values of c, for a full voltage cycle, with a frequency of 3 kHz at a discharge length of 5 cm.

Fig. 5 .
Fig. 5. NH 3 conversion when implementing MgAl 2 O 4 packing in the plasma zone, found from experiments and simulations, compared with the NH 3 conversion obtained from an empty reactor at a similar residence time.Plasma power 15 W and frequency of 3 kHz, flow rate of 100 Nml/min, and discharge gap of 4.5 mm.In the model, the effect of the packing is simulated by using a higher c of 0.35, corresponding to a more uniform plasma, in line with the model developed by van't Veer et al. (2020b).

Fig. 6 .
Fig. 6.Calculated number density as a function of time for unpacked plasma (outer electrode length of 2 cm andc = 0.08) of (a) neutral and vibrationally excited species and (b) radicals and charged species in the gas phase, and similarly for packed plasma (outer electrode length of 5 cm andc = 0.35) of (c) neutral and vibrationally excited species and (d) radicals and charged species.

Fig. 9 .
Fig. 9. Schematic reaction pathways for NH 3 decomposition into H 2 and N 2 in a micro-discharge and its afterglow, for plasma-only.

Table 2
Reactor and micro-discharge specification used in the model.NH 3 conversion as function of SEI obtained after 1 h, with either varying plasma power (at constant flow rate of 100 Nml/min) or varying flow rate (at constant power of 15 W), at a frequency of 3 kHz and a discharge volume of 10 cm 3 .