Foundations of plasma catalysis for environmental applications

As mentioned above in section 2.2, all surfaces exposed to a plasma naturally acquire a negative surface charge. This charge effectively changes the electronic structure of the surface, and thus also the electronic structure of the catalyst. As the catalytic action of a material is ultimately determined by its electronic structure [30], it is thus not unlikely that the catalytic efficiency of any given material would be different in a thermal catalytic setup and a plasma–catalytic setup.

Moreover, charging is a reversible process that does not directly change the morphology, structure or other physical properties of the catalyst. In a study by Kim et al [26], the synergistic effect was also found to be reversible, and surface charging could indeed be responsible for the experimental observations. However, there are currently no direct experimental works validating or falsifying this hypothesis. Recent atomistic simulations (discussed in section 3.1), however, clearly demonstrate the potential of surface charge to significantly alter the catalytic process and thus induce a synergetic effect [31].

Also, the importance of charge in determining the efficiency or yield of a plasma–catalytic process should depend on the magnitude of the charging, or more precisely, on the surface charge density, and on the distribution of that charge density. Peeters et al estimated the plasma-induced surface electron density on alumina to be of the order of 10¹⁵–10¹⁷ m⁻² in their atmospheric-pressure dielectric barrier discharge (DBD) [32], in agreement with direct measurement of surface charges on dielectric targets exposed to ionization waves obtained by 'Pockels effect' based techniques (see section  4.3.1). While such significant charge densities can be expected to have at least some effect on the catalytic behaviour, it remains to be conclusively demonstrated that surface charge can be a dominant factor in inducing plasma–catalytic synergy.

2.3.2.1. Excited species.

2.3.2.2. Radicals.

Both electrons and electromagnetic fields are known to induce or modify chemical processes. Indeed, they are the root cause for the existence of technological plasmas in the first place. Also, at a surface, they may induce or modify reactions. Electron-induced desorption, either due to electron-impact induced thermal heating or by direct interaction of the electron with the bonding and antibonding orbitals, has been well-known for a long time [38]. A typical example relevant to plasma catalysis is the desorption of CO from a TiO₂ surface through electron-impact induced CO₂ dissociation. Additionally, electrons may also ionize surface-adsorbed species to form anions, which subsequently desorb from the surface [39].

Electric fields are also known to impact surface processes. This may be of particular importance on rough surfaces and when field lines concentrate near local surface irregularities. Although it is difficult to investigate this effect separately from other factors, and in particular from charges, a recent computational study (see section 3.1.2) indeed showed that the application of an electric field might change the adsorption energy of CO₂ at a Cu surface [40]. Therefore, the existence of the electric field changes the thermodynamics of the process, which in turn may modify the plasma–catalytic process relative to the thermal-catalytic process if the effect is sufficiently large.

Finally, while photons have been considered to be of possible importance in contributing to a synergetic effect, in particular when using photocatalytic materials as the catalyst, there is at present no clear evidence supporting this.

Any (heterogeneous) catalytic process requires the adsorption and desorption of reactants and products on and from the catalyst surface. If the plasma, therefore, changes the surface morphology, structure, or any of its other physical or electronic properties, the catalytic process is likely to be influenced. Such catalyst modifications are indeed quite often observed in plasma–catalytic setups. Stere et al [41] provided a nice example of plasma modification of catalyst activity. They observed that the Ag/Al₂O₃ catalyst in their atmospheric-pressure DBD was active towards NO_x reduction at temperatures at which the catalyst should be inactive in a thermal-catalytic setup. This, therefore, clearly demonstrates a synergistic plasma–catalytic effect.

In situ catalyst regeneration was reviewed recently by Lee et al [42]. In particular, two direct pathways to in situ catalyst regeneration are reduction of (partially) oxidized catalyst material to the metallic structure and the removal of carbon deposit to de-passivate the catalyst.

Of course, one could argue that plasma-induced catalyst modification, activation or regeneration is not a fundamental process but rather the convoluted result of possibly many, more elementary, plasma–surface interactions, ultimately leading to the observed catalyst activity. Regardless, if such plasma-induced catalyst modification may be controlled or tuned, it does provide a reliable means to induce or enhance synergy in plasma catalysis.

Another effect that may be important in plasma catalysis, is catalyst heating. Indeed, the catalyst temperature determines its 'thermal' activity, and also determines the rate of many elementary processes such as surface diffusion and desorption. Moreover, spatially and temporally localized heating of the catalyst surface may affect the surface processes. This catalyst heating, however, is again rather a net result of a variety of surface processes rather than a separate fundamental process. For a more thorough discussion in the context of plasma catalysis, we refer the reader to [43].

Finally, highly reactive plasma-generated species such as radicals may be stabilized on the inner surfaces of voids in the catalyst material [44]. This, in turn, leads to increased surface retention times and, therefore, to possible higher catalyst activity. Below a certain limit, defined by the Debye length, the discharge cannot penetrate into the pores, as discussed in more detail in section 3.3 below. Larger pore sizes, however, can have a distinct effect on the plasma chemistry [45].

Similar to the plasma modification and activation of a catalyst, the occurrence of microdischarges in the pores of a catalyst is not in itself a truly fundamental plasma–surface interaction but may effectively contribute to the overall plasma–catalytic process.

Atomic-scale simulations provide a representation of the system to be studied with atomistic resolution. A variety of techniques exist to gain information from this atomic-scale representation: static calculations may optimize the critical points (energy minima and barriers) in a process, MD simulations provide the trajectories of the atoms through space and time, and enhanced sampling techniques, such as metadynamics or replica exchange MD, allow the calculation of free energy profiles along the (often reduced) reaction coordinate.

The critical factor in all of such calculations is how the interactions, viz the energies and forces, between the atoms, molecules and surface, are accounted for. These interactions can either be described classically or quantum mechanically.

In the classical approach, a so-called force field is constructed that yields the potential energy of the system as a function of the positions of the atoms. Forces between the atoms are obtained as the negative gradient of the potential energy function. The complexity of such force fields may vary from very simple, such as the Lennard-Jones potentials, to much more complex, such as the Reax family of force fields. In general, fairly complex expressions are needed to enable the force field to accurately represent the near-infinite number of possible atomic configurations and the corresponding energies and thus yield sensible chemistry. The main advantage of this approach is that it does not require the solution of the electronic structure problem and is therefore computationally fast.

Alternatively, one may resort to a quantum-based approach to attain a higher level of accuracy. This, of course, comes at the price of a higher computational cost. In quantum-based simulations, the electronic structure of the system is solved, subject to a number of assumptions and approximations. Due to its computational efficiency, the approach taken in the (plasma) catalysis community is invariably so-called density functional theory (DFT) calculations, in which all physical and chemical properties of the system are derived from the electron density instead of from the much more complex electronic wavefunction. The most important choice to make in any DFT calculation is, in essence, the same as in classical simulations: how to represent the energy? In DFT, the energy is expressed as a functional of the electron density, which itself is a function of space. As a rule of thumb, the higher the level of theory of the functional, the more accurate the calculation will be, but also the higher the computational cost will be.

If one wishes to calculate atomic trajectories, the equations of motion need to be integrated, requiring a discretization of time. To maintain a stable trajectory for this time integration, the time step must be sufficiently small, typically of the order of a femtosecond. The simulated period is inevitably very short—at most of the order of microseconds in the case of classical force fields, and of the order of nanoseconds in the case of DFT-based MD, depending, of course, on the system size and complexity of the force description (classical force field or DFT energy functional). Still, as the atomic connectivity may be reevaluated at each step, this indeed allows the study of the actual dynamic trajectories in a chemical reaction. Importantly, if the force field or functional is indeed suitable for the process to be studied, no assumptions regarding possible mechanisms need in principle to be made.

The main limitation of MD simulations is the very short time scale that can be accessed in the simulation. Indeed, thermal processes typically occur on μs—ms timescales, which is beyond the reach of atomistic simulations. Solutions to the time scale problem exist, viz accelerated MD, such as, e.g. temperature accelerated dynamics [48] or collective variable-driven hyperdynamics [49]. Alternatively, enhanced sampling of the free energy profile of a process may be both more efficient and yield more information. An example of this approach is presented in section 3.1.2.2 below.

Besides explicitly and deterministically calculating atomic trajectories, it is also possible to follow the system evolution stochastically, based on a set of probabilities for transitions between states, in a so-called kinetic Monte Carlo approach. Various implementations exist and were evaluated in the context of plasma catalysis by Marinov and Guerra [50, 51]. A major advantage of these models is that the coupling between the surface chemistry and gas-phase chemistry is relatively straightforward. The timescale that can be handled is the nanoseconds-to-minutes range, while the calculations are still very fast compared to MD simulations. A major disadvantage is that the simulations require a list of possible species as well as events that can take place, with appropriate rate coefficients. This limits what can (and cannot) happen in the simulation. So far, the application of this type of modelling to plasma catalysis has been limited.

In contrast to the extensive body of computational (mainly DFT) studies of thermal catalysis, the number of works on plasma catalysis using atomic-scale simulations remains very limited. This is partly due to the computational cost of (reliable) DFT calculations and the unpredictable suitability of force fields, which are generally not optimized for plasma–catalytic processes. An additional reason is the non-existence of methodologies capable of modelling certain aspects of plasma catalysis, such as surface charging. Only recently have methods been developed that allow such aspects of plasma–catalyst interactions to be described.

Moreover, the stochastic nature of many surface processes, such as simple surface diffusion required for L–H kinetics, leads to an exponential distribution in reaction times. To dynamically simulate surface reactions thus seems a near-impossible task, which is further complicated by the wide range of flux ratios of species reaching the surface. For instance, for every ion reaching the surface, perhaps 10⁶ neutrals would need to be accounted for. It is clear that this cannot be accomplished in a single dynamic simulation effort.

Instead, atomic-scale simulations typically approach the problem by one of two options. The first option is to statically calculate system properties of interest, such as, e.g. the reaction energy as a function of the progress of a reaction. This can be accomplished using sampling techniques such as metadynamics or alternatively by barrier finding techniques such as nudged elastic band calculations. This information can subsequently be used as input in, e.g. microkinetic models as described in section 3.2. The second option is to dynamically simulate reactions focusing on, e.g. a single reaction or a single parameter such as surface charge.

In the remainder of section 3.1.2, we shall describe what is currently known from atomistic calculations about fundamental factors of influence specific to plasma catalysis, viz surface charge, electric fields and vibrational excitation.

3.1.2.1. Surface charge and electric fields.

As discussed above (sections 2.2 and 2.3.1), a solid in contact with plasma accumulates a negative surface charge due to the influx of free electrons. Excess surface electrons can reach densities of the order of 10¹⁷ m⁻² and may remain trapped for long times, up to days [32, 52]. Since excess charge at the surface may modify the electronic structure of the material, capturing charge-induced changes in surface reactions requires a quantum chemical approach. Bal et al developed a DFT-based technique to add charges to a periodic surface slab [31]. Divergence of the energy is avoided by inserting a counter charge in the gas phase above the charged slab. This setup effectively corresponds to a negatively charged surface with a positive space charge next to it. The surface charge density can be tuned by varying the lateral dimensions of the surface. Note that this approach is valid only for DFT-codes based on an atom-centred basis set (such as, e.g. CP2K), and would not be suitable for plane-wave based codes (such as, e.g. VASP).

Using this methodology, Bal et al investigated how charging a dielectric Al₂O₃ surface loaded with a single metal atom (Ti, Ni or Cu) as the catalyst would affect its chemical reactivity [31]. It was found that the metal atom adsorbed less strongly on the surface, with a decrease in adsorption energy of about 1 eV. This was explained by the charge-induced change in the support electron affinity: the metal was found to adsorb as an M²⁺ species, thus reducing the surface upon adsorption. Upon adding a negative surface charge, the support is already reduced and therefore becomes more resistant against further reduction by adsorption of the metal. This, in turn, leads to lowered adsorption energies.

When allowing CO₂ to adsorb on the charged surface, Bal et al observed that the adsorption energy changes significantly, in particular on Ni and Cu: whereas the CO₂ adsorption energy on the neutral Cu/Al₂O₃ surface is about 0.5 eV, it increases to about 1.5 eV on the charged surface. This adsorption energy is similar to that for CO₂ adsorption on neutral Ni/Al₂O₃. This is shown in figure 5(a). Moreover, when CO₂ was considered, it was found that the overall reaction energy was also significantly influenced by surface charge. In particular, CO₂ dissociation was found to be much less endothermic on the charged surface, as shown in figure 5(b).

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These observations can be rationalized by inspecting the partial density of states. Essentially, the M–CO₂ bond is formed by the overlap of the metal d-orbitals with the CO₂ antibonding π^* orbitals. The resulting bonding states are lowered in energy relative to the neutral systems due to the increased overlap between the d-orbitals and the CO₂ antibonding π^* orbitals. This effectively strengthens the M–CO₂ bond and weakens the C–O bonds in CO₂. Thus, surface charging activates the CO₂ molecule upon adsorption. From a chemical perspective, charging makes the surface more basic and thus more prone to react with the Lewis acid CO₂. Similarly, and also using DFT calculations, Jafarzadeh et al found that adsorption energies of CO₂ on TiO₂-supported Ni₅ and Cu₅ catalyst clusters substantially increase upon charging, by up to 2 eV [53].

Large electric fields are also found in common plasma–catalytic setups [54], which can polarize the surface. The electronic and thus chemical properties of a catalyst can hence be significantly altered through plasma exposure without changing its actual chemical composition. Recently, Jafarzadeh developed the (as yet) only model specific to plasma catalysis, incorporating both charging and electric fields [40]. The authors investigated the effect of charge, electric fields and the combination of both on the adsorption and activation of CO₂ on various Cu-surfaces. When only an electric field was applied, the partial charges on the adsorbed CO₂ and the adsorption energy were predicted to increase. Concurrently, C–O bond lengths were observed to increase, thus activating the molecule towards dissociation. When combining the electric field with excess surface electrons, this effect is enhanced, leading to binding and reaction energies shifted by up to 1 eV. It was thus concluded that the presence of both surface charge and an electric field might be a key factor in enhancing CO₂ conversion in plasma catalysis.

Whether or not this effect is indeed dominant, or at least can be dominant in plasma catalysis, remains to be validated. Indeed, the surface charges investigated in these studies (about 0.09 C m⁻²), as well as the values of the electric field strength (up to 250 V nm⁻¹), are rather high. Regardless, simulations like these demonstrate the crucial importance of methodological developments in elucidating specific mechanisms operative in plasma catalysis.

3.1.2.2. Vibrational excitation.

As discussed in section 2, the presence of vibrationally excited molecules has also been presumed and, for some processes, demonstrated to be important in plasma catalysis [55]. Indeed, the average vibrational temperature of specific chemically active normal modes can be well above 1000 K in plasmas that are otherwise at room temperature [46]. The effect of vibrational excitation of gas-surface reactions is usually studied through explicit quasi-classical trajectory studies, which can only model molecular beams at fixed translational and vibrational energies.

However, such state-resolved molecular beams are a poor representation of the broad energy distributions found in a plasma. Moreover, these simulations are highly demanding and time-consuming: up to 10⁶ trajectories have to be calculated for a single condition, which is only feasible when an efficient classical interatomic potential is parametrized for the system a priori and precludes more wide-ranging studies over several catalysts, reactions, or conditions. Nevertheless, a recent preliminary study used a simplified analytical model, the so-called Fridman–Macheret model (which was, however, untested for surface reactions) to include the effect of vibrational excitation in a kinetic model of catalytic NH₃ synthesis. The model predicted a rate increase by up to five orders of magnitude and a shift in relative catalyst activities, analogous to the charging effects mentioned above [11].

Employing an ensemble-based approach to investigate the effect of vibrational non-equilibrium on chemical reactivity [56], Bal et al attempted to quantify the importance of this vibrational non-equilibrium on dissociative chemisorption of H₂ and CH₄ on Ni catalysts [35]. These authors found that vibrational excitation can indeed very efficiently lower the apparent free energy barrier to dissociation at the surface. The free energy barrier for dissociative chemisorption is shown in figure 6 for H₂ and CH₄ on Ni in figure 6.

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Further, it is observed that the rate enhancement is not captured well by the Fridman–Macheret model and that an accurate assessment of the importance of vibrational excitation requires consideration of the vibrational temperature, the specific modes that are excited, the degeneracy of these modes, and the presence of steps and terraces, which also affects the impact of vibrational excitation. Although this study shows that significant rate enhancements can be expected at low temperatures, the lowering of the apparent free energy barrier is limited at more realistic temperatures (T_vib ∼ 1500 K), so the rate enhancement will also be limited. The authors, therefore, concluded that the potential impact of vibrationally excited CH₄ on the overall catalytic process may be minor.

The continuity equations for the species densities in 0D plasma chemistry models are written in their simplest form as:

$$\begin{equation}\frac{\mathrm{d}{n}_{i}}{\mathrm{d}t}={\sum }_{j}\left\{\left({a}_{ij}^{(2)}-{a}_{ij}^{(1)}\right){k}_{j}\prod\limits _{\text{l}}{n}_{\text{l}}^{{a}_{ij}^{(1)}}\right\}\end{equation} \tag{ 1 }$$

with a_ij ⁽¹⁾ and a_ij ⁽²⁾ the stoichiometric coefficients of species i, at the left and right-hand side of a reaction j, respectively, n_l is the species density at the left-hand side of the reaction, and k_j is the rate coefficient of reaction j.

The rate coefficients of chemical reactions between neutral species or ions are usually adopted from literature and are typically calculated from Arrhenius equations, expressing the dependence on gas temperature. The rate coefficients of electron impact reactions are usually obtained from energy-dependent cross-sections integrated over the EEDF. The latter is then calculated with a Boltzmann solver, which is commonly incorporated in plasma chemistry models.

Besides the species densities, the electron and gas temperatures can also be calculated from similar (energy-balance) equations, again based on production and loss terms, as defined by the power deposition or by the electric field, and by chemical reactions. For more details, we refer to an interesting tutorial review paper by Hurlbatt et al [62].

The balance equations yield the time-evolution of the species densities, electron and gas temperature, averaged over the plasma reactor volume; spatial variations due to transport in the plasma are typically not considered, although 1D fluid models describing detailed plasma chemistry and accounting for diffusion, migration and convection, have also been developed for plasma catalysis (gas-conversion) applications (e.g. [63]). In addition, several methods exist to account for spatial variations in 0D chemical kinetics models, for instance, the so-called h_l factor, which describes the relationship between the central ion density and the ion density at the sheath edge; see details in [62]. Moreover, the effect of diffusion and losses due to chemical reactions at the catalytic surface is typically considered by an additional loss term in the balance equations [64].

Finally, spatial variations can also be accounted for by translating the time-variation of the balance equations into a spatial variation, i.e., as a function of distance travelled through the plasma reactor, based on the gas flow rate, hence considering the plasma reactor as a plug flow reactor. This also allows spatial variations of input parameters, such as applied power or gas temperature, to be considered. Note that this feature is particularly useful in accounting for the filamentary behaviour of a DBD, which is the reactor type primarily used in plasma catalysis, as illustrated for instance in [65, 66]. This method is computationally much more manageable than accounting for filament formation in 1D, 2D or 3D fluid models.

Typically about 100 different species, including the electrons, various types of molecules, radicals, ions and (electronically and vibrationally) excited species, are included in such plasma chemistry models, which react in (above) 1000 reactions. As shown by Hurlbatt et al [62], the number of chemical reactions to be considered typically rises more or less linearly with the number of species included.

The possibility of describing detailed plasma chemistry is the main advantage of this type of model, but at the same time also their main weakness, i.e., the need for accurate rate coefficients or cross-sections for all reactions. Indeed, the latter are subject to uncertainties, which limits the accuracy and predictive power of chemical kinetics models. Hence, there is a strong need for model validation. The effect of the uncertainties can be evaluated by Monte-Carlo simulations, which use a large number of combinations of rate coefficients randomly generated within their reported uncertainties, hence providing information on the uncertainty of the model output results attributable to the rate coefficients. This method was first developed by Turner for an He/O₂ plasma [67–69] and later also illustrated for a CO₂ plasma [70] and a CO₂/CH₄ mixture [71]. Although reliable rate coefficients and cross-sections are needed for all kinds of plasma models, this is especially true for chemical kinetics models, which focus precisely on studying complex chemistries.

Obviously, the more reactions included in such models, the more complicated it is to evaluate the model uncertainty. Hence, while it is tempting to include all possible reactions for all species, this complexity may also limit the predictive power. Turner [67, 68] demonstrated that reaction schemes could be drastically reduced, even up to 85%, without significantly affecting the output [68].

Plasma chemistry models are very popular for plasma catalysis applications because they can handle many different plasma species and chemical reactions. Some examples for CO₂ splitting, CH₄ conversion, as well as for CO₂/CH₄, CO₂/H₂, CO₂/N₂, CO₂/H₂O, CH₄/O₂ and N₂/H₂, and their combinations can be found in, e.g. [72–77].

Surface kinetics models solve the continuity equations for the fractional coverage of all surface species as a function of time, again based on production and loss terms:

$$\begin{equation}\begin{array}{c}\frac{\mathrm{d}{\theta }_{x}}{\mathrm{d}t}=\sum\limits _{i,\text{production}}{c}_{x,i}{r}_{i}-\sum\limits _{i,\text{loss}}{c}_{x,i}{r}_{i}\end{array},\end{equation} \tag{ 2 }$$

where θ_x is the fractional coverage of species x, c_x,i is the stoichiometric coefficient of this species in the production and loss reactions i and r_i are the rates of the corresponding reactions. These rates are calculated as the difference between the rates of the forward and reverse reactions:

$$\begin{equation}\begin{array}{c}{r}_{i}={k}_{i,f}\prod\limits _{{x}_{f}}{({a}_{{x}_{f}})}^{{c}_{{x}_{f},i}}-{k}_{i,r}\prod\limits _{{x}_{r}}{({a}_{{x}_{r}})}^{{c}_{{x}_{r},i}}\end{array},\end{equation} \tag{ 3 }$$

where k_i,f and k_i,r are the rate constants of the forward and reverse reactions, respectively, and a_xf and a_xr are the activities of the reactant species x_f and the product species x_r , respectively. The activities are assumed equal to the fractional coverages for surface species and to the partial pressures (in bar) for gas-phase species. While in plasma chemistry models, the rate coefficients are typically adopted from literature (or databases), in surface chemistry models, the rate constants are usually calculated from transition state theory:

$$\begin{equation}\begin{array}{c}k=\frac{{k}_{\text{B}}T}{h}\;\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{{\Delta}{G}^{{\ddagger}}}{RT}\right)=\frac{{k}_{\text{B}}T}{h}\;\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{{\Delta}{H}^{{\ddagger}}}{RT}\right)\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{{\Delta}{S}^{{\ddagger}}}{R}\right)\end{array},\end{equation} \tag{ 4 }$$

where k_B is the Boltzmann constant, T is the temperature, h is Planck's constant, R is the ideal gas constant and ΔG^‡, ΔH^‡ and ΔS^‡ are the Gibbs free energy, enthalpy and entropy of activation, respectively. The latter are typically obtained by DFT calculations, and are also available for many catalyst materials in databases, such as the CatApp database [78].

By solving the differential equations to steady-state $\left(\frac{\mathrm{d}{\theta }_{x}}{\mathrm{d}t}=0\right)$ for all species, and inserting the steady-state coverages back into the rate equations, the steady-state reaction rates can be obtained, which provide the product formation TOFs, a common term in catalysis. More information about such models can be found in [79].

Chemical kinetics models are very useful for chemical reaction pathway analysis, to study the most important production and loss processes for various species, both in the plasma and at the catalyst surface. In this way, they can pinpoint limitations for the production of some species, and thus also propose solutions on how to overcome these limitations.

Hong et al developed a chemical kinetics model for NH₃ synthesis by plasma catalysis, accounting for surface reactions at the catalyst surface [64]. The loss and production rates due to the surface reactions were included as additional loss or source terms, consisting of the rate coefficients multiplied by the free surface site density. The model revealed that the surface-adsorbed N atoms, N(s), were mainly formed by dissociative adsorption of ground-state N₂ molecules, as well as by N₂ molecules in the first vibrational level, and by direct adsorption of N atoms. H(s) were also mainly formed by dissociative adsorption from ground-state H₂ molecules, but also by direct adsorption of H atoms, while dissociative adsorption from vibrationally excited H₂ molecules seemed less important. In addition, the rate of H(s) formation was calculated to be four orders of magnitude higher than the rate of N(s) formation. The model did not only account for stepwise hydrogenation on the surface, which is the dominant pathway in conventional catalysis, but also for reactions between plasma radicals and surface-adsorbed species, i.e., E–R reactions, and the E–R reaction of NH₂ radicals with H(s) was indeed reported to be more important for the NH₃ synthesis [64].

van't Veer et al developed a similar model for plasma–catalytic NH₃ synthesis, again for a simple catalyst metal and paying most attention to the plasma chemistry [80]. This model focused on the role of the filamentary microdischarges (FMs) and their afterglows, typical of DBD plasmas. The model revealed that most of the NH₃ production occurs in the afterglows, while during the microdischarges, the NH₃ is actually decomposed upon electron impact dissociation. However, during the microdischarges, electron-impact dissociation of N₂ and H₂ also creates N and H atoms, which form NH radicals. These species adsorb onto the surface and are subject to hydrogenation, leading to the formation and desorption of NH₃.

Electron-impact dissociation of N₂ followed by adsorption of N atoms was identified as the rate-limiting step, rather than dissociative adsorption of N₂ at the catalyst surface, like in thermal catalysis. In addition, despite the fact that vibrational excitation is stated to be of minor importance in DBD plasmas, electron-impact dissociation from vibrationally excited N₂ levels was predicted to contribute ca. 8% to the overall N₂ dissociation in the plasma. The larger this contribution, the more energy-efficient the overall NH₃ synthesis, as the required dissociation energy is reduced by vibrational excitation. Overall, just like the model of Hong et al, this model revealed that both E–R and L–H reactions play a role in plasma–catalytic NH₃ synthesis. The pathways predicted by the model during the microdischarges (a) and subsequent afterglows (b) are illustrated in figure 7.

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Mehta et al developed a more detailed surface microkinetics model for plasma–catalytic NH₃ synthesis, but without a plasma chemistry model, thus not accounting for plasma radicals and only considering vibrational excitation [11]. They reported that vibrationally excited N₂, as produced by the plasma, can drastically enhance the NH₃ synthesis rates on catalyst materials that are kinetically limited by N₂ dissociation, and thus, that the optimal catalytic material in plasma catalysis would be different from thermal conditions [11]. In addition, the model revealed that due to the non-thermal plasma excitation, the NH₃ yields could exceed equilibrium limits [81]. Engelmann et al studied the impact of different vibrational distribution functions on the catalytic dissociation of N₂ and the subsequent production of NH₃, and also included radical reactions, to illustrate the contribution of these species and their corresponding reaction pathways. Their model was applied to a large range of catalyst materials and revealed that when radical adsorption and E–R reactions determine the reaction pathways, the NH₃ synthesis becomes virtually independent of the catalyst material [36]. These model predictions are confirmed by various experimental data [37], indicating that in most common (DBD) plasma–catalytic conditions, radical adsorption and E–R reactions indeed dictate the plasma–catalytic NH₃ synthesis mechanisms.

Engelmann et al [82] also developed a similar surface microkinetics model for plasma–catalytic non-oxidative coupling of CH₄ for a range of different metal catalyst surfaces, and the overall conclusion was that the optimal catalyst material depends on (i) the desired products and (ii) the plasma conditions. Indeed, plasma conditions that favour vibrational excitation of CH₄ could significantly enhance C₂H₄ formation on most catalysts, like Pt, Rh, Pd and Cu, while C₂H₆ formation was promoted on the more noble catalysts, like Ag. On the other hand, plasma conditions that give rise to many radicals, such as CH₃, CH₂, C₂H₅ and C₂H₃, cause a high selectivity towards C₂H₄ on all catalysts, hence including noble catalysts as well [82].

Finally, microkinetics models were also developed for plasma–catalytic CO₂ hydrogenation into CH₃OH [83] and oxidative coupling of CH₄ [84]. Plasma-generated radicals and intermediates were found to increase the calculated CH₃OH production rate by 6–7 orders of magnitude compared to thermal catalysis on a Cu(111) surface, showing the potential of plasma–catalytic CO₂ hydrogenation into CH₃OH [83]. Also, in the case of plasma–catalytic oxidative coupling of CH₄, the plasma-generated radicals and intermediates largely enhance the oxygenated product yields [84]. In addition, the model revealed the role of individual radicals in the surface processes, as summarized in figure 8.

• Strongly dehydrogenated carbonaceous species (CHCH, CH, C) strongly induce coking, and their formation should be avoided.
• O radicals counteract coking, so their partial pressure should be tuned against that of the carbonaceous radicals, but they also lead to deep oxidation to CO₂.
• The more hydrogenated carbonaceous radicals (CH₃, CH₂) are in general beneficial, as they bind less strongly to the catalyst and lead to H^* formation on the surface, yet they also cause coking at high partial pressures.
• H radicals appear beneficial by promoting hydrogenation of CH₃O^* and HCOO^*, yielding CH₃OH and HCOOH, respectively. Moreover, high H partial pressures can potentially form more free surface sites by removing excess O^* via H₂O formation.
• CH₃O and CH₃OO radicals are important precursors to both CH₃OH and CH₂O. Increasing their partial pressures thus also strongly enhances CH₃OH and CH₂O formation.

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In general, these chemical kinetics models can reveal how various plasma species affect the catalyst surface chemistry. This can guide alterations of the plasma composition to improve the formation of desired products.

A fluid model is based on solving conservation equations for the densities of the various plasma species, similar to equation (1) in section 3.2.1 above, but in addition also account for spatial gradients. Moreover, transport of the species is described by migration in the electric field (for the charged species), diffusion due to concentration gradients, and convection. In addition, Poisson's equation is usually solved, for a self-consistent calculation of the electric field distribution, based on the charged species densities. Finally, gas heating can be calculated by a heat transfer model, and the gas flow dynamics by the Navier–Stokes equations, although static gas conditions are also often assumed, depending on the application and the research question under study.

Zhang et al developed a 2D fluid model to study the plasma behaviour in inter-particle macro (10–400 μm) pores for a DBD plasma operating in a homogeneous mode in helium [85, 86]. The model revealed that the plasma species can only be generated inside pores with diameter ⩾30 μm. This can be correlated with the Debye length, which is in this order for the typical conditions of a helium plasma in glow discharge mode (i.e., electron temperature and density of 3 eV and 10¹⁷ m⁻³).

In general, modelling predicted that plasma formation inside pores occurs more easily at larger pore size and applied voltage [85], which was also observed experimentally [87, 88]. In addition, the dielectric constant of the catalyst support also plays a role [86]. Modelling revealed that for small dielectric constants, ionization inside the pores appears to occur more easily. The reason is that for large dielectric constants, the polarization of the left sidewall of the pore counteracts that of the right sidewall, reducing the net electric field, and thus the electron temperature and electron-impact ionization inside the pore are lower. To our knowledge, no experiments have investigated the plasma behaviour inside catalyst pores with different dielectric constants. Hence, these model predictions still have to be validated by experiments, but they suggest that the most common catalyst supports, i.e., Al₂O₃ and SiO₂, with dielectric constants around 8–11 and 4, respectively, can more easily promote plasma formation inside catalyst pores than, e.g. ferroelectric materials with dielectric constants above 300. Finally, also the pore shape determines how easily plasma can be formed inside catalyst pores because it greatly affects the electric field enhancement. Indeed, modelling predicted that the electric field is significantly enhanced near tip-like structures, which affects the electron-impact ionization and thus plasma formation [89].

While μm-sized pore sizes are of interest for structured catalysts, catalytic supports typically have pores in the nm range. Fluid modelling, however, cannot be applied to nm-sized pores because the mesh size would be too small for a fluid description. To gain insight into whether plasma can penetrate into such small pores, PIC-MCC simulations must be applied. They are based on calculating the trajectory of a large number of individual particles (so-called super-particles, typically various types of ions, and the electrons) using Newton's laws, while the collisions of these super-particles are treated with random numbers, which are compared with the collision probabilities, defined by the collision cross-sections. The electric field distribution is calculated self-consistently from the positions of the charged super-particles. For this purpose, the positions of the super-particles are projected onto a grid to obtain a charge density distribution, from which the electric field distribution can be calculated with Poisson's equation.

Most applications of plasma catalysis use reactive gases, like air, CO₂, hydrocarbons and their mixtures, rather than helium. The reactive gas plasmas are typically filamentary, and the plasma density inside the filaments can be much higher than in a homogeneous plasma in glow discharge mode. This can induce a much smaller Debye length and enable the plasma to penetrate into smaller catalyst pores.

Figure 9 illustrates the calculated electron number density profile inside pores with different diameters, obtained from PIC-MCC simulations in dry air, for an applied voltage of −8 kV [90]. The electron density inside the pore is negligible for a pore diameter of 400 nm, while it reaches a maximum inside pores with diameter of 600 nm and above. Hence, these PIC-MCC simulations predict that plasma streamer formation can occur in pores of 600 nm and above but not in smaller pores. This behaviour is again correlated with the Debye length, which is calculated to be 415 nm for this case (dry air, atmospheric pressure and applied voltage of −8 kV). In general, we can conclude that the Debye length is an important criterion for plasma streamer penetration into catalyst pores, i.e., plasma streamers can only penetrate into pores with diameter larger than the Debye length.

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The Debye length depends on the electron density and temperature in the plasma streamer, but it is typically in the order of a few 100 nm up to 1 μm at typical DBD conditions in air. Hence, this is the typical range of pore sizes in which plasma streamers can penetrate. This has consequences for plasma catalysis, as it determines the catalyst surface area exposed to plasma, and thus it will affect the plasma–catalytic performance. Note that catalytic supports (such as zeolites) typically have pores in the (few) nm range, which will thus not allow plasma streamer penetration inside the pores. In this case, however, plasma species might still be able to diffuse into the pores, depending on their lifetime. This diffusion process could be described by Monte-Carlo simulations, which could then also include detailed catalytic surface reactions, but to our knowledge, such modelling efforts have not yet been reported in the context of plasma catalysis.

Finally, PIC-MCC simulations also revealed that the dielectric constant of the support material plays an important role in the plasma streamer behaviour inside the pores, i.e., through surface charging, which determines the streamer penetration and discharge enhancement [52]. At small dielectric constants, surface charging causes the plasma to spread inside the pore, leading to somewhat deeper plasma streamer penetration than for larger dielectric constants, in line with the fluid model predictions discussed above.

The catalyst (or catalytic packing) can affect the plasma behaviour in various ways. A catalytic packing in a packed-bed DBD reactor can cause local electric field enhancements at the contact points between the beads, and also change the discharge behaviour (from volumetric filaments to more surface discharges). This has been demonstrated by both experiments (see section 4 below) and modelling.

Modelling a packed bed DBD reactor is quite challenging because of the 3D geometry and the large number of mesh points needed to resolve the space near the contact points between the packing beads. In fact, modelling a packed bed DBD reactor in 3D is not yet feasible within a realistic calculation time. Instead, Van Laer and Bogaerts developed two complementary axisymmetric 2D fluid models to approximate the 3D geometry, i.e., a so-called 'contact point' model and a 'channel of voids' model [54]. The combination of both models can account for the two important features of a packed-bed DBD reactor, i.e., (i) the contact between the beads, yielding local electric field enhancement due to polarization effects, and (ii) the fact that the voids between the beads are connected, allowing the gas to travel from one side of the discharge gap to the other [54].

Fluid modelling for a helium DBD plasma revealed that at low applied voltage, the plasma is confined to the contact points, reflecting the properties of a Townsend discharge, while at higher applied voltage, more typical of a DBD, the discharge spreads out more into the bulk of the reactor, from one void space to the other [54], in qualitative agreement with intensified charge-coupled device (ICCD) camera experiments [91–93].

The dielectric constant of the packing beads also affects the plasma behaviour [94]: a larger dielectric constant leads to a more pronounced electric field enhancement, and thus also higher electron temperature, but only up to a certain value, while the electron density drops, due to a change in discharge behaviour. Indeed, as the dielectric constant increases, the plasma can no longer travel through the channels between the voids, and the electrons (and ions) are more easily absorbed at the walls and the surface of the packing beads. A similar effect was obtained for smaller packing beads, where modelling also predicted a lower electron density due to electron losses at the surface of the beads, as well as more pronounced electric field enhancements, due to the many contact points [95].

Streamer propagation in a packed bed DBD reactor has also been described by 2D fluid models [96, 97]. In this case, air plasmas were modelled as they exhibit filamentary characteristics. The models predicted that the dielectric constant of the packing beads dictates whether FMs or surface discharges are formed [97]. Indeed, at small dielectric constants (e.g. ε = 5, characteristic for SiO₂), plasma ignition between the beads occurs as surface discharges or surface ionization waves (SIWs), created due to electric field components parallel to the dielectric surfaces, resulting from surface charging. These SIWs can then connect with the surface of adjacent beads. In contrast, at large dielectric constants (e.g. ε = 1000, characteristic for ferroelectric materials, such as BaTiO₃), modelling predicted localized FMs between the contact points of the beads, while at intermediate dielectric constants, a mix of local filamentary and surface discharges was predicted, in good qualitative agreement with ICCD measurements [97].

Note that the localized FMs between the beads may limit the catalyst activation due to the limited catalyst surface area in contact with the plasma. This may have implications for the efficiency of plasma catalysis. Indeed, although modelling predicted the most pronounced local electric field enhancement at large dielectric constants [94], at the same time, the catalyst surface area in contact with the plasma is more limited due to the localized discharges. Depending on the relative importance of both effects, packing materials with a large or small or intermediate dielectric constant will perform the best in plasma catalysis, as indeed demonstrated in experiments (e.g. [98, 99]).

Plasma streamer propagation through packed-bed DBD reactors in dry air was also described by PIC-MCC simulations [100, 101], revealing similar trends as the fluid models above. Furthermore, more sophisticated packing structures, such as honeycomb packing and three-dimensional fibre deposition (3DFD) structures, were also simulated [102]. The calculations revealed how the plasma streamer propagates along the dielectric surface, yielding a surface discharge, and that it is limited to one channel. In other words, the streamers in different channels of a honeycomb-structured catalyst are completely separated. As a consequence, when the honeycomb channels are parallel to the electrodes, the discharge is much weaker than when the channels are perpendicular to the electrodes. In the latter case, the plasma streamer can develop over a much longer distance, yielding the production of more reactive plasma species by electron-impact reactions. This may explain why in plasma catalysis applications, the channels of honeycomb-structured catalysts are mostly perpendicular to the electrodes (see, e.g. [87, 103].

In contrast to the separate channels of a honeycomb-structured catalyst, when using a so-called 3DFD structure, the plasma streamers can freely distribute into different channels, causing discharge enhancement due to surface charging on the dielectric walls of the structured catalyst. This gives rise to a broad plasma distribution, which is not limited to one channel, as was the case for the honeycomb structure. This is illustrated in figure 10 for the plasma streamer propagation in a so-called 1-3-5 stacking architecture, as obtained from PIC-MCC simulations [102]. This broader plasma distribution could be beneficial for plasma catalysis, because a larger catalyst surface area will be exposed to the plasma.

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Note that the examples and models in this section all apply to packed-bed DBD reactors (or other, more sophisticated packing geometries in DBD reactors). This is the most common geometry for plasma catalysis due to the easy incorporation of the catalyst inside the plasma. Moreover, packed bed DBDs allow intimate coupling between plasma and catalyst, due to the small plasma volume, which cannot be reached in other plasma types, where volume processes may be dominant. Nevertheless, plasma catalysis can also be performed in other plasma setups, like microwave (MW) or gliding arc (GA) plasmas or (atmospheric-pressure) glow discharges. However, this is typically performed in a post-plasma catalysis configuration (e.g. [104]), because most catalysts would not withstand the high temperatures in these 'warm' plasmas, although fluidized or spouted bed configurations are under investigation as well (e.g. [105]). In post-plasma catalysis, however, there is no direct contact between the short-lived reactive plasma species or other plasma components (like the electric fields) and the catalyst, and the catalyst will not affect the plasma behaviour (like the local electric field enhancements, described above). For this reason, we believe, modelling up to now has focused on packed-bed DBD reactors, at least on the reactor scale.

Of course, the models for the plasma and surface kinetics and for plasma behaviour inside catalyst pores, described in sections 3.2 and 3.3, could also be applied to other types of plasmas, at least when in direct contact with a catalyst, such as being investigated in some in situ diagnostics studies (e.g. low-pressure glow discharges; see section 4 below).

'Packed bed' configurations are reactors allowing the circulation of a gas flow while being filled with solid particles to increase the efficiency of the exchanges between the gas and solid phases. The combination of a packed bed reactor (PBR) with a plasma was first considered in the 1990s, mainly for the treatment of diesel engine exhausts, the removal of nitrogen oxides (so-called deNOx), and soon after for the treatment of VOCs in indoor air [107–109]. All these applications require the direct use of air at atmospheric pressure to generate the plasma with strong constraints on energy consumption. This has naturally led to the use of DBD to couple the PBR to the plasma, but other plasma sources can be coupled with packed beds.

The gas space between the solid particles (or 'voids') cannot be too small; otherwise, the plasma will not develop between the particles. If powders with particles of a few microns are used, a preferential path for the plasma will tend to be established above the catalyst bed and not through the core of the powder. DBD-PBRs are therefore usually filled with millimetre-sized particles, leaving at least a few hundred microns of space between particles. This simple constraint can already be a problem in evaluating and comparing the catalytic activity of different materials. Indeed, good practice in assessing the activity of a catalyst requires determining parameters such as selectivity, or turnover frequency (TOF or site-normalized catalytic reaction rates), or turnover numbers in ideal reactor configurations (perfectly mixed batch reactors or plug flow reactors, for instance) in which the results are reproducible and above all, independent of mass and heat transport [110]. The presence of relatively large voids between the particles can cause some of the gas to pass through the reactor without interacting with the catalytic surface, and affects the mass and heat transport phenomena to the surface depending on the geometric arrangement of the catalytic bed. This difficulty is already significant, simply from the point of view of stable molecules in classical catalysis, but in addition, DBD-PBRs add the problem of the distribution of plasma filaments within the packed bed and the diffusion of short-lived species (radicals, vibrationally or electronically excited molecules) to the surface. This effect of catalytic packing on the plasma development has been discussed from a modelling point of view in section 3.4. Experimentally, the difficulty of optical access in packed bed configurations and the randomness in time and space of plasma filaments forces us to study the effect of packing in more or less simplified systems. The effect of the packing configuration on the plasma development is mostly studied with fast ICCD imaging to characterize the localisation of the plasma in the bed. In [92], ICCD imaging was used in a plane-to-plane packed bed DBD configuration showing preferential plasma initiation at the points of contact between catalyst beads. However, such a three-dimensional packed bed configuration does not allow the visualisation of plasma development in the whole volume of the catalyst bed. This is why 'simplified' packed bed configurations are often used to perform fast imaging.

Examples of such simplified configurations are shown in figure 12, which gives examples of ICCD imaging taken from [111–113] in PBR configurations ranging from the most complex, with random packing, in figure 12(a) to the simplest, with only a single bead, in figure 12(d).

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Figure 12(a), from [92], obtained with a microscope above a plane-to-plane packed bed DBD with random packing, shows the tendency of filaments to ignite close to the contact points of the beads. Figure 12(a), from [111], shows different types of plasma filaments in a PBR between two mesh electrodes and relates these discharge modes to the ones observed in a pin-to-plane corona configuration with the same catalyst bead (figure 12(b)). The 2D PBR shown in figure 12(c), from [112], allowed for a detailed study of the path taken by the filaments and its dependence on the spacing between beads and their dielectric permittivity (comparing quartz and zirconia). The extreme simplification of the case of an isolated bead shown in figure 12(d), taken from [113], allows a very detailed study of the development of the plasma on the surface of a bead of a given material but obviously does not allow the importance of the junctions between beads of catalysts to be studied, for example. It is worth mentioning here that configurations from [111, 112] are not, strictly speaking, DBDs since a plasma channel can be established that connects the two metal electrodes without being stopped by the charge deposition on an insulating barrier. Another example of experimental study of streamer propagation on a single catalyst bead with metallic pin electrodes is given in [114]. The advantage of metal electrodes to perform fast imaging is the lower jitter on ignition time, which helps to synchronize the acquisition of the ICCD camera, but the absence of dielectric covering the electrode can modify the mechanism of initial breakdown since no surface charge is accumulated.

All these configurations are complementary and give valuable information on the type of discharge that can develop in PBRs. In particular, simplifying the packing makes comparisons with models possible, as shown in [112], in which a fluid model reproduced the different behaviour of discharges in the 2D packed bed. It is only the combined study of all these PBR configurations that allows links to be made between the physics of individual discharges, the effects of electric field reinforcement induced by the catalytic bed arrangement, and finally, the resulting statistical spatial distribution in a large volume reactor. In an application-oriented DBD-PBR, only statistical or time- and space-averaged electrical data can give some indication of the discharge behaviour (see section 4.3). Simplified 2D or single bead configurations give real access to the type of discharge initiated with fast imaging but also spatially and temporally resolved spectroscopic information, as obtained with interferometric filters in [111].

These studies have provided evidence of different types of discharge behaviour. When the local electric field is enhanced by the catalyst beads, the applied voltage required to ionize the gas at this location is lowered. These localized field enhancements can thus generate partial discharges (PDs) that do not necessarily cross the entire inter-electrode gap. This can be the case, for example, at the poles of a catalyst bead in contact with the dielectric barrier, especially if the permittivity of the material is high (the left-hand image figure 12(d) from [113] and in [115]), at the junction between two beads (as indicated by 'PD' in figure 12(b')), or when the distance between two catalyst particles is reduced, or in the vicinity of metal particles deposited on the catalyst support (as in the bottom-left image in figure 12(c) from [112] and also in [96, 116]). The term 'PD' here refers to the fact that these filaments do not bridge the entire gap between the electrodes. They are sometimes referred to as 'FMs', which is not a very specific name because all discharges observed in these configurations are of micrometre diameter and filamentary. These PDs or FMs are mostly ionization waves through the gas voids, as distinct from the ionization waves propagating along the surface of the beads that are also observed (SIW, or SIWs, as shown in figure 12(c)). The 'primary streamer' denoted by 'PS' in figure 12(b') is also a SIW, as is the filament seen in the right-hand image of figure 12(d). Both filaments through the gas voids and SIWs are probably streamers, as will be discussed in section 4.2.2, but the small dimension and low emission intensity of the PD make an experimental distinction between an ionization wave and simple electron avalanches very difficult.

The SIW can be triggered by the accumulation of charges carried by a gas void ionization wave (or PD or FM) on the surface of the catalyst bead and is primarily ignited at the location of the most intense applied electric field. The SIW generally has a higher electric field and electron density, as expected from the literature on DBDs and flashover (see section 4.2.2). When the packing material has high dielectric permittivity, it induces higher local electric field enhancement, promoting more numerous PDs at lower applied voltage [117]. As a result, low permittivity materials will induce longer streamers along the surface for the same average power transferred to the gas. In contrast, high permittivity materials will generate more numerous discharges that are more localized in high applied electric field areas [13, 14]. It is, however, interesting to note that the dielectric permittivity depends on the frequency. The reinforcement of the applied electric field is well determined by the low-frequency dielectric permittivity (because the high voltage supplies of the DBDs are generally only at a few kHz). On the other hand, the electric field variation during the passage of an ionization wave (of the order of nanoseconds) corresponds to the GHz frequency range, for which the permittivity values can significantly decrease, as suggested in [119]. For small particles, the permittivity also depends on the grain size.

For the optimization of the chemical conversion efficiency of a DBD-PBR, many characteristics of the catalyst bed arrangement are important: the fraction of the void volume compared to the total volume of the reactor is, of course, important for the residence time of the gas and the possibility to generate the plasma, but the average size distribution of the voids, the number of contact points between catalyst particles, the angularity of the shape of the catalyst particles (which can reinforce the electric field) and, of course, the permittivity will affect the number and the location of the ionization waves generated at a given power. All these macroscopic parameters are essential to control the volume fraction of the voids in which the plasma can be ignited or not. This will determine the probability that a molecule will pass through a plasma filament. In [120], by comparing a Monte Carlo model with experimental data on the filament distribution in a plane-to-plane DBD and NH₃ production in a packed bed DBD, it has been shown that the ratio of the discharge volume to the reactor volume determines the plasma reactor efficiency.

In addition to the importance of macroscopic packing parameters, the surface parameters usually controlled in catalysis remain decisive for the chemical reactivity in DBD-PBRs. In thermal catalysis, the notion of 'pores' typicaly refers to cavities or channels within the catalyst with a characteristic dimension less than 100 nm. The porosity (often written θ) is then the ratio of the total pore volume to the apparent volume of the particle or powder (excluding interparticle voids). As shown in section 3.3.2, these dimensions are too small for a plasma to be ignited in the pores. Nevertheless, the porosity θ will influence the reactivity of stable molecules in the material and whether short-lived species can diffuse into the catalyst. In particular, for sub-50 nm pores, for which diffusion occurs mainly by the collision of molecules with pore walls (Knudsen diffusion), the stability of radicals or excited states of molecules produced by the plasma after a few collisions with the surface is a key parameter that is unfortunately usually unknown. The number of active sites, the BET surface area, the crystalline or amorphous structure, and the reducibility, are all determining parameters in the activity of a catalyst, but they can all be modified by the action of the plasma on the material, either transiently or permanently, because of strong electric fields or efficient oxidizing species.

Very little is known about the role of voids at the scale of a few microns, between the macroscopic scale of the packing and the surface properties at the nanoscale. In section 3.3.2, it has been shown that models predict the possibility of initiating plasmas in micron-scale voids. This possibility has been suggested experimentally but only from energy measurements [121, 122].

There are still many questions about the development of filamentary plasmas in packed beds. To better understand these discharges, one should not neglect studies dedicated to the interaction of ionization waves with dielectric surfaces carried out in fields other than plasma catalysis, in simpler but nevertheless relevant configurations.

The literature describing the physics of DBDs without catalytic beds is, of course, also relevant to understanding the physics of discharges in DBD-PBRs. Indeed, DBD-PBR configurations can be seen as a set of dielectric surfaces placed with different orientations to the applied electric field, from surfaces perpendicular to the applied field (which includes the dielectric barriers themselves) to surfaces parallel to it. Such configurations have been studied in numerous works focused on avoiding 'flashover', i.e., the initiation of ionization waves on different material surfaces. PBRs can also be seen as a set of small empty spaces of dimensions typically smaller than a millimetre. This viewpoint corresponds to the study of the initiation of discharges in small voids, which can lead to the breakdown of insulating materials. These studies do not involve catalytic materials and do not capture some specific aspects of PBRs, such as the field enhancement at particle contact points. Still, they are nevertheless helpful to understand the development of discharges in PBRs.

The plasma discharge in a DBD can develop either in a filamentary streamer regime or, in some particular conditions, as a Townsend discharge or even a glow-like discharge [123, 124]. One of the main criteria for the transition to the streamer regime is the size of the increase of the effective ionization coefficient (α_eff = α − η, with α the ionization coefficient and η the attachment coefficient) for the gas with the reduced electric field E/N, where E is the electric field and N is the gas number density. Indeed, when α_eff increases strongly with E/N, the local increase of the charge density induced by electron avalanches will be very sensitive to electric field inhomogeneities, which tends to satisfy locally Meek's criterion responsible for the initiation of a streamer [125]. The typical molecular gases used in plasma–catalysis applications (CO₂, CH₄, air, H₂O, etc) all tend to have a strong dependence of α_eff on E/N, except for N₂, which can be favourable for the Townsend discharge regime [126]. The Townsend discharge corresponds to a low-current electron avalanche regime which does not strongly modify the applied potential. The glow-like regime only happens in a DBD when the current in the Townsend discharge increases sufficiently to have a large reservoir of adsorbed charges homogeneously spread over the cathode dielectric surface, which can sustain the discharge in the manner (in fact, the mechanism is charge desorption from dielectric) of secondary electron emission from a metallic cathode in a 'real' glow discharge. The homogeneity of the surface charge on the cathode side is critical to maintaining the glow-like discharge. Otherwise, the local charge amplification is responsible for the transition to streamers as measured by the Pockels technique on different dielectric materials deposited on top of a BSO crystal [127]. In most PBR applications, the gases used, the inhomogeneity of surface charges, and the local field reinforcement due to the shape of the catalytic surface make the formation of a Townsend or glow-like discharge unlikely, at least in the large voids (>100 μm). In small voids, however, a Townsend discharge could occur. From a terminology point of view, 'micro-discharges' or 'filaments' are therefore more of a visual description, and 'PD' and 'SIW' characterize the localization of the plasma. Most of the time, the plasma in a DBD-PBR develops as an ionization wave through a streamer mechanism either in gas voids or on a surface. Nevertheless, the properties of the streamers (electric field, electron density, etc) are modified by contact with the surface and especially by its capacitance.

In a plane-to-plane DBD, like in a DBD-PBR, it is observed experimentally that, at constant power, higher capacitance of the dielectric barrier results in fewer but more intense streamers with higher electron density, and higher gas temperature [128]. A high dielectric permittivity (ε_r) barrier in a plane-to-plane geometry will lower the voltage necessary to achieve the breakdown field, but the streamer will nevertheless ignite as soon as the minimum breakdown field is reached (imposed by the α_eff of the gas considered), independently from the ε_r of the barrier. However, when the ionization front approaches the surface of the high-ε_r barrier, the polarization of the material will reinforce the field between the front and the surface, speeding up the streamer towards the surface. The charge deposition on the surface will then depend on the capacitance of the barrier proportional to ε_r/d, with d the thickness of the dielectric barrier. The velocity and the length of the propagation of the streamer along the surface in the direction perpendicular to the applied electric field will be controlled by ε_r/d. This can be nicely described by a simple model of resistors and capacitances in series, as shown by Akishev et al [129]. Fluid models, as in [130], also show the role of ε_r/d on the radial expansion, as well as the importance of surface charge density in reignition behind a dielectric barrier in the middle of the gap. A similar influence of high ε_r materials is observed in DBD-PBRs: gas-phase streamers approaching high ε_r poles of catalyst beads will develop with higher electric field and electron density, while only a weak radial spreading around the beads is observed due to the large capacitance of the beads. As a result, only PDs instead of long streamers around the surface are preferentially formed on high permittivity beads if the voltage is kept relatively low.

In contrast to the case of a dielectric surface perpendicular to the applied electric field, which can slow down the SIW because of charge deposition, when the dielectric surface is parallel to the applied field, the SIW is faster than in the gas phase. This has been extensively studied in the literature on flashover prevention with various materials and even with different surface shapes [131–133]. Figure 13, from [134], shows a similar configuration studied for lamp ignition with two pin electrodes applying an electric field parallel to BK7 glass or an Al₂O₃ surface in argon.

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When the dielectric surface is close enough to the pin-to-pin axis, the streamer tends to connect to the surface. The velocity of streamers along the surface is always much higher than through the gas phase for all pressures, peak voltages and distances. This could be due to the polarization of the dielectric surface induced by the applied field or the accumulation of surface charges from previous streamers helping the propagation on the surface. However, the higher ε_r of Al₂O₃ than BK7 seems to have very little influence in this case.

The plane-to-plane or pin-to-plane DBD, as well as the typical 'flashover' setups, have the advantage of better control of the plasma discharge and the orientation of the dielectric surface with respect to the applied field. The influence of catalytic surfaces in these configurations should be more thoroughly investigated. The problem of discharges in very small voids (<100 μm) is also little studied. Discharges in very small gaps have mostly been studied with metallic electrodes to understand the deviation from Paschen's law [135]. Nevertheless, a few studies conducted on the aging of insulating materials and the appearance of plasma in small defects discuss the possible effect of surface charging in small dielectric voids and the consequent field enhancement [136, 137]. Another application of discharges in small voids is the development of ferroelectrets. In [138], an example of DBD with a polycarbonate barrier and a 70 μm gap seems to ignite in the Townsend regime, which might be because charge amplification is not sufficient in such small voids to start a streamer. This could suggest that Townsend discharges can occur in small voids of catalyst pores of a few tens of micrometres even though the wall charging of such voids obviously depends strongly on the material.

The importance of the macroscopic shape and size of catalyst particles/beads in packed bed DBDs has been discussed in the previous sections. Other possible methods of combining plasma and catalysts are discussed here, either with different catalyst supports or with plasma sources other than DBDs.

Better control of the spatial arrangement of the catalyst in the reactor volume can be achieved by using structured one-piece catalyst supports such as monoliths or ceramic foams [139]. For example, materials such as cordierite provide parallel channels typically of 1 mm width and several centimetres length, inside which various catalysts can be deposited. These channels must be placed in the direction of gas flow, which is why they are mostly used with metal electrodes pierced at each end of the monolith. This corresponds to a 'corona' discharge configuration but one in which a 'spark' whose current is limited only by the power source (DC or AC) could connect the two electrodes if the voltage is sufficient [140–142]. These monoliths can also be used in DBDs [143], but in this case, since the applied field is perpendicular to the direction of the gas channels, the applied field must be high enough to allow the re-ignition of the streamers in each channel crossed, which depends strongly on the charge deposition on the channel walls [130]. However, recent techniques for the fabrication of these monoliths provide structures with both axial and radial channels, which gave better toluene conversion efficiency in a coaxial DBD in [144] by facilitating streamer initiation in the radial direction. Another possibility to impose a macroscopic spatial distribution of the catalyst is to use ceramic foams as a support either in DBD [45] or corona [87] configuration. Besides the control of the size of the macroscopic voids using a monolithic support allows the heat transfer from the centre of the catalytic bed to the walls of the reactor to be improved, preventing local overheating thanks to the better thermal conductivity of the solid compared to the gas [144].

The improvement of heat transfer can also be one of the motivations for coupling the plasma with a fluidized bed reactor (P-FBR) [145, 146]. In a fluidized bed, the gas flow is sufficient to displace the catalyst particles (typically a few hundred micrometres in diameter) and induce a recirculation that improves the exchange between the gas phase and the surface. In a P-FBR, the fluidization mode of the powder bed is largely influenced by the charge acquired by the particles exposed to the plasma [146]. Most of the works dealing with the coupling of a plasma with a fluidized bed were aimed at functionalizing the surface of powders using various plasma sources (RF capacitively or inductively coupled plasmas, MW plasmas, DBDs), often at reduced pressure. For environmental plasma–catalysis applications, a few studies were done with GAs [147], but otherwise, mainly DBDs have been trialled for P-FBRs [148–150]. The comparison of the conversion efficiency between the same DBD reactor in 'PBR' or FBR regimes can be complicated because if the same catalytic powder is used in both configurations, the PBR bed may be too compact to allow streamer initiation in the core of the catalytic bed.

Whatever the type of catalyst support (beads, pebbles, monoliths, powders, etc), it is obvious that most of the work carried out on plasma–catalyst coupling has been done with DBDs, mainly because of their simplicity of implementation. Nevertheless, other sources of non-thermal plasmas can be coupled with catalysts. At atmospheric pressure, corona discharges, nanosecond repetitively pulsed plasmas and GAs are sources having clear advantages for some applications. However, some issues are to be considered in coupling them to catalysts. By definition, in a corona discharge configuration, the plasma does not transition to an arc because of the non-uniformity of the applied electric field, which implies that in a part of the inter-electrode gap, the field is no longer sufficient to sustain the plasma discharge. If the inter-electrode space is filled with a catalyst in such a configuration, then the entire catalyst bed is not exposed to the same plasma conditions [151]. In nanosecond repetitively pulsed plasmas, for which the transition to an electric arc is prevented by the very short duration of the voltage pulse (typically <20 ns), the interaction with a catalyst is limited by the volume of plasma generated and the impedance matching to limit power reflection. With GAs, since fluid dynamics are essential to their proper operation, the catalyst can only be positioned downstream of the discharge [152] or in a fluidized bed, as mentioned above [147]. RF and MW discharges are only rarely used in combination with catalysts. The reason is that, just like with GA plasmas, these discharges reach very high gas temperatures at atmospheric pressure (up to several thousand kelvins). These very high temperatures could be limited by pulsing the plasma or by using sufficiently large gas flows, but instead, the catalysts used with these types of discharges are most of the time placed downstream of the plasma to avoid damaging the material. For instance, degradation of vinyl chloride has been investigated with a Pt/Al₂O₃ catalyst in the near post-discharge region of an atmospheric-pressure RF jet [153]. MW plasmas are somewhat more often used with catalysts at atmospheric pressure because they can activate catalytic reactions simply by heating (MW-heated reactions) in addition to enhancing catalytic reactions by species produced in the plasma (MW-enhanced catalytic reactions), as described in a recent review paper [154]. Since the catalyst must be placed downstream of the MW plasma source, not all reactive species reach the surface. The catalyst can then sometimes be beneficial (NH₃ synthesis from N₂ and CH₄ with Co/γ-Al₂O₃ catalyst in [155]), but it can also promote undesirable reverse reaction processes (back-reactions forming CO₂ from CO are promoted on the surface of Rh/TiO₂ catalyst downstream of an Ar/CO₂ MW plasma in [156]). For many molecular gas mixtures, the maximum conversion efficiency of a MW or RF discharge without catalysts is not at atmospheric pressure but between 50 and 200 mbar. It is in this pressure range that these plasmas are furthest from equilibrium, in particular with vibrational temperatures much higher than the gas temperature. In general, catalytic processes are less efficient at reduced pressure due to the lower flux of molecules reaching the surface. It is, therefore, necessary to keep the plasma out of equilibrium at the highest possible pressure, which can be achieved by pulsing RF and MW discharges, as shown by recent works on CO₂ plasmas [157]. Until now, the only works using RF [158], MW [159, 160] or even DC glow discharge [161, 162] sources at reduced pressure are essentially fundamental studies that take advantage of the possibility of measuring radicals and vibrationally excited molecule densities in such discharges at a few millibar to study their interaction with catalytic surfaces.

The great diversity of plasma–catalyst coupling reactors makes their comparison challenging. Moreover, in many cases, the reactors aiming at optimizing the conversion efficiency do not allow in situ measurements, and the only experimental data that can be easily obtained are the densities of stable molecules at the reactor outlet and the electrical data of the reactor. These data are obviously useful, in particular for evaluating the performance of a given reactor, but they are often insufficient to draw conclusions on the real mechanisms of the interaction of the plasma with the catalyst. Simply comparing the performance of one plasma source with another requires care because of the limitations of the parameters commonly used.

To illustrate this point, we consider differences between the fundamental meaning of parameters such as 'yield' (Y_i in %) or 'gas hourly space velocity' (GHSV, h⁻¹) in thermal catalysis and plasma–catalysis.

Y_i is the molar fraction of the initial limiting reactant (i.e., the molecule having the smallest mole number/stoichiometric coefficient ratio for the reaction considered) transformed into a given product. When the yield obtained with two different catalysts is discussed in thermal catalysis, it gives information about how the two catalysts affect the limiting reactant. In plasma catalysis, it is not only the stable species of the inlet gas that reach the surface of the catalyst but also the reactants produced from electron impact processes in the plasma. Two different catalysts can affect these electron impact processes differently by modifying the plasma itself and, consequently, the flow of reactants arriving on the surface. A difference in the yield obtained with two catalysts is therefore much more difficult to relate to a surface reactivity with respect to the molecules at the reactor inlet than in thermal catalysis.

The GSHV is the ratio between the volumetric flow rate of reactants and the catalyst volume. As an example, we consider here the case of a particular catalyst with two different morphologies, i.e. beads of either 1 mm (B1) or 2 mm (B2) in diameter. The volume of a B2 bead is therefore eight times larger than that of a B1 bead. If the same DBD reactor is filled with a packed bed of B2 beads or with eight times as many B1 beads, the total catalyst volume will remain the same, and thus at constant reactant flow rate, the GHSV will be the same. However, the packed bed with B1 beads will have smaller voids on average and many more junctions between the beads that will reinforce the electric field locally. Therefore, as discussed in the previous sections, the number and distribution of streamers will be different. The comparison of two catalysts at constant GHSV is, therefore, less straightforward than in thermal catalysis, mainly because the reactive medium (gas and plasma together) is inhomogeneous. This plasma inhomogeneity in plasma catalysis systems is also important to consider when discussing the performance of different plasma–catalyst reactors as a function of specific energy input (SEI).

Parameters such as SEI, residence time (t_res), power (P_w) and gas temperature (T_g) are very often used to compare the results of molecule conversions with different catalysts or plasma sources. While these parameters are essential, they can be more complicated to analyse than they initially appear.

The energy density transferred to the gas (SEI) in a plasma catalysis reactor is often expressed (in J l⁻¹) as the ratio of the power to the volumetric flow rate:

$$\begin{equation}\text{SEI}=\frac{{P}_{\text{w}}}{{\varphi }_{\text{vol}}}.\end{equation} \tag{ 5 }$$

The SEI (or 'specific energy consumption', or 'energy cost') is also often defined in eV molecule⁻¹ or in J molecule⁻¹ by:

$$\begin{equation}\text{SEI}=\frac{{P}_{\text{w}}\cdot {t}_{\text{res}}}{{N}_{\text{mol}}},\end{equation} \tag{ 6 }$$

where P_w is the power transferred to the gas, t_res the residence time of the gas in the 'active zone' volume and N_mol the absolute number of molecules treated. In catalysis, the residence time often designates the inverse of the GSHV. Here t_res is the time spent by a molecule in the active plasma volume.

As will be shown in section 5, the SEI is a useful parameter to compare the performances of very different plasma sources. Moreover, equation (5) can be calculated a priori in any reactor, even if nothing is known about in situ parameters. It only requires measuring the average power injected into the reactor and the inlet gas flow rate. From an application point of view, this definition could be sufficient to choose an energy-efficient process (although the energy efficiency of the power generator used to ignite the plasma should also be taken into account to obtain the real power consumption). However, several problems can arise in interpreting the SEI in terms of plasma–catalyst interaction mechanisms.

First of all, in most experiments, the gas flows are regulated by mass-flow controllers that impose a standard volumetric flow rate (ϕ_std) referenced to the standard conditions of pressure and temperature. The volumetric flow rate ϕ_vol in equation (5) is then related to ϕ_std by

$$\begin{equation}{\varphi }_{\text{vol}}={\varphi }_{\text{std}}\frac{{P}_{\text{std}}}{{P}_{x}}\frac{{T}_{x}}{{T}_{\text{std}}}\end{equation} \tag{ 7 }$$

with P_std and T_std the pressure and temperature in standard conditions (respectively 101.325 kPa and 273.15 K) and P_x and T_x the pressure and temperature of the gas in the experiment. Obviously, in order to compare measurements made at different total gas pressures, this normalization of the volumetric flow rate must be taken into account. However, the gas temperature is not always known in plasma–catalytic reactors. With higher gas temperature, the residence time of the gas in the plasma zone will be shorter since t_res can be written as follows

$$\begin{equation}{t}_{\text{res}}=\frac{{V}_{\text{reac}}}{{\varphi }_{\text{std}}}\frac{{P}_{x}}{{P}_{\text{std}}}\frac{{T}_{\text{std}}}{{T}_{x}}\end{equation} \tag{ 8 }$$

with V_reac the volume of the reactor or volume of the active plasma zone. In a PBR, V_reac depends on the packing fraction and the typical size of voids and can be challenging to determine precisely. For example, in [120], a parameter of the fraction of the gas volume occupied by the plasma makes it possible to account for the efficiency of production of NH₃, illustrating that the characteristic time that is really important in this case is the time spent by the molecules in the plasma filaments rather than in the gas void regions. V_reac can also be inaccurate, for instance, because the volume occupied by the plasma can vary with power and pressure in a MW discharge. Moreover, equation (8) implicitly supposes laminar flow, which is not necessarily the case [163]. In any case, the gas temperature in the plasma has to be known to estimate t_res.

4.2.2.1. Power (P_w) and electrical measurements.

The simplest way to determine the instantaneous power dissipated in the plasma should be to measure the voltage (U(t)) and current (I(t)) of the discharge and apply P_w(t) = U(t) ⋅ I(t). This can be done in corona or nanosecond repetitively pulsed discharges, for instance, although the short characteristic times of these discharges require special attention to the bandwidth of all the electrical measurement elements, and even the length of the cables used in order not to induce a shift between the voltage and current signals, which would result in a large error in the power calculation. The principle of a DBD, on the other hand, is to limit the current by the capacity of the dielectric. Determining the power actually transferred to the gas by the product of voltage and current signals then requires subtracting the voltage across the dielectric capacitance, which depends on the amount of charge adsorbed on it. It is then simpler to determine an average power by plotting a Lissajous figure (or charge-voltage (Q–V) diagram) as first proposed for DBDs by Manley [164]. In figure 14 (adapted from [165]), the DBD reactor is represented by two capacitances in series, the gas capacitance (C_g) and the dielectric capacitance (C_die). The Lissajous figure is an X–Y plot of the charge accumulated on a measuring capacitor (C_m) placed in series with the DBD reactor as a function of the voltage applied across the DBD reactor. When there is no plasma, the voltage measured on C_m is proportional to the voltage on the equivalent capacitance of the whole DBD reactor cell (C_cell = C_gas C_die/(C_gas + C_die)) corresponding to the slope between A and B (or between C and D) on the Q–V diagram (figure 14(b)). When the plasma is ignited in the gas, this corresponds to a channel with a certain conductivity in parallel with the gas capacitance (resistance R in the diagram). The charges transferred by the plasma will induce an additional increase of the voltage V_die on the dielectric, which will result, via the displacement current, in an increase of V_m on C_m. In the Q–V diagram, the slope of the plot between points B and C (or between D and A) while the plasma is ignited is now given by C_die. It can be easily shown that the difference in height between points B and C gives the total charge transferred ΔQ through the gas during a half period of the power supply. The area bounded by the Q–V diagram gives the average power transferred to the gas in a full discharge cycle according to equation (9), with T the period of the voltage cycle:

$$\begin{equation}{P}_{\text{w}}=\frac{1}{T}{\int }_{0}^{T}{V}_{\text{cell}}(t)\mathrm{d}{Q}_{\text{cell}}(t).\end{equation} \tag{ 9 }$$

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The details of the calculation can be found in many papers [165, 166]. Beyond the determination of the average power, the shape of the Lissajous figure contains other interesting information. The ideal parallelogram shown in figure 14(b) is only obtained if the voltage at which breakdown occurs is the same for all the filaments in the volume of the DBD reactor, which can be the case, for instance, in an empty plane-to-plane DBD.

When the plasma is ignited with different applied voltages at different locations in the reactor, the angles at points B and D become less well defined, and the resulting cycle shape is shown on figure 14(c). This is the typical shape obtained when averaging the signals over many voltage cycles, but in general, from one period to another of the power supply, the position of points B and D is erratic. This shape can often be observed in DBD-PBRs since the local field reinforcements of the catalyst beads and the variable size of voids affect the breakdown voltage required at different positions in the reactor. Figure 14(d) shows another feature that can appear in particular in PBRs. The slope of the Q–V diagram during the plasma 'ON' phases (between points B and C and D and A) corresponds to the capacitance C_die of the whole dielectric of the reactor only if there is enough charge transferred on average to cover the entire dielectric surface. When the applied voltage is only slightly higher than the minimum breakdown voltage, it often happens that the plasma filaments are ignited only in certain areas of the reactor, especially in PBRs. The slope of the Q–V diagram in segments B and C then corresponds to an effective capacitance related to only a part of the total surface of the reactor dielectric, and this effective capacitance increases with the amplitude of the applied voltage [167]. The cycle shapes can also be strongly disturbed when the reactor dimensions are very small or when a pulsed power supply with sub-microsecond rise time is used instead of a sinusoidal power supply. In these two cases, the charge transfer will take place on very short time scales (typically a few tens of nanoseconds), which gives the Q–V diagram a shape very far from a parallelogram. The determination of the value of C_die can then be difficult, but the amount of charge transferred can still be obtained [168, 169]. Many more details about possible deformations of Q–V diagrams and practical points to consider for good measurements can be found in [165].

The previous examples illustrate that an identical Q–V diagram area (i.e. identical average power) can be obtained with very different shapes of the Q–V plot corresponding to different plasma behaviour. To compare the effect of two catalysts in a DBD-PBR, it is therefore not sufficient to compare at constant power because of the inhomogeneity of the energy deposition. Additional information is needed to interpret how the power is distributed in the reactor volume. In addition to the Lissajous figures, it can be interesting to perform a statistical analysis on the current peaks of the plasma filaments. In a PBR reactor, the number of current peaks per half period of the voltage is too high to isolate the current of an individual filament. It is nevertheless possible to study how the statistical distribution of the current peak amplitudes is affected by the catalyst introduced into the reactor, provided that the electrical measurement system (current probe, oscilloscope, etc) has sufficient bandwidth to avoid an artificial smoothing of the fast current peaks. As a first approach, the amplitudes of the current peaks over a single period of the voltage can be compared for different catalysts [170, 171]. It is also quite simple with a modern oscilloscope to perform a more detailed statistical study of the distribution of events as a function of their amplitude at different times of the voltage period as shown in figure 15, or even to study the average charge transferred by different types of filaments in the presence or absence of catalyst [28, 172, 173].

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The measurement of Lissajous figures using a capacitor in series with the reactor has the advantage of not missing any of the charges transferred through the gas even if the bandwidth of the measurement system is not very high. However, combining Lissajous measurements with a statistical analysis of the current peaks to obtain more detailed information on the plasma distribution in the presence of various catalysts is a practical approach that can be used even when the reactor configuration does not offer any optical access to perform in situ plasma measurements.

The importance of energy deposition inhomogeneity in the interpretation of plasma–catalysis results is not limited to DBDs. RF or MW plasma sources also induce inhomogeneous energy deposition with different regimes depending on the working pressure, as recently shown, for example, in [163] for MWs. Thus, even if the power transferred to the gas is correctly measured (e.g. by correct subtraction of the power lost in the tuning box in the case of RF discharges), it is still necessary to characterize the spatial gradients in the plasma to understand the mechanisms in the induced chemistry.

4.2.2.2. Gas temperature (T_g) and catalyst surface temperature (T_cat).

The plasma–catalyst interaction is reciprocal. It is as important to know how the catalyst influences the electronic properties in the plasma (electron density n_e, electron temperature T_e and electric field E) as it is to know the effect of the plasma on the material via the surface field E_s and surface charges σ.

Recently, several techniques have been used to obtain measurements of n_e, T_e and E in ionization waves at atmospheric pressure, but all require devices in which the location and timing of the ionization waves are well controlled. For example, the electric field can be measured by Stark polarization spectroscopy, and n_e, T_e by Thomson scattering in He or Ar jet plasmas impacting on various dielectric or metallic surfaces [182–184]. The electric field in air streamers can be measured with excellent spatial and temporal resolution by cross-correlation spectroscopy (CCS) using the ratio of emission lines corresponding to electronic states excited by electron impact at different energies. This technique has, for example, highlighted the importance of the pre-breakdown phase, which can last up to a few microseconds before reaching the Meek criterion threshold, triggering the initiation of a streamer from the anode of a pin-to-pin DBD [184]. CCS could also be adapted to measure the development of streamers in CO₂ [185]. The influence of remaining surface charge on the development of successive SIWs studied with a similar technique in [186] has demonstrated the strong enhancement of E/N in surface streamers. Electric-field-induced second-harmonic generation (E-FISH) is a recent laser-based technique to measure the electric field with very high time resolution (typically tens of picoseconds), although questions remain as to the exact spatial resolution that can be achieved [187]. The influence of the decay rate of surface charge on the electric field and dynamic of SIWs in a nanosecond pulsed surface DBD have been studied with E-FISH on epoxy resin and PTFE in [188]. All these examples show that the spatio-temporal evolution of the electric field in ionization waves in contact with catalytic surfaces can be measured with these techniques.

Measurements of surface electric field and surface charges on the dielectric have also made significant progress. Electrostatic probes can be limited in spatial and temporal resolution, but the 'Pockels' technique based on change of light polarization through an electro-optic crystal has already been used for some time to determine the surface charge pattern of streamers impacting dielectric surfaces [189]. This technique has been used, for instance, to investigate the role of surface charge on the transition from a diffuse to filamentary DBD in He/N₂ mixtures [190]. The main limitation of this technique is the necessity to use electro-optical crystals (mostly BSO) as the dielectric. A variant of this technique called Mueller polarimetry has recently been developed to separate the depolarization, diattenuation and birefringence components of the signal for use on more complex surfaces. As a test case, the field induced by an atmospheric-pressure plasma jet (APPJ) in He impacting organic tissue could be determined [191]. With the same technique, the axial and radial component of surface electric field induced in a BSO crystal at the impact of an ionization wave generated by a helium APPJ was monitored with spatial and temporal resolution. Figure 16, taken from [192], shows the comparison of these measurements with the results of a 2D fluid model of the APPJ, showing excellent agreement for both the surface electric field component as well as the surface charge density.

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It is worth noting here that in all these measurements [189–192], the surface charge density is between 1 and 100 nC cm⁻² (in agreement with the ∼160 nC cm⁻² estimated in [32] and mentioned in section 2.3.1) irrespective of the gas in which the ionization waves are generated because it is the capacitance of the dielectric material that primarily controls the maximum achievable surface charge density. Whether by Mueller polarimetry or by other techniques being developed (e.g. IR spectroscopy of surface charges in [193]), the measurement of σ on catalytic surfaces is becoming possible.

Radicals and vibrationally excited molecules play a major role in the plasma–catalyst synergy due to their high chemical reactivity (see section 2). Because they are very reactive, their absolute density and their lifetime at atmospheric pressure are respectively very small and short, making them highly challenging to measure. In addition, all absorption measurement techniques that are often suitable for radicals and vibrational temperature measurement are poorly suited to the small dimensions and inhomogeneity of atmospheric-pressure plasmas. Measurements at atmospheric pressure are, therefore, often limited to OES. For instance, in [194], OES was performed on CH(A²∆) radicals in a packed bed DBD for methane steam reforming. The rotational temperature of this radical was shown to be in equilibrium with the gas temperature, which allowed the determination of T_g in the catalytic bed. On the other hand, the measured vibrational temperature only corresponds to the vibrational temperature of the excited electronic state of this radical, which is not necessarily in equilibrium even with the ground state of CH. The main difficulty of OES measurements is the uncertainty surrounding the link between the properties measured on excited electronic states and the bulk properties of the gas. Nevertheless, in [194], it was observed that the vibrational temperature of CH(A²D) is affected by the presence of the nickel catalyst.

More direct measurements of radicals and vibrational temperature (T_v) at atmospheric pressure would be beneficial. Two-photon laser-induced fluorescence (TALIF) can be used to measure the densities of various radicals (O, H, OH, etc) with good spatial and temporal resolution. One of the difficulties at atmospheric pressure is the characteristic time of the quenching of the state excited by the laser beam. However, the development of 'fast-TALIF' (with a picosecond or even femtosecond laser) has given excellent results in flames and is starting to be used in atmospheric-pressure plasmas [195]. A limitation to using fast TALIF in plasma–catalysis systems, however, is that it is difficult to measure close to (typically within 1 mm of) the surface. Mass spectrometry can be performed in atmospheric-pressure plasmas, providing information about stable molecules, and also radicals and even ions [196], which would be interesting for sampling done at a catalytic surface exposed to the plasma. Infrared absorption spectroscopy measurements performed directly through the plasma is a powerful technique to measure the vibrational temperature of molecules [197]. The approach has been applied recently at high pressure with FTIR in an RF discharge [198] and in a nanosecond discharge with quantum cascade laser absorption [199]. The same measurements could be performed with a catalytic surface despite the limitations of line-of-sight integrated techniques.

A complementary approach for gaining understanding of the interaction with catalysts, is to use low-pressure discharges in which the radical densities and vibrational temperatures can be precisely determined. For instance, in [200], the vibrational de-excitation of N₂ on various catalysts was investigated in a low-pressure RF discharge. In [201], silica fibres commercially available as catalyst supports were placed on the inner wall of a low-pressure glow discharge in CO₂. It has been shown that the very high recombination probability of O atoms on this material was responsible for an increase of vibrational temperature of both CO₂ and CO, highlighting the importance of CO₂ vibrational quenching by O atoms.

Many techniques commonly used for the characterization of catalysts (x-ray diffraction, O₂ chemisorption, Fourier-transform Raman, x-ray photoelectron spectroscopy, NMR, TEM, etc) are difficult to use in situ under direct plasma exposure. It is, of course, always interesting to use these techniques before and after exposing the catalyst to plasma to check the permanent structural changes caused by the plasma. However, to really understand the plasma–catalyst interactions, it is also necessary to have access to the temporal evolution and to the reversible phenomena under plasma exposure. The surface measurement technique that has been the most developed for in situ measurements to date remains infrared absorption, whether by diffuse reflectance infrared Fourier transform spectroscopy [202], transmission through pellets [203], or attenuated total reflectance [204]. These variants of broadband infrared absorption techniques on surfaces allow the temporal evolution of stable molecules adsorbed on the catalyst to be followed. If these measurements can be associated with measurements of the composition of the gas phase produced by the plasma, they become a powerful tool to study the coupled chemical kinetics of the gas and adsorbed phases. However, it must be kept in mind that the molecules detected by IR on the surface are primarily those that accumulate there and thus are not necessarily the most reactive species. A method to increase the sensitivity of IR absorption detection and, therefore, to have access to species with lower surface densities is polarization-modulation infrared reflection-absorption spectroscopy (PM-IRAS). The oxidation of CH₄ by plasma on Ni and SiO₂ surfaces has recently been studied with PM-IRAS in combination with OES and mass spectrometry to monitor both gas and surface species [205]. As PM-IRAS relies on reflections, it is, however, more often used on metal surfaces.

Temperature programmed desorption is another technique commonly used to identify species adsorbed on catalyst surfaces. TPD has recently been adapted to study CO₂ hydrogenation in DBDs with Co and Cu catalysts [174]. The gas-phase composition was also monitored with gas chromatography and mass spectrometry. Pre-treatment of the surface with isotopically labelled CO₂ allowed the authors to track the exchange of atoms between the gas and the surface. Isotopic labelling is a powerful technique that has already been used, for instance, in [206] to investigate the chemical pathways in NH₃/D₂/N₂ in a DBD-PBR filled with lead zirconate titanate catalyst.

Even techniques based on x-rays, which in principle are only applicable at very low pressure, become accessible for in situ structural analysis of catalysts thanks to the brightness of synchrotron radiation. In [177], it was shown that the structure of Pd particles supported on Al₂O₃ in a DBD-PBR was not affected by the plasma.

All these characterization techniques associated with in situ measurements of the plasma phase are undoubtedly essential to improve our understanding of the fundamental mechanisms of plasma–catalyst interactions and should eventually allow quantitative comparisons with the models described in section 2.

The use of combinations of non-thermal plasmas and catalytic materials to remove VOCs has been studied for decades. Several reviews have been published, for example [208–212].

The standard approach is the use of a DBD combined with a packed bed of catalytic material. The VOC is adsorbed on the catalyst surface before oxidation by species generated by the plasma. The VOCs are typically at low concentrations, and the adsorption acts as a pre-concentration step before plasma treatment [9]. A wide range of VOCs has been treated, including chain hydrocarbons, aromatics and, more recently, chlorinated species.

The most widely used catalytic materials are metal oxides, such as TiO₂, Al₂O₃, SiO₂ and CeO₂. Metal oxides are less expensive than the metal-loaded catalysts typically used for thermal catalysis and in plasma–catalytic gas conversion. MnO₂, which has poor thermal catalytic activity, is also widely used because it efficiently decomposes the ozone produced by the plasma as well as adsorbing VOCs. The application of metal oxides in plasma removal of VOCs provides an example of the different catalytic materials used for plasma and thermal catalysis applications. Indeed, strictly speaking, the metal oxides are not true catalysts since while they facilitate reactions, they do not lower their energy barriers.

Three main approaches can be distinguished: continuous in-plasma catalysis and post-plasma catalysis, which are differentiated by the location of the catalytic bed in relation to the plasma, and sequential in-plasma catalysis, in which adsorption of the VOC and plasma regeneration take place sequentially [213, 214]. Kim et al calculated that reactive species such as O (³P) and OH, with respective lifetimes of 50 μs and 100 μs, must be produced within about 60 μm of the catalyst surface for interactions to occur [214]. Therefore, such species will not be active in post-plasma catalysis; the dominant reactive species will be ozone, whose lifetime is several minutes. Indeed, in some implementations, the only role of the plasma is to produce ozone [6].

Sequential and continuous in-plasma catalysis can both give excellent removal of VOCs. The sequential approach can substantially decrease energy use, but this can be at the expense of less complete oxidation of the VOCs to CO₂ [215]. Sequential operation also offers the possibility of using oxygen as the plasma gas, which increases the decomposition rate and removes the possibility of NO_x formation [216].

Thermal catalytic approaches for the removal of NO_x from exhaust gases include selective catalytic reduction (SCR) using ammonia (NH₃-SCR) and hydrocarbons (HC-SCR). HC-SCR has a poor activity below 300 °C and requires the addition of HC, although this may be provided by unburned fuel. NH₃-SCR can operate at lower temperatures but requires a separate tank of NH₃.

The use of a plasma can avoid problems such as the requirement for expensive noble metal catalysts, the need for high temperatures, particularly in HC-SCR, and the formation of N₂O instead of N₂ as the product of NO_x reduction.

Post-plasma catalysis is widely used since stable intermediate species can be produced by the interaction of the plasma with exhaust gases. The plasma partially oxidizes the NO and hydrocarbons to form NO₂ and oxygenates (alcohols and aldehydes), as well as organic nitroso-compounds such as CH₃ONO and HNO₂ [9]. The species then interact with the catalyst to form, ideally, N₂, CO₂ and H₂O.

An example, analogous to that mentioned in section 2.3.4 [40], is given in figure 17 [217]. The simulated exhaust gas contained 435 ppm NO, 10 ppm NO₂, 6000 ppm C₂H₄, 8% O_2, and the balance was N₂. A DBD reactor partially oxidized the NO to NO₂ and converted the C₂H₄ to HCHO, CH₃ONO₂ and other organic species. The gas mixture then passed over an Ag/Al₂O₃ catalyst, where the organics were removed, and up to 90% of the NO_x was reduced to N₂. The catalyst temperature was 240 °C, which is too low to activate C₂H₆; however, the organics produced by the plasma were activated and could contribute to NO_x reduction. The strong synergistic effect of the plasma and catalyst is clear; the catalyst alone had a removal efficiency of only 7% [217].

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In-plasma catalysis has also been shown to reduce NO_x strongly. Complete oxidation of the hydrocarbon in the plasma decreases NO_x reduction since the beneficial intermediate organic species are not available, so it is important to limit the reaction temperature to ensure only partial oxidation occurs [218]. In situ measurements indicate that the plasma may play a role in cleaning the surface of the catalyst, reducing deactivation [202, 218]. In both post- and in-plasma catalysis, the role of the intermediate species formed in the plasma is critical to allowing HC-SCR to proceed at relatively low temperatures, below the usual activation temperature of the catalyst.

Plasma can also enhance NH₃-SCR. It has been demonstrated that the NO_x conversion rate in NH₃-SCR is increased at low temperatures (below 250 °C) if the NO₂/NO ratio is increased to 50%. This suggests that post-plasma catalysis, with the plasma used to partially oxidize the NO, can be advantageous [218]. This has been confirmed experimentally. For example, Rajanikanth et al [219] found that treating the exhaust gas from a diesel generator with a plasma before passing to an NH₃-SCR reactor increased the NO_x removal efficiency from 10% to 90%, with the NO₂/NO ratio after the plasma stage and the NO_x removal efficiency increasing with the plasma energy density. Moreover, the NO_x removal efficiency increased much less rapidly with the plasma energy density once the NO₂/NO ratio reached 50%, confirming that this is an optimum ratio.

NH₃ production from N₂ and H₂ is the simplest example of plasma–catalytic gas production. The reaction is exothermic

$$\begin{equation}3{\mathrm{H}}_{2}\!+\!{\mathrm{N}}_{2}\to 2\mathrm{N}{\mathrm{H}}_{3}\quad \!\!{\Delta}{H}^{0}=-91.8\enspace \mathrm{k}\mathrm{J}\;\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}=-0.951\enspace \mathrm{e}\mathrm{V},\end{equation} \tag{ 10 }$$

where ΔH⁰ is the change in enthalpy, but has a large energy barrier due to the strong triple bond of the N₂ molecule.

The Haber–Bosch process uses a thermal catalyst to reduce the energy barrier through reactions between surface-adsorbed N and H atoms. The reaction mechanism is given in table 1. Appropriate catalysts have to bind N₂ molecules sufficiently strongly to allow easy dissociation, but not so strongly that they limit desorption or slow the hydrogenation reactions. Iron-based catalysts are typically used since they satisfy this requirement and are relatively inexpensive. However, high temperatures (at least 700 K) are required for catalyst activation. At such temperatures, the chemical equilibrium production of NH₃ is negligible. From Le Chatelier's principle, increasing the pressure increases the conversion yield since there are fewer product than reactant molecules; however, only by increasing the pressure to 100 bar can an acceptable yield of 15% be obtained.

The energy cost of the Haber–Bosch process is typically very low, about 0.1 MJ mol⁻¹ (corresponding to an energy yield of 600 g (kWh)⁻¹), excluding the energy cost of H₂ production. However, at the smaller scales (∼10 t day⁻¹) compatible with renewable energy sources, 0.4 MJ mol⁻¹ (corresponding to 150 g (kWh)⁻¹) is typical [211].

Applying a nonequilibrium plasma allows the reaction to proceed at ambient temperature and pressure, although higher temperatures have proved advantageous. Most experiments have used packed-bed DBDs; MW and rf discharges have also been tested. Figure 18 summarizes the energy yields and NH₃ concentrations that have been achieved and shows a suggested target range of 100–200 g (kWh)⁻¹ energy yield and 1% conversion yield [8]. Energy costs of 1.8 MJ mol⁻¹ (corresponding to 30 g (kWh)⁻¹) have been achieved, but only at yields below 1%. Yields up to 9% have been demonstrated, but the best energy costs for yields above 1% are about 4 MJ mol⁻¹ (corresponding to 15 g (kWh)⁻¹) [8, 211, 220].

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While it is possible to produce NH₃ in a plasma through gas-phase reactions alone (see figure 1(a)), the presence of surfaces, particularly catalysts, significantly increases the conversion yield. Two main mechanisms have been proposed [8].

The first is by providing vibrational energy to N₂ molecules to promote their dissociative adsorption. This is an example of the vibrational and electronic excitation for thermodynamically downhill reactions mentioned at the start of section 5.2, which may lead to a change in the optimum catalyst. The dominant reaction mechanism, illustrated in figure 1(d), is essentially the same as that shown in table 1, with the addition of vibrational excitation of N₂ and H₂. Mehta et al [11, 221] predicted using microkinetic modelling that metals that bind N₂ weakly will be favoured since N₂ activation is the rate-limiting step. This corresponds to a shift in the peak of the volcano curve away from the iron-based catalysts used in the Haber–Bosch process toward cobalt- and nickel-based catalysts, which bind N₂ less tightly, as shown in figure 19.

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The second proposed mechanism is the dissociation of N₂ in the plasma, which has been called surface-enhanced plasma-driven NH₃ synthesis [8]. Here, dissociation of N₂ occurs predominantly in the gas phase. The reaction mechanism becomes more complex. Important reactions include adsorption of N on the catalyst, after which L–H reactions with surface-adsorbed H occur (this has also been called plasma-enhanced semi-catalytic NH₃ synthesis [12], as discussed in section 2.1) and E–R reactions of N with surface-adsorbed H. The reaction mechanisms are illustrated in figures 1(b) and (c), respectively.

Detailed kinetic modelling of the reactions occurring in packed-bed DBDs has been performed [64, 80, 222], as discussed in some detail in section 3.2.3. Together with experimental studies, the models indicate the importance of temperature in determining the dominant mechanisms. Kinetic modelling predicts that at low temperatures, surfaces become saturated with adsorbed N and NH₃, leaving limited sites available for dissociative adsorption of N₂ or adsorption of N. Increasing the temperature, particularly above about 500 K, is predicted to free surface sites for N adsorption [221]. Measurements, such as those shown in figure 20, demonstrate that an enhancement of NH₃ production occurs in the presence of a catalyst at higher temperatures, which is attributed to the dissociative adsorption of vibrationally excited N₂ and adsorption of N. The presence of the plasma significantly increases the NH₃ production, indicating the ability of plasma catalysis to exceed thermal equilibrium limits [13, 223].

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The energy requirements of different gas-phase reactions, shown in table 2, provide insights into the energy efficiency of NH₃ production using a plasma. It is clear that ionization of N₂ or H₂, and dissociation of H₂, in the plasma are ixncompatible with a target energy yield of 100 g-NH₃ (kWh)⁻¹. Vibrational and electronic activation, and possibly dissociation, of N₂ are likely to be compatible, depending on the energy requirements of the many other reactions that will occur.

The reduced electric field (E/N) in MW and GA reactors is typically around 50 Td (1 Td = 10⁻²¹ V m²). In contrast, DBD reactors have reduced electric fields over 200 Td, which is appropriate for direct electron impact dissociation and ionization.

An examination of the energy transferred to different electron-impact processes, shown in figure 21, indicates that vibrational excitation of N₂ and dissociation of H₂ are dominant below 20 Td, electronic excitation of N₂ and dissociation of H₂ between 20 and 200 Td, and ionization of N₂ and H₂ and dissociation of N₂ above 200 Td. Hence, DBD reactors tend to couple energy to ionization reactions and N₂ dissociation.

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The data indicate that, for plasma-only processes, GAs and MW discharges should have higher energy yields. However, as shown in figure 18, only low energy yields have been obtained. Moreover, such discharges are only compatible with post-plasma catalysis because of their high gas temperatures. The lifetime of vibrationally excited N₂ molecules is only about 40 ns [224], so post-plasma catalysis will not be able to make use of such molecules.

DBD reactors are unlikely to provide the required energy efficiency, even in the presence of a catalyst, since ionization and dissociation reactions will dominate over vibrational and electronic excitation processes. This indicates the need for new strategies. One possibility is to use H₂O as the precursor molecule rather than H₂ [225]. This saves the large amount of energy (237 kJ mol⁻¹) required to produce the H₂ from water. For a typical water electrolyzer energy requirement of 0.35 MJ mol⁻¹, the target energy cost to produce NH₃ from N₂ and H₂O is around 1.2 MJ mol⁻¹, approximately twice that for production from N₂ and H₂. The approach is complicated by the competing reactions to form NO_x , however. Innovative approaches, such as using an electrochemical reactor to produce H₂ from H₂O and coupling this to a N₂ plasma through a proton-conducting membrane, are being developed [226].

Transforming CO₂ into valuable products using renewable energy is an attractive element of a sustainable low-carbon economy. Potential products include CO, CH₄, olefins and liquid fuels. A major challenge is the thermodynamic stability of CO₂; substantial energy is required for its dissociation.

There is an extensive effort to apply plasmas for the conversion of CO₂ to useful products. Many reactions are being investigated. The include CO₂ splitting to form CO and O₂, CO₂ hydrogenation to form CH₄, CO and methanol, CO₂ reforming with CH₄ to form syngas (CO and H₂), higher hydrocarbons and oxygenates, and CO₂ reduction with water to form syngas. The reader is referred to reviews of CO₂ conversion [6, 227] for more detailed discussions of mechanisms and progress.

CO₂ reforming with CH₄, known as dry reforming, will be discussed in section 5.2.3. Here we consider CO₂ splitting and CO₂ hydrogenation. A comparison of the two processes provides insights into the applicability of plasma catalysis to different chemical reactions.

CO₂ splitting proceeds via the reaction

$$\begin{equation}\mathrm{C}{\mathrm{O}}_{2}\to \mathrm{C}\mathrm{O}+1/2{\mathrm{O}}_{2}\quad {\Delta}{H}^{0}=283\enspace \mathrm{k}\mathrm{J}\;\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}=2.93\enspace \mathrm{e}\mathrm{V}.\end{equation} \tag{ 11 }$$

While the reaction is endothermic at room temperature, the equilibrium conversion increases at temperatures above about 1500 K because of the entropy contribution to the Gibbs free energy. It is instructive to consider the different excitation mechanisms and their energy requirements compared to the enthalpy of formation of CO. Direct electron-impact dissociative excitation, $\mathrm{e}+\mathrm{C}{\mathrm{O}}_{2}\to \mathrm{C}\mathrm{O}+\mathrm{O}\left({}^{1}\mathrm{S}\right)+\mathrm{e}$, requires an electron energy of around 11.5 eV. A single vibrational excitation allows the bound CO + O(³P) state to be accessed: $\mathrm{e}+\mathrm{C}{\mathrm{O}}_{2}\left(\nu > 1\right)\to \mathrm{C}\mathrm{O}+\mathrm{O}\left({}^{3}\mathrm{P}\right)+\mathrm{e}$. This reduces the energy barrier to 5.5 eV. The stepwise vibrational excitation mechanism, in which overpopulation associated with the initial vibrational excitation is transferred up the vibrational ladder by excitation exchange in collisions between CO₂ molecules, has a threshold electron energy of only 0.3 eV.

As noted for the case of NH₃ production, MW and GA reactors have electron energies suited to transferring energy to vibrational excitation, as shown in figure 22 for the case of CO₂. In contrast, DBD reactors have reduced electric fields above 200 Td, which is appropriate for direct electron-impact dissociation.

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DBDs have only reached about 20% energy efficiency for CO₂ splitting, with typical values below 10% [227]. This is a consequence of the high reduced electric field, typically above 200 Td, which yields average electron energies of 2 to 3 eV [228], too high for the efficient population of CO₂ vibrational levels, as shown in figure 22. The addition of a packed bed to the DBD generally increases the conversion, with a strong dependence on the packing material and its size [117], without changing the energy efficiency greatly. The increased conversion is generally attributed to affecting the physical parameters of the discharge, with no strong evidence of a contribution due to catalysis. A useful catalyst would need to assist the dissociation of vibrationally excited CO₂ molecules on the surface.

MW and GA plasmas have been found to give far higher energy efficiencies than DBDs for CO₂ conversion [6, 227]. This is partly a consequence of the more favourable E/N and partly because of the higher gas temperatures, which give a higher equilibrium yield and efficiency. However, MW and GA plasmas are generally incompatible with in situ plasma catalysis because of the high temperatures. Post-plasma catalysis has not been tested extensively. A problem is the lifetime of the vibrationally excited CO₂ molecules, which is limited by collisions with ground-state molecules (VT relaxation); the relaxation rate increases with translational temperature, with the lifetime falling below 1 μs for temperatures above 1000 K [229]. The development of lower temperature sources would allow the catalyst to be placed closer to the reaction zone and also increase the lifetime of vibrationally excited molecules.

While the energy efficiency obtainable using a DBDs is unavoidably limited by their high E/N, their suitability for in situ catalysis makes possible direct production of value-added chemicals when a hydrogen-containing precursor is added to CO₂. This contrasts with the need for an additional synthesis step (e.g. a Fischer–Tropsch process) to convert the CO and H₂ to useful compounds.

CO₂ hydrogenation is an exothermic process; for example, the reaction to produce CH₄ (known as CO₂ methanation or the Sabatier reaction) is

$$\begin{equation}\mathrm{C}{\mathrm{O}}_{2}\!+\!4{\mathrm{H}}_{2}\to \mathrm{C}{\mathrm{H}}_{4}\!+\!2{\mathrm{H}}_{2}\mathrm{O}\quad \!\!{\Delta}{H}^{0}\!=\!-165.3\enspace \mathrm{k}\mathrm{J}\;\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}=-1.71\enspace \mathrm{e}\mathrm{V}.\end{equation} \tag{ 12 }$$

A wide range of products can be obtained in addition to CH₄. These include methanol, other alcohols, aldehydes and acids.

The simplest example is methanation (reaction (12)). If the H₂ is obtained by electrolyzing water, the process is a method of converting CO₂ to CH₄ using renewable energy [230, 231]. Nickel-based catalysts are typically used for thermal catalysis, with a temperature of 300 to 400 °C required. The equilibrium CO₂ conversion is around 90% at 350 °C and 1 bar. As for NH₃ production, Le Chatelier's Principle indicates that this can be improved by increasing the pressure or reducing the temperature [231]. A plasma process offers the possibility of operation at a reduced temperature, allowing, in principle, higher CO₂ conversion.

CO₂ conversion and CH₄ yield of up to 80% have been obtained using plasma catalysis in DBD reactors, as shown in figure 23. Note that the CH₄ yield is the product of the CO₂ conversion and the CH₄ selectivity, so the best selectivity approaches 100%. The presence of a catalyst greatly improves the performance compared to the use of a plasma alone. For example, Ahmad et al [232] obtained CO₂ conversion of 60% and CH₄ selectivity above 97% at 150 °C using an Ni/Al₂O₃ catalyst in a DBD plasma. The synergy between the plasma and the Ni catalyst was demonstrated by the greatly reduced (<10%) CO₂ conversion obtained both when Al₂O₃ alone was used and when the Ni/Al₂O₃ catalyst was placed downstream of the plasma (post-plasma catalysis). OES measurements showed the presence of vibrationally excited CO₂, CO and other species, indicating the occurrence of excitation and dissociation of CO₂ in the plasma. This is in accordance with the results of Parastaev et al [174], who used isotope-labelled CO₂ and temperature-programmed plasma–surface reaction techniques to provide evidence that dissociation of CO₂ occurred mainly in the gas phase, with CO dissociatively adsorbed on the catalyst and hydrogenated to form CH₄.

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The energy efficiency of the plasma processes is shown in figure 23. It is clear that the use of a catalyst improves the energy efficiency and the conversion and yield in DBD reactors. However, the energy cost remains too high, despite the inherent advantages of plasma reactors, such as lower-temperature operation and suitability for coupling to renewable electricity sources. As shown in figure 22, the electron energy in DBDs is preferentially coupled to electronic excitation and dissociation of CO₂. The lowest-energy mechanism (vibrational excitation of CO₂ to promote dissociative adsorption on the catalyst) is therefore not favoured. It is important to note that the catalysts that are optimal for thermal catalysis are unlikely to be so for plasma catalysis. As noted for NH₃ synthesis in section 5.2.1, vibrational excitation of the precursor will shift the volcano curve to weaker binding of the reactants and products. Dissociation of CO₂ in the gas phase will favour catalysts suitable for reacting CO with H, rather than CO₂.

A possibly more attractive case is the synthesis of methanol

$$\begin{equation}\mathrm{C}{\mathrm{O}}_{2}+3{\mathrm{H}}_{2}\to \mathrm{C}{\mathrm{H}}_{3}\mathrm{O}\mathrm{H}+{\mathrm{H}}_{2}\mathrm{O}\quad {\Delta}{H}^{0}=-49.5\enspace \mathrm{k}\mathrm{J}\;\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}\!=\!-0.513\enspace \mathrm{e}\mathrm{V}.\end{equation} \tag{ 13 }$$

The reaction mechanism for thermal catalysis proceeds via the adsorption of CO₂ to produce adsorbed formate (HCOO) or CO intermediates, followed by stepwise hydrogenation reactions. As for NH₃ production and CO₂ methanation, the reaction is favoured by low temperatures and high pressures because it is exothermic and reduces the number of molecules. However, low temperatures limit the activation of the catalyst, so typically temperatures of 200 to 350 °C and pressures of 17 to 100 bar are used.

Plasma catalysis again offers the possibility of low temperature and atmospheric pressure reactions. Wang et al [233] demonstrated CO₂ conversion of 21% in a DBD packed with Cu/Al₂O₃ catalyst at 30 °C and 1 bar, which is comparable to that reported for thermal catalysis. A feature of the reactor was the use of a water ground electrode to maintain a low temperature in the reactor. The selectivity for methanol (54%) was lower than in thermal catalysis, and the energy cost was around 11.5 MJ mol⁻¹ of methanol (119 eV molecule⁻¹). This is about nine times higher than that for industrial-scale thermal catalysis.

Hydrocarbon conversion includes a wide range of reactions. The most extensively examined is the dry reforming of CH₄, the reaction of CH₄ and CO₂ to produce syngas (a mixture of CO and H₂)

$$\begin{equation}\mathrm{C}{\mathrm{O}}_{2}\!+\!\mathrm{C}{\mathrm{H}}_{4}\to 2\mathrm{C}\mathrm{O}+2{\mathrm{H}}_{2}\quad {\Delta}{H}^{0}=247\enspace \mathrm{k}\mathrm{J}\;\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}=2.56\enspace \mathrm{e}\mathrm{V}.\end{equation} \tag{ 14 }$$

The thermal catalytic process has to be carried out at high temperatures, i.e., 900 to 1200 K, to ensure the entropy increase outweighs the enthalpy decrease, giving a negative Gibbs free energy. Unlike CO₂ methanation, lower pressures are favoured because the number of product molecules exceeds the number of reactant molecules.

Dry reforming by thermal catalysis has been studied for close to a century, without wide industrial implementation. A particular problem is soot deposition and the resulting catalyst deactivation [6]. A target energy cost for commercial plasma dry reforming to produce syngas of 4.27 eV per molecule of CH₄ and CO₂ converted, corresponding to an energy efficiency of 60% [6]. The theoretical conversion and energy efficiency, assuming chemical equilibrium, are shown in figure 24. An energy efficiency of 60% is possible at 1500 K, the lowest temperature for which complete conversion can occur.

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The non-equilibrium nature of non-thermal plasmas allows reactions to occur under conditions that are not thermodynamically accessible. A collection of results for different discharge types is shown in figure 25. DBD reactors without packing have achieved conversions of up to 60%, but at an energy cost of over 20 eV per molecule. GAs have achieved energy costs as low as 0.75 to 2.6 eV per molecule with a conversion of 40 to 80%. Promising results have also been obtained for nanosecond-pulsed discharges, spark discharges and atmospheric-pressure glow discharges.

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Most experiments relevant to plasma catalysis have used packed-bed DBD reactors. The review by Mehta et al [221] noted the critical role of the reactor temperature. The results of Kim et al [26], shown in figure 26, demonstrate the point. At low temperatures, for which ΔG > 0, the presence of a plasma, irrespective of the presence of packing or a catalyst, leads to CH₄ conversion. In contrast, at high temperatures, for which ΔG < 0, a plasma alone or a plasma with non-catalytic packing is inactive. However, the combination of a plasma and catalyst leads to improved conversion compared to thermal catalysis.

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The results illustrate several of the points elucidated in section 5.2. The first is that bond breaking in the plasma is required for thermodynamically uphill reactions to proceed. In this case, the plasma-driven conversion is predicted to be initiated by electron-impact dissociation of CO₂ and CH₄. The second is that standard catalysts will not be effective for thermodynamically uphill reactions since they will be active for both forward and backward reactions. While different authors have reported an increase or decrease in CO₂ and CH₄ conversion upon packing the reactor with a catalyst or support, this is usually attributed to the effects of the packing on the discharge characteristics [221].

The final point illustrated is that, for thermodynamically downhill reactions, the vibrational excitation of molecules can increase reaction rates in the presence of an appropriate catalyst. The significant enhancement of CH₄ conversion at higher temperatures in the presence of a plasma and Ni catalyst was attributed to the reduction of the energy barrier due to the interaction of vibrationally excited CH₄ with Ni sites, based on the dependence of the reaction rate on CH₄ partial pressure [235]. Sheng et al [236] reached similar conclusions from a study of a DBD reactor packed with lanthanum-modified Ni/Al₂O₃ catalyst at 400 to 700 °C. They observed a strong influence of plasma catalysis for 100 kHz excitation and a weak influence for 12 kHz excitation. Noting that the lifetime of bending-mode vibrational excitation of CH₄ is 31 μs, they attributed the difference to the influence of vibrationally excited CH₄, whose interaction with the catalyst would be much more significant for the 100 kHz excitation, with half-cycle period of 5 μs, compared to 12 kHz with half-cycle period of 42 μs.

For the low-temperature regime, a wide range of products is obtained, including CO, H₂, C₂–C₄ hydrocarbons and oxygenates (methanol, ethanol, formic acid, acetic acid, etc). Plasmas on their own are not selective, although the input ratio of CO₂ to CH₄ has an influence on the products. However, the combination of a plasma and catalyst does allow the product selectivity to be manipulated. For example, Wang et al [237] were able to alter the selectivity to gaseous and liquid products using Cu/Al₂O₃, Au/Al₂O₃ and Pt/Al₂O₃ catalysts. In particular, Cu/Al₂O₃ was selective towards acetic acid, and Au/Al₂O₃ and Pt/Al₂O₃ allowed the production of formic acid, which was not accessible without a catalyst. This result illustrates the potential of plasma catalysis to directly produce valuable chemicals and fuels, for which the required energy efficiency would be significantly lower (perhaps a factor of 2 to 3) than for syngas production because of the avoidance of an additional step for beneficiation of the syngas [6].

Post-plasma catalysis has been found to be effective for both gliding-arc discharges and atmospheric-pressure glow discharge plasma jet [6]. For example, Allah and Whitehead [238] found an increase in CH₄ and CO₂ conversion of 20% and 16%, respectively, and a 22% increase in energy efficiency when an NiO/Al₂O₃ catalyst bed was placed in contact with the afterglow of a GA discharge. It seems likely that the location of catalyst in the afterglow is critical given the short lifetimes of the species produced in the plasma.