**3. Electron paramagnetic resonance**

cation oxygen cation

The magnetic interactions in spinel ferrites can be easily understood by considering two B sites and one A site about an oxygen, see Figure 3. The center and right side of this figure, where the large circle represents the oxygen ion, the small circle above it stands for the cation on the A site, and the two small circles below represent B sites. Note that this arrangement is 3D, but for this schematic illustration, it has been simplified on a plane. Nickel ferrite is an inverse spinel, Ni2+ goes to B sites, one ferric ion occupies the other B site, and the other Fe3+ is located on the A site. All magnetic interactions between cations are antiparallel (superexchange).

A

A

B B

B B

**Figure 3.** Schematic spin arrangements in spinel ferrites. Left: a section of the crystal structure showing the cation occu‐ pancy about an oxygen. Center: the ferrimagnetic spin orientation of the crystal sites for nickel ferrite. Right: the anti‐

There are A–O–B interactions between the cation on A site and the cations on B sites, and an B–O–B interaction between the cations on the two B sites. However, due to the axial symmetry of oxygen *p*-orbitals, superexchange interaction becomes more efficient when cations and oxygen are in an axial arrangement. This makes a strong difference between interactions; A– O–B interaction is far more efficient than B–O–B interactions since the latter has a 90° angle, while the former is closer to 180°. As a result, both spins on B sites are antiparallel to the A spin. The magnetic moment of Fe3+ on A site cancels with the magnetic moment of Fe3+ on B site, and the resulting magnetic moment is the spin value for nickel Ni2+ (2.3 Bohr magnetons), as shown in Figure 3 center. This is a strong interaction; the Curie transition is about 858 K.

**Figure 2.** Superexchange interactions in ferrites.

214 Advanced Electromagnetic Waves

ferromagnetic structure for the zinc ferrite.

Electron paramagnetic resonance (EPR) or electron spin resonance (ESR) is a technique of observing resonance absorption of microwave power by unpaired electron spins aligned with a magnetic field [4]. The electron paramagnetic resonance (EPR) spectroscopy is similar to the nuclear magnetic resonance (NMR) except for the fact that EPR arises from the interaction between unpaired electrons and electromagnetic radiation.

The history of EPR can be told beginning with the Stern–Gerlach experiment in 1921. They observed that a beam of silver atoms split into two lines when it was subjected to a magnetic field. In contrast with the line splitting in optics found by Zeeman in 1896, these phenomena could not be explained by the angular momentum of the electrons.  Three more years passed before Uhlenbeck and Goudsmit found an explanation for these anomalous Zeeman effect when they postulated the spin [5,6].

The development of the EPR was furthered by the World War II since after the war was over, there was available a great amount of microwave instruments from the radar equipment used in the war. It was in 1945 when a Russian physicist, Zavoisky, observed the first EPR spectrum. He observed a radiofrequency absorption line from a CuCl2⋅2H2O sample. One year later, the first NMR spectrum was observed and through the first decade both techniques developed simultaneously. Nevertheless, EPR spectroscopy had a few challenges from lack of microwave components and limited microwave power to expensive instrumentation and consequently was left behind by NMR for a couple of decades [4–6].

It was until the 1980s that the instrumentation became cheaper and more manageable and the first pulse EPR was released to the market. A decade later the high field spectrometer was released and since then the interest in EPR as a characterization technique has considerably increased.

The spin angular momentum *S* gives rise to a magnetic moment *μ* =– g*μ*B*S*, where *g* is the g factor; its value for free electrons is *g* = 2.0023193043617 and *μ*B is the Bohr magneton. When the electrons are subjected to an external field *H* (it is customary to place the field along the *z* axis), the energy levels of the degenerate spin states split depending on their quantum magnetic moment *m*s = ± 1/2 and the strength of the magnetic field as shown in Figure 4 [4–6].

**Figure 4.** Splitting of the energy levels of an electron spin in a magnetic field at the resonance frequencies.

When the irradiation at a given frequency *ω*0 is the same as the energy difference ∆*E* between both states, a resonant absorption takes place. This frequency is named the Larmor frequency *ω*0 = –γ *H*0 after J. Larmor [6]:

$$
\Delta W = \hbar \alpha\_0 = \text{g}\,\mu\_\text{g}H \tag{1}
$$

The detection of that absorption is the most important principle of this spectroscopy.

For temperatures above the Curie temperature, the magnetic moments in an external field obey the Bloch equations. These equations follow the Larmor theorem where the motion of the magnetic moments in a magnetic field originates a torque [6–9]:

$$
\hbar \frac{d\mathbf{M}}{dt} = \mathbf{M} \times \boldsymbol{\gamma} \mathbf{H} \tag{2}
$$

To detect the absorption, there is an oscillating microwave field **H**1 = (*Hx*,*Hy*,0) = (*H*1cos(*ω*mw*t*), *H*1sin(*ω*mw*t*),0) aside from the external magnetic field along the *z* axis. This magnetic field deviates the magnetization away from its equilibrium position. To describe accurately the motion of the magnetization vector, it is important to take into account the relaxation effects. The relaxation time has two components, the longitudinal relaxation time, which is the average time in which the magnetization vector returns to its thermal equilibrium state, and the transverse relaxation time, which characterizes the loss of coherence in the transverse plane due to spin interactions [5–8].

The evolution of the magnetization as a function of time and its dependence of the magnetic field is given by the equation motion derived by F. Bloch [5–6]:

Characterization of Magnetic Phases in Nanostructured Ferrites by Electron Spin Resonance http://dx.doi.org/10.5772/61508 217

$$i\hbar \frac{d\mathbf{M}}{dt} = \mathbf{M}(t) \times \gamma \mathbf{H}(t) - \mathbf{R}(\mathbf{M}(t) - \mathbf{M}\_0) \tag{3}$$

whereγ is the gyromagnetic ratio, **H** = (*H*1cos(*ω*mw*t*), *H*1sin(*ω*mw*t*),*Hz*), and **R** is the relaxation tensor given by [6]:

$$\mathbf{R} = \begin{pmatrix} 1/T\_2 & 0 & 0 \\ 0 & 1/T\_2 & 0 \\ 0 & 0 & 1/T\_1 \end{pmatrix} \tag{4}$$

Relaxation phenomena need to be taken into account to describe the motion of the magneti‐ zation vector. *T*1 is the longitudinal relaxation time; this parameter characterizes the process that makes the magnetization vector return to its thermal equilibrium. *T*2 is the transverse relaxation time which describes the loss of coherence in the transverse plane due to spin-spin interactions.

**Figure 4.** Splitting of the energy levels of an electron spin in a magnetic field at the resonance frequencies.

*ω*0 = –γ *H*0 after J. Larmor [6]:

216 Advanced Electromagnetic Waves

due to spin interactions [5–8].

When the irradiation at a given frequency *ω*0 is the same as the energy difference ∆*E* between both states, a resonant absorption takes place. This frequency is named the Larmor frequency

> m

For temperatures above the Curie temperature, the magnetic moments in an external field obey the Bloch equations. These equations follow the Larmor theorem where the motion of the

g

To detect the absorption, there is an oscillating microwave field **H**1 = (*Hx*,*Hy*,0) = (*H*1cos(*ω*mw*t*), *H*1sin(*ω*mw*t*),0) aside from the external magnetic field along the *z* axis. This magnetic field deviates the magnetization away from its equilibrium position. To describe accurately the motion of the magnetization vector, it is important to take into account the relaxation effects. The relaxation time has two components, the longitudinal relaxation time, which is the average time in which the magnetization vector returns to its thermal equilibrium state, and the transverse relaxation time, which characterizes the loss of coherence in the transverse plane

The evolution of the magnetization as a function of time and its dependence of the magnetic

0 *B* D= = h (1)

**M** h **M H** (2)

*W gH* w

The detection of that absorption is the most important principle of this spectroscopy.

*dt* = ´

magnetic moments in a magnetic field originates a torque [6–9]:

field is given by the equation motion derived by F. Bloch [5–6]:

*d*

Electron paramagnetic resonance is a very useful technique to study the properties of bulk paramagnetic compounds including their transitions to the magnetic ordered state. Below this temperature, ferromagnetic resonance (FMR) or antiferromagnetic resonance (AFMR) are detected. EPR in paramagnetic samples give information such as the resonance active ion valence and the symmetry of the ligand environment. In the case of nanoparticles, the theory of EPR is not quite the same as in bulk; however, a study of the thermal variations of EPR spectra can be very informative because of the high sensibility of the EPR technique [10].

Let's recall that magnetic resonance is observable only in materials that contain a sufficient number of permanent magnetic dipoles; if the origin of these dipoles is electronic, then the resonance is detectable with a population even fewer than 1011 dipoles [8].

The first paramagnetic resonance absorption in metals due to the conduction electrons was observed by Feher and Kip [8]. The conduction electrons have an effect on the shape and intensity of the resonance lines. However, until the theoretical study of Dyson, there were not many studies in conduction electron paramagnetic resonance in metals [11].

In a metal, the electrons are assumed to diffuse as free particles and the magnetic moments of each of them can be seen as free-particle moments. When the metal is placed in a radiofre‐ quency electromagnetic field and at the same time in a perpendicular uniform magnetic field, a certain macroscopic magnetization is created as a result of the magnetic moments of the conduction electrons. The penetration of the radio frequency field into the metal is modified by the magnetization. Actually, only the layers near the surface contribute, since the excitation field *H*1 penetrates only a small depth into the metal. This is called the skin effect [11]. The magnetization *M* shows a resonant behavior and becomes large when the frequency of the field is nearly equal to the resonant frequency. The absorption field observed is a measure of the total energy absorbed in the metal both by eddy currents and by the resistive out of phase component of the magnetization.

There are four assumptions which need to be taken into account to study the dependence of the line width [8,11]:

These assumptions give as a result a finite line width proportional to 1/*U* in the resonance signal from nondiffusing electrons. The penetration of the radio frequency field into the metal will be limited by the skin depth, which is given by [11] In a metal, the electrons are assumed to diffuse as free particles and the magnetic moments of each of them can be seen as free-particle moments. When the metal is placed in a radiofrequency electromagnetic field and at the same time in a perpendicular uniform magnetic field, a certain macroscopic magnetization is created as a result of the magnetic moments of the conduction electrons. The penetration of the radio frequency field into the metal is modified by the magnetization. Actually, only the layers near the surface contribute, since the excitation field *H*1 penetrates only a small depth into the metal. This is called the skin effect [11]. The magnetization *M* shows a resonant behavior and becomes large when the frequency of the field is nearly equal to the resonant frequency. The absorption field observed is a measure of the total energy absorbed in

the metal both by eddy currents and by the resistive out of phase component of the magnetization.

2. Each electron moves as an independent classical particle with random changes in their direction.

conduction electrons and to move with constant velocity.

$$\mathcal{S} = \left(\mathbf{c}^2 \mid 2\pi\sigma\alpha\phi\right)^{1/2} \tag{5}$$

where *c* is the speed of light, *σ* is the conductivity of the metal, and *ω* is the radio frequency. If the skin depth is larger than the main free path, we are in the domain of the classical skin effects; if it is equal to the main free path, then we are in the anomalous case. In fact, unlike paramagnetic insulators, in which the varying part of the magnetization depends on the magnitude of the applied oscillating field, in metals, there is also a dependence of the local values of the oscillating field on the magnetization because of the skin depth. A typical spectrum (metallic Na) is shown in Figure 5. 3. The spin of each particle is a quantum independent variable. It is unaffected by collisions and only the local magnetic field has an effect on them. 4. Given any time interval *t* and *U,* a volume relaxation time there is a probability ~exp(-*t*/*U*) that the spin state of an electron will not be randomly distributed by collisions during this interval. These assumptions give as a result a finite line width proportional to 1/*U* in the resonance signal from nondiffusing electrons. The penetration of the radio frequency field into the metal will be limited by the skin depth, which is given by [11] 2 1/ 2 (*c* / 2) (5) where *c* is the speed of light, is the conductivity of the metal, and is the radio frequency. If the skin depth is larger than the main free path, we are in the domain of the classical skin effects; if it is equal to the main free path, then we are in the anomalous case. In fact, unlike paramagnetic insulators, in which the varying part of the magnetization depends on the magnitude of the applied oscillating field, in metals, there is also a dependence of the local values of the oscillating field on the magnetization because of the skin depth. A typical spectrum (metallic Na) is shown in Figure 5.

Figure 5. Typical first derivative EPR spectrum observed in colloidal samples of Na, with mean diameter particle small compared to the skin depth. The basic parameters and the definition of *R* are indicated. Adapted from Feher and Kip [8]. **Figure 5.** Typical first derivative EPR spectrum observed in colloidal samples of Na, with mean diameter particle small compared to the skin depth. The basic parameters and the definition of *R* are indicated. Adapted from Feh‐ er and Kip [8].

7

The magnetic susceptibility in metals has a diamagnetic component due to the circulation of electrons in the field *H*. This is opposed by the normal paramagnetic component due to unpaired electrons. This is related with another EPR parameter that has been studied in metals: the *g* factor [8,12]. The relation between the resonance values of the constant magnetic field *H*0 and the frequency is determined by the magnitude of the *g* factor of the conduction electrons. The existence of internal interactions in a metal leads to a shift in the value of the *g* factor.

Experimentally, the *g* factor has been measured in different paramagnetic metals giving rise to values very close to the *g* free electron value *g* = 2.0023 as shown in Table 3. This is a measure of the spin-orbit coupling. It has been possible to study *S*-state ions in metals in order to understand the interaction between the conduction electrons and the inserted ions.

**Table 3.** Experimental values for the *g* shift. Adapted from Feher and Kip [8].

EPR spectroscopy has made contributions in understanding the bonding and the electronic structure of molecular species with metal–metal bonds. Some of the information obtained through this technique includes determining whether unpaired electrons reside in metal-based or ligand-based molecular orbitals, giving information of the metal center's total electronic spin, which also provides information of its oxidation state, broadly have information of the distribution of the unpaired electrons between metals and organic ligands [13].


*2.11. Flow Cytometry*

SCs were seeded at a density of 5 × 105 cells/well in 6-well culture plates (Corning, Corning, NY, USA) to detect the cell cycle distribution. The cultivation process was carried out as described above and according to a method described previously [25]. After harvesting at 24, 48 and 72 h, the cells were fixed in 70% ice-cold ethanol at −20 ◦C for cell cycle analysis. Before the samples were analyzed by flow cytometry using a Becton Dickinson Fluorescence Activating Cell Sorter Aria (BD Biosciences, San Diego, CA, USA), the cells were centrifuged at 200× *g* and 4 ◦C for 5 min, re-suspended in 1 mL PBS, treated with 100 μL 200 mg/mL DNase-free RNase, incubated at 37 ◦C for 30 min, and treated with 100 μL 1 mg/mL propidium iodide (PI, Sigma-Aldrich, St. Louis, MO, USA) at room temperature (25 ◦C) for 10 min (n = 6).

#### *2.12. Protein Synthesis*

To measure protein synthesis, a nonradioactive technique called surface sensing of translation (SUnSET) was used [26,27]. In this study, 1 μg/mL puromycin (Millipore, Waltham, MA, USA) was added to all wells for an additional 30 min of culture, and puromycin was detected by western blotting with an anti-puromycin antibody (Millipore, Waltham, MA, USA, Table S2). The total protein concentration was determined by BCA (Thermo-fisher, Waltham, MA, USA).

#### *2.13. Immunofluorescence Staining*

SCs were cultured for 96 h for the proliferation rescue assay and differentiation rescue assay. First, SCs were fixed in 4% paraformaldehyde for 30 min and then permeabilized with 0.1% Triton-X-100 for 10 min. After blocking with 1% bull serum albumin (BSA) and 10% goat serum for 30 min, the SCs were stained with primary antibodies for 90 min and then probed with goat anti-rabbit IgG (Table S2). In addition, the nuclei were labeled with 4 ,6-diamidino-2-phenylindole (DAPI, Sigma-Aldrich, St. Louis, MO, USA) for 5 min at room temperature. Images were obtained using immunofluorescence microscopy.

#### *2.14. Rapamycin Inhibition*

After Lys deficiency for 48 h, Lys rescue medium was added alone or combined with 20 or 50 nmol/L (nM) rapamycin for another 48 h. After a total of 96 h, cell viability was measured by MTT assay, and cell proliferation was measured by cell count assay. In addition, cell samples were collected to detect protein synthesis and the mTORC1 pathway by western blotting.

#### *2.15. Statistical Analysis*

The data were analyzed using Statistical Analysis System software (SAS, Version 9.2; SAS Institute, Cary, NC, USA). For control group and Lys deficiency group comparisons, the results were analyzed by t-test. For control group, Lys deficiency group and Lys rescue group comparisons, the mean data were assessed for significance using Tukey's test. The data are expressed as the mean ± S.E.M. Differences between treatments were considered statistically significant when *p* < 0.05 and extremely significant when *p* < 0.01.

#### **3. Results**

#### *3.1. Skeletal Muscle Growth in Piglets Relies on Dietary Lys Supplementation*

To determine the effects of dietary Lys supplementation on the skeletal muscle growth of weaned piglets, we developed the experimental design shown in Supplemental Table 1. After the piglets (initial body weight: control = 8.42 ± 0.11 kg versus Lys deficiency = 8.42 ± 0.08 kg) were fed the Lys-restricted diet for 14 d, we found that the growth of the piglets (final body weight: control = 11.91 ± 0.18 kg versus Lys deficiency = 11.33 ± 0.18 kg) was significantly suppressed (Table S4). In detail, compared with those of the control group, the relative weights of the longissimus dorsi muscle, extensor carpi radialis muscle, semimembranosus muscle, total forequarters muscle and total hindquarters muscle were significantly decreased by dietary Lys deficiency for 14 d (Table S4).

After dietary Lys deficiency for 14 d, the piglets received a diet we supplemented to match the level in the control diet for another 14 d. Obviously, the final weight of the piglets in the Lys rescue group was significantly increased compared with that of the piglets in the Lys deficiency group (Table 1). Moreover, compared with those after Lys deficiency for 28 d, the relative weights of the longissimus

dorsi muscle, lateral head of triceps of brachii muscle, extensor carpi radialis muscle, biceps femoris muscle, semimembranosus muscle, semitendinosus muscle, cranial tibial muscle, soleus muscle, lateral head of gastrocnemius muscle and total hindquarters muscle were all increased in the Lys rescue group, which was subjected to dietary Lys deficiency for 14 d and re-supplemented for another 14 d (Table 1). Collectively, these findings suggest that skeletal muscle growth in piglets relies on dietary Lys supplementation.

**Table 1.** Effect of dietary Lys re-supplementation on the skeletal muscle growth of weaned piglets on 28 d (n = 5, %) 1.

1 Values without the same small letters within the same line indicate a significant difference (*p* < 0.05).


2. Literature overview on modeling for plasma-based CO2 conversion

Describing a detailed plasma chemistry in 2D or 3D models, with 100s of species and chemical reactions, is not yet feasible, due to excessive calculation times. Therefore, a detailed plasma chemistry is typically described by 0D chemical kinetic models or sometimes by 1D fluid models. The first papers on CO2 plasma chemistry modeling were published back in 1987–1995 but were applied to CO2 lasers [22–24]. Some papers also studied the vibrational kinetics of CO2 for gas flow applications [25, 26]. Rusanov et al. [27] were the first to develop a model for CO2 conversion in a MW plasma, based on particle and energy conservation equations for the neutral species, and an analytical description of the vibrational distribution function.

In the last decade, the research on plasma-based CO2 conversion experienced a clear revival, and quite some plasma chemistry models have been developed in literature, for either pure CO2 splitting [7, 28–48] or CH4 (of interest for hydrocarbon reforming) [49–52], as well as in various mixtures, that is, CO2/CH4 [53–66], CH4/O2 [66–72], CO2/H2O [73], and CO2/H2 [74, 75], of interest for producing value-added chemicals, or in mixtures of CO2/N2 [76, 77] or CH4/N2 [78–83], more closely mimicking reality, as N2 is a major component in effluent gases. Recently, we gave an overview of such 0D models for plasma-based CO2 and CH4 conversion [84], and we also presented a very comprehensive plasma chemistry model for CO2 and CH4 conversion in mixtures with N2, O2, and H2O [85]. These plasma chemistry models can provide detailed information on the underlying chemical reaction pathways for the conversion or product formation.

Furthermore, to investigate which reactor designs can lead to improved CO2 conversion, 2D or even 3D fluid models can be used; they offer a good compromise between level of detail and calculation time. To our knowledge, the number of 2D models for describing CO2 conversion is very limited [86, 87], and there exist no 3D models yet for this purpose. Most of the 2D/3D fluid models developed up to now in the literature for the typical plasma reactors used for CO2 conversion are developed in argon or helium, or sometimes air, with limited chemistry, to reduce the calculation time.

For packed bed DBD reactors, different types of modeling approaches have been developed. Chang [88] presented a 0D plasma chemistry model, simply predicting the enhancement factor of the electric field in the voids between the packing pellets from the ratio of the dielectric constant of the pellets and the gas phase. Takaki et al. [89] applied a simplified time-averaged 1D model in N2, based on solving the transport equations and Poisson's equation. Zhang et al. [90] performed 2D particlein-cell/Monte Carlo collision (PIC/MCC) simulations for the filamentary discharge behavior in a parallel-plate packed bed DBD reactor in air. Kang et al. [91] developed a 2D fluid model for a DBD with two stacked ferroelectric beads and studied the propagation of the microdischarges, but no plasma species were explicitly considered. Russ et al. [92] applied a 2D fluid model for studying transient microdischarges in a packed bed DBD operating in dry exhaust gas. Based on a 2D fluid model for a packed bed reactor with dielectric rods, Kruszelnicki et al. [93] presented a very interesting and detailed study on the mechanism of discharge

### Modeling for a Better Understanding of Plasma-Based CO2 Conversion DOI: http://dx.doi.org/10.5772/intechopen.80436

propagation in humid air, reporting that the discharges can generally be classified in three modalities: positive restrikes, filamentary microdischarges, and surface ionization waves. They observed that the type of discharge dominating the production of reactive species depends on the dielectric facilitated electric field enhancement, which is determined by the topography and orientation of the dielectric lattice. Finally, they demonstrated that photoionization plays an important role in discharge propagation through the dielectric lattice, because it seeds initial charge in regions of high electric field, which are difficult to access for electrons from the main streamer [93]. Van Laer et al. [94–96] developed two complementary 2D fluid models to describe a packed bed DBD in helium, to elucidate the electric field enhancement between the packing beads, and the effect of the dielectric constant of the packing beads, as well as the gap size and bead size. Wang et al. [97] applied a 2D fluid model to a packed bed DBD in air, studying the behavior of positive restrikes, filamentary microdischarges, and surface discharges, as well as the transition in discharge modes upon changing the dielectric constant of the packing beads. Finally, Kang et al. [98] also presented a 2D fluid model to study surface streamer propagation in a simplified packed bed reactor, in comparison with experimental data, obtained from time-resolved ICCD imaging.

For MW plasmas, a large number of models were presented in the literature, and we refer to [99] for a recent overview. Van der Mullen et al. [100–102] as well as Graves et al. [103] developed self-consistent 2D fluid models, based on Maxwell's equations for the electromagnetic field and plasma fluid equations, assuming ambipolar diffusion. Some of these models were applied to intermediate pressure coaxial microwave discharges [102], while others describe atmospheric pressure cylindrical (surfaguide or surfatron) MW plasmas [101, 103]. Although being very valuable, these models did not apply to the application of CO2 conversion. Recently, Georgieva et al. [99] performed a comparison between two fluid models, based on the coupled solution of the species conservation equations and Poisson's equation (i.e., so-called non-quasi-neutral approach) on the one hand and on a quasi-neutral approach on the other hand, but again these models were developed for argon.

For low-current nonthermal GA discharges (typically near 1 A or below), some simple 1D analytical or semi-analytical models have been developed [104–109], including the plasma string model [104] and the Elenbaas-Heller model, assuming an equilibrium plasma, with the radius of the plasma channel being constant [105– 107] or with a correction based on an analytical relation between the electric field and the electron and gas temperatures for non-equilibrium plasma [108] or focusing on the discharge electrical parameters [109]. These simple models cannot describe the complex behavior of the GA, such as the unsteady behavior in time and space, arc restrike, non-equilibrium effects, effects of flow patterns, etc., and they did not include a detailed chemistry. Gutsol and Gangoli [110] presented a simple 2D model of a GA, in a plane parallel to the gas flow and perpendicular to the discharge current, which provided very useful information about the gas-discharge interaction. Within our group, we developed a 2D non-quasi-neutral fluid model for the arc gliding process in an argon GA [111], and we compared the glow and arc mode in this setup [112]. We also presented a 2D quasi-neutral model [113], which was also applied in 3D modeling for a classical (diverging electrode) GA [114] and a reverse vortex flow (RVF) GA (also called GA plasmatron; GAP) [115]. These models were developed for argon, but we also developed a 1D fluid model [44] and two different 2D models [86, 87] for a (classical or RVF) GA in CO2, considering the detailed plasma chemistry of CO2 conversion. An overview of both 0D chemical kinetic models and 2D/3D fluid models for plasma reactors of interest for CO2 conversion was presented in [116].

(typically based on 2D, or even 3D, fluid models), and we will show some characteristic examples from our own research, to illustrate how such models can give more insight in the underlying mechanisms. First, however, we will present a brief overview of the different models relevant to CO2 conversion that have been

2. Literature overview on modeling for plasma-based CO2 conversion

and chemical reactions, is not yet feasible, due to excessive calculation times. Therefore, a detailed plasma chemistry is typically described by 0D chemical kinetic models or sometimes by 1D fluid models. The first papers on CO2 plasma chemistry modeling were published back in 1987–1995 but were applied to CO2 lasers [22–24]. Some papers also studied the vibrational kinetics of CO2 for gas flow applications [25, 26]. Rusanov et al. [27] were the first to develop a model for CO2 conversion in a MW plasma, based on particle and energy conservation equations for the neutral species, and an analytical description of the vibrational distribution function.

Describing a detailed plasma chemistry in 2D or 3D models, with 100s of species

In the last decade, the research on plasma-based CO2 conversion experienced a clear revival, and quite some plasma chemistry models have been developed in literature, for either pure CO2 splitting [7, 28–48] or CH4 (of interest for hydrocarbon reforming) [49–52], as well as in various mixtures, that is, CO2/CH4 [53–66], CH4/O2 [66–72], CO2/H2O [73], and CO2/H2 [74, 75], of interest for producing value-added chemicals, or in mixtures of CO2/N2 [76, 77] or CH4/N2 [78–83], more closely mimicking reality, as N2 is a major component in effluent gases. Recently, we gave an overview of such 0D models for plasma-based CO2 and CH4 conversion [84], and we also presented a very comprehensive plasma chemistry model for CO2 and CH4 conversion in mixtures with N2, O2, and H2O [85]. These plasma chemistry models can provide detailed information on the underlying chemical reaction path-

Furthermore, to investigate which reactor designs can lead to improved CO2 conversion, 2D or even 3D fluid models can be used; they offer a good compromise between level of detail and calculation time. To our knowledge, the number of 2D models for describing CO2 conversion is very limited [86, 87], and there exist no 3D models yet for this purpose. Most of the 2D/3D fluid models developed up to now in the literature for the typical plasma reactors used for CO2 conversion are developed in argon or helium, or sometimes air, with limited chemistry, to reduce the calcula-

For packed bed DBD reactors, different types of modeling approaches have been developed. Chang [88] presented a 0D plasma chemistry model, simply predicting the enhancement factor of the electric field in the voids between the packing pellets from the ratio of the dielectric constant of the pellets and the gas phase. Takaki et al. [89] applied a simplified time-averaged 1D model in N2, based on solving the transport equations and Poisson's equation. Zhang et al. [90] performed 2D particlein-cell/Monte Carlo collision (PIC/MCC) simulations for the filamentary discharge behavior in a parallel-plate packed bed DBD reactor in air. Kang et al. [91] developed a 2D fluid model for a DBD with two stacked ferroelectric beads and studied the propagation of the microdischarges, but no plasma species were explicitly con-

sidered. Russ et al. [92] applied a 2D fluid model for studying transient

microdischarges in a packed bed DBD operating in dry exhaust gas. Based on a 2D fluid model for a packed bed reactor with dielectric rods, Kruszelnicki et al. [93] presented a very interesting and detailed study on the mechanism of discharge

ways for the conversion or product formation.

tion time.

8

reported in literature.

Plasma Chemistry and Gas Conversion