Energy storage and transfer in non-equilibrium CO2 plasmas

Citation for published version (APA):Grofulovic, M. (2019). Energy storage and transfer in non-equilibrium CO2 plasmas. Technische UniversiteitEindhoven.

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Energy storage and transfer in

non-equilibrium CO2 plasmas

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische UniversiteitEindhoven, op gezag van de rector magnificus prof.dr.ir. F. P. T. Baaijens,voor een commissie aangewezen door het College voor Promoties, in het

openbaar te verdedigen op woensdag 2 oktober 2019 om 13:30 uur

door

Marija Grofulovic

geboren te Bor, Servie

Dit proefschrift is goedgekeurd door de promotoren en de samenstelling van depromotiecommissie is als volgt:

voorzitter: prof.dr.ir. G. M. W. Kroesen1e promotor: dr. R. A. H. Engeln2e promotor: prof. dr. V. L. Guerra (Universidade de Lisboa)copromotor: prof.dr.ir. M. C. M. van de Sandenleden: Prof.Dr.rer.nat. T. Gans (University of York)

dr. H. Fernandes (Universidade de Lisboa)prof.dr.ing. A. J. M. Pemenprof.dr. L. L. Alves (Universidade de Lisboa)

Het onderzoek dat in dit proefschrift wordt beschreven is uitgevoerd in overeen-stemming met de TU/e Gedragscode Wetenschapsbeoefening.

UNIVERSIDADE DE LISBOA

INSTITUTO SUPERIOR TECNICO

EINDHOVEN UNIVERSITY OF TECHNOLOGY

Energy storage and transfer in non-equilibriumCO2 plasmas

Marija Grofulovic

Supervisors: Doctor Vasco GuerraDoctor Richard Engeln

Co-supervisor: Professor Doctor ir. M.C.M. van de Sanden

Thesis specifically prepared to obtain the PhD Degree in

Technological Physics Engineering

2019

This thesis was performed in the framework of a joint protocol between InstitutoSuperior Tecnico, University of Lisbon, and Eindhoven University of Technology.

The research received funding from the Portuguese FCT - Fundacao para aCiencia e a Tecnologia, under grant PD/BD/ 105884/ 2014 (PD-F APPLAuSE).

Energy storage and transfer in non-equilibrium CO2 plasmas / by Marija Gro-fulovicEindhoven: Technische Universiteit Eindhoven, 2019 - Proefschrift.

A catalogue record is available from the Eindhoven University of TechnologyLibraryISBN: 978-90-386-4849-1

Printed by proefschriftenprinten.nlCover by Igor Dordevic

Copyright c© 2019 Marija Grofulovic

Summary

Energy storage and transfer in non-equilibrium CO2 plasmas

The steady growth of greenhouse gases in the atmosphere is undoubtedly oneof the major concerns for the 21st century, making their conversion one of themajor scientific and technological challenges nowadays. An efficient storageof energy in chemical compounds produced from CO2 emissions, in particularin hydrocarbon-based fuels, which could be straightforwardly integrated intothe existing transport infrastructure, would be extremely interesting fromenvironmental, economical and societal points of view. In order to do so, CO2

must be captured and recycled and the energy stored as a fuel, using greenelectricity all along the transformation process. The combustion of this so-called solar fuel releases the initial CO2 and the stored energy, completing theCO2 neutral energy loop. Hydrocarbon based fuels of this type would be analternative to the conventional fossil fuels, providing the same energy density,without further increasing the emission of CO2.

The main task within this strategy is to maximize the energy efficiencyof the CO2 dissociation. This is a strongly endothermic process where non-equilibrium plasma may be useful, providing the possibility to enhance specificreaction channels and suppress others by controlling the electron density, electrontemperature and gas temperature. The important advantages of non-thermalplasmas for dissociating CO2 are the high energy efficiency and instantaneousstart and stop of operation, which is relevant considering the intermittency ofrenewable sources. By tailoring the electron energy distribution function, theenergy input into the relevant vibrational levels can be maximized while keepinga relatively low gas temperature. These conditions may favour the up-pumpingof vibrational quanta and enhance dissociation.

This thesis consists on a modeling and experimental investigation of the mainsteps involved in plasma decomposition of CO2, including electron kinetics,input of energy in the low v-levels by low-energy electrons, up-pumping ofvibrational quanta and coupled kinetics of the discharge under study. Theplasma of our choice is a CO2 glow discharge, operated in a low-pressure regime(mbar range). Glow discharges are suitable for gaining fundamental knowledgeon plasma kinetics, which is a starting point for further investigation of CO2

activation. The advantage of a glow discharge is the homogeneity of the positivecolumn, which, together with the ability of using many diagnostics to do time-resolved measurement, allows the investigation of the time evolution of thevibrational temperatures (and the densities of vibrationally excited states) andvalidation of the respective rate coefficients.

The first step of this study is the investigation of the electron kinetics, inorder to understand in detail how the electrons gain energy from the electricfield and how this energy is transferred, through collisions, into CO2 vibrational

i

ii

excitation and dissociation. As a result, an electron-impact cross section setfor CO2 was proposed. The set is validated from the comparison betweenthe calculated swarm parameters and the available experimental data. Theimportance of superelastic collisions with CO2(010) molecules at low valuesof the reduced electric field is pointed out. These cross sections, compiled forkinetic energies up to 1 keV, are part of the IST-LISBON database with LXCat.Furthermore, the electron impact dissociation cross section was studied, byevaluating the available cross sections and proposing a strategy for obtainingthe dissociation rate coefficients.

A vital aspect in the investigation is to understand the role of vibrationallyexcited states, which can store energy for long times. They can then bedirectly involved in dissociation and other chemical reactions or can be theirprecursors. The energy input into low vibrational levels and its redistributionby V-V and V-T processes is addressed by coupling the rate balance equationsfor ≈ 70 CO2 vibrational levels with the electron kinetics. The model islimited to a low excitation regime, which is sufficient to describe very wellthe vibrational temperature dynamics, experimentally obtained in millisecondpulsed DC glow discharges. The so called ‘single pulse’ experiment is performedin such conditions that ensure a negligible influence of the dissociation products.The residence time of the plasma and the off time are chosen in such a way asto allow the gas to fully renew, leaving the reactor with most of CO and O2

removed. This is suitable for the validation of a model that does not includespecies other than CO2(ν). The results confirm the non-equilibrium nature of alow-pressure CO2 plasma, with the characteristic temperature of the asymmetricmode, T3, well above the vibrational temperature corresponding to the othertwo modes and of the gas temperature. The elevation of T3 above the gastemperature reaches around 500 K in the first millisecond of the discharge, atthe studied conditions (p = 5 Torr, I = 50 mA, ∆t = 5 ms), while the relaxationof all three vibrational temperatures shows a similar behaviour.

Many processes in plasmas are governed by the gas temperature. The ratecoefficients, as well as the diffusion coefficients and the surface kinetics aredependent on the temperature value. For this reason, a precise description ofthis parameter is pertinent for plasma modeling and plasma characterization. Inthis thesis, the calculation of the temporal evolution of the gas temperature innon-equilibrium CO2 plasmas is performed. The model is based on the solutionsto the time-dependent gas thermal balance equation, coupled to the electron andvibrational kinetics. The simulation results are compared with experimentaldata, obtained in a ms pulsed glow discharge. Very good agreement withthe experimental data confirms the validity of the model and the collisionaldata used. The results show that the dominant heating mechanisms are thevibrational energy exchanges.

The vibrational energy transfer from vibrationally excited N2 to the asym-metric mode of CO2 is well-known from the studies of CO2-N2 lasing systems.

iii

N2 vibrations can serve as an energy reservoir that can efficiently populateCO2 vibrational levels. Besides, N2 is an important impurity in most industrialgasflows, so it can impact the kinetics of CO2 conversion. The influence of N2

admixtures to a CO2 plasma is investigated experimentally by employing in siturotational Raman spectroscopy in a ms pulsed glow discharge. The advantage ofthe rotational Raman spectroscopy is the ability of detecting numerous Ramanactive molecules in the spectral range of a single measurement, which makes thistechnique beneficial for investigating gas mixtures. Spatiotemporally resolvedgas temperature and molecular densities are examined, in pure CO2 and indifferent compositions of CO2-N2. Additionally, the impact of O2 addition isexamined, as O2 is a product of CO2 conversion. It is observed that relativecompositions are nearly constant during the pulse and along the axis of thereactor. The rotational temperature is shown to be independent on the amountof N2 present, exhibiting nearly the same temperature profile in all the studiedmixtures. The amount of O2, however, leads to lower temperature values atcorresponding times. Furthermore, the effect that N2 has on CO2 vibrationsis inspected by examining the ratio between the intensity of even and oddnumbered CO2 peaks in Raman spectrum. It is demonstrated that addition ofN2 has a beneficial effect on CO2 decomposition, which might be interpretedas an evidence of the vibrational transfer between the excited N2 and CO2

molecules. On the other hand, the addition of O2 had a negative effect on CO2

conversion, which might be attributed to the vibrational quenching of CO2 byO2, and/or to the enhancement of recombination with CO producing CO2.

Contents

Summary i

1 General introduction 1

1.1 CO2 and climate change . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Plasma-based conversion of CO2 . . . . . . . . . . . . . . . . . 5

1.3 Dissociation of CO2 . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4 Different configurations of gas discharges for CO2 plasma study 12

1.5 Literature overview on modeling of non–equilibrium CO2 plasmas 15

1.6 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2 Electron-neutral scattering cross sections for CO2 29

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.2 The cross section set . . . . . . . . . . . . . . . . . . . . . . . . 32

2.3 Swarm calculations . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.4 Dissociation of CO2 . . . . . . . . . . . . . . . . . . . . . . . . 43

2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3 Relaxation of vibrational energy in CO2 discharges 59

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.2 Description of the model . . . . . . . . . . . . . . . . . . . . . 62

3.3 Estimation of vibrational rates: general overview . . . . . . . . 62

3.4 Vibration-vibration and vibration-translation energy exchanges 64

3.5 Spontaneous emission . . . . . . . . . . . . . . . . . . . . . . . 67

3.6 Rate balance equations for CO2 vibrational levels . . . . . . . . 67

3.7 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.8 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

iv

Contents

4 Input of vibrational energy in CO2 discharges 834.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854.2 Description of the model . . . . . . . . . . . . . . . . . . . . . 874.3 Vibrational kinetics . . . . . . . . . . . . . . . . . . . . . . . . . 884.4 Electron kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . 904.5 Maintenance electric field . . . . . . . . . . . . . . . . . . . . . 954.6 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . 964.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

5 Modelling of the time-dependent gas temperature in CO2 1115.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1135.2 Heat transfer equation . . . . . . . . . . . . . . . . . . . . . . . 1145.3 Model details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . 1195.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1275.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6 A rotational Raman study in CO2-N2 and CO2-O2 1336.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1356.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1376.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1406.4 CO2 conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . 1456.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1476.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

7 Conclusions 155

v

Chapter 1

General introduction

1

1.1. CO2 and climate change

1.1 CO2 and climate change

Carbon dioxide (CO2) is known, along with other greenhouse gases, for beingimportant in sustaining a habitable temperature for the planet. Due to the rapidgrowth in fossil fuel consumption, the emission of anthropogenic greenhousegases has been increasing steadily since the industrial revolution in the early20th century. This resulted in a planetary warming impact. The heat-trappingnature of CO2, along with its increased amount in the atmosphere, is widelyrecognized as the reason for many of the observed changes in the climate system.The atmosphere and ocean have warmed (see figure 1.1), the Greenland andAntarctic ice sheets have decreased, the global sea level is rising, the acidity ofsurface ocean waters has increased, and glaciers are retreating almost everywherearound the world [1, 2].

1 9 6 0 1 9 7 0 1 9 8 0 1 9 9 0 2 0 0 0 2 0 1 0 2 0 2 0

0 . 0

0 . 5

1 . 0

Y e a r

3 2 03 4 03 6 03 8 04 0 04 2 04 4 0

Figure 1.1: The change in global temperature relative to the 20th century average(blue curve), and the atmospheric concentrations of the carbon dioxide (orange curve).The temperature data are retrieved from [3], and the CO2 concentrations data aretaken from [4].

As a response to the ongoing concerns for climate changes, the renewableenergy production has increased drastically in the past decade [5]. Figure1.2 depicts the change in electricity production by different sources in 2017compared with the previous year, and the share in global generation. It iseasily seen that renewables accounted for ∼ 50% of the global increase ofelectricity generation, whilst their share of total energy generation was 25%,which is second only to coal in that year. The major contribution comes fromhydropower which, in spite of strong increases in wind and solar PV generation,is the dominant source of renewable electricity generation, with a share of65% in overall renewables output [6]. The fraction of energy produced from

3

Chapter 1. General introduction

renewables increased by 1.3% from the end of 2017 to the same time in 2018,while compared to the total net production, they accounted for 26.4%. Thehighest growth is accomplished in solar energy, 18.2% compared to the sameperiod of the previous year [7].

R e n e w a b l e s C o a l G a s O i l N u c l e a r0

1 0 0

2 0 0

3 0 0

4 0 0E l e c t r i c i t y g e n e r a t i o n i n 2 0 1 6 - 2 0 1 7C h a n g e i n e l e c t r i c i t y g e n e r a t i o n i n 2 0 1 6 - 2 0 1 7

Electr

icity g

enera

tion (

TWh)

1 0 . 3 1 %3 . 9 %

2 3 . 2 5 %

3 7 . 4 1 %

2 5 . 1 3 %

Figure 1.2: Electricity production change (left) and electricity production in 2017(right) by different sources. Data retrieved from [6].

Despite the satisfactory trend, some challenges intrinsic to renewable energyhave to be addressed. Firstly, it is important to stress that the majorityof renewable sources provide electrical energy, whilst most of the industrialchemical processes use heat as the source of energy. Therefore, one of theimportant steps, that is already being considered worldwide is replacement ofthe fossil fuel based equipment [8]. Another drawback of the renewable energy isits local and intermittent nature. Many of these resources are highly dependenton weather conditions. The inconsistency of the energy production from solarenergy systems or wind turbines is impractical and does not match the demandfor electrical energy. For this reason, the technology of energy storage is beingreinforced, leading to numerous solutions and to a steady growth in the storagecapacity as the technology progresses [9, 10].

The energy storage technologies can be classified as mechanical, electrical,thermal and chemical, depending on the type of energy being stored. Theyall have different characteristic and their own disadvantages, which makesit difficult to select a single technology for all applications. However, theuniversal challenge is to meet the energy density, storage efficiency, and goodtranspontability of hydrocarbon fuels. Among all the approaches, the ones thatstand out are based on conversion of electricity into fuel, which is favorable forsectors that do not rely on electrical energy directly [11, 12]. For instance, thescheme in which excess electricity generated by wind or solar power is convertedand stored into non-fossil hydro carbon based fuels would benefit from theexisting infrastructure. The carbon input needed for the fuel synthesis can beobtained from CO2 captured directly from air and from large-scale sources,

4

1.2. Plasma-based conversion of CO2

eg. fossil-burning powerplants [13, 14]. Therefore, this “carbon capture andutilisation (CCU)” scheme considers CO2 as a viable resource rather than awaste [15–18]. The electrical energy surpluses from renewable resources arethen used to reduce the captured CO2 to CO. This step, the CO2 dissociation,is the key process of this strategy and there are numerous approaches suggestedin order to find the most efficient way. The next step incorporates the well-established Fischer-Tropsch process that creates hydrocarbons from syngas (COand H2 mixture) [8]. The combustion of solar fuels releases CO2 and the energyused to create them, which closes the CO2-neutral energy cycle [17, 19].

1.2 Plasma-based conversion of CO2

An alternative way to start the Fischer–Tropsch process is to produce syngasfrom water and CO2. In this case, dissociation of CO2 into CO and O2 wouldenable synthetic fuel production using water, CO2 and electricity. Due to thelimitations of conventional thermal approaches, new technologies are beinginvestigated in order to achieve efficient CO2 dissociation. One of them isthe utilization of non-thermal plasma technologies. The main advantage islinked with its non-equilibrium nature, allowing selective excitation of certainprocesses.

The main idea behind plasma assisted dissociation of CO2 is to use low-energy electrons to introduce energy into the vibrational degrees of freedom,subsequently pumped up to the dissociation limit [20]. In order to maximize thestorage of energy in CO2 vibrations, a thorough investigation of the complexinterplay between electron and vibrational kinetics must be conducted. Thissection gives a brief introduction to non–equilibrium plasma, CO2 vibrationsand main mechanisms of CO2 dissociation in non-equilibrium plasma, whichwill be important throughout this thesis.

CO2 vibrations

CO2 is a triatomic molecule with a carbon atom in its center, covalentlydouble bonded to two oxygen atoms. It has three normal vibrational modes:the symmetric stretching, the double degenerate bending vibration and theasymmetric stretching mode, characterized by quantum numbers ν1, ν2 and ν3respectively (see figure 1.3). The symmetric mode of vibration corresponds tomotions in which the oxygen atoms oscillate symmetrically with respect to thecarbon, as shown in figure 1.3 a). In this motion the electric dipole moment doesnot change, therefore the symmetric mode is inactive in the infra-red (which isnot the case for the bending and the asymmetric mode) but appears stronglyin the Raman spectrum. In vibrations associated to the asymmetric mode, thecarbon atom oscillates along the intermolecular axis with respect to the oxygen

5

Chapter 1. General introduction

atoms (see figure 1.3 b). The bending mode of vibrations corresponds to thevibrations in which the carbon atom oscillates along the axis perpendicular tothe intermolecular axis (figure 1.3 c)). Due to the degeneracy of the bendingvibration mode, an additional quantum number l2, associated with an angularmomentum, is needed to fully describe a CO2 vibrational state. l2 can takethe values l2 = ν2, ν2 − 2, ν2 − 4, ...1 or 0, depending on the parity of ν2. TheCO2 vibrational state can then be specified in the form CO2(ν1ν

l22 ν3), known

as Herzberg’s notation [21].

a) b)

c)

Figure 1.3: Normal vibrational modes of a CO2 molecule. a) Symmetric stretchingmode, characterized by quantum number ν1. b) Asymmetric stretching mode of vibra-tion, with quantum number ν3. c) Bending mode with vibrations in two orthogonalplanes.

To calculate the energy of any CO2 vibrational level, one can simply employthe formula for the energy of vibrational levels of a molecule with doubly

6

1.2. Plasma-based conversion of CO2

Table 1.1: Spectroscopic constants used for the calculation of CO2 vibrational energy,taken from [22].

Constant Value (cm−1)

ω1 1354.31ω2 672.85ω3 2396.32χ11 -2.93χ12 -4.61χ13 -19.82χ22 1.35χ23 -12.31χ33 -12.47g22 -0.97

degenerate vibrations:

E

hc(ν1, ν2, ...) =

∑k

ωk

(νk +

dk2

)+

∑k≥j

χkj

(νk +

dk2

)(νj +

dj2

)+

∑k≥j

gkj lklj , (1.1)

where c is the speed of light and h is Planck constant. The quantities χk,j = χj,kare anharmonicity coefficients, whilst ωk are normal frequencies. In this equationdk = 1 if k refers to a non-degenerate level and 2 in case of a double-degeneratevibration. For non-degenerate vibrations, the energy coefficients gkj are equalto zero, as well as lk. As CO2 has three normal modes of vibration, one of whichis double-degenerate, the previous expression can be written in the followingform:

E

hc(ν1, ν2, l2, ν3) =

3∑k=1

ωk

(νk +

dk2

)

+

3∑k=1

3∑j≤k

χkj

(νk +

dk2

)(νj +

dj2

)+ g22l

22. (1.2)

7

Chapter 1. General introduction

The experimentally obtained values of χ11, χ12, χ13, χ22, χ23, χ33; the frequenciesω1, ω2 and ω3; and g22 for CO2 are given by Suzuki [22] and presented in table1.1.

In some diatomic molecules, such as CO2, it may occur that the energies ofdifferent vibrational levels are nearly equal, which is in literature referred toas accidental degeneracy. Fermi has noticed that the interaction between somevibrations of CO2 with similar energies, more specifically the interaction between(ν1, ν

l22 , ν3) and ((ν1 − 1), (ν2 + 2)l2 , ν3) leads to a perturbation, called Fermi

resonance [23]. These levels, in fact, “repel” each other, meaning that one ofthem is shifted up and the other down, thus the actual levels are not accuratelydescribed by the expression (1.2). It is important to note that in a symmetricmolecule, such as CO2, the Fermi resonance can happen only between levelswith the same quantum number l2, which arises from the symmetry type of theeigenfunctions describing these vibrational levels [21, 22, 24]. As a consequenceof a strong perturbation, eigenfunctions corresponding to the perturbing levelsare strongly mixed so that the two observed levels cannot be unambiguouslyallocated to each level separately. Therefore, the resulting wave functions are alinear combination of the original wave functions. More on the calculation ofthe energy correction of perturbed levels can be found in the study of Ambertand Pembert [25] and also in [21, 22].

For this reason, in the following chapters we will treat the groups of Fermiresonant levels as one single effective level. The vibrational energy of thiseffective level is determined through the average of the vibrational energies ofall the individual levels. We introduce the index f that specifies the number ofindividual levels within an effective level CO2(ν1ν

l22 ν3f). This notation is used

in chapters 3 and 4.

Non-equilibrium plasma

Plasma is often referred to as the fourth state of matter. It is a quasi-neutralionized gas, meaning that concentrations of negatively charged particles (elec-trons and negative ions) and positively charged particles are well balanced. Byapplying heat or more commonly a strong electric field, a neutral gas is turnedinto a highly reactive environment. Plasmas usually constitute of free electrons,positive and negative ions, atoms, and molecules that can be rotationally, vibra-tionally or electronically excited. In plasmas, as in neutral gases, temperatureis determined by the average energies of plasma species and their degrees offreedom. Therefore, as a multi-component system, a plasma can have multiplecharacteristic temperatures, e.g. rotational (Trot), vibrational (Tν), electrontemperature (Te), ion (Ti) and neutral gas “temperature” (T0) [20, 26, 27].

Based on the relative temperature related to different species, plasmas canbe classified as thermal and non-thermal (cold). The work presented is thisthesis is concerned with cold plasmas, more specifically with weakly ionized,

8

1.3. Dissociation of CO2

low pressure gas discharges In gas discharge plasmas, the chain of variousprocesses is initialized by the activity of electrons. After being accelerated bythe electric field, electrons transfer their energy in collisions with heavy-particles.Various processes may occur as a consequence of the inelastic collisions, suchas excitations of the internal degrees of freedom, dissociation and ionization.Elastic and inelastic collisions between electrons typically and heavy particlesare characterized by the corresponding cross sections [28, 29]. Since their massis much smaller, electrons lose only a small fraction of their energy. For thisreason, the electron temperature surpasses the temperatures related to heavyparticles. Non-thermal plasmas do not fulfil the requirements for thermodynamicequilibrium, so they are also called non-equilibrium plasmas. In gas discharges,the vibrational temperature can be much higher than the temperature describingheavy neutrals (usually referred to as translational or gas temperature). Theusual relationship between the temperatures in a non-equilibrium plasma is asfollows [20, 27]:

Te > Tν > Trot ≈ Ti ≈ T0.

On the other hand, the temperatures in thermal plasmas equilibrate quicklyafter the ignition via collisions of different particles. Since in this case localthermodynamic equilibrium (LTE) is established, thermal plasmas are charac-terized by a single temperature at each point of space. An example of thermalplasmas in nature is the solar plasma.

1.3 Dissociation of CO2

Decomposition of CO2 is a strongly endothermic process where a non-equilibriumplasma can prove advantageous in comparison with other thermal techniques.The decomposition starts by dissociation of CO2:

CO2 → CO + O, ∆H = 5.5 eV/mol, (1.3)

and it is followed by O conversion into O2 either by recombination or by areaction with vibrationally excited CO2*:

O + CO∗2 → CO + O2, ∆H = 0.3 eV/mol. (1.4)

By combining the reactions above, the process of CO2 decomposition and itsenthalpy can be represented as

CO2 → CO +1

2O2, ∆H = 2.9 eV/mol. (1.5)

The limiting step of CO2 decomposition is dissociation (reaction (1.3)) whichcan occur in different reaction pathways in non-equilibrium plasma conditions.

9

Chapter 1. General introduction

0 . 1 0 . 2

0

1

2

3

4

5

6

7

8

9

1 0

1 1

C O ( 1Σ+ ) + O ( 3 P )

C O ( 1Σ+ ) + O ( 1 D )

3 B 2

Poten

tial e

nergy

(eV)

r O - C O ( n m )

1Σ+1 B 2 C O ( 1Σ+ ) + O ( 1 S )

Figure 1.4: The potential energy diagram of CO2 as a function of the O-CO bondlength. Arrows indicate different dissociation mechanisms: two different channels fordirect electron impact dissociation, represented by blue arrows; the ladder-climbingmechanism is indicated by the orange arrow, together with the vibrational levels ofasymmetric mode; a combination of these two mechanisms is shown by red arrow.

The most effective one incorporates the selective stimulation of vibrationalexcitation, specifically of the asymmetric mode of vibrations. This is supportedby the fact that the major fraction of the discharge energy is transferredto CO2 vibrations by electrons of rather low energy, Te ≈ 1 eV, typical fornon-equilibrium conditions [20, 30, 31].

10

1.3. Dissociation of CO2

Figure 1.4 illustrates the potential energy of a CO2 molecule as a func-tion of the O-CO distance, with mechanisms of CO2 dissociation relevant fornon-equilibrium conditions [20, 32, 33]. As one can see from the figure, thestraightforward dissociation of a vibrationally excited CO2 molecule results ina creation of an O atom in an electronically excited state O(1D):

CO2 → CO + O(1D) (1.6)

The required electron energy is about 7 eV. A higher dissociation effectivenessis achieved when the stepwise vibrational excitation results in the transitionCO2(1Σ+)→CO2(3B2) at the point of intersection of the corresponding poten-tial curves:

CO∗2(1Σ+)→ CO∗2(3B2)→ CO(1Σ+) + O(3P). (1.7)

The activation energy of this process is Ea = 5.5 eV, which is much smallerthan in reaction (1.6). Figure 1.4 shows 21 vibrational levels of the asymmetricmode with energies up to the activation energy of reaction (1.7). Therefore, theefficient CO2 splitting predominantly proceeds by electron impact vibrationalexcitation of the lowest vibrational levels, followed by vibrational–vibrational(VV) collisions, gradually populating the higher vibrational levels, which thenlead to dissociation of the CO2 molecule. Due to this stepwise vibrationalexcitation process, energy efficiency in non-equilibrium conditions can be veryhigh without a significant amount of kinetic energy, which makes this thedesirable channel of CO2 dissociation [20].

CO2 dissociation can occur through direct electron impact excitation ofelectronically excited states CO2(1B2) and CO2(3B2). Direct electron impactprovides the transition from the ground state to CO2(1B2), according to theFrank-Condon principle, requiring electron energis of about 7 eV. Subsequently,the transition to CO2(3B2) leads to dissociation, creating O atom and CO inthe ground states. Electronic excitation dissociation can occur through differentchannels, creating electronically excited O(1S) [34], or CO(a3Π) [28], whichrequires even higher electron energy, around 12 eV. The CO2 decomposition bydirect electron impact can be dominant in plasmas with high reduced electricfield values, where vibrational excitation is suppressed. However, due to otherprocesses being stimulated by energetic electrons, such plasmas do not providean energetically efficient conversion of CO2. The energy threshold of electronicexcitation dissociation can be significantly reduced by the prior vibrationalexcitation, therefore combining the aforementioned processes.

11

Chapter 1. General introduction

1.4 Different configurations of gas discharges for CO2

plasma study.

In recent years, plasma–based methods for reduction of CO2 have been thefocus of many studies. Non-equilibrium plasmas offer an immensely differentenvironment for various processes in comparison with the typical thermalconditions. The key challenge for practical use is to find the proper regimeand optimal plasma parameters. Many different plasma configurations andoperating conditions were investigated and they all complement the overallimage of the processes occurring in CO2 plasma. Additionally, numerical modelsare created to investigate the underlying mechanisms and their dependence onthe discharge parameters.

Dielectric-barrier discharges

Dielectric barrier discharges (DBDs), well-known for its industrial applicationfor ozone production [35], are investigated in many works on CO2 conversion.In general they operate at atmospheric pressure and alternating voltage (1-100 kV) and a frequency of a few Hz to MHz. The majority of the research wasconducted using coaxial reactors [36–40], which sometimes have beads inside inorder to increase the local electric field (packed bed DBD) [41–44]. Parallel platereactors are mostly used in order to be accessible for optical diagnostics [45].CO2 DBD discharges have a filamentary character. Moreover, a modeling studyhas reported that the volume of micro–discharges makes 1-10% of the total gasvolume [46, 47]. For this reason, it is difficult to apply in situ diagnostics, asthe detection volume will most likely not comprise only the ionized gas [48].

Due to the high electric fields, processes in DBD discharges are dominantlydriven by electrons, including dissociation of CO2 [49]. This explains the lowefficiencies that were observed in both experimental and modeling studies [50].

Microwave discharges

Microwave (MW) discharges are very popular plasma sources for the investiga-tion of CO2 conversion, because they can provide a strong non–equilibrium thatstimulates the vibrational ladder climbing mechanism. As the name suggests,MW discharges are operated by applying microwaves with frequency between300 MHz and 10 GHz. They can have different configurations, such as cavityinduced plasmas, electron cyclotron resonance plasmas, free expanding atmo-spheric plasma torches and the ones that are most commonly used for CO2

conversions studies, surface–wave discharges.An important parameter in MW discharges is pressure, as it highly affects

the dominant set of reactions in the plasma. As a matter of fact, at higherpressure three body reactions are present and the three body recombination

12

1.4. Different configurations of gas discharges for CO2 plasma study

CO + O + M → CO2 + M is limiting the effective CO2 conversion [51]. Thisis seen as a disadvantage of MW discharges, as industrial applications favourthe operation at atmospheric pressure. Operation of a MW plasma is alsoaffected by its temperature, which is shown to be a critical parameter. Typicalgas temperature in MW CO2 plasmas in the non–equilibrium regime is ∼1000− 2000 K, while vibrational temperatures range from 3000 K to 8000 K.If pressure increases, a MW plasma can evolve to a thermal regime, whichresults in a temperature growth up to 14000 K [33]. At these conditions, itis more likely that thermal splitting is the dominant mechanism instead ofplasma assisted dissociation of CO2 [52, 53]. Modeling studies have also statedthat the temperature should be kept low to prevent vibrational-translational(VT) energy relaxation, in order to achieve an efficient vibrational-excitationdissociation [50, 54].

An additional advantage of MW discharges is that they can be made acces-sible for in situ diagnostics [48]. Various experimental works have investigatedmolecular compositions, gas and vibrational temperatures in MW plasmas bymeans of FTIR spectroscopy, Rayleigh scattering, or optical emission spec-troscopy [33, 52, 53, 55].

Gliding arc discharges

The gliding arc (GA) discharge is a transient type of plasma that provides somebenefits of both thermal and non–thermal systems. While operating at highcurrents, GA transforms from a quasi–equilibrium arc to a non–equilibriumplasma [56]. The GA operates at atmospheric pressure, which is advantageousfor their utilization on large scale. Another benefit is that the conditions in GAcan stimulate dissociation of CO2 through the vibrational excitation [57, 58].

Two main reactor geometries are used for CO2 conversion. The classicconfiguration with two planar electrodes treats only a small fraction of thegas passing through, therefore limiting the conversion [50, 58, 59]. Reversevortex flow GAs have been developed in recent years to maximize the energyand conversion efficiency by permitting longer residence times in the dischargezone. They are also called ‘gliding arc plasmatron’ (GAP) and are investigatedtheoretically and experimentally by numerous works [57, 60–65].

DC glow discharges

DC glow discharges have a very simple design and are the most well knownsource of non–equilibrium plasmas. The usual configuration consists of a longglass tube with the positive anode at one end and a negative cathode at theother. Although some different reactor designs are more used for processing,the simple arrangement with a glass tube has a huge advantage of symmetryand has been well studied. The emission light pattern in a glow discharge tube

13

Chapter 1. General introduction

- +

Figure 1.5: The cylindrical DC glow discharge reactor.

shows sequences of dark and bright luminous regions. This fact alone showsthat the plasma behaviour is quite complicated. The positive column representsa weakly ionized non-equilibrium low-pressure plasma.

A dark space near the cathode, called Aston dark space, is produced due tothe low electron energy insufficient to excite molecules and to produce radiation.When electron gain enough energy for electronic excitation, the cathode glowis observed. Further acceleration of electrons makes ionization events moreprobable, leading to an increase of electron density and a very weak radiation.The corresponding region is called the cathode dark space or Crookes dark space.The high electron density provided by ionization in the Crookes dark spaceresults in a decrease of the electric field and electron energy. Consequently, abright layer is created whit strong radiation, called negative glow. The adjacentregion is the Faraday dark space where the electrons do not have the energyrequired for radiation, as they are decelerated transiting from the negative glowregion. This is where the cathode layer ends. The length of the cathode layeris inversely proportional to pressure [20, 27, 66].

The next region is the positive column, a well known example of a non-equilibrium low-ionization plasma. Here, the ion concentration is lower and theelectron energy is around 1-2 eV, which is enough to excite atoms and producelight emission. The positive column length can be increased by moving awaythe electrodes from each other, whilst the anode layer thickness stays the same.Therefore, at proper conditions and reactor length, the positive column can beextended so that it almost connects the electrodes. Near the anode, a negativespace charge is created by pulling out the electrons from the positive columnand repelling the positive ions. Sometimes, the anode glow can be observed,being brighter than the positive column [20, 27, 66].

Some of the advantages of a DC glow discharge that we would like to highlighthere iare their simple geometry and homogeneity of the positive column. Thismakes them accessible for many diagnostics, e.g. FTIR, Raman scattering etc[67, 68]. The experimental results are furthermore very convenient for validationof 0D self-consistent kinetic models with a large number of reactions and a

14

1.5. Literature overview on modeling of non–equilibrium CO2 plasmas

complex electron, vibrational and chemistry kinetics. DC glow discharges aretherefore extremelly valuable for fundamental research [69–72].

CO2 glow discharges were studied in the past for the investigation of CO2

lasing systems, exploiting their capability of exciting vibrational levels [73–80].The results of these works are important for the CO2 reduction research, as theyalso benefit from the selective excitation of the asymmetric mode. However,only the excitation of ν3 = 1 is significant for lasing, therefore these works lackin the information on the excitation of higher levels.

Chapters 3 and 4 of this thesis benefit from an experiment conducted in apulsed DC glow discharge [67, 68], allowing the validation of the results of a 0Dkinetic model of CO2 plasma with the experimental results. The schematic ofthe reactor used in the experiment is illustrated in figure 1.5. The cylindricallyshaped reactor is made of pyrex, with a 2 cm inner diameter and a length of23 cm. The electrodes are 17 cm apart, in a short radial extension oppositeto the inlet and outlet of the gas. The conditions under study, along with thereactor’s design, are such that the cylindrical part of the plasma correspondsto the positive column only. The same reactor was used for the experimentalinvestigation employing rotational Raman scattering in pulsed DC dischargesin CO2, CO2/N2 and CO2/O2, shown in chapter 6

1.5 Literature overview on modeling of non–equilibriumCO2 plasmas

Numerical modeling of non–equilibrium plasmas is a powerful tool for un-derstanding the complicated mechanisms and their dependence on dischargeparameters such as reduced electric field, gas temperature, pressure, or elec-tron density. Modeling of CO2 plasmas is nowadays popular in the scientificcommunity due to its importance in the production of CO2-neutral fuels andfor aerospace applications. Numerous papers are published involving pureCO2 [29, 40, 46, 47, 54, 59, 65, 71, 72, 81, 82, 82–91] as well as mixtures withother gases, such as CO2-CH4 [92–95], CO2-N2 [96, 97], CO2-H2 [98, 99] andCO2-H2O [100] in different discharge conditions.

The first works on CO2 plasma chemistry were motivated by CO2 lasers [101–103]. One of the first models of CO2 conversion was presented by Rusanov etal [31]. A 0D kinetic model applied to DBD discharges is presented in [47, 104],including chemical reaction kinetics and some low lying CO2 vibrational levelsand one effective level accounting for some higher levels of symmetric andbending modes. A more extensive model applied to DBD and MW plasmas,that takes into account a few low-lying symmetric stretching and bending modelevels and 21 levels in the asymmetric mode, up to the dissociation energyof 5.5 eV, is presented by Kozak and Bogaerts [54, 81]. A similar strategywas adopted in[49, 84–86], which addresses in detail the dependence of the

15

Chapter 1. General introduction

electron energy distribution function on the concentration of electronically andvibrationally excited states. The detailed and very extensive investigation ofvibrational kinetics, motivated by reentering bodies in the Mars atmosphere ina dissociation-recombination regime by Armenise and Kustova contains severalthousand levels [105–107]. The work by Gordiets et al proposes a divisionof vibrational levels into multiplets with an equilibrium distribution of thelevels within each multiplet [108, 109]. In the study presented in [59, 63], a 0Dmodel was applied to the non–equilibrium region of a GA discharge in specificoperating conditions not accounting for the transport processes explicitly.

1.6 Thesis outline

Numerous works undertaken in the field of CO2 conversion have approachedthe topic in different manners aiming to reveal the influences of gas pressure,flow, temperature, temperature gradients, the ideal reduced electric field fordischarge operation, the precise role of the dynamics of the internal degrees offreedom, or how to control the shape of the non–equilibrium electron energyand vibrational distributions in order to increase the energy and conversionefficiency. The work presented in this thesis presents a fundamental studyproviding a physical insight into different elementary phenomena.

Chapter 2 investigates the electron kinetics in CO2. This is done by solvingthe homogeneous electron Boltzmann equation, in the usual two-term expansionin spherical harmonics, using the numerical code LoKI-B (LisbOn KIneticsBoltzmann solver) [110], already developed by the N-PRiME group of Institutode Plasmas e Fusao Nuclear (IPFN). As a result, an electron-impact crosssection set for CO2 was proposed. The set is validated from the comparisonbetween the calculated swarm parameters and the available experimental data.These cross sections, compiled for kinetic energies up to 1 keV, are a partof the IST-LISBON database with LXCat. Moreover, the electron impactdissociation cross section was studied, by evaluating the available cross sectionsand proposing a strategy for obtaining the dissociation rate coefficients.

The aim of the study presented in chapters 3 and 4 is to understand in detailthe interplay between the electron and vibrational kinetics, i.e. the energytransfers between electrons and the low vibrational levels of the CO2 molecules.The study involves the coupled solution of the homogeneous electron Boltzmannequation and a system of rate balance equations describing the time-evolutionof the CO2 molecules in low v-levels, accounting for inelastic and superelasticelectron-vibrational (e-V) energy exchanges, vibration-vibration (V-V) energyexchanges and vibration-translation (V-T) energy exchanges in CO2 plasmas.Specifically, a detailed model accounting for the vibrational kinetics of the lowerlevels of each vibration mode and of the lower mixed levels has been developed,with the relevant rate coefficients being validated in sequential steps. First, in

16

1.6. Thesis outline

chapter 3, we have analysed the vibrational relaxation in the afterglow of a DCpulsed discharge at p = 5 Torr and I = 50 mA and validated the V-T and V-Vrate coefficients used. Then we extended the model from chapter 3 to the activedischarge, in order to investigate the input of vibrational energy in the plasmaand to validate the electron impact cross sections and rate coefficients for thee-V processes. The model is validated through the comparison of the calculatedtime-dependent concentrations of several individual vibrational levels of CO2

with the experimental results obtained in a ms pulsed glow discharge.Chapter 5 presents the modeling study of the gas temperature evolution

and heat transfer mechanisms in CO2 discharges in non-equilibrium. Gas tem-perature calculations are based on the solutions of the gas thermal balanceequation under time-dependent situations, coupled to the electron and vibra-tional kinetics. The simulation results are compared with the time-resolvedtemperature measurements obtained in a ms pulsed glow discharge, operatingat low pressure.

In chapter 6, the temperature dynamics of CO2 is investigated by in siturotational Raman spectroscopy in the same type of a discharge as in the previouschapters. Spatiotemporally resolved rotational temperatures and molecularcompositions are obtained in pure CO2, and in CO2-N2 and CO2-O2 discharges.It is shown that the whole positive column of the glow discharge under study(figure 1.5) is homogeneous, therefore the time evolution obtained correspondsto the entire plasma volume. The vibrationally averaged nuclear spin degeneracyis examined, which provided an insight into the vibrational kinetics of CO2.

Finally, chapter 7 contains the general conclusions and the main resultsobtained in the thesis.

17

Chapter 1. General introduction

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[70] V. Guerra, P. A. Sa, and J. Loureiro, “Kinetic modeling of low–pressurenitrogen discharges and post–discharges,” Eur. Phys. J. Appl. Phys., 28,125–152, 2004.

[71] M. Grofulovic, T. Silva, B. L. M. Klarenaar, A. S. Morillo-Candas,O. Guaitella, R. Engeln, C. D. Pintassilgo, and V. Guerra, “Kinetic

23

Chapter 1. General introduction

study of CO2 plasmas under non-equilibrium conditions. II. Input ofvibrational energy,” Plasma Sources Sci. Technol., 27, 115009, 2018.

[72] T. Silva, M. Grofulovic, B. L. M. Klarenaar, O. Guaitella, R. Engeln,C. D. Pintassilgo, and V. Guerra, “Kinetic study of CO2 plasmas undernon–equilibrium conditions. I. Relaxation of vibrational energy,” PlasmaSources Sci. Technol., 27, 015019, 2018.

[73] C. Dang, J. Reid, and B. K. Garside, “Detailed vibrational populationdistributions in a CO2 laser discharge as measured with a tunable diodelaser,” Appl. Phys. B, 27, 145–151, 1982.

[74] C. Dang, J. Reld, and B. K. Garside, “Dynamics of the CO2 lower laserlevels as measured with a tunable diode laser,” Appl. Phys. B, 31, 163–172,1983.

[75] I. I. Zasavitskii, R. S. Islamov, M. A. Kerimkulov, Y. B. Konev, V. N.Ochkin, S. Y. Savinov, N. N. Sobolev, M. V. Spiridonov, and A. P.Shotov, “Kinetics of formation of the CO2 molecule distributions over thevibrational-rotational levels in the active medium of a waveguide CO2

laser,” J. Sov. Laser Res., 11, 361–375, 1990.

[76] D. Toebaert, P. Muys, and E. Desoppere, “Spatially resolved measurementof the vibrational temperatures of the plasma in a dc-excited fast-axial-flow CO2 laser,” IEEE Journal of Quantum Electronics, 31, 1774–1778,1995.

[77] M. Spiridonov, C. Leys, D. Toebaert, S. Sazhin, E. Desoppere, P. Wild,and S. M. P. McKenna-Lawlor, “Investigation of the active medium ofa direct-current-excited fast-axial-flow CO2 laser using a tunable diodelaser,” J. Phys. D: Appl. Phys., 27, 962–969, 1994.

[78] K. Siemsen, J. Reid, and C. Dang, “New techniques for determiningvibrational temperatures, dissociation, and gain limitations in CW CO2

lasers,” IEEE J. Quantum Electron., 16, 668–676, 1980.

[79] T. Kishimoto, N. Wenzel, H. Grosse-Wilde, G. Lupke, and G. Marowsky,“Experimental study of a CO2 laser plasma by coherent anti-stokes ramanscattering (cars),” Spectrochim. Acta B, 47, 51 – 60, 1992.

[80] R. K. Brimacombe, J. Reid, and T. A. Znotins, “Gain dynamics of the4.3 µm CO2 laser,” Appl. Phys. B, 36, 115–124, 1985.

[81] T. Kozak and A. Bogaerts, “Splitting of CO2 by vibrational excitation innon-equilibrium plasmas: a reaction kinetics model,” Plasma Sources Sci.Technol., 23, 045004, 2014.

24

1.7. References

[82] S. Ponduri, M. M. Becker, S. Welzel, M. C. M. Van De Sanden, D. Loffha-gen, and R. Engeln, “Fluid modelling of CO2 dissociation in a dielectricbarrier discharge,” J. Appl. Phys., 119, 093301, 2016.

[83] P. Koelman, S. Heijkers, S. Tadayon Mousavi, W. Graef, D. Mihailova,T. Kozak, A. Bogaerts, and J. van Dijk, “A comprehensive chemical modelfor the splitting of CO2 in non-equilibrium plasmas,” Plasma ProcessPolym., 14, 1600155, 2017.

[84] L. D. Pietanza, G. Colonna, G. D’Ammando, A. Laricchiuta, andM. Capitelli, “Electron energy distribution functions and fractional powertransfer in ”cold” and excited CO2 discharge and post discharge condi-tions,” Phys. Plasmas, 23, 013515, 2016.

[85] L. Pietanza, G. Colonna, G. D’Ammando, A. Laricchiuta, and M. Capitelli,“Non equilibrium vibrational assisted dissociation and ionization mecha-nisms in cold CO2 plasmas,” Chem. Phys., 468, 44 – 52, 2016.

[86] L. D. Pietanza, G. Colonna, G. D’Ammando, A. Laricchiuta, andM. Capitelli, “Vibrational excitation and dissociation mechanisms of CO2

under non-equilibrium discharge and post-discharge conditions,” PlasmaSources Sci. Technol., 24, 042002, 2015.

[87] M. S. Moss, K. Yanallah, R. W. K. Allen, and F. Pontiga, “An investigationof CO2 splitting using nanosecond pulsed corona discharge: effect of argonaddition on CO2 conversion and energy efficiency,” Plasma Sources Sci.Technol., 26, 035009, 2017.

[88] A. Berthelot and A. Bogaerts, “Modeling of CO2 splitting in a microwaveplasma: How to improve the conversion and energy efficiency,” J. Phys.Chem. C, 121, 8236–8251, 2017.

[89] A. Berthelot and A. Bogaerts, “Modeling of plasma-based CO2 conversion:lumping of the vibrational levels,” Plasma Sources Sci. Technol., 25,045022, 2016.

[90] J. F. de la Fuente, S. H. Moreno, A. I. Stankiewicz, and G. D. Stefanidis,“A new methodology for the reduction of vibrational kinetics in non-equilibrium microwave plasma: application to CO2 dissociation,” React.Chem. Eng., 1, 540–554, 2016.

[91] T. Silva, M. Grofulovic, L. Terraz, C. D. Pintassilgo, and V. Guerra,“Modelling the input and relaxation of vibrational energy in CO2 plasmas,”J. Phys. D: Appl. Phys., 51, 464001, 2018.

25

Chapter 1. General introduction

[92] M. Kraus, W. Egli, K. Haffner, B. Eliasson, U. Kogelschatz, andA. Wokaun, “Investigation of mechanistic aspects of the catalytic CO2

reforming of methane in a dielectric-barrier discharge using optical emis-sion spectroscopy and kinetic modeling,” Phys. Chem. Chem. Phys., 4,668–675, 2002.

[93] W. Wang, A. Berthelot, Q. Zhang, and A. Bogaerts, “Modelling of plasma-based dry reforming: how do uncertainties in the input data affect thecalculation results?,” J. Phys. D: Appl. Phys., 51, 204003, 2018.

[94] C. De Bie, J. van Dijk, and A. Bogaerts, “The dominant pathways forthe conversion of methane into oxygenates and syngas in an atmosphericpressure dielectric barrier discharge,” J. Phys. Chem. C, 119, 22331–22350, 2015.

[95] L. M. Zhou, B. Xue, U. Kogelschatz, and B. Eliasson, “Nonequilibriumplasma reforming of greenhouse gases to synthesis gas,” Energy & Fuels,12, 1191–1199, 1998.

[96] S. Heijkers, R. Snoeckx, T. Kozak, T. Silva, T. Godfroid, N. Britun,R. Snyders, and A. Bogaerts, “CO2 conversion in a microwave plasmareactor in the presence of N2: Elucidating the role of vibrational levels,”J. Phys. Chem. C, 119, 12815–12828, 2015.

[97] R. Snoeckx, S. Heijkers, K. V. Wesenbeeck, S. Lenaerts, and A. Bogaerts,“CO2 conversion in a dielectric barrier discharge plasma: N2 in the mixas a helping hand or problematic impurity?,” Energy Environ. Sci., 9,999–1011, 2016.

[98] C. De Bie, J. van Dijk, and A. Bogaerts, “CO2 hydrogenation in adielectric barrier discharge plasma revealed,” J. Phys. Chem. C, 120,25210–25224, 2016.

[99] B. Eliasson, U. Kogelschatz, B. Xue, and L.-M. Zhou, “Hydrogenationof carbon dioxide to methanol with a discharge-activated catalyst,” Ind.Eng. Chem. Res., 37, 3350–3357, 1998.

[100] R. Snoeckx, A. Ozkan, F. Reniers, and A. Bogaerts, “The quest for value-added products from carbon dioxide and water in a dielectric barrierdischarge: A chemical kinetics study,” ChemSusChem, 10, 409–424, 2017.

[101] A. Cenian, A. Chernukho, V. Borodin, and G. Sliwinski, “Modeling ofplasma-chemical reactions in gas mixture of CO2 lasers I. gas decompo-sition in pure CO2 glow discharge,” Contrib. Plasma Phys., 34, 25–37,1994.

26

1.7. References

[102] A. Cenian, A. Chernukho, and V. Borodin, “Modeling of plasma-chemicalreactions in gas mixture of CO2 lasers. II. theoretical model and itsverification,” Contrib. Plasma Phys., 35, 273–296, 1995.

[103] H. Hokazono and H. Fujimoto, “Theoretical analysis of the CO2 moleculedecomposition and contaminants yield in transversely excited atmosphericCO2 laser discharge,” J. Appl. Phys., 62, 1585–1594, 1987.

[104] A. Ozkan, A. Bogaerts, and F. Reniers, “Routes to increase the conversionand the energy efficiency in the splitting of CO2 by a dielectric barrierdischarge,” J. Phys. D: Appl. Phys., 50, 084004, 2017.

[105] I. Armenise and E. V. Kustova, “State–to–state models for CO2 molecules:From the theory to an application to hypersonic boundary layers,” Chem.Phys., 415, 269–281, 2013.

[106] I. Armenise and E. Kustova, “Sensitivity of heat fluxes in hypersonic CO2

flows to the state-to-state kinetic schemes,” AIP Conf. Proc., 1786, 1–8,2016.

[107] I. Armenise, “Excitation of the lowest CO2 vibrational states by electronsin hypersonic boundary layers,” Chem. Phys., 491, 11 – 24, 2017.

[108] B. F. Gordiets, N. N. Sobolev, and L. A. Shelepin, “Kinetics of physicalprocesses in CO2 lasers,” 26, 1968.

[109] B. F. Gordiets, A. N. Stepanovich, K. U. Grossmann, and K. H. Vollmann,“Model of the Vibrational kinetics of CO2 in the upper atmosphere,”Geomagn. Aeronomy, 34, 699–701, 1995.

[110] A. Tejero-del Caz, V. Guerra, D. Goncalves, M. Lino da Silva, L. Marques,N. Pinhao, C. Pintassilgo, and L. Alves, “The LisbOn KInetics Boltzmannsolver,” Plasma Sources Sci. Technol., 28, 043001, 2019.

27

Chapter 2

Electron-neutral scattering crosssections for CO2: a complete andconsistent set and an assessmentof dissociation

This chapter proposes a complete and consistent set of cross sections for electroncollisions with carbon dioxide (CO2) molecules, published in the IST-Lisbondatabase with LXCat. The set is validated from the comparison between swarmparameters calculated using a two-term Boltzmann solver and the availableexperimental data. The importance of superelastic collisions with CO2(010)molecules at low values of the reduced electric field is pointed out. It is arguedthat a deconvolution of the cross sections describing generic energy losses atspecific energy thresholds into cross section describing individual processes isstill surrounded by significant uncertainties. An important example of theseuncertainties is with the dissociation of CO2, for which the total electron impactdissociation cross section has not yet been unambiguously identified. Theavailable dissociation cross sections are evaluated and discussed, and a strategyto obtain electron-impact dissociation rate coefficients is suggested.1

1The results presented here were published as Electron-neutral scattering cross sectionsfor CO2: a complete and consistent set and an assessment of dissociation, Marija Grofulovic,Luıs L. Alves and Vasco Guerra, 2016 Journal of Physics D: Applied Physics, 49, 395207.

29

2.1. Introduction

2.1 Introduction

Carbon dioxide (CO2) is an important component of our atmosphere anda dominant constituent of the atmospheres of Venus and Mars. It has beenextensively studied in the last few years, due to its importance for dry reforming,and space mission studies and to its effect on climate change [1–3]. The latterhas recently put forward the idea of CO2 conversion as one of the major scientificand technological challenges nowadays and has set the goals for fundamentalexperimental research and plasma modeling [4–10]. In particular, an efficientstorage of energy in chemical compounds produced from CO2 emissions wouldbe extremely interesting from environmental, economical and societal points ofview. The main task to achieve this efficient storage of energy is to maximizethe energy efficiency of the dissociation of CO2. Low-temperature plasmas canpromote CO2 dissociation both by direct electron impact and by an indirectroute passing through vibrational excitation [4–7], but the kinetic mechanismsleading to dissociation are not yet completely understood.

Electron collisions with molecules initiate all the processes in gas discharges,thus representing the starting point for plasma chemistry. A reliable quantifica-tion of a complete set of electron-impact cross section is of immense significancefor the study of the electron kinetics and the calculation of accurate electronenergy distribution functions (EEDFs). In addition, it is desirable to identify theexcited states and mechanisms corresponding to all the cross sections requiredto calculate the EEDFs, in order to get a deeper insight into the elementaryprocesses occurring in plasmas. Electron-impact dissociation of CO2, in partic-ular, has been of interest for many years. However, despite the numerous worksaddressing the question, the cross section for this process remains a missingpiece of the puzzle [11–21]. In fact, there is no consensus on this matter andthe lack of experimental data regarding the dissociation rate coefficient makesthe validation of the electron-impact dissociation cross section of CO2 a verychallenging subject.

To allow the physical interpretation of experiments and meet the demandsof modelling, a comprehensive cross section set with interest for plasma physicsshould be more than a simple collection of data. The electron momentum loss, allthe inelastic energy loss processes and electron number changing processes (e.g.,ionization and attachment), as well as an identification of relevant superelasticgain processes, should be properly described. A set that provides the afore-stated description is said to be complete. An EEDF can be calculated when acomplete set of cross sections is used as input to a Boltzmann solver or to MonteCarlo/Particle-in-Cell codes. The result depends on the working conditions andmay deviate considerably from a Maxwellian. The transport parameters andcollision rate coefficients can then be calculated from the first two moments ofthe Boltzmann equation. An equally important requirement a cross section setshould fulfill is the ability to reproduce measured electron transport parameters

31

Chapter 2. Electron-neutral scattering cross sections for CO2

and rate coefficients. A set that meets this requirement is said to be consistent.One of the strategies to determine a complete and consistent cross sectionset includes adjusting iteratively the magnitudes and/or shapes of an existingcompilation of data (if possible within experimental uncertainty) to improve theagreement between calculated and measured swarm parameters. This “swarmderivation” method is very useful and widely used in the low-temperatureplasma community, but undermines the uniqueness of the cross section set andmay complicate the identification of individual collision processes.

The aims of this study are to propose a complete and consistent set ofelectron-neutral scattering cross sections for CO2 and to assess the available crosssections for dissociation. The set is swarm derived, based on the calculationsfrom the two-term Boltzmann solver BOLSIG+ [22], and is published on theIST-Lisbon database with LXCat. In addition, the existing dissociation crosssections are compared and evaluated, leading to a recommended procedure tocalculate the rate coefficients of CO2 dissociation by electron impact.

The organization of this chapter is as follows. The next section is devotedto the description of the complete and consistent set of electron-impact crosssections for CO2. The comparison of the two-term Boltzmann calculation of theswarm parameters with the existing measurements is presented and discussed insection 2.3, where the importance of the superelastic collisions at low reducedelectric fields (E/N . 10 Td, where E is the electric field and N is the gasdensity; 1 Td = 10−21 Vm2) is also pointed out. Section 2.4 evaluates andrecommends cross sections for providing the electron-impact rate coefficients forCO2 dissociation. Finally, the concluding remarks are summarized in section2.5.

2.2 The cross section set

This section proposes a swarm-derived complete and consistent set of electron-neutral scattering cross sections for CO2, included in the IST-Lisbon databasewith LXCat. The set was compiled mostly from Phelps [11] and it includes 17cross sections defined up to 1000 eV, describing dissociative attachment, effectivemomentum transfer, eleven vibrational excitations energy losses (correspondingeither to the excitation of individual levels or groups of vibrational levels),superelastic collisions with the CO2(010) vibrational state, excitation of twogroups of electronic states and ionization. These cross sections are outlined intable 2.1 and summarized in figure 2.1. They assure a valid prediction of theswarm parameters when used in a two-term Boltzmann solver and for reducedelectric fields below 1000 Td, as shown and discussed in section 2.3. Note thatother works might contain interesting data for some individual processes, yetnot forming a complete and consistent set of cross sections. This is the caseof Itikawa’s compilation [12], that was not adopted here as starting point for

32

2.2. The cross section set

defining our dataset because it yields calculated swarm parameters stronglydeviated from the experiments.

A small number of modifications was made in regard to the original set byPhelps [11]. First, the cross section for superelastic collisions with the first levelof the bending mode was included and should be considered as a part of theset. As a matter of fact, due to its low energy threshold (∼0.08 eV), this levelpresents a non-negligible population even in thermal conditions (see below)hence influencing the electron kinetics, especially at low values of the reducedelectric field. Second, the cross section for the electronic excitation at 10.5 eVand the ionization initially limited to 100 eV, were extended up to 1000 eVand replaced by the total ionization cross section from Itikawa [12], respectively.Then, as the effective momentum-transfer cross section corresponds to the sumof the elastic momentum-transfer, the total excitation and the ionization crosssections, the extension of the inelastic cross sections for electron energies above100 eV required modifying accordingly the effective momentum–transfer in thesame energy region. Finally, the effective momentum–transfer cross section wasslightly increased for electron energies below 0.1 eV, in order to compensate forthe additional gain of energy associated with the superelastic collisions.

The cross sections include the eight excitations to the groups of vibrationallevels schematically denoted in table 2.1. Electron impact vibrational excitationand de-excitation between the ground level υ0 and level υ1 ≡ (010) are givenby reactions (3a)–(3b). This dominant de-excitation is the only superelasticprocess taken into account in the swarm analysis, although a second superelasticprocess can be taken into account for a more accurate calculation of thetransport parameters at low values of the reduced electric field, typically below∼ 1 Td. Reactions (4a)–(10) correspond to the electron impact vibrationalexcitation from the ground level υ0 to the remaining groups of vibrationallevels υi. In principle, processes (3a) to (9b) describe the excitation of theCO2 vibrational levels with the lowest energy thresholds. The vibrational levelsassociated with the energy losses υ1 − υ4 are clearly identified. Notably, theoriginal cross section for υ2 from [11] corresponds to the sum (020)+(100). Ina recent work, Celiberto et al [23, 24] calculated new cross sections for theelectron-impact resonant vibrational excitation of several transitions of thesymmetric mode, (υi, 0, 0)→ (υf , 0, 0), with υi = 0, 1, 2 and υf in the intervalυi ≤ υf ≤ 10. Therefore, we have de-convoluted the cross section for υ2 intwo separate channels, as indicated in table 2.1, by subtracting the excitationcross section of the symmetric stretching mode (100) given in [23, 24] from thetotal excitation cross section by Phelps [11]. These two individual cross sectionsassociated with υ2 are also considered separately in [13], based on data fromBiagi [25]. Furthermore, by using the spectroscopic constants reported in [4]and the energy thresholds from Phelps’ set, it is possible to further suggestthat the identification of the vibrational excitation generically indicated in [11]as (0n0) + (n00) is as follows: υ5 with the excitation of levels (200), (040),

33

Chapter 2. Electron-neutral scattering cross sections for CO2

(a)

0.01 0.1 1 1010-26

10-25

10-24

10-23

10-22

10-21

10-20

10-19

Cro

ss s

ectio

n (m

2 )

Energy (eV)

vib (010) 0.083 eV vib (100) 0.167 eV vib (020) 0.167 eV vib (030)+(110) 0.252 eV vib (001) 0.291 eV vib (200) 0.339 eV vib (040)+(120)+(011) 0.339 eV vib (050)+(210)+(130)+(021)+(101)0.422 eV vib (300) 0.505 eV vib (0n0)+(n00) 0.505 eV vib (0n0)+(n00) 2.5 eV superelastic 010->000 Diss. attachment

(b)

Figure 2.1: Summary of the IST-Lisbon set of electron–impact cross sections for CO2,as a function of the electron kinetic energy: effective momentum transfer, electronicexcitations and ionization (a) and vibrational excitations and dissociative attachment(b).

34

Table 2.1: Summary of the processes considered in the cross section set proposed.

No. Heavy–species products Configuration of final CO2 state Threshold [eV]

(1) Effective momentum–transfer CO2(υ0) (000)(2) Dissociative attachment CO+O−

(3a) Vibrational excitation CO2(υ1) (010) 0.083(3b) Superelastic deexcitation CO2(υ0) (000)(4a) Vibrational excitation CO2(υ2a) (020) 0.167(4b) Vibrational excitation CO2(υ2b) (100) 0.167(5) Vibrational excitation CO2(υ3) (030) + (110) 0.252(6) Vibrational excitation CO2(υ4) (001) 0.291(7a) Vibrational excitation CO2(υ5a) (200) 0.339(7b) Vibrational excitation CO2(υ5b) (040) + (120) + (011) 0.339(8) Vibrational excitation CO2(υ6) (050) + (210) + (130) + (021) + (101) 0.422(9a) Vibrational excitation CO2(υ7a) (300) 0.505(9b) Vibrational excitation CO2(υ7b) (060) + (220) + (140) 0.505(10) Vibrational excitation CO2(υ8) (0n0) + (n00) 2.500(11) Electronic excitation CO2(e1) 7.0(12) Electronic excitation CO2(e1) 10.5(13) Total ionization CO+

2 13.3

Chapter 2. Electron-neutral scattering cross sections for CO2

(120) and (011); υ6 with (050), (210), (130), (021) and (101), having energythresholds between 0.42 and 0.46 eV; and υ7 with (300), (060), (220) and (140),having energy thresholds between 0.50 and 0.51 eV, as well as contributionsfrom other vibrational states with thresholds between 0.54 and 2.5 eV. The crosssections for the excitation of the symmetric stretching mode with υ5 and υ7were separated from the cross sections for the other excitation mode, using thesame procedure as for υ2 and the data from [23, 24], as indicated also in table2.1. An additional deconvolution of processes with υ3 − υ8 and the addition ofcross sections for other vibrational excitations may lead to an improvement ofthe swarm analysis and would certainly be significant to get a more completeinsight into CO2 plasmas. On-going work by R. Celiberto, V. Laporta andco-workers may provide invaluable data to pursue this task [23, 24].

Reactions (11)–(12) generically represent the excitation of electronic states.We believe that the corresponding cross sections describe various processes,including CO2 dissociation. Polak and Slovetsky [17] refer to a group of stateswith energy thresholds ≈ 8 eV, the triplets 3Σ+

u , 3Πg,3∆u and 3Σ−u and the

singlets 1Πg,1Σ−u and 1∆u. The same states are tabulated by Itikawa [12], who

indicates energy thresholds in the range 8.15-9.32 eV as given by [26], althoughan energy threshold as low as 4.9 eV is given by Rabalais et al [27] for the lowestlaying state 3Σ+

u [12]. The same sates are also identified in [28, 29], where anenergy threshold of 7.35 eV is given for the 3Σ+

u state. A second group of states,with energy thresholds of about 11 eV is identified in [12, 26, 29], 1Σ+

u , 3Πu

and 1Πu. The two groups of electronically excited states just described are verylikely included in reactions (11) and (12), respectively, but the separation ofthe lumped cross sections into individual processes seems to be beyond reach atpresent. Moreover, these cross sections may contain other mechanisms and thepossible role of these states in dissociation is far from clear. An assessment ofdissociation is carried out in section 2.4 and the reader should refer to it forfurther details. Notably, in [13] the two electronic excitation cross sections areassigned in a simplified way to the excitation of the lowest state in each group,3Σ+

u and 1Σ+u .

The non-conservative processes considered are ionization, described by re-action (13), and dissociative attachment, represented by reaction (2). Themaximum value of the dissociative attachment cross section is not very high(∼ 10−22 m2), so in general it does not contribute significantly to CO2 decom-position [13]. However, it may be important for the discharge maintenance, byaffecting the charged particle balance.

It is worth noting that the superelastic process in (3b) is considered usingthe Klein-Rosseland relation and the vibrational excitation cross section at0.083 eV. When the population of the vibrationally excited states is high enough,the excited molecules can effectively transfer energy back to the electrons. Thelow energy threshold of the (010) state makes it important to account forsuperelastic collisions even for gas temperatures around room temperature,

36

2.3. Swarm calculations

Tg = 300 K, since the relative population of this state is already about 8% inthis case. The energy gained in these processes is especially noticeable at lowreduced electric fields, while for E/N & 10 Td (and Tg = 300 K) the EEDF isbarely affected by superelastic mechanisms (cf. section 2.3).

The cross section set presented in this section is available in the IST-Lisbondatabase with LXCat [30]. At present, the IST-Lisbon database includescomplete and consistent sets of electron scattering cross sections for argon,helium, nitrogen, oxygen, hydrogen, methane and carbon-dioxide, issued by theGroup of Gas Discharges and Gaseous Electronics, now renamed N-PlasmasReactive: Modelling and Engineering (N-PRiME) group with Instituto dePlasmas e Fusao Nuclear, Instituto Superior Tecnico, Lisboa, Portugal.

2.3 Swarm calculations

In this section the set of electron–impact cross sections for CO2 proposed hereis validated from the comparison between calculated and measured values ofelectron transport parameters, namely the reduced mobility, µN , the charac-teristic energy, uk = DT /µ (DT is the transverse diffusion coefficient), thereduced longitudinal diffusion coefficient, DLN , and the reduced Townsendeffective ionization coefficient, αeff/N . The calculations are performed usingthe freeware package BOLSIG+, a numerical solver based on the two-termapproximation of the electron Boltzmann equation [22], and are compared withthe measurements available in several databases of the LXCat open-accesswebsite [31–34]. All calculations are made using three sets of cross sections:the IST-Lisbon set proposed in this work; the Phelps set [11, 35]; and a setobtained by excluding the superelastic cross section from IST-Lisbon.

Since the current set was developed to be used in a two-term Boltzmannsolver, it should not be used in conditions where the anisotropic correctionsbecome too significant. In practice, taking into account the precision in thepower balance, the magnitude of the anisotropic correction and the agreementwith the experimental swarm data, the current set can be used safely in anyBoltzmann solver for reduced electric fields lower than 1000 Td and using anenergy grid extending up to 1000 eV. In other cases multi-term expansionsor Monte Carlo methods accounting for the anisotropy of the cross sectionsshould be used. An example of a freely available software accounting for thisanisotropy is the MagBoltz code by Stephen Biagi [36–38].

In typical conditions of swarm experiments, the electron transport parame-ters are functions essentially of the local reduced electric field strength, E/N.However, dependences on the gas temperature, Tg, may be evidenced at lowvalues of E/N , usually for ∼ 1− 10 Td and below [39]. As anticipated in theprevious section, this is also the case of CO2. The dependence is mainly anoutcome of the superelastic collisions with vibrationally excited molecules in the

37

Chapter 2. Electron-neutral scattering cross sections for CO2

0 . 0 1 0 . 1 1 1 0 1 0 0 1 0 0 00 . 0

0 . 5

1 . 0

1 . 5

2 . 0

2 . 5

3 . 0

3 . 5

1 0 1 0 0

2 . 4

2 . 8

3 . 2

I S T - L i s b o n I S T - L i s b o n n o s u p e r e l a s t i c P h e l p s

B o r t n e r 1 9 5 7 F r o m m h o l d 1 9 6 0 P a c k e t a l 1 9 6 2 S c h l u m b o h m 1 9 6 5 E l f o r d 1 9 6 6 W a g n e r e t a l 1 9 6 7 E l f o r d 1 9 8 0 R o z n e r s k i e t a l 1 9 8 4 H a s e g a w a 1 9 9 4 E T H Z 2 0 1 5 K o r o l o v 2 0 1 6

E / N ( T d )

µN

(1024

m-1 V-1 s-1 )

(a)

0 . 0 1 0 . 1 1 1 0 1 0 0 1 0 0 01 0 - 3

1 0 - 2

1 0 - 1

1 0 0

1 0 1

1 0 2

d (104 m

s-1 )

E / N ( T d )

B o r t n e r 1 9 5 7 F r o m m h o l d 1 9 6 0 P a c k e t a l 1 9 6 2 S c h l u m b o h m 1 9 6 5 E l f o r d 1 9 6 6 W a g n e r e t a l 1 9 6 7 E l f o r d 1 9 8 0 R o z n e r s k i e t a l 1 9 8 4 H a s e g a w a 1 9 9 4 E T H Z 2 0 1 5 K o r o l o v e t a l 2 0 1 6 I S T - L i s b o n I S T - L i s b o n n o

s u p e r e l a s t i c P h e l p s

(b)

Figure 2.2: Measured and calculated reduced electron mobility (a) and drift velocity(b) in CO2 at Tg = 300 K, as a function of E/N in CO2. The symbols are experimentaldata (see text) and the lines are calculation results obtained using a two–termBoltzmann solver with the following cross section sets: IST-Lisbon with (———)and without (- - - - -) the superelastic process included; and Phelps (- - - - -). Theinsert in (a) is is a zoom over the peak region of the reduced electron mobility.

38

2.3. Swarm calculations

0.00 0.05 0.10 0.15 0.20

1

10

100

1000

EE

DF

(eV

-3/2)

Energy (eV)

superelastic included superelastic not included

(a)

0 5 10 1510-6

10-5

10-4

10-3

10-2

10-1

100

Energy (eV)

superelastic included superelastic not included

EE

DF

(eV

-3/2)

(b)

Figure 2.3: Electron energy distribution function in CO2 obtained with the IST-Lisbon cross section set for 1 Td (a) and 50 Td (b), with (——) and without (- - - - -)the superelastic process included.

(010) bending mode, whose population depends on Tg. Notice that swarm ex-periments correspond typically to conditions of negligible vibrational excitationby electron impact, so that the populations of the vibrationally excited states

39

Chapter 2. Electron-neutral scattering cross sections for CO2

0 . 0 1 0 . 1 1 1 0 1 0 0 1 0 0 00 . 0 1

0 . 1

1

D LN (10

24 m

-1 s-1 )

E / N ( T d )

F i n k e t a l 1 9 6 5 S c h l u m b o h m 1 9 6 5 W a g n e r e t a l 1 9 6 7 Y o s h i n a g a 2 0 1 3 U r q u i j o 2 0 1 3 K o r o l o v e t a l 2 0 1 6 I S T - L i s b o n I S T - L i s b o n n o s u p e r e l a s t i c P h e l p s

Figure 2.4: Measured and calculated reduced longitudinal diffusion coefficient inCO2 at Tg = 300 K, as a function of E/N . The symbols are experimental data (seetext) and the lines are calculations using a two–term Boltzmann solver. The crosssection sets used in the calculations are IST-Lisbon with (——) and without (- - - - -)the superelastic process included; and Phelps (——).

can be assumed to follow a Boltzmann distribution at the gas temperature.In any case, at low E/N the plasma tends to a thermal equilibrium situation,with the electron temperature similar to the gas temperature. The previousconsiderations imply that the population of the (010) vibrationally excited state(with 0.083 eV excitation energy and statistical weight of 2) must be given asinput parameter to the code. For guidance, the Boltzmann relative populationof this level at Tg = 300 K is 0.076.

In principle, the electron swarm parameters may depend on the way theelectron density is changing along the swarm. Since the measurements canadopt different conditions and configurations, the choice of the growth modelincluded in the calculations may be relevant for the purpose of comparingthe calculations with the experimental data. The calculations presented inthis work were performed assuming one of the following situations: “steady-state Townsend” (SST), which considers an exponential growth of the electroncurrent between the electrodes; or “pulsed Townsend” (PT), in which thespatially averaged electron number density increases exponentially in time.The SST formulation was used for the calculations of µN , uk and αeff/N .

40

2.3. Swarm calculations

0 . 0 1 0 . 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 00 . 0 1

0 . 1

1

1 0

E / N ( T d )

D T/µ (eV

) S k i n k e r 1 9 2 2 B a i l e y e t a l 1 9 3 2 R e e s 1 9 6 2 W a r r e n e t a l W a r r e n e t a l 1 9 6 2 ( T g = 1 9 5 K ) I S T - L i s b o n ( T g = 3 0 0 K ) I S T - L i s b o n ( T g = 1 9 5 K ) I S T - L i s b o n n o s u p e r e l a s t i c ( T g = 3 0 0 K ) P h e l p s ( T g = 3 0 0 K )

Figure 2.5: Measured and calculated characteristic energy in CO2 as a functionof E/N . The symbols are experimental data (see text). The lines are calculationresults obtained using a two–term Boltzmann solver at different temperatures, withthe following cross section sets: IST-Lisbon 195 K (- - - - -) and 300 K with (——)and without (- - - - -) the superelastic process included; and Phelps 300 K (——).

Conversely, the results for DLN were obtained using the PT model, becausethe longitudinal diffusion cannot be measured in SST experiments [40]. At lowE/N the results are unaffected by the choice of the growth model, since in thiscase the rate of production of new electrons is sufficiently low and, therefore,the electron number density is approximately constant. The values of µN , ukand of αeff/N , calculated using the SST and PT models, differ by 1% and 5%at 200 Td, respectively, the differences increasing to 10% and 15% for higherE/N.

Figure 2.2 presents the calculated and measured values of the reducedmobility and drift velocity υd = (µN)(E/N), the latter being the parametermeasured in swarm experiments. The measurements are taken from the DUT-TON, LAPLACE and ETHZ databases [41–59] and from Korolov et al [60, 61].All the calculations are in reasonable agreement with the measurements overthe full range of values of E/N. As it can be seen, both IST-Lisbon and Phelpscross section sets reproduce very well the reduced mobility for the lower valuesof E/N , within 1% of the measurements. This is mainly due to the adequatechoice of the effective momentum–transfer cross sections in these sets. The

41

Chapter 2. Electron-neutral scattering cross sections for CO2

influence of superelastic collisions is also clearly visible, revealing that Phelps’set would give worse results if superelastic collisions would be added to it,thus suggesting that this complete set was deduced to fit measurements atTg = 300 K only. It is also worth noting that the IST-Lisbon calculated peak ofthe reduced mobility, at E/N ≈ 20 Td, fits very well the recent measurementsprovided by ETHZ [32] and by Korolov et al [60, 61].

The influence of superelastic collisions with CO2(010) is further illustratedin figures 2.3 (a) and 2.3 (b), which show the EEDFs calculated at 1 Td and50 Td, respectively, with and without the inclusion of the superelastic process.The effect can be seen in both cases, even if superelastic collisions are not veryimportant at higher reduced electric fields. This is well-known from studies inother gases, noticeably nitrogen [62], since for high values of E/N the electronsgain most of their energy from the electric field. A detailed study of the influenceof superelastic collisions in CO2 was recently published in [14, 63].

The reduced longitudinal diffusion coefficient, DLN , calculated and mea-sured, is shown in figure 2.4. The IST-Lisbon cross section set yields goodagreement (within 7%) between the two-term Boltzmann calculations and themeasurements by Wagner et al [55], at low E/N . The inclusion of the superelas-tic mechanism (3b) is mainly responsible for the differences of ∼ 40% observedbetween the results of the various datasets for, E/N <10 Td.

The ratio of the transversal electron diffusion coefficient to the electronmobility is a measurable quantity with dimensions of energy expressed ineV, known as the characteristic energy, uk. As it is well-known, when theEEDF is Maxwellian uk = kT/e, where T is the electron temperature, k theBoltzmann constant and e the electron charge. In other cases there is no simplerelation between the average and the characteristic energies. Nevertheless,DT /µ provides a very useful energy scaling, since the average electron energy isnot easily accessible from experiments. The comparison between calculated andmeasured values of DT /µ as a function of E/N is shown in figure 2.5, for twovalues of the gas temperature, 195 and 300 K. The results strikingly expose theimportance of superelastic collisions. In fact, while the IST-Lisbon cross sectionset gives uk in good agreement with the measurements for both values of thegas temperature, Phelps’ set yields predictions at 300 K that wrongly matchthe experimental data measured at 195 K by Warren et al [56]. The sameoccurs when superelastic collisions are excluded from the IST-Lisbon set. Thegas temperature affects uk at very low E/N, in a situation where the electronsgain a considerable amount of energy in elastic and superelastic collisions withthe target molecules. Accordingly, the inclusion of superelastic collisions yieldscharacteristic energies in significantly better agreement with the measurements.In the region E/N < 10 Td, the predictions differ from the measurements by8% at 195 K and by 5% at 300 K. The only available data for E/N > 100 Td,measured by Schlumbohm [50, 51], deviates significantly (by a factor of 2) fromthe calculations made with either sets.

42

2.4. Dissociation of CO2

1 0 0 1 0 0 0 1 0 0 0 01 0 - 2 4

1 0 - 2 3

1 0 - 2 2

1 0 - 2 1

1 0 - 2 0

1 0 - 1 9α

eff/ N

(m2 )

T o w n s e n d 1 9 0 2 B h a l l a e t a l 1 9 6 0 C o n t i e t a l 1 9 6 7 H u r s t 1 9 0 6 S c h l u m b o h m 1 9 6 2 & 1 9 6 5 K o r o l o v e t a l 2 0 1 6 U r q u i j o 2 0 1 3 I S T - L i s b o n I S T - L i s b o n n o s u p e r e l a s t i c P h e l p s

E / N ( T d )

Figure 2.6: Calculated and measured reduced effective ionization coefficient versusthe reduced electric field (E/N ) in CO2. The lines are results from two–term Boltzmanncalculations corresponding to the calculations made with the cross sections from IST-Lisbon with (——) and without (- - - - -) the superelastic process included; andPhelps (- - - - -). The symbols are experimental data (see text).

The reduced Townsend ionization coefficient, α/N , is defined as the numberof ionization events per unit distance in the drift direction, normalized to theneutral number density. Figure 2.6 compares calculations and measurements ofthe reduced effective ionization coefficient, defined as αeff/N = α/N − η/N ,where η is the corresponding attachment coefficient. The contribution of electronattachment is noticeable only at the lower values of electric field, around 100 Td.All sets tested here are able to reproduce fairly well the measured αeff/N(within 2%) for E/N < 200 Td, yielding results that deviate up to 40%, forhigher E/N .

2.4 Dissociation of CO2

The growing interest in the plasma assisted conversion of greenhouse gases(mainly CO2 and CH4) into chemical compounds and liquid fuels has brought toattention the complexity of CO2 dissociation, since it corresponds to the limitingstep for achieving an efficient energy storage. The dissociation of CO2 is astrongly endothermic process, which makes non-equilibrium plasma technologies

43

Chapter 2. Electron-neutral scattering cross sections for CO2

promising candidates for defining an energy-efficient reaction path [6, 7]. Thegreat potential of non-equilibrium plasmas is due to the presence of energeticelectrons that can initiate chemical reactions unattainable by ordinary thermalmechanisms, e.g. through vibrational ladder-climbing processes. Indeed, anefficient dissociation path can be induced by electrons with energies of only∼1 eV, by transferring energy to the asymmetric stretching mode of the CO2

molecule [4]. Under favourable conditions the vibrational quanta can be pumped-up to the dissociation limit during the relaxation process, due to non-resonantvibration-vibration energy exchanges.

These considerations are at the basis of the considerable work conducted inthe 1970s and 1980s [4, 64–67], aiming to use vibrational energy to achieve thedissociation process rather than promoting the direct electron impact process,with the belief that the activation energy of the former is much smaller than thatof the latter. Nevertheless, dissociation through electronic excitation can be adominant mechanism in some plasmas, for example in non-equilibrium plasmaswith high values of reduced electric fields, such as dielectric barrier discharges, orwhen plasma is generated by degradation of very energetic particles. Either way,in order to optimize plasma–assisted conversion of CO2, a profound knowledgeof all dissociative channels is needed, including the direct route by electronimpact. Surprisingly, the CO2 dissociation cross section by electron impact ispoorly known to date. As a matter of fact, the cross sections for the dissociationof CO2 through electronic excitation are reported by several authors, but theyvary significantly, both in magnitude and shape, and many unknowns regardingthis issue remain.

The cross section set proposed in this work contains two electronic excitationcross sections, with thresholds at 7 eV and 10.5 eV, both originating from thePhelps database. Hake and Phelps derived the original cross sections from aswarm analysis [20], and they were later modified by Lowke and Phelps [11] inaccordance with newer measurements. Since the 10.5 eV cross section in [11] islimited to 100 eV, we included an extension up to 1 keV, as stated in section 2.2.To the best of our knowledge, the two electronic excitation cross sections do notcorrespond to any specific process, but rather to a combination of mechanismslumped as a global energy loss, including the excitations of levels 3Σ+

u , 3Πg,3∆u, 3Σ−u , 1Πg,

1Σ−u and 1∆u around 8− 9 eV and 1Σ+u , 3Πu and 1Πu around

11 eV, as described in section 2.2. These excitation levels most likely representdissociative channels, but they may contain more than just dissociation.

Several authors have identified the process with the threshold at 7 eV asthe channel of CO2 dissociation. One recent example is the work of Pietanza etal [14], which considers the 7 eV cross section from the Phelps database as thedissociative channel, while the 10.5 eV cross section is assumed to correspondto electronic excitation without dissociation. This standpoint is also adoptedin the work of Wiegand et al [19], where the measured dissociation rate in theCO2 laser gas mixture is reported to be in agreement with the measurements of

44

2.4. Dissociation of CO2

5 10 15 20 25 300

5

10

15

C

ross

sec

tion

(10-2

1 m

2 ) Polak (i) Polak (ii) Polak total Phelps 7eV Phelps 10.5eV Cosby and Helm Itikawa Corvin and Corrigan

Energy (eV)

Figure 2.7: Cross sections for the electron–impact dissociation of CO2, proposed bydifferent authors.

Corvin and Corrigan [15] and the calculations of Nighan [68] performed with the7 eV Phelps cross section. Capezzuto et al [18] acknowledges the research effortsby Wiegand and Nighan, considering that the same cross section correspondsto the electron-impact dissociative excitation

e− + CO2 → e− + CO∗2 → e− + CO + O, (2.1)

and used it to calculate the rate coefficient of CO2 dissociation. Comparingthe calculations of Wiegand and Nighan to their measurements, Capezzutoand co-workers conclude that equation (2.1) and the 7 eV cross section cannotrepresent the sole mechanism of CO2 dissociation.

Cross sections of CO2 dissociation are also offered by Corvin and Corrigan[15]. However, what was measured was not the cross section, but the dissociationrate coefficient. Then, assuming a Maxwellian EEDF, they estimated a crosssection with threshold at 6.1 eV, constructed in order to give a rate coefficientin agreement with their own measurements.

Cosby and Helm [21] measured the absolute cross section for the dissociationof CO2, using electron beam techniques. They found a higher threshold, near

45

Chapter 2. Electron-neutral scattering cross sections for CO2

12.0± 0.8 eV, corresponding to two dissociation channels:

CO∗2 → CO(X) + O(1S) (2.2)

CO∗2 → CO(a) + O(3P). (2.3)

According to their predictions, O(1S) and CO(a) represent 73% and 27%,respectively, of the dissociation products. In his compilation of CO2 crosssections [12], Itikawa includes the dissociation cross section leading to theproduction of O(1S) measured by LeClair and McConkey [16]. The cross sectionis obtained by measuring the radiation of the neutral fragment using a solid Xedetector. They conclude that besides (2.2) many other channels contribute tothe production of O(1S). The cross sections compiled by Itikawa are taken asrepresentative of the total dissociation in [5, 13, 69–73].

In a very thorough work published in 1976, Polak and Slovetsky develop amethod of computing the dissociation cross sections giving rise to the productionof neutral species [17]. Using this method, they calculated the electron-impactdissociation cross sections for hydrogen, nitrogen, oxygen, nitric oxide, carbonmonoxide, carbon dioxide, methane and other saturated hydrocarbons, stressingthe importance of a complex mechanism involving a multiplicity of channelsleading to dissociation. Regarding CO2, they address three channels representedby the following cross sections:

1. cross section of dissociation with formation of the CO(a) molecule;

2. cross section of dissociation by excitation of allowed transitions from∆Eik = 7− 9 eV states;

3. cross section of dissociation by excitation of forbidden transitions from∆Eik = 7− 9 eV states.

In their work it is stated that about 40% of the cross section (i) corresponds tothe direct formation of CO(a) molecules, the remaining representing cascadetransitions from higher triplet states of the CO molecule, resulting also fromCO2 dissociation. The excitation cross section (ii) of levels to which opticaltransitions are allowed, observed at ∆Eik = 7− 9 eV during light absorption,are computed from the absorption spectra. In what follows, the cross section(iii) is ignored, as it is much smaller than (i) and (ii). The total dissociationcross section from [17] (i.e. the sum of (i), (ii) and (iii)) differs significantlyfrom Corvin’s cross section, both in shape and magnitude (see figure 2.7).

The work by Polak and Slovetsky gives a very interesting framework toanalyse the problem. On the one hand, dissociation cross sections are calculatedas the result of individual excitations of different electronically excited states, notthrough the measurement of excited products (which accounts for only a fractionof dissociation) or lumped energy losses. On the other hand, their method was

46

2.4. Dissociation of CO2

30 40 50 60 70 80 90 100 110

10-5

10-4

10-3

10-2

10-1

100

101

Rat

e co

effic

ient

(10

-16 m

3 s-1)

E/N (Td)

Corvin exp Corvin Phelps 7eV Phelps 10.5eV Itikawa Cosby&Helm Polak total Polak (i) Polak (ii)

Figure 2.8: Dissociation rate coefficient of CO2 as a function of E/N, calculatedusing different dissociation cross sections. The symbols represent the measurementsby Corvin and Corrigan.

applied to several other molecules with success, which gives some confidence touse these cross sections as starting point for CO2. The identification in [17] oftwo groups of states, one with energy thresholds around 7− 9 eV and the otheraround 11 eV, may suggest an association of these excitations with the crosssections at 7 and 10.5 eV from the Phelps and the IST-Lisbon datasets. Thecomparison of the cross sections (i) and (ii) with those proposed here for theelectronic excitations is given in figure 2.7, revealing some similarity in shape,but a much smaller magnitude for the data in [17]. These results give a firstsuggestion that the 7 eV and 10.5 eV cross sections probably include more thanjust dissociation. For completeness, figure 2.7 depicts as well the cross sectionsproposed in [12, 15, 21].

The rate coefficient of CO2 dissociation can be calculated as a function ofthe reduced electric field according to

k =

(2

me

)1/2 ∫ ∞0

uσ(u)f(u)du (2.4)

whereme is the electron mass, f(u) is the EEDF defined so that∫∞0u1/2f(u)du =

1 and σ(u) is the cross section for dissociation by electron impact. Herein, the

47

Chapter 2. Electron-neutral scattering cross sections for CO2

dissociation rate coefficient is calculated from (2.4) using the cross sectionsreported by Corvin and Corrigan [15], Polak and Slovetsky [17], Cosby andHelm [21], Itikawa [12] and Phelps electronic excitation [11] (very similar toours), with an EEDF obtained using the IST-Lisbon cross sections proposed inthis work. The results are shown in figure 2.8. It can be seen that the 7 eVPhelps cross section and the Polak and Slovetsky total cross section lead torate coefficients with comparable values, especially for E/N ∼ 50 Td. Corvin’scross section yields a rate coefficient in reasonably good agreement with theirexperimental measurements, but this is of little significance since it just reflectsthe way the cross section was derived. It is also interesting to note that thethree cross sections assigned to dissociation with the formation of excited prod-ucts, the calculations by Polak and Slovetskii (i) and the later measurementsby Itikawa and by Cosby and Helm, all give results within the same order ofmagnitude for E/N & 35 Td. This reinforces the idea that the cross sectionsfrom [17] establish an interesting starting point to analyse the question. Forinstance, Phelp’s cross section at 10.5 eV clearly overestimates dissociation withthe formation of excited products. Moreover, the 7 eV cross section seems alsoto overestimate dissociation at higher values of E/N .

Although the calculations are compared with a single set of experimentalmeasurements, the results suggest that the 7 eV and 10.5 eV cross sectionsare likely to include more than dissociation. To test this hypothesis, theswarm analysis was repeated for the IST-Lisbon set, but this time replacing theelectronic excitation cross sections at 7 eV and 10.5 eV with those of Polak andSlovetsky (ii) and (i). The resulting cross section set fails to predict the expectedbehaviour of the reduced Townsend effective ionization coefficient, as shown infigure 2.9. This constitutes an additional confirmation that some electron energylosses are missing in the cross sections from [17], probably not ascribable todissociation, making it delicate to directly assign any of the electronic excitationcross sections from Phelps or IST-Lisbon datasets to dissociation.

Taking into account the information available to date, namely: a) theacceptable agreement between the dissociation rates calculated using Polak andSlovetsky’s cross sections (i) and the later measurements adopted in Itikawafor the same processes; b) that the cross sections in [17] are based on a theorythat predicts an additional channel which currently remains difficult to assessexperimentally (as the products are not excited); and c) that the theory in[17] was also applied with success to other molecules; we currently suggestusing the IST-Lisbon set to calculate the EEDF and the electron transportparameters, and later integrating Polak and Slovetsky’s total cross section withthe calculated EEDF in order to obtain a first estimation for the dissociationrate. Further theoretical and experimental work is desirable, investigating theinfluence of the different cross section sets on dissociation and the validity ofthis recommendation.

48

2.5. Conclusions

1 0 0 1 0 0 0 1 0 0 0 01 0 - 2 4

1 0 - 2 3

1 0 - 2 2

1 0 - 2 1

1 0 - 2 0

1 0 - 1 9

T o w n s e n d 1 9 0 2 B h a l l a e t a l 1 9 6 0 C o n t i e t a l 1 9 6 7 H u r s t 1 9 0 6 S c h l u m b o h m 1 9 6 2 & 1 9 6 5 U r q u i j o 2 0 1 3 I S T - L i s b o n I S T - L i s b o n w i t h P o l a k ’ s d i s s o c i a t i o n c . s .

α eff

/ N (m

2 )

E / N ( T d )

Figure 2.9: Calculated and measured reduced effective ionization coefficient in CO2,as a function of E/N. The symbols are experimental data (see text). The lines arecalculation results obtained using a two–term Boltzmann solver with the followingcross section sets: IST-Lisbon (——); IST-Lisbon, replacing the electronic excitationcross sections at 7 eV and 10.5 eV with Polak’s (i) and (ii) (——).

2.5 Conclusions

This chapter proposes a swarm–derived complete and consistent electron-impactcross section set for CO2, which is included in the IST-Lisbon database atLXCat, deduced from an improvement to the Phelps database [11]. Superelasticcollisions with CO2 (010) molecules are considered in this work, as it is clearlyshown they are important to study the energy transfers between electrons andCO2 molecules, at low reduced electric fields. Additionally, an effort was madeto deconvolute the original vibrational excitation cross sections.

The new IST–Lisbon set yields accurate predictions of the characteristicenergy giving the correct dependences with the gas temperature; this is veryevident for E/N < 10 Td and is impossible to obtain if superelastic collisionsare not taken into account. The proposed cross sections are able to producereduced electron mobilities that are in good agreement with the measured datawithin a large range of E/N values, as well as good predictions of the reducedTownsend ionization coefficient.

49

Chapter 2. Electron-neutral scattering cross sections for CO2

This work addresses as well the problem associated with CO2 dissociation,reviewing the available electron-impact dissociation cross sections. In particular,the dissociation coefficient is calculated upon integration of the EEDFs obtainedusing the IST-Lisbon set, over the different cross sections associated withdissociation available in the literature. The results strongly suggest that ourcross sections for electronic excitation, based on Phelps [11] and with energythresholds at 7 eV and 10.5 eV, most likely include not only dissociative channelsbut also some additional contributions.

Despite the numerous works on CO2, electron-impact dissociation is still notcompletely understood, with different authors making different assumptions andusing different cross sections to calculate the dissociation rates. We considerthat the cross sections calculated by Polak and Slovetsky [17] addressing i) theformation of O(3P)+CO(a) and ii) the dissociation by excitation of allowedtransitions, and provide a good basis for understanding and analysing theproblems of CO2 dissociation. As a matter of fact, these cross sections givedissociation rate coefficients through mechanism i) similar to the ones obtainedusing the experimental cross section reported in [12] and total dissociation ratesin reasonable agreement with the measurements from [15].

At present, we suggest using Polak and Slovetski’s cross section [17] tocalculate the dissociation rate coefficient of CO2, upon integration of a previouslycalculated EEDF. However, this cross section should not be used in a Boltzmannsolver to calculate the EEDF nor it is part of the IST-Lisbon dataset. Theuse of the electronic excitation at 7 eV may provide a simpler and reasonablealternative to this procedure. Notice that the cross sections from [17] producea dissociation rate coefficient comparable to the one calculated with the Phelps7 eV cross section at E/N ∼ 40 Td, which is the reduced field favouring theindirect dissociation route through vibrational excitation.

Work is in progress to verify the influence of the different cross sections inthe overall kinetics of CO2 plasmas in different types of discharges, namely bytesting the influence of the cross section set proposed in this work and of thecross sections for dissociation assumed by different authors in the models of thePLASMANT group in Antwerpen [74]. Preliminary results seem to indicatethat Polak and Slovetski’s cross section may lead to a too low dissociationrate and that the 7 eV excitation may provide better results. On the otherhand, very recent experimental results, conducted by the group LPP at EcolePolytechnique, show very good agreement with the rates for the electron impactdissociation calculated with Polak’s cross sections. Detailed descriptions of theexperiment and the results are given in the paper by Morillo-Candas et al [75].Moreover, the experimental estimation of the electron impact dissociation crosssection obtained by the same group shows a very good agreement with Polak’sresults [76]. Further work is needed in order to clarify this question and todefine a dissociation cross section for CO2. In addition, a deconvolution of thecurrent vibrational excitation cross sections and/or the inclusion of additional

50

2.5. Conclusions

vibrational excitation channels would also contribute to improve our knowledgeof the energy transfer made in CO2.

51

Chapter 2. Electron-neutral scattering cross sections for CO2

2.6 References

[1] A. Bultel and J. Annaloro, “Elaboration of collisional-radiative models forflows related to planetary entries into the Earth and Mars atmospheres,”Plasma Sources Sci. Technol., 22, 25008, 2013.

[2] E. Kustova and E. Nagnibeda, “On a correct description of a multi-temperature dissociating CO2 flow,” Chem. Phys., 321, 293 – 310, 2006.

[3] V. L. Kovalev and M. Y. Pogosbekyan, “Simulation of heterogeneous atomrecombination on spacecraft heat shield coatings using the methods ofmolecular dynamics,” Fluid Dynamics, 42, 666–672, 2007.

[4] A. Fridman, Plasma chemistry. Cambridge: Cambridge University Press,2008.

[5] T. Kozak and A. Bogaerts, “Splitting of CO2 by vibrational excitation innon-equilibrium plasmas: a reaction kinetics model,” Plasma Sources Sci.Technol., 23, 045004, 2014.

[6] A. Bogaerts, T. Kozak, K. van Laer, and R. Snoeckx, “Plasma-basedconversion of CO2: current status and future challenges,” Faraday Discuss.,183, 217–232, 2015.

[7] G. J. van Rooij, D. C. M. van den Bekerom, N. den Harder, T. Minea,G. Berden, W. A. Bongers, R. Engeln, M. F. Graswinckel, E. Zoethout,and M. C. M. van de Sanden, “Taming microwave plasma to beat thermo-dynamics in CO2 dissociation,” Faraday Discuss., 183, 233–248, 2015.

[8] T. Silva, N. Britun, T. Godfroid, and R. Snyders, “Optical characterizationof a microwave pulsed discharge used for dissociation of CO2,” PlasmaSources Sci. Technol., 23, 025009, 2014.

[9] F. Brehmer, S. Welzel, M. C. M. van de Sanden, and R. Engeln, “CO andbyproduct formation during CO2 reduction in dielectric barrier discharges,”J. Appl. Phys., 116, 123303, 2014.

[10] O. Taylan and H. Berberoglu, “Dissociation of carbon dioxide using amicrohollow cathode discharge plasma reactor: effects of applied voltage,flow rate and concentration,” Plasma Sources Sci. Technol., 24, 015006,2015.

[11] J. J. Lowke, A. V. Phelps, and B. W. Irwin, “Predicted electron transportcoefficients and operating characteristics of CO2–N2–He laser mixtures,”J. Appl. Phys., 44, 4664–4671, 1973.

52

2.6. References

[12] Y. Itikawa, “Cross sections for electron collisions with carbon dioxide,” J.Phys. Chem. Ref., 31, 749–767, 2002.

[13] S. Ponduri, M. M. Becker, S. Welzel, M. C. M. Van De Sanden, D. Loffhagen,and R. Engeln, “Fluid modelling of CO2 dissociation in a dielectric barrierdischarge,” J. Appl. Phys., 119, 093301, 2016.

[14] L. D. Pietanza, G. Colonna, G. D’Ammando, A. Laricchiuta, andM. Capitelli, “Electron energy distribution functions and fractional powertransfer in ”cold” and excited CO2 discharge and post discharge conditions,”Phys. Plasmas, 23, 013515, 2016.

[15] K. K. Corvin and S. J. B. Corrigan, “Dissociation of carbon dioxide inthe positive column of a glow discharge,” J. Chem. Phys., 50, 2570–2574,1969.

[16] L. R. LeClair and J. W. McConkey, “On O(1s) and CO(a3π) productionfrom electron impact dissociation of CO2,” J. Phys. B, 27, 4039, 1994.

[17] L. Polak and D. Slovetsky, “Electron impact induced electronic excitationand molecular dissociation,” Int. J. Radiat. Phys. Chem., 8, 257 – 282,1976.

[18] P. Capezzuto, F. Cramarossa, R. D’Agostino, and E. Molinari, “Contribu-tion of vibrational excitation to the rate of carbon dioxide dissociation inelectrical discharges,” J. Phys. Chem., 80, 882–888, 1976.

[19] W. J. Wiegand, M. C. Fowler, and J. A. Benda, “Carbon monoxideformation in CO2 lasers,” Appl. Phys. Lett., 16, 237–239, 1970.

[20] R. D. Hake and A. V. Phelps, “Momentum-transfer and inelastic-collisioncross sections for electrons in O2, CO, and CO2,” Phys. Rev., 158, 70–84,1967.

[21] P. C. Cosby and H. Helm, “Dissociation rates of diatomic molecules,” Tech.Rep. WL-TR-93-2004, Wright Laboratory Report, OH 45433-7650, 1992.

[22] G. J. M. Hagelaar and L. C. Pitchford, “Solving the Boltzmann equation toobtain electron transport coefficients and rate coefficients for fluid models,”Plasma Sources Sci. Technol., 14, 722, 2005.

[23] R. Celiberto, V. Laporta, A. Laricchiuta, J. Tennyson, and J. Wadehra,“Molecular physics of elementary processes relevant to hypersonics: Electron-molecule collisions,” Open Plasma Phys. J., 7, 33, 2014.

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Chapter 2. Electron-neutral scattering cross sections for CO2

[24] R. Celiberto, I. Armenise, M. Cacciatore, M. Capitelli, F. Esposito,P. Gamallo, R. K. Janev, A. Lagana, V. Laporta, A. Laricchiuta, A. Lom-bardi, M. Rutigliano, R. Sayos, J. Tennyson, and J. M. Wadehra, “Atomicand molecular data for spacecraft re-entry plasmas,” Plasma Sources Sci.Technol., 25, 033004, 2016.

[25] Biagi S Cross sections used by Magboltz 7.1. http://rjd.web.cern.ch/rjd/cgi-bin/cross.

[26] H. Nakatsuji, “Cluster expansion of the wavefunction, valence and rydbergexcitations, ionizations, and inner-valence ionizations of CO2 and N2Ostudied by the sac and sac CI theories,” Chem. Phys., 75, 425 – 441, 1983.

[27] J. W. Rabalais, J. R. McDonald, V. M. Scherr, and S. P. McGlynn, “Elec-tronic spectoscopy of isoelectronic molecules. ii. linear triatomic groupingscontaining sixteen valence electrons,” Chem.Rev., 71, 73–108, 1971.

[28] R. I. Hall, A. Chutjian, and S. Trajmar, “Electron impact excitation andassignment of the low-lying electronic states of CO2,” J. Phys. B-At. Mol.Phys., 6, L264–L267, 1973.

[29] N. W. Winter, C. F. Bender, and W. A. Goddard, “Theoretical assignmentsof the low-lying electronic states of carbon dioxide,” Chem. Phys. Lett.,20, 489 – 492, 1973.

[30] L. L. Alves, “The IST-LISBON database on LXCat,” J. Phys.: Conf.Series, 565, 012007, 2014.

[31] Dutton database www.lxcat.net retrieved on May 2015.

[32] ETHZ database www.lxcat.net retrieved on May 2015.

[33] LAPLACE database www.lxcat.net retrieved on May 2015.

[34] UNAM database www.lxcat.net retrieved on May 2015.

[35] Phelps database www.lxcat.net retrieved on May 2015.

[36] http://magboltz.web.cern.ch/magboltz/.

[37] S. Biagi, “A multiterm boltzmann analysis of drift velocity, diffusion, gainand magnetic-field effects in argon-methane-water-vapour mixtures,” Nucl.Instr. Meth. Phys. Res. A, 283, 716 – 722, 1989.

[38] S. Biagi, “Monte carlo simulation of electron drift and diffusion in countinggases under the influence of electric and magnetic fields,” Nucl. Instr. Meth.Phys. Res. A, 421, 234 – 240, 1999.

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[39] M. A. Ridenti, L. L. Alves, V. Guerra, and J. Amorim, “The role ofrotational mechanisms in electron swarm parameters at low reduced electricfield in N2, O2 and H2,” Plasma Sources Sci. Technol., 24, 035002, 2015.

[40] L. C. Pitchford, L. L. Alves, K. Bartschat, S. F. Biagi, M. C. Bordage, A. V.Phelps, C. M. Ferreira, G. J. M. Hagelaar, W. L. Morgan, S. Panchesh-nyi, V. Puech, A. Stauffer, and O. Zatsarinny, “Comparisons of sets ofelectron–neutral scattering cross sections and swarm parameters in noblegases: I. argon,” J. Phys. D: Appl. Phys., 46, 334001, 2013.

[41] V. Bailey and J. Rudd, “CVI. the behaviour of electrons in nitrous oxide,”Phil. Mag., 14, 1033–1046, 1932.

[42] M. Bhalla and J. Craggs, “Measurement of ionization and attachmentcoefficients in carbon dioxide in uniform fields,” Proc. Phys. Soc. London,76, 369–377, 1960.

[43] V. Conti and A. Williams Contributed papers of the Eight InternationalConference on Phenomena in Ionized Gases, Vienna, (Springer-Verlag,Vienna, 1967), 19, 23, 1967.

[44] M. Elford, “The drift velocity of electrons in carbon dioxide at 293K,”Austr. J. Phys., 19, 629, 1966.

[45] X. Fink Helv. Phys. Acta., 38, 717, 1960.

[46] L. Frommhold, “Eine untersuchung der elektronenkomponente von elektro-nenlawinen im homogenen feld ii,” Zeitschrift fur Physik, 160, 554–567,1960.

[47] H. Hurst, “XLV. genesis of ions by collision and sparking-potentials incarbon dioxide and nitrogen,” Phil. Mag., 11, 535–552, 1906.

[48] J. Pack, R. Voshall, and A. Phelps, “Drift velocities of slow electrons inkrypton, xenon, deuterium, carbon monoxide, carbon dioxide, water vapor,nitrous oxide, and ammonia,” Phys. Rev., 127, 2084–2089, 1962.

[49] J. A. Rees, “Measurements of townsend’s energy factor k1 for electrons incarbon dioxide,” Austr. J. Phys., 17, 462, 1964.

[50] H. Z. Schlumbohm, “Messung der driftgeschwindigkeiten von elektronenund positiven ionen in gasen,” Zeitschrift fur Physik, 182, 317–327, 1965.

[51] H. Z. Schlumbohm, “Stoßionisierungskoeffizient α, mittlere elektronenen-ergien und die beweglichkeit von elektronen in gasen,” Zeitschrift fur Physik,184, 492–505, 1965.

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Chapter 2. Electron-neutral scattering cross sections for CO2

[52] H. Z. Schlumbohm, “Elektronenlawinen in elektronegativen gasen,”eitschrift fur Physik, 166, 192–206, 1962.

[53] M. F. Skinker, “LXXXVIII. the motion of electrons in carbon dioxide,”Phil. Mag., 44, 994, 1922.

[54] J. Townsend, “LXVI. the conductivity produced in gases by the aid ofultra-violet light,” Phil. Mag., 3, 557–576, 1902.

[55] E. B. Wagner, F. J. Davis, and G. S. Hurst, “Time-of-flight investigationsof electron transport in some atomic and molecular gases,” J. Chem. Phys.,47, 3138–3147, 1967.

[56] R. W. Warren and J. H. Parker, “Ratio of the diffusion coefficient to themobility coefficient for electrons in He, Ar, N2, H2, D2, CO, and CO2 atlow temperatures and low E

p ,” Phys. Rev., 128, 2661–2671, 1962.

[57] M. Elford and G. Haddad, “The drift velocity of electrons in carbon dioxideat temperatures between 193 and 573 k,” Aust. J. Phys., 33, 517, 1980.

[58] H. Hasegawa Aust. J. Phys., 48, 357, 1994.

[59] W. Roznerski and K. Leja, “Electron drift velocity in hydrogen, nitrogen,oxygen, carbon monoxide, carbon dioxide and air at moderate e/n,” J.Phys. D: Appl. Phys., 1, 279, 1984.

[60] I. Korolov, M. Vass, and Z. Donko 23rd Europhysics Conference on theAtomic and Molecular Physics of Ionized Gases (ESCAMPIG), Bratislava,2016, 2016.

[61] M. Vass, I. Korolov, D. Loffhagen, N. Pinhao, and Z. Donko, “Electrontransport parameters in CO2: scanning drift tube measurements andkinetic computations,” Plasma Sources Sci. and Technol., 26, 065007,2017.

[62] J. Loureiro and C. M. Ferreira, “Coupled electron energy and vibrationaldistribution functions in stationary N2 discharges,” J. Phys. D: Appl. Phys.,19, 17–35, 1986.

[63] L. Pietanza, G. Colonna, G. D’Ammando, A. Laricchiuta, and M. Capitelli,“Non equilibrium vibrational assisted dissociation and ionization mechanismsin cold CO2 plasmas,” Chem. Phys., 468, 44 – 52, 2016.

[64] I. A. Semiokhin, Y. P. Andreev, and G. Panchenkov Russ. J. Phys. Chem.,38, 1126, 1964.

[65] A. N. Maltsev, E. N. Eremin, and L. V. Ivanter Russ. J. Phys. Chem., 41,633, 1967.

56

2.6. References

[66] Y. P. Andreev, I. A. Semiokhin, Y. Voronkov, V. A. Sirotkina, and V. A.Kaigorodov Russ. J. Phys. Chem., 45, 1587, 1971.

[67] V. D. Rusanov, A. A. Fridman, and G. V. Sholin, “The physics of achemically active plasma with non-equilibrium vibrational excitation ofmolecules,” Sov. Phys.—Usp., 24, 447, 1981.

[68] W. Nighan, “Effect of molecular dissociation and vibrational excitation onelectron energy transfer in CO2 laser plasmas,” Appl. Phys. Letters, 15,355–357, 1969.

[69] T. Kozak and A. Bogaerts, “Evaluation of the energy efficiency of CO2

conversion in microwave discharges using a reaction kinetics model,” PlasmaSources Sci. Technol., 24, 015024, 2015.

[70] R. Aerts, T. Martens, and A. Bogaerts, “Influence of vibrational states onCO2 splitting by dielectric barrier discharges,” J. Phys. Chem. C, 116,23257–23273, 2012.

[71] R. Snoeckx, Y. X. Zeng, X. Tu, and A. Bogaerts, “Plasma-based dryreforming: improving the conversion and energy efficiency in a dielectricbarrier discharge,” RSC Adv., 5, 29799–29808, 2015.

[72] R. Snoeckx, S. Heijkers, K. V. Wesenbeeck, S. Lenaerts, and A. Bogaerts,“CO2 conversion in a dielectric barrier discharge plasma: N2 in the mixas a helping hand or problematic impurity?,” Energy Environ. Sci., 9,999–1011, 2016.

[73] S. Heijkers, R. Snoeckx, T. Kozak, T. Silva, T. Godfroid, N. Britun,R. Snyders, and A. Bogaerts, “CO2 conversion in a microwave plasmareactor in the presence of N2: Elucidating the role of vibrational levels,”J. Phys. Chem. C, 119, 12815–12828, 2015.

[74] A. Bogaerts, W. Wang, A. Berthelot, and V. Guerra, “Modeling plasma-based CO2 conversion: Crucial role of the dissociation cross section,”Plasma Sources Sci. Technol., 25, 2016.

[75] A. Morillo-Candas, C. Drag, J.-P. Booth, V. Guerra, and O. Guaitella,“Oxygen atom kinetics in CO2 plasmas ignited in a DC glow discharge,”Plasma Sources Sci. Technol., 28, 075010, 2019.

[76] A. Morillo-Candas, B. Klarenaar, T. Silva, R. Engeln, R. Guerra, andO. Guaitella, “Time-evolution of the CO2 conversion studied by in situFTIR absorption and isotopic exchange,” 24th International Symposiumon Plasma Chemistry, 2019.

57

Chapter 3

Kinetic study of low-temperatureCO2 plasmas undernon-equilibrium conditions:relaxation of vibrational energy

A kinetic model describing the time evolution of ∼ 72 individual CO2(X1Σ+)vibrational levels during the afterglow of a pulsed DC glow discharge is developed.The results of the simulations are compared with the experimental resultsobtained in a pulsed DC glow discharge and its afterglow at pressures of afew Torr and discharge currents of around 50 mA by means of in situ Fouriertransform infrared spectroscopy. The very good agreement between the modelpredictions and the experimental results validates the kinetic scheme consideredhere and the corresponding vibration–vibration and vibration–translation ratecoefficients. In this sense, it establishes a reaction mechanism for the vibrationalkinetics of these CO2 energy levels and offers a firm basis to understand thevibrational relaxation in CO2 plasmas. It is shown that first-order perturbationtheories, namely, the Schwartz–Slawsky–Herzfeld and Sharma–Brau methods,provide a good description of CO2 vibrations under low excitation regimes.1

1The results of this chapter were partially presented in Kinetic study of CO2 plasmasunder nonequilibrium conditions. I. Relaxation of vibrational energy, T. Silva, M. Grofulovic,B. L. M. Klarenaar, A.S. Morillo-Candas, O. Guaitella, R. Engeln, C.D. Pintassilgo, V.Guerra, 2018 Plasma Sources Science and Technology, 27, 015019.

59

3.1. Introduction

3.1 Introduction

The study of CO2 discharges has been a subject of many publications sincethe sixties, when the CO2 laser was invented [1]. More recent studies aremotivated by aerospace applications and the production of CO2-neutral fuels.Non-equilibrium plasmas are particularly interesting for the later purpose,where energetic electrons coexist with relatively cold gas molecules. Undernon-equilibrium conditions, the electrons transfer the energy they gained fromthe electric field to the excitation of the vibrational degrees of freedom of the gasmolecules, which strongly promotes their decomposition [2–4]. The interest inspace exploration has reinforced the modeling of CO2 discharges because of theirkey role in the heat generation on the surface of space-crafts [5], prediction ofgas dynamic parameters on the trajectory of space vehicles during atmosphericentry [6], oxygen production in Mars [7], etc.

For all the applications, it is of crucial interest to have a comprehensivemodel of electron, vibrational, chemical and surface kinetics in CO2 plasmas. Tothat end, several such models have been developed in recent years. For instance,Kozak and Bogaerts [8] have considered a very extensive plasma chemistry thattakes into account the first low-lying symmetric levels and various asymmetriclevels up to the dissociation limit. Armenise and Kustova [6] have developed astate-to-state relaxation model which takes into account the complete mixing ofthe various CO2 vibrational modes, which leads to a total of ∼ 9000 differentCO2 vibrational states and, accordingly, to a very high computational costs.Despite the high relevance of all of these studies, the discrepancies betweenthe formulations raises the question on the advantages and disadvantages ofeach approach. The comparison between theoretical results and experimentallymeasured values is of paramount importance to validate the correctness ofparticular approach, and it is unfortunately usually missing in these studies.

In order to understand the energy exchanges in CO2 plasmas, we havedeveloped a CO2 kinetic model and have validated it against experimental data.This chapter presents the relaxation of vibrational energy in CO2 plasma takinginto account the V–T and V–V exchanges, while the input of vibrational energywith the electron impact processes is described in chapter 4. More specifically,the vibrational energy exchanges in CO2 discharges and post-discharges areinvestigated using a detailed self-consistent model describing the time evolutionof the various CO2(X1Σ+) vibrational levels measured in [9]. Our study islimited to a low excitation regime involving at most these 72 vibrational levels.The modeling results are compared with the measurements presented in [9].

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Chapter 3. Relaxation of vibrational energy in CO2 discharges

3.2 Description of the model

The kinetic model developed in this work to study low-pressure pulsed DCdischarges and their afterglows is used in two coupled modules, one describingthe discharge and the other the post-discharge. In this chapter, we discuss indetail the post-discharge module, while the discharge module is presented inchapter 4. The input parameters to the simulations are the discharge pressure,current, pulse length and the tube radius, while the gas temperature profile inthe pulse is taken from experiment (cf. section 3.7).

At present, a low excitation regime is assumed, in which only a few vibra-tional levels are excited, namely the levels corresponding to quantum numbersup to νmax1 = 2 and νmax2 = νmax3 = 5, where ν1, ν2 and ν3 denote, respectively,the vibrational quantum numbers associated with the symmetric stretching,bending and asymmetric stretching modes, resulting in a total of 72 vibrationallevels. These low excitation conditions can be obtained under the experimentalconditions considered in the present work, with millisecond pulse durationsand a discharge current of 50 mA. Some of the levels included in the modelare effective levels corresponding to groups of vibrationally excited states inFermi resonance that are difficult to resolve and, therefore, are observed lumpedtogether (cf. section 1.2). All the information regarding the vibrational levelsactually used, the grouping into effective levels, notation used and calculationof V-V and V-T rate coefficients is thoroughly presented in [10] and is brieflyreviewed in section 4.3.

The solutions obtained in the end of the discharge pulse can be used as initialconditions for the post-discharge module, where the system of rate balanceequations is solved including the same V-T and V-V exchanges, while neglectingall the electron impact processes. This approximation is justified since, besidesthe decay of the electron density, the timescale for electron energy relaxationis much shorter than the relaxation time of the vibrational energy [4, 11, 12].Accordingly, electron impact processes are not expected to play any significantrole in the vibrational kinetics of the post-discharge in the ms timescale understudy.

3.3 Estimation of vibrational rates: general overview

The populations of the CO2 vibrational levels are largely controlled by theV-V and V-T energy exchanges [13]. Therefore, an accurate estimation of thereaction rates up to the dissociation limit is of utmost interest for the CO2

decomposition applications. However, experimental data for V-V and V-Tenergy exchanges in CO2 are limited to lower quantum numbers. Numerousstudies were dedicated to determination of these rates using acoustic methods[14], shock tube studies [15] and laser-induced vibrational fluorescence analysis

62

3.3. Estimation of vibrational rates: general overview

[16]. Since these studies were focused on understanding of the CO2 laser systems,they were limited to first six vibrational levels of CO2 molecule and to thetemperature range relevant for the laser systems, i.e. a few hundred degreesCelsius. This makes the available rates insufficient for a proper description ofCO2 discharges under non-equilibrium conditions with the complex vibrationalkinetics.

There are several theoretical approaches that allow the calculation of thereaction rates for the vibrational exchanges (see table 3.1). They can becategorized as follows:

• first-order perturbation theories (FOPTs);

• forced harmonic oscillator (FHO) model;

• quantum–classical trajectory (QCT)

FOPTs are based on collinear collision models, hence they are used in caseswhere transition probabilities are much smaller than unity, using the first Bornapproximation [17]. This requires the interaction energy to be small comparedwith the translational kinetic energy. The most commonly used FOPT methodis the SSH method, developed by Schwartz, Slawsky, and Herzfeld [18, 19].In short, SSH assumes that strong, short-range, repulsive forces are effectivein producing vibrational transitions. It is a very convenient method sincethe expressions for the state-specific relaxation rates are rather simple [3].However, SSH theory overestimates the vibrational transition probabilities athigh temperatures and/or high quantum numbers [20]. The most extensive SSHstudy regarding CO2 vibrational kinetics was conducted by Herzfeld [21, 22],taking into account many V-V and V-T energy exchanges of the first CO2

vibrational levels. Several papers published by Kozak and Bogaerts [8, 23],Armenise and Kustova [6], and Sahai et al [24] have used these results, togetherwith a scaling-law formulation, to describe CO2 vibrational kinetics up to thedissociation limit. However, it has been noted by Capiteli et al [11] and Silva etal [10] that in some cases the reaction rates calculated from the SSH theory havevalues that are too large for higher vibrational quantum numbers, which leadsto unphysical transition probabilities. Therefore, the prediction of reactionrates near the dissociation limit should be improved by developing scaling lawsmore appropriate than the ones used by the SSH theory.

Another FOPT theory, developed by Sharma and Brau, assumes that vibra-tional energy exchanges occur due to long-range multipole interactions and it isapplicable to near-resonant processes involving molecules with large moments ofvibrational transitions [25–27] as is the case of V-V transfers on the asymmetricstretching mode. This theory predicts a possible decrease of the reaction rateswith the gas temperature, contrary to the SSH theory.

63

Chapter 3. Relaxation of vibrational energy in CO2 discharges

Table 3.1: Summary of different theories potentially applicable to the study ofvibrational exchanges in CO2 discharges and post-discharges.

Method Multi- Temp. Intermolecular Ref.quantum range potential

FOPT (SSH) Noa Low Repulsive (short-range) [6, 8, 22, 34, 35]FOPT (SB) No Low Attractive (long-range) [25–27, 36]

FHO Yes High Anyb

QCT Yes Any Any [32, 33]

a Extended versions of the original SSH theory include two-quantum transitions [35].b This implies the use of steric factors and the limitation of a 1D description [28].

The FHO is a semi-classical analytical method developed from a non-perturbative analytical theory. In this theory, the interaction between particlesis described by a detailed Morse intermolecular potential, meaning that bothshort-range repulsive forces and any long-range attractive forces are accountedfor [28]. Studies performed on many systems, such as N2-O2, N2-N2, andO2-O2 have shown that the FHO is able to predict the vibrational rates veryaccurately over a wide range of translational temperatures and vibrationalquantum numbers, including multi-quanta jumps [29, 30].

A more general approach is taken in the QCT method which assumes arealistic intermolecular interaction potential energy surface (PES) [31]. TheQCT is computationally expensive since it employs the Monte Carlo methods ofstatstical sampling of the kinetic and internal energy of the colliding particles.Some works were dedicated to the investigation of energy transfers in CO2–CO2

collisions [32, 33], however the number of transitions that were studied islimited and validation against experimental data is somewhat difficult. Thequalitative behavior of the QCT was investigated in [33] by analyzing theV–T energy transfers associated with the CO2 bending mode, which shown anunderestimation of the SSH probabilities in the lower temperature range.

3.4 Vibration-vibration and vibration-translation energyexchanges

The vibrational energy transferred to the CO2 molecules in electron impactprocesses during the on-time of a pulsed DC glow discharge is primarily re-distributed among different V-V and V-T channels. The complete set of V-Tand V-V reactions is the basis of our afterglow kinetic model. First, we takeinto account transfers of vibrational energy from one mode into translationalkinetic energy, while the other two modes remain unchanged. These processes

64

3.4. Vibration-vibration and vibration-translation energy exchanges

are denoted as V-T1, V-T2 and V-T3 in the text below respectively for thesymmetric stretching, bending and asymmetric stretching modes . Similarly, thevibrational energy may be transferred from one molecule to another within thesame vibrational mode, while the other two modes stay unchanged (V-V1, V-V2

and V-V3). Finally, one can consider the processes that affect simultaneouslytwo or more vibrational modes. Such reactions are represented as V-T4 andV-V4.

The processes considered by our model can be categorised as follows:

a) V-T exchanges:

V − T1 : CO2((ν1 + n)νl22 ν3f) + CO2 ←→ CO2(ν1νl22 ν3f) + CO2,

V − T2 : CO2(ν1(ν2 + n)l2+nν3f) + CO2 ←→ CO2(ν1νl22 ν3f) + CO2,

V − T3 : CO2(ν1νl22 (ν3 + n)f) + CO2 ←→ CO2(ν1ν

l22 ν3f) + CO2,

V − T4 : CO2((ν1 + n)(ν2 + j)l2+j(ν3 + k)f) + CO2 ←→CO2(ν1ν

l22 ν3f) + CO2,

b) V-V exchanges:

V −V1 : CO2((ν1 + n)νl22 ν3f) + CO2((µ1 + n′)µm22 µ3f)←→

CO2(ν1νl22 ν3f) + CO2(µ1µ

m22 µ3f),

V −V2 : CO2(ν1(ν2 + n)l2+nν3f) + CO2(µ1(µ2 + n′)m2+n′µ3f)←→

CO2(ν1νl22 ν3f) + CO2(µ1µ

m22 µ3f),

V −V3 : CO2(ν1νl22 (ν3 + n)f) + CO2(µ1µ

m22 (µ3 + n′)f)←→

CO2(ν1νl22 ν3f) + CO2(µ1µ

m22 µ3f),

V −V4 : CO2((ν1 + n)(ν2 + j)l2+j(ν3 + k)f) +

CO2((µ1 + n′)(µ2 + j′)m2+j′(µ3 + k′)f)←→

CO2(ν1νl22 ν3f) + CO2(µ1µ

m22 µ3f),

where n, n’, j, j’, k, and k’ represent arbitrary numbers (positive, negative, orzero).

The data for the V-T and V-V rate coefficients are taken from the reportpublished by Blauer and Nickerson [34] where the first 14 vibrational levelsof CO2 are considered (with νmax1 = 2, νmax2 = 5 and νmax3 = 1). Therates given in the report are either experimental or calculated using the SSH

65

Chapter 3. Relaxation of vibrational energy in CO2 discharges

theory. The calculations made by Blauer and Nickerson take into account theFermi resonance. The report provides many rates for the transitions wherethe quantum numbers ν1 and ν2 change, while ν3 stays the same. Only a fewtransitions are given with the deactivation of the first excited level ν3. Ourmodel uses all the rate coefficients published in [34]. Additionally, they areused to estimate the rates of the transitions in which ν3 changes as well.

The rate coefficients for the transitions involving the modifications of higherν3 levels are computed for the fundamental transitions whilst the remainingones are scaled using the scaling law described in [3]. A similar approach isused by Armenise and Kustova [6] and Kozak and Bogaerts [8].

One important vibrational mechanism included in our model that deservesspecial attention is the V-V3 exchange

CO2(00011) + CO2(00011)←→ CO2(00001) + CO2(00021). (3.1)

Reaction (3.1) represents the nearly resonant collisional up-pumping processesalong the asymmetric mode of vibration, that is expected to be important innon-equilibrium CO2 plasmas. The experimental measurement of the rate forthis transition was determined by Kreutz et al employing diode laser absorptionmeasurements [37]. Their result yields 1.7 × 10−10 cm3s−1 at 298 K, whichis very close to the calculated value of 2.1×10−10 cm3s−1 at 300 K given byPack [38]. Since for Tg lower than 1200 K the vibrational energy exchangessuch as 3.1 should be dominated by long-range interactions [3], we used the SBtheory [36] and the results from [37, 38] to obtain a formula of the rate constantdependent on the gas temperature, Tg. According to the SB theory, the ratecoefficients decrease with the gas temperature. However, one should be carefulwhen calculating rate constants for higher temperatures (Tg > 1200 K) andhigher quantum numbers, where a mixed contribution of short- and long-rangeforces become important and the rate coefficient start to increase with Tg. TheSSH and SB scaling for higher quantum number would give unrealisticallylarge values for the corresponding rates. A list of the ‘core’ processes and thecorresponding rate coefficients taken from the literature and used in the modelis given in table 3.2.

The kinetic scheme includes 72 CO2 vibrational levels, with approximately350 V-T and 600 V-V direct reactions. The corresponding rate coefficient forthose reactions are fitted by the following expression

k(cm3s−1) = 1.66 · 10−24 exp(A+BT−1/3g + CT−2/3g ), (3.2)

where A, B and C are fitting constants, given in table 3.2.

66

3.5. Spontaneous emission

Table 3.2: Vibrational energy transfer reactions of CO2 used for the scaling ofthe similar reactions including higher vibrational numbers, with the correspondingreferences. The coefficients A, B, and C are to be used in expression (3.2).

No. Reactions Scaling Ref.

(1) CO2(00011) + CO2 ←→ CO2(01101) + CO2 SSH [34]A = 53.9; B = −407; C = 824

(2) CO2(00011) + CO2 ←→ CO2(10002) + CO2 SSH [34]A = 54.6; B = −404; C = 1096

(3) CO2(00011) + CO2 ←→ CO2(11102) + CO2 SSH [34]A = 43.6; B = −252; C = 685

(4) CO2(00011) + CO2(00001)←→ CO2(10002) + CO2(01101) SSH [34]A = 34.8; B = −88; C = 23

(5) CO2(00011) + CO2(00011)←→ CO2(00001) + CO2(00021) SB [37]A = 29.8; B = 22; C = −40; Tg < 1200 K

(6) CO2(00011) + CO2(01101)←→ CO2(00001) + CO2(01111) SB [38]A = 30.8; B = 13; C = −23; Tg < 1200 K

(7) CO2(10012) + CO2(00001)←→ CO2(10002) + CO2(00011) SB [38]A = 30.8; B = 14; C = −36; Tg < 1200 K

3.5 Spontaneous emission

The loss or gain of vibrational quanta may also occur through radiative processes,contributing to the infrared spectra of CO2. The model presented here follows[10] and includes the vibrational transitions ν + 1→ ν within each mode of theCO2 molecule, by emission of a single photon (3.3).

CO2((ν1 + 1), νl22 , ν3, f)→ CO2(ν1, νl22 , ν3, f) + hν,

CO2(ν1, (ν2 + 1)l2+1, ν3, f)→ CO2(ν1, νl22 , ν3, f) + hν,

CO2(ν1, νl22 , (ν3 + 1), f)→ CO2(ν1, ν

l22 , ν3, f) + hν. (3.3)

The Einstein coefficients for the spontaneous emission are taken from Blaueret al. [34] and Rothman et al. [39]. Absorption of radiation is not takeninto account. Note that these mechanisms were found to be negligible for thedischarge pulse under the current conditions and in practice can be disregardedfrom the analysis of the discharge phase.

3.6 Rate balance equations for CO2 vibrational levels

The concentrations of 72 vibrational levels of CO2 are determined in this workby solving a system of 72 time-dependent rate balance equations accounting for

67

Chapter 3. Relaxation of vibrational energy in CO2 discharges

the corresponding creation and loss molecular mechanisms. A general form of arate balance equation for a level ν may be written as:

dnνdt

=

(dnνdt

)V−T

+

(dnνdt

)V−V

+

(dnνdt

)hν

. (3.4)

Every term on the right-hand side represents one type of mechanisms includedin the model. They can symbolically be written as follows:

(dnνdt

)V−T

=∑w

nw[CO2]Pw,ν −∑w

nν [CO2]Pν,w, (3.5)(dnνdt

)V−V

=∑

ν′,w,w′

nν′nwQw,w′

ν′,ν −∑

ν′,w,w′

nνnw′Qw′,w

ν,ν′ , (3.6)

(dnνdt

)hν

= nν+1Aν+1,ν − nνAν,ν−1. (3.7)

Here, [CO2] denotes the CO2 molecular density, while P , Q and A are therate coefficients for the V-T, V-V and spontaneous emission respectively. Thesubscripts represent the initial and the final states of the colliding molecules.The system is closed by assuming that the CO2 gas density equals the sum ofall vibrational states densities:

[CO2] =∑ν

nν . (3.8)

The gas temperature, gas pressure and the corresponding initial concentra-tions of the vibrational levels are given as input to our simulations. In sections3.8 and 4.6, the results of our simulations are compared with the experimentaldata. For the initial values of the concentrations of the vibrational levels, wehave taken the measured ones and estimated the rest of the levels by assumingthe Boltzmann distribution at experimentally obtained vibrational temperaturesT1,2 and T3 [9].

3.7 Experiment

The experimental results were obtained by time-resolved in situ Fourier Trans-form Infrared spectroscopy (FTIR) in a pulsed DC glow discharge, allowing thedetermination of the population of the same vibrational levels of CO2 describedin the model [9, 10]. The measurements were performed in flowing conditions,at pressures between 1 and 5 Torr and pulsed plasma current in the range10-50 mA. The inner tube diameter of the reactor is 2 cm. The measuredinfrared transmittance spectra is then analysed using the algorithm developed

68

3.7. Experiment

by Klarenaar et al described in detail in [9]. Additionally, the electric fieldwas measured with two tungsten probes that are inserted in the dischargetube 8.5 cm apart and the steady-state value was then compared with theself-consistent reduced electric field calculated in the model.

Table 3.3: Summary of the experimental conditions in the single pulse experimenttaken as input for the model.

Parameter Working conditions

Type of discharge DC pulsed dischargePressure 5 TorrTube radius 1 cmTube length 23 cmDischarge current 50 mAOn-off time 5-150 msFlow rate 166 sccm

Infrared absorption is a line of sight integrated technique, which can bringsome difficulties for the comparison with modeling results. First, part of thegas along the optical path is not excited by the plasma. This dead volume isassumed to be at thermal equilibrium in the fitting algorithm and accounts forabout 26% of the total volume of the reactor. The second issue is that slowprocesses such as the cumulative dissociation of CO2 over repetitive plasmapulses can lead to an axial profile along the tube length which relates to anaverage molecular density in the absorption measurement results. However,since in this work we are focusing on the ‘single pulse’ measurement, this lastquestion does not come into play.

The ‘single pulse’ measurement was made with a gas flow rate of 166 sccmof CO2, 5 ms plasma-on time and 150 ms off time, at p = 5 Torr and I = 50 mA[9, 10]. A summary of the experimental conditions is given in table 3.3. Atthese conditions, there is no significant dissociation during a single pulse andthe residence time (∼ 100 ms) is shorter than the off time, allowing the gas tofully renew, leaving the reactor with most of CO and O2 removed. Accordingly,collisions of CO2 with CO, O and O2 are expected to play a negligible role inthe CO2 vibrational kinetics. The results of this measurement are, therefore,suitable for the comparison with the model predictions and confirmation ofboth vibrational energy transfers (V-V and V-T) and e-V rate coefficients, sinceonly e-V processes need to be added to the model where the CO2-CO2 V-Tand V-V rate coefficients have been validated [10].

The experimental time-resolved gas temperature data is used as an input inour calculations for all the studied conditions. Figure 3.1 shows the experimentalgas temperature during the post-discharge in the single-pulse measurement

69

Chapter 3. Relaxation of vibrational energy in CO2 discharges

0 . 0 0 0 0 . 0 0 2 0 . 0 0 4 0 . 0 0 6 0 . 0 0 8 0 . 0 1 03 0 0

4 0 0

5 0 0

6 0 0

7 0 0

8 0 0

E x p e r i m e n t a l d a t a E x p o n e n t i a l f i t

p = 5 T o r r

Gas t

empe

rature

(K)

T i m e ( s )

Figure 3.1: Gas temperature profile during the afterglow of a pulsed DC glowdischarge at p = 5 Torr, I = 50 mA, and ∆t = 5 ms. The symbols represent theexperimental values and the solid line refers to the fit according to formula (3.9).

together with the fitted temperature used in the model, that is described bythe following expression:

Tg(t) = Tc + (T0 − Tc) exp(−αt), (3.9)

where Tc, T0 and α are fitting constants. The values of the fitting constants forthe post-discharge in the single pulse experiment, i.e. p = 5 Torr, I = 50 µA,are Tc = 350.7 K, T0 = 683.9 K and α = 347.7 s−1.

3.8 Results

This section presents the analysis of the modeling results of post-discharge andcompares it with the experimental data obtained in the FTIR study, brieflypresented in section 3.7.

Figure 3.2 depicts the normalized density of the first vibrational level ofthe bending mode during the afterglow of a pulsed DC discharge operatingat p = 5 Torr, I = 50 ms and 5-150 ms on-off cycle. The figure shows threedifferent sets of results: i) the temperature profile represented by expression(3.9), which fits the experimental data; ii) constant gas temperature at 300 Kin the absence of the V–V mechanisms; and iii) constant gas temperature at200 K in the absence of the V–V mechanisms.

70

3.8. Results

1 0 - 6 1 0 - 5 1 0 - 4 1 0 - 3 1 0 - 2 1 0 - 1- 3 . 5

- 3 . 0

- 2 . 5

- 2 . 0

- 1 . 5

- 1 . 0

C O 2 ( 0 1 1 0 1 ) - 5 T o r r ( s i n g l e p u l s e )E x p e r i m e n tM o d e l ( r e a l T g p r o f i l e ) M o d e l ( T g = 3 0 0 K ; N o V - V )M o d e l ( T g = 2 0 0 K ; N o V - V )

Log[N

011 01

)/N0⋅g]

T i m e ( s )

Figure 3.2: Normalized density of the CO2(01101) state during the post-discharge atp = 5 Torr, I = 50 mA, and ∆t = 5 ms. The dashed lines correspond to the calculatedvalues using constant gas temperature at 200 and 300 K, whilst the solid line representsthe results obtained with the experimental temperature profile. Spontaneous emissionis not considered in these calculations.

The first case represents our base model, and shows a very good agreementwith the experimental results. Both the calculations and the experiment shownearly constant values of the density until ∼ 10−4 s. After that time thedensity of CO2(01101) exhibits a drop until the moment when the creation anddestruction mechanisms are in equilibrium (∼ 10−2 s). The other two curvesin figure 3.2 show an incorrect prediction of the CO2(01101) density evolution.Since in the scenarios ii) and iii) V-V exchanges are absent, the relaxation ofthis level is driven purely by V-T processes, and the only difference between ii)and iii) is in the gas temperature. Clearly, higher temperature leads to a fasterrelaxation, due to the higher values of the V-T rate coefficients according tothe SSH theory.

The temporal evolution of the populations of first four levels of the bendingmode during the post-discharge is shown in figure 3.3, evidencing the goodagreement between the model predictions and the experiment even for highervibrational levels. Similarly to CO2(01101), the relaxation of each vibrationallevel starts at ∼ 10−4 s. The relaxation of the CO2(05501) level is not showndue to the rather noisy experimental data in this case. The good agreementbetween the measurements and calculations for these higher levels reinforces

71

Chapter 3. Relaxation of vibrational energy in CO2 discharges

1 0 - 5 1 0 - 4 1 0 - 3 1 0 - 2 1 0 - 1

- 1 0

- 8

- 6

- 4

- 2

C O 2 ( 0 v 2l 2 0 1 ) - 5 T o r r

( E x p e r i m e n t ) ( M o d e l ) v 2 = 1 v 2 = 1 v 2 = 2 v 2 = 2 v 2 = 3 v 2 = 3 v 2 = 4 v 2 = 4

Log[N

0v2l2 01

/N 0⋅g]

T i m e ( s )

Figure 3.3: Normalized density of different states of the CO2 bending mode ofvibration, for p = 5 Torr, I = 50 mA, and ∆t = 5 ms.

the validity of the CO2 vibrational kinetic scheme presented in this work. Thesteady-state regime at the end of the afterglow is observed starting at ∼ 10−2 sfor the various CO2 levels presented in the figure 3.3. This is the result ofthe thermal equilibrium that is established at that time so that the calculatedpopulation of each level corresponds to the Boltzmann distribution. Note thatthe experimental data do not reach the region of this thermal equilibrium.

A comparison between the experimental and modeling results for the othermodes of vibration, is shown in figure 3.4; the relaxation of the first level ofthe asymmetric mode is shown in panel a), whilst the first two levels of thesymmetric mode, CO2(10002) and CO2(20003) are presented in the panel b) ofthe same figure. It is easily seen that the characteristic relaxation times are ofthe same order as observed in figures 3.2 and 3.3. In the first panel, one mayobserve some discrepancy between the calculated and measured values at theend of the post-discharge. The measured data exhibit a slightly faster decay,than what the model predicts. This comparison can be improved by includingspontaneous emission, as shown later.

72

3.8. Results

- 1 0

- 9

- 8

- 7

- 6

- 5

- 4

1 0 - 6 1 0 - 5 1 0 - 4 1 0 - 3 1 0 - 2 1 0 - 1

- 1 1- 1 0- 9- 8- 7- 6- 5- 4- 3- 2

C O 2 ( 0 0 0 1 1 ) - 5 T o r r

E x p e r i m e n t M o d e l

Log[N

000 11

))/N0)⋅g

]

a )

b )

C O 2 ( v 1 0 0 0 f ) - 5 T o r r ( E x p e r i m e n t ) ( M o d e l )

v 1 = 1 v 1 = 1 v 1 = 2 v 1 = 2

Log[N

v100 0f/N

0⋅g]

T i m e ( s )

Figure 3.4: Normalized density of a) first CO2 vibrational level of the asymmetricmode and b) different CO2 vibrational levels of the symmetric mode of vibration. Theexperimental conditions are p = 5 Torr, I = 50 mA, and ∆t = 5 ms.

A usual way of describing the degree of vibrational excitation and non-equilibrium of CO2 is by the “temperatures” of each normal mode, calculatedfrom the populations of the corresponding excited levels. These temperaturesare obtained from the actual densities of the individual CO2 vibrational levels.For instance, the characteristic temperature of the asymmetric mode, T3, isobtained by fitting the calculated densities of the CO2(000ν31) levels, withν3 = 1 − 5, to a Boltzmann distribution. The characteristic temperature ofthe effective symmetric (which include the Fermi resonant states) and bendingmodes, T1 and T2, respectively, are also obtained from Boltzmann plots. Indeed,

73

Chapter 3. Relaxation of vibrational energy in CO2 discharges

1 2 3 4 5

- 2 5

- 2 0

- 1 5

- 1 0

- 5

0

A s s y m m e t r i c B e n d i n g 0 s 0 s 1 0 - 4 s 1 0 - 4 s 1 0 - 3 s 1 0 - 2 s

v

Log[N

v/N0⋅g]

Figure 3.5: Vibrational distribution functions calculated for the CO2 asymmetricstretching mode (dashed line) and the bending mode of vibration (solid line) atdifferent times in the afterglow, for p = 5 Torr, I = 50 mA.

the calculated vibrational distribution functions of the asymmetric and bendingvibrational modes during the afterglow shown in figure 3.5 are very close tostraight lines. Figure 3.6 illustrates the comparison between the experimentaland modeling results of the characteristic vibrational temperatures, T3 and T12,for different experimental conditions of the pulsed DC glow discharge. Panel a)shows the temporal evolution of the vibrational and gas temperatures for thesingle-pulse experiment. The very good agreement between the simulation andthe experiment is expected, as the individual densities shown in figures 3.2, 3.3and 3.4 already exhibit the good agreement with the measurements.

Figure 3.6b) presents experimental data corresponding to different operatingconditions. The pressure and current have the same values as in the single-pulseexperiment. However, the flow rate is smaller (7.4 sccm) and the pulse on-offcycle is 5-10 ms. According to this conditions, it is expected to observe an accu-mulation of the CO2 decomposition products. For this reason, the experimentalresults are compared to the calculations obtained with the CO2 partial pressure,using the experimentally determined decomposition fraction. The calculationsshow a slightly slower relaxation than in the experiment. Therefore, this effectmight be attributed to the influence of CO2 decomposition product and theircontribution to the evolution of the CO2 vibrational population. Figure 3.6

74

3.8. Results

4 0 0

6 0 0

8 0 0

4 0 0

6 0 0

8 0 0

1 0 0 0

1 0 - 6 1 0 - 5 1 0 - 4 1 0 - 3 1 0 - 2 1 0 - 1

4 0 0

6 0 0

8 0 0

1 0 0 0

3 T o r r ( M u l t i - p u l s e m e a s u r e m e n t )

c )

b )

E x p e r i m e n t T 3 T 1 2 T g

M o d e l T 1 2 T 3

5 T o r r ( M u l t i - p u l s e m e a s u r e m e n t )

5 T o r r ( S i n g l e - p u l s e m e a s u r e m e n t )

a )

Temp

eratur

e (K)

T i m e ( s )

Figure 3.6: Temporal evolution of the vibrational temperatures T3 and T12 for threedifferent experimental conditions. a) Single-pulse experiment, detailed in section 3.7.b) Multi-pulse experiment, with 5-10 ms on-off time and p = 5 Torr. c) Multi-pulseexperiment, with 5-10 ms on-off time and p = 3 Torr. The gas temperature profilesare represented by cross symbols.

c) shows the values of the temperatures corresponding to a pressure of 3 Torrand 5-10 ms duty cycle. In this case, the agreement between the experimentand the modeling results is still fairly good, with slightly slower relaxation of

75

Chapter 3. Relaxation of vibrational energy in CO2 discharges

- 1 0

- 8

- 6

- 4

1 0 - 5 1 0 - 4 1 0 - 3 1 0 - 2 1 0 - 1- 1 0

- 8

- 6

- 4

C O 2 ( 0 0 0 1 1 ) - 5 T o r r ( s i n g l e - p u l s e ) E x p e r i m e n t M o d e l ( r a d i a t i o n ) M o d e l ( n o r a d i a t i o n )

a )

C O 2 ( 0 0 0 1 1 ) - 3 T o r r ( m u l t i - p u l s e ) E x p e r i m e n t M o d e l ( r a d i a t i o n ) M o d e l ( n o r a d i a t i o n )

Log[N

000 11

/N 0⋅g]

T i m e ( s )

b )

Figure 3.7: Normalized density of CO2(00011) with and without the spontaneousemission included. The experimental conditions in a) are p = 5 Torr, I = 50 mA, and∆t = 5 ms, whilst the pressure is p = 3 Torr for the multi-pulse experiment shown inb).

the simulation prediction. Nevertheless, it can be seen that even with thatour simplified kinetic scheme (with a correction of the pressure) leads to areasonable description of the experimental observations for the afterglow andcan be used as a basis for their interpretation even for a multi-pulse experiment,where the CO2 decomposition products are present.

The effect of the spontaneous emission was examined by including theradiative transfer from several CO2 vibrational levels that give rise to theinfrared spectra of CO2. The absorption of radiation is, however, not consideredin our calculations, so the loss of vibrational quanta by spontaneous emission is

76

3.9. Conclusions

not compensated by the corresponding inverse reactions. Figure 3.7 shows thepopulation of the first vibrational level of the asymmetric mode measured in : a)the single-pulse experiment at 5 Torr, and b) in the multi-pulse experiment, at3 Torr. The results show that inclusion of the spontaneous emission processesleads to a slightly faster decay of vibrationally excited states, giving a betteragreement with experimental data. This is a consequence of the rather highspontaneous emission coefficients for the vibrationally excited levels of theasymmetric mode of vibration.

3.9 Conclusions

We have developed a kinetic model describing the temporal evolution of severalindividual CO2 vibrational levels during the afterglow of a CO2 discharge,under a low excitation regime. A total of 72 vibrational levels was considered,corresponding to νmax1 = 2, νmax2 = 5 and νmax3 = 5. The creation and lossmechanisms for these CO2 vibrational levels were considered, including V-V andV-T energy exchanges. The modeling results were compared to the measureddensities of CO2 vibrationsl states, presented in the FTIR study of Klarenaaret al [9]. The good comparison between the experimental data obtained bytime-resolved in situ FTIR spectroscopy in a pulsed DC glow discharge andthe simulation results served as a validation of the model.

By directly comparing the afterglow dynamics of various individual vibra-tionally excited levels, as pursued in this work, we have established the V–Tand V–V reaction mechanism for the levels taken into account and defineda set of elementary processes and corresponding rate coefficients validatedagainst suitable experiments. In this context, with the strength of this model,future work can be built on the firm bases established here. Despite the goodagreement between the experimental data and our model predictions, there arestill many open challenges and directions to pursue for further investigation.For instance, the study of higher excitation of CO2 molecules and influence ofCO2 decomposition products on the overall kinetics. This will allow furtherapplications of the model to realistic plasma conditions. This effort will involvecomputation of the rate coefficients for the energy transfers between the colli-sional partners that are not considered in this model, such as CO2-CO, CO2-O,CO-CO, etc.

The major future challenge is the calculation of the reaction rates relatedto highly excited CO2 levels. It was mentioned in this work that first-orderperturbation theories, namely the SSH and SB approaches, are suitable for de-scribing of CO2 vibrations under low excitation regimes. However, an extensivestudy related to the scaling of vibrational rates up to the dissociation limitmust be undertaken. Special attention must be paid to the rate coefficientsof the V–V energy exchanges on the asymmetric stretching mode (V–V3), a

77

Chapter 3. Relaxation of vibrational energy in CO2 discharges

process that is critical for the accurate calculation of CO2 dissociation rates,for two reasons: on the one hand, they quickly become unrealistically large forhigher quantum numbers than those considered here if no correction is made tothe first-order perturbation theories; on the other hand, their dependence isaltered as Tg increases, corresponding to an evolution from a regime dominatedby long-range interactions (described by the SB theory) to one dominated byshort-range interactions (described by the SSH theory).

78

3.10. References

3.10 References

[1] C. K. N. Patel, “Selective excitation through vibrational energy transferand optical maser action in N2-CO2,” Phys. Rev. Lett., 13, 617–619, 1964.

[2] A. Fridman, Plasma chemistry. Cambridge: Cambridge University Press,2008.

[3] G. B. F. Capitelli M, Ferreira C M and O. A. I, Plasma Kinetics inAtmospheric Gases. Berlin: Springer, 2000.

[4] L. D. Pietanza, G. Colonna, G. D’Ammando, A. Laricchiuta, andM. Capitelli, “Electron energy distribution functions and fractional powertransfer in ”cold” and excited CO2 discharge and post discharge conditions,”Phys. Plasmas, 23, 013515, 2016.

[5] I. Armenise and E. Kustova, “Sensitivity of heat fluxes in hypersonic CO2

flows to the state-to-state kinetic schemes,” AIP Conf. Proc., 1786, 1–8,2016.

[6] I. Armenise and E. V. Kustova, “State–to–state models for CO2 molecules:From the theory to an application to hypersonic boundary layers,” Chem.Phys., 415, 269–281, 2013.

[7] V. Guerra, T. Silva, P. Ogloblina, M. Grofulovic, L. Terraz,M. Lino da Silva, C. D. Pintassilgo, L. L. Alves, and O. Guaitella, “Thecase for in situ resource utilisation for oxygen production on mars by non-equilibrium plasmas,” Plasma Sources Sci. Technol., 26, 11LT01, 2017.

[8] T. Kozak and A. Bogaerts, “Splitting of CO2 by vibrational excitation innon-equilibrium plasmas: a reaction kinetics model,” Plasma Sources Sci.Technol., 23, 045004, 2014.

[9] B. L. M. Klarenaar, R. Engeln, D. C. M. van den Bekerom, M. C. M.van de Sanden, A. S. Morillo-Candas, and O. Guaitella, “Time evolutionof vibrational temperatures in a CO2 glow discharge measured with infraredabsorption spectroscopy,” Plasma Sources Sci. Technol., 26, 115008, 2017.

[10] T. Silva, M. Grofulovic, B. L. M. Klarenaar, O. Guaitella, R. Engeln,C. D. Pintassilgo, and V. Guerra, “Kinetic study of CO2 plasmas undernon–equilibrium conditions. I. Relaxation of vibrational energy,” PlasmaSources Sci. Technol., 27, 015019, 2018.

[11] M. Capitelli, G. Colonna, G. D’Ammando, and L. D. Pietanza, “Self-consistent time dependent vibrational and free electron kinetics for CO2

dissociation and ionization in cold plasmas,” Plasma Sources Sci. Technol.,26, 055009, 2017.

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Chapter 3. Relaxation of vibrational energy in CO2 discharges

[12] V. Guerra, P. A. Sa, and J. Loureiro, “Relaxation of the electron energydistribution function in the afterglow of a N2 microwave discharge includingspace-charge field effects,” Phys. Rev. E, 63, 046404, 2001.

[13] T. Silva, M. Grofulovic, L. Terraz, C. D. Pintassilgo, and V. Guerra,“Modelling the input and relaxation of vibrational energy in CO2 plasmas,”J. Phys. D: Appl. Phys., 51, 464001, 2018.

[14] F. D. Shields, C. C. Warf, and H. E. Bass, “Acoustical method of obtainingvibrational transition rates tested on CO2/N2 mixtures,” J. Chem. Phys.,58, 3837–3840, 1973.

[15] R. E. Center, “Vibrational relaxation of CO2 by O atoms,” J. Chem.Phys., 59, 3523–3527, 1973.

[16] R. Huddleston and E. Weitz, “A laser-induced fluorescence study of energytransfer between the symmetric stretching and bending modes of CO2,”Chem. Phys. Lett., 83, 174 – 179, 1981.

[17] A. P. W and F. R, Molecular Quantum Mechanics. Cambridge: New York:Oxford University Press, 2005.

[18] D. Rapp and T. Kassal, “Theory of vibrational energy transfer betweensimple molecules in nonreactive collisions,” Chemical Reviews, 69, 61–102,1969.

[19] R. N. Schwartz, Z. I. Slawsky, and K. F. Herzfeld, “Calculation of vibra-tional relaxation times in gases,” J. Chem. Phys., 20, 1591–1599, 1952.

[20] V. Joly and A. Roblin, “Vibrational relaxation of CO2(m,nl, p) in a CO2-N2 mixture. part 1: Survey of available data,” Aerosp. Sci. Technol., 3,229 – 238, 1999.

[21] K. F. Herzfeld, “Deactivation of vibration by collision in CO2,” Discuss.Faraday Soc., 33, 22–27, 1962.

[22] K. F. Herzfeld, “Deactivation of vibrations by collision in the presence offermi resonance,” The Journal of Chem. Phys., 47, 743–752, 1967.

[23] T. Kozak and A. Bogaerts, “Evaluation of the energy efficiency of CO2

conversion in microwave discharges using a reaction kinetics model,” PlasmaSources Sci. Technol., 24, 015024, 2015.

[24] A. Sahai, B. Lopez, C. Johnston, and M. Panesi, “A reduced order max-imum entropy model for chemical and thermal non-equilibrium in hightemperature CO2 gas,” in 46th AIAA Thermophysics Conference, Ameri-can Institute of Aeronautics and Astronautics Inc, AIAA, 2016.

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[25] W. A. Rosser, A. D. Wood, and E. T. Gerry, “Deactivation of vibrationallyexcited carbon dioxide (ν3) by collisions with carbon dioxide or withnitrogen,” The Journal of Chem. Phys., 50, 4996–5008, 1969.

[26] W. A. Rosser, R. D. Sharma, and E. T. Gerry, “Deactivation of vibrationallyexcited carbon dioxide (001) by collisions with carbon monoxide,” TheJournal of Chem. Phys., 54, 1196–1205, 1971.

[27] R. L. Taylor and S. Bitterman, “Survey of vibrational relaxation data forprocesses important in the CO2-N2 laser system,” Rev. Mod. Phys., 41,26–47, 1969.

[28] M. L. da Silva, J. Loureiro, and V. Guerra, “A multiquantum datasetfor vibrational excitation and dissociation in high-temperature O2–O2

collisions,” Chem. Phys. Letters, 531, 28 – 33, 2012.

[29] M. L. da Silva, V. Guerra, and J. Loureiro, “State-resolved dissociationrates for extremely nonequilibrium atmospheric entries,” J. Thermophys.Heat. Tr., 21, 40–49, 2007.

[30] I. V. Adamovich, S. O. MacHeret, J. W. Rich, and C. E. Treanor, “Vibra-tional Energy Transfer Rates Using a Forced Harmonic Oscillator Model,”J Thermophys. Heat Transfer, 12, 57–65, 1998.

[31] D. A. Andrienko and I. D. Boyd, “Rovibrational energy transfer anddissociation in O2–O collisions,” The Journal of Chem. Phys., 144, 104301,2016.

[32] M. Bartolomei, F. Pirani, A. Lagana, and A. Lombardi, “A full dimensionalgrid empowered simulation of the CO2 + CO2 processes,” Journal ofComputational Chemistry, 33, 1806–1819, 2012.

[33] A. Lombardi, N. Faginas-Lago, L. Pacifici, and G. Grossi, “Energy transferupon collision of selectively excited CO2 molecules: State-to-state crosssections and probabilities for modeling of atmospheres and gaseous flows,”The Journal of Chem. Phys., 143, 034307, 2015.

[34] J. A. Blauer and G. R. Nickerson, “A survey of vibrational relaxation ratedata for processes important to CO2–N2–H2O infrared plume radiation,”Report Ultrasystems, Inc., 1973.

[35] K. N. Seeber, “Radiative and collisional transitions between coupled vibra-tional modes of CO2,” J. Chem. Phys., 55, 5077–5081, 1971.

[36] R. D. Sharma and C. A. Brau, “Energy transfer in near-resonant molecularcollisions due to long-range forces with application to transfer of vibrationalenergy from ν3 mode of CO2 to N2,” J. Chem. Phys., 50, 924–930, 1969.

81

Chapter 3. Relaxation of vibrational energy in CO2 discharges

[37] T. G. Kreutz, J. A. O’Neill, and G. W. Flynn, “Diode laser absorptionprobe of vibration-vibration energy transfer in carbon dioxide,” J. Phys.Chem., 91, 5540–5543, 1987.

[38] R. T. Pack, “Analytic estimation of almost resonant molecular energytransfer due to multipolar potentials. VV processes involving CO2,” J.Chem. Phys., 72, 6140–6152, 1980.

[39] L. S. Rothman, R. L. Hawkins, R. B. Wattson, and R. R. Gamache,“Energy levels, intensities, and linewidths of atmospheric carbon dioxidebands,” J. Quant. Spectrosc. Radiat. Transfer, 48, 537–566, 1992.

82

Chapter 4

Kinetic study of CO2 plasmasunder non-equilibriumconditions: input of vibrationalenergy

This chapter continues the investigation of vibrational energy exchanges in non-equilibrium CO2 plasmas in low-excitation conditions. The previous chapteraddresses a theoretical and experimental investigation of the time relaxation of∼ 70 individual vibrational levels of ground-state CO2(X 1Σ+) molecules duringthe afterglow of a pulsed DC glow discharge, operating at pressures of a few Torrand discharge currents around 50 mA, where the rate coefficients for vibration-translation (V-T) and vibration-vibration (V-V) energy transfers among theselevels are validated. Herein the investigation is focused on the active discharge,by extending the model with the inclusion of electron impact processes forvibrational excitation and de-excitation (e-V). The time-dependent calculateddensities of the different vibrational levels are compared with experimental dataobtained from time-resolved in situ Fourier Transform Infrared spectroscopy.It is shown that the vibrational temperature of the asymmetric stretchingmode is always larger than the vibrational temperatures of the bending andsymmetric stretching modes along the discharge pulse, the latter two remainingvery nearly the same and close to the gas temperature. The general goodagreement between the model predictions and the experimental results validatesthe e-V rate coefficients used and gives confidence that the proposed kineticscheme provides a solid basis to understand the vibrational energy exchangesoccurring in CO2 plasmas.1

1The results presented here were published as Kinetic study of CO2 plasmas undernon-equilibrium conditions. II. Input of vibrational energy, M. Grofulovic, T. Silva, B. L. M.

83

Chapter 4. Input of vibrational energy in CO2 discharges

Klarenaar, A.S. Morillo-Candas, O. Guaitella, R. Engeln, C.D. Pintassilgo, V. Guerra, 2018Plasma Sources Science and Technology, 27, 115009.

84

4.1. Introduction

4.1 Introduction

The modelling of CO2 plasmas under non-equilibrium conditions has been thesubject of considerable interest in the past decades, with a significant attentiondrawn in the more recent years. The first studies were associated with thediscovery of the CO2 laser [1, 2], while more recent works are mainly motivatedby environmental issues [3, 4], aerospace applications [5–8] and focus on CO2

dissociation. Progress in any plasma technology that uses molecular gasesis indissolubly linked with the understanding of the various kinetics involved(i.e. electron, vibrational, chemical and surface kinetics) and their coupling.For plasma-based CO2 conversion, a central piece of the puzzle to be solvedresides in a deep understanding of the detailed mechanisms of the up-pumpingof vibrational quanta along the vibrational ladder [9]. Indeed, the main ideabehind the process of plasma CO2 decomposition is that the non-equilibriumnature of the plasma provides promising conditions for the energetically efficientCO2 dissociation. The typical energy of the electrons in the plasma stronglyfavours vibrational excitation, promoting the input of vibrational quanta inlow levels and subsequent up-pumping during relaxation [9], while keeping thegas temperature relatively low and thus limiting the losses into gas heating.The vibrationally excited molecules can then become more reactive and lead todissociation at a low energy cost.

State-to-state kinetic models, where the different vibrational levels aretreated as independent species, constitute a powerful tool to investigate thevibrational energy transfer and relaxation in molecular plasmas. However, al-though the ladder climbing mechanism is relatively well understood for diatomicgases [10], an accurate description and study of vibrational energy exchangesin polyatomic gases such as CO2 remains very challenging. The underlyingreason is the complex geometry of the CO2 molecule, which has four vibrationalmodes (one symmetric stretching mode, two degenerate bending modes, andone asymmetric stretching mode) resulting in a multitude of vibrational levelsand a large number of reactions. Another difficulty is the lack of knowledgerelated to CO2 rate coefficients for energy exchanges between the translationaland vibrational degrees of freedom (V-T transitions) and among the vibrationallevels (V-V transitions). Additionally, there are no cross sections available forthe manifold of electron-impact direct and stepwise excitation of vibrationallyexcited states (e-V processes). Therefore, the state-to-state modelling of CO2

discharges is currently impossible without involving approximate theories forscaling over scarce data to obtain the inaccessible rates.

Several strategies to tackle the problem have been proposed in the last fewyears. Kozak and Bogaerts [4] have modelled microwave and dielectric barrierdischarges, taking into account only a few low-lying symmetric stretching andbending mode levels, whilst the asymmetric mode levels (000n) are includedup to a dissociation energy of 5.5 eV assuming the energy levels of a Morse

85

Chapter 4. Input of vibrational energy in CO2 discharges

oscillator (corresponding to n = 21 bound vibrational levels). Despite theconsiderable success of this model and the breakthrough it represents, some ofthe rate coefficients it considers are disputable [11] and the formulation neglectsto a large extent inter-mode coupling and the increased density of levels near thecontinuum, an idealisation of the system that may prove appropriate but requiresfurther investigation. A similar approach was adopted by the Bari group, whichaddresses in detail the dependence of the electron energy distribution function onthe concentration of electronically and vibrationally excited states [3]. The studyof vibrational kinetics in the hypersonic boundary layer of reentering bodies inthe Mars atmosphere in a dissociation-recombination regime by Armenise andKustova [6] contains several thousand levels and disregards free electrons. In amore recent work by Armenise [12] electrons are included in the kinetic scheme,which nevertheless accounts only a very limited number of electron impactprocesses. This very impressive and detailed model is difficult to apply atpresent to the description of gas discharges, due to the too extensive vibrationalkinetics and the very simplified electron kinetic scheme. Another possibility,suggested by Gordiets et al [13, 14], is to divide vibrational levels into multipletswith an equilibrium distribution of the levels within each multiplet.

In this study we follow a different approach, aimed at understanding vi-brational energy transfers in CO2 plasmas. Specifically, we develop a detailedmodel accounting for the vibrational kinetics of the lower levels of each vibrationmode and of the lower mixed levels, with the relevant rate coefficients beingvalidated in sequential steps. In chapter 3 we have analysed the vibrationalrelaxation in the afterglow of a DC pulsed discharge at pressures p = 3− 5 Torrand discharge current I = 50 mA and validated the rate coefficients used todescribe the vibration-translation (V-T) and vibration-vibration (V-V) energyexchanges. The simple geometry and homogeneity of pulsed DC dischargesmake them accessible to a series of diagnostics and suitable to the developmentof 0D self-consistent kinetic models accounting for very complex vibrational andchemical kinetics. For this reason, they are ideal for fundamental studies, bothexperimental [15, 16] and theoretical [10, 17]. We now extend the model to theactive discharge, with the inclusion of electron impact processes of vibrationalexcitation and de-excitation (e-V) and ionization, in order to gain insight intothe input of vibrational energy in the plasma by electron impact and to validatethe electron impact cross sections and rate coefficients for the individual e-Vprocesses taken into account.

The definition of the relevant e-V transitions to consider and the choice of therespective cross sections is far from straightforward. On the one hand, the crosssections available from swarm derived sets include only a very limited numberof individual collisional processes. Moreover, most of these cross sections referto “energy losses” corresponding to the excitation of lumped levels [18]. It istherefore necessary to establish procedures to deconvolute the original crosssections and to calculate the missing ones, such as Fridman’s approximation

86

4.2. Description of the model

[4, 9]. On the other hand, a set of cross sections for the resonant excitation of upto 10 vibrational levels in each mode was recently calculated by Laporta and co-workers using R-matrix codes [19]. These new data are very exciting and opennew possibilities for research, but are still difficult to use in state-to-state models.In fact, although the calculations seem to provide results for the symmetricstretching mode in good agreement with data from the literature, non-resonantcontributions may be of importance for the bending and asymmetric modes.

The current model couples the electron Boltzmann equation, using the usualtwo-term expansion approximation, and a system of rate balance equationsdescribing the creation and loss of both the low vibrational levels of CO2 andof CO+

2 ions. The e-V processes’ cross sections are obtained from a directdeconvolution of the available lumped cross sections according to the statisticalweights of the various levels and the missing cross sections are generated usingFridman’s approximation. The model is validated through the comparison ofthe calculated time-dependent concentrations of several individual vibrationallevels of CO2 with the experimental results obtained in a millisecond pulsedglow discharge.

The organization of the chapter is the following. Section 4.2 gives a generaldescription of the kinetic model developed to describe the CO2 plasma inlow-excitation regime and the selection of the collisional data. The details onvibrational and electron kinetics are presented in sections 4.3 and 4.4 respectively.A description of the method employed to calculate the maintenance electricfield is given in section 4.5. Section 4.6 presents the comparison betweenthe measured and calculated time-dependent densities of various vibrationallyexcited CO2 levels and the discussion of the results. Finally, the conclusionsare given in the section 4.7.

4.2 Description of the model

The kinetic model developed here studies millisecond pulsed DC dischargesand their afterglows, under low-pressures of a few millibars. The two coupledmodules can be distinguished, one describing the post-discharge and the otheris dedicated to the active discharge study. The post-discharge is analysed in theprevious chapter, while here we are continuing the study of the same type ofdischarges during the pulse, by extending the model with additional processesinvolving electron kinetics.

The input parameters in the simulations are the discharge pressure, current,pulse length and the tube radius and gas temperature profile taken fromexperiments. The time-dependent electron density profile is estimated from themeasured temporal variations of the discharge current and electric field, whileassuming an exponential growth estimated from the CO2 ionization coefficient

87

Chapter 4. Input of vibrational energy in CO2 discharges

and ensuring that the self-consistent value obtained for the steady-state currentat the end of the pulse matches the input parameter to the model.

The discharge module couples the solutions to the homogeneous electronBoltzmann equation and a system of rate balance equations for various individualvibrational levels of CO2(X 1Σ+) and for CO+

2 ions. This system takes intoaccount the processes of excitation and de-excitation of the vibrational levelsby electron impact (e-V processes), vibration-vibration (V-V) and vibration-translation (V-T) energy exchanges, electron impact ionization and ambipolardiffusion to the wall. Using the rate coefficient 6.6×10−8 cm3s−1 reported in [3],we estimate that the loss rate of charged particles by electron-ion recombinationis about 25–50 times smaller than by ambipolar diffusion.

The model describes CO2 discharges in a low excitation regime, where onlya few vibrational levels are excited, namely the levels corresponding to quantumnumbers up to νmax1 = 2 and νmax2 = νmax3 = 5, where ν1, ν2 and ν3 are thevibrational quantum numbers associated with the symmetric stretching, bendingand asymmetric stretching modes,respectively. The low excitation conditionsare met in experiment considered in this work, with millisecond pulse durationand a discharge current of 50 mA.

The self-consistent reduced electric field is determined from the electronand ion rate balance equations, using the requirement that under steady-stateconditions the total rate of ionization must compensate the rate of electron lossby ambipolar diffusion to the wall, under the assumption of a quasi-neutraldischarge. Once the self-consistent sustaining field and electron density areobtained for a steady-state situation, the system of rate balance equationsfor the heavy particles is solved in time for the length of the pulse, using theelectron excitation rates derived for the steady-state case. This is obviously anapproximation, but it has proved very satisfactory in the study of O2, N2-O2 andN2-CH4 pulsed discharges in previous works [17, 20–22]. As initial conditionsfor the system of rate balance equations, the populations of various vibrationallevels are assumed to follow a Boltzmann distribution corresponding to theexperimental initial vibrational temperatures. The solutions corresponding tothe end of the discharge pulse are then used as initial conditions for the post-discharge module. Both modules solve the system of rate balance equationsincluding the same V-T and V-V exchanges, while taking into account theelectron impact processes in the discharge module.

4.3 Vibrational kinetics

The CO2 molecule in its ground electronic state is linear and possesses threenormal vibrational modes: the symmetric stretching, the double degeneratebending vibration and the asymmetric stretching. These modes are characterizedby quantum numbers ν1, ν2 and ν3 respectively. The degeneracy of the bending

88

4.3. Vibrational kinetics

vibration mode requires one more quantum number to fully describe the CO2

vibrational state, l2, associated with an angular momentum, which can take thevalues l2 = ν2, ν2 − 2, ν2 − 4, ...1 or 0. The vibrational state of the molecule canthen be identified in principle as CO2(ν1ν

l22 ν3). However, polyatomic molecules,

due to their multidimensional nature, commonly exhibit the so-called “Fermiresonance,” which refers to an accidental energy degeneracy between certainvibrational modes. In the case of CO2, the modes ν1 and 2ν2 have very closevibrational energies and the same type of symmetry, resulting in a couplingbetween the CO2(ν1ν

l22 ν3) and CO2((ν1 − 1)(ν2 + 2)l2ν3) levels to form new

states that are assumed to be in local equilibrium. Note that all the vibrationallevels coupled together have the same orbital quantum number l2, since thosewith different l2 cannot perturb each other [23].

Following [11], in the present model the CO2 vibrational levels under Fermiresonance are considered as one single effective level. The vibrational energy ofthis effective level is determined through the average of the vibrational energiesof all the individual levels in the effective level, calculated using the anharmonicoscillator approximation [24], while its statistical weight is determined throughthe sum of the statistical weights of the individual states. These effective levelsare denoted in this work by CO2(ν1ν

l22 ν3f), where the ν1, ν2 and ν3 quantum

numbers correspond to the level with highest ν1; the ranking number f is alwaysequal to ν1+1 and indicates how many individual levels are accounted for inthe effective level. For instance, the level CO2(20003) stands for the coupling ofthe three levels CO2(2000), CO2(1200) and CO2(0400).

A detailed description of the vibrational energy exchanges in molecularcollisions requires the knowledge of the corresponding state-specific V-T and V-V rate constants, which are available for several vibrational transitions betweenthe lowest states. This is, however, not sufficient for a full characterization ofthe vibrational kinetics, since the rate coefficients of many other transitionsare still missing. For this reason, there has been an extensive effort along theyears to develop theories to calculate unavailable rate coefficients for vibrationalenergy transfers [25–29]. In this work, we use the rate constants for the low-lying levels given in the survey of Blauer and Nickerson [30], while for thehigher levels and missing transitions we have used the scaling laws based onthe Schwartz-Slawsky-Herzfeld (SSH) [25] and Sharma-Brau (SB) [27] theories.

Despite its limitations, the SSH theory provides a fairly simple expressionfor the rate constants and it is commonly used in many kinetic models withevident success [3, 4, 6, 7]. The current low-excitation conditions do notinvolve transitions with too high probabilities and the first order perturbationapproaches of the SSH and SB theories were shown to be valid [11]. The situationis different regarding collisions of highly vibrationally excited molecules and/orhigh gas temperatures (Tg >1500 K), as pointed out in [11]. The thoroughanalysis of the vibrational energy relaxation in the CO2 post-discharge is

89

Chapter 4. Input of vibrational energy in CO2 discharges

1 0 1 0 0

0

2 0

4 0

6 0

8 0

1 0 0 0 . 2 9 e V ( 0 0 0 1 ) 0 . 1 7 e V ( 1 0 0 0 ) 0 . 0 8 e V ( 0 1 1 0 ) o t h e r m o d e s d i s s o c i a t i o n i o n i z a t i o n e l . e x c i t .

T e = 2 e V

η (%)

E / N ( T d )

T e = 1 e V

Figure 4.1: Fraction of electron energy transferred to different channels of vibrationalexcitation, electronic excitation, dissociation and ionization of CO2, as a function ofthe reduced electric field (E/N ), calculated from the corresponding cross sections ofthe electron impact reactions.

presented in the previous chapter, where the rate constants for the V-T andV-V energy exchanges used here have been validated.

4.4 Electron kinetics

The electron energy distribution function (EEDF) is self-consistently calculatedby solving the steady-state, homogeneous electron Boltzmann equation inthe two-term expansion approximation. The electron Boltzmann equation issolved taking into account elastic and inelastic collisions between electronsand CO2(X 1Σ+) molecules, including vibrational excitation energy losses(corresponding either to the excitation of individual levels or of groups ofvibrational levels), superelastic collisions with CO2 vibrational excited states,excitation of two groups of electronic states and ionization. The complete andconsistent cross sections set used for calculation of EEDF is available at theIST-Lisbon database published at LXCat and is described in detail in chapter2.

90

4.4. Electron kinetics

Superelastic collisions with vibrationally excited molecules in the dischargedo not affect noticeably the current results due to the low degree of vibrationalexcitation in the conditions under investigation. The same conclusion hasbeen drawn recently by Pietanza et al [31]. Moreover, it has been shown thatsuperelastic collisions with electronically excited states of CO2 can have a stronginfluence in shaping the EEDF in the early instants of the post-discharge [3, 31].However, electron impact processes in the afterglow are not expected to giveany significant contribution to the results in the present conditions, as discussedin section 3.2, and are neglected in our simulations.

Once a validated electron impact cross section set is available, an importantstep in the study of the electron kinetics is to understand in depth how theenergy gained by the electrons from the electric field is transferred throughcollisions into the different channels. Regarding CO2 conversion, the mostrelevant pathways for electron energy transfer are CO2 vibrational excitationand dissociation [9]. In low-pressure discharges, the initial energy input necessaryfor vibrational excitation of stable CO2 molecules is provided by electrons ofenergies ∼1 eV. Figure 4.1 illustrates the fraction of energy transferred fromthe electrons into the different channels of CO2 excitation and ionization, asa function of the reduced electric field, E/N, in a pure CO2 discharge. Thefractional power losses to the different CO2 excitation channels are calculatedas the ratio between the electron energy transferred per unit time and volume,using the cross sections for the corresponding electron-impact reactions [18],and the total power per unit volume gained from the field. The results arein agreement with the literature [9, 31, 32], showing that the major portionof the discharge power is transferred from the plasma electrons to vibrationalexcitation of CO2 molecules when the electron temperature is around 1-2 eV,or, equivalently, for reduced electric fields of about 40-80 Td. At higher reducedelectric fields, the electronic excitation, dissociation and ionization channels areactivated.

Another crucial information provided after the calculation of the EEDF isthe value of the various electron-impact rate coefficients. Regarding the e-Vexcitation from a state i to a state j, the corresponding coefficient is given by

Cij =

√2

m

∫ ∞0

uσij(u)f(u) du (4.1)

where σij is the corresponding cross section, m is the electron mass, u theelectron energy, and f(u) the EEDF, normalized according to the condition∫∞0f(u)√udu = 1. As the cross section set used in this work to calculate the

EEDF includes only a limited number of cross sections corresponding eitherto the excitation of individual levels or groups of vibrational levels from theground level [18], two very challenging steps are the choice of cross sections for:i) the excitation of each individual level that is included in the model from the

91

Chapter 4. Input of vibrational energy in CO2 discharges

ground state; and ii) the transitions between vibrationally excited levels, whilekeeping the compatibility with [18].

In order to deconvolute the cross sections presented in [18] (used to obtainthe EEDF) into the individual cross sections for the levels included in theheavy-particle rate balance equations [11], it is assumed that the electron energyis equally distributed amongst the levels lumped inside each of the cross sectionsconsidered in [18], weighted by the statistical weight of the excited states. Thestatistical weight of a CO2(ν1ν

l22 ν3) level depends only on the l2 quantum

number, being 1 for l2 = 0 and 2 (corresponding to two possible directions ofrotation) otherwise. The statistical weight of a CO2(ν1ν2ν3) level (i.e., includingall possible values of l2 compatible with ν2) depends only on the bending mode,gν1ν2ν3 = ν2 + 1. In practice, if C0j is the rate coefficient for the excitationof the individual level j from the ground-state and Co is the rate coefficientcalculated from the original cross section of the IST-Lisbon data set containingthe required process, the individual electron impact rate coefficient is obtainedfrom

C0j =gjgoCo , (4.2)

where gj and go are the corresponding statistical weights, go corresponding tothe sum of the statistical weights of all the individual levels contained in theoriginal cross section. As an example, the rate coefficient for the excitationof the CO2(11102) level, containing the two degenerate levels CO2(1110) andCO2(0310), with statistical weight g11102 = g0310 + g1110 = 4, is calculated asC11102 = 4

6Cυ3 , where the rate coefficient Cυ3 is calculated using the originalcross section denoted as CO2(υ3) in [18], corresponding to the energy loss at0.252 eV and accounting for the total excitation of the levels (030) and (110)(regardless of the quantum number l2), with statistical weight go = g030 +g110 =4 + 2 = 6 (or, equivalently, go = g0330 + g0310 + g1110 = 2 + 2 + 2 = 6). Thefull list of vibrational excitation processes by electron impact considered in thiswork is given in the table 4.1, accounting for 32 excitations of the ground-stateCO2(00001) molecules and 115 stepwise excitations, as well as the correspondingoriginal cross sections and the fractions gj/go.

For the transitions from the ground state to the higher vibrationally excitedlevels that are not included in any of the cross sections from the data set [18],i.e., j = 2, 3, 4, 5 and i = 0 in the asymmetric mode, we have used the Fridmanapproximation [9], based on the semiempirical formula

Cij =exp[−α(i− j − 1)]

1 + βiC01. (4.3)

This expression allows us to scale an excitation rate coefficient Cij for anytransition between vibrational levels i and j, provided that the rate coefficientsC01 is known. The magnitude of the rate coefficient is altered depending onthe parameters α and β, specific of each plasma species. In the case of CO2,

92

Table 4.1: Electron impact reactions included in the model. The rate coefficients are calculated using the cross sections (andnotation) presented in [18].

No Reaction Cross section Notes1a e + CO2(000i1)→ e + CO2(011i1) υ1 i = 0, 1, 2, 3, 4, 51b e + CO2(0jj01)→ e + CO2(0(j + 1)(j+1)01) υ1 1 ≤ j < 52a e + CO2(000i1)→ e + CO2(022i1) 2/3 υ2a2b e + CO2(0jj01)→ e + CO2(0(j + 2)(j+2)01) 2/3 υ2a3a e + CO2(000i1)→ e + CO2(033i1) 1/3 υ33b e + CO2(0jj01)→ e + CO2(0(j + 3)(j+3)01) 1/3 υ34a e + CO2(000i1)→ e + CO2(044i1) 1/5 υ5b4b e + CO2(01101)→ e + CO2(05501) 1/5 υ5b5 e + CO2(000i1)→ e + CO2(055i1) 1/8 υ66a e + CO2(0ii01)→ e + CO2(0ii11) υ46b e + CO2(1kk02)→ e + CO2(1kk12) υ4 k = 0, 1, 2, 36c e + CO2(2mm03)→ e + CO2(2mm13) υ4 m = 0, 16d e + CO2(000j1)→ e + CO2(000(j + 1)1) υ47a e + CO2(0ii01)→ e + CO2(0ii21) Eq. (4.3)7b e + CO2(1kk02)→ e + CO2(1kk223 Eq. (4.3)7c e + CO2(2mm03)→ e + CO2(2mm23) Eq. (4.3)7d e + CO2(000j1)→ e + CO2(000(j + 2)1) Eq. (4.3)8a e + CO2(0ii01)→ e + CO2(0ii31) Eq. (4.3)8b e + CO2(1kk02)→ e + CO2(1kk32) Eq. (4.3)8c e + CO2(2mm03)→ e + CO2(2mm33) Eq. (4.3)8d e + CO2(000j1)→ e + CO2(000(j + 3)1) Eq. (4.3)9a e + CO2(0ii01)→ e + CO2(0ii41) Eq. (4.3)9b e + CO2(1kk02)→ e + CO2(1kk42) Eq. (4.3)

9c e + CO2(2mm03)→ e + CO2(2mm43) Eq. (4.3)9d e + CO2(00011)→ e + CO2(00051) Eq. (4.3)10a e + CO2(0ii01)→ e + CO2(0ii51) Eq. (4.3)10b e + CO2(1kk02)→ e + CO2(1kk52) Eq. (4.3)10c e + CO2(2mm03)→ e + CO2(2mm53) Eq. (4.3)11a e + CO2(000i1)→ e + CO2(100i2) υ2b11b e + CO2(10002)→ e + CO2(20003) υ2b12 e + CO2(000i1)→ e + CO2(200i3) υ5a+2/10 υ5b13 e + CO2(000i1)→ e + CO2(111i2) 2/3 υ314 e + CO2(000i1)→ e + CO2(122i2) 2/5 υ5b15 e + CO2(000i1)→ e + CO2(133i2) 1/4 υ616 e + CO2(000i1)→ e + CO2(211i3) 3/8 υ6

4.5. Maintenance electric field

α = 0.5 for the asymmetric mode and the value of β is unknown [9], which inour case is irrelevant, since Fridman’s approximation is used only when i = 0.

For the cross sections for the stepwise excitation of levels j from i > 0,we have chosen a different strategy, due to the unknown β parameter, whichwould be necessary for the Fridman approximation. Alternatively, we haveused a simple threshold reduction, by keeping the magnitude and shape ofthe 0→ (j − i) cross section, but with a shift in the threshold to account forthe anharmonicity of the oscillator. This approach has been used for nitrogenin [10] and compared with other hypotheses and more accurate cross sectioncalculations in [33]. Despite the differences between the different approaches,the results and discussion by Colonna et al [33] strongly suggest that this simpleapproximation is appropriate in the present context.

Different scaling laws can be used to obtain the unknown cross sectionsand the determination of the best choice of cross sections for electron collisionsinvolving transitions between vibrational levels of CO2 is still subject to largeuncertainties. This subject will be further investigated in the future.

The rate constants for superelastic collisions are obtained from the Klein-Rosseland relation

σji(u) =gigj

u+ Eiju

σij(u+ Eij) , (4.4)

which represents the microscopic reversibility of the collision processes.

4.5 Maintenance electric field

The value of maintenance reduced electric field during the pulse is obtainedby solving the continuity equations for the positive ions CO+

2 , coupled to thesystem of equations for vibrational levels and adopting the quasineutrality ofthe discharge. The crucial requirement is that under steady-state conditionsthe total rate of ionization must compensate exactly for the rate of electron lossby ambipolar diffusion to the wall. In the presence of n species of positive ions,the ambipolar diffusion coefficient for a certain species i, Da,i, reads

Da,i = Di − µi

∑n+1j=1 njDj∑n+1j=1 njµj

i = 1, ...., n+ 1,

where Di and µi are the free diffusion coefficient and the mobility for the speciesi and the species with index n+1 corresponds to electrons [10]. Accordingly,the values of Dn+1 and µn+1 are negative, as well as the value of the electrondensity nn+1 = −ne. In the present case, the only positively charged particlesincluded in the model are CO+

2 ions and the expression above simplifies to theusual expression [9]. In the calculation of the ambipolar diffusion coefficient we

95

Chapter 4. Input of vibrational energy in CO2 discharges

use the mobility of CO+2 in CO2 given in [34], whilst the corresponding free

diffusion coefficients is calculated using the Einstein relation, as suggested in[35].

1 0 - 5 1 0 - 4 1 0 - 3 1 0 - 22

3

4

5

6

7

8

Electr

on de

nsity

(109 cm

-3 )

T i m e ( s )

Figure 4.2: The electron density profile estimated from the temporal evolution ofthe discharge current and electric field.

4.6 Results and discussion

This section presents and discusses the results of the model, together with thecomparison with pertinent experimental data reported in [15]. All the resultsshown here correspond to the active part of the ‘single pulse’ measurement,i.e., p = 5 Torr, I = 50 mA for a pulse of 5 ms and 150 ms off time (seesection 3.7), during the active part of the discharge. The calculated value ofthe reduced electric field in these conditions is E/N = 55 Td, in excellentagreement with the measured value at the end of the pulse, which is around54 Td. Except otherwise noted, the measured time-resolved gas temperatureprofile from [15] (reproduced in figure 4.9) is used as an input to the model,while the electron density profile is estimated from the temporal evolution ofthe discharge current and electric field, as discussed in section 3.2. To facilitatethe discussion, this set of conditions is hereafter referred to as the “referencemodel.” The time-dependent electron density profile is shown in figure 4.2.The steady-state value ensures the self-consistent calculation of the dischargecurrent to match the experimental value I = 50 mA.

96

4.6. Results and discussion

1 0 - 6 1 0 - 5 1 0 - 4 1 0 - 3 1 0 - 2

- 1 4

- 1 2

- 1 0

- 8

- 6

- 4

C O 2 ( 0 0 0 ν3 1 ) M o d e l

E x p e r i m e n t : ν3 = 1 ν3 = 2

Log[N

v3/N 0⋅g]

T i m e ( s )

Figure 4.3: Normalized density of the CO2(00011) and CO2(00021) states duringthe active part of a pulsed DC discharge at p = 5 Torr, I = 50 mA, ∆tpulse = 5 ms,as a function of the discharge on-time. The symbols correspond to the experimentalvalues, whilst the solid lines correspond to the simulation results.

The temporal evolution of the calculated and measured normalized popula-tions of the first two vibrationally excited levels of the asymmetric stretchingmode are presented in figure 4.3. Both the calculations and the experimentaldata show a fast growth of the CO2(000ν31) populations in the first millisecondof the pulse. Subsequently, the gas heating enhances the energy exchanges tothe translational degrees of freedom, leading to a population drop at about1 ms. This can be confirmed by inspection of figures 4.4 and 4.5.

Figure 4.4 shows the time-evolution of the population of the CO2(00011)level calculated from our reference model and when constant values of gastemperature along the discharge pulse are considered. The results reveal ahigher population for this level at lower gas temperatures, in accordance withthe results from [8], demonstrating the importance of cooling down the gas foran effective excitation of the asymmetric mode. Furthermore, the calculationsmade at constant Tg do not exhibit a local maximum of the population at 1 mson-time, indicating that this effect is dominated by the modification of the V-Vand V-T rate coefficients with the gas temperature.

97

Chapter 4. Input of vibrational energy in CO2 discharges

1 0 - 5 1 0 - 4 1 0 - 3 1 0 - 2- 8

- 7

- 6

- 5

- 4

- 3

- 2

C O 2 ( 0 0 0 1 1 ) E x p e r i m e n t R e f . m o d e l T = 1 0 0 K T = 3 0 0 K T = 5 0 0 K

T i m e ( s )

Log[N

ν3/N 0⋅g]

Figure 4.4: Normalized density of the CO2(00011) states for the same conditionsas in figure 4.3. Closed black symbols correspond to the experimental values, whilethe lines represent the simulation results calculated with different values of the gastemperature.

Figure 4.5 shows the net contribution of the dominant populating anddepopulating mechanisms of the first level of the asymmetric mode, wherethe full and dashed lines correspond, respectively, to net creation and netloss mechanisms (i.e., the dashed lines are multiplied by -1). In the earlyinstants of the discharge, this level is mainly created by electron impact fromthe ground-state,

e + CO2(00001) e + CO2(00011) .

Once the population of the second asymmetric level becomes large enough,V-V reactions within the asymmetric mode depopulating ν3 = 2 become thedominant creation mechanism,

CO2(00021) + CO2(00001) CO2(00011) + CO2(00011) .

Finally, as the gas temperature increases V-T deactivation to the bending andsymmetric modes starts to play an important role,

CO2(00011) + CO2 CO2(11102, 10002) + CO2 ,

98

4.6. Results and discussion

1 0 - 5 1 0 - 4 1 0 - 3 1 0 - 2

1 0 1 5

1 0 1 6

1 0 1 7

1 0 1 8

1 0 1 9

Cr

eatio

n-Los

s rate

s (cm

-3 s-1 )

T i m e ( s )

C O 2 ( 0 0 0 1 1 )

C O 2 ( 0 0 0 0 1 ) + e < - > C O 2 ( 0 0 0 1 1 ) + e C O 2 ( 0 0 0 1 1 ) + C O 2 < - > C O 2 ( 1 0 0 0 2 ) + C O 2 C O 2 ( 0 0 0 1 1 ) + C O 2 < - > C O 2 ( 1 1 1 0 2 ) + C O 2 C O 2 ( 0 0 0 1 1 ) + C O 2 ( 0 0 0 1 1 ) < - > C O 2 ( 0 0 0 0 1 ) + C O 2 ( 0 0 0 2 1 ) C O 2 ( 0 0 0 1 1 ) + C O 2 ( 0 1 1 0 1 ) < - > C O 2 ( 0 0 0 0 1 ) + C O 2 ( 0 1 1 1 1 )

Figure 4.5: Net contribution of several mechanisms to the creation and the loss ofCO2(00011). The dashed lines represent loss mechanisms, i.e. they are multiplied by-1 in the plot.

justifying the decrease in the population for on-times around 1 ms.Panels a) and b) of the figure 4.6 show the time-dependent populations

of the first two levels of the symmetric mode and the first three levels ofthe bending mode, respectively. The simulation results are in generally goodagreement with the experimental data, albeit predicting a slightly slower growthof the populations as compared with the experiment. It can be observed fromthe figures that the discrepancy is more prominent with the increase of thequantum number. The reasons for this difference are not yet clear. Possibleexplanations may involve more complex deconvolution procedures of the lumpedcross sections and/or an influence of vibrational transfers from the asymmetricmode in collisions involving oxygen molecules or excited atoms. Ongoinginvestigation should cast light into this question. Preliminary results pointtowards a higher likelihood of the latter mechanisms, but at this stage it ispremature to draw definitive conclusions.

99

Chapter 4. Input of vibrational energy in CO2 discharges

- 1 0

- 5

1 0 - 5 1 0 - 4 1 0 - 3 1 0 - 2- 1 0

- 5

0

a ) C O 2 ( ν 1 0 0 0 f )

M o d e lE x p e r i m e n t :

ν1 = 1 ν1 = 2

Log[N

ν1/N 0⋅g]

b ) C O 2 ( 0 ν l2 0 1 )

M o d e lE x p e r i m e n t :

ν2 = 1 ν2 = 2 ν2 = 3

Log[N

ν2/N 0⋅g]

T i m e ( s )Figure 4.6: Normalized density of several states a) in the symmetric mode and b)in the bending mode of vibration during the active discharge in the same conditionsas in the figure 4.3. Symbols correspond to the experimental values, while the solidlines correspond to the model predictions.

100

4.6. Results and discussion

Figure 4.7: Time-resolved vibrational distribution function of the lower vibrationallevels of the asymmetric mode, normalized to the ground-state density, a) in the activeCO2 discharge; b) during the post-discharge, for the same conditions as in figure 4.3.Red dashed lines indicate the energies of the first five levels of the asymmetric mode.

101

Chapter 4. Input of vibrational energy in CO2 discharges

Figure 4.8: Time-resolved vibrational distribution function of the lower vibrationallevels of the bending mode, normalized to the ground-state density, a) in the activeCO2 discharge; b) during the post-discharge, for the same conditions as in figure 4.3.Red dashed lines indicate the energies of the first five levels of the bending mode.

102

4.6. Results and discussion

1 0 - 6 1 0 - 5 1 0 - 4 1 0 - 3 1 0 - 2

3 0 04 0 05 0 06 0 07 0 08 0 09 0 0

1 0 0 01 1 0 0

2 x 1 0 - 4 4 x 1 0 - 4

3 4 0

3 6 0

T 1 T 2 T 3 T 2 E x p . T 3 E x p . T g a s

Temp

eratur

e (K)

T i m e ( s )

Figure 4.9: Comparison between calculated and measured vibrational temperatures:T1, T2 and T3 correspond to the symmetric stretching, bending and asymmetricstretching modes of vibration, respectively. The insert shows that the calculated T1

and T2 are nearly equal. The measurements assume a common temperature T1 = T2.The experimental gas temperature profile is represented by the black solid line.

Figure 4.7 shows the calculated vibrational distribution function (VDF) ofthe levels in the asymmetric mode during the discharge a) and afterglow b).Clearly, the VDF deviates from a Boltzmann distribution during the discharge,in contrast with the afterglow regime, where a Boltzmann distribution is quicklyestablished, although a complete thermalisation only takes place at times∼ 10−3 − 10−2 s. On the other hand, the VDF of the bending mode exhibitsa Boltzmann distribution both during the active discharge and the afterglowregime, as shown in figures 4.8a) and 4.8b), respectively. The excitation ofthe bending mode during the pulse is slower than what is observed in theasymmetric mode, whilst the behavior in the post-discharge is similar for bothmodes with comparable thermalization times.

The degree of vibrational excitation and non-equilibrium of CO2 can becharacterised by the “temperatures” of each normal mode, calculated from thepopulations of the corresponding excited levels. In particular, the characteristictemperature of the asymmetric mode, T3, is obtained by fitting the calculateddensities of the CO2(000ν3=1-5) levels to a Treanor distribution, while the

103

Chapter 4. Input of vibrational energy in CO2 discharges

characteristic temperature of the effective symmetric (which include the Fermiresonant states) and bending modes, T1 and T2, respectively, are obtained fromsimple Boltzmann plots. Figure 4.9 shows the time evolution of the calculatedthree temperatures along the discharge pulse, together with the values forT3 and T1,2, obtained experimentally, where T1,2 is a common temperatureassumed for the symmetric and bending modes [15]. The simulation resultsconfirm the validity of the assumption that the temperatures T1 and T2 arenearly the same, associated with the Fermi resonance between the symmetricand the bending modes of vibration and with the similarity of the energiesand rate coefficients involving Fermi and non-Fermi bending levels. Therefore,the two characteristic temperatures T1,2 and T3 suffice for a simple descriptionof the extent of vibrational excitation. For the conditions under analysis, T3,exhibits a fast elevation of 500 K above Tg and T1,2 in good agreement with themeasurements, confirming the preferential excitation of the asymmetric modeand the strong non-equilibrium nature of the discharge.

The influence of the electron density temporal profile (ne) used as inputto our simulations can be asserted by inspection of figure 4.10, showing themeasured and calculated effective temperatures of the asymmetric mode, T3using the reference model and three different values of ne kept constant alongthe full duration of the pulse. Inspection of the figure confirms that consideringthe constant steady-state value of the electron density along the pulse yieldsthe correct final result for T3, as it should, but leads to an overestimationof the temperature up to times of the order of 10 ms. On the other hand,the simulation performed with an electron density of 2.5 × 109 cm−3 leadsto the same predictions as the reference model for times up to ∼ 5 × 10−4 s,but produces underestimated values of T3 at the end of the discharge pulse.Naturally, taking a constant value ne = 5× 109 cm−3 results in an intermediatesituation as compared to the two extreme cases. Figure 4.10 shows that a goodqualitative description can be made assuming a constant electron density alongthe discharge pulse, but that quantitative analysis must take into account morerealistic temporal profiles for ne.

4.7 Conclusions

The present work studies the state-to-state kinetics of the first 72 low-lyinglevels of CO2 plasma during the active discharge, corresponding to νmax1 = 2,νmax2 = 5 and νmax3 = 5 with energies up to about 2 eV. The model was validatedby comparing the calculated populations with the time-resolved in situ FTIRmeasurement realized in a pulsed DC glow discharge [15]. Mechanisms relatedto the V-V and V-T energy exchanges were previously examined in the studyof the CO2 afterglow presented in chapter 3. To describe the active discharge,

104

4.7. Conclusions

1 0 - 5 1 0 - 4 1 0 - 3 1 0 - 2

4 0 0

5 0 0

6 0 0

7 0 0

8 0 0

9 0 0

1 0 0 0

1 1 0 0

n e p r o f i l e E x p e r i m e n t n e = 2 . 5 x 1 0 9 c m - 3

n e = 5 . 0 x 1 0 9 c m - 3

n e = 7 . 5 x 1 0 9 c m - 3

Temp

eratur

e (K)

T i m e ( s )

Figure 4.10: Measured () and calculated vibrational temperature T3 using theelectron density profile from figure 4.2 (—) and using constant electron densities of2.5× 109 cm−3 (- - -), 5× 109 cm−3 (- - -), and 7.5× 109 cm−3 (- - -).

a detailed set of electron-impact excitation and de-excitation processes is addedto the list of reactions taken into account previously in the post-discharge.

The very good agreement between the model predictions and the experimen-tal results validates the correctness of our description, despite some differencespersisting in the time-evolution of the populations of the symmetric and bend-ing excited states. The present results confirm the non-equilibrium nature oflow-pressure CO2 plasmas, with a characteristic temperature of the asymmetricvibration mode, T3 well above the vibrational temperatures of the other twomodes and of the gas temperature, Tg. T3 exhibits a maximum during thedischarge pulse, which for the conditions under study (pressure p = 5 Torr anddischarge current I = 50 mA) occurs at about 1 ms on-time, strongly connectedwith the gas heating along the pulse and the increased contribution of V-Tdeactivation with Tg.

The investigation further corroborates the validity of the often made assump-tion of equality of the vibrational temperatures of the symmetric and bendingmodes, T1,2. This opens the possibility of using a state-to-state approach tobenchmark and establish domains of validity of three-temperature (Tg, T12 andT3) macroscopic descriptions of CO2 plasmas trying to capture some essential

105

Chapter 4. Input of vibrational energy in CO2 discharges

features of non-equilibrium phenomena, as it has been done for the case of nitro-gen [36]. If the appropriate conditions are met, such semi-empirical approachescan be useful for reducing the computational cost of handling a large numberof elementary processes

Future work will analyse in detail some of the assumptions made here,such as the procedure for deconvolution of lumped cross sections, Fridman’sapproximation and the scaling laws for missing electron-impact processes, theassumptions regarding the electron density profile, or the utilisation of thevibrational resonant excitation cross section from [19]. Work is in progress toextend our investigation to higher excitation regimes, in order to study bothelectron impact and vibrational dissociation of CO2, which do not play a relevantrole in the conditions studied in this work. This task involves many challenges.For instance, electron impact collisions with all dissociation by-products mustbe included, as well as vibrational energy exchanges between different partners(CO2-CO, CO2-O, CO-CO, etc.). The effect that the extended vibrationalladder will have on the EEDF should also be taken into account, following, e.g.,the procedure described in [37]. Another complex endeavour is to validate thescaling methods for the calculation of V-V and V-T rate coefficients appropriatefor the higher excitation, since the first-order perturbation theories used inthis work, namely SSH and Sharma Brau, do not provide a valid descriptionof these exchanges at high temperatures and high vibrational numbers. Sucha comprehensive model will offer a valuable insight into fundamental reactionmechanisms in CO2 plasmas.

106

4.8. References

4.8 References

[1] W. J. Wiegand, M. C. Fowler, and J. A. Benda, “Carbon monoxideformation in CO2 lasers,” Appl. Phys. Lett., 16, 237–239, 1970.

[2] A. Cenian, A. Chernukho, V. Borodin, and G. Sliwinski, “Modeling ofplasma-chemical reactions in gas mixture of CO2 lasers I. gas decompositionin pure CO2 glow discharge,” Contrib. Plasma Phys., 34, 25–37, 1994.

[3] M. Capitelli, G. Colonna, G. D’Ammando, and L. D. Pietanza, “Self-consistent time dependent vibrational and free electron kinetics for CO2

dissociation and ionization in cold plasmas,” Plasma Sources Sci. Technol.,26, 055009, 2017.

[4] T. Kozak and A. Bogaerts, “Splitting of CO2 by vibrational excitation innon-equilibrium plasmas: a reaction kinetics model,” Plasma Sources Sci.Technol., 23, 045004, 2014.

[5] A. Bultel and J. Annaloro, “Elaboration of collisional-radiative models forflows related to planetary entries into the Earth and Mars atmospheres,”Plasma Sources Sci. Technol., 22, 25008, 2013.

[6] I. Armenise and E. V. Kustova, “State–to–state models for CO2 molecules:From the theory to an application to hypersonic boundary layers,” Chem.Phys., 415, 269–281, 2013.

[7] R. Celiberto, I. Armenise, M. Cacciatore, M. Capitelli, F. Esposito,P. Gamallo, R. K. Janev, A. Lagana, V. Laporta, A. Laricchiuta, A. Lom-bardi, M. Rutigliano, R. Sayos, J. Tennyson, and J. M. Wadehra, “Atomicand molecular data for spacecraft re-entry plasmas,” Plasma Sources Sci.Technol., 25, 033004, 2016.

[8] V. Guerra, T. Silva, P. Ogloblina, M. Grofulovic, L. Terraz,M. Lino da Silva, C. D. Pintassilgo, L. L. Alves, and O. Guaitella, “Thecase for in situ resource utilisation for oxygen production on mars by non-equilibrium plasmas,” Plasma Sources Sci. Technol., 26, 11LT01, 2017.

[9] A. Fridman, Plasma chemistry. Cambridge: Cambridge University Press,2008.

[10] V. Guerra, P. A. Sa, and J. Loureiro, “Kinetic modeling of low–pressurenitrogen discharges and post–discharges,” Eur. Phys. J. Appl. Phys., 28,125–152, 2004.

[11] T. Silva, M. Grofulovic, B. L. M. Klarenaar, O. Guaitella, R. Engeln,C. D. Pintassilgo, and V. Guerra, “Kinetic study of CO2 plasmas under

107

Chapter 4. Input of vibrational energy in CO2 discharges

non–equilibrium conditions. I. Relaxation of vibrational energy,” PlasmaSources Sci. Technol., 27, 015019, 2018.

[12] I. Armenise, “Excitation of the lowest CO2 vibrational states by electronsin hypersonic boundary layers,” Chem. Phys., 491, 11 – 24, 2017.

[13] B. F. Gordiets, N. N. Sobolev, and L. A. Shelepin, “Kinetics of physicalprocesses in CO2 lasers,” 26, 1968.

[14] B. F. Gordiets, A. N. Stepanovich, K. U. Grossmann, and K. H. Voll-mann, “Model of the Vibrational kinetics of CO2 in the upper atmosphere,”Geomagn. Aeronomy, 34, 699–701, 1995.

[15] B. L. M. Klarenaar, R. Engeln, D. C. M. van den Bekerom, M. C. M.van de Sanden, A. S. Morillo-Candas, and O. Guaitella, “Time evolutionof vibrational temperatures in a CO2 glow discharge measured with infraredabsorption spectroscopy,” Plasma Sources Sci. Technol., 26, 115008, 2017.

[16] B. L. M. Klarenaar, M. Grofulovic, A. S. Morillo-Candas, D. C. M. van denBekerom, M. A. Damen, M. C. M. van de Sanden, O. Guaitella, andR. Engeln, “A rotational Raman study under non-thermal conditions in apulsed CO2 glow discharge,” Plasma Sources Sci. Technol., 27, 045009,2018.

[17] C. D. Pintassilgo, O. Guaitella, and A. Rousseau, “Heavy species kineticsin low-pressure dc pulsed discharges in air,” Plasma Sources Sci. Technol.,18, 025005, 2009.

[18] M. Grofulovic, L. L. Alves, and V. Guerra, “Electron-neutral scatteringcross sections for CO2: a complete and consistent set and an assessment ofdissociation,” J. Phys. D: Appl. Phys., 49, 395207, 2016.

[19] V. Laporta, J. Tennyson, and R. Celiberto, “Calculated low-energy electron-impact vibrational excitation cross sections for CO2 molecule,” PlasmaSources Sci. Technol., 25, 06LT02, 2016.

[20] C. D. Pintassilgo, G. Cernogora, and J. Loureiro, “Spectroscopy study andmodelling of an afterglow created by a low-pressure pulsed discharge inN2-CH4,” Plasma Sources Sci. Technol., 10, 147, 2001.

[21] C. D. Pintassilgo, V. Guerra, O. Guaitella, and A. Rousseau, “Modellingof an afterglow plasma in air produced by a pulsed discharge,” PlasmaSources Sci. Technol., 19, 055001, 2010.

[22] D. Marinov, V. Guerra, O. Guaitella, J.-P. Booth, and A. Rousseau,“Ozone kinetics in low-pressure discharges: vibrationally excited ozone andmolecule formation on surfaces,” Plasma Sources Sci. Technol., 22, 055018,2013.

108

4.8. References

[23] G. Herzberg, Molecular spectra and molecular structure. Vol.2: Infraredand Raman spectra of polyatomic molecules. 1945.

[24] I. Suzuki, “General anharmonic force constants of carbon dioxide,” J. Mol.Spectrosc., 25, 479–500, 1968.

[25] R. N. Schwartz, Z. I. Slawsky, and K. F. Herzfeld, “Calculation of vibra-tional relaxation times in gases,” J. Chem. Phys., 20, 1591–1599, 1952.

[26] D. Rapp and D. Englander-Golden, “Resonant and near-resonantvibrational-vibrational energy transfer between molecules in collisions,”J. Chem. Phys., 40, 573–575, 1964.

[27] R. D. Sharma and C. A. Brau, “Energy transfer in near-resonant molecularcollisions due to long-range forces with application to transfer of vibrationalenergy from ν3 mode of CO2 to N2,” J. Chem. Phys., 50, 924–930, 1969.

[28] A. E. DePristo, S. D. Augustin, and R. Ramaswamy, “Quantum numberand energy scaling for nonreactive collisions,” J. Chem. Phys., 71, 850–865,1979.

[29] I. V. Adamovich, S. O. MacHeret, J. W. Rich, and C. E. Treanor, “Vibra-tional Energy Transfer Rates Using a Forced Harmonic Oscillator Model,”J Thermophys. Heat Transfer, 12, 57–65, 1998.

[30] J. A. Blauer and G. R. Nickerson, “A survey of vibrational relaxation ratedata for processes important to CO2–N2–H2O infrared plume radiation,”Report Ultrasystems, Inc., 1973.

[31] L. D. Pietanza, G. Colonna, G. D’Ammando, A. Laricchiuta, andM. Capitelli, “Electron energy distribution functions and fractional powertransfer in ”cold” and excited CO2 discharge and post discharge conditions,”Phys. Plasmas, 23, 013515, 2016.

[32] T. Silva, N. Britun, T. Godfroid, and R. Snyders, “Optical characterizationof a microwave pulsed discharge used for dissociation of CO2,” PlasmaSources Sci. Technol., 23, 025009, 2014.

[33] G. Colonna, V. Laporta, R. Celiberto, M. Capitelli, and J. Tennyson,“Non-equilibrium vibrational and electron energy distributions functions inatmospheric nitrogen ns pulsed discharges and µs post-discharges: the roleof electron molecule vibrational excitation scaling-laws,” Plasma SourcesSci. Technol., 24, 035004, 2015.

[34] L. Viehland and E. Mason, “Transport properties of gaseous ions over awide energy range, IV,” Atomic Data and Nuclear Data Tables, 60, 37 –95, 1995.

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Chapter 4. Input of vibrational energy in CO2 discharges

[35] S. Ponduri, M. M. Becker, S. Welzel, M. C. M. Van De Sanden, D. Loffhagen,and R. Engeln, “Fluid modelling of CO2 dissociation in a dielectric barrierdischarge,” J. Appl. Phys., 119, 093301, 2016.

[36] M. Lino da Silva, V. Guerra, and J. Loureiro, “Two-temperature modelsfor nitrogen dissociation,” Chem. Phys., 342, 275–287, 2007.

[37] L. D. Pietanza, G. Colonna, G. D’Ammando, A. Laricchiuta, andM. Capitelli, “Vibrational excitation and dissociation mechanisms of CO2

under non-equilibrium discharge and post-discharge conditions,” PlasmaSources Sci. Technol., 24, 042002, 2015.

110

Chapter 5

Modelling of the time-dependentgas temperature in low-pressureCO2 discharges andpost-discharges

This chapter presents a modelling study of the time-dependent variation ofthe gas temperature in a millisecond DC pulsed discharge and its afterglow inCO2. A self-consistent model is developed based on the solutions to the time-dependent gas thermal balance equation under the assumption of a parabolicgas temperature profile across the discharge tube, coupled to the electron andvibrational kinetics. The calculations are validated through a comparison withexperimental data obtained before by time-resolved FTIR in pulsed DC glowdischarges at p = 5 Torr and I = 50 mA. Additionally, modelling results are alsocompared with the gas temperature measured in this work by rotational Ramanspectroscopy in continuous DC CO2 discharges at pressures p = 1 − 5 Torrand current I = 40 mA. The very good agreement with the experimental dataconfirms the validity of the model and of the reaction mechanism proposed.The results show that the dominant gas heating mechanisms are the vibrationalenergy exchanges.

111

5.1. Introduction

5.1 Introduction

Gas temperature and heat transfer mechanisms in plasmas are important forfundamental research and many applications. In fact, small variations in the gastemperature may greatly affect the processes therein, since the rate coefficientsof chemical reactions and diffusion coefficients are strongly dependent on thisparameter [1]. Moreover, the gas temperature has an indirect impact on thevalue of the reduced electric field (E/N) at constant pressure [1, 2].

Many works have been dedicated to the determination of gas temperaturein plasmas, developing different theoretical approaches [3, 4], experimentalmethods [5–8] or both [4, 9–13], focusing on different systems such as nitrogen[3, 9, 13], air [3, 11, 14–16], argon [4, 17], hydrogen [5] etc. Modelling of energytransfer in plasmas is particularly important for understanding the gas heatingmechanisms. According to the plasma system under study, gas temperaturecalculations can be based on the solutions to the gas thermal balance equationunder steady-state [9, 10, 17, 18] or time-dependent situations[11–13, 15]. Forthe formulation of the gas thermal balance equation it is important to determinethe main gas heating mechanisms for a given plasma discharge. These processesinclude volume heating sources from elastic collisions between electrons andheavy particles, electron-ion recombination and exothermic reactions betweenheavy particles. The presence of the wall can also affect greatly the heattransfers. In principle, one should consider the diffusion of metastable states,neutralization of ions and atomic recombination at the wall. The contributionof different processes is determined by the plasma operating conditions andgaseous composition. While in some plasmas heating is dominated by theprocesses at the wall, as in microwave discharges in argon [17], in microwaveand glow discharges in pure N2 the main sources of gas heating are vibration-to-vibration (V-V) and vibration-to-translation (V-T) energy exchanges involvingvibrationally excited molecules [9] or both, as in air plasmas [11, 19].

To the best of our knowledge, only a few studies have been dedicated to thecalculation of the temperature dynamics in CO2 plasmas. In recent years, CO2

plasmas have been extensively studied, motivated by the ongoing interest innovel solar fuels [20, 21]. The ultimate aim of widening the understanding ofdifferent kinetic mechanisms involves the detailed knowledge of the heat transfermechanisms in CO2 plasmas. Furthermore, the surface kinetics is highly affectedby the temperature near the wall and the neutral density in the plasma dependsdirectly on the temperature, for a given pressure [22]. This chapter presentsa modelling study of the time-dependent evolution of the gas temperature ina CO2 millisecond pulsed DC glow discharge, extending the model presentedin chapters 3 and 4 of this thesis. The discharge is produced in a cylindricaltube of radius R = 1 cm at low pressures (p = 5 Torr) and current I = 50 mA.The modelling results are compared with experimental data obtained by in situinfrared absorption spectroscopy (presented in chapter 3). Additionally, the

113

Chapter 5. Modelling of the time-dependent gas temperature in CO2

model is validated through a comparison with the new measurement presentedin this chapter, employing rotational Raman spectroscopy in a continuous DCdischarge at p = 1− 5 Torr and I = 40 mA.

The next section is devoted to the formulation of the time-dependent heattransfer equation. The details of the model are presented in section 5.3, togetherwith the relevant data on the thermal conductivity and heat capacity for CO2,which are input to the model. The main mechanisms taken into account aredetailed as well. The results of our simulation are analyzed in section 5.4,including the self-consistent calculations of the gas temperature during thepulse and the afterglow. The temporally resolved gas temperature is validatedthrough a comparison with the experimental data. Finally, the main conclusionsare summarized in section 5.5.

5.2 Heat transfer equation

Under isobaric conditions and assuming that heat conduction is the predominantcooling mechanism, the gas temperature T (r, t) is described by

nmcp∂T

∂t= λg∇2T +Qin, (5.1)

where cp is the molar heat capacity of the gas at constant pressure, λg is thethermal conductivity, nm is the molar density and Qin is the total net powerper volume unit transferred to gas heating [11].

In the discharge under study, the plasma is axially homogeneous. Therefore,the model considers a radially averaged gas temperature, Tg(t), given by

Tg(t) =1

πR2

∫ 2π

0

∫ R

0

T (r, t)r dθdr, (5.2)

where R represents the tube radius.A further assumption usually considered for the discharges under study is

that the gas temperature has a parabolic radial profile of the form

T (r, t) = T0(t)− (T0(t)− Tw)( rR

)2, (5.3)

where T0(t) and Tw denote the gas temperature at the tube axis and at thewall, respectively. Taking this into account, equation (5.2) reduces to

Tg(t) =1

2(T0(t) + Tw) . (5.4)

114

5.3. Model details

Now we can write the derivative in equation 5.1,

λg∇2T = λg1

r

∂

∂r

(r∂T

∂r

)=

4λg(Tw − T0)

R2. (5.5)

Replacing T0 from equation (5.4), we have

nmcp∂Tg∂t

=8λg(Tw − Tg)

R2+Qin. (5.6)

Under steady state conditions, this expression takes the form

Qin =8λg(Tw − Tg)

R2. (5.7)

5.3 Model details

From the previous discussion, it is clear that the first step in finding the solutionsof the heat balance equation is to identify the required input thermodynamicdata: the thermal conductivity and the heat capacity. Next, it is crucial toinclude all the relevant heating and cooling mechanisms.

The subject under study here is the discharge that was investigated inchapters 3 and 4 with the same reaction kinetics, but with one additionaldifferential equation for the gas temperature, coupled with the rest of thesystem. Whilst in 3 and 4 the measured temporally resolved gas temperaturewas given as an input to the model, here the Tg(t) is calculated from (5.1),together with the densities of different vibrationally excited states of CO2.

Thermodynamic data

The thermal conductivity λg and the molar heat capacity cp are both inputto equation (5.6) and at the same time are dependent on the gas temperature.Different data can be found in the literature, obtained theoretically [24, 27, 30,31] or experimentally [23]. Usually the calculated parameters do not accountfor the non–equilibrium nature of plasma. However, many works focused on theheat transfer in plasmas have described the temperature dynamics very well byusing the simple thermal conductivity and heat capacity without including thecontribution from the vibrational and electronic degrees of freedom [11, 13, 32],as these contributions are expected to be small in the usual discharge conditions.Moreover, under the conditions studied in this work, λp and cp are reportedto be pressure independent [30, 33]. A general formulation for non-equilibriumconditions is given in [27, 34].

Figure 5.1 illustrates the thermal conductivity of CO2 as a function of thegas temperature, published in different works. It is easily seen that for the

115

Chapter 5. Modelling of the time-dependent gas temperature in CO2

2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0

2 0

4 0

6 0

8 0

1 0 0λ (

10-5 W

K-1 cm-1 )

T ( K )

G u p t a 1 9 7 0 V e s o v i c 1 9 9 0 , K o z a k e t a l 2 0 1 4 N A S A t e c h . r e p o r t 1 9 9 5 K u s t o v a a n d N a g n i b e d a 2 0 0 6

Figure 5.1: Thermal conductivity of CO2 as a function of the gas temperatureaccording to Gupta [23], Vesovic et al [24], Kozak and Bogaerts [25], NASA technicalreport [26] and Kustova and Nagnibeda [27].

2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 0 2 0 0 0

3 0

4 0

5 0

6 0

7 0

c p (J /

mol

K)

T ( K )

E n g i n e e r i n g T o o l B o x K o z a k 2 0 1 4 N I S T - J A N A F T h e m o c h e m i c a l T a b l e s / C h a s e 1 9 9 8

Figure 5.2: Temperature dependence of the molar heat capacity of CO2 accordingto the Engineering ToolBox [28], Kozak and Bogearts [25] and NASA technical report[29].

temperature range important for this work (up to 1000 K), there is a goodagreement among different sources. For instance, the work published by Vesovicet al [24] shows the spread of data obtained by different authors covering thetemperature range between 186 K and 1350 K. The data were recently fitted tothe expression

λg = 0.071 Tg − 2.33 [10−5Wcm−1 K−1], (5.8)

116

5.3. Model details

and used for calculating the heat transfer mechanisms in CO2 plasmas in [32].A very extensive set of transport property data for various gases and theirmixtures is documented in [26], providing coefficients to calculate the thermalconductivity given by the formula

lnλg = A lnTg +B

Tg+

C

T 2g

+D [Wcm−1K−1], (5.9)

obtained by fitting the data. The fitting parameters for a large temperaturerange are given in table 5.1. The calculations of Kustova and Nagnibeda [27]apply to strongly non–equilibrium conditions, therefore they include variouscontributions to thermal conductivity, i.e. λ(Tg) = λtr + λrot + λvib,12 + λvib,3corresponding to the translational, rotational, and vibrational degrees of freedom.The corresponding thermal conductivity shown in figure 5.1 represents theirresults in the case of thermal equilibrium, i.e. Tg = T12 = T3, which are ina satisfactory agreement with the other sources. In highly non–equilibriumplasmas the contributions of vibrational degrees of freedom depend not only onthe gas temperature, but also on the vibrational temperature, and may affectgreatly the total thermal conductivity [27, 34].

The molar heat capacity cp, retrieved from [28, 29, 32] is depicted in figure5.2. It can can be seen that the theoretically obtained data from the Engineeringtoolbox [28] and NIST-JANAF [29] databases match very well. The NIST-JANAF thermochemical tables provide a large amount of data for differentgases. In case of CO2, the molar heat capacity can be described by the Shomateequation,

cp = A+B · t+ C · t2 +D · t3 + E/t2 [Jmol−1K−1], (5.10)

where t = Tg/1000 and the coefficients A, B, C and D are given in table 5.1.The heat capacity used in the work of Kozak and Bogaerts [32] represents themodified data from the NIST-JANAF report in such a way that the contributiondue to translational and rotational degrees freedom, as well as the vibationalsymmetric mode levels are taken into account [32, 35].

In the present work, the radially averaged gas temperature is always below700 K, and above the room temperature. Therefore, we may conclude fromfigures 5.1 and 5.2 that in that temperature range no distinction can be madebetween the different sources analysed and any of them can be used. However,for modeling different plasma configurations where higher temperatures arereached, one should consider carefully the contributions of the internal degrees offreedom and undertake a thorough analysis of the data available in the literaturefor higher temperature range. Here we have used the thermal conductivity from[32] and the molar heat capacity from [29].

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Chapter 5. Modelling of the time-dependent gas temperature in CO2

Table 5.1: Thermal capacity and specific heat retrieved from different sources.

λ [10−5Wcm−1K−1] Reference Temperature (K)

0.071 Tg − 2.33 [24, 32] 200 - 1350

exp(0.0514 lnTg − 47.445/Tg + 3129.593/T 2g + 0.341) [26] 300 - 1000

exp(0.0675 lnTg − 11.284/Tg − 6913.262/T 2g + 0.204) [26] 1000 - 5000

−10.05 + 9.04 · 10−2Tg − 13.58 · 10−6T 2g [23] 373 - 1350

cp [Jmol−1K−1]

a 24.997 + 55.19 · t− 33.69 · t2 + 7.95 · t3 − 0.14/t2 [29] 298 - 1200

58.17 + 2.72 · t− 0.49 · t2 + 0.039 · t3 − 6.45/t2 [29] 1200 - 6000

16.25 + 81.18 · t− 62.88 · t2 + 17.65 · t3 + 0.16/t2 [32] 300 - 1200

5839− 2.59 · t+ 1.39 · t2 − 0.26 · t3 − 4.82/t2 [32] 1200 - 3000

b 61.23− 40.92 exp(−T/560.18) [28] 250 - 2000

a t=temperature (K)/1000.b The data are retrieved from [28] where they cover the range of 175 - 6000 K. Forconvenience, the data are fitted in this work to the expression in the table, covering the gastemperature range of 250 - 2000 K.

Heat transfer mechanisms in CO2

The time-evolution of Tg in a plasma is governed by different elementary pro-cesses. For millisecond pulsed discharges, the populations of CO2 vibrationallevels become important, leading to energy exchanges that contribute signifi-cantly to the gas temperature increase during the discharge and to its relaxationin the afterglow. Our simulations are based on a 0D kinetic model that de-termines the solutions of a coupled system of time-dependent rate balanceequations for ∼70 vibrational levels of CO2. The collisional data used in thiswork are detailed in [36, 37] and references therein. Once the solutions areknown for some pulse duration, they are used as initial conditions for the samesystem of equations to obtain the solutions corresponding to the afterglow, withthe assumption that electron impact processes are negligible.

In the present work, the term Qin in equation (5.6) includes: i) the powertransferred from the electrons to the heavy particles in elastic collisions; and ii)

118

5.4. Results and discussion

the power consumed or released in heavy particle reactions. The only heavyparticle interactions considered in the model are vibration–translation (V-T)and vibration–vibration (V-V) energy exchanges, including the non-resonantV-V processes. The contributions i) and ii) may be calculated in the followingway.

The elastic collisions of electrons with CO2 molecules, Qel, is calculatedfrom the average energy transferred to CO2 molecules, Pel:

Qel = ne[CO2]Pel, (5.11)

where ne and [CO2] are the densities of electrons and CO2, respectively, and Pelis calculated from the integration of the electron energy distribution function(EEDF) over the electron energy and the electron cross section for momentumtransfer. The EEDF is calculated using the two-term Boltzmann solver LoKI[38].

The heating contribution originating from the interactions between vibra-tionally excited CO2 molecules may be represented in a general form

QV T = [CO2]∑ν

kV T [CO2(ν)]∆EV T , (5.12)

and

QV V =∑ν,ω

kV V [CO2(ν)][CO2(ω)]∆EV V , (5.13)

where kV T and kV V represent the rate coefficients for the corresponding vibra-tional energy exchanges, and ∆EV T and ∆EV V are the energies released in asingle reaction, i.e. the difference between the energies of the reaction productsand the energies of the reactants, CO2(ν) and CO2(ω) present generic CO2

vibrational levels. The full list of processes taken into account in (5.12) and(5.13) is given in chapters 3 and 4.

5.4 Results and discussion

FTIR study: single-pulse experiment

This section analyses the calculated time-resolved gas temperature in a low-pressure CO2 plasma. The results of the simulations are validated by comparingthe calculated gas temperature with the experimental data obtained from time-resolved in situ Fourier transform infrared spectroscopy (FTIR) in a pulsed DCglow discharge, with 5 ms plasma-on time and 150 ms off time, at p=5 Torrand I =50 mA. The inner tube diameter of the reactor is 2 cm. The experimentis detailed in [8]. Due to a high flow rate and a long off time, all dissociation

119

Chapter 5. Modelling of the time-dependent gas temperature in CO2

0 5 1 0 1 5 2 03 0 0

4 0 0

5 0 0

6 0 0

7 0 0P l a s m a o n

E x p M o d e l T w = 3 5 0 K

T g (K)

T i m e ( m s )

I = 5 0 m Ap = 5 T o r r

Figure 5.3: Temporal evolution of the radially averaged gas temperature Tg for apulsed discharge in CO2 at a pressure of 5 Torr with a pulse duration of 5 ms anda current of 50 mA and the corresponding afterglow. The solid line represents themodelling results, whereas the symbols are experimental data.

0 5 1 0 1 5 2 00

2

4

6

8

1 0 P l a s m a o n

Heati

ng ra

te (10

4 K/s)

T i m e ( m s )

V - T V - V

Figure 5.4: Heating rates of the V-V and V-T mechanisms in a 5 ms pulsed dischargein CO2 at pressure of 5 Torr and current of 50 mA and the corresponding afterglow.

products leave the reactor between two subsequent pulses. For this reason, theexperiment is suitable for the comparison with the present model that doesnot include chemical kinetics and species other than electrons and vibrationallyexcited CO2 [36, 37, 40].

The calculated temporal evolution of the radially averaged gas temperatureis shown in figure 5.3 together with the measured data. For the reduced electric

120

5.4. Results and discussion

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 00

2

4

6 P l a s m a o n C O 2 ( 0 1 1 0 ) + C O 2 ( 0 3 3 0 ) - > C O 2 ( 0 0 0 0 ) + C O 2 ( 0 2 2 0 ) C O 2 ( 1 2 2 0 ) + C O 2 ( 1 1 1 0 ) - > C O 2 ( 0 3 3 0 ) + C O 2 ( 1 0 0 0 ) C O 2 ( 1 1 1 0 ) + C O 2 ( 1 1 1 0 ) - > C O 2 ( 1 0 0 0 ) + C O 2 ( 0 3 3 0 ) C O 2 ( 0 1 1 0 ) + C O 2 - > C O 2 ( 0 0 0 0 ) + C O 2 C O 2 ( 1 0 0 0 ) + C O 2 - > C O 2 ( 0 1 1 0 ) + C O 2 C O 2 ( 0 2 2 0 ) + C O 2 - > C O 2 ( 0 1 1 0 ) + C O 2

Gas h

eatin

g rate

(104 K/

s)

T i m e ( m s )Figure 5.5: Time-resolved gas heating rates of the most important mechanisms in a5 ms pulsed discharge in CO2 at p = 5 Torr and I = 50 mA.

0 1 2 3 4 50

1 0

2 0

3 0

4 0

η R (%)

T i m e ( m s )

I = 5 0 m Ap = 5 T o r r

Figure 5.6: Temporal evolution of the fractional power transferred to gas heatingduring the pulse of a CO2 DC discharge, operated at p = 5 Torr and I = 50 mA.

field, we have used in our simulation the measured value of E/N = 55 Td. Thewall temperature, Tw, which is an input parameter to our model (see equation(5.6)), is assumed to have a constant value of 350 K. Clearly, the calculated gastemperature compares very well with the experiment, with some observablediscrepancies in the active part, especially during the last 2 ms of the pulse.The good agreement of the predictions with the measured data implies that

121

Chapter 5. Modelling of the time-dependent gas temperature in CO2

2 4 6 8 1 0

0 . 1

1

1 0Nu

mber

dens

ities (

1016

cm-3 )

T i m e ( m s )

C O 2 ( 0 0 0 0 ) C O 2 ( 0 1 1 0 ) C O 2 ( 0 0 0 1 ) C O 2 ( 1 0 0 0 )

P l a s m a o n

Figure 5.7: The absolute number densities of the ground state CO2 and vibrationallyexcited CO2(1000), CO2(0110) and CO2(0001) during the pulse and the afterglow ina 5 ms pulsed discharge in CO2 at pressure of 5 Torr and current of 50 mA.

0 1 2 3 4 5 6 7

4 0 0

6 0 0

8 0 0

E x p . T w = 5 0 0 K T w = 3 5 0 K T w = 3 2 3 + 0 . 4 5 ( T g - 3 7 5 K )

T g (K)

T i m e ( m s )

I = 5 0 m Ap = 5 T o r r

Figure 5.8: Temporal evolution of the radially averaged gas temperature Tg in CO2

during the active discharge. The different curves correspond to calculations madeimposing different wall temperature values as input: (—) 500 K; (- - -) 350 K; (– · –)dependence on Tg from [39]. The symbols represent the experimental data.

the role of vibrational kinetics is paramount in gas heating mechanisms in CO2

plasma under the studied conditions.

122

5.4. Results and discussion

The contributions of V-T and V-V mechanisms to gas heating are plotted infigure 5.4 during the pulse and the afterglow. As seen in the figure, the heatingrates increase steadily in the first ∼ 2 ms of the pulse, when a saturation isreached. The elastic collisions between electrons and CO2 molecules contributeinsignificantly to gas heating with ∼ 1%.

Heating rates of the most important reactions for gas heating during thepulse and the afterglow are reported in figure 5.5. Clearly, the highest gasheating rates correspond to the vibrational energy exchanges involving thebending and symmetric vibrational modes. In the first instants of the pulse,the dominant contribution to gas heating is due to the following reaction

CO2(0110) + CO2 ↔ CO2(0000) + CO2, (5.14)

with a relative contribution of ∼ 60% at the very beginning. After t = 1 ms thedominant reaction for gas heating is

CO2(0110) + CO2(0330) ↔ CO2(0000) + CO2(0220), (5.15)

contributing with ∼ 30% to the total heating rates.The fractional power spent on gas heating, ηR, obtained as the ratio between

the total gas heating rate and the discharge power, i.e. the power gained bythe electron from the applied field, is reported in figure 5.6. The power thatelectrons gain from the electric field is obtained using the Boltzmann solverLoKI [38], whilst the electron density used in the model is reported in chapter4. The figure shows that ηR grows in the first ∼ 2 ms, after which its valueremains in the range of 30-35%.

Figure 5.7 plots the time-dependent variations of the absolute densities ofthe vibrational ground state CO2(X1Σ+) and of the first vibrational statesof the different vibrational modes. During the pulse, the concentrations ofCO2(1000) and CO2(0110) increase steadily, with a slightly faster growth in thefirst millisecond of the discharge. The very high density of CO2(0110) has animpact on the gas heating rates, as it can be seen by the high contributions fromreactions (5.14) and (5.15). The characteristic behavior of the first asymmetriclevel of excitation, as reported in chapter 4 is also evident in our currentcalculation. Its population increases rapidly during the pulse and at t ∼0.7 msit reaches the highest value, decreasing afterwards. A detailed analysis of thisphenomenon is given in [37, 40].

To test the sensitivity of the model to the value of Tw, we have performedcalculations for the active part of the discharge using different values for thewall temperature, Tw = 500 K (full curve) and Tw = 350 K (dashed curves), aswell as assuming a temporal evolution of Tw dependent on the gas temperature,as suggested in some recent works [22, 39]. The results are shown in figure 5.8.It can easily be seen that using Tw = 500 K, we obtain a very good agreement

123

Chapter 5. Modelling of the time-dependent gas temperature in CO2

0 1 0 2 0 3 0 4 0

4 0 0

5 0 0

6 0 0

7 0 0 P l a s m a o nI = 5 0 m AT w = 3 5 0 K

T g (K)

T i m e ( m s )

C O 2 p = 1 T o r r C O 2 p = 5 T o r r

Figure 5.9: Calculated temporal evolution in CO2 for pressures of 1 Torr (green)and 5 Torr (blue). The wall temperature in both cases is 350 K and the pulse durationis 5 ms.

with the experiment up until t = 4 ms. However, this value seems unrealisticallyhigh. Calculations made with the Tw dependent on the gas temperature assuggested in [39] yield overestimated values of Tg for later times of the discharge.This approach is, however, rather attractive, especially for time-resolved studiesas it models the wall temperature more realistically, describing its dependenceon Tg.

The calculated temporal evolutions of Tg in CO2 at two different pressures,1 and 5 Torr, are shown in figure 5.9. As expected, at 5 Torr the gas gets muchhotter, 200 K higher at the end of the pulse. The relaxation in both cases showsa similar behavior, being slightly slower at higher pressure, as expected.

The modeling results for longer afterglow times are shown in figure 5.10. Itis easily seen that a complete relaxation takes place at ∼35 ms. Additionally, wehave calculated the temperature as a function of time for two hypothetical cases:i) the afterglow where only the heat conduction is taken into account, meaningthat the term Qin is discarded from equation (5.6); ii) Tg calculated only forthe active discharge for longer times. We can observe that the temperaturedecay becomes faster when only the heat conduction is included, which is due tothe neglected heat transfers originating from the vibrational energy exchanges.Figure 5.10 also shows that the temperature becomes constant after 20 ms ofthe pulse duration, meaning that at that time the vibrational kinetics reachessteady-state conditions.

124

5.4. Results and discussion

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 03 0 0

4 0 0

5 0 0

6 0 0

7 0 0

8 0 0

T w = 3 5 0 K

T g (K)

T i m e ( m s )

I = 5 0 m Ap = 5 T o r r

P l a s m a o n

1

2

3

Figure 5.10: Radially averaged gas temperature Tg in a CO2 discharge with p =5 Torr and I = 50 mA during a 5 ms pulsed plasma and the corresponding afterglow(1) and additional simulation made for the following situations: (2) - when only heatconduction is taken into account in the afterglow (black dashed–dotted curve); (3) -The temporal evolution of Tg during the active part, shown for times longer than thepulse duration (dashed black line).

Figure 5.11 depicts the cooling rate as a function of time, in the pulse andthe corresponding afterglow. Clearly, the shape is very similar to the modelingresults shown in figure 5.10. The cooling rate depends on λg and the gastemperature relative to the temperature at the inner wall. For this reason, itshows the same behavior, increasing in the active part, and decreasing in theafterglow.

Rotational Raman scattering measurements: Continuous DCdischarge

To extend the study of the gas temperature dynamics in a CO2 discharge,we have measured rotational Raman spectra in continuous CO2 plasmas atpressures of p = 1 − 5 Torr, and I = 40 mA, at constant flow of 7.4 sccm.The CO2 glow discharge was ignited in a cylindrical Pyrex tube with a 2 cminner diameter and 23 cm length. Raman scattered light is collected from thefocal point of a pulsed Nd:YAG laser (532 nm, 100 mJ/pulse, 100 Hz), focusedinside the reactor. Rayleigh scattered and stray light is removed by using avolume Bragg grating, after which the remaining light enters a spectrometerand is detected by an ICCD camera. The rotational Raman spectra are fitted

125

Chapter 5. Modelling of the time-dependent gas temperature in CO2

0 1 0 2 0 3 0 4 0

0

1

2

3P l a s m a o n

I = 5 0 m Ap = 5 T o r r

Coolin

g rate

(105 K/

s)

T i m e ( m s )

Figure 5.11: Cooling rate by heat conduction in a 5 ms pulsed discharge in CO2 atpressure of 5 Torr and current of 50 mA and the corresponding afterglow.

to determine the rotational temperature. The setup is described in previouspublications [6, 41], dedicated to the Raman study in similar discharges operatedin a pulsed regime.

The main difference between the continuous plasma and the single-pulseexperiment lies in the influence of the chemical kinetics. Indeed, in the single-pulse experiment the conditions are tailored in such a way to ensure the absenceof dissociation products. On the other hand, in continuous plasma there is anoticeable dissociation of CO2, typically of the order of 20% [6], so that O, O2

and CO are present. Therefore, a fully accurate description of a continuousCO2 plasma should include the collisions between electrons and CO2, CO andO2; all the V-V and V-T energy exchanges in a CO2/CO/O2 system; and thekinetics of O atoms. Although our model is lacking the full kinetics of suchplasma, it is of interest to compare the simulation results to the measurements,in order to estimate the significance of the processes included in the model,namely, the role of the vibrational kinetics of CO2.

The gas temperatures are determined for several pressures from the rangeof 1-5 Torr, as shown in figure 5.12. The modeling results are obtained for theexperimental conditions of current and pressure, which are input parameters inour calculations. As expected, the temperature rises as the pressure increases.It can be seen that the model predicts very well the gas temperature in acontinuous CO2 plasma. The good agreement obtained despite the fact thatthe model does not account for the amount of CO, O2 and O present in the

126

5.5. Conclusions

1 2 3 4 54 5 05 0 05 5 06 0 06 5 07 0 07 5 08 0 0

T g

P r e s s u r e ( T o r r )

E x p e r i m e n t M o d e l , T w = 3 5 0 K

I = 4 0 m A

Figure 5.12: Pressure dependence of the gas temperature in a continuous DCdischarge in CO2, operated at p = 1− 5 Torr and I = 40 mA. The measured valuesare represented by the orange symbols. Calculation are performed using Tw = 350 Kfor the wall temperature.

discharge, suggests the dominance of the V-V and V-T mechanisms in the heattransfers to the gas. In fact, the excess of CO2 in our modelling system seemsto compensate almost exactly for the missing processes.

5.5 Conclusions

This chapter presents a self-consistent model that provides the time-dependentradially averaged gas temperature both in a millisecond pulsed and in a con-tinuous CO2 discharge. The model is based on the coupled solutions to thegas thermal balance equation, the electron Boltzman equation and a systemof rate balance equations for ∼70 CO2 vibrational levels. The calculations aremade for a cylindrical geometry. The temperature dependence of the thermalconductivity and the heat capacity is taken into account and a modest overviewof these parameters available in the literature is included.

The validation of the model is done through a comparison with two differentexperiments. The first one is an in situ FTIR study in a millisecond pulsedDC discharge, whilst the second experiment is a rotational Raman study in acontinuous plasma. A very good agreement between modelling predictions andmeasurements is obtained in the first case, where the temporal evolution of thegas temperature matches very well the measured data. The good agreement

127

Chapter 5. Modelling of the time-dependent gas temperature in CO2

implies that the vibrational kinetics dominates the energy transferred to gasheating in the single-pulse experiment and confirms the reaction mechanismproposed in [36] and [37].

The second experiment corresponds to a different plasma, containing dissoci-ation products, therefore, including the influence of the corresponding chemicalkinetics, that is excluded in our model. However, a very good agreement be-tween the measurements and the simulation is still obtained. This implies theimportance of the V-V and V-T processes for the heat transfers in a CO2 plasma.Moreover, it suggests the validity of using the present simplified model as a toolto calculate the gas temperature in CO2 operating in more complex conditions.Future work should include the dissociation of CO2 molecules and chemicalkinetics in a CO2/CO/O2/O system, including the corresponding vibrationallyexcited states and energy exchanges between them in order to accurately de-scribe and to fully understand the heating mechanisms in a non-equilibriumCO2 plasma.

128

5.6. References

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[38] A. Tejero-del Caz, V. Guerra, D. Goncalves, M. Lino da Silva, L. Marques,N. Pinhao, C. Pintassilgo, and L. Alves, “The LisbOn KInetics Boltzmannsolver,” Plasma Sources Sci. Technol., 28, 043001, 2019.

[39] A. Morillo-Candas, C. Drag, J.-P. Booth, V. Guerra, and O. Guaitella,“Oxygen atom kinetics in CO2 plasmas ignited in a DC glow discharge,”Plasma Sources Sci. Technol., 28, 075010, 2019.

[40] T. Silva, M. Grofulovic, L. Terraz, C. D. Pintassilgo, and V. Guerra,“Modelling the input and relaxation of vibrational energy in CO2 plasmas,”J. Phys. D: Appl. Phys., 51, 464001, 2018.

[41] M. Grofulovic, B. L. M. Klarenaar, O. Guaitella, V. Guerra, and R. Engeln,“A rotational raman study under non-thermal conditions in pulsed CO2-N2

and CO2-O2 glow discharges,” Plasma Sources Sci. Technol, 28, 045014,2019.

132

Chapter 6

A rotational Raman study undernon-thermal conditions in pulsedCO2-N2 and CO2-O2 glowdischarges

This chapter employs in situ rotational Raman spectroscopy to study the effectof N2 and O2 addition to CO2 in pulsed glow discharges in the mbar range.The spatiotemporally resolved measurements are performed in CO2 and 25%,50% and 75% of N2 or O2 admixture, in 5-10 ms on-off cycle, 50 mA plasmacurrent and 6.7 mbar total pressure. The rotational temperature profile isnot affected by adding N2, ranging from 400 K to 850 K from start to endof the discharge pulse, while the addition of O2 decreases the temperatureat corresponding time points. Molecular number densities of CO2, CO, O2

and N2 are determined, showing the spatial homogeneity along the axis ofthe reactor and uniformity during the cycle. The measurements in the N2

containing mixtures show that CO2 conversion factor α increases from 0.15 to0.33 when the content of N2 is increased from 0% to 75%, demonstrating thepotential of N2 addition to enhance the vibrational pumping of CO2 and itsbeneficial effect on CO2 dissociation. Furthermore, the influence of admixtureson CO2 vibrations is examined by analysing the vibrationally averaged nuclearspin degeneracy. The difference between the fitted odd averaged degeneracyand the calculated odd degeneracy assuming thermal conditions increases withthe addition of N2, demonstrating the growth of vibrational temperatures inCO2. On the other hand, the addition of O2 leads to a decrease of α, which

133

Chapter 6. A rotational Raman study in CO2-N2 and CO2-O2

might be attributed to quenched vibrations of CO2, and/or to the influence ofthe back reaction in the presence of O2.1

1The results presented here are published as A rotational Raman study under non-thermalconditions in pulsed CO2-N2 and CO2-O2 glow discharges, M. Grofulovic, B. L. M. Klarenaar,O. Guaitella, V. Guerra, and R. Engeln, 2019 Plasma Sources Science and Technology, 28,045014.

134

6.1. Introduction

6.1 Introduction

Reduction of carbon-dioxide for solar fuels production is a matter of largescientific and industrial interest [1]. Non-thermal plasmas are a promisingcandidate to achieve efficient dissociation of CO2, as they offer a selectiveactivation of certain chemical processes [2]. Vibrational excitation, for instance,may lead to the dissociation of CO2 molecules without a significant amount ofkinetic energy. A large number of publications have addressed this issue, bothexperimentally [3–5] and theoretically [6–11], often highlighting the relevance ofthe selective excitation of the asymmetric stretch vibration of CO2. Furthermore,N2 addition might be interesting per se, as it can have a positive repercussionon CO2 dissociation.

Some recent works have studied CO2-N2 mixtures, motivated mostly byreentry problems [12, 13] and by their application to CO2 conversion [14–17].In the latter case, the reason for considering the effect of N2 is twofold. Firstly,N2 is the main impurity in most industrial gasflows, so the influence it mayhave on the kinetics and chemistry of a plasma has to be considered. Secondly,the vibrational energy transfer from vibrationally excited N2 to the asymmetricmode of CO2 can be beneficial for vibrational dissociation of CO2. Vibrationallyexcited N2 serves as an energy reservoir due to a high degree of vibrationalexcitation that can be easily reached and very slow relaxation, which maystrongly affect the plasma properties [18]. The effect it has on CO2 vibrationsis well-known from the studies of CO2-N2 maser/laser systems in the 60’s[19–22], reporting that the selective excitation of the asymmetric mode of CO2

by nearly resonant vibrational energy transfers from N2 enhances lasing power.Current research on plasma-based CO2 conversion in presence of N2 is donewith dielectric barrier discharges (DBD)[14–16] and microwave plasmas (MW)[17], with the main focus on increasing the CO2 conversion rate and energyefficiency.

This work addresses the experimental investigation of a pulsed glow dischargein CO2-N2 in the mbar range. The investigation is further extended to CO2-O2

mixtures, since the effect of O2 is relevant for CO2 conversion, given that O2

is a product of CO2 dissociation. Despite having fairly low conversion andenergy efficiencies, glow discharges are easily accessible for different diagnosticsand proved to be very convenient for validation of complex numerical models[6, 23, 24].

The study conducted in the present work employs rotational Raman spec-troscopy, which provides spatiotemporally resolved rotational temperatures(Trot) and number densities of heavy particles in the plasma. Utilization ofrotational Raman spectroscopy has been demonstrated for measuring rotationaltemperatures in CO2 in DBD discharges [25, 26]. In a recent work by Klarenaaret al [4], this technique was performed in a CO2 glow discharge in the mbarrange. The obtained Trot and composition were shown to be in good agreement

135

Chapter 6. A rotational Raman study in CO2-N2 and CO2-O2

Figure 6.1: a) Schematic representation of the Raman setup. Raman scattered lightis collected from the focal point of a pulsed Nd:YAG laser, focused inside the reactor.Rayleigh scattered and stray light is removed by using a volume Bragg grating, afterwhich the remaining light enters a spectrometer and is detected by an ICCD camera.b) The clock of the laser is used for triggering of the plasma power supply and theintensifier (figure courtesy of B. L. M. Klarenaar).

with the FTIR study [3] and to have good spatial homogeneity over the lengthof the reactor. The present study is performed on the same reactor, under equaloperating conditions and using the same experimental setup as in [4]. Theability of detecting numerous Raman active molecules in the spectral rangeof a single measurement makes rotational Raman spectroscopy pertinent forinvestigating gas mixtures. Furthermore, rotational Raman spectroscopy is usedto gain insight on vibrational excitation of CO2. Vibrations of CO2 moleculesaffect its nuclear degeneracy, which can be expressed by a ratio between theintensity of even and odd numbered CO2 peaks [4, 27]. Hence, this ratio is usedto inspect the effect of N2 addition on CO2 vibrations.

The organization of this chapter is the following. Section 6.2 gives a generaldescription of the experimental setup and measurement procedure employedin this work. The analysis of the rotational temperature and relative gas

136

6.2. Experiment

composition in different gas mixtures is presented in section 6.3. Section 6.4discusses the observed impact of admixtures on vibrational excitation anddissociation of CO2. Finally, the conclusions are given in section 6.5.

6.2 Experiment

The reactor used in the experiment is made of pyrex. It is cylindrically shapedwith a 2 cm inner diameter and a length of 23 cm, while the electrodes areplaced 17 cm apart (see figure 6.1a). It is operated under flowing conditionsusing CO2, N2 and O2 inflows, controlled at 7.4 sccm total flow rate and aconstant pressure. Unless otherwise noted, the pressure is kept at 6.67 mbarwith a discharge current of 50 mA. All the measurements were performed with5 ms plasma-on time and 10 ms off time.

A complex optical setup is used to focus the light of a pulsed Nd:YAG laser(532 nm, 100 mJ/pulse, 100 Hz) inside the plasma reactor resulting in a beamwaist of 70 µm. Rayleigh scattered and stray light is removed by using a volumeBragg grating, which acts as an ultra-narrow-band notch filter. The light isthen focused onto the 50 µm entrance slit of the spectrometer (Jobin-Yvon, HR640, equipped with a Horiba, 530 15 Holographic Grating, 2400 l/mm, blazed at400 nm), after which the spectrally resolved light is detected with an intensifiedcamera (ICCD). The frequency range of this spectrometer- ICCD combinationis 183 cm−1 with a resolution of 0.143 cm−1. The spectral broadening isdetermined to be Voigt shaped with a FWHM of 1.55 cm−1, with an equalGaussian and Lorentzian contribution. The wavelength sensitivity of the fulldetection branch is determined using the black-body radiation of a W-ribbonlamp and used for calibrating the measured spectra.

The power supply for the plasma reactor and the gating of the intensifier aretriggered by using the laser clock. In order to match the 10 ms laser cycle withthe 15 ms plasma cycle, every third laser pulse is used to trigger two consecutiveplasma cycles, controlling the phase difference by setting a delay between laserclock and the start of the two plasma pulses (see figure 6.1b).

The gate of the intensifier is triggered by one in every three laser pulses withthe gate duration of 70 ns, which is long enough to collect the laser light and tooshort for plasma emission to be recorded. For every time resolved measurementthe position of the detection arm is fixed at the center of the reactor, i.e. at8.5 cm, while the selection of time points (0.0, 0.7, 1.4, 2.0, 3.0, 4.9, 5.2, 6.0, 7.5,10.0, and 12.5 ms) is made by varying the laser pulse phase with respect to theplasma cycle. Each measurement has accumulation time of 45 min resulting inaveraging 90,000 laser pulses per measurement. Possible pressure fluctuationsduring such a long measurement are addressed by using a scroll pump anda pressure gauge with feedback to an automated valve, which maintains thepressure constant. Laser focal point could change its position over time due to

137

Chapter 6. A rotational Raman study in CO2-N2 and CO2-O2

533 534 535 536Wavelength (nm)

10-2

100dataExcl. from fitTotal fitCO

2

COO

2

N2

533 534 535 536

10-2

100

Inte

nsity

(no

rmal

ized

)

532 533 534 535 536 537Wavelength (nm)

10-2

100

a)

t = 4.9 ms; 25% N2- CO2; Trot = 830.8 K

t = 0.0 ms; 25% N2- CO2;

Trot = 387.6 K

t = 4.9 ms; 75% N2- CO2; Trot = 850.2 Kc)

b)

Figure 6.2: Rotational Raman spectra (Stokes only) measured at 8.5 cm, in thecenter of the reactor. The measurements are taken at a) 0.0 ms, in CO2-25%N2, b)4.9 ms, in CO2-25%N2 and c) 4.9 ms in CO2-75%N2. Solid black line represents thefit on the data, while the contributions of CO2, CO, O2 and N2 peaks are indicatedby colored lines.

heating of the laser, which is monitored by a camera and actively corrected witha feedback loop to a kinematic mirror mount. The influence of the fluctuationsin the laser power are considered by continuously monitoring in order to adjustthe intensity of the Raman spectra. Spatially resolved measurements are doneby translating the reactor along the axis with respect to the laser focal pointwhile keeping the phase constant.

Before starting a series of measurements, it is necessary to calibrate thewavelength axis by measuring a Raman spectrum in pure N2 gas. The N2

spectrum is also used for calibrating the intensity which is required to obtainmolecular number densities. For every series of measurements, a background

138

6.2. Experiment

measurement is taken with covered fiber opening in the detection branch.ICCD settings are kept the same during the calibration, background and themeasurement series.

The measured spectra are analyzed by using an algorithm which calcu-lates spectrally broadened rotational Raman spectra for mixtures of differentmolecules. The total spectrum is calculated as a sum of the individual spectraof the molecular species present in the system, including the spectral broadeningin a form of Voigt profile. This algorithm and the underlying theory are detailedin the work of Klarenaar et al [4].

The spatiotemporally resolved number densities obtained in the experimentare then utilized for the analysis of the conversion of CO2, characterized by theCO2 conversion factor α [3, 4, 28],

α =[CO]

[CO2]i=

[CO]

[CO] + [CO2]f, (6.1)

where [CO] and [CO2] are the number densities of CO and CO2, respectively. Itis assumed here that the difference between [CO2] before and after the dischargeequals to [CO], i.e. [CO2]i − [CO2]f = [CO], where the indexes i and f refer toinitial (before the discharge) and final (after the discharge) concentrations. Itis assumed here that no carbon deposition occurs, which has been checked bylooking at the carbon balance with FTIR measurement downstream a similarplasma [28]. As the determination of [CO] is subject to some uncertainty (seesection 6.3), α is additionally calculated by substituting the density of CO bytwice the density of O2. This introduces the assumption that the amounts of Oatoms and NOx species created in the discharge are negligible. The conversionfactor α presented is the weighted average from the two calculations.

For CO2-O2 mixtures the CO density cannot be simply replaced by twicethe density of O2, as there is an initial amount of oxygen. An alternativeway of calculating α can be derived from expression (6.1), assuming that[O2]f = [O2]i + [O2]diss and [O2]diss = 1/2[CO] is being produced by thedissociation of CO2:

α =FO2

f /FCO2

f − FO2i /FCO2

i

1/2 + FO2

f /FCO2

f

, (6.2)

where FO2

f and FCO2

f are the final, and FO2i and FCO2

i are the initial molecularfractions of O2 and CO2 relative to the total number density. α is thenrepresented as weighted average of the calculations made by both of thisexpressions.

139

Chapter 6. A rotational Raman study in CO2-N2 and CO2-O2

6.3 Results

Rotational Raman spectra

Figure 6.2 displays three different examples of rotational Raman spectra, corre-sponding to different time points and/or different initial gas composition. Allthe spectra are measured in the center of the reactor at 0.0 ms - panel a) and at4.9 ms - panels b) and c). Accurate description of the data (presented by orangecircles) is evident from the good comparison with the total fit, represented bythe solid black line. Contributions of the lines corresponding to CO2, CO, O2

and N2 is depicted by the lines of different colors, while gray circles show thedata excluded due to deformation by the notch-filter.

Panels a) and b) show spectra measured in the same mixture, i.e. CO2-25%N2, at the beginning and at the end of the pulse, respectively. Clearly, thetemperature growth relates to the higher scattering intensity of the peaks atlarger wavelengths. Contribution of N2, CO and O2 peaks in panels a) and b)is more explicit at larger wavelengths where the intensity of CO2 peaks is lower.O2 and N2 peaks, however, are significant at smaller wavelengths as well. Forinstance, it is easy to observe their contributions at 533.7 nm, 534.1 nm and534.4 nm. Since CO peaks are explicit mostly at larger wavelengths, fitting of COdensity is generally less accurate. Panel c) shows the spectrum corresponding toCO2-75%N2 with more dominant N2 lines, affecting the spectrum significantlyeven at small wavelengths (see the peak at 532.3 nm) due to a larger amount ofN2 in the plasma. The contribution of odd rotational peaks of CO2 is readilyobserved in the panels b) and c) as a reduced depth of the minima of CO2

peaks.

Temperature profile

Temperatures determined from the time-resolved measurement are shown infigures 6.3a) and 6.3b) in mixtures containing CO2 and different amounts ofN2 and O2, respectively, including a 95% fitting uncertainty. The rotationaltemperature measured in pure N2 is shown in 6.3a). The black dashed lines inboth panels represent the temperatures obtained in the measurements in pureCO2 at the same conditions, previously presented in [4]. It can be observed infigure 6.3a) that the presence of N2 up to 75% in the mixture does not affectthe Trot evolution: the initial temperature of ∼ 400 K quickly increases atignition and reaches ∼ 830 K at the end of the plasma pulse. On the otherhand, a higher amount of O2 results in lower temperatures at correspondingtimes (see figure 6.3b). The temperature in pure N2 is ∼ 300 K lower than thetemperature in CO2 and CO2-N2 discharges at the end of the pulse. In theafterglow, Trot exponentially decreases towards the initial temperature with thesimilar relaxation times in all cases.

140

6.3. Results

4 0 0

6 0 0

8 0 0

0 2 4 6 8 1 0 1 2 1 4

4 0 0

6 0 0

8 0 0

2 5 % N 2 5 0 % N 2 7 5 % N 2 p u r e C O 2 p u r e N 2

a ) P l a s m a o nT rot

(K)

t ( m s )

2 5 % O 2 5 0 % O 2 7 5 % O 2 p u r e C O 2

b )

Figure 6.3: The rotational temperature versus time for different initial gas mixturescontaining CO2 and a) 25%, 50% and 75% of N2; and b) 25%, 50% and 75% of O2.The grey dashed line depicts the rotational temperature measured in N2, whilst theblack dashed line represents the rotational temperature in pure CO2, reported in [4].The total pressure is p=6.67 mbar, I=50 mA and pulse duration is ∆t=5 ms.

In complex media, such as CO2, N2 and O2 plasmas, understanding of thegas heating requires a thorough investigation of the interplay between electron,vibrational and chemical kinetics and surface processes. The contribution ofthe heat conduction, for instance, which is the dominant cooling mechanismduring the afterglow, is estimated using the values of thermal conductivityand molar heat capacity presented in [29] and is very similar in N2 and O2.This indicates that different temperature profiles in CO2-N2 and CO2-O2 aredue to some heat transfer mechanisms other than conduction, and can mostlikely be attributed to the different vibrational kinetics in N2 and O2. As itis well known, in N2 and N2-O2 discharges operating in conditions similar tothose under study, the electrons transfer their energy very efficiently to thenitrogen vibrational states [30], which results in a highly populated vibrationaldistribution function (VDF) of N2(X,v) [24, 30, 31]. This is in sharp contrastwith O2, where only a small fraction of the electron energy is transferred to thevibrational states [32] and the VDFs of O2(X,v) are much less populated [31].The difference between the Trot profiles in pure N2 and in CO2-N2 indicates

141

Chapter 6. A rotational Raman study in CO2-N2 and CO2-O2

0246

0 2 4 6 8 1 0 1 2 1 40

2 5

5 0

7 5

N (

1022

m-3 ) a ) P l a s m a o n

C O 2 O 2 C O N 2

Gas c

ompo

sition

(%)

t ( m s )

b )

Figure 6.4: Fitting results from the time-resolved rotational Raman measurementsin 25% N2 and 75% CO2 initial plasma composition. a) Absolute molecular numberdensities of CO2, N2, CO and O2. b) The gas composition, assuming that speciesother than CO2, N2, CO, and O2 are not present in significant amounts. The totalpressure is p=6.67 mbar, I=50 mA and pulse duration is ∆t=5 ms.

that vibrational energy exchanges between CO2 and N2 play an important rolein heat transfer mechanisms.

Molecular number densities

The temporally resolved fitted number densities of CO2, N2, CO, and O2 areshown for the CO2-25%N2 mixture in figure 6.4a), including a 95% fittinguncertainty. The presence of other rotationally active species was not indicatedby the rotational Raman spectra, hence it is assumed that plasma does notcontain significant amounts of molecules other then CO2, N2, CO, and O2 only.A certain amount of atomic oxygen, which is not rotationally active, might beformed. However, at the studied conditions it is expected to be relatively low[33].

All number densities change significantly with time during a plasma cycle:they decrease as the plasma heats up during the on time, and increase backto the initial value as the temperature drops in the afterglow. However, therelative gas compositions are nearly constant during the cycle, which is shown

142

6.3. Results

0246

0 2 4 6 8 1 0 1 2 1 40

2 5

5 0

7 5

N (10

22 m

-3 )

C O 2 O 2 C O S p a t i a l l y - r .

a ) P l a s m a o nGa

s com

positi

on (%

)

t ( m s )

b )

Figure 6.5: Fitting results from the time-resolved rotational Raman measurementsin CO2-25%O2. a) Absolute molecular number densities of CO2, CO and O2. b) Thegas composition, assuming other species than CO2, CO, and O2 are not present insignificant amounts. In both panels diamonds indicate the results from the spatially-resolved measurements shown in figure 6.6, measured at t = 4.9 ms at the center ofthe reactor.

in figure 6.4b). They are obtained as a ratio between the number density andthe total gas density at each time point. The important point to note here isthat the amount of N2 remains 25% during the discharge, proving that there isno observable conversion of N2 at these conditions. Some small amounts of NOx

are most likely created. However, taking the results on N2-O2 discharges from[34, 35] as a reference, their concentrations are expected to be small and seemto be below the detection limit. To fully investigate this issue, some of highsensitive detection methods should be used, e.g. the infrared tunable diode laserabsorption spectroscopy (TDLAS) [36, 37] or quantum cascade laser absorptionspectroscopy (QCLAS) [38].

Similar plots show number densities and relative composition of CO2, CO,and O2 in figures 6.5a) and b) for the CO2-25%O2 mixture. Clearly, the numberdensities vary between different time points in accordance with the ideal gas law,as in the previous case, while the relative composition is nearly constant withtime. Figure 6.6 depicts the spatially resolved number densities and relativecomposition for CO2-25%O2, measured at the very end of the discharge, i.e.

143

Chapter 6. A rotational Raman study in CO2-N2 and CO2-O2

0

2

4

0 2 4 6 8 1 0 1 2 1 40

4 0

8 0

N (10

22 m

-3 ) C O 2 O 2 C O T i m e - r .

a )

P o s i t i o n ( c m )

Gas c

ompo

sition

(%) b )

Figure 6.6: Fitting results from the spatially-resolved rotational Raman measurementin CO2-25%O2, corresponding to the end of the pulse, t = 4.9 ms. Absolute molecularnumber densities of CO2, CO and O2 are shown in panel a) and relative gas compositionassuming other species than CO2, CO, O2, are not present in significant amounts isshown in panel b). In both panels diamonds indicate the results from the time-resolvedmeasurements shown in figure 6.5, measured at the same timing in the center of thereactor.

4.9 ms. The diamonds in figure 6.5 indicate the fitted values obtained from thespatially resolved measurements. Similarly, diamonds in figure 6.6 indicate theresults from the time-resolved measurement at equal time and position. Theagreement between time- and spatially-resolved measurements at correspondingtimes and positions in both figures shows good reproducibility over differentexperimental sessions, demonstrating the reliability of the diagnostic techniqueand the obtained results. The spatial homogeneity of the discharge shown infigure 6.6 is stimulated by the diffusion and convection due to the gas flow,as discussed in [4]. Therefore the whole positive column can be consideredhomogeneous and the time evolution measured is reflecting the change of thewhole plasma volume and not only of the evolution at one given position.

144

6.4. CO2 conversion

0 . 0

0 . 1

0 . 2

0 . 3

0 . 4

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0

0

5

1 0

1 5

2 0

N 2 - C O 2 O 2 - C O 2

α

a )

b )

CO co

ntent

(%)

C o m p o s i t i o n ( % N 2 ; O 2 )

Figure 6.7: a) The conversion factor α in CO2-N2 (the blue solid line) as a functionof N2 fraction and in CO2-O2 (the dashed orange line) as a function of O2 fraction inthe gas mixture. b) The content of CO relative to the total gas density, for differentgas mixtures.

6.4 CO2 conversion

The CO2 conversion factor α, calculated by employing expressions (6.1) and(6.2), is plotted in figure 6.7a) as a function of the N2 and O2 fractions. Theresults show that an increase of the N2 fraction leads to a higher value of α,which demonstrates its beneficial influence on CO2 conversion. The physicalmechanism responsible for the N2 induced enhancement of CO2 dissociationmay reside in the vibrational energy transfer from N2(v) to CO2 molecules.

145

Chapter 6. A rotational Raman study in CO2-N2 and CO2-O2

Nearly resonant fast vibrational transfer between vibrationally excited N2 andthe asymmetric ν3 mode of CO2 is well-known from the studies of processesimportant for CO2-N2 lasers [19–21], and is assumed to be a pathway for anefficient excitation of the levels in the asymmetric CO2 mode. A high degree ofvibrational excitation of this mode would then facilitate dissociation [2].

Despite having an increase of α with the addition of N2, the amount of COproduced in the discharge does not change significantly by varying the amountof N2 between 0 and 75%, as shown in figure 6.7b). This is due to the smallerfraction of CO2 initially present in the gas mixtures, compensating to someextent the enhancement of the CO2 dissociation caused by the presence of N2.

To investigate the vibrational excitation of CO2 in different mixtures, wecan examine the fitted vibrationally averaged nuclear degeneracy of the oddrotational levels of CO2. The vibrations of the CO2 molecule affect its nucleardegeneracy, which in practice can be observed from the variations in the ratiobetween the intensity of even and odd numbered CO2 peaks in the rotationalRaman spectra [39, 40]. Elevations of the odd vibrationally averaged nucleardegeneracy, 〈gJ,o〉, above the degeneracy calculated for thermal conditions atTrot = T12 = T3, 〈gJ,o〉th, are an indication of non-thermal conditions in theplasma [4]. This is shown in figures 6.8a) and b) for CO2-25%N2 and CO2-75%N2, respectively. Evidently, both panels show that during the on time〈gJ,o〉 is above 〈gJ,o〉th, with higher elevations for CO2-75%N2. During thepost-discharge, 〈gJ,o〉 and 〈gJ,o〉th are nearly equal at corresponding times whenthere is a smaller amount of N2 present, which is in contrast with what weobserve in CO2-75%N2, where the elevations of 〈gJ,o〉 above 〈gJ,o〉th indicatethat the plasma did not thermalise during the afterglow. Panel c) of thesame figure displays the difference between the fitted odd averaged degeneracyand the degeneracy calculated for thermal conditions, 〈gJ,o〉 − 〈gJ,o〉th, fordifferent gas mixtures. This difference is larger during the discharge than itis in the post-discharge, when CO2 vibrations relax, as shown in panels a)and b). Moreover, 〈gJ,o〉 − 〈gJ,o〉th increases with N2 content, indicating highervibrational temperatures of CO2. Figures 6.8b) and c) show that the vibrationalexcitation of CO2 still persists in the post-discharge in the case of CO2-75%N2,due to the V − V ′ exchange process [41]

CO2(000ν) + N2(υ)↔ CO2(000(ν + 1)) + N2(υ − 1).

The work by Heijkers et al [17], focused on modeling and experimental inves-tigation of MW discharges in CO2-N2 mixtures, reports that the dissociation ofvibrationally excited CO2 by collisions with heavy particles in the plasma is thedominant channel for the destruction of CO2 in mixtures having more than 30%of N2. Electron impact dissociation from ground state and from vibrationallyexcited states is found to be important only in the MW discharge containingsmaller fractions of N2, giving a contribution of 25% and 42%, respectively.

146

6.5. Conclusions

Studies performed on DBD discharges have also reported that dissociation ofCO2 is enhanced by the addition of N2, however the physical mechanism behindit is driven by the electrons. Addition of N2 decreases electron attachment rates,which leads to higher current pulses in DBD and enhances electron impactdissociation [14, 16, 42], while reactions with metastable N2(A3Σ+

u ) moleculeswith CO2 are dominant at large fractions of N2 [16].

Contrary to N2, an increase of the O2 fraction is observed to have a negativeimpact on CO2 dissociation, as shown in figure 6.7. One reason might bethe quenching of vibrationally excited CO2 by O2 molecules, resulting in adecrease of dissociation involving vibrationally excited CO2 molecules. Anotherpossibility is the enhancement of recombination with CO producing CO2; this“back reaction” is very slow at room temperature [8], but it is not unreasonableto consider that its rate coefficient can be significantly higher if the reactioninvolves vibrationally excited CO molecules. To fully understand the processesresponsible for the observed effects, it is necessary to model these plasmasand to further study the kinetics of O atoms and O2 molecules in mixturescontaining large amounts of oxygen.

6.5 Conclusions

In this work, rotational Raman spectroscopy was used to investigate spatiotem-porally resolved rotational temperatures and number densities in CO2-N2 andCO2-O2 gas mixtures excited by a pulsed dc discharge. Spectra are recorded atdifferent times during the discharge pulse and attributed to the contributionsof CO2, O2, CO and N2, where the contribution of CO2 peaks originates fromeven and odd rotational levels. Moreover,the vibrationally averaged nuclear de-generacies, related to the vibrational excitation of CO2, are studied in presenceof different fractions of N2 and O2.

The rotational temperature is observed to have the very similar profileswith 25%, 50% and 75% of N2 admixtures as in pure CO2 plasma, reaching850 K at the end of the pulse. In CO2-O2 plasmas, Trot decreases with a higherfraction of O2. The observed temperature difference between CO2-25%O2 andO2-75%CO2 at the end of the pulse reaches 250 K.

Number densities and relative compositions of CO2, N2 , CO, and O2 aredetermined for different admixtures of N2 and O2. It is observed that therelative compositions are nearly constant during the pulse and also along theaxis of the reactor. The fitted number densities are utilized for the analysisof the CO2 conversion factor α. It is demonstrated that addition of N2 hasa beneficial effect on CO2 decomposition. In CO2-N2 α is determined toamount to 0.17, 0.23 and 0.33 for 25%, 50% and 75% of N2 in its mixtures,respectively, which might be interpreted as an evidence of the vibrationalenergy transfer between vibrationally excited N2 and CO2 molecules and its

147

Chapter 6. A rotational Raman study in CO2-N2 and CO2-O2

0 . 0

0 . 2

0 . 4

0 . 6

0 2 4 6 8 1 0 1 2 1 40 . 0

0 . 1

0 . 2

0 . 3

0 . 2

0 . 4

0 . 62 5 % N 2 + 7 5 % C O 2

T h e r m a l F i t t e d

7 5 % N 2 + 2 5 % C O 2 T h e r m a l F i t t e d

c )

t ( m s )

2 5 % N 2 5 0 % N 2 7 5 % N 2

<gJ,o

> - <g

J,o> th

a ) P l a s m a o n

b )<gJ,o

>

Figure 6.8: The fitted odd vibrationally averaged nuclear degeneracy of CO2 (—–)and the calculated odd degeneracy assuming thermal conditions, calculated usingthe fitted rotational temperature (- - -), for a) CO2-25%N2 and b) CO2-75%N2. c)The difference between the fitted odd averaged degeneracy and the calculated odddegeneracy assuming thermal conditions in different compositions of CO2-N2.

importance of vibrational excitation of CO2 on dissociation. This is supportedby the fact that the difference between the fitted odd averaged degeneracyand the calculated degeneracy for thermal conditions at Trot increases with

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6.5. Conclusions

higher amounts of N2 present in plasma. However, the interplay of electronand vibration kinetics, complex chemistry as well as the presence of metastablestates has to be considered for a comprehensive and unambiguous interpretationof the observed results. Further investigation demands a detailed kinetic modelto fully understand the relevant processes occurring in CO2-N2 and CO2-O2

glow discharges.

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Chapter 6. A rotational Raman study in CO2-N2 and CO2-O2

6.6 References

[1] A. Bogaerts, T. Kozak, K. van Laer, and R. Snoeckx, “Plasma-basedconversion of CO2: current status and future challenges,” Faraday Discuss.,183, 217–232, 2015.

[2] A. Fridman, Plasma chemistry. Cambridge: Cambridge University Press,2008.

[3] B. L. M. Klarenaar, R. Engeln, D. C. M. van den Bekerom, M. C. M.van de Sanden, A. S. Morillo-Candas, and O. Guaitella, “Time evolutionof vibrational temperatures in a CO2 glow discharge measured with infraredabsorption spectroscopy,” Plasma Sources Sci. Technol., 26, 115008, 2017.

[4] B. L. M. Klarenaar, M. Grofulovic, A. S. Morillo-Candas, D. C. M. van denBekerom, M. A. Damen, M. C. M. van de Sanden, O. Guaitella, andR. Engeln, “A rotational Raman study under non-thermal conditions in apulsed CO2 glow discharge,” Plasma Sources Sci. Technol., 27, 045009,2018.

[5] N. Britun, T. Silva, G. Chen, T. Godfroid, J. van der Mullen, and R. Sny-ders, “Plasma-assisted CO2 conversion: optimizing performance via mi-crowave power modulation,” J. Phys. D: Appl. Phys., 51, 144002, 2018.

[6] M. Grofulovic, T. Silva, B. L. M. Klarenaar, A. S. Morillo-Candas,O. Guaitella, R. Engeln, C. D. Pintassilgo, and V. Guerra, “Kinetic studyof CO2 plasmas under non-equilibrium conditions. II. Input of vibrationalenergy,” Plasma Sources Sci. Technol., 27, 115009, 2018.

[7] T. Silva, M. Grofulovic, B. L. M. Klarenaar, O. Guaitella, R. Engeln,C. D. Pintassilgo, and V. Guerra, “Kinetic study of CO2 plasmas undernon–equilibrium conditions. I. Relaxation of vibrational energy,” PlasmaSources Sci. Technol., 27, 015019, 2018.

[8] T. Kozak and A. Bogaerts, “Splitting of CO2 by vibrational excitation innon-equilibrium plasmas: a reaction kinetics model,” Plasma Sources Sci.Technol., 23, 045004, 2014.

[9] M. Capitelli, G. Colonna, G. D’Ammando, and L. D. Pietanza, “Self-consistent time dependent vibrational and free electron kinetics for CO2

dissociation and ionization in cold plasmas,” Plasma Sources Sci. Technol.,26, 055009, 2017.

[10] P. Diomede, M. C. M. van de Sanden, and S. Longo, “Insight into CO2

dissociation in plasma from numerical solution of a vibrational diffusionequation,” J. Phys. Chem. C, 121, 19568–19576, 2017.

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6.6. References

[11] J. F. de la Fuente, S. H. Moreno, A. I. Stankiewicz, and G. D. Stefanidis, “Anew methodology for the reduction of vibrational kinetics in non-equilibriummicrowave plasma: application to CO2 dissociation,” React. Chem. Eng.,1, 540–554, 2016.

[12] V. Joly and A. Roblin, “Vibrational relaxation of CO2(m,nl, p) in a CO2-N2 mixture. part 1: Survey of available data,” Aerosp. Sci. Technol., 3,229 – 238, 1999.

[13] V. Joly, C. Marmignon, and P. Jacquet, “Vibrational relaxation ofCO2(m,nl, p) in a CO2-N2 mixture. part 2: Application to a one-dimensional problem,” Aerosp. Sci. Technol., 3, 313 – 322, 1999.

[14] R. Brandenburg and A. Sarani, “About the development of single microdis-charges in dielectric barrier discharges in CO2 and CO2/N2 gas mixtures,”Eur. Phys. J. Spec. Top., 226, 2911–2922, 2017.

[15] M. Schiorlin, R. Klink, and R. Brandenburg, “Carbon dioxide conversionby means of coplanar dielectric barrier discharges,” Eur. Phys. J. Appl.Phys., 75, 24704, 2016.

[16] R. Snoeckx, S. Heijkers, K. V. Wesenbeeck, S. Lenaerts, and A. Bogaerts,“CO2 conversion in a dielectric barrier discharge plasma: N2 in the mixas a helping hand or problematic impurity?,” Energy Environ. Sci., 9,999–1011, 2016.

[17] S. Heijkers, R. Snoeckx, T. Kozak, T. Silva, T. Godfroid, N. Britun,R. Snyders, and A. Bogaerts, “CO2 conversion in a microwave plasmareactor in the presence of N2: Elucidating the role of vibrational levels,”J. Phys. Chem. C, 119, 12815–12828, 2015.

[18] J. Loureiro, V. Guerra, P. A. Sa, C. D. Pintassilgo, and M. L. da Silva,“Non-equilibrium kinetics in N2 discharges and post-discharges: a fullpicture by modelling and impact on the applications,” Plasma Sources Sci.Technol., 20, 024007, 2011.

[19] C. K. N. Patel, “Selective excitation through vibrational energy transferand optical maser action in N2-CO2,” Phys. Rev. Lett., 13, 617–619, 1964.

[20] R. L. Taylor and S. Bitterman, “Survey of vibrational relaxation data forprocesses important in the CO2-N2 laser system,” Rev. Mod. Phys., 41,26–47, 1969.

[21] W. J. Witteman and G. V. D. Goot, “High-power infrared laser withadjustable coupling-out,” J. Appl. Phys., 37, 2919–2919, 1966.

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Chapter 6. A rotational Raman study in CO2-N2 and CO2-O2

[22] S. Ono and S. Teii, “Vibrational temperature in a weakly ionised CO2-N2-He discharge,” J. Phys. D. Appl. Phys., 18, 441, 1985.

[23] T. Silva, M. Grofulovic, L. Terraz, C. D. Pintassilgo, and V. Guerra,“Modelling the input and relaxation of vibrational energy in CO2 plasmas,”J. Phys. D: Appl. Phys., 51, 464001, 2018.

[24] V. Guerra and J. Loureiro, “Self-consistent electron and heavy-particlekinetics in a low-pressure N2-O2 glow discharge,” Plasma Sources Sci.Technol., 6, 373, 1997.

[25] F. Brehmer, S. Welzel, B. L. M. Klarenaar, H. J. van der Meiden, M. C. M.van de Sanden, and R. Engeln, “Gas temperature in transient CO2 plasmameasured by Raman scattering,” J. Phys. D: Appl. Phys., 48, 155201,2014.

[26] B. L. M. Klarenaar, F. Brehmer, S. Welzel, H. J. van der Meiden, M. C. M.van de Sanden, and R. Engeln, “Note: Rotational Raman scattering onCO2 plasma using a volume Bragg grating as a notch filter,” Rev. Sci.Instrum., 86, 046106, 2015.

[27] D. van den Bekerom, J. M. P. Linares, T. Verreycken, E. M. V. Veldhuizen,S. Nijdam, W. Bongers, R. V. de Sanden, and G. J. V. Rooij, “The impor-tance of thermal dissociation in CO2 microwave discharges investigatedby power pulsing and rotational Raman scattering,” Plasma Sources Sci.Technol., 28, 055015, 2019.

[28] B. L. M. Klarenaar, A. S. Morillo-Candas, M. Grofulovic, R. V. de Sanden,R. Engeln, and O. Guaitella, “Excitation and relaxation of the asymmetricstretch mode of CO2 in a pulsed glow discharge,” Plasma Sources Sci.Technol., 28, 035011, 2018.

[29] C. D. Pintassilgo, V. Guerra, O. Guaitella, and t. Rousseau, “Study of gasheating mechanisms in millisecond pulsed discharges and afterglows in airat low pressures,” Plasma Sources Sci. Technol., 23, 025006, 2014.

[30] J. Loureiro and C. M. Ferreira, “Coupled electron energy and vibrationaldistribution functions in stationary N2 discharges,” J. Phys. D: Appl. Phys.,19, 17–35, 1986.

[31] V. Guerra and J. Loureiro, “Non-equilibrium coupled kinetics in stationaryN2-O2 discharges,” J. Phys. D: Appl. Phys., 28, 1903–1918, 1995.

[32] G. Gousset, C. M. Ferreira, M. Pinheiro, P. A. Sa, M. Touzeau, M. Vialle,and J. Loureiro, “Electron and heavy-particle kinetics in the low pressureoxygen positive column,” J. Phys. D: Appl. Phys., 24, 290–300, 1991.

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6.6. References

[33] A. Morillo-Candas, C. Drag, J.-P. Booth, V. Guerra, and O. Guaitella,“Oxygen atom kinetics in CO2 plasmas ignited in a DC glow discharge,”Plasma Sources Sci. Technol., 28, 075010, 2019.

[34] C. D. Pintassilgo and V. Guerra, “Kinetic mechanisms in air plasmas,”Plasma Phys. Control. Fusion., 61, 014026, 2018.

[35] C. Riccardi and R. Barni, Chemical Kinetics in Air Plasmas at AtmosphericPressure. 2012.

[36] Y. Ionikh, A. Meshchanov, J. Ropcke, and A. Rousseau, “A diode laserstudy and modeling of NO and NO2 formation in a pulsed dc air discharge,”Chem. Phys., 322, 411 – 422, 2006.

[37] A. Rousseau, L. V. Gatilova, J. Ropcke, A. V. Meshchanov, and Y. Z.Ionikh, “NO and NO2 production in pulsed low pressure dc discharge,”Appl. Phys. Lett., 86, 211501, 2005.

[38] S. Welzel, L. Gatilova, J. Ropcke, and A. Rousseau, “Time-resolved study ofa pulsed dc discharge using quantum cascade laser absorption spectroscopy:NO and gas temperature kinetics,” Plasma Sources Sci. Technol., 16,822–831, 2007.

[39] M. Schenk, T. Seeger, and A. Leipertz, “Time-resolved CO2 thermometryfor pressures as great as 5 MPa by use of pure rotational coherent anti-Stokes Raman scattering,” Appl. Opt., 44, 6526–6536, 2005.

[40] F. Vestin, K. Nilsson, and P. E. Bengtsson, “Validation of a rotationalcoherent anti-Stokes Raman spectroscopy model for carbon dioxide usinghigh-resolution detection in the temperature range 294-1143 K,” Appl.Opt., 47, 1893–1901, 2008.

[41] D. Marinov, D. Lopatik, O. Guaitella, M. Hubner, Y. Ionikh, J. Ropcke,and A. Rousseau, “Surface vibrational relaxation of N2 studied by CO2

titration with time-resolved quantum cascade laser absorption spectroscopy,”J. Phys. D. Appl. Phys., 45, 175201, 2012.

[42] M. Schiorlin, R. Klink, and R. Brandenburg, “Carbon dioxide conversionby means of coplanar dielectric barrier discharges,” Eur. Phys. J. Appl.Phys., 75, 24704, 2016.

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Chapter 7

Conclusions

This final chapter summarizes the most relevant results obtained in the PhDproject. The general conclusions are highlighted and some recommendationsfor future work are proposed.

• The first task within the project was the investigation of the electronimpact cross sections for CO2, presented in chapter 2. As a result, a swarm–derived complete and consistent set was proposed, which is currently partof the IST–LISBON database at LXCat. It is concluded that the inclusionof superelastic collisions with CO2(010) is important for an accurateprediction of the swarm parameters at low reduced electric fields. Morespecifically, it is shown that the calculated values of the characteristicenergy are correct only when the superelastic collisions are taken intoaccount, which is very evident for E/N < 10 Td.

• Different electron impact dissociation cross sections available in the litera-ture are reviewed and discussed. The analysis strongly suggests that thecross sections with energy thresholds at 7 eV and 10.5 eV from our setmost likely include more than dissociative channels. The calculated crosssection given by Polak and Slovetsky is considered as a good basis forstudying direct electron impact dissociation. We have therefore proposeda strategy for obtaining electron impact dissociation rate coefficients.Polak’s cross section should be used upon integration of a previouslycalculated EEDF, although it should not be used in a Boltzmann solverfor obtaining the EEDF.

Uncertainty around the electron impact cross sections for CO2 is stillpresent, especially considering the direct electron impact dissociation.Further work is needed to deepen the knowledge on the electron impactprocesses in CO2 plasmas. The inclusion of additional excitation tohigh vibrational levels is highly important for the investigation of plasma

155

Chapter 7. Conclusions

assisted CO2 conversion to CO, which can diminish the uncertaintyinherent to the usual scaling formulas used for the estimation of unknownvibrational excitations.

• Chapters 3 and 4 present a kinetic model describing the time evolutionof ∼ 70 individual vibrational levels of CO2(X1Σ+) in a pulsed DC glowdischarge. First, the V-V and V-T reaction mechanisms are validatedthrough a comparison with experimental data in chapter 3, where thepost-discharge is analysed.

Next, the model is extended in chapter 4 with the electron impact processesin order to describe the active discharge. A very good agreement with theexperiment is again observed, despite some differences in the evolutionsof the populations of the symmetric and bending excited states, whichserves as a validation of our kinetic model.

The results show a rapid growth of the CO2(000ν31) populations duringthe first millisecond of the pulse. The subsequential gas heating enhancesthe V-T mechanisms, leading to a drop of asymmetric mode’s populations.The characteristic temperatures associated with each vibrational modeare calculated from the corresponding populations. It is confirmed thatthe usual assumption of T1 and T2 being nearly equal is valid. Therefore,the two characteristic temperatures, T1,2 and T3 are sufficient for a simpledescription of vibrational excitation of CO2. As expected, T3 exhibits afast growth at the same time as the associated populations. The elevationof T3 reaches ∼ 500 K above above T12 and Tg at about 1 ms of the pulseunder the studied conditions (p = 5 Torr and I = 50 mA), which is in goodagreement with the measurements. This confirms the non-equilibrium na-ture of CO2 plasmas under low-pressures and the preferential excitation ofthe asymmetric stretching mode. The populations of different vibrationallevels during the afterglow show a similar behaviour, with the relaxationof each vibrational level starting at ∼ 10−4 s, while the beginning of thesteady state regime is observed from ∼ 10−2 s.

• One of the major challenges for future work is the calculation of thereaction rates for vibrational energy transfers related to the higher CO2

vibrational levels, were the SSH and SB theories are no longer suitable.Furthermore, the inclusion of CO2 decomposition products and highervibrational excitation in the overall kinetics is an important and complexdirection for future work. It will involve the energy exchanges betweendifferent collisional partners, such as CO2-CO, CO2-O2, CO2-O, etc. Theinfluence of the high-v levels upon the EEDF should also be considered.

• Chapter 5 presents a self-consistent model based on the coupled solu-tions to the gas thermal balance equation and a system of rate balance

156

equations that provides the temporal evolution of the radially averagedgas temperature in low-temperature CO2 plasmas. The very good agree-ment between the modeling results and the two different experimentsis observed. The first one is the single-pulse experiment, also used forthe validation of the modelling results in chapters 3 and 4, specificallytailored to match the kinetics involved in the model, which excludes thedissociation products. The second experiment corresponds to a continuousDC discharge, where there is noticeable dissociation of CO2. However, avery good agreement between the experiment and the modeling results isstill obtained, implying the significance of the V-V and V-T transfers forthe gas heating.

Future work should include the dissociation of CO2 and the correspondingchemical kinetics of a CO2/CO/O2/O system.

• An experimental investigation of the time-resolved gas temperature andmolecular densities in CO2-N2 and CO2-O2 pulsed discharges is presentedin chapter 6 by employing rotational Raman spectroscopy. The measuredrotational temperatures are shown to have very similar profiles for differentamounts of N2, whilst the larger amounts of O2 lead to a decrease ofthe temperature. The relative compositions are observed to be nearlyconstant during the pulse and along the axis of the reactor. The measureddensities are utilized to determine the conversion factor, α, in order toestimate the influence of N2 and O2 additions on CO2 decomposition. InCO2-N2 α amounts to 0.17, 0.23 and 0.33 for 25%, 50% and 75% of N2.This could be interpreted as an evidence of the vibrational energy transferbetween vibrationally excited N2 and CO2 molecules and its positiveeffect on CO2 dissociation. The examination of the difference betweenthe fitted odd averaged degeneracy and the calculated degeneracy forthermal conditions at Trot showed an increase when a higher amount ofN2 is present in plasma, confirming the relation between the amount ofN2 and the vibrational excitation of CO2.

To fully describe the systems studied in the experiment, it is necessaryto perform a modelling study of CO2-N2 and CO2-O2 glow dischargesincluding the details of the underlying kinetics.

157

List of publications

1. A rotational Raman study under non-thermal conditions inpulsed CO2-N2 and CO2-O2 glow dischargesM. Grofulovic, B.L.M. Klarenaar, O. Guaitella,V. Guerra and R. Engeln,Plasma Sources Science and Technology, 28, 045014, 2019.

2. Kinetic study of CO2 plasmas under non-equilibrium conditions.I. Relaxation of vibrational energyT. Silva, M. Grofulovic, B.L.M. Klarenaar, A.S. Morillo-Candas, O. Guaitella,R. Engeln, C.D. Pintassilgo, V. Guerra, Plasma Sources Science andTechnology, 27, 015019, 2018.

3. Kinetic study of CO2 plasmas under non-equilibrium conditions.II. Input of vibrational energyM. Grofulovic, T. Silva, B. L. M. Klarenaar, A.S. Morillo-Candas, O.Guaitella, R. Engeln, C.D. Pintassilgo, V. Guerra, Plasma Sources Scienceand Technology, 27, 115009, 2018.

4. A rotational Raman study under non-thermal conditions in apulsed CO2 glow dischargeB.L.M. Klarenaar, M. Grofulovic, A.S. Morillo-Candas, D.C.M. van denBekerom, M.A. Damen, O. Guaitella, M.C.M. van de Sanden, and R. En-geln, Plasma Sources Science and Technology, 27, 045009, 2018.

5. Excitation and relaxation of the asymmetric stretch mode ofCO2 in a pulsed glow dischargeB.L.M. Klarenaar, A.S. Morillo-Candas, M. Grofulovic, M.C.M. vande Sanden, R. Engeln, and O. Guaitella, Plasma Sources Science andTechnology, 28, 035011, 2019.

159

List of publications

6. Modelling the input and relaxation of vibrational energy in CO2

plasmasT. Silva, M. Grofulovic, L. Terraz, C.D. Pintassilgo, V. Guerra, Journalof Physics D: Applied Physics, 51, 464001, 2018.

7. The case for in situ resource utilisation for oxygen productionon Mars by non-equilibrium plasmasV. Guerra, T. Silva, P. Ogloblina, M. Grofulovic, L. Terraz, M. Linoda Silva, C.D. Pintassilgo, L.L. Alves and O. Guaitella, Plasma SourcesScience and Technology, 26, 11LT01, 2017.

8. Reply to Comment on The case for in situ resource utilisationfor oxygen production on Mars by non-equilibrium plasmasV. Guerra, T. Silva, P. Ogloblina, M. Grofulovic, L. Terraz, M. Linoda Silva, C.D. Pintassilgo, L.L. Alves and O. Guaitella, Plasma SourcesScience and Technology, 27 (2), 2018.

9. Electron-neutral scattering cross sections for CO2: a completeand consistent set and an assessment of dissociationM. Grofulovic, L.L. Alves and V. Guerra, Journal of Physics D: AppliedPhysics, 49, 395207, 2016.

160

Conference contributions

• 28th International Symposium on the Physics of Ionized Gases (SPIG),Belgrade, Serbia (2016)“Swarm Analysis and Dissociation Cross Sections for CO2”, M. Grofulovic,L.L. Alves and V. Guerra.

• 69th Annual Gaseous Electronics Conference (GEC), Bochum, Germany(2016)“IST-LISBON database with LXCat: Electron scattering cross sections foroxygen and carbon dioxide”, M. Grofulovic, V. Guerra, P. Coche and L.LAlves.

• 69th Annual Gaseous Electronics Conference (GEC), Bochum, Germany(2016)“Inter-comparison of calculation techniques of the electron Boltzmannequation for the analysis of swarm parameters in CO2”, M. Grofulovic, D.Loffhagen, N.R. Pinhao, L.L. Alves, V. Guerra, I. Korolov, M. Vass, Z.Donko.

• 23rd Europhysics Conference on Atomic and Molecular Physics of IonizedGases (ESCAMPIG) Bratislava, Slovakia (2016)“Intercomparison of calculation techniques of the electron Boltzmannequation for the analysis of swarm parameters in CO2”, M. Grofulovic, D.Loffhagen, N.R. Pinhao, L.L. Alves, V. Guerra, I. Korolov, M. Vass, Z.Donko.

• 23rd Europhysics Conference on Atomic and Molecular Physics of IonizedGases (ESCAMPIG), Bratislava, Slovakia (2016)M. Grofulovic, V. Guerra and L.L. Alves, “CO2 electron impact crosssections: a complete and consistent set and an assessment of dissociation”.

161

Conference contributions

• 33rd International Conference on Phenomena in Ionized Gases (ICPIG),Estoril , Portugal (2017)M. Grofulovic, T. Silva and V. Guerra, “Sensitivity and uncertaintyanalysis of a kinetic model for CO2 non-equilibrium plasmas”.

• 70th Annual Gaseous Electronics Conference (GEC), Pittsburgh, USA(2017)M. Grofulovic, T. Silva, B. Klarenaar, A. S. Morillo-Candas, O. Guaitella,R. Engeln, C. Pintassilgo and V. Guerra, “Vibrational kinetics of non-equilibrium CO2 plasma discharge in low-excitation regime”.

• 28th Workshop on the exploration of low-temperature plasma physics,Rolduc, The Netherlands (2017)M. Grofulovic, T. Silva, B. Klarenaar, A. S. Morillo-Candas, O. Guaitella,R. Engeln, C. Pintassilgo and V. Guerra, “Vibrational kinetics of non-equilibrium CO2 plasma discharge in low-excitation regime”.

• 24th Europhysics Conference on the Atomic and Molecular Physics ofIonized Gases (ESCAMPIG 2018), Glasgow, UKM. Grofulovic, B.L.M. Klarenaar, M.C.M. van de Sanden, V. Guerra,O. Guaitella, R. Engeln, “A rotational Raman study under non-thermalconditions in pulsed CO2/N2 and CO2/O2 glow discharges”.

• 24th International symposium on plasma chemistry (ISPC), Naples, Italy(2019)M. Grofulovic, T. Silva, V. Guerra, O. Guaitella, R. Engeln, C.D. Pintas-silgo, “Modelling of the time-dependent gas temperature in low-pressureCO2 and N2 discharges”.

162

Acknowledgements

First and foremost, I would like to thank my supervisors, Vasco Guerra,Richard Engeln and Richard van de Sanden for their guidance and support.Thank you for always being available for discussions, giving me feedback andinvaluable suggestions throughout this project. I would also like to thank youfor your engagement and commitment in making the joint protocol betweenthe IST and TU/e possible.

I owe my gratitude to Gerrit Kroesen, Timo Gans, Luıs Alves, HoracioFernandes and Guus Pemen for being in the committee and for making thetime to read the manuscript and to participate in my defense ceremony.

This thesis is the result of the research conducted at two great universitiesand, naturally, includes contributions of the colleagues from both IST in Lisbonand TU/e in Eindhoven, whom I thank greatly. First I owe my gratitude to theN-PRiME group in Lisbon, that welcomed me after the APPLAuSe trainingand offered me the opportunity to do this research in a friendly and inspiringenvironment. Tiago, thank you for being there since the beginning of thisproject, for sharing the good and the bad during our modeling adventure andfor your contribution to this thesis. I am also grateful for your friendship andthe fun we had during my stay in Lisbon. I want to thank as well Polina andLoann for going through the PhD together, for all the meetings, conferences andWOTANs. Of course, I am very grateful for starting this journey with my friendsand colleagues from the APPLAuSE program. We had some hectic periods inthe first year, but we made it through. Adwiteey, it was almost fun reportingto each other about the stress level while finalizing our theses. Susana andAna, thank you for your friendship and help with sometimes uncomprehensiblebureaucracy. Susana, I enjoyed very much reminiscing about Portugal withyou during cold rainy days in Eindhoven.

My experimental work in Eindhoven brought many new challenges, andit would not have been the same without Bart, Mark and Alex in the lab.Together with Richard, you made me feel as a part of your group, which I amimmensely grateful for. Bart, thank you for trusting me with your setup andfor contributing to this thesis. I have learnt a great deal from our discussionsduring my year in Eindhoven. Thank you for pushing me to overcome my fear

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Acknowledgements

of breaking things, while reminding me of the trouble we will both be in ifthat happens. I am also grateful to Mark and Alex for working together inthe lab and for jumping in when help was needed. I enjoyed very much ourconversations during coffee breaks about the milestones, problems with setupsor just contemplating life. Alex, it would not have been the same without yourpositivity! I also owe my gratitude to the entire PMP group for welcoming mein Eindhoven and for the fun we had at the borrels. Rene, I am especiallygrateful for your contagious life enthusiasm and for helping me learn the virtuesof the Dutch sarcasm.

I am also indebted to Olivier for welcoming me in his lab in Paris morethan once. Thank you for all the invaluable discussions and also for bringing aglass tube from Paris, which helped me finalizing one chapter of this thesis. Iespecially enjoyed the after-work discussions in the lab’s mezzanine in Paris.I thank Ana Sofia, Elmar, Pedro and others for making these times soamazing. Ana Sofia, I am glad that, although being far from each other, wemanaged to share the news about our results and challenges on a daily basis.

My sincere gratitude goes to Sasa Gocic, thanks to whom I started theresearch in non-equilibrium plasma. Thank you for your encouragement fromthe beginning!

Finally, I will forever be grateful to my family. Zahvalna sam mami i tatijer nisu dozvoljavali da strah pobedi radoznalost i entuzijazam. Hvala vam zapozitivan pogled na buducnost, sto je olaksalo svaku tesku odluku. Hvala stonam nikada niste svaljivali teret nedostajanja. Hvala mojoj miloj sestri Jeleniza humor i njen poseban wit. Hvala mojim dragim Trujicima za nesebicnupomoc u svim lepim, a i teskim trenucima. Veliko hvala Dikicima za brigui podrsku od prvog dana naseg poznanstva. Najvece hvala Marku koji jeprolazio kroz svaki korak mojih studija zajedno sa mnom, delio sve probleme iradosti. Bez tebe ova teza ne bi bila ista (mozda bolja?). Hvala!

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Curriculum Vitae

Marija Grofulovic was born on 05-01-1990 in Bor, Serbia. After finishing theSpecialized physics program for gifted students in 2009 at “Svetozar Markovic”high school in Nis, Serbia, she studied Physics at the University of Nis. In 2014she graduated within the Group for Experimental and Applied Physics. Duringthe studies, she was awarded scholarships from the Ministry of Youth andSport and the Ministry of Science of Republic of Serbia. After her graduation,she started working as a teaching associate at the Physics Department of theFaculty of Science and Mathematics, University of Nis.

In 2015 she was selected for the doctoral program APPLAuSE – AdvancedProgram in Plasma Science and Engineering, hosted by IPFN in Lisbon. HerPhD project was carried out in the framework of a double doctorate protocolbetween IST from the University of Lisbon, in Portugal and the TU/e, in theNetherlands, granting a degree in Technological Physics Engineering and inapplied Physics, respectively. The project was supervised by dr. Vasco Guerra,dr. Richard Engeln and Prof.dr.ir. Richard van de Sanden. The results arepresented in this thesis.

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