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Streamer propagation in a packed bed plasma reactor for plasma catalysis applicationsWeizong Wang1, Hyun-Ha Kim2, Koen Van Laer1 and Annemie Bogaerts1

1. Research group PLASMANT, Department of Chemistry, University of Antwerp,

Universiteitsplein 1, BE-2610 Wilrijk-Antwerp, Belgium

2. National Institute of Advanced Industrial Science and Technology (AIST), 16-1 Onogawa, Tsukuba, Ibaraki 305-8569, Japan

E-mail: wangweizong@gmail..com ; Annemie.bogaerts@uantwerpen.be

1 Modelling streamer propagation: Description of photoionization

To correctly calculate the propagation of the streamer, we need to include extra equations in the model, to account for photoionization. In N2-O2 mixtures, photoionization occurs when O2 molecules absorb photons, which are emitted as a result of the quenching of highly excited N2 molecules from the singlet states b1П, b’1Σu

+ and c’41Σu

+ (in the following equations these states are lumped together as state “u”) [1]. Classically, the rate of this process would be calculated using an integral radiation transfer model, such as the model of Zheleznyak et al. [2].

Sph (r )=∭V '

❑ I (r ) g (r )4 π r2 dV '

(S1)

This expression shows that the photoionization rate Sph(r) as a function of the position vector r, equals the volume integral of the product of the rate of emission of photons, I(r), with g(r), which is a function of the photon absorption rate by O2. However, this method is computationally quite expensive. In 2007, Luque et al. proposed a novel approach, allowing to effectively replace the classical integral model by a set of Helmholtz differential equations, significantly simplifying the solution process [3]. The photoionization rate can then be represented as the sum of a number of solutions of Helmholtz equations:

Sph (r )=∑j

Sphj (r )∭

V '

❑ I (r ) g (r )4 π r2 dV ' (S2)

with terms:

Sphj (r )=∭

V '

❑ I (r ) A j pO2

2 e−λ j pO 2r

4 πr dV '

(S3)

In these equations, j stands for the total number of Helmholtz equations (see below), pO2 stands for the partial pressure of O2 in the gas mixture and Aj and λj are fitting parameters, defined against the integral model of Zhelznyak. The Helmholtz equations themselves, which represent the actual problem of radiation transport in a gas, are then defined as follows:

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∇2 Sphj (r )−( λ j pO 2)

2 Sphj (r )=−A j pO2

2 I (r ) (S4)

The aforementioned I(r), the emission rate of photons, is given by:

I (r )=pq

p+ pqξ νu ne Si (r )

(S5)

In this expression, pq/(p+pq) accounts for the probability of quenching, i.e., the non-radiative deexcitation of the excited state of N2 after collision with another molecule, in which p is the gas pressure and pq the quenching pressure of the excited states (here indicated as lumped state “u”), ξ stands for the photoionization efficiency, νu is the electron impact excitation frequency for states u, ne

is the electron number density and Si ( r⃗ ) the electron impact ionization rate.

From comparison between the expression of Sph(r) by Zheleznyak et al. and by Luque et al., it is clear that:

g (r )pO2

=( pO2r )∑

jA je

− λ j pO2r (S6)

To retrieve the fitting parameters Aj and λj, the function g(r)/ pO2 is fitted against a number of

exponents (j) multiplied by pO2r. This number of exponents can change depending on the pressure

range of the fit. For atmospheric pressures, a minimum of 3 is required. This number thus defines the number of Helmholtz equations to be solved (see above). The values for the fitting parameters, A j and λj, are taken from the paper of Bourdon et al., in which this three exponential fit is performed, resulting in the fitting parameters shown in table S1 [4]. The summation of the solutions of the three Helmholtz differential equations, using these three pairs of parameters, gives the total reaction rate for photoionization of O2, which is included in the model, as explained in the next section.

Table S1: Fitting parameters of the three exponential fit, as obtained from Bourdon et al. [4]

j Aj (cm-2 Torr-2) λj (cm-1 Torr-1)

1 1.986 × 10-4 0.0553

2 0.0051 0.1460

3 0.4886 0.89

2. Plasma chemistry included in the model

Table S2: Dry air reaction set used in the model, with rate coefficients, and references where these data are adopted from. The electron impact reactions are described by energy dependent cross sections. Te and Tg are the electron temperature and gas temperature (in K), respectively. Reactions R25 and R30 stand for radiative decay, described by an Einstein transition probability, instead of a rate coefficient. In R39 and R40, M stands for any third body.

Nr. Reaction Rate coefficient Ref

R1 e + N2 → e + N2 cross-section [5]

R2 e + O2 → e + O2 cross-section [5]

R3 e + N2 → N2+ +2e cross-section [5]

R4 e + O2 → O2+ + 2e cross-section [5]

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R5 e + N2 → e + N2A cross-section [5]

R6 e + N2 → e + N2B cross-section [5]

R7 e + N2 → e + N2C cross-section [5]

R8 e + N2 → e + N2a1 cross-section [5]

R9 e + N2 → e + N + N cross-section [5]

R10 e + O2 → e + O + O cross-section [5]

R11 e + O2 → e + O + O1D cross-section [5]

R12 N + O2 → NO + O 1.10 x 10-20 Tg e-3150/Tg m3 s-1 [6]

R13 N + NO → N2 + O 1.05 x 10-18 (Tg)-0.5 m3 s-1 [6]

R14 O + O3 → O2 + O2 2.00 x 10-17 e-2300/Tg m3 s-1 [6]

R15 O + O + N2 → O2 + N2 2.76 x 10-46 e-720/Tg m6 s-1 [6]

R16 O + O + O2 → O2 + O2 2.45 x 10-43 Tg-0.63 m6 s-1 [6]

R17 O + O2 + N2 → O3 + N2 5.58 x 10-41 Tg-2 m6 s-1 [6]

R18 O + O2 + O2 → O3 + O2 8.61 x 10-43 Tg-1.25 m6 s-1 [6]

R19 N2A + O2 → N2 + O + O 1.70 x 10-18 m3 s-1 [6]

R20 N2A + O2 → N2 + O2 7.50 x 10-19 m3 s-1 [6]

R21 N2A + O → N2 + O1D 3.00 x 10-17 m3 s-1 [6]

R22 N2A + N2A → N2 + N2B 7.70 x 10-17 m3 s-1 [6]

R23 N2A + N2A → N2 + N2C 1.60 x 10-16 m3 s-1 [6]

R24 N2B + N2 → N2A + N2 3.00 x 10-17 m3 s-1 [6]

R25 N2B → N2A + hν 1.50 x 105 s-1 [6]

R26 N2B + O2 → N2 + O + O 3.00 x 10-16 m3 s-1 [6]

R27 N2a1 + N2 → N2 + N2 2.00 x 10-19 m3 s-1 [6]

R28 N2a1 + O2 → N2 + O + O1D 2.81 x 10-17 m3 s-1 [6]

R29 N2C + N2 → N2B + N2 1.00 x 10-17 m3 s-1 [6]

R30 N2C → N2B + hν 3.00 x 107 s-1 [6]

R31 N2C + O2 → N2A + O + O 3.01 x 10-16 m3 s-1 [6]

R32 O1D + N2 → O + N2 2.57 x 10-17 m3 s-1 [6]

R33 O1D + O2 → O + O2 4.00 x 10-17 m3 s-1 [6]

R34 N2+ + O2 → N2 + O2

+ 6.00 x 10-17 m3 s-1 [6]

R35 e + N2+ → N + N 8.31 x 10-12 (Te)-0.5 m3 s-1 [6]

R36 e + O2+ → O + O 5.99 x 10-11 (Te)-1 m3 s-1 [6]

R37 e + e + N2+ → N2 + e 1.40 x 10-20 (Te)-4.5 m6 s-1 [6]

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R38 e + e + O2+ → O2 + e 1.40 x 10-20 (Te)-4.5 m6 s-1 [6]

R39 e + N2+ + M → N2 + M 3.21 x 10-35 (Te)-1.5 m6 s-1 [6]

R40 e + O2+ + M → O2 + M 3.21 x 10-35 (Te)-1.5 m6 s-1 [6]

R41 O2 + hν → e + O2+ Sph [3]-[4]

The rates of the first eleven reactions (R1-R11) are obtained by Bolsig+, a software program that solves the Boltzmann equation for the electrons, using the collision cross sections from the LXCat database, to generate the electron impact reaction rates as a function of the mean electron energy [5]-[7]. It also calculates the transport coefficients of the electrons as a function of mean energy. The reaction rate coefficients of the other reactions (except R41), namely the chemical reactions between neutral species, electron-ion recombination reactions and radiative decay from the excited species (R25, R30), are taken from literature [6]. Some of these expressions contain the electron temperature or gas temperature. The reaction rate of the last reaction, i.e., photoionization (R41), is calculated from the Helmholtz differential equations, as explained in previous section.

3. Streamer propagation for a packing with dielectric constant = 5

Figure S1: Evolution of the electron temperature distribution over 12 ns, for a packing with r = 5.Note that the maximum electron temperature is much higher than 6 eV, i.e., up to hundreds of

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eV near the edge of the surface ionization wave, but only in a very limited area. The maximum scale in the legend is however set at 6 eV, in order to better visualize the electron temperature in the rest of the discharge area.

Figure S2: Evolution of the electron impact ionization rate distribution over 12 ns, for a packing with r = 5.

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Figure S3: Evolution of the photoionization rate distribution over 12 ns, for a packing with r = 5.

Figure S4: Net positive charge distribution at 3 ns, 3.5 ns, 4 ns and 10 ns, for a packing with r = 5, to show the large positive space charge at the head of the streamer (positive restrike), followed by a quasi-neutral column (see section 4.1 in the main paper).

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Figure S5: Electron number density distribution, with (right) and without (left) including the photoionization effect at 5 ns, for a packing with r = 5, illustrating that photoionization clearly enhances the electron density and makes the streamer much wider, and the gap more filled with plasma, in spite of the fact that the photoionization rate is two orders of magnitude lower than the electron impact ionization rate (see main text and figures S2 and S3).

4. Streamer propagation for a packing with dielectric constant = 1000

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Figure S6: Evolution of the electron temperature distribution over 6 ns, for a packing with εr = 1000. Note that the maximum electron temperature is much higher than 6 eV, i.e., up to hundreds of eV near the edge of the ionization wave, but only in a very limited area. The maximum scale in the legend is however set at 6 eV, in order to better visualize the electron temperature in the rest of the discharge area.

Figure S7: Evolution of the electron impact ionization rate distribution over 6 ns, for a packing with εr = 1000.

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Figure S8: Evolution of the photoionization rate distribution over 6 ns, for a packing with εr = 1000.

5. Comparison with experimental observations

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Figure S9: Experimental imaging of the microdischarges in a packed bed reactor, by fast ICCD camera imaging of the visible emission using a microscope lens and an observation gate width of 1 μs with a positive high voltage output of 10 kV. (a) Alumina, εr = 9; (b) Zirconia, εr = 25; (c) BaTiO3, εr = 2600. The left figures show the location of the packing beads without discharge, to better understand the right figures, which illustrate the images of dicharge plasma. For BaTiO 3, a lower applied voltage of 8.4 kV was used, because the pulsed voltage could not reach a higher value due to the large capacitance of the packed bed.

6. Production of reactive species

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Figure S10: Fraction of electron energy transferred to different channels of dissociation and ionization of O2 and N2, in a 80% N2/20% O2 mixture, as a function of the reduced electric field (E/N, with E the electric field and N the gas number density), as calculated from the corresponding cross sections of the electron impact reactions. This illustrates that O2 dissociation is by far the most important process, especially at low E/N, because of the lower threshold level of electron impact dissociation than for N2 (12.6 eV vs 15.6 eV), but its relative importance drops above E/N = 100, while N2 dissociation becomes gradually more important. This explains why the N atom density rises while the O atom density drops upon higher dielectric constant of the packing (characterized by a more pronounced electric field enhancement, and thus higher E/N); see main text.

Figure S11: Reaction rates of electrons impact dissociation and ionization of O2 and N2, in a 80% N2/20% O2 mixture, as a function of the average electron energy, as calculated from the corresponding cross sections of the electron impact reactions.

References[1] G. V. Naidis, Plasma Sources Sci. Technol. 15 (2006) 253-255.[2] M. B. Zheleznyak, A. K. Mnatsakanyan and S. V. Sizykh, High Temp. 20 (1982) 357-362.[3] A. Luque, U. Ebert, C. Montijn and W. Hundsdorfer, Appl.Phys. Lett. 90 (2007) 081501.[4] A. Bourdon, V. P. Pasko, N. Y. Liu, S. Célestin, P. Ségur and E. Marode, Plasma Sources Sci. Technol. 16 (2007) 656–678.[5] Siglo Database, www.lxcat.net, retrieved on July 19, 2016.[6] J. Poggie, I. Adamovich, N. Bisek and M. Nishihara, Plasma Sources Sci. Technol. 22 (2013) 015001.[7] G. J. M. Hagelaar and L. C. Pitchford, Plasma Sources Sci. Technol. 14 (2005) 722.

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