Characterization of dielectric barrier discharge in air applying current measurement, numerical simulation and emission spectroscopy

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1 Characterization of ielectric barrier ischarge in air applying current measurement, numerical simulation an emission spectroscopy Priyaarshini Rajasekaran, ikita Bibinov an Peter Awakowicz nstitute for Electrical Engineering an Plasma Technology, Ruhr-Universität Bochum, Universitätstr. 5, 448 Bochum, Germany Abstract. Dielectric barrier ischarge (DBD) in air is characterize applying current measurement, numerical simulation an optical emission spectroscopy (OES). For OES, a non-calibrate spectrometer is use. This iagnostic metho is applicable when cross-sectional area of the active plasma volume an current ensity can be etermine. The nitrogen emission in the spectral range of 38 nm- 46 nm is use for OES iagnostics. Electric fiel in the active plasma volume is etermine applying the measure spectrum, well-known Frank-Conon factors for nitrogen transitions an numerically- simulate electron istribution functions. The measure electric current ensity is use for etermination of electron ensity in plasma. Using the etermine plasma parameters, the issociation rate of nitrogen an oxygen in active plasma volume are calculate, which can be use by simulation of the chemical kinetics.

2 . ntrouction Dielectric barrier ischarge (DBD) in air has a wie fiel of application because of the simplicity of electrical scheme of excitation, consumption of ambient air at atmospheric pressure as working gas an low average electric current. This ischarge can, for example, activate surfaces of ifferent materials before painting or prouce biologically-active molecules like nitric oxie an ozone close to the treate surface (such as human skin) that are useful for skin therapy. For safe an effective application of the DBD, optimisation of treatment process requires ischarge characterisation or in other wors, the etermination of the gas temperature an plasma parameters (electron istribution function EDF an electron ensity). Applying these ata, the plasma chemical kinetics can be simulate an the treatment conitions can be optimize. Several experimental methos such optical emission spectroscopy (OES), measurement of V- characteristics an microphotography, an simulations are necessary for the characterization of plasma evices such as the DBD []. OES in combination with numerical simulation is use for the etermination of gas temperature, electron velocity istribution function (f(e) in ev -3/ ) an electron ensity (n e in m -3 ) of ifferent ischarge moes of a DBD in air [,,3]. The electric fiel is etermine from the intensity ratio of spectral bans of nitrogen [4]. For the etermination of n e, the absolute intensity of nitrogen emission is use, an for this absolutely-calibrate spectrometers are employe. The calibration of spectral evices is not always feasible ue to the requirement of relate equipments (such as tungstenribbon lamp [5]), an lack of expertise. n this paper, we present a metho of characterizing the DBD in air by implementing a noncalibrate spectrometer for measuring the emission spectra. n aition, current measurements an numerical simulation are use. Electric current is a function of both the electric fiel an the electron ensity, an therefore current measurements can eliver aitional information that complement OES [6]. The electric fiel in the active plasma is etermine from the intensity ratio of + (B-X,-) an (C-B,-) while the electron ensity at that electric fiel is etermine from the measure electric current ensity.. DBD evice an plasma iagnostics. DBD evice The DBD evice use in this work [] consists of a ring-shape copper electroe (iameter = 8 mm) covere with ceramic (Al O 3 ) of mm thickness. Objects of high capacitance or groune electroes of ifferent materials an profiles (flat or pointe) can serve as the counter electroe. A high voltage pulse supply (trigger frequency = 3 Hz; maximum amplitue = kv []) is applie on the DBD electroe to ignite plasma in ambient air between the electroes. Each trigger pulse initiates a

3 ntensity (counts nm - s - ) sequence of high voltage pulses an ampe oscillations; the frequency within each sequence is khz. At the same experimental conitions such as applie voltage, trigger frequency an interelectroe istance, a homogeneous ischarge an a stochastic-filamentary ischarge are obtaine, respectively, with glass an aluminium as the groune electroe [3]. A single-filamentary ischarge [] is ignite when a pointe electroe such as a groune spike is use. n this work, the homogeneous DBD is consiere for iscussion. The gap between the DBD-electroe an glass plate is 3. mm.. Plasma iagnostics Optical emission spectroscopy is performe using a grating spectrometer (Ocean Optics QE65, spectral range = 33-4 nm, spectral resolution ~.5 nm) calibrate in wavelength by the manufacturer but the spectral efficiency remains unknown. The observe spectrum of plasma in air ( in countsnm - s - ) shows bans of neutral an ionic emissions of molecular nitrogen (figure ). The ischarge current is measure using a current monitor (Pearson 63). The traces are recore using an oscilloscope (LeCroy Waverunner 4 Xi - A, GHz) (figure ). The average plasma uration is etermine at FWHM (full with at half maximum) of the measure current profile which amounts to ns, an the current-amplitue is.94 A. (-) (-) (C-B) (-) (-3) + (B-X,-) Wavelength (nm) Figure. Emission spectrum of air-dbd showing ifferent vibrational bans of neutral nitrogen molecules (C-B), an + (B-X,-) at 39 nm.

4 Current (A) Time (ns) Figure. Measure current in homogeneous DBD in air with glass as the counter electroe. nterelectroe istance amounts to 3. mm. 3. Plasma characterization Plasma characterization refers to the etermination of gas temperature an plasma parameters namely the electron istribution function an electron ensity. The gas temperature (T g in K) in the active plasma channel is etermine using emission of (C-B,-) at 337. nm with the assumption that the rotational temperature (T rot ) of iatomic molecules is equal to the gas temperature at atmospheric-pressure conition. Electron istribution function is simulate using reuce electric fiel- etermine using measure intensity ratio of (C-B) an + (B-X) emissions. Electron ensity is etermine using the measure electric current ensity an the rift velocity calculate for the etermine electric fiel. The gas temperature an the plasma parameters are all average over time an space. 3.. Determination of electric fiel from intensity ratio n our previous work [6], it has been shown that only irect excitation of (C-B,-) at 337. nm an + (B-X,-) at 39.4 nm ue to electron-impact of groun state neutrals (X) occur in the homogeneous moe of the DBD in air [3], an the step wise excitation via nitrogen metastables (A) an groun state of molecular ion + (X) can be neglecte. Accoringly, the intensity ratio of these emissions is written as: ( BX,) ( CB,) Q Q ( B) ( C) k k ( B) ( C) n n e e Q Q ( B) ( C) k k ( B) ( C) ()

5 where, Q A' k ( B) ( B) ( B) q A' k qo O an Q ( C) A, A k k ( C) ( C) q qo O A' an A are the corresponing Einstein coefficients [7], ( ) k B q, ( ) k C ( ) q, k B qo, ( ) k qo C (in m3 s - ) are the rate constants for quenching of + (B) an (C) excite states uring collision with an O [5], an O (in m -3 ) are the ensities of an O at etermine gas temperature, k an k (C) (in m 3 s - ) are the rate constants, respectively, for electron impact excitation of (C-B,-) an + (B-X,-) emission from (X), an n e (in m -3 ) is the electron ensity. The quenching factors Q an Q ( epen slightly on the gas temperature because of temperature epenencies of C) ( B) (B) gas ensity an quenching rate constants accoring to Arrhenius formula. iscusse later. This effect will be The rate constants for electron-impact excitation of nitrogen emissions epen on the electron velocity istribution function (f v (E) in ev -3/ ) an the corresponing cross-section σ (in m ) [8]. k an k ) (C are calculate using () for varie electric fiel values: (B) k exc 4 fv (E) e E σ m exc (E) E, () where, e an m are elementary charge (in C) an mass of an electron (in kg). Here, E is the kinetic energy of electrons (in ev). f v (E) is normalize to fulfil (3): 4 f (E) E E v f v (E) is simulate by solving the Boltzmann equation in local approximation (nitrogen/ oxygen = 78%/ %) for varie electric fiel values [9]. The program coe EEDF evelope by Prof. A P apartovich [] is use for this purpose. k, k (B) ) (C an the ratio between these rate constants for ischarge in air are liste in table. (3)

6 Reuce electric fiel E/ in T Electron-impact excitation rate constant for Ratio of excitation rates of nitrogen emissions excluing quenching + (B-X,-) (C-B,-) ( B ) k exc in m 3 s - (C) kexc in m 3 s ( B ) k - exc ( C ) k.55e-35.7e E E-7.74E- 3.77E-7 6.5E-3 6.6E-9.49E E- 3.95E-8.3E-4.3E-.E-7 9.6E-4 6.3E-.58E-7.44E-3 4.E-9 4.4E-7 5.E E E E-3 8.5E E-7.39E-.37E-8.5E-6.6E- 4.5E-8.4E-6.87E E-8.68E-6 3.8E E-8.95E-6 4.9E- 8.36E-7.E-6 6.5E- 3.86E-7.46E E- 3.46E-7.7E-6 9.8E E-7.95E-6.7E E-7 3.7E-6.6E E E-6.45E E-7 3.6E-6.65E E E-6.87E E E-6.9E E-7 4.5E-6.3E- 48.E-6 4.3E-6.55E- 5.4E E-6.78E- exc Table. Ratio of nitrogen emissions (excluing quenching) etermine using (3) for ifferent electric fiel values at atmospheric pressure in air. When using a calibrate spectrometer, the intensities of nitrogen emission (C-B,-) an + (B- X,-) are calculate by integration of measure intensities ( ) correcte to efficiency of spectrometer ( in photons per count) (4). The measure spectrum is integrate in to an 3 to 4 spectral ranges, respectively, for etermination of + (B-X,-) ( nm) an (C-B,-) ( nm) intensities. The efficiency of the spectrometer is a smooth function of wavelength an can be presente as constants (, ) in short integrating intervals

7 ), ( ), ( B C X B (4) But the spectrometer use in this experiment is not calibrate, an therefore for the use of equation (4) one nees aitional information an assumptions. We assume that the efficiency is a linear function of wavelength an we fin the slope of this function. But to etermine ratio of efficiency values at = 337 nm an = 39 nm, linearity in a such a broa spectral range cannot be vali for the spectrometer use. To solve this problem, we use emission bans of (C-B,-) at = 38 nm an (C-B,-3) at = 46 nm that are close to + (B-X,-) at = 39 nm an linearity of efficiency curve of spectrometer in the range of nm is vali. We integrate emission spectrum in spectral rages 5 to 6 (376.5 to 38.5 nm an 7 to 8 ), an 7 to 8 (4 to 46.5 nm) corresponingly for (C-B,-) an (C-B,-3). n orer to etermine the intensity of (C-B,-), the calculate intensities of (C-B,-) an (C-B,-3) are correcte to the ratio of corresponing Frank-Conon factors (5). The branching factors of emission from excite vibrational level (C,) that correspons to the Frank-Conon factors are well known [] an inepenent of plasma conitions ) B, (C ) X, (B R R FCF FCF FCF FCF , (5) where, an n our opinion, the efficiency of usual UV/VS gratings spectrometer can be, with goo accuracy, assume as linear (6) in the spectral range of nm. Taking into account (5), we receive (7) FCF FCF R FCF FCF R

8 ( Q k ) (BX,) (B) (B) R38.4 R 46 (C B, ) Q (C) k (C) 38 R R.4 R (6) (7) Applying (7) an (4), we etermine electron istribution function using the non-calibrate spectrometer. 3.. Measure current as a iagnostic tool n the DBD, electric current (i) flows between the electroes through a efine plasma volume with cross section S an there is no current loss to the surrouning. This allows the use of measure current as a iagnostic tool for plasma characterization. The current ensity (j in A m - ) is a function of electron ensity an rift velocity (v in m s - ) of electrons (8), which in turn is a function of electric fiel. i j ne e v (8) S v etermine for ifferent electric fiel values an measure current ensity are use in (9) to etermine n e which itself becomes a function of the electric fiel: n e j F(E / ) (9) e v The electron rift velocity use in (9) to etermine n e for ifferent electric fiel values is presente in table. As was shown [6], a combination of OES an current measurement allows etermination of electron istribution function an electron ensity in the active plasma volume.

9 Table. Electron rift velocity (v in m s - ) for ifferent electric fiel values use for the etermination of electron ensity. Reuce electric fiel E/ in T Electron rift velocity v in m s E E E E4.E5.9E5 4.47E5 6.64E5 8.8E5.96E5.E5 4.7E5 6.4E5 8.57E5 3.7E5 3.85E E E E E E E E E E5

10 ntensity (a.u.) 4. Results an Discussion To etermine gas ensity in the plasma an the rate constants of reactions between gas species, we etermine the gas temperature at DBD conitions. At that rotational istribution in (C-B,-) emission (figure 3) is applie. The emission spectrum of (C-B,-) is simulate at variable rotational temperature an compare with the measure one. Rotational temperature of nitrogen molecules, which is equal to the gas temperature at atmospheric pressure conitions, is etermine in fitting proceure. Applying this metho, T g in the homogeneous DBD is etermine as K Experiment T rot = 36+3K (nm) Figure 3. (C-B,-) emission ban measure (broken line) an simulate (soli line) at 36K. The measure spectrum is shifte for clarity. Using (4), we calculate the ratio of intensities of nitrogen emissions at 36 K an DBD conitions in air (table 3). These calculate values are also presente in figure 4. Using this ata an measure emissions, the ratio of nitrogen emissions calculate using (8) amounts to that correspons to 4 T which is the electric fiel at the stuie DBD conition.

11 Table 3. Ratio of observe nitrogen emissions etermine using (4) for ifferent electric fiel values in air at atmospheric pressure Reuce electric fiel E/ in T Ratio of observe nitrogen emissions in air at 36 K in atmospheric pressure ( BX,) ( CB,) k k ( B) exc ( C ) exc 8.76E E E E-5.4E E E E-3 8.E-3 3.5E E E E E-3 3.5E- 3.39E E- 36.9E- 38.E- 4.5E- 4.86E E E E E- Q Q ( B) ( C)

12 ntensity ratio.. E-3 E-4 E-5 E-6 E-7 E-8 E-9 E- E- E E/ (T) Figure 4. Ratio of nitrogen emissions (incluing quenching at T g =36K etermine using (4) for ifferent electric fiel values. The ata pertaining to this curve is also presente in table 3. The point () correspons to measure ratio of intensities of nitrogen emissions in the homogeneous DBD reporte here. At our experimental conitions, the homogeneous DBD fills the entire gap between electroes, an hence the circular cross-section of the active plasma volume amounts to m. The average electric current is.47 A an the current ensity amounts to Am -. Applying graphical metho for (4) an (9) (figure 5), we etermine the average electron ensity as m -3 at 4 T in the homogeneous moe. These values are in goo agreement with those etermine using absolutely an relatively-calibrate spectrometer [6].

13 n e (m -3 ).5x 8.x 8.5x 8.x 8 5.x E/ (T) Figure 5. Graphical interpretation of equations (7,9) for homogenous DBD. Broken line presents electric fiel (E/ = 4 T) etermine applying ratio of nitrogen intensities (7). - applying 4T 7 measure current ensity (9). n 3.6 m -3. e To etermine the influence of gas temperature on the calculate ratio of the quenching factors, we calculate the ratio Q (B) Q (C) at variable gas temperatures. This ratio is equal to 6.55 at 3 K an ecreases to.7 % (of 6.55) at K. Therefore, we conclue that the influence of gas temperature on plasma parameters is negligible. However, the influence of gas temperature cannot be neglecte while etermining the rate of prouction of nitrogen an oxygen atoms uring electron-impact issociation of their molecules because the ensity of gas species ( an O ) epen on the gas temperature. Furthermore, the rate constants of chemical reactions also epen on the gas temperature. Therefore, for the simulation of plasma chemical kinetics, the etermination of gas temperature is essential. The plasma parameters an the gas temperature can be use for the simulation of chemical kinetics an the etermination of species fluxes reaching the treate surface. The rate constants for electron- O impact issociation of nitrogen an oxygen molecules in air ( k an k iss iss in m 3 s - ) for varie electric fiels are presente in table 4. The issociation rates ( R molecules at plasma conitions are calculate using (): M iss. in m -3 s - ) of nitrogen an oxygen

14 R M iss k n () M M iss e where, M = or O corresponingly. n the homogeneous ischarge at DBD conitions (E/=4 T, n e =3.6 7 m -3 ), R m -3 s - O an R. 7 m -3 s -. iss. iss. Table 4. Rate constants for electron impact issociation of nitrogen an oxygen by variation of electric fiel. Reuce electric fiel E/ in T Dissociation rate constants by electron impact +e +e O +eo +e k in m 3 s - k O - in m 3 s iss 4.54E-.87E E E E-8 3.E E-7 9.E-7.6E-6.77E-6.46E-6.7E E E E E E E-6.8E-5 6.7E-6.36E-5 7.3E E E-6 6.E E E-5 9.5E E E E-5.E E-5.6E E-5.E E-5.6E E-5.E E-5.3E E-5.7E E-5.3E E-5.33E E-5.36E-5 iss The metho of using a non-calibrate spectrometer for characterization of ischarges in air at atmospheric-pressure conitions is applie in assumption of linearity of the efficiency function of the spectrometer in spectral range of about 5 nm. The metho iscusse in this work can be applie when a usual grating spectrometer is use. By application of an echelle spectrometer operate in numerous optical orers that possesses efficiency curve which is rugge profile with sharp contour

15 that cannot be escribe as a linear function of wavelength also by such small spectral range, this metho is not applicable. To numerically-simulate emission spectrum at ifferent gas temperature that can be use for the etermination of gas temperature in the experiment, the program coe use was evelope by our group specially for this purpose []. Similar simulation can also be performe using applications like "Specair" an "LFBASE". To simulate electron istribution function an to calculate the rift velocity of electrons, the Boltzmann equation can be numerically solve using the program BOLSG. (These applications an programs are available as freeware that can be ownloae from their respective websites)

16 5. Conclusion The combination of current measurement, numerical simulation an OES has been applie for the etermination of plasma parameters at DBD conitions in air. For OES, a non-calibrate spectrometer is use. Electric fiel an electron istribution function are etermine using the measure unaltere emission spectrum of nitrogen, the well-known Frank-Conon factors of nitrogen emission an the calculate rate constants for electron-impact excitation of these emissions. Electron ensity is etermine using measure electric current ensity an rift velocity that epen on the electric fiel. The etermine plasma parameters can be use for calculation of issociation rates at DBD conitions an for simulation of plasma chemical kinetics.

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