Kinetic Study of Atmospheric Pressure Nitrogen Plasma Afterglow Using Quantitative Electron Spin Resonance Spectroscopy

Quantitative electron spin resonance spectroscopy is used to measure nitrogen atom density in atmospheric pressure dielectric barrier discharge afterglow. The experiment shows that oxygen injection into early afterglow increases the nitrogen dissociation in certain parts of the afterglowwhile it is decreased in the rest of the afterglow. Numerical kineticmodelling supports and explains the experimental data while the best fit provides some a priori unknown parameters such as initial concentrations and rate constants.


Introduction
Nonequilibrium cold plasmas at atmospheric pressure and especially dielectric barrier discharges are getting increased attention of both basic and applied research.They are widely used in many industrial applications from ozone production [1] and lighting [2] to plasma surface modifications [3].Their main advantages over other competing technologies are the ease-of-use, economy, and environmental considerations [4].Besides the already established applications, there is rapid expansion of atmospheric pressure plasmas into new areas, such as plasma-chemical synthesis of substances which are difficult to attain by other techniques [5][6][7], plasma medicine [8], material disinfection and sterilisation [9], and use in cosmetics [10] or in fashion industry [11].
Nitrogen plasmas are often used as a source of high density nitrogen atoms.Molecular nitrogen is rather inert gas, but atomic nitrogen is quite reactive, which is made use of in plasma deposition of nitride films [12] or plasma nitridation [13].Although the low pressure plasmas are currently dominating this field, there is strong incentive for research and development of nitrogen plasma sources operating at atmospheric pressure [14].
In order to develop new plasma-chemical technologies it is important to understand the elementary processes taking place in both the active plasma and plasma afterglow.
Nitrogen, despite being a simple diatomic molecule, has quite complex plasma chemistry and kinetics, especially in mixtures with oxygen [15,16].As stated above, the nitrogen atoms play a significant kinetic role due to their high reactivity.Their concentration is then one of the most important parameters to be experimentally determined.Although there is broad range of experimental techniques able to detect N atoms, for example, optical emission spectroscopy, only few of them are suitable for absolute, not relative, measurements.UV absorption spectroscopy [17], NO titration [18], mass spectroscopy (MS) [19], laser induced fluorescence (LIF) [20], and catalytic probes [21], for example, are widely used.Another challenge is an operation of such diagnostic technique in atmospheric pressure, which, for example, greatly increases quenching in LIF, complicates pumping in MS, or totally changes the plasma chemistry (NO titration).
In this paper, the electron spin/paramagnetic resonance (ESR/EPR) [30][31][32] method is used for N atom density determination.This method is very useful for detection and identification of paramagnetic particles and especially radicals [33][34][35].Although the method is routinely used in chemistry, its use in plasma physics is relatively rare.Since the pioneering works [36][37][38], other, mostly laser based methods appeared which are now considered mainstream.
Electron spin or paramagnetic resonance (ESR/EPR) is essentially microwave absorption spectroscopy [39] on Zeeman split [40] levels.The transitions with very low energy separation between the upper and the bottom levels (as is the case in microwave spectroscopy) are very easily disturbed by the collisions with other particles.The collisional/pressure broadening of absorption line can be quite pronounced [41,42], especially for gas phase atomic and molecular lines with very low natural linewidths.This makes most of the species (for extensive list, see [43]), including, for example, atomic oxygen, difficult to detect in atmospheric pressure plasmas.However, the particles in s-state, such as nitrogen or hydrogen atoms in ground state, do not exhibit pressure broadening and can be detected by ESR/EPR even at atmospheric pressure.
There are a number of works, both theoretical and experimental, dealing with low pressure plasma diagnostics by ESR/EPR method [44][45][46][47][48][49][50].However, due to abovementioned difficulties of pressure broadening, the diagnostics of atmospheric pressure plasmas by EPR/ESR is rather unresearched topic, as our previous paper [51] is, to authors' best knowledge, still the only one published.
Although the nitrogen and oxygen plasmas are studied for very long time, there is still intensive research [52][53][54] going on.The discharges in N 2 -O 2 mixtures have very complicated plasma kinetics and some effects, especially in mixtures with low O 2 /N 2 ratio, are not fully explained yet.In our previous work [55] it was reported that adding of small amount of oxygen into a low pressure nitrogen plasma afterglow causes an increase of nitrogen atom density.In this paper we extend the study of the influence of oxygen admixture on the nitrogen afterglow to atmospheric pressure.

Experimental Set-Up.
The experimental apparatus is depicted in Figure 1.Nitrogen plasma at atmospheric pressure was produced using industrial ozoniser LifeTech 50.It is based on coaxial dielectric barrier discharge, excited by 25-35 W power at 15 kHz frequency.The stainless steel inner electrode has approx.2 cm diameter and is separated by 0.7 mm plasma gap and 2.5 mm thick corundum (Al 2 O 3 ) ceramics from the outer electrode which is realised by an aluminium foil tightly wrapped around the ceramic tube.The discharge tube is approx.15 cm long.Although the metal electrode in direct contact with plasma can significantly reduce N atom density in the effluent due to increased surface recombination/reassociation, this design [56] is well established in industrial ozonisers.
The discharge was operated in flowing (12 standard litres per minute) nitrogen, coming from pressurised cylinder (Messer-Griesheim, purity 99.995%) via pressure reduction valve.The volumetric flow rate of nitrogen was measured by flowmeter with floating element (rotameter UPLS-R3).Downstream from the plasma source, the oxygen is optionally introduced.The oxygen comes from pressurised cylinder (Messer-Griesheim, purity 99.995%) via Hastings mass flowcontroller maintaining the oxygen flow at 7.5 sccm (standard cubic centimetre per minute).The tubing is made from polyethylene and stainless steel.
The oxygen is introduced into the afterglow tube just downstream from the plasma generator using an inlet threeway valve.This configuration permits presetting the oxygen flow on the flow-controller and rapidly switches on and off the oxygen admixture.The distance between the output port of the plasma generator and the inlet of oxygen is 6 cm.The afterglow tube is made of fused silica with 10 mm outer diameter and 8 mm inner diameter.This tube passes through ESR/EPR spectrometer resonator and ends in another outlet three-way valve.In normal operation the plasma afterglow vents into open atmosphere and the afterglow tube length (approx.2.5 metres) together with high gas flow prevents any back-diffusion of air into the afterglow or plasma.In second position of this outlet valve the whole apparatus can be pumped down by the rotary vane oil vacuum pump.This is used for calibration by molecular oxygen at reduced pressure and for degassing/cleaning as before every measurement series the whole plasma system is evacuated to pressure about 10 Pa to remove residual impurities.After that, the nitrogen flow is switched on and the outlet three-way valve is turned to normal position.Then the discharge is run 1 hour at maximum power to burn-in the plasma generator and remove the possible contamination off the electrode.Only after such procedure are the experiments started.
The distance from the inlet of oxygen admixture to the measuring ESR/EPR resonator can be changed by shifting the whole plasma system.To ease this, the plasma system including afterglow tube is placed on nonmagnetic rails parallel to ESR/EPR resonator axis.The furthest possible position is limited by the rail length to 90 cm.However, in the present study the maximum extension was not used as the ESR/EPR signal in this extreme position was already difficult to measure.The minimum distance in which the measure could be carried out is about 20 cm.Although it is mechanically possible to place the discharge closer to the resonator, at shorter distances the magnetic field of the ESR/EPR spectrometer electromagnet affected the plasma generator.
The ESR/EPR spectrometer JEOL JES-PE is specially adapted for use in plasma physics.It is classical continuous wave spectrometer [34] using klystron source operating at X band and with standard sensitivity around 10 10 paramagnetic particles in the interaction volume of TE 011 resonator.The output voltage of the analogue spectrometer is measured by digital voltmeter (Metra M1T390, 5 digits) and transmitted to a personal computer via GPIB.The ESR/EPR signal is analysed and postprocessed using custom software.It automatically identifies the spectral lines and calculates their peak-to-peak height, peak-to-peak width , and area under the absorption line  N (as ESR/EPR lines are typically [34] recorded in the form of derivation, double integration is needed).

The Principle of Measurement and Calibration Procedure.
The ESR/EPR phenomenon is based on resonant absorption of microwave photons by transition between Zeeman split [40] energy levels.Typically, the resonance is achieved by variable magnetic field (which sets the energy level splitting) while the microwave frequency (i.e., photon energy) is fixed.The area under absorption spectral line is proportional [38] to the concentration of absorbing paramagnetic particles.The proportionality constant depends on spectrometer settings and the transition probability (Einstein coefficient).After a calibration of the spectrometer by a known sample it is possible to measure the concentration of paramagnetic particles absolutely [57].
In this work, the spectrometer calibration [44] is carried out using molecular oxygen O 2 .The measuring resonator is filled with gaseous molecular oxygen at known concentration (calculated from pressure and temperature), its intensive spectral line C (the traditional naming, found in many papers, e.g., [38,41,43,44]) is recorded, and corresponding double integral  C is calculated.Using the same settings of the spectrometer, the ESR/EPR line of atomic nitrogen is recorded and its double integral  N is calculated.Knowing the Einstein coefficients of both species the concentration of atomic nitrogen is given by simple relation The numeric constant in this formula is the ratio of Einstein coefficient of molecular oxygen line C and that of one component of atomic nitrogen triplet [43].
As the oxygen calibration is carried out in the flowregime, due to Hagen-Poiseuille law [58] there exist pressure gradients along the tube, making the pressure in the ESR/EPR resonator slightly different from the one indicated by pressure meter.The vacuum conductivity of the tube depends [59] on pressure, too.Moreover, as at low pressures the partial pressure of O 2 could be smaller than the total pressure indicated due to small vacuum leaks, finite base pressure of the pump used, or degassing from walls, it is better to record O 2 line for several indicated pressures than to rely on single value only.The result of such calibration measurement is shown in Figure 2.
The ESR/EPR lines of atomic nitrogen are extremely narrow and therefore sensitive to any broadening [41].The ground state of nitrogen N( 4 S 3/2 ) has zero orbital magnetic momentum and its paramagnetism is given only by the electron spin.In that case there should be no collision induced broadening; its spectral linewidth should be independent of pressure [60].In work [61] this was studied in the pressure range from 50 to 600 Pa and in temperature range from 80 to 300 K.It was found that with decreasing temperature the apparent linewidth  = 6 T remained constant, while the integral and thus the concentration [N] decreased.The linewidth was thus independent of N atom density, which suggested that the role of spin-spin relaxation at these N concentrations (around 10 13 -10 14 cm −3 ) is negligible.In present work, a similar measurement of N( 4 S 3/2 ) linewidth was carried out in pure nitrogen afterglow but at atmospheric pressure.Practically the same value  = 6.4 T was observed.The linewidth (and spectral line shape) being constant, the concentration of N atoms should be directly proportional to the absorption line height and by consequence also to the peak-to-peak height of the measured (i.e., absorption derivative) line.It can be advantageous to use this peak-to-peak height over the spectral line integral as the latter exhibits much higher statistical variations due to an increased influence of a noise overlaying the line shoulders.
However, a presence of other paramagnetic particles can affect even the s-states.The experimental result, nitrogen spectral linewidth as a function of molecular oxygen admixture, is shown in Figure 3.The changing nitrogen linewidth prevents the use of simple line height as concentration indicator and the integral must be used instead.This effect is consistent with [60].

Experimental Results.
Electron paramagnetic/spin resonance was used to measure the concentration of atomic nitrogen N( 4 S 3/2 ) in atmospheric pressure discharge afterglow.This density [N] was measured along fused silica tube in pure nitrogen afterglow and with 625 ppm of oxygen injected into the early afterglow; see Figure 4.
The most important result is the fact that the two curves apparently intersect.It means that a small admixture of oxygen can cause both an increase and a decrease in concentration of nitrogen atoms, depending on which part of the afterglow is observed.This nontrivial behaviour is a typical demonstration of complexities inherent in N 2 -O 2 kinetics.
In flowing kinetic studies, if the gas velocity is known, the spatial distribution of measured species can be transferred to their temporal evolution.Sometimes the same gas velocity in the whole cross-section (i.e., plug flow) is assumed without any further consideration.However, there can be a significant radial gradient of gas velocity due to a shear flow and a boundary layer.While a laminar flow in circular tube produces well-known parabolic velocity profile, in a welldeveloped turbulent flow the shear zone is thin compared to the tube diameter, so the plug flow is appropriate.The character of flow in a tube can be deduced from the Reynolds number [62]

𝑅 = 𝑢𝑑/],
where  is mean flow velocity,  is the inner tube diameter, and ] is cinematic viscosity.For nitrogen at standard pressure and temperature ] = 1.50 ⋅ 10 −5 m 2 s −1 according to [63], which gives  = 2100 for our experimental conditions.This value falls in critical Reynolds number range  = 1800-2300 where a transition between the laminar and the turbulent flow happens [64].One can expect that the inhomogeneity caused by the lateral oxygen inlet together with other imperfections introduces some additional turbulence.Based on this reasoning, there is enough turbulence to consider the plug flow as a valid approximation in this paper, too.
In that case, the radially uniform flow velocity is approx.4 m/s.Using this value, the measured dependence of the nitrogen atom density on position in the afterglow (Figure 4) was recalculated to the dependence on time; see Figure 5.
It is experimentally impossible to measure the concentration near the oxygen inlet (i.e., at times close to  = 0 s) as the T-piece (needed for the inlet) cannot pass through the ESR/EPR measuring resonator opening and the close distance between the plasma generator and the ESR/EPR electromagnet would magnetically influence the plasma generator and the plasma itself.However, if one excludes a backdiffusion, it is evident that with or without oxygen admixture the value at  = 0 s must be the same; that is, both curves must start at the same initial value depicted in Figure 5 by red circle.While this common initial value is a priori unknown 0.00 0.0 0.5 it effectively sets the probable shapes of both curves (with and without oxygen admixture) in the unmeasurable region.These are shown in Figure 5 using the dashed lines.One can see that the case without oxygen admixture should be simply governed by losses while the case with oxygen admixture initially exhibits some process producing the nitrogen atoms and only later the losses dominate.Higher losses of N with O 2 present cause the steeper descent of this curve and so both curves intersect.

Kinetic Modelling of Plasma Afterglow in Pure Nitrogen.
The model is based on collisional processes between the principal species in the nitrogen afterglow: N 2 molecules, electronically excited molecules N 2 (A), atoms N(S), N(P), and N(D), and it takes into account also the wall processes.The model is focused on N( 4 S) and so the species N 2 (X,v) despite being another important energy carrier is not included as it cannot directly cause N 2 dissociation and it does not exhibit very strong quenching by nitrogen atoms (which N 2 (A) does).An overview of the main plasmachemical processes based on [28] is presented in Table 1.
The kinetic equations describing the processes in Table 1 were transformed to a set of differential equations and solved numerically using the Euler method.As this method might be unstable for rapidly changing functions, it is necessary to use sufficiently small time-step.This convergence was verified in the presented model.Some parameters, such as  2 and initial concentrations of N( 4 S) and N 2 (A), are a priori unknown and must be determined by fitting to the experimental data.The concentration of molecular nitrogen [N 2 ] = 2.77⋅10 19 cm −3 at standard pressure and temperature was used as one of initial values.
The reaction (1) describes the volume recombination and the reaction (2) the wall recombination of atomic nitrogen in ground state N( 4 S).The model includes the reactions of the N( 2 P), N( 2 D), and N 2 (A) metastables, too.However, significant simplifications are possible.In the experiment, only the N( 4 S) concentration is actually measured.Moreover, the metastable N atoms generally end in ground state (reactions (4)-( 6)).So the reaction (3) effectively produces one N( 4 S) atom and is equivalent to N 2 (A) deexcitation.
Further simplification stems from the mutual ratio of [N 2 (A)] and [N( 4 S)].Although these values are a priori unknown, they can be roughly estimated.A rough estimation of the initial concentration [N 2 (A)] 0 of 10 11 cm −3 can be taken from papers [65][66][67], which used sufficiently similar conditions to the present ones (atmospheric pressure nitrogen afterglow operated in similar tube diameter and similar input power).As the visual extrapolation of pure nitrogen curve (red hollow diamonds) in Figure 5 gives the initial value of [N( 4 S)] 0 around 10 13 cm −3 , one may safely assume that Using these simplifications, the "full" model of Table 1 is effectively reduced to the set of kinetic equations ( 1), ( 2 In the first few milliseconds there is a big difference between the full and the reduced models due to the reaction (3).But in later reaction times, in which the real experiment is carried out (as discussed above, due to experimental constraints it is not possible to measure at afterglow positions before 0.06 s), there is nearly negligible difference between the full and the reduced models.Taking into account the experimental error around 10% and an assumption about initial values 10 11 cm −3 < [N 2 (A)] 0 < [N( 4 S)] 0 , one can safely use the reduced model only.1)-( 7)) and reduced (see ( 1), ( 2), (3), and ( 7)) models for several initial ratios between [N( 4 S)] and [N 2 (A)].The least squares fit of experimental data by this reduced model is shown in Figure 7 and gives the values of previously unknown parameters: [N( 4 S)] 0 = 3.3 ⋅ 10 13 cm −3 and  2 = 3.1 s −1 .To the rate constant  2 exists corresponding coefficient (probability) of surface recombination/reassociation  = 1.24 ⋅ 10 −6 which is in good agreement with [68] where they get  lit = 1.35 ⋅ 10 −6 .Following the reasoning of the previous paragraph, one may assume that these values do not strongly depend (see Figure 6) on the initial concentration of N 2 (A) (for sufficiently small [N 2 (A)] 0 ).
The inclusion of vibrationally excited nitrogen molecules is necessary as these have even greater importance [73] in N 2 + O 2 plasma afterglow.In a nitrogen pink afterglow the vibrationally excited molecules carry a significant part of energy in the afterglow [74,75].This energy is then responsible for the formation of N 2 (A), N 2 (a  ) and finally for the ionisation of N 2 molecules.Although the pink afterglow was not observed [76] in atmospheric pressure plasma, one may assume [73,77] the concentration of N 2 (V = 12) greater than 5 ⋅ 10 13 cm −3 at afterglow position of 15 ms.
The concentration of molecular oxygen [O 2 ] = 1.56 ⋅ 10 16 cm −3 is calculated according to the ideal gas law from the experimental conditions (625 ppm of O 2 in N 2 at atmospheric pressure and room temperature).
The reaction set of Table 2 can be further reduced as follows.Kinetic reaction ( 22) is negligible to the reaction (12) because  22 is about two orders of magnitude smaller than  12 .For the same reason, reaction (15) can be neglected with respect to reaction (14).Furthermore, (26), according to the numerical calculations, has not significant influence on the concentration of N( 4 S), so it can be omitted, too.
Most of the equations describe the loss of ground state metastable atom N( 4 S).Equation ( 13) describes production of N( 4 S) but its contribution is not significant in comparison with the losses due to reactions (8), (9), and (10).This is in contrast with the experiment, where an increase in N( 4 S) concentration is observed when oxygen is added.Using the larger equation set of [28] does not help either.To explain the [N( 4 S)] increase, ( 23) is needed, where vibrationally excited molecule in the electronic ground state N 2 (X,v) produces N atom and nitric oxide molecule by reacting with oxygen atom [69,77].
The heterogeneous reactions in the model include the wall deexcitation of N 2 (X,v), see (24), and N 2 (A), see (25).
As usual, the kinetic model must be supplemented by the initial concentrations.The initial value of [N( 4 S)] 0 was taken from the pure nitrogen model.Due to the adsorption of oxygen on the walls of the afterglow tube [78][79][80][81], a smaller value of the wall recombination coefficient  2 (change from 3.1 s −1 to 0.5 s −1 ) was assumed.Atomic oxygen wall recombination coefficient  16 was considered to be same as  2 for simplicity.Rate constants for wall deexcitation (24) and (25) were taken to be the same for both species, that is,  24 =  25 , with estimated value in range of 1-10 s −1 to correspond to [82].The precise value of  24 and  25 is calculated by fitting the model to the experimental data.
Figure 8 shows the calculated temporal evolution of concentrations of main species considered in the present model in short (a) and long (b) time scales.The dominant species (besides the parent N 2 and O 2 ) are the nitrogen and oxygen atoms.Interestingly, despite the very unfavourable ratio of [O 2 ]/[N 2 ] = 625 ppm, there are more oxygen atoms than nitrogen atoms in the late afterglow.Electronically and vibrationally excited nitrogen molecules disappear quickly.Both oxides of nitrogen, nitrogen dioxide NO 2 and nitric oxide NO, remain after 0.1 s constant, [NO] being approx.10 times higher than [NO 2 ].
Full comparison of the model and the experiment is shown in Figure 9 for both cases, with and without the oxygen admixture.Values of a priori unknown parameters obtained

Figure 1 :
Figure 1: Schematic drawing of the experimental set-up.

Figure 2 :
Figure 2: Calibration of EPR spectrometer using the line C of molecular oxygen.Linear dependency of absorption line integral  C (i.e., double integral of measured signal) on oxygen pressure validates the calibration process and its slope provides a constant [O 2 ]/ C needed for the calibration.

Figure 3 :
Figure 3: Linewidth of N atom ground state ( 4 S 3/2 ) EPR line as a function of oxygen admixture.

3 )Figure 4 :
Figure 4: Spatial distribution of the nitrogen atom concentration (in ground state) along the afterglow tube for two cases: with and without 625 ppm oxygen admixture.

N 2 + 4 S) (10 13 cm − 3 )Figure 5 :
Figure 5: Data from the previous figure recalculated from distance to time.The rough estimation of initial [N] value at  = 0 s is shown, too.The sketch of a reasonable time evolution is shown by dashed lines.

3 )Figure 7 :
Figure7: Fit of the kinetic model of the pure nitrogen afterglow given by reduced reactions from Table1to the experimental data, giving the previously unknown initial value [N( 4 S)] 0 = 3.3 ⋅ 10 13 cm −3 and the value of  2 .

Figure 8 :
Figure 8: The temporal evolution of main species considered in the reduced kinetic model of N 2 -O 2 afterglow.For clarity, the data are shown in two time scales.

Table 1 :
Main plasma-chemical reactions in the pure nitrogen afterglow.