Institute of Physics Publishing Plasma Sources Science and Technology Plasma Sources Sci. Technol. 13 (2004) 668-674 PII: S0963-0252(04)85669-X Simultaneous measurement of N and O densities in plasma afterglow by means of NO titration P Vašina, V Kudrle, A Tálský, P Botoš, M Mrázková and M Meško Department of Physical Electronics, Masaryk University, CZ-61137 Brno, Czech Republic E-mail: vasina@physics.muni.cz Received 10 February 2004 Published 12 October 2004 Online at stacks.iop.org/PSST/13/668 doi:10.1088/0963-0252/13/4/016 Abstract In this work we describe a method based on NO titration that permits us to measure at the same time the absolute concentrations of N and O atoms in the gas phase. This method is suitable for low concentrations of oxygen atoms. We also discuss the validity of the titration method, especially the influence of the reaction time. It was used to study the influence of O2 admixture on the degree of dissociation of nitrogen in the afterglow. The results of the NO titration technique were compared with those obtained by means of electron paramagnetic resonance and with the relative values determined from emission of N2(53 ng-A3 1. Introduction One can observe growing interest in non-equilibrium kinetics of low pressure plasmas in nitrogen, oxygen and their mixtures. It is caused by the need of various branches of science, for example, physics of the upper atmosphere or plasma physics and technology (cleaning of pollutants, plasma processing). In many studies various authors [1-5] have observed that even a small admixture of oxygen into nitrogen (or inversely, nitrogen into oxygen) changes the dissociation degree of the main gas substantially. In order to obtain a better understanding of this phenomenon it is necessary to know the absolute densities of both N and O. There are also many other types of experiment, where the absolute concentration of atomic nitrogen and/or oxygen in a plasma afterglow is needed. As the atoms are radical species, their detection may be difficult. There are only a few methods giving reliable absolute data, for example, two photon absorption laser induced fluorescence (TALIF) [6], nitrogen oxide, titration [7, 8] and electron paramagnetic resonance (EPR) [9, 10]. Due to its simplicity, NO titration is the most widely used. However, in most published works the experimental data are evaluated using the theory for an ideal case. In some circumstances, this can introduce substantial errors. Recently, a method using NO titration for simultaneous measurement of N and O concentrations was reported [11] and then used [12, 13]. It is carried out in the region where [NO]^[N]. It is well suited for higher oxygen atom concentrations but is quite insensitive for lower O densities. Unfortunately, this low [O] region is very interesting for studying the increase of the dissociation rate of nitrogen when a very small molecular oxygen admixture (under 1%) is added [14,15]. We have developed an NO titration variant especially for this range, which is presented in this paper. It is based on fitting data in the [NO]^[N] region by a theoretical curve and gives the absolute values of [N] and [O] rather easily. As we wanted to test its correctness, the results from the NO titration were compared with those of various other methods, such as EPR and optical emission spectroscopy (OES). 2. Titration by NO in nitrogen Into a flow of partially dissociated nitrogen gas a small quantity of NO is added. Among the possible chemical reactions, these are the most important: N + NO^N2 + 0, (1) N + 0(+N2) NO*(+N2), (2) NO + O^NO^. (3) 0963-0252/04/040668+07$30.00 © 2004 IOP Publishing Ltd Printed in the UK 668 Table 1. Values of rate constants of reactions (l)-(3) that were used in our calculations. For reaction (2) we assumed the nitrogen pressure to be 400 Pa, which gives ^2^2] =9.1 x 10~16 cm3 s_1. Reaction Value Reference (1) k, = 1.6 X 10" -10cm3s-' [16] (2) k2 = 9.1 X 10" -33 cm6s-' [17] (3) h = 6.4 X 10" -17 3 -1 cm s [18] Reaction (1) is very fast (see table 1) and converts all the available N atoms and NO molecules to O atoms. If there are more N atoms than NO molecules, reaction (2) follows and produces excited NO*. It then radiates in the UV region as an NOyS system (B 2Yl-X 2n, k « 320 nm). On the other hand, if [NO]>[N], then reaction (3) produces NOj, which radiates as a green-yellow continuum (A 2B\-X 2A\) around 570 nm. This can be used to measure the absolute concentration of N atoms by NO titration. It is sufficient to slowly increase the flow of NO and record the optical emission spectra of NO* and NOj. At the moment (the so-called dark point) when the NO* bands have decreased to zero and NOj continuum is just about to appear, the densities of the introduced NO and the initial N are the same. As the NO flow is easily measurable by a flow-controller, this method has been used by many authors. To find the dark point with good accuracy in a classical way, one needs to carry out many measurements. However, it is possible to achieve the same accuracy with fewer experimental points if the shape of the solution of (l)-(3) is considered. If reaction (1) is finished, the intensity of NO* radiation is proportional to the actual values of [N] and [O]. As a result of reaction (1) each NO molecule produces one O atom and consumes one N atom. The dependence 7No = /([NO]o) is then 7N0 « [N][0] = ([N]0 - [NO]0)[NO]0 = [N]0[NO]0 - ([NO]0)2, (4) where the subscript 0 denotes the initial densities (without the influence of the products of reactions (l)-(3)). This is the equation of a parabola with one root at zero and the second root at the dark point. A good use of this fact is that by fitting of experimental data by a parabola we can determine the position of the dark point precisely even from sparse data. In spite of the ease of use of the NO titration method certain problems may arise. The 'ideal' behaviour (see figure 1) is observed only for a limited range of reaction times. However, in many published works the authors have recorded emission spectra from a region too close to the NO inlet. In that case the reactions are not over and the observed results are distorted (see figure 2). The experimental evidence of this effect is presented later in figure 8. It is clear that there is no longer even a dark point. As a quick cure some authors [19] suggest taking the intersection of the two lines as the dark point. Unfortunately this is not valid, because (i) the scaling of curves will influence the position of the dark point and (ii) even for the same scale for both curves the position of the intersection depends on the reaction time. In some cases the error of such quick estimation may be relatively important as is demonstrated in figure 2. Therefore it is necessary to either correct for insufficient reaction time or, even better, to avoid short reaction times altogether. Because we neglected Measurement of N and O density Figure 1. Production of excited molecules in the course of NO titration in nitrogen afterglow at a pressure of 400 Pa. The three curves correspond to different concentrations of N atoms: 8, 10 and 12 xl014cm-3. l—1—1—1—1—1—1—1—1—1—1—1—1—1—1—1—1—1—1—1—r NO concentration [ 10 s cm"3 ] Figure 2. Distortion of the ideal case due to insufficient reaction time. The intersection of the NO* and NOj curves moves away from the correct value of 1 x 1015 cm-3 for too-short reaction times. all other processes except (l)-(3), long reaction times pose no problem. 3. NO titration in N2-O2 mixtures When the afterglow of nitrogen-oxygen discharges is studied, the set of reactions (l)-(3) remains the same but the initial conditions are different. The solution for sufficient reaction times (reaction (1) completed) has the form /no « ([N]0 - [NO]0)([O]0 + [NO]0) = -([NO]0)2 +([N]0-[0]o)[NO]o + [N]0[0]o. (5) In comparison with the case of pure nitrogen, a new factor appears—the initial concentration of O atoms. It is again an equation of a parabola, Ifioix) = ax2 + bx + c, (6) where the coefficients a, b and c follow b/a = [O]o — [N]o and c/a = —[N]q[0]o- So by fitting the experimental dependence 669 P Vašina et al Figure 3. Production of excited molecules in the course of NO titration in nitrogen + oxygen afterglow for various oxygen atom concentrations. The nitrogen atom concentration is fixed at 1 x 1015 cm-3 and the pressure is 400 Pa. It is seen that for rising oxygen content the dark point does not move but the shape of the NO* curve changes. 10" 10" I 10,! g 10 i c o O 10" TT711T-........I oxygen nitrogen nitrogen oxide nitrogen dioxide. T 10-' "T" 10'" 10'5 1—1 10"4 10'a 10* 10' Time [ s ] Figure 4. Time development of important species in the course of NO titration in nitrogen + oxygen afterglow. Curves were calculated for a pressure of 400 Pa, [N]o = 1 x 1015 cm-3 and [O]0 = 2.5 x 1014cm-3. 7N0 = /([NO]o) by a parabola, we obtain the results -b — yjb2 — 4ac [N]0 [O]0 2a -b + -Jb2 — Aac 2a (7) (8) Now one of the roots moves with the initial O concentration to the value — [O]o, but the second one remains fixed at [N]o as shown in figure 3. Therefore, the dark point does not shift and even in the presence of O atoms the standard method of [N] measurement by NO titration works. Measured data exhibiting these parabolic dependences are shown later in figure 9 in the experimental part of this paper. In figure 4 the time evolution of the densities of important species during the course of NO titration is shown. At time t = 0, NO molecules (2.5 x 1014 cm-3) were ideally 0 w 10 10 10' Reaction time [ s ] Figure 5. Relative error of [N] and [O] estimation as a function of the reaction time. Curves were calculated for a pressure of 400 Pa, [N]0 = 1 x 1015 cm"3 and [O]0 = 5 x 1014 cnr3. mixed with N of concentration 1 x 1015 cm-3 and O atoms of concentration 1 x 1015cm-3. We can see that for t < 10~4 s [N] and [NO] decreases due to reaction (1). At time teq, in this case around 1 x 10~4 s, an equilibrium between the NO loss due to reaction (1) and the production due to reaction (2) is established. For times higher than 1 x 10~4 s, the resulting [NO] value is given by [NO] fc2[N2][N][Q] *i[N] + *3[0]' (9) where [O] is the total density of O atoms, which includes not only the initial O atoms but also those produced by reaction (1). Because k^[0]