Atomic oxygen in a cold argon plasma jet: TALIF spectroscopy in ambient air with modelling and measurements of ambient species diffusion

Figure 2 illustrates the setup and the principle of the TALIF measurement system. By mounting the jet on a three-axis manipulator, it is possible to move the jet through the detection volume along the axes of a self-defined coordinate system, yielding space-resolved measurements of the oxygen distribution. The detection volume is defined by the overlapping foci of the laser beam (d = 200 µm) and the imaging volume of the fluorescence light (d = 500 µm). The fluorescence is detected by a gated photomultiplier synchronized to the 10 Hz pulsed nanosecond laser beam.

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As the plasma jet operated in argon produces excited argon species (²P $^{\circ}_{3/2}$ 4p), radiating at 842.42 nm close to the oxygen fluorescence light, the use of an interference filter (FWHM = 1 nm; T = 50%, λ₀ = 844.5 nm) in front of the photomultiplier is necessary in order to reduce stray light and increase the signal-to-noise ratio.

Figure 3 shows the oxygen resonance and the variation of the laser energy yielding the relative oxygen fluorescence signal normalized over the square of the laser energy. The signal is proportional to the square of the laser energy in the low energy regime. This guarantees that apart from negligible spontaneous emission no competitive processes like photo-dissociation take place which could prohibit a quantitative analysis. The calibration measurements were performed at the defined origin (0,0,0) of the coordinate system close to the nozzle with an argon flow of 5 slm and 50 sccm of O₂ admixture defined as standard conditions.

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For the absolute calibration of the oxygen signal a reference measurement at the same position in a controlled xenon atmosphere is performed [2], which means comparing the atomic oxygen fluorescence signal to the fluorescence signal of a known density of xenon according to

$$\begin{equation} n_{\rm O} =\left( {\frac{\eta _{{\rm Xe}} T_{{\rm Xe}} \sigma _{{\rm Xe}} a_{{\rm Xe}}^{32} }{\eta _{\rm O} T_{\rm O} \sigma _{\rm O} a_{\rm O}^{32} }} \right)\frac{n_{{\rm Xe}} }{S_{{\rm Xe}} }S_{\rm O}. \end{equation} \tag{ 1 }$$

Here S_O denotes the normalized oxygen TALIF signal (see figure 3), n are the ground-state densities of the excited species, T and η are optical properties of the experimental setup, a³² the quenching-corrected branching ratios of the observed fluorescence transitions (see section 3.3) and σ are the two-photon excitation cross sections [3]. The lower index denotes the species whereas the upper index refers to the transition. The normalized xenon TALIF signal S_Xe of the known xenon density n_Xe is gained from the reference measurements under a variation of the laser energy at different xenon pressures (see figure 3). For high laser energies a non-proportional behaviour due to saturation effects can be observed. From the comparable measurements in xenon using equation (1) the atomic oxygen density under standard conditions and the defined origin is determined to be n_O = 2.75 × 10¹⁵ cm⁻³.

At atmospheric pressure, quenching becomes relevant and needs to be considered. It is implicitly considered in the calibration (see equation (1)) through the effective branching ratios for the oxygen and the xenon excited states:

$$\begin{equation} a^{32}=\frac{A^{32}}{A^{31}+A^{32}+Q^{(3)}}\tqs {\rm with~}Q^{(3)}=\sum\nolimits_q {k_q^{(3)} } n_q , \end{equation} \tag{ 2 }$$

where A denotes the spontaneous emission rate of the excited state and Q⁽³⁾ the effective quenching rate, depending on quenching partner densities n_q and the corresponding quenching coefficients $k_q^{(3)}$ taken from [6]. Equation (2) shows that quenching reduces the effective branching ratios of the spontaneous emission of the excited states. In the case of oxygen, neutral ground-state argon atoms and oxygen and nitrogen molecules are considered to be the most efficient quenching partners. In xenon atmospheres only self-quenching by xenon atoms takes place.

The spectrum of the jet between 115 and 140 nm is measured with a 0.5 m VUV scanning monochromator (Acton Research Corp., VM 505) with a grating of 1200 g mm⁻¹ blazed at 150 nm. A photomultiplier (PM) tube (Thorn/EMI, 9635 QB) with a sodium salicylate entrance window is used to detect the VUV radiation. The optical emission is measured end on by placing the jet nozzle in the axis of the optical system, consisting of a measuring aperture, imaging mirror and entrance slit, which are located in a vacuum chamber with a pressure in the range of 2 × 10⁻⁶ mbar. The plasma jet is positioned in ambient air at different distances axially to the MgF₂ window, which seals the vacuum chamber. A detailed description of the VUV setup is given in [7].

When the jet is operated in ambient air, ambient air species diffuse into the jet's effluent from the ambient atmosphere leading to photo-absorption of the VUV radiation generated inside the core plasma. This results in intensity dips in the measured ${\rm Ar}_2^\ast$-excimer second continuum in the region of 120–135 nm (figure 4). By increasing the distance between the jet nozzle and the MgF₂ window the intensity of these dips decreases, which means that more VUV photons are absorbed. On the one hand, this is due to the longer absorption path length. On the other hand, the oxygen concentration inside the effluent increases in the axial direction, which also leads to a higher absorption rate. The effect of an increasing nozzle distance is displayed in figure 4. While at 4 mm distance hardly any intensity dips were detected, at 10 mm distance significant absorption dips are noticeable. From the dip intensity I located at 124.6 nm the optical depth τ = −ln(I/I₀) is calculated for varying nozzle distances. In order to determine the background intensity I₀ the Ar excimer continuum was fitted by a polynomial as exemplarily displayed in figure 4.

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In figure 5 the calculated optical depths in the wavelength range 123–126.5 nm are shown for different nozzle window distances. It can be observed that the optical depth steeply increases for longer distances. This disproportionately high slope of the optical depth reveals that the oxygen density must increase in the axial direction.

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A verification that the absorption around 124.6 nm is due to molecular oxygen is achieved by the following experiment. An absorption cell with two magnesium fluoride windows at each end is mounted between the plasma jet and the entrance of the VUV emission measuring system (figure 6).

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The gap spacing L between the two MgF₂ windows is 5 mm. Either pure argon (0.3 slm) or argon mixed with a minority flow of oxygen (1 sccm to 6 sccm) is fed into this region. The gas flux and the geometry of the cell assembly prevent air leaking into the absorption path, and the plasma jet positioned on one side of the cell acts as a background radiation source. The distance between the jet nozzle and the MgF₂ window is 4 mm and hence the visible effluent touches the cell window. The transmitted VUV radiation of the jet, especially that around the argon excimer second continuum, is detected spectrally resolved after passing the absorption cell. The calculated optical depths, for different flows of oxygen mixed to the constant argon flow rate of 0.3 slm, are presented in figure 7.

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A comparison of the optical depth spectra, measured along the downstream axis and in the absorption cell shows almost identical values and shape. Hence, it is most likely that molecular oxygen diffuses into the effluent from the ambient air.

From the maxima of the profiles in figure 7 obtained in the absorption cell the photo-absorption cross section σ for the given experimental setup is calculated using the relation σ = 1/L · dτ/dn, where L and n are the absorption length (5 mm) and the density of admixed molecular oxygen, respectively. The cross section calculated from this measurement is 9.3 × 10⁻¹⁸ cm² with an uncertainty of about 10%. The cross section value of oxygen at 124.6 nm found in the literature is 10.2 × 10⁻¹⁸ cm² [8].

Diffusion of molecular oxygen into the effluent of the jet with a velocity field u is described by the stationary convection–diffusion equation (u · ∇)n = DΔn, where D is the diffusion coefficient for diffusion of air into argon. Assuming a velocity field u = u(r, z)e_z directed in the axial direction with a flux of 5 slm through a tube of radius r₀ and neglecting transport by diffusion over convectional transport in the axial direction, we obtain the expression

$$\begin{equation} u/D\partial _z n=\Delta _r n. \end{equation} \tag{ 3 }$$

Here Δ_r denotes the radial component of the Laplace operator in cylindrical coordinates. The axial dependence of the factor u/D is approximated by the function u/D = u₀/D₀ (1−sz) with slope s, while the radial velocity profile and the initial values u(z = 0) and D(z = 0) determine the factor u₀/D₀. Setting the boundary condition n(z = 0) = n₀θ(r − r₀), where θ(r) denotes the Heaviside step function, equation (3) yields the on-axis solution

$$\begin{equation} n(z)=n_0 \exp ({-r_0^2 }/{4P(z))},\tqs P(z)=\int_0^z {\frac{D}{u}\,{\rm d}z'.} \end{equation} \tag{ 4 }$$

To obtain an integrable expression, P⁻¹(z) is expanded to first order in z, yielding

$$\begin{equation} n(z)=n_0 k\exp ({-r_0^2 u_0 }/{4D_0 z)}, \end{equation} \tag{ 5 }$$

where $k=\exp ({r_0^2 u_0 s}/{8D_0 })\gtrsim 1$. Integration from z = 0 to the nozzle distance z_n and multiplication with σ provides a theoretical expression for the optical depth

$$\begin{equation} \tau _{{\rm th}} (z_{\rm n} )=n_0 k\sigma \left( {\beta \,{\rm Ei}\left( {-\frac{\beta }{z_{\rm n} }} \right)+z_{\rm n} \exp \left( {-\frac{\beta }{z_{\rm n} }} \right)} \right). \end{equation} \tag{ 6 }$$

Here Ei(x) is the exponential integral function, and $\beta ={r_0^2 u_0 }/{4D}$ is a numerical constant which can be used as a fitting parameter.

A numerical solution for the density of ambient species was obtained solving the isothermal Navier–Stokes equations with the standard k–ε turbulence model [9] using COMSOL 4.2. The diffusion of ambient species is described by the equation for the conservation of mass

$$\begin{equation} \nabla (\rho x_{{\rm air}} {\bit{u}})=\nabla \cdot (\rho D_{\rm T} \nabla x_{{\rm air}} ),\tqs D_{\rm T} =\nu _{\rm T} /Sc, \end{equation} \tag{ 7 }$$

where ρ is the mass density, x_air is the mole fraction of air and ν_T is the turbulent viscosity. The turbulent Schmidt number is estimated by Sc = 0.7 [10]. Equation (7) was decoupled from the Navier–Stokes equations assuming identical molar masses of argon and ambient air. In figure 8 the on-axis density obtained from a simulation of the free jet—as is the case for the TALIF measurements—is compared with simulations with a wall placed in front of the jet at various distances from the nozzle—as is the case for the UV-absorption measurements. It is observed that the wall does not change the on-axis density of ambient species and the theoretical formula (5) is applicable for distances up to 11 mm. With the presented solution of the convection–diffusion equation, the on-axis density of indiffusing ambient species into both laminar and turbulent flows from a cylindrical tube can be estimated.

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The fit of τ_th to the measured optical depth according to (6) is displayed in figure 9. The factor n₀kσ is calculated assuming k = 1.

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The on-axis density profile of oxygen corresponding to the fit is displayed in figure 10. Within the first 3 mm from the nozzle hardly any molecular oxygen is found in the effluent. For distances greater than 4 mm a steep oxygen density increase is obtained. Its concentration lies in the same order of magnitude as is intentionally admixed to the argon feed gas. For greater distances the density function saturates to the ambient air oxygen concentration level.

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Compared with the numerical simulation, the measured density is lower by a factor of 0.5 in the range 6–12 mm. This is in good agreement, as the simulations are of a more qualitative nature, neglecting gas heating and electrohydrodynamic forces. Furthermore it is noted that the value of the Schmidt number can be tuned to fit the experimental data, but should be determined by independent measurements.