The influence of metastable species and rotational quantum numbers on the derivation of OH (A– X), NO-γ (A–X) and N2 (C–B) bands rotational temperatures in an argon gas-liquid-phase plasma discharge

In this work, the rotational temperatures of the atmospheric pressure AC-excited argon gas-liquid-phase discharge estimated by employing disparate spectroscopic methods on the rotational structure of molecular OH (A–X), NO-γ (A–X), and N2 (C–B) bands-spectra emanating from the gas-phase discharge region were compared with those obtained from the liquid-phase region to analyze their variations based on the metastable species and rotational quantum numbers. The electrical characteristics and images of the discharge were also examined to analyze the discharge nature. Realization of the estimated values for rotational temperatures, as an estimation of the gas temperature, depend on thermalization of the accounted excited rotational population levels. Excitations to higher rotational quantum numbers (Nʹ) inhibited thermalization of the rotational distributions, and the rotational temperatures were found to increase proportionally with excitations to higher Nʹ numbers. The phenomenon of rotational excitation to higher Nʹ numbers was particularly prominent for the wet discharge region, and thus, substantially higher rotational temperatures were obtained. The excitation to higher Nʹ numbers is related to the basic production processes largely those involving and N2 (A) metastable states that populate predominantly the levels with large Nʹ numbers (e.g., Nʹ=8 and Nʹ=25, respectively for OH and NO), and thus, their contemplated rotational population is not indicative of the kinetic gas temperature. With respect to spectral diagnostics techniques, the Boltzmann plot constructed by adopting a unique single fitting model (compared to the conventional double fitting models approach used for liquid discharges) only calculating the rotational population of the Q1 branch of OH (A–X) for lower Nʹ numbers (Nʹ ≤ 4) affords the opportunity to estimate the gas temperature in wet plasma discharge.


I. INTRODUCTION
Over the last several decades, non-equilibrium discharges on and within liquid surfaces have rapidly evolved because of their great impact in diverse fields such as cancer treatment, lithotripsy, plant growth enhancement, water decontamination, chemical analysis, and nanoparticle synthesis [1][2][3][4][5][6][7][8]. In comparison to conventional atmospheric pressure glow discharges excited between metallic electrodes, the chemistry and physics related to plasma discharges in liquids electrodes are somewhat less well understood. This is because these discharges are typically excited in both the gas-and liquid-phases, and are relatively chaotic in nature [9]. Moreover, in the discharge assembly where the liquid typically serves as one of the electrodes, it is found that the electrodes tend not only to evaporate but also undergo deformation. These factors add significant complexity to the experimental configuration, and the associated discharge processes become fairly intricate when compared with the non-thermal gas-phase discharges (plasmas) between metallic electrodes.
Investigations conducted to evaluate the non-equilibrium plasmas on and within liquid surfaces have revealed a broad range of methodologies, applications, and phenomena whereby a large number of articles have addressed this specific topic [8,10]. The advances in plasma diagnostics necessarily comes up against the need to characterize comprehensively the fundamental processes occurring in such plasmas and also to develop and apply adequate models which can substantiate the characterization techniques. In this regard, optical emission spectroscopy has long been accepted as a valuable technique for characterizing and exploring the basic physical parameters of plasmas and is frequently applied to predict the rotational temperature (Trot) of plasmas based on measurement of the excited rotational population distributions of various diatomic molecules such as OH (A-X), NO-γ (A-X), and N2 (C-B). Therefore, it is important to have an in-depth understanding of this particular characterization technique, especially for the case of atmospheric pressure non-equilibrium plasmas generated in a gas-liquid environment or in a complex mixture comprising various molecular species. It is often not the case that the densities of the considered excited rotational states for the case of the diatomic molecules (in non-equilibrium plasmas) are in thermal equilibrium with the translational temperature (gas temperature, Tgas) [11]. Non-Boltzmann distributions which are witnessed in the rotational spectra of non-equilibrium plasmas obviously demonstrate the significance of being able to inspect carefully the rotational structure of the spectra.
As for conventionally applied methodologies, in many cases, the Trot of non-equilibrium plasmas has often been predicted from the emission band of OH (A-X) [12]. In the case of a discharge operating in humid conditions, the population of higher rotational quantum numbers ( ) is substantially overpopulated, and shows a clear deviation from the Boltzmann law. It is accepted that this overpopulation is less dominant for lower numbers. Thus, in the Boltzmann plot method, a two-temperature fitting methodology is typically adopted to characterize the population of rotational levels. And the Trot of OH (A-X) comes from the slope of the linear fit corresponding to the populations with low numbers. One of the major disadvantages of this technique is that it is necessary to access highly resolved spectra to construct the plot for the whole range of numbers along with the corresponding populations. Thus, as an alternative, a calculation using LIFBASE software calculation has also been used in numerous investigations to derive the Trot from poorly resolved rotational structure of OH (A-X) [13][14][15][16]. This software has also been employed for other molecular bands to calculate the Trot. For example, it was used to derive the Trot from the gamma-band system of NO [NO-γ (A-X)] [15]. Besides, in other works, as an alternative to OH (A-X) and NO-γ (A-X), the nitrogen second positive system [SPS N2 (C-B)] bands were calculated with SPECAIR software to approximate the Trot [17][18][19]. The latter are convenient for calculating the partially resolved emission spectra; however, their main drawback is that an assumption is made that the obtained shape of the populated rotational distribution is Boltzmann/non-Boltzmann. Irrespective of such a drawback, the former techniques have been applied successfully to measure the Trot in many plasma discharges. Nonetheless, their utilization for OH (A-X), NO-γ (A-X), and SPS N2 (C-B) diatomic molecular emission transition bands have resulted in discrepancies among the derived Trot, especially in respect of discharges on and within liquids.
In an atmospheric pressure vapor bubble plasma discharge, for instance, a non-Boltzmann distribution was demonstrated for the OH (A-X) rotational structure, in which rotational states with rotational numbers > 10 were overpopulated, and the yielded Trot of 8800 K was much higher than the Tgas of 1550 K as derived from the Trot of N2 (C) [19]. This clearly means that a non-Boltzmann rotational distribution is characterized by the production mechanism that leads to an efficient excitation of OH (A) to higher numbers. A non-equilibrium distribution of OH (A-X) has also been found and investigated in other studies [10], and discrepancies were reported among the predicted Trot of OH (A-X) and N2 (C-B) at atmospheric pressure. In an argon gas-liquid-phase discharge, the OH (A-X) band rotational population adaptation in a Boltzmann plot resulted in a Trot value which was comparatively higher than the Tgas, and this was ascribed to the fact that the production process was boosted as a consequence of diffusion of water content in the discharge region [20]. Non-Boltzmann behavior is not only realized for OH (A-X) band rotational distribution; for example, highly populated higher rotational levels were also observed for N2 (C) in a N2O bubble discharge in water [11]. The Trot of N2 (C) was found to be higher than for cases in which the plasma was filled with air and N2. The high value of Trot was associated with N2 (C) excitation through the processes such as dissociative electron recombination of N2O + and dissociative electron excitation of N2O that result in rotational excitation to higher numbers in a N2O discharge. Besides, overpopulation of the N2 (C) higher excited levels in an argon-water discharge was demonstrated to be result of dissociative excitation of H2O via the ( 3 P2) state [23] . In this discharge, the predicted Trot of N2 (C-B) was also found to be higher than the expected Tgas as well. Apart from these situations, the emission spectra have been studied for the presence of diatomic molecules such as N2, NO, OH, etc., which were measured in an open-air discharge with electrodes based on the use of tap water [21]. The predicted Trot values obtained from OH (A-X), and particularly, NO-γ (A-X), exceeded substantially the estimated Trot of N2 (C-B), and consequently the Tgas. The difference in the calculated Trot was associated with the impact of the production mechanisms, as well as with the decay of the excited states.
The common trend identified in the characterization studies on such plasma discharges initiated on and within liquid surfaces is the utilization of spectroscopic diagnostics to predict the Trot. Additionally, investigations seek to introduce improvements, especially in respect to the domains of the production processes (e.g., involving metastable dissociative excitation or electron impact excitation or dissociative electron recombination of ions etc.,), in different discharge media, and on the effects of the surrounding environment (e.g., N2, O2, and water vapor content) to understand the non-equilibrium nature of the plasmas. The production processes involved in exciting the molecule to a certain rotational state with numbers determine the occurrence of rotational-translational equilibrium. This means that detailed investigation of the elementary production mechanisms and the population of the generated rotational levels (in a certain domain of interest) in molecules under study is highly desirable before considering their population distribution as a measure of the Tgas.
Against a background of the above factors, a study simultaneously involving multiple molecular species (e.g., OH (A-X), NO-γ (A-X), and N2 (C-B)) to determine Trot and Tvib could prove to be imperative to provide a broader perspective to the awareness of the various production mechanisms and the rotational populations in certain ranges of numbers, especially in the case where argon is used as the plasma fill gas in a wet environment, because the presence of ( 3 P2) stable states governs the formation chemistries of a humid plasma discharge, which in turn produces numerous reactive nitrogen and oxygen species ((e.g., OH (A), N2 (A), and SPS N2 (C)). Concerning the derivation of the rotational and vibrational temperatures of the considered diatomic molecules, we are mainly interested in utilizing conventional spectroscopic-based diagnostics such as the Boltzmann plot and related software modules such as LIFBASE and SPECAIR. However, unlike a number of studies that have adopted double fittings models approach to fit the rotational level populations in the Boltzmann plot to estimate the OH (A-X) band Trot (equivalent to Tgas) [11,12], in the present work, only a single fitting model has been successfully adopted to fit the rotational structure of OH (A-X) in a wet discharge region. The Boltzmann plot with a single fitting has often been used to determine the Tgas in conventional gas discharges between metallic electrodes, nonetheless, adaptation of this model has resulted in higher Trot of OH (A-X) for the plasma discharges in a humid environment [22].
The objective of this study is to characterize the atmospheric pressure AC-excited argon gas-liquid-phase discharge using spectroscopic diagnostic techniques. Moreover, the electrical properties of the discharge are analyzed by an electrical method; in addition, the discharge is evaluated visually by capturing high speed images. The formation mechanisms for the populated non-equilibrium rotational levels of various diatomic molecules are realized qualitatively by investigating the optical emission spectra.
The key contribution of the present work is the successful utilization of the single fitting Boltzmann plot model to derive the Trot of OH (A-X) in a wet environment; moreover, discrepancies in the measured Trot corresponding to the same discharge region are elaborated based on the excitation mechanisms (particularly those involving metastable states) and the numbers. Based on analysis of (1) the hydroxyl OH band due to the electronic transition from the upper state to the ground state , (2) the gamma-band system of nitric oxide NO-γ due to the electronic transition from the upper state to the ground state , and (3) the second positive system of nitrogen SPS N2 due to the electronic transition from the upper state to the lower state , the Trot and the vibrational temperatures (Tvib) are determined from a single spatially resolved spectrum (in the spectral range 200 to 415 nm) being recorded in the corresponding region of the discharge in the gas-or liquid-phase. By employing different methodologies, fourteen distinct temperatures were measured and comparisons made for a discharge region in the gas-phase with that in the liquid-phase, that is, the Boltzmann plot Trot of OH (A-X), LIFBASE Trot and Tvib of OH (A-X), LIFBASE Trot and Tvib of NO-γ (A-X), and SPECAIR Trot and Tvib of N2 (C-B). The production mechanisms and the rotational populations for the various diatomic molecules are thoroughly discussed to explain the causes of the variations in the Trot in a humid discharge.

II. EXPERIMENTAL SETUP
A schematic sketch of the experimental device is exhibited in Figure 1 (a), and the optical configuration for experimentation is displayed in Figure 1 (b). The gas-liquidphase (two-phase) discharge assembly comprises of a cylindrical stainless-steel (CSS) electrode (outer diameter 2.0 mm) kept in a coaxial mannar inside a fused quartz tube with inner diameter of 5.5 mm. From the end view of the fused quartz tube, the CSS electrode is adjusted at a gap of 8.0 mm. The discharge assembly is installed in an acrylic glass chamber filled with deionized water (DIW). For generation of the two-phase plasma, argon gas (99.99% pure) is injected through the CSS electrode with a flow rate of 1.2 slpm, and then the discharge assembly is lowered below the surface (D-=10 mm) of DIW by adjusting a micrometer caliper. The gap spacing is 8.0 mm, which is the separation between the tip of CSS electrode and the DIW surface. Before conducting experiments, the chamber is filled each time with 400 ml of fresh DIW. A cooling setup is attached with the two-phase reactor to control the temperature of the DIW at 25℃. The CSS electrode of the discharge assembly is connected with a high voltage AC power supply (Corona Lab CTP-2000K) with the driving frequency fixed at 22 kHz, and the DIW electrode is grounded. The voltage and current waveforms are recorded by an oscilloscope (Tektronix DPO4034) with a high-voltage probe (Tektronix P6015A) and a current probe (Tektronix TCP0030A), respectively. The visible light emission patterns of the discharge are recorded using a Canon camera (EOS7d). Spectroscopic measurements are performed with a multichannel spectrometer (Avantes Avaspec; grating 1800 grooves mm -1 ). Spatially resolved emission spectra are obtained using the optical setup outlined in Figure 1(b). This optical arrangement for experimentation is analogous to the one adopted in a previous study concerned with measurement of the spatial emission profiles [16].

A. DESCRIPTION OF THE DISCHARGE OPTICAL
EMISSION PATTERNS The discharge first started at the tip of the CSS electrode, and became localized just above the breakdown threshold (Vrms = 2430 V) for the plasma gas. When the Vrms, d value was raised to a higher level, the discharge expanded suddenly and occupied the entire interelectrode spacing volume (Vrms, = 2490 V). It was noted that just after the breakdown, the Irms, d value of the discharge current was only 2 mA. When Vrms, d was further increased from 2430 to 4700 V, the Irms, d increased from 2 to 20 mA. These values for the discharge current were much smaller than those occurring in conventional atmospheric plasmas excited between metallic electrodes [23,24]. This is because current was flowing through the DIW electrode.
In the gas-phase (inside the quartz tube), the discharge formed in a stable constricted channel. Whereas, in the liquid-phase it evolved as a plume-like shape (PLS), as typically observed in a conventional plasma jet in the gas phase [25]. The question then arises as to whether the PLS structure sustained in the gas-phase (which results from the gaseous discharge flowing into the liquid-phase) or in the liquid-phase. In an attempt to enhance our understanding of these basic processes, typical images of the discharge, which are displayed in Figure 2, were analyzed. A computer code routine was used to measure the dimensions of the discharge in the liquid-phase (below the opening surface of the quartz tube). The hole generated as a consequence of gas flowing in the downstream direction was short in length (~2 mm) relative to the length of the PLS (~6 mm) in the liquid-phase (Figure 2(a)). Moreover, with an increase in the Vrms, d value, the length of the PLS structure also increased in both the radial (from ~2 mm to up to ~4 mm) and the downstream directions (from ~6 mm to up to ~8 mm) (Figures 2(b) and (c)). In contrast, expansion of the conventional plasma jet plume in the gas phase typically occurs in the direction of the stream. Visually, it was also noticed that the structure of the PLS was not stable and it moved around at the onset value of the applied voltage, although, to some extent, it still retained the plume shape, as shown in Figure 2. A distinctive phenomenon of direct-liquid discharges is their unstable nature. Our experiments confirmed that such direct-liquid discharges were highly unstable and spread in a chaotic manner in the liquid-phase. Such discharges are also called streamer discharges [26]. Another interesting phenomenon was the reduction in length of the PLS, this being observed by recording an image of the discharge at 8 min after initiation. The property associated with the shortening of the length of the discharge is also a factual phenomenon observed for direct-liquid discharges whereby an escalation in liquid conductivity occurs [27]. Thus, in the present experiments, the evidence for shortening of the length of the PLS is consistent with the discharge existing in the liquidphase. Based on these observations it can be concluded that the structure of the PLS was not that of a gas-phase discharge, rather it was a liquid-phase discharge might be consisting of multiple nonstationary streamers. Here a short description is given to explain the breakdown mechanism for a discharge (PLS structure) in the liquidphase. The breakdown mechanism in liquids is relatively intricate than in gases. Liquids are more compact in comparison to gases and also exhibit a short-range order. Historically, there were two schools of thought related to the formation of discharge in liquids. The first theory was based on the electron multiplication, and second theory was based on the bubble breakdown mechanism. In liquid discharges, electron avalanche process can be negligible due to the shorter range of high electric field, moreover, scattering cross sections are large as a consequence electron do not gain sufficient energy to initialize impact ionization [26]. Besides, free electrons by and large are not present in the water. Even if they are in water, they are immediately solvated (1 ps time scales). Thus, here electron avalanche phenomenon is less probable because of the utilization of high purity DIW (3 µs cm -1 ). Moreover, powered electrode is located at a distance of 8.0 mm from the liquid surface. So, one may assume that electric field at the liquid surface should be weaker to boost the impact ionization, converting it into an electron avalanche, and then further triggering the multiplication of electron avalanches. Thus, the propagation of discharge in liquid most probably can be the result of micro-bubbles formation in the liquid-phase. According to bubble theory, formation of micro bubbles requires joule heating (provided by the high gas temperature of discharge at the liquid surface). These bubbles believed to serve as a source of local electrical breakdown which further begin the breakdown process and initiate the streamers.
The increase in length of the PLS with increase in the applied voltage from Vrms, d = 4700 V to Vrms, d = 5500 V (power increases from Pdis, in = 72 W to Pdis, in = 146 W), as shown in Figure 2, may be associated with increased dissociation processes. This implies that the discharge is responsible for sustaining an increased dissociation of the plasma, consequently it gains length at higher applied voltages. In contrast, by keeping the discharge current constant, when the exposure time of the discharge is extended by up to 10 min, clearly results in a reduction in the length of the PLS. At the longer exposure time, the number of ions are increased as a result of the dissociation and ionization of water molecules. Furthermore, in the presence of air, gaseous acidic contamination products such as and species are produced. These species may be responsible for the increased electrical conductivity of the liquid (Figure 2), resulting in a shorter length of the PLS. At the edge of the discharge channel, an increasing σe weakens the electric field in the Maxwellian relaxation time and discontinue the further process of dissociation [28]. At this stage, extension of the discharge requires more energy to sustain the discharge in order to compensate for the reduction in the electric field near the channel edge. Nevertheless, it is evident that the discharge power, in this case, has decreased due to a drop in the discharge voltage after operation for 10 min. Thus, ultimately a reduction in the electric field is accompanied by a shortening of the PLS length.

B. VOLTAGE AND CURRENT WAVEFORM
The voltage and current waveforms corresponding to the discharge images in Figures 2(b) and 2(c) are presented in Figures 3(a) and 3(b), respectively. Just after initiation of the discharge, the recorded current waveform indicates a discharge current pulse (DCP) situated at rising edge of every half-period ( Figure 3). According to the results, a decrease in the amplitude of the DCP is detected with increasing applied voltage, and a sinusoidal-like current waveform without a DCP is witnessed with the further increase in applied voltage, as shown in Figure 3(b). The current waveforms with the aforementioned characteristics were also reported and discussed in our previous studies [16,29], where focus was given to the temporal evolution and variation in shapes of the waveforms (for description of the nature of the discharge). At that time, minimal consideration was given to explaining the underlying discharge mechanisms that control the emergence of the DCP.
Herein, an analysis is conducted on the current waveforms in an attempt to understand the reasons for the appearance and disappearance of the DCP under different discharge conditions. A characteristics time period (CTP) during which magnitude of the discharge current maintains at a certain minimum level whereby the corresponding discharge voltage rises continuously from zero to a certain value is observed initially for all the current waveforms, an example of which is displayed in Figure 3(a). Starting from the current waveform in Figure 3(a), the discharge current remains at a minimum for a time period of 5 µs. Afterwards, a rise in the discharge current is seen with further increase in the discharge voltage. For the case in Figure 3(b), the discharge current remains at a minimum with a continuously increasing discharge voltage in a similar manner to that observed for the case in Figure 3(a).
In contrast, in this case, the CTP is much shorter as the discharge current starts increasing after 2 µs. This is due to the fact that Pdis, in is raised to 146 W, implying that more power is absorbed into the discharge compared to the case for 72 W in Figure 3(a). This clearly indicates that Pdis, in is an important parameter that may reduce the CTP followed by the extinction of the DCP on the current waveform. To validate this assumption in Figure 3(a), the instantaneous power of the discharge (Pdis, ins) was measured within the CTP and compared with the Pdis, ins for the case in Figure  3(b). It may be seen that Pdis, ins within the CTP in Figure 3(a) is 14 W, a value which is much less than 110 W, as measured for the case in Figure 3(b). This shows that for the discharge of Figure 3(a), the conductivity is much weaker during the CTP, and continuously increasing the discharge voltage may trigger an electron avalanche (to sustain the discharge before it dies out), which abruptly elevates the discharge current. In Figure 3(b), in contrast, the conductivity of the discharge during the CTP is much higher, so a smoother current waveform is obtained. Therefore, it is clear that the discharge power during the CTP is crucial for the appearance and disappearance of the DCP on the current waveform. A relationship between the CTP and DCP can also be inferred from inspection of the current waveform, namely, that a larger CTP is followed by the DCP. For example, in the present case, a CTP of 5 µs results in the emergence of the DCP and no DCP is observed on the current waveform for a relatively smaller CTP of 2 µs. Here the two-phase discharge in the reactor based on the appearance of DCP on the current waveform is considered to be in a streamer-like mode [9].

C. COMPARISON OF THE OPTICAL EMISSION SPECTRA OF THE DISCHARGE REGIONS IN THE GAS-AND LIQUID-PHASES
The two-phase discharge is further characterized by recording the spatially resolved emission spectra for two distinct locations in the discharge, that is, (1) in the gas-phase (1.0 mm from the tip of the CSS electrode) and (2) in the liquid-phase (4.0 mm from the inlet of the quartz tube), as illustrated in the inserts of Figure 4. The discharge region inside the quartz tube remains in the gas-phase due to the high flow rate (1.2 slpm) of the plasma gas, whereas the discharge region below the inlet to the quartz tube corresponds to the liquid-phase (wet environment). The purpose of recording spectra at these two distinct locations in the discharge is to identify the prevailing production mechanisms for the molecular species of interest. In the spectral range from 200 to 415 nm, the emission spectra for both locations are dominated by OH (A-X) and the SPS N2 (C-B). In the spectral range from 650 to 815 nm, argon atomic lines are clearly dominant. In addition, the prominent atomic hydrogen Balmer alpha line (656 nm) and the atomic oxygen line (777 nm) are detected in both emission spectra. It is noted that the SPS N2 (C-B) emission bands are more intense in the case of the spectra recorded in the gas-phase; in contrast, the OH (A-X) emission band is more intense in the liquid-phase (Figure 4). The important chemical reactions governing the discharge chemistries are described below. The •OH is one of the most active radicals with the highest oxidation potential, 2.85 V, and thus considered crucial in advanced oxidation processes. The emission intensity of OH (A-X) is much higher in the liquid-phase discharge region compared to that in the gas-phase, as revealed in ]. [30] (R1) A large amount of energy (12.6 eV) is required to ionize the water molecule, thus this reaction R1 would be feasible for directly yielding the •OH production. Electron-impact dissociation of a water molecule proceeds to OH (X) via , [ ]. [30] (R2) The resultant OH (X) via electron-impact in the plasma: , [ ]. [31] (R3) Electron-ion recombination reactions have also been proposed as a possible route for OH (A) production: ], [32] (R4) , [ ] . [33] (R5) Last but not least, a dissociative excitation reaction of H2O with the ( 3 P2) stable state is also crucial for the production of OH (A): and is frequently proposed in several studies [34,37,38]. The ( 3 P2) stable state is resosnant with the Rydberg levels of a water moledule, and thus, in a wet environment, reaction R6, in particular, seems critical for the formation of ]. [40] (R9) According to a simulation-based study conducted on describing the chemical kinetics of humid argon discharges, the excitation to N2 (A) state was suggested through the following reaction: , [ ]. [34,41] (R10) Besides, the occurrence of the ( 3 P2) states is most probably the origin of N2 (C) through the Penning reaction with N2 (X): , [ ]. [42] (R11) The SPS N2 (C-B) transitions are relatively much weaker for the liquid-phase discharge region, as shown in Figure 4(b). Also, the first negative system of nitrogen FNS ambient atmospheric air discharges was not witnessed for the discharge in the wet region. In contrast, its presence was confirmed for the discharge region in the gas-phase. The required threshold energy to produce FNS (B-X) via a molecule in the N2 (X) state is about 18.8 eV, a level which is less probable through electronimpact processes due to a shift in the electron energy distribution function (EEDF) to the lower energy region in a relatively higher humidity [43]. Apart from these, frequently proposed reaction pathways for the production of atomic O are , [34] (R12) . [44] [45] In an argon discharge, atomic O• can also be produced from states through the following reaction: [ ]. [34] (R14) The discussion concerning the chemical reaction pathways indicates that the discharge chemistries operating in the gas and liquid discharge locations are different according to the relative humidity and the availability of contaminant impurities (e.g., N2, O2) arising due to diffusion from the ambient air. These impurities are responsible for the production of various atomic and molecular species (e.g., OH, N2 (A), N2 (C), O, and H) and hence there is a degree of versatility in the discharge chemistry of the plasma discharge depending on the measurement location in the discharge. In connection with the production of these species, the roles of and N2 (A) metastable states are important through reactions R6, R9-R11, and R14.

D. SPECTROSCOPIC METHODS FOR DETERMINATION OF THE ROTATIONAL TEMPERATURE (Trot)
In the present work, the extracted Trot from OH (A-X), NOγ (A-X), and SPS N2 (C-B) bands in a discharge region situated in the gas-phase are compared with region of the discharge in the liquid-phase. Disparate spectroscopic diagnostics methods (e.g., the Boltzmann plot, LIFBASE software, and SPECAIR software) are exploited for derivation of the Trot from rotational structure of the considered diatomic molecules. The production processes for the discharge are predicted qualitatively by investigating the recorded spatially resolved emission spectra, and the fractional population histograms are calculated through the LIFBASE simulation. It is important to point out that the Trot for the OH (A-X), NO-γ (A-X), and SPS N2 (C-B) bands are measured simultaneously from a single spatially resolved emission spectrum (recorded in the spectral range of 200 to 415 nm according to the optical setup of Figure 1 (b)) recorded either for the discharge region in the gas-or the liquid-phase. The optical emission spectra are measured right after initiation of the two-phase discharge under the same conditions as mentioned in Figure 2(c). Two distinct discharge locations are selected for gathering of the respective optical emissions: (i) for the gas-phase at a location 1.0 mm apart from the CSS electrode tip, and (ii) for the liquid-phase at a location 4.0 mm away from the opening surface of the fused quartz tube. Note that for measurement of the liquid-phase, the recorded molecular spectrum for SPS N2 (C-B) is weak, and evidence for NO-γ (A-X) is completely absent in both the gas-and liquid-phases discharge regions; therefore, in this experiment, argon as a feed gas is mixed with 0.5% nitrogen to facilitate the recording of prominent emission signals for the SPS N2 (C-B) and NO-γ (A-X) bands. The OH molecular structure in the spectral range 306-310 nm comprises mainly three branches [Q1, R2, and P1]. In this work, the Q1 branch is selected to construct the Boltzmann plot. The line details of the Q1 branch are provided in the inset of Figure 5. There are various advantages to be gained by selecting the Q1 branch, namely, (i) the band is situated in a relatively less dense region of the OH (A-X) spectrum, so lines in this branch from Q1(1) to Q1(6) are well isolated; (ii) self-absorption of lines that appear in the wavelength range for this branch is not strong compared with the other lines except for Q1 (3). Lines that undergo strong self-absorption result in a dip in the plot, and thus there is an alteration in the slope of the Boltzmann plot, which leads to an inaccurate estimation of the temperature. Therefore, the Q1(3) line that undergoes a strong self-absorption together with the neighboring line Q21(3) is eliminated from the Boltzmann plot calculation [22]; (iii) the lower rotational numbers of the Q1 branch from to , corresponding to lines Q1(1) to Q1 (6), are feasible for minimizing the phenomenon of overpopulation. Thus, the Q1 branch seems suitable for determining the Trot from the OH (A-X) rotational-vibrational system . The distribution of intensities for the rotational population is given by the following formula [46] (1) with factor the rotational energy , the rotational constant, h the Plank's constant, kB the Boltzmann constant, the wavenumber for the rotational transition , the emission coefficient, and Qr the rotational partition function.
The LIFBASE software offers spectral simulation of various molecular bands including NO-γ (A-X), OH (A-X), CH (A-X), etc. [13]. This program is based on the most frequently used assumption attributed to the supposition that the rotational and vibrational levels populations are distributed in accord with the Boltzmann law. Using the LIFBASE software, the OH (A-X) spectral range from 306 to 310 nm is fitted according to the simulation. In the fitting process, Trot is fixed at first to a certain value so that the smallest residual is compensated by varying the vibrational temperature (Tvib) to obtain a best correspondence of the experimental spectrum with the calculated one. Note that the fitting process requires the measurement of a slit function (spectral line broadening due to instrumental broadening). In the gas temperature range from 300 to 6000 K, spectral lines broadening results primarily outcome in convolution of the optical emission spectrum, generating the slit function considered to be a Gaussian, with a full width at half maximum (FWHM). The slit function is determined by measuring the emission from a Hg lamp which emits a welldefined atomic line at 404 nm and is deemed to be almost a Gaussian distribution (FWHM=0.0656 nm). The UV spectral range from 241 to 249 nm of the gamma-band system of NO was selected for analysis and compared with the calculated simulated spectrum. Besides, spectral simulation of the SPECAIR software also offers the facility of manipulating and fitting spectra [18]. Similar to the LIFBASE, SPECAIR also assumes that rotational populations of molecules in certain energy states are Boltzmann distributed. Unlike the LIFBASE, SPECAIR facilitates the spectral fitting of SPS N2 (C-B). That is why, it is often used for approximation of the Trot of SPS N2 (C-B). In the present case, the SPS N2 (C-B) bands at 353 and   The Trot values for OH (A-X) and SPS N2 (C-B) acquired using the LIFBASE and SPECAIR software are 1120±70 K and 1100±65 K, respectively. These methods generated fits which are concordant with the experimental measurements (Figures 7 and 8), suggesting the thermalized behavior for the rotational population distribution. Consequently, the predicted Trot values can also be approximated as Tgas for the gas-phase. This is due to the fact that quenching collisions are less dominant with water molecules. That is, the translational-rotational energy exchange remains faster than the electronically excited state quenching. Under such conditions, the diatomic molecular rotational distribution is equilibrated with the translational distribution and the assumption of Trot being equivalent to Tgas is validated.

FIGURE 7. Fitting of the OH (A-X) emission spectrum by using the LIFBASE spectral simulation to measure Trot and Tvib, for the case of a discharge region in the gas-phase. The fitting of the spectra is achieved by assuming a Boltzmann distribution for vibrational level (0-0). The insert displays the histogram for the fractional population calculated by the simulation.
For the case of NO-γ (A-X), the same fitting procedure is applied using LIFBASE. In spite of the fact that fitting of the spectra in Figure 9 is quite reasonable and thermalized distribution can be expected, it is known, however, that the obtained Trot value is higher than the predicted temperatures based on using other methods applied to OH (A-X) and SPS N2 (C-B), and thus, the Trot manifestation for Tgas will overestimate the Tgas in the gas-phase. In this scenario, presumably thermalization is not achieved completely even though the fitting does indicate the Boltzmann distribution is realized. The fractional population histogram of NO-γ (A-X) calculated by the LIFBASE software predicts a maximum rotational population for =16 (Figure 9), which means that the NO-γ (A-X) excited rotational levels are overpopulated for higher numbers. This phenomenon can be interpreted as an indication of there being residual chemical energy through the production mechanisms of the molecules [15]. For these molecules at atmospheric pressure, electronically excited state quenching becomes faster than translational-rotational energy exchange, and thus, leads to a non-Boltzmann distribution. To elaborate further on this phenomenon, detailed discussion of the formation processes will be presented later in Section III (F). The Trot value from the Boltzmann plot increases to 1474±80 K for a discharge region in the liquid-phase, indicating non-Boltzmann behavior (Figure 10). Similarly, using the LIFBASE and SPECAIR methodologies, an increase in Trot is also observed (Table 1). However, using the latter methods, a substantial increase in Trot is witnessed. For example, when the LIFBASE method was applied to the NOγ (A-X) spectrum recorded for a discharge region in the liquid-phase, the Trot value obtained was 3900±180 K. The Tvib values measured from the spectra of OH (A-X), NO-γ (A-X) and N2 (C-B) are more than twice those of the corresponding Trot values (Table 1). This may be explained by the way the vibrational energy transfer occurs, mostly as a consequence of electron collisions. The electron temperature (Te) typically falls in the range 1-2 eV, which is a much higher temperature compared to that for a heavy particle.
The lower value of Trot (1474±80 K) is the consequence of using the Q1 branch with low rotational numbers from to . Though the estimated Trot from selected rotational lines in the liquidphase is still higher than the temperature of the discharge in the gas-phase, it is not related to the actual Tgas. This phenomenon is evaluated further by means of examples. In the first case, the Q1(6) line of the Q1 branch is excluded, and thus, lines from Q1 to Q5 corresponding to the rotational numbers from to are employed for constructing the Boltzmann plot. Exclusion of the Q1(6) line from the calculation results in a noticeable drop in Trot from 1474±80 K to 1265±50 K; nevertheless, Trot is still higher compared to the gas discharge region [see Figure 11(a)]. Thus in the second case, only lines from Q1 (1) to Q1(4) corresponding to the rotational numbers from to of the Q1 branch, are accounted by constructing the Boltzmann plot [ Figure  11(b)]. Using these lines, a linear fitting is quite reasonable, and the thermalized distribution is represented by a straight line, of which the slope is dependent on the Trot. In this case the derived Trot (1070±35 K) is in good agreement with the Trot value predicted by the Boltzmann plot in the gas-phase, and, in addition, also with those values inferred theoretically using the LIFBASE OH (A-X) and SPECAIR SPS N2 (C-B) calculations as applied to the spectra of the discharge region in the gas-phase, as can be seen in Table 1. The transition probability of any given rotational structure is roughly proportional to the rotational number. With 2017 3 increasing rotational number the population term declines rapidly since the rotational energy varies roughly as the square of the rotational number [47]. Therefore, moving along the optical branch with increasing rotational number, the intensity of the lines is boosted at first, and acquires a maximum value, but thereafter the intensity decreases. This type of emission intensity distribution shows a good linear fitting, as also observed for the case of the Q1 branch in Figure 6. However, the spectrum recorded for the discharge region in the liquidphase reveals an increase in emission intensity at first with increasing rotational number and reaches a maximum at the Q1(3) line; neverthless, the intensity starts to increase again after the Q1(4) line, unlike the emission intensity distribution of the Q1 branch (Figures 6 and 10). This means for the case of the discharge spectrum in the liquid-phase with increasing rotational number, the aforementioned condition does not remain valid. Thus, the linear fittings carried out based on including the Q1(5) and Q1(6) lines will deviate from the Boltzmann distribution, as shown in Figures 10 and 11(a). In a vapor bubble discharge at atmospheric pressure, the Boltzmann plot of OH (A-X) shows that the rotational states with a number larger than >10 clearly overpopulated [19]. Consequently, the rotational states with only lower numbers are thermalized. The Boltzmann plot constructed for the emission spectrum of OH (A) collected for a plasma jet in argon-water also has rotational population distributions acquired based on two linear fits; namely, the temperature from the rotational distribution with lower numbers ( < 13) is 625 K, and the attained temperature for rotational distribution with higher numbers 13 < < 25 is 5000 K [48]. A substantial difference between the Trot is clear for rotational distributions having different numbers, and clearly the distribution belonging to higher numbers is not representative of Tgas.
It must be appreciated that the construction of Boltzmann plots in the aforementioned studies by employing two linear fittings to the rotational population distribution requires sophisticated spectrometers to record the spectra at high resolution. In contrast, a well-resolved Q1 branch spectrum (utilized for Boltzmann fitting in our case) can be recorded even with a spectrometer with a grating of 1800 grooves/mm. More than that, using the Q1 branch for construction of the Boltzmannn plot undoubtedly has technical merit in terms of ease of calculation by employing only a single fit to the population distrubution. However, it is suggested that before applying the linear fit, the emission intensity distribution of lines from Q1(1) to Q1(6) of the Q1 branch should be carefully examined, such that the line intensities in the branch are increasing at first and then decreasing, and later, the obtained fitting should also be inspected carefully to clarify whether the rotational distribution concurs with Boltzmann or not. In a humid environment, fitting of NO-γ (A-X) and OH (A-X) using LIFBASE and fitting of SPS N2 (C-B) using SPECAIR results in much higher calculated values of Trot (Table 1). This means that non-Boltzmann behavior occurs for the higher rotational states of the employed bands. It is woth mentioning that the temperature parameter attributed to the overpopulation of the higher rotational states (for the cases of OH (A-X), NO-γ (A-X), and SPS N2 (C-B)) falls in the range 2800 to 3900 K and this would seem to be independent of the nature of the discharge (such as glow or streamer type), the discharge current (Irms, d=30 mA), the pressure (ambient air), and the discharge feed gas (argon). This is considered a straightforward scenario whereby the rotational populations are a consequence of the formation processes, and thus, evaluation of the higher rotational populations can be performed by predicting possible production mechanisms based on analysis of the emission spectra of the discharge regions in the gaseous and wet environments.
In non-equilibrium plasmas, various essential reactions associated with OH (A) excitation are outlined in Section III (C). For the electron-impact excitation, a larger rate coefficient in comparison to the dissociative excitation of water suggests that direct excitation from OH (X) to OH (A) may be the governing reaction (reactions R1 and R3). Electron-ion recombination reactions (R4 and R5) may also produce overpopulation of higher rotational levels of OH (A). Apart from these processes, it has already been discussed in Section III (C) that ( 3 P2) stable state and the Rydberg levels of the water molecule are resonant with each other [34,37,38], and thus, OH (A-X) production is stimulated in a wet environment via reaction R6. As shown in Figure 4, with the identical discharge conditions, the absolute intensity for OH (A-X) increases more than two orders of magnitude in the discharge region in the liquidphase compared to the location in the gas-phase. This phenomenon confirms in a qualitative way the increased formation of OH (A-X) in a wet environment and also implies that the ( 3 P2) stable state induce dissociative excitation of water molecules through R6 such that this pathway could be responsible for large excitations to higher rotational levels of the produced OH (A) state. These results imply that the OH (A-X) rotational levels population is populated via the formation process, and therefore, the deduced Trot is overestimated because the rotational population distribution is non-Boltzmann. This hypothesis can be validated by the fractional population histogram that predicts the highest population for =8, comparatively higher than =4 as predicted for a gas-phase discharge spectrum of OH (A-X) (Figures 7 and 12). Due to this phenomenon, the fitted OH (A-X) spectrum (assuming the Boltzmann distribution using LIFBASE) for a discharge region in the liquid-phase yields a Trot (3400±170 K) much higher than Trot (1120±70 K) of a discharge region in the gasphase.
The OH spectrum recorded for a pulsed discharges operated in helium or argon bubbles in tap water was compared with a reference spectrum calculated by using LIFBASE to obtain the Tgas [49]. It was shown that, the OH (A-X) rotational population is sensitive to the formation process, especially situating at higher numbers, and these are better to be characterized with a two-temperature fitting distribution. A discharge sustained between metallic and liquid electrodes characterized by conducting spatial measurements of the Trot of OH (A-X) shown that, the deduced values of Trot using LIFBASE are drastically higher near the liquid electrode region (reaches to 3100 K at the liquid surface) compared to a region near the metallic electrode (1050 K), and explicitly indicates the nonthermalization of the considered rotational levels population, populated by the formation process [16]. This means that, regardless of the spectroscopic technique employed, to represent the kinetic tempetaure, the rotational population (occuring at low or high numbers) must be thermalized for kinetic temperature representation.
In our previous work on an atmospheric discharge in argon sustained between liquid and metal electrodes using spatial measurements, it was shown that the absolute emissoin intensity of NO-γ (A-X) absolute intensity increases in a wet environment nearby region of the liquid electrode surface [16]. A similar case is observed in the present work, where an increased emission of NO-γ (A-X) is observed for the spectrum recorded (with argon as a feed gas mixed with 0.5% nitrogen) for a wet discharge region. In the case of argon as the plasma-forming gas, a reaction involving •OH and N [ ]. [34] (R15) is commonly proposed for the formation of the NO• radical, especially in humid environments. As has been seen, generation of •OH is efficient in humid environments and this clearly increases one of the reactants of R15. A study conducted to understand the chemistry of an atmospheric pressure plasma in argon using kinetic modeling shown that, N is exclusively generated from the ( 3 P2) stable state [34], and consequently, R15 is promoted to increase the yielding of NO•. However, here to explain the overpopulation phenomenon, it is also important to take into account the possible excitation mechanisms where, for example, NO (A) generation is most often the result of direct excitation instead of involving dissociation processes. For a plasma in He-N2 mixtures and for a plasma in N2 or N2-O2 or N2-NO mixtures, respectively, driven by a pulsed RF and by a high-voltage pulse, a reaction involving NO (X) and N2 (A) , [50,51] (R16) was proposed as the dominant excitation mechanism for the production of the NO (A) excited state [50,51]. In a N2-O2 discharge excited by means of a pulsed RF, the excitation mechanism to NO (A) with comparatively large excitation of higher rotational levels ( > 20) was also attributed to R16 [52]. Large deviations were witnessed for the Trot from the Tgas. As illustrated, the chemical generation of NO• is stimulated in a wet environment through R15, and, therefore, one of the reactants in R16 is increased. In a study on a humid argon discharge where the yielding of N2 (A) by the ( 3 P2) stable state reaction (R10) with N2 (X) was proposed Ar * [34], the subsequent excitation mechanism R16 becomes crucial in the wet environment for the excitation of NO from the ground state (X) to the excited-state (A), and this thus leads to a rotational population of rotational levels which is overpopulated in the higher numbers. For the case of a discharge in a wet environment, the LIFBASE simulation predicts highest population for =25 in comparison with =16, as estimated for the gas-phase discharge spectrum (Figures 9 and 13). Thus, the predicted Trot (3900±180 K) of NO-γ (A-X) is perceptibly higher for a humid discharge compared to the Trot (1600±110 K) for a discharge in the gasphase. The Trot of OH (A-X), NO-γ (A-X), N2 (C-B), and O2 (B-X) were compared for a discharge ignited between liquid electrodes (tap water) in air at atmospheric pressure were compared with their estimated Trot of 2600 K, 3800 K, 2200 K, and 2200 K, respectively [21]. The Trot of OH (A-X) and NO-γ (A-X) were substantially higher compared to other molecular transitions in the humid discharge. The differences in the various Trot are associated with a differences in the production mechanisms operating in the discharge, as well as with the decay processes of the excited states. If the results reported elsewhere [21] are compared with those found in the present study based on using argon as a fill gas mixed with 0.5% nitrogen, the reaction mechanisms involving the excitation to higher rotational levels of the monitored molecules should be different. This is because generation of OH (A-X), NO-γ (A-X), and N2 (C-B) is critically influenced both directly and indirectly by the presence of the ( 3 P2) stable states (via R6, R9-R11, R15, and R16), which are absent in the previously referenced study [21]. This is the reason why the results for the estimated Trot [21] are different from those of the present study. For example, the attained value of Trot from the N2 (C-B) is much higher than the expected Tgas, while in [21] the estimated Trot for N2 (C-B) denotes the actual Tgas.
The SPS N2 (C-B) is commonly used for estimating Trot using SPECAIR, and a particular focus is the case of atmospheric discharges with air as the main plasma-forming gas [17]. Typically, intense emission of SPS N2 (C-B) is witnessed in the spectra of an atmospheric DBD plasma generated for argon-water vapor mixtures [48]. Spatially resolved measurements performed on an argon discharge in a gas-liquid environment have shown increased emission of SPS N2 (C-B) near the liquid surface [16]. A similar phenomenon was observed in the present experiments, where an increased emission of SPS N2 (C-B) was repeatedly observed in the spectrum for the liquid discharge region while comparing the spectra (recorded with argon as a feed gas mixed with 0.5% nitrogen) for discharge locations in the gas-phase and liquid-phase environments. A nitrogen discharge excited with pulsed RF in the pressure range 2.4 mTorr-1.5 Torr was investigated in an attempt to understand the production mechanism of N2 (C) [53]. It was found that the formation of N2 (C) was predominantly the consequence of N2 (X) excitation [53]. In the afterglow region where there is a drop in the Te, the Pooling reaction R9 involving N2 (A) and N2 (A) metastable states interaction becomes the dominant excitation mechanism. Another study conducted on a corona discharge has shown that the Te quickly decreases as a result of higher pressure (atmospheric pressure), and the afterglow production mechanism of N2 (C) is govern by the Pooling reaction (R9) [50]. For direct-liquid discharges excited with DC, N2 (C) excitation was also considered the result of the Pooling reaction (R9) [19].
The predominant excitation of N2 (C) via the Pooling reaction requires a N2 (A) metastable state density much higher than that in the ground state N2 (X), and in several cases, this condition might not be achieved. To investigate Ar * the influence of filling gases (such as Ar, N2, N2O, air, etc.) particularly focusing on the rotational distribution of OH (A-X), higher rotational excitation of N2 (C) was also reported for discharges in bubbles in water and atmospheric glow discharges sustained with liquid electrodes [11]. In a N2O discharge excited with DC, the measured Trot (2400±200 K) of N2 (C-B) was substantially exceeded than those measured in Air (1850±150 K) and N2 (1850±150 K) discharges [11]. The high value of Trot was ascribed as the result of N2 (C) excitation through the production mechanisms such as electron and ion (N2O + ) recombination and excitation through electron dissociation in a N2O discharge. The rotatoinal temperatures as predicted from the SPS N2 (C-B) (captured from an atmospheric pressure plasma jet) were 1000 K and 1500 K, respectively, for the case of pure argon and argon water (0.76%) mixtures [48]. The rise in the derived value of the Trot was connected to the excitation of N2 (X) through (reaction R11). In fact, the presence of the ( 3 P2) state in the discharge leads to their interaction with other species (e.g., N2, H2O, O2, etc.), thus, causing a large range of nitrogen and oxygen species. As regard to the excitation of N2 (C), the Penning excitation of N2 (X) via the stable state could be important. This is because this process is a near resonance and is often proposed for the production of the N2 (C) state, especially, for the case of discharges involving argon or argon mixed with small fractions of nitrogen as plasma-forming gases. Also, the density of produced molecules in the N2 (C) state indicates a certain distribution that relies on the electronic state of ( 3 P2 or 3 P0).
Based on what has already been discussed, it seems likely that both reactions R9 and R11 are important with regard to the formation of N2 (C). However, one should be aware that reaction R16 involving N2 (A) metastable as reactant to excite NO (X) to NO (A) has been extensively proposed as a means to populate the rotational levels to higher numbers even greater than > 20 [52]. In the existing case, similar results are witnessed for the case of NO (A) whereby the highest population is perceived for =25 ( Figure 13). This implies that the density of the N2 (A) metastable state is sufficient in the wet discharge region. Based on this and on the larger rate coefficient ( ) for the Pooling reaction (R9) compared to the Penning reaction (R11) ( ), it is suggested that the Pooling reaction is the mechanism that could potentially excite NO (A) to a much larger rotational excitation in the wet environment. Irrespective of the rate constants, an alternative explanation relates to the fact that the energies of the stable states for and are 11.5 eV and 11.7 eV [54], respectively, while the threshold energy requirement for excitation of N2 (X) to N2 (C) is only 11.1 eV [55]. Comparing the respective energies, the excitation of N2 (X) to N2 (C) by ( 3 P2) stable state may be proposed. However, generation of the N2 (A) metastable species via ( 3 P2) stable species could be more favorable through reactions R10 and R11 given that the species lies at 6.2 eV above the ground state [54]. N2 (A) are the sole input species that result in the occurrence of the Pooling reaction, and thus, may boost the Pooling reaction R9 to produce the N2 (C) state. In such a case as mentioned above, the rotational population is thus populated by the formation process that, by and large, excite the N2 (C) to higher rotational levels, and as a result, the obtained populated rotational states are nonthermalized. This is the reason that the Trot (2700±130 K) predicted using the N2 (C-B) is appreciably overestimated in the discharge region in the liquid-phase compared to the Trot (1100±65 K) for a discharge region in the gas-phase ( Figures  8 and 14).

IV. CONCLUSIONS
This research has concerned studies on the experimental diagnostics of the argon gas-liquid-phase (two-phase) plasma discharge. From the recorded electrical signals, the pulses on the current waveforms were identified as the typical streamer-like behavior of the argon two-phase discharge. Image analysis indicated that discharge propagation through the liquid-phase (after the gas-phase discharge) depends on liquid properties and on discharge power input. Several spectroscopic diagnostics techniques (e.g., Boltzmann plot, LIFBASE, and SPECAIR simulation methods) were used to extract the Trot and Tvib from the simultaneously recorded OH (A-X), NO-γ (A-X), and SPS N2 (C-B) diatomic molecular spectra either attained from discharge region in the gas-or in liquid-phase. The variations in temperatures in the gas-and liquid-phases of the discharge were inspected based on the metastable speices and rotational quantum numbers. In the gas-phase, the Trot measurements for the considered diatomic molecules were in good agreement, except for that estimated by NO-γ (A-X). Furthermore, the Trot were found to be substantially higher in the humid environment for all the considerd diatomic molecules.
In a humid environment, the calculated Trot (1070±35 K) via the Boltzmann plot and attaind with a unique single fitting model (in comparison with that of a conventional two linear fittings models adopted for liquid discharges, as reported in the literature) only involving the rotational distribution of the lower rotational quantum numbers (from to ) of the Q1 branch of OH (A-X) provided a Trot value that was found in excellent agreement with Tgas predicted by other methods (e.g., LIFBASE and SPECAIR simulation methods) in the gasphase region. The overestimation of Trot from various diatomic molecules come from the excitation of rotational population to higher numbers: for example this phenomenon was more pronounced for the case of NO (A) in the humid environment, where the maximum population occurred at =25, resulted in the highest Trot (3900±180 K) compared to the estimated Trot values for other molecular bands. This result provides evidence supporting the hypothesis of a strong Trot dependence on the numbers. Accordingly, excitation to higher numbers was elucidated as the aftermath of the production processes, whereby the Boltzmann distribution for the considered rotational states was inhibited, and not related to the kinetic temperature. As for the totality of the production processes occurring in the aforementioned experiments in the argon discharge, these were ( 3 P2) and N2 (A) metastable based-processes that prevail practically exclusively in the liquid-phase region and favor the formation of various nitrogen and oxygen species (e.g., OH (A), NO (A), N2 (A), and SPS N2 (C)). This also gave support to the hypothesis proposed regarding the involvement of metastable species governing the chemistry of the argon discharge.
The Boltzmann method involving only a single fitting over the low numbers of the Q1 branch of OH (A-X) has advantageous over the double Boltzmann plot model in a way that Q1 branch rotational structure acquisition does not require sophisticated spectrometers compulsory for double fittings models to acquire highly resolved rotational structure. More than that, the attained fitting having the capability of detecting the deviation from the Boltzmann distribution compared to the simulation fitting methods (such as LIFBASE and SPECAIR). Besides, considering the case of simulation techniques, even with satisfactory fitting, and expecting them to be of the Boltzmann form by shape, the predicted Trot values were significantly higher than the actual Tgas.