Indigo Carmine Degradation in Water Induced by a Pulsed Positive Corona Discharge in Air: Discharge and Postdischarge Effects

: In recent years, one of the fastest growing technological applications in the ﬁeld of nonthermal plasmas is the degradation of organic contaminants of water. In this work, the degradation of indigo carmine (IC) in water induced by a pulsed positive corona discharge operating in ambient air is reported. Degradation levels in different volumes of IC in solution with distilled water treated with different plasma exposure times immediately after discharge (0 h), and in the postdischarge up to 24 h were examined. To explain the IC discoloration in the postdischarge phase, a chemical model was developed. The stability of the reactive species in solution nitrate (NO 3 − ), nitrite (NO 2 − ) and hydrogen peroxide (H 2 O 2 ), as well as the properties of the solution (electrical conductivity, pH) were also measured. The results suggest that the hydroxyl radical (OH˙) as well as ozone (O 3 ) are the main oxidizing species during the discharge phase, being primarily formed in the gas phase through plasma-mediated reactions and then transferred to the liquid by diffusion, while the OH˙ production in the bulk liquid through the decomposition of peroxinitrous acid (O=NOOH) plays a major role in the IC degradation during the postdischarge. These results are associated with a noticeably increase in the energy-yield values observed at 24 h post-treatment.


Introduction
A plasma is a quasineutral gas of charged and neutral particles that exhibits collective behavior [1]. On a laboratory scale, the most usual mode of plasma generation is through electrical discharges in a gaseous medium [2]. These are usually divided into two broad categories: (i) thermal discharges, where the energies of the heavy particles are of the order of the electron energy (~1 eV = 11,600 K) [3]; and (ii) nonthermal discharges, where the electron energy is much higher (~1-5 eV) than the energy of the heavy particles (~300-3000 K) [3]. In the latter group, the electrical energy applied to the discharge is mainly delivered to the electrons, which in turn excite by collisions with the molecules of the gas where the discharge is established, thus generating large amounts of reactive oxygen and nitrogen species (RONS) and UV radiation in air or similar gas mixtures [4].
The applications of nonthermal discharges are wide, and in recent years, there has been a growing interest in nonthermal plasmas in (and in contact with) liquids due to their multiple technological applications, encompassing areas such as agriculture, medicine, anism of pollutant degradation is associated with the most reactive species (OH˙, O 2˙− , O 3 ) formed in the gas phase during the discharge, which enter in the liquid bulk, react with the contaminant molecule, and fragment it. However, the results are highly dependent on the configuration of the discharge, as well as how the energy is deposited in the plasma.
In this work, the degradation of indigo carmine (IC) induced by a pulsed positive corona discharge operating in air is reported. Two volumes of IC solution in distilled water (50 and 100 mL) were treated with different plasma exposure times (10-30 min). Discharge and postdischarge effects on the IC degradation and the concentration of longlived species in the aqueous phase (NO 3 − , NO 2 − and H 2 O 2 ), were investigated up to 24 h after treatment. In addition, a chemical model to explain the IC chromogenic-bond degradation in the postdischarge phase via the O=NOOH decomposition was developed. Moreover, for each of these volumes, the energy yield was estimated as the amount of dye degraded per kWh delivered to the discharge (g/kWh).

Pulsed Positive Corona Discharge
A (positive) pulsed corona discharge in open air in contact with liquid was used in the experiments. The discharge was powered with a capacitive pulsed source, capable of delivering voltage pulses with a time-width of~100 ns, an amplitude of~10 kV, and a pulse repetition frequency of~42 Hz. The operation of the source is based on the charging of a capacitor bank (C = 224 nF) to a voltage level of 1500 V, which is in turn discharged by a thyristor onto a pulse transformer with ferrite core (Figure 1a).
Plasma 2022, 5, FOR PEER REVIEW 3 Pollutant degradation (such as pharmaceuticals, pesticides and organic dyes) in water induced by nonthermal plasma discharges in (and in contact with) liquids has been extensively studied, as summarized in a recent review articles [15,18]. The principal mechanism of pollutant degradation is associated with the most reactive species (OH˙, O2˙¯, O3) formed in the gas phase during the discharge, which enter in the liquid bulk, react with the contaminant molecule, and fragment it. However, the results are highly dependent on the configuration of the discharge, as well as how the energy is deposited in the plasma.
In this work, the degradation of indigo carmine (IC) induced by a pulsed positive corona discharge operating in air is reported. Two volumes of IC solution in distilled water (50 and 100 mL) were treated with different plasma exposure times (10-30 min). Discharge and postdischarge effects on the IC degradation and the concentration of longlived species in the aqueous phase (NO3¯, NO2¯ and H2O2), were investigated up to 24 h after treatment. In addition, a chemical model to explain the IC chromogenic-bond degradation in the postdischarge phase via the O=NOOH decomposition was developed. Moreover, for each of these volumes, the energy yield was estimated as the amount of dye degraded per kWh delivered to the discharge (g/kWh).

Pulsed Positive Corona Discharge
A (positive) pulsed corona discharge in open air in contact with liquid was used in the experiments. The discharge was powered with a capacitive pulsed source, capable of delivering voltage pulses with a time-width of ~100 ns, an amplitude of ~10 kV, and a pulse repetition frequency of ~42 Hz. The operation of the source is based on the charging of a capacitor bank (C = 224 nF) to a voltage level of 1500 V, which is in turn discharged by a thyristor onto a pulse transformer with ferrite core (Figure 1a). The plasma reactor was set in a wire-to-plate electrode configuration with electrodes made in AISI 304 (Figure 1b). The anode consisted of an arrangement of 10 wires of 0.2 mm in diameter and 100 mm in length with a separation between them 10 mm. These wires were placed parallel and at a certain distance from the cathode, which consisted of a square reservoir with a side of 140 mm and a height of 10 mm, containing the distilled water or IC solution to be treated in the form of a thin layer. Two volumes of the liquid to be analyzed were used: 50 and 100 mL; and in both cases the same gas gap of 3 mm was maintained between the surface of the liquid and the wires that form the anode.
Discharge voltage (V) was obtained as the difference between the CH1 and CH2 voltage signals (Figure 1a). A high-voltage probe (Tektronix P6015A, 1000X, 3 pF, 100 MΩ) The plasma reactor was set in a wire-to-plate electrode configuration with electrodes made in AISI 304 (Figure 1b). The anode consisted of an arrangement of 10 wires of 0.2 mm in diameter and 100 mm in length with a separation between them 10 mm. These wires were placed parallel and at a certain distance from the cathode, which consisted of a square reservoir with a side of 140 mm and a height of 10 mm, containing the distilled water or IC solution to be treated in the form of a thin layer. Two volumes of the liquid to be analyzed were used: 50 and 100 mL; and in both cases the same gas gap of 3 mm was maintained between the surface of the liquid and the wires that form the anode.
Discharge voltage (V) was obtained as the difference between the CH1 and CH2 voltage signals (Figure 1a). A high-voltage probe (Tektronix P6015A, 1000X, 3 pF, 100 MΩ) was used to measure CH1, while a coaxial shunt resistor (T&M SDN-414-025, 0.25 Ω, 1200 MHz) was used in CH2 to infer the discharge current (I). The signals of both channels were recorded with a 4-channel digital oscilloscope (Tektronix TDS 2004C, sampling rate 1 GS s −1 , bandwidth 70 MHz). Due to the difference in length between the measurement lines (the cable used in CH1 has a length of approximately 3 m, while the corresponding to CH2 has length of 1.5 m) a delay of approximately 10 ns in the voltage signal with respect to the current signal was measured. Figure 2a shows typical voltage and current waveforms of the discharge for each applied voltage pulse. The voltage pulse reached a maximum value of ≈11 kV, while the current pulses reached a maximum near to 30 A, with a time width of ≈40 ns. was used to measure CH1, while a coaxial shunt resistor (T&M SDN-414-025, 0.25 Ω, 1200 MHz) was used in CH2 to infer the discharge current (I). The signals of both channels were recorded with a 4-channel digital oscilloscope (Tektronix TDS 2004C, sampling rate 1 GS s −1 , bandwidth 70 MHz). Due to the difference in length between the measurement lines (the cable used in CH1 has a length of approximately 3 m, while the corresponding to CH2 has length of 1.5 m) a delay of approximately 10 ns in the voltage signal with respect to the current signal was measured. Figure 2a shows typical voltage and current waveforms of the discharge for each applied voltage pulse. The voltage pulse reached a maximum value of ≈11 kV, while the current pulses reached a maximum near to 30 A, with a time width of ≈40 ns. The instantaneous power and energy dissipated in the discharge are shown in Figure  2b. The instantaneous power (the product of V I) oscillated with the same frequency as the discharge current, reaching a maximum around 200 kW, while the average power per pulse was ≈21 kW. The energy per pulse, calculated as the time integral of the instantaneous power, reached a value of ≈21 mJ. Taking into account the pulse repetition frequency, the corresponding mean power resulted at about 0.9 W.

Treatments and Statistical Analysis
Volumes of 50 and 100 mL of distilled water (pH ≈ 5.2 and electrical conductivity ≈ 5 µS/cm) or IC solution subjected to different plasma exposure times were studied: 0 (control), 10, 20 and 30 min. Each of these experiments was performed in triplicate. Statistical analyses were performed with the R 4.1.1 software, R Core Team, R Foundation for Statistical Computing (Vienna, Austria) [19]. Data are shown as mean values ± SEM.

IC Degradation
To study the IC degradation, 50 and 100 mL of a 20 mg/L dye solution (5,5′-Indigo sulfonic acid sodium salt, Cicarelli) were treated with plasma and the absorbance was measured at 285 and 610 nm [10,20] immediately at the end of the treatment and at 24 h after discharge. The treated samples were stored at room temperature in sterile flasks, tightly capped and in the dark for 24 h and the absorbance was remeasured at these wavelengths. The results are shown as percentage degradation of the IC with respect to the The instantaneous power and energy dissipated in the discharge are shown in Figure 2b. The instantaneous power (the product of V I) oscillated with the same frequency as the discharge current, reaching a maximum around 200 kW, while the average power per pulse was ≈21 kW. The energy per pulse, calculated as the time integral of the instantaneous power, reached a value of ≈21 mJ. Taking into account the pulse repetition frequency, the corresponding mean power resulted at about 0.9 W.

Treatments and Statistical Analysis
Volumes of 50 and 100 mL of distilled water (pH ≈ 5.2 and electrical conductivity ≈ 5 µS/cm) or IC solution subjected to different plasma exposure times were studied: 0 (control), 10, 20 and 30 min. Each of these experiments was performed in triplicate. Statistical analyses were performed with the R 4.1.1 software, R Core Team, R Foundation for Statistical Computing (Vienna, Austria) [19]. Data are shown as mean values ± SEM.

IC Degradation
To study the IC degradation, 50 and 100 mL of a 20 mg/L dye solution (5,5 -Indigo sulfonic acid sodium salt, Cicarelli) were treated with plasma and the absorbance was measured at 285 and 610 nm [10,20] immediately at the end of the treatment and at 24 h after discharge. The treated samples were stored at room temperature in sterile flasks, tightly capped and in the dark for 24 h and the absorbance was remeasured at these wavelengths. The results are shown as percentage degradation of the IC with respect to the initial concentration: % = 100 (1 − A/A 0 ), where A is the absorbance of the treated sample and A 0 is the absorbance of the untreated sample.

pH and Electrical Conductivity
The levels of pH and electrical conductivity were determined using a HI 8314 pH meter (Hanna) with a range of 0 to 14 and a resolution of 0.01; and a CYBERSCAN COND 610 conductivity meter (Oakton Instruments, Vernon Hills, IL, USA) with a measurement range of 0 to 500 mS/cm with an accuracy of 1%. Both instruments were calibrated prior to the determinations using standard solutions (buffer pH 7, buffer pH 4 and KI 0.01 M solution with σ = 1413 µS/cm at 25 • C). The determinations were performed at the end of the plasma treatments.

Hydrogen Peroxide Measurement
A method using peroxidase was used [21]. The method is based on the reaction of H 2 O 2 with a mixture of 4-aminophenazone and phenol to give as product a red quinoneimine (4-(p-benzoquinonamonoimino)-phenazone) that exhibits an absorption maximum at 505 nm.

Nitrate Measurement
The UV method was used [21]. Hydrochloric acid was added in a ratio water:HCl = 50:1 and the absorbance at 220 nm (A 220 ) and 275 nm (A 275 ) was measured. These values were used to obtain the corrected absorbance (A = A 220 − 2 A 275 ).

Nitrite Measurement
Nitrite concentration was measured using Griess reagents (I and II) [21]. This technique consists of detecting a color change of the solution to a pink when nitrite react sequentially with sulfanilic acid and α-naphthylamine. After adding the reagents, the sample is allowed to react for 20 min and the absorbance at 520 nm is measured.
At the same time, calibration curves and their respective quality controls were processed for the determination of the reactive species. Using these curves, the concentrations of the compounds in mg/L were calculated. The standards and quality controls were prepared with analytical quality drugs, with known concentrations and within the range of the measured concentrations.
Measurements of the reactive species in activated water were made at the end of the plasma treatment, at 5 h and 24 h after treatment, in order to correlate these concentrations with the results obtained in the IC degradation. The treated samples were stored at room temperature (25 ± 2 • C) in sterile flasks, tightly capped and in the dark.

Modeling of IC Degradation in the Postdischarge Phase
A chemical model to estimate the degradation rate of the IC chromogenic bond in the postdischarge phase via the O=NOOH decomposition was developed. To this end, the value of the third-order rate coefficient for the production of O=NOOH under the conditions considered was obtained [22].

pH and Electrical Conductivity in PAW
The levels of pH and electrical conductivity of PAW were measured immediately after treatment with plasma. The variation of these variables can be seen in Figure 3. The pH showed a significant decrease from ≈5.2 to 3.8 with increasing plasma exposure time and decreasing volume (Two-way ANOVA, p < 0.05). The pH variation depends on the type of discharge and gas used. The decrease in the pH of aqueous solutions treated with electrical discharges in air is mostly attributed to the formation of nitric and nitrous acids in solution [17].
The electrical conductivity increased significantly with treatment time for both volumes studied with an approximately linear dependence. For the 50 mL volume, the conductivity reached a significantly higher value, close to double, compared to 100 mL for all plasma exposure times. This is expected due to the higher level of gas-liquid interaction at the interface area in the thinner water layer. The increase in conductivity with plasma exposure time is associated with acidic effects and the formation of NO 2 − and NO 3 − ions in water [17].  The electrical conductivity increased significantly with treatment time for both umes studied with an approximately linear dependence. For the 50 mL volume, the ductivity reached a significantly higher value, close to double, compared to 100 mL f plasma exposure times. This is expected due to the higher level of gas-liquid intera at the interface area in the thinner water layer. The increase in conductivity with pl exposure time is associated with acidic effects and the formation of NO2¯ and NO3 in water [17].

Concentration of Reactive Species in PAW
In all cases, reactive species increased significantly with plasma exposure tim with decreasing volume of water (two-way ANOVA, p < 0.05) ( Figure 4). The increa the concentration of reactive species as the volume decreases was also documente other authors [23,24], suggesting that the species responsible for the variation of pH ductivity and formation of secondary species are formed at the gas-liquid interfac then transferred to the bulk liquid, and that the generation rate of the species doe depend on the treated volume. In plasma-liquid discharges, water evaporation enh the generation of OH˙ and H2O2 in the gas phase, which in turn are transported t plasma-liquid interface based on their solubility coefficients [12], thus promoting th mation of secondary species in the water phase.

Concentration of Reactive Species in PAW
In all cases, reactive species increased significantly with plasma exposure time and with decreasing volume of water (two-way ANOVA, p < 0.05) (Figure 4). The increase in the concentration of reactive species as the volume decreases was also documented by other authors [23,24], suggesting that the species responsible for the variation of pH, conductivity and formation of secondary species are formed at the gas-liquid interface and then transferred to the bulk liquid, and that the generation rate of the species does not depend on the treated volume. In plasma-liquid discharges, water evaporation enhances the generation of OH˙and H 2 O 2 in the gas phase, which in turn are transported to the plasma-liquid interface based on their solubility coefficients [12], thus promoting the formation of secondary species in the water phase.    (Figure 4), reaching a maximum of ≈7.2 mg/L in 50 mL and ≈3.3 mg/L in 100 mL. H 2 O 2 formed in the gas phase by the discharge has a high Henry's law solubility coefficient (≈9 × 10 -2 M -3 Pa -1 ), so almost all H 2 O 2 (g) rapidly transfers to the liquid bulk [12]. Although H 2 O 2 has a relatively high oxidation potential, its direct oxidation effect in water is low because it does not react significantly with most organic compounds. However, this species involves processes that affect water chemistry, including the formation of OH˙radicals by reacting with nitrite through the formation of peroxynitrous acid [17]. Consequently, this advanced oxidation chemistry generates much more reactive species than H 2 O 2 ; for this reason, nonthermal discharges produce very efficient processes for organic-compound degradation and water disinfection.

NO 3
− and NO 2 − concentrations increased significantly with plasma exposure time, reaching peak values of ≈15.6 mg/L for NO 3 − and ≈2.2 mg/L for NO 2 − (Figure 4) in 50 mL, obtaining a ratio of 1:7, similar to that established by other authors in solution [10]. Similar concentrations have been described by other authors using plasma equipment with a voltage of 15 kV and exposure time of 5 min [25].
Nitric oxide (NO) formed through dissociated oxygen and nitrogen in air discharges via the Zeldovich reactions reacts with oxygen or ozone to form nitrogen dioxide (NO 2 ), which upon dissolving in water leads to the formation of NO 2 − and NO 3 − ions through electron capture by NO 2 or through oxidation of NO [17]: In these reactions, it can be clearly seen that the formation of these ions in solution contributes to the drop in pH by the release of H + ions into the water.

Time Evolution of the Concentration of Reactive Species in the Postdischarge
The stability of the reactive species in PAW up to 24 h after treatment is presented in Figure 5. The results corresponded to 50 mL sample volume treated for 30 min. The NO 3 − concentration remained stable for 24 h with a value of 15.7 mg/L immediately after treatment, and 15.5 mg/L after 24 h of storage. Similar results were reported by Vlad et al. [24], who showed that nitrate was also stable in solution for 20 days after treatment.  [24], who showed that nitrate was also stable in solution for 20 days after treatment.  A significant decrease in hydrogen peroxide from 7.1 mg/L to 4 mg/L was observed after 24 h of storage time ( Figure 5). Other authors [25,26] have documented decreases in hydrogen peroxide concentration after storage of plasma-treated solutions for 24 h. A significant drop in NO 2 − concentration from 2.3 mg/L to 0.5 mg/L at 24 h was also observed. Previous studies have also reported a significant decrease in nitrite and an increase in nitrate concentration after 48 h [25] or 7 days of storage [26]. The NO 2 − to NO 3 − disproportionation reaction is as follows [17]: which is strongly pH-dependent and is not expected to be a significant pathway of nitrite loss under the conditions considered (proceeds faster at pH < 3.5). On the other hand, the peroxynitrous acid formation is an important pathway by which nitrite and hydrogen peroxide are consumed in the aqueous phase [17]: Reaction (4) is of particular importance in plasmas in contact with water because of the large amount of H 2 O 2 produced in discharges of this type. In acidic solutions, the predominant form of peroxynitrite is the protonated form (pKa = 6.8), which decays to OH˙and NO 2˙r adicals via (5), and to NO 3 − via (6), with their corresponding branching values [13]: b values reported in the literature vary between 0.15 and 0.4 [13]. Although both radicals in reaction (5) can recombine to form nitric acid, the rate constant of that reaction (>3 × 10 4 L mol −1 s −1 ) is several orders of magnitude lower than most of the rate constants of the destruction OH˙reactions (10 7 ÷ 10 10 L mol −1 s −1 ), so the reactivity of peroxynitrous acid is determined primarily by the OH˙radicals formed from (5) [17].

IC Degradation: Discharge and Postdischarge Effects
Indigo carmine degradation immediately after discharge (0 h) increased with both plasma exposure time and decreasing volume (Two-way ANOVA, p < 0.05), showing a significant difference between treatments. Maximum values for the degradation of the IC unsaturated bond (measured at 285 nm) at 0 h was obtained for a plasma exposure time of 30 min: 81.3% and 86% for sample volumes of 100 mL and 50 mL, respectively (Figure 6a), while corresponding values for the IC chromogenic bond (measured at 610 nm) at the same plasma exposure time were 93.4% and 99.1%, respectively (Figure 6b). These results can be primarily associated to the diffusion into the liquid of O 3 and OH˙(main oxidizing species for the IC dye [27]) generated in the gas phase through plasma-mediated reactions. It should be noted that due to their short lifetime (<1 ns), plasma-generated OH˙radicals are not expected to diffuse far beyond a thin boundary layer (of the order of 100 nm to 10 µm) near the gas-liquid interface [13]. As for O 3 , it is worth mentioning that despite its hydrophobicity and low Henry's law diffusion coefficient, the diffusion of O 3 in the liquid volume is favored, since upon entry it reacts with the IC molecule, being rapidly consumed in solution [10].
It is also observed that for low plasma exposure times (<20 min) the IC degradation of both the chromogenic and unsaturated bonds at 24 h post-treatment was higher than 0 h; with the IC degradation for 50 mL being higher than 100 mL (Figure 6). Such a marked difference in the IC degradation between measurements at 0 h and 24 h post-treatment suggests that the OH˙production in the bulk liquid through the decomposition of the O=NOOH pathway (5) plays a major role in the IC degradation in the postdischarge [13]. Moreover, the difference in IC degradation between volumes could be related to a change in the level of the gas-liquid interaction. As quoted before, the concentration of nitrite and hydrogen peroxide-which increases the availability of OH˙radicals-significantly increased their concentration at lower volume, leading to more oxidants in solution. However, for higher plasma exposure times, the IC degradation was almost independent of both the volume treated and the post-treatment time, thus indicating that the IC degradation limit was already reached. unsaturated bond (measured at 285 nm) at 0 h was obtained for a plasma exposure time of 30 min: 81.3% and 86% for sample volumes of 100 mL and 50 mL, respectively ( Figure  6a), while corresponding values for the IC chromogenic bond (measured at 610 nm) at the same plasma exposure time were 93.4% and 99.1%, respectively (Figure 6b). These results can be primarily associated to the diffusion into the liquid of O3 and OH˙ (main oxidizing species for the IC dye [27]) generated in the gas phase through plasma-mediated reactions. It should be noted that due to their short lifetime (<1 ns), plasma-generated OH˙ radicals are not expected to diffuse far beyond a thin boundary layer (of the order of 100 nm to 10 µm) near the gas-liquid interface [13]. As for O3, it is worth mentioning that despite its hydrophobicity and low Henry's law diffusion coefficient, the diffusion of O3 in the liquid volume is favored, since upon entry it reacts with the IC molecule, being rapidly consumed in solution [10]. It is also observed that for low plasma exposure times (<20 min) the IC degradation of both the chromogenic and unsaturated bonds at 24 h post-treatment was higher than 0 h; with the IC degradation for 50 mL being higher than 100 mL (Figure 6). Such a marked difference in the IC degradation between measurements at 0 h and 24 h post-treatment suggests that the OH˙ production in the bulk liquid through the decomposition of the O=NOOH pathway (5) plays a major role in the IC degradation in the postdischarge [13]. Moreover, the difference in IC degradation between volumes could be related to a change in the level of the gas-liquid interaction. As quoted before, the concentration of nitrite and hydrogen peroxide-which increases the availability of OH˙ radicals-significantly increased their concentration at lower volume, leading to more oxidants in solution. However, for higher plasma exposure times, the IC degradation was almost independent of both the volume treated and the post-treatment time, thus indicating that the IC degradation limit was already reached.

Modeling of the IC Degradation in the Postdischarge Phase
In the postdischarge phase (i.e., without the generation of reactive species formed in the gas-phase by the plasma) it is reasonable to assume that the IC chromogenic bond degradation is due to the interaction of the dye molecule with the OH˙radical, formed through the O=NOOH decomposition in the bulk liquid. The O=NOOH is formed via reaction (4) (i.e., NO 2 − + H 2 O 2 + H + → O=NOOH + H 2 O); and quickly decomposes via (5) and (6) [13]. The formation rate of O=NOOH obtained from reaction (4) is as follows: where k 4 is the third-order rate coefficient of (4)  and H + , respectively. It is worth noting that estimating the formation rate of O=NOOH (and consequently the formation of OH˙radicals in solution) necessarily implies knowing the k 4 value, which is pH-dependent. To estimate the k 4 value for the given conditions, the procedure developed by Lukes et al. was followed [22]. Due to the fact that during the postdischarge the pH data remained within a value of 3.87 ± 0.02, the corresponding concentration of H + (=10 −pH ) was almost constant. Under such conditions, the third-order reaction (7) can be simplified to a pseudo-second-order reaction as d[ where k 4 SO ≡ k 4 [H+] is the pseudo-second-order rate constant of reaction (4). Moreover, the rate of O=NOOH formation (7) can be expressed in terms of the rate of disappearance of reactants, as The integration of (8) and (9) between t = 0 and t gives: where the zero subscript indicates species concentrations at t = 0 in the postdischarge. The experimental data for this analysis were used from post-treatment evolution of [NO 2 − ] and [H 2 O 2 ] in a sample volume of 50 mL of PAW treated for 20 min (Figure 7a). The plot of (10) as a function of the time together with the corresponding linear fit is presented in Figure 7b. the rate of O=NOOH formation (7) can be expressed in terms of the rate of disappearance of reactants, as The integration of (8) and (9) between t = 0 and t gives: where the zero subscript indicates species concentrations at t = 0 in the postdischarge. The experimental data for this analysis were used from post-treatment evolution of [NO2¯] and [H2O2] in a sample volume of 50 mL of PAW treated for 20 min (Figure 7a). The plot of (10) as a function of the time together with the corresponding linear fit is presented in Figure 7b.  It is worth noting that as reactions other than the decomposition of O=NOOH arising from stable RONS in water (i.e., H 2 O 2 , NO 2 − , and NO 3 − ) do not significantly oxidize indigo carmine, the measured concentrations of these species in PAW can be used to estimate the corresponding concentrations in IC solution. Measurements of NO 2 − and H 2 O 2 in PAW and in IC solution were similar (data not shown). Moreover, as the O 3 would react with indigo carmine almost instantly [13], neglectable concentrations of O 3 in IC solution are expected in the postdischarge.
Once the k 4 value was determined for the given experimental conditions, it is possible to model the IC chromogenic bond degradation related to the O=NOOH decomposition based on the following bulk-liquid reactions: where (11) corresponds to the IC destruction by the OH˙radicals, while (12) and (13) correspond to the processes of formation and destruction of OH˙radicals and ONOO=H, respectively. Since the timescale for the IC degradation under the given conditions (~1 h) is very large compared to the lifetimes of OH˙and O=NOOH (the decomposition rate of O=NOOH is 0.13 + 0.87 [H+], s −1 [29]) it is reasonable to assume that such species are in instantaneous equilibrium (i.e., the accumulation terms in (12) and (13) are taken as zero). Under such assumption, (11) can be rearranged as [13]: with the branching value b being the parameter of the model. Figure 8 shows The good agreement between the experimental degradation data for t genic bond and those obtained through the model (Figure 8) support the h during the postdischarge phase, the most important mechanism of IC disc interaction with the OH˙ radical formed in the liquid bulk through the dec O=NOOH [13].

Subproducts of the IC Degradation
The degradation of IC in water is a good indicator of the amount of reactive species produced, in particular ozone [30]. The molecule of IC in co reactive species generated by the plasma fragments, leads to the formation intermediates, such as isatin-5-sulfonic acid, which gives a yellowish or col ance to the treated solution [30]. One way to corroborate the fragmentation ecule in isatin-5-sulfonic acid is by measuring the absorbance at 250 nm [1 ately after discharge. Figure 9 shows the significant increase in absorbance the 50 mL samples of IC treated 30 min. The good agreement between the experimental degradation data for the IC chromogenic bond and those obtained through the model (Figure 8) support the hypothesis that during the postdischarge phase, the most important mechanism of IC discoloration is by interaction with the OH˙radical formed in the liquid bulk through the decomposition of O=NOOH [13].

Subproducts of the IC Degradation
The degradation of IC in water is a good indicator of the amount of oxygen-based reactive species produced, in particular ozone [30]. The molecule of IC in contact with the reactive species generated by the plasma fragments, leads to the formation of fragmented intermediates, such as isatin-5-sulfonic acid, which gives a yellowish or colorless appearance to the treated solution [30]. One way to corroborate the fragmentation of the IC molecule in isatin-5-sulfonic acid is by measuring the absorbance at 250 nm [10,31] immediately after discharge. Figure 9 shows the significant increase in absorbance at 250 nm for the 50 mL samples of IC treated 30 min.

Energy Yield G50
The energy yield G50 of the discharge was determined as the ratio between the amount of the converted IC and the energy required for 50% IC conversion: G50 = 1.8 × 10 6 C0 V0 M0/(P t50) [g/kWh], where C0 is the molar concentration of the control IC, V0 is the treated volume in liters, M0 is the molecular weight of the IC in grams, P is the average power of the plasma reactor in watts, and t50 is the time in seconds required for 50% conversion [16]. Although the G50 value is usually calculated at 0 h, its calculation at 24 h becomes relevant if the treated liquid is not used immediately, having a storage time of at least 1 day. The G50 values obtained at 0 h and 24 h post-treatment are shown in Table 1.  Table 1 shows that regardless of the volume of the sample, the energy yield G50 values calculated at 0 h are almost constant, with a value of around 5 and 6 g/kWh for the unsaturated and chromogenic bonds, respectively, indicating that the ratios t50/V0 are remarkably constant under the present conditions. These dependences are strengthened by the fact that in the discharge phase both O3 and OH˙ are mainly formed in the gas phase through plasma-mediated reactions and then transferred to the liquid by diffusion; and that the generation rate of species does not depend on the sample volume. (Note that the rate of degradation through the O=NOOH pathway is dependent on the bulk concentrations of H2O2 and NO2and thus changes with sample volume.) On the other hand, the energy yield G50 values calculated at 24 h postdischarge decrease noticeably as the sample volume increases. This result is related to the higher concentration of NO2¯ and H2O2 in aqueous phase at the lower volume, which in turn increases the availability of OH˙ radicals in the liquid bulk through the pathway (5). It is also worth noting that large increases in the energy yield values are observed at 24 h post-treatment due to the beneficial effects

Energy Yield G 50
The energy yield G 50 of the discharge was determined as the ratio between the amount of the converted IC and the energy required for 50% IC conversion: G 50 = 1.8 × 10 6 C 0 V 0 M 0 /(P t 50 ) [g/kWh], where C 0 is the molar concentration of the control IC, V 0 is the treated volume in liters, M 0 is the molecular weight of the IC in grams, P is the average power of the plasma reactor in watts, and t 50 is the time in seconds required for 50% conversion [16]. Although the G 50 value is usually calculated at 0 h, its calculation at 24 h becomes relevant if the treated liquid is not used immediately, having a storage time of at least 1 day. The G 50 values obtained at 0 h and 24 h post-treatment are shown in Table 1.  Table 1 shows that regardless of the volume of the sample, the energy yield G 50 values calculated at 0 h are almost constant, with a value of around 5 and 6 g/kWh for the unsaturated and chromogenic bonds, respectively, indicating that the ratios t 50 /V 0 are remarkably constant under the present conditions. These dependences are strengthened by the fact that in the discharge phase both O 3 and OH˙are mainly formed in the gas phase through plasma-mediated reactions and then transferred to the liquid by diffusion; and that the generation rate of species does not depend on the sample volume. (Note that the rate of degradation through the O=NOOH pathway is dependent on the bulk concentrations of H 2 O 2 and NO 2 − and thus changes with sample volume.) On the other hand, the energy yield G 50 values calculated at 24 h postdischarge decrease noticeably as the sample volume increases. This result is related to the higher concentration of NO 2 − and H 2 O 2 in aqueous phase at the lower volume, which in turn increases the availability of OH˙radicals in the liquid bulk through the pathway (5). It is also worth noting that large increases in the energy yield values are observed at 24 h post-treatment due to the beneficial effects induced by the O=NOOH decomposition. For instance, the energy yield G 50 for the degradation of the unsaturated bond calculated at 24 h and for the 50 mL volume is higher than that