Effects of frequency and pulse width on electron density, hydrogen peroxide generation, and perfluorooctanoic acid mineralization in a nanosecond pulsed discharge gas-liquid plasma reactor

Nonthermal plasma formed in or in-contact with a liquid medium is of interest due to a wide range of applications in material processing, medical treatment, agriculture, and water purification.^1–3 The most common ways of making nonthermal plasma for technological applications are to use electrical discharges formed from AC, DC, or pulsed electric fields.⁴ Plasma-contacting liquids can be generated in various reactor configurations including direct discharge in the liquid, discharge in a gas phase over the liquid, and discharges formed in multiphase environments such as liquid sprays or foams.⁵ Nonthermal plasma-contacting liquid water with a gas phase carrier such as argon or helium generates highly reactive species such as •OH, •O, •H, O₂^•−, aqueous electrons (e⁻_aq), and molecular species such as H₂, O₂, and H₂O₂.^6–8 H₂O₂ is a stable species that can be used as an indirect measurement of •OH.⁹ Hydroxyl radicals, •OH, are strong oxidizing species and can degrade many organic compounds such as phenols, benzene, and toluene⁶ and organic dyes such as methylene blue.¹⁰ Singh et al.¹¹ suggest that both oxidative and reductive species play important roles in the degradation of some organic pollutants such as perfluorooctanoic acid (PFOA).

In our previous studies using a nanosecond pulsed discharge in a gas-liquid flowing reactor where the plasma is generated at the gas-liquid interface,¹² H₂O₂ production and the time-averaged electron density and gas temperature varied with pulse frequency and input voltage.¹³ In order to develop plasma reactors for chemical applications, it is necessary to determine how the production rate of reactive species depends upon plasma properties such as electron density.^14,15 In the present study, we expand our previous work to investigate the dependency of the electron density on pulse frequency and pulse width using time-resolved spectroscopy. Electron density is determined from the full width half area (FWHA) of $Hα$ Stark broadening and the full width half maximum (FWHM) of $Hβ$ Stark broadening.¹⁶ Two different nanosecond power supplies were used to provide a large range of pulse frequency (1–100 kHz) and pulse width (40–200 ns).

Perfluoroalkyl substances (PFAS), such as PFOA, are widely used in applications such as fire-fighting foams, nonstick cookware, and paint adhesives.¹⁷ PFAS are very difficult to degrade and, thus, are persistent in the environment¹⁸ and have been detected in drinking water, ground water, oceans, lakes, rivers, and other surface water bodies.^19,20 PFOA received the most attention due to its high bio-accumulation potential, persistence, toxicity, and ubiquitous presence in the environment.²¹ The United States Environmental Protection Agency (USEPA) released a lifetime health advisory level of PFOA of 0.07 μg/l in 2016.²¹ On the industrial scale, it is possible to remove PFAS such as PFOA from water efficiently by physical adsorption on activation carbon.²² However, for a complete destruction of the PFAS, the activated carbon much be incinerated at high temperatures above 1000 K resulting in high operating cost.²³ Recent studies have demonstrated that nonthermal plasma was more efficient for the removal of persistent chemicals and anticipated carcinogens such as PFOA^24–26 than sonolysis,²⁷ electron beams,²⁸ and similar to electrochemical oxidation.²⁹ In recent studies, Johnson et al.³⁰ studied the effect of pulse frequency and pulse width on one of the common PFAS, i.e., perfluorooctanoic sulfonate (PFOS) degradation. Johnson et al.³⁰ reported that with an increase in pulse frequency and pulse width, the energy yield of PFOS degradation decreased and the main factor affecting the PFOS degradation was the contact time between the plasma and the solution. Our previous work³¹ demonstrated that PFOA mineralization to fluoride (F⁻) was optimum at 5 kHz³¹ when the pulse frequency was varied between 0.25 and 10 kHz at 16 kV and 40 ns with the EHT power supply. In contrast, the formation of H₂O₂ increased monotonically with pulse frequency.³¹ This significant difference in behavior for PFOA mineralization and H₂O₂ formation with pulse frequency motivates the present study with regard to determining how the plasma properties are affected by power delivery characteristics and how they, in turn, affect the chemical reaction processes.

In this study, temporal evolution of electron density and electron temperature at different pulse parameters were reported. The effects of pulse parameters and plasma electron density on chemical reactions were determined through the analysis of degradation of a model organic contaminant (PFOA) and the formation of H₂O₂. A novel result of correlation between the peak electron density in a single pulse and mineralization of PFOA to F⁻ was reported. Chemical scavengers were used to evaluate the role of •OH in the degradation pathway. Glycerol³² was used as a liquid-phase •OH scavenger and CO was used as a gas-phase •OH scavenger. The study shows that the optimal frequency for PFOA degradation reported in our earlier study corresponds to the maximum electron density generated during a single discharge event.

The continuous gas-liquid flowing film reactor system used in this study, as shown in Fig. 1, is similar to that used in the previous work.³¹ De-ionized (DI) water was supplied to the system with a high-pressure reciprocating pump and argon was the carrier gas. The high-pressure gas and de-ionized water were fed into the reactor through a stainless-steel capillary tube with 0.5 mm inner diameter. The liquid flows along the internal reactor walls and the gas flows through the central core. The plasma channel propagates along the gas-liquid interface as shown in previous studies.^15,31

Two nanosecond pulsed power supplies were used in this study including one commercially manufactured by Eagle Harbor Technologies, Inc (EHT) (NSP-120-20, Seattle, Washington) and a customized power supply manufactured by Airity Technologies, LLC (AT) (Palo Alto, California) to maximize the range of pulse frequency used in this study. EHT power supply has the capability to vary the pulse width (20–240 ns), input voltage (0.2–20 kV), and pulse frequency (single to 10 kHz) using front panel knobs. While the EHT power supply could achieve maximum pulse frequency of 10 kHz, with the AT power supply, much higher pulse frequency of 100 kHz could be achieved.

As shown in Fig. 1, the stainless-steel inlet (0.5 mm ID) and outlet (1 mm ID) capillary tubes serve as electrodes. The negative lead of the power supplies was attached to the inlet and the positive lead is connected to the outlet. The EHT power supply was used to vary the pulse frequency and pulse width in the ranges of 1–10 kHz and 40–200 ns, respectively.

A commercially available function generator (Rigol 1022Z, Portland, OR) was utilized to vary the pulse frequency between 5 and 100 kHz using AT. The pulse width of AT was constant at 220 ns. The AT power supply has an internal voltage transformation and a pulse stage that provides voltage gains of 100–130 times depending upon the load and pulse width settings. A variable DC power supply (Sorensen XHR 600-1.7, British Columbia, Canada) was used to supply the input voltage for the AT power supply. Different input DC voltages were used for different pulse frequencies because the average power must be limited to about 12.5 W during continuous operation for safety reasons. The input DC voltages used for different frequencies are shown in Table I.

Liquid solutions exiting the reactor were collected and analyzed separately to determine H₂O₂ and F⁻ concentrations. H₂O₂ was quantified using the titanium oxysulfate sulfuric acid complex colorimetric test with a UV-vis spectrophotometer (Lambda 35, PerkinElmer, Waltham, MA).³³ The liquid samples were analyzed for F⁻ using a perfectION™ fluoride ion-selective electrode connected to a SevenGo pro™ portable meter (Seven2Go™ S8 Pro Fluoride kit, Mettler Toledo, Switzerland). Fluoride calibration curves were made before each measurement due to the slow drift of the voltage response. Different concentrations of potassium fluoride (KF) solutions that were adjusted for ionic strength and pH using total ionic strength adjustment buffer (TISAB III) and 15% sodium acetate, respectively, were used to make the calibration curves.

The production rate (mol/s) and energy yield (mol/J) were calculated using the following equations:

Electrical diagnostics were performed with an oscilloscope (Tektronix MDO 3014; Beaverton, OR). Two HV probes (TektronixP6015A, 1/1000; Beaverton, OR) and a current transformer (Pearson Electronics, model 6585; Palo Alto, CA) placed across and around the reactor, respectively, were connected to the oscilloscope. The two voltage probes were connected together at the grounds to generate a floating reference. The two voltage values from the oscilloscope were added together to measure the breakdown voltage across the reactor. The energy per pulse was determined by Eq. (3).^13,34 Figure 2 shows example voltage and current waveforms for EHT and AT power supplies. The rise time of the EHT power supply is ∼20 ns while that of the AT power supply is ∼220 ns,

V is the instantaneous voltage, I is the instantaneous current, and t is the time period of a single pulse.

Total discharge power was determined by multiplying the energy per pulse by the pulse frequency. The discharge power data for all experiments including those to measure H₂O₂ and F⁻ are given in the supporting information (Table S4,⁷⁷ Table S5,⁷⁷ and Table S6⁷⁷).

Optical emission spectroscopy was used to determine the electron density variation within a single pulse by placing the reactor across the slit of the imaging spectrometer (HRX Spectra Pro 750). An iCCD camera (PIMax 3 by Princeton Instruments, New Jersey, USA) was attached to the spectrometer.

The analysis of Stark broadened spectral line profiles is a common plasma diagnostic tool,¹⁶ and the electron density can be determined using the full width at half maximum (FWHM) of H_β (Ref. 35) and full width at half area (FWHA) of $Hα$⁠.³⁶ However, when the plasma density is higher than 10¹⁶ cm⁻³, the $Hβ$ spectral lines become too broad because of significant Stark broadening³⁷ and often interfere with other spectral lines; therefore, fitting it becomes too complex. In our gas-liquid reactor, the time-resolved electron density was determined using the FWHA of the Stark-broadening of $Hα$ and the FWHM of Stark broadening of $Hβ$⁠. We have considered additional line broadening mechanisms, e.g., Doppler broadening and van der Waals broadening. Resonance broadening is typically neglected unless the element density (H) is large.³⁸ 

The Doppler broadening and van der Waals broadening were determined using the following equations:³⁹ 

The gas temperature was found to be 600 K in our previous work using the OH band at 310 nm.¹² For H_α, the values of $λD$ and $λvdw$ were 0.0115 and 0.0651 nm, respectively. For H_β, the values of $λD$ and $λvdw$ were 0.0085 and 0.0627 nm, respectively.

The instrumental broadening of the $Hα$ line was determined for different gratings using a Hg(Ar) lamp with a slit width of $10μm$ as shown in Table II. There were two different gratings that were used in this study, i.e., 150 and 1200 g/mm. The higher the number the better the resolution. We utilized the 150 g/mm data when the FWHA of the $Hα$ was large (>3 nm) and 1200 g/mm data when the FWHA was small (<3 nm).

The electron density was determined from Stark broadening of $Hα$ and $Hβ$ bands using Eqs. (6) and (7), respectively, and corrected using diagnostic maps given in Gigosos et al.¹⁶ 

Figure 3(a) shows an example of the temporal evolution of H_α when we used the EHT power supply at 16 kV, 40 ns, and 10 kHz. We observed that the FWHM of H_α decreases with time in a single pulse. Figures 3(b) and 3(c) show examples of Voigt fits for $Hα$ and $Hβ$⁠, respectively.

The opacity effect was evaluated using the following equation:⁴⁰ 

where $Ta$ is the temperature of the absorbing atoms, $re$ is the radius of the electron $(2.82×1013cm)$⁠, $fik$ is the absorption oscillator strength (0.641 for $Hα$ and 0.119 for $Hβ$⁠), $λ0$ is the transition wavelength (656.28 nm for $Hα$ and 486.13 nm for $Hβ$⁠), d is the thickness of the absorbing homogeneous plasma (0.035 cm, plasma diameter⁴¹), M is the atom mass $(1.67355×10−24g)$ of hydrogen, and c is the speed of light. $ni$ is the population density of the lower level that is calculated using the following equation:⁴⁰ 

$Na$ is the density of absorbers $(2.2×1018cm−3)$⁠, i.e., H. The H density is calculated assuming complete dissociation of water at a concentration equivalent to a saturated vapor at 300 K. The saturated vapor pressure was calculated using the Antoine equation⁴² and the water concentration was determined using the ideal gas law. $Ta$ was estimated for the upper limit of electron temperature of T_e ≈ 1 eV.⁴⁰ Using the parameters given above, $τ(λ0)∼10−4–10−5≪1$ for $Hα$ and $Hβ$⁠, respectively, making the lines optically thin.

The excitation temperature analysis was dependent on the intensities of $Hα$ and $Hβ$ since the lines are optically thin. The ratio of line intensities with wavelengths $λpq$ and $λp′q′$ is given by the following equation:^38,40

where A is the Einstein coefficient of the transition, g is the degeneracy of the level, E is the energy of the upper level in the transition, and $I(p→q)$ and $I(p′→q′)$ are the intensities of lines. We considered transition $p→q$ to be $Hα$ and $p′→q′$ to be $Hβ$⁠, $kB$ is the Boltzmann constant, and $Tex$ is the excitation temperature. The parameters used in this analysis are from Kramida⁴³ and are shown in Table III.

The intensities were obtained from data collected using 150 g/mm grating in the spectrometer.

In local thermodynamic equilibrium (LTE), the excitation temperature $(Tex)$ is equal to electron temperature $(Te)$⁠.⁴⁴ For LTE, the condition shown in Eq. (11) must be satisfied, i.e., the rate of electron collisions with the given species having the largest energy gap [E(p) – E(q)] should be larger than the radiative decay by at least a factor of 10,

where $kB$ is the Boltzmann constant (8.63 × 10⁻⁵ eV/K), $Te$ is the excitation temperature, and [E(p) – E(q)] is the energy gap for $Hα$⁠, i.e., 1.89 eV. For maximum excitation temperature observed in this study (0.8 eV), $ne≥1.9×1015cm−3$⁠. For $Tex≈Te$⁠, electron density should be greater than or equal to $1.9×1016cm−3$ and the electron density reported in this study is ∼10¹⁷ cm⁻³. Hence, in our case, $Tex$ is equivalent to $Te$⁠.

Figure 4(a) shows that for increasing frequency from 1 to 10 kHz, the energy per pulse (E) and breakdown current per pulse (I) decreased from 0.98 to 0.71 mWs and 0.66 to 0.6 mAs with the EHT power supply. However, the total discharge power (P) increased from 0.98 to 7.1 W in the same interval. Figure 4(b) shows that E increases approximately linearly from 0.92 to 2.34 mWs with an increase in pulse width from 40 to 160 ns and then increases to 2.44 mWs when we increase the pulse width to 200 ns. Figure 4(b) shows that variation in pulse width between 40 and 200 ns using EHT causes saturation of E, I, and P starting at ∼200 ns. E, I, and P at 16 kV, 2 kHz, and 200 ns were 2.44 mWs, 3.42 mAs, and, 4.88 W, respectively. Figure 4(c) shows that with an increase in frequency from 1 to 60 kHz, E and I decreased from 0.22 to 0.1 mWs and 0.20 to 0.06 mAs, respectively. E and I levels off between 60 and 70 kHz at 0.1 mWs and 0.06 mAs, respectively, and then increased to 0.12 mWs and 0.11 mAs at 100 kHz, respectively. P increased linearly from 0.22 to 7.01 W with an increase in frequency from 1 to 50 kHz and levels off between 50 and 70 kHz. P increased from 7.04 to 11.53 W when the frequency is increased from 70 to 100 kHz.

As discussed in Sec. II C, the energy per pulse and total discharge power are dependent on the breakdown current and breakdown voltage. It was observed that there was no significant change in breakdown voltage when pulse frequency and pulse width were varied with EHT. However, different input high voltages to AT resulted in different breakdown voltages and different current per pulse. This explains the trends in the energy per pulse, breakdown current per pulse, and total discharge power. When compared with EHT, AT had lower breakdown voltage, breakdown current, and energy per pulse, which can be attributed to using power supplies at different input voltages, i.e., 16 kV for EHT and 5.1–6.2 kV for AT. The electrical diagnostics data can be found in the supporting information (Table S1⁷⁷, Table S2⁷⁷, and Table S3⁷⁷).

Figure 5(a) shows the electron density $(Ne)$ variation with frequency from 1 to 10 kHz using the EHT power supply at 16 kV and 40 ns. The peak $Ne$ increased from 1.90 × 10¹⁸ to 3.94 × 10¹⁸ cm⁻³ with increasing frequency from 1 to 5 kHz. With an increase in frequency from 5 to 10 kHz, the peak $Ne$ decreased to 1.85 × 10¹⁸ cm⁻³. Therefore, at a frequency of 5 kHz, the $Ne$ was highest using the EHT power supply. Figure 5(b) shows that with an increase in pulse width from 40 to 200 ns, the peak $Ne$ in a single pulse increases from 2.28 × 10¹⁸ to 4.45 × 10¹⁸ cm⁻³. Figure 5(c) shows the electron density when we varied the pulse frequency between 5 and 100 kHz using the AT power supply. In this case, the peak $Ne$ increases from 9.91 × 10¹⁷ to 1.42 × 10¹⁸ cm⁻³ with an increase in frequency from 5 to 20 kHz. With further increase in pulse frequency from 20 to 100 kHz, there is a decrease in peak $Ne$ to 9.5 × 10¹⁷ cm⁻³. Therefore, the AT power supply had an optimal frequency of 20 kHz, where the peak $Ne$ was maximum.

We were able to resolve $Hβ$ and calculate the Stark broadening from 150 ns after the initiation of the pulse at 16 kV, 40 ns, 10 kHz using the EHT power supply. Figure 5(d) shows that the $Ne$ calculated using $Hα$ was the same as $Ne$ calculated using $Hβ$⁠, and this observation is consistent with Yubero.³⁹ 

For comparison of plasma parameters to similar discharges where plasma is generated on the liquid interface or is found in contact to it, most ubiquitous results are reported on plasma-jet in contact with liquid. In a recent study, Slikboer and Walsh⁴⁵ used a pulsed 5 μs Ar jet operated at 16 kHz frequency in contact with water grounded through a series of resistors (1–680 kΩ) to mimic different liquid conductivities. The electron density and temperature values were found to be in the range of 10¹⁴–10¹⁵ cm⁻³ and 1–3.5 eV, respectively. In a similar study, Slikboer and Walsh,⁴⁶ the same team of authors, investigated the plasma generated by Ar jet operated by a AC 5 kV generator at 23 kHz. The maximum electron densities and temperatures were 6 × 10¹⁴–6.3 × 10¹⁴ cm⁻³ and 3.1–3.3 eV for the floating liquid case and 1.1 × 10¹⁵ cm⁻³ and 4.3 eV in the grounded liquid case. A plasma He jet powered by a square 6 kV pulse, with a duration of 1 μs and a frequency of 5 kHz, was also studied when impinging on water by Klarenaar et al.⁴⁷ The maximum electron density and electron temperature were determined to be ∼1.7 × 10¹⁷ cm⁻³ and ∼3 eV, respectively. Oldham et al.⁴⁸ and Yatom et al.⁴⁹ studied the Ar RF jet in contact with liquid for RF powers from 20 to 50 W and found peak values of $Ne$ to be 8 × 10¹⁵ cm⁻³ and $Te∼1eV$⁠. Simeni et al.⁵⁰ also studied nanosecond pin-to-liquid discharge in He at a pressure of 100 Torr. Maximum electron densities and temperatures measured were ∼10¹⁵ cm⁻³ and 3.5 eV. As one can see in the present study, we show that the electron density obtained in the thin-film reactor powered by the nanosecond HV pulse is significantly higher than in systems previously investigated.

However, further investigation is required to determine the reason for optimal frequencies that give maximum peaks in $Ne$⁠. Yet, as discussed below (Sec. III D), these results have significant influence on observable chemical reactions of PFOA and, therefore, are connected to the chemical activity of the plasma.

Due to higher electron density at the beginning of the pulse, the $Hβ$ with both EHT and AT power supplies was not resolvable. At the end of the decay of the electron density, the electron density was sufficiently low to form a resolvable $Hβ$ peak in order to determine the intensity. Figure 6(a) shows the variation of $Te$ when the frequency varied between 1 and 10 kHz at 16 kV and 40 ns using the EHT power supply. $Te$ varied between 0.4 and 0.6 eV at various frequencies. It was observed that the decay of $Te$ was slower as the frequency increases. Figure 6(b) shows the variation of $Te$ when pulse width was varied between 40 and 200 ns using the EHT power supply at 16 kV and 2 kHz. The $Hβ$ was resolvable later in the pulse as the pulse width increased, and this is due to the increase in peak $Ne$ with increases in pulse width. $Te$ varies between 0.35 and 0.55 eV when we varied the pulse width. Figure 6(c) shows the variation of $Te$ between 0.4 and 0.8 eV when the frequency was varied between 5 and 100 kHz with the AT power supply.

Literature suggests that the reactive species generated by nonthermal plasma, including both oxidative and reductive species, e.g., •OH, e⁻_aq, and Ar⁺, cause a step-wise degradation reaction mechanism of PFOA resulting in the release of fluoride, F⁻.^25,51–53 In the previous work,³¹ using 50 ppm PFOA dissolved in DI water, the production rate of F⁻ $(RF−)$ increased from 2.2 × 10⁻⁹ to 1.57 × 10⁻⁸ mol/s with the increase in pulse frequency from 0.25 to 5 kHz. $RF−$ then decreased from 1.57 × 10⁻⁸ to 7.98 × 10⁻⁹ mol/s when the pulse frequency was increased from 5 to 10 kHz.³¹ Comparing electron density variation in a single pulse (discussed in Sec. III B) with the F⁻ production rate in our previous work, Bulusu et al.³¹ as shown in Fig. 7(a), it is clear that the $RF−$ directly correlates with the peak electron density where both have maximum at 5 kHz.

Figure 7(b) shows that $RF−$ increases from 1.27 × 10⁻⁸ to 2.41 × 10⁻⁸ mol/s with an increase in pulse width from 40 to 200 ns at 16 kV and 2 kHz. Similar to the effect of frequency on the production rate of F⁻ using the EHT power supply, $RF−$ follows the same trend as the peak electron density when varying pulse width where both increase monotonically with pulse width.

Figure 7(c) shows that $RF−$ increases from 1.22 × 10⁻⁸ to 1.79 × 10⁻⁸ mol/s with an increase in frequency from 5 to 20 kHz using the AT power supply. When the frequency was increased from 20 to 100 kHz, $RF−$ decreases from 1.79 × 10⁻⁸ to 1.05 × 10⁻⁸ mol/s. Similar to the cases shown above when we varied frequency and pulse width with the EHT power supply, $RF−$ follows the same trend as the peak electron density in a single pulse with the AT power supply. It is notable that the optimal frequency shifts from 5 kHz with the EHT power supply to 20 kHz with the AT power supply.

Figure 7(d) shows the trends of percentage defluorination with the initial concentration of PFOA for the cases of 12.5 and 200 ppm and the EHT power supply. In this range of concentration, i.e., 12.5–200 ppm, the percentage defluorination follows the same trend as the peak $Ne$ supporting our hypothesis that defluorination depends on the key plasma property of peak $Ne$⁠. The initial concentration of PFOA had a significant effect on $RF−$⁠. $RF−$ with 200 ppm PFOA was an order of magnitude higher when compared with $RF−$ at 12.5 ppm PFOA. The fluoride data can be found in the supporting information (Table S10⁷⁷).

As shown in Fig. 8(a), and in our previous work, the energy yield of F⁻ production $(EYF−)$ decreases with the increase in frequency with the EHT power supply from 0.25 to 10 kHz from 9.12 × 10⁻⁹ to 0.87 × 10⁻⁹ mol/J. Figure 8(b) shows that with an increase in pulse width from 40 to 200 ns, the total discharge power increased from 1.93 to 5.11 W. This increase in total discharge power resulted in the decrease in $EYF−$ from 6.94 × 10⁻⁹ to 4.83 × 10⁻⁹ mol/J. When the frequency was increased from 5 to 100 kHz with the AT power supply, the total discharge power increased from 0.99 to 11.4 W as shown in Fig. 8(c). $EYF−$ decreased from 7.96 × 10⁻⁹ to 0.91 × 10⁻⁹ mol/J. The power data can be found in the supporting information (Table S7⁷⁷, Table S8⁷⁷, and Table S9⁷⁷). It was observed that the decay of energy yield was linear when the pulse width was varied between 40 and 200 ns with the EHT power supply compared with the exponential drops when varying frequency with both power supplies. This suggests that increasing pulse width is more advantageous to improve $EYF−$⁠.

Table IV shows $EYF−$ for mineralization of PFOA to F⁻ using various nonthermal plasma reactors. The best $EYF−$ reported in other plasma systems was 3.42 × 10⁻⁹ mol/J.⁵² The highest $EYF−−$ in our previous work³¹ was 9.12 × 10⁻⁹ mol/J. The highest $EYF−$ with the AT power supply in the present work was 7.96 × 10⁻⁹ mol/J at 5 kHz. The optimum power setting for mineralization/degradation of PFOA was 16 kV, 2 kHz, and 200 ns using EHT where $NF−$ was 23.55 × 10⁻⁹ mol/s and $EYF−$ was 4.83 × 10⁻⁹ mol/J. The gas-liquid continuous film flow reactor is more efficient than other studies using plasma with Ar bubbles,⁴⁷ DBD plasma,⁴⁹ self-pulsing DC plasma,⁵⁰ DC plasma with Ar⁴⁶ and O₂⁵¹ bubbles, gliding arc,⁵² and mesoporous plasma.⁵³ The exact reason for the higher efficiency cannot be determined without further data on electron density and other properties for all of the various reactor configurations. The high electron density and the nanosecond pulses may play important roles in improving the energy yields for this chemical process.

Saleem et al.⁵⁰ suggest that the degradation of perfluoroalkyl substances is induced by electrons (plasma electrons and aqueous electrons), producing highly reactive perfluoroalkyl radicals which then react with •OH. In the present work, liquid- and gas-phase •OH scavengers and their effects on H₂O₂ formation were used to help elucidate the role of •OH on PFOA mineralization. With 1M glycerol dissolved in DI water, a 90% decrease in H₂O₂ concentration was found for 16 kV, 40 ns, and 5 kHz at 2 ml/min using the EHT power supply. Similarly, at 12% CO in the gas phase and DI water in the liquid phase, the H₂O₂ concentration was completely depleted. We introduced the •OH scavengers to 50 ppm PFOA dissolved in DI water and measured the F⁻ production. As shown in Table V, when 1M glycerol was used as a liquid phase •OH scavenger, we did not observe a significant change in the production of F⁻. However, when 12% CO in the gas phase was used as an •OH scavenger, we observed a significant decrease in the production of F⁻. This suggests a possible reaction of PFOA with •OH within the gas-liquid interfacial film to form F⁻ near the gas phase rather than the reaction of •OH through attack from the liquid phase.

Since the DC input voltage for the AT power supply was different at different frequencies, the H₂O₂ data are plotted with discharge power in Fig. 9. Total discharge power data analysis can be found in Sec. III A. Figure 9(a) shows the variation of $NH2O2$ with P using the EHT power supply with frequency in the range of 1–10 kHz. $RH2O2$ increases linearly from 3.04 × 10⁻⁸ to 2.02 × 10⁻⁷ mol/s with the increase in P. With the increase in P, $EYH2O2$ varied slightly between 3.10 × 10⁻⁸ to 2.85 × 10⁻⁸ mol/J. The levelling off of $EYH2O2$ is because the $NH2O2$ and P increased by the same factor when the pulse frequency increased.

Figure 9(b) shows the variation of $NH2O2$ with P when we varied the pulse width between 40 and 200 ns using the EHT power supply. $NH2O2$ increased from 5.79 × 10⁻⁸ to 1.91 × 10⁻⁷ mol/s with the increase in P. When the pulse width increased from 40 to 120 ns, $RH2O2$ increased linearly from 5.80 × 10⁻⁸ to 1.36 × 10⁻⁷ mol/s. It was observed that $RH2O2$ deviates from linearity when the pulse width was increased from 120 to 200 ns. $RH2O2$ increases from 1.36 × 10⁻⁷ to 1.91 × 10⁻⁷ mol/s. $EYH2O2$ gradually increased from 3.16 × 10⁻⁸ to 3.92 × 10⁻⁸ mol/J. The increase in $EYH2O2$ with the increase in pulse width is due to the larger increase in $RH2O2$ than the increase in P.

Similarly, when we increased frequency with the AT power supply between 1 and 100 kHz, $RH2O2$ increased linearly with increases in P as shown in Fig. 9(c). $RH2O2$ increased linearly from 0.69 × 10⁻⁸ to 3.58 × 10⁻⁷ mol/s. $EYH2O2$ levels off with the increase in P around 3.1 × 10⁻⁷ mol/J. Similar to when the pulse frequency of the EHT power supply was varied, P and $RH2O2$ increase by the same factor when the pulse frequency was increased with the AT power supply. The $EYH2O2$ determined in this study was comparable to our previous work.^31,41,64

As shown in Fig. 10(a), variation in the pulse parameters of frequency and pulse width affected $NH2O2$⁠; however, $RH2O2$ increased linearly with P irrespective of the pulse characteristics or the power supply. Figure 10(b) shows that $EYH2O2$ was constant around 3 × 10⁻⁸ mol/J with variation in pulse characteristics with the exception of higher pulse widths with the EHT at 16 kV and 2 kHz, 200 ns, i.e., 3.95 × 10⁻⁸ mol/J. This suggests that longer pulse widths may lead to higher $EYH2O2$⁠.

These data are in agreement with the literature,^12,13 which suggests that $RH2O2$ increases with increase in P. It was observed that there was no change in $RH2O2$ with 50 ppm PFOA dissolved in DI water (Table S7,⁷⁷ Table S8,⁷⁷ and Table S9⁷⁷). The H₂O₂ results in this section show that there is a significant difference in the dependence of $RH2O2$ on plasma properties and pulse properties than those for PFOA degradation. $RH2O2$ was dependent on the total discharge power irrespective of the peak electron density, unlike PFOA. It was also observed that the $RF−$ was at least one order of magnitude lower than $RH2O2$⁠. The contrast between $RH2O2$ and $RF−$ from PFOA illustrates the significant differences in the mechanism in the plasma on these two species. One possible explanation for this would be that •OH recombination for the formation of H₂O₂ (reaction R2 in Table VI) and the attack of •OH on PFOA takes place at different locations in the interfacial region. Further discussion of the role of •OH in PFOA mineralization is given in Sec. III G.

Figure 11 shows a schematic of the gas-liquid interface with corresponding reactions. Rumbach et al.⁶⁶ suggest that plasma in contact with liquid involves length scales on the order of magnitude of 1 nm to capture the free radical chemistry at the interface. Tachibana and Yasuoka⁶⁷ suggest the thickness of a gas-liquid interface to be 0.3–1 nm. Figure 11 shows the density profile of water approximated from Zhang et al.⁶⁰ where the density of H₂O, as determined by molecular dynamic simulations, increases approximately linearly from the gas phase to the liquid phase in a 1 nm interfacial film region. Our previous work¹³ shows that plasma propagates along the gas-liquid interface in our reactor. Water vaporizes into the film region where it dissociates to form •OH and •H (among other reactions) (reaction R1 in Table VI).⁶⁸ Some •OH recombines within the gas-liquid interfacial film to form H₂O₂ (reaction R2 in Table VI). The H₂O₂ dissolves rapidly into the liquid phase.^69–71 CO reacts with the gas-phase •OH to form CO₂ (reaction R3 in Table VI), which escapes to the gas phase. Glycerol scavenges the •OH in the bulk liquid (reaction R4 in Table VI).

PFOA is a surfactant⁷² with a length of 8 Å.⁷³ Zhang et al.⁶⁰ used molecular dynamics to determine the density profiles of a similar compound oligo(ethylene oxide)-2-perfluorooctyl at the gas-liquid interface. We approximated the profiles of PFOA to follow similar patterns to those found by Zhang et al.⁶⁰ since PFOA also has a hydrophobic end and a hydrophilic end (acid group).⁷⁴ The density of the hydrophobic region of PFOA would, thus, be highest in the gas phase at the edge of the interface as indicated in Fig. 11. The density of the hydrophilic end of PFOA (acid group) would be higher in the gas-liquid film region where the water density is higher. As suggested by Thagard et al.,⁷⁵ the hydrophobic end is exposed to the gas phase while the hydrophilic end is exposed to the water, still within the gas-liquid film region, where the possible attack of •OH and •H take place. The decrease in F⁻ production when using 12% CO suggests that •OH plays an important role (but significantly not the only role) within the gas-liquid film on the mineralization of PFOA. If the hydrophilic end group falls within the gas-liquid film, but not fully in the liquid phase as shown in this figure, then •OH, •H, or even e⁻ from the plasma might directly attack the PFOA hydrophilic region leading to the dependency of $NF−$ on peak $Ne$⁠. This dependency of mineralization of PFOA to form F⁻ on peak $Ne$ can be used to optimize the degradation of PFOA by optimizing the peak $Ne$ to higher values.

The dependencies of $RF−$ per pulse and $RH2O2$ per pulse on energy per pulse (discussed in Sec. III A) are shown in Fig. 12. As shown in Fig. 12(a), it was observed that $RH2O2$ per pulse follows the same trend as the energy per pulse when varying the frequency and pulse width. $NH2O2$ per pulse decreased from 3.04 × 10⁻¹¹ to 2.02 × 10⁻¹¹ mol when the energy per pulse decreasing from 0.98 to 0.71 mWs when the pulse frequency was varied between 1 and 10 kHz at 16 kV, 40 ns using EHT. However, $RF−$ per pulse does not follow the same trend as the energy per pulse. $RF−$ per pulse decreased from 7.73 × 10⁻¹² mol to 7.99 × 10⁻¹³ mol with the increase in pulse frequency from 1 to 10 kHz. As shown in Fig. 12(b), it was observed that $RH2O2$ per pulse increased from 2.90 × 10⁻¹¹ to 9.56 × 10⁻¹¹ mol when the energy per pulse increased from 0.92 to 2.44 mWs. When the pulse width was varied between 40 and 200 ns at 16 kV, 2 kHz using EHT, $RF−$ per pulse increased from 6.35 × 10⁻¹² to 1.2 × 10⁻¹¹ mol with the increase in pulse width from 40 to 200 ns. As shown in Fig. 12(c), $RH2O2$ per pulse decreased from 5.69 × 10⁻¹² to 3.59 × 10⁻¹² mol when the energy per pulse decreasing from 0.19 to 0.11 mWs when the pulse frequency was varied between 5 and 100 kHz using AT. $RF−$ per pulse decreased from 2.44 × 10⁻¹²  to 1.04 × 10⁻¹³ mol with the increase in pulse frequency from 1 to 10 kHz.

A possible explanation for the trend of $RF−$ per pulse versus energy per pulse is that $RF−$ per pulse is not solely dependent on the peak electron density. $RF−$ per pulse could also depend on the reaction rates of PFOA with other plasma-formed species such as •OH and •H at the gas-liquid interface. The peak $Ne$ plays an important role in PFOA degradation; however, further investigation is necessary to study the effects of pulse parameters such as pulse frequency and pulse width on the reaction rates of PFOA at the gas-liquid interface. The data reported on temporal evolution of electron density in Sec. III D will be beneficial in future work because the electron density is the major input parameter in studying the chemical pathways in Ar + H₂O plasma.⁷⁶ 

It was observed that the peak $Ne$ increased from 2.28 × 10¹⁸ to 4.45 × 10¹⁸ cm⁻³ with the increase in pulse width from 40 to 200 ns with the EHT power supply at 16 kV, 2 kHz, and 200 ns. However, an optimum frequency was observed with both power supplies where the peak electron densities were maximal. With the EHT power supply, at 16 kV, 40 ns, and 5 kHz, the peak $Ne$ was 3.94 × 10¹⁸ cm⁻³ and with the AT power supply, at 20 kHz, the peak $Ne$ was 1.42 × 10¹⁸ cm⁻³. The peak $Ne$ for the EHT power supply was higher when compared with that for the AT power supply at the optimum frequency. One possible reason could be the difference in operating conditions of the two power supplies. However, further work is required to explain the reason behind the optimum/resonant frequencies for EHT and AT.

PFOA was used as an example and the mineralization/degradation of PFOA was directly correlated to the peak electron density. The highest defluorination of PFOA was observed at the frequency with peak $Ne$⁠. H₂O₂ formation at different pulse frequencies and pulse widths were also reported because H₂O₂ is often used as an indicator or a proxy for •OH formation. It was observed that the formation of H₂O₂ was dependent on total discharge power unlike PFOA that was dependent on peak $Ne$⁠. It was also observed that $RF−$ from PFOA was at least one order of magnitude lower than $RH2O2$⁠. The contrast between $RH2O2$ and $RF−$ from PFOA illustrates the significant differences in the mechanism of plasma on these two species. 12% CO was used as an •OH scavenger in the gas phase and a significant drop in F⁻ formation from PFOA was observed. This suggests that •OH plays an important role in the degradation of PFOA, but that this does not interfere with the formation of H₂O₂. It was also observed that the mineralization/degradation of PFOA was dependent on plasma properties such as electron density but could also depend on the surface reaction rates of PFOA with other plasma-formed species such as •OH and •H in the gas-liquid interfacial film. Based on the results reported, insights into the reaction mechanism for the formation of H₂O₂ and the degradation of PFOA at the gas-liquid interface are provided. On a final note, the correlation between peak $Ne$ and F⁻ from PFOA reported in this work could be used in making the treatment of ground water using nonthermal plasma more efficient through implementation of control strategies to optimize electron density.

This material is based upon support from the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award No. DE-SC-0021371. The work by Shurik Yatom was supported by the Princeton Collaborative Research Facility (PCRF), which is supported by the U.S. Department of Energy (DOE) under Contract No. AC02-09CH11466. Plasma diagnostic resources used in this work were provided by PCRF. The authors would like to thank Youneng Tang (Department of Civil and Environmental Engineering, FAMU-FSU College of Engineering, Tallahassee, USA) and Rachel Gallan (Department of Chemical and Biomedical Engineering, FAMU-FSU College of Engineering, Tallahassee, USA) for fruitful discussions.

The authors have no conflict to disclose.

Radha Krishna Murthy Bulusu: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal). Shurik Yatom: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Validation (equal); Writing – review & editing (equal). Christopher W. Patterson: Investigation (supporting). Robert J. Wandell: Investigation (supporting); Writing – review & editing (supporting). Bruce R. Locke: Conceptualization (lead); Formal analysis (equal); Funding acquisition (lead); Methodology (equal); Project administration (lead); Supervision (lead); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material. In addition, raw data will also be supplied upon reasonable request.