T S Nguyen

C Rond
email: rond@lspm.cnrs.fr

A Vega

X Duten

S Forget

Investigation of hydrogen peroxide formation after underwater plasma discharge

Keywords: Underwater plasma, pulsed electrical discharge, pin-to-pin geometry, electrode erosion, hydrogen peroxide formation

This paper reports investigations on the formation of hydrogen peroxide resulting from micro-pulse plasma discharges obtained in pin-to-pin configuration underwater.

In particular, this study reports the influence of the discharge regime (cathode regime with and without breakdown, and anode regime) as well as that of the discharge energy (from 10 to 45 mJ per pulse). It has been shown that the H 2 O 2 production is higher for high energy and anode regime. In addition, the variation of the pulse width (from 50 to 500 µs) highlights the dependence of the chemical processes induced by the discharge according to the regime. Considering two different electrode materials (tungsten and platinum), we do not observe any significant influence of the electrode material on the H 2 O 2 production, whereas the injected energy depends on the high voltage electrode material. Finally, the erosion of the electrodes have been studied using in-situ optical microscopy and SEM. It is shown that the erosion mechanisms strongly depend on materials, regimes and the polarity of the electrodes.

Introduction

The study of electrical discharges formed under water is of great interest because of their large applications in material, environmental and biomedical sciences [START_REF] Akiyama | Streamer discharges in liquids and their applications[END_REF][START_REF] Bruggeman | Non-thermal plasmas in and in contact with liquids[END_REF][START_REF] Locke | Electrohydraulic discharge and nonthermal plasma for water treatment[END_REF][START_REF] Locke | Special Issue on Plasmas and Liquids[END_REF][START_REF] Šunka | Pulse electrical discharges in water and their applications[END_REF].

Indeed a series of physical and chemical processes formed by discharges in the water lead to the production of various reactive chemical species such as radicals (OH, H, O), molecular species (H 2 O 2 , H 2 , O 2 , O 3 ) and solvated electron (e -) [START_REF] Bruggeman | Non-thermal plasmas in and in contact with liquids[END_REF][START_REF] Šunka | Pulse electrical discharges in water and their applications[END_REF][START_REF] Lukes | Role of solution conductivity in the electron impact dissociation of H2O induced by plasma processes in the pulsed corona discharge in water[END_REF][START_REF] Kirkpatrick | Hydrogen, oxygen, and hydrogen peroxide formation in aqueous phase pulsed corona electrical discharge[END_REF][START_REF] Malik | Water purification by electrical discharges[END_REF]. Their concentrations are obviously strongly dependent on the experimental conditions. In the frame of industrial applications, there is a need to determine these relationships in order to master and optimize the process. Most of the underwater discharges have been performed using pin-to-plate electrode configuration, of which the works of Locke and Lukes groups [START_REF] Lukes | Role of solution conductivity in the electron impact dissociation of H2O induced by plasma processes in the pulsed corona discharge in water[END_REF][START_REF] Kirkpatrick | Hydrogen, oxygen, and hydrogen peroxide formation in aqueous phase pulsed corona electrical discharge[END_REF][START_REF] Grymonpré | Hybrid gas-liquid electrical discharge reactors for organic compound degradation[END_REF][START_REF] Joshi | Formation of hydroxyl radicals, hydrogen peroxide and aqueous electrons by pulsed streamer corona discharge in aqueous solution[END_REF][START_REF] Lukes | The catalytic role of tungsten electrode material in the plasmachemical activity of a pulsed corona discharge in water[END_REF][START_REF] Lukes | Hydrogen peroxide and ozone formation in hybrid gas-liquid electrical discharge reactors[END_REF][START_REF] Holzer | Influence of High Voltage Needle Electrode Material on Hydrogen Peroxide Formation and Electrode Erosion in a Hybrid Gas -Liquid Series Electrical Discharge Reactor[END_REF][START_REF] Sahni | Quantification of Hydroxyl Radicals Produced in Aqueous Phase Pulsed Electrical Discharge Reactors[END_REF][START_REF] Medodovic | Primary chemical reactions in pulsed electrical discharge channels in water[END_REF][START_REF] Locke | Review of the methods to form hydrogen peroxide in electrical discharge plasma with liquid water[END_REF][START_REF] Locke | Analysis and review of chemical reactions and transport processes in pulsed electrical discharge plasma formed directly in liquid water[END_REF] are major contributions in valuable insights in chemical analysis. As an example, it has been shown that the early chemical activity is related to OH and H radicals formed by electron collisions with water molecules in the plasma channel [START_REF] Lukes | Role of solution conductivity in the electron impact dissociation of H2O induced by plasma processes in the pulsed corona discharge in water[END_REF]. It has been also demonstrated that the rate production of molecular hydrogen and hydrogen peroxide is 1:2 [START_REF] Kirkpatrick | Hydrogen, oxygen, and hydrogen peroxide formation in aqueous phase pulsed corona electrical discharge[END_REF] and that the recombination of hydroxyl radicals is the major pathway to H 2 O 2 formation [START_REF] Sahni | Quantification of Hydroxyl Radicals Produced in Aqueous Phase Pulsed Electrical Discharge Reactors[END_REF][START_REF] Medodovic | Primary chemical reactions in pulsed electrical discharge channels in water[END_REF]. A special attention has been paid on the study of hydrogen peroxide production according to the experimental conditions such as the discharge treatment time [7, 9-13, 18, 19] the solution conductivity [START_REF] Lukes | Role of solution conductivity in the electron impact dissociation of H2O induced by plasma processes in the pulsed corona discharge in water[END_REF][START_REF] Kirkpatrick | Hydrogen, oxygen, and hydrogen peroxide formation in aqueous phase pulsed corona electrical discharge[END_REF][START_REF] Lukes | The catalytic role of tungsten electrode material in the plasmachemical activity of a pulsed corona discharge in water[END_REF], the discharge power [START_REF] Lukes | Role of solution conductivity in the electron impact dissociation of H2O induced by plasma processes in the pulsed corona discharge in water[END_REF][START_REF] Kirkpatrick | Hydrogen, oxygen, and hydrogen peroxide formation in aqueous phase pulsed corona electrical discharge[END_REF][START_REF] Joshi | Formation of hydroxyl radicals, hydrogen peroxide and aqueous electrons by pulsed streamer corona discharge in aqueous solution[END_REF][START_REF] Lukes | Hydrogen peroxide and ozone formation in hybrid gas-liquid electrical discharge reactors[END_REF], the gas flow [START_REF] Grymonpré | Hybrid gas-liquid electrical discharge reactors for organic compound degradation[END_REF][START_REF] Međedović | Platinum catalysed decomposition of hydrogen peroxide in aqueous-phase pulsed corona electrical discharge[END_REF], the reactor configuration [START_REF] Lukes | Hydrogen peroxide and ozone formation in hybrid gas-liquid electrical discharge reactors[END_REF], the pH [START_REF] Međedović | Platinum catalysed decomposition of hydrogen peroxide in aqueous-phase pulsed corona electrical discharge[END_REF] and the electrode material [START_REF] Lukes | The catalytic role of tungsten electrode material in the plasmachemical activity of a pulsed corona discharge in water[END_REF][START_REF] Holzer | Influence of High Voltage Needle Electrode Material on Hydrogen Peroxide Formation and Electrode Erosion in a Hybrid Gas -Liquid Series Electrical Discharge Reactor[END_REF][START_REF] Međedović | Platinum catalysed decomposition of hydrogen peroxide in aqueous-phase pulsed corona electrical discharge[END_REF][START_REF] Lukeš | Erosion of needle electrodes in pulsed corona discharge in water[END_REF]. These discharges can produce about k=5.10 -7 M/s of H 2 O 2 with high energy consumption (about 1 J/pulse). An exhaustive review discussing the methods to form hydrogen peroxide in electrical discharges with liquid water is available [START_REF] Locke | Review of the methods to form hydrogen peroxide in electrical discharge plasma with liquid water[END_REF]. It reports that the energy yields are within the range from 0.5 to 1 g.kWh -1 for a very wide range of types of discharge suggesting that a common mechanism drives the H 2 O 2 formation.

In order to reduce this consumption, a needle-to-needle underwater discharge was used with low pulse energy (about 10 mJ) using reduced voltage (< 4 kV) but high frequency (10 kHz) and bipolar pulses [START_REF] Potocký | Needle electrode erosion in water plasma discharge[END_REF]. The electrodes, made either in stainless steel or tungsten, are 1 mm diameter and the solution conductivity is high (from 500 to 1250 µS/cm). They have measured H 2 O 2 concentration up to 5 mM independently of the type of plasma discharge (bridged or not). However, it is known that the erosion of needle electrode involves the modification of the electrical field distribution since it is very sensitive to the electrode curvature radius. It is then possible to observe time evolution of the discharge characteristics, whi ch is not suitable for industrial applications.

As a consequence, in parallel to the H 2 O 2 production measurements, several studies focused on electrode erosion in underwater pulsed discharge [START_REF] Lukes | The catalytic role of tungsten electrode material in the plasmachemical activity of a pulsed corona discharge in water[END_REF][START_REF] Holzer | Influence of High Voltage Needle Electrode Material on Hydrogen Peroxide Formation and Electrode Erosion in a Hybrid Gas -Liquid Series Electrical Discharge Reactor[END_REF][START_REF] Potocký | Needle electrode erosion in water plasma discharge[END_REF][START_REF] Lukeš | Erosion of needle electrodes in pulsed corona discharge in water[END_REF][START_REF] Goryachev | Mechanism of electrode erosion in pulsed discharges in water with a pulse energy of ∼ 1[END_REF][START_REF] Liu | Comparison and Evaluation of Electrode Erosion Under High -Pulsed Current Discharges in Air and Water Mediums[END_REF]. In particular these studies investigated the catalytic effect of W which leads to H 2 O 2 decomposition [START_REF] Lukes | The catalytic role of tungsten electrode material in the plasmachemical activity of a pulsed corona discharge in water[END_REF][START_REF] Holzer | Influence of High Voltage Needle Electrode Material on Hydrogen Peroxide Formation and Electrode Erosion in a Hybrid Gas -Liquid Series Electrical Discharge Reactor[END_REF][START_REF] Potocký | Needle electrode erosion in water plasma discharge[END_REF][START_REF] Kirkpatrick | Effects of Platinum Electrode on Hydrogen, Oxygen, and Hydrogen Peroxide Formation in Aqueous Phase Pulsed Corona El ectrical Discharge[END_REF][START_REF] Patel | Theoretical models of the electrical discharge machining process. II. The anode erosion model[END_REF][START_REF] Dibitonto | Theoretical models of the electrical discharge machining process. I. A simple cathode erosion model[END_REF][START_REF] Xu | An electrochemical discharge drilling method of small deep holes[END_REF][START_REF] Yerokhin | Plasma electrolysis for surface engineering[END_REF]. Possible mechanisms causing electrodes erosion by electrical discharge in water include melting, evaporation, electron/ion bombardment, sputtering, oxidation, cavitation… [START_REF] Goryachev | Mechanism of electrode erosion in pulsed discharges in water with a pulse energy of ∼ 1[END_REF][START_REF] Kumar | Erosion and lifetime evaluation of molybdenum electrode under high energy impulse current[END_REF]. As mentioned previously, most of the studies dealt with pin-to-plane configuration and they focused on the erosion of the HV-pin electrode [START_REF] Lukes | The catalytic role of tungsten electrode material in the plasmachemical activity of a pulsed corona discharge in water[END_REF][START_REF] Holzer | Influence of High Voltage Needle Electrode Material on Hydrogen Peroxide Formation and Electrode Erosion in a Hybrid Gas -Liquid Series Electrical Discharge Reactor[END_REF][START_REF] Goryachev | Mechanism of electrode erosion in pulsed discharges in water with a pulse energy of ∼ 1[END_REF] according to electrode material or solution conductivity. In particular, Lukes et al [START_REF] Lukes | The catalytic role of tungsten electrode material in the plasmachemical activity of a pulsed corona discharge in water[END_REF][START_REF] Lukeš | Erosion of needle electrodes in pulsed corona discharge in water[END_REF] have reported that the anodic electrolysis is the significant form of erosion of the HV electrode [START_REF] Anik | Effect of pH on the Anodic Behavior of Tungsten[END_REF] which can represent 40% of the total erosion process for tungsten or stainless steel electrodes [START_REF] Lukes | The catalytic role of tungsten electrode material in the plasmachemical activity of a pulsed corona discharge in water[END_REF][START_REF] Lukeš | Erosion of needle electrodes in pulsed corona discharge in water[END_REF][START_REF] Liu | Comparison and Evaluation of Electrode Erosion Under High -Pulsed Current Discharges in Air and Water Mediums[END_REF]. In addition, thermal processes of erosion involving melting and condensation have been suggested [START_REF] Lukes | The catalytic role of tungsten electrode material in the plasmachemical activity of a pulsed corona discharge in water[END_REF][START_REF] Lukeš | Erosion of needle electrodes in pulsed corona discharge in water[END_REF][START_REF] Goryachev | Mechanism of electrode erosion in pulsed discharges in water with a pulse energy of ∼ 1[END_REF][START_REF] Liu | Comparison and Evaluation of Electrode Erosion Under High -Pulsed Current Discharges in Air and Water Mediums[END_REF]. Potocký et al [START_REF] Potocký | Needle electrode erosion in water plasma discharge[END_REF] have investigated the erosion of tungsten and stainless steel needle electrodes and the presented results suggest that the erosion mechanisms are similar on HV and GND for both materials and are also related to electrolysis and thermal processes. One mean of reducing the erosion issue is to decrease the diameter of the electrode enough that the discharge characteristics do not depend anymore on the shape of the tip, resulting in the pin-topin geometry that we used in the present work.

In this paper, we report the measurement of H 2 O 2 production and electrodes erosion after underwater discharge using pin-to-pin configuration and low energy for different discharge regimes. Considering these experimental conditions, two different regimes have been identified (cathode and anode regimes) in which three different cases of discharge occur. A detailed description is given in [START_REF] Rond | Time-resolved diagnostics of a pin-to-pin pulsed discharge in water: pre-breakdown and breakdown analysis[END_REF]. As a summary, the cathode regime involve the case 1, in which a bush-like structure propagates from the cathode to the anode, a glow discharge appears on the cathode and no breakdown occurs between the two electrodes; and the case 2, where the bushy structure still appears at the cathode but the discharge spans the electrode gap causing the breakdown. The anode regime corresponds to the case 3, where a filament structure appears and propagates from the anode to the cathode leading to several successive breakdowns.

In this work, a series of experiments were performed for different cases of discharge by changing the applied voltage, the pulse frequency and the pulse duration in order to determine the production of hydrogen peroxide. We also report the effect of different electrode materials (Tungsten and Platinum) on the production of hydrogen peroxide. The final section presents a study of the electrode erosion by the pulsed electrical discharge in water according to the material and the case of the discharge.

Experimental set-up

The scheme of the experimental set-up is presented in Fig. 1. Pin electrodes of 100 µm diameter are covered by an insulating capillary tube. The length of both pin electrodes protruded from the capillary tube in water is about 400 µm (±100 µm).

The distance between the two electrodes is set at 2 mm for all experiments. Most of the experiments are performed using tungsten electrodes, but use of platinum is also considered (see parts 3. The conductivity of the solution is kept constant at σ=200 µS/cm for various experiments by using sodium chloride (NaCl). A magnetic stirring bar at the bottom of the reactor with speed of 200 rpm is used to homogenize the solution.

The concentration of hydrogen peroxide is determined by measuring the absorbance at 410 nm of the product of 2 mL sample with 1 mL of titanyl ions giving a yellowcolored complex [START_REF] Eisenberg | Colorimetric determination of hydrogen peroxide[END_REF]. These ex-situ measurements are performed in Avaspec-DHC2048XL spectrometer. Measurements are performed every 5 minutes during the 30 min long experiment. Uncertainty on H 2 O 2 concentration is estimated to be lower than 2%. Both electrodes are imaged on a CCD Camera (IDS Imaging Development Systems) through a homemade microscope with a (×2)-magnification. A long working distance objective (Mitutoyo plan apochromatic, infinity corrected) was used to take into account the dimension of the reactor and coupled to a tube lens with a f=200 mm focal length. This optical system allowed in situ and real time measurement of the variation of the electrodes length during the plasma discharge (presented in Fig. 1) with an accuracy of about 98%. Morphology and composition of the electrodes after the discharge are also studied ex-situ by using Scanning Electron Microscopy (SEM) and Energy-Dispersive X-ray spectroscopies (EDX) respectively.

For both, H 2 0 2 and electrode length measurements, a minimum of three measurements have been carried out for each experimental condition in order to ensure the reproducibility of the observed phenomena, and to provide reliable analysis of the results.

H 2 O 2 measurements

Basic experimental conditions involve tungsten wire for both electrodes and a pulse frequency fixed at 50 Hz (if no other specification).

Characteristics of the discharge

Fig. 2(a) shows the typical voltage and current waveforms obtained for one pulse with different applied voltages (4, 6 and 9 kV). Detailed analysis of the waveforms can be obtained in [START_REF] Rond | Time-resolved diagnostics of a pin-to-pin pulsed discharge in water: pre-breakdown and breakdown analysis[END_REF]. The value of the applied voltage has been determined in order to obtain the three cases of discharge mentioned previously with f=50 Hz [START_REF] Rond | Time-resolved diagnostics of a pin-to-pin pulsed discharge in water: pre-breakdown and breakdown analysis[END_REF][START_REF] Rond | Influence of applied voltage and electrical conductivity on underwater pin-to-pin pulsed discharge[END_REF]. Indeed, even if the occurrence of the different cases is random for given initial conditions, it is possible to identify a set of experimental conditions that makes a case dominant. Accordingly, case 1, case 2 and case 3 of the discharge correspond to applied voltages of 4 kV, 6 kV, and 9 kV respectively. ). We observe that most of the energy is deposited in the liquid during the first 50 µs of the discharge. Since the variation of the waveforms from pulse to pulse is lower than 10%, we determine the average energy per pulse by considering the average of all the waveforms measured (every 5 min) during the experiment. As an example for the experimental conditions reported in Fig. 2, the average energy per pulse delivered for case 1 is about 12 mJ, for case 2 is 24 mJ and for case 3 is 45 mJ (reported on Fig. 3(b)). We also determined the total energy of the process by integrating the average energy per pulse over the total duration of the experiment considering the fr equency of the pulse generation. Considering the same example, we obtained a total energy equal to 1.1 kJ for case 1, 2.4 kJ for case 2 and 4.1 kJ for case 3.

Production of H 2 O 2

The time evolution of H 2 O 2 production was obtained by sampling 2 mL of the solution every 5 min (Fig. 3 1. Values from about 10 -3 g/h (case 1) to 10 -2 g/h (case 3) were obtained, and are about one order of magnitude lower than those reported in [START_REF] Locke | Review of the methods to form hydrogen peroxide in electrical discharge plasma with liquid water[END_REF]. This difference may be due to the lower energy used in this work, as detailed below. The formation of hydrogen peroxide by pulsed corona discharge in deionized water use to be represented by the global reaction [START_REF] Kirkpatrick | Hydrogen, oxygen, and hydrogen peroxide formation in aqueous phase pulsed corona electrical discharge[END_REF][START_REF] Joshi | Formation of hydroxyl radicals, hydrogen peroxide and aqueous electrons by pulsed streamer corona discharge in aqueous solution[END_REF][START_REF] Medodovic | Primary chemical reactions in pulsed electrical discharge channels in water[END_REF]:

6 H 2 O 2 H 2 O 2 + 4 H 2 + O 2 (1)
Reaction ( 1) is assumed to be directly initiated by the discharge, to be zero-order (considering that the water concentration remains constant) [START_REF] Joshi | Formation of hydroxyl radicals, hydrogen peroxide and aqueous electrons by pulsed streamer corona discharge in aqueous solution[END_REF] and to dominate the other reactions [START_REF] Kirkpatrick | Hydrogen, oxygen, and hydrogen peroxide formation in aqueous phase pulsed corona electrical discharge[END_REF]. Measurements of [H 2 O 2 ] corresponding to case 3 show linear increase in relation to the time, which could be expressed as: , k 1 is the rate constant of reaction (1). This equation shows that reaction (1) dominates the H 2 O 2 production. As a consequence, the rate constant k 1 can be estimated from the slope of the plot, being equal to about = 4.7×10 -7 M/s. This model is not perfectly adapted to describe H 2 O 2 production for case 1 and case 2 because of the presence of an ignition delay. Nevertheless, by using the same approach for case 2 (from 10 min), the estimation of the rate constant provides 2.3×10 -7 M/s, which is 2 times lower than for case 3. The differences between the ignition delay and the estimated rate constant according to the cases suggest that the chemical processes strongly depend on the discharge regime. The values of these rate constants are in good agreement with measurements obtained for needle-to-plate configurations [START_REF] Kirkpatrick | Hydrogen, oxygen, and hydrogen peroxide formation in aqueous phase pulsed corona electrical discharge[END_REF][START_REF] Grymonpré | Hybrid gas-liquid electrical discharge reactors for organic compound degradation[END_REF][START_REF] Joshi | Formation of hydroxyl radicals, hydrogen peroxide and aqueous electrons by pulsed streamer corona discharge in aqueous solution[END_REF][START_REF] Holzer | Influence of High Voltage Needle Electrode Material on Hydrogen Peroxide Formation and Electrode Erosion in a Hybrid Gas -Liquid Series Electrical Discharge Reactor[END_REF]. Using this configuration, the authors have reported up to [H 2 O 2 ] = 2 mM after 30 min, but these performances have been obtained using a very high energy (about 40 times higher than this work) [START_REF] Grymonpré | Hybrid gas-liquid electrical discharge reactors for organic compound degradation[END_REF]. For the same duration, Potocky et al. [START_REF] Potocký | Needle electrode erosion in water plasma discharge[END_REF] have reported H 2 O 2 concentrations equal to 1.8 mM in unbridged conditions (similar to case 1) and equal to 2.7 mM in bridged conditions (similar to case 2 or case 3). These values have been obtained using a needle-to-needle geometry with low energy (10 mJ/pulse) but for high er solution conductivities (at least 500 µS/cm) and higher electrode diameter (1 mm).

As reported in Fig. 2(b), the energy delivered to the discharge depends on the case. efficiency. The calculations of the corresponding energy yield for each case are reported in Table 1. We obtain energy yields from 1.5 g/kWh -1 (case 1) to 4,7 g/kWh - 1 (case 3), which are close to the values reported in [START_REF] Locke | Review of the methods to form hydrogen peroxide in electrical discharge plasma with liquid water[END_REF].

Considering these results, two different parameters are responsible for the increase in H 2 O 2 production: the increase in the energy and the change of the discharge case. In order to discriminate the influence of these two parameters on H 2 O 2 production, the effect of the frequency and the pulse width was inspected.

Case 1 Case 2 Case 3

Production rate (g/h) 9.10 -4 4.10 -3 10 -2

Energy yield (g/(kWh) 1,5 3,3 4,7

Table 1.Hydrogen peroxide production rate and energy yields

Variation of the pulse frequency on the production of H 2 O 2

In order to study independently the influence of both the total energy and the discharge case on H 2 O 2 production, we have performed experiments by decreasing the pulse frequency. This study focuses on only case 2 and case 3 experiments since H 2 O 2 production is very low for case 1.

It is to notice that changing the frequency of the pulse has an influence on the total energy consumption, and also on the characteristics of the discharge. Indeed whereas only case 2 is observed for 6kV-50Hz and 6kV-25Hz, a mix of case 1 and case 2 appears for 6kV-5Hz (Fig. 4). In order to isolate the influence of the total energy only, we have to adjust the applied voltage to ensure that only case 2 is present at 5 Hz, which is the case for U = 8kV. We note that these two experimental conditions (6kV-5Hz and 8kV-5Hz) give similar results in terms of energy and H 2 O 2 production (Fig. 4) since the mix of case 1 and case 2 involves mainly case 2 experiments. The same approach justifies the change of the applied voltage used to obtain only case 3

for different frequencies (e.g. 11kV-5Hz, 10kV-25Hz to obtain the whole discharge process is case 3) (Fig. 4). This means that in order to keep the same case, the decrease of the frequency has to be compensated by increasing the applied voltage. Fig. 4 shows that, for a given case (either for case 2 or case 3), the increase of the energy involves the increase of [H 2 O 2 ]. The evolution is almost linear with a coefficient equal to about 0.12 mM/kJ for both cases. This value is lower than those estimated from Fig. 3(b) (0.19 mM/kJ), which includes the influence of both the total energy and the discharge case. It confirms that both parameters exercise comparable influence on H 2 O 2 production. This result is also observable directly on Fig. 4 which shows that for a same total energy, the concentration of H 2 O 2 in case 3 is greater than that in case 2. For example at 2.5 kJ, case 3 conditions (10kV -25Hz) produce twice more H 2 O 2 than case 2 conditions (6kV-50Hz). These results are in good agreement with the rate constants estimated previously which have shown that is 2 times lower than . These results confirm that chemical processes involved in the discharge mechanisms strongly depend on the discharge regime (case). They are consistent with [START_REF] Locke | Review of the methods to form hydrogen peroxide in electrical discharge plasma with liquid water[END_REF], which suggests that the power is not the only parameter determining H 2 O 2 production.

Effect of pulse duration on the production of H 2 O 2

In order to analyze the effect of the discharge regime on the H 2 O 2 production, the length of the pulse duration is changed from 50 to 500 µs. Fig. 5 presents the results obtained for case 2 (6 kV) and case 3 (9 kV). We observe that increasing the pulse duration from 50 to 500 µs involves a low increase of the deposited energy equal to 25% for case 2 (from 1.8 kJ to 2.25 kJ) and to 12% for case 3 (from 3.7 kJ to 4.1 kJ).

Indeed, as mentioned previously (Fig. 2(b)), most part of the energy is deposited before 50 µs (before the first breakdown).

Uncertainty of [H 2 O 2 ] (2%) is not discernable

Whereas the variation of the energy is similar for both cases, the influence of the pulse duration is different on H 2 O 2 production. From 50 to 500 µs, the concentration of H 2 O 2 increases by 100% for case 2 (from 0.15 to 0.3 mM), but by only 10% for case 3 (from 0.72 to 0.78 mM) (Fig. 5). This result shows that the chemical kinetics initiated by the discharge was very different for case 2 and case 3. Experiments at 50 µs give information on what happens during the pre-breakdown and the breakdown: the chemical mechanisms are much more efficient for case 3 than for case 2 for these stages. To increase the pulse duration from 50 µs to 500 µs means increasing the post-breakdown duration. During this phase H 2 O 2 production is much more efficient for case 2 than for case 3. H 2 O 2 production seems to be mainly driven by the initial stage of the discharge in case 3 whereas the tail of the discharge has also a significant influence for case 2. These results confirm that the chemical processes induced by the discharge are very different according to the regime.

Effect of different electrode materials on H 2 O 2 formation

We have shown that case 3 is more efficient than case 2 for H 2 O 2 production. Even if energy cost and chemical efficiency are important parameters of the process, its durability is also essential. The weak point of such process is the lifetime of the electrodes. According to the physical and chemical mechanisms occurrin g during the discharge, and to the nature of electrode material, the erosion phenomena are very different [START_REF] Goryachev | Mechanism of electrode erosion in pulsed discharges in water with a pulse energy of ∼ 1[END_REF]. Before studying the erosion processes, we propose to investigate for our experimental conditions the influence of the electrodes material on the H 2 O 2 production.

Fig. 6 shows H 2 O 2 concentration obtained using electrodes in tungsten (dotted curve), platinum (solid curve) and a combination of platinum for the anode and tungsten for the cathode (dash and dot curve). The measurements have been performed for 3 different applied voltages and during 30 min of discharge, except for experiments using platinum electrodes at 6 kV and 9 kV (solid curve) because of the total erosion of the cathode (GND) after 10 min. For case 1 and case 2, the electrode material has no influence on the total energy consumed after 30 min of discharge, as already observed by [START_REF] Holzer | Influence of High Voltage Needle Electrode Material on Hydrogen Peroxide Formation and Electrode Erosion in a Hybrid Gas -Liquid Series Electrical Discharge Reactor[END_REF]. For case 3 we observe that the total energy consumed during the experiment is about 20% higher for Pt-W electrodes than for W-W electrodes (using the same applied voltage).

On the whole range of energy, the influence of the electrode material on the H This result is consistent with [START_REF] Holzer | Influence of High Voltage Needle Electrode Material on Hydrogen Peroxide Formation and Electrode Erosion in a Hybrid Gas -Liquid Series Electrical Discharge Reactor[END_REF][START_REF] Potocký | Needle electrode erosion in water plasma discharge[END_REF], which have reported no influence of the electrode material on the initial H 2 O 2 formation rates. However, it has been shown that after several tens of minutes of discharge, tungsten particles dissolved into the bulk solution via the electrodes erosion, lead to H 2 O 2 decomposition by catalysis reactions [START_REF] Lukes | The catalytic role of tungsten electrode material in the plasmachemical activity of a pulsed corona discharge in water[END_REF][START_REF] Holzer | Influence of High Voltage Needle Electrode Material on Hydrogen Peroxide Formation and Electrode Erosion in a Hybrid Gas -Liquid Series Electrical Discharge Reactor[END_REF]. Moreover, it has been shown that hydrogen peroxide concentration can be affected when Pt is used (depending on the pH) [START_REF] Međedović | Platinum catalysed decomposition of hydrogen peroxide in aqueous-phase pulsed corona electrical discharge[END_REF]. Therefore, in addition to limiting the process, the erosion of electrodes by electrical discharge in water can modify the chemical activity in the solution. Even if such catalytic effect has not been observed in our conditions, the erosion of tungsten and platinum electrodes is investigated in detail in the next section.

Erosion of electrodes

The erosion of the electrodes is estimated from the decrease of the length of the protruding part with time. In situ measurements have been performed every 5 min using an IDS camera. Even though the measurements have shown that the erosion is all around the electrodes, the variation of the length is a good indicator to describe the erosion process. Fig. 7 shows the time evolution of the normalized length of positive (HV) and ground (GND) electrodes for experiments performed with either W or Pt at 3 different applied voltage (i.e. different energies per pulse which involve different cases). It is obvious that the erosion of both materials (tungsten and platinum) increase s with the discharge time. However, the erosion of electrodes strongly depends on the material, the case and the energy per discharge.

It is to notice that for case 1 (e.g. discharge in cathode regime without breakdown), the erosion of both electrodes is not significant for both materials (decrease lower than 10%), except for W-anode which shows a fast decrease (85%) after 10 min of discharge. The variation of the electrodes length for case 2 (e.g. discharge in cathode regime with breakdown) is significant for W-anode (55%) and Pt-cathode (85%) but negligible for W-cathode (15%) and Pt-anode (5%). This work does not highlight the influence of the breakdown phenomena on the erosion process for cathode regime neither on W or Pt electrodes, whereas Potocký et al. have shown that the erosion rate for an unbridged discharge was lower than for a bridged discharge with W electrodes [START_REF] Potocký | Needle electrode erosion in water plasma discharge[END_REF].

Nevertheless, when dealing with electrodes discharge -induced erosion, several processes might be considered, as presented in other works [START_REF] Međedović | Platinum catalysed decomposition of hydrogen peroxide in aqueous-phase pulsed corona electrical discharge[END_REF][START_REF] Lukeš | Erosion of needle electrodes in pulsed corona discharge in water[END_REF][START_REF] Liu | Comparison and Evaluation of Electrode Erosion Under High -Pulsed Current Discharges in Air and Water Mediums[END_REF]. One of these processes concerns electrochemical reactions that may occur at the electrodes surface. In the case of tungsten electrodes, the anodic oxidation of W to WO 3 [START_REF] Depetris-Wery | Potentiels standards d'oxydo-réduction en solution aqueuse-Application aux traitements de surface en voie humide[END_REF],

followed by the oxide dissolution into tungstate ions, WO 4 2- [START_REF] Anik | Effect of pH on the Anodic Behavior of Tungsten[END_REF], is to be considered:

(

This mechanism could explain the W-anode length decrease presented in Fig. 7(a)

whereas no significant change is observed for the cathode.

For the platinum electrodes, a significant length variation is only observed at the cathode. Once again, we might take into account the possible cathodic reactions taking place during the process, one of these being oxygen reduction:

(4)

In addition, the presence of chloride ions might have a role in the erosion of Pt electrodes [START_REF] Matsuoka | Degradation of polymer electrolyte fuel cells under the existence of anion species[END_REF] according to the reactions:

(5)

Thus, cathodic reduction of oxygen added to an easier oxidation of Pt electrodes in the presence of chloride ions could explain the significant length change observed at the Pt-cathode.

Regarding breakdown conditions, the erosion of both electrodes is always more important for case 3 (initiation of the discharge from the anode) than for case 2 (from the cathode), which is expected since the energy per pulse is higher in case 3 than in case 2 (Fig. 2(a)). Furthermore, for W electrodes (Fig. 7(a)), erosion is more important at the anode than at the cathode, showing respective variations of 55%/15% for case 2 and 90%/45% for case 3. This result is consistent with experiments performed in plate-plate configuration [START_REF] Liu | Comparison and Evaluation of Electrode Erosion Under High -Pulsed Current Discharges in Air and Water Mediums[END_REF]. Liu et al. suggested that a larger amount of mass is lost from the anode since the arc develops from the anode. This phenomenon can only explain case 3 results since for case 2 the discharge is initiated from the cathode.

In contrast, for platinum electrodes (Fig. 7(b)) erosion is less intense at the anode than at the cathode, showing respective variations of 5%/85% for case 2 and 30%/90% for case 3. These results justify experiments performed with a combination of material using platinum for the anode and tungsten for the cathode. This configuration gives the best result in terms of electrodes erosion. We point out that the evolution of the electrodes showed similar behavior to Fig. 7(a) for cathode and Fig. 7(b) for anode (not shown here).

The decreases in the length are almost linear for all the conditions presented in Fig. 7 , except for the tungsten anode electrode in case 1 (as already reported), and in case 2, for which a fast decrease occurs after 20 min of discharge. These results will be discussed below.

The morphology of the electrodes exposed to the discharge is studied with electronic microscopy. Fig. 8 shows SEM images of anode and cathode for W and Pt electrodes after plasma discharge in water. Complementary SEM images (pin orientation and higher magnification) are provided in supplementary material 1 . These images confirm the results shown in Fig. 7. The initial shapes of the electrodes are sharp and they became rounded after discharge exposure, except for HV-Pt, GND-W and more slightly for GND-Pt used in case 1 (Fig. 8 The results show the diversity of the surface states according to the polarity and the materials, which confirms that many physical and chemical processes take action on electrodes erosion during pulse discharges in water [START_REF] Lukeš | Erosion of needle electrodes in pulsed corona discharge in water[END_REF][START_REF] Goryachev | Mechanism of electrode erosion in pulsed discharges in water with a pulse energy of ∼ 1[END_REF][START_REF] Liu | Comparison and Evaluation of Electrode Erosion Under High -Pulsed Current Discharges in Air and Water Mediums[END_REF].

We remind that case 1 corresponds to cathode initiation of the discharge which does not span the electrodes gap. Based on previous studies [START_REF] Potocký | Needle electrode erosion in water plasma discharge[END_REF][START_REF] Lukeš | Erosion of needle electrodes in pulsed corona discharge in water[END_REF][START_REF] Liu | Comparison and Evaluation of Electrode Erosion Under High -Pulsed Current Discharges in Air and Water Mediums[END_REF], we can state that for case 1, the dominant process that causes the electrode erosion is electrochemistry involving anodic electrodissolution (anodic oxidation + electrolyte dissolution). Indeed, the erosion process is only significant for HV -W electrode, which presents a lower standard potential than platinum. This result is also confirmed by EDX measurements which reports almost 17% of oxygen on the HV-W surface whereas no

[O] trace is detected for other electrodes. It has been suggested that electrolysis is

(b) (c)

most predominant before the formation of the conductive channel in the water but when electrons arrive to the anode, they inhibit the anodic electrodissolution [START_REF] Lukeš | Erosion of needle electrodes in pulsed corona discharge in water[END_REF].

As a consequence, we observe that for case 2 (cathode initiation with breakdown), the body of HV-W also shows typical patterns for electrochemical oxidation process, i.e. the surface is not smooth anymore whereas the tip of the electrode, which receives a high electron bombardment through the conductive channel, shows mainly protrusions. On the contrary, the HV-Pt electrode presents a smooth surface. Thermal processes are primarily responsible for the erosion which is due to melting (evaporation can also be considered) followed by condensation. The differences observed on the surface roughness can be explained by the physical prop erties of tungsten and platinum. Tungsten has much higher thermal conductivity than platinum which leads to a faster solidification of the tungsten surface after melting. As a result, the molten tungsten part quickly solidifies to produce a thorny structure on the tip of electrode surface, while a slower solidification of platinum leads the smoother electrode surface [START_REF] Lukes | The catalytic role of tungsten electrode material in the plasmachemical activity of a pulsed corona discharge in water[END_REF][START_REF] Holzer | Influence of High Voltage Needle Electrode Material on Hydrogen Peroxide Formation and Electrode Erosion in a Hybrid Gas -Liquid Series Electrical Discharge Reactor[END_REF][START_REF] Lukeš | Erosion of needle electrodes in pulsed corona discharge in water[END_REF]. Both ground electrodes also show patterns characteristic to thermal processes but we also report spherical cavities that can be due to ions bombardment.

For case 3, the energy per pulse is higher so the electrochemical and bombardment processes are no more significant in comparison to thermal effect. Surface patterns of the electrodes are quite similar to those observed for case 2, except for GND-Pt which shows smooth crater like surface with no more cavities.

It is to notice that cracks have been observed on W-electrodes which can be explained by the fact that at high temperatures, tungsten recrystallizes and becomes brittle [START_REF] Ceccato | Filamentary plasma discharge inside water: initiation and propagation of a plasma in a dense medium[END_REF], whereas platinum is known to be fragile. This property can explain the break of the electrode tip reported for HV-W in case 1 and case 2 after 10 and 20 minutes of discharge, respectively.

Conclusion

We studied the formation of hydrogen peroxide in water by pin-to-pin micro-pulsed discharge and the resulting electrodes erosion. We have estimated concentrations of H 2 O 2 for the three different discharge modes of operation: case 1 (cathode regime -no breakdown), case 2 (cathode regimebreakdown) and case 3 (anode regimebreakdowns). Besides different mechanisms, the cases also consume different total energies (estimated over 30 min of process): case 1 -1.1 kJ, case 2 -2.2 kJ and case 3 -4.1 kJ. We report that the concentration of H 2 O 2 changes with both the cases and the energy, the influence of these two parameters being in the same order of magnitude. On the one hand, we have reported that the hydrogen peroxide concentration increases linearly with the total energy. On the other hand , we have shown that, for a given energy, case 3 produces more H 2 O 2 than case 2. The highest concentration of H 2 O 2 is formed for discharges propagating from the anode. Moreover, we have highlighted that the post discharge plays an important role in case 2, whereas it does not affect significantly the concentration of H 2 O 2 in case 3.

These results confirm that the two discharge regimes (catho de and anode) involve very different initiation and propagation mechanisms, which result in different chemical mechanisms.

Finally, we have demonstrated that the production of H 2 O 2 does not depend on the electrode materials by comparing tungsten and platinum. Regarding the strong erosion occurring during the process, we have performed experiments with a combination using W-cathode and Pt-anode that allows improving the process lifetime. Time evolution of the electrodes' length and SEM images provide new and complementary results in order to study the erosion processes according to the discharge cases, the material and the polarity of the electrodes. We suggest that for case 1, the dominant process of electrode erosion is electrochemistry (anodic oxidation followed by electrolyte dissolution) which is only significant at the anode.

For case 2 and case 3, this process is no more significant but thermal processes are dominant in the erosion process. This work contributes to a better understanding of pin-to-pin micro-pulsed discharges in water. H 2 O 2 measurements together with the erosion study highlight very different mechanisms involved in the discharge according to the case. Studying H 2 O 2 concentration is the first step to study the complex chemical activities in the solution after plasma discharge. Chemical components are thought to have many applications in wastewater treatment, medicine, and biology.

  5 & 4). The pin-to-pin geometry of electrodes has been used in two different reactors for two different kinds of experiments. Experiments investigating H 2 O 2 concentration during the discharge are performed in a 200 mL cylinder glass reactor, whereas experiments dedicated to the variation of electrodes length involve a 150 mL rectangular reactor including two parallel silica windows for optical access. Changing the shape and the volume of the vessel does not involve significant variations on the final results on either H 2 O 2 or electrodes measurements (lower than the estimated uncertainties). The high voltage pulsed power supply consists of a low inductance capacitor (C = 1 nF) charged by a 30 kV DC high voltage supply passing through a 30 kΩ resistor which discharges through a fast high voltage solid-state switch (Behlke HTS 301-03-GSM). The positive high voltage pulse has a rising time equal to 30 ns and adjustable pulse duration from Δt = 50 µs to 1 ms. The pulse frequency is adjusted from f = 5 Hz to 100 Hz and the voltage range is between U = 4 kV and 11 kV. Discharge voltage and current waveforms are measured via a Tektronix high voltage probe connected to the high voltage electrode and a 10 Ω resistor connected with the ground electrode respectively. Both signals are recorded by a digital oscilloscope (Lecroy HDO9104) every five minutes during the 30 min long experiment.

Fig. 1

 1 Fig. 1 Schematic diagram of the experiment set-up (150 mL rectangular reactor is shown).

Fig. 2

 2 Fig.2 Typical electrical waveforms of pin-to-pin discharge generated in water: V = 200 mL, f = 50 Hz, Δt = 500 µs, 2 mm of gap, and σ = 200 µS/cm); (a) Voltage and Current signals and (b) Time evolution of the energy per pulse

Fig. 3

 3 Fig. 3 Hydrogen peroxide concentration for three different cases (applied voltages). (a) Concentration of H 2 O 2 as a function of time. (b) Final concentration of H 2 O 2 as a function of total energy (measured after 30 min) (V = 200 mL, f = 50 Hz, Δt = 500 µs, 2 mm of gap, σ = 200 µS/cm). Uncertainty of [H 2 O 2 ] (2%) is not discernable.

Fig. 3 (

 3 Fig.3(b) presents the H 2 O 2 concentration measured after 30 min of discharge according to the total energy consumed during the experiment. The highest the total energy, the highest the H 2 O 2 concentration, and the relationship is quite linear with a coefficient of about 0.19 mM/kJ which can be interpreted as the H 2 O 2 formation

Fig. 4 H

 4 Fig. 4 H 2 O 2 concentration according to the total energy for 2 different cases (V = 150 mL, Δt = 500 µs, 2 mm of gap, σ = 200 µS/cm) -couples "applied voltagefrequency" are reported. Uncertainty of [H 2 O 2 ] (2%) is not discernable.

Fig. 5 H

 5 Fig. 5 H 2 O 2 production measured for different pulse durations (Δt =50,100,500 µs) and reported for 2 different cases (V = 200 mL, f = 50 Hz, 2 mm of gap, σ= 200 µS/cm).

Fig. 6 .

 6 Fig. 6. The effect of electrode material on the production of H 2 O 2 by the discharge in water (V = 200 mL, f = 50 Hz, Δt = 500 µs, 2 mm of gap, σ = 200 µS/cm). HV means anode and GND is for cathode. Uncertainty on [H 2 O 2 ] is not discernable (2%)

2 O 2 production

 22 is low. At very low energy (1.08 kJ), H 2 O 2 is not detected either with Ptelectrodes or with Pt-W electrodes, whereas a low concentration is measured with Welectrodes ([H 2 O 2 ] = 0.065 mM). For medium energy (~2 kJ), the concentrations of H 2 O 2 are similar whatever the electrode material (~0.25 mM). Finally at high energy (4-5 kJ) the concentration of H 2 O 2 generated after using the combination of two different materials for the electrodes is similar to the production obtained with Welectrodes (for a given energy).

Fig. 7

 7 Fig. 7 Variation of normalized length of anode and cathode electrodes as a function of time, (a) tungsten electrodes, (b) platinum electrodes (V = 150 mL, f = 50 Hz, Δt = 500 µs, 2 mm of gap, σ = 200 µS/cm). Uncertainty of measurement is not discernable (2%)

  (a)); as well as for HV-Pt and GND-W used in case 2 (Fig.8(b)), conditions for which the erosion process is not significant.

Fig. 8

 8 Fig. 8 SEM images of the eroded tip of tungsten and platinum electrodes after the electrical discharge obtained for (a) case 1 (4kV), (b) case 2 (6 kV) and (c) case 3 (9kV), anode and cathode are shown on left and right respectively (V = 150 mL, f = 50Hz, Δt = 500µs, 2mm of gap, and σ = 200 µS/cm) with a ×500 magnification

Acknowledgment

This work bearing the reference ANR-11-LABX-086 has benefited from State aid managed by the National Research Agency under the Future Investments program with the reference number ANR-18-IDEX-0001

The authors would like to thank the technical support in LSPM and LPL for providing the SEM, EDX and UV-Vis analyses.


T S Nguyen

N Fagnon

A Vega

X Duten

S Forget

C Rond
email: rond@lspm.cnrs.fr

Cr(VI) reduction by microsecond pin-to-pin discharges generated in an aqueous solution

Keywords: electrical discharge, water depollution, Cr(VI) removal

The total reduction of Cr(VI) by microsecond pin-to-pin electric discharge generated in aqueous solution has been reported. [Cr(VI)] and [H 2 O 2 ] were measured simultaneously by UV-vis absorption spectroscopy during the process. The kinetics of the Cr(VI) reduction resulting from the discharges is found to be pseudo zero order rate. The influence of the electron properties has been studied by varying the applied voltage and the electrode gap showing a better reduction for a higher electric field. In addition pH and conductivity of the solution have been measured before and after the process. The analysis of the chemical kinetics has been completed by varying the pulse duration of the discharge. The results show that the reduction occurs both during the plasma and the post plasma phases. It is also noted that the increase of the pulse duration involves a better Cr(VI) reduction, a higher [H 2 O 2 ] production and a more important change in conductivity.

Introduction

Hexavalent chromium Cr(VI) pollution in water represents a current health and society issue worldwide since this compound is a CMR agent (Carcinogenic, Mutagenic and Reprotoxic). This pollution is mainly related to industrial applications in many fields such as energy production, waste and wastewater managements, paints and pigments, metal plating, tanning and steel industries [1,2]. The effluent from these industries can contain Cr(VI) at concentrations ranging from tenths to hundreds of mg/L. These values are much higher than the recommended dose thresholds. Chromium emission limits in the aquatic environment are mainly regulated on a national scale (no universal regulation), depending on the source of pollution, the receiving water body and the chromium speciation. As an example for drinking water, the European Union and the United States of America have set the above limit to 0.05 mg/L and 0.1 mg/L of total chromium respectively, whereas World Health Organization suggests 0.05 mg/L for Cr(VI) [1].

Different techniques are considered to remove Cr(VI) from wastewaters either using chemical treatment (chemical reduction, adsorption, ion exchange, electrocoagulation), biological approaches (biosorption, bioaccumulation, bioreduction, phytoremediation) or physical processes (permeable reactive barriers, solidification) [3][4][5]. Most of them involve the reduction process of Cr(VI) to the less mobile and less toxic form Cr(III). Most techniques reach high removal efficiency (>90%) but few of them report a total removal which represents a limitation since heavy metals are highly toxic even at very low concentration [START_REF] Wilbur | Toxicological profile for chromium, Agency for Toxic Substances and Disease Registry (US)[END_REF]. Moreover, none of these techniques has become dominant since they all involve different pros and cons. For example, biological methods are considered as potential and eco-friendly but the processes take a lot of time to be completed [2,4,5].

Among the physico-chemical methods, plasma in interaction with liquid can be considered as a promising remediation technology since first studies show encouraging results [START_REF] Bobkova | [END_REF][8][START_REF] Chen | Reduction of aqueous chromium(VI) by plasmatreatment of wastewater[END_REF][START_REF] Zhang | [END_REF][11][12][START_REF] Du | Plasma Remediation Technology for Environmental Protection[END_REF][START_REF] Jiang | [END_REF][START_REF] Harianti | AIP Conference Proceedings[END_REF][START_REF] Wang | [END_REF][17][18]. For example, Wang et al. reported that the energy efficiency of Cr(VI) reduction in glow discharge plasma (GDP) is higher than those in semiconductor photocatalysis and comparable to that in electrolytic reduction with Fe electrode [START_REF] Wang | [END_REF]. But to the best of our knowledge, no plasma-liquid interaction (PLI) techniques has reported a total removal of Cr(VI), only almost 100% of reduction is reported [11,[START_REF] Du | Plasma Remediation Technology for Environmental Protection[END_REF]17]. One of the main drawback of these processes is the pseudo 1 st order kinetics that involves an exponential decay of [Cr(VI)]. As a consequence the initial decrease of [Cr(VI)] is fast but the total removal is not obtained. As an example, some works reported a decrease by a factor of two of the initial [Cr(VI)] concentration in about 2 min but a horizontal asymptote is reached after 3 min of process corresponding to a non-zero concentration [START_REF] Bobkova | [END_REF]18].

It is known that discharges above or inside a solution results in the formation of reactive species in the liquid phase such as H 2 O 2 ,  H,  OH or solvated electrons. A list of reactions have been detailed in several papers [18][19][20] and examples are reported in Table 1 (reactions 1-4). These species can be involved in the redox processes between Cr(VI) and Cr(III). Some of the main reduction mechanisms of Cr(VI) by PLI discussed in the literature have been reported in Table 1 [START_REF] Bobkova | [END_REF]11,17,21]. Reactions are reported by considering either the ion global form of Cr(VI) (Reaction 5) or the more specific forms (Reactions 6-12). Indeed Cr(VI) exists in solution with different speciation according to pH including H 2 CrO 4 , HCrO 4 -, CrO 4 2-and CrO 7 2- [2,5]. The removal of Cr(VI) is known to be more efficient in an acidic environment. This effect could be attributed to three reasons [START_REF] Jiang | [END_REF]: (i) The pH of the solution affects the existing form of Cr(VI) in the solution, and the oxidation potential of Cr(VI) increases when the pH decreases, then facilitating the reduction process ; (ii) Under acidic conditions, the amount of H + ions is increased, which enhances the reducing efficiency of the process (reactions Despite several studies that have reported the feasibility of Cr(VI) reduction by PLI, the total removal is still challenging as well as the identification of the reactions mechanisms for Cr(VI) reduction [21].

This work reports a plasma in liquid process able to completely reduce Cr(VI) in solution. Moreover, parametric studies on the applied voltage and the interelectrode gap is performed in order to better understand the mechanisms mainly responsible for Cr(VI) reduction. In addition to [Cr(VI)] measurements, chemical analyses of the solution have been performed reporting the variation of the pH and the conductivity as well as the hydrogen peroxide concentration during the PLI process. Finally, the pulse duration is varied to provide new insights into kinetics analysis of Cr(VI) reduction.

Experimental set up

A description of the plasma set-up has been previously detailed in [22,23]. A general schematic of the microsecond plasma system in liquid using a pin-to-pin configuration is shown in Electrical measurements are performed using a HV probe (LeCroy PMK 20 kV, 1000:1, 100 MHz), a shunt current (R=10 Ω connected to Lecroy PP023 probe) and an oscilloscope (HDO9104 -1GHz, Teledyne LeCroy). Typical voltage and current waveforms are reported in Fig. S1 and values of injected energy are also provided in Table S1, in supplementary file. Readers can refer to [22,24] for the description of the electrical signals. In summary, two main regimes of discharge can be identified using the electrical signals: one regime only reports a transient current corresponding to the plasma formation at the electrode tips (bush-like structures) whereas the other one involves a breakdown (resulting from the plasma connection across the gap) which results in voltage drop and current peak as well as strong light emission (see Fig. S2, in supplementary file). It is noted that the distribution of the two discharge regimes during the process is monitored thanks to a dedicated data processing program. For both regimes the plasma discharge occurs during the first 10 µs according to both light emission and current signals. More specifically the charges are mainly injected during the first ten microseconds for no breakdown and even faster for breakdown since the breakdown phenomenon is not measured after 4 µs. From 10 µs to the end of the pulse duration, the voltage is about 1-2 kV and the current is too small to be detected by the acquisition system (<1 mA).

Cr(VI) solution with a concentration equal to 50 mg/L ( 0. In this paper all the results will be discussed in terms of [Cr(VI], including all the forms of the species. The measurements of Cr(VI) concentration have been performed every 15 minutes during the treatment process by sampling 2 mL of the treated solution and using UV-vis absorption spectrophotometry at 350 nm (AvaSpec-2048 XL, Avantes). Moreover additional measurements using DPC (1.5-diphenylcarbazide), a reagent forming a complex with Cr(VI) that ensures selectivity and lower detection limit [25], are also performed periodically to confirm the results for low concentrations.

The concentration of H 2 O 2 is measured by a colorimetric method using ammonium metavanadate (NH 4 VO 3 ) [START_REF] Vasko | Microplasmas for gas phase hydrogen peroxide production[END_REF]. The method is based on measuring the absorption at 440 nm of the complex NH 4 [VO(O 2 )SO 4 ] formed by the reaction between H 2 O 2 and NH 4 VO 3 under acidic conditions. The measurements are performed every 15 minutes by mixing 2 mL of the treated solution with 1 mL of 0.06 M NH 4 VO 3 . We note that this method allows measuring [H 2 O 2 ] and [Cr(VI)] simultaneously.

Measurements of [Cr(VI)

] and [H 2 O 2 ] have been repeated several times for the same experimental condition and the corresponding standard deviation is calculated (example for [Cr(VI)] in Fig. S3 in supplementary file). The corresponding values are reported as error bars in the figures.

The measurements of the conductivity and the pH of the treated solution are performed before and after the process using dedicated probes (SensION+ EC71, HACH and SensION MM340, HACH, respectively). The experiments are performed at room temperature and only a slight increase in liquid temperature is reported after 2 h of process.

Different initial parameters are changed within this study: the inter-electrode distance is equal to either 2 or 5 mm using micrometer control system; the applied voltage is changed from U = 2 kV to 11 kV and the pulse duration varies from Δt = 10 µs to 1 ms. The repetition rate of the process is constant and equal to 50 Hz. The process duration is defined to be equal to maximum 2 hours.

Results and discussions

Kinetics of the Cr(VI) reduction

For all the conditions used in the frame of this work (changing the applied voltage, the pulse duration or the gap), it is reported that the evolution of Cr(VI) concentration during PLI process is linear with time (coefficient of determination R² > 0.98). As an illustration, Fig. 2 shows the results obtained for different applied voltages. This linear trend is very different from other evolutions reported in the literature for Cr(VI) reduction by PLI which have shown exponential decay [START_REF] Bobkova | [END_REF]11,17,18]. These works generally refer to first order kinetics which involves that (i) the reverse process (oxidation) occurs along with the reduction process and (ii) the rate of reduction is related to the initial concentration of Cr(VI) [START_REF] Bobkova | [END_REF]. In this work, the linear evolution refers more to pseudo-zero order mechanism. In accordance with this result, it is also observed in Fig. 2 that the reduction rate does not strongly depend on the initial concentration of Cr(VI) when it is divided by two: it is equal to 0.4 mg.L -1 /min for 47 mg/L and to 0.32 mg.L -1 /min for 23.5 mg/L. It is known that two general conditions can result in zero-order rates [START_REF] Petrucci | General chemistry : principles and modern applications[END_REF]:

-Only a small part of the reactants are in a configuration (place or state) in which they are able to react, and this amount is continually supplied from a larger pool (as for catalyze). We can consider that this effect happens if Cr(VI) is reduced at the interface between the gas phase and the liquid, the interface acting like the catalyst for the reactivity limitation.

-For multi-components process, the concentration of one reactant is much greater than those of other(s). This assumption is possible if Cr(VI) reduction is directly related to H 2 O (aqueous solution) or to species produced in abundance by H 2 O dissociation.

Then considering a pseudo-zero order assumption, the kinetics of Cr(VI) concentration can be written as:

with the rate constant of the reduction process. Of course the rate constant is effective, including the concentrations of species generated by the discharge that participate in the reduction process [START_REF] Bobkova | [END_REF]. The measurements show that the reduction rate increases with the applied voltage, from 0.21 mg.L -1 /min at 7 kV to 0.53 mg.L -1 /min at 11 kV (Fig. 2). It is to notice that no reduction is observed for 2 kV, suggesting that electrolysis effect alone cannot reduce Cr(VI) (also shown by [17]). Moreover it is observed that Cr(VI) is totally reduced in 120 min of PLI process (with gap = 2 mm and pulse duration = 500 µs) at 9 kV and in 90 min at 11 kV.

The distribution of breakdown/no breakdown discharge changes with the applied voltage (Table S2 in supplementary file). As expected, the number of breakdowns increases with the applied voltage. Additional measurements are performed by changing the interelectrode gap from 2 to 5 mm in order to avoid breakdown phenomenon. In this case, Cr(VI) reduction is still significant (Fig. S4 in supplementary file), e.g. the reduction rate is equal to 0.39 mg.L -1 /min for 10 kV. These new result show that breakdown does not play a main role in Cr(VI) reduction. Moreover it is observed that increasing the gap from 2 to 5 mm leads to slightly decrease the reduction rate. As an example for applied voltage of 9 kV, the reduction rate decreases from 0.4 to 0.35 mg.L -1 /min for 2 and 5 mm respectively.

Results obtained by changing the gap and the applied voltage suggest that electric properties of the plasma has an influence on Cr(VI) reduction mechanisms. To go further, additional measurements dedicated to the chemical analysis of the process, such as pH, conductivity and [H 2 O 2 ] are discussed hereafter.

pH evolution

In this work, the maximum variation of pH observed after two hours of process is an increase of 0.1 (from 2.3 to 2.4) which corresponds to an increase in [H + ] equal to 1 mM. In acid conditions Cr(VI) reduction can either consume or produce H + , by reactions 6-8 and 5 (Table 1) respectively [START_REF] Zhang | [END_REF]12,[START_REF] Harianti | AIP Conference Proceedings[END_REF]17]. However it is noted that changes in pH at values around 2 might be affected by buffer capacity of water, so the variation in pH could not be directly related to variation in [H + ]. In our conditions the pH variation is not directly related to the Cr(VI) reduction since the same increase of 0.1 is observed for a Cr(VI) reduction rate equal to 0.21 mg.L -1 /min (7 kV) and 0.53 mg.L -1 /min (11 kV). The increase in [H + ] during plasma discharge in aqueous liquid can also be related to other processes as reactions 2 and 4 (Table 1).

This result is consistent with the literature showing that hydronium ions are deeply involved into Cr(VI) chemistry. It is reported that the variation of the pH during the Cr(VI) reduction does not depend on the plasma type (above or inside the liquid) but it relies on the initial pH of the solution: for acid solution, the pH slightly increases whereas for initial pH>5, the pH of the solution decreases during the process [11,12,17].

Change in solution conductivity

At the beginning of the experiments, the solution conductivity is about 4 mS/cm. After two hours of plasma process, the conductivity decreases significantly depending on the experimental conditions. This result has been also observed in other papers for above and inside liquid processes, e.g. in [17] the conductivity decreases from 5 to 4.6 mS/cm after 20 min of GDP in Cr(VI) solution.

Fig. 3 reports the change in conductivity after 2 hours of process in relation to the reduction rate for 2 and 5 mm gaps. It shows that the decrease of the conductivity is more important for high reduction rate, but no direct relationship is observed. Indeed, a given reduction rate is related to different changes in conductivity depending on the gap. As an example, for a reduction rate equals to about 0.2 mg.L -1 /min, the change in conductivity is equal to -0.23 and -0.44 mS/cm for 5 and 2 mm respectively (at 7 kV). The decrease of the solution conductivity is related to the global chemical activity initiated by the plasma, not only the Cr(VI) reduction.

Wang et al. assumed that, because the mobility of H + is much higher than that of Cr 3+ , the decay of the solution conductivity is a consequence of the production of Cr 3+ (due to Cr(VI) reduction) and the decrease of [H + ] (pH increase) [17]. This correlation between the variations of pH and conductivity is not observed in our conditions since the variation of the pH is always close to 0.1 whereas the change in conductivity varies from -0.23 to -0.99 mS/cm. However the mobility of chromium in aqueous fluids strongly depends on its oxidation state. In contrast to Cr 3+ species, Cr(VI) is considered to be relatively mobile [START_REF] Watenphul | [END_REF] [29] so the reduction of Cr(VI) in Cr(III) can result in the decrease of the solution conductivity. This assumption can only explain partially the results observed in Fig. 3 since a total reduction of Cr(VI) does not involve the same final conductivity. Indeed, it is noted that reduction efficiency of 100% is obtained at 10 kV for both gaps but with very different changes in conductivity, being equal to -0.53 and -0.98 mS/cm for 5 and 2 mm respectively. Fig. 3 shows that the decrease of the conductivity is more important with high applied voltage and low interelectrode gap, i.e. with high electric field. For example, at 5 mm gap the variation of the conductivity is equal to -0.23 mS/cm for 7 kV and -0.53 mS/cm for 10 kV. It is also observed that for 10 kV the variation changes from -0.53 to -0.98 mS/cm when the gap decreases from 5 to 2 mm. These results confirm that the reaction mechanisms strongly depend on the electron properties initially generated by the discharge. The chemistry activated by the plasma is complex and results in the production and the consumption of a lot of other species that can also modify the conductivity. The electric discharge initiates the generation of reactive oxidizing or reducing species such as  H,  OH, H 2 O 2 , . These species can diffuse in the liquid phase and induce oxidation/reduction reactions with dissolved elements. To give a first insight of the chemical activity, simultaneous measurements of [H 2 O 2 ] and [Cr(VI)] have been performed for different experimental conditions.

Measurements of H 2 O 2 concentration

The species that are the most effective in reducing Cr(VI) have not been identified yet, but some works assume that H 2 O 2 can play a major role [START_REF] Chen | Reduction of aqueous chromium(VI) by plasmatreatment of wastewater[END_REF]12,21]. Although H 2 O 2 and Cr(VI) reactions are quite slow and require acidic medium (Table 1), H 2 O 2 is very interesting to monitor because it is a long lived specie and one of the major products formed in aqueous solution by PLI. The literature highlights the role of H 2 O 2 in Cr(VI) reduction for PLI above liquid showing that hydrogen peroxide plays a major role but it is not the sole factor [START_REF] Chen | Reduction of aqueous chromium(VI) by plasmatreatment of wastewater[END_REF]12,21]. However comparisons between Cr(VI) and H 2 O 2 concentrations have never been presented for direct PLI in Cr(VI) solution. Some studies have been performed in more complex solutions including phenol [START_REF] Harianti | AIP Conference Proceedings[END_REF] or arsenic [START_REF] Jiang | [END_REF], which leads to more difficult chemical analysis. In this work, the concentration of H 2 O 2 and Cr(VI) are measured simultaneously by UV-Vis absorption method (as detailed in section 2). Fig. 4 shows the relation between [Cr(VI)] and [H 2 O 2 ] for different applied voltages and gaps (in molar concentration). For a given condition, four measurements are presented corresponding to different sampling times [START_REF] Harianti | AIP Conference Proceedings[END_REF]45,90, and 120 minutes). It is shown that the higher values of [H 2 O 2 ], the lower Cr(VI) concentrations. We note a good agreement with the literature [START_REF] Du | Plasma Remediation Technology for Environmental Protection[END_REF][START_REF] Jiang | [END_REF]30] showing that the reduction of Cr(VI) in an acidic environment increases when the concentration of H 2 O 2 increases. We also note that the relationship between [Cr(VI)] and [H 2 O 2 ] is not linear. For example, Cr(VI) concentration decreases significantly (from 0.9 mM to about 0.4 mM) despite very low H 2 O 2 concentrations (less than 0.1 mM). In particular, for 7 kV half of the Cr(VI) is reduced after 120 minutes for both gaps, and the concentration of H 2 O 2 is equal to about 0.1 mM for 2 mm and 0.05 mM for 5 mm. Moreover, for 10 kV we can observe that [Cr(VI)] is completely removed when [H 2 O 2 ] is about 0.3 mM for 5 mm gap, while in the case of 2 mm, the complete removal of Cr(VI) is achieved when [H 2 O 2 ] is about 0.42 mM. These phenomena can be explained by the fact that H 2 O 2 is not the only species involved in the reduction of Cr(VI). As an example, Chandana et al. have reported that in acidic medium, Cr(VI) reduction depends on both H 2 O 2 and H + [12]. To go further on this assumption, measurements of [H 2 O 2 ] without Cr(VI) in solution have been performed in the same experimental conditions. Results have been given after 30 min of discharges (at 9 kV -50 Hz) (Fig. S5 )] would be related to a consumption of about 0.35 mM of H2O2, which is very low comparing to 0.62 mM. This result confirms that there are several processes taking place simultaneously in Cr(VI) reduction.

Discussion

To complete the analysis of the reduction process, the pulse duration is varied from 10 µs to 1 ms. Fig. 5 presents the reduction rate (and also the corresponding reduction efficiency after 2 hours) according to the pulse duration. It is shown that the reduction rate increases significantly with the pulse duration for the two gaps (2 and 5 mm). As shown in Fig. S2, whatever the regime discharge (breakdown or no breakdown) the charges are mainly delivered into the discharge during the first microseconds. As a consequence the pulse duration of 10 µs ensures that the whole plasma phase is taken into account despite the variability of the experiments. The plasma phase generates reactive species which can diffuse into the solution and be responsible for Cr(VI) reduction. For 10 µs the reduction efficiency is close to 35% and the reduction rate is about 0.1-0.15 mg.L -1 /min for the two gaps (Fig. 5). Despite the short duration of the plasma, its effect is significant on Cr(VI) reduction (almost 40% of efficiency). The gap has only a slight effect on the process; the short gap provides a slight better reduction. Reducing the gap changes the electric field and then the electron properties of the plasma, e.g. presence of breakdowns has been reported for 2 mm gap (Table S2). Although consequences on the chemical activity are expected, no direct effect of the gap is observed on the reduction rate during 10 µs-long discharges.

Between 10 and 25 µs the reduction process strongly depends on the gap, it is higher for 2 mm than for 5 mm, the reduction efficiency being equal to 63% and 36% respectively. The chemistry during this post-plasma phase mainly involves long-lived species (such as H 2 O 2 ). The production of these species depends on the gap so it can be assumed that their production depends on the electric field. Moreover, these species are significantly produced after 10 µs so they should result from multi-steps mechanisms. An example of such mechanisms could be the succession of reaction A or A' and reaction B:

H 2 O + e-=>  OH + H - (E th =5.3 eV) (reaction A) H 2 O + e-=>  OH +  H + e- (E th =7 eV) (reaction A')  OH +  OH (+M) => H 2 O 2 (+M) (reaction B)
Primary reactions A and A' both involve electrons as reactants but have different threshold energy (about 5.5 and 7 eV respectively [31]). Their reaction rate depends on both the electron energy and the electron density, therefore it depends on the electric field. It can be assumed that for 5 mm gap, the low electric field involves mainly reaction A whereas at 2 mm the higher electric field involves higher electron density and more reaction A' which results in a higher production of  OH. Then secondary reactions (B) take place which results in higher production of H 2 O 2 for 2 mm gap, and then higher Cr(VI) reduction.

From 25 µs to 1000 µs, the reduction rate continues to increase with the pulse duration showing quite parallel evolution for both gaps. It can be assumed that the chemical mechanisms are the same for both gaps. As a consequence the additional effect previously identified for 2 mm gap has no longer effect. It is possible that the very low current delivered by the DC power supply during this time interval (< 1 mA, not quantifiable in our experimental conditions) and/or the low applied electric field (high voltage < 2 kV) promote Cr(VI) reduction by low energy mechanisms. But it should be reminded that no reduction effect is obtained for applied voltage equal to 2 kV (Fig. 2). Then these low energy mechanisms should involve species previously produced during the plasma phase.

Fig. 5 Reduction rate of Cr(VI) according to the pulse duration after pin-to-pin discharges in Cr(VI) solution (47 mg/L, σ=4 mS/cm, pH=2.3) V = 100 mL, U= 9 kV, electrodes length = 0±10 μm, f = 50 Hz, duration of 120 min Fig. 6 presents a comparison between the evolutions of [Cr(VI)], [H 2 O 2 ] and the change in conductivity for different pulse durations. First, it is observed for the two gaps that with longer pulse duration, H 2 O 2 concentration increases and the decrease in conductivity is higher. These results confirm that the reactivity of the solution changes with the pulse duration and also that the variation depends on the gap, being higher for 2 mm than for 5 mm. Regarding the conductivity, the main difference between 2 and 5 mm is observed for short pulse durations (Δt < 100 µs): for 5 mm gap, the variation of the conductivity is quite constant (-0.35 mS/cm) whereas for 2 mm gap a strong variation is observed (from -0.35 to -0.1 mS/cm). On the opposite, for [H 2 O 2 ] the difference between 2 and 5 mm gaps appears for long pulse duration. For Δt > 250 µs, [H 2 O 2 ] remains lower than 0.15 mM for 5 mm gap while it increases to 0.4 mM for 2 mm gap.

To summarize, the increase of the pulse duration involves a better Cr(VI) reduction, a higher [H 2 O 2 ] production and a more important change in conductivity. But no direct relationship between the three parameters can be easily highlighted. Due to the high complexity of the intertwined mechanisms involved in plasma process, the variation of the conductivity cannot be related to species production or consumption.

Conclusion

The These variations are also related to higher decrease of the conductivity. On the contrary, the slight pH increase does not depend significantly on the experimental conditions. These results highlights the significant influence of the electric properties of the plasma on chemical mechanisms and so on the Cr(VI) reduction.

To complete the analysis of the kinetics, the influence of the pulse duration on the chemical properties of the solution has been studied. The increase of the pulse duration involves a better Cr(VI) reduction, a higher [H 2 O 2 ] production and a more important change in conductivity. Moreover it has been shown that despite the short duration of the plasma phase (<10 µs), its effect is significant on Cr(VI) reduction leading to maximum 40% of reduction efficiency. In addition the post plasma stage is also very efficient for Cr(VI) degradation since the reduction rate increases from about 0.15 mg.L -1 /min to 0.4 mg.L -1 /min when the pulse width rises from 10 to 500 µs.

Fig. 1 .

 1 The high voltage pulsed power supply consists of a low inductance capacitor (C = 1 nF) charged by a 30 kV DC high voltage power supply (Ultravolt 30A24-P30) through a 30 kΩ resistor, and a fast-high voltage solid-state switch (Behlke HTS 301-03-GSM). The 200 µm-diameter electrodes are in platinum (Pt). The tips of the electrodes do not protrude from the insulator in the solution.

Fig. 1

 1 Fig. 1 Experimental set-up of pin-to-pin discharge in liquid (side view)

Fig. 2

 2 Fig. 2 Time evolution of Cr(VI) concentration according to the applied voltage for 2 mm gap obtained during pin-to-pin discharges in Cr(VI) solution (47 mg/L, σ=4 mS/cm, pH=2.3) V = 100 mL, ∆t = 500 μs, electrodes length = 0±10 μm, f = 50 Hz. The empty symbols refer to [Cr(VI)] 0 =23.5 mg/L (σ=4 mS/cm, pH=2.3)

Fig. 3

 3 Fig.3Change in solution conductivity according to the reduction efficiency after pin-to-pin discharges in Cr(VI) solution (47 mg/L, σ=4 mS/cm, pH=2.3) V = 100 mL, ∆t = 500 μs, electrodes length = 0±10 μm, f = 50 Hz, duration of 120 min

Fig. 4

 4 Fig. 4 Evolution of Cr(VI) concentration according to H 2 O 2 concentration measured after pin-to-pin discharges in Cr(VI) solution (47 mg/L, σ=4 mS/cm, pH=2.3) V = 100 mL, Δt=500 µs, electrodes length = 0±10 μm, f = 50 Hz

Fig. 6

 6 Fig. 6 Evolution of [H 2 O 2 ], [Cr(VI)] and change in conductivity according to pulse duration for (a) 2 mm gap and (b) 5 mm gapfor pin-to-pin discharges in Cr(VI) solution (47 mg/L, σ=4 mS/cm, pH=2.3) V = 100 mL, U=9 kV, electrodes length = 0±10 μm, f = 50 Hz, duration of 120 min

Table 1 Examples of mechanisms involved in Cr(VI) reduction by PLI process in aqueous solution [7, 11, 17-21]

 1

  in supplementary file). The concentration of H 2 O 2 is about 10 times higher when there is no Cr(VI) in the initial solution: [H 2 O 2 ]=0.68 mM without Cr(VI) and 0.057 mM with Cr(VI) (Δ[H 2 O 2 ]=0.62 mM). It confirms that H 2 O 2 is consumed by Cr(VI) reduction. But during the same duration, [Cr(VI)] decreases by only 0.23 mM. If considering that Reaction(8) of Table 1 is the main pathway for Cr(VI) reduction, this decrease of [Cr(VI

  results of this study prove that microseconds electrical discharge in solution can totally remove dissolved Cr(VI). The simultaneous measurements of [Cr(VI)] and [H 2 O 2 ] are reported for the first time for this experimental configuration, i.e. direct discharge in aqueous Cr(VI) solution. Additional measurements of pH and conductivity complete the chemical analysis of the process. Time evolution of [Cr(VI)] shows a linear behavior reflecting pseudo-zero order rate which is different from first order systematically reported by the literature. This result involves that the oxidation process is negligible which is in accordance with the total C(VI) removal obtained in this work. Increasing the applied voltage and decreasing the gap result in increasing the reduction rate of Cr(VI) and [H 2O 2 ].

Acknowledgements

This work bearing the reference ANR-11-LABX-086 has benefited from State aid managed by the National Research Agency under the Future Investments program with the Reference Number ANR-18-IDEX-0001. The authors thank Benjamin Dufour for valuable discussions about the chemical activity of water.