Damien Breilly

Sami Fadlallah

Vincent Froidevaux

Frédéric Lamaty

Florent Allais
email: florent.allais@agroparistech.fr

Thomas-Xavier Métro
email: thomas-xavier.metro@umontpellier.fr

Sustainability and efficiency assessment of lignin derived phenolic synthons' allylation: in solution versus ball-milling

come

Introduction

Composed of p-hydroxyphenylpropanoids units, lignins are a natural and abundant polyphenolic resource that is gaining more and more interest and value in the chemical industry. Indeed, lignins can be used as macromolecular polyols 1 or (bio)-catalytically depolymerized to prepare monophenolics such as vanillin, syringaldehyde, or 4-hydroxyphenyl ethanol. [START_REF] Abu-Omar | Guidelines for Performing Lignin-First Biorefining[END_REF] Among the various phenolics that can be readily obtained from lignins, vanillin is probably the most promising, by being mainly produced from the hydrolysis-oxidation of lignosulfonate coming from paper industries. In order to meet the world demand of vanillin, 15% of the general production comes from this lignosulfonate revalorization which would have been burned otherwise. [START_REF] Fadlallah | Are Lignin-Derived Monomers and Polymers Truly Sustainable? An in-Depth Green Metrics Calculations Approach[END_REF][START_REF] Calvo-Flores | Lignin as Renewable Raw Material[END_REF][START_REF] Fache | Vanillin Production from Lignin and Its Use as a Renewable Chemical[END_REF] These renewable phenolics constitute a great source of valuable synthons for the production of bio-based alternatives to petroleum-based phenolic/aromatic bioactive compounds -such as antioxidants, [START_REF] Reano | Chemo-Enzymatic Preparation and Characterization of Renewable Oligomers with Bisguaiacol Moieties: Promising Sustainable Antiradical/Antioxidant Additives[END_REF] UV filters, [START_REF] Horbury | Investigating Isomer Specific Photoprotection in a Model Plant Sunscreen[END_REF][START_REF] Horbury | Towards Symmetry Driven and Nature Inspired UV Filter Design[END_REF][START_REF] Horbury | Exploring the Photochemistry of an Ethyl Sinapate Dimer: An Attempt Toward a Better Ultraviolet Filter[END_REF][START_REF] Peyrot | Innovative Bio-Based Organic UV-A and Blue Light Filters from Meldrum's Acid[END_REF][START_REF] Peyrot | Expeditious and Sustainable Two-Step Synthesis of Sinapoyl-Lmalate and Analogues: Towards Non-Endocrine Disruptive Biobased and Water-Soluble Bioactive Compounds[END_REF][START_REF] Rioux | Sustainable Synthesis of P-Hydroxycinnamic Diacids through Proline-Mediated Knoevenagel Condensation in Ethanol: An Access to Potent Phenolic UV Filters and Radical Scavengers[END_REF][START_REF] Toldo | Mechanistic Aspects of the Photophysics of UVA Filters Based on Derivatives[END_REF] monomers and corresponding polymers. [START_REF] Fadlallah | Are Lignin-Derived Monomers and Polymers Truly Sustainable? An in-Depth Green Metrics Calculations Approach[END_REF] In the literature, many groups -including URD ABI -have reported several works on the use of vanillin [START_REF] Savonnet | Divanillin-Based Epoxy Precursors as DGEBA Substitutes for Biobased Epoxy Thermosets[END_REF] and p-hydroxycinnamate esters (e.g., ethyl ferulate [START_REF] Pion | Chemo-Enzymatic Preparation of New Bio-Based Bisand Trisphenols: New Versatile Building Blocks for Polymer Chemistry[END_REF][START_REF] Maiorana | Structure Property Relationships of Biobased N-Alkyl Bisferulate Epoxy Resins[END_REF] and ethyl sinapate [START_REF] Jaufurally | Optimization of the Laccase-Catalyzed Synthesis of (±)-Syringaresinol and Study of Its Thermal and Antiradical Activities[END_REF][START_REF] Janvier | Syringaresinol: A Renewable and Safer Alternative to Bisphenol A for Epoxy-Amine Resins[END_REF] ) as bio-based synthons for the synthesis of poly-epoxidized phenolics as sustainable and non-toxic alternative to endocrine disruptive bisphenol A (BPA). So far, the epoxidation process used to access these BPA substitutes involved epichlorohydrin. To circumvent the use of this chlorinated reagent, pioneer work on the use of a two-step allylation/lipase-catalyzed epoxidation demonstrated that one could replace epichlorohydrin-based glycidylation to synthesize epoxides from phenols such as vanillin. [START_REF] Aouf | Chemo-Enzymatic Functionalization of Gallic and Vanillic Acids: Synthesis of Bio-Based Epoxy Resins Prepolymers[END_REF] Building on this finding, we decided to green up this strategy further through the use of mechanochemical allylation. Allylation is an easy and quick reaction to functionalize hydroxylic group with a reactive and versatile double bound, which is widely used in multistep synthetic pathways. The first group who applied allylation on vanillin was Ayer et al. in 1991 (Scheme 1, first step), to synthesize a molecule inhibiting the growth of pathogens. [START_REF] Ayer | Synthesis of (+/-) Arthrographol[END_REF] Then, Detterbeck et al. used it in order to create hydroxylated aryldihydrobenzofuran systems as key structures to obtain natural compounds. [START_REF] Detterbeck | An Improved and Versatile Method for the Rapid Synthesis of Aryldihydrobenzofuran Systems by a Boron Tribromide-Mediated Cyclization Reaction[END_REF] Later on, Breloy et al., who aimed to develop a green vanillin-based photoinitiator for free-radical polymerization of acrylated monomer, performed vanillin allylation to avoid radical side reaction on phenols during polymerization. [START_REF] Breloy | Vanillin Derivative as Performing Type I Photoinitiator[END_REF] Still in the polymer field, Han et al. carried out the allylation of vanillin to ease the curing of a phtalonitrile resin. [START_REF] Han | Phthalonitrile Resins Derived from Vanillin: Synthesis, Curing Behavior, and Thermal Properties[END_REF] Willing to enhance the bioactivity of vanillin-based chalcones, Sharma et al. also implemented this allylation step. [START_REF] Sharma | Economical Synthesis and Antiplasmodial Evaluation of Vanillin Derived Allylated Chalcones and Their Marked Synergism with Artemisinin against Chloroquine Resistant Strains of Plasmodium Falciparum[END_REF] It is noteworthy to mention that some researchers, such as Yu et al., took advantage of the resulting allyloxy group to perform Claisen rearrangement (Scheme 1, second step). [START_REF] Yu | Renewable Reactive Diluents as Practical Styrene Replacements in Bio-Based Vinyl Ester Thermosets[END_REF] Scheme 1: Allylation in solution [START_REF] Ayer | Synthesis of (+/-) Arthrographol[END_REF] followed by Claisen rearrangement [START_REF] Yu | Renewable Reactive Diluents as Practical Styrene Replacements in Bio-Based Vinyl Ester Thermosets[END_REF] Generally, allylation of vanillin is carried out in solution in organic solvents, such as DMF, acetone or ethanol, in the presence of potassium carbonate as a base. Although these reaction conditions allow the isolation of allylated vanillin in high yields, they also present some drawbacks such as the toxicity and the quantities of the solvent used, [START_REF]Request for Assistance in Preventing Adverse Health Effects from Exposure to Dimethylformamide (DMF)[END_REF] long reaction times or the need to perform the reaction at relatively high temperature (such as in refluxing EtOH or acetone). Due to the critical importance of vanillin and other renewable phenolic compounds (e.g., ethyl ferulate) as well as their allylated counterpart, the development of efficient and sustainable allylation conditions is of high interest. Based on previous successes in the field, [START_REF] Friščić | Mechanochemistry for Synthesis[END_REF][START_REF] Howard | Mechanochemistry as an Emerging Tool for Molecular Synthesis: What Can It Offer?[END_REF][START_REF] James | Mechanochemistry: Opportunities for New and Cleaner Synthesis[END_REF] we therefore envisaged using mechanochemistry to produce allylated phenols. Mechanochemistry can be defined as the field of science that studies chemical transformations facilitated by mechanical energy. [START_REF] Michalchuk | Mechanical Alloying, Mechanochemistry: What Is in a Name? Front[END_REF] It has been demonstrated in many cases that mechanochemistry allows the development of more efficient and sustainable alternatives to the processes classically performed in solution. [START_REF] Ardila-Fierro | Sustainability Assessment of Mechanochemistry by Using the Twelve Principles of Green Chemistry[END_REF] Mechanochemical allylation of vanillin was therefore attempted by milling vanillin with K2CO3 and allyl bromide.

Results and discussion I) Mechanochemical allylation of vanillin a. Optimization of reaction conditions by planetary ball milling

At first, 143.7 mg of vanillin were reacted with 130.6 mg of K2CO3 (1.0 eq) in a 20 mL reactor made of zirconium oxide (noted ZrO2) containing 80 beads of the same material (5 mm diameter). After 5 min milling at 850 rpm in a planetary ball-mill (at room temperature), 90.4 µL of allyl bromide (1.1 eq) were added to the reactor and the reaction mixture was agitated at 850 rpm. After 1 h of milling, an HPLC analysis of the crude revealed that ~37% of vanillin was allylated (Table 1, entry 1). Here, the number of parameters that could be optimized being quite large (mechanical parameters adding to the chemical ones), performing a Design of Experiments (DoE) and Response Surface Methodology (RSM) was not adapted. [START_REF] Uy | Optimization by Design of Experiment Techniques[END_REF] It was thus decided to implement classic One Variable At a Time approach (OVAT) to optimize the mechanochemical allylation of vanillin. Before studying and optimizing the mechanical parameters, it was decided to first investigate the chemical parameters and more specifically, the reaction time and the excess of allyl bromide, which is a liquid at ambient temperature (Table 1). Indeed, it is widely known in mechanochemistry that adding small amounts of a liquid can dramatically influence the course of the reaction. This technique, called Liquid-Assisted Grinding (LAG), often enables to increase homogeneity of the reaction mixture but also to accelerate and control selectivity of a reaction. [START_REF] Denlinger | Liquid-Assisted Grinding and Ion Pairing Regulates Percentage Conversion and Diastereoselectivity of the Wittig Reaction under Mechanochemical Conditions[END_REF][START_REF] Belenguer | Reliable Mechanochemistry: Protocols for Reproducible Outcomes of Neat and Liquid Assisted Ball-Mill Grinding Experiments[END_REF][START_REF] Hasa | Mechanochemical Synthesis of Multicomponent Crystals: One Liquid for One Polymorph? A Myth to Dispel[END_REF] To quantify LAG solvent added in the bulk, the η value was defined in the literature as the liquid volume added per total mass of reagents. [START_REF] Friščić | The Role of Solvent in Mechanochemical and Sonochemical Cocrystal Formation: A Solubility-Based Approach for Predicting Cocrystallisation Outcome[END_REF] In this work, η will be calculated based on the total mass of the following reagents: phenol, potassium carbonate and allyl bromide. [START_REF] Michalchuk | Mechanical Alloying, Mechanochemistry: What Is in a Name? Front[END_REF] Their signification is explained in the SI. b Estimated based on the surface areas of the peaks visible on the HPLC chromatograms. No side products could be detected in any of the experiments performed. Yields are presented as an average of three samples taken at three different spots of the reaction mixture. The standard deviation therefore represents the homogeneity of the distribution of the reactants and products in the reaction mixture.

In our case, it was expected that allyl bromide could both play the role of a reactant and of a beneficial liquid additive. Therefore, the quantity of allyl bromide was increased to 1.5 and 4.0 equivalents (Table 1, entries 2 and 3). Counterintuitively, increasing the equivalents of allyl bromide did not favor the conversion of vanillin towards allylated vanillin. On the opposite, the yield dropped down to ~28% when using 4.0 equivalents of allyl bromide, while no other side products could be detected (Table 1, entry 3). Similar tendency was observed when the reaction time was raised to 3 hours (Table 1, entries 4-6). This confirmed the deleterious effect of allyl bromide as a liquid additive was stronger than the positive effect that would have been expected from increasing the excess of this reactant. It was hypothesized here that the excess of allyl bromide led to a less homogeneous distribution of the reactants, which is essential in solvent-free synthesis and could explain the lower yields. Additionally, increasing the reaction time did not significantly improve the yield, neither led to the formation of side products, whatever the excess of allyl bromide used (Table 1, entries 4-6). Finding a suitable liquid additive was thus the next step of this study. Ten polar aprotic solvents and EtOH, which is a commonly used solvent for allylation, were then tested as liquid additives: acetone, EtOAc, anisole, dimethylcarbonate, DMF, DMSO, diethyl malonate, acetonitrile, Cyrene® and -valerolactone (Table 2). Vanillin and K2CO3 were first milled for 5 min before allyl bromide and the liquid additive were added and milled.

Among the different LAG tested, DMF allowed for the highest yield (79%, Table 2, entry 6) while the use of diethyl malonate and DMSO provided the lowest (12% and 14%, respectively, Table 2, entries 7 & 8). DMF is a widespread and efficient solvent for many chemical processes, yet its toxicity is an incentive to the development of safer and more sustainable alternatives. [START_REF] Camp | Bio-Available Solvent Cyrene: Synthesis, Derivatization, and Applications[END_REF][START_REF] Yeboue | Peptide Couplings by Reactive Extrusion: Solid-Tolerant and Free from Carcinogenic, Mutagenic and Reprotoxic Chemicals[END_REF][START_REF](EC) No 1272/2008[END_REF] Among the solvents commonly recognized as more sustainable (i.e., EtOH, acetone, EtOAc, anisole, dimethylcarbonate), 40 yields unfortunately did not exceed 40% (Table 2, entries 1 to 5). Yields obtained with other alternative solvents (acetonitrile, Cyrene® and -valerolactone) did not provide better results (Table 2, entries 9 to 11). Of note, the low yield in the case of Cyrene® could be explained by its capacity to undergo K2CO3-mediated deprotonation and subsequent homo-oligomerization through Michael-addition, aldol condensation or allylation. [START_REF] Diot-Néant | Sustainable Synthesis and Polycondensation of Levoglucosenone-Cyrene-Based Bicyclic Diol Monomer: Access to Renewable Polyesters[END_REF] Well-aware that DMF is not the ideal liquid additive because of its reproductive toxicity, reducing its concentration from 0.2 µL/mg to 0.1 µL/mg was attempted (Table 2, entry 12). Unfortunately, this resulted in a decrease in yield from 79% to 48% (Table 2, entries 6 vs 12). By combining the aforementioned optimized parameters (i.e., 1.5 eq. of allyl bromide and 0.2 µL of DMF as LAG), while increasing the milling time to 3 hours, the yield reached 98% (Table 2, entry 13).

Table 2: Liquid additive screening for the mechanical allylation of vanillin a Vanillin: K2CO3 1:1, 20 mL ZrO2 reactor, 80 ZrO2 beads (32 g, d = 5 mm), rotational speed: 850 rpm, total mass of reagents: 400 mg. Symbols utilized in this scheme are those proposed by Michalchuk et al. [START_REF] Michalchuk | Mechanical Alloying, Mechanochemistry: What Is in a Name? Front[END_REF] Their signification is explained in the SI. b All liquid additive were utilised in quantities corresponding to η = 0.2 µL/mg. η is defined as the volume of liquid additive over the total mass of reactants. 36 c Estimated based on the surface areas of the peaks visible on the HPLC chromatograms.

No side products could be detected in any of the experiments performed. Yields are presented as an average of three samples taken at three different spots of the reaction mixture. The standard deviation therefore represents the homogeneity of the distribution of the reactants and products in the reaction mixture.

In parallel with the optimization of the chemical parameters, the influence of the mechanical parameters on the yield was studied: quantity, diameter and material of beads (Table 3), as well as rotational speed (Table 4). Indeed, such parameters will influence on the energy transferred to the reaction mixture, and hence on the course of the reaction. For instance, under otherwise equal conditions, beads made of a dense material, such as stainless steel (ρstainless steel = 7.8 g cm -3 ), will provide more energy to the system on every impact than a less dense material, such as ZrO2 (ρzirconium oxide = 5.9 g cm -3 ). In total, three diameters and two materials were tested (i.e., 3, 5 or 10 mm diameter beads made of ZrO2 or stainless steel) (Table 3). As a reminder, using 5 mm ZrO2 beads without any liquid additive provided allylated vanillin with a yield of ~37% after 1 h of milling (Table 1, entry 1). Changing the material of the beads and reactor to stainless steel, while keeping other parameters constant, slightly reduced the yield to 32% (Table 3, entry 1). Using larger stainless steel beads (10 mm diameter) also reduced the yield (to 20%, Table 3,entry 2), yet smaller 3 mm beads increased the yield (to 40%, Table 3, entry 3). The same tendency was observed with ZrO2 beads: yield decreased to 23% with 10 mm diameter beads (Table 3, entry 4 compared to Table 1, entry 1) and increased to 42% with 3 mm diameter beads (Table 3, entry 5 compared to Table 1, entry 1). a Vanillin:K2CO3:allyl bromide 1:1:1.1, reaction time: 1 h, rotational speed: 850 rpm. For each material, the total weight of beads was kept constant (32g for ZrO2 beads, 40g for stainless steel ones) and the 20 mL reactor was made of the same material than the beads (ZrO2 or stainless steel). Symbols utilized in this scheme are those proposed by Michalchuk et al. [START_REF] Michalchuk | Mechanical Alloying, Mechanochemistry: What Is in a Name? Front[END_REF] Their signification is explained in the SI. b Estimated based on the surface areas of the peaks visible on the HPLC chromatograms. No side products could be detected in any of the experiments performed. Yields are presented as an average of three samples taken at three different spots of the reaction mixture. The standard deviation therefore represents the homogeneity of the distribution of the reactants and products in the reaction mixture.

Another parameter allowing to easily modulate the induced mechanical energy is the rotational speed. Without any liquid additive, lowering the frequency to 600 rpm decreased the yield down to 19% (Table 4, entry 1 vs ~37% in Table 1 entry 1). Adding DMF as a liquid additive (η = 0.2 µL/mg) and increasing the excess of allyl bromide to 1.5 equivalents led to a better yield of 55% (Table 4, entry 2). Yet, the highest yield (93%) was obtained when running the reaction with a rotational speed of 850 rpm, the maximal acceptable rotational speed for our equipment (Table 4, entry 3). The latter results showed that lowering this parameter did not improve the yield, suggesting that higher-energy reaction conditions were needed here. No side products could be detected in any of the experiments performed. Yields are presented as an average of three samples taken at three different spots of the reaction mixture. The standard deviation therefore represents the homogeneity of the distribution of the reactants and products in the reaction mixture. c η is defined as the volume of liquid additive over the total mass of reactants. [START_REF] Friščić | The Role of Solvent in Mechanochemical and Sonochemical Cocrystal Formation: A Solubility-Based Approach for Predicting Cocrystallisation Outcome[END_REF] It is expressed in µL/mg.

After having varied the different parameters of the reaction individually from each other (stoichiometry, reaction time, material of reactors, quantity, material and size of beads, as well as rotational speed), the allylation was performed using the optimal conditions (i.e., 1.5 eq of allyl bromide, DMF η = 0.2 µL/mg, 20 mL ZrO2 reactor, 32 g of 3 mm ZrO2 beads, 3 h, 850 rpm) leading to a quantitative conversion of vanillin. After recovery of the reaction mixture from the reactor with EtOAc, water and 1M NaOH aqueous solution, the aqueous phase was extracted with EtOAc. Combined organic phases were dried, filtered and concentrated to furnish pure allylated vanillin in 87% isolated yield.

b. Comparison with reaction in solution

To evaluate the advantages brought by the aforementioned mechanochemical conditions compared to those in solution, an allylation reaction was performed in solution under classical stirring by using DMF as a solvent. [START_REF] Breloy | Vanillin Derivative as Performing Type I Photoinitiator[END_REF] The reaction was conducted at 50 °C with the minimal volume of DMF required to obtain a homogeneous solution under stirring, which corresponded to a η ratio of 0.84 µL/mg in these conditions. The temperature of the reaction was set at 50 °C to be as close as possible to the milling conditions (50 °C was the temperature of the reaction media in the ball-mill right after milling was stopped in the best conditions described in the previous paragraph). Like in ball-milling conditions, a complete conversion was attained after 3 h of reaction and the allylated vanillin was isolated in 86% yield (87% isolated yield for ball-milling conditions). Yet, one can highlight that under these solutionbased conditions, the amount of DMF reached more than 4 times the amount required under ballmilling (η = 0.84 µL/mg in solution vs η = 0.2 µL/mg for ball-milling).

II) Mechanochemical allylation of ethyl ferulate

The allylation of vanillin being successful by using ball milling, it was decided to apply these conditions to ethyl ferulate, a naturally occurring synthon of interest that has been used for the synthesis of renewable compounds such as non-toxic alternatives to endocrine disruptive bisphenol A. [START_REF] Reano | Chemo-Enzymatic Preparation and Characterization of Renewable Oligomers with Bisguaiacol Moieties: Promising Sustainable Antiradical/Antioxidant Additives[END_REF][START_REF] Maiorana | Structure Property Relationships of Biobased N-Alkyl Bisferulate Epoxy Resins[END_REF] At first, 180 mg of ethyl ferulate was reacted with 112 mg of K2CO3 (1.0 eq) in a 20 mL ZrO2 reactor containing 80 beads of the same material (5 mm diameter). As for vanillin, after 5 min milling at 850 rpm at room temperature, 77.6 µL of allyl bromide (1.1 eq) were added to the reactor and the reaction mixture was agitated at 850 rpm. After 3 h of milling, an HPLC analysis of the crude revealed that 49% of ethyl ferulate was allylated (Table 6, entry 1).

In the same conditions, only ~37% of vanillin was allylated (Table 1, entry 1), thus demonstrating a better reactivity of ethyl ferulate compared to vanillin in these conditions. As for vanillin in the same conditions (Table 1, entry 5), increasing the excess of allyl bromide to 1.5 equivalents and the milling time to 3 hours did not significantly improve the yield (50%, Table 5, Entry 2). Yet when DMF was used as a liquid additive (η = 0.2 µL/mg), ethyl ferulate was converted almost quantitatively (97% yield, Table 5, entry 3). After work-up, allylated ethyl ferulate was isolated with 82% yield. Of note, allylated vanillin is a liquid in our reaction conditions. On the opposite, allylated ethyl ferulate is a solid. Gratifyingly, in these reaction conditions, yield does not seem to be influenced by the physical states of the reactants and products. Although it is known that "hot spots" can be generated during milling, it is worth mentioning that, in our reaction conditions, no trace of the thermally-favored Claisen rearrangement product (Scheme 1, second step) was detected neither for vanillin nor for ethyl ferulate. a Vanillin:K2CO3 1:1, rotational speed: 850 rpm, beads and reactor are made of ZrO2. For each size of beads, the total weight of beads was kept constant (32 g). Symbols utilized in this scheme are those proposed by Michalchuk et al. [START_REF] Michalchuk | Mechanical Alloying, Mechanochemistry: What Is in a Name? Front[END_REF] Their signification is explained in the SI. b Estimated based on the surface areas of the peaks visible on the HPLC chromatograms. No side products could be detected in any of the experiments performed. Yields are presented as an average of three samples taken at three different spots of the reaction mixture. The standard deviation therefore represents the homogeneity of the distribution of the reactants and products in the reaction mixture.

III) Scale-up and benchmarking

This mechanochemical allylation reaction was further studied at a higher scale. For this, a Retsch PM100 planetary ball mill equipped with a 250 mL stainless steel reactor containing ~2080 stainless steel beads (3 mm diameter) was utilized (instead of the Fritsch P7 and 20 mL ZrO2 reactor). Thus, 1.61 g of vanillin produced 1.94 g of allylated vanillin (95% isolated yield, Scheme 2) after having been milled for 3 h at 400 rpm in the 250 mL reactor. Following a similar procedure, 2.05 g of ethyl ferulate furnished 2.24 g of allylated ethyl ferulate (92% isolated yield, Scheme 2).

Scheme 2: Mechanochemical allylation of vanillin and ethyl ferulate at the gram scale (for meaning of symbols please see ref 30) The efficiency and the environmental impact for the allylation of vanillin under mechanochemical and solution conditions were then compared (Table 6). As one cannot compare the sustainability of processes based only on their yields, the E factor was calculated for all selected procedures. E factor, which represents how many kgs of waste are produced for a kg of product, is nowadays largely accepted as a useful and simple measure to rapidly give an idea on the sustainability of a chemical reaction. [START_REF] Fadlallah | Are Lignin-Derived Monomers and Polymers Truly Sustainable? An in-Depth Green Metrics Calculations Approach[END_REF][START_REF] Roschangar | Overcoming Barriers to Green Chemistry in the Pharmaceutical Industry -the Green Aspiration Level TM Concept[END_REF][START_REF] Fadlallah | Cellulose-Derived Levoglucosenone, a Great Versatile Chemical Platform for the Production of Renewable Monomers and Polymers[END_REF][START_REF] Sheldon | The E Factor: Fifteen Years On[END_REF] Although many conditions describing the allylation of vanillin with K2CO3 and allyl bromide were reported in the literature, only the reaction conditions with the best yield and E factor are detailed in the table 6. As quantities of "work-up solvents" (such as those used for extraction, washing, cristallization or column chromatography) are not always indicated in publications, E factors were first calculated without taking them into account (corresponding E factor being identified as "simple E factor" and abbreviated "sEF"). [START_REF] Roschangar | Overcoming Barriers to Green Chemistry in the Pharmaceutical Industry -the Green Aspiration Level TM Concept[END_REF] Thus, here sEF will account for all reagents, products and "reaction" solvents, as opposed to "work-up" solvents. While DMF was the best liquid additive for the allylation of vanillin in a ball-mill (furnishing allylated vanillin in 95% isolated yield), less problematic solvents such as acetone and ethanol provided better yields when used under classical stirring conditions (100% and 98%, Table 6, entries 1 and 2, respectively). [START_REF] Srikrishna | Synthesis of (±)-12-Methoxyherbertenediol Dimethyl Ether[END_REF][START_REF] Hoffmann | A Straightforward Approach towards Cyclic Photoactivatable Tubulysin Derivatives[END_REF] Yet these procedures presented sEF above 3, indicating that they produced more than 3 times the amount of waste than the amount of allylated vanillin. A lower sEF of only 2.47 could be obtained by Ayer et al. when using DMF as a solvent, albeit the reaction lasted 68 hours. [START_REF] Ayer | Synthesis of (+/-) Arthrographol[END_REF] Other research groups obtained allylated vanillin in shorter reaction times by using DMF, yet by running the reaction at higher temperatures (65 and 70 °C, Table 6, entries 4 and 5, respectively), and with higher sEF (5.46 and 5.51, respectively, Table 6, entries 4 and 5). [START_REF] Chate | Antimicrobial Screening of Novel 2-(5-(4-(Allyloxy)-3-Methoxyphenyl)-1H-Pyrazol-3-Yl)Phenols Analogues of 2-(4-(Allyloxy)-3-Methoxyphenyl)-4H-Chromen-4-Ones[END_REF][START_REF] Kevwitch | Vanillin and O-Vanillin Oligomers as Models for Dendrimer Disassembly[END_REF] These differences led us to perform the vanillin allylation reaction with DMF as a solvent under classical stirring conditions while i) trying to minimize as much as possible the amount of DMF ii) keeping the same excesses of K2CO3 and allyl bromide as for the ball milling conditions. In such conditions, allylated vanillin could be obtained in 86% yield after 3 hours of reaction at 50 °C in DMF, with a sEF of 4.09. When performing the allylation in a ball-mill by using DMF as a liquid additive, allylated vanillin was isolated in yields comparable to the previously described procedures in solution (87% and 95% isolated yields for ball-milling conditions, Table 6, entries 7 and 8, respectively; 86-100% yield range for reactions performed in solution). Yet, the ball-milling conditions enabled to reach the lowest sEF of 2.33 and 2.06, for the mg-scale and the gram-scale synthesis, respectively (Table 6, entries 7 and 8). Similar trend was also obtained for the allylation of ethyl ferulate, with sEF of 1.98 and 1.66, for the mg-scale and gram-scale respectively. Such results clearly highlight the capacity of ball-milling to drastically reduce the need for "reaction" solvent, while keeping overall efficiency (in terms of yield and reaction time). Although many publications do not mention the quantities of solvent used during work-up steps, the E factor taking into account these solvents (defined as "complete E factor" and abbreviated "cEF") was calculated when possible. [START_REF] Roschangar | Overcoming Barriers to Green Chemistry in the Pharmaceutical Industry -the Green Aspiration Level TM Concept[END_REF] Thus, the procedure developped by Kevwitch et al. presented a cEF of 14 (Table 6, entry 5). In our hands, performing the allylation in solution in DMF at 50 °C resulted in a higher cEF of 91 (Table 6, entry 6). This significative difference can be explained by the difference in scale at which the reactions were performed. In our hands, 6.6 mmoles of vanillin were engaged in the allylation reaction while 670.4 mmoles were used in the procedure described by Kevwitch et al. Performing the reaction at such scale (more than 100 grams of vanillin were allylated) enabled to drastically minimize the work-up solvent quantities, which was not possible in our small scale reaction conditions. The same "scale effect" is visible when looking at the cEF values for the allylation reactions performed in the ball-mill: the mg-scale ball-mill procedure requires more work-up solvents (cEF = 268, Table 6, entry 7) than the one performed at the gram-scale (cEF = 124, Table 6, entry 8). Yet, our results show that when performed at a similar scale, the ball-mill procedure uses more work-up solvents than the procedure in solution (Table 6, entry 8 vs entry 6). A detailed analysis of these differences in cEF indicates that a large portion of the work-up solvents used in the ball-mill process corresponds to the amount of solvent required to recover the reaction mixture from the ball mill reactor. Of note, such excess in work-up solvents could be easily avoided by using continuous mechanochemical equipment such as extruders. [START_REF] Isoni | Screwing NaBH 4 through a Barrel without a Bang: A Kneaded Alternative to Fed-Batch Carbonyl Reductions[END_REF][START_REF] Yeboue | Peptide Couplings by Reactive Extrusion: Solid-Tolerant and Free from Carcinogenic, Mutagenic and Reprotoxic Chemicals[END_REF]

Conclusions

The present work demonstrates that mechanochemistry is a versatile and efficient method for the allylation of biobased phenols such as vanillin and ethyl ferulate. It is shown that mechanical parameters (i.e. rotational speed, material, size and number of beads, liquid additive) are as important as the chemical parameters (i.e. stoichiometry, reaction time). Both of them were examined for the allylation of vanillin and their effects on the yield were reported. For example the bead choice enabled to double the yield. Allylated products were isolated in high yields (vanillin: 87%, ethyl ferulate: 82%). Better results were obtained when the method was scaled-up to the gram scale furnishing allylated vanillin and allylated ethyl ferulate with 95% and 92% isolated yield, respectively. Finally, E factors were calculated and compared to results obtained in solution, taking into account the work-up solvents (cEF) or not (sEF). Thus, sEF values clearly highlighted the capacity of ball-milling to drastically reduce the need for "reaction" solvent. On the opposite, the solution strategy revealed better E factors values (cEF) when the work-up solvents were taken into account. A detailed analysis of these differences in cEF indicated that a large portion of the work-up solvents used in the ball-mill process corresponded to the amount of solvent required to recover the reaction mixture from the ball mill reactor, which could be avoided by using continuous mechanochemical equipment such as extruders. Overall, these results highlight i) the great potential of mechanochemistry to enable the development of both efficient and waste-less allylation of lignin-derived phenolic synthons and ii) the need to study higher-scale and continuous mechanochemical processes, such as by using extruders, to further improve efficiency and sustainability of such mechanochemical processes.

Experimental Section

 Chemicals

Vanillin (99%), allyl bromide (99%) and potassium carbonate (99%) were all purchased from Sigma Aldrich. Ethyl ferulate was synthesized following the already reported procedure. [START_REF] Abu-Omar | Guidelines for Performing Lignin-First Biorefining[END_REF] Sodium hydroxide was purchased from Fischer scientific. Cyrene® was graciously provided by Circa group. All other solvents were obtained from VWR, Sigma Aldrich, Fischer Scientific and Alfa Aesar.

 Materials

Small scale mechanochemical reactions were performed in a Fritsch Pulverisette 7 premium line planetary ball mill with 20 mL inner-volume reactors containing 3, 5, or 10 mm diameter beads. Reactors and beads were made of zirconium oxide (noted ZrO2) or stainless steel. Gram scale mechanochemical reactions were performed in a Retsch PM100 planetary ball mill with a 250 mL innervolume reactor and 3 mm diameter beads, both made of stainless steel. Reactions were performed at room temperature, without control of the temperature by external heating or cooling. A slight increase in reactor temperature was observed, due at least in part to bead frictions during grinding.

 Chemical Analysis

UHPLC UHPLC analyses were performed on an Agilent technologies 1220 Infinity LC using a Chromolith high resolution RP-18e 50-4.6 mm column and a linear gradient of 0 to 100% CH3CN/0.1% TFA in H2O/0.1% TFA over 3 min, detection at 214 nm. Flow rate: 3 mL/min.

LCMS

Mass spectra were obtained using a LCMS with ESI using a Water Alliance 2695 as LC, coupled to a Waters ZQ spectrometer with electrospray source, a simple quadrupole analyzer and a UV Waters 2489 detector. Analyses were carried out using a linear gradient of 0 to 100% CH3CN/0.1% TFA in H2O/0.1% TFA over 2.5 min, detection at 214 nm. Flow rate: 3 mL/min. NMR NMR analyses were performed at the "Plateforme d'Analyse et de Caractérisation" of the Pôle Chimie Balard, Université de Montpellier. [START_REF] Laurichesse | Original Polyols Based on Organosolv Lignin and Fatty Acids: New Bio-Based Building Blocks for Segmented Polyurethane Synthesis[END_REF] H NMR spectra were recorded on a Bruker Avance III HD 400 MHz spectrometer and chemical shifts are reported in ppm using DMSO-d6 peak as an internal standard (2.50 ppm). Peaks are reported as s = singlet, d = doublet, t = triplet, q = quadruplet, m = multiplet; coupling constant are reported in Hz. [START_REF] Toldo | Mechanistic Aspects of the Photophysics of UVA Filters Based on Derivatives[END_REF] C NMR spectra were recorded on a Bruker Avance III HD 101 MHz spectrometer and are reported in ppm using DMSO-d6 peak as an internal standard (39.52 ppm).

FTIR IR spectra were recorded on an Agilent Cary 630 FTIR Spectrometer and are reported in cm -1 .

 Methods and procedure

General procedure for the mechanochemical allylation of vanillin at small scale The total mass of reagents (vanillin, potassium carbonate and allyl bromide) was fixed at 400 mg for all small scale assays. Vanillin (1.0 eq) and potassium carbonate (1.0 eq) were added in the reactor.

Beads were then added. The reactor was closed and stirred at the chosen rotational speed for 5 min to obtain a homogeneous mixture. If any, LAG solvent (80 µL, 0.2 µL/mg) was added followed by the addition of allyl bromide (1.1-1.5 eq). The reactor was closed and stirred for 1 to 3 cycles of 1 h separated by 30 min breaks. The reactor was opened and three reaction samples were collected at different locations in the reactor and solubilized in a mixture of aqueous 1M HCl and acetonitrile (50/50 v/v) for further analysis by HPLC. The reaction mixture inside the reactor was then solubilized with 5 mL of EtOAc, 5 mL of H2O, and finally 10 mL of an aqueous solution of sodium hydroxide 1M was added. The crude solution was then transferred into a separatory funnel and the organic layer was recovered.

The aqueous layer was extracted twice with 10 mL of EtOAc. The combined organic layers were then dried over anhydrous magnesium sulfate, filtered and concentrated under vacuum to afford allylated vanillin as a pale yellow liquid.

Optimized conditions for the mechanochemical allylation at small scale 3-Methoxy-4-(2-propen-1-yloxy)benzaldehyde (allylated vanillin), CAS: 22280-95-1 Vanillin (129 mg, 0.85 mmol) and potassium carbonate (117.2 mg, 0.85 mmol, 1.0 eq) were added in the reactor. 370 ZrO2 beads of 3 mm diameter (32 g) were then added. The reactor was closed and stirred at 850 rpm for 5 min to obtain a homogeneous mixture. DMF (80 µL, 0.2 µL/mg) and allyl bromide (110 µL, 1.27 mmol, 1.5 eq) were then added. The reactor was closed and stirred at 850 rpm following 3 cycles of 1 h separated by intervals of 30 min. Three samples were collected at different locations in the reactor and solubilized in a mixture of aqueous 1M HCl and acetonitrile (50/50 v/v) for further analysis by HPLC where no trace of vanillin was detected. The reaction mixture inside the reactor was then solubilized with 5 mL of EtOAc, 5 mL of H2O, and finally 10 mL of an aqueous solution of sodium hydroxide 1M was added. The crude solution was then transferred into a separatory funnel and the organic layer was recovered. The aqueous layer was then extracted twice with 10 mL of EtOAc. The combined organic layers were then dried over anhydrous magnesium sulfate, filtered and concentrated under vacuum to afford allylated vanillin as a pale yellow liquid (143 mg, 87% isolated yield). 3-[3-Methoxy-4-(2-propen-1-yloxy)phenyl]-2-propenoic acid ethyl ester (allylated ethyl ferulate), CAS: 54744-76-2 Ethyl ferulate (164 mg, 0.74 mmol) and potassium carbonate (102 mg, 0.74 mmol, 1.0 eq) were added in the reactor. 370 ZrO2 beads of 3 mm diameter (32 g) were then added. The reactor was closed and stirred at 850 rpm for 5 min to obtain a homogeneous mixture. DMF (80 µL, 0.2 µL/mg) and allyl bromide (96.4 µL, 1.11 mmol, 1.5 eq) were then added. The reactor was closed and stirred at 850 rpm following 3 cycles of 1 h separated by intervals of 30 min. Three samples were collected at different locations in the reactor and solubilized in a mixture of aqueous 1M HCl and acetonitrile (50/50 v/v) for further analysis by HPLC where no trace of vanillin was detected. The reaction mixture inside the reactor was then solubilized with 5 mL of EtOAc, 5 mL of H2O, and finally 10 mL of an aqueous solution of sodium hydroxide 1M was added. The crude solution was then transferred into a separatory funnel and the organic layer was recovered. The aqueous layer was then extracted twice with 10 mL of EtOAc. The combined organic layers were then dried over anhydrous magnesium sulfate, filtered and concentrated under vacuum to afford allylated ethyl ferulate as a pale orange powder (160 mg, 82% isolated yield). C NMR (ppm, 101 MHz, DMSO-d6) δ (ppm): 166.7 (s), 149.9 (s), 149.3 (s), 144.7 (s), 133.6 (s), 127.2 (s), 122.9 (s), 118.0 (s), 115.9 (s), 113.0 (s), 110.7 (s), 68.9 (s), 60.0 (s), 55.8 (s), 14.4 (s).

Reaction in a 250 mL stainless steel reactor in the PM100 planetary ball mill (scale-up assay) 3-Methoxy-4-(2-propen-1-yloxy)benzaldehyde(allylated vanillin), CAS: 22280-95-1 The total mass of reagents (vanillin, potassium carbonate and allyl bromide) was fixed at 5 g for all scale-up assays. Vanillin (1.61 g, 10.58 mmol) and potassium carbonate (1.46 g, 10.56 mmol, 1.0 eq) were added in the reactor. 2080 stainless steel beads of 3 mm diameter (180 g) were then added. The reactor was closed and stirred at 400 rpm for 5 min to obtain a homogeneous mixture. DMF (1.0 mL, 0.2 µL/mg) and allyl bromide (1.38 mL, 15.90 mmol, 1.5 eq) were then added. The whole reactor was stirred at 400 rpm following 3 cycles of 1 h separated by 1 h breaks. Three samples were collected at different locations in the reactor and solubilized in a mixture of aqueous 1M HCl and acetonitrile (50/50 v/v) for further analysis by HPLC. The reaction mixture inside the reactor was then solubilized with 50 mL of EtOAc, 50 mL of H2O, and finally 50 mL of an aqueous solution of sodium hydroxide 1M was added. The crude solution was then transferred into a separatory funnel and the organic layer was recovered. The aqueous layer was then extracted twice with 50 mL of EtOAc. The combined organic layers were then dried over anhydrous magnesium sulfate, filtered and concentrated under vacuum to afford allylated vanillin as a pale yellow liquid (1.94 g, 95% isolated yield).

3-[3-Methoxy-4-(2-propen-1-yloxy)phenyl]-2-propenoic acid ethyl ester (allylated ethyl ferulate), CAS: 54744-76-2 The total mass of reagents (ethyl ferulate, potassium carbonate and allyl bromide) was fixed at 5 g for all scale-up assays. Ethyl ferulate (2.05 g, 9.23 mmol) and potassium carbonate (1.28 g, 9.26 mmol, 1.0 eq) were added in the reactor. 2080 Stainless steel beads of 3 mm diameter (180 g) were then added. The reactor was closed and stirred at 400 rpm for 5 min to obtain a homogeneous mixture. DMF (1.0 mL, 0.2 µL/mg) and allyl bromide (1.2 mL, 13.84 mmol, 1.5 eq) were then added. The whole reactor was stirred at 400 rpm following 3 cycles of 1 h separated by 1 h breaks. Three samples were collected at different locations in the reactor and solubilized in a mixture of aqueous 1M HCl and acetonitrile (50/50 v/v) for further analysis by HPLC. The reaction mixture inside the reactor was then solubilized with 50 mL of EtOAc, 50 mL of H2O, and finally 50 mL of an aqueous solution of sodium hydroxide 1M was added. The crude solution was then transferred into a separatory funnel and the organic layer was recovered. The aqueous layer was then extracted twice with 50 mL of EtOAc. The combined organic layers were then dried over anhydrous magnesium sulfate, filtered and concentrated under vacuum to afford allylated ethyl ferulate as a pale orange powder (2.24 g, 92% isolated yield).

Allylation reaction in solution

Vanillin (1 g, 6.57 mmol) and potassium carbonate (0.908 g, 6.57 mmol, 1.0 eq) were added in a 10 mL round-bottom flask. A minimum quantity of DMF (2.6 mL) and allyl bromide (0.85 mL, 9.82 mmol, 1.5 eq) were added. The reaction was stirred for 3 h at 50 °C and then concentrated under vacuum. The crude was analyzed by [START_REF] Laurichesse | Original Polyols Based on Organosolv Lignin and Fatty Acids: New Bio-Based Building Blocks for Segmented Polyurethane Synthesis[END_REF] H NMR to determine the conversion. The reaction mixture inside the reactor was then solubilized with 20 mL of EtOAc, 20 mL of H2O, and finally 20 mL of an aqueous solution of sodium hydroxide 1M was added. The crude solution was then transferred into a separatory funnel and the organic layer was recovered. The aqueous layer was then extracted twice with 20 mL of EtOAc. The combined organic layers were then dried over anhydrous magnesium sulfate, filtered and concentrated under vacuum to afford allylated vanillin as a pale yellow liquid (1.09 g, 86% isolated yield).

1 H

 1 M.p.: 70-74 °C NMR (ppm, 600 MHz, DMSO-d6) δ (ppm): 7.58 (d, J = 16.0 Hz, 1H), 7.37 (S, 1H), 7.21 (d, J = 8.4, 1H), 6.97 (d, J = 8.4, 1H), 6.56 (d, J = 15.9, 1H), 6.12 -5.94 (m, 1H), 5.39 (d, J = 17.3, 1H), 5.26 (d, J = 10.5, 1H), 4.59 (d, J = 5.3, 2H), 4.17 (q, J = 7.1, 2H), 3.81 (s, 3H), 1.25 (t, J = 7.1 Hz, 3H).

13

 13

Table 1 :

 1 Optimization of the chemical parameters for the allylation of vanillin

	Entry a	Allyl bromide equivalents	Reaction time (h)	Yield b (%)
	1	1.1	1	37 ± 8
	2	1.5	1	36 ± 4
	3	4.0	1	28 ± 4
	4	1.1	3	40 ± 5
	5	1.5	3	40 ± 1
	6	4.0	3	38 ± 1

a Vanillin: K2CO3 1:1, 20 mL ZrO2 reactor, 80 ZrO2 beads (32 g, d = 5 mm), rotational speed: 850 rpm, total mass of reagents: 400 mg. Symbols utilized in this scheme are those proposed by

Michalchuk et al.

Table 3 :

 3 Influence of size and number of beads for the mechanical allylation of vanillin

	Entry	Bead and reactor material a	Bead diameter (mm)	Yield b (%)
	1	Stainless steel	5	32 ± 3
	2	Stainless steel	10	20 ± 1
	3	Stainless steel	3	40 ± 1
	4	ZrO2	10	23 ± 3
	5	ZrO2	3	42 ± 3

Table 4 :

 4 Influence of the rotational speed on the allylation of vanillin by planetary ball-milling

	Entry a	LAG	Allyl bromide equivalents	Speed (rpm) Yield b (%)
	1	No LAG	1.1	600	19 ± 2
	2	DMF η = 0.2 c	1.5	600	55 ± 5
	3	DMF η = 0.2 c	1.5	850	93 ± 2
	a Vanillin:K2CO3 1:1, reaction time: 1 h, 20 mL ZrO2 reactor, 80 ZrO2 beads (32 g, d = 5 mm).

b Estimated based on the surface areas of the peaks visible on the HPLC chromatograms.

Table 5 :

 5 Mechanochemical allylation of ethyl ferulate

	Entry a	LAG	AllylBr eq.	Reaction time (h)	Bead diameter (mm)	Yield b (%)
	1	No LAG	1.1	1	5	49 ± 2
	2	No LAG	1.5	3	5	50 ± 6
	3	DMF η = 0.2	1.5	3	3	97 ± 1

Table 6 :

 6 Comparison of reaction conditions, yields and simple and complete E factors for the allylation of vanillin Work-up solvents were not taken into account in the calculation of the E factor. c Work-up solvents were taken into account in the calculation of the E factor. d n.a.: not applicable (information not available in the original publication, e.g. volume of solvent used for column chromatography purification). e Reaction run under ultrasonication. f 80 ZrO2 beads (32 g, d = 3 mm) in a 20 mL ZrO2 reactor. g Temperature reached a maximum of ~50 °C right after milling was stopped. h 2080 stainless steel beads (180 g, d = 3 mm) in a 250 mL stainless steel reactor.

	Entry	Author, year	Solvent	Reaction time (h)	Temp. (°C)	Scale (mmoles) a	Isolated yield (%)	Simple E Factor (sEF) b	Complete E Factor (cEF) c
		Srikrishna
	1	et al.,	Acetone	5	Reflux	16.4	100	3.61	n.a. d
		2007 45
		Hoffmann
	2	et al.,	Ethanol	6	Reflux	99.9	98	3.34	n.a. d
		2014 46
	3	Ayer et al., 1991 20	DMF	68	RT	80.2	99	2.47	n.a. d
	4 e	Chate et al., 2012 47	DMF	1	65	6.6	92	5.46	n.a. d
		Kevwitch
	5	et al.,	DMF	24	70	670.4	96	5.51	14
		2012 48
	6	This work, in solution	DMF	3	50	6.6	86	4.09	91
	7 f	This work, ball-milling at mg-scale	DMF	3	Self-heating g	0.8	87	2.33	268
	8 h	This work, ball-milling at g-scale	DMF	3	Self-heating	10.6	95	2.06	124

a Number of mmoles of vanillin involved in the reaction. b

Acknowledgements

The authors are grateful to CHRYSO Saint-Gobain, Grand Reims, Département de la Marne, Grand Est Region, Université de Montpellier and Centre National de la Recherche Scientifique (CNRS) for their financial support.


Marc Gouttefarde
email: marc.gouttefarde@lirmm.fr

Mariola Rodriguez

Cyril Barrelet

Pierre-Elie Hervé

Vincent Creuze

Jose Gorrotxategi

Arkaitz Oyarzabal

David Culla

Damien Sallé

Olivier Tempier

Stéphane Caro
email: stephane.caro@ls2n.fr

Nicola Ferrari

Marc Chaumont

Gérard Subsol

The Robotic Seabed Cleaning Platform: An Underwater Cable-Driven Parallel Robot for Marine Litter Removal

Keywords: Marine litter, underwater robots, cable-driven parallel robots

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

It is estimated that about 70% of marine debris sinks to the seabed where it will fragment in micro and nano plastics. On overall, tens of million tons of waste and debris are estimated to lie on the seafloors of seas and oceans worldwide. Significant efforts to reduce sea and ocean pollution are thus of fundamental importance. Besides, developing new techniques for the removal of marine litter is needed. In this context, the European Union project MAELSTROM [START_REF]European union's H2020 project MAELSTROM[END_REF] aims at designing and integrating technologies to identify, remove, sort and transform all types of collected marine litter into valuable raw materials. In this project, two systems are considered for marine litter removal. The first one is developed by The Great Bubble Barrier and consists in catching plastic pollution in rivers before it reaches the ocean, using bubbles. The second one is presented in the present paper: The Robotic Seabed Cleaning Platform. It mainly consists of a floating platform that supports the base elements of a 6-DOF Cable-Driven Parallel Robot (CDPR) actuated by eight winches. The mobile platform of this CDPR can work underwater and is equipped with sensors to control the underwater mobile platform motion and detect & identify marine litter to be removed. To achieve efficient and selective removal, an aspiration system to suck up smaller litter and a gripper to grasp and remove larger items, e.g. tires, are also installed on the CDPR underwater mobile platform.

Existing solutions for removal of marine litter lying on the seabed can be highly harmful to the marine ecosystem, e.g., dredges and bottom trawl nets. Human divers can also remove litter from the seabed but this work can put them in danger and their actions are limited in time and litter weight. Another option for marine litter removal is to use robotic systems. For instance, there exist autonomous surface vehicles to remove floating pollution such as the low cost, zero greenhouse emissions WaterShark [4] and the multi-purpose Jellyfishbot [START_REF]Jellyfishbot: Surface robot for the cleaning and the depollution of water surfaces[END_REF]. Besides, to remove litter from the seabed, underwater robots [START_REF] Antonelli | Underwater Robots: Motion and Force Control of Vehicle-Manipulator Systems[END_REF] can be used. Both autonomous underwater vehicles and Remotely Operated Vehicles (ROV) allow to reach seabed at depth of several tens or hundreds of meters. For example, the SeaClear project [START_REF]European union's H2020 project SeaClear[END_REF] aims at deploying a system consisting of an unmanned surface vehicle, an unmanned aerial vehicle, a small ROV and a larger ROV. The unmanned surface vehicle is the mothership that deploys the aerial vehicle and the two underwater robots. The aerial vehicle can search litter from the air (in clear water) and helps the navigation of the surface vehicle while the small ROV scan the seabed at close range. The larger ROV removes litter with a gripper and suction device. The SeaClear system should thus be able to operate autonomously over large distances but can remove rather small lightweight objects from the seafloor. Moreover, ROV may take time to stabilize before being able to grasp a litter, thus impairing efficiency. Hence, one advantage of the Robotic Seabed Cleaning Platform introduced in this paper is its capability to efficiently and selectively remove relatively large and heavy objects, as well as smaller ones, since it is based on a CDPR which constitutes a (relatively) accurate and fast positioning system. Numerous previous papers on underwater cables exist in the literature, from their physical modeling, e.g. [START_REF] Boyer | Geometrically exact kirchhoff beam theory: Application to cable dynamics[END_REF][START_REF] Buckham | Formulation and validation of a lumped mass model for low-tension rov tethers[END_REF], to their use as ROV umbilical, e.g., [START_REF] Laranjeira | Catenary-based visual servoing for tether shape control between underwater vehicles[END_REF][START_REF] Viel | Self-management of the umbilical of a ROV for underwater exploration[END_REF], where the cables are usually used in low tension contrary to the case of CDPRs where tensed cables transmit motion and force. In fact, few previous works deal with marine and underwater CDPRs. In [START_REF] Ghaffar | Study on cable based parallel manipulator systems for subsea applications[END_REF], the idea of a 6-DOF underwater mobile platform connected to surface ships by more than 6 cables is presented but there is no specific underwater modeling, design, control or experiments introduced in this paper. In [START_REF] Horoub | Workspace analysis of a gough-stewart type cable marine platform subjected to harmonic water waves[END_REF][START_REF] Horoub | Influence of cables layout on the dynamic workspace of a six-dof parallel marine manipulator[END_REF], the workspace, dynamic performances and various cable configurations of a Gough-Stewart type floating cable-driven marine platform subjected to waves are studied. The winches are placed on the surface mobile platform and the cables anchored on the seabed (mooring cables). Computer simulations are reported but no prototype and experiments are presented. Moreover, the concept of underwater robot actuated in a hybrid fashion by thrusters and cables is introduced in [8] and further studied in numerical simulations in [START_REF] Sacchi | Analysis of hybrid cable-thruster actuated rov in heavy lifting interventions[END_REF], but no experiment or prototype has been presented at the time of writing the present paper.

Hence, the contribution of this paper is to introduce the Robotic Seabed Cleaning Platform (RSCP) design, control and experimental testing to remove marine litter lying on the seabed of Venice lagoon. To the best of the authors' knowledge, it is the first time an underwater CDPR is designed and used. The paper is organized as follows. In Section 2, an overview of the RSCP is presented. Then, in Sections 3 and 4, the RSCP design and control are described, respectively. Finally, Section 5 presents the results of the first RSCP cleaning campaign in Venice lagoon while Section 6 concludes the paper.

Presentation of the Robotic Seabed Cleaning Platform

The RSCP consists mainly of a CDPR installed and operated from a floating barge. The mobile platform of the CDPR can work underwater and is equipped with selective cleaning tools that allow the removal of legacy small (micro-plastics > 5 mm) and large items on the seabed, as well as floating plastics in the water column, in a beneficial way for the marine ecosystem. The main components of the RSCP are presented in Fig. 1 where the mobile platform is shown outside of the water. In the CAD view of Fig. 2, the mobile platform is shown working underwater. The 6-DOF mobile platform of the RSCP is driven by eight cables in a suspended configuration similar to the one of the CoGiRo CDPR [START_REF] Gouttefarde | Geometry selection of a redundantly actuated cable-suspended parallel robot[END_REF]. Four base frame posts are secured to the floating platform (floating barge), the latter being made of several modules (pontoons) assembled together. Each post has two winches and pulleys that route the cable from the winch to the top of the post where a swiveling output pulley directs the cable toward the mobile platform. One of the pulley located near the winch at the bottom of the post is equipped with a load pin and thereby allows the measurement of the cable tension. The mobile platform can move down in the water below the floating barge which has a rectangular hole (inner pool) in its middle. An aspiration system to suck up smaller litter in the water column and seabed below the hole in the floating barge, as well as a gripper to remove larger items, are installed on the CDPR underwater mobile platform. A control room hosts the electronic and control cabinets, the control PCs and the human operator(s) of the RSCP.

A picture of the RSCP during first tests on the ground in Tecnalia's facilities in Spain is shown in Fig. 3. The mobile platform is the beige structure in the middle of the picture. After its setting up in Tecnalia's facilities, the RSCP was disassembled and moved to Venice in Italy for its first underwater cleaning campaign (cf Section 5), as shown in Fig. 4.

Design of the Robotic Seabed Cleaning Platform

The RSCP components have been designed to be used in a harsh outdoor maritime environment. The maximum depth of operation of the underwater mobile platform is directly correlated to the size of the floating barge. Besides, the rigidity of the barge depends on the size of its inner pool. A compromise has been found in the design of the floating barge to reach the required depth of operation (between 15 to 20 m) while maximizing its rigidity. The CAD of the floating barge final design is shown in Fig. 5.

The floating barge, designed for both still waters and sea operations, is composed of several pontoons. Two metallic posts are fixed on two steel bases located on the same pontoon to avoid relative displacements between the swiveling output pulleys of the CDPR. The two other posts are also mounted on another single pontoon. During the experiments reported in Section 5, the relative displacement between two opposite posts mounted on different pontoons has been estimated by means of measurements with a total station. When middle size waves are shaking the floating barge, the relative movement is around +/-5 mm, which was deemed to be an acceptable value. The floating barge is maintained in position, depending on the depth of the cleaning, by anchor feet or wire anchors to the seafloor. The floating barge is displaced from a cleaning spot to another one by a tugboat.

As shown in Fig. 6, each cable goes out of the winch is guided by pulleys to a movable carriage. This carriage has a vertical translation to move the upper swiveling pulleys from a the lower position to an upper position, the latter being 2.5 m higher than the former. On the one hand, when the carriage is at the top of the post (parking position), this reconfiguration capability allows the CDPR mobile platform to be out of the water for assembly and maintenance operations and for moving the floating barge from spot to spot. On the other hand, when the carriage is at the bottom of the post (working position), it allows having the robot inside the water for marine litter removal operations with increased operational workspace. The marine litter removal operations are also possible in parking position, but the CDPR workspace size is reduced. The design of the supporting structure of the winches and pulleys is suitable for any kind of pontoons and floating barge and is independent of the height of the pontoon. The location of the posts on the floating barge has been defined by optimizing the workspace of the CDPR with methods well known in the state of the art.

The calibration of the positions of the swiveling pulleys (points A i ) is made with the help of a total station that measures reflective targets closed to the pulleys as shown in Fig. 7. For practical reasons, it is not possible to measure directly the positions of the cable-platform connection points B i as they are virtual points at the center of rotation of universal joints. Hence, as shown in Fig. 8, a 3D printed plastic part installed around point B i is used to measure 2 reflective targets. The position of point B i is at the middle of the measured targets. The plastic part is removed from point B i once it has been measured and installed to the next point B i . Besides, three reflective targets are fixed on the mobile platform to measure its pose. The positions of these targets are measured just before or after the position measurements of the points B i . This platform pose measurement is required to calibrate the initial pose of the platform.

The underwater mobile platform, shown in Fig. 9, is a classic steel welded structure, protected by a marine resistant paint. The cable attachment points (points B i ) are made with stainless steel universal joints. All bearings at points A i and B i are Igus plastic bearings to avoid corrosion. The cables are nonrotating steel wires of diameter 12 mm. They are generously greased with a bio sea water compatible grease, to prevent corrosion.

Sensors and control system

Various sensors are located on the floating floating barge including a pressure sensor to compensate for the atmospheric pressure and two RTK GPS placed at two different locations on the floating barge to estimate the position and orientation (around the vertical axis) of the floating barge based on position measurements from a global navigation satellite system. It thus allows to position the RSCP on top of a previously generated bathymetry map of the seabed environment, allowing to identify "hotspots", to position the barge inner pool above one of these hotspots and to make the CDPR mobile platform dive to reach it. This capability turned out to be a key enabling feature in the highly turbid water of Venice lagoon. Moreover, the CDPR has eight force sensors placed at fixed (non swiveling) routing pulleys to measure the cable tensions as well as encoders in the winch motors.

The sensors located inside the underwater platform shown in Fig. 9 comprise five IP cameras which enable the human operator located in the control room on the floating barge to see the surrounding of the underwater platform (provided that water turbidity is not too high). Several other sensors, listed below, are also integrated into the so-called "smart camera" system, shown in Fig. 10, which is fixed to the mobile platform on one of its edge. The smart camera mainly consists of the following components. A camera used for visual servoing: The camera enables a marine litter to be seen by the operator who can click on the litter in the camera image so that the CDPR mobile platform approaches the litter automatically. One depth (pressure) sensor to measure the depth of the mobile platform (distance with respect to the sea surface). One IMU used mainly to measure the orientation of the underwater mobile platform. A Doppler Velocity Log (DVL) which is a hydro-acoustic sensor integrating four acoustic beams to measure the distance of the mobile platform to the seabed and its velocity with respect to the seabed. The DVL estimates velocity relative to the sea bottom by sending acoustic waves from four angled transducers and then measure the frequency shift (Dopplers effect) from the received echo. By combining the measurements of all four transducers and the time between each acoustic pulse, it is possible to estimate the speed and direction of movement. Since the DVL also indicates the altitude with respect to the seabed (from the range measurements achieved by the four beams), it can be used to build a local map of the seabed slope (sea ground surface) such as illustrated in Fig. 12. To this end, the pressure sensors on the floating barge and on the underwater mobile platform are also used to determine the depth of the mobile platform with respect to the floating barge and the altitude of the floating barge with respect to the seabed. Subsequently, the two GPS on the floating barge can be used to locate the local map in a global earth coordinate system. This allows either estimating previously located underwater litter positions and/or to build a map of the (removed) litters.

The control system of the CDPR of the RSCP used in the experiments reported in Section 5 consists of the CDPR teleoperation control and the perception system for underwater vision. Regarding the CDPR teleoperation control, the pilot (human operator) uses estimated underwater mobile platform pose as well as the cameras located on the mobile platform to drive the underwater mobile platform using a joystick. The joystick commands issued by the pilot are Regarding the perception system for underwater vision, the camera in the smart camera system is used as the underwater perception system. It notably enables visual servoing: Once a marine litter is seen by the human operator (at relatively closed range from the camera because of water turbidity), the latter can click on the litter in the camera image and the CDPR mobile platform approaches the litter automatically. Figure 12 shows the HMI of the underwater perception system. On the left, the depth map built with the DVL measurement is shown. In the middle, the human operator can see the image from the camera of the smart camera system (here shown in turbid water with very little visibility range). The operator can click on a point in this image, where a possible litter to be removed is located, so that the mobile platform moves toward this point. On the right of the HMI, the bathymetry map is shown. It is centered on the RSCP inner pool (the orange rectangle). The red rectangle is the safe working zone where no collision between the RSCP and the CDPR cables can happen. In the HMI bottom part, various sensor values and other information are displayed.

Experiments in Venice

The RSCP was tested in September 2022 in Venice lagoon in Italy where it performed a cleaning campaign. Despite highly turbid water, the cleaning campaign was a success since many marine litters of several different types were removed from the seabed, as shown in Fig. 13. To deal with the very low visibility due to the turbidity of the lagoon water, real-time image enhancement was used to improve the perception of the marine litter with the cameras on-board the CDPR underwater mobile platform.

Conclusion

This paper presented the Robotic Seabed Cleaning Platform. It mainly consists of a floating platform that supports the base elements of a 6-DOF CDPR actuated by eight winches. The mobile platform of this CDPR can work underwater and is equipped with sensors to control the underwater mobile platform motion and detect & identify marine litter to be removed. To achieve efficient and selective removal, an aspiration system to suck up smaller litter and a gripper to grasp and remove larger items, e.g. tires, are also installed on the CDPR underwater mobile platform. To the best of the authors' knowledge, it is the first time an underwater CDPR is designed and used. The Robotic Seabed Cleaning Platform was successfully experimented in Venice lagoon where many marine litters of several different types were removed from the seabed.

Fig. 1 .

 1 Fig. 1. The main components of the RSCP.

Fig. 2 .

 2 Fig. 2. A CAD view of the RSCP with the CDPR mobile platform working underwater.

Fig. 3 .

 3 Fig. 3. The RSCP during tests in Tecnalia's facilities.

Fig. 4 .

 4 Fig. 4. The RSCP in Venice lagoon.

Fig. 5 .

 5 Fig. 5. CAD of the final design of the floating barge.

Fig. 6 .

 6 Fig. 6. Final CAD design of the metallic posts (left subfigure) and the swiveling output pulleys (right subfigure).

Fig. 7 .

 7 Fig. 7. Calibration: Determination of the positions of the points Ai from the target measurements.

Fig. 8 .

 8 Fig. 8. Calibration: 3D plastic parts used to measure the positions of points Bi.

Fig. 9 .

 9 Fig. 9. Close-up view of the underwater mobile platform including 3 reference points on the platform (reflective targets).

Fig. 10 .

 10 Fig.10. The waterproof underwater capsule of the smart camera system (left) and the smart camera system description with reference frames fixed to it (right).

  interpreted as desired operational velocities, i.e., linear and angular velocities of the underwater mobile platform. These velocities are integrated to provide desired positions and orientations of the mobile platform that are converted into desired winch motor positions by means of the inverse kinematics of the CDPR. These desired joint motor positions are sent on the fly to the drive setpoint controllers which are in charge of the feedback position control of the motors. The Human-Machine Interface (HMI) of the CDPR is shown in Fig 11. It allows the human operator (pilot) to monitor various sensor values and to choose between different control modes. The human operator can see the videos from the IP cameras placed on-board the underwater mobile platform in a dedicated screen.

Fig. 11 .

 11 Fig. 11. HMI of the CDPR: 1. Winch axis information area; 2. Secondary commands for individual or combined motion of the cables, motion command to calibration position, and enabling post vertical carriage linear movements using the joystick; 3. Mobile platform position and orientation information area; 4. Manual commands area including initialization (calculation of the Cartesian pose computed using the winch motor positions by means of forward kinematics), manual move with joystick enabling & speed override setting, and robot status; 5. Automatic command area including pointto-point motion command (actual to destination pose) and CNC trajectory program execution; 6. Cable tension monitoring area: Force sensor values in Kg.

  4

Fig. 12 .

 12 Fig. 12. HMI of the underwater perception system.

Fig. 13 .

 13 Fig. 13. The RSCP removing a tire from the water (left) and various litters collected by the RSCP during the cleaning campaign in Venice lagoon.

As shown in the following videos of the RSCP experiments in Venice: https://youtu.be/1EVQm-0yyRY and https://youtu.be/16k3-Bp4FCI

Acknowledgments

This work was supported by the European Union's H2020 Program (H2020-FNR-2020) under the grant agreement No. 101000832 (MAELSTROM project).


K Ardaneh

R Giust

B. Morel P-J Charpin

F Courvoisier

Electron heating and radiation in high aspect ratio sub-micron plasma generated by an ultrafast Bessel pulse within a solid dielectric

When propagating inside dielectrics, an ultrafast Bessel beam creates a high aspect-ratio cylinder of plasma with nanometric diameter that extends over several tens of micrometers to centimeters. We analyze the interaction between the intense ultrafast laser pulse and the plasma rod using particle-in-cell simulations. We show that electrons are heated and accelerated up to keV energies via transit acceleration inside the resonance lobes in the vicinity of the critical surface and compute their radiation pattern.

INTRODUCTION

Ultrafast lasers are ideal tools to deposit energy within the bulk of transparent materials [START_REF] Gattass | [END_REF]. This has applications for laser micromachining, for the generation of new material phases as well as for the generation of warm dense matter. Thanks to the nonlinear ionization, the infrared radiation of the laser can generate, early in the pulse, a plasma of electrons and holes in the bulk of transparent dielectrics [2]. The interaction of the trailing part of the laser pulse can heat the plasma if proper conditions are met. Then, depending on the energy density that has been deposited within the plasma, phase change can occur, even at sub-picosecond time scale via non-thermal melting if the ionization rate of the solid is sufficiently high (only few %) [3,4]. In this case, the material can quickly reach the warm dense matter regime, in which the material is at solid density but with temperatures on the order of 1-10 eV [5,6] . This is a challenging state still under study which is relevant for the modeling of many astrophysical objects [7]. The phase change triggers also a series of physical phenomena in the material such as shockwave emission, void formation [8], densification around the void [9]. In the densified regions around voids formed within the bulk, the extreme temperatures and pressures reached within a short time can lead to the formation of new material phases as it has been observed in sapphire and silicon [10,11]. Finally, the formation of voids inside the material has useful applications for laser cutting or drilling of transparent materials. High-speed (typ. 1 m/s) cutting of glass with the stealth dicing technology is one of the most relevant examples [START_REF] Mishchik | Frontiers in Ultrafast Optics: Biomedical, Scientific, and Industrial Applications XVI, Proc. SPIE 9740[END_REF][START_REF] Meyer | [END_REF][14][15].

In these three domains of applications, it is clear that a challenge is to reach the largest energy density as possible over the largest volume possible. However, it is well-known that nonlinear filamentation of Gaussian beams prevents reaching extreme energy densities inside dielectrics. In contrast, we recently demonstrated that it is possible with Bessel beams [START_REF] Ardaneh | High energy density plasma mediated by collisionless resonance absorption inside dielectrics[END_REF].

Zeroth-order Bessel beams, also called "diffractionfree" beams, constitute a propagation-invariant solution to the wave equation [START_REF] Durnin | [END_REF]. They are featured by a conical flow of light directed toward the optical axis. The conical interaction creates an interference pattern, characterized by an intense central lobe surrounded by several other circular lobes of lower intensity. Importantly, when propagating inside transparent solids, an ultrafast laser pulse shaped as a Bessel beam can generate a nano-plasma rod with a length that is adjustable independently of the diameter. Recent work has shown that the length of this plasma rod can be scaled from tens of micrometers to 1 cm [15].

We have recently demonstrated that 100 fs Bessel beams can generate elongated plasma rods with over critical plasma density in sapphire Al 2 O 3 [START_REF] Ardaneh | High energy density plasma mediated by collisionless resonance absorption inside dielectrics[END_REF], in the regime corresponding to the formation of high aspect ratio nanovoids [18]. In contrast with the case of the Gaussian beam, all the pulse energy in the Bessel beam impinges with a relatively large incidence angle toward the plasma rod generated early in the pulse along the optical axis. This configuration is ideal to trigger resonance absorption. In reference [START_REF] Ardaneh | High energy density plasma mediated by collisionless resonance absorption inside dielectrics[END_REF], we have demonstrated the occurrence of resonance absorption inside sapphire by comparing experimental results to particle-in-cell (PIC) simulations. The strong energy transfer between the laser wave to the core of the plasma opens the possibility to reach the warm dense matter regime and to produce temperatures on the order of 10 eV. This explains the opening of high aspect ratio nano channels inside several dielectrics upon Bessel beam femtosecond illumination. Importantly, the conical geometry of Bessel beams is invariant along the propagation. This implies that results obtained with Bessel beams of only several tens of micrometers in length can be extrapolated to several centimeters.

A key question is the understanding of the microphysics of the interaction of the Bessel beam with the sub-micron plasma, at moderate intensities (typically 10 14 W/cm 2 ). For this, we have used Particle-In-Cell (PIC) simulations to investigate the electron plasma wave generation, particle heating and acceleration, as well as the radiation emitted by the accelerated particles.

SIMULATIONS

Our PIC simulations are based on the interaction of a Bessel-Gauss beam [19] with a preformed plasma. The 100 fs laser pulse, with a central wavelength of 800 nm, is polarized along x-direction. We assume that nonlinear ionization has produced early in the pulse a plasma and we model the interaction of the most intense part of the laser pulse with this pre-plasma. We used the numerical code EPOCH [20], without ionization, and the numerical scheme is detailed in reference [START_REF] Ardaneh | Femtosecond laser-induced sub-wavelength plasma inside dielectrics: I. field enhancement[END_REF]. We maintained the numerical heating at a negligible level over the duration of the simulation (320 fs). The pre-plasma is a plasma rod extending over the whole longitudinal length of the box (because of the invariance of the Bessel beam), and its transverse cross-section is elliptically-shaped. The profile is Gaussian and is the same as the one matching our experimental results, as shown in reference [START_REF] Ardaneh | High energy density plasma mediated by collisionless resonance absorption inside dielectrics[END_REF]: the critical radius is 190 nm along the polarization direction (x axis) and 380 nm in the other direction, as shown in Fig. 1(a). The peak intensity of the pulse is 610 14 W/cm 2 , for a pulse duration of 100 fs.

FIELD AMPLIFICATION AND PARTICLE ACCELERATION

Figure 1(b) shows the evolution of the E x component of the electric field in time, on a segment placed along the x direction at the propagation distance corresponding to the highest intensity reached in the Bessel-Gauss beam [START_REF] Boucher | [END_REF]. We first observe the field enhancement in the region where the permittivity decreases because of the presence of plasma ( |x| < 190 nm). A strong field amplification occurs on the critical surfaces, that are indicated with dashed lines in Fig. 1(a). The field reaches a maximum value of 1 GV/cm. This corresponds to an amplification factor of approximately 7 in comparison with the input laser field.

At the critical surface, the resonance absorption takes place. The wave conversion phenomenon creates electron plasma waves. We plot in Fig. 2(a) the density of electrons at the peak of the pulse, in x -z plane. The white line shows the contour at the critical density. We see plasma oscillations taking place. To allow a clearer visualization of the plasma waves, we computed the electrostatic field, that is shown in Fig. 2(b). It has been derived from the density ρ using Gauss's law in the Fourier k-space, E ES x = -jkρ(k)/k 2 / 0 . We can observe that, in the sub-critical region, outside the plasma, the electron plasma waves are quickly damped. This arises from the efficient Landau damping. In the over-critical region, the field oscillations are due to electron sound waves [START_REF] Ardaneh | Femtosecond laser-induced sub-wavelength plasma inside dielectrics: I. field enhancement[END_REF]23]. They penetrate relatively deeply into the overcritical region and we observe that they are curved. The propagation of these waves into the overcritical region is attributed to the fact that the temperature is highly inhomogeneous in the plasma. This is also the reason of the variation of the spatial period along x, hence the variation of the apparent curvature of the fringes. This structure will have a strong impact on the acceleration of electrons as we will see below.

The heating of the particles has been investigated in Ref. [START_REF] Ardaneh | High energy density plasma mediated by collisionless resonance absorption inside dielectrics[END_REF]. In summary, the wave particle energy exchange is very efficient: we observe the heating of the electron population mainly around the critical surfaces. In Fig. 2(c), we show the particle distribution in the phase space x -p x after the pulse (135 fs). We evaluated the main component temperature to be 1.3 eV, and a hot electrons component at 70 eV. In addition, we observe in Fig. 2(c), two tails expanding outwards, at high momentum, outside the plasma.

These tails correspond to highly accelerated particles with energies up to 7 keV. Figure 1 provides a glimpse on the physical mechanism of the acceleration. We have selected out 1000 of the most energetic particles and have traced their trajectories. In Fig. 1(b), we have plotted a selection of 8 representative trajectories. Two of them show highly accelerated particles that escape from the plasma. The other 6 are accelerated by the same mechanism, but remain trapped by a static electric field generated by a double layer formation that will be explained later. The acceleration mechanism is the same in all cases: in the different sub-figures 1(c-h), we see that the particles undergo transit acceleration, which occurs when a particle travels through a highly non-uniform electromagnetic field [24][25][26]. The electrons gain energy by riding on the electron plasma wave, that is curved in the x -t space. The effective acceleration occurs on a distance of less than 60 nm, when crossing the high resonance field. Depending on the exact position of the particle with respect to the plasma wave, the acceleration is more or less efficient. We see that the curvature of the plasma wave is a key to obtain a progressive acceleration of the particle while it remains on the peak of the wave.

Particle acceleration and heating transfer a fraction of the electrons away from the main plasma, as it is also apparent on the x -p x representation of Fig. 2(c). This generates a so-called double layer on either sides of the plasma. These double layers are apparent in Fig. 1 because they generate a static E-field that is superimposed to the laser pulse. Importantly, this static field has an amplitude that is as high as the resonance field of the laser pulse itself (on the order of GV/cm). This static Efield even remains after the laser pulse has vanished. Its damping is governed by the collisions inside the plasma.

RADIATION PATTERN

One of the major advantages of PIC codes is the possibility to access the full information about the particle dynamics, e.g., the position and the momentum as a function of time. If this information can be retrieved and stored for a number of particles, it is then feasible to post-process the radiation associated with a particular set of particles. The radiation diagnostic uses the information from the particle trajectories, position and momentum over time, and determines the energy being radiated by an accelerated charged particle.

Let us consider a particle at position r 0 (t) at time t. At the same time, we observe the radiated electro-magnetic fields from the particle at position r. Due to the finite velocity of light, we observe the particle at an earlier position r 0 (t ) where it was at the retarded time t = t -R (t ) /c, where R (t ) = |r -r 0 (t ) | is the distance from the charged particle (at the retarded time t ) to the observer. Using the Liénard-Wiechert potentials, the total energy W radiated per unit solid angle per unit frequency from a charged particle moving with instantaneous velocity β = v/c under acceleration β = a/c can be expressed as [START_REF] Jackson | Classical Electrodynamics[END_REF]:

d 2 W dωdΩ ∝ ∞ -∞ n × [(n -β) × β] (1 -β • n) 2 e iω(t-n•r(t)/c) dt 2 (1)
Here, n = R (t ) /|R (t ) | is a unit vector that points from the particle retarded position towards the observer. The observer's viewing angle is set by the choice of n (x sin θ cos φ + ŷ sin θ sin φ + ẑ cos θ).

Figure 3 shows the total radiated energy from an ensemble of 100 randomly selected electrons traced in the simulations that we computed using Eq. ( 1). The distribution is plotted as a function of the angles (θ, φ) in Fig. 3(left). The forward direction corresponds to values of θ below 90 • . We observe that the forward signal shows maxima at (θ, φ) ≈ (0, π/2) and (0, 3π/2), perpendicular to the electron acceleration in the x-direction, which indeed corresponds to the pump laser polarization direction. The emission follows the well-known power distribution per solid angle Ω emitted by a single particle [START_REF] Jackson | Classical Electrodynamics[END_REF]:

dP dΩ ∝ | β| 2 (1 -β cos θ) 3 1 - sin 2 θ cos 2 φ γ 2 (1 -β cos θ) 2 (2)
where γ is the Lorentz factor. Noticeably, the power shows a much higher signal in the angles corresponding to the forward direction than for the backward direction (90 • < θ ≤ 180 • ). This behaviour could be explained by the coherence of the phases of the dipole moments induced along the plasma rod. A more detailed analysis of the radiation spectrum, out of the scope of the present article, shows the presence of second harmonic generation and of THz radiation in the forward direction.

In conclusion, we have investigated the interaction between a moderately intense laser pulse shaped as a Bessel beam with a nanoplasma rod using particle-in-cell simulations. We have demonstrated that resonance absorption generate plasma waves inside plasma. These plasma waves are highly damped in the sub-critical region while plasma sound waves can propagate over several hundreds of nanometers inside the overcritical plasma. The analysis of the trajectories of the most energetic particles shows that the main acceleration mechanism is transit acceleration. It occurs at the critical layer when particles are trapped inside a plasma wave and gain energy until they are released at the critical surface. Because of the heating of the electron gas, two double layers form on either sides of the nano-plasma. The most energetic particles, with energies up to 7 keV can escape the plasma while part of the hot electrons remain trapped by the potential well due to the electrostatic field of the double layer. Overall, our results enable us to gain insights into the micro physics of the laser-plasma interaction that this relevant for the understanding of the different mechanisms of the deposition of the femtosecond laser pulse energy inside dielectrics. Our results reveal a rich physics which can be exploited in several fields of applications: laser-matter interaction, laser micro-machining, warm dense matter and high energy density physics inside solids, as well as the generation of electrostatic fields and terahertz radiation.

FIG. 1 .

 1 FIG. 1. (a) Cross section of the 2D density profile of the plasma. The black solid line shows the density profile at y = 0 along x-direction. The critical density nc is 1.7 × 10 21 cm -3 (b) Ex component of the electric field as a function of time and x position. The solid colored lines correspond to the projection in the plane of 8 particle trajectories. Their energy is indicated using the color code. (c-h) Zoom-in views of the acceleration of the electrons as they leave the plasma, together with the exact value of the field Ex(x, y = yp, z = zp, t) sampled at the particle position (xp,yp,zp, t).

FIG. 2 .

 2 FIG. 2. (a) Plasma density at the time corresponding to the peak intensity in the plane y = 0, which is parallel to the polarization direction. The white solid line shows the contour at the critical density(b) Longitudinal component of the electric field, which allows the visualization of the plasma density waves. (c) x -px phase space of the electron population at a time 135 fs after the peak of the pulse.

FIG. 3 .

 3 FIG. 3. (left)The total energy radiated per unit solid angle per unit frequency from the accelerated electrons. (right) Configuration of the angles. The laser polarization is along the x axis

Acknowledgments : The research leading to these results has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No 682032-PULSAR), Région Bourgogne Franche-Comté, I-SITE BFC project (contract ANR-15-IDEX-0003), and the EIPHI Graduate School (ANR-17-EURE-0002). We acknowledge the support of PRACE HPC resources under the Project "PULSARPIC" (PRA19 4980 and RA5614), and GENCI resources under projects A0070511001 and A0090511001.

Data availability statement: Data will be made available on reasonable request.