Julien Rosselgong

Maud Chemin

Cédric Cabral

Gauvin Hemery

Jean-Michel Guigner

Guillaume Chollet

Gilles Labat

Denilson Da

Silva Perez

Frédérique Ham-Pichavant

Etienne Grau

Jean- Michel Guigner

Stéphane Grelier
email: sgrelier@enscbp.fr

Sébastien Lecommandoux
email: lecommandoux@enscbp.fr

Henri Cramail
email: cramail@enscbp.fr

Synthesis and self-assembly of Xylan-based amphiphiles: from bio-based vesicles to antifungal properties

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

and their high loading capacity with propiconazole as an antifungal active molecule was shown. The resulting vesicles loaded with propiconazole in a microfluidic process, proved to significantly improve the antifungal activity of propiconazole, demonstrating the high potential of such xylan-based amphiphiles.

1-Introduction

Knowing that the fossil fuel available on earth will be spent in the foreseeable future that the barrel price is quite volatile and because of environmental issues, the development of new chemicals from renewable resources is nowadays a strategic research area. Among the available renewable biomass, polysaccharides such as starch, pectin, cellulose and hemicelluloses, gums or arabinogalactan confer diverse functions of food reserve, cementing, ion balancing, structure, defense or cell adhesion [1]. Within the last two decades, there has been a growing interest in lignocellulosic biomass, which is a sustainable resource to produce fuels, chemicals and materials [2][START_REF] Ragauskas | The Path Forward for Biofuels and Biomaterials[END_REF][START_REF] Deutschmann | From Plant Biomass to Bio-Based Chemicals: Latest Developments in Xylan Research[END_REF]. Contrarily to cellulose that is the most industrialized polysaccharide, woody hemicelluloses are less valued. The most abundant hemicellulosic polymers are xylans, essentially linear heteropolysaccharides, accounting for 25-35% of the dry biomass of woody tissues. Extensive literature data report on the isolation, characterization, derivatization and applications of xylans [START_REF] Izydorczyk | Cereal Arabinoxylans: Advances in Structure and Physicochemical Properties[END_REF][START_REF] Ebringerova | Xylans of Industrial and Biomedical Importance[END_REF][START_REF] Ebringerova | Xylan and Xylan Derivatives -Biopolymers with Valuable Properties, 1. Naturally Occurring Xylans Structures, Isolation Procedures and Properties[END_REF][START_REF] Mäki-Arvela | Synthesis of Sugars by Hydrolysis of Hemicelluloses-A Review[END_REF][START_REF] Sun | Preparation of (1→4)-β-d-Xylooligosaccharides from an Acid Hydrolysate of Cotton-Seed Xylan: Suitability of Cotton-Seed Xylan as a Starting Material for the Preparation of (1→4)-β-d-Xylooligosaccharides[END_REF]. However, the chemical modification and the degradation of hemicelluloses into oligosaccharides are still a challenging task that would open the route to biomacromolecular engineering. Amphiphilic copolymers are composed of hydrophilic and hydrophobic segments that confer the behavior of self-assembly to these systems. Such materials can self-organize into nanoscale-size objects such as micelles, wormlike micelles or vesicles in solution, can form some well-defined assemblies at interfaces such as air-liquid, liquid-solid or air-solid and have been studied in the past recent years as nanosized reactors, nano-patterned surfaces for lithography, organic-inorganic mesostructures and drug delivery systems [START_REF] Blanazs | Self-Assembled Block Copolymer Aggregates: from Micelles to Vesicles and their Biological Applications[END_REF].

Polysaccharides-based amphiphiles are of particular interest due to their biocompatibility, bioactivity and biodegradability. Polysaccharides-based block copolymers can be designed using different methods, such as enzymatic polymerization, ring-opening polymerization, reversible-deactivation radical polymerization or end-to-end coupling [START_REF] Schatz | Polysaccharide-Containing Block Copolymers: Synthesis, Properties and Applications of an Emerging Family of Glycoconjugates[END_REF]. In the last case, many oligosaccharides from amylose [START_REF] Ziegast | Linear and Star-Shaped Hybrid Polymers. Part IV. Phosphorolytic Syntheses with Di-, Oligo-and Multifunctional Primers[END_REF], cellulose [START_REF] Yagi | Synthesis and Characterization of Cellulose-b-Polystyrene[END_REF], chitosan [START_REF] Tornoe | Peptidotriazoles on Solid Phase: [1,2,3]-Triazoles by Regiospecific Copper(I)-Catalyzed 1,3-Dipolar Cycloadditions of Terminal Alkynes to Azides[END_REF], dextran [START_REF] Bernard | Preparation of a xanthate-terminated dextran by click chemistry: Application to the synthesis of polysaccharide-coated nanoparticles via surfactant-free ab initio emulsion polymerization of vinyl acetate[END_REF], maltoheptaose [START_REF] Li | Synthesis and characterization of novel amphiphilic block copolymers based on maltoheptaose and poly(ε-caprolactone)[END_REF], xyloglucan [START_REF] Lohmann | Hybrid Block Copolymers Incorporating Oligosasaccharides and D Synthetic Blocks Grown by Controlled Radical Polymerization[END_REF], hyaluronan [START_REF] Upadhyay | Biomimetic Doxorubicin Loaded Polymersomes from Hyaluronan-block-Poly(γ-benzyl glutamate) Copolymers[END_REF], galactan [START_REF] Bonduelle | Multivalent Effect of Glycopolypeptide Based Nanoparticles for Galectin Binding[END_REF] and others have been coupled to synthetic blocks, making such bioconjugates of major interest especially for biomedical applications.

The aim of this contribution is to develop high added-value xylan derivatives, by designing fully bio-based amphiphilic oligomers. Beechwood xylans were first degraded into xylooligosaccharides by acidic hydrolysis [START_REF] Sun | Preparation of (1→4)-β-d-Xylooligosaccharides from an Acid Hydrolysate of Cotton-Seed Xylan: Suitability of Cotton-Seed Xylan as a Starting Material for the Preparation of (1→4)-β-d-Xylooligosaccharides[END_REF]. The hydrolysis conditions were previously optimized in order to obtain well-defined xylo-oligosaccharides, i.e. oligomeric chains of about six xylose units that have only one methylglucuronic acid unit positioned at the nonreductive chain end [START_REF] Chemin | Synthesis and characterization of functionalized 4-Omethylglucuronoxylan derivatives[END_REF][START_REF] Chemin | Well-defined oligosaccharides by mild acidic hydrolysis of hemicelluloses[END_REF]. The xylo-oligomers were then functionalized from their reductive end with an azide moiety, providing them the ability to couple with alkynefunctionalized fatty acid derivatives using 'click chemistry'. The obtained amphiphilic bioconjugates were finally studied according to their self-assembly properties that were demonstrated using three different methods: direct solubilization, thin-film rehydration followed by extrusion and microfluidics. Thereafter the resulting amphiphilic self-assembled nanostructures were characterized via dynamic light scattering (DLS), static light scattering (SLS) and transmission electron microscopy (TEM). Loading experiments were conducted by microfluidics to encapsulate either nile red, further detected by confocal microscopy or propiconazole to undergo antifungic biological evaluation. High loading capacity, together with significant improvement of the antifungal activity of propiconazole were demonstrated.

2-Experimental

Materials

Xylans from beechwood (MGX) were purchased from Symrise and ultrafiltrated prior reaction [START_REF] Chemin | Synthesis and characterization of functionalized 4-Omethylglucuronoxylan derivatives[END_REF]. Methyl oleate (MeOl, 83.5%) and methyl ricinoleate (MeRic, 90.9%) were donated by ITERG and used without further purifications. Copper(II) sulfate and baryum hydroxide (Ba(OH) 2 ) were obtained from Prolabo. Cuprisorb was purchased from Seachem. Ethanol (96.0%, EtOH) was obtained from VWR international. Propiconazole (solution 100 ng/µl in MeOH), sulfuric acid (ACS reagent, 95.0-98.0%, H 2 SO 4 ), 2-aminoethyl chloride (99.0%), sodium cyanoborohydride (95%), sodium azide (reagent plus, ≥99.5%), propargyl alcohol (99%), 1,5,7-triazabicyclo[4.4.0]dec-5-ene (98%, TBD), nile red (for microscopy), ethyl acetate, magnesium sulfate, dimethyl sulfoxide (DMSO), sodium L-ascorbate and tetrahydrofuran (THF) were purchased from Sigma Aldrich and used without further purification. Dialysis was conducted using a Spectra/Por®6 MWCO 100-500 Da membrane.

Synthesis procedures

Dilute acidic hydrolysis of xylan.

A scale up experiment, times 120 for the comparison of mass of MGX involved, was performed compared to the acidic hydrolysis described previously [START_REF] Chemin | Synthesis and characterization of functionalized 4-Omethylglucuronoxylan derivatives[END_REF][START_REF] Chemin | Well-defined oligosaccharides by mild acidic hydrolysis of hemicelluloses[END_REF] and is detailed in the supplementary information.

Reductive amination and functionalization with sodium azide. The overall reaction allowing the functionalization of the XOS with an azide group is shown in Scheme 1A. The first step includes a reductive amination of the aldehyde present at the terminal end of the XOS following an adapted procedure [START_REF] Schatz | Polysaccharide-block-polypeptide Copolymer Vesicles: Towards Synthetic Viral Capsids[END_REF]. An amount of 10 g of XOS was dissolved in deionized water at 100g.L -1 . 2-chlorethylamine hydrochloride (15 Eq.) was added under stirring. The mixture was stirred at 50°C for 3 days and NaBH 3 CN was added in 3 portions (3 * 5 Eq.) every day. After cooling down, the mixture was precipitated 3 times in EtOH, resulting in 6.84g of brown powder after freeze-drying. In a second step, the obtained XOS-NH-(CH 2 ) 2 -Cl was dissolved in 40 mL of deionized water and reacted overnight with sodium azide (4 Eq.) at 80°C. The mixture was first cooled down to room temperature then to 0°C with an ice bath. An amount of 3.7 g of KOH was added to the mixture which was then allowed to stir for another hour at 0°C [START_REF] Huynh | Preparation of 'click' hydrogels from polyaspartamide derivatives[END_REF]. The final product, XOS-NH-(CH 2 ) 2 -N 3 , was purified by precipitation in EtOH, solubilized in deionized water then freeze-dried yielding 6.84 g of a pale brown powder.

Transesterification of fatty acid methyl ester. Both MeOl and MeRic fatty acid methyl esters (FAME) were functionalized with an alkyne group following the synthesis depicted in Scheme 2B. In a typical transesterification procedure, 10 Eq. of propargyl alcohol and 0.1 Eq. of TBD were added to 10 g of MeOl. The mixture was stirred at 100°C for 4 hours under a gentle flux of N 2 . To follow, the mixture was placed for 4 hours at 100°C under dynamic vacuum. After cooling down to room temperature, 200 mL of ethyl acetate where added to the mixture followed by 4 consecutive washes with 50 mL of deionized water. The organic phase was dried using MgSO 4 , filtered, then finally dried under high vacuum to yield 7.5 g of pale yellow oil of alkyne functionalized MeOl.

Huisgen cycloaddition. Amphiphilic bioconjugates were produced by 'click' reactions between azide functionalized XOS and alkyne functionalized FAME via the Huisgen cycloaddition as presented in Scheme 1C. In a typical Huisgen cycloaddition, 2 g of XOS azide functionalized were added in a 20 mL solution of DMSO and let under stirring overnight at 30°C. Alkyne functionalized FAME, for example MeRic (0.627 g, 1 Eq.) was added to the mixture. After 15 min, the sodium ascorbate (0.369 g, 1 Eq.) was introduced in the reaction mixture followed by the addition of CuSO 4 (0.292 g, 1 Eq.) 15 min later. The reaction was allowed to stir for 24 hours at 30°C. Yet, 20 mL of deionized water was added to the mixture with 1.168 g of Cuprisorb (4 weight eq. of CuSO 4 ) [START_REF] Anastasaki | Aqueous Copper-Mediated Living Radical Polymerisation of N-Acryloylmorpholine, SET-LRP in Water[END_REF], a powerful copper absorbent, and stirred overnight. Cuprisorb beads were separated by centrifugation (3800 rpm, 5°C, 25 min) and the reaction solution was dialyzed (MWCO: 100-500 Da) for 4 days against deionized water then freeze-dried to afford 0.689 g of pale green powder (yield ≈ 25 %).

Self-assembly procedures

Direct solubilization. Bioconjugates obtained after 'click' reaction between azide functionalized XOS and alkyne functionalized FAME, either XOS-b-MeOl or XOS-b-MeRic depending on the FAME used, were dispersed in filtered deionized water (using a 0.45 µm cellulose acetate filter) or in filtered chloroform (using a 0.45 µm PTFE filter) at a concentration of 10 mg.mL -1 , then diluted to 1 mg.mL -1 and 0.1 mg.mL -1 using filtered solvents. Solutions were magnetically stirred for 24 hours at room temperature and filtered through cellulose acetate or PTFE filters without significant loss prior size characterization by DLS, SLS and TEM.

Thin-film hydration method followed by extrusion. An amount of 50 mg of bioconjugates XOS-b-MeOl and XOS-b-MeRic was dispersed in filtered THF at a concentration of 10 mg.mL -1 and stirred overnight in a 50 mL round bottom flask. THF was removed from the flask via rotary evaporation followed by high vacuum to form a thin film. This film was rehydrated dropwise using 5 mL of filtered deionized water. The solution was then gently stirred at room temperature for 3 hours, then extruded back and forth 15 times through 0.4 µm polycarbonate membranes prior size analysis by DLS.

Microfluidics method using Dolomite's micromixer system. Bioconjugates XOS-b-MeOl or XOS-b-MeRic were dispersed in THF at a concentration of 2 mg.mL -1 and stirred overnight before filtration using a 0.45 µm PTFE filter. The resulting solution was mixed with filtered deionized water using the Dolomite's micromixer system in order to create the selfassembled objects. This system was composed of a microfluidic device (Mitos micromixer chip, lamination-based compact glass microfluidic device), two precision pumps (Mitos-P-Pump flow control, one filled with the bioconjugate in THF solution and the other one with filtered deionized water), fluidic elements (linear connector 4-way and a H interface to enable fluidic connection between the tubing and chip), a microscope (Meros TCU-100) and software to achieve microfluidic mixing (flow control center) and to observe the mixing chip (capture OEM). The key component in the system was the micromixer chip that allowed rapid mixing of the two streams from low to high flow rate ratios (50 µL.min -1 < flow rate < 1000 µL.min -1 ). THF containing bioconjugates was mixed with filtered deionized water at different flow rates (from to 200 to 1000 µL.min -1 ) and the resulting solutions were collected for 5 min then analyzed through light scattering methods. When changing one flow rate parameter, a waiting time of 1 min was respected before the resultant solution was started to be collected.

Loading procedure

Microfluidics method using Dolomite's micromixer system. For nile red loading, 300 µL of a solution of nile red in acetone (10 -4 M) were added to 3 mL of THF containing 6 mg of bioconjugate XOS-b-MeOl. The process of self-assembly used was similar as described above in using a flow rate of 200 µL.min -1 of THF/acetone containing bioconjugate and nile red mixed with a flow rate of 600 µL.min -1 of filtered deionized water. The sample obtained was purified by dialysis (MWCO: 1000 Da) for 2 days against deionized water prior light scattering and confocal microscopy analyses. For propiconazole loading, from 300 µL to 1500 µL of a solution of propiconazole in methanol (100ng/µL) were added to 4 mL of THF containing 8 mg of bioconjugate XOS-b-MeOl. The process of self-assembly used was similar as described above in using a flow rate of 200 µL.min -1 of THF/MeOH containing bioconjugate and propiconazole mixed with a flow rate of 600 µL.min -1 of filtered deionized water. The sample obtained was purified by dialysis (MWCO: 1000 Da) for 2 days against deionized water prior light scattering and antifungal biological evaluation.

Characterization methods

Nuclear Magnetic Resonance (NMR). Analyses were performed at 298 K on a

Bruker AVANCE I apparatus equipped with a 5 mm probe operating at 400.2 MHz for 1 H.

An amount of 20 mg of material was dissolved/dispersed in 0.5 mL of deuterated solvent (CDCl 3 , Eurisotop; 99.5 atom%D, D 2 O, Eurisotop; 99.9 atom%D or DMSO-d6, Eurisotop; 99.8 atom%D) and 128 scans were recorded for 1 H experiments, 4096 for 13 C experiments.

The spectra obtained by proton-detected Heteronuclear Single-Quantum Correlation (HCQC) were acquired over a spectral width of 20,000 Hz for 13 C and 4,000 Hz for 1 H with 1024 data points; 256 increments collected and a delay between two pulses of 1.5 s. Spectra were analyzed using Bruker Topspin software.

Size Exclusion Chromatography (SEC). SEC analyses of MGX and XOS were

performed on a Spectra-Physics Analytical system equipped with a TSK PWH 13 µm guard column, a TSK gel G2000PW column and a TSK gel G3000PW column along with a refractive index detector (model RID-10A) from Shimadzu. The system was calibrated with 6 Shodex pullulan standards ranging from 5.9.10 3 to 375.10 3 g.mol -1 and one oligosaccharide laminarihexaose from Megazyme with M = 990.9 g.mol -1 . A phosphate eluent was used (NaNO 3 0.2 M, Na 2 HPO 4 0.01M adjusted to pH = 9) and running at 0.5 mL.min -1 . SEC analyses of FAME and their alkyne functionalized entities were performed on an Ultimate 3000 system from Thermoscientific, equipped with three G2000, G3000 and G4000 TOSOH HXL gel columns (300 x 7.8 mm) (exclusion limits from 1000 Da to 400 000 Da) at a flowrate of 1 mL.min -1 . Columns temperature was held at 40°C. The system also includes a multi-angle light scattering detector, MALLS and differential refractive index detector, dRI, from Wyatt technology. THF was used as the eluent and polystyrenes as standards.

Matrix Assisted Laser Desorption/Ionisation-Time of flight (MALDI-TOF).

MALDI-TOF analyses were performed on a Voyager apparatus (Applied Biosystems) equipped with a laser pulsed N 2 (337 nm) and an ionisation source assisted by a matrix with a time of flight analyser. Spectra were recorded in positive mode. Samples or 2,5dihydroxybenzoic acid matrix (FlukaChemika; 2,5-DHB > 98.5 %) were solubilised in deionised water at 10 mg.mL -1 . Then, solutions were prepared at a volume ratio matrix: sample 10:1. Finally, 1 or 2 µL of the prepared solutions were deposited on a plate that was dried under vacuum prior analysis.

Dynamic Light Scattering (DLS) and Static Light Scattering (SLS). Dynamic

Light Scattering (Malvern DLS) was used to obtain particle average sizes and their size distribution by using a Malvern ZetaSizer Nano ZS instrument equipped with a standard HeNe laser emitting at 632.8 nm. As a first approach, measurements were carried out with this device at a single angle of 90° and at 25°C. Particle sizes and their size distribution were determinate by the cumulative method (second order). Appropriated dispersants were selected (H 2 O, CHCl 3 or various THF/H 2 O mixtures) depending on the self-assembly procedure.

Moreover, to accurately determine the gyration radius (Rg) and the hydrodynamic radius (R H ) of the nano-objects formed by the bioconjugates, multi-angle light-scattering analysis (ALV DLS) was performed using an ALV laser goniometer, with a 22 mW linearly-polarised laser (632.8 nm HeNe) and an ALV-5000/EPP multiple tau digital correlator (125 ns initial sampling time). All the measurements were performed at a constant temperature of 25°C. The accessible scattering angles range from 30 to 150°. The solutions were placed in 20 mm diameter glass cells. Data were acquired using the ALV correlator control software, and the counting time was fixed for each sample at 15 s for dynamic diffusion measurements. The hydrodynamic radius was calculated from the diffusion coefficient using the Stokes-Einstein relation and the gyration radius was calculated from a Guinier plot.

Transmission Electron Microscopy (TEM). TEM images were acquired on a

Hitachi H7650 microscope working at 80kV and equipped with an ORIUS SC1000 11MPx camera. Samples were prepared by direct deposition of a 1 mg.mL -1 droplet on carbon grids (300 mesh Cu-300LD from Pacific Grid Tech.). For CHCl 3 , the droplet was allowed to dry entirely, while for H 2 O, the liquid was removed after 2 min using a filter paper. After drying, a droplet of uranyl acetate 0.5 % in water was deposited. After 2 min the rest of liquid was removed using a filter paper.

Cryo-Transmission Electron Microscopy (cryo-TEM). Cryo-TEM micrographs

were obtained as following. A drop of suspension at a concentration of 6 mg/mL was deposited on a "quantifoil"® (Quantifoil Micro Tools GmbH, Germany) carbon membrane.

The excess of liquid on the membrane was absorbed with a filter paper and the membrane was quench-frozen quickly in liquid ethane to form a thin vitreous ice film. Once placed in a Gatan 626 cryo-holder cooled with liquid nitrogen, the samples were transferred in the microscope and observed at low temperature (-180°C). Cryo-TEM images were recorded on ultrascan 2k CCD camera (Gatan, USA), using a LaB6 JEOL 2100 (JEOL, Japan) cryo microscope operating at 200kV with a JEOL low dose system (Minimum Dose System, MDS) to protect the thin ice film from any irradiation before imaging and reduce the irradiation during the image capture.

Laser Scanning Confocal Microscopy (LSCM). LSCM images were acquired on an

inverted Leica TCS SP5 microscope equipped with an HCX PL APO 63X, NA 1.4 oil immersion objective in fluorescence mode. The laser outputs were controlled via the Acousto-Optical Tunable Filter (AOTF) and one collection window using the Acousto-Optical Beam Splitter (AOBS) and photomultiplicators (PMT) as follows: Nile Red was excited with a laser at 561 nm (12.5%) and measured with emission settings at 571nm-624nm. The Helium-Neon laser at 633 nm (14%) was only used in transmission mode. Images were collected in simultaneous mode using a resonant scanner at 8000 Hz in bidirectional mode at a resolution of 512*512 pixels.

Antifungal biological evaluation.

Fungal strains used in this study are part of the FCBA collection from Bordeaux. 10 mL of bioconjugate XOS-b-MeOl loaded with propiconazole solutions at several concentrations were filtered with 0.2 µm PES sterile filters then added to 65 mL of malt/agar (4%/2%). The final solutions were then split in three plates and experiments were performed in three independent biological repeats were the strain Trametes versicolor (CTB 863A) was propagated and incubated at 22°C and 70% of relative humidity. Radial growth assay was performed on malt/agar medium supplemented prior solidification with bioconjugate XOS-b-MeOl loaded with propiconazole. One plug of fungal mycelia was put on supplemented medium to evaluate the ability of bioconjugate XOS-b-MeOl loaded with propiconazole to affect fungal growth. Agar plates were incubated at 22°C and 70% of relative humidity until complete growth.

3-Results and discussion

3.1-Synthesis procedures

Dilute acidic hydrolysis of xylan. The production of well-defined XOS by mild sulfuric acid hydrolysis of beechwood xylans was recently reported by Chemin et al. [START_REF] Chemin | Synthesis and characterization of functionalized 4-Omethylglucuronoxylan derivatives[END_REF][START_REF] Chemin | Well-defined oligosaccharides by mild acidic hydrolysis of hemicelluloses[END_REF] and its scale up is reproducible and allow the production of 75 g of XOS per batch.

Reductive amination and functionalization with sodium azide. The XOS formed by controlled hydrolysis of MGX were functionalized by reductive amination of the aldehyde chain-end followed by a nucleophilic substitution with sodium azide. Hence, an azide function was introduced to the extremity of the XOS (Scheme 2A). Figure SS1 shows the Fourier transform infrared (FTIR) spectra of the XOS before (black, bottom) and after (red, top) reductive amination followed by reaction with sodium azide: clearly, a specific band appears at 2100 cm -1 corresponding to the azide function [START_REF] Diaz | Click Chemistry in Materials synthesis. 1. Adhesive Polymers from Copper-Catalyzed Azide-Alkyne Cycloaddition[END_REF]. Figure 1 represents the 1 H NMR spectra in D 2 O of XOS before (bottom) and after (top) reductive amination with 2aminoethyl chloride followed by reaction with sodium azide. The top spectrum reveals the appearance of new signals for the modified XOS at 2.4-2.8 ppm (4H, -CH 2 -CH 2 -N 3 ) corresponding to the ethylazide chain-end. According to previous DOSY experiments, one can conclude that the azide moiety is really linked to the XOS chain-end [START_REF] Chemin | Synthesis and characterization of functionalized 4-Omethylglucuronoxylan derivatives[END_REF].

Transesterification of fatty acid methyl ester. Vegetable oils are easily accessible and in large quantities. Many articles and reviews deal with the functionalization of triglycerides and fatty acids for the synthesis of bio-sourced polymers [START_REF] De Espinosa | Synthesis of Star-and Block-Copolymers using ADMET: Head-to-Tail Selectivity During Step-Growth Polymerization[END_REF][START_REF] Meier | Plant Oil Renewable Resources as Green Alternatives in Polymer Science[END_REF][START_REF] More | Vegetable-Based Building-Blocks for the Synthesis of Thermoplastic Renewable Polyurethanes and Polyesters[END_REF][START_REF] Petrovic | Polyurethanes from Vegetable Oils[END_REF][START_REF] Hong | Biopolymers from Vegetable Oils via Catalyst-and Solvent-Free "Click" Chemistry: Effects of Cross-Linking Density[END_REF][START_REF] Ogunniyi | Castor Oil: A Vital Industrial Raw Material[END_REF][START_REF] Maisonneuve | Structure-Properties Relationship of Fatty Acid-Based Thermoplastics as Synthetic Polymer Mimics[END_REF][START_REF] Biermann | Oils and Fats as Renewable Raw Materials in Chemistry[END_REF]. The transesterification of fatty esters is a catalyzed reaction generally carried out in the bulk at rather high temperature (120°C) [START_REF] Jérôme | One Pot" and Selective Synthesis of Monoglycerides over Homogeneous and Heterogeneous Guanidine Catalysts[END_REF][START_REF] Jérôme | One Pot" and Selective Synthesis of Monoglycerides over Homogeneous and Heterogeneous Guanidine Catalysts[END_REF]. In this study, the methyl oleate (MeOl) and the methyl ricinoleate (MeRic) were used as mono-unsaturated C18 fatty esters as the latter can be produced with a relatively high purity and only differ by the presence or not of one OH group linked to the fatty acid backbone. These substrates were functionalized by transesterification reaction with propargyl alcohol in the presence of TBD used as a catalyst (Scheme 1B) [START_REF] Lebarbé | Methyl 10-Undecenoate as a Raw Material for the Synthesis of Renewable Semi-Crystalline Polyesters and Poly(ester-amide)s[END_REF] to yield fatty esters bringing an alkyne end-group that could be further Huisgen cyclo-addition. 'Click chemistry' was reported as a concept of 'green chemistry' in 2001 by Kolb et al. [START_REF] Kolb | Click Chemistry: Diverse Chemical Function from a Few Good Reactions[END_REF]. The reactions are characterized by presenting a good selectivity, a simple experimental device with a minimum of synthetic steps, aqueous and oxygen application, tolerance to numerous chemical groups and quantitative yields. A widely used 'click' reaction is typically the azide-alkyne cyclo-addition catalyzed with Cu (I) or Huisgen cyclo-addition. The concept has further been extended to other reactions with, for example, the thiol-ene addition, the Diels-Alder cyclo-addition or the thiol-yne addition [START_REF] Lligadas | Monomers and Polymers from Plant Oils via Click Chemistry Reactions[END_REF].

Herein, the XOS-NH-(CH 2 ) 2 -N 3 were coupled with both fatty ester derivatives alkynefunctionalized through an azide-alkyne cyclo-addition, as presented in Scheme 1C. This reaction was carried out accordingly to a previously reported protocol [START_REF] Upadhyay | Biomimetic Doxorubicin Loaded Polymersomes from Hyaluronan-block-Poly(γ-benzyl glutamate) Copolymers[END_REF]. The reaction solvent DMSO was chosen as it solubilizes well both hydrophilic and hydrophobic segments but also because it is the only solvent to fully solubilize the final amphiphilic bioconjugate soformed. The amount of catalytic system CuSO 4 /sodium ascorbate was reduced to 1 equivalent compared to azide or alkyne functions, as its removal is the limiting factor of the purification step and an excess of it was not necessary to achieve a full conversion. FTIR spectra presented in Figure S6 shows the XOS azide functionalized and the bioconjugate XOS-b-MeOl after the 'click' reaction: the total disappearance of the characteristic azide band at 2100 cm -1 in the bioconjugate proves that the 'click' reaction was total. Cuprisorb was used in the purification process before the dialysis step because it is known to be a powerful copper absorbant [START_REF] Anastasaki | Aqueous Copper-Mediated Living Radical Polymerisation of N-Acryloylmorpholine, SET-LRP in Water[END_REF]. The final purification step of dialysis is probably the limiting factor for the overall reaction as the relatively small bioconjugate obtained, around 1,300 g.mol -1 , is susceptible to go through the dialysis membrane. The final bioconjugates were analyzed by 1 H NMR in DMSO-d6 (Figure 4

3.2-Self-assembly properties

As described in the experimental part, the self-assembly behavior of the two amphiphilic bioconjugates XOS-b-MeOl and XOS-b-MeRic was studied using three different methods such as direct solubilization, thin-film rehydration and microfluidics, each method having its own advantages and drawbacks. The resulting self-assembled objects were characterized in size and shape using four techniques: a routine single-angle dynamic light scattering at 90° (Malvern DLS), a multi-angle light scattering (ALV DLS and static light scattering SLS), a transmission electron micrograph (TEM) or a cryo-transmission electron microscope (cryo-TEM) allowing to determine, respectively, particle sizes and their distribution (Malvern DLS), hydrodynamic (R H ) and gyration radii (Rg) and the nano-object shape defined by the ratio of the two previous radius (ALV DLS), the shape and size of the dry nano-objects (TEM) and finally the shape and size of the nano-objects directly in aqueous conditions (cryo-TEM). Subsequently, laser scanning confocal microscopy (LSCM) was used to determine the incorporation of the nile red dye in the nano-objects.

Direct solubilization. Both bioconjugates XOS-b-MeOl and XOS-b-MeRic were solubilized either in water or in chloroform at a concentration of 10 mg.mL -1 and then diluted to 1 mg.mL -1 then 0.1 mg.mL -1 . Particle sizes obtained through DLS measurements are compiled in Table 1 and in Table S1.

For the bioconjugates dissolved in water, their hydrodynamic radii (R H ) measured at 90° range from 87 nm to 106 nm (0.163 ≤ PDI ≤ 0.193) for the XOS-b-MeOl bioconjugate and from 88 nm to 91 nm (0.192 ≤ PDI ≤ 0.230) for the XOS-b-MeRic bioconjugate with, in every cases, a monomodal size distribution. For both bioconjugates, the R H values are relatively stable within the range of concentrations studied with some relatively high PDI.

Particles are still detected at the lowest concentration, meaning that 0.1 mg.mL -1 is above the critical aggregation concentration. Furthermore, from SLS and multi-angle light scattering measurements (ALV) performed at a concentration of 1 mg.mL -1 , a R g = 91 nm and a R H = 104 nm were obtained for the XOS-b-MeOl system and a R g = 66 nm and R H =61 nm for the XOS-b-MeRic system. In both cases, the ratio R g /R H ≈ 1 suggests a vesicular morphology of the self-assembled nano-object [START_REF] Chécot | From Supramolecular Polymersomes to Stimuli-Responsive Nano-Capsules Based on Poly(diene-b-peptide) Diblock Copolymers[END_REF][START_REF] Kratochvil | Classical Light Scattering from Polymer Solutions[END_REF][START_REF] Benoit | Light Scattering from Polymer Solutions[END_REF]. This was confirmed by TEM analyses, as presented in Figure 6, where spherical objects with a hole in the center can be observed: at high magnification, the membrane of the vesicles can be detected. Higher resolution imaging was achieved when using cryo-TEM: the nano-objects formed could be observed in aqueous solution as shown in Figure 7 (A-D) and vesicular shape was confirmed with an accurate definition of the membrane of the vesicle. Nevertheless, the TEM and cryo-TEM pictures show similarly a high size polydispersity of the nano-objects, confirming the obtained results through DLS measurements at 90° (Malvern) with a PDI ≈ 0.2. For the chloroform system, only the highest concentration of 10 mg.mL -1 was analyzed through DLS measurements at 90° (Malvern). When solubilizing XOS-b-MeOl and XOS-b-MeRic in this solvent, aggregates are formed and removed after filtration so that the two lowest concentrations of 1 mg.mL -1 and 0.1 mg.mL -1 could not be distinguished by lack of signal. The nano-objects detected at 10 mg.mL -1 have a R H = 74 nm for the XOS-b-MeOl and a R H = 89 nm for the XOS-b-Ric with, in both cases, relatively high PDI ≈ 0.18. The selfassembly properties in chloroform were not further exploited.

Thin-film hydration method followed by extrusion. This method was originally developed for liposomes preparation. It involves first the formation a thin lipid film in a round-bottom flask by rotary evaporation of an organic solvent. Upon the slow addition, then agitation of the dispersion medium (typically water of a buffer), heterogeneous liposomes (different size and multi-lamellar) are formed. Then, after extrusion through polycarbonate membranes, homogeneous small liposomes are obtained [START_REF] Samad | Liposomal Drug Delivery Systems: an Update Review[END_REF]. Even if not a perfect solvent for the systems XOS-b-MeOl and XOS-b-MeRic, we chose THF to disperse the bioconjugates and create the thin-film because of its low boiling point (66°C). A full solubilization of the bioconjugates could have been obtained only in DMSO however this solvent would not be removed to create the thin film due to its high boiling point (189°C). Upon addition of water, large nano-objects were formed, up to 128 nm for the XOS-b-MeOl system and 189 nm for the XOS-b-MeRic system, as evidenced by DLS measurements (see Table 2, entries 1 & 3). However, their distribution is multimodal showing three peaks with accordingly very high PDI = 0.35 for the XOS-b-MeOl system and PDI = 0.38 for the XOS-b-MeRic system. Extrusion through polycarbonate membrane followed the rehydration process and was performed through a 0.4 µm membrane. The solutions containing a multimodal distribution of nano-objects were forced to pass through the membranes back and forth 15 times by applying a relatively high pressure. The obtained solutions after extrusion presented nanoparticles with lower particle sizes, i.e. 74 nm for the XOS-b-MeOl system and 86 nm for the XOS-b-MeRic system (see Table 2, entries 2 & 4). Moreover, their distributions became monomodal, even if the PDI stayed relatively high: PDI = 0.23 for the XOS-b-MeOl system and PDI = 0.28 for the XOS-b-MeRic system.

For an analysis by multi-angle light scattering, the initial solutions after rehydration were too polydisperse to be investigated properly. However, the R g and R H could be measured for the extruded solutions, giving a set of data presented in Table 2, entry 2 for the XOS-b-MeOl and entry 4 for the XOS-b-MeRic. The obtained results for these 2 solutions were very similar, giving a shape factor R g /R H ≈ 1 in all cases, meaning that the shape of the nano-objects formed was vesicular with a radius being around 45 nm. The sample XOS-b-MeOl was also analyzed by cryo-TEM as shown in Figure 7 (E,F) and once again vesicular shape could clearly be observed with sizes and PDI confirming the light scattering experiments.

Microfluidic micromixer experiments. Due to optimized and stable mixing parameters, the preparation of self-assembled nano-objects via microfluidic systems may provide nanostructures with a better control over size in a high throughput manner. Such method used for the preparation of polymersomes (vesicles) was recently reviewed [START_REF] Bleul | Techniques to Control Polymersome Size[END_REF]. The first approaches described generating polymersomes using double emulsion microfluidics produced giant vesicles in the micrometer range [START_REF] Shum | Microfluidic Fabrication of Monodisperse Biocompatible and Biodegradable Polymersomes with Controlled Permeability[END_REF][START_REF] Habault | Droplet Microfluidics to Prepare Magnetic Polymer Vesicles and to Confine the Heat in Magnetic Hyperthermia[END_REF]. Using very fast and controlled mixing processes, Prud'homme first evidenced the ability to form small size and reproducible polymer vesicles [START_REF] Johnson | Mechanism for Rapid Self-Assembly of Block Copolymer Nanoparticles[END_REF][START_REF] Saad | Principles of Nanoparticle Formation by Flash Nanoprecipitation[END_REF]. Later, the use of micromixer devices, as presented by Maskos and coll., enabled control over size and shape of polymersomes below 100 nanometers [START_REF] Thiermann | Size Controlled Polymersomes by Continuous Self-Assembly in Micromixers[END_REF][START_REF] Bleul | Continuously Manufactured Magnetic Polymersomes -a Versatile Tool (not only) for Targeted Cancer Therapy[END_REF].

Recently, Le Fer et al. [START_REF] Fer | Design and Self-Assembly of PBLG-b-ELP Hybrid Diblock Copolymers Based on Synthetic and Elastin-Like Polypeptides[END_REF] reported the self-assembly of amphiphilic copolypeptide containing an Elastin-like polypeptide copolymerized with an γ-benzyl-L-glutamate block using the Dolomite micromixer chip, similar system used in the present study. This system allowed the fast mixing of at least two sources of different solutions in a laminar flow, permitting to vary the flow rate (D) of each solution and obtaining in the final mixed solution different solvent ratios (SR). We chose to mix a solution of THF containing the bioconjugate at a concentration of 2 mg.mL -1 with water to obtain the self-assembled nano-objects. In the first set of experiments, we increased the flow rate of THF containing the bioconjugate (D THF ) with respect to the flow rate of water (D H2O ) with a factor of 2 between D THF and D H2O in order to keep a final SR equal to 2. The final solutions were analyzed by DLS at 90° in order to evaluate the R H of the nano-objects. The results are compiled in Table S2 (entries 11-16).

In comparison with the two methods described previously, the PDI of the nano-objects formed was very low (0.04 < PDI < 0.08). However, no special trend could be observed for the size of the nano-objects formed (Table S2). In a second set of experiments, the flow rate D THF was kept constant at 200 µL.min -1 while the flow rate D H2O increased gradually from 200 µL.min -1 to 1000 µL.min -1 (i.e. SR 1 to 5). Figure 7 shows the trend observed for the evolution of the R H and the PDI when this set of experiments was repeated 3 times (DLS data are shown in Table 3 and in Table S2). For both bioconjugates, XOS-b-MeOl and XOS-b-MeRic, a similar trend was observed: when increasing the flow rate D H2O , the R H of the nanoobjects decreased first drastically from 200 µL.min -1 to 400 µL.min -1 , then slowly from 400 µL.min -1 to 1000 µL.min -1 while the PDI slightly increased. The repeatability of these experiments proved that the size of the nano-objects formed could be fine-tuned in these conditions. To further study the morphology of the nano-objects formed, THF was removed under vacuum. The characteristics of the resulting nanoparticles are summarized in Table 3.

One can note that the size of nanoparticles obtained at high THF content significantly increased after THF removal, probably because the self-assemblies are very dynamic under these conditions. For higher water content in the final solvent mixture, R H measured after THF evaporation are relatively similar than before. In that case, the nano-particles were rapidly kinetically frozen, in agreement with previous experiments [START_REF] Johnson | Mechanism for Rapid Self-Assembly of Block Copolymer Nanoparticles[END_REF][START_REF] Saad | Principles of Nanoparticle Formation by Flash Nanoprecipitation[END_REF][START_REF] Fer | Design and Self-Assembly of PBLG-b-ELP Hybrid Diblock Copolymers Based on Synthetic and Elastin-Like Polypeptides[END_REF]. 3), corresponding to the lowest ratio D THF /D H2O = 200/200 and the highest ratio D THF /D H2O = 200/1000 giving respectively the largest and the smallest nano-objects. Previously determined sizes were confirmed and the ratio R g /R H close to ≈ 1 again confirmed the presence of vesicular morphologies for all these samples.

3.3-Loading experiments and preliminary biological evaluation

Nile red loading. The nile red hydrophobic fluorescent dye was co-solubilized firstly in acetone at a concentration of 10 -4 M, then with the THF containing XOS-b-MeOl prior to self-assembly in microfluidics. The mixing with water was performed using a mixing ratio 200-600 (using a flow rate of 200 µL.min -1 of THF/acetone containing bioconjugate and nile red mixed with a flow rate of 600 µL.min -1 of filtered deionized water) in order to obtain nano-objects not in a metastable state with kinetics of self-assembly relatively fast. The hydrophobic dye should be loaded in the hydrophobic membrane of the vesicles, as confirmed by confocal microscopy observations in Figure S8 (see also video in Supporting Information).

Of course, the resolution of the confocal microscope is too low to detect the dye in the membrane but it can be clearly seen that the repartition of the dye is homogeneous through the sample and that it is trapped within small nano-objects with low PDI. This loading experiment was conducted as a proof of concept to show that hydrophobic dye could be encapsulated inside le membrane of the vesicles.

Propiconazole loading and antifungic biological evaluation. Propiconazole is a fungicide used in agriculture, well-known to inhibit the growth of fungi such as trametes versicolor [START_REF] Bleul | Techniques to Control Polymersome Size[END_REF]. Five different samples were tested in this study (see Figure 7, D-H) when propiconazole was loaded in XOS-b-MeOl nano-objects by microfluidics at different concentrations, in comparison with three controls (see Figure 7, A-C). These controls correspond to the trametes versicolor fungi growth in presence of pure water (control 1), XOS-b-MeOl nano-objects (control 2) and with XOS-b-MeOl nano-objects and

[propiconazole] = 33.7 nmol.mL -1 added on this solution (control 3). All three controls were shown negative and full fungi growth was observed after 17 days (see Figure 7, A-C), even if kinetics studied made on control 1 and 3 showed that full fungi growth was achieved as fast as 12 days (see Figure 8). Figures 7 and8 show that control 3, where self-assembled nanoparticles were not loaded with propiconazole, were less efficient than the loaded nanoparticles with different amount of propiconazole. Interestingly, fungal growth was almost fully inhibited in all cases when propiconazole was loaded in XOS-b-MeOl nanoparticles by microfluidics (see Figure 7, D-H) at least up to 17 days. A concentration-dependence growth inhibition was observed, and interestingly, a significant growth inhibition could be maintained for propiconazole concentration as low as 8.4 nmol.mL -1 . Kinetics studies presented in Figure 10 showed that after 13 days, full inhibition of fungal growth was observed for propiconazole loaded in XOS-b-MeOl nano-objects at 33.7 and 42.1 nmol.mL -1 where control 1 and 3 presented at this stage full growth of the fungi. The active agent rate release is not constant as full inhibition occurs until 12 days and then slowly decreases linearly from 13 days: as shown in Figure 8, there is full inhibition up to about 12 days at two concentrations of fungicide. By 14 days fungal growth occurs and slowly increases to 27 days. The experiment was carried out until 27 days where the two propiconazole loaded in XOS-b-MeOl sample exhibit both an inhibition of fungi superior to 60%. 100% growth was achieved when the fungus has occupying the whole agar plate (i.e. 100 % of its surface. Similarly, the percentage of inhibition was calculated depending on the surface of the agar plate not covered by the fungus.

4-Conclusions

This work led to the synthesis of bio-based amphiphilic oligomers starting from xylans, which are potential byproducts in the paper/pulp industry. After acidic hydrolysis of the xylans to generate well-defined oligomers, the aldehyde function of the reducing end of these oligomers of xylan were then functionalized with an azide group to allow their coupling to fatty acid derivatives by 'click chemistry'. Fully bio-sourced bioconjugates were then produced and their self-assembly behavior was studied using three different methods.

The direct solubilization of XOS-b-MeOl and XOS-b-MeRic bioconjugates formed vesicular morphology in water, as evidenced by a combination of TEM, cryo-TEM and light scattering experiments, with a radius around 90 nm and a relatively high polydispersity. The main advantage of the direct solubilization is the easiness of the preparation that neither require the use of another solvent nor a complex experimental set up. Nevertheless, such a simple approach is not suitable for efficient loading of active materials.

Alternatively, the film-rehydration followed by extrusion method was performed by using THF to form the initial multilamellar film of bioconjugates. As judged by multi-angle DLS combined with SLS, nano-size vesicles were obtained, as confirmed by cryo-TEM. This method has the potentiality to load drugs in the nano-objects formed. Depending on their polarity, different active ingredients can be incorporated in the process by dissolution in the organic solvent for hydrophobic molecules or dissolution in the water for hydrophilic ones.

Nile red was loaded in the membrane of the vesicle using this technique by simply adding the fluorescent dye in the THF/bioconjugate mixture used to prepare the starting polymer film. Finally, a microfluidic set up using a micromixing chip was used to self-assemble bioconjugates in a controlled and reproducible nanoprecipitation approach. Again, vesicles were formed, with a low polydispersity and high reproducibility, as demonstrated by scattering and TEM techniques. In using a third pump for the mixing in the chip or in dissolving a dye/drug in the organic solvent or in the water phase, loading of both hydrophilic and hydrophobic drugs could be easily achieved. This has been first demonstrated by loading nile red, a hydrophobic dye, previously dissolved in the THF containing bioconjugates. Then propiconazole, a potent anti-fungic molecule was loaded at different concentrations. The evaluation of the anti-fungic activity of propiconazole loaded into our bioconjugate XOS-b-MeOl vesicles was then compared to free propiconazole and evidenced the enhanced activity of the drug encapsulated by reducing significantly the growth of trametes versicolor (i.e selfassembled nanoparticles not loaded with propiconazole were less efficient in slow delivery than the loaded nanoparticles with different amount of propiconazole).

  engaged in coupling reactions with XOS-NH-(CH 2 ) 2 -N 3 , giving access to bio-sourced and amphiphilic bioconjugates. Due to the relatively low boiling point of propargyl alcohol (115°C), a large excess of the latter was used (10 equivalents) and the reaction temperature was decreased to 100°C. These two experimental parameters have the advantage of limiting the auto condensation of MeRic by transesterification on itself.1 H NMR analyses, presented in Figure2A(MeOl) and Figure2C(MeRic), clearly show that the conversion is complete with the disappearance of the -CH 3 of the ester at 3.62 ppm and the appearance of the protons resulting from the propargyl alcohol at 2.4 ppm (H≡) and 4.6 ppm (-CH 2 -O). SEC analyses in THF, presented in Figure3B(MeOl) and Figure3D(MeRic), show a slight increase in molar mass (from 480 g.mol -1 to 500 g.mol -1 for MeOl and from 450 g.mol -1 to 480 g.mol -1 for MeRic) and no signal attributable to a possible polymerization side-reaction.

  ) after freeze-drying. Both spectra, for XOS-b-MeOl and XOS-b-MeRic, show the characteristic peaks of the FAME, at 0.5-2.5 ppm, of the XOS at 3-5.5 ppm and the triazole peak at 8.1 ppm confirming the expected structure of the amphiphilic bioconjugates. 1 H NMR analyses in D 2 O, selective solvent of the XOS segment and in CDCl 3 , selective solvent of the fatty acid segment, gave a first insight on the amphiphilic nature of the bioconjugates as shown in the Figure S7 and S8. It is revealed that in D 2 O mainly the domain of chemical shift belonging of the XOS is resolved and in CDCl 3 , only the domain of chemical shift corresponding to the fatty acid is resolved. This indicates that the two solvents are selective of a self-assembly structure that hides the hydrophobic groups of the FAME in D 2 O and the hydrophilic group of the XOS in CDCl 3 . This self-assembly process is discussed in the following part of the manuscript.

Finally, the most

  relevant samples were analyzed by multi-angle light scattering after THF evaporation: sample XOS-b-MeOl with SR 1 & 5 and sample XOS-b-MeRic with SR 1 & 5 (see entries 1, 5, 6 & 10 in Table

Fig. 1 1 H

 1 Fig. 1 1 H NMR spectra in D 2 O of xylo-oligosaccharides before (blue) and after (red) reductive amination with 2-aminoethyl chloride followed by reaction with sodium azide.

Fig. 2

 2 Fig. 2 Fatty Acid Methyl Ester transesterification with propargyl alcohol. 1 H NMR spectra in CDCl 3 of the methyl oleate (A) before (blue) and after (red) transesterification with propargyl alcohol, of the methyl ricinoleate (C) before (blue) and after (red) transesterification with propargyl alcohol; GPC traces in THF of the methyl oleate (B) before (black) and after (red) transesterification with propargyl alcohol and of the methyl ricinoleate (D) before (black) and after (red) transesterification with propargyl alcohol using a RI detector calibrated with PMMA.

Fig. 3

 3 Fig. 3 Overlaid spectra of the 1 H NMR of the bioconjugates XOS-b-MeOl (bottom) and XOSb-MeRic (top) in DMSO-d6.

Fig. 4

 4 Fig. 4 TEM images obtained for the bioconjugates XOS-b-MeOl and XOS-b-MeRic after direct solubilization in H 2 O (1 mg.mL -1 ) and stained with uranyl formate.

Fig. 5 Fig. 6

 56 Fig. 5 Cryo-TEM images obtained after direct solubilization in H 2 O (6 mg.mL -1 ) for the bioconjugates XOS-b-MeOl (A, B) and XOS-b-MeRic (C, D) and after thin-film rehydration followed by extrusion for the bioconjugate XOS-b-MeOl (E, F).

Fig. 7

 7 Fig. 7 Picture of the fungal growth after propagation of the strain Trametes versicolor on malt/agar (4%/2%) plates incubated at 22°C and 70% of relative humidity for 17 days, B), D-F) and for 19 days, A), C), G), H). A) control 1 with water added to the malt/agar medium, B) control 2 with [XOS-b-MeOl] self-assembled by microfluidics added to the malt/agar medium, C) control 3 with [XOS-b-MeOl] self-assembled by microfluidics followed by addition of [propiconazole] = 33.7 nmol.mL -1 added to the malt/agar medium and D-H) with [XOS-b-MeOl] self-assembled by microfluidics with an increasing amount [propiconazole] = (D) 8.4, (E) 16.9, (F) 25.3, (G) 33.7, (H) 42.1 nmol.mL -1 added to the malt/agar medium.

Fig. 8

 8 Fig. 8 Kinetic evolution of the fungal growth after propagation of the strain Trametes versicolor on malt/agar (4%/2%) plates incubated at 22°C and 70% of relative humidity for control 1 with water added to the malt/agar medium, control 3 with [XOS-b-MeOl] selfassembled by microfluidics followed by addition of [propiconazole] = 33.7 nmol.mL -1 added to the malt/agar medium and with [XOS-b-MeOl] self-assembled by microfluidics with [propiconazole] = 33.7 and 42.1 nmol.mL -1 added to the malt/agar medium.

Acknowledgements

This work is financially supported by the Aquitaine Council, FCBA, ITERG and ANR-10-EQPX-16-XYLOFOREST. The authors thank P. Castel (CESAMO, Institut des Sciences Moléculaires, Université de Bordeaux, Talence (33), France) for MALDI-TOF MS experiments. The transmission electron microscopy (TEM) was done in the Bordeaux Imaging Center, a service unit of the CNRS-INSERM and Bordeaux University, member of the national infrastructure France BioImaging, so the authors thank S. Lacomme for the training. E. Ibarboure (Laboratoire de Chimie des Polymères Organiques, LCPO, Université de Bordeaux, Pessac (33607), France) is acknowledged for confocal microscopy measurements. Finally, M. Coloignier (ITERG, 11 rue Gaspard Monge, Parc Industriel, Pessac, (33600), France) is thanked for advices in the XOS hydrolysis scale-up and fruitful discussions.

Conflicts of interest

There are no conflicts to declare. g.mol -1 . In the present study, we have followed this set of conditions while scaling up the acidic hydrolysis from 500 mg of ultrafiltrated xylans (the initial raw material needs to be purified by ultrafiltration to remove a population of aggregated xylans using tangential flow filtration with a 0.45 µm pore size membrane) to 120 grams (in testing 5 grams and 20 grams scale in between) of this starting material in order to obtain a large batch of hydrophilic segment which would be the foundation of the elaboration of amphiphilic bioconjugates. The XOS produced were characterized by size exclusion chromatography (SEC), I H, 13 MeGlcA unit [1]. However the MALDI-TOF spectrum presented in Figure S5 gives a better insight on the structure of the XOS: two main populations can be observed, the minor one with no MeGlcA branching unit with a DP n of xylose units varying from 3 to 9 and the major one with one MeGlcA branching unit and with a DP n of xylose units varying from 3 to 12. dispersed in THF at a concentration of 2 mg/mL then filtered using a 0.45 µm PTFE filter.

Direct solubilization DLS at 90° (Malvern)

Supporting


José Alberto De La Paz

Adeline Bonvalet

Manuel Joffre
email: manuel.joffre@polytechnique.edu

Frequency-Domain Two-Dimensional Infrared Spectroscopy using an Acousto-Optic Programmable Dispersive Filter

We report on multidimensional spectroscopy in the mid-infrared performed using a calomel-based acousto-optic programmable dispersive filter. Although the associated spectral resolution is currently not as good as what has been previously reported using time-domain interferometers or other pulse-shaping technologies, the extreme compactness of the calomel crystal allows a straightforward implementation in a pre-existing pump-probe setup. Furthermore, the frequency-domain approach allows easy measurement of 2D slices of the multidimensional spectrum associated with a given pump frequency. We demonstrate our method with the measurement of the mid-infrared spectrum of carboxy-hemoglobin in three spectrotemporal dimensions.

Introduction

Two-dimensional infrared (2DIR) spectroscopy has been established in the last two decades as the most advanced form of femtosecond vibrational spectroscopy. Indeed, 2DIR spectroscopy has been shown to be an invaluable tool for investigating vibrational dynamics, as well as couplings between vibrational modes [START_REF] Hamm | Concepts and methods of 2D infrared spectroscopy[END_REF].

It shares many conceptual and experimental aspects with the other form of multidimensional spectroscopy, namely two-dimensional electronic spectroscopy (2DES) [START_REF] Gallagher Faeder | Two-dimensional electronic correlation and relaxation spectra: Theory and model calculations[END_REF], which is a powerful tool for investigating electronic structure and dynamics using visible or ultra-violet femtosecond pulses. Among the different implementations of multidimensional spectroscopy, the so-called pump-probe geometry is probably the most straightforward [START_REF] Gallagher Faeder | Two-dimensional electronic correlation and relaxation spectra: Theory and model calculations[END_REF][START_REF] Hamm | Structure of the amide I band of peptides measured by femtosecond nonlinear-infrared spectroscopy[END_REF][START_REF] Cervetto | Double-resonance versus pulsed Fourier transform two-dimensional infrared spectroscopy: An experimental and theoretical comparison[END_REF][START_REF] Deflores | Two dimensonal Fourier transform spectroscopy in the pump-probe geometry[END_REF][START_REF] Shim | Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide[END_REF][START_REF] Myers | Two-color two-dimensional Fourier transform electronic spectroscopy with a pulse-shaper[END_REF]. Based on a standard pump-probe setup, this approach yields the multidimensional pump-probe signal S(ω s , ω p , T ), resolved as a function of the probe frequency ω s , the pump frequency ω p , and the waiting time T , also known as the pump-probe delay. Whereas the probe frequency is almost always resolved using a grating spectrometer placed on the transmitted probe beam, two different methods can be distinguished for resolving the pump frequency. In the frequency-domain approach [START_REF] Hamm | Structure of the amide I band of peptides measured by femtosecond nonlinear-infrared spectroscopy[END_REF], the measured signal is recorded as a function of the center frequency of a tunable narrow-band pump pulse, e.g. using a Fabry-Perot etalon. In the time-domain (or Fourier-transform) approach, the pump-probe signal is recorded as a function of the time delay between two broadband pump pulses, yielding the exciting pump frequency by Fourier-transform spectroscopy [START_REF] Gallagher Faeder | Two-dimensional electronic correlation and relaxation spectra: Theory and model calculations[END_REF][START_REF] Lepetit | Two-dimensional nonlinear optics using Fourier-transform spectral interferometry[END_REF].

In combination with the pump-probe geometry, another major simplification can be achieved by inserting a programmable pulse shaper in the pump beam, thus allowing to directly filter the incident broadband pulse into a two-pulse sequence (for time-domain multidimensional spectroscopy) or a tunable narrow-band pulse (for frequency-domain multidimensional spectroscopy). Indeed, in the spectral domain extending from the near-IR to the UV, pulse shapers allowing complete control of the spectral amplitude and phase are routinely available. The two leading pulse-shaping technologies rely either on a zero-dispersion line (ZDL) including a liquid-crystal [START_REF] Weiner | Femtosecond pulse shaping using spatial light modulators[END_REF] or acousto-optic [START_REF] Dugan | High-resolution acousto-optic shaping of unamplified and amplified femtosecond laser pulses[END_REF] modulator placed in the Fourier plane, or on a more compact acousto-optic programmable dispersive filter (AOPDF) [START_REF] Verluise | Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter: pulse compression and shaping[END_REF]. Applications to 2DES have been successfully demonstrated both with ZDL [START_REF] Gundogdu | Multidimensional coherent spectroscopy made easy[END_REF][START_REF] Shim | How to turn your pump-probe instrument into a multidimensional spectrometer: 2D IR and Vis spectroscopies via pulse shaping[END_REF] and AOPDF [START_REF] Myers | Two-color two-dimensional Fourier transform electronic spectroscopy with a pulse-shaper[END_REF][START_REF] Tyagi | Two-Color Two-Dimensional Electronic Spectroscopy Using Dual Acousto-Optic Pulse Shapers for Complete Amplitude, Phase, and Polarization Control of Femtosecond Laser Pulses[END_REF] pulse shapers. In the mid-infrared (MIR) spectral domain, pulse shaping technologies have matured more recently due to an initial lack of suitable modulators.

Yet, direct pulse shaping of MIR pulses has been eventually demonstrated with a ZDL using a germanium transverse acousto-optic modulator [START_REF] Shim | Femtosecond pulse shaping directly in the mid-IR using acousto-optic modulation[END_REF] or deformable mirror [START_REF] Cartella | Pulse shaping in the mid-infrared by a deformable mirror[END_REF]. Recently, the availability of suitable calomel (Hg 2 Cl 2 ) crystals has also made possible the demonstration of a MIR AOPDF pulse shaper in a device of only a few-cm length [START_REF] Tournois | Design of acousto-optic programmable filters in mercury halides for mid-infrared laser pulse shaping[END_REF][START_REF] Maksimenka | Direct mid-infrared femtosecond pulse shaping with a calomel acousto-optic programmable dispersive filter[END_REF]. However, until now, only the ZDL approach has been applied to 2DIR spectroscopy [START_REF] Shim | Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide[END_REF].

In this article, we report on the first application of a calomel AOPDF for 2DIR spectroscopy. By inserting a 22-mm thick calomel crystal and collecting the diffracted beam, we can readily transform a standard pumpprobe setup into a 2DIR spectrometer, as previously demonstrated for 2DES [START_REF] Myers | Two-color two-dimensional Fourier transform electronic spectroscopy with a pulse-shaper[END_REF][START_REF] Tyagi | Two-Color Two-Dimensional Electronic Spectroscopy Using Dual Acousto-Optic Pulse Shapers for Complete Amplitude, Phase, and Polarization Control of Femtosecond Laser Pulses[END_REF]. We demonstrate our method with the measurement of 2DIR spectra in carboxy-hemoglobin (HbCO), using the frequency-domain approach.

Methods

Fig. 1 shows our MIR femtosecond pump-probe setup. As described elsewhere [START_REF] Kemlin | Transient Two-Dimensional Infrared Spectroscopy in a Vibrational Ladder[END_REF], the MIR source consists of a 1-kHz Titanium:Sapphire regenerative amplifier (Libra-HE, Coherent) delivering 4-mJ, 800-nm, 100-fs pulses that are down-converted in a two-stage nonlinear setup in order to deliver horizontally-polarized, 20-µJ, 100-fs pulses centered at 5.1 µm (or 1950 cm -1 ). After recombination with a He:Ne alignment laser, a coated ZnSe beam splitter (BS) splits the incoming beam into pump and probe beams, with 16 µJ devoted to the pump. With the AOPDF removed and mirror M located in a position suitable for reflecting dotted-line beam We first align this standard pump-probe setup and optimize the differential pump-probe signal, measured in HbCO using broadband pump pulses and a 500-Hz mechanical chopper (not shown) inserted on the pump beam. In a second step, we insert the calomel AOPDF (MIR Dazzler, Fastlite) on the pump beam, just after a half-wave plate (HWP) with its neutral axis initially horizontally aligned. Due to the required 47 o incidence angle [START_REF] Tournois | Design of acousto-optic programmable filters in mercury halides for mid-infrared laser pulse shaping[END_REF] on the 22-mm long calomel crystal, the beam undergoes a significant lateral displacement. After translation of mirror M in order to collect the beam shown as dotted line (2), and appropriate adjustment of the pump-probe delay, the pump-probe signal is recovered and re-optimized. In a third step, the no-longer needed mechanical chopper is removed and the HWP neutral axis is rotated by 45 o , so that the beam incident on the calomel crystal is now vertically polarized, i.e. along the crystal ordinary axis. The AOPDF software is parametrized so that an acoustic wave is sent through the transducer to the crystal at a repetition rate of 500 Hz, properly synchronized with the laser amplifier. The acoustic waveform is chosen for diffracting a narrow-band pump pulse centered at 1951 cm -1 , tuned to the n = 0 to n = 1 CO stretch transition in HbCO.

After diffraction on the acoustic wave from vertical back to horizontal polarization, the shaped beam acquires an external angle of 11.0 o with respect to the incident beam [START_REF] Tournois | Design of acousto-optic programmable filters in mercury halides for mid-infrared laser pulse shaping[END_REF] (see solid line in Fig. 1). Mirror M is thus translated accordingly and rotated clockwise by half the diffraction angle, or 5.5 o , so that the diffracted beam is sent along the previous direction of the pump beam. The differential pump-probe signal is then monitored by subtracting even (AOPDF OFF) from odd (AOPDF ON) probe spectra, allowing to recover and re-optimize the pump-probe signal by fine adjustment of the pump mirror placed just before the lens (again after proper adjustment of the pump-probe delay). After this straightforward three-step procedure, we are now able to record pump-probe spectra with a pump pulse shape controlled by the AOPDF.

A well-known issue in 2DIR and 2DES is that even a small amount of scattered pump will be strongly enhanced through spectral interference with the probe, thus providing an unwanted contribution to the measured differential pump-probe signal. Furthermore, as the relative phase between pump and probe pulses is not locked, the interference pattern is unstable which makes it more difficult to remove by a mere subtraction. It has been shown previously that phase cycling provides an elegant method to address this issue [START_REF] Shim | Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide[END_REF][START_REF] Myers | Two-color two-dimensional Fourier transform electronic spectroscopy with a pulse-shaper[END_REF][START_REF] Bloem | Enhancing signal detection and completely eliminating scattering using quasi-phase-cycling in 2D IR experiments[END_REF]. This is easily implemented here, by applying with the pulse shaper a π phase shift to every other diffracted pump pulse, thus changing the sign of the interference pattern. The detrimental scattered pump interference then averages out. where N is the number of different pump frequencies.

For frequency-domain 2DIR spectroscopy, we use a convenient feature of the Dazzler known as the "sequence" mode, allowing preloading of a series of waveforms that can be applied on a pulse-by-pulse basis and repeated continuously. As shown in Fig. 2, a scan of N different pump pulse frequencies can be achieved by preloading a series of 2N pump waveforms, with the pump center frequency changing every other pump pulse and a π phase shift between odd and even pump pulses, as discussed above. This pump-pulse sequence is applied to the AOPDF at a repetition rate of 500 Hz, so that even probe pulses can be used for recording reference spectra, when no pump is applied to the sample. The total pulse sequence thus corresponds to 4N

probe pulses, and is repeated every 4N msec for appropriate data averaging of the 2DIR spectrum.

Results and discussion

We now demonstrate the approach outlined in the previous section with the measurement of a series of 2DIR spectra in HbCO. The preparation of the sample (heme concentration 10 mM, cell thickness 100 µm) has been described elsewhere [START_REF] Falvo | Ultrafast Dynamics of Carboxy-Hemoglobin: Two-Dimensional Infrared Spectroscopy Experiments and Simulations[END_REF]. For each value of the waiting time T , the 2DIR spectrum is averaged by scanning The spectra shown in Fig. 3 are typical of 2DIR spectroscopy [START_REF] Hamm | Concepts and methods of 2D infrared spectroscopy[END_REF], with a positive peak at 1951 cm -1 due to ground state bleaching and stimulated emission (n = 0 to n = 1 CO stretch transition) and a negative peak at 1926 cm -1 due to excited state absorption (n = 1 to n = 2 transition, downshifted due to the 25-cm -1 anharmonicity). The 2DIR signal then decays with increasing waiting time due to vibrational relaxation back to the ground state. At early waiting times, the axis of the elliptic 2DIR response is observed to be only slightly tilted with respect to the vertical, in contrast with high-resolution HbCO 2DIR spectra previously reported [START_REF] Falvo | Ultrafast Dynamics of Carboxy-Hemoglobin: Two-Dimensional Infrared Spectroscopy Experiments and Simulations[END_REF] where the center line was observed to be almost exactly along the diagonal. This behavior can be attributed to the large spectral-resolution anisotropy in the present measurement. Indeed, the probe spectral resolution is better than 1 cm -1 whereas the pump spectral resolution is limited by the pump spectral width, which we measured to be about 8 cm -1 FWHM. This value is not quite sufficient to resolve the anti-diagonal width of the 2DIR spectrum, known to be about 5 cm -1 at early waiting times [START_REF] Falvo | Ultrafast Dynamics of Carboxy-Hemoglobin: Two-Dimensional Infrared Spectroscopy Experiments and Simulations[END_REF]. However, a change in center line slope can still be observed in Fig. 3 when the waiting time increases, evidencing the expected spectral diffusion at longer time scales. Although time-domain multidimensional spectroscopy is known to provide in principle a better spectral resolution than frequency-domain multidimensional spectroscopy [START_REF] Cervetto | Double-resonance versus pulsed Fourier transform two-dimensional infrared spectroscopy: An experimental and theoretical comparison[END_REF][START_REF] Shim | Automated 2D IR spectroscopy using a mid-IR pulse shaper and application of this technology to the human islet amyloid polypeptide[END_REF], there are at least two reasons favoring the frequency-domain approach when pulse shaping is achieved using an AOPDF. First, diffraction efficiency is maximized in case of a single-frequency acoustic wave, thanks to the coherent contribution of the entire crystal when a single frequency is diffracted. Second, when an AOPDF is programmed for diffracting a two-pulse sequence, the maximum available delay will be limited by the duration of the acoustic wave associated with each pulse. This results in a compromise between diffraction efficiency (related with the acoustic pulse duration) and spectral resolution (related with the maximum delay), which is not encountered in the frequency-domain approach used here. An additional advantage of the frequency-domain approach is that a 2D slice of S(ω s , ω p , T ) for a specified pump frequency ω p can be readily obtained by programming the corresponding frequency on the AOPDF and recording the pump-probe spectrum as a function of the waiting time. This is illustrated in Fig. 4(a), showing the time evolution of the pump-probe spectrum with an excellent signal to noise ratio. Fig. 4(b) shows the time dependence of the height of the two peaks, which is observed to be in perfect agreement with an exponential fit with a time constant T 1 ≈ 22.3 ps, in good agreement with values previously reported for HbCO [START_REF] Lim | Protein Fluctuations are Sensed by Stimulated Infrared Echoes of the Vibrations of Carbon Monoxide and Azide Probes[END_REF][START_REF] Kemlin | Transient Two-Dimensional Infrared Spectroscopy in a Vibrational Ladder[END_REF]. This slicing feature should prove particularly useful for measuring excited state lifetimes using transient 2DIR spectroscopy in a vibrational ladder [START_REF] Kemlin | Transient Two-Dimensional Infrared Spectroscopy in a Vibrational Ladder[END_REF].

Conclusion

To summarize, we have demonstrated the use of a calomel AOPDF for frequency-domain 2DIR spectroscopy.

Thanks to the remarkable compactness of the pulse shaper, a straightforward three-step alignment procedure allows to transform a standard MIR pump-probe experiment into a 2DIR spectrometer. Although the current 8-cm -1 frequency resolution along the pump frequency axis remains modest when compared to time-domain 2DIR spectrometers, the slicing ability of the frequency-domain approach makes it particularly attractive for transient 2DIR spectroscopy. In particular, the evolution with respect to the waiting time of specific peaks of the 2DIR spectrum can be easily recorded with an excellent signal to noise ratio.

Funding

Fondation de l'Ecole polytechnique (PhD Track program).

( 1 )

 1 , the setup shown in Fig.1is merely a standard pump-probe setup. Pump and probe pulses are focused on the sample using a CaF 2 lens L (focal length 40 mm), and the transmitted probe beam is spectrally analyzed using a Chirped-Pulse Up-conversion (CPU) system[START_REF] Lee | Removing cross-phase modulation from midinfrared chirped-pulse upconversion spectra[END_REF][START_REF] Anna | Measuring absorptive two-dimensional infrared spectra using chirped-pulse upconversion detection[END_REF].

Figure 1 :

 1 Figure 1: Experimental setup for 2DIR spectroscopy using an Acousto-Optic Programmable Dispersive Filter (AOPDF). (BS) Beam splitter, (HWP) Half-Wave Plate, (L) lens, (M) Mirror mounted on a motorized rotation stage around the vertical axis and on a translation stage along the direction of the reflected beam. Dotted lines (1) and (2) show alternate paths used during the alignment procedure (see text).

Figure 2 :

 2 Figure 2: Schematic view of the 4N pulse sequence used in the 2DIR measurement,

1 (Figure 3 :

 13 Figure 3: Set of 2DIR spectra measured for the specified values of the waiting time T . The color scale is common to all plots and shows the relative change in differential transmission (in percents). (Visualization 1) Full 3D set with waiting time T varying between -3 and +48 ps. (Visualization 2) Full 3D set with linear interpolation on pump wavenumber and waiting time axes.

Figure 4 :

 4 Figure 4: (a) Dependence of the pump-probe signal as a function of time delay, for a pump frequency tuned to 1951 cm -1 . (b) Time dependence of induced absorption (blue disks) and induced bleaching (red diamonds) peak amplitude. The solid line shows an exponential fit, yielding a vibrational time constant T 1 ≈ 22.3 ps.

Acknowledgments

We wish to thank Mathias Herzog and Raman Maksimenka from Fastlite for their invaluable help in configuring the sequence mode of the AOPDF.


L Bizet

K Mathis
email: kevin.mathis@cnes.fr

P Saffré

D Halm

M Gueguen

P Francescato

M Jacquesson

A COMPREHENSIVE TOOL TO SIMULATE COMPOSITE LAY-UPS IN PRESSURE VESSELS

Composite pressure vessels made by filament winding processes are commonly used in aerospace design due to weight saving compared to metal parts. This technique involves complexities in analyzing the geometry especially in the dome section. Tools already exist to predict the geometrical characteristics like winding angle, ply thickness or some singularities. However they are limited to specific sequence dome lay-up. A numerical tool has been developed to simulate windings layer after layer.

The goal is to deal with any kind of sequence dome layup calculation. To ensure this there are three main challenges that are seldom cited in scientific literature. The first is when the geometry of the current ply overlaps the inferior ply. The second is the management of convex parts of a ply. Finally, our mathematical tool is able to deal with the accumulation of composite fibers near the polar boss outer radius.

INTRODUCTION

The winding process produces composite tanks capable of withstanding high internal pressures. The very high specific properties of these materials lead to structures with remarkable rigidity and strength for a contained mass. The filament winding continuously deposits composite fibers on a mould or a mandrel with a rotational movement. This manufacturing method is particularly suitable for revolution structures. In the space industry this technology is already used for some motor cases or tanks. To best design and optimize these structures it becomes necessary to integrate the simulation of the winding process of composite structures.

The performance of a composite structure depends on the adequacy between the loading directions and the distribution of the fibrous reinforcement. In the case of the filament winding process, a reliable estimation of the mechanical behaviour of the structure is conditioned by the most exact simulation possible of the fiber path, in particular in the domes, considered as the most delicate parts to simulate. Several studies [START_REF] Vasiliev | New generation of filament-wound composite pressure vessels for commercial applications[END_REF][START_REF] Koussios | Influence of laminate thickness approximation methods on the performance of optimal filamentary pressure vessels[END_REF][START_REF] Wang | A new method for predicting dome thickness of composite pressure vessels[END_REF][START_REF] Wang | Dome thickness prediction of composite pressure vessels by a cubic spline function and finite element analysis[END_REF][START_REF] Leh | Multi-sequence dome lay-up simulations for hydrogen hyper-bar composite pressure vessels[END_REF] have allowed the development of successive winding models that enable the complex geometry of domes to be managed. However, these models remain limited with regard to the strong disparity of possible windings. The objective of this work is to propose a tool for simulating the filament winding of any winding sequences on generic revolution geometries.

The ultimate aim is to use the model developed in an optimization procedure in which lay-up orientation, stacking sequence and filament winding parameters are significant parameters.

BASIC ASPECTS

Winding angle determination

Geodesic winding provides to the best winding stability by finding the shortest fiber path between two points on any surface. However, non-geodesic winding increases the scope of the geodesic winding technique through the use of the slippage tendency of the fibers on their supporting surface. Descriptions of geodesic and non-geodesic winding methods can be found in [START_REF] Carvalho | Optimization of filament wound parts based on non-geodesic winding[END_REF][START_REF] Zu | Design of filament-wound domes based on continuum theory and non-geodesic roving trajectories[END_REF][START_REF] Kim | Optimal design of filament wound structures under internal pressure based on the semi-geodesic path algorithm[END_REF]. For the purposes of future optimization, it is desirable to have a general equation to describe both geodesic and non-geodesic winding. The following equation [START_REF] Zu | Design of filament-wound domes based on continuum theory and non-geodesic roving trajectories[END_REF] is valid:

𝑑𝛼 𝑑𝑧 = 𝜆 [ sin 𝛼 tan 𝛼 𝑟 - 𝑟" 1 + 𝑟 ′ 2 cos 𝛼] - 𝑟 ′ tan 𝛼 𝑟 ( 1
)
where  is the angle between the fiber tow and the meridian direction of the dome,  the slippage coefficient of the fiber tows on the supporting surface and r and z the radial and axial coordinates of the dome, as shown in Fig. 1.

Depending on the sign of , the path will be lengthened or shrunk and thus influence the positioning of the radius at the turn-around of the continuous fiber. Usually this differential equation is solved by a Runge-Kutta method to order 4. The main problem with this method of resolution is the number of integration points required to ensure convergence of results. We will see in the proposed developments that this method of resolution, although used by all the routines allowing the multi-sequence simulation of filament winding, is not sufficiently adapted due to the inherent nature of the differential equation Eq. 1.

Figure 1. Geometry of the liner

To ensure the continuity of the winding between the cylindrical section of the tank and the dome, the following equation [START_REF] Zu | Design of filament-wound domes based on continuum theory and non-geodesic roving trajectories[END_REF] is used :

𝜆 = 𝜆 𝑚𝑎𝑥 cos ( 𝜋 2 𝑟 -𝑟 𝑡𝑢𝑟𝑛 𝑅 -𝑟 𝑡𝑢𝑟𝑛 ) ( 2
)
where R is the external equator radius of the tank (including the thickness of the plies) in the cylindrical section, 𝑟 𝑡𝑢𝑟𝑛 the radius at the turn-around point and 𝜆 𝑚𝑎𝑥 the arbitrary top value of the slippage coefficient.

The arbitrary top value 𝜆 𝑚𝑎𝑥 can be an optimization parameter as long as |𝜆 𝑚𝑎𝑥 | ≤ 𝜆 𝑙𝑖𝑚 where 𝜆 𝑙𝑖𝑚 is the slippage limit coefficient which depends on practical winding parameters.

Thickness determination

Once the radius at the turn-around point determined by the resolution of Eq. 1, it is necessary to determine the evolution of the thickness of the composite layer of the cylindrical section up to this radius at the turn-around point. Leh [START_REF] Leh | Multi-sequence dome lay-up simulations for hydrogen hyper-bar composite pressure vessels[END_REF] presented several formulations of thickness. It shows that Wang's formulation [START_REF] Wang | A new method for predicting dome thickness of composite pressure vessels[END_REF] is one of the most recent methods and presents very good results in comparison with the experimental one. It is based on the use of a double formulation to reflect as accurately as possible the thickness evolution:

𝑡(𝑟) = 𝑛 𝑅 𝑚 𝑅 𝑡 𝑝 𝜋 [arccos ( 𝑟 𝑡𝑢𝑟𝑛 𝑟 ) -arccos ( 𝑟 𝑏 𝑟 )] for 𝑟 2𝑏 ≤ 𝑟 ≤ 𝑅 (3)
and

𝑡(𝑟) = 𝐴 + 𝐵𝑟 + 𝐶𝑟 2 + 𝐷𝑟 3 for 𝑟 𝑡𝑢𝑟𝑛 ≤ 𝑟 ≤ 𝑟 2𝑏 (4)
where 𝑛 𝑅 , 𝑚 𝑅 are the number of pseudo-plies (±𝛼 𝑅 ) and their quantity in the cylindrical section, 𝑡 𝑝 is the thickness of a fiber tow or tape, b is the width of a fiber tape, 𝑡 𝑅 and 𝛼 𝑅 are the thickness of the layer and the initial winding angle on the cylindrical part, respectively. The parameters 𝑟 𝑏 and 𝑟 2𝑏 are the radius at one and two tape-width distances, respectively, from the turn-around point, and A, B, C and D the four coefficients of the method presented in [START_REF] Wang | A new method for predicting dome thickness of composite pressure vessels[END_REF] and defined using boundary conditions (pseudo-ply thickness at the turn-around radius, continuity of the thickness and the curvature in 𝑟 2𝑏 between Eqs. 3 and 4, and constant material volume between 𝑟 𝑡𝑢𝑟𝑛 and 𝑟 2𝑏 ).

Lay-up determination

In the multi-sequence lay-up of a dome, prediction is a tricky process, given that the determination of both winding angle and thickness is based on the current supporting surface topology, which, in a multi-layer layup, depends on the previous supporting surface topologies. The classical process presented by Leh [START_REF] Leh | Multi-sequence dome lay-up simulations for hydrogen hyper-bar composite pressure vessels[END_REF] is as follows:

 recovery and storage in internal variables of geometric data (in the form of elliptical liner definition parameters) and winding sequence parameters,  a definition of the coordinates according to z and r and a discretization of this geometry,  the calculation of first and second derivatives of current shape line by the finite difference method to solve Eq. 1,  the resolution of Eq.1 by a Runge-Kutta method to order 4 in order to obtain the value of the radius at the turn-around of the current layer,  the calculation of the overthickness to be applied to the previous layer thanks to the Wang's formulation,  normal calculation and application of the previously determined overthickness at each integration point,  smoothing of new points calculated by a B-spline,  the looping of all these steps for each layer described by the sequence of the winding angles. The operation of the routine can be schematized according to the graph of Fig. 2.

Figure 2. General dome lay-up calculation algorithm

This process has some limitations not compatible with configuration extensions. Thus the tool is not able to deal with winding lay-up other than increasing initial winding angle lay-up. It consequently does not make possible to cover a layer n with the layer n + 1. It is also highly unstable when covering a convex shape. As shown in Fig. 3, if the integration step is too large, there is a possibility that the normals at two (or more) integration points intersect.

This results in the creation of points for the new layer that will no longer be ordered in an increasing z when the overthickness is added.

IMPROVEMENTS

Digital processing of the evolution of 𝒅𝜶/𝒅𝒛

All the identified authors use the Runge-Kutta algorithm at order 4 (RK4) to solve Eq. 1 for determining the radius at the turn-around point of the current layer. The main problem with this resolution method is it is highly dependent on the number of integration points resulting from the geometric discretization of the current layer.

As we can see in Fig. 4, the problem is strongly nonlinear: the closer we get to 𝛼 = 90°, the more the influence of the discretization step is preponderant. This is problematic because the calculation error via RK4 is strongly related to discretization and consequently to calculation time. The resolution model should also be validated by optimizing the calculation step to reach a cumulative error below an admissible threshold. Eq. 1 is an equation whose sensitivity to parameters makes it difficult to solve by explicit numerical methods. The closer we get to 𝛼 = 90° the more sensitive it is and the less relevant the RK4 algorithm is to solve it. Works using this algorithm do not quantify the error associated with the resolution of this problem with this method. The solution to enable the algorithm to converge is then to define an extremely fine step without obtaining information on the cumulative error.

There are many powerful resolution algorithms, originally optimized to run on low-performance machines, alternative to explicit methods. This is the case with the LSODA [START_REF] Brown | Reduced storage matrix methods in stiff ODE systems[END_REF] algorithm, which offers many advantages. The first is that it is able to manage different resolution methods in the same calculation. Thus, it can switch from an Adams method to a BDF method automatically depending on the degree of stiffness of the differential equation. The algorithm is also independent of the calculation step imposed. The code automatically manages the step needed to solve the problem based on the calculated error to ensure convergence. Once solved on the number of steps strictly necessary, the function then re-interpolates at the integration points specified initially.

Instabilities due to convex zones

Due to the reduction in the number of integration points compared to a purely explicit routine, the code is then sensitive to the problem of overlapping instability of convex areas (Fig. 3) : physically meaningless loops may appear (Fig. 5a, Fig. 5b). It is therefore necessary to introduce a specific function to erase these loops (Fig. 5b). This function detects each segment consisting of two successive integration points intersecting another segment of the original curve. In order to limit the calculation time, the function must only take into account the convex parts of the curve to be checked. The outputs of this function are all the intersection points of the curve as well as two series of z and r coordinates of the erased instability loops.

Figure 5. Resolution of instabilities related to convex shapes of geometries for the current layer

In addition, a smoothing function is required to ensure the stability of the next layer simulation (Fig. 6). The degree of the smoothing function will depend on the geometric dimensions of the wound body and the thickness of the composite layers.

Figure 6. Smoothing of layer n with layer n -1

This smoothing function has to manage the different possible winding angle sequences:  sequence with equal initial angles (Fig. 7a),  sequence with decreasing initial angles (Fig. 7b),  sequence with increasing initial angles (Fig. 7c),  sequence with alternation of the three previous types.

Layers overlapping the barrel of the boss

Modelling the helical layers overlapping the barrel of the boss is a development which is less dealt with in the literature, although [START_REF] Moussaïd | Analyse et intégration des spécificités liées au procédé de fabrication dans les modèles de calcul des structures composites[END_REF] addresses this issue. In order to take into account these overlappings which may occur near the boss (Fig. 8), a method is proposed to transfer the overthickness. [START_REF] Moussaïd | Analyse et intégration des spécificités liées au procédé de fabrication dans les modèles de calcul des structures composites[END_REF] considers a linear extension tangent to the curve at the radius of the boss 𝑟 𝑏𝑜𝑠𝑠 to be the support for the calculation of the current layer. It then proposes that the volume defined by the winding for 𝑟 < 𝑟 𝑏𝑜𝑠𝑠 be reported with respect to the location of

(b) (a) (a) (b) (c)
the curve presenting the maximum thickness (𝑟 𝑡𝑚𝑎𝑥 ) and satisfying several conditions:  the thickness is redefined by: 𝑡(𝑟) = 𝐴 + 𝐵𝑟 + 𝐶𝑟 2 for 𝑟 𝑏𝑜𝑠𝑠 ≤ 𝑟 ≤ 𝑟 𝑡𝑚𝑎𝑥 (5)

 the volume for a radius smaller than 𝑟 𝑏𝑜𝑠𝑠 is distributed between 𝑟 𝑏𝑜𝑠𝑠 and 𝑟 𝑡𝑚𝑎𝑥 ,  continuity of thickness at 𝑟 𝑡𝑚𝑎𝑥 ,  continuity of slope at 𝑟 𝑡𝑚𝑎𝑥 .

Figure 8. Micrograph of storage tanks studied in [10]

The problem with this approach is twofold. First of all, the expression of the thickness in 𝑟 2 does not allow to take into account geometries with an inflection point, which is often the case. On the other hand, as can be seen in Fig. 9, this approach does not work if the radius at maximum thickness (𝑟 𝑡𝑚𝑎𝑥 ) is also less than 𝑟 𝑏𝑜𝑠𝑠 . A satisfactory routine should be able to handle overlapping layers on the boss. The most common function whose curve has an inflection point is a polynomial function of degree 3. Rather than reasoning about the redefinition of the overthickness to be applied, the geometry of the current layer is directly modified once it has been calculated. It is therefore first necessary to extend the spatial domain of the lower layer which will serve as a support for the calculation of the current layer for the values of 𝑟 < 𝑟 𝑏𝑜𝑠𝑠 . Note that a second order spline has been finally chosen (Fig. 10a).

As one of the conditions on the polynomial of degree 3 used to smooth this kind of layer regards a volume equivalence, it is necessary to be able to perform a numerical integration. To do this, a polynomial definition of z is chosen as a function of r. A new geometry is then defined as:

𝑧 = 𝐴 + 𝐵𝑟 + 𝐶𝑟 2 + 𝐷𝑟 3 (6)
This new geometry is defined over a transfer length 𝐿 𝑒𝑥 .

To determine the parameters A, B, C and D it is necessary to introduce 4 conditions, namely:  continuity at fixed 𝐿 𝑒𝑥 ,  continuity of the slope at 𝐿 𝑒𝑥 ,  slope equal to the one of previous layer at 𝑟 = 𝑟 𝑏𝑜𝑠𝑠 ,  conservation of the area between 𝑟 𝑏𝑜𝑠𝑠 and 𝑟 𝑏𝑜𝑠𝑠 + 𝐿 𝑒𝑥 for initial formulation and polynomial formulation. Once the equation system is solved, it is then possible to switch back to a definition of r as a function of z to establish the new geometry. The routine is then able to manage the layers overlapping the barrel of the boss (Fig. 10a) and to propose a redefinition of the geometry in a polynomial of degree 3 (Fig. 10b). From a physical point of view, the only value that the winding angle can take in the vicinity of the boss end is 𝛼 = 90°. This corresponds to the tilting of the fiber during winding at the radius at the turn-around point. Indeed, a value lower would mean that the winding head hits the boss barrel.

If the initial winding angle at the cylinder/dome junction is fixed by the process, there is only one parameter left to ensure these conditions, i.e. . This parameter is then optimized to ensure that the winding is feasible. To do this, the routine solves Eq. 1 backwards from the radius at the turn-around point 𝑟 𝑡𝑢𝑟𝑛 = 𝑟 𝑏𝑜𝑠𝑠 with a definition of  set by a value of 𝜆 𝑚𝑎𝑥 . The idea is then to compare the value of the calculated initial winding angle with the value of the imposed initial winding angle and this by modifying the value of the parameter 𝜆 𝑚𝑎𝑥 during optimization process. For this one must defined a cost function:

Δ = 𝛼 0 (𝜆 𝑚𝑎𝑥 ) -𝛼 0 (7)
Thanks to an adapted algorithm, it's possible to optimize this calculation by minimizing this cost function, i.e. by searching for the root of: Δ = 0, -𝜇 𝑠 < 𝜆 𝑚𝑎𝑥 < 𝜇 𝑠 [START_REF] Kim | Optimal design of filament wound structures under internal pressure based on the semi-geodesic path algorithm[END_REF] where 𝜇 𝑠 is the static friction coefficient, the maximum value of the sliding coefficient beyond which it becomes impossible to wind. Thus it is possible to identify the 𝜆 𝑚𝑎𝑥 value that satisfies both 𝛼 = 𝜋 2 at the barrel of the boss and α = 𝛼 0 for 𝑟 = 𝑅.

CONCLUSION

The work presented here allows the development of a generic filament winding routine to simulate any sequence. It is not limited to specific geometries (which must be axisymmetric) and is suitable to any winding sequence. This is made possible by a number of functions developed such as smoothing or winding stabilization functions on convex geometries. Particular attention is paid to a physical interpretation of certain parameters such as the definition of the slip coefficient or the management of the winding angle in the vicinity of the boss. The interest of this approach is to propose the integration of a simulation module of the winding process, flexible enough to be adaptable to the geometrical peculiarities of the motor cases or tanks, in a design and optimization tool for wound composite structures sizing.

Figure 3 .

 3 Figure 3. Overlap instability for convex areas due to the interweaving of normals close to integration points Finally, another critical point consists in the absence of possibility to model the covering of the barrel of the boss by several layers of composite. Indeed this routine foresees that only the first layer reaches the barrel of the boss. Then, because only sequences of increasing winding angles are managed, the other layers can only be modelled with increasing radii at the turn-around point.

Figure 4 .

 4 Figure 4. Winding angle variation  according to z

Figure 7 .

 7 Figure 7. Smoothing routine applied in sequence of equal (a), decreasing (b) and increasing (c) initial winding angles

Figure 9 .

 9 Figure 9. Volume transfer defined by a winding for 𝑟 𝑡𝑢𝑟𝑛 < 𝑟 𝑏𝑜𝑠𝑠

Figure 10 .

 10 Figure 10. Layer overlapping the barrel of the boss (a) and geometrical definition in the form of polynomial of degree 3 (b)

Acknowledgments

This research is supported by the French Space Agency (CNES).