Khantutta-Kim Tremblay-Parrado

Clément Bordin

Samuel Nicholls

Benoit Heinrich

Bertrand Donnio

Luc Avérous

Renewable and Responsive Cross-Linked Systems Based on Polyurethane Backbones from Clickable Biobased Bismaleimide Architecture

A new biobased bismaleimide architecture from methyl oleate, consisting of an aliphatic branched structure, denoted methyl oleate bismaleimide (MO BMI), was synthesized and fully characterized. MO BMI was used as a cross-linking agent to obtain networks by using linear biobased furan bearing PUs via the Diels-Alder reaction and compared with more conventional aromatic or aliphatic bismaleimides (BMIs). These networks can be defined as dissociative covalent adaptable networks (CANs). Different linear biobased PUs were synthesized by using rapeseed-based polyol, hexamethylene diisocyanate, and (furan-2,5-diyl)dimethanol as a chain extender. The furan content was controlled by varying the hard segment content. Compared to conventional BMIs, MO BMI as biobased cross-linker impacts particularly the materials performance and the mechanical properties, for example an increase of the elasticity. MO BMI also yields most consistent advanced properties in terms of thermal recyclability and self-healing.

Introduction

Polymer science has been established as a distinct field of organic chemistry for over 100 years. [START_REF] Staudinger | Über Polymerisation[END_REF][START_REF] Frey | Celebrating 100 years of "polymer science": Hermann Staudinger's 1920 manifesto[END_REF] Since that era, the invention of plastics has drastically changed our daily lives. However, most plastics are based on synthetic macromolecules that originate from nonrenewable petroleum resources. [START_REF] Bioplastics | Bioplastics Market Development Update[END_REF] Recently, the worldwide polymer industry has performed considerable progress to ensure the development of sustainable polymers with lower environmental impact using renewable feedstocks. Nevertheless, continued progress for these materials to contain advanced materials properties such as a controlled end-of-life to improved waste management is still required.

Renewable feedstocks are very diverse such as vegetable oils, woods, sugars, and polysaccharides from annual cultures. Plant oils are of particular interest as their innate chemical architectures allow for a vast panel of potential chemical modifications. [START_REF] Ronda | Vegetable oils as platform chemicals for polymer synthesis[END_REF] They are also of interest from an industrial perspective, as they are highly accessible at rather low production cost with low toxicity. [START_REF] Lligadas | Renewable polymeric materials from vegetable oils: a perspective[END_REF] Vegetable oils as well as their fatty acid derivatives have been widely used for the synthesis of polymers such as polyesters, [START_REF] Pan | High Biobased Content Epoxy-Anhydride Thermosets from Epoxidized Sucrose Esters of Fatty Acids[END_REF][START_REF] Duarte | The unrevealed potential of elemental sulfur for the synthesis of high sulfur content bio-based aliphatic polyesters[END_REF] polyamides, [START_REF] Hablot | Dimer acid-based thermoplastic bio-polyamides: Reaction kinetics, properties and structure[END_REF][START_REF] Türünç | Fatty acid derived renewable polyamides via thiolene additions[END_REF] epoxy resins, [START_REF] Tan | Biobased Epoxidized Vegetable Oils and Its Greener Epoxy Blends: A Review[END_REF] and quite prominently polyurethanes (PUs). [START_REF] Hablot | Polyurethanes Based on Castor Oil: Kinetics, Chemical, Mechanical and Thermal Properties[END_REF][START_REF] Bueno-Ferrer | Structure and Morphology of New Bio-Based Thermoplastic Polyurethanes Obtained From Dimeric Fatty Acids[END_REF][START_REF] Desroches | From Vegetable Oils to Polyurethanes: Synthetic Routes to Polyols and Main Industrial Products[END_REF][START_REF] Pfister | Recent Advances in Vegetable Oil-Based Polyurethanes[END_REF] PUs are a leading polymer family, with their production ranked sixth among all polymers. [START_REF] Carré | From the synthesis of biobased cyclic carbonate to polyhydroxyurethanes: a promising route towards renewable non-isocyanate polyurethanes[END_REF] Because of their wide structural variability, PUs are used for applications such as, the building, transportation, and furniture industries. (16) Although the use of plant oils for the synthesis biobased PUs is on the raise, [START_REF] Miao | Vegetable-oil-based polymers as future polymeric biomaterials[END_REF] limited research has exploited these biobased structures to develop advanced materials, to achieve for instance, dynamic and adaptable materials with high recyclability and extended lifetimes.

In the past 20 years, the introduction of dynamic cross-links in polymers has developed a new generation of polymer materials that can be reprocessed like thermoplastics, all the while maintaining the benefits of thermosets. This incorporated feature allows for the possibility of advanced properties such as healing, reprocessability, and extended material lifetimes and can reduce the consumption of energy and resources as well as reduce waste. [START_REF] Fortman | Approaches to Sustainable and Continually Recyclable Cross-Linked Polymers[END_REF] These networks have been defined as covalent adaptable networks (CANs) [START_REF] Kloxin | Covalent Adaptable Networks (CANs): A Unique Paradigm in Cross-Linked Polymers[END_REF] based on dynamic covalent bonds that can assemble and disassemble by "dissociative" or "associative" means when exposed to specific stimuli. [START_REF] Denissen | Vitrimers: permanent organic networks with glass-like fluidity[END_REF] In associative CANs, dynamicity occurs by a substitution reaction between an existing cross-link and a pending reactive group, whereas in dissociative CANs, cross-links are cleaved back into their individual reactive moieties before re-forming again. Dissociative CANs have been predominately studied [START_REF] Gandini | Macromolecular materials based on the application of the Diels-Alder reaction to natural polymers and plant oils[END_REF](22)[START_REF] Sun | Architecture-transformable polymers: Reshaping the future of stimuli-responsive polymers[END_REF] -more specifically those cross-linked via Diels-Alder (DA) adducts formed between furan and maleimide moieties. The DA reaction between furan and maleimide functions is defined as a click cycloaddition reaction and occurs at modest temperatures (below 90 °C), whereas the retro-DA (r-DA) reaction occurs predominately between 110 and 130 °C. [START_REF] Chen | A Thermally Remendable Cross-Linked Polymeric Material[END_REF] Although there have been increasing reports of biobased CANs, associative [START_REF] Dhers | A fully bio-based polyimine vitrimer derived from fructose[END_REF] and dissociative [START_REF] Gandini | Macromolecular materials based on the application of the Diels-Alder reaction to natural polymers and plant oils[END_REF][START_REF] Duval | Reversible crosslinking of lignin via the furanmaleimide Diels-Alder reaction[END_REF][START_REF] Buono | Thermally healable and remendable lignin-based materials through Diels -Alder click polymerization[END_REF][START_REF] Duval | Biobased and Aromatic Reversible Thermoset Networks from Condensed Tannins via the Diels-Alder Reaction[END_REF][START_REF] García-Astrain | Synthesis and evaluation of functional alginate hydrogels based on click chemistry for drug delivery applications[END_REF][START_REF] Yoshie | Self-healing of biobased furan polymers: Recovery of high mechanical strength by mild heating[END_REF] alike, limited research has explored the use of the thermoreversible DA in biobased cross-linked PUs. [START_REF] Tremblay-Parrado | Renewable Responsive Systems Based on Original Click and Polyurethane Cross-Linked Architectures with Advanced Properties[END_REF][START_REF] Hu | Biobased Reprocessable Polyhydroxyurethane Networks: Full Recovery of Crosslink Density with Three Concurrent Dynamic Chemistries[END_REF][START_REF] Zhang | Nonisocyanate route to 2,5-bis(hydroxymethyl)furan-based polyurethanes crosslinked by reversible diels-alder reactions[END_REF] The aim of this study is to explore reversible cross-linked PUs based on vegetable oils using the thermally reversible furan-maleimide DA reaction, with a particular interest in studying the changeability of cross-links localized on hard segments and the use of an original and biobased bismaleimide. As depicted in Scheme 1, (furan-2,5-diyl)dimethanol (FDM) is used as a furan bearing chain extender incorporated into the linear polymer backbone and further cross-linked with the use of different bismaleimides (BMIs). In this frame, we report the synthesis of a new methyl oleate-based BMI (MO BMI), which to our knowledge is the first of its kind. The topic of the synthesis and use of maleimide-bearing architectures having recently been explored in depth by Dolci and co-workers affirms this, as no such architectures were reported. [START_REF] Dolci | Maleimides As a Building Block for the Synthesis of High Performance Polymers[END_REF] The use of this new MO BMI is compared to aromatic and aliphatic fossil-based BMIs. These fossil-based BMIs are commercially available. The aromatic bismaleimide chosen was 1,1′-(methylene di-4,1-phenylene)bismaleimide (MP BMI), and the aliphatic fossil-based bismaleimide chosen was a polypropylene (PPO)-based BMI (PPO BMI) with a degree of polymerization (DP) of 3. The corresponding materials were synthesized with varying furan contents and different cross-linkers. They are studied for advanced properties such as thermal reprocessability and self-healing ability.

Experimental Section

Reagents and Materials Methyl oleate (MO) from sunflower oil was kindly supplied by ITERG (France). It is a fatty acid with an acid value of 0.34 mg KOH/g and an iodine value of 77 g of I2/100 g. Biobased polyester polyol (purchased from Oleon, France) was derived from dimeric fatty acids from rapeseed oil with purity greater than 98% and weight-average molar mass (Mw) around 3000 g/mol. Hydroxyl and acid values were 33.7 and 0.253 mg/g of KOH, respectively. 2-Chloro-4,4,5,5-tetramethyl-1,3,2dioxaphospholane (CL-TDP, 95%), 6-maleimidohexanoic acid (6-MHA, 95%), hydrogen peroxide (H2O2, 30% w/v aqueous solution), chromium(III) acetylacetonate (99.99%), [D6]dimethyl sulfoxide (DMSO, 100%, 99.96% atom D), chloroform-d (CDCl3, 100%, 99.96% atom D), amberlyst 15, 1,4-butanediol (BDO, 98%), oxalyl chloride (99%), and cholesterol (>99%) were purchased from Sigma-Aldrich. 1,1′-(Methylene di-4,1-phenylene)bismaleimide (95%, MP BMI) was purchased from Alfa Aesar. N,N-Dimethylformamide (DMF, 99.8%), chloroform (99.8% stabilized with amylene), glacial acetic acid (GAA, >99%), and ethyl acetate (EA, 95%) were purchased from Fisher Scientific. Amberlite IR-120 H was from Fluka Chemicals. Poly(propylene oxide)-based bismaleimide (PPO BMI) with DPn = 3 was obtained from Specific Polymers (Castries, France). 2,3,4,5,6-Pentafluorobenzaldehyde (PFB, 98%) and (furan-2,5-diyl)dimethanol (FDM, 97%) was purchased from Fluorochem. Reagents and solvents from commercial suppliers were used without additional purification.

Syntheses and Materials Preparations Epoxidation of Methyl Oleate from Sunflower Oil

The epoxidation of methyl oleate (MO) was conducted by the in situ formation of peracetic acid from glacial acetic acid and H2O2 and was adapted from Arbenz et al. [START_REF] Arbenz | Elaboration and Properties of Innovative Biobased PUIR Foams from Microalgae[END_REF] In a two-necked round-bottom flask, equipped with a magnetic stirrer and a dropping funnel, MO (1 mol equiv of unsaturations), Amberlite IR-120 H (25 wt % of MO), and glacial acetic acid (0.5 mol equiv) were inserted into the flask and dissolved at 0.5 mL/g of MO in toluene. The solution was stirred to 70 °C, and then 1.5 mol equiv of H2O2 was added dropwise. The mixture was stirred at 70 °C for 7 h. The solution was diluted in ethyl acetate. The Amberlite IR-120 H was filtered off, and the solution was washed with distilled water until a neutral pH was attained. The organic phase was dried with anhydrous sodium sulfate and then filtered. The solvent was evaporated under reduced pressure. Methyl 8-(3-octyloxiran-2-yl)octanoate (MOO) was dried under vacuum overnight at 50 °C. The reaction product, methyl 8-(3-octyloxiran-2yl)octanoate (MOO), was a clear light yellow oil. [START_REF] Staudinger | Über Polymerisation[END_REF] H NMR (400 MHz, CDCl3): δ = 3.63 (s, 3H, (C═O)OCH3), 2.9 (m, 2H, CHOCH), 2.3 (t, 2H, CH2C(═O)), 1.6 (m, 2H, CH2CH2C(═O)), 1.3-1.0 (m, 24H, aliphatic CH2), 0.9 (t, 3H, CH3). [START_REF] Desroches | From Vegetable Oils to Polyurethanes: Synthetic Routes to Polyols and Main Industrial Products[END_REF] C NMR (400 MHz, CDCl3): δ: 174 (C═O), 57.2 (OCH3), 57.2 (HC-O-CH), 51.4 (OCH3), 34.0 (CH2-C(═O)), 31.9-22.7 (aliphatic CH2), 14.1 (CH3).

Methyl 8-(3-Octyloxiran-2-yl)octanoate (MOO)

Ring-Opening by Butane-1,4-diol of Methyl 8-(3-Octyloxiran-2-yl)octanoate

In a round-bottom flask, equipped with a magnetic stirrer, MOO (1 mol equiv of epoxy), Amberlyst 15 (4 wt % of MOO), and butane-1,4-diol (10 mol equiv) were introduced. The mixture was stirred at 75 °C for 10 h. The solution was diluted in ethyl acetate, and the Amberlyst 15 was filtered off. The solution was washed with distilled water until a neutral pH was attained, and the excess of BDO was removed. The organic phase was dried with anhydrous sodium sulfate and then filtered. The solvent was evaporated under reduced pressure. Methyl 10-hydroxy-9-(4-hydroxybutoxy)octadecanoate (MO Diol) was dried under vacuum overnight at 50 °C. The reaction product, MO Diol, was a clear light yellow oil.

Methyl 10-Hydroxy-9-(4-hydroxybutoxy)octadecanoate (MO Diol) [START_REF] Staudinger | Über Polymerisation[END_REF] H NMR (400 MHz, CDCl3) δ: 3.63 (s, 3H, (C═O)OCH3), 3.65-3.45 (m, 1H, CHOH) and (m, 2H, CH2OH), 3.47 (t, 2H, CH2OCH), 3.10 (q, 1H, CH2OCH), 2.3 (t, 2H, CH2C(═O)), 1.6 (m, 2H, CH2CH2C(═O)), 1.3-1.0 (m, 28H, aliphatic CH2), 0.9 (t, 3H, CH3). [START_REF] Desroches | From Vegetable Oils to Polyurethanes: Synthetic Routes to Polyols and Main Industrial Products[END_REF] C NMR (400 MHz, CDCl3) δ: 174 (C═O), 83.0 (CH2CHOH), 72.7 (CHOH), 70.5 (CH2CHOH), 51.4 (OCH3), 34.0 (CH2-C(═O)), 31.9-22.7 (aliphatic CH2), 14.1 (CH3).

Chlorination of 6-Maleimidohexanoic Acid 6-MHA (1 mol equiv) was placed in a two-necked, flamedried round-bottomed flask flushed with argon and charged with a magnetic stirring bar. Anhydrous ethyl acetate was then added, and the solution was cooled to 0 °C under a flow of nitrogen. An excess of oxalyl chloride (1.5 mol equiv) was then added dropwise at 0 °C (15 min) and finally heated at 50 °C for 3 h. The excess of oxalyl chloride and solvent was evaporated under vacuum. The product, 6maleimidoundecanoyl chloride (6-MHC), was obtained as a low-melting yellow solid and used without any further purification. [START_REF] Staudinger | Über Polymerisation[END_REF] H NMR (400 MHz, CDCl3, δ (ppm)): 6.69 (s, 2H, CH-ring), 3.56 (t, 2H, CH2-N), 2.89 (t, 2H, CH2(C═O)Cl), 1.71 (m, 2H, CH2CH2(C═O)Cl), 1.60 (m, 2H, CH2CH2-N), 1.3 ppm (m, 2H, CH2CH2CH2-N). [START_REF] Desroches | From Vegetable Oils to Polyurethanes: Synthetic Routes to Polyols and Main Industrial Products[END_REF] C NMR (400 MHz, CDCl3) δ: 174 ((C═O)Cl), 170 (CO-ring), 135 (CH-ring), 46.7 (CH2(C═O)Cl), 39.0 (CH2N), 29.3-25.0 (aliphatic chain carbons).

6-Maleimidohexanoyl Chloride (6-MHC)

Synthesis of Methyl Oleate Bismaleimide (MO BMI)

MO Diol was esterified with 1.2 equiv of 6-MHC with respect to the amount of total hydroxy groups. In agreement with different green chemistry principles, the reaction was catalyst-free at 65 °C. CHCl3 was added to homogenize the reaction mixture. At the end of the reaction, a brown viscous product was obtained. Methanol was added to quench the unreacted 6-MHC, and the mixture was left stirring for an additional 30 min. The solvents were then evaporated under vacuum, and the resultant MO BMI products finally dried under high vacuum for 24 h

Methyl Oleate Bismaleimide (MO BMI) [START_REF] Staudinger | Über Polymerisation[END_REF] H NMR (CDCl3, 400 MHz) δ: 6.69 (s, 4H, CH-ring), 4.61 (m, 1H, CHO(C═O)), 4.06 (t, 2H, (C═O)OCH2), 3.63 (s, 3H, (C═O)OCH3), 3.56 (t, 4H, CH2-N), 3.47 (t, 2H, CH2OCH),), 3.25 (q, 1H, CH2OCH), 2.30 (m, 6H, CH2(C═O)O), 1.20-1.80 (multi, 40H, CH2), 0.9 (t, 3H,CH3). [START_REF] Desroches | From Vegetable Oils to Polyurethanes: Synthetic Routes to Polyols and Main Industrial Products[END_REF] C NMR (400 MHz, CDCl3) δ: 174 (CH2(C═O)), 171 (CO-ring), 134 (CH-ring), 51.4 (OCH3), 39.0 (CH2N), 34.0 (CH2-C(═O)), 31.9-22.7 (aliphatic CH2), 14.1 (CH3).

Study of the DA Reaction between MO BMI and FDM MO BMI (200 mg) was dissolved in [D6]DMSO (2 mL) in a 10 mL round-bottom flask. (Furan-2,5-diyl)dimethanol (FDM) was added to obtain a furan/maleimide ratio of 1:1 (mol/mol). The solution was placed in an oil bath regulated to 65 °C, and samples (200 μL) were taken at regular intervals over 4 days. The samples were further diluted to 650 μL and analyzed by 1 H NMR to determine the reaction conversion and endo/exo ratio of the DA adducts.

Synthesis of PUs Based on FDM All glassware and reactants were previously dried. PUs were synthesized by a two-step polymerization process. Three different kinds of PUs films were prepared by a two-step synthesis process by varying the content of hard segments (HS) in wt %, based on diisocyanate and FDM, by 5, 10, and 20%. First, for the prepolymerization step, in a three-necked round-bottom flask flushed with nitrogen, the biobased rapeseed polyester polyol was added to hexamethylene diisocyanate (HDI), and the mixture was mechanically stirred at 70 °C for ∼2 h until an appropriate NCO value was attained.

During the synthesis, aliquots were extracted to determine the NCO content to control and follow the NCO consumption during the reaction. A specific method has been performed to determine isocyanate content by reaction with 1 equiv of N-dibutylamine to give NCO content (in wt %). The prepolymer sample (≈1.2 g) was diluted in a standard solution (20 mL) of dibutylamine (0.2 M) in THF for the reaction with the unreacted diisocyanate. The amine excess was back-titrated with a 0.5 aqueous solution of HCl. The NCO content (wt %) was determined via eq 1:

(1) in which Vblank (mL) is the HCl solution volume required for a blank titration of the dibutylamine solution, while Vs is the volume required for the prepolymer titration and ms is the prepolymer weight. This result was used for the addition for the precise amount of FDM. The appropriate amount of FDM is dissolved in anhydrous DMF (1 mL/g FDM) and added to the above-mentioned reaction system and stirred for 3 h. The ratio of -NCO/-OH functional groups was fixed to 1.05 in all cases.

Cross-Linking of PUs by Each BMI

The PU was dissolved in anhydrous DMF. The respective amount of each bismaleimide was added in a 1:1 furan to maleimide ratio (mol/mol). The reaction mixture was stirred at 70 °C for 12 h to allow for the DA adducts to form. The solution was poured into a polytetrafluoroethylene mold and put into the oven to evaporate the solvent (70 °C, 48 h). Solvent traces were removed under vacuum at 70 °C for 24 h. Cross-linked PU systems using MO BMI were labeled PU-HS5-MOBMI, PU-HS10-MOBMI, and PU-HS20-MOBMI. Two additional cross-linked PUs were obtained by using linear PU-HS20 with cross-linked with a reference and conventional BMI, MP BMI, or PPO BMI and denoted as PU-HS20-MPBMI or PU-HS20-PPOBMI.

Study of the Reprocessability Behavior of PUs PU films were reprocessed by compression molding in a tile mold (10 cm × 10 cm × 1 mm) at 140 °C in a LabTech Scientific press hot press. First, the films were cut in several small pieces and placed in the center of the tile and left to undergo a 10 min preheating cycle to soften the material. This was followed by several venting steps, and the material was pressed with a constant applied force of 16 MPa between both plates for 15 min. The square materials were then cured at 60 °C in an oven for 48 h and postcured for 24 h at room temperature.

Study of Self-Healing Behavior

The macroscopic self-healing ability of material was analyzed on a dumbbell-shaped sample cut in half and then healed. The dumbbell was cut in the middle and subsequently healed by placing the halves in contact for 1 h at 120 °C, followed by 60 °C overnight, and then 24 h at room temperature and 50% RH, and was then tested by uniaxial tensile tests to evaluate the recovery of the integrity of the self-healed dumbbells.

Methods Iodine Value

The iodine value (IV) was determined by using the Wijs method to quantify the double-bond content according to ISO 3961:2018(E).

Hydroxyl Value

The hydroxyl value (HV) was determined by the esterification method using a 1 M solution of phthalic anhydride in pyridine (ASTM 4274-99) for the MO Diol and the biobased polyester polyol. The appropriate mass of sample was dissolved (1.25 g for MO Diol and 7.5 g for the polyester polyol) in 20 mL of phthalic anhydride solution, heated to 130 °C under reflux for 45 min, and cooled at room temperature. Pyridine was added (10 mL) from the top of the reflux to collect all reactions products; the last 20 mL of pyridine and 30 mL of water were added. The solution was titrated with 1 M potassium hydroxide (KOH) solution with phenolphthalein solution as indicator. The HV was determined in mg of KOH g -1 , as described in eq 2.

(

) 2
where Vblank (mL) and Vs (mL) are the volumes of KOH solution required for blank and polyol sample titrations, respectively. C (mol L -1 ) is the KOH solution concentration, and Ws (g) is the polyol weight.

NMR Spectroscopy All NMR spectra were recorded on a Bruker Ascend 400 or 500 MHz spectrometer. Sample were dissolved in deuterated chloroform (CDCl3) or deuterated dimethyl sulfoxide ([D6]DMSO) with contents between 8-10 and 20-30 mg/mL for 1 H NMR and [START_REF] Desroches | From Vegetable Oils to Polyurethanes: Synthetic Routes to Polyols and Main Industrial Products[END_REF] C NMR spectroscopy, respectively. The calibration of 1 H and [START_REF] Desroches | From Vegetable Oils to Polyurethanes: Synthetic Routes to Polyols and Main Industrial Products[END_REF] C NMR spectra was performed by using the chloroform peaks at δ = 7.26 and 77.16 ppm, respectively, and the DMSO peak at δ = 2.50 ppm as references. [START_REF] Tremblay-Parrado | Renewable Responsive Systems Based on Original Click and Polyurethane Cross-Linked Architectures with Advanced Properties[END_REF] P NMR analysis was performed by 2-chloro-4,4,5,5-tetramethyl-1,3,2-dioxaphospholane as a phosphylating agent. Scans (128) were recorded with a 15 s delay and a spectral width of 80 ppm (180-100 ppm). Cholesterol was used as an internal standard, as described in standard protocols. [START_REF] Spyros | Quantitative determination of the distribution of free hydroxylic and carboxylic groups in unsaturated polyester and alkyd resins by 31P-NMR spectroscopy[END_REF] In the case of quantitative 1 H NMR spectroscopic analysis, 20 mg was dissolved in [D6]DMSO (0.5 mL) for each sample before the addition of a standard solution (100 μL) of pentafluorobenzaldehyde in [D6]DMSO. Thirty-two scans were collected with 10 s delay.

Fourier Transform Infrared Spectroscopy (FTIR) For FTIR spectroscopy of experimental samples, a blank background was performed prior to examining samples (32 scans, resolution 4 cm -1 ) on a Nicolet 380 spectrometer equipped with an ATR diamond module (FTIR-ATR) in reflection mode.

Thermal Gravimetric Analysis (TGA) Sample weighing between 1 and 3 mg were evaluated by TGA (TA Instruments Hi-Res TGA Q5000) at a heating rate of 10 °C min -1 from 25 to 700 °C, without oxidative atmosphere, under a nitrogen flow rate atmosphere at 25 mL min -1 .

Differential Scanning Calorimetry (DSC)

In standard aluminum pans, samples between 1 and 3 mg in weight were examined by DSC (TA Instruments Q200) under a nitrogen flow at 50 mL min -1 . For crosslinked PUs, a single heating ramp of 10 °C min -1 was used over the same aforementioned temperature range. Non-cross-linked materials were evaluated by using a cyclical heating ramp.

Uniaxial Tensile Tests Uniaxial tensile testing was performed on an Instron model 5567 H, USA, at strain rate of 20 mm min -1 on dumbbell specimens of approximately 30 × 5 × 1 mm 3 . For each synthesized or reprocessed PU, five dumbbell samples were tested.

Swelling Index and Gel Content Determination

The swelling ratio (SR) for each PU was determined between dried (mi) and swollen samples (ms) in DMF according to eq 3.

(3) PU samples of approximately 10-20 mg were swollen in 15 mL of solvent over an entire day. Three repetitions were examined for each PU formulation. The insoluble fraction (IF) was determined by drying the swollen sample (mf) according to eq 4:

(4)

Small-and Wide-Angle X-ray Scattering (SWAXS)

The SWAXS patterns were obtained with a transmission Guinier-like geometry. A linear focalized monochromatic Cu Kα1 beam (λ = 1.5405 Å) was obtained by using a sealed-tube generator (600 W) equipped with a bent quartz monochromator. In all cases, samples were filled in homemade cells of 1 mm path. The scattering curves were recorded with a curved Inel CPS120 counter gas filled and corrected from air scattering contribution.

Scheme 2. Global Reaction Pathway of MO BMI

Results and Discussion

Analysis of Synthesis of MO BMI The alkene moiety of methyl oleate (MO) was used as the reaction site to yield a MO-based BMI as depicted in Scheme 2. First, MO underwent an in situ epoxidation with peroxyacetic acid as the oxidizing agent to yield MOO. This type of epoxidation is routinely used on vegetable oils. [START_REF] Petrović | Epoxidation of soybean oil in toluene with peroxoacetic and peroxoformic acids-kinetics and side reactions[END_REF] Other pathways for epoxidations using, for example, presynthesized oxidizing agents such as m-chloroperoxybenzoic acid (mCPBA) require large quantities of solvents. Thus, the in situ epoxidation method abides more precisely to the principles of green chemistry. The FTIR spectrum of MOO (Figure 1b) shows the disappearance of the double bonds at ṽ = 3009 cm -1 and the appearance of the C-H bending associated with appearance of epoxides at ṽ = 825 cm -1 . By 1 H NMR spectroscopic analysis (Figure 2b), the structure is confirmed with the disappearance of the vinyl and allyl protons at δ = 5.35 and 2.0 ppm, respectively, and by the appearance of the epoxide and protons alpha to the epoxides at δ = 2.90 and 1.45 ppm, respectively. The results of the [START_REF] Desroches | From Vegetable Oils to Polyurethanes: Synthetic Routes to Polyols and Main Industrial Products[END_REF] C NMR spectroscopic analysis of MOO agreed with the assigned structure as depicted in Figure S1 of the Supporting Information. Thereafter, MOO underwent a ring-opening reaction with BDO to give MO Diol as the main product along with a diester diol as a side product (chemical structure in Figure S2). This diester as a side product is shown also by size exclusion chromatography (SEC) as depicted in Figure S3. The protocol developed by Palaskar et al. was slightly altered and improved. [START_REF] Palaskar | Original diols from sunflower and ricin oils: Synthesis, characterization, and use as polyurethane building blocks[END_REF] The reaction was for instance limited to 10 h compared to 20 h, since the transesterification between the ester moiety and BDO largely took place after 10 h. Figure S4 illustrates that at 10 h all epoxy moieties have been opened by BDO,and the transesterification reaction begins to take place. Furthermore, the purification step for the removal of BDO consisted solely of water-based washing as opposed to vacuum distillation to avoid further side reactions. The HV was determined by two methods: a chemical esterification titration method using phthalic anhydride and quantitative 31 P NMR which gave similar and reproducible results (Figure S5 and Table S1). The HV of MO Diol is 223 mg of KOH/g. This is relatively close to the theoretical value of 258 mg of KOH/g if only the MO Diol product was achieved without diester side product. The FTIR spectrum of MO Diol (Figure 1c) shows the disappearance of C-H bending associated with the epoxides at ṽ = 825 cm -1 , the appearance of a broad band between ṽ = 3600 and 3100 cm -1 corresponding to the hydroxyl groups, and the appearance of a C-O stretch of newly formed alcohols. The 1 H NMR spectrum of the MO Diol along with proton assignments is presented Figure 2c. The chemical structure of MO Diol is confirmed by the appearance of peaks at δ = 3.65 ppm (e) (CH2OH), 3.60 ppm (h) (CH-OH), 3.47 ppm (f) (CH2OCH), and 3.10 ppm (g) the proton adjacent to ether bond. The results of the analysis of [START_REF] Desroches | From Vegetable Oils to Polyurethanes: Synthetic Routes to Polyols and Main Industrial Products[END_REF] C NMR of the MO Diol agreed with the assigned chemical structure as depicted in Figure S1.

MO BMI was finally synthesized by the esterification of the hydroxyl groups of MO Diol by 6-MHA. Similarly to previously reported work, [START_REF] Duval | Reversible crosslinking of lignin via the furanmaleimide Diels-Alder reaction[END_REF][START_REF] Buono | Thermally healable and remendable lignin-based materials through Diels -Alder click polymerization[END_REF] 6-MHA was transformed into an acyl chloride derivative, 6-MHC, to increase the reactivity of the reaction (Scheme S1). The success of this transformation reaction is attested by the 1 H NMR spectra of 6-MHA and 6-MHC and the corresponding proton assignments found in Figure S6. The derivatization of MO Diol was then conducted by using 1.2 equiv of 6-MHC under catalyst-free conditions to Figure 2d), [START_REF] Desroches | From Vegetable Oils to Polyurethanes: Synthetic Routes to Polyols and Main Industrial Products[END_REF] C NMR (Figure S1), SEC, and quantitative 1 H NMR (Figure S7) to determine the maleimide content of MO BMI reported to be 1.83 mmol/g. The FTIR spectrum of MO BMI evidenced the disappearance of a broad band between ṽ = 3600 and 3100 cm - 1 corresponding to the hydroxyl groups and C-O stretch of alcohols. Furthermore, the N-C═O amide stretch of the maleimide ring is detected at ṽ = 1701 cm -1 as well as the C-H bend associated with the maleimide ring at ṽ = 826 and 696 cm -1 . The 1 H NMR spectrum of MO BMI was analyzed and evidenced by the appearance of a strong signal at δ = 6.7 ppm belonging to the maleimide ring double-bond protons. The SEC chromatograms of MO BMI, MO Diol, and 6-MHA are presented in Figure S3. When evaluating these chromatograms purely in terms of retention times, we observed that MO BMI has an increased retention time in comparison to the MO Diol starting material due to the successful esterification by 6-MHC. Nevertheless it is important to note that within the chromatogram of MO BMI the evidence of the excess use of 6-MHC is clearly observed at lower retention times (∼8.7 min) where a weight-average molar mass corresponding to 6-MHA is seen. Quantitative 1 H NMR (in [D6]DMSO) was used to determine the maleimide content by using the C-H bending signal at δ = 7.1 ppm as this signal is free from overlap from other MO Diol signals. This calculation is further depicted by Figure S7 and Table S2.

Analysis of DA Cycloaddition of MO BMI and FDM

To confirm and study the DA adduct formation by [START_REF] Staudinger | Über Polymerisation[END_REF] H NMR of MO BMI when exposed to furan moieties, MO BMI was reacted with FDM in DMSO at 65 °C (Figure 3a). As depicted in Figure 3b, the 1 H NMR spectrum and proton assignment confirm the formation of the DA adduct. The proton assignment was confirmed by using the 1 H NMR of initial reactional entities and compared to the literature. [START_REF] Froidevaux | Study of the Diels-Alder and retro-Diels-Alder reaction between furan derivatives and maleimide for the creation of new materials[END_REF] To quantify the conversion, proton signals f1 (in the furan) and f1′ (in the adduct) were used as they are free from overlap with other signals (Figure 3b). The conversion was calculated by eq 5 for the proton set f1 and f1′ as follows: (5) where Intf1 and Intf1′ represent the integral values of their respective protons. In Figure 3c, the trend of the conversion with respect to time at 65 °C is shown. As similarly reported in the literature, [START_REF] Adzima | Rheological and Chemical Analysis of Reverse Gelation in a Covalently Cross-Linked Diels-Alder Polymer Network[END_REF][START_REF] Scheltjens | A self-healing polymer network based on reversible covalent bonding[END_REF] an equilibrium conversion of 88% was obtained after 78 h of reaction time. A limited conversion was reached due to the thermodynamic equilibrium between the forward and retro reaction at 65 °C. [START_REF] Buono | Thermally healable and remendable lignin-based materials through Diels -Alder click polymerization[END_REF][START_REF] Adzima | Rheological and Chemical Analysis of Reverse Gelation in a Covalently Cross-Linked Diels-Alder Polymer Network[END_REF][START_REF] Scheltjens | A self-healing polymer network based on reversible covalent bonding[END_REF] Decreasing the reaction temperature could increase the final conversion, nevertheless leading to slower reaction kinetics. Moreover, proton signals f1′ were used to assess the presence of the two diastereomers of the DA adduct (endo and exo) with respect to time (Figure 3b), as the chemical shift differs for each diastereomer. The kinetically favored endo adduct is first formed at 80%. An equilibrium between the two diastereomers starts after 78 h (50 wt %).

Analysis of the Synthesis of Biobased Cross-Linked PUs

Cross-linked biobased PUs containing thermoreversible DA adducts were synthesized. Scheme 1 depicts the synthesis of (i) the control systems (linear PUs; recations 1 and 2) and (ii) the cross-linked PUs (reactions 1-3). Furthermore, the synthesis of the PU control systems and PU backbone used for cross-linked PUs was represented structurally in Scheme S2. Different PUs were obtained by varying the HS% in the PU structure. The HS% is the mass of HDI and FDM with respect to the mass of the global structure. The HS% in the PU systems was varied either as 5, 10, or 20%. The nomenclature of all PU systems prepared is summarized in Table 1. As previously mentioned, three different BMIs were explored as cross-linkers: a synthesized biobased BMI, MO BMI, and two fossil-based BMIs. The fossil-based aromatic BMI chosen was MP BMI, and the aliphatic fossil-based BMI chosen was PPO BMI. The chemical structures of both these conventional fossil-based BMIs are illustrated in Figure 4. All PU networks after postcuring (linear and cross-linked) were insoluble in conventional solvents (CHCl3, DMSO, THF, and DMF) and were thus examined by FTIR. In Figure 5, a comparison of the FTIR spectra of PU-HS5, PU-HS10, PU-HS20, polyester polyol, and FDM is presented. In the spectra of the three linear control PUs (Figure 5a-c), no peak was found at ṽ = 2270 cm -1 (NCO stretching band), and the disappearance the hydroxyl stretches (approximately at ṽ = 3600 to 3025 cm -1 ) associated with the hydroxyls of polyester polyol and FDM is observed. Furthermore, the FTIR spectra of PU-HS5, PU-HS10, and PU-HS20 could be used to highlight the main structural differences between them. As expected, the main variations are related to the increasing content of HS%, leading to higher concentration of urethane groups (-NH-C═O-O-). This is highlighted by the increasing vibrations of -NH stretching and bending (ṽ = 3335 and 1550 cm -1 , respectively) as well as the C═O stretching from the urethane group (ṽ = 1680 cm -1 ) from PU-HS5 to PU-HS20. The FTIR spectra of all cross-linked PU networks compared to their control PU and bismaleimides are displayed in Figure 6 and Figure S8. Figure 6 displays the FTIR spectra of PU-HS20 (Figure 6a) compared to the cross-linked PU networks PU-HS20-PPOBMI (Figure 6b), PU-HS20-MPBMI (Figure 6d), and PU-HS20-MOBMI (Figure 6f) with their respective BMIs: PPO BMI (Figure 6c), MP BMI (Figure 6e), and MO BMI (Figure 6g). The FTIR spectrum of MP BMI distinguishes itself by the C-C stretches of the aromatic ring at ṽ = 1500 cm -1 (Figure 6e). It was observed that PS-HS20-PPOBMI and PU-HS20-MPBMI lose the prevalence of the peaks associated with the HS concentration (N-H stretch, bend, and urethane C═O (ṽ = 1550 cm -1 ). In Figure S8 it can be observed that for each PU network cross-linked with MO BMI, PU-HS5-MOBMI (Figure S8b), PU-HS10-MOBMI (Figure S8d), and PU-HS20-MOBMI (Figure S8f), the carbonyl stretch corresponding to the urethane of the control PU-HS5 (Figure S8a), PU-HS10 ( Figure S8c), and PU-HS20 (Figure S8e) becomes masked by the carbonyl stretch of the amide of the maleimide. Furthermore, the N-H stretch of the urethane at (ṽ = 3335 cm - 1

Table 1. Linear PU (Control) and Cross-Linked Systems: Nomenclature and Corresponding Formulations

) becomes slightly less prevalent, most specifically in the case PU-HS20-MOBMI. Moreover, as all PU cross-linked networks are cross-linked via DA reaction, the disappearance of the C-H bending of maleimide ring (ṽ = 826 and 692 cm -1 ) is observed. Mechanical, Thermal, and Structural Evaluations of Biobased Cross-Linked PUs TGA was used to evaluate the thermal stability of PU materials. Detailed TGA results can be found in Figure S9. In Table 2, the initial thermal degradation (T5%) is reported. The T5% for all materials is considerably above the r-DA reaction of ∼120 °C, allowing for the r-DA reaction to take place without any significant thermal degradation of materials. Control PUs (PU-HS5, PU-HS10, and PU-HS20) exhibit decreased T5% with increasing HS ratio. As described in a previous study of our group, [START_REF] Bueno-Ferrer | Relationship between morphology, properties and degradation parameters of novative biobased thermoplastic polyurethanes obtained from dimer fatty acids[END_REF] for equivalent biobased PU materials, initial degradation takes place in the HS domain, and the thermal degradation is directly linked to the HS content. When comparing control PUs with their respective cross-linked materials, the T5% decreased for cross-linked materials. This is primarily linked to the thermal degradation of the BMIs used. As previously mentioned, the temperature at which the initial thermal degradation takes place for cross-linked materials is above that of the r-DA, thus allowing the degradation of free BMIs to take place. The range at which initial degradation begins in cross-linked PUs is well pass the temperature at which significant degradation takes place for the reported BMIs. This is adamant when comparing control PUs to their counterparts cross-linked by MO BMI. The prevalence of MO BMI considerably decreases the T5% due to its decreased thermal stability. Furthermore, upon comparison of T5% of control PU-HS20 to cross-linked PU materials, the lowest T5% reported is that of PU-HS20-MOBMI, whereas PU-HS20-PPOBMI and PU-HS20-MPBMI were observed to be 30 °C higher due to their respective higher thermal stability. This can be linked to the long-chain aliphatic nature of MO BMI as well as traces of reagents from synthesis of MO BMI allowing for lower thermal stability. In contrast, the PU material PU-HS20-MPBMI exhibits the highest T5% in comparison to other cross-linked PU-HS20 materials, and this could be related to the aromaticity of the cross-linker allowing for higher thermal stability.

The glass transition temperatures (Tg) were determined by DSC. To avoid degradation, the Tg of all materials were recorded from -80 to 175 °C as reported in Table 2. A single heating ramp was used for cross-linked PUs. Detailed DSC thermograms can be found in Figure S10. The Tg of all PU materials were observed in a very short window, from -51 to -48 °C. As a general trend, the Tg of cross-linked materials increased (due to cross-linking) when compared to their control counterparts with the exception of PU-HS5-MOBMI. Endothermic peaks corresponding to the r-DA reaction did not seem to appear clearly in any cross-linked PU due to the consequently predominant Tg related to the HS domains and could not be studied.

The mechanical properties of all PUs were evaluated at room temperature by uniaxial tensile tests. They are reported in Table 2 and Figure S11. For control PUs, results indicated that increased HS content led to increased tensile strength and decreased elongation, with the exception of PU-HS5, which exhibited a predictable lower tensile strength but also surprisingly lower elongation at break. As expected, the Young's modulus increased due to the increasing HS content of the control PU materials.

For PU materials that are cross-linked by MO BMI ( Figure S11a), the building block MO BMI tends to have a softening effect compared to the other systems. These PU materials present an increased elongation break and a strong decrease in Young's modulus and tensile strength. This behavior was most apparent in PU-HS10-MOBMI and PU-HS20-MOBMI. This can be explained by the aliphatic and branched long chains of MO BMI. Furthermore, as MO BMI was synthesized with an excess of 6-MHC, the neutralized 6-MHC by methanol gave the corresponding methyl ester, which certainly cause soften in the materials. Nevertheless, the cross-linking does not counter this softening effect due to MO BMI architecture or of remnant reagents. In contrast, PU-HS20 cross-linked by conventional BMIs PPO BMI and MP BMI led to the expected increase in Young's modulus and tensile strength but surprisingly similar elevated elongation at break (Figure S11b). Other research groups have used FDM as part of synthesis of polymer backbones, such as polyesters [START_REF] Zhang | Interplay between crystallization and the Diels-Alder reaction in biobased multiblock copolyesters possessing dynamic covalent bonds[END_REF] and PUs, [START_REF] Gu | Recyclable bio-based crosslinked polyurethanes with self-healing ability[END_REF] both cross-linked by varying amounts of MP BMI, where the PU study exhibited similar behavior. This could perhaps be explained by the fact that the cross-linking took place in the HS domain. This could be further developed in studying PU networks with constant HS content and cross-linked by varying the amount of BMI. Given that the cross-linking takes places in the HS, there seems to be an interplay between the phase segregation of the materials and the DA reaction, especially evident with short BMIs. This was further investigated by small-and wide-angle X-ray scattering (SWAXS) to observe the SWAXS patterns of these PUs. Nevertheless, it is apparent the structure of the BMIs played an evident role in improving the material properties, as PU-HS20-MPBMI reported higher Young's modulus than PU-HS20-PPOBMI. However, the PUs cross-linked with different conventional BMIs reported similar tensile strength. 2. The PUs crosslinked by MO BMI appear to have decreased swelling ratios (SRs) with respect to the linear counterpart but as well experienced decreased in insolubility fraction (IF). This is highly likely due to remnants reagents and byproducts carried over from the MO BMI synthesis, as depicted in the 1 H NMR and [START_REF] Desroches | From Vegetable Oils to Polyurethanes: Synthetic Routes to Polyols and Main Industrial Products[END_REF] C NMR spectroscopic analyses (Figure 2 and Figure S1). Some questions remain open, and at this level it is difficult to fully conclude whether the decreasing in swelling is solely due to cross-linking or rather soluble mass transferred to the organic solvent phase. Additional investigations could be needed on this point. In contrast, a significant decrease in SRs and increase in IFs is evidently apparent in PUs cross-linked by the conventional BMIs. Lastly, the SWAXS patterns of some synthesized PUs are shown in Figure 7. As shown in Figure 7a, from the PU-HS5 and PU-HS10 curves, it cannot be excluded that the appearance of an upturn instead of a peak pertains to a completely irregular distribution of hard and soft segments. However, the explanation is more probably the same as for PU-HS20, with namely the presence of a crystalline fraction. The steep upturn shown by PU-HS20 and above all the broadened reflections overlapping the broad wide-angle signal (blue arrows) are indeed clear proof for a scattering contribution from crystallites dispersed in the amorphous matrix. This contribution masks the peak from hard-soft alternation in PU-HS20 and probably also in PU-HS10 and PU-HS5. The average crystallite size in PU-HS20 is ∼10 nm, as estimated from reflection width using the Scherrer equation with shape factor K = 0.9. As depicted in Figure 7b, in addition to the wide-angle scattering signal at 1.4 Å -1 from lateral distances between molecular segments, patterns exhibit a broad peak in the small-angle range reflecting the hard-soft alternation in the elastomeric structure. [START_REF] Charlon | structure and properties of fully biobased thermoplastic polyurethanes, obtained from a diisocyanate based on modified dimer fatty acids, and different renewable diols[END_REF] The periodicity of this alternation, i.e., the long period L = 2p/q* deduced from peak maximum q*, is 74-75 Å for PU-HS20-MOBMI, 75-76 Å for PU-HS20-PPOBMI, and 65-66 Å for PU-HS20-MPBMI. The thickness of the hard segments slabs, i.e., the short period S deduced from the scattering profile using the one-dimensional correlation function, [START_REF] Goderis | Use of SAXS and linear correlation functions for the determination of the crystallinity and morphology of semi-crystalline polymers[END_REF] is 15 Å for PU-HS20-MOBMI and PU-HS20-PPOBMI and 12 Å for PU-HS20-MPBMI. However, the hard segment slabs are constituted of neat HDI or of HDI juxtaposed to furan and possibly engaged in adduct with bismaleimide. These elastomers are indeed more complex than the two-phase model used for the scattering curve analysis, and the short periods therefore represent average values of the weighted individual hard segment configurations.

Evaluation of the Remendable and Self-Healing Behaviors

As an advanced property, reprocessability was studied by using PU materials cross-linked by conventional BMIs and PU-HS10-MOBMI and reported in Figure 8 and Table S3. The reprocessability of these PUs was evaluated by comparing the mechanical properties of original materials processed by solvent casting to materials reprocessed by compression molding. Of all materials evaluated, PU-HS10-MOBMI seems to best preserve its static mechanical properties over two hot press reprocessing cycles, with only experiencing a loss in Young's modulus after a second reprocessing cycle. PU-HS20-PPOBMI seems to preserve its Young's modulus over all processing cycles whereas PU-HS20-MPBMI evidenced an apparent decrease over reprocessing cycles. Although the aromatic nature for the MP BMI yields superior mechanical properties, it can affect the reprocessing ability of the material by compression molding. The high melting temperature of MP BMI (∼150 °C) can be affecting the reprocessing ability of materials, specifically during the curing step (DA reaction) of the procedure as this limits the local mobility of MP BMI in the material. Nevertheless, PU-HS20-MPBMI loss in Young's modulus and tensile strength remains quantitatively superior than PU-HS20-PPOBMI for the respective reprocessing step. The notable lack of preservation of material properties over processing cycles can be attributed to the inability of the material to maintain its cross-linking density when exposed to this thermal treatment.

As previously mentioned, dissociative CANs often exhibit varying cross-link densities after reprocessing, which in turn affect the mechanical properties due to chain rearrangement, vitrification, and cross-link ruin. [START_REF] Kloxin | Covalent Adaptable Networks (CANs): A Unique Paradigm in Cross-Linked Polymers[END_REF] Furthermore, since there is an interplay between the hydrogen bonding due to the phase segregation of the materials and the DA reaction, exposing the material to different reprocessing procedures could enhance reprocessability. For example, curing temperatures higher than 60 °C but lower than 90 °C, for the DA reaction to take place, could increase the kinetics of the DA reaction in the material but as well enhance local mobility.

As an advanced property, the self-healing ability of PU-HS10-MOBMI was also evaluated. The initial 120 °C heating allows the r-DA to take place but as well as promotes adhesion, whereas the 60 °C heating cycle allows for the network to be re-formed by the DA reaction. After thermal treatment, the cut dumbbells have recovered their integrities. As depicted in the stress-strain curved of the initial and healed sampled displayed in Figure 9, the healed sample seems to almost fully recover in Young's modulus and attain about 50% of the initial tensile strength. Because of their toughness, PU-HS20-PPOBMI and PU-HS20-MPBMI samples could not be easily tested for self-healing. In contrast, an adhesion test could be further developed to further characterize these stiffer materials by examining the adhesion between two pieces of these material on larger surfaces areas.

Conclusion

A new approach of producing cross-linked vegetable oil-based PUs via the thermoreversible furanmaleimide DA reaction was studied and successfully developed. Linear PUs were synthesized by using rapeseed-based polyol, HDI, and FDM, a furan containing chain extender. By using FDM as chain extender, we can explore the cross-linking of PUs in the HS domain. The furan content was varied in PUs by varying the HS content (5, 10, and 20%). Furthermore, to ultimately avoid the use of fossilbased BMIs and provide a new branched BMI, an original biobased methyl oleate BMI (MO BMI) derived from sunflower oil was synthesized and fully characterized. The PUs were cross-linked by MO BMI as well as two conventional and fossil-based BMIs: 1,1′-(methylenedi-4,1-phenylene)bismaleimide and PPO-based BMI. Control PUs (without BMI cross-linking) generally exhibited increased Young's modulus and tensile strength and decreased elongation with increasing HS content. However, when these PUs were cross-linked by MO BMI, MO BMI tends to have a softening effect on the material, with increased elasticity. The long branched aliphatic chains of MO BMI as well of shortcomings of its synthesis process can be attributed to the reported behavior. In contrast, PUs cross-linked with shorter linear BMIs would yield increased Young's modulus, tensile strength, Tg, and IF and decreased SR. PUs cross-linked by MO BMI exhibited the most consistent thermal recyclability and heat-induced selfhealing. Nevertheless, PUs cross-linked by conventional BMIs showed promising thermal recyclability which requires further optimization by modified thermal treatments. Future efforts consist of further examining the temperature-dependent viscoelastic behavior of these CANs to further improve thermal recyclable behavior.

These PU networks are reported for the first time with such a high biobased content (90 wt %).

Synthesizing such networks provides a holistic approach to sustainable material design by incorporating sustainable raw materials but as well as attempting to control the end life of materials as a means to reduce energy and waste. This innovative work contributes to the development of biobased intrinsically dynamic architectures for a wide range of material domains.

ABBREVIATIONS

Scheme 1 .

 1 Scheme 1. Illustration of the General Synthesis of Biobased Thermoreversible PU-Based Systems Using (Furan-2,5-diyl)dimethanol and Different BMIs (MO BMI, MP BMI, and PPO BMI)

Figure 1 .

 1 Figure 1. FTIR spectra (a) MO, (b) MOO, (c) MO Diol, and (d) MO BMI with the assignations of the main peaks.

Figure 2 . 1 H

 21 Figure 2. 1 H NMR spectra of (a) MO, (b) MOO, (c) MO Diol, and (d) MO BMI, with the assignations of the main signals and the corresponding chemical structures.

Figure 3 .

 3 Figure 3. (a) Reaction scheme between FDM and MO BMI. (b) 1 H NMR of spectra of mixture of FDM and MO BMI after 10 min and 24 h. (c) Conversion and percentage of endo structure with respect to time and 65 °C.

Figure 4 .

 4 Figure 4. Chemical structure of both conventional maleimide-terminated BMIs used as cross-linkers.

Figure 5 .

 5 Figure 5. FTIR spectra of from top to bottom: (a) PU-HS5, (b) PU-HS10, (c) PU-HS20, (d) rapeseedbased polyol, and (e) FDM.

Figure 6 .

 6 Figure 6. FTIR spectra of from top to bottom: (a) PU-HS20, (b) PU-HS20-PPOBMI, (c) PPO BMI, (d) PU-HS20-MPBMI, (e) MP BMI, (f) PU-HS20-MOBMI, and (g) MO BMI.

Figure 7 .

 7 Figure 7. SWAXS patterns of (a) PU-HS5, PU-HS10, and PU-HS20 and (b) PU-HS20-MOBMI, PU-HS20-PPOBMI, and PU-HS20-MPBMI.

Figure 8 .

 8 Figure 8. Uniaxial tensile tests to compare the mechanical results of initial and reprocessed materials PU-HS20-MPBMI, PU-HS20-PPOBMI, and PU-HS10-MOBMI: (a) Young's modulus, (b) tensile strength (σ), and (c) elongation (ε).

Figure 9 .

 9 Figure 9. Uniaxial tensile tests: stress-strain curves of healed samples PU-HS10-MOBMI.

Table 2 . Main Characterizations of Synthesized Biobased PUs

 2 SR = swelling ratio. d IF = insoluble fraction. All PUs were characterized by swelling tests in DMF. Results are reported in Table

	PU system	TGA	DSC	Young's	σ a	ε b	SR c in	IF d
		T5%	Tg	modulus	[MPa]	[%]	DMF	[%]
		[°C]	[°C]	MPa]			[%]
	PU-HS5	348	-49	2.33 ± 0.21	0.55 ± 0.01	91 ± 14	40 ± 3	97.6 ± 0.1
	PU-HS10	322	-49	2.73 ± 0.15	0.88 ± 0.01	155 ± 4	167 ± 18	97.5 ± 4.4
	PU-HS20	281	-51	5.64 ± 1.12	1.73 ± 0.08	74 ± 8	137 ± 6	93.5 ± 1.0
	PU-HS5-MOBMI	339	-51	1.80 ± 0.12	0.57 ± 0.02	102 ± 13	42 ± 1	96.4 ± 0.1
	PU-HS10-MOBMI	298	-48	3.80 ± 0.05	0.35 ± 0.01	299 ± 15	105 ± 2	91.2 ± 1.6
	PU-HS20-MOBMI	230	-51	0.17 ± 0.01	0.15 ± 0.01	114 ± 9	116 ± 5	84.8 ± 3.0
	PU-HS20-PPOBMI	261	-48	6.20 ± 1.03	2.28 ± 0.21	114 ± 9	70 ± 11	97.1 ± 1.3
	PU-HS20-MPBMI	268	-48	13.4 ± 1.81	2.07 ± 0.06	97 ± 12	69 ± 2	96.1 ± 0.6

a Tensile strength. b Elongation. c

  6-MHA, 6-maleimidohexanoic acid; 6-MHC, 6-maleimidohexanoyl chloride BDO, 1,4-butanediol; BMI, bismaleimide; CAN, covalent adaptable network; DA, Diels-Alder; DSC, differential scanning calorimetry; FDM, (furan-2,5-diyl)-dimethanol; HDI, hexamethylene diisocyanate; HS, hard segments; HV, hydroxyl value; IF, insolubility fraction; IV, iodine value; MO, methyl oleate; MO Diol, methyl 10hydroxy-9-(4-hydroxybutoxy)octadecanoate; MOO, methyl 8-(3-octyloxiran-2-yl)octanoate; MP BMI, 1′-(methylene-di-4,1-phenylene) BMI; Mw, weight-average molecular weight; NCO, isocyanate; PPO BMI, poly(propylene oxide)-based BMI; PU, polyurethane; r-DA, retro-Diels-Alder; SEC, size exclusion chromatography; SR, swelling ratio; SWAXS, small-and wide-angle X-ray scattering; TGA, thermal gravimetric analysis.

ACKNOWLEDGMENTS

The authors thank Programme d'investissements d'avenir (PIA) of BPI-France for their financial support and Iterg (France) for kindly providing technical grade methyl oleate. The authors also thank the R&D Team of Soprema (France). In memory of Pr. Jean-Pierre Pascault (1943-2020), a top researcher and great man who has always sympathetically followed the project.

FUNDING

This study was funded by the Programme d'investissements d'avenir (PIA) of BPI-France.

NOTES

The authors declare no competing financial interest.

SUPPORTING INFORMATION

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.macromol.0c01115.


Yinshi Zhou

Francois Ollivier

Pascal Challande

Régis Marchiano

Vincent Valeau

David Marx

Christian Prax

DESIGN AND USE OF A THREE-DIMENSIONAL ARRAY OF MEMS MICROPHONES FOR AEROACOUSTIC MEASUREMENTS IN WIND-TUNNELS †

This paper introduces a three-dimensional (3D) microphone array associated with a dedicated beamforming algorithm for aeroacoustic sources identification in an anechoic windtunnel. The array is arranged into a tunnel geometry composed of three nearly perpendicular planar sub-arrays consisting of 768 digital Micro ElectroMechanical Systems (MEMS) microphones enclosing the 3/4 open test-section of the wind-tunnel. This setup enables to scan a volume containing the potential noise sources in the wind-tunnel flow. Digital MEMS microphones allow significant cost reduction and lower complexity for large array systems. Several spatial arrangements of the microphones were investigated in terms of resolution and signal-to-noise ratio using synthetic noise sources in order to find the optimal one under manufacturing constraints. The coordinates of the microphones after installation of the array system were obtained by using a method based on the differential times of arrival. The array processing algorithm is based on a 3D implementation of the beamforming technique, associated to the Clean-SC method extended to applications involving dipolar sources, in order to improve the spatial resolution of the 3D sound maps. The application results presented in this study concern the dipolar broadband noise sources radiated by two wall-mounted NACA 0012 airfoils.

INTRODUCTION

Microphone arrays are nowadays very common tools in wind-tunnels for performing experimental aeroacoustics studies. Most of the time, planar arrays are used. Such arrays are powerful tools to identify the sources of sound in a plane parallel to the array, but their resolution is bad perpendicularly to the array so that they fail to perform source identification in three dimensions. However, this aspect is important for studying the sound radiation of obstacles which are strongly three-dimensional (3D). Such studies can be achieved only by using 3D arrays, measuring the sound radiation over a large solid angle around the source, in order to capture the 3D patterns of the radiation.

In 2010, Dougherty [START_REF] Dougherty | Jet noise beamforming with several techniques[END_REF] reported the design of a cylindrical cage array of 105 pressure transducers enclosing a jet. Diverse beamforming techniques were evaluated to investigate the noise sources at low frequency. Padois et al. [START_REF] Padois | 3D source localization in a closed wind-tunnel using microphone arrays[END_REF] used four sub-arrays of 48 microphones mounted on the walls of the closed test-section of a wind-tunnel, and applied their system to the aelioan tones produced by a cylinder. Porteous et al. [START_REF] Porteous | Threedimensional beamforming of dipolar aeroacoustic sources[END_REF] used two perpendicular arrays of 31 microphones to investigate the radiation of cylinders and airfoils; the originality of their study was the use of a 3D beamforming algorithm (associated to the CLEAN-SC deconvolution technique [START_REF] Sijtsma | CLEAN based on spatial source coherence[END_REF]) taking into account the dipolar nature of the radiation. In 2017, Ernst et al. [START_REF] Ernst | A three-dimensional microphone array for wind tunnel application[END_REF] designed a 3D array by optimizing the microphone positions in order to reduce the side lobes in three-dimensional space. In the present study, some measurements are carried out in a wind-tunnel with an open test-section. A large array has been designed, with a tunnel shape totally enclosing the test-section. Such an array requires a high number of microphones (of the order of several hundreds), in order to reach a targeted operational frequency range reaching frequencies of the order of 10 kHz.

Large microphone arrays are still rare nowadays because the technological barriers remain numerous: the congestion of the connections, the complexity of the electronic design and manufacturing of the system, maintenance complexity to replace faulty channels, the difficulty and time required to deploy the system in situ. To defeat these locks, a strategy is to propose an architecture dividing the array into sub-arrays. The advantage lies in the ability to position subsets over a large area, and in the fact that it requires a number of wires lower than the number of microphones. Silverman et al. were pioneers in making large arrays in the late 1990s, with the Huge Microphone Array, made up of 512 electret microphones [START_REF] Silverman | The huge microphone array (HMA)[END_REF]. The architecture was broken down into 16-microphone modules containing the analog-to-digital conversion and then connected by optical fiber to the master interface. The LOUD array, designed at MIT in 2004, has long been the largest network, equipped with 1020 channels [START_REF] Weinstein | A 1020-node microphone array and acoustic beamformer[END_REF]. In this purpose, the team designed the most modular structure possible: the instrumentation chain is compacted closer to each microphone. This has two important advantages: (i) ease of manufacture and maintenance: all modules are identical, and can easily be replaced in the event of a failure, (ii) the signal transmission is entirely digital. But this array of transducers was still very complex and its shape was only two-dimensional. In 2004, Humphreys et al. [START_REF] Humphreys | Application of MEMS microphone array technology to airframe noise measurements[END_REF] designed a planar array of 128 analog microphones which solved the problem of complexity of the conditioning stage. The application to a scaled landing gear indicated performances equivalent to arrays of measurement microphones.

In this study, we propose to use a massive multi-channels antenna in order to build a 3D array: the MegaMicros system, developed at Institut d'Alembert [START_REF] Vanwynsberghe | Design and implementation of a multi-octave-band audio camera for realtime diagnosis[END_REF]. This new generation of array is based on the use of a large number of digital MEMS (Micro Elec-troMechanical Systems) microphones (up to 1024). This 3D array will be used in this paper to investigate the noise produced by two wall-mounted NACA 0012 airfoils.

The present paper is structured as follows. In Section 2, the data acquisition system is first briefly presented. In Section 3, the experimental set-up (wind-tunnel, test cases) and the characteristics of the 3D array (response of the microphones, design and optimization of the array geometry) are presented. The array processing techniques used, based on 3D beamforming, are introduced in Section 4, followed by results concerning the two wallmounted airfoils located in the wind-tunnel test section . The paper ends with a set of conclusions (Section 5).

The acoustic data acquisition system allows to synchronously acquire up to 1024 digital signals from MEMS microphones and 16 other signals from analog channels. The 1024 MEMS microphones are divided into 128 bundles of 8 microphones. Each microphone is inserted in a small PCB card (see Fig. 1). In each bundle, the 8 microphones are controlled by a buffer card (see Fig. 1) linked to the data acquisition system with a RJ45 cable (see Fig. 2). First, the data acquisition system collects all the signals acquired by each channel (digital and analog ones). The MEMS microphones are ICS-43434 microphones developed by InvenSense. These microphones deliver digital signals: the whole instrumentation chain is directly included on the chip (the transducer, an amplifier and a 24 bits AD converter). From the microphone to the interface, signals are handled with I2S serial protocol. The sampling frequency can be chosen by the user up to 50 kHz. Then, the 24-bit integer samples are converted to 32-bit floats before multiplexing and transfer via the USB 3.0 serial bus to the host PC.

EXPERIMENTAL SET-UP

Wind-tunnel and test models

Wind tunnel The anechoic wind-tunnel BETI of the PPRIME Institute is an open circuit wind-tunnel for aerodynamic and aeroacoustic studies. The wind-tunnel flow is drawn by fan assemblies downstream the test section with suction. Figure 3 shows the sketch of a part of the wind-tunnel. The open test section with a wood plank as bottom is located in an anechoic room of 90 m 3 allowing a cutoff frequency of 200 Hz. The length of the test section in wind-tunnel flow direction is 1.44 m. The wind-tunnel flow is firstly accelerated in a tunnel with decreasing section area (with a contraction ratio of 10), and enters the test section from a rectangular nozzle of (0.7 × 0.7) m 2 . At the nozzle exit, the boundary layer thickness is of the order of 10 mm, and the turbulence intensity of the free-stream flow is about 1.5 %. The flow is then sucked through a collector of dimensions (width × height) (1.00 × 0.87) m 2 . The maximum free-stream velocity of the wind-tunnel flow is up to 60 m/s (216 km/h). The coordinate system (O, x, y, z) used for the experiments in this paper is presented in Fig. 3. The origin of the coordinate system is located at the center of line AB (see Fig. 3). Axis x follows the wind-tunnel flow direction, and axis z follows the vertical direction. Test models The test models under study are two wall-mounted finite length NACA 0012 airfoils with a flat-ended tip and sharp trailing edge. They both have a chord length C = 200 mm. The short NACA 0012 airfoil has a span length L 1 = 400 mm and its leading edge is located 350 mm downstream of the nozzle exit at zero-angle of attack. The long NACA 0012 airfoil has a span length L 2 = 458 mm and its leading edge is located 450 mm downstream of the nozzle exit at zero-angle of attack. The airfoil models are mounted vertically to the bottom of the open test section as shown in Fig. 4. The distance between them in the y direction is 200 mm. For the two wall-mounted airfoils, a tripping device using a rough band (sandpaper) with a width of 15 mm is placed at a distance of 10 mm from the leading edge along the span at one side of the airfoil surface. Hence, a forced transition of boundary layer can occur on the side with such devices and a natural transition of boundary layer can occur on the other side of the airfoil surface. The rotation axis of the NACA airfoils are located at 66.6 mm (a third of the chord length) from the leading edge. The angle of attack is defined as positive when the tripping device is on the pressure side of the airfoil. In this paper, results are given for angle of attack at 4 • and a flow speed of 50 m/s, corresponding to a chord-based Reynolds number of 6.66 × 10 5 . Tonal noise generation is eliminated at these testing conditions, and it is the broadband noise that dominates the noise radiation.

Response of the MEMS microphones

In order to characterize the frequency response the MEMS microphones, 32 elements of a same lot of ICS-43434 have been tested in an anechoic room, using the protocol described in [START_REF] Vanwynsberghe | Design and implementation of a multi-octave-band audio camera for realtime diagnosis[END_REF].The average response of this set is presented on Fig. 5, together with the intervals of variation in relative amplitude and phase.

The tested set shows a very good homogeneity in terms of sensitivity with less than 3 dB dispersion over the band comprised between 80 Hz and 10 kHz. Concerning the phase homogeneity, it should be noticed that it is very good up to 6kHz. At higher frequencies the relative phase between the microphones grows significantly which is likely to affect the performance of the beamforming process.

Another important point needed to be addressed is the exposure of the microphones to the wind stream. When embedded in a moderate wind, the microphones without any protection are exposed to turbulence and produce saturated signals, hence unusable. Therefore it was required to design the array so as to locate the microphones outside the locus of turbulence. Meanwhile, their distribution was to allow a surrounding view of the aeroacoustic sources while ensuring the best possible characteristics in terms of dynamics and resolution.

Array design

The minimum distance to the shear layer, the need to avoid the turbulent regions around the collector intake and manufacturing constraints determined a conical shape of array enlarging from the nozzle to the collector intake of the wind tunnel. The structure of the array is shown in Fig. 6. It is a cone with rectangular base surrounding the flow like a tunnel (see also Fig. 4). The length of the edges of square 1 (vertices 1, 2, 3 and 4) is L 1 =1200 mm and that of square 2 (vertices 5, 6, 7 and 8) is L 2 =1535 mm. The distance between the two squares is L D =1157 mm. For each of the four sides (A, B, C and D), there are 16 bars (spaced by a distance of 75 mm on square 1 and 96 mm on square 2) . The bars of length 1.8 m have U-shaped section. On each bar there are two bundles of microphones (so 16 microphones on each bar) uniformly spaced by a distance of 72 mm. Each bundle is connected to the acquisition system with an RJ45 cable. The theoretical performances of such an arrangement of the microphones are discussed in the next section. The experiments in this paper were conducted using only 3 sides (A, B and C) enclosing the Â3 4 open test section of the wind tunnel with 768 microphones.

Optimization of the microphones distribution

On the inner surface of the cone surrounding the wind-tunnel flow, various distributions of the microphones could be chosen accounting for the manufacturing constraints and optimal array processing characteristics. Therefore, numerical simulations were conducted to estimate the point spread functions of the possible distributions. Four distributions where compared: fully random ("Aleat"), stream-wise logarithmic ("Log16"), regular 1 ("Reg16") and regular 2 ("Reg24"). They are presented in Fig. 7. To estimate their performances, a harmonic point source is simulated at the center of the volume for investigation. It emits a harmonic signal at a chosen frequency. The signals received at the microphones are polluted by a level driven random noise. Using these signals, a standard beamforming is processed to recover the source. Figure 8 presents a typical result showing the reconstructed acoustic intensity in 3 perpendicular planes intersecting at the source point. The Point Spread Function (PSF) presents two line plots indicating, with respect to the distance to the source over the solid angle 4π, the average relative acoustic level (blue line) and the maximum relative acoustic level (red line).

The investigation established firstly that the random and logarithmic distributions did not provide a significant improvement in terms of dynamics of reconstruction compared to the regular distributions. Therefore, for ease of assembly, the choice was the most regular distribution (Reg16, ie., 16 microphones with a regular longitudinal spacing, on 64 bars with a regular transverse spacing). At high frequency (5kHz) and high noise level (0dB SNR) as shown by Fig. 8, the antenna provides a resolution of a few centimeters with very good dynamic of the order of 10dB in the vicinity of the source up to 15dB at 0.5m and more.

Geometrical calibration of the array

In order to ensure a proper resolution of the inverse problem, the true positions of the microphones have to be assessed. Since the array structure is rigid, this assessment is not critical, the relative positions being well known. Anyway, for a final check of the setup, a thorough geometrical calibration procedure was led. Based on the measurements of relative time of flights between a number of sources and the microphones, it followed the prescriptions of Vanwynsberghe et al. [START_REF] Vanwynsberghe | A robust and passive method for geometric calibration of large arrays[END_REF] to estimate the individual positions of the microphones.

A small loudspeaker was located successively at 29 different positions of the space surrounding the array (12 outside, 17 inside), emitting at each position a broadband signal allowing to implement in the following a generalized cross correlation based process to derive the required set of DTOAs (Differential Time of Arrival). The robust DTOA procedure finally provided a geometry very close to the one measured during the building process, and the latter was used in the array signal process to identify the aeroacoustic

ARRAY PROCESSING TECHNIQUE AND RESULTS

Array processing technique

3D beamforming Conventional beamforming is the standard array processing technique for noise source identification [START_REF] Johnson | Array signal processing: concepts and techniques[END_REF][START_REF] Mueller | Aeroacoustic measurements[END_REF]. Consider an array consisting of M microphones located in the far-field of noise sources for identification with x m describing their position. A scanning domain, which is discretized and represented by a scanning grid (described by the position x f ), contains the potential noise sources. It is a plane, generally parallel to a planar array for 2D beamforming and a volume for 3D beamforming.

For each point x f , the frequency-domain beamforming function is given by the following equation:

A(x f , ω) = e H C t e M 2 -M , (1)
where C t is obtained by setting the diagonal elements of the Cross Spectral Matrix (CSM) as zero. The CSM is defined as C = P P H with H being the Hermitian transpose operator. This matrix C has an Hermitian symmetry (C mn (ω) = C * nm (ω)). P = (P (x 1 , ω)...P (x M , ω)) T contains the Fourier transforms of the signals recorded by each microphone with T indicating the transpose operator. The steering vector e = (e(x 1 , x f , ω)...e(x M , x f , ω)) T allows the microphone array to "steer" to different scanning points x f , and depends on a source model. Sound maps can be obtained by mapping the beamformed values A(x f , ω) to the corresponding scanning domain.

For 3D beamforming, the assumption of monopole noise source with uniform radiation is not always appropriate. The flow-induced noise with the presence of solid boundaries tends to have a dipolar radiation [START_REF] Howe | The influence of solid boundaries upon aerodynamic sound[END_REF]. According to [START_REF] Porteous | Threedimensional beamforming of dipolar aeroacoustic sources[END_REF][START_REF] Liu | Beamforming correction for dipole measurement using two-dimensional microphone arrays[END_REF], the steering function for a point dipole source is given by:

e d (x m , x f , ω) = exp(-jωτ (x m , x f )) ξ • x m -x f r m , (2)
with r m = |x m -x f |, c 0 being the speed of sound and ξ being the orientation of the dipole source. The time delay τ (x m , x f ) is simply r m /c 0 for a quiescent medium. The steering vector allows to exhibit a main lobe at the position of a dipolar source on sound maps. However, appropriate assumption of the dipole orientation should be made, otherwise it may lead to ambiguous lobes on sound maps.

The wind-tunnel flow can involve significant effects (refraction, convection) on sound propagation, and methods based on ray tracing [START_REF] Amiet | Refraction of sound by a shear layer[END_REF][START_REF] Koop | Investigation of the systematic phase mismatch in microphone-array analysis[END_REF][START_REF] Rakotoarisoa | Array processing for the localisation of noise sources in hot flows[END_REF] can be used to compute the time delay τ (x m , x f ). Note that noise sources on sound maps are subjected to apparent shift downstream if these influences are not considered. In this paper, a 3D implementation of the Amiet's method [START_REF] Bahr | Shear layer time-delay correction using a non-intrusive acoustic point source[END_REF] was used for the beamforming technique. The shear layers of the wind-tunnel were simplified to two vertical planes and a horizontal plane with no thickness. The acoustic rays in the wind-tunnel are not straight from source to microphone because of the convection effect by the wind-tunnel flow and refraction effect by the shear layer. In this paper, only the angle corrections due to the shear layers of the wind-tunnel are addressed, and the existence of the wake of the airfoils is not accounted for in the Amiet's method.

Deconvolution The main lobes of the beamforming sound maps are used to identify the location of noise sources. However, they provide the source location and its distribution only approximately because the size of the lobes are frequency-dependent. Moreover, side lobes may contaminate the beamforming results because they can overlap between them and even with main lobes. This makes it difficult to obtain the real distribution of noise source. To improve the spatial resolution in all frequency bands and remove the side lobes from the sound maps, the deconvolution method CLEAN-SC (Sijtsma [START_REF] Sijtsma | CLEAN based on spatial source coherence[END_REF]) can be associated to the BF technique. This method is not computationally expensive and can be extended to 3D applications for dipolar noise sources, which was initially developed by Porteous et al. [START_REF] Porteous | Threedimensional beamforming of dipolar aeroacoustic sources[END_REF]. Although it is not efficient at low frequencies and for source regions containing coherent noise (Bahr and Cattafesta [START_REF] Bahr | Wavenumber-frequency deconvolution of aeroacoustic microphone phased array data of arbitrary coherence[END_REF]), it is used in this paper based on its good compromise between efficiency and computational cost.

Results

Acoustic measurements were conducted with the 768 digital MEMS microphones and a microphone (GRAS 40F) placed outside the flow above the airfoil surface at the level of the trailing edge of the longer airfoil. The experiment data were transmitted using 769 channels including an analogical channel for the GRAS microphone. They were obtained for a sampling time of 5 s with a sampling frequency of 50 kHz. The analogical data were used to compute the far-field spectrum of the two wall-mounted airfoils in flow. For the acoustic spectrum and sound maps, the Welch's method of spectral estimation was used, and the frequency resolution was 20 Hz.

In order to compute the sound maps, 236 channels of acoustic data were selected from the acoustic database containing 768 channels. The scanning domain is a cube of dimension 0.6 m × 0.6 m × 0.6 m containing a 3D scanning grid of 226981 points (61 3 ) (see Fig. 9), for which the grid was composed of cubes with an edge length of 10 mm. As explained above, a dipolar noise source model was used for beamforming processing. Therefore, the steering vectors were computed based on Eq. ( 2), with the dipole orientation perpendicular to the airfoils' surfaces. The 3D sound maps were presented in a third-octave band [2828 Hz; 3564Hz] of centre frequency 3175 Hz, which were obtained by summing all the beamforming results in this band. Fig. 11 shows the sound maps of the two wall-mounted airfoils in the third-octave band [2828 Hz; 3564Hz] at angle of attack of α = 4 • and incoming velocity U ∞ = 50 m/s. In Fig. 11(a), the beamforming result illustrates some lobes around the trailing edges of the two wall-mounted airfoils. A lobe with large size along the trailing edges may indicate some noise sources. However, regular appearance of some lobes of almost the same size in the direction perpendicular the airfoils' surfaces is observed, which introduces the ambiguity for the distribution of the noise sources. In Fig. 11(b), the CLEAN-SC technique allows a better spatial resolution for the sound map. The safety factor and clean beamwidth for CLEAN-SC were set respectively as 0.99 and 5 cm. After removing the side lobes, the distribution of the broadband noise generated by the airfoils is clearly observed. For the longer airfoil, the noise source distributes evenly along the trailing edge of the airfoil with higher sound intensity toward the wing tip area. For the airfoil with short span, this tendency is stronger with the wing tip noise dominating the noise generation of this airfoil. It is suggested that the wing tip flow has more influence on the flow mechanism in the mid-span area at the trailing edge of the short airfoil and thus on the corresponding noise source distribution.

CONCLUSIONS

This paper introduces the design of a 3D microphone array and its first application to aeroacoustic source identification in an anechoic wind-tunnel. Digital MEMS microphones and the designed data acquisition system through USB connection allow a large amount of data channels for the 3D array. A 3D array was installed in the wind-tunnel, made of three planar arrays enclosing the open test section. The coordinates of the microphones were estimated, based on the measurements of relative time of flights between a number of sources and microphones. The arrangement of the microphones was chosen in order to optimize the resolution and dynamics of the array, by using simulations,

The array system was applied to the broadband aeroacoustic radiation of two wallmounted finite NACA 0012 airfoils of different span lengths. An acoustic database containing 769 channels of data (768 MEMS channels and an analogical channel) was obtained. 236 channels of data were selected from the database for array signal processing. A 3D conventional beamforming algorithm with a dipolar noise source model was used, associated to the deconvolution method CLEAN-SC. The flow effects on sound propaga- tion were taken into account by using the Amiet's method. The broadband noise sources generated by the two airfoils were successfully identified on the 3D sound maps, in terms of distribution, in a third-octave band.

Figure 1 :

 1 Figure 1: Photograph of a buffer card and of a microphone card.

Figure 2 :

 2 Figure 2: Photograph of the acoustic data acquisition system. The colored cables are RJ45 linking the buffer cards to acquisition system.

Figure 3 :

 3 Figure 3: Sketch of the test section of the anechoic wind-tunnel of the PPRIME Institute.

Figure 4 :

 4 Figure 4: Photograph of the experimental setup. The tunnel-shaped 3D array encloses the nozzle, the two wall-mounted airfoils and the collector from the left to the right in the picture.

Figure 5 :

 5 Figure 5: Measured frequency response of a set of 32 MEMS microphones -The measurement protocol follows the procedure depicted in [19]. Red line -Average ; Blue shaded area : variation interval over the set.

Figure 6 :

 6 Figure 6: 3D model of the array structure.

Figure 7 : 4

 74 Figure 7: 4 Microphones distribution configurations for the numerical simulation of the PSF.

  sources.

Figure 8 :

 8 Figure 8: Simulated characteristics of the final array with three panels and 768 microphones. The test case concerns a monopole point source located at the center point of the investigated volume. The signal is harmonic with a frequency of 5 kHz. A random noise is added to the microphone signals with a 0 dB SNR. The floor is considered as a perfectly reflective plane.

Figure 9 :

 9 Figure 9: Schematic depicting the positions of microphones of the 3D array with black points and the two wall-mounted airfoils. The cube with dashed edges of dimension 0.6 m × 0.6 m × 0.6 m presents the 3D scanning grid for the beamforming. The blue plane indicates the bottom of the open test section of the wind tunnel.

Fig. 10

 10 Fig.10shows the wideband far-field spectrum of the noise generated by the two wallmounted airfoils at angle of attack α = 4 • and incoming velocity U ∞ = 50 m/s. The acoustic spectrum in the band [2828 Hz; 3564Hz] is the part between the blue lines (see Fig.10).Fig.11shows the sound maps of the two wall-mounted airfoils in the third-octave band [2828 Hz; 3564Hz] at angle of attack of α = 4 • and incoming velocity U ∞ = 50 m/s. In Fig.11(a), the beamforming result illustrates some lobes around the trailing edges of the two wall-mounted airfoils. A lobe with large size along the trailing edges may indicate some noise sources. However, regular appearance of some lobes of almost the same size in the direction perpendicular the airfoils' surfaces is observed, which introduces the ambiguity for the distribution of the noise sources. In Fig.11(b), the CLEAN-SC technique allows a better spatial resolution for the sound map. The safety factor and clean beamwidth for CLEAN-SC were set respectively as 0.99 and 5 cm. After removing the side lobes,

Figure 10 :

 10 Figure 10: Far-field acoustic power spectral density (dB/Hz ref. 2.10 -5 Pa) for the two wallmounted finite airfoils at angle of attack α = 4 • and incoming velocity U ∞ = 50 m/s. The two blue lines present the third-octave band [2828.4 Hz; 3563.6Hz]. The dash-dot line presents its center frequency 3174.8 Hz.

Figure 11 :

 11 Figure 11: Sound maps for the wall-mounted finite airfoils at incoming velocity U ∞ = 50 m/s and angle of attack α = 4 • , at a third-octave band [2828 Hz; 3564Hz] of centre frequency 3175 Hz (a): 3D dipolar beamforming; (b): CLEAN-SC technique. The 3D isosurface in each sound map is plotted at 6 dB below the maximum. The shadows present the 3D beamforming results projected in different directions.

ACKNOWLEDGEMENTS

The authors warmly acknowledge Jacques Marchal, Hugo Dutilleul, Hélène Moingeon, Christian Ollivon (Institut d'Alembert), and Pascal Biais, Janick Laumonier, Laurent Philippon, Philippe Szeger, Jean-Christophe Vergez (Institut PPRIME) for their invaluable technical support. This work is supported by Agence Nationale de la Recherche (ANR) and China Scholarship Council.