Yohan Cosquer
email: yohan.cosquer@isae-supaero.fr

Patrice Longère
email: patrice.longere@isae-supaero.fr

Olivier Pantalé
email: olivier.pantale@enit.fr

Claude Gailhac
email: claude.gailhac@cnim.com

Identification of armour technological solutions following experiment-simulation correlation


Yohan Cosquer
email: yohan.cosquer@isae-supaero.fr

Patrice Longère

Olivier Pantalé

Claude Gailhac

Methodology to optimise ballistic protection systems based on an experiment/simulation correlation

This work presents a methodology aimed to optimise multi-layer and multi-material ballistic protection systems using an experiment/simulation correlation. This methodology is applied to minimise the mass of an armour steel-aluminium alloy protection system.

INTRODUCTION

Ballistic protections usually result from an incremental and empirical approach and accordingly strongly depend on the experience and know-how of the manufacturer. Yet, in order to improve their specific ballistic resistance, current ballistic protections are more and more complex, based on multi-layer and multi-material systems, see [START_REF] Crouch | The Science of Armour Material[END_REF], and thus require the optimisation of a great number of parameters (e.g. layering order, thicknesses, number of layers, etc). In this context, numerical simulation-aided design has become indispensable, see for example [START_REF] Paman | An optimization scheme for a multilayer armour module against 7.62 mm armour piercing projectile[END_REF]. The methodology developed in the present work relies on a correlation between experiments and simulations following three steps: (i) calibration and verification of a numerical model, (ii) validation of the model and (iii) use of the model in an optimisation process.

Results of impact experiments involving simple configurations are used to feed an automatic calibration process based on numerical simulations performed with the explicit commercial finite element code Abaqus coupled to the Isight optimisation software. More specifically, the model parameters that depend on the strain rate and related to damage and rupture are identified at this stage (step (i)). Step (ii) validates the parameters of the previously calibrated model, comparing the experimental and numerical results obtained by impact tests on more complex configurations (not used in step (i)). If the correlation fails, a corrective loop is added between step (i) and step (ii) until the results match. As mentioned above, step (iii) aims to optimise a multi-component ballistic protection system (stacking order, layer thickness, etc.) for a given threat, in order to determine the best ballistic performance-mass ratio compromise.

RESULTS AND CONCLUSIONS

This procedure has been applied to a bi-layered protection system, composed of an armour steel (MARS 380) plate and an aluminium alloy plate, impacted by a tungsten carbide projectile similar to a 7,62×51 AP8 ammunition core. Impact tests are carried out with a single stage gas launcher available in STIMPACT platform of Institut Clément Ader Lab. Model parameters were calibrated and verified in step (i) with a single plate (armour steel and aluminium alloy separately), and validated in step (ii) in a bi-layered configuration. Fig. 1 shows a good agreement between experimental and numerical results (8.8 mm MARS 380 armour steel ("MS8.8") as front layer and 8.0 mm aluminium alloy ("AA8") as rear layer, "MS8.8-AA8"). According to Fig. 1, the ballistic limit velocity ( BL v ) is close to 720 m/s.

Finally, the position and thickness of each plate were optimised in step (iii). Table 1 reports some final optimised 1, a ballistic protection with an aluminium alloy as a front plate and an armour steel plate as a rear plate could be 7% lighter than the opposite configuration against the considered threat (tungsten carbide projectile at 345 m/s). This study allowed to optimise a ballistic protection system with a relatively low number of experiments, and paves to way to more complex optimisations (e.g. regarding materials, number of layers, air gaps, etc).

  Fig.1 Comparison between experiments and simulations of a tungsten carbide projectile impacting a bi-layered protection system: 8.8 mm-thick MARS 380 armour steel as front layer and 8.0 mm-thick aluminium alloy as rear layer ("MS8.8-AA8")

Table 1

 1 Optimisation results. Threat: tungsten carbide projectile at 345 m/s According to Table

ACKNOWLEDGMENTS

The authors acknowledge the financial support of French Association Nationale de la Recherche et de la Technologie (ANRT) and the high-performance computing support by French Calcul en Midi-Pyrénées (CalMiP).


C Royer

François Poulet

Jean-Michel Reess

C Pilorget

V Hamm

Thierry Fouchet

Sylestre Maurice

Roger C Wiens

Olivier Forni

Franck Montmessin

J.-M Reess

F Mont- Messin

The Calibration of the Infrared Spectrometer of SuperCam/Mars2020: Results and Prediction of the Future Performance on Mars

come   L'archive ouverte pluridisciplinaire

Introduction:

The Mars 2020 Rover will be launched in July 2020 to explore Jezero Crater. The objective of this roving laboratory is to characterize the habitability of Mars, past or present, through the use of a versatile scientific payload, and to prepare for sample return.

The SuperCam instrument on board the Mars 2020 Rover will play a central role in the Mars habitability investigation by providing rapid, synergistic, fine-scale mineralogy, chemistry, and color imaging [1]. Using color imaging for context, SuperCam combines coaligned Raman-fluorescence, visible/infrared reflectance, and laser-induced breakdown spectroscopy coupled to a microphone covering broad areas at remote distances.

This abstract focuses on the IRS instrument and its ground radiometric calibration. IRS is a near-infrared point spectrometer (1.15 mrad field of view) which ranges from 1.3 µm to 2.6 µm covering major silicate and hydrated mineral absorption features [2]. Signal measured by this instrument will contain the Mars target spectral signature convolved by the instrument response function and possibly other instrument-specific effects.

The IRS instrument has thus to be fully calibrated in a controlled laboratory environment with illumination conditions as similar as possible to Martian observations.

The calibration products will be used to simulate mineral mixtures expected in a sedimentary context such as that expected at Jezero crater, so as to prepare the future observations. IRS concept: IRS works in reflectance spectroscopy: the science scene is illuminated by the Sun and IRS collects the scattered light carrying Mars' ground spectral signatures, which allow us to deduce the composition of the selected terrains and retrieve the abundances of the detected compounds from spectral modeling. IRS uses an Acousto-Optic Tunable Filter (AOTF) as a dispersive system which provides a higher diffraction efficiency than a classical grating. It also does not require any moving part. The light beam that passes through the AOTF is focused on two photodiodes (the additional second is redundant). By tuning the AOTF frequency with the integrated radiofrequency (RF) generator, a spectrum is sequentially built channel by channel with a spectral sampling varying over the spectral range from 2 to 10 nm. The spectral resolution of IRS is 26 cm -1 (FWHM), which corresponds to 5 to 20 nm on the instrument spectral range. This shall enable identification of many of the minerals (silicates, hydrated minerals, oxides, salts).

Calibration goals and requirements:

The radiometric calibration of IRS has been performed using IAS and LESIA joint developed facilities [START_REF] Royer | 9 th Int. Conf. Mars[END_REF][START_REF] Royer | [END_REF]. It consisted in a campaign of spectra acquisitions, under various thermal and instrumental conditions. Its main objective was the derivation of the Instrumental Transfer Function (ITF), which provides the relationship between the measured digital numbers (in DN) and incident radiance (in W/m 2 /sr/µm) on the telescope aperture, over a parameter space covering the entire science operational range. The calibration provides the relationship: 𝑆 = 𝐹(𝜙, 𝑓 𝑅𝐹 , 𝑃 𝑅𝐹 , 𝑇 𝑠𝑝 , 𝑇 𝑝ℎ , 𝑡 𝑖𝑛𝑡 )

with S: integrated signal (including dark current and thermal background), in ADU, 𝜙: incident radiance from science scene, 𝑓 𝑅𝐹 : RF frequency supplying the AOTF, 𝑃 𝑅𝐹 : RF power supplying the AOTF, 𝑇 𝑝ℎ : temperature of the detector cooled by the thermoelectric cooler (TEC), 𝑇 𝑠𝑝 : temperature of the instrument, 𝑡 𝑖𝑛𝑡 : integration time (Fig. 1). All these parameters are necessary to be tested to fully understand the instrument's behavior towards internal and external conditions.

In terms of precision, the calibration had to respect the following requirements: absolute accuracy shall be better than 20%, and 1% in relative (namely between contiguous spectral channels).

1868.pdf 51st Lunar and Planetary Science Conference (2020)

Results: After the calibration campaign, data reduction was divided into three steps: 1) development of an instrument response model that describes the instrument behavior with respect to integration time and input flux. This model appeared to be linear with integration time and following a power-law with flux. The resulting transfer function is given by: 𝑆 = 𝐼𝑇𝐹 𝑓𝑎𝑐 × 𝑡 𝑖𝑛𝑡 × 𝜙 𝐼𝑇𝐹 𝑒𝑥𝑝 where ITFfac and ITFexp are respectively the factor and the exponent of the transfer function. 2) derivation of the ITF parameters according to the previously established model, from high SNR, high spectral resolution data, in every condition (Fig. 2). Note that modulations in ITF parameters are due to instrument transmission features (mainly AOTF) and not setup contamination (water residuals for example). Due to the lack of measurements in warm conditions (Tph > -70°C), the ITF interpolation domain is (Tsp, Tph) ∈ ([-35, -5], [-90, -70])°C, which covers the nominal operational mode of IRS.

3) uncertainty evaluation of the ITF in typical Martian conditions in terms of temperature and ambient illumination. Table 1 summarizes the error sources and their weight in the error budget. These uncertainties are in accordance with the calibration requirements.

Absolute error

Modelling of spectra:

A radiometric model of IRS has been developed to simulate observations on the Martian surface. This model generates reflectance spectra from illumination conditions, thermal environment and scene composition, and the SNR of the observation is calculated using the calibration-based noise model of the instrument (Fig. 3). As result, the simulator allow us to check the SNR vs. measurement duration in various expected operation conditions. A first version of this simulator shall be presented during the meeting.

Figure 1 :

 1 Figure 1: Parameter space sampled during IRS calibration. Dots represent the sampled points except for the wavelength where the whole spectral range is measured (256 spectral channels), and the integration time which has been calculated to cover the entire dynamic of the detectors (up to saturation).

Figure 2 :

 2 Figure 2: ITF parameters at Tsp=-20°C, Tph=-90°C. Top: factor of the transfer function. It has the dimension of a conversion factor between radiance and numerical signal. Bottom: exponent of the transfer function. This parameter models the non-linearity with flux.

Figure 3 :

 3 Figure 3: Simulation of an IRS reflectance measurement of a synthetic scene (selected from [5], but considering linear mixture), at Tsp=-30°C, Tph=-90°C. These very favorable conditions (cold instrument, Sun at zenith, perihelion) yield high SNR data. This simulation does not take into account atmospheric contributions (multiple scattering by aerosols and absorption features by atmospheric gaseous components)

Table 1 :

 1 Summary of contributions to the error budget for the calibration setup [6] and the derived ITF parameters.

	Relative error


Do faults trigger folding in the lithosphere ? Muriel Gerbault, Evgenii E.B. Burov, Alexei A.N.B. Poliakov, Daignières Marc To cite this version: Muriel Gerbault, Evgenii E.B. Burov, Alexei A.N.B. Poliakov, Daignières Marc. Do faults trigger folding in the lithosphere ?. Geophysical Research Letters, 1999, 26 (2), pp.271-274. ird-00388016 upper crust a) Single layer faulting and folding b) Crust and mantle biharmonic folding c) Crust and mantle coupled folding


Florian Cuminet

Sylvain Caillol

Éric Dantras

Éric Leclerc

Cédric Totée

Olivier Guille

Vincent Ladmiral
email: vincent.ladmiral@enscm.fr

Synthesis of a transesterification vitrimer activated by fluorine from an α,α-difluoro carboxylic acid and a diepoxy

An α,α-difluorodicarboxylic acid (P-DAF) was easily synthesized in two steps from diiodobenzene and reacted with a commercial diepoxy (BDGE). The electron-withdrawing effect of the fluorinated group activated the polymerization and gelation readily happened at room temperature. After curing at 150 °C a novel dynamic material was obtained. The P-DAF/BDGE material exhibited a high gel content (94 %) and was able to flow when heated. This material could be successfully reshaped by compression molding under mild conditions (1.5 h at 150 °C). This new material demonstrates that catalyst-free transesterification vitrimers can be prepared from difunctional monomers.

Introduction

Thermosets are polymers made of a network of covalent bonds. Thanks to this structure, they are endowed with high chemical resistance, as they do not solubilize in organic solvents, and high thermal resistance, as they do not flow upon heating. [START_REF] Pascault | Thermosetting Polymers[END_REF] In the current context of pursuit for greener and more sustainable polymers, thermosets are raising concerns as they cannot be easily recycled. [START_REF] Pickering | Wiley Encyclopedia of Composites[END_REF] An answer to this issue is the use of reversible covalent bonds to prepare the network, since such bonds can be broken into reactive species able to re-associate with similar partners elsewhere in the network and form new bonds of the same nature. [START_REF] Leibler | [END_REF][4][5][6][7] At low temperatures, the bonds are unreactive and the network is permanent, whereas upon heating exchange reactions between reversible bonds can take place. This feature allows the polymer chains to rearrange at the local scale, and the material to flow at the macroscopic scale and be recycled. The most extensively studied chemistry for such materials is probably the Diels-Alder and retro-Diels-Alder reactions. 8,9 However, the dissociative nature of this reaction often induces a dramatic loss of the network integrity during the reprocessing steps. 10 In 2005, Bowman et al. introduced a dynamic network in which covalent bonds exchanges proceeded via an associative mechanism triggered by visible light. 11 In such exchange mechanisms the crosslinking density does not decrease, as a new bond is formed when another is broken, simultaneously. Thereby, the number of crosslinks remains the same even when the network rearranges. Later, in 2011, the same idea was implemented in polyester networks, using transesterification reactions triggered by heat. 12 The exchange reaction was promoted by a Zn II catalyst so that the rearrangements at high temperature were fast enough to induce a flow of the material. Because the viscosity of these polymers evolves linearly with temperature as silica glasses, and because they can be shaped the same way, they were called vitrimers. This discovery generated a strong emulation within the polymer scientists community, leading to the discovery of many other exchange reactions and their implementation in vitrimers: carbonates, 13 dioxaborolanes, 14,15 olefins, 16 vinylogous urethanes [17][18][19] and imines [20][21][22][23] are just a few examples of exchangeable functions that have been reported in vitrimers thus far. The major drawback of the polyester vitrimers is the use of an external catalyst, usually Zn 2+ , triazabicyclodecene or phosphines. 24 However, these catalysts are suspected to leach out of the material or to induce premature ageing upon reprocessing. [25][26][27] To overcome this issue, some strategies were developed to synthesize catalyst-free transesterification vitrimers. Hyperbranched epoxy monomers were synthesized from BADGE and a trifunctional alcohol before curing with succinic anhydride. The resulting relatively loose network and the high content of free hydroxy groups favored the mobility and the catalyst-free transesterification. 28 The effect of high hydroxy group concentration alone was also reported. 29,30 Another strategy is to embed a catalytic function in the network. For example, tertiary amines integrated in a polyester network were proved to act as an internal catalyst and activate the material flow. 31 Finally, the addition of activating groups in the direct vicinity of the ester links can also promote the transesterification reaction. 32 Oxime-esters are a representative example of this strategy. 27 Recently, the activation of the transesterification reaction thanks to vicinal fluorinated groups was demonstrated. 33 In particular, the careful design of ,,-trifluoro and α,α-difluoro polycarboxylic acids, from a tetrathiol and a triphenol respectively, allowed the synthesis of catalystfree polyester vitrimers. 34,35 The present work aimed at the diversification of such fluorinated monomers and of the properties of the materials obtained thereof. Inspired by the work of Poutrel et al. on the synthesis of crosslinked vitrimers from a mix of diepoxides and sebacic acid, 10 a catalystfree transesterification vitrimer was synthesized from a simple difunctional α,α-difluorodicarboxylic acid and a commercially available difunctional epoxy. The gelation of diepoxy-diacid "2+2" systems for classical thermosets is well known 36 and was also reported for vitrimers. 10 In 2+2 systems, the ring opening of the epoxy by the acid cannot explain the gelation alone. Side reactions, such as direct esterification and epoxy homopolymerization also occur as the curing is done at high temperatures, thus inducing the crosslinking. [START_REF] Pascault | Thermosetting Polymers[END_REF] The goal of this work is to study the feasibility of a crosslinked network at lower temperature with fluorinated dicarboxylic acids. The activation of the transesterification by fluorine is expected to be beneficial for the crosslinking density. In this context, a novel α,α-difluorodiacid (P-DAF) was synthesized in two scalable steps from 1,4-diiodobenzene. P-DAF was reacted with commercial butanediol diglycidylether (BDGE) to obtain an insoluble crosslinked material which resistance to solvents, mechanical properties and flow properties were studied. The P-DAF/BDGE vitrimer ability to be reprocessed was also assessed.

Results and Discussion

Monomer Synthesis

A novel α,α-difluorinated bis-carboxylic acid (P-DAF, Figure 1) was synthesized for the first time, following procedures described for monofunctional analogues. 37,38 The conditions for this reaction feature several advantages. First, the corresponding diester is synthetized in DMSO, which is a nontoxic solvent. The temperature of the reaction is 60 °C, which is relatively mild. In addition, the purification procedure is much easier and more convenient than the silica gel chromatography previously reported, especially for large-scale syntheses. 34 Indeed, the reaction conditions used to prepare α,α-difluorinated carboxylic acids from a tri-phenol induce a partial oxidation of the latter, thus requiring a purification on silica gel to obtain the pure target monomer. Here, the purification of the crude product is easily scalable, as the desired compound is isolated by a simple recrystallization in ethanol. The overall yield after the first recrystallization was 42 %. Nevertheless, this yield was improved by removing the solvent and performing a second recrystallization to reach an overall yield of 54 %. Finally, a straightforward saponification using a potassium carbonate aqueous solution in methanol led to the pure desired diacid P-DAF as a white powder, without further purification.

Vitrimer Network Synthesis

Figure 1. Vitrimer synthesis from P-DAF and BDGE P-DAF was mixed with BDGE at room temperature (ca. 20°C) and a gel formed after after 8 h. The resulting gel was then cured at 150 °C for 3 h (Figure 1 and3a). As previously described, 34,35 fluorine atoms enhance the acid reactivity towards the epoxy, allowing the ring opening to happen significantly at room temperature (RT). A FTIR monitoring was performed over the first two hours of reaction at RT (Figure S1). The shift of the acid C=O band to the ester around 1761 cm -1 was too narrow to follow the conversion of these functions. Nevertheless, the intensity of the epoxy band at 914 cm -1 clearly decreased over time, which indicates that the opening of the epoxy by the acid occurs at RT (Figure S2). Additionally, this reaction could also be observed using 13 C high resolution magic angle spinning (HRMAS) NMR spectroscopy. No deuterated solvent was used, which is common in solid state NMR, but rather uncommon for HRMAS NMR experiments. The high resolution obtained in 13 C allowed to acquire spectra without lock, and calibrate them using the peaks at 26 and 71 ppm of the butanediol core of BDGE. In addition, the outstandingly fast acquisition (256 scans, 0.1 s per scan) of these 13 C spectra allowed to qualitatively monitor the reaction by this technique. The progressive disappearance of the epoxy signals at 44 ppm (R-CH-O-CH 2 ) and 51 ppm (R-CH-O-CH 2 ) was easily followed over the course of 6 h, when they completely disappeared (Figures 2 andS3). Attempts to follow the reaction by 1 H HRMAS NMR failed because the signal resolution was too poor. 19 F HRMAS NMR could not be used either to follow the ester formation. Indeed the difference in chemical shifts of the α-difluoroacids and α-difluoroesters was too small (-102.1 ppm for P-DE and -103.0 ppm for P-DAF in solution 19 F NMR, Figures S4 andS5).

After gelation at room temperature, a DSC of the resulting material was performed to check whether the polymerization was complete. Two consecutive heating ramp from -100 °C to +250 °C were applied (Figure S6). On the first heating ramp a T g is visible at 13 °C, and a small endothermic peak can be observed between the T g and the maximum temperature. On the second heating ramp, this endothermic phenomenon is absent and the T g increased to 27 °C. This result suggests that a curing step at higher temperature is necessary to finish the polymerization reaction. This was confirmed by the relatively low gel content observed after the polymerization at room temperature (50-60 % in polar solvents, Table S1). The end of the polymerization was also followed by monitoring the evolution of the dynamic storage modulus E' of the material with time, first at 150 °C (Figure S7) and then at 170 °C (Figure S8). At 150 °C, the storage modulus increased during 80 minutes from 0.5 to 3.7 MPa, before reaching a plateau. The analysis was stopped after 100 min. Then, a second step at 170 °C was applied, to check whether the polymerization was over or if a higher temperature would extend it again. No significant evolution of the modulus (which ranged between 4.0 and 4.5 MPa at this temperature) was observed. This result suggested that a curing step of 80 min at 150 °C was sufficient to finish the polymerization. This curing time was nonetheless doubled to ensure a complete curing; and the BDGE/P-DAF gel obtained at room temperature was cured for 3 h at 150 °C.This treatment produced a flexible light brown material (Figure 3b). The swelling index (SI) and gel content (GC) of the BDGE/P-DAF material were determined in a series of solvents (Table S2). Polar solvents showed the highest affinity with the polymer, as the swelling index was 237, 148, 159 and 136 % in dimethylsulfoxide (DMSO), dichloromethane (DCM), water and tetrahydrofuran (THF), respectively. This is not surprising since the network contains many polar functions such as esters, hydroxyl and -CF 2 groups. The material exhibited a gel content of 96 % in THF, thus confirming the crosslinked structure of the material. The morphology of the C=O FTIR band in the 1780-1710 cm -1 area (Figure S9) did change after the curing step at 150 °C. Unfortunately, the bands of the acid and of the ester are hardly distinguishable. Nevertheless, a very weak band centered on 2631 cm -1 which can be ascribed to the O-H stretching of carboxylic acid disappeared after the curing at 150 °C (Figure S10). This confirmed that a small amount of unreacted carboxylic acid remained in the material after the polymerization at room temperature. This residual unreacted -COOH groups are probably due to the lack of mobility of the reactive species after the gelation occurred.

Obtaining a crosslinked network from a difunctional epoxy and a difunctional carboxylic acid seems counterintuitive if only the reaction of epoxide opening by acids is considered. In this case, the polymerization would indeed lead to linear polymer chains and the material would be a thermoplastic. However, if other reactions happen concomitantly to the epoxy ring-opening, in particular transesterification, then 3D network can be formed. 36 The epoxy opening by a carboxylic acid leads to primary and secondary β-hydroxyl esters (Scheme 1).

Scheme 1. Epoxide opening by a carboxylic acid leads to a. secondary or b. primary β-hydroxyl ester.

Then, the dangling hydroxy groups can undergo transesterification with an ester of another chain/segment. This leads to crosslinks and to the formation of "sacrificial" polyol oligomers (Figure 4). This mechanism was clearly explained and theorized recently for non-fluorinated epoxy-acid vitrimers made from difunctional acids and is represented for the present system in Figure 4. 10

Figure 4. Expected structures of a diepoxy-diacid "2+2" polymer (a). if only epoxy opening by the acid is considered (b). if transesterification and Fisher esterification are taken into account (crosslinked network: blue, orange and pink segments and soluble sacrificial oligomers in red).

In addition, other minor side reactions could increase the degree of crosslinking of the network: 1) Fisher esterification with the remaining traces of carboxylic acid groups (Figure 5a), 2) transesterification leading to the formation of sacrificial oligomers (Figure 4), or 3) irreversible formation of ether bonds (Figure 5b). [START_REF] Pascault | Thermosetting Polymers[END_REF]10 Although these reactions only happen to a small extent, they generate crosslinks which can be beneficial to the formation of 3D network.

Vitrimer Characterization

The thermal stability of the BDGE/P-DAF vitrimer was assessed by TGA under air. The temperature of 2 % mass loss was 262 °C whereas 5 % mass loss was attained at 321 °C (Figure S11, Table 1). The T g measured by DSC was 27 °C (Figure S6). This value is rather low considering the aromatic nature of the diacid, and shows that BDGE brings flexibility to the network, as expected. This feature also translates on the DMA experiment, with T α = 47 °C. The values of the storage modulus were E' G = 1.9 GPa and E' R = 11 MPa on the glassy plateau and on the rubbery plateau respectively (Figure S12, Table 1), which is consistent with similar networks reported previously. 28,29,34,39,40 The flow properties of the BDGE/P-DAF vitrimer were studied by stress-relaxation in the time domain. To assess the role of fluorine in the flow properties, a non-fluorinated counterpart called BDGE/P-DA was prepared by reaction of 1,4-phenylenediacetic acid and BDGE at XXX °C for xxx h. A 10 % torsionnal strain was applied and full stress relaxation was observed for the fluorinated BDGE/P-DAF material at 210 °C after 45900 s (12 h 45 min, the end of the curve is noisy because of the apparatus technical limitations to keep the applied strain constant at low torque). The same experiment was performed on the non-fluorinated BDGE/P-DA counterpart. The relaxation was much slower, as only 37 % of the applied stress was relaxed after the same duration. This proves the significant effect of the α,α-difluoro group to activate transesterification and allow the material to flow (Figure 6). The relaxation modulus was monitored for isotherms ranging from 170 to 210 °C (Figure 7). The stress relaxation data were fitted with a Kohlraush-Williams-Watts equation and the obtained relaxation times τ KWW were plotted in an Arrhenius diagram (Figure 7 inset). The value obtained from the curve at 170 °C was discarded, because the data at this temperature was considered inaccurate. Indeed, the relaxation seemed faster than expected compared to the other isotherms. This is likely due to a slow slipping of the sample at lower temperatures for long experiment times, in spite of the experimental efforts implemented to overcome this issue. This translates clearly on the Arrhenius plot when the 5 isotherms values are plotted. Thus, only the isotherms from 180 °C to 210 °C were considered. The τ KWW values followed a linear fit, proving the vitrimer follows the Arrhenius law, and the activation energy was determined to be E a = 118±8 kJ mol -1 (Figure 7 inset). hv The reprocessing ability of the vitrimer was successfully assessed by compression molding. Samples were diced into ≈ 1 mm 3 pieces and reprocessed by compression molding for 1.5 h at 150 °C under a 6 ton load (Figure 8). The vitrimer chemical stability upon reshaping was checked by FTIR (Figure 9). A slight increase of the -OH band and the appearance of a weak band at 1630 cm -1 were observed. These may be caused by a slight water intake of the material from ambient moisture before reprocessing. The value of T g obtained by DSC dropped from 27 °C for the pristine material to -2 °C for the reprocessed material (Table 2 and Figure S13). The swelling index of 136 % before reprocessing increased to 308 % after reprocessing, whereas the gel content slightly decreased from 96±1 % to 93±1 % (Table 2). The water intake could lead to plasticization, or to some hydrolysis at high temperature in the heating press. By DMA the T α shifted from 47 °C to 30 °C before and after reprocessing, respectively and the modulus on the rubbery plateau decreased from 11 to 7 MPa (Table 2 and Figure S14). The T α ascribes for the effects of both plasticization and possible hydrolysis, whereas the modulus on the rubbery plateau depends only on the crosslinking density, thus the decrease observed can be ascribed to hydrolysis during reprocessing. This hypothesis of a plasticization effect after hot pressing remains plausible, as the sample is constrained between two plates which hinder water evaporation. When a reprocessed sample underwent an annealing treatment in an oven for 3 h at 150 °C, in which water is free to escape from the material, the T g and the T α reached values (T g = 20°C, T α = 40°C) close to those of the material before reprocessing. This results are consistent with a water plasticizing effect. Nevertheless, the modulus on the rubbery plateau was not recovered (6 MPa) which suggest partial hydrolysis. The change in the gel content, though very limited, also supports this hypothesis.

Therefore, the behaviour of the material is most likely due to a combination of both plasticization and hydrolysis (Table 2).

Figure 9. FTIR spectra of the P-DAF/BDGE vitrimer before and after reprocessing by compression molding

Conclusion

Catalyst-free transesterification vitrimers were synthesized from P-DAF, an α,α-difluorodicarboxylic acid and a commercially available diepoxy. P-DAF was easily synthesized in two steps and purified by recrystallization. The α,α-difluoro groups proved to activate P-DAF reactivity towards epoxy ring opening, as the reaction with the diepoxy BDGE readily happened at room temperature. This bulk polymerization resulted in a gelled material. After completion of the curing at 150 °C for 3 h, an insoluble thermosetting material was obtained. Transesterification concomitant to the epoxy-acid reaction during the curing was responsible for the crosslinking of the network. The P-DAF/BDGE material relaxed stress when a constant strain was applied at temperatures ranging from 170 to 210 °C. The dynamic properties of this material are due to bond exchanges by transesterification activated by the inductive effect of the α-CF 2 groups to the ester bonds. The relaxation times at different isotherms followed the Arrhenius equation, which is consistent with the behavior of a vitrimer. The P-DAF/BDGE vitrimer was then successfully reprocessed by compression molding for 1.5 h at 150 °C under a 6-ton load to give homogeneous reshaped samples, without the need for any added catalyst. The feasibility of such α,α-difluoro activated vitrimers from difunctional monomers will simplify the synthesis of other similar materials, as difunctional species are more available than tri-or tetra-functional ones. This could benefit in the future to a better understanding of the structure/properties relationship in such materials, but also to their potential synthesis on larger scales.

Experimental Section

Materials

Copper powder (Aldrich, 99 %), 1,4-diiodobenzene (Fluorochem, 98 %), 1,4-butanediol diglycidyl ether (BDGE, Aldrich, ≥ 95 %, 1,1,1-Tris(4-hydroxyphenyl)ethane ("TPE", Sigma-Aldrich, 99 %), 1,8-Diazabicyclo(5.4.0)undec-7-ene (DBU, Fluorochem, 98 %), ethyl bromodifluoroacetate (Fluorochem, 98 %), 1,4-phenylenediacetic acid (ABCR, 97 %) were used as received. Solvents were supplied by VWR Chemicals. Deuterated solvents were supplied by Eurisotop (99.8 %).

Synthetic Procedures

Synthesis of diethyl 2,2'-(1,4-phenylene)bis(2,2-difluoroacetate) (P-DE): 1,4-diiodobenzene (41.3 g, 125 mmol, 1 equiv.) was dissolved in DMSO (300 mL) in a 500-mL round-bottom flask. Copper powder (42.17 g, 664 mmol, 5.3 equiv.) was added under vigorous stirring to obtain a suspension. Ethyl bromodifluoroacetate (51.0 g, 251 mmol, 2 equiv.) was then added. The flask was sealed with a septum and heated to 60 °C for 7 hours. The crude mixture was cooled to room temperature, poured in a mixture of ice and saturated ammonium chloride aqueous solution (1.5 L) under vigorous magnetic stirring. The aqueous solution was extracted 4 times with ethyl acetate (4 x 500 mL). The combined organic layers were washed 4 times with saturated aqueous ammonium chloride (4 x 400 mL) and twice with brine (2 x 400 mL), dried with MgSO 4 and concentrated under reduced pressure. The solvent was removed under high vacuum to afford 38 grams of an orange solid-and-oil mixture. The crude product was taken in a minimum of cold ethanol, inducing a crystallization of 17 grams of the pure diester (white solid, 42 %). The filtrate was concentrated under reduced pressure and the same operation was repeated to afford another 4.9 grams of the diester (off white solid, 12 %).

Synthesis of 2,2'-(1,4-phenylene)bis(2,2-difluoroacetic acid) (P-DAF):

In a 250-mL round-bottom flask, 9.4 g of diester P-DE were dissolved in 80 mL of methanol. Then, 80 mL of a 1M potassium carbonate aqueous solution was added under magnetic stirring and the reaction was left to proceed overnight at room temperature. The crude mixture was then precipitated in 300 mL of 1M HCl, extracted with ethyl acetate (3 x 200 mL), washed twice with brine (2 x 150 mL), dried over Na 2 SO 4 and the solvent was removed under reduced pressure to afford 7.7 g of the pure diacid (white solid). Synthesis of BDGE/P-DA reference material: 0.97 g (10 meq ; EEW=97 g/eq) of 1,4phenylenediacetic acid was mixed with 1.19 g of BDGE at 90 °C to obtain a homogeneous light brown mixture. The mixture was cast in aluminum molds and left overnight in an oven at 120 °C. The mixture was not cured and a subsequent 1 h step at 180 °C was applied. The curing was checked by DSC and no remaining exothermic phenomenon was observed.

Synthesis of BDGE/P-DAF vitrimer: 1 g (7.5 meq COOH, HEW=133) of P-DAF and 1.067 g (7.5 meq epoxy, EEW=142) of butanediol diglycidyl ether (BDGE) were mixed together manually at room temperature until P-DAF was totally dissolved. A viscous clear yellowish solution was obtained and quickly cast in PTFE molds. The solution was left to gel at room temperature, typically for 8 hours. Then, a brittle gel was obtained, unmolded and left for 3 h in an oven at 150 °C.

Instrumentation NMR: 1 H, 13 C and 19 F were acquired on a Bruker Avance 400 MHz spectrometer at 23 °C. External reference was tetramethylsilane (TMS) with chemical shifts given in ppm. Samples were dissolved or diluted in 0.5mL of CDCl 3 or DMSO-d 6 depending on their solubility. FTIR: FTIR spectra were acquired on a ThermoScientific Nicolet iS50 FT-IR equipped with an attenuated total reflectance cell (ATR). The data were analyzed using the software OMNIC Series 8.2 from Thermo Scientific. HRMAS: High resolution MAS NMR experiments were carried out on a Varian VNMRS 600 MHz spectrometer equipped with a wide bore magnet (B0 = 14.1 T). Prior to HRMAS NMR experiments, the BDGE and the P-DAF were manually mixed together in a beaker, and injected in a 4 mm quartz zirconia HRMAS rotor insert with a 1 mL syringe. No solvent was added and the calibration was made using the peaks at 72 and 26 ppm of the BDGE, as observed in liquid NMR. Experiments were performed at room temperature. The sample spinning rate was 5 kHz. 13 C NMR spectra were recorded at 20 °C, 38 kHz for spectral width, 15 kHz for transmitter frequency offset, 0.1 s for acquisition time, 256 scans (NS) with a 45 ° pulse (5.5 µs) and a relaxation delay at 1 s . [START_REF] Pascault | Thermosetting Polymers[END_REF] H decoupling was applied during the whole sequence. The outstandingly short overall acquisition time compared to usual 13 C experiments allowed to obtain spectra within a few minutes and to monitor qualitatively the polymerization reaction for several hours. Mechanical analysis: Dynamic Mechanical Analyses were carried out on Metravib DMA 25 with Dynatest 6.8 software. Uniaxial stretching of samples (1 × 2 × 6 mm 3 ) was performed while heating at a rate of 3 °C min -1 from -90 °C to 150 °C, at a f=1 Hz frequency. Relaxation experiments were performed on a ThermoScientific Haake Mars 60 rheometer equipped with a electric heating cell and a textured 8-mm plane-plane geometry. A 10 % torsional strain was applied on 8 mm diameter and 2 mm thickness circular samples, and the relaxation modulus evolution with time was monitored. The curing checking experiment was performed on a TA Ares G2 at a given temperature (150 or 170 °C) by applying a 0.1 % deformation at ω = 1 rad.s -1 under a normal force of 100 grams every 2 minutes, and monitoring G'.

TGA: Thermogravimetric thermograms were recorded on a TA TGA G50 appliance using a 40 mL min - 1 flux of synthetic air as purge gas. Approximately 10 mg of sample were used for each analysis. Ramps from 20 to 500 °C were applied at a rate of 20 °C min -1 . DSC: Analyses were carried out using a NETZSCH DSC200F3 calorimeter. The calibration was performed using adamantane, biphenyl, indium, tin, bismuth and zinc standards. Nitrogen was used as purge gas. Approximately 10 mg of sample were placed in perforated aluminum pans and the thermal properties were recorded between -100 °C and the temperature of 2% mass loss T d2% at 20 °C min -1 . The reported values are the values measured during the second heating ramp.

Reprocessing: the material was cut into 1 x 1 x 1 mm 3 pieces and then pressed in a PTFE mold for 1.5 h at 150 °C under a 6 tons load using a Carver 3960 manual heating press.

Conflicts of interest

There are no conflicts to declare.

Figure 3 .

 3 Figure 3. a. Crosslinked material after 8 h at room temperature (ca.20 °C); and b. after 3 h at 150 °C

Figure 5 .

 5 Figure 5. Possible side reactions during the curing step at 150 °C a. Fisher esterification, b. etherification by epoxy opening by an alcohol

Figure 6 .

 6 Figure 6. Stress relaxation experiments on fluorinated P-DAF/BDGE and non-fluorinated P-DA/BDGE at 210 °C with a 10 % strain.

Figure 7 .

 7 Figure 7. Normalized stress-relaxation curves from 170 to 210 °C for BDGE/P-DAF vitrimer fitted with the Kohlraush-Williams-Watts equation (KWW) and Arrhenius plot of the τ KWW relaxation times obtained.

Figure 8 .

 8 Figure 8. P-DAF/BDGE vitrimer before and after reprocessing by compression molding, front lighting (center) and backlit (right) Table 2. Properties of P-DAF/BDGE vitrimer pristine, after reprocessing and after subsequent annealing Pristine Reprocessed b Annealed c T g (°C) 27 -2 20 T α (°C) 47 30 40 SI (%) a 136 308 -GC (%) a 96±1 93±1 -E' R (MPa) 11 7 6 a in THF b 1.5 h, 150 °C, 6 tons in press c 3 h, 150 °C in oven

1 H

 1 NMR 400MHz DMSO-d 6 (Figure S15): δ (ppm) 7.80 (s, 4 H, aromatic protons), 4.31 (quad, 4 H, CH 2 ), 2.50 (DMSO), 1.21 (t, 6 H, CH 3 ). 19 F NMR 377 MHz, DMSO-d 6 (Figure S16): δ (ppm) -102.1. 13 C NMR 101 MHz, DMSO-d 6 (Figure S17): δ (ppm) 163.2 (RCOOR, J C-F = 36 Hz), 135.4 (C IV aromatic, J C-F = 26 Hz), 126.6 (CH aromatic, J C-F = 6 Hz), 113.3 (CF 2 , J C-F = 252 Hz), 64.2 (CH 2 ), 40.0 (DMSO), 14.0 (CH 3 ). HRMS (ESI+) Calc. for [M+H] + 323.0901, found 323.0902. FTIR spectrum: Figure S18.

1 H

 1 NMR 400MHz DMSO-d 6 (Figure S19): δ (ppm) 7.76 (s, 4 H, aromatic protons). 19 F NMR 377 MHz, DMSO-d 6 (Figure S20): δ (ppm) -103.0. 13 C NMR 101 MHz, DMSO-d 6 (Figure S21) : δ (ppm) 165.1 (RCOOR, J C-F = 33 Hz), 135.9 (C IV aromatic, J C-F = 27 Hz), 125.6 (CH aromatic, J C-F = 168 Hz), 113.5 (CF 2 , J C-F = 250 Hz), 40.0 (DMSO). HRMS (ESI-) Calc. for [M-H] -265.0129, found 265.0135. FTIR spectrum: Figure S22.

Table 1 .

 1 Thermal properties of the BDGE/P-DAF vitrimer

	T 2% loss (°C) T 5% loss (°C)	T g (°C)	T α (°C)	E' G (GPa) a E' R (MPa) b	SI (%) c	GC (%) c

Acknowledgements

This work was funded by the Institut Carnot Chimie Balard CIRIMAT (16CARN000801). The authors would like to thank Dr. Marc Guerre and Dr. François Tournilhac for fruitful discussions.


Philippe Pouletaut

Yoann Tatarenko

M Li

Venus Joumaa

Mashhour Chakouch

John R Hawse

Walter Herzog

Simon Chatelin

Sabine F Bensamoun

Characterization of the passive mechanics at three different structural levels of the muscle

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