Thibaut Lalire

Belkacem Otazaghine

Aurélie Taguet

Claire Longuet

Correlation between multiple chemical modification strategies on graphene or graphite and physical / electrical properties Authors

Keywords: Graphene, Graphite, Nanocomposite, Electrical conductivity, Functionalization, Copolymer

Chemical modifications of carbon based materials are often used to improve their dispersion in polymer matrix and increase the nanocomposite electrical properties. This work concerned the control of graphene and graphite physical and chemical structure thanks to different chemical modification (oxidation, copolymer functionalization and reduction). This article exposes a complete study of different chemical modifications impact on graphene and graphite microstructure, chemical structure, and its relative electrical property. A first oxidation step by Hummers or nitric acid method was necessary to further graft a copolymer of methyl methacrylate and hydroxyethyl methacrylate via a versatile "grafting onto" covalent functionalization. Hummers' and nitric acid methods were considered as strong and soft oxidation treatments, respectively. Reduction steps were also performed using hydrazine or thermal treatments to recover high electrical conductivity. Chemical modifications of graphene and graphite were characterized by X-ray diffraction, Raman spectroscopy, thermogravimetric analysis, Fourier transform infrared spectroscopy and pyrolysis-gas chromatography-mass spectrometry. Moreover, a new method for the electrical measurement of the modified particles is presented in this work. This measurement requires adhesive tape and an electrical circuit with a diode using the four probes protocol, it allows the evaluation of the electrical conductivity of the graphene and graphite samples in powder state. Finally, the electrical resistances of the different graphene and graphite submitted to all the chemical treatments are reported.

Introduction

Carbon fillers like carbon black, carbon nanotube, graphite or graphene are widely used for nanocomposite applications in order to improve mechanical, thermal and/or electrical properties of polymer matrices [START_REF] Papageorgiou | Mechanical properties of graphene and graphene-based nanocomposites[END_REF], [START_REF] Balandin | Superior thermal conductivity of single-layer graphene[END_REF]. The last decades, graphene and other 2D materials [START_REF] Li | Ultrathin Nickel-Cobalt Phosphate 2D Nanosheets for Electrochemical Energy Storage under Aqueous/Solid-State Electrolyte[END_REF], [START_REF] Liu | Recent progress on graphene-analogous 2D nanomaterials: Properties, modeling and applications[END_REF] attracted much attention thanks to remarkable properties due to their 2D structure with high aspect ratio and high surface area. This exceptional structure made graphene one of the most promising particle for polymer nanocomposites elaboration. Its 2D structure mostly composed of carbon atoms with low defect concentration provides high electrical conductivity due to a solid carbon pathway for electrons [START_REF] Zhu | Graphene and graphene oxide: Synthesis, properties, and applications[END_REF].

However, the final performances of a nanocomposite is also affected by the dispersion of the nanoparticles in the matrix and the quality of the particle/matrix interface [START_REF] Wang | Graphene and graphene derivatives toughening polymers: Toward high toughness and strength[END_REF]. The strong Van der Waals interactions between π-π bonds of graphene sheets and the lack of affinity with polymer matrices entailed inevitably the aggregation of the graphene particles. That is why obtaining a percolated network in the nanocomposite is difficult and requires high content of graphene. The percolation is an essential element that corresponds to the formation of graphene sheets network and impact strongly composite electrical properties [START_REF] Nan | Physical properties of composites near percolation[END_REF].

A poor interface/interphase can lead to an unbinding of the nanoparticle from the polymer matrix and have an impact on polymer and nanocomposite property [START_REF] Fu | Some basic aspects of polymer nanocomposites: A critical review[END_REF]. To counter this phenomenon, chemical modifications of graphene as oxidation and functionalization are used to allow a better affinity with polymer matrices [START_REF] Ege | Graphene Oxide/Polymer-Based Biomaterials[END_REF], [START_REF] Wan | Improved dispersion and interface in the graphene/epoxy composites via a facile surfactant-assisted process[END_REF]. High compatibility between graphene and the polymer matrix allows to produce performant nanocomposite. Graphene surface modification is an effective way to improve the robustness of the polymer/particle interface. This allows charge transfer and also exploit the extraordinary properties of this carbon material [START_REF] Mohan | Graphene-based materials and their composites: A review on production, applications and product limitations[END_REF], [START_REF] Ma | Covalently bonded interfaces for polymer/graphene composites[END_REF], [START_REF] Zainal Abidin | Surface functionalization of graphene oxide with octadecylamine for improved thermal and mechanical properties in polybutylene succinate nanocomposite[END_REF]. The compatibility of graphene and polymer matrices can be improved by grafting polymer chains on graphene [START_REF] Yang | Functionalization of Graphene and Applications of the Derivatives[END_REF], [START_REF] Tang | Grafting of polyester onto graphene for electrically and thermally conductive composites[END_REF]. Several methods were developed such as "grafting from", "grafting through" or "grafting onto" [START_REF] Liu | Recent advances in covalent functionalization of carbon nanomaterials with polymers: Strategies and perspectives[END_REF], [START_REF] Sekhavat Pour | Polymer grafted graphene oxide: For improved dispersion in epoxy resin and enhancement of mechanical properties of nanocomposite[END_REF], [START_REF] Eskandari | Polymer grafting on graphene layers by controlled radical polymerization[END_REF], [START_REF] Han | Surface/Interface Engineering of Carbon-Based Materials for Constructing Multidimensional Functional Hybrids[END_REF], [START_REF] Quan | Graphene and its derivatives as versatile templates for materials synthesis and functional applications[END_REF]. From this chemical modification methods, the synthesis of a conductive and compatible modified graphene with polymer matrices is possible [START_REF] Héctor Aguilar-Bolados | Synthesis of sustainable, lightweight and electrically conductive polymer brushes grafted multi-layer graphene oxide[END_REF], [START_REF] Park | Graphene-polyethylene nanocomposites: Effect of graphene functionalization[END_REF], [START_REF] Guimont | Grafting of polyethylene onto graphite oxide sheets: A comparison of two routes[END_REF]. The "grafting from" procedure is defined by the introduction of an initiator moiety to proceed to the grafting of polymer chains from different polymerization techniques. The "grafting through" approach is similar, but it requires the introduction of a polymerizable function during the first step. Then, a polymerization step allows the grafting of polymer chains by copolymerization with comonomers. For the "grafting onto" strategy, the polymer chains are first synthesized before to be grafted onto the graphene oxide (GO). An organic functional group from the polymer chain is generally used to form the covalent bond by condensation reaction with the reactive GO functional groups. By comparison, the "grafting onto" is a practical approach which allows the control of the polymer chain structure but the grafting density is lower compared to "grafting from" method [START_REF] Liu | Recent advances in covalent functionalization of carbon nanomaterials with polymers: Strategies and perspectives[END_REF], [START_REF] Rubio | Grafting from versus Grafting to Approaches for the Functionalization of Graphene Nanoplatelets with Poly(methyl methacrylate)[END_REF]. Functionalization of pristine graphene can be directly obtained [START_REF] Yang | Functionalization of Graphene and Applications of the Derivatives[END_REF], [START_REF] Park | Covalent Functionalization of Graphene with Reactive Intermediates[END_REF] but graphene oxide (GO) is usually selected as the starting material for the grafting of the organic groups. Indeed, reactivity of hydroxyl, carboxyl, and epoxy functions of GO allows the introduction of a large variety of chemical groups which can make carbon materials compatible with various polymer matrices. Hummers' method is the most common synthesis for graphene oxide. This method entails high defects on graphite or graphene structure and the formation of sp 3 domains due to appearance of functional groups from the oxidation reactions. This strong modification leads of a drop of the electrical property due to the sp 2 network deterioration [START_REF] Feicht | Defects in Graphene Oxide as Structural Motifs[END_REF], [START_REF] Park | Highly dispersible edge-selectively oxidized graphene with improved electrical performance[END_REF]. However, this chemical modification is necessary for stable dispersion, graphite exfoliation and for the formation of reactive functional sites allowing functionalization. Since graphene oxide is an electric insulator, a chemical or thermal reduction step allows the recovery of electrical properties. Hydrazine hydrate or high temperature treatments are generally used as reduction reaction [START_REF] Zhu | Experimental study on the reducibility of graphene oxide by hydrazine hydrate[END_REF], [START_REF] Huh | Thermal Reduction of Graphene Oxide[END_REF]. In this case, graphene modification with polymer chains can be associated with a good electrical conductivity for conductive nanocomposite elaboration [START_REF] Tan | Grafting of copolymers onto graphene by miniemulsion polymerization for conductive polymer composites: Improved electrical conductivity and compatibility induced by interfacial distribution of graphene[END_REF]. Non-covalent functionalization is also possible by using surfactant to improve graphene dispersion in the matrix without damaging the graphene structure [START_REF] Meng | Effect of interface modification on PMMA/graphene nanocomposites[END_REF]. However, surfactants can interact with polymer matrix and alters its properties. Indeed, a high concentration of surfactant is sometimes necessary and decreases mechanical properties of the nanocomposite [START_REF] Tkalya | The use of surfactants for dispersing carbon nanotubes and graphene to make conductive nanocomposites[END_REF]. In this study, we will focus on chemical modification control of graphene and graphite to adjust their electrical properties. The objective is to further promote a good graphene or graphite dispersion in a poly(methyl methacrylate) (PMMA) matrix.

In the literature, several chemical modification methods were tested on graphite and graphene [START_REF] Layek | A review on synthesis and properties of polymer functionalized graphene[END_REF]. However, most of the time, these chemical modifications impact on electrical property of the particles were not completely investigated. In this article, two types of oxidation treatments have been examined. The first method based on Hummers' method is a strong oxidation reaction using strong acids and oxidants. The second method is a soft oxidation procedure easier to implement and leading to less defects on the graphene sheets structure.

Firstly, the objective was to characterize these two procedures and determine the impact on graphite and graphene morphology and chemical structure. Secondly, oxidized particles have been modified by adding a copolymer agent using the "grafting onto" method. The efficiency of the grafting of copolymer chains has been also compared for the two oxidation methods.

Then, hydrazine hydrate reduction and thermal reduction were performed in order to recover a suitable structure for the modified graphene sheets and improve the electron transfer. In parallel to the oxidation and grafting reactions, we characterized the effect of these modifications on the electrical conductivity of the treated graphene and graphite particles.

Materials and methods

Raw materials

Graphene KNG 180 (Xiamen Knano), methyl methacrylate (MMA, Sigma-Aldrich), nitric acid (Sigma Aldrich), graphite (Sigma-Aldrich), sulfuric acid (Sigma Aldrich), potassium permanganate (Sigma Aldrich), Hydrogen peroxide 33% (Panreac), Hydrochloric acid 37% (Panreac), 2-hydroxyethyl methacrylate (HEMA, Sigma-Aldrich), hydrazine hydrate (Sigma-Aldrich), azobisisobutyronitrile (AIBN, Sigma-Aldrich), acetonitrile (Fisher), toluene (Fisher), acetone (Merck Schuchardt OHG) were used as received without any further purification.

Soft oxidation of graphene and graphite: Nitric acid method

Graphene and graphite were firstly oxidized (Fig. 1a) by following the procedure inspired by Zubair et al. [START_REF] Zubair | Effect of modified graphene and microwave irradiation on the mechanical and thermal properties of poly(styrene-co-methyl methacrylate)/graphene nanocomposites[END_REF]. Into a 50 mL flask equipped with a condenser, 2 g of graphene or graphite and 20 mL of concentrated nitric acid (60 wt%) were introduced. The mixture was then stirred and heated at solvent reflux for 15 h. The mixture was centrifuged at a speed of 5000 rpm to eliminate the liquid phase and then washed with deionized water until pH 5-7 was obtained.

Finally, the obtained graphene and graphite oxide was dried under vacuum before characterization. The obtained graphene and graphite oxides were named GOxN and GrOxN, respectively.

Strong oxidation of graphene and graphite: Hummers' method

The second method used is an improved Hummers' method [START_REF] Chen | An improved Hummers method for eco-friendly synthesis of graphene oxide[END_REF]. This method consists in mixing 1 g of graphite or graphene with 3 g of KMnO4. 45 mL of H2SO4 were added in order to penetrate between the sheets and to achieve the oxidation with KMnO4. The solution was stirred at 40 °C during 24 h. When the oxidation was complete, the solution turned brown. 80 mL of hydrogen peroxide (33%) and deionized water (1:15) were added to the mixture. 15 mL of HCl (37%) and deionized water (1:9) were mixed with 25 mL of the graphene or graphite oxide suspension in order to remove metal ions. Finally, around 15 washes were necessary to remove acid species to reach a pH between 6 and 6.5. The obtained graphene or graphite oxide suspension was freeze-dried during 24 h in order to obtain a dry powder. The obtained graphene and graphite oxides were named GOxH and GrOxH, respectively.

Thermal and chemical reduction (r1 and r2)

Particles were thermally reduced at 250 °C under air during 1 h (this treatment was noted r1).

The chosen temperature rise was 3 °C/min in order to avoid deflagration phenomenon of GrOxH or GOxH [START_REF] Kim | Self-propagating domino-like reactions in oxidized graphite[END_REF]. The obtained reduced graphene and graphite oxides from the thermal method were named GOxH-r1 and GrOxH-r1, respectively.

The chemical reduction (noted r2) of GOxH or GrOxH was also tested using hydrazine hydrate.

A 3 mg/mL solution of GOxH or GrOxH in water was introduced in a flask. Then hydrazine hydrate was added at a rate of 1 µL for 3 mg of GOxH or GrOxH. The mixture was then heated at 80 °C during 12 h under stirring. The obtained solution was filtered with a fritted glass filter under vacuum [START_REF] Park | Hydrazine-reduction of graphite-and graphene oxide[END_REF]. The obtained reduced graphene and graphite oxide from the hydrazine method were named GOxH-r2 and GrOxH-r2, respectively.

Synthesis of P(MMA-co-HEMA) copolymer

The synthesis consisted in a radical copolymerization of methyl methacrylate (MMA) and 2hydroxyethyl methacrylate (HEMA) with a molar ratio MMA/HEMA = 95/5. Into a 100 mL flask fitted with a condenser, 10 g (0.1 mol) of MMA, 0.68 g (5.2 × 10 -3 mol) of HEMA, 0.16 g (9.7 × 10 -4 mol) of AIBN and 20 g of acetonitrile were introduced. Argon was bubbled through the mixture for 15 min. Then the mixture was stirred and heated at 80 °C for 3 h. After reaction, the copolymer of methyl methacrylate and hydroxyethyl methacrylate P(MMA-co-HEMA) was purified by precipitation in methanol. A schematic representation of the grafting agent structure is available in Fig. 1b. SEC analysis was used to characterize the obtained copolymer, a polydispersity index of 1.47 was determined with a Mn of 35000 g.mol -1 equivalent PMMA. 1 H NMR (Figure S1) confirmed the expected structure.

Functionalization of oxidized graphene and graphite

After particles oxidation (Fig. 1a), the P(MMA-co-HEMA) copolymer was grafted to GOxH, GrOxH, GOxN and GrOxN by an esterification reaction (Fig. 1b). The esterification occurs by condensation of the hydroxyl groups of the copolymer chains with the carboxylic acid functions of the oxidized particles. 1 g of GOxN (or GrOxN, GrOxH, GOxH), 0.1 g of the P(MMA-co-HEMA) copolymer, 50 mL of toluene and 1 mg (1.04 × 10 -5 mol) of methanesulfonic acid were introduced into a 50 mL flask equipped with a Dean Stark apparatus. The mixture was then stirred and heated at solvent reflux for 15 h. The Dean Stark apparatus eliminated the water formed during the reaction. The mixture was then centrifuged at a speed of 5000 rpm to eliminate the liquid phase and washed three times with acetone. The powder was dried under vacuum before characterization. The different grafted samples were listed in Table 1.

Table 1. List of the modified graphite and graphene samples, the different treatments used and the type of notation chosen.

Materials

Characterization methods

Fourier transform infrared spectroscopy (FTIR) was used to evaluate the graphene oxidation.

Analyses were conducted on a BRUKER Vertex 70 spectrometer using an attenuated total reflection (ATR) process. Spectra were obtained from 32 scans with a resolution of 4 cm -1 at room temperature in a wavenumber range between 4000 cm -1 and 400 cm -1 .

Thermogravimetric analysis (TGA) was carried out to evaluate the oxidation rate of graphene oxide and graphite oxide and to measure the grafting rate after modification with P(MMA-co-HEMA) copolymer. Grafting rate is determined thanks to TGA values:

𝐺𝑟𝑎𝑓𝑡𝑖𝑛𝑔 𝑟𝑎𝑡𝑒 = 𝑚 𝑐𝑜𝑝𝑜 𝑙𝑜𝑠𝑠 𝑚 𝑠𝑎𝑚𝑝𝑙𝑒
where 𝑚 𝑐𝑜𝑝𝑜 𝑙𝑜𝑠𝑠 is the mass of copolymer grafted on graphene or graphite and msample is the powder mass analyzed by TGA.

Initial rate is determined with graphene (or graphite) and copolymer mass introduced in the reaction:

𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑟𝑎𝑡𝑒 = 𝑚 𝑐𝑜𝑝𝑜 𝑚 𝐺 + 𝑚 𝑐𝑜𝑝𝑜
where 𝑚 𝑐𝑜𝑝𝑜 and 𝑚 𝐺 are the mass of copolymer and graphene or graphite used for the reaction, respectively.

Grafting efficiency was calculated as followed:

𝐺𝑟𝑎𝑓𝑡𝑖𝑛𝑔 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 (%) = 𝐺𝑟𝑎𝑓𝑡𝑖𝑛𝑔 𝑟𝑎𝑡𝑒 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑟𝑎𝑡𝑒 × 100
In our synthesis conditions, molar concentration of copolymer is fixed at 2.86.10 -6 mol/g of graphene or graphite.

These measurements were performed on a TGA 8000 apparatus from PERKIN ELMER under nitrogen atmosphere at a gaz flow of 40 mL/min. For each analysis the sample (5 ± 2 mg) was first maintained at 110 °C during 15 min to remove physisorbed water and then heated up to 600 °C at 10 °C/min. TGA thermograms start at 110 °C in this article.

X-ray diffraction (XRD) was used to obtain informations about the morphological changes for graphene and graphite after oxidation and functionalization. The diffractometer used is a BRUKER D8 Advance apparatus with a Cu Kα radiation (λ = 0.1542 nm). XRD technique was used to confirm the delamination and exfoliation phenomena observed for graphene after Hummer's method oxidation. XRD characterizations are based on the Bragg's law (equation ( 1)) to determine the interlayer distance [START_REF] Ice | Polychromatic X-ray Microdiffraction Characterization of Local Crystallographic Structure and Defect Distributions[END_REF], [START_REF] Li | The preparation of graphene oxide and its derivatives and their application in bio-tribological systems[END_REF]:

𝑑 002 = 𝑛𝜆 2𝑠𝑖𝑛𝜃
With d002 is the interlayer distance, λ is the wavelength, n is the diffraction order and θ is the diffraction angle.

The Debye Scherrer's law (equation ( 2)) was used to determine the graphene and graphite thicknesses [START_REF] Krasnikova | Functionalization, modification, and characterization of carbon nanofibers[END_REF], [START_REF] Gao | Influence of filler size on the properties of poly(lactic acid) (PLA)/graphene nanoplatelet (GNP) nanocomposites[END_REF], [START_REF] Jun | Highly conductive interconnected graphene foam based polymer composite[END_REF]:

𝐷 002 = 0.89𝜆 𝐹𝑊𝐻𝑀 (𝑟𝑎𝑑)𝑥 𝑐𝑜𝑠𝜃
With D002 corresponding to the thickness of the particle, λ to the wavelength, FWHM to the full width middle high of the peak, and θ is the diffraction angle.

Raman spectroscopy was used to analyze defects in graphene or graphite structure before and after chemical modifications. Spectra were obtained using a RENISHAW spectrometer with a confocal microsocope. Raman apparatus was used with a laser source of 532 nm.

Scanning electron microscope (SEM) micrographs were performed on an Environmental

Scanning Electron Microscope equipped with Energy Dispersive X-ray spectroscopy (ESEM-EDX) (Quanta 200 FEG) from the FEI Company. Pyrolysis-gas chromatography-mass spectrometry (Py-GC/MS) analytical setup consisted of an oven pyrolyzer connected to a GC/MS system. A pyrolyzer equipped with an electrically heating platinum filament (Pyroprobe 5000 from CDS Analytical) was used for the pyrolysis step under helium. Each sample (less than 1 mg) was introduced in a quartz tube between pieces of quartz wool. A coiled probe enabled the pyrolysis of the whole. The sample was heated directly at 900 °C (during 15 s) before gases formed during pyrolysis were drawn to the gas chromatograph (during 5 min). The pyrolyzer apparatus is connected to a gas chromatograph (450-GC from Varian) by means of a transfer line heated at 270 °C. The GC initial temperature of 70 °C was held for 0.2 min, and then raised to 310 °C at 10 °C/min. The Varian Vf-5 ms capillary column (30 m × 0.25 mm) used for separation was under helium (1 mL/min) with a split ratio set to 1:50. After separation, the pyrolysis products were introduced to the ion trap analyzer of the 240-MS mass spectrometer (Varian) through the direct-coupled capillary column. The NIST mass spectral library was used to identify the pyrolysis products.

Results

FTIR, TGA and Py GC/MS characterization of oxidized and functionalized graphene and graphite

The different modified samples were characterized to confirm and compare the amounts of oxidation and the exfoliation degree obtained with the two oxidation methods used.

From the Hummers' oxidation (leading to GOxH and GrOxH), several oxide groups are present on the oxidized structures as confirmed by the FTIR analysis (Fig. 2). The wide band at 3500 cm -1 observed for GOxH and GrOxH corresponds to -OH bonds, and signals of carbonyl and carboxyl groups are identified at 1250 cm -1 and 1710 cm -1 , respectively. The presence of the C=C bonds is confirmed by the band at 1625 cm -1 .

Fig. 2. FTIR of graphene and graphite samples after Hummers' oxidation and functionalization with the copolymer.

After grafting of P(MMA-co-HEMA) copolymer, the band corresponding to C-O bond at 1220 cm -1 is broader for GrOxH-PMMA compared to GrOxH that confirms the presence of ester groups from the copolymer. The band at 1730 cm -1 is characteristic of the C=O of the ester group from methacrylate units. This band proves also the copolymer presence on the graphene and graphite samples after the grafting step.

As for native graphene and graphite, GOxN and GrOxN absorb IR due to a low oxidation level.

The oxidation and then the functionalization with the copolymer were not proved by the FTIR analyses for these samples.

The TGA of the oxidized particles by nitric acid shows a low oxidation rate with a percentage of residue reaching 98.9 wt% for GOxN compared to 99.1 wt% for graphene. The same result was obtained with GrOxN. However, the obtained functionalized graphene and graphite display a higher loss mass with a residue of 95.5 wt% for GOxN-PMMA and 98 wt% for GrOxN-PMMA. The grafting efficiency in our reaction conditions is 14 % and 8 % for GOxN-PMMA and GrOxN-PMMA, respectively. These results prove that a very low oxidation was obtained with nitric acid, but is enough to produce carboxyl groups on the graphene sheets to allow, by esterification, the grafting of the P(MMA-co-HEMA) copolymer chains.

TGA of the graphene and graphite oxidized by the Hummers' method display higher oxidation rates (Fig. 3a,b). A strong mass loss appears at 200 °C reaching 30 wt% corresponding to the degradation of labile oxide groups. As for the oxidation with nitric acid, the oxidation by the Hummers' method allows the formation of carboxylic acid groups that can react with P(MMA-co-HEMA) copolymer to functionalize graphite and graphene oxide. GrOxH-PMMA displays a weak degradation at 200 °C compared to GrOxH (around 12 wt% loss and 33 wt%, respectively). The same observation is conducted for GOxH compared to GOxH-PMMA. Indeed, an in-situ reduction occurs during the synthesis due to the temperature condition at 110 °C in toluene. To verify this hypothesis the same reaction was carried out with GrOxH and GOxH without the grafting agent, GrOxH-Toluene/110 °C and GOxH-Toluene/110 °C respectively. These curves show the expected in-situ reduction during the synthesis with a lower mass loss. However, a mass loss at 450 °C, for GOxH-Toluene/110 °C and GrOxH-Toluene/110 °C, is also observed probably due to the decomposition of the trapped solvent between graphene sheets [START_REF] Au | Thermal Decomposition of Ternary Sodium Graphite Intercalation Compounds[END_REF], [44]. Due to this trapped solvent, the copolymer grafting efficiency calculation is difficult. Indeed, trapped toluene quantity varies when this procedure is reproduced with GOxH or GrOxH.

Py-GC/MS allows to confirm the presence of the copolymer agent grafting for GOxN-PMMA, GrOxN-PMMA, GOxH-PMMA and GrOxH-PMMA samples. The chromatograms obtained for the pyrolysis of GOxN-PMMA and GrOxN-PMMA show the presence of a major peak at 3 min attributed to methyl methacrylate (MMA) (Fig. 4). For GrOxH-PMMA and GOxH-PMMA, several main peaks are observed in addition to the MMA signal during the pyrolysis, which reflects a higher degradation of the structure in comparison with GOxN-PMMA and GrOxN-PMMA. Indeed, Hummers' oxidation creates more defects than oxidation with nitric acid. These degradations can be attributed to structural weakness due to the strong oxidation reaction of the Hummers' method, which disturbs the sp 2 structure. The MMA peak attributed to the decomposition of the grafted PMMA chains is more intense for GOxH-PMMA than GrOxH-PMMA. This result implies a higher grafting efficiency for GOxH-PMMA, this will be explained later in the study. Moreover, presence of a weight loss due to release of toluene is confirmed also with this analysis which can prove the solvent trapping between sheets.

Morphological characterization of oxidized and functionalized graphene and graphite

After confirming oxidation and functionalization, the evolution of the morphology and the stacking structure of these materials have been studied. Information about exfoliation degree and defect concentration is essential for predicting the graphene and graphite capacity to improve the final properties of polymer based nanocomposites, especially electrical conductivity [START_REF] Yan | Effect of graphene oxide with different exfoliation levels on the mechanical properties of epoxy nanocomposites[END_REF]. SEM images were investigated in order to observe the impact of chemical treatments on sheets structure. Fig. 5 shows graphite and graphene particles before and after Hummers' and nitric acid oxidations. Before oxidation, Fig. 5 a and d show a compact stacking of sheets corresponding to graphite and graphene materials, respectively. After nitric acid oxidation, the morphology did not change and stay compact for oxidized graphite and graphene samples (Fig. 5 b and e, respectively). During the Hummers' oxidation, the creation of new functional groups in the intercalated position between the carbon sheets facilitate their exfoliation [START_REF] Hou | High-quality preparation of graphene oxide via the Hummers' method: Understanding the roles of the intercalator, oxidant, and graphite particle size[END_REF]. The SEM images of the graphite and graphene oxidized seems to prove the high exfoliation degree phenomenon (Fig. 5 c andf, respectively) with clearly more flexible and transparent sheets. The XRD analysis provides additional morphological information and confirm SEM observations. The typical diffractogram of graphite (Fig. 6a) shows a main peak at 26.4° corresponding to an interlayer distance of 0.337 nm and after calculation a carbon sheets stacking of 64 layers [START_REF] Zhang | Characterization of graphene oxide: Variations in reported approaches[END_REF]. This small interlayer distance combined with strong Van der Walls interactions between sheets make the exfoliation difficult. Therefore, the use of only an ultrasonication step is not enough. Oxidation is one of the chemical ways to allow the increase of the interlayer distance. A graphene diffractogram should not show peaks due to the monolayer structure. In this study, the used commercial graphene displays a peak at 26.4°. It assumes that this commercial graphene structure is similar as graphite with 46 layers. The soft oxidation method with nitric acid is not enough to obtain intercalation of oxide groups between layers, as shown by the peak (0 0 2) at the same 2θ degree position before and after oxidation (Fig. 6a). Results are similar after functionalization for GOxN-PMMA and GrOxN-PMMA. The copolymer grafting does not change the interlayer spacing and leaves the morphology unchanged. The localization of the grafting is assumed to be only on the edge and not between graphene sheets.

On the contrary, the oxidation of graphite and graphene using the Hummers' method leads to a displacement of the (0 0 2) peak from 26.4° to 10.5° and to 11° on the XRD diffractograms, respectively (Fig. 6 b). At this 2θ position, the interlayer distance is 0.835 nm and 0.801 nm for GrOxH and GOxH, respectively due to the intercalation of oxide groups between the sheets.

The interlayer distance also depends of the content of water adsorbed in the material [START_REF] Sun | Structure evolution of graphene oxide during thermally driven phase transformation: Is the oxygen content really preserved?[END_REF]. By using Equation (2), the number of layers can be calculated and are reported in Table 2.

Hummers' method displays a high exfoliation degree from 65 to 9 layers for graphite and 46 to 9 for commercial graphene, which agrees with SEM images. AFM images of GrOxH after deposition on silica wafer (Figure S3) confirmed a partial graphite exfoliation with a measured thickness of 2 and 4 nm. Same number of layers was obtained for GOxH. These results proves that GrOxH and GOxH obtained by Hummers' oxidation can be finally considered as a multilayer graphene oxide [START_REF] Wick | Classification framework for graphene-based materials[END_REF]. S4 proves that by putting GOxH in toluene at 110 °C it is possible to decrease the interlayer spacing by reduction of oxygenated groups. As the grafting of P(MMAco-HEMA) copolymer occurs at the edge of the graphene sheets and not in the internal structure it does not allow to increase the interlayer spacing. In the case of grafting in the internal structure, the interlayer can increase [START_REF] Guimont | Grafting of polyethylene onto graphite oxide sheets: A comparison of two routes[END_REF], [START_REF] Zhang | Effect of grafted graphene nanosheets on morphology evolution and conductive behavior of poly(methyl methacrylate)/poly(styrene-: Co -acrylonitrile) blends during isothermal annealing[END_REF]. The broad peak at 12° for GrOxH-PMMA (and less pronounced for GOxH-PMMA) can be assigned to the presence of the oxygenated groups in some part of the graphene particles that were not fully reduced.

Since electrical conductivity depends on the graphene structure such as the defect concentration, Raman spectroscopy was used to evaluate the concentration of defects in the graphene and graphite sheets structure of the chemically modified samples [START_REF] Pimenta | Studying disorder in graphite-based systems by Raman spectroscopy[END_REF]. For pristine graphite or graphene, two bands appear at 1351 cm -1 and 1581 cm -1 , corresponding to the D and G bands, respectively. The G band corresponds to the E2g optical phonon whereas the D band corresponds to the A1g optical phonon [START_REF] Kaniyoor | A Raman spectroscopic investigation of graphite oxide derived graphene[END_REF]. The comparison of D and G band intensities (ID/IG ratio) of particles modified from nitric acid method shows that the structure of graphene is preserved even after oxidation and functionalization (Fig. 7 a). On the other hand, oxidation by Hummers method leads to a strong degradation of the graphene and graphite structure due to the introduction of sp 3 clusters confirmed with a higher ID/IG ratio (Fig. 7 b). For samples GOxH and GrOxH, the value is closed to 1 which reveals the presence of high concentration of defects or disorders in the sheets structure. After functionalization, the ID/IG ratio increases strongly for GOxH-PMMA compared to GrOxH-PMMA. This increase in defects has been attributed to a higher grafting efficiency of the copolymer grafting agent for GOxH-PMMA.

Thermal and chemical reduction of oxidized and functionalized graphene and graphite

Reduction of graphite and graphene oxide

Reduction of graphene or graphite oxide obtained from Hummers' method is necessary to recover a sp 2 structure and good electrical properties. The reduction method can be a chemical or a thermal treatment [START_REF] Mohan | Characterisation of reduced graphene oxide: Effects of reduction variables on electrical conductivity[END_REF], [START_REF] Pang | Composites of craphene with large aromatic molecules[END_REF]. By comparing hydrazine reduction and thermal reduction, mass losses occur at different temperatures when samples are analyzed by TGA. We assume that hydrazine reduction and thermal reduction decompose different oxygenated groups.

Indeed, the thermograms comparison shows different degradation profiles. After reduction, the elimination of the intercalated oxygenated groups leads to a restacking of the carbon sheets as shown by XRD (Fig. 9a) with a displacement of the peak from 10.5° to 24°

for both GrOxH-r2 and GrOxH-r1. This latter displacement corresponds to an interlayer spacing of 0.376 nm close to the graphite structure and confirms a restacking due to oxygenated groups decomposition. The broad peak of the graphite oxide particles reduced by the thermal treatment (GrOxH-r1) means that a low thickness of the particle is preserved after reduction with also a low number of layers. The combination of the (0 0 2) peak enlargement and the shift at 24° corresponds to particles of around 8 layers determined with Scherrer's equation. It proves that the number of layers remains the same after the reduction of GrOxH. The same restacking phenomenon (Fig. 9a) is observed with the GrOxH reduced with hydrazine hydrate (GrOxH-r2) which can prove indirectly, the elimination of the intercalated oxygenated groups [START_REF] Pei | The reduction of graphene oxide[END_REF]. SEM images confirms the flexibility and the high degree of exfoliation with clear wrinkled and transparent particles (Fig. 9b,c).

Reduction of functionalized graphite and graphene

Reduction after the functionalization

GrOxH-PMMA and GOxH-PMMA were thermally reduced at 250 °C (leading to GrOxH-PMMA-r1 and GOxH-PMMA-r1) in order to decompose functional groups that disrupt sp 2 structure and which do not participate to the reaction with the grafting agent. A clear mass loss gap is observed between GrOxH-r1 and GrOxH-PMMA-r1 which proves the grafting agent stability during the thermal reduction (Fig. 10a). An identical phenomenon is obtained with the hydrazine hydrate reduction (GrOxH-PMMA-r2 and GOxH-PMMA-r2) which confirms also the stability of the grafted copolymer. Py-GC/MS also proves the presence of the copolymer grafting after the hydrazine hydrate reduction with the characteristic peak of the methyl methacrylate (peak number 1 in Fig. 10b). Molecules containing nitrogen atoms are also released during the pyrolysis step of the reduced samples. Indeed, during the reduction, hydrazine hydrate reacts with GO and can also form nitrogen-carbon bonds.

Reduction treatment before the functionalization

Another chemical sequence modification has been tested to evaluate the impact of the reduction treatments on the functionalization efficiency and also on the electrical conductivity. It is known that hydrazine hydrate reacts mostly with the epoxy groups and maintain the majority of carboxylic acid groups on graphite and graphene oxide [START_REF] Krishna | Hydrazine and Thermal Reduction of Graphene Oxide: Reaction Mechanisms, Product Structures, and Reaction Design[END_REF]. So, the chemical reduction of GrOxH and GOxH can be performed before the functionalization with the copolymer grafting agent. TGA (Fig. 11a) shows that the copolymer grafting after the hydrazine reduction (GOxH-r2-PMMA) is effective due to a higher mass loss of GOxH-r2-PMMA compared to GOxH-r2.

Moreover, a thermal treatment after this procedure (hydrazine reduction followed by copolymer functionalization) removed other functional groups, which was not used for the copolymer grafting. Indeed, the sample obtained after this third step (GOxH-r2-PMMA-r1) did not highlight a mass loss at 200 °C contrary to GOxH-r2-PMMA. Moreover, the functionalized particles (GOxH-r2-PMMA and GOxH-r2-PMMA-r1) have a similar mass loss of 15 wt% between 250 °C and 400 °C corresponding to the decomposition of grafted copolymer chains. This proves that the grafted copolymer was not affected by the following thermal treatment at 250 °C. Considering the proportion of the grafting agent and graphene used during the functionalization reaction, the grafting efficiency in our reaction conditions is still 100 % after the hydrazine reduction. This result confirms also that all the copolymer chains incorporated during the reaction were fully grafted on GOxH-r2 which is due to a high concentration of acid carboxylic groups even after hydrazine reduction. The presence of the copolymer after the grafting reaction was proved also by Py-GC/MS (Fig. 11b). Py-GC/MS reveals numerous peaks but the identification of the copolymer is confirmed by the presence of methyl methacrylate (peak number 4 in Fig. 11b). Presence of molecules containing nitrogen atoms (peak 2 and 6 of Fig. 11b) is also observed. This was attributed to the formation of functional groups containing nitrogen atoms by the reaction of hydrazine hydrate with GOxH and GrOxH during the reduction reaction. Several other peaks appear on the chromatogram due to the different chemical treatments which lead to the creation of defects.

Electrical conductivity measurement on oxidized and functionalized graphite and graphene

In the perspective to produce electrically conductive nanocomposites, electrical tests were carried out on these various samples directly on the powders (Figure S5). Four samples were prepared for each powder in order to check the reproducibility of the method. As it was demonstrated previously, the different samples tested have different chemical structure and morphology. To measure their electrical resistance, a tape with two adhesive faces was placed on a glass and then each powder sample was spread on the other surface (as presented in the scheme in Figure S5). The dimension of the tape and the power mass was identical for each sample. The objective is to measure the impact of the different chemical modifications on the electrical properties. A diode was added to the electrical circuit to confirm the conductive property of the powder. The four probes installation was elaborated to determine the resistance of the powder. A green color presented in Table 3 corresponds to the lit diode (Figure S5).

Chemical reactions on graphite and graphene obviously disturbed the sp 2 carbon structure and led to a drop of the electrical conductivity. However, these modifications are often necessary before the incorporation of graphite and graphene in polymer matrices to improve the particle dispersion and the particle/polymer interface quality. Pristine materials display very low resistance, 49.8 ± 0.4 Ω for G and 114 ± 3 Ω for Gr. Modifications from Hummers' method showed high destruction of the graphene and graphite structure. These results are confirmed by the electrical measurements in which no current is detected (Figure 12a). On the contrary, chemical modifications with nitric acid method displayed lower defects and a preservation of most of the structure. Indeed, slightly higher resistances are obtained compared to pristine materials with 100 ± 3 Ω for GOxN and 169 ± 5 Ω for GrOxN. After functionalization with the P(MMA-co-HEMA) copolymer, resistances increase inevitably. Resistances of 2566 ± 85 Ω and 57762 ± 1681 Ω are reached for GOxN-PMMA and GrOxN-PMMA, respectively (Figure 12b). For GrOxN-PMMA, the resistance increases strongly while GOxN-PMMA maintains a low resistance. This phenomenon can be due to a lower specific surface area of graphite than graphene. Specific surface areas of 2.91 m 2 /g and 22.17 m 2 /g were obtained by

BET analyses of graphite and graphene, respectively. The low specific surface area combined with the copolymer grafting, hinders electrons displacements [START_REF] Mohan | Brunauer-Emmett-Teller (BET) specific surface area analysis of different graphene materials: A comparison to their structural regularity and electrical properties[END_REF]. The thermal reduction at 250 °C allows to reduce the resistance but it needs higher temperature under control atmosphere to improve the decomposition of all oxygenated groups. Hydrazine reduction method allows to strongly decrease the resistance for GOxH-r2 and GrOxH-r2 which reaches 1067 ± 54 Ω and 47622 ± 1066 Ω, respectively. The hydrazine hydrate reduction method decomposed most of the epoxide groups in the sp 3 structure and allows to recover better electrical property. However, the same reduction on functionalized particles (GOxH-PMMA-r2 and GrOxH-PMMA-r2) does not allow to obtain better electrical properties due to the presence of a large quantity of copolymer grafted. The presence of the grafted copolymer chains is supposed to prevent the access of hydrazine hydrate, because of steric hindrance, to the graphene structure and also to the oxygenated groups. Thermal reduction at 250 °C is more efficient to reduce the resistance in the presence of the copolymer grafting.

By changing the chemical modification sequences, the particle structure is modified and electrical properties are different. A first reduction by hydrazine of GrOxH or GOxH (GrOxH-r2, GOxH-r2), decomposed preferably epoxide groups while keeping carboxylic acid groups which can react by esterification with the copolymer grafting agent [START_REF] Kim | Epoxide reduction with hydrazine on graphene: A first principles study[END_REF]. After the functionalization, resistance increases until 6113 ± 97 Ω for GOxH-r2-PMMA and until 409058 ± 8900 Ω for GrOxH-r2-PMMA (Figure 12a). By adding a thermal reduction step, measured resistances decrease until 4576 ± 64 Ω for GOxH-r2-PMMA-r1 and 232684 ± 2998 Ω for GrOxH-r2-PMMA-r1. With an extension of thermal reduction time until 6 h at 250 °C, resistance of GOxH-r2-PMMA-r1 (6 h) reaches 1203 ± 3 Ω and 122652 ± 1505 Ω for GrOxH-r2-PMMA-r1 (6 h). The final step with the thermal reduction allows to decompose the oxygenated groups which didn't participate to the functionalization. The elimination of these residual groups improves even more the electrical conductivity. This part proved that the control of each chemical modification step and also the sequence of these steps have an impact on the material electrical properties. According to the needs and the targeted applications, electrical property can so be adjusted.

Discussion

Regarding electrical resistance values, hydrazine reduction before functionalization is the suitable way to obtain an exfoliated modified and conductive graphene. Hydrazine allows to recover electrical property thanks to the decomposition of a high quantity of oxygenated groups localized in the internal structure such as epoxide and open ways for electrons circulation. Raman spectra (Figure S6 and Table S1) confirms the diminution of oxygenated groups with a FWHM reduction of D band and G band after hydrazine treatment compared to GOxH. A high D band intensity of GOxH-r2 can be explained by the presence of vacancy defects after the subsequent chemical modifications (strong oxidation and reduction) [START_REF] Muzyka | Characterization of graphite oxide and reduced graphene oxide obtained from different graphite precursors and oxidized by different methods using Raman spectroscopy[END_REF]. The presence of vacancy defects does not allow to recover the electrical conductivity of the started material (graphene or graphite), but they seem to have a lower impact on electrical conductivity compared to the oxidation which create sp 3 domains in the structure. Electrons can find a pathway between vacancy defects. The functionalization on GOxH-r2 (GOxH-r2-PMMA) does not result in an augmentation of the FWHM. However, the ID/IG ratio increases after the grafting due to the presence of the copolymer mainly on the edge and not in the internal structure, since the D band is sensitive to edge defects [START_REF] Mohan | Improvements in electronic structure and properties of graphene derivatives[END_REF]. Consequently, the presence of the copolymer increases the electrical conductivity. Hydrazine reduction after the functionalization (GOxH-PMMA-r2) is less effective than before the copolymer grafting (GOxH-r2-PMMA) due to the steric hindrance of the grafted copolymer which prevents hydrazine hydrate access to the internal structure.

By modifying graphene with the soft chemical sequence (OxN), reduction steps were not necessary to obtain an electrically conductive and modified graphene. However, in this way, particles are not exfoliated.

With graphite as the starting material, electrical resistances were higher compared to commercial graphene for each chemical modifications. Specific surface area is probably the parameter that influences this gap of electrical conductivity.

Conclusion

This study showed that for graphene and graphite it was possible to control the particles morphology and structure and therefore their electrical properties by the aid of different chemical methods and treatments. A strong oxidation treatment by Hummers' method allowed to obtain exfoliated graphene and graphite with a highly reduced numbers of layers and an increased interlayer spacing (between 9 and 10 and around 0.3 nm, respectively for both GrOxH and GOxH). Using nitric acid, oxidation allowed to create reactive site for the functionalization but the product was not exfoliated and both GrOxN and GOxN keep their original structures.

The functionalization of graphene and graphite was done using a simple and versatile "grafting onto" method which allowed the grafting of a suitable copolymer via an esterification reaction.

As expected, grafting of P(MMA-co-HEMA) copolymer on both GrOxN and GOxN leads to highly conductive particles but with low amounts of grafted PMMA chains. On the contrary, the oxidation by Hummer's method was much more efficient to create reactive sites. Moreover, by using Hummers' method graphite can be used as a less expensive and more available product than graphene. Copolymer grafting on GrOxH and GOxH are very efficient but leads to very high resistance. Hence, those nanoparticles need a reduction step to recover their electrical conductivity.

Electrical results obtained were in accordance with the physical and chemical characterizations carried out on all the nanoparticles. Resistance measurements showed that it is possible to adjust nanoparticles property of our started material via different chemical modifications such as functionalization, oxidation, thermal and chemical reduction.

These results demonstrate the possibility to combine high electrical property and graphene covalent bonding modification to further improve dispersion in polymer matrix in the perspective of the high nanocomposite performance elaboration. To complete this work, a next study will be focus also on the impact of these modifications on nanoparticles localization in an immiscible PMMA/PS blend. This will assess to evaluate the effect of these different treatments on the electrical conductivity of the obtained composite materials. One objective will be to selectively disperse those functionalized graphene or graphite into a PS/PMMA blend to try to reach a double percolation phenomenon. We assume that the most interesting modified nanoparticles that would be selectively dispersed in a PMMA/PS polymer blends would be GOxH-r2-PMMA, GOxH-r2-PMMA-r1, GOxN-PMMA, GOxN and GOxH-r2 because of their high electrical conductivity and also their different morphology.

CRediT authorship contribution statement

Fig. 1 .

 1 Fig. 1. Schematic representations of (a) graphene oxidation and (b) Functionalization of graphene oxide in toluene with P(MMA-co-HEMA) copolymer as grafting agent.

3 :

 3 Graphite oxide functionalized with P(MMA-co-HEMA) GO-PMMA Graphene oxide functionalized with P(MMA-co-HEMA) functionalization with P(MMA-co-HEMA)GOxH-PMMA-r2Step 1: functionalization of GOxH with P(MMA-co-HEMA)Step 2Thermal reduction at 250 °C

Fig. 3 .

 3 Fig. 3. TGA of (a) modified graphite and (b) modified graphene samples. GrOxH (toluene) and GOxH (toluene) were obtained from GrOxH and GOxH powders dispersed in toluene and heated at solvent reflux in the same grafting synthesis conditions than GrOxH-PMMA and GOxH-PMMA, respectively without the copolymer agent incorporation. Thermogram of P(MMA-co-HEMA) copolymer is available in Figure S2.

Fig. 4 .

 4 Fig. 4. Py-GC/MS chromatograms of modified graphene and graphite samples.

Fig. 5 .

 5 Fig. 5. SEM images of (a) graphite, (b) GrOxN, (c) GrOxH, (d) graphene, (e) GOxN and (f) GOxH.

Fig. 6 .

 6 Fig. 6. XRD diffractograms of graphite and graphene samples oxidized and functionalized with P(MMA-co-HEMA) copolymer using (a) nitric acid and (b) Hummers' method.

Fig. 7 .

 7 Fig. 7. Raman spectra of graphene and graphite before and after modifications from (a) nitric acid and (b) Hummers' methods.

Fig. 8

 8 Fig.8shows the effective thermal and chemical reduction of Hummers' oxidized graphene and graphite. Indeed, the absence of weight loss at 200 °C for GrOxH-r1 and GrOxH-r2 compared to GrOxH and GOxH proves the effectiveness of the reductions.

Fig. 8 .

 8 Fig. 8. TGA of (a) GrOxH-r1 (thermal reduction), GrOxH-r2 (chemical reduction) and GrOxH, and (b) GOxH-r1, GOxH-r2 and GOxH.

Fig. 9 .

 9 Fig. 9. (a) XRD diffractograms of reduced GrOxH by hydrazine hydrate (GrOxH-r2) and thermal treatment (GrOxH-r1). SEM images of (b) GrOxH-r1 and (c) GrOxH-r2.

Fig. 10 .

 10 Fig. 10. (a) TGA and (b) Py-GC/MS after reduction treatment of functionalized graphite and graphene.

Fig. 11 .

 11 Fig. 11. (a) TGA of oxidized graphene after hydrazine reduction, copolymer grafting and thermal treatment; (b) Py-GC/MS of GOxH-r2-PMMA-r1.

Fig. 12 .

 12 Fig. 12. (a) Impact of Hummers' method and following chemical modifications on graphene and graphite electrical property, (b) Impact of nitric acid sequence on graphene and graphite electrical property.

  Lalire: Formal analysis, Methodology, Investigation, Writingoriginal draft. Claire Longuet: Writingreview & editing, Supervision. Aurélie Taguet: Writingreview & editing, Supervision. Belkacem Otazaghine: Conceptualization, Writingreview & editing.

Table 2 .

 2 Calculation performed from XRD diffractograms showing the impact of two different oxidation methods on graphite and graphene interlayer distance and thickness.

	Materials Peak	Interlayer	FWHM	Particle	Layers
		position (°)	spacing (nm)	(rad)	thickness (nm)	number
	Graphite 26.42	0.337	0.0066	21.33	63-64
	GrOxH	10.58	0.835	0.0174	7.91	9-10
	GrOxN	26.42	0.337	0.0064	21.99	65-66
	Graphene 26.42	0.337	0.0090	15.64	46-47
	GOxH	11.03	0.801	0.0188	7.32	9-10
	GOxN	26.42	0.337	0.0094	14.97	44-45
	XRD patterns of GOxH-PMMA and GrOxH-PMMA are plotted in Fig. 6b. After
	functionalization, the peak at 10.4° shifts to 24.9° for both GrOxH-PMMA and GOxH-PMMA
	which indicates that the interlayer distance decreases from 0.835 and 0.801 nm, respectively to
	0.357 nm. This shift is assigned to a partial restacking after the functionalization. Indeed,
	functionalization is performed at 110 °C and reduction of labile groups can occur at this
	temperature. Figure

Table 3 .

 3 Powder sample resistance values.

Acknowledgements

We gratefully acknowledge Thierry MICHEL (Laboratoire Charles Coulomb, UMR 5221 CNRS, Univ Montpellier) for Raman spectroscopy analyzes, Jean-Claude ROUX (C2MA, PCH, IMT Mines Alès) for SEM images and Monica PUCCI (LMGC, IMT Mines Ales, Univ Montpellier) for AFM images.

Ecole Doctorale Sciences Chimiques Balard (Univ Montpellier) finances this work.


Nolwenn Fougeron
email: nolwenn.fougeron@univ-grenoble-alpes.fr

Nathanaël Connesson

Grégory Chagnon

Thierry Alonso

Laurent Pasquinet

Manuelle Bahuon

Eugénie Guillin

Antoine Perrier

Yohan Payan

New pressure ulcers dressings to alleviate human soft tissues: a finite element study

Keywords: Finite Element Analysis, Pressure Ulcers, Dressing, Soft Tissues, Internal Strains

Pressure Ulcers (PU) are real burdens for patients in healthcare systems, affecting their quality of life.

External devices such as prophylactic dressings may be used to prevent the onset of PU. A new type of dressing was designed to alleviate soft tissue under pressure, with the objective to prevent PU and to improve the healing conditions of category-1 and category-2 wounds. The mechanical interactions of this dressing with a generic model of human skin/hypodermal soft tissue was simulated using the Finite Element (FE) method. Different cases with intact skin tissues and injured tissues with a category-2 PU, with and without dressings in place, were modeled.

The tissues were deformed under compressive load; internal strains were computed. The results showed a clear benefit from the use of the dressing to reduce the peak internal strains both in the intact and injured tissues models by 17 to 25 %, respectively. The intact soft tissues model was evaluated via sacral pressure measurements performed on one healthy volunteer. Results showed a good agreement between pressure measurements and estimations both with and without the dressing in place; particularly under the bony prominence and in surrounding tissues. As a conclusion, the importance of dressings to maintain a proper biochemical environment for the healing of PU is incontestable. Yet, new concepts of dressings may be developed to prevent the onset of PU, but also to provide local stress and strain reliefs and create mechanical conditions as less damaging as possible for the tissues.

Introduction

In Europe and North America 7 to 23 % of patients in healthcare facilities develop Pressure Ulcers (PUs) with an increased risk for older patients, people with spinal cord injuries or comorbidities [START_REF] Demarré | The cost of prevention and treatment of pressure ulcers: A systematic review[END_REF]. PUs have terrible consequences on the quality of life of patients including longer hospitalisation time, social isolation and pain.

PUs are localised wounds that propagate in the soft tissues after a detrimental external loading. Short time but intense load application is sufficient to cause tissue wounds while reduced loads applied for an extended period of time can also lead to PUs [START_REF] Loerakker | Temporal effects of mechanical loading on deformation-induced damage in skeletal muscle tissue[END_REF]. Pressure or shear loads applied at the skin level may lead to significant internal strains [START_REF] Gefen | Our contemporary understanding of the aetiology of pressure ulcers/pressure injuries[END_REF]. When these strains exceed the cell ability to deform, in most cases under bony prominence, this eventually leads to cell death and the development of PUs [START_REF] Ceelen | Compression-induced damage and internal tissue strains are related[END_REF][START_REF] Bouten | Compressive deformation and damage of muscle cell subpopulations in a model system[END_REF][START_REF] Oomens | Can loaded interface characteristics influence strain distributions in muscle adjacent to bony prominences?[END_REF].

To reduce the prevalence of PUs, external medical devices are used to redirect external loads away from areas prone to PUs such as the sacrum or the heel. More particularly, dressings have been demonstrated to have a prophylactic effect [START_REF] Walker | Prophylactic dressing to minimize sacral pressure injuries in high-risk hospitalized patients: A pilot study[END_REF][START_REF] Miller | Analysis of the Pressure Distribution Qualities of a Silicone Border Foam Dressing[END_REF]. Finite element (FE) modelling is a known tool to estimate internal tissue strains and stresses, since these quantities cannot be measured in-vivo [START_REF] Ceelen | Validation of a numerical model of skeletal muscle compression with MR tagging: A contribution to pressure ulcer research[END_REF]. Consequently, FE models have played a key role to assess the ability of dressings to alleviate soft tissues [START_REF] Peko Cohen | Dressings cut to shape alleviate facial tissue loads while using an oxygen mask[END_REF][START_REF] Gefen | Pressure ulcer prevention dressing design and biomechanical efficacy[END_REF][START_REF] Lustig | How patient migration in bed affects the sacral soft tissue loading and thereby the risk for a hospital-acquired pressure injury[END_REF][START_REF] Soh | Computational modeling of the thin muscle layer, panniculus carnosus, demonstrates principles of pressure injury and prophylactic dressings[END_REF]. Most studies report a decrease of the strain energy density and stress in soft tissues, with various dressings [START_REF] Sieracki | Finite Element Analysis Modeling of a Novel Silicone Dressing[END_REF] considering a supine position. This was also confirmed with head-of-bed elevation [START_REF] Schwartz | A Computer Modeling Study to Assess the Durability of Prophylactic Dressings Subjected to Moisture in Biomechanical Pressure Injury Prevention[END_REF][START_REF] Levy | Assessment of the Biomechanical Effects of Prophylactic Sacral Dressings on Tissue Loads: A Computational Modeling Analysis[END_REF].

However, only few studies focusing on PUs compute the strains correlated to cell death in soft tissues [START_REF] Keenan | A review of foot finite element modelling for pressure ulcer prevention in bedrest: Current perspectives and future recommendations[END_REF] and none of the models proposed in the literature were evaluated with experimental data. Only one study shows the effect of dressings on tissues with a PU [START_REF] Schwartz | The biomechanical protective effects of a treatment dressing on the soft tissues surrounding a non-offloaded sacral pressure ulcer[END_REF]. Yet, the used model accounted for a category-4 wound which is not representative of the majority of clinical cases.

Urgo RID is currently developing a new concept of dressing that can be used both to prevent PUs and to improve the healing process for PUs as deep as category-2 PU. To do so, the objective is to reduce the internal strains in the wound and in surrounding tissues. This study aims at developing a parametric FE model of the interaction between intact soft tissues, the Urgo RID dressing and the lying surface. This model was evaluated with regard to pressure estimations which were compared with experimental data. The parametric model was used to assess the prophylactic properties of the dressing and its ability to reduce tissues strains in the presence of a category-2 PU.

Materials and methods

Dressing model

Dressing description

The new Urgo RID (Urgo Research, Innovation & Development, Chenôve, France) dressing is an improved version of UrgoStart Plus Border ® dressing, currently under study and development. The novelty of the dressing consists in adding a deformable and protective layer. This layer is made of alveoli that can be removed in a subject-specific manner in order to unload the wound and its surrounding tissues (Figure 1). To model the mechanical behavior of this new dressing, we proposed to build an FE model with two layers. A first component, referred as "dressing layer 2", was supposed to model the UrgoStart Plus Border ® dressing which is in contact with the skin. In a first approximation this layer was approximated by a single material. The second component, the protective layer was modeled as a deformable layer glued with "dressing layer 2" and was referred as "dressing layer 1".

Mechanical tests and modeling of "dressing layer 1"

Compressive mechanical tests were performed on the "dressing layer 1" (Figure 2, right panel). Creep tests showed an increase by 12 % of the stretch ratio for a constant compressive force maintained for 30 min.

"Dressing layer 1" was modelled as a compressible homogeneous isotropic material following an hyperelastic Blatz-Ko law [START_REF] Lee | Finite element modeling for predicting the contact pressure between a foam mattress and the human body in a supine position[END_REF]. Stretch ratio values were increased by 12 % to account for the creep resulting from the extended used of the dressing. The initial strain shear modulus, 1.00 kPa, was optimized using a curve fitting method with Matlab (Figure 2). "Dressing layer 1" was modelled as a hollow cylindrical layer with a radius of 125.0 mm, a central opening surface of 255.6 mm², larger than the PU surface, and a thickness of 5.2 mm. It was meshed in Ansys Mechanical APDL with 3 612 hexahedral elements (SOLID185).

Mechanical tests and modeling of "dressing layer 2"

Tensile mechanical tests were performed on specimens from the "dressing layer 2" cut at 0.0°, 22.5°, 45.0° and 90.0° according to the orientation of the dressing with the spine (Figure 2, left panel). These tests revealed the orthotropy of the dressing. Additional creep tests showed an increase by 16 % of the stretch ratio for a constant tension force maintained for 30 min. Thus, the "dressing layer 2" was modeled as a linear homogenous orthotropic material. Stretch ratio values were increased by 16 % to account for the creep resulting from the extended used of the dressing. Young moduli were optimized using a curve fitting method with Matlab. The resulting Young modulus in the principal direction, i.e. in the spine direction, was 4.40 MPa, whereas the secondary direction, orthogonal to the spine direction in the dressing plane, was 1.80 MPa. An FE inverse method based on compression tests performed on both dressing layers was used to assess the Young modulus in the transverse direction of the dressing which, eventually, was set to 0.03 MPa.

The Poisson coefficient was set to 0.25 according to literature data [START_REF] Schwartz | A Computer Modeling Study to Assess the Durability of Prophylactic Dressings Subjected to Moisture in Biomechanical Pressure Injury Prevention[END_REF]. This "dressing layer 2" was modeled as a cylindrical layer with a radius of 125.0 mm and a thickness of 3.5 mm, and meshed in Ansys Mechanical APDL with 2 476 hexahedral elements (SOLID185).

Soft tissues/dressing interaction

Modeling of the sacral area

This study focused on the dressing ability to i) prevent PU within intact soft tissues, and to ii) reduce further damage of injured tissues, with a category-2 PU, using parametric FE models. One healthy volunteer (male, 40 years old, 94 kg, 1.73 m) was included for the modeling and for the experimental setup (described in part 2.3.1).

The volunteer gave his informed consent as required by the Helsinki declaration (1964). In both intact and injured tissues models, two cases of analysis were performed, without and with the dressing placed at the skin surface. In both models the subject was simulated in a supine position on a mattress with linear elastic isotropic homogenous properties. The mattress height was set to 50 mm and its Young modulus to 230 kPa [START_REF] Lee | Finite element modeling for predicting the contact pressure between a foam mattress and the human body in a supine position[END_REF].

Intact tissues model

The sacral area was modeled as one layer of dermis and one layer of adipose tissues. By means of ultrasound images collected onto the volunteer, the dermis thickness was set to 1.3 mm while the adipose tissue thickness was 13.3 mm under the bony prominence and 22.3 mm outside the bone. The bone boundary was modeled by a portion of sphere with a radius of curvature of 110.0 mm. A bony prominence, approximated by an elliptical surface, with a height of 5.2 mm, was added to the model (Figure 4). The length of the sacral area model was 250.0 mm, i.e. twice the dressing one, to reduce free boundary effect close to the dressing area. This geometry was meshed in Ansys Mechanical APDL using hexahedral linear elements (SOLID185) with a mixed pressuredisplacement formulation. A mesh convergence study was performed on the displacement of the adipose tissues' nodes. Eventually, the complete mesh was composed of 15 936 elements (Figure 5, left panel).

The skin was modelled with an Isihara's et al. law [START_REF] Isihara | Statistical theory of rubber-like elasticity. IV. (Two-dimensional stretching)[END_REF] (equivalent to a Yeoh constitutive law with the parameter C30 equals to zero). Material parameters were optimized using a curve fitting method with Matlab from the experimental data of Ni Annaidh et al. [START_REF] Ní Annaidh | Characterization of the anisotropic mechanical properties of excised human skin[END_REF] who did uniaxial tensile tests on skin samples collected in the sacral region (Table 1). The adipose tissue layer was modeled with a Yeoh law [START_REF] Yeoh | Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates[END_REF] and parameters were optimized according to the equibiaxial test data of Sommer et al. [START_REF] Sommer | Multiaxial mechanical properties and constitutive modeling of human adipose tissue: A basis for preoperative simulations in plastic and reconstructive surgery[END_REF] (Table 1).

All incompressibility parameters were supposed equal and were computed from the formula provided in Mott et al. [START_REF] Mott | The bulk modulus and Poisson's ratio of "incompressible" materials[END_REF]:

(1) 𝐷𝐷 1 = 𝐷𝐷 2 = 𝐷𝐷 3 = 3(1-2𝜈𝜈) 2𝐶𝐶 10 (1+𝜈𝜈)
With ν, the Poisson's ratio, set to 0.4999, to account for the nearly incompressibility of soft tissues. C10 (MPa) C20 (MPa) C30 (MPa) D1 (MPa -1 ) D2 (MPa -1 ) D3 4). This geometry was also meshed using hexahedral linear elements (SOLID185) with a mixed pressure-displacement formulation. The resulting mesh was composed of 18 664 elements (Figure 5, right panel).

The soft tissues surrounding a PU are usually stiffer than healthy tissues [START_REF] Agam | Pressure ulcers and deep tissue injury in wheelchair users: A bioengineering perspective[END_REF]. Three areas were therefore defined both for the skin and the adipose tissues to account for this local stiffening. For both tissues, the C10 coefficient was multiplied by 1, 1.5 or 2 for the areas nearest to the wound [START_REF] Edsberg | Microstructural and mechanical characterization of human tissue at and adjacent to pressure ulcers[END_REF] to define soft, medium and rigid material, respectively.

Boundary conditions and loading

Nodes between skin and adipose tissue, skin and "dressing layer 2", and, between "dressing layer 2" and "dressing layer 1", were tied (Figure 5). Friction tests were performed to assess the coefficient of friction between the support and the dressing layer 2, set to 0.62. A coefficient of friction of 0.43 was set between the skin and the mattress [START_REF] Call | Enhancing pressure ulcer prevention using wound dressings: What are the modes of action?[END_REF].

A vertical force of 47 % of the subject body weight was simulated, to account for the weights of thighs, pelvis and abdomen body segments [START_REF] Plagenhoef | Anatomical Data for Analyzing Human Motion University of Massachusetts -Amherst[END_REF]. Considering the symmetry of the model, half of the resulting force, 217 N, was applied to a pilot node, located at the center of the bony prominence. All nodes at the boundary between the sacrum and the adipose tissues, in a radius of 68.5 mm, were tied in displacement with the pilot node. This radius was equal to half the distance between the sacroiliac crests measured on the sacrum 3D reconstruction of the volunteer (Figure 5). The bottom nodes of the mattress were fixed.

Model validation

Experimental setup

The volunteer was wearing tights and laid in supine position on a rigid support, holding his legs up to exacerbate the loading on the sacrum to account for a worst-case scenario. A Tekscan 5250 pressure sensor (Tekscan, South Boston, USA) with 44x44 sensors was positioned between the rigid support and the sacral region.

The calibration was performed according to the manufacturer protocol. The sensor could measure pressures up to 1 724 kPa with a 5 mm resolution. Three acquisitions of 30 s were recorded for all configurations. First measurements were performed without the dressing. Pressures were then measured with the dressing placed between the rigid support and the pressure sensor (Figure 6, left panel). For such a case, the alveoli located at the position of the previously measured peak pressure were removed.

Experimental setup model

The intact tissues model was used for the evaluation. Yet loads were adapted to the performed experiments (Figure 6, right panel). Since the experiment aimed to load solely the sacrum prominences, only nodes in a radius of 37 mm around center of the model were tied to the pilot node. Because of the symmetry in the model, half the forces measured during the experiments without and with the dressing, respectively 291 N and 245 N, were applied to the pilot node as vertical forces. Considering the experimental setup, the subject was simulated as lying on a rigid support.

Internal strains with the intact tissues model

Green-Lagrange maximal shear strains are assumed to be a relevant numerical biomarker for PU prevention [START_REF] Ceelen | Compression-induced damage and internal tissue strains are related[END_REF] and were computed from the simulations. The Region Of Interest (ROI) consisted of all soft tissues elements included in a radius lower than 19.5 mm. This value included the soft tissues below the surface surrounding the bony prominence where strains should be as low as possible according to clinician experts. The dressing helped to decrease the internal strains in the ROI. The volumes of soft tissues above strains thresholds are presented in Figure 8. The peak strain in the ROI was estimated to 0.42 without dressing. This value decreased to 0.23 with the dressing.

Internal strains with the injured tissues model

Assuming a category-2 PU developed, the dressing was also able to reduce the internal strains (Figure 9)

in the ROI. The peak strain was estimated to 0.43 without dressing, and decreased to 0.30 with the dressing.

Discussion

This study focused on a new approach based on a parametric model of the sacral area, interacting with a new dressing developed by Urgo RID, to investigate internal strains in the context of PU prevention. Thus, the FE method was used to model intact and injured tissues. To evaluate the model, one volunteer participated to measurements of pressures at the interface between the sacral region and the dressing, in a worst-case scenario.

These measures were compared to the pressure estimated with the model.

FE estimations of the pressure showed a good agreement with measurements with and without the dressing. Yet estimated peak pressures, up to 217 kPa, revealed an overloading of the tissues during the experiment.

This was performed on purpose to account for the worst-case scenario. In fact, clinical pressures as measured at the interface with the sacral areas do not exceed 15 kPa [START_REF] Bader | Bioengineering considerations in the prevention of medical devicerelated pressure ulcers[END_REF][START_REF] Defloor | The effect of position and mattress on interface pressure[END_REF]. Peak pressure estimations were close to the measured pressure with an error up to 24 kPa. Errors may be explained by numerical geometrical non-linearities at the dressing boundary and also by the resolution of the pressure sensor, that may not capture local extrema.

Internal strains were also estimated with and without the dressing. Loadings was modified to assess clinically relevant internal strains. As expected, the presence of the dressing resulted in a decrease of the soft tissues strains in intact tissues surrounding the bony prominence. The reduction of the peak strain by 45 %, highlighted the prophylactic effect of the dressing like in other literature studies [START_REF] Walker | Prophylactic dressing to minimize sacral pressure injuries in high-risk hospitalized patients: A pilot study[END_REF][START_REF] Sieracki | Finite Element Analysis Modeling of a Novel Silicone Dressing[END_REF][START_REF] Schwartz | The biomechanical protective effects of a treatment dressing on the soft tissues surrounding a non-offloaded sacral pressure ulcer[END_REF][START_REF] Peko Cohen | Sacral Soft Tissue Deformations When Using a Prophylactic Multilayer Dressing and Positioning System: MRI Studies[END_REF]]. Yet, this study focuses on a new dressing based on the combination with a honeycombed deformable layer. Considering injured soft tissues with a category-2 PU, results showed a decrease of the internal strains surrounding the PU with a reduction of the peak strain by 30 %. To our knowledge, this study is the first attempt to numerically investigate the ability of a dressing to reduce strains of category-2 sacral PU. A similar attempt was proposed for category-4 PU [START_REF] Schwartz | The biomechanical protective effects of a treatment dressing on the soft tissues surrounding a non-offloaded sacral pressure ulcer[END_REF] and showed also a benefit of the dressings on the internal stresses. Direct comparison between both models was not possible since, in the present study, soft tissues were modelled between the bone and the wound bottom. To our knowledge, no other literature studies provided internal strains data in the human sacral area when lying on a rigid surface.

Some limitations may impact these findings. The parametric approach involved a simplification of the geometry that may lack accuracy to estimate isolated stress/strain concentration areas. Some parameters of the models had to be defined arbitrarily since they could not be measured such as the Poisson's ratio for soft tissues.

A preliminary study revealed that this coefficient could be set between 0.4999 and 0.499 to account for a soft tissues' volume change from 2 % to 18 % respectively. The impact of this parameter on the results of the simulation clearly indicates that further investigation should be conducted to evaluate its value. It is however important to mention that the efficacy of the dressing is still satisfying if the Poisson's ratio is changed to 0.499. In addition, the duration of the loading was not investigated [START_REF] Gefen | Strain-time cell-death threshold for skeletal muscle in a tissue-engineered model system for deep tissue injury[END_REF]. The time parameter may, however, be implemented in further work since tissues and dressings may have viscoelastic properties. The time parameter may also be modelled to consider the biochemical and biophysical phenomenon that were not studied here such as the inflammation or ischemia [START_REF] Gefen | Our contemporary understanding of the aetiology of pressure ulcers/pressure injuries[END_REF]. Further work may also focus on the implementation of clinical parameters such as the head-of-bed elevation and the use of a mattress to assess the efficacy of the dressing in a clinical environment [START_REF] Lustig | How patient migration in bed affects the sacral soft tissue loading and thereby the risk for a hospital-acquired pressure injury[END_REF] but also extend this work to more subjects to account for geometrical but also material properties discrepancies in different populations. Finally, this model provided results applicable to category-2 PU and may not be extended to deeper wounds as this should involve further developments.

Eventually, this study highlights the potential of a new dressing which may benefit the PU healing process an also act as a prophylactic device with the implementation of a FE model. The FE method allows scientists, industry partners and clinicians, to assess data such as the internal strains that cannot be measured in vivo but are still fundamental to evaluate the risk of development of a PU.

Figure 1 :

 1 Figure 1: The new dressing design developed by Urgo RID

Figure 2 :

 2 Figure 2: Material parameters optimization of the dressing layers. The optimization was processed after a correction by the creep ratio. (Left) "Dressing layer 2". (Right) "Dressing layer 1" hyperelastic response.

Figure 3 :

 3 Figure 3: Optimization of the material parameters of the adipose tissue (left) and the skin (right) 2.2.3. Injured tissues model

Figure 4 :

 4 Figure 4: Models of the dressing/soft tissues coupling with intact (top) and injured soft-tissues (bottom).

Figure 5 :

 5 Figure 5: Models of the dressing interaction with intact (left) and injured (right) tissues. Pink areas represent the nodes tied to the pilot node.

Figure 6 :

 6 Figure 6: Experimental setup (left) and associated models (right) without (top) and with (bottom) the dressing. Pink areas represent the nodes tied to the pilot node. Pressure sensor and dressing thicknesses were exaggerated for illustration

Figure 7 :

 7 Figure 7: Pressure measurements (top) and estimations (bottom) obtained without (left) and with (right) dressing.

Figure 8 :

 8 Figure 8: A) Strains in the sagittal plane. The dark square circled the ROI. B) Volume of soft tissues in ranges of strains for the intact tissues model without (grey triangles) and with the dressing (black squares) in the ROI. Green, orange and red regions are safe, potentially injurious and injurious domains of strains respectively [4].

Figure 9 :

 9 Figure 9: A) Strains in the sagittal plane. The dark square circled the ROI. B) Volume of soft tissues in ranges of strains for the injured tissues model without (grey triangles) and with the dressing (black squares) in the ROI. Green, orange and red regions are safe, potentially injurious and injurious domains of strains respectively [4].

Table 1 :

 1 Soft tissues material parameters.

	(MPa -1 )

Acknowledgement

Conflict of interest

This study was supported by Urgo RID.