Bonnal Thomas

Elodie Prud'homme

Solene Tadier
email: solene.tadier@insa-lyon.fr

Genevieve Foray

Infrared mapping of inorganic materials: a supervised method to select relevant spectra

Keywords: Iterative Boundary Least Squares Method, Infrared Spectroscopy, Multivariate Curve Resolution, Inorganic Materials, Hyperspectral Imaging, Chemical Imaging

Spectroscopic imaging is expanding thanks to new instrumental concepts, technological developments, easier use and lower costs. This leads to collect and to handle huge hyperspectral databases. Among data providing useful information, there may also be unwanted information (i.e., either biased or irrelevant with respect to the information one wants to retrieve from the analysis). The classical approach aims at building a spectra library, which contains both informative spectra and outliers, so as to train learning algorithms. However, reference spectra cannot always be acquired, especially for samples prone to ageing or changes when exposed to humidity, temperature... Thus, building a library with reference spectra is not always possible.

To handle this issue, a new supervised method (SSMS for Supervised Selective Method based on SIMPLISMA) has been designed and is described in this article, to identify and exclude unwanted spectra from the resolution process when no library is available. SSMS relies on a supervised exclusion of the unwanted spectra. It ensures both a quick treatment and an accurate

Introduction

Recent developments in advanced techniques for material analysis, such as characterizations in 3D [START_REF] Maire | X-ray tomography and three-dimensional image analysis of epoxy-glass syntactic foams[END_REF][START_REF]Development of optical models and non-supervised methods to solve bilinear problems: application to vibrationnal mapping[END_REF] or in complex environments [START_REF] Xiao | Analysis of liquid suspensions using Scanning Electron Microscopy in transmission: estimation of the water film thickness using Monte Carlo simulations[END_REF], and an easier access to cutting-edge techniques lead to deal with a larger and larger amount of data (large scanned areas and volumes, monitoring of the evolution of a sample vs. time, large number of replicates...). In particular, the use of spectroscopy techniques (e.g., Raman [START_REF] Bannerman | Visualising phase change in a brushite-based calcium phosphate ceramic[END_REF], NMR [START_REF] Puig-Castellví | 1H NMR metabolomic study of auxotrophic starvation in yeast using Multivariate Curve Resolution-Alternating Least Squares for Pathway Analysis[END_REF] or terahertz [START_REF] Yamaguchi | Brain tumor imaging of rat fresh tissue using terahertz spectroscopy[END_REF]) requires to handle hyperspectral databases. More specifically, Fourier-Transform Infrared (FT-IR) microscopy is employed to obtain chemical mapping of ma-terials and has known very interesting developments in the past few years [START_REF] Offroy | Infrared chemical imaging: Spatial resolution evaluation and super-resolution concept[END_REF][START_REF] Nasse | High-resolution Fourier-transform infrared chemical imaging with multiple synchrotron beams[END_REF][START_REF] Amarie | Nano-FTIR chemical mapping of minerals in biological materials[END_REF].

Along with spectra providing useful information on the samples composition, these hyperspectral databases may also contain biased data (outof-measurement ranges, noise, artifacts. . . ) or unwanted information (e.g., linked to mounting resin or stand). Therefore, such big data analysis requires a thorough pre-processing stage to exclude non useful information and keep only the relevant spectra. Data, which are out-of-range or characterized by a too low signal-to-noise ratio, are relatively easily removed from databases.

However, the identification of misinformative or unwanted information is based on preconceptions on their spectral characteristics or on their detection by learning algorithms (e.g. Random Forest classifier, Support Vector Machines, artificial Neural Networks). The latter approach is highly efficient but requires the algorithms to be trained on an available database. Such IR spectral libraries including relevant spectra and outliers are scarce, especially for inorganic materials.

In this work, a home made selective robust method, called SSMS (Supervised Selective Method based on SIMPLISMA), has been developed to eliminate non useful spectra based on statistical considerations without needing any training database. SSMS enables to identify irrelevant spectra without any a priori knowledge of the material. Such an automatic treatment becomes essential to enable the analysis of large databases. SSMS algorithm is detailed and illustrated on the obtaining of chemi-cal maps issued from FT-IR microscopy acquisitions. The use of a particular set-up, called static attenuated total reflection (s-ATR), is shown to be an efficient tool for the mapping of inorganic materials. A granular composite used for construction applications, containing a very sensitive ettringite binder, was successfully studied avoiding cross-contamination and surface degradation issues. SSMS permitted to exclude spectra related to artifacts linked to the s-ATR set-up without any preconceptions on the material. Chemical maps were obtained using a Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) procedure. It is shown how SSMS can be used as an efficient pre-processing step in the analysis of any type of hyperspectral database.

Theoretical background

FT-IR spectroscopy

Infrared spectra can be obtained from different acquisition modes measuring reflected beam, transmitted beam or a combination of both [START_REF] Bassan | Reflection contributions to the dispersion artefact in FTIR spectra of single biological cells[END_REF]. The intensity I of these measured beams is then compared to the intensity I 0 of the incident beam. To do so, absorbance A and reflectance R are defined as A(ω) = log 10 (I 0 (ω)/I(ω)) = -log 10 (R(ω)), ω being the wavenumber.

The transmission mode is not applicable for most minerals since they are dense and absorbent. Focusing on the reflective mode, three different optical phenomena have been exploited for FT-IR spectra acquisitions: specular, diffuse and total reflections, the latter one occurring when the incident angle is larger than the critical angle of the studied material.

The amount of light detected by the sensor is the key parameter to obtain exploitable spectra (i.e., bands relative to covalent bonds are predominant in the spectra). It can be influenced by material parameter as 1) the roughness of material surface and 2) the material nature. 1) An increase of the sample roughness leads to an increase of the scattered light and to a decrease of the signal-to-noise ratio [START_REF] Macdonald | Dispersion analysis of FTIR reection measurements in silicate glasses[END_REF]. 2) The imaginary refractive index influences the spatial distribution of the light scattered by the material [START_REF] Bassan | Resonant Mie scattering in infrared spectroscopy of biological materialsunderstanding the 'dispersion artefact[END_REF][START_REF] Bassan | Reflection contributions to the dispersion artefact in FTIR spectra of single biological cells[END_REF]. This may result in modulations and distortions in spectra [START_REF] Miljković | Line shape distortion effects in infrared spectroscopy[END_REF]. Moreover, in a quantitative study, a minimal number of photons has to be detected to obtain a measurement included in the linearity range of the sensor. This may be achieved by increasing the number of scans or by minimizing the roughness of the material. Acquiring a spectrum using the specular reflection is the easiest technique to implement, as it does not require any specific set-up: the infrared beam is directly projected through the ambient air at the surface of the sample. A sensor placed above the sample then records the reflected beam (Fig. 1.a).

Crystals, which are used to achieve Attenuated Total Reflection ATR, have no absorption in the infrared range and a much higher refractive index than the studied material. The incident infrared beam travels through the ambient air and then through the ATR crystal before reaching the surface of the sample beyond the critical angle. Thus, total internal reflection occurs, maximizing the amount of reflected light. Practically, a vertical load is ap-

FT-IR microscopy

To obtain a 2D FT-IR map (( x, y) plane), the sample is placed on a micrometric (x, y, z) motorized stage to scan its surface, which enables the acquisition of FT-IR spectra at different locations.

The spatial resolution of the resulting map is theoretically limited by the diffraction limit described by the Rayleigh criterion r:

r = 0.61.λ N A ( 1
)
Where λ is the wavelength and N A is the numerical aperture of the optical system. The numerical aperture is defined by N A = n. sin θ and depends on the incident medium (n: refractive index of incident medium: air or ATR crystal) through which the light travels. It also depends on θ, the half angle of the cone of incident light [START_REF] Chan | Attenuated total reflection Fouriertransform infrared (ATR-FTIR) imaging of tissues and live cells[END_REF]. The spatial resolution is the minimal distance for which two adjacent points can be separated and is theoretically equal to 2r. In practice, optical aberrations lead to a worse spatial resolution [START_REF] Chan | New opportunities in micro-and macroattenuated total reflection infrared spectroscopic imaging: spatial resolution and sampling versatility[END_REF]. Thus, the actual spatial resolution has to be experimentally measured.

Methods based on optical reference targets are often used [START_REF] Offroy | Infrared chemical imaging: Spatial resolution evaluation and super-resolution concept[END_REF][START_REF] Offroy | Pushing back the limits of Raman imaging by coupling super-resolution and chemometrics for aerosols characterization[END_REF] but Kazarian [START_REF] Kazarian | Micro-and Macro-Attenuated Total Reflection Fourier Transform Infrared Spectroscopic Imaging[END_REF] recently suggested a more accurate method when ATR crystals are involved in the acquisition process.

Finally, a distinction has to be made between the spatial discretization arisen from the step of the motorized stage and the actual spatial resolution [START_REF] Chan | Attenuated total reflection Fouriertransform infrared (ATR-FTIR) imaging of tissues and live cells[END_REF].

To acquire a FT-IR map in specular reflection, no additional set-up is required (Fig. 1.a).

For ATR, the crystal, located above the sample, is motionless. The stage moves vertically up (z direction) to make the contact between the sample and the crystal. Then, the stage keeps going up until a specified stress (∼ 10 N ) ensures a good contact between the sample and the crystal: a spectrum is recorded. Then the stage moves down before switching to the next location (( x, y) plane) (Fig. 1.b).

The crystal focuses the incident beam and ensures a higher spatial resolution.

However, cross-contamination may be induced by the (x, y) displacements.

Moreover, with a crystal diameter of few hundreds of microns, localized loads of about 80 M P a are generated. They may lead to residual imprints in case of sample with weak mechanical properties [START_REF] Bonnal | Towards chemical imaging: Fourier transform infrared mapping on organo-mineral materials[END_REF]. Caution should be taken for sensitive material to avoid or check for such artifacts.

The static-ATR (s-ATR) set-up enables performing ATR without applying successive localized loads onto the sample. The crystal has a conical shape with a half-sphere on its top (Fig. 1.c). The bottom flat surface is about ten times larger than usual ATR crystals and is put in contact with the sample only once for the whole acquisition process. The resulting block {crystal + sample} is fixed on the motorized stage. When the stage moves, the location of the incident beam on the upper base of the crystal is changed (Fig. 1.c), enabling the acquisition of FT-IR microscopy maps. This minimizes damage at the surface, avoids potential cross contamination issues and prevents any pressure loss between the crystal and the sample. However, this technique is seriously affected by surface imperfections: a high roughness can lead to signal loss for some areas. In addition, a lack of parallelism between the two sample faces can hinder the contact between the crystal and the sample. This contact is ensured by applying a localized load, which may lead to one residual imprint (Fig. 2).

Finally, some of the spectra acquired with this set-up are aberrant (i.e., to the authors' knowledge, not corresponding to the actual material). These artifacts will be further denoted 's-ATR artifacts' and discussed later in the manuscript.

Spatial resolutions and other comparative items of the different set-ups are summarized in Table 1, while their schematic views are displayed in Fig. 1.

Actual spatial resolutions have been provided by the manufacturer of the mi-croscope used in this study.

Obtaining a FT-IR map from acquired spectra: bilinear modelling

First of all, the following hypotheses have to be made to obtain a FT-IR map: (i) the studied material is made of p compounds, (ii) each compound is isotropic and (iii) its characteristics remain unchanged versus time. It is important to note that a compound may be composed by a mixture of several chemical phases.

The Beer-Lambert law links absorbance values A(ω) for a wavenumber ω with the molar attenuation coefficient , the concentration of absorbing species c and the path length l: A(ω) = (ω).l(ω).c.

Working on relative quantities of a mixture of p compounds, this law can also be expressed by:

A(ω) = p i=1 s i (ω).c i (2)
with s i and c i the spectrum and the relative concentration related to each

compound i ∈ [1; p], respectively. Acquiring one FT-IR spectrum per loca- tion, a 3D data matrix D 3D of dimensions [x × y × m] is constructed [19]. x
and y are the numbers of acquisitions in the two spatial directions ( x, y). m is the number of wavenumbers for which absorbance values are recorded. As most chemometrics tools are not designed to directly handle 3D matrices, the two spatial indexes are combined to store the data in a 2D matrix:

[x, y, m] → [n, m], n ∈ [1; x × y] (3)
D 3D [x×y×m] → D [n×m] (4)
Finally, the application of the Beer-Lambert law to the matrix of data leads to consider the following bilinear problem:

D [n×m] = C [n×p] . S t [p×m] + E [n×m] (5)
S is the matrix of spectra relative to each compound, C the matrix of concentrations and E the matrix of residual errors [START_REF] De Juan | Multivariate Curve Resolution (MCR). Solving the mixture analysis problem[END_REF].

Material and methods

Material

A construction material has been fabricated to illustrate the method developed in this work. A cylinder (diameter: 30 mm, height: 50 mm) of granular composite has been prepared with equal weights of ground silica and limestone filler. Their granular size distribution was comprised in the range [0.3; 300] µm, the carbonate filler being smaller than the siliceous one.

They were binded together with an ettringite binder, based on calcium aluminate cement and anhydrite. This granular composite with ettringite binder was elaborated according to Michel et al. [START_REF] Michel | Développement de composites à matrice minérale et à renfort textile[END_REF]. This material includes non stable ettringite hydrates. Carbonate groups may be incorporated over time, which drastically influences the composition and the properties of the material. The phases, which are formed in small amounts during this process, are poorly crystalline. Thus, their identification and characterization are challenging.

For FT-IR microscopy observations, a 4×4×4 mm 3 cube was extracted from the core of the cylindrical sample. One surface of the cube was resurfaced using a target surfacing system EM TCP (Leica microsystems, Germany) with a milling step of 1µm, followed by a polishing (Fig. 2.a). array sensor cooled with liquid nitrogen was used, leading to an effective pixel size of 6.25 µm × 6.25 µm. Its inferior limit of linearity corresponds to 5 % of the incident beam. Actual spatial resolutions of the set-ups (Table 1) were evaluated by the manufacturer using a USAF 1951 spatial resolution target. The stage moved by a (( x, y) plane) step of 25 µm. The scanned area was about 300 × 515 µm 2 leading to a map composed of 48 × 82 pixels.

FT-IR microscopy equipment and acquisition parameters

Spectra were collected with a spectral resolution of 8 cm -1 in the Infrared range between 717 and 4000 cm -1 , with 16 scans per spectrum. Omnic Picta T M software was used to acquire FT-IR maps.

Description of the resolution process

The resolution process developed in the following sections aims at obtaining relevant chemical maps describing the spatial distribution of each compound at the surface of the material.

A schematic view of the preprocessing steps is shown in figure 3. As detailed in section 2.3, once one FT-IR spectrum has been acquired per location, a 3D data matrix of dimensions [x × y × m] is built (Fig. 3, Step 1 ). Finally, the bilinear problem is described by equation ( 5):

D [n×m] = C [n×p] . S t [p×m] + E [n×m]
S is the matrix of spectra relative to each compound, C the matrix of concentrations and E the matrix of residual errors.

In our application, the number of compounds (and their related spectra) is a priori unknown leading to an under-determined system of equations. Thus, a first step is needed to determine the number of compounds and their relative spectra. The resolution of this step will be described in section 4.1. It permits to obtain an over-determined system, which can then be solved to find the maps of relative concentrations, as detailed in section 4.2.

In this work, all data preprocessing and resolution techniques were implemented in a home-made algorithm encoded with Matlab R2015a using Curve Fitting, Global Optimization and Statistics & Machine Learning toolboxes.

Initialization of the iterative process

• Data preprocessing Before solving the bilinear problem, outlier spectra had to be excluded from the resolution process in order to avoid chemically non-meaningful solutions. Spectra with values out of the linearity range of the MCT sensor (linearity threshold of 1.3 in absorbance) were therefore removed from the data (Fig. 3, Step 2 : deep blue). Spectra with a too low signal-to-noise ra- tio (highest absorbance value lower than 0.4 for this study) were also removed (Fig. 3, Step 3 : blue).

• Supervised Selection Method for Spectra (SSMS)

After the exclusion of outlier spectra by the previous data preprocessing stage, a classical approach would consist in two more steps: (i) determining of p, the number of compounds, and (ii) first guess for the matrix S.

However, the use of the s-ATR set-up induces artifacts (Table 1), resulting in biased spectra, which would not be identified using this classical approach.

Due to their singularity, these biased spectra would be assimilated to fictive compounds. This could lead to misjudge the number of compounds p and hence the matrix S of spectra.

To deal with this problem, the algorithm Supervised Selection Method for Spectra (SSMS) was developed to solve the whole issue at once: solving the two steps (i) and (ii) all together including the detection of s-ATR artifacts and the exclusion of related spectra.

SSMS uses SIMPLISMA, an iterative algorithm designed by Windig et Guilment [START_REF] Windig | Interactive self-modeling mixture analysis[END_REF] to select the most singular spectra out of a database. In SIM-PLISMA, at each iteration, the purest spectrum is selected as the one which forms the "most orthogonal" hypercube with the spectra already selected.

For more details about the SIMPLISMA algorithm, see [START_REF] Windig | Interactive self-modeling mixture analysis[END_REF][START_REF] Windig | Self-modeling mixture analysis of categorized pyrolysis mass spectral data with the SIM-PLISMA approach[END_REF][START_REF] Sánchez | Application of SIMPLISMA for the assessment of peak purity in liquid chromatography with diode array detection[END_REF].

SSMS consists in the following steps:

i First evaluation of the number of compounds P all based on a Principal Component Analysis (PCA). Then, a threshold has to be set to determine the number of compounds. In this work, the Kaiser's criterion (intensity of components higher than 1) was used to give a first estimation of P all [START_REF] Rencher | Principal Component Analysis[END_REF][START_REF] Wold | Principal component analysis[END_REF](Fig. 3, Step 4 : green). As a validation for this estimation of P all , a second criterion was based on the slope change in the plot of component intensity vs. component index (obtained from PCA). Segregation methods could also have been used but, as for PCA, they would also require a criterion or a threshold to be fixed.

Since spectra containing s-ATR artifacts are singular, they may be considered as pure spectra by SIMPLISMA and contained in P all .

ii Application of SIMPLISMA to select a number P 0 ≈ αP all of spectra out of the preprocessed database (i.e., initial database -outlier spectra) (Fig. 3, Step 5 : purple). The coefficient α ensures that the number P 0 of selected spectra is small enough to be easily and accurately checked by the operator, but large enough to contain at least one spectrum representative of each actual compound and of each unwanted spectrum.

iii Examination of the P 0 spectra, supervised selection and exclusion of the P 1 spectra presenting s-ATR artifacts among P 0 (Fig. 3, Step 6 : half light blue, half purple symbolizing the spectra first selected within P 0 (purple ones) and then excluded by the operator). At this stage, it is also possible to select and exclude spectra, which do not present any interest for a specific study (e.g., those of a mounting resin).

iv Back to the preprocessed data matrix (i.e., initial database -outlier spectra): all unwanted spectra, presenting a correlation coefficient > 0.95 with the aforementioned P 1 spectra are identified by statistical considerations in the preprocessed data matrix (i.e., initial database -outlier spectra) and excluded from the bilinear problem (Fig. 3, Step 7 : light blue). At this stage, a reduced matrix is obtained, which only contains relevant spectra with respect to the study.

v PCA on the reduced database (i.e., obtained after Step 7 ) to find p (Fig. 3, Step 8 : green).

vi Selection of the p most different spectra using SIMPLISMA on the remaining P 0 -P 1 spectra (Fig. 3, Step 9 ).

vii The p spectra selected previously form the first estimation of the matrix of spectra S ((Fig. 3, Step 10 : red, yellow and orange).

At this point, SSMS gives a first guess of p, the number of compounds, and of S their relative spectra. Like for every other statistical methods, the process of resolution has then to be applied with different numbers of compounds around this first estimation ( [...p -1, p, p + 1, ...]) (see [START_REF]Development of optical models and non-supervised methods to solve bilinear problems: application to vibrationnal mapping[END_REF]: chapter 2, section 3 for further details).

Multivariate Curve Resolution -Alternating Least Squares (MCR-ALS)

With a first estimation of the matrix S, it is now possible to solve the bilinear problem with a regular ALS method. Constraints and iterative process are detailed thereafter.

Constraints:

To obtain chemically acceptable solutions, different kinds of constraints can be taken into account:

Physical constraints Non-negativity of spectra and concentrations, normalization of spectra or sum of relative concentrations equal to one (closure) are quite easy to handle with an ALS process [START_REF] Tauler | Calculation of maximum and minimum band boundaries of feasible solutions for species profiles obtained by multivariate curve resolution[END_REF][START_REF] De Juan | Multivariate Curve Resolution (MCR). Solving the mixture analysis problem[END_REF].

Model constraints When an evolutive process is studied with a known physicochemical model, specific constraints arising from this model can be applied [START_REF] Juan | Multivariate Curve Resolution (MCR) from 2000: Progress in Concepts and Applications[END_REF].

Statistical constraints From statistical considerations, such as local rank analysis [START_REF] Juan | Local rank analysis for exploratory spectroscopic image analysis[END_REF][START_REF] Juan | Use of local rankbased spatial information for resolution of spectroscopic images[END_REF], the number of compounds can be imposed in the resolution process.

Spectra normalization and closure cannot be used together [START_REF] Tauler | Calculation of maximum and minimum band boundaries of feasible solutions for species profiles obtained by multivariate curve resolution[END_REF]. In this study, spectra have been normalized ( D i D i ) before ALS process but closure was applied during ALS to remain in a linear resolution. In addition, tolerances k were included in all the constraints, leading to the following inequalities:

• All absorbance values in the range [0, L sensor ], 0 -1 ≤ S ij ≤ L sensor + 1 (6)
With L sensor the upper limit of linearity of the sensor (the upper limit in absorbance corresponds to the inferior limit in transmittance).

• Non-negativity of concentrations and local rank constraints,

0 -2 ≤ C ij ≤ C local rank,ij + 2 (7)
Fixed Size Image Window-EFA algorithm (FSIW-EFA) [START_REF] Juan | Use of local rankbased spatial information for resolution of spectroscopic images[END_REF] was used to evaluate C local rank , which was a matrix only composed of 1 and 0 (absence of a compound was marked by a 0).

• Closure.

1

-3 ≤ p j=1 C ij ≤ 1 + 3 (8)
As the number of compounds was considered to be well-defined, the sum of relative concentrations was closed to one in all acquisitions.

Iterative process:

Under these constraints, the iterative process consisted in successive evaluations of C and S until convergence was achieved:

• Evaluation of C:

min C D -C.S t    0 -2 ≤ C ij ≤ C local rank,ij + 2 1 -3 ≤ p j=1 C ij ≤ 1 + 3 (9)
• Evaluation of S:

min S D -C.S t 0 -1 S ij L sensor + 1 (10)
• Evaluation of the quality of the reconstructed data (Lack of Fit):

LoF = D -C.S t 2 D 2 (11)
In this study, the function lsqlin in Matlab R2015a was used to deal with the constrained linear least-squares problem. If spectra normalization had been chosen instead of imposing closure, the function fmincon could have been used to deal with non linear constraints.

Results and discussion

SSMS applied on a granular composite with an ettringite binder

The new methodology developed in this work is illustrated step by step on a s-ATR map (48 X 82 pixels, i.e. 3936 spectra) acquired on a mineral It has also led to exclude 1654 spectra (42.02% of the database) because of a too low signal to noise ratio (Fig. 3 step 3 , Fig. 4.g). Then, using a PCA study on the remaining spectra, P all was found to be equal to 4 (Fig. 3 step 4 ). To make sure that at least one spectrum for each actual compound and one spectrum for each possible artifact was selected, α was set to 4. Hence, using SIMPLISMA, P 0 = 16 spectra have been selected in the database (Fig. 3 step 5 ). Thus, with α equal 4 (same order of magnitude as P all ), it became possible for the operator to accurately examine each of the P 0 = 16 spectra out of the 3936 initial spectra. As a result, P 1 = 1 spectrum presenting s-ATR artifacts has been identified by the operator among the P 0 spectra (Fig. 3 step 6 , Fig. 5.a). 54 spectra (1.37% of the database) were correlated to the previous spectrum and were therefore excluded from the bilinear problem (Fig. 3 step 7 , Fig. 4.f). Then, a PCA was used to find the number of compounds on the reduced database. Similarly to the previous estimation, p = 4 compounds were found (Fig. 3 step 8 ). Thus, the number of compounds defined before and after SSMS (i.e., before and after excluding the irrelevant spectra from the database) was the same (Fig. 6.a). In this case, SSMS led to exclude only 1.37% of the database, which explains why it did not impact on the number of compounds found by a PCA. However, if SSMS had been used to remove more spectra (e.g., all the spectra corresponding to a mounting resin), the number of compounds found after SSMS In an IR spectrum, each band is representative of the vibration of a covalent bond within its environment in the material. Thus, the four compounds could be clearly identified thanks to their characteristic bands, well described in literature (Table 2). The first compound was identified as silica (Fig. 7.a).

The second compound was identified as crystalline calcium carbonate with the presence around 1400 cm -1 and around 740 cm -1 of characteristic vibration bands of carbonate group (Fig. 7.b). The combination of compounds 1 and 2 formed the granular structure. The third compound was associated to the ettringite binder thanks to the OH bonds around 3630 cm -1 and to the sulfate bonds at 1088 cm -1 [START_REF] Olphen | Data Handbook for Clay Materials and Other Nonmetallic Minerals[END_REF]. The small shoulder at 1020 cm -1 (Fig. 7.c) may be assigned to Al -O bonds, due to the presence of gibbsite in the material.

Gibbsite is a classical phase formed simultaneously with ettringite. Due to its poor crystallinity, very few techniques are able to track gibbsite. This highlights the important role played by infrared analysis in phase identification. Compound 4 was identified as ettringite containing carbonate groups (Fig.

7.d).

The combination of compounds 3 and 4 formed the binder phase.

From the matrix C, chemical mapping of each compound may also be displayed (Fig. 8). The maps highlight the presence of different areas: zones where one compound was highly predominant (relative concentration close to 1, red to brown colours), zones where several compounds were present (green to yellow colours) and zones where spectra have been excluded from the resolution by SSMS (grey).

The main part of these grey zones, blue areas in Fig. 4.g, corresponds to spectra with a too low signal to noise ratio. This was due to an insufficient contact between the s-ATR crystal and the sample. This may have arisen from an insufficient planarity of the sample surface, from the sample roughness (including open pores) or from the presence of phases with different mechanical properties. In addition, the possible creep of the sample during long acquisitions should not completely be excluded. Indeed, as summarized in Table 1, the use of a s-ATR crystal requires a very flat and even surface.

Surprisingly, the remaining grey areas, deep and light blue in Fig. 4, are located in the middle of closed zones where one compound was highly predominant. Comparing Fig. 4 and Fig. 8, spectra in these areas were excluded from the analysis for two different reasons:

• absorbance values out of the linearity range of the sensor (Fig. 4.h,

6.06% of the database)

A high absorbance, thus a low reflectance (A ∼ 1/R) implies that there was an insufficient number of photons hitting the sensor during the acquisition.

This occurred in zones assigned to granular silica (compound 1). For such absorbent materials, a higher number of scans would permit to reduce the signal to noise ratio; a longer duration of acquisition (per scan) would permit to collect more photons and perform a reliable measurement.

• occurrence of s-ATR artifacts (Fig. 4.f, 1.37% of the database) Spectra assigned to these artifacts were only found right in the middle of zones where carbonate ettringite (compound 4) was predominant. Looking at one of the spectra excluded from the resolution process by SSMS (Fig. 5.a)

and at the spectrum corresponding to carbonate ettringite (compound 4, Fig. 7.d), the unique band of the first one (at 786 cm -1 ) matches perfectly with the main band of the latter (Si -O -Si vibration).

However, all the values displayed by the spectrum presented in Fig. 5.a are: (i)

within the linearity range of the sensor and (ii) above the defined threshold for the signal-to-noise ratio (higher absorbance value > 0.4). This implies that (i) the acquisition parameters (duration and scans number) were adapted and (ii) the local contact between the s-ATR crystal and the material was properly done. Therefore, the relative intensities displayed by the s-ATR artifacts spectrum can be considered as correct: there is no other hidden band in the spectrum (for instance due to a scale effect). Thus, it was considered that this spectrum really contained only one band, which is physically non possible for any material. Finally, it was hard to determine the physical origin of such s-ATR artifacts spectra. One explanation could arise from the occurrence of distortions in spectra acquired in reflection modes due to Mie scattering effect as shown by Bassan et al. [START_REF] Bassan | Reflection contributions to the dispersion artefact in FTIR spectra of single biological cells[END_REF]. Another comprehensive study on distortion effects occuring in reflection [START_REF]Development of optical models and non-supervised methods to solve bilinear problems: application to vibrationnal mapping[END_REF] showed that they also may stem from material dispersion.

Implications of the use of SSMS and s-ATR acquisitions

All in all, a new supervised method has been developed in this work:

SSMS combined with ALS. This method permitted to handle a set of 3936 FT-IR spectra to obtain a relevant chemical mapping of compounds present in an ettringite binder.

In this work, a PCA on the hyperspectral database led to the same number of compounds with or without the exclusion of the s-ATR artifacts spectra thanks to SSMS. But, without SSMS, the 4 selected spectra and their related maps had no chemical meaning. Moreover, as already discussed, SSMS can also be used to exclude spectra of no interest for a specific study. In this case, the number of compounds found by a PCA would be changed after SSMS.

In SSMS, thresholds and a correlation coefficient have to be adjusted for each study. Since the operator has to intervene in the process, SSMS requires the operator to have enough hindsight and expertise for his study. However, such a requirement holds true for all statistical methods applied on physical problems.

On the other hand, the main interest of SSMS lies precisely in the fact that it is based on statistical considerations. Thus, SSMS can be used to identify all kinds of artifacts in all kinds of database without any restriction on material nature and characterization mean; more generally, SSMS may be used for all types of problems with few adaptations.

The s-ATR crystal is an interesting set-up for the acquisition of valuable data to map the relative concentrations of compounds in a material. Thanks to this set-up, no relative motion occurred between the s-ATR crystal and the sample all along the acquisition: cross-contamination and successive stamps, experienced in previous studies on materials with similar properties [START_REF] Bonnal | Towards chemical imaging: Fourier transform infrared mapping on organo-mineral materials[END_REF], were avoided here. However, the s-ATR crystal left one unique imprint of around 500 µm in diameter in the sample (Fig. 2.b). Noteworthy, this mark could be used to easily find the imaged zone for complementary characterizations (such as SEM-EDX).

In addition, and as discussed in the previous section, some of the acquired spectra presented s-ATR artifacts, which remain unexplained until now.

As highlighted in Table 1, using the s-ATR set-up also requires the sample to have a very low roughness and a very flat surface for the contact between the crystal and the sample to be perfect on a relatively large surface area (around 1 mm 2 ). This requires a meticulous preparation and polishing of the surface of the sample prior to analysis. On this aspect, one very interesting feature of the SSMS approach is illustrated on the granular composite with ettringite binder in Fig. 4: this new method enables to highlight zones of the sample, where the surface state has to be improved (Fig. 4.g), as well as zones where the acquisition parameters have to be optimized (Fig. 4.h) to map more completely the sample. In other words, SSMS proved to be very efficient to identify issues in specific zones: in addition to permit to obtain relevant chemical maps of a material, SSMS can also be used as a powerful tool to adapt one's method (sample preparation, acquisition parameters) for the specific zones one wants to map.

Conclusions

A new supervised method, called SSMS, has been developed to deal with the analysis of hyperspectral data.

Experimental acquisitions may lead to unexpected biased information, which can have different origins, such as the acquisition technique, the environment, the analyzed sample. To obtain relevant information from the database, it is fundamental to be able to exclude all of these biased data without impacting on the informative ones. This selection is easily carried out with classical filtering methods when the origin and the characteristics of the biased data are known. SSMS is a powerful tool to handle this problem in the general case and exclude biased data when all their sources cannot be predicted.

Moreover, SSMS is a preprocessing method, and thus can be coupled with a reliable physical model to obtain quantitative chemical information. In addition, the combined use of SSMS and of a physical model permits to identify the sources of the biased data. Thus, it becomes possible to improve the experimental method (sample preparation, acquisition parameters...).

All steps involved in SSMS are described and justified in this article. The interest and the gain provided by SSMS is illustrated on the analysis of data acquired with a FT-IR microscope using a disregarded set-up (static-ATR).

Relevant chemical maps of a complex inorganic material are obtained coupling FT-IR microscopy data with the Beer Lambert law. Maps are analyzed, sources of biased data are identified thanks to SSMS and discussed.

Finally, such a supervised preprocessing opens a new route to obtain more reliable quantitative information and to improve the experimental protocols.

Figure 1 :

 1 Figure 1: Schematic view of FT-IR microscopy set-ups: a) Specular Reflection, b) ATR Crystal and c) Static ATR.

  plied on the crystal to ensure a neat material/crystal interface. This induces stresses at the interface (Fig.1.b).

FTa

  Pixel size; b CC: Cross-Contamination; c Perturbations due to heterogeneous scattering; d May disturb the structure or deform samples; e 's-ATR' artifacts will be discussed in section 5 of this article.

Figure 2 :

 2 Figure 2: Optical micrography of the granular composite with ettringite binder: a) surface state before acquisition, and b) s-ATR crystal imprint in the material after s-ATR acquisition.

A

  FT-IR microscope Nicolet T M iN 10 from ThermoFisher Scientific (USA) has been used. The only set-up used in this study was the static-ATR, using a Germanium crystal (refractive index: 4, top diameter: 9.525 mm, bottom diameter: 0.350 mm). The aperture was 100 µm × 100 µm. The focus of the beam due to combined use of the Cassegrain reflector and of the Ge crystal led to a projected size of the IR beam of 25 µm × 25 µm. A Mercury Cadmium Telluride (MCT)

Figure 3 :

 3 Figure 3: Schematic view of data preprocessing (steps 1 to 3) and initialization with SSMS (steps 4 to 10). x, y, m and p are the numbers of acquisitions in the two spatial directions ( x, y), the number of wavenumbers and the number of compounds respectively. Step numbers and color code defined here are recalled in the text to explain the whole process. The figure shows how irrelevant spectra (in color) are excluded from the database, step after step. The color code is consistent with colors used in Fig.4 & Fig. 5.

Figure 4 :

 4 Figure 4: Spatial distribution after SSMS method of spectra assigned to: a) compound 1 in yellow, b) compound 2 in orange, c) compound 3 in red, d) compound 4 in brown, e) a mixture of several compounds in green, f) s-ATR artifacts in light blue. Spectra with: g) a too low signal to noise ratio and h) values above linearity range are represented in and deep blue respectively. A pixel is assigned to one of the previous items if their spectra match (correlation coefficient > 0.95). The projected pixel size is about 6.25 × 6.25 µm 2 per pixel, the map is composed of 48 × 82 pixels.

Figure 5 :

 5 Figure 5: Infrared spectra of the granular composite with s-ATR set-up. a) Spectrum identified by the operator among the P 0 spectra as corresponding to s-ATR artifacts (step 6; in this example only P 1 = 1 spectrum was excluded from the P 0 spectra) and b) first estimation of the matrix S obtained by SSMS prior to MCR-ALS, as schemed in Fig.3, Step 10: compound 1 in yellow, compound 2 in orange, compound 3 in red and compound 4 in brown.21

Figure 6 :

 6 Figure 6: a) Intensities of the first components (PCA) before and after SSMS b) evolution of the Lack of Fit criterion vs. ALS iteration.

Figure 7 :

 7 Figure 7: Normalized spectra obtained after SSMS coupled with ALS resolution: a) compound 1, b) compound 2, c) compound 3, and d) compound 4.

Figure 8 :

 8 Figure 8: Maps of relative concentrations obtained by a s-ATR acquisition coupled with SSMS-ALS resolution for the granular composite with an ettringite binder: a) compound 1 assigned to silica, b) compound 2 -calcium carbonate, c) compound 3 -silicate ettringite + gibbsite, and d) compound 4 -carbonated ettringite. Analysed surface area was 300 × 515 µm 2 . contourf function on Matlab R2015a has been used to obtain smoothed representations in the mapping.

Table 1 :

 1 Summary of FT-IR microscopy set-ups to obtain FT-IR maps in reflection

Acknowledgments:

The authors would like to thank R. Pujol (Univ.

Lyon, INSA Lyon) for fruitful discussions.

Funding: This work was supported by the French Ministry of Higher Education and Research and ENS Paris-Saclay.

would have been different than the one found before. In addition, more than the determined number of compounds, SSMS brought a real benefit in the determining of the spectra of S: without SSMS, the spectrum of the second compound obtained with SIMPLISMA was an artifact spectrum (data not shown); whereas using SSMS, the first four spectra corresponding to the p = 4 compounds were all chemically meaningful (Fig. 5.b).

To save time, SIMPLISMA was performed on the P 0 -P 1 = 15 purest spectra rather than on the reduced database (Fig. 3 step 9 ). Finally, the matrix S was built (Fig. 3 In a first approximation, the spatial distribution of the four compounds was found with a correlation coefficient higher than 0.95 (Fig. 4.a,.b,.c & .d).

Chemical maps: computation and analysis

The linearity limit of the MCT sensor has been taken equal to L sensor = 1.3 in absorbance in the ALS resolution. To release the constraints, 1 2 and 3 were fixed equal to 10 -4 . The evolution of the iterative process is illustrated by the Lack of Fit criterion. As shown in Fig. 6.b, convergence of the iterative process was achieved after 13 iterations. During the convergence, spectra selected by SSMS evolved (band shifts, band intensities, smoothing).

After the 13 th iteration, only non-significant modifications occurred.

Once the bilinear problem was solved, matrices S and C were obtained.

The matrix S contained spectra corresponding to the p = 4 compounds (Fig. 7).


Lestriez

D Mazouzi

R Grissa

M Paris

Z Karkar

L Huet

D Guyomard

L Roué

T Devic

B Lestriez
email: bernard.lestriez@cnrs-imn.fr

CMC-citric acid Cu(II) cross-linked binder approach to improve the electrochemical

Keywords: silicon, carboxymethyl cellulose, citric acid, copper, coordination chemistry

diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The use of silicon as negative electrode active material in Li-ion batteries could significantly increase their energy density compared to commercial ones based on graphite.

However, several difficulties associated with the strong volume expansion and contraction of the active material during its lithiation and delithiation have prevented their implementation in commercial batteries. [START_REF] Obrovac | Alloy negative electrodes for Li-ion batteries[END_REF] Indeed, these volume variations cause the passivation layer formed on the surface of the active material (the solid-electrolyte interphase (SEI)) to rupture, leading at each cycle to additional degradation of the electrolyte on the reducing surface of lithiated silicon. Moreover, these volume variations lead more or less rapidly during cycling to a mechanical failure (loss of cohesion/adhesion) of the electrodes and a drop in capacity. For many years and until very recently, many studies have been carried out and have led to significant progress in understanding these problems and in the way to solve them at least partially, thanks to new materials, additives for electrolytes, binders and conducting additives for electrode formulation optimization. [START_REF] Kasavajjula | Nano-and bulk-silicon-based insertion anodes for lithium-ion secondary cells[END_REF][START_REF] Szczech | Nanostructured silicon for high capacity lithium battery anodes[END_REF][START_REF] Wu | Designing nanostructured Si anodes for high energy lithium ion batteries[END_REF][START_REF] Su | Silicon-Based Nanomaterials for Lithium-Ion Batteries: a review[END_REF][6][START_REF] Obrovac | Si-alloy negative electrodes for Li-ion batteries[END_REF] Polymeric binders play an active role in maintaining the electrode morphology and in helping to stabilize cracked silicon particles along with the SEI layer. [START_REF] Mazouzi | Critical roles of binders and formulation at multiscales of silicon-based composite electrodes[END_REF][START_REF] Li | Water Soluble Binder, an Electrochemical Performance Booster for Electrode Materials with High Energy Density[END_REF][START_REF] Chen | Exploring Chemical, Mechanical, and Electrical Functionalities of Binders for Advanced Energy-Storage Devices[END_REF][START_REF] Kwon | The Emerging Era of Supramolecular Polymeric Binders in Silicon Anodes[END_REF][START_REF] Bresser | Alternative binders for sustainable electrochemical energy storage -the transition to aqueous electrode processing and bio-derived polymers[END_REF] The first class of suitable binders for silicon-based electrodes are natural and/or water soluble. They possess polar groups (e.g. -COOH, -OH, -NH2) able to strongly interact with or chemically graft to the active particle surface through hydrogen or covalent bonds. They are able to maintain a good level of mechanical strength when soaked in the liquid electrolyte. They have good filmforming ability to deposit as conformal coating at the surface of the silicon particles and possess acceptable Li + conductivity (thanks to the presence of polar groups) to work as protective artificial SEI. [13] Self-healing property, based on strong but noncovalent binder-binder and binder-silicon particles supramolecular interactions, such as ion-dipole and hydrogen interactions, is considered as mandatory for durable cycling because these interactions are permanently stressed by the silicon volume expansion and contraction. [14] Finally, ramified or cross-linked macromolecular architectures are considered superior to linear ones because the presence of numerous ramifications shall result in superior adhesion and cohesion strength. [START_REF] Kwon | The Emerging Era of Supramolecular Polymeric Binders in Silicon Anodes[END_REF] The second class of suitable binders are aromatic ones (including electronically conductive polymers). Their in situ electrochemical reduction lead to a hydrogen containing carbon coating around the silicon particles, reducing electrolyte decomposition and improving electronic contact. [START_REF] Obrovac | Si-alloy negative electrodes for Li-ion batteries[END_REF] Whatever the binder type, the size and the shape of the carbon conductive additives are important to level the mechanical stress within the stacking of particles. The processing conditions of the electrode slurry plays a lot on the homogeneity in the distribution of the different materials and thus on the efficiency of the binder and the carbon additive. Finally, the interface with the copper current collector can be designed through chemical or mechanical treatments to increase the adhesion with the electrode. [START_REF] Mazouzi | Critical roles of binders and formulation at multiscales of silicon-based composite electrodes[END_REF] We recently discovered a simple post-processing treatment that improves very significantly the mechanical strength and the cyclability of silicon-based composite electrodes made with an acidic linear non-aromatic aqueous binder. This treatment, called maturation, consists of storing the electrode under humid atmosphere (about 80% relative humidity (RH))

for at least 2-3 days before drying and cell assembly. [START_REF] Hernandez | A film maturation process for improving the cycle life of Si-based anodes for Li-ion batteries[END_REF][START_REF] Hernandez | A facile and very effective method to enhance the mechanical strength and the cyclability of Si-based electrodes for Li-ion batteries[END_REF] Compared to a standard (nonmatured) electrode, a matured electrode shows: (i) in its pristine and dry states, a significantly higher hardness, peel and scratch resistance, and (ii) upon electrochemical cycling, a much better resistance to cracking and delamination from the current collector, lower and more reversible volume expansion. [START_REF] Vanpeene | Dynamics of the morphological degradation of Si-based anodes for Li-ion batteries characterized by in-situ Xray tomography[END_REF] The effectiveness of this maturation treatment was observed for negative electrodes made with various silicon powders and for binders bearing carboxylic functional groups, either carboxymethyl cellulose (CMC) mixed with citric acid (CA) or polyacrylic acid (PAA). The effectiveness of maturation was also observed with respect to the calendering of silicon-based electrodes. Calendering is essential to achieve a high volume fraction of active material, and a high coating volumetric capacity. [START_REF] Du | High Energy Density Calendered Si Alloy/Graphite Anodes[END_REF] However, this mechanical treatment is observed to deteriorate the mechanical strength of the electrode, likely by degrading the bonds between the binder and/or the current collector surface or the binder itself, inducing a decrease of the cycling stability. If applied as a post-calendering treatment, the maturation step restores and even improves the mechanical strength of the electrode, which makes possible to cycle calendered electrodes with high active mass loading and low porosity. [START_REF] Karkar | How silicon electrodes can be calendered without altering their mechanical strength and cycle life[END_REF] The improvement of the electrode cohesion with maturation was attributed to the fortification of the binder connections between silicon particles, as a result of some dewetting of the binder layer adsorbed on the free surface of the silicon particles to concentrate at the contact points between silicon particles. The improvement of the electrode adhesion to the copper current collector was attributed to the formation of copper-carboxylate coordination bonds between the current collector and the electrode binder, as a result of an atmosphericinduced corrosion of copper activated by the acidic functional groups of the binder. [START_REF] Hernandez | A facile and very effective method to enhance the mechanical strength and the cyclability of Si-based electrodes for Li-ion batteries[END_REF] In this follow-up study, a better understanding of the maturation process is achieved. In particular, the critical role of the atmospheric-induced corrosion of the current collector is addressed. It is discovered that oxidized copper species can migrate into the electrode to physically crosslink the binder phase through the formation of copper carboxylate coordination bonds. Very interestingly, the pre-addition of a small amount of copper salt in the electrode slurry allows to reach similar level of performance improvement than maturation, but without the need of exposing the electrode for several days to humid atmosphere.

Experimental

Materials

Ball-milled Si powder was used as active material. Si powder (99.999%, 20 mesh, Materion) was loaded and sealed under argon atmosphere into a 55 ml stainless-steel vial containing two 11.1 mm/5.4 g and one 14.3 mm/11.5 g diameter/mass stainless-steel balls. The ball-to-powder mass ratio was 5:1. Milling was performed for 20 h using a SPEX 8000 mixer (1080 rpm). The as-milled Si powder consists of micrometric agglomerates (median size ∼6 µm, SBET ∼12 m 2 g - 1 ) made of sub-micrometric particles more or less welded together [START_REF] Gauthier | A low-cost and high performance ball-milled Si-based negative electrode for high-energy Li-ion batteries[END_REF]. The conductive additive was ultrathin platelets of graphite consisting in the as-received state of short stacks of graphene sheets (diameter ∼15 µm, thickness ∼5-10 nm, SBET = 74 m 2 g -1 , GM15 grade from XGSciences). The binder was carboxymethyl cellulose (CMC) (DS = 0.9, Mw = 700 000, Sigma-Aldrich). Citric acid (CA) and KOH (Sigma-Aldrich) were used to prepare the pH3 buffer solution (0.17 M citric acid + 0.07 M KOH) as slurry medium.

Electrode preparation

For the standard electrode, a slurry was prepared by mixing 160 mg of silicon, 24 mg of GM15 conductive additive in 1 mL of CMC binder in pH3 buffer solution using a Fritsch Pulverisette 7 mixer at 500 rpm for 1 h with 3 silicon nitride balls (9.5 mm diameter). The pH3 buffering of the slurry promotes covalent bonding (esterification) between -OH groups present on the surface of Si particles and -COOH groups of CMC, which improves the mechanical and electrochemical stabilities of the electrode. [START_REF] Mazouzi | Silicon composite electrode with high capacity and long cycle life[END_REF][START_REF] Tranchot | Impact of the slurry pH on the expansion/contraction behavior of silicon/carbon/carboxymethylcellulose electrodes for Li-ion batteries[END_REF] The slurry was tape casted by using a doctor blade onto a 25 µm thick copper current collector (PI-KEM, purity 99.9%, cold-rolled Cu foil) and dried 12 h at room temperature and then 2 h at 100°C under vacuum. Citric acid (CA) and KOH salts, which are not eliminated upon drying, contribute to the mass of the electrodes. The Si areal mass loading was typically 1.4 to 1.6 mg cm -2 . Matured electrode was obtained by storing the standard electrode under humid atmosphere (about 80% RH) for 3 days before final drying at 100°C and cell assembling. For the Cu-containing electrode, the slurry was prepared as for the standard electrode, except that the 1 mL of CMC binder in pH 3 buffer solution also contains a certain amount of CuSO4 (CuSO4,5H2O, Alfa Aesar, purity 99.9%).

Reference samples were also prepared for the sake of complementary characterizations.

For infrared (IR) spectroscopy and X-ray photoelectron spectroscopy (XPS) analyses, Si/CMC/CA/KOH/CuSO4 samples were prepared in the same way as for their corresponding electrodes but without the carbon additive. After drying at 100°C under vacuum, a small amount of the film was scratched from the copper current collector. For XPS analysis, a Si/CMC sample referred as pH7 was prepared without using a CA/KOH buffer solution. Another sample analogous to the binder phase of a Cu-containing electrode was prepared with CMC/CA/KOH/CuSO4 in the same proportion as for the Cu-0.05 electrode.

Characterization

Na, K and Cu contents in the matured electrodes were measured by inductively coupled plasma optical emission spectroscopy (ICP-OES, 5110 ICP-OES Instrument).

Diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy characterizations were done with a vertex 70 Bruker spectrometer equipped with a Harrick HVC accessory, in the 400-4000 cm -1 range. No baseline correction was applied.

Solid state magic angle spinning nuclear magnetic resonance (MAS NMR) spectra were acquired on a 500 MHz Bruker Avance III using a 4mm MAS probe. For both 1 H- 29 Si and 1 H-13 C Cross-Polarization (CP) spectra, the contact time was set to 2 ms. The recycle delay between scans was set to 2 s and the MAS frequency to 11 kHz and 10 kHz for 13 C and 29 Si acquisitions, respectively. TPPM15 1 H decoupling scheme was used during all acquisitions with radiofrequency strength of 60 kHz. Spectra were referenced against TMS (tetramethylsilane).

XPS measurements were performed with a Kratos Axis Nova Instrument, using a monochromated Al Kα source (1486.6 eV) operating at 300 W. The instrument base pressure was 5 × 10 -10 Torr. The sample area analyzed was about 700 µm × 300 µm. A pass energy (PE) of 80 eV, with an all over instrumental resolution of 0.9 eV measured on Fermi edge, was used to acquire wide range survey spectra. A PE of 40 eV was used to acquire narrow spectra of the C 1s, O 1s, Si 2p, Cu 2p and Na 1s levels with an all over instrumental resolution of 0.55 eV measured on Fermi edge. All data were acquired using charge compensation with low energy electrons gun in order to have homogenous surface potential. This is necessary to have accessible chemical information. XPS data were analyzed using the CasaXPS software (version 2.3.19) using Gaussian/Lorentzian (30% Lorentzian) line shapes and Shirley background correction. All spectra were calibrated with Hydrocarbon C1s photoemission set to 285.0 eV binding energy. In order to check for reproducibility, all XPS measurements are carried out in three independent areas of the samples.

All NMR, IR and XPS characterizations were done on samples dried at 100°C under vacuum.

Electrochemical measurement

Swagelok type half cells were assembled with the silicon electrodes (0.785 cm 2 disc) in a glovebox under argon atmosphere. A borosilicate glass-fiber (Whatman GF/D) was used as a separator and was soaked with an electrolytic solution of 1 M LiPF6 in ethylene carbonate (EC) and dimethyl carbonate (DMC) (1:1) with 10 wt. % fluoroethylene carbonate (FEC) (Solvionic, purity 99.9%). A lithium foil (Aldrich, purity 99.9%) was used as the counter and reference electrode. The cycling tests were performed at room temperature in galvanostatic mode at full capacity over the potential window of 1-0.005 V versus Li + /Li with a VMP multichannel electrochemical workstation (Bio-Logic). The current density was fixed at 96 mA per g of Si (C/40) for the first cycle, then at 193 mA g -1 Si (C/20) for cycles 2 to 5 and then at 385 mA g -1 Si (C/10) for the following ones. The gravimetric capacities of the electrodes are given per mass of Si.

Results

Table 1 gives the as prepared standard and Cu-containing electrodes compositions. The composition of the matured electrode is expected to be identical to the standard one. However, its composition in Na, K and Cu was measured by ICP-OES (see below). The molar ratio of the amount of copper to the amount of carboxylate groups is also given in Table 1. This ratio is calculated as follows:

/ = 3 × + 0.9 ×
where nCA is the number of moles of citric acid, which has three carboxylates per molecule, and nHCMC is the number of moles of CMC repetition (anhydroglucose) units, which has 0.9 carboxymethyl groups per unit.

ICP-OES measurements were done to quantify the elemental composition in K, Na and Cu of the electrode matured for various durations. Results are given in Table 2. K and Na are internal standard. They come from the citric acid/KOH buffer and the Na-CMC binder, while

Cu was not part of the electrode formulation in this case. We assume that its presence is not due to the mechanical removing of the electrode from the current collector as we took care to not scratch the collector. Otherwise Cu would be heterogeneously distributed, in contradiction with the XPS analysis which confirm the homogeneity of the electrode. The most likely origin of the presence of copper in these electrode is the result of its atmospheric corrosion by the organic acids present in the electrode, respectively citric acid and the acidic form of carboxymethyl cellulose. [START_REF] Hernandez | A facile and very effective method to enhance the mechanical strength and the cyclability of Si-based electrodes for Li-ion batteries[END_REF][START_REF] Gil | Initial Atmospheric Corrosion of Copper Induced by Carboxylic Acids[END_REF] Indeed, traces of corrosion were previously observed at the surface of the collector. [START_REF] Hernandez | A facile and very effective method to enhance the mechanical strength and the cyclability of Si-based electrodes for Li-ion batteries[END_REF] We assume that the copper ions released during this atmospheric corrosion could have migrated into the humidified electrode during maturation. The amount of Cu in the electrode increases almost linearly with the duration of maturation to reach 1.67 wt.% of the total electrode mass after 7 days of maturation, which corresponds to / equal to 0.18.

One can notice that the amounts of K and Na stay constant, which attests of the good reproducibility of the composition of the electrode samples. Surprisingly, the un-matured electrode also contains traces of Cu. This might reflect the small corrosion of the current collector in contact with the acid electrode slurry during the casting and the drying steps.

Finally, by maturing the electrode for 2-3 days or deliberately adding about 2.5 wt.% of CuSO4 ( / = 0.11) in the electrode, one has the same electrode composition in the end, except for sulfate ions.

The electrochemical behavior (discharge capacity vs. cycle number) is shown in Figure 1 for the three types of electrodes. It confirms the much better cyclability of the matured electrode compared to the standard case, as already shown in previous works. [START_REF] Hernandez | A film maturation process for improving the cycle life of Si-based anodes for Li-ion batteries[END_REF][START_REF] Hernandez | A facile and very effective method to enhance the mechanical strength and the cyclability of Si-based electrodes for Li-ion batteries[END_REF][START_REF] Vanpeene | Dynamics of the morphological degradation of Si-based anodes for Li-ion batteries characterized by in-situ Xray tomography[END_REF][START_REF] Karkar | How silicon electrodes can be calendered without altering their mechanical strength and cycle life[END_REF] The Cu-containing electrodes also display better cyclability than the standard electrode. The discharge capacity retained after 100 cycles for the different electrodes is plotted against the molar ratio of the amount of copper to the amount of carboxylates in Figure 2. The trend is very clear. The retained capacity evolves considerably with the increase of / , up to a critical value of approximately 0.11. For a higher ratio, there is no longer any improvement in performance. The particular case of the matured electrode coincides with the trend curve of the electrodes in which copper has been deliberately added. It should be noted that in our previous work [START_REF] Hernandez | A facile and very effective method to enhance the mechanical strength and the cyclability of Si-based electrodes for Li-ion batteries[END_REF], we observed that 2 days were enough to get the maximum benefits from maturation. Leaving the electrode longer did not decrease or improve its cycling.

This result is explained with this Figure 2 which shows that beyond a critical copper content there is no change in performance.

The 1 H- 13 C CP-MAS NMR spectrum of a reference sample (in green) that does not contain citric acid but only Si particles and CMC is in agreement with the literature report for CMC [14] with resonances of C1 (carboxylate/ic group) at 179 ppm, C2 at 106 ppm, and substituted C3 at 64 ppm, respectively (Figure 3a). A first possible explanation for this loss of signal is an increase of mobility of both CMC and citric acid after maturation which would impede the polarization transfer from 1 H to 13 C in the CP experiment. However, such an explanation is ruled out since no more signal was obtained by running a 1 H-13 C CP-MAS experiment at lower temperature (230K) for which residual mobility is too low to hinder CP transfer. Therefore, the most likely explanation for the loss of signal is the commitment of a fraction of the carboxylate groups belonging to both species in coordination bonds with copper ions throughout the whole electrode volume. Indeed, paramagnetic Cu(II) will ruin the CP polarization transfer by strongly decreasing the rotating frame spin lattice relaxation times (T1ρ).

Additional information can be obtained from 29 Si NMR spectroscopy. The 1 H- 29 Si CP-MAS spectra of the reference, standard and matured electrodes look similar (Figure 3b), all composed of three resonances. The ones at -80 ppm and -100 ppm originate from the bulk and the surface of the silicon particles, respectively [START_REF] Pietraβ | 29Si High Resolution Solid State Nuclear Magnetic Resonance Spectroscopy of Porous Silicon[END_REF]. The broad resonance at about -10 ppm suggests the formation of Si-C linkages (e.g. silane). The unexpected signal at -167 ppm in the spectrum of the standard electrode could be tentatively attributed to Si5H12 molecules. [START_REF] Hahn | Si-NMR-spektroskopische Untersuchungen von geradkettigen und verzweigten Silanen[END_REF] These silanes could be formed during the slurry mixing by high energy ball-milling through scission of the CMC chains and grafting to the silicon particles surface. In contrast with the 1 H- Si ester bonds formed between the carboxylate groups of CMC and/or CA and the silanols at the silicon particles surface [START_REF] Hochgatterer | Silicon/Graphite Composite Electrodes for High-Capacity Anodes: Influence of Binder Chemistry on Cycling Stability[END_REF][START_REF] Delpuech | Critical Role of Si Nanoparticles Surface on Lithium Cell Electrochemical Performance Analyzed by FTIR, Raman, EELS, XPS, NMR and BDS Spectroscopies[END_REF] in agreement with the concomitant decrease of the band located at ca. 1990 cm -1 and attributed to SiOH groups (see the reference Si material Figure 4a).

Nevertheless, the presence of purely organic R-C(=O)-O-R' ester formed by the reaction between CMC and CA is also possible. [START_REF] Koo | Highly Cross-linked Polymeric Binder for High-performance Silicon Negative Electrodes in Lithium Ion Batteries[END_REF] There are also two less intense peaks centered at ca. 1610 cm -1 and 1405-1425 cm -1 , and corresponding to the anti-symmetric (νasym(CO2 -) and symmetric vibrations (νsym(CO2 -)) of the carboxylate groups respectively. With maturation, the intensity of the peak at 1728 cm -1 decreases while that of the carboxylate centered at 1610 cm - 1 increases. A very similar trend is observed upon the deliberate addition of CuSO4: the band at 1720-1730 cm -1 decreases while the band at 1610 cm -1 increases (Figure 4b). These changes indicate that maturation caused the hydrolysis of the ester bonds, restoring carboxylate moieties. Knowing that carboxylate groups interact more strongly with copper(II) than alkaline ions, these groups are very likely involved in citrate-copper and CMC-copper coordination bonds. Asymmetric and symmetric carboxylates bands are known to be sensitive to the neighboring cations, and thus a good probe of the coordination. [START_REF] Liu | Copper(II) carboxymethylcellulose (CMC-CuII) as an efficient catalyst for aldehyde-alkyne-amine coupling under solvent-free conditions[END_REF] Unfortunately, considering the copper to carboxylate ratio in play (here 0.05 to 0.43), both bands likely contain here not only contributions from copper(II) carboxylates bonds, but also sodium and potassium carboxylate bonds precluding any complete analysis.

Nevertheless, some changes are visible: first, upon increasing the amount of CuSO4, whereas the position of the asymmetric band remains unchanged, a shift of the symmetric vibration band from ca. 1405 to 1425 cm -1 is observed (see insert on contribution [START_REF] Sivakumar | Characterization of MHz pulse repetition rate femtosecond laser-irradiated gold-coated silicon surfaces[END_REF][START_REF] Lisovskyy | Transformation of the structure of silicon oxide during the formation of Si nanoinclusions under thermal annealings[END_REF][START_REF] Liu | Selective area in situ conversion of Si (0 0 1) hydrophobic to hydrophilic surface by excimer laser irradiation in hydrogen peroxide[END_REF]. It is first worth noting that both elemental and oxidized silicon components relative to the electrode prepared at pH7 (figure 5b) present a higher FWHM (Full Width at Half Maximum) than the ones relative to the electrodes prepared at pH3 (figures 5e and h). The former electrode presents also a higher global oxidized Si/elemental Si ratio. This can be attributed to the presence of more intermediate surface species SixOy at pH7, which are eliminated at acidic pH. Note that the Si2/Si3 ratio increases from pH7 to pH3 (from 0.4 to 1.1), which is again in agreement with the formation of Si-based ester at acidic pH. This ratio decreases (from 1.1 to 0.3) after the electrode maturation, supporting again the partial hydrolysis of the Si-ester bonds.

The copper element is detected on the matured electrodes, and to a lesser extent in the standard ones (pH3 and pH7) (Figures 5c, f and i respectively). This is in agreement with the ICP results and corroborates our hypothesis of copper migration for the matured electrode. The Cu 2p core peaks are also split in two components due to the spin-orbit coupling phenomena (Cu 2p3/2 and Cu 2p1/2 with an area ratio of 2). It is worth to mention that the analysis of Cucontaining samples by XPS is challenging because of the copper reduction under the X-ray beam, impeding a quantitative analysis of the different oxidation states, especially in copperpoor samples. In order to be able to carry a comparative study, we fixed the measurement time constant for all the samples (30 min) and thus assume that the amount of copper reduced under the beam is the same for all the samples. Note that the metallic copper is characterized by a Cu 2p3/2 component appearing at 933.1 eV. However, the Cu(II) environment is generally recognized by a Cu 2p3/2 component at 935.0 eV and a first satellite peak at 940.9 eV [START_REF] Biesinger | Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Sc, Ti, V, Cu and Zn[END_REF]. If we consider the Cu 2p core peaks of the standard (pH3 and pH7), both contain a low amount of copper (0.2-0.3 at%), all in the reduced state. In line with the ICP measurement, this value reaches 0.7 at% for the maturated electrode, in which both reduced and oxidized copper are detected. Finally, the AC-CMC-Cu reference sample (figure 5k) contains a high proportion of copper (9.5 at%), with 0.4 at% the reduced state. All these analyses first suggest than in our experimental conditions, ca. 0.4 at% Cu is reduced under the beam, but also that copper is at least partially in the +II oxidation state in the maturated electrode.

XPS analyses were also conducted on the Si-electrodes prepared on a Cu-free substrate and to which were added different amounts of CuSO4. The corresponding Si 2p XPS spectra are shown in Figure 6. The same silicon environments Si1, Si2 and Si3 are found as for the Sielectrodes prepared on a copper current collector (Figure 5). Nevertheless, we note a shift of the global Si spectra to higher binding energies with the addition of higher amounts of CuSO4.

We assume that this phenomenon rather originates from a more oxidant environment than from the formation of new species. Note that, unlike for the matured Si-electrode (Figure 5e), the Si2/Si3 ratio remains almost constant with the addition of CuSO4. Indeed, these electrodes were not exposed to humid atmosphere contrarily to the matured electrode, and thus numerous ester bonds remain, in fair agreement with the IR results.

The C 1s XPS cores peaks corresponding to the Si-electrodes containing different amounts of CuSO4 (Figure S1) show also four carbon environments (C1, C2, C3 and C4).

Nevertheless, in this case, the evolution of the C4/C3 ratio seems to be more complex. Indeed, a different mechanism seems to be involved in the copper reactivity with the Si-based electrode compared to the case of a matured electrode where the Si-based esters are partially hydrolyzed to form Cu-based ester and RCOO -carboxylates. This is again in agreement with IR analysis, which suggests different coordination patterns in the matured electrode than in the electrodes containing different amounts of CuSO4 deliberately added. Given that the Si and Cu-based esters contributions are not dissociable (contribution C4), it is challenging to understand this different mechanism from the carbon peaks evolution. The Cu amount detected by XPS for this samples series of Si-based electrodes performed on a Cu-free substrate (Figure S2) is in agreement with the added amount of CuSO4. Nevertheless, as previously detailed, it is quite challenging to consider the Cu oxidation number evolution given that this latter is reduced to Cu-metal under the X-ray beam.

Z. Yan and M.N. Obrovac [START_REF] Yan | Selecting inactive materials with low electrolyte reactivity for lithium-ion Cells[END_REF] have found that the electrolyte is reduced in nonnegligible quantity at low potential on metallic copper. This electrolyte reactivity is enhanced when this one contains vinylene carbonate (VC). Table 3 gives the coulombic efficiency (CE) and the irreversible capacity loss at the 1st and between the 2nd and the 100th cycles. In the case at hand, if the copper, which was deliberately added (or non-deliberately as a consequence of maturation) to the Si-based electrodes, was present in the metallic form, as nanoparticles for example, then the CE at the 1st cycle and for the following ones should decrease with the increase of the Cu content. The reverse trend is in fact observed (Table 3). The CE increases and the irreversible capacity loss decreases with an increase of the Cu content (Figure 7). This trend is in agreement with the XPS and IR analyses, which indicate that copper is rather present as cations involved in coordination bonds with the carboxylate moieties of the CA and CMC.

In another work, Y. Gu et al., [START_REF] Gu | The effects of cross-linking cations on the electrochemical behavior of silicon anodes with alginate binder[END_REF] added a Ni 2+ salt to the alginate binder in silicon-based electrodes. They found that only ca. 10% on the Ni 2+ was reduced to Ni 0 after cycling, suggesting that the coordination bond is stable in the 100 mV -1V potential window. Moreover, they even observed an increase of the CE and a decrease of the amount of electrolyte degradation products for cations containing electrodes, suggesting a better stability of the SEI thanks to the addition of the cations. Our results are clearly in line with the work of Y. Gu et al.

Another information about the possible reduction of oxidized Cu species or the reduction of electrolyte on Cu is obtained by looking at differential capacity curves. Indeed, in their study, Yan and Obrovac observed on differential capacity curves one weak cathodic peak at 2.27 V and two strong cathodic peaks at 0.9 V and 1.3 V. [START_REF] Yan | Selecting inactive materials with low electrolyte reactivity for lithium-ion Cells[END_REF] In the present study, the differential capacity of the first cycle does not clearly show extra peaks in Cu-containing electrode (Figure S3), which could be due to the fairly low amount of Cu in our electrodes compared to the study of Yan and Obrovac. However, the peak at 0.9-1.0V that corresponds to the FEC reduction on these silicon-based electrodes, according to our previous work, [START_REF] Karkar | A comparative study of polyacrylic acid (PAA) and carboxymethyl cellulose (CMC) binders for Si-based electrodes[END_REF] appears to be shifted to higher potential and its intensity is increased with higher Cu content. A study specifically dedicated to this phenomenon will have to be undertaken to explain this evolution.

Discussion

The initial atmospheric corrosion of copper induced by organic acids (formic, acetic, and propionic acid) was finely studied by Gil and Leygraf. [START_REF] Gil | Initial Atmospheric Corrosion of Copper Induced by Carboxylic Acids[END_REF] In their experimental conditions (exposure in 120 ppb (volume parts per billion) of carboxylic acid concentration in air (gas phase), 95% relative humidity, 20°C, and up to 4 days of exposure), they found that the corrosion products formed are mainly cuprous oxide or cuprite (Cu2O), copper carboxylate, and water or hydroxyl groups. Two spatially separated main pathways, occurring at different sites of the copper surface, have been identified, as schematized in Figure 8.

The physically adsorbed water layer allows electrochemical reactions. The dominant ones are the oxidation of copper (anodic reaction: Cu → Cu + + e -) and reduction of oxygen (cathode reaction: ½ O2 + H + + 2 e -→ 2OH -). The first pathway for acid-induced atmospheric corrosion consists of proton-induced dissolution of Cu + ions, subsequent reaction of the Cu + ions with hydroxyl ions produced in the reduction of oxygen, and formation and precipitation of cuprite (Cu2O). The second pathway consists of carboxylate-induced dissolution of Cu + ions, formation of dissolved Cu + or Cu 2+ carboxylate species, that eventually precipitate as copper(II) carboxylate. The first pathway is initially very fast but levels off, grows more uniformly over the surface forming a layer up to about 15 nm thickness. The second pathway exhibits a more linear growth, with the formation of localized precipitates. The strength of the acid affects the corrosion process. A higher corrosion rate and domination of second pathway occurred with the stronger formic acid, because the stronger the acid, the higher the concentration of both protons and carboxylate ions for ligand exchange at the hydroxylated surface. For weaker acetic acid the first pathway dominated.

The conditions are different in our case, in particular because there is a mixture of organic acids (citric acid and the acid form of CMC) and because they are already present in the electrode in a significant amount. The exposure of the electrode to the humid atmosphere will cause the formation of a film of water on the surface of the electrode (in all its porosity) and on the surface of the copper collector. The acids present in the electrode and in the vicinity of the collector will be able to absorb this moisture or dissolve therein. It should therefore lead to the corrosion of the copper collector, with the formation of Cu2O-deposits and copper carboxylates.

However, the presence of the electrode above the collector and the wet film on its surface can promote the diffusion of these copper carboxylates, and more particularly the low weight complexes formed with citric acid. As for the complexes formed between the CMC and the Cu 2+ ions, their diffusion into the electrode from the current collector is less likely due to the multitude of attachment points of the long chains of CMC with the surface of the collector but also with the surface of the silicon or graphene particles. In the volume of the electrode, the absorption of water by the citric acid / CMC phase can lead to its swelling and to the formation of micro-gels in which the copper citrates (diffusing from the interface with the collector) could mix. After the maturation stage, the removal of the water by the drying stage would then lead to the formation of mixed copper complexes of citric acid and CMC. This would result in the formation of a very original three-dimensional network consisting of this mixture of CMC, citric acid, and Cu 2+ ions. The nodes of this cross-linked network resulting from the formation of Cu 2+ bridges or sequences of Cu 2+ and citric acid linkers between the carboxylate lateral groups of the CMC chains.

These results are in line with previous studies focusing on alginate binders. It was indeed reported that the addition of cations (Ca 2+ , Ba 2+ , Zn 2+ , Mn 2+ , Al 3+ ) to sodium alginate gives rise to a net improvement of the cyclability of silicon and silicon-carbon based negative electrodes. [START_REF] Gu | The effects of cross-linking cations on the electrochemical behavior of silicon anodes with alginate binder[END_REF][START_REF] Yoon | Improvement of Desolvation and Resilience of Alginate Binders for Si-Based Anodes in a Lithium Ion Battery by Calcium-Mediated Cross-Linking[END_REF][START_REF] Liu | A High-Performance Alginate Hydrogel Binder for the Si/C Anode of a Li-Ion Battery[END_REF][START_REF] Zhang | A Coordinatively Cross-Linked Polymeric Network as a Functional Binder for High-Performance Silicon Submicro-Particle Anodes in Lithium-Ion Batteries[END_REF][START_REF] Wu | Multiple Hydrogel Alginate Binders for Si Anodes of Lithium-Ion Battery[END_REF] The cyclability improvement was related to the cross-linking of the alginate binder through the formation of carboxylate-cation coordination bonds, which significantly enhanced the mechanical strength of such electrode compared to the sodium alginate-based one. The examination of the influence of the cation size and charge showed that alginate-cation gels presenting the higher hardness and better retention of capacity upon cycling, were obtained from Al 3+ and Ba 2+ ions. [START_REF] Yoon | Improvement of Desolvation and Resilience of Alginate Binders for Si-Based Anodes in a Lithium Ion Battery by Calcium-Mediated Cross-Linking[END_REF] The amount of cations was also found to be critical: a ratio of 0.1 to 0.15 cation per alginate seemed optimal for achieving the better capacity retention. [START_REF] Karkar | A comparative study of polyacrylic acid (PAA) and carboxymethyl cellulose (CMC) binders for Si-based electrodes[END_REF][START_REF] Liu | A High-Performance Alginate Hydrogel Binder for the Si/C Anode of a Li-Ion Battery[END_REF] Matured electrodes show much superior mechanical strength, with three times higher resistance to peeling and seven times higher resistance to scratching than the standard electrode.

[16] These superior mechanical properties may be ascribed to the physical cross-linking of the binder phase through the ligand (carboxylate)-Cu 2+ coordination bonds. Recent reviews have highlighted a superiority trend of chemically cross-linked binders through covalent bonds, with respect to linear or ramified uncross-linked binders for silicon-based electrodes. [START_REF] Li | Water Soluble Binder, an Electrochemical Performance Booster for Electrode Materials with High Energy Density[END_REF][START_REF] Chen | Exploring Chemical, Mechanical, and Electrical Functionalities of Binders for Advanced Energy-Storage Devices[END_REF][START_REF] Kwon | The Emerging Era of Supramolecular Polymeric Binders in Silicon Anodes[END_REF] of binding networks are formed in such electrode compared to the matured one. In particular, the amount of Si-CMC/CA ester bonds appear significantly different in both electrodes, the maturation causing the hydrolysis of numerous of these bonds. But these IR and XPS analyses relate to the as-prepared electrodes, just before cell assembling; the evolution of these microstructures upon cycling is largely possible. In particular, the reminiscence of the Si-CMC/CA ester bond upon lithium (de)alloying has never been proved. The similar electrochemical performance of the matured and CuSO4-containing electrodes may suggest that the key parameter controlling the mechanical stability of the electrodes is the presence of Cu(II) ions distributed in the binder phase allowing for self-healing mechanical properties.

Finally, the beneficial influence of the addition of Cu 2+ cations on the CE could be explained as follow. It was shown that binders such as alginate or CA/CMC behave as artificial SEI.

[39,45-47] This is because they can form a thin electronically insulating and lithium conducting coating at the surface of the silicon particles. However, this binder layer may be disrupted during cycling as a consequence of the silicon particles volume variations. As described into more details in the Discussion section, the addition of cations to these binders improves their mechanical properties, which could be at the origin of better mechanical stability of the preformed artificial SEI and thus improved CE.

Conclusion

The superior mechanical strength of the matured electrode is due for a large part to the migration of Cu 2+ ions from the current collector across the electrode thickness. These cations coordinate with the carboxylate groups of the carboxymethylcellulose binder and of citric acid to form a physically cross-linked network provided with both elastic and self-healing properties.

As a result of this superior mechanical strength, the cyclability of matured electrode is largely enhanced with respect to un-matured one.

The same level of performance can however be achieved for a non-matured electrode by deliberately adding these Cu 2+ ions in the electrode slurry, even if different coordination pattern is formed. In both cases, the maximum level of performance improvement is reached for a copper content of about 1 wt% that corresponds to a molar ratio of copper to carboxylates equal to about 0.11.

The convenience of the second approach, together with the myriad of possibilities associated with the selection of cations of various size and charge, polymers, and/or smaller organic molecules carrying various types and numbers of organic ligands, is offering a very attractive and also vertiginous avenue to explore for designing a novel class of binders for lithium-ion battery silicon-based electrodes, [START_REF] Devic | Addressing the Challenges through Coordination Chemistry[END_REF] and more generally for negative and positive composite electrodes for various types of batteries and also super-capacitors.

  The signals of other carbons from the ring and the chain are poorly resolved and span from 70 to 90 ppm. The spectrum for the standard electrode (in red) shows in addition the characteristic resonances for citric acid, namely the CH2 group at 44 ppm (C4), and the carboxylate/ic group at 173 ppm (C5) is more intense than for the reference sample. The central carbon atom C6 is expected at 75 ppm, thus overlaps with the main resonance of CMC. On the spectrum of the matured electrode (in blue), there is a huge loss of signal. The resonance of the citric acid (C4) as well as those of the carboxylate/ic groups of citric acid and CMC (C1 and C5) are no longer visible. Only the signals of C atom of the CMC ring remain discernible.

13 C

 13 CP-MAS spectra, the 1 H-29 Si CP-MAS signal of the electrode is still observable after maturation. Therefore, the complexation of copper by CMC and citric acid does not take place in the vicinity of the Si particle surfaces. Finally, the 1 H-29 Si CP-MAS signal spectrum of the matured electrode shows significant modification in the relative intensities of the 3 resonances as compared to the reference and standard electrodes. Since no loss of Si-C linkages (at -10 ppm) is expected during maturation, the relative increase in -80 and -110 ppm resonances intensities can be ascribed to better efficiency of the CP magnetization transfer. This improvement could proceed from water molecules and/or more CMC / citric acid -COOH groups interacting with the surface of the Si particles. In fact, the latter hypothesis is well supported by IR and XPS characterizations as shown below.Diffused reflectance IR Fourier transform (DRIFT) spectra of the pristine silicon powder and of the electrodes, without however the carbon additive in their composition, are shown in Figure4a. In the carbonyl region, the standard electrode shows an intense peak at ca. 1720-1730 cm -1 , which is attributed to the vibration of a C=O group engaged in R-C(=O)-O-

Figures 5 .

 5 Figures 5. The C 1s core peaks (figures 5a, d, g and j respectively) show the presence of four main components: the one at 285.0 eV (C1) is attributed to the hydrocarbon contribution (C-C/C-H), which is mainly contained in surface contamination, classically detected on the sample surfaces. The component located at 286.7 eV (C2) is assigned to alkyl C-O species, mainly contained in the CMC and CA compounds. The peak detected at 288.1 eV (C3) could be attributed to the carbon O-C=O contained in sodium or potassium carboxylate RCOONa orRCOOK[START_REF] Zou | Heterogeneous Ti3SiC2@C-Containing Na2Ti7O15 Architecture for High-Performance Sodium Storage at Elevated Temperatures[END_REF]. The carbon appearing at 289.1 eV (C4) is assigned to a different environment of the carboxyl group, which could be either a carboxylic acid RCOOH[START_REF] Louette | Poly(acrylic acid) (PAA) XPS Reference Core Level and Energy Loss Spectra[END_REF], an ester (R-C(=O)-OR'), or a Si or Cu-carboxylate bond (R-C(=O)-O-Si-or R-C(=O)-O-Cu-)). Indeed, the C 1s XPS core peak of the CMC-AC-Cu reference compound (without silicon) (Figure5j) shows also the presence of both environments, which is in agreement with our peak assignments. Note that the C4/ C3 ratio increases from pH7 to pH3, in line with the formation of (R-C(=O)-O-Si-) ester bonds in acidic pH as previously observed.[START_REF] Delpuech | Critical Role of Si Nanoparticles Surface on Lithium Cell Electrochemical Performance Analyzed by FTIR, Raman, EELS, XPS, NMR and BDS Spectroscopies[END_REF][START_REF] Mazouzi | Silicon Composite Electrode with High Capacity and Long Cycle Life[END_REF] For the matured electrode, the C4/C3 ratio decreases as the consequence of the hydrolysis of the ester bonds, as already observed by the IR experiments. As the signal of RCOOH, R-C(=O)-O-Si-, R-C(=O)-OR' and R-C(=O)-O-Cu-overlap, no information regarding the amount of copper-carboxylate bonds can be extracted from this analysis.The Si 2p core peaks (Figures5b, e and h) are split in two components Si 2p3/2 and Si 2p1/2 due to the spin-orbit coupling effect. Each Si 2p (Si 2p3/2-Si 2p1/2) couple corresponding to one component is identified with a defined color. Three slightly asymmetric contributions are identified for the standard (at pH7 and pH3) and matured electrodes. The first one (Si1), with a Si 2p3/2 peak located at 98.7 eV, is assigned to the elemental silicon. The second one (Si2) (Si 2p3/2 at 102.1 eV) is attributed to the Si-based ester and SiOx (x<2) type environments, and the third peak (Si3) (Si 2p3/2 at 103.1 eV) can be assigned to surface SiO2 and SiOH

Figure 1 .

 1 Figure 1. Comparison of the electrochemical performance between standard, matured, andCuSO4-added electrodes cycled at full capacity.

Figure 2 .

 2 Figure 2. The discharge capacity retained after 100 cycles vs. the molar ratio of the amount of copper to the amount of carboxylates for the different electrodes: standard, matured, and those prepared by addition of CuSO4 in their slurry formulation.

Figure 3a. 1 H

 1 Figure 3a.1 H-13 C CP-MAS NMR spectra on standard (red, b) and matured (blue, a) electrodes (without carbon in their composition) scrapped of the copper collector. The spectrum of an electrode prepared without citric acid is also shown as reference (green, c).

Figure 3b. 1 H

 1 Figure 3b.1 H-29 Si CP-MAS NMR spectra on standard (red, b) and matured (blue, a) electrodes (without carbon in their compositions) scrapped of the copper collector. The spectrum of an electrode prepared without citric acid is also shown as a reference (green, c).

Figure 4 .

 4 Figure 4. DRIFT spectra of (a) the as-milled silicon powder, the standard and the matured electrodes (without carbon additive in their composition) removed from the copper collector; (b) of electrodes prepared with various amounts of CuSO4 (also without carbon additive in their composition). Insert: zoom of the 1800-1200 cm -1 region.

Figure 5 .

 5 Figure 5. C 1s-K 2p, Si 2p and Cu 2p XPS core peaks of a silicon electrode (at pH=7) ((a), (b), and (c) respectively), the standard Si-electrode (pH=3) ((d), (e) and (f) respectively, the matured electrodes ((g), (h) and (i) respectively) and an AC-CMC-Cu mixture powder ((j) and(k) respectively).

Figure 6 .

 6 Figure 6. Si 2p XPS core peaks of a silicon electrode deposited on a Cu-free substrate and containing different amounts of CuSO4 ([Cu]/[COOH] ratio =0 (a), 0.054 (b), 0.107 (c), 0.214 (d) and 0.429 (e).

Figure 7 .

 7 Figure 7. The 1 st cycle irreversible capacity loss vs. the copper content in the different electrodes.

Figure 8 .

 8 Figure 8. Schematic description of possible pathways for acid-induced atmospheric corrosion of copper. Reprinted from Reference [23], Copyright 2007, with permission from The Electrochemical Society.

  The capacity retention is already significantly improved for the lower amount of CuSO4 (1.30 wt%,

	/	= 0.054) and reaches similar or slightly superior capacity retention than the matured
	electrode for 2.5 wt% of CuSO4 (	/	= 0.11). For larger amounts of CuSO4 (4.84 and
	9.3 wt%,

/

= 0.21 and 0.43), there is no longer any performance improvement.

  Crosslinked binders are stiffer than linear binder and therefore, during the delithiation of the active mass, they afford better elastic recovery of the electrode expansion that happened during lithiation. However chemical cross-links are prone to irreversible and permanent rupture when stretched above a critical deformation point. Contrarily to covalent bonds, coordination bonds are labile. That means they are exchangeable and reversible, which afford self-healing properties to the resultant polymer-cation networks.[START_REF] Lai | A Rigid and Healable Polymer Cross-Linked by Weak but Abundant Zn(II)-Carboxylate Interactions[END_REF] The recent reviews also emphasized another class of binders endowed with self-healing properties, which result from the presence of hydrogen bonding moieties in the binder. Hydrogen bonds, if reversible, are however weak, which minimizes the ability of such binders to give elastic recovery properties. Because coordination bonds are stronger than hydrogen bonds but still reversible, it appears that they might be the more suitable type of bond to rely upon for building a tough and resilient siliconbased electrode.Physical cross-linking of the CMC/CA with (carboxylate)-Cu 2+ coordination bonds can also be achieved by deliberately adding Cu(II) salt in the electrode slurry, allowing for similar level of electrochemical performance enhancement. However, both IR and XPS spectroscopies suggest that different coordination patterns and Si-CMC/CA bonding and thus different types

Table 1 .

 1 Electrode formulations as prepared with RCu/COOH molar ratio.

	Wt%	Si	GM15 CMC	CA	Na	K	Cu	SO4	/
	Standard 73.3	11.0	6.7	7.8	0.65	0.64	0	0	0
	Cu-0.05	72.3	10.9	6.6	7.7	0.65	0.63	0.50	0.8	0.054
	Cu-0.11	71.4	10.7	6.5	7.6	0.64	0.62	0.99	1.5	0.107
	Cu-0.21	69.7	10.5	6.3	7.4	0.62	0.61	1.94	2.9	0.214
	Cu-0.43	66.5	10.0	6.1	7.1	0.59	0.58	3.70	5.6	0.429

Table 2 .

 2 Cu, K and Na quantity in the composition of the matured electrode as a function of the maturation duration, with [Cu] to [COOH in CMC+CA] molar ratio.

	Days of	Na	K	Cu	[ ]
	maturation	(wt%)	(wt%)	(wt%)	[	]
	0 (Standard)	0.57	0.68	0.34	0.037
	2	0.56	0.61	0.81	0.089
	4	0.54	0.62	1.27	0.140
	7	0.53	0.62	1.67	0.183

Table 3 .

 3 Coulombic efficiency (CE) and irreversible capacity loss at the first cycle and theirmean value (at each cycle) between the 2 nd and 100 th cycle for each sample.

		Coulombic efficiency		Irreversible loss
			(%)	(mAh g -1 per cycle)
	sample	1 st cycle	mean value between 2 nd and 100 th cycle	1 st cycle	mean value between 2 nd and 100 th cycle
	Standard	78 ±1	95.6	805	92
	Matured 2 days 83 ±1	99.6	643	23
	Cu-0.05	82 ±1	99.4	702	26
	Cu-0.11	82 ±1	99.4	670	25
	Cu-0.21	83 ±1	99.4	622	25
	Cu-0.43	86 ±1	99.8	564	19

Acknowledgements

The authors thank the Natural Sciences and Engineering Research Council (NSERC) of Canada and the Centre National de la Recherche Scientifique (CNRS) of France for supporting this work. D. M. is grateful to the University of Nantes for invited stay.