Sofia Perticarari

Tom Doizy

Patrick Soudan

Chris Ewels

Camille Latouche

Dominique Guyomard

Fabrice Odobel
email: fabrice.odobel@univ-nantes.fr

Philippe Poizot
email: philippe.poizot@cnrs-imn.fr

Joel Gaubicher
email: joel.gaubicher@cnrs-imn.fr

Prof Philippe Poizot

Intermixed Cation-Anion Aqueous Battery Based on an Extremely Fast and Long-Cycling Di-Block Bipyridinium-Naphthalene Diimide Oligomer

Aqueous batteries, particularly those integrating organic active materials functioning in a neutral pH environment, stand out as highly promising contenders in the stationary electrochemical storage domain, owing to their unparalleled safety, sustainability and low-cost materials. Herein, a novel di-block oligomer (DNVBr), serving as the negative electrode of an all-organic aqueous battery, is shown to offer exceptional output capabilities. The battery's performance is further enhanced by a unique intermixed p/n-type storage mechanism, which is able to simultaneously exchange light and naturally abundant Na + , Mg 2+ and Cl -. Reaching up to 105 mAh/g, this system shows remarkable capacity retention for several thousand cycles (6500 cycles, ~40 days) in various neutral electrolytes, including raw ocean water (~3000 cycles, ~75 days). The surprisingly fast kinetics of this di-block oligomer allow to attain an unmatched specific capacity of near to 60mAh/g electrode while entirely devoid of conducting additives, and more than 80mAh/g electrode with 10% carbon additive, as well as displaying an a real capacity as high as 3.4mAh/cm 2 at C rate. Full cell validation was demonstrated over 1600 cycles by virtue of a commercial TEMPO molecule, which permitted an energy density of close to 40Wh/kg materials at C rate in a self-pH-buffered and inexpensive aqueous electrolyte.

Introduction

By virtue of their high energy efficiency, facile scalability, intrinsic safety, not to mention low cost and environmental compatibility, aqueous batteries are being increasingly considered as a novel and promising technology for grid storage [START_REF] Poizot | Progress in all-organic rechargeable batteries using cationic and anionic configurations: Toward low-cost and greener storage solutions?[END_REF][START_REF] Poizot | Perspectives in Lithium Batteries[END_REF][START_REF] Li | Rechargeable Lithium Batteries with Aqueous Electrolytes[END_REF] . Despite recent progress, [START_REF] Poizot | Progress in all-organic rechargeable batteries using cationic and anionic configurations: Toward low-cost and greener storage solutions?[END_REF][START_REF] Liang | Universal quinone electrodes for long cycle life aqueous rechargeable batteries[END_REF][START_REF] Hatakeyama-Sato | An Ultrahigh Output Rechargeable Electrode of a Hydrophilic Radical Polymer/Nanocarbon Hybrid with an Exceptionally Large Current Density beyond 1 A cm -2[END_REF][START_REF] Whitacre | An aqueous electrolyte, sodium ion functional, large format energy storage device for stationary applications[END_REF][START_REF] Lee | Manganese hexacyanomanganate open framework as a high-capacity positive electrode material for sodium-ion batteries[END_REF][START_REF] Häupler | Aqueous zinc-organic polymer battery with a high rate performance and long lifetime[END_REF][START_REF] Dong | All-Organic Rechargeable Battery with Reversibility Supported by "Waterin-Salt[END_REF][START_REF] Wan | An Aqueous Rechargeable Zinc-Organic Battery with Hybrid Mechanism[END_REF][START_REF] Xu | Energetic Zinc Ion Chemistry: The Rechargeable Zinc Ion Battery[END_REF][START_REF] Toussaint | Development of a Rechargeable Zinc-Air Battery[END_REF] however, these systems are still associated with a relatively low energy density of below 50Wh/kgcell, or insufficient cycle life [START_REF] Toussaint | Development of a Rechargeable Zinc-Air Battery[END_REF] , which is detrimental to their economic viability by perpetuating the issues of both unit cost and/or durability of active materials. A device of this sort needs to be able to supply an adequate amount of cycles over a sufficient time span in order to equalize energy storage costs to around 100 $/kWh. Furthermore, the extensive utilization of batteries for both domestic and large-scale applications that would result from the global energy transition, would further restrict our already limited, unequally distributed and monopolized metal resources. The design of suitable host materials displaying optimal potential and high chemical/electrochemical stability hinges upon resolving these challenging issues.

In this regard, substituting transition metal-based materials with organic ones appears to be a very favorable approach 1,2 since these materials provide several distinct advantages: (i) their extraction is not restricted to specific geographical areas, making them of particular interest in countries such as Europe where certain key raw materials are scarce; (ii) low-cost organic chemistry can provide a virtually infinite number of compound modifications with appropriate functional groups (hydrophobic, electron attractor/donor, favorable pi-stacking interactions, etc.), which permits the tuning of their solubility, molecular mass and chemical reversibility, as well as the adjustment of their redox potential, thereby optimizing the cell voltage without triggering overwhelming O2 or H2 evolutions. By way of reminder, in an electroactive organic group, the latter property arises from the change in its charge state, whereas for inorganics it stems from the change in the valence of the transition-metal or element; (iii) they can undergo multi-electron redox reactions which can lead to a much higher specific capacity. Lastly, it is worth noting that their low volumetric density is evidently not as great a hindrance with respect to stationary applications as it is to itinerant ones.

From a general perspective, and based on several exhaustive studies reviewing organic redox materials [START_REF] Poizot | Progress in all-organic rechargeable batteries using cationic and anionic configurations: Toward low-cost and greener storage solutions?[END_REF][START_REF] Poizot | Perspectives in Lithium Batteries[END_REF][START_REF] Schon | The rise of organic electrode materials for energy storage[END_REF][START_REF] Zhao | Advanced Organic Electrode Materials for Rechargeable Sodium-Ion Batteries[END_REF][START_REF] Yao | Molecular ion battery: a rechargeable system without using any elemental ions as a charge carrier[END_REF][START_REF] Janoschka | Powering up the Future: Radical Polymers for Battery Applications[END_REF][START_REF] Zhao | Molecular Engineering with Organic Carbonyl Electrode Materials for Advanced Stationary and Redox Flow Rechargeable Batteries[END_REF][START_REF] Gracia | Polymers with redox properties: materials for batteries, biosensors and more[END_REF][START_REF] Song | Towards sustainable and versatile energy storage devices: an overview of organic electrode materials[END_REF] it is clear that although many n-type organic materials such as quinones and diimides can be designed for the anode side fairly "easily" (potentials below -0.3 V vs. Saturated Calomel Electrode (SCE) or 2.95 V vs. Li + /Li) due to the carbonyl/enolate redox moiety, it is much more challenging to find cathodic n-type materials with sufficient potentials to produce a voltage of >1 V. Quite synchronously, while the redox potentials of the viologen group match up with the negative side, the potentials of other p-type organic materials are a fit for the positive side. It is for this reason that cationic (n-type) rocking-chair aqueous batteries only make use of hybrid cells that combine inorganics (cathode) and organics (anode). Yao's group [START_REF] Liang | Universal quinone electrodes for long cycle life aqueous rechargeable batteries[END_REF] aptly illustrate this point with the use of a polypyrene-4,5,9,10-tetraone negative electrode (220 mAh/gmaterial) paired with LiMn2O4. This full cell can sustain ~90 Wh/kgmaterials for more than 3000 cycles at 0.23 A/g (3500 h cycling) with near to 100% coulombic efficiency.

Another interesting hybrid cationic cell was demonstrated by Wu and co-workers [START_REF] Wu | Rocking-Chair Ammonium-Ion Battery: A Highly Reversible Aqueous Energy Storage System[END_REF] using an ammonium Ni-based Prussian white as the cathode paired with a 3,4,9,10perylenetetracarboxylic diimide in 1 M (NH4)2SO4. The cell delivered 43Wh/kgmaterials at 1.5C, but displayed a rather moderate capacity retention (67% upon 1000 cycles at 3C rate). Thus far, the only full organic rocking-chair aqueous cells are p-type ones (anionic configuration), and both of them were put forward by the same group (Nishide, Oyaizu and co-workers): their thin film batteries were designed using a TEMPO redox polymer derivative, with poly (2,2,6,6tetramethylpiperidin-4-yl) acrylamide (PTMA) as the cathode, paired with either a highly crosslinked polyviologen hydrogel (poly-(tripyridiniomesitylene)) [START_REF] Sano | Polyviologen Hydrogel with High-Rate Capability for Anodes toward an Aqueous Electrolyte-Type and Organic-Based Rechargeable Device[END_REF] enabling ~1.3 V over 2000 cycles, or with poly(N-4,4'-bipyridinium-N-decamethylene dibromide) leading to 2000 cycles with a 1.2 V average voltage [START_REF] Chikushi | TEMPO-substituted polyacrylamide for an aqueous electrolyte-typed and organic-based rechargeable device[END_REF] . Recently, Truhlar, Wang and co-workers demonstrated a full organic "dual-ion" cell (cations and anions are drawn from the electrolyte, as opposed to a "rocking-chair" system) based on p-type polytriphenylamine and n-type polynaphthalene diimide polymers as the positive and negative materials, respectively [START_REF] Dong | All-Organic Rechargeable Battery with Reversibility Supported by "Waterin-Salt[END_REF] . The authors determined that nearly 53 Wh/kgmaterials and 32 kW/kgmaterials can be obtained for 1 mg/cm 2 electrodes using a 21 m LiTFSI water-in-salt electrolyte. Lastly, we previously reported a possible new avenue for designing aqueous batteries using an organic material wherein a p-type viologen and n-type naphthalene diimide moieties merge together into a short oligomer, thus allowing the exchange of both anions and cations in a narrow potential range, and showing encouraging performance [START_REF] Perticarari | Dual Anion-Cation Reversible Insertion in a Bipyridinium-Diamide Triad as the Negative Electrode for Aqueous Batteries[END_REF] .

In light of the above, even though remarkable progress has already been made, further material innovation is required in order to ultimately obtain a low-cost, green and long-lasting aqueous battery for renewable energy storage.

In the present work we identify an advanced p/n-type organic scaffold that exchanges simultaneously cations and anions in a high cation to anion ratio and over almost all of its potential range, and with greatly improved capacity (up to 82 mAh/gelectrode), cyclability (over 6500 cycles), chemical stability (3000 cycles in ocean water) and conductivity, thereby bringing us quite a bit closer to being able to build competitive devices. This point was demonstrated by pairing a commercial TEMPO small molecule for use as the cathode material, thus attaining up to 40 Wh/kgmaterials at a C rate.

RESULTS

Synthesis

In order to attain the objective of water-insoluble p/n-type redox active compounds providing optimal performance, a new "di-block" oligomer (DNVBr, Scheme 1) was designed. The latter contains naphthalene diimide repeating units (referred to as NDI) coupled to bipyridinium units (referred to as Violo) by a propyl linker. As mentioned in the introduction, being able to synthesize active materials at a low cost constitutes a sine qua non condition for making ionaqueous batteries, a technology of choice for stationary applications. In this spirit, DNVBr was synthesized by following two elementary reaction steps (Scheme1): firstly, the intermediate NDI 3 was obtained, in a yield of 89%, by an imidization reaction between the naphthalenetetracarboxylic dianhydride NDA (1) and the 3-bromopropylammonium bromide (2), according to the customary procedure [START_REF] Matsunaga | Photoinduced Color Change and Photomechanical Effect of Naphthalene Diimides Bearing Alkylamine Moieties in the Solid State[END_REF] . The second step was a nucleophilic substitution between compound 3 and the 4,4'-bypiridine. The final dark brown product (DNVBr in Scheme 1) is completely insoluble in most organic solvents, thus preventing its characterization by Size-Exclusion Chromatography and by Mass Spectrometry analysis, thereby precluding the precise determination of this new material's polydispersity. However, thanks to its solubility in trifluoroacetic acid (TFA), the 1 H-NMR and [START_REF] Schon | The rise of organic electrode materials for energy storage[END_REF] C-NMR spectra were successfully recorded (Figures S1-S2), showing that a polydisperse mixture of oligomers was produced. The degree of oligomerization was deduced by the integration of the specific signals into the 1 H-NMR spectrum, and led to an estimated average degree of oligomerization equal to 3±1 (for further details see Figure S1 and accompanying explanations). This result was replicated across several reaction batches and by different experimentalists.

FT-IR/ATR analyses confirm the presence of both the imide and the bipyridinium units via the existence of the characteristic stretching bands of the C=O (1702, 1656 cm -1 ), C=N + (1640 cm - 1 ) and C=N (1577 cm -1 ) bonds (Figure S3). The thermal stability of the new product was tested by means of TGA-MS/DSC analysis, showing that DNVBr is stable up to 300°C and contains approximately 5wt% adsorbed water (Figure S4). In addition, the FT-IR spectrum indicates a large band at 3400 cm -1 that may correspond to the solvation sphere around the Br -counteranion.

Electrochemical behavior of DNVBr:

The "di-block" nature of DNVBr is characterized by two redox units: the viologen one, ensuring anion exchange (p type); and the NDI one, retaining/releasing cations (n type) according to the following reactions: and Noteworthy, the second electron reduction of Violo + could not be achieved, even with a potential as low as -1.V vs. SCE in an aqueous electrolyte. The theoretical specific capacity of the Viologen moiety substituted by a propyl group on one side and bearing Br -as the counter anions, (M w =374.12 g/mol), is 74.6 mAh/g for a one-electron reaction. However, the capacity of the naphthalenediimide, also functionalized by a propyl linker on one side, is 16% higher (86.7 mAh/g) for one electron and 132% higher for two electrons (173.3 mAh/g). Accordingly, the theoretical specific capacity of DNVBr is 90.31 mAh/g (5e  ) for n=1, 99.78 mAh/g (8e  ) for n=2 and 104.8 mAh/g (11e  ) for n=3, while that of MNV is at most 90 mAh/g (4e  ) (Figure S5).

In conclusion, by comparison to conventional inorganic and organic materials previously reported, several unique advantages can be gleaned from the specific molecular structure of DNV. Indeed, (i) NDI brings both a high hydrophobicity which mitigates dissolution issues during battery operation and a large specific capacity while (ii) the propyl linker provides flexibility as well as robustness, which prevents the capacity fading observed for NDI [START_REF] Perticarari | Dual Anion-Cation Reversible Insertion in a Bipyridinium-Diamide Triad as the Negative Electrode for Aqueous Batteries[END_REF] , and

(iii) the viologen units are in the "charged state" and allow p-type redox processes (anionic), which could potentially mitigate both the ionic depletion occurring within the porosity of ultrathick electrodes (> mm) [START_REF] Barnett | PHEV Battery Cost Assessment[END_REF][START_REF] Dillon | Microstructural design considerations for Li-ion battery systems[END_REF] as well as electrode volume variations upon cycling. As will be demonstrated throughout this paper, the extended length and specific molecular structure of DNVBr offer us numerous advantages over the first di-block compound of this kind [START_REF] Perticarari | Dual Anion-Cation Reversible Insertion in a Bipyridinium-Diamide Triad as the Negative Electrode for Aqueous Batteries[END_REF] (referred to as MNV), making it one of the most attractive negative electrode materials for aqueous batteries: DNVBr was found to (i) support light counter anions (Br -and Cl -) without dissolving in any of the aqueous electrolytes (ii) display unmatched performance without carbon additive, (iii) show an intermixed cation-anion mechanism over almost all of its potential range, and (iv) demonstrate outstanding cyclability.

The cyclic voltammogram (CVs) of DNVBr in NaClO 4 2.5 M is shown in Figure 1a, along with that of MNV. The electrochemical profile of both compounds is characterized by three main reversible peaks (denoted by I, II and III, respectively) that are much broader in the case of DNVBr. We note that the peak potentials of II could only be distinctively identified upon oxidation for DNVBr and upon reduction for MNV, by limiting the potential cut-off (Figure 1a). Under these conditions, the estimated equilibrium potential for II DNVBr (approximated to Ei=1/2(E i peak,ox + E i peak,Red )) is 20 mV lower than for DNVBr (Table S2).

Using the same approximation, the potential differences between I DNVBr and I MNV on one side, and III DNVBr and III MNV on the other side, are +30 and +60 mV respectively (Table S2). Lastly, DNVBr is characterized by lower polarizations for I and III. Most especially, the maximum intensity of III red MNV is at 0.901 V, which is 107 mV lower than that of DNV (0.794 V).

Described in more detail below, these changes in equilibrium potential and polarization give DNVBr a decisive advantage over MNV as regards its specific capacity. Galvanostatic tests of DNVBr and MNV at 0.3 A/g (4C rate) highlight the fact that moving from MNV to DNVBr has a profound effect on the electrochemical profile. In particular, the two potential plateaus that are observed for MNV mirror the occurrence of phase transformations [START_REF] Perticarari | Dual Anion-Cation Reversible Insertion in a Bipyridinium-Diamide Triad as the Negative Electrode for Aqueous Batteries[END_REF] , whereas the smooth profile of DNVBr suggests solid solution type processes. Reduction of these materials down to 1 V at 4C rate permits to recover a specific capacity on oxidation of 89 mAh/g for DNVBr, and 83 mAh/g for MNV (Figure 1b). However, in order to mitigate hydrogen evolution in neutral and molar range electrolytes, such a low cutoff potential can only be used at high current loads (typically 2.4 A/g -32C-rate). At lower currents, long cycling is typically performed down to -0.75 or even -0.85 V. Under these conditions, the absence of a potential plateau, as well as the mitigated polarization and 60 mVhigher potential of step III, allows DNVBr to reach 85 mAh/g (+36% vs. MNV) at -0.85 V (Figure 1b). We note that at C/5, DNVBr achieves 107 mAh/g upon oxidation (Figure S6), which is close to the theoretical value expected for n=3 (105 mAh/g).

Specific insertion mechanism of DNVBr:

The specificities of the DNVBr insertion mechanism that are responsible for its superior performance were pinpointed by UV-Vis spectroelectrochemistry, EQCM, operando synchrotron XRD, as well as spin-polarized DFT calculations.

An overview of the UV-Vis spectral changes observed while cycling DNVBr from 0 to 1.1 V vs. SCE is shown in Figure 2a, while the corresponding solid-state speciation is reported in Figure 2b. The latter is shown by plotting the relative intensity of the specific bands for each species as a function of the scan number. For the sake of clarity, the evolution of the five most representative wavelengths are reported in Figure 2b. The first drop in intensity of the red curve associated with the neutral NDI (372 nm) occurs during scan 280 (E = 0.21 V), at the expense of the NDI radical anion at 452 nm (dark blue curve). This transformation, which is characterized by an isosbestic point (Figure S7), ends at scan 480 (E = 0.51 V) and thereby accounts for the first reduction peak (I) in the CV plot (Figure 2a). It is worth noting, however, that the maximum intensityof the dark blue curve associated with the NDI radical anion keeps increasing until scan 532 (Figure 2b), which corresponds to E = 0.60 V in Figure 2a. This demonstrates that a second component is at play at this wavelength. Based on the literature findings [START_REF] Bird | Electrochemistry of the viologens[END_REF] , this corresponds to the radical viologen moiety (Table 1). The behavior of the viologen redox center can also be tracked by the band at 533 nm (light blue curve, Figure 2b), which grows on top of that pertaining to the radical NDI • (Figure 2a, Table 1 and Figure S7). From scan 314 on (E = 0.26V in Figure 2a) the intensity of this band increases due to the formation of NDI •-, but an inflexion point occurs at scan 390 (E = 0.39V in Figure 2a) which mirrors the appearance of the viologen cation radical. This intermixing of both the NDI • and Violo •+ is further supported in Figure 2b by the opposite slope changes of the light and dark blue curves in the vicinity of scan 480 (E = 0.51 V in Figure 2a): (i) the negative inflexion of the dark blue curve corresponds to the end of the NDI to NDI • transformation whereas, (ii) the positive inflexion of the light blue curve is associated with the maximum of intensity of the CV peak II in Figure 2a. Consistently, this CV peak can confidently be ascribed to the reduction of Violo 2+ to Violo •+ . Finally, the band at 452 nm (dark blue curve) decreases during the third electrochemical process due to the reduction of NDI • into its dianionic quinoid form NDI 2 . The appearance of the NDI dianion can indeed be identified from the band at 401 nm (Figure 2b, pink curve), for which the slope changes from scan 493 (E = 0.53 V in Figure 2a). Notably, this characteristic is therefore unique to DNVBr, since the dianionic quinoid form NDI 2 was not detected for MNV even at potentials as low as -0.75V [START_REF] Perticarari | Dual Anion-Cation Reversible Insertion in a Bipyridinium-Diamide Triad as the Negative Electrode for Aqueous Batteries[END_REF] . Taking the NDI/NDI • redox couple as an example, this transformation is characterized by an isosbestic point (Figure S7) confirming that these redox centers are not involved in side reactions. The production of NDI 2 can also be detected at 372 nm (Table 1) as the intensity of the red curve increases above I/Imax(I/I0)=1 from the same scan number (Figure 2b). The two NDI 2 bands stop growing as the intensity of the low-potential CV peak (III, in Figure 2a) tends toward zero in the vicinity of scan 800 (E = 0.98 V). The subsequent increase in reduction current at 0.92 V (scan 780, Figure 2a) is therefore mainly attributed to H2 evolution. Lastly, one can see that the intensity of the two blue curves, as well as the red and pink ones, increases slightly from scan 780 up until the end of the reduction. Accordingly, it appears that (i) both the NDI • and the viologen subunits are still active until the very end of the reduction, and (ii) further reduction of the viologen radical cation into its neutral form does not occur under our conditions, which is an important feature considering that the neutral form is known to induce considerable volume variations and poor reversibility [START_REF] Bird | Electrochemistry of the viologens[END_REF] . Upon reverse scan, the oxidation of the electro-generated species reverts to the initial spectra. An asymmetry appears between the end of reduction (from scan 650 to 900) and the beginning of oxidation (scan 900 to 1250). This asymmetry, comparable to the one observed in the electrochemical curve, is characterized by two features: (i) the drop of intensity in the radical viologen bands (dark and light blue curves) is more pronounced at the beginning of the oxidation process than the corresponding increase in intensity at the end of the reduction, and (ii) the NDI 2 starts decreasing upon oxidation around 50-100 scans later than one would expect judging by its behavior upon reduction.

Overall, these results demonstrate that DNVBr shows an intermixed p-n type electroactivity over nearly its entire potential range, a property which has never yet been encountered in the battery field to our knowledge. This particularity, which stems primarily from the stabilization of its dianionic quinoid units (NDI 2 ) to high potentials, accounts for the high specific capacity of DNVBr. It is anticipated that such an extended anionic-cationic ingress-release in opposite flows (see EQCM results below) could potentially mitigate volume variations in the electrode, which would be an even greater advantage since thick ones are mandatory for decreasing levelized energy costs.

It is worth noting that, a very similar solid state speciation is observed when using Mg(ClO4)2

1.25 M as the electrolyte (Figure S8).

The electrogravimetric behavior of DNVBr measured by EQCM (Figure S9) provides valuable information supporting the dual cationic/anionic insertion processes of DNVBr. Indeed, on reduction three successive steps are observed: a first gain in mass that can be attributed to the uptake of cationic species occurs upon formation of the radical anion (NDI • ) during the electrochemical step (I); this process is followed by a mass loss, consistent with the reduction of the p-type Viologen to its cationic form (Violo + ) during (II) and the concomitant release of anions; finally, the low potential step (III) is associated with a second gain in mass that supports the reduction of the radical anion (NDI • ) to its dianionic form NDI 2 . Therefore, the EQCM finding is in agreement with the UV-Vis inferred description of electrochemical behavior.

Given the intricate intermixing of the p/n-type electrochemical processes, a qualitative analysis would, however, require a dedicated study and is thus beyond the scope of this paper.

Nevertheless, based on the present results, calculations suggest an important co-insertion of water molecules during cation ingress: eighteen H 2 O molecules per cation during step I, and thirteen during III; while during II, the departure of one ClO 4  anion would be counterbalanced by the ingress of two H 2 O molecules (details are reported in Figure S9). The structural evolution of solid state oligomers or polymers during electrochemical ion insertion is certainly a challenging issue given the poor crystallinity of this class of materials.

Synchrotron XRD, however, reveals fairly unexpected behavior for DNVBr. Indeed, although the smooth electrochemical profile of DNVBr suggests solid-solution type processes, no peak shifts were detected during the entire electrochemical process (reduction and oxidation). Rather, the intensity of DNVBr peaks (referred to as phase P0) at 6.35°, 8.15°, 9.40° and 12.55° starts decreasing as soon as the reduction begins (scan 5). This is most clearly visible for the main peaks at 6.35°, 8.15° and 9.40° in Figure S10a. Disappearance of P0 occurs upon the appearance of a a new set of peaks at 2.33°, 8.03° and 11.79° (the corresponding phase being referred to as P1). The P0 to P1 phase transformation is completed upon scan 18 (QQ 0 = 61.5 mAh/g). It is worth noting that the new peak at 2.33° corresponds to a very large d-spacing (d =33 Å), which could either be due to a superstructure or the uptake of a large amount of water molecules, as suggested by EQCM analysis. From scan 18 up until the end of the reduction (scan 24, QQ 0 = 81.4 mAh/g), P1 peaks decrease. However, a thorough examination of the data did not reveal the emergence of a new set of peaks, leaving us to conclude that an amorphous compound is formed (referred to as P2). This amorphization-type transformation is tentatively ascribed to further water uptake and a swelling of the structure during Na insertion and concomitant formation of NDI 2-. Unlike during the reduction step, where the two phase transformations are merged into a single large electrochemical envelop (Figure 3), the oxidation is characterized by two main peaks I and (II+III) as previously described in Figures 1 and2. Remarkably, P1 reforms during the (II+III) oxidation process and reaches a maximum when the current response drops to nearly zero at scan 37. As expected from Figure 1 and 2, the corresponding capacity is (QQ red ) = 48.4 mAh/g, which is 66% of the total capacity upon oxidation (73.0 mAh/g).

During step I, a second phase transformation characterized by the full disappearance of P1 occurs upon the appearance of a very broad peak from 6° to 11° (the latter can be better observed in Figure S10b). The angular range of this peak encompasses the initial DNVBr peaks, and therefore suggests that the corresponding re-oxidized phase (referred to as P0*) resembles

DNVBr. This intriguing contradiction between the smooth potential behavior (Figure 1) that suggests a solid solution type structural conduct, and the formation of new structural phases, has never been reported to our knowledge. As shown by the XRD diagrams in Figure S11, DNVBr is much less crystalline than MNV, which indicates a phase transformation associated with a potential plateau [START_REF] Toussaint | Development of a Rechargeable Zinc-Air Battery[END_REF] . The DNVBr molecule, which is nearly three times longer, is expected to inhibit long-range ordering and favor crystalline strains, this effect being presumably more pronounced at the surface of the grains. In this possible scenario, the potential being a surface measurement, we tentatively propose that the relatively less disordered inner part of the grains would favor the formation of the new phases, thereby leaving the surface with a wide variety of ionic and electronic states, and therefore a sloppy profile throughout the redox process.

To further support the unique properties of DNVBr, we used local spin density functional theory to model DNV and MNV as isolated solvent-free molecules. Both systems were fully geometrically optimized, and with the molecules in the neutral charge state (i.e. with full charges received from counter-anions, which are not explicitly included). In agreement with the experiment, both molecules are initially polarized with charge transfer from the Violo to the NDI. In MNV, 0.5e is donated from Violo to NDI (0.25e from each of the two Violo groups), whereas in DNV the ratio of NDI to Violo groups is different and as a result the Violo groups are more positive (+0.43e on average) and the NDI less negative (-0.44e).

Figure 4 shows the calculated Kohn-Sham electron eigenvalues for the DNV molecule. The molecule has a wide 3.3eV separation of filled and empty levels with nine additional states (labeled a-i in Figure 4) with nearly degenerate energy at the Fermi level. These mid-gap levels contain eight electrons in the neutral species. In the experimental crystal environment, the degeneracy of these states will be lifted by the presence of the counter anions. Since these will be distributed stochastically amongst available interstitial sites in the crystal, we expect the ordering of these levels a-i to vary between DNV molecules, which explains the redox peak broadening seen in experiment compared to the previous MNV studies. Since the system initially contains only anions, in general these will tend to localize near the positive Violo groups, stabilizing states a-c and pushing up empty states d-i. The first states to populate during electron addition will thus be these lowest unoccupied states d-i on the NDI. Once these molecules are charged, further electron addition to the sample will then be to the remaining DNV molecules with empty Violo states near the Fermi level (ac).

Importantly, as charge is added to the DNV molecule these states split further (see Figure S12), while we expect the counter-ions to redistribute in response to charge filling. Furthermore, as electrons are added these gap states are driven upwards in energy and eventually encounter the higher energy empty states above them, which are more delocalized between Violo and NDI groups (Figure S12). This is consistent with the observed increase in sample conductivity at lower potentials (see below). Most interestingly this effect could corroborate the intermixed Violo-NDI character upon electron filling.

Additionally, the gap states in DNV are distributed across multiple groups of the same type (see Thus an important conclusion from the calculations is that the electron filling of DNV pushes towards a more intermixed p-/n-type behavior and its order on the Violo and NDI groups depends on the distribution and diffusion behavior of the counter ions in the crystal.

Electrochemical performance and optimization of DNVBr electrodes

The capacity retention of the DNVBr performance in NaClO 4 2.5 M was examined using variations in current and potential cut-off (Figure 5), and it was found that when using a 0.75V cut-off both the specific capacity and cyclability are comparable to that of MNV. However, as expected from Figure 1b, as soon as the cut-off is set to 0.85 V a significant capacity gain is observed for DNVBr, irrespective of the current load. The latter is close to 85 mAh/g at 0. Owing to the unique chemical structure of DNVBr (Scheme 1), two approaches for optimizing its specific capacity can be envisioned. The first consists in turning the two terminal pyridinium groups into redox active viologen units (1 e  each) by quaternization, while the second aims at decreasing the mass of the molecule by using lighter counter-anions. Taking n=3 for DNVBr (Scheme 1), bromine anions do represent 23% of the molecular mass. Accordingly, substituting Br  for Cl  and achieving the quaternization of the two terminal pyridinium moieties with methyl groups would lead to a specific capacity of 137.6 mAh/g (13 e  , M w = 2532.9 g/mol; considering n=3), which represents a gain of 31%. Unfortunately, the extremely low solubility of DNVBr in all solvents, except for trifluoroacetic acid (TFA), prevents further chemical modifications. However, the anionic exchange of Br  by Cl  could readily be achieved by simple immersion in an aqueous solution of NaCl 6 M at 50°C, witnessing a high anionic mobility within the DNV scaffold. Within the 0.75 ≤ E ≤ 0 V potential window, and by using 0.3 A/g (4C), this facile ionic exchange leads to a capacity gain of approx. 11.5% at 32C rate for DNVCl (Figure 5b).

As highlighted in Figures 1 and2, the positioning of the NDI • /NDI 2 redox couple (III) in the vicinity of practical cut-off potentials is a means of improving the electrochemical performance of DNVBr. Adjusting the level of this redox couple to a higher position than that observed in NaClO 4 2.5 M would indeed be one way to optimize the specific capacity. Bearing in mind that the free enthalpy of formation of each new redox state of organic materials depends on how much the charge (and/or radical) is stabilized, a convenient way of increasing the NDI-related potentials consists in augmenting the strength of the interaction between the counter ion and the NDI radical or di-anion [START_REF] Hernández-Burgos | Increasing the Gravimetric Energy Density of Organic Based Secondary Battery Cathodes Using Small Radius Cations (Li+ and Mg2+)[END_REF] . Based on Fajans' rule [START_REF] Fajans | Struktur und Deformation der Elektronenhüllen in ihrer Bedeutung für die chemischen und optischen Eigenschaften anorganischer Verbindungen[END_REF] that ϕ=Z/r², this approach is demonstrated here by changing the cation of the electrolyte from Na + (ϕ Na+ = 0.96 Å -2 ) to the much more polarizing Mg 2+ (ϕ Mg2+ = 3.86 Å -2 ).

-0,4 -0,3 -0,2 -0,1 0 0,1 0,2 0,3 -0,8 -0,7 -0,6 -0,5 -0,4 -0,3 -0,2 -0,1 Indeed, as pointed out by Abrũna and Dichtel [START_REF] Deblase | Cation-Dependent Stabilization of Electrogenerated Naphthalene Diimide Dianions in Porous Polymer Thin Films and Their Application to Electrical Energy Storage[END_REF] , the stabilization effect by the Mg +2 cation induces shifts as large as +240 mV and +700 mV for NDI/NDI  and NDI  /NDI 2 respectively, in a porous polymer derivative when substituting 0.1 M TBAClO 4 with 0.1 M Mg(ClO 4 ) 2 in acetonitrile. In our case, substituting Mg(ClO 4 ) 2 for NaClO 4 , while keeping the cation concentration constant [Na + ] = [Mg 2+ ] = 2.5 M, permits an increase in the two redox processes associated with the formation of NDI  and NDI 2 by +52 mV and +75 mV respectively (Figure 6a). Interestingly, these increments in potential are still positive (+25 mV for NDI/NDI  and +27 mV for NDI  /NDI 2 , respectively), and remain so even with a lower concentration of salt [Mg 2+ ] = 1.25 M (Figure 6a). These shifts are in the same order of magnitude (100 mV) as those observed by Y. Yao in an aqueous electrolyte (estimated to be approx. 120 mV from results reported in the supplementary information [START_REF] Liang | Universal quinone electrodes for long cycle life aqueous rechargeable batteries[END_REF] ), and are much less pronounced than those described in the work of Abrũna and Dichtel [START_REF] Deblase | Cation-Dependent Stabilization of Electrogenerated Naphthalene Diimide Dianions in Porous Polymer Thin Films and Their Application to Electrical Energy Storage[END_REF] . This mitigated effect in aqueous electrolytes is tentatively ascribed to the higher permittivity and solvating ability of water molecules, which presumably better shields the guest cation interaction from the DNVBr electron density. This hypothesis would corroborate the large amount of water involved in the insertion/de-insertion process as suggested by EQCM results. Nevertheless, Figure 6b shows that when maintaining a 0.75 V cut-off, the potential shift of the NDI  /NDI 2 redox couple is large enough to induce a significant increase in the capacity, from 63 to 75 mAh/g, without having a detrimental effect on the cyclability. We note that, as expected, the magnesium electrolyte has no effect when the cut-off is set to -0.85 V during the 2.4 A/g periods (Figure 6b).

As stated before, the high NDI/Violo ratio provides substantial hydrophobicity to DNV, which results in absolute insolubility in aqueous media, as opposed to MNV [START_REF] Perticarari | Dual Anion-Cation Reversible Insertion in a Bipyridinium-Diamide Triad as the Negative Electrode for Aqueous Batteries[END_REF] . Taking advantage of this property, and to further demonstrate the interest in using the DNV derivative for low-cost grid storage, long cycling experiments were conducted both in Na perchlorate and, more interestingly, in ocean water electrolytes (Figures 7a,b). In both cases, DNVBr shows remarkable cycling behaviors and coulombic efficiencies from 0.15 A/g (2C) (4C in NaClO 4 ) to 2.4 A/g (32C), with an impressive capacity retention of 82.8% and 77.7% upon 6500 (936 hours) and 2570 (1019 hours) cycles in NaClO 4 2.5 M and ocean water, respectively, making it one of the most stable electrode materials for use as the negative electrode of aqueous batteries. We note that the pH was found to increase from neutrality to approx. 9.3 upon 6600 cycles in NaClO 4 , which could potentially trigger a hydrolysis of the CN bonds. However, no attempt was made to optimize the cyclability using pH buffers in the present work. Further cycling in ocean water was conducted by opening the electrochemical window from (0; 0.75V) to (0; 0.85V) and decreasing the cycling rate to 0.15 A/g (2C) and 0.3 A/g (4C). Under these conditions a gain in capacity of 20% was achieved, permitting the storage of nearly 60 mAh/g upon 3000 cycles (1800 hours). These values compare well with those of previously demonstrated aqueous batteries [START_REF] Liang | Universal quinone electrodes for long cycle life aqueous rechargeable batteries[END_REF][START_REF] Lee | Manganese hexacyanomanganate open framework as a high-capacity positive electrode material for sodium-ion batteries[END_REF][START_REF] Häupler | Aqueous zinc-organic polymer battery with a high rate performance and long lifetime[END_REF][START_REF] Kim | An Aqueous Sodium Ion Hybrid Battery Incorporating an Organic Compound and a Prussian Blue Derivative[END_REF][START_REF] Yao | Aqueous Energy Storage Devices with Organic Electrode Materials[END_REF] , with the added advantage of using low-cost (Na), sustainable (ocean water) and neutral electrolytes. It is worth mentioning that in ocean water the capacity drops by approx. 10 mAh/g when increasing the current load from 0.6 A/g (8C rate) to 38 mAh/g at 1.2 A/g (16C rate) whereas in NaClO 4 2.5 M, under the same conditions, the drop is only approx. 3 mAh/g. Ragone tests confirm this trend (Figure S14) which matches the electrolyte conductivity values (Table S3). Additionally, because similar Ragone profiles are obtained for both NaCl and NaClO 4 with the same concentration (2.5 M, Figure S14), it is the ionic conductivity of the electrolyte rather than the nature of the anion that rules the kinetics of these electrochemical reactions. Aside from some rare examples [START_REF] Deunf | Reversible anion intercalation in a layered aromatic amine: a high-voltage host structure for organic batteries[END_REF][START_REF] Deunf | Solvation, exchange and electrochemical intercalation properties of disodium 2,5-(dianilino)terephthalate[END_REF] , the use of organic materials for electrochemical storage in both aqueous and non-aqueous media is hampered by the large quantities of carbon additives (typically >30 wt.%) [START_REF] Muench | Polymer-Based Organic Batteries[END_REF] that are required in order to compensate for their relatively low electronic conductivity. Added to the intrinsically low volumetric density of organic materials, this flaw makes the efficient design of the electron percolating [START_REF] Fongy | Electronic and Ionic Wirings Versus the Insertion Reaction Contributions to the Polarization in LiFePO4 Composite Electrodes[END_REF] network and the optimization of the electrode thickness [START_REF] Hatakeyama-Sato | An Ultrahigh Output Rechargeable Electrode of a Hydrophilic Radical Polymer/Nanocarbon Hybrid with an Exceptionally Large Current Density beyond 1 A cm -2[END_REF][START_REF] Singh | A systematic study of thick electrodes for high energy lithium ion batteries[END_REF][START_REF] Wang | Formulation and characterization of ultra-thick electrodes for high energy lithium-ion batteries employing tailored metal foams[END_REF] even more critical to reducing the cost of stored energy. These two key points, scarcely studied in the literature [START_REF] Hatakeyama-Sato | An Ultrahigh Output Rechargeable Electrode of a Hydrophilic Radical Polymer/Nanocarbon Hybrid with an Exceptionally Large Current Density beyond 1 A cm -2[END_REF][START_REF] Iordache | From an Enhanced Understanding to Commercially Viable Electrodes: The Case of PTCLi4 as Sustainable Organic Lithium-Ion Anode Material[END_REF] , were investigated for DNVBr composite electrodes by using varying amounts of carbons, mixing protocols and areal capacity. We note that carbon nanotubes were not considered in this work owing to their elevated price, even though they have been shown to significantly reduce the percolation threshold of electroactive organic-based composite electrodes [START_REF] Hatakeyama-Sato | An Ultrahigh Output Rechargeable Electrode of a Hydrophilic Radical Polymer/Nanocarbon Hybrid with an Exceptionally Large Current Density beyond 1 A cm -2[END_REF][START_REF] Iordache | From an Enhanced Understanding to Commercially Viable Electrodes: The Case of PTCLi4 as Sustainable Organic Lithium-Ion Anode Material[END_REF] . Contrary to most of the electroactive organic materials published thus far [START_REF] Poizot | Progress in all-organic rechargeable batteries using cationic and anionic configurations: Toward low-cost and greener storage solutions?[END_REF] , we demonstrate below that at 1C, a rate that is compatible with renewable energy storage, the best specific capacity per mass of the whole electrode is obtained with a carbon black content as low as 10wt%.

Let us first consider the electrical property of a standard thin electrode of 0.7 mAh/cm 2 where 25% carbon additive was hand-mixed with DNVBr (referred to as DNVBr-HM-25%). In this case, EIS measurements show that the resistance associated with the semi-circle decreases slightly from approx. 5.5 ohms to 3.5 ohms during the reduction process from the initial state to 0.64 V, and then remains constant irrespective of the state-of-charge (Figure S15b). Given the high conductivity of the electrolyte (Table S3), this behavior indicates that DNVBr charge transfer resistance is not detectable, and that it is instead the response of the percolating carbon additive network which is measured. Such low cell resistance is expected to induce a barely detectable polarization of 4.5 mV if the current increases from 0.3 A/g (4C rate) to 2.4 A/g (32 C rate). This point is illustrated in Figure S16 where a negligible polarization and a drop in specific capacity are indeed observed while the current load is multiplied by a factor of 8 both on discharge and on charge, from 4C to 32C. There are thus two points worth noting from these results: (i) 25% carbon additive constitutes a large excess of carbon additive and (ii) DNVBr seems to be associated with extremely fast intrinsic kinetics (that includes charge transfer, phase boundary displacement, solid state ionic diffusivity and electron conductivity), which do not appear to substantially limit the electrode properties, even at rates of up to 32C.

The electrical behavior of DNVBr itself was therefore unraveled by decreasing the weight fraction of the carbon additive to 10 wt% (DNVBr-HM-10%). The resulting EIS measurements do indeed show a correlation between the state-of-charge and the value of the resistance that is ascribed to a charge transfer mechanism (Rct) (Figure 8a, fits with the data reported in Figure S17): (i) a marked decrease in Rct during the reduction process, (ii) an increase in Rct upon completion of the reduction, and (iii) a reverse trend during oxidation. We note the presence of the same evolution during the second cycle (Figure S17). The intriguing increase of Rct observed at the end of the reduction process can tentatively be ascribed to the drastic change in the electronic state of the molecule from a dual-radical form (NDI • and Violo •+ ) to a radical/quinoid one (NDI 2 and Violo •+ ). However, further research needs to be devoted to this point since this "electronic" transformation is paired with the structural evolution of the solid (P1 to P2), as shown in Figure 3. The results nonetheless show that the reduction of DNVBr is accompanied by a significant decrease in Rct, which supports DFT findings. They also show that, except for the most oxidized states, Rct remains as low as 13 to 45 ohms, which opens up the possibility for a further increase in active material loading. In order to confirm this, we tested DNVBr without any carbon additive. We found only one other example of an organic material having been shown to be electro-active without carbon additive [START_REF] Deunf | Reversible anion intercalation in a layered aromatic amine: a high-voltage host structure for organic batteries[END_REF] . Results reported in The effect of the surrounding composite electrode on the overall performance was further investigated by studying the influence of a ball milling step (BM) using different carbon contents. These samples are referred to as DNVBr-BM-X%, where X stands for the weight fraction of carbon additive (5 < X < 20). SEM images, as well as specific surface values derived from BET analysis, are reported in Figures S18, S19 and S20, confirming that the ball milling step strongly favors inter-particle contacts. The cyclability of these electrodes is reported in Figure S21. Fits to the EIS data (Figure S22 and S23) clearly show that as the carbon content drops from 20 wt.% to 5 wt.% the resistance (Rct) sharply increases from 11 to 1850 ohms (Figure S23). This trend is most prominent between 10 wt.% and 5 wt.%, suggesting that a threshold lies in between these two compositions. Ragone plots performed upon oxidation (Figure 9a) indeed show that with 5 wt.% carbon additive, 70% of the full capacity (which is 94 mAh/g DNVBr as observed for DNVBr-20-BM) is obtained at 0.22C, while with 10 wt.% of carbon additive, full capacity can be attained. Importantly, out of the four samples DNVBr-10-BM shows the best specific capacity up to C rate in terms of electrode mass (Figure 9b), with a gain as high as 30% at C/4 rates (82 mAh/g electrode ) vs. DNVBr-20-BM (69 mAh/g electrode ).

Increasing the amount of carbon additive above 10wt% is therefore only necessary for highrate uses. In this regard, it is to be noted that DNVBr-BM- Due to the fact that aqueous battery technology requires electrodes to be several mAh/cm 2 so as to reach the 100 $/kWh target, we also demonstrate in Figure 9c that the performance of DNVBr-HM-25 implemented in a thick electrode of 8 mAh/cm 2 (76.5 mg/cm 2 of DNVBr, 0.53< thickness < 0.78 mm, Figure S24) shows similar cyclability and Coulombic efficiency at 1C rate to a 1 mAh/cm 2 (9.6 mg/cm 2 of DNVBr, 65 m) (Figure 9c), yet possesses a much higher areal capacity (3.4 mAh/cm 2 vs. 0.55 mAh/cm 2 ).

In conclusion, DNVBr is a unique and highly promising electroactive organic material that can simultaneously exchange both inexpensive as well as abundant cations (such as Na and Mg)

and anions (Cl  ), and can reach more than 100 mAh/g at an optimal potential of 0.55 V vs.

SCE with remarkable capacity retention and Coulombic efficiency in several neutral electrolytes, including ocean water. Thanks to the intrinsically high kinetics of the material, straightforward electrode engineering was shown to enable a significant optimization of the overall performance by increasing the active material content from 75 to 95%, and the surface capacity from 0.65 to 3.6 mAh/cm 2 .

Electrochemical performance of full cells

To further demonstrate the interest of DNVBr, a full organic cell was assembled in the discharge state using a commercial p-type TEMPO derivative (4-HydroxyTEMPObenzoate, referred to as 4HT) as the active material of the positive electrode. A comprehensive study of the 4HT material being out of the scope of this paper, we put forward a proof of concept of the cell using three electrodes set up in order to follow the electrochemical response of the two electrodes. We note that, at this stage of the study, and with 4HT being slightly soluble in NaClO4 2.5 M, we used a more concentrated NaClO4 electrolyte (arbitrarily saturated). It is worth noting this cell is a hybride, p-type (anionic) rocking chair battery, and dual ion since DNVBr still needs to draw sodium cations from the electrolyte. To mimic the galvanostatic cycling of a real battery, no potential restrictions were applied to the two working electrodes.

Rather, the cell voltage was controlled between 0 and 1.8 V. Under these conditions, the best capacity ratio was found to be nearly 1.0, resulting in the highest average discharge voltage of 1.07 V (Figure 10a) and the best cyclability (Figure 10b). This output average voltage is comparable to the currently most promising Na (1.1-1.4 V), Li aqueous based systems (1.1 V) [START_REF] Liang | Universal quinone electrodes for long cycle life aqueous rechargeable batteries[END_REF][START_REF] Gao | An Aqueous Symmetric Sodium-Ion Battery with NASICON-Structured Na3MnTi(PO4)3[END_REF] and mixed Li/Na cells [START_REF] Whitacre | An aqueous electrolyte, sodium ion functional, large format energy storage device for stationary applications[END_REF] . The specific energy density of this new cell is 36 Wh/kg by mass of the two active materials at C rate, which is competitive with recent sodium-based aqueous batteries (27 [START_REF] Lee | Manganese hexacyanomanganate open framework as a high-capacity positive electrode material for sodium-ion batteries[END_REF] -42 [START_REF] Whitacre | An aqueous electrolyte, sodium ion functional, large format energy storage device for stationary applications[END_REF][START_REF] Gao | An Aqueous Symmetric Sodium-Ion Battery with NASICON-Structured Na3MnTi(PO4)3[END_REF] Wh/kg) but still lower than the Li-aqueous mixed inorganic/organic battery recently achieved (92 Wh/kg 7 ). We note, however, that all these batteries use at least one inorganic material which is associated with larger grey energy [START_REF] Poizot | Clean energy new deal for a sustainable world: from non-CO2 generating energy sources to greener electrochemical storage devices[END_REF] .

Moreover, because of the high ionic conductivity of the electrolyte (9.6 S/cm) and rapid reaction of the electrodes in the present cell, 98.4% of the maximum discharge capacity was retained at 8C rate, while at nominal rates of 16C (1.2 A/g) and 32C (2.4 A/g), 97.1% and 95% of the capacity was still available, respectively. When compared to the state-of the art of Na and Li aqueous batteries, an excellent cyclability could be achieved, with 80% of the initial capacity being retained after 1200 cycles (600 hours). The Coulombic efficiency stays remarkably high (>99.93%) at high rates, and higher than 99.57% at 1C rate (Figure 10b). With respect to corrosion issues, it is instructive to note that charging the cell up to 1.8V did not provoke any strong deviation of the pH which self-buffers to around 5 (Figure 10b).

Conclusion:

All of the above results serve to demonstrate the uniqueness and efficiency of the proposed diblock bipyridinium-naphthalene diimide oligomer (DNV) in maintaining a high capacity, as well as in sustaining long-term cycling, in several molar range and neutral aqueous electrolytes, such as ocean water, for several thousand cycles. Furthermore, the capacity for anionic exchange, electrolyte tailoringand the design of highly-loaded (8 mAh/cm When glove bags were used, electrolytes were degassed with argon bubbling for 1h within the glove bag prior to use. Experimental errors related to capacity values were always below 5% using our protocols and set-up, and both glove bags and glove box environments were found to lead to similar electrochemical results.

Electrochemical impedance measurements were performed from 180 kHz to 100 mHz with a perturbation voltage of 7mV. Power tests on charge were carried out using the "single charge technique" consisting of OCV relaxations until ΔU/t = 1 mV/h between each current pulse from I max to I min . All experiments were conducted twice in order to ensure reproducibility.

Synthetic Procedures:

All commercially obtained solvents and reagents were used without further purification unless noted below. The 1,4,5,8-naphthalenetetracarboxylic dianhydride, 4,4'-bipyridyl, 3bromopropylammonium bromide and sodium perchlorate were purchased from Sigma-Aldrich.

Compound 3: A mixture of naphthalene tetracarboxylic dianhydride (536 mg, 1.99 mmol), 3-3-bromopropylammonium bromide (1.64 g, 7.5 mmol) and Et 3 N (1.0 mL) in AcOH (10 mL) was refluxed for 24 h. The reaction mixture was filtered and thoroughly washed with water and MeOH to give 3, as a white solid (900 mg, 89%). This compound was used in the next reaction without further purification. [START_REF] Poizot | Progress in all-organic rechargeable batteries using cationic and anionic configurations: Toward low-cost and greener storage solutions?[END_REF] H NMR (300 MHz, DMSO-d 6 ): δ 8.69 (s, 4H), 4.19 (t, J = 6.9 Hz, 4H), 3.64 (t, J = 6.9 Hz, 4H), 2.24 (q, 4H).

Compound

DNVBr:

In a sealed tube, N,N'-Bis(2-bromoethyl)-1,4,5,8naphthalenetetracarboxylic 1,8:4,5-diimide 3 (500 mg, 0.984 mmol) was added to 4,4'bipyridine (154 mg, 0.984 mmol) (4) in anhydrous DMF (10ml). The reaction mixture was reacted for 4 days at 130°C. After cooling down to room temperature, the dark brown precipitate was filtered and thoroughly washed with methylene chloride yielding 180 mg of final product 5. The dark brown product obtained is totally insoluble in organic solvents, preventing its characterization by Size Exclusion Chromatography and by Mass spectrometry analyses, and therefore precluding the determination of its polydispersity. Accordingly, the yield of the last step could not be accurately determined. [START_REF] Poizot | Progress in all-organic rechargeable batteries using cationic and anionic configurations: Toward low-cost and greener storage solutions?[END_REF] Ionic exchange (DNVCl): 50 mg of DNVBr was dispersed in aqueous 6 M solution of NaCl.

The suspension was stirred for 4 days at 50°C. Subsequently, the precipitate was washed several times with water, dried at 60°C under vacuum overnight to finally obtain 40 mg of DNVCl.

The final product was characterized by SEM-EDS (Figure S25), 1 HNMR (Figure S26) and TGA-MS/DSC (Figure S27). Electrode preparation: All electrodes contained 5wt% PTFE as the binder and only the DNVBr/carbon additive ratio was varied. However, unless otherwise specified, the electrode composition remained 70 wt% active material, 25 wt% Ketjen Black, and 5 wt% PTFE. The DNVBr BM electrodes were prepared by ball milling the mixture of active material and conductive carbon for one hour at 700 rpm using the Pulverisette 7 classic line (Fritsch). To this end, a total amount of 100 mg of the mixture was introduced along with 0.25 mL of water and three silicon nitride balls. The slurry was then dried and mixed with PTFE in order to obtain electrode compositions of DNVBr/KB/PTFE ranging from 75/20/5 to 90/5/5. The mixture was pressed at 5 tons on a stainless steel (AISI 304L) grid current collector. Unless otherwise specified, the electrodes were in the 0.6 to 0.7 mAh/cm 2 range.

Thick electrodes of 8 mAh/cm² were made in two steps. Firstly, a pellet was obtained by pressing a mixture of 70 wt% active material, 25 wt% Ketjen Black, and 5 wt% PTFE at 5 tons.

Secondly, this pellet was placed between two stainless steel grids and pressed at 2 tons in order to mitigate contact resistance with the current collector.

Scheme 1 :

 1 Scheme 1: Synthetic route to compound DNVBr having n = 3±1.

Scheme 2 :Scheme 3 :

 23 Scheme 2: Reversible one-electron reduction of both viologen (Violo) and naphthalene diimides (NDI) redox-active moieties in blue and red, respectively.

Figure 1 :

 1 Figure 1: (a) Typical cyclic voltammogram of DNVBr (blue) and MNV (red) measured in NaClO 4 2.5 M at a scan rate of 2 mV/s between 0 and -1 V vs. SCE. Limitation of the potentials (pink and light blue) was performed to enable a better description of the electrochemical reaction, denoted as II. (b) Comparison of DNVBr and MNV galvanostatic charge discharge profiles at 0.3 A/g (4C rate) in NaClO 4 2.5 M between 0 and -1 V vs. SCE.

Figure 2a :Figure 2b :

 2a2b Figure 2a: UV-vis spectroelectrochemical spectra and corresponding CVs of DNVBr measured in NaClO 4 2.5 M at a scan rate of 0.5 mV/s.

Figure 3 :

 3 Figure 3: Evolution of XRD diagrams of DNVBr upon subtraction of the background during 1 st reduction (scan 0-24) and oxidation (scans 25-49). The double arrow on the right-hand side represents the domain associated with the existence of P2.

Figure 4 :

 4 Figure 4: Calculated LDA-DFT Kohn-Sham eigenvalues (eV) for an isolated DNV molecule, showing the realspace wave function distribution on the molecule for states at the Fermi level. Level offset is for visual clarity and does not represent symmetry equivalent states. The molecule is in the neutral charge state, i.e. after charge transfer from nominal counter-anions, which are not included explicitly in the calculation.

Figure

  Figure 4a-c, h,i), differently to the smaller MNV molecule (Figure S13 for comparison). The

Figure 5 :

 5 Figure 5: (a) Capacity retentions on oxidation for (violet) DNVBr and (light blue) MNV in NaClO 4 2.5 M according to the standard cycling protocol (see experimental section). The red curve is associated with the capacity retention of DNVBr using a modified standard protocol (see experimental section) within 0.85 ≤ E ≤ 0 V as potential window and current loads as specified in the figure. (b) Cycling curves of DNVCl (blue) and DNVBr (pink) in NaClO 4 2.5 M using the standard cycling protocol (see experimental section).

Figure 6 a

 6 Figure 6 a) Incremental capacity curve on cycle 4 derived from galvanostatic cycling of DNVBr at 0.3A/g (4C rate); b) Cycling curves of DNVBr in NaClO 4 2.5 M (blue) and Mg(ClO 4 ) 2 1.25 M (red) using the standard cycling protocol (see experimental section).

Figure 7 :

 7 Figure 7: Cyclability and corresponding coulombic efficiency curves for DNVBr in (a) NaClO 4 2.5 M and (b) ocean water.

FigureFigure 8 a

 8 Figure S6 demonstrate the most unexpected capability of DNVBr, showing it to deliver nearly

Figure 9 :

 9 Figure 9: a) Ragone plots of DNVBr performed during oxidation with different percentages of carbon: 20 wt.% Kb (light blue), 15 wt.% Kb (dark blue), 10 wt.% Kb (red), 5 wt.% Kb (orange). The relative capacity "Q/Q Max " in a) refers to the maximum one Q max , as obtained for 20 wt.% Kb BM at C/10 rate and the specific capacity refers to the mass of active material, in b) the specific capacity refers to the mass of electrode. c) Comparison of experimental surface capacity, cyclability and Coulombic efficiency for 1 and 8 mAh/cm 2 electrodes of DNVBr-HM-25 in saturated NaClO 4 electrolyte at 1C rate.

Figure 10 :

 10 Figure 10: a) Potential-capacity profile of both 4HT and DNVBr electrodes of 0.65 mAh/cm 2 , b) Cyclability of the full cell at different C rates along with pH values of the electrolyte. C and D stand for charge and discharge rate, respectively. The inset shows that most of the cycling time was performed at C-rate, c) Voltage-capacity profile of the full cell, at C rate on charge, and from C to 32C rate on discharge, and d) the corresponding Ragone plot.

  [START_REF] Poizot | Progress in all-organic rechargeable batteries using cationic and anionic configurations: Toward low-cost and greener storage solutions?[END_REF] H NMR (300 MHz, TFA-d 1 ): δ 9.36 (m, 16H), 9.23 (d, J = 6.4 Hz, 4H), 8.99 (m, 22H), 8.64 (m, 20H), 5.12 (m, 16H), 4.59 (m, 17H), 2.82 (m, 16H).

Table 1 : Attribution of the most representative UV-Vis absorption bands relative to the reduction and oxidation of DNVBr in NaClO 4 2.5M.

 1

  15 and DNVBr-BM-20 can still achieve 47 mAh/g and 64 mAh/g per mass of electrode, respectively, at a currents as high as

	9.6 A/g (88 C), which competes well with best results obtained for similar areal capacity
	organic-based electrodes as reported by Oyaizu and Nishide 5 (0.8mAh/cm 2 PTAm-SWNT
	hybride electrodes with optimized current collector/electrode interface), and by Y. Yao 4 (0.5
	mAh/cm 2 electrodes of PPTO).

  [START_REF] Poizot | Perspectives in Lithium Batteries[END_REF] ) or devoid of conducting additives electrodes is shown to provide excellent prospects for future performance enhancement. Coupled with a commercial TEMPO derivative and a sodium electrolyte, this full organic aqueous battery ensures a long cycle life, extremely fast kinetics, as well as promising energy density values, thereby placing DNVBr among the top contenders for largescale energy storage. Electrode preparation") and all the pouch cells were mounted in a glove bag under constant argon flow. Electrodes were insulated from one another using a microfiber glass separator impregnated with 150 L of electrolyte before sealing at 180°C. activated carbon Norit 1600, 10 wt% Ketjen Black, and 10 wt% PTFE) was used to ensure that its potential remained in the 0; +0.3 region vs. the Saturated Calomel Electrode (SCE), which was used as the reference electrode. All tests were performed within either a glove bag (Aldrich) under N 2 flow or a glove box (Braun) under Ar with less than 1ppm O 2 .

	section ("Electrochemical tests were performed using either SP 300 or VMP potentiostats from Bio-logic
	SAS (Claix, France). DNVBr was characterized by cyclic voltammetry, potentiodynamic and
	galvanostatic cycling in NaClO 4 (1.25M and 2.5 M), ocean water (coast of Pornic, France,
	salinity of S=34) and in Mg(ClO 4 ) 2 (1.25 M and 2.5M) aqueous electrolytes. Based on Dittmar's
	Acronyms Law (C ion (mol/kg)=S*(Ionic factor)) was used to determine the precise composition of the
	EQCM, electrochemical quartz crystal microbalance; EIS, electrochemical impedance spectroscopy; NDI, Naphthalene diimide; Violo, Bipyridinium salt; XRD, X-Ray diffraction ocean water as follows:
	Ions	Ionic factor (mmol/kg) Dittmar Law C (mol/kg) C (Mol/l)
	Na +	13.402	0.455668 0.46683187
	Mg 2+	1.509	0.051306	0.052563
	Ca 2+	0.2938 0.0099892 0.01023394
	K +	0.2916 0.0099144 0.0101573
	Cl -	15.597 0.530298 0.5432903
	SO 4 2-	0.807 0.027438 0.02811023
	Br -	0.02404 0.00081736 0.00083739
	F -	0.00195 0.0000663 6.7924E-05
	DNVCl was characterized by galvanostatic cycling in NaClO 4 2.5 M. 4HT was characterized
	by galvanostatic cycling insaturatedNaClO 4 aqueous electrolytes. A standard cycling test is
	defined as a series of successive galvanostatic periods of 20 cycles at 0.3A/g (4C), 20 cycles at
	0.6A/g (8C), and 20 cycles at 1.2A/g (16C) in a (0; -0.75V) potential window, followed by 100
	cycles at 2.4A/g (32C) in a (0; -0.85V) potential window. A threefold-size counter-electrode
	(80 wt%

  H NMR (300 MHz, TFA-d 1 ): δ 9.34 (m, 13H), 9.23 (d, J = 6.4 Hz, 4H), 8.99 (m, 18H), 8.64 (m, 17H), 5.13 (m, 14H), 4.60 (m, 18H), 2.82 (m, 14H). FT-IR/ATR (cm -1 ):3382, 2990, 1702 (C=O imide asym.), 1656 (C=O imide sym.), 1640 (C=N+), 1577(C=N), 1449, 1376, 1331, 1242, 1178, 1050, 1013, 970, 814, 766.

c

Acknowledgements

JG and SP wish to thank: Dr. Antonio Jesus Fernandez Ropero (CIC Energigune), Dr.

Guillaume Ledain (IMN), and Nicolas Stephan (IMN) for their help with SEM pictures; Dr. Christelle Gautier (MOLTECH Anjou) for her technical assistance with EQCM measurements performed at Moltech Anjou in Dr. E. Levillain's group; Dr. V. Silvestre and B. Charrier (CEISAM, University of Nantes) for their help with NMR spectrometers, and Prof. Bernard Humbert (IMN) for fruitful discussions regarding FTIR data. JG and SP are also grateful to synchrotron SOLEIL for funding proposal 20160193 on the CRISTAL beamline, and Dr. Erik Elkaim (SOLEIL) for technical assistance with the beamline. JG is thankful to Nathalie Cochennec-Laureau (IFREMER) for providing salinity measurements and Dittmar's method for ion composition determination. All of the above-mentioned authors contributed to the present manuscript, and all have approved the final version.

Experimental Section

Characterization techniques:

1 H-NMR spectra were acquired using a Bruker ARX 300 MHz spectrometer. [START_REF] Schon | The rise of organic electrode materials for energy storage[END_REF] C-NMR spectra were recorded on a Bruker 500 MHz, operating at 125MHz, using a dual 1H/13C cryoprobe.

Spectra were recorded at room temperature. Chemical shifts are reported in ppm, and coupling constant in Hz. Multiplicity is presented in the following way: s = singlet, d= doublet, t = triplet, q = quintuplet, m = multiplet. Thermal analyses were performed with a NETZSCH STA 449F3 device under Argon atmosphere. Fourier transform infra-red spectroscopy (FTIR) spectra were collected with a Bruker Vertex 70 device in ATR mode, using a DTGS detector at a resolution of 4 cm -1 . Scanning electron microscopy (SEM) was performed using a JEOL JSM-7600F microscope. Energy-dispersive X-ray spectroscopy (EDS) was performed with a Hitachi HF-2000.

UV-Vis Spectroelectrochemistry of DNVBr was conducted using a BUNDLE-FLAME-ABS Ocean Optics spectrometer under N 2 atmosphere in an airtight glove bag. Each scan was recorded from 250 to 1050 nm within approx. 0.7s. Electrochemical quartz-crystal microbalance (EQCM) was performed with a Stanford Research Systems QCM200 Digital Controller and a QCM25 Crystal Oscillator (5 MHz Crystal). Operando X-ray diffraction was performed at SOLEIL synchrotron on the CRISTAL beamline using a 2D MAR detector. We used a home-made pouch cell bearing three electrodes sealed in Mitsubishi Escal Neo transparent films. The working electrode containing 70 wt.% active material, 25 wt.% Ketjen Black EC-600JD, and 5 wt.% PTFE was precisely aligned in the center of the pouch cell; a carbon reference electrode located was on one side, and a three-fold oversized carbon counter electrode (80 wt% activated carbon Norit 1600, 10 wt% Ketjen Black, and 10 wt% PTFE) on the other side. All the electrodes were prepared following the procedure described in the next


Hmamouche Youssef

Ochs Magalie

Prévot Laurent

Chaminade Thierry

Exploring the Dependencies between Behavioral and Neuro-physiological Time-series Extracted from Conversations between Humans and Artificial Agents

Keywords: Multimodal Signals Processing, Conversation, Machine Learning, Human-human and Human-machine Interactions, Functional MRI

Whole-brain neuroimaging using functional Magnetic Resonance Imaging (fMRI) provides valuable data to localize brain activity in space and time. Here, we use a unique corpus including fMRI and behavior recorded when participants discussed with a human or a conversational robot. Temporal dynamic is crucial when studying conversation, yet identifying relationship between the participants' behavior and their brain activity is technically challenging given the time resolution of fMRI. We propose here an approach developed to extract neurophysiological and behavioral time-series from the corpus and analyse their causal relationships. Preprocessing entails the construction of discrete neurophysiological time-series from functionally well defined brain areas, as well as behavioral time-series describing higher-order behaviors extracted from synchronized raw audio, video and eyetracking recordings. The second step consists in applying machine learning models to predict brain activity on the basis of various aspects of behavior given knowledge about the functional role of the areas under scrutiny. Results demonstrate the specificity of the behaviors allowing the predictions of the activity in functional brain areas.

INTRODUCTION

In neuroimaging, signal processing and machine learning techniques have become very useful, especially in explaining or predicting the brain activity based on external signals related to behavior. Meanwhile, analysis of temporal relationships between behavior and brain activity is an important step towards the investigation of the brain bases of natural social behaviors. This requires datasets comprising synchronized neurophysiological and behavioral time series recorded during unconstrained social interactions. In this paper, we propose to develop an approach to investigate a fMRI dataset acquired when participants were having a bidirectional natural conversation with a fellow human or a conversational robot [START_REF] Birgit | Brain activity during reciprocal social interaction investigated using conversational robots as control condition[END_REF]. This dataset is unique in that participants' behaviour is unconstrained and therefore different for each individual recording. Thus, the classical approach of contrasting two or more well controlled experimental conditions can't be used. The proposed approach consists instead in using behavioral recordings to predict fMRI responses in local-ized brain areas.

Existing works (cf. Section 2) have a major drawback in the sense that they use one or a small number of behavioral signals that are derived from very controlled tasks. Our contribution therefore consists in handling complex multimodal behavioral signals acquired during the unconstrained conversation and derive from them features that are relevant to predict brain activity in well-defined functional regions of interest. This contribution is divided in two parts. First, we propose a way of extracting representative time series(the behavioral features) from multimodal behavioral data acquired when participants discuss with a fellow human or a robot. These recordings include speech produced by the two interlocutors, as well as eyetracking signals of the participant while viewing videos of the human or artificial interlocutor. Then, we propose an approach to predict the discretized BOLD (Blood-Oxygen-Level-Dependent) signal, that measures the hemodynamic changes associated with brain activity, in well-defined functional areas from the behavioral features, using supervised machine learning algorithms. Our hypothesis is that only relevant behavioral features will be efficient in predicting the activity in a given brain area given domain knowledge about the function of this area.

The rest of the paper is organized as follows, after presenting existing related work (Section 2), we describe the fMRI experiment and recorded behavioral data in Section 3. Then, we formulate the problem in Section 4. We then present and discuss our results in Section 5, and summarize our approach and results in Section 6.

RELATED WORK

In the literature, many approaches based on multiple linear regression have been proposed to address the problem of fMRI signals prediction. In [START_REF] Mitchell | Predicting Human Brain Activity Associated with the Meanings of Nouns[END_REF], the fMRI neural activation associated to meanings is predicted based on a large text data. The brain regions studied are in the sensory-motor cortex. The model used consists of transforming the meaning of text into semantic features, then building a regression model that expresses the fMRI brain activity as a linear combination of input semantic features. The authors show a prediction accuracy of 0.62 or higher, but on each participant independently. This issue has also been addressed with multi-subject approach, that is, by concatenating data from multiple subjects. For example, in [START_REF] Huth | Natural speech reveals the semantic maps that tile human cerebral cortex[END_REF], the goal was to predict voxels activity measured via the BOLD signal based on the speech meaning. The used data are collected from an fMRI experiment performed on 7 subjects. The brain areas predicted are from the cerebral cortex (the lateral and ventral temporal cortex, lateral and medial parietal cortex, and superior and inferior prefrontal cortex). The methodology adopted is based first on constructing predictive variables using semantic features extracted from natural language. Second, dimension reduction using Principal Component Analysis (PCA) is applied to reduce the number of the predictive variables. Then, a prediction model is learned based on multiple linear regression with regularization to predict the BOLD signal. The prediction results and the principal components of the predictive variables are both combined to classify brain areas according to the semantic features categories.

In addition to the semantic features, other behavioral signals have been analyzed by studying the effect of a single predictive variable on the brain activity. For example, the reaction time is used to predict activity in specific brain regions [START_REF] Yarkoni | BOLD Correlates of Trial-by-Trial Reaction Time Variability in Gray and White Matter: A Multi-Study fMRI Analysis[END_REF]. In [START_REF] Chen | A Gaussian mixture regression approach toward modeling the affective dynamics between acousticallyderived vocal arousal score (VC-AS) and internal brain fMRI bold signal response[END_REF], the acoustically-derived vocal arousal score [START_REF] Bone | Robust Unsupervised Arousal Rating: A Rule-Based Framework with Knowledge-Inspired Vocal Features[END_REF]) is used to predict the BOLD signal using the Gaussian mixture regression model. In [START_REF] Knops | Recruitment of an Area Involved in Eye Movements During Mental Arithmetic[END_REF], the authors predict the BOLD signal in the posterior parietal cortex based on eye movement data using a multivariate regression model.

More general approaches try to predict the brain activity of various areas using different types of signals at the same time. For example, in [START_REF] Desouza | Correlating Behavioral Responses to fMRI Signals from Human Prefrontal Cortex: Examining Cognitive Processes Using Task Analysis[END_REF], correlations are analyzed using linear regression between the BOLD signal and behavioral features computed from observed facial expressions, reaction time and eyetracking data.

DATASETS ACQUISITION AND PROCESSING

In this section, we describe the experimental paradigm, the data recorded in this experiment, and describe our analysis. The data is collected from an fMRI experiment described in [START_REF] Birgit | Brain activity during reciprocal social interaction investigated using conversational robots as control condition[END_REF].

The experiment involves twenty five participants, and consists of four sessions, each containing six conversations of 60 seconds each, three with a human and three with a conversational robot alternatively. A "advertising campaign" provides a cover story: participants are informed that they should guess what is the message brought by images in which the fruits appear either as 'superheroes' or 'rotten fruits'. The conversations between the participant and either a confederate of the experimenter or a FURHAT conversational robot [START_REF] Al Moubayed | Furhat: A back-projected human-like robot head for multiparty human-machine interaction[END_REF] (controlled by the confederate in a Wizard-of-Oz mode, unbeknown to the participant), are about single images of the purported "advertising campaign". The experiment design is illustrated in Figure 1

Time Series Extraction

We process the recorded behavioral and neurophysiological signals in order to extract representative features, then we construct structured time series for each subject that can be used for machine learning models. This processing is illustrated in Figure 3.

Processing fMRI Signals

Standard functional MRI acquisition procedures were used, described in details in [START_REF] Birgit | Brain activity during reciprocal social interaction investigated using conversational robots as control condition[END_REF]. BOLD signal 3-dimensional images are recorded in the whole brain every 1.205 seconds. Standard SPM12 preprocessing procedures are used [START_REF] Penny | Statistical Parametric Mapping: The Analysis of Functional Brain Images[END_REF], including correction for time delays in slice acquisition ("slice timing"), image realignment, magnetic field inhomogeneities correction, normalization to the standard MNI space using the DARTEL [START_REF] Ashburner | A fast diffeomorphic image registration algorithm[END_REF] procedure for coregistration of individual participants' anatomy, and finally spatial smoothing with a 5-mm full-width halfmaximum 3-dimensional Gaussian kernel. Extraction of the signal in regions of interest is performed using the conn toolbox (Whitfield-Gabrieli and Nieto-Castanon, 2012), and includes several denoising procedures, firstly a linear detrending using a high-pass filter with a threshold of 128 seconds, secondly using realignment parameters to calculate nuisance regressors related to participants' movement during scanning, thirdly taking heartbeat and breathing recordings to remove physiological artifacts with the PhysIO toolbox [START_REF] Kasper | The PhysIO Toolbox for Modeling Physiological Noise in fMRI Data[END_REF], and finally extracting BOLD signal in the white matter and cerebrospinal fluid and using the 5 first eigen variate of the timeseries as nuisance representing signal fluctuations in non-cortical brain tissues. A 275-area parcellation based on functional and anatomical connectivity patterns [START_REF] Fan | The Human Brainnetome Atlas: A New Brain Atlas Based on Connectional Architecture[END_REF] defines regions of interest (ROI) for the whole brain, and specific regions are chosen based on their anatomical location. Continuous time-series (385 time points) are extracted for each ROI and each session and participant representing the mean activity after denoising.

For the current demonstration, we focus on 5 ROIs chosen in order to validate our approach using well-defined functional areas: the Fusiform Gyrus ROI corresponds to the Fusiform Face Area involved in face perception, the left and right Motor Cortex ROIs support speech production, and the left and right Superior Temporal Sulcus ROIs are involved in speech perception.

Processing Multimodal Behavioral Signals

During conversations, different types of behavioral data are recorded for both the participant and his interlocutor: video of the interlocutor, gaze movements of the participant using an eyetracking system, and the speech of both of them. For each of these modalities, several time series are computed to represent the evolution over time of different variables for both the participant and his interlocutor.

First, speech to text transformation is performed manually, then automatic annotation and segmentation are applied using SPPAS [START_REF] Bigi | SPPAS -multi-lingual approaches to the automatic annotation of speech[END_REF]. From the obtained transcriptions, we have extracted many linguistic time series such as the Speech activity (the presence the speech), Overlap (presence of speech of both interlocutors), Laughters, Filled-breaks and the Reaction time. The reaction time in our case represents the amount of time taken by an interlocutor to speak after the other interlocutor finishes his turn. We consider this amount positive if there is a delay between the speaking turns and negative in case of overlap.

We also consider specific features like interpersonal Particles items, i.e., words that may express the mood of the speaker (e.g., but, well, maybe), Discourses markers, which are expressions used to make the discourse organized (e.g., I mean, so, therefore, okay) [START_REF] Schiffrin | Discourse markers[END_REF], and Feedback lexical items, which represent words used for reaction, perception and understanding (e.g., yes, no, okay, right) [START_REF] Gravano | Affirmative cue words in task-oriented dialogue[END_REF].

The time series categorizing these features are resampled according to the fMRI acquisition frequency by considering the percentage of their existence in each time bin. Figure 2 illustrates an example of resampling the speech activity. Note that if we make direct projection on the expected axis, we may lose information between two consecutive fMRI acquisitions concerning the quantity of speech or silence that have occurred. That is why at each point we consider the percentage to have a sort of summary of what happens after the previous point.

The speeches are also analyzed via lexical richness based on two metrics from [START_REF] Ochs | Toward an automatic prediction of the sense of presence in virtual reality environment[END_REF], that consider the number of the different words (typetoken ratio) and the number of adjectives plus the number of adverbs resp., divided by the number of to- tal words in the text of each speaking turn. Sentiment analysis is also considered by calculating the polarity and the subjectivity using the Pattern library [START_REF] Smedt | Pattern for python[END_REF]. The polarity score fluctuates between -1 (negative behavior) and 1 (positive behavior), while the subjectivity is between 0 (objective) and 1 (personal). The method of their calculations is based first on manual association of the polarity and the subjectivity scores to a set of adjectives among the most used. Second, another set is extracted with the most frequent nouns and the predecessor adjectives as features. Finally, a kNN classifier is learned to determine the scores of neighbor adjectives of those manually annotated [START_REF] Smedt | Pattern for python[END_REF].

From videos, we used pre-trained models from Openface [START_REF] Baltrusaitis | OpenFace 2.0: Facial Behavior Analysis Toolkit[END_REF] to extract 68 facial landmarks and 17 facial action units, which categorize facial movements [START_REF] Bartlett | Classifying facial action[END_REF]. The 3D coordinates of gaze movements (3 features) and head pose translations and rotations (6 features) are also extracted. The time series associated with these features are constructed by analyzing each image of the videos. In this case, the resampling task is less difficult compared to speech features, because all the variables have the same frequency and the same number of observations. From raw eyetracking data, we compute the speed of the gaze movements. Then, we project the gaze coordinates on visual stimulation using the extracted landmarks to localize where the subject is looking in at each time step (face, eyes, mouth). The saccades are also detected by the used eyetracking system, and added to the extracted features.

Table 1 summarizes all the extracted predictive features. After gathering and resampling them in addition to the BOLD signal, we build multivariate time series for each subject with the same number of observations.

ANALYTICAL APPROACH

One hypothesis of this work is that the activity in functional brain areas is mainly determined by what participant experiences, described here by behavioral signals. Therefore, we try to predict the processed BOLD signal based only on the history of behavioral features. Note that it is possible to predict the activity of a brain area based on its previous observations and the previous observations of other related areas. Accordingly, auto-regressive models can be used in this situation, such as the ARIMA (Auto-Regressive Integrated Moving Average) [START_REF] Box | Time series analysis: forecasting and control[END_REF] model to predict a single time series, or the co-intregrated vector auto-regressive models for multivariate prediction of non-stationary time series [START_REF] Johansen | Estimation and hypothesis testing of cointegration vectors in gaussian vector autoregressive models[END_REF].

In our research work, our goal is to better understand the behavioral features related to the brain activity by comparing human-human and human-machine interaction. Consequently, we focus on the behavioral features to predict the BOLD signal.

Feature Selection

Domain knowledge allows us to determine the set of possible behavioral signals responsible for the activation of each brain area. For example, to predict the BOLD signal of the Fusiform Gyrus area, which is involved in face perception [START_REF] Kanwisher | The fusiform face area: a cortical region specialized for the perception of faces[END_REF], we can use features derived from video and eyetracking signals, in order to take into account the visual simulation and the gaze movement of the participant to evaluate where he is looking. For some complex brain areas, this is not sufficient, especially when multiple modalities are involved, because the set of generated predictive features may be large. In this case, we use automatic feature selection to refine the input features before applying prediction models.

Prediction

The BOLD signal results from a function called the Hemodynamic Response Function (HRF), which determines the activation delay after receiving a trigger event, which peaks close to 5 seconds after the event [START_REF] Gössl | Bayesian modeling of the hemodynamic response function in bold fmri[END_REF]. This delay is a key parameter in our approach to model the dynamic between the BOLD signal and the behavioral features.

Let Y (t) be a variable representing the discretized BOLD signal of a given brain area of one subject, and

X(t) = {X 1 (t), X 2 (t), . . . , X k (t)}, is a k-dimensional
time series representing the behavioral variables. The first formulation that comes to mind is to expresses each value of the BOLD signal at time t as a function of the predictive features at time t -5s. This process can be written as follows:

Y (t) = f (X 1 (t -5s
), X 2 (t -5s), . . . , X k (t -5s))+U(t),

(1) where U(t) is the vector of errors of the model, and f is the function that we want to find.

Considering the fact that the 5s delay is not fix for all subjects and brain areas, but varies around 5s, it can be more relevant to include more than one values around the 5s. Consequently, as an improvement of equation 1, our formulation can be expressed as follows:

Y (t) = f (X 1 (t -4s), X 1 (t -5s), X 1 (t -6s), (2) . . . , X k (t -4s), X k (t -5s), X k (t -6s) +U(t),
As mentioned in Section 1, our approach is based on discretizing the variable describing local brain activity into binary variable (activation or not). The motivation behind the discretization is that instead of predicting the exact value of the BOLD signal, we start by predicting if a brain area is active or not. In our case, classification models can be used to approximate the function f . The other possibility is to keep the BOLD signals continuous and use multiple regression to predict them, which is the classical approach in the literature [START_REF] Mitchell | Predicting Human Brain Activity Associated with the Meanings of Nouns[END_REF][START_REF] Huth | Natural speech reveals the semantic maps that tile human cerebral cortex[END_REF][START_REF] Knops | Recruitment of an Area Involved in Eye Movements During Mental Arithmetic[END_REF][START_REF] Desouza | Correlating Behavioral Responses to fMRI Signals from Human Prefrontal Cortex: Examining Cognitive Processes Using Task Analysis[END_REF]. In our case, we evaluate both approaches by using multiple regression, then discretizing the predictions in order to compare all models with same prediction accuracy measures.

RESULTS

In this section, we present the prediction procedure used, the obtained prediction scores, and discuss the results.

Prediction Procedure

The pre-processed time series of each subject are restructured in such a way to have a target variable and the lagged behavioral variables as predictive features according to Equation 2. The data of all subjects are concatenated, and randomly shuffled to train and test the models on all observations. The prediction procedure is based on a 10-fold-cross validation to find the parameters of the prediction models on the training set (80% of the data). Second, feature selection and dimension reduction methods are applied with different reduction sizes to find the most relevant lagged variables. Her we evaluate two methods, the Recursive Feature Elimination [START_REF] Guyon | Gene selection for cancer classification using support vector machines[END_REF] and the Principal Component Analysis [START_REF] Tipping | Probabilistic principal component analysis[END_REF]. Afterwards, prediction models are tested on 20% of the data. This procedure is repeated 5 times to test the models on all data. Finally, we select the model and the predictive features leading to the best prediction scores for each brain area.

The experiments are conducted on human-human and human-robot conversations separately in order to compare the differences between the two conditions in terms of the selected behavioral features activating specific brain areas. In both cases, the data (training and test sets) consists of 9180 observations. In this paper, we concentrate on five brain areas: Fusiform Gyrus Area involved in face perception, left and right Motor Cortex for speech production, and left and right Superior Temporal Sulcus for speech perception and social cognition. These areas are chosen in order to validate our approach before investigating all brain areas in future works.

We evaluated classical classifiers using the Sickitlearn machine learning library [START_REF] Pedregosa | Scikitlearn: Machine learning in python[END_REF]: SVM, Random Forest (RF), and Gradient Boosting (GB). The RIDGE model (regression with regularization) is also evaluated with the idea of predicting the continuous BOLD signal, then discretiz- ing the predictions. We use also the Long Short Term Memory (LSTM) network from the Tensorflow library [START_REF] Abadi | Tensorflow: A system for largescale machine learning[END_REF]. Finally, a baseline classifier is evaluated with random predictions using 3 strategies: stratified, most frequent, and uniform, where the appropriate strategy of each target variable is chosen in the training step.

Prediction Scores

Figure 4 shows a comparison between the evaluated classifiers in terms of the mean and the standard deviation of the weighted F-score over the 5 prediction tests. 1 The results show that globally almost all models outperform the baseline, and they are close for brain areas involved in speech perception and production. Overall, the best f-scores are between 0.65 and 0.7, except for the Fusiform Gyrus area that we found the most difficult to predict, where only the Random Forest Gradient Boosting classifier that are slightly better than the baseline.

Discussion

The proposed prediction process allows to identify the features that elicit the local activation of the brain areas, and to compare the difference between the situations where a participant is talking with a human or a robot. For the Fusiform Gyrus area (face perception), the selected features for human-human conversations are head movements and facial action units with the random forest classifier, while from humanmachine conversations, eyetracking features (i.e., the speed of gaze coordinates, saccades and whether the participant is looking at the face of the robot) are also needed. This can be explained by the fact that our scenario for the talking head does not express significant facial movements compared to the human. For left and right Motor cortex areas, which are involved in speech production, the obtained results confirm the hypothesis that the best predictions are obtained using only the speech activity of the participant. For these areas, we found no difference between human-human and human-machine conversations. For left and right Motor cortex areas, the obtained results confirm the hypothesis that the best predictions are obtained using only the speech activity of the participant. For these areas, we found no difference between human-human and human-machine conversations. For left and right Superior Temporal Sulcus, only the Speech activity of the interlocutor is needed for human-robot interactions. For human-human interactions, different linguistics features are selected for the right {Speech activity, Filled-breaks, Feedbacks, and Discourses markers}, compared to the left area, for which just the Speech activity is required. These brain areas are an interesting example to compare humanhuman and human-machine, as we see the absence of social cognition features where the interlocutor is a robot.

Let us note that each prediction model selects its own best predictors for each brain area. Nevertheless, there is some sort of stability in this selection over all models. For example, all the models select the speech activity of the participant to predict left and right Motor Cortex areas. They differs a little for left and right Superior Temporal Sulcus. For instance, the Random Forest model selects linguistics features involved in perception, while the SVM includes some facial action units. One explanation might be that different behavioral features may provide the same predictive information. In our case, we select the final best predictors based on the best model for each brain area.

We can conclude that the local activation of the studied brain areas involved in speech production and perception can be predicted, allowing us to identify causal dependencies between behavioral and neuro-physiological time series, and compare human-human and human-machine interactions. Importantly, the relevant features are in complete agreement with the social cognitive neuroscience literature. One limit that we face concerns the prediction of the Fusiform Gyrus area activity. Although the features selected to predict the activity of this area are logical, improving the prediction performances requires further investigation, and particularly to compare prediction for the human and robot agent given the differences in their head movements and facial expression.

CONCLUSION

In this paper, we propose an approach to predict the activity in specific brain areas based on the multi-modal behavioral signals of human-human and human-machine conversations. This is a worthwhile alternative to the classical approach that consists in predicting continuous fMRI signals directly using multiple regression. The results show that the discretized BOLD signals of brain areas involved in speech perception and production are predictable based only on linguistics time series. In future works, we plan to explore all brain regions and to define higher-order behavioral features. The approach proposed here confirms the links between behavioral variables and the functional brain areas under scrutiny, but more importantly paves the way to discover new dependencies between behaviour and local activity across the whole brain in a natural social interaction.

  and two conversational sequences are illustrated in examples (1) (Subject-Confederate) and (2) (Subject-Furhat).

  est vraiment pourrie cette framboise. S : Oui, je trouve aussi C : Tu penses ce c'est pour nous faire penser à quoi? S : Je sais pas, contre le gaspillage alimentaire? C : Ouais bonne idée. [...] (2) F: Elle est vraiment pourrie cette framboise. S : Oui, je trouve aussi F : Tu penses ce c'est pour nous faire penser à quoi? S : Je sais pas, contre le gaspillage alimentaire? F : Ouais bonne idée. [...]

Figure 1 :

 1 Figure 1: The experiment procedure.

Figure 2 :

 2 Figure 2: Example of resampling speech features (the speech activity).

Figure 3 :

 3 Figure 3: Extracting structured time series from raw multimodal signals.

Fus ifor m

 m Gyr us Lef t Mot or Cor tex Lef t Sup erio r Tem por al Sul cus Rig ht Mot or Cor tex Rig ht Sup erio r Tem por al Sul Fus ifor m Gyr us Lef t Mot or Cor tex Lef t Sup erio r Tem por al Sul cus Rig ht Mot or Cor tex Rig ht Sup erio r Tem por al Sul cus Prediction accuracy for human-human (a) and human-robot (b) interactions, based of the F-score measures. The values represent the mean of the F-scores over 5 prediction experiments, while the error bars represent the standard deviations.

Table 1 :

 1 The extracted behavioral features.

	Modality	Features
	Speech	Speech activity, Particles items,
		Discourse Markers, Overlap, Re-
		action Time, Filled-breaks, Feed-
		backs, Laughters, Lexical Rich-
		ness, Polarity, Subjectivity.
	Video	Facial Action Units (17 vari-
		ables), Head pose coordinates (6
		variables), Gaze coordinates (3
		variables).
	Eyetracking data Gaze movement of the partici-
		pant (2 variables), and 4 binary
		variables categorizing resp. the
		presence of saccades, and if the
		participant is looking at the face,
		the eyes of the mouth of the inter-
		locutor.
	Raw Signals
	Speech	Time Series Representation
	Video
	Eyetracking
	data
	fMRI signals

We only showed the results based on f-score as it resumes the precision and the recall. These measures are also calculated, more details about their results in addition to the scores of each subset of behavioral features can be found in https://github.com/Hmamouche/NeuroTSConvers.