Nathan Coutard

Bertrand Reuillard

Tran Ngoc Huan

Fabrice Valentino

Reuben T Jane

Solène Gentil

Eugen S Andreiadis

Alan Le Goff

Tristan Asset

Frédéric Maillard

Bruno Jousselme

Adina Morozan

Sandrine Lyonnard

Vincent Artero
email: vincent.artero@cea.fr

Pascale Chenevier
email: pascale.chenevier@cea.fr

Impact of ionomer structuration on the performance of bio-inspired noblemetal-free fuel cell anodes

Molecular-engineered bio-inspired catalysts hold promise for the next generation of protonexchange membrane fuel cells (PEMFCs). Yet, their implementation in catalytic layers with Nafion ionomer faces nanocomposite formulation issues. Here, we use various DuBois nickel catalysts immobilized on carbon nanotubes to exemplify how self-assembly at the mesoscale affects H2 oxidation anode performances. We exploited the reversible activity of these catalysts together with potential-step chronoamperometry to locally produce H2 and probe mass transport within the catalytic layer. Small-angle neutron scattering studies serve to build a model, describing how the surface functionalization drives the structuration of the ionomer and impacts the diffusion of protons and gas from and to catalytic centres. This study thus demonstrates that implementation of unconventional catalysts in catalytic layers requires the redesign of the whole system of materials. Based on such information, catalytic layer formulation was optimized, allowing order of magnitude performance enhancement of noblemetal free PEMFCs.

Introduction

Hydrogen gas is a promising storage framework for renewable energies through the combination of water-splitting, in electrolysers or photoelectrochemical cells, [START_REF] Ardo | Pathways to electrochemical solar-hydrogen technologies[END_REF] with fuel cells (FC), releasing energy from hydrogen as supply/demand dictates. [START_REF] Armaroli | The Hydrogen Issue[END_REF] Proton exchange membrane (PEM) devices are an attractive technology, but they rely on the powerful catalytic properties of platinum, the replacement of which by lower cost and more abundant materials is a requisite for economic viability. [START_REF] Stephens | Toward sustainable fuel cells[END_REF][START_REF] Kongkanand | The Priority and Challenge of High-Power Performance of Low-Platinum Proton-Exchange Membrane Fuel Cells[END_REF] Noble metal-free hydrogen FC are classically based on the alkaline technology [START_REF] Steele | Materials for fuel-cell technologies[END_REF] or exploit hydrogenase enzymes in homemade laboratory experimental setups. [START_REF] Xu | Optimizing the power of enzyme-based membrane-less hydrogen fuel cells for hydrogen-rich hydrogen-air mixtures[END_REF][START_REF] Szczesny | A gas breathing hydrogen/air biofuel cell comprising a redox polymer/hydrogenase-based bioanode[END_REF][START_REF] Mazurenko | Impact of substrate diffusion and enzyme distribution in 3D-porous electrodes: a combined electrochemical and modelling study of a thermostable H2/O2 enzymatic fuel cell[END_REF] However, none of them allow taking advantage of the low internal resistance, compactness and high stability of PEMFCs optimized over the last decades. [START_REF] Steele | Materials for fuel-cell technologies[END_REF] The combination of a bio-inspired molecular approach [START_REF] Artero | Bioinspired catalytic materials for energy-relevant conversions[END_REF] with nanochemical tools, through the attachment of mimics [START_REF] Dubois | Development of Molecular Electrocatalysts for Energy Storage[END_REF][START_REF] Dutta | Designing electrochemically reversible H2 oxidation and production catalysts[END_REF] of the active sites of hydrogenases (Fig. 1b) on multi-wall carbon nanotubes (MWNTs) has allowed to prepare nickel-based nanomaterials with unique properties for bidirectional catalysis (hydrogen evolution and oxidation) under conditions compatible with PEM technology. [START_REF] Coutard | Molecular engineered nanomaterials for catalytic hydrogen evolution and oxidation[END_REF][START_REF] Jaouen | Toward Platinum Group Metal-Free Catalysts for Hydrogen/Air Proton-Exchange Membrane Fuel Cells[END_REF][START_REF] Tran | Noncovalent Modification of Carbon Nanotubes with Pyrene-Functionalized Nickel Complexes: Carbon Monoxide Tolerant Catalysts for Hydrogen Evolution and Uptake[END_REF][START_REF] Gentil | Carbon-Nanotube-Supported Bio-Inspired Nickel Catalyst and Its Integration in Hybrid Hydrogen/Air Fuel Cells[END_REF][START_REF] Huan | Bioinspired noble metal-free nanomaterials approaching platinum performances for H2 evolution and uptake[END_REF][START_REF] Goff | From Hydrogenases to Noble Metal-Free Catalytic Nanomaterials for H-2 Production and Uptake[END_REF] Their active sites are nickel(II) bisdiphosphine complexes [START_REF] Dubois | Development of Molecular Electrocatalysts for Energy Storage[END_REF][START_REF] Dutta | Designing electrochemically reversible H2 oxidation and production catalysts[END_REF] bearing amine pendant bases directly inspired from the structure of the dithiomethylamine cofactor found at the active site of [FeFe]-hydrogenases (Fig. 1a). [START_REF] Lubitz | Hydrogenases[END_REF][START_REF] Evans | Mechanism of hydrogen activation by [NiFe] hydrogenases[END_REF][START_REF] Hidalgo | Infrared Spectroscopy During Electrocatalytic Turnover Reveals the Ni-L Active Site State During H2 Oxidation by a NiFe Hydrogenase[END_REF] During H2 oxidation, these amine groups polarize the H-H bond to facilitate its heterolytic cleavage into proton and hydride. Reversely, they serve as proton relays to promote protonation of metal-hydride intermediate towards H2 evolution. [START_REF] Dutta | Designing electrochemically reversible H2 oxidation and production catalysts[END_REF] In this study, we focus on three previously described catalysts immobilized on MWNTs represented in Fig. 1. They are named 1 Arg ([Ni(P2 Cy N2 Arg )2] 6+ ), 1 Ester ([Ni(P2 Cy N2 Ester )2] 2+ ) and 1 Py ([Ni(P2 Cy N2 Py )2] 2+ ) after their anchoring groups, an arginine, [START_REF] Dutta | Arginine-Containing Ligands Enhance H2 Oxidation Catalyst Performance[END_REF] an activated ester [START_REF] Goff | From Hydrogenases to Noble Metal-Free Catalytic Nanomaterials for H2 Production and Uptake[END_REF] and a pyrene. [START_REF] Tran | Noncovalent Modification of Carbon Nanotubes with Pyrene-Functionalized Nickel Complexes: Carbon Monoxide Tolerant Catalysts for Hydrogen Evolution and Uptake[END_REF] The anchoring group are designed for stable grafting on appropriately functionalized MWNTs (Fig. 1b) through polycationic/polyanionic electrostatic or -cation interactions, [START_REF] Gentil | Carbon-Nanotube-Supported Bio-Inspired Nickel Catalyst and Its Integration in Hybrid Hydrogen/Air Fuel Cells[END_REF] covalent amide linkage [START_REF] Goff | From Hydrogenases to Noble Metal-Free Catalytic Nanomaterials for H2 Production and Uptake[END_REF] and π-stacking of the pyrene moiety on MWNT, [START_REF] Tran | Noncovalent Modification of Carbon Nanotubes with Pyrene-Functionalized Nickel Complexes: Carbon Monoxide Tolerant Catalysts for Hydrogen Evolution and Uptake[END_REF] respectively. While optimisation of the three-dimensional structure of the electrodes yielded current densities up to 40 mAcm -2 in the case of MWNT-NH3 + /1 Ester , [START_REF] Huan | Bioinspired noble metal-free nanomaterials approaching platinum performances for H2 evolution and uptake[END_REF] power densities in technologically relevant setups remain below expectations. Indeed, when formulated with Nafion ionomer in a catalytic layer assembled with a NRE 212 Nafion membrane and assessed in a compact PEMFC, 1 Py yielded only 23 µWcm -2 power output. [START_REF] Tran | A noble metal-free proton-exchange membrane fuel cell based on bio-inspired molecular catalysts[END_REF] Further optimization is therefore clearly required to find alternative formulations of the catalytic layers that account for the specificity of these innovative catalytic hybrid materials. [START_REF] Artero | Bioinspired catalytic materials for energy-relevant conversions[END_REF][START_REF] Yang | Towards systems materials engineering[END_REF] The use of Nafion is widely adopted in the formulation of Pt/C-based catalytic inks as it both enhances proton transport throughout the thickness of the electrode and provides good contact with the PEM in a compact fuel cell. [START_REF] Kraytsberg | Review of Advanced Materials for Proton Exchange Membrane Fuel Cells[END_REF] However, while perfluorinated sulfonic acid membranes have been thoroughly investigated, [START_REF] Mauritz | State of understanding of Nafion[END_REF][START_REF] Kusoglu | New Insights into Perfluorinated Sulfonic-Acid lonomers[END_REF] less information is available for Nafion-containing catalytic layers. [START_REF] Li | Defining Nafion Ionomer Roles for Enhancing Alkaline Oxygen Evolution Electrocatalysis[END_REF][START_REF] Yarlagadda | Boosting Fuel Cell Performance with Accessible Carbon Mesopores[END_REF][START_REF] Artyushkova | Structural correlations: Design levers for performance and durability of catalyst layers[END_REF][START_REF] Wang | Impact of Catalyst Ink Dispersing Methodology on Fuel Cell Performance Using in-Situ X-ray Scattering[END_REF] The Nafion covering of the carbon support is often heterogeneous, composed of clusters that fail to impregnate the support smaller porosities, hence greatly hindering the proton conductivity in the latter. [START_REF] Lopez-Haro | Three-dimensional analysis of Nafion layers in fuel cell electrodes[END_REF][START_REF] Pan | Current challenges related to the deployment of shape-controlled Pt alloy oxygen reduction reaction nanocatalysts into low Pt-loaded cathode layers of proton exchange membrane fuel cells[END_REF] The morphology of the clusters might be tuned through the degree of graphitization or the functionalization of carbon black, [START_REF] Yang | Investigation of the Interaction between Nafion Ionomer and Surface Functionalized Carbon Black Using Both Ultrasmall Angle X-ray Scattering and Cryo-TEM[END_REF][START_REF] Orfanidi | The Key to High Performance Low Pt Loaded Electrodes[END_REF] which in turn impacts direct access of catalytic active sites to the electrolyte. To the best of our knowledge, no such information is currently available for carbon nanotubes-based catalytic layers, although the latter hold promises to reach technological PEMFC benchmarks. [START_REF] Coutard | Molecular engineered nanomaterials for catalytic hydrogen evolution and oxidation[END_REF][START_REF] Jaouen | Toward Platinum Group Metal-Free Catalysts for Hydrogen/Air Proton-Exchange Membrane Fuel Cells[END_REF][START_REF] Jha | Functionalized Single-Walled Carbon Nanotube-Based Fuel Cell Benchmarked Against US DOE[END_REF] In addition, Nafion was originally selected for being the best compromise as ionomer in the very case of Pt/C catalysts. [START_REF] Steele | Materials for fuel-cell technologies[END_REF] The whole system of materials within the catalytic layer may have to be redesigned for implementing alternative catalysts as even fewer data is available regarding the interaction of Nafion with alternative noble-metal free catalysts. [START_REF] Jaouen | Toward Platinum Group Metal-Free Catalysts for Hydrogen/Air Proton-Exchange Membrane Fuel Cells[END_REF][START_REF] Artyushkova | Structural correlations: Design levers for performance and durability of catalyst layers[END_REF][START_REF] Jha | Functionalized Single-Walled Carbon Nanotube-Based Fuel Cell Benchmarked Against US DOE[END_REF][START_REF] Wu | Nanostructured Nonprecious Metal Catalysts for Oxygen Reduction Reaction[END_REF][START_REF] Wang | Recent Insights into the Oxygen-Reduction Electrocatalysis of Fe/N/C Materials[END_REF][START_REF] Chlistunoff | Nafion Induced Surface Confinement of Oxygen in Carbon-Supported Oxygen Reduction Catalysts[END_REF][START_REF] Chlistunoff | On the use of Nafion® in electrochemical studies of carbon supported oxygen reduction catalysts in aqueous media[END_REF]

Results and discussion

Overwiew of catalytic systems

Surface concentrations of the three catalysts immobilized on MWNTs (Fig 1) have been determined by cyclic voltammetry (CV) in CH3CN through integration of the Ni II /Ni I signal and found similar in all three cases (Table 1). All three systems were already demonstrated to reversibly catalyse H2 evolution and oxidation when drop-cast on one side of a gas diffusion layers (GDL) fed with H2 from the back and immersed in 0.5 M H2SO4 electrolyte in threeelectrode half-cell configuration. [START_REF] Tran | Noncovalent Modification of Carbon Nanotubes with Pyrene-Functionalized Nickel Complexes: Carbon Monoxide Tolerant Catalysts for Hydrogen Evolution and Uptake[END_REF][START_REF] Gentil | Carbon-Nanotube-Supported Bio-Inspired Nickel Catalyst and Its Integration in Hybrid Hydrogen/Air Fuel Cells[END_REF][START_REF] Goff | From Hydrogenases to Noble Metal-Free Catalytic Nanomaterials for H2 Production and Uptake[END_REF] Structural differences in the outer sphere of nickel entail distinct catalytic behaviours, as previously reported: linear sweep voltammetry (LSV) measurements (Fig. S1) indeed show that MWNT-NH3 + /1 Ester and MWNT/1 Py are biased towards H + reduction [START_REF] Tran | Noncovalent Modification of Carbon Nanotubes with Pyrene-Functionalized Nickel Complexes: Carbon Monoxide Tolerant Catalysts for Hydrogen Evolution and Uptake[END_REF][START_REF] Goff | From Hydrogenases to Noble Metal-Free Catalytic Nanomaterials for H2 Production and Uptake[END_REF] while MWNT-COO -/1 Arg is biased towards H2 oxidation. [START_REF] Gentil | Carbon-Nanotube-Supported Bio-Inspired Nickel Catalyst and Its Integration in Hybrid Hydrogen/Air Fuel Cells[END_REF][START_REF] Dutta | Arginine-Containing Ligands Enhance H2 Oxidation Catalyst Performance[END_REF][START_REF] Gentil | A Nanotube-Supported Dicopper Complex Enhances Pt-free Molecular H-2/Air Fuel Cells[END_REF] Chronoamperometry (CA) measurements showed that the catalytic activity of all three systems is sustained for hours under such conditions, [START_REF] Tran | Noncovalent Modification of Carbon Nanotubes with Pyrene-Functionalized Nickel Complexes: Carbon Monoxide Tolerant Catalysts for Hydrogen Evolution and Uptake[END_REF][START_REF] Gentil | Carbon-Nanotube-Supported Bio-Inspired Nickel Catalyst and Its Integration in Hybrid Hydrogen/Air Fuel Cells[END_REF][START_REF] Goff | From Hydrogenases to Noble Metal-Free Catalytic Nanomaterials for H2 Production and Uptake[END_REF] supporting stability of both molecular catalyst structure and surface grafting.

Catalytic behaviour in presence of Nafion

For MWNT/1 Py /Nafion or MWNT-NH3 + /1 Ester /Nafion anodes integrated in a compact PEMFC, the low activation energies measured in a previous work for H2 oxidation [START_REF] Tran | A noble metal-free proton-exchange membrane fuel cell based on bio-inspired molecular catalysts[END_REF] suggested that the current density is limited by mass transport in the bulk of the electrode. To gain more insight into the effect of Nafion on the performances of the Ni-based catalysts, we first studied inks formulated with a Nafion to MWNT dry mass ratio of 1, i.e. with a composition similar to that used in the above mentioned study, [START_REF] Tran | A noble metal-free proton-exchange membrane fuel cell based on bio-inspired molecular catalysts[END_REF] co-dispersed via sonication in ethanol and drop-cast onto GDL used as a conductive support. Note that the catalyst content represents 40-45% of the dry mass of these inks. Confirming our previous observations, the addition of Nafion to MWNT/1 Py turns off almost all activity (Table 1 and Fig. S2). When mixed with MWNT-NH3 + /1 Ester , Nafion triggers a fourfold drop in oxidation current (Table 1 and Fig. S3). However the presence of Nafion impacts H + reduction or H2 oxidation currents measured at MWNT-COO - /1 Arg anodes to a lesser extent (Table 1 and Fig. S4), mirroring the situation observed for ultralow loaded MWNT/Pt systems fabricated using a polyol method (Fig S5). [START_REF] Asset | Activity and Durability of Platinum-Based Electrocatalysts Supported on Bare or Fluorinated Nanostructured Carbon Substrates[END_REF] Several scenarios can lead to a drop of activity when adding Nafion to the MWNT-catalyst composite ink: i) the catalyst might be chemically inactivated by Nafion through interactions affecting the amine positionning in the second coordination sphere of nickel; ii) the catalyst might electrically disconnect from the MWNT; iii) the catalyst might lose access to its substrates, H + or H2; iv) the catalyst might be unable to release the product H2 or H + .

The lack of detrimental effect of CF3SO3H, mimicking perfluorosulfonic chains of Nafion, on the catalytic activity of DuBois's catalysts immobilized onto MWNTs (Fig. S6) does not indicate that Nafion's sulfonate groups strongly interact with amine groups in the second coordination sphere of nickel. In addition, data shown in Figure S2-4 show that the catalytic bias (i.e. the ratio between oxidation and reduction currents) is only marginally affected by the presence of Nafion in the case of MWNT-COO -/1 Arg and MWNT-NH3 + /1 Ester : For MWNT NH3 + /1 Ester (Fig S3), there is a two-fold effect on the catalytic bias induced by the presence of Nafion that may be accounted for to such Nafion-catalyst interactions. While the same effect may be valid for MWNT/1 Py , a complete loss of current at all potentials is observed (Fig. 3a To account for such changes, we then hypothesized that while Nafion plays its expected protontransport role for MWNT-COO -/1 Arg /Nafion, it might prevent H2 access to the catalytic sites in MWNT-NH3 + /1 Ester /Nafion and in MWCNT/1 Py /Nafion. Recent literature has shown that H2 mass transport can use different channels than H + in hydrated Nafion. [START_REF] Schalenbach | Gas Permeation through Nafion. Part 1: Measurements[END_REF][START_REF] Schalenbach | Gas Permeation through Nafion. Part 2: Resistor Network Model[END_REF][START_REF] Takeuchi | Hydrogen Permeation in Hydrated Perfluorosulfonic Acid Polymer Membranes: Effect of Polymer Crystallinity and Equivalent Weight[END_REF] Scanning electron microscopy (SEM) images recorded for the three systems (Fig. 2) revealed that, for the same loading in catalytic ink, MWNT-COO -/1 Arg displays a thickness (~ 10 µm) five times greater than that of the other systems (~ 2 µm). Looking more closely at individual nanotubes in the composites (Fig. 2), differences are observed in the association of the MWNTs and Nafion: in MWNT-NH3 + /1 Ester /Nafion and MWNT/1 Py /Nafion, MWNTs are wrapped in a Nafion matrix to form a packed layer, while the MWNT-COO -/1 Arg /Nafion composite appears loosely arranged in balls of entangled MWNTs and Nafion. Such a porous structure being more suitable for gas and electrolyte diffusion, we concluded that mesoscale morphology is the major driver for catalytic performances in such hybrid materials.

To inquire about the effect of Nafion wrapping, we took advantage of the reversible catalytic activity of this family of catalysts and designed a potential-step chronoamperometric measurement. By first probing the electrodes under nitrogen flow at -100 mV vs. RHE for 60 seconds to accumulate hydrogen locally, then suddenly switching the potential to +300 mV vs.

RHE, H2 was produced at the catalytic site just before probing its oxidation.

These measurements were performed on MWNT/1 Py , MWNT-NH3 + /1 Ester and MWNT-COO - /1 Arg with and without Nafion (Fig. 3). In all cases, the measurements allow to warrant that the catalysts are electrochemically accessible and capable of bidirectional reversible catalysis in the absence of Nafion (dotted lines). Despite the difference in catalytic bias among the catalysts, they are all able to produce hydrogen continuously during the reduction phase and to oxidize the available hydrogen after the potential step. Only a very small part of the hydrogen produced during the reduction phase is oxidized after the step and the current drops within 2 seconds, because of the hydrogen fast diffusing away.

The picture is different in the presence of Nafion (continuous lines). First the MWNT/1 Py /Nafion catalytic layer shows a complete loss of current at all potentials (Fig. 3a), again indicating either detachment of the catalyst from the MWNTs or complete mass transport inhibition. Additional control measurements performed with other combinations between nickel catalysts and functionalized MWNTs (Fig. S9) also show that the catalytic activity is almost completely inhibited by Nafion in all the cases where the catalyst is not strongly attached to the MWNTs. This is an indication for a strong affinity of Nafion for MWNT and/or DuBois catalyst that will destabilize the catalyst-MWNT contact required in supported catalysis.

As a contrary, the catalytic H2 evolution activity of MWNT-COO -/1 Arg /Nafion increases in the presence of Nafion (Fig. 3c), showing that 1 Arg stays active and electrically connected to MWNTs. At the potential step, the oxidation current produces a peak and then falls to zero within 2 seconds, as in the absence of Nafion. The electrochemical behaviour of 1 Arg in the presence of Nafion is thus essentially similar to that without Nafion. It shows that the overall catalytic behavior of the DuBois catalyst (substrate capture and release, pendant amine movements to the active site) is not affected by the polyanionic ionomer and rules out the possibility that Nafion inactivates the catalyst via strong interactions with the positively charged arginine moieties.

Finally, the MWNT-NH3 + /1 Ester /Nafion electrode also shows an increase in proton reduction current (Fig. 3b), and then features a transient oxidation current over more than 30s. Integrating the current indicates that a huge part (>50%) of the hydrogen produced in the 30s before the potential step is oxidized in the 30s after. This transient signal drops significantly with a lower amount of Nafion (Fig. S7). Taken together, these data indicate a singular behaviour for MWNT-NH3 + /1 Ester /Nafion: H2 produced locally at the 1 Ester site accumulates in its vicinity when Nafion is present and remains temporarily trapped, available for local oxidation, highlighting limited mass transport from the catalyst in the composite. Furthermore, in potential-step chronoamperometry tests under H2 flow (Fig. S8), under conditions where MWNT-COO -/1 Arg /Nafion delivers 22 mAcm -2 steadily, [START_REF]Arg is slightly inhibited in the presence of H2 feed, a typical behaviour for product-hindered catalytic kinetics which has been reported for such catalysts and hydrogenase enzymes[END_REF] the oxidation current from MWNT-NH3 + /1 Ester /Nafion is slightly enhanced compared to tests under N2 flow, showing that H2 hardly permeates towards the catalyst. As a consequence of local H2 accumulation, the proton reduction current is slightly inhibited at equilibrium (i.e. in the presence of H2, Fig. S3), a typical behaviour for product-hindered catalytic kinetics which has been reported for such reversible catalysts [START_REF] Dutta | Designing electrochemically reversible H2 oxidation and production catalysts[END_REF] and hydrogenase enzymes. [START_REF] Lubitz | Hydrogenases[END_REF] To gain further structural insight, we recorded small angle neutron scattering (SANS) data for the three systems (Fig. 4). Samples of MWNT/catalyst/Nafion (MWNT/Nafion mass ratio 1/1)

were drop-casted on quartz glass as a dry layer, and then equilibrated for 3 days in a chamber at 98 % relative humidity (RH) at room temperature. A sample of dry MWNT-COOH served as a reference. All SANS 1D profiles (Fig. 4a) show a decaying intensity characterized by oscillatory features and a local minimum around values of the scattering vector Q~0.06 Å -1 , corresponding to a characteristic distance d ~ 10 nm. These profiles are typical of the form factor P(Q) of relatively monodisperse, infinite cylindrical particles such as carbon nanotubes (see supporting information for details). All catalyst SANS profiles have a lower intensity in the region of the form factor oscillation due to a loss of contrast between the cylinder and the solvent, indicating that a different material has been added on the cylinder. In the dry material, the high-Q intensity decays as Q -4 (so-called Porod's behaviour) indicating sharp interfaces between the scattering particles and the surrounding medium. By contrast, a flat signal is observed in the hydrated samples due to incoherent scattering from hydrogen atoms, e.g. water captured during the hydration step. Sample MWNT-COO -/1 Arg /Nafion shows a 10 times higher flat signal, proving a much higher hydrophilicity. This enhanced ability to bind water might constitute a significant advantage for 1 Arg as compared with the other DuBois catalysts in the catalytic process, as water is required for substrate entry/product release paths. Thus, these SANS data picture our samples as a brightly scattering network of MWNTs surrounded by an organic material with different degrees of water uptake.

For closer analysis, the profiles were fitted with a core-shell cylinder model (see supplementary information for details), taking the core diameter, the shell thickness, the scattering length density of the shell (SLDshell) and of the medium (SLDmedium) as adjustable parameters (Fig. 4b). Note that in case of hydrated materials a constant background is added to account for the high-Q plateau. The MWNT-COOH reference SANS profile fits very well to a model with an empty core of 4.2 ± 0.1 nm diameter and a 2.4 ± 0.1 nm thick carbon shell (see model in supplementary information and fitted SLD profiles in Fig. S10), as expected from TEM images of MWNT (Fig. 4a inset). Deviation from the cylinder form factor at low Q values (<0.02 Å - 1 ) is due to scattering by the MWNT entangled network at the micron-scale, but the mesh size could not be investigated because of the limited range at low Q.

The MWNT/1 Py /Nafion and MWNT-NH3 + /1 Ester /Nafion profiles show a very good fit with a carbon shell of larger thickness (2.7 ± 0.1 and 2.9 ± 0.1 nm respectively) and lower shell scattering length density (SLDshell = 6.5 ± 0.5 10 -6 Å -2 instead of 10 ± 1 10 -6 Å -2 ) than control.

These results are congruent with the observation of MWNTs surrounded by organic material.

Interestingly, the MWNT-NH3 + /1 Ester /Nafion data shows a significant excess intensity in the range Q~0.1-0.3 Å -1 , that is not accounted for by the core-shell model but can be understood as an additional scattering peak (see below). The MWNT-COO -/1 Arg /Nafion profile is different: the fitted shell has the same characteristics as for MWNT-COOH, but the scattering length density of the medium rises up to 1.8 ± 0.5 10 -6 Å -2 (instead of 0 ± 0.2 Å -2 in the previous cases), a value that approaches that of a matrix of hydrated Nafion and/or 1 Arg . Besides, the SANS profile shows a strong additional signal at Q~0.1-0.3 Å -1 , a region where the peak of hydrated Nafion is usually reported in the literature (yellow crosses). [START_REF] Rubatat | Fibrillar structure of Nafion: Matching Fourier and real space studies of corresponding films and solutions[END_REF] The excess of signal around Q~0.1-0.3 Å -1 reads better after subtraction of the MWNT-COOH reference SANS profile (Fig. 4c). Then an intense, well-defined correlation peak appears, centered at Qpeak=0.12 Å -1 , i.e. corresponding to mean separation distances of ~ 5 nm. Note that this peak appears identical in the catalyst-free MWNT-COOH/Nafion control sample (black line) and can be safely assigned to the nanoscale structure of hydrated Nafion. Indeed, the so-called ionomer peak due to hydrophilic/hydrophobic phase segregation was reported at position Q=0.12 Å -1 in bulk Nafion membranes equilibrated at 98% RH. [START_REF] Gebel | The kinetics of water sorption in Nafion membranes: a small-angle neutron scattering study[END_REF] Moreover, we notice that this ionomer peak is also present in the MWNT-NH3 + /1 Ester /Nafion sample, although much less pronounced.

The same features and difference of behaviour among the three catalytic systems was observed on samples in contact with excess water, therefore indicating that hydration in liquid water

does not modify the nature of the interactions found between Nafion and the various MWNTs.

The present MWNT/catalyst/Nafion systems thus appear to adopt two types of nanoscale structural organization depending on the nature of catalyst and distinct catalyst-Nafion interactions. In the case of MWNT-COO -/1 Arg /Nafion, the ionomer forms bulk-like domains composed of hydrophobic polymer fibers and aqueous channels as reported for pure Nafion. [START_REF] Rubatat | Fibrillar structure of Nafion: Matching Fourier and real space studies of corresponding films and solutions[END_REF] This structure interacts poorly with MWNT-COO -/1 Arg , just providing a water-rich matrix as described in Scheme 3d. By contrast, in the MWNT/1 Py /Nafion, Nafion hydrophobic chains stick at the MWNT surface as a polymer surfactant, so that no ionomer is available to form a developed fibre/channel structure, as described in Scheme 3e. Indeed, the 1:1 Nafion to MWNT dry mass ratio implies that Nafion would wrap as a 1.4 nm thick shell if covering the MWNT evenly, which more or less corresponds to a monolayer. This Nafion/MWNT interaction then competes with the -stacking of 1 Py onto MWNT and probably leads to displacement of the catalyst from their surface. Finally, the MWNT-NH3 + /1 Ester /Nafion system has an intermediate behaviour, though closer to the inefficient structure of MWNT/1 Py /Nafion.

Meso-scale structuration of the MWNT/catalyst/Nafion catalytic layer

A contrasted picture of their meso-scale arrangement, depicted in Fig. 5, arises from the combined analysis of the electrochemical behaviour and SANS profiles of our series of MWNT/catalyst/Nafion composites. Although the three grafting methods attain approximately the same loading of catalyst on MWNT (Table 1) in the absence of Nafion, the bond type has a significant impact on the physicochemical behaviour of the MWNT network, and consequently on the structuration of the MWNT/Nafion composite. The very efficient π-π interaction used in MWNT/1 Py construct relies on the hydrophobic nature of the MWNT surface, but the very same mechanism happens to disturb Nafion self-organization, as was previously observed with other hydrophobic substrates. [START_REF] Luo | Flexible Carbon Nanotube-Polymer Composite Films with High Conductivity and Superhydrophobicity Made by Solution Process[END_REF][START_REF] Borges | Morphology of Supported Polymer Electrolyte Ultrathin Films: A Numerical Study[END_REF][START_REF] Modestino | Controlling Nafion Structure and Properties via Wetting Interactions[END_REF] Measurement of active site loading under aqueous conditions (Fig. S11) revealed that competition of 1 Py and Nafion backbone for the hydrophobic surface of MWNTs induces a massive (> 85%) desorption of the catalyst (Scheme 4a), [START_REF] Chlistunoff | Nafion Induced Surface Confinement of Oxygen in Carbon-Supported Oxygen Reduction Catalysts[END_REF][START_REF] Wood | Nafion Structural Phenomena at Platinum and Carbon Interfaces[END_REF] which is the likely cause for the complete loss of electrocatalytic activity for both H2 production and oxidation. We cannot however exclude that some catalyst remain trapped between MWNTs and Nafion, with mass transport from and to the electrolyte being fully stopped. It thus proves impossible to use hydrophobic interactions both for grafting the catalyst on the MWNT support, and for making ionomer ion-conducting paths in the same active layer. The covalent binding strategy used in MWNT-NH3 + /1 Ester avoids this competition pitfall (Scheme 4b). Nevertheless, the required functionalization of the MWNTs by amine moieties turns them into MWNT-NH3 + polycations, and thus induces a strong affinity for the Nafion as a polyanion. This leads to a tight wrapping of most of the Nafion around the MWNT-NH3 + as observed in similar systems. 52 53 This Nafion shell reduces H2 diffusion to and from the MWNT surface, explaining the observed transient currents. However, part of the MWNT-NH3 + /1 Ester material remains uncovered with Nafion and connected to few ionomer bulk-like domains (Fig. 4c), therefore able to achieve bidirectional electrocatalysis. Finally, the ionic interaction between anionic MWNT-COO -and cationic 1 Arg proves much more favourable (Scheme 4c). First, although not covalently bound, 1 Arg does not significantly desorb from MWNT-COO -by competition with the anionic moieties of Nafion. Indeed, CV measurements performed in aqueous potassium phosphate electrolyte at a pH value corresponding to negligible H2 evolution catalysis indicate that 70-85% of the active sites remain electrochemically connected to MWNTs after Nafion addition (Fig. S12). Second, the MWNT-COO -/1 Arg and Nafion have no strong affinity, so that both can independently organize into the desired electron-and ion-conductive networks respectively. The MWNT-COO -/1 Arg /Nafion composite thus provides the best mesostructure for electrocatalysis in the series.

Optimization of performance and implementation in PEMFC

From these data, the MWNT-COO -/1 Arg /Nafion composite proves the best choice for implementation in a PEMFC. Membrane-electrode assemblies (MEAs) were fabricated by drop-casting MWNT-COO -/1 Arg /Nafion on a GDL and subsequent hot-pressing of the electrode against a side of an activated Nafion NRE-212 membrane. MEAs fabrication was first optimized for H2 oxidation currents (Table S1) and electrode homogeneity. The best currents (28 mAcm -2 current at 300 mV overpotential in half-cell configuration) arise for a Nafion to MWNT (0.36 mgMWNTcm -2 ) dry weight ratio of 1, catalytic loading in 1 Arg of 0.2 µmolcm -2 (125 µgcm -2 ) and MEA prepared by hot-pressing for 60 s at 80 °C and 1000 kgcm - 2 . This yields a flat catalytic layer with quite homogeneous thickness of 20 µm, with very few MWNTs intruding into the GDL pores (SEM images in Fig. S13). The MEA was completed with a cathode consisting of Co/N/MWNT catalyst [START_REF] Morozan | Electrochemical performance of annealed cobalt-benzotriazole/CNTs catalysts towards the oxygen reduction reaction[END_REF] and Nafion, drop-cast on a GDL and hotpressed under the same conditions. Mounted in a 0.126 cm 2 fuel cell setup, this noble-metal free PEMFC displayed an open circuit voltage of 820±5 mV and a maximum power output of 325±2 µWcm -² at 415 mV (Fig. 6), resulting in a 15-fold improvement compared to the performance of the previously reported MEA based on MWNT/1 Py /Nafion (23 µWcm -² at 500 mV). [START_REF] Tran | A noble metal-free proton-exchange membrane fuel cell based on bio-inspired molecular catalysts[END_REF] Although MWNT-COO -/1 Arg possesses a ~3-fold higher H2 oxidation activity than MWNT/1 Py (Fig. S1), the difference in the intrinsic activity between the distinct active sites cannot alone explain the observed improvement observed here, which again points to the better compatibility of MWNT-COO -/1 Arg with Nafion (Fig. S4) as compared to MWNT/1 Py (Fig. S2).

Conclusion

In this study, we have designed an effective approach to efficiently integrate molecularengineered bio-inspired catalysts with Nafion ionomer in a membrane electrode assembly.

While Nafion may slightly affect the subtle positioning of amine groups in the second coordination sphere of nickel and the intrinsic catalytic bias of the catalysts, the major issue relies in the control of both the electronic connection of the catalysts with the carbon-based support and the mass transport within the catalytic layer. Combining SANS, SEM and electrochemical measurements, we have shown that the structuration of Nafion ionomer in a catalytic ink is deeply influenced by the surface functionalization of MWNTs. Mixing MWNTs functionalized with hydrophilic carboxylate functions and Nafion yields a porous catalytic layer promoting mass transport of protons and gas, therefore with the desired functionality for integration in PEMFC. By contrast, unfavourable interactions take place when the carbon nanotubes are either functionalized with ammonium sites or left unfunctionalized, leading to a detrimental effect of Nafion addition on mass transport of product and substrate within the catalytic layer. As a consequence, the catalytic performance of the electrode does not always reflect the intrinsic properties of the catalysts. Our results show that, even within the same family of catalysts, the grafting strategy appears crucial as it not only influences the catalyst reactivity at the molecular scale but also the nanocomposite self-assembly at the mesoscale.

This finding led to a 15-fold improvement of the performance of platinum-group metal-free membrane electrode assemblies and opens novel perspective regarding the optimization of active layers for operating electrocatalytic devices. More generally, our findings imply that implementing novel catalysts including ultra-small Pt particles, 4, 39 transition metal nitrogendoped carbon (TM/N/C) ORR catalysts [START_REF] Jaouen | Cross-Laboratory Experimental Study of Non-Noble-Metal Electrocatalysts for the Oxygen Reduction Reaction[END_REF][START_REF] Shao | Recent Advances in Electrocatalysts for Oxygen Reduction Reaction[END_REF] and bio-inspired catalysts [START_REF] Chlistunoff | On the use of Nafion® in electrochemical studies of carbon supported oxygen reduction catalysts in aqueous media[END_REF] may require reengineering the electrode composite, [START_REF] Yang | Towards systems materials engineering[END_REF] with special attention to intermolecular interactions.

A favourable impact of positive charges on carbon black was recently reported in the case of low Pt-loaded electrodes, favouring triple-point boundaries. [START_REF] Orfanidi | The Key to High Performance Low Pt Loaded Electrodes[END_REF] The cationic functionalization of the support studied here with bio-inspired Ni catalysts shows an opposite effect, suggesting that surface functionalisation of the electrode is certainly instrumental to control the microstructure of the active layer and enhance global catalytic performances. A thorough investigation including all components of the catalytic layer should be undertaken when using unconventional catalysts in H2 technologies, or in emerging electrocatalytic processes such as CO2 valorization [START_REF] Lim | How to make the most of carbon dioxide[END_REF] and N2 reduction to NH3. [START_REF] Van Der Ham | Challenges in reduction of dinitrogen by proton and electron transfer[END_REF] Finally, we note that the pyrene-based grafting method has gained a great popularity in molecular science for the oxygen reduction reaction as well as other multi-electron multi proton catalysis such as water splitting (hydrogen evolution [START_REF] Li | Graphene-Supported Pyrene-Modified Cobalt Corrole with Axial Triphenylphosphine for Enhanced Hydrogen Evolution in pH 0-14 Aqueous Solutions[END_REF] and water oxidation [START_REF] Creus | A Million Turnover Molecular Anode for Catalytic Water Oxidation[END_REF] ) or CO2 reduction. [START_REF] Blakemore | Noncovalent immobilization of electrocatalysts on carbon electrodes for fuel production[END_REF][START_REF] Reuillard | Tuning Product Selectivity for Aqueous CO2 Reduction with a Mn(bipyridine)-pyrene Catalyst Immobilized on a Carbon Nanotube Electrode[END_REF][START_REF] Maurin | Noncovalent Immobilization of a Molecular Iron-Based Electrocatalyst on Carbon Electrodes for Selective, Efficient CO2-to-CO Conversion in Water[END_REF] In these fast growing domains, the fatal effect of Nafion competition on catalysts immobilized by -stacking should be considered as a serious Achilles' heel of the pyrene functionalization.

Experimental Procedures

Resource Availability

Lead contact: Pascale Chenevier (pascale.chenevier@cea.fr) with a ZEISS Ultra 55+ Electron Microscope, using an electron beam at 5.0 kV.

Transmission Electron Microscopy (TEM) images were acquired with a Cs-probe corrected FEI Titan Themis microscope at 80 kV.

Electrochemical measurements

Electrochemical experiments were carried out using a Bio-Logic SP300 potentiostat and a three-electrode electrochemical cell. For aqueous electrochemical measurements, the working electrode was the GDL-MWNT assembly, the counter-electrode was either titanium or platinum wire and the RE-2CP (Hg/Hg2SO4/sat. K2SO4; calibrated versus RHE in 0.5 M H2SO4) was used as reference electrode. Non-aqueous voltammograms were measured against an Ag/AgCl/3M KCl reference electrode and referenced to the Fc +/0 couple by the addition of an internal standard after the final experiment. Cyclic voltammetry and chronoamperometry experiments were recorded in a homemade miniaturized half-cell setup, [START_REF] Goff | From Hydrogenases to Noble Metal-Free Catalytic Nanomaterials for H2 Production and Uptake[END_REF][START_REF] Reuillard | Noncovalent Integration of a Bioinspired Ni Catalyst to Graphene Acid for Reversible Electrocatalytic Hydrogen Oxidation[END_REF] in aqueous 0.5 M H2SO4 purged with argon. Gases were provided in the back of the GDL at atmospheric pressure (Patm) and 20 mLmin -1 and atmospheric pressure with the use of Bronkhorst Mass-Flows through Swagelok fittings.

Small Angle Neutron Scattering

SANS measurements were performed on the D22 spectrometer at the Institut Laue Langevin (ILL, Grenoble, France) and on the PAXY spectrometer at the Laboratoire Léon Brillouin (LLB, Paris, France). Two configurations were used to cover an extended Q-range, from 4 × 10 -3 to 0.6 Å -1 and 7× 10 -3 to 0.6 Å -1 (ILL and LLB experiments, respectively), Q being the scattering vector defined as Q = (4π/λ)sin(θ/2) where λ is the wavelength of the incident neutron beam, and θ the total scattering angle. The isotropic 2D patterns recorded in the two configurations were radially averaged to obtain the 1D scattered intensities I(Q), and further corrected using standard procedures (detector efficiency, background, and empty cell subtraction) using PASINET and GRASP data reduction in-house softwares. As data taken in the two configurations were perfectly overlapping in the intermediate Q-region, the I(Q) were merged to obtain a single profile for each sample. Prior to the SANS experiment, the hydrated materials deposited on quartz window were inserted in round cells and maintained at 98% RH by equilibrating them in a fixed vapor pressure environment. Absolute intensities were obtained by normalized I(Q) by the mass of MWNTs in each sample. Fitted data are shifted for clarity and therefore plotted in arbitrary units. Spectra fitting was performed using SASView software. The best fits were obtained with the core-shell cylinder form factor and the hard-sphere structure factor, with a size dispersity of 40% in core radius, shell thickness and length.

SANS 1D profile fitting

SANS profiles were fitted using the SASView software, with the core-shell cylinder model.

This corresponds to the following model: and α is the angle between cylinder axis and q, Vs is the total volume, Vc is the volume of the core, L is the length of the core, R is the radius of the core, T is the thickness of the shell, ρc is the scattering length density of the core, ρs is the scattering length density of shell, ρsolv is the scattering length density of the solvent, and background is the background level. J1 is the first order Bessel function.

𝐼(𝑞, 𝛼) = 1 𝑉 𝑠 𝐹 2 (
Synthesis P Cy 2 N PhCH 2 CH 2 COOH 2
To a suspension of paraformaldehyde (408 mg, 13.6 mmol) in degassed, dry ethanol (60 mL) cyclohexylphosphine (0.88 mL, 6.68 mmol) was added drop-wise. The suspension was heated at 78 °C overnight under argon, after which 3-(4-aminophenyl)propionic acid (1.1 g, 6.65 mmol) was added, and the solution stirred at 78 °C for an additional night. After cooling in the freezer at -18 °C for several hours, the voluminous white precipitate was filtered with cannula and washed several times with ethanol. The precipitate was then recrystallized from DMF and water, filtered and dried to give 1.63 g of a white powder (2.67 mmol, 80%);

Grafting and ink preparation

MWNT-COO -/1 Arg

Adapting from a recently developed procedure, [START_REF] Gentil | Carbon-Nanotube-Supported Bio-Inspired Nickel Catalyst and Its Integration in Hybrid Hydrogen/Air Fuel Cells[END_REF] This suspension (200 µL) was mixed in a 3:1 ratio with a 3 mgmL -1 solution (67µL) of 1 Arg in pH 6, aqueous, 0.1 M MES:HEPES (1:1 v/v) buffer. 20 µL of this suspension were then drop cast directly onto a 0.126 cm² circular area of GDL and air-dried.

MWNT-NH 3 + /1 Ester

As described in our early work for similar complexes bearing activated ester function, [START_REF] Huan | Bioinspired noble metal-free nanomaterials approaching platinum performances for H2 evolution and uptake[END_REF][START_REF] Goff | From Hydrogenases to Noble Metal-Free Catalytic Nanomaterials for H-2 Production and Uptake[END_REF] MWNTs (2.5 mg) are dispersed by sonication in 25 mL abs. EtOH, and filtered onto a 5 cm² circular piece of GDL. 4-aminoethyl)benzene diazonium tetrafluoroborate (25 mg in 50 mL degassed MeCN / 0.1 M nBu4NBF4) was electrochemically reduced onto the MWNT layer through cyclic voltammetry by recording 2 cycles at 20 mVs -1 between 0.5 V and -0.8 V vs.

Ag/AgCl, yielding MWNT-NH3 + . Amine coverage before grafting has been estimated around 2 % (N/C ratio) corresponding to about one atom of nitrogen per 40 MWNT surface carbon atoms. [START_REF] Chenevier | Hydrogenase enzymes: Application in biofuel cells and inspiration for the design of noble-metal free catalysts for H2 oxidation[END_REF] The electrode was then soaked in a 1 mmolL -1 solution of 1 Ester in DMF in the presence of 10 eq. of 2,6-lutidine overnight, then rinsed with DMF, MeCN and air-dried. Fig. S15 presents the cyclic voltammetry characterization of the MWNT-NH3 + /1 Ester . Fig. S16 shows the stability of a MWNT-NH3 + /1 Ester electrode during both H2 production and oxidation at 300 mV overpotential.

Alternative strategies for modification of the MWNTs were employed to ensure that the behaviour of the MWNT-NH3 + /1 Ester system did not arise from the electrodeposition of the diazonium salt. Following the protocol for the synthesis of MWNT-COOH, replacing the 6amino-2-naphtoic acid by 4-(2-aminoethyl)aniline yielded MWNT-NH3 + . Although the overall areal current densities were lower with this functionalization mode, no qualitative difference was observed when compared to the MWNT-NH 3 + made by electrodeposition of the diazonium salt. Even more interestingly, the order of the addition of Nafion for the Nafion-containing electrodes, whether it was added as described above or deposited on top of the electrodes (200 µLcm -2 ) after electroreduction of diazonium, was proven to have no qualitative effect on either electrochemistry results or the aspect of individual MWNTs in SEM images. Addition of Nafion was done by dropcasting a 5 wt. % in lower aliphatic alcohols and water onto the electrode to reach a 1:1 Nafion:MWNTs dry mass ratio (typically 125 µL per cm 2 ).

MWNT/1 Py

This grafting method was also described in our previous work. [START_REF] Tran | A noble metal-free proton-exchange membrane fuel cell based on bio-inspired molecular catalysts[END_REF] No prior modification of the MWNTs was required, and they were simply dispersed in abs. EtOH by sonication (6 mgmL - 1 ) and diluted to 2 mL with abs. EtOH either without or with Nafion (1:1 Nafion:MWNTs dry mass ratio). This MWNT suspension was mixed in a 3:1 ratio with a 1 mmolL -1 solution of 1 Py in DCM and 20µL of this mixture were drop-casted onto a 0.126 cm² circular area of a GDL and air-dried.

MWNT/Pt (ULL Pt)

The deposition of the Pt nanoparticles onto the various MWNT was performed through the following process: 42 a given amount of Pt salt was dissolved in a 2:1 ethylene glycol:deionized water (18.2 MΩ cm) solution (for a typical synthesis, 88 mg of Pt salt in 100 mL of solution). Then, the solution was brought to pH 12.5, using a deionized water solution saturated in NaOH and vigorously stirred under argon atmosphere for 1 h. The temperature was then increased to 120 °C and maintained for 3 h. Meanwhile, MWNTs were dispersed in a 1:1 ethylene glycol:deionized water solution, aiming a 1 % theoretical weight fraction of Pt onto the carbon support (wt. %). The solution containing the Pt colloidal solution and the dispersed carbon support were mixed and the pH of the solution was decreased down to 2.5

to allow the nanoparticles deposition onto the carbon support. After t = 22 h, the solution was filtered, washed and dried for t = 45 min at T = 110 °C.

The obtained dry powder was then dispersed in EtOH at 3 mgmL -1 , with or without Nafion solution (1:1 Nafion:MWNTs dry mass ratio) and deposited onto a GDL in order to obtain a final surface loading of 7 or 14 µgcm -² of Pt.

Membrane-electrode assembly

The anode was a MWNT-COO -/1 Arg electrode with Nafion to MWNT-COOH dry mass ratio of 1, prepared as follows: 3 mg of MWNT-COOH were dispersed by sonication in 1 mL of absolute EtOH in the presence of 5 wt. % Nafion solution (75 µL). This suspension (200 µL) was mixed in a 3:1 ratio with a 3 mgmL -1 solution (67 µL) of 1 Arg in pH 6 aqueous 0. 1 M MES:HEPES (1:1) buffer. This ink was deposited on GDL at a loading of 160 µLcm -² (corresponding to 125 µg.cm -² 1 Arg ) and air-dried. 0.126 cm 2 anodes were then punched out.

A Nafion membrane sheet (NRE-212, 50 µm thick, Alfa Aesar) was activated prior to use following a standard procedure [START_REF] Pujiastuti | Effect of various concentration of sulfuric acid for Nafion membrane activation on the performance of fuel cell[END_REF] in 4 steps at 80 °C: 30 min in 3 wt. % H2O2 aqueous solution, 30 min in deionized water, 30 min in H2SO4 (0.5 M) and then 30 min in deionized water. The activated membrane was stored in distilled water and superficially dried before use.

The Co/N/MWNT oxygen-reduction cathode was prepared as described in previous work._ENREF_54 [START_REF] Morozan | Electrochemical performance of annealed cobalt-benzotriazole/CNTs catalysts towards the oxygen reduction reaction[END_REF] 20 mg of this Co/N/CNT catalyst was dispersed under sonication in a 3:1 (v/v) mixture of EtOH and H2O (1.04 mL) in the presence of 5 wt. % Nafion solution (160 µL).

The ink was sonicated for 60 minutes. 400 µl of this ink were deposited on the GDL (5 cm 2 )

substrate and dried at 80 °C under ambient atmosphere leading to a final catalyst loading of around 1333 µgcm -2 . The drop-casting was repeated twice to get a final loading of 4 mgcm -2 .

0.126 cm 2 cathodes were then punched out.

Half-MEA measured in Table S1 were prepared by pressing 0.126 cm 2 anodes with a conditioned Nafion NRE-212 membrane at various temperatures and pressures for 1 min.

Full MEA were prepared by pressing 0.126 cm 2 anode and cathode against either side of a Nafion NRE-212 membrane at 80°C and 1000 kgcm -2 for 1 min. The as-prepared MEA was further assembled in the single-cell PEMFC. Polytetrafluoroethylene (PTFE) gaskets (FuelCellStore) with ~5 mm diameter holes were used at both anode and cathode side. The gasket thickness were chosen to achieve ca. 15 % compression of the electrodes.

Fuel cell measurements

Testing PEMFC tests were performed with a single-cell fuel cell (5 cm 2 active area, Paxitech) with serpentine flow field using an in-house fuel cell bench and a Bio-Logic potentiostat with 1 Arg , middle: 1 Ester , bottom: 1 Cy ) mixed with Nafion (MWNT/Nafion 1:1 dry mass ratio) deposited on GDL. In all images, the catalytic layer is face up.

Figures titles and Legends

  ), again indicating detachment of the catalyst from the MWNTs or complete mass transport inhibition as discussed below. The catalytic bias of MWNT-COO -/1 Arg is almost unchanged, although addition of Nafion (Fig S4) induces a change of the shape of the linear scan voltammograms.

  MWNTs (50 mg) are sonicated in 150 mL of argon-degassed DMF for 45 minutes. 1.5 g of 6-amino-2-naphtoic acid and 1.1 mL of isoamyl nitrite are added, to trigger the in situ formation of 2-naphthoic acid 6-diazonium and its subsequent reduction onto the MWNTs. The reaction vessel is purged with argon, closed then heated under stirring at 80 °C for 12 hours. After cooling, the MWNTs are filtered on a 0.45 µm Teflon filter, sonicated overnight in 150 mL of DMF then filtered again. They are rinsed thoroughly with hot DMF and EtOH and dried under vacuum to yield around 50 mg of MWNT-COOH. 6 mg of MWNT-COOH are then dispersed by sonication in 1 mL of abs. EtOH. The suspension was diluted with abs. EtOH, either without or with Nafion (1:1 Nafion:MWNTs dry mass ratio, 150 µL of a 5% solution) to reach a final volume of 2 mL.

a 10 A

 10 load. Stainless steel gas tubing (Swagelock) was connected to BronkHorst mass flow controllers providing the flow rates for humidified H2 and O2 of 80 mLmin -1 , downstream of the fuel cell. For the tests, humidifier's temperatures were 80 °C. The gas outlets were let at atmospheric pressure. Heating cartridges (PID, RS Components) were connected to the fuel cell and allowed fine control (2 °C) over the temperature of the cell as a whole. Before measurement with a Bio-Logic SP-300 potentiostat, the fuel cell was degassed with N2 for 20 minutes prior to purging the anode and cathode with H2 and O2 respectively. Polarization curves were recorded by scanning the cell voltage from open circuit voltage (OCV) down to 0.3 V at a scan rate of 2 mVs -1 .

Fig. 1 . 1 Fig. 2 :

 112 Fig. 1. Molecular-engineered catalytic materials: a: Three molecular complexes for H2

Fig. 3 :

 3 Fig. 3: (a, b, c) Potential-step chronoamperometry measured for the MWNT/catalyst electrodes

Fig. 4 :

 4 Fig. 4: SANS data and models for the self-organization of MWNTs and ionomer in the samples.

Fig. 5 :

 5 Fig. 5: Schemes representing the ionomer and catalyst arrangement in the MWNT network in the MWNT/1 Py /Nafion (a), MWNT-NH3 + /1 Ester /Nafion (b) and MWNT-COO -/1 Arg /Nafion (c)

Fig. 6 :

 6 Fig. 6:. Power curve of a MWNT-COOH/1 Arg /Nafion | Nafion NRE-212 membrane |

Table 1 :

 1 Electrode composition (Ni/C ratio from energy-dispersive X-ray spectroscopy (EDX) measurements and site loading from CV measurements) and H2 oxidation current densities of the three systems. Site loading is measured in the absence of Nafion and Ni/C ratio is given in the Nafion-containing electrodes (1:1 Nafion/MWNT dry mass ratio). jox is given at 300 mV vs. the reversible hydrogen electrode (RHE), after stabilization of the current.

	Electrode			MWNT-NH3 +	MWNT-COO -	MWNT
				/1 Ester	/1 Arg	/1 Py
	Ni/C atomic ratio (%)		0.3	0.3	0.6
	Catalytic	sites	loading	2.7 ± 0.5	2.5 ± 0.5	3.1 ± 0.5
	(nmolcm -²)
	MWNTs loading (mgcm -²)	0.50 ± 0.01	0.36 ± 0.05	0.36 ± 0.05
	jox w/o Nafion (mAcm -²)	2.1 ± 0.3	20 ± 3	2.3 ± 0.3
	jox w/ Nafion (mAcm -²)	0.5 ± 0.1	17 ± 3	0.0 ± 0.1

  Materials Availability : this study did not generate new unique reagent or material Data and Code Availability: this study does not use unpublished codes, software and algorithm MHz for 31 P. Solvent peaks were used as internal references relative to Me4Si for 1 H chemical shifts; H3PO4 (85%) was used as external reference for 31 P NMR spectra. All 31 P NMR spectra were proton decoupled. Electrospray ionization mass spectrometry (ESI-MS) spectra were recorded with a Bruker Daltonics Esquire 3000 Plus device. The elemental

	analyses were carried out on a C, H, N analyser (SCA, CNRS). Scanning Electron
	Microscopy (SEM) images and Energy Dispersive X-ray spectroscopy (EDX) were acquired
	aminoethyl)benzene diazonium tetrafluoroborate, 22, 64 [Ni(MeCN)6](BF4)2, 65
	[Ni(P Cy 2N CH 2 Pyrene 2)2](BF4)2 (1 Py ) 23 and [Ni(P Cy 2N Arginine 2)2](BF4)2 (1 Arg ) 21 were synthesized
	according to published procedures. For the Pt/MWNT electrocatalysts, the platinum salt
	(H2PtCl6 . xH2O, 99.9% metal basis) was purchased from Alfa Aesar, the ethylene glycol from
	Roth (Rotipuran > 99.9 %) and the NaOH from Sigma-Aldrich 99.99 %, Merck. MilliQ water
	was systematically used.
	Instrumentation
	NMR spectra were recorded at room temperature in 5 mm tubes on a Bruker AC 300

Materials

All chemicals and solvents, including the Nafion perfluorinated resin solution (5 wt. % in lower aliphatic alcohols and water), were purchased from Sigma-Aldrich and used without further purification unless otherwise stated. UP-NC7000WT MWNTs (purity >90% in carbon) were obtained from Nanocyl (Belgium) and used as received. The gas diffusion layers (GDL w/o MPL) were purchased from Paxitech (Grenoble, France). (4spectrometer equipped with a QNP probe head, operating at 300.0 MHz for 1 H, and 121.5

N PhCH 2 CH 2 COOPht 2

  with water, ethanol and ether to give 595 mg of a light yellow product (0.66 mmol, 88%);[START_REF] Ardo | Pathways to electrochemical solar-hydrogen technologies[END_REF] H NMR (CDCl3): δ 7.81 -7.91 (m, 8 H, pht), 7.08 (d, 2 J = 8 Hz, 4 H, NC6H4), 6.66 (d, 2 J = 8 Hz, 4 H, NC6H4), 4.31 (t, 3 J = 13.5 Hz, 4 H, PCH2N), 3.57 (d, 2 J = 15

	Hz, 4 H, PCH2N), 2.93 (m, 8 H, CH2CH2COO), 1.35 -1.99 ppm (m, 22 H, C6H11); 31 P NMR
	(CDCl3): δ -39.64 ppm.
	1 Ester
	In an argon-purged Schlenck flask, 130 mg P Cy 2N PhCH 2 CH 2 COOPht 2 (0.144 mmol) and 26.7 mg
	[Ni(MeCN)6](BF4)2 (0.057 mmol) were dissolved in ~5 mL dry, degassed acetonitrile and
	stirred overnight at room temperature under argon. The purple solution was filtered and the
	solvent removed to give 102 mg of [Ni(P Cy 2N PhCH 2 CH 2 COOPht 2)2](BF4)2 (1 Ester ) as a purple
	powder (0.05 mmol, 88%); 1 H NMR (CD3CN): δ 7.88 (s, 16 H, pht), 7.27 (d, 2 J = 8.3 Hz, 8
	H, NC6H4), 7.04 (d, 2 J = 8.3 Hz, 8 H, NC6H4), 4.09 (d, 2 J = 14.1 Hz, 4 H, PCH2N), 3.83 (d,
	2 J = 14.2 Hz, 4 H, PCH2N), 3.75 (d, 2 J = 14.5 Hz, 4 H, PCH2N), 3.56 (d, 2J = 13.9 Hz, 4 H,
	PCH2N), 3.02 (s, 16 H, CH2CH2COO), 1.39 -2.22 ppm (m, 44 H, C6H11); 31 P NMR	1 H
	NMR (DMSO-d6): δ 11.97 (s, 2H, COOH), 6.95 (d, 2 J = 7.4 Hz, 4 H, NC6H4), 6.46 (d, 2 J = (CD3CN): δ 6.34 ppm; mass spectrometry (ESI + ): m/z 929.7 [M-2BF4 -] 2+ ; cyclic
	7.6 Hz, 4 H, NC6H4), 4.13 (d, 2 J = 13.7 Hz, 4 H, PCH2N), 3.89 (d, 2 J = 13.3 Hz, 4 H, voltammetry: ½ (Epa + Epc) = -0.65 and -1.11 V vs. Fc +/0 (Fig. S14); elemental analysis
	PCH2N), 3.31 (s, 8 H, CH2CH2COO), 1.07 -2.90 ppm (m, 22 H, C6H11); 31 P NMR (DMSO-(%) calculated for C100H108B2F8N8NiO16P4: C, 59.05; H, 5.35; N, 5.51; found: C, 56.95; H,
	d6): δ -42.22 ppm. 5.33; N, 5.52.
	P Cy 2 To a solution of P Cy 2N PhCH 2 CH 2 COOH 2 (459 mg, 0.75 mmol) in 15 mL DMF was added N-
	hydroxyphthalimide (489 mg, 3 mmol) and N-(3-dimethylaminopropyl)-N′-
	ethylcarbodiimide hydrochloride (577 mg, 3 mmol) and the mixture stirred overnight. The

yellow suspension was added drop-wise to rapidly stirred water to precipitate the product, which was collected by filtration and recrystallized from chloroform and diethyl ether, then washed copiously

Acknowledgements

This work was supported by the Ministère de la transition écologique et solidaire and the Agence Nationale de la Recherche (Labex ARCANE, CBH-EUR-GS, ANR-17-EURE-0003), the CEA PTC program on Materials and Processes and the Fuel Cells and Hydrogen 2 Joint Undertaking (FCH-JU, GAN 779366). FCH-JU receives support from the European Union's Horizon 2020 research and innovation programme, Hydrogen Europe and Hydrogen Europe research. PC and SL acknowledge ILL and LLB for beam time allocation, and Alexis Chennevière, Jacques Jestin and Lionel Porcar for their help as local contact. The authors thank Dr. Ahmed Ghedjatti for providing TEM imaging.

Declaration of Interests

The authors declare no conflict of interest.


Fei Jiang

Hugues Berry

Marc Schoenauer

Supervised and Evolutionary Learning of Echo State Networks

Keywords: Neural networks, Evolutionary algorithms, Control

A possible alternative to topology fine-tuning for Neural Network (NN) optimization is to use Echo State Networks (ESNs), recurrent NNs built upon a large reservoir of sparsely randomly connected neurons. The promises of ESNs have been fulfilled for supervised learning tasks, but unsupervised ones, e.g. control problems, require more flexible optimization methods -such as Evolutionary Algorithms. This paper proposes to apply CMA-ES, the state-of-the-art method in evolutionary continuous parameter optimization, to the evolutionary learning of ESN parameters. First, a standard supervised learning problem is used to validate the approach and compare it to the standard one. But the flexibility of Evolutionary optimization allows us to optimize not only the outgoing weights but also, or alternatively, other ESN parameters, sometimes leading to improved results. The classical double pole balancing control problem is then used to demonstrate the feasibility of evolutionary (i.e. reinforcement) learning of ESNs. We show that the evolutionary ESN obtain results that are comparable with those of the best topology-learning methods.

Introduction

It has long been known to Neural Networks practitioners that a good design for the topology of the network is an essential ingredient for a successful application of Neural Networks to a given learning task. The critical issue then becomes that of learning the appropriate weights. Echo State Networks (ESNs) [START_REF] Jaeger | The Echo State Approach to Analysing and Training Recurrent Neural Networks[END_REF], that were recently proposed for supervised learning of time series, can be seen as an alternative approach based on a large reservoir of neurons with random, constant (non-learned) and sparse connectivity. Learning is thus restricted to the outgoing connections only. In the supervised learning case, this efficiently transforms the learning process into a simple quadratic optimization problem. The situation changes dramatically with unsupervised learning tasks, such as control ones: no input-output example being available, the learning problem can no longer be set as quadratic. Evolutionary Computation provides a possible solution for such situations, as long as some fitness is available. This paper addresses the following issues: are Evolutionary Algorithms (EAs) a viable method to train ESNs in general and on reinforcement learning tasks in particular? Furthermore, are ESNs an alternative to topology learning in the framework of control problems? Finally, Evolutionary Algorithms can learn to adjust more than just the weights of the outgoing connections of the ESN. Does this improve the learning power of ESNs?

The paper is organized as follows. Section 2 introduces ESNs and our evolutionary algorithm. The supervised task case (time-series prediction) is addressed in Section 3. Moreover, Evolutionary Learning opens up the field of reinforcement learning to ESNs. We address this issue with a canonical example, the double pole balancing problem [START_REF] Stanley | Efficient reinforcement learning through evolving neural network topologies[END_REF][START_REF] Igel | Neuroevolution for reinforcement learning using evolution strategies[END_REF][START_REF] Dürr | Neuroevolution with Analog Genetic Encoding[END_REF], in Section 4. Finally, Section 5 sums up the paper and sketches directions for on-going and further researches.

Background

Echo State Networks

Echo state networks (ESN) are discrete time, continuous state, recurrent neural networks using a sigmoidal activation function for all neurons [START_REF] Jaeger | The Echo State Approach to Analysing and Training Recurrent Neural Networks[END_REF]. A typical ESN is shown in figure 1: the input layer is totally connected to the hidden layer (the reservoir ) whose neurons are themselves totally connected to the output layer. Note that the output layer can also be connected backward to the reservoir. To generate the reservoir, one connects N neurons randomly (with independent uniform distribution) up to a user-defined connection density α. The weight of these connections are randomly chosen, then scaled so that the spectral radius of the reservoir, ρ (i.e. the largest modulus among the eigenvalues of the reservoir weight matrix) is less than a prescribed value < 1 (see e.g. [START_REF] Jaeger | Tutorial on training recurrent neural networks[END_REF]). The main point in ESN is that only the weights from the reservoir nodes to the output ones are to be learned. Any supervised learning problem using some mean-square error objective thus reduces to a quadratic optimization problem that can be quickly solved by any deterministic optimization procedure, even for very large values of N . ESNs have been shown to perform surprisingly well in the context of supervised learning, in particular for time series prediction. They have also been successfully used in the context of (supervised) robot control learning [START_REF] Jaeger | NIPS 2006 Workshop on Echo State Networks and Liquid State Machines[END_REF]. The idea beyond Evolutionary Learning for Echo State Networks is to replace the gradient descent used to optimize the outgoing weights in Jaeger's approach [START_REF] Jaeger | Tutorial on training recurrent neural networks[END_REF] by an Evolutionary Algorithm (EA). We first present the Evolutionary Algorithm that will be used throughout the paper, the Covariance Matrix Adaptation Evolution Strategy, aka CMA-ES.

CMA-ES

The CMA-ES is a well-established and state-of-the-art Evolutionary Algorithm in continuous domain evolutionary computation [START_REF] Hansen | Adapting arbitrary normal mutation distributions in evolutionstrategies: the covariance matrix adaptation[END_REF][START_REF] Hansen | Completely derandomized self-adaptation in evolution strategies[END_REF][START_REF] Hansen | Evaluating the CMA evolution strategy on multimodal test functions[END_REF]. At iteration step t, λ > 1 offspring individuals x ∈ R n are generated by sampling a multi-variate normal distribution: x = m t + σ t × N (0, C t ), where m t is the average of the best individuals of the previous generation, N (0, C t ) is a normally distributed variable with mean 0 and n × n covariance matrix C t , and σ t > 0 is a scaling parameter, the step-size. After those λ individuals have been sampled, evaluated on f , and sorted according to their objective function values, the distribution parameters m t , σ t , and C t are updated for a new iteration step using the sorted population and cumulated information about the whole optimization path. It has been shown experimentally that the covariance matrix C t approximates the inverse of the Hessian matrix of the problem at hand near the optimum, and CMA-ES can hence be considered a quasi-second order optimization method. Importantly, CMA-ES is almost a parameter-free algorithm. Only the number of offsprings λ is crucial to the evolution success and must possibly be adapted to account for the ruggedness of the fitness landscape at hand. In our case, the default value [START_REF] Hansen | Completely derandomized self-adaptation in evolution strategies[END_REF], that increases logarithmically with the dimension n of the problem (number of unknown parameters): λ = 4 + 3 ln(n), was found to be well adapted.

Supervised Learning of ESN

In order to validate the Evolutionary approach to ESN learning, we first replicate Jaeger's initial setting [START_REF] Jaeger | The Echo State Approach to Analysing and Training Recurrent Neural Networks[END_REF], but using an Evolutionary Algorithm in lieu of its gradient-based quadratic optimization procedure.

The Original Settings

In this toy example, the aim is to train the network to produce a univariate time-series output, y teach (n) = 1 2 u 7 (n) (where n is time) from a univariate input given by u(n) = sin(n/5). The network output is given by y

(n) = f ( N i=1 w out i × x i (n)), where w out i denotes the weight of the i-th output con- nection, x i (n) is the state of the i-th neuron, f (x) = (1 -e -ax )/(1 + e -ax )
and a is the half-slope of f at zero activation. Like in Jaeger's original paper, the reservoir consists of N = 100 randomly connected neurons (independent uniform distribution). Its weights are set to 0, +0.4 or -0.4 with probabilities 0.95, 0.025, 0.025 respectively (sparse connectivity of 5%). They are then scaled so that the spectral radius of the reservoir is ρ ≈ 0.88. The input weights (from the input to all neurons in the reservoir) are set to +1 or -1 with equal probability. Direct links from inputs to outputs or backward links from outputs to the reservoir are not used here. The fitness to minimize is the Mean Square Error of the network, computed between time steps 101 and 300:

mse train = 1/200 300 n=101 (y(n) -atanh(y teach (n))) 2 .

Which parameter to optimize?

In Jaeger's original paper [START_REF] Jaeger | The Echo State Approach to Analysing and Training Recurrent Neural Networks[END_REF], the output weights were optimized with a gradient method, resulting in a reported error mse ≈ 3.5 × 10 -15 [START_REF] Jaeger | The Echo State Approach to Analysing and Training Recurrent Neural Networks[END_REF]. But a critical parameter in ESN tuning seems to be the spectral radius, that is usually advised to be < 1 [START_REF] Jaeger | The Echo State Approach to Analysing and Training Recurrent Neural Networks[END_REF] though different values have been proposed in the literature for different problems. Hence it seems a good idea to use the spectral radius as a free parameter to be optimized by CMA-ES: it only adds one dimension to the problem. The procedure goes as follows: the weights of the recurrent connections within the reservoir are first scaled so that the spectral radius of the connection matrix takes the value prescribed by the additional optimized parameter. The weights are of course set back to their original values before the evaluation of next individual. Jaeger's original sigmoidal function was tanh, corresponding to the case a = 2 for the transfer function f above. However, if both the output weights and the sigmoid slopes a are optimized, the dimension of the optimization problem is twofold. Hence, we examined the case where only the slopes a are optimized.

Comparative Measures

Because CMA-ES, like all EAs, is a stochastic optimization procedure, no strong conclusion can be drawn in absence of a thorough statistical analysis of the performances. Here 15 different networks have been used, and for each network, 5 runs of CMA-ES were launched with different random seeds (and hence starting points). To have a global performance measure, we used an estimator of the success performance called the "SP1 measure" [START_REF] Hansen | Evaluating the CMA evolution strategy on multimodal test functions[END_REF][START_REF] Auger | Performance evaluation of an advanced local search evolutionary algorithm[END_REF], which is the number of evaluation of the fitness function that is needed to reach a given fitness level, divided by the fraction of runs that did reach that fitness value. SP1 can thus be viewed as the computational effort required to reach a given performance level.

Results

Three variants of the ESN evolutionary optimization have thus been compared: (i) optimizing the output weights only, denoted Std in the following; (ii) optimizing the output weights plus the spectral radius, denoted Rho; and (iii) optimizing the sigmoidal slopes only, denoted Slopes. Figure 2 shows the SP1 plots for a 100 neuron reservoir and confirms that CMA-ES (Std) can be as precise as the gradient method reported in [START_REF] Jaeger | The Echo State Approach to Analysing and Training Recurrent Neural Networks[END_REF] (i.e. with a mse of the order of 10 -15 ), though undoubtedly requiring a much greater computational effort. Interestingly, the results show that optimizing only the reservoir slopes (Slopes) yields precisions that are also similar to the original ESN learning method. Note however that with smaller reservoir sizes (e.g. N = 30), optimizing the reservoir neuron slopes (Slopes variant) yielded even better fitness than the standard procedure (not shown). This, however, has a cost and requires almost 100-folds more evaluations, due to the fact that very few runs do find such low fitness values. Finally, Figure 2 also evidences that increasing the search space fails to improve precision: the Rho variant yields the worst precision in this supervised task. Taken together, these results validate the use of Evolutionary Learning for supervised tasks. We now turn to the study of a reinforcement learning task.

Reinforcement Learning of ESN

The double pole balancing problem without velocity information is a benchmark learning task for the evaluation of neuroevolution methods -i.e. methods that evolve both the topology and the weights of neural networks [START_REF] Stanley | Efficient reinforcement learning through evolving neural network topologies[END_REF][START_REF] Gruau | A comparison between cellular encoding and direct encoding for genetic neural networks[END_REF][START_REF] Gomez | Solving non-markovian control tasks with neuroevolution[END_REF][START_REF] Igel | Neuroevolution for reinforcement learning using evolution strategies[END_REF][START_REF] Dürr | Neuroevolution with Analog Genetic Encoding[END_REF]. Albeit they don't belong to supervised learning methods, evolutionary methods are based on the evaluation of some individual fitness. This fitness can be considered as a feedback or a kind of reward emitted by the environment, so that such neuroevolution methods are considered as reinforcement learning methods. The system consists of a cart (mass =1 kg) moving along the x axis, and two poles of different lengths (l 1 = 1 m, l 2 = 0.1 m) and masses (m 1 = 0.1 kg, m 2 = 0.01 kg) that are connected to the cart by a hinge. The poles have a single degree of freedom (their angle θ 1 and θ 2 w.r.t. the vertical). The challenge is to keep both poles up (i.e. within given bounds for their angles) as long as possible using the ESN output, which is interpreted as a force F x applied to the cart (F x ∈ [-10 N, 10 N]). In all experiments (in this paper as well as in previous works), the dynamics of this mechanical system was solved using fourth-order Runge-Kutta method with a step size of 0.01 s.

Fitness(es)

To avoid heavy computational cost many, if not all, previous works in the evolutionary literature addressing the double pole balancing problem [START_REF] Gruau | A comparison between cellular encoding and direct encoding for genetic neural networks[END_REF][START_REF] Gomez | Solving non-markovian control tasks with neuroevolution[END_REF][START_REF] Stanley | Efficient reinforcement learning through evolving neural network topologies[END_REF][START_REF] Igel | Neuroevolution for reinforcement learning using evolution strategies[END_REF][START_REF] Dürr | Neuroevolution with Analog Genetic Encoding[END_REF] have used a simplified fitness (thereafter referred to as F cheap ): a single trial is run for every individual in the population, starting from the same state (θ

1 (0) = 4.5 o , θ1 (0) = θ 2 (0) = θ2 (0) = x(0) = ẋ(0) = 0).
f stable =    0 if t < 100 0.75 t i=t-100 (|x(i)| + | ẋ(i)| + |θ 1 (i)| + | θ1 (i)|)
otherwise where t denotes the number of time steps during which the system remained inside the success domain and f stable quantifies the cart stability during the last 100 time steps. At every generation, the best individual for fitness F cheap undergoes two generalization tests. The first test is passed if the individual keeps the system within the success domain during 100, 000 further time steps. The second test is passed if the individual as well succeeds in balancing the system for 1, 000 time steps starting from 625 different initial positions. When one individual succeeds for at least 200 of those 625 trials, the run is stopped and this individual is returned as the solution.

However, though this simplified fitness does save a lot of computational resources, it is a poor fitness with respect to the overall goal of the optimization. For instance, individuals are commonly obtained that have a very high fitness but never pass the first generalization test, while some others pass all generalization tests but with a rather low F cheap . Hence we propose here a new fitness (F gen. ) that takes into account all 3 tests described above: F gen. = F cheap + 10 -5 n I + 30n S /625 where n I is the number of iterations where the system was maintained within the success domain during the first generalization test, and n S is the number of generalization trials passed by the controller during the second one. The constants 10 -5 and 30 were chosen by trial and error.

Experimental conditions

The size of the reservoir was fixed here to N = 20: initial experiments indicated that larger reservoirs did not improve the results. To study the variability with respect to the reservoir topology, 20 different reservoirs were generated and 11 independent runs of CMA-ES were made for each reservoir. Each reservoir was initialized as described in section 3.1, except for the fixed weights: here, the reservoir connectivity was 10% and non-zero weights were randomly initialized between [-1, 1]. At the beginning of each run, the activity of all neurons in the reservoir was zeroed, and the network was run for 20 iterations before control actually began and the fitness started to accumulate. As mentioned in Section 2.2, CMA-ES is almost a parameter-free algorithm. However, Igel advises in his paper [START_REF] Igel | Neuroevolution for reinforcement learning using evolution strategies[END_REF] to impose a lower bound on the actual lower eigenvalue of the covariance matrix during CMA-ES runs. Indeed, our preliminary results confirmed that, without this constraint, the solutions systematically evolves toward "Bang-Bang" types of motor control, that do not seem very efficient for the task at hand. We were able to solve this issue by imposing a lower bound of 0.05 on the step-size σ. Finally, the presented results were obtained with the Std and Rho variants of the evolutionary ESN learning (Section 3.2).

Results and Discussion

All results are summarized in Table 1. Every line in the table gives the results of one variant of the algorithm (two spectral radii, 0.6 and 0.95 were tried for the Std variant, and variant Std -Opt will be discussed later). For each variant, the 220 runs (11 runs for each of the 20 different reservoir initializations) are here grouped together. Each sub-table shows the average number of needed evaluations averaged over the successful runs (column Avg Eval.), its standard deviation (Std Dev.), the number of tests (out of 625) passed during the third generalization test (Generalization), and, most importantly, the percentage of success (% success), i.e. of runs where the best individual did pass the 3 tests. Using the "cheap" fitness F cheap , a first striking result is the very low performance of the Std variants (whatever the spectral radius): less than 7% of the runs did pass the 3 generalization tests in these cases. Things are better for the Rho variant: more than half of the runs succeeded, with an average cost of 23, 571 evaluations, which amounts to an SP1 value of about 45, 300. This value is still worse than NEAT (≈ 33, 000 evaluations [START_REF] Stanley | Efficient reinforcement learning through evolving neural network topologies[END_REF]) and AGE (≈ 25, 000 evaluations [START_REF] Dürr | Neuroevolution with Analog Genetic Encoding[END_REF]), but within the same order of magnitude.

As expected, the results really improve when using the new fitness, that takes into account the generalization ability of the network: the Rho variant almost always find a solution (except for one run out of 220). Even the Std ones improve a lot over their results with the cheap fitness. More importantly, using the new fitness allows all variants to reach performances that are comparable to those of NEAT (≈ 33, 000 evaluations [START_REF] Stanley | Efficient reinforcement learning through evolving neural network topologies[END_REF]) and AGE (≈ 25, 000 evaluations [START_REF] Dürr | Neuroevolution with Analog Genetic Encoding[END_REF]), though of course those results can hardly be compared, as they were obtained using a different fitness. Indeed, the found SP1 values for Std-0.60, Std-0.95, and Rho variants respectively were 19, 342, 19, 808 and 21, 658. Spectral Radius. It has always been advocated by ESN pioneers that the upper bound on the spectral radius was important for successful ESN use, and the results for both Std variants with different spectral radius seem to confirm this. However, the most remarkable fact here is that for all settings, the Rho variant, that explicitly optimizes the spectral radius, almost always gives the best results. This is surprising when compared to the situation in the supervised context (Section 3.4), where the Rho variant performed the worst of all. Further experiments were run, using the Std variant but fixing the spectral radius to the final value found by the Rho method (see the lines "Std -Opt" in Table 1). Though it generally slightly improves the results over an arbitrary value like 0.6 or 0.95, it does not allow to reach the same level of performance as the Rho method itself. The important feature is thus that ρ is allowed to vary during the optimization, and not the final value it reaches. A final advantage about the Rho variant, is that it seems to be able to provide controllers that generalize very well, if evolution (using the new fitness) is continued after the first network has passed the 200-tests of the last generalization test: all resulting networks are able to successfully solve more than 500 out of the 625 test cases, with a peak at 555 for one network. Unfortunately, the previously published studies do not report this kind of result, except for one sentence in [START_REF] Dürr | Neuroevolution with Analog Genetic Encoding[END_REF] that mentions that one network successfully solved 525 test cases. Reservoir topologies. The results obtained with the the double pole problem were found to vary a lot among the different (random) realizations of the connections (i.e. the non-zero weights) in the reservoir, for the same value of the density of connection. Indeed, in the case of methods with low performance, all the successful runs often stem from a small number of initial reservoir topologies, while a majority the initial reservoir topologies fail to generate even a single success. Together with the differences noted in the supervised learning context, this makes a clear picture that the topology of the reservoir matters. Why, and how to take advantage of this fact, is left to further work.

The question is now open: whereas reservoir computing has been proposed as a possible alternative to fine tuning of the weights in Neural Networks, it might be the case that tuning the topology of the reservoir allows to obtain more efficient ESNs. Further work will address this research question, and two main directions can be imagined. The network can be built using different topological classes (e.g. small world, scale free, . . . ); identifying classes of networks that are efficient for a given type of problem (i.e. such that randomly built networks from this class have a very high probability to solve the problem at hand) would indeed relieve the programmer from the task of optimizing the topology, restricting the search space to a fraction of the parameter space, where CMA-ES proved to be an efficient tool. It might be the case, however, that for reservoir computing, problem-specific topology tuning is nevertheless required anew for each problem. The main difficulty will then be to design efficient techniques for tuning the topology of large networks, as most existing methods do not really scale up to hundreds of neurons or more. Some hints have been recently given with Hyper-NEAT [START_REF] Stanley | Compositional Pattern Producing Networks: A Novel Abstraction of Development[END_REF] on the one hand, and with the different approaches based on Genetic Regulatory Networks, starting with AGE, though other GRN approaches can be envisioned, too (see e.g. [START_REF] Banzhaf | Artificial Regulatory Networks and Genetic Programming[END_REF]).

Conclusion

Several recent studies have attempted to couple EAs with ESNs, mostly using supervised learning [START_REF] Schmidhuber | Training recurrent networks by evolino[END_REF]. A limited number of works have used reinforcement learning to optimize ESNs with EAs, in which the network tasks were time series predictions [START_REF] Xu | Direct adaptive control: an echo state network and genetic algorithm approach[END_REF][START_REF] Ishu | Identification of motion with echo state network[END_REF] or robust spatial pattern formation ("flag" problems [START_REF] Devert | Robust multi-cellular developmental design[END_REF]). To our knowledge, our study is the first one to show the feasibility of the EA-ESN couple for motor control tasks. On addition, previous articles restricted evolutionary optimization to the reservoir weights [START_REF] Schmidhuber | Training recurrent networks by evolino[END_REF] or more frequently the outgoing weights of the ESN. Here we show that optimizing additional ESN parameters could indeed be efficient.

In a supervised context, the results on a standard time series prediction problem reach the same precision when optimizing the output weights than the original results obtained using quadratic optimization, and further optimizations fail to improve this precision. For reinforcement learning tasks, the good news is that the Evolutionary Learning of ESNs works. Moreover, optimizing more than just the outgoing weights does improve the results. Furthermore, there seems to be a high dependency of the results on the topology of the reservoir, at least for the small sizes experimented with here. Hence, the results presented here do not satisfactorily answer the question of where ESNs stand between the two extremes of neuroevolution today: evolutionary optimization of the weights of a fully recurrent neural network (as proposed in [START_REF] Igel | Neuroevolution for reinforcement learning using evolution strategies[END_REF]) and carefully crafted developmental systems that evolve the topology of highly efficient NNs for a given task [START_REF] Stanley | Efficient reinforcement learning through evolving neural network topologies[END_REF][START_REF] Dürr | Neuroevolution with Analog Genetic Encoding[END_REF]. Further experiments using more reliable test problems, and larger reservoir sizes, are needed to definitely address this issue. Additionally, a side take-home lesson from this paper concerns the usefulness of the double pole balancing problem as a benchmark for evolutionary control in general: the answer is clearly negative for us now (but had been claimed by others before), at last with the kind of fitness used up to now to tackle the problem.

Acknowledgments

The simulator of the double pole balancing problem relies on the source code kindly provided by Kenneth O. Stanley.

Fig. 1 .

 1 Fig. 1. Schematic view of an Echo State Network. Plain arrows stand for weights that are randomly chosen and remain fixed, while dashed arrows represent the weights to be optimized.

Fig. 2 .

 2 Fig. 2. Comparative SP1 measures for the case N = 100, in log-log scale.

Table 1 .

 1 Experimental results for the double pole balancing.

		Cheap Fitness	New Fitness
	Method	Avg.	Std. Genera-	% Avg.	Std. Genera-	%
		Eval.	Dev. lization success Eval.	Dev. lization success
	Std -0.95 14960	6291 234	6.8% 16303 11511 209	82.3%
	Std -0.60 16639 17037 225	6.8% 16886 11073 211	87.3%
	Rho	23571 10175 241	52.7% 19796 6770 224	91.4%
	Std -Opt 19168 21782 232	9.5% 15965 11813 208	86.8%