Marc Grosjean

Elise Lorenceau

Unstable growth of bubbles from a constriction

published or not. The documents may come

Unstable growth of bubbles from a constriction

I. INTRODUCTION

Among the successes of microfluidics is the possibility of forming large assemblies of drops or bubbles almost identical at high throughput (of the order of 100 Hz) [START_REF] Anna | Formation of dispersions using "flow focusing" in microchannels[END_REF][START_REF] Huerre | Bubbles and foams in microfluidics[END_REF][START_REF] Anna | Droplets and bubbles in microfluidic devices[END_REF]. These entities, dispersed in a continuous liquid phase and used as microreactors containing active ingredients at a concentration changing from drop to drop, allows analysis and screening of chemical reactions with unprecedented throughput [START_REF] Song | Reactions in droplets in microflulidic channels[END_REF][START_REF] Brouzes | Droplet microfluidic technology for single-cell high-throughput screening[END_REF][START_REF] Guo | Droplet microfluidics for high-throughput biological assays[END_REF][START_REF] Baret | Surfactants in droplet-based microfluidics[END_REF]. Bubbles and drops are also found in other fields of engineering where they are generally dispersed in a continuous liquid phase, themselves then being qualified as the dispersed phase (firefighting foam or sparkling drinks [START_REF] Stevenson | Foam Engineering: Fundamentals and Applications[END_REF]). There are many methods to make monodisperse bubbles or drops such as shearing crude emulsion to split it into droplets [START_REF] Mason | Emulsification in viscoelastic media[END_REF][START_REF] Bibette | emulsion science: basic principles -an overview[END_REF] or blowing on an interface [START_REF] Basaran | Small-scale free surface flows with breakup: Drop formation and emerging applications[END_REF][START_REF] Salkin | Generating soap bubbles by blowing on soap films[END_REF][START_REF] Hamlett | Blowing big bubbles[END_REF]. One commonly used in microfluidics and called flow-focusing consists in forming bubbles (or drops) by deforming an air/liquid interface placed at the end of a tube (of square, rectangular or circular section) from a reservoir whose pressure increases [START_REF] Anna | Formation of dispersions using "flow focusing" in microchannels[END_REF]. In the dripping regime, three distinct steps can be identified: (1) a phase of quasi-static deformation of the interface fixed to the end of the tube which, by bending, changes from a flat geometry to that of a quasi-hemispherical cap with a radius equal to that of the tube. (2) a rapid growth (generally in less than 100 milliseconds) of this hemisphere until reaching a final almost spherical shape of radius much greater than that of the tube. (3) Finally, pinch-off regime with detachment of the bubble from the constriction [START_REF] Garstecki | Mechanism for flow-rate controlled breakup in confined geometries: A route to monodisperse emulsions[END_REF][START_REF] Dollet | Role of the channel geometry on the bubble pinch-off in flow-focusing devices[END_REF]. Depending on the geometry of the system used, gravity or viscous friction forces produce the work necessary to stretch the neck separating the spherical bubble to the point of spontaneous rupture driven by capillary forces [START_REF] Eggers | Nonlinear dynamics and breakup of freesurface flows[END_REF][START_REF] Eggers | Physics of liquid jets[END_REF]. When nothing disturbs the bubble, it remains attached to the end of the constriction or tube, as beautifully illustrated in the magnificent paintings "Les bulles de savon" of J.S. Chardin, E. Manet or J. Bail [START_REF]Les bulles de savon[END_REF].

To obtain the most peaked bubble size distribution, the time of the pinch-off regime (3), which is intrinsically variable as a result of hydrodynamic instability, must be much shorter than the time of growth regimes (1) and [START_REF] Huerre | Bubbles and foams in microfluidics[END_REF]. Thus, the pinching dynamics of fluid necks have been studied with great care, revealing the importance of convection [START_REF] Garstecki | Mechanism for flow-rate controlled breakup in confined geometries: A route to monodisperse emulsions[END_REF][START_REF] Ganan-Calvo | Perfectly monodisperse microbubbling by capillary flow focusing: An alternate physical description and universal scaling[END_REF], swirl [START_REF] Herrada | Generation of small mono-disperse bubbles in axisymmetric t-junction: The role of swirl[END_REF], confinement [START_REF] Hagedorn | Breakup of a fluid thread in a confined geometry: droplet-plug transition, perturbation sensitivity, and kinetic stabilization with confinement[END_REF], presence of surfactants or not [START_REF] Van Hoeve | Bubble size prediction in co-flowing streams[END_REF]. On the contrary, the dynamics of phases (1) and ( 2) have been much less explored, the implicit hypothesis being that the duration of this phase is controlled by the flow rate of the dispersed phase and the volume of the bubble at the threshold of breakup. However, what sets this flow rate is not always obvious. For pressure-driven flow of the dispersed phase, nonlinear variations of the gas flow rate, induced by hydrodynamic feedback in the outlet channel have been reported in several studies [START_REF] Raven | Periodic microfluidic bubbling oscillator: Insight into the stability of two-phase microflows[END_REF][START_REF] Raven | Dry microfoams: formation and flow in a confined channel[END_REF][START_REF] Sullivan | The role of feedback in microfluidic flow-focusing devices, Philosophical transactions of the royal society A-mathematical physical and engineering sciences[END_REF]. For flow-rate driven flow, this difficulty should not exist, yet we reveal in this work that the compliance of the system -which arises here from the gas compressibility -induces a mechanical coupling between the deformation of the interface at the constriction and the pressure in the gas reservoir. This coupling can induce large fluctuations in the flow rate that lead to unstable bubble formation modes. We therefore study the first steps of bubble growth at an imposed flow rate in a geometry reminiscent of the one used by children when they blow a bubble from a tube. By comparing experimental results with an analytical model, we predict the final bubble volume. In particular, we show that the initial volume of the reservoir comprising the gas -usually not considered -is a key parameter of this process.

II. EXPERIMENT

The soap film is made of a mixture of Sodium Dodecyl Sulfate (SDS) at a concentration of 24 mmol/L, which is 3 times larger than the CMC, 20% of glycerine and deionized water. The solution is used at least 3 days after it has been made to ensure that the hydrolysis of SDS into dodecanol is achieved [START_REF] Bergeron | Equilibrium measurements of oscillatory disjoining pressures in aqueous foam films[END_REF]. The liquid/air surface tension, γ, is measured prior to any experiment using the pendant drop technique [START_REF] Daerr | Pendent drop an imagej plugin to measure the surface tension from an image of a pendent drop[END_REF] and we systematically found γ = 23 ± 2 mN/m. The soap film is deposed at the extremity of a needle -tube in the following -of external radius, a, ranging between 0.3 and 0.83 mm. The other extremity of the tube is connected to a reservoir composed of two syringes of volumes V 1 and V 2 (see Fig. 1). The total volume of the reservoir V -which includes V 1 , V 2 , V d the dead volume of the valve and the tube and Ω the volume comprised between the film and the outlet of the tube -varies between 1 and 50 mL. A first syringe, connected to a syringe pump (KdScientific), is used to reduce the volume of the reservoir at a flow rate -dV 1 /dt = Q, with Q equal to 1 or 2 µL/s. A second syringe serves to change the initial total volume of the reservoir V (t = 0) = V 0 . The deformation of the soap film is monitored by a camera Marlin from Allied Vision.

At t = 0, the syringe pump and the camera are triggered simultaneously (the error associated with this manual triggering is estimated at less than one second). The reduction of the volume of the reservoir increases the pressure and bends the soap film. The liquid film is much softer than the rest of the elements containing the compressed gas (syringe tube and connectors), then we assume that only the film is deformable. To avoid premature rupture of the soap film, a transparent plastic box is placed around the bubble to limit its evaporation. This allows an easy observation of stable bubbles for several minutes. We made sure that this plastic box is not completely airtight so that the external pressure around the bubble is the atmospheric pressure.

III. EXPERIMENTAL RESULTS

In our experiments, we have observed that it exist two clearly different regimes for a bubble to swell, a quasistatic one and a second highly dynamic. Those two regimes are illustrated in Fig. 2.a) and b). In both cases V 0 is identical while a is 2.8 times bigger in b) than in a). The bubble in Fig. 2.b), swelled from a large tube, continuously inflates step by step while the swelling of the bubble in Fig. 2.a) is unstable and takes place in less than 5 ms. To go further, we report in Fig. 3 the evolution of h, the height of the bubble, defined in Fig. 1, as a function of time, t, at same flow rate and radius but for different V 0 . As we can see, we can make a distinction between two regimes, a first for V 0 < 10 mL where the growth of the bubble is continuous and a second for V 0 ≥ 10 mL, where the swelling is unstable. In this second regime, the curves are S-shaped with a near-vertical zone meaning that the height of the bubble, h, changes from one to several millimeters in less than 5 ms.

The non-monotonic evolution of the radius of curvature, R, of the soap film is a crucial point to explain the distinction of regime observed in experiment. This radius is both constrained by a, the radius of the tube, and the evolution of the pressure, P , which follows the Laplace's law P = P 0 + 4γ/R, where the factor 4 arises from the presence of two liquid/air interfaces.

At first, the pressure in the reservoir is identical to the atmospheric pressure and the film is flat, thus R → ∞. When the volume of the reservoir decreases due to the push syringe action, the pressure increases. Then, the soap film bends, R decreases and Laplace-over pressure increase in agreement. However, due to geometrical con-FIG. 3. Bubble's height, h as a function of time, t for a = 0.83 mm, Q = 2 µL/s and different V0. For V0 = 42, 30 and 20 mL, the bubbles inflate very rapidly while for V0 = 1 and 10 mL, the bubbles inflate continuously. For each curve, the time origin is adjusted so that the data collapses at long times. The recording of the different curves is stopped just before the explosion of the bubbles.

straint, R cannot reach a value smaller than a which correspond to a maximal pressure P * = P 0 + 4γ/a. At this point any compression of the volume by the push syringe triggers a second step of the film dynamic. The compression of the reservoir by the push syringe can not be balance with an increase of the pressure because R is now increasing with the bubble bending. The bubble is in a non-equilibrium state in which compressed air has been store in the reservoir. To recover an equilibrium state, the bubble as to inflate until that the decompression of the stored air is done. This event has a very short characteristic time fully separate from the push syringe speed and an amplitude dependant of the quantity of compressed air stored. After, any further compression from the syringe pump is compensated by an increase of the bubble size.

IV. MODEL

To understand these results, we write simple thermodynamic arguments stemming from the conservation of n, the number of gas moles in the reservoir. This is valid if the whole system is gas tight, hence if the rate of mole transfer dn/dt due to the permeability k of the soap film is negligible. From Fick's law, dn/dt = -kA∆C, where k is the soap film permeability, A ≈ 4πR 2 the area of the bubble and ∆C the difference of gas concentration between the reservoir and the atmosphere surrounding the bubble. Using R ∼1 mm, k ∼ 1 mm/s, a typical value from literature for SDS surfactants without salts [START_REF] Hadji | Impact of fluorocarbon gaseous environments on the permeability of foam films to air[END_REF][START_REF] Krustev | An apparatus for the measurement of the gas permeability of foam films[END_REF], and ∆C = 4γ/(RR u T 0 ), where R u = 8.31 J/mol/K is the universal gas constant and T 0 = 298 K the room temperature, we find dn/dt ∼ 2 10 -10 mol/s. As the bubble typically forms in 100 s, the variation of moles in the bubble due to the permeability of the soap film is δn ∼ 2 10 -8 mol. This is very small when compared to n 0 = P 0 V 0 /(R u T 0 ) ≈ 1.210 -3 mol, thus we assume the system to be air tight and consider n to be constant. Writing the conservation of n for an isothermal transformation, yields:

1 = (1 + 4γ P 0 R )(1 + Ω V 0 - Qt V 0 ) ( 1
)
Where Ω is the volume of the spherical cap above the tube of radius a. Since R > a, with a ranging between 0.3 and 0.83 mm, 4γ RP0 < 4γ aP0 << 1, we make a Taylor expansion of Eq. 1 and express the geometrical quantities Ω and R as a function of h, the height of the spherical cap (see Fig. 1), using the geometrical relations 2hR = h 2 + a 2 and Ω = πh/2(a 2 + h 2 3 ). We also introduce the dimensionless parameters x = h/a, τ = 2Qt πa 3 , so that Eq. 1 finally writes:

τ = x 1 + x 2 3 + Bx x 2 + 1 (2)
With B = 16γV 0 πa 4 P 0 . The numerical resolution of Eq.

2 is plotted in figure 4 for various values of B. Two types of bubble growth are observed: for small values of B, x increases as τ increases and the bubble formation is monotonic and proceeds continuously. This is in agreement with the observations of Fig. 2 and3, which revealed continuous bubble formation for large values of a and small values of V 0 . For larger values of B (typically B ≥ 38 on figure 4), the curves corresponding to the numerical solution of Eq. 2 are S-shaped with nonmonotonic variation of τ as a function of x, which is not physical since τ -the dimensionless time -should always increases. Thus, when dx/dτ is negative, there is no physical solution to the equation, and the dimensionless height suddenly jumps from one value to another. In the following, we call x 1 the maximum value of x before the jump and x 2 the minimum value of x after the jump.

To determine x 1 and x 2 , we proceed as follows. We first calculate x 1 , the dimensionless height at the onset of the formation of an unstable bubble, for which dτ dx x=x1 = 0. Hence x 1 is a solution of:

B -1 1 + x 2 3 -x 2 + 1 = 0 (3)
Using X = 1 + x 2 , Eq. 3 can be reduced to a polynomial of degree 3:

B -1 X 3 -X + 2 = 0 (4)
We seek for solutions larger than one using the Cardan method [START_REF] Cardano | Ars magna or The Rules of Algebra[END_REF]. For B ≤ 27, there is no real solution larger than one for Eq. 4, hence dτ dx > 0 and the formation of the bubble is continuous.

For B ≥ 27, two real solutions exist, but only one, X 1 , is larger than one, increases with B, and is physically consistent when B → ∞:

X 1 = 2 B 3 cos 1 3 arccos -3 3 B + 4π 3 (5)
Thus, the instability is triggered, as soon as x > x 1 , where x 1 = √ X 1 -1, with X 1 given by Eq. 5. To determine x 2 , the dimensionless height of the bubble after the unstable swelling, we assume that the swelling is instantaneous and writes τ (x 1 ) = τ (x 2 ) using Eq. 2. This leads to a 4th order polynomial equation in x 2 :

x 4 2 +x 1 x 3 2 +(x 2 1 +4)x 2 2 +x 1 1 - 3B x 2 1 + 1 x 2 +3+x 2 1 + 3B x 2 + 1 = 0 (6) Since x 1 is
also a solution of Eq.6 we factor by (x 2 -x 1 ) to reduce the polynomial of degree 4 to a polynomial of degree 3:

x 3 2 +2x 1 x 2 2 +(4+3x 1 2 )x 2 - 3B x 1 (1 + x 1 2 ) + 3 x 1 + x 1 = 0 ( 7
) Eq. 7 can also be solved analytically using the Cardan method after the change of variable X 2 = x 2 + 2x1 3 [START_REF] Cardano | Ars magna or The Rules of Algebra[END_REF], which leads to: with D = 27q 2 + 4p 3 , q = 43 27

X 2 = 3 1 2 (-q + D 27 ) - 3 1 2 (q + D 2 ) (8)
x 3 1 + 63 27 x 1 -3Bx1 (1+x 2
1 ) and p = 5 3 x 2 1 +4. x 1 and x 2 are plotted in Fig. 5 and discussed in the following section.

V. RESULTS

We now discuss the outcomes of the model. In Figure 5, we plot the simple analytical expressions of x 1 and x 2 as a function of B. For B < 27, x 1 and x 2 are not defined and the bubble growth proceeds continuously. For B = 27, Eq. 5 and 8 insures X 1 = 3 and

X 2 = 5 3 √ 2, hence x 1 = x 2 =
√ 2, as highlighted by the black dot of coordinate (27, √ 2), which superimposes with the two curves of Fig. 5. For B -→ ∞, Eq. 3 gives x 1 -→ 1 as observed in Fig. 5. Since B increases with V 0 and decreases with a, this suggests that for large V 0 and/or small a, the instability is triggered as soon as h -→ a, hence when the bubble reaches a shape very close to the hemisphere in agreement with the Laplace pressure limit set by the radius of the tube. Then imposing x 1 in Eq. 7 yields to x 2 ∼ 3 2 B 1/3 . In this asymptotic limit, which correctly reproduces the full calculation of x 2 for B ≥ 10 3 as highlighted by the dashed line Fig. 5, the height of the bubble at the end of the instability is of the order of a 3 2 B 1/3 .

In this limit of large B, the bubble is quasi-spherical and its volume Ω right after the jump is Ω = π 6 h 3 . Therefore, our model predicts a final bubble volume equal to V 0 4γ aP0 , which is surprisingly proportional to V 0 the volume of compressed gas upstream of the constricted zone modulated by the ratio of the Laplace pressure over the atmospheric pressure.

The comparison of this theoretical findings with the experimental data is not immediate for the following reasons. First, the determination of ax 1 , the height of the bubble at the onset of the instability is delicate due to the small range of variation of x 1 , so we do not propose experimental data points on Fig. 5 conserning x 1 .Second, the data of figure 3 shows a very fast growth of the bubble, but not instantaneous. Thus, to experimentally extract the height ax 2 corresponding to the end of the instability, we use the following arbitrary criterion: the bubble is in the unstable mode as soon as dh/dt is greater than af where f is the acquisition frequency of the camera. Despite this arbitrary criterion, the corresponding experimental data show a remarkable agreement with the model as illustrated in figure 5. The model thus confirms the importance of V 0 and a for bubble sizing and gives a direct relation between those parameters which could have direct application in microfluidic engineering processes.

VI. DISCUSSION

The system we describe -namely ejection of a large volume of gas when the pressure in the microfluidic reservoir exceeds a critical value -is analogous to what could be observed when following the volume of gas ejected from a macroscopic pressure cooker equipped with a weighted valve. In these cookers, the charging phase where the pressure increases in the tank is contained by the weight of the valve, is followed by a discharging phase, where a large volume of gas is ejected very quickly when the pressure exceeds the threshold supported by the valve. Beyond that, the gas flow rate out of the cooker remains constant. In the problem we study, the constriction of the tube, a, that imposes the maximum capillary pressure that the system can support is then equivalent to the valve of the pressure cooker. Recently, Keiser & al [START_REF] Keiser | Intermittent air invasion in pervaporating compliant microchannels[END_REF] have shown that a similar behavior can also be observed in a dead-end microchannel containing a constriction, initially filled with water. The unstability is then driven by the pervaporation of the liquid through the channels. Yet, in their case, the water being incompressible, it is the compliance of the elastic channels that allows the variation of pressure of the water. As for our system, the kinetics of fluid escape depends on the volume under tension. Magdelaine & al.[32] who studied a gaseous system very similar to the one considered here where the volume of compressed gas ejects into water rather than into a bubble, also highlights the importance of the volume of the pressurized reservoir. By adopting a very different formalism from ours and introducing the pinching kinetics of the gas jet ejected into the water, they produce a comprehensive model predicting the number of bubbles formed during the compression of a gaseous syringe. In general, in these two-phase systems, it is the compliance of the system, whether it comes from the compressibility of the gas or the elasticity of the microfluidic channels, which is at the origin of this instability as thoroughly discussed in [START_REF] Van Loo | Droplet formation by squeezing in a microfluidic cross-junction[END_REF] for two-phase microfluidics flow.

In view of these results, two points seem interesting to discuss.

The first point of interest concerns the formation of monodisperse bubbles in microfluidic geometries where the interface is confined in a constriction, like flowfocusing. Experimentalists in this field are well aware that the bubble size distributions produced in this type of geometry when the gas phase is flow-rate driven are more difficult to control and less peaked (with standard deviations higher than 20%) than when the gas is driven at controlled pressure [START_REF] Ward | Microfluidic flow focusing: Drop size and scaling in pres-sure versus flow-rate-driven pumping[END_REF]. This explains why pressuredriven gas control is often preferred to flow-rate gas control. Our work sheds light on this point : taking typical values a = 100 µm, V 0 = 1 mL, it comes B ∼ 1000, which clearly shows that those devices are in the unstable regime highlighted here. This suggests that the volume of the syringe containing the gas, V 0 , a parameter usually not considered, must be taken into account to set the bubbles size.

Second, the proposed model, in very good agreement with the experiments, allows to predict the unstable growth regime (B > 27) as well as the amplitude of this phase, set by a(x 2 -x 1 ). Since it is based on quasi-static arguments, it does not perfectly capture the growth dynamics of the bubble in the unstable regime. Indeed, for B > 27, we predict that the height h/a jumps from x 1 to x 2 instantaneously (see Fig. 4), which is neither physical nor confirmed by experiments. As can be seen in Fig. 3, the growth is very fast but not infinite because in practice, this expansion regime is limited by a dissipative process being either inertia of the gas, viscosity of the gas or liquid or rheology of the interface. A detailed follow-up of the bubble growth kinetics using a high-speed camera in the limit where it is limited by the interfacial rheology, seems to us a promising prospect for this work, since it could open the way to a new characterization of the interfacial rheology of surfactants in elongation.

VII. CONCLUSION

We have shown that the growth of bubbles blown in geometries with non-zero compliance can exhibit unstable regimes. Our experimental and theoretical study reveals the importance of the coupling between the constriction zone on which the interface is anchored and the volume of the tank in which the gas is compressed. The use of these unstable regimes to probe elongational interfacial rheology seems to us among the most promising perspective of this work.

FIG. 1 .

 1 FIG. 1. Experimental setup: the bubble of radius of curvature R and height h is connected to a large reservoir of volume V constituted by the volume of the two syringes, V1 and V2, the dead volume of the connectors V d and the volume of the spherical cap, Ω, of the bubble. The volume V1 is decreased at a flow rate Q thanks to a syringe pump.

FIG. 2 .

 2 FIG. 2. These two image sequences shows two bubbles swelled from reservoirs of identical volume V0 = 10 mL. In a) a = 0.3 mm and in b) a = 0.83 mm. The thumbnails are separated by 5 ms except for the first ones that display the tube before the beginning of the soap films' compression. In a way to superposed the two swellings Q = 2 µL/s in a) and Q = 1 µL/s in b).

FIG. 4 .

 4 FIG. 4. The theoretical dimensionless height x as a function of dimensionless time τ for different values of B calculated using Eq. 2. Two regimes are observed: for B ≤ 19, x is defined unequivocally as a function of τ and the slope dx/dt always reaches a finite value, whereas for B ≥ 38, x is multivalued and the slope dx/dt reaches an infinite value.

FIG. 5 .

 5 FIG. 5. Analytical solutions x1 of Eq. 5 and x2 of Eq. 7 as a function of B. The two curves meet for B = 27 at x1 = x2 = √ 2. For B < 27, x1 and x2 are not defined as the bubble inflates continuously. For B -→ ∞, x1 -→ 1 and x2 ∼ ( 3 2 B) 1/3 . The green stars correspond to experimental data.

ACKNOWLEDGMENTS

The authors thank Jerome Giraud for his technical help and Ludovic Keiser, Philippe Marmottant and Benjamin Dollet for fruitful discussions. This work is supported by funding from Pack Ambition Recherche 2021 of the region AURA -SELFI project.

AUTHOR CONTRIBUTIONS

M.G. designed the research, conducted the experiments and made the model. M.G and E.L discussed the results and wrote the article.

CONFLICTS OF INTEREST

There are no conflict to declare.


Md Estak Ahmed

Abhijit Nayek

Alenka Križan

Nathan Coutard

Adina Morozan

Ghosh Somdatta

Reiner Dey

Leif Lomoth

Vincent Hammarström

Abhishek Artero

Dey

Somdatta Ghosh Dey

Reiner Lomoth

Leif Hammarström

Vincent Artero
email: vincent.artero@cea.fr

Abhishek Dey

A bidirectional bioinspired [FeFe]-hydrogenase model

Introduction

Attaining the goal of a clean and sustainable energy cycle is the need of the next decades.

Abundant sunlight and water have encouraged the development of a H 2 /O 2 based energy cycle.

The H 2 and O 2 can be generated from water via electrolysis using sunlight as the source of energy either using solar panel to generate the current needed for electrolysis or by photo(electro)catalysis. [START_REF] Fujishima | Electrochemical Photolysis of Water at a Semiconductor Electrode[END_REF][START_REF] Bard | Artificial Photosynthesis: Solar Splitting of Water to Hydrogen and Oxygen[END_REF][START_REF] Heller | Hydrogen-Evolving Solar Cells[END_REF][START_REF] Maeda | Photocatalytic Water Splitting: Recent Progress and Future Challenges[END_REF][START_REF] Kudo | Heterogeneous photocatalyst materials for water splitting[END_REF][START_REF] Maeda | New Non-Oxide Photocatalysts Designed for Overall Water Splitting under Visible Light[END_REF][START_REF] Ardo | Pathways to electrochemical solar-hydrogen technologies[END_REF][START_REF] Kibsgaard | Considerations for the scaling-up of water splitting catalysts[END_REF][START_REF] Luan | Stepping Towards Solar Water Splitting: Recent Progress in Bismuth Vanadate Photoanodes[END_REF] Similarly, H 2 and O 2 can be combined back in a fuel cell to generate electricity. [START_REF] Diat | Proton channels[END_REF][START_REF] Cracknell | Enzymes as Working or Inspirational Electrocatalysts for Fuel Cells and Electrolysis[END_REF][START_REF] Matsumoto | Molecular Catalysis in a Fuel Cell[END_REF] This process, in principle, is sustainable and can have minimum carbon footprint thereby addressing the concern of depleting fossil fuel and the carbon footprint associated with them at the same time. The key to the success of this cycle is the availability of earth abundant metal-based cheap and efficient catalysts for the two half cells involved (Equation i & ii). So far only noble metals have been found suitable as catalysts which has deterred large scale practical implementation of a H 2 /O 2 based energy cycle. [START_REF] Beni | Electrocatalytic oxygen evolution on reactively sputtered electrochromic iridium oxide films[END_REF] Apart from the price, the poisoning of the noble metal catalysts by common impurities in H 2 O (energy storage) and H 2 (energy release) has concerned energy scientists and technologists attempting to venture in to large-scale solar energy storage applications. In addition, catalyst degradation leads to the leaching of ions that diffuse through the electrolyte, resulting in membrane damages, reducing the lifetime of the whole system and compromising the recyclability of these expensive catalysts. While biofuel cells using H 2 ases [START_REF] Vincent | Electricity from low-level H2 in still airan ultimate test for an oxygen tolerant hydrogenase[END_REF][START_REF] Wait | Characteristics of Enzyme-Based Hydrogen Fuel Cells Using an Oxygen-Tolerant Hydrogenase as the Anodic Catalyst[END_REF][START_REF] Rüdiger | Enzymatic Anodes for Hydrogen Fuel Cells based on Covalent Attachment of Ni-Fe Hydrogenases and Direct Electron Transfer to SAM-Modified Gold Electrodes[END_REF][START_REF] Fasano | Reversible or Irreversible Catalysis of H+/H2 Conversion by FeFe Hydrogenases[END_REF][START_REF] Land | Characterization of a putative sensory [FeFe]-hydrogenase provides new insight into the role of the active site architecture[END_REF] in membrane-less configuration are demonstrated, these enzymes are degraded by O 2 and inhibited by CO, which are additional barriers against their use under practical conditions. [START_REF] Stiebritz | Hydrogenases and oxygen[END_REF][START_REF] Lambertz | O2 Reactions at the Six-iron Active Site (H-cluster) in [FeFe]-Hydrogenase[END_REF][21] H 2 H + + e -(E = -0.059 V. pH) (i)

O 2 + 2H + + 2e - H 2 O (E = 1.23 -0.059 V. pH) (ii)
In the past two decades, there have been substantial developments of catalysts for electrochemical hydrogen generation by electrolysis of acidic-to neutral aqueous electrolytes and several Earth-abundant metal-based catalysts are now known to compete with noble metals for hydrogen generation. [START_REF] Seh | Combining theory and experiment in electrocatalysis: Insights into materials design[END_REF] Tolerance to oxygen during hydrogen evolution is another issue for practical implementation and some major developments in those directions are already underway. [START_REF] Ahmed | Oxygen-Tolerant H2 Production by [FeFe]-H2ase Active Site Mimics Aided by Second Sphere Proton Shuttle[END_REF][START_REF] Wakerley | Oxygen-tolerant proton reduction catalysis: much O2 about nothing?[END_REF][START_REF] Mondal | Development of air-stable hydrogen evolution catalysts[END_REF] On the contrary, noble metal-free alternatives in electrocatalytic hydrogen oxidation is limited to the series of catalysts designed by DuBois and Shaw. [START_REF] Dutta | Designing electrochemically reversible H2 oxidation and production catalysts[END_REF][START_REF] Smith | Reversible Electrocatalytic Production and Oxidation of Hydrogen at Low Overpotentials by a Functional Hydrogenase Mimic[END_REF][START_REF] Dubois | Development of Molecular Electrocatalysts for Energy Storage[END_REF][START_REF] Wilson | Hydrogen Oxidation and Production Using Nickel-Based Molecular Catalysts with Positioned Proton Relays[END_REF] As far as biomimetic systems are concerned, most mimics of the active site of [FeFe]-hydrogenases models that can activate H 2 only react stoichiometrically in organic solvents [START_REF] Wang | Catalytic Activation of H2 under Mild Conditions by an [FeFe]-Hydrogenase Model via an Active μ-Hydride Species[END_REF] and only one [START_REF] Camara | Combining acid-base, redox and substrate binding functionalities to give a complete model for the [FeFe]-hydrogenase[END_REF] has been shown to achieve a few turnovers for H 2 oxidation with ferrocenium used as the oxidant.

Therefore, biomimetic electrocatalysis for H 2 oxidation is yet to be achieved. Even more challenging is the discovery of synthetic catalysts able to mediate both H 2 production and oxidation under the same set of experimental conditions. Such bidirectional catalysis has so far only been observed for platinum, hydrogenase enzymes and the above-mentioned DuBois/Shaw catalysts.

We recently developed oxygen tolerant hydrogen evolution [Fe 2 ] catalysts which are inspired by the binuclear azadithiolato (ADT) bridged active site of [FeFe]-H 2 ases (Figure 1). [START_REF] Ahmed | Oxygen-Tolerant H2 Production by [FeFe]-H2ase Active Site Mimics Aided by Second Sphere Proton Shuttle[END_REF] These catalysts are prolific in their application and can be easily integrated with cheap and abundant electrode materials both via adsorption and covalent attachment. [START_REF] Dey | Electrochemical Hydrogen Production in Acidic Water by an Azadithiolate Bridged Synthetic Hydrogenese Mimic: Role of Aqueous Solvation in Lowering Overpotential[END_REF][START_REF] Ahmed | H2 evolution catalyzed by a FeFehydrogenase synthetic model covalently attached to graphite surfaces[END_REF][START_REF] Dey | Electrocatalytic O2 Reduction by [Fe-Fe]-Hydrogenase Active Site Models[END_REF] The [Fe 2 ] catalysts (see for example complex 1 in Figure 1) differ in their design from previously reported ones in their substitution of the aromatic ring. We observed that inclusion of an alkyl substituent in the ortho position of the aryl substitution on the nitrogen bridgehead results in an rotation that suppresses the delocalization of the amine lone pair into the aromatic ring (Figure 1, bottom). [START_REF] Ahmed | Oxygen-Tolerant H2 Production by [FeFe]-H2ase Active Site Mimics Aided by Second Sphere Proton Shuttle[END_REF] As a result of this loss of electronic delocalization, the basicity of this aliphatic-like amine function increases, allowing its protonation at near neutral pH's, contrary to a para substituted/unsubstituted aryl amine (aniline, as in complex 2 in Figure 1) that can only be protonated under quite acidic conditions. [START_REF] Dey | Electrochemical Hydrogen Production in Acidic Water by an Azadithiolate Bridged Synthetic Hydrogenese Mimic: Role of Aqueous Solvation in Lowering Overpotential[END_REF] A direct consequence of protonation of the nitrogen at higher pH's is catalytic hydrogen evolution at higher pH (i.e. near neutral conditions). [START_REF] Dey | Electrochemical Hydrogen Production in Acidic Water by an Azadithiolate Bridged Synthetic Hydrogenese Mimic: Role of Aqueous Solvation in Lowering Overpotential[END_REF] Another consequence of the presence of the aromatic ortho substituent lies in the change of conformation of the amine function, with the nitrogen lone pair now pointing towards the first coordination sphere of an iron center and allowing for a remarkable resistance to reactive oxygen species and tolerance to O 2 during H 2 evolution. [START_REF] Ahmed | Oxygen-Tolerant H2 Production by [FeFe]-H2ase Active Site Mimics Aided by Second Sphere Proton Shuttle[END_REF][START_REF] Dey | Electrocatalytic O2 Reduction by [Fe-Fe]-Hydrogenase Active Site Models[END_REF] Figure 1. Top: structure of the active site of [FeFe]-H 2 ase (H-cluster, H ox ) and [Fe 2 ] subsite mimics 1 and 2. Bottom: crystal structures of ortho (1) and para (2)-substituted complexes showing unfavorable delocalization of the nitrogen lone-pair in 1 due to perpendicular orientation of the planes in the ortho substituted complex.

In this report, we show that another feature of such bio-inspired hydrogenase mimics with "rotated" aryl groups is their unique capability to oxidize hydrogen back to proton in both organic and aqueous medium under both homogeneous and heterogeneous conditions, respectively, making them the first series of bidirectional bio-inspired [FeFe]-H 2 ase complexes.

Their overpotential requirements for electrochemical hydrogen oxidation are moderate (<400 mV) and the large catalytic rate allowed the implementation of catalyst 1 in a membrane-less fuel cell setup with current densities and power densities up to 60 Acm 2 and 31 Wcm 2 at 0.6 V cell voltage.

Results

Hydrogen Evolution and Oxidation under Aqueous Conditions

As previously reported, the hydrogen evolution reaction (HER) is catalyzed by 1 adsorbed on edge plane graphite (EPG) electrode from water, thus under heterogeneous conditions, at near neutral pH (pH 5.5) with mild overpotential requirements (160-180 mV, Figure 2a). [START_REF] Ahmed | Oxygen-Tolerant H2 Production by [FeFe]-H2ase Active Site Mimics Aided by Second Sphere Proton Shuttle[END_REF] The enhanced basicity of the nitrogen lone pair can also be advantageous for the hydrogen oxidation reaction (HOR) as it can facilitate the heterolysis of the HH bond by stabilizing the incipient proton, leaving a hydride bound to the Fe 2 S 2 cluster. Indeed, when the 1-modified EPG electrode is swept at potential negative enough for H 2 evolution to occur (Figure 2a, green and blue lines), a peak at 525 mV vs RHE is observed in the return anodic scan. Note that the solution does not contain any added H 2 to begin with. This signal is not observed if the cathodic scan is stopped before the HER process (Figure 2a, orange line). This anodic peak also appears when anodic linear sweeps are performed after bulk electrolysis has been performed at -475 mV vs RHE to produce H 2 (Figure 2b, red line). The intensity of the oxidation peak increases with increased electrolysis time (Figure 2b, inset), i.e. as the concentration of H 2 in the solution increases. These data are suggestive of HOR by complex 1 of the H 2 generated in-situ by HER by the same complex. The HOR current is not observed when the electrode is rotated (Figure 2b, purple line)

as the generated H 2 flows away from the electrode upon rotation. Finally, hydrogen oxidation was confirmed by monitoring the HOR current at 425 mV vs RHE under various partial pressures of H 2 in H 2 /N 2 mixtures (Figure 2c) with the HOR current increasing linearly with H 2 partial pressure (Figure 2d) as is expected for heterogeneous electrocatalysis where the substrate diffuses from bulk solution. [START_REF] Dey | Electrocatalytic O2 Reduction by [Fe-Fe]-Hydrogenase Active Site Models[END_REF] . The HOR current is not observed in complex 2 which does not have the o-substituent implying that the delocalization of the bridgehead nitrogen lone pair into the ring makes it unable to activate H 2 (Figure S2). For heterogeneous electrocatalysis, the I cat /I p ratio is the direct measure of the turnover frequency at saturation (TOF max ). It is a convenient way of defining the catalytic efficiency of a heterogeneous electrocatalysts. The TOF max of complex 1 for H 2 oxidation is calculated to be ~ 1.6 s -1 under 1 atm. of H 2 . To check the stability of complex 1 long-term controlled potential electrolysis (CPE) has been carried out. The stable electrolysis current (Figure S3) implies that the catalyst is stable even after 11 h of electrolysis under catalytic conditions. Moreover, ATR-FTIR of complex 1 physisorbed on EPG surface, before and after controlled potential electrolysis shows that the complex is stable even after a few hours of electrolysis (Figure S4). 2c.

Hydrogen Oxidation in Organic Solvents

To experimentally confirm HOR and determine the faradic efficiency of this process, we shifted to homogeneous non-aqueous conditions. These conditions allow us to quantify the formation of protons, i.e., the products of H 2 oxidation by capturing them with a well-defined base such as N,N-diisopropylethylamine (i-Pr 2 NEt). The cyclic voltammetry of a 1 mM solution of complex 1 in CH 3 CN solution under 1 atm of H 2 in the presence of i-Pr 2 NEt (5 mM) shows an anodic catalytic oxidation which increases with the addition of i-Pr 2 NEt (Figure 3a) suggestive of electrochemical oxidation of H 2 by complex 1. The current increases linearly with square root of partial pressure of H 2 (Figure 3b & 3b, inset) consistent with a 1 st order dependence of the homogeneous catalytic process on H 2 . [START_REF] Roy | Molecular Cobalt Complexes with Pendant Amines for Selective Electrocatalytic Reduction of Carbon Dioxide to Formic Acid[END_REF][START_REF] Ahmed | Homogeneous Electrochemical Reduction of CO2 to CO by a Cobalt Pyridine Thiolate Complex[END_REF] The electrocatalytic HOR process mediated by 1 has a half peak potential of 750 mV vs Fc +/0 . The apparent standard potential of H 2 oxidation in CH 3 CN is -1.14 V vs Fc +/0 using 18.1 as the pKa value of i-Pr 2 NEt in acetonitrile [START_REF] Kelly-Rowley | Molecular Recognition of Enolates of Active Methylene Compounds in Acetonitrile. The Interplay between Complementarity and Basicity and the Use of Hydrogen Bonding to Lower Guest pKas[END_REF] and -0.07 V vs Fc +/0 as the thermodynamic proton reduction potential value. [START_REF] Smith | Reversible Electrocatalytic Production and Oxidation of Hydrogen at Low Overpotentials by a Functional Hydrogenase Mimic[END_REF][START_REF] Fourmond | H2 Evolution and Molecular Electrocatalysts: Determination of Overpotentials and Effect of Homoconjugation[END_REF] This indicates that the overpotential (electrochemical driving force) requirement for HOR catalyzed by complex 1 is ~400 mV in acetonitrile solution. This value compares well with the HOR overpotential requirement displayed in acetonitrile by most DuBois' catalysts. [START_REF] Wilson | Hydrogen Oxidation and Production Using Nickel-Based Molecular Catalysts with Positioned Proton Relays[END_REF][START_REF] Yang | Two Pathways for Electrocatalytic Oxidation of Hydrogen by a Nickel Bis(diphosphine) Complex with Pendant Amines in the Second Coordination Sphere[END_REF][START_REF] Tard | Structural and Functional Analogues of the Active Sites of the [Fe]-, [NiFe]-, and [FeFe]-Hydrogenases[END_REF][START_REF] Adamska-Venkatesh | Spectroscopic Characterization of the Bridging Amine in the Active Site of [FeFe] Hydrogenase Using Isotopologues of the H-Cluster[END_REF][START_REF] Rodríguez-Maciá | Intercluster Redox Coupling Influences Protonation at the H-cluster in [FeFe] Hydrogenases[END_REF] The proton generated from oxidation of H 2 is converted to i-Pr 2 NEtH + cation. Quantification of the i-Pr 2 NEtH + cation by [START_REF] Fujishima | Electrochemical Photolysis of Water at a Semiconductor Electrode[END_REF] H NMR during the course of a bulk electrolysis (BE) experiment carried out in 0.5 mM CD 3 CN solution (6 ml) of the catalyst in presence of large excess of i-Pr 2 NEt (10 M) at -0.7 V vs Fc +/0 under 1 atm of hydrogen (charge passed = 136 C over 10 h) shows the gradual depletion of the signal corresponding to H 2 at 4.57 ppm and growth in the signal corresponding to i-Pr 2 NEtH + at 7.59 ppm (Figure 3c). There is no appreciable decay (only 6%) or change in the UV-visible spectra before and after long term BE experiments of the complex indicating that this complex is quite stable under these conditions (Figure S5). Quantification of the i-Pr 2 NEtH + signal and its ratio with the charge consumed yields the FY to be 82 ± 3% (Table S1). The turnover number (TON) after 10 h of electrolysis ranges between 192 and 204 (taking into account a 6% decay of the catalyst during the reaction). No HOR is observed for complex 2

under the same conditions commensurate with the proposal that the basicity of the bridgehead nitrogen is key to H-H heterolysis (Figure S6).

Time-resolved FTIR Spectroscopy

Rapid scan FTIR spectroscopy was employed to investigate the mechanism of HER catalysis by complex 1. FTIR spectroscopy is a useful tool for discerning changes in the electronic density on metal carbonyls due to the sensitivity of the carbonyl peaks to their electronic environment. As both reduction and protonation alter the electronic density on the diiron core, the carbonyl peaks could be used to gain information on the electronic and protonation state of complex 1.

An acetonitrile solution containing complex 1 and excess CoCp 2 (electron source) was rapidly mixed with excess malonic acid (proton source, pKa = 15 in acetonitrile) using a stopped flow mixing table and monitored using FTIR spectroscopy (Figure 4). The earliest recorded spectrum (< 8 ms) showed three pronounced peaks (2076, 2038 and 1998 cm -1 ) which correspond to those of the resting complex 1 in the Fe(I)Fe(I) state. As more time elapsed, these three peaks disappeared and four new peaks appeared at 2028, 1975, 1930 and 1885 cm -1 . No major differences could be observed between the IR spectra recorded at 2 min and 50 min, suggesting species 1 was rapidly and quantitatively converted to another long-lived species. This newly formed species had its carbonyl peaks red shifted by 50-70 cm -1 with respect to 1, as well as an additional, forth peak at 1885 cm -1 . The shift to the lower wavenumbers implied reduction of the diiron core. The shift magnitude was in good agreement with a shift expected for a Fe(0)Fe(I) core. A similar spectrum had already been experimentally observed for another diiron azadithiolate complex by Aster et al. [START_REF] Aster | ligand protonation and the alleged proton-shuttling role of the azadithiolate ligand in catalytic H2 formation with FeFe hydrogenase model complexes[END_REF] The N-protonated, singly reduced form of their diiron azadithiolate complex had its carbonyl peaks at 1880, 1935, 19600 and 2020 cm -1 (Table 1). [START_REF] Aster | ligand protonation and the alleged proton-shuttling role of the azadithiolate ligand in catalytic H2 formation with FeFe hydrogenase model complexes[END_REF] Similarities between the two spectra, i.e., the magnitude of the peak shift upon reduction as well as the number of carbonyl peaks suggested that the long-lived species could be the N-protonated, singly reduced species 1H (scheme 1). The DFT computed FTIR data of both 1 and 1H agree reasonably well with that of the experimental data (Figure 5a). 1930, 1975, 2028 1890, 1935, 1960, 2020 To obtain further information on the structure of and the redox state of the two iron centers, Mössbauer spectrum was recorded at 90 K for both the complexes 1 and 1H and summarizes the data in Table 2. The Mössbauer spectrum of parent complex 1 shows one doublet with isomer shift δ iso = -0.065 ± 0.01 mm.s -1 and quadrupole splitting ΔE Q = 0.83 ± 0.01 mm.s -1 (relative to α Fe ) (Figure 6a) attributed to the two identical Fe(I) centers in its butterfly Fe 2 S 2 cluster core.

Mössbauer spectroscopy

These values are in agreement with those obtained for the structurally related diiron complex [Fe 2 (μ-SCH 2 OCH 2 S)(CO) 6 ] (IS, δ iso = -0.02 mm.s -1 ; QS, ΔE Q = 0.81 mm.s -1 (relative to α Fe ). [START_REF] Song | Novel Single and Double Diiron Oxadithiolates as Models for the Active Site of [Fe]-Only Hydrogenases[END_REF][START_REF] Apfel | Models for the Active Site in [FeFe] Hydrogenase with Iron-Bound Ligands Derived from Bis-, Tris-, and Tetrakis(mercaptomethyl)silanes[END_REF] The Mössbauer data of 1H (one electron reduced protonated species), on the other hand, exhibits a quadrupole doublet with an isomer shift δ iso = -0.049 ± 0.01 mm.s -1 relative to α Fe and a quadrupole splitting ΔE Q = 0.79 ± 0.02 mm.s -1 (Figure 6b), which implies the two Fe centers in 1H is identical as well. Thus, the electronic structure of the 1H species is best described as Fe(0.5)Fe(0.5), consistent with the fact that the LUMO is a Fe-Fe * orbital and addition of 1e - to this orbital results in a delocalized mixed-valent Fe(0.5)Fe(0.5) state. The X-band EPR of 1H at 77 K shows a rhombic signal with g x = 2.07, g y = 2.06, and g z = 1.99 (Figure S7) consistent with an S = 1/2 overall spin state. -0.065 ± 0.01 -0.049 ± 0.01

ΔE Q (mm s -1 )
0.83 ± 0.01 0.79 ± 0.02

Proposed Mechanism

Complex 1 can produce as well as oxidize hydrogen, thus reproducing a unique characteristic of the active sites of natural hydrogenases. Complex 2 does not show HOR at all but exhibits HER activity in highly acidic solutions. Hydrogenases can perform both conversions generally without any substantial overpotential requirement, contrary to the complex observed here that exhibit bidirectional activity but with overpotential requirement for both processes. Of note, a putative sensory [FeFe]-hydrogenase enzyme has been recently described with a unique bidirectional irreversible behavior quite similar to the activity reported here for complex 1, [START_REF] Fasano | Reversible or Irreversible Catalysis of H+/H2 Conversion by FeFe Hydrogenases[END_REF][START_REF] Land | Characterization of a putative sensory [FeFe]-hydrogenase provides new insight into the role of the active site architecture[END_REF] catalyzing HER with an overpotential requirement of 180 mV and HOR with an overpotential requirement of 400 mV, both measured at the onset of the catalytic waves in aqueous medium under heterogeneous conditions). The first redox process observed for 1 (Fe(I)Fe(I) state) is found around 345 mV vs RHE and shifts by 50 mV per pH unit towards positive potential, indicating that the first reduction of 1 is accompanied by protonation to form the Fe(0.5)Fe(0.5)-NH species 1H, which could be isolated and characterized as described above. Note that the HER mechanism for these complexes in organic medium are different. [START_REF] Tschierlei | Spectroscopically characterized intermediates of catalytic H2 formation by [FeFe] hydrogenase models[END_REF] Sweeping to more negative potentials, position of inflexion of HER potential is then shifted by 57 mV/ pH unit (Figure S8), suggesting that the second reduction process is also coupled to protonation resulting in H 2 evolution catalysis and regeneration of 1, which immediately equilibrates with the electrode and the solution to form 1H in the Fe(0.5)Fe(0.5)-NH resting state. 1H is however unable to activate H 2 so that HOR activity is only observed at more positive potentials, where 1 is the predominant species. Actually, 1H is an intermediate in both HER and HOR (see below) processes but is inert toward both protons and H 2 substrates. 1H predominates between +425 mV and -275 mV vs RHE and hence no catalysis is observed in this potential window, explaining the irreversible behavior. By contrast, the two consecutive reduction of the 2Fe active site and the proximal Fe 4 S 4 cubane occur at similar potentials in reversible hydrogenases. 21 To gain additional insights into H 2 activation, a theoretical gauging of the mechanism (G16 [START_REF] Mj | Gaussian 03, C.02[END_REF] , B3LYP functional [START_REF] Perdew | Density-functional approximation for the correlation energy of the inhomogeneous electron gas[END_REF][START_REF] Becke | Density-functional exchange-energy approximation with correct asymptotic behavior[END_REF] We include in Scheme 1 the isomerization between terminal and bridging hydride derivative which is found quasi thermo-neutral. This is at variance with classical [Fe2] mimics for which the bridging form is significantly more stable and constitute the natural route for HER catalyzed by 2. In addition, the impossibility for the ammonium proton to be positioned close to the transient terminal hydride ligand [START_REF] Ezzaher | Evidence for the Formation of Terminal Hydrides by Protonation of an Asymmetric Iron Hydrogenase Active Site Mimic[END_REF] reported by Rauchfuss and coworkers [START_REF] Camara | Combining acid-base, redox and substrate binding functionalities to give a complete model for the [FeFe]-hydrogenase[END_REF] react with H 2 in the Fe(II)Fe(I) state. Such a deviation of the reactivity relative to electronic structure is due to the difference in the ligand environments in these systems. In the natural active site, a CN -ligand and a thioether ligand replaces two π-acid CO ligands in complex 1, resulting in increased electron density of the diiron cluster. The same is true for the FcFe 2 complex where the diphosphine ligand replaces the two -acid CO ligands in 1. This is why the Fe(II)Fe(I) mixed valent state is required to oxidize H 2 in the enzyme active site and FcFe 2 complex while the Fe(I)Fe(I) state of complex 1 can react with H 2 . Of note, this increased electron density in the active site also makes hydrogenases able to evolve H 2 from a Fe(I)-Fe(II)-H 2 state, [START_REF] Amanullah | Biochemical and artificial pathways for the reduction of carbon dioxide, nitrite and the competing proton reduction: effect of 2nd sphere interactions in catalysis[END_REF][START_REF] Senger | Protonation/reduction dynamics at the [4Fe-4S] cluster of the hydrogen-forming cofactor in [FeFe]-hydrogenases[END_REF][START_REF] Sommer | Proton Coupled Electronic Rearrangement within the H-Cluster as an Essential Step in the Catalytic Cycle of [FeFe] Hydrogenases[END_REF][START_REF] Kleinhaus | FeFe]-Hydrogenases: maturation and reactivity of enzymatic systems and overview of biomimetic models[END_REF] which is more oxidized by one redox equivalent than the Fe(I)-Fe(I)-H 2 state required for 1 to cycle.

Of note, the mechanism observed for the complex in non-aqueous conditions depends on whether reduction/oxidation is achieved chemically or electrochemically. While 1 -and 1H are observed when Cp 2 Co is used as the reductant, these species are not observed during electrochemical reduction (Figure S10, see also the comment in the Supporting Information).

Therefore, the bidirectional mechanism observed for the adsorbed complex in aqueous conditions is at variance with that occurring at the vicinity of an electrode in non-aqueous, and homogeneous, conditions in the presence of mild proton sources such as malonic acid and/or mild bases such as i-Pr 2 NEt. Under these conditions, HER proceeds directly from the Fe(0)Fe(0) state (Figure S10); Similarly, we posit that the 1H species produced from HOR rapidly disproportionate to generate 1 and protonated forms of 1 2-. This discrepancy between catalytic behaviors for HER/HOR is reminiscent for that of the initial series of DuBois complexes, which displayed various reactivity when solubilized in acetonitrile [START_REF] Tschierlei | Spectroscopically characterized intermediates of catalytic H2 formation by [FeFe] hydrogenase models[END_REF] or adsorbed on electrode and assayed in acidic aqueous conditions. 60

HOR in a membrane-less fuel cell setup

The good catalytic performance measured for H 2 oxidation of complex 1/EPG electrodes in mildly acidic solution prompted us to integrate them in H 2 /O 2 fuel cell devices. As 1 is active in near neutral aqueous environment (pH 5.6) and cannot withstand the highly acidic conditions required for implementation in Proton-Exchange Membrane (PEM) fuel cells, we turned to a membrane-less fuel cell architectures that has been developed for biocatalysts and other bioinspired catalysts. The selectivity of these (bio)catalysts makes them unsensitive to potential substrate crossover, which allows saving the cost of membrane. Instead a liquid electrolyte is used. To that end, we prepared gas diffusion electrodes (GDEs) circumventing solution H 2 masstransport limitation. Commercial Sigracet gas diffusion layer (GDL) substrates covered with a microporous layer were drop-casted with an ink based on the complex 1, carbon black and CH 2 Cl 2 . Best results were found with a carbon black/complex 1 mass ratio of 2 corresponding to a loading of 60 nmol.cm -2 . These GDEs were first assessed under a back flow of H 2 at atmospheric pressure in three-electrode half-cell configuration (see SI), as previously described, 60,61 using a 0.1 M KPF 6 aqueous electrolyte (pH 5.6). Figure 7 shows the typical cyclic voltammograms recorded under these conditions, confirming the property of the heterogenized complex 1 to catalytically oxidize H 2 with onset overpotential requirement of ~0.2

V and current densities reaching 0.4 mA.cm -2 at 0.8 V overpotential. For comparison, the polarization curve recorded on a commercial Pt/C electrode (0.5 mg Pt .cm -2 ) is also shown on Figure 7. Noteworthy, the Pt loading (2.5 10 -6 mol Pt cm -2 ) is ~20 fold higher than that of iron (1.2 10 -7 mol Fe cm -2 ). Figure S11 shows that both electrodes display specific catalytic current density (expressed in A mol M cm -2 ) in the same range.

Figure 7.

CV of a complex 1/carbon black GDE (carbon black/ complex 1 mass ratio of 2, 60 nmol complex 1 .cm -2 ) (red solid line), a carbon black GDE (black solid line) and of a conventional Pt/C (0.5 mg Pt .cm -2 ) GDE (grey solid line) in 0.1 M aqueous KPF 6 pH = 5.6 adjusted with HCl and under back-flow H 2 (1 atm H 2 , S = 0.38 cm 2 , ν = 10 mV s -1 , 20°C).

The complex 1/carbon black GDEs were then integrated in the above mentioned unconventional membrane-less H 2 /O 2 fuel cell setup using continuously degassed 0.1 M KPF 6 electrolyte adapted from our previous report [START_REF] Gentil | Carbon-Nanotube-Supported Bio-Inspired Nickel Catalyst and Its Integration in Hybrid Hydrogen/Air Fuel Cells[END_REF][START_REF] Gentil | A Nanotube-Supported Dicopper Complex Enhances Pt-free Molecular H2/Air Fuel Cells[END_REF] and operated at 25°C. The complex 1-based anode was coupled with a cathode based on a commercial 0.5 mg Pt .cm -2 GDE installed in a second electrode holder fed with pure O 2 at atmospheric pressure (Figure S12). GDEs used in this setup allow each catalyst to work at the interface between the electrode, the liquid electrolyte ensuring proton mass transport, and the gas phase supplied by a back flow of their respective substrates, i.e. H 2 or O 2 . However, this proof-of-concept setup could lead to a significant performance drop linked to possible O 2 crossover to the complex 1-based anode. This was minimized via N 2 bubbling in the electrolyte. The distance between cathode and anode was set to 0.5 cm. Figure 8 displays the polarization and power curves recorded by scanning the cell voltage from open circuit voltage (OCV) down to 0.25 V at a scan rate of 0.5 mV s -1 using the anode sample characterized in Figure 7. The membrane-less fuel cell device based on the complex 1 as anode catalyst delivers a maximum power density of 31 μW cm -2 at 0.60 V and is characterized by an OCV of 0.9 V. Similar results were obtained for three other fuel cells devices with power output ranging from 10 to 31 μW cm -2 . For comparison, catalyst-free carbon black anode and Pt/Cbased GDE were also integrated as anodes in the same fuel cell setup, resulting in OCVs of 0.68 V and 1.06 V and power output of 6 ± 1 and 85 ± 6 μW cm -2 at 0.6 V cell voltage, respectively.

The four membrane-less fuel cell devices prepared with the complex 1 anode catalyst all display performances significantly better to those with only carbon black at the anode, as far as both OCV and power output is concerned. When compared to Pt/C-based GDE, the OCV observed for complex 1/GDE are very similar with a power output of around 30% of that of Pt/C GDE. This membrane-less fuel cell device is the first example using a mimic of the active site of

[FeFe]-hydrogenase as the anode catalyst. Although not as efficient as the Pt-free membrane-less H 2 /O 2 fuel cell reported by some of us based on an arginine derivative of the nickel bisdiphosphine catalysts that displays 150 µW.cm -2 at 0.2V, [START_REF] Gentil | A Nanotube-Supported Dicopper Complex Enhances Pt-free Molecular H2/Air Fuel Cells[END_REF] this new device already outperforms previously-designed zero-gap fuel cells integrating mimics of the active sites of

[NiFe]-hydrogenases delivering 11 µW cm -2 with an OCV of 0.3 V 12 and 25 µW cm -2 with an OCV of 0.42 V 64 and including noble metals as part of the catalysts' composition. The low power densities observed in these proof-of concept devices can however be improved by several orders of magnitude through optimization of the composition and structuration of the electrodes, as demonstrated for zero-gap Pt-free PEM fuel cells based on immobilized DuBois nickel bisdiphosphine catalysts with a 2 orders of magnitude improvement, [START_REF] Gentil | Carbon-Nanotube-Supported Bio-Inspired Nickel Catalyst and Its Integration in Hybrid Hydrogen/Air Fuel Cells[END_REF][START_REF] Tran | A noble metal-free proton-exchange membrane fuel cell based on bio-inspired molecular catalysts[END_REF][START_REF] Coutard | Impact of ionomer structuration on the performance of bio-inspired noble-metal-free fuel cell anodes[END_REF] or biofuels cells based on natural hydrogenases that were first reported with a 5µW.cm -2 power density [START_REF] Vincent | Electrocatalytic hydrogen oxidation by an enzyme at high carbon monoxide or oxygen levels[END_REF] and have now reached over 8 mA.cm -2 . 68,69

Conclusion

After two decades of biomimicry of the active site of [FeFe]-hydrogenase, a subtle modification of the bridging azadithiolate ligand allowed us to design the first diiron mimic with hydrogen oxidation activity, as a result of (i) a preferred conformation positioning the nitrogen lone pair toward the H 2 binding site and (ii) an increased basicity of the amine function due to hindered delocalization of the nitrogen lone-pair allowing for heterolytic H 2 cleavage. This is therefore the first diiron complex able to activate H 2 via a mechanism reminiscent of that followed by the enzyme. This system however uses oxidation states of the active site lower by one unit to activate both protons and H 2 . The lack of reversibility for bidirectional catalysis can be explained by the existence of a potential window at which an intermediate of both HER and HOR cycles predominates and the catalytic bias towards HER over HOR could be rationalized based on the kinetic barriers required to activate protons and H 2 , respectively. Structural variations, such as modifications of the iron ligand sets and modifications of the substituents in the ortho position of the aryl-ADT ligand could allow to tune the potentials of the redox processes and the kinetics for substrates binding, so as to obtain reversible bidirectional catalytic behavior or modify the catalytic bias. Noteworthy, this system showed quite high stability with ~200 turnovers under bulk conditions. It can therefore be considered as a novel blueprint for the preparation of costeffective HOR catalysts made of one of the most abundant transition metals and is a promising candidate to be integrated at the anode of hybrid biofuel cells. [START_REF] Gentil | Carbon-Nanotube-Supported Bio-Inspired Nickel Catalyst and Its Integration in Hybrid Hydrogen/Air Fuel Cells[END_REF] Experimental section.

Materials

Complex 1 was synthesized according to previously reported procedure. [START_REF] Ahmed | Oxygen-Tolerant H2 Production by [FeFe]-H2ase Active Site Mimics Aided by Second Sphere Proton Shuttle[END_REF] Syntheses of all the complexes were performed either under anaerobic atmosphere or in an Ar Glove Box from Mössbauer cryostat for liquid nitrogen connected with Lake Shore-325 temperature controller unit. Measurements were performed at 90K. Data acquisition was performed using a 512 channel analyzer. Isomer shifts were referenced versus -iron metal foil at the same temperature. The simulation of experimental data was performed using the Normos-A Mössbauer Fit programmes Site and Dist.

For fuel-cell measurements, commercial carbon black Vulcan VXC72 was obtained from Cabot and used as received. Gas diffusion layer (GDL) Sigracet 39-BC with hydrophobic treatment (5 wt % PTFE) and microporous layer was purchased from SGL Carbon GmbH (Germany).

Platinum gas diffusion electrodes with 0.5 mg Pt cm -2 (60% Pt on Vulcan carbon support) were purchased from FuelCellStore. Oxygen gas and hydrogen gas (Air Liquide ultrapure quality) were of 99.995% and 99.999% purity, respectively.

UV-Vis Spectroscopy

UV-Vis absorption data were recorded in an Agilent technologies spectrophotometer model 8453 fitted with a diode-array detector. During the experiments, anaerobic cuvettes (path length 1 cm) with rubber septum were used.

NMR Spectroscopy

All the NMR spectra were recorded on Bruker DPX-400 or DPX-500 spectrometers at room temperature.

FTIR Spectroscopy

FT-IR spectra of the complexes are recorded by a Perkin-Elmer Frontier FT-IR spectrometer in a CaF 2 window. ACN solution of the complex 1 (500 L; 2 mM) was prepared in a vial, and reduced by using fifty equivalents of cobaltocene inside the glove box, then 50 equivalents of malonic acid were added to it. The sample was injected in the anaerobic FTIR setup and tightly sealed. The cell was taken out from the box for data collection.

Time-resolved spectroscopy

Solutions of complex 1 (0.0015 mmol, 0. The wavenumber region 1000-4000 cm -1 was scanned every 50 ms with the resolution of 2 cm -1 .

Mössbauer Spectroscopy ACN solutions of the complex 1 (150 L; 40 mM) was prepared inside the glove box, and the Fe I Fe I state data was collected. Then the sample was reduced using fifty equivalents of cobaltocene and fifty equivalents of malonic acid was added to it inside a glove box. With this sample the data was collected for the intermediate. In each of the cases mentioned above, 150 L sample was taken in a custom-made Nylon capsule, froze with liquid N 2 inside the glove box, and immediately taken out, attached to the sample holder (immersed into liquid N 2 ) using a screw joint, and inserted into the cryostat maintained at 90K for data collection (Figure S1).

EPR Spectroscopy

The X-band EPR spectrum of 1H was recorded with a Bruker EMX X-band spectrometer operating at a field modulation of 100 kHz with a modulation amplitude of 10 G and microwave radiation power of 1.03 mW at 77 K.

Electrochemical Measurements

Cyclic Voltammetry: All electrochemical experiments were performed using a CH Instruments

Figure 3 .

 3 Figure 3. Electrochemical data for 1 in acetonitrile medium under homogeneous conditions. (a) Cyclic voltammetry of 1 in acetonitrile and Linear sweep voltammetry in the presence of different concentration of base; (inset) Peak current vs concentration of base plot. (b) Linear sweep voltammetry of 1 in acetonitrile at different H 2 concentrations in presence of 5 mM i-Pr 2 NEt (scan rate: 100 mV s -1 ). (inset) Peak current vs square root of partial pressure of H 2 plot (c) 1 H NMR of complex 1 in CD 3 CN after different time of bulk electrolysis; initial (black line), 40 min (yellow line), 90 min (red line), 140 min (blue line), 250 min (green line), and 420 min (purple line), in the presence of large excess (10 M) of i-Pr 2 NEt.

Figure 4 .

 4 Figure 4. Time-resolved FTIR spectra recorded after the rapid mixing of the complex 1, CoCp 2 and malonic acid. Times indicated in the legend are relative to the rapid mixing event.

Figure 5 .

 5 Figure 5. (a) FTIR data of complex 1 (navy trace) and chemically synthesized 1H (red trace) in acetonitrile medium. (b) DFT optimized FTIR data of complex 1 calculated in various redox and protonation states.

Figure 6 .

 6 Figure 6. Mössbauer spectra of (a) 1 and (b) 1H recorded at 90 K.

2 binding to 1 Scheme 1 .

 211 Scheme 1. Proposed mechanistic cycle(s) for HER and HOR catalyzed by heterogenized complex 1 in aqueous electrolyte, including a HER route via bridged hybride intermediate. Computed E 0 and Δ r G 0 values are indicated.[START_REF] Reiss | The absolute potential of the standard hydrogen electrode: a new estimate[END_REF]

Figure 8 .

 8 Figure 8. Polarization (filled marks) and power (empty marks) curves for Pt/C | aq. KPF 6 | complex 1/C (red marks) and Pt/C | aq. KPF 6 | C (no anode catalyst, grey marks) membrane-less fuel cell device; anode and cathode were fed with pure H 2 and O 2 (1 atm , 10 ml min 1 , 20°C) and the electrolyte was degassed 0.1 M KPF 6 adjusted to pH = 5.6.

  6 mL), CoCp 2 (Sigma Aldrich, 100 equivalents, 3 mL) and malonic acid (Sigma Aldrich, 25 equivalents, 3 mL) in acetonitrile were prepared under argon atmosphere inside Unilab (MBraun) glove box. Acetonitrile (UVASOL, Sigma Aldrich) was dried by refluxing in CaH 2 and degassed using freeze-pump-thaw technique. The three solutions were transferred from the glove box to the rapid mixing accessory in gas-tight transfer syringes. Malonic acid solution was mounted on the first drive syringe. Solutions of complex 1 and CoCp 2 were mounted on the second drive syringe and mixed by pushing the liquid from the drive to the transfer syringe and back three times. Stopped-flow experiments were initiated immediately after mixing of the solutions containing complex 1 and CoCp 2 . The experiments were conducted on SFA-20 rapid mixing accessory provided by TgK Scientific. The optical cell incorporated in the rapid mixing accessory consisted of two CaF 2 windows and had the optical path length of 0.5 mm. The nominal dead time of the stopped-flow setup was <8 ms. Rapid scan FTIR measurements were performed on a Bruker Vertex 70v spectrometer with a MCT detector.

(

  model CHI 710D Bi-potentiostat Electrochemical Analyzer). Reference electrodes, Teflon® plate material evaluating cell (ALS Japan) were purchased from CH Instruments. A Pt wire electrode was used as a counter electrode. The measurements were made against a leak proof Ag/AgCl aqueous reference electrode (satd. KCl). Anaerobic experiment was performed within a 5 neck S3 water jacket electrochemical cell brought from PINE Instruments or in a 4-neck custom made electrochemical cell by thoroughly degassing the whole set up with Ar gas.Preparation of modified Edge PlaneGraphite electrode: The edge plane graphite (EPG) electrodes were freshly polished and cleaned with polishing kit before each single experimental use. A 200 μL portion of a dilute solution (∼1 mM, in CHCl 3 ) was uniformly drop casted on cleaned EPG disc (3.5 mm diameter) fitted within a shaft. After CHCl 3 evaporation, the surface was washed with CHCl 3 thoroughly and then ethanol to remove any loosely bound catalyst on the surface and washed with triple distilled water. Aqueous electrochemical measurements: All the electrochemical experiments were performed using a CH Instruments (model CHI 710D Electrochemical Analyzer). Reference electrodes, Pt counter electrodes were purchased from CH Instruments. The rotating ring disk electrochemical (RRDE) set up from Pine Research Instrumentation (E6 series Change Disk tips with AFE6M rotor) was used to obtain the RDE and LSV data on modified EPGs. A Pt wire was used as a counter electrode. The measurements were made against an Ag/AgCl aqueous leak proof reference electrode (satd. KCl). Anaerobic CV experiment was performed within a 5 neck S3 water jacket electrochemical cell brought from PINE Instruments by thoroughly degassing the whole set up with Ar gas. The cyclic and rotating disk electrode voltammograms were recorded in 0.1 M KPF 6 water solution with all of the complexes adsorbed onto the EPG disc held within a shaft (Pine Instruments, AFE6MB). Non-aqueous electrochemical measurements: Electrochemical measurements were carried out in MeCN solution (Merck, HPLC gradient grade 99.99%), 0.1 M Bu 4 NClO 4 (Sigma-Aldrich, for electrochemical analysis ≥99%, used as received), under argon (cyclic voltammetry, CV) or nitrogen (controlled potential electrolysis, CPE) atmosphere at 20-25 °C using a CH Instruments (model CHI 710D Electrochemical Analyzer). For CV experiments, a 4-neck custom made electrochemical cell was used. Potentials were referred to an Ag/AgCl (satd. KCl) reference electrode in MeCN + 0.1 M Bu 4 NClO 4 and measured potentials were calibrated through the use of an internal Fc/Fc + standard. A glassy carbon electrode (CV, LSV) and a glassy carbon plate electrode (CPE) were used as a working electrode. The auxiliary electrode was a Pt wire in MeCN + 0.1 M Bu 4 NClO 4 solution. Bulk electrolyses and coulometry were carried out in a 4neck custom made electrochemical cell using a glassy carbon plate electrode. The reference electrode was externally calibrated vs Fc + /Fc. The electrochemistry was performed after saturating the acetonitrile solution with H 2 gas (45 mins purging).H 2 concentration dependence using mass flow meter:The H 2 concentration dependence experiments in aqueous medium (heterogeneous conditions) were done using Mani-Flow (BRONKHORST) gas flow meter, which was connected with a digital Power Supply Flow Indicator Controller (PSFIC) (EUTECH SYSTEMS). Using PSFIC one can control the mass flow rate of the gas. In this experiment we used two different digital gas flow meters with full setup (One for H 2 gas control and another for Argon gas control). The outlet from these two flow meters were put into a closed vessel through a rubber septum, in which two gases are mixed and form a homogeneous gas mixture. Another outlet of this closed vessel was connected to the electrochemical cell. During the H 2 concentration dependence experiment different types of H 2 /Ar gas mixture were used. During the experiments, each time the gas mixture was purged for 45 mins into the solution and then the data was recorded. During homogeneous study, the H 2 partial pressure dependence experiments were done by using CVG Technocrafts India mass flow meter purchased from Chemix. Mass flow rate of the gases were controlled manually during the experiments using regulator. Instead of digital flow meter the other procedures were same as heterogeneous study.

Table 1 . CO Stretching frequencies

 1

		Experimental IR	Previously reported IR
		stretching frequencies of complex 1 (cm -1 )	stretching frequencies of an adt complex. 43
	1	1998,2038,2076	1994, 2034, 2075
	1H	1885,

Table 2 . Experimental Mössbauer data recorded at 90 K Mössbauer parameters Complex 1 Complex 1H δ iso (mm s -1 )

 2

  IR data are measured on the Perkin-Elmer FTIR Frontier instrument. The CaF 2 windows for FTIR spectroscopy were purchased from Sigma Aldrich. The anaerobic setup for FTIR spectroscopy was purchased from PerkinElmer. All the NMR spectra were recorded on Bruker DPX-400 or DPX-500 spectrometers at room temperature. The mass spectra are recorded on an

	MBRAUN. Complex 1 was synthesized using standard Schlenk techniques. 2-Ethylaniline and the solvents were used fresh after distillation, purchased from Merck. Thionyl chloride (SOCl 2 ) was purchased from Spectrochem Pvt. Ltd. (India). p-formaldehyde, superhydride (Li[HBEt 3 ], 1 M in THF), N,N-diisopropylethylamine, malonic acid and bis(cyclopentadienyl)cobalt(II) were purchased from Sigma-Aldrich chemicals Pvt. Ltd., and anhydrous Na 2 SO 4 was purchased from Merck Specialities, Pvt. Ltd. (India). During electrochemistry the solvent (acetonitrile) was used after distillation with proper drying agent. Silica (60-120 mesh), for column chromatography, was purchased from SISCO Pvt. Ltd. (India). Edge Plane Graphite (EPG) discs were purchased from Pine Instruments. Glassy carbon plate (1 mm thick, type1) was purchased from Alfa Aesar. technologies spectrophotometer model 8453 fitted with a diode-array detector. Mössbauer spectra were recorded in an alternating constant WissEl Mössbauer spectrometer, which consists of an MR 360 drive unit, an MVT 1000 velocity transducer, and an LND-45431 proportional counter mounted on an MB-600 Mössbauer bench with cryostat stand. The system was operated in a horizontal transmission geometry with source ( 57 Co in Rh-matrix), absorber and detector in a The FT-QTOF Micro YA263 instrument. UV-Vis absorption data were recorded in an Agilent linear arrangement. The temperature was controlled and maintained using MBBC-N20106

Acknowledgments

This work was supported by the Indo-French Center for the Promotion of Advanced Research (IFCPAR/CEFIPRA grant n° 5405-1), the French National Research Agency (Labex program, ARCANE, Graduate school of Chemistry, Biology and Health of Univ. Grenoble Alpes, CBH-EUR-GS, ANR-17-EURE-0003) and Department of Science and Technology, India, Grant DST/TMD/HFC/2K18/90. M.E.A. and A. N. acknowledgesCSIR (SRF) and DST-Inspire for the fellowship, respectively.

Bulk electrolysis and NMR spectroscopy:

The BE experiment was done in a custom made 4 neck electrochemical cell with glassy carbon (2×2.25 cm 2 ) working electrode. After saturating the acetonitrile-d 3 solution (containing 0.5 mM complex 1 and 10 M diisopropylethylamine) with H 2 gas the BE experiment was performed. After different time interval of BE, 450 L solution was syringe out anaerobically from the electrochemical cell and took into an NMR tube; after performing 1 H NMR, the solution was put back into the electrochemical cell anaerobically and then again performed the BE experiment. During the experiments occasionally H 2 gas was purging (after 90 mins and 240 mins). The amount of ammonium produced was quantified from the integration values of the new peak which is generating and increasing with time at 7.59 ppm.

We consider the integration of the CH 2  peak at 3.78 ppm is 1.

The faradic yield (FY) was determined by the equation (iv) and reported in Table S1.

Membrane-less fuel cell measurements Preparation and characterization of the electrodes

Catalyst ink was prepared using the following formulation: 100 µl of a 2 mg ml -1 dispersion of Vulcan VXC72 in CH 2 Cl 2 were mixed with 50 µl of a solution of 1 in CH 2 Cl 2 (4 mM). This formulation corresponds to a Vulcan VXC72-to-Fe2 mass ratio of 2:1. Then, an aliquot of 50 µl of the catalyst ink was deposited on the microporous layer of a 1.13 cm 2 GDL to reach a loading of 30 µg cm -2 of 1 (0.06 µmol cm -2 or 60 nmol cm -2 ). The working gas diffusion electrodes (GDEs) with the deposited catalyst layer was used in a three-electrode cell configuration described elsewhere [START_REF] Goff | From Hydrogenases to Noble Metal-Free Catalytic Nanomaterials for H2 Production and Uptake[END_REF] and in the membrane-less fuel cell configuration (Figure S10). The blank working electrodes used in the experimental setups consisted of GDEs with 0.09 mg Vulcan cm -2 .

Membrane-less fuel cell setup

The membrane-less fuel cell experimental setup is show in Figure S10 and consists of two halfcell holders with the GDEs placed face-to-face in a special glass cell filled with degassed electrolyte. The cathode is a commercial GDE with 0.5 mg Pt •cm -2 . Polarization curves were recorded by scanning the cell voltage from open circuit voltage (OCV) down to 0.25 V at a scan rate of 0.5 mV s -1 and 25°C, under a back-flow of H 2 (1 atm, 10 ml min 1 ) at the anode and a back-flow of O 2 (1 atm, 10 ml min 1 ) at the cathode.

Computational Details

The geometries were optimized in Gaussian 16 software [START_REF] Mj | Gaussian 03, C.02[END_REF] using the B3LYP functional, [START_REF] Perdew | Density-functional approximation for the correlation energy of the inhomogeneous electron gas[END_REF][START_REF] Becke | Density-functional exchange-energy approximation with correct asymptotic behavior[END_REF] 6-311g* basis set and PCM-dispersion model. Frequency calculations were performed to ensure the presence of a minimum. The single point calculations were calculated using the same functional but a 6-311+g* basis set and 10 -10 convergence criteria. Reduction potentials were calculated vs Fc/Fc + and 271 kCal/mol for proton. 70

Associated Content

Supporting Information

Detailed experimental conditions, preparation and characterization of electrodes, fuel cell experimental setup and other addition information are available free of charge in the online version of the paper. Correspondence and requests for materials should be addressed to V.A. and A.D.

Notes

The authors declare no competing financial interests.


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