Dr Amanda Lyn Robinson

Eva Bannermann

Dr Régis Guillot

Christian Herrerro

Katell Sénéchal-David

Pr Eric Rivière

Frédéric Banse
email: frederic.banse@universite-paris-saclay.fr

Jean-Noël Rebilly
email: jean-noël.rebilly@universite-paris-saclay.fr

Dr Eva Bannerman

Dr Christian Herrero

Jean-Noël Rebilly

Dr J-N Rebilly

Significant effect of 2nd sphere interactions on the reductive activation of O2 by non-heme iron(II) complexes. Application to the electroassisted oxidation of thioanisole

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

Introduction

Redox iron metalloenzymes activate O 2 to achieve the selective oxidation of a variety of molecules in very mild conditions. [START_REF] Bertini | Handbook of metalloproteins[END_REF][START_REF] Meunier | [END_REF][3][4][5][6] For this purpose, several crucial patterns are ubiquitous in both heme and non-heme systems. The first is the so-called reductive O 2 activation process. [4] Due to its triplet spin state, dioxygen cannot react spontaneously with singlet organic substrates. To trigger its reactivity, enzymes formally reduce it with two electrons to generate a species capable of carrying out the 2-electron oxidation of the substrate. The electron input is achieved by redox cofactors, either bound to the metal (for instance -ketoglutarate in non-heme -KG-dependent enzymes) [5,[7][8] or distant from it, like NADPH, a source of two electrons which are sequentially transferred to the metal active site thanks to a reductase. [2-3, 5, 9] The control of the sequential electron input is crucial in cytochromes P450 in order to achieve the formation of the reactive species and avoid its overreduction. In the catalytic cycle, [START_REF] Meunier | [END_REF] (P)Fe III is reduced to (P)Fe II by the first electron, which can then bind O 2 to form the superoxo species (P)Fe III -OO•. The second electron reduces it to Fe III -peroxo (P)Fe III -OO -, which is then protonated to form Fe III -hydroperoxo (P)Fe III -OOH. Another protonation of the distal O atom of hydroperoxo induces the heterolytic O-O bond cleavage to form the active species, compound I, (P •+ )Fe IV =O. The key aspect of O 2 activation is thus the injection of an electron in an Fe II /O 2 adduct. This strategy was used with model systems by injecting electrons via an electrode. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] Recently, we studied the activation mechanism of O 2 by the complex [(TPEN)Fe II ](PF 6 ) 2 . [25][26] It was characterized in cyclic voltammetry by the presence of a "prewave", assigned to the reduction of the Fe II /O 2 adduct, occurring before the reduction of free O 2 (e.g. at a more positive potential), making the O 2 reduction process less energetic. However, this potential gain remained limited. Exploiting the push strategy of cytochrome P450 (i.e. increasing the donating character of the 1 st coordination sphere to favor the Fe II to O 2 electron transfer and formation of the superoxo species), we achieved the reductive activation of O 2 by the complex [(L 2 )Fe III (OTf)], L 2 being a dianionic ligand, at a potential 500 mV higher than with [(TPEN)Fe II ](PF 6 ) 2 . [27] Cytochromes P450 also use pull effects in order to favor O 2 activation: 2 nd sphere cationic, acidic, and hydrogen bonding residues form an hydrogen bonding network between the distal O atom in the (P)Fe III -OO• and the bulk. [START_REF] Meunier | [END_REF] They stabilize the negative charge forming at the distal O atom of the nascent (P)Fe III -OO -, and thus favor the reduction of its precursor (P)Fe III -OO•. With this strategy in mind, we herein report a new ligand L 5 2(OH) derived from the classic pentadentate aminopyridine ligand L 5 [START_REF] Meunier | [END_REF] by appending an OH hydrogen-bond donor on the ortho position of one of the pyridines. Unexpectedly, L 5 2(OH) shows two types of binding modes with different 2 nd sphere hydrogen bonding patterns, which can be selectively obtained by a judicious choice of the metal salt. Addition of the 2 nd sphere group generates a 90-mV gain in the O 2 activation potential when it is structurally oriented to be able to develop a H-bond with the proximal O in the Fe/O 2 adduct and an even larger gain of 250 mV when the H-bond donor is oriented is such a way that it cannot. We propose a putative interaction with the distal O atom (intra-or intermolecularly, to rationalize this observation. This suggests that a controlled pull effect can significantly reduce the energetic cost of the O 2 activation process.

Results and Discussion

Ligand synthesis L 5 2(OMe) was synthesized from 6-methoxy-2pyridinecarboxaldehyde and N,N'bis(2pyridylmethyl)ethylenediamine following a procedure reported for ligand L 5 2 . [28][29][30] Demethylation of L 5 2(OMe) was achieved using a nucleophile (Cl -) in acidic medium (Scheme 1) to yield L 5 2(OH) bearing a 2-pyridone group (Supporting Information, Synthetic procedures and Figures S1-S8). [31] N OH) . Another common feature is the binding mode of the 2-pyridone group of L5 2(OH) . The iron center is bound through the nitrogen, which loses its hydrogen and transfers it to the neighboring oxygen atom. Thus, the 2-pyridone is bound to the metal in its tautomer form, 2-hydroxypyridine. This coordination-induced equilibrium displacement between 2-pyridone and 2hydroxypyridine was already reported by Szymczak with TPAtypes ligands. [32][33] However, depending on the complex, two binding modes of these pentadentate ligands can be distinguished.

Synthesis and characterization of complexes

In [L5 2(OH) FeCl](PF6) the two pyridyl groups sitting in trans positions are linked to two different amines of the ethylene diamine bridge (Figure 1 a/) and lie in nearly perpendicular planes. As a result of this arrangement, one of the pyridyl groups sits in the equatorial plane of the complex (with respect to the Fe-Cl axis), while the other two sit in planes that nearly contain the Fe-Cl axis (scheme 2a). This binding mode will be referred to as the "classical mode" as it is, to the best of our knowledge, the only one reported in the CDCC for Fe(II) complexes of pentadentate ligand L 5 2 and its derivatives bearing the same coordinating pentadentate amino-pyridine backbone with pyridines unfunctionalized on the ortho position. [30,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] Conversely, in [L5 2(OH) Fe(OTf)](OTf) (2) (Figure 1 b/), the two pyridyls in trans positions are connected to the same amine group of the ethylene diamine bridge. These two groups lie in the equatorial plane (with respect to the Fe-X axis, X = OTf -) while the third pyridine lies in the plane that nearly contains the Fe-OTf axis (Scheme 2b). This binding mode will be referred to as the "alternative mode", as, to the best of our knowledge, it is the first time such a wrapping is reported in an Fe II complex of L 5 2 ligand derivatives. The Fe-N bond lengths sit in the range 2.20-2.25 Å for the complex [L5 2(OH) FeCl](PF6) (1) displaying the classical binding mode, and in the range 2.15-2.25 Å for the complexe [L5 2(OH) Fe(OTf)](OTf) (2) displaying the alternative binding mode. This suggests a high spin state (S = 2) in all cases, as bond distances are expected to be close to 2 Å for a low spin state (S = 0). [34,51] This result is in line with a (N 5 )Fe II (X), where X is an anionic, -donating, exogenous ligand. Finally, L 5 2(OH) complexes display specific hydrogen bonds in the crystal, thanks to the OH group of 2-hydroxypyridine, which acts as a H-bond donor. In the structure of [L5 2(OH) FeCl](PF6) (1), 2hydroxypyridine sits in the axial plane  ax2 (Figure 1a, Scheme 2a, classical mode) and is preorganized to hydrogen-bond to the chloro ligand occupying the axial site (d Cl…H = 2.208 Å). This pattern can only occur in complexes displaying the classical mode (Scheme 2a). Such a pattern was already observed with other ligands bearing 2-hydroxypyridine, [32][33] 2-(alkylamino)pyridine [52- 54] or 2-(acylamino)pyridine [42] groups. In [L5 2(OH) Fe(OTf)](OTf) (2), displaying the alternative mode, 2hydroxypyridine sits in the equatorial plane  eq (Scheme 2b, alternative mode) and cannot generate hydrogen bonding with the bound O atom of triflate. Instead, the OH group projects outward and is hydrogen-bonded to the unbound triflate in the unit cell (d TfO…H = 1.642 Å). Comparison of the structure of [L5 2(OH) FeCl](PF6) (1) and parent complex deprived of hydroxy group [L5 [START_REF] Meunier | [END_REF] FeCl](BPh4) [34] shows a similar coordination sphere. However, the Fe-N bond length between the iron and the bound 2-hydroxypyridine in (1) is increased with respect to [L5 [START_REF] Meunier | [END_REF] FeCl](BPh4) (2.235 Å instead of 2.171 Å) due to the increased bulk, while the Cl-Fe-N angle involving 2-hydroxypyridine in (1) is decreased from 106.79° to 101.40° with respect to [L5 [START_REF] Meunier | [END_REF] FeCl](BPh4), in line with the optimization of hydrogen bonding.

Solution characterization

In the following electrochemistry discussion, the coordination sphere of the species will be described using (N 5 c ) for the classical pentadentate binding mode and (N 5 a ) for the alternative one, and (N 4 ) for the tetradentate binding mode (decoordination of one pyridine). The cyclovoltammogram (CV) of [L5 2(OH) FeCl](PF6) (1) in MeCN shows a predominant quasi reversible wave at E 1/2 = 0.7 V (E = 120 mV, Figure S11), assigned to a complex in which L5 2(OH) binds in a pentadentate fashion, and completes its coordination sphere with an anionic exogenous ligand, by analogy with parent complexes. [30] On the reverse scan (reduction), three waves are detected suggesting equilibria with the solvent at the Fe III state:

E p c = 0.92 V ([(N 5 c )Fe III (MeCN)] 3+ species), E p c = 0.64 V ([(N 5 c
)Fe III Cl] 2+ species) and E p c = 0.34 V ([(N 4 )Fe III Cl 2 ] + species. [30] At more negative potentials, a reduction wave at E p c = -1.81 V is tentatively ascribed to the reduction of a pyridine bound to Fe II , by analogy with the Zn II titration of the ligand where a similar wave is observed at E p c = -1.73 V (Figure S9). In the [L5 2 Fe(MeCN)](PF6)2 complex, [50] a similar reduction wave is observed at -1.70 V (Figure S9c). The UV-vis absorption spectrum of [L5 2(OH) FeCl](PF6) (1) in MeCN displays MLCT absorption bands at = 372 nm (= 1920 M -1 .cm -1 ) (Figure S12). The low values of the extinction coefficients are in line with a high spin state, confirmed by Evans NMR (84% HS at 300 K in CD 3 CN, Figure S13). A high spin state is consistent with a (N 5 )Fe II Cl formulation. Thus, the structure of S15) shows an oxidation wave at E p a = 1.03 V of a poorly reversible couple, ascribed to [(N 5 a )Fe II (MeCN)] 2+ . On the reverse scan, the reduction of the corresponding species is found at E p c = 0.89 V (E 1/2 = 0.96 V, E = 140 mV), along with another wave at E p c = 0.49 V. By analogy with parent complexes, these reduction potentials are ascribed to species [(N 5 a )Fe III (MeCN)] 3+ , and [(N 5 a )Fe III (OH)] 2+ respectively (Table S1). As expected, the labile triflato ligand is substituted by MeCN. The UV-vis spectrum in MeCN of the crystals of S17) displays MLCT absorption bands at = 362 nm (= 1510 M -1 .cm -1 ). NMR characterization by the Evans method indicates the complex is predominantly HS (76%) in CD 3 CN at 300 K (Figure S18). At this point, the reason for the appearance of this unusual alternative coordination mode of a L 5 2 -type ligand in [L5 2(OH) Fe(OTf)](OTf) (2) was puzzling. A first hypothesis was that the bulkiness of the bound anion might direct the binding mode of the ligand: with the larger triflato (vs chloro), the classical binding mode could be sterically disfavored. However, Que et al. reported the structure of [(BnTPEN)Fe II (OTf)](OTf), with a L 5 2 -type ligand bearing a benzyl pendant group instead of methyl and the complex displayed the classical binding mode. [35] It thus appears that this alternative wrapping likely results from the simultaneous presence of the OH group in the ortho position of pyridine and a bound triflate (vide infra). To confirm this hypothesis, we synthesized the complex [L5 2(OMe) Fe(OTf)](OTf) (3).

[L5 2(OH) FeCl](PF6) (1) is retained in solution. The CV of crystaIs of [L5 2(OH) Fe(OTf)](OTf) (2) (Figure
[L5 2(OH) Fe(OTf)](OTf) (2) (Figure

[L 5 2(OMe) Fe(OTf)](OTf) (3)

[L5 2(OMe) Fe(OTf)](OTf) (3) was synthesized by reaction of Fe II (OTf) 2 with the ligand L5 2(OMe) in MeOH, followed by precipitation by addition of diethyl ether.

Solid state characterization

Single crystals of [L5 2(OMe) Fe(OTf)](OTf) (3) were obtained by diffusion of diethyl ether in a methanolic solution of the complex. The X-ray structure of [L5 2(OMe) Fe(OTf)](OTf) (3) is displayed in Figure 2. The L5 2(OMe) ligand is bound in the alternative binding mode (Scheme 2), as observed in the structure of 1). The OMe group of the methoxypyridine lies in the equatorial plane. A bound triflate in [L5 2(OMe) Fe(OTf)](OTf) (3) completes the coordination sphere. The Fe-N bond lengths sit in the range 2.15-2.23 Å in line with a high spin complex. [34,51]

[L5 2(OH) Fe II (OTf)](OTf) (2) (Figure

Solution characterization

The CV of crystaIs of [L5 2(OMe) Fe(OTf)](OTf) (Figure S20) shows a quasi-reversible oxidation wave at E 1/2 = 0.98 V (E = 130 mV), ascribed to the [(N 5 a )Fe III/II (MeCN)] 3+/2+ couple. On the reverse scan, a minor reduction wave is observed at E p c = 0.52 V. By analogy with parent complexes, this reduction potential is ascribed to the reduction of a [(N 5 a )Fe III (X)] 2+ species, X being an anion (triflate or hydroxide). The structure of [L5 2(OMe) Fe(OTf)] + is not maintained in solution and the triflato ligand is, as expected, exchanged for MeCN. The UV-vis spectrum in MeCN of the crystals of [L5 2(OMe) Fe(OTf)](OTf) (3) (Figure S21) is very similar to the one of [L5 2(OH) Fe(OTf)](OTf) (2) (see above Figure S17) : the complex displays a MLCT absorption band at = 364 nm (= 1600 M -1 .cm -1 ) in MeCN. NMR characterization by the Evans method indicates the complex is predominantly HS (91%) in CD 3 CN at 300 K (Figure S22). [L5 2(OH) Fe(OTf)](OTf) and [L5 2(OMe) Fe(OTf)](OTf) also display very similar NMR spectra (Figure S23) supporting the fact they display the same binding mode. L5 2(OMe) were to bind Fe II in the classical binding mode, the 2hydroxypyridine or 2-methoxypyridine would be forced to lie in one of the axial planes  ax1 or  ax2 (Scheme 2). In the case of L5 2(OMe) , the methyl group of the methoxy would project outwards for steric reasons, thus forcing the lone pairs of oxygen to be oriented towards the binding site of triflate. A repulsive electrostatic interaction would then develop between them and the lone pairs of the binding O atom of triflate (Scheme 3). In the case of L5 2(OH) , a hydrogen bond between the OH group of 2hydroxypyridine (H-bond donor) and the bound O atom of triflate would be expected to form by analogy with the structure of [L5 2(OH) FeCl](PF6) (1). The lone pairs of the O atom of 2hydroxypyridine would thus be oriented outwards but repulsive electrostatic interactions would develop between them and the lone pairs of the F atoms of triflate, given the orientation imposed to the bound counterion by the hydrogen bond (Scheme 3). Conversely, in the alternative mode, where the functionalized pyridine lies in the equatorial plane (Schemes 2 and 3), the repulsive interactions vanish. With the less bulky chloride in [L5 2(OH) FeCl](PF6) (1), no repulsive interaction is present and the classical binding mode remains the favored one. It is even further stabilized by hydrogen bonding. Drastic effects of such unfavorable interactions are not unprecedented in coordination chemistry. Izzet et al reported the comparative binding properties of Cu II complexes of tripodal ligands grafted onto a calix [6]arene cavity via ether bridges. Depending on the cap, the orientation of the lone pairs of the O atoms of the ether bridges could be controlled and oriented either outwards or towards the binding site within the cavity. In the former case, the complex was able to bind a variety of anions whereas in the latter case, anion binding was completely discarded. [55] By the choice of the starting iron salt (chloride or triflate), it is thus possible to selectively obtain complexes in the classical or alternative binding mode of L5 2(OH) . Each mode displays a different H-bonding pattern with the ligand on the 6 th coordination site. Our aim being to study the impact of such hydrogen bonds on the performance of O 2 reductive activation, we needed an easily exchangeable ligand at the 6 th site of iron. Triflate fulfills this requirement and [L5 2(OH) Fe II (OTf)](OTf) (2) is a good candidate to study the alternative binding mode. However, for the classical binding mode, [L5 2(OH) FeCl](PF6) (1) is not, as chloride is a strong competitor of O 2 for coordination. Attempts to remove chloride using silver nitrate and isolate the resulting complex were unsuccessful. We thus tried to isolate a complex starting from the Fe(H 2 O) 6 .(BF 4 ) 2 salt, as the counterions are not coordinating and the remaining ligand, H 2 O, is perfectly suited to fit in the classical binding mode and to develop a hydrogen bond with the ortho OH group without repulsive interactions.

[(L 5 2(OH) )Fe(OH)]BPh 4 (4)

[(L5 2(OH) )Fe(OH)]BPh4 (4) was obtained by the addition of NaBPh 4 to a methanol solution containing equimolar amounts of L5 2(OH) and [Fe(H2O)6](BF4)2. Single crystal suitable for X-ray diffraction were obtained in the methanol filtrate. Ligand L5 2(OH) acts as pentadentate ligands wrapping around the pseudo-octahedral iron center and leaving a 6 th position available for an hydroxo ligand (Figure 3). L5 2(OH) is bound in the classical binding mode, and the first coordination sphere is similar to that of iron in [L5 2(OH) FeCl](PF6) by replacing Cl -by OH -. However, while 2-hydroxypyridine sits in the  ax2 plane in [L5 2(OH) FeCl](PF6), it lies in the  ax1 plane in the case of [(L5 2(OH) )Fe(OH)]BPh4 (4). The Fe-N bond lengths are in the range of 2.20-2.25 Å suggesting a high spin state. [34,51] Fe-OH bond length is 1.955 Å, and the length of the intramolecular H-bond between the 2hydroxypyridine and the O atom of the bound hydroxo ligand is 1.668 Å. Due to the reduced bulkiness of OH -vs Cl -, the N (py-OH) -Fe-X angle (X = Cl or OH) is reduced from 101.4° (Cl -) to 87.6° (OH -). Interestingly, an intermolecular H-bond also develops in the unit cell with an external methanol molecule and the bound hydroxo ligand (d(H MeOH -O OH ) = 1.902 Å).

Solid state characterization

Solution characterization

The CV of [(L5 2(OH) )Fe(OH)]BPh4 (Figure S25) displays a major reversible couple at E 1/2 = 0.58 V (E = 80 mV) and a much weaker one at E 1/2 = 0.95 V (E = 80 mV) ascribed to [(N 5 a )Fe II (OH)] + and ([(N 5 a )Fe II (MeCN)] 2+ species respectively. An additional irreversible wave is observed in oxidation at E p a = 0.82 V, ascribed to the oxidation of BPh 4 -. The CV is in line with the structure, with a predominant [(N 5 a )Fe II (OH)] + form. The UV-vis spectrum in MeCN (Figure S26) displays an MLCT absorption band at = 389 nm (= 1600 M -1 .cm -1 ). The spectrum is close to the one of the chloro analogue [(L5 2(OH) )FeCl]PF6  = 372 nm, = 1920 M -1 .cm -1 ) in MeCN).

As the BPh 4 -counterion is electroactive and might interfere in the O 2 activation process, [56][57] we carried out the synthesis of its BArF analogue.

[(L 5 2(O-) )Fe] 2 (BArF) 2 (5)

[(L5 2(O-) )Fe]2(BArF)2 (5) was obtained by reacting equimolar amounts of L5 2(OH) and [Fe(H2O)6](BF4)2 in the presence of a base (NaOMe, 1 equiv.) in MeOH. Addition of KBArF did not induce precipitation of the compound. The product was isolated by addition of water to the methanol solution, which induced its precipitation. Single crystals suitable for X-ray diffraction were obtained by diffusion of pentane into a CH 2 Cl 2 solution of the complex.

Solid state characterization

The BArF analogue of [(L5 2(OH) )Fe(OH)](BArF) does not crystallize as a mononuclear species, but as a dinuclear one formulated as [(L5 2(O-) )Fe]2(BArF)2 (5) (Figure 4). The ligand is present in the dimer in its deprotonated form L5 2(O-) . It binds each of the Fe II centers in a pentadentate fashion analogous to L5 2(OH) in the classical binding mode. More specifically, the binding mode is the same as L5 2(OH) in [L5 2(OH) FeCl](PF6), with the functionalized pyridine sitting in the axial plane  ax2 (Scheme 2a). The 6 th binding site is occupied by the O atom of the L5 2(O-) ligand of the other Fe center. The two complexes are thus arranged in a head-to-tail fashion and the O-pyridyl groups are thus bridging the two iron centers. The Fe-N bond lengths (N amine and N py ) sit in the range 2.19-2.31 Å. The Fe-N (py-O-) bonds are slightly shorter (2.13-2.15 Å), in line with a more donating character of the (py-O -) group, and the Fe-O bond lengths are in the range 1.97-1.98 Å. This suggests a high spin state locally for each Fe center. [34,51] Magnetic studies of [(L5 2(O-) )Fe]2(BArF)2 (5) (Figure S28) show that the dimer consists of two high spin Fe II complexes that are antiferromagnetically coupled with a very weak constant (J = -1 cm -1 ).

Solution characterization

The CV of [(L5 2(O-) )Fe]2(BArF)2 (Figure S29) displays three quasireversible oxidation waves in the Fe III/II region at E 1/2 = 0.35 V (E = 90 mV), E 1/2 = 0.65 V (E = 140 mV) , E 1/2 = 0.97 V (E = 170 mV), assigned to a [(N 4 )Fe III/II (X) 2 ] +/0 , a [(N 5 )Fe III/II (X)] 2+/+ and a [(N 5 )Fe III/II (MeCN)] 3+/2+ species (X = monoanion, likely OH -). The potential of the 0.65 V wave could also correspond to the Fe III Fe III /Fe III Fe II wave of the dimer itself. Upon addition of HClO 4 (up to 1 equiv. vs Fe), the first two Fe III/II waves vanish in favor of the 3 rd one, in line with acid-base related species (Figure S30,S31). It can be concluded that the dimer is present in various forms in equilibrium in solution (Scheme 4). This equilibrium can be displaced towards a quasi-single species [(L5 2(OH) )Fe(MeCN)] 2+ upon addition of 1 equiv. HClO 4 (vs Fe). Comparison with the CV of [(L5 2(OH) )Fe(OTf)](OTf) (Figure S31, Table S1) shows that the Fe III/II couples are similar but not exactly the same, especially on the reverse scan upon [(N 5 )Fe III (X)] 2+ reduction. The difference is ascribed to different binding modes of L5 2(OH) . The addition of HClO 4 can also be followed by [START_REF] Bertini | Handbook of metalloproteins[END_REF] H NMR (Figure S32). The complexes before and after addition remains mostly paramagnetic (Figure S33). The spectrum of the final complex displays peaks that are similar to those found in

Electrochemical studies of the reductive activation of dioxygen

2 nd sphere interactions are crucial to control the activation of dioxygen in natural systems. In cytochrome P450, cationic residues and H-bond donors form an uninterrupted hydrogen bond network between the bulk (water medium) and the distal O atom in the Fe/O 2 adduct. This makes the reduction of Fe III -OO• to Fe III -OO -easier, as it stabilizes the nascent negative charge, subsequently protonating the distal O to form Fe III -OOH. [START_REF] Meunier | [END_REF] As evidenced by the structures reported above, the L5 2(OH) ligand in the classical binding mode would be constrained to generate a hydrogen bond with the proximal O atom of a Fe/O 2 adduct, while in the alternative binding mode, it could not. In order to evaluate more quantitatively the impact of this 2 nd sphere hydrogen bond donor (OH) on the O 2 activation process in both binding modes of

Impact of the binding mode of the ligand.

As control experiments, we first recorded the CVs under air of complexes deprived of hydrogen bond donor, bound in the alternative binding mode. Both display very similar CVs under air (Figure 5) that are very close to that reported for complex [(TPEN)Fe)(PF6)2. In the [(TPEN)Fe)(PF6)2 case, the O 2 activation mechanism was studied in detail by a combination of spectroscopy of reaction intermediates and simulation of CVs. [25] The wave observed at -1 V vs SCE corresponds to the reduction of free O 2 to superoxide (Figure 5b). In the presence of an Fe II complex, another wave appears at a slightly higher potential (-0.76 V for [(L5 2 )Fe II (MeCN)](PF6)2, -0.72 V for [(L5 2(OMe) )Fe(OTf)](OTf)). It corresponds to the reduction of the Fe II /O 2 adduct (to Fe III -OO -in a 1 st step) and thus to the potential of the reductive activation of O 2 at the iron center. The mechanism at work at the prewave has been previously described as the square scheme represented in scheme 5. [25] Scheme 5. Square scheme representing the reductive O2 activation process, involving two pathways, an EC one (electrochemical-chemical) and a CE one

[( L5
(chemical-electrochemical).
Thus, the value of the prewave potential quantifies the efficiency of the complex in this process. This preliminary result shows that (i) both complexes are not very efficient O 2 activators as they display a prewave that remains very close to that of the reduction of free O 2 , (ii) the binding mode of L 5 2 -type ligands does not make a significant difference in the activation potential, and (iii) improvement of this activation potential can be expected from ligand tuning.

Impact of the hydrogen bond donor in the classical binding mode

To evaluate the impact of the hydrogen bond donor in the classical binding mode, the [(N 5 c )Fe II (MeCN)] 2+ species has to be generated in solution by reaction of the dimeric Under air, the addition of acid slightly shifts the first prewave from -0.74 V to -0.81 V and induces the appearance of a 2 nd one at -0.65 V. Both prewaves grow in intensity during the HClO 4 titration (Figure 6 and S35). The two species present in solution,

[(L5 2(OH) )Fe(MeCN)] 2+ and [(L5 2(OH) )Fe(OH)] + , can thus be considered as responsible for the two observed prewaves. When an anion is bound to Fe, as in [L5 2(OH) FeCl](PF6), a prewave is observed at -0.74 V (Figure S36). By analogy, the -0.81 V wave can thus be ascribed to the O 2 activation by a complex with a bound anion, i.e. [(L5 2(OH) )Fe(OH)] + species, and consequently, the new wave at -0.65 V is likely due to the O 2 activation by [(L5 2(OH) )Fe(MeCN)] 2+ in the classical binding mode. The intensity increases of the overall CV in reduction (Figure S35) is ascribed to the presence of protons in the reaction medium, as a result of equilibrium (i): protonation can indeed favor extra electron input at the prewaves. This is confirmed when pentafluorophenol is used as a source of protons (pKa = 20.11 in MeCN) [58] instead of HClO 4 (pKa = 1.57 in MeCN). [59] Under Ar, its addition to [(L5 2+ species, but a major [(L5 2(OH) )Fe(X)] + one (X = anion). (Figure S37). Under air, only a prewave at -0.78 V is observed, assigned to the activation of O 2 by [(L5 2(OH) )Fe(X)] + with its intensity increasing with the amount of pentafluorophenol used (Figure S38). However, no extra prewave at more positive potential is observed, even in the presence of extra protons in the reaction medium. This also confirms that the prewave at -0.

Impact of the hydrogen bond donor in the alternative binding mode

When a hydrogen bond donor is added in the ortho position of one of the pyridines in the alternative binding mode ([L5 2(OH) Fe(OTf)](OTf)), a single prewave is observed at -0.50 V (Figure 7). When compared to its counterpart deprived of hydrogen bond donor [L5 2(OMe) Fe(OTf)](OTf), this represents a gain of 220 mV for the prewave potential and thus the O 2 activation process. The potential gain observed in the classical binding mode is understandable as the electron input into the Fe II /O 2 adduct is expected to generate an Fe III -OO -species in the 1 st step. The presence of a hydrogen bond donor able to interact with the nascent anionic peroxo ligand would stabilize the species and thus favor the activation process.

In the case of the alternative mode, this potential gain is more puzzling as the OH group, located in the equatorial plane, cannot directly interact with the bound peroxo. Several hypotheses can be proposed to rationalize this observation (Scheme 6): i) the involvement of residual water molecules as relays between the equatorial OH group and the bound peroxo , ii) the decoordination of the hydroxypyridine upon oxidation, as this ligand becomes more labile in the absence of intramolecular hydrogen bond. The peroxo species could then be stabilized by H-bonding to the dangling 2-pyridone , iii) H bonding occurs intermolecularly, between the Fe III -OO -group of one complex and the bound The fact that the potential gain is even larger in the alternative mode than in the classical mode is at first counter-intuitive. However, whereas the OH group in the classical mode is structurally constrained to interact only with the proximal O in an end-on bound Fe III -peroxo species, the hydrogen-bonding pattern is much more flexible in the alternative mode. In hypothesis i) involving a water relay, a hydrogen bonding network involving not only the proximal, but also the distal O atom of an end-on bound Fe III -peroxo species can also be considered. In hypothesis ii), decoordination allows the dangling 2-pyridone to hydrogen bond to the distal O atom. Finally, in hypothesis iii), bulkiness will favor the H bonding interaction with the distal O atom as well (Scheme 6).

As a negative charge develops on this distal O atom upon electron input in the Fe II /O 2 adduct, the Fe III -peroxo species would be better stabilized in the latter case, hence a better potential gain in the alternative binding mode case.

Electroassisted oxidation of thioanisole

In the case of reference complex [(TPEN)Fe II ](PF 6 ) 2 , the prewave for the activation of O 2 was overlapping with the reduction wave of free dioxygen. As a consequence, the energetic cost of the activation of O 2 was not significantly reduced by the presence of the complex, and the reduction of the Fe/O 2 adduct to yield a potentially active Fe III -peroxo was also accompanied by the generation of free superoxide with uncontrollable reactivity. In the case of [L5 2(OH) Fe II (OTf)](OTf), the prewave is significantly shifted to more positive potentials (energetic gain) and it is fully extracted from the reduction wave of free O 2 , so no free superoxide is generated at this potential. We thus attempted the electroassisted oxidation of a substrate (thioanisole), using reductive activation of O 2 by [L5 S2). At the end of the electrolysis and after removal of the electrolyte and complex, the solution was analyzed by GC. The chromatogram shows a peak corresponding to the sulfoxide product, corresponding to a concentration of 0.24 ± 0.03 mM (Figure S44). Control experiments when the complex is absent, show no formation of sulfoxide. Also, when commercial Fe II (OTf) 2 is used instead of the catalyst, only 0.03 mM of sulfoxide is obtained (Figure S43, Table S2).

Sulfone is also detected in the chromatogram for the runs and controls, but in the same quantities as the traces present in the commercial thioanisole substrate (Figures S43-S47, Table S3). It can be concluded that no sulfone is obtained by reductive activation of O 2 and that the sulfoxide product is not obtained by the reduction of the traces of sulfone present in the substrate. Assuming a 2-electron activation of O 2 is involved in the oxidation of thioanisole according to equation (ii), a faradaic yield of 16.2 ± 3.2 % can be estimated. O 2 + 2 e -+ 2 H + + S → H 2 O + S=O (ii) We attempted to increase the reaction yield by addition of a source of protons (2,2,2-trifluoroethanol, 200 equiv. vs Fe). While the overall charge increases from around 1.7 to 3.5 C, the yield in sulfoxide product is not affected, suggesting that the extra electrons injected in solution are lost for the oxidation reaction (Figure S47, Table S2). This could be due to a "decoupling" phenomenon, well-known in natural systems, [START_REF] Meunier | [END_REF] between the reductive activation of O 2 and the oxidation of the substrate that can occur when protons induce the decoordination of a peroxo moiety from iron by release of H 2 O 2 , or even the subsequent reduction of the peroxo to water.

Conclusion

We report the synthesis of a new pentadentate ligand L 5 2(OH) bearing a 2-pyridone moiety. Upon coordination to iron, 2pyridone isomerizes to 2-hydroxypyridine, generating a 2 ndsphere hydrogen-bond donor. L 5 2(OH) can display two binding modes for iron: a classical one, which is displayed by all the pentadentate aminopyridine ligands that are parent of L 5 2(OH) and an alternative one. We showed that each binding mode can be selectively obtained by a judicious choice of the metal salt, as a result of a subtle interplay between the bulkiness of the bound counterion and the hydrogen bond ability and bulkiness of the 2hydroxypyridine moiety. In the classical binding mode, 2hydroxypyridine lies in an axial plane and its OH group can be hydrogen-bonded to the exogenous ligand. In the alternative mode, it is in the equatorial plane and this intramolecular hydrogen-bond pattern vanishes, but can occur intermolecularly instead. In all cases, the addition of the H-bond donor on the ligand backbone significantly improves the reductive activation of O 2 by an iron complex: in the classical mode, it represents a 90-mV gain on the reduction potential, while in the alternative mode we achieve gains of up to 220 mV. Compared to the uncatalyzed activation (reduction of free O 2 at -1 V vs SCE), it represents a remarkable gain of 350 and 500 mV respectively. We took advantage of this significant potential gain to attempt the electroassisted oxidation of a substrate. This allowed us to achieve the oxidation of thioanisole to methylphenyl sulfoxide at -0.5 V vs SCE using [L5 2(OH) Fe II (OTf)](OTf), with faradaic yields of around 16 %.

We recently reported the ability to obtain an important gain in the activation potential by tuning the donating ability of the ligand backbone. [27] Together with the present results, this shows that a rational bioinspired strategy allows to considerably reduce the energetic cost of electroassisted oxidation processes. In the future, we plan to combine these "push" and "pull" effects within one single scaffold to further optimize the energetic efficiency of complexes for both O 2 activation and the oxidation of substrates.

Scheme 1 .

 1 Scheme 1. Synthetic scheme of L5 2(OMe) and L52(OH) .

[L 5 2 (

 2 OH) FeCl](PF 6 )(1) and [L 5 2(OH) Fe(OTf)](OTf)(2) [L5 2(OH) FeCl](PF6)(1) was synthesized by reaction of Fe II Cl 2 with L5 2(OH) in methanol followed by precipitation upon addition of NaPF 6 . [L5 2(OH) Fe(OTf)](OTf) (2) was synthesized by reaction of Fe II (OTf) 2 with ligand L5 2(OH) (see Supporting Information).Solid state characterizationSingle crystals of [L5 2(OH) FeCl](PF6) (1) and [L5 2(OH) Fe(OTf)](OTf) (2) were obtained from the methanol/Et 2 O filtrate during synthesis. The XRD structures of [L5 2(OH) FeCl](PF6) (1) and [L5 2(OH) Fe(OTf)](OTf) (2) are displayed in Figure 1. In both complexes, ligand L5 2(OH) act as a pentadentate ligand wrapping around the pseudo-octahedral iron center and leaving a 6 th position available for an exogenous ligand (chloride or triflate).

Figure 1 .

 1 Figure 1. Views of the metal cations in the XRD structures of complexes of [L5 2(OH) Fe II (Cl)](PF6) (1) (a/), [L5 2(OH) Fe II (OTf)](OTf) (2) (b/). Fe is in orange, C in grey, N in blue, O in red, Cl in green, F in lime, S in yellow. Hydrogen atoms are omitted for clarity, except for those involved in hydrogen bonds.

Scheme 2 .

 2 Scheme 2. Description of the two binding modes with L5 2 -type ligands. Classical mode (a/), and alternative mode (b/).

Figure 2 .

 2 Figure 2. View of the metal cation in the XRD structures of complexes of [L5 2(OMe) Fe(OTf)](OTf) (3). Fe is in orange, C in grey, N in blue, O in red, Cl in green, F in lime, S in yellow. Hydrogen atoms are omitted for clarity, except for those involved in hydrogen bonds.

Scheme 3 .

 3 Scheme 3. Views of the repulsive electrostatic interactions that would develop in the discarded classical binding mode of L5 2(OMe) and L5 2(OH) in comparison with the absence of such interactions in the favored alternative binding mode.

Figure 3 .

 3 Figure 3. View of the metal cation in the XRD structure of [(L5 2(OH) )Fe(OH)]BPh4 (4). Fe is in orange, C in grey, N in blue, O in red. Hydrogen atoms are omitted for clarity, except for those involved in hydrogen bonds.

Figure 4 .

 4 Figure 4. View of the metal cations in the XRD structures of complexes of [(L5 2(O-) )Fe]2(BArF)2 (5). Fe is in orange, C in grey, N in blue, O in red. Hydrogen atoms are omitted for clarity.

[(L5 2 (Scheme 4 . 2 ( 5 )

 2425 Scheme 4. Equilibria in solution upon dissolution of dimer [(L5 2(O-) )Fe]2(BArF)2 (5) in MeCN, and in situ generation of [(L5 2(OH) )Fe] 2+ as a single species upon addition of 1 equiv. aqueous HClO4 (vs Fe).

L5 2 (

 2 OH) , we studied the reductive activation of O 2 by two of the above mentioned complexes: [L5 2(OH) Fe II (OTf)](OTf)(2), which yields the [(N 5 a )Fe II (MeCN)] 2+ species in MeCN solution (alternative mode), and the dimeric [(L5 2(O-) )Fe]2(BArF)2, as the addition of 1 equiv. HClO 4 (per Fe) generates in situ the [(N 5 c )Fe II (MeCN)] 2+ species (classical mode). CVs of the complexes were recorded under air at [Fe] = 1.62 mM, which is the solubility of O 2 in MeCN in these conditions, and allows us to maintain a Fe:air (1:1) ratio through all the CVs.

Figure 5 .

 5 Figure 5. CVs at GC electrode of [L5 2 Fe II (MeCN)](PF6)2 (blue trace) and [L5 2(OMe) Fe(OTf)](OTf) (red trace), ([Fe] = 1.62 mM in MeCN, NBu4PF6 0.1 M, CE = Pt; Ref = SCE, 0.1 V.s -1 ) under air. Full scale (a/) and zoom on the reduction part (b/).

2 )

 2 Fe II (MeCN)](PF6)2, with ligand L5 2 bound in the classical binding mode, and [(L5 2(OMe) )Fe(OTf)](OTf), with ligand L5 2(OMe)

[(L5 2 (Figure 6 .

 26 Figure 6. Compared CVs at GC electrode ([Fe] = 1.62 mM in MeCN, NBu4PF6 0.1 M, CE = Pt; Ref = SCE, 0.1 V.s -1 ) under air of [L5 2 Fe II (MeCN)](PF6)2 and of a solution of [(L5 2(O-) )Fe]2(BArF)2 and HClO4 (1 equiv. per Fe).

  65 V is due to the O 2 activation by [(L5 2(OH) )Fe(MeCN)] 2+ in the classical binding mode. Comparison of the prewaves observed with [(L5 2(OH) )Fe(MeCN)] 2+ (-0.65 V) and [(L5 2 )Fe(MeCN)] 2+ (-0.76 V) shows that the addition of the OH hydrogen-bond donor in the ortho position of one pyridine in the classical binding mode is responsible for a 90-mV shift of the prewave to more positive potentials.

Figure 7 .

 7 Figure 7. Compared CVs at GC electrode ([Fe] = 1.62 mM in MeCN, NBu4PF6 0.1 M, CE = Pt; Ref = SCE, 0.1 V.s -1 ) under air of [L5 2(OH) Fe II (OTf)](OTf) (red trace) and [L5 2(OMe) Fe II (OTf)](OTf) (blue trace).

Scheme 6 .

 6 Scheme 6. Proposed interpretation for the hydrogen bonding networks' involvement in the reductive O2 activation taking place in the classical and alternative binding modes of L5 2(OH) .

  [START_REF] Meunier | [END_REF]

  [START_REF] Meunier | [END_REF]

Acknowledgements

This work was supported by the Agence Nationale de la Recherche (GOAL Project, ANR-22-CE07-0037-01).

Keywords: non-heme iron complex • O 2 activation • thioanisole oxidation • 2 nd sphere • pull effect

Supporting Information

Synthetic procedures, spectroscopic characterization and analysis. The authors have cited additional references within the Supporting Information. [28,[60][61][62][63][64]


Jean-Christophe Perrin
email: jean-christophe.perrin@univ-lorraine.fr

Assma El Kaddouri

Laouès Guendouz

Christine Mrad

Kévin Mozet

Jérôme Dillet

Sebastien Leclerc

Olivier Lottin

Sébastien Leclerc

NMR contributions to the study of water transfer in proton exchange

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

Introduction 1.General information on PEMFC

A proton exchange membrane fuel cell (PEMFC) is an electrochemical converter that combines hydrogen and oxygen to produce electrical energy, water, and thermal energy. Among different types of fuel cells, PEMFC technology currently dominates the market due to its suitability for portable applications (< 1 𝑘𝑊) and transportation sector (~ 100 𝑘𝑊 for automotive vehicles). To achieve these power levels, one or several stacks of individual cells are used, with each cell capable of producing up to 1 𝑊/𝑐𝑚² of active surface area. The operational principle of a single cell is relatively simple, but its engineering is rather complex. The various components must possess the required properties to fulfill the necessary requirements for proper functioning, including uniform supply of reactants, separation of anode (where the hydrogen oxidation half-reaction occurs) and cathode (where the oxygen reduction half-reaction occurs) compartments, charge transport across the membrane-electrode assembly, and evacuation of produced water without impeding reactant transport. The different components constituting a PEMFC cell are as follows ( • The membrane-electrode assembly (MEA), which consists of electrodes where electrochemical reactions take place, and is made out of carbon black, platinum nanoparticles, and ionomer. The electrodes must support the catalyst, have good electronic and ionic conductivity, enable the diffusion of reactive gases to reaction sites, and facilitate water evacuation. Main components of a PEMFC cell.

• The ionomer electrolyte membrane, at the center of the cell. Currently, the membrane has a thickness of less than 15 𝜇𝑚 and ensures efficient transport of protons from the anode to the cathode as well as water diffusion from the cathode to the anode, while providing electronic insulation between the two compartments.

• The gas diffusion layer (GDL), which enables uniform distribution of reactants to the electrodes and facilitates water management within the cell through hydrophobic treatment. Its thickness ranges from 200 to 400 𝜇𝑚, with pore sizes of approximately 10 𝜇𝑚. A microporous layer, typically more hydrophobic with smaller pores, can be placed between the electrode and the GDL to enhance electrical contact and limit electrode flooding by liquid water.

• The flow field plates that distribute reactants and remove excess water and gases. They also ensure compression of the different layers and allow for the collection of electrical current.

PFSA membranes consist of a fully fluorinated polymer chain to which are grafted fluorinated pendant chains terminated by a sulfonic acid group. Nafion is the best-known PFSA polymer. It is composed of a hydrophobic fluorocarbon backbone derived from polytetrafluoroethylene -PTFE-. The pendant chains are terminated by hydrophilic sulfonate groups (-𝑆𝑂 3 --), neutralized by a counterion (𝐻 + in acid medium). Currently sold by the Chemours Company, it was introduced in the 1960s by DuPont, then used in numerous industrial processes, such as production of sodium hydroxide by brine electrolysis, or more recently, in sensors (humidity sensors, biosensors). Nafion has been studied in laboratories and industry for about 60 years (1).

Water in PEM membranes

Water plays a fundamental role in the operation of a PEMFC: it is the product of the electrochemical reaction, the material that fills the membrane's porous microstructure, and the transport medium for protons transferred from the anode to the cathode. While the polymeric backbone provides the membrane's mechanical properties, the sulfonic acid function confers its water sorption and swelling properties. Conventionally, the amount of water present in the polymer structure is quantified by the parameter 𝜆, representing the average number of water molecules adsorbed on each sulfonic acid unit:

𝜆 = [𝐻 2 𝑂] [𝑆𝑂 3 𝐻] equation 1
In Nafion membranes, 𝜆 varies between 0 and around 10 to 15 when the air relative humidity rises from 𝑅𝐻 = 0% to 𝑅𝐻 = 100%, while the relative change in membrane volume (swelling) is significant, typically ~15%, between the dry and saturated states. The "performance" of an ionconducting membrane is quantified by its ionic conductivity, measured in 𝑆. 𝑐𝑚 -1 . The more efficient the ionic transport, the better the membrane material performs as an electrolyte. At a given temperature, the proton conductivity of ionomer membranes varies tremendously as a function of water content [START_REF] Cornet | Sulfonated polyimide membranes: a new type of ion-conducting membrane for electrochemical applications[END_REF][START_REF] Sone | Proton conductivity of Nafion 117 as measured by a four-electrode AC impedance method[END_REF]. As water is essential for proton transport, the study of water diffusion through the membrane is crucial for PEMFC applications. The mechanisms of proton transport in Nafion have been studied and debated in the literature (4). It is accepted that there are two main modes of conduction: the mass diffusion of hydronium ions 𝐻 3 𝑂 + , also known as the vehicular mechanism, and the transfer of protons via hydrogen bonds from one vehicle to another. These processes are strongly coupled to the reorganization of the environment: both the migrating species and the solvent. A third mechanism, surface diffusion, has also been proposed at low hydration. The correlation between the mechanisms depends on the state of water confinement and therefore on the degree of hydration of the membrane. In these materials, it is the simultaneous existence of ionic functionalities and a hydrophobic backbone that is at the origin of the nano-phase separation between hydrophilic and hydrophobic domains, which generates a network of multi-connected "pores" accessible to water. In the case of Nafion, numerous and sometimes competing structural models have emerged since the 1980s. All studies show that the structure is complex and organized at different spatial scales. In the model from Rubatat et al. [START_REF] Rubatat | Evidence of elongated polymeric aggregates in Nafion[END_REF]6), the basic brick is an aggregate of cylinder-or ribbon-shaped polymer chains. These elongated objects are arranged in bundles to form organized zones with a characteristic size of about 500 Å (Figure 2.). Finally, the bundles are organized isotropically on a larger scale. Diagram of several "cylinder bundles" in Nafion. This drawing shows very schematically organized zones with a characteristic size of around 500Å (circled in dotted line) and completely disordered zones.

(the parallelism between the cylinders is exaggerated). Figure from ref (6).

Hydrated membranes are mixed polymer/water matrix systems containing particularly complicated confinement matrices, since the interaction of water and charges, swelling and the multi-scale nature of the structure have to be considered. In such structures, the water diffusion coefficient depends on the time scale probed by the experimental technique used. The molecular scale, studied by quasi-elastic neutron scattering, reveals rapid diffusion over a characteristic time of the order of picoseconds [START_REF] Perrin | Quasielastic neutron scattering study of water dynamics in hydrated nafion membranes[END_REF]. In contrast, self-diffusion probed by pulsed-field gradient NMR (PGSE-NMR) methods reveals a diffusion coefficient averaged over a time of the order of milliseconds [START_REF] Zhao | Diffusion and Interfacial Transport of Water in Nafion[END_REF]. Between the two, water diffusion undergoes slowdowns at the so-called "intermediate" scale, that can be probed by field cycling NMR relaxometry [START_REF] Perrin | Water dynamics in ionomer membranes by field-cycling NMR relaxometry[END_REF][START_REF] Perrin | Water dynamics in lonomer membranes by field-cycling NMR relaxometry[END_REF][START_REF] Perrin | Water dynamics in ionomer membranes by field-cycling NMR relaxometry[END_REF].

NMR study of water properties in PFSA membranes

From the earliest days, NMR was used to study diffusion in liquids [START_REF] Hahn | Spin Echoes[END_REF]. From 1965 onwards, with the application of pulsed field gradient methods by Stejskal and Tanner (Stejskal and Tanner 1965), the magnetic field gradient intensity could be chosen strong enough to allow measurement of diffusion in porous media. The methods involved are sensitive to molecular motion and therefore reveal information about porous structures that impede molecular movement [START_REF] Price | Pulsed-field gradient nuclear magnetic resonance as a tool for studying translational diffusion: Part 1. Basic theory[END_REF][START_REF]Diffusion NMR of Confined Systems[END_REF]. NMR methods have also been used for a long time to study fuel cell materials, particularly membranes, and can even be said to have played a part in the development of PEMFC. NMR has been extensively exploited because the methods are well suited to the study of molecular motion in fuel cell membranes. Water is abundant and the phenomena to be studied are numerous and sufficiently complex to mobilize a large number of researchers [START_REF] Suarez | Nuclear Magnetic Resonance of Polymer Electrolyte Membrane Fuel Cells[END_REF]. In PFSA membranes, the situation is ideal, as proton NMR only provides information on adsorbed water, while fluorine NMR can probe the chemical structure of the perfluorinated skeleton. In hydrocarbon materials, the situation is more complex, but filtering of the matrix signal is relatively straightforward, so that the water signal is accessible. The review article by Yan et al. [START_REF] Yan | Applications of NMR Techniques in the Development and Operation of Proton Exchange Membrane Fuel Cells[END_REF] details in this sense the contributions of the different techniques to research on core materials. The article by Zhang et al.

(17) reviews studies using MRI as a "diagnostic tool" for fuel cells.

proton NMR spectra in PFSA membranes.

The main feature of proton NMR spectra of Nafion-type PFSA membranes is an intense resonance line of liquid nature, broadened by the resolution of the spectrometer (Figure 3). This line is generally detected at a chemical shift between 6.5 and 12 𝑝𝑝𝑚 relative to the TMS reference and is attributed to the water present in the ionic domains. First, no significant broadening occurs as the water content of the membrane decreases, although the transverse relaxation time 𝑇 2 drops significantly. A broadening appears only at very low water content (𝜆 < 2), indicative of a significant reduction in molecule mobility. In all cases, the line shape is highly asymmetrical, indicating the existence of one or more other components, albeit unresolved. These additional components may correspond to protons that cannot be exchanged with those of the main water population on the characteristic time scale of the measurement: 𝐻 + counterions or impurities introduced by synthesis. As the amount of water in the membrane increases, the main resonance line shifts towards the low chemical shifts (𝛿) [START_REF] Bunce | Proton NMR method for the quantitative determination of the water content of the polymeric perfluorosulfonic acid Nafion-H[END_REF][START_REF] Wakai | Analysis of the Hydration Process and Rotational Dynamics of Water in a Nafion Membrane Studied by H-1 NMR Spectroscopy[END_REF]: the network of hydrogen bonds becomes denser, the water interacts less and less with the polymer chains, and becomes increasingly mobile. This dependence of 𝛿 on 𝜆 inspired Bunce et al. [START_REF] Bunce | Proton NMR method for the quantitative determination of the water content of the polymeric perfluorosulfonic acid Nafion-H[END_REF] to develop a method for determining the absolute amount of water in a Nafion membrane through the direct measurement of 𝛿. The problem of choosing a reference state arose immediately: it is known that it is practically impossible to remove all the water from a PFSA membrane other than by heating it to high temperatures (21).

NMR relaxation and water mobility

The interactions between the proton magnetic moments in a sample can often come from a variety of sources. The measurement of the proton NMR relaxation parameters (𝑇 1 , 𝑇 2 ) provides information on the origin of the modulations, i.e., on the molecular dynamics of the spin carriers, by revealing the nature of the modulations of the interactions between the spins in the system and, consequently, the nature of the relaxation mechanisms. In the case of dipolar interaction between spins with random rotational motion, the BPP model [START_REF] Bloembergen | Relaxation effects in Nuclear Magnetic Resonance Absorption[END_REF] shows that the correlation function is an exponential of the form 𝑒𝑥𝑝(-𝑡/𝜏 𝑐 ), where 𝜏 𝑐 is a correlation time characteristic of the motion.

Two modulation ranges can be distinguished as a function of this time: a fast regime -also called "extreme narrowing"when the correlation time is much less than the inverse of the Larmor frequency, (𝜔 0 𝜏 𝑐 << 1) and a slow regime if the correlation time is much higher than this value, (𝜔 0 𝜏 𝑐 >> 1). In the fast modulation regime, the relaxation rates 𝑅 1 and 𝑅 2 are equal and proportional to 𝜏 𝑐 . In Nafion, the time evolution of nuclear magnetization recorded during the socalled CPMG measurement (used to measure 𝑇 2 ) and inversion-recovery measurement (to measure to reach the conditions of extreme narrowing of liquid water at 1/𝜆 = 0 for which 𝑅 1 (200 𝑀𝐻𝑧) ≈ 𝑅 2 (20𝑀𝐻𝑧). We also observe that bulk water appears as the infinite dilution limit of 𝑅 1 (𝜆) for 1 𝜆 ⁄ → 0. The evolution of 𝑅 1 at "high" field indicates that 𝑅 1 (𝜆 → 0) reaches the maximum value of the relaxation rate at 𝜔 0 2𝜋 = 200 𝑀𝐻𝑧 ⁄ . This property is representative of molecular dynamics with a characteristic time 𝜏 𝑐 such that 𝜔 0 𝜏 𝑐 = 1, i.e., 𝜏 𝑐 ≈ 1𝑛𝑠 a value well below that of bulk water (≈ 1𝑝𝑠). Adapted from reference [START_REF] Perrin | [END_REF].

To go one step further, temperature and Larmor frequency can be used as experimental parameters to study dynamics on "short" or "intermediate" time scales, respectively. In 1999, MacMillan et al. produced a comprehensive study of the restriction of molecular motion by the presence of "pores", by measuring the temperature evolution of proton, deuteron, and fluorine relaxation times in hydrated Nafion membranes with different water contents [START_REF] Macmillan | An nmr investigation of the dynamical characteristics of water absorbed in Nafion[END_REF][START_REF] Macmillan | relaxation in Nafion -The low temperature regime[END_REF]. The authors have identified a transition temperature, above which the water in the clusters behaves like bulk water. Below this temperature, the slopes of the 𝑇 1 (𝑇) and 𝑇 2 (𝑇) curves are much steeper, indicative of a situation in which molecular movement is restricted. The transition temperature depends on the water content of the membrane, and ranges from -10°𝐶 to 13°𝐶 for high and low water contents respectively. The authors note that this transition does not correspond to a liquid ↔ solid phase transition, which was later confirmed by further relaxation and diffusion studies [START_REF] Guillermo | NMR and Pulsed Field Gradient NMR Approach of Water Sorption Properties in Nafion at Low Temperature[END_REF][START_REF] Wakai | H-1 NMR Analysis of Water Freezing in Nanospace Involved in a Nafion Membrane[END_REF].

Furthermore, no structural transition is possible since for the same temperature ranges, no discontinuities are observed in the fluorine relaxation curves. An important finding of the MacMillan et al. study is that, in the high-temperature limit (𝑇 > 270°𝐾), 𝑇 1𝜌 = 𝑇 2 ≠ 𝑇 1 , which is unusual behavior and not understandable within the framework of the BPP model [START_REF] Bloembergen | Relaxation effects in Nuclear Magnetic Resonance Absorption[END_REF]. This model predicts that, in the so-called "extreme narrowing" regime, the three relaxation times 𝑇 1 , 𝑇 2 The main conclusions of NMR relaxometry studies are as follows ( 18):

• The evolution of proton relaxation rates as a function of Larmor frequency measured over the entire hydration range shows little variation, a sign that the interaction between water and the polymeric surface is not very intense.

• The proton and deuteron relaxation dispersions, normalized to the relaxation rates of water and heavy water (compared in Figure 4-(b) for low hydration), are very distinct, meaning that molecular reorientation modulating the intramolecular dipolar interaction is not the main contribution to relaxation. The difference between the two profiles proves that there is at least one other relaxation mechanism, corroborating the findings of MacMillan's study.

• Proton relaxation contains an intramolecular component that can be evaluated by relaxation measurements on heavy water (at identical hydration) and subtracted. The resulting intermolecular contribution contains a component due to the interaction between water protons and fluorine nuclei in the matrix, and another due to the modulation by translational motion of water molecules of the 𝐻 -𝐻 dipolar interaction between protons belonging to different molecules. It has been shown that the 𝐻 -𝐹 dipolar interaction is in the minority at low frequencies and for water contents above 𝜆 ≈ 6. In this hydration range, all dispersions follow a logarithmic distribution. They were then interpreted within the framework of a dipolar relaxation model by translational diffusion in a locally two-dimensional medium [START_REF] Korb | Confinement effects on dipolar relaxation by translational dynamics of liquids in porous silica glasses[END_REF]. For higher water contents, the relaxation of water protons is almost exclusively due to intramolecular components.

In conclusion, we can state that the non-wetting nature of the perfluorinated Nafion membrane induces relatively low-dispersion relaxation profiles. The transition from 2𝐷 to 3𝐷 diffusion during hydration is a realistic hypothesis for interpreting the evolution of intermolecular dipolar interaction relaxation profiles as a function of water content. This transition takes place around 𝜆 = 5 -6. These results support a structural model of Nafion based on the existence of elongated aggregates, organized in locally lamellar domains at the nanometric scale. A small increase in the size of the inter-lamellar space, due to the introduction of additional water, induces a rapid disappearance of the 2𝐷 behavior and the establishment of the 3𝐷 regime, which is directly reflected by the significant variation in dispersion profiles observed over a restricted hydration range, from 𝜆 = 3.7 to 𝜆 = 5.6.

PFGNMR and diffusion at the micrometer scale

In a pulsed field gradient diffusion (PFG-NMR) measurement, motion detection is based on the analysis of the attenuation of the NMR signal, known as spin echo, resulting from the dephasing of nuclear spins under the combined effect of translational motion and the application of perfectly controlled field gradient pulses [START_REF] Price | Pulsed-field gradient nuclear magnetic resonance as a tool for studying translational diffusion: Part 1. Basic theory[END_REF]. In contrast to the relaxation methods described in the previous paragraph, the spatial scale associated with the measurement is directly linked to the duration of motion observation set by the user (diffusion delay ∆). In the case of free diffusion, the value of the self-diffusion coefficient does not depend on the observation time, as the rootmean-square displacement is a linear function of time. As the self-diffusion coefficient of free pure water at 25°𝐶 is around 2.3. 10 -9 𝑚 2 . 𝑠 -1 (29), the scale probed along the direction of application of the field gradient in this case is de √2𝐷 𝑠 ∆ ≈ 5 to 25 𝜇𝑚 for ∆ = 5 to 150 𝑚𝑠. In the case where the fluid (water for example) is confined, the displacement will depend on the diffusion delay, the size of the confinement domain and the bulk diffusion coefficient. In the Nafion membrane, the PFG-NMR method has been used since the 1990s to study the link between water sorption, molecular diffusion, and ionic conductivity [START_REF] Zawodzinski | Comparative study of water uptake by and transport through ionomeric fuel cell membranes[END_REF][START_REF] Kreuer | On the development of proton conducting materials for technological applications[END_REF]. More recently, other studies have used this method to elucidate proton transport mechanisms [START_REF] Privalov | Transport Mechanism in Nafion Revealed by Detailed Comparison of 1H and 17O Nuclear Magnetic Resonance Diffusion Coefficients[END_REF]. The values of the water diffusion coefficient 𝐷 𝑠 increase strongly with water content, in the range 2. 10 -8 < 𝐷 𝑠 < 6.5. 10 -6 𝑐𝑚 2 /𝑠 13 [START_REF] Zhao | Diffusion and Interfacial Transport of Water in Nafion[END_REF][START_REF] Maldonado | Characterization of polymer electrolyte Nafion membranes: Influence of temperature, heat treatment and drying protocol on sorption and transport properties[END_REF][START_REF] Gong | Self-diffusion of water, ethanol and decafluropentane in perfluorosulfonate ionomer by pulse field gradient NMR[END_REF]. The value in the saturated membrane is lower than that measured for pure liquid water at the same temperature by a factor ~ 4 (23. 10 -6 𝑐𝑚 2 /𝑠). This may be related to the tortuosity of the medium (Figure 5). In general, diffusion is activated by temperature. Assuming that the diffusion coefficient follows an Arrhenius law, the activation energy extracted varies between 31.6 and 19.2 𝑘𝐽/𝑚𝑜𝑙 as 𝜆 increases from ~3 to ~13. By comparison, the activation energy extracted from the Arrhenius plot of the diffusion coefficient of liquid water over the same temperature range is 16.7 𝑘𝐽/𝑚𝑜𝑙. The continuity between the values in Nafion and liquid water is good; diffusion in liquid water then appears as the infinite dilution limit of the diffusion of water in Nafion. Water in Nafion thus acquires the same diffusive behavior as free water when hydration is at its maximum. However, as hydration decreases, the energy cost becomes much higher.

Impact of chemical degradation

The degradation and ageing of PEMFC materials have been the target of numerous experimental and theoretical studies [START_REF] Zaton | Current understanding of chemical degradation mechanisms of perfluorosulfonic acid membranes and their mitigation strategies: a review[END_REF][START_REF] Dubau | A review of PEM fuel cell durability: materials degradation, local heterogeneities of aging and possible mitigation strategies[END_REF]. Membrane aging and the alteration of its properties is a particularly important issue. During the operation of a PEMFC, the membrane undergoes significant modifications, of various origins (mechanical, chemical, electrochemical and/or hygrothermal), which can affect the performance of the cell, or even lead to its shutdown. The problem of membrane ageing is difficult to solve, as it is the consequence of simultaneous and coupled mechanisms. It must therefore be tackled using a multi-analytical experimental approach.

The effects induced by the use of a Nafion XL membrane in a fuel cell stack at constant intensity over a long period have been studied by proton and fluorine NMR [START_REF] Robert | Towards a NMR-Based Method for Characterizing the Degradation of Nafion XL Membranes for PEMFC[END_REF]. An example of the results is shown in Figure 6. The XL membrane is a tri-layer composite membrane with a PFSA- The 𝐻 1 -𝑁𝑀𝑅 spectrum of the new XL100 membrane shows a second resonance peak at around 7.6 𝑝𝑝𝑚. Pulsed field gradient and relaxation experiments show a complex behavior, with (at least) two components [START_REF] Robert | Towards a NMR-Based Method for Characterizing the Degradation of Nafion XL Membranes for PEMFC[END_REF]. Initially attributed to the water present in the PTFE reinforcement, this second population could correspond instead to hydronium ion protons, an attribution made by Han et al. in Nafion NR211 (39) (the NR211 membrane is a monolayer, with a nominal thickness of 25 𝜇𝑚, based on chemically stabilized PFSA polymer). After fuel cell operation, the sorption curve shows a reduced water uptake capacity, while the resonance line attributed to water shifts towards the lowest chemical shifts, which is contrary to the behavior observed in new membranes: the water's chemical environment has therefore been modified. The self-diffusion coefficient, meanwhile, follows the usual logic, with a lower value in the saturated membrane after operation (containing less water than the new membrane). The 𝐹 19 spectra show that operation has altered the polymer, as the ion exchange capacity (denoted IEC in the figure) is lower after operation. This may be due to the partial loss of ionic sulfonic groups as a result of side-chain scissions caused by radical attack (40, 41) (Figure 7). Indeed, it is known in the literature that various mechanisms, such as the formation of hydrogen peroxide by reduction of oxygen followed by the scission of 𝐻 2 𝑂 2 catalyzed by the presence of metal cations [START_REF] Pozio | Nafion degradation in PEFCs from end plate iron contamination[END_REF] or the simultaneous reaction of the two gaseous reactants 𝐻 2 and 𝑂 2 on the platinum surface of electrodes in an operating cell [START_REF] Mittal | Membrane degradation mechanisms in PEMFCs[END_REF], can lead to the formation of the radicals 𝐻 • and 𝐻𝑂 • .

Membrane imaging and operando MRI

As NMR is non-invasive and selective, it is a method of choice for the operando study of water transfer in PEMFC cells. However, MRI is incompatible with ferromagnetic, paramagnetic or electrically conductive materials. Carbonated layers are key elements in the design of PEMFC cells and cannot be easily replaced due to their multiple roles in the system. The general advancement of MRI methods in the PEMFC research field has been limited in particular by the existence of carbon-based gas diffusion layers (GDLs). During the experiment, the radiofrequency (RF) waves generated by the excitation/reception radio-frequency coil must reach the measurement volume to excite the spins and collect the NMR signal in return. These signals are strongly attenuated by conductive materials, resulting in considerable losses and severe distortions and artifacts. Despite these disadvantages, MRI has been the target of much attention from the PEMFCs scientific community from 2004 until around 2012 [START_REF] Bedet | Magnetic resonance imaging of water distribution and production in a 6 cm(2) PEMFC under operation[END_REF][START_REF] Tsushima | Magnetic resonance imaging of the water distribution within a polymer electrolyte membrane in fuel cells[END_REF][START_REF] Minard | Magnetic resonance imaging (MRI) of PEM dehydration and gas manifold flooding during continuous fuel cell operation[END_REF][START_REF] Wang | In situ quantification of the in-plane water content in the Nafion (R) membrane of an operating polymer-electrolyte membrane fuel cell using H-1 micro-magnetic resonance imaging experiments[END_REF][START_REF] Feindel | Use of hydrogen-deuterium exchange for contrast in (1)H NMR microscopy investigations of an operating PEM fuel cell[END_REF](50)[START_REF] Zhang | Magnetic resonance imaging of water content across the Nafion membrane in an operational PEM fuel cell[END_REF][START_REF] Zhang | Zero-mode TEM parallel-plate resonator for high-resolution thin film magnetic resonance imaging[END_REF]. A major step in the field of operando MRI of PEMFCs has been achieved by the Balcom's group, who have used a prototype surface coil as an integrated radio-frequency resonator in the fuel cell prototype. In this configuration, the planar resonator serves simultaneously as a reactant supply plate for the cell and as a current collector [START_REF] Zhang | Zero-mode TEM parallel-plate resonator for high-resolution thin film magnetic resonance imaging[END_REF]. A probe of related design was introduced at the same time as this work for biomedical histology [START_REF] Meadowcroft | Direct magnetic resonance imaging of histological tissue samples at 3.0T[END_REF]. The aim of this development was to increase NMR sensitivity and spatial resolution. Using this methodology, the authors were able to obtain one-dimensional water content profiles with a resolution of 6 𝜇𝑚 (51). The authors clearly capture the partial dehydration of the membrane on the anode side, even at room temperature. This very good spatial resolution was made possible here by the innovative design of the RF coil. The design avoids problems of RF field shielding by conductive layers (carbon electrodes and electrode support, gas diffusion layers), as the resonator generates a magnetic field parallel to the plane of the membrane-electrode

HO• HO• HO• H• H•
assembly rather than normal to it, as is the case in "standard" configurations where the RF field is generated by a volume probe or surface coil. Although significant progress was made during the few years when MRI imaging of operating cells was being developed, the number of studies suddenly declined after 2012. It is still unrealistic to be able to carry out a time-and space-resolved MRI study of PEMFC operation under true operating conditions (particularly in terms of temperature) and on a prototype that enables realistic operation in terms of electrochemical performance. The incompatibility of materials rules out measurements on commercial PEMFC, and even the possibility of seeing the water in GDL, while the need for fast experiments with good spatial resolution means using small RF coils and a low field of view, which limits the size of the cell. Finally, and perhaps the most limiting factor, the thickness of the membranes currently in use is less than 20 µ𝑚. The resolution of MRI methods is therefore unsuitable for high-quality operando studies. That said, imaging methods can be used to study membrane properties ex-situ, outside the fuel cell system. This approach, detailed in the next paragraph, is the one that has been most widely followed in recent years for fundamental studies of diffusion in stressed membranes and water transfer at membrane interfaces.

NMR and MRI in a single proton exchange membrane

The strategy used for accessing NMR measurements on a single membrane involves the development of suitable radio-frequency (RF) NMR instrumentation coupled to dedicated devices, enabling the sample to be subjected to controlled mechanical and hydric stresses.

Water self-diffusion in a membrane under traction / compression

The emission of the RF field and the detection of the NMR signal are both performed by a copper wire loop of diameter 𝑑 = 10 𝑚𝑚. The dimensions are sufficiently small compared to the wavelength at 100 𝑀𝐻𝑧. When the electronic circuit is tuned and matched by a symmetrical capacitive circuit, the coil has a good quality factor of around 𝑄~110. In this geometry, the plane of the membrane is close to the coil and therefore exposed to a strong RF magnetic field, ensuring a significant gain in signal-to-noise ratio. The plane of the membrane is located within the linearity zone of the RF field, i.e. at around 𝑑 4 ⁄ = 2.5 𝑚𝑚.

• For the traction experiments the dimensions of the membrane were chosen so that the coil covers part of the stretched sample as uniformly as possible (away from the ends). The mini-tensile machine was made out of polycarbonate and PTFE (Figure 8(a)). It consisted of two sliding jaws, which moved symmetrically with respect to the center of the sample. This means that, whatever the stretch ratio, the center of the sample always coincided with the center of the RF coil, the center of the field gradient coils, and the center of the magnet homogeneity zone.

• For the compression experiments, an NMR-compatible device was developed to quantify the evolution of the water content of a PFSA membrane exposed to a variable and balanced normal stress in a controlled relative humidity environment (Figure 8(b)). The body (36 × 44 𝑚𝑚) of the compression cell consists of a chamber, a movable piston, a lid and a chamber cover made of polyetheretherketone (PEEK). The 5 𝑚𝑚-diameter membrane sample is placed between two porous quartz discs (pore size 15 to 40 µ𝑚) to allow water to drain away when pneumatic pressure is applied. Brass screws and nuts were used to tighten the assembly, with polymethyl methacrylate (PMMA) spacers. The NMR coil was positioned around the lower porous disk below the plane of the membrane. To maintain constant, homogeneous humidity conditions in the membrane environment, a flexible hose was placed close to the membrane between the two spacers to supply humid air at a fixed relative humidity (15% < 𝑅𝐻 < 98%).

The traction and compression systems were inserted in a Bruker Biospec 24/40 imager, equipped with a 3-axis field gradient sheath producing a maximum intensity of 20 𝐺𝑎𝑢𝑠𝑠/𝑐𝑚 (0.2 𝑇/𝑚).

The combination of two orthogonal field gradients in the (𝑥𝑦) plane made it possible to modify the orientation of the magnetic field gradient relatively to the plane of the membrane, and thus control the direction of diffusion coefficient measurement. A stimulated spin-echo sequence (PGSTE) with unipolar magnetic field gradients was used to perform the experiments. The results show a clear drop in content and diffusion coefficient with increasing stress. The relative effect on diffusion is much greater than on water content, in agreement with the strong acceleration of diffusion at low water content (Figure 5 and Figure 9(b)). The effect of a change in microstructure is also experienced throughout the hydration range.

Water transfer at the membrane/humid air interface

Ex-situ membrane imaging can be effectively used to study phenomena taking place at the interfaces between the membrane and an external humid atmosphere. Among the phenomena of interest is the transfer of water from a gaseous phase to the membrane interior. The experiment which aims to subject a membrane to a flow of humid air on one side and a flow of dry air on the other corresponds to the gas-phase pervaporation process. It consists in three phases:

• water sorption in the membrane on the wet air side;

• diffusion of water through the structure;

• water desorption on the dry air side.

Sorption and desorption can be accompanied by interface resistance phenomena, controlled by the boundary layer in the gas flow, the gas ↔ liquid phase change and the surface properties (morphology, hydrophobicity) of the membrane (Figure 10). While boundary layer effects can be minimized by imposing a high gas flow rate, the other two resistances cannot be avoided. However, their impact on the overall phenomenon is more or less important, depending on the relative values of the resistance due to diffusion inside the membrane 𝑅 𝐷 and the interface resistances 𝑅 𝑖𝑛𝑡 .

(a) (b)

Figure 10 (a) Illustration of the effect of an interfacial resistance on the steady-state water content at the interface.

The non-linear water profile results from the concentration dependence of the diffusion coefficient.

(b) Zooming in on the interface reveals the presence of two resistances in series, one of which is due to the boundary layer effect and the other to the morphology of the thin PTFE-rich layer on the membrane surface.

Experimental results acquired when a Nafion N1110 membrane is subjected to a moisture gradient between its two faces are shown in are also more open and less tortuous as moisture increases [START_REF] Kusoglu | New Insights into Perfluorinated Sulfonic-Acid lonomers[END_REF]. In the limiting case where the membrane surface is in equilibrium with liquid water, we anticipate a very sharp drop in interface resistance, down to a value close to zero [START_REF] Satterfield | Non-fickian water vapor sorption dynamics by nafion membranes[END_REF][START_REF] Monroe | A vaporization-exchange model for water sorption and flux in Nafion[END_REF][START_REF] Majsztrik | Water Permeation through Nafion Membranes: The Role of Water Activity[END_REF]. The water conduction channels are then predominantly oriented towards the surface, this configuration being the one that minimizes surface energy, and a water film forms and propagates towards the interior of the material. By subtracting the constant value of resistance due to limitations to mass transfer at the interface due to the boundary layer phenomenon 𝑅 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 , we can determine an approximate value of resistance due to the morphological skin effect (𝑅 𝑠𝑘𝑖𝑛 ). This effect, which appears here to dominate interface resistance over a wide humidity range, stems from the highly hydrophobic nature of the surface, comparable to that of Teflon. This condition is due to the pendant chains carrying the ionic sites, which are oriented at the interface towards the interior of the material over a thickness of a few nanometers [START_REF] Hwang | Understanding Water Uptake and Transport in Nafion Using X-ray Microtomography[END_REF]. This results in a lower water content over a short distance. In conclusion, the limitations to steady-state water transfer in Nafion come mainly from interface effects when the condition is of the "humid air" type. When air humidity is low, resistance due to diffusion can be significant, as can that due to interface hydrophobicity. If the gas flow rate is sufficiently high, the boundary layer effect can be limited. In the transient regime, another limitation, arising from polymer relaxation under the effect of chain rearrangement associated with swelling, must be considered when modeling the overall phenomenon.

Conclusion

PEMFC fuel cells are electrochemical converters that play a significant role in the energy mix. Understanding the properties of proton exchange electrolyte membranes is critical for creating efficient and long-lasting materials. Advanced experimental methods are required for this.

In this article, we reviewed a number of studies that investigated water behavior in Nafion reference membranes using NMR spectroscopy, field cycling NMR relaxometry, PFG-NMR, and MRI imaging. Over the year this membrane has evolved into a model system on which new approaches can be tested. Despite the large number of studies that have been published in the literature, research on the Nafion membrane is not yet complete. Studies are currently focused on understanding the membrane's degradation mechanisms and the strategies to be followed to limit them. Other studies are being carried out on alternative materials. One option is to introduce modifications into hydrocarbon host membranes, with the aim of giving them good ionic conduction properties and improved durability. The quest for the "ideal" membrane, which would have all the advantages of Nafion without its shortcomings, is therefore still ongoing.

Funding

This research has received funding from the European Union's EIT Raw Materials project nº 19247 ALPE: "Advanced Low-Platinum hierarchical Electrocatalysts for low-T fuel cells".

Figure 1

 1 Figure 1):

Figure 1 .

 1 Figure 1.

Figure 2 .

 2 Figure 2.

Figure 3 . 1 H

 31 Figure 3. 1 H NMR spectra of low-water content Nafion 112, measured at 200 𝑀𝐻𝑧, 25°𝐶, and normalized to the maximum intensity. Adapted from reference (18).

𝑇 1 )Figure 4 . 1 ⁄

 141 Figure 4. The values of 𝑅 2 ( 𝐻) = 1

  Figure 4 (a) Proton relaxation rate in a Nafion 112 membrane at room temperature as a function of 1 𝜆 ⁄ . Adapted from reference (18). (b) Normalized proton and deuteron relaxation profiles in Nafion 112 at 𝜆 = 3.7.

  et 𝑇 1𝜌 converge to a single value. Since 𝑇 1 represents the longitudinal relaxation time at high frequency, 𝑇 1𝜌 the longitudinal relaxation time at low frequency, and since 𝑇 1𝜌 = 𝑇 2 in this temperature range, the authors attribute the relatively short values of 𝑇 1 ( 𝐻) 1 to the presence of an additional relaxation mechanism at low frequency. In Nafion, the movement of confined water is slowed down by interactions with the material's surfaces. Processes appear that are much slower than molecular movements in the bulk: several elementary steps are then required for a molecule to lose the correlation of its initial orientation or position. The additional relaxation mechanism suggested by MacMillan et al. has been identified and studied using the NMR relaxometry method (field-cycling NMR). In this method, the Larmor frequency at which the nuclear spins relax is used as a parameter[START_REF] Kimmich | NMR Tomography Diffusometry Relaxometry[END_REF] to extract information on the slow movements of water molecules: typically from 10 𝜇𝑠 𝑡𝑜 1 𝑛𝑠 in the membranes studied here, corresponding to Larmor frequencies between 10 𝑘𝐻𝑧 and 400 𝑀𝐻𝑧. The shape and amplitude of the dispersions are indeed characteristic of modulations by spin carrier dynamics of the interactions responsible for relaxation. To be exploitable, however, the data must be interpreted within the framework of theoretical models, which are only valid if the mechanisms behind nuclear relaxation are clearly identified. Proton relaxation is governed by the dipolar interaction. In water, a proton is in dipolar interaction with the second proton of the same molecule and with other neighboring protons belonging to different molecules. Intramolecular dipolar interactions (between protons of the same molecule) are modulated by molecular reorientations, while intermolecular dipolar interactions are modulated by variations in the radius-vector joining the protons, i.e. by translational diffusion. Measuring the proton relaxation time alone is therefore not enough to directly assess the respective proportion of relaxation due to the intra-and inter-molecular components of the dipolar interaction. In the case of deuteron, on the other hand, relaxation is largely due to rotational modulation of the intramolecular coupling between the deuteron's quadrupole moment and the electric field gradient carried by the 𝑂 -𝐷 bond. This interaction is strong, and the dipole-dipole interaction is negligible. The measurement of 𝑇 1 ( 𝐻) 2 can therefore be directly interpreted in terms of rotational motion. The two contributions, rotational and translational, can be distinguished and separated by measuring the two relaxation times 𝑇 1 ( 𝐻) 1 and 𝑇 1 ( 𝐻) 2 .

Figure 5 .

 5 Figure 5. Influence of water content 𝜆 and drying temperature on the evolution of the self-diffusion coefficient and proton conductivity in Nafion N115. From reference (21).

Figure 6 .

 6 Figure 6. (a) and (b) 𝐻 1 NMR spectra of Nafion XL100 membranes before and after PEMFC operation. (c) Comparison of membrane sorption isotherms before and after operation. (d) 𝐹 19 NMR spectra of new XL100 and NR211 membranes and the tri-layer membrane after operation. Adapted from (36).

Figure 7 .

 7 Figure 7. Schematic representation of possible radical attacks in Nafion during fuel cell operation, proposed by Ghassemzadeh et al. (44).

Figure 9 (

 9 Figure 8 (a) Mini-tensile machine and surface coil developed for measuring the water self-diffusion coefficient in membranes under tension. Figure from reference (54, 55). (b) Compression mini-machine and surface coil developed to characterize the effect of compressive stress on water diffusion properties. Figure from reference (56)

Figure 9 ( 1 . 7 .

 917 Figure9(a) shows the evolution of the diffusion coefficient in a single Nafion N1110 membrane (250 µ𝑚 nominal thickness) equilibrated at 𝜆 = 4 ± 0.5 for different stretching ratios. In the unstretched sample (𝐷𝑅 = 1), the lamination process induces a weak alignment of the Nafion membrane structure, resulting in a ~ 10% anisotropy of the water diffusion coefficient. Before stretching, the aggregates of polymer chains, assembled in lateral size domains of around 800 Å, are randomly oriented on a micrometric scale. A weak orientation order exists, however, in membranes that were laminated (N112, N115, N117, N1110), but not in those obtained by castingevaporation, for which the order is orthogonal to the plane of the membrane. Measurements in the 𝐷𝐷, 𝑇𝑃 and 𝑇 directions for increasing draw ratios demonstrate that the diffusion tensor is cylindrically symmetrical around the stretching direction with excellent approximation. When stretched, the domains rotate in the tensile direction. The symmetry of the structure is uniaxial, as is that of the diffusion tensor. The diffusion anisotropy increases strongly to reach 2.5 for 𝐷𝑅 = 1.7. Beyond this point, the domains deform, probably introducing an alignment of polymer chain aggregates along the tensile direction. At room temperature, systematic membrane rupture occurs at 𝐷𝑅 ~ 2.2 .

Figure 11 . 2 where

 112 Figure 11