Rémi Plamont

Jessica Tami

Juan-Ramón Jiménez

Amina Benchohra

Omar Abou Khaled

Geoffrey Gontard

Yanling Li

Rodrigue Lescouëzec

Remi Plamont

Juan-Ramon Jimenez

Omar Khaled

Rodrigue Lescouezec
email: rodrigue.lescouezec@upmc.fr

A soluble cyanide-bridged Fe 4 Ni 4 box encapsulating a Cs + ion: synthesis, structure and electronic properties

Keywords: molecular cage, cyanide ligand, electronic communication, caesium

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

Introduction

Polymetallic cyanide assemblies have attracted considerable interest because of their interesting electronic properties. These properties often arise from the ability of the cyanide ligand to promote efficient electronic communication between the metal ions it binds, through its set of  and  frontier orbitals that are involved in the coordination bonds. The electronic communication is revealed, for example in mixed valence compounds by the presence of a strong metal-metal charge transfer band, which can give rise to intense colour. This is the case of Prussian blue, a mixed valence compound of class II (partially delocalized electron) of the formula Fe III 4 [Fe II (CN) 6 ] 3 . nH 2 O. This material is the first synthetic coordination polymer and was used as a blue pigment by painters during the 18 and 19 th centuries. compounds, which all exhibit cubic structure where the octahedral metal ions are linked through linear cyanide bridges. Their electronic properties can be tuned by selecting the metal ion and by tuning the synthetic condition to control the stoichiometry of the compound. The range of application for these emblematic cyanide-based coordination polymers is large and continuously broadening. For example redox active PBA have been recently explored for water oxidation catalysis.

[2] The electronic delocalization through the M-CN-M' bridges and the possible insertion of alkali ions was taken into profit recently to use PBA as cathode material in ion batteries. [3] When the metal ions bear unpaired electrons, the electronic communication gives rise to a magnetic exchange interaction through the cyanide bridge (so-called superexchange interaction). Contrary to the oxo bridge, another efficient magnetic linker, the ambidentate character of the cyanide ligand and the use of stable cyanide building blocks, makes designing heterometallic compounds easier. [4] Moreover, the linear shape of the cyanide together with the rigidity of the M(CN) 6  x- building block allows a good control on the topology of the final compounds. It is also possible to control the nature and the strength of the magnetic interaction using simple consideration. In particular, it has been shown that an adequate choice of the metal ions allows controlling the nature and the strength of the magnetic exchange interaction. [5] This allowed M. Verdaguer et coll. to obtain the first molecular-based magnet with a Curie temperature above room temperature, a VCr PBA.

[6] The electronic communication through the cyanide bridge also allows, in some cases, the preparation of interesting mixed valence bistable systems, showing photo-induced electron transfer in the M-CN-M' unit. The phenomenon was first observed by O. Sato in a FeCo Prussian blue analogue [7] and it has been thoroughly investigated in order to better understand the phenomenon. [8] In the last two decades, more attention has been devoted to the synthesis of magnetic systems having reduced dimensionality. Beside the curiosity-driven research, several reasons have motivated these works. Low-dimensional systems represent interesting models to help rationalizing the magnetic properties of non-stoichiometric PBA. In contrast with PBA, they can also be soluble, although the stability of polymetallic species is rarely investigated. Low-dimensional systems can also show original physical properties. One possible synthetic strategy consists in using partially-blocked cyanide building block of the general formula [M(L)(CN) x ] n-(where L is a ancillary ligand) instead of hexacyanometallate during the self-assembly process. For example, we first showed that by using the known [Fe(L)(CN) 4 ] - complex toward cobalt aqua-complexes (L= 2,2'-bipyridine or 1,10-phenanthroline), we could obtain magnetic one-dimensional chain compounds. [ 9 ] We later designed new pyrazolylborate-based [Fe( R Tp)(CN) 3 ] -cyanide building block (Tp is a tris-(pyrazolyl)borate anion), which shows reduced coordination ability with only three cyanide ligands oriented in facial geometry.

[10] These precursors were largely used and led to many low-dimensional compounds showing interesting properties. [11] Although the intrinsic anisotropy of the magnetic properties of the building block is not underlined in these works, these precursors were proven successful to design slow relaxation systems. [12] In fact, from a magnetic point of view, these Fe III low-spin complexes are remarkably anisotropic because of the first order spin-orbit coupling contribution in the d 5 low-spin configuration. [13] The versatility of the pyrazolyl ligand, which allows adjusting the electronic properties of the complexes was also useful in designing FeCo switchable compounds [ 14 ][ 15 ] and multifunctional systems.

[ 16 ] The search for new kinds of cyanide-based coordination assemblies is also interesting from a pure fundamental reason, and it has motivated us to look for new synthetic approaches. By using oxo-bridged polymetallic reactants toward the [Fe(Tp)(CN) 3 ] - building block, we obtained for example the largest cyanide-based coordination cluster containing sixty Fe metal ions. [17] More recently, our interest has been devoted to the design of molecular models of the PBA.

In particular, we have focused our attention on the synthesis of cyanide-bridged octametallic cages A{Fe 4 Co 4 } containing an inserted alkali ion, A. [ 18 ] These boxes are obtained by reacting the fac-

[Fe(Tp)(CN) 3 ] -building block with fac-[Co( pz Tp)(H 2 O) 3 ] 2+
in presence of a templating alkali cation. They represent interesting molecular models which allow in depth studying the influence of the alkali ion on the electronic properties of the box, particularly on the photomagnetic effect. One of their specificities is to show a remarkable stability in organic solvent, even under boiling conditions. In this context, we started exploring if these cages could be obtained with other metal ions and with other blocking ligand. In this paper we report a new {Fe 4 Ni 4 } neutral cage containing an encapsulated Cs + ion. The R Tp ligand we used here is a new heteroscorpionate, [START_REF] Scorpionates | The coordination chemistry of polypyrazolylborate ligands, S. Trofimenko[END_REF] with the R group being N(Me) 2 . We thus describe in this work, the synthesis of the new ligand, the Cs{Fe 4 Ni 4 } cage, its structure, and its solution and solid-state studies, which allowed us to probe the electronic properties of the cage and its stability in solution.

Experimental

General methods

FT-IR spectra were collected in the 200-4000 cm -1 range. Measurements were carried out on a Vertex 70

Brüker instrument using the attenuated total reflection (ATR) technique on solid samples (with a 4 cm -1 resolution). The intensity of the absorption band is indicated as w (weak), m (medium), s (strong), vs (very strong), and br (broad).

NMR spectra were recorded on a Bruker Avance 400 spectrometer. The chemical shifts, δ, are expressed in parts per millions (ppm) and are referenced using IUPAC recommendations. All the measurements of the paramagnetic sample were carried out after thermal stabilization.

Mass spectrometric analyses (ESI mode MS mode) were performed on a micro-TOF Bruker mass spectrometer. The Cs-cube was measured in dichloromethane by direct infusion with the ESI-source set at 180°C and a capillary voltage set at 4500 V.

Elemental analyses (C, H, N) were carried out by combustion analysis using a vario MICRO cube apparatus from Elementar.

DC and AC Magnetic susceptibility measurements were carried out using respectively a Quantum Design MPMS-XL7 magnetometer and a PPMS-9 susceptometer. The DC measurements were performed in the temperature range 2 -300 K under a 0.2 T magnetic field. A lower field of 0.05 T was also used in the low temperature range (2 -40 K) to avoid saturation effect. A fresh sample of the Cs-cube was filtered from the mother solution and wrapped in a PVC film just before its introduction into the MPMS at 120 K under helium flow. It was frozen in the magnetometer before purging under vacuum in order to prevent the evaporation of the crystallized solvent molecules. The DC magnetic susceptibility values were corrected from the diamagnetism of the molecular constituents and of the sample holder. The AC measurements were carried out on a sample prepared in the same manner as that described above. The measurements were taken at 3 K at different static magnetic fields, from 0 to 4999 Oe. The AC amplitude was set to 10 Oe and the frequency range varied from 10 to 9900 Hz. No ac susceptibility signals were observed.

Cyclic voltammetry measurements were carried out at room temperature in a standard cell equipped with a platinum wire counter electrode, a calomel reference electrode (ECS) and a glassy-carbon working electrode using an AUTOLAB PGSTAT 100 electrochemical analyser. The measurements were performed in dichloromethane with 0.1 M [Bu 4 N][PF 6 ] as the supporting electrolyte at scan rates of 100 mV s -1 . The redox potentials were determined by using ferrocene/ferrocenium couple (Fc/Fc + ) as an internal reference.

Syntheses

Synthesis of NMe2

Tp dimethylamino-tris(pyrazolyl)borate. In a three-necked round bottom flask, sodium pyrazolate, NaPz (0.7 g, 7.7 mmol) and pyrazolyl, HPz (1.04 g, 15 mmol) were dissolved under argon in 10 mL of dried THF. To this solution, 1.35 mL of tris(dimethylamino)borane, B(N(Me) 2 ) 3 (7.7 mmol) and 10 mL of toluene were added. The reaction mixture was refluxed for 24 h. After cooling the reaction mixture to room temperature, a white precipitate was filtered and washed with 10 mL of dried hexane, affording 1.4 g of white powder. The compound was stored in argon. Yield: 65%

X-ray crystallography

Red prismatic crystals of complex 1 suitable for X-ray diffraction studies were grown by diffusion of hexane into a solution of 1 in dichloromethane at room temperature. A single crystal was selected, mounted and transferred into a cold nitrogen gas stream. Intensity data was collected with a Bruker Kappa-APEX2 system using fine-focus sealed tube Mo-Kα radiation. Unit-cell parameters determination, data collection strategy, integration and absorption correction were carried out with the Bruker APEX2 suite of programs. The structure was solved with SHELXT-2014 and refined anisotropically by full-matrix least-squares methods with SHELXL-2014 using the WinGX suite. The structure contains a lot of disorder. The counter-anion to the caesium ion is missing. Other analyses identified it as being a tetrafluoroborate but it couldn't be located on the fourier difference map. It is believed to be somewhere between the cube and the channels of disordered solvent (vide infra) but disordered on too many positions. The cubes are statistically disordered with iron and cobalt atoms roughly occupying the same positions within the structure. Several atoms of the trispyrazolylborate ligands are located on average positions between two or more possible conformations. As a result, some of these atoms seem to be much too close from one another, most notably C3 to C11A, C3 to C11B, C16 to C17 and C16 to C18. The caesium atom is not effectively located at the center of the cube, which explains the remaining electron density calculated on its position. The structure also contains very large channels of severely disordered and partially evaporated molecules of dimethylformamide and/or diethylether, which couldn't be properly located. PLATON-SQUEEZE was instead used for the final refinement cycle to further refine the structure while accounting for the corresponding unassigned electron density. The structure was deposited at the Cambridge Crystallographic Data Centre with number CCDC 1588704 and can be obtained free of charge via www.ccdc.cam.ac.uk.

R1 = Σ(|Fo| -|Fc|)/Σ|Fo| ; wR2 = [Σw(Fo 2 -Fc 2 ) 2 /Σw(Fo 2 ) 2 ] 1/2 b S = [Σw(|Fo| -|Fc|) 2 /(No-Np)] 1/2

Results and discussion

Structure

Despite our efforts, the crystallographic data obtained on single crystals of 1 are of limited quality. However they allow the confirmation of other analytical data obtained by mass spectrometry, elemental analysis, FT- crystallizes in the P2 1 /n monoclinic space group. The octametallic complex exhibits a cubic core made of M-CN-M' edges and trispyrazolyl-borate ancillary ligands occupying the eight corners (Figure 1). A caesium alkali ion occupies the centre of the {Fe 4 Ni 4 } box.

The compound 1 is thus similar to the Cs{Fe II 4 Co III 3 Co II } cube that was recently reported. [18] The asymmetric unit is made of a cube edge, where one metal has a occupancy of 1 and the other 1/3. The Fe and Ni metal ions, and the Tp and NMe2 Tp ancillary ligands are indiscernible. Thus the bond distances and angles are averaged values and cannot be analysed in detail. However, the Fe-CN-Ni bond length, ca. 5.11 Å, is as expected for a Fe III -CN-Ni II bridge. [21] The cubic molecules are quite well isolated from each other by the organic shell formed by the ligand and the shortest intermolecular M … M distance is ca. 11.6 Å.

1 H and 133 Cs NMR

The 1 H NMR spectrum of 1 was recorded in CD 2 Cl 2 . It shows various strongly shifted signals that account for the paramagnetic nature of the molecule (Figure 2). At 300 K, the 1 H signals spread in a large chemical shift range, from ca. + 58 to -55 ppm. Despite the presence of eight paramagnetic centres in the molecules, the peaks half-width remains moderate so that reliable peak integration can be obtained. Beside the residual solvent peaks, eight paramagnetic signals are expected when taking into account the cubic symmetry of the molecule: (i) 6 different proton signals integrating for 12 H each are assigned to the pyrazolyl protons of the two scorpionate ligands; (ii) one proton signal integrating for 4 H due to the BH groups of the four equivalent Tp ligands; (iii) one signal integrating for 24 H, assigned to the methyl groups of the four equivalent NMe2 Tp ligands. The peak intensity allows the unambiguous assignment of the BH at + 40.0 ppm and the methyl groups at +1.5 ppm. The peak of the Tp ligand can be identified by comparing the 1 H spectrum of 1 to that of the PPh 4 [Fe III (Tp)(CN) 3 ] [22] or NBu 4 [Fe III (Tp)(CN) 3 ] precursors obtained in the same solvent at the same temperature (see Figure S1). As the BH signal is very similar in both cases (+40 ppm in 1 and +42 ppm in the precursor), we assumed that the 1 H pyrazolyl signals were not significantly affected by the coordination to the Ni(II). In fact, three proton signals very similar to those of the PPh 4 [Fe III (Tp)(CN) 3 ] precursor are found at -12.8 , -15.7 and -54.7 ppm. The broadest signal at -54.7 can be assigned to the proton Ha, which is located close to the metal ion (Fe … Ha < 4 Å). In fact, the proton signals located close to the metal paramagnetic source are broadened because of the larger contribution of the electron-nuclei dipolar interaction. This interaction lead to a faster magnetic relaxation and a broadening of the NMR signals. [START_REF]Solution NMR of paramagnetic molecules[END_REF] The other two signals, Hb (-15.7 ppm) and Hc (-12.8 ppm) were assigned by comparison with those found in the PPh 4 [Fe(Tp)(CN) 3 ] precursor. The three remaining strongly shifted signals integrating for 12H each, were thus assigned to the three pyrazolyl protons of the four equivalent NMe2 Tp ligands coordinated to the Ni(II) ions. Because of the larger half-width of the signal located at +32.8 ppm, it is reasonable to assign this signal to the proton located close to the Ni paramagnetic source, Ha'. The other two signals at +57.8 and +49.4 ppm are assigned to Hb' and Hc'. Finally, it is worth noticing that the 1 H NMR of 1 does not show any other paramagnetic or diamagnetic signals (expect those of the residual solvent molecules). This accounts for the purity of the sample and the robustness of the cubic cage in organic solvent.

The 133 Cs spectrum of 1 was also recorded at 300 K in CD 2 Cl 2 (Figure 2, inset). Although 133 Cs has a quadrupolar nucleus, its quadrupole moment is very weak and its receptivity is good so that well-resolved thin signal can be obtained in solution. [START_REF] Harris | [END_REF] In the present case, only one thin 133 Cs signal is observed, which is consistent with the presence of only one caesium site in a cubic surrounding. The 133 Cs signal is remarkably shifted to up-field at -780 ppm, far away from the diamagnetic range (vs. CsNO 3 ;  in D 2 O). This accounts for an efficient electronic communication between the paramagnetic sources and the inserted alkali ion. The observed chemical shift can be compared with two reference compounds. The measured value (-780 ppm) is smaller than that observed in the three-dimensional CsNi II [Co III (CN) 6 ] Prussian blue analogue (-946 ppm at 298 K), [25] where each caesium ion is located inside a cubic cage formed by four paramagnetic Ni(II) ions and four diamagnetic Co(III) ions, and it is larger than that observed in the Cs{Fe II 4 Co III 3 Co II } molecular cage (-236 ppm at 300 K) [18] where only one paramagnetic high-spin

Co II ion is present. The observed paramagnetic chemical shift consists of two contributions,  para =  dip +  con : (i)  dip is the dipolar contribution due to the through space electron-nucleus dipolar magnetic interaction;

(ii)  con is a contact term due to the spin delocalization onto the observed nucleus. As mentioned in the two reference works, the dipolar contribution is expected to be positive or negligible. The negative experimental chemical shift can thus only be explained by a negative contact contribution. This implies some spin transfer from the paramagnetic sources to the central Cs atom, either directly from the metal frontiers orbitals to the caesium, [25] or indirectly through the interaction of the Cs + ion with the CN ligands. [18]

Cyclic voltammetry

The cyclic-voltamogramm of 1 (Figure 3) has been recorded in CH 2 Cl 2 (see details in the experimental section). It shows four quasi-reversible redox waves corresponding to the successive reduction of the Fe III ions:

[Fe III 4 Ni II 4 ]/[Fe III 3 Fe II Ni 4 ] -, E°1 /2 = -0.36 V; [Fe III 3 Fe II Ni II 4 ] -/[Fe III 2 Fe II 2 Ni II 4 ] 2-, E°1 /2 = -0.47 V; [Fe III 2 Fe II 2 Ni II 4 ] 2-/[Fe III Fe II 3 Ni II 4 ] 3-, E°1 /2 = -0.65 V; [Fe III Fe II 3 Ni II 4 ] 3-/[Fe II 4 Ni II 4 ]
4-, E°1 /2 = -0.86 V (versus ferrocene, Fc). As expected, the first redox potential at -0.36 V is significantly higher compared to that of the precursor [Fe III (Tp)(CN) 3 ] -(E°1 /2 = -0.89 V, vs Fc). [26] This is consistent with the coordination of Lewis acids (the Ni(II) ions) on the nitrogen of the cyanide ligands. The donation from the nitrogen to the Ni(II) ions reduces the electronic density of the whole {Fe(Tp)(CN) 3 } subunit and makes the Fe II/III oxidation more difficult. The effect decreases on the second, third and fourth reduction waves as the cage becomes more and more negatively charged. In fact, the last reduction wave is found at about the same potential as that of the free [Fe(Tp)(CN) 3 ] -complex. It is interesting to compare this effect with that observed in related {Fe 4 M 4 } cages containing similar ancillary scorpionate ligands with other metal ions coordinated on the nitrogen cyanide atoms. The shift of the potential of the {Fe II/III (Tp)(CN) 3 } redox potential to higher values is much more important in the {Fe III 4 Fe II 4 } cages reported by Oshio et coll.. [ 27 ] In that case the nitrogen is coordinated to the very acidic Fe III ions and the redox waves are located approximately 1.4 V above those found in our {Fe 4 Ni 4 } cage. The effect is similar in our recently reported Cs{Fe 4 Co 4 } cage. [18] The redox potentials are shifted by ca 1.15 V in comparison to 1. In these last cases, the potential of the {Fe II/III (Tp)(CN) 3 } units in the cage become high compare to that of the coordinated neighbour (initially Fe II and Co II ion) and an electron transfer occurs during the synthesis between the neighbour metal ions.

It is also interesting to compare the differences between the four successive Fe II /Fe III redox waves in these cubes. These shifts account for an efficient electronic communication between the four iron ions in the {Fe 4 Ni 4 } cage. The interaction can be quantified by the comproportionation constants, K c , which reflects the relative stability of the mixed valence states with respect to its (monovalent) reduced and oxidation forms.

The comproportionation constant is calculated through the expression K c = exp(FE/RT), where E is the difference between successive oxidation waves. E values of 0.23, 0.25 and 0.24 V for the four redox waves yield to K c of 7.3 x 10 3 , 1.5 x 10 4 and 1.0 x 10 4 . These values are in the expected range for mixedvalence Class II compounds. [28] Here it is worth noticing that this interaction takes place between second neighbours through the -CN-Ni-NC-bridge. The obtained values are about 10 times bigger than those found in the above mentioned {Fe 4 Fe 4 }, [27] {Fe 4 Co 4 }, [18] molecular cubes, thus suggesting a larger communication between the iron ions in 1.

It is worth underlining here that both NMR and electrochemistry studies account for the stability of the cube in solution. These results are also coherent with the mass spectrometry experiment, which shows a molecular peak corresponding to {Li,1} + at 2871.45 g/mol. The simulated isotopic distribution is perfectly coherent with the experimental one as shown in the Figure 4.

Magnetic properties

The magnetic properties of a polycrystalline sample of 1 have been investigated in the temperature range of 2-300 K. The  M T versus T plots of 1 is shown in Figure 5 ( M being the molar magnetic susceptibility per {Fe III 4 Ni II 4 } unit). The values of the  M T product at room temperature (7.9 cm 3 K mol -1 ) is in agreement with the expected value considering the following set of uncoupled spin carriers: four low-spin iron(III) ions exhibiting magnetic orbital contribution (ca.  M T ≈ 0.5-0.8 cm 3 K mol -1 , with g av ≈ 2.6) and four nickel(II) ions (ca.  M T ≈ 1.1 cm 3 K mol -1 with g ≈ 2.1).

[10][29] Upon cooling, the  M T value decreases smoothly down to ca. 125 K, where  M T value reaches 7.3 cm 3 K mol -1 . This smooth decrease is ascribed to the spinorbit coupling effect of the four Fe III low-spin ions. Below 125 K, the  M T value increases rapidly, reaching a maximum at 5 K of 16.5 cm 3 K mol -1 . Then a slight decrease is observed due to the combined effects of the magnetic ground state anisotropy and the intermolecular interaction. The strong increase is in agreement with an intramolecular ferromagnetic interaction. This is as expected for a Fe-CN-Ni moieties where the magnetic orbitals on both metal ions (t 2g and e g , respectively) are orthogonal [START_REF]Molecular Magnetism[END_REF] as previously observed in other cyanide bridged FeNi complexes.

[29] The isothermal magnetization of 1 versus magnetic field (Figure S2)

shows that the magnetic moment tend to saturate with increasing of the magnetic field and reaches the value of 11.8 μ B at 7 T, indicating a ground spin state of S = 6 for 1, which is in agreement with a ferromagnetic interaction. In order to evaluate the overall coupling constant of the ferromagnetic interactions through the cyanide bridge, the following spin Hamiltonian (eq. 1) has been used to fit the experimental  M T data in the temperature range of 30 K -300 K by using a free software, Phi. where J iso is the isotropic coupling constant between the low-spin Fe III and the Ni II ions, S Fek is the spin operator for low spin Fe III (S Fek = ½, k = 1 -4) and S Nik , the spin operator for Ni II (S Nik = 1, k = 1 -4), g Ni and g Fe , are the Landé factors of the Ni II and Fe III ions respectively, β is the Bohr magneton, and H is the applied magnetic field. The best fit gives: J iso = 4.95 cm -1 , g Ni = 2.0 and g Fe = 2.2. The two later values are obviously too low compared to the expected g Ni and g Fe values (see above). However, although the simplified spin hamiltonian under-estimate the Landé factors of the metal ions, it allows a fair estimation of the average ferromagnetic coupling constant, J iso . Here, the J iso value obtained is reasonable and is of the same magnitude as that reported in the literature for Fe III -Ni II ferromagnetic couplings through the cyanide linker. [21][32] Finally ac susceptibility measurements were carried out at a low temperature in order to probe the occurrence of slow magnetic relaxation in the S = 6 ground spin-state. Although both low-spin Fe III ion and Ni II ion show magnetic anisotropy in distorted octahedral geometry, no out-of-phase signal was detected (at zero magnetic field and under the application of small dc field). The absence of slow magnetic relaxation in 1 is coherent with the high symmetry of the octametallic complex.

Conclusion

In the present work, we showed that the synthetic approach that we recently used to prepare FeCo switchable states. Moreover the 133 Cs NMR shows that a noticeable amount of spin density is transferred from the paramagnetic centres to the inserted caesium ion. This brings an experimental proof of the occurrence of a through-bond electronic interaction between the inserted caesium and the paramagnetic box. This study also reveals an efficient electronic interaction between the second neighbour iron ions. Additionally, the electronic interaction trough the cyanide bridge between the first neighbour is revealed by the occurrence of a ferromagnetic superexchange interaction between the Fe(III) and Ni(II) ions, which leads to a S=6 ground spin state. The absence of slow magnetic relaxation despite the presence of anisotropic paramagnetic ions is likely due to the high symmetry of the molecule. Our synthetic efforts are now focusing on the design of new

  [1] Many Prussian blue analogues can be obtained by simply reacting hexacyanometallate with hexaaqua complexes. The resulting insoluble Prussian blue analogues (PBA) of general formula A x M' 4 [M(CN) 6 ] (8+x)/3 [] (4-x)/3 . nH 2 O (A is an alkali cation, M and M' are six coordinated transition metal ions, [] represents a [M(CN) 6 ] vacancy) are non-stoichiometric

)

  Hβ eq. 1

  cubic cages containing tris(pyrazolyl)borate ancillary ligands and an inserted alkali ion can be extended to the use of other metal ions or other functionalized scorpionate ligands. The new Cs{Fe 4 Ni 4 } cationic cage can be obtained in single crystals in good yield. As for the parent Cs{Fe 4 Co 4 } cube, it is soluble and stable in organic solvent as demonstrated by the NMR and electrochemistry studies. The cyclo-voltammetry study also shows the remarkable redox flexibility of the Cs{Fe 4 Ni 4 } cage, which shows five accessible redox

Table 1 .

 1 Crystallographic data and structure refinement for 1.

	Empirical formula	C 101 H 117 B 8 Cs Fe 4 N 67 Ni 4 O 3 ,
	Formula weight
	Temperature	130(1) K
	Wavelength 0	0.71073 Å
	Crystal system	trigonal
	Space group	R -3
	Unit cell dimensions	a = b = 20.4574(15) Å
		c = 39.943(3) Å,
		α = β = 90°,
		γ = 120°
	Volume	V = 14477(2) Å 3
	Z	3
	Absorption coefficient	0.910 mm -1 ,
	min / max transmission	0.64 / 0.86
	Theta range for data collection	1.26° to 26.54°,
	Reflections collected	57632
	Independent reflections	6634, (R int = 0.051)
	Observed reflections [I>2σ(I)]	6634
	completeness	0.988
	restraints / parameters,	140 / 354
	a Final R indices [I > 2σ(I)]	R1 = 0.1228, wR2 = 0.4259 (all data)
	b Goodness-of-fit on F2	1.606
	Largest diff. peak and hole	5.16 / -0.92 e.Å -3
	a

Acknowledgements

We are gratefull to the CNRS, le ministère de l'enseignement et de la recherche and the Agence Nationale de la Recherche (ANR-JST program, MoMa project, ANR-14-JTIC-0001), and the National Science Foundation (CHE-1659782).

Supplementary materials

The structure was deposited at the Cambridge Crystallographic Data Centre with number CCDC 1588704.

Copy of this information may be obtained free of charge on application to CCDC, 12 Union Road, Cambridge CB2 1EZ, UK (Fax: +44 1223 336 033; E-mail: deposit@ccdc.cam.ac.uk or www: http://www.ccdc.cam.ac.uk). Supplementary data associated with this article: 1 H NMR spectra of NBu 4 [Fe(Tp)(CN) 3 ] in CD 2 Cl 2 at 300 K (figure S1) ; Curve of the magnetization versus applied magnetic field (H) for 1 at 2 K (figure S2)


Nicolas Dubouis

Alessandra Serva

Elodie Salager

Michael Deschamps

Mathieu Salanne
email: mathieu.salanne@sorbonne-universite.fr

Alexis Grimaud
email: alexis.grimaud@college-de-france.fr

The fate of water at the electrochemical interfaces: electrochemical behavior of free water vs. coordinating water.

ABSTRACT:

The water reduction which produces hydrogen is one key reaction for electrochemical energy storage. While it has been widely studied in traditional aqueous electrolytes for water splitting (electrolyzers), it also plays an important role for batteries. Indeed, the reduction of water at relatively high potential prevents the practical realization of high-voltage aqueous batteries, while water contamination is detrimental for organic batteries electrolytes. Nevertheless, recent studies pointed towards the positive effect of traces of water for Li-air batteries as well as for the formation of solid-electrolyte-interphase. Herein, we provide a detailed understanding of the role of the solvation on water reduction reaction in organic electrolytes.

Using electrochemistry, classical molecular dynamics simulations and nuclear magnetic resonance spectroscopy, we were able to demonstrate that 1) the hydrophilicity/hydrophobicity of the species inside the electrochemical double-layer directly controls the reduction of water and 2) water coordinating strong Lewis acids such as Li + cations is more reactive than "free" water (or non-coordinating) water molecules.

Table of Content

Introduction

The influence of traces of water in organic electrolytes for Li-ion batteries (LIBs) electrochemistry has been a subject of interest since their commercialization in the 90s'.

Indeed, its presence is detrimental for the stability of the electrode materials and of the electrolytes and degrade the cycling performances of the system owing to its influence on the formation and the nature of the solid-electrolyte-interphase (SEI). [START_REF] Aurbach | The Electrochemical Behavior of Lithium Salt Solutions of γ-Butyrolactone with Noble Metal Electrodes[END_REF][START_REF] Aurbach | The Electrochemistry of Noble Metal Electrodes in Aprotic Organic Solvents Containing Lithium Salts[END_REF][START_REF] Aurbach | The Correlation Between the Surface Chemistry and the Performance of Li-Carbon Intercalation Anodes for Rechargeable "Rocking-Chair" Type Batteries[END_REF][START_REF] Aurbach | X-Ray Photoelectron Spectroscopy Studies of Lithium Surfaces Prepared in Several Important Electrolyte Solutions. A Comparison with Previous Studies by Fourier Transform Infrared Spectroscopy[END_REF][START_REF] Xu | Electrolytes and Interphases in Li-Ion Batteries and Beyond[END_REF] With the goal of improving the performances of LIBs, most of studies were often focusing on the practical impact of water added into Li-containing electrolytes. Nevertheless, a regain of interest was recently observed as water traces in organic electrolytes were found to promote the performances for other battery chemistries, especially the oxygen redox chemistry which is at the heart of the lithium-air batteries, [START_REF] Meini | The Effect of Water on the Discharge Capacity of a Non-Catalyzed Carbon Cathode for Li-O2 Batteries[END_REF][START_REF] Aetukuri | Solvating Additives Drive Solution-Mediated Electrochemistry and Enhance Toroid Growth in Non-Aqueous Li-O 2 Batteries[END_REF][START_REF] Staszak-Jirkovský | Water as a Promoter and Catalyst for Dioxygen Electrochemistry in Aqueous and Organic Media[END_REF][START_REF] Liu | Cycling Li-O2 Batteries via LiOH Formation and Decomposition[END_REF][START_REF] Aurbach | Advances in Understanding Mechanisms Underpinning Lithium-air Batteries[END_REF][START_REF] Liu | The Effect of Water on Quinone Redox Mediators in Nonaqueous Li-O2 Batteries[END_REF] and the solvation properties of divalent cations such as Mg-ion. More recently, novel classes of safe superconcentrated aqueous or hybrid aqueous/non-aqueous electrolytes were proposed, highlighting that water redox activity would drastically be governed by its solvation (free water vs. cation-coordinating water). [START_REF] Suo | Water-in-Salt" Electrolyte Enables High-Voltage Aqueous Lithium-Ion Chemistries[END_REF][START_REF] Suo | Advanced High-Voltage Aqueous Lithium-Ion Battery Enabled by "Water-in-Bisalt[END_REF][START_REF] Yamada | Hydrate-Melt Electrolytes for High-Energy-Density Aqueous Batteries[END_REF][START_REF] Leonard | Water-in-Salt Electrolyte for Potassium-Ion Batteries[END_REF][START_REF] Wang | Hybrid Aqueous/Non-Aqueous Electrolyte for Safe and High-Energy Li-Ion Batteries[END_REF] Thus, playing on water solvation appears as a promising strategy to tune its reactivity and help the design of new battery chemistries.

As the standard redox potential for water oxidation (OER:

H 2 O = ½ O 2 + 2 H + + 2 e -)
is relatively high and the reaction suffers from sluggish kinetics, it makes this reaction unlikely to occur at potential at which positive electrodes are working. In contrast, most efforts have been placed on the other half reaction of water electrolysis, namely the hydrogen evolution reaction (HER: H 2 O + e -= ½ H 2 + OH -), which occurs 1.23 V lower than water oxidation and shows a relatively fast kinetics, therefore making this reaction more likely to take place during batteries operation. The HER was largely studied in aqueous media, and its mechanism was shown to be drastically dependent on weak interactions that are controlled by the nature of the electrode, the pH, the applied potential or the electrolyte composition. [START_REF] Subbaraman | Enhancing Hydrogen Evolution Activity in Water Splitting by Tailoring Li + -Ni(OH) 2 -Pt Interfaces[END_REF][START_REF] Strmcnik | Improving the Hydrogen Oxidation Reaction Rate by Promotion of Hydroxyl Adsorption[END_REF][START_REF] Ledezma-Yanez | Interfacial Water Reorganization as a pH-Dependent Descriptor of the Hydrogen Evolution Rate on Platinum Electrodes[END_REF][START_REF] Dubouis | Interfacial Interactions as an Electrochemical Tool To Understand Mo-Based Catalysts for the Hydrogen Evolution Reaction[END_REF] However, the precise role played by the solvation of water at the electrochemical interface is difficult to assess experimentally owing to the dual role played by water as reactant and as solvent. To alleviate this complexity, few studies were thus carried out in organic electrolytes and pointed towards the importance of the cation on the water reduction reaction. [START_REF] Suárez-Herrera | Voltammetry of Basal Plane Platinum Electrodes in Acetonitrile Electrolytes: Effect of the Presence of Water[END_REF][START_REF] Ledezma-Yanez | Hydrogen Oxidation and Hydrogen Evolution on a Platinum Electrode in Acetonitrile[END_REF][START_REF] Ledezma-Yanez | Influence of Water on the Hydrogen Evolution Reaction on a Gold Electrode in Acetonitrile Solution[END_REF] Intrigued by the critical role played by water solvation on its redox activity, we decided to study, in this work, the relative reactivity of free water molecules when compared to coordinating water molecules. For that, we re-investigated the redox activity of water in organic solvents. Indeed, this strategy allows to 1) tune the solvation properties of water by modifying the nature of the cation and 2) modulate the cation-water association by the use of a cation chelating agent and therefore control the relative proportion of "free" vs. coordinating water molecules. Combining electrochemical measurements with classical molecular dynamics (MD) simulations and nuclear magnetic resonance (NMR) spectroscopy, we demonstrate that the solvation strength of water molecules in the bulk of the electrolyte is largely correlated to its presence at the electrochemical interface. As a result, we could highlight that the free water molecules are less reactive than the coordinating ones at a negatively polarized electrode. This finding opens new avenues for tuning the redox activity of water in organic solvents to either develop moisture sensitive organic systems or aqueous batteries with enhanced performances.

Influence of the supporting cation on water reduction. Prior to discuss the effect of solvation structure on the water reduction, it is worth mentioning that two mechanisms exist for the HER. Indeed, in dry ACN with 10 mM HClO 4 a first peak is observed at around 0 V vs. SHE, similarly to what is measured in water with 10 mM HClO 4 (Figure 1). This first peak therefore involves the reduction of protons. By adding H 2 O into ACN, a second reduction event is seen starting at a more negative potential at around -0.75 V vs. SHE. This second event, that occurs at a similar potential than what is measured in water-based electrolyte, is associated with the splitting of water molecules and is characterized by a greater overpotential as a result of the energy penalty required to break O-H bonds from water. [START_REF] Strmcnik | Improving the Hydrogen Oxidation Reaction Rate by Promotion of Hydroxyl Adsorption[END_REF][START_REF] Dubouis | Interfacial Interactions as an Electrochemical Tool To Understand Mo-Based Catalysts for the Hydrogen Evolution Reaction[END_REF] These two mechanisms are therefore ubiquitous and coexist in aqueous electrolytes for pH > 2, [START_REF] Strmcnik | Improving the Hydrogen Oxidation Reaction Rate by Promotion of Hydroxyl Adsorption[END_REF][START_REF] Dubouis | Interfacial Interactions as an Electrochemical Tool To Understand Mo-Based Catalysts for the Hydrogen Evolution Reaction[END_REF] as well as in organic electrolytes as shown Figure 1, with the difference that a peak which intensity depends on the amount of H 2 O is visible in organic electrolytes due to the limited concentration of water when compared to aqueous solution and/or the precipitation of a passivation layer. (see discussion below) Finally, we can conclude that in the absence of protons, water reduction is expected to take place well below 0 V vs. RHE in organic electrolytes, independently of the solvation structure and the nature of the cation. We then investigated the effect of cation hydrophilicity on the reduction of water in acetonitrile in the presence of 10,000 ppm (~ 400 mM) of water (Figure 2). Interestingly, three different electrochemical behaviors can be distinguished. While almost no cathodic current was observed with tetrabutylammonium (TBA + ) cations (orange), a large cathodic current was measured with Li + (purple) and Na + (green) cations. Comparing these results with dry electrolytes for which no cathodic current is measured (Figure S1) and with the result obtained in aqueous electrolyte where a reduction event is measured in a similar potential range (< -0.75 V vs. NHE) (Figure 1), this cathodic current can be attributed to water reduction: H 2 O + e -= ½ H 2 + OH -. Second, the shape for the reduction current was found dependent on the cation. Hence, a reduction wave is observed for Na + while a reduction peak is seen for Li + cations. This difference is explained by the formation of a passivation layer (the so-called solid electrolyte interphase SEI). This passivation layer could result from the reaction of Li Intrigued by this difference of reactivity for water upon reductive conditions, the solvation structure for water molecules was analyzed for the different supporting salts by classical MD simulations. To shed light on the cations first solvation shell, the radial distribution functions (RDFs) between the cations and the oxygen atom of water molecules were then calculated (Figure 3a). Li + and Na + cations have a stable first solvation shell (very sharp first peak in the RDFs), while only a broad low intensity peak at long distances is observed for the TBA + cation. In particular, the Li-O water and Na-O water first shell distances obtained in this work are 2.06 Å and 2.38 Å, respectively, consistent with those previously reported in the literature for aqueous solutions. [START_REF] Newsome | Lithium Ions in Aqueous Solution[END_REF][START_REF] Cartailler | Lithium Bromide in Acetonitrile and Water: A Neutron Scattering Study[END_REF][START_REF] Mähler | A Study of the Hydration of the Alkali Metal Ions in Aqueous Solution[END_REF] A good agreement was also found for Cation-N ACN as shown in Figure S2. [START_REF] Cartailler | Lithium Bromide in Acetonitrile and Water: A Neutron Scattering Study[END_REF][START_REF] Spångberg | The Solvation of Li+ and Na+ in Acetonitrile from Ab Initio-Derived Many-Body Ion-solvent Potentials[END_REF] The number of water molecules in the first solvation shell of the cation is rather large (about 2.7) for Li + , it slightly decreases for Na + and finally goes almost to zero for TBA + cation, which shows the possibility of accommodating a larger number of organic solvent molecules in its solvation shell (see Figure 3b). The direct consequence is that the percentage of "free" water molecules rapidly increases moving from

Li + to Na + and finally to TBA + cation, as shown in Figure 3c. The different complexing ability of the three cations with water thus reveals a different hydrophilic character following Li + > Na + > TBA + . The marked passage from hydrophilic Li + cation to hydrophobic TBA + cation is also confirmed by the evaluation of the cation-water cage lifetime (Figure 3c and Figure S3), that indeed is one order of magnitude larger for Li + and Na + than for TBA + , suggesting a reduced (almost zero) cation-H 2 O affinity for the TBA + cation. To experimentally assess these different interactions of water with the aforementioned cations, 1 H nuclear magnetic spectroscopy (NMR) was employed (Figure 3d). The Li + > Na + > TBA + is in agreement with the predictions made by MD simulations (Figure 3c).

As a result, this spectroscopic study demonstrates that the lower electronic density observed around protons for solvated Li + cations is due to the strong Lewis acidity of Li + cations, which also suggests a greater Brønsted acidity for these protons due to electron withdrawing from the water molecule.

Having demonstrated the different hydrophilicity for the cations considered in this work, its impact on the water reduction reaction can then be rationalized. As the electrode is negatively polarized, cations are migrating with their solvation shells toward the negative electrode. In the presence of TBA + cations, the resulting double-layer is hydrophobic (as shown by the short lifetime of water molecules in its first solvation shell, Figure 3c) and water cannot access the surface of the electrode even though the concentration of free water is found greater than for Li + and Na + cations. This explains the absence of cathodic current associated with the reduction of water for TBA + (Figure 2). On the contrary, hydrophilic lithium and to lesser extent sodium cations migrate to the electrochemical interface together with their solvation shell comprised of water molecules, allowing water to be reduced. Furthermore, not only the nature of the cation dictates the presence of water at the electrochemical interface, but the cation affinity for water also modifies the onset potential for water reduction. Hence, the considerable difference in the onset potential for H 2 O reduction measured for Li + and Na + cations (~ 250 mV) in Figure 2 cannot fully be explained by the difference of water content or lifetime of water molecules in the cations solvation shell. Indeed, such a potential shift would result, applying the Nernst equation, in an interfacial concentration of water 4 orders of magnitude greater for lithium than for sodium, while MD simulations demonstrate that the ratio of water in the solvation shell of Li + and Na + cations is closer to 1.6:1 and the lifetime of water molecules in the solvation shell is not drastically modified (Figure 3c). Thus, this difference in onset potential is likely to originate from pure kinetics limitations. As the initial Volmer step (H 2 O + e -= H ads + OH -) is expected to be the rate determining step for water reduction in these experimental conditions, [START_REF] Strmcnik | Improving the Hydrogen Oxidation Reaction Rate by Promotion of Hydroxyl Adsorption[END_REF][START_REF] Suárez-Herrera | Voltammetry of Basal Plane Platinum Electrodes in Acetonitrile Electrolytes: Effect of the Presence of Water[END_REF][START_REF] Lutz | Role of Electrolyte Anions in the Na-O2 Battery: Implications for NaO2 Solvation and the Stability of the Sodium Solid Electrolyte Interphase in Glyme Ethers[END_REF] the electrochemical activity is going to be driven by its activation energy that, according to the linear free energy relationship approximation, must vary linearly with the difference of energy between the products states and the reactants states of this step. [START_REF] Gileadi | Physical Electrochemistry[END_REF] The greater electronic withdrawing interaction between

Li + cations and oxygen atom from H 2 O could thus be partly responsible for a weakening of the O-H bond of water molecules (destabilization of the reactants state), in agreement with the 1 H NMR results that show more acidic protons (Figure 3d). This effect would thus facilitate water reduction by lowering the transition state energy as a result of an easier proton adsorption and a stronger association of Li + with OH -produced during the HER (stabilization of the products state). As divalent cations such as Mg 2+ , which are more hydrophilic than monovalent ones, are used, this effect becomes even more important since the measured water reduction potential is less negative (Figure S4). Finally, we could show that the nature of the organic solvent on the double-layer formation and water reduction is weak. For that, ACN was replaced by a solvent with a greater dielectric constant, namely ethylene carbonate (EC) dissolved into dimethyl carbonate (DMC), and similar electrochemical observations were made with the presence of a reduction event starting at around -0.75 V vs. SHE with Li + while no reduction is observed with TBA + (Figure S5). This result confirms that organic solvent molecules play a minor role under negative polarization at the electrochemical interface when compared to the role played by cations. In other words, the concentration of water is always greater at the electrochemical interface than in the bulk of the electrolyte independently of the polarizability of the solvent.

"Free water" vs. cation-coordinating water. Having established that the use of hydrophilic cations such as Li + enables an easy reduction of water at the electrochemical interface under negative polarization, we then investigated the reactivity of "free" water molecules in organic solvent independently of the use of hydrophobic cation. For that, crown ether (12-Crown-4) was used as an additive to selectively "trap" Li + cations and therefore release water molecules from their solvation shell, thus making them "free". We first validated this strategy by studying the water solvation using [START_REF] Aetukuri | Solvating Additives Drive Solution-Mediated Electrochemistry and Enhance Toroid Growth in Non-Aqueous Li-O 2 Batteries[END_REF] Li and 1 H NMR (Figure 4a). As the crown ether/Li + ratio increases closer to 1, the chemical shift for [START_REF] Aetukuri | Solvating Additives Drive Solution-Mediated Electrochemistry and Enhance Toroid Growth in Non-Aqueous Li-O 2 Batteries[END_REF] Li was found to be downfield (higher chemical shift), indicating a change of the Li + solvation shell and its association with the crown ether molecules. [START_REF] Masiker | 7Li NMR Chemical Shift Titration and Theoretical DFT Calculation Studies: Solvent and Anion Effects on Second-Order Complexation of 12-Crown-4 and 1-Aza-12-Crown-4 with Lithium Cation in Several Aprotic Solvents[END_REF] The opposite trend was found for the 1 H signal from H 2 O for which the chemical shift undertakes an upfield, demonstrating a greater electronic density. From these observations, it can be concluded that "free" water molecules are released when adding 12-Crown-4 to the electrolyte following the reaction:

[Li(H 2 O) x ] + + crown -> [Li(Crown) 1 ] + + x H 2 O "free" .
The electrochemical behavior of these solutions was then studied, and a shift to more negative potentials as well as a decrease of the cathodic current were found with increasing 12-Crown-4 concentration (Figure 4b). Hence, we can conclude that "free" water molecules are more difficult to reduce than "coordinating" water molecules in organic media, as seen by the more negative potential required for their reduction. This finding is in agreement with the results discussed above for which water molecules strongly coordinating hydrophilic Lewis acid such as Li + cations were found to be reduced at lower onset potentials.

Furthermore, we can tentatively assign the decrease of the reduction peak intensity to a reduced concentration of "free" water molecules at the electrochemical interface when

Conclusions

Combining electrochemical and NMR spectroscopy measurements with molecular dynamics simulations, we could demonstrate that the ability of water to solvate cations dictates its electrochemical reduction. Indeed, upon negative polarization cations migrate to the electrochemical interface with their solvation shell. For hydrophilic cations such as Li + or Na + , water can thus be reduced while we could demonstrate that the use of hydrophobic cations such as large organic cations almost suppresses the water reduction. Not only the affinity of cation with water is critical, but a stronger Lewis acid cation such as Li + weakens the O-H bond of water molecules thus lowering the energy barrier required for the hydrogen evolution reaction. This effect is further exemplified when chelating Li + with crown ether molecules to release so-called "free" water molecules that, as we demonstrate, require a greater overpotential to be reduced than molecules participating to cation solvation shell.

Based on this conclusion, the use of highly concentrated Li + -based aqueous electrolytes would certainly not lead to an extension of the cathodic part of the electrochemical window of water, as it would instead increase the amount of coordinating water molecules with weakened O-H bonds present at the electrochemical interface. [START_REF] Vatamanu | Ramifications of Water-in-Salt Interfacial Structure at Charged Electrodes for Electrolyte Electrochemical Stability[END_REF][START_REF] Li | Capacitive Performance of Water-in-Salt Electrolyte in Supercapacitors: A Simulation Study[END_REF][START_REF] Mceldrew | Theory of the Double Layer in Water-in-Salt Electrolytes[END_REF] Rather, the use of hydrophobic ions and/or coating strategies 37 should be privileged for developing aqueous batteries with enhanced performances as it repulses water away from the electrochemical interface and thus prevents its reduction. However, water can be used as an additive in organic electrolytes as its reduction can trigger the formation of degradation products that can passivate the negative electrode. Alternatively, this understanding of the cationic influence on water reduction may also rationalize the detrimental role of water sometimes observed in metal plating experiments. Eventually, more remains to be done to understand both the kinetics and thermodynamics origin for such effect in order to implement this strategy into electrochemical energy storage devices.

Figure 1 .

 1 Figure 1. Cyclic voltammograms recorded at 50 mV.s -1 on a platinum electrode in electrolytes

Figure 2 .

 2 Figure 2. Cyclic voltammograms recorded over a Platinum electrode in acetonitrile

Figure 3 .

 3 Figure 3. Influence of the cation nature (Li + : purple, Na + : green and TBA + : orange) in

  compared to [Li(H 2 O) x ] + .

Figure 4 .

 4 Figure 4. Influence of the 12-Crown-4 concentration in 100 mM LiClO 4 in acetonitrile containing 10,000 ppm of water electrolytes on a) Li + (left) and H 2 O (right) NMR chemical

  + with OH -formed upon water reduction and the subsequent precipitation of LiOH (Li + + H 2 O + e -= ½ H 2 + LiOH (s) ), as previously observed in similar systems,[START_REF] Aurbach | The Electrochemistry of Noble Metal Electrodes in Aprotic Organic Solvents Containing Lithium Salts[END_REF][START_REF] Irr | Voltammetric Studies of Lithium Salt-Acetonitrile Solutions Containing Traces of Water[END_REF][START_REF] Dubouis | The Role of the Hydrogen Evolution Reaction in the Solid-electrolyte Interphase Formation Mechanism for "Water-in-Salt[END_REF] or from the possible reactivity of the organic solvent with OH -. In both case, NaOH or any other

Na-based product formed upon reduction is too soluble to passivate the electrode surface owing to the weaker affinity (weaker Lewis acidity) of Na + cations with hydroxile anions or other anions than Li + cations.

[START_REF] Irr | Voltammetric Studies of Lithium Salt-Acetonitrile Solutions Containing Traces of Water[END_REF][START_REF] Lutz | Role of Electrolyte Anions in the Na-O2 Battery: Implications for NaO2 Solvation and the Stability of the Sodium Solid Electrolyte Interphase in Glyme Ethers[END_REF]

Acknowledgments

Supporting information

Material and methods, molecular dynamics simulation methods, figures S1 to S5

Conflicts of Interest

The authors declare no conflict of interest.


teaching and research institutions in France or abroad, or from public or private research centers.

Diversity of fungal DyP-type peroxidases and their potential contribution to organic matter degradation


Nathalie Lorrain
email: nathalie.lorrain@univ-rennes1.fr

Parastesh Pirasteh

Pauline Girault

Paul Azuelos

Jonathan Lemaitre

Mohammed Guendouz

Isabelle Hardy

Monique Thual

Joël Charrier

J Lemaître

Submicron gap reduction of micro-resonator based on porous silica ridge waveguides manufactured by standard photolithographic process

Keywords: Micro-resonator, Porous silicon, Oxidation, Technological process, Gap reduction

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.

I. Introduction

Porous silicon (PS) is a material of which the optical properties have been widely studied for many applications [START_REF] Torres-Costa | Application of nanostructured porous silicon in the field of optics. A review[END_REF] such as optoelectronics [START_REF] Bisi | Porous silicon: a quantum sponge structure for silicon based optoelectronics[END_REF] and also, over the past decade, for chemical [START_REF] Dhanekar | Optical measurement of trace level water vapours using functionalized porous silicon: selectivity studies[END_REF][START_REF] Jalkanen | Optical gas sensing properties of thermally hydrocarbonized porous silicon Bragg reflectors[END_REF] and biological [START_REF] Chan | Porous silicon microcavities for biosensing applications[END_REF][START_REF] Dhanekar | Porous silicon biosensor: Current status[END_REF] sensing applications.

PS is easily fabricated by electrochemical etching of silicon [START_REF] Lehmann | On the morphology and the electrochemical formation mechanismof mesoporous silicon[END_REF]. The tunability of the porosity and of the thickness of PS layers, which depends on the fabrication parameters, allows optoelectronic components such as filters [START_REF] Lorenzo | Porous silicon-based rugate filters[END_REF][START_REF] Ilyas | Porous silicon based narrow line-width rugate filters[END_REF], Bragg grating [START_REF] Rea | A porous silicon-based Bragg grating waveguide sensor for chemical monitoring[END_REF] and optical waveguides [START_REF] Weiss | Porous Silicon Optical Waveguides[END_REF] to be developed.

The large internal surface of PS and its biocompatibility are significant advantages for biosensing applications [START_REF] Dhanekar | Porous silicon biosensor: Current status[END_REF]. Indeed, PS is a real potential host for various molecules which can either be in solution in the pores, or grafted onto the internal surface. However, as the surface of PS is strongly hydrophobic, thermal oxidation and chemical adaptation must be applied respectively to stabilize and functionalize the internal surface of the PS layer to obtain subsequent efficient molecules attachment [START_REF] Dhanekar | Porous silicon biosensor: Current status[END_REF]. In most of the cases, these molecules can be detected by a change in the refractive index of the PS, induced by their presence inside the pores. Indeed, the refractive index is a weighted average of the refractive indices of silicon, silica and of molecules present or grafted in the pores.

Integrated optical PS sensors using refractive index variations [START_REF] Weiss | Current status and outlook for silicon-based optical biosensors[END_REF] have already been the subject of several studies, the number of which continues to grow due to the interest of this porous material in order to increase the sensor sensitivity. Furthermore, PS sensors can be integrated on Photonic Integrated Circuits (PIC) which provide a route towards small, low-cost and very rugged optical systems and could therefore be a game-changer for sensor systems.

In the field of integrated optics applied to bio-detection, micro-resonators (MRs) are certainly the most compact structures that allow to achieve very low optical detection limits and high sensitivities [START_REF] Chao | Design and Optimization of Microring Resonators in Biochemical Sensing Applications[END_REF][START_REF] Ciminelli | Labelfree optical resonant sensors for biochemical applications[END_REF][START_REF] Ciminelli | High performance SOI microring resonator for biochemical sensing[END_REF]. Combining a MR structure and a porous material such as PS, is of great interest to enhance sensor characteristics as the interaction between the molecules to be detected and the optical wave is optimized as it occurs in the core of the porous waveguide instead of in the evanescent part for MR based on bulk materials [START_REF] Hutter | Theoretical Study of Porous Silicon Waveguides and Their Applicability for Vapour Sensing[END_REF]. Very promising values of sensitivities have already been obtained with one MR based on PS for salt solution [START_REF] Rodriguez | Porous silicon ring resonator for compact, high sensitivity biosensing applications[END_REF], glucose detection [START_REF] Girault | Racetrack micro-resonators based on ridge waveguides made of porous silica[END_REF] or with different ethanol-water dilutions [START_REF] Caroselli | Experimental study of the sensitivity of an porous silicon ring resonator sensor using continuous in-flow measurements[END_REF]. Moreover very promising low limit of detection has been calculated especially by cascading a PS MR with a reference MR based on polymers [START_REF] Azuelos | Theoretical investigation of Vernier effect based sensors with hybrid porous silicon-polymer optical waveguides[END_REF].

A MR is an interferometer constituted of an access waveguide, in which light propagates, and a cavity, separated by a submicron gap, in which light is coupled. At the output of the access waveguide, the spectral response of the MR presents lacks of transmitted light for specific wavelengths that resonate in the cavity. The presence of the molecules in contact with the MR results in a shift of the resonant wavelengths which increases as the concentration of molecules increases.

Low-loss waveguides supporting single-mode propagation are required for MR sensing [START_REF] Landgraf | Polymer Microring Resonator Directly Patterned by Multilevel-Nanoimprint: Integration into Biosensor System with a Miniaturized Microfluidic System[END_REF].

Moreover, for sensing applications, the contrast between on/off resonant intensity has to be the highest as possible to ease the detection of the wavelength shift. A high contrast is obtained for a critical coupling ratio of the light between the access waveguide and the resonant cavity. Critical coupling corresponds to a balance between the energy coupled into the resonator and the energy loss in the resonator. The energy coupling into the resonator mainly depends on the gap separation between the cavity and the access waveguide, and also on the optical losses: the lower are the losses, the wider gap can be considered, which is easier to be obtained from a technological point of view in relation to the resolution of the manufacturing process [START_REF] Chao | Design and Optimization of Microring Resonators in Biochemical Sensing Applications[END_REF]. A racetrack geometry can be considered with a coupling distance which aim is to increase the gap and ease the fabrication [START_REF] Dai | Compact Microracetrack Resonator Devices Based on Small SU-8 Polymer Strip Waveguides[END_REF]. Nevertheless, in the goal of the miniaturization of the device, the length of the coupling region has to be minimized and a low gap which can be technologically obtained is preferred.

Concerning the fabrication, we have demonstrated recently the proof of concept of a racetrack MR based on porous silica ridge waveguides manufactured using standard photolithographic process, which is a low cost method [START_REF] Girault | Racetrack micro-resonators based on ridge waveguides made of porous silica[END_REF]. Due to the theoretical photolithography resolution limit of 0.4 µm [START_REF] Maalouf | An improvement in standard photolithography resolution based on Kirchhoff diffraction studies[END_REF] and the experimental resolution, the smallest gap of 0.5 µm was taken into account into the photolithographic mask [START_REF] Girault | Racetrack micro-resonators based on ridge waveguides made of porous silica[END_REF]. However, experimental gaps of 0.7 µm have been obtained instead of 0.5 µm aimed because of a lateral etching of the ridge waveguides occurring during the process [START_REF] Girault | Racetrack micro-resonators based on ridge waveguides made of porous silica[END_REF].

In the present work, we propose a proof of concept in order to reduce the gap between a racetrack resonator and the porous silica-based access waveguide by standard photolithography followed by an oxidation step to take advantage of the phenomenon resulting from silicon volume expansion. The choice of a racetrack geometry is chosen in order to optimize the coupling while keeping in mind the miniaturization of the component. Porous silica, obtained by complete thermal oxidation of PS, has been preferred to partially oxidized PS as the optical losses are lower [START_REF] Dhanekar | Porous silicon biosensor: Current status[END_REF][START_REF] Ferrand | Optical losses in porous silicon waveguides in the nearinfrared: Effects of scattering[END_REF][START_REF] Charrier | Optical study of porous silicon buried waveguides fabricated from p-type silicon[END_REF].

In a first part, the fabrication method of the MR based on porous silica ridge waveguides is described. Then the design of the MR taking into account the refractive index and the condition of single mode propagation are presented. Eventually, the microstructural and optical characterizations are reported and discussed.

II. Fabrication method of racetrack MR based on porous silica ridge waveguides

The studied racetrack MR is based on porous silica ridge waveguides which were obtained from a photolithographic process of three porous silicon layers of different porosities followed by a complete oxidation treatment. These three consecutives PS layers have been prepared by electrochemical etching at ambient temperature (20°C) of a heavily doped P (100) silicon substrate with a 5 m.cm resistivity and using applied current densities of 4, 10 and 90 mA/cm 2 respectively and for specific times. The electrolyte was formed by combining hydrofluoric acid (50 %) with ethanol and deionized water in the ratio of 2-2-1 respectively. The first PS layer (4 mA/cm²) is a thin barrier layer with a very low porosity (around 6%) on the top of the two other porous layers. This first upper porous layer plays the role of a "technological barrier" that prevents the other deeper porous layers from being infiltrated by the resin during the subsequent photolithographic process which is necessary to create the ridge porous waveguides. The second (10 mA/cm²) and the third (90 mA/cm²) porous layers constitute the core and the lower cladding layers respectively of the PS waveguides. The corresponding porosity of the core and the cladding layers are respectively of 50 % and 80 % (Table I).

Then, PS ridge waveguides constituting the MR have been implemented using a large scale standard photolithographic process performed on the three porous silicon layers. The process is described in Figure 1 (a, b andc). A positive photosensitive resin layer (S1805) was deposited by spin coating on the top of the structure. Patterns were then produced under UV exposure through a well-defined chrome mask designed using Olympios software. To obtain the ridge waveguides, a trifluoromethane CHF 3 plasma RIE/ICP was performed in order to remove the sacrificial layer and the core layer from either side of the mask. Then a final etching is performed on the whole surface to remove the sacrificial layer.

Given the electrochemical etching used for the manufacture of PS layers, it is necessary to always proceed in the same way (temperature, identical configuration of the electrolytic cell) to obtain a reproducible PS characteristics.

Due to the inhomogeneity of porous silicon on the wafer edges, special care is taken to perform photolithography on the homogeneous part in the center of the wafer.

Moreover it is really necessary to respect the conditions of the reactive ion etching which is a very important step of the photolithography process to obtain a reproducibility of porous silica waveguides with similar shape and dimensions with uncertainties in the order of 50 nm.

After the photolithographic process, the obtained porous silicon ridge waveguides were completely oxidized, to obtain porous silica ridge waveguides, by a thermal treatment in two steps: the first one at 300°C under air during one hour followed by the second step at 960 °C during one hour under humid oxygen.

Moreover during the complete oxidation, a volume expansion of PS occurs depending on the porosity and the morphology of the pores [26 -29]. The porosities of the core and the confinement layers are reduced and the dimensions of the ridge waveguides are increased which implies a reduction of the gap between the straight and the curved waveguides (Figure 1.d). The porosities of the core and the cladding layers after complete thermal oxidation and the associated refractive indices are also reported in Table I.

These porosities and associated refractive indices at 1550 nm have been determined from reflectivity measurements of two single PS and porous silica layers whose fabrication parameters correspond to those of the ridge waveguides. From the thicknesses measured by scanning electron microscopy, porosities and then refractive indices have been determined by the adjustment of the calculated reflectance spectra of each porous layer with experimental one using Bruggemann model [START_REF] Astrova | Effective refractive index and composition of oxidized porous silicon films[END_REF][START_REF] Lorrain | Functionalization control of porous silicon optical structures using reflectance spectra modeling for bio sensing applications[END_REF]. It should be noted that these porosities have been chosen for a sensor application and, from a mechanical point of view, to avoid the detachment of the core of the waveguide due to the stresses generated in the material by the volume expansion. Regardless of these aspects, in order to take advantage of the volume expansion in the core of the waveguide to reduce the gap, a low porosity with a small pore diameter will be necessary [START_REF] Toth | Origin and FEM-assisted evaluation of residual stress in thermally oxidized porous silicon[END_REF]. Thus, with regard to all these aspects, an initial porosity of 50% which gives after oxidation a porosity of 20%, has been chosen. This porosity allows to obtain pore diameters in an estimated range [10 -30 nm] that is sufficient for detection applications that we have already conducted for example in reference [START_REF] Hiraoui | Towards a biosensor based on anti-resonant reflecting optical waveguide fabricated from porous silicon[END_REF][START_REF] Girault | Porous silicon micro-resonator implemented by standard photolithography process for sensing application[END_REF].

III. Design of racetrack MR based on porous silica ridge waveguides

In this part, the design of the racetrack porous silica MR is detailed in terms of geometrical parameters.

The dimensions of the ridge waveguides have to be chosen to provide single mode propagation at 1550 nm. Using the effective refractive index method [START_REF] Westerveld | Extension of Marcatili's analytical approach for rectangular silicon optical waveguides[END_REF], the effective refractive index of the porous silica core ridge waveguides has been calculated as a function of its width and height for three different TE and TM modes: the fundamental mode 00, the mode 01 and the mode 10.

From these results, the dimensions of the ridge waveguide required to obtain only single mode (mode 00) propagation for both the TE and TM modes, were deduced.

Figure 2 reports the lowest dimension limits (width and height) of the 00, 01 and 10 TE modes propagation that involve solutions to the Maxwell equations [START_REF] Okamoto | Fundamentals of optical waveguides[END_REF]. Thus, the hatched area between the lowest limits of the 00 mode (fundamental mode), the 01 and 10 modes, represents the single mode propagation region. For TM modes, the curves are similar to TE modes but are slightly shifted towards higher dimension values. Thus, the results indicate the range of width and the associate height of porous silica ridge waveguide that could allow single mode propagation. Based on these results, a width of 2 µm and a height of 1 µm have been aimed. Then, for these chosen dimensions, an effective refractive index of 1.235 ± 0.020 for the TE mode and 1.209 ± 0.020 for the TM mode were calculated using the effective index method.

Similar values were obtained from the Finite Difference Generic (FDG) method which is a full vectorial solver using Olympios software. The accuracies on the calculated refractive indices take into account the measurement errors on the refractive index of the core and cladding porous silica layers.

The top view and the cross section of the porous silica racetrack MR design are presented in Figure 3. As already mentioned in introduction, the separation (gap) "g" between the straight waveguide and the MR (Figure 2) is an important parameter which contributes to the coupling coefficient. Considering the theoretical resolution limit of photolithography of 0.4 µm [START_REF] Maalouf | An improvement in standard photolithography resolution based on Kirchhoff diffraction studies[END_REF], the minimal gap of 0.5 µm has been considered in the photolithographic mask. To obtain a sufficient coupling ratio with gap less of 1 µm between the straight and the curved waveguides, the MR is designed as a racetrack with an internal radius R of 50 µm and a coupling length L c of 40 µm:

the radius of 50 µm has been chosen with respect to a compromise between the optical losses (due to the waveguide curvature) and the miniaturization of the structure.

Indeed, in these conditions, the coupling ratio, calculated as a function of the gap by the method described in a previous study [START_REF] Girault | Racetrack micro-resonators based on ridge waveguides made of porous silica[END_REF] and based on Marcatilli method [START_REF] Okamoto | Fundamentals of optical waveguides[END_REF] for TE and TM modes, becomes more and more significant when decreasing the gap down to 0.7 µm (Figure 4.a). This trend clearly shows the interest of reducing the gap. Aside from the benefit of lower losses due to the decrease of the refractive index contrast that allows an evanescent wave more important, as illustrated in Figure 4.a, the full oxidation is also a mean to obtain a sufficient coupling rate, close to the critical coupling rate which is of about 30% in this case by considering similar losses as in reference [START_REF] Rodriguez | Porous silicon ring resonator for compact, high sensitivity biosensing applications[END_REF]. Considering the same design, and taking into consideration the indices of non-oxidized porous silicon core and cladding layers, much lower coupling rate values would be obtained for the same gap range (Figure 4.b).

IV. Characterizations of the racetrack MR

Scanning Electron Microscopy (SEM) has been performed on the porous silicon racetrack MR just after the photolithographic process (Figure 5) and after the complete oxidation step (Figure 6) in order to determine the experimental ridge waveguide dimensions and the experimental gap. After the complete oxidation step, the height of the waveguide is slightly increased of 0.1 µm as well as its mean width which reaches 2.05 µm (Figure 6.a). The waveguide dimensions which are obtained always allow a single modal propagation of the light (Figure 2).

The width of 2.05 µm for the two waveguides is confirmed by the top view of the coupling region (Figure 6.b). An expansion ratio of about 17% in width reduces consequently the gap: the mean value of the gap is 0.45 ± 0.05 µm (Figure 6.c). Thus the oxidation performed after the photolithographic process reduces the gap by nearly 40%. A schema of the width evolution of the waveguide is reported on Figure 7: initially planned on the mask (Figure 7.a), after the photolithographic process (Figure 7.b) and after the complete oxidation (Figure 7.c). Moreover, the width and the height before and after the thermal oxidation as well as the corresponding expansion ratio are reported in Table II for the core and the cladding layers. Table II: Height and width of the core and cladding layers of the ridge waveguide before and after the complete thermal oxidation and the corresponding expansion ratio. After the photolithographic process, the real separation distance between the two PS waveguides is higher than expected by a mean value of 0.25 µm because of an additional lateral etching that occurred in the core PS layer. This phenomenon had been already observed in a previous study [START_REF] Girault | Racetrack micro-resonators based on ridge waveguides made of porous silica[END_REF].

Core waveguide

Before oxidation

After oxidation

Expansion

Then, as already mentioned previously, during the complete oxidation step of PS waveguides, an increase in volume of silicon crystallites occurs [26 -29]. This volume expansion is due to the transformation of silicon into silica and induces a reduction of the porosity and also an increase of the ridge waveguide dimensions.

In the core waveguide, the increase of the height is about 11% and the one of the width waveguide is of 17%. This width expansion allows to reach a gap of 0.45 µm that is not possible to obtain if, as in our previous study [START_REF] Girault | Racetrack micro-resonators based on ridge waveguides made of porous silica[END_REF], the standard photolithographic process is performed after the oxidation step of the PS layers. The expansion rate values reported in Table II reveal an anisotropic character of the expansion volume all the more marked in the core layer (lower porosity). The photolithography process was initially carried out on straight guides in the same way as the micro-resonators in order to predict the expansion volume. Very similar lateral expansions with less than 0.5% of difference have been obtained showing the reproducible process if it is carried out in a strictly identical way from the elaboration of porous silicon layers to the photolithography process.

This inhomogeneity of the expansion ratio results from the anisotropic porous structure constituted of columnar pore shape, perpendicular to the silicon substrate [START_REF] Lehmann | On the morphology and the electrochemical formation mechanism of mesoporous silicon[END_REF] and typical of the electrochemical etching of P + orientated (100) silicon substrates. Thus, when the porosity is higher, the width expansion occurs more within the pores inducing a decrease of the pore diameter instead of an increase of the total width. Nevertheless, even with an initial porosity of 80% in the cladding, the width expansion remains significant (9%). So the reduction of the gap with such a core porosity would be also obtained using the method of porous silica waveguide fabrication described in this paper.

Then, after having shown the feasibility of reducing the gap in porous silica-based MR, it is important to show that the MRs are optically operational. Using the experimental method described in our previous studies [START_REF] Girault | Racetrack micro-resonators based on ridge waveguides made of porous silica[END_REF], the experimental spectral response of the porous silica MR has been measured and is reported in Figure 8.a.

The transmitted response shows peaks that corresponds to resonance wavelengths. The difference between two resonance wavelengths (Free Spectral Range: FSR) is of 4.35 nm which corresponds to the aimed one considering the effective index and the geometrical parameters of the racetrack cavity.

An extinction ratio of 25 dB has been obtained and corresponds to the contrast between the maximum of transmitted light and the minimal one at resonant wavelengths. Using the equations defined in a previous study on polymers MR [START_REF] Girault | Racetrack micro-resonators based on ridge waveguides made of porous silica[END_REF], the theoretical transmission has been calculated and then adjusted to match the experimental one (Figure 8.a).

The adjustment of the resonance shape is performed by modifying the coupling ratio and the propagation losses in the MR with the assumption that the coupling losses are negligible. The wavelength difference, or free spectral range (FSR), is adjusted from the group index [START_REF] Lehmann | On the morphology and the electrochemical formation mechanism of mesoporous silicon[END_REF].

The adjustment of the calculated spectrum to the experimental one has been obtained with a coupling ratio of 30% and a field attenuation constant "a" of 0.86, which corresponds to propagation losses per length unit of 32 dB/cm. To match the experimental FSR, the group index was adjusted to 1.4194. According to Figure 4, a gap of 0.45 -0.5 µm allows to reach a coupling ratio of about 30 -40% for the TM mode and for waveguide dimensions of 2 µm x 1 µm. The selected polarization in the experiment presented in Figure 8.a is then the TM mode. As the real dimensions are of 2.05 µm x 0.9 µm, we have calculated again the coupling ratio for these dimension and the same parameters as in figure 4 and verified that a coupling ratio of about 30 % can be obtained for a gap of 0.45 -0.5 µm.

The corresponding normalized transmission is reported in Figure 8.b. The contrast obtained is nearly of 100% which means that the critical coupling is reached. This demonstrates that the coupling of the light between the access waveguide and the racetrack cavity is optimal as a maximum contrast is obtained. Despite the lateral over lateral etching that occurs due to the porous nature of the layers, this experiment shows clearly that we have succeed in making a ridge porous silica racetrack MR with low gap of about 0.45 -0.5 µm by taking advantage of the volume expansion of silicon that occurs during oxidation of the ridge PS waveguides. Such gap value allows to reach the critical coupling of around 30% in this case.

If oxidation had been carried out before the photolithographic process, as in our previous study [START_REF] Girault | Racetrack micro-resonators based on ridge waveguides made of porous silica[END_REF], a gap of 0.75 µm instead of 0.45 µm would have been obtained. In this case, the coupling ratio for the same mode (TM) would be 6% (8% for the TE mode). The calculated transmission spectra of the porous silica MR with a gap of 0.75 µm, taking into consideration the same conditions (refractive indices, dimensions, optical losses) except for the coupling ratio

Conclusion

In this paper, a new method of processing racetrack MR based on porous silica ridge waveguides has been demonstrated in the objective to obtain lower gap between the straight access waveguide and the racetrack cavity. The method consists first in performing the standard photolithographic process on PS layers to obtain the ridge PS waveguides and then to carry out their complete oxidation in order to obtain porous silica waveguides. The method adopted previously consisted in oxidizing the PS layers before the processing of the ridge porous silica waveguides. In both method, a lateral etching occurs, reduces significantly the width of the ridge waveguide and increases consequently the gap. Such phenomenon resulted in the use of larger coupling distance (Lc) in the design of the racetrack.

The method demonstrated in this paper allows to use lower coupling distances and so to miniaturize further PS ridge waveguides MRs. To do so, the fabrication process takes advantage of the volume expansion of silicon that occurs during the full oxidation of PS ridge waveguides.

The volume expansion is all the more marked when the porosity of the core is low. In this work, we demonstrated a gap reduction of about 40% that has been obtained due to the expansion phenomena with an initial porosity of 50%. The resulting porosity after oxidation (20 %) remains sufficient for sensor application for gases or small molecules as proteins which can be easily grafted on porous silica after an appropriate functionalization of its high specific surface.

Figure 1 :

 1 Figure 1: Schema of the photolithographic process used for the fabrication of porous silica ridge waveguides: a) deposit of a photosensitive resin and exposure under UV; b) wet etching development of the photosensitive resin; c) dry etching of the porous silicon (sacrificial and core layers) under the unprotected area. Gap "g" between the straight

Figure 2 :

 2 Figure 2: Solutions of the Maxwell equations for the 00, 01 and 10 TE modes as a function of the porous silica ridge waveguide dimensions. The hatched area between the fundamental mode (00) and the 01 and 10 modes curves represents the waveguide dimensions range for which only single mode propagation is possible.

Figure 3 :

 3 Figure 3: Schema of: (a) top view of the porous silica racetrack MR and (b) cross section of the waveguide.

Figure 4 :

 4 Figure 4: Coupling ratio as a function of the gap between the straight and the curved waveguide of a racetrack MR with a radius of 50 µm, a coupling length of 40 µm, and aimed waveguide dimensions of 2 µm (width) x 1 µm (height) (a) Porous silica (complete oxidized porous silicon) based MR (b) non-oxidized-porous-silicon based MR.

Figure 5 :

 5 Figure 5: SEM observations after the photolithographic process: (a) Porous Silicon waveguide section; (b) Top view of the MR with a low magnification; (c) Top view of the coupling area at a higher magnification.

Figure 6 :

 6 Figure 6: SEM observations after complete oxidation: (a) Cross section of porous silica waveguide; (b) Top view of the MR with a low magnification; (c) Top view of the coupling area at a higher magnification.

Figure 7 :

 7 Figure 7: Schema of the top view of the coupling region of core waveguides reporting the width and the gap between the two waveguides: (a) as planned on the mask, (b) after the photolithographic process and (c) after the complete oxidation step.

Figure 8 :

 8 Figure 8 : Transmission spectra for one polarization of light of the porous silica racetrack MR : (a) Experimental and calculated spectra (gap of 0.45µm), (b) normalized experimental spectrum (gap of 0.45µm), (c) Calculated spectra for gaps of 0.45 µm and 0.75µm.

  shows a lower contrast compared to the transmission spectra of the porous silica MR with a gap of 0.45 µm (Figure8.c). This comparison clearly demonstrates the interest of reducing the gap.Without the over lateral etching effect, the gap could be further reduced. If we take into account the reduction obtained of 40%, for a minimum gap before oxidation of 0.5 µm, limited by the resolution of the standard photolithography technique, a gap of 0.3 µm could be obtained after oxidation of the MR. Such a value would further allow to miniaturize the MR by reducing the coupling length and radius of curvature of the MR. It would also allow the use of slightly larger waveguides, respecting the single modal conditions, up to 2.3 µm (width) x 1.5 µm (height) which would induces lower optical losses.

Table I :

 I Porosity and associated refractive index at 1550 nm for the PS core and cladding layers just after the electrochemical etching process and after complete thermal oxidation.

	After electrochemical anodization
	Porous silicon layers	Core	Cladding
	Current density (mA/cm²)	10	90
	Porosity (%)	50	80
	Refractive index	1.92	1.68
	After complete oxidation
	Porous silica layers
	Porosity (%)	20	60
	Refractive index	1.35	1.17

ACKNOWLEDGMENTS

This work is supported by the BIOCAP project, the ANR MIDVOC funded by the French Research Ministry, and the ARED funded by the Conseil Départemental des Côtes d'Armor and the Région Bretagne. The authors thank the CCLO (Centre Commun Lannionnais d'Optique) platform for its technical support in this work.