Martien Duvall

Deffo Ayagou

Mai Tran

Bernard Tribollet

Jean Kittel
email: jean.kittel@ifpen.fr

Eliane Sutter

Nicolas Ferrando

Christophe Mendibide

Claude Duret-Thual

Thi Tuyet

Electrochemical impedance spectroscopy of iron corrosion in H 2 S solutions

Keywords: Corrosion, iron, H2S, EIS, porous electrode

Introduction

Corrosion of metallic materials in the oil and gas industry has been a significant concern over the last decades and has major financial and environmental implications. H2S and CO2 are two main corrosive agents in the oil and gas industry.

Several studies have been carried out to understand the corrosion of steel in a CO2 medium, and there is a relative consensus on the mechanisms, which are often related to the formation of an iron carbonate scale. Depending on the conditions, such scale may have a protective action through a blocking effect, or provide no protection at all. Electrochemical impedance spectroscopy (EIS) represents an interesting technique to study the evolution with time of corrosion reaction, as it is usually performed at the corrosion potential. Most EIS studies of CO2 corrosion were conducted at ambient temperature and in NaCl solutions saturated with CO2 at atmospheric pressure [START_REF] Altoé | Evaluation of oilfield corrosion inhibitors in CO2 containing media: A kinetic study[END_REF][START_REF] Carvalho | Corrosion rate of iron and iron-chromium alloys in CO2 medium[END_REF][START_REF] Almeida | New insights on the role of CO2 in the mechanism of carbon steel corrosion[END_REF][START_REF] Lee | The effect of trace amount of H2S on CO2 corrosion investigated by using EIS technique[END_REF][START_REF] Lee | EIS investigation of CO2/H2S corrosion[END_REF]. Typical impedance diagrams contain a high frequency (HF) capacitive loop followed by an inductive loop at low frequency (LF). The HF loop has typical resistance value of several hundreds of Ω.cm² and a characteristic frequency of a few hertz, corresponding to a capacitance around 100 µF/cm². This capacitance value is typical of the double-layer at a bare metal surface [START_REF] Grahame | The electrical double layer and the theory of electrocapillarity[END_REF]. It is also well admitted that the resistive component corresponds to the charge transfer associated with the faradaic response [START_REF] Almeida | New insights on the role of CO2 in the mechanism of carbon steel corrosion[END_REF][START_REF] Lee | The effect of trace amount of H2S on CO2 corrosion investigated by using EIS technique[END_REF]. The inductive behavior at low frequency is often attributed to relaxation of intermediate adsorbates [START_REF] Almeida | New insights on the role of CO2 in the mechanism of carbon steel corrosion[END_REF][START_REF] Gabrielli | The Nature of the Passive Film on Iron .2. Ac Impedance Studies[END_REF]. The low frequency behavior seems however less reproducible, as some studies also showed a capacitive loop in the mHz frequency domain instead of the inductive loop [START_REF] Almeida | New insights on the role of CO2 in the mechanism of carbon steel corrosion[END_REF]. Similar shapes of impedance curves were obtained in CO2 environments with traces of H2S at concentrations up to at least 100 ppm vol. with respect to CO2 [START_REF] Altoé | Evaluation of oilfield corrosion inhibitors in CO2 containing media: A kinetic study[END_REF][START_REF] Carvalho | Corrosion rate of iron and iron-chromium alloys in CO2 medium[END_REF]. Unfortunately, it was not possible to extract capacitance values from these publications, since Nyquist plots did not include characteristic frequencies.

It results from all these studies that low alloy steel corrosion in CO2 saturated solution at ambient temperature results in a capacitive loop associated with the charge transfer resistance in parallel with the double layer capacitance. An additional contribution, either inductive or capacitive can also be observed at lower frequencies, in the mHz domain.

Compared to CO2, electrochemical measurements in H2S environments seem to be much more difficult, and the shape of impedance diagrams vary a lot between various studies. Ma et al. published several papers on pure iron exposed to H2SO4 / Na2SO4 solutions with dissolved H2S introduced as Na2S [START_REF] Ma | The influence of hydrogen sulfide on corrosion of iron under different conditions[END_REF][START_REF] Ma | Theoretical interpretation on impedance spectra for anodic iron dissolution in acidic solutions containing hydrogen sulfide[END_REF]. In these studies, pH range varied from 0.7 to 3.5, and dissolved H2S concentration was 0.4 mmol/L, corresponding to the equilibrium with gaseous H2S at a partial pressure of 4 mbar. Impedance diagrams measured at the corrosion potential showed two capacitive loops, and were interpreted with the equivalent circuit shown in Figure 1.a. In this circuit, CPEdl and Rt were respectively attributed to the double layer capacitance and charge transfer resistance, corresponding to the HF capacitive loop. Rt values between 13 and 72 Ω.cm 2 and Cdl values between 25 and 140 µF.cm -² were derived from equivalent circuit fitting. CPEa and Ra are associated with relaxation of adsorbed species, which was supposed to proceed slower and to correspond to the LF arc. These authors also measured impedance diagrams at various anodic potentials in order to promote the anodic reaction versus the cathodic contribution [START_REF] Ma | The influence of hydrogen sulfide on corrosion of iron under different conditions[END_REF][START_REF] Ma | Theoretical interpretation on impedance spectra for anodic iron dissolution in acidic solutions containing hydrogen sulfide[END_REF]. At the more anodic potentials, an inductive loop appeared at low frequency. This led the authors to use The same equivalent circuit as Figure 1.a was used by Veloz et al. to describe experimental results on mild steel exposed to a brine (30 g/L NaCl) solution buffered at pH 3.5 by sodium acetate and acetic acid, saturated by 1 bar dissolved H2S (0.1 mol/L) [START_REF] Veloz | Electrochemical study of carbon steel corrosion in buffered acetic acid solutions with chlorides and H2S, Electrochim[END_REF]. Tests were performed for short exposure times, after which no iron sulfide or any other corrosion product layer was detected by XRD analysis. In these conditions, charge transfer resistance in the order of 150 Ω.cm 2 and a double layer capacitance of 60 µF.cm -2 were measured.

A last study used the same equivalent circuit (Figure 1.a) for the interpretation of impedance data in H2S [START_REF] Tang | Test methods for the evaluation of materials for wet H2S service[END_REF]. Similarly to the studies by Ma et al., test solutions were prepared with H2SO4 and Na2SO4, and H2S was introduced as Na2S. However, temperature was raised to 90 °C, while all previous studies were conducted at ambient temperature. Impedance plots obtained in presence of H2S at the corrosion potential consisted of two capacitive loops. Rt and Cdl values were extracted by curve fitting with the equivalent circuit of Figure 1.a. The values of the double layer capacitance presented in this paper were of the order of mF/cm 2 which is much higher than expected values for a double layer capacitance, in the order of ten to a few hundred μF/cm 2 [START_REF] Grahame | The electrical double layer and the theory of electrocapillarity[END_REF][START_REF] Tang | Test methods for the evaluation of materials for wet H2S service[END_REF]. The reasons for such high values were not commented.

Significantly different shapes of impedance results were obtained by Arzola et al. [START_REF] Arzola | The effect of H2S concentration on the corrosion behavior of API 5L X-70 steel[END_REF]. They performed tests in 30 g/L NaCl solutions with various H2S concentrations ranging from 100 mass ppm to 2550 mass ppm (i.e. corresponding to equilibrium with 30 mbar to 700 mbar H2S). pH of test solutions varied from 5.3 (for 100 ppm H2S) to 4.1 (2550 ppm H2S). Measurements were performed immediately after immersion, and repeated after 24 hours exposure. Impedance diagrams were quite different from those obtained by previous authors. They consisted of a capacitive loop at high frequency interpreted by the charge transfer resistance in parallel to the double layer capacitance, followed by a 45° tail at low frequency assumed to represent a diffusion process (Figure 1.c). Rct values immediately after immersion were comprised between 300 Ω.cm 2 at the higher H2S content and 1315 Ω.cm 2 at 100 ppm H2S.

These values increased respectively to 460 Ω.cm 2 and 2060 Ω.cm 2 after 24 hours exposure. Unfortunately, capacitance values were not reported in the paper, and since no frequency information was given in the Nyquist plots, it was also impossible to evaluate these values from the frequency at the maximum of the imaginary part of the impedance. The low frequency contribution (45° tail) was not analyzed in the paper. It was just stated that it could correspond to diffusion through the iron sulfide film formed at the metal surface.

In summary, two different impedance shapes are presented in available literature on H2S corrosion of low alloy steels. The first type of results shows a HF behavior dominated by the anodic charge transfer resistance and the double layer capacitance, while low frequency characteristics correspond to relaxation of adsorbed species (Figure 1.a and 1.b). This type of result was obtained for short immersion times, and it was mentioned that no surface precipitation was visible after the tests. Indeed, these tests were performed at low pH or in presence of acetate, which retards iron sulfide precipitation. In that case, impedance response is mainly dominated by anodic reactions.

The second type of result shows a different behavior, with a 45° tail at low frequency, interpreted by diffusion limitation (Figure 1.c). In that case, presence of iron sulfide scale was observed. In addition, impedance measurements were performed at short immersion time and then repeated after 24 hours, and a significant increase of the high frequency semi-circle (interpreted as Rt) was observed, and was associated with a decrease of the corrosion rate. [START_REF] Ma | The influence of hydrogen sulfide on corrosion of iron under different conditions[END_REF][START_REF] Ma | Theoretical interpretation on impedance spectra for anodic iron dissolution in acidic solutions containing hydrogen sulfide[END_REF][START_REF] Arzola | The effect of H2S concentration on the corrosion behavior of API 5L X-70 steel[END_REF]. For the sake of simplicity, electrolyte resistance was removed from these equivalent circuits.

The first aim of this paper is thus to examine the evolution with time of EIS spectra of pure iron exposed to water containing dissolved H2S. Contrary to what already exists in the literature, time evolution over a few weeks will be examined, allowing significant iron sulfide precipitation. This time-scale is representative of sulfide stress cracking (SSC) qualification tests as per NACE TM0177, which constitute one field of application of this project [START_REF] Nace Tm | Laboratory Testing of Metals for Resistance to Sulfide Stress Cracking and Stress Corrosion Cracking in H2S Environments[END_REF].

Experimental procedure

This study is part of a project of which main objective is to study the impact of oxygen pollution on SSC. Hydrogen permeation is thus used as the central experimental method, together with EIS measurements. The experimental set-up thus consists in a Devanathan-Stachurski system shown in Figure 2 [START_REF] Devanathan | The mechanism of hydrogen evolution on iron in acid solutions by determination of permeation rates[END_REF]. The apparatus is composed of twin cells separated by the iron membrane. The cells are equipped with double jacket in order to maintain the temperature at 24 ± 2°C. In this experimental system, test specimens consisted in pure iron membranes, annealed under vacuum at 900 °C for 30 minutes (chemical composition provided in Table 1Table 1). These membranes were thus exposed on one side to the corrosive environment containing H2S where EIS measurements were made (designated as charging side), while the other side was exposed to 0.1 M sodium hydroxide and maintained at an anodic potential of 250 mV vs. Hg/HgO (1M KOH) for hydrogen permeation measurement (designated as detection side). The exit face covered by palladium following well established procedures [START_REF] Manolatos | Necessity of A Palladium Coating to Ensure Hydrogen Oxidation During Electrochemical Permeation Measurements on Iron[END_REF]. Membrane thickness was in the order of 0.5 mm, and the exposed area was 17 cm² on both sides. Details on hydrogen permeation measurement procedure were given in a previous paper [START_REF] Deffo-Ayagou | Corrosion of Pure iron and Hydrogen Permeation in the Presence of H2S with O2 contamination[END_REF].

Table 1: Chemical composition of test material (mass. ppm) EIS measurements were carried out with the iron membrane as working electrode, an Ag/AgCl reference electrode and a platinum mesh as auxiliary electrode. A perturbation of +/-10 mV amplitude around the corrosion potential was applied with a range of frequency of 10 kHz to 1 mHz. Each EIS measurement was preceded by an open circuit potential (OCP) measurement of about 2 hours. OCP and EIS measurements were then repeated over 3 to 4 weeks. Specific precautions were taken to avoid interferences between electrochemical measurements performed simultaneously on both sides of the membrane.

In addition to the permeation membrane, pure iron flat specimens (0.9 cm x 0.9 cm x 0.05 cm) were also introduced into the charging side. These coupons were used for weight-loss corrosion rate evaluation, as well as surface analysis by scanning electronic microscopy (SEM) and X-ray diffraction (XRD). The total surface of iron specimens exposed in the charging side was thus close to 23 cm², while the volume of test solution was 0.6 L.

Test solution at the entry side consisted in 35 g/L NaCl dissolved in distilled water.

Continuous bubbling of pure H2S was maintained during all experiments, resulting in a dissolved H2S concentration around 0.1 M, and an initial pH around 3.8 -4.

Results

Since one main goal of this study is to evaluate the evolution of H2S corrosion over a few weeks, changes in the test solution are likely to occur. Indeed, as iron corrosion proceeded, alkalinity is released by the cathodic reaction (reduction of protons and H2S). It results in pH increase, until iron sulfide saturation is reached. As shown on Figure 3Figure 3, initial pH corresponding to the test solution saturated with 1 bar H2S is 3.9. After 1 day, a plateau was reached around pH 4.3 -4.5, corresponding to FeS saturation. Typical evolution with time of exposure of Nyquist diagrams are presented in Figure 4Figure 4. For short exposure times (2 to 152 hours), Nyquist diagrams consist of a capacitive loop at high and medium frequencies, and a LF contribution which could correspond to a 45° linear tail or to the start of a second capacitive loop with a very low characteristic frequency. Throughout all exposure period, the corrosion potential varied in a narrow range, between -690 and -700 mV vs. Ag/AgCl. These impedance diagrams are similar to those obtained by Arzola et al. [START_REF] Arzola | The effect of H2S concentration on the corrosion behavior of API 5L X-70 steel[END_REF]. In addition, and as previously observed by these authors, the diameter of the capacitive loop increases with time.

At longer immersion times, some overlap between the HF capacitive loop and the LF contribution occurs. It becomes difficult to distinguish the various contributions to the impedance, which seems to be flattened and to tend towards a single line at 45°. Before impedance analysis, all raw experimental data were validated using Kramers-Kronig transformations. In addition, validity of impedance measurements at high frequency also had to be questioned. Indeed, at very high frequency, the impedance of the system may be simplified as the resistance of the electrolyte in series with the system capacitance (CHF), corresponding to:

HF e HF C R Z  1   Equation 1
Considering that the measurement noise is close to 1 %, all impedance values for which HF C  1 is lower than 1 % of Re cannot be trusted. For our system, Re was

Code de champ modifié

Code de champ modifié above 1 % of Re is 360 rad/s, i.e. a frequency of 57 Hz. This value is much lower than that usually considered for impedance measurements of corrosion processes.

However, it is a direct consequence of the huge capacitance values obtained in the case of H2S corrosion, resulting in a translation of impedance data to lower frequencies. The reasons for this surprisingly high capacitance value will be discussed later in the paper.

In order to determine the nature of the impedance, and to choose the model accordingly, measurements at various potentials around the corrosion potential (Ecorr)

were performed (Figure 5Figure 5). It was observed that the diameter of the HF arc decreased as the potential was more anodic, suggesting that the impedance is dominated by anodic reactions. This result will be used in the next section of the paper in order to establish the global impedance model of the system. Immediately after immersion, hydrogen permeation increases up to 60 µA/cm², followed by a slow decrease down to a plateau at 40 µA/cm², reached after a few days. Since permeated hydrogen was generated by the cathodic reaction (proton and/or H2S reduction) during the corrosion process, it may be interesting to compare corrosion current density and hydrogen permeation current density (Jperm). This comparison will be carried out in the next section of the paper.

Discussion

Impedance diagrams obtained for tests at short time immersion (Figure 4Figure 4.a)

are similar to those obtained by Arzola et al. [START_REF] Arzola | The effect of H2S concentration on the corrosion behavior of API 5L X-70 steel[END_REF]. However, the equivalent circuit used by these authors corresponds to a cathodic impedance, while the results of The values of model parameters corresponding to these fitted impedances are gathered in Table 2Table 2. In order to derive capacitance values from the CPE (constant phase elements) corresponding to the double layer capacitance used in the impedance model, the Brug's relationship was used [START_REF] De Levie | Electrochemical response of porous and rough electrodes[END_REF][START_REF] Hirschorn | Determination of effective capacitance and film thickness from constant-phaseelement parameters[END_REF]:

     1 1 1 1      t e dl R R Q C Equation 2
Corrosion current densities (Jcorr) were calculated from Rt using the Stern and Geary relationship with an anodic tafel coefficient (ba) of 40 mV, as usually observed in H2S environments [START_REF] Brug | The analysis of electrode impedances complicated by the presence of a constant phase element[END_REF] :

t a corr R b J 3 . 2  Equation 3
It must be remarked that for this type of anodic behavior with an adsorption intermediate step, the polarization resistance as determined by linear polarization or by the low frequency limit of the real part of the impedance shall not be used for corrosion rates evaluation with the Stern and Geary equation, since it does not coincide with the charge transfer resistance. For comparison, the hydrogen permeation current densities at various exposure times are also reported in Table 2Table 2.

Table 2: Component values of equivalent circuit of Figure 1.a giving the best fit of experimental impedance at various exposure times.

The most interesting fact about this analysis of impedance results at short exposure times lies in the very good match between corrosion current densities and hydrogen permeation current densities at various exposure times. Such result was, in fact, expected. Indeed, at high H2S content and for thin steel membranes, the permeation efficiency often reaches values close to 100 %, meaning that all hydrogen produced by the cathodic reaction actually enters into the metal. This comparison also offers a direct validation of the consistency of the impedance model, confirming the validity of corrosion current density evaluation.

The other parameter which is worth examining is the double layer capacitance. It can immediately be noted that Cdl values exceed by at least one order of magnitude usual values for metal corrosion. It is believed that these high values are associated with the rapid formation of a conductive iron sulfide scale. Indeed, this capacitance applies to all conductive surfaces of the electrode. Consequently, it increases as the iron sulfide film is growing, and its evolution with time gives information on the true surface of the scale. At the beginning of the test, i.e. after less than a few hours immersion, its value is already quite high at 2.7 mF/cm². Since typical double-layer capacitance on metal surfaces shall be in the order of 100 µF/cm², this result implies iron sulfide scaling has already started to form, providing a high effective surface [START_REF] Grahame | The electrical double layer and the theory of electrocapillarity[END_REF].

It was confirmed by visual observation that scaling was already present a few minutes after immersion. After 150 hours of exposure, the double layer capacitance reached 30 mF/cm², i.e. 300 times higher than the expected value. It can thus be inferred that the real cathodic surface reaches about 300 times that of the initially exposed iron surface. The assumption of the impact of iron sulfide scale on impedance is supported by SEM observations showing a highly porous structure offering a high effective surface (Figure 6Figure 6). Finally, it can be remarked that the CPE coefficients are quite stable between 47 hours and 152 hours exposure, with respectively 0.73 and 0.89 for CPEa and CPEdl. The deviation from a purely capacitive behavior might be explained by 2D heterogeneities at the metal surface and by the rapid formation of the conductive iron sulfide scale. These values of αa and αdl are also in the same order as those obtained by Ma et al at various pH [START_REF] Ma | The influence of hydrogen sulfide on corrosion of iron under different conditions[END_REF][START_REF] Ma | Theoretical interpretation on impedance spectra for anodic iron dissolution in acidic solutions containing hydrogen sulfide[END_REF].

This observation of high capacitance values led us to introduce a specific component in the impedance model in order to account for the iron sulfide film. The porous electrode model was used to determine a physical model for the impedance of this conductive and porous layer iron sulfide film. According to the theory developed by de Levie [START_REF] Zheng | Electrochemical mechanism and model of H2S corrosion of carbon steel[END_REF], the impedance of a pore is given by:

         0 0 0 0 coth Z R l Z R Z pore Equation 4
where l is the pore length, R0 is the electrolyte resistance for one-unit length pore, with units of Ω.cm -1 , and Z0 is the interfacial impedance (also expressed per surface unit and per unit length of the pore, with units of Ω.cm). It is also common to express R0 and Z0 in function of the pore radius (r), and of the interfacial impedance per surface unit (Zeq) as:

2 0 r R    Equation 5 r Z Z eq  2 0  Equation 6
where  is the electrolyte resistivity. This resistivity is considered as uniform inside all pores. Indeed, test solution contains a relatively high NaCl concentration (0.6 M) that should be sufficient to hinder concentration gradients of reactive ions inside the pores. Another simplification made by de Levie is adopted here; i.e. that the axial concentration gradient inside the pores is negligible.

Depending on the value of l and r, the coth function in Equation 4 admits two limiting situations. If the argument is close to zero (i.e. pores with small length or large radius), then coth(X) is equal to 1/X. In such a case, Equation 4simplifies to:

rl Z l Z Z eq pore  2 / 0   Equation 7
The film behaves as a plane electrode, and its impedance is inversely proportional to the number of pores n and to the surface of pores:

rl n Z n Z Z eq pore plane film  2 / ,   Equation 8
The other limiting situation corresponds to long and thin pores, for which the argument X in the coth function takes high values. Then coth(X) tends towards 1,

meaning that 0 0 Z R Z pore 
. The film behaves as a semi-infinitely deep porous system, with an impedance proportional to the square root of the interfacial impedance, resulting in a 45° inclination of Nyquist plots:

2 3 , 2 r n Z Z eq porous film    Equation 9
These two limiting situations correspond to model systems, for which all pores have the same geometry. In practice, and as illustrated by SEM observations of the FeS layer, there is a distribution of pore size and geometry, leading to the co-existence of both behaviors in parallel. The total impedance of the film is then given by:

1 , 1 , 1      porous film plane film film Z Z Z Equation 10
As a consequence, as soon as the iron sulfide film builds-up at the metal surface, this film impedance has to be added in parallel to the faradaic contribution of Figure 1.a.

The complete impedance of the system is then given by the following equivalent circuit:

Figure 9: Equivalent circuit for the corrosion of pure iron in H2S containing environment with the formation of a conductive and porous FeS layer.

In the present case, and since the faradaic cathodic impedance is negligible (see Figure 5Figure 5), only the double layer capacitance is taken into account in the interfacial impedance Zeq for both film contributions:

  * ,* ,* 1   j Q Z eq eq  Equation 11
where* represents alternatively the parameters associated with the plane electrode or with the porous electrode contributions in the expressions of Zfilm (Equations 8 to 10).

Although it may seem quite complicated, this impedance model still presents several simplifying assumptions. First, as in the original development of the transmission line model by de Levie, it is considered that the ohmic drop along the pores is negligible.

It is also considered that there is no axial concentration gradient inside the pores.

Then, in the expression used for the film impedance (Equation 10), the pores where the coth term plays a role (i.e. different from the two limiting cases described above) are neglected. It means that equation 10 correctly represents situations where the iron sulfide film behaves as a plane electrode or as a porous electrode, or both in parallel. But it presents some weaknesses when the pores geometry is so that simplifications of the coth function are not valid (i.e. argument value is neither close to zero nor close to infinite). A more robust approach to describe the impedance of this film would consist in considering a distribution of pore sizes. This type of approach is often used for energy storage applications, where porous electrodes are used to maximize current densities [START_REF] Huang | Theory of Impedance Response of Porous Electrodes[END_REF][START_REF] Kant | Theory of the Electrochemical Impedance of Mesostructured Electrodes Embedded with Heterogeneous Micropores[END_REF][START_REF] Lasia | Impedance of porous electrodes[END_REF][START_REF] Song | Electrochemical impedance spectroscopy of porous electrodes: the effect of pore size distribution[END_REF]. Equivalent circuit approaches then becomes inappropriate, and numerical resolutions are required. The validity of these assumptions will be further discussed after comparing electrochemical data with weight-loss and hydrogen permeation measurements, at the end of this paper.

The model was then used to analyze impedance spectra obtained at various immersion times. For short immersion times, when the iron sulfide film is thin with relatively large pores, it was found that the film impedance is only composed of Zfilm,plane, i.e. a purely capacitive contribution. This film capacitance being in parallel with the double layer capacitance of the initial model of Figure 1.a, the equivalent circuit is fully equivalent to the circuit of As already mentioned, the similarity between corrosion and permeation current densities is remarkable. The permeation efficiency is maintained at values close to 100 % even at longer exposure times. In addition, and considering the total time of exposure, an average corrosion current density of 45 µA/cm² was obtained, corresponding to a corrosion rate of 530 µm/year. This value is in very good agreement with weight loss measurements performed on small coupons, exhibiting a corrosion rate of 490 µm/year. This result also confirm that it was reasonable to restrain Rt values in the range 400 -500 Ω.cm² when fitting impedance obtained at long exposure times. This good correlation also validates the simplifying hypothesis describes above, at least for the determination of Rt, which is the only parameter used for the analysis of corrosion.

It can finally be noted that the new model proposed in this paper is consistent with literature data, while giving new insights in unexplained results from the literature. For short immersion times, when no film formation occurs or when the iron sulfide film remains sufficiently thin, the film behaves as a pure capacitance. It results in high values of capacitance, while the faradaic contribution is dominated by the anodic reactions with an adsorbed intermediate, as proposed by Ma et al. [START_REF] Ma | The influence of hydrogen sulfide on corrosion of iron under different conditions[END_REF][START_REF] Ma | Theoretical interpretation on impedance spectra for anodic iron dissolution in acidic solutions containing hydrogen sulfide[END_REF]. The same model also allows representing the results of Veloz et al. [START_REF] Veloz | Electrochemical study of carbon steel corrosion in buffered acetic acid solutions with chlorides and H2S, Electrochim[END_REF], and it gives a physical explanation for the high capacitance values obtained in this paper.

For longer exposure times, a flattening of impedance diagrams is observed, tending towards a 45° line. For this system, where impedance is dominated by the anodic reactions and for which the reactive species are available at high concentration in the solution, diffusion limitation is unlikely to take place. The porous electrode behavior, associated with the conductive iron sulfide scale that forms at the electrode surface, gives a physical explanation for observed impedance.

CONCLUSION

Corrosion of pure iron in H2S saturated 35g/L NaCl solution was studied for 3 to 4

weeks. An impedance model was proposed, with two distinct contributions: i/ a faradaic anodic impedance consisting of a two-step reaction with charge transfer and adsorption -desorption and, ii/ the impedance of the conductive and highly porous iron sulfide (mackinawite) film. This impedance model is fully compatible with previous proposals of the literature, and its physical meaning is now well established, which was not completely available yet in the case of film formation. The main impact of this scale is to induce extremely high values of double-layer capacitance, due to the huge increase of effective surface which can reach nearly 600 times that of the geometrical surface of the metallic electrode.

The analysis of impedance data also allowed determining the evolution with time of the charge transfer resistance, from which the corrosion current density could directly be estimated. Corrosion rates evaluated from impedance data were perfectly correlated with weight loss measurements. It was also found that corrosion current density was nearly identical to the hydrogen permeation current density over the whole duration of the tests. This permeation efficiency of 100 % was expected in our test conditions, i.e. high H2S content and thin metal membrane. Therefore, hydrogen permeation provides a direct and independent measurement of the cathodic current density, also corresponding to the corrosion current density.

This impedance model will now be used to study the impact of environmental parameters on iron corrosion in H2S environment. In the second part of this paper, a study of the effect of continuous ingress of oxygen in the H2S environment will be proposed.

  another equivalent circuit, claimed to represent anodic dissolution (Figure 1.b). Although they look quite different, it can be shown that both circuits of Figure 1.a and b correspond to a similar analytical expression of the impedance of anodic dissolution through an adsorbed intermediate [10]. For such system, and depending on surface coverage and constant parameter values, the low frequency contribution may correspond either to a capacitive arc (Figure 1.a) or to an inductive loop (Figure 1.b).

Figure 1 :

 1 Figure 1: Equivalent circuits and corresponding impedance diagram used in the literature to describe iron corrosion in presence of H2S[START_REF] Ma | The influence of hydrogen sulfide on corrosion of iron under different conditions[END_REF][START_REF] Ma | Theoretical interpretation on impedance spectra for anodic iron dissolution in acidic solutions containing hydrogen sulfide[END_REF][START_REF] Arzola | The effect of H2S concentration on the corrosion behavior of API 5L X-70 steel[END_REF]. For the sake of

Figure 2 :

 2 Figure 2: Experimental set up (Devanathan-Stachurski type cell).

Figure 3 :

 3 Figure 3: pH evolution of test solution consisting of 35 g/L NaCl solution saturated with 1 bar H2S at 24 °C, with iron coupons exposed to corrosion.

Figure 4 :

 4 Figure 4: Nyquist diagrams of pure iron exposed to a 35 g/L NaCl solution saturated with 1 bar H2S at 24 °C for short (a) and long (b) exposure times.

Figure 5 :

 5 Figure 5: Nyquist diagram of pure iron exposed to a 35 g/L NaCl solution saturated with 1 bar H2S at 24 °C. Measurements at Ecorr -50 mV, Ecorr, and Ecorr + 50 mV.

Figure 6 :

 6 Figure 6: SEM observation of corrosion deposits formed at iron surface after 620 hours exposure to a 35 g/L NaCl solution saturated with 1 bar H2S at 24 ° C.

Figure 7 :

 7 Figure 7: Hydrogen permeation for a 0.5 mm thick pure iron membrane exposed to a 35 g/L NaCl solution saturated with 1 bar H2S at 24 °C.

Figure 5Figure 5

 5 Figure 5Figure 5 clearly indicate that the measured impedance is dominated by the anodic reactions. Consequently, impedance results were analyzed with the model of Figure 1Figure 1.a proposed in the literature to describe anodic impedance of iron corrosion in presence of H2S[START_REF] Ma | The influence of hydrogen sulfide on corrosion of iron under different conditions[END_REF][START_REF] Ma | Theoretical interpretation on impedance spectra for anodic iron dissolution in acidic solutions containing hydrogen sulfide[END_REF]. EIS spectra fitting were carried out with SIMAD ® software developed by the LISE laboratory. Curve fitting was applied to extract the various physical parameters describing the impedance of the system. Satisfactory fitting results were obtained for impedance measurements performed between 2 and 152 hours of exposure, as illustrated in Figure8Figure8. In order to illustrate the inconsistency of HF measurements above a few tens of Hertz, impedance data were represented after subtraction of the resistance of the electrolyte. This representation illustrates the inconsistency of HF measurements, resulting in erratic phase angles.

Figure 8 :

 8 Figure 8: Comparisons between experimental (open symbols) and fitted impedance (lines) measured after 2 hours (a), 47 hours (b) and 152 hours (c) exposure, using the equivalent circuit of Figure 1.a.

Figure 1 .

 1 Figure10Figure10, for the experimental data obtained after 437 and 572 hours.

Figure 10 :

 10 Figure 10: Comparisons between experimental (open symbols) and fitted impedance (lines) measured after 437 hours (a) and 572 hours (b) exposure, using the equivalent circuit of Figure 9Figure 9.

Figure 11 :

 11 Figure 11: Comparison of Jperm with Jcorr determined from Rt values determined by EIS fitting with the model of Figure 9Figure 9.

Figure 1 :

 1 Figure 1: Equivalent circuits and corresponding impedance diagram used in the literature to describe iron corrosion in presence of H2S[START_REF] Ma | The influence of hydrogen sulfide on corrosion of iron under different conditions[END_REF][START_REF] Ma | Theoretical interpretation on impedance spectra for anodic iron dissolution in acidic solutions containing hydrogen sulfide[END_REF][START_REF] Arzola | The effect of H2S concentration on the corrosion behavior of API 5L X-70 steel[END_REF]. For the sake of simplicity, electrolyte resistance was removed from these equivalent circuits.

Figure 2 :Figure 3 :Figure 4 :Figure 5 :

 2345 Figure 2: Experimental set up (Devanathan-Stachurski type cell).

Figure 6 :

 6 Figure 6: SEM observation of corrosion deposits formed at iron surface after 620 hours exposure to a 35 g/L NaCl solution saturated with 1 bar H2S at 24 ° C.

7 :

 7 Hydrogen permeation for a 0.5 mm thick pure iron membrane exposed to a 35 g/L NaCl solution with 1 bar H2S at 24 °C.

Figure 9 :Figure 10 :Figure 11 :

 91011 Figure 9: Equivalent circuit for the corrosion of pure iron in H2S containing environment with the formation of a conductive and porous FeS layer.

Table 1 :

 1 Chemical composition of test material (mass. ppm)

	Al	Cr	Cu	Mn	Ni	Si	Ti	C	P	S	Fe
	107	133	55	240	159	100	5	18	60	48	Bal

Table 2 :

 2 Component values of equivalent circuit of Figure1.a giving the best fit of experimental impedance at various exposure times.

		2 hours	47 hours	152 hours
	Re (Ω.cm²)	143	140	139
	Qa	0.13	0.09	0.09
	αa	0.78	0.74	0.73
	Ra (Ω.cm²)	910	1594	3202
	Qdl	0.003	0.013	0.026
	αdl	0.89	0.90	0.89
	Cdl (mF.cm -2 )	2.6	13.4	29.4
	Rt (Ω.cm²)	276	381	435
	Jcorr (µA.cm -2 )	63	46	40
	Jperm (µA.cm -2 )	55	46	42

Misen forme : Police :(Par défaut) Arial, 12 pt, Anglais (États-Unis) Mis en forme : Police :(Par défaut) Arial, 12 pt, Anglais (États-Unis)

Mis en forme : Police :(Par défaut) Arial, 12 pt, Anglais (États-Unis)

Acknowledgements

The authors kindly thank Alexandre Bonneau for his participation in the implementation of the experimental setup. Remy Mingant is also warmly acknowledged for his active participation in the analysis and modeling of impedance data. The contribution of IFPEN analysis department in the surface characterization and test solution analysis is also greatly acknowledged.


François Catzeflis
email: francois.catzeflis@univ-montp2.fr

Yann Gager
email: yann.gager@gmail.com

Manuel Ruedi
email: manuel.ruedi@ville-ge.ch

Benoit De Thoisy
email: bdethoisy@pasteur-cayenne.fr

The French Guianan endemic Molossus barnesi (Chiroptera: Molossidae) is a junior synonym for M. coibensis

Keywords:

The taxonomy of the small Neotropical Molossus species has been notoriously difficult due to a lack of adequate comparative material. One taxon in particular, M. barnesi Thomas, 1905 was believed to be restricted to a narrow stretch of coastal areas around Cayenne, in French Guiana and was so far represented only by three female specimens. It was variously considered as a species on its own, or synonymized with M. molossus or M. coibensis. Thanks to the discovery of several mixed colonies of these small molossids in two localities in French Guiana, we could obtain and measure a large sample (nearly 200 specimens) of adult individuals to better assess their morphological variation. Owing to largely bimodal and non-overlapping distributions of external measurements such as forearm length, we could demonstrate the existence of two sympatric morphotypes, the smaller one corresponding to M. barnesi and the larger one to M. molossus. Univariate and multivariate comparisons of cranio-dental and external characters further suggest that the new series of barnesi from French Guiana do not differ notably from specimens assigned to M. coibensis from elsewhere. Molecular reconstruction based on the barcode gene (CO1) confirmed their genetic distinctness, but also the overall close relationships (mean divergence of 1.7 %) of all assayed taxa in this group. Although none of the haplotypes are shared across taxa, haplotypes of M. coibensis from Panama and M. barnesi from French Guiana are mixed in a single, poorly supported cluster, suggesting that these animals could represent a single biological species. Based on all evidences, we thus recommend treating barnesi as a junior synonym of M. coibensis, a species now widely and continuously distributed from Central America to Middle South America.

Introduction

The Order Chiroptera represents one fifth of all extant Mammals with well over 1116 recognized species [START_REF] Simmons | Order Chiroptera[END_REF], but the true diversity still remains underestimated in many places and taxonomic issues are continuously revised. Molecular data and phylogenetic reconstructions coupled with careful morphological comparisons provide an integrative framework that helps to better understand the evolution of this biodiversity and has been applied successfully in bat taxonomy [START_REF] Goodman | The use of molecular and morphological characters to resolve the taxonomic identity of cryptic species: the case of Miniopterus manavi (Chiroptera, Miniopteridae)[END_REF]. We apply here such an integrative approach to resolve the taxonomic status of small Neotropical molossid bats of the genus Molossus. [START_REF] Thomas | New Neotropical Molossus, Conepatus, Nectomys, Proechimys, and Agouti, with a note on the genus Mesomys[END_REF] described Molossus barnesi (Molossidae) from a single female specimen collected at Cayenne, French Guiana. Since then, this taxon was variously considered as a species on its own, or synonymized with other small Neotropical molossids. For instance, M. barnesi was synonymized with M. molossus by [START_REF] Freeman | A multivariate study of the family Molossidae (Mammalia, Chiroptera) : Morphology, ecology, evolution[END_REF] or [START_REF] Brosset | The bats of French Guiana: a taxonomic, faunistic and ecological approach[END_REF], while [START_REF] Dolan | Systematics of Middle American mastiff bats of the genus Molossus[END_REF] and [START_REF] Eger | Family Molossidae[END_REF] rather classified it within M. coibensis (another small Molossus species originally described by [START_REF] Allen | New bats from tropical America, with note on species of Otopterus[END_REF] from the Island of Coiba, Panama). Although the first authors did not justify their taxonomic decision, Dolan compared the holotypes and considered that barnesi fell within the morphological variation of a series of Central American M. coibensis. More recently, [START_REF] Simmons | The mammals of Paracou, French Guiana, a Neotropical lowland rainforest fauna. Part 1, Bats[END_REF] caught two small Molossus during a large survey of mammals conducted at Paracou (ca. 80 km north-west from Cayenne), French Guiana. They also compared this new material with the holotype of barnesi and with several other small-sized Neotropical Molossus and showed that these new specimens corresponded well to barnesi. However, they concluded that M. barnesi was a taxon on its own and clearly distinct (generally smaller-sized and with different pelage and dental patterns) from any other recognized species, including M. coibensis or M. molossus. They also confirmed that M. barnesi was so far only known from these 2 localities in French Guiana. [START_REF] Gregorin | Molossus aztecus and other small Molossus (Chiroptera: Molossidae) in Brazil[END_REF] challenged this taxonomic view arguing that the morphological characters distinguishing M. barnesi and M. coibensis were too variable in a broader geographic context or were overlapping between the few known (n=3) individuals of barnesi compared to the more numerous specimens assigned to M. coibensis. [START_REF] Gregorin | Molossus aztecus and other small Molossus (Chiroptera: Molossidae) in Brazil[END_REF] further mentioned the biogeographical issue regarding the much localized occurrence of barnesi (i.e. restricted to a small coastal area of French Guiana) versus the widespread distribution of M. coibensis, supposed to live in a region comprised between southern Mexico and the Brazilian Mato Grosso (Correa da [START_REF] Correa Da Costa | First record of Molossus coibensis (Chiroptera: Molossidae) in the Brazilian Amazon[END_REF]. More recently, the distribution of M. coibensis was extended even farther towards the south-east of Brazil, with a new locality in the Atlantic Forest biome (Pimental et al., 2014).

As the source of most of these taxonomic controversies appears to be a lack of appropriate comparative material of M. barnesi, and because no DNA characters have been examined so far in this context, we report here the comparative morphological and molecular analyses of a series of new specimens of M. barnesi collected in two localities of French Guiana where this taxon lives in sympatry with typical populations of M. molossus. We also use DNA sequences of extralimital material of other small Neotropical Molossus species, including a series of M. coibensis, to reassess their taxonomic status.

Material and methods

Over 200 small molossid bats living under several tin roofs of traditional houses were caught at Remire-Montjoly between November and December 2007 (collectors Maël Dewynter and Julien Jemin) and at Cacao in July 2012 (collectors Francois Catzeflis and Manuel Ruedi), both locations being set along the coastal region of north-east French Guiana. The locality of Remire-Montjoly (04°52'30'' N; 52°16'30'' W) lies in the eastern suburbs adjacent to the city of Cayenne, with surrounding habitats highly anthropized and consisting of a patchwork of private houses, gardens, and small forest fragments. The locality of Cacao (04°34'30'' N; 52°27'10'' W) lays ca. 45 km to the south of Cayenne and is set in an agricultural landscape comprised of various orchards and small plots of organic vegetables, with some secondary forest remains in its immediate vicinity.

Capture methods included mist nets (2.6 × 6 m and 2.6 x 9 m; mesh size = 16 mm) set close to the edges of roofs from where the molossids were leaving their roost at dusk. Upon capture, bats were held temporarily in individual cotton bags. Prior to release, each animal was aged (only adults with completely fused phalangeal epiphyses were considered), sexed and measured for the following three external measurements (with a dial calliper to the nearest 0.1 mm): forearm length (FA; taken from the tip of the elbow to the wrist with the wing held closed), length of metacarpal of third (MC3) and of fourth digit (MC4; measured on the dorsal side of the wing held flat on a solid surface, from the basis of the wrist to the tip of the metacarpal). A selection of 50 specimens (see list in Appendix A) were kept and euthanized following the guidelines of the American Society of Mammalogists for the use of wild mammals in research [START_REF] Sikes | Guidelines of the American Society of Mammalogists for the use of wild mammals in research[END_REF]. These specimens were preserved as scientific vouchers for further morphological and genetic analyses. A fragment of chest muscle was kept in 95% ethanol and specimens were fixed for one day in 10% buffered formalin, and stored in 70% ethanol. As no specific decree conserving bats outside protected areas exist in French Guiana, no specific legal authorization was required for captures and handling of bats.

Morphology

Reproductive status was acquired from external characteristics (e.g. enlarged nipples or testis) or from gross examination of dissected specimens [START_REF] Racey | Reproductive assessment of bats[END_REF]. In addition to the three external characters taken on all bats (FA, MC3 and MC4), tibia length (TI), tail length (TL), wingspan (WS), weight (expressed in grams) and length of mid-dorsal fur (DF) were also recorded on each vouchered specimen. Nine cranio-dental measurements were taken on the cleaned skulls with a dial calliper (accurate to 0.05 mm) following the methods detailed in [START_REF] Simmons | The mammals of Paracou, French Guiana, a Neotropical lowland rainforest fauna. Part 1, Bats[END_REF] except when noted: greatest length of skull (bone-to-bone: GLS), maxillary toothrow length (MTL), condylo-incisive length (CIL), breadth across canines (BaC), zygomatic breadth (ZB), mastoid breadth (MB), braincase breadth (BB), post-orbital breadth (PB) and outer breadth across molars (BaM). Because sexual dimorphism is common in Molossidae, including in the genus Molossus [START_REF] Freeman | A multivariate study of the family Molossidae (Mammalia, Chiroptera) : Morphology, ecology, evolution[END_REF][START_REF] Willig | Secondary sexual dimorphism and phylogenetic constraints in bats: A multivariate approach[END_REF], we determined its significance with Mann-Whitney tests (as implemented in the software PAleontological STatistics: [START_REF] Hammer | PAST: Paleontological statistics software package for education and data analysis[END_REF]. As most historic specimens are females and also to avoid the confounding factor of sexual dimorphism, the following global morphological comparisons were based only on a subset of 48 female molossids. This subset included 21 M. barnesi from French Guiana (including the two females studied by [START_REF] Simmons | The mammals of Paracou, French Guiana, a Neotropical lowland rainforest fauna. Part 1, Bats[END_REF], 19 M. molossus from French Guiana (including nine specimens studied by [START_REF] Simmons | The mammals of Paracou, French Guiana, a Neotropical lowland rainforest fauna. Part 1, Bats[END_REF], the holotype of M. barnesi , at the London Natural History Museum) and a series of seven females of M. coibensis from Brazil (Universidade Federal do Pará Campus de Bragança: vouchers numbers LJCC-13, LJCC-14, LJCC-16 to -20) assigned to this taxon by Correa da [START_REF] Correa Da Costa | First record of Molossus coibensis (Chiroptera: Molossidae) in the Brazilian Amazon[END_REF].

Morphological shape variation, determined for six cranial (GLS, CIL, MTL, BaM, BB, and PB) and one external (FA) measurements, was analysed using a Principal Component Analysis Biplot on scaled data (PCA Biplot, [START_REF] Core | R: A language and environment for statistical computing[END_REF].

Molecular analyses

DNA was extracted with the NucliSENS EasyMag robot (Biomérieux, Craponne, France) following manufacturer's recommendations for tissue extraction. The barcoding fragment of the mitochondrial gene Cytochrome oxydase 1 (CO1) was amplified as recommended by [START_REF] Borisenko | DNA barcoding in surveys of small mammal communities: a field study in Suriname[END_REF]. After amplification, PCR products were sent for purification and sequencing at Cogenics (Takeley, UK), using the same primers as for amplifications. Of the ca. one hundred sequences of small Molossus already available in GenBank, we selected a subset of 15 distinct haplotypes to represent 1 or 2 individuals each of the taxa coibensis, molossus and rufus living in the areas of sympatry (Panama, Ecuador and the Guiana Shield). Together with these 15 sequences retrieved from GenBank (Accession numbers in Appendix B), the six sequences generated here were aligned and checked manually with MEGA 6.0 [START_REF] Tamura | MEGA6: Molecular Evolutionary Genetics Analysis version 6.0[END_REF] for absence of gaps or stop codons, to ensure that these were not pseudogenes.

Phylogenetic relationships between samples were evaluated with neighbour-joining (NJ), maximum likelihood (ML) and Bayesian procedures, and using two Eumops species (two exemplars each of E.

hansae and E. auripendulus -accession numbers in Appendix B) as outgroups. The Tamura-Nei model (TN93) with gamma (G) rate parameter and a proportion of invariant sites (I) was identified with MEGA 6.0 as the best-fitting nucleotide substitution model. Ten thousand replicates were used for maximum likelihood and neighbour-joining analyses, yielding support values as Bootstrap Percentage (BP). The Bayesian approach was carried out with MrBAYES 3.2 [START_REF] Ronquist | MrBayes 3.2: efficient Bayesian phylogenetic inference and model choice across a large model space[END_REF]. Markov Chain Monte Carlo (MCMC) simulations were run twice independently for 10 million generations with four simultaneous chains, using a sample frequency of one every 1,000 and a burn-in of 3 million trees. Support values are indicated as Posterior Probabilities (PP) and were calculated from the remaining trees.

Together with the phylogenetic trees, we estimated the haplotype network of Molossus spp. sequences using Network 4.5.0. and the Median Joining (MJ) network algorithm [START_REF] Bandelt | Median-joining networks for inferring intraspecific phylogenies[END_REF].

Results

Capture sessions at Remire-Montjoly and Cacao yielded 196 adult Molossus bats. We plotted the distribution of FA lengths measured in these colonies for each sex separately. Measurements of the 128 females (53 from Remire-Montjoly and 75 from Cacao) and 68 males (27 and 41, respectively) show clear bimodal distributions, with little or no overlap between the two morphotypes found in syntopy (Figure 1). According to these clear differences, all females with a forearm smaller than 37.1 mm and all males with a FA smaller than 37.4 mm were assigned to the M. barnesi morphotype, whereas the larger specimens were assigned to M. molossus, as suggested by [START_REF] Simmons | The mammals of Paracou, French Guiana, a Neotropical lowland rainforest fauna. Part 1, Bats[END_REF]. As expected, all other external measurements correlated with size differed significantly between those two species identified by their forearm size (Table 1). Intraspecific sexual dimorphism, whereby males are larger than females, was also significant in the digit measurements (MC3 and MC4) of M. barnesi but not in those of M. molossus, as shown in Table 2.

Cranio-dental measurements also revealed the existence of a significant overall sexual dimorphism (p < 0.01), with males being larger that female at most variables (GLS, CIL, ZB, MB, BB and BaC).

Significant intraspecific sexual dimorphism was also evident in the skulls of both species (p < 0.01 for all variables except BaM in M. barnesi, and except MTL and PB in M. molossus). Regardless of the sex, skulls of M. molossus were longer than in M. barnesi, with all antero-posterior measurements (GLS, CIL, MTL, PB) being significantly different (p<0.01), whereas these two taxa had similar skull breadth (as measured by ZB, MB, BaM, BB, BaC; p > 0.05; Table 3).

Discussion

The newly collected material of M. barnesi sampled close to the type-locality in French Guiana adds to the only three historical specimens (all females) reported so far by [START_REF] Simmons | The mammals of Paracou, French Guiana, a Neotropical lowland rainforest fauna. Part 1, Bats[END_REF]. The now enlarged samples provide an appropriate series for assessing morphological variation and sexual dimorphism in this highly localized taxon. In two different localities (Cacao and Rémire-Montjoly), these small molossids were captured in strict sympatry (i.e. under the same tin roof) with another, larger species (M. molossus). It is, however, unclear whether individuals live really in intermixed clusters or whether they form species-specific social groups occupying different portions of the same building. According to the principle of competitive exclusion verified in other sibling species of bats living in sympatry [START_REF] Arlettaz | Trophic resource partitioning and competition between the two sibling bat species Myotis myotis and Myotis blythii[END_REF], these two species should even differ at some ecological aspects but this has still to be ascertained with proper evidences. Synanthropic roosts occupied simultaneously by 2 or 3 species of small molossids were also reported in the Brazilian Atlantic Forest (M. molossus, M. coibensis, M. rufus) by [START_REF] Pimenta | First occurrence of Molossus coibensis Allen, 1904 (Chiroptera, Molossidae) in Atlantic Forest[END_REF] and in central Panama (M. molossus, M. coibensis, and M. bondae) by [START_REF] Gager | The value of molecular vs morphometric and acoustic information for species identification using sympatric molossid bats[END_REF], whereas the syntopic occurrence of M. coibensis and M. molossus in outside roosts is already known from Ecuador (McDonough et al., 2011), from Guyana [START_REF] Lim | Species diversity of bats (Mammalia: Chiroptera) in Iwokrama Forest, Guyana, and the Guianan subregion: implications for conservation[END_REF]) and from Brazil [START_REF] Pimenta | First occurrence of Molossus coibensis Allen, 1904 (Chiroptera, Molossidae) in Atlantic Forest[END_REF].

Despite more of less pronounced sexual dimorphism exhibited by both species, highly significant morphometric differences exist between the distinctly smaller M. barnesi versus the larger M. molossus in French Guiana. This clearly supports the taxonomic distinction proposed by [START_REF] Simmons | The mammals of Paracou, French Guiana, a Neotropical lowland rainforest fauna. Part 1, Bats[END_REF]. In particular, wing measurements (FA, MC3, MC4 and WS) are all very discriminant, with little or no overlap between those two sympatric species. Our large samples of both Molossus species in French Guiana further show that the sexual dimorphism is more pronounced in M. barnesi than in M. molossus, as illustrated by external measurements such as forearm or third and fourth metacarps. Due to an overall significant sexual dimorphism (males being generally larger than females), these external differences are even more obvious when values are sorted by sex, as detailed in Table 2. Another external character mentioned by [START_REF] Simmons | The mammals of Paracou, French Guiana, a Neotropical lowland rainforest fauna. Part 1, Bats[END_REF], i.e. the length of dorsal hairs measured in the mid-dorsum (DF), is less useful for the discrimination of both species because several individuals caught in sympatry in French Guiana and in south-east Brazil [START_REF] Pimenta | First occurrence of Molossus coibensis Allen, 1904 (Chiroptera, Molossidae) in Atlantic Forest[END_REF] had intermediate values (about 3.0 mm).

Regarding the cranio-dental variables, we observed that M. barnesi and M. molossus have similar measurements in the breadth of the skull (expressed by ZB, MB, BaM, BB or BaC) but differ for length measurements (i.e. GLS, CIL, MTL or PB). Thus, the skull of M. barnesi is relatively shorter than that of M. molossus for similar breadth. This difference again corroborates earlier remarks on skull shape mentioned for those two species in Brazil [START_REF] Pimenta | First occurrence of Molossus coibensis Allen, 1904 (Chiroptera, Molossidae) in Atlantic Forest[END_REF]. Another qualitative discriminant character proposed by [START_REF] Simmons | The mammals of Paracou, French Guiana, a Neotropical lowland rainforest fauna. Part 1, Bats[END_REF] and also noted by [START_REF] Pimenta | First occurrence of Molossus coibensis Allen, 1904 (Chiroptera, Molossidae) in Atlantic Forest[END_REF] is the shape of the upper incisors (Figure 3). The six illustrated specimens indeed show that M. barnesi have slightly shorter and more convergent (spatulate) upper incisors, whereas those of M. molossus are more elongated and tapering (pincer-like), but these qualitative differences are sometimes difficult to evaluate on single specimens.

Although various morphological and morphometric characters support the existence of three distinct species of Molossus living in sympatry in French Guiana (the small M. barnesi and M. molossus and the much larger M. rufus, [START_REF] Simmons | The mammals of Paracou, French Guiana, a Neotropical lowland rainforest fauna. Part 1, Bats[END_REF], their CO1 sequences are very similar (differing by about 1.7% nucleotides substitutions), indicating that these haplotypes derive from a recent common mitochondrial ancestor. None of the sequenced bats shared the same haplotype (Figure 3 -right panel) but the number of assayed individuals here is not enough to establish firmly if time since their separation was long enough to lead to reciprocal monophyly of lineages in each species. When other extralimital sequences of other small Molossus are included in the molecular analyses, notably those of M. coibensis from Ecuador and Panama, the separation of taxa does not improve, as sequences are globally all very closely related (Figure 3). This indicates that most mitochondrial lineages in this group diverged recently from each others. Based on a much larger data set, [START_REF] Gager | The value of molecular vs morphometric and acoustic information for species identification using sympatric molossid bats[END_REF] also found very closely related CO1 sequences between morphologically distinct M. coibensis and M. molossus from Panama, Ecuador, Guyana and Suriname. Whereas the usefulness of DNA barcoding has proven its effectiveness in several other studies of bat identification (e.g. [START_REF] Clare | DNA barcoding of Neotropical bats: species identification and discovery within Guyana[END_REF]Clare et al., , 2011;;[START_REF] Lim | Review of species richness and biogeography of bats (Chiroptera) from the Guiana subregion of South America with comments on conservation[END_REF], this example of morphologically recognizable taxa which do not show necessarily appreciable genetic differentiation indicates that more rapidly evolving genes (such as some fastevolving nuclear introns or the mitochondrial control region) might be necessary to reach a better phylogenetic resolution.

Even if barcodes are of limited use in this group [START_REF] Borisenko | DNA barcoding in surveys of small mammal communities: a field study in Suriname[END_REF], haplotypes of M. barnesi from French Guiana are intertwined with those of geographically more distant M. coibensis from Panama and Ecuador and do not form distinct haplogroups (Figure 3). Notably, the later include representative sequences of M. coibensis sampled close to the type-locality of this taxon in Panama and identified with multiple morphological, bioacoustics and molecular characters [START_REF] Gager | The value of molecular vs morphometric and acoustic information for species identification using sympatric molossid bats[END_REF].

Again, such close genetic relatedness and lack of reciprocal monophyly calls into question the taxonomic distinctness of these two taxa.

Based on our new univariate and multivariate morphological comparisons, we further demonstrate that animals assigned to M. coibensis from Brazil (Correa da [START_REF] Correa Da Costa | First record of Molossus coibensis (Chiroptera: Molossidae) in the Brazilian Amazon[END_REF] and to M. barnesi from French Guiana are indistinguishable, whereas all M. molossus are clearly set apart on this morphospace (Figure 2). Although none of the specimens of M. coibensis from near the type-locality in Panama could be added to this multivariate analysis, measurements of the type specimen (Table 4) and direct morphological comparisons made by earlier researchers [START_REF] Dolan | Systematics of Middle American mastiff bats of the genus Molossus[END_REF][START_REF] Eger | Family Molossidae[END_REF][START_REF] Gregorin | Molossus aztecus and other small Molossus (Chiroptera: Molossidae) in Brazil[END_REF]) also confirm that coibensis and barnesi cannot be distinguished elsewhere. Given all available genetic and morphologic evidences, we thus recommend to consider M. barnesi as a junior synonym of M. coibensis. This proposed synonymy would also solve the critical issue raised by [START_REF] Gregorin | Molossus aztecus and other small Molossus (Chiroptera: Molossidae) in Brazil[END_REF] concerning the apparent lack of M. coibensis in some areas of the Guiana Shield [START_REF] Lim | Review of species richness and biogeography of bats (Chiroptera) from the Guiana subregion of South America with comments on conservation[END_REF], whereas it is found further south to the Mato Grosso and the Atlantic Forest biome in Brazil [START_REF] Paglia | Annotated checklist of Brazilian mammals[END_REF][START_REF] Correa Da Costa | First record of Molossus coibensis (Chiroptera: Molossidae) in the Brazilian Amazon[END_REF][START_REF] Pimenta | First occurrence of Molossus coibensis Allen, 1904 (Chiroptera, Molossidae) in Atlantic Forest[END_REF]. Given the anthropophilous character of the species in French Guiana (reported so far as M. barnesi) and elsewhere, we anticipate that more localities of M. coibensis throughout South America will fill gaps between the current scattered occurrences for this species. In conclusion, we concur with [START_REF] Gregorin | Molossus aztecus and other small Molossus (Chiroptera: Molossidae) in Brazil[END_REF] that a more global taxonomic review concerning other small taxa of the genus Molossus living in tropical South America is needed, as the exact number of distinct biological species contained in this group is still debated. Unusually divergent barcode sequences of a small Molossus sp. found in the Kanuku Mountains of Guyana [START_REF] Lim | Species diversity of bats (Mammalia: Chiroptera) in Iwokrama Forest, Guyana, and the Guianan subregion: implications for conservation[END_REF] even suggest that additional cryptic species might occur in the region [START_REF] Clare | DNA barcoding of Neotropical bats: species identification and discovery within Guyana[END_REF]. Table 1. External measurements for small molossids caught in syntopy at Remire-Montjoly and Cacao, in French Guiana. All females with a forearm smaller than 37.1 mm and all males with a forearm smaller than 37.4 mm were assigned to the M. barnesi morphotype, whereas the larger specimens were assigned to M. molossus. Values are mean ± one standard-deviation (minimum and maximum); n = sample size. See Material and Methods for abbreviations of measurements. W stands for weight, expressed in grams, while all other variables are expressed in mm. M. molossus from French Guiana (including 11 specimens studied by [START_REF] Simmons | The mammals of Paracou, French Guiana, a Neotropical lowland rainforest fauna. Part 1, Bats[END_REF].

Tables

M. barnesi

Abbreviations: PC = Principal Component; var. = variance. molossus (MHNG-1972(MHNG- .020, 1972(MHNG- .022 and 1972.023).023). The scale bar is 3.0 mm.

  An analysis of variance (ANOVA) for size variation at one external (FA) and six cranio-dental measurements (GLS, CIL, MTL, BaM, BB, and PB) of the 48 female reference specimens indicates that M. molossus is clearly larger than M. barnesi and M. coibensis (post-hoc Tuckey test: p = 0.0001 and p = 0.0323, respectively), while females M. coibensis and M. barnesi do not differ significantly (p = 0.7998). The PCA Biplot based on those same variables explained a high percentage of the total variation, 45.5% being associated to the first and 26.0% to the second component. This PCA Biplot indicates that the seven M. coibensis from Brazilian Para and all specimens of M. barnesi from French Guiana (including the holotype of barnesi) form completely overlapping groups, while individuals of M. molossus are set in a distinct cluster (Figure2). Table 4 compares our French Guianan sample consisting of 11 males and 20 females (including the holotype) M. barnesi with a sample of 21 males (including the type of coibensis) and 23 females M. coibensis taken in Panama (sample #19 from Chiriquí, La Concepcíon, in Dolan, 1989). As already mentioned by Dolan (1989), measurements of the female holotype of barnesi (BMNH-5.1.8.7) fall within the range of female specimens of M. coibensis from Central America. Similarly, the male holotype of coibensis (AMNH-18731) conforms well to the variation of males M. coibensis from Panama or from those of M. barnesi from French Guiana. The phylogenetic reconstructions (Figure 3 -left panel) based on CO1 sequences indicate that small Molossus assayed form various monophyletic clades which appear very closely related to each other, differing by an average of 1.7 % substitutions (range 0.0 -2.0 %). In particular, sequences of M. coibensis from Ecuador and Panama and those of M. barnesi from French Guiana differ by less than 1.5% substitutions. Sequences of M. molossus from French Guiana, Ecuador, Panama, Suriname and Guyana and those of M. rufus from French Guiana and Guyana each form monophyletic taxa (BP support 71% and 95%, respectively), whereas sequences of M. coibensis and M. barnesi are intertwined. The MJ network which shows in more details relationships of the various haplotypes (Figure 3 -right panel) further indicates that the COI haplotypes of M. barnesi and M. coibensis derive from the same haplogroup, whereas those of M. molossus and M. rufus are set further apart.

Figure 1 .

 1 Figure 1. Distribution of forearm lengths for 128 females (left) and 68 males (right) of Molossus spp. caught in syntopy at two localities in French Guiana. The smaller animals correspond to the M. barnesi morphotype (represented in dark gray, FA smaller than 37.1 or 37.4 mm for females and males, respectively); the larger animals correspond to the M. molossus morphotype (represented in light gray, FA larger than 36.5 or 37.3 mm for females and males, respectively).

Figure 2 .

 2 Figure 2. Principal Component Analysis Biplot with confidence ellipses based on six cranio-dental (GLS, CIL, MTL, BaM, BB, and PB) and one external (FA) measurements measured in 48 female specimens of Molossus spp. The legend for species is as follows: M. barnesi (black squares), M. coibensis (light gray point-up triangles) and M. molossus (gray circles). Notice the position of the holotype of M. barnesi (black diamond), which is placed in the middle of the groups including all M. barnesi from French Guiana and those of M. coibensis from Brazil. Specimens of M. molossus from French Guiana form a distinct cluster. The dataset comprises the holotype of M. barnesi (BMNH-5.1.8.7), seven M. coibensis from Brazilian Para (Correa da Costa et al., 2013), 21 M. barnesi and 19

Figure 3 .

 3 Figure 3. Left: Maximum likelihood tree showing the phylogenetic relationships among 16 CO1 barcodes of the following Molossus spp.: M. barnesi (French Guiana), M. coibensis (Ecuador, Panama), M. rufus (French Guiana; Guyana), and M. molossus (Ecuador, French Guiana, Guyana, Panama, Suriname). Each individual is identified with its voucher number (see details in the Appendix B). Bootstrap support from NJ / ML and posterior probabilities (PP) from a Bayesian analysis are shown above and below major nodes, respectively. The tree was rooted with sequences of Eumops hansae and E. auripendulus. Right: Median-Joining network for 14 different CO1 haplotypes (Hap) of Molossus spp. (see Appendix B for linking haplotype number and specimen details).

Figure 4 .

 4 Figure 4. Frontal view of the upper dentition of three Molossus barnesi (top row) and three M. molossus (bottom). The shape of upper incisors are more or less species-specific, i.e. more spatulate in M. barnesi (from left to right: MHNG-1979.023; 1979.026 and 1979.029) versus pincerlike in M.

Table 2 .

 2 Three wing measurements (FA, MC3, MC4) of small Molossus spp. caught in syntopy at the localities of Remire-Montjoly and Cacao in French Guiana. Values (in mm) are expressed as the mean ± one standard deviation (minimum -maximum); n = sample size. The p value of the last column represents the significance of sexual dimorphism investigated with Mann-Whitney tests.

			M. barnesi
		females	n	males	n	p
	FA	34.8 ± 0.7	95	35.9 ± 0.7	47	< 0.0001
		(32.9 -36.3)		(33.9 -37.3)
	MC3	34.0 ± 0.8	83	34.6 ± 0.8	44	< 0.0001
		(32.0 -35.5)		(32.5 -36.0)
	MC4	32.4 ± 0.9	83	32.8 ± 0.9	44	0.0204
		(30.0 -34.5)		(31.0 -34.5)
			M. molossus
		females	n	males	n	p
	FA	39.0 ± 0.8	33	39.4 ± 1.2	21	0.4087
		(37.3 -40.8)		(37.4 -41.6)
	MC3	38.8 ± 1.2	29	38.4 ± 1.2	19	0.2479
		(36.0 -41.5)		(37.0 -40.5)
	MC4	36.6 ± 0.9	29	36.6 ± 1.2	19	0.3813
		(34.0 -38.0)		(35.0 -39.5)

Table 3 .

 3 Mean, standard deviation and ranges of 9 cranio-dental measurements (expressed in mm) taken on skulls of M. barnesi (n = 30) and M. molossus (n = 20) caught in syntopy in French Guiana.Males and females were not distinguished. Significance of differences was investigated with Mann-Whitney (p values). See Material and Methods for abbreviations of these cranio-dental variables.

		M. barnesi	M. molossus	p
	GLS	16.1 ± 0.6	16.6 ± 0.7	0.0078
		(15.4 -17.5)	(15.5 -17.9)
	CIL	14.9 ± 0.5	15.7 ± 0.5	<0.0001
		(14.2 -15.9)	(14.5 -16.3)
	ZB	10.6 ± 0.3	10.5 ± 0.4	0.9420
		(10.1 -11.2)	(9.8 -11.2)
	MB	10.2 ± 0.5	10.1 ± 0.4	0.5438
		(9.3 -11.1)	(9.4 -10.9)
	MTL	5.9 ± 0.2	6.2 ± 0.2	<0.0001
		(5.5 -6.3)	(5.6 -6.5)
	BaM	7.6 ± 0.2	7.6 ± 0.3	0.3233
		(7.2 -8.1)	(7.0 -8.1)
	PB	3.8 ± 0.1	3.6 ± 0.2	0.0011
		(3.5 -4.1)	(3.3 -4.0)
	BB	8.9 ± 0.2	8.8 ± 0.3	0.0721
		(8.5 -9.2)	(8.4 -9.3)
	BaC	4.3 ± 0.2	4.4 ± 0.2	0.0537
		(4.0 -4.6)	(4.0 -4.8)

Acknowledgements

We first would like to acknowledge Maël Dewynter and Julien Jemin for generously sharing their data on the molossids which they caught at Remire-Montjoly as well as Julien Claude for helping with some statistical analyses of morphological variation. Laurent Vallotton provided appreciated help in the field in Cacao. Skulls were prepared by Michel Gillioz at the Natural History Museum of Geneva (Switzerland). The study received financial support from the Agence Nationale de la Recherche through an "Investissement d'Avenir" grant (CEBA, ref. ANR-10-LABX-25-01). Fieldwork at Cacao (French Guiana) was funded by French National Research Agency Project ANR 06-SEST-20 IAEL attributed to the MIVEGEC (UMR IRD 224-CNRS 5290) laboratory of Montpellier, France.

Appendix B. List of animals with CO1 barcoding fragment: 15 individuals retrieved from GenBank and 6 individuals (indicated with §) sequenced for this study. Abbreviations for specimen numbers: MHNG = Muséum d'histoire naturelle de Genève (Switzerland); ROM = Royal Ontario Museum (Toronto, Canada). The column "Haplotype" provides the haplotype number for animals of the MJ network of right panel in Figure 3.


Eugenia Martinez-Ferrero

David Grosso

Cédric Boissière

Clément Sanchez

Olivier Oms

Dominique Leclercq

André Vioux

Fabien Miomandrec

Pierre Audebert

Cédric Boissiere

Fabien Miomandre

Electrochemical investigations into ferrocenylphosphonic acid functionalized mesostructured porous nanocrystalline titanium oxide

come

Introduction

During the last two decades, the development of organic-inorganic hybrid materials has been associated with the evolution of sol-gel process. [1][2][START_REF] Clearfield | Progress in Inorganic Chemistry[END_REF] Furthermore, a wide class of hybrids involves the covalent bonding of the organic and the inorganic components through the use of coupling molecules. Some of us have recently demonstrated the potentialities of phosphonate and phosphinate groups in the coupling of organic components to metal oxides. 4- 8 Actually, this coupling is quite stable and difficult to hydrolyze.

Meanwhile the apparition of the first micellar templated materials prepared by sol-gel route has introduced a new type of extremely interesting materials due to their highly organized structure [9][10] . Usually, they present a narrow mesopore size distribution easily tunable between 2 and 30 nm, mesoporous cavities of defined geometry (lamellar, spherical or cylindrical) with various degrees of connectivity and a large porous volume (sometimes higher than 1cm [START_REF] Clearfield | Progress in Inorganic Chemistry[END_REF] .g -1 ). Their preparation by the recently developed Evaporation Induced Self Assembly (EISA) process allowed their rapid and easy shaping as nanometric powders, monoliths, fibers, and thin films of optical quality and controlled thickness. [11][12][13] Due to their very specific porous network, these new materials are thus highly promising candidates for electrochemical investigations, allowing to establish a relationship between the mesostructure and the electron transfer properties within the structure. Cyclic voltammetry and chronoamperometry in turn are choice methods to investigate the specific features of electron transfer in materials. We have already demonstrated that electrochemistry was a suitable tool for the investigations of the nanostructure of materials prepared by sol-gel chemistry [14][15][16][17] and in particular that the fractal dimension of oxide colloids could be determined by electrochemical investigations. 18 Ferrocenylphosphonic acid has been shown to be a redox-active pH-responsive molecules for which the variations of the half-wave potential of the acid and their salts results from an electrostatic stabilization and not from the nature of the cations. The electrochemical studies of different metal ferrocenylphosphonates have been reported; particularly the redox half wave potential has been shown to be quite sensitive to the bonding mode to the metal atoms. [19][20][21][22] In this paper we report the anchoring of ferrocenic phosphonic acid onto TiO 2 particles, and we describe the electrochemical behavior of ferrocenylphosphonic acid grafted onto nanocrystalline mesostructured anatase titanium dioxide thin films prepared by EISA process, presenting a specific 2D grid-like pore shape. We show the mode of bonding of the ferrocenylphosphonic acid and how the fine analysis of the electron transfer dynamics is indicative of the anisotropic repartition of the ferrocenyl groups within the film, allowing us to estimate the diffusion coefficient characteristic of the charge transfer with pores. The results shed some light on the efficiency of the charge transfer process between grafted organic components and the mesoporous semiconducting TiO 2 film, which might be important for the improvement of Dye Sensitized Solar Cells (D.S.S.C.) efficiency.

Experimental section

Synthesis

Ferrocenylphosphonic acid was prepared according to the literature procedure. 19 Anchoring of FcPO 3 H 2 on TiO 2 particles was performed as reported in the liierature. 5 1.42g of TiO 2 particles (P25 Degussa) with an average particle size of 21 nm and a specific surface area of 45±5 m 2 g -1 were added to 144 mg (0.54 mmol) of ferrocenylphosphonic acid in 50 ml of methanol. The suspension was stirred at room temperature for 24 h and the powder was filtered off and washed successively three fold with 30 ml methanol, and two fold with 30 ml acetone and 30 ml diethyl ether, and dried 12 h under vacuum at room temerature.

The mesoporous TiO 2 films were prepared as previously reported in the literature. [23][24][25] First we prepared a solution containing TiCl 4 as inorganic precursor, a volatile solvent made of ethanol and water, and Pluronic F127 block copolymers (HO(CH 2 CH 2 -O) 106 (CH 2 CH(CH 3 )-O) 70 (CH 2 -CH 2 -O) 106 H) as structuring agents. All reagents were used as provided by Sigma-Aldrich company. The following solution composition was adopted: TiCl 4 :EtOH:H 2 O:F127 with molar ratios of 1:40:10:0.005. This transparent and slightly viscous solution was stirred 15 minutes at room temperature for homogenization. The solution was then deposited by dip coating at the surface of a SnO 2 :F (FTO) substrate at constant speed rate of 2.5 mm.s -1 in controlled atmosphere. The liquid layers were evaporated at a fixed Relative Humidity (RH) of 15% then transferred and aged in a sealed environmental chamber with a RH fixed either at 70% for 18 hours. Then, the following thermal treatment was applied: 24 hours at 130°C and 3 hours at 350°C for densification of amorphous TiO 2 , 10 minutes flash heating at 500°C and 5 minutes flash heating at 550°C. As reported in literature, flash treatments induced the transformation of amorphous TiO 2 into Anatase TiO 2 nanocrystals of about 7-8 nm. 24,26 The functionalizations were performed by soaking the nano-crystallized mesoporous films into a 1•10 -4 M ethanolic solution of ferrocenylphosphonic acid during 3 h. A continuous stirring was applied to keep the solution homogeneous. The resulting samples were rinsed several times with absolute ethanol and dried in air.

Environmental Ellipsometric Porosimetry

Environmental Ellipsometric Porosimetry (EEP) investigations were performed with a Variable Angle Ellipsometer 2000U from Woolam in the range 400-1000 nm by varying the relative humidity of the atmosphere over the TiO 2 films. The porous volume of TiO 2 films was calculated with the Brugemann Effective Medium Approximation (BEMA) from the optical properties of void and of a TiO 2 reference film prepared without structuring agent with the same thermal history as its mesoporous counterpart. The fractions of porous volume filled with water during the analysis were calculated with BEMA from a mix of the dry mesoporous film and the film completely saturated with water. All the details of experimental setup and data treatments have been previously described. 27

Electrochemistry

Cyclic voltammetry of modified TiO 2 particles was performed on the powder by means of a Radiometer Analytical PGZ 100 potentiostat in a three-electrode cell. A platinum cavity microelectrode provided by the "réseau micro électrode à cavité" of CNRS (France), was used as working electrode, a platinum wire as auxiliary electrode, and a saturated calomel as reference electrode. The electrolyte was KCl (1M in water) and the scan rate was 100 mV s -1 .

The electrochemical response of the functionalized mesoporous TiO 2 films was analyzed using slow and fast scan rate cyclic voltammetry and fast chronoamperometry using an efficient ohmic drop compensation equipped with a home-built potentiostat. 28 The medium used for analysis was acetonitrile (SDS, Spectroscopic Grade), with TBAP (Fluka, puriss.) 0.1 M as the supporting electrolyte. The working electrode was a SnO 2 :F (FTO) plate coated with the TiO 2 film, a part of which was masked so that an area of c.a. 1 cm 2 was in contact with the electrolytic solution. A platinum wire was used as a counter electrode with an Ag|AgCl reference electrode. Solutions were degassed by argon bubbling for 15 minutes prior to each experiment.

Results and discussion

Anchoring of FcPO 3 H 2 on titania particles.

The possibility of anchoring of ferrocenylphosphonic acid on a titania surface has been checked by reacting the acid with TiO 2 particles (P25 Degussa) in methanol at room temperature. The solution was then filtered off and the powder was thoroughly washed to remove unreacted and physisorbed species and then dried before analysis. Elemental analysis shows 0.66 wt% of P corresponding to 2.8 coupling molecules per nm 2 of TiO 2 . The 31 P NMR spectrum (fig) shows a rather broad signal at δ = 24.1 ppm, similar in shape to the ones observed for phenylphosphonate/TiO 2 particles. 5 The chemical shift is different from the ones of crystalline FcPO 3 H 2 which shows two peaks in the solid state at 26. 19,21,22 This suggests that one P-OH group of the ferrocenylphosphonic acid is not bonded to the surface and remains free. The results show that ferrocenylphosphonic acid is strongly bonded to the titanium oxide particles by two oxygen titanium bonds.

Structural analysis of TiO 2 nanocrystallized electrode

Careful studies of the calcination process of mesostructured electrode have shown that aging and crystallization of the amorphous TiO 2 to nanocrystalline anatase involved a simultaneous dramatic reorganization of the mesoporous architecture. As-prepared films exhibit body centered cubic mesostructure (space group Im3m) with organized domains preferentially aligned with their [110] direction normal to the interface, 24,26 as shown in the figure 1A. After consolidation of the inorganic mesostructure at 130 °C for 30 min and removal of the surfactant at 350 °C, the unidirectional shrinkage induced by the drying and thermal treatment applies perpendicularly to the surface and provokes the transformation of the initial mesostructure into a contracted cubic structure having orthorhombic symmetry.

Upon crystallization at 500 °C, this latter structure is turned into a grid-like structure of bidirectional mesoporous parallel network standing perpendicular to the substrate surface percolating from the TiO 2 air interface to TiO 2 -FTO electrode (Fig. 1B andC, TiO 2anatase). 25 The thermal treatment was pushed up to 550°C in order to enlarge connectivities between mesopores.

After impregnation of the calcined film with ferrocenylphosphonic acid, the volumetric analysis of the electrode was performed via spectroscopic ellipsometry. TiO 2 impregnated films were perfectly fitted between 400 nm and 1100 nm with a cauchy single layer model, strongly suggesting that the organic probe was homogeneously dispersed within the porous network. Finally, the measurement of the static water contact angle informs about the wettability of the surface. The measurements have been performed with water drops of 2.5 μL on several samples and the average value was determined. TiO 2 surfaces are hydrophilic allowing the expansion of the water drop and, thus, give low contact angles of 27º. On the contrary, the anchoring of the phosphonic acid on the titania left the hydrophobic terminal ferrocene groups on the surface promoting a contact angle value of 50º after dipping in the ferrocenylphosphonic acid solution and washing. The increase of the contact angle corroborates the presence of hydrophobic molecules onto the surface.

The water adsorption-desorption isotherm obtained by EEP is given in the figure 2. From measurements performed in dry air, we determined the TiO 2 film thickness at 221 nm and the total porous volume of the film is 0.40 cm 3 .cm -3 . As the RH increased, the porous film exhibited a slow uptake of water and a sudden steep adsorption at 70% of RH, characteristic of surfactant templated mesoporous films with a narrow pore size distribution. [26][27][29][30][31][32] Upon desorption, a large hysteresis characteristic of pores restrictions appears. The parameters of the porous network, that is, pore large diameter, small diameter and size of restrictions were calculated from the isotherm at 7.6 nm, 2.9 nm and 1.4 nm respectively. From these analyses, one can deduce that the TiO 2 used for electrochemical analysis exhibits a porous network characteristic of the grid-like structure previously reported and made of anisotropic mesoporous cavities connected with each other by four microporous windows, as schemed in the figure 3.

Electrochemistry

The response in cyclic voltammetry of the ferrocene moieties included in the mesoporous titanium dioxide film is represented in Fig. 4 at various scan rates. The signal exhibits very well behaved peaks, with a tailing characteristic of a diffusion-limited current.

The redox potential of the electroactive moieties is + 270 mV vs. AgCl|Ag. Taking into account a ΔE 1/2 of 50 mV between AgCl and SCE (calomel), this value is the same than the one found for the modified titanium dioxide particles. and the same mode of anchoring of the phosphonic acid with one P-OH group of the ferrocenylphosphonic acid not bonded to the surface can be proposed. The low increase in the hydrophobicity of the surface after grafting could be explained by the presence of these remaining hydrophilic groups.

Nevertheless, a very interesting feature is the evolution of the peak currents with the scan rate in log-log scale (fig. 5a). First of all, a linear relationship (slope of α = 0.65 ±0.02) is obtained on nearly 4 orders of magnitude of scan rate, showing that there is no transition in the mass transfer regime on the explored timescale. In the case of electron hopping between redox sites homogeneously distributed in an isotropic medium, a proportionality of the peak current with the square root of scan rate is expected, since hopping can be assimilated to a diffusion process, as shown by Laviron 33 and Andrieux. 34 This is not the case here, since electron diffusion cannot be assumed to be isotropic, but rather restricted within the "channels" of the mesoporous structure. Further investigation to fully understand this really unusual behavior is currently under progress but requires modelization of the diffusion process in geometry like the one schemed in figure 3.

On the other hand, since it is sometimes uneasy to analyze cyclic voltammograms accurately in terms of rate constants, we turned to chronoamperometry measurements. This technique has the advantage to eliminate the difficulties linked to slow electron exchange rate constants at the electrode (provided that the potential step is chosen far enough from the peak potential). As a consequence, it also enables to have insights into the electron pseudodiffusion kinetics, as forecast 17 and demonstrated in previous situations. 18 Potential steps at least 200 mV above the ferrocene oxidation potential are applied here, and the current vs time is plotted on a bilogarithmic scale. The results are shown in Fig. 5b. It is clear that a linear relationship is also observed on several orders of magnitude, but with a slope different from the classical value (-0.65 instead of -0.5). Thus, the chronoamperometry measurements confirm the results obtained from cyclic voltammetry as concerns the non-isotropic electron diffusion process in this kind of material. This very unusual behavior has never been observed so far in a modified electrode.

From the current variation with time or scan rate, it is possible to draw an estimation of the apparent diffusion coefficient for electron transfer between ferrocene moieties; [START_REF] Bard | Electrochemical Methods[END_REF]

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = . nF RT D v t 2 l =
where n is the number of electron exchanged per ferrocene unit (n = 1), A is the active area of the electrode, c Fe is the volumic concentration of Fe in the material and p is the slope of the I vs. v relationship (other symbols have their usual meanings). The iron amount can be deduced from integration of the CV curve obtained at very low scan rate (10 mV.s -1 ), assuming that all the ferrocene moieties of the material layer are oxidized at this timescale. A concentration of ca. 8.10 -5 mol.cm -3 , corresponding to ca. 0.2 % (in mass) of Fe vs. TiO 2 was found.

From this value of c Fe and taking the geometric area of the electrode (1 cm 2 ), a diffusion coefficient D app of ca. 4•10 -10 cm 2 .s -1 was obtained from the CV analysis. This value is in good agreement with similar measurements in the case of adsorbed redox molecules in mesoporous films of TiO 2 , [START_REF] Mckenzie | [END_REF] where the great amount of adsorbed molecules made the diffusion process much more likely to be due to electron hopping than to actual motion of species in solution, thus making the comparison with our results suitable.

In such conditions, the transition between the diffusion limited (at short timescale) and the thin layer (at long timescale) regimes can be estimated to occur for the following scan rate: where λ is the thickness of the material layer deposited on the electrode (λ = 221 nm). Equation (2) gives v t = 20 mV.s -1 , which validates the assumption made for the calculation of c Fe . This means that a thin-layer behavior is likely to be observed at scan rates much lower than this transition value.

  7 and 29.6 ppm. The half wave potential of the ferrocenyl group is + 230 mV/SCE. This value is very closed to those found for FcPO 3 HNa (E 1/2 = + 246 mV/SCE in H 2 O), (FcPO 3 H) 2 Zn•2H 2 O (E 1/2 = + 235 mV/SCE in H 2 O), (FcPO 3 H) 2 Cd•3.5H 2 O (E 1/2 = + 238 mV/SCE in H 2 O), and (FcPO 3 H) 2 Mn•3H 2 O (E 1/2 = + 243 mV/SCE in H 2 O), whereas it is far from the half wave potentials of FcPO 3 Na 2 (86 mV/SCE), (FcPO 3 ) 2 Cd•2H 2 O (132 mV/SCE ) and (FcPO 3 ) 2 Mn•2H 2 O (135 mV/SCE ).

  in the case of cyclic voltammetry, the Randles-Sevcik relationship can be written: ‡

Fig. 1 (

 1 Fig. 1 (adapted from reference 27) Illustration of the mesoporous TiO 2 architecture obtained at (A) 300 °C (closed contracted bcc) and (B) 500 °C (open grid-like). TEM picture of the open grid like structure stabilized at 500 °C (C).

Fig. 1 (

 1 Fig. 1 (adapted from reference 27) Illustration of the mesoporous TiO 2 architecture obtained at (A) 300 °C (closed contracted bcc) and (B) 500 °C (open grid-like). TEM picture of the open grid like structure stabilized at 500 °C (C).

Fig. 2 A

 2 Fig.2 A) Water adsorption-desorption isotherm obtained from EEP measurements after impregnation of ferrocenylphosphonic acid. B) Pore size distribution of (circles) small axis and (triangles) large axis of ellipsoidal pores obtained from the adsorption branch of the isotherm.

Fig. 3

 3 Fig. 3 Nanocrystallized TiO 2 porous network parameters obtained from EEP analysis assuming ellipsoidal pore geometry.

Fig. 4 Fig. 5 a

 45 Fig. 4 CVs of the ferrocene grafted mesoporous

P. Audebert, S. Sadki and S. Sallard, J. Phys.Chem. B, 2003Chem. B, , 107, 1321. .

Acknowledgements

The authors thank the NOE FAME for financial support and integration activities, and the "réseau microelectrode à cavité" of CNRS France for the gift of a cavity microelectrode. E. M-F thanks the Conselleria d'Empresa, Universitat i Ciència of the Generalitat Valenciana for a postdoctoral fellowship.

Conclusions

We have described the preparation of functionalized mesoporous titanium oxide layers, and the first fast electrochemical study allowing us to have insights on the mode of anchoring of the ferrocenylphosphonic acid and the short range charge transfer features inside the film. Surprisingly, a very unusual time-current dependence has been observed, which could be indicative of restricted charge pseudo-diffusion within the localized mesopores. Further investigations are in progress to model the electron transfer in such peculiar geometry of modified electrodes. On the other hand, the quality of the charge transfer at the hybrid organic-inorganic interfaces demonstrates that this transfer between the grafted organic component and the mesoporous titania is likely not the limiting step in the preparation of high efficient D.S.S.C. 37 Notes and references ‡ Despite the non-classical diffusion mode observed here, we use the Randles-Sevcik equation, which should provide an estimation of the order of magnitude of the electronic diffusion coefficient.