Andrea Bedon
email: abedon@efestoinnovation.it

Jean Paul Viricelle

Mathilde Rieu

Simone Mascotto

Antonella Glisenti
email: antonella.glisenti@unipd.it

Single Chamber Solid Oxide Fuel Cells selective electrodes: a real chance with brownmillerite-based nanocomposites

Keywords: Single-Chamber Solid Oxide Fuel Cell, brownmillerites, iron oxide nanocomposites, selective electrodes

In this contribution brownmillerite-based nanocomposite cathode for Single-Chamber Solid Oxide Fuel Cells is developed. These cells can be very attractive especially for small and cheap devices because of the absence of seals. The efficiency of SC-SOFCs is strictly connected to the selectivity of anode and cathode, the bottleneck for this technology. The development of a cathode inert in fuel oxidation is particularly challenging. Our strategy is to start from a catalytically un-active support (CFA=Ca2FeAl0.95Mg0.05O5) and induce the formation of iron oxide based nanoparticles, expected to activate oxygen. Symmetric (CFA+FeOx/CGO/CFA+FeOx) and complete cells (CFA+FeOx/CGO/Ni-CGO) are studied in air and methane/oxygen 2:1 mixture. The Area Specific Resistance of CFA+FeOx is less than 1/3 that of CFA. The high selectivity allows to reach an efficiency of 25%; power still needs to be increased but we demonstrated the possibility to develop selective low cost electrodes. The effect of air, methane/oxygen exposure and the heat treatments were carefully investigated.

Introduction

Solid Oxide Fuel Cell technology is in a period of great development and since now, has been reserved to stationary applications, due to their size and their thermomechanical fragility.

A particular type of SOFC has been proposed and studied: Single Chamber SOFC (SC-SOFC). A SC-SOFC [START_REF] Hibino | Simplification of Solid Oxide Fuel Cell System Using Partial Oxidation of Methane[END_REF][START_REF] Brett | Intermediate temperature solid oxide fuel cells[END_REF] resolves most of the flaws of a traditional SOFC and in principle would have several advantages [START_REF] Yano | Recent advances in single-chamber solid oxide fuel cells[END_REF][START_REF] Kuhn | Single-Chamber Solid Oxide Fuel Cell Technology-From Its Origins to Today's State of the Art[END_REF], especially for small and cheap devices. In the SC-SOFCs both the electrodes are immersed in the same atmosphere. The obtainment of an effective sealing at high temperature is complicated, and tight connections between the cell and the other sealing elements can be the source of tensions leading to failures. For Single Chamber devices, cell design becomes more compact, and in general fabrication is easier. Moreover, specific applications can be devised; an example is the use of SC-SOFCs operating with exhaust gases in thermal engines [START_REF] Briault | Anode supported single chamber solid oxide fuel cells operating in exhaust gases of thermal engine[END_REF]. In this application the cell might be embedded at the outlet of engine and could turn unburned hydrocarbons present in the exhaust gas into electricity allowing, for instance the energy supplying of electronic devices in vehicles; such application can also consider all cases in which hydrocarbons are burnt, as in stationary power plants After start-up, SC-SOFCs can operate without external heating, because the direct oxidation of fuel by oxygen is exothermal and can sustain autonomously the cell, at expense of a fraction of efficiency. The main drawbacks are the low efficiency due to parasitic reactions, and the risk of explosion related to the presence of fuel and oxygen in the same mixture. For safety reasons, SC-SOFCs are fed only with methane and rarely with hydrogen; methane at the anode is subjected to partial oxidation and the syngas produced is the real fuel [START_REF] Riess | On the single chamber solid oxide fuel cells[END_REF].

In SC-SOFCs the selectivity of electrode materials for the respective electrochemical reaction is critical, and has been the main restrain to a large diffusion of these devices. No material turned out to have the selectivity required, and only a maximum 8% efficiency has been reached [START_REF] Kuhn | Single-Chamber Solid Oxide Fuel Cell Technology-From Its Origins to Today's State of the Art[END_REF]. Instead, great advancements were accomplished in cell design, with indisputably good results in terms of cell power [START_REF] Shao | A thermally self-sustained micro solid-oxide fuel-cell stack with high power density[END_REF].

Coplanar cells are electrolyte plates in which both the electrodes are printed on the same side [START_REF] Kuhn | Miniaturization limits for single-chamber micro-solid oxide fuel cells with coplanar electrodes[END_REF][START_REF] Kuhn | Single-chamber micro solid oxide fuel cells : Study of anode and cathode materials in coplanar electrode design[END_REF].

Flow-through cells (also named Mixed Reactant Cell) in which the gas mixture is forced through repeated porous layers of cathode, electrolyte and anode are another possibility. [START_REF] Riess | Catalytic Requirements for Mixed Reactant Fuel Cells[END_REF] Riess [START_REF] Riess | On the single chamber solid oxide fuel cells[END_REF][START_REF] Riess | Significance of impeded reactions in solid state electrochemistry-Conspicuous examples[END_REF][START_REF] Riess | The significance of impeded reactions in solid state electrochemistry[END_REF][START_REF] Riess | Catalysis of electrochemical processes and the suppression of chemical ones are needed in mixed reactant fuel cells -Can this be achieved?[END_REF], stressed the importance of the selectivity of the electrodes on SC-SOFCs performance. A SC-SOFC is operated in an anomalous way compared to other cells. A strong imbalance in fuel (methane)/oxygen ratio, which ranges between 1 and 2 [START_REF] Rembelski | In situ reduction and evaluation of anode supported single chamber solid oxide fuel cells[END_REF][START_REF] Morel | Temperature and performance variations along single chamber solid oxide fuel cells[END_REF] and a high gas flow, allow a large part of the fuel to pass through the cell unreacted.

The oxygen poor mixture is necessary to promote selective methane partial oxidation to syngas at the anode [START_REF] Riess | On the single chamber solid oxide fuel cells[END_REF]. The cathode should not be able to catalyse methane oxidation, and hardly methane can be used directly for electrochemical oxidation. Syngas is the real fuel so feeding this mixture of methane and oxygen is a way to feed fuel only at the anode. Feeding directly with syngas would lead to loss of performances, because the cathode is able to electrocatalyse its oxidation. A fake but effective selectivity of the anode can be created with a fuel rich mixture, but the cathode must be selective by itself. A single chamber cell with an efficient cathode could operate with low flows and reach high fuel utilization efficiencies, up to 25% each cell and to 1-(3/4) n for a stack of n cells [START_REF] Riess | On the single chamber solid oxide fuel cells[END_REF].

Electrochemical reactions require limited residence times, while chemical reactions, that should be suppressed in a SC-SOFC, take longer times; as a reference, 10 ms is a suitable time for electrocatalysis reactions while being low enough to avoid catalytic effect [START_REF] Riess | The significance of impeded reactions in solid state electrochemistry[END_REF]. Thus, high flow is a mean to decrease residence times and to avoid the catalytic effect of the used materials, but that entails a very low fuel utilization; residence time is also influenced by materials porosity, cell geometry and gas flow. Anode activity is stressed by the mixed atmosphere (stability, deactivation due to the reduction/oxidation cycles) [START_REF] Yang | Single-chamber solid oxide fuel cells with nanocatalyst-modified anodes capable of in situ activation[END_REF] [START_REF] Faes | A review of RedOx cycling of solid oxide fuel cells anode[END_REF][START_REF] Wang | Redox Tolerance of Thin and Thick Ni/YSZ Anodes of Electrolyte-Supported Single-Chamber Solid Oxide Fuel Cells under Methane Oxidation Conditions[END_REF]. Aim of the present work is to developed a perovskite/brownmillerite nanocomposite in which the perovskite is selected for catalytic selectivity toward oxygen reduction and the brownmillerite for ionic and electronic conductivity: this is expected to help obtaining a selective cathode for SC-SOFC.

Several materials, mainly perovskites, have been considered interesting to improve selectivity and stability of cathode: ferrites, cobaltates, manganates [START_REF] Gadacz | Voltage Oscillations in Single-Chamber Fuel Cells Operating under a C 3 H 8 /O 2 Mixture[END_REF][START_REF] Viricelle | Development of Single Chamber Solid Oxide Fuel Cells (SCFC)[END_REF][START_REF] Rembelski | Characterization and Comparison of Different Cathode Materials for SC-SOFC: LSM, BSCF, SSC, and LSCF[END_REF][START_REF] Yin | Anode-supported single-chamber solid oxide fuel cell based on cobalt-free composite cathode of Nd0.5Sr0.5Fe0.8Cu0.2O3-δ-Sm0.2Ce0.8O1.9 at intermediate temperatures[END_REF][START_REF] Sun | Fabrication and characterization of anodesupported single chamber solid oxide fuel cell based on La0.6Sr0.4Co0.2Fe0.8O3-δ-Ce0.9Gd0.1O1.95 composite cathode[END_REF][START_REF] Gaudillère | Alternative perovskite materials as a cathode component for intermediate temperature single-chamber solid oxide fuel cell[END_REF][START_REF] Morales | Intermediate temperature single-chamber methane fed SOFC based on Gd doped ceria electrolyte and La0.5Sr0.5CoO3-δ as cathode[END_REF][START_REF] Zhang | A comparative study of La0.8Sr0.2MnO3 and La0.8Sr0.2Sc0.1Mn0.9O3 as cathode materials of single-chamber SOFCs operating on a methane-air mixture[END_REF][START_REF] Zhang | Initialization of a methane-fueled single-chamber solid-oxide fuel cell with NiO+SDC anode and BSCF+SDC cathode[END_REF][START_REF] Wei | Enhanced performance of a single-chamber solid oxide fuel cell with an SDC-impregnated cathode[END_REF]: among these we focused on iron containing ones.

All materials used as SOFC cathodes are Mixed Ionic Electronic Conductive (MIEC) oxides or composites of MIEC materials [START_REF] Sun | Cathode materials for solid oxide fuel cells: a review[END_REF]. Several perovskite based oxides show good oxygen ion mobility and conductivity [START_REF] Gong | Dynamic Octahedral Breathing in Oxygen-Deficient Ba0.9Co0.7Fe0.2Nb0.1O3-δ Perovskite Performing as a Cathode in Intermediate-Temperature SOFC[END_REF][START_REF] Sun | Recent Advances in Perovskite-Type Oxides for Energy Conversion and Storage Applications[END_REF][START_REF] Yang | Insight into the Structure and Functional Application of the Sr0.95Ce0.05CoO3-δ Cathode for Solid Oxide Fuel Cells[END_REF] as well as electronic conductivity [START_REF] Yang | Perovskite Sr1-xCexCoO3-δ (0.05 ≤ x ≤ 0.15) as Superior Cathodes for Intermediate Temperature Solid Oxide Fuel Cells[END_REF] but are characterized by high catalytic activity in oxidation. Because of this reason, among MIECs the choice has been restricted to a brownmillerite (A2B2O5) of the type Ca2FeAlO5 (CFA) [START_REF] Geffroy | Rational selection of MIEC materials in energy production processes[END_REF]. In principle, CFAbased oxides are less reactive than perovskites toward oxidation and are characterized by a good chemical stability. The brownmillerite structure differs from the perovskite one for the presence of ordered oxygen vacancies in the (010) plane. Depending on the B cation and on the synthesis procedure, fully (Ibm2 and Pnma) or not fully (Icmm) ordered structures can be obtained. The presence of cations that prefer tetrahedral coordination (as Al) contribute to increase the stability.

The distribution of Al and Fe in Ca2FeAlO5 follows the "homogeneous layer principle": [START_REF] Tao | Atomic occupancy mechanism in brownmillerite Ca 2 FeAlO 5 from a thermodynamic perspective[END_REF] Al and Fe tend to form homogeneous octahedral layers or tetrahedral chains rather than mixed layers or chains of two elements along the b axis. To improve conductivity, a small amount of magnesium was inserted, so the actual formula of CFA is Ca2FeAl0.95Mg0.05O5 [START_REF] Malveiro | Magnesium doping on brownmillerite Ca2FeAlO5[END_REF]. Also Co-doping was considered in literature for improving conductivity [START_REF] Thundiyil | Bifunctional Oxygen Reduction and Evolution Activity in Brownmillerites Ca2Fe(1-x)CoxO5[END_REF][START_REF] Li | Electrode properties of Co-doped Ca2Fe2O5 as new cathode materials for intermediate-temperature SOFCs[END_REF][START_REF] Cascos | Structural and electrical characterization of the Co-doped Ca2Fe2O5 brownmillerite: Evaluation as SOFC -cathode materials[END_REF] in our work we decided to avoid the use of Critical Raw Materials and Mg was preferred. The substitution of Al(III) with Mg(II) should help increasing Fe(IV) amount for charge compensation. Mg also affects the structure having a high octahedral site preference (higher than Fe(III)) and enhances the number of iron cations in tetrahedral environment; its solubility in CFA is low (< 0.1) [START_REF] Malveiro | Magnesium doping on brownmillerite Ca2FeAlO5[END_REF]. After its synthesis by citric acid route, CFA has been characterized by means of XRD, TPR, SEM, XPS, EDX and N2 adsorption isotherms; its catalytic activity towards methane oxidation has been measured; once verified the low activity toward methane oxidation, CFA was selected as the MIEC support for the catalytically active phase.

Following literature, that underline the capability of iron containing oxides to dissociatively chemisorb oxygen [START_REF] Bligaard | Heterogeneous Catalysis in Chemical Bonding at Surfaces and Interfaces[END_REF][START_REF] Cox | Transition Metal Oxides: An Introduction to Their Electronic Structure and Properties[END_REF][START_REF] Miyano | Electron energy-loss spectroscopy study of oxygen chemisorption and initial oxidation of Fe(110)[END_REF][START_REF] Sakisaka | Electron-energy-loss-spectroscopy study of oxygen chemisorption and initial oxidation of Fe(100)[END_REF] and our previous experience, the supporting CFA powder has been impregnated with iron and thermally treated with the aim of inducing the formation of a catalytically active iron based active phase enclosed in a brownmillerite. We refer to this second material as CFA + FeOx. Catalysis and electrocatalysis are diffuse applications of these nanocomposition techniques. [START_REF] Carollo | No Title. Hydrog. Fuel Cells[END_REF][START_REF] Perin | Cu@LaNiO3 based nanocomposites in TWC applications[END_REF][START_REF] Bedon | Rational Development of IT-SOFC Electrodes Based on the Nanofunctionalization of La 0.6 Sr 0.4 Ga 0.3 Fe 0.7 O 3 with Oxides. PART 1: Cathodes by Means of Iron Oxide[END_REF] To the best of our knowledge brownmillerite-based nanocomposites are not so diffused and some few example concerns composites of the type perovskite/brownmillerites. [START_REF] Ortiz-Vitoriano | A novel one step synthesized Co-free perovskite/brownmillerite nanocomposite for solid oxide fuel cells[END_REF][START_REF] Lo Faro | Solid oxide fuel cells fed with dry ethanol: The effect of a perovskite protective anodic layer containing dispersed Ni-alloy @ FeOx core-shell nanoparticles[END_REF] Symmetrical cells with Cerium Gadolinium Oxide (CGO) electrolyte have been prepared using both CFA and CFA + FeOx for electrochemical impedance spectroscopy (EIS) tests. The electrode firing temperature has been optimized; complete cells with a Ni/CGO anode have been fabricated

and their polarization curves have been measured. The same treatments necessary to assure electrode/electrolyte adhesion have been carried out to the CFA + FeOx powders to better investigate the evolution of nanocomposite during the device optimization.

Synthesis and characterization

CFA has been synthesized with a solid combustion synthesis. Precursors CaCO3, Fe, Al(NO3)3 and Mg(OH)2 were dissolved in water with the help of HNO3 when needed. Citric acid in amount 1.9 times the cations in solution was then added. The solution was neutralized adding drop-bydrop NH4OH; water was eliminated by mildly heating on hot plate, gel formation happens at the end of this step. Increasing of hot-plate heating over 250°C triggers gel self-combustion. The obtained powder was grinded and calcined at 1050°C for 6h.

Iron oxide was deposited on CFA via a wet impregnation procedure in the amount of 10% mol. [START_REF] Schwarz | Methods for Preparation of Catalytic Materials[END_REF][START_REF] Kung | Transition Metal Oxides Surface Chemistry and Catalysis[END_REF]. An aqueous solution of Fe(II) was prepared, and CFA was added to it. The suspension was covered and kept under stirring for one day. Mild heating on a hot plate was employed to evaporate water. The obtained powder was finally treated at 550°C for 6 hours.

Cells for EIS and polarization measurements are electrolyte supported and prepared by screen printing the material to be tested on both sides of a CGO pellet (diameter 20 mm, thickness 1.4 mm). The electrolyte was prepared by pressing the CGO powder (GDC10-TC, Fuel Cell Materials) and treating the so-obtained pellet at 1350°C for two hours. An ink was prepared by mixing the electrode (CFA or NiO) powder with a fraction of CGO powder, and adding binder V400 (ESL, commercial) and solvent T404 (ESL, commercial) to adjust viscosity. The ink deposition is carried out by means of a serigraphy machine. The layer is then dried in an oven at 100°C for 15 minutes.

For symmetrical cells two layers on each side of the CGO pellets were printed; for complete cells cathode was printed with two CFA layers and anode with four NiO layers. Anodes were treated at 1200°C and cathodes were treated at 1000, 1050, and 1100°C, to evaluate the temperature better ensuring a good electrical contact between the electrolyte and the electrodes. Treatments at temperatures lower than 1000°C have been found not to be sufficient to ensure enough mechanical stability to the electrodic layer. Finally, a gold grid is printed from a gold ink (8880-H, ESL, commercial) on both the electrodes, and the cell is treated a last time at 850°C for two hours.

In order to evaluate the performances of the materials for SOFC operation, EIS tests were performed on the following symmetrical cells: two CFA/CGO/CFA cells and two CFA+FeOx/CGO/CFA+FeOx cells, each cell treated at a different temperature (1000°C to 1100°C). Impedances of the cell were measured under air (normal operating condition for a double cell SOFC cathode), under a 20% CH4 10% O2 atmosphere and then a second time under air. Data were collected with Solartron 1286 Electrochemical Interface and Solartron 1255 Frequency Response Analyzer devices. Prior to test, complete cells require anode activation, consisting in a reduction of NiO to Ni, carried out with a 5 min. treatment under CH4 10% in N2 at 600°C, then cell measurements were carried out under a 20% CH4 10% O2 atmosphere. For the polarization curves of complete SC-SOFC, a Keithley 2400 SourceMeter was used. Selectivity tests of the cathodes were performed by sealing two alumina tubes at both sides of a complete cell with a commercial cement (Aremco Ceramabond 571). Tests were carried out on following cells: Ni-CGO/CGO/CFA, Ni-CGO/CGO/CFA+FeOx and also Ni-YSZ/YSZ/CFA+FeOx. An Autolab PGSTAT204 was used to keep the cell working during the test, voltage was set at 0.4V to obtain the maximum power. A thermocouple at each side measured the cell temperature. An ESS Evolution quadrupole was used to measure composition of the cathode exhaust; the instrument was calibrated with a CO2 standard to obtain quantitative data. Each cathode was flushed with 140 sccm of a 20% CH4 and 10% O2 gas mixture.

X-ray photoelectron spectroscopy (XPS) measurements were carried out with a Perkin Elmer Φ 5600ci Multi Technique System. The spectrometer was calibrated by assuming the binding energy (BE) of the Au 4f7/2 line to be 84.0 eV with respect to the Fermi level. Both extended spectra (survey -187.85 eV pass energy, 0.5 eV•step -1 , 0.05 s•step -1 ) and detailed spectra (for Ca 2p, Fe 2p, Al 2p, Mg 1s, O 1s and C 1s -23.50 eV pass energy, 0.1 eV•step -1 , 0.1 s•step -1 ) were collected with a standard Al Kα source working at 250 W. The standard deviation in the BE values of the XPS line is 0.10 eV. The atomic percentage, after a Shirley-type background subtraction [START_REF] Shirley | High-resolution x-ray photoemission spectrum of the valence bands of gold[END_REF], was evaluated by using the PHI sensitivity factors [START_REF] Wanger | Handbook of X-ray Photoelectron Spectroscopy[END_REF]. The peak positions were corrected for the charging effects by considering the C 1s peak at 285.0 eV and evaluating the BE differences [START_REF]Practical Surface Analysis in Auger and X-ray Photoelectron Spectroscopy[END_REF].

X-ray diffraction (XRD) analyses were performed with a Bruker D8 Advance diffractometer with Bragg-Brentano geometry using a Cu Kα radiation (40 kV, 40 mA, λ = 0.154 nm). The data were collected at 0.03° at a counting time of 10 s step -1 in the (2θ) range from 10° to 60°. The crystalline phases were identified by the search-match method using the JCPDS database.

Temperature Programmed Reduction (TPR) was performed with an Autochem II 2920 Micromeritics, equipped with a Thermal Conductivity Detector (TCD). The TPR measurements were carried out in a quartz reactor by using 50 mg of sample and heating from RT to 900°C at 10°C min -1 under a constant flow of H2 5% in Ar (50 ml•min -1 ). TPR samples were previously outgassed with He (50 ml•min -1 ) at room temperature.

Nitrogen adsorption isotherms were measured at 77K with a Micromeritics ASAP 2020 plus instrument. Superficial area by BET model has been calculated from adsorption curves. DFT calculations were carried out with built-in software of the instrument. Transmission electron microscopy (TEM) and selected area electron diffraction (SAED) measurements were carried out on a JEOL JEM 1011. The sample was grinded into a fine powder, which was suspended in toluene by sonication and dropped on a carbon coated 400 mesh TEM grid. The excess of solvent was removed with a filter paper and by drying the grid under air.

The catalytic activity was measured placing 100mg of CFA in the middle of a vertical quartz tube, with a 7% O2, 14% CH4 gas mixture flowing upside, with a 100 sccm flow. The exhaust composition was measured with a GC.

Results and discussion

XRD

CFA pattern (Figure 1Sa -Supporting Information) matches with a brownmillerite phase Ca2FeAlO5: the magnesium concentration is only minimal and insufficient to produce significant deviations from parent Ca2FeAlO5 structure but probably un-favours crystalline order. Brownmillerite's crystal structure is similar to the perovskite's one, from which it can be obtained with the ordered removal of one oxygen atom every six [START_REF] Johnsson | Crystallography and Chemistry of Perovskites[END_REF]. With this transformation, each layer every two of the perovskite becomes a layer of tetrahedral [START_REF] Shaula | Ionic conductivity of brownmillerite-type calcium ferrite under oxidizing conditions[END_REF], and symmetry changes from cubic to orthorhombic. A small krotite (CaAl2O4) impurity is also present.

After the impregnation with Fe-based solution the phase composition is deeply changed (Figure 1Sb): three new phases appeared, all of them containing calcium, oxygen and one other element between Fe and Al. Their formation suggests the decomposition of the brownmillerite, with Fe and Al cations separating in two different phases. One possible phase could be Ca2Fe2O5, which is very similar to the original Ca2FeAlO5 and has the same brownmillerite structure. In fact, srebrodolskite is the name of a mineral with composition Ca2Fe2O5 and the brownmillerite crystalline structure. The mayenite (Ca12Al14O33), despite its formula similar to the brownmillerite (that would be Ca14Al14O35) has a very different crystalline structure. A treatment at 1050°C, which replicates the firing of the electrodes to make them adhere to the electrolyte, restores the original Ca2FeAlO5 phase (Figure 1Sc). This means that when preparing a cell with the iron impregnated powder, the electrode is deposited as a mixture of Ca12Al14O33, Ca2Fe2O5, CaCO3, and then reverts to the pristine brownmillerite during the firing. Traces of the spinel CaAl2O2 are again observed, and there still is some trace of calcite, close to the detection limit. It is possible that CFA decomposes in Ca2Fe2O5 and CaAl2O4. In general, signal/noise ratio is worse than as-synthesized brownmillerite.

N2 isotherms and superficial area

The specific surface area of CFA is low, 1.7 m 2 /g; the CFA isotherm is type II (Figure S2). CFA + FeOx treated at 1050°C has a higher specific surface area, 17.1 m 2 /g, and the isotherm is type V (Figure S2). This is consistent with the phase modifications observed by means of XRD. Other than the different curve shape, in CFA + FeOx also a hysteresis loop appeared. Loops in gas physisorption measurements form due to capillary condensation of the adsorbate and identify the presence of mesoporosity. This loop shape, of type H3, is associated to disordered pores. From adsorption curves it is possible to perform DFT calculations to analyse the CFA + FeOx treated at 1050°C pore distribution. Such procedure reveals a porosity distribution with average pore size of 22 nm.

SEM and TEM

CFA powder, Figure 1, is in form of conglomerated particles of size around 200 nm; the shape of the particle appears smooth and irregular, no particular feature is observed. In the image of CFA + FeOx powder, some crystals with an octahedral shape and 1μm size are mixed with smaller and less defined particles. The morphology change is a result of the formation of a new crystal phase (see XRD) and the presence of a highly porous structure. After the 1050°C thermal treatment the original dense structure is restored. Contrary to CFA, after the thermal treatment CFA + FeOx is an agglomerate of very different size of particles, from around 200 nm to more than 1 µm. This different size distribution can be a consequence of the formation of a composite structure with different chemical compositions. During the treatment the atoms moved along the existing structures and recombined maintaining the shape of the bigger particles. Thus, the final structure (evidenced in Figure 2) has a shape reminiscent of an octahedron. Detailed information on the local structure of the different materials were obtained by TEM and SAED analyses (Figure 2). CFA is characterized by cubic-like grains agglomerated dense structures typical of sintered systems. In CFA+FeOx the material decomposition is evident. Here a highly mesoporous structure with pore size of approx. 20 nm is evidenced, in very good agreement with the nitrogen physisorption analysis. Also, anisotropic crystalline particles appear, which significantly differ from those in CFA. After the firing step at 1050 °C the material sintered structured is restored. Along with the cubic-like particles, the elongated structures observed in CFA+FeOx are still present. To get precise information on the chemical nature of the observed materials, electron diffraction studies were performed. In case of CFA, due to the large thickness of the agglomerates and the overlap of crystallites with different orientation, SAED patterns were not easy to be assigned. However, we successfully identified the presence of crystalline planes belonging to the Ca2FeAlO5 structure (01-070-1499). The nanostructured nature of CFA+FeOx provided more insightful results. Among other phases, the presence of Ca5Fe2O5 (00-030-0226) reflections was demonstrated in good agreement with the XRD results. In CFA+FeOx after sintering, the two crystalline structures clearly indicate the presence of two different crystal habits confirming the presence of a nanocomposite material. From the cubic-like particles we found evidences of Ca2FeAlO5 phase, confirming the XRD results. The anisotropic crystals present very clearly the Ca5Fe2O5 structure. The high intensity of the (161) reflection agrees very well with the anisotropic form of the crystal. Evidently, this brownmillerite phase formed after the Fe-solution impregnation step is maintained after firing. The missing information in XRD about the presence of this phase can be justified by the strong crystallographic overlap with the similar Ca2FeAlO5 brownmillerite structure.

XPS and EDX

Quantitative analysis of samples composition is shown in Table 1. In general, XPS suggests an excess of oxygen, consistent with surface hydroxylation. As typically observed in perovskite structures, XPS reveals a superficial segregation of the A-site cation. Regarding the B cations there is a relative abundance of Al compared to Fe instead of the nominal 1:1 ratio. Traces of Mg have been detected. The deposition of iron oxide, unexpectedly, favours the surface segregation of Al and this situation is not significantly affected by the following treatment at 1050 °C. The amounts of cations determined by EDX are more in accordance with nominal compositions indicating that the segregation is limited to few surface monolayers.

Nominal

TPR

The TPR curves are shown in Erreur ! Source du renvoi introuvable.3, and the area of the peaks are summarized in Erreur ! Source du renvoi introuvable.. TPR profile of CFA reveals only two very small peaks at 450°C and 600°C. The only species that can be reduced below 1000°C is iron. [START_REF] Kayaalplee | Template-free mesoporous La0.3Sr0.7Ti1-xFexO3±δ for CH4 and CO oxidation catalysis[END_REF][START_REF] Kayaalp | Pt Nanoparticles Supported on a Mesoporous (La,Sr)(Ti,Fe)O3-δ Solid Solution for the Catalytic Oxidation of and CH4 ACS Appl[END_REF] The area of the peaks is too small to account for the Fe(III)→Fe(II) reduction; this means that the observed signals correspond only to the reduction of small amounts of Fe(IV) to Fe(III) and, successively, of Fe(III) to Fe(II). The presence of Fe 4+ in this brownmillerite is not unexpected [START_REF] Waerenborgh | Fe4+ formation in brownmillerite CaAl0.5Fe0.5O2.5+δ[END_REF] and probably the Mg atoms inserted in the Ca2FeAlO5 structure are involved in its formation. The amount of Fe 4+ ions, as determined by these measurements, roughly corresponds to the amount of magnesium, suggesting that iron atoms were oxidized to 4+ to balance magnesium 2+ charge, in accordance with literature. [START_REF] Malveiro | Magnesium doping on brownmillerite Ca2FeAlO5[END_REF] TPR profiles of Ca2FeAlO5 report [START_REF] Tian | Development of a Steel-Slag-Based, Iron-Functionalized Sorbent for an Autothermal Carbon Dioxide Capture Process -Supporting Information[END_REF] only one small reduction peak at 700-800 °C, so confirming this interpretation. Only the beginning of the curve corresponding to the reduction to Fe(0) is observed (above 800°C). [START_REF] Kayaalplee | Template-free mesoporous La0.3Sr0.7Ti1-xFexO3±δ for CH4 and CO oxidation catalysis[END_REF][START_REF] Kayaalp | Pt Nanoparticles Supported on a Mesoporous (La,Sr)(Ti,Fe)O3-δ Solid Solution for the Catalytic Oxidation of and CH4 ACS Appl[END_REF] The impregnation with iron heavily modifies the TPR profile in agreement with the phase transitions observed by XRD.

Ca2Fe2O5 is the phase to be related with the TPR response as it is the only one containing iron;

indeed, observed peaks are compatible with what described in literature about this phase [START_REF] Hirabayashi | Formation of brownmillerite type calcium ferrite (Ca2Fe2O5) and catalytic properties in propylene combustion[END_REF]; the higher hydrogen consumption can be related also to the increased specific surface area. The two peaks between 400°C and 600°C are compatible with the presence of Fe2O3 that, according to literature [START_REF] Liang | Comparison of reduction behavior of Fe2O3, ZnO and ZnFe2O4 by TPR technique[END_REF], would be reduced with two non-resolved peaks having area ratio 1:8, as observed here. The signal at temperature lower than 400 °C is consistent with the reduction of Fe(IV). After the treatment at 1050°C a shape similar to pristine CFA is obtained again, due to the lower porosity of the material after sintering. The peak positions match very well with those of CFA-FeOx. This likely indicates that besides the regeneration of the CFA phase, after firing Ca2Fe2O5 is still present in the material. Due to the strong similarity between the two brownmillerite phases their presence in the XRD data is difficult to discern.

Catalytic activity of the powders

The catalytic activity of the electrodes used in SC-SOFCs is very important, as it has been mentioned in the introduction. For the efficiency's sake it is important to use, as starting point, materials with the lowest catalytic activity for methane oxidation. To obtain a result as close as possible to real cell operation, the same fuel/oxygen ratio used in SC-SOFCs has been used, the results are shown in Figure 4. The activity of CFA towards methane oxidation is low. Onset temperature is around 500°C, then activity increases slowly with temperature, and at 600°C it is only modest (around 15% of oxygen conversion). The reaction reaches completion at 660°C, the reactivity is considered low enough for making the material an adequate starting point.

Electrochemical Impedance Spectroscopy and fuel cells performances

The area specific resistance (ASR) determined as a function of temperature is summarized, for all the materials, in Figure 5. The electrochemical performance is not very different when comparing CFA treated at 1000°C and 1100°C, and CFA+FeOx treated at 1000°C. A significant decrease is observed, in contrast, in CFA+FeOx treated at 1100°C (i.e. when the brownmillerite structure is reconstructed). In all cases but CFA 1000°C, the resistance increases in CH4+O2 atmosphere but then significantly decreases when it is switches to air again. The lower resistance is obtained in CFA+FeOx 1100°C after treatment in CH4+O2.

) The differences between the cathodes CFA and CFA + FeOx are small but significant. CFA is entirely composed by Ca2FeAl0.95Mg0.05O5 brownmillerite. CFA + FeOx originally was Ca2FeAl0.95Mg0.05O5, then the FeOx induced the decomposition into at least 4 phases: srebrodolskite, mayenite, calcite (XRD). Finally, the thermal treatment during electrode firing, reversed phases to Ca2FeAlO5 and Ca2Fe2O5..

1000/T (1/K) CFA 1000°C Air CFA 1000°C CH4+O2 CFA 1000°C Air II CFA 1100°C Air CFA 1100°C CH4+O2 CFA 1100°C Air II 1 1,5 2 2,5 3 3,5 1,05 1,1 1,15 1,2 1,25 log(ASR
For the sake of clarity, only 620 °C EI spectra have been reported. Figure 6 shows the Nyquist plots, Figure 7 is the Bode plot of the phase, and Figure 8 shows the frequency shifts depending on temperature of the observed processes. It is possible to get some insight about mechanisms of the reaction. The way oxygen turns from molecular (in gas phase) to anion (in the electrolyte) depends heavily on cathode characteristics, including geometrical ones as porosity, tortuosity, thickness, and chemical ones (surface active sites, electron exchange, etc), ionic and electronic conductivity. The different atmospheres the sample experiences in this series of tests, (air followed by CH4+O2 followed by air) can affect the ongoing process and modify the sample. When changing from air to oxygen/methane mixture, surface sites undergo reduction, and the amount of oxygen vacancies increases. [START_REF] Kayaalplee | Template-free mesoporous La0.3Sr0.7Ti1-xFexO3±δ for CH4 and CO oxidation catalysis[END_REF][START_REF] Kayaalp | Pt Nanoparticles Supported on a Mesoporous (La,Sr)(Ti,Fe)O3-δ Solid Solution for the Catalytic Oxidation of and CH4 ACS Appl[END_REF] These effects sum, and when reverting to oxygen, equal results are never obtained. Instead, a second measurement (not reported for sake of clarity) under CH4 + O2 always gives the same results of the first one.

Under air, up to three different resistive processes can be distinguished: on the basis of their frequency they can be labelled as High Frequency (HF), Medium Frequency (MF) and Low Frequency (LF); the latter is observed only in some samples and conditions.

The resistance of the HF process is highly dependent on oxygen concentration in all the samples, and its apex frequency is dependent on the temperature. It is fitted with a R//CPE element (Figure 5). The frequency close to 10 4 Hz in SOFCs can be attributed to the O 2-transfer at the electrode/electrolyte interface [START_REF] Ringuedé | Oxygen reaction on strontium-doped lanthanum cobaltite dense electrodes at intermediate temperatures[END_REF], the observed capacitance around 10 -5 Fcm -2 , compatible with a double layer, is consistent with this interpretation [START_REF] Yang | Oxygen exchange kinetics on a highly oriented La0.5Sr0.5CoO3-?? thin film prepared by pulsed-laser deposition[END_REF]. The O 2-transfer depends on the phases really composing the interface. These phases can differ from the bulk ones, and their formation can be influenced by the atmosphere (hence pO2) [START_REF] Adler | Factors governing oxygen reduction in solid oxide fuel cell cathodes[END_REF]. This phenomenon has already been observed in other cases, as for YSZ/LSM interfaces [START_REF] Kawada | Reaction Between Solid Oxide Fuel-Cell Materials[END_REF], and related to changes of the impedance response [START_REF] Liu | Significance of interfaces in solid-state cells with porous electrodes of mixed ionicelectronic conductors[END_REF]. In this particular case, however, the different degree of aggregation and oxidation of iron oxide clusters, can deeply effect the electronic properties (Electron affinity, Fe-O and Fe-Fe bond strength) and thus the electrochemical response [START_REF] Wang | Sequential Oxygen Atom Chemisorption on Surfaces of Small Iron Clusters[END_REF].

The MF process depends on the atmosphere, its apex frequency is strongly influenced by the temperature and is well fitted be a R//CPE. It is the main contribution to resistance, and probably represents the oxygen reduction process; its resistance slightly increases from air to CH4+O2 and strongly decreases when going back to air. The reduction of some superficial sites, carried out by methane, can potentially modify catalytic activity permanently, and could be at the base of the changes of the resistance. Experimental and theoretical evaluation demonstrated, in fact, that in particular cases, the strain in the iron particles and the forces between the methane and the nearsurface iron and oxygen atoms can induce the dissociative chemisorption of methane [START_REF] Motozuka | Methane adsorption and dissociation on mechanochemically activated iron-particle surfaces[END_REF].

The LF process is very well fitted by a Warburg element, the change of atmosphere from air to CH4+O2 make it disappear, and only in the samples treated at 1100°C it is observed again during the second measurement in air. CFA + FeOx never features it. Diffusive processes at very low frequencies can be associated to oxygen diffusion inside the porosities of the electrode [START_REF] Flura | Identification and modelling of the oxygen gas diffusion impedance in SOFC porous electrodes: application to Pr2NiO4+δ[END_REF], but in this case the decrease of resistance when pO2 decreases excludes this interpretation (diffusion of oxygen is easier when it is more concentrated, not the opposite). So, this process could be related to the electrode diffusion of oxygen ions (either superficial or bulk, depending on preferred path).

Focusing on bulk, a decrease of pO2 can induce an increase of vacancies of CFA and speeds up ionic conduction; on the other hand, diffusion of O 2-in bulk electrode is in general observed ad higher frequencies [START_REF] Grunbaum | Rate limiting steps of the porous La0.6Sr0.4Co0.8Fe0.2O3-δ electrode material[END_REF]. Considering surface, beside oxygen vacancies change, it has to be considered that active sites can be modified by atmosphere and the mobility of adsorbed oxygen can vary depending on pO2.

The reason why the LF process is observed only in some case is that this process is related to a specific path for the conduction of oxygen; consistently, its presence indicates that only under these conditions oxygen moves via the path the LF semicircle is associated with. The process is very temperature sensitive (Figure 8), and tends to shift at higher frequency and disappear at increasing temperature. This remarkable change suggests a change of the limiting phenomenon.

Such a result would be in accordance with a surface diffusion.

As observed, in general, overall resistance is higher when the atmosphere is changed to CH4+O2, because of a significant increase of the resistances associated to the HF and MF processes. So, it appears that the LF process is able in some way to ease the other two processes, in fact when it is present, the overall resistance is lower than the case in which the HF and MF processes are alone.

After all, considering the performances observed with these measurements, the performance of CFA is mediocre, compared to other materials; its ASR is one order of magnitude higher than state of the art materials. Nonetheless, this material shows a remarkably low activation energy, close to 0.02 eV. This value is even lower than state-of-the-art LSCF [START_REF] Tai | Structure and electrical properties of La1-xSrxCo1-yFeyO3. Part 1. The system La0.8Sr0.2Co1-yFeyO3[END_REF], as can be seen in Table S3. This makes CFA an interesting candidate for high temperature cells. have been fired at the temperature that allowed to reach the lowest resistance during EIS measurements, so 1000°C for CFA and 1100°C for CFA + FeO x . The results of these measurements prove that CFA actually work as cathode for single chamber fuel cells. Compared to state-of-the-art cells, the power output is low, as it could be expected from the high ASR from single chamber measurements. In any case, it is remarkable that a material never tested for this application, without any kind of noble, toxic, rare or expensive component, is able to operate a fuel cell. ASR of CFA and CFA + FeO x as measured by EIS in symmetric cell, were almost similar, nonetheless power obtained from polarization curve are quite different. In fact, CFA + FeO x is able to produce a power output three times higher than CFA, reaching values close to 20 mWcm - 2 . We attribute this finding to the formation of the more conductive Ca 2 Fe 2 O 5 phase, which is retained after firing, as showed by TEM. [START_REF] Shukl | First principles investigations of structure, stability and electronic properties of polar Ca 2 Fe 2 O 5 (010) surfaces[END_REF] So, the phase transformation after impregnation with an iron solution, was effectively able to improve the performances of the material. Power output of a cell with CFA based cathode could be even better in double chamber architecture: as measured by means of EIS, the resistance in air is 1/3 the one under the atmosphere single chamber cells operate, so better values would be probably obtained under atmospheres richer in oxygen.

As already mentioned, selectivity of the cathode is one of the most difficult and important issues in SC-SOFCs. In order to verify if the selectivity target has been reached, some preliminary test has been performed on the same cathodes tested in complete cells. Ideally, from the outlet of the cathode only oxygen, methane and inert gases should be found. All the product of a combustion (as CO2 and CO) are result of parasitic undesired reactions. The results were found to be identical in both the tests of CFA and CFA + FeOx, this means that the processes involved in the parasitic reactions were only catalytic: if electrocatalysis was involved, it would have had some dependence on the cell power.

During the selectivity tests, a concentration of 400 ppm of CO2 was detected, and no CO was found, with no difference depending on electrolyte (YSZ/CGO) or cathode (CFA or CFA + FeOx).

The absence of variations in the cells suggests that the traces of CO2 originate from non-catalysed direct oxidation. This is confirmed by the absence of difference between the CGO and YSZ-based cells, standing the relevant differences in catalytic activity. Considering methane Low Heating Value (LHV) as a reference and comparing with the gas flow, this methane conversion corresponds to a power loss of 30 mW. This is a very promising result: if the power loss were the same also at the anode side, the cell would have been able to convert into energy 25% of the consumed fuel.

The similarity of CO2 formation observed with CGO and YSZ-based cells, means methane loss due to catalytic activity is low, so there is significant room for selectivity improvement.

Then, an optimization of the electrode deposition would be appropriate, as well as a more accurate gas management. With those described improvements, a SC-SOFC based on CFA has strong chances of attaining the best efficiency ever for a SC-SOFC. On the other hand, as it was in the premises of this work, the power output would not compare with current double chamber SOFC, but this is evidently the price to pay for selectivity.

Conclusions

A specific material for cathodes of SC-SOFCs, Ca2FeAl0.95Mg0.05O5, has been designed aiming to obtain a material with specific properties in terms of process efficiency. During the material design, the requirement of a high final power output was deliberately dropped in order to maximize the results. CFA and its derivative CFA + FeOx have been successfully synthesized and completely characterized. Symmetrical cells with CFA and CFA + FeOx have been fabricated and tested by means of EIS, the respective electrode firing temperatures have been optimized. ASR were calculated, obtaining high overall values, but in line with expectations. Then, complete cells have been prepared and tested as power output and, preliminary, efficiency. Results confirm initial targets were reached, as cell showed an optimal efficiency.

ASSOCIATED CONTENT Supplementary Material. The following files are available free of charge.

XRD patterns (PDF), N2 physisorption.

  Field emission-scanning electron microscopy and EDX measures were carried on a Zeiss SUPRA 40VP. Morphological and EDX analysis were carried out setting the acceleration voltages at 20 kV. The powder was positioned on the sample holder by means of a high vacuum conductive Cbased adhesive and analysed without any further treatment.

Figure 1 .

 1 Figure 1. SEM images of CFA (above, left), CFA + FeOx (above, right) and CFA + FeOx (below) treated at 1050°C. Red circles highlight octahedron-like particles.

Figure 2 :

 2 Figure 2: TEM micrographs and corresponding SAED patterns of CFA, CFA+FeOx, and

Figure 3

 3 Figure 3 TPR profiles of synthesized powders.

Figure 4 .

 4 Figure 4. Oxygen conversion of CFA in fuel rich mixture (CH4/O2=2). flow 100 sccm, CH4=14%, O2=7%.

Figure 5 .

 5 Figure 5. Above: model circuit used for EIS data fitting. Middle: ASR of CFA tested sample. Below: ASR of CFA + FeOx tested samples.

Figure 6 .

 6 Figure 6. Nyquist plot of impedance spectra of symmetric cells at 620°C. A: CFA tested at 1000°C. B: CFA tested at 1100°C. C: CFA + FeOx tested at 1000°C. CFA + FeOx tested at 1100°C. Orange: first test under air. Blue: second test under air. Green: test under CH4 + O2.

Figure 7 .

 7 Figure 7. Bode plots of impedance phase of symmetric cells at 620°C. A: CFA tested at 1000°C. B: CFA tested at 1100°C. C: CFA + FeOx tested at 1000°C. CFA + FeOx tested at 1100°C. Orange: first test under air. Blue: second test under air. Green: test under CH4 + O2.

Figure 8 .

 8 Figure 8. Bode plot of the impedance phase of CFA treated at 1100°C under air (first measurement), showing the frequency shifts of the resistive processes depending on temperature.

Figure 9 .Figure 9

 99 Figure 9. Polarization curves and power of cells with CFA treated at 1000°C (left) and CFA+FeOx (right) treated at 1100°C (right) cathodes. Anode is Ni/CGO and electrolyte is CGO

Table 1 .

 1 Summary of quantitative analysis by means of XPS and EDX on powders. Abundances are indicated as atomic % relative concentrations. Numbers in brackets refer to calculation considering only cations.

				XPS			EDX
						CFA+FeOx		CFA + FeOx CFA + FeOx
		CFA	CFA+FeOx	CFA	CFA + FeOx	1050°C	CFA		1050°C
	Ca	22.2	22.0	18.0	15.9	17.4
		(50.0)	(48. 8)	(66.4)	(56.6)	(61.3)	(49.1)	(51.2)	(47.8)
	Fe	11.1	12.1	2.9	3.1	3.2
		(25.0)	(26.8)	(10.7)	(11.0)	(11.3)	(22.3)	(24.6)	(24.6)
	Al	10.6	10.4	5.0	8.0	6.9
		(23.7)	(23.2)	(18.5)	(28.5)	(24.2)	(27.0)	(24.2)	(26.8)
	Mg	0.6	0.6	1.2	1.1	0.9
		(1.3)	(1.2)	(4.4)	(3.9)	(3.2)	(1.6)		(0.81)
	O	55.6	55.0	72.9	71.9	71.6
	Fe/Al	1.06	1.16	0.58	0.39	0.47	0.83	1.02	0.92
	(Fe+Al)/Ca	0.97	1.02	0.52	0.70	0.58	1.00	0.95	1.08

Table 2 .

 2 Hydrogen consumption in mol of H2/mol of CFA and CFA+FeOx before and after the treatment at 1050°C necessary to reconstruct the brownmillerite structure.

		450°C	650°C
	CFA	0.010	0.012
	CFA + FeOx	0.005+0.045	0.172
	CFA + FeOx 1050°C	0.009	0.016

ACKNOWLEDGMENT

The authors want to express their gratitude to Dr. Clematis from University of Genova, for his great help in the interpretation of EIS spectra.


Alexandre Lecoeur

Maria Bernard

Sandrine Lagarrigue

Tatiana Zerjal

Evaluate the impact of abiotic stressors (heat and suboptimal diet) on the gut microbiota of two chicken lines diverging in feed efficiency, using the 16S rRNA high throughput sequence technology

Evaluate the impact of abiotic stressors (heat and suboptimal diet) on the gut microbiota of two chicken lines diverging in feed efficiency, using the 16S rRNA high-throughput sequence technology.

Alexandre LECOEUR 1,2 , Maria BERNARD 1,3 , Sandrine LAGARRIGUE 4 ,Tatiana ZERJAL 1

Animal model

Objectives:

1. Is feed efficiency (genotypes) linked to gut microbiota composition? 2. Under abiotic stress (feed or heat), is there a difference in microbiota composition between lines? 3. Are these changes dependent on the genetic background of the chicken?

Experimental design DNA from the caecum was extracted and the V3V4 region of the 16S rRNA gene was amplified and sequenced in paired end 2x250bp on an Illumina Miseq sequencer. OTU were constructed with the FROGS pipeline, with a filtering step on low abundance (<5.10 -5 ) and on a presence prevalence of at least 50% in at least one group. Taxonomical affiliations were obtained using NCBI Blast+ against the SILVA 132 database (filtered on pintail > 50).

Finally, in total 2,381,417 sequences were kept and distributed into 555 OTU that belonged to 6 phyla, 11 classes, 12 orders, 30 families (26 known), 98 genus (80 known), 141 species (32 known).

Technical approach and bioinformatics analysis

Microbiota composition analysis

As previously described in litterature, the Firmicutes and the Bacteroidetes are the main phyla in the gut microbiota. Despite the high intra group variability (SD until 17.6%), we observed significant line and condition effects. Indeed, Bacteroidetes are more abundant in the R-line than in the R+ line, and this is the opposite for the Firmicutes or the Actinobacteria. The Proteobacteria abundance increase in the heat stress condition. Line and condition effects are also visible at the genus level.

genera abundance distribution showing different evolution among groups

Bacteroides a well-known propionate producer often linked to high fiber diets, strongly decreases in both stressed conditions in the R-line, and only in the heat stress group for the R+ line. Short-chain fatty acid producers, like Subdoligranulum, or Faecalibacterium, present dynamic changes between conditions, and these changes are more pronounced in the R+ line.

Microbiota composition analysis

Alpha diversities indices show:

• Under optimal conditions, a strong richness difference exist between lines, with R+ line presenting reduced flora diversity. This difference is not observed under stressful conditions. This is mainly due to the huge increase of richness in R+ in under feed and heat conditions. • The abiotic stresses impact the eveness of OTU abundance as Shannon and

InvSimpson increase. This means there is more abundant OTU than in optimal conditions.

Bray-Curtis beta diversities, as well as Jaccard and Unifrac, revealed a strong condition effect. Moreover, this analysis confirmed that microbiota composition differs between lines but these differences are reduced (in HS) or even erased (in FS) in stressed conditions.

MDS plot of Bray -Curtis

Perspectives

There is still work to do to identify precise OTU involved in microbiota dynamics under these abiotic stresses and how it relates to feed efficiency parameters.

Our experiment lack of sensitivity to determine the taxonomy of each OTU. A finer taxonomy will allow us to estimate microbiota functions for example using PICRUSt2.

Acknowledgment

This study was part of the ChickStress project funded by the ANR and the european project Feed-a-Gene. We are also thanksfull to the Migale bioinformatics plateform for providing us computing infrastructure and support. Under optimal reared conditions, increased gut diversity is associated with increased feed efficiency. This could imply that the R-line, to reach its high feed efficiency, needs a rich flora to guarantee the maximum of efficiency from a relatively reduced feed intake. On the contrary, the R+ line that has a feed intake larger than expected, probably does not require a very efficient microbiota because it exceeds in nutrients.

Conclusions and Perspectives

Under stressful conditions, major changes are observed in the R+ line reaching the level observed in the R-line. This increasing richness probably reflects the need to guarantee microbiota functionality in response to host requirements under constraints.

1

  Université Paris -Saclay, INRAE, AgroParisTech, GABI, 78350, Jouy-en-Josas, France, 2 Université de Paris, Paris Diderot, Master Biologie Informatique, 75013 Paris, 3 INRAE , SIGENAE, 78350 Jouy -en-Josas, France, 4 INRAE, Agrocampus-Ouest, PEGASE, 35590 Saint-Gilles, France Chicken lines divergently selected for feed efficiency R

FROGS

  F.Escudié et al, FROGS: Find, Rapidly, OTUs With Galaxy Solution, Bioinformatics 2018, doi: 10.1093/bioinformatics/


Hamidreza Rezaei
email: hamidreza.rezaei@imt-atlantique.fr

Nathalie Bostel
email: nathalie.bostel@univ-nantes.fr

Vincent Hovelaque
email: vincent.hovelaque@univ-rennes1.fr

Olivier P Éton
email: olivier.peton@imt-atlantique.fr

Agadir -Morocco "New advances and challenges for sustainable and smart industries" A FINANCE DRIVEN SUPPLY CHAIN NETWORK DESIGN MODEL

Keywords: Supply chain, network design, facility location, finance, Adjusted Present Value, Z-score

We propose a supply chain network design model focusing on the interactions between logistic and financial considerations. From the logistic point of view, this model determines the optimal location of production facilities and the assignment of these facilities to customers. From the financial point of view, it plans logistics decisions such that a financial indicator is maximized. We propose to use the Adjusted Present Value (APV) as the objective function.

INTRODUCTION

Supply Chain Network Design (SCND) aims at optimizing strategic decisions such as "where" and "when" to locate facilities. It also determines the capacity of facilities and product flows in logistics networks. The primary goal in classical SCND models is to maximize the profit or, equivalently, to cut logistics costs.

In this paper we focus on the interactions between the logistic and financial considerations in SCND. At least two financial impacts must be studied. The first one concerns the funding of logistics decisions. There are several means to finance big investment over a long term horizon. This funding may use internal financial resources that the company accumulated prior to the investment. In this case, the investment decision must be anticipated. It can also be financed by borrowing. These two funding levers modify the financial structure of the company and, subsequently, some of its financial ratios. This may have a considerable impact on the future value of the company.

The importance of incorporating financial considerations into strategic decisions, in particular supply chain management decisions, has been reported many times in the literature. [START_REF] Shapiro | Challenges of strategic supply chain planning and modeling[END_REF] discusses the links between supply chain, demand, and corporate financial decisions at the strategic level. He mentions the strong interaction between the financial factors and the strategic planning of firms and organizations. In the context of closed-loop supply chain network design, [START_REF] Ramezani | Closed-loop supply chain network design: A financial approach[END_REF] mention that the majority of studies consider the financial aspects as endogenous variables, and only very few studies consider these aspects as exogenous variables used in constraints and in the objective function. It is striking to see that financial considerations are very often considered in the literature as side constraints, but are never in the core of the decision model. The goal of this paper is to fill this gap by proposing a mathematical model for the joint optimization of the supply chain network design and of the firm's value.

FINDING A RELEVANT FINANCIAL OBJECTIVE FUNCTION

Capital structure optimization

The question of defining the optimal capital structure (Modigliani and Miller, 1963) refers to the debt over equity ratio. This question arises when large investments must be decided, which is exactly the case in strategic supply chain management decisions. The corresponding large investments can be financed by the equity and by the debt. In the first case, the necessary funds are supported by the shareholders or generated by the firm's activities. In the second case, they are borrowed from banks and financial institutions. The most significant incentive of debt financing, called tax shield benefit (TSB) is related to the corporate income tax system. Given that the interest expenses associated with the debt are tax-deductible, the TSB is proportional to the corporate tax rate as well as the amount borrowed to the bank. It is thus, easy to calculate.

The main risk of debt financing is the possibility of bankruptcy if a firm is unable to repay debts.

There is a vast literature dedicated to the evaluation of bankruptcy cost. We consider the expected bankruptcy cost, which combines an estimation of the cost of bankruptcy, denoted BC and the probability π of going bankrupt. The expected bankruptcy cost EBC is estimated as follows (Damodaran, 2012):

EBC = π × BC.
The valuation of the bankruptcy cost BC follows the model of Leland (1994). Let U V represent the unlevered value of the firm, i.e. its value under all-equity financing. When bankruptcy occurs, a firm loses a fraction 0 ≤ β ≤ 1 of its unlevered value. Then, [START_REF] Myers | The capital structure puzzle[END_REF] introduced the trade-off theory, in which the TSB is balanced by the dead-weight bankruptcy cost. According to this theory, there is a debt to equity ratio, driving the firm to its maximum value.

BC = β × U V.
This mechanism is illustrated by Figure 1. When the debt level increases (horizontal axis), both the value of TSB and BC increase. It is assumed that the tax shield, represented by the black solid line increases roughly linearly, while BC is nonlinear. Thus, the firm's value (represented by the blue curve) first increases, then reaches an optimal value and then decreases. The highest point of the firm's value curve helps determine the optimal debt value.

Z-score

The Z-score is an econometric scoring tool, developed in the late 60s (Altman, 1968;Beaver, 1968), used in decisions to grant credit limits. It is one of the most popular bankruptcy predictors for companies and organizations. Its main use is to establish a probability of default at 2 years on the basis of 5 financial ratios. We use the following Z-score formula for private manufacturing companies:

z = 0.717X 1 + 0.847X 2 + 3.107X 3 + 0.420X 4 + 0.998X 5 , (1)
where X 1 is the Working capital/Total assets ratio, X 2 is the Retained Earnings/Total assets ratio, X 3 is the Earnings Before Interest and Taxes (EBIT)/Total assets ratio, X 4 is the Book value of equity/Book value of total liabilities ratio and X 5 is the Sales/Total Assets ratio.

The primary goal of the Z-score is to predict bankruptcy. Its value can be converted to a probability π of bankruptcy with a logistic function (see, e.g. Hillegeist et al. (2014) and Kallunki and Pyykkö (2013)).

π = e -z 1 + e -z .

(2)

Adjusted Present Value (APV)

Let us first recall the definition of the Net present Value (NPV). It is defined as the value of a project's future cash flows (positive or negative), translated into today's money i.e., the difference between a project's value and its costs over time. Given a set T of time periods, the values of the profit and fixed assets at each period t ∈ T and the cost of equity r E ,

N P V = t∈T P rof itt-F ixedAssett (1+r E ) t
is used as an objective function in numerous SCND papers, especially in models describing real-life applications or complex supply chains.

The Adjusted Present Value (APV), proposed by [START_REF] Myers | Interactions of corporate financing and investment decisions-implications for capital budgeting[END_REF] is mainly used for the valuation of investment projects. Practically, it is calculated as follows:

AP V = N P V + T SB -EBC. (3)
The main principle of the APV is to adjust the unlevered value of the firm by considering the debt effect. The total enterprise value equals the sum of the values of the operating assets plus the present value of debt tax shields. The main contribution of our mathematical model is to adopt APV as the objective function in a classical SCND model, instead of classical cost based objective functions, so as to maximize the overall firm's value.

PROBLEM SETTINGS AND MATHE-MATICAL FORMULATION

Problem statement

We consider a supply chain consisting of a set I of customers delivered from a set J of potential production centers belonging to the same company. Customers' locations and demands are known and considered deterministic over a time horizon T decomposed in discrete time periods, typically years. We also define T * = T \{0}. The main goal of the SCND problem is to select a subset of production centers among the whole set J and to assign customers' demand to these production centers, at each time period, so as to maximize the adjusted present value of the company.

Satisfying customers' demand requires a certain number of logistic decisions: opening production facilities, setting production levels and carrying the goods from facilities to customers. The mathematical model presented in this section aims at determining the list of Expected Bankruptcy cost (EBC)

Figure 1 -Trade-off theory for the determination of the optimal debt value candidate facilities selected, and the product flows from these facilities to customers at each time period, in order to maximize an objective function based on both financial and logistic goals. Since one of the main goals of this paper is to show the interactions between logistic and financial decisions, we adopted a set of simple logistic rules that are not too constraining. We assume that there is no closing option for the facilities. In other words, once a facility is selected, it will stay open until the end of the time horizon. The generalization of this work to a network with both opening and closing options does not raise theoretical difficulties.

The main assumption is that it is not mandatory to serve every particular customer's demand. This can be justified by at least two reasons. First, some customers may be simply too far from production centers, so that delivering them would result in a loss of money. Second, enforcing the delivery to all customers would generate unrealistic solutions in which large fixed cost would be paid to open facilities that deliver only a few customers. We do not impose any single sourcing constraint: customers can be delivered from distinct facilities at distinct periods. However, no partial satisfaction of a particular customer's demand is authorized. Moreover, if a customer's demand is satisfied within a given time period, then it must be satisfied again in all subsequent time periods. Unsatisfied customers' demands are simply lost ; back-orders are not authorized. For each time period, the fraction of the total demand that is satisfied is called fill rate.

All supply chain operations have a potentially large cost that must be financed with either debt or equity.

Companies generally mix debt financing and equity financing. Thus, for a given decision, the amount to be borrowed to banks and the duration of repayment varies with respect to this mix. We define a set B of available bank offers. Each bank offer is modeled by a tuple containing the maximum amount of money that can be borrowed, an interest rate and a repayment duration.

Incorporating financial decisions into an SCND problem amounts to select a subset of candidate bank offer and optimize the financial flows of the company. The objective function of the optimization problem considered is to maximize the firm's value at the end of the time horizon, where the APV described in section 2.3 is used as a proxy for the firm's value. We consider only two modes for financing supply chain strategic decisions: equity (using the available cash accumulated in previous periods) and debt (selecting bank offers). This study does not consider capital increase, which decision depends on strategic objectives that can hardly be modeled by mathematical models. Moreover, our decision making framework does not consider any decision at the tactical or operational decision levels. The next sections detail the proposed MILP formulation. Section 3.2 describes the variables and constraints related to logistic decisions. Section 3.3 does the same for financial decisions. Section 3.4 describes the calculation of the APV.

MOSIM'20 -November 12-14, 2020 -Agadir -Morocco

Logistic constraints

For any j ∈ J and t ∈ T , the binary variables y jt equal 1 if the facility j ∈ J is selected at period t ∈ T , and 0 otherwise. As mentioned before, once a facility is selected, it cannot be closed later. Besides, the number of facilities selected is bounded above by a number J max . These assumptions are modeled by constraints ( 4) and ( 5).

y j,t-1 ≤ y jt ∀j ∈ J, t ∈ T * (4) j∈J,t∈T * y jt -y j,t-1 ≤ J max (5)
Constraints ( 6), ( 7), ( 8) and ( 9) are related to the delivery of customers. Due to different trade rules between geographical areas as well as various logistic constraints, it might be practically impossible to deliver some customers from some facilities. Thus, we introduce the binary notation v ij which is set at value 1 if the customer i ∈ I can be delivered by the facility j ∈ J. Moreover, we denote by q ijt the quantity delivered by facility j ∈ J to customer i ∈ I at time period t ∈ T .

With these notations, constraints (6) set q ijt to 0 if customer i ∈ I cannot be served by facility j ∈ J or if facility j ∈ J is not operating at period t. The binary variables θ it take value 1 if customer i ∈ I is served at period t ∈ T , and 0 otherwise. Constraints (7) calculate the total quantity delivered to each customer. It is either 0 (when θ it = 0) or the value of the customer's demand.

According to the constraints (8), once a customer is served, it will be served at all subsequent periods. The capacity constraints (9) enforce the total quantity shipped by one facility j ∈ J to be at most equal to its capacity k j . Note that with these constraints, one can model several possible sizes of facilities, by setting several candidate facilities, with distinct capacities, at the same location.

q ijt ≤ v ij d it y jt ∀i ∈ I, j ∈ J, t ∈ T * (6) j∈J q ijt = d it θ it ∀i ∈ I, t ∈ T * (7) θ it ≥ θ i,t-1 ∀i ∈ I, t ∈ T * (8) i∈I q ijt ≤ k j y jt ∀j ∈ J, t ∈ T * (9)
The constraints (10)-( 13) calculate the costs related to the manufacturing and transportation of goods. Each candidate facility j ∈ J has a fixed cost f j , which is paid once when the facility is selected, as well as the processing cost µ j for each unit of product processed by this facility. We consider a unit transportation cost w. Without loss of generality, it is the same in the whole network. The distance dist ij between two locations j ∈ J and i ∈ I is denoted as dist ij .

Constraints (10) calculate the total processing cost P rocCost t at time period t ∈ T by summing the processing costs at every production center. Constraints (11) give an estimate of the total transportation cost T rnCost t at period t ∈ T . Constraints (12) compute the sum of the fixed cost of selected candidate locations. Finally, constraints (13) calculate the total amount of logistic expenses Exp t at time period t ∈ T .

P rocCost t = j∈J µ j i∈I q ijt ∀t ∈ T * (10)
T rnCost t = w × i∈I j∈J dist ij × q ijt ∀t ∈ T * (11) F ixedCost t = j∈J f j × y jt ∀t ∈ T * (12)
Exp t = P rocCost t + T rnCost t + F ixedCost t ∀t ∈ T * (13) Considering a selling price p i to customer i ∈ I, the total revenue Rev t at period t ∈ T is calculated with constraints (14).

Rev t = j∈J i∈I p i × q ijt ∀t ∈ T * (14)

Financial constraints

In this section, we present the financial constraints that relate to debt, equity, or a combination of both.

Debt Financing

Debt refers to the money borrowed to financial institutions on certain conditions subject to return. We MOSIM'20 -November 12-14, 2020 -Agadir -Morocco

The constraints (15) introduce the upper bounds Z b while the constraints ( 16) calculate the value of Repay bt for each bank-offer and each period of interest, with the corresponding financial mathematics formula.

Borrow bt ≤ Z b , ∀b ∈ B, t ∈ T * (15)

Repay bt = Borrow bt b α b (1 + α b ) N b (1 + α b ) N b -1 ∀b ∈ B, t ∈ [t b + 1, t b + N b ] (16)
We define D bt as the current debt associated with bank offer b ∈ B at time period t ∈ T \{0}. Given the interest rate α b , the value of the interest at period t is given by constraints (17). The constraints (18) model the calculation of the current value D bt of the debt related to bank offer b at period t. It is the value at the preceding period, augmented by the interest I bt as well as the possible additional amount borrowed, and decreased by the amount repaid. In constraints (19), we define the total debt Debt t of the company at period t. Constraints (20) state that this total debt should not exceed some maximal level M axDebt.

I bt = α b D b,t-1 ∀b ∈ B, t ∈ T * (17) D bt = D b,t-1 + I bt + Borrow bt -Repay bt ∀b ∈ B, t ∈ T * (18) Debt t = b∈B D bt ∀t ∈ T (19) Debt t ≤ M axDebt ∀t ∈ T (20)

Equity Financing

Equity refers to the money supported by shareholders and also a portion of the generated revenues plowed back into the company after paying out the expenses as well as the shareholders' dividends. Assuming that there is no possibility of capital increase, equity is defined in the form of internal funds. Internal funds, which are used to be invested for the firms' long-term purposes, are a portion of cash left over for the companies. Thereby, internal funds at period t ∈ T , IF t , are restricted by the available cash at the end of the preceding period, Cash t-1 , as stated in constraints ( 21)

IF t ≤ Cash t-1 ∀t ∈ T. (21)
In order to introduce constraints related to cash management, we first define intermediate notations in equations ( 22) to ( 26). First, the depreciation represents a yearly decrease of tangible assets' value over time. There are different methods to depreciate the firm's assets. Following Laínez et al. ( 2007), we implement the straight-line approach to calculate the depreciation of each facility j ∈ J as a function of its initial value, IV j , salvage value, SV j , and lifetime, LT j , according to the constraints ( 22).

Dep j = IV j -SV j LT j ∀j ∈ J (22)
Constraints ( 23) define the yearly changes in the value of the fixed asset, ∆F A t . It results from the opening cost o j of the facilities and from the depreciation Dep j .

∆F A t = j∈J (o j (y jt -y j,t-1 ) -Dep j × y j,t-1 ) ∀t ∈ T (23)
The net changes in debt liabilities due to the bank at period t ∈ T , ∆Lib t , is computed by the constraints (24). In constraints (25), the Earning Before Interest and Taxes (EBIT) at period t ∈ T , denoted EBIT t , is the difference between the firm's revenues and expenses (before interest and tax) at period t ∈ T . A depreciation factor is considered for all open facilities.

EBIT t = Rev t -Exp t - j∈J Dep j × y j,t-1 ∀t ∈ T (25)
In constraints (26), N OP AT t expresses the net operating profit after taxes of period t ∈ T . By definition, it is obtained by subtracting the interest expenses from the EBIT at period t ∈ T , and then multiplying the result by the term (1 -τ ), where τ is the firm tax rate.

N OP AT t = (EBIT t - b∈B I bt ) × (1 -τ )
MOSIM'20 -November 12-14, 2020 -Agadir -Morocco ∀t ∈ T (26)

At the strategic decision level, the level of cash at period t ∈ T , Cash t , is a function of available cash at the end of the preceding period, Cash t-1 , net operating profit after tax, N OP AT t , net changes in longterm investment, ∆F A t , and net changes in longterm liabilities, ∆Lib t . Constraints (27) represent the above-mentioned relation.

Cash t = Cash t-1 -∆F A t + N OP AT t + ∆Lib t ∀t ∈ T (27)
Constraints ( 28) explain how facility location decision are funded, either by internal funds (IF t ) or by the debt.

j∈J o j (y jt -y j,t-1 ) = b∈B (Borrow bt ) + IF t ∀t ∈ T (28)

Objective function

The objective function to be maximized is the Adjusted Present Value (APV), briefly introduced in equation ( 3). The detailed formulation of APV is given by equation ( 29).

AP V = t∈T F CF t (1 + r E ) t + t∈T b∈B τ × I bt (1 + α b ) t -π × BC (29)
The first term of this objective function is based on the Future cash flows (F CF t ), that measure the firm's ability to generate cash. In other words, F CF t is defined as the difference between both operating and non-operating cash inflows and outflows. Constraints (30) indicate how to calculate this indicator.

F CF t = (1 -τ )EBIT t -∆F A t ∀t ∈ T, (30)
In equation ( 29), the parameter r E represents the cost of equity.

The second term of the objective function represents the net present value of the Tax Shield Benefit (TSB). The last term is the Expected bankruptcy Cost (EBC), which mainly depends on the Z-score value. The following set of equations defines the Zscore components listed in section 2.2.

The total assets for every period t ∈ T , denoted T A t , is expressed by constraints (31). They include the cash at period t and the book value at period t ∈ T , which is calculated as the accumulated changes in fixed assets value, ∆F A t , from period 1 to t.

T A t = Cash t + t t =1 ∆F A t ∀t ∈ T (31)
The retained earnings are defined as the net income left over for the company after distributing the dividends to its shareholders. With regards to ignoring the capital expenditures, no dividends are considered. Therefore, RE t , which represents the value of retained earnings at the period t, is simply obtained using the constraints (32).

RE t = RE t-1 + N OP AT t ∀t ∈ T (32)
The book value of equity equals the sum of the retained earnings and the paid-in capital by the shareholders. However, ignoring capital expenditure, BE t , which is the book value of equity at period t ∈ T is represented by the constraints (33).

BE t = RE t ∀t ∈ T (33)
The book value of liabilities, BL t , is defined as the portion of long-term debts due to the bank at period t ∈ T . It is formulated in the constraints (34).

BL t = b∈B t t =1 (Borrow bt -Repay bt + I bt ) ∀t ∈ T (34)
Finally, the sales, at period t ∈ T are directly given by the variables Rev t defined by the equation ( 14).

Note that the Z-score components used in the mathematical model (X 2 = RE t /T A t , X3 = EBIT t /T A t , X4 = BE t /BL t and X5 = Rev t /T A t ) are all nonlinear. The linearization of these ratios is fully detailed in [START_REF] Rezaei | An adjusted present value based supply chain network design model[END_REF].

NUMERICAL EXPERIMENTS

This section presents the computational experiments conducted to evaluate the performance of the pro-posed mathematical model. To this aim, we generated a set of instances. The number of customers in these instances is between 60 and 180, and the number of candidate facilities is always 10% of the number of customers. Extensive details about the data generation can be found in [START_REF] Rezaei | An adjusted present value based supply chain network design model[END_REF].

FCF is used as an objective function in many SCND models. Thus, the impact of handling financial indicators in our model is highlighted through a comparison between the results of APV maximization and of the FCF maximization. Concretely, we compare two models: (i) a restricted model whose objective function is t F CF t and where the only equity financing constraints considered are those related to F CF t and (ii) an exhaustive model whose objective function is the APV and with all constraints considered.

For each instance, the network configurations obtained under F CF and AP V maximization are shown in Table 1. The first column of the table represents the instance name, built from the number of customers and the coordinates pattern (R=random, C=clustered). The next five columns detail the list of facilities opened at each time period. The eight column represents the fill rate reached in the final period. In order to compare the FCF-and APVdriven solutions, we have a posteriori calculated the APV corresponding to solution obtained under FCF maximization. The percentage indicated in the ninth column represents the gap between both APVs.

To get a more detailed picture of the model's decision mechanism, Figures 2 and 3 present the optimal network configurations for instance 150-C, obtained under FCF or APV maximization, respectively. The second reason is the time value of money, which is ignored by FCF. Opening facility 7 at period 2 rather than at period 1 as well as opening facility 14 at period 3 rather than at period 2 leads to a lower fill rate (we recall that the firm is nonsensitive to the consumer's behavior and that no back-order cost is assumed for unsatisfied customers), higher tax shield benefit and lower investment value due to the time value of money.

CONCLUSION

In this paper, we proposed an extension of traditional supply chain network models, driven by financial considerations. We propose to use the Adjusted Present Value (APV) as a performance indicator and show that this indicator enables decision makers to find a trade-off between logistic and financial priorities. The mathematical model is tractable by state of the art mixed integer linear programming solvers for realistic sizes of instances, opening perspectives for reallife applications. The numerical experiments show that using APV instead of traditional indicators does not bring considerable changes in the final configuration of the supply chain, but modifies its temporal implementation and can increase the firm value up to around 10%. Besides, focusing on the firm value rather on logistic costs tends to decrease the fill rate, i.e. the satisfaction of customers' demand. Further research could aim at investigating the trade-offs between the interest of various supply chain stakeholders.

ACKNOWLEDGMENT

This work has been supported by ANR under the FILEAS-FOG -ANR-17-CE10-0001 project. Modigliani, F. and Miller, M. H. (1963). Corporate income taxes and the cost of capital: a cor-

  u e c o n s i d e r i n g o n l y t a x s h i e l d ( U V + T S B ) Tax shield benefit (TSB)

  consider a set B of bank offers, each of them consisting of an upper bound Z b on the amount borrowed, a duration N b (in years) of reimbursement, an interest rate α b . The variables Borrow bt represent the amount of bank offer b borrowed at period t. If some bank offer b ∈ B is activated at period t b , then the reimbursement period is the interval [t b + 1, t b + N b ]. The amount of bank offer b repaid at period t ∈ [t b + 1, t b + N b ] is denoted Repay bt .

(

  Borrow bt -Repay bt + I bt ) ∀t ∈ T (24)

Figure 2 -

 2 Figure 2 -Instance 150-C: network under FCF maximization

Table 1 -

 1 Network configuration under FCF and APV

	under APV max-

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