Camélia Matei Ghimbeu
email: camelia.ghimbeu@uha.fr

Joanna Górka

Virgine Simone

Loïc Simonin

Sébastien Martinet

Cathie Vix-Guterl

Insights on the Na + ion storage mechanism in hard carbon: Discrimination between the porosity, surface functional groups and defects

Keywords:

Sodium ion batteries (SIBs) using hard carbon as negative electrode hold the promise of being low cost alternative to lithium ion batteries (LiBs). However, the Na + storage mechanism in hard carbons is not fully understood yet and the attribution of Na storage in the sloping and plateau regions of the sodiation/desodiation curves remains still controversial. The current work employs N 2 , Kr and CO 2 gases to correctly assess the changes in hard carbon porosity induced by different pyrolysis temperature of cellulose. The sloping capacity was found to decrease with the decrease of the specific area of ultramicropores measurable only by CO 2 adsorption, while the plateau capacity demonstrated an opposite behavior. The high temperature derived carbons (> 1400 °C) present no porosity which disqualifies the attribution of plateau region to the adsorption of Na + in the nanopores but rather the insertion between the pseudo-graphitic domains. Temperature programmed desorption coupled with mass spectrometry (TPD-MS) was performed to determine the nature and the quantity of oxygen surface functional groups followed by oxygen chemisorptions to assess the amount of carbon edge defects expressed by active surface area (ASA) values. A decrease in the amount of oxygen groups and active surface area with the increase of the pyrolysis temperature was observed which is accompanied by a decrease of the sloping capacity. These results shed light in the storage mechanisms, the sloping region being ascribed mainly to the interaction of Na + with carbon edge defects and adsorption in the microporosity while the plateau region assigned to the intercalation of Na + in the pseudo-graphitic nanodomains.

Introduction

Growing energy demands as well as high availability of sodium sources are main driving forces for recent rapid development in the area of sodium ion batteries (SIBs), which hold the promise of being low cost alternative to lithium ion batteries (LiBs) for large-scale electric storage applications [START_REF] Irisarri | Review-hard carbon negative electrode materials for sodium-ion batteries[END_REF][START_REF] Luo | Na-ion battery anodes: materials and electrochemistry[END_REF][START_REF] Kang | Update on anode materials for Na-ion batteries[END_REF][START_REF] Gorka | Recent progress in design of biomassderived hard carbons for sodium ion batteries[END_REF][START_REF] Dahbi | Negative electrodes for Na-ion batteries[END_REF]. At early stage of the development of SIBs it was discovered that graphite, extensively used as anode material in LiBs, shows very limited electrochemical performance in SIBs. In place of graphite, hard carbons became most commonly used materials as anodes [START_REF] Irisarri | Review-hard carbon negative electrode materials for sodium-ion batteries[END_REF][START_REF] Luo | Na-ion battery anodes: materials and electrochemistry[END_REF][START_REF] Kang | Update on anode materials for Na-ion batteries[END_REF][START_REF] Gorka | Recent progress in design of biomassderived hard carbons for sodium ion batteries[END_REF][START_REF] Dahbi | Negative electrodes for Na-ion batteries[END_REF], even though they were displaying rather modest capacities, poor cycling stability and initial current efficiency when compared to lithium ion batteries.

Hard carbons are usually prepared by pyrolysis of organic polymers or sugars at high temperatures and their structure can be described as planar hexagonal network of carbon atoms without ordering in the c direction. The amorphous areas are mixed with more graphitic layers in which strong cross-linking immobilizes and prevents the development of true graphitic structure even at high temperatures. From fundamental and comprehensive studies viewpoint, phenolic resin-derived carbons are very promising for electrochemical Na-storage due to precise control of the carbon's physical and chemical properties [START_REF] Hasegawa | Hard carbon anodes for Na-ion batteries: toward practical use[END_REF]. But lately, thanks to a low cost, large producibility and promising performance, hard carbons obtained from wide range of biomass-derived precursors were brought into the spotlight. They include different forms of cellulose, lignin, peanut skins and shells, banana and shaddock peel, wood [START_REF] Zou | Evaluating the storage behaviour of superior low-cost anode material from biomass for high-rate sodiumion batteries[END_REF] as well as a bit less obvious choice for carbon precursors such as peat moss and algal blooms [START_REF] Gorka | Recent progress in design of biomassderived hard carbons for sodium ion batteries[END_REF].

Speaking about material's performance, even though there is a growing number of reports published each year on the subject, the https://doi.org/10.1016/j.nanoen.2017.12.013 sodium insertion mechanism is not fully understood and the relationship between the texture and microstructure of carbon materials and their performance not fully established. Especially, what affects the irreversible capacity loss, low initial Coulombic efficiency and poor rate performances. The initial irreversible capacity loss is usually associated with SEI formation, although it is also suspected that some of Na ions can be trapped in the graphene edges and defects between the graphene planes [START_REF] Lotfabad | Origin of non-SEI setalted coloumbic efficiency loss in carbons tested against Na and Li[END_REF].

The most used mechanism to describe the sodium storage in hard carbons is the so-called "falling card" model and was proposed by Stevens and Dahn in 2000 [START_REF] Stevens | High capacity anode materials for rechargeable sodium-ion batteries[END_REF]. In this model, the sloping part of the galvanostatic curve (1-0.1 V, vs. Na + /Na) is associated with Na + intercalation between the graphene sheets in turbostatic domains while the low voltage plateau (0.1-0 V, vs. Na + /Na) is ascribed to the insertion of Na + into the nanocavities or nanopores. In 2012, Cao et al. [START_REF] Cao | Sodium ion insertion in hollow carbon nanowires for battery applications[END_REF] firstly suggested based on experimental and theoretical approaches that the sloping region is associated to the Na + adsorption while the plateau region ascribed to the Na + insertion between the graphene layers. Similar mechanism was latter on confirmed by Ding et al. [START_REF] Ding | Carbon nanosheet frameworks derived from peat moss as high performance sodium ion battery anodes[END_REF]. More recently, several other works pointed out that Na storage mechanisms ascribed by "falling-card" model in these two regions is not straightfull, the sloping region being associated to the Na binding on carbon vacancies [START_REF] Lotfabad | High-density sodium and lithium ion battery anodes from banana peels[END_REF] or the plateau region associated to the Na insertion in graphene domains [START_REF] Ding | Carbon nanosheet frameworks derived from peat moss as high performance sodium ion battery anodes[END_REF][START_REF] Lotfabad | High-density sodium and lithium ion battery anodes from banana peels[END_REF][START_REF] Bommier | New mechanistic insights on Na-ion storage in nongraphitisable carbon[END_REF].

The link between SEI formation and the surface area of the electrode observed at first for LIBs seems to be valid for SIBs as well. The irreversible capacity loss during the first cycle decreases with the decrease of specific surface area [START_REF] Irisarri | Review-hard carbon negative electrode materials for sodium-ion batteries[END_REF][START_REF] Simone | Hard carbon derived from cellulose as anode for sodium ion batteries: dependence of electrochemical properties on structure[END_REF]. It should be mentioned that the carbon surface is formed by basal and edge planes and their amount may change depending on the carbon precursors, carbonization treatments or post-treatment modification. The carbon total surface area involves mainly the basal planes and is widely determined in many works by nitrogen physisorption at 77 K using the BET method. However, it is well known that such gas do not allow to assess the ultramicropores (pores < 0.7 nm). Less concerns on the determination of ultramicropores was given for hard carbons that can be achieved by using slightly smaller gas probe molecule such CO 2 at a higher temperature (273 K), conditions favoring the gas diffusion inside the narrowest micropores. Hard carbons characterized by low nitrogen BET surface area give different electrochemical performances and the existence of such small pores may probably explain in some extent the different performances but to our knowledge not yet investigated in detail.

On the other hand, the edge planes include several types of defects (stacking faults, vacancies, dislocations) placed on the prismatic faces and inside the hexagonal network which constitute the so-called active sites or active surface area (ASA). Their amount depends on the carbon crystallite size/orientation, structural order and vacancy/impurity concentration [START_REF] Ehrburger | Active surface area of microporous carbons[END_REF][START_REF] Ehrburger | The concept of active sites applied to the study of carbon reactivity[END_REF][START_REF] Laine | The importance of active surface area in the carbon-oxygen reaction[END_REF] and can be quantified by the amount of oxygen surface complexes formed by oxygen chemisorptions at 300 °C followed by quantification of formed CO and CO 2 groups using temperature programmed desorption coupled with mass spectrometry (TPD-MS) [START_REF] Ehrburger | Active surface area of microporous carbons[END_REF][START_REF] Ehrburger | The concept of active sites applied to the study of carbon reactivity[END_REF][START_REF] Laine | The importance of active surface area in the carbon-oxygen reaction[END_REF][START_REF] Vix-Guterl | Surface characterisations of carbon multiwall nanotubes: comparaison between surface active sites and Raman spectroscopy[END_REF]. It has been shown that these active sites induce different reactivity of carbon with gases and electrolytes. Particularly, we have highlighted in several works that the ASA is an important parameter governing the irreversible capacity of graphite in lithium ion batteries [START_REF] Beguin | Correlation of the irreversible lithium capacity with the active surface area of modified carbons[END_REF][START_REF] Bernardo | Influence of graphite surface properties on the first electrochemical C. Matei Ghimbeu et al. lithium intercalation[END_REF][START_REF] Matei Ghimbeu | Influence of graphite characteristics on the electrochemical performance in alkylcarbonate LiTFSI electrolyte for Li-ion capacitors and Li-ion batteries[END_REF]. More recently we have demonstrated that the active sites are involved in the mechanism of electrochemical double layer supercapacitor formation leading to the improvement of the capacitance in aqueous and organic electrolytes [START_REF] Moussa | Relationship between the carbon nano-onions (CNOs) surface chemistry/defects and their capacitance in aqueous and organic electrolytes[END_REF].

However, no works linking the carbon defects amount (ASA) with electrochemical performances of Na-ion batteries are published. It is worth to note the work of Bommier et al. [START_REF] Bommier | New mechanistic insights on Na-ion storage in nongraphitisable carbon[END_REF] where a relationship between the slope capacity and the defects estimated as the ratio I D /I G from Raman Spectroscopy was established. The defect determination by Raman can be linked in some extent to ASA as demonstrated by Vix-Guterl et al. [START_REF] Vix-Guterl | Surface characterisations of carbon multiwall nanotubes: comparaison between surface active sites and Raman spectroscopy[END_REF], however, the Raman is not sensitive to the defects induced by the presence of micropores < 2 nm [START_REF] Lahaye | The chemistry of carbon surfaces[END_REF]. Theoretical studies pointed out recently the importance of graphene defects in the interaction with Na + [START_REF] Datta | Defective graphene as a high-capacity anode material for Na-and Ca-ion batteries[END_REF][START_REF] Tsai | Ab initio study of sodium intercalation into disordered carbon[END_REF].

Later on, it was discovered that not only specific surface area of the electrode material could be entirely responsible for irreversible capacity but also the amount of functional groups on carbon's surface could play significant role. The reactivity and electronic conductivity of carbon surface can also be modified by introducing N-and O-containing functionalities. This approach turned out to be very beneficial to improve the electrochemical performance of SIBs as well as doping with heteroatoms such as boron, phosphorus and fluorine [START_REF] Wang | Fluorine-doped carbon particles derived from Lotus Petioles as high-performance anode materials for sodium-ion batteries[END_REF][START_REF] Wu | Nitrogen-doped porous carbon nanosheets as low-cost,high-performance anode material for sodiumion batteries Heng-guo Wang[END_REF][START_REF] Ruan | A phosphorus/N-doped carbon nanofiber composite as an anode material for sodium-ion batteries[END_REF][START_REF] Tang | Sulfur-doped carbon spheres with hierarchical micro/mesopores as anode materials for sodium-ion batteries[END_REF].

As one can see from the discussion above, porosity, surface chemistry and defects of hard carbons are key factors affecting their electrochemical performance. Since there is a lack of systematic studies addressing this issue, the goal of this work is to investigate and establish clear relationships between the materials porosity, structure and chemistry and their electrochemical capacity in the sloping and plateau regions. Different gas probing molecules (N 2 , CO 2 and Kr) were used to correctly asses the hard carbon porosity while the surface chemistry and the amount of defects were determined by TPD-MS. An overall picture of the evolution of the sloping and plateau capacities with the microporosity, amount of functional groups, amount of defects and the interlayer spacing is drawn as a function of hard carbon pyrolysis temperature.

Experimental

Hard carbon synthesis/modification

Several hard carbon samples were prepared by two steps pyrolysis of cellulose (Aldrich, microcrystalline powder) according to our previous work [START_REF] Simone | Hard carbon derived from cellulose as anode for sodium ion batteries: dependence of electrochemical properties on structure[END_REF]. Both heat treatments were performed under argon atmosphere in a horizontal tube furnace. In the first step, the temperature was increased to 200 °C using a fast heating rate (20 °C/min) followed by slow heating rate (1 °C/min) up to 450 °C then were cooled down to room temperature. In the second step, the as-prepared materials were pyrolysed to the final temperature (3.33 °C/min), maintained for 1 h and cooled down then to room temperature. The six different samples were synthesized using temperatures between 1000 °C and 1600 °C and they are labeled as HC-T, where T denotes the annealing temperature (Table 1).

To increase the amount of oxygenated groups, the HC-1400 carbon was modified with concentrated nitric acid (HNO 3 ). A certain amount of carbon (~2 g) was immersed in 40 mL of HNO 3 and heated under reflux at 60 °C for 1 h. After cooling down, the solution containing the carbon was filtered and the recovered carbon washed with plenty distillate water followed by drying at 80 °C. The resulting oxidized material was denoted HC-1400ox. Half of the HC-1400ox oxidized carbon was heat treated further up to 900 °C under hydrogen in order remove the oxygen functional groups. The resulting reduced carbon was named HC-1400red.

Characterization methods

Nitrogen, Kr and CO 2 adsorption isotherms were measured on ASAP2020 porosity analyzer from Micromeritics at 77 K (N 2 and Kr) and 273 K (CO 2 ). Prior to the analysis, the materials were outgassed under primary vacuum at 300 °C during one night. The BET specific surface area S BET was calculated in the relative pressure range, P/P 0 of 0.05-0.3. The micropore pore size distributions (PSD) were determined from the adsorption branch of isotherms using the 2D NLDFT heterogeneous surface model for carbon materials for N 2 and CO 2 gases implemented in SAIEUS (Micromeritics) [START_REF] Jagiello | Carbon slit pore model incorporating surface energetical heterogeneity and geometrical corrugation[END_REF][START_REF] Jagiello | 2D-NLDFT adsorption models for carbon slit-shaped pores with surface energetical heterogeneity and geometrical corrugation[END_REF]. X-ray diffraction analysis was performed with a powder diffractometer D8 ADVANCE A25 from Bruker in Bragg-Brentano reflexion geometry θ -θ. The diffractometer is equipped with a LynxEye XE-T high resolution energy dispersive 1-D detector (Cu Kα 1 , 2 ), leading to ultra fast X-ray diffraction measurements. Transmission electron microscopy (TEM) was used to observe the structure of each sample. TEM images were acquired using a JOEL ARM-200F microscope with working voltage of 200 kV.

The surface functionality of hard carbon was analyzed by temperature programmed desorption coupled with mass spectrometry. The material is heat-treated in vacuum with a heating rate of 5 °C/min up to 950 °C. The oxygen functional groups are decomposing in CO and CO 2 during the heating process and are continuously quantitatively detected by a mass spectrometer. Water and H 2 are evolved as well from the material. Before experiments, the mass spectrometer was calibrated using N 2 (m/z = 28), H 2 (m/z = 2), CO (m/z = 28), CO 2 (m/z = 44) and H 2 O (m/z = 18). The total amount of each gas released was computed by time integration of the TPD curves. The active surface area (ASA) was determined as described in the literature [START_REF] Bernardo | Influence of graphite surface properties on the first electrochemical C. Matei Ghimbeu et al. lithium intercalation[END_REF]. In summary, the hard-carbon surface is cleaned in a first step by outgassing at 950 °C for 30 min under high vacuum (10 -4 Pa). In a second step, the hard carbon surface is exposed to di-oxygen atmosphere at 300 °C (di-oxygen pressure: 66.5 Pa) during 10 h allowing the carbon defects to react and to form surface oxygen complexes. After the removal of di-oxygen, the sample is heat-treated up to 950 °C and the oxygenated complexes formed are decomposed into CO and CO 2 and their amount is quantitatively determined subsequently by mass spectrometry. The surface area occupied by the chemisorbed oxygen (ASA) can be calculated by taking into account the number of mole for each gas desorbed and considering the area of an edge carbon site that chemisorbs an oxygen atom as 0.083 nm 2 [START_REF] Bernardo | Influence of graphite surface properties on the first electrochemical C. Matei Ghimbeu et al. lithium intercalation[END_REF].

Electrochemical tests

Electrode slurries were prepared with the formulation 80 wt% hard carbon, 10 wt% Carbon black (super C45 from Timcal-Imerys) and 10 wt% PVDF (1015 from Solvay) in N -methyl pyrrolidone (NMP) solvent. Slurries were coated onto aluminium foils and dried overnight at 55 °C. The 2-electrode coin cells were assembled in an argon filled glovebox. A Celgard 2400 polyethylene separator was put between both electrodes with a Viledon® membrane used as an electrolyte reservoir. Sodium metal (Aldrich, 99.9%) was used as a counter electrode. The electrolyte was a 1 M solution of NaPF 6 (Stella Chemifa, min 98% pure) in ethylene carbonate/dimethyl carbonate (EC/DMC-UBE America Inc.-ratio 1/1 in volume). The amounts of water and HF in the electrolyte were measured at laboratory to be less than 30 ppm. The electrochemical tests were carried out using an Arbin BT2000 battery cycler. The electrodes were tested upon cycling with a constant current corresponding to a C /10 rate (37. 2 mA/g) followed by a constant voltage of 10 mV at the end of discharge step only (i.e. sodium uptake).

Results and discussion

As highlighted in the introduction, the porosity of hard carbons is an important parameter that influences the battery performance, particularly the first irreversible capacity. Usually, the most employed probe molecule to evaluate the textural properties of hard carbons is the nitrogen. However, the nitrogen gas cannot correctly asses the entire porosity of very low surface area materials and in such case Kr adsorbate is recommended. In addition, the very small pores, called ultramicropores (< 0.7 nm) cannot be as well determined by nitrogen and in this case CO 2 is considered the most appropriate in this aim [START_REF] Cychosz | Recent avances in the textural characterization of hierarchically structured nanoporous materials[END_REF]. Such small pores may contribute to the Na + storage mechanism and often not taken into consideration in most of the works. The majority of hard carbon present low surface area when determined by nitrogen adsorption, but information about the ultramicropores are not provided to better compare the materials issued from different precursors and synthesis procedures. Therefore, to completely asses the porosity of hard carbon in this work, N 2 , Kr and CO 2 adsorption was performed. The nitrogen adsorption/desorption isotherms at 77 K were firstly measured and except the sample treated at 1000 °C (HC-1000) which present a nitrogen surface area of ~80 m 2 /g, the thermal treatments at higher temperatures yielded in very low surface area carbon materials (Table 1). As expected, the whole series of samples follows the trend of gradual lowering of BET surface area as the temperature of thermal treatment increases, with quite abrupt drop when temperature exceeds 1000 °C (Table 1) [START_REF] Irisarri | Review-hard carbon negative electrode materials for sodium-ion batteries[END_REF][START_REF] Hasegawa | Hard carbon anodes for Na-ion batteries: toward practical use[END_REF][START_REF] Simone | Hard carbon derived from cellulose as anode for sodium ion batteries: dependence of electrochemical properties on structure[END_REF][START_REF] Li | Hard carbon microtubes made from renewable cotton as high-performance anode material for sodium-ion batteries[END_REF].

The nitrogen adsorption measurements revealed that most of the carbons treated at high temperature in the series possess low surface area close to the detection limit of the technique and because of that they are not distinct enough to differentiate between samples. That is why using probe molecules with different sizes, shapes and different saturation pressures was behind the idea of performing Kr and CO 2 adsorption measurements.

While Kr adsorption is well known to have greater accuracy in estimating porosity of small surface area materials and thin films compared to nitrogen, one can clearly see that all Kr isotherms and derived BET values obtained are very close to each other and smaller than the nitrogen ones (Fig. S1 and Table 1). Based on that, it is impossible to discriminate between samples. The evident discrepancy between BET values obtained from Kr and N 2 adsorption measurements is most likely due to different saturation pressure Kr condenses at and bigger size of Kr molecule.

Among N 2 , Kr and CO 2 only CO 2 adsorption measurements brought more insight into the textural properties of studied carbons. The smaller size of CO 2 molecule and the higher saturation pressure make it much better for accessing pores smaller than 1 nm, so-called ultramicropores [START_REF] Cychosz | Recent avances in the textural characterization of hierarchically structured nanoporous materials[END_REF]. The CO 2 adsorption isotherms along with the pore size distribution determined by 2D-NLDFT model are shown in Fig. 1. We can see that the materials present high CO 2 adsorption volumes which decreases significantly particularly for temperatures higher than 1300 °C. The CO 2 specific area is significantly much higher compared to nitrogen one and comprised between 406 m 2 /g and 5 m 2 /g (Fig. 1 c). The same behavior was observed on other types of disordered carbons [START_REF] Béguin | A better understanding of the irreversible lithium insertion mechanisms in disordered carbons[END_REF][START_REF] Zhang | Correlation between microstructure and Na storage behaviour in hard carbon[END_REF]. The pore size distribution (Fig. 1b) show a high intense peak centered around 0.45 nm for HC-1000 carbon and in addition a less intense and broad peak with sizes > 1.0 nm. The larger pore size were more accurately determined by nitrogen adsorption/desorption isotherms (Fig. S1) which reveals uniform pore with average size centered around 1.3 nm.

Increasing the annealing temperature, the pore volume determined by NLDFT on CO 2 isotherm significantly diminishes (Fig. 1b, Table S1) but their size become larger, i.e., 0.45 nm for HC-1000 to 0.59 nm for HC-1600. However, it is clear that the amount of such larger pores is very limited in the present materials as highlighted by the pore size distribution (Fig. 1b). The decrease of the pore volume is mainly associated to the microporosity closure during the thermal annealing at higher temperature. This is usually explained by the so-called "falling cards model" [START_REF] Dahn | The "falling cards model" for the structure of microporous carbons[END_REF][START_REF] Buiel | Model of micropore closure in hard carbon prepared from sucrose[END_REF] which assumes that the increasing of the annealing temperature induce graphene layers organization and further lead to the microporosity collapsing and the formation of larger pores. Indeed, the organization of the hard carbons with the increase in the temperature is evidenced also here by the decrease of the graphene interlayer distance, d-space (Table 1). The increase of micropore size with the increase in the annealing temperature was underlined by Small Angle X-ray Scattering (SAXS) measurements in other works as well [START_REF] Simone | Hard carbon derived from cellulose as anode for sodium ion batteries: dependence of electrochemical properties on structure[END_REF][START_REF] Buiel | Model of micropore closure in hard carbon prepared from sucrose[END_REF].

The evolution of the carbon specific surface area with the annealing temperature by using the three gases is shown in Fig. 1c. Except the carbon HC-1000 which has a measurable surface area by using nitrogen, the other carbons present similar surface area. When Kr is used, same similar low surface area is determined. On the contrary, employing CO 2 , high surface area is seen but this are gradually decreases with the increase of the pyrolysis temperature. This suggest that the materials are mainly ultramicroporous (pore size < 0.7 nm), except the HC-1000 where some microporosity (pore size > 0.7 nm) is also observed.

The type and quantities of oxygenated functional groups present on the carbon surface maybe another important parameter in the interactions with the electrolyte. Thus, the carbon surface functionality was analyzed by TPD-MS technique and the desorption rate of each gas evolved during the thermal treatment is plotted vs. temperature as shown in Fig. 2a. During the hard carbon heating, the decomposition of the functional oxygenated groups occur leading to the formation of gases such as CO and CO 2 . The type of CO x groups released and their release temperature give indication about their nature. Typically, the CO 2 derives from acidic groups, i.e., carboxyl or anhydride groups while CO is formed by decomposition of more basic or neutral groups such as, carbonyl, phenol, ether and/or quinone groups [START_REF] Figueiredo | Modification of the surface chemistry of activated carbons[END_REF].

For simplicity reasons, only one typical TPD-MS desorption curve is shown for HC-1150 carbon (Fig. 2a). We noticed an intense and large CO desorption peak comprised between 400 and 950 °C indicating the presence of a large pallet of oxygenated groups such as anhydrides, phenols, ethers and quinones [START_REF] Moussa | Relationship between the carbon nano-onions (CNOs) surface chemistry/defects and their capacitance in aqueous and organic electrolytes[END_REF][START_REF] Matei Ghimbeu | Influence of surface chemistry on the adsorption of oxygenated hydrocarbons on activated carbons[END_REF][START_REF] Ruiz | Effects of thermal treatment of activated carbon on the electrochemical behaviour in supercapacitors[END_REF]. The CO 2 evolution is significantly much lower and is mainly located between 200 and 700 °C suggesting the presence of carboxyl and anhydride groups [START_REF] Moussa | Relationship between the carbon nano-onions (CNOs) surface chemistry/defects and their capacitance in aqueous and organic electrolytes[END_REF][START_REF] Matei Ghimbeu | Influence of surface chemistry on the adsorption of oxygenated hydrocarbons on activated carbons[END_REF][START_REF] Ruiz | Effects of thermal treatment of activated carbon on the electrochemical behaviour in supercapacitors[END_REF]. The materials are characterized also by a large peak of water release (100-600 °C). At low temperatures this can be assigned to physisorbed water in carbon porosity while at much higher temperatures to chemisorbed water. This can be an indication of water desorbed due to the dehydration reactions of neighbour carboxyl groups leading to the formation of anhydrides which decomposes at higher temperature concomitantly to both CO and CO 2 gases. Furthermore, a peak of hydrogen is observed at high temperature (> 800 °C) which is typical for the cleavage of the C-H bonds and carbon structural organization.

The integration of CO and CO 2 desorption peaks allows to quantify the amounts of the oxygenated groups released from the carbon surface as seen gather in Table 1. According to Table 1, the amount of CO evolved is higher than CO 2 in good agreement with the desorption profiles intensity. The total amount of oxygen groups evolution (CO x : CO + CO 2 groups) with the annealing temperature of cellulose is presented in Fig. 2b and a decrease of the amount of CO x groups is seen with the increase of the pyrolysis temperature. The same tendency is observed for water and hydrogen gases.

After removing the oxygen functional groups from the carbon surface by the in-situ TPD-MS treatment up to 950 °C under vacuum, the surface defect concentration was determined in terms of active surface area by exposing the carbon to oxygen at 300 °C overnight. Oxygen functionalities are formed and a subsequent TPD-MS analysis allows to quantify them and to calculate the ASA. The ASA values obtained for all carbons are listed in Table 1 while its evolution with the temperature of cellulose annealing temperature shown in Fig. 2b.

The ASA decreases from 44 m 2 g -1 for HC-1000 to 1 m 2 g -1 for HC-1600, therefore, the amount of defects diminishes with the increase of the annealing temperature similarly as the amount of oxygen groups. This maybe understood by the formation of edge defects, vacancies, dangling bonds during the pyrolysis treatment and once exposed to air such defects are highly reactive towards oxygen from air and induce the formation of oxygen groups. It can be supposed that the functional groups are anchored on carbon defects. This is coherent with the fact that the amount of functional groups and the amount of defects are varying in the same manner with the annealing temperature.

The increase in the short-range ordering of the carbon with the temperature was proven as well by the decrease of the interlayer spacing d (002) from 3.88 to 3.72 Å (Table 1), as previously determined by XRD analysis [START_REF] Simone | Hard carbon derived from cellulose as anode for sodium ion batteries: dependence of electrochemical properties on structure[END_REF]. The high resolution transmission electron microscopy (HRTEM) images (Fig. S2, Supporting Information's) performed on the lowest and highest temperature treated materials, i.e., HC-1000 and HC-1600 show the increase of ordered structure containing graphitic domains with the increase of the temperature. More staked graphene layers are observed in line with the selected area electron diffraction (SAED) analysis demonstrating more defined diffractions rings (Fig. S2, Supporting information's).

As previously demonstrated for Li ion batteries, ASA differences may induce a modification in carbon reactivity towards the electrolyte and direct the electrolyte decompositions and further the formation of SEI layer [START_REF] Bernardo | Influence of graphite surface properties on the first electrochemical C. Matei Ghimbeu et al. lithium intercalation[END_REF][START_REF] Ng | Correlations between surface properties of graphite and the first cycle specific charge loss in lithium-ion batteries[END_REF]. In the case of Na-ion batteries, the influence of ASA on electrochemical performances was not yet evaluated.

Fig. S3 (Supporting information's), shows the first charge/discharge cycle for all hard carbons and we notice that the first reduction capacity was around 360 mAh/g for all materials (Table S1, Supporting information's). The evolution of the irreversible, reversible, slope and plateau capacities with the pyrolysis temperature of cellulose is provided in Fig. S4 (Supporting information's). It can be observed that the irreversible capacity and the sloping capacity follow the same trend, i.e., decrease of the capacity with the increase of the cellulose annealing temperature while for the reversible and plateau capacities an opposite behavior is seen. To go more in details about the key parameters behind these trends one must be considered that during the thermal pyrolysis several events occurs giving rise to modifications of several carbon characteristics. To recall, the specific surface area, the amount of oxygen surface groups, the active sites (amount of defects) and the dspace decreases with the increase of the pyrolysis temperature. Thanking into consideration the similar variation of these characteristics with the temperature, the main difficulty and challenge here is to highlight the main important carbon characteristic influencing the electrochemical performances. For simplicity reasons, the slope capacity and plateau capacity which are subject of controversial mechanisms explanations in the literature will be discussed in more details in relation with carbon characteristics.

Regarding the sloping and the irreversible capacity, a notable dependence on the pyrolysis temperature is observed, i.e., decrease of the capacity with the increase in the annealing temperature which translates as well in coulombic efficiency variation with the temperature, i.e., increase from 72% for HC-1000 to 84% for HC-1600 °C. The irreversible capacity is closely related to the formation of the solid electrolyte interphase (SEI) due to the interaction of carbon surface with the electrolyte. Several works pointed out that the irreversible capacity can be correlated to the carbon accessible surface area quantified as BET surface area with nitrogen adsorbent [START_REF] Simone | Hard carbon derived from cellulose as anode for sodium ion batteries: dependence of electrochemical properties on structure[END_REF][START_REF] Bommier | Predicting capacity of hard carbon anodes in sodium-ion batteries using porosity measurements[END_REF][START_REF] Ponrouch | High capacity hard carbon anodes for sodium ion batteries in additive free electrolyte[END_REF]. Generally, the decrease of the BET surface area induces a decrease of the irreversible capacity. However, no correlation concerning the surface area of ultramicropores (pores < 0.7 nm) was established up to now. We determined the surface area of such small pores by CO 2 adsorption and interestingly we can see that the sloping capacity is increasing with the increase of specific surface area (Fig. 3a). We noticed that the same trend as for nitrogen BET surface area is found, suggesting that small pores (< 0.7 nm) are as well involved in the Na + storage mechanism which was not considered before. The same trend as for the sloping capacity is seen for the irreversible capacity (Fig. S5, Supporting information) while the plateau capacity show an opposite behavior, i.e., decrease of the capacity with the increase of specific surface area.

Other factors than porosity affecting the capacities are the carbon surface chemistry (oxygen functional groups) and the amount of defects. Although the oxygen functional groups amount may be assessed by other techniques than TPD-MS, i.e, XPS or Boehm titration, the active sites may be assessed precisely only by oxygen chimisorption followed by TPD-MS, explaining the lack of studies measuring such parameter on carbons. Fig. 3b links the sloping capacity and the amount of oxygen functional groups and a correlation maybe established, i.e., the higher the amount of oxygenated groups, the higher the sloping is obtained. The same trend is observed for the ASA as well. Therefore, the amount of functional groups and of defects induces similar effect on the sloping capacity.

In the case of plateau capacity, an opposite behavior than the sloping capacity was observed, i.e., the higher the amount of oxygenated groups and defects the smaller the plateau capacity is obtained (Fig. S5b, Supporting information).

In order to discriminate between the effect of oxygen surface groups and the ASA, the HC-1400 carbon was oxidized by nitric acid in order to increase the amount of surface groups (HC-1400ox) [START_REF] Figueiredo | Modification of the surface chemistry of activated carbons[END_REF]. A part of the obtained oxidized material (HC-1400ox) was annealed further in hydrogen up to 900 °C to remove the formed surface groups (HC-1400red). This kind of treatment was proven to be efficient to remove oxygenated groups from graphitic materials while keeping rather similar ASA [START_REF] Moussa | Relationship between the carbon nano-onions (CNOs) surface chemistry/defects and their capacitance in aqueous and organic electrolytes[END_REF]. A schematic representation of modification procedure is provided in Fig. S6, Supporting information. The performed oxidation and the reduction treatments have a great impact in the modification of surface chemistry, ASA but also specific surface area (Table 2).

The oxidation of HC-1400 material induces as expected a significant increase in the amount of functional groups and in addition an increase in the porosity and active surface area on the obtained HC-1400ox. When the later one is subject of hydrogen reduction (HC-1400red), most of functional groups are removed, the CO x quantities being similar to the pristine HC-1400, as highlighted in Table 2. In the same time, the ASA decreases compared to HC-1400ox (31 m 2 g -1 for HC-1400ox vs. 21 m 2 g -1 for HC-1400red) but still remains significantly higher than pristine HC-1400 (6.8 m 2 g -1 ). As for the porosity, the reduction treatment of HC-1400ox has only limited effect.

Considering that the new obtained materials present higher surface area and ASA than HC-1400 and also higher amount of functional groups in the case of HC-1400ox, this triggers as expected an increase in the irreversible capacity from 65 mAh/g for pristine HC-1400 to 170 mAh/g for modified carbons, HC-1400ox and HC-1400red, respectively (Table 2). The columbic efficiency decreases as well from 82.7% (HC-1400) to 48.2% (HC-1400red) suggesting that the electrolyte is consumed irreversibly.

If we compare in more details the HC-1400ox and HC-1400red, we can noticed that the specific surface areas determined by nitrogen and CO 2 are slightly higher for HC-1400red. In addition, a significant difference is observed in the amount of oxygen groups (CO x ), the HC-1400ox present 5x higher amount of surface groups (1.25 mmol/g) compared to HC-1400red (0.23 mmol/g). With the increase of the amount of oxygen groups (HC-1400ox), the amount of desorbed physisorbed water is increasing also due to the improvement of the hydrophilic behavior (Fig. 4a). The porosity also influences the amount of Fig. 3. (a) Correlation between the sloping capacity and plateau reversible capacity with the CO 2 surface area; (b) correlation between carbon sloping capacity and the total amounts of CO x groups desorbed during TPD measurements and the active surface area (c) and correlation between carbon sloping capacity and the ratio ASA/BET CO 2 .

Table 2

Textural, surface chemistry, active surface area and electrochemical performances of HC-1400, HC-1400ox and HC-1400red.

Materials

BET N 2 m 2 g -1 BET CO 2 m 2 g -1

COx mmol/g ASA m 2 g -1 1 st insertion capacity mAh/g adsorbed water and this is clearly seen by comparing HC-1400 and HC-1400red. The later one has rather low amounts of oxygen groups but desorbs higher water amounts (Fig. 4a) which is related to its higher porosity compared to HC-1400 (Table 2). Hence, both surface chemistry and porosity influence the amounts of water adsorbed on carbon. This is an important issue to take into account; on one hand, the interactions with the electrolyte can be modified giving rise to undesired side reactions, and on the other hand, from more practical point of view, such electrodes containing water in their porosity must be outggased at temperatures up to 200 °C (temperature where the water release is finished). Another consequence of surface modification of HC-1400 by oxidation and reduction is the formation of C-H bonds, the amounts of hydrogen released increasing for the HC-1400ox and more significantly for HC-1400red which was hydrogen treated (Fig. 4a).

Concerning the ASA values, the HC-1400ox have an ASA of 31 m 2 /g while the thermal annealing under hydrogen decreases the ASA to 21 m 2 /g (HC-1400red). Therefore, the main important difference between the two materials is the high amount of surface groups of HC-1400ox compared to HC-1400red. It is interesting to notice that such increase in oxygen functional groups does not induce significant difference in the shape of charge/discharge curves and the irreversible capacity (Fig. 4b and Table 2), suggesting that the amount of surface groups is not the main parameter influencing the irreversible capacity and the sloping region capacity. The slightly higher irreversible capacity for HC-1400red may be linked to its higher porosity (Table 2). Another reason may be the higher amounts of C-H bonding. Such bonds proved to be able to link with the Na + and Li + inducing the formation of C-Na or C-Li bonds [START_REF] Stevens | The mechanisms of lithium and sodium insersion in carbon materials[END_REF] and also to favor the graphite exfoliation in EC-based electrolytes [START_REF] Bernardo | Influence of graphite surface properties on the first electrochemical C. Matei Ghimbeu et al. lithium intercalation[END_REF].

Regarding the plateau capacities of HC-1400ox and HC-1400red, it can be seen that they are decreasing compared to pristine HC-1400 (Fig. 4b). This may be explained on one hand by the increase of the specific surface area but also of active surface area ASA (Table 2).

Notwithstanding the ASA is the most pertinent parameter influencing the capacity, still the porosity must be taken into account. In such case, it is useful to calculate the density of active sites as a ratio between ASA and the BET CO 2 surface area [START_REF] Moussa | Relationship between the carbon nano-onions (CNOs) surface chemistry/defects and their capacitance in aqueous and organic electrolytes[END_REF]. In Fig. 3c, the correlation between the density of active sites and the slopping capacity is shown. It can be seen that the sloping capacity diminish rather linearly with the increase of the density of active sites suggesting the main importance of the defects in the sloping region. The HC-1000 material deviates from the linear shape of the correlation and this may be due to the fact that in such case the material contains not only ultramicropores detectable by CO 2 but also larger pores which were detected by nitrogen (Fig. S1a, Supporting information) and not taken into account here.

Gathering most of the results in Fig. 5, one can see that the carbon characteristics (microporosity, oxygen surface groups, active surface area and d 002 space) are decreasing with the increase of the pyrolysis temperature. Interestingly, the sloping capacity is decreasing almost linearly in the same way while the plateau capacity varies in an opposite way. To further discuss the founding of this work in relation to previous works one must consider firstly the porosity of hard carbons. The gas adsorption measurements performed in this work highlighted that the hard carbon is composed at low temperature of micropores and in addition of ultramicropores, measureable only with CO 2 gas. Such small pores are usually not measured and not considered in most of the works when discussing the performances of hard carbon. A great quantity of micropores/ultramicropores are formed at low pyrolysis temperature (< 1400 °C) while the plateau capacity is low (Fig. 3a). By increasing the pyrolysis temperature (> 1400 °C), all the pores are removed while the plateau capacity increases (Fig. 3a). We establish a relationship between the plateau capacity and the surface area of ultramicropores, i.e., increase of plateau capacity with the decrease of the surface area (Fig. 5). This trend is in contradiction with the classical proposed mechanisms of Na-storage where the plateau capacity is often related to the insertion/adsorption of Na in the carbon porosity. At this stage the materials have no porosity, therefore, sodium filling mechanism in the nanopores is questionable. Our results join the results of Cao et al. [START_REF] Cao | Sodium ion insertion in hollow carbon nanowires for battery applications[END_REF] who firstly proposed the assigning of the plateau region to the insertion/extraction of Na + between the carbon layers. They performed theoretical calculations on the energy required for Na-ion insertion into carbon as a function of carbon interlayer distance, and predicted an interlayer distance of ~0.37 Å to be suitable to enable Naion insertion between the carbon layers.

In the same line, Ding et al. [START_REF] Ding | Carbon nanosheet frameworks derived from peat moss as high performance sodium ion battery anodes[END_REF] ascribed the plateau region of a pyrolytic carbon to insertion of Na between the graphitic layers instead of micropores. Qiu et al. [START_REF] Qiu | Manipulating adsorption-insertion mechanisms in nanostructured carbon materials for high-efficiency sodium ion storage[END_REF] calculated the theoretical plateau capacity of cellulose-derived hard carbons considering Na saturated filling in the micropores and they observed a linear relationship with the microporous volume. However, the comparison with the experimental values showed a rather opposite behavior demonstrating once again that the micropore filling mechanism cannot explain the evolution of plateau capacity. This was further confirmed by using micro/mesoporous carbons which exhibited only a single sloping region, therefore absence of a plateau region.

In addition to micropores, the hard carbons present at low temperature oxygen functional groups (carboxyl, lactones, ethers, quinones) and defects (edge defects, vacancies, staking faults…). As determined by TPD-MS, the amount of oxygen functional groups and the amount of active sites (defects) are decreasing both with the increase in the pyrolysis temperature. We established as well that the sloping capacity decrease with the decrease of the functional groups and amount of defects (Fig. 5). Moreover, controlled surface oxidation/reduction on HC-1400 allowed discriminating between the importance of functional groups and defects in the storage mechanism. The results showed that the functional groups are significantly less important in the storage mechanisms compared with defects. Similar dependence was found in our previous studies performed on graphite materials in Li-ion batteries Fig. 5. Schematic representation of the evolution of hard carbon microstructure with the annealing temperature of cellulose along with sodium insertion (a) and evolution of hard carbons characteristics (V micro CO 2 (cm 3 /g); d 002 -space (nm); COx groups (mmol/g) and ASA (10 2 m 2 /g) and sloping and plateau capacities vs. the annealing temperature of cellulose. [START_REF] Bernardo | Influence of graphite surface properties on the first electrochemical C. Matei Ghimbeu et al. lithium intercalation[END_REF].

Other recent works pointed out as well the Na + storage in the sloping region occurs via interactions of sodium with the carbon edge defects [START_REF] Lotfabad | Origin of non-SEI setalted coloumbic efficiency loss in carbons tested against Na and Li[END_REF][START_REF] Bommier | New mechanistic insights on Na-ion storage in nongraphitisable carbon[END_REF][START_REF] Datta | Defective graphene as a high-capacity anode material for Na-and Ca-ion batteries[END_REF][START_REF] Tsai | Ab initio study of sodium intercalation into disordered carbon[END_REF][START_REF] Li | Hard carbon microtubes made from renewable cotton as high-performance anode material for sodium-ion batteries[END_REF]. Particularly, Bommier et al. [START_REF] Bommier | New mechanistic insights on Na-ion storage in nongraphitisable carbon[END_REF] found a linear relationship between the carbon defects estimated by I D /I G ratio from Raman spectroscopy and the sloping capacity. This trend is in well agreement with the correlation we established herein between the active surface area and the sloping capacity. Theoretical studies were conducted as well [START_REF] Datta | Defective graphene as a high-capacity anode material for Na-and Ca-ion batteries[END_REF][START_REF] Tsai | Ab initio study of sodium intercalation into disordered carbon[END_REF] on graphenes having a disordered structure in which mainly mono-vacancy, di-vacancy and Stone-Wales defects were considered. These studies come to the same conclusion that the sloping part is indeed related to the storage of Na in the carbon defects. The strong ionic binding energy between the Na + adsorption and the defects may effectively overcome the van der Waals interactions between the graphenes planes and make possible the sodiation. Local probe in-situ and ex-situ analyses such as 23 Na solid-state NMR and pair distribution function indicated in the sloping region a mechanism where Na + is first adsorbing on pore surface and defects. Such defects would favor also larger graphene interplanar distances and therefore Na + insertion. At higher voltages (plateau region), rather Na quasimetallic species are formed [START_REF] Stratford | Mechanistic insights into sodium storage in hard carbon anodes using local probes[END_REF]. Such scenario based on adsorption of Na-ions on carbon pores and defects in the sloping region and their further intercalation with the formation of NaC x compounds in the plateau region was recently proposed by Qiu et al. [START_REF] Qiu | Manipulating adsorption-insertion mechanisms in nanostructured carbon materials for high-efficiency sodium ion storage[END_REF].

Therefore, based on the results obtained herein we can conclude that the sloping region is related to the Na + storage/adsorption in the carbon porosity and carbon defects and in less extent to disordered pseudo-graphitic domains. The plateau region could be ascribed to Na + intercalation between the graphitic carbon planes. This is sustained by the increase in sloping capacity with the removal of pores and defects and the opposite behavior with the plateau capacity (Fig. 5). These results provide a complete overall picture of the Na-ion storage mechanism in the sloping and plateau regions and their evolution with the main hard carbon characteristics (porosity, surface functionalities, defects and structure) over a large range of annealing temperatures and is summarized is Fig. 5.

Conclusions

A series of hard carbon were prepared via the pyrolysis of cellulose at temperatures ranged between 1000 and 1600 °C in order to systematically evaluate the porosity, surface chemistry and defects in relation with the Na storage mechanism in the sloping and plateau regions.

Several gases were used in order to properly asses the carbon porosity. Except the carbon treated at low temperature (HC-1000) which shows a measureable BET surface area, the other materials exhibit low surface areas when nitrogen is used as probe molecule, in agreement with many works. On the contrary, when CO 2 is used, high surface areas is evidenced which are related to the presence ultramicropores (pore size < 0.7 nm). The porosity was found to decrease with the increase of the temperature and for high temperatures (> 1400 °C) no porosity was detected in the materials neither by nitrogen or CO 2 adsorption. The plateau capacity was found to increase with the decrease of the porosity which clearly disqualifies the classical mechanism of its attribution to the adsorption of Na + in the nanopores. We assigned the plateau capacity rather to the insertion of Na + in the graphitic nanodomains.

The carbon surface functionalities and active surface area related to carbon edge defects were quantitatively determined by TPD-MS and a decrease in their amounts with the increase of the temperature was demonstrated. The sloping region was found to decrease with the decrease of the amount of active sites; therefore, the sloping region ascribed to the insertion of Na + between the graphene layers is strongly influenced by the carbon defects.

In summary, we found that the sloping region is related to the Na ions interaction with the carbon edge defects and their adsorption into porosity and in less extent to its insertion into the carbon pseudo-graphitic nanodomains. The plateau region was attributed to the insertion of Na + into the graphitic structure, the pore nanofilling mechanism being excluded.

Fig. 1 .

 1 Fig. 1. CO 2 adsorption isotherms (a), the corresponding 2D-NLDFT pore size distribution (b) and the evolution of the specific surface area (N 2 , Kr and CO 2 ) for hard carbons obtained at different annealing temperatures (c).

Fig. 2 .

 2 Fig. 2. Representative TPD-MS thermal desorption profiles for HC-1150 carbon (a) total desorbed quantities of oxygen functional groups, COx and the active surface area, ASA recorded for all carbon materials derived from cellulose pyrolysed at different temperatures (b).

Fig. 4 .

 4 Fig. 4. (a) Desorbed gas quantities (CO x , H 2 O and H 2 ) as determined by TPD-MS analyses for HC-1400 carbons; (b) First charge-discharge curve of hard carbons cycled at a C/10rate where C = 37.2 mA/g between 10 mV and 3 V of modified hard carbons tested against sodium metal at 37.2 mA/g with 1 M NaPF 6 in EC: DMC (1:1) between 50 mV and 3 V.

Table 1

 1

	Hard carbon characteristics including specific surface area determined by several gases,
	d-002 space obtained by XRD patterns, CO x desorbed quantities and ASA determined by
	TPD-MS.
	Sample BET N2	BET Kr	BET CO2	V micro CO2	d 002-space Å CO x	ASA
	m 2 /g	m 2 /g	m 2 /g	cm 3 /g		mmol/g	m 2 /g
	HC-1000 83	1.74	406	0.21	3.885	0.58	44
	HC-1150 15	1.83	380	0.18	3.834	0.33	20
	HC-1300 6	1.93	255	0.13	3.827	0.26	12
	HC-1400 5	1.91	40	0.02	3.730	0.20	7
	HC-1600 8	1.86	3	0.006	3.720	0.014	1

Acknowledgements

The authors acknowledge financial support of this work through the European Union's Horizon 2020 Program (project NAIADES, call: LCE10-2014, Contract no. 646433) and the RS2E network. The French General Directorate for Armament (DGA) is acknowledged for cofunding of the Ph.D. thesis of Virginie Simone. The authors thank Dr. Loic Vidal for performing the HRTEM/SAED. Dr. Joseph Denzer is acknowledged for the valuable discussions concerning the TPD-MS analysis.

Competing financial interests

The authors declare no competing financial interest.

Appendix A. Supporting information

Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.nanoen.2017.12.013.


Mourad Djahmoum

Omar El Kechai

Dr Pascal Marchet
email: pascal.marchet@unilim.fr

O El Kechaï

Elaboration and Characterization of Materials from the LaMnO 3 -BiMnO 3 Binary System

Keywords: perovskites, solid solution, phase transitions, semiconductor materials, ceramics

The study of the La(1-x)BixMnO3 system was carried out using X-ray diffraction and electrical measurements. A continuous solid solution was evidenced for the LaMnO3 rich part of this system (x ≤ 0.6). According to the analyses of XRD results, a rhombohedral symmetry ( 3 ) was observed for x ≤ 0.4 and a cubic structure for x = 0.5. The structural study allowed to determine an increase of the mean perovskite lattice parameter, together with a decrease of the rhombohedral angle up to a cubic symmetry for x = 0.5. For x > 0.6, the system is no more single-phased. Impedance measurements were carried out for ceramics in a wide frequency range (100 Hz -1 MHz), between room temperature and 800°C. The exponential decrease of the AC conductivities (σAC) and the room temperature values correspond to a semiconducting behavior. DC conductivity measurements (σDC) were also performed below room temperature (25K < T < 300K). The results evidence for a metal-insulator phase transition. For the exponential part of the σDC curves, the gap energy is between 0.1 and 0.2 eV, confirming the semiconductor behavior of these materials.

Introduction

Perovskite based materials have a long history and are studied now for more than 70 years. Indeed, they present a wide range of interesting physical properties, like dielectric properties, ferroelectricity / piezoelectricity, magnetic properties, superconductivity, metallic conductivity… [1][2] Such a large range of properties allows a large field of applications such as piezoelectric transducers, magnetic recording heads, energy storage, cathode materials for solid oxide fuel cells (SOFC), catalyzers for oxydo-reduction (car motors)… In 1994, the discovery of intrinsic giant magnetoresistance phenomena in La1-xAxMnO3 compounds induced a new field of interest for perovskite compounds because of their potential technological applications. [3][4][5] Indeed, such materials exhibit fascinating physical phenomena such as colossal magnetoresistance, metal-insulator phase transitions, charge ordering and orbital ordering. Such properties result from an interplay between magnetic, transport and structural properties . [4] At the present time, one of the most studied system is La(1-x)AxMnO3, "A" ion being generally a divalent alkaline-earth ion (Ca 2+ , Sr 2+ or Ba 2+ ). [4,6] Substituting around 30% (x=0.3) in the La(1-x)CaxMnO3 and La(1-x)SrxMnO3 systems led to a quite complex phase diagram and allowed to obtain a change from paramagnetic-insulating LaMnO3 pure compound to ferromagnetic-metallic behavior at room temperature. More recently, these studies were extended to other lanthanide-based compounds. [7] However, a more recent study on La(1-x)MgxMnO3 (x = 0.10, 0.25, 0.50) reported for a rhombohedral 3 symmetry and a semiconducting behavior. [8] Stoichiometric LaMnO3 can be prepared by different routes and is paramagnetic and insulating at room temperature (TN ≈ 145 K), with an orthorhombic symmetry (space group Pnma). [9,10] In the literature, the physical properties of LaMnO3 are reported as very sensitive to parameters such as temperature, pressure, chemical substitution or the route used for elaboration. When heated in air atmosphere, oxidation of manganese occurs, from Mn III to Mn IV , leading to a non-stoichiometric LaMnO3+δ compound with rhombohedral symmetry (space group 3 ). [11][12][13] In a similar way, a change of manganese oxidation state can occur for La1-tMnO3+δ compounds, also leading to a rhombohedral distortion. [11][12][13] In 2002, it was suggested that the study of the LaMnO3 -BiMnO3 system would be interesting. [14] Indeed, the substitution of lanthanum by alkaline-earth ions induces the transition from antiferromagnetic to ferromagnetic metallic state. On the contrary, this substitution in BiMnO3-based manganites destroys the ferromagnetic order, leading to a spin glass behavior. [14] Both LaMnO3 and BiMnO3 compounds, which are end-members of this solid solution, present a perovskite structure but their physical properties are different. Indeed, BiMnO3 can only be obtained by high-pressure synthesis: BiMnO3 perovskite compound decomposes around 600 °C into Bi2O3 and Bi2Mn4O9. [15] BiMnO3 is an insulating ferromagnetic compound at low temperature (TC = 102 K) and presents at room temperature a monoclinic structure with space group C2/c. [16,17] Now, there are only a few reports devoted to the LaMnO3 -BiMnO3 system. The first study evidenced for a solid solution La(1-x)BixMnO3 up to x < 0.65. For samples prepared in air, the symmetry is rhombohedral up to x = 0.4, while higher Bi content leads to tetragonal symmetry. [14] The solid-solution limit was later confirmed around x = 0.6, all the compositions being rhombohedral. [18] More recently, the solid solution limit was reported for x = 0.7, the symmetry changing from orthorhombic (x < 0.35) to pseudo cubic and then to BiMnO3 tetragonal type for x ≥ 0.5. But this study didn't report of the X-ray diffraction patterns or structural arguments. [19,20] The La0.94Bi0.06MnO3 composition was later described as orthorhombic, but the reported X-ray diffraction pattern corresponds more to a rhombohedral symmetry. [21] In addition, a more recent paper reported a change from orthorhombic to cubic symmetry around x = 0.3. [22] The structural evolution of the La(1-x)BixMnO3 solid-solution and the upper solubility limit remain thus as unclear.

Concerning the electrical properties, only three papers report electrical properties. Metalinsulator transitions and large magnetoresistance effects were observed for low Bi-doping levels (x < 0.4), while insulating behavior was reported for higher doping levels (x ≥ 0.4). [18] Nevertheless, the exponential decrease of the resistivity as a function of temperature and the values of resistivity at room temperature (1 to 10 Ω.m) seem to correspond more to a semiconducting behavior. [18] Furthermore, the second paper including electrical properties reported metal conduction for x > 0.1, but the corresponding curves evidence for a decrease of resistivity as a function of temperature. [19,20] As a consequence, the electrical properties remain unclear for this system.

To sum up, a La(1-x)BixMnO3 solid solution exists for the LaMnO3 rich part of the system, but there are discrepancies concerning the upper solubility limit. In addition, there is no agreement concerning the crystalline symmetry and its evolution with Bi-content. Indeed, to our knowledge, structural refinements were never reported for this system. Moreover, there are only few reports concerning the electrical properties of Bi-substituted LaMnO3 and the corresponding results present some discrepancies. Therefore, the aim of the present study is the investigation of: (i) the structural evolution of the La(1-x)BixMnO3 solid solution and (ii) of the electrical properties for the corresponding compositions.

Materials and methods

The La(1-x)BixMnO3 compounds (x = 0 to x = 1) were elaborated by classical solid-state reaction using Mn2O3 (Aldrich, 99.8%), Bi2O3 (Interchim, 99.075%), and La2O3 (Alfa Aesar, 99.998%) as raw materials. After weighing in stoichiometric amounts, the mix was homogenized in an agate mortar. The powders were then calcined in air in alumina crucibles for 10 to 12 hours between 900 and 1000 °C, using a 10 °C/min heating rate and natural cooling of the furnace. After synthesis, the powders were crushed and studied by X-ray diffraction at room temperature using a θ/2θ diffractometer (Bruker D8 advance, Cu Kα1 radiation, λ = 1.5406 Å) for 2θ angles ranging from 10 to 120°. The structure and lattice parameters of the observed phases were calculated using Rietveld refinement with the Jana 2006 software. [23] The powders were then pressed into cylindrical pellets (φ = 10 mm, e = 1 mm, P ≈ 250 MPa) and sintered between 900 and 1100 °C for 10 hours, depending on the composition. The relative densities of the pellets were determined by geometrical method to be around 90-95% of theoretical density. The pellets were then electroded using silver paint before study of their alternative current (AC) electrical properties by impedance measurements (100 Hz -1 MHz, Agilent 4294A), between room temperature and 800 °C. The measured complex admittance Y = 1/Z is thus such as Y = G + jB. This measurement allows a calculation of the approximate values of the AC conductivity (σAC): σAC = G . (t / S), t being the thickness of the measured sample and S its cross section.

For the LaMnO3 rich part of the solid solution (x =0 to x = 0.6), bar-shaped samples were cut in the cylindrical pellets, with dimensions typically around 1 mm x 1 mm x 8-10 mm. Then a fourpoint measurement method was used in order to determine the thermal evolution of resistivity below room temperature. Their direct current (DC) electrical properties were studied between 25 and 300 K using a closed-cycle helium cryostat (Leybold ROK 10-300 and cryogenerator RW2). A constant current source and a digital multimeter were used to determine the current -voltage characteristics at each selected temperature.

Results and discussion

Structural evolution for the La(1-x)BixMnO3 solid solution

The X-ray diffraction patterns (x = 0 to x = 1) are represented figure 1. The solid solution is not continuous: a single-phase perovskite compound is observed from pure LaMnO3 up to x = 0.6.

From x = 0.7 to x = 0.8, a perovskite compound is present together with Bi2Mn4O9 and Bi2O3. For x ≥ 0.8, the perovskite compound disappears and only Bi2Mn4O9 and Bi2O3 are observed. Therefore, the limit of the solid solution can be estimated to correspond to x = 0.6, in agreement with previous results. [14,18] Indeed, perovskite BiMnO3 can only be synthesized under pressure and decomposes around 600°C into Bi2O3 and Bi2Mn4O9. [15] Logically, the same decomposition occurs for the BiMnO3-rich compositions of this system. However, the structural evolution does not correspond to the reported one. In our case, a rhombohedral symmetry ( 3 space group) is observed up to x = 0.5. For x = 0.6, the symmetry is difficult to determine but seems to be orthorhombic. Troyantchuk et al. reported an evolution from rhombohedral (up to x = 0.4) to tetragonal. [14] Zhao et al. reported a rhombohedral symmetry up to x = 0.60. [18] Ogawa et al. observed an evolution from orthorhombic to pseudo-cubic (x = 0.4) and then tetragonal symmetry (x = 0.5 -0.7), [19,20] while Paul Joseph et al reported an orthorhombic symmetry from x = 0 to x = 0.2, and a cubic structure for x = 0.3 to x = 0.5. [22] Logically, the symmetry of the La(1-x)BixMnO3 compounds depends of their thermal history, like for pure LaMnO3. [24,25] But our observations correspond more to those of Zhao, who only reported qualitative considerations for this system, without any structural calculation. [18] Therefore, the lattice parameters, rhombohedral angle and cell volume were determined by Rietveld refinement for the continuous part of the solid solution, using the 3 space group in hexagonal setting. The results of the refinement are reported table 1. An example of the result of Rietveld refinement for x = 0 is represented figure 2. Since the 3 space group in hexagonal setting corresponds to a multiple cell, the pseudo-cubic parameters corresponding to a distorted primitive perovskite cell were calculated using the following relationships:

ah = 2ap . sin( ∝ ) ch = 6ap . 1 - ( ∝ )
Where ah and ch are hexagonal lattice parameters, ap is the pseudo-cubic lattice parameter and αp the rhombohedral distortion angle of the pseudo-cubic lattice (αp would be 90° for a perfectly cubic cell).

Logically, the "a" pseudo-cubic parameter increases with the increasing bismuth content (figure 3).

These results agree well with the ionic radius of twelve coordinated Bi 3+ ion (1.38 -1.40 Å) which is higher than the one of La 3+ ion (1.32 Å). [26] The results also evidence for a decrease of the rhombohedral angle from ≈ 90.5° (x = 0) to 90° for x = 0.5. This last value indicates a cubic symmetry for x = 0.5. The refinement in 3 space group allowed obtaining low values of reliability parameters (Gof ≈ 1.2 %, Rp = 5,35 %, Rwp = 6.83 %, Table 1). [27] These values indicate very satisfactory structural refinements for X-ray diffraction patterns, testifying for the rhombohedral symmetry close to LaMnO3 and its evolution toward cubic symmetry with increasing x values.

Electrical properties

For the continuous part of the solid solution (x = 0 to x = 0.6), the AC electrical properties (admittance modulus |Y| and phase angle θ) were determined up to 800 °C (figure 4). The admittance modulus is between 7.10 -3 and 12 S at room temperature, together with a negative phase angle close to 0°. This value of the phase angle indicates a conductor or a semiconducting material at room temperature. Indeed, phase angle would be close to 90° for an insulating (dielectric) material. The conductivity values σAC at room temperature (20° C, 1 kHz) calculated from the admittance modulus are between 9.10 -1 and 10 -7 S.m -1 . Therefore, these materials appear more as semiconducting materials (10 -8 S.m -1 ≤ σ ≤ 10 2 S.m -1 ) than insulating (σ ≤ 10 -12 S.m -1 ). [START_REF] Moulson | Electroceramics, materials properties applications[END_REF] In addition, the AC conductivity values at room temperature confirm the structural results (table 2). For the continuous part of the solid solution, the conductivities does not change significantly. Except for x = 0 (σAC = 6.5 10 -4 S.m -1 ) for which the value does not depend on frequency, the other σAC values fluctuate between 6.6 10 -3 S.m -1 and ≈ 1 S.m -1 (0.1 ≤ x ≤ 0.6). Then, for the two-phase range (x > 0.6), the obtained value are three orders of magnitude lower, around 10 - 6 -10 -7 S.m -1 .These values confirm that the samples containing more than 60% Bi (x > 0.6) have a different behavior, in agreement with their two-phase character. Moreover, for the continuous part of the solid solution (0 ≤ x ≤ 0.6), the plot of Log (Z) as a function of 1/T gives access to an approximate value of the gap energy around 0.1 -0.2 eV (this calculation is based on the admittance results of figure 4 and is not represented here).

In order to confirm these values, and to search for metal-insulating phase transitions, the electrical behavior was studied below room temperature (25 K -300 K) by four points DC measurements. The samples of La(1-x)BixMnO3 (0 ≤x ≤0.6) were cut in the form of parallelepiped bars in order to be able to calculate their resistivity. The results of these measurements are represented figure 5. For all samples, the resistivity increases first with the temperature, reaches a maximum and then decreases. These phenomena corresponds well to a metal-insulator phase transition, as previously reported for La1-xA 2+ xMnO3, [3][4][5][6] or for the La(1-x)BixMnO3 system close to LaMnO3. [18,19] For x = 0, the temperature of the maximum is 240K. Compared to previously published results, this value confirms that this samples in non-stoichiometric, with a Mn 4+ content around 30%. [24] A similar maximum is also observed for x = 0.1 and x = 0.2. However, for the low temperature part, the slope of the curve is high for x = 0 -0.2, while the curves appear more "flat" for x = 0.3 -0.6 (figure 5). In contrast, all the curves present a similar exponential decrease for the high temperature part, which corresponds well to a semiconductor behavior.

For the exponential part of the curves of figure 5, the values of the resistivity extracted from the current-voltage (I-V) measurements allowed to plot the ln(σ) as a function of 1/T relationships (figure 6). Using these curves, the values of the activation energy Ea were calculated for the singlephase perovskite compositions x=0 to 0.6 (figure 6) using the relationship σ = σ e ( ) , σDC being the DC conductivity, Ea the bandgap energy, k the Boltzmann constant and T the temperature.

The results correspond to Ea values around 0.2 eV for LaMnO3 and 0.3 eV for the other compositions.

They present only little change with composition. It should be noted that these values are lower than the band gap reported for "pure" LaMnO3 (≈1 eV), [START_REF] Shaterian | [END_REF]30] However, these values correspond well to the estimated one in the same system (0.05 -0.34 eV). [20]

Conclusion

We have characterized the physicochemical properties of La(1-x)BixMnO3 (x = 0.1 to 1) ceramics prepared by conventional solid state synthesis. The study of lanthanum substitution by bismuth confirms the existence of a continuous solid solution for the lanthanum-rich part of this system (0 ≤

x ≤ 0.6). According to the results reported in the literature, the compositions rich in bismuth are biphasic (x > 0.6). For this solid solution, the substitution of lanthanum by bismuth implies a decrease of the rhombohedral distortion of LaMnO3 and leads to a cubic symmetry for x = 0.5. The study of AC electrical properties reveals a semi-conducting behavior, the substitution of lanthanum by bismuth resulting in a decrease of the conductivity at room temperature. DC measurements performed from 25 to 300 K confirm the occurrence of a phase transition, associated to metal-insulating phase transition. However, the behavior of the insulating phase corresponds to an exponential decrease of the conductivity with increasing temperature, which means a semiconductor behavior. For the semiconductor part of the resistivity curves, the gap energy was determined to be around 0.1 -0.2 eV, which is lower than the value reported for "pure" LaMnO3 (≈ 1 eV). [START_REF] Shaterian | [END_REF] Figure

Figure 1 :Figure 2 :

 12 Figure 1: X-ray diffraction patterns for the La(1-x)BixMnO3 system (x = 0 to 1)

Figure 3 :

 3 Figure 3: Evolution of the "a" lattice parameter of the rhombohedral cell and of the "α" rhombohedral angle as a function of composition for the continuous part of the La(1-x)BixMnO3 solid solution.

Figure 4 :

 4 Figure 4: Results of AC measurements above room temperature: (A) Evolution of the admittance modulus |Y| and (B) of the phase angle as a function of temperature for the single-phases perovskite compositions (x = 0 to x = 0.6) of the La(1-x)BixMnO3 solid solution.

Figure 5 :

 5 Figure 5: Evolution of the DC resistivity as a function of temperature for the single-phases perovskite compositions of the La(1-x)BixMnO3 solid solution (x = 0 to x = 0.6).

Figure 6 :

 6 Figure 6: Ln(σ) as a function of 1/T extracted from the DC resistivity curves for the La(1-x)BixMnO3 solid solution (x = 0 to x = 0.6).

Figure 1 :Figure2:

 1 Figure 1: X-ray diffraction patterns for the La(1-x)BixMnO3 system (x = 0 to 1)

Figure 3 :

 3 Figure 3: Evolution of the "a" lattice parameter of the rhombohedral cell and of the "α" rhombohedral angle as a function of composition for the continuous part of the La(1-x)BixMnO3 solid solution.

Figure 4 :

 4 Figure 4: Results of AC measurements above room temperature: (A) Evolution of the admittance modulus |Y| and (B) of the phase angle as a function of temperature for the single-phases perovskite compositions (x = 0 to x = 0.6) of the La(1-x)BixMnO3 solid solution.

Figure 5 :

 5 Figure 5: Evolution of the DC resistivity as a function of temperature for the single-phases perovskite compositions of the La(1-x)BixMnO3 solid solution (x = 0 to x = 0.6).

Figure 6 :

 6 Figure 6: Ln(σ) as a function of 1/T extracted from the DC resistivity curves for the La(1-x)BixMnO3 solid solution (x = 0 to x = 0.6).

Table caption Table 1 :

 caption1 Structural parameters and reliability factors obtained after Rietveld refinement of La(1x)BixMnO3 X-ray diffraction patterns

Table 2 :

 2 conductivity values (σAC) at room temperature (20°C) extracted from the admittance measurements

Table 1 :

 1 Structural parameters and reliability factors obtained after Rietveld refinement of La(1x)BixMnO3 X-ray diffraction patterns

	Composition Space group X value	LaMnO3 0	La0.9Bi0.1MnO3 0.1	La0.8Bi0.2MnO3 R3 c 0.2	La0.7Bi0.3MnO3 0.3	La0.6Bi0.4MnO3 0.4	La0.5Bi0.5MnO3 0.5
	a hexa (Å)	5.5267	5.5205	5.5239	5.5272	5.5285	5.5251
	c hexa (Å)	13.3541	13.3748	13.4064	13.4126	13.4741	13.5373
	a rhombo (Å)	3.8904	3.8894	3.8941	3.8962	3.9027	3.9072
	α rhombo (°) V (Å 3 )	90.519 351.95	90.417 352.835	90.357 354.10	90.357 354.70	90.192 357.02	89.989 357.66
	U iso La/Bi	0.0102	0.0120	0.0168	0.0211	0.0240	0.0192
	U iso Mn	0.00682	0.001	0.001	0.001	0.001	0.001
	x oxygen	0.55456	0.54885	0.54984	0.55273	0.54704	0.55056
	GOF	1.25	1.18	1.16	1.15	1.16	1.21
	Rp (%)	5.35	5.03	5.82	6.32	6.6	7.16
	WRp (%)	6.83	6.29	7.27	7.9	8.25	8.93
				Sigma (S.m -1 )
	x	100 Hz	1 kHz	10 kHz	100 kHz	1 MHz
	0	6.5E-04	6.5E-04	6.5E-04	6.4E-04	6.4E-04
	0.1	4.0E-01	4.0E-01	3.9E-01	2.4E-01	6.6E-03
	0.2	9.8E-03	9.8E-03	9.8E-03	9.8E-03	9.4E-03
	0.3	9.0E-01	8.9E-01	8.4E-01	4.7E-01	5.6E-02
	0.4	1.9E-01	1.9E-01	1.9E-01	1.6E-01	1.1E-02
	0.5	2.0E-01	2.0E-01	1.9E-01	1.7E-01	1.4E-02
	0.6	9.4E-02	9.3E-02	9.3E-02	9.0E-02	2.0E-02
	0.7	8.7E-07	1.0E-06	1.8E-06	5.0E-06	1.4E-05
	0.8	1.0E-07	3.4E-07	1.1E-06	3.0E-06	1.6E-05
	0.9	2.7E-08	9.9E-08	3.9E-07	8.3E-07	1.7E-06
	1	1.0E-07	1.9E-07	4.6E-07	9.4E-07	1.8E-06

Table 2 :

 2 conductivity values (σAC) at room temperature (20°C) extracted from the admittance measurements


P Chrin
email: phok.chrin@laplace.univ-tlsefr

M Pietrzak-David

P Maussion
email: pascalmaussion@laplace.univ-tlsefr

Renewable electricity production with some wasted second-life components

Keywords: Pico-hydro generation, induction generator, reused components, waste components, renewable energy, second-life I Stator phase resistance R r : Rotor phase resistance L ls : Stator leakage inductance L lr : Rotor leakage inductance L ms : Stator magnetization inductance L mr : Rotor magnetization inductance L sr : Stator to rotor mutual inductance Transformation matrix II

Renewable energy systems are playing an important role to reduce CO2 emission and provide electricity for daily use in rural areas. But brand new components with up-todate technology could be far too expensive for many potential users (rural communities in many developing countries. As a consequence, turning waste components into energy production systems could be a good opportunity to reach these two goals simultaneously. In this paper, a disposal induction motor, a car battery and an Uninterrupted Power Supply (UPS) are combined together in order to generate electrical energy from pico-hydro power. The control of the RMS output voltage and frequency is presented with a comprehensive state-space model, simulation and experimental validation results are provided.

INTRODUCTION

A lot of induction motors and other electronic devices are disposed and replaced every year. Some of them are still functioning and can have a "second life". It is well known that environmental issues take more and more importance in the field of energy production and that recycling part of the waste to make "new things" will be a good opportunity either for household or industry applications. For these reasons, the way to turn a disposed induction motor into an induction generator is being studied in this paper together with its control.

In order to generate electric energy, many different methods were applied on induction generators (IG) [START_REF] Murthy | a novel self-excited self-regulated single phase induction generator[END_REF]- [START_REF] Madawala | Modeling and Analysis of a Novel Variable-Speed Cage Induction Generator[END_REF]. At the same time, renewable energy resources could be combined to get more energy or to avoid intermittence. Self-excited induction generator (SEIG) is one of the solutions which was introduced in [1] by using capacitors. Voltage and frequency are not controlled although they need to be operated at constant value under a certain range. In [START_REF] Pena | A doubly fed induction generator using back-to-back PWM converters supplying an isolated load from a variable speed wind turbine[END_REF], Double Fed Induction Machine (DFIM) can generate constant frequency and voltage for the renewable energy applications. But it is a high cost system which not suitable for pico-hydro power in the rural areas of developing countries. Simple low cost solution using a 3-phase induction motor as a single phase generator has been proposed [START_REF] Madawala | Modeling and Analysis of a Novel Variable-Speed Cage Induction Generator[END_REF]. Later on, the model of an induction generator with the capacitors was presented in [START_REF] C H R I N | Modeling of 3-phase Induction Machine as Single Phase Generator for Electricity Generation from Renewable Energies in Rural Areas[END_REF].

This paper presents a complete model of a single phase induction generator with a re-used Un-interrupted Power Supply (UPS), a push-pull inverter which is commonly used for PC network supply. Some papers [START_REF] Kim | How to reuse PC power supply for renewable energy applications[END_REF]-[10] already studied the re-use of full PC supplies [START_REF] Kim | How to reuse PC power supply for renewable energy applications[END_REF] or parts of them [9] [10] but the re-use of an inverter is the original approach developed in this study. Some examples of old components are shown in Fig. 1(a) and Fig. 1(b): wasted induction motors and standalone UPS together with a lot of different electronic devices which are disposed each year. As an example, [START_REF]Conservation and Recovery Electronics Waste Management in the United States through 2009[END_REF] indicates that 14 to 20 billion PC's were thrown away in 2006. It is shown in [START_REF]Basel Conference Addresses Electronic Wastes Challenge[END_REF], that almost 52 billion of computers have been trashed or recycled in USA in 2010 for a total weight of 423 000 tons. Unfortunately, only 40% of them are recycled as incineration remains the PC final destiny in most of the cases. There is certainly room for a second-life of part of them! So, the first section of this article describes the complete state-space model of the waste induction generator and UPS. The next section presents the design of the controller for this generation system. The last section gives experimental results and discussions. The classical well-known modeling of the 3-phase squirrel cage induction motor can be found in [START_REF] Krause | Analysis of Electric Machinery and Drive Systems[END_REF] with the stator voltage and rotor voltage equations. For this motor, the rotor voltages are equal to zero. In [START_REF] Madawala | Modeling and Analysis of a Novel Variable-Speed Cage Induction Generator[END_REF], the author had developed and modeled it as the single phase induction generator which forms four order state space equation with two component input vector (excitation voltage and output voltage). A complex model is obtained by adding of two capacitors; excited capacitor and output capacitor [START_REF] Madawala | Modeling and Analysis of a Novel Variable-Speed Cage Induction Generator[END_REF], [START_REF] C H R I N | Modeling of 3-phase Induction Machine as Single Phase Generator for Electricity Generation from Renewable Energies in Rural Areas[END_REF]. This complex model had also valid both cases with and without capacitors. Consequently, the state space equation of the model without capacitor is given as [START_REF] C H R I N | Modeling of 3-phase Induction Machine as Single Phase Generator for Electricity Generation from Renewable Energies in Rural Areas[END_REF]:

̇= [ ] + [ ] (1)
where u=[v se v so ] T is input vector x=[i se , i so , i rα i rβ ] T is state space vector [v rabc ]=0 for a squirrel cage induction machine

A. Modeling of the single phase IG with capacitors

Capacitors are used to compensate the reactive power of induction generator as shown in Fig. 2. The capacitor currents are added in [START_REF] Murthy | a novel self-excited self-regulated single phase induction generator[END_REF] to model where the excitation and output voltage, v se and v so are the state variables of new model.

= = - = = - (2)
In [START_REF] Ojo | An analysis of single phase self-excited induction generators[END_REF], C e , C o , i Ce , i Co , i e , and i L are the excitation capacitor, output capacitor, excitation capacitor current, output capacitor current, input excitation current and load current, respectively.

Fig. 2. Induction generator with two capacitors for reactive power compensation

The excitation phase of the induction generator is connected to an UPS circuit as shown in Fig. 3. The push-pull DC/AC inverter is used in the UPS circuit to step-up the voltage from V dc =24V DC to 110V AC and 230V AC. The RMS value of the output voltage of the push-pull inverter depends on the battery DC voltage and its duty ratio for the switching MOSFET T1 and T2 and the transformation ratio of the transformer. The equivalent circuit of the transformer referring to the secondary winding is shown in Fig. 4.

A new state space model of the single phase induction generator with capacitors can be re-written as follows in [START_REF] C H R I N | Modeling of 3-phase Induction Machine as Single Phase Generator for Electricity Generation from Renewable Energies in Rural Areas[END_REF]:

̇= [ ] + [ ] (3)
where x c =[v se v so i se i so i rα i rβ ] T is new state vector and u c =i e is the new input vector with its state and control matrices: The secondary winding of transformer is connected to one phase of induction motor shown in Fig. 4 where the output voltage equation of at the secondary winding can be expressed as in (4):

[ ] = , [ ] = -1/ 0 00 0 -1/ 00 , [ ] = [1/ 0 × ] , [ ] = 0 0 0 -1/ , [ ] = ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ - √ √ - - √ - √ - √ ( ) - - √ ( ) ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ [ ] = ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ - 0 0 - 0 0 √ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ with = -( + ) + , = /2-2( + )( + ) - ( + ) = + , = + , = ( + ) + , = + + = /2-2( + )( + ) - ( + ))
= + + (4)
where R eq = R' 1 +R 2 and X eq =X' 1 +X 2 , (X eq =2πfL eq ) R' 1 =(N 2 /N 1 ) 2 R 1 , X' 1 =(N 2 /N 1 ) 2 X 1 In order to form the total state space equation of the system in Fig. 3, equations (3) and ( 4) are re-written as follows:

= - - 1 + 1 ̇= [ ] + [ ] (5)
The total state-space model of IG and UPS circuit is used to the describe behavior of the generation system where a new input vector, , and a new state variable, i e , are added.

̇= [ ] + [ ] (6)
where = i s t he s y s te m s t a t e vector, = is the system input vector and with

[ ] = [ , ][ ] [ ][ ] , [ ] = - , [ ] = [ ], [ ] = [-1/ 00 000 ] , [ ] = [ ], [ ] = [1/ 0 × ]
The transfer function of input voltage, , to output voltage, v so , can be determined from the total state space equation [START_REF] Madawala | Modeling and Analysis of a Novel Variable-Speed Cage Induction Generator[END_REF]. Replacing by k Tr v 1 , then the transfer function of total system can be defined as:

( ) = = ( -)( -) ( -)( -) … ( -) (7)
where z 1,2 and p 1,.. The re-used UPS, initially devoted to standalone computer supply includes a sine-modified inverter at the frequency of 100Hz. In our modified version, the driver circuit is based on t he c l as s ic a l d riv e r I C S G 352 4 . I t c re a te s t he 2 s w itc hi ng signals necessary to drive the 2 MOSFETs of the push-pull inverter as shown in Fig. 5. In order to use this UPS for isolated grid supply, the switching frequency is changed to 50Hz and its controller is re-design to maintain constant the RMS output voltage of the IG whatever the load. Fig. 6 shows the modified UPS used to control IG.

( ) = ( ) ( ) (9)
V.

NUMERICAL APPICATION AND EXPERIMENTS The induction generator operates in the following conditions: rotational speed of IG is Nr=1540 rpm of course over the synchronous speed, nominal load resistance is R L = 220Ω which emulates a motor load at its nominal power, PWM duty ratio of UPS is d=20%, excitation capacitor is C e =10mF while the output capacitor is C o =5mF and the battery voltage V dc =25.9V. The capacitor values are determined by calculating the required reactive power of the IG. The motor parameters and transformer are given in appendix.

Fig. 9 shows the simulation results of whole system, singlephase induction generator SPIG, car battery and UPS. The corresponding experimental results given in Fig. 10 which are in good agreement for different operational conditions validate the simulation results. Fig. 11 shows the location of the poles and zeros map of the transfer function H o (s). R o t o r r e s i s t o r i n c r e a s e s w i t h temperature, will only slightly influence the location of pole P 1 , P 2 which are always compensated by zeros Z 1 and Z 2 . This behaviour does not affect system stability. H o (s) includes an excitation capacitor, C e , and a transformer equivalent inductance, L eq which vary while the other parameters are kept constants. It can be seen that their variations could affect the system performances. For example, when the input capacitor is increased, the damping ratio decreases. Besides, a higher inductance value makes the pole move towards to the origin. These two parameters create complex conjugated poles p5 and p6, whose very low damping ratio may lead to high overshoot. But they can be turned into design parameters: Setting a chosen open loop bandwidth below -100rad/s and a damping ratio higher than 0.1 will lead to L eq < 5mH and C e >10uF. The prototy pe of IG, U PS, car batte ry and the contro l scheme were assembled together in order to verify the performance of this original type of energy generation system only based on disposed components. A step down transformer is used to step down output voltage of generator and connected to a rectifier for obtaining the feedback signal. The RMS value of feedback signal can be measured from the output of fullwave rectifier with its appropriated filter capacitor. This value is approximately equal to maximum of value of input signal where the RMS value can be obtained. The induction generator was subjected to a step load change 220Ω to 150Ω and its output voltage response is recorded, shown in Fig. 15. The settling time of RMS output voltage is about 150ms and its frequency remains the same as excited voltage which is 50Hz.

VI. CONCLUSION

Pico-hydro generation using disposed and wasted components, especially a 3-phase squirrel cage induction motor and a UPS, has been presented in this paper. First the whole system architecture and state-space model of the 7 th order was described. Some suggestions about the total system sizing were made using the Zero-Pole placement analysis. A PI controller has been designed in order to control the output voltage of the induction generator. The controller of a re-used UPS has been modified and connected to the excited phase. Test results have shown that the induction generator and PI controller exhibits good RMS output voltage regulation and adequate transient response to the step-load change. This research work is suitable for electricity application in rural areas of developing countries where the cost of installation must be very low and where only disposal UPS, car battery and induction motors can be found in large quantities at an affordable price. Future work will deal with higher power induction machines, resonant controllers for non-linear loads such as the rectifiers embedded in smartphone chargers, TV and other home appliances.

Fig. 1 (

 1 Fig. 1(a): electrical machines as wasted components

Fig. 3 .

 3 Fig. 3. Complete system architecture with IG, 2 capacitors for reactive power compensation and UPS

Fig. 5 .

 5 Fig. 5. Gate signal for T1 and T2 MOSFETs of the UPS

Fig. 6 . 1 Fig. 8 .

 618 Fig. 6. Circuit Board of disposed UPS to control IG

Fig. 9 .

 9 Fig. 9. Simulation results of output voltage, Vso, battery current, Idc, excitation voltage, Vse, and excitation current Ise

Fig. 10 .

 10 Fig. 10. Experimental results of output voltage, Vso, battery current, Idc, excitation voltage, Vse, and excitation current Ise

Fig. 11 .

 11 Fig. 11. Pole-Zero Map of Ho(s) for Leq and Ce varying Fig. 12 shows the pole and zero map of H o (s) when the load R L changes from 85Ω to 255Ω and the output capacitor from 0.5uF to 6.5uF. With C o =6.5uF, the conjugated poles P3 and P4 still move inside the red designed location (bandwidth>100 rad/s and damping ratio>0.45). R L and output capacitor C o values can be defined as 85Ω <RL<255Ω and C o < 6.5uF.

Fig. 12 .

 12 Fig. 12. Pole-Zero Map of Ho(s) for RL and Co variations Bode plots of the open loop transfer function T(s) are shown in Fig. 13. They have high dc gain to regulate the RMS value of the output voltage and the crossover frequency is set by the controller gain k c , it remains far below the switching frequency. The phase margin at the crossover frequency is greater than 45 o . This result confirms that a simple PI controller is successful for the control of the RMS output voltage of this

Fig. 13 .

 13 Fig. 13. Overall open loop frequency response of T(s)

Fig. 14 .

 14 Fig. 14. Simulation time response of the output voltage of the IG with re-used UPS during load change from 220Ω to 150Ω

ACKNOWLEDGMENT

The authors would like to warmly thank M. Olivier DURRIEU from LAPLACE for his valuable contribution.

APPENDIX

: Inductance of the primary winding. L2=7.66mH

: Inductance of the secondary winding.