Abdelghani El Mouat

Taha El Assimi

Mustapha Raihane

Jérémy Ternel

Hervé Bricout

Eric Monflier

Sébastien Tilloy

Mohammed Lahcini

Exploiting hydrohydroxymethylated sunflower oil grafted on polycaprolactone as biodegradable coating material of water-soluble fertilizers

Keywords: In-situ polymerization, Polycaprolactone, grafting form, biobased oil, slow-release fertilizer

Biodegradable materials based on branched-architecture vegetable oil have attracted much interest in recent years. In the present study, hyperbranched poly( caprolactones) were prepared and used as coating materials to prepare slow release diammonium phosphate (DAP) fertilizer. Firstly, the sunflower oil was hydrohydroxymethylated by one-pot two-step process using Rh(acac)(CO)2 as catalyst, and triethylamine as ligand. Next, the bio--caprolactone) (SFO-O-PCLs) were prepared in open air by in-situ ring-opening polymerization of -caprolactone using hydroxymethylated sunflower oil as macro-4) as catalyst. The structures of the prepared polymers (SFP-O-PCL) were confirmed by nuclear magnetic resonance ( 1 H NMR) and the infrared spectroscopy (FTIR). Furthermore, the molecular weights of SFP-O-PCL were determined by size exclusion chromatography (SEC), the thermal stability and morphology of the coated film were evaluated respectively by thermogravimetric analysis (TGA) and the scanning electron microscopy (SEM). As the hydrophobic / hydrophilic balance is a key parameter in the coating of fertilizer domain, the hydrophobic character of the prepared SFP-O-PCL was also assessed by measuring the water contact angle (WCA). The final part of this contribution was devoted to the study of phosphorus (P2O5) kinetic released in water from coated and uncoated DAP granules. Thus, it was found that the prepared coating materials exhibited good performance in delaying the release of phosphorus and open a wide perspective for combining the advantages of hydrophobic polyesters and biobased oil.

1.Introduction

Fertilizers have an important role in agriculture. They provide nutrients to crops and also improve the physical, biological and chemical properties of the soil [START_REF] Sharma | A Review on the Effect of Organic and Chemical Fertilizers on Plants[END_REF]. However, as the main nutrients in conventionally used fertilizers are nitrogen, phosphorus and potassium (N, P, K), their excessive use leads to the depletion of the world's reserves of these valuable and non-renewable elements [START_REF] Anderson | Aquaculture: Its role in the future of food[END_REF]. In addition, recent studies on the long-term availability of these agrochemicals have confirmed a rapid release of these nutrients from fertilizers into the soil during the direct application process. This application method results in the loss of a large amount of these nutrients (about 40-70% of nitrogen, 80-90% of phosphorus, and 50-70% of potassium) that cannot be absorbed by the crops. In fact, the low efficiency of conventional fertilizers leads to variable mobility of nutrients and losses such as runoff, fixation, eutrophication, and volatilization, which have been shown to have a negative impact on the ecosystem by contaminating aquatic resources and the atmosphere [START_REF] Chien | Chapter 8 Recent Developments of Fertilizer Production and Use to Improve Nutrient Efficiency and Minimize Environmental Impacts[END_REF][START_REF] Viets | The environmental impact of fertilizers, C R C Crit[END_REF].

Therefore, to enhance the fertilizers efficiency, improve stability and reduce their environmental impact, coating approach has been investigated during the last decades to obtain a slow and controlled nutrients release from the water soluble fertilizer granules (SCRF) [START_REF] Rindt | Sulfur Coating on Nitrogen Fertilizer to Reduce Dissolution Rate[END_REF][START_REF] Blouin | Sulfur-Coated Fertilizers for Controlled Release: Pilot Plant Production[END_REF]. Indeed, many previous studies have investigated synthetic polymers as hydrophobic coating material such as polyethylene, poly (acrylic acid-co-acrylamide), poly (butyl methacrylate), polystyrene and others [7 10]. However, these coating materials are non-biodegradable and have raised doubts about the sustainability of such alternative. Moreover, it has been estimated that around 50 kg/ha of plastic residue could be cumulated each year in soils and consequently could affects its quality [START_REF] Trenkel | Slow-and Controlled-Release and Stabilized Fertilizers: An Option for Enhancing Nutrient Use Ef ciency in Agriculture[END_REF]. Thus, research investigations were later oriented on the potential uses of polysaccharides as biodegradable coating materials of granular fertilizers. Indeed, cellulose, chitosan and other polysaccharides were used as sustainable coating materials to overcome such biodegradability issue [12 15]. However, the use of these polysaccharides as coating materials has not led to the expected results, due to their highly hydrophilic character, poor mechanical properties, and their insolubility in organic solvents. Actually, organic solvent affords a uniform coating thickness during the coating processes which could not be unfortunately ensured when water is used as solvent as the granular fertilizers to be coated are water-soluble. Taking into consideration the above conclusions, researchers have recently focused their investigations on hydrophobic biopolymers-based coating such as aliphatic polyesters [START_REF] Assimi | Overview on progress in polysaccharides and aliphatic polyesters as coating of water-soluble fertilizers[END_REF]. In spite the fact that the new approach adopted lead to the elaboration of original coating materials characterized by their biodegradability and hydrophobic character [17 20], it should be noted that the marketability of the coating materials based on aliphatic polyesters remain so far constrained.

Meanwhile, vegetable oil, as a biobased material, has attracted attention in recent years due to its availability, renewable nature, high hydrophobicity, biodegradability, and low cost. However, most vegetable oils have limited technological application in their original forms because of their specific chemical and physical properties. To work around this, vegetable oils are often modified by hydrogenation, interesterification, fractionation or blending with other moieties [START_REF] Idris | Interesterified palm products as alternatives to hydrogenation[END_REF]. Recently, in the coating fertilizers field, we reported for the first time the possibility of using only vegetable oil as a coating material for fertilizers [START_REF] Sofyane | Properties of Coated Controlled Release Diammonium Phosphate Fertilizers Prepared with the Use of Bio-based Amino Oil, JAOCS[END_REF]. In this study, Priamine 1071®, a commercial amino oil, was chosen because of its high hydrophobicity character to prevent rapid water penetration into the fertilizer granules, and also for its low viscosity to avoid the use of solvent in the coating process. With this oil, the rate of nutrient (phosphate) released into the water after coating was significantly delayed, but it was very difficult to dry the encapsulated granules after the coating process which led to granules stick.

To circumvent this problem, it has been reported that it is necessary to cross-link the vegetable oil by combining it with other materials. In this respect, recent studies cross-linked hydroxylated vegetable oils using polyisocyanates have shown high efficiency for fertilizer coating. In this case, the drying problem encountered when using neat oils has been surmounted [START_REF] Desroches | From vegetable oils to polyurethanes: Synthetic routes to polyols and main industrial products[END_REF]. Nevertheless, the use of isocyanates as cross-linking agents is generally very harmful to human health [START_REF] Miao | Vegetable-oil-based polymers as future polymeric biomaterials[END_REF]. Therefore, the idea of this work is not to cross-link vegetable oils to effectively coat phosphate fertilizers, but to use them as a carrier for the grafting of aliphatic polyesters to develop biodegradable coating materials without employing a harmful cross-linking agent.

Among the most widely studied aliphatic polyesters is poly( caprolactone) (PCL) due to its high biodegradability, mechanical properties, and hydrophobic character and miscibility with a wide variety of other polymers. The poly( caprolactone) is widely synthetized by the ring opening polymerization (ROP) of -caprolactone using stannous octoate as a catalyst. Indeed, the ring opening polymerization of -caprolactone affords polymer with high molecular weight and lower dispersity [START_REF] Labet | Synthesis of polycaprolactone: a review[END_REF]. The most used catalyst for the ring opening polymerization are tin(II) and tin (IV) complexes [ 26 28], but tin-octoate is by far the catalyst that has usually used thanks to its effectiveness in the in-situ ROP of -caprolactone even in presence of organic and inorganic fillers [START_REF] Boujemaoui | Facile preparation route for nanostructured composites: Surface-initiated ring-caprolactone from high-surface-area nanopaper[END_REF][START_REF] Lahcini | Harnessing synergies in tin-clay catalyst for the preparation of poly( -caprolactone)/halloysite nanocomposites[END_REF]. However, as all those tin catalysts required inert gas condition to control polymerization process and to avoid drop down of molecular mass of the polymer [START_REF] Robert | Ring-Opening Polymerization of Lactide To Form a Biodegradable Polymer[END_REF]. Therefore, this synthetic approach is complicated by the presence of physically or chemically adsorbed water and the high number of hydroxyl groups in polyols oils, which leads to the grafting of only low molecular weight polymers. For instance, Gokhan Acik recently reported the ring--CL using stannous octoate as a catalyst and soybean oil hydroxyl groups (SBO-OH) as macro-initiators (polyol), the grafting of PCL onto oil was achieved but under strict experimental requirements, such as drying of solvent and reagents and working under anhydrous conditions, must be applied to ensure control of the polymerization [START_REF] Acik | Bio-based Poly( -caprolactone) from Soybean-Oil Derived Polyol via Ring-Opening Polymerization[END_REF]. With the aim of circumventing the disadvantage of using tin octoate as the standard catalyst for the ROP of cyclic esters, we have investigated a new catalyst based on tetra(alkynyl)tin to prepare a high molar mass grafted biodegradables polymers on hydroxylated organic and inorganic fillers [START_REF] Lahcini | Harnessing synergies in tin-clay catalyst for the preparation of poly( -caprolactone)/halloysite nanocomposites[END_REF][START_REF] Kadib | Luinstra, -caprolactone)-grafted guar gum by surface-initiated ring-opening polymerization[END_REF][START_REF] Nabgui | Synthesis and antibacterial behavior of Bio-composite materials--caprolactone)/Bentonite[END_REF]. Indeed, tetra(phenylethynyl)tin was found as efficient catalyst for the ring opening polymerization of lactide and -caprolactone even in open air at high (monomer)/(catalyst) ratio in the presence of silica nanoparticles [START_REF] Kalmi | Tetrakis Sn(IV) Alkoxides as Novel Initiators for Living Ring-Opening Polymerization of Lactides[END_REF]. In fact, the stability of tin-alkynyl bond (Sn--R) in air allows a short time synthesis without inert atmosphere requirement. In addition, the hydrolysis of tetra(phenylethynyl)tin catalyst like stannous octoate affords tin oxide, nontoxic compound approved by the FDA for internal use in human [START_REF]Agency for Toxic Substances and Disease Registry (ATSDR). Toxicological Profile for Tin[END_REF].

In this contribution, we report the synthesis in open air of a series of biodegradable polymeric materials via in-situ ring-opening polymerization (grafting from) of -caprolactone in the presence of hydrohydroxymethylated sunflower oil as a macro-4)

as a catalyst. Sunflower oil has been hydrohydroxymethylated (SFO-OH) before the grafting from according to the one-pot two-step process adapted in previous works where the first step is the hydroformylation of the carbon-carbon double bonds (C=C), followed by a subsequent reduction of the formyl group [START_REF] Vanbésien | Rhodium-catalyzed one pot synthesis of hydroxymethylated triglycerides[END_REF]. It should be noted that the one-pot tandem reaction is atom-economical, proceeds very cleanly, and lead to highly reactive primary alcohol than the secondary generally obtained by opening the epoxide ring of epoxidized oils. Once the synthesis was completed, the prepared material was fully characterized to approve the covalent linkage between poly( caprolactone) (PCL) polymerized and hydrohydroxymethylated sunflower (SFO-OH), and to investigate its thermal stability and surface propriety. Afterward, granular fertilizer of diammonium phosphate (DAP) were coated by the prepared material (SFO-O-g-PCL) using a laboratory rotary drum. Finally, the kinetic release of nutrients (phosphorus) in water was studied to evaluate the slow-release proprieties of the coated fertilizer proposed (SRF).

2.Experimental section 2.1 Materials

DAP, a granular diammonium phosphate fertilizer was received from OCP Group (Morocco), Very High Oleic Sunflower Oil (VHOSO) was provided by Oleon (France) (composition in Table 1SI), poly( caprolactone) (PCL) 90000 gmol -1 -caprolactone (CL), methanol, toluene, and tetrahydrofuran -caprolactone (CL) were distilled before their uses, hydroxylated sunflower oil, and tetra(phenylethynyl)tin were synthesized.

Synthesis procedures

One-pot synthesis of hydrohydroxymethylated sunflower oil (SFO-OH)

The hydrohydroxymethylation of sunflower oil was carried out following a previously published procedure [START_REF] Vanbésien | Rhodium-catalyzed one pot synthesis of hydroxymethylated triglycerides[END_REF]. In a typical catalytic experiment, Rh(acac)(CO)2 (7.8 mg, 0.030 mmol), triethylamine stainless-steel autoclave (Parr instrument company) equipped with a mechanical stirrer. Then, the reactor was sealed, the reaction mixture was stirred and heated at the desired temperature (typically 80 °C). Later, the reactor was pressurized with a mixture of CO and H2 (1:1 ratio) at desired pressure (typically 80 bar). When the reaction is completed, the apparatus is allowed to cool down to room temperature and depressurized. The catalyst was removed by filtration on Celite. The solvent was separated from products under vacuum and the hydrohydroxymethylated sunflower oil was ready to be used in the polymerization.

4)

The synthesis pathway of tetra(phenylethynyl)tin catalyst was inspired from previous published work [START_REF] Jousseaume | A general route to alkylene-, arylene-, or benzylene-bridged ditin hexachlorides and hexaalkynides[END_REF]. In fact, a three-necked flask was charged with 9 g of phenylacetylene. Furthermore, toluene was added to butyllithium in hexane. Then 5 g of Sn(IV)chloride in dry toluene was added to the solution under stirring at 70 °C. Finally, the obtained solution was filtrated, and the solvent was evaporated under vacuum. A yellow solid residue was obtained and recrystallized from toluene.

In-situ ring opening polymerization (ROP) of -CL from hydrohydroxymethylated sunflower oil

The synthesis approach of poly( caprolactone) grafted from hydrohydroxymethylated sunflower oil (SFO-O-g-PCL) was carried out in solvent-free conditions by using 5 different ratios of monomer/catalyst/oil ( -CL/ Sn(CCPh)4/ SFO-OH) of 50/1/1 (P1), 50/1/3 (P2), 50/1/5 (P3), 100/1/3 (P4) and 1000/1/3 (P5) in open air. It should be noted that the hydroxyl groups in the sunflower oil act as a co-initiator to initiate the ring-opening polymerization (ROP) of -CL. The tin catalyst was used in stock solution in dry toluene. The hydrohydroxymethylated sunflower oil (SFO-OH) was solubilized in -caprolactone ( -CL), afterwards, the catalyst in stock solution in dry toluene was added to the mixture and stirred at room temperature for 2 h. Then, the polymerization was conducted at 140 °C for a period of 1 h. At the end of the reaction, the resulting product was dissolved in a minimum of THF, then precipitated in cold methanol and the resulting product was filtered and dried in a vacuum oven at 50 °C for 24 h.

Coating of granular fertilizers (DAP)

Firstly, the prepared materials SFO-O-g-PCL were solubilized in THF (5%w.t.), then spherical granules (3-4 mm of diameter) of fertilizer were selected and loaded onto a laboratory rotary drum (see figure 2SI). The coating was applied by maintaining rotation speed at 100 rpm and alternation of injection/heating inside the pan. In fact, the injection was assured using an appropriate syringe and the heating by using heat flow tube of about 50 °C. After the coating process, the granules were weighed, and the percentage coating was calculated using equation (1):

Equation (1)

Mi and Mf are the fertilizer weights before and after coating respectively.

Phosphorus release test in water

The experiments were performed at room temperature. Uncoated and coated DAP granules (100 mg)

were immersed in 250 mL beakers of distilled water, the system was homogenized with slight and continuous stirring. Samples of 100 L were taken at different time intervals, diluted, and analyzed by spectrophotometer. The release kinetics of phosphorus in distilled water was determined by colorimetric methods (AFNOR-T90-023) using Ammonium-molybdate/ascorbic acid reagent. The colored complex was analyzed at a wavelength of 880 nm using an ultraviolet-visible spectrophotometer (UV-2600, Shimadzu).

Characterization methods

Nuclear magnetic resonance (

Fourier transform-infrared spectroscopy (FT-IR)

Structural interactions were investigated using Fourier transform infrared spectrophotometer (FTIR) (Prestige-21) using a bright ceramic light source, a high sensitivity DLATGS detector and highthroughput optical elements. The analysis was performed at room temperature in a range of wave numbers between 450 and 4000 cm -1 .

Size exclusion chromatography (SEC)

Steric exclusion chromatography (SEC) was used to determine the molecular weight of the prepared polymers. Measurements were performed on high resolution GPC/SEC Agilent chromatography equipped with two RI and UV sensors connected to PL-gel (MIXED-C column). Tetrahydrofuran was used as eluent in the chromatographic system, with rate flow of 1 cm 3 min -1 . The molecular weight distribution was calculated based on the specific calibration curve of poly(styrene) certified (PS calibration Kit S-M2-10).

Thermogravimetric analysis (TGA)

The TGA was performed to investigate the thermal stability of prepared materials (SFO-O-g-PCL).

TGA measurement was performed using the TA Instruments Q500 analyzer at a heating rate of 10 °C min -1 under nitrogen atmosphere (40 cm 3 min -1 ). The experiments were performed with a temperature ramp of 10 °C/min in the range of 20-600 °C.

Scanning electronic microscopy (SEM)

The surface morphology and thickness of the coated granules were determined by scanning electron microscopy (SEM), observations were recorded on Vega 3 TESCAN with a conventional tungsten heated cathode, intended for high vacuum and low vacuum operations. All samples were previously sputter-coated with Au-Pd in argon plasma to assure their conductivity.

Contact angle measurement

Contact angle measurements of water droplets on the prepared material surface were performed on EASY DROP machine. Measurements were carried out at room temperature with 2 L water droplets.

Results and discussion

SFO-OH synthesis

The hydrohydroxymethylated sunflower oil was obtained by one-pot two-step process using Rh(acac)(CO)2 as catalyst, and triethylamine as ligand. The reaction was carried out at 80 °C under 80 bar CO/H2 (1:1). The first step is hydroformylation of the C=C double bonds, followed by reduction of the formyl group. In this process, the carbon-carbon double bonds can remain unchanged or be isomerized, allowing the hydroxymethyl groups to be randomly located [START_REF] Vanbésien | Rhodium-catalyzed one pot synthesis of hydroxymethylated triglycerides[END_REF].

Scheme 1. One pot tandem rhodium-catalyzed hydrohydroxymethylation (HHM) of sunflower oil (SFO-OH)

SFO-O-g-PCL synthesis

As mentioned above, the SFO-O-g-PCL polymeric materials were prepared by in-situ ring-opening polymerization (ROP) of -CL using SFO-OH as a macro-4 as a catalyst in solvent free conditions. The polymerization was performed in open air. The mechanism suggested for this synthesis is similar to that already reported in previous studies [START_REF] Lahcini | Harnessing synergies in tin-clay catalyst for the preparation of poly( -caprolactone)/halloysite nanocomposites[END_REF][START_REF] Kadib | Luinstra, -caprolactone)-grafted guar gum by surface-initiated ring-opening polymerization[END_REF][START_REF] Nabgui | Synthesis and antibacterial behavior of Bio-composite materials--caprolactone)/Bentonite[END_REF]. In fact, PCL is grafted form hydroxyl groups of sunflower oil (SFO-OH) through the ring opening polymerization reaction of The Infrared spectroscopy was performed to identify functional groups of hydrohydroxymethylated sunflower (SFO-OH), the neat PCL and the prepared materials SFO-O-g-PCL. (Figure 3 and Figure 1SI). In fact, characteristic broad bands of sunflower hydroxyl groups (OH) at around 3416 cm -1 and an intense carbonyl band at 1743 cm -1 of C=O are clearly evidenced. Meanwhile, Neat PCL spectra shows similar vibration of carbonyl function (C=O) at 1743 cm -1 , but narow one was detected at 3443 cm -1 that is asigned to PCL OH groups. It souhld be noted that C-H vibration characterized by two bands around 2857-2949 cm -1 were revealed for both sunflower and neat PCL spectras. For structural investigation of the prepared material (SFO-O-g-PCL), PCL fingerprints were clearly revealed from FTIR spectra of SFO-O-g-PCL. Furthemore, a significant increase was observed on hydroxyl (OH) vibration of SFO-O-g-PCL compared to neat PCL which could be due to the contribution of hydrohydroxymethylated sunflower in the prepared material as the grafting of PCL onto SFO-OH leads to polymers with three terminal hydroxyl groups (scheme 2) whereas neat PCL possesses only one. The molecular weight of all prepared polymers was determined using steric exclusion chromatography (SEC). Table 1 summarized the molecular weights Mn and the dispersity D of prepared polymers. In fact, the high molecular weight (28000 g.mol -1 ) was obtained with the highest monomer/catalyst/ SFO-OH ratio (P5: 1000/1/1). Furthermore, the effect of hydrohydroxymethylated sunflower ratio on the polymerization reaction was also studied 50/1/1 (P1), 50/1/3 (P2), 50/1/5 (P3).

The molecular weight of polymer decreases by increasing the SFO-OH/monomer ratio. For the PCL obtained with 50/1/5 molar ratio, the molar mass presented the lowest value; it is probably due to the increase of the polymerization sites (hydroxyl co-initiator), which leads to more polymer chains but with shorter chain lengths. The explanation of this results is in good agreement with the assumption that a higher content of hydroxyl group of SFO-OH leads to a higher catalyst-co-initiator, which could generate a higher number of short chains of PCL (Scheme 2) [START_REF] Labet | Synthesis of polycaprolactone: a review[END_REF][START_REF] Lahcini | Harnessing synergies in tin-clay catalyst for the preparation of poly( -caprolactone)/halloysite nanocomposites[END_REF][START_REF] Kalmi | Tetrakis Sn(IV) Alkoxides as Novel Initiators for Living Ring-Opening Polymerization of Lactides[END_REF]. Analogically, the decrease of SFO-OH ratio leads to a low catalyst-co-initiator, which implies long polymeric chains, thus a high molecular weight (Table 1).

The dispersity of the synthesized polymers, remained lower than 1.6 (1.22 1.55) indicating that the polymerization proceeds at least partially by a controlled mechanism with little transesterification side reactions favored by the higher temperature. The thermal properties of all prepared polymers were investigated by TGA analysis to evaluate the effect of the incorporation of SFO-OH in PCL on the thermal stability of the prepared materials (SFO-O-g-PCL). Indeed, as presented in figure 4 and Figure 3SI, the thermal degradation of the prepared materials (P1, P2, P3, P4 and P5) occurred in a single step while thermal degradation of the neat PCL starts at 340 °C with a weight loss of 5% followed by total degradation at around 480 °C. It should be noted that the molecular mass of synthetized polymers (SFO-O-g-PCL) was significantly lower compared to neat PCL (90000 g.mol -1 ) used as reference sample. As consequence, the drop down in term of thermal stability could be clearly noticed from figure 4. Generally, this degradation behavior is attributed to a transesterification, as secondary reaction that occurs at high temperatures [START_REF] Lahcini | The use of tetra(phenylethynyl)tin as an initiator for the ring-opening polymerization of lactide[END_REF]. The hydrophobic/hydrophilic balance was evaluated by determining the contact angle value of droplet water deposed on the prepared materials surfaces. Actually, the hydrophobic character of fertilizer coating materials is a key paramter towards inhibiting water penetration on the fertilizer core. To better evaluate the effect of introducing SFO-OH into PCL towards the coating of water-soluble fertilizers, the granular diammonium phosphate fertilizer and SFO-O-g-PCL (P5) were selected. Indeed, this choice was motivated by the fact that P5 has the highest molecular weight which is required to form stable coating films as well as its lower contact angle which would control the penetration of water into the granule through the coating film. Table . 2 summarized the coating content of selected material, its

Mn and its contact angle value. It should be noted that the prepared material was able to be dried at the end of the coating process. The morphology and thickness of the SFO-O-g-PCL coating achieved by a rotary drum was investigated by SEM. Firstly, SEM image (Figure 6 B and C) of the cross-section allows the determination the coating thickness that is around 50 µm. Furthermore, it has been approuved that the coating process developped in this study affords a unifome thickness as reported in previous published work [START_REF] Meziane | Polylactide/cellulose acetate biocomposites as potential coating membranes for controlled and slow nutrients release from water-soluble fertilizers[END_REF][START_REF] Hassan | Polymethyl methacrylate -gcarboxy-methylcellulose as an amphiphilic coating material for slowrelease fertilizer[END_REF].

Phosphorus release study

In this last part, the kinetic study of the cumulative phosphorus (P2O5) released in water from coated and uncoated DAP granules was studied. According to previous investigation [START_REF] Assimi | R. -caprolactone)-g-Guar Gum and -caprolactone)-g-Halloysite Nanotubes as Coatings for Slow-Release DAP Fertilizer[END_REF][START_REF] Rui Lan | Prediction of Release Characteristics of Film-Coated Urea from Structure Characterization Data of the Film[END_REF], the release rate depends on the hydrophobicity, molecular weight, and the thickness of the coating materials. Figure 7 presents the release rate of phosphorus from uncoated and coated DAP granules in distilled water. In fact, the coated fertilizers present a significant slow-release properties. The delay of phosphorus release from coated fertilizers was clearly observed compared to the uncoated one in which less than 2 hours were enough to reach the total release. Meanwhile, the release of phosphorus from coated fertilizer by neat PCL presents the slowed release kinetic compared to prepared material (P5). The later statement was due to the high hydrophobic character of neat PCL that protects well the coated granules and avoids water penetration into fertilizer core. The prepared material (P5) exhibits slow phosphorus release behavior in distilled water, and only 32% was released in the first 10 hours. Indeed, we suggest that the difference in term of slow-release performances noticed between the prepared and neat PCL coating was due to the differences in molecular weight and hydrophobic character. It has been reported before that high molecular weight inhibits the hydrolysis of the polymeric chain and consequently the delaying performance will be enhanced [START_REF] Assimi | R. -caprolactone)-g-Guar Gum and -caprolactone)-g-Halloysite Nanotubes as Coatings for Slow-Release DAP Fertilizer[END_REF]. To conclude, the prepared material P5 proposed in this study as a granular fertilizer coating agent showed a promising result and opens a great opportunity to combine hydrophobic polyesters with biobased oils towards new applications. and the covalent bonding of PCL with hydrohydroxymethylated sunflower was approved by 1 H NMR and infrared spectroscopy. As revealed from SEC measurment, the PCL molecular weight grafted on the biobased oil could reach 28000 gmol -1 with high monomer to catalyst ratio. Moreover, the films formed from the prepared polymers showed a slight decrease in term of hydrphobic property which was probably due to the presence of hydroxyl fuctions as a polar groups. Furthermore, the thermal stability of the prepared material was compared to the neat PCL and a significant decrease was noticed, which could be related to the lower molecular weight of grafted PCL on SFO-OH oil. Furthemore, the prepared SFO-g-PCL (P5) and neat PCL were used for coating diammonium phosphate (DAP) granular fertilizer.

From SEM observation, an uniform coating thickness was achieved without cracks or failures. The invistigation of phosphorus release in distilled water from diammonium phosphate (DAP) coated granules and uncoated ones was carried out and it was found that granules coated with SFO-O-g-PCL and neat PCL show slow release of nutrients compared to uncoated granules.

In fact, the use of prepared material (P5: SFO-O-g-PCL) as coating agent of granular fertilizer displays

promising result that open the opportunity of combining hydrophobic polyesters and biobased oil toward original coatings materials for fertilizers.

- 4 andScheme 2 .

 42 Scheme 2. Proposal mechanism of the in-situ ROP -caprolactone in the presence of hydroxylated sunflower oil

Figure 1 :Figure 2 .

 12 Figure 1 : Proposed structure of SFO-O-g-PCL

Figure 3 .

 3 Figure 3. FTIR spectroscopy of Neat PCL, SFO-OH, and SFO-O-g-PCL (P5)

Figure 4 .

 4 Figure 4. TGA curve of the SFO-O-g-PCL polymers and Neat PCL.

Figure 5 shows

 5 the values of the angles measured with the EASY DROP. In that regards, the results provide more information about the hydrophobicity/hydrophilicity balance by varying the oil and monomer ratios in the prepared materials SFO-O-g-PCL. Although the hydrophobic character was relatively preserved for all prepared SFO-O-g-PCL materials in comparison to neat PCL, the slight decrease in hydrophbic character could be due to the additional OH groupe localized in PCL end chain grafted from the hydrohydroxymethylated sunflower.

Figure 5 .

 5 Figure 5. Contact angle values of PCL and PCL composites.

  Secondly, from the figures 6A, it was observed that the uncoated granule has a rough surface while the coating makes the surface smoother as observed from figure 6C. On the other hand, EDX analysis on the uncoated granule reveals phosphorus and nitrogen signals, whereas in the case of the coated granule, only carbon and oxygen signals were detected which are the only elements constituting the coating material and indicating also the absence of failures and cracks on the surface of the coating.

Figure 6 .

 6 Figure 6. SEM images of granule surfaces (A) uncoated DAP, cross-section of coated DAP (B and C) and their EDX analyses

Figure 7 .

 7 Figure 7. The release curves of P in water from uncoated and coated DAP by Neat PCL, the prepared coating agent SFO-O-g-PCL (P5) 4. Conclusions : In this research work, poly( caprolacotone) (PCL) was grafted from hydrohydroxymethylated sunflower oil (SFO-OH) following in-situ ring openning polymerization (ROP) approach by using efficient tin based catalyst in open air. The prepared polymers (SFO-O-g-PCL) were fully characterized

  OH), the prepared materials were analyzed by 1 H NMR. NMR spectra were recorded at 298K on a Bruker Avance III HD 300 NanoBay spectrometer equipped with a 5 mm broadband probe BBFO with Z-gradients, operating at 7.05 T field strength (300 MHz for 1 H nuclei and 75 MHz for 13 C nuclei).

1

H-NMR)

-caprolactone) (PCL) into hydrohydroxylated sunflower oil (SFO-

Table 1 .

 1 Results of SEC characterization of PCL

	SFO-O-g-PCL	Mn (g/mol)	Mw (g/mol)
	P1 :50/1/1	23641	31286	1.32
	P2 :50/1/3	21832	28231	1.29
	P3 :50/1/5	13210	16197	1.22
	P4 :100/1/3	18330	23922	1.30
	P5 :1000/1/3	28666	44466	1.55
	Mn, Mw, and determined by steric exclusion chromatography (SEC)

Table 2 .

 2 Coating content, Mn, and contact angle of P5 coating materials

	DAP Coating	Coating content	Mn (g/mol) b	WCA (°) c
		(wt%) a
	P5 :1000/1/3	17	28666	66,7

Acknowlegment:

Financial support from Projet Prioritaire (PPR1/2015/73) and the University of Artois is acknowledged for funding this work.


Pablo Stoliar

Julien Tranchant

Benoit Corraze

Etienne Janod

Marie-Paule Besland

Federico Tesler

Marcelo Rozenberg

Laurent Cario
email: laurent.cario@cnrs-imn.fr

A Leaky-Integrate-and-Fire Neuron Analogue realized with a Mott insulator

Keywords: Leaky-integrate-and-fire, Neuron, Mott insulator

During the last half century, the tremendous development of computers based on von

Neumann architecture has led to the revolution of the information technology. However, von Neumann computers are outperformed by the mammal brain in numerous data-processing applications such as pattern recognition and data mining. Neuromorphic engineering aims to mimic brain-like behavior through the implementation of artificial neural networks based on the combination of a large number of artificial neurons massively interconnected by an even larger number of artificial synapses. In order to effectively implement artificial neural networks directly in hardware it is mandatory to develop artificial neurons and synapses. A promising advance was made in recent years with the introduction of the components called memristors that might implement synaptic functions. In contrast, the advances in artificial neurons have consisted in the implementation of silicon-based circuits. However, so far, a single component artificial neuron that would bring an improvement comparable to what memristors had brought to synapses is still missing. Here, we introduce a simple two-terminal device, which can implement the basic functions leaky integrate and fire of spiking neurons.

Remarkably, we found that it is realized by the behavior of strongly-correlated narrow-gap Mott insulators subject to electric pulsing.

Introduction

During the last half century, the tremendous development of computers has led to the revolution of the information technology. Nevertheless, the way computers store and process the information has scarcely changed since their inception and relies on the concepts proposed by von Neumann in the 40's. This von Neumann architecture, based on a clear separation between the memory and the processing unit, is extremely powerful in many cases such as high-speed processing of large data streams. However, von Neumann computers are outperformed by the mammal brain in numerous data-processing applications such as pattern recognition and data mining. [1,[START_REF] Mead | Proc. IEEE[END_REF][START_REF] Jain | [END_REF][START_REF] Boahen | Neuromorphic Microchips[END_REF]5,6,7,8] In fact, the brain is organized with a very different architecture, based on a network of closely connected neurons and synapses.

Neuromorphic engineering aims to mimic brain-like behavior through the implementation of artificial neural networks based on the combination of a large number of artificial neurons massively interconnected by an even larger number of artificial synapses. [ 2 , 3 ] In most cases, artificial neural networks are software-implemented in conventional hardware; they are programmed in computers with standard architectures, i.e. on von Neumann architectures. In principle, a much more efficient way to that goal would be to use the so-called neuromorphic systems that allow a direct hardware implementation, that is, systems where each neuron and each synapse consists in a dedicated set of components in an electronic circuit. [ 4 , 5 ] In order to effectively implement artificial neural networks directly in hardware and integrated in high-density chips, it is mandatory to develop two types of devices: artificial neurons and synapses. [ 6 ] The key aspect here is the requirement of a vast number of these interconnected basic building blocks. Therefore any improvement in reducing the complexity, size, and power dissipation in their implementation has a huge impact on the efficiency of the whole neuromorphic system. A promising advance was made in recent years with the introduction of the components called memristors, which are highly-scalable two-terminal devices that might implement synaptic functions. [ 8 , 9, 10] Memristors have a history dependent resistance, which may be exploited to encode a synaptic weight in a neuromorphic circuit. Moreover, they may also be integrated into high-density cross-bar arrays, which simplify the interconnection between a high number of neurons. [11] In contrast, the advances in artificial neurons have consisted in the implementation of silicon-based circuits employing many standard electronic components. A first simplification was recently achieved with the multicomponent neuristor designed with several memristors, resistances and capacitors, and that aims to mimic the action potential of the biological neuron. [12] However, so far, a single component artificial neuron that would bring an improvement comparable to what memristors had brought to synapses is still missing. [START_REF] Indiveri | Neuromorphic Silicon Neuron Circuits[END_REF] Here, we introduce a simple two-terminal device, which can implement a basic function of spiking neurons, namely the leaky integrate and fire.

Remarkably, we found that it is realized by the behavior of strongly-correlated narrow-gap Mott insulators subject to electric pulsing. [14,15,16]

Results and discussion

The lacunar spinel compounds AM4Q8 (A = Ga, Ge; M = V, Nb, Ta, Mo; Q = S, Se) containing transition-metal tetrahedral clusters are narrow gap Mott insulators with Mott-Hubbard gaps in the order of 0.1-0.3 eV. [17] Conventional density functional calculation of the band structure yields partially filled bands, however, strong local electronic repulsion turn these materials into correlated insulators. [18] Pressure, doping or electric field can destabilize this electronic state, "melting" the Mott insulating phase into a correlated metal phase. [17,18,19,20] Both, in pressure driven or electronic doping driven insulator-to-metal transition, the physics is well accounted for by the Dynamical Mean Field Theory. [18,21] The mechanism behind the destabilization of the Mott state upon electric field, which brings the quantum system out of equilibrium, was found recently to be related to an electronic phenomena, namely an avalanche breakdown. [14] It is not the purpose of this paper to describe the physics behind this new mechanism of resistive switching and to compare it with other mechanisms reported in the literature. These issues are addressed in recent review papers. [22] However we give hereafter a brief summary on the volatile resistive switching observed above a threshold electric field of a few kV/cm in the AM4Q8 compounds. Under an electric pulse exceeding the threshold electric field these narrow gap insulators undergo a dramatic resistive transition from a high to a low resistance state as described elsewhere. [14,15] This phenomenon may be observed using a simple circuit made of a two-terminal narrow-gap Mott insulator crystal connected in series with a load resistor (see Fig. 1 (a)). Fig. 1(b) displays a typical resistive transition observed on a GaTa4Se8 sample at 74K during a voltage pulse exceeding a threshold voltage Vth. A sudden lowering of the voltage across the sample occurs after a (voltage dependent) delay time hereafter called tFIRE and equal to 89 µs in this case. This lowering of the sample voltage is concomitant with an increase of the current intensity through the sample (called hereafter "firing" event). As a consequence, a resistive transition from a high to a low resistance state is observed (see bottom panel in Fig. 1(b)). An essential feature of this transition is that when the voltage pulse on the sample ends the sample returns to its original high resistance value after a brief delay time. This resistive transition is therefore called volatile. This volatile transition is due to the unique ability of the Mott material to locally commute between a stable insulator state and a metastable conductive state, through an electric-field driven insulator to metal transition. [15,14,20] The conductive state is characterized by metastable metallic filamentary structures bridging the electrodes and fading in time after the pulse. [16] Previous numerical modeling studies have suggested that the relaxation of the metastable metallic domains within the conducting filaments is thermally activated. [16] To gain more understanding of this relaxation phenomenon, the evolution of the resistance after the pulse is terminated was measured and is presented in Fig. 1(c). This measurement provides the insight that the relaxation involves in fact two successive processes. Initially, right after the pulse is over, the resistance rises sharply. This may be ascribed to the filamentary conductive structure rapidly tapering itself and losing percolation. Then, once the filament is destroyed the resistance follows a long-time exponential relaxation law. This may be associated to the isolated metallic granular domains that get further reabsorbed through a thermally activated behavior as suggested by previous numerical modeling studies. [16] According to these studies, the relaxation time may be simply characterized by fitting the long time relaxation with an exponential form. Hence, we assume the form,

( ) 0 / 1 R e R t τ - - =
(1) which provides the satisfactory fit shown in Fig. 1(c). In Eq. ( 1), R0 denotes the resistance of the pristine sample, and τ the experimental relaxation time. From the fit we can extract τ = 518 ± 100 µs. This value of τ is related to the energy barrier of the metastable metallic state, which is material dependent.

The volatile nature of the resistive transition described here prevents its use to implement synaptic functions like Spike-Timing-Dependent-Plasticity (STDP), which requires a non-volatile resistive switching as found in memristors. In contrast, the two features described above, namely a delay time tFIRE and a relaxation time τ open the way to the implementation of a novel functionality "Leaky Integrate and Fire" (LIF), which realizes an analogue to a basic spiking neuron behavior. Fig. 2 illustrates this functionality. It demonstrates the spiking response of the current (i.e. firing) after a number of voltage pulses NFIRE are applied. The main idea is to apply a train of short pulses with duration tON and separation tOFF such that tON < tFIRE and tOFF < τ. For instance, in Fig. 2(a) we have tON = 20µs < tFIRE = 89 µs (cf. Fig. 1(b)) and tOFF=30µs < τ = 518 µs, which yields a resistive transition in the GaTa4Se8 system after NFIRE = 6 pulses. The fact that the transition can be triggered with pulses of shorter duration than tFIRE demonstrates that the effect is cumulative, i.e. integrated by the system. Moreover, Fig. 2(a) brings about the third feature of the LIF neuromorphic functionality. Indeed, the applied pulse-time elapsed until the firing (~ 6 x 20 µs) is longer than tFIRE = 89 µs. This deviation from perfect integration is of course simply due to the relaxation between pulses (i.e. during tOFF), which in other words realizes the leaky feature. Thus, NFIRE depends (at a given VPULSE) on the values of tON and tOFF. Hence, raising tON or tOFF should have opposite effects on the leaky integration and lead respectively to a decrease or an increase of NFIRE which is in fact seen in Figs. 2b-c.

This "Leaky Integrate and Fire" functionality can be well understood within the framework of the model of the resistive transition in narrow-gap Mott insulators describe in details in reference [16]. To summarize, in that model the system is represented as a discretized 2D array of cells that form a resistor network (see Fig. 2). As depicted in Fig. 2(a), each cell may be in either one of two phases, which correspond to the two physical states of the system: a stable high-resistivity Mott insulator (MI) or a metastable low-resistivity correlated metal (CM). The key assumptions of the model are that the transition MI→CM can be induced by the action of a local electric field ~qΔV, with a transition rate PMI→CM = c ( )

T k V q E B B e / ∆ - -
, where EB is the energy barrier with respect to the insulator state, ΔV is the voltage drop on the cell, c is a constant and q is set to unity. It is further assumed that the cells excited to the metastable state relax back thanks to a thermal activation law with a rate PCM→MI = c ( )

T k E E B M B e / - -
, where EB-EM represents the energy barrier (see Fig. 3a).

The key quantity here nCM = NCM/N is the ratio of the number of correlated metallic cells (NCM) to the total number of cells (N). [16] Its dynamics follows

( ) ∑ - → - → + - = ∂ ∂ cells MI CM MI MI CM CM CM P N t p P n n t 1 , (2)
where the first (loss) term account for the relaxation of CM cells back to the MI state and the second (gain) term accounts for excitation of MI cells to the CM state. Since EB >> kBT, the rate PMI→CM and therefore the gain term only become significant during the voltage pulses.

Hence the function p(t) assumed to be p(t)=1 during the pulses and 0 otherwise is introduced to account for the fact that no CM sites are created without voltage. Note that while the relaxation rate PCM->MI is independent of the voltage on the cell, the excitation rate PMI->CM depends on the cell's local drop ΔV. This introduces a strong non-linearity in the problem.

The dynamical behavior can, nevertheless, be investigated in detail by numerical simulations. [16] As evidenced in reference [23] the firing event, i.e. the sudden growth of a filament that percolates through the system, is found to occur when the fraction nCM attains a critical value nC. An example of the evolution of nCM vs time is shown in Fig. 3(c). It is interesting to observe, that the growth of the filament occurs abruptly (compare Fig. 3(d), 3(e) and Fig.

3(f))

, due to the strong non-linearity of Eq. ( 2). Until the firing event, and during the action of the applied voltage, the fraction nCM increases approximately linearly in time (see Fig. 3(c)). This is because the CM cells form sparse isolated clusters (nCM << 1), hence the electric field remains rather homogeneous through the system, yielding an almost constant production rate of CM cells, except when the number of CM cells becomes very close to the critical value nC.

There, the non-linear behavior kicks in, the production rate increases sharply and the filament percolates through the system. An important notion to realize is that for the firing event to occur, the production rate should dominate over the relaxation, which requires the applied voltage to be larger than a finite threshold value VTH. [START_REF] Indiveri | Neuromorphic Silicon Neuron Circuits[END_REF] Thus, we may rewrite Eq. ( 2) as ( )

t p A P n n t MI CM CM CM + - = ∂ ∂ → ; V > VTH, nCM < nC ( 3
)
where A is the production rate and nC is a (model parameter dependent) critical value where the conductive filament formation suddenly occurs.

In this study we have applied this model of resistive transition to the case of train of short pulses. Importantly, Fig. 4 demonstrates that the qualitative behavior found in the case of a single pulse also occurs for application of a train of pulses, i.e., adopting a p(t) that subsequently switches between 1 and 0, during respective intervals tON and tOFF. Specifically, during tON the CM fraction growth linearly in time (integrate), and during the tOFF it decays exponentially in time (leaky). Hence, the modeling (Fig. 4) reproduces nicely the qualitative dependence of NFIRE with tON and tOFF as observed experimentally (Fig. 2). Moreover, it confirms that the formation of the metallic path is a sudden process occurring during a single pulse (Fig. 4d to 4g).

As we shall see below, the central result of the present work is to demonstrate that thanks to this behavior the Mott system can be considered as an analogue of a spiking neuron.

Specifically, the dynamics given by Eq. ( 3) is analogous to the transfer function of the leaky integrate-and-fire model (LIF) of spiking neuromorphic systems. [24] These systems are a class of artificial neural networks that deal with data represented as sequences of pulses, or "spikes". The LIF model aims to describe a basic function of the neuron behavior related to the accumulation of electric charge through the cellular membrane (Fig. 4(a)). Following early work of Lapicque's, the LIF model sketched in Fig. 4(b) represents the membrane as a capacitor with a leaking resistor in parallel. [25] The increase in the membrane potential, resulting of synaptic processes (i.e., spikes arriving from other neurons) is generally modeled as current pulses that inject electrical charges into the capacitor. When the voltage reaches a given threshold the neuron fires an output electric spike. The nature of this output spike (that would represent the action potential in biological neurons) as well as the concomitant reset of the capacitor charge are usually not considered part of the model . [24,26] Within the LIF model of an artificial neuron that has one synaptic excitatory input-current the time dependence of the voltage v across the membrane is ( )

t s C w RC v v t + - = ∂ ∂ 1 , (4)
with R the leaky resistance and C the capacitance of the membrane. s(t) represents a train of spikes arriving to the neuron. In fact, a peculiarity of the LIF model and of spiking neuromorphic systems in general, is that the information is encoded in the timing of the spikes (i.e., temporal sequence) not in their amplitude, width, etc. [14] . Furthermore, we should note that in actual neuromorphic hardware, spikes may adopt electric pulses of arbitrary shape since only their timing is relevant. The effect of the incoming spikes is controlled by the synaptic weight w, which we assume a constant since the LIF model does not include the behavior of synapses.

At this stage the equivalence between the behavior of Mott insulators and the behavior of artificial neurons based on the LIF model becomes clear, as both, Eqs. ( 3) and ( 4), are analogous. Figure 5 and Table 1 summarize the equivalence between our Mott system and the LIF model. In the former, incoming spikes are represented by a train of voltage pulses and the output spike is a current pulse. As highlighted in Fig. 5, a key feature of the analogy is that the role of charge accumulation in the LIF model is played in the Mott system by the accumulation of correlated metallic sites.

Finally, we illustrate the experimental validation of Eq. ( 3) by computing the predicted number of spikes (i.e. pulses) required to produce a fire event for a train with given parameters tON and tOFF and applied voltage V. In this case, the expression for the required number of pulses NFIRE can be obtained in closed form, under the simplifying assumption that the production rate of CM sites, remains constant in time (see Eq. ( 3)), (5) Since NFIRE is an integer number of pulses, we use the ceiling function which maps a real number to the smallest following integer. It is worth noting that Eq. ( 5) does not contain any free parameter. Both tFIRE and the relaxation time τ are indeed obtained experimentally for a given fixed applied voltage. For our experimental conditions, we determined τ = 518 μs and tFIRE = 89 μs (cf Fig. 1). Fig. 6(a) and 6 (b) show the parametric dependence of NFIRE with tON and tOFF measured experimentally along with the theoretical prediction using Eq. ( 5). The simultaneous agreement for the behavior of NFIRE as a function of both, tON and tOFF, provides a remarkable validation of our neuromorphic Mott device as an analogue of an artificial neuron with the LIF functionality.

( )                     - - - = τ τ τ / 1

Conclusion

We have demonstrated that the LIF neuron model can be implemented by a single component device based on a Mott insulator compound. The system implements all three basic spiking neuron processes: Leaky, Integrate and Fire. It is important to note that, this novel functionality of our Mott device goes even beyond the LIF model, as it readily implements a Firing spike by delivering an outgoing current pulse. In fact, this is one of the most complex part to implement by neuromorphic hardware. Hence, the downscaling of this simple two-terminal device may open the way for the realization of long sought after dense spiking neuromorphic networks.

In the reviewing process of our article several interesting works were published that aims to realize artificial neurons with graphene oxide [ 27 , 28 ] or RRAM materials [ 29 ]. All these studies fully confirm that the realization of downscalable artificial neurons will rapidly emerge as an active field of research in neuromorphic engineering. (b). The relaxation of the resistance is shown in (c), and the fit of the long-time relaxation with Eq. ( 1) in (d). For the sake of the demonstration these experiments were performed at 74 K using as sample a slice of GaTa4Se8 crystal so that the resistive switching can reach almost three orders of magnitude. The inter-electrodes distances was about 40 µm which explains the large voltage needed to trigger the switching. A simple downscaling would reduce both the voltages and currents required to operate the device. (d-g) show snapshots of the microscopic state of the resistor network during each of the 4 pulses shown in panel (a). We observe that the formation of the conductive bridge is a sudden process, which occurs within the duration of a single pulse, i.e., in that case the fourth one.

Fig. 1 .

 1 Fig.1. Experimental setup (a) and typical resistive switching experiments obtained on applying a long single voltage pulse(b). The relaxation of the resistance is shown in(c), and the fit of the long-time relaxation with Eq. (1) in (d). For the sake of the demonstration these experiments were performed at 74 K using as sample a slice of GaTa4Se8 crystal so that the resistive switching can reach almost three orders of magnitude. The inter-electrodes

Fig. 2 .

 2 Fig. 2. Experimental resistive switching obtained by applying trains of short pulses of various tON and tOFF. Using tON = 20 µs and tOFF = 30 µs leads to NFIRE =6 (a). Increasing tON to 30 µs leads to a decrease of NFIRE to 4 (b).Increasing tOFF to 80 µs leads to an increase of NFIRE to 8 (c).

Fig. 3 .

 3 Fig. 3. Description of the energy landscape (a) and 2D resistor network (b) used for the modeling of the resistive switching in reference (16). Typical output of the model (c) showing before resistive switching the linear increase with time of the fraction of metallic sites. Figs. (d) and (e) display the resistance network at different time before resistive switching. A few metallic sites are created randomly. Fig. f shows, on the other hand, that the resistive switching is associated with the formation of a filamentary metallic path between the bottom and top electrodes.

Fig. 4 .

 4 Fig. 4. Modeling of resistive switching obtained with trains of short pulses of various tON and tOFF Panels (a-c). Panels(d-g) show snapshots of the microscopic state of the resistor network during each of the 4 pulses shown in panel (a). We observe that the formation of the conductive bridge is a sudden process, which occurs within the duration of a single pulse, i.e., in that case the fourth one.

Fig. 5 .

 5 Fig. 5. Schematic representation of a biological neuron receiving input spikes from other neurons and triggering an ouput action potential when the membrane potential reaches the threshold value (a). The LIF artificial neurons based on Lapicke's model reproduces the evolution of the membrane potential thanks to an RC circuit accumulating electrical charges (b). The Mott artificial neuron sketched in (c) reproduces the LIF behavior thanks to the accumulation of correlated metallic sites.

Fig. 6 .

 6 Fig. 6. Evolution of the number of pulses necessary to "fire" the Mott Neuron versus the pulse duration tON (a) and the separation time between pulses tOFF (b). Remarkably the parameter-free theoretical prediction established for the LIF model (Eq.5, see in text), shown as red curves, reproduces nicely the experimental dependences.

Table 1

 1 Comparison of variables and equations used in the LIF and Mott neuron models. Both models are analogue and lead to the same equation for the number of pulse for FIRE. The ceiling function maps a real number to the smallest following integer.

							LIF model												Mott LIF neuron
	Integrated variable		Membrane potential ν									Fraction metallic regions n CM
	Model	t ∂ ∂	v	=	-	v	RC 1	+	C w	s	( ) t						t ∂ ∂	n CM	=	-	n CM	P CM	→	MI	+	A	p	( ) t
	Input variable			Dirac delta function									Voltage pulse
	Output variable						Not defined												Current pulse
	Leaking time-constant								RC														1/P CM→MI
	Synaptic input				s	=	( ) ∑ -i i t t δ							p	=	i ∑	[ H	( ) ( --i t H t t	-	t	i	-	t	ON	) ]
	Spike contribution								w/C														A t ON
	Number of pulses for FIRE			N	FIRE	=	ceiling	      	1	-	ln	  	e	OFF t	/τ	-t	/ FIRE OFF ON t t	τ (	e	OFF t	/τ	-	) 1	  	      

Acknowledgements

The authors thanks the Région Pays de la Loire for funding the present work in the framework of the "Pari Scientifique Neuro-Mott" and J. Gesrel for his help in preparing the figures.

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Revised: ((will be filled in by the editorial staff))

The table of contents entry should be 50-60 words long, and the first phrase should be bold.

The mammal brain is based on a network of closely connected neurons and synapses.

The implementation of artificial neural networks directly in hardware requires therefore to develop artificial neurons and synapses that can be integrated in high-density chips. Here, we demonstrate that a two-terminal device made of narrow-gap strongly-correlated Mott insulators implement the processing functions of the leaky-integrate-and-fire artificial neuron.