Sobhan Razm
email: sobhan.razm@imt-atlantique.fr

Nadjib Brahimi
email: nadjib.brahimi@rennes-sb.com

Alexandre Dolgui
email: alexandre.dolgui@imt-atlantique.fr

Ramzi Hammami
email: ramzi.hammami@rennes-sb.com

Designing Bioenergy Supply Chains under Social Constraints

Keywords: Sustainable development, Biofuel production, Bioenergy supply chains, Biomass, Optimization, Social concerns

The use of renewable energy, as a clean alternative to fossil fuel, has become very attractive. It has environmental advantages and leads to regional development. This study proposes an optimization model for the design of bioenergy supply chains under social concerns. The social concerns involve the unemployment rate and the vulnerability to changes during an economic crisis. The areas that are mostly exposed to these social issues are chosen as initial potential locations for installing the biorefineries. Installing a biorefinery can generate jobs for the people of these areas. This leads to the sustainable development in the areas. The applicability of the developed model is shown through a case study. The results demonstrate that the proposed approach leads to the generation of a large number of job positions which has an important impact on the social development of these regions.

Introduction

The design and management of bioenergy supply chains have gotten attention in the recent years [START_REF] Nur | A two-stage stochastic programming model for biofuel supply chain network design with biomass quality implications[END_REF]. However, the cost of the bioenergy supply chain (SC) network is one of the most significant obstacles in developing bioenergy supply chains [START_REF] Yue | Biomass-to-bioenergy and biofuel supply chain optimization: Overview, key issues and challenges[END_REF]. For example, one of the major costs is incurred in the collection and transportation of biomass to the biorefineries. Collecting, processing, and transporting biomass feedstocks from supply sites to the biorefineries have also environmental and social impacts [START_REF] Awudu | Uncertainties and sustainability concepts in biofuel supply chain management: A review[END_REF].

The location of the biorefinery is a critical issue [START_REF] Santibañez-Aguilar | Sequential use of geographic information system and mathematical programming for optimal planning for energy production systems from residual biomass[END_REF] in terms of reducing these costs [START_REF] Awudu | Stochastic production planning for a biofuel supply chain under demand and price uncertainties[END_REF] as well as GHG emissions (e.g. because of less transportation). The location of the biorefinery is also important, since it can generate new jobs and lead to sustainable development in a given region [START_REF] Razm | A multi-objective mathematical model to redesign of global sustainable bioenergy supply network[END_REF]. As a result, it is important to incorporate the concepts of sustainability into the design and planning of the bioenergy supply chain networks. Consequently, this study is seeking to answer the following questions:

1. How to design and manage the bioenergy supply chains that transform biomass into biofuel and bioenergy?

2. How to determine the purchased biomass quantities, the output quantities of bioenergy and biofuel, and the inventory decisions in order to minimize the supply chain costs while considering social constraints?

Consequently, the contributions of this paper are as follows: 1) Developing a mathematical model for designing and managing the bio-refineries. 2) Incorporating the social concerns into the network design of the bioenergy supply chain. 3) Applying the developed model to a case study. The remainder of the paper is organized as follows. The literature review is presented in Section 2. The definition of the problem is presented in Section 3. The model formulation is presented in Section 4. The results are described in Section 5. Finally, the conclusion and some suggestions to extend the study are presented in section 6.

2

Literature review

In recent years, modeling and optimization of the bioenergy supply chains have attracted the researchers. For example, some studies focused on the geographical dispersion to find biomass sources and supply capacities [START_REF] Nguyen | Supplier selection and operation planning in biomass supply chains with supply uncertainty[END_REF]. Some studies were more focused on the locations of bio-refinery and production capacities [START_REF] Schmidt | Potential of biomass-fired combined heat and power plants considering the spatial distribution of biomass supply and heat demand[END_REF]. A group of studies considered the whole network (more integrated). They used different types of biomass (the agricultural and forest residues) to generate biofuel in the design of bioenergy supply chains [START_REF] Marvin | Economic optimization of a lignocellulosic biomass-to-ethanol supply chain[END_REF][START_REF] Razm | A global bioenergy supply network redesign through integrating transfer pricing under uncertain condition[END_REF]. In terms of sustainability, a MILP model was proposed by [START_REF] Rabbani | Developing a sustainable supply chain optimization model for switchgrass-based bioenergy production: A case study[END_REF] to design the bioenergy supply chain network. They used switchgrass as biomass feedstock. Three objectives (economic, environmental, and social objectives) were considered to optimize the following decisions: i) determining the amount of collected biomass, ii) determining the maximum capacity in the biomass collecting centers, iii) determining the locations of power plants and the capacities. The augmented ε-constraint and TOPSIS approach were used as a hybrid method to generated Pareto-optimal solutions for decision makers. However, their study focused only on generating electricity (power plant), and the generated jobs were not jobs with high impacts on the area. They did not pay attention very well to the important social concerns such as high unemployment rate, and high vulnerability to changes in the markets in an economic crisis.

Designing a biofuel supply chain could generate jobs for the local residents (in the territory), as well as protect the environment [START_REF] D'amore | Strategic optimisation of biomass-based energy supply chains for sustainable mobility[END_REF]. Nevertheless, in the literature, most of the researchers focused only on economic aspects, and less attention has been made to sustainability, especially the social aspects of the bioenergy supply chains. This is a gap in the bioenergy SC literature that needs to get more attention. In addition, in the real world, generating the jobs in a territory where has a very low unemployment rate could not be considered a very efficient design of the bioenergy SC (in terms of sustainable development). Generating the jobs which are not close (not relevant) to the skills of the local people, who may lose their jobs in the economic crisis, could not make a high social impact on the territory. These are the factors which motivate this paper versus the state of the art. The outcomes of the bioenergy SC literature review are shown in Table 1. As shown in Table 1, there is an essential research gap in the literature to optimal design and planning of the bioenergy supply chains under social sustainability constraints such as high unemployment rate, and high vulnerability to changes in the markets in an economic crisis. This study tries to fill this research gap.

Problem definition

The bioenergy supply chain network gets started with supplying raw materials (biomass) for the biorefineries and will end with the customers (markets). As shown in Fig. 1, biomass 𝑟 ∈ 𝑅 is collected from the supply site 𝑠 ∈ 𝑆. The biomass can be sent and processed by biorefinery at location 𝑏 ∈ 𝐵 using technology 𝑎 ∈ 𝐴. The biomass is converted to bioenergy 𝑒 ∈ 𝐸 to sell in location 𝑏 ∈ 𝐵, or is converted to biofuel 𝑓 ∈ 𝐹 to sell in market 𝑐 ∈ 𝐶.

The biomass feedstocks are forest residues and agricultural residues. Bioenergy refers to heat and electricity. Biofuel refers to bio-oil and pellet. These conversions of biomass can be done by different processes such as thermochemical, chemical, and biochemical. The generated biofuel is sent to different markets. The generated bioenergy is either used in the bio-refinery or sold to local heat grids/systems.

Social sustainability

Iran's Ministry of Economic Affairs and Finance proposed an index of agricultural and forest vulnerability based on the research done by Isfahan University of Technology's college of agricultural engineering. The index is used to resist against changes in the agricultural and forest commodity markets that is 𝒱 = 𝔇 × (100 -𝜉). In this equation, 𝔇 is the agricultural and forest dependency index. It is a part of employment revenue in the area that is obtained from the agricultural and forest parts. 𝜉 is diversity index. It shows the economic diversity in the area. 𝜉 takes value in (0,100). 𝜉=0 means that the society (the area) is completely dependent on a part. 𝜉=100 means that the society is equally dependent on each of the defined parts. After normalizing, 𝒱 (The agricultural and Forest vulnerability Index) is obtained in (0,100) for each area. 𝒱=100 means the area is highly vulnerable to changes in the markets (e.g., in an economic crisis). For example, the values of 𝒱 for 23 territories are shown in Table 2. These values can be obtained from the statistics office of each country.

Table 2. The values of 𝒱 for each territory.

Concentrating on the high unemployment rate in the areas with high vulnerability could generate social impact. Consequently, when a job with a higher employment rate is generated in a territory with a higher vulnerability (job with a high impact), it can generate more social profit. Given the ruined jobs of the aboriginal people of the biorefinery's territory (caused by an economic crisis), various job categories are generated in the biorefineries that are close to the skills of the aboriginal people. For instance, the farmers who have lost their jobs can be employed in combustion stations. The individuals who have worked in the corporations relating to oil can be employed in the pyrolysis technology stations. According to the Iranian statistics office, a lot of farmers have lost their jobs in the last economic crisis, so their unemployment rate is high (equal to 11.23%). These farmers could be employed in the combustion stations. As a result, the social profit is generated by the social impact of the job generation.

The jobs generated for local people by installing the biorefinery could be defined into three main categories depending on the average unemployment rate (ℷ 𝑤 ), consulting with Renewable Energy and Energy Efficiency Organization.Table 3 shows these categories.

Table 3. Jobs categories generated by installing the bio-refineries.

The unemployment rates can be determined by the statistics office of each country. Therefore, in another study, the values of the unemployment rate may change. The social impact (𝜫 𝒘,𝒃 ) of the generated job in the category w in the territory b is calculated by 𝜫 𝒘,𝒃 = ℷ 𝒘 × 𝓥 𝒃 . Then, the territories with high vulnerability and high unemployment rates are chosen as candidate locations for the biorefineries (see Fig. 2), in order to maximize the social impact. The vulnerability rate and unemployment rate for each territory can be obtained from the statistics office of each country. Model formulation:

The objective of the proposed model is to minimize the total costs of the supply chain.

The decisions determined by this model are as follows: 1) determining the amount of the purchased and transported biomass to the bio-refineries, 2) selecting the biomass suppliers, 3) selecting the optimal locations of the bio-refineries, 4) determining the capacity and type of the technologies considered in each bio-refinery, 5) determining the amount of the assigned biomass to the technologies, 6) determine the amount of biofuel and bioenergy to sell to customers.

Fig. 1. General framework of the supply chain

Because of page limitation imposed by the conference, we opt for a verbal description of the proposed model. The detailed mathematical formulation is available from the authors upon request. It consists of a Mixed Integer Linear Programming formulation that can be described as follows:

5

Results and discussion

The proposed model was coded in GAMS 24 and solved using the CPLEX solver. Using the case study, the model was implemented with an Intel Core i3, 2.13 GHz processor with 4GB of RAM. The results are presented in the following.

Bioenergy supply chain structure

In this part, the optimal design obtained by the model is presented. The optimal locations of the biorefineries are presented in Fig. 3 that minimize the total cost of the bioenergy supply chain. The total cost of the bioenergy SC that was obtained from the model is equal to 637.5M$. Fig. 3 also shows the area of the customers and the amount of satisfied demand during the planning horizon. The satisfied biofuel demand is illustrated by yellow colors (pale to dark), and the satisfied pellet demand is shown by green colors (pale to dark). Table 5 shows the different types and capacities of the technologies that are optimally installed in the biorefineries.

The social impacts of the bioenergy supply chain

This part investigates the effect of the bioenergy network on the territories (the society), where bio-refineries are installed. Therefore, first, the social profit (𝕾 𝒘,𝒃 ) of the generated job w (the work hours) in territory b is defined as follows: 𝕾 𝒘,𝒃 = 𝜫 𝒘,𝒃 × 𝕿 𝒘,𝒃 ; 𝕿 𝒘,𝒃 = (𝕳 + 𝕵) (P1)

Where 𝜫 𝒘,𝒃 is the social impact of the installed biorefinery that was defined in Section 3.1. 𝕳 is the number of work hours (hourly work) within the job category w required to operate technology a. In other words, 𝕳 is corresponding to the work hours that are required to converting the biomass to bioenergy and biofuel (hours/tonne of biomass).

𝕵 is the number of work hours (salaried work) within job class w required to operate technology a (hours/year). 𝕵 is corresponding to the work hours that are required to keeping the bio-refinery open during the year (e.g., administrative staff). These work hours (Hourly-wage work and salaried work) can change by changing the type of technology and its capacity. Table 4 shows the assumptions of these work hours. They come from reports made by [START_REF] Heat | Power catalog of technologies[END_REF] and also from consulting with the Renewable Energy and Energy Efficiency Organization. In addition, work hours that are required for pyrolysis and pellet technologies come from different studies [START_REF] Campbell | A feasibility study guide for an agricultural biomass pellet company[END_REF][START_REF] Razm | A two-phase sequential approach to design bioenergy supply chains under uncertainty and social concerns[END_REF].

Next, given the optimal design of the bioenergy supply chain obtained in Section 5.1, the social profit of the bioenergy SC can be calculated using equation (P1) and Table 5. If the social impact (𝜫 𝒘,𝒃 ) in (P1) is substituted by value 1, the number of jobs is obtained. As shown in Table 5, the optimal design obtained from the model causes social profit (up to 48.84) by generating 262 jobs. These jobs have a high impact on the society, because they are generated in the territories with two features: i) high vulnerability in an economic crisis, and ii) high unemployment rate.

Conclusion

In this paper, a model was proposed to design bioenergy supply chains under social consideration. Unemployment rate and vulnerability to changes during an economic crisis were considered as social concerns. The areas that are mostly exposed to these social issues were chosen as initial potential locations for installing the bio-refineries. The applicability of the developed model was shown through a case study. The results demonstrated that the proposed approach leads to the generation of a large number of job positions which has an important impact on the social development of these regions.

In the future studies, first, initial capacities can be considered, or instead of using old technologies, the new technologies can be considered in the model in order to increase the production yield (efficiency). Second, it would be interesting to consider product recycling inside the biorefinery after generating the products. Finally, carbon pricing policies or decisions corresponding to the carbon trading can be added to the model.

Fig. 2 .

 2 Fig. 2. Initial suggested locations for installing the bio-refineries

Fig. 3 .

 3 Fig. 3. Optimal structure of the bioenergy supply chain.

Table 1 .

 1 The bioenergy SC literature vs. this study

	Article	Modeling ap-		Social sustainability		Final products
		proach
		Mathematical Programming MoMILP MILP MINLP	Objective function	jobs with high impacts High unemploy-ment rate (index) High vulnerability in an economic crisis (index)	Other indices	Electricity	Pellet	Heat	Biofuel (bioethanol, bio-oil, biodiesel)
	[13]	X	3						X
	[14]	X	2		food				X
					versus
					fuel
	[15]	X

X [16] X 1 X [17] X 2,3 X [5] X 2 X [18] X 1 X [9] X 3 X [19] X 2 X [20] X 1 X Proposed model X 1 X X X X X X1= minimizing (expected) total cost/annual cost/unit cost. 2= maximizing (expected) total profit/annual profit/annual income/net cash. 3= maximizing (expected) net present value


Gustavo Galleani
email: gugalleani@yahoo.com.br

Alain Abou Khalil

Lionel Canioni

Marc Dussauze

Evelyne Fargin

Thierry Cardinal
email: thierry.cardinal@icmcb.cnrs.fr

Andrea S S De Camargo

Fluorine and sodium depletion followed by refractive index modification imprinted on fluorophosphate glass surface by thermal poling

Keywords: glass, thermal poling, fluorophosphate, refractive index modification 1

INTRODUCTION

Thermal poling is a very powerful technique for local modification of optical, electrical and chemical properties in glass surface. [START_REF] Dussauze | Thermal Poling of Optical Glasses: Mechanisms and Second-Order Optical Properties[END_REF] It comprises in employing a dc electric field below the glass transition temperature (Tg) and cooling the glass before removing the dc bias developing an increase of mobility of charge carriers, mainly alkali and alkaline-earth cations [START_REF] Delestre | Towards second-harmonic generation micropatterning of glass surface[END_REF][START_REF] Dussauze | Correlation of large SHG responses with structural characterization in borophosphate niobium glasses[END_REF][START_REF] Guimbretìre | Correlation between second-order optical response and structure in thermally poled sodium niobium-germanate glass[END_REF][START_REF] Dussauze | Enhanced Raman scattering in thermally poled sodium-niobium borophosphate glasses[END_REF][START_REF] Clare | A Comparison of the structural role of Na+ network modifying cations in sodium silicate and sodium fluoroberyllate glasses[END_REF] and also some anionic species, as first considered in 1963 by Von Hippel et al, [START_REF] Hippel | Photocurrent, space-charge buildup, and field emission in alkali halide crystals[END_REF] being responsible for the creation of a expended layer of few hundred of nanometers up to several micrometers depending on the experimental parameters. [START_REF] Luo | Large second-harmonic signal in thermally poled lead glass-silica waveguides[END_REF] This process induces at the anode side depletion of cations, structural reorganization, [START_REF] Malakho | Second-harmonic generation in sodium and niobium borophosphate glasses after poling under field-assisted silver ions anodic injection[END_REF][START_REF] Poirier | Second Harmonic Generation in Sodium Tantalum Germanate Glasses by Thermal Poling[END_REF] change of the surface reactivity, [START_REF] Dussauze | Accurate Second Harmonic Generation Microimprinting in Glassy Oxide Materials[END_REF][START_REF] Lipovskii | 2D-structuring of glasses via thermal poling: A short review[END_REF] wettability and modification in surface potential, [START_REF] Lind | Modifying the surface wetting behavior of soda-lime silicate glass substrates through thermal poling[END_REF] modifications of the index and induced second-order nonlinear response (change in optical properties). [START_REF] Karam | The effect of the sodium content on the structure and the optical properties of thermally poled sodium and niobium borophosphate glasses[END_REF][START_REF] Brennand | Planar waveguides in multicomponent glasses fabricated by field-driven differential drift of cations[END_REF] Surface patterning of those modifications have been recently demonstrated using structured electrodes. [START_REF] Alvarado | Patterning of the Surface Electrical Potential on Chalcogenide Glasses by a Thermoelectrical Imprinting Process[END_REF][START_REF] Lepicard | Micro-structuring the surface reactivity of a borosilicate glass via thermal poling[END_REF] Indeed, glasses treated by thermal poling have prominent potential for applications in materials with multiple functionalities as photonic integrated circuits for instance. Looking more specifically to the modifications of the optical properties, it is in consequence possible to develop in a glass by thermal poling, arrays of microlenses, micro-optic devices such as waveguides and diffraction gratings [START_REF] Lepicard | Long-lived monolithic micro-optics for multispectral GRIN applications[END_REF].

The patterning of these modifications can be done using structured electrodes that act like stamps to control the surface properties in the micrometer scale, paving the way for design of these functional elements. [START_REF] Dussauze | Spatial and geometry control of second order optical properties in inorganic amorphous materials[END_REF] Upon thermal poling, mobile ions present in the glass composition drift to the cathode, resulting in a sodium depleted zone on the anodic side. In most glass compositions described in the literature, the mobility of sodium cations and oxygen are the main drifted species responsible for the compositional changes, even if the thermal poling is also reported to promote migration of bigger alkalis, such as potassium or alkaline earth ions such as calcium but in a less extent. [START_REF] Janicki | Ellipsometry-based study of poled glass refractive index depth profiles[END_REF] Hence, the resulting poled layer is mainly composed by the network-former compounds and shows different chemical and physical surface properties as compared to the original glass. Thermal poling effect has been substantially studied in several oxide glasses such as silica glass [START_REF] Myers | Large second-order nonlinearity in poled fused silica[END_REF], silicates [START_REF] Raskhodchikov | Mechanism of Thermal Charge Relaxation in Poled Silicate Glasses in a Wide Temperature Range (From Liquid Nitrogen to Glass Melting Temperature)[END_REF][START_REF] Redkov | How Does Thermal Poling Produce Interstitial Molecular Oxygen in Silicate Glasses?[END_REF], phosphates [START_REF] Dussauze | Structural rearrangements and secondorder optical response in the space charge layer of thermally poled sodium-niobium borophosphate glasses[END_REF], tellurides [START_REF] Ferreira | Second harmonic generation in poled tellurite glass[END_REF][START_REF] Narazaki | Effect of poling temperature on optical second harmonic intensity of sodium zinc tellurite glasses[END_REF], heavy metal oxides [START_REF] Poirier | Second Harmonic Generation in Sodium Tantalum Germanate Glasses by Thermal Poling[END_REF], as well as chalcogenide glasses. [START_REF] Guo | Large second-order nonlinearity in thermally poled Ge-Sb-Cd-S chalcogenide glass[END_REF][START_REF] Dussauze | Photosensitivity and second harmonic generation in chalcogenide arsenic sulfide poled glasses[END_REF] These works have assisted to better understand the mechanism happening in the development of properties in different kind of glasses. The atomic structure of the glass adjusts the compositional changes that take places during the treatment by poling, rearranging the "parent" glass structure with local coordination changes, condensation reactions and injecting protons or other counter-ions to maintain the charge-balance requirements to the glass network.

On the other way, oxyfluoride glasses have not been yet used, to the best of our knowledge, as materials in thermal poling. The role of conductive fluorine ions migration in the optical and structural properties is still unknown and could be explored to promote great changes in glass properties. One promising system is the use of fluorophosphate glasses as host for the development of optical devices from thermal poling. They offer the promise of emerging the profitable optical properties of fluoride with the advantageous mechanical properties of oxide glasses. They have been extensively described in literature for photonic applications, taking its optical properties advantages. [START_REF] Ebendorff | Fluoride phosphate and phosphate glasses for photonics[END_REF][START_REF] Zou | Transmission loss characteristics of fluorophosphate optical fibers in the ultraviolet to visible wavelength region[END_REF] In this context, the aim of this work is on engineering fluorophosphate glass material to tailor their optical properties upon thermal poling. The migration of not only cationic species, but also fluorine upon poling treatment is explored and the impact on the glass surface property and structure is investigated. A particular attention is targeted on the impact of the thermal poling using a microstructured electrode on the refractive index modification.

EXPERIMENTAL PROCEDURE

Oxyfluoride vitreous sample with the molar composition 50Na(PO3)2-20GdF3-20BaF2-10CaF2

(mol %), labelled as NPGF, was prepared by the conventional melt-quenching method. To avoid fluorine losses, powder precursors were mixed and melted at 950 C in a capped platinum crucible in an electric furnace for 20 min. Finally, the melted glass was cooled rapidly in a brass mold kept at 20

C below the glass transition temperature (Tg = 290 ⁰C) and kept in a resistive oven for 4 h to remove residual stresses.

Prior poling, the glass transition temperature was determined by differential scanning calorimetric (DSC) measurements performed using a TA Instruments 2910 calorimeter at a heating rate of 10 C.min -1 and placing glass pieces of around 20 mg into the Al pans under nitrogen atmosphere and Raman measurements were done on a spectrometer HR800 (Horiba/Jobin Yvon) in backscattering mode using a continuous laser operating at 532 nm was used.

Thermal poling was then performed under a N2 flow of 6 L/min. Polished glass sample was heated at 250 C and the DC voltage was raised to 1.2 kV with a 350 V/min rate and left at these conditions for 30 min. The glass was then cooled down to room temperature before removing the dc bias. The anode consisted of a home-prepared patterned ITO electrode facing the sample. In the present work, they were made by laser ablation of a 100 nm thick indium tin oxide (ITO) layer (8-12 Ω sq -1 ) deposited on a microscope glass slide using a nanosecond YAG laser source at 1064 nm with a scanning speed of 1000 mm/s at pulse energy of 150 J. The pattern was inscribed on the electrode placed on a microscope stage controlled by a software. The final ITO coated microscope slide was then composed of alternating conductive and nonconductive areas. After structured, the ITO free side of the electrode was covered by a gold conductive thin film to ensure conductivity. A piece of silicon wafer was used on the cathode side, and a soda lime glass was used in the middle of the silicon and the sample to avoid reduction of the sample at the cathode.

Secondary ion mass-spectrometry (SIMS) evaluations were performed on a PHI Adept 1010 dynamic SIMS system. Excitation of secondary ion emission was made by a focused primary ion beam of Cs + at 2 KeV. For the negative secondary ions, sample was biased to -30 keV and for positive ions + 30 kV. A qualitative distribution of elements in poled sample was examined by etching of the surface with ion beam. An area of 300 x 300 m 2 was scanned. Etching rate was obtained from the profundity of the crater measured by optical profilometry Infrared reflectance spectra were recorded in reflection mode prior and after poling treatment to achieve details on the structural modifications related with the charge migrations in a Vertex 70V spectrometer in a primary vacuum. The equipment is equipped with a deuterated triglycine sulfate detector, a globar type source and a mid/far infrared range beam splitter. Kramers-Krönig analysis were used to calculate the absorbance spectra from these spectra. [START_REF] Kamitsos | Infrared reflectance spectra of lithium borate glasses[END_REF] Atomic Force Microscopy (AFM) measurements were performed at the samples by an AFM Dimensions Icon (Bruker) using a PFQNE-AL cantilever.

The refractive index change ∆n was evaluated using a commercial quantitative phase imaging QWLSI sensor, SID4Bio by PHASICS in transmission mode placed on a microscope. An intensity image and a phase image showing the optical path difference (OPD) produced by the transmitted light is the final output of the wave front sensor.

RESULTS AND DISCUSSION

Bulk glass characterization

The oxyfluoride vitreous sample 50NaPO3-20GdF3-20BaF2-10CaF2 obtained using classical melt quench technique and the thermal properties were analyzed by DSC and is shown in Prior to imprinting, an ITO patterned electrode has been prepared. An illustrative representation of the prepared electrode is depicted in Figure 2. After laser irradiation, electrode structuring simply consisted of a 1 cm 2 surface area, which half of the electrode was non-structured (in yellow in the figure 2, with conductive area) for macroscopic measurements, and the other half consists of structures of 30 μm x 30 μm of ablated square (white in the figure 2), distanced by 10 μm conductive lines. The structured electrode is then used as "stamps" during the imprinting poling process. The thermal poling was then performed under nitrogen at 250 C and 1.2 kV to avoid proton injection. After 30 minutes of poling, the glass sample was cooled to 25 C and the initial applied electric field removed. Figure 3a shows, using white light microscopy, that the structured pattern was faithfully transposed to the glass poled surface by leaving a clear optical contrast at the surface. In Figure 3b, the degradation of the ITO electrode used as anode after the poling process was observed.

This observation could give the first indication of a hypothesis of possible fluorine loss during the process within the anode side leading to the corrosion of the ITO layer, but further characterization and studies need to be done for prove such hypothesis. where the real trend of SIMS total ion signal can be drawn.

In Figure 5, the depth profile of positive and negative charges is inferred as counts per second signal as a function of surface depth. For both charge profile, the first few tens of seconds are because of charge distribution stabilization in the SIMS method, no real trend can be drawn up to 25 nm. The depth of the crater during the total exposure of the glass surface during the SIMS thickness has been determined at 400 nm by measuring the optical profilometry, as shown in supporting information (Figure S1). The evolution of the concentration profile of the positive species Na, Gd, P and Ba are shown in Figure 5a. One can notice that the sodium depletion occurs on a depth of about ~180 nm, assuming that the sputtering speed remains constant during the whole SIMS analysis, while the relative concentration of the Gd and Ba increases. Regarding the phosphorus cation, the profile appears expected to create an oxygen enriched glass layer in the 180 nm poled region with a low concentration of fluorine anions and sodium cations inducing a possible large chemical and physical property variations.

Structural evolution of the glass after poling.

The poling procedure induces clear modification of the surface material composition on a depth up to 180 nm. Such modification is expected to produce important changes of the glass network which can be explored using IR vibrational spectroscopy.

Prior poling, Raman and Infrared spectroscopy have been conducted as reported in Figure 6a and 6b (black curve), respectively. Raman spectra of oxyfluoride phosphate glasses with similar composition (NaPO3-BaF2-YF3) have been previously studied and the structure described in literature.

[38] The Raman spectrum is formed mainly of a band at ~1040 cm -1 which is assigned to PO3 symmetric stretching modes of P2(O,F)7 dimers, in Q (1) units, and a band at 1110 cm -1 , assigned to PO2 stretching modes of metaphosphate groups. The band near 900 cm -1 suggest the existence of P-F bonding, [START_REF] Galleani | Rare-earth doped fluoride phosphate glasses: structural foundations of their luminescence properties[END_REF][START_REF] Galleani | BiF3Incorporation in Na/Ba Mixed Network Modifier Fluoride-Phosphate Glasses: Structural Studies by Solid-State NMR and Raman Spectroscopies[END_REF] and the band observed near 740 cm -1 is assigned to the P-O-P symmetric stretching mode of bridging oxygen between two phosphate tetrahedral in short chains, such as Q (1) species. At lower frequency, the bands in the region 450-650 cm -1 are typically bands of alkaline-earth bonded to fluorine species observed in pure fluoride glasses. [START_REF] Poulain | Multicomponent fluoride glasses[END_REF] At 540 cm -1 i.e. the band has been assigned to NaF. [START_REF] Brow | Effect of fluorine on the structure of phosphate glass[END_REF] Regarding the infrared spectroscopy, the bands in the region 1000-1250 cm -1 were assigned to νasPO3 2-(PO3F, Q 1 ) units, normally present at 1090 cm -1 for fluorophosphate glasses and νasPO2 - (PO3/2F, Q 2 ) units at 1150 cm -1 . At 900 cm -1 the band is due to νasym(POP) stretching vibration of Q 1 in chains and/or P-F bonding and at 735-745 cm -1 of POP ring stretching mode. At 500 cm -1 the band is generally to ν(POP) for phosphates, [START_REF] Rai | Effect of gamma irradiation on the structure and valence state of Nd in phosphate glass[END_REF] while for fluoride glasses can be assigned to the stretching modes of M-F bonds. [START_REF] Djouama | Structural investigation of fluorophosphate glasses by 19F, 31P MAS-NMR and IR spectroscopy[END_REF] Some of these network chains bring negative charges that are balanced by Na + charges, so it is expected modifications at these units after sodium depletion, but not only, since fluorine also due a role in these units, possibly causing modifications on it.

The structure of our NPGF glass as described by Raman above consists in the most part of Q 1 units in P2(O,F)7 dimers and the presence of some metaphosphate groups (Q 2 units). It is known that sodium ions dominantly interact with phosphate units rather than fluoride species in fluorophosphate glasses. [START_REF] Zhang | Precipitation of Er 3+ -doped Na5Y9F32 crystals from fluorophosphate glasses: An advanced solid-state NMR spectroscopic study[END_REF][START_REF] Galleani | BiF3Incorporation in Na/Ba Mixed Network Modifier Fluoride-Phosphate Glasses: Structural Studies by Solid-State NMR and Raman Spectroscopies[END_REF][START_REF] Strojek | Medium-range order in sodium phosphate glasses: A quantitative rotational echo double resonance solid state NMR study[END_REF] Therefore, it is reasonable to believe that sodium departures will affect mainly these phosphate units. The fluorine anions can be present in different anionic units as Gd-F, Na-F, Ba-F, but also be present in different Q 1 linked to phosphorus, forming P-F bonds, denoted as Q 1 1F, Q 1 2F, which means one Q 1 unit having one F and two F, respectively, which has been proven to exist in previously studies by 19 F{ 31 P}double-resonance and 2D 31 P{ 19 F} HMQC experiments by nuclear magnetic resonance in similar glasses, showing that F ions have bond connectivity with these phosphorus species. [START_REF] Zhang | Precipitation of Er 3+ -doped Na5Y9F32 crystals from fluorophosphate glasses: An advanced solid-state NMR spectroscopic study[END_REF][START_REF] Galleani | BiF3Incorporation in Na/Ba Mixed Network Modifier Fluoride-Phosphate Glasses: Structural Studies by Solid-State NMR and Raman Spectroscopies[END_REF] To get information about the structural modifications after poling, a comparison of absorptions obtained by IR reflectance was used. IR in reflection mode allows to probe submicron surface layer of the thermal poled sample and get information about these modifications, depicted in Figure 6b. The spectra were acquired at the anode side prior poling (in black) and after poling (in red) between 400 and 1500 cm -1 . The crucial region with modifications in this section is ~ 1040 cm -1 . One can see that thermal poling treatment induced a significant decrease of the absorption for the band ~1040 cm -1 , described above to belong to (FPO3 2-) Q 1 units. It is assumed here that the changes are mainly connected to the Na + and F -depletion layer observed by SIMS in Figure 5, which leads to the decrease of the Q 1 units. Previous report of NaPO3(1-x)Fx glasses [START_REF] Brow | Effect of fluorine on the structure of phosphate glass[END_REF] have shown a decrease in the band ~ 1040 cm -1 as the F content in the glass is lower. The extend of modification related to each ion is difficult at this point, since both are present at these units.

Refractive index modification by thermal poling

To better characterize the optical changes induced by the imprinted structure in the poled glass, the variation of the refractive index Δn is an essential parameter, and for that, the SID4Bio wave front sensor by PHASICS was used. The phase image of the imprinted structure in NPGF glass is shown in The optical path difference between the virgin glass and the zone affected by the poling treatment can be written as follow:

𝑂𝑃𝐷 = 𝑂𝑃 𝑥 -𝑂𝑃 1 , (1)
𝑂𝑃 𝑥 = 𝑛 𝑎𝑖𝑟 . 𝑑 𝑥 + 𝑛 𝑥 . 𝑑 𝑝 ,

𝑂𝑃 1 = 𝑛 𝑔𝑙𝑎𝑠𝑠 . (𝑑 𝑝 + 𝑑 𝑥 ), (2)
where nair is the refractive index of air (nair = 1), nglass is the refractive index of our NPGF glass (nglass = 1.53), dp is the poled layer thickness determined by SIMS (180 nm), dx is the topological change profile obtained by AFM and nx is the refractive index of the poled layer. The OPD is the optical phase difference between the optical phase in the poled zone (OPx) and the outside of the poled zone (OP1)

Based on the average depth and phase contrast profile obtained for the same region of the imprinted poled glass, the refractive index profile could be obtained and the Δn profile (Δn = nxnglass) is shown in Figure 7. A positive Δn up to ~0.06 was observed in the poled region, showing that the departure of fluorine and sodium impact the refractive index. Considering that a reduction of the sodium content should tend to decrease the refractive index, as observed in previously reported thermal poled sodium borophosphate glasses, [START_REF] Karam | The effect of the sodium content on the structure and the optical properties of thermally poled sodium and niobium borophosphate glasses[END_REF] and that the fluorine departure is expected to have the opposite effect. [START_REF] Oto | Fluorine doped silica glass fiber for deep ultraviolet light[END_REF] Since the fluorine anions has much less polarizability than the oxygen, injection of fluorine in silica glass has been used to produce step-index fibers i. e., [START_REF] Oto | Resistivity for deep-UV laser irradiation in fluorine doped silica glass fiber[END_REF][START_REF] Tsukuma | Refractive index, dispersion and absorption of fluorine-doped silica glass in the deep UV region[END_REF] being the fluorine responsible to decrease the refractive index. Similar approach was also responsible for refractive index decrease in phosphate glasses. [START_REF] Brow | Effect of fluorine on the structure of phosphate glass[END_REF] Therefore, in our case, as we observe fluorine departure (ejection of fluorine in the poled layer), the opposite effect is expected, so the fluorine departure observed after poling treatment is considered to be the main phenomenon driving the refractive index change in our glass.

The formation of a rich oxygen layer during poling is then definitely promoting a highest refractive index when compared to the original oxyfluoride glass. These changes can be correlated with structural rearrangements upon poling. Following sodium departure linked to Q 1 phosphate groups, charge compensation is done by the formation of additional P-O-P linkages. The role of fluorine ions departure on the structural change is more complex and conclusions could not be unraveled, since fluorine can be present in different anionic units bonded to phosphorus or the other ions present in glass matrix. Therefore, the question remains open and future work is necessary to comprehend the role of fluorine drift and its impact on the chemical reactivity of the glass surface for instance since the oxide layer is expected to show different resistance to water as compared to the oxyfluoride "virgin" glass.

CONCLUSION

In this work, the use of thermal poling in fluorophosphate glass as an imprinting process to induce optical modification has been demonstrated. It was described not only cationic migration towards anode (sodium in our case), but also fluorine anionic migration towards cathode from the glass network occurs upon poling treatment, forming a controlled oxide richer layer under the glass surface in contact with the anode compared to the original glass. The distribution of sodium and fluorine in the glass were analyzed and revealed that a 180 nm layer with less sodium and fluorine was created.

It has been shown that using micro-structured electrodes it was possible to faithfully transfer the electrode pattern to the glass poled surface through the electrostatic imprint process during poling treatment. Topological changes have been also observed with a surface variation of -60 nm of amplitude and the phase contrast image analysis has allowed evidencing that a positive n variation of 0.06. These results open huge perspectives for implementing flat micro-optical components under the fluorophosphate glass surface with high refractive index contrast by controlling cations and anions migrations.

Figure 1 .

 1 The sample exhibit a glass transition temperature (Tg) of 290 C obtained from the onset point of the DSC curve and an onset crystallization temperature (Tx) of 380 C. The thermal stability against crystallization corresponding to the temperature difference between Tg and Tx is ΔT = 90 C, high enough to obtain large pieces of glasses suitable for the thermoelectrical polarization investigation.

Figure 1 . 3 . 2 .

 132 Figure 1. DSC curve of the oxyfluoride NPGF glass.

Figure 2 .

 2 Figure 2. Schematic representation of the patterned electrode used in this work. The contact and noncontact zones are represented in yellow and white, respectively.

Figure 3 .Figure 4 .

 34 Figure 3. (a) Micrography of the surface imprinted micropattern of the NPGF glass after thermal poling treatment. (b) Microscope image of the structured electrode surface degraded after poling.

Figure 5 .

 5 Figure 5. SIMS profile from the anode entering inside the glass for positive (a) and negative (b) ions on the NPGF oxyfluoride glass after poling treatment. The vertical dot line represents the initial point

  constant. Concerning the anions profile shown in figure5b, on can observe an increase of the oxygen and the phosphorus relative concentration while the proportion of fluorine decreases also on a depth about 180 nm. The relative concentration evolution of hydroxyls appears fairly constant along the whole thickness investigated. Based on the SIMS investigation, a clear depletion of sodium and fluorine is observed, which results in an increase in the relative concentration of the less mobile ions (Ba, Gd, P) which form the resulting glass network in the poled affected thickness. Based on the profile investigation, one can propose that the sodium ions have been carried along the electric field from the anode to the cathode while the fluorine anions went through the inverse route. The observed degradation of the ITO electrode after poling shown in Figure3is in line with such hypothesis and the attack of the ITO layer by the fluorine species. The whole process occurring during the poling is then

Figure 6 .

 6 Figure 6. (a) Raman spectra of the NPGF oxyfluoride glass. (b) Comparison of absorption coefficients () obtained by the reflectance spectra Kramers-Kronig transformation of the NPGF glass prior (black curve) and after (red curve) poling recorded under vacuum. Asterisks highlights the positions with spectral modifications.

Figure 7a and displaysFigure 7 .

 7 Figure7aand displays a positive optical path difference (OPD) in the poled zone (darker areas in the image). The value of ∆n was calculated by dividing the OPD by the thickness (l) of the imprinted region (∆n = 𝑂𝑃𝐷⁄l). Considering the thickness (l) of the poled layer determined above by SIMS and the optical profilometry (FigureS1), the qualitative value of Δn of the imprinted structures was determined. In order to evaluate the refractive index change, the surface topology (by AFM) in the poled region has been considered and compared to the phase contrast image showed in Figure7.

Acknowledgments

Authors would like to acknowledge the Brazilian funding agencies FAPESP -Fundação de Amparo à Pesquisa do Estado de São Paulo (Project N. 2013/07793-6, CEPID program); CAPES -Coordenação de Aperfeiçoamento de Pessoal de Nível Superior; CNPq -Conselho Nacional de Desenvolvimento Científico e Tecnológico (Universal project 130562/2018-1). GG personally acknowledges funding by FAPESP grant 2019/12442-4 for a postdoctoral fellowship.


Elias Al Sarraf

Basile Radisson

Christophe Almarcha

Bruno Denet

Joel Quinard

Elias Al-Sarraf

Joël Quinard

Flame instability in a Hele-Shaw cell: thickness effect

Introduction

Hydrodynamic flame instabilities (see the recent book [START_REF] Clavin | Combustion waves and fronts in flows[END_REF] for a review) can be important for turbulent burning, particularly at high pressure [START_REF] Fogla | [END_REF] and there are some hopes that they can be simulated using a model equation such as the Sivashinsky nonlinear equation [3] for the flame front propagation. However precise experimental studies of the hydrodynamic instability are relatively scarce, and even the propagation of a laminar flame in a tube can lead to a very complex non-linear evolution if the tube is large enough [4]. It has been suggested in [5] and first obtained experimentally in [START_REF] Abid | Ronney Spring Technical Meeting[END_REF], to study flames in a quasi two dimensional configuration in a Hele-Shaw cell. We will show here that this configuration allows quantitative measurements of the growth rates of the instability and of the nonlinear evolution, and study the effect of the cell thickness on the instability properties of propane air flames.

Specific Objectives

.

We study here, following the paper [START_REF] Almarcha | [END_REF], where qualitative results in this configuration were presented, flames propagating in a Hele-Shaw burner where the flame dynamics is more easily recorded with a high-speed camera than in a cylindrical burner.

The burner consists of two glass plates 0.50 m wide and 1.5 m high, separated by a gap width of 4.7 or 3.8 mm. After each run, the airflow is opened and maintained until the tube walls have cooled to ambient temperature. The flow of combustible, (propane in this article), is then adjusted to the desired equivalence ratio and a 2D inverted V-flame is ignited at the top of the burner with a lighter. Closing the valve at the bottom of the burner then stops the flow and the downward flame propagation is recorded thanks to a high-speed camera (Fig. 1).

It will be shown in this paper that it is possible in this configuration to measure the growth rates of the instability for different equivalence ratios and cell thicknesses.

These measurements lead to important parameters of the non-linear modelling with the Sivashinsky equation: a cut-off wavelength λc and a characteristic growth rate σ of the most unstable perturbation with wavelength λmax~2λc. Let us recall that in the literature, the growth rates of the Darrieus-Landau instability have only been measured twice, first by Clanet and Searby for very lean propane air flames [8] by using an acoustic field to create initially a plane flame, then by Truffaut and Searby [9] for rich propane air flames by studying the development of the instability on an oblique flame. The present Hele-Shaw configuration leads to another type of measurement, but naturally the thickness of the cell plays a role in the value of the growth rates we obtain, we discuss here these effects.

Figure 1: Experimental set-up

Results and Discussion

Experiments are performed with propane-air mixtures whose laminar flame speeds in a tube are known. Introducing a plate with periodic indentations a few centimeters above the burner exit, it is possible to force the flame response at the desired wavelength, (wave vector K=2π/λ). The initial flame contour appears relatively flat (Fig. 2), then Fourier analysis of the successive records of the flame contour can give access to the linear growth rate of the excited perturbations of the flame (the slope of the linear regime in Fig. 3). Using this procedure, we obtain the growth rate for different wavelengths of perturbations (we will show figures of growth rate versus wave vector for different thicknesses in Figures 5 and6). Let us note however that it is difficult to measure growth rates for wave vectors very far from the most amplified wave vector, which is observed anyway even without specific forcing. This method for measuring growth rates does not work in all cases, the inverted V flame at the top of the burner is cellular itself for rich propane air mixtures (equivalence ratio 1.3 for instance), so the above method is not available in this case. For propane, the results will be reported for lean or stoichiometric propane air mixtures.

Having obtained the growth rate of the instability, this growth rate is an essential ingredient of a nonlinear modelization of the flame. The Sivashinsky equation [3] essentially describes the normal propagation of a front submitted to an instability corresponding to the growth rate we have just measured. We show in Figure 4 in this configuration. In the pioneering paper by Joulin and Sivashinsky suggesting to use this experimental configuration [5], these authors analyzed (unfortunately without including Markstein lengths) two effects which modify the usual Darrieus Landau instability in tubes. The first effect is the Saffman Taylor effect: the dispersion relation is modified by friction terms, which increase the growth rate. The second effect is the role of heat losses, studied in a low gas expansion case. Another type of study are the two papers by Kang Baek and Im [10] [11], which also study friction and heat losses effects, but numerically. We could summarize the results of these papers in the following simplified way; both Joulin Sivashinsky and Kang Baek Im argue that the Saffman Taylor effects are small for a typical value of the thickness.

For the heat losses, Kang Baek Im obtain, with an effective two dimensional analysis, that heat losses reduce the growth rate for large Lewis number, and increase the growth rate for low Lewis number.

In the propane air case of the present paper, we have obtained results, as explained before, for lean or stoichiometric mixtures. So the Lewis number we have are typically larger than one. We give growth rates for two thicknesses (4.7 mm and 3.8 mm) and for two values of the equivalence ratio (0.9 and 1). In Figure 5 is shown the case equivalence ratio 0.9. The red, upper curve corresponds to a thickness 4.7 mm, the green lower curve to 3.8 mm. It can be seen that the growth rate is lower for a smaller thickness, suggesting, in agreement with theory, that the Saffman Taylor effects are small and that the heat losses is the most important effect, leading in a Hele Shaw cell for lean propane to lower growth rates.

In Figure 6 is shown the stoichiometric case, with the same type of curves, red curve 4.7 mm, green curve 3.8 mm. It is seen that the larger thickness always corresponds to a more unstable case for low wavevectors: this would suggest that the effective gas expansion in the cell is lower for a smaller thickness. The situation is less clear for higher wave vectors; it seems that the curve for a smaller thickness decreases more slowly than the 4.7 mm case. This could be interpreted as saying that with heat losses the Markstein number is lower with heat losses, which is also suggested by the solid curves in both Figures 5 and6, which are a fit of the experimental points with the classical dispersion relation of Clavin and Garcia-Ybarra [12] for flames in tubes. Note also the lower effective expansion ratio E (ratio of density on both sides of the flame) in both figures for the smaller thickness.

Conclusions

We have seen in this paper that the Hele-Shaw burner configuration is extremely useful, quantitative results difficult to obtain in 3D have been obtained here, both for the dispersion relation of the hydrodynamic instability and even for the non linear evolution. The growth rates are not completely modified compared to the few measurements we have for 3D flames, however for propane air lean or stoichiometric mixtures, the effective expansion ratio is lower with heat losses, but the Markstein length is also lower. It also seems that in our experiments in a Hele Shaw burner, heat losses effects are larger than Saffman Taylor friction effects.

Figure 2 :

 2 Figure 2: Flame front at successive moments, close to the top of the Hele Shaw cell, showing the linear development of the hydrodynamic instability

Figure 3 :

 3 Figure 3: Amplitude of the Fourier mode versus time, showing the linear regime

  a comparison with experimental results: Fig 4.a, experimental fronts at different time superimposed on the same figure, Fig 4.b evolution given by the Sivashinsky equation, starting from the experimental front highlighted in black. Although not all the features of the experiments can be obtained by the model equation, the agreement is very good on a time of approximately 10 times the characteristic time of the instability (the characteristic time is the inverse of the growth rate of the most unstable wavenumber). The cusps on the different fronts correspond to the red points and the width of the domain shown in Figure 4 is 16 cm.

Figure 4 :

 4 Figure 4: Non-linear evolution (flame fronts at different times) of the instability for an equivalence ratio of 0.9 and a Hele-Shaw thickness of 3.8 mm Fig 5.a: experiment, Fig 5.b Sivashinsky equation,

Figure 5 :

 5 Figure 5: Growth rate of the instability versus wavevector for propane air flames with equivalence ratio of 0.9 and a Hele-Shaw thickness of 4.7 mm (red) and 3.8 mm (green). Solid curves: fit with a Clavin Garcia dispersion relation (expansion ratio E, Markstein number Ma).

Figure 6 :

 6 Figure 6: Growth rate of the instability versus wavevector for propane air flames with equivalence ratio of 1.0 and a Hele-Shaw thickness of 4.7 mm (red) and 3.8 mm (green). Solid curves: fit with a Clavin Garcia dispersion relation (expansion ratio E, Markstein number Ma).

Acknowledgements

We are grateful to Guy Joulin for many stimulating discussions. This work was supported by the French National Research Agency (project PDF) under agreement and it has been carried out in the framework of the Labex MEC (ANR-10-LABX-0092) and of the A*MIDEX project (ANR-11-IDEX-0001-02), funded by the "Investissements d'Avenir" French Government Program, managed by the French National Re-search Agency (ANR).