Maria Ponomar

Valentina Ruleva

Veronika Sarapulova

Natalia Pismenskaya

Victor Nikonenko
email: v_nikonenko@mail.ru

Alina Maryasevskaya

Denis Anokhin

Dimitri Ivanov

Jeet Sharma

Vaibhav Kulshrestha

Bruno Ameduri

Structural Characterization and Physicochemical Properties of Functionally Porous Proton-Exchange Membrane Based on PVDF-SPA Graft Copolymers

Keywords: Conductivity, diffusion permeability, energy production and storage, ion transport, 39 proton-exchange membranes, fuel cell, graft copolymer, electrochemical characterization, porous 40 structure

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Sustainable development of the modern society is closely connected to efficient and safe production and usage of energy. Mankind is constantly searching for new clean sources of energy based on concepts that are ecologically and economically appropriate for the long-term future. Polymer electrolyte membrane fuel cells (PEMFCs) can generate electricity using hydrogen (or other fuel). Polymer electrolyte membrane water electrolyzers (PEMWEs) can generate hydrogen. Coupled together, PEMFCs and PEMWEs can form the basis of an efficient green hydrogen zero-carbon technology for energy production and storage [START_REF] Pan | A Review of Membranes in Proton Exchange Membrane Fuel Cells: Transport Phenomena, Performance and Durability[END_REF][2][START_REF] Sun | Hybrid Inorganic-Organic Proton-Conducting Membranes Based on SPEEK Doped with WO3 Nanoparticles for Application in Vanadium Redox Flow Batteries[END_REF]. It is noted that the main features of such systems enlist low operating temperature, high energy-conversion efficiency, low emission, quiet operation and easy scale-up [START_REF] Pan | A Review of Membranes in Proton Exchange Membrane Fuel Cells: Transport Phenomena, Performance and Durability[END_REF][START_REF] Wang | Technological Status, and Fundamentals of PEM Fuel Cells -A Review[END_REF]. Proton exchange membrane is a major component in these devices and channelizes the conduction of protons from the anode to the cathode.

Numerous studies and review papers have been devoted to the study of PEM [START_REF] Pan | A Review of Membranes in Proton Exchange Membrane Fuel Cells: Transport Phenomena, Performance and Durability[END_REF][START_REF] Prater | Polymer Electrolyte Fuel Cells: A Review of Recent Developments[END_REF][START_REF] Ogungbemi | Fuel Cell Membranes -Pros and Cons[END_REF][START_REF] Neburchilov | A Review of Polymer Electrolyte Membranes for Direct Methanol Fuel Cells[END_REF][START_REF] Kusoglu | New Insights into Perfluorinated Sulfonic-Acid Ionomers[END_REF][START_REF] Talukdar | Comparative Investigation into the Performance and Durability of Long and Short Side Chain Ionomers in Polymer Electrolyte Membrane Fuel Cells[END_REF][START_REF] Peighambardoust | Review of the Proton Exchange Membranes for Fuel Cell Applications[END_REF][START_REF] Ahmad | An Overview of Proton Exchange Membranes for Fuel Cells: Materials and Manufacturing[END_REF][START_REF] Kayumov | Ammonium Form of Nafion Plasticized by Dimethyl Sulfoxide[END_REF] and suggest that the characteristics of the PEM has a significant effect on the performance and durability of the PEMFCs. Among all commercial samples for the PEMFC applications, the most used membranes are perfluorosulfonic acid (PFSA) due to its stability, long-term performance, mechanical strength and low conduction resistance [START_REF] Safronova | Mechanical Properties and Influence of Straining on Ion Conductivity of Perfluorosulfonic Acid Nafion®-Type Membranes Depending on Water Uptake[END_REF][START_REF] Moukheiber | Investigation of Ionomer Structure through Its Dependence on Ion Exchange Capacity (IEC)[END_REF]. Standard reference PFSA used in energy conversion systems is Nafion® membrane, developed by the DuPont Company, which consists of an aliphatic perfluorinated backbone with ether-linked side chains bearing sulfonated cation exchange sites. However, despite all the advantages of the Nafion -like PFSA membranes, there are several challenges viz dehydration induced inoperability at high temperatures, gas/fuel crossover, high cost of materials and production of harmful wastes [START_REF] Ogungbemi | Fuel Cell Membranes -Pros and Cons[END_REF][START_REF] Mu'min | Electrospun Phosphonated Poly(Pentafluorostyrene) Nanofibers as a Reinforcement of Nafion Membranes for Fuel Cell Application[END_REF][START_REF] Hickner | Alternative Polymer Systems for Proton Exchange Membranes (PEMs)[END_REF]. Hence, the use of complex fluorine chemistry involved in the PFSA PEM fabrication method is not only the reason for the high stability in oxidative and reductive conditions of these membranes, but also for their high price and environmental hazards [START_REF] Peighambardoust | Review of the Proton Exchange Membranes for Fuel Cell Applications[END_REF]. Noteworthy, that cost of the membrane is an important point because the PEM material is one of the major contributors (along with catalysts in these systems) to the cost of the membrane electrode assembly [START_REF] Du | Recent Advances in Electrode Design Based on One-Dimensional Nanostructure Arrays for Proton Exchange Membrane Fuel Cell Applications[END_REF]. These shortcomings and the need for environmentally friendly and cheap power generation systems have initiated a worldwide research effort to develop alternative PEMs for fuel cells.

Today, the alternate membranes designs to Nafion® are partially fluorinated membranes, membranes with hydrocarbon polymer matrixes, inorganic-organic hybrid membranes, acid-base complexes and grafting membranes by irradiation [START_REF] Ogungbemi | Fuel Cell Membranes -Pros and Cons[END_REF][START_REF] Peighambardoust | Review of the Proton Exchange Membranes for Fuel Cell Applications[END_REF][START_REF] Hickner | Alternative Polymer Systems for Proton Exchange Membranes (PEMs)[END_REF]. Introducing additives in the membrane, i.e. ionic liquids [START_REF] Chen | Enhanced Performance of Ionic-Liquid-Coated Silica/Quaternized Poly(2,6-Dimethyl-1,4-Phenylene Oxide) Composite Membrane for Anion Exchange Membrane Fuel Cells[END_REF][START_REF] Elumalai | Phosphonate Ionic Liquid Immobilised SBA-15/SPEEK Composite Membranes for High Temperature Proton Exchange Membrane Fuel Cells[END_REF][START_REF] Arias | Hybrid Membranes of Sulfonated Poly Ether Ether Ketone, Ionic Liquid and Organically Modified Montmorillonite for Proton Exchange Membranes with Enhanced Ionic Conductivity and Ionic Liquid Lixiviation Protection[END_REF][START_REF] Hooshyari | Novel Composite Membranes Based on PBI and Dicationic Ionic Liquids for High Temperature Polymer Electrolyte Membrane Fuel Cells[END_REF] and inorganic compounds [START_REF] Singh | PEO Nanocomposite Polymer Electrolyte for Solid State Symmetric Capacitors[END_REF][START_REF] Bae | Asymmetric Silica Composite Polymer Electrolyte Membrane for Water Management of Fuel Cells[END_REF][START_REF] Wang | Advance Fuel Cells Using Al2O3-NNaAlO2 Composite as Ion-Conducting Membrane[END_REF][START_REF] Munavalli | Development of Novel Sulfonic Acid Functionalized Zeolites Incorporated Composite Proton Exchange Membranes for Fuel Cell Application[END_REF][START_REF] Ozden | Evaluation of Sulfonated Polysulfone/Zirconium Hydrogen Phosphate Composite Membranes for Direct Methanol Fuel Cells[END_REF][START_REF] Kudashova | Physicochemical Properties and Performance Characteristics of Perfluorinated Membranes Bulk Modified with Platinum during Operation in Proton Exchange Membrane Fuel Cell[END_REF] is used to improve mechanical strength, thermal stability, ionic conductivity, water behavior and other properties of the PEM. Detailed review on the effects of some dopants on PFSA membrane behavior can be found in Ref. [START_REF] Safronova | Approaches to the Modification of Perfluorosulfonic Acid Membranes[END_REF].

Among this variety of polymers and dopants, partially fluorinated membranes based on the PVDF copolymers attract special attention [START_REF] Liu | Progress in the Production and Modification of PVDF Membranes[END_REF][START_REF] Kang | Application and Modification of Poly(Vinylidene Fluoride) (PVDF) Membranes -A Review[END_REF][START_REF] Rajput | Dehydrofluorinated Poly(Vinylidene Fluoride-Co-Hexafluoropropylene) Based Crosslinked Cation Exchange Membrane for Brackish Water Desalination via Electrodialysis[END_REF][START_REF] Li | Improved Surface Property of PVDF Membrane with Amphiphilic Zwitterionic Copolymer as Membrane Additive[END_REF][START_REF] Das | Partial Sulfonation of PVdF-Co-HFP: A Preliminary Study and Characterization for Application in Direct Methanol Fuel Cell[END_REF][START_REF] Mahmoud | High Hydroxide Ion Conductivity with Enhanced Alkaline Stability of Partially Fluorinated and Quaternized Aromatic Copolymers as Anion Exchange Membranes[END_REF][START_REF] Fontananova | Effect of Additives in the Casting Solution on the Formation of PVDF Membranes[END_REF]. Such membranes are cheaper, easy to manufacture and flexible in changing properties [START_REF] Liu | Progress in the Production and Modification of PVDF Membranes[END_REF][START_REF] Kang | Application and Modification of Poly(Vinylidene Fluoride) (PVDF) Membranes -A Review[END_REF]. By varying the synthesis conditions, different exchange capacity, water content, porosity and degree of cross-linking of such materials can be achieved. Significant improvement of the propertied of the PVDF-based membranes intended for direct methanol fuel cells can be achieved by incorporating sulfonated Fe3O4@SiO2 nanorods [START_REF] Ranjani | Sulfonated Fe3O4@SiO2 Nanorods Incorporated SPVdF Nanocomposite Membranes for DMFC Applications[END_REF] or sulfonated graphene oxide [START_REF] Hariprasad | SPVdF-HFP/SGO Nanohybrid Proton Exchange Membrane for the Applications of Direct Methanol Fuel Cells[END_REF] into the PVDF structure. In addition, membranes with PVDF copolymers matrix can be suitable not only for PEMFC applications but also in electrodialysis, electro deionization, membrane electrolysis, etc. [START_REF] Rajput | Dehydrofluorinated Poly(Vinylidene Fluoride-Co-Hexafluoropropylene) Based Crosslinked Cation Exchange Membrane for Brackish Water Desalination via Electrodialysis[END_REF][START_REF] Sarapulova | Transport and Electrochemical Characteristics of CJMCED Homogeneous Cation Exchange Membranes in Sodium Chloride, Calcium Chloride, and Sodium Sulfate Solutions[END_REF][START_REF] Ran | Ion Exchange Membranes: New Developments and Applications[END_REF][START_REF] Hossain | Preparation of Porous Poly(Vinylidene Fluoride) Membranes with Acrylate Particles for Electrodialysis Application[END_REF][START_REF] Zuo | Desalination of Water with a High Degree of Mineralization Using SiO2/PVDF Membranes[END_REF][START_REF] Prakash | High Efficiency Direct Methanol Fuel Cell Based on Poly(Styrenesulfonic) Acid (PSSA)-Poly(Vinylidene Fluoride) (PVDF) Composite Membranes[END_REF].

This work reports systematic studies on the synthesis and pivotal physicochemical/ion transport properties of a PVDF-based sulfonated proton exchange membrane.

The electrochemical attributes of the synthesized fluorinated membranes were compared with those of commercially available PFSA-based PEMs and cation exchange membranes with sulfonated PVDF matrix designed for electrodialysis application. This comparison allows to determine the most promising applications of fabricated membranes and outline ways of their further improvement.

Results and discussion

In this research, polyvinylidene fluoride-based membranes PEM-RCF and PEM-RCF-2 were synthesized. The chemical modification of PVDF to prepare membranes was achieved as follows: first, dehydrofluorination of PVDF in basic medium [START_REF] Rajput | Dehydrofluorinated Poly(Vinylidene Fluoride-Co-Hexafluoropropylene) Based Crosslinked Cation Exchange Membrane for Brackish Water Desalination via Electrodialysis[END_REF] led to PVDF containing double bond in the backbone (D-PVDF). Such double bond could react with 3-sulfopropyl acrylate (SPA) and 1H, 1H, 2H-perfluoro-1-hexene (PFH) un-der radical initiation to lead to the membranes [START_REF] Sharma | Spectroscopic Evidence and Mechanistic Insights on Dehydrofluorination of PVDF in Alkaline Medium[END_REF]. Figure 1 illustrates the reaction steps and synthetic strategy adopted for PEMs fabrication.

Structural Characteristics of the Membranes under Study

The perturbations in melting behaviour and crystallinity of functionally modified PVDF via grafting of 3-Sulfopropyl acrylate and 1H, 1H, 2H-Perfluoro-hex-1-ene were studied using DSC technique. Consequently, the melting of PVDF phase is observed for PEM-RCF (Figure 2(a)), and for PEM-RCF-2 (Figure 2(b)), with an onset temperature of 121 °C and 127 °C, respectively. The reduction of melting temperature in comparison with pure PVDF might be caused by disturbance of the crystalline phase of PVDF by small fraction of grafted side chains according to Flory's approach [START_REF] Flory | Theory of Crystallization in Copolymers[END_REF]. The enthalpy is 18.2 J/g for PEM-RCF and 17.2 J/g for PEM-RCF-2. Given the melting enthalpy of 104.5 J/g for 100% crystalline PVDF [START_REF] Nakagawa | Annealing Effects in Poly(Vinylidene Fluoride) as Revealed by Specific Volume Measurements, Differential Scanning Calorimetry, and Electron Microscopy[END_REF], the degree of crystallinity are estimated to be 17% and 16% for PEM-RCF and PEM-RCF-2, respectively. The indexation of the WAXS peaks results in the identification of the α-phase of PVDF [START_REF] Martins | Electroactive Phases of Poly(Vinylidene Fluoride): Determination, Processing and Applications[END_REF] , as shown in Figure 3(a). The peaks are broadened due to the small lateral crystal size (5-6 nm). The SAXS curve for the PEM-RCF-2 membrane, as shown by the red line in Figure 4(b), exhibits a significant peak L1=Lc+La=7.9 nm, characteristic of the lamellar stacking in PVDF, which includes alternating crystalline (Lc) and amorphous (La) layers [START_REF] Prakash | High Efficiency Direct Methanol Fuel Cell Based on Poly(Styrenesulfonic) Acid (PSSA)-Poly(Vinylidene Fluoride) (PVDF) Composite Membranes[END_REF][START_REF] Sharma | Spectroscopic Evidence and Mechanistic Insights on Dehydrofluorination of PVDF in Alkaline Medium[END_REF]. The absence of this peak in PEM-RCF, indicated by the red line in Weight fraction of absorbed water WSAXS can be estimated by assuming a typical scenario where the thickness of the crystalline and amorphous layers in lamellar stacks is equal, i.e., Lc=La=0.5L1. Taking into account the densities of the amorphous and α-crystal phase of PVDF of 1.73 and 1.92 g/cm 3 [START_REF] Dallaev | Brief Review of PVDF Properties and Applications Potential[END_REF], respectively, one can estimate WSAXS as:

21 21 () () w S A X S w c c a a LL W L L L L          (1)
where w, c and a represent the densities of water, the crystalline and the amorphous phase of PVDF, respectively. Water content in PEM-RCF-2 after treatment in sulfuric acid, as calculated from equation [START_REF] Pan | A Review of Membranes in Proton Exchange Membrane Fuel Cells: Transport Phenomena, Performance and Durability[END_REF], is approximately 7% by weight. In contrast, a similar treatment of PEM-RCF does not lead to any noticeable changes in the membrane morphology (Figure 4(a), black line). During heating and subsequent crystallization, the lamellar morphology of both membranes becomes more pronounced, i.e. the intensity of the main interference peak, or the long period, increases, while its position shifts to 13.5 and 15.2 nm for PEM-RCF and PEM-RCF-2, respectively (Figure 4(a)(b), blue lines).

Since the recrystallization of the membranes occurs in a dry state, the increase of the long period can be associated with lamellar thickening of α-crystals. This structural change could negatively influence water uptake and proton diffusion across the amorphous regions, showing a direct correlation between crystal and supramolecular structures and the transport properties of the membranes under study. SEM images of both PEM-RCF membranes (Figure 5) reveal porous structure. As evidenced, PEM-RCF is more porous, with variation of pore diameters in the range of 56-138 nm and a pore density of 1.4×10 9 cm -2 . These factors might have a great impact on the transport characteristics. Table 1 provides a summary of the structural information on the membranes. 1 in the swollen state in equilibrium with 0.05M HCl solution

Structural characteristics of the membranes used for comparison

The transport properties of ion-exchange membranes (ionic conductivity, permselectivity and some other) are controlled by their porous structure, including pore size distribution, their direction in space and possible agglomeration, and the physicochemical characteristics of the pore walls [START_REF] Kreuer | Transport in Proton Conductors for Fuel-Cell Applications: Simulations, Elementary Reactions, and Phenomenology[END_REF][START_REF] Nikonenko | Ion Transfer in and Through Charged Membranes: Structure, Properties, and Theory[END_REF]. In order to get an idea of the porous structure of the designed membranes, their transport and electrochemical properties were compared with the corresponding properties of some commercial membranes.

Two perfluorosulfonated membranes, Nafion® 117 (Dupont) and MF-4SK (Plastpolymer, Russia) are chosen as usual references of PEM for fuel cells. These membranes consist of an aliphatic perfluorinated backbone and ether-linked side chains with sulfonated cation exchange sites. The pore structure is schematized as a system of hydrated clusters with a diameter of about 4 nm, which are connected by channels with 1 nm in diameter and length [START_REF] Gierke | The Morphology in Nafion Perfluorinated Membrane Products, as Determined by Wide-and Small-Angle x-Ray Studies[END_REF]. The relatively large clusters (the aggregates of fixed sulfo groups with mobile counterions) condition high ionic conductivity, and the presence of narrow channels creates electrostatic barrier for the anion transport, which ensures high permselectivity of these membranes [START_REF] Mauritz | State of Understanding of Nafion[END_REF]. The channels ensure the percolation [START_REF] Larson | Percolation Theory of Residual Phases in Porous Media[END_REF] of the membrane, the degree of which can be different in regard of counterions and co-ions [START_REF] Zhang | The Trade-off between Membrane Permselectivity and Conductivity: A Percolation Simulation of Mass Transport[END_REF]. According to the standard contact porosimetry data [START_REF] Divisek | A Study of Capillary Porous Structure and Sorption Properties of Nafion Proton-Exchange Membranes Swollen in Water[END_REF][START_REF] Berezina | Characterization of Ion-Exchange Membrane Materials: Properties vs Structure[END_REF][START_REF] Kononenko | Porous Structure of Ion Exchange Membranes Investigated by Various Techniques[END_REF], most of the pores contained in these membranes have a radius less than 10 nm. However, there are also pores with a radius of up to 50 nm, but there are no macropores with a radius higher than 100 nm.

Cation-exchange CJMC-3 and CJMC-4 membranes (ChemJoy Polymer Materials, Hefei, China) are chosen for the comparison, since their ion exchange matrix is based on polyvinylidene fluoride (PVDF) functionalized with sulfonic -3

SO

 groups, and crosslinked with an aromatic agent, similar as the novel membranes under study. Membranes of this type contain nanometer-scale pores. In addition, the crosslinking degree of the CJMC-3 ion-exchange matrix is relatively low, it contains polyester reinforcing fiber, which causes the presence of macropores localized at the matrix/reinforcement fiber interface [START_REF] Sarapulova | Transport and Electrochemical Characteristics of CJMCED Homogeneous Cation Exchange Membranes in Sodium Chloride, Calcium Chloride, and Sodium Sulfate Solutions[END_REF].

A track-etched polyethylene terephthalate membrane with the provisional name TEM#811 (made by the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, Dubna, Russia) [START_REF] Apel | Track-Etching[END_REF][START_REF] Apel | Creation of Ion-Selective Membranes from Polyethylene Terephthalate Films Irradiated with Heavy Ions: Critical Parameters of the Process[END_REF] is added for the comparison, since it contains through pores with a radius of 20 nm and pore density of 5×10 9 (estimated by SEM [START_REF] Nichka | Modeling the Conductivity and Diffusion Permeability of a Track-Etched Membrane Taking into Account a Loose Layer[END_REF])

comparable with the pores of the PEM-RCF membrane (Table 1). The pore walls contain cation-exchange hydroxyl and carboxyl groups within an ion-conducting gel loose layer of thickness of a few nm.

The thicknesses of Nafion® 117, MF-4SK, CJMC-3 and CJMC-4 membranes are relatively close: 230 m [START_REF] Safronova | New Cation-Exchange Membranes Based on Cross-Linked Sulfonated Polystyrene and Polyethylene for Power Generation Systems[END_REF], 190-230 m [START_REF] Berezina | Electrotransport Properties and Morphology of MF-4SK Membranes after Surface Modification with Polyaniline[END_REF], 185 m [START_REF] Sarapulova | Transport and Electrochemical Characteristics of CJMCED Homogeneous Cation Exchange Membranes in Sodium Chloride, Calcium Chloride, and Sodium Sulfate Solutions[END_REF] and 128 m (our data), respectively; while that of TEM#811 is significantly less: 10 m [59].

Transport Characteristics

Some characteristics of the membranes under study are presented in Table 2. Comparison of the membranes in Table 2 shows that the PVDF-based membranes (the PEM-RCF one and the CJMC ones) are characterized by a relatively high water content despite the fact that the PEM-RCF and the CJMC-3 display low exchange capacities. Only the PEM-RCF-2 membrane having an extremely low exchange capacity is distinguished by a low W value, according to the SAXS result, water in this sample is localized in the amorphous regions and probably does not form continuous channels. Nevertheless, there is a maximum amount of water per mole of fixed groups for both membranes. The high water content in the manufactured sample PEM-RCF can be partly caused by a fairly high density of macropores and their large radius. However, even when assuming that these pores are through, a simple evaluation shows that their volume fraction is insignificant and amounts to about 8%. It is more likely that the high water content is due to the presence of hydrophilic fragments specially introduced into the polymer matrix, which contain oxygen and sulfonate groups (Figure 1). These hydrophilic fragments should contribute to the formation of a system of nanopores similar to that in Nafion® and other PEM [START_REF] Tsang | Alternative Proton Exchange Membranes by Chain-Growth Polymerization[END_REF][START_REF] Deng | Membrane Architectures for Self-Humidifying Proton Exchange Membrane Fuel Cells[END_REF], which contains ionic clusters and channels (Figure 6 PEM-RCF sample turns out to be an order of magnitude higher than that of PEM-RCF-2 sample, which evidently is due to the low exchange capacity of the latter. The temperature dependences of the membrane conductivity presented in Arrhenius coordinates have classical linear shape [START_REF] Yurova | Nafion / Surface Modified Ceria Hybrid Membranes for Fuel Cell Application[END_REF][START_REF] Cappadonia | Conductance of Nafion 117 Membranes as a Function of Temperature and Water Content[END_REF][START_REF] Damay | Transport Properties of Nafion TM Composite Membranes for Proton-Exchange Membranes Fuel Cells[END_REF][START_REF] Kopitzke | Conductivity and Water Uptake of Aromatic-Based Proton Exchange Membrane Electrolytes[END_REF] (Figure 8).

The diffusion permeability, P, of both membranes decreases as the NaCl concentration of the external solution increases. Apparently, this decrease is due to the fact that with increasing external solution concentration, the membranes lose water. The latter is caused by a decrease in the difference in osmotic pressure between the internal and external solutions (the "swelling pressure" [START_REF] Helfferich | Ion Exchange[END_REF]), which leads to shrinkage of the membrane matrix and narrowing the pores [START_REF] Helfferich | Ion Exchange[END_REF]. The decrease of P in the case of PEM-RCF-2 is very strong, at the NaCl concentration of 1.5 M the value of P of this membrane is 50 times lower than that of the PEM-RCF membrane. It seems that the channel conductance regarding the co-ion (Cl -) becomes so low that the co-ion percolation of the PEM-RCF-2

membrane is lost at a certain external solution concentration.

Comparison of transport and electrochemical characteristics of synthesized and commercial membranes

The activation energy of conductivity, found according to Equation (9) (Section 3.3) from the ln * -1/T dependences (Figure 8(b)) is equal to 8.6 kJ mol -1 (for the PEM-RCF membrane) and 9.7 kJ mol -1 (for the PEM-RCF-2 membrane), which is close to that of 9.4 kJ mol -1 for Nafion® 117 as obtained by Yurova et al. [START_REF] Yurova | Nafion / Surface Modified Ceria Hybrid Membranes for Fuel Cell Application[END_REF]. Note that the activation energy of proton transfer in aqueous solutions of acids including the case where such a solution is in a macropore is about 5 kJ/mol [START_REF] Yaroslavtsev | Высокомолекулярные соединения[END_REF]. It is known that the activation energy for conductivity is equal to the sum of the activation energy for proton migration and half the energy for the formation of defects in the membrane. It decreases in the presence of large pores, the proton transport in which occurs by the Grotthuss mechanism [START_REF] Paddison | Proton Conduction Mechanisms at Low Degrees of Hydration in Sulfonic Acid-Based Polymer Electrolyte Membranes[END_REF][START_REF] Voropaeva | Transport Properties of Hydrous-Silica-Modified MF-4SK Membranes[END_REF].

On the contrary, the activation energy of conductivity increases if the transferred protons are located at a large distance from each other (low concentration of fixed groups) in pores of small radius. A similar effect is observed also, if the pores are isolated [START_REF] Liu | An Overview of the Proton Conductivity of Nafion Membranes through a Statistical Analysis[END_REF].

Our data indicate that the sizes of the pores, which are formed in the synthesized membranes in conditions of a relatively dilute bathing solution (0.05 M HCl), are comparable to the pore sizes formed in the Nafion®-117 membrane.

The conductivity of the PEM-RCF membrane in the H + -form is about three times higher than that in Na + -form (Figs. 7 and8). At 25 °C and when the bathing solution concentration is 0.05 M, in the first case, the PEM-RCF conductivity is about 3.0 mS cm -1 , while in the second case, 1.0 mS cm -1 . A similar ratio is observed for Nafion® membranes. For example, at 25 °C and close concentrations, the conductivity of a Nafion® 425 membrane is 16 mS cm -1 , and 3.6 mS cm -1 , in H + -and Na + -form, respectively [START_REF] Demina | Effect of Counter-and Co-Ions on the Structural Transport Parameters of Sulfoacid Cationite Membranes[END_REF].

For Nafion® 117 this ratio is slightly higher: 51 mS cm -1 [69] and 9.3 mS cm -1 [START_REF] Stenina | Ion Mobility in Nafion-117 Membranes[END_REF] in 0.05 M HCl and 0.05 M NaCl solutions, respectively. The higher conductivity of cationexchange membranes in the H + -form in comparison with the Na + -form is due to the higher mobility of H + ions. However, the increase in membrane conductivity (3-5 times) is lower than the increase in ion mobility in free solution: the mobility/diffusion coefficient of H + in aqueous solutions is about 7 times higher than that of Na + . In the literature, two mechanisms of proton transport in cation-exchange membranes are discussed [START_REF] Kreuer | Transport in Proton Conductors for Fuel-Cell Applications: Simulations, Elementary Reactions, and Phenomenology[END_REF][START_REF] Nikonenko | Ion Transfer in and Through Charged Membranes: Structure, Properties, and Theory[END_REF]: vehicular motion, which is the movement of the center of mass of proton in an aqueous environment, and the Grotthuss mechanism, which is proton shuttling through hydrogen bonded network. The contribution of the Grotthuss shuttling, which determines the high mobility of H + ions, increases with increasing water content in a cationexchange membrane. The shape of the concentration dependences of the conductivity of the membranes presented in Figure 9 can be explained using the microheterogeneous model [START_REF] Zabolotsky | Effect of Structural Membrane Inhomogeneity on Transport Properties[END_REF]. This model considers the membrane as a microheterogeneous swollen medium, which consists of two phases: i) The intergel phase is an electrically neutral solution, which is located in the center of the macro-and mesopores. It is assumed that this solution is identical to the external equilibrium solution; ii) The gel phase combines all the other components of the membrane: it is a microporous medium containing the polymer chains with fixed groups (sulfonate groups in our case); the charge of the fixed groups is compensated by a charged aqueous solution filling the hydrophilic domains of the membrane. There are mobile counterions (carrying a charge of the same sign as the fixed ions) and, in smaller quantities, co-ions (carrying the opposite sign of charge). The gel phase involves also inert filler (if any) and reinforcing fabric (if any). The conductivity of the gel phase,  , to a first approximation, is considered a constant value, which depends on the counterion diffusion coefficient, , in this phase, and on its exchange capacity, :

Conductivity and diffusion permeability

2 ii z D Q F RT   (2)
The value of is related to the exchange capacity of the membrane Q:

1 / Q Q f  (3)
where f1 is the volume fraction of the gel phase. The volume fraction of the intergel phase f2=1-f1.

In the case where (1) the solution concentration is close to the concentration of the iso-conductance point (where the conductivities of the membrane and solution are equal), and (2) the membrane contains approximately an equal number of pores, which are connected between them in parallel and in series (regarding the direction of the current flow), the conductivity of the membrane ( ), that of the gel phase ( ) and the electrically neutral solution in the intergel spaces (κ) are related to each other by the following equation:

1 2 * f f     (4)
Using Equation (4), it is not difficult to find the values of f2 and f1, as well as , if the experimental results are presented in the vs.

(or vs.

) coordinates, since , when assuming that the electrolyte solution conductivity is proportional to its concentration C.

It follows from equation ( 4) that in dilute solutions the main contribution to the membrane conductivity comes from the conductivity of the gel phase. As the concentration of the external solution increases, the conductivity of the intergel space makes an increasing contribution. Moreover, the higher the value of f2, the more significant this contribution is, which manifests itself in an increase in the slope of the vs. (or vs.

) dependence. Indeed, in the region of dilute solutions (about 0.1 M), the conductivity of membranes increases in the series TEM#811≤PEM-RCF<CJMC-4≈MF-4-SK<CJMC-3<Nafion® 117 (Figure 9(a)), that is, symbatically with the value of the exchange capacity of swollen membranes (Table 2). An increase in the external solution concentration leads to an increase in conductivity of all membranes. The highest growth

As Table 2 shows, the f2app values are the highest in the case of TEM#811 and PEM-

RCF having large open pores. In contrast, the perfluorosulfonated membranes do not have large pores, and the values of this parameters is close to 0.1. The CJMC-4 membrane based on PVDF, similarly, has a small f2app value. However, its homologue, the CJMC-3 membrane, has an increased f2app value, which should be due to the presence of macropores between the polyester reinforcing fiber and the membrane matrix.

If the conductivity of ion-exchange membranes (IEMs) is controlled by counterions, then the diffusion permeability is controlled by co-ions. When an electrolyte diffuses through a membrane, counterions cannot leave the membrane without being accompanied by co-ions due to the electroneutrality conditions. The co-ion concentration, A c , is low in ion-exchange membranes due to the Donnan exclusion effect: co-ions are electrostatically pushed out by the fixed ions [START_REF] Helfferich | Ion Exchange[END_REF]. However, co-ions are excluded only from the gel phase containing the fixed ions. They are not pushed out from the central parts of the macro-and mesopores, where their concentration is the same as in the external solution.

The co-ion concentration in the gel phase, under the first approximation, is inversely proportional to the fixed ions concentration, i.e. to the exchange capacity:

2 D A K c C Q  (6)
Equation ( 6) is obtained from the Donnan equation [START_REF] Helfferich | Ion Exchange[END_REF] in the case of 1:1 electrolyte under the condition that C<< . The value determines the degree of electrostatic (Donnan) exclusion of co-ions from the gel phase; a low value of facilitates the sorption of co-ions, hence, advantages the electrolyte diffusion through the membrane. Another parameter, which controls the membrane diffusion permeability is f2. The latter determines the membrane volume fraction of the in which the electrostatic exclusion of coions is absent. Indeed, Figure 9(b) shows that among the studied membranes, two groups can be distinguished: a group (PEM-RCF, TEM#811 and CJMC-3 membranes) with low (Q) and high f2 (f2app), which is characterized by elevated values of P, and a group (CJMC-4, MF-4SK and Nafion® membranes) with elevated (Q) and low f2 (f2app), which is endowed with a high diffusion permeability.

With increasing concentration, the effect of co-ion exclusion weakens, since its driving force is the Donnan potential (the difference in potential in the membrane gel phase and in the equilibrium solution), which is close to the ratio C/ [START_REF] Helfferich | Ion Exchange[END_REF]. Thus, an increase in the solution concentration should lead to an increase in the membrane diffusion permeability. Indeed, this trend can be seen for all compared membranes, except for the PEM-RCF (Figure 9(b)). The diffusion permeability of this membrane decreases as the external concentration increases. Thus, an increase in the solution concentration should lead to an increase in the diffusion permeability of the membranes. Indeed, this trend can be seen for all compared membranes, with the exception of the PEM-RCF. As we wrote in Section 3.3, the reason for such a dependence in the case of PEM-RCF is a decrease in the degree of membrane percolation with respect to co-ions. This decrease is due to the loss of water by the membrane upon contact with a concentrated solution: shrinkage of the membrane results in narrowing the pores, which hinders the ion transport, primarily, the co-ion transport.

The reason for this behavior of the PEM-RCF membrane is the low concentration of fixed groups, causing the appearance of singularities in its structure as compared to conventional IEMs (Figure 6). Since the number of fixed ions in a cluster is almost independent of their average concentration in the membrane, a decrease in their concentration primarily leads to an increase in the distance between clusters [START_REF] Hsu | Ion Transport and Clustering in Nafion Perfluorinated Membranes[END_REF][START_REF] Gebel | Structural Evolution of Water Swollen Perfluorosulfonated Ionomers from Dry Membrane to Solution[END_REF]. Thus, the length of channels in the PEM-RCF membrane should be longer and their radius smaller than the corresponding parameters in such membranes as Nafion® 117 and MF-4SK.

Dehydration of the membrane causes a decrease in swelling and, consequently, a decrease in cluster size, as well as a decrease in the radius of inter-cluster channels [START_REF] Gebel | Structural Evolution of Water Swollen Perfluorosulfonated Ionomers from Dry Membrane to Solution[END_REF].

These structural changes cause a sharp decrease in the diffusion coefficient, especially of co-ions. This phenomenon is due to the fact that along with a decrease in the radius of clusters and channels when contacting with concentrated solutions, there is an increase in the concentration of fixed groups per volume of water sorbed by the membrane [START_REF] Helfferich | Ion Exchange[END_REF][START_REF] Drozdov | The Effects of PH and Ionic Strength on Equilibrium Swelling of Polyampholyte Gels[END_REF][START_REF] Kozmai | A Simple Model for the Response of an Anion-Exchange Membrane to Variation in Concentration and PH of Bathing Solution[END_REF]. As shown in [START_REF] Kamcev | Equilibrium Ion Partitioning between Aqueous Salt Solutions and Inhomogeneous Ion Exchange Membranes[END_REF][START_REF] Geise | Fundamental Water and Salt Transport Properties of Polymeric Materials[END_REF], an increase in the concentration of fixed groups should lead to a stronger electrostatic exclusion of co-ions from the channels, which causes an increase in their resistance against co-ions. The high resistance of some channels may cause them to be completely impermeable to co-ions. The need to search for longer pathways of co-ion transport will lead to a sharp increase in the tortuosity factor, which can also be interpreted as a decrease in the degree of membrane percolation with respect to co-ions. These effects are particularly strong in the case of non-crosslinked polymers, such as the PEM-RCF matrix. Polymer chains of Nafion® 117 and MF4-SK membrane matrix also do not contain additional cross-linking. However, during the manufacturing process, these membranes are subjected to a special temperature treatment that results in the formation of crystallites from the main chains of the polymer. It gives commercial Nafion® 117 and MF-4SK membranes additional rigidity [START_REF] Zawodzinski | A Comparative Study of Water Uptake By and Transport Through Ionomeric Fuel Cell Membranes[END_REF]. Therefore, the influence of external electrolyte concentration on pore size and moisture content is less evident in these membranes. The described phenomenon of membrane shrinkage in concentrated solutions is almost absent in the case of the TEM#811 track membrane, since it is based on hydrophobic material that is not capable of swelling.

Membrane selectivity

An important property of IEM is selectivity with respect to counterion transport, which can be characterized by ("true") ionic transport numbers, (Figure 10). According to equation ( 12) (Section 3.3), in the first approximation when the counterion transport numbers are close to one, the is proportional to the membrane conductivity and inversely proportional to its diffusion permeability. The low ion transport characteristics of the PEM-RCF-2 sample cause a specific shape of its current-voltage curve, which resembles the CVCs of bipolar membranes [START_REF] Wilhelm | Current-Voltage Behaviour of Bipolar Membranes in Concentrated Salt Solutions Investigated with Chronopotentiometry[END_REF]. The current-voltage curves of all other membranes have a shape characteristic of others IEMs obtained in many studies [START_REF] Sarapulova | Transport and Electrochemical Characteristics of CJMCED Homogeneous Cation Exchange Membranes in Sodium Chloride, Calcium Chloride, and Sodium Sulfate Solutions[END_REF][START_REF] Filippov | New Approach to Characterization of Hybrid Nanocomposites[END_REF][START_REF] Akberova | Effect of the Resin Content in Cation-Exchange Membranes on Development of Electroconvection[END_REF][START_REF] Kozaderova | Electrochemical Characteristics of Thin Heterogeneous Ion Exchange Membranes[END_REF][START_REF] Melnikov | Transport Properties of Bilayer and Multilayer Surface-Modified Ion-Exchange Membranes[END_REF][START_REF] Güler | Monovalent-Ion-Selective Membranes for Reverse Electrodialysis[END_REF][START_REF] Krol | Concentration Polarization with Monopolar Ion Exchange Membranes: Current-Voltage Curves and Water Dissociation[END_REF][START_REF] Park | An Approach to Fouling Characterization of an Ion-Exchange Membrane Using Current-Voltage Relation and Electrical Impedance Spectroscopy[END_REF][START_REF] Mishchuk | Concentration Polarization of Interface and Non-Linear Electrokinetic Phenomena[END_REF]. Initial linear region I of the CVCs shown in Figure 11a corresponds to the formation of diffusion layers near the IEM surface, one of which is depleted in ions and the other is enriched. At i<0.9ilim Lev , electric current is transported by electrodiffusion: ions move under the influence of electric potential gradient and concentration gradient. The sloping plateau (region II of the CVC) occurs when there is a deficit of electric charge carriers in the depleted solution layer at the membrane boundary. The electrolyte concentration near the membrane surface approaches zero, which causes a rapid resistance increase. A very small increase in current leads to a significant increase in the potential difference, which results in the appearance of a sloping plateau on the CVC. Further rapid growth of the current (region III in Figure 11(a)) is due to the appearance of new mechanisms of the charge transport. These include (1) electroconvection: the transfer of a volume containing a space electric charge under the action of a potential gradient [START_REF] Rubinstein | Electroconvection at an Electrically Inhomogeneous Permselective Membrane Surface[END_REF], and (2) "water splitting": the generation of H + and OH -ions due to the dissociation of water molecules with the catalytic participation of functional groups of the IEM [START_REF] Zabolotskii | Dissociation of Water Molecules in Systems with Ion-Exchange Membranes[END_REF]. The slope and length of region II are controlled by the rate of these two charge transfer mechanisms, electroconvection and water splitting. There is a critical value of the potential drop (different for each membrane), which corresponds to the onset of intensive electroconvection and/or water splitting.

Electrochemical characteristics

The intersection of the tangents drawn to regions I and II of the CVC gives the value of the experimental limiting current, ilim exp . As can be seen from Figure 11, the ilim exp value for the membranes presented in Figure 11(a) agrees reasonably well with the theoretical estimation of theoretical limiting current density ilim Lev using equation ( 14) (Section 3.3).

The CVC of the PEM-RCF membrane has the same characteristic regions as those of the other IEMs. The difference is that region II is more diffuse, its slope is much larger, and its length is much shorter than that of the other membranes (excluding TEM#811).

Only in the case of PEM-RCF and TEM#811, a negative slope of region III is noted. This slope corresponds to the negative differential resistance of the membrane system: at a small increase in current there is a decrease, rather than an increase, in the potential EO transport through the membrane pores is caused by the action of an external electric force on the space charge localized in the double electric field at the surface of the pore walls. The rate of EO transport increases with increasing potential drop. EO flow through the membrane pores induces a "fresh" more concentrated solution from the bulk solution into the depleted diffusion layer. This "fresh" solution leads to a decrease in the resistance of the membrane system and the negative diffusion resistance. It is possible that PEM-RCF has a small number of through pores, which makes the effect described above possible.

If the concentration of fixed sulfonate groups of the PEM-RCF sample is increased, a quantitative match of its CVC with the corresponding curves obtained for PEM and IEMs can be expected. Improvement of the electrochemical properties of this sample can be achieved by increasing the number of side chains with sulfonate groups during the synthesis process or by filling its macropores with an ionic liquid or solid polyelectrolyte, as demonstrated in previous studies [101-104].

Materials and Methods

Chemicals

In this work, distilled water (electrical conductivity of 3 ± 0.5 μS cm -1 ; pH = 5.5 ± 0. and Azobisisobutyronitrile (AIBN, radical initiator) were supplied from Sigma Aldrich.

Solvents (as dimethyl acetamide, DMAc) for membrane casting were procured from Qualigens Chemical Ltd while common reagents like iso-propyl alcohol (IPA), sodium hydroxide and sodium chloride from B. Hiten chemical distributor. All reagents were used without procession (Except, AIBN, which was recrystallized in ethanol prior to copolymer synthesis).

Membrane Preparation. Synthesis of polyvinylidene fluoride copolymer

The formation of unsaturated site in PVDF is desirable strategy for the copolymerization of monomers viz. 3-sulfopropyl acrylate potassium salt (SPA) and 1H, 1H, 2H-Perfluoro-1-hexene (PFH) and to synthesize the desired copolymers.

a. Dehydrofluorination of polyvinylidene fluoride (PVDF)

The dehydrofluorination of polyvinylidene fluoride (PVDF) was carried out using previous reported method [105]. In brief, a 10 w/v % of vacuum dried PVDF powder was prepared in DMAc solvent. Further, the homogenous solution of PVDF was then subjected to dehydrofluorination using 0.5 M NaOH/isopropyl alcohol (IPA) reagent at During addition of monomers, the relative input ratio of 3-sulfopropyl acrylate potassium salt: 1H, 1H, 2H-Perfluoro-1-hexene was 9:1 w/w %.

Finally, the synthesised copolymers with buff and cream coloured solution texture were allowed to dissolve in dimethylacetamide (DMAc) solvent to prepare a homogenous solution. The obtained copolymer mixture was blade-casted to desired thickness and dried for 24 h to obtain the membrane.

Methods of Membrane Characterization

The morphology and physical properties of the membrane were studied by small (SAXS) and wide angle (WAXS) X-ray scattering, scanning electron microscopy and differential scanning calorimetry.

The SAXS/WAXS measurements were carried out at laboratory Xenocs Xeuss 3.0 system equipped with a GeniX3D copper micro-focus tube operating at 60 kV and 0.59 DSC experiments were performed with a Mettler Toledo DSC 3+ instrument. The protocol was the same for both samples: two heating and cooling runs with the temperature range from -50 to 250 °C and rates equal to 10 K/min, annealing at room temperature for one day and repeating the same heating/cooling runs. STARe software was used to obtain the enthalpies of phase transitions.

Prior to the next measurements, all membrane samples were subjected to standard salt treatment in NaCl solutions [START_REF] Berezina | Characterization of Ion-Exchange Membrane Materials: Properties vs Structure[END_REF].

The contact angles of the membrane were measured by sessile drop method as reported earlier [START_REF] Ponomar | Sessile Drop Method: Critical Analysis and Optimization for Measuring the Contact Angle of an Ion-Exchange Membrane Surface[END_REF]. A drop of distilled water was placed on the surface of the swollen sample and the image was captured with an optical microscope. Then the contact angle of the surface was obtained by image processing. The measurements were repeated at least 10 times at different points of the membrane surface and the values were averaged.

The ion exchange capacity (Q) is determined by the static method [START_REF] Berezina | Characterization of Ion-Exchange Membrane Materials: Properties vs Structure[END_REF]107]. For this purpose, protons of fixed -SO3H groups were replaced with sodium ions using a 0.1 M NaCl solution. Then the amount of removed H + ions was found by titration with a 0.02 M NaOH solution. Q is found as the ratio of the number of moles of the H + ions to the mass of the swollen membrane. Detailed information on this and other physico-chemical methods of membrane characterization can be found in the Supplementary Materials.

Water content (W) of the membranes is found by the gravimetric method. This method consists of drying a swollen wet membrane in the H + form, equilibrated with distilled water, initially of mass mwet, to an air-dry state while weighing on an analytical balance to a constant mass value (mdry). The gravimetric water content is calculated according to the formula:

The ion exchange capacity and water content also provide values for the membrane hydration number (nm, mol H2O / mol -SO3 -) [START_REF] Berezina | Effect of Conditioning Techniques of Perfluorinated Sulphocationic Membranes on Their Hydrophylic and Electrotransport Properties[END_REF], which is the average number of water molecules per functional group. The nm is calculated according to the formula [START_REF] Berezina | Effect of Conditioning Techniques of Perfluorinated Sulphocationic Membranes on Their Hydrophylic and Electrotransport Properties[END_REF][START_REF] Ermakova | Structural and Electrosurface Characteristics of Sulfonated Cation-Exchange Perfluoropolymer Membranes in 1 : 1 Electrolyte Solutions[END_REF]:

m w W n MQ  ( 8
)
where Mw is the molar mass of water (18 g mol -1 ).

The electrical conductivity ( * ) of the membrane was determined by the differential method using a clip-like cell [108,109]. The membrane resistance is determined as the difference between the resistances of the space between the electrodes with the solution and the membrane and only with the solution.

The activation energy of the membrane conductivity is determined by the tangent of the slope of the temperature dependence of  * in Arrhenius coordinates [START_REF] Safronova | New Cation-Exchange Membranes Based on Cross-Linked Sulfonated Polystyrene and Polyethylene for Power Generation Systems[END_REF][START_REF] Cappadonia | Conductance of Nafion 117 Membranes as a Function of Temperature and Water Content[END_REF]110]:

* ln (1 / ) a c t d ER dT   (9)
To obtain the diffusion permeability of the membranes, a two-chamber flow cell

Current-voltage characteristics (CVC) of the membranes were studied in a flowthrough four-chamber cell. The scheme of the cell as well as the principle of its operation are described in [START_REF] Sarapulova | Transport and Electrochemical Characteristics of CJMCED Homogeneous Cation Exchange Membranes in Sodium Chloride, Calcium Chloride, and Sodium Sulfate Solutions[END_REF]. The potential drop across a membrane under study was measured using two silver/silver chloride electrodes connected to the Luggin capillaries. Further relevant details are given in Supplementary materials.

The value of the theoretical limiting current density was calculated by the Lévêque equation obtained within the convection-diffusion ion transport model for a flat channel with an ideally selective membrane [114]:

1 / 3 2 lim 1 .4 7

(1 )

L e v F D z C hV i h t L D        ( 14
)
where D is the electrolyte diffusion coefficient, z+ is the counterion charge number, h is the intermembrane distance, t+ is the electromigration transport number of the counterion in the solution, V is the average linear flow velocity of the solution, and L is the length of the active part of the membrane surface.

All experiments were conducted at a temperature of 25 °C excluding the measurement of the temperature dependence of membrane conductivity.

As for further characterization of the developed membranes, the membranes should be tested for gas permeation and chemical stability, following, for example, the procedure suggested in Ref.

[115].

Conclusions

Using a relatively inexpensive material, an attempt has been made to synthesize a graft copolymer that contains hydrophobic fluorine-containing backbones (polyvinylidene fluoride, PVDF, and Perfluoro-1-hexene, PFH) and hydrophilic side chains (3-Sulfopropyl acrylate, SPA). One of the two synthesized membranes (PEM-RCF) demonstrates properties proper to proton-conducting (Nafion® 117, MF-4SK) and ion-exchange membranes (CJMC-3, CJMC-4). It has a low surface resistance (0.9 Ω cm 2 ), characterized by an activation energy of fixed groups (8.6 kJ mol-1), close to the activation energy of fixed sulfonate groups of the Nafion® 117 membrane (9.4 kJ mol-1), but is inferior to this and other membranes selected for comparison in selectivity. This disadvantage appears to be caused by the relatively small amount of hydrophilic sulfonatecontaining moieties introduced into the copolymer during the synthesis step and formation of regular lamellar stacks of α-crystals of PVDF. These α-crystals act as a barrier to ion transport. In addition, the ion transport and electrochemical characteristics of PEM-RCF are negatively affected by open extended macropores formed in the membrane, probably at the casting manufacturing stage. Eventually, the influence of PFH hydrophobic spacers suggest decrement in ion migration aptitude and reduction in conducting phase since, the structure is dense and occupied by inert copolymer of PVDF and PFH. These shortcomings can be overcome by changing the synthesis conditions, for example by using high boiling dry solvents and the casting of membrane in vacuum environment at very low humidity and/or filling the macropores of the synthesized membrane with cationic ionic liquids or a solid polyelectrolyte such as Nafion®.

Figure 1 .

 1 Figure 1. Synthetic route adopted for PEM-RCF and PEM-RCF-2 preparation. Black colour indicates the hydrophobic component (PVDF and PFH), blue colour indicates the hydrophilic component of the copolymer (SPA). AIBN is azobisisobutyronitrile; IPA is isopropyl alcohol.

Figure 2 .

 2 Figure 2. DSC traces of PEM-RCF (a) and PEM-RCF-2 (b). Red curves represent the first heating cycle, brown curves correspond to the second heating cycle, and blue curves indicate the cooling phase.

Figure 4 (

 4 Figure 4(a), suggests a less ordered structure, potentially enhancing the membrane's transport properties, since proton transport predominantly occurs through the amorphous regions. Interest-ingly, after the treatment of PEM-RCF-2 described in section 3.3, the SAXS peak shifts to smaller angles corresponding to long period L2=9.0 nm because of water absorption into the interlamellar amorphous regions (Figure 4(b), black line).

Figure 3 .Figure 4 .

 34 Figure 3. WAXS diffractogram of the PEM-RCF membrane with peak indexation.

Figure 5 .

 5 Figure 5. SEM surface images of PEM-RCF (a) and PEM-RCF-2 (b).

  ); the latter are filled with an aqueous electrolyte solution. The rather high hydrophilicity of the synthesized polymer is also indicated by the smallest contact angle of the PEM-RCF surface (40 °) among other studied membranes (Table 2). Noteworthy the contact angle of the PVDF-based CJMC-3 membrane is also small despite its low exchange capacity. This small value might be due to the presence of open extended macropores on the surface of CJMC-3 membrane[START_REF] Sarapulova | Transport and Electrochemical Characteristics of CJMCED Homogeneous Cation Exchange Membranes in Sodium Chloride, Calcium Chloride, and Sodium Sulfate Solutions[END_REF].

Figure 6 .

 6 Figure 6. Probable structure of a swollen PEM-RCF membrane. EDL is electrical double layer.

Figure 7 Figure 7 .Figure 8 .

 778 Figure 7 exhibits the concentration dependences of the conductivity and integral diffusion permeability coefficient of the synthesized membranes in sodium chloride solutions. Figure 8 presents the temperature dependences of the conductivity of these membranes in a 0.05M HCl solution.

Figure 9 Figure 9 .

 99 Figure9shows the concentration dependences of conductivity and integral diffusion permeability of the PEM-RCF sample as well as the commercial membranes selected for comparison. Figure10presents the counterion transport numbers in these membranes. We measured the characteristics of the CJMC-4 in this study; the data for other commercial membranes are taken from the literature: Nafion® 117[START_REF] Stenina | Ion Mobility in Nafion-117 Membranes[END_REF], MF-4SK[START_REF] Berezina | Effect of Conditioning Techniques of Perfluorinated Sulphocationic Membranes on Their Hydrophylic and Electrotransport Properties[END_REF], TEM#811 track-etched membrane[START_REF] Sarapulova | Electrochemical Properties of Ultrafiltration and Nanofiltration Membranes in Solutions of Sodium and Calcium Chloride[END_REF], CJMC-3[START_REF] Sarapulova | Transport and Electrochemical Characteristics of CJMCED Homogeneous Cation Exchange Membranes in Sodium Chloride, Calcium Chloride, and Sodium Sulfate Solutions[END_REF].

  in conductivity is manifested by the track-etched TEM#811 membrane and the novel PEM-RCF membrane. Apparently, it is due to the extended relatively large open pores, which have these membranes. It is difficult to use the narrow concentration range in the dilute solution region when measuring conductivity, as required by Equation (4). The requirement of an equal number of parallel and serial connections between the pores is also not always met. Therefore, to quantify the rate of increase in conductivity with increasing concentration, it is convenient to use the apparent volume fraction of intergel solution[START_REF] Sarapulova | Transport Characteristics of CJMAED TM Homogeneous Anion Exchange Membranes in Sodium Chloride and Sodium Sulfate Solutions[END_REF]:

Figure 10 .

 10 Figure 10. Concentration dependence of the counterion transport number in the synthesized membrane PEM-RCF, Nafion® 117 [79], MF-4SK [63], TEM#811 [62], CJMC-3 [38] and CJMC-4; if the data were taken from a reference, it is indicated. The solid lines are guides to the eye. Nafion® 117 and CJMC-4 membranes, which do not contain macropores and apparently have a well-balanced combination of hydrophobic and hydrophilic components of the ion exchange matrix, as well as a sufficiently high exchange capacity, are characterized by a very high selectivity. The combination of these properties ensures an only slight decrease in the selectivity of these membranes with increasing electrolyte concentration in the external solution. The values of counterion transport numbers in the TEM#811 track membrane and the synthesized PEM-RCF sample are more sensitive to external electrolyte concentration. However, in the case of dilute (≤0.1 M) solutions, exceeds 0.9. The transport numbers of the cations should become even greater, approaching one, with further dilution of the solution. Since PEMs in fuel cells are in contact with water, the selectivity of PEM-RCF should not be a barrier to its use in this application.

Figure 11

 11 Figure11shows the current-voltage curves (CVC) of the synthesized samples as well as commercial ion exchange membranes in a 0.05 M HCl solution or in a 0.02 M NaCl solution. The values of current densities are normalized by theoretical limiting current density ilim Lev to offset differences caused by unequal values of diffusion coefficients of H + and Na + cations in solution. For the same reasons, the ohmic resistance of the space between the Luggin measuring capillaries containing the membrane and the unpolarized solution was subtracted from the measured potential differences.

Figure 11 .

 11 Figure 11. Current-voltage characteristics of PEM-RCF sample and commercial ion exchange membranes (the membrane names are indicated near the curves) (a) as well as PEM-RCF-2 sample (b). The CVCs of PEM-RCF, PEM-RCF-2, CJMC-3 and CJMC-4 membrane are measured in 0.05 M HCl solutions, that of Nafion® 117, MF-4SK and TEM#811, in 0.02M NaCl solutions. The black dashed line corresponds to i=ilim Lev . The blue arrows indicate the direction of current sweep during the CVC measurement of the PEM-RCF-2 membrane.

  drop. Such effect could be caused by electroosmotic (EO) transport of solute through open or extended solution pores. The theoretical possibility of sufficiently intense electroosmosis through TEM#811 pores was discussed in our recent publication [100].

  2; 25 °C), solid NaCl of the analytical grade (JSC Vecton), liquid standards HCl and NaOH (JSC Lenreaktiv) were used to prepare solutions. Polyvinylidene fluoride, PVDF (Solef ® , Mn = ⁓ 230,000 and melt flow index = 6-8 g per 10 min; temperature = 230 °C) was purchased from Solvay and dried at 45 °C before chemical modification. The 3-sulfopropyl acrylate (hydrophilic monomer), 1H, 1H, 2H-perfluoro-1-hexene (fluorinated spacer)

27 ± 2

 2 °C for 12 h. Finally, the dehydrofluorination reaction was quenched by precipitating the brown coloured polymer from cold water. To eliminate the interference of any trapped solvent, the dehydrofluorinated PVDF was washed multiple times until free from bound DMAc and the modified PVDF was dried in vacuum at 75 °C for 24 h.b. Synthesis of polyvinylidene fluoride-co-(3-sulfopropyl acrylate) and polyvinylidene fluoride-co-(3-sulfopropyl acrylate)-co-perfluoro-1-hexene copolymerSimple one-pot free radical polymerization was adopted to synthesize copolymer of dehydrofluorinated PVDF and 3-sulfopropyl acrylate potassium salt akin Yadav et al[106]. For the synthesis of polyvinylidene fluoride-co-(3-sulfopropyl acrylate), a 15 w/v % polymer solution of dehydrofluorinated PVDF was prepared at 45 ± 2°C in N2 atmosphere. To this solution, 10 w/v % of 3-sulfopropyl acrylate potassium salt was added and allowed to mix homogenously. Thereafter, the temperature of reaction mixture was set to 80 ± 2°C allowed to further dissolve completely and Azobisisobutyronitrile (radical initiator) was added at 2 mol % of monomer concentration in final reaction mixture. The obtained solution was continued to react for 16 h and the colour changes from pale brown to off white. Finally, the reaction was quenched and allowed to slow dry in vacuum oven for 24 h at 60 °C to yield the desired polyvinylidene fluoride-co-(3sulfopropyl acrylate) copolymer. Furthermore, to understand the influence of fluorinated spacer, the copolymer was fine-tuned and modified. Akin the procedures adopted for polyvinylidene fluoride-co-(3-sulfopropyl acrylate) synthesis, the polyvinylidene fluoride-co-(3-sulfopropyl acrylate)-co-perfluoro-1-hexene copolymer was synthesized.

mA with 1 .

 1 5406 Å wavelength. Samples were placed in an evacuated chamber and illuminated with monochromatic X-rays in transmission geometry. The scattered intensity was recorded using a Dectris Eiger2 1M detector implemented in a long vacuum flight tube at two different sample-to-detector distances of 68 mm and 0.7 m. The accessed q values, with |q| = 4πsin(ϴ)/λ, where ϴ is the Bragg angle and λ -wavelength, cover a range from 0.015 Å -1 to 3.0 Å -1 . The degree of crystallinity of the membranes was estimated from the results of WAXS. 1D diffraction curve was decomposed in IgorPro, WaveMetrics Software. The crystal size was calculated with Scherrer equation from 110 peak. To study the influence of water penetration into hydrophilic domains SAXS measurements were performed for both dry and swollen membranes. The next protocol was used: boiling in milliQ for 6 hours and keeping in 3M H2SO4 at 50°C for 5 hours after.SEM experiments were performed with a Zeiss Crossbeam 550. Membrane samples were attached to carbon tape and examined without sputtering at an accelerating voltage of 1 kV at the accelerating voltage of 1kV.

  was used[111]. The membrane separated two compartments: distilled water was circulated through one of them (I), and a NaCl solution of a given concentration, CII, was pumped through the other (II). Diffusion permeability coefficient, P, is determined based on the rate of ion diffusion transport through the membrane under the concentration gradient between the solution II and distilled water: J is the diffusion flux density, dmb is the membrane thickness.The differential diffusion permeability coefficient, P * , related to concentration CII, is found when knowing the dependence P(CII) [112]: of co-ion (t-* ) in the membranes under study is obtained using the experimental values of  * and P * on the base of the relationship deduced by comparing the Onsager and the Kedem-Katchalsky transport equation systems [112]: R and T are the Faraday constant, gas constant and temperature; t+app is the apparent counterion transport number; g is the activity factor, and C is the electrolyte concentration of the bathing solution (in this study, it varied in the range of 0.1 -1.5 mol L - 1

Table 1 .

 1 Structural characteristics of the PEM-RCF and PEM-RCF-2 membranes.

	Membrane

Degree of crystallinity, % PVDF phase Grain size from XRD, nm Diameter of open extended pores, nm Pore density, pores/cm 2 Membrane thickness, 1 dmb, µm DSC WAXS

	PEM-RCF	17	18	α	5	5 56-138	1.4×10 9	29±2
	PEM-RCF-2	16	19	α	6	5 20-58	2.8×10 8	86±2

Table 2 .

 2 Some physicochemical characteristics of the membranes

	Membrane	Q, mmol g -1 wet	Water content, W, gH2O/gwet, %	nm, mol H2O/mol functional groups	Area resistance, R, Ω cm 2	7 f2app	Contact angle, (wet), grad
	PEM-RCF	1 0.12 ± 0.02	3 26 ± 2	3 122	5 0.9± 0.05	0.81	40 ± 2
	PEM-RCF-2	1 0.08 ± 0.01	3 7 ± 2	3 52	5 571 ± 3	-	-
	TEM#811	1 0.064 ± 0.003 [62]	4 6.5 [59]	4 43 [59]	5 0.3 [62]	0.95 [62]	62 ± 3
	Nafion® 117	1 0.71 [60]	3 14.8 [60]	3 14 [60]	6 0.82 [60]	0.1-0.15 [63]	8 108.1±0.7 [64]
	MF-4SK	2 0.58 [63]	3 16.7 [63]	3 16 [63]	-	0.05 [63]	77.5±2.6 [65]
	CJMC-3	1 0.63 ± 0.05 [38]	4 30 ± 3 [38]	4 27 [38]	5 2.2 ± 0.3 [38]	0.33 [38]	51±2 [66]
	CJMC-4	1

1.2 ± 0.1 4 29 ± 3 4 13 6 2.5± 0.1 0.09 64±

1 [66]

1 -equilibrium exchange capacity (H + was replaced by Na + and titrated); 2 -total exchange capacity (H + directly titrated by OH -); 3 -in H + form; 4 -in Na + form; 5 -in 0.5 M NaCl; 6 -in 0.2 M NaCl; 7 -determined from measurements of electrical conductivity in NaCl (section 2.4); 8 -in dry state. Values obtained in this study are presented in bold.

30, 2022. J.S. acknowledges the financial support from Indo-French Centre for the Promotion of Advanced Research (IFCPAR/ CEFIPRA), University Grant Commission (UGC, File No. 191620048179) and French National Center for Scientific Research (CNRS) for research facilities under the Raman-Charpak Fellowship (RCF) program [OM offer no.: IFC/ /4141/RCF2022/375]. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Acknowledgments: B.A. and the team of authors are grateful to French Fluorine Network.

Funding: A.M., D.A., B.A. and V.N. acknowledge financial support from the Ministry of Science and Higher Education of the Russian Federation within State Contract 075-15-2022-1117 from June

Supplementary Materials: Supporting information on membrane characterization methods can be

Conflicts of Interest:

The authors declare no conflict of interest.


Ilyass Moummad
email: ilyass.moummad@imt-atlantique.fr

Romain Serizel
email: romain.serizel@loria.fr

Nicolas Farrugia
email: nicolas.farrugia@imt-atlantique.fr

PRETRAINING REPRESENTATIONS FOR BIOACOUSTIC FEW-SHOT DETECTION USING SUPERVISED CONTRASTIVE LEARNING

Keywords: Contrastive learning, representation learning, transfer learning, few-shot learning, bioacoustic sound event detection

Deep learning has been widely used recently for sound event detection and classification. Its success is linked to the availability of sufficiently large datasets, possibly with corresponding annotations when supervised learning is considered. In bioacoustic applications, most tasks come with few labelled training data, because annotating long recordings is time consuming and costly. Therefore supervised learning is not the best suited approach to solve bioacoustic tasks. The bioacoustic community recasted the problem of sound event detection within the framework of few-shot learning, i.e. training a system with only few labeled examples. The few-shot bioacoustic sound event detection task in the DCASE challenge focuses on detecting events in long audio recordings given only five annotated examples for each class of interest. In this paper, we show that learning a rich feature extractor from scratch can be achieved by leveraging data augmentation using a supervised contrastive learning framework. We highlight the ability of this framework to transfer well for five-shot event detection on previously unseen classes in the training data. We obtain an F-score of 63.46% on the validation set and 42.7% on the test set, ranking second in the DCASE challenge. We provide an ablation study for the critical choices of data augmentation techniques as well as for the learning strategy applied on the training set. Our code is available on Github.

INTRODUCTION

Sound Event Detection (SED) is the task of recognizing sound events, including determining their onsets and offsets, as well as recognizing them. SED has many applications in bioacoustics such as monitoring of biodiversity, studying animal behavior and identifying species. Automatic bioacoustic SED provides significant value in our understanding of animal populations and their interactions, as well as individuals and their behaviors. Standard SED systems leverage supervised learning as well as semi-supervised learning (DCASE Challenge Task 4) and have shown strong results in the recent years [START_REF] Chan | A comprehensive review of polyphonic sound event detection[END_REF][START_REF] Dang | A survey of deep learning for polyphonic sound event detection[END_REF][START_REF] Turpault | Sound event detection in domestic environments with weakly labeled data and soundscape synthesis[END_REF]. Numerous works focused on bird vocalization due to availability of large bird sound datasets [START_REF] Stowell | Automatic acoustic detection of birds through deep learning: the first bird audio detection challenge[END_REF][START_REF] Lasseck | Acoustic bird detection with deep convolutional neural networks[END_REF]. BirdNet [START_REF] Kahl | Birdnet: A deep learning solution for avian diversity monitoring[END_REF] is a notable work for bird monitoring, able to identify nearly one This work was co-funded by the AI@IMT program and the company OSO-AI. 1 : https://github.com/ilyassmoummad/dcase23_ task5_scl thousand bird species. The approach involves training a model in a supervised fashion using a vast dataset comprising over one million labeled bird recordings, using extensive data-preprocessing and data augmentation techniques.

However, such a large scale data collection for training systems is not always feasible in bioacoustics. The challenge lies not only in obtaining annotations but also in acquiring the audio samples themselves (e.g. for rare species or fields that are difficult to reach). As a consequence, bioacoustics SED is considered as a collection of numerous small-data problems, each requiring specialized systems for their individual solutions. Thus, the community of bioacoustics recasted bioacoustic SED as a few-shot learning (FSL) problem [START_REF] Nolasco | Learning to detect an animal sound from five examples[END_REF][START_REF] Nolasco | Few-shot bioacoustic event detection at the dcase 2022 challenge[END_REF].

FSL is a machine learning problem where a model has to learn to adapt to new classes of data unseen during training with only few labeled samples. FSL is adapted for many applications where acquisition or annotation is expensive or time consuming. The annual challenge on detection and classification of acoustic scenes and events (DCASE) organized a third edition for the task of few-shot bioacoustic sound event detection. This task focuses on SED in a FSL setting for mammal and bird vocalizations. The goal is to create a system that learns from five exemplar vocalizations (shots) to detect instances of these vocalizations in test audio recording.

Prototypical networks (ProtoNets) [START_REF] Snell | Prototypical networks for few-shot learning[END_REF] were proposed as a baseline to solve the FSL problem of detecting animal sound events in the DCASE challenge [START_REF] Nolasco | Few-shot bioacoustic event detection at the dcase 2022 challenge[END_REF]. ProtoNets, a meta-learning framework, have been state-of-the-art FSL audio systems in the recent years [START_REF] Heggan | Metaaudio: A few-shot audio classification benchmark[END_REF][START_REF] Wang | Who calls the shots? rethinking few-shot learning for audio[END_REF]. The goal of meta-learning training is to develop models that can quickly adapt to new tasks with minimal data by simulating the test scenario within the training process. In Computer Vision, simple transfer learning methods have been shown to outperform meta-learning methods in FSL [START_REF] Tian | Rethinking few-shot image classification: a good embedding is all you need?[END_REF][START_REF] Bendou | Easy-ensemble augmented-shot-yshaped learning: State-of-the-art few-shot classification with simple components[END_REF] in several datasets such as MiniImageNet and TieredImagenet, in which case the domain shift between the training data and the few shot generalization is small enough. Here, we propose to test transfer learning to solve FSL problems for the bioacoustic SED [START_REF] Nolasco | Few-shot bioacoustic event detection at the dcase 2022 challenge[END_REF].

As the generalization capability of the feature extractor is crucial for efficient transfer learning, we propose to train a model using the supervised contrastive learning framework (SCL) [START_REF] Khosla | Supervised contrastive learning[END_REF]. Numerous contrastive learning methods have been proposed in the selfsupervised learning (SSL) literature [START_REF] Chen | A simple framework for contrastive learning of visual representations[END_REF][START_REF] Caron | Unsupervised learning of visual features by contrasting cluster assignments[END_REF][START_REF] Fonseca | Unsupervised contrastive learning of sound event representations[END_REF], but the fundamental concept of pulling together positive pairs and pushing apart negative pairs remains the same across these approaches. The positive pairs consist of similar samples, while negative pairs consist of dissimilar samples. The selection of these pairs can be achieved through various means, such as data augmentation techniques [START_REF] Chen | A simple framework for contrastive learning of visual representations[END_REF] and/or utilizing class labels as in done in SCL [START_REF] Khosla | Supervised contrastive learning[END_REF]. The representa- tions learned using this framework have shown competitive transfer learning performance with SSL and cross-entropy (CE) learning on a variety of downstream tasks in vision [START_REF] Khosla | Supervised contrastive learning[END_REF]. In audio, the works of Moummad et al. [START_REF] Moummad | Learning audio features with metadata and contrastive learning[END_REF] and Nasiri et al. [START_REF] Nasiri | Soundclr: contrastive learning of representations for improved environmental sound classification[END_REF] have demonstrated strong generalization capabilities of SCL. Following the training of the feature extractor using SCL on the training set, the learned model is transferred to the validation set to conduct hyperparameter search. The optimal hyperparameter setting determined from this process is then employed on the test set for evaluation. In summary, our contribution revolves around the proposition of employing supervised contrastive learning to train a feature extractor that can be transferred to new few-shot bioacoustic sound event detection tasks.

METHOD

This section provides a comprehensive overview of the methodology employed in this study (Figure 1). Firstly, we present the SCL framework utilized for pre-training a good feature extractor model. Secondly, we describe the data augmentation techniques employed to enhance the diversity and robustness of the learned features. Finally, we detail our transfer learning strategy for adapting the pretrained model to effectively tackle novel tasks.

Supervised Contrastive Learning

SCL consists in learning an embedding space in which the samples with the same class labels are close to each other, and the samples with different class labels are far from each other. Formally, a composition of an encoder f and a shallow neural network h called a projector (usually a MLP with one hidden layer) are trained to minimize the distances between representations of samples of the same class while maximizing the distances between representations of samples belonging to different class. After convergence, h is discarded, and the encoder f is used for transfer learning on downstream tasks. The supervised contrastive loss (SCL) is calculated as follows:

L SCL = i∈I -1 |P (i)| p∈P (i) log exp (zi • zp/τ ) s∈S(i) exp (zi • zs/τ ) (1

Data Augmentation

Data augmentation is crucial for learning a good feature extractor as advocated by the SSL literature [START_REF] Chen | A simple framework for contrastive learning of visual representations[END_REF][START_REF] Khosla | Supervised contrastive learning[END_REF][START_REF] Caron | Unsupervised learning of visual features by contrasting cluster assignments[END_REF], ?]. To this end, we adopt several augmentation modules derived from the audio representation learning domain [START_REF] Fonseca | Unsupervised contrastive learning of sound event representations[END_REF][START_REF] Wang | Multi-format contrastive learning of audio representations[END_REF][START_REF] Niizumi | Byol for audio: Exploring pre-trained generalpurpose audio representations[END_REF]. The following augmentations are sequentially applied in the prescribed order and are iteratively employed twice on the same data, with the exception of spectrogram mixing, which is exclusively applied to a single view (based on our experimental findings, this configuration demonstrated superior performance). To demonstrate the significance of each augmentation technique, an ablation study is conducted in the subsequent section.

-Spectrogram mixing: we add background sounds using random samples from the same batch. The mixing follows:

x1 = αx1 + (1 -α)x2
. where x1 is considered as a view of x1 and x2 is a random sample from the batch.

-Frequency shift: we approximate frequency shift by shifting the spectrogram upwards by few bands. -Random crop: we crop a patch from the spectrogram along the time axis. -Spectrogram resize: this augmentation is applied after the crop to restore the spectrogram to its original size. -Power gain: we attenuate the power of the spectrogram by multiplying it with a coefficient sampled uniformly between 0.75 and 1. -Additive white Gaussian noise: we add a small additive white Gaussian noise to the view

Transfer Learning

After training the feature extractor, we transfer the model to the validation and test tasks. Each audio file is treated independently as a separate SED problem (as the challenge rules specify). We extract the features of the five positive annotated prototypes (shots) indicating the occurrence of the event of interest. We select intervals preceding the positive events as for the negative prototypes indicating the absence of the event. We train a binary classifier on these two prototypes using cross-entropy loss. The encoder layers can be either frozen or fine-tuned. We use a sliding window along the audio file (starting from the end of the fifth positive shot) to select queries for making predictions. The class activity is determined independently in each query window using the classifier. The onsets and offsets decision is made based on the precise moment when the label for the window transitions from a negative class to a positive class and from a positive class to a negative class, respectively.

EXPERIMENTS

Data

The bioacoustic few-shot sound event detection DCASE task development set consists of a training set and a validation set, for more details we refer the reader to the description of the task in 2022 [START_REF] Nolasco | Few-shot bioacoustic event detection at the dcase 2022 challenge[END_REF] as these sets did not change from the previous edition.

Training

We train our system on the official training set. We select all the positively annotated segments within each audio file. We compute Mel spectrogram features with a FFT of size 512, a hop length of 128, a number of mels of 128 and a sampling rate of 22.05 kHz. Each positive annotated segment from the training set is chunked into patches of length 200 ms with 100 ms overlap. We apply minmax normalization on each patch.

Validation and test

For each audio file, we extract the first five positively annotated segments. The duration of these segments varies due to the wide range of animals and classes covered by the dataset. Following the approach proposed by Tang et al. [START_REF] Tang | Few-shot embedding learning and event filtering for bioacoustic event detection technical report[END_REF], we determine the window length based on the mean duration of the events in the file. To compute Mel spectrogram features, we employ identical parameters and normalization technique as those used during the training phase. The shift size equals to half of the window length to predict the class for each query window along the remaining duration of the audio.

Model

We use a ResNet [START_REF] He | Deep residual learning for image recognition[END_REF] consisting of three blocks, each comprising three convolutional layers. The feature maps of these convolutions have sizes of 64, 128, and 256, respectively. Following each convolutional layer, we apply batch normalization and a leaky rectified linear unit (ReLU) activation function. Max pooling operations are performed after each block. Specifically, we employ a 2x2 kernel for the first and second blocks, while for the third block, we use a 1x2 kernel. This choice is made to preserve frequency information by avoiding excessive pooling of the frequency bands, as suggested by Hertkorn [START_REF] Hertkorn | Few-shot bioacoustic event detection : Don ' t waste information technical report[END_REF].

To ensure consistent output dimensions despite varying input lengths, we incorporate adaptive max pooling at the end of the network. This pooling operation is configured to yield a desired output size of (8, 1), resulting in a latent vector of size 8 x 256 = 2048. A MLP projector is added, consisted of a hidden layer with a dimension of 2048 and an output layer with a dimension of 512.

Training details

Data augmentation

The spectrogram mixing coefficient α is sampled from a β(5, 2) distribution. The frequency shift size is uniformly sampled between 0 and 10. The crop size (i.e. how much total duration is kept from the original audio) in the Random crop augmentation is uniformly sampled between 60% and 100%. Power gain augmentation is achieved by multiplying the mel spectrogram with a coefficient uniformly sampled between 0.75 and 1. The additive white Gaussian noise is incorporated by adding noise with a mean of zero and a variable standard deviation, which is uniformly chosen between 0 and 0.1.

Training and evaluation

We train our model from scratch on the training set using SCL framework with a temperature τ = 0.06 using SGD optimizer with a batch size of 128, a learning rate of 0.01 with a cosine decay schedule, momentum of 0.9, and a weight decay of 0.0001 for 50 epochs. After training, we discard the MLP projector and transfer the encoder to the validation and test sets by training a linear binary classifier on the pretrained representations. In this phase we used random resized crop along the time axis with a crop size ranging from 90% to 100% of the original size. We submitted four distincts systems to the challenge : freezing all pretrained layers (Frozen), or finetuning the last, two last and all layers (FineTune-1, FineTune-2 and Finetune-3). We optimize our systems using Adam optimizer with a learning rate of 0.01 for 20 epochs for the first system, and 40 epochs with a learning rate of 0.001 for the others. The selection of these hyperparameters is based on evaluation conducted on the validation set.

Results

The performance of our four systems on the validation set is presented in Table 1. For PB dataset, where events are short (therefore only few patches are available, because we divide longer events into multiple chunks), the first system outperforms the others, indicating that fine-tuning degrades the performance when only few positive patches are present. Conversely, for the HB dataset, where events tend to be longer, the third and fourth systems outperform the others. This indicates that finetuning a greater number of layers is advantageous when more positive patches are present. The second system demonstrates satisfactory performance across all datasets, outperforming the other systems across all datasets with a max F1 score of 63.46%. It is important to note that our results on the validation set exhibit significant variability, primarily attributed to the instability of our proposed cross-entropy adaptation strategy. We acknowledge this limitation and plan to address it in future work.

Table 2 displays the performance scores of our systems on the test sets. Remarkably, the ranking order of these systems on the test set aligns with that observed on the validation set. This consistency further validates the robustness and generalizability of our models across different datasets. [START_REF] Chen | A simple framework for contrastive learning of visual representations[END_REF], which has the same formula as SCL but without positive label pairs. We perform these studies on the validation set using the first system Frozen, where we freeze all layers, as it better captures the impact of the pre-training strategy. We use the same hyperparameter setting described in 3.3 for all experiments except for CE training where we use a learning rate of 0.0001 after thorough exploration. Additionally, we modify the training duration for Sim-CLR, extending it to 100 epochs. This adjustment is made to account for the longer training requirements typically associated with self-supervised approaches. To ensure reliable results, we trained the model five times on the training set and conducted five evaluations for each run, resulting in a total of twenty-five runs per experiment. The analysis presented in Table 3 indicates that certain data augmentation techniques have a negative impact on the model's performance. Surprisingly, these effects were not evident during the challenge submission due to the limited number of experiments conducted at that time. Notably, the data augmentation setting that yielded the highest score was the setting without the additive white Gaussian noise to the spectrogram. This finding suggests that this particular augmentation strategy was either enforcing an invariance that is not beneficial for the downstream task at hand, or that the task becomes hard given the small size of the training dataset.

We can observe from the results of Table 4 that SCL consis-tently outperforms both SimCLR and CE frameworks for transfer learning. The superior performance of SCL highlights its efficacy in capturing discriminative features. These findings emphasize the importance of incorporating SCL as a powerful framework for advancing feature representation learning, particularly for enhancing transferability in downstream tasks.

DISCUSSION AND PERSPECTIVES

In this study, we have provided a comprehensive description of a simple approach for bioacoustic few-shot sound event detection.

We have detailed the methodology behind the systems we developed and submitted for the DCASE 2023 challenge task five. Our approach involves pretraining a feature extractor using supervised contrastive learning and data augmentation on the training set, followed by training binary classifiers on positive and negative prototypes for each audio file in the validation/evaluation sets. We proposed four systems. The first system, which utilized a linear classifier on frozen representations, demonstrated the robustness and transferability of the learned features. When fine-tuning the last layer (the second system) or the last two layers (the third system), the performance is increased. However, our current adaptation strategy, involving training classifiers on available shots, showed performance instability. We also note the gap in performance between the validation and the test sets. HB validation dataset is made of controlled lab recordings, which may make the detection easier, while PB recordings are in the wild with noisy background. Settings of the test set are more close to PB than HB [START_REF] Nolasco | Learning to detect an animal sound from five examples[END_REF]. To address the limitation and instability of our approach, future work will explore more effective adaptation techniques such as meta-learning. Notably, the winning systems in the 2022 and 2023 editions of the DCASE bioacoustic few-shot sound event detection challenge (Tang et al. [START_REF] Tang | Few-shot embedding learning and event filtering for bioacoustic event detection technical report[END_REF]; Du et al. [START_REF] Yan | Multi-task frame level system for few-shot bioacoustic event detection[END_REF]) employed a frame-level approach, offering a higher time resolution capability compared to our window-level approach.

Exploring the frame-level approach, as well as a proposal-based approach [START_REF] Wolters | Proposal-based few-shot sound event detection for speech and environmental sounds with perceivers[END_REF] for detecting variable length temporal regions of interest, which has not been previously investigated in this task, will be considered for future research. Combining representation learning (meta-learning, self-supervised learning, or supervised learning) is a promising direction for learning useful representation leveraging knowledge from large data, that can transfer well to new tasks.

Figure 1 :

 1 Figure 1: Overview of the proposed framework

  )where i ∈ I = {1...2N } is the index of an augmented sample within a training batch, containing two views of each orig-inal sample. These views are constructed by applying a data augmentation function A twice to the original samples. zi = h(f (A(xi))) ∈ R D P where DP is the projector's dimension. P (i) = {p ∈ I : yp = yi} is the set of indices of all positives in the two-views batch distinct from i sharing similar label with i. |P (i)| is its cardinality, S(i) = {s ∈ I : s ̸ = i}, the • symbol denotes the dot product, and τ ∈ R + * is a scalar temperature parameter that controls the penalty strength on hard negative samples.

Table 1 :

 1 Performance of different systems on the validation set; freezing all layers, fine-tuning one, two or all three layers. Table 3 presents our ablation study on data augmentation. Additionally, Table 4 compares pre-training methods : SCL, crossentropy training (CE), and the self-supervised training method Sim-CLR

	System	Precision Recall F1-score	Pr	HB Re	F1	Pr	ME Re	F1	Pr	PB Re	F1
	Frozen	71.41	55.19	62.26	77.14 81.57 79.29 65.45 69.23 67.28 72.64 36.17 48.29
	FineTune-1	73.93	55.59	63.46	82.95 82.32 82.63 67.69 84.61 75.21 72.72 33.33 45.71
	FineTune-2	72.90	55.14	62.79	79.73 89.72 84.43 74.60 90.38 81.73 65.57 31.06 42.19
	FineTune-all	67.08	51.58	58.32	81.20 91.38 85.99 58.75 90.38 71.21 65.00 27.65 38.80
				*We highlight in bold the best scores for each metric
	Table 2: F-score on the test sets of the different submissions
			F-score
	Frozen	35.6% (35.3 -36.0)
	FineTune-1	42.7% (42.2 -43.1)
	FineTune-2	38.3% (37.9 -38.7)
	FineTune-all 34.4% (33.9 -34.8)
		*with 95% confidence interval
	3.5. Ablation study

Table 3 :

 3 Ablation of Data augmentation on the validation set

	DA removed	Mean	[Min, Max]
	Frozen (with all DAs) 56.47 [49.37, 62.39]
	-Spectrogram mixing 56.59 [47.99, 64.65]
	-Frequency shift	58.60 [49.73, 66.18]
	-Time stretch	55.68 [49.20, 62.83]
	-Power gain	56.02 [47.04, 63.01]
	-Additive noise	59.04 [52.68, 67.47]

*Best score is highlighted in bold

Table 4 :

 4 Ablation of the pretraining methods on the validation set

	Method	Mean	[Min, Max]
	CE	51.96 [43.013-57.42]
	SimCLR 50.89	[39.28-57.41]
	SCL	56.27	[49.37, 62.39]

*Highest F-score is highlighted in bold