Jie Yu

Jesús González-Cobos
email: jesus.gonzalez-cobos@ircelyon.univ-lyon1.fr

Frederic Dappozze

Nicolas Grimaldos-Osorio

Philippe Vernoux

Angel Caravaca
email: angel.caravaca@ircelyon.univ-lyon1.fr

Chantal Guillard
email: chantal.guillard@ircelyon.univ-lyon1.fr

First PEM photoelectrolyser for the simultaneous selective glycerol valorization into value-added chemicals and hydrogen generation

Keywords: Photoelectrocatalysis, Polymer electrolyte membrane, Glycerol, Electrolysis, Hydrogen

The photoelectrocatalytic (PEC) valorization of glycerol is emerging for the co-generation of hydrogen and value-added organics like glyceraldehyde (GAD) or dihydroxyacetone (DHA). In this work, we have designed, tested and optimized a pioneering photoelectrolyser with a non-noble metalbased photoanode (WO 3 ), operating in near-neutral conditions and using .a proton-exchange membrane (PEM) which ensures the elution of a purified hydrogen stream from the cathode side while selectively oxidizing glycerol on the anode. The influence of light irradiation, external bias and cell temperature has been investigated, leading to GAD and DHA production rates of 11.1 and 5.2 mmol m -2 h -1 at 60 ºC and 1.2 V, along with 44.0 mmol H 2 m -2 h -1 . The long-term stability of the photoelectrolyser has also been validated and the particularities of this system with respect to other conventional devices have been discussed. PEC stands as a promising sustainable technology for the simultaneous H 2 generation and biomass valorization.

Introduction

Glycerol is an important by-product (~2.2 Mt worldwide in 2019 [START_REF] Dias Da Silva Ruy | Market Prospecting and Assessment of the Economic Potential of Glycerol from Biodiesel[END_REF]) of the production of biodiesel as an alternative to fossil fuels and of soap manufacture. Being largely available and cheap, its valorization is not only encouraged for the global consensus on carbon neutralization, but also highly economically profitable. This is especially relevant when dealing with the selective production of its primary 3C oxidation products, glyceraldehyde (GAD) and dihydroxyacetone (DHA), which are key precursors in the synthesis of cosmetics, polymers and biodegradable emulsifiers [START_REF] Karimi Estahbanati | Current developments and future trends in photocatalytic glycerol valorization: photocatalyst development[END_REF][START_REF] Mendoza | Selective production of dihydroxyacetone and glyceraldehyde by photo-assisted oxidation of glycerol[END_REF][START_REF] Houache | Study on catalyst selection for electrochemical valorization of glycerol[END_REF][START_REF] Arcanjo | Glycerol valorization: Conversion to lactic acid by heterogeneous catalysis and separation by ion exchange chromatography[END_REF][START_REF] Simões | Electrochemical valorisation of glycerol[END_REF]. Besides, green hydrogen is regarded as one of the most important energy carriers for global energy transformation and development, given its high gravimetric energy density and its potential environmentally friendly implementation [START_REF] Montini | Nanostructured Cu/TiO 2 photocatalysts for H 2 production from ethanol and glycerol aqueous solutions[END_REF][START_REF] Schichtl | Characterizing Sustained Solar-to-Hydrogen Electrocatalysis at Low Cell Potentials Enabled by Crude Glycerol Oxidation[END_REF]. In this sense, a promising pathway for simultaneous glycerol valorization into value-added chemicals and pure green hydrogen is the photoelectrocatalysis (PEC) using renewable energy sources. This technology is more efficient than photocatalysis (PC) because external voltage can promote the separation of photogenerated electrons and holes. Therefore, PEC has gradually attracted the attention of academia and industry in recent years [START_REF] Gong | Advances in solar energy conversion[END_REF][START_REF] Li | Implementation of ferroelectric materials in photocatalytic and photoelectrochemical water splitting[END_REF][START_REF] Lu | Photoelectrochemical hydrogen production from biomass derivatives and water[END_REF].

Glycerol-upgrading by PEC process is composed of two half-reactions: glycerol electrooxidation/oxygen evolution reaction (OER) at the anodic catalyst, and hydrogen evolution reaction (HER) at the cathodic catalyst. Despite recent several achievements, four main bottlenecks need to be addressed: i)

There is insufficient attention on both half-reactions simultaneously, i.e., glycerol oxidation and hydrogen evolution. Many studies are focused only on the cathodic hydrogen production and the anodic reactions are to some extent ignored. The products of the glycerol electrooxidation have not been analyzed in some cases [START_REF] Caravaca | H2 production by the photocatalytic reforming of cellulose and raw biomass using Ni, Pd, Pt and Au on titania[END_REF][START_REF] Seferlis | Photoelectrocatalytic electricity and/or H2 production from alcohols: the effect of TiO2 film Thickness[END_REF][START_REF] Sheng | Constructing 1D hierarchical heterostructures of MoS2/In2S3 nanosheets on CdS nanorod arrays for enhanced photoelectrocatalytic H2 evolution[END_REF][START_REF] Reddy | Photocatalytic reforming of biomass derived crude glycerol in water: a sustainable approach for improved hydrogen generation using Ni (OH) 2 decorated TiO2 nanotubes under solar light irradiation[END_REF][START_REF] Iervolino | Photocurrent increase by metal modification of Fe2O3 photoanodes and its effect on photoelectrocatalytic hydrogen production by degradation of organic substances[END_REF][START_REF] Raptis | Renewable energy production by photoelectrochemical oxidation of organic wastes using WO3 photoanodes[END_REF] and, when they have been,

the reaction has not always resulted in the production of the desired primary products. For example, in some cases, the selectively obtained product is glycerate [START_REF] Bhattacharjee | Reforming of Soluble Biomass and Plastic Derived Waste Using a Bias-Free Cu30Pd70| Perovskite| Pt Photoelectrochemical Device[END_REF][START_REF] Bashiri | Enhanced hydrogen production over incorporated Cu and Ni into titania photocatalyst in glycerol-based photoelectrochemical cell: Effect of total metal loading and calcination temperature[END_REF][START_REF] Lima | Glycerol (photo)electro-oxidation on carbon supported Ag nanoparticles modified with low amounts of Pt. Activity, selectivity and the effect of visiblelight irradiation[END_REF], glycolate [START_REF] Lima | Glycerol (photo)electro-oxidation on carbon supported Ag nanoparticles modified with low amounts of Pt. Activity, selectivity and the effect of visiblelight irradiation[END_REF][START_REF] Perini | Photoelectrochemical oxidation of glycerol on hematite: thermal effects, in situ FTIR and long-term HPLC product analysis[END_REF], lactate [START_REF] Lima | Glycerol (photo)electro-oxidation on carbon supported Ag nanoparticles modified with low amounts of Pt. Activity, selectivity and the effect of visiblelight irradiation[END_REF] or formate [START_REF] Wang | CoNiFe-LDHs decorated Ta3N5 nanotube array photoanode for remarkably enhanced photoelectrochemical glycerol conversion coupled with hydrogen generation[END_REF][START_REF] Huang | Converting glycerol aqueous solution to hydrogen energy and dihydroxyacetone by the BiVO4 photoelectrochemical cell[END_REF][START_REF] Liu | Selective photoelectrochemical oxidation of glycerol to high value-added dihydroxyacetone[END_REF][START_REF] Wu | Solar-driven valorisation of glycerol on BiVO4 photoanodes: effect of co-catalyst and reaction media on reaction selectivity[END_REF].

ii)

The utilization of precious metals like Pt [START_REF] Lima | Glycerol (photo)electro-oxidation on carbon supported Ag nanoparticles modified with low amounts of Pt. Activity, selectivity and the effect of visiblelight irradiation[END_REF][START_REF] Maslova | Solar-driven valorization of glycerol towards production of chemicals and hydrogen[END_REF][START_REF] Li | Photocatalytic hydrogen generation using glycerol wastewater over Pt/TiO2[END_REF][START_REF] Ribao | Challenges arising from the use of TiO2/rGO/Pt photocatalysts to produce hydrogen from crude glycerol compared to synthetic glycerol[END_REF][START_REF] Maslova | Highly-dispersed ultrafine Pt nanoparticles on microemulsion-mediated TiO2 for production of hydrogen and valuable chemicals via oxidative photo-dehydrogenation of glycerol[END_REF], Au [START_REF] Dodekatos | Plasmonic Au/TiO 2 nanostructures for glycerol oxidation[END_REF][START_REF] Guo | Photocatalytic glycerol oxidation on Au x Cu--CuS@ TiO 2 plasmonic heterostructures[END_REF][START_REF] Shen | others, Promotion mechanisms of Au supported on TiO2 in thermal-and photocatalytic glycerol conversion[END_REF] and Pd [START_REF] Jedsukontorn | Photoinduced glycerol oxidation over plasmonic AU and AuM (M= Pt, Pd and Bi) nanoparticle-decorated Tio2 photocatalysts[END_REF][START_REF] Abis | Plasmonic oxidation of glycerol using AuPd/TiO 2 catalysts[END_REF][START_REF] Ruberu | Selective alcohol dehydrogenation and hydrogenolysis with semiconductor-metal photocatalysts: toward solar-to-chemical energy conversion of biomass-relevant substrates[END_REF], either as main active phase or as co-catalyst, decreases the PC and PEC economic competitiveness. In particular, in this work, the concern of replacing the noble metals has been focused on the anodic catalyst.

iii) Most of the studies are carried out under harsh reaction conditions, i.e., using acid (e.g., H 2 SO 4 ) [START_REF] Liu | Selective photoelectrochemical oxidation of glycerol to high value-added dihydroxyacetone[END_REF][START_REF] Tang | Fabrication of MOFs' derivatives assisted perovskite nanocrystal on TiO2 photoanode for photoelectrochemical glycerol oxidation with simultaneous hydrogen production[END_REF][START_REF] Luo | Selective Photoelectrocatalytic Glycerol Oxidation to Dihydroxyacetone via Enhanced Middle Hydroxyl Adsorption over a Bi2O3-Incorporated Catalyst[END_REF][START_REF] Vo | Unveiling the crystallographic facet dependence of the photoelectrochemical glycerol oxidation on bismuth vanadate[END_REF] or alkaline concentrated solutions (e.g., KOH, NaOH) [START_REF] Bhattacharjee | Reforming of Soluble Biomass and Plastic Derived Waste Using a Bias-Free Cu30Pd70| Perovskite| Pt Photoelectrochemical Device[END_REF][START_REF] Bashiri | Enhanced hydrogen production over incorporated Cu and Ni into titania photocatalyst in glycerol-based photoelectrochemical cell: Effect of total metal loading and calcination temperature[END_REF][START_REF] Lima | Glycerol (photo)electro-oxidation on carbon supported Ag nanoparticles modified with low amounts of Pt. Activity, selectivity and the effect of visiblelight irradiation[END_REF][START_REF] Perini | Photoelectrochemical oxidation of glycerol on hematite: thermal effects, in situ FTIR and long-term HPLC product analysis[END_REF][START_REF] Wang | CoNiFe-LDHs decorated Ta3N5 nanotube array photoanode for remarkably enhanced photoelectrochemical glycerol conversion coupled with hydrogen generation[END_REF] as electrolytes, increasing the safety risks of storage and transportation and environmental hazards in large-scale production. For instance, Wang et al. proposed a CoNiFe-LDHsdecorated Ta 3 N 5 nanotube array for the simultaneous generation of anodic formate and cathodic hydrogen in a 1.0 M NaOH electrolyte, [START_REF] Wang | CoNiFe-LDHs decorated Ta3N5 nanotube array photoanode for remarkably enhanced photoelectrochemical glycerol conversion coupled with hydrogen generation[END_REF] while the highest DHA selectivities (above 50%) have been reached by using solutions with pH = 2 [START_REF] Liu | Selective photoelectrochemical oxidation of glycerol to high value-added dihydroxyacetone[END_REF][START_REF] Tang | Fabrication of MOFs' derivatives assisted perovskite nanocrystal on TiO2 photoanode for photoelectrochemical glycerol oxidation with simultaneous hydrogen production[END_REF][START_REF] Luo | Selective Photoelectrocatalytic Glycerol Oxidation to Dihydroxyacetone via Enhanced Middle Hydroxyl Adsorption over a Bi2O3-Incorporated Catalyst[END_REF][START_REF] Vo | Unveiling the crystallographic facet dependence of the photoelectrochemical glycerol oxidation on bismuth vanadate[END_REF]. There are very few PEC works performed under neutral or near-neutral conditions [START_REF] Wu | Solar-driven valorisation of glycerol on BiVO4 photoanodes: effect of co-catalyst and reaction media on reaction selectivity[END_REF][START_REF] Gu | Interface-modulated nanojunction and microfluidic platform for photoelectrocatalytic chemicals upgrading[END_REF][START_REF] Yu | WO3-based materials for photoelectrocatalytic glycerol upgrading into glyceraldehyde: Unravelling the synergistic photo-and electro-catalytic effects[END_REF][START_REF] Liu | Selective photoelectrochemical oxidation of glycerol to high value-added dihydroxyacetone[END_REF] and only two of them achieved the selective generation of C 3s , by Gu et al. [START_REF] Gu | Interface-modulated nanojunction and microfluidic platform for photoelectrocatalytic chemicals upgrading[END_REF] and by this group [START_REF] Yu | WO3-based materials for photoelectrocatalytic glycerol upgrading into glyceraldehyde: Unravelling the synergistic photo-and electro-catalytic effects[END_REF]. In both cases, WO 3 -based anodes showed to be excellent materials for the selective glycerol oxidation, with selectivities up to c.a. 90% for GAD+DHA.

iv)

Apart from the unavoidable purification concerns regarding anodic liquid products (their separation from the liquid electrolyte), the generation of pure H 2 stream from glycerol electrolysis/photoelectrolysis is not ensured in the traditional 3-electrode PEC cells, unless there is a complete absence of any other gaseous products derived from the anode (e.g., CO

or CO 2 from undesired glycerol oxidation reactions under neutral or acid conditions, or O 2 from the competitive water oxidation reaction at high enough potentials) [START_REF] Çetinkaya | Selective photoelectrocatalytic oxidation of glycerol by nanotube, nanobelt and nanosponge structured TiO2 on Ti plates[END_REF][START_REF] Augugliaro | Heterogeneous photocatalysis and photoelectrocatalysis: from unselective abatement of noxious species to selective production of high-value chemicals[END_REF].

Furthermore, the non-separation of the anodic and cathodic compartments may lead to side reduction reactions or poisoning phenomena at the cathode due to adsorbed organics adsorption. This is the case of the above-mentioned works, where both anodic and cathodic half-reactions took place in the same gas/liquid compartment. In view to its practical application, this configuration may increase the process complexity and economical cost due to the need for hypothetical products post-purification operations.

Polymer electrolyte membrane (PEM) cells using a thin solid electrolyte membrane to separate anode and cathode electrodes show several advantages with respect to liquid electrolyte cells, such as the separation of any possible gaseous oxidation products from the cathodic hydrogen effluent, typically lower ohmic resistance, higher compactness and better fluid dynamics, which lead to improved durability and efficiency [START_REF] Malik | Comparative study and analysis between Solid Oxide Fuel Cells (SOFC) and Proton Exchange Membrane (PEM) fuel cell--A review[END_REF][START_REF] Cognard | Benefits and limitations of Pt nanoparticles supported on highly porous antimony-doped tin dioxide aerogel as alternative cathode material for proton-exchange membrane fuel cells[END_REF]. PEM cells have been widely used in the field of electrocatalytic hydrogen generation from alcohols [START_REF] Coutanceau | Electrochemical conversion of alcohols for hydrogen production: a short overview[END_REF][START_REF] Rodr\'\iguez-Gómez | Boosting hydrogen and chemicals production through ethanol electro-reforming on Pt-transition metal anodes[END_REF][START_REF] De Lucas-Consuegra | A novel sputtered Pd mesh architecture as an advanced electrocatalyst for highly efficient hydrogen production[END_REF][START_REF] Lamy | Kinetics analysis of the electrocatalytic oxidation of methanol inside a DMFC working as a PEM electrolysis cell (PEMEC) to generate clean hydrogen[END_REF][START_REF] Sapountzi | Hydrogen from electrochemical reforming of C1--C3 alcohols using proton conducting membranes[END_REF][START_REF] Caravaca | Electrochemical reforming of ethanol--water solutions for pure H2 production in a PEM electrolysis cell[END_REF]. In particular, glycerol electrolysis was studied in PEM configuration with a proton-conducting membrane by Kim et al. [START_REF] Kim | Selective glycerol oxidation by electrocatalytic dehydrogenation[END_REF], Marshall and Haverkamp [START_REF] Marshall | Production of hydrogen by the electrochemical reforming of glycerol--water solutions in a PEM electrolysis cell[END_REF],

and Fan et al. [START_REF] Fan | High Entropy Alloy Electrocatalytic Electrode toward Alkaline Glycerol Valorization Coupling with Acidic Hydrogen Production[END_REF]. There are also several works using an anion-exchange membrane, from the groups of Linares [START_REF] De Paula | Electrochemical reforming of glycerol in alkaline PBIbased PEM reactor for hydrogen production[END_REF][START_REF] De Paula | Influence of the anolyte feed conditions on the performance of an alkaline glycerol electroreforming reactor[END_REF], Vizza [START_REF] Bambagioni | Self-sustainable production of hydrogen, chemicals, and energy from renewable alcohols by electrocatalysis[END_REF] and Schuhmann [START_REF] Morales | Electrocatalytic conversion of glycerol to oxalate on Ni oxide nanoparticles-modified oxidized multiwalled carbon nanotubes[END_REF][START_REF] Brix | Electrocatalytic Oxidation of Glycerol Using Solid-State Synthesised Nickel Boride: Impact of Key Electrolysis Parameters on Product Selectivity[END_REF][START_REF] Brix | others, Structure-Performance Relationship of LaFe1-xCoxO3 Electrocatalysts for Oxygen Evolution, Isopropanol Oxidation, and Glycerol Oxidation[END_REF]. However, the employed anodes were found to mainly produce glycerate [START_REF] Kim | Selective glycerol oxidation by electrocatalytic dehydrogenation[END_REF][START_REF] De Paula | Electrochemical reforming of glycerol in alkaline PBIbased PEM reactor for hydrogen production[END_REF][START_REF] De Paula | Influence of the anolyte feed conditions on the performance of an alkaline glycerol electroreforming reactor[END_REF][START_REF] Bambagioni | Self-sustainable production of hydrogen, chemicals, and energy from renewable alcohols by electrocatalysis[END_REF], tartronate [START_REF] De Paula | Electrochemical reforming of glycerol in alkaline PBIbased PEM reactor for hydrogen production[END_REF][START_REF] De Paula | Influence of the anolyte feed conditions on the performance of an alkaline glycerol electroreforming reactor[END_REF][START_REF] Bambagioni | Self-sustainable production of hydrogen, chemicals, and energy from renewable alcohols by electrocatalysis[END_REF][START_REF] Brix | Electrocatalytic Oxidation of Glycerol Using Solid-State Synthesised Nickel Boride: Impact of Key Electrolysis Parameters on Product Selectivity[END_REF] or formate [START_REF] Fan | High Entropy Alloy Electrocatalytic Electrode toward Alkaline Glycerol Valorization Coupling with Acidic Hydrogen Production[END_REF][START_REF] Morales | Electrocatalytic conversion of glycerol to oxalate on Ni oxide nanoparticles-modified oxidized multiwalled carbon nanotubes[END_REF][START_REF] Brix | Electrocatalytic Oxidation of Glycerol Using Solid-State Synthesised Nickel Boride: Impact of Key Electrolysis Parameters on Product Selectivity[END_REF][START_REF] Brix | others, Structure-Performance Relationship of LaFe1-xCoxO3 Electrocatalysts for Oxygen Evolution, Isopropanol Oxidation, and Glycerol Oxidation[END_REF]. Therefore, to the best of our knowledge, the present study is the first one that simultaneously investigates the production of hydrogen and the selective glycerol valorization to GAD or DHA in a PEM cell, for either glycerol electrolysis or photoelectrolysis. Furthermore, the photoelectrocatalytic route is also herein explored, for the first time, to boost the glycerol selective oxidation in a PEM configuration.

To date, there are very few studies in literature employing compact PEM cell configurations under PEC conditions and they were used for water splitting at room temperature, either in liquid-phase [START_REF] Zhang | Enhancing hydrogen evolution by photoelectrocatalysis of water splitting over a CdS flowers-loaded TiO2 nanotube array film on the Ti foil substrate[END_REF][START_REF] Li | Effect of water and annealing temperature of anodized TiO2 nanotubes on hydrogen production in photoelectrochemical cell[END_REF][START_REF] Marschall | Composite protonconducting polymer membranes for clean hydrogen production with solar light in a simple photoelectrochemical compartment cell[END_REF][START_REF] Stoll | Solar fuel production in a novel polymeric electrolyte membrane photoelectrochemical (PEM-PEC) cell with a web of titania nanotube arrays as photoanode and gaseous reactants[END_REF] or in gas-phase [START_REF] Stoll | Solar fuel production in a novel polymeric electrolyte membrane photoelectrochemical (PEM-PEC) cell with a web of titania nanotube arrays as photoanode and gaseous reactants[END_REF][START_REF] Kang | Water Vapor Photoelectrolysis in a Solid-State Photoelectrochemical Cell with TiO2Nanotubes Loaded with CdS and CdSe Nanoparticles[END_REF][START_REF] Amano | Photoelectrochemical gaselectrolyte-solid phase boundary for hydrogen production from water vapor[END_REF]. Thus, the application of the PEC approach to glycerol electrolysis in a PEM device is totally innovative.

In this work, a PEM Photoelectrolyser was designed to perform the separated glycerol oxidation to high value-added products in the anode compartment, together with the simultaneous green H 2 generation in the cathodic compartment. Monoclinic WO 3 synthesized by a simple hydrothermal method with proper crystallinity, acidity and redox properties (oxygen vacancies due a ratio of W 5+ /W 6+ of ~18%/82%) was selected as the photoanode electrode due to its high selectivity towards GAD under near-neutral pH conditions observed in our previous work [START_REF] Yu | WO3-based materials for photoelectrocatalytic glycerol upgrading into glyceraldehyde: Unravelling the synergistic photo-and electro-catalytic effects[END_REF]. The operation parameters of this cell have been optimized, focusing not only on the applied potential but also on the cell temperature. This latter key parameter could significantly affect the reaction kinetics, mass transfer and photo-or electro-induced charge separation rate, but has been only scarcely studied in a three-electrode cell configuration. For this purpose, the bifunctional PEM system, dedicated not only on the anodic glycerol selective oxidation but also on the cathodic green energy H 2 generation, has been studied under (thermo)catalytic (TC), photocatalytic (PC), electrocatalytic (EC) and combined PEC conditions. The performance of the system has been evaluated in terms of obtained photocurrent, product selectivity, faradaic efficiency and stability, and the synergy between photo-and electroinduced mechanisms has been discussed. Thus, we believe that this study provides a meaningful reference for PEC technology in the solar-to-chemical energy conversion in academic research and industrial application.

Experimental section

Preparation of WO 3 photoanode

The synthesis procedure of monoclinic WO 3 was based on that reported in a previous study [START_REF] Yu | Glyceraldehyde production by photocatalytic oxidation of glycerol on WO3-based materials[END_REF].

Typically, 0.6 g of WCl 6 (Sigma-Aldrich) was firstly dissolved in Ethanol (99.8% purity, Sigma-Aldrich) solution (120 mL) and transferred to a 200 mL of Teflon-lined stainless-steel autoclave for hydrothermal treatment at 180 o C for 12 h. Then, the light-blue WO 3 was carefully withdrawn and washed using Ethanol and deionized water 3 times. The collected powder was dried at 80 o C overnight. Finally, the bright yellow monoclinic WO 3 with high crystallinity and suitable oxygen defects (with a ratio of W 5+ /W 6+ of ~0.18/0.82 as determined in ref [START_REF] Yu | WO3-based materials for photoelectrocatalytic glycerol upgrading into glyceraldehyde: Unravelling the synergistic photo-and electro-catalytic effects[END_REF]) was obtained by postcalcination treatment at 450 o C for 1 h (5 o C min -1 of heating rate) in air. Samples were well-grinded before use. A catalyst ink was prepared by mixing the obtained WO 3 catalyst powder with a 5 wt.% Nafion (Sigma-Aldrich) perfluorinated resin solution in aliphatic alcohols and water (to reach a WO 3 :Nafion wt. ratio of 1:1) and 5 mL isopropanol (HPLC-isocratic grade, Carlo Erba Reagents).

Then, the ink was sprayed with an aerograph on a carbon cloth (W1S1011, FuelCellStore) electrodesupport with a thickness of 410 µm and an area of 5.3 cm 2 . The alcohol/water solvent was evaporated at 80 ºC, and the catalyst loading on the carbon cloth was controlled by weight measurement, reaching a value of 3.5 mg cm -2 . Details on the physicochemical characterizations of this WO 3 material can be found in our previous [START_REF] Yu | WO3-based materials for photoelectrocatalytic glycerol upgrading into glyceraldehyde: Unravelling the synergistic photo-and electro-catalytic effects[END_REF].

Membrane Electrode Assembly (MEA) and PEM cell setup

The synthesized carbon cloth-supported WO 3 was used as the photoanode, and a commercial carbon cloth-supported Pt (20% wt.)/C (Fuel Cell Store) with a loading of 0.2 mg•cm -2 was used as cathode.

In the latter case, the carbon cloth behaves as gas diffusion layer (GDL) with a microporous layer (MPL) and a thickness of 365 µm. In the former case, the carbon cloth with a MPL and a thickness of 410 µm serves as a substrate which is a low-cost alternative to GDL materials. A Nafion TM 117 membrane was used as the proton-exchange membrane (PEM) with a thickness of 183 μm, which does not only serve as a solid electrolyte, but also as a physical separator for the obtained redox products. Prior to assembly, the membrane was pretreated by successive immersions in 3 different 150 mL-solutions, 3% wt. H 2 O 2 , 0.5 M H 2 SO 4 and deionized water, in that order. The membrane electrode assembly (anodic photoelectrode/PEM/cathodic electrode) was prepared by hot-pressing under 1 metric ton at 120 o C for 3 min. In this MEA, the anode electrode was placed facing the membrane by the carbon cloth side that was not sprayed with the catalyst ink, while the commercial cathode electrode was placed facing the membrane by the catalyst-MPL side (Fig. 1).

Figure 1. Scheme of the Proton-exchange membrane (PEM) photoelectrocatalytic (PEC) cell set-up employed in this study.

The employed (photo)electrochemical cell was adapted from a 5 cm 2 -commercial electrochemical cell (Dioxide Materials), by designing and constructing one of the two bipolar plates, i.e., the anode side, to house a suitable quartz window for the PEC measurements. The PEC was also modified to introduce heating resistance rods (see Fig. S1 in Electronic Supplementary Information). The MEA was held between two Teflon gaskets to ensure the correct sealing of the Photoelectrolyser and was placed in a way that the catalyst-sprayed side of the photoanode faces the cell window (3.8 cm 2 ).

As depicted in Fig. 1, a temperature control system was used, and 30 mL-solutions of 0.1 M glycerol and pure water (pH 5.5 both) were continuously fed (recycled) by means of a peristaltic pump (ISMATEC SA, Switzerland) through the anode and cathode sides of the cell from the respective reservoirs at a flow rate of approximately 3 mL min -1 each.

Electrochemical characterization

An Origalys OGBO5A electrochemical station (OrigaLys ElectroChem SAS, Rillieux-la-Pape, France) was used to measure the photoelectrochemical properties of the PEC PEM system, by feeding either 0.1 M glycerol (or pure water) to the anodic side of the cell, while feeding pure water to the cathodic side. Photocurrent, linear sweep voltammetry (LSV), cyclic voltammetry (CV), and open circuit potential (OCP) measurements were performed. The transient photocurrent tests were carried out at different applied cell potentials from 0.3 V to 1.5 V with 15 seconds of irradiation interval, using a LED UV lamp as the light source (41 mW cm -2 ), with an incidence area of 1 cm 2 . Prior to these measurements, the system was kept in dark conditions for 2 min to stabilize the current derived from the external bias. CV was recorded between 0 and 1.5 V (cell potentials) at a scan rate of 10 mV s -1 for 10 cycles under light irradiation. All the tests presented in this study were carried out in the same system, without changing the electrodes nor the membrane.

TC/PC/EC/PEC glycerol oxidation

PEC experiments were carried out under ultraviolet light using the same setup and LED UV lamp above mentioned. The PEC was measured under different applied cell voltages, between 0. (GAD/DHA)

(tartronic acid)

(glycolic acid)

(oxalic acid)

(formic acid) (

The total amount (N t,i , in mmol) of unreacted glycerol and of each produced chemical, i, at a given time (i.e., sampling time), t, was calculated from the concentration values quantified by HPLC, according to equation ( 6):

where V t (in L) and (in mM) are the solution volume and the concentration of the chemical i in the cell, respectively, at the time t, V s is the sample volume (i.e., 6 x 10 -4 L) and, thus, the term [ ] stands for the accumulated amount of product or unreacted glycerol collected in previous samplings.

The Glycerol conversion (in %) at a given time was calculated according to equation ( 7):

Where V 0 (in L) and C 0,glycerol (in mM) stand for the initial electrolytic solution volume and glycerol concentration, respectively, and N t,glycerol is the unreacted amount of glycerol at a given time, t.

The Yield (in %) and the Selectivity (in %) of every product were calculated at a given time, t, according to equations ( 8) and ( 9), respectively:

(8) (9)
where f i is the stoichiometric factor of the product i with respect to glycerol (i.e., according to reactions (1-5)).

Then, the faradaic efficiency of each target product, FE (in %) was calculated through equation ( 10).

Where N i and N e (in mmol) stand, respectively, for the number of electrons/holes that would be transferred for the EC/PEC production of the quantified amounts of product i, and those electrochemically transferred according to the measured electric charge, Q (in C), which can be calculated, at a given time, through equations ( 11) and ( 12):

(11) (12)
Where n e,i is the number of mol of electrons/holes theoretically transferred for the production of each mol of target product i (i.e., according to reactions (1-5)), F is the Faraday constant (96485 C mol e- -1

) and I (in mA) is the current obtained at a given time, t (in h).

Results and discussion

Photoelectrochemical characterization

The homemade WO 3 photoanode was coated on a commercial carbon cloth and tested in the PEC proton-exchange membrane (PEM) cell shown in Fig. 1 and Fig. S1, where a commercial Pt/C electrode behaved as the cathode. Through the quartz window, the UV light with a radiation density of 41 mW cm -2 activates the photocatalyst to excite electrons to the conduction band (e - CB ), leaving the same number of holes in the valence band (h + VB ), which may participate in the glycerol valorization (reactions (1-5)) and/or water oxidation (reactions [START_REF] Seferlis | Photoelectrocatalytic electricity and/or H2 production from alcohols: the effect of TiO2 film Thickness[END_REF][START_REF] Sheng | Constructing 1D hierarchical heterostructures of MoS2/In2S3 nanosheets on CdS nanorod arrays for enhanced photoelectrocatalytic H2 evolution[END_REF]). Meanwhile, the resultant protons and electrons are transferred to the cathode through the proton-exchange membrane and the external circuit, respectively, leading to the hydrogen evolution reaction (HER, reaction [START_REF] Reddy | Photocatalytic reforming of biomass derived crude glycerol in water: a sustainable approach for improved hydrogen generation using Ni (OH) 2 decorated TiO2 nanotubes under solar light irradiation[END_REF]). Hence, the external bias contributes to separating the photo-generated electrons from the holes, thus hindering their recombination and increasing the holes availability for oxidation reactions, while the PEM configuration is expected to improve the EC performance and allows the elution of a purified H 2 cathodic stream.

(

) (14) 13
Transient photocurrent response tests were performed at different applied cell potentials (0.3, 0.6, 0.9, 1.2 and 1.5 V) and temperatures (25, 40, 60 and 80 o C) to investigate the photoelectrochemical performance of the synthesized photoanode in 0.1 M glycerol (Fig. 2). A first sharp decrease of the current is typically observed for the first seconds which is mainly due to the decay of the capacitive current, after which rather stable photocurrents have been obtained in all cases.

Both currents and photocurrents increase with the cell voltage at any reaction temperature. One can observe that this PEM PEC system is electrocatalytically active in a potential range (0.3-1.5 V) in which other WO 3 -based photoanodes [START_REF] Raptis | Renewable energy production by photoelectrochemical oxidation of organic wastes using WO3 photoanodes[END_REF][START_REF] Gu | Interface-modulated nanojunction and microfluidic platform for photoelectrocatalytic chemicals upgrading[END_REF][START_REF] Yu | WO3-based materials for photoelectrocatalytic glycerol upgrading into glyceraldehyde: Unravelling the synergistic photo-and electro-catalytic effects[END_REF][START_REF] Yu | Glyceraldehyde production by photocatalytic oxidation of glycerol on WO3-based materials[END_REF] were inactive in a 3-electrodes cell configuration under dark conditions. Indeed, the high contribution of the electrocatalytic activity likely diminished the effect of the increase of the photocurrent due to the light irradiation. It suggests that the PEM configuration implies an especially important upgrading from the electrocatalytic (rather than photocatalytic) point of view. It could be attributed to the compactness of the MEA configuration, which leads to presumably much lower ohmic losses between anode and cathode, as well as enhanced interaction between the catalyst/support/electrolyte elements, than a 3-electrodes cell. Also, the use of carbon cloth as catalyst support and gas diffusion electrode herein increases the electrode roughness and enhances the diffusion of reactants and products, thus favouring their access to the catalyst active sites. For instance, at 60 o C, the obtained current (in the dark) was enhanced from 0.4 to 3.1 mA at cell voltages from 0.3 to 1.5 V, with photo-induced current increments from 0.1 to 0.5 mA, respectively, upon illumination, which denotes a slight increasing trend of the generated photocurrent with the applied voltage. The rise of the temperature also favored the obtained currents, reaching a value at 1.5 V that was four times higher at 80 ºC than that at 25 o C. However, this influence was much less pronounced on the photo-generated currents, with similar current increases upon illumination above 40 ºC, which can be attributed to a likely detrimental temperature effect on the charge carriers' separation [START_REF] Chen | Effects of reaction temperature on the photocatalytic activity of TiO2 with Pd and Cu cocatalysts[END_REF][START_REF] Umar | Photocatalytic degradation of organic pollutants in water, Organic Pollutants-Monitoring[END_REF]. On the other hand, if we compare these transient photocurrent tests in the presence of glycerol (Fig. 2) with those performed in pure water at the same temperatures and applied potentials (Fig. S2), we can observe that the obtained current intensities in the dark are all in the same range and are probably strongly related to the large capacitive current of the photoanode, as typically found on carbonsupported photoanodes [START_REF] Gomis-Berenguer | Photoelectrochemical response of WO3/nanoporous carbon anodes for photocatalytic water oxidation[END_REF], and maybe also to its EC activity for water electrooxidation in the experiments performed at 1.5 V. However, very interestingly, there is a significant increase in the photo-generated current upon irradiation in the presence of glycerol, which acts as a hole-scavenger and benefits the separation of photo-induced charges [START_REF] Ibadurrohman | Photoelectrochemical performance of graphene-modified TiO2 photoanodes in the presence of glycerol as a hole scavenger[END_REF][START_REF] Chong | Impact of glycerol as scavenger for solar hydrogen production from water[END_REF]. It should also be noted that the photocurrent densities obtained in this work are lower than those reported in other studies with conventional 3-electrodes PEC cells, for instance using BiVO 4 -based photoanodes [START_REF] Wu | Solar-driven valorisation of glycerol on BiVO4 photoanodes: effect of co-catalyst and reaction media on reaction selectivity[END_REF][START_REF] Vo | Unveiling the crystallographic facet dependence of the photoelectrochemical glycerol oxidation on bismuth vanadate[END_REF]. However, the performance of the WO 3 electrode used herein would be expected to be enhanced after a further upgrading in terms of morphology, structure and composition.

Cyclic voltammetry (CV) tests have also been performed upon UV irradiation, and the 10 th cycle obtained at each temperature is shown in Fig. 3, both in the presence and in the absence of glycerol.

At low cell potential (0-0.3 V), apart from some cathodic hydrogen evolution on the WO 3 electrode, cathodic and anodic peaks were expected due to the intercalation/de-intercalation of H + in the WO 3 [START_REF] Upadhyay | On the supercapacitive behaviour of anodic porous WO3-based negative electrodes[END_REF][START_REF] Gupta | Phase transformation in tungsten oxide nanoplates as a function of post-annealing temperature and its electrochemical influence on energy storage[END_REF][START_REF] Sfaelou | Mesoporous WO3 photoanodes for hydrogen production by water splitting and PhotoFuelCell operation[END_REF]. Then, during the forward scan in pure water (Fig. 3a), an increase in the anodic current can be observed at 0.5-0.6 V, likely due to the intercalation of oxygen into the vacancies of the photoanode oxide network [START_REF] Grenier | Electrochemical oxygen intercalation into oxide networks[END_REF][START_REF] Liang | Tungsten blue oxide as a reusable electrocatalyst for acidic water oxidation by plasma-induced vacancy engineering[END_REF], followed by the oxygen evolution curve at higher potentials. On the other hand, in the presence of glycerol (Fig. 3b), the anodic peaks obtained at low potentials were likely overlapped with the current increase derived from glycerol oxidation. Indeed, under cell voltages below c.a. 0.7 V, the obtained currents are higher in glycerol solution than in pure water (e.g., 2.4 mA with 0.1 M glycerol vs. 1.8 mA with pure water at 0.6 V and 80ºC), which can be attributed to the low onset oxidation potential of glycerol oxidation (typically lower than 0.4 V vs. RHE on Wbased electrodes [START_REF] Wu | Solar-driven valorisation of glycerol on BiVO4 photoanodes: effect of co-catalyst and reaction media on reaction selectivity[END_REF][START_REF] Gu | Interface-modulated nanojunction and microfluidic platform for photoelectrocatalytic chemicals upgrading[END_REF][START_REF] Yu | WO3-based materials for photoelectrocatalytic glycerol upgrading into glyceraldehyde: Unravelling the synergistic photo-and electro-catalytic effects[END_REF]). Then, in the potential range of 0.7-1.5 V, the currents obtained in the presence of glycerol are lower, and a reasonable hypothesis is the partial poisoning of the catalyst surface by adsorbed reaction intermediates at this potential range. However, as the potential or temperature are further increased and these surface species are desorbed/oxidized, the currents obtained in glycerol solution reach again similar values than those obtained in pure water (e.g., 6.6 and 6.7 mA, respectively, at 1.5 V and 80ºC), derived from the contribution from oxygen evolution reaction and the oxidation of fresh glycerol and its derived molecules. Thus, from the transient photocurrent and CV measurements, it is clear the beneficial influence of both the cell voltage and temperature on the overall photo-electro-catalytic activity of the PEM Photoelectrolyser. It is worth noting that, under given PEC operation conditions, the expected hydrogen production rate in this PEM cell is directly related to the obtained current intensity, since both glycerol oxidation and water oxidation reactions at the anode imply the reduction of protons at the cathode. Thus, regardless of the products obtained in the anodic side of the cell, an increase in both parameters, i.e., potential and temperature, was found to be beneficial when dealing with the maximization of the obtained current intensity and, therefore, of the hydrogen production on the cathode side (reaction ( 15)). However, for the optimization of the bifunctional Photoelectrolyser, the anodic performance for biomass valorization (in terms of products selectivity) must be also evaluated.

Glycerol valorization by PEC

The operation conditions of the PEM PEC system have also been optimized for the selective glycerol valorization to produce high-value-added products, by focusing on the obtained liquid products, and with special interest in GAD and DHA, claimed as the most valuable ones.

Effect of cell voltage

In all the tests, under light irradiation on the WO 3 photoanode, GAD and DHA were obtained as the main products, along with some formic acid (FA) and trace amounts of glycolic (GA), tartronic (TA), and oxalic (OA) acids. Other unknown product was also detected by HPLC in some cases and, given that the overall liquid products selectivity always remained below 100% in all cases, significant amounts of CO 2 were also expected to be evolved, derived from glycerol mineralization. However, it should be noted that the use of a PEM membrane to separate anodic and cathodic compartments still ensures the elution of pure H 2 gas stream from the latter in any case. Fig. 4a-c and Fig. 4d-f show the dynamic results obtained at 60ºC under photocatalytic (PC) conditions (i.e., in the absence of any electric polarization) and under PEC conditions at 1.2 V, respectively, while Fig. S3 shows those obtained under intermediate cell voltages between 0.3 and 1.2 V. Note that all concentration profiles shown in the manuscript refer only to the anodic liquid products that have been identified. In all cases, one can observe that the concentration of the target liquid products in the cell linearly increased with time, leading to constant production rates (11.1 and 5.2 mmol m -2 h -1 for GAD and DHA, respectively) upon increasing glycerol conversion with an average consumption rate of 42.0 mmol m -2 h -1 . Thus, increasing yields and larger or, at least, stable selectivities were obtained with the reaction time. When comparing the obtained GAD production rate with those reported in the field of electrocatalytic glycerol oxidation, it is noteworthy that there are only two studies using flow-through electrochemical reactors where GAD was quantitatively generated, by means of Pt-based anodes. The GAD production rate obtained herein on the WO 3 photoanode in the near-neutral media is similar to that obtained at 60ºC using a Pt/C catalyst and a Nafion membrane (15.6 mmol m -2 h -1 ) [START_REF] Kim | Selective glycerol oxidation by electrocatalytic dehydrogenation[END_REF], and lower than that reported with a membrane-less configuration at room temperature using a Pt 9 Bi 1 /C catalyst (1950 mmol m -2 h -1 ) [START_REF] González-Cobos | Development of bismuth-modified PtPd nanocatalysts for the electrochemical reforming of polyols into hydrogen and value-added chemicals[END_REF]. However, in the latter case, strongly alkaline conditions were employed (0.5 M NaOH) and the glycerol feeding rate was also two orders of magnitude higher than in the present work (40 vs. 0.3 mmol min -1 ). Regarding the external bias influence, in our previous study using a similar WO 3 photoelectrode for the selective glycerol oxidation in a conventional PEC reactor, the light showed to be the trigger of the reaction while the external voltage seemed to promote the separation of photogenerated electrons and holes in the photocatalyst, thus raising the PEC activity and the GAD and DHA yields, in particular, highlighting the promising properties of this photoelectrode for the selective glycerol valorization [START_REF] Yu | WO3-based materials for photoelectrocatalytic glycerol upgrading into glyceraldehyde: Unravelling the synergistic photo-and electro-catalytic effects[END_REF]. A similar promoting effect of the external bias on the DHA and GAD yields was observed in the PEM Photoelectrolyser (Fig. 5). Under purely PC conditions, GAD and DHA were already selectively generated with a cell concentration after 6 h of 0.50 and 0.26 mmol L -1 , respectively. Their production was very similar upon 0.3 V but increased upon the application of higher cell voltages to reach 1.29 and 0.61 mmol L -1 for GAD and DHA after 6 h, respectively.

Similar glycerol conversions were reached under all applied potentials after 6 hours-test, i.e., 4.2-4.7%. Given the negligible current obtained at low potentials (i.e., 0.3 V, Fig. S4a) the conversion observed under such conditions is rather attributed to a bare thermos-catalytic decomposition of glycerol as will be shown below. However, what is most interesting is that GAD and DHA yields were increased by more than 2 times from 0.3 V to 1.2 V (Fig. S3e-h). Indeed, in the case of GAD, the yield showed to increase linearly in this potential range, at a rate of 0.82% V -1 . On the other hand, the GAD+DHA selectivity gradually increased with the applied potential from c.a. 15.2% (0.3 V) to 38.3% (1.2 V) (Fig. S3i-l). With respect to purely PC conditions (Fig. 4), the GAD and DHA selectivity only slightly increased, but the corresponding glycerol conversion more than doubled by PEC at 1.2 V after 6 h on stream. This explains the enhanced yield of the desired products at 1.2 V compared with the purely PC conditions. Besides, the influence of the potential was even greater on the obtained current, and therefore on the hydrogen production at the cathode (Fig. 5 and Fig. S4a). Given the important competition of glycerol overoxidation reactions expected in the studied potential range, the enhanced C 3s selectivity by PEC upon increasing potentials is of especial relevance. Apart from being the first photoelectrocatalytic study of glycerol oxidation in a PEM-type cell, the obtained selectivity results also stand out with respect to the published works on purely electrocatalytic systems.

Table 1 collects a selection of results obtained on glycerol electrooxidation in all kinds of flowthrough cells, like compact PEM electrolysers [START_REF] Kim | Selective glycerol oxidation by electrocatalytic dehydrogenation[END_REF][START_REF] Marshall | Production of hydrogen by the electrochemical reforming of glycerol--water solutions in a PEM electrolysis cell[END_REF][START_REF] Fan | High Entropy Alloy Electrocatalytic Electrode toward Alkaline Glycerol Valorization Coupling with Acidic Hydrogen Production[END_REF][START_REF] De Paula | Electrochemical reforming of glycerol in alkaline PBIbased PEM reactor for hydrogen production[END_REF][START_REF] De Paula | Influence of the anolyte feed conditions on the performance of an alkaline glycerol electroreforming reactor[END_REF][START_REF] Bambagioni | Self-sustainable production of hydrogen, chemicals, and energy from renewable alcohols by electrocatalysis[END_REF], other flow reactors employing polymer electrolyte membranes [START_REF] Morales | Electrocatalytic conversion of glycerol to oxalate on Ni oxide nanoparticles-modified oxidized multiwalled carbon nanotubes[END_REF][START_REF] Brix | Electrocatalytic Oxidation of Glycerol Using Solid-State Synthesised Nickel Boride: Impact of Key Electrolysis Parameters on Product Selectivity[END_REF][START_REF] Brix | others, Structure-Performance Relationship of LaFe1-xCoxO3 Electrocatalysts for Oxygen Evolution, Isopropanol Oxidation, and Glycerol Oxidation[END_REF][START_REF] Houache | Selective Electrooxidation of Glycerol to Formic Acid over Carbon Supported Ni1--x M x (M= Bi, Pd, and Au) Nanocatalysts and Coelectrolysis of CO2[END_REF] and recently explored membrane-less configurations [START_REF] González-Cobos | Development of bismuth-modified PtPd nanocatalysts for the electrochemical reforming of polyols into hydrogen and value-added chemicals[END_REF][START_REF] Houache | Selective Electrooxidation of Glycerol to Formic Acid over Carbon Supported Ni1--x M x (M= Bi, Pd, and Au) Nanocatalysts and Coelectrolysis of CO2[END_REF][START_REF] Houache | Influence of Pd and Au on electrochemical valorization of glycerol over Ni-rich surfaces[END_REF][START_REF] Houache | Modification of nickel surfaces by bismuth: Effect on electrochemical activity and selectivity toward glycerol[END_REF][START_REF] Shubair | Electrolysis of glycerol to value-added chemicals in alkaline media[END_REF].

Although the glycerol conversion values in literature (the reported ones) were in several cases higher than those obtained herein, one can stress that most of the anodes were tested in strongly alkaline electrolytes and proved to be completely unselective for GAD or DHA. The main products usually are GRA, TA or FA, with only two cases where bulk GAD production was reported using platinum-group metal (PGM) catalysts [START_REF] Kim | Selective glycerol oxidation by electrocatalytic dehydrogenation[END_REF][START_REF] González-Cobos | Development of bismuth-modified PtPd nanocatalysts for the electrochemical reforming of polyols into hydrogen and value-added chemicals[END_REF], as mentioned above. Moreover, it is also noteworthy that, in conventional EC systems, the increase of the applied potential, in the range studied herein, typically results in the generation of increasingly oxidized glycerol products (e.g., glyceric, hydroxypyruvic and tartronic acids), which is evident from the decrease of GAD selectivity with the cell voltage in the two aforementioned works [START_REF] Kim | Selective glycerol oxidation by electrocatalytic dehydrogenation[END_REF][START_REF] González-Cobos | Development of bismuth-modified PtPd nanocatalysts for the electrochemical reforming of polyols into hydrogen and value-added chemicals[END_REF]. This contrasts with the stable GAD and DHA selectivity obtained herein, likely due to the selective PEC behavior of the WO 3 material, and represents one of the main advantageous aspects of the proposed PEC technology compared to conventional EC. It must be also noted that, in terms of obtained current densities, those obtained in this work are c.a. 2 orders of magnitude lower than those reported with conventional EC glycerol electrolysers, as it is also typically found in the field of PEC water splitting [START_REF] Zhang | Enhancing hydrogen evolution by photoelectrocatalysis of water splitting over a CdS flowers-loaded TiO2 nanotube array film on the Ti foil substrate[END_REF][START_REF] Li | Effect of water and annealing temperature of anodized TiO2 nanotubes on hydrogen production in photoelectrochemical cell[END_REF][START_REF] Marschall | Composite protonconducting polymer membranes for clean hydrogen production with solar light in a simple photoelectrochemical compartment cell[END_REF][START_REF] Stoll | Solar fuel production in a novel polymeric electrolyte membrane photoelectrochemical (PEM-PEC) cell with a web of titania nanotube arrays as photoanode and gaseous reactants[END_REF]. This is likely influenced by the different nature of the materials employed as anodes/photoanodes and to the different light-and electrolyteexposed surface phenomenon taking place. However, the PEC approach offers the possibility of operating at lower voltages than conventional EC systems, with the consequent energy saving, while employing renewable energy sources. This, along with the outstanding C 3 selectivity found in this integrated system could make PEC an efficient and sustainable alternative technology for glycerol valorization after the proper photoelectrode engineering and operation conditions optimization. [79]

a Data drawn or estimated from the information reported in the articles (RT: Room temperature; polarization in terms of cell voltage unless otherwise stated). b Selectivity values for the main products obtained (minor when not specified). GAD: Glyceraldehyde; DHA: Dihydroxyacetone; FA: Formate; GA: Glycolate; TA: Tartronate; GRA: Glycerate; LA: Lactate; OA: Oxalate; AA: Acetate; HPA: Hydroxypyruvate. c Faradaic efficiency (FE) values (selectivity not reported).

Effect of cell temperature

Fig. 6 and Fig. S5 show the effect of cell temperature on the PEC performance, in the range from 25 to 80 ºC, at a fixed applied cell potential of 1.2 V, in order to provide the strongest possible capability to accelerate photo-induced charge separation without water oxidation occurrence. As opposed to the cell voltage, the temperature did not have a significant promoting effect on the PEC glycerol valorization. GAD and DHA production was only slightly enhanced by heating up to 60°C and even decreased at 80 ºC. Although there are very few publications about the effect of reaction temperature on PC and PEC performances, in general terms, the temperature increase is expected to enhance the reaction kinetics and electrolyte conductivity, as reported for water splitting [START_REF] Katakis | Photocatalytic splitting of water: increase in conversion and energy storage efficiency[END_REF][START_REF] Velázquez | Effect of reaction temperature and sacrificial agent on the photocatalytic H2-production of Pt-TiO2[END_REF] and organic matter degradation [START_REF] Ghasemi | Kinetics and thermodynamics of photocatalytic degradation of organic pollutants in petroleum refinery wastewater over nano-TiO2 supported on Fe-ZSM-5[END_REF][START_REF] Hu | Temperature effect on the photocatalytic degradation of methyl orange under UV-vis light irradiation[END_REF]. For instance, Velazquez et al. [START_REF] Velázquez | Effect of reaction temperature and sacrificial agent on the photocatalytic H2-production of Pt-TiO2[END_REF] found a positive effect of the cell temperature in the PC production of H 2 from water and water/methanol solutions. However, the rise of the temperature may also hinder the charge carriers' separation, as recently reported, for instance, by Chen et al. [START_REF] Chen | Effects of reaction temperature on the photocatalytic activity of TiO2 with Pd and Cu cocatalysts[END_REF]. These authors observed that the PC activity of TiO 2 -based materials for the degradation of methylene blue decreased at temperatures higher than 70 ºC. Moreover, the temperature may also strongly influence the products' desorption and reactants' adsorption, which are typically considered the rate-limiting steps in PC systems at temperatures below 20 ºC and above 80 ºC, respectively [START_REF] Umar | Photocatalytic degradation of organic pollutants in water, Organic Pollutants-Monitoring[END_REF][START_REF] Herrmann | Heterogeneous photocatalysis: fundamentals and applications to the removal of various types of aqueous pollutants[END_REF]. For these reasons, the temperature range of 20-80 ºC seems to be optimum for the PEC oxidation of organic matter. In the present work, the glycerol conversion values reached after 6 hours-test slightly increased from 2.8 to 4.9% in this temperature range, with stable low GAD and DHA yields of 0.9-1.2% and 0.4-0.5%, respectively (Fig. S5e-h). Regarding the selectivity obtained for the identified liquid products (Fig. S5i-l), the overall value after 6-hours test slightly decreased from 55 to 42% by heating from 25 to 60 ºC. In particular, fairly stable selectivity values of 26-34% and 12-16% were obtained for GAD and DHA, respectively. These values therefore denote a significant overoxidation of glycerol and/or its derived products (> 50%) to CO 2 or other organic compounds, especially at 80 ºC, in which case the C 3 product selectivity clearly shows a decreasing trend with time and with the GLY conversion (Fig. S5l). Indeed, the amount of the aforementioned unknown liquid product detected by HPLC increased with the temperature (see Fig. S6). Likewise, the obtained current after 6 hours seemed to find an optimum at 60 o C (Fig. 6 and Fig. S4b). As previously mentioned, this current can be directly related to the production of hydrogen at the cathode. Thus, in view of these experiments, we can conclude that the maximum operating temperature to enhance both the hydrogen generation (at the cathode) and the selective glycerol valorization (at the anode) by PEC is 60 ºC. Under these conditions, the application of an optimum cell voltage of 1.2 V allows to obtain stable GAD and DHA production rates at the anode side of 11.1 and 5.2 mmol m -2 h -1 , respectively, and a simultaneous H 2 production rate at the cathode side of 44.0 mmol m -2 h -1 , as estimated from a steady-state current intensity of c.a. 1.25 mA.

Stability evaluation

In order to evaluate the stability of the system, another PEC measurement was performed under relatively harsh conditions (1.2 V, 80 o C) for three successive days, with 3 successive operation periods of 9 hours (27 h in total) (Fig. S7). After each pulse, the cell was cooled down to room temperature and the flow kept running. Results after 6 hours are similar to those reported in Fig. 6 and, interestingly, the targeted value-added products, GAD and DHA, were still the main obtained products after 27 h, reaching yields of 3.6% and 1.5%, respectively, with a still low formic acid yield of 0.3% and an increase in the glycerol conversion up to ~40%, i.e., around 8 times higher than that reached in the short-term experiment (6 h), with an average consumption rate of 79.6 mmol m -2 h -1 .

According to the continuous increase in glycerol conversion and the stable current intensity observed during this test (with a decrease of c.a. 0.1 mA in the last 24 hours, Fig. S7e), the proposed PEM Photoelectrolyser using a WO 3 photoanode showed not only the capability for simultaneous hydrogen generation and glycerol valorization, but also a good stability in long-term operation. However, it should be noted that, under the studied operation conditions, GAD and DHA production rates slowed down for the last operation hours, with a presumably increase of CO 2 formation. Consequently, the joint selectivity of the targeted C 3 compounds continuously decreased for the 27 hours-test, down to 13.4%. In view to the practical application of the PEC PEM cell for the selective glycerol valorization, higher solution volumes should be treated, thus operating under low-conversion conditions and, preferably, the targeted products should be continuously separated from the anode effluent and collected, in order to avoid their recycling and overoxidation. On the other hand, the repeatability of the PEC measurements has also been verified by replicating those performed under reference PEC conditions (an applied bias of 1.2 V and a cell temperature of 60ºC and 80ºC), as it can be observed in Fig. S8.

Technology comparison with EC, TC and PC

The PEC performance of the PEM cell for glycerol valorization has also been evaluated in a broader context by comparing the above-discussed results with those obtained at different temperatures under purely electrocatalytic (EC), photocatalytic (PC) and thermocatalytic (TC) conditions, i.e., by removing the light irradiation, the external bias, and both stimuli, respectively. An overview of the results obtained with the different technologies can be found in Fig. S9. Among them, the only technology capable to produce value-added organics and pure hydrogen gas separately, apart from PEC, is the electrocatalysis. In this way, glycerol electro-oxidation (reactions (1-5)) takes place on the WO 3 catalyst surface releasing protons and electrons that are transferred through the proton-exchange membrane and the external circuit, respectively, to the Pt cathode, where H 2 evolves. Fig. 7 and Fig. S9i-l show the liquid products distribution obtained by EC glycerol oxidation at different temperatures between 25 and 80 ºC under an applied cell voltage of 1.2 V. The temperature increase is expected to enhance the reaction kinetics, the mass transport and the membrane electrical conductivity. Indeed, the PEM cell configuration has been widely employed for hydrogen production from alcohols electro-reforming at temperatures closed to 80 ºC [START_REF] Lamy | Kinetics analysis of the electrocatalytic oxidation of methanol inside a DMFC working as a PEM electrolysis cell (PEMEC) to generate clean hydrogen[END_REF][START_REF] Sapountzi | Hydrogen from electrochemical reforming of C1--C3 alcohols using proton conducting membranes[END_REF][START_REF] Caravaca | Electrochemical reforming of ethanol--water solutions for pure H2 production in a PEM electrolysis cell[END_REF][START_REF] Marshall | Production of hydrogen by the electrochemical reforming of glycerol--water solutions in a PEM electrolysis cell[END_REF][START_REF] De Paula | Electrochemical reforming of glycerol in alkaline PBIbased PEM reactor for hydrogen production[END_REF]. However, in the present case, although a significant EC activity for GAD production (0.382 mmol L -1 ) was observed at room temperature, it was still much lower than that obtained by PEC of (1.059 mmol L -1 ) and the heating showed a clear detrimental effect on the selective glycerol valorization, which became negligible at 80 ºC. Instead, the obtained currents increased with the temperature, as expected from the previous results on transient photocurrent measurements in dark conditions (Fig. 2). This enhanced EC activity can be mainly attributed to glycerol overoxidation reactions to gaseous CO 2 or other compounds which, in turn, are expected to be favored by hydroxyl or oxygen radicals generated from water [START_REF] Xue | Electrochemical and photoelectrochemical water oxidation for hydrogen peroxide production[END_REF][START_REF] Zhang | Near-complete suppression of oxygen evolution for photoelectrochemical H2O oxidative H2O2 synthesis[END_REF]. The EC behavior is therefore different from that observed in PEC measurements, in which both the GAD/DHA production rates and the obtained currents were slightly enhanced with temperature up to 60 ºC (Fig. 6). Hence, if this dual compartment cell is used for pure EC reactions at 1.2 V, a high temperature is favorable for hydrogen production, while a low temperature is beneficial for selective glycerol valorization. Besides, a suitable external voltage is also necessary for the hydrogen generation by EC. For instance, at a low cell voltage of 0.3 V, the obtained current was negligible, even at 60 ºC (Fig. S10), and the observed glycerol oxidation products were likely derived from a purely thermocatalytic (TC) process, as can be observed in Fig. S9. Glycerol can be fully converted into DHA, glyceric acid or other organic compounds by TC at temperatures between 25 and 160 ºC by using 1-10 bar oxygen, as reviewed by Dodekatos et al. [START_REF] Dodekatos | Recent Advances in Thermo-, Photo-, and Electrocatalytic Glycerol Oxidation[END_REF]. In this work, the measurements carried out in the absence of any light irradiation or external bias showed a negligible TC activity of the WO 3 catalyst at room temperature, but significant GAD production rates were observed upon increasing the temperature (Fig. S9a-d), even overpassing those obtained by electrocatalysis, which can be attributed to the promoting effect of EC operation on organic molecules mineralization and thus CO 2 generation, as will be discussed below. On the other hand, it is important to note that under either PEC or EC conditions, not only fresh glycerol but any other organic product derived from concurrent EC/PEC/TC/PC conversion processes is prone to be further oxidized.

Regarding pure PC reactions (Fig. S9e-h), the WO 3 photoanode showed an important production of GAD, with an optimum temperature of 40 ºC in this case. As discussed in section 3.2.2, the sensitivity to temperature in the range of 25-80 ºC mostly stems from the influence on the recombination efficiency of photogenerated electrons and holes in WO 3 [START_REF] Chen | Effects of reaction temperature on the photocatalytic activity of TiO2 with Pd and Cu cocatalysts[END_REF][START_REF] Umar | Photocatalytic degradation of organic pollutants in water, Organic Pollutants-Monitoring[END_REF]. This was also evidenced in the PEC measurements performed at different temperatures (Fig. 6) although, in this operation mode, the optimum value was 60 ºC. Another sign of the temperature effect on the PC activity was noticed by analyzing the time response of the open circuit potential (OCP) upon illumination (Fig. S11). At 25 ºC, the decay in the OCP for the first seconds under light irradiation was higher than that observed at 80 ºC, which could be linked to a higher photoactivity in the former case due to a higher accumulation of photogenerated electrons [START_REF] Gomis-Berenguer | Photoelectrochemical response of WO3/nanoporous carbon anodes for photocatalytic water oxidation[END_REF][START_REF] Carrera-Crespo | Unrevealing the effect of transparent fluorine-doped tin oxide (FTO) substrate and irradiance configuration to unmask the activity of FTO-BiVO4 heterojunction[END_REF]. This pioneering analysis of the glycerol oxidation results obtained in all operation modes, i.e., PEC, PC and EC, demonstrates that PEC performance for glycerol valorization, in terms of target C 3 -product yield, is not only better than that obtained by PC, due to the promotional effect of the external bias on the charge carriers separation, but also greater than the sum of the individual yields obtained by PC and EC, at a given cell temperature. The superior PEC performance was especially evident at high temperatures. In fact, at 80 ºC, the production rates of GAD, DHA and all other identified liquid products were negligible (with glycerol conversion values of 2-5%) in all configurations except in PEC.

The synergistic effect between photo-and electro-catalysis was also found in terms of obtained current intensity, and thus hydrogen generation. For instance, one can observe that the steady-state current intensities obtained by PEC at 1.2 V at different temperatures (Fig. 6) were higher than those obtained by EC (Fig. 7) in all cases, with enhancements from 32% (at 80ºC) to 154% (at 40ºC). This demonstrates that the application of an external potential facilitates the separation of the charge carriers and thus increases the availability of the photogenerated holes for the glycerol oxidation reactions. At the same time, the light irradiation and the consequent generation of those charge carriers can enhance the overall number of electrons transferred between the photoanode and the cathode for their consumption in HER. In other words, PEC technology proves to be the most promising among the explored technologies for the synthesis of both hydrogen and value-added C 3 compounds.

Electron transfer efficiency assessment

In order to get more insights into the reactions preferably taking place on the WO 3 photoanode, the faradaic efficiency (FE) obtained under the different PEC and EC operation conditions has also been evaluated, along with the total organic carbon (TOC) measurements. Fig. 8a 8a). The charge enhancement observed by increasing the temperature, and also by operating in the Photoelectrolyser configuration with respect to EC, can be linked to an increase in the consequent hydrogen production as above discussed. The improvements in the production rates of GAD and DHA by PEC vs. EC observed in the previous section were even greater than the respective increases in the transferred charges, which denotes that the faradaic efficiency (FE) values of the selective glycerol valorization reactions were higher by PEC than by EC, as can be observed in Fig. 8b and Fig. 8c.

The influence of the temperature on the faradaic efficiency was different depending on the operation mode, i.e., EC or PEC. The FE values obtained for the targeted C 3 products by pure electrocatalysis strongly decreased with the temperature, from 25.7% at room temperature to less than 1% at 80 ºC (Fig. 8b). This denotes that, in dark conditions, the increase in the electric charge transferred from the WO 3 catalyst with the temperature (Fig. 8a) is mostly attributed to the enhancement of glycerol overoxidation reactions, CO 2 probably being the main obtained product, especially at high temperature. However, in the tests performed under both light irradiation and external bias (Fig. 8c), the FE values obtained for GAD+DHA were higher and much more stable with the temperature, decreasing from 49.9% (25 ºC), to 30.3% (80 ºC). At this high temperature, the C 3 FE even increased to 40.1% when the measurement was extended from 6 to 27 hours, indicating the good stability of C 3 FE. To understand this FE enhancement with time, one must take into account that the long-term decrease in the current density is more pronounced than the corresponding decrease in the C 3 production. The higher C 3 production by PEC is also evidenced by the higher stability of the TOC value obtained under these conditions. Fig. S12a and S12b show the variation of the TOC with the temperature under EC and PEC conditions, respectively. In the former case, a decreasing trend was obtained between 25 and 60ºC, with an average value of 3589 ± 82 mg L -1 , while the TOC was more stable in this temperature range under PEC conditions, with an average value of 3603 ± 33 mg L -1 . In the latter conditions, a significant TOC decrease was only observed at 80ºC. Thus, the results obtained in this operation mode seem to indicate that the increased number of electrons transferred under PEC conditions by increasing the temperature from 25 to 60 ºC is mainly derived from the selective glycerol oxidation reactions. One can conclude that, from the energy efficiency point of view, the Photoelectrolyser is also more favorable for the simultaneous hydrogen generation and glycerol valorization than the conventional EC configuration. These results open new doors in the application of the PEC approach to the electrolysis of organic molecules easily adapting commercially available PEM cells, although further efforts should be made to maximize their photo-and photoelectrocatalytic features, for instance, by optimizing the light source, the light-exposed photoelectrode surface and, very specially, by tailoring more efficient photoelectrodes through the tuning of their nanostructure and/or composition.

Conclusions

A photoelectrocatalytic (PEC) cell with a proton-exchange membrane (PEM) configuration has been developed, for the first time, for the simultaneous glycerol valorization and green H 2 generation under soft pH conditions. For this purpose, a WO 3 catalyst which is selective for glyceraldehyde (GAD) and dihydroxyacetone (DHA) production has been employed as photoanode. The electrocatalytic (EC), photocatalytic (PC) and thermocatalytic (TC) effects have been assessed and the following conclusions can be drawn from this study:

-An increase of the temperature and, specially, the voltage enhances the current generated by the photoelectrolyser, and thus the hydrogen production rate at the cathode. The cell voltage has also a positive effect up to 1.2 V on the selective glycerol oxidation to C 3 compounds at the anode, in contrast to conventional EC systems, due to the enhanced photogenerated charge carriers' separation.

-Under optimum PEC operation conditions, 60 ºC and 1.2 V, stable GAD and DHA production rates of 11.1 and 5.2 mmol m -2 h -1 are obtained, respectively, along with the simultaneous production of 44.0 mmol H 2 m -2 h -1 . Under such conditions, the selectivity of GAD+DHA reaches 38% after 6 hours operation, corresponding with 4.5% glycerol conversion.

-In this PEM configuration, the WO 3 photoanode shows a much higher EC activity in dark conditions than conventional PEC systems operating in batch configuration. The increase of either the temperature (up to 80 ºC) or the cell voltage (up to 1.2 V) enhances the EC hydrogen production at the cathode and favours the deep oxidation of glycerol and/or its derived molecules, likely to CO 2 , vs.

glycerol partial oxidation at the anode.

-Under PC conditions, the catalyst shows a high selectivity for GAD production with an optimum operation temperature of 40 ºC. While the direct electron transfer from the anode under EC conditions favours the glycerol mineralization, the holes photogenerated by PC seem to be rather involved in the selective glycerol oxidation reactions to produce the targeted C 3s .

-A strong synergistic effect is observed between electro-and photo-catalytic effects. Thus, PEC proves to be the most promising among the explored technologies studied for the synthesis of both hydrogen and GAD/DHA in a PEM cell, as well as from the energy efficiency point of view.

3 and 1. 2 V

 2 , and at different temperatures between 25 and 80 ºC. Purely PC, EC and TC experiments were also carried out at different cell temperatures in the absence of either external bias, light irradiation or both, respectively. Prior to all measurements, the cell and all lines of the experimental setup were systematically deep cleaned. Then, the anolyte and catholyte solutions were initially flowing through the cell for 30 min under dark and open-circuit conditions, at room temperature, to achieve the adsorption-desorption equilibrium of glycerol on the surface of the WO 3 catalyst. Then, the PEC/PC/EC/TC measurements were initiated and, every hour, a sample (0.6 mL) was collected from the anode solution and immediately filtered by a Millipore 0.45 µm (hydrophilic PVDF) membrane using a plastic syringe. The reaction time was generally 6 h, except for the long-term experiment (27h). The concentrations of glycerol and derived products were analyzed by a Shimadzu SPD-M20A ultrafast high-performance liquid chromatography (HPLC) equipped with a Transgenomic ICSep ICE-COREGEL-87H3 organic acid column. 5 mmol L -1 of H 2 SO 4 with a flow rate of 0.7 mL min -1 served as the mobile phase and the column temperature was 30 o C. The products of glycerol oxidation were determined by the ultraviolet detector at the wavelength of 210 nm. Glycerol was analyzed by the refractive index detector (RID). The concentration of total organic carbon (TOC) of the solutions before and after the PEC tests were measured using a Shimadzu TOC-VCPN analyzer equipped with an auto-sampler.According to the liquid products detected, the photo-(or electro-)catalytic reactions (1-5) were assumed to take place on the WO 3 catalyst surface, by considering the transfer of either holes left in the valence band (h + VB ) upon illumination (under PEC or PC operation conditions) or electrons (e -, under EC conditions).

Figure 2 .

 2 Figure 2. Transient photocurrent response at different cell voltages (0.3-1.5 V) and temperatures (25-

Figure 3 .

 3 Figure 3. Cyclic voltammetry (CV) performed in the Photoelectrolyser at different temperatures (25-80 ºC) under UV light irradiation (41 mW cm -2 ) using (a) water or (b) 0.1 M glycerol as anodic solution, and water as cathodic solution. Scan rate: 10 mV s -1 . The 10 th cycle is shown in each case.

Figure 4 .

 4 Figure 4. (a,d) Time evolution of liquid products concentration in the anodic solution, and evolution

Figure 5 .

 5 Figure 5. Influence of the cell voltage on the liquid products concentration in the anodic solution and

Figure 6 .

 6 Figure 6. Influence of the Photoelectrolyser temperature on the liquid products concentration in the

Figure 7 .

 7 Figure 7. Influence of the cell temperature on the liquid products concentration in the anodic solution

Figure 8 .

 8 Figure 8. (a) Comparison of the charge transferred during electrocatalytic (EC) and

7

 7

  .

Table 1 .

 1 Glycerol (GLY) oxidation selectivity reported with different flow-through electrochemical cells.

	Cell configuration	Membrane / Separator	Anode	Anolyte	Operation conditions a	GLY conv. / % a	Main liquid products (Selectivity / %) a,b	Ref.
	PEC PEM cell with MEA	Nafion 117	WO 3 / Carbon cloth	0.1 M GLY	60 ºC, 1.2 V, 6 h	4.5	GAD (26) + DHA (12) + FA (2) + GA + TA	This work
		Nafion 115	Pt (20 wt.%) / C	0.1 M GLY	60 ºC, 1 V, 5 h	9	GRA (80) + GAD (8)	[52]
		Nafion 212	Pt (20 wt.%) / RuIrO x	8.5 M GLY	70 ºC, 5 mA cm -2 , 0.5 h		Liquid products not analyzed	[53]
	PEM cell with	Proton-exchange	CoNiCuMnMo / Carbon cloth	0.1 M GLY + 1 M KOH	RT, 10 mA cm -2 , 12 h	-	FA (FE = 93.5%) c	[54]
	MEA	KOH-doped	PtRu / C (20 wt.%	1 M GLY + 4 M KOH	60 ºC, 20 mA cm -2	-	TA (61) + GRA (31) + GA + LA	[55]
		PBI	metal)	2 M GLY + 4 M KOH	75 ºC, 80 mA cm -2	-	TA (45) + GRA (36) + OA + FA + GA	[56]
		Tokuyama A006	Pd-(NiZn) / C / Ni mesh	1.1 M GLY + 2 M KOH	RT, 19 mA cm -2 , 15 h	-	TA (36) + GRA (35) + GA + OA + FA	[57]
	3-electrode membrane-separated cell	Fumasep FAA-3-PK-130	NiO x / O-MWCNT / Carbon paper Ni x B / Carbon paper 0.5 M GLY + 2 M KOH 0.1 M GLY + 1 M KOH LaFe 0.31 Co 0.69 O 3 / Carbon paper 1 M GLY + 1 M KOH	1.5 V vs. RHE, 6 h 1.54 V vs. RHE, 4 h 1.59 V vs. RHE, 24 h	80 10 15	FA (55) + OA + GA + GRA + AA FA (55) + TA (17) + GA (11) + GRA + OA FA (17) + GA (6) + GRA + LA + OA + AA	[58] [59] [60]
		Fumasep FAA-3-PK-75	Ni 9 Au 1 / C	2 M GLY + 2 M KOH	20 ºC, 1.5 V	-	FA (-) d + LA (-) d	[79]
			Pt 9 Bi 1 / C / Carbon cloth	2 M GLY + 0.5 M NaOH	RT, 0.55 V, 4 h	6	GAD (80) + GRA (10) + HPA + TA	[78]
	Compact		Ni 8 Pd 2 / C	0.1 M GLY + 1 M KOH	50 ºC, 1.3 V, 6 h	28	GRA (47) + FA (39) + GA + TA + OA + LA	[80]
	membrane-less cell	Filter paper	Ni 9 Bi 1	0.1 M GLY + 1 M KOH	50 ºC, 1.3 V, 6 h	25	GRA (41) + FA (38) + TA + OA + GA + LA	[81]
			Ni 95 Bi 5 / C	0.1 M GLY + 1 M KOH	75 ºC, 1.35 V, 3 h	<10	FA (51) + GRA (31) + GA + TA + LA	[82]
			Ni 8 Pd 2 / C	0.1 M GLY + 1 M KOH	20 ºC, 1.55 V, 6 h	73	100)

  shows the electric charges transferred in the EC and PEC measurements performed for 6 h-each at different temperatures, as calculated from the intensity vs. time curves. The accumulated charges transferred in the PEC reactions were 4.53, 6.93, 7.62 and 7.79 mA•h at 25, 40, 60 and 80

o C, respectively. These values are 1.77, 2.54, 2.10 and 1.32 times higher than those obtained in pure EC processes at the corresponding temperatures (PEC/EC ratios in Fig.

d In this case, the anodic glycerol oxidation is coupled with cathodic CO 2 reduction (mainly to CO). No quantitative data on glycerol conversion or anodic products selectivity.

Acknowledgments

This work was financially supported by the China Scholarship Council (Grant No. 201906740016).

The authors would like to thank Frederic Bourgain (fabrication of Photoelectrolyser) of IRCELYON.

Author Contributions

Declaration of Competing Interest

The authors reported no declarations of interest.


Mohamad Jouni

Daniele Picone

Mauro Dalla Mura

Mauro Dalla

Reconstruction of Spectra from Interferometric Measurements (poster)

teaching and research institutions in France or abroad, or from public or private research centers.

Reconstruction of Spectra from Interferometric Measurements

Mohamad Jouni, mohamad.jouni@grenoble-inp.fr Daniele Picone, daniele.picone@grenoble-inp.fr Mauro Dalla Mura, mauro.dalla-mura@grenoble-inp.fr Grenoble Images Parole Signal Automatique UMR CNRS 5216 -Grenoble Campus 38400 Saint Martin d'Hères -FRANCE

I. Context

We want to reconstruct spectra from interferograms. A simple inversion is not straightforward, and the data are scarce. We exploit our knowledge of the acquisition model. -2-wave model:

Examples of data acquisition sources

A(δ l , σ) = (1 + R 2 (σ) -2R(σ) cos(2πσδ l ))T 2 (σ) ≈ C 0 + C 1 cos(2πδ l σ) -∞-wave model: A(δ l , σ) = 1 1+R 2 (σ)-2R(σ) cos(2πσδ l ) T 2 (σ) ≈ C 0 + ∞ n=1 C

1 2

 1 Devices: Dispersive spectrometers and Interferometers Example targets: Monochromatic sources and spectral references II. Problem Statement Acquisition and Inversion Pipelines Direct model: y = Ax + e, where: -x ∈ R K (unknown): spectral radiance, in the domain of wavenumbers σ. -y ∈ R L (observed): interferogram, in the domain of optical path differences (OPDs) δ. -A ∈ R L×K is the discretized acquisition model, and depends on δ and σ.-e ∈ R L is the noise, which we assume to be Gaussian. Goal: Estimate the value of x such that x = argmin x Model (knowledge the system) Theoretical: following the physical interferometric phenomena / models[START_REF] Hecht | Optics[END_REF]:

1 2

 1 n cos(2πnδ l σ) Raw data: following the raw monochromatic acquisitions of a real device. Characterized: fitting a model with the monochromatic acquisitions of a real device[START_REF] Picone | Interferometer response characterization algorithm for multiaperture Fabry-Perot imaging spectrometers[END_REF]. (Model-based)Based on the condition numbers from the singular values plots, the inversion problem is ill-posed.Conventional methods (SVD-based approaches) [3]Inverse discrete cosine transform (IDCT) Psuedo-inverse (e.g., raw data) Truncated singular value decomposition (TSVD) Ridge regression (RR)Iterative methods: Loris-Verhoeven (LV) algorithm[START_REF] Loris | On a generalization of the iterative soft-thresholding algorithm for the case of non-separable penalty[END_REF] Solve x = argmin x ∥y -Ax∥ 2 2 + λ g(Lx) where: λ is the regularizing parameter g(•) is the regularization term (e.g., sparsity) -L is a linear domain transformation (e.g., DCT or identity)


domain: spi nlin

text:
Let us consider the following continuous-time system

ẋ = f (x) + g(x)u, x ∈ R n , u ∈ R nin , (1)
ξ = h(x) , ξ ∈ R nout , (2)
where f (x), g(x) and h(x) are sufficiently smooth vector functions. Linear system i.e. f (x) = Ax, g(x) = B and h(x) = Cx, there exists an observability condition:

The linear system is observable if and only if

Rank        C CA . . . CA n-2 CA n-1        = n (3)
For nonlinear systems, the observability depends on the input, is local and there are no stopping criteria. Besides, there exist several definitions of observability as local [5], generic [3] etc. In a very simplified way, we can refer to the implicit functions theorem and find out on which order the output function ξ must be derived with respect to time. This leads to the simple test: (1) . . .

Rank         dξ dξ
dξ (n) . . .         = n (4)
where ξ (j) denotes the i th derivative of ξ with respect to time and

d• := ( ∂• ∂x1 , ..., ∂• ∂xn ).
Let us consider the well-known Rossler dynamics [11]:

ẋ1 = -x 2 -x 3 ẋ2 = x 1 + ax 2 (5) ẋ3 = b + x 3 (x 1 -c)
If we consider ξ = x 1 as output, then (4) becomes

Rank   dξ dξ (1) dξ (2)   = Rank   1 0 0 0 -1 -1 -(1 + x 3 ) -a -(x 1 -c)  
which has a state singularity in x 1 = a + c due to the nonlinearity. Now, if we consider ξ = x 2 as output, then (4) becomes

Rank   dξ dξ (1) dξ (2)   = Rank   0 1 0 1 a 0 a 1 -a 2 -1   .
Since the seminal work of , the flatness concept is used in many applications. Definition 1:

The dynamic (1) with x ∈ R n and u ∈ R nin , is zero-flat if there locally exist n out = n in smooth functions h i = h i (x), where 1 ≤ i ≤ n out having the following property: there exist an integer q and smooth functions γ i , 1 ≤ i ≤ n, and δ j , 1 ≤ j ≤ n in , such that locally

x i = γ i (h, ḣ, . . . , h (q-1) ) and u j = δ j (h, ḣ, . . . , h (q) ), (6)
The function h = (h 1 , . . . , h nout ) T is called a flat output.

Example, let us consider again the Rossler dynamic ( 7) with ξ = x 2 and add an input that appears linearly in the equation describing the time derivative of x 3 . The resulting controlled system reads:

ẋ1 = -x 2 -x 3 ẋ2 = x 1 + ax 2 (7) ẋ3 = b + x 3 (x 1 -c) + u ξ = x 2
It holds that ∂ξ ∂u = 0, ∂ξ (1) ∂u = 0, ∂ξ (2) ∂u = 0 and ∂ξ (3) ∂u = -1. All the properties like observability, controllability, input-output link hold without state singularity as it would hold for a linear system. In [10,9]... a symbolic algorithm is proposed to check whether a system is flat or not along with an assessment of the quality of flatness.

Outline

Continuous-time systems analysis Discrete-time system analysis Graph-based approach for discrete-time systems

J-P Barbot et a.
Toulouse, France, October 2023 8 / 17

Let us now consider the invariant discrete-time system

x + = G(x, u) , x ∈ R n , u ∈ R nin (8) ξ = h(x) , ξ ∈ R nout . ( 9
)
where x + stands for x(k + 1) and x stands for x(k). Moreover, we consider discrete-time dynamic with nonlinearity in u, because the composition of functions generally kills the input linearity e.g.

x + 1 = x 2 2 and x + 2 = u give x ++ 1 = u 2 . Definition 2: The invariant discrete system (8)-( 9) is globally universally causally observable, if ∀x ∈ R n and ∀u ∈ R nin there exists l ∈ R * and a function F such that

x -l = F (ξ, ξ -, ..., ξ -l , u, u -, ..., u -(l-1) ) ( 10
)
where • -stands for •(k -1) and • -l stands for •(k -l).

Definition 3: The invariant discrete system (8)-( 9) is locally universally causally observable at x 0 := x(0), if ∀u ∈ R nin , there exist V x0 a neighborhood of x 0 , l ∈ R * and a function F x0 such that ∀x ∈ V X0

x -l = F x0 (ξ, ξ -, ..., ξ -l , u, u -, ..., u -(l-1) ) ( 11)

Proposition:

The pair ⌈G, ξ⌉ is locally universally observable at x 0 if and only if there exists l > 0 such that ∀u ∈ R nin the observability matrix

O ξ l (x 0 ) = d(h(x 0 )) d(h • G(x 0 , u)) . . . d(h • G •l (x 0 , u)) , (12)
is of rank n where G

•2 (x 0 , u) is equal to G(G(x 0 , u), u + ), G •3 (x 0 , u) = G(G(G(x 0 , u), u + ), u ++ )
, and so on.

As a discrete-time counterpart of flatness for continous-time systems (let us recall [4]), the definition of a zero-flat nonlinear discrete-time system was given in [7]: Definition 4:

The nonlinear discrete-time input-output system ( 8)-( 9) is zero-flat if

The discrete-time nonlinear canonical form given in [8] makes a connection between controllabilty, observability and flatness [7, 2]:

x

+ 1 = x 2 + a 1 (x 1 ) x + 2 = x 3 + a 2 (x 1 , x 2 ) . . . = . . . ( 13
) x + n-1 = x n + a n-1 (x 1 , x 2 , ..., x n-1 ) x + n = a n (x 1 , x 2 , ..., x n , u)
Systems ( 13) with a n (x 1 , x 2 , ..., x n , u) = a(x 1 , x 2 , ..., x n ) + bu and x 1 as output ξ are zero-flat. In fact

x 1 = ξ, x 2 = + i -a 1 (ξ), x 3 = ξ ++ -a 1 (ξ + ) -a 2 (ξ, ξ + -a 1 (ξ)
) and so on recursively. Consequently, from the fact that every x i is function of y, y + , ...y i+ and that x + n = a n (x 1 , ..., x n ) + bu, there exists a function F in (ξ, ξ + , ..., ξ (n+1)+ ) such that u = F in (ξ, ξ + , ..., ξ (n+1)+ ).

Let us consider the nonlinear discrete-time system:

x + 1 = x 1 + x 2 2 x + 2 = u (14) ξ = x 1
The change of coordinates

ζ 1 = ξ and ζ 2 = ξ + x 2 2 gives ζ + 1 = ζ 2 ζ + 2 = ζ 2 + u 2 (15) ξ = ζ 1
This coordinate change is not a global diffeomorphism, the singularity is at x 2 = 0. Thus, even if the system ( 15) is observable the system ( 14) is not observable. Moreover, there is also a commandability in both system representations (i.e. ( 14) and ( 15) where x 2 respectively ζ 2 can only increase.

The aim is to propose a graph-based methodology [6,1] in order to verify that for a given discrete map (1) with u = 0 (autonomous system), the controlled system with input u ∈ R nin and measurement ξ ξ ξ ∈ R nin admits ξ ξ ξ as a flat output. This approach is restricted to discrete-time systems that can be written in the controlled form:

Σ :

x + = Ax + Bu, ξ ξ ξ = Cx (16)
where the entries of matrices A ∈ R n×n and B ∈ R n×nin may be non constant but may depend on the output ξ ξ ξ ∈ {x 1 , x 2 , ..., x n }. Proposition Consider the structured linear discrete-time system Σ described by ( 16). The output denoted by ξ ξ ξ ∈ {x 1 , x 2 , ..., x n }, associated to set of vertices Ξ, is generically a flat output if and only if, in the associated digraph G(Σ), the following three conditions hold:

Let us consider the Henon map described by

x + 1 = 1 -ax 2 1 + x 2 x + 2 = bx 1 (17) ξ ξ ξ = x 1
where a and b are real numbers. When applying a control input u on the second component x 2 , the resulting dynamics can be rewritten like x + = Ax + Bu + f (ξ ξ ξ) with A = -aξ ξ ξ 1 b 0 , B = 0 1 .

x x 1 2 u J-P Barbot et a. Toulouse, France, October 2023 16 / 17

x 1 = ξ = F state,1 (ξ)

x 2 = ξ + -1 + aξ 2 = F state,2 (ξ, ξ + ) u = ξ ξ ξ ++ -1 + aξ ξ ξ ++ -bξ = F in (ξ, ξ + , ξ ++ )

J-P Barbot et a. Toulouse, France, October 2023

Toulouse, France, October 2023

There exists an integer k and a function F state , such that, the state x can be rewritten as a function of the output, that is x = F state (ξ, ξ + , ..., ξ +k )

There exists an integer k and a function F in , such that, the control input can be rewritten as a function of the output that is u = F in (ξ, ξ + , ..., ξ +(k+1) ).J-P Barbot et a.Toulouse, France, October 2023

J-P Barbot et a.Toulouse, France, October 2023

η(U, Ξ) = n in .

All the maximum U-Ξ linkings have the same length.

Every cycle in the digraph G(Σ) covers at least an element of V ess (U, Ξ).J-P Barbot et a.Toulouse, France, October 2023

Outline

Continuous-time systems analysis Discrete-time system analysis Graph-based approach for discrete-time systems


domain: phys spi

text:
Group-Delay (ns)

Abstract-We showcase here the experimental demonstration of demultiplexing terahertz channels with up to 200 Gbit/s aggregated data-rate, using 4 carrier frequencies. The demonstration is carried out in the 300 GHz band. Best error vector magnitude obtained values are in the range 6-9%, with 50 Gbit/s per channel, enabled by a recently-reported novel substrateless integrated passive demultiplexer, which was developed specifically to serve the particular requirements of terahertz waves.

I. INTRODUCTION

erahertz (THz) technology is receiving rapidly increasing attention for an envisioned application in the communications field. Specifically, the frequency range around 300 GHz is very attractive from a good compromise of technology performance and atmospheric window between 250 and 320 GHz. Significant advances have been achieved for transmitters, receivers and related lab demonstrations. Among the multiple challenges of THz communications [1], passive functions as filtering, multiplexer/demultiplexer, duplexing, antennas are also mandatory to consider. Here we showcase the use of a recently developed THz multiplexer [2] in the 300 GHz band, thoroughly characterize its frequency differentiation and dispersion properties, and demonstrate that it is able to support a 4-channels signal with 200 Gbit/s aggregated data-rate.

II. TRANSMISSION AND DISPERSION ANALYSIS

The THz demux deployed here is described in detail in [2]. This device is implemented in a broadband substrateless all-silicon platform that offers freedom to define arbitrary guide curvatures [3], which the demux exploits for tailored wave-tunneling from a curved guide into an adjacent slab in order to achieve a frequency-scanning focused beam. The demux is shown in the Fig. 1. The demux is incorporated in two THz testbeds. The first one is used to measure the transmission characteristics and the dispersion characteristics using a set of 2 frequency extenders coupled to vector network analyzer (VNA). In this case, injection is done at the common port, and signal is extracted from each individual channel port. The measured transmission characteristics are shown in Fig. 2. The 4 channels were well identified, and centered at 330, 350, 370 and 390 GHz. One important feature is also a flat group delay (GD) performance of the device, which is of critical importance to avoid signal degradation due to dispersion. An example (channel 2) is shown in Fig. 3, and the flat GD in-band is clearly visible. Daniel Headland [START_REF] Song | Terahertz communications: challenges in the next decade[END_REF][START_REF] Headland | Gratingless integrated tunneling multiplexer for terahertz waves[END_REF] , Withawat. Withayachumnankul [START_REF] Headland | Unclad Microphotonics for Terahertz Waveguides and Systems[END_REF] , Masayuki. Fujita [START_REF] Headland | Gratingless integrated tunneling multiplexer for terahertz waves[END_REF] , Tadao Nagatsuma [START_REF] Headland | Gratingless integrated tunneling multiplexer for terahertz waves[END_REF] , Pascal Szriftgiser (4) and Guillaume. Ducournau (5*) The Fig. 5 shows the EVM evolution with the relative received power, corresponding to the lowest EVM obtained for the channel 1 (329 GHz).

Fig. 5 EVM performances curves for all channels.

IV. CONCLUSION

We have thoroughly characterized the transmission and dispersion of a recently reported passive four-channel terahertz demux [2]. The device is shown to support an aggregate data rate of 200 Gbit/s using a 16-QAM modulation format. This clearly illustrates the potential for practical applications of terahertz waves. The channel characteristics will be shown in greater detail at the conference.

Fig. 1 .

 1 Fig. 1. Photograph of the 4 channel tunneling demultiplexer.

Fig. 2 .

 2 Fig. 2. Transmission characteristics of the THz demultiplexer. VNA measurement is done in the 220-325 GHz/325-500 GHz bands (CH1), and 325-500 GHz band for CH2-4.

Fig. 3 .

 3 Fig. 3. Transmission characteristics of the 350 GHz channel and measured group delay, found to be flat and close to 0.51 ns.

  COMMUNICATION DEMONSTRATIONThe THz demultiplexer was then tested in a data communication setup. A 16-QAM with 12.5 GBaud was successfully transmitted in all the channels, resulting in a 4x50 = 200 Gbit/s aggregated data-rate. The constellations for the reference and transmitted 16-QAM signals are shown in Fig.4, and a clearly defined pattern of symbols can be observed, and corresponding EVM for all channels, in the range 5.6~8.5%.

Fig. 4

 4 Fig.4 16-QAM transmission in all channels (up: references, down, after demultiplexing).

1

  Optoelectronics and Laser Technology Group, Department of Electronics Technology, Universidad Carlos III de Madrid, 28911 Leganés, Spain 2 Graduate School of Engineering Science, Osaka University, 560-8531 Toyonaka, Japan 3 Terahertz Engineering Laboratory, The University of Adelaide, SA 5005, Australia 4 PhLAM Laboratoire de Physique des Lasers, Atomes et Molécules, 59650 Villeneuve d'Ascq, France 5 Univ. Lille, CNRS, Centrale Lille, ISEN, UPHF, UMR 8520 -IEMN, F-59652 Villeneuve d'Ascq, France.

	200 Gbit/s terahertz tunneling demultiplexer in 300 GHz band
	*Email: guillaume.ducournau@univ-lille.fr

ACKOWLEDGMENT

The characterization work conducted at IEMN, France, was supported by the 'Contrat de Plan Etat Region' (CPER) WAVETECH @HdF project and Haut-de-France Regional council, IEMN UHD flagship project, and MEL-I-site TERIL-WAVES project. The characterization testbed are also supported by the PEPR project 'FUNTERA' funded by ANR (Agence Nationale de la Recherche) and France 2030, grant ANR-22-PEEL-0006, dedicated to THz converters.