Keywords: propagation channel measurements, maritime environment, two-ray model, WiMAX

This paper presents studies, carried out by Télécom Bretagne, concerning new radio technologies (mainly WiMAX, 802.16e) in the maritime environment. The aim of these studies is to reinforce the quality and the robustness of such transmissions. Several measurements were set up to characterize the propagation channel in maritime environment in order to study the communication performances of WiMAX. This characterization was obtained by specific experimental devices, developed and implemented by Télécom Bretagne. The experimentations were carried out at frequencies of 3.5 GHz (Licensed WiMAX Band in France) and 5.8 GHz (Free Band in France). Similar studies [1] and [2] were already carried out, but they did not take into account all the environment characteristics, namely tides and coast relief masking. Our study looks at these parameters for a better understanding of the propagation in operational transmission environments. In this paper, measurements were carried out by measuring the mean received power both for several distances over the sea and for a coastal point-to-point link during long periods. Part of the work presented in this paper has been obtained during the Ex'treme project.

I. INTRODUCTION

As mentioned in [START_REF] Garroppo | Wimax Testbed For Interconnection Of Mobile Navy Units In Operational Scenarios[END_REF] and [START_REF] Yattoun | A Millimetre communication system for IVC[END_REF], a basic model being able at a first order to apply to the propagation in maritime environment is the two-ray model. This model takes into account one direct path between the transmitter and the receiver and another path refracted by the sea. For this model, it is possible to calculate the level of the received field at a given point, according to: the distance between the transmitter and the receiver, the relative heights of the transmitter and the receiver from the sea, the wave polarization, the working frequency, the conductivity, the relative permittivity of the sea and the transmitted power.

The present study aims at evaluating the levels of accuracy of this model and at examining two other causes of modification of the propagation channel:

• the masking effects due to the coastal relief and islands situated between the transmitter and the receiver,

• the tide effects that modifies the refraction conditions of the indirect path. The paper will show various propagation characteristics observed during our experiments.

II. MEASUREMENTS

A. Measurement Locations

The measurements were carried out in the Brest harbour. The navigation conditions were good. Indeed the climate was gentle and the waves not very high. Figure 1 represents the locations where the measurements were carried out and an example of two routes covered by the boat with transmitting equipments (in yellow the forward route and in white the backward route). The point 1 (IFREMER site) indicates the receiver location for all the experimentations and the point 2 (Le Caro site) notices one other spot, in order to have a pointto-point fixed connection above the sea. The Brest harbour presents various types of environments, also defined in paper [START_REF] Konstantinos | Measurements and Wideband Channel Characterization for Over-the-sea Propagation[END_REF] in which four types of environments and five groups of measurements are mentioned.

B. Measurement Equipments

At the transmitting site (the boat), two kinds of signals may be generated: a continuous sine wave or a pulsed one. The system involves two generators, one for the carrier frequencies 3.5 GHz or 5.8 GHz and the other one for the pulse shaped

Experimental measurements of propagation characteristics for maritime radio links

Yvon-Marie Le Roux, Jacky Ménard, Claude Toquin, Jean-Pierre Jolivet, Fabien Nicolas Institut Télécom -Télécom Bretagne, UMR CNRS 3192 Lab-STICC, Brest, France Email: yvon.leroux@telecom-bretagne.eu signals. The pulsed wave is built with a switch and a band pass filter. Two horn antennas are installed on the boat, the first at a height of 12 meters above sea level and the second one at a height of 3 meters above sea level. At the receiving site, two systems were available, namely a spectrum analyzer controlled by a computer and a second system build with PXI cards. A controller, a signal analyzer, a frequency converter and a data storage device constituted this last one. This acquisition system can record the received signal with 80 dB magnitude range and a 20 MHz bandwidth centred on a programmable frequency included between a few tens kHz and 6 GHz. These two systems received the signal transmitted by means of a horn antenna followed by a filter and a low noise amplifier. This antenna was placed at the point number 1 with a height of 52 meters.

The antennas were 12 dB horn antennas with 120° horizontal aperture and 30° vertical aperture. A GPS equipped a PC on the boat. The time and the position data were recorded for each trip. These data make possible to readjust the recordings of the signal received according to the real distance between the transmitter and the receiver. These data were confirmed by the equipment of the ship. The GPS information was also used for clock synchronization of the Tx an Rx devices.

The following pictures represent the devices used for the experimentations.

Throughout this paper, all the presented results concern the 3.5 GHz frequency.

III. MEASUREMENT RESULTS

A. Theoretical Results

As indicated in the introduction a basic model being able to apply to the propagation in maritime environment is the tworay model. It takes into account a direct way between the transmitter and the receiver and a way refracted by sea surface. We consider this model for simulate the propagation over the sea, the figures 4 and 5 show simulation examples.

B. Experimental Results

These preceding characteristics were verified during experiments and some measurement results are presented now. Geographical representations have been obtained from "Google Earth". Figure 6 represents an example of route during which measurements were carried out. Fig. 6. Example of route where the measurements were carried out (Max Tx-Rx distance = 14 km).

The following figure shows measurement results for the level of the received field, on this "mixed" course, corresponding to the two-ray model previously described but involving also some partial or total masking effects.

Results shown figure 7 compares the levels of theoretical values from the two-ray model, and measured ones of the received signal for a distance from A to C. There is a good agreement between the theoretical values of field attenuation and the measurements. The level differences at the beginning of the travel are mainly due to antenna effects. Indeed, the Tx and Rx antennas has only 30 degrees vertical apertures, and the receiving antenna at point A was located at 52 meters above the sea, whereas the transmitting antenna was onboard a small ship. The sharp level fluctuation at the end of the record (position B) is a masking effect due to a small island.

For a better understanding of the masking effects, other experimentations were realized. The following figures show some obtained results. Figure 8 shows a trip with an important masking effect and figure 9 shows the measurement results received field levels on this way. Here two effects are opposed: increase of the field level with the reduction of the transmitter-receiver distance and the masking effect growing when the boat gets closer the coastal point. In this configuration, it is the first that prevails slightly. At the point B, the mask effect causes a reduction of 25 dB as previously indicated to the passage behind the island.

C. Tide effects

In the two-ray model, the relative heights of Tx and Rx antennas are important characteristics in calculation equation. In our situation, the effective antenna heights of course varied with the tide effects, which imply a modification of the indirect path. To evaluate this phenomenon the figure 12 presents the results of the field level received over a radio link between Tx and Rx on the ground, but above sea. Figure 13 presents the hours of tides corresponding to the measurement period.

These figures show the strong incidence of tides on the point-to-point fixed connection above sea. We note that for this link geometry, the maximum of the field levels were obtained for tide heights from approximately 1 and 6 meters. The minimum of the field levels were obtained for tide heights from approximately 2.5 meters.

Other descents of the field levels occur near 7 meters of tide heights, indicating that in the event of strong tide (over 8 meters), a minimum of field level would again be reached.

Other complementary results confirm the influence of the sea state but this influence requires to be better quantified by new studies and experiments. Obviously, these tide effects also exist for radio links between a boat and the ground and should be taken into account.

IV. DATA ANALYSIS AND SYSTEM IMPACTS

The theoretical results and the experimental validations show that the propagation channel in maritime environment has diversity at three dimensions:

• a polarization diversity which is present until distances ranging between 10 meters and 500 meters. Experimental studies in cross polarizations must be made to consolidate this observation, • the vertical polarization mode is better adapted starting from distances of a few hundred meters, • a horizontal space diversity (and temporal for a transmitter and/or a receiver in mobility). This diversity, inversely proportional to the Tx-Rx distance is thus reduced with this distance, • a vertical space diversity proportional to the relative height variations of the transmitting and receiving antenna. The results confirm also that the masking effects are more or less important according to the distance relatives to the masks. Moreover, the influence of the sea states is certain on two levels and request still to be quantified in experiments:

• pointing defaults of the receiving and/or transmitting antennas [START_REF] Wen | A novel Frame work to simulate Maritime Wireless Communication Networks[END_REF] and [START_REF] Ang | Signal Strength Sensitivity and Its Effects on Routing in Maritime Wireless Networks[END_REF],

• modification of the refraction conditions of the indirect way. Studies and experimental complements are necessary to refine the description of the channel behaviour, in particular for the presence of obstacles (coastal relief, large ship …) near one or both connection ends, being able to create complex situations of multi-paths.

To take benefit from these diversities of the propagation channel in maritime environment, the following solutions on the systems could be examined:

• throughput and/or emission power adaptability according to the reception level and/or the signal to noise ratio (thus depending from distance and masking effects), • taking advantage of the natural channel diversity: o using two transmitting and/or two receiving antennas with orthogonal polarizations (vertical and horizontal), with a reception strategy to be determined (combining, best level, …). This solution would be useful until approximately 1000 m (in harbour and harbour approach). Beyond 1000 m, vertical polarization is preferable, o take advantage from channel horizontal diversity by using two (or more) receiving antennas approximately distant of half of the maximum interval between two fading, with a reception strategy to be determined (combining, best level, …). But the effectiveness of the solution depending on the Tx-Rx distance is proportional to the size of the ships concerned. o exploit the channel vertical diversity by using two (or more) transmitting antennas and/or two (or more) reception antennas separated by the height from approximately half of the maximum interval between two fading in altitude, with a reception strategy to be determined (recombination, best level, …). Vertical and polarization diversities could be combined. The solution would be effective for connections between two points at ground and above the sea, for connections between a ground point and a ship, and for connections between two ships, with however a respectively decreasing efficiency for these three cases. • control the Tx-Rx antenna pointing.

V. LINKED MARITIME PROJECTS

A. Ex'treme project

This project proposes the implementation of a broadband connectivity between the ground and the ships on sea. It will offer broadband services, mainly to increase the safety on the sea and to exchange information at short distances from the coast.

Moreover this project is based on complementary radio technologies to ensure IP services towards the passengers and the members of crew. The Ex'treme project is pioneer in the sector of the broadband services on the sea. This is because the existing IP Mobile service offers are not yet really dedicated to the maritime field.

The public concerned is mainly: pleasure boats, passenger liner, fishing vessels and ships of service. Moreover a great range of services will be proposed to these users: information on safety, the management and diffusion of an alarm, video transmissions, video monitoring, videoconference and applications of collaborative work, Internet access... The partners of this project are: Alcatel Business Systems, Thomson-GrassValley, IFREMER, C2 Innovativ'Systems, Morgan'Conseil, Chantiers de l'Atlantique, and Télécom Bretagne.

B. ImaginLab project

ImaginLab project is a test and experimental regional platform, adopted by FUI 6. It will make it possible to test new products and services. The infrastructure design and installation are carried out jointly by the pole Images & Réseaux and the UEB (Université Européenne de Bretagne), this later one having delegated its mission to Télécom Bretagne.

The infrastructure is made up of three inter-connected technological platform. The "Internet du futur" platform, located in Lannion, works on IMS (IP Multimedia Subsystem) architecture. The "Images en mobilité" platform, located in Rennes, will be used to diffuse mobile television services. The "haut débit sans fil" platform, located in Brest, will make it possible to test high-speed services on radio links, such as applications intended for the professionals or accessible services from a boat located near the coasts.

In this project, Télécom Bretagne uses its knowledge in the wireless transmission domain. These studies will relate to the wave propagation studies in different environments (urban, suburban, white zones and maritime areas).

C. Palmyre project

The Palmyre project consists in a realization of a modular platform for the evaluation of both systems and new communication concepts in frequency bands going from HF to microwaves, within realistic experimental situations. This platform is being developed by a hardware and software infrastructure group Partners of this project are teams from the " Institut d'Électronique et de Télécommunications" in Rennes, the "Laboratoire d'Électronique des Systèmes Temps Réel" from University of Bretagne Sud, the "Micro-ondes, Electronique and Signal & Communications departments" from Télécom Bretagne and the "Université de Bretagne Occidentale" in Brest.

D. Navtrack project

The general concept of this project is constituted of two technical guidelines:

• the first consists in locating in real-time all the boat race actors, using a radio transmission (868 MHz) to transmit GPS data, which are decoded on ground. A suited cartography traces the trajectories. The virtual images are enriched by environmental data (wind, currents, tide…) • the second aims at transmitting on line the images of the boat race by a radio transmission at 5.8 GHz. Partners of this project are teams from "DETI", "Ecole Navale -IRENav", "AGESSI", "Technopole Brest Iroise", "Electronique department from Télécom Bretagne" in Brest and from " SeatizenPro" in Villeneuve-Loubet.

VI. CONCLUSION AND PERSPECTIVES

This paper presented experimental researches carried out by the CaPSyS team of Télécom Bretagne on the new radio technologies in the maritime environment. This characterization of the propagation channel is necessary to understand the behaviour of radio waves in a maritime environment. Moreover, with this study, the performances of WiMAX systems can be analyzed according to the characteristics enumerated above. It is thus possible to take advantage of this analysis to propose some improvements of the transmission systems for better performances.

Télécom Bretagne develops new testing systems, in particular multi-channel receiving and transmitting systems, in order to explore the channel diversities quoted previously (MIMO spatial and polarization diversities) and for a better understanding of the propagation mechanisms in operational transmission environments (terrestrial as well as maritime). WiMAX (or others) transmission systems will also be operated simultaneously with channel sounding equipments, in order to compare the propagation channel characteristics with transmission performances.

These studies have been partially funded by: Brittany Regional Council, Finistere Council, Brest Metropole Oceane and Europe (FEDER).

Fig. 1 .

 1 Fig. 1. Example of routes (Max Tx-Rx distance = 27 km).

Fig. 4 .

 4 Fig. 4. Simulation with two-ray model: level of the received field according to the length Tx-Rx.

Fig. 5 .

 5 Fig. 5. Simulation with two-ray model: level of the received field according to the length Tx-Rx. From the simulated results we can notice what follows: • the average slope of path loss is proportional to the Tx-Rx distance approximately up to the radio electric horizon, as for a connection in free space, • the average slope of path loss is proportional to the squared of the Tx-Rx distance, approximately beyond the radio electric horizon, • the horizontal polarization presents major and recurrent fading (up to 60 dB) depending on the Tx-Rx distance, • the vertical polarization presents major and recurrent fading (up to 30 dB) depending on the Tx-Rx distance, • the fading of horizontal and vertical polarizations are phase opposite until a distance of few hundred meters, • the distance interval between fading for both the horizontal and vertical polarizations exceeds the hundred meters for transmitter-receiver distances greater than approximately 1 km.

Fig. 2 .

 2 Fig. 2. Transmitting devices.

Fig. 3 .

 3 Fig. 3. Receiving devices.

Fig. 7 .

 7 Fig. 7. Level comparison of the measured received signal with simulated values. In blue: measurements, in green: simulations

Fig. 8 .Fig. 9 .Fig. 11 .

 8911 Fig. 8. Example of route with an important masking effect.

Fig. 12 .

 12 Fig. 12. Received field level according to the Universal Time.

Fig. 13 .

 13 Fig. 13. Tide according to Universal Time.


Elodie Anxolabéhère-Mallart

Julien Bonin

Claire Fave

Marc Robert
email: robert@univ-paris-diderot.fr

Small-molecule activation with iron porphyrins using electrons, photons and protons: some recent advances and future strategies

Substituted tetraphenyl Fe porphyrins are versatile molecular catalysts for the activation of small molecules (such as O 2 , H + or CO 2 ), which could lead to renewable energy storage, the direct production of fuels or new catalytic relevant processes. Herein, we review the recent studies of these earth-abundant metal catalysts for the electrochemical activation of dioxygen on the one hand and for the photostimulated reduction of carbon dioxide on the other hand. These two prototype reactions illustrate how mechanistic studies are the only rational approach to gain fundamental insights into the elementary steps that drive the catalysis and for identification of the key intrinsic parameters controlling the reactivity, offering in turn the possibility to rationally tune the structure of the catalysts as well as the catalytic conditions.

Introduction

Nature has developed systems that are able to harness the oxidizing power of O 2 to produce energy (e.g. in the aerobic respiration process) and chemical compounds (e.g. in various oxygenation process, such as those encountered in oxygenase activity). In these processes, kinetic barriers prevent O 2 from reacting with organic substrates and being reduced to H 2 O. These barriers, therefore, must be overcome in order to exploit and control the reactivity. The same is true regarding CO 2 activation, which has been included by nature as a substrate for photosynthesis, ultimately generating chemical energy (under the form of carbohydrates) to fuel the activity of photosynthetic organisms. During the multi-electron and multi-proton processes that lead to reduced products, catalysis is mandatory to overcome the kinetic barriers and to achieve selectivity control.

Among the many molecular catalysts, iron tetraphenyl porphyrin complexes (Fig. 1) have long been used as homogeneous and heterogeneous Oxygen Reduction Reaction (ORR) or oxygen activation catalysts, as well as in CO 2 reduction processes. As far as O 2 is concerned, recent reviews on heterogeneous 1 and homogeneous 2 cases have detailed the nature of catalytic systems, including a description of many Fe porphyrins. The early development of Fe porphyrins catalysts for O 2 activation stem from efforts to mimic the enzymatic activity related to the uses of O 2 , such as O 2 reduction in cytochrome c oxidase or O 2 activation for the oxidation reaction in cytochrome P450. 3,[START_REF] Momenteau | [END_REF] Fe porphyrins are capable of facilitating oxygen activation by an inner-sphere reaction, essentially through the binding of O 2 to Fe(II) ion in concert with an electron transfer from Fe to O 2 leading to the concomitant oneelectron reduction of O 2 and the oxidation of Fe(II) to Fe(III) (i.e. formation of the superoxo adduct Fe(III)OO • ). The development of new Fe porphyrins-based catalysts aim at two objectives: (1) improving the efficiency of the 4e -reduction of O 2 to H 2 O in fuel cells, and (2) realizing O 2 activation through partial and controlled reduction of O 2 bound at the Fe active site. This activation occurs via sequential e -and H + transfers Fig. 1 Schematics of: (A) hangman porphyrins, 20 (B) the α 4 -FeFc 4 complex, 21 (C) and (D) Fe(III) 5,10,15,20-tetrakis (carboxyphenyl) porphyrins. 22 to realize O-O bond cleavage and to generate a high-valent reactive Fe-oxo species capable of oxidizing organic substrates. In the first section of this perspective, we review recent papers dealing with electrochemical O 2 reduction/activation using Fe porphyrins. We emphasize that the inhomogeneity of the experimental conditions (i.e. aqueous or organic medium, covalently bound to an electrode, or solubilized molecular catalyst, and so on) prevents any direct comparison of the performances of the various systems.

Remarkably, the role of iron tetraphenyl porphyrins as molecular catalysts for small-molecule activation is of course not restricted to O 2 -containing systems. These bio-inspired complexes also bind carbon oxides; for example, Fe(II) species strongly interact with CO, while the nucleophilic Fe(0) quickly coordinates to CO 2 , which opens up a rich catalytic chemistry to the multi-electrons and multi-protons reduction of gases. The catalytic processes for CO 2 reduction are generally of the ECEC or ECCE type (where E is an electron transfer step and C a chemical reaction (here protonation)), parallelling catalytic schemes observed for O 2 reduction, although the oxidation states of the iron centre are not the same for the two reactions. A method of choice for the clean generation of Fe(0) is electrochemistry, which has been extensively used since the pioneering work of Savéant et al. 5 It has also led to important mechanistic insights and in some cases to a deep understanding of the elementary steps of catalysis. [6][7][8] The mechanistic knowledge helped tuning the substituents on the phenyl rings of the ligand and optimizing the performances. In particular, the derivatives bearing either -OH groups or positively charged trimethylammonio groups on the phenyl moieties (Fig. 4) proved to be among the best molecular catalysts for the CO 2 -to-CO conversion, both in terms of selectivity (close to 100%), intrinsic rate and long-term stability (several days in the best cases). [9][10][11] Catalysts are highly active in organic solvent and in water as well.

Inspired by these studies, we developed a homogeneous photostimulated approach for achieving the visible lightdriven reduction of CO 2 . 12,13 In such an approach, the electrode is replaced by a molecular sensitizer that absorbs photons, while electrons are ultimately provided by a sacrificial donor. Following a parallel strategy to the electrochemical studies, i.e. developing a rational, methodic mechanistic approach, we have been able in the last 5 years to devise systems for the efficient and selective catalysis of the CO 2 , not only to CO in organic solvent and aqueous solutions, but also to more reduced products, such as methane, employing only an earth-abundant metal and a simple organic sensitizer. These studies will be the object of the second section of this perspective.

Electrochemical activation and reduction of O 2

It is now well established that there is a strong correlation between the structure of the catalyst and its oxygen activation or ORR catalytic activity. In this sense, coordination of an axial ligand, modification of the secondary coordination by an acidic group and physisorption or grafting of the catalyst on a surface actively participate in the catalytic activity.

O 2 binding to Fe porphyrins O 2 binding to the Fe centre is the first step in the activation process. DFT calculations 14 have been performed for better understanding the mechanism of the reversible O 2 binding by heme. It has been demonstrated that O 2 is in its singlet state when coordinating to the metal. Although this aspect has not yet been systematically explored, several studies have evidenced that the nature of the ligand trans to the O 2 binding plays a role in the reactivity of the Fe(III)-superoxo Fe(III)OO • adduct. The effects of axial ligands ("push effect") on the electronic structure and O 2 reduction have been reported in a recent review in which the authors discuss the ground state electronic structure of Fe porphyrins bearing various axial ligands (imidazole, phenolate and thiolate). 15 In this work, through the analysis of the differences in kinetics and selectivity for ORR, the authors present a quantitative understanding of the push effect, i.e. the ability of axial ligands to activate the O-O bond cleavage through an electron-donating effect. A DFT calculation study by Kasai suggested that imidazole ligand axial coordination weakens the O-O bond in O 2 adducts, thus favouring 4e -O 2 -reduction catalysis. 16 A related study by Naruta et al. reported that the formation of the Fe(III)-hydroperoxo (Fe(III)OOH) reactive species involved in the O-O bond cleavage reaction is enhanced thanks to the increase of the pK a values of Fe(III)OO • and Fe(III)OO species resulting from imidazole axial coordination to the iron ion. 17

Ligand modification and secondary coordination sphere effects

From early studies by Momenteau [START_REF] Momenteau | [END_REF] and Collman 18 and inspired by the protein environment of metalloenzyme active sites, the rational design of porphyrin ligands has allowed for the development of more sophisticated structures. Advances in porphyrin-and corrole-based ORR catalysts were addressed thoroughly in a recent review by Cao. 19 In particular, Fe porphyrin complexes with hydrogen-bonding groups in the secondary coordination sphere have been synthesized, such as the so-called hangman porphyrins (Fig. 1A) developed by Nocera, 20 showing an enhancement of O 2 activation. These systems allow tuning the acid-base properties of bound O 2 intermediates, and it was shown that protonation control of these intermediates plays a crucial role in O-O bond cleavage.

Electrochemical O 2 catalytic activation using Fe porphyrins has been studied both in aqueous and in organic media. Recent studies of water soluble Fe(III) tetra-N-methylpyridinium porphyrins have reported O 2 to H 2 O reduction with high catalytic performance in 0.1 M HOTf (k cat = 6.04 × 10 4 M -1 s -1 ). Although this specific aspect was not further detailed, the authors observed an enhancement of the turnover frequency in the presence of protonated imidazole. 23 Matson et al. also reported the 4e -/4H + reduction of O 2 using Fe(III) tetra-N-pyri-dinium porphyrins derivatives with high selectivity (<15% H 2 O 2 ). 24 Looking at another type of porphyrin ligand modification, Dey's group showed that electron-withdrawing ester groups in the β-pyrrolic position of Fe(III) tetraphenylporphyrin induce a positive shift (200 mV) of the formal Fe(III)/Fe(II) potential in both organic and aqueous media and of the onset potential of ORR as compared to the unsubstituted porphyrin. 25 Electrochemical studies of O 2 reduction in organic solvents have been mainly performed in N,N-dimethylformamide (DMF) and acetonitrile (ACN). After reporting ORR studies with the non-substituted archetype porphyrin Fe(III)(TPP)Cl (TPP = 5,10,15,20-tetraphenylporphyrin, Fig. 4), 26 Mayer et al. studied the influence of the local proton source in the secondary coordination sphere with Fe(III) 5,10,15,20-tetrakis (carboxyphenyl)porphyrins incorporating carbonyl groups in the ortho and para positions (Fig. 1C andD). The authors reported a higher selectivity for H 2 O production in the case of the orthosubstituted derivative, which was attributed to the involvement of the carboxylic groups as protonating agents or proton relays. 22 In a more recent analysis of the ORR performance within a series of Fe porphyrins, Mayer's group showed experimental evidence, supported by computational studies, that the free energies for O 2 binding to the Fe were linearly correlated to the catalyst E 1/2 reduction potential. From this analysis, they demonstrated that decoupling of the properties of the first coordination sphere (E 1/2 , K O 2 ) from the influence of the second coordination sphere (basicity of the superoxide intermediate, pK a ) seems to be a promising way to overcome the scaling relationship and thus to facilitate the design of new, efficient catalysts. 27 In this period, Dey's group also made an important contribution to the O 2 electrochemical activation studies with various Fe porphyrin derivatives, with catalysts in solution (homogeneous conditions) or with surface-modified electrodes. Using the α 4 -FeFc 4 porphyrin complex (Fig. 1B), they analyzed the role of the secondary coordination sphere effect for facilitating ORR catalysis. 21,28,29 They found that the α 4 -FeFc 4 complex could act both as a homogeneous catalyst (in an organic solvent in the presence of acid) and as a heterogeneous catalyst (in an aqueous medium, pH 1-9) for ORR, and proposed that the triazole residues offer an efficient proton-transfer pathway into the active site.

Influence of the electrode surface

Since Collman's early work with a catalytic system attached to an electrode, 30,31 surfaces have proven to be an efficient interface to tune and to boost O 2 activationas well as to study intermediatespecies. In some cases, the surface itself or a surface modified either by an organic molecule or by a polymer can be considered as an "axial" ligand. 32 In a similar way, Chlistunoff Q4 and Sansinena reported a 300 mV positive shift of the O 2 reduction in an acidic medium for a catalytic system corresponding to a mixture of Fe porphyrin and carbon Vulcan impregnated with polyvinylimidazole in comparison with the catalyst in solution or supported on graphene surface. 33 An original approach used a honeybee silk film as the surface.

The presence of the silk films favoured cleavage of the O-O bond by playing the role of an axial ligand to the heme centre. 34 Costentin et al., revisiting the catalytic activity of the extensively studied para derivative of Fe(III) 5,10,15,20-tetrakis (N-methylpyridyl)porphyrin, recently showed that although the amount of adsorbed catalyst on a glassy carbon electrode was very small, the catalytic activity found its origin in the heterogeneous contribution over the homogeneous contribution (k het = 780 s -1 , k hom = 30 s -1 ). 35 Liu and co-workers reported another approach by anchoring biomimetic ORR electrocatalysts onto the surface through a pre-functionalization with imidazole derivatives, which led to a remarkably high ORR activity. A DFTPPFe porphyrin (DFTPP = 2,6-difluorotetraphenylporphyrin) was grafted onto multi-walled carbon nanotubes (MWCNTs) surface previously modified by imidazole through the axial position (Fig. 2). The ORR catalytic activities of the DFTPPFe-Im-CNTs, DFTPPFe-CNTs (a simple mixture of the porphyrin and CNTs) and the Pt/C catalyst were studied and compared by using a rotating ring-disc electrode. The DFTPPFe-Im-CNTs exhibited a higher ORR activity (high selectivity in the direct 4e -/4H + reduction) and also superior stability (90% of the initial current for the DFTPPFe-Im-CNTs is retained compared to only 57% for the Pt/C catalyst under the same conditions). 36 Dey also reported the use of ammonium tetrathiomolybdate (ATM) for forming self-assembled adlayers on gold electrodes, which are robust and stable in aqueous environments and can be used to physisorb Fe porphyrin catalysts. The modified electrodes showed better performance in terms of stability during the hydrodynamic electrochemical experiments unlike the selfassembled monolayer (SAM) of thiols on Au/Ag. The rate of interfacial charge transfer could be tuned by controlling the thickness of the ATM layer by varying the deposition time. 37 Very recently, Elbaz and co-workers used a modified graphene oxide surface with benzimidazole and reacted it with a Fig. 2 Schematic representation of the bio-inspired ORR catalyst (DFTPP)Fe-Im-CNTs (Ar = aryl) covalently anchored to the surface of multiwalled CNTs. 36 Fe(III)tetrakis(1-methyl-4-pyridyl)porphyrin. The presence of this surface bound-axial ligand boosted the 4e -/4H + reduction by facilitating the reduction of peroxide anion. 38 Finally, one may note the work of Mayer and co-workers who evaluated the performance of several substituted Fe porphyrin complexes for ORR electrocatalysis in different homogeneous and heterogeneous media. They observed that the selectivity for 4e -reduction to H 2 O vs. 2e -reduction to H 2 O 2 varied substantially from one medium to another for a given catalyst. One important conclusion of this work is that any comparison of the selectivity results from supported and soluble molecular ORR electrocatalysts must be interpreted with caution, as selectivity is a property not only of the catalyst structure (which notably includes the presence or not of a proton relay on the porphyrin ligand) but also the nature of the surrounding medium (solvent, acido-basic species and nature of the film in case of supported catalysis). 39

Detection of intermediates and mechanistic insights

In order to gain insights into the mechanism of Fe porphyrin electrocatalysts reducing O 2 , Dey and co-workers developed a set-up for coupling a rotating disc (RDE) or rotating-ring-disc electrochemistry (RRDE) with resonance Raman spectroscopy. The studies were conducted in buffered aqueous solutions with Fe catalyst immobilized on a thiol SAM-covered Au disc electrode though axial ligand binding (thiolate, imidazole). These experiments probed the system under steady state conditions. A combination of oxidation and spin-state marker bands and metal ligand vibrations provided for the in situ identification of O 2 -derived intermediates formed on the electrode surface. 40,41 Interestingly with the system where a thiolate was bound to the Fe center, highly oxidizing species were generated at the electrode during electrocatalytic O 2 reduction. These reactive species could in principle act as an oxidant for triggering catalytic processes. 32,42,43 Upon combining the same SERRS-RDE (SERRS: surface enhanced resonance Raman spectroscopy) method with a measurement of the H/D isotope effects, the group recently reported that the rate of O 2 reduction, ∼10 4 to 10 5 M -1 s -1 for simple Fe porphyrins, was limited by the O-O bond cleavage rate of a ferric peroxide intermediate species. SERRS-RDE probes the system in operando when it is under steady state conditions, such that any species that has a faster formation rate as compared to its decay rate, including the rate determining species, would accumulate and can be identified. It is also reported that the selectivity of the ORR is determined by the protonation site of the ferric peroxide intermediate and can be controlled by installing pre-organized second sphere residues in the distal pocket. The 4e -/4H + reduction of O 2 entails protonation of the distal oxygen of the Fe III -OOH species, while 2e -/2H + reduction requires the proximal oxygen to be protonated. Very recently Dey and co-workers highlighted an unprecedented 4e -/4H + behaviour (>90% selectivity) of Fe porphyrin complexes containing a basic residue when adsorbed on EPG (edge pyrolytic graphite) electrodes. DFT calculations showed that the hydroperoxide is stabilized by H-bonding, resulting in an elongation of the O-O bond and promotion of proton transfer to the distal oxygen. 44 Finally, in a recent and detailed account incorporating all the recent studies based on the SERRS-RDE method, Dey and co-workers reviewed the various factors (e.g. the binding of axial ligands and incorporation of second coordination sites) determining the rate and selectivity of the electrocatalytic reduction of O 2 by Fe porphyrin complexes. 46 We have reported the electrochemical generation of the intermediates species Fe(III)OO peroxo and Fe(III)OOH hydroperoxo using simple commercially available Fe(III) tetrakis( pentafluorophenyl)porphyrin (Fe(III)F 20 TPP) in DMF, thus mimicking the first step of O 2 activation cycle (Fig. 3). The experimental set-up allowed the measurement of the oxidation potential of the peroxo (E = 0.5 V vs. SCE) from the electroreduction of the superoxo adduct at a moderate potential (-0.60 V vs. SCE) and the EPR detection of the hydroperoxo.

It is worth mentioning here that this electrochemical approach coupled to spectroscopy is an appropriate method to generate and characterize reactive species, 45 complementary to the one reported by Dey.

The control of the reductive activation of O 2 with bioinspired catalysts remains challenging, in particular for predicting the final products of the reaction, i.e. H 2 O, H 2 O 2 or SO (with S = substrate). Our ability to design a single catalyst so as to favour a specific product remains out of reach. In Nature, selectivity is controlled by the active site of the metalloenzyme yielding H 2 O (O 2 + 4e -+ 4H + → H 2 O, cytochrome c oxidase) or oxygenated molecules (RH + O 2 + 2e -+ 2H + → ROH + H 2 O, cytochrome P450). In other words, tuning the exact structure of the ligand around the metal active site could allow triggering a specific reaction and the ability to discriminate between the two major pathways. Along these lines, we have shown in the above paragraphs that the use of electrochemical tools and techniques, through a precise adjustment of the electrode potential and control of the pH, allows tuning the formation of some key intermediates and to further characterize them with complementary coupled spectroscopic methods. Although obtained on model systems that are not the most cat-Fig. 3 Catalytic scheme for the electrochemical reductive activation of O 2 and of the final products in the presence of iron porphyrin catalyst. 45 alytically active ones, gathering all these data is a necessary step to better understand the reductive activation of O 2 in the ORR reactions.

Photostimulated reduction of CO 2

Light-induced catalyst activation

Following pioneering studies by Neta et al. in the early 1990s, [47][48][49] we have demonstrated in the last years that Fe porphyrins are efficient molecular catalysts for photochemically induced CO 2 reduction to CO 12,13,50 but also to CH 4 , 51 both in organic 52 and in aqueous 53,54 environments. In this approach, a key aspect lies in efficient catalyst activation, which requires three successive electron transfers (ET) to the catalyst centre to reach the Fe(0) active state. Starting from the Fe(III) state, the first ET can occur through homolytic bond-breaking of the Fe-Cl (eqn (1)) bond under irradiation of the ligand-to-metal charge transfer (LMCT) band of the porphyrin (around 330 nm). The low efficiency of the process combined with the use of deleterious (see below) UV light makes it necessary to include a sacrificial electron donor (SD, eqn ( 2)), typically a tertiary amine. The yield and rate of formation of the Fe(II) state is then greatly enhanced. The two subsequent ETs, leading to Fe(I) and ultimately to Fe(0) species (eqn (3)-( 5)), occur by a bimolecular reductive quenching reaction between the porphyrin excited state and the SD. The oxidation of the latter generates the SD •+ radical cation, which undergoes a dismutation-like acid-base reaction (eqn (6)) and generates a reducing and reactive radical able to reduce another Fe(III) centre (eqn (7)). As a side reaction, the protonated form of SD is also formed in this process, which is a species that could play an important role in the mechanism, being a strong acid donor, as exposed later.

FeðIIIÞ À Cl À! hv FeðIIÞ þ Cl • ð1Þ
FeðIIIÞ þ þ SD À! hv FeðIIÞ þ SD •þ ð2Þ
FeðIIÞ þ SD À! hv FeðIÞ À þ SD •þ ð3Þ
FeðIÞ À þ SD À! hv Feð0Þ 2À þ SD •þ ð4Þ
2FeðiÞ À ⇄ Feð0Þ 2À þ FeðiiÞ ð 5Þ SD •þ þ SD ! SDH þ þ SD • -SD ð6Þ
SD • -SD þ FeðiiiÞ þ ! SD þ -SD þ FeðiiÞ ð 7Þ
The catalytic active Fe(0) species bind to CO 2 and upon protonation and further reduction afford CO and a water molecule. Depending on the acid content of the solution ( pK and concentration) and of the nature of the substituents on the porphyrin ligand, the sequencing of electron and proton transfers and their degree of coupling (concerted vs. sequential steps) may vary.

Catalysis analysis and quantification

To analyse and quantify the catalytic performances, we made intensive use of a combination of spectroscopic and chromatographic studies. Collecting UV-Visible absorption spectra during the course (typically, several hours) of irradiation indeed allowed identifying some intermediates. This approach was, however, only tractable when no other absorbing species, such as a photosensitizer, was present in the reaction solution. We thus demonstrated that the formation of the Fe(II) could be readily achieved and that, upon defined conditions, Fe(I) and/ or Fe(II)-CO could be observed, meaning that these species somehow accumulated. Fe(0), being highly reactive, was formed in very low quantity and had a short lifetime, consequently it could not be observed spectroscopically. Moreover, the various Fe redox states of the porphyrin usually had similar and strong absorption spectra, mainly in the Soret band region, so that spectral overlap was frequently encountered. We were, however, able to attribute each Fe state to its spectral signature by conducting spectroelectrochemical measurements and using previously reported data. 12,55 Spectroscopic measurement is also a pertinent tool to track for degradation of the system. It is known that the hydrogenation of the porphyrin macrocycle, leading to the parent chlorin and phlorin compounds, is associated with an increase in UV (<300 nm) absorption corresponding to the loss of ligand conjugation. Gas chromatography (GC), coupled (GC-MS) or not with mass spectrometry, was the second tool utilized for catalysis evaluation. By analysing the gas composition in the solution headspace along the irradiation course, it was possible to precisely quantify the number of catalytic turnover (TON) as well as the catalytic selectivity (CS) towards the detected products. The absence or presence of liquid products was checked by ionic chromatography or by NMR (formate, formaldehyde, methanol). Note that in all cases, checks that the reaction products were indeed issued from the CO 2 were carefully performed by NMR or GC/MS, or both, upon photo-experiments with labelled 13 CO 2 .

Catalyst structure and reaction partners

The catalytic system used in the photochemical approach was a combination of several components, each of them being a potential lever to drive the process into the desired direction. The first element is the catalyst itself, and along years, several derivatives bearing various groups on the phenyl rings have been prepared in our lab. 56,57 Structural modifications allow modulating the standard potential of the iron centre through an inductive (through structure) effect. A more positive standard potential of the Fe(I)/Fe(0) redox couple facilitates the electron-transfer step but at the expense of a decrease in the intrinsic activity of the reduced porphyrin(0).

Second coordination sphere effects, such as through space effects, can counterbalance the previous decrease. For example, the introduction of internal OH groups (Fe-o-OH and Fe-o-OH-F10,Fig. 4) can provide H-bond stabilization of the Fe(0)-CO 2 adduct and canfurther act as a protonating agent.

The introduction of positively charged groups (trimethylammonio groups) at the periphery of the phenyl rings (Fe-p-TMA, Fig. 4) can also lead toa stabilization of the partial negative charge borne by the O atoms of the CO 2 inthe adduct. In these two cases, the intrinsic activity of the porphyrins is greatly enhanced. Another distinct advantage of using Fe-p-TMA is the possibility to perform the catalysis in water (see below) (Table 1). We equally explored various sacrificial electron donors (SD), starting from typical amines (TEA, TEOA, DiPEA) and using also very efficient donors, such as BIH (Fig. 5, bottom). A drawback is their degradation to by-products during catalysis. It is known that both tertiary amines and EDTA evolve, upon oxidation, into aminyl radicals and then to iminium species and, in the presence of water, to secondary amines and short aldehydes. 59,60 Once oxidized, BIH quickly releases one proton and then a second electron to form a cationic dead-end species. 60 To date, no detectable degradation of our system could be attributed to these secondary reactions.

To ensure an efficient visible light absorption and to allow irradiation in the visible range, several photosensitizers (PS), both inorganic and organic have been tested (Fig. 5, top and middle). Since CO 2 reduction requires the concomitant transfer of several protons, external acids with various pK (water, phenol, trifluoroethanol) have been employed to enhance the catalysis, keeping in mind that a balance should be kept for the acid strength, since a too weak acid will only weakly boost the process while a too strong one may favour competitive hydrogen evolution. Finally, even if most of our studies have been performed in an organic solvent (acetonitrile) to ensure a suitable solubility of each component and particularly of CO 2 , we recently managed to carry out the photostimulated catalysis in aqueous solutions, which constitutes a key target for applications but still presents major challenges to be addressed.

Photoinduced CO 2 reduction to CO

In a first approach, the remarkable optical properties of Fe porphyrin were exploited to trigger a catalytic process without the assistance of a sensitizer, which remains rare in the literature. We started with the unmodified Fe tetraphenylporphyrin (FeTPP, Fig. 4) and with two analogues bearing -OH groups in all ortho, ortho′ positions of the four phenyls (Fe-o-OH, Fig. 4), or -OH groups and -F atoms on the phenyl rings (Fe-o-OH-F 10 , Fig. 4). 12 We showed that these three catalysts can achieve CO 2 conversion to CO at a moderate rate and with limited selectivity. We also identified intrinsic limitations due to three factors. First, near-UV (ca. 300 nm) irradiation was required but induced a progressive photodegradation of the catalyst; then, a competitive pathway for H 2 formation was observed thanks to the presence of the acidic protonated form of the SD; finally, modified porphyrins stabilized the adduct formed with CO 2 but this made it necessary for the injection of an extra electron to cleave the C-O bond, and no other species but Fe(0) itself, whose concentration was low, was reductive enough to achieve this step. More recently, another analogue bearing four positively charged trimethylammonio groups (Fe-p-TMA, Fig. 4) has been used in association with BIH (Fig. 5) as an SD. 50 First, we demonstrated that the introduction of the trimethylammonio groups made the catalyst active under visible light, preventing photodegradation. Second, the competitive H 2 pathway was bypassed since selective CO formation was observed. Third, the four positively charged groups played a strong stabilizing role since no loss of activity, albeit modest, was observed over 60 h reaction. This was taken as evidence that the Fe-p-TMA analogue possessed key features for CO 2 photostimulated reduction.

Photoinduced CO 2 reduction to CH 4

Having in hand a promising catalyst, we then combined it with a photosensitizer (PS). This classical, simple strategy was already employed with the Fe-o-OH, for which we showed that with both an inorganic (Ir( ppy) 3 , Fig. 5) or an organic (9-CNA, Fig. 5) sensitizer, catalysis for CO production was enhanced. 13 Beyond a better absorption in the visible range, the use of these two PSs greatly improved both the catalytic selectivity, with no or negligible amount of H 2 formed, and the stability of the system, since CO formation increased linearly with irradiation time. This was also the first example of the association of an abundant metal-based catalyst and a low-cost organic sensitizer (9-CNA, Fig. 5). In the case of Fe-p-TMA, the use of Ir( ppy) 3 as PS turned out to be even more remarkable. Indeed this system could realize the eight-electron reduction of CO 2 to CH 4 at ambient temperature and pressure upon visible light irradiation. 51 Starting from CO 2 as a substrate, CO is an intermediate product and the selectivity towards CH 4 was 17%. When using CO directly as the substrate, simply by saturating the solution with the gas, the formation of CH 4 was obtained with a selectivity above 80%, with H 2 being the only by-product detected. To circumvent the use of a noble-metal based PS, we very recently replaced it by a phenoxazine-based organic PS (Phen, Fig. 5). 52 In this case too, CO 2 or CO could be used as a starting material to form CH 4 . Compared with Ir ( ppy) 3 , Phen is significantly more efficient as a PS, producing, under similar conditions, almost twice the amount of CH 4 with a quantum yield multiplied by ca. three. In both cases, the rationale resided in the high reducing character of the triplet excited state of, respectively, Ir( ppy) 3 (E°(Ir(IV)/ 3 Ir(III)*) = -1.73 V vs. SCE, Table 2) and accumulation of the Fe(II)-CO intermediate. In other words, the key to produce methane lies in the ability to activate the CO bound to the Fe(II) complex, using highly reducing species before the CO could be released from the metal centre. For all of these studies, GC/MS experiments were performed under a 13 CO 2 or 13 CO atmosphere, respectively, and confirmed that the produced CH 4 originated from CO 2 or CO, respectively. Until now, we have not been able to achieve methane formation at an electrode since there is no accumulation of the Fe(II) species that are necessary to react with CO.

Photoinduced CO 2 reduction in aqueous solutions

Another important physical property of Fe-p-TMA is its solubility in aqueous solutions thanks to its positively charged trimethylammonio groups. Water as a solvent remains a challenge in the catalytic transformation of CO 2 with molecular compounds, in particular for solubility reasons, but also for selectivity issues with the competitive H 2 evolution. CO 2 solubility is much lower in water than in most commonly used organic solvents (e.g. by a factor of ca. 5 when compared to DMF or ACN) and both water-soluble catalysts and visible-light PSs are rare. However, we demonstrated that a typical organic dye, namely purpurin (PP, Fig. 5), could be employed as a PS in combination with Fe-p-TMA in aqueous solution (containing 10% acetonitrile) to achieve the production of CO from CO 2 reduction over 2 days of irradiation. 53 The catalytic process was, in this case, limited by progressive PP degradation, since catalytic activity could be restored upon adding fresh sensitizer. Even though the rate remained modest, the selectivity towards CO was excellent (above 95%) with very little formation of H 2 . This illustrates the remarkable potential of Fe-p-TMA and its high affinity for CO 2 . To solve PS degradation, we also tried to employ a water-compatible analogue of Ir( ppy) 3 , namely Ir( ppy) 2 (bpy) (Fig. 5). In acetonitrile/H 2 O (3 : 7 v/v) solution, upon visible-light irradiation, CO was the major CO 2reduction product (75% selectivity), with H 2 and CH 4 formed in minor amounts (16% and 9% selectivity, respectively). The efficiency of the catalytic system was, however, severely limited by two factors, first the low CO 2 solubility and most importantly by the instability of the iridium PS in the presence of CO, because of a deleterious ligandation/deligandation process and concomitant loss of activity. Even though the performances and/or stability in aqueous solutions remained modest, these works can be considered as a proof of concept and could open the door to new developments of aqueous photocatalytic processes.

Mechanism under photochemical conditions

A global photochemical catalytic scheme is presented in Fig. 6. Electron injection in the system is insured by a photochemical event (Photo-ET) through oxidative quenching reaction with the PS. Once the catalyst active form, Fe(0), is formed, it combines with CO 2 to form a Fe(II)-CO 2 adduct. In acidic conditions, i.e. if protons are readily available, a competitive H 2 formation may occur through a hydride formation to form Fe(0). Otherwise, Fe(II)-CO 2 leads to Fe(II)-CO and the release of CO, giving back Fe(II) and closing the cycle. Under conditions exposed earlier, CH 4 formation is accomplished through a a From its monoanionic to its dianionic form.

mechanistic pathway that has not yet been deciphered and for which we are conducting intensive ongoing experimental and theoretical studies.

Conclusions and perspectives

We have illustrated in this perspective how a careful, rational mechanistic approach may bring a valuable contribution to the understanding of the intrinsic factors governing electrochemical O 2 activation and photostimulated CO 2 reduction by tetraphenyl Fe porphyrin catalysts under mild conditions.

In the case of dioxygen, such an approach could help in monitoring the partially reduced oxygen species (PROS) produced during O 2 reduction, thus generating high valent Q species, such as Fe(IV) •+ -oxo or Fe(V)-oxo (Fig. 3). These highly oxidizing species could serve as an oxidant for catalytic reac-tion with an organic substrate. It is clear that controlling the competition between the reaction of these crucial high-valent intermediates with the substrate (upper left part in Fig. 3) and their reduction by electron transfer from the electrode (leading to the 4e -reduction product, H 2 O, Fig. 3) is still a challenging issue. Designing new Fe porphyrins bearing rationally designed functional groups on the second coordination sphere and/or grafted on the electrode surface with various spacers may help prevent unwanted reactions and prevent triggering oxidation reactions of the substrates. Ultimately, such approaches will also be beneficial towards the transposition of the oxidation strategy to photoinduced processes, opening a route to sustainable oxidation processes using only solar light. Then, helped by the fundamental understanding and control of O 2 activation, one can foresee the development of industrial synthetic processes that will take due account of environmental and economic constraints.

Regarding the carbon dioxide photostimulated catalysis with visible light, Fe porphyrins have also emerged as versatile and highly active catalysts. Much remains to be done in terms of mechanistic studies, especially for the understanding of the 8e -/8H + reduction to methane, which will involve the combination of spectroscopic studies, such as time-resolved infrared spectroscopy, and quantum calculations. Such studies are a necessary step towards expanding the range of products that could be obtained from the catalytic conversion of CO 2 . Fuels, such as methanol, and multi-carbon products are among the most important targets that currently remain inaccessible. In this connection, developing multi-metallic complexes for triggering cooperativity between metal centres, as naturally performed by enzymes, such CO dehydrogenase (CODH) should be explored. Another important aspect is to increase the efficiency of the photoprocesses through a better collection of the light (quantum efficiencies remain low when using molecular sensitizers despite recent progress) and of the chargetransfer reactions. Several strategies may be envisioned, among which the association of the catalysts to photoelectrodes and the development of metal-organic frameworks 68 seem appealing. The replacement of amines as sacrificial electron donors by water or by developing valuable oxidation process that would be coupled to CO 2 reduction is also an important challenge. Finally these studies pave the way towards solar-driven CO 2 conversion employing water as a proton source, which could have a significant impact in changing current industries into a low carbon economy.

Fig. 4

 4 Fig. 4 Tetraphenyl Fe porphyrin catalysts for photostimulated CO 2 reduction.

Fig. 5

 5 Fig. 5 Top, middle: Main organic and inorganic sensitizers employed for the CO 2 photostimulated conversion. Bottom: Typically used sacrificial donors.

Table 1

 1 Standard redox potentials (V vs. SCE) for Fe porphyrins (in DMF)58

		FeTPP	Fe-o-OH	Fe-o-OH-F 10	Fe-p-TMA
	Fe(III)/Fe(II)	-0.21	-0.34	-0.12	-0.10
	Fe(II)/Fe(I)	-1.05	-1.16	-0.99	-0.95
	Fe(I)/Fe(0)	-1.67	-1.57	-1.51	-1.47

Table 2

 2 Standard redox potentials (V vs. SCE) for electron donors and sensitizers

	Sacrificial electron donors (SD) (in acetonitrile for amines, in H 2 O for
	EDTA)
		TEA 61	TEOA 62	DiPEA 63	EDTA 62	BIH 64
	E ox (SD •+ /SD)	+1.0	+0.82	+0.5	0.92	+0.33
	Photosensitizers (PS) (in acetonitrile)
		PS + /PS*	PS*/PS -	PS + /PS	PS/PS -
	9-CNA 65					-1.58
	PP 53					-0.66 a
	Phen 66	-1.80			+0.65
	61 61 Ru(bpy) 3 Ir(ppy) 3 Ir(ppy) 2 (bpy) 67	-0.81 -1.73 -0.85		+0.77 +0.31 +0.68	+1.29 +0.77 +1.25	-1.33 -2.19 -1.42

Acknowledgements

Partial financial support to M. R. from the Institut Universitaire de France (IUF), from the French National Research Agency (ANR-116BS07-024-03, Cathymetoxy) to C. F. and from Labex Michem to E. A. M. are warmly thanked. Dr Heng Rao, Dr Mathilde Routier, Ms Celia Achaibou, Dr Rachel Oliveira and Dr Luciana C. Schmidt are gratefully acknowledged for the work accomplished in the lab on these topics.

Conflicts of interest

The authors declare no competing financial interest.


Patrick Meyer
email: patrick.meyer@telecom-bretagne.eu

Progressive methods in multiple criteria decision analysis

Keywords: Multiple criteria decision analysis, Progressive methods, Choquet integral, Multiattribute value theory, Bipolar-valued outranking relation MSC classification (2000) 05C20, 90B50

de Mons, under the joint supervision of Raymond Bisdorff and Marc Pirlot. The thesis is

Introduction and structure of the doctoral dissertation

Our work mainly focusses on the study and the development of progressive methods in the field of multiple criteria decision analysis (MCDA), i.e., iterative procedures presenting partial conclusions to the decision maker (DM) that can be refined at further steps of the analysis. The thesis is divided into three parts. The first one is intended to be a general analysis of the concept of progressiveness. The last two parts develop progressive methods related first to multiattribute value theory (MAVT) and second to outranking methods. In the following sections, we briefly present our main contributions to these subjects.

MCDA

Information

Elicitation Recommendation

Information

Interactivity

Progressiveness

Output

Partial conclusion Exploitation

Input Initialisation

Fig. 1 General scheme of a progressive MCDA process

On the concept of progressiveness in MCDA

A progressive MCDA method is an iterative procedure which presents intermediate recommendations to the DM which have to be refined at further steps of the MCDA. The concept of progressiveness therefore intervenes in practice in the determination of the recommendation, rather than in the elicitation of a DM's preferences. Figure 1 represents progressiveness in an MCDA method. As one can see, it is a framework around interactivity, that controls the construction of a final recommendation via intermediate partial conclusions.

The entry point to a progressive method is an initialisation phase which generates a first recommendation in accordance with the DM preferences, via an interactive questioning. If the DM is not completely satisfied with this output, a progressive process can then be initiated to further refine the partial conclusion. This can be done by enriching the currently available data by further information, by solving issues related to missing data or by focussing on a subset of alternatives to refine the recommendation.

These iterations are continued until the DM accepts the current recommendation as the final one. In practice this means that he is satisfied with it or that he can get along with it on his own to elaborate his final decision.

The necessity of such methods in real-world applications can be illustrated via a short example. Consider a recruitment procedure in a company. At different steps of this process, new information is collected from the applicants and inappropriate candidates are rejected on the basis of the currently available information. Consequently the final best applicant is determined in a progressive manner.

The use of a progressive decision analysis method can be motivated by (at least) three reasons. First, it can be justified by prudence, as the ultimate recommendation does not necessarily have to be reached in one step. Second, progressiveness is also motivated by economic constraints. Indeed, at a given moment, only limited financial or temporal resources may be available. Third, as the DM's preferences, as well as the final recommendation, are actively constructed via small steps, such methods are motivated by a constructive approach [START_REF] Dias | On the constructive and other approaches in decision aiding[END_REF] to the problem.

On the choice problematique in an outranking framework

The second part of our thesis deals with the choice problematique, which is the typology of decision problems dealing with the determination of a single alternative which can be considered as the best one.

Our research is based on the so-called bipolar-valued outranking relation representing the credibility of the validation of outranking situations between all pairs of alternatives. We introduce and discuss a set of five pragmatic principles which should guide a progressive search for a single best alternative: -P 1 : Non-retainment for well motivated reasons; -P 2 : Minimal size; -P 3 : Efficient and informative refinement; -P 4 : Effective recommendation; -P 5 : Maximal credibility. These principles are thoroughly discussed and translated into properties in a bipolarvalued outranking digraph. These then lead to the new graph theory-related object of maximally determined strict outranking hyperkernel, which is considered as an appropriate choice recommendation in a progressive MCDA context. Note that the Rubis choice method [START_REF] Bisdorff | Rubis: a bipolar-valued outranking method for the best choice decision problem. 4OR[END_REF] implements this concept and allows to determine the choice recommendation.

In our work we also study the k-choice problematique, which is the typology of decision problems dealing with the choice of k > 1 best alternatives [START_REF] Meyer | Exploitation of a bipolar-valued outranking relation for the choice of k best alternatives[END_REF]. We show that different definitions of the k-choice problematique can be given: -Search for the first k best alternatives (k first-ranked); -Search for a set of k alternatives better than any other coalition of k alternatives (best k-team); -Search for a set of k alternatives better than all the other alternatives (best k-committee). In the dissertation each of these definitions is detailed and their resolution is presented via extensions of the Rubis method.

On Choquet integral-based MAVT and Kappalab

The last part of our thesis deals with Choquet integral-based MAVT. In this context, we studied the extension of the Choquet integral to take fuzzy partial evaluations into account to produce a fuzzy output. In particular, we show how the overall fuzzy evaluations obtained via this aggregation operator can be used in MCDA to solve the choice and the ranking problematiques.

An important issue in Choquet integral-based MAVT concerns the determination of the parameters of the underlying capacity. In our work we present these so-called capacity identification methods from a common general point of view and discuss our proposal, which allows to find an approximate solution, even if the Choquet integral is too poor to model the DM's preferences (Grabisch et al. 2008).

A further achievement of our doctoral work is our collaboration to the Kappalab package [START_REF] Grabisch | kappalab: non additive measure and integral manipulation functions[END_REF] for the GNU R statistical system. It allows to solve MCDA problems via Choquet integral-based MAVT and contains all the identification methods proposed in the literature as well as our personal contributions (see also [START_REF] Grabisch | A decade of application of the Choquet and Sugeno integrals in multicriteria decision aid. 4OR[END_REF].


Raymond Bisdorff

Patrick Meyer

Yannis Siskos

come   L'archive ouverte pluridisciplinaire

OR and the management of electronic services - EURO'2004 One of the most important concerns of the European Union is the provision and continuous improvement of goods and services within the Europe of today and tomorrow. Among the technologies used for this purpose, the Internet has become a powerful vehicle of services rather than just a repository of information. Many organizations are struggling to put their core business competences on the Internet as a collection of e-services, while customers may retrieve these services from the web and fuse them into combinations of new value-adding e-services in different ways.

The 17 articles gathered in this feature issue originate in the 20th EURO Conference, held in Rhodes Islands in July 2004. The main theme of the conference -OR AND THE MANAGEMENT OF ELECTRONIC SERVICES -dealt with the contribution of operational research philosophies, methods and techniques to the design, performance and delivery of e-services. Finally selected papers target towards the academic and practical aspects of e-Commerce, e-Business and e-Government.

The present feature issue starts consequently with a corresponding review paper by G.I. Doukidis, K. Pramatari and G. Lekakos which aims at giving insight into the relation between operations research and the management of electronic services. The authors summarise the various aspects in which operations research may support the management of electronic services, taking into account the different characteristics of alternative electronic media, such as the Internet, mobile communications, interactive television, etc.

The following papers, more or less close to the overall theme, are organized along six principal top-ics: Management of electronic services, financial modelling and engineering, multiple criteria decision analysis, data mining and knowledge management, networks and electronic services, and mathematical programming.

Management of electronic services

Three papers directly relay to the main theme of the EURO 2004 conference.

C.D. Tarantilis, C.T. Kiranoudis, and N.D. Theodorakopoulos: A web-based ERP system for business services and supply chain management. Application to real-world Process Scheduling. The authors present a system developed for attacking business problems and managing real-world business processes ranging from simple office automation procedures to complicated supply chain planning.

M. Louta, I. Roussaki, and L. Pechlivanos: An Intelligent Agent Negotiation Strategy in the Electronic Marketplace Environment. In their paper, the authors present a dynamic multilateral negotiation model and construct an efficient negotiation strategy based on a ranking mechanism that does not require a complicated rationale on behalf of the buyer agents. The framework proposed considers both contract and decision issues, is based on real market conditions, and has been empirically evaluated.

E. Grigoroudis, Ch. Litos, V.A. Moustakis, Y. Politis, and L. Tsironis: The assessment of userperceived web quality: Application of a satisfaction benchmarking approach. Here the authors present a pilot user satisfaction survey concerning the major cellular phone service providers in Greece. The analysis is based on a multiple criteria preference disaggregation approach for satisfaction benchmarking analysis.

Financial modelling and engineering

Ch. Tofallis: Investment Volatility: A Critique of Standard Beta Estimation and a Simply Way Forward. The author reviews the common interpretations that are applied to beta in finance and show that the standard method of estimation -least squares regression -is inconsistent with these interpretations. Consequently he presents an alternative beta estimator which is more appropriate, as well as being easier to understand and to calculate.

T. Shibata: O.R. Applications: The Impacts of Uncertainties in a Real Options Model under Incomplete Information. This paper examines the impact with respect to the uncertainty of the underlying state variable, profit uncertainty, on the real options model in a situation of incomplete information.

G.D. Samaras, N.F. Matsatsinis, and C. Zopounidis: A Multicriteria DSS for Stock Evaluation Using Fundamental Analysis. This paper describes a Multiple Criteria Decision Support System which aims at presenting an evaluation of the Athens Stock Exchange (ASE) stocks, on the basis of the fundamental analysis ratios method. The system, intended for both institutional and private investors, incorporates a large volume of relevant information and operates in real-world conditions.

Multicriteria decision analysis

E. Erkut, A. Karagiannidis, G. Perkoulidis, and St. A. Tjandra: A Multicriteria Facility Location Model for Municipal Solid Waste Management in North Greece. In this paper, the authors compare and contrast regional and prefectural Solid Waste Management (SWM) planning in Central Macedonia. Following this analysis, they present a new multiple criteria mixed-integer linear programming model to solve the location-allocation problem for municipal SWM at the regional level.

C.A. Bana e Costa, and J.-Cl. Vansnick: A critical analysis of the eigenvalue method used to derive priorities in AHP. A lot of research has been devoted to the critical analysis of the Analytic Hierarchy Process (AHP), from various perspectives. Here the authors address a fundamental problem concerning the meaning of the priority vector derived from the principal eigenvalue method used in AHP. The role of AHP's consistency ratio is also analysed.

Data mining and knowledge management

The first paper in this category is based on a semi-plenary presentation.

S. Olafsson, X. Li, and Sh. Wu: Operations Research and Data Mining. This paper provides a survey of the intersection between operations research and data mining. The primary goals of the paper are to illustrate the range of interactions between the two fields, present some detailed examples of important research work, and provide comprehen sive references to other important work in the area.

G. Mavrommatis: Learning Objects and Objectives towards Automatic Learning Construction. The author presents a method that creates instructionally sound learning experiences by means of learning objects. The method distinguishes two kinds of learning objects properties and proceeds in two major steps: the course creation and the alternative learning sources selection.

Networks and electronic services

S. Yaiparoj, F. Harmantzis, and V. Gunasekran: On the Economics of GPRS Networks with Wi-Fi integration. Wi-Fi provides an appealing opportunity for GSM/GPRS operators to enhance their data capability. By integrating both networks, operators are able to provide 3G-like services. However, both networks have different data rates and capacity, which makes economics of the network integration and pricing of services a challenging issue. In this paper, the authors therefore introduce a novel pricing model for GPRS networks integrated with Wi-Fi networks.

Y.-M. Wang, C. Parkan, and T. Elhag: Optimal aggregation of fuzzy preference relations with an application to broadband internet service selection. This paper investigates the aggregation of multiple fuzzy preference relations into a collective fuzzy preference relation in fuzzy group decision analysis and proposes an optimization based aggregation approach to assess the relative importance weights of the multiple fuzzy preference relations.

N. Nikolic: Statistical Integration of Erlang's Equations. Establishing analytical description of a queuing system is in the form of a system of first-order differential equations. There are two commonly used methods of solving this system: analytical and numerical. Both are exact and reliable, but also very complicated. The author presents a third solution method that can be realized by mathematical statistics.

Mathematical programming

The first paper in this last category is based again on a semi-plenary presentation.

A. Caprara: Constrained 0-1 Quadratic Programming : Basic Approaches and Extensions. The author describes the simplest technique to tackle 0-1 Quadratic Programs with linear constraints among those that turn out to be successful in practice. The proposed technique is completely general and is by far the most successful one in several other cases, such as Quadratic Knapsack.

Z. Lukac ˇ, Kr. S ˇoric ´, and V. Vojvodic ´: Production Planning Problem with Sequence Dependent Setups as a Bilevel Programming Problem. The problem of processing n products on two machines may be formulated as a bilevel mixed 0-1 integer programming problem. The objective of the leader problem is to assign the products to the machines in order to minimize the total sequence dependent setup time, while the objective of the follower problem is minimize the production, storage and setup cost of the machine.

Z. Laslo, B. Keren, and H. Ilani, Minimizing Task Completion Time with the Execution Set Meth-od. The authors seek an arrangement of a network of assembling operations and an execution plan that divides the task operations among the conveyers by minimizing the overall task completion time. They use linear programming optimization, subject to reasonably general rules for distributing the operation-fragments among the conveyers.

Raymond