Cédric Plesse
email: acedric.plesse@u-cergy.fr

Alexandre Khaldi
email: balexandre.khaldi@isen.iemn.univ-lille1.fr

Caroline Soyer
email: ccaroline.soyer@univ-valenciennes.fr

Eric Cattan
email: deric.cattan@univ-valenciennes.fr

Dominique Teyssié
email: edominique.teyssie@u-cergy.fr

Claude Chevrot
email: fclaude.chevrot@u-cergy.fr

Frédéric Vidal
email: gfrederic.vidal@u-cergy.fr

PEDOT based Conducting IPN Actuators. Effects of electrolyte on actuation

Keywords: Interpenetrating Polymer Network (IPN), electronic conducting polymer, poly(3, 4ethylenedioxythiophene), actuators, electrolyte, Ionic liquid

Actuators from conducting IPNs architecture are described. The electroactive materials are based on several PEO/elastomer IPNs as solid polymer electrolytes in which the conducting polymer Poly(3,4-ethylenedioxythiophene) (PEDOT) is gradually dispersed, i.e. its content decreases from the outside towards the centre of the film. Influence of the electrolyte on the actuation properties has been studied. Moreover, the effect of actuator thickness has been investigated. It is shown that the decrease of the thickness leads to fast response systems presenting large deformations at frequencies above 100 Hz.

Introduction

Electronic conducting polymers (ECPs) have attracted attention notably because of possible dimensional changes due to the counter-ion (and solvent molecule) expulsion/incorporation during oxidation or reduction processes. Providing an ionic conducting medium is available, ECPs can be used as the active component in actuators or artificial muscles and lead to interesting potential applications (robotics, prosthetics, microvalves, etc.). [START_REF] Baughman | Molecular electronics[END_REF][START_REF] Smela | [END_REF][START_REF]Polymer Sensors and Actuators[END_REF][START_REF] Madden | [END_REF][5]. ECPs such as polyaniline, polythiophene and their derivatives have been studied; nevertheless polypyrrole (PPy) is the most widely studied ECP as active component in actuators [START_REF] Spinks | Conjugated Polymer actuators: fundamentals in[END_REF]. Consequently many studies on actuators are based on self-standing PPy film or PPY film/ no volume change film (PPY/ NVC) [START_REF] Sansiñena | Electroactive Polymer Actuator as Artificial Muscles[END_REF] bilayer structure for which the PPy film is connecting as a working-electrode in a classical 3 electrochemical cell. The first actuators capable of a reversible bending movement in air were also made of PPy [START_REF] Baughman | Molecular electronics[END_REF]. These actuators are constructed using two PPY film electrodes and a solid polymer electrolyte (SPE) film in a (PPy//SPE//PPy) sandwich configuration. These trilayered actuators opened the possibility of getting ECP based actuators working out of a liquid electrolyte. However a delamination process was reported that limits the actuator's lifetime [START_REF] Smela | [END_REF]9]. To overcome the delamination process Spinks et al. used a porous membrane as the SPE. The membrane acts a reservoir for the ionic electrolyte and provides improved adhesion to the ECP layers that are deposited on the membrane. The adhesion improvement is attributed to the rough nature of the porous membrane.

PEDOT has received particular attention in recent years. PEDOT displays a high structural regularity due to the exclusive 2-5 linkage resulting from the presence of the 3,4-ethylenedioxy substituent. It has also been described as a chemically and thermally [10] stable polymer exhibiting a particularly high electrochemical stability [11][12][13] in the doped state. Moreover the donor properties of alkylenedioxy substituent as well as the rigid and planar 3,4-ethylenedioxythiophene (EDOT) conjugated rings lead to a low-band-gap polymer (Eg ∼ 1.6 eV). Indeed, PEDOT can be easily oxidized [14][15][16] and it presents high visible contrasts upon electrochemical switching, being transparent light blue in its p-doped state and dark blue in its dedoped one [17][18][19]. As an ECP that undergoes dimensional changes resulting from redox processes, PEDOT is potentially attractive for the design of electrochemical actuators [20]. Nevertheless unlike PPy, PEDOT based actuators have not received particularly high attention. Only few groups are currently dealing with PEDOT based actuators [21,22]. Likewise, fundamental studies on actuation properties have been hardly carried out because PEDOT can not form a self-standing film. Several years ago an original polymer architecture was proposed by our laboratory by developing an actuator based both on Interpenetrating Polymer Networks and on PEDOT [22]. The linear electronic conducting polymer is then entangled within an interpenetrating polymer network (IPN) SPE matrix and its controlled inhomogeneous mass distribution mimics the sandwich like configuration. The IPN structure ensures a good compatibility between PEDOT and the SPE matrix and totally prevents delamination. Conducting IPN actuator is thus similar to a layered one but for the fact that it is a one-piece device instead of being a trilayered device. As for conventional PPy based actuators, the ion movements are principally responsible for the volume change that produces an actuation response. The extent and speed of actuation is influenced by the nature of ions that move during the redox reaction as well as the speed at which the ion move. The behavior of conducting IPN actuators is then sensitive to the electrolyte nature and to the SPE matrix characteristics. Their influences are described in the present paper.

Experimental

Materials

Polytetrahydrofurane (PTHF, Terathane® Mw = 2900 g mol -1 ), polybutadienehydroxyl functionalized (HTPB, Mw = 2800 g.mol -1 ), methoxy poly(ethylene glycol) methacrylate (PEGM475 Mw = 475 g mol -1 ), poly(ethylene glycol) dimethacrylate (PEGDM750, Mw = 750 g mol -1 ; dibutyltin dilaurate (DBTDL 95%), obtained from Aldrich were used without further purification. Nitrile butadiene rubber with 44 wt % acrylonitrile content (NBR, Mw = 230 000 g mol -1 , Perbunan 4456F) was provided by Lanxess. 3,4-ethylenedioxythiophene (EDOT) (Bayer) was distilled under reduced pressure at 90°C prior to use. Dichloromethane (VWR), toluene (VWR), methanol (VWR), lithium perchlorate (Aldrich), anhydrous iron III chloride (Acros) and Desmodur® N3300 (5.2 × 10 -3 moles of NCO for 1 g of Desmodur®) (Bayer) were used without further purification. Dicyclohexylperoxidicarbonate (DCPD) (Groupe Arnaud) and 1-ethyl-3methylimidazolium bis-(trifluoromethylsulfonyl)-imide (EMITFSI) (Solvionic) was used as received.

Synthesis of IPNs, conducting IPNs and actuators. Solid Polymer Electrolytes (SPE) (PEO/PB, PEO/PTHF, PEO/NBR IPNs) have been synthesized according to procedures described elsewhere [23][24][25]. Conducting IPNs have been synthesized by chemical oxidative polymerization of EDOT according to procedure described elsewhere [22,24,[START_REF] Festin | Proceeding of SPIE -Smart Structures and Materials 2011 -EAPAD[END_REF]. The edges of the conducting IPNs were cut off in order to avoid short-circuit between the two faces of the device. The conducting IPNs were immersed in electrolyte (salt/solvent or neat EMITFSI ionic liquid) for a swelling step. In the case of salt/solvent electrolytes, the actuators are tested immediately after the desired amount of electrolyte has been incorporated. In the case of EMITFSI ionic liquid, the actuator is kept in air without further precaution.

Actuator characterizations. The conducting IPNs were maintained horizontal with steel clamps in order to ensure electrical contact with the VMP Bio-logic (Science Instrument) potentiostat. Electrochemical studies were carried out by connecting the counter electrode and the reference electrode together on one side of the actuator and by connecting the working electrode to the other side. The displacement response was stimulated by applying a square or triangle wave potential from ±2 to ±5 V and recorded with a numeric camera and a laser displacement sensor (ILD 1401-5, Micro-Epsilon) fitted to a computer.

The actuator position was characterized by calculating the curvature  (cm -1 ) as described elsewhere [START_REF] Uchida | [END_REF]. The strain ε of the device was calculated using equation ( 1

): 100 ) ( 2 2    L D Dw  (1)
where D is the displacement from the unactivated position to the activated position, L the length of the sample and w the thickness of the sample.

Scanning electron microscopy and energy dispersion spectroscopy (EDS).

Scanning electron microscopy (SEM) was performed using a Carl Zeiss AG-ULTRA 55 by GEMINI® with a field emission gun at 2-10 kV. The SEM is equipped with an energy dispersion spectrometer allowing a sulfur mapping on dry conducting IPN (HV = 10 kV).

Results and Discussion

Conducting IPN synthesis

The preparation of PEO based IPNs is among the most efficient approaches in Solid Polymer Electrolyte (SPE) design suppressing PEO crystallinity at ambient temperature and ensuring polymer flexibility. Moreover in the chosen PEDOT-based materials the presence of ethylene oxide units in both the PEO network and the ethylenedioxy function of PEDOT will ensure a compatibilizing effect [22]. In order to further improve the ionic conductivity, short PEO side chains can be introduced in the structure of the IPNs as dangling chains leading to the design of a branched PEO network [28].The flexibility of the chains is thus expected to be less restricted than in an unbranched network and the amount of volume available for the migration of ions would be much higher. In the present paper the PEO based IPN SPE matrix is composed either of a polybutadiene (PB) or Nitrile Butadiene Rubber (NBR) or polytetrahydrofurane (PTHF) partner according to the nature of the desired application. The synthesis and the characterization of these PEO based IPN matrices have been described elsewhere. A series of PEO based IPNs were prepared, namely the 80/20 (w/w) PEO/PB, the 60/40 (w/w) PEO/NBR and the 50/50 (w/w) PEO/PTHF. The conducting IPNS are obtained from the above described SPE. The PEO-based IPN film is swollen with EDOT which is subsequently polymerized to PEDOT. The EDOT-swollen IPNs are immersed in a 1.5 mol L -1 FeCl 3 aqueous solution for various lengths of time leading to the formation of PEDOT inside the IPN. The preferential PEDOT distribution as a thin layer towards the surface of the film has been evidenced from EDS. For polymerization duration of 18 h, the quantity in the central part of the film is low enough to ensure that no short-circuiting occurs. The general procedure for the synthesis of conducting IPN is described Figure 1.

Effects of the salt and solvent

A series of conducting IPNs were prepared according to the procedure described above. As synthesized via chemical oxidation of the monomer, PEDOT is present in the IPN in the charged conducting state. The FeClO 4 dopant anion is fixed during the oxidative polymerization, but may be exchanged during the electrolyte swelling process. Therefore before actuation experiments, dry conducting IPNs were dipped in different salt/solvent combination solutions (10 -1 mol L -1 ). The mass quantity of electrolyte in the conducting IPN was controlled by the time duration of immersion in the salt/solvent solution.

After salt uptake in LiClO 4 /acetonitrile, a strip of conducting IPN (10x6x0.25 mm 3 ) was subjected to a constant voltage of 2 V applied between the two sides of the actuator film. The actuator bends and reach a positive curvature value of 0.4 cm -1 in 60s (Figure 2-A). The actuation direction corresponds to an increase in volume at the anode and a decrease in volume at the cathode indicating that a positive charge on the PEDOT backbone is balanced by the incorporation of ClO 4 -. This mechanism with ClO 4 -incorporation /expulsion has been already described in PPy actuators [5,[START_REF] Skaarup | Ionic Motion ibn Polypyrrole doped with ions of different sizes[END_REF] but it is shown here that a different behavior is achieved on PEDOT based actuators. Skaarup et al. [START_REF] Skaarup | Ionic Motion ibn Polypyrrole doped with ions of different sizes[END_REF] have found that for PPy actuators in LiClO 4 /acetonitrile electrolyte, ClO 4

-is a non-mobile specie. The mobile anion mechanism is further confirmed when the conducting IPN actuator is dipped in NBu 4 ClO 4 / acetonitrile electrolyte. Indeed NBu 4 + cation is much more bulky than Li + and should be immobilized. As show in Figure 2, the actuator bends in the same direction with similar capacity which confirms that the mechanism is governed by an anion exchange. In the range of 5-15wt% salt, the electrolyte content has only a weak influence on the rate and strain when a voltage of 2V is applied. Different solvents can be used for the electrolyte and could have an impact on the actuation behavior since interactions between the SPE, the PEDOT and the solvent can be modified. Conducting IPN actuators are now swollen in LiClO 4 / H 2 O electrolyte. This system shows more complex behavior as illustrated in Figure 3. Depending on the amount of loaded LiClO 4 , significantly different results are obtained. The amount of LiClO 4 loaded in the actuator seems to have a major and unexpected role on the curvature. For a content of 9wt% LiClO 4 , the actuator remains motionless during the first 3 seconds while applying a voltage of +2V. Then, the actuator bends and reaches a positive curvature value of 0.35 cm -1 after 40s. Therefore, since PEDOT electrode volume expansion and contraction are observed during oxidation and reduction respectively, the actuation mechanism seems to be mainly governed by an anion movement. In the case of actuators containing 11 and 16wt% LiClO 4 , a particular behavior is observed while applying +2V. Indeed, during the first 3 seconds the devices bend in the opposite direction to the previous case and after this period, the bending direction is reversed. The curvature values at 30s decrease when the amount of LiClO 4 increases. Finally, for the sample containing 20wt% LiClO 4 , only the opposite movement is observed. The actuator bends in the first 3 seconds and hold a constant position (-0.12 cm -1 ). Likewise, Li + cation is not immobile anymore and a competition mechanism seems to be involved. Indeed in the case of an electrolyte comprising two mobile ions, a competition mechanism could take place, leading to the successive deformation of the actuator in one direction then in the other. In the case of conducting IPN actuator based on PEDOT, the three behaviors, namely mechanism of anion or cation movement or both successively, seem to be observed as function of loaded LiClO 4 . All the above experiments show the complexity of the processes involved in conducting actuators. To our best knowledge such behavior as a function of salt concentration has not been described before.

Different solvents and salts have been tested as electrolyte. Finally the best actuation performances are obtained with the following electrolytes i.e. LiClO 4 / propylene carbonate (PC) and EMITFSI. Conducting IPN is actuated in LiClO 4 / PC and the optimum performances of 1.1 cm - 1 curvature at a rate of 0.5 cm -1 /s is achieved. This electrolyte allows the largest bending as shown in Figure 4 and the direction as well as the amplitude of the bending movement indicates that the mechanism is mainly governed by the anion movement. Likewise, PC can not only swell the PEO and the elastomer partners but has also the ability to diffuse in the PEDOT partner. Therefore PC electrolyte can enable plasticizing and softening all the partners of the conducting IPN which result in higher strain. However the main drawback of LiClO 4 / PC electrolyte is the solvent evaporation. For instance conducting IPN actuator can be cycled over 3h before the bending deformation stops due to PC evaporation. After being immersed again for a few hours in LiCLO 4 / PC solution the actuator fully recovers its working capacity [30]. In order to prevent the evaporation process ionic liquid (IL) has been used as electrolyte. Indeed ILs are non-volatile compounds and have been successfully used for electromechanical actuators [31][32][33]. In the presence of ethyl-3methylimidazolium bis-(trifluoromethylsulfonyl)imide (EMITFSI) as IL, the actuator can be operated in open air over one month and be stored over a period of 6 months at least without any precaution and be operated again immediately. In the presence of EMITFSI, the actuation is dominated by cation movement [34] giving an actuation curvature of -0.4 cm -1 at quite low rate (Figure 4). Compared with LiClO 4 / PC electrolyte, conducting IPN actuators are less efficient in the presence of EMITFSI, however it should point out that the major advantage obtained from EMITFSI is the extended cycling. For instance EMITFSI allows the conducting IPN actuator to be operated in air for one month without drying. In this configuration an actuator film has been subjected to 7 × 10 6 bending motions (f = 10 Hz) without degradation and/or delamination [30].

Conducting Polymer actuators with fast response

In order to investigate the response speed of conducting IPN actuators, thin IPN based SPEs have been elaborated and have been used as starting material for the conducting IPN synthesis. In principle, ionic EAPs, such as conducting polymer actuators, present slow responses since they are based on ion motions inside polymer membrane. In the case of ECP actuators, it is commonly accepted that actuation mainly results from the redox process of the conducting polymer which is limited by ion diffusion. However, several examples of ionic EAPs presenting high actuation frequency have been described. For instance, Spinks et al [35] have described a fast-response actuator, based on polypyrrole, which displays a resonance peak as high as 90 Hz depending on the sample size. Recently Asaka et al [36] have reported a beam shaped actuator consisting of singlewalled carbon nanotubes (SWNTs), ionic liquid, PVDF and polyaniline as an additive. Bending deformation was measured in the frequency range between 5 mHz and 100 Hz. Nevertheless the strains are low at high frequencies, Since the actuation mechanism is dominated by mass transfer, the actuation is determined by the diffusion rates and distances [START_REF] Madden | [END_REF]35]. Therefore, conducting polymer actuators with fast response can be obtained by decreasing the thickness of the SPE. Then, the previously described IPN SPEs have been synthesized as thin films. For instance 50/50 PEO/PTHF or 50/50 PEO/NBR IPNs present a final thickness of 10 and 30 µm respectively. Thin actuators were prepared from PEO/elastomer and EDOT according to the procedure described elsewhere [22,24]. As shown in Figure 5, by the control of the polymerization condition (EDOT content, temperature, FeCl 3 concentration and time), trilayer configuration can still be obtained despite the use of very thin membranes. Afterward PEO/PTHF/PEDOT or PEO/NBR/PEDOT conducting IPNs are swollen with EMITFSI (140wt%). The study of the electrochemical behaviour of these systems has been performed by cyclic voltametry at different scan rates. Figure 6 presents the cyclic voltametry of PEO/PTHF/PEDOT beam (2.6 mm×1.2 mm×0.020 mm) between -2 and 2 V in open air (twoelectrode system, scan rate of 50 mV s -1 ). The actuator exhibits a symmetric voltamogram with two distinct oxidation peaks at -0.5 and 0.5 V and two distinct reduction peaks at 0.5 and -0.6 V. This behaviour has been already observed in the case of electropolymerized PEDOT studied in EMITFSI [37]. Since EMI + cation is the involved ion in the redox process [37], this electrochemical behaviour has been attributed to the presence of two coexisting zones corresponding to two different PEDOT morphologies in which cation diffusion is different. Figure 7-A presents voltamperograms of this actuator in a 2 electrode setup for increasing scan rates between 50 and 1.10 5 mV.s -1 (corresponding to frequencies between 6.25 mHz and 5 Hz) with potential windows between 4 and 10 V (from + 2V to + 5V). Redox process can be observed for every studied scan rate. When the scan rate increases, only one oxidation and reduction peak is observed. Moreover, oxidation and reduction peak potentials present an anodic and cathodic shift respectively. Then, a broadening of the applied potential window is necessary. Conducting polymer overoxidation can still be avoided since the frequency is high enough, typically above 1 Hz. This is due to the huge ohmic drop in the thickness of the sample (serial resistance) [37]. As a consequence, the effective potential is much lower than the applied potential and does not lead to PEDOT degradation. The consumed charge is reported on figure 7-B. As the frequency increases, the electrochemical charge decreases: from 19.1 to 0.4 mC.cm -2 for a + 5 V potential windows and from 42.3 to 0.003 mC.cm -2 for +2V potential window. In other words, less and less PEDOT can undergo the redox process since ion diffusion remains the limiting step. The redox process of ECP based actuators is not well known at high frequencies but one can suppose that the capacitive component of the charge may become preponderant. In this case, the system starts to behave like a capacitor, mainly ruled by ion migration under the electric field. However, recent studies have described that a redox process can occur for polyaniline at frequencies as high as 1000 Hz [38]. These results allow making the assumption that a small fraction of the ECP can still undergo a redox process, even at high frequency. Next, displacement measurements were recorded at an applied square-wave voltage of ±5.0 V at different frequencies. Figures 8-A and B present the frequency dependence of the generated strain for PEO/PTHF/PEDOT (thickness: 20 µm) and PEO/NBR/PEDOT (thickness: 90 µm) actuators respectively. For PEO/PTHF/PEDOT actuator, the strain is almost constant up to 100Hz, between 0.1 and 0.2 %. A slight increase can be observed when the applied frequency is increased and may be due to a Joule effect taking place through the thickness of the sample. This Joule effect leads to a temperature increase and then to an increase of the ionic conductivity of the SPE. In the case of the PEO/NBR/PEDOT thin actuators, the strain decreases as the frequency increases, from 3.7% at 1 Hz to 1.3% at 100 Hz. This behaviour has been already observed by several authors [35,36] and is consistent with the decrease of the electrochemical charges as a function of the frequency. However, for both conducting IPNs, when the frequency reaches 100 Hz, the tip displacement sharply increases. A maximum strain can be observed at 125 Hz and 156 Hz for PEO/PTHF/PEDOT and PEO/NBR/PEDOT respectively. This strain amplification is related with the fundamental resonance frequency of the beam and is dependent of the geometrical dimensions of the actuator. This behaviour has been previously observed in the frequency response [35] of trilayer actuators based on polypyrrole, with a resonance peak observed as high as 90 Hz. The resonance peak occurs when the actuator is operated near the system's natural frequency.

Conclusion

Actuators from conducting IPNs architecture have been demonstrated and lead to a bending deformation with different electrolytes i.e; salts and solvents. For a LiClO 4 /organic solvent electrolyte, only the anion is mobile whereas for LiClO 4 /water system mixed ion movement can occur according to the amount of salt loaded. The actuator thickness can also affect the actuation rate and fast response has been obtained by decreasing the thickness of the SPE. Thin actuators show a mechanical resonance higher than 100Hz for an applied potential of ±5V.

Figure 1 :

 1 Figure 1 : Schematic procedure for the synthesis of conducting IPN actuators

Figure 2 :

 2 Figure 2: Curvature as a function of time for a PEO/PB/PEDOT conducting IPN actuator under 2 V. electrolyte: (A) LiClO 4 /acetonitrile and (B) tBuNClO 4 /acetonitrile

Figure 3 :

 3 Figure 3 : Curvature as a function of the time for a PEO/PB/PEDOT conducting IPN actuator swollen by LiClO 4 /H 2 O under 2 V. Amount of loaded LiClO 4 : (■) 9 %, (□) 11 %, (Δ) 16 %, (▲) 20 %.

Figure 4 :

 4 Figure 4: Curvature as a function of the time for a PEO/PB/PEDOT conducting IPN actuator swollen by (■) LiClO 4 /PC or (Δ) EMITFSI.

Figure 5 :

 5 Figure 5: SEM images of the cross-section of the conducting IPNs: (A) PEO/NBR/PEDOT and (B) PEO/PTHF/PEDOT. Energy Dispersive Spectroscopy with sulfur atom mapping (light grey) of the conducting IPNs: (C) PEO/NBR/PEDOT and (D) PEO/PTHF/PEDOT.

Figure 6 :

 6 Figure 6: Cyclic voltametry of PEO/PTHF/PEDOT conducting IPN swollen with EMITFSI in a 2 electrode configuration. Scan rate: 50 mV.s -1 .

Figure 7 :

 7 Figure 7: (A) cyclic voltametry of PEO/PTHF/PEDOT conducting IPN swollen with EMITFSI in a 2 electrode configuration at different scan rates. (B) Consumed charge Q during cyclic voltametry as a function of the applied frequency with (♦) + 2V and (□) + 5 V electrochemical windows.

Figure 8 :

 8 Figure 8: Frequency dependence of the generated strain for (A) PEO/PTHF/PEDOT (2.56x1.2x0.02 mm 3 ) and (B) PEO/NBR/PEDOT (3.27x1.22x0.09 mm 3 )thin actuators in open-air under + 5V square wave potential. Strain measured at 1 mm from the clamped beam.

Acknowledgements

This work was funded by the French Ministry of Research (Action Concertée Incitative: MUSARIP), by the ANR project "IN-ART" ANR-09-BLAN-0110 and by the Fondation d'Entreprise EADS "OVMI-2". Authors would like to thank COST (European Cooperation in Science and Technology) in the framework of ESNAM (European Scientific Network for Artificial Muscles) -COST Action MP1003.


Ngoc Tan Nguyen

Cédric Plesse

Frédéric Vidal

Caroline Soyer

Sébastien Grondel

John D W Madden

Eric Cattan
email: eric.cattan@univ-valenciennes.fr

Microfabricated PEDOT trilayer actuators: synthesis, characterization, and modeling

Keywords: IEAP micro actuator, PEDOT, layer by layer, force generation, modeling, dynamic beam theory, Bond Graph

Conducting polymer actuators have long been of interest as an alternative to piezoelectric and electrostatic actuators due to their large strains and low operating voltages. Recently, poly (3,4-ethylenedioxythiophene) (PEDOT) -based ionic actuators have been shown to overcome many of the initial obstacles to widespread application in micro-fabricated devices by demonstrating stable operation in air and at high frequencies, along with microfabrication compatible processing using a layer by layer method that does not require any handling. However, there is still a need for characterization, prediction, and control of the actuator behavior. This paper describes the fabrication and characterization of thin trilayers composed of a 7 µm thick solid polymer electrolyte (SPE) sandwiched between two 2.1 µm thick PEDOT-containing layers. Beam properties including capacitance, elastic moduli of the layers, and the extent of charge driven strain, are applied to predict curvature, frequency response and force generation. The actuator is represented by an electrical circuit, a mechanical system described via dynamic beam theory, and a strain-to-charge ratio for the electro-mechanical coupling matrix, which together predict the actuator curvature and the resonant response. The success of this physical model promises to enable design and control of micro-fabricated devices.

INTRODUCTION

Electro active polymers (EAPs) has attracted interest in both academic and industrial fields since their mechanical and electrical characteristics have the potential for widespread application, for instance: locomotion systems [START_REF] Mcgovern | Finding NEMO (novel electromaterial muscle oscillator): A polypyrrole powered robotic fish with real-time wireless speed and directional control[END_REF] , steerable micro catheters 2 , micro pumps [START_REF] Ramírez-García | Biomimetic, low power pumps based on soft actuators[END_REF][START_REF] Wu | TITAN: A conducting polymer based microfluidic pump[END_REF] , micro actuators [START_REF] Wilson | New materials for micro-scale sensors and actuators. An engineering review[END_REF][START_REF] Pede | A general-purpose conjugated-polymer device array for imaging[END_REF][START_REF] Kiefer | The application of polypyrrole trilayer actuators in microfluidics and robotics[END_REF] . Poly(3,4-ethylenedioxythiopene) (PEDOT) based-actuators have received a lot of attention due to their properties such as: low density, biocompatibility [START_REF] Smela | Conjugated Polymer Actuators for Biomedical Applications[END_REF] , high stress, high power/weight ratio [START_REF] Mazzoldi | Conducting Polymer Actuators: Properties and Modeling[END_REF] , significant displacement (up to 1%), and low operating voltages [START_REF] Smela | Conjugated Polymer Actuators for Biomedical Applications[END_REF] in solution or in open-air [START_REF] Khaldi | Conducting interpenetrating polymer network sized to fabricate microactuators[END_REF] . They can be electronically controlled with reasonable frequency response and are potentially suitable for microscale applications. Actuating layers have been applied in bilayer [START_REF] Cho | A solid state actuator based on the PEDOT/NBR system[END_REF] , trilayer [START_REF] Citerin | Characterization of a new interpenetrated network conductive polymer (IPN-CP) as a potential actuator that works in air conditions[END_REF][START_REF] Zainudeen | PEDOT and PPy conducting polymer bilayer and trilayer actuators[END_REF][START_REF] Plesse | Synthesis and characterization of conducting interpenetrating polymer networks for new actuators[END_REF] , and multilayer [START_REF] Ikushima | A practical multilayered conducting polymer actuator with scalable work output[END_REF] structures in which conducting polymer electrode (CPE) layers are directly in contact with solid polymer electrolyte (SPE) layers accommodating ion flow. However, due to the large charge fluxes required, and the significant electronic and ionic resistances of CPE and SPE layers, speed of charging and actuation has been slow. These important rate-limiting factors are reducing the response speed of the actuator [START_REF] Tina Shoa | Rate Limits in Conducting Polymers[END_REF] . A new clean-room compatible process, referred to as Layer-by-Layer (LbL) [START_REF] Maziz | Top-down Approach for the Direct Synthesis, Patterning, and Operation of Artificial Micromuscles on Flexible Substrates[END_REF] , has been recently been demonstrated which removes the need for manual handling and promises to make the fabrication of conducting polymer actuators highly automated. It also enables thin layers and short device lengths, enabling fast actuation. In the LbL fabrication process of a trilayer structure, there is a need to creat CPE layers. PEDOT can be polymerized insitu via electropolymerization [START_REF] Hulvat | Liquid-crystal templating of conducting polymers[END_REF] or via vapour phase polymerization (VPP) [START_REF] Winther-Jensen | Base inhibited oxidative polymerization of 3,4ethylenedioxythiophene with iron(III)tosylate[END_REF] . In the VPP method, PEDOT thin films were fabricated by spin-coating an oxidant solution onto silicon substrate and then exposing this substrate to a monomer vapor.

The interpenetrating polymer network (IPN) situated between two PEDOT electrodes plays a role of an electronic insulator and an ion transfer membrane. For operation in open air, the trilayer actuator needs to be introduced to the electrolyte, which is necessary for the redox process, where during the oxidation and reduction ions flow through the ion transfer membrane. To improve the mechanical properties and ionic conductivity of this SPE, an IPN matrix of two cross-linked polymers: polyethylene oxide (PEO) and nitrile-butadiene rubber (NBR) [START_REF] Plesse | Synthesis and characterization of conducting interpenetrating polymer networks for new actuators[END_REF][START_REF] Vidal | Conducting IPN actuators: From polymer chemistry to actuator with linear actuation[END_REF] has been designed and controlled. For the purpose of control and to predict the actuator's behavior, researchers have developed models. Madden [START_REF] Madden | Conducting polymer actuators[END_REF] came up with an analytical model based on the diffusive elastic metal phenomenon to describe chemical process between electrolyte and polymer electrode that can be applied to a trilayer actuator, and which was further extended by Shoa [START_REF] Shoa | Analytical modeling of a conducting polymer-driven catheter[END_REF] . This chemical model was linked to the mechanical deformation by an experimentally determined strain-to-charge ratioan empirical constant that relates injected ionic charge density to strain [START_REF] Madden | Conducting polymer actuators[END_REF] . Alici [START_REF] Alici | Bending modeling and its experimental verification for conducting polymer actuators dedicated to manipulation applications[END_REF] also proposed an analytical model in which emphasizes the effects of the interface between electrolyte and polymer electrode and models it as a capacitor and a resistor.

This previous work has employed equivalent circuit models. A related alternative that is explored here is Bond Graph methodology. It appears to be a promising candidate as it allows easy access to power transformation, stored power, and dissipated power inside these actuators. Bond Graph language has shown its flexibility in working with different energy domains and feasibility to describe interactions between systems [START_REF] Karnopp | System dynamics : modeling and simulation of mechatronic systems[END_REF] . These characteristics provide an approach for the design of actuators and further, the design of complete actuated robots while retaining the physical structure of the model [START_REF] Nishida | Multi-scale distributed parameter modeling of ionic polymer-metal composite soft actuator[END_REF] . Few works in modeling IEAP actuators using Bond Graphs have been proposed. Byung-Ju Yi concentrated on diffusion in separator layer and electrodes of ionic polymer-metal composites (IPMCs) and did not describe the mechanical response. The model was not verified by experiments [START_REF] Yi | Modeling of EAPs as multiple energy domain systems: A bond graph approach[END_REF] . Nishida developed a more complex model on IPMCs type using distributed port-Hamiltonian [START_REF] Nishida | Multi-scale distributed parameter modeling of ionic polymer-metal composite soft actuator[END_REF] , while Bowers built a Bond Graph model of bilayer actuators operating in a liquid environment [START_REF] Bowers | MSc thesis title: Modeling, Simulation, and Control of a Polypyrrole-Based Conducting Polymer Actuator[END_REF] . Since ionic EAP actuators inherently involve energy flow in multiple energy domains: mechanical, electrical, simultaneously with chemical domain, a thorough model for explaining the behavior of this actuator is required. Regarding the work that has been accomplished on fabrication and modeling of trilayer actuators, there is a need to improve the fabrication process and develop a more adaptable model to predict actuator behavior. Within this work, an improvement in the LbL process to synthesize an ultrathin trilayer structure in a cleanroom environment will be described. A key advance is the precise control of the VPP by using a vacuum heating plate allowing the fine control of pressure and temperature during the process. Following this step, the microbeam dimensions and composition were studied under scanning electron microscope (SEM), via energy-dispersive X-ray (EDX) analysis and through mechanical, electrochemical and electromechanical testing. In next step, an IEAP actuator model is being developed. An RC electrical circuit is represented for physical model, the electromechanical coupling matrix is based on the accepted relationship between the strain and the volumetric charge density (strain is proportional to charge density multiplied by an empirically derived strain to charge ratio), and a mechanical model is coupled in based on the modal superposition method to treat Euler-Bernoulli dynamic beam equations for beam displacement. This model will provide physical insight into IEAP actuator behavior, which should enable designers to optimize the system through identified critical parameters. Furthermore, the model can then be expanded to describe complex actuator geometries and interactions with other systems.

EXPERIMENTAL SECTION

Fabrication

The synthesis of a trilayer actuator is based on the LbL method which was first described by Maziz 28 , where all the layers are spin coated and deposited on top of previous layers. The overall process is shown in Fig. 1. In this study, the LbL process has been adapted to clean room compatible microfabrication. The first PEDOT electrode layer was synthesized by mixing Poly(ethylene glycol) methyl ether methacrylate (PEGM) (50 wt. %) and Poly(ethylene glycol) dimethacrylate (PEGDM) (50 wt. %), known as PEO precursors, with Fe(III) p-toluene sulfonate oxidant solution in butanol. PEO precursors were added to this layer, and to all the subsequent layers, and polymerized finally throughout the trilayer structure to improve the adhesion between the layers as well as increase ionic conductivity. A solution was stirred during 10 min and spin coated on a 2-inch silicon wafer. The oxidant solution coated wafer was then placed on a vacuum hot plate for EDOT VPP at 45 o C for 50 minutes under vacuum. EDOT monomer droplets were placed in the vacuum system on a glass slides situated around the wafer to obtain a homogenous PEDOT layer. on semi-IPN with PEO prec carbonate (DC lend was spin 45 min at 50 o improve adh s synthesized i VPP was car wt. % of PEO at treatment. ctrode layer, yer. The heat tr ator DCPD in rosslinking to also a micro-p welled in ioni int (Fig. 1).

1. actuato to pattern the femtosecond l ometric mirror as several hun DOT:NBR/PE e three layers NBR/PEO lay d in Table 1.

Trilaye

In this sectio volumetric ca play an impor

Volu

The apparent determined b setup, the co reference elec three electrod (I-E) curve, s 0.7 V at scan

The capacitan lowest and t

As described 53x10 6 F/m 3 t In this sectio determine the which the ac trilayer actua ionic resistan creating an el At

Ioni ic conductivit ty of SPE layer

You

The measure measurement (Fig. 6). The L m is the leng of the beam. T The results s approximatel

Dam

In mechanica frequencies w actuator was quickly relea measurement

(5) ely.

(6) (7) function of (8) (9) (10) ss is given by an be rewritten

Matchin

The beam m properties are to demonstra displacement match betwee

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.2 Experim 2.2.1 Trilaye

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	NBR and 80 w wt. % of cyclo ohexanone) w
	radical initiat tor dicyclohex xyl peroxydic
	degassed. Th he resulting ho omogenous bl
	then placed in n the vacuum m hot plate for
	the PEO netw work to form in n each layer t
	The second P PEDOT electro ode layer was
	spin coated o on the bilayer r, and EDOT
	electrode. Du uring this step p, DCPD (3 w
	between all th hree layers du uring final hea
	After EDOT	VPP for the e second elec
	polymerize P	EO precursor rs in every lay
	During this p period, the fre	e radical initia
	PEO precurso ors in the thre e layers are cr
	The microact tuator fabricat tion includes a
	and a last ste ep where the t trilayer was sw
	actuator until l it reaches the e saturated poi
	mental results er structure 2Several meth hods have been
	reactive-ion e etching 10, 30 . I
	length 400 fs , spot size 10
	dimensions o	f the actuator
	SEM and ED DX. Fig. 2a de
	7.0 μm, and		2.1 μm, resp
	highlighted in n green, and t
	after immersi ion in EMImT
	Fig.2 2. tructure of t
	imag ge confirming th
	layer r is red (not to s

.1.2.4 The

	In this section n, an accurate e model, low-o order, lumped d-parameter re epresentation	of distributed d elements to d describe beam
	displacement t based on E Euler-Bernoull li beam theo ory is given.	The number r of suitable	retaining m modes and the
	incorporation n of the beam'	s damping rat tio are also ex xplained.
	Karnopp 38 in ntroduced the e first model B Bond Graph t to describe re esults of solvin ng Euler-Bern noulli beam e equation using
	separation of f variables me ethod. A simil ar method can n be used to d derive the ion nic EAP actuat tor model in t this paper, bu
	with different t boundary co onditions. The	Euler-Bernou ulli equation	for dynamic be eam is adapted d as follows:
					, ,		,	,	,
	where	is e equivalent flex xural rigidity o of trilayer actu uators which i is calculated a as follows:
					2		/ /	.
	Fig. 8. G Global word Bo nd Graph mode el of ionic EAP ung's modulu PE layer's You Here is SP us, while and d are cross s section and wi idth of the bea actuator. am, respective
	The set of bou undary condit tions for an io onic EAP beam m with clampi ing at one end d are:
	3.1.2 Bond G Graph model l of EAP actu uators	, |	0;	, ,	0	.
	tem 32 . After s ubtracting the e ystem can be ng each subsy Graph describin d, the Bond G ph is obtained rd Bond Grap Once the wor involving in t the electrical, the coupling, and the mech hanical variabl les. derived from the equations In the case of f an applied po oint force at th he other free e end: s , 0 ; , .
	3.1.2.1 Elec ctrical model The separatio an nd a function only , on of variable of time, , es method beg gins by assum : ming the displa acement	,	can be sep parated into a	(1)
					,		.
	highest peak er the form of voltage unde f current. The al e k and y is tota r each compon he response to l represents th ctrical model bility. The ele predictive ab o the applied In this work, we start by employing re elatively simpl le models for nent, and just tify these cho oices based on n Substituting ( (8) into (6), th he solution for r this equation n is in form of f mode shape f functions:
	steady state. ymer electrod nducting poly nside the con dation state in hange in oxid o promote ch age is used to applied volta es, leading to This was no ot o ,
	insertion or re and quite low emoval of cha w frequency o arge, and a ch operation ( 4 ange in electr rode volume. S Since the mod del is designed d for thin (18 and the contri ibution of mode is: 40 ), the el lectrodes are r represented by y one capacit or (Fig. 4). T This model has ) actuators s s 2 2 ,
	Bottom CPE apacitors . T he series of ca ance and th sists of resista actuators cons rcuit of EAP a equivalent cir This part is de escribed by the e . 0.1 Hz) E layer been shown, electrical resp resistance in some cas ponse of con which depe es, to be suf nducting polym ends on the i fficient to pro mer 33-34 . The onic conduct ovide a good e SPE layer o ivity and dim description o of conducting mensions of S of oxidation r polymer actu SPE. Accordi rate or in oth uator can be ingly, the sim her words, the modeled as a mple electrica e where yi elds equation n: 1 1, mode frequ encies , mod de mass a al and model da amping 2 in w which dampin ng ratio is f found by expe eriment. The m model stiffnes
	following equ 3.1.2.2 Elec uation: ctro-mechani Once mode s as: , hape function cal coupling , or in dif fferential form , m: ∑ ns and c contribution fu functions ∑	32.8 S/cm m quation (8) ca determined, eq have been d . .	(2)
	Based on the elements is es relationship b stablished as f between total follows: global mode el of actuator 3In three prev vious sections , the physical l model, the e force , and total char rge in the elec 0 ctrodes electro-mecha anical couplin ng, and the me , the coupling echanical mo	matrix of 2 2 2
	, d divided into organized and he model are o elements in th built. To form m the global m model, it is a m matter of conn small subsyst tems as depict 0 ted in Fig. 9. , , necting all thre ee sub models s by bond elem ments in a Bon	(3)
	where , is tip is the total vo oltage applied d, is strain t to charge ratio o 35 , p displacemen nt in the vert tical direction n at position along the l is the TORS Young's mod dulus of the C CPE layer, and d length of actu uator. This m model does no ot
	consider the s sensor respons se (e.g. effect	of externally	applied displa acement on vo oltage), which h is known to b be small 36 .
	3.1.2.3 Mec chanical mod del
							rical sub syste em, the electr ro-mechanica al
	ystems are sh , and beam tem. The mec force is that g hown in Fig. 8 displacement chanical system enerated at th 8. The input to t , . The m is driven by he tip, but this r o the actuator. Since ionic E EAP actuators s have a smal ll e be considered d as a thin be eam. Moreove er, this type o f y n this case, E n bending of fects results in m coupling eff neration from The force gen ratio between n thickness an nd length 2 / ≪ ≪ 1 , this can actuator oper rates at quite low frequen ncy 4 40 , so in Euler-Bernoull li beam theor ry is perfectly y s could be gen eralized. The pairs of inputs and outputs s (voltage/cur rrent, force/ve elocity) provid de information n about power suitable in ter rm of accurac cy, computatio onal simulatio on, and time s saving, to pre dict beam dyn namic behavi or 34, 37 . Other r
	possible meth hods not used transmission.	here include R Rayleigh, She ear, and Timos shenko. Ionic Fig. 9. EAP ac ctuator's Bond Graph global m model.

ACKNOWLEDGMENTS

This project received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 641822 -MICACT. This work was partly supported by the French Government through the National Research Agency (ANR) under program PIA EQUIPEX LEAF (ANR-11-EQPX-0025), RENATECH, MICRO-TIP projects, and Natural Sciences and Engineering Research Council of Canada.


domain: spi phys

text:
Alexandre Bontemps
email: alexandre.bontemps@isen.iemn.univ-lille1.fr

Sebastien Grondel
email: sebastien.grondel@univ-valenciennes.fr

Thomas Vanneste
email: thomas.vanneste@iemn.univ-lille1.fr

Samuel Dupont
email: samuel.dupont@univ-valenciennes.fr

Eric Cattan
email: eric.cattan@univ-valenciennes.fr

Modeling and evaluation of power transmission of flapping wing nano air vehicle

Keywords: Bioinspiration, mechatronic, MEMS, nano air vehicle, Bond Graph, compliant link, electromagnetic actuation I

In the last decade researchers pursued the development of tiny flying robots inspired by natural flyers. Within this context our main objective is to devise a flying robot-mimicking insect in terms of kinematics and scale using MEMS technologies. For this purpose, an original design has been developed around resonant thorax and wings by the way of an indirect actuation and a concise transmission. Using such a design prototypes with a wingspan of 3 cm and a mass of 22 mg able to lift 75 % of their weights are achieved. As a part of this global goal, this paper presents an innovative power modeling of a flapping-wing nano air vehicle (FWNAV) actuation-transmission system, aiming at a better comprehension of the power transmission from power source to wings, thus allowing future optimization of the actuation efficiency. Considering the multiphysics nature of the prototype a mechatronic approach has been chosen bringing thus a unique model for the whole system. This model has been realized thanks to Bond Graph formalism, which has the crucial advantage to be adapted to multiphysics systems and energetic analysis. After an experimental validation, it is demonstrated that the main parameter conditioning the overall efficiency of the FWNAV is the interaction between coil's current and magnet remanent magnet flux density.

INTRODUCTION

Among flying species observed in nature, insects certainly demonstrate the most impressive aerial capacities in terms of hovering, backward flight or sudden acceleration. Moreover, their great robustness allows them to fly after a shock or with damaged wings. Insect diversity therefore brings multiple solutions to generate lift through original design in actuation, structure and wings. For all these reasons, several studies [START_REF] Ennos | A comparative study of the flight mechanism of Diptera[END_REF][START_REF] Combes | Flexural stiffness in insect wings I. Scaling and the influence of wing venation[END_REF][START_REF] Dickinson | Wing Rotation and the Aerodynamic Basis of Insect Flight[END_REF][START_REF] Ellington | The Aerodynamics of Hovering Insect Flight. I. The Quasi-Steady Analysis[END_REF] as well as observations and experimental data [START_REF] Dudley | Mechanics of forward flight in bumblebees: II. Quasi-steady lift and power requirements[END_REF][START_REF] Dickinson | The wake dynamics and flight forces of the fruit fly Drosophila melanogaster[END_REF][START_REF] Fry | The aerodynamics of hovering flight in Drosophila[END_REF] on mechanical, kinematical and aerodynamic characteristics of insects, have been carried out. To understand flapping flight and the creation of lift, different strategies have been developed. The one chosen here is based mostly on a heuristic approach to design prototypes with simple wing geometries and a single actuator to generate lift and control the prototype attitude. Very few advanced prototypes with geometric characteristics and masses close to those of an insect exist for more realistic studies [START_REF] Wood | Microrobot Design Using Fiber Reinforced Composites[END_REF][START_REF] Dargent | Micromachining of an SU-8 flapping-wing flying micro-electro-mechanical system[END_REF][START_REF] Groen | Improving flight performance of the flapping wing MAV DelFly II International Micro Air Vehicle conference and competitions[END_REF][START_REF] Park | Development of bio-mimetic composite wing structures and experimental study on flapping characteristics Robot[END_REF][START_REF] Lee | MEMS wing technology for a batterypowered ornithopter Micro Electro[END_REF]. This might be due to the fact that traditional robotic mechanisms and macro-scale manufacturing methods can be extremely inefficient on an insect scale due to undesirable surface effects such as adhesion, friction and wear [START_REF] Wood | Microrobot Design Using Fiber Reinforced Composites[END_REF]. To overcome this problem, different solutions using MEMS manufacturing processes have been investigated in recent years [START_REF] Dargent | Micromachining of an SU-8 flapping-wing flying micro-electro-mechanical system[END_REF][START_REF] Bontemps | Design and performance of an insect-inspired nano air vehicle Smart[END_REF][START_REF] Tai | Titanium-alloy MEMS wing technology for a micro aerial vehicle application Sensors[END_REF]. For the construction of an insect-inspired Flapping-Wing Nano Air Vehicle (FWNAV), one priority is to obtain large wing displacements with kinematics similar to those of insects. Another one is to maximize the power-to-weight ratio of the prototype, which requires optimizing the power transmission from the battery to the wings. Therefore, the actuator, as well as the structure, has to be carefully designed to satisfy this compromise. To reach a satisfying structure both priorities have been yet explored. The first one dealing with the design of structure and wings is detailed in a previous paper, demonstrating prototypes able to generate a mean lift force up to 75 % of their weights as measured by an in-house force sensor [START_REF] Bontemps | Design and performance of an insect-inspired nano air vehicle Smart[END_REF]. The second one presented in this paper is focused on the energetic transmission within the prototype. This study proposes a model of the power transmission in order to evaluate and recognize hypothetical weaknesses. This efficiency analysis is also of great interest in an energetic outlook and especially for autonomy problematic. Moreover, this model of actuation and transmission consists in a first step towards a global model of the prototype. Since, the studied system combines both the mechanical and electromagnetic fields, a Bond Graph of the system has been set up to obtain a model in a unique formalism. Indeed, this kind of modeling is widely used for multiphysics systems. The first part of the paper is dedicated to an overview of the prototype and its actuation principle. Second, the global model and its compounds are widely detailed. The different parameters of both mechanical and electromagnetic submodels are then established thanks to different measurements and analytical studies. Finally, the global model is validated with experimental comparison and the efficiency is determined and discussed.

II. PRINCIPLE

The prototype (figure 1) is primarily composed of a tergum and a pair of wings connected together through compliant links. A central electromagnetic actuator mimicking dorso-ventral muscles of insects is completing the system to initiate and sustain a vibration in the tergum. The transmission of this vibration to the wings needs to be as straightforward as possible, mainly to maximize the system efficiency; therefore, the transmission part is a crucial element of our design. Different solutions have been experimented [15] and the best tradeoff between performance and conception has been found with compliant links [15]. This kind of architecture is realized in SU-8 EPOXY ® , which is a photosensitive resin commonly used in MEMS technologies to design micro-mirrors amongst others systems with impressive results [20], [21].Moreover, this material has interesting mechanical properties which are similar to those of insect's wing [START_REF] Bao | Design and fabrication of insect-inspired composite wings for MAV application using MEMS technology[END_REF]. Besides the enhanced transmission, the actuation has to be optimized in order to maximize the vibration amplitude of the tergum and thus increase the flapping angle and ultimately the lift generated by the wings. The electromagnetic actuator is constituted of a magnet stuck to the tergum, which is slipped into a fixed copper coil glued to the thorax, as presented in figure 2. This architecture is easy to manufacture, what is a real advantage at this scale. A cylindrical neodymium-iron-boron magnet (Ni-N48 HKCM®) has been selected, with a thickness of 500 µm and a diameter of 1.5 mm corresponding to a magnet mass of 6.25 mg. The internal magnetic flux provided by the manufacturer is 1.4 T. The coil is made in-house using a 40-µm radiusrcopper covered with a layer of varnish. The coil diameter R is fixed at 2 mm, leaving a 250-µm gap between the coil and the magnet in order to avoid any friction. The electromagnetic force is generated by an interaction between the current travelling the coil and the remanent magnetic field of the magnet that could be expressed by the equation 1. where i a is the current inside the coil flowing along e θ , and B the magnetic flux density passing through the coil. Only the vertical component of the force is here constructive, indeed the magnet and the coil are supposed to be perfectly concentric and cylindrical. In this case, the integral of the radial component of the force on the coil is null, and the vertical component of the force is generated exclusively by the interaction between B r (the radial component of the magnetic flux density) and i a .

III. MODELING

As a first step towards a complete prototype model, this paper presents the actuator and transmission parts of the model, composed of two blocks (figure 3 (a)). First an electromagnetic system, shown on the figure 4, composed of the coil and the magnet modeling the transformation of the electric power P a (U a , i a ) into a mechanical power P m (F e , ) through interaction of both electric fields generated in the coil and remanent magnetic fields of the magnet. Second, a mechanical resonator, shown in the figure 5, constituted of the magnet, the tergum and the links. The mechanical resonator will dissipate or store power under different ways resulting in a mechanical power P u (F u , ) transmitted to the wings.

The system studied here is composed by the ensemble coil, magnet, tergum and links (figure 3 (b)). Although, this modeled system highlighted in the red frame in the figure 3 (a) does not take into account the wings or the battery, the battery is still present via a source S f of an electrical flux i a . The main goal of this analysis is to compare the input power P a injected in the coil with the mechanical one available to move the wings. For this purpose, the two blocks, i.e. the electromagnetic system and the mechanical resonator, are firstly studying separately before being coupled to form the global model. These relationships are expressed by these two equations:

{

In the other hand, the mechanical system composed of the magnet, the tergum and the links (MTL-system) is identified as a spring-mass system (figure 5 (a)). This resonator could be characterized by a C-element for its stiffness (1/k eq ), a Ielement for its mass (m eq ) and a R-element for its damping (R eq ) as represented on the figure 5 (b). Finally, a 1-junction is used to express the Newton's second law (equation 2): ̈ ̇ In order to characterize all parameters (R b, R eq , m eq k eq and k em (z)) of the both blocks different tools and method have been used and are presented in section B. 1. It has to be duly noted that the coil is only represented by a resistor as a more complete study realized in [15] proved that its inductive behavior can be neglected mainly due to the low frequency of the current i a . The electromagnetic coupling coefficient k em (z) depends of the coil radius R, the whorl number n and the mean radial compounds of the magnetic flux density crossing the whole coil B m (z). A finite elements simulation [START_REF] Bontemps | Design and performance of an insect-inspired nano air vehicle Smart[END_REF] has been used to establish this last parameter. For this purpose, B m (z) has been evaluated along z-axis at a radial distance d of 250 µm from the magnet. This value represents the technological minimum that could be reached considering the handmade assembly [START_REF] Bontemps | Design and performance of an insect-inspired nano air vehicle Smart[END_REF].

Then an 8-whorls coil made of a 60-µm radius wire is considered and the sliding average of the mean radial magnetic flux density, B m (z) is calculated on the bobine height (h bob , figure 2). The determination of these parameters allows evaluating the electromagnetic actuator system.

2) Mechanical resonator First, the equivalent mass m eq of the system is determined through experimental method. Thus the different component of the MTL-system are weighted on a high-precision scale (Mettler Toledo XP-26), able to measure 1 µg. 13 samples have been weighted and the equivalent masses obtained are between 5.97 and 6.85 mg. This mass mostly corresponds to the magnet that is around 6 mg. Second, a modal analysis has been run in order to determine the first resonant frequency of the MTL-system. Indeed, considering the equation 3, the knowledge of m eq and f 1 enables to figure out the equivalent stiffness of the system, k eq .

√

To realize this modal analysis, a finite element simulation has been set up with each link clamped at its thorax side, as presented on the figure 6. Moreover, a parametric analysis has been developed by changing, in one hand the beam thickness, which plays a major role in beam stiffness according to equation 4, and in the other hand the SU-8 Young's modulus. Indeed, thanks to different studies it is known that this modulus could vary roughly between 3.5 to 5.5 GPa. Thanks to these simulations and considering m eq variations, the equivalent stiffness lies between 17 N.m -1 and 37.8 N.m -1 . In order to confirm these simulation results, an experimental bench composed of a Femtotools ® force sensor and a micrometric displacement pad has been set up (figure 7). The force sensor is fixed to the pad and displaced by 10-µm steps; at each step, while the reaction force exerted by the MTLsystem on the sensor is measured. Considering Hooke's law (equation 5), the knowledge of F r allows to determine experimentally the equivalent stiffness k eq of the system.

For a global displacement of 90 µm in both directions, data interpolation exhibits an equivalent stiffness of 18.7 N.m -1 in one direction and 19.6 N.m -1 in the other direction. Hence, these experimental results confirm the analytical value previously obtained with finite element analysis. The last parameter, which needs to be evaluated, is the equivalent damping R eq . This parameter overlays numerous damping mechanisms (thermoelastic, viscoelastic, aerodynamic, clamping, etc.) that are very difficult to evaluate analytically. Consequently, another test bench has been set up in order to experimentally evaluating this parameter. First, the MTL-system is excited to its first resonant frequency f 1 . Second, when the resonator has reached a stable state, the excitation is stopped and the transient deceleration of the resonator is monitoring thanks to a Keyence LK G-32 displacement sensor. The envelop curves could be expressed as an exponential decrease where ξ could be determined with the equivalent parameters R eq , k eq and m eq : √ With the mean values of k eq and m eq previously determined, 19.1 N.m -1 , 6.29 mg respectively, the equivalent damping obtained is between 0.00045 and 0.001. These results are also summarized in the table 2 for clarity sake. To form the complete Bond Graph model of our prototype, each sub-model, the electromagnetic system of the figure 4 (b) and the mechanical resonator of the figure 5 (b), just has to be coupled together, here via a serial connection.

IV. SIMULATION & EXPERIMENTAL VALIDATION

Even if the complete Bond Graph model up and running, its validation, among other things, with experimental data is primordial to evaluate the soundness of the above determined parameters before rushing in further investigations such as the power efficiency. To check the model ability, the resonator response is simulated for sinusoidal current input of different values (i a ) and frequencies (f). The magnet displacement z obtained with the simulation exhibits the typical response of a mechanical resonator. It should be noted that the resonant frequency of 267 Hz is independent of the displacement amplitude (figure 8) highlighting the absence of any non-linearity in the system. To measure experimentally and compare magnet displacement with simulations results an experimental bench has been set up. The thorax of the prototype is fixed and the actuator is powered by an external source while the fundamental resonant frequency of the wings is manually adjusted and the magnet displacement tracked. In order to preserve the same load between the simulation and the experimentation, the wings of the prototype are cut as near as possible from the links. As presented on the figure 9, first tests highlight a very good correlation between experimental results and simulations. Nevertheless, for large magnet displacement, an increase of the resonant frequency due to geometric non-linearities is appearing. The Duffing equation [START_REF] Duffing | Erzwungene Schwingungen bei veranderlicher eigenfrequenz[END_REF] proposes to model these non-linearities by the addition of a non-linear stiffness k nl . In this case the equation 2 becomes: ̈ ̇

Through a heuristic approach, a value of 126 . 10 6 N.m -3 has been chosen for k nl . As demonstrated on the figure 10, a satisfying correlation in frequency shift as well as in the response amplitude is observed which validates the complete Bond Graph model. In order to evaluate the actuator efficiency, the power available for the wings corresponding to the one stored under kinematics P I (F I , ) and potential energy P C (F C , ) in the mechanical resonator need to be evaluated. Considering the results obtained above, the complete Bond Graph model has been used to evaluate the efficiency of the MTL-system.

Its efficiency η t can be defined as the ratio between the input power P a and the power transmitted to the wings P u . In our case, i.e. without wing model, this power corresponds to the sum of P I (F I , ) and P C (F C , ).

It could also been expressed as the product of the electromagnetic sub-model efficiency η e and mechanical submodel η m . This indicator is evaluated with the Bond Graph model presented in precedent sections with 20-SIM® software. The results obtained exhibit an overall efficiency of 1.4 %. Indeed, for an electrical input power P a of 288 µW, corresponding to a current (rms) of 60 mA and a voltage (rms) of 4.8 mV, the mechanical output power available to actuate wings P u is 4.6 µW. To refine this analysis, η e , η m are examined separately.

In one hand, the figure 11(a) brings to light that the power dissipated through Joule effect in the coil represents 98 % of whole losses. In the other hand, mechanical damping in the resonator dissipates only 27 % of the whole losses as it could be seen in the figure 11(b). This analysis leads to the conclusion that main energetics losses come from electromagnetic actuator and more precisely from the coil. In order to increase the actuator efficiency two ways might be followed, first reduce the current into the coil and second decrease the coil resistance. The counterpart of such measure is that the radial compound of the magnetic flux density needs to be increased at the coil neighborhood to maintain the electromagnetic force generated F e . This paper proposes a Bond Graph model of a FWNAV actuator composed of a linear electromagnetic actuator and a mechanical resonator which has been experimentally validated and used to evaluate actuator's efficiency. This energetic evaluation indicates that the electromagnetic actuator and more precisely the interaction between coils current and magnet remanent magnet flux density needs to be improved. The main way to improve this interaction is in the coil, indeed different material might replace the cupper, its position could also been optimized. A more complete model integrating wings will be available in the near future allowing a global evaluation of a FWNAV efficiency.

Figure 1 :

 1 Figure 1: General presentation of the prototype architecture

Figure 2 :

 2 Figure 2: Diagram of the electromagnetic actuator with the different parameters and a view of the field lines

Figure 3 :

 3 Figure 3: (a) Bond Graph representation of the whole system, the red frame corresponding to the modeled system. (b) Schematic view of the modeledsystem composed of coil, magnet, tergum and links A. Bond Graph model In one hand, the electromagnetic part is modeled with three elements as it is presented in the figure 4 through an electrical equivalent circuit and a Bond Graph model: a R-element representing the coil resistor (R b ), and a variable gyrator (MGY) with a parameter k em (z) symbolizing the transformation of electrical power into mechanical one [17]. This last element expresses the relation between the current in the coil i a and the mechanical force generated F e . The radial compounds of the magnetic flux density crossing each whorl of the coil is considered as equal to the mean radial compounds of the magnetic flux density crossing the whole coil B m (z), which still depends of the magnet vertical position z. R and n represent the coil diameter and its whorl number, respectively. To connect these both elements a 1-junction is used to indicate that the current generator, the resistor and the gyrator are serially connected.

Figure 4 :

 4 Figure 4: (a) Representation of the electromagnetic system (a) through an electrical equivalent circuit, (b) through Bond Graph formalism

Figure 5 :

 5 Figure 5: (a) Representation of the mechanical resonator (a) through a springmass representation, (b) through Bond Graph formalism B. Parameter estimation 1) Electromagnetic system To obtain the coil resistance R b analytical calculi has been compared to experimental measurements; results obtained are summarized in the table1. It has to be duly noted that the coil is only represented by a resistor as a more complete study realized in[15] proved that its inductive behavior can be neglected mainly due to the low frequency of the current i a .

Figure 6 :

 6 Figure 6: Modal analysis through the finite element method figuring the MTLsystem

Figure 7 :

 7 Figure 7: Experimental set-up used to evaluate the stiffness of the MTLsystem

Figure 8 :

 8 Figure 8: MTL-system mechanical response symbolized by the displacement of the magnet z for different sinusoidal excitations of amplitude ia and a frequency f.

Figure 9 :

 9 Figure 9: Comparison of MTL-system response in simulation (lines) and in experimental (dots) results for small magnet displacement (less than 200 µm)

Figure 10 :

 10 Figure 10: Comparison of MTL-system response between experimental results (green dots), linear simulation (blue line) and non-linear simulation (red line) V. EFFICIENCY EVALUATION

Figure 11 :

 11 Figure 11: Presentation of simulation results: (a) Efficiency characterization of electromagnetic sub-model, input power (blue line) and power dissipated through Joule effect (red line). (b) Efficiency of mechanical sub-model, input power (blue line), power dissipated (red line) and output mechanical power (green line) VI. CONCLUSION & PERSPECTIVES

Table 1 :

 1 Comparison of 8-whorls coil resistance different wire diameters

	Wire
	diameter
	[µm]

Resistance value [mΩ]

		Theoretical values	Measured values
	25	435	[425-577]
	40	170	[175-182]
	60	75	[65-93]

Table 2 :

 2 Recap of the theoretical, measured and used values in the Bond Graph model for the mechanical parameters

		Theoretical values	Measured values	Used value
	keq[N.m -1 ]	[17;37.8]	[18.7;19.6]	19.1
	meq [mg]	[6.16;7.04]	[5.97;6.85]	6.78
	Req		[0.00045;0.001]	0.00085

ACKNOWLEDGMENT

This research was financially supported by the Agence Nationale de la Recherche (ANR-09-BLAN-0110), and the Fondation d'Entreprise EADS.


H 2 O + H + + 2e → H 2 + OH - M 3+ + 3OH -→ M(OH) 3 avec M = Am,

  TRACES D'EMETTEURS ALPHA DANS LES RESEAUX PUBLICS Jacques de Sanoit, Michal Pomorski et Philippe Bergonzo Laboratoire Capteurs Diamant, CEA-Saclay, 91191, Gif sur Yvette Objectifs Surveillance des actinides à l'état de traces dans l'eau potable Détection et identification des émetteurs alpha Gain de temps car pas de préparation de sources en laboratoire Faible limite de détection (< 1Bq/L) Décontamination rapide du capteur et réutilisation immédiate Un concept original Détecteur alpha immergé électrochimiquement assisté Fenêtre d'entrée du détecteur alpha en matériau diamant dopé au bore (B-NCD) Matériau B-NCD fonctionnant en mode cathodique Dépôt d'hydroxydes d'actinides sous courant d'électrolyse (électroprécipitation)

  Pu, Cm, Np ... Mesure spectrométrique aprés dépôt Décontamination du détecteur par voie électrochimique Schéma de principe du dispositif incluant l'électronique associée J. de Sanoit, M. Pomorski et C. Mer, Brevet Francais n o 1058150 du 7 octobre 2010 Electroprécipitation Montage expérimental utilisé pour l'électroprécipitation des ions des actinides (gauche) schéma (droit) photo avec un détecteur de type BNCD/Si-PIN électrochimiquement assisté avec un effluent réel (CEA-DAM, Valduc) contenant de faibles quantités de 239 Pu et de 244 Cm Résultats : Mode comptage avec Am-241 Spectres α obtenus avec un détecteur de type BNCD/Si électrochimiquement assisté avec des solutions étalons d' 241 Am. Conditions : Volume de l'électrolyte 40 ml ; pH 4.5, J c = 6 mA/cm 2 ; agitation 10 3 rot. min -1 Variation du taux de comptage (s -1 ) en fonction de la quantité présente d' 241 Am dans l'électrolyte. (Données extraites de la figure ci-dessus) Résultats : Influence d'un interférent hydrolysable : le fer

  Comparaison des spectres α du 239 Pu et du 244 Cm obtenus avec un détecteur de type BNCD/Si-PIN électrochimiquement assisté en l'absence et en présence de fer à la concentration de 8 • 10 -5 M

	Résultats : Rendements de dépôt et de decontamination
	241 Am en solution	Taux de comptage	Rendement	Taux de comptage	Rendement de
	(Bq)	avant	d'électropré	après	décontamination
		décontamination	cipition (%)	décontamination	(%)
		(s -1 )		(s -1 )
	0.59	0.059	20.0	2.76 • 10 -4	99.53
	1.18	0.073	12.4	6.49 • 10 -4	99.11
	2.87	0.199	13.9	2.63 • 10 -4	99.86
	5.74	0.389	13.6	3.60 • 10 -4	99.90
	14.15	0.821	11.6	8.41 • 10 -4	99.90
	Conclusions et Perspectives
	Le principe de fonctionnement d'un détecteur de rayonnement
	électro-chimiquement assisté permettant la spectrométrie des émetteurs
	alpha en solution est expérimentalement démontrée
	La décontamination électrochimique du détecteur avant sa réutilisation

immédiate est une procédure rapide et efficace L'optimisation des conditions de dépôt des actinides sur la fenêtre d'entrée du détecteur sera étudiée dans le cadre du projet CSOSG franco-allemand Le système développé dans le cadre d'ActiFind sera potentiellemnt industrialisable sous la forme d'un système portable de terrain permettant d'obtenir des données d'identification des émetteurs alpha dans les situations d'urgence.

llCreated with L A T E Xbeamerposter l'ANR finance ACTIFIND dans le cadre de l'appel CSOSG 2011 contact: jacques.desanoit@cea.fr, michal.pomorski@cea.fr