Larry Bliven

Valérie Billat

Piotr Sobieski

A Guissard

Hubert Branger

Jean-Paul Giovanangeli

Communiqué on veering wind effects on scatterometry from the sea-surface

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


H Branger

L Bliven

A Ramamonjiarisoa

A LABORATORY INVESTIGATION ON ELECTROMAGNETIC BIAS IN SEA LEVEL MEASUREMENTS BY MICROWAVE ALTIMETERS

Keywords:

To contribute to a better understanding of the Electromagnetic Bias in radar altimetry, a serie of ex]periments was conducted in the I.M.S.T. large wind wave facility using a focused beam radar set at 13.5 GHz frequency. For pure wind wave fields we found the bias to be a quadratic function of each of the commonly used prurameters, namely the significant wave height, the wind speed, the water elevation skewness and significant sl!}pe. The bias divided by the significant waveheight is a linear function of these parameters. The coefficients in bias representation as a function of either the significant waveheight or the wind speed are significantly different from values obtained in field 1<xperiments. This led us to conclude that none of the latter parameters can be taken solely to account for all observed bias variations. Instead, dimensionless parameters such as the wave skewness or a dimensionless waveheight are shown to be more appropriate. They include more or less explicitely the state of development of the wind wave field of interest.

INTRODUCTION

A radar altimeter determines its range by measuring the round-trip time of a pulse of electromagnetic waves to the sea-surface. The mean reflecting surface differs in efovation from the the mean sea level. The difference, called the Electromagnetic (E.M.) Bias, is probably the lar gest remaining source of error for which no fully sa1isfactory algorithm is yet established for correc tions. E.M. Bias, which obviously depends on the hydrodynamic electromagnetic properties of the sea surface, is commonly considered as a fixed percentage of the significant wave height (SWH). Such iut approximation is not precise enough to achieve the range accuracy of a few centimeters required for the next spacebome altimeter TOPEX POSEIDON mission. Modulations of the ocean wave• field by non linear wave-wave interactions, currents or residual swell would probably lead to E.M. Bias modulations that should• be considered to improve the accuracy of the prediction.

Wind-wave research tank laboratory experiments enable systematic exploration of the influence of geophysical parameters on physical processes under accurately controlled and repetable conditions. Our purpose w�•s to make simultaneous and collocated high spatial resolution measurements of both sea surface elevation and nadir backscattered power in the large I.M.S.T. wind-wave research tank (40mx3mxlm -figure 1-a) under numerous well controlled environmental conditions. A focused beam radar set at 13.5 GHz frequency was mounted above the tank. The 3 cm spot size allowed us to visualize the sea wave trough/crest asymetry of the backscattered response and moreover to compute the "radar seen" sea surface wave height distribution.

Our main objectives were: a) to compare the radar seen wave height distribution with the actual wave height distribution, the E.M. Bias beeing the difference between the means of the two distributions.

b) to relate the computed E.M. Bias values with standard geophysical parameters characterizing the wave field, such as the significant wave height, the wind speed, the wave height skewness and the significant slope. c) to compare the wind-wave tank E.M. Bias values with open field measurements in order to give some clues for the prediction of all the observed Bias variations.

The experimental arr angement is described in section 2. Data processing procedures are detailed in section 3. Main results are shown in section 4 and discussed in section 5.

EXPERIMENT AL ARRANGEMENT

The operating frequency was 13.5GHz, one of the future TOPEX mission operating frequency. We used a focused beam radar set in a bistatic configuration (figure 1-b). The transmit and n;ceive horns were located at the same but opposite 10• off nadir angle. The bistatic configuration is equivalent to a nadir monostatic configuration because, in both cases the scattering facets are the zero slope facets of the sea waves. Before hitting the sea surface, the microwaves were focused by a 30" diameter dielectric lens. The spot size was found to be 3 cm at the one meter focal lenght. The dielectric lens which had been first designed by Parsons and Miller [1) for the NASNGSFC Wallops Flight Facility, was kindly lent to I.M.S.T. The radar system we used was derived from the scatterometer designed by Bliven et al [2]. Absorbing material at appropriate locations reduced multipath reflection. The signal to noise ratio was found to be excellent, namely 60dB.

The mean reflected power from water surface at rest at a level h, namely P .Pl,l(h), was determined _as follows: starting with the tank tull of water, we drained it slowly while acquiring on a computer the-water level h delivered by a capacitance probe, and the radar backscattered power

-�-� �\ \ I \ I \ I \\ \ (b) ---- - P ca1(h).
In order to prevent the tank water height level dependence on the backscattered power, we defined a Reflectivity coefficient r(t) as : r(t) = P(t) IP ca1(h(t)) P(t) and h(t) beeing respectively the backscattered power and the water elevation at instant t. r(t) ranged from 0 to 1 , the maximum value corresponding to a flat horiwntal sea surface all over the illuminated spot.

The water surface elevation and slopes were measured using 3 capacitance probes with 5mm separation in an L. configuration located within the radar spot. The probes delivered a range measurement with a ± 0.2mm precision. Test runs made with and without the wave gauges, showed that the reflectivity coefficients were decreased by less than 1 % when the probes were present within the radar spot. The mean wind speed was measured with a Pitot tube with a precision of a few cm/s. Measurements, made at 28m, were free from reflection from the wave absorber. The elevation h(t) was determined from a single probe. The sea wave along-wind and cross-wind slopes were obtained by differenciating the elevation readings from two adjacent probes and dividing by the 5 mm spatial separation.

W e combined the lOdB Gain radar signal and the 20dB Gain one to perform a double decade high precision backscattered signal P(t). The reflectivity coefficient r(t) was computed, as previously defined, using P(t), h(t), and the calibrated Look-up table P ca1(h). In order to compute the E. M. Bias, we performed a "radar seen sea surface distribution" ( [l]) : the elevation measurements were sorted into a fixed number of elevation bins. If "i" is the index of the elevation bin, Ni the number of observations sorted in that bin, r i j the reflexion coefficient -0f sample i sorted in bin j, then :

Jm

-the "actual elevation pdf value" of bin number "i" is equal to the ratio of the number of samples that belong to this bin to the total number of data samples:

(1) -the "radar seen elevation pdf value" of bin number "i" is set by normalizing the sum of the reflected power of all the samples that belong to this bin by the total amount of reflected power:

(2)

The E. M. Bias, was directly derived from expressions (1) and ( 2

IL USTRATIVE RESULTS

A set of 93 experiments under well controlled conditions have been conducted (wind speed from 0 to 15m/s, paddle wave generator from l . lHz to 2. lHz, and combinations of both wind waves and paddle waves). The Wav@ propagation

• : f •O m /< I U= t.7m/s ••-� Wavo U=2.7m/s �-� Wav• U= ,,0 m/s • -• � Wav@ ••••• � WavP U= tt.Om/s F' igures 2:
(a) samples of time vanat10ns of the water deflection surface level and the reflected radar signal at various wind speed.

short presentation which follows will concern only the cases of pure wind waves. A subsequent article [START_REF] Branger | An investigation on electromagnetic bias in radar altimetry[END_REF] will re:port on more detailed results from the complete set of experiments.

Figure 2(a) displays typical samples of the time variations of the water deflection level and the corresponding radar reflected signal. With the water surface at rest (U=Om/s) no parasitical reflection is observed. At U=l.7m/s, the radar appears to be sensitive to small . water surface • oscillations of few centimeters wavelengths. The fact of interest with regard to the electromagnetic bias is seen at U=2.7m/s and U=4m/s, namely, the reflection is much larger over the wave trough than over the wave crest. Then, the radar signal oscillates at the frequency of the dominant wave. For wind speed higher than about 8m/s, a large enhancement of the reflected signal is observed in front of breaking crests. These results confirm previous observations by Lifermann [START_REF] Lifermann | [END_REF] under similar environmental conditions whitch related the signal enhancement above the particular geometry of the breaking crests as identified by Bonmarin [START_REF] Bonmarin | Geometric properties of deep-water breaking waves[END_REF]. The variations above will be discussed in detail in [START_REF] Branger | An investigation on electromagnetic bias in radar altimetry[END_REF]. The discussions will take benefit of theoretical or semi empirical relationships established within the field of wind waves development ( [START_REF] Sverdrup | Wind, Sea and Swell[END_REF], [START_REF] Deardorff | Aerodynamic theory of wave growth with constant wave steepness[END_REF], [START_REF] Hasselmann | Measurements of wind wave growth and swell decay during JONSW AP[END_REF]). [START_REF] Melville | Measurements of E.M. Bias in Radar Altimetry[END_REF]. Clearly neither U nor SWH can be taken as a single parameter to account for all observed bias variations. A dimensionless variable characterizing the state of development of the wind wave fields need clearly to be introduced. At least the influence of the fetch have to be considered explicitly or implicitly. The respective bias from laboratory and fields observations would correspond to different ranges of appropriate parameters. This is preliminarly illustrated by figures 5 and 6 which report on our laboratory results together with some values from fields observations ( [START_REF] Melville | Measurements of E.M. Bias in Radar Altimetry[END_REF], [START_REF] Choy | Bias of 10 GHz radar altimeter measurements of M.S.L[END_REF], [START_REF] Melville | Measurements of E.M. Bias at Ku and C bands[END_REF]). The parameters are respectively the wave height skewness A.t and the adimensionless significant height, g*SWH/U , introduced by Rodriguez [START_REF] Rodriguez | Ocean Skewness and the Skewness Bias in Altimetry: a Geosat study[END_REF], related with the dimensionless fetch, g*XJU2.

Within extended ranges of parameters values, the continuous variations of the bias is quite striking. This would be of crucial interest to determine the bias evolutions with much higher accuracy. Detailed investigation in that matter is under way. • Laboratory;� Melville et al [START_REF] Melville | Measurements of E.M. Bias in Radar Altimetry[END_REF]; x Melville et al [START_REF] Melville | Measurements of E.M. Bias at Ku and C bands[END_REF]; OChoy et al [START_REF] Choy | Bias of 10 GHz radar altimeter measurements of M.S.L[END_REF]; -average curve estimated from these data

  3. DATA PROCESSINGBefore beeing digitized at 300 Hz on the l.M.S.T. HP-1000 computer, the two analog lOclB and 20dB Gain Radar output and the three wave gauges analog signals were low-pass filtered with a cutoff frequency of 100 Hz to avoid aliasing effects. For each experiment run, 30000 0 samples per line were recorded, representing a time span per test of 16 min 40 s.

Figures 1 :

 1 Figures 1: (a) Schematic view of the I.M.S.T. large wind-wave facility l :Fan 2:Electrohydraulic wavemaker 3:Radar Device (b) View in the vertical plan of the measuring equipment l :Radar Transmitter 2:Dielectric lens 3:Radar Receiver 4:Capacitance wire gauges 5:Pitot tube

  ) by differentiating the mean values of the two distributions: E.M. Bias = }:: h i *(pdfRadar(i)-pdf Height (i)) (3) I The standard deviation: cr , the skewness : A3 and the kurtosis : K4, of the surface elevation distribution and of the radar distribution were also estimated. Moreover, we computed for each experiment the significant wave height (SWH = 4 * cr ), the dominant frequency n0 of the energy containing the waves (from FFT analysis), the dominant wavelenght 10 of the energy containing the waves (from the linear dispersion relat i onship for deep water gravity waves), and the significant slope ( § = SWH I 4 * 10 ).

3 (

 3 b) probability density functions of waveheight (-) and "radar seen waveheight" (--). Wind speed respectively: 1.7; 3.1; 4.1; 5.5; 6.6; 7.7; 8.9; 10.2; 11.6; 14.1 m/s, from the bottom to the top of the figure. ((••• .. ••)Gaussian distribution).

Figure 2 (

 2 b) shows the probability density functions (p.d.f) of the actual waveheight and the radar seen waveheight as defined in section 3 with increasing wind speed. Two facts are obviously of main interest : a) both distributions exhibit larger and larger asymetry b) the distributions depart more and more each other, the radar p.d.f being more asymetrical than the wav(fheight p.d.f. Detailed investigation on the p.d.f will be found in[START_REF] Branger | An investigation on electromagnetic bias in radar altimetry[END_REF].

Figure 3

 3 Figure 3 shows the absolute bias as defined by expression (3) as a function of U,SWH,A.3 and §. They are commonly used parameters in analysing the electromagnetic bias. The correlation of the E.M. Bias with each of these parameters yields :

5 .

 5 PRELIMINARY DISCUSSIONS While the bias from fields observations remains generally smaller than about 5% of SWH, laboratory measurements yield significantly larger values. In addition, these values evolue rapidly with respect to U, SWH, etc ... If we want to predict the E.M. Bias with the algorithm: "EM.B.(%SWH) =-a -b*U", b should be of order 0.8 in the tank and of order 0.2 in open field

  Acknowledgments: the authors are particularly grateful .to Dr C. Parsons who generously lent them the dielectric lens. We especially thank B. Zucchini for his diligent laboratory work. This work was supported by C.N.E.S. (Centre National d'Etudes Spatiales), contract N'90/8002/854, by O.N.R. contract N'l 46n0/03, and by N.A.S.A. contract N'l 61/80/23.

Figure 3 :

 3 Figure 3: The absolute E.M. Bias (cm) as a function of wind speed ( 8 ), significant wave height ( e ), waveheight skewness ( O) and significant slope ( o ).

Figure 4 :

 4 Figure 4: as in figure 3 except E.M. Bias(%SWH) replaces E.M. Bias(cm).

Figure 5 :Figure 6 :

 56 Figure 5: The relative E.M. Bias(%SWH) as a function of waveheight skewness: 0 Laboratory; A field (Choy et al [12]);---JACKSON's theoretical law ([6])


domain: spi chim phys

text:
Laurence Ourry

Damien Le Roy

Samir Mekkaoui

Thierry Douillard

Anne-Laure Deman

Vincent Salles
email: vincent.salles@univ-lyon1.fr

Damien Le Roy

Magnetic filaments for anisotropic composite polymers

Keywords: nanofilaments, magnetic anisotropy, electrospinning, polymer composite

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Magnetic composite polymers are part of new multifunctional materials that aroused considerable interest over the past two decades. The nature, size, concentration of the magnetic particles added in the polymer matrix modify the magnetic behaviors of the composite [START_REF] Thévenot | Magnetic responsive polymer composite materials[END_REF]. Magnetic multifunctional materials address numerous applications such as microelectromechanical systems (MEMS) for sensors and actuators [START_REF] Pirmoradi | A magnetically controlled MEMS device for drug delivery: Design, fabrication, and testing[END_REF][START_REF] Nikkhah | Engineering microscale topographies to control the cell-substrate interface[END_REF][START_REF] Digabel | Magnetic micropillars as a tool to govern substrate deformations[END_REF][START_REF] Erb | Actuating Soft Matter with Magnetic Torque[END_REF] controlled drug delivery based on thermoresponsive materials or magnetic guidance [START_REF] Thévenot | Magnetic responsive polymer composite materials[END_REF], bioinspired microstructures [START_REF] Erb | Self-shaping composites with programmable bioinspired microstructures[END_REF][START_REF] Alfadhel | A magnetic nanocomposite for biomimetic flow sensing[END_REF], microfluidics functions such as micro-object trapping [START_REF] Faivre | Magnetophoretic manipulation in microsystem using carbonyl iron-polydimethylsiloxane microstructures[END_REF] [START_REF] Yu | Control of magnetic field distribution by using nickel powder@PDMS pillars in microchannels[END_REF] or fluidics components [START_REF] Li | Design and fabrication of microfluidic mixer from carbonyl iron-PDMS composite membrane[END_REF] [START_REF] Kim | Hydrodynamic focusing micropump module with PDMS/nickel-particle composite diaphragms for microfluidic systems[END_REF].

Fine control of the magnetic properties is required to optimize their implementation.

In particular, the development of composite materials with anisotropic magnetic properties opens up many perspectives. This magnetic anisotropy can be achieved through the creation of chains of magnetic particles or the use of magnetic nano-or micro-filaments. This first approach is versatile and easy to implement, through the application of a magnetic pattern during the composite fabrication, and permits to enhance the magnetic response in the direction of the chain [START_REF] Fragouli | Dynamical formation of spatially localized arrays of aligned nanowires in plastic films with magnetic anisotropy[END_REF][START_REF] Tokarev | Nanostructured Soft Matter with Magnetic Nanoparticles[END_REF][START_REF] Ghosh | Soft polymer magnetic nanocomposites: Microstructure patterning by magnetophoretic transport and self-assembly[END_REF]. S. Marchi et al. reported that the deflection of a composite polymeric membrane is increased when particles are aligned in the matrix and the magnetic field is applied along the chains, compared to disordered composite [START_REF] Marchi | Highly Magneto-Responsive Elastomeric Films Created by a Two-Step Fabrication Process[END_REF]. In the field of microfluidics, the increased magnetic susceptibility along the chains of particles, amplify generated magnetophoretic forces [START_REF] Mekkaoui | Anisotropic composite polymer for high magnetic force in microfluidic systems[END_REF]. Besides, magnetic composite at relatively low concentration (up to 10 wt%), can form arrays of isolated and well-defined chains of magnetic particles homogeneously distributed within the polymer matrix. These structures were found to act as efficient magnetic flux micro-concentrators and were used as micro-traps in microdevices [START_REF] Mekkaoui | Arrays of high aspect ratio magnetic microstructures for large trapping throughput in lab-on-chip systems[END_REF], notably in the scope of single cell or single bead analysis systems [START_REF] Hosic | Microfluidic Sample Preparation for Single Cell Analysis[END_REF] [START_REF] Narayanamurthy | Microfluidic hydrodynamic trapping for single cell analysis: Mechanisms, methods and applications[END_REF]. Indeed, magnetic micro-traps permitted to capture thousands of isolated beads [START_REF] Li | Design and fabrication of microfluidic mixer from carbonyl iron-PDMS composite membrane[END_REF].

However, if the results are promising, the chains of particles are relatively porous, and so the magnetic flux guides are discontinuous [START_REF] Roy | Anisotropic ferromagnetic polymer: A first step for their implementation in microfluidic systems[END_REF]. In this regard, continuous magnetic structures with high aspect ratio, such as nanofibers, would be highly beneficial. The synthesis of magnetic nanofilaments with strong saturation magnetization and good dispersion in polymer matrixremains a challenge.

Magnetic composite polymers based on magnetic fillers with a cylindrical shape are reported in the literature, [START_REF] Digabel | Magnetic micropillars as a tool to govern substrate deformations[END_REF][START_REF] Keshoju | Mechanical characterization of magnetic nanowirepolydimethylsiloxane composites[END_REF][START_REF] Vega | Tuning the magnetic anisotropy of Co-Ni nanowires: comparison between single nanowires and nanowire arrays in hard-anodic aluminum oxide membranes[END_REF] , with fillers obtained using a porous and sacrificial template. This fabrication process presents a low production rate and is suitable for only a few materials. Since the beginning of the 21 st century, numerous kinds of filaments have been produced using a unique and versatile process called "electrospinning" (ES). Briefly, a polymer solution is stretched under an electric field to produce solid filaments with a final diameter in the range of micrometer or nanometrer scale, with an adjustable production rate by sizing correctly the setup.

More than polymer filaments, inorganic wires can be produced if metallic salts or specific precursors are introduced in the raw polymer solution.

Particularly, the state of the art on ES shows that a lot of oxide filaments have been produced and studied in the last two decades. Some of those articles are about electrospun magnetic (nano)filaments, made of cobalt [START_REF] Rakhi | Substrate dependent selforganization of mesoporous cobalt oxide nanowires with remarkable pseudocapacitance[END_REF], nickel [START_REF] Kyoung | Production of beads like hollow nickel oxide nanoparticles using colloidal-gel electrospinning methodology[END_REF] or iron oxides [START_REF] Eid | Iron-based 1D nanostructures by electrospinning process[END_REF] [START_REF] Eid | Magnetic properties of hematite nanotubes elaborated by electrospinning process[END_REF], or even of mixed Co/Fe [START_REF] Ju | Fabrication and characterization of cobalt ferrite ( CoFe 2 O 4 ) nanofibers by electrospinning[END_REF] and Ni/Fe oxides [START_REF] Li | Magnetic nanofibers of nickel ferrite prepared by electrospinning[END_REF]. Moreover, one can notice a previous work of our group dealing with the synthesis of electrospun iron carbide filaments used as fillers in a Polyurethane matrix [START_REF] Fiorido | Bifunctional organic/inorganic nanocomposites for energy harvesting, actuation and magnetic sensing applications[END_REF]. To our knowledge, only one article is related to the fabrication of pure iron electrospun filaments [START_REF] Shao | Preparation of pure iron nanofibers via electrospinning[END_REF], but the authors did not study the magnetic properties of such nanomaterials.

The present study is part of the development of new multifunctional material, Fe magnetic nanofibers/PDMS (polydimethylsiloxane). PDMS matrix presents numerous advantages. This elastomer, widely used in microfluidics, is biocompatible, non-toxic, and easily micropatterned by soft-lithography. In addition, PDMS-based composites permit to solve issues linked to heterogeneous integration of magnetic materials with polymers.

We performed a complete study of structural and magnetic properties of electrospun fibers, with different chemical compositions and/or different metal oxidation degrees in view to select a PDMS filler combining a high magnetization at saturation and a good dispersion ability in the PDMS matrix. Taking into account this guideline, a final composite was prepared by filling a PDMS matrix with aligned Fe nanofibers in order to assess the interest of such composites for microfluidic devices.

Materials and methods

Magnetic filaments

All solutions of this study contained at least an iron salt, iron(III) nitrate nonahydrate (98% of purity, Sigma Aldrich), or iron(II) acetate (Sigma Aldrich), and an electrospinnable polymer which can be polyvinyl pyrrolidone (PVP, Mw ∼ 1 300 000 Da, Acros Organics) or polyvinyl alcohol (PVA, Mw ∼ 72 000 Da, Chang Chun Petrochemical Co.) (Table S1).

Fe solutions: The solution with iron salt solely contained 9 wt% of PVA in deionised water and 0.768 g of iron nitrate (mPVA/miron=1.5). 4.8 mL of acetic acid (a.a.) was then added to 5mL of the previous solution.

Fe-Co solution: in 7 mL of absolute ethanol, PVP was first dissolved (10 wt%) before adding 0.283 g of iron acetate and 0.236 g of cobalt nitrate (Sigma Aldrich) (nFe/nCo=2).

Then, 1.5 mL of a.a. and 0.7 mL of deionized water were finally added to the previous mixture.

Fe-Ni solution: 0.329 g of iron acetate was dissolved in 7 mL of a solution containing 7 wt% of PVP in absolute ethanol. Simultaneously, 0.275 g of nickel nitrate hexahydrate (Sigma Aldrich) was mixed with 0.5 mL of deionized water before blending the two solutions together. Finally, 1 mL of a.a. was poured to the solution.

All solutions were stirred overnight at room temperature before electrospinning experiments.

Electrospinning: After overnight stirring, transparent and homogeneous solutions containing metal salts and polymers were ready to be electrospun. The electrospinning setup was mainly composed of a syringe-pump to adjust the solution feeding rate (0.02-1 mL/h), a high voltage supplier (0-30 kV), and an aluminum foil as a sample collector (ground electrode) positioned at a few centimeters from the spinneret. The solution was loaded into a plastic syringe and then extruded through a stainless steel needle (inner diameter of 0.51 mm) connected to the high voltage supply. Filaments were produced during several hours in the air before being removed from the target and cut in different pieces hanged on a silica gibbet fixed onto a crucible, specially designed to improve the treatment's reproducibility.

Thermal treatment: Heat treatments in the air were performed in a muffle furnace.

Regarding Fe-based filaments, those made with PVP were pyrolysed 4h at 550°C (5°C/min) whereas those containing PVA were treated during 5h at 500°C (2°C/min).

For samples containing Fe and Co or Ni, a higher temperature of treatment was set: 2h at 800°C for Fe-Ni samples and 4h at 800°C for Fe-Co filaments, with a heating ramp of 3 °C.min -1 in both cases. Treatments with reducing atmosphere were carried out with a mixture of argon and hydrogen (Ar/H2, 90/10 or 95/5) in a tubular furnace (3°C.min -1 , 400°C, 1h), with a gas flow rate ranging from 0.4 to 0.7 L/min.

Composites with PDMS matrix

The best nanofiber candidate was used as filler to realize magnetic composite. The dispersion of synthesised nanofibers (0.23 wt%) into PDMS prepolymer (Sylgard from Samaro) was performed using an ultrasonic processor (Sonics Materials TM , 500W, tapered 3 mm diameter sonotrode). Sonication conditions were the following: 25% amplitude, 30 seconds cycles with a 33% duty cycle for 10 min. The bucket containing the mixture was positioned in a beaker filled with ice in order to limit the rise in temperature due to sonication. Then, the curing agent was thoroughly mixed with the mixture, with a ratio 10/1 w/w of monomer/curing agent. The composite membranes of circular and square shapes, 5 mm diameter and diagonal respectively, were obtained using molds realized with dry 50 µm thick photoresist (Ethertec ®). We poured the composite on the mold and removed the excess with a blade. The reticulation was performed in an oven at 70 °C for 3 hours. During reticulation, the first batch of composite membranes was submitted to a 130 mT uniform magnetic field, created in the gap of two permanent magnets, in order to align nanofibers. The second batch of the composite membranes was reticulated without the presence of a magnetic field.

Characterization techniques

The morphology of the electrospun filaments was characterized by scanning electron microscopy SEM (FEI, Quanta FEG 250) and by transmission electron microscopy TEM (JEOL, 2100F). For SEM observations, samples were fixed on aluminum holders covered with carbon tape before deposition of a gold-palladium coating (5 nm) by sputtering. For TEM samples, a small amount of fibers is dispersed in ethanol, and using the same ultrasound probe as the one above-mentioned for the composite preparation. Two drops of this solution are consecutively deposited onto a TEM grid (copper grid with a carbon membrane) before observation. Additional crystalline information was brought by X-ray diffraction (XRD) experiments (Philipps PW 3040/60 PANalytical X'Pert PRO (CuKα radiation; λ = 1.5406 Å at 40 kV and 30 mA). The average crystallite size was calculated with the Scherrer method. Moreover, the magnetic properties were investigated with a Quantum Design SQUID magnetometer to obtain the magnetization hysteresis loops at 310 K in a magnetic field of 40 kOe. For magnetization measurements, fibers were directly poured into a capsule, whereas composite films were placed on a silicon substrate.

Confocal observations were performed on composites, with a confocal microscope (Zeiss LSM 800), placing a composite slice between two glass slides. For 3D reconstruction, a series of 9 images were acquired, with a distance of 6 µm along the z axis between each image. Each image was an average of 2 images using the software (ZEN) function "averaging". Finer observations of composites were carried out using a FIB/SEM workstation (NVision 40; Carl Zeiss Microscopy GmbH, Oberkochen,

Germany) combining a SIINT zeta FIB column (Seiko Instruments Inc. NanoTechnology, Japan) with a Gemini I SEM column. The NVision 40 platform is also equipped with a multi-nozzle SIINT gas injection system. The angle between the FIB and SEM columns was 54°. FIB/SEM nano-tomography (FIB-nt) was performed following a precise protocol (see Supporting Information).

Results and discussion

Microstructural properties

Each material was prepared after the optimization of its electrospinning and thermal treatment parameters. Detailed conditions are presented in Table S1 (see Supporting Information). According to the kind of gas flowing into the furnace, iron, nickel and cobalt salts were either oxidized (under air) or reduced (under Ar/H2). Thermal treatment in air at 550°C of electrospun filaments made of PVA and iron nitrate leads to the crystallization of pure α-Fe2O3 (hematite) (Fig. 1). A fine analysis of the pattern excluded any presence of ɣ-Fe2O3 (maghemite). A subsequent treatment under reducing atmosphere (Ar/H2) allowed to deoxidize the material into Fe3O4, and even in pure iron (ferrite) when the amount of hydrogen was raised from 5 to 10%.

For filaments prepared with an iron amount twice that of Co or Ni, the resulting material had the same Fe/Ni ratio, leading to CoFe2O4 and NiFe2O4 phases, respectively. By deoxidizing NiFe2O4 at 600°C under Ar/H2 (95/5), another material was achieved (see Fig. S1 and Fig. S2). Three peaks on the XRD pattern of the corresponding sample, named "FeNi", were present. The peaks at 2 theta values of 43.6° and 50.8° correspond to the phase Fe0.64Ni0.36 (JCPDS sheet: 00-047-1405), with a perfect difference of relative intensity between the two peaks, as reported in the JCPDS sheet. The peak at 44.6° can be assigned to the presence of Fe0.94Ni0.06 (Kamacite, JCPDS sheet: 00-037-0474) and/or to pure Fe (Ferrite, JCPDS sheet: 00-006-0696). Moreover, taking first into account the relative intensities, we can assume that the amount of the Fe0.64Ni0.36 phase is in the majority. Then, since the pristine nFe/nNi ratio of the material equaled 2, we can guess that an excess of iron should denote the presence of pure iron, explaining the peak present at 44.6°. Considering the Fe-Cobased alloy, the peak located at 44.7° was assigned to the presence of metallic cobaltiron alloy (Co3Fe7) (Table S3). This compound could be assigned to a local lack of oxygen during the thermal treatment because of the presence of PVP chains, which are made of a large amount of carbon. In turn, Co3Fe7 is an appealing material as it is expected to exhibit a higher magnetization than pure Fe. According to the Slater-Pauling curve that describes the average atomic magnetic moments in binary alloys of the 3d transition metal series, against the number of valence (3d+4s) electrons, Co3Fe7 would lead to a magnetization in the excess of 1900 kA/m [START_REF] Coey | Micromagnetism, domains and hysteresis[END_REF]. However, our attempts to form metallic structures by annealing of the CoFe2O4 filaments under a reducing atmosphere did not fully eliminate the oxide phase, which led to mixed structures with a relatively low magnetization. In the following only single phase structures will be discussed. The average crystallite size was calculated from the XRD patterns with the Scherrer method (Table S2). The crystals of all samples are assumed to have a spherical shape (due to the calculation method), with a diameter ranging from 30 to 70 nm. These values are in good agreement with our observations in a transmission electron microscope. On SEM pictures (Fig. 2), elongated structures were observed with a diameter lower than 500 nm, except for the FeNi sample that did not present any fibrous morphology after treatment under Ar/H2 (90/10) of NiFe2O4 filaments. It is noteworthy that fibers of Fe2O3, Fe3O4 and pure Fe have a diameter which is lower than 100 nm. Thus, these three materials can be named as "nanofibers". Some particles of the Fe sample have a rounded shape. In this specific case, the reducing atmosphere induces a loss of oxygen that can lead to a particle coalescence explaining the decrease of the aspect ratio of the fibers.

Magnetic properties

We investigated the influence of the shape and microstructure of the synthesized nanofibers on their magnetic properties, in a SQUID magnetometer. We measured room temperature magnetization curves M-H of nanofibers.

In table 1, we present the magnetization of the different fibers and compare with bulk values. The spontaneous magnetization for each compound is comparable with bulk values showing that the metallic phases are relatively pure, and that potential oxidation remains limited. In particular, the largest discrepancy is measured for Fe fibers, in which the magnetization is 21% less than the one of bulk Fe. As compared to previous work on Fe nanofibers the magnetization of our fibers is relatively large [START_REF] Vega | Tuning the magnetic anisotropy of Co-Ni nanowires: comparison between single nanowires and nanowire arrays in hard-anodic aluminum oxide membranes[END_REF].

Considering a fiber diameter of 48 nm that is the crystallite size determined by XRD, the magnetization reduction would correspond to a superficial "magnetically dead" layer of less than 3 nm thick.

Fe2O3 fibers exhibit extremely small net magnetization, confirming the predominant antiferromagnetic -Fe2O3 (hematite) phase with respect to ferromagnetic -Fe2O3 (maghemite) phase as observed on the XRD pattern. * estimated from ref. [START_REF] Coey | [END_REF] Metallic and oxide fibers show drastically different magnetic behaviors, as reveal the M-H loops of figure 3. Oxide fibers exhibit magnetization hysteresis while metallic Fe, Fe-Ni fibers show nearly reversible magnetization reversal process, as could be expected considering the intrinsic magnetic properties of these materials. Indeed, coercivity highly depends on the material's microstructure and its intrinsic magnetic hardness. The magnetic hardness is characterized by a dimensionless parameter that is the ratio of anisotropy to dipole energy and scales with √|𝐾 1 | 𝑀 𝑆 ⁄ [START_REF] Eid | Magnetic properties of hematite nanotubes elaborated by electrospinning process[END_REF]. Table 2 shows that the oxide compounds present larger magnetic hardness values as compared to Fe and FeNi favoring the larger coercive field. One can notice that the coercive field can be under-estimated since the nanofibers are not rigidly fixed into the capsule during SQUID measurement. Besides microstructure considerations would favor larger coercivity in oxide fibers.

Based on XRD Debye Scherrer analysis (Table S2), the crystallites size ranges from 30 to 70 nm independently to the material. This is in the critical range of the magnetic domain length scale. The general picture that describes the dependence of coercive field with particle size presents a maximum at the critical size that separates single domain to multidomain structure. [START_REF] Xu | Microfluidic microsphere-trap arrays for simultaneous detection of multiple targets[END_REF][31] The crystallites size is comparable to the maximum single domain particle size of oxides, if not smaller, but greater than the one of the considered metals. As a result, one could expect the magnetic structure to break into multidomain structure in metallic fibers but to remain single domain in oxides, which again favors coercivity.

Both Fe and NiFe fibers show no hysteresis but exhibit different M-H loop shapes. The magnetization reversal of NiFe fibers is progressive while the it occurs in a two-step process for Fe fibers, with an abrupt magnetization change in the low field region followed by a progressive approach to saturation. In both cases, the saturation of the magnetization is reached for an applied field of around 10 kOe. This is significantly larger than the expected anisotropy field from the intrinsic magnetocrystalline contribution (inferior to 1 kOe in Fe and less in Fe-Ni alloys). This shows that the predominant contribution to the anisotropy is not of magnetocrystalline origin, but could be the contribution of the fiber shape and the microstructure.

In addition, provided the lower magnetization of Fe fibers as compared to bulk Fe, one cannot discard a secondary phase, like Fe-O formed at the fibers' surface.

Magnetic composite polymer

Fe nanofibers/PDMS composite were realized with a concentration of 0.23 wt%. When no magnetic field was applied during the polymer reticulation, nanofibers were distributed in disorder in the polymer matrix. However, when an external magnetic field was applied, nanofibers have self-ordered in chain-like agglomerates. The magnetic pattern and the exposure time of the composite to this pattern influence the organization of the fibers [START_REF] Zhu | Fabrication of polydimethylsiloxane composites with nickel particles and nickel fibers and study of their magnetic properties[END_REF]. These first experiments subjected the composite to a homogeneous magnetic field of 130 mT and a time of 2 hours, corresponding to the cross-linking time of the PDMS matrix.

Before complete PDMS reticulation, nanofibers orient themselves relatively to the magnetic field, and dipolar interactions guide the fibers motion: (i) dipole-dipole attraction in the direction of the applied field forming high aspect ratio chains along the flux lines and (ii) dipole-dipole repulsion within the orthogonal plane to the applied field vector leading to a self-distancing between adjacent chains [START_REF] Odenbach | Ferrofluids: magnetically controllable fluids and their applications[END_REF]. We studied nanofiber organization using confocal microscopy and FIB/SEM (see part 4 of S.I.). The fibers' alignment leads to an anisotropic response, as shown in Fig. 5. As expected from magnetostatic energy considerations, the easy magnetization axis is found along the global orientation of the nanofibers. However, as compared to other work on oriented Fe and Co nanofibers [START_REF] Graeser | Magnetically anisotropic cobalt and iron nanofibers via electrospinning[END_REF] the anisotropy is less pronounced. The relatively low reduced remanence along the easy axis, below 50%s, and weaker anisotropic response could be explained by the presence of superparamagnetic domains. Indeed the nanocrystals in the present work are smaller, so the population of superparamagnetic grains is expected to be larger. Taking into account the shape of the pure iron fibers (Fig. 2), during the thermal treatment, fibers with elongated shapes can merge and form 3D multi-branched structures. Thus, the initial expected uniaxial shape anisotropy of individual fibers can be biased. In these 3D structures, the easy-magnetization direction is expected to be the best compromise between all the contributions of the constituting branches.

These complementary experiments enable

Conclusions

Fibers of different magnetic materials, metals, Fe and FeNi, and oxides Fe3O4, Fe2O3, CoFe2O4, NiFe2O4, were produced using electrospinning. Their morphology was characterized by SEM and TEM and additional crystalline information were obtained by X-ray diffraction (XRD) experiments. Except for FeNi sample that did not present any fibrous morphology after heating treatment, Fe, Fe3O4, Fe2O3, CoFe2O4 and NiFe2O4, fibers shown diameter lower than 500 nm. The average crystallite size, calculated from the XRD patterns with the Scherrer method, ranged from 30 to 70 nm. Concerning magnetic properties, metallic and oxide fibers presented drastically different magnetic behaviors, in agreement with the intrinsic magnetic properties of these materials.

We have thus succeeded in synthesizing pure iron nanofibers that have a magnetization at saturation of 171 emu/g, no hysteresis and a diameter lower than 100nm. These NFs are excellent candidates for the realization of magnetic composite polymers. We have performed first experiments by integrating these filaments in a PDMS matrix at a concentration of 0.23 wt%, and a magnetic field was applied during reticulation to self-organize iron fibers in the matrix. As shown by 3D structural characterization, performed by FIB-nt and confocal microscopy, Fe nanofibers selfordered in elongated agglomerates in the PDMS matrix when a magnetic field was applied during composite cross-linking. Such alignment of the fibers leads to an enhanced anisotropic magnetic response. Such magnetic multifunctional material is promising for numerous applications.

Figure 1 :

 1 Figure 1: XRD spectra of samples after heat treatment; α-Fe2O3 (Rhombohedral, space group:

Figure 2 :

 2 Figure 2: TEM pictures of electrospun samples after thermal treatment; Insets correspond to

Figure 3 :

 3 Figure 3: Room temperature magnetization curves of fibers: (a) Fe3O4, Fe2O3, CoFe2O4,

  to perform 3D structural characterization of the composite at different scales. Confocal microscopy allows observing a composite volume of 620 x 620 x 50 µm³ with a voxel of 500 x 200 x 200 nm 3 and FIB/SEM a composite volume of 23.25 x 17.52 x 15.7 μm³ with a voxel of 25x25x25 nm 3 . Confocal microscopy gives an overview of the nanofiber composite organization in the polymer matrix. Fig. 4-a shows Fe nanofibers self-ordered in elongated chains in the PDMS matrix. Chain diameters range from µm to tens of µm, they are aligned along the magnetic flux lines. The distribution of the chains in the volume is rather homogeneous as chains are present over the entire thickness and surface of the sample, as shown in Fig. 4-b. FIB/SEM allows to have a closer look at the morphology and orientation of the agglomerates (Fig. 4-c). Visible chain-like agglomerates possess a high aspect ratio with a diameter of the order of 2 µm, and are localized at different thicknesses of the composite, as highlighted by Confocal microscopy. Although both chains are oriented in the same direction, we can observe a slight angular dispersion, which could be due to the repulsive force of the neighboring chains, on top of the image.

Figure 4 :

 4 Figure 4: a) 3D reconstruction of confocal images of the composite (PDMS + Fe fibers),

Figure 5 :

 5 Figure 5: Magnetization of composites with isotropic fibers orientation (white circle),

Table 1 :

 1 Fiber spontaneous magnetizations at room temperature. Comparison with bulk values.

	Material	s exp. (emu/g)	s bulk (emu/g)
	Fe	171	218[32]
	NiFe	143	146.7[33]*
	-Fe2O3	<2.5	0.5 [31]
	Fe304	94	92[23]
	CoFe2O4	84.5	80 [23]
	NiFe2O4	88.6	50 [23], 55 [34]

Table 2 :

 2 Magnetic properties and grain size of synthesized fibers. Comparison with intrinsic magnetic properties of the materials.

	Materials	Coercive field	Magnetic	XRD	Maximum single
		(kOe)	hardness	crystallite size	domain particle
			parameter	(nm)	size (nm) [37]
	Fe		0.12	48	10
	NiFe		0.1	40	1.6
	Fe304	0.57	0.84	47	38
	CoFe2O4	0.93	0.21	30	160
	NiFe2O4	0.28	0.48*	67	-
	* calculated assuming same density between CoFe2O4 and NiFe2O4

Acknowledgments

This work was financially supported by the "Institut Carnot Ingénierie@Lyon". The authors are grateful to Nanolyon technological platform for access to microfabrication facilities, ILM Tech (Centre de Magnétométrie de Lyon) for access to the SQUID characterization, CTµ (Centre Technologique des Microstructures, microscopies.univ-lyon1.fr) for the access to the SEM and TEM microscopes used in this work and CLyM (Consortium Lyon Saint-Etienne de Microscopie) for FIB/SEM characterization. Dr. Rodica Chiriac and François Toche are warmly acknowledged for their help regarding the TGA experiments. Finally, the authors thank Jérôme Degouttes and Nicolas Terrier for their technical support.