Amandine Maetz

Luc Delmotte

Georges Moussa

Joseph Dentzer

Stephan Knopf

Camélia Matei Ghimbeu

Joseph Denzer

Camelia Matei Ghimbeu
email: camelia.ghimbeu@uha.fr

Facile and sustainable synthesis of nitrogen-doped polymer and carbon porous spheres

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

Nanostructured carbon materials with controlled texture, structure, morphology and surface chemistry witness a large pallet of utilizations such as absorbents, electrodes for batteries and supercapacitors, catalyst, fuel cells or gas sensors [1][2][3][4][5][6] . Particularly, nanoporous carbon spheres have considerably attracted attention in the recent years due to their tunable particle size/shape, improved pore accessibly providing faster molecular diffusion and specific structure containing open edges inducing specific reactivity with molecules 2;7;8 . Several synthetic approaches have been proposed during the time to design carbon spheres with different particle sizes, tunable pore size/geometry and graphitization levels. Firstly, chemical vapor deposition (CVD) routs were employed, involving the thermal pyrolysis of hydrocarbons (toluene, benzene, hexane, methane, acetylene etc.) at high temperature (600°C to 1200°C) in the presence or not of a metallic-based catalyst 7 . Such approach allows to obtain graphitic carbon spheres but uniform particles is difficult to be achieved. In addition, the inconvenient including high temperature reactions, toxic and dangerous carbon precursors and sacrificial use of catalyst limited the extensive use of such approach. Hard-templating pathways involves the use of silica or latex particles which are filled with carbon precursors by wet impregnation or by CVD with hydrocarbon gases. This step is followed by the dissolution of the template with strong acids or bases allowed to obtain well defined carbon spheres with controlled ordered porosity 9;10 . The obtained carbon spheres correspond to the negative replicas of silica/latex spheres. Despite the good control of carbon spheres characteristics obtained by hard-template, the long synthesis process related to the preparation of hard templates and their dissolution with hazardous HF or NaOH are considered as the main drawbacks of this approach.

More recently, the soft-template route emerged as an alternative approach. Commercially available block copolymer soft templates easily decomposable thermally are being used as pore and structure directing agents together with thermosetting polymers resins as carbon source under hydrothermal conditions. 60 Carbon spheres with well controlled mesoporosity were achieved only in few cases and their preparation remains a challenge 11;12 Besides, the low carbon yield, high cost and restrained choice of templates are important issues to be overcome. Hydrothermal route carbonization route (HTC) in aqueous 65 medium at low temperatures (< 300°C) and under pressure (~1 MPa) was found to be a sustainable and efficient process to transform sugar-based precursors (glucose, fructose, cellulose, biomass etc.) into carbon spheres, without the use of templates 13- 15 . 70 However, such carbons are obtained with low yield and present limited porosity, therefore, supplementary additives or post activation treatments are required in order to adjust the porosity 16- 18 . A significant progress in the preparation of carbon spheres was 75 recently achieved by modification of Stöber method 19;20 . Originally developed for the preparation of silica particles by a sol-gel reaction under hydrothermal conditions, it has been demonstrated that this method can be extended to the preparation of monodisperse phenolic-resin polymer spheres and therefore, 80 by thermal decomposition for carbon spheres preparation. Phenolic-resins are of great interest due to their high thermal stability and high carbon yield useful for practical application. Mainly, phenol-formaldehyde based resins are used [21][22][23] , although these precursors are highly toxic and/or carcinogen. As 85 alternative to these toxic precursors we have recently proposed green resins based on phloroglucinol and glyoxylic acid in order to prepared mesoporous carbons powders and films 24 . In addition to the toxic precursors often used in the Stöber method, non-aqueous solvents and hydrothermal treatments (60 90 to 220°C) are required to obtain carbon spheres. Another important key of the Stöber synthesis is the catalyst employed which will direct the particle morphology and size. Ammonium hydroxide is usually employed in such synthesis but its pungent smell and its toxicity for environment direct researchers to evaluate novel catalysts. Song et al. 25 proposed the use of urea in this aim. In the present work, trietylenediamine (TEDA) is used for the first time as catalyst and stabilizer for resin polymer/carbon spheres synthesis. A non-exhaustive literature table gathering several synthesis conditions (type of precursors, solvents, catalysts, synthesis temperature and time) is provided is Table S1(Supporting Information) in order to illustrate these points 20-22;25-36 . Although, efforts have been committed to use green carbon precursors, low synthesis temperatures, aqueous solvents or shorter synthesis periods 14;34;35 , no synthesis methods gathering all these positive requirements have been reported yet. Moreover, the synthesis mechanisms are rarely studied although they may shed light in the understanding of the formation of such structures and in the design of materials with improved characteristics.

Therefore, we propose a simple, fast and green synthesis strategy to design carbon spheres with controlled particle shape and size. The synthesis involves the use of green resins precursors and TEDA catalyst dissolved in water at room temperature followed by a short aging periods which allows to obtain monodisperse polymer resin and carbon spheres. The particle size can be tuned from 500 nm to 10 µm by varying the synthesis time or molar ratio between the resin and the catalyst. The synthesis mechanism is studied by coupling [START_REF] Tekin | Clean Technologies 100 and[END_REF] C and 1 H NMR spectroscopy, TPD-MS and XPS analysis.

MATERIALS AND METHODS

Chemicals

Phloroglucinol (1,3,5-benzentriol, C6H6O3), glyoxylic acid monohydrate (C2H2O3•H2O) and triethylenediamine, TEDA (C6H12N2, also called 1,4-Diazabicyclo [2.2.2] octane or DABCO) were purchased from Sigma-Aldrich and used as received without any further purification.

Material Synthesis

The polymer and carbon porous materials were synthesized via a modified Stöber method 20 . However, compared to literature, our synthesis involves green precursors, water solvent and room temperature conditions, most of the works being performed under hydrothermal conditions (see Table S1, Supporting Information).

Typically, phloroglucinol (0.82g) and glyoxylic acid (0.72g) were dissolved in water (40 mL) at room temperature (25 °C) and ambient pressure, followed by the addition of TEDA (0.36 g) under stirring. The obtained solution was left aging in static conditions (no stirring) for 24 h at 25°C, a phase separation occurs and the upper layer solution is discarded while the solid polymer product is recovered and dried. In some cases, centrifugation was used to recover the polymer spheres having small sizes. Subsequently, a thermopolymerisation at 80°C for one night followed by another one at 150°C was performed to cross-link the polymer resin framework in the material. The obtained materials were pyrolysed at 600°C (2°C/min) under inert atmosphere (Ar) for 1 hour. The pyrolysis was as well performed on the as-synthesized polymer spheres (without thermopolymerization step at 80/150°C) in order to evaluate the necessity of such step. A 65 schematic representation of main synthesis steps is provided in Figure 1 and Figure S1 (Supporting Information).

The influence of several parameters on the particle size and morphology was investigated. Only one parameter was changed on one time while keeping the others unmodified. The water 70 volume investigated was: 10, 40 and 400 mL, the TEDA amount was: 0.09, 0.18, 0.36 and 0.72 g while the synthesis time was: 30 min, 1h, 3h, 6h and 24h.

Material Characterization

The materials morphology was evaluated by scanning electron 75 microscopy (SEM) analysis using a FEI Quanta 400 scanning electron microscope. The particle size was measured using the SEM images and ImageJ software. The textural properties of the materials were investigated with a Micromeritics ASAP 2420 instrument using N2 adsorbate at -196 °C. Prior to the analysis, 80 the samples were out-gassed overnight in vacuum at 300°C on the degassing port followed by 4h out-gassing on the analysis port 37 .

The BET (Brunauer-Emmett-Teller) surface area (SSA) was calculated from the linear plot in the relative pressure range of 0.01-0.05 while the micropore volume (Vmicro) was determined 85 using the Dubinin-Radushkevich (DR) equation. The total pore volume was obtained at relative pressure P/P0 of 0.99. The pore size distributions (PSD) were determined from the adsorption branch of nitrogen isotherms using the NLDFT standard slit pore model for carbon materials implemented in SAIEUS software 90 (Micromeritics) 38;39 .

The polymer resin structure was studied by solid-state [START_REF] Tekin | Clean Technologies 100 and[END_REF] C and 1 H magic angle spinning (MAS). NMR spectra were obtained at a frequency of 100.6 MHz, 400.13MHz respectively on a Bruker Avance 400 NMR spectrometer. X-ray photoelectron 95 spectroscopy (XPS) was performed with a VG Scienta SES 200-2 spectrometer equipped with a monochromatized Al Kα X-ray source (1486.6 eV) and a hemispherical analyzer. The pass energy was 100 eV. Thermo-gravimetric analysis (TGA) was used to study the mass loss during the polymer spheres 100 carbonization by heating with 2°C min -1 up to 900°C under nitrogen (METTLER-TOLEDO TGA 851e). The type of species evolved during the carbonization of polymer resin were analyzed by temperature programmed desorption coupled with mass spectrometry 40;41 . A small quantity of cured resin (~ 5 mg) was 105 introduced in a quartz tube place inside of a furnace and heattreated in vacuum up to 950°C. The gases evolved during the heating process were continuously detected by a mass spectrometer.

RESULTS AND DISCUSSION

Polymer and carbon spheres were prepared by a facile and green synthesis approach. Phloroglucinol and glyoxylic acid were dissolved in water followed by the addition of TEDA. A colorless solution is obtained which turned rapidly into a turbid one (few minutes later). After 30 min of reaction a solid product is observed on the bottom of the balloon (Figure 2) and its quantity increases with the increase of the reaction time. This is accompanied as well by the modification of the product color from pale yellow (< 1h), to orange (3-6h) and red-brown (24 h) suggesting more advance polymerization and cross-linking between the precursors with the reaction time proceeding. The recovered phenolic-resin polymer was thermopolymerized and thermally decomposed at 600°C to obtain the carbon materials. Figure 3 shows the evolution of carbon morphology with the synthesis time. In the first stages of the synthesis (10 to 30 min) spherical particles with narrow uniform size of about 500 nm are formed (Figure 3a-b). As the reaction progresses (1 to 6h), these particles tend to merge forming bigger particles with sizes of ~3-4 µm as seen in the in-set of Figure 3d. Therefore, agglomerated small particles and large particles coexist (Figure 3c-e). For time periods longer than 6h, mostly large individual particles with uniform shape and size are obtained (Figure 3e-f).

LaMer mechanism 42 can be considered to explain the formation of the spheres. This involves nucleation of particles and a growth step. The nucleation proceeds with constant monomer concentration until the monomer concentration falls below the critical level of nucleation (supersaturation level) and the nucleation ends. The resulting nuclei grow uniformly by diffusion of solutes toward the particle surfaces until the final size is attained 42 . This mechanism seems to not be valid in this case, in agreement with other works 43;44 where the particles prepared are the result of aggregation of much smaller subunits rather than continuous growth by diffusion of species from the solution towards the surfaces of nuclei. A broad range of size distribution is observed during the growth step, indicating the occurrence of several nucleation events 45 . The final particle size uniformity could be achieved through a self-sharpening growth process where the small particles grow more rapidly than the larger ones.

The influence of the amount of TEDA on the size and shape of carbon spheres was investigated. The TEDA play a double role in the synthesis, i.e., stabilizer in the formation of the particles and nitrogen source to incorporate heteroatoms in the particles. For TEDA amounts smaller than 0.09 g (Figure 4a), the particle shape is irregular and the particles tend to merge to form agglomerates. Between 0.18 and 0.36 g of TEDA (Figure 4b-c), the particles present smooth and homogeneous spherical shape and the size slightly increases with the amount of TEDA but they become more homogenous in size. To better understand the modification of carbon morphology with 60 the TEDA amount, the pH of the solution vs. TEDA amount was monitored (see Figure S2, Supporting Information). With the increase of the amount of TEDA form 0.09 g to 0.72 g, the pH significantly increases from 0 to 3.5-4. Therefore, for highly acidic conditions 0 to 1, irregular and agglomerated spheres are For pH values higher than 3, no spheres are formed. This could be related to the negative effect of such pH on the polymerization of phloroglucinol with glyoxylic acid and on the H + bonding of the resin with the TEDA. As a result, the pH interval range from 1 to 2.5 seems the most convenient one to form uniform spherical particles.

The impact of the solvent amount on the sphere formation was evaluated using 10, 40 and 400 mL of water. As noticed in Figure 5, such parameter influences both the morphology and the size of the particles. At low water volumes (10 mL), the particles exhibit a flower-like morphology with average sizes of about 10 µm. The flower particles are composed of "petals" of quasi-spherical particles with 2-3 µm of diameter. When the volume of water is increased to 40 mL, the particles become spherical and their diameter decreases to 5-7 µm (Figure 5b). Further increase in the amount of water to 400 mL has an effect only on the particle size, which reduces to 2-4 µm. The decrease of the particle size with the increase of the water content in a mixture of ethanol/water has been reported by other authors. This behavior may be induced by the decrease of surface tension of the solution, resulting in smaller primary emulsion droplets and finally smaller particle spheres. The formation of carbon flowers may be a result of a saturation of solution with precursors.

The textural properties of the carbon spheres were investigated and typically nitrogen adsorption/desorption isotherms and the pore size distribution are shown in Figure 6.

The isotherms are of type I (Figure 6a), characterized by an important increase in nitrogen adsorption volume at low relative pressures (P/P0 < 0.1) indicating the formation of microporous carbon spheres and a plateau which tend to increase between 0.1 and 1, suggesting the existence of larger micropores. This is in line with the pore size distribution showing mainly uniform pore size centered around 0.6 nm (Figure 6b) and some larger micropores comprised between 0.9 and 1.6 nm. The specific surface area and the total pore volume are ranged between 415 and 490 m 2 •g -1 and 0.19-0.23 cm 3 •g -1 , respectively (Table 1). The formation mechanism of polymer and carbon spheres derived from phloroglucinol-glyoxylic acid resin in the presence of TEDA was never studied and is worth to be investigated. For this aim, the NMR technique was employed to determine the structure 55 of the resins, XPS to study its composition, while the thermal analyses (TGA and TPD-MS) were employed to understand the decomposition of polymer resin spheres and its transformation into carbon spheres.

Figure 7 shows the [START_REF] Tekin | Clean Technologies 100 and[END_REF] C and 1 H CP-MAS (cross-polarization 60 magic angle spinning) NMR spectra of the as-synthesized polymer resins spheres at 25°C, thermopolymerized at 80°C and 150°C, respectively. At 25°C, the [START_REF] Tekin | Clean Technologies 100 and[END_REF] C spectra of polymer spheres exhibit several peaks placed at 178, 154, 106, 96, 44 and 38 ppm corresponding to the carbon atoms involved in different moieties 65 of phenolic resins formed by the polymerization reactions between the phloroglucinol and glyoxylic acid in the presence of TEDA. Except the peak from 44 ppm, all the other peaks were observed belong to phloroglucinol/glyoxylic acid resins and described in detail in our previous works 21,24 . For clarity reasons 70 they are reported in the in-set of the Figure 7a and described briefly herein.

The peak from 176 ppm corresponds to carbon atoms of carboxylic acid group of glyoxylic acid or its derivates. The two peaks placed at 154 ppm and 96 ppm are associated to carbon atoms in phloroglucinol, i.e., unsaturated aromatic carbons bonded with OH group (154 ppm) and to the CH unsaturated bond in the phenyl ring (96 ppm), respectively. The presence of those peaks indicates some un-reacted phloroglucinol and glyoxylic acid at this stage of reaction (25°C). 10 However, a part of phloroglucinol reacted with glyoxylic acid by an electrophilic aromatic substitution mechanis 21,24 forming the trihydroxy-phenylacetic acid, identified in NMR by the peak placed at 105 ppm. The small peak from 38 ppm indicates further cross-linking of trihydroxy-phenylacetic acid with phloroglucinol via different mechanisms, with the formation of carboxylic acid and/or lactone bridges between the phloroglucinol rings 46 . The most intense peak noticed at 44 ppm is assigned to carbon atoms bonded with positively charged nitrogen of TEDA molecule. TEDA may link to phloroglucinol/glyoxylic acid resin via oxygen 20 coming from trihydroxy phenylacetic acid as schematically shown in the in-set of Figure 1 and7. This is evidence that the TEDA is integrated in the backbone of phenolic resin.

With the increase of the temperature at 80 and 150°C, we observe progressive evolution of the glyoxylic acid and phloroglucinol peaks towards unique peaks. At 80°C, the 106 and 96 ppm resonance peaks become closer and merge to one single peak at 150°C, suggesting highly substituted phenyl ring and higher cross-linking. In the same way the 178 and 154 ppm peaks related to phloroglucinol and glyoxylic acid did not progress very much 30 at 80°C, but at 150°C they merge as well into a single peak with intermediate position, i.e., 159 ppm. Therefore, at 150°C, all initial precursors reacted to form a cross-linked phloroglucinol/glyoxylic acid/TEDA resin.

The 1 H NMR exhibit mainly two peaks at 25°C, at 5.8 and 3.0 ppm which are assigned to protons involved in phenyl ring of phloroglucinol and in TEDA, respectively. By increasing the temperature to 80°C and 150°C, the 5.8 ppm peak intensity significantly decreases indicating highly substituted 40 phloroglucinol and better cross-linking, while the 3.0 ppm peak become wider indicating protons involved in rigid (cross-linked) structures. These observations are in good agreement with the [START_REF] Tekin | Clean Technologies 100 and[END_REF] C NMR results showing increase cross-linking with the increase of the temperature.

45

The surface chemistry of thermopolymerized polymer spheres and of the derived carbon spheres was analyzed by XPS. The XPS survey spectra (not shown here) revealed that the amounts of nitrogen, oxygen and carbon before carbonization are 5.3, 22.7 and 72.0 at.%. After carbonization the amounts of 55 nitrogen and oxygen decreases to 3.1 and 7.7 at.%, respectively, while the carbon amount increases to 87.9 at.%.

Figure 8a shows the high-resolution N1s XPS spectra. For polymer spheres the peak show mainly two contributions at 400 eV and 402 eV corresponding to N atoms involved in TEDA and 60 positively charges N + in TEDA, respectively, involved in the phenolic resin (Fig. 7a down). After the thermal treatment of polymer spheres, the obtained carbon spheres present a N1s peak which was deconvoluted into five main components peaks i.e., pyridinic nitrogen (398eV), pyrrolic nitrogen (400eV), quaternary 65 nitrogen (401eV), pyridine oxide (403 eV) and nitrogen oxides (404 eV), as schematically shown in the in-set of Fig. 7a (up). This result confirms the incorporation of nitrogen groups into the polymer and carbon framework.

The high-resolution C1s XPS spectra (Figure 8b) of 70 thermopolymerized polymer spheres show two merged peaks placed at 285 and 286 eV which are deconvoluted into five components. The most intense peak is placed at 284.7 and is related to C-C and C-H bonds in polymer resin, the second important contribution is placed at 286.5 and corresponds to C-O 75 bonds, the peak at 285.9 is related to C-N and C-N + bonds, while two other smaller contributions from 287.7 and 288.8 eV, are assigned to C=O and O-C=O bonds. After carbonization the C1s present only one intense peak at 284.5 eV which is assigned to graphite-like sp2 carbon 47 . A tail of asymmetric C 1s peak at 80 higher binding energies is originated from the presence of carbon atoms bonded to nitrogen (C=N and C-N) and different oxygenfunctional groups (C-OR, C=O and O=C-O). Those oxygen groups are in less quantity than in the polymer spheres, therefore, were removed during the carbonization.

To better understand the transformation of polymer spheres into carbon spheres, thermal analysis techniques, i.e., TGA and TMD-MS were employed. Figure 9 shows the TGA profile under nitrogen of as-synthesized and thermopolymerized at 150°C polymer spheres. For the assynthesized polymer spheres, three main peaks are observed. The first one is placed between 25 and 100°C, with a maximum at 60°C and can be related to physisorbed water on the material. The second peak is ranged between 100 and 200°C, with a maximum at 150°C which may be assigned to water or other species evolved during the polymerization/polycondensation reactions between the phloroglucinol and glyoxylic acid. The third peak is 20 located between 250 and 400°C with a maximum at 300°C and may be attributed to the decomposition of polymer resin. When the polymer spheres are thermopolymerized at 150°C, the peak at 60°C related to physisorbed water is still observed but is less intense while the peak at 150°C is not any longer visible, indicating the well cross-linking of the polymer spheres. The peak at 300°C becomes as well less defined. The yield in carbon of thermopolymerized polymer is about 55 wt.% at 600°C and 45 wt. % at 900°C, which is an advantage of resin precursor. The morphology of the polymer spheres are well conserved, however, 30 shrinkage of particle size during the thermopolymerization step and thermal treatment is observed (Figure 9b-e). The assynthesized polymer particles have an average size of 6.2 µm (inset Figure 9b) which decreases to 5.4 µm during the thermopolymerization step (~ 13 % shrinkage, Figure 9c) and to 35 4.8 µm during the thermal treatment (~ 12 % shrinkage, Figure 9e), therefore, a total of 25% of shrinkage. These observations are in good agreement with other works 20;25;28;29;34 where shrinking of polymer particle between 12 and 30 % was observed during the carbonization step. The shrinkage rate was found to depend 40 by the polymer composition, structure and thermal annealing conditions. It is worth to note that, if the as-synthesized polymer particles are directly carbonized, the average particle size decreases to 4.6 µm (26 % shrinkage, Figure 9d), thus, the final shrinkage of the particle and their size is rather similar as in the 45 case of thermopolymerized particles.

Therefore, the obtainess of carbon spheres is not conditioned by the thermopolymerization step, even if such step is performed in most of previous works 20;21;25;29;30;32;33 The experimental pressure curve is higher in intensity than the calculated pressure, implying the evolvement of supplementary gaseous species from the material during heating than the calibrated ones. For more details, the calibrated gases desorption profiles vs. the temperature can be seen in Figure 10b. The most intense peaks are corresponding to H2O, CO, CO2 and H2, while smaller contribution of CH4 and NH3 is detected as well.

The CO2 peak is very large, comprised between 200 and 600°C. The CO2 formation is usually attributed to the decomposition of acidic groups such as carboxylic (~200-300°C) and/or anhydride groups (> 300°C) 41;48 . The latest one decomposition is accompanied by the evolution of CO gas as well. The CO peak is placed between 200 and 800°C and corresponds at low temperature to the decomposition of acidic groups such 10 anhydrides as mentioned above, and at higher temperatures to the decomposition of more basic groups such as phenol, quinones, lactones and ethers 37;48;49 .

The water peak presents two maxima at 300°C and 450°C which may be related to the in-situ reactions between functional groups during the TPD-MS experiment. The first peak, may be linked to the desorption of water formed due to the reaction between two neighbor carboxylic groups (-COOH) of glyoxylic acid with the formation of anhydrides groups which subsequently decomposes at higher temperature (450°C) with the formation of water and 20 concomitantly of CO and CO2. This suggests the cross-linking and the further decomposition (carbonization) of polymer spheres. A high intense peak of H2 is noticed for temperatures higher than 600°C due to the structural organization of carbon through C-H bond cleavage. Smaller amounts of CH4 and NH3 are released during this process but in smaller extent.

Besides these gases, other species are observed by MS. Firstly, we investigate the existence of mass signals coming from TEDA (Figure S3a, Supporting Information), and no peaks related to this molecule were found. However, peaks with m/z = 26, 53 and 80 were detected (Figure 10c) which were found to correspond to pyrazine (Figure S3b, Supporting Information). This means that TEDA transformed into pyrazine at around 200°C, by eliminating ethane molecules, observed as well at this temperature is small quantities. A closer look to the peaks of pyrazine (Figure 10c)

show the presence of a secondary peak for the mass m/z = 26 at around 700°C, which do not correspond to pyrazine but rather to the hydrogen cyanide (HCN). This compound present 2 main mass signals at m/z = 26 and m/z = 27 (Figure S3c, Supporting Information), and it can be clearly confirmed with the peak at m/z 40 = 27, that the peak at 600°C belongs to HCN. Therefore, the removal of nitrogen from the carbon structure when increasing the temperature well above 600°C occurs.

Conclusions

A simple and sustainable synthesis approach to design polymer and carbon spheres was developed. Such approach employs green concepts, i.e., green precursors and catalysts, water as solvent and room temperature conditions, therefore, easily scalable and answering to practical and industrial requirements. Particles with uniform shape and size that could be tuned between 500 nm and 10µm were obtained by varying the synthesis conditions. The surface charges, surface tension and polymerization rate are some of the key factors influencing the particle size and morphology. The carbon particles are microporous and exhibit specific surface areas up to 490 m 2 •g -1 and nitrogen in their structure. Insights on the synthesis mechanism of polymer and carbon spheres were assessed be coupling several techniques. The structure of polymer resin spheres and its evolution with the temperature was determined by [START_REF] Tekin | Clean Technologies 100 and[END_REF] C NMR and XPS while their decomposition behavior along with the evolved species during the carbon sphere 60 formation was monitored by TPD-MS. The as-designed materials can be easily functionalized with other heteroatoms and/or metallic nanoparticles and further employed for a wide range of applications.

Figure 1 :

 1 Figure 1: Schematic illustration of the synthesis of polymer and carbon spheres using green precursors and conditions.

Figure 2 :

 2 Figure 2: Photos of solution evolution during the time.

Figure 3 :Figure 4 :

 34 Figure 3: SEM images of carbon spheres obtained using different synthesis times: (a) 10 min, (b) 30 min, (c) 1h, (d) 3h, (e) 6h and (f) 24h; (TEDA quantity: 0.36 g, water volume: 40 mL).55

  65formed probably due to the insufficient quantity of positive nitrogen charges delivered by the TEDA at the external part of the particles. Such charges, localized at the external part of the resin allow to stabilize the morphology and to avoid the agglomeration of the particles.

Figure 5 :

 5 Figure 5: SEM images of carbon spheres obtained using different water volumes: (a) 10 mL, (b) 40 mL and (c) 400 mL; (TEDA quantity: 0.36 g, synthesis time: 24h).

45 Figure 6 :

 456 Figure 6: (a) N2 adsorption/desorption isotherms and (b) their corresponding NLDFT pore size distribution of carbon spheres synthesized under different time periods conditions (TEDA amount: 0.36 g, water amount: 40 mL, synthesis time: 6h).

Figure 7 :

 7 Figure 7: 13 C and 1 H NMR spectra for phenolic resin polymer 5

Figure 8 :

 8 Figure 8: XPS spectra of polymer spheres thermo-polymerized (down) and derived carbon spheres (up): N1s (a) and C1s (b) high 50

5 Figure 9 :

 59 Figure 9: TGA under inert atmosphere of the as synthesized and thermopolymerized at 150°C polymer spheres (a); SEM pictures of as-synthesized (b) and thermopolymerized polymer spheres at 150°C (c) and their corresponding carbon spheres (d and e); inset: particle size distribution; (TEDA amount: 0.36 g, water 10

Figure 10 :

 10 Figure 10: TPD-MS desorption spectra of polymer spheres thermo-polymerized at 150°C (a) evolution of measured and calculated pressures, (b) desorption profiles of calibrated gases and (c), (d) desorption profiles of non-calibrated gases. (TEDA amount: 0.36 g, water amount: 40 mL, synthesis time: 6h).

  70

Table 1 :

 1 Textural properties of carbon materials synthesized

	30min	466	0.20	0.17
	1h	490	0.23	0.20
	3h	415	0.19	0.15
	6h	471	0.21	0.18
	24h	452	0.21	0.19

50 under different experimental conditions. Materials SSA, m 2 •g -1 Vt, cm 3 •g -1 Vmicro, cm 3 •g -1

Acknowledgements

65

The authors thank Samar Hajjar and Gauthier Schrodj for the help provided with the XPS and TGA analyses through the technical platform of IS2M. Financial support of this work by the French National Research Agency (ANR) project Genesis (ANR-13-BS08-0004-02) is acknowledged.


P Martinet
email: martinet@lasmea.univ-bpclermont.fr

E Cervera
email: ecervera@inf.uji.es

Stacking Jacobians Properly in Stereo Visual Servoing

Most visual servoing applications are concerned with geometrically modeled objects. In this paper, the problem of controlling a motion by visual servoing around an unknown object with a stereovision system is addressed. The main goal is to move the end-effector around the object in order to observe several viewpoints of the object for other tasks, e.g. inspection or grasping. The present work uses the well-known imagebased visual servoing approach with a point, but the importance of the relationship between the end-effector and camera frames is clarified and emphasized. This relationship is needed for properly stacking the Jacobians or interaction matrices of each camera. A comparison with a visual servoing approach with a direct stacking of the Jacobians is presented. The centroid of a region, obtained by color segmentation, is used to move around the observed object. Experiments are developed on a PA-10 robot connected to a real time stereovision system, with two cameras mounted on the end-effector. Experimental results demonstrate the importance of a proper definition of the stacked Jacobians, to avoid undesired motions in the servoing task. Particularly, when turning around an unknown object, undesired motions on roll angle of the stereovision system can be avoided.

Introduction

Visual servoing applications have grown significantly since the last decade. Though in the first approaches, the scene observed by the camera was relatively simple, many works concerning unknown and complex objects have been developed recently.

Some methods require an initial learning step to obtain information characterizing the interaction between the sensor apparatus and the environment [START_REF] Deguchi | Image based simultaneous control of robot and target object motions by direct image interpretation method[END_REF][START_REF] Jägersand | Experimental evaluation od uncalibrated visual servoing for precision manipulation[END_REF]. In this case, it is necessary to get information from a predefined trajectory. To do so, the method proposed by Berry et al. [START_REF] Berry | Real time visual servoing around a complex object[END_REF] performs automatic motions around an unmodeled object in order to learn this interaction.

In this paper, the problem of moving around an object is addressed: no geometric model is needed and a stereovision system is used. Many works have been done in the field of visual servoing using a stereovision system [START_REF] Crowley | Comparison of kinematic and visual servoing for fixation[END_REF][START_REF] Hager | Robot hand-eye coordination based on a stereo vision[END_REF][START_REF] Maru | Manipulator control by visual servoing with stereo vision[END_REF]. Most of them use the stereovision system to recover the depth. Others use the epipolar constraint in order to execute the point to point matching process.

Recent developments in stereo-visual servoing have proved the theoretical soundness of the approach. Lamiroy et al. [START_REF] Lamiroy | Controlling robots with two cameras: How to do it properly[END_REF] present a solution to integrate the epipolar constraint directly in the control law. They rewrite the minimization problem under the optimization of the epipolar constraint, and show that, in the noiseless case and using rigid control points, both the classical and constrained approaches are identical.

Malis et al. [START_REF] Malis | Multicameras visual servoing[END_REF] have formalized a multi-cameras visual servoing approach. They consider a system with N cameras which delivers a set s = (s

T 1 s T 2 • • • s T N ) T of sensor signals (dim(s i ) = n i ).
Assuming that each sensor signal can control all the end-effector d.o.f m (m ≤ n i ), they rewrite the global interaction relationship as:

ṡ =      L 1 0 • • • 0 0 L 2 • • • 0 . . . . . . . . . . . . 0 0 • • • L N           1 M e 2 M e . . . N M e      e v = LM e e v (1)
where L i represents the interaction matrix (or Jacobian matrix) of the i th camera, and i M e the transformation matrix between the velocity of the i th camera and the robot end-effector velocity. They define a global task function e = Cṡ = N i=1 k i e i as a weighted mean of the task function relative to each camera, and demonstrate some properties in convergence and stability.

In our work, this scheme is applied to a stereo rig composed of two cameras. We show that less d.o.f. can be controlled, by defining an appropriate hybrid task.

The paper outline is as follows: first, the modeling aspect is developed; secondly, the task-function approach is applied to obtain the control law. Next, results obtained at video rate with our robotic platform vision system are shown. Finally, some conclusions and possible extensions are presented.

Modeling

The main goal of this work is the positioning of the end-effector with respect to a fixed object, and to perform motions around it. A stereo rig is rigidly attached to the end-effector. No model of the object is known a-priori, thus limiting the choice of features for tracking [START_REF] Berry | Real time visual servoing around a complex object[END_REF]. Nevertheless, the position of the cameras in the end-effector frame and its intrinsic parameters are roughly known, without any special calibration.

The proposed approach uses 2D features extracted from regions in the image, segmented by color. Such features can be the centroid of the region, its size, the aspect ratio, and the angle of its first axis of inertia.

In this first work, only a point feature (the centroid of the blob) is used. Its observation by the stereo pair mounted on the end-effector makes possible the 3D positioning task. At the same time, the 3 remaining d.o.f are used for a secondary task, e.g. moving the end-effector around the object while keeping the fixed relative position.

Our stereovision system is composed of two parallel cameras. Figure 1 illlustrates the case when both cameras observe a 3D point P .

Let us define F e as the Cartesian frame attached to the end-effector, F l as the frame attached to the left camera, and F r as the frame attached to the right camera.

The feature vector is defined as s = (u l , v l , u r , v r ) T where (u l , v l ) T and (u r , v r ) T are the image coordinates of the point, observed by the left and right cameras respectively.

First control law: real stereo

Let e v be the kinematic screw applied to the robot end-effector. According to the multi-cameras visual servoing formulated in equation [START_REF] Berry | Real time visual servoing around a complex object[END_REF], the relationship between the time derivative of the feature vector and the end-effector screw is

ṡ = L l l M e L r r M e e v = L st e v (2)
where • L l and L r are the interaction matrices relative to the left and right cameras respectively, defined by (i = r or l) :

- F u z 0 u i z u i v i F v -F u - u 2 i F u v i F u F v 0 - F v z v i z F v + v 2 i F v - u i v i F u - u i F v F u
• l M e and r M e are the transformation matrices of the screw between the left and right camera frames and the end-effector frame. Given frames F e and F i , the relationship between the screws is

i v = i M e e v (3)
where the transformation matrix i M e is

i M e = i R e i t e × i R e O 3 i R e (4)
Though the resulting interaction matrix L st is the same as that obtained by Maru et al. [START_REF] Maru | Manipulator control by visual servoing with stereo vision[END_REF], our development is somewhat simpler and it is easier to generalize to other configurations of the cameras.

Second control law: stacked-mono

It is widely accepted in monocular visual servoing that the interaction matrix (the jacobian) of a set of points is constructed by stacking every interaction matrix of each single point.

One is tempted to apply this method directly to stereo vision, and thus, a simpler interaction matrix is obtained, if both matrices l M e and r M e are neglected.

In this case, the fusion of the sensor information is processed directly in the interaction matrix despite of the frame where they are defined. So, a more classical form is obtained:

ṡ = L l L r e v = L sm e v (5)
The interaction matrix is similar to that obtained by stacking the matrices of several points, hence the name of the control law.

Theoretical comparison

It can be shown that the null space of the stereo interaction matrix L st is always spanned by the three vectors

        0 z -y 1 0 0                 -z 0 x 0 1 0                 y -x 0 0 0 1         (6)
which are in fact the same for the null space of the interaction matrix associated to a 3D point p e = (x, y, z) T in the robot end-effector frame

L 3D = -I 3 [p] × =   -1 0 0 0 -z y 0 -1 0 z 0 -x 0 0 -1 -y x 0   (7)
The interaction matrix L st can be rewritten as:

L st = L st 3D L 3D (8)
where the matrix L st 3D is defined as:

L st 3D =   ∂s l ∂ l p l R e ∂sr ∂ r p r R e   (9)
thus it is composed of the partial derivatives of the image points with respect to the velocity of the 3D point.

The matrix is full rank, i.e., its null space is empty, since there is no motion of the 3D point which leaves both images unaffected. Indeed, only the motion along the projection ray leaves an image constant, but, since the cameras are not coincident, their projection rays are obviously different. Consequently, the null space of matrix L st is the same as that of L 3D .

In our experiments, only one point is used, thus 3 d.o.f. of the end-effector remain free for moving around the object.

In the second control law, excepting in some singular cases, the dimension of the null space of the interaction matrix L sm is always 2. The reason is that the 3D relationship between both image points has been lost. As a consequence, in the equilibrium state (when the 3D point is centered in regard with the stereovision sensor apparatus), only 2 d.o.f. are available to perform motions around the object.

We show in the experiments that an undesired rotation around the z axis is present as a side-effect, due to the wrong dimension of the null space of the interaction matrix.

Control

The control law used in this study is based on the Task function formalism [START_REF] Samson | Robot Control. The task function approach[END_REF], firstly applied to visual servoing by Espiau et al. [START_REF] Espiau | A new approach to visual servoing in robotics[END_REF]. In this approach, the control is directly specified in terms of regulation in the image. It may be noted that this approach has the advantage of avoiding the intermediate step of the 3D estimation of the target with regard to the end effector [START_REF] Martinet | Vision based control law using 3d visual features[END_REF][START_REF] Wilson | Relative end-effector control using cartesian position based visual servoing[END_REF]. For a given robotics task, a target image is built, corresponding to the desired position of the end effector with regard to the environment. If the image jacobian is not full rank (number of d.o.f > number of independent visual features), it is possible to use an hybrid task. In an hybrid task, the primary task e 1 maintains a visual constraint during the trajectory, while the secondary task e 2 can be seen as representing a minimization of a secondary cost h s .

A global task function e is then defined as:

e = W + e 1 + γ(I n -W + W) ∂h s ∂r T ( 10
)
where W + and (I n -W + W) are two projection operators which guarantee that the camera motions due to the secondary task are compatible with the regulation of s to s * . W is a full rank matrix with the same null space as that of the interaction matrix. The parameter γ is used to tune the preponderance between the primary and the secondary task.

Considering a motionless environment, the control law has the following expression:

v = -λe -γ(I n -W + W) ∂ ∂t ∂h s ∂r T ( 11
)
This control law is applied to both presented modelings, where matrix W is defined as follows for each control law:

Real stereo Stacked-mono W L * 3D L * sm
The symbol * is used to precise that the corresponding expression is evaluated at the equilibrium situation.

The stereo system consists of two NTSC color cameras mounted on the end-effector of a Mitsubishi PA-10 manipulator. Cameras are coarsely positioned, being approximately mounted with the same orientation, and at equal distances from the end-effector's origin. No calibration procedure has been used.

A video-rate color segmentation system is used which extracts colored regions from an image and delivers the coordinates of its centroid, its aspect ratio, and the orientation of its major axis of inertia.

Each camera is connected to one of such image processing systems. Though the system is capable of sustaining a 60 Hz frame rate, only even or odd frames are used, due to alignment problems with interlaced frames, thus reducing the frame rate to 30 Hz.

An overview of the stereovision system is depicted in Fig. 2. Though our setup is equivalent to the presented by Maru et al. [START_REF] Maru | Manipulator control by visual servoing with stereo vision[END_REF], it must be noted that our task is under-constrained, and a secondary task has been defined for the motion around the object. Their object is modeled as a square and the feature vector is composed of four points (the corners).

Estimation of depth

In Fig. 1, f represents the focal length. We can write:

sin(α) = u l Fu = x l z l sin(β) = ur Fu = xr zr ( 12
)
and finally:

x l = x r + b ( 13
)
where F u = f du is the focal length along of the u axis. With the relations 12 and 13, the depth of the observed point can be estimated as:

z = z r = z l = b. F u u l -u r ( 14
)
As a result, it is very simple to show one of the main advantages of a stereovision system in regard with a monocular vision system: the estimation of the depth. This estimation can be provided by:

ẑ = b. F u u l -ur
The Mitsubishi PA-10 manipulator has 7 d.o.f and is mounted on a mobile platform (XR4000 from Nomadic Inc.). In this implementation, the arm is only used and controlled as a Cartesian frame with 6 d.o.f.

The experimentation has been split in two steps. In the first step, a positioning task is executed during 300 iterations (one iteration corresponds to 33 ms). Then, the second step consists in a secondary task using a sinusoidal wave translation signal in x and y direction (T x = A x .ω x .cos(ω x .t) , T y = -A y .ω y .sin(ω y .t) with A x = A y = 0.6 m and ω x = ω y = 0.2π rd/s). The aim of the secondary task is to describe a circle trajectory on a sphere while fixing the object centered in the image plane at a given distance.

The following table shows the different parameters (intrinsic and extrinsic) of both cameras, which have been roughly estimated:

F u F v b 300 450 118mm
The gains in the control laws are fixed to 1 for λ and 1/5 for γ.

Positioning task

In this paragraph, some results obtained in the real context when using both laws (real stereo and stackedmono) are compared. The curves or graphs on the left side correspond to the stacked-mono control law, while those on the right side correspond to the real stereo. The reference feature to reach at the equilibrium is arbitrary fixed to s * = (40, 0, -40, 0)

T .

Figure 3 presents the servoing task during all the experimentation (both positioning and moving around the object).

Figure 4 gives the trajectories of the 2D points (left and right) in the same image plane.

Figures 5,6, and 7, present the servoing task only during the positioning task. The sensor signals and the control vector have an exponential decay, but there is a persistent offset at the equilibrium. In fact, the sensor apparatus is not well calibrated, and the equilibrium sensor vector has been defined without taking into account this fact. To solve this problem, one way is to learn the desired sensor vector at the equilibrium with the uncalibrated sensor. This is the reason why, in the stacked-mono approach, there exists a persistent rotation velocity in z direction (Ω z ). However, in the real stereo, this motion is cancelled due to the proper choice of matrix W.

Secondary task

Summary and Conclusions

This paper has presented for the first time the application of stereo vision in an under-constrained visual servoing task. It has been shown that problems can appear if the relationships between frames are not properly taken into account. Particularly, it concerns some uncontrolled motions which can bring the robot in its joints limits.

On the contrary, when the modeling is correctly done, the use of a 3D point observed by a stereo vision system is sufficient to perform motions around an unknown and complex object. The choice of the centroid of the blob in both image planes is not the ideal invariant feature to perform this kind of task. As explained in [START_REF] Berry | Real time visual servoing around a complex object[END_REF], the center of a global bounding box is more relevant when using complex object. Future developments will concern the extension of the approach to a set of points, and other visual features (orientation and size of the blob).

First theoretical studies indicate that, when using two points in stereo, the null space of matrix L st remains the same as that of L 3D , which corresponds to a rotation around the line joining both points. With additional points, the null space is empty, thus we are interested in finding out which other properties are shared by both interaction matrices.

Figure 1 :

 1 Figure 1: Stereovision: Case of a 3D Point.

Figure 2 :

 2 Figure 2: Overview of the stereovision system.

Figure 3 :Figure 4 :

 34 Figure 3: Sensor signals during the whole task

Figures 8 , 9 ,Figure 5 :Figure 7 :

 8957 Figures 8,[START_REF] Martinet | Vision based control law using 3d visual features[END_REF], and 10, present the servoing task during the secondary task. The sensor signals do not remain in their equilibrium values: an offset due to the tracking error is present. In addition, in figures 9 and 10 the effect of the secondary task can be verified: the translation velocities T x and T y produce rotation velocities on Ω y , Ω x and a translation velocity on T z (this corresponds to the vectors v 1 = ( 0, z, -y, 1, 0, 0 ) T v 2 = ( -z, 0, x, 0, 1, 0 ) T of the kernel of the image jacobian).Finally, in figure 10 (right side) the effect of the

Figure 8 :Figure 10 :

 810 Figure 8: Evolution of the errors

Acknowledgement

This work is partially funded by the Valencian Government under grant GV99-67-1-14, and a grant for a temporal stay of P. Martinet at Jaume-I University.