K.-S Lin

Ruey-Bing Li

Frank Lee

Li-Cheng Lou

Su-Wei Chiu

K.-S Lin

Kuen-Song Lin

Synthesis, characterization, and application of carbon cubes

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

Carbon nanotubes (CNTs) synthesized in the arcdischarge apparatus was first discovered by Iijima in 1991 as nested structures of concentric shells, which stimulated a worldwide research effort to improving their synthesis, structure determination, and physical properties calculation and identification [START_REF] Iijima | Helical Microtubules of Graphitic Carbon[END_REF]. The unique carbon nanotubes are predicted to possess novel mechanical and electrical properties since their regular, periodic structure, and quantum size [START_REF] Tong | Field Emission from Aligned Multi-walled Carbon Nanotubes[END_REF][START_REF] Dillon | Storage of Hydrogen in Singlewalled Carbon Nanotubes[END_REF][START_REF] Guo | Catalytic Growth of Single-walled Nanotubes by Laser Vaporization[END_REF]. These properties suggest enormous potential applications for CNTs include such as novel nanoscale electronic devices, tips for scanning probe microscopy, hydrogen storage media, reinforcing materials for carbon matrix composites, and catalyst supports [START_REF] Dillon | Storage of Hydrogen in Singlewalled Carbon Nanotubes[END_REF][START_REF] Guo | Catalytic Growth of Single-walled Nanotubes by Laser Vaporization[END_REF][START_REF] Hone | Thermal Conductivity of Single-walled Carbon Nanotubes[END_REF][START_REF] Dresselhaus | Physics of Carbon Nanotubes[END_REF]. Realization of these commercial scale uses will require scaleable, economical synthesis methods. In the recent years, methods for synthesizing metalcatalyzed CNTs has been pursued by a variety of methods including laser or arc evaporation of a metal praphite composite target, hydrocarbon pyrolysis or CO disproportionation on a metal catalyst in high temperatures [START_REF] Jiang | A Catalytic-assembly Solvothermal Route to Multiwall Carbon Nanotubes at a Moderate Temperature[END_REF][START_REF] Wang | A Novel Route to Multiwalled Carbon Nanotubes and Carbon Nanorods at Low Temperature[END_REF][START_REF] Liu | Large-scale Synthesis of Carbon Nanotubes by an Ethanol Thermal Reduction Process[END_REF][START_REF] Sun | Functionalized Carbon Nanotubes: Properties and Applications[END_REF][START_REF] Liu | Single-source Precursor Route to Carbon Nanotubes at Mild Temperature[END_REF]. The laser or arc evaporation provides little control over process condition, thus producing many undesired by-products, a low CNTs yield, and posing physical separation challenges [START_REF] Li | Adsorption of Cadmium (II) from Aqueous Solution by Surface Oxidized Carbon Nanotubes[END_REF][START_REF] Li | Lead Adsorption on Carbon Nanotubes[END_REF][START_REF] Hamon | End-group and Defect Analysis of Soluble Single-walled Carbon Nanotubes[END_REF][START_REF] Branca | Characterization of Carbon Nanotubes by TEM and Infrared Spectroscopy[END_REF][START_REF] Zhang | Effect of Chemical Oxidation on the Structure of Single-walled Carbon Nanotubes[END_REF]. In contrast, high temperature furnaces offer a high degree of control over the hydrocarbon identity, temperature, and reaction time, all of which can be optimized for product purity [START_REF] Chen | Solution Properties of Singlewalled Carbon Nanotubes[END_REF][START_REF] Wong | Covalently-functionalized Single-walled Carbon Nanotube Probe Tips for Chemical Force Microscopy[END_REF][START_REF] Bahr | Functionalization of Carbon Nanotubes by Electrochemical Reduction of Aryl Diazonium Salts: A Bucky Paper Electrode[END_REF][START_REF] Xing | Sonochemical Oxidation of Multiwalled Carbon Nanotubes[END_REF][START_REF] Mickelson | Fluorination of Single-wall Carbon Nanotubes[END_REF]. However, these methods are energy intensive and produce relatively low quantities of CNTs. In addition, neither method is readily scaleable for bulk commercial production.

On the contrary, a novel and innovatory catalyticassembly benzene-solvothermal route to MWCNTs by using a reduction of hexachlorobenzene on metallic K in the presence of Co/Ni catalyzer in a autoclave has been used. Comparatively the reaction temperature of this CNTs synthesis system is much lower than others. The valency and fine structure of Co and Ni atom used as the catalyzer precursor of CNTs formation have also not been well studied. The concurrence of nucleation of the Co/Ni metal nanoparticles and CNTs growth within a reactive hydrocarbon atmosphere creates a complex transient chemical environment, making it difficult to study the inception and growth processes in CNTs synthesis.

By using XANES/EXAFS spectroscopy, the valency and fine structure of these complex metals in the synthesis of CNTs has been investigated. The XANES/EXAFS spectra offer the basic knowledge of understanding the oxidation states and fine structures of Co and Ni atom in the complex catalytic precursor to a further study on the distribution/dispersion and interaction mechanism of these metals. XANES/EXAFS spectroscopy is also an excellent technique for characterizing the valency and local structure of Co/Ni metals in catalyzer precursor with short-range order [START_REF] Vlaic | Characterisation of Heterogeneous Catalysts by EXAFS[END_REF][START_REF] Conradson | Application of X-ray Absorption Fine Structure Spectroscopy to Materials and Environmental Science[END_REF][START_REF] Koningsberger | XAFS Spectroscopy in Catalysis Research: AXAFS and Shape Resonances[END_REF][START_REF] Lytle | The EXAFS Family Tree: a Personal History of the Development of Extended X-ray Absorption Fine Structure[END_REF]. Thus, the main objective of the present study was to investigate the fine structures, oxidation states, fine structures or surface chemical modification of MWCNTs and Co/Ni atoms dispersed in the catalyzer precursor of MWCNTs synthesis by TEM, XRPD, EDS or XANES/EXAFS spectroscopy. The chemical-modified with concentrated H 2 SO 4 /HNO 3 solution of MWCNTs used for the adsorptive enhancement of Pb(II) removal was also studied.

EXPERIMENTAL

The MWCNTs synthesis was conducted in a batch system. 100 mL of benzene was placed into a 250 ml PTFE-lined stainless steel 316 autoclave, and then 15 grams hexachlorobenzene and 20 grams metallic potassium were added. After that, 15 mL of benzene was added until approximately 70-80% of the autoclave's capacity was filled. Finally, 700 mg of catalyzer precursor were also added. The catalyzer precursor was prepared by dissolving one gram of CoCl 2 6H 2 O and NiCl 2 6H 2 O mixture (Co/Ni = 1 in mole ratio) in 100 mL of absolute ethanol, followed by drying in an 353 K and calcining at 423 K in a flowing air. All the chemicals used are highpurity (ACS grade). The sealed autoclave was heated at 503-623 K for 8-12 hr, and then cooled to room temperature in the furnace naturally. The obtained samples were repeatedly and sequentially washed with absolute ethanol, dilute acid, de-ionized double distilled water to remove the residual impurities, such as chlorides and remaining catalyzer, and finally vacuum-dried at 343-353 K for 6-10 hr.

In order to more thoroughly examine the adsorptive efficiencies of 50-100 mg/L Pb with monochromatic CuK α radiation (MAC Sience, MXP18). The XANES/EXAFS spectra were collected at the Wiggler beamline 17C1 at the National Synchrotron Radiation Research Center (NSRRC) of Taiwan. The electron storage ring was operated with an energy of 1.5 GeV and a current of 100-200 mA. A Si(111) DCM was used for providing highly monochromatized photon beams with energies of 1 to 15 keV and resolving power (E/ Δ E) of up to 7000. Data were collected in fluorescence or transmission mode with a Lytle ionization detector [START_REF] Lytle | The EXAFS Family Tree: a Personal History of the Development of Extended X-ray Absorption Fine Structure[END_REF] for Co (7709 eV) and Ni (8333 eV) K edge experiments at room temperature. The photon energy was calibrated by characteristic preedge peaks in the absorption spectra of Co and Ni standards. The raw absorption data in the region of 50 to 200 eV below the edge position were fit to a straight line using the leastsquare algorithms. The fitted pre-edge background curves were extrapolated throughout all data range, and subtracted and normalized to minimize the effect of the MWCNT sample thickness. The near-edge structure in an absorption spectrum covers the range between the threshold and the point at which the EXAFS begins [START_REF] Vlaic | Characterisation of Heterogeneous Catalysts by EXAFS[END_REF][START_REF] Conradson | Application of X-ray Absorption Fine Structure Spectroscopy to Materials and Environmental Science[END_REF][START_REF] Koningsberger | XAFS Spectroscopy in Catalysis Research: AXAFS and Shape Resonances[END_REF]. The XANES extend to an energy of the order of 50 eV above the edge. The k 2 -weighted and EXAFS spectra were Fourier transformed to R space over the range between 2.5 and 12.5 Å -1

. The EXAFS data were analyzed by using the UWXAFS 3.0 program and FEFF 8.0 codes [START_REF] Vlaic | Characterisation of Heterogeneous Catalysts by EXAFS[END_REF][START_REF] Conradson | Application of X-ray Absorption Fine Structure Spectroscopy to Materials and Environmental Science[END_REF][START_REF] Koningsberger | XAFS Spectroscopy in Catalysis Research: AXAFS and Shape Resonances[END_REF][START_REF] Lytle | The EXAFS Family Tree: a Personal History of the Development of Extended X-ray Absorption Fine Structure[END_REF].

RESULTS AND DISCUSSION

The TEM microphotographs were used to investigate the morphologies, crystallinity, and microstructure of MWCNTs synthesized by using Co/Ni catalyzer precursors with metallic K. Morphological observations of MWCNTs synthesized by using Co/Ni catalyzer precursors were shown in Figure 1. Figure 1(a) showed the MWCNTs have a bamboo-like structure with an average length of 1500 nm. The inner diameter of MWCNTs is 20 nm and outer diameter 45 nm in average. The inner tube is subdivided by single-or multi-graphite layer, which may be formed by the surface diffusion of carbon cluster on the larger Co/Ni catalytic nanoparticles across the wall of carbon nanotubes. The MWCNTs having irregular-shaped were showed in Figure 1(b). The MWCNTs without amorphous carbon coating typically have open ends when were acid-or ultrasonic-purified previously.

Figure 2 represented the metallic K was found in MWCNTs synthesized by using Co/Ni catalyzer precursors at T = 503-623 K for 12 h identified with energy dispersive spectrometer (EDS). The postulated equation and reaction mechanism of MWCNTs synthesis may be described as following: n C 6 Cl 6 + n K → 6n KCl + poly aromatic hydrocarbons (+ benzene at 503-623 K) → MWCNTs (+ Co/Ni for 8- The XRPD pattern shown in Figure 3 indicated that the abstraction of Cl from hexachlorobenzene and formation of the KCl precipitate may be involved in the early stage of the synthesis process of MWCNTs. Since KCl powders can be easily dissolved in water, the high removal efficiency of KCl from MWCNTs samples by washing with water was found (shown in Figures 3 (b The EXAFS data of Co/Ni precursor residues revealed that the nanophase metallic Co or Ni particles had a central Co (or Ni) atom of a coordination number of 2.92 ± 0.05 (or 5.96 ± 0.05) primarily Co-Co with a bond distance of 2.49 ± 0.05 Å (or 2.48 ± 0.05 Å ). These results may offer a further explanation of how the yield and structure of MWCNTs formed by catalytic-assembly benzene-solvothermal route depend on the species of the Co/Ni metal catalysts. However, this result combining with TEM images (Figures 1(a) and(b)) might indicate that some MWCNTs having bending structure, and at the close end of the tubes, the catalytic Co/Ni metal particles exist clearly, which may suggest that the Co/Ni metal particles are responsible for the nucleation of the MWCNTs. The concurrence of nucleation of the Co/Ni metal nanoparticles and MWCNTs growth within a reactive hydrocarbon atmosphere (e.g. benzene) creates a complex transient chemical environment, making it difficult to study the inception and growth processes in MWCNTs synthesis.

Since the unique adsorptive properties of carbon nanotubes, it suggests enormous potential applications for MWCNTs on environmental technologies. Adsorptive removal of toxic metals such as Pb(II) cations by surfacemodified MWCNTs is an appealing pollution control and metallic resource recovery alternative. Since the sake of chemical decoration and modification of K-MWCNTs, the first cap opening of MWCNTs may be finished and therefore the active functional groups are observed. Laboratory-scale experiments were carried out to provide information concerning the feasibility for Pb(II) adsorption system of MWCNTs, and determined if further developments would be warranted.

In order to more thoroughly examine the adsorptive efficiencies of 50-100 mg/L Pb(II), different oxidants of chemical modifications of MWCNTs surfaces for adsorption enhancement included HNO 3 , KMnO 4 or Na 2 S processes were performed. Experimentally, the Pb(II) adsorptive efficiencies of K-MWCNTs were KMnO 4 > HNO 3 > Na 2 S modification processes in series. Interestingly, these methods are all effective in opening the caps of MWCNTs but are very different in oxidation ability.

The surface roughness and abundance of effective functional groups such as OH, COOH or NO on the MWCNTs after surface modification also vary. Since using KMnO 4 in alkali solution as a moderate oxidant, the caps of MWCNTs may be not effectively opened. Similarly, dilute HNO 3 solution may purify the MWCNTs and etch the nanotubes from the terminal and the defects on the nodes or sidewalls. However, the relatively mild oxidant of HNO 3 solution may not able to generate abundant NO, OH or COOH functional groups eventually.

The experimental results of higher Pb(II) adsorptive removal efficiency of MWCNTs indicated that the KMnO 4 may provide abundant and more effective -OH or COOH functional groups on MWCNTs. Moreover, the MWCNTs possessed COOH functional groups on the surface of defect structures during chemical oxidation of HNO 3 and the -NO functional groups were observed on the K-MWCNTs surface of defect structures.

CONCLUSIONS

The

Figure 1

 1 Figure 1 TEM images of (a) bamboo-like and (b) irregular-shaped of MWCNTs synthesized by using Co/Ni catalyzer precursors with metallic K at T = 503-623 K for 12 hr.

Figure 2

 2 Figure 2 EDS measurement of MWCNTs synthesized by using Co/Ni catalyzer precursors with metallic K at T = 503-623 K for 12 hr.

Figure 3

 3 Figure 3 XRPD patterns of (a) KCl standard, (b) unwashed MWCNTs with KCl crystals, (c) washed MWCNTs with KCl contaminants synthesized by Co/Ni catalyzer precursors at T = 503-623 K for 12 h.

  ) and (c)). KCl was the main species and over 95% of K + cations was formed as KCl in the synthesis process of MWCNTs by using Co/Ni catalyzer precursors at at T = 503-623 K for 8-12 hr.Since the valency and fine structure of Co and Ni atom used as the catalyzer precursor of MWCNTs formation have not been well studied, therefore the catalytic redox mechanisms effected by the Co/Ni catalyzer precursor in the growth of MWCNTs may be determined by using XANES and EXAFS spectra.

Figure 4

 4 Figure 4 (a) NANES of Co/Ni precursor residue samples (solid lines) compared with Co(0,II) or Ni(0,II) powder standards and (b) Fourier transform (FT) of the metallic Co and Ni K-edge EXAFS of the carbon nanotubes synthesized by using Co/Ni catalyzer precursors at T = 603 K for 8-12 hr. The best fitting of the EXAFS spectrum is expressed by the dotted lines. Bond Distance(Å) FT Magnitude (a.u.) Intensity (a.u.) 2θ (degree)

Figure 5

 5 Figure 5 The adsorption curves of 100 mg/L Pb(II) on surface-modified MWCNTs with (a) KMnO 4 , (b) HNO 3 , (c)Na 2 S, and (d) non-modification procedures.

  potential synthesis route of MWCNTs with reductive metallic K of catalytic hexachlorobenzene-thermal routes in the presence of Co/Ni catalyst precursors at 503-623 K for 12 hr was investigated. The characteristics identification of as-synthesized MWCNTs and environmental application of lead cations adsorptive removal by MWCNTs were also studied. Experimentally, TEM microphotos showed the MWCNTs have a bamboolike structure with an average length of 1500 nm. The inner diameter of CNTs is 20 nm and outer diameter 45 nm in average. The XRPD patterns indicated that the abstraction of Cl from hexachlorobenzene and formation of the KCl precipitate may be involved in the early stage of the synthesis process of MWCNTs. From the XANES spectra, the Co/Ni catalyst precursors of the MWCNTs syntheses were all metallic Co or Ni species. Furthermore, the EXAFS spectra of Co/Ni precursor residues revealed that the metallic Co or Ni nanoparticles had a central Co (or Ni) atom of a coordination number of 2.92 ± 0.05 (or 5.96 ± 0.05) primarily Co-Co with a bond distance of 2.49 ± 0.05 Å (or 2.48 ± 0.05 Å). Finally, in the view of environmental application, the Pb(II) adsorptive efficiencies of MWCNTs were KMnO 4 > HNO 3 > Na 2 S modification processes in series.


Umberto Arena
email: umberto.arena@unina2.it

Maria Laura Mastellone

PRODUCTION OF MULTI-WALL CARBON NANOTUBES BY MEANS OF FLUIDIZED BED PYROLYSIS OF VIRGIN OR RECYCLED POLYMERS

The paper studies in depth a new technique for mass production of MWCNTs that is based on thermal cracking of polymers in a solid-gas fluidized bed reactor, operated under specific thermal and hydrodynamic conditions. The paper provides information about the phenomenology of interactions between the bed material and the polymer particles injected into the fluidized bed reactor, which in turn affect the mechanism of formation of MWCNTs. Results obtained with different reactor temperature and bed materials are reported in terms of yield and quality of obtained MWCNTs, all characterized by TG-DTA, SEM and TEM microscopy and Raman spectroscopy. It is noteworthy that high-quality MWCNTs were obtained from virgin or recycled polyolefins as well as from recycled polyethylene terephtalate.

INTRODUCTION

A great effort has been recently devoted to the synthesis methodology and the production technology of carbon nanotubes (CNTs), since the actual high cost of production limits their use in the industrial market: there is a general accordance that as new techniques to fabricate CNTs on a large scale emerge, they will find their way in a relevant number of applications [START_REF]Carbon Nanotubes[END_REF][START_REF]Nanoscience and nanotechnologies: opportunities and uncertainties[END_REF][START_REF] Ebbesen | Carbon Nanotubes Preparation and Properties[END_REF]. Present methods for production of CNTs utilize graphite, carbon monoxide or hydrocarbons for the construction of the carbon skeleton of CNT, but all these methods usually require critical operating conditions that are very expensive, and then strongly restrict the fields of applications of these nanostructures [START_REF]Carbon Nanotubes[END_REF][START_REF] Ebbesen | Carbon Nanotubes Preparation and Properties[END_REF]. A number of procedures to obtain MWCNTs, has been recently proposed. In particular, the catalytic chemical vapour deposition carried out by feeding gaseous hydrocarbons in a continuous bench scale reactor has been described [START_REF] Wang | [END_REF] as a process that could potentially give mass production of MWCNTs at reasonable costs, even though there is still the problem of keeping both catalysts and CNT product, fluidized during the whole growing period, within the reactor. Other Authors [5][6][7] claim the possibility to obtain carbon nanotubes by means of different high-temperature thermolysis processes, generally carried out under reducing atmosphere, and applied to carbonaceous substrates (as bulk polymers) that fill metallic templates.

This paper reports new experimental results related to a new method for MWCNT production by means of a continuous pyrolysis process of virgin or recycled polymers [START_REF] Arena | Polymer Degradation and Stability[END_REF]. The technique allows to obtain carbon nanotubes having quality similar to MWCNTs available on the market even when the starting materials were polymers coming from post-consumers waste collection and recycling. The reactor used is an atmospheric bubbling fluidized bed (BFB), i.e. a gas-solids contacting reactor in which a bed of solid particles are transformed into a fluidlike state trough suspension in a gas [START_REF] Kunii | Fluidization Engineering[END_REF]. Compared to other system of gas-solids contacting systems, fluidized beds have some rather unusual and useful properties: the heat and mass transfer between gas and particles are very high when comparing with those of other gas-solid reactors; the good quality of contact between gas and solids reactants increases their fractional conversions; the rapid and good mixing of solids leads to almost uniform isothermal conditions throughout the reactor, so allowing a reliable process control [START_REF] Arena | Pyrolysis and Gasification of Solid Wastes in Fluidized Bed Reactors[END_REF][START_REF] Arena | chapter "Fluidized Bed Pyrolysis of Plastic Wastes[END_REF].

EXPERIMENTAL

The tested materials were recycled polymers (polyethylene, PE, polypropylene, PP, polyethylene terephtalate, PET, and packaging derived fuel, PDF, which is a mixture of the three polymers).

The experimental apparatus is the bubbling fluidized bed reactor 110 mm ID, made of high-temperature austenitic stainless steel, which is schematically described in Figure 1. The reactor was equipped with a continuous plastics feeder located at the reactor top; pressure and temperature transducers located at the bed bottom and along the reactor; a conditioning line that addresses the produced gas to the on-line analyzers. Nitrogen was used to fluidize the bed. Throughout the duration of the experiment the on-line gas analyzers allowed the identification and measurement of the hydrocarbon concentrations in the gas phase. The composition of produced gas as well as the temperature and pressure inside the reactor were continuously monitored and recorded during the test by a data acquisition unit. Part of the pyrolysis gas was sent to the hood via a preferential route and occasionally collected by means of a sample bag, and part to the conditioning line connected to different analysers. Solid phase was continuously collected from the bottom and the top of the reactor: in particular, the tubes upstream the conditioning line were disassembled after each experiment in order to collect the solids and to re-establish a clean condition. The samples were then purified and quality of obtained MWCNTs was determined by using termogravimetrical analysis (TG), Raman spectroscopy, SEM and TEM microscopy [START_REF] Arena | Polymer Degradation and Stability[END_REF].

PHENOMENOLOGY OF INTERACTIONS BETWEEN POLYMERS AND BED MATERIAL

The peculiar interaction between polymer and bed materials was already studied by the authors [START_REF] Arena | [END_REF] and indicated as the phenomenon that promotes a very fast thermal cracking of polymer chain with the contemporaneous production of light hydrocarbons, aromatics, waxes and carbon nanotubes. Just after the injection into the hot fluidized bed, a very fast heat transfer mechanism leads the polymer pellet external surface up to the softening temperature. Several bed particles stick therefore on the plastic surface, forming an aggregate that has the external shell made of bed particles and the internal core made of polymer not yet molten [START_REF] Arena | [END_REF]. When the temperature further increases, the surface of the pellet reaches the melting temperature and the polymer flows throughout the bed particles of the external shell, so forming a uniform coating over and between them. The described progress of heating leads to the cracking of the carbon-carbon bonds of the polymer chain, i.e. to the beginning of a fast pyrolysis process, that starts when the polymer has already covered the bed particles. Therefore, it is not related to the whole molten pellet, but to a layer of polymer which coats and adheres on the external surfaces of single bed particles [START_REF] Arena | [END_REF]. The microphotographs reported in Figure 2 show the peculiar morphology of the polymer layer (Fig. 2A) that covers the bed material (Fig. 2B) and a detail of this layer, which is completely strewn by a sort of "hair" (Fig. 2C). Figure 3 supports this finding by showing an agglomerate formed by the "hair" grown on the particle surface. Investigation with other techniques (TEM, X-

A C B

Ray, Raman) demonstrated that these "hair" can be classified as nanotubes and nanofibers having diameters between 10 and 150nm [START_REF] Arena | Polymer Degradation and Stability[END_REF]. The pictures are related to particles collected from the bed during a test carried out with a recycled PET but they are very similar to those obtained with PE, PP or PDF mixture. Photographs 4A and B show MWCNT agglomerates formed on the surface of a sand particle, in a test carried out by pyrolysing virgin polypropylene, while photographs of Figure 5A and B show, again in a test carried out with virgin PP, a bush of MWCNTs and nanofibers that fills the space between some surface irregularities of an alumina particle and a detail of carbon nanotubes agglomerate. These microphotographs suggest that the MWCNT formation occurs on the bed particle surface, starting from the layer of polymer that fast cover the bed material just after the polymer particle injection into the reactor. A catalytic effect of the bed material surface could be possible, even though the substantial same behaviour was observed by using quartz and silica sand as well as alumina. The MWCNTs formed on the bed particle surface are then moved towards other areas of the bed or towards the reactor walls by the phenomenon of attrition [13], i.e. the mechanical abrasion of the bed materials connected to the continuous rubbing that bed particles operate each other as a consequence of their uninterrupted movement in the fluidlike state of the bed. The fluidizing gas is finally able to entrain the produced MWCNT agglomerates and carry them of the reactor together with flue gases.

EXPERIMENTAL RESULTS

A series of experiments were carried out with virgin PP and recycled PET in the described bubbling fluidized bed reactor by changing some operating parameters that can affect the quality and yield of obtained carbon nanotubes.

The set of utilized operating conditions is reported in Table 1. The fluidizing velocity was kept fixed even though its effect could be very important as a consequence of its influence on the released volatiles residence time in the reaction zone [START_REF] Mastellone | The Fifth World Congress on Particle Technology[END_REF]. The temperature range was fixed by taking into account that pyrolysis of polymers carried out in BFB at bed temperatures lower than 480°C led to defluidization of the with consequent shut down of the reactor [START_REF] Arena | [END_REF]. On the other hand, reactor temperature higher than 700°C could make more expensive the process due to the amount of required thermal energy without any advantages in terms of yields. The bed material was changed in order to investigate if it acts as a catalyst of the MWCNT formation. The material utilized in the largest part of experiments was quartz sand, even though silica sand and alumina were also used, with similar results (as already shown by Figures 4 and5).

The design of the apparatus was optimized in order to obtain the maximum solids collection efficiency. In fact, the MWCNT agglomerates, together with other carbonaceous structures, as well as tar and char, are drifted out of the freeboard region by means of fluidizing gas. The solids fraction was recovered from the internal reactor wall and from the external tubes connecting the reactor exit with the conditioning line. The total solids amount and the specific MWCNT yield found in the external tubes were much higher than those obtained from internal wall of the reactor (Table 2). This could be explained with the large presence of waxes and highboiling compounds stuck on the reactor wall that contaminate the MWCNTs, as it was demonstrated by a parallel investigation with TG measurements under inert and oxidizing conditions [START_REF] Mastellone | The Fifth World Congress on Particle Technology[END_REF]. Experiments have been also carried out by adding ferrous oxide as particles having a 20-350µm size range and a loading ratio Fe 2 O 3 /sand equal to 0.0069. This choice was based on two considerations: the individuation, by means of TEM/EDX investigation, of the presence of ferrous nanoparticles inside the carbon nanotubes; the known dehydrogenation effect of the ferrous catalysts during heavy hydrocarbons cracking. As it was unexpected, the presence of the ferrous particles led to a decreasing in the yield and quality of nanotubes, as shown during SEM and TEM investigations and as reported in Table 2. The "solids yield", y s , represents the ratio between the amount of total solids collected at the end of a test and the amount of PP or PET fed during the test. The "purified solids yield", y p , represents the ratio between the amount of purified solids obtained by the purification process of the solids collected for each test and the amount of these latter solids. The purified solids were then characterized by means of TG-DTA, SEM and TEM microscopy and Raman spectroscopy in order to verify if they really were MWCNTs and to estimate their purity. Figures 6 and7 report SEM and TEM photos of the purified solids samples of tests #1 and #2. They clearly show the presence of MWCNTs. On the contrary, the SEM/TEM investigation indicates the absence of MWCNTs at 700°C with quartz sand bed and at 600°C with a quartz sand/Fe 2 O 3 bed. In particular, at temperature equal 700°C there is a massive production of fullerenes instead of nanotubes, as showed in Figure 8. The experiment carried out by feeding PET at 600°C led to a mass production of MWCNTs as demonstrated by Raman investigation and by SEM and TEM pictures reported in Figure 9. The "MWCNT yield", obtained by multiplying the "purified solids yield" by the "solids yield", is reported in the last column of Table 2. The MWCNT yield can be used to estimate the rate of MWCNT that can be obtained in a continuous production that uses the proposed pyrolysis of polymers in BFB reactor.

CONCLUSIONS

The reported experimental results demonstrate that the proposed process allows the production of high-quality MWCNTs, in a relatively large quantity and at low cost by means of bubbling fluidized bed pyrolysis of polymers. The starting polymers can be virgin or recycled PE and PP, as already demonstrated [START_REF] Arena | Polymer Degradation and Stability[END_REF] A phenomenology of the MWCNT growth starting from a thin layer of polymer which covers the surface of bed particles is proposed and supported by several SEM images. The effect of bed material type (silica sand, quartz sand, alumina, ferrous oxide-sand mixture) is reported. In particular, the presence of ferrous oxide, even with small loading ratio, did not allow MWCNT formation while the other bed materials utilized in several experiments gave good results. It is not yet clear if the bed materials act as catalyst in some way or only as support for the polymer layer. The effect of temperature was investigated by carrying out experiments with polypropylene at 500, 600 and 700°C. The maximum MWCNT yield was obtained by performing an experiment at 600°C. At 700°C there is a predominance of other nano-structures as fullerenes. TG-DTA, SEM, TEM and, in some cases, Raman spectroscopy were used in order to confirm the carbon nanotubes presence in the purified solids. Some experiments carried with PET at 600°C demonstrated that a mass production of MWCNTs can be obtained also with this polymer.

Figure 1 .Figure 2

 12 Figure 1. The bubbling fluidized bed reactor used for carrying out all the experiments

Figure 5

 5 Figure 5 MWCNT agglomerates formed on the surface of bed particles in tests with PP in a bed of alumina.

Figure 4

 4 Figure 4 MWCNT agglomerates formed on the surface of bed particles in tests with PP in a bed of quartz sand.

Figure 3

 3 Figure 3 SEM picture of MWCNT agglomerate at the surface of a bed particle in a test with PET.

Figure 6 .

 6 Figure 6. MWCNTs obtained after purification of samples produced with PP at 500°C: (A) SEM picture; (B)TEM picture.

Figure 7

 7 Figure 7 MWCNTs obtained after purification of samples produced with PP at 600°C: (A) SEM picture; (B)TEM picture.

Figure 8 .

 8 Figure 8. Nanotubes and other nanostructures obtained after purification of samples produced with PP at 700°C: (A) SEM picture; (B)TEM picture.

Figure 9

 9 Figure 9 MWCNTs obtained with PET at 600°C: (A-B) SEM pictures of not purified samples; (C-D) TEM pictures of purified samples.

Table 2

 2 as well as PET or Experimental results of tests on MWCNT yield for the experiments with virgin PP. mixtures of these polymers.

	Test # Pol.	Bed material	Temperature,
				°C
	1	PP	Quartz sand	500
	2	PP	Quartz sand	600
	3	PP	Quartz sand/Fe 2 O 3	600
	4	PP	Quartz sand	700
	5	PET	Quartz sand	600
	Table 1 Operating conditions utilized for the
	experiments with virgin PP.

© TIMA Editions / ENS 2005 ISBN: 2-916187-02-2


Cédric Lachat

François Pellegrini

Cécile Dobrzynski

Gabriel Staffelbach

Fast parallel remeshing for accurate large-eddy simulations on very large meshes

Keywords: distributed mesh, parallel remeshing, large-eddy simulation, LES maillage distribué, remaillage parallèle, méthode LES

Numerical simulations on very large meshes, such as large-addy simulations (LES), cannot be performed without resorting to distributed-memory parallelism. For these methods, a sufficient precision can only be achieved by remeshing dynamically the areas that need it. Such a remeshing must therefore be performed in parallel. This paper presents the coarse-grain parallel remeshing method which has been devised and implemented in the PaMPA library for handling distributed meshes in parallel. This method is validated in the context of an industrial LES simulation on a helicopter turbine combustion chamber, on a mesh of more than one billion elements.

Introduction

Parallel remeshing methods can be categorized into two major families. The first one, the study of which started by the end of the 1990s, is that of fine-grained parallel methods. They aim at performing concurrently the elementary remeshing primitives, such as element subdivision, edge flipping, or node insertion or removal, on the same mesh. However, such a fine-grained parallelism is difficult to implement, due to the amount of fine-grained synchronization and locking that must be implemented in order to preserve mesh consistency when two neighboring elements are processed concurrently. Moreover, it implies using shared-memory parallelism, which is not scalable for a large number of processing elements. The second family, the study of which started in the early 2000s, overcomes these issues by considering coarse-grain parallelism only. Larger, non-overlapping areas of the mesh are defined, on which existing sequential remeshing libraries can be applied concurrently and independently. Such methods can be used either in a sharedmemory, or a distributed-memory context.

We consider this second approach to be more scalable, that is, to allow for the processing of larger meshes on a larger number of processing elements, while preserving parallel efficiency. In order to validate this assumption, a comprehensive software framework for handling distributed meshes and using sequential remeshers in a distributed memory context had to be created. This was the purpose of Cédric Lachat's PhD thesis [START_REF] Lachat | Conception et validation d'algorithmes de remaillage parallèles à mémoire distribuée basés sur un remailleur séquentiel[END_REF], which resulted in the creation of the PaMPA software [START_REF]Pampa: Parallel mesh partioning and adaptation[END_REF]. This software has been designed to fulfill the needs of numerical solver writers, by providing relevant abstractions of mesh components. The algorithms it implements have been designed to scale up to handle mesh sizes above a billion elements, to be used in frontier simulations. This paper is structured as follows. Section 2 provides an overview of existing methods used to perform remeshing using several processing elements. Section 3 presents the method that has been devised and implemented in PaMPA. Section 4 evidences the efficiency of PaMPA in an industrial context, for performing a scientific simulation on meshes remeshed up to above one billion elements. Then comes the conclusion.

State of the art

Two different reasons may motivate the use of remeshing during a numerical simulation. The first one is to reduce numerical inaccuracy induced by an inadequate mesh. Most often, this occurs when the mesh is too coarse. Yet, a too fine mesh may induce numerical error as well, and wastes too much compute time. The second reason is a changing geometry: moving bodies, deformations, etc. Sequential remeshers face physical limits which hinder their practical use. The hardest limit is that of available memory per processing element (PE), but run time also becomes a strong concern for very large meshes. This is why many authors investigated parallel remeshing. Sharedmemory parallelism is a straightforward way to reduce run time, at the expense of only small modifications to existing sequential remeshing algorithms, namely by adding locking mechanisms that prevent multiple PEs to process simultaneously the same or neighboring elements. However, shared-memory parallelism cannot scale to a large number of processing elements, because of memory bottlenecks. Moreover, all large-scale parallel architectures implement a distributedmemory model. Hence, on-the-fly remeshing of distributed meshes used in large-scale simulations requires distributed-memory parallel remeshing methods. In the case where the physical nodes of the parallel cluster comprise several cores, shared-memory parallelism can be used at the node level, but explicit message passing still has to be performed across machine nodes. There exist two main families of remeshing algorithms. The first one [START_REF] Castanos | The dynamic adaptation of parallel mesh-based computation[END_REF][START_REF] Laemmer | Parallel mesh generation[END_REF][START_REF] Oliker | Parallel tetrahedral mesh adaptation with dynamic load balancing[END_REF][START_REF] Oliker | Plum: Parallel load balancing for adaptive unstructured meshes[END_REF][START_REF] Chrisochoides | Parallel delaunay mesh generation kernel[END_REF][START_REF] Casagrande | Parallel mesh adaptation[END_REF][START_REF] Lawlor | Parfum: a parallel framework for unstructured meshes for scalable dynamic physics applications[END_REF], which may seem the most natural, involves fine-grain parallelization of existing sequential remeshing primitives and methods, such as Delaunay triangulation [START_REF] George | Delaunay triangulation and meshing: application to finite elements[END_REF], frontal methods [START_REF] Owen | A survey of unstructured mesh generation technology[END_REF] and edge subdivision [START_REF] Muthukrishnan | Simple algorithm for adaptive refinement of three-dimensional finite element tetrahedral meshes[END_REF]. However, in a distributed-memory context, synchronization across PEs amounts to exchanging messages across PEs which own neighboring elements, to make sure that, e.g., a node is not created on the same edge by several PEs at the same time. Such fine-grained communications usually lead to significant performance drops, due to the latency of the communication subsystem [START_REF] Maerten | Drama: A library for parallel dynamic load balancing of finite element applications[END_REF]. This is why a second family [START_REF] Coupez | Parallel meshing and remeshing[END_REF][START_REF] Basermann | Dynamic load-balancing of finite element applications with the drama library[END_REF][START_REF] Dobrzynski | Parallel mesh adaptation[END_REF][START_REF] Tremel | Parallel remeshing of unstructured volume grids for cfd applications[END_REF][START_REF] Cavallo | Parallel unstructured mesh adaptation method for moving body applications[END_REF][START_REF] Ramadan | A parallel two mesh method for speedingup processes with localized deformations: application to cogging[END_REF][START_REF] Loseille | Parallel generation of large-size adapted meshes[END_REF][START_REF] Menier | Numerical methods and mesh adaptation for reliable rans simulations[END_REF][START_REF] Benard | Mesh adaptation for large-eddy simulations in complex geometries[END_REF][START_REF] Digonnet | Massively parallel anisotropic mesh adaptation[END_REF][START_REF] Yılmaz | Parallel mesh generation, migration and partitioning for the elmer application[END_REF] of coarser-grain methods has been investigated, which uses existing sequential remeshers as black boxes within an iterative framework. Coarse-grained methods have strong benefits, but possess some drawbacks as well. While shared-memory, fine-grained methods implicitly balance the workload across PEs, which share the queue of elements to be remeshed, coarse-grained, distributed-memory methods require much more elaborate mechanisms to achieve parallel efficiency. For instance, the mesh has to be distributed across the PEs using some partitioning tool [START_REF] Maerten | Drama: A library for parallel dynamic load balancing of finite element applications[END_REF], mesh pieces of equivalent workload have to be assigned to the PEs [START_REF] Tremel | Parallel remeshing of unstructured volume grids for cfd applications[END_REF] (which requires to estimate a priori the remeshing workload of a piece), and the number of pieces should match the number of PEs [START_REF] Chrisochoides | Simultaneous mesh generation and partitioning for delaunay meshes[END_REF][START_REF] Verhoeven | Dynamic load balancing in a 2d parallel delaunay mesh generator[END_REF], among other constraints. PaMPA pushes these ideas further, by implementing them in a generic and scalable framework for handling distributed meshes of any types of elements, as will be presented in the next section.

Parallel remeshing in PaMPA

As we have seen, due to technological limitations and especially memory bottlenecks, parallel remeshing on a large number of PEs can only be addressed using distributed-memory parallelism. Also, users may want to keep using the parallel remeshing library that they are used to. Hence, we have devised a coarse-grained parallel framework for taking advantage of existing sequential remeshers in a distributed-memory context.

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Our method

Our method for parallel remeshing is an iterative algorithm made of two nested loops. The outer loops iterates the remeshing process until all elements satisfy the user-provided quality criterion. It starts by computing the quality of all elements according to the user-provided metric. All elements that do not respect this quality criterion are flagged for remeshing. The criterion may involve metrics such as smallest or largest edge length, or element geometry (quality), possibly considering anisotropy requirements. Then, the sub-mesh comprising all the tagged elements is passed to the inner loop. The outer loop stops when an inner loop does not bring enough improvement to the mesh, that is, when the ratio of tagged elements between two iterations of the outer loop becomes close to 1.

The inner loop, depicted in Figure 1, comprises five consecutive steps. It splits the groups of elements to be remeshed into pieces that will be remeshed concurrently on as many PEs as possible by a third-party, sequential remesher. Unlike [START_REF] Benard | Mesh adaptation for large-eddy simulations in complex geometries[END_REF][START_REF] Loseille | Parallel generation of large-size adapted meshes[END_REF], sizes of subdomains are independent from the maximum mesh size allowed by the sequential remesher. In the following, we will provide further details on each of these five steps. A thorough description of all of the sketched algorithms can be found in [START_REF] Lachat | Conception et validation d'algorithmes de remaillage parallèles à mémoire distribuée basés sur un remailleur séquentiel[END_REF].

Tagging of elements to be remeshed

The purpose of the first step is to determine the set of elements that need to be remeshed during the inner loop. Step 1a, which represents the initialization phase of the inner loop, yields the tags that have been computed at the beginning of the outer loop, without any further processing. In subsequent inner iterations, corresponding to step 1b, tags are removed from the elements that have been successfully remeshed. Elements which belong to the skin of the remeshed areas usually remain tagged, because the sequential remesher has been prevented from modifying them in order to reintegrate the remeshed areas.

Computation of independent pieces

This step aims at computing pieces of the mesh that can be remeshed independently from each other. Three constraints must be satisfied.

• Firstly, pieces must contain mostly elements that have been tagged. However, because remeshers often have to modify the neighboring elements of an element being refined, a piece may contain additional un-tagged elements that form a skin around the considered tagged elements.

• Secondly, the size of the pieces must be big enough to leave room for work to the sequential remesher. Yet, there must be enough pieces not to leave any PE idle. Hence, the size of the pieces may depend on the number of PEs. Also, it has to be bounded by the PE's available memory.

• Thirdly, the size of the frontier, that is, the number of elements that are adjacent to elements that do not belong to the piece, must be as small as possible, so that the aspect ratio of the piece to remesh is as high as possible, in order to constrain the remesher as little as possible in its operations. This third criterion may be evaluated using the isoperimetric quotient metric, which ranges from 0 to 1. A value of 1 indicates that the surface of the piece is minimized with respect to its volume, as it is the case for a sphere.

In the context of our algorithm, we consider the frontier of a piece, that is, the elements that are connected to elements that do not belong to the piece, and which should not be modified by the Figure 1: Sketch of the inner loop of our algorithm, showing its five steps. In the first step (1a, 1b), elements that still need to be remeshed (the gray area) are tagged. In the second step, independent pieces are computed. In the third step, pieces are redistributed across PEs, each PE gathering all the data of a given piece, so as to balance the load of subsequent work. In the fourth step, sequential remeshing is concurrently performed on each PE. In the fifth, last step, remeshed pieces are reintegrated into the distributed mesh. This five-step loop iterates until no tagged element remains.

sequential remesher. In order to decrease the number of outer iterations, our aim is to minimize the number of these elements. Since this metric is not taken into account by parallel graph partitioners, we tried out several algorithms to obtain the pieces, and evaluated their output with respect to the frontier metric.

The most efficient method on average, for out test cases, consists in partitioning the dual Inria graph of the mesh. The desired number of parts is determined by estimating the number of nodes that will be created or removed by the remeshing process. Each of the tagged elements is assigned a weight that represents an estimation of the amount of work that the remesher will spend to process this element. The parallel partitioner PT-Scotch is used to partition this weighted dual graph into the desired number of pieces.

Extraction of the pieces to be remeshed

The pieces that have been computed at the previous step may span across multiple PEs. The goal of this step is therefore to gather all the fragments of a given piece to the same PE, so that PEs can work on centralized instances of the pieces that they have to remesh. All the entities adjacent to an element that belongs to some piece are copied to the destination PE for this piece. Consequently, some entities (e.g. nodes) may be duplicated across several PEs, if they are part of elements that belong to different pieces and which are to be processed by different PEs.

The assignment of pieces to PEs is also performed by using the Scotch partitioner. Its aim is to balance the estimated remeshing workload of the pieces across the PEs, while migrating as little data as possible across PEs, by favoring the assignment of pieces to PEs that already hold most, or at least some, of their data. To perform this assignment, a constrained partitioning is computed on a bipartite graph, as shown in figure 2. This graph comprises two sets of vertices: weighted vertices that represent the pieces, and fixed vertices that represent the PEs. A piece vertex is connected to a PE vertex if some of the data of the piece are originally stored on this PE. The weight of the edge depends on the amount of data on the PE. Hence, minimizing the cut of the partition of piece vertices amounts to minimizing data migration.

Remeshing of the pieces

Every piece, now on the form of a centralized submesh, is processed concurrently by an instance of the sequential, third-party remesher. In order to be able to reintegrate the remeshed pieces into the distributed mesh, frontier elements must never be modified by the remesher. Also, if a remesher instance fails when remeshing some piece, the original piece structure is preserved, with its tags remaining set, so as to be processed in a subsequent outer loop. Our framework is therefore resistant to remesher failure.

Reintegration of the remeshed pieces

Once the pieces have been remeshed, they have to be reintegrated into the unmodified part of the distributed mesh. This requires to merge the new topological information, as well as the new values associated with the new mesh entities. The tags of elements which need to be remeshed but which belong to the skin of the pieces are kept, since these elements could not be remeshed. Once this step is complete, a new iteration of the inner loop can take place. After all the tagged elements have been remeshed, the new distributed mesh may be repartitioned and redistributed, so as to rebalance workload across the PEs.

Our parallel remeshing method has been implemented in the PaMPA parallel library. An interface has been defined, which allows one to use any sequential remesher that allows some of the elements of the mesh that is passed to it not to be modified.

Load balancing

The remeshing process, which may significantly modify the structure of the mesh, is likely to create load imbalance and/or communication overhead if remeshed mesh data is not properly redistributed. Redistribution can conveniently take place at two steps: during reintegration of the pieces and when the distributed mesh is built.

Load balancing during reintegration

The load balancing strategy that we implemented at reintegration time is the following. When a piece comes entirely from a single PE, all the elements of the remeshed piece are sent back to this PE. When a piece is shared by more than one PE, the elements of the remeshed piece are distributed across the involved PEs, in the same proportion as they were distributed in the original piece. The rationale for this strategy is that if the mesh is to be uniformly remeshed, as it is the case for instance when creating a dense distributed mesh from some coarse mesh produced by a mesher, the increase in the number of elements is likely to be uniformly distributed.

In order to select the destination PE for each remeshed element, while minimizing communication at a local scale, the remeshed piece is partitioned into as many parts as there are involved PEs. Scotch is used to compute a constrained sequential mapping (and not only a partitioning), with fixed vertices, of the dual graph of the remeshed piece, as shown in Figure 3. Vertices that represent skin elements are fixed to their origin PE, while vertices that represent other elements, which belong to the interior of the piece, are not constrained. Then, a target architecture for mapping with Scotch is built, comprising as many target vertices as there are PEs sharing the piece. The capacity of each target vertices is set according to the ratio of elements located on each PEs before remeshing took place. Load balancing after the new distributed mesh is built The previous local load balancing technique does not yield balanced meshed when remeshing is not uniform: a small group of

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PEs may be overloaded by many newly created elements, or underloaded if the part of the mesh they own is coarsened. PE overloading not only creates computing inefficiency, but may also lead to remesher failure, when the memory of some PE gets full. Consequently, if, at the end of an iteration, the difference between the smallest and largest subdomains is higher than 25%, an additional, global repartitioning is performed, using PT-Scotch Ṡince, to date, parallel repartitioning is not available in PT-Scotch only parallel partitioning from scratch is performed.

Interfacing with the sequential remesher

Remeshing libraries are usually complex software. An advantage of our method is that it does not require profound changes in their code. Our only requirement is that these libraries should keep untouched a provided list of elements: those who correspond to the skin of the piece to remesh. To date, we have coupled our parallel software framework with Mmg3d, the 3D remesher of the mmg platform [START_REF] Dapogny | Three-dimensional adaptive domain remeshing, implicit domain meshing, and applications to free and moving boundary problems[END_REF]. Mmg3d is an open-source software for simplicial remeshing based on local mesh modifications. A metric tensor field is provided at the vertices of a given triangulation. The remeshing process is controlled by two criteria: the boundary approximation and the metric field. An ideal surface model of the initial mesh is built, based on third-order Bézier patches. Then, the maximal distance between the piecewise linear representation of the boundary and this ideal surface is controlled along the surface remeshing process. The compliance of the remeshing with the size map is checked by checking edge lengths. Given a metric field prescription, the lengths of all mesh edges of the final optimized mesh should be as close as possible to that prescribed by the metric field, and mesh quality has to be as close as possible to the optimal unit value. Vertices are inserted in the volumic mesh using an anisotropic Delaunay kernel, and all the usual mesh operators (that is, collapse, edge swap, node relocation) are used.

Parallel interpolation

Currently, no interpolation is performed after parallel remeshing. Interpolation can take place at two different times: either sequentially at the end of each sequential remeshing task, before reintegrating the remeshed piece into the original mesh, or in parallel at the end of the whole remeshing process. On the one hand, with the first approach, several interpolations may be performed successively on the same area of the mesh, resulting in numerical inaccuracy. On the other hand, the second approach is very difficult to implement, because PEs may not own the same pieces of the mesh before and after remeshing and redistribution. Some global communication has to take place, in order to match the geometry of the remeshed mesh with that of the original mesh. For the sake of simplicity, we plan to follow the first approach. However, to mitigate the inaccuracy issue, we will favor as much as possible the production of large pieces, whose inner mesh elements will be more likely to reach optimal sizes in only one remeshing pass.

Experiments with an industrial test case

Mesh generation of the complex geometries encountered in industrial cases if often limited by the capabilities of meshing software and by the user's experience. Knowing where to set the highest resolution so as to get the most accurate results requires a lot of expertise. However, most meshing tools only provide global mesh refinement, where all the elements of the domain are scaled (up or down) to increase (or decrease) the discretization. Mesh adaptation is consequently a powerful tool allowing for targeted mesh refinement.

The industrial test case that we present in this report concerns a gas turbine (see Figure 4). This experiment took place as a follow-up to a study on the impact of mesh resolution impact on soot prediction in combustion [START_REF] Lamouroux | ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition[END_REF]. In this study, large eddy simulation (LES) was used to predict the combustion characteristics of the system, including soot creation. Mesh discretization is a highly critical aspect of LES for capturing the physics of the problem, and mesh convergence is a critical diagnostic for the validity of the results. In this experiment, a standard quality mesh comprising 11 millions of tetrahedra was used as first guess. From this first mesh, three consecutive levels of refinement were generated, up to 1 billion of elements. The first level of refinement can usually be achieved via the standard meshing tools and global refinement. However, more detailed meshes are out of reach from standard tools, as memory and time become an issue. In this study, generating a first homogeneously refined mesh from the 33 million tetrahedra case up to 200 million elements required 7 hours to compute, and 7 more hours to dump to disk, with mixed quality results. As a more viable alternative, PaMPA was used, using selective refinement, to increase mesh resolution inside the elbow-shaped combustion chamber without modifying the refinement in the outer case zone where no combustion takes place, leading to a 220 million elements mesh (see Figure 5). Subsequently, PaMPA was used a second time to remesh the geometry further, so as to increase the resolution up to 1 billion elements in the same combustion region as before. This last refinement level is out of reach of current stateof-the-art meshing tools with acceptable time and resources constraints, that is, using less than 1 Tb of memory and taking less than 1 week for the meshing process. With PaMPA, the third level of remeshing took 10 minutes on 120 Intel E5-2680v4 Broadwell Xeon cores running at 2.40 GHz. To avoid I/O and memory bottlenecks, as each core can only address 4 GB of memory, partitioned input and output files were generated and coalesced using the mdist and mcat tools of the PaMPA distribution, respectively. The pre-and post-processing phases took 40 minutes each on a single Haswell core at 2.4 GHz.

Conclusion

The parallel remeshing framework implemented in PaMPA allowed us to process an industrial test case for a LES simulation that could not be tackled with prior state-of-the-art tools. The approach that we considered, which is based on distributed-memory, coarse-grained parallelism, needs to balance evenly remeshing workload across all PEs. This requires to estimate accurately enough the remeshing workload attached to each element, and to create as many independent pieces as there are PEs assigned to the user.

Although PaMPA has proved its usefulness and exhibits good scalability on thousands of PEs for large meshes [START_REF] Lachat | Conception et validation d'algorithmes de remaillage parallèles à mémoire distribuée basés sur un remailleur séquentiel[END_REF], some of the algorithms implemented to date can be reworked in order to further improve parallel efficiency.

For instance, at the time being, element redistribution after remeshing is considered independently for each remeshed piece. This may result in overloading or underloading some PEs, which requires a subsequent, global redistribution step. A more efficient solution might be to consider element redistribution collectively on all pieces. Element redistribution would be performed in a localized way so as to share evenly the workload associated with the new elements, eliminating the need for subsequent global redistribution. Also, in order to reduce data movement and redistribution time, parallel repartitioning should be used instead of parallel partitioning from scratch. This requires an improvement of the PT-Scotch software.

Another slight improvement might be to consider vertex partitioning rather than edge partitioning, when creating the pieces to remesh. Indeed, with edge partitioning, two layers of untouched, skin elements are created between two pieces, which reduces piece sizes and thus Finally, PaMPA could be interfaced with more sequential remeshing tools. Some work has been carried out concerning Tetgen and GMSH, to enlarge the potential user base of PaMPA.

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Figure 2 :

 2 Figure 2: Bipartite graph used to extract pieces to PEs.

Figure 3 :

 3 Figure 3: Constrained partitioning with fixed vertices to preserve the same ratio of elements accross PEs.

Figure 4 :

 4 Figure 4: Cut view of the temperature field inside a gas turbine demonstrator.

Figure 5 :

 5 Figure 5: Top: increasing refinement of the mesh from 11 to 220 millions of elements. Bottom: detailed view

RR n°9133

avenue de la Vieille Tour 33405 Talence Cedex Publisher Inria Domaine de Voluceau -Rocquencourt BP 105 -78153 Le Chesnay Cedex inria.fr ISSN 0249-6399


Gou-Jen Wang
email: giwang@dragon.nchu.edu.tw

Wen-Chiao Chang

IMITATION OF THE ION DIFFUSION AND ION PUMPING MECHANISMS OF A LIVING CELL BY NANOPOROUS ALUMINA MEMBRANE

Diffusion and pumping of ions are two major mechanisms of the ion channels in real cell membranes. The main goal of this research is to imitate the ion diffusion and pumping properties of a real cell membrane using the inorganic porous alumina membrane. The diameters of the pores on the membrane, typically ranged from 10 nm to 100nm, can be controlled by the type of electrolyte used to fabricate the alumina membrane.

An electrochemistry bath that used the alumina membrane as filter to separate solutions with concentration gradient was built to investigate its diffusion and pumping properties. Experimental results indicated that the ion diffusion and pumping mechanisms of a real cell can be artificially imitated by the inorganic porous alumina membrane.

INTRODUCTION

Cell is the basic unit in a living body that can completely perform the sign of life. Cell membrane is one of the major components of a living cell. The controlled and selective flow of ions through biological channels in cell membranes enables efficient communication of biological information within cells inside a living body [START_REF] Jiang | The open pore conformation of potassium channels[END_REF]. Passive transport and active transport are two main manners of the ion transport. The driving forces of the passive transport and the active transport are diffusion and ionpumping, respectively. Diffusion property allows ions to travel from higher concentration area to lower concentration area. On the contrary, ion-pumping transports ions against the direction of electrochemical potential with energy coming from the hydrolysis of ATP [START_REF]Cell Physiology. Academic[END_REF]. Diffusion property has been well-known. However, the ion-pumping mechanism has still been under investigated. Recently, the Feynman's Ratchet and Pawl theory has been adopted to characterize the ion-pumping principles [START_REF] Siwy | Preparation of synthetic nanopores with transport properties analogous to biological channels[END_REF][START_REF] Siwy | Fabrication of a Synthetic Nanopore Ion Pump[END_REF][START_REF] Siwy | Origen of 1/f α noise in membrane channel currents[END_REF][START_REF] Siwy | A nanodevice for rectification and pumping ions[END_REF][START_REF] Siwy | Rectification and voltage gating of ion currents in a nanofabricated pore[END_REF]. In which, conical nanopores in polyethylene terephthalate (PET) and polymide foils were produced by track-etching technique [START_REF] Fleischer | Nuclear Tracks in Solids: Principles and Applications[END_REF] to biomimic the transports of ions against electrochemical gradient.

In contrast to polymers, the inorganic porous alumina membrane (AAO) [START_REF] Whitesides | Molecular self-assembly and nanochemistry: a chemical strategy for the synthesis of nanostructures[END_REF][START_REF] Park | Block copolymer lithography: periodic arrays of ~10 11 holes in 1 square centimeter[END_REF][START_REF] Masuda | Ordered metal nanohole arrays made by a two-step replication of honeycomb structures of anodic alumina[END_REF] that can be easily fabricated by dipping an aluminum foil into an electrolytic bath in which the aluminum metal was electrically anodized was adopted to imitate the cell membrane. The diameters of the pores on the membrane, typically ranged from 10 nm to 100nm, can be controlled by the electrolyte in the electrolytic bath. In addition, porous alumina membrane possesses other advantages such as conveniently to fabricate large membrane with relatively low cost and having good mechanical and chemical properties.

FABRICATION OF POROUS ALUMINA MEMBRANE

The procedure to fabricate the porous alumina membrane [START_REF] Lehmann | Formation mechanism and properties of electrochemically etched tranches in Ntype silicon[END_REF][START_REF] Wang | Fabrication and characterization of anodic aluminum oxide template[END_REF] is well known and does not require expensive instrumentation. Figure 1 diagrammatically illustrates the fabrication procedures of the porous alumina membrane. The procedures include (i) electropolishing aluminum foil (99.9995% Al, 96% sulfuric acid, 85% phosphoric acid, and DI water with 1:1:1 ratio) (ii) 1 st anodization (0.3M oxalic acid) (iii) etching (50% phosphoric acid) (iv) 2 nd anodization (0.3M oxalic acid) (v) removing aluminum substrate (CuCl 2 +HCl) (vi) removing barrier (6% phosphoric acid). Figure 2 shows the SEM images of the porous alumina membrane used in this research.

PREPARATION OF ION PUMP

An electrochemistry bath that used the porous alumina membrane as filter to separate solutions with different concentrations was built to conducting the experiments of ion diffusion and pumping. (1) Diffusion experiments Without externally electrical potential, the ion diffusion mechanism was investigated. The average diameter of the pores in the porous alumina membrane is about 60 nm. Figure 5 illustrates the current curves of different concentration gradients of KCl. It is found that both the current intensity and its variation gradient are proportional to the concentration gradient. Since the concentration gradient was the most at the beginning, the current intensity variations were more apparent during the first couple seconds. When the concentrations in each side of the electrochemistry bath were approaching equilibrium, the current intensity variations became inconspicuously.

c 1 /c 2 =100 c 1 /c 2 =4 c 1 /c 2 =2 Figure 5.

Current curves of different concentration gradients on diffusion experiments

In general, pores with diameter of 60 nm should allow both the cation (K + ) and anion (Cl -) to penetrate simultaneously. i.e. the net current should be zero. Consequently, there should be other causes to the recorded current. One of the feasible reasons is the mobility difference between K + and Cl -. K + navigates faster than Cl -; therefore, net cations traveling through the membrane contribute to the recorded current. The electroosmotic-flow effect inside the pores may be another possibility to the net current.

(

2) Ion pumping experiments

When an electrical potential opposite to the concentration gradient was applied, the ion pumping mechanism was investigated. Figure 6 compares the diffusion and ion-pumping properties of the porous alumina membrane under 100-fold concentration gradient of KCl (c 1 /c 2 =100). The ion-pumping property was observed through the recorded against gradient current (Figure 6b). (b) Ion-pumping (0.1 V) Figure 6. Ion-pumping properties of the porous alumina membrane Figure 7 schematically describes the ion-pumping mechanism. After a potential voltage being applied, cations in the lower concentration area penetrate the membrane toward the electrode of the higher concentration bath. On the contrary, anions in the higher concentration bath move to the electrode of the lower concentration area. Cations and anions are hereby separated. As time goes on, variation of the amount of the moving ions gradually decrease; therefore, the current intensity reaches its stable value (Figure 6b). Experimental results show that the current intensity is proportional to the applied voltage. As observation time went on, the current intensities were getting smaller. It is also found that current intensity is inversely proportional to the concentration gradient. The reason is that the smaller the concentration of the solution is, the amount of ions inside the solution is rarer; therefore, the total amount of ions can contribute to the transport are fewer. (3) Dependence of the pumping on the diameter of the pore Porous alumina membranes with different pore diameters were fabricated to examine the dependence of the pumping property on the diameter of the pores. Figure 9 shows the relationship between the pumping property and the pore diameter. The recorded current is found to be proportional to the diameter of the pore.

Gou-Jen Wang and Wen-Chiao Chang Imitation of the Ion Diffusion and Ion Pumping Mechanisms of a Living Cell

Gou-Jen Wang and Wen-Chiao Chang Imitation of the Ion Diffusion and Ion Pumping Mechanisms of a Living Cell

CONCLUSIONS

Diffusion and pumping of ions are two major mechanisms of the ion channels in real cell membrane. In this research, the porous alumina membrane was adopted to imitate the ion diffusion and pumping properties of a real cell membrane. The diameters of the pores on the membrane can be controlled by the electrolyte used to fabricate the membrane. Furthermore, the porous alumina membrane possesses other advantages such as conveniently to fabricate large membrane with relatively low cost and having good mechanical and chemical properties.

An electrochemistry bath that used the nanoporous membrane as the filter to separate solutions with concentration gradient was built to examine the diffusion and pumping properties of the alumina membrane. Without externally electrical potential, the ion diffusion mechanism was investigated. When an electrical potential opposite to the concentration gradient was applied, the ion pumping mechanism was investigated.

Ion diffusion and pumping mechanisms of a real cell were artificially imitated through the experiments.

Subheadings

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  Wang and Wen-Chiao Chang Imitation of the Ion Diffusion and Ion Pumping Mechanisms of a Living Cell

Figure 1 .

 1 Figure 1. Fabrication procedures of the porous alumina membrane

2 c 1 > c 2 Figure 3 .Figure 4 .

 21234 Figure 3. Schematic diagram of the electrochemistry bath

Figure 7 .Figure 8

 78 Figure 7. Schematic illustration of the ion-pumping mechanism Figure 8 depicts the current intensities measured at different time intervals for different concentration gradient of the electrochemistry bath, under several oppositely electrical potentials.Experimental results show that the current intensity is proportional to the applied voltage. As observation time went on, the current intensities were getting smaller. It is also found that current intensity is inversely proportional to the concentration gradient. The reason is

Figure 8 .

 8 Current intensities measurement for different concentration gradients

Figure 9 . 4 )Figure 10 .

 9410 Figure 9. Dependence of the pumping property on the diameter of the pore (4) Dependence of the pumpingon the porous coverageThere kinds of membranes with different porous coverage were prepared to dig out the influence of the porous coverage percentage on the ion pumping property. The directly proportional dependence of the pumping property on the porous coverage percentage was illustrated in Figure10.

© TIMA Editions / ENS 2005 ISBN: 2-916187-02-2

ACKNOWLEDGEMENTS

The authors would like to address their graduate to the National Science Council of Taiwan for financial support under grant NSC-94-2212-E-005-010. The work was conducted in the Center of Nanoscience and Nanotechnology at the National Chung-Hsing University, Taiwan.