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• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
  • B01J—CHEMICAL OR PHYSICAL PROCESSES, e.g. CATALYSIS OR COLLOID CHEMISTRY; THEIR RELEVANT APPARATUS
  • B01J23/00—Catalysts comprising metals or metal oxides or hydroxides, not provided for in group B01J21/00
  • B01J23/70—Catalysts comprising metals or metal oxides or hydroxides, not provided for in group B01J21/00 of the iron group metals or copper
  • B01J23/74—Iron group metals
  • B01J23/745—Iron
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
  • B01J—CHEMICAL OR PHYSICAL PROCESSES, e.g. CATALYSIS OR COLLOID CHEMISTRY; THEIR RELEVANT APPARATUS
  • B01J21/00—Catalysts comprising the elements, oxides, or hydroxides of magnesium, boron, aluminium, carbon, silicon, titanium, zirconium, or hafnium
  • B01J21/18—Carbon
  • B01J21/185—Carbon nanotubes
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
  • B01J—CHEMICAL OR PHYSICAL PROCESSES, e.g. CATALYSIS OR COLLOID CHEMISTRY; THEIR RELEVANT APPARATUS
  • B01J23/00—Catalysts comprising metals or metal oxides or hydroxides, not provided for in group B01J21/00
  • B01J23/70—Catalysts comprising metals or metal oxides or hydroxides, not provided for in group B01J21/00 of the iron group metals or copper
  • B01J23/74—Iron group metals
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
  • B01J—CHEMICAL OR PHYSICAL PROCESSES, e.g. CATALYSIS OR COLLOID CHEMISTRY; THEIR RELEVANT APPARATUS
  • B01J23/00—Catalysts comprising metals or metal oxides or hydroxides, not provided for in group B01J21/00
  • B01J23/70—Catalysts comprising metals or metal oxides or hydroxides, not provided for in group B01J21/00 of the iron group metals or copper
  • B01J23/74—Iron group metals
  • B01J23/75—Cobalt
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  • B01J31/00—Catalysts comprising hydrides, coordination complexes or organic compounds
  • B01J31/02—Catalysts comprising hydrides, coordination complexes or organic compounds containing organic compounds or metal hydrides
  • B01J31/06—Catalysts comprising hydrides, coordination complexes or organic compounds containing organic compounds or metal hydrides containing polymers
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  • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
  • B01J—CHEMICAL OR PHYSICAL PROCESSES, e.g. CATALYSIS OR COLLOID CHEMISTRY; THEIR RELEVANT APPARATUS
  • B01J37/00—Processes, in general, for preparing catalysts; Processes, in general, for activation of catalysts
  • B01J37/02—Impregnation, coating or precipitation
  • B01J37/0201—Impregnation
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B82—NANOTECHNOLOGY
  • B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
  • B82Y30/00—Nanotechnology for materials or surface science, e.g. nanocomposites
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B82—NANOTECHNOLOGY
  • B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
  • B82Y40/00—Manufacture or treatment of nanostructures
• • C—CHEMISTRY; METALLURGY
  • C01—INORGANIC CHEMISTRY
  • C01B—NON-METALLIC ELEMENTS; COMPOUNDS THEREOF; METALLOIDS OR COMPOUNDS THEREOF NOT COVERED BY SUBCLASS C01C
  • C01B32/00—Carbon; Compounds thereof
  • C01B32/15—Nano-sized carbon materials
  • C01B32/158—Carbon nanotubes
  • C01B32/16—Preparation
  • C01B32/162—Preparation characterised by catalysts
• • D—TEXTILES; PAPER
  • D01—NATURAL OR MAN-MADE THREADS OR FIBRES; SPINNING
  • D01F—CHEMICAL FEATURES IN THE MANUFACTURE OF ARTIFICIAL FILAMENTS, THREADS, FIBRES, BRISTLES OR RIBBONS; APPARATUS SPECIALLY ADAPTED FOR THE MANUFACTURE OF CARBON FILAMENTS
  • D01F9/00—Artificial filaments or the like of other substances; Manufacture thereof; Apparatus specially adapted for the manufacture of carbon filaments
  • D01F9/08—Artificial filaments or the like of other substances; Manufacture thereof; Apparatus specially adapted for the manufacture of carbon filaments of inorganic material
  • D01F9/12—Carbon filaments; Apparatus specially adapted for the manufacture thereof
  • D01F9/127—Carbon filaments; Apparatus specially adapted for the manufacture thereof by thermal decomposition of hydrocarbon gases or vapours or other carbon-containing compounds in the form of gas or vapour, e.g. carbon monoxide, alcohols
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
  • B01J—CHEMICAL OR PHYSICAL PROCESSES, e.g. CATALYSIS OR COLLOID CHEMISTRY; THEIR RELEVANT APPARATUS
  • B01J23/00—Catalysts comprising metals or metal oxides or hydroxides, not provided for in group B01J21/00
  • B01J23/16—Catalysts comprising metals or metal oxides or hydroxides, not provided for in group B01J21/00 of arsenic, antimony, bismuth, vanadium, niobium, tantalum, polonium, chromium, molybdenum, tungsten, manganese, technetium or rhenium
  • B01J23/24—Chromium, molybdenum or tungsten
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
  • B01J—CHEMICAL OR PHYSICAL PROCESSES, e.g. CATALYSIS OR COLLOID CHEMISTRY; THEIR RELEVANT APPARATUS
  • B01J23/00—Catalysts comprising metals or metal oxides or hydroxides, not provided for in group B01J21/00
  • B01J23/38—Catalysts comprising metals or metal oxides or hydroxides, not provided for in group B01J21/00 of noble metals
  • B01J23/40—Catalysts comprising metals or metal oxides or hydroxides, not provided for in group B01J21/00 of noble metals of the platinum group metals
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
  • B01J—CHEMICAL OR PHYSICAL PROCESSES, e.g. CATALYSIS OR COLLOID CHEMISTRY; THEIR RELEVANT APPARATUS
  • B01J23/00—Catalysts comprising metals or metal oxides or hydroxides, not provided for in group B01J21/00
  • B01J23/70—Catalysts comprising metals or metal oxides or hydroxides, not provided for in group B01J21/00 of the iron group metals or copper
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
  • B01J—CHEMICAL OR PHYSICAL PROCESSES, e.g. CATALYSIS OR COLLOID CHEMISTRY; THEIR RELEVANT APPARATUS
  • B01J35/00—Catalysts, in general, characterised by their form or physical properties
  • B01J35/60—Catalysts, in general, characterised by their form or physical properties characterised by their surface properties or porosity
  • B01J35/61—Surface area
  • B01J35/613—10-100 m2/g
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
  • B01J—CHEMICAL OR PHYSICAL PROCESSES, e.g. CATALYSIS OR COLLOID CHEMISTRY; THEIR RELEVANT APPARATUS
  • B01J35/00—Catalysts, in general, characterised by their form or physical properties
  • B01J35/60—Catalysts, in general, characterised by their form or physical properties characterised by their surface properties or porosity
  • B01J35/61—Surface area
  • B01J35/615—100-500 m2/g
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B01—PHYSICAL OR CHEMICAL PROCESSES OR APPARATUS IN GENERAL
  • B01J—CHEMICAL OR PHYSICAL PROCESSES, e.g. CATALYSIS OR COLLOID CHEMISTRY; THEIR RELEVANT APPARATUS
  • B01J37/00—Processes, in general, for preparing catalysts; Processes, in general, for activation of catalysts
  • B01J37/02—Impregnation, coating or precipitation
  • B01J37/0201—Impregnation
  • B01J37/0203—Impregnation the impregnation liquid containing organic compounds
• • C—CHEMISTRY; METALLURGY
  • C01—INORGANIC CHEMISTRY
  • C01B—NON-METALLIC ELEMENTS; COMPOUNDS THEREOF; METALLOIDS OR COMPOUNDS THEREOF NOT COVERED BY SUBCLASS C01C
  • C01B2202/00—Structure or properties of carbon nanotubes
  • C01B2202/02—Single-walled nanotubes
• • C—CHEMISTRY; METALLURGY
  • C01—INORGANIC CHEMISTRY
  • C01B—NON-METALLIC ELEMENTS; COMPOUNDS THEREOF; METALLOIDS OR COMPOUNDS THEREOF NOT COVERED BY SUBCLASS C01C
  • C01B2202/00—Structure or properties of carbon nanotubes
  • C01B2202/06—Multi-walled nanotubes

Definitions

• the present invention relates to a process for preparing carbon fibrils and / or nanotubes from a carbon source integrated with the catalyst used for their preparation, as well as the catalyst material and its manufacturing process.
• Carbon fibrils and carbon nanotubes are recognized today as materials presenting great advantages, because of their mechanical properties, of their relations of form
• the carbon fibrils generally have a mean diameter ranging from 50 nm to a micron, greater than that of the carbon nanotubes.
• the fibrils are composed of more or less organized graphitic zones (or turbostratic stacks) whose planes are inclined at variable angles with respect to the axis of the fiber. They are often hollow in the central axis.
• the carbon nanotubes are terminated by hemispheres consisting of pentagons and hexagons of structure close to fullerenes.
• nanotubes composed of a single sheet this is called SWNT (acronym for Single Wall Nanotubes) and nanotubes composed of several concentric layers then called MWNT (acronym for Multi Wall Nanotubes).
• SWNTs are generally more difficult to manufacture than MWNTs.
• the production of carbon nanotubes may be implemented by various methods such as electrical discharge, the r laser ablation or chemical vapor deposition (CVD)
• a carbon source is injected at a relatively high temperature over a catalyst, said catalyst being able to consist of a metal supported on an inorganic solid.
• a metal supported on an inorganic solid iron, cobalt, nickel and molybdenum are preferentially mentioned and among the supports there is often alumina, silica or magnesia.
• Possible carbon sources are methane, ethane, ethylene, acetylene, ethanol, methanol, acetone or even CO + H2 synthesis gas (HIPCO process).
• the ashes consist of transition metal and alumina, silica or magnesia.
• the metal is often encapsulated and little subject to cause undesirable effects, but this is not the case of the mineral support which, if it is not eliminated by a binding acidic treatment, can prove harmful in applications such as thin films or fibers, because of the particle size.
• US2006 / 0115409 describes a process in which the preparation of carbon nanotubes (CNTs) is carried out by in situ decomposition of a mixture comprising polyethylene glycol as organic material and carbon source, in the presence of a catalyst. metallic.
• the mixture consisting of the metal catalyst dispersed in the polyethylene glycol is previously prepared in a solvent medium before the CNT formation step which itself is carried out in two stages by heating at temperatures of 200-400 ° C., respectively, at the first time. step then 400-1QOO 0 C in the second step.
• the invention provides a catalyst material for the preparation of fibrils and / or mono- or multi-walled carbon nanotubes comprising:
• one or more multivalent transition metals chosen from those of group VIB, chromium Cr, molybdenum Mo, tungsten W, or those of group VIIIB, iron Fe, cobalt Co, nickel Ni, ruthenium Ru, Rh rhodium, Pd palladium, Os osmium, Ir irium, Pt platinum or mixtures thereof, and a solid organic substrate selected from polymers, copolymers and terpolymers which contain only carbon and hydrogen.
• the organic substrate is a polymer with a BET specific surface area of less than 200 m 2 / g, for example between 0.1 m 2 / g and 50 m 2 / g.
• a BET specific surface area of less than 200 m 2 / g, for example between 0.1 m 2 / g and 50 m 2 / g.
• the organic substrate is chosen from polymers, copolymers or terpolymers, in which at least a part of the units comprises butadiene and / or styrene.
• the organic substrate is selected from core-shell polymers (methacrylate / butadiene / styrene terminology) or crosslinked polystyrene / divinylbenzene polymers.
• the transition metal may be chosen from iron Fe, cobalt Co, or nickel Ni, or a mixture thereof.
• the amount of transition metal (s) is advantageously up to 50% by weight of the final catalyst material, preferably from 1 to 30% and more preferably from 1 to 15% by weight of the final catalyst material.
• the organic substrate is a porous support in which the metal is impregnated, preferably, in which the impregnation rate of the support is up to 40%.
• the catalyst material according to the invention is in the form of solid particles whose diameter is between 1 micron and 5 mm.
• the invention also relates to the process for preparing the catalyst material described above by contacting the organic substrate with a solution containing at least one of said transition metal (s) in the form of salt, preferably under a dry gas sweep. This step is usually followed by a reduction of the deposited metal. To do this, the deposited metal is advantageously reduced under a reducing gas scan such as hydrogen.
• the solution is an aqueous solution metal nitrate, especially iron nitrate.
• the denitrification of the catalyst takes place under an inert atmosphere.
• the contacting is carried out at a temperature between room temperature and the boiling temperature of the solution, and the quantity of liquid, at any time, in contact with the substrate is just sufficient to ensure the formation of a film on the surface of the particles.
• the invention also relates to a process for the preparation of fibrils and / or mono- or multi-walled carbon nanotubes comprising the steps of: a) providing a catalyst material as defined above; b) growth of the carbon fibrils and / or nanotubes by thermal decomposition of the organic substrate by heating the catalyst material at a temperature of between 300 and 1200 ° C. in the presence of a hydrocarbon gas composition optionally comprising a reducing gas; c) cooling and recovery of fibrils and / or carbon nanotubes formed.
• the invention relates more particularly to a process as described above, wherein the hydrocarbon gas is ethylene, used in the presence of hydrogen as a reducing gas, the gas composition containing at least 20% by volume of hydrogen.
• step b) is carried out on a fluidized bed in the presence of the hydrocarbon gas and optionally reducing gas, more preferably in the presence of ethylene and hydrogen.
• the reducing gas is present in step b) of preparing the carbon nanotubes, so that the reduction of the metal of the catalyst material occurs in-situ during step b).
• the process according to the invention allows the manufacture of carbon fibrils and / or nanotubes both by decomposition of the organic support and chemical vapor deposition, so that its productivity is maximum.
• the aim of the invention is to provide a catalyst material for the preparation of mono- or multi-walled carbon fibrils and / or nanotubes comprising one or more particular multivalent transition metals and a hydrocarbon polymeric organic substrate.
• the organic substrate
• the organic substrate is solid and advantageously porous. It may have a BET specific surface area of less than 200 m 2 / g, and preferably between 1 m 2 / g and 50 m 2 / g.
• the substrate is chosen from polymers, copolymers or terpolymers which contain only carbon and hydrogen, and which, as a result, lead to a higher yield of ordered fibrils and / or nanotubes.
• the organic substrate is chosen from polymers, copolymers or terpolymers in which at least part of the units comprise butadiene and / or styrene. More preferably, it is chosen from the core-bark polymers of the methacrylate / butadiene / styrene type or the polystyrene / divinylbenzene type crosslinked polymers or the methacrylate / butadiene / styrene MBS (BET surface area of 1 to 5 m 2 / g) sold in particular by Arkema.
• BET surface area of 1 to 5 m 2 / g sold in particular by Arkema.
• the particle size of the substrate is advantageously chosen to allow good fluidization of the catalyst during the synthesis reaction of carbon fibrils and / or nanotubes. In practice, to ensure correct productivity, it is preferred that the substrate particles have a diameter of between 20 and 500 ⁇ m. Multivalent transition metals.
• the transition metal is a multivalent metal selected from those of group VIB such as chromium Cr, molybdenum Mo, tungsten W, or those of group VIIIB such as iron Fe, cobalt Co, nickel Ni, ruthenium Ru, rhodium Rh, palladium Pd, osmium Os, Ir irium, platinum Pt or mixtures thereof.
• the metal is selected from iron Fe, cobalt Co, or nickel Ni, or a mixture thereof.
• the metal consists of iron only.
• the catalyst material More preferably still, the metal consists of iron only.
• the organic substrate represents the support on which the metal is coated.
• the metal may be in the form of a film, but as otherwise the support is preferably porous, a portion of the metal may also be located in the pores of the catalyst.
• a catalyst with a metal impregnation rate of up to 40%, preferably 10 to 35% can be obtained.
• the amount of transition metal (s) generally represents up to 50% by weight of the final catalyst.
• the amount of metal represents 1 to 30%, or even 1 to 15%, of the weight of the final catalyst.
• the final catalyst is typically in the form of particles whose diameter is between 1 micron and 5 mm, preferably between 10 and 500 microns.
• the catalyst is prepared by contacting the organic substrate as described above with a solution containing at least one transition metal (as) as defined above, in salt form.
• the contacting is in principle carried out at a temperature between room temperature and the boiling point of the solution.
• the amount of impregnating solution is determined so that at any time the substrate particles are in contact with a sufficient amount of solution to ensure the formation of a surface film on said substrate particles.
• an impregnation of the substrate occurs when the organic substrate is brought into contact with the solution.
• the impregnation of the substrate particles is advantageously carried out under a dry gas sweep, for example by means of an aqueous solution of metal in salt form, for example iron nitrate or cobalt acetate or nitrate. cobalt or a mixture of the two metals.
• metal in salt form for example iron nitrate or cobalt acetate or nitrate. cobalt or a mixture of the two metals.
• a catalyst material is provided as described above.
• the growth of fibrils and / or carbon nanotubes is carried out.
• This is carried out by thermal decomposition, preferably on a fluidized bed, of the organic substrate by heating the catalyst material at a temperature of between 300 and 1200 ° C., preferably between 500 and 700 ° C., in the presence of a composition.
• hydrocarbon gas optionally comprising a reducing gas such as hydrogen.
• a hydrocarbon gas is preferably introduced alone or in the presence of hydrogen.
• the hydrocarbon gas may especially be chosen from: methane, ethane, ethylene, acetylene, ethanol, methanol, acetone and their mixtures, or even synthesis gas CO + H 2 (HIPCO process ). It is preferably a hydrocarbon such as methane, ethane, ethylene or acetylene, with ethylene being preferred for use in the present invention.
• the hydrocarbon gas, such as ethylene, introduced into the reactor acts as a complementary source of carbon in the preparation of the carbon fibrils and / or nanotubes and can be combined if necessary with hydrogen or with a hydrogen / hydrogen mixture.
• inert gas such as nitrogen.
• the gas composition preferably comprises from 20 to 100% hydrogen, from 0% to 85% and more generally from 5 to 80% of hydrocarbon gas such as ethylene and optionally inert gas in addition. It is still preferred that the hydrocarbon gas be present in greater quantity (by volume) than the reducing gas.
• volume ratio of hydrogen to hydrocarbon gas is advantageously between 1: 2 and 1: 4, better still, between 1:25 and 1:35 and even better, close to 1: 3.
• Hydrogen allows the cleaning of the catalyst surface, prevents the formation of carbon fibers having an anarchic organization, and promotes the production of ordered carbon fibers and / or carbon nanotubes. It may further allow the reduction of the metal deposited on the catalyst.
• the reduction of the catalyst takes place in situ in the synthesis reactor of carbon nanotubes, introducing the catalyst at the reaction temperature; thus, the catalyst does not see the air and the metal remains in unoxidized metal form.
• This process has the advantage of allowing high productivity and obtaining products having a very low ash content of less than 15%, preferably less than 4%.
• Fibrils and carbon nanotubes mono- or multifilets.
• the products obtained have lengths ranging from 1 ⁇ m to 7 or 8 ⁇ m.
• the diameters are between 20 and 250 nm, and particularly for the carbon nanotubes of diameters between 10 and 60 nm. Nanotubes are mainly multifilets.
• the fibrils and / or nanotubes obtained according to the process of the invention described above can be used as agents for improving the mechanical and / or thermal properties and / or electrical conductivity in polymeric compositions or be used to prepare dispersions in solvents.
• the fibrils and / or nanotubes obtained can be used in many fields, in particular in electronics (depending on the temperature and their structure, they can be conductors, semiconductors or insulators), in mechanics, for example for the reinforcement of composite materials ( carbon nanotubes are a hundred times stronger and six times lighter than steel) and electromechanical (they can lengthen or contract by charge injection). It is possible, for example, to mention the use of carbon nanotubes in macromolecular compositions intended, for example, for the packaging of electronic components, for the manufacture of fuel lines (fuel oil), antistatic coatings (or coating), in thermistors, electrodes for supercapacities, etc.
• a catalyst is prepared from methacrylate / butadiene / styrene (MBS) and iron nitrate.
• MBS methacrylate / butadiene / styrene
• the MBS sold by Arkema under reference C223 is a core-shell structure, consisting of an elastomeric core of butadiene surrounded by a crown consisting of a layer of methylmethacrylate
• the median diameter is of the order of 200 to 250 ⁇ m.
• a 3 1 reactor equipped with a double jacket heated to 100 0 C is introduced 30 g of MBS and nitrogen sweeps from bottom to top.
• the MBS particles are then in a prefluidization state.
• a pump 54 g of a solution of iron nitrate nonahydrate containing 5.4 g of iron are then continuously injected.
• the target ratio (mass of metal / mass of catalyst) being 15% of iron metal
• the duration of addition of the solution is 2 h
• the rate of addition of the liquid is substantially equal to the rate of evaporation of the water.
• the catalyst is then heated to 18O 0 C in the reactor for 4 hours to effect denitrification.
• the actual iron content of the catalyst at the end of the operation is 13%.
• the same catalyst is prepared without denitrification; as soon as it is put back into the air, the composition
• MBS / Fe begins to oxidize slowly, giving off smoke.
• a black powder consisting of 32% of iron oxide and 68% of carbon.
• Example 3 Preparation of the Polymeric Metal Catalyst No. 3
• a catalyst is prepared from the same amount of MBS by adding 160 g of solution of iron nitrate nonahydrate, ie 16 g of iron.
• the catalyst preparation and the impregnation are carried out in the same manner as in Example 1, with the exception of the duration of addition which is of the order of 6.5 h. Denitrification is continued for 4 hours. The actual iron content of the catalyst is 23% at the end of the operation.
• This catalyst is prepared from an aqueous solution of cobalt acetate.
• the actual cobalt content of the catalyst at the end of the operation is 12%.
• a catalytic test is carried out by introducing a temperature between 600 and 700 ° C, a mass of about 2.5 g of catalyst in a reactor of 5 cm in diameter and 1 m in effective height, equipped with a disengagement to prevent entrainment of fine particles to downstream.
• the gases are composed of hydrogen and ethylene (25% / 75% vol / vol) with a total flow rate between 100 and 300 Nl / h.
• the catalyst is introduced in five portions per 0.5 gram to avoid too much gas evolution. Between each introduction, we wait 10 minutes.
• the gas flow rate is sufficient for the solid to be well above the fluidization limit velocity, while remaining below the rate of flight.
• the fibers obtained in tests 1 to 4 are well ordered and present either with well-organized graphitic planes parallel to the axis, or with planes inclined with respect to the axis of an angle of about 30 °. fish).
• Productivity is expressed in grams of carbon produced per gram of metal introduced.

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