CN108682821A - A kind of preparation method of lithium ion battery cobalt-based metal oxide composite electrode - Google Patents

A kind of preparation method of lithium ion battery cobalt-based metal oxide composite electrode Download PDF

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Publication number
CN108682821A
CN108682821A CN201810516906.7A CN201810516906A CN108682821A CN 108682821 A CN108682821 A CN 108682821A CN 201810516906 A CN201810516906 A CN 201810516906A CN 108682821 A CN108682821 A CN 108682821A
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China
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preparation
temperature
cobalt
lithium ion
based metal
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CN201810516906.7A
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王迎
吴胜祥
赖超
王庆红
范诗佳
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Jiangsu Normal University
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Jiangsu Normal University
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    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01MPROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M4/00Electrodes
    • H01M4/02Electrodes composed of, or comprising, active material
    • H01M4/36Selection of substances as active materials, active masses, active liquids
    • H01M4/362Composites
    • H01M4/366Composites as layered products
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01MPROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M10/00Secondary cells; Manufacture thereof
    • H01M10/05Accumulators with non-aqueous electrolyte
    • H01M10/052Li-accumulators
    • H01M10/0525Rocking-chair batteries, i.e. batteries with lithium insertion or intercalation in both electrodes; Lithium-ion batteries
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01MPROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M4/00Electrodes
    • H01M4/02Electrodes composed of, or comprising, active material
    • H01M4/36Selection of substances as active materials, active masses, active liquids
    • H01M4/48Selection of substances as active materials, active masses, active liquids of inorganic oxides or hydroxides
    • H01M4/52Selection of substances as active materials, active masses, active liquids of inorganic oxides or hydroxides of nickel, cobalt or iron
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01MPROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M4/00Electrodes
    • H01M4/02Electrodes composed of, or comprising, active material
    • H01M4/36Selection of substances as active materials, active masses, active liquids
    • H01M4/58Selection of substances as active materials, active masses, active liquids of inorganic compounds other than oxides or hydroxides, e.g. sulfides, selenides, tellurides, halogenides or LiCoFy; of polyanionic structures, e.g. phosphates, silicates or borates
    • H01M4/583Carbonaceous material, e.g. graphite-intercalation compounds or CFx
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/10Energy storage using batteries

Abstract

The present invention relates to a kind of lithium ion battery preparation method of cobalt-based metal oxide composite electrode, the electrode material is then prepared through two step high-temperature heat treatments using cobalt-based metal organic framework compound as presoma;The electrode material has the various structures advantages such as graduation hole, N doping, extra granular size.The preparation method that the present invention uses is simple and effective, prepared combination electrode material shows excellent storage lithium performance, the presence of the graduate pore structure of material internal and carbon nanotube can keep the structural stability of electrode well, and more multichannel is provided for lithium ion transport, to ensure that the lithium ion battery using the material preparation still has excellent cyclical stability at higher current densities.

Description

A kind of preparation method of lithium ion battery cobalt-based metal oxide composite electrode
Technical field
The present invention relates to the cobalt based metal oxides that a kind of nitrogen-doped carbon can be used for lithium ion battery and carbon nanotube coat Object combination electrode material and preparation method thereof.
Technical background
Lithium ion battery has many advantages, such as that energy density is high, has a safety feature, memory-less effect, be widely used with it is all kinds of In portable electronic device.However, in order to promote the growth requirement of electric vehicle and large scale electric network equipment, people are to lithium ion More stringent requirements are proposed for the high rate performance and stored energy capacitance of battery.When traditional graphite material is as negative electrode of lithium ion battery, Its theoretical lithium storage content is only 372mAh/g, it is difficult to meet actual demand, therefore is developed with higher capacity, more excellent high rate performance New electrode materials be just particularly important.Transition metal oxide with higher theoretical lithium storage content has just obtained extensively Concern, wherein CoC3OC4Theoretical lithium storage content be up to (890mAh/g), be it is a kind of relatively have future negative electrode of lithium ion battery material Material, still, CoC3OC4The insertion of lithium ion abjection during can occur larger volume change, and then dusting, fall off, make At the irreversible decaying of capacity;In addition CoC3OC4Electric conductivity it is poor, cause its high rate performance undesirable.
It is the effective ways for improving material electrochemical performance that the particle size of electrode material, which is reduced to Nano grade,.Nanometer Grade electrode material usually has higher specific surface area and more reactivity sites, while nano level electrode material can also The stress generated in volume expansion is effectively relieved, shortens electrons/ions transmission range, to keeping the structural stability of material and carrying High electrode high rate performance plays good effect.Nano material and carbon base body are subjected to the conduction that recombination energy further increases material Property, transition metal oxide/carbon composite electrode of various structures is had reported at present.However traditional transition metal oxide/ Carbon composite, particles' interaction is poor, although electrons/ions transmission speed in single nano material enhances, Transmission rate between nano material is still undesirable.It up to the present, can be there are no a kind of cobalt-based metal oxide electrode material Higher current density (>Realize that high power capacity conservation rate and long circulation life, problem above limit lithium ion battery under 10A/g) Application surface hinders the more preferable development of lithium ion battery industry.
The excellent carbon nanotube of electric conductivity is introduced in cobalt-based metal oxide/carbon composite, prepares cobalt-based metal Oxide/carbon/carbon nanotube composite mesh structure, between the ion/electron transfer rate and strengthening material improving nanometer materials Material structural stability plays an important role.In addition, the introducing of hetero atom nitrogen can also enhance wetting capacity of the electrolyte to electrode material. The method that tradition prepares cobalt-based metal oxide/nitrogen-doped carbon/carbon nano tube compound material is generally required carbon with physical method Nanotube and target product progress are compound, or need to introduce additional carbon source or nitrogen source, and preparation method is complicated, and transition in product Metal oxide and carbon base body intermolecular forces are poor, can not ensure that electrode material still has at higher current densities and preferably follow Ring stability.Based on the above analysis, the present invention proposes a kind of nanoscale still at higher current densities with long circulation life Cobalt metal oxide/nitrogen-doped carbon/carbon nano-tube combination electrode and preparation method thereof.
Invention content
The present invention in order to realize lithium ion battery at higher current densities still have higher capacity retention ratio and cycle the longevity Life, it is proposed that it is a kind of using cobalt-based metal organic framework compound be presoma, preparation have both graduation pore structure, N doping and The electrode structure and preparation method thereof of cobalt-based metal oxide/nitrogen-doped carbon/carbon nano tube compound material of nano effect.The party Method simple possible, is easy to large-scale production at stable structure.
The technical solution adopted by the present invention is to prepare cobalt-based metal organic framework compound first with coprecipitation, so The cobalt-based metal organic framework compound of preparation is subjected to high temperature cabonization afterwards, then to product under acetylene/argon gas mixed gas Secondary heat treatment is carried out, target product is obtained after fully oxidized.It is as follows:
(1) cobalt salt, 2-methylimidazole are dispersed in water, stirring or ultrasound are allowed to be uniformly dispersed;Subsequent static ageing 12h is then centrifuged for separation, drying obtains dried powder;
(2) powder is subjected to high-temperature heat treatment under an argon atmosphere;
(3) the above-mentioned powder for preparing under acetylene/argon gas mixed gas is subjected to secondary high-temperature processing, product is collected after cooling Carry out subsequent processing;
(4) will after secondary high-temperature is handled powder, be transferred to air atmosphere and aoxidized at low temperature.
Cobalt salt described in step (1) is CoC (NOC3)2·6H2OC、CoCCl2·6H2OC or CoC (CH3COCOC)2· 6H2Any one or more in OC
The molar ratio of 2-methylimidazole and cobalt salt described in step (1) is 10:1~70:1, best proportion 39:1;
Calcination temperature described in step (2) is 500~950 DEG C;
Heat treatment time described in step (2) is 1-4h;
Heating rate described in step (2) is 1 DEG C/min~10 DEG C/min, and optimal heating rate is 3 DEG C/min;
Acetylene content is 10~30% volume ratios in acetylene/argon gas mixed gas described in step (3);
Secondary heat treatment temperature described in step (3) is 350~700 DEG C of C/min, and processing time is 5~60min, most preferably Processing time is 20min;
Heating rate described in step (3) is 1 DEG C/min~10 DEG C/min, and optimal heating rate is 5 DEG C/min;
Oxidization time described in step (4) is 10~48h, and oxidizing temperature is 100~200 DEG C, optimum reaction condition 200 It is reacted for 24 hours at DEG C;
The present invention obtains cobalt-based metal oxygen using cobalt-based metal organic framework compound as presoma after substep high-temperature process Compound/nitrogen-doped carbon/carbon nano-tube combination electrode, preparation method is simple, and without introducing additional carbon source or nitrogen source, product In generated in-situ nitrogen-doped carbon/carbon nanotube conducting matrix and cobalt-based metal oxide combine closely, can guarantee electrode material In multiple charge and discharge process still with higher reactivity and the structure stablized.
Description of the drawings
Fig. 1 is cobalt-based metal oxide/nitrogen-doped carbon/carbon nano tube compound material prepared in the embodiment of the present invention 1 SEM figure.
Fig. 2 is cobalt-based metal oxide/nitrogen-doped carbon/carbon nano tube compound material prepared in the embodiment of the present invention 1 TEM figure.
Fig. 3 is cobalt-based metal oxide/nitrogen-doped carbon/carbon nano tube compound material prepared in the embodiment of the present invention 3 Cycle performance figure of the lithium ion battery of preparation under 15A/g electric currents.
Specific implementation mode:
Embodiment 1:
The cobalt salt of selection is CoC (NOC3)2·6H2OC, the molar ratio for controlling 2-methylimidazole and cobalt salt is 30:1, it stirs Static hatching 12h after 10min is mixed, product centrifuges, is dry.Powder is transferred in tube furnace after drying, argon gas protection lower 5 DEG C/min is warming up to 550 DEG C and keeps the temperature 2h, after cooled to room temperature, carry out secondary high-temperature heat treatment.Acetylene volume is selected to contain Acetylene/argon gas mixed gas that amount is 10%, 5 DEG C/min are warming up to 550 DEG C, keep the temperature 10min, collection of products.By above-mentioned powder It is placed under 200 DEG C of air atmosphere and aoxidizes for 24 hours, obtain final product.
SEM and the TEM figure such as Fig. 1, Fig. 2 institutes for cobalt-based metal oxide/nitrogen-doped carbon/carbon nanotube that the present embodiment obtains Show.
Embodiment 2:
The cobalt salt of selection is CoC (Cl)2·6H2OC, the molar ratio for controlling 2-methylimidazole and cobalt salt is 60:1, stirring Static hatching 12h after 10min, product centrifuge, are dry.Powder is transferred in tube furnace after drying, and lower 5 DEG C of argon gas protection/ Min is warming up to 600 DEG C and keeps the temperature 3h, after cooled to room temperature, carries out secondary high-temperature heat treatment.Select acetylene volume content be 20% acetylene/argon gas mixed gas, 3 DEG C/min are warming up to 500 DEG C, keep the temperature 15min, collection of products.Above-mentioned powder is placed in 36h is aoxidized under 150 DEG C of air atmosphere, obtains final product.
Embodiment 3:
The cobalt salt of selection is CoC (NOC3)2·6H2OC, the molar ratio for controlling 2-methylimidazole and cobalt salt is 39:1, it stirs Static hatching 12h after 10min is mixed, product centrifuges, is dry.Powder is transferred in tube furnace after drying, argon gas protection lower 3 DEG C/min is warming up to 600 DEG C and keeps the temperature 2h, after cooled to room temperature, carry out secondary high-temperature heat treatment.Acetylene volume is selected to contain Acetylene/argon gas mixed gas that amount is 15%, 5 DEG C/min are warming up to 600 DEG C, keep the temperature 10min, collection of products.By above-mentioned powder It is placed under 200 DEG C of air atmosphere and aoxidizes 48h, obtain final product.
Product cycle performance test under the current density of 15A/g is as shown in Figure 3
Embodiment 4:
The cobalt salt of selection is CoC (CH3COCOC)2·6H2OC, the molar ratio for controlling 2-methylimidazole and cobalt salt is 70: 1, static hatching 12h after 10min is stirred, product centrifuges, is dry.Powder is transferred in tube furnace after drying, argon gas protection Lower 10 DEG C/min is warming up to 700 DEG C and keeps the temperature 4h, after cooled to room temperature, carries out secondary high-temperature heat treatment.Select acetylene body Acetylene/argon gas mixed gas that product content is 30%, 1 DEG C/min are warming up to 700 DEG C, keep the temperature 10min, collection of products.It will be above-mentioned Powder is placed under 250 DEG C of air atmosphere and aoxidizes 36h, obtains final product.
As can be seen from Figure 1 it is graduate polyhedral structure that this method, which prepares product, and polyhedron is by nano-scale particle Second Aggregation forms, while many generated in-situ carbon nanotube networks of sample surfaces homoepitaxial.TEM is further confirmed Product division center prepared by this method is CoC3OC4, outer layer coated nitrogen-doped carbon base carbon nanotube successively.It can be seen in Fig. 3 Going out to prepare product has excellent storage lithium performance, still has higher capacity to protect after 5000 weeks under the high current density of 15A/g Holdup and the cycle life stablized.

Claims (10)

1. a kind of lithium ion battery preparation method of cobalt-based metal oxide composite electrode comprising following steps:
(1) cobalt salt, 2-methylimidazole are dispersed in water, stirring or ultrasound are allowed to be uniformly dispersed;Subsequent static ageing 12h, so It centrifuges afterwards, drying obtains dried powder;
(2) powder is subjected to high-temperature heat treatment under an argon atmosphere;
(3) the above-mentioned powder for preparing is subjected to secondary high-temperature processing under acetylene/argon gas mixed gas, collecting product after cooling carries out Subsequent processing;
(4) will after secondary high-temperature is handled powder, be transferred to air atmosphere and aoxidized at low temperature.
2. preparation method according to claim 1, it is characterised in that:Cobalt salt described in the step (1) is CoC (NOC3)2·6H2OC、CoCCl2·6H2OC or CoC (CH3COCOC)2·6H2Any one or more in OC.
3. preparation method according to claim 1, it is characterised in that:2-methylimidazole described in step (1) and cobalt salt Molar ratio is 10:1~70:1..
4. preparation method according to claim 1, it is characterised in that:Calcination temperature described in step (2) is 500~950 ℃。
5. preparation method according to claim 1, it is characterised in that:Heat treatment time described in step (2) is 1-4h.
6. preparation method according to claim 1, it is characterised in that:Heating rate described in step (2) be 1 DEG C/min~ 10℃/min。
7. preparation method according to claim 1, it is characterised in that:In acetylene/argon gas mixed gas described in step (3) Acetylene content is 10~30% volume ratios.
8. preparation method according to claim 1, it is characterised in that:Secondary heat treatment temperature described in step (3) is 350 ~700 DEG C/min, processing time is 5~60min, and the optimization process time is 20min.
9. preparation method according to claim 1, it is characterised in that:Heating rate described in step (3) be 1 DEG C/min~ 10 DEG C/min, optimal heating rate is 5 DEG C/min.
10. preparation method according to claim 1, it is characterised in that:Oxidization time described in step (4) is 10~48h, Oxidizing temperature is 100~200 DEG C, and optimum reaction condition is to be reacted for 24 hours under 200 DEG C of C.
CN201810516906.7A 2018-05-25 2018-05-25 A kind of preparation method of lithium ion battery cobalt-based metal oxide composite electrode Pending CN108682821A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111463406A (en) * 2020-04-09 2020-07-28 江苏师范大学 Preparation method of cobalt-doped zinc-based metal selenide composite electrode for lithium ion battery
CN112098486A (en) * 2020-09-18 2020-12-18 湖北中烟工业有限责任公司 N, P co-doped nano carbon-based framework material modified electrode and preparation method and application thereof

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104681810A (en) * 2015-01-11 2015-06-03 北京工业大学 Cobaltosic oxide nitrogen-doped carbon nanotube three-dimensional composite electrode material for lithium ion battery and manufacturing method of electrode material
CN106082167A (en) * 2016-06-13 2016-11-09 西南大学 The carbon nano tube compound material of porous carbon supporting base end portion coated metal granule and the preparation method of derivant, product and application
CN106229541A (en) * 2016-07-27 2016-12-14 安徽师范大学 A kind of N C/Co3o4hollow ball shaped nanometer material and its preparation method and application

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104681810A (en) * 2015-01-11 2015-06-03 北京工业大学 Cobaltosic oxide nitrogen-doped carbon nanotube three-dimensional composite electrode material for lithium ion battery and manufacturing method of electrode material
CN106082167A (en) * 2016-06-13 2016-11-09 西南大学 The carbon nano tube compound material of porous carbon supporting base end portion coated metal granule and the preparation method of derivant, product and application
CN106229541A (en) * 2016-07-27 2016-12-14 安徽师范大学 A kind of N C/Co3o4hollow ball shaped nanometer material and its preparation method and application

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
GANG HUANG 等: "Metal Organic Frameworks Route to in Situ Insertion of Multiwalled Carbon Nanotubes inCo3O4 Polyhedra as Anode Materials for Lithium-Ion Batteries", 《ACS NANO》 *

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111463406A (en) * 2020-04-09 2020-07-28 江苏师范大学 Preparation method of cobalt-doped zinc-based metal selenide composite electrode for lithium ion battery
CN111463406B (en) * 2020-04-09 2022-03-25 江苏师范大学 Preparation method of cobalt-doped zinc-based metal selenide composite electrode for lithium ion battery
CN112098486A (en) * 2020-09-18 2020-12-18 湖北中烟工业有限责任公司 N, P co-doped nano carbon-based framework material modified electrode and preparation method and application thereof

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