CN110348054B - Method for calculating electric conductivity of particle reinforced material containing hard core-soft shell structure - Google Patents
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Abstract
The invention discloses a method for calculating the conductivity of a particle reinforced material containing a hard core-soft shell structure body, which comprises the following steps: determining geometric parameters of the hard core; calculating the rejection volume of the soft shell; calculating the volume fraction of the soft shell; calculating the percolation threshold of the soft shell; the conductivity of the particulate reinforcement material of the hard core-soft shell structure was calculated. The invention overcomes the technical bottlenecks that the prior art can not describe the process of sudden change of the conductivity of the particle reinforced material caused by the percolation of the intermediate layer and the numerical simulation efficiency is low and the precision is difficult to ensure, so that the calculation method of the conductivity of the particle reinforced material has universality and representativeness.
Description
Technical Field
The invention belongs to the technical field of composite material micromechanics and material engineering, and particularly relates to a hard core-soft shell structure body technology.
Background
In recent years, materials such as carbon fibers, carbon nanotubes, and silver nanowires have received increasing attention due to their excellent rigidity and strength, and high thermal and electrical conductivity. Researchers have used these particles as reinforcing agents to add to the matrix, and only a small amount of the particles can greatly improve the conductivity of the whole material. The material is an ideal material in the engineering fields of electronics, sensors, aerospace, shielding and the like. The research and prediction of the conductivity of the particle reinforced material are very challenging scientific problems, and have great significance for the research and development of material science. A quantitative correlation mechanism of the microstructure and the macroscopic property of the material is disclosed, and the regulation of the macroscopic property of the material through the microstructure is an important way for realizing the 'customized' design of the particle reinforced material. Studies have shown that due to processing and material properties, inter alia, an intermediate layer is present around the particles, which is different from the properties of the particles and the matrix material, and this system is typically a core-shell structure, as shown in figure 1.
In recent years, researchers have observed through scanning electron microscopy and tomography that intermediate layers around particles penetrate each other to form a complex network, and the complex network is one of main paths for transmission of media such as current, heat, magnetic current and the like in the material, and particularly when the intermediate layer network is subjected to percolation, the conductivity of the material is changed. The current prediction method of the percolation threshold of the interlayer network ignores the overlapping effect between interlayers and the influence of the geometric characteristics of particles, and no clear method is available for acquiring the percolation threshold of the interlayer network around non-spherical particles, so that the application of the percolation threshold in practice is limited. In the aspect of predicting the effective performance of the particle reinforced material, an effective approximate theoretical method of the micromechanics of the composite material is created in recent decades, such as: the Mori-Tanaka mechanism, the differential effective medium approximation and the generalized self-consistent method cannot describe the conductivity evolution mechanism of the particle reinforced material under the condition that the intermediate layer is subjected to percolation. Based on this, it is urgent to establish a method for calculating the conductivity of a particulate reinforcing material containing a hard core-soft shell structure, which has a clear concept, is convenient to operate, and has a wide application range.
Disclosure of Invention
In order to solve the technical problems mentioned in the background art, the invention provides a method for calculating the conductivity of a particle reinforced material containing a hard core-soft shell structure.
In order to achieve the technical purpose, the technical scheme of the invention is as follows:
a method for calculating the conductivity of a particle reinforced material containing a hard core-soft shell structure body comprises the following steps:
(1) determining geometric parameters of the hard core;
(2) calculating the rejection volume of the soft shell according to the geometric parameters of the hard core;
(3) calculating the volume fraction of the soft shell according to the geometric parameters of the hard core and the volume fraction of the particles;
(4) taking a critical volume fraction of particles as a characteristic quantity of a percolation threshold of the soft shell, wherein the critical volume fraction of the particles is obtained according to the rejection volume of the soft shell, the critical volume fraction of the soft shell and geometric parameters of the hard core, and the critical volume fraction of the soft shell is obtained through the volume fraction of the soft shell;
(5) calculating the conductivity of the hard core-soft shell structure according to the volume fraction of the soft shell and the volume fraction of the particles; and calculating the conductivity of the particle reinforced material of the hard core-soft shell structure according to the conductivity of the hard core-soft shell structure and the percolation threshold of the soft shell.
Further, in the step (1), the hard core is considered as a sphere body, and when the height is H and the diameter is D, the aspect ratio α is H/D, and the equivalent diameter D iseq＝D(1+1.5α)1/3。
Further, in step (2), the repulsive volume of the soft shell is calculated by the following formula:
in the above formula, Sc＝(1+α)πDeq 2A-23，
A＝1+1.5α，B＝1+0.5α，
Is the repulsive volume of the soft shell and t is the thickness of the soft shell.
Further, in step (3), the volume fraction of the soft shell is calculated by:
in the above formula, phisIs the volume fraction of the soft shell, phicIs the volume fraction of the particles, λ ═ t/DeqS is the sphericity of the granule, s ═ 1+ 1.5. alpha.)2/3/(1+α)。
Further, in step (4), the percolation threshold of the soft shell is calculated by:
in the above formula, phic cIs the critical volume fraction of the particles,i.e. percolation threshold of the soft shell, phic sIs the critical volume fraction of the soft shell,
is the repulsive volume of the soft shell, gcs(φc c)＝(1-φc c/2)/(1-φc c)3。
Further, in step (5), the electrical conductivity of the hard core-soft shell structure is calculated according to the following formula:
in the above formula, σcsIs the conductivity, σ, of the hard core-soft shell structuresIs the conductivity, σ, of the intermediate layercIs the electrical conductivity of the particles in the axial direction, F (alpha) is the depolarization factor,
the conductivity of the particulate reinforcement of the hard core-soft shell structure was then calculated according to the following formula:
in the above formula, σeffIs the conductivity, σ, of the particulate reinforcing materialmIs the conductivity of the matrix, P is the percolation probability of percolation of the soft shell,
Lpeis the side length of a representative volume element.
Adopt the beneficial effect that above-mentioned technical scheme brought:
the method can predict the conductivity of the particle reinforced material based on the geometric parameters of the non-spherical particles and the percolation effect of the intermediate layer, overcomes the technical bottlenecks that the prior art can not describe the process of mutation of the conductivity of the particle reinforced material caused by the percolation of the intermediate layer and has low numerical simulation efficiency and difficult guarantee of precision, and ensures that the method for calculating the conductivity of the particle reinforced material has universality and representativeness. The method has clear concept and simple and convenient operation, and has important significance for application and popularization in the field of composite materials.
Drawings
FIG. 1 is a schematic diagram of the conductive principle of a representative volume element of a particulate reinforcing material containing a hard core-soft shell structure;
FIG. 2 is a flow chart of a method of the present invention;
FIG. 3 is a comparison graph of conductivity calculation method and experimental results, which includes two sub-graphs (a) and (b).
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings.
The invention designs a method for calculating the conductivity of a particle reinforced material containing a hard core-soft shell structure body, which comprises the following steps as shown in figure 2:
step 1: determining geometric parameters of the hard core;
step 2: calculating the rejection volume of the soft shell according to the geometric parameters of the hard core;
and step 3: calculating the volume fraction of the soft shell according to the geometric parameters of the hard core and the volume fraction of the particles;
and 4, step 4: taking a critical volume fraction of particles as a characteristic quantity of a percolation threshold of the soft shell, wherein the critical volume fraction of the particles is obtained according to the rejection volume of the soft shell, the critical volume fraction of the soft shell and geometric parameters of the hard core, and the critical volume fraction of the soft shell is obtained through the volume fraction of the soft shell;
and 5: calculating the conductivity of the hard core-soft shell structure according to the volume fraction of the soft shell and the volume fraction of the particles; and calculating the conductivity of the particle reinforced material of the hard core-soft shell structure according to the conductivity of the hard core-soft shell structure and the percolation threshold of the soft shell.
In this embodiment, the step 1 is implemented by the following preferred scheme:
considering the hard core as a sphere column, the height is H, the diameter is D, the length-diameter ratio alpha is H/D, and the equivalent diameter Deq＝D(1+1.5α)1/3。
In this embodiment, the step 2 is implemented by the following preferred scheme:
the repelled volume of the bladder is calculated by:
in the above formula, Sc＝(1+α)πDeq 2A-23，
A＝1+1.5α，B＝1+0.5α，
Is the repulsive volume of the soft shell and t is the thickness of the soft shell.
In this embodiment, the step 3 is implemented by the following preferred scheme:
the volume fraction of the soft shell is calculated by:
in the above formula, phisIs the volume fraction of the soft shell, phicIs the volume fraction of the particles, λ ═ t/DeqS is the sphericity of the granule, s ═ 1+ 1.5. alpha.)2/3/(1+α)。
In this embodiment, the step 4 is implemented by adopting the following preferred scheme:
the percolation threshold of the soft shell is calculated by:
in the above formula, phic cIs critical for the particleVolume fraction, i.e. percolation threshold of the soft shell, phic sIs the critical volume fraction of the soft shell,
is the repulsive volume of the soft shell, gcs(φc c)＝(1-φc c/2)/(1-φc c)3。
In this embodiment, the step 5 is implemented by the following preferred scheme:
the conductivity of the hard core-soft shell structure was calculated according to the following formula:
in the above formula, σcsIs the conductivity, σ, of the hard core-soft shell structuresIs the conductivity, σ, of the intermediate layercIs the electrical conductivity of the particles in the axial direction, F (alpha) is the depolarization factor,
the conductivity of the particulate reinforcement of the hard core-soft shell structure was then calculated according to the following formula:
in the above formula, σeffIs the conductivity, σ, of the particulate reinforcing materialmIs the conductivity of the matrix, P is the percolation probability of percolation of the soft shell,
Lpeis the side length of a representative volume element.
According to the conductivity calculation method, the actual experimental data can be brought in for verification, and the multi-wall carbon nano-tube reinforced aluminum oxide composite material is usedMaterials for example, the conductivity of a dealuminated matrix is σm＝10-12S/m, conductivity of the multi-walled carbon nanotube is sigmac＝6×102S/m, the conductivity of the intermediate layer was taken to be 10 of the conductivity of the substrate14Multiple, i.e. sigmas＝1014σmThe length-diameter ratio of the carbon nanotube is 100, and the diameter of the carbon nanotube is 20 nm. The theoretical prediction result and the experimental result of the conductivity based on the present invention are shown in fig. 3 (a), and the thickness t of the intermediate layer is 0.6nm, which are highly consistent with each other.
In addition, taking the single-walled carbon nanotube reinforced polyimide composite material as an example, CP2 polyimide is selected as a substrate, and the conductivity of the polyimide is sigmam＝6.3×10-16S/m, the diameter of single-wall carbon nanotube is 1.4nm, the length is 3 microns, and the conductivity is sigmac0.6S/m, the thickness of the intermediate layer is 0.35nm, and the conductivity of the intermediate layer is 10 of that of the substrate13Multiple, i.e. sigmas＝1013σmThe theoretical prediction result and the experimental result of the conductivity based on the present invention are shown in fig. 3 (b), and both have high consistency.
The embodiments are only for illustrating the technical idea of the present invention, and the technical idea of the present invention is not limited thereto, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the scope of the present invention.
Claims (6)
1. A method for calculating the conductivity of a particle reinforced material containing a hard core-soft shell structure body is characterized by comprising the following steps:
(1) determining geometric parameters of the hard core;
(2) calculating the rejection volume of the soft shell according to the geometric parameters of the hard core;
(3) calculating the volume fraction of the soft shell according to the geometric parameters of the hard core and the volume fraction of the particles;
(4) taking a critical volume fraction of particles as a characteristic quantity of a percolation threshold of the soft shell, wherein the critical volume fraction of the particles is obtained according to the rejection volume of the soft shell, the critical volume fraction of the soft shell and geometric parameters of the hard core, and the critical volume fraction of the soft shell is obtained through the volume fraction of the soft shell;
(5) calculating the conductivity of the hard core-soft shell structure according to the volume fraction of the soft shell and the volume fraction of the particles; and calculating the conductivity of the particle reinforced material of the hard core-soft shell structure according to the conductivity of the hard core-soft shell structure and the percolation threshold of the soft shell.
2. The method for calculating the electrical conductivity of the particulate reinforcing material containing hard core-soft shell structures as claimed in claim 1, wherein in the step (1), the hard core is considered as a sphere column, and the height is recorded as H, the diameter is recorded as D, the length-diameter ratio α is H/D, and the equivalent diameter D is recorded as Deq＝D(1+1.5α)1/3。
3. The method for calculating the electrical conductivity of a particulate reinforcing material containing a hard core-soft shell structure according to claim 2, wherein in the step (2), the repulsive volume of the soft shell is calculated by the following formula:
in the above formula, Sc＝(1+α)πDeq 2A-2/3，
A＝1+1.5α，B＝1+0.5α，
Is the repulsive volume of the soft shell and t is the thickness of the soft shell.
4. The method for calculating the electrical conductivity of a particulate reinforcing material containing a hard core-soft shell structure according to claim 2, wherein in the step (3), the volume fraction of the soft shell is calculated by the following formula:
in the above formula, phisIs the volume fraction of the soft shell, phicIs the volume fraction of the particles, λ ═ t/DeqS is the sphericity of the granule, s ═ 1+ 1.5. alpha.)2/3/(1+α)。
5. The method for calculating the electrical conductivity of a particulate reinforcing material containing a hard core-soft shell structure according to claim 4, wherein in the step (4), the percolation threshold of the soft shell is calculated by the following formula:
in the above formula, phic cIs the critical volume fraction of the particles, i.e. the percolation threshold of the soft shell, phic sIs the critical volume fraction of the soft shell,
is the repulsive volume of the soft shell, gcs(φc c)＝(1-φc c/2)/(1-φc c)3。
6. The method for calculating the electrical conductivity of a particulate reinforcing material containing a hard core-soft shell structure according to claim 5, wherein in the step (5), the electrical conductivity of the hard core-soft shell structure is calculated according to the following formula:
in the above formula, σcsIs the conductivity, σ, of the hard core-soft shell structuresIs the conductivity, σ, of the intermediate layercIs the electrical conductivity of the particles in the axial direction, F (alpha) is the depolarization factor,
the conductivity of the particulate reinforcement of the hard core-soft shell structure was then calculated according to the following formula:
in the above formula, σeffIs the conductivity, σ, of the particulate reinforcing materialmIs the conductivity of the matrix, P is the percolation probability of percolation of the soft shell,
Lpeand t is the thickness of the soft shell, which is the side length of a representative volume unit.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2014209476A1 (en) * | 2013-06-24 | 2014-12-31 | International Business Machines Corporation | Injection of a filler material through implosion |
| CN106777822A (en) * | 2017-01-22 | 2017-05-31 | 河海大学 | Two-dimentional high-content particle strengthens composite three-phase meso-mechanical model and method for building up |
| CN109370155A (en) * | 2018-10-17 | 2019-02-22 | 中国人民解放军陆军工程大学 | Field causes non-linear conducing composite material preparation method, obtained composite material and application |
Family Cites Families (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8231808B2 (en) * | 2008-05-27 | 2012-07-31 | Hong Kong University Of Science And Technology | Percolation efficiency of the conductivity of electrically conductive adhesives |
| WO2015135463A1 (en) * | 2014-03-11 | 2015-09-17 | The Hong Kong University Of Science And Technology | Electrical and thermal conductive paste composition and method of reducing percolation threshold and enhancing percolating conductivity using the same |
| US10340520B2 (en) * | 2014-10-14 | 2019-07-02 | Sila Nanotechnologies, Inc. | Nanocomposite battery electrode particles with changing properties |
| US10013523B2 (en) * | 2016-03-29 | 2018-07-03 | Mentor Graphics Corporation | Full-chip assessment of time-dependent dielectric breakdown |
| US11704457B2 (en) * | 2017-06-16 | 2023-07-18 | University Of Cincinnati | Methods, software, and apparatus for porous material or medium characterization, flow simulation and design |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2014209476A1 (en) * | 2013-06-24 | 2014-12-31 | International Business Machines Corporation | Injection of a filler material through implosion |
| CN106777822A (en) * | 2017-01-22 | 2017-05-31 | 河海大学 | Two-dimentional high-content particle strengthens composite three-phase meso-mechanical model and method for building up |
| CN109370155A (en) * | 2018-10-17 | 2019-02-22 | 中国人民解放军陆军工程大学 | Field causes non-linear conducing composite material preparation method, obtained composite material and application |
Non-Patent Citations (3)
| Title |
|---|
| Excluded volumes of anisotropic convex particles in heterogeneous media: Theoretical and numerical studies;Wenxiang Xu 等;《Computers, Materials and Continua》;20160131;第52卷(第1期);第25-40页 * |
| 石墨烯表面改性及其在聚合物导电复合材料中的应用研究;胡圣飞 等;《高分子材料科学与工程》;20170831;第33卷(第8期);第184-190页 * |
| 软物质系颗粒材料组成、微结构与传输性能之间关联建模综述;许文祥 等;《物理学报》;20160930;第65卷(第17期);第82-105页 * |
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