Characterization Method for Thermal Conductive Pathways of Particle Reinforced Polymer Matrix Thermal Conductive Composites

Abstract

The present invention provides a method for characterizing the heat conduction paths of a particulate-reinforced polymer-based thermal conductive composite material, belonging to the technical field of thermal conductive composite materials. The method of the present invention comprises the following steps: S1: determining the critical spacing for the formation of heat conduction paths between particles; S2: based on the critical spacing, statistically obtaining the particle IDs that form heat conduction paths with each particle within a representative volume element to form a complete list of heat conduction path particle IDs within the representative volume element; S3: using a cyclic search algorithm to calculate the number of heat conduction clusters within the representative volume element and the particle IDs included in each cluster; S4: outputting the number of heat conduction clusters, the particle IDs included in each cluster, the size of each cluster, and the cluster distribution information, and quantitatively characterizing the three-dimensional heat conduction network inside the composite material based on the above information. The method of the present invention is applicable to particulate-reinforced polymer-based composite materials with multiple particle sizes, and realizes the quantitative description of the particle dispersion state and heat conduction paths inside the composite material.

Description

Technical Field

[0001] The present invention belongs to the technical field of thermal conductive composite materials, and relates to a method for characterizing the thermal conduction path of a particle-reinforced polymer-based thermal conductive composite material. Background Art

[0002] High molecular polymers such as silicone rubber and epoxy resin are widely used in the field of electronics and electricity. Due to the low thermal conductivity of high molecular materials, the thermal conductivity of the composite material can be effectively improved by introducing inorganic filler particles with high thermal conductivity and good insulation properties into the polymer matrix. The macroscopic thermal conductivity of the material is closely related to the number of thermal conduction paths formed by the effective contact of micro-particles with each other. The filling density of the filler particles and the filler grading scheme are the key factors affecting the thermal conduction path of the composite material. Accurately characterizing the thermal conduction path of the multi-particle-size filled composite material is an important means to realize the microscopic design of the high thermal conductivity composite material.

[0003] At present, it is still difficult to directly characterize the three-dimensional thermal conduction path inside the composite material by experimental methods. Generally, the structural morphology pictures of the filler particles inside the composite material are taken by scanning electron microscopy, and then the obtained pictures are numerically processed. On the other hand, a representative volume element of the composite material can also be established, and the thermal conduction performance of the actual composite material system can be evaluated by numerically characterizing the thermal conduction path inside the representative volume element. Generally, based on the position information, particle size information of the filler particles and the determination conditions for forming a thermal conduction path between particles, the thermal conduction path inside the composite material is quantified. It is recorded in the literature ("A method for calculating the particle contact probability for quantitatively characterizing the thermal conduction path of particles", Composites Science and Technology, 2021, 210: 108808) that the particle contact probability is positively correlated with the thermal conductivity of the composite material. The molecular simulation post-processing software Ovito and VMD can calculate the cluster size formed between particles according to the set cut-off radius, and output information such as the number of clusters, the maximum cluster size, the particle ID included in the cluster, and the cluster size distribution.

[0004] However, the particle contact probability only gives the ratio of the number of particles that are in contact with each other to form a thermal conduction path to the total number of particles that may be in contact, and does not give the specific thermal conduction path and its distribution. It is difficult to characterize the influence of the filler particle size and the relative volume content of the filler on the thermal conduction path by this method; the conventional molecular simulation post-processing software can only process the filling system with uniform particle sizes, while there is a certain distribution of the filler sizes in general polymer-based composite materials. Therefore, there are great limitations in numerically characterizing the thermal conduction path of the composite material by using the conventional molecular simulation post-processing software. Summary of the Invention

[0005] The object of the present invention is to provide a method for characterizing the heat conduction path of a particle-reinforced polymer matrix thermal conductive composite material, which is applicable to multi-sized particle-reinforced polymer matrix composite materials, and realizes the quantitative description of the particle dispersion state and heat conduction path inside the composite material.

[0006] To achieve the above object, the present invention provides a method for characterizing the heat conduction path of a particle-reinforced polymer matrix thermal conductive composite material, comprising the following steps:

[0007] S1: Determine the critical spacing for forming a heat conduction path between particles;

[0008] S2: Based on the critical spacing, count the particle IDs that form a heat conduction path with each particle in the representative volume element, and form a complete list of heat conduction path particle IDs in the representative volume element;

[0009] S3: Use a cyclic search algorithm to calculate the number of heat conduction clusters in the representative volume element and the particle IDs included in each cluster;

[0010] S4: Output the number of heat conduction clusters, the particle IDs included in each cluster, the size of each cluster, and the cluster distribution information, and quantitatively characterize the three-dimensional heat conduction network inside the composite material based on the above information.

[0011] Preferably, the step S1 is specifically as follows:

[0012] For particles of different particle sizes, establish a heat conduction calculation model of a two-particle composite material corresponding to the particle size, set the particle thermal conductivity, matrix thermal conductivity, thermal resistance between the particle and the matrix interface, and contact thermal resistance between particles according to the actual material properties, calculate the heat flux density between two particles at different center distances, obtain the change curve of the heat flux density with the particle spacing, and take the particle spacing corresponding to 80% of the maximum heat flux density as the critical spacing of the heat conduction path, that is, when the center distance d of two particles satisfies d ≤ d c it is determined that a heat conduction path is formed between the two particles.

[0013] Preferably, the step S2 is specifically as follows:

[0014] Assume that the representative volume element contains N particles of different sizes. For particle i, calculate the distance d between the centers of the remaining N - 1 particles and particle i respectively, and count the particle IDs with d ≤ d c and record them in the heat conduction path particle ID list of particle i, where i represents the particle ID;

[0015] Repeat the above method, and successively count all the particles in the representative volume element to form the corresponding heat conduction path particle ID list, and finally form a complete list of heat conduction path particle IDs in the representative volume element.

[0016] Preferably, step S3 is specifically as follows:

[0017] According to the complete list of thermal conduction path particle IDs, mark the particle IDs that form a thermal conduction path with particle 1 as the first-level particles of cluster 1; take the first-level particles as the search objects, and mark the particle IDs that form a thermal conduction path with the first-level particles as the second-level particles of cluster 1; and so on, until the number of thermal conduction path particles determined according to the searched particle IDs is 0, indicating that all the particles included in cluster 1 have been found;

[0018] Then take the smallest particle ID not included in cluster 1 as the search particle, repeat the above cyclic search process, and determine all the particles included in cluster 2;

[0019] And so on, until the complete list of thermal conduction path particle IDs of the representative volume element is completely searched, indicating that all the particles that can form a thermal conduction path in the representative volume element have been included in a certain cluster;

[0020] Count the number of particles and particle IDs included in each cluster, and then calculate the total volume of the particles included in each cluster according to the particle diameter.

[0021] Preferably, in step S4, the cluster size includes the total number of particles included in a single cluster and the total volume of the particles included in a single cluster.

[0022] Preferably, count the relative number of the number of particles included in each cluster with respect to the total number of all particles, and count the relative volume of the total volume of the particles included in each cluster with respect to the total volume of all particles; the relative number to a certain extent represents the cluster size.

[0023] Preferably, in step S4, the cluster distribution information is the number distribution and volume distribution information.

[0024] Preferably, in step S4, quantitatively characterizing the three-dimensional thermal conduction network inside the composite material based on the output information is specifically as follows:

[0025] Based on the output information, determine the largest cluster in the representative volume element; if the relative volume of the particles included in the largest cluster is large, it indicates that there are more thermal conduction paths in the composite material and the thermal conductivity is better; otherwise, it indicates that there are fewer thermal conduction paths in the composite material and the thermal conductivity is worse.

[0026] The advantages of the present invention adopting the above technical solutions are:

[0027] 1) General molecular simulation post - processing software, such as Ovito and VMD, can only process filling systems with uniform particle sizes. However, the fillers in actual composites generally have a certain size distribution. The method of the present invention can respectively give the critical spacing for forming a heat - conduction path between particles according to filler particles of different sizes, and determine the particle IDs that form a heat - conduction path with each particle based on this critical spacing. The method of the present invention is not limited by particle size and can process filler particle filling systems with any particle size distribution.

[0028] 2) Since scanning electron microscope images are two - dimensional images, numerical processing based on the images can only characterize the dispersion state of fillers on a certain plane inside the composite material. Although this method is based on the actual material system, two - dimensional information cannot reflect the construction of three - dimensional heat - conduction paths inside the actual composite material. The present invention provides a set of accurate, effective, and convenient methods for characterizing three - dimensional heat - conduction paths inside the composite material by analyzing a representative volume element that is very close to the dispersion state of fillers inside the actual composite material and is macroscopically infinitesimal and microscopically infinite.

[0029] 3) The particle contact probability is positively correlated with the thermal conductivity of the composite material, but this value cannot intuitively reflect the three - dimensional structure of the heat - conduction paths inside the composite material, let alone analyze the distribution of the heat - conduction paths. The present invention gives the particle IDs included in each heat - conduction cluster, and the three - dimensional structure of the heat - conduction paths can be conveniently obtained by molecular simulation post - processing software. Description of the Drawings

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or in the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0031] Figure 1 It is a schematic diagram of the complete list of particle IDs for heat - conduction paths and the cluster cyclic search algorithm;

[0032] Figure 2 It is a flowchart of the cluster cyclic search algorithm;

[0033] Figure 3 It is the cluster distribution diagram of three representative volume element models in the composite material in Example 1. (a) is the cluster number distribution, and (b) is the cluster volume distribution;

[0034] Figure 4Three-dimensional structure diagrams of the largest thermal conduction clusters of three representative volume element models in the composite material in Example 1. (a) represents the volume element model with f1 = 0.05, f2 = 0.6, and f3 = 0.35. (b) represents the volume element model with f1 = 0.25, f2 = 0.15, and f3 = 0.6. (c) represents the volume element model with f1 = 0.75, f2 = 0.1, and f3 = 0.15. Detailed implementation mode

[0035] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0036] The present invention provides a method for characterizing the thermal conduction path of a particle-reinforced polymer-based thermal conduction composite material. Based on the position and particle size information of the filler particles and the determination conditions for forming a thermal conduction path between particles, an accurate and quantitative description of the thermal conduction path inside the composite material is realized, and the microscopic regulation and prediction of the thermal conductivity of the composite material are achieved. The method of the present invention includes the following steps:

[0037] S1: Determine the critical spacing for forming a thermal conduction path between particles;

[0038] S2: Based on the critical spacing, count the particle IDs of the particles that form a thermal conduction path with each particle in the representative volume element, and form a complete list of the particle IDs of the thermal conduction path particles in the representative volume element;

[0039] S3: Use a cyclic search algorithm to calculate the number of thermal conduction clusters in the representative volume element and the particle IDs included in each cluster;

[0040] S4: Output the number of thermal conduction clusters, the particle IDs included in each cluster, the size of each cluster, and the cluster distribution information, and quantitatively characterize the three-dimensional thermal conduction network inside the composite material based on the above information.

[0041] Among them, the specific content of step S1 is as follows:

[0042] For particles with different particle sizes, a thermal conduction calculation model of a two-particle composite material corresponding to the particle size is established respectively. According to the actual material properties, the particle thermal conductivity, matrix thermal conductivity, thermal resistance between the particle and the matrix interface, and contact thermal resistance between particles are set. The heat flux density between two particles at different center distances is calculated, and the change curve of the heat flux density with the particle distance is obtained. The particle distance corresponding to 80% of the maximum heat flux density is taken as the critical spacing of the thermal conduction path, that is, when the center distance d of two particles satisfies d ≤ d cWhen it is determined that a heat conduction path is formed between the two particles.

[0043] As Figure 1 shown, the specific steps of step S2 are as follows:

[0044] Assume that the representative volume element contains N particles of different sizes. For particle i, calculate the distances d between the centers of the remaining N - 1 particles and the center of particle i respectively, and count the particle IDs with d ≤ d c and record them in the heat conduction path particle ID list of particle i, where i represents the particle ID;

[0045] Repeat the above method, and successively count all the particles in the representative volume element to form the corresponding heat conduction path particle ID lists, and finally form the complete heat conduction path particle ID list of the representative volume element.

[0046] As Figure 2 shown, the specific steps of step S3 are as follows:

[0047] According to the complete heat conduction path particle ID list, mark the particle IDs that form a heat conduction path with particle 1 as the 1st - level particles of cluster 1; take the 1st - level particles as the search objects, and mark the particle IDs that form a heat conduction path with the 1st - level particles as the 2nd - level particles of cluster 1; and so on, until the number of heat conduction path particles determined according to the searched particle IDs is 0, indicating that all the particles included in cluster 1 have been found;

[0048] Then take the smallest particle ID not included in cluster 1 as the search particle, and repeat the above cyclic search process to determine all the particles included in cluster 2;

[0049] And so on, until the entire complete heat conduction path particle ID list of the representative volume element is searched, indicating that all the particles that can form a heat conduction path in the representative volume element are included in a certain cluster;

[0050] Count the number of particles and particle IDs included in each cluster, and then calculate the total volume of the particles included in each cluster according to the particle diameters.

[0051] Among them, the cluster size in step S4 includes the total number of particles included in a single cluster and the total volume of the particles included in a single cluster. Count the relative number of the number of particles included in each cluster with respect to the total number of all particles, and count the relative volume of the total volume of the particles included in each cluster with respect to the total volume of all particles; the relative number represents the cluster size to a certain extent. The cluster distribution information in step S4 is the number distribution and volume distribution information.

[0052] Among them, the specific method of quantitatively characterizing the three - dimensional heat conduction network inside the composite material based on the output information in step S4 is as follows:

[0053] Determine the largest cluster within the representative volume element based on the output information; if the relative volume of the particles included in the largest cluster is large, it indicates that there are more heat conduction paths in the composite material and better heat conduction performance; otherwise, it indicates that there are fewer heat conduction paths in the composite material and poorer heat conduction performance.

[0054] Example 1

[0055] Randomly fill three types of spherical Al2O3 filler particles with different particle sizes in the silicone grease matrix, where the diameters of the large particles, medium particles, and small particles are 70μm, 50μm, and 10μm respectively. The volume contents of the large particles, medium particles, and small particles are represented by f1, f2, and f3, and the volume content of the particles is defined as the ratio of the total volume of the particles of the same size to the total volume of all particles. The particle filling volume fraction is 60 vol.%. The particles are randomly and uniformly distributed in the matrix, and 3 representative volume elements of the composite material filled with different graded filler particles are established to characterize the heat conduction paths inside the composite material.

[0056] Adopt the characterization method of the present invention, and the specific process is as follows:

[0057] (1) Establish three two-particle composite material models of 70μm - 70μm, 50μm - 50μm, and 10μm - 10μm. Set the intrinsic thermal conductivity of the Al2O3 filler to 30 W / (m·K), the particle-matrix interface thermal resistance to 2.2×10 -8 m 2 ·K / W, and the filler-filler contact thermal resistance to 2×10 -7 m 2 ·K / W. Calculate the heat flux density of the two particles at different center distances, and obtain the change curve of the heat flux density with the particle distance. Take the particle distance corresponding to 80% of the maximum heat flux density as the critical distance d c of the heat conduction path, that is, when the center distance d of the two particles satisfies d ≤ d c , it is determined that a heat conduction path is formed between the two particles.

[0058] (2) According to the heat conduction path determination condition determined in the first step, for each particle i, calculate the distance d between the centers of the remaining N - 1 particles and particle i, and count the particle IDs with d ≤ d c , and record them in the heat conduction path particle ID list. Through cyclic calculation, a complete list of the heat conduction path particle IDs of the representative volume element is formed.

[0059] (3) Calculate the number of heat conduction clusters in the representative volume element. According to the complete list of heat conduction path particle IDs, mark the particles forming a heat conduction path with particle ID = 1 as the first-level particles of Cluster 1; then use the first-level particle IDs as the search objects, and mark the particle IDs of the particles forming a heat conduction path with the first-level particles as the second-level particles of Cluster 1. And so on, until the number of particles forming a heat conduction path with the searched particle ID is 0, indicating that all the particles included in Cluster 1 have been found. Then use the smallest particle ID not included in Cluster 1 as the first search particle of Cluster 2, and repeat the above loop search process to determine all the particles included in Cluster 2. Until the complete list of heat conduction path particle IDs of the representative volume element is completely searched, indicating that all the particles that can form a heat conduction path are included in a certain cluster.

[0060] (4) Output the number of heat conduction clusters, the particle IDs included in each cluster, the size of each cluster, and the cluster distribution information. Count the number and relative number of particles included in each cluster. The relative number to some extent represents the size of the cluster; calculate the total volume of the particles included in each cluster according to the particle diameter and the relative volume of the cluster relative to the total volume of all particles.

[0061] Output the number distribution and volume distribution of heat conduction clusters in the representative volume element. The cluster distributions of the three representative volume element models are as Figure 3 shown. It can be seen that the relative number and relative volume of the particles included in the largest cluster are much larger than those of other clusters, so the largest cluster forms the main heat conduction path inside the composite material. Figure 4 The particles in [Figure] show the largest clusters in three representative volume elements. Among them, in the composite material representative volume element model with f1 = 0.75, f2 = 0.1, f3 = 0.15, the relative volume of the particles included in the largest cluster is the largest, and more heat conduction paths can be formed inside the composite material, which is beneficial to the improvement of the heat conduction performance. In the composite material representative volume element model with f1 = 0.25, f2 = 0.15, f3 = 0.6, the relative volume of the particles included in the largest cluster is the smallest, and the heat conduction performance of this model is predicted to be relatively poor. In short, by calculating the heat conduction clusters, the three-dimensional heat conduction network inside the composite material is quantitatively characterized, which is convenient for predicting the heat conduction performance of composite materials filled with different gradations of fillers.

[0062] The advantages of the present invention adopting the above technical solutions are:

[0063] 1) General molecular simulation post-processing software, such as Ovito and VMD, can only process filling systems with uniform particle sizes. However, the filler sizes in actual composites generally show a certain distribution. The method of the present invention can respectively give the critical spacing for forming a heat conduction path between particles according to filler particles of different sizes, and determine the particle IDs that form a heat conduction path with each particle based on this critical spacing. The method of the present invention is not limited by particle size and can process filler particle filling systems with any particle size distribution.

[0064] 2) Since scanning electron microscope images are two-dimensional images, the numerical processing based on the images can only characterize the filler dispersion state on a certain plane inside the composite material. Although this method is based on the actual material system, two-dimensional information cannot reflect the construction of the three-dimensional heat conduction path inside the actual composite material. The present invention provides a set of accurate, effective and convenient methods for characterizing the three-dimensional heat conduction path inside the composite material by analyzing the representative volume element that is very close to the filler dispersion state inside the actual composite material and is macroscopically infinitesimal and microscopically infinite.

[0065] 3) The particle contact probability is positively correlated with the thermal conductivity of the composite material, but this value cannot intuitively reflect the three-dimensional structure of the heat conduction path inside the composite material, let alone analyze the distribution of the heat conduction path. The present invention gives the particle IDs included in each heat conduction cluster, and the three-dimensional structure of the heat conduction path can be conveniently given by the molecular simulation post-processing software.

[0066] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for characterizing the heat conduction path of a particulate-reinforced polymer-based thermal conductive composite material, characterized in that, Including the following steps: S1: Determine the critical spacing for forming a heat conduction path between particles; S2: Based on the critical spacing, count the particle IDs of the particles that form a heat conduction path with each particle within the representative volume element to form a complete list of the particle IDs of the heat conduction path particles within the representative volume element; S3: Use a cyclic search algorithm to calculate the number of heat conduction clusters within the representative volume element and the particle IDs included in each cluster; S4: Output the number of heat conduction clusters, the particle IDs included in each cluster, the size of each cluster, and the cluster distribution information, and quantitatively characterize the three-dimensional heat conduction network inside the composite material based on the above information; The specific content of step S1 is as follows: A thermal conductivity calculation model of bi-particle composite materials corresponding to different particle sizes is established respectively. According to the actual material properties, the particle thermal conductivity, matrix thermal conductivity, thermal resistance between the particle and the matrix interface, and contact thermal resistance between particles are set. The heat flux density between two particles at different center distances is calculated, and the variation curve of the heat flux density with the particle distance is obtained. The particle distance corresponding to 80% of the maximum heat flux density is taken as the critical distance of the heat conduction path, that is, when the center distance between the two particles meets , it is determined that a heat conduction path is formed between the two particles.

2. The method for characterizing the heat conduction path of the particulate-reinforced polymer-based thermal conductive composite material according to claim 1, wherein The specific content of step S2 is as follows: Suppose the representative volume element contains N particles of different sizes. For particle i , calculate the distances from the remaining N- 1 particle to the center of the sphere of particle i respectively. Count the d particle IDs and record them in the list of particle IDs of the heat conduction path of particle . Here, i represents the particle ID; i represents the particle ID. Repeat the above method, successively count all the particles within the representative volume element to form the corresponding list of particle IDs of the heat conduction path, and finally form a complete list of the particle IDs of the heat conduction path particles within the representative volume element.

3. The method for characterizing the heat conduction path of the particulate-reinforced polymer-based thermal conductive composite material according to claim 2, wherein The specific content of step S3 is as follows: According to the complete list of the particle IDs of the heat conduction path, mark the particle IDs of the particles that form a heat conduction path with particle 1 as the first-level particles of cluster 1; use the first-level particles as the search objects, and mark the particle IDs of the particles that form a heat conduction path with the first-level particles as the second-level particles of cluster 1; and so on, until the number of heat conduction path particles determined according to the searched particle IDs is 0, indicating that all the particles included in cluster 1 have been found; Then use the smallest particle ID not included in cluster 1 as the search particle, repeat the above cyclic search process to determine all the particles included in cluster 2; And so on, until the complete list of the particle IDs of the heat conduction path particles within the representative volume element is completely searched, indicating that all the particles that can form a heat conduction path within the representative volume element are included in a certain cluster; Count the number of particles and the particle IDs included in each cluster, and then calculate the total volume of the particles included in each cluster according to the particle diameter.

4. The method for characterizing the heat conduction path of the particulate-reinforced polymer matrix thermal conductive composite material according to claim 3, wherein In step S4, the size of the cluster includes the total number of particles included in a single cluster and the total volume of the particles included in a single cluster.

5. The method for characterizing the heat conduction path of the particulate reinforced polymer matrix thermal conductive composite according to claim 4, wherein, Count the relative number of the number of particles included in each cluster with respect to the total number of all particles, and count the relative volume of the total volume of the particles included in each cluster with respect to the total volume of all particles; To a certain extent, the relative number represents the size of the cluster.

6. The characterization method of the heat conduction path of the particulate-reinforced polymer-based thermal conductive composite according to claim 1, characterized in that, In step S4, the cluster distribution information is the quantity distribution and volume distribution information.

7. The method for characterizing the heat conduction path of the particulate-reinforced polymer-based thermally conductive composite material according to claim 1, characterized in that, The specific content of quantitatively characterizing the three-dimensional heat conduction network inside the composite material based on the output information in step S4 is as follows: Based on the output information, determine the largest cluster within the representative volume element; if the relative volume of the particles included in the largest cluster is large, it indicates that there are more heat conduction paths in the composite material and the heat conduction performance is better, otherwise, it indicates that there are fewer heat conduction paths in the composite material and the heat conduction performance is worse.

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