CN108009317A - A kind of conductivity studies emulation of composite material and modeling method - Google Patents

Abstract

Conductivity studies emulation and modeling method the invention discloses a kind of composite material; including the generation of controllability single-root carbon nano-tube model automatization, the generation of controllability reunion carbon nanotubes model automatization and FEM calculation; compared with prior art; the present invention establishes curvature of space random distribution carbon nano tube/epoxy resin composite material Three-dimension Numerical Model using FInite Element and discloses its thermal conduction mechanism; the emulation of the automation generating process of main protection controllability carbon nanotubes and modeling method, lay the foundation for the technical research in future.

Description

A Simulation and Modeling Method for Thermal Conductivity Research of Composite Materials

technical field

The invention relates to the technical field of thermal conduction simulation of nanomaterial polymer composite materials, in particular to a research simulation and modeling method for thermal conductivity of carbon nanotube/epoxy resin composite materials.

Background technique

Since the discovery of carbon nanotubes in 1991, they have attracted widespread attention of scientists due to their excellent mechanical properties, electrical conductivity and thermal conductivity. In recent years, increasing the thermal conductivity of polymers by adding carbon nanotubes to the epoxy-based polymer matrix has become a research hotspot. Carbon nanotubes can be divided into single-walled carbon nanotubes (SWCNTs), multi-walled carbon nanotubes (MWCNTs) and carbon nanofibers (CNFs). Compared with most nanofillers, carbon nanotubes can significantly enhance the thermal conductivity of composite materials, while maintaining a certain degree of insulation in composite materials.

With the improvement of computer simulation technology, more and more research tends to use numerical methods to quantitatively explore the influence of relevant parameters of carbon nanotubes on thermal conductivity, and try to use numerical methods to explain the depth mechanism of carbon nanotubes' thermal conductivity. Li Qianqian, based on the molecular dynamics method, explored the interface characteristics of carbon nanotubes and silicon, and found that the thermal conductance of the interface increases with the increase of temperature and the increase of the force between interface atoms, and explains the reasons for these two phenomena. As the temperature rises, more phonons are excited, which promotes the heat transfer; the atoms near the interface will vibrate intensified as the force increases, the phonon coupling becomes better, and the heat transfer level is improved, but there is no Explain how the improvement of interface thermal conductivity affects the overall thermal conductivity of composite materials. Song Yunpeng, based on the molecular dynamics simulation results, after different functional groups modify carbon nanotubes, the decrease in thermal conductivity is not much different, that is to say, the modification type has little effect on the thermal conductivity of CNTs. Zhou, S. used the finite element method (FEM) in 2012 to simulate and analyze the influence of spatially randomly distributed straight carbon nanotubes in the matrix on the overall thermal conductivity of the material, involving the interface thermal resistance between carbon nanotubes and the matrix, However, due to the complexity of the research, the contact thermal resistance between carbon nanotubes and the actual shape factors of carbon nanotubes in the matrix have not been considered. Therefore, it is necessary to establish a numerical model of carbon nanotubes/epoxy resin composites that is closer to the actual shape, and at the same time quantitatively explore the volume content of carbon nanotubes, the thermal conductivity of the carbon nanotubes and the matrix interface, and the contact thermal conductivity between carbon nanotubes and the thermal conductivity of the composite material. The combined effect of rate is necessary. This patent uses the finite element method (FEM) to establish a three-dimensional numerical model of curved carbon nanotubes/epoxy resin composites with random distribution in space to explore its thermal conduction behavior.

Contents of the invention

The object of the present invention is to provide a thermal conductivity research simulation and modeling method of composite materials in order to solve the above problems.

The present invention achieves the above object through the following technical solutions:

The present invention comprises the following steps:

(1) Automatic generation of controllable single carbon nanotube model: under the condition of existing computing resources, the diameter of carbon nanotube is set to 1nm, and the initial length is set to 100nm. In order to successfully generate this model in ANSYS finite element software, Using the method of splicing multiple straight cylinders and connecting them with arcs at the junction points to generate spatially curved carbon nanotubes, use matlab software to generate the first straight cylinder, its position and direction are random, and generate the first straight cylindrical carbon nanotubes Finally, according to the set bending angle, the end point of the first straight cylinder is used as the starting point of the second straight cylinder to generate the following carbon nanotubes. It is connected by an arc, and the curvature of the arc is controllable. The bending of the carbon nanotubes in the model is controlled between 0-96°, and so on, until the total length of the carbon nanotubes reaches the set length, that is, a single 3D-worm-like carbon is generated. Nanotubes: After the first CNT is generated, the subsequent carbon nanotubes need to detect the interference between them and the previously generated carbon nanotubes, that is, the contact depth. If the contact depth is greater than the set value, discard it and continue to generate ;

(2) Automatic generation of controllable agglomerated carbon nanotube models: the degree of agglomeration of carbon nanotubes is controlled by controlling the number of groups of agglomerated carbon nanotubes and the number of carbon nanotubes contained in each group of carbon nanotubes. First, randomly generate an agglomeration point within the volume range of 100×100×100nm ³ , and then generate a certain number of carbon nanotubes near the agglomeration point, so that a group of agglomerated carbon nanotubes is generated, and the rest of the agglomerated carbon nanotubes are similarly The method is generated until the preset degree of agglomeration is reached, and the remaining carbon nanotubes are randomly distributed to ensure that the volume content of carbon nanotubes in the model is the same;

(3) Finite element calculation: using a cube of 100×100×100nm ³ as the representative volume element solution domain, the calculation formula of thermal conductivity Kc is:

Where k _c is the thermal conductivity of the composite material, in w/(m k); Tz+ is the average temperature of the heat flow surface, in k; Tz- is the average temperature of the normal temperature surface, in k; q _z is The heat flux density applied on the heat flow surface, the unit is w/m ² ; Δz is the distance between the heat flow surface and the normal temperature surface, the unit is m; the heat flow load is applied to each of the six surfaces of the model by statistical methods, and the corresponding opposite surface Applying a normal temperature load, a thermal conductivity can be calculated for each pair of surfaces, and the final thermal conductivity of the composite material is the average value of six thermal conductivity calculation results.

The beneficial effects of the present invention are:

The present invention is a thermal conductivity research simulation and modeling method of composite materials. Compared with the prior art, the present invention adopts the finite element method to establish a three-dimensional numerical model of spatially curved and randomly distributed carbon nanotube/epoxy resin composite materials to reveal its The heat conduction mechanism mainly protects the simulation and modeling methods of the automatic generation process of controllable carbon nanotubes, laying the foundation for future technical research.

Description of drawings

The generation process of Fig. 1 single carbon nanotube;

Figure 2 A single carbon nanotube produced by controlling the bending angle;

In Fig. 2: (a) bending angle 0-10°, (b) bending angle 40°-60°, (c) bending angle 80°-90°;

Fig. 3 is a carbon nanotube agglomeration model;

Fig. 4 is the example of carbon nanotube/epoxy resin heat conduction model;

In Fig. 4: (a) randomly distributed carbon nanotube model, (b) finite element discrete model;

Fig. 5 is the thermal conductivity calculation result of the randomly distributed carbon nanotube model and the agglomerated carbon nanotube model;

Fig. 6 is the schematic diagram of heat flow network of dispersion model and reunion model;

In Figure 6: (a) heat flow network of dispersed carbon nanotubes, (b) heat flow network of agglomerated carbon nanotubes;

Fig. 7 is the relation of model thermal conductivity and carbon nanotube effective length;

Fig. 8 is a schematic diagram of the interference process.

Detailed ways

The present invention will be further described below in conjunction with accompanying drawing:

1. Automatic generation of controllable single carbon nanotube model:

In order to explore the influence of structural factors of carbon nanotubes such as dispersion, shape, and size on the thermal conductivity of composite materials, it is necessary to simulate the three-dimensional shape of carbon nanotubes more realistically. Under the condition of existing computing resources, the diameter of carbon nanotubes is set to is 1nm, and the initial length is set to 100nm. In order to successfully generate this model in ANSYS finite element software, the method of splicing multiple straight cylinders and connecting them with arcs at the junctions is used to generate spatially curved carbon nanotubes. Use matlab software to generate the first straight cylinder, its position and direction are random. After the first straight cylindrical carbon nanotubes are generated, according to the set bending angle, the end of the first straight cylindrical is used as the starting point of the second straight cylindrical to generate the following carbon nanotubes, and the angle between the front and rear is within the controlled angle range Inside, two sections of straight cylinders are connected by an arc, and the curvature of the arc is controllable, as shown in Figure 1. When the included angle θ exceeds a certain value, the carbon nanotubes will yield, which brings great difficulties to the modeling. However, since the yield point in the actual sample is very small compared with the whole carbon nanotube, the The overall thermal conductivity of the model has little effect, so the yielding phenomenon is negligible in our model. The bending of carbon nanotubes in the model is controlled between 0-96°. By analogy, until the total length of the carbon nanotube reaches the set length, that is, a single 3D-worm-like carbon nanotube is generated, as shown in FIG. 2 .

As shown in Figure 8: After the first CNT is generated, the subsequent carbon nanotubes need to detect the interference between them and the previously generated carbon nanotubes, that is, the contact depth. If the contact depth is greater than the set value, it will be discarded. , continue generating. Since the interference detection between randomly curved carbon nanotubes is difficult, the curved carbon nanotubes are divided into multiple segments of straight cylinders, and the arcs are divided into multiple segments of small cylinders to improve its accuracy. In this way, only the newly generated curved carbon nanotubes It only needs to perform interference detection between each section of the straight cylinder part of the tube and each section of the straight cylinder part of the bent carbon nanotube, and the interference detection judgment between the straight cylinders is relatively simple. The interferometric detection judgment program we generated can control the degree of contact between all carbon nanotubes, including the case that all carbon nanotubes are not in contact at all.

2. Automatic generation of controllable agglomerated carbon nanotube model

The dispersion quality of carbon nanotubes has a great influence on thermal conductivity, which indicates that it is necessary to establish a carbon nanotube aggregation model. The agglomeration degree of the carbon nanotubes is controlled by controlling the group number of the agglomerated carbon nanotubes and the number of carbon nanotubes contained in each group of carbon nanotubes. First, an agglomeration point is randomly generated within the volume range of 100×100×100nm ³ , and then a certain number of carbon nanotubes are generated near the agglomeration point, so that a group of agglomerated carbon nanotubes is formed. The rest of the agglomerated carbon nanotubes are also generated in the same way until the preset degree of agglomeration is reached, and the remaining carbon nanotubes are randomly distributed to ensure the same volume content of carbon nanotubes in the model. The results are shown in Figure 3.

3. Finite element calculation: Considering the shape and diameter of carbon nanotubes and existing computing resources, this patent uses a cube of 100×100×100nm ³ as a representative volume element solution domain. Figure 4 is an example of a carbon nanotube/epoxy resin thermal conductivity model. Thermal conductivity Kc is calculated as formula 1:

Where k _c is the thermal conductivity of the composite material, in w/(m k); Tz+ is the average temperature of the heat flow surface, in k; Tz- is the average temperature of the normal temperature surface, in k; q _z is The heat flux applied on the heat flow surface, the unit is w/m ² ; Δz is the distance between the heat flow surface and the normal temperature surface, the unit is m. Apply a heat flow load on each of the six faces of the model using a statistical method, and apply a normal temperature load to the corresponding opposite face. A thermal conductivity can be calculated for each pair of faces. The final thermal conductivity of the composite material is the result of six thermal conductivity calculations. average value.

Example:

Effect of Carbon Nanotube Distribution on Thermal Conductivity

Four pairs of thermal conductivity calculation models with volume contents of 0.059vol%, 0.200vol%, 0.300vol and 0.380vol% of carbon nanotubes were established, and each volume content contained a model of uniform dispersion of carbon nanotubes and carbon nanotubes Although there is a certain degree of reunion in the model, the thermal conductivity of these four pairs of models is calculated by finite element. The physical parameters of the materials used are shown in Table 1, and the calculation results are shown in Figure 5.

Table 1 Physical parameters of epoxy resin and carbon nanotubes in the calculation model

When the volume content of carbon nanotubes is 0.200vol%, the calculation results show that the difference between the well-dispersed model thermal conductivity (0.210w/(mk)) and the agglomerated model thermal conductivity (0.181w/(mk)) is 16%. , the difference with the experimental result of 23% is small, which verifies the validity of the model.

It can be seen from Fig. 5 that the dispersion of carbon nanotubes and the interfacial thermal conductivity Csm have a great influence on the thermal conductivity of the model at low volume content, which can be explained by the heat flow network: carbon nanotubes pass through the thermal common node in the whole Model space forms a fast heat transfer network. Due to its very high thermal conductivity, carbon nanotubes form a certain area of heat-affected zone around them. When the heat-affected zone of one carbon nanotube overlaps with the heat-affected zone of another carbon nanotube, then Heat can be transferred rapidly through the heat-affected zone, this overlapping area is called the heat common node. If the heat-affected zones of all carbon nanotubes have overlapping areas, heat can be quickly transferred through the formed heat-conducting network. The heat flow network diagrams of the dispersion model and the agglomeration model are shown in Fig. 6, respectively. The thermal conductivity depends on the transfer efficiency of the heat flow network. The heat flow network efficiency is determined by the distribution and quantity of heat common nodes: the higher the distribution quality and number of heat common nodes in space, the higher the heat flow network efficiency and the higher the thermal conductivity of the model; When the number is poor but the number is large, the efficiency of the heat flow network is still very low. The agglomerated carbon nanotube model can also form a heat flow network (as shown in Figure 2(b)), but there is no connecting channel between the local networks, so the thermal conductivity is low.

The effect of carbon nanotube morphology on thermal conductivity

The morphology of carbon nanotubes is characterized by the effective length,

η=L _c /L _l (2)

Wherein η is the effective length, L _c is the linear distance between two ends of the carbon nanotube, and L ₁ is the length of the curve of the carbon nanotube. The reason why the effective length can characterize the morphology of carbon nanotubes better than the bending angle is because it takes into account both the bending angle and the bending direction. So far, there is no numerical model to quantitatively study the effect of effective length on the thermal conductivity of composites. Under the same volume content (0.300vol%), four models with effective lengths of carbon nanotubes of 0.45, 0.57, 0.75 and 0.98 were established and the thermal conductivity was calculated. The results (Figure 7) show that the effective length of carbon nanotubes has a great influence on the thermal conductivity of the model. When the content of carbon nanotubes is 0.300vol%, the effective length increases from 0.45 to 0.98, and the thermal conductivity of the model increases from 0.28w/( mk) increased to 0.40w/(mk). The larger the effective length of the carbon nanotubes, the higher the thermal conductivity of the model, because the curling of the carbon nanotubes leads to self-agglomeration.

The effective length is a physical quantity that characterizes the shape of carbon nanotubes. The smaller the effective length, the more curved the carbon nanotubes, that is to say, the curling of the carbon nanotubes will reduce the effective length. The curling phenomenon can be understood as the self-agglomeration of carbon nanotubes.

The basic principles and main features of the present invention and the advantages of the present invention have been shown and described above. Those skilled in the industry should understand that the present invention is not limited by the above-mentioned embodiments. What are described in the above-mentioned embodiments and the description only illustrate the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will also have Variations and improvements are possible, which fall within the scope of the claimed invention. The protection scope of the present invention is defined by the appended claims and their equivalents.

Claims (1)

1. A thermal conductivity research simulation and modeling method of composite material, is characterized in that, comprises the following steps: (1) Automatic generation of controllable single carbon nanotube model: under the condition of existing computing resources, the diameter of carbon nanotube is set to 1nm, and the initial length is set to 100nm. In order to successfully generate this model in ANSYS finite element software, Using the method of splicing multiple straight cylinders and connecting them with arcs at the junction points to generate spatially curved carbon nanotubes, use matlab software to generate the first straight cylinder, its position and direction are random, and generate the first straight cylindrical carbon nanotubes Finally, according to the set bending angle, the end point of the first straight cylinder is used as the starting point of the second straight cylinder to generate the following carbon nanotubes. It is connected by an arc, and the curvature of the arc is controllable. The bending of the carbon nanotubes in the model is controlled between 0-96°, and so on, until the total length of the carbon nanotubes reaches the set length, that is, a single 3D-worm-like carbon is generated. Nanotubes: After the first CNT is generated, the subsequent carbon nanotubes need to detect the interference between them and the previously generated carbon nanotubes, that is, the contact depth. If the contact depth is greater than the set value, discard it and continue to generate ; (2) Automatic generation of controllable agglomerated carbon nanotube models: the degree of agglomeration of carbon nanotubes is controlled by controlling the number of groups of agglomerated carbon nanotubes and the number of carbon nanotubes contained in each group of carbon nanotubes. First, randomly generate an agglomeration point within the volume range of 100×100×100nm ³ , and then generate a certain number of carbon nanotubes near the agglomeration point, so that a group of agglomerated carbon nanotubes is generated, and the rest of the agglomerated carbon nanotubes are similarly The method is generated until the preset degree of agglomeration is reached, and the remaining carbon nanotubes are randomly distributed to ensure that the volume content of carbon nanotubes in the model is the same; (3) Finite element calculation: using a cube of 100×100×100nm ³ as a representative volume element solution domain, the calculation formula of thermal conductivity Kc is: <mrow><msub><mi>k</mi><mi>c</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>q</mi><mi>z</mi></msub><mi>&amp;Delta;</mi><mi>z</mi></mrow><mrow><msub><mi>T</mi><mrow><mi>Z</mi><mo>+</mo></mrow></msub><mo>-</mo><msub><mi>T</mi><mrow><mi>Z</mi><mo>-</mo></mrow></msub></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow> Where k _c is the thermal conductivity of the composite material, the unit is w/(m k); Tz+ is the average temperature of the applied heat flow surface, the unit is k; Tz- is the average temperature of the applied normal temperature surface, the unit is k; q _z is The heat flux density applied on the heat flow surface, the unit is w/m ² ; Δz is the distance between the heat flow surface and the normal temperature surface, the unit is m; the heat flow load is applied to each of the six surfaces of the model by statistical methods, and the corresponding opposite surface Applying a normal temperature load, a thermal conductivity can be calculated for each pair of surfaces, and the final thermal conductivity of the composite material is the average value of six thermal conductivity calculation results.