Method for creating simulation model of composite material with filler dispersed in polymer, and simulation method using the simulation model

Abstract

To provide a method for creating a simulation model of a composite material with a filler dispersed in a polymer, that allows a dispersion structure in a near-field region of a filler particle model, to be freely controlled.SOLUTION: A method in which a computer creates a simulation model of a composite material with a filler dispersed in a polymer, includes the steps of: randomly arranging filler particle models at coordinates not overlapping each other in a model creation region; and newly arranging a filler particle model in the model creation region where filler particle models are already arranged. The step of newly arranging a filler particle model includes the steps of: setting the coordinates of a filler particle model to be newly arranged, on the basis of the coordinates of the filler particle models already arranged and a preset distance between filler particle models; and newly arranging a filler particle model at the set coordinates, on the basis of the upper limit particle coordination number that is preset.SELECTED DRAWING: Figure 2

Description

Technical Field

[0001] The present invention relates to a method for creating a simulation model of a composite material in which a filler is dispersed in a polymer, and a simulation method using the simulation model.

Background Art

[0002] In a composite material in which a filler is blended with a polymer, the properties change depending on the dispersion form (morphology) of the filler. Therefore, in the development of various composite materials, the influence of the dispersion form of the filler on various properties is predicted by simulation. Since the accuracy of the simulation depends largely on the simulation model, some methods for creating the model have been proposed.

[0003] For example, there has been proposed a method for creating a simulation model of a heterogeneous material, which includes a step of dispersing and generating particle models in a modeling region sequentially, and when generating the particle models, controlling the generation positions of the particle models so that an allowable value of the distance between the center of gravity of the already arranged particle models and the center of gravity of the newly generated particle models decreases each time the number of the particle models increases by a set number (Patent Document 1).

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, according to the studies by the present inventors, in the conventional method for creating a simulation model, the modeling of the dispersion structure in the vicinity of filler particles (primary particles) has been insufficiently studied, and it has been difficult to freely control the short-distance network structure formed by filler particle models.

[0006] The present invention has been made in view of such circumstances, and an object of the present invention is to newly provide a method for creating a simulation model that can freely control the dispersion structure in the vicinity of filler particle models in a method for creating a simulation model of a composite material in which a filler is dispersed in a polymer.

Means for Solving the Problems

[0007] The gist of the present invention is as follows in [1] to [9] below. [1] A method for a computer to create a simulation model of a composite material in which a filler is dispersed in a polymer, randomly arranging filler particle models at non-overlapping coordinates in a model creation region, including a step of newly arranging a filler particle model in a model creation region where a filler particle model has already been arranged, The step of newly arranging the filler particle model includes a step of setting the coordinates of the filler particle model to be newly arranged based on the coordinates of the filler particle model already arranged and a preset distance between filler particle models, and a step of newly arranging a filler particle model at the set coordinates based on a preset upper limit particle coordination number. A method for creating a simulation model. [2] The method for creating a simulation model according to [1], wherein the step of newly arranging the filler particle model is repeated until a preset filler filling rate is satisfied. [3] The step of setting the coordinates of the filler particle model to be newly arranged is selecting an arbitrary filler particle model from the already arranged filler particle models, and setting, as the coordinates of the filler particle model to be newly arranged, the coordinates at which the distance between the coordinates of the selected arbitrary filler particle model and the coordinates of the filler particle model to be newly arranged is the preset distance between filler particle models. The method for creating a simulation model according to [1] or [2]. [4] The step of newly arranging a filler particle model at the set coordinates based on the preset upper limit particle coordination number is when the particle coordination number of the filler particle model in the model creation region is less than or equal to the preset upper limit particle coordination number, newly arranging a filler particle model at the set coordinates. The method for creating a simulation model according to any one of [1] to [3]. [5] The method for creating a simulation model according to any one of [1] to [4], wherein the preset upper limit particle coordination number is 3 or 4. [6] The method for creating a simulation model according to any one of [1] to [5], wherein the preset upper limit particle coordination number is set by the following formula. (Formula) Upper limit particle coordination number = π of the filler particle model / (1 - [filler filling rate [volume %] × 0.01]) [7] The method for creating a simulation model according to any one of [1] to [6], wherein the preset distance between filler particle models is the distance between the center-of-gravity coordinates of the preset filler particle models and is 0.9 times or more and 1.0 times or less the diameter of the filler particle model. [8] The method for creating a simulation model according to any one of [1] to [7], wherein the composite material is a composite material in which a conductive filler is dispersed in a polymer. [9] A simulation method including a step of analyzing the characteristics of a simulation model created by the method for creating a simulation model according to any one of [1] to [8].

Advantages of the Invention

[0008] According to the present invention, the dispersion structure in the vicinity of the filler particle model can be freely controlled.

[0009] According to the present invention, since the short-distance network structure formed between filler particle models can be controlled, it can contribute to improving the accuracy of simulation.

[0010] For example, according to an embodiment of the present invention, in the simulation of the electrical conductivity characteristics of a composite material, the deviation between the tendency of the volume resistivity value obtained by simulation and the tendency of the volume resistivity value obtained by measuring the actual composite material can be suppressed, so it can contribute to improving the accuracy of simulation. In this regard, in the conventional simulation of the electrical conductivity characteristics of a composite material, the dispersion structure in the vicinity of filler particle models cannot be freely controlled, and it was difficult to create a simulation model that reflects the dispersion structure in the actual composite material. Therefore, there was a tendency for a deviation to occur between the volume resistivity value obtained by simulation and the volume resistivity value obtained by measuring the actual composite material. Specifically, for example, in the simulation under the condition of a low filler filling rate, it is difficult to reproduce the short-distance network structure formed between filler particles. As a result, the volume resistivity value obtained by simulation tends to be higher in resistance than the measured value of the actual composite material, and there were problems with the accuracy of the simulation. According to an embodiment of the present invention, even in the simulation under the condition of a low filler filling rate, the tendency to increase in resistance can be suppressed, so it is very excellent in that it can improve the accuracy of the simulation.

[0011] In addition, in the conventional simulation method, since the simulation model is composed of complex elements, even if an ideal filler dispersion structure is found, it has often been difficult to reflect that ideal dispersion structure in the development of actual composite materials. According to one embodiment of the present invention, since it is possible to perform relatively simple modeling considering the inter-particle distance between filler particle models and the particle coordination number of the filler particle models, when an ideal filler dispersion structure is found from the results of the simulation, it is also excellent in that it is relatively easy to reflect it in the development of actual composite materials.

Brief Description of the Drawings

[0012]

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Embodiments for Carrying Out the Invention

[0013] A method for creating a simulation model according to an embodiment of the present invention (hereinafter sometimes referred to as this embodiment) is a method in which a computer creates a simulation model of a composite material in which fillers are dispersed in a polymer. It is characterized in that the positions of the filler particle models are controlled based on a preset filler particle model inter-distance, and the coordination number of the filler particle models is controlled based on a preset upper limit coordination number. Thereby, the dispersion structure in the vicinity region of the filler particle models can be freely controlled. Hereinafter, embodiments of the present invention will be described in detail.

[0014] In this embodiment, the method for creating a simulation model and the simulation method are executed by a computer. The computer is, for example, an information processing device such as a personal computer provided with an arithmetic processing unit (CPU), a ROM, a working memory, a storage device such as a magnetic disk, an input device such as a keyboard and a mouse, a display device such as a display, etc. In this, a processing routine stored in advance is executed by the cooperation of software and hardware.

[0015] In this embodiment, the composite material to be modeled and analyzed is a composite material in which fillers are dispersed in a polymer.

[0016] Examples of the polymer include rubber, resin, elastomer, etc. Specifically, but not limited to the following, ethylene-propylene-diene monomer terpolymer (EPDM), acrylic rubber, urethane rubber, styrene-butadiene-styrene block polymer (SBS), styrene-isobutylene-styrene block polymer (SIBS), styrene-butadiene (SB) copolymer, styrene-isoprene (SI) copolymer, styrene-isoprene-styrene (SIS) copolymer, styrene-ethylene-butylene (SEB) copolymer, styrene-ethylene-butylene-styrene (SEBS) copolymer, styrene-ethylene-propylene (SEP) copolymer, styrene-ethylene-propylene-styrene (SEPS) copolymer, hydrogenated copolymers of the above, ethylene-propylene copolymer (EPR), butadiene rubber (BR), isoprene rubber (IR), styrene-butadiene rubber (SBR), liquid isoprene rubber (liquid IR), liquid butadiene rubber (liquid BR), liquid styrene-butadiene rubber (liquid SBR), liquid styrene-isoprene rubber (liquid SI), liquid styrene-ethylene-propylene rubber (liquid SEP), liquid isoprene-butadiene rubber (liquid IR-BR), etc.

[0017] Examples of the filler include carbon black, silica, talc, calcium carbonate, carbon fiber, carbon nanotube, etc. Examples of the conductive filler include conductive carbon-based fillers such as conductive carbon black, carbon nanotubes, and graphite.

[0018] Figures 1 to 3 are flowcharts showing an example of the main processing procedures for creating the simulation model according to this embodiment. The flowchart shows an example of the embodiment. The method for creating the simulation model of the present invention is not limited to the order of the flowchart.

[0019] <Step S1> The method for creating a simulation model according to this embodiment includes step S1 of setting parameters such as the filler filling rate. In step S1, in addition to the filler filling rate, for example, the size (radius, diameter, volume, etc.) of the filler particle model, the shape of the filler particle model (sphere, oblate spheroid (prolate ellipsoid, flattened ellipsoid), plate-like body, cylindrical shape, etc.), the range of the model creation area, the distance between filler particle models, the criterion for calculating the coordination number of filler particle models, the upper limit coordination number, etc. are set in advance.

[0020] <Step S2> The method for creating a simulation model according to this embodiment includes step S2 of randomly arranging filler particle models at non-overlapping coordinates with each other in the model creation area. In step S2, for example, among the total number corresponding to the filler filling rate set in step S1, a plurality of filler particle models corresponding to a part of the number are randomly arranged at coordinates where the filler particle models do not overlap with each other.

[0021] Specifically, step S2 randomly selects an arbitrary coordinate in the model creation area using, for example, a uniform random number or the like, and sequentially arranges the filler particle model at the selected coordinate. In the process of this process, when the selected coordinate overlaps with another filler particle model that has already been arranged, the selection of the coordinate is redone and a new different coordinate is randomly selected. Step S2 ends the process, for example, when a part of the ratio or number among the total number is reached.

[0022] The number or ratio of the filler particle models arranged in step S2 is appropriately set in advance according to the purpose of the simulation and the characteristics of the filler. For example, the number of filler particle models corresponding to about 0.3 - 20%, 1 - 10%, or 1 - 5% of the total number corresponding to the filler filling rate is arranged.

[0023] FIG. 4 is a diagram for explaining an example of the process of step S2. For the sake of convenience, FIG. 4 shows a three-dimensional model creation region 1 and a filler particle model 2 which is a three-dimensional sphere, represented in two dimensions (the same applies to the figures after FIG. 4). Step S2 is, for example, a step of randomly arranging a plurality of filler particle models 2 at non-overlapping coordinates in the initial state of the model creation region 1 (a state where the filler particle model does not exist). As shown in FIG. 4, after the execution of step S2, a plurality of filler particle models 2 are arranged, but the coordinates of the filler particle models 2 do not overlap with each other, and they are arranged in a predetermined dispersed state with an interval between them.

[0024] Similar to the conventional simulation model, the model creation region 1 is the entire region where the periodic boundary condition is defined, or an arbitrary-shaped partial region extracted from the region where the periodic boundary condition is defined, or an arbitrary-shaped partial region extracted from the space where the periodic boundary condition is not defined. The range of the model creation region 1 is set in advance.

[0025] The filler particle model arranged in the model creation region 1 is a model of the primary particles of the filler. The shape of the filler particle model is generated by approximately modeling shapes such as a sphere, an oblate spheroid (prolate ellipsoid, flattened ellipsoid), a plate-like body, a cylindrical body, etc., and parameters for specifying the size such as the radius, diameter, volume, etc. (the size of the region occupied in the model creation region) are defined in advance. Also, when performing various characteristic simulations described later, characteristic parameters (such as conductivity) that are separately required are set. In this embodiment, a spherical filler particle model is set, but filler particle models of other shapes may be used, or two or more types may be used in combination. Also, in this embodiment, other regions except the region where the filler particle model is created are defined as the polymer model.

[0026] <Step S3> The method for creating a simulation model according to this embodiment includes step S3 of newly arranging an additional filler particle model 3 in a model creation region 1 including a plurality of filler particle models 2 arranged in step 2. Step S3 controls the coordinates of the filler particle model 3 to be newly arranged based on the filler particle models 2 already arranged. For example, it includes step 31 of setting the coordinates of the filler particle model 3 to be newly arranged based on the coordinates of the filler particle models 2 arranged in step S2. In step 31, for example, an arbitrary filler particle model 2 is randomly selected from among the plurality of filler particle models 2 already arranged based on a uniform function or the like (step 311). The selected filler particle model 2 serves as a reference or starting point for generating the filler particle model 3 to be newly arranged.

[0027] Next, based on the coordinates of the selected filler particle model 2 and the preset distance d between filler particle models, the coordinates of the filler particle model 3 to be newly arranged are selected (step 312). Step S312 is a step of controlling the relative coordinates between the coordinates of the selected filler particle model 2, which serves as the starting point of the filler particle model 3 to be newly arranged, and the coordinates of the filler particle model 3 to be newly arranged among the filler particle models 2 already arranged. Specifically, for example, the coordinates of the filler particle model 3 to be newly arranged are randomly selected from among the coordinate groups where the distance from the coordinates of the selected filler particle model 2 is the preset distance d between filler particle models, using, for example, a uniform random number or the like. By performing such processing, for example, it becomes possible to model considering the filler dispersion structure in an actual composite material, such as making the probability of the filler particle model being isolated extremely small.

[0028] The preset distance d between the filler particle models can be appropriately set according to the purpose of the simulation and the characteristics of the filler. For example, from the perspective of freely controlling the short-distance network, the distance at which the surface of the already arranged filler particle model 2 contacts the surface of the newly arranged filler particle model 3, the distance at which a predetermined gap is formed between the surfaces of the filler particle models, or the distance at which the filler particle models share a predetermined overlapping region, etc., can be determined based on appropriate criteria.

[0029] In one embodiment of the present invention, the preset distance d between the filler particle models can be set as the distance between the centers of gravity of the filler particle models, and the preset distance between the filler particle models is, for example, 0.9 times or more and 1.5 times or less, 0.9 times or more and 1.0 times or less, etc. of the diameter of the filler particle model. Specifically, for example, the distance set by the following formula can be cited as an example. (Formula) Distance d between filler particle models = diameter of filler particle model × α (where α is 0.9 or more and 1.5 or less)

[0030] Also, in the embodiment of creating the electrical conductivity simulation model, it is preferable that α in the above formula is less than 1.0, and preferably 0.9 or more and 0.95 or less.

[0031] Next, the step of selecting the coordinates of the newly arranged filler particle model 3 based on the coordinates of the selected filler particle model 2 and the preset distance d between the filler particle models will be described (step 311, step 312). In FIG. 5 schematically showing a filler particle model in a partial area of the model creation area 1, there are a plurality of already arranged filler particle models 2a, 2b,... etc. When the filler particle model 2a is randomly selected from among the plurality of already arranged filler particle models 2a, 2b,... etc., an arbitrary coordinate randomly selected from a group of coordinates via a preset distance d between filler particle models (in FIG. 5, the diameter of the filler particle model) from the center-of-gravity coordinates of the filler particle model 2a is set as the coordinate of the filler particle model 3 to be newly arranged. Specifically, in FIG. 5, an arbitrary coordinate randomly selected from among the center-of-gravity coordinates of the filler particle models 3a, 3b, 3c,... etc. is set as the coordinate of the filler particle model 3 to be newly arranged. That is, in FIG. 5, the filler particle models 3a, 3b, 3c,... etc. become one of the candidates for the filler particle model to be newly arranged. Next, when each of the conditions described later is satisfied, the filler particle model 3 is newly arranged at the set coordinate.

[0032] Next, in the present embodiment, the same process is repeated. That is, an arbitrary filler particle model 2 is randomly selected from among the plurality of already arranged filler particle models 2..., an arbitrary coordinate is randomly set from a group of coordinates via a preset distance d between filler particle models from the center-of-gravity coordinates of the selected filler particle model 2, and when each of the conditions described later is satisfied, a series of processes of newly arranging the filler particle model 3 at the set coordinate are repeated, and the filler particle model 3 is newly arranged sequentially until a preset filler filling rate is achieved.

[0033] In addition, in FIG. 5 above, the case where the diameter of the filler particle model is set as the preset distance d between filler particle models is illustrated. However, as shown in FIG. 6, for example, when creating a conductive property simulation model, etc., the distance d between filler particle models is preferably set to a predetermined distance shorter than the diameter of the filler particle model (a distance where the filler particle models slightly overlap).

[0034] As described above, based on the coordinates of the selected filler particle model 2 and the preset distance d between the filler particle models, the coordinates of the filler particle model 3 to be newly arranged are set. However, when each of the following conditions is satisfied, the filler particle model 3 is newly arranged at the set coordinates. That is, in the method for creating a simulation model according to the present embodiment, as shown in step 313 of FIG. 3 and step 32 of FIG. 2, (1) the coordinates of the filler particle model 3 to be newly arranged are such that the distance from the coordinates of other filler particle models does not become less than the preset distance between the filler particle models (the filler particle models do not overlap excessively), and (2) the coordination number of the filler particle model is equal to or less than the preset upper limit coordination number.

[0035] <Step S313> First, step S313 is a step of controlling the relative coordinates between the coordinates of other filler particle models excluding the filler particle model that serves as the starting point of the filler particle model to be newly arranged among the already arranged filler particle models 2 and the coordinates of the filler particle model to be newly arranged. That is, step S313 is a step for suppressing the excessive overlap of the coordinates of the filler particle model to be newly arranged with the coordinates of other filler particle models arranged in the model creation region. Specifically, among the already arranged filler particle models, the relative coordinates between the filler particle model that serves as the starting point of the filler particle model to be newly arranged (the selected filler particle model) and the coordinates of the filler particle model to be newly arranged are controlled by the preset distance d between the filler particle models. On the other hand, if the relative coordinates between the coordinates of other filler particle models (non-selected filler particle models) excluding the filler particle model that serves as the starting point of the filler particle model to be newly arranged among the already arranged filler particle models and the coordinates of the filler particle model to be newly arranged are not controlled, there is a possibility that the coordinates of the filler particle model to be newly arranged and the coordinates of other filler particle models (non-selected filler particle models) will overlap excessively. Therefore, step S313 controls such overlap.

[0036] Taking FIG. 7 as an example for explanation. As shown in FIG. 7 which schematically shows the filler particle models in a partial area of the model creation area 1, there are a plurality of already arranged filler particle models 2a, 2b,... etc. When the filler particle model 2a is randomly selected from among the plurality of already arranged filler particle models 2a, 2b,... etc., any coordinate randomly selected from the coordinate group via the preset distance d between filler particle models (in this embodiment, the diameter of the filler particle model) from the center-of-gravity coordinates of the filler particle model 2a is assumed to be a candidate for the coordinates of the newly arranged filler particle model 3. However, since the distance d' between the center-of-gravity coordinates of the filler particle model 3b and the center-of-gravity coordinates of another filler particle model 2b is less than the preset distance d between filler particle models (in this embodiment, the diameter of the filler particle model), the center-of-gravity coordinates of the filler particle model 3b are not set as the coordinates of the newly arranged filler particle model 3.

[0037] As an example of the processing when the above conditions are not satisfied, for example, again, any filler particle model 2 is randomly selected from among the plurality of already arranged filler particle models 2 based on a uniform function or the like (step 311), and any coordinate randomly selected from the coordinate group via the preset distance d between filler particle models (in this embodiment, the diameter of the filler particle model) from the center-of-gravity coordinates of the selected filler particle model is selected as a candidate for the coordinates of the newly arranged filler particle model 3 (step 312), and it is determined whether the above conditions are satisfied (see FIG. 3). When the above conditions are satisfied, the selected coordinates are set as the coordinates of the newly arranged filler particle model.

[0038] In FIG. 7 above, the steps of step 312 and step 313 are executed based on the preset filler particle model distance d, but it can be set appropriately differently according to the purpose of the simulation or the like. For example, while setting the distance between the filler particle models in step 312, that is, the distance between the coordinates of the newly arranged filler particle model 3 and the coordinates of the starting filler particle model 2 as the first filler particle model distance d1, the preset filler particle model distance in step 313, that is, the distance between the coordinates of the other filler particle model 2 excluding the starting filler particle model 2 and the coordinates of the newly arranged filler particle model 3 can also be individually set as the second filler particle model distance d2.

[0039] <Step S32> Next, a step (step 32) will be described on the condition that the coordination number of the filler particle model is less than or equal to the upper limit coordination number. As described above, based on the coordinates of the selected filler particle model 2 and the preset filler particle model distance d, the coordinates of the newly arranged filler particle model 3 are set. However, in the method for creating a simulation model according to the present embodiment, a step (step 32) on the condition that the coordination number of the filler particle model is less than or equal to the preset upper limit coordination number is important. Specifically, this step is conditional on the coordination number of each of the selected filler particle model 2, the filler particle model 3 newly arranged starting from the selected filler particle model 2, and the unselected filler particle model 2 being less than or equal to the preset upper limit coordination number.

[0040] The method for creating a simulation model according to the present embodiment includes a step of presetting the upper limit coordination number and a step of presetting a criterion for calculating the coordination number of the filler particle model. The step of presetting the upper limit of the particle coordination number is a step of presetting the upper limit of the particle coordination number in consideration of the purpose of the simulation, the characteristics of the filler, the filler filling rate, etc. The upper limit of the particle coordination number can be set, for example, based on the empirical formula of powder engineering. Specifically, for example, the upper limit of the particle coordination number can be preset by the following formula. (Formula) Upper limit of particle coordination number = Pi (π) of the filler particle model / (1 - [filler filling rate [volume%] × 0.01]) Specific examples of the preset upper limit of the particle coordination number are appropriately set according to the purpose of the simulation and the characteristics of the filler. As a conductive property simulation model, for example, about 3 to 5 or 3 to 4 can be mentioned.

[0041] The step of presetting the criteria for determining the coordination number of the filler particle model is a step of presetting the criteria for determining the coordination number of any filler particle model in the model creation area. Here, the coordination number is a concept in powder engineering and means the number of contact points with other particles existing on the surface of one particle. In the present invention, however, the criteria can be appropriately set in consideration of the purpose of the simulation and the characteristics of the filler to be targeted. For example, in addition to the case where the criteria are set based on the number of contact points with other filler particle models existing on the surface of one filler particle model, for example, the criteria can be set based on the number of other filler particle models in contact with one filler particle model. Furthermore, even if one filler particle model and other filler particle models are not geometrically in contact, in cases where they are close to each other, etc., considering the purpose of the simulation and the characteristics of the filler being targeted, there may be cases where it is appropriate to consider them as being in contact. Therefore, it is also possible to set based on the number of filler particle models having coordinates in the surrounding area of one filler particle model. Specifically, for example, assuming a surrounding area formed when expanding its volume at an arbitrary magnification in a similar shape with the center-of-gravity coordinates of one filler particle model as the center, it may be based on the number of other filler particle models having center-of-gravity coordinates in the said surrounding area. Also, for example, assuming a surrounding area with the center-of-gravity coordinates of one filler particle model as the center and a radius of a distance 1.0 times to 1.5 times the diameter of the said filler particle model, it may be based on the number of other filler particle models having center-of-gravity coordinates in the said surrounding area.

[0042] FIG. 8 will be described as an example. The preset upper limit of the particle coordination number is 3, and the criterion for determining the particle coordination number of the filler particle model is based on the number of other filler particle models in contact with one filler particle model. In the arrangement of FIG. 8 schematically showing the filler particle models in a partial area of the model creation area 1, since the particle coordination number of the filler particle model 3b becomes 4, the center-of-gravity coordinates of the filler particle model 3b are not set as the coordinates of the filler particle model 3 to be newly arranged. Specifically, in FIG. 8, in a state where there are already 4 filler particle models, the filler particle model 2a is randomly selected (step 311), and when setting the center-of-gravity coordinates of the filler particle model 3b as the coordinates via the preset distance d between filler particle models (in this embodiment, the diameter of the filler particle model) from the center-of-gravity coordinates of the filler particle model 2a, since the particle coordination number of the filler particle model 3b becomes 4, the center-of-gravity coordinates of the filler particle model 3b are not set as the coordinates of the filler particle model 3 to be newly arranged.

[0043] Next, taking FIG. 9 as an example, an explanation will be given. The preset upper limit of the particle coordination number is 3, and the criterion for determining the particle coordination number of the preset filler particle model is based on the number of other filler particle models in contact with one filler particle model. In the arrangement of FIG. 9 schematically showing the filler particle models in a partial region of the model creation region 1, since the particle coordination number of the filler particle model 2a becomes 4, the center-of-gravity coordinates of the filler particle model 3b are not set as the coordinates of the filler particle model 3 to be newly arranged. Specifically, in FIG. 9, in a state where there are already four filler particle models, the filler particle model 2a is randomly selected (step 311), and when the center-of-gravity coordinates of the filler particle model 3b are set as the coordinates via the preset distance d between the filler particle models (in this embodiment, the diameter of the filler particle model) from the center-of-gravity coordinates of the filler particle model 2a, since the particle coordination number of the filler particle model 2a becomes 4, the center-of-gravity coordinates of the filler particle model 3b are not set as the coordinates of the filler particle model 3 to be newly arranged.

[0044] Next, taking FIG. 10 as an example, it will be described. The preset upper limit of the particle coordination number is 3, and the criterion for determining the particle coordination number of the preset filler particle model is to set a surrounding region with a radius of a distance (D) 1.1 times the diameter of the filler particle model centered on the center-of-gravity coordinates of one filler particle model, and use the number of other filler particle models having the center-of-gravity coordinates in the surrounding region as the criterion. In the arrangement of FIG. 10 schematically showing the filler particle models in a partial region of the model creation region 1, since the particle coordination number of the filler particle model 2a becomes 4, the center-of-gravity coordinates of the filler particle model 3b are not set as the coordinates of the filler particle model 3 to be newly arranged. Specifically, in FIG. 10, in a state where there are already 4 filler particle models, the filler particle model 2a is randomly selected (step 311), and when the center-of-gravity coordinates of the filler particle model 3b are set as the coordinates via the preset distance d between the filler particle models (in this embodiment, the diameter of the filler particle model) from the center-of-gravity coordinates of the filler particle model 2a, since the particle coordination number of the filler particle model 2a becomes 4, the center-of-gravity coordinates of the filler particle model 3b are not set as the coordinates of the filler particle model 3 to be newly arranged.

[0045] Next, taking FIG. 11 as an example for explanation. The preset upper limit of the particle coordination number is 3, and the criterion for determining the particle coordination number of the preset filler particle model is based on the number of other filler particle models in contact with one filler particle model. In the arrangement of FIG. 11 schematically showing the filler particle models in a partial region of the model creation region 1, since the particle coordination number of the filler particle model 2 becomes 4, the barycentric coordinates of the filler particle model 3b are not set as the coordinates of the filler particle model 3 to be newly arranged. Specifically, in FIG. 11, when there are already five filler particle models, the filler particle model 2a is randomly selected (step 311), and when the barycentric coordinates of the filler particle model 3b are set as the coordinates via the preset distance d between the filler particle models (in this embodiment, the diameter of the filler particle model) from the barycentric coordinates of the filler particle model 2a, since the particle coordination number of the filler particle model 2 becomes 4, the barycentric coordinates of the filler particle model 3b are not set as the coordinates of the filler particle model 3 to be newly arranged.

[0046] As an example of the process when the conditions regarding the upper limit of the particle coordination number are not satisfied, for example, again, an arbitrary filler particle model 2 is randomly selected from among the plurality of already arranged filler particle models 2 based on a uniform function or the like (step 311), the processes of steps 312 to 314 are performed, and the determination as to whether the conditions of step S32 are satisfied is repeatedly made. When the conditions of step S32 are satisfied, a new filler particle model is arranged at the coordinates selected in step 312.

[0047] By repeating the above steps, filler particle models are newly arranged sequentially. When the preset filler filling rate is satisfied, the creation of the simulation model is terminated (step S4: see FIG. 1). The simulation model obtained by the method for creating a simulation model according to this embodiment is schematically shown in FIG. 12.

[0048] In the above-described embodiment, for convenience of explanation, after determining the condition of step 313, the condition of step 32 is determined. However, the order of the two conditions is not limited. If both conditions are satisfied, a new filler particle model may be arranged for processing.

[0049] In one embodiment of the present invention, it can be used as a simulation model used in various simulation methods. Further, it can be used as a base model of a simulation model used in various simulation methods, and can be applied, for example, to the creation of a simulation model used in a simulation method using the molecular dynamics method.

[0050] In the embodiment of the present invention, it is mainly a two-phase model of a filler particle model and a polymer model, but it is not limited thereto, and other model elements may be included.

[0051] Furthermore, the method for creating a simulation model according to the present embodiment has an advantage in that a simulation model can be freely created without using a TEM image or the like obtained by observing an actual composite material. However, it is also possible to acquire an image such as a TEM image obtained by observing an actual composite material and create a simulation model based on the image.

[0052] <Simulation method using a simulation model> A simulation method including a step of analyzing the characteristics of the simulation model will be described by taking a conductivity simulation method as an example. However, the present invention is not limited to the conductivity simulation method, and can also be applied to, for example, a simulation method of mechanical properties such as durability.

[0053] Define the interface between the filler particle model and the polymer model created above as an interface layer model. As an example of the interface layer model, for example, a position element in which at least one adjacent element among the position elements of the filler particle model becomes a polymer model can be defined as the interface layer model.

[0054] Also, in the simulation model, a positive electrode element and a negative electrode element as electrode elements are added. The positive electrode element and the negative electrode element are models corresponding to electrodes with high conductivity. The positive electrode element is located at one end in the left - right direction of the simulation model, and the negative electrode element is located at the other end in the left - right direction. A predetermined positive electrode potential is set for the positive electrode element, and a predetermined negative electrode potential, for example, a ground potential, is set for the negative electrode element.

[0055] Next, based on the preset conductivity of the filler particle model, the preset conductivity of the polymer model, the preset conductivity of the interface layer model, the preset conductivity of the positive electrode element, and the preset conductivity of the negative electrode element, set the conductivity between adjacent position elements. The conductivity between adjacent position elements is set to different conductivities according to the types of the adjacent position elements respectively. In this way, a simulation model for analyzing conductivity characteristics is created.

[0056] The analysis of the conductivity characteristics can be performed according to a conventionally known method. For example, with the input condition that a predetermined positive electrode potential is applied to the positive electrode element and a predetermined negative electrode potential is applied to the negative electrode element, perform an analysis of the electrical resistance value between the positive electrode element and the negative electrode element. Also, it is possible to analyze the conduction path and the like based on the current value for each position element.

Example

[0057] Using the method for creating a simulation model according to the above - described embodiment, a simulation model SM1 was created and a conductivity characteristic simulation was performed. Various parameters are as follows. In the simulation model SM1, the preset upper limit of the particle coordination number is a numerical value set based on the above formula (the circumference ratio π of the filler particle model / (1 - [filler filling rate [volume%] × 0.01])). Further, the criterion for determining the preset particle coordination number of the filler particle model is assumed to be the surrounding area centered on the center of gravity coordinates of one filler particle model and with a radius of 1.0 times the diameter of the filler particle model, and is based on the number of other filler particle models having the center of gravity coordinates in the surrounding area (for example, refer to Fig. 10). (Parameter) ·Radius of the filler particle model 5 voxels ·Model creation area 512×512×256 voxels 3 ·Distance between filler particle models Diameter of the filler particle model (10 voxels) × 0.93 ·Upper limit of the particle coordination number 3 ·Filling rate of the filler particle model 5.0 vol% ·Resistance value of the filler particle model 10 -2 Ω·cm ·Resistance value of the polymer model 10 12 Ω·cm ·Resistance value of the interface layer model 10 0 Ω·cm ·Initial condition Potential 0 in all voxels (electrodes are each 2 voxels thick) ·Convergence condition Change amount of the total potential sum < 10 0 or 1 million loops

[0058] Also, except when not setting the upper limit of the particle coordination number (no limit on the upper limit of the particle coordination number), in the same manner as the simulation model SM1, a simulation model SM2 was created and a conductive property simulation was performed.

[0059] <Evaluation of the particle coordination number> Since the simulation model SM2 was created without setting an upper limit on the particle coordination number, the number of filler particle models with a particle coordination number of 4 or more (specifically, the particle coordination number is 4 to 9) was about 1000 (out of a total of about 6400 filler particle models). In contrast, since the simulation model SM1 was created with a limited upper limit on the particle coordination number, the particle coordination number of all filler particle models was 3 or less, and there were substantially no filler particle models with a particle coordination number of 0.

[0060] <Evaluation of Conductivity Simulation> In conventional conductivity simulations, it is difficult to reproduce the short-distance network structure formed by filler particles. As a result, especially under conditions of low filler filling rates (for example, 5 to 8% or less), the volume resistivity obtained by simulation tends to be higher than the measured value of the actual composite material, and there are problems with the accuracy of the simulation. As a result of performing conductivity simulations using simulation model SM1 (with a limit on the upper particle coordination number) or simulation model SM2 (without a limit on the upper particle coordination number), it was confirmed that the volume resistivity obtained using simulation model SM1 was significantly lower than that of simulation model SM2. Specifically, as shown in Fig. 13, it was confirmed that the volume resistivity (Ω·cm) of simulation model SM1 was significantly lower than that of simulation model SM2 and approached the measured value. The number of N for each simulation model is 45.

Industrial Applicability

[0061] The present invention provides a new method for creating a simulation model of a composite material in which a filler is dispersed in a polymer, and is particularly useful, for example, as a method for creating a simulation model used in a conductivity simulation method.

Explanation of Signs

[0062] 1 Model creation area 2(2a…) Filler particle model 3(3a…) Filler particle model (filler particle model to be newly arranged)

Claims

1. A method for a computer to create a simulation model of a composite material in which fillers are dispersed in a polymer, comprising: randomly arranging filler particle models at non-overlapping coordinates in a model creation area; including the step of newly arranging a filler particle model in the model creation area where the filler particle model has already been arranged; the step of newly arranging the filler particle model includes: setting the coordinates of the filler particle model to be newly arranged based on the coordinates of the filler particle model already arranged and the preset distance between filler particle models; including the step of newly arranging a filler particle model at the set coordinates based on a preset upper limit particle coordination number; A method for creating a simulation model.

2. The method for creating a simulation model according to claim 1, wherein the step of newly arranging the filler particle model is repeated until a preset filler filling rate is satisfied.

3. The step of setting the coordinates of the filler particle model to be newly arranged includes: selecting an arbitrary filler particle model from among the filler particle models already arranged; setting, as the coordinates of the filler particle model to be newly arranged, the coordinates at which the distance between the coordinates of the selected arbitrary filler particle model and the coordinates of the filler particle model to be newly arranged is equal to the preset distance between filler particle models. The method for creating a simulation model according to claim 1 or 2.

4. The step of newly arranging a filler particle model at the set coordinates based on the preset upper limit particle coordination number includes: when the particle coordination number of the filler particle model in the model creation area is less than or equal to the preset upper limit particle coordination number, newly arranging a filler particle model at the set coordinates. The method for creating a simulation model according to claim 1 or 2.

5. The method for creating a simulation model according to claim 1 or 2, wherein the preset upper limit particle coordination number is 3 or 4.

6. The method for creating a simulation model according to claim 1 or 2, wherein the preset upper limit particle coordination number is set by the following formula: (Formula) Upper limit particle coordination number = π of the filler particle model / (1 - [filler filling rate [volume%] × 0.01])

7. The pre-set filler particle model inter-distance is the distance between the center-of-gravity coordinates of the pre-set filler particle models, and is 0.9 times or more and 1.0 times or less the diameter of the filler particle model. The method for creating a simulation model according to claim 1 or 2.

8. The method for creating a simulation model according to claim 1 or 2, wherein the composite material is a composite material in which a conductive filler is dispersed in a polymer.

9. A simulation method including a step of analyzing the characteristics of a simulation model created by the method for creating a simulation model according to claim 1 or 2.

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