Method for creating simulation model of composite material in which filler is dispersed in polymer, and simulation method using said simulation model

Abstract

Provided is a simulation model creation method capable of freely controlling a dispersion structure in a neighboring region of a filler particle model in a simulation model of a composite material in which a filler is dispersed in a polymer.　In this simulation model creation method, a computer creates a simulation model of the composite material, and the method comprises a step for randomly arranging filler particle models at coordinates that do not overlap each other in a model creation region, and a step for newly arranging a filler particle model in a model creation region in which a filler particle model is already arranged, the step for newly arranging the filler particle model including a step for setting coordinates of the newly arranged filler particle model on the basis of coordinates of the already arranged filler particle model and a preset inter-filler particle model distance, and a step for newly arranging a filler particle model at the set coordinates on the basis of a preset upper-limit particle coordination number.

Description

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

[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.

[0002] The properties of composite materials made by blending fillers with polymers change depending on the filler's dispersion form (morphology), so in the development of various composite materials, simulations are used to predict the effect of the filler's dispersion form on various properties. Since the accuracy of simulations depends heavily on the simulation model, several methods for creating such models have been proposed.

[0003] For example, a method for creating a simulation model of a heterogeneous material has been proposed, which includes a step of generating particle models in a dispersed manner in a modeling area, and controlling the generation positions of the particle models so that, when generating the particle models, an allowable value for the distance between the centers of gravity of an already placed particle model and a newly generated particle model is reduced every time the number of the particle models increases by a set number (Patent Document 1).

[0004] Patent No. 5854067

[0005] However, according to the studies of the present inventors, conventional methods for creating simulation models have not sufficiently considered the modeling of the dispersion structure in the vicinity of filler particles (primary particles), making it difficult to freely control the short-range network structure formed by filler particle models.

[0006] The present invention has been made in consideration of the above circumstances, and provides a new method for creating a simulation model of a composite material in which a filler is dispersed in a polymer, which method allows for free control of the dispersion structure in the area surrounding the filler particle model.

[0007] The gist of the present invention is the following [1] to [9]. [1] A method for creating a simulation model of a composite material in which a filler is dispersed in a polymer, by using a computer, comprising: randomly arranging filler particle models at non-overlapping coordinates in a model creation area; and newly arranging a filler particle model in a model creation area in which a filler particle model has already been arranged, the step of newly arranging the filler particle model comprising: setting coordinates of the newly arranged filler particle model based on the coordinates of the already arranged filler particle model and a predetermined distance between the filler particle models; and arranging the new filler particle model at the set coordinates based on a predetermined upper limit particle coordination number. [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 predetermined filler filling rate is satisfied. [3] The method for creating a simulation model according to [1] or [2], wherein the step of setting the coordinates of the newly placed filler particle model comprises: selecting an arbitrary filler particle model from among filler particle models already placed; and setting, as the coordinates of the newly placed filler particle model, coordinates at which the distance between the coordinates of the selected arbitrary filler particle model and the coordinates of the newly placed filler particle model is a preset filler particle model-to-filler model distance. [4] The method for creating a simulation model according to any of [1] to [3], wherein the step of newly placing a filler particle model at the set coordinates based on the preset upper limit particle coordination number comprises: placing a filler particle model at the set coordinates when the particle coordination number of the filler particle model in the model creation region is equal to or less than the preset upper limit particle coordination number. [5] The method for creating a simulation model according to any 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 of [1] to [5], wherein the preset upper limit particle coordination number is set by the following formula:(Formula) Upper limit particle coordination number = Pi of filler particle model π / (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 predetermined distance between filler particle models is the distance between coordinates of centers of gravity of the predetermined filler particle models, and is 0.9 to 1.0 times the diameter of the filler particle models. [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 comprising a step of analyzing characteristics of a simulation model created by the method for creating a simulation model according to any one of [1] to [8].

[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, it is possible to control the short-range network structure formed between filler particle models, which can contribute to improving the accuracy of the simulation.

[0010] For example, according to one embodiment of the present invention, in a simulation of the conductive properties of a composite material, it is possible to suppress the deviation between the volume resistivity trends obtained by the simulation and the volume resistivity trends obtained by measuring the actual composite material, thereby contributing to improved simulation accuracy. In this regard, conventional simulations of the conductive properties of composite materials have been unable to freely control the dispersion structure in the vicinity of filler particle models, making it difficult to create a simulation model that reflects the dispersion structure in the actual composite material. This has resulted in a tendency for the volume resistivity values ​​obtained by the simulation to deviate from the volume resistivity values ​​obtained by measuring the actual composite material. Specifically, for example, in simulations under conditions with a low filler filling rate, it is difficult to reproduce the short-range network structure formed by the filler particles. As a result, the volume resistivity values ​​obtained by the simulation tend to be higher than the measured values ​​of the actual composite material, posing a challenge to the accuracy of the simulation. According to one embodiment of the present invention, it is possible to suppress the tendency for high resistance even in simulations under conditions with a low filler filling rate, which is extremely advantageous in terms of improving the accuracy of the simulation.

[0011] Furthermore, in conventional simulation methods, because simulation models are composed of multiple elements, even if an ideal filler dispersion structure is found, it is often difficult to reflect the ideal dispersion structure in the development of an actual composite material. According to one embodiment of the present invention, it is possible to perform relatively simple modeling that takes into account the interparticle distance between filler particle models and the particle coordination number of the filler particle model, and therefore, when an ideal filler dispersion structure is found from the results of the simulation, it is advantageous in that it is relatively easy to reflect the result in the development of an actual composite material.

[0012] FIG. 1 is a flowchart showing an example of a processing procedure of a simulation model creation method according to an embodiment of the present invention. FIG. 2 is a flowchart showing an example of a processing procedure of a simulation model creation method according to an embodiment of the present invention. FIG. 3 is a schematic explanatory diagram for explaining a simulation model creation method according to an embodiment of the present invention. FIG. 4 is a schematic explanatory diagram for explaining a simulation model creation method according to an embodiment of the present invention. FIG. 5 is a schematic explanatory diagram for explaining a simulation model creation method according to an embodiment of the present invention. FIG. 6 is a schematic explanatory diagram for explaining a simulation model creation method according to an embodiment of the present invention. FIG. 7 is a schematic explanatory diagram for explaining a simulation model creation method according to an embodiment of the present invention. FIG. 8 is a schematic explanatory diagram for explaining a simulation model creation method according to an embodiment of the present invention. FIG. 9 is a diagram showing an example of a simulation model obtained by the simulation model creation method according to an embodiment of the present invention. FIG. 10 is a diagram showing a result obtained by a simulation method according to an embodiment of the present invention.

[0013] A simulation model creation method according to one embodiment of the present invention (hereinafter sometimes referred to as this embodiment) is a method for creating a simulation model of a composite material in which a filler is dispersed in a polymer by a computer, and is characterized in that the position of the filler particle model is controlled based on a preset distance between the filler particle models, and the particle coordination number of the filler particle model is controlled based on a preset upper limit particle coordination number. This makes it possible to freely control the dispersion structure in the region near the filler particle model. The embodiment of the present invention will now be described in detail.

[0014] In this embodiment, the simulation model creation method and the simulation method are executed by a computer. As in the conventional simulation model creation method, the computer executes a processing routine stored in advance in an information processing device such as a personal computer provided with a central processing unit (CPU), ROM, working memory, storage devices such as a magnetic disk, input devices such as a keyboard and a mouse, and a display device such as a monitor, through cooperation of software and hardware.

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

[0016] The polymer includes rubber, resin, elastomer, etc., and specific examples thereof include, but are not limited to, 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, Examples of the copolymer include 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), and liquid isoprene-butadiene rubber (liquid IR-BR).

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

[0018] 1 to 3 are flowcharts showing an example of the main processing steps of a simulation model creation method according to this embodiment. The flowcharts show an example of an embodiment. The simulation model creation method of the present invention is not limited to the order of the flowcharts.

[0019] <Step S1> The simulation model creation method according to this embodiment includes step S1 of setting parameters such as a filler filling rate, etc. 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 (sphere, oblate spheroid (prolate spheroid, oblate spheroid), plate-like body, cylinder, etc.) of the filler particle model, the range of the model creation region, the distance between filler particle models, the criterion for calculating the particle coordination number of the filler particle model, the upper limit particle coordination number, etc. are set in advance.

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

[0021] Specifically, step S2 randomly selects arbitrary coordinates in the model creation area using, for example, uniform random numbers, and sequentially places filler particle models at the selected coordinates. If, during this process, the selected coordinates overlap with other filler particle models already placed, the coordinate selection is redone and new, different coordinates are randomly selected. Step S2 ends the process, for example, when a certain percentage or number of the total number is reached.

[0022] The number or proportion of filler particle models to be placed in step S2 is set in advance as appropriate depending on the purpose of the simulation and the characteristics of the filler. For example, filler particle models are placed in a number corresponding to approximately 0.3 to 20%, 1 to 10%, or 1 to 5% of the total number corresponding to the filler filling rate.

[0023] FIG. 4 is a diagram illustrating an example of the processing of step S2. For convenience, FIG. 4 shows a three-dimensional model creation region 1 and a three-dimensional spherical filler particle model 2 in two dimensions (the same applies to the following figures). Step S2 is, for example, a step of randomly arranging multiple filler particle models 2 at coordinates that do not overlap with each other in the initial state of the model creation region 1 (a state in which no filler particle models exist). As shown in FIG. 4, after execution of step S2, multiple filler particle models 2 are arranged, but the coordinates of the filler particle models 2 do not overlap with each other and are arranged at intervals from each other in a predetermined dispersed state.

[0024] As in conventional simulation models, the model creation region 1 may be the entire region for which periodic boundary conditions are defined, a partial region having an arbitrary shape extracted from a region for which periodic boundary conditions are defined, or a partial region having an arbitrary shape extracted from a space for which periodic boundary conditions are not defined. The range of the model creation region 1 is set in advance.

[0025] The filler particle model placed in the model creation region 1 is a model of 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 (a prolate spheroid, an oblate spheroid), a plate, or a cylinder, and parameters for specifying dimensions such as radius, diameter, and volume (the size of the area occupied in the model creation region) are defined in advance. In addition, when performing various characteristic simulations described below, additional characteristic parameters (e.g., conductivity) that are required are set. In this embodiment, a spherical filler particle model is set, but filler particle models of other shapes may also be used, or two or more types may be used in combination. In addition, in this embodiment, the area other than the area where the filler particle model is created is defined as a polymer model.

[0026] <Step S3> The simulation model creation method according to this embodiment includes step S3 of newly arranging an additional filler particle model 3 in a model creation region 1 including the plurality of filler particle models 2 arranged in step S2. Step S3 controls the coordinates of the newly arranged filler particle model 3 based on the filler particle models 2 already arranged. For example, step S31 includes setting the coordinates of the newly arranged filler particle model 3 based on the coordinates of the filler particle model 2 arranged in step S2. In step S31, for example, an arbitrary filler particle model 2 is randomly selected from the plurality of already arranged filler particle models 2 based on a uniform function or the like (step S311). The selected filler particle model 2 serves as a reference or starting point for generating the newly arranged filler particle model 3.

[0027] Next, 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 newly placed filler particle model 3 are selected (step S312). 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 newly placed filler particle model 3, and the coordinates of the newly placed filler particle model 3. Specifically, for example, the coordinates of the newly placed filler particle model 3 are randomly selected using, for example, uniform random numbers from a group of coordinates whose distance from the coordinates of the selected filler particle model 2 is the preset distance d between the filler particle models. By performing such processing, for example, it is possible to minimize the probability of a filler particle model being isolated, thereby enabling modeling that takes into account the filler dispersion structure in an actual composite material.

[0028] The predetermined distance d between filler particle models can be set appropriately depending on the purpose of the simulation and the characteristics of the filler. For example, from the viewpoint of freely controlling the short-range network, the distance d can be set based on an appropriate standard, such as the distance at which the surface of an already placed filler particle model 2 comes into contact with the surface of a newly placed 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.

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

[0030] In an embodiment in which a conductive characteristic simulation model is created, it is preferable that α in the above formula is less than 1.0, and more preferably 0.9 or more and 0.95 or less.

[0031] Next, the steps of selecting the coordinates of a newly placed filler particle model 3 based on the coordinates of the selected filler particle model 2 and a preset distance d between the filler particle models will be described (steps S311 and S312). In FIG. 5 , which schematically shows filler particle models in a partial region of the model creation region 1, there are multiple filler particle models 2a, 2b, etc. already placed, and if a filler particle model 2a is randomly selected from the multiple filler particle models 2a, 2b, etc. already placed, then any coordinates randomly selected from a group of coordinates across the preset distance d between the filler particle models (in FIG. 5 , the diameter of the filler particle model) from the centroid coordinates of the filler particle model 2a are set as the coordinates of the newly placed filler particle model 3. Specifically, in FIG. 5 , any coordinates randomly selected from the centroid coordinates of filler particle models 3a, 3b, 3c, etc. are set as the coordinates of the newly placed filler particle model 3. 5, filler particle models 3a, 3b, 3c, etc. are candidates for the filler particle model to be newly placed. Next, if the conditions described below are satisfied, a filler particle model 3 is newly placed at the set coordinates.

[0032] Next, in this embodiment, the same process is repeated. That is, an arbitrary filler particle model 2 is randomly selected from the plurality of filler particle models 2 already arranged, arbitrary coordinates are randomly set from a group of coordinates at a predetermined distance d between filler particle models from the coordinates of the center of gravity of the selected filler particle model 2, and if the conditions described below are satisfied, a new filler particle model 3 is arranged at the set coordinates. By repeating this series of processes, new filler particle models 3 are sequentially arranged until the predetermined filler filling rate is satisfied.

[0033] Note that Figure 5 above illustrates an example in which the diameter of the filler particle model is set as the preset distance d between the filler particle models. However, as shown in Figure 6, when creating, for example, a conductive property simulation model, it is preferable to set the distance d between the filler particle models to a predetermined distance shorter than the diameter of the filler particle model (a distance at which the filler particle models slightly overlap).

[0034] As described above, the coordinates of the newly placed filler particle model 3 are set based on the coordinates of the selected filler particle model 2 and the preset distance d between the filler particle models, and the filler particle model 3 is newly placed at the set coordinates when the following conditions are met: That is, in the method for creating a simulation model according to this embodiment, as shown in step S313 of Fig. 3 and step S32 of Fig. 2, the conditions are: (1) the distance between the coordinates of the newly placed filler particle model 3 and the coordinates of other filler particle models is not less than the preset distance between the filler particle models (filler particle models do not overlap excessively), and (2) the particle coordination number of the filler particle model is equal to or less than a preset upper limit particle coordination number.

[0035] <Step S313> First, step S313 is a step of controlling the relative coordinates of the filler particle model to be newly placed and the coordinates of the filler particle model other than the filler particle model that serves as the starting point of the filler particle model to be newly placed among the already placed filler particle models 2. That is, step S313 is a step of preventing the coordinates of the newly placed filler particle model from excessively overlapping with the coordinates of the other filler particle models placed in the model creation area. Specifically, the relative coordinates of the filler particle model (selected filler particle model) that serves as the starting point of the filler particle model to be newly placed among the filler particle models that have already been placed are controlled by a preset distance d between the filler particle models. On the other hand, if the relative coordinates of the other filler particle models (non-selected filler particle models) among the filler particle models that have already been placed, excluding the filler particle model (selected filler particle model) that serves as the starting point of the filler particle model to be newly placed, and the coordinates of the filler particle model to be newly placed are not controlled, there is a possibility that the coordinates of the newly placed filler particle model will overlap excessively with the coordinates of the other filler particle models (non-selected filler particle models), and therefore such overlap is controlled in step S313.

[0036] 7 will be taken as an example. As shown in FIG. 7 , which schematically illustrates filler particle models in a partial region of the model creation region 1, when a plurality of filler particle models 2a, 2b, etc. are already arranged and a filler particle model 2a is randomly selected from the plurality of already arranged filler particle models 2a, 2b, etc., it is assumed that any coordinates randomly selected from a group of coordinates at a predetermined filler particle model-to-filler particle model distance d (in this embodiment, the diameter of the filler particle model) from the centroid coordinate of the filler particle model 2a are set as candidates for the coordinates of the newly arranged filler particle model 3. However, since the distance d′ between the centroid coordinate of the filler particle model 3b and the centroid coordinate of another filler particle model 2b is less than the predetermined filler particle model-to-filler particle model distance d (in this embodiment, the diameter of the filler particle model), the centroid coordinate of the filler particle model 3b is not set as the coordinate of the newly arranged filler particle model 3.

[0037] As an example of processing when the above condition is not satisfied, for example, an arbitrary filler particle model 2 is randomly selected again from the plurality of filler particle models 2 already placed based on a uniform function or the like (step S311), and arbitrary coordinates are randomly selected from a group of coordinates across a preset filler particle model-to-filler particle model distance d (in this embodiment, the diameter of the filler particle model) from the centroid coordinates of the selected filler particle model as candidates for the coordinates of a newly placed filler particle model 3 (step S312), and it is determined whether the above condition is satisfied (see FIG. 3 ). If the above condition is satisfied, the selected coordinates are set as the coordinates of a new filler particle model.

[0038] 7, steps S312 and S313 are executed based on a preset distance d between filler particle models, but this distance can be set differently as appropriate depending on the purpose of the simulation, etc. For example, the distance between filler particle models in step S312, i.e., the distance between the coordinates of the newly placed filler particle model 3 and the coordinates of the starting filler particle model 2, can be set as the first distance d1 between filler particle models, while the distance between filler particle models preset in step S313, i.e., the distance between the coordinates of the filler particle models 2 other than the starting filler particle model 2 and the coordinates of the newly placed filler particle model 3, can be individually set as the second distance d2 between filler particle models.

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

[0040] The method for creating a simulation model according to this embodiment includes a step of presetting an upper limit particle coordination number and a step of presetting a criterion for calculating the particle coordination number of a filler particle model. The step of presetting an upper limit particle coordination number is a step of presetting an upper limit particle coordination number taking into consideration the purpose of the simulation, the characteristics of the filler, the filler filling rate, etc. The upper limit particle coordination number can be set, for example, based on an empirical formula in powder engineering. Specifically, the upper limit particle coordination number can be set in advance, for example, using the following formula: (Formula) Upper Limit Particle Coordination Number = Pi of Filler Particle Model / (1 - [Filler Filling Rate [volume %] × 0.01]) Specific examples of the preset upper limit particle coordination number are set appropriately depending on the purpose of the simulation and the characteristics of the filler, and for a conductive property simulation model, examples include 3 to 5 particles or 3 to 4 particles.

[0041] The step of presetting a criterion for determining the particle coordination number of a filler particle model is a step of presetting a criterion for determining the coordination number of an arbitrary filler particle model in the model creation region. Here, the particle coordination number is a concept in powder engineering, meaning the number of contact points with other particles present on the surface of a particle. In the present invention, however, an appropriate criterion can be set taking into consideration the purpose of the simulation and the characteristics of the target filler. For example, the criterion can be set based on the number of contact points with other filler particle models present on the surface of a filler particle model. Alternatively, the criterion can be set based on the number of other filler particle models in contact with a filler particle model. Furthermore, even if a filler particle model and other filler particle models are not geometrically in contact with each other, in cases where they are close to each other, it may be appropriate to consider them to be in contact, taking into consideration the purpose of the simulation and the characteristics of the target filler. Therefore, the number of filler particle models with coordinates in the surrounding area of ​​a filler particle model can also be set as the criterion. Specifically, for example, a surrounding region formed when the volume of a filler particle model is enlarged to a similar shape by an arbitrary magnification factor around the coordinates of the center of gravity of the filler particle model may be assumed, and the number of other filler particle models having coordinates of their centers of gravity in the surrounding region may be used as the reference.Furthermore, for example, a surrounding region may be assumed around the coordinates of the center of gravity of a filler particle model, with a radius of 1.0 to 1.5 times the diameter of the filler particle model, and the number of other filler particle models having coordinates of their centers of gravity in the surrounding region may be used as the reference.

[0042] FIG. 8 will be taken as an example. If the preset upper limit particle coordination number is three and the criterion for determining the particle coordination number of a preset filler particle model is the number of other filler particle models in contact with one filler particle model, then in the arrangement of filler particle models shown in FIG. 8 , which schematically illustrates filler particle models in a partial region of the model creation region 1, the particle coordination number of filler particle model 3b is four, and therefore the coordinates of the center of gravity of filler particle model 3b are not set as the coordinates of the newly placed filler particle model 3. Specifically, in FIG. 8 , when four filler particle models already exist, filler particle model 2a is randomly selected (step S311) and the coordinates of the center of gravity of filler particle model 3b are set as coordinates separated by a preset filler particle model-to-filler particle model distance d (in this embodiment, the diameter of the filler particle model). As a result, the particle coordination number of filler particle model 3b becomes four, and therefore the coordinates of the center of gravity of filler particle model 3b are not set as the coordinates of the newly placed filler particle model 3.

[0043] 9 will be taken as an example. If the preset upper limit particle coordination number is three and the criterion for determining the particle coordination number of a preset filler particle model is the number of other filler particle models in contact with one filler particle model, then in the arrangement of filler particle models shown in FIG. 9 , which schematically illustrates filler particle models in a partial region of the model creation region 1, the particle coordination number of filler particle model 2a is four, and therefore the coordinates of the center of gravity of filler particle model 3b are not set as the coordinates of the newly placed filler particle model 3. Specifically, in FIG. 9 , when four filler particle models already exist, a filler particle model 2a is randomly selected (step S311) and the coordinates of the center of gravity of filler particle model 3b are set as coordinates separated from the coordinates of the center of gravity of filler particle model 2a by a preset filler particle model-to-filler model distance d (in this embodiment, the diameter of the filler particle model). As a result, the particle coordination number of filler particle model 2a becomes four, and therefore the coordinates of the center of gravity of filler particle model 3b are not set as the coordinates of the newly placed filler particle model 3.

[0044] 10 will be taken as an example. In the case where the preset upper limit particle coordination number is 3, and the criterion for determining the particle coordination number of a preset filler particle model is to set a surrounding region having a radius of a distance (D) 1.1 times the diameter of one filler particle model as the center, and to use the number of other filler particle models having gravity center coordinates in the surrounding region as the criterion, in the arrangement of filler particle models in a partial region of the model creation region 1 as shown in FIG. 10 , the particle coordination number of filler particle model 2a is 4, and therefore the gravity center coordinates of filler particle model 3b are not set as the coordinates of the newly placed filler particle model 3. Specifically, in FIG. 10 , in a state where four filler particle models already exist, a filler particle model 2 a is randomly selected (step S311), and the coordinates of the center of gravity of a filler particle model 3 b are set as coordinates via a predetermined filler particle model-to-filler particle model distance d (in this embodiment, the diameter of the filler particle model) from the coordinates of the center of gravity of the filler particle model 2 a. Since the particle coordination number of the filler particle model 2 a becomes four, the coordinates of the center of gravity of the filler particle model 3 b are not set as coordinates of the newly placed filler particle model 3.

[0045] 11 will be taken as an example. If the preset upper limit particle coordination number is three and the criterion for determining the particle coordination number of a preset filler particle model is the number of other filler particle models in contact with one filler particle model, then in the arrangement of filler particle models shown in FIG. 11 , which schematically illustrates filler particle models in a partial region of the model creation region 1, the particle coordination number of filler particle model 2 is four, and therefore the coordinates of the center of gravity of filler particle model 3b are not set as the coordinates of the newly placed filler particle model 3. Specifically, in FIG. 11 , when five filler particle models already exist, filler particle model 2a is randomly selected (step S311) and the coordinates of the center of gravity of filler particle model 3b are set as coordinates separated by a preset filler particle model-to-filler particle model distance d (in this embodiment, the diameter of the filler particle model). Therefore, the coordinates of the center of gravity of filler particle model 3b are not set as the coordinates of the newly placed filler particle model 3.

[0046] As an example of processing when the condition regarding the upper limit particle coordination number is not satisfied, for example, an arbitrary filler particle model 2 is randomly selected again from the plurality of filler particle models 2 already arranged based on a uniform function or the like (step S311), and the processing of steps S312 to S314 is performed while repeatedly determining whether or not the condition of step S32 is satisfied. If the condition of step S32 is satisfied, a new filler particle model is arranged at the coordinates selected in step S312.

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

[0048] In the above embodiment, for the sake of convenience, the conditions of step S313 are judged before the conditions of step S32 are judged, but the order of the two conditions is not limited, and processing may be performed such that a new filler particle model is placed when both conditions are satisfied.

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

[0050] Furthermore, in the embodiment of the present invention, a two-phase model consisting mainly of a filler particle model and a polymer model is used, but the present invention is not limited to this and may include other model elements.

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

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

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

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

[0055] Next, the conductivity between adjacent positional elements is set based on the conductivity of the preset filler particle model, the conductivity of the preset polymer model, the conductivity of the preset interface layer model, the conductivity of the preset positive electrode element, and the conductivity of the preset negative electrode element. The conductivity between adjacent positional elements is set to a different conductivity depending on the type of each adjacent positional element. In this way, a simulation model for conductive property analysis is created.

[0056] The analysis of the electrical conductivity can be performed according to a conventionally known method, for example, by applying a predetermined positive potential to the positive element and a predetermined negative potential to the negative element as input conditions, and then analyzing the electrical resistance between the positive element and the negative element. Furthermore, the electrical conductivity path can also be analyzed based on the current value for each position element.

[0057] A simulation model SM1 was created using the simulation model creation method according to the above embodiment, and a conductive property simulation was performed. Various parameters were as follows. In the simulation model SM1, the preset upper limit particle coordination number was a value set based on the above formula (π / (1-[filler filling rate [volume %] × 0.01])). The criterion for determining the particle coordination number of the preset filler particle model was the number of other filler particle models with center coordinates in a surrounding region, centered on the center of gravity of one filler particle model and with a radius of 1.0 times the diameter of the filler particle model (see, for example, FIG. 10 ). (Parameters) Radius of filler particle model: 5 voxels Model creation region: 512 × 512 × 256 voxels 3Distance between filler particle models: Diameter of filler particle model (10 voxels) × 0.93 Upper limit particle coordination number: 3 Filler particle model filling rate: 5.0 vol% Resistance value of filler particle model: 10 -2 Ω cm ・Resistance value of polymer model 10 12 Ω cm Resistance value of interface layer model 10 0 Ω cm Initial condition: Potential 0 in all voxels (electrodes are 2 voxels thick each) Convergence condition: Change in total potential < 10 0 Or 1 million loops

[0058] A simulation model SM2 was created in the same manner as the simulation model SM1 except that the upper limit of the particle coordination number was not set (there was no limit on the upper limit of the particle coordination number), and a simulation of the conductive properties was performed.

[0059] <Evaluation of Particle Coordination Number> Simulation model SM2 was created without setting an upper limit on the particle coordination number, and therefore the number of filler particle models with a particle coordination number of 4 or more (specifically, a particle coordination number of 4 to 9) was approximately 1,000 (out of a total of approximately 6,400 filler particle models). In contrast, simulation model SM1 was created with a limited upper limit on the particle coordination number, and therefore all filler particle models had a particle coordination number of 3 or less, and there were essentially no filler particle models with a particle coordination number of 0.

[0060] <Evaluation of Conductive Property Simulation> Conventional conductive property simulations have difficulty reproducing the short-range network structure formed by filler particles. As a result, the volume resistivity values ​​obtained by the simulation tend to be higher than the measured values ​​of the actual composite material, especially under conditions of low filler loading (e.g., 5-8% or less), resulting in issues with simulation accuracy. Conductive property simulations were performed using simulation model SM1 (with a limit on the upper particle coordination number) and simulation model SM2 (without a limit on the upper particle coordination number). It was confirmed that the volume resistivity values ​​obtained using simulation model SM1 were significantly lower than those obtained using simulation model SM2. Specifically, as shown in FIG. 13 , the volume resistivity (Ω·cm) of simulation model SM1 was significantly lower than that of simulation model SM2 and approached the measured value. Note that the number of Ns for each simulation model was 45.

[0061] Although the above examples show specific embodiments of the present invention, the examples are merely illustrative and should not be construed as limiting. Various modifications that are obvious to those skilled in the art are intended to fall within the scope of the present invention.

[0062] 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 as a method for creating a simulation model used in, for example, a conductivity simulation method.

[0063] 1 Model creation area 2 (2a...) Filler particle model 3 (3a...) Filler particle model (newly placed filler particle model)

Claims

1. A method for creating a simulation model of a composite material in which a filler is dispersed in a polymer by a computer, comprising the steps of: randomly arranging filler particle models at non-overlapping coordinates in a model creation area; and newly arranging a filler particle model in the model creation area in which a filler particle model has already been arranged, wherein the step of newly arranging the filler particle model comprises the steps of: setting coordinates of the newly arranged filler particle model based on the coordinates of the already arranged filler particle model and a predetermined distance between the filler particle models; and newly arranging the filler particle model at the set coordinates based on a predetermined upper limit particle coordination number.

2. The method for creating a simulation model according to claim 1, further comprising repeating the step of arranging new filler particle models until a preset filler filling rate is satisfied.

3. A method for creating a simulation model as claimed in claim 1 or 2, wherein the step of setting the coordinates of the newly placed filler particle model comprises the steps of: selecting an arbitrary filler particle model from among filler particle models already placed; and setting, as the coordinates of the newly placed filler particle model, coordinates such that the distance between the coordinates of the arbitrary filler particle model selected and the coordinates of the newly placed filler particle model is a preset filler particle model-to-filler particle model distance.

4. A method for creating a simulation model as described in any one of claims 1 to 3, wherein the step of newly placing a filler particle model at the set coordinates based on the predetermined upper limit particle coordination number is a step of newly placing a filler particle model at the set coordinates when the particle coordination number of the filler particle model in the model creation area is equal to or less than the predetermined upper limit particle coordination number.

5. A method for creating a simulation model according to any one of claims 1 to 4, wherein the preset upper limit particle coordination number is three or four.

6. The method for creating a simulation model according to any one of claims 1 to 5, wherein the preset upper limit particle coordination number is set by the following formula: Upper limit particle coordination number = pi of filler particle model / (1 - [filler filling rate [volume %] x 0.01]) 7. A method for creating a simulation model according to any one of claims 1 to 6, wherein the predetermined distance between filler particle models is the distance between the center of gravity coordinates of the predetermined filler particle models, and is 0.9 to 1.0 times the diameter of the filler particle models.

8. A method for creating a simulation model according to any one of claims 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 comprising a step of analyzing characteristics of a simulation model created by the method for creating a simulation model according to any one of claims 1 to 8.

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