JP2015079450A - Method for creating simulation model of composite material - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for creating a simulation model of a composite material in which fillers are dispersedly disposed inside a high polymer material.SOLUTION: A method includes: a first process S1 of setting, to a computer, a first simulation model disposed with a string-like high polymer model in which a high polymer material is discretized by a high polymer particle model and a block-like filler model in which fillers are discretized by a limited number of filler particle models, in an optional three-dimensional space; and a second process S2 in which the computer defines a bond for bonding both the particle models between at least one filler particle model positioned in the surface of the filler model of the first simulation model and the high polymer particle model positioned near the filler particle model, and sets a second simulation model.

Description

  The present invention relates to a method for creating a simulation model of a composite material in which fillers are dispersed in a polymer material.

  Conventionally, molecular simulation has been performed on a composite material in which fillers are dispersed in a polymer material. In molecular simulation, a simulation model simulating a composite material is defined in a virtual three-dimensional space on a computer. The simulation model is defined, for example, by discretizing a polymer material, filler molecules, and the like with a particle model (mass point in the equation of motion). Each particle model is sequentially calculated in time series in accordance with classical mechanics under potential and the like. Thereby, the physical property etc. of the said composite material are analyzed.

  For example, as a composite material, molecular simulation of a silica-containing rubber in which silica is added as a filler in a matrix rubber may be performed. In this case, for example, a composite material model a as visualized in FIG. 12 is defined in the computer. The composite material model a includes a polymer model b for expressing the matrix rubber and a filler model c for expressing the filler. The polymer model b is defined by connecting a finite number of polymer particle models b1 in a string form with a chain model b2 so as to represent a molecular chain of rubber. The filler model c is defined as a lump by connecting a finite number of filler particle models c1 with a chain model c2 so as to represent spherical filler particles.

  The composite material model a further defines a bond d that connects at least one filler particle model c1 located on the surface of the filler model c and one polymer particle model b1 of the polymer model b. The bond d constrains the relative distance between the two models, and corresponds to, for example, a coupling agent that bonds the filler surface and the matrix rubber in an actual composite material. Such a bond d affects the degree of bonding between rubber and silica, and the arrangement and number thereof have an important influence on the analysis of the physical properties of the composite material.

JP 2013-186746 A JP 2013-108951 A

  When defining the above-mentioned bond d, first, the filler particle model c1 located on the surface of the filler model c must be specified. However, since the filler particle model c1 is arranged three-dimensionally and the number thereof is very large, it is difficult to specify which one is located on the surface by a computer.

  Conventionally, it has been considered that a filler model is defined as a sphere and a bond is defined in a filler particle model positioned at the apex of a regular polyhedron inscribed therein (Related Art 1). However, this method has a problem that the number of bonds is limited to the number of vertices of the regular polyhedron, and an arbitrary number of bonds cannot be defined. Further, the filler model has to be defined by a sphere, and there is a problem that it lacks versatility.

  As another method, a method in which a filler particle model c1 and a polymer particle model b1 within a predetermined distance R in a predetermined range are combined with each other sequentially or using a pseudo-random number is also considered. (Related technology 2). However, this method has a problem in that the bond may be biased to a specific position.

  The present invention has been devised in view of the above circumstances, and a method for easily identifying a filler particle model located on the surface of a filler model and efficiently creating a simulation model of a composite material. It is intended to provide.

  The present invention is a method for creating, using a computer, a simulation model of a composite material in which fillers are dispersed in a polymer material. A first simulation model in which a string-like polymer model discretized by a model and a massive filler model discretized by a finite number of filler particle models are arranged in an arbitrary three-dimensional space is set. Between the at least one filler particle model located on the surface of the filler model of the first simulation model and the polymer particle model located near the filler particle model. A second step of defining a bond for connecting the particle model and setting a second simulation model. The second step divides the three-dimensional space into a plurality of regions using a first polyhedron including one of the polymer particle models and a second polyhedron including one of the filler particle models. Between the polymer particle model and the filler particle model included in at least one of a pairing step and a pair of the first polyhedron and the second polyhedron that are adjacent to each other in the three-dimensional space And a bonding step for defining the bond.

  In the composite material simulation model creation method according to the present invention, the first polyhedron and the second polyhedron are preferably Voronoi-divided polyhedrons.

  In the method for creating a simulation model of a composite material according to the present invention, the combining step includes an extraction step of extracting all filler particle models belonging to the second polyhedron in contact with the first polyhedron, and the extracted filler Defining a bond between a determination step of determining at least one filler particle model from among the particle models, the determined filler particle model, and the polymer particle model located closest to the filler particle model; And a bond definition step.

  In the method for creating a simulation model of a composite material according to the present invention, it is preferable that the determination step and the bond definition step are repeatedly performed until the number of bonds reaches a predetermined upper limit.

  In the method for creating a simulation model of a composite material according to the present invention, the determining step may determine the next filler particle model so that the distance from the filler particle model that has already been determined does not fall below a predetermined value. desirable.

  In the first step of the present invention, a first simulation model is set on a computer. The first simulation model is defined in a virtual three-dimensional space for numerical calculation by a computer. A string-like polymer model obtained by discretizing a polymer material with a finite number of polymer particle models. The filler model is arranged in the space in a lump shape obtained by discretizing the filler with a finite number of filler particle models.

  In the second step of the present invention, the computer sets a second simulation model. The second simulation model combines both particle models between at least one filler particle model located on the surface of the filler model of the first simulation model and a polymer particle model located near the filler particle model. For this purpose, a bond is defined.

  The second step of the present invention includes a dividing step of dividing the three-dimensional space into a plurality of regions using a polyhedron. As the polyhedron, a first polyhedron including one of the polymer particle models and a second polyhedron including one of the filler particle models are used.

  The second step further includes a combining step. In the bonding step, a bond is defined between the polymer particle model and the filler particle model included in at least one of the pair of the first polyhedron and the second polyhedron that are adjacent to each other in the three-dimensional space. The

  As described above, in the present invention, the filler particle model located on the surface of the filler model can be easily specified as belonging to the second polyhedron in contact with the first polyhedron. Therefore, according to the method of the present invention, the creation of the simulation model is made efficient. Further, according to the method of the present invention, it is possible to create a simulation model in which the definition and number of bonds can be arbitrarily set and changed.

It is a flowchart of embodiment of the process sequence of this invention. It is a top view which shows the 1st simulation model of the filler compounded rubber visualized. It is a flowchart of one embodiment of the 1st process. It is a top view of the visualized matrix rubber model. It is a top view of the visualized filler rubber model. It is a flowchart of one Embodiment of a 2nd process. It is a top view of the 1st simulation model which shows a division process. It is a top view of the 1st simulation model which shows a determination process. It is a top view of the 2nd simulation model in which a bond was defined. (A) is a filler model obtained according to the method of the present embodiment, and (B) is a filler model obtained according to a conventional method, both of which are identified as surface filler particles are displayed in white. . (A) is a filler model obtained according to the method of the present embodiment, and (B) is a filler model obtained according to a conventional method. Both filler particles whose bond can be defined at a distance are displayed in black. Has been. It is the top view by which the simulation model of the composite material was visualized.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
The present invention is a method for creating, using a computer, a simulation model of a composite material in which fillers are dispersed in a polymer material.

  In the present specification, the “polymer material” is a concept including at least a resin, rubber, and elastomer. The “filler” is not particularly limited as long as it reinforces the polymer material as a matrix, but is a concept including at least carbon black, silica, and the like.

  In this specification, the “simulation model” is “numerical data” defined in a computer and used for numerical calculation of molecular simulation. In this embodiment, the simulation model is represented as a diagram. These are visualized by replacing numerical data of a simulation model with, for example, a figure imitating an actual molecular structure. These simulation models can also be displayed through a display device or the like connected to a computer.

  FIG. 1 shows an embodiment of the processing procedure of the present invention. In the present embodiment, first, the first process is performed (step S1). In the first step, as shown in FIG. 2, a first simulation model 2 is defined on a virtual three-dimensional space (x, y, z) defined in a computer (book omitted). In the first simulation model 2, a string-like polymer model 3 and a massive filler model 4 are arranged in a three-dimensional space.

  FIG. 3 shows an example of a more specific processing procedure of the first step. In the first step of the present embodiment, first, the polymer model 3 is set (step S11).

  In FIG. 4, one embodiment of the polymer model 3 is visualized. The polymer model 3 of this embodiment has a linear three-dimensional structure composed of a plurality of polymer particle models 3a and a chain model 3b connecting these polymer particle models 3a and 3a. Have.

  Each polymer particle model 3a can represent an atom of a polymer material or an aggregate thereof. The polymer particle model 3a may be discretized by either a coarse-grained particle model as in the present embodiment or a so-called “Full Atom model” that captures all atoms as particle models.

  The polymer particle model 3a is treated as a mass point of the equation of motion in, for example, molecular simulation based on molecular dynamics. Accordingly, parameters such as mass, volume, diameter, charge and / or initial coordinates are given to each polymer particle model 3a. Each of these parameters is input to the computer as numerical information.

  The chain model 3b specifies the relative positions of the polymer particle models 3a and 3a. Further, the chain model 3b can change the bond length, bond angle or dihedral angle between the polymer particle models 3a and 3b by external force or internal force based on the physical properties of the polymer material to be analyzed. The polymer model 3 is constrained. The chain model 3b is input to the computer device as vector information, for example.

  Furthermore, in order to perform molecular dynamics calculation, a potential function is defined between the polymer particle models 3a and 3a.

  Next, as shown in FIG. 3, in the first step, the filler model 4 is set (step S12).

  In FIG. 5, one embodiment of the filler model 4 is visualized. The filler model 4 of this embodiment has a multilayer and spherical three-dimensional structure composed of a plurality of filler particle models 4a and a chain model 4b connecting these filler particle models 4a and 4a. Yes.

  Each filler particle model 4a represents an aggregate of filler atoms of the composite material. The filler particle model 4a may be discretized by any of the so-called “Full Atom model” that captures all atoms as particle models in addition to the coarse-grained particle model as in the present embodiment.

  The filler particle model 4a is also handled as a mass point of the equation of motion in the molecular simulation based on molecular dynamics. Accordingly, each filler particle model 4a is given parameters such as its mass, volume, diameter, charge and / or initial coordinates. Each of these parameters is input to the computer as numerical information.

  As with the chain model 3b described in the polymer model 3, the relative positions of the filler particle models 4a and 4a are specified for the chain model 4b. Further, the chain model 4b is a filler model 4 so that the bond length, bond angle or dihedral angle between the filler particle models 4a and 4b can be changed by external force or internal force based on the physical properties of the filler to be analyzed. Is restrained. The chain model 4b is input to the computer device as vector information, for example. Further, a potential function is defined between the filler particle models 4a and 4a in order to perform molecular dynamics calculation.

  Next, as shown in FIG. 3, in the first step, molecular dynamics calculation is performed using the polymer model 3 and the filler model 4 (step S13).

  In the molecular dynamics calculation, as shown in FIG. 2, the previously defined polymer model 3 and filler model 4 are contained in a three-dimensional space (also called “cell”) having a predetermined volume. Initially arranged at random. In the molecular dynamics calculation, for example, Newton's equation of motion is applied on the assumption that all the arranged models 3 and 4 follow classical mechanics within a predetermined time. The movement of all polymer particle models 3a and filler particle models 4a at each time is tracked. As a result, each of the models 3 and 4 can gradually change from an artificial initial arrangement to an equilibrium state.

  Next, as shown in FIG. 3, in the first step, it is determined by molecular dynamics whether or not the polymer model 3 and the filler model 4 are sufficiently relaxed (step S14). In the molecular dynamics calculation of this embodiment, it is considered that the structure has been relaxed when the computer finishes a certain number of repetitive steps.

  Next, when the polymer model 3 and the filler model 4 are sufficiently relaxed (Y in step S14), all the positional information and the like of the polymer model 3 and the filler model 4 in this state are stored in the computer. Thereby, the first simulation model 2 is defined in the computer (step S15).

  Next, returning to FIG. 1, in the present embodiment, the second step is performed (step S2). In the second step, in the first simulation model 2 shown in FIG. 2, at least one filler particle model 4a located on the surface of the filler model 4, and a polymer particle model 3a located near the filler particle model 4a, In the meantime, a bond for bonding both particle models 4a and 3a is defined (the bond is not shown in FIG. 2).

  FIG. 6 shows an example of a detailed processing procedure of the second step. As shown in FIG. 6, in the second step, first, a division step is performed (step S21). In the dividing step, the computer divides the three-dimensional space of the first simulation model 2 into a plurality of regions using the first polyhedron and the second polyhedron.

  FIG. 7 shows a plan view of the first simulation model 2 for explaining the dividing step. In FIG. 7, the chain model 3b of the polymer model 3 and the chain model 4b of the filler model 4 are each omitted. The polymer particle model 3a is indicated by a white circle, and the filler particle model 4a is indicated by a black circle.

  The first polyhedron 5 is a polyhedron including only one of the polymer particle models 3a. The second polyhedron 6 is a polyhedron including only one of the filler particle models 4a. In the dividing step, the space of the first simulation model 2 is divided using only the first polyhedron 5 and the second polyhedron 6. As a method for obtaining such polyhedrons 5 and 6, Voronoi division (Tiessen division) is employed in the present embodiment. Voronoi division is a method of dividing a space by a region closest to each generating point when a plurality of generating points (corresponding to a particle model) are defined in a certain three-dimensional space. That is, it is a method of dividing the nearest neighbor region of each generating point while defining a plane that bisects a straight line connecting adjacent generating points. The Voronoi boundary demarcates the polyhedra that are in contact with each other. The position information of each polyhedron 5 and 6 can be stored in the computer by the dividing step.

  Next, as shown in FIG. 6, an extraction process is performed (step S22). In the extraction step, all filler particle models 4a belonging to the second polyhedron 6 that is in contact with the first polyhedron 5 are extracted. FIG. 8 shows the first simulation model 2 in which the second polyhedron 6 in contact with the first polyhedron 5 is lightly colored in order to visually explain the extraction process. In the extraction process, as colored in FIG. 8, all filler particle models 4a belonging to the second polyhedron 6 that is in contact with the first polyhedron 5 at the Voronoi boundary are stored in a computer, for example.

  Thus, according to the present embodiment, the filler particle model 4 a located on the surface of the filler model 4 is easily specified as belonging to the second polyhedron 6 in contact with the first polyhedron 5.

  Next, as shown in FIG. 6, a determination process is performed (step S23). In the determination step, one filler particle model 4a is determined from the filler particle models 4a extracted in the extraction step. In the present embodiment, one filler particle model 4a is extracted at random from the extracted filler particle models 4a.

  Next, in the present embodiment, it is determined whether or not the distance between the determined filler particle model 4a and the previously determined filler particle model 4a is equal to or greater than a predetermined distance Rmin (step S24). . If the filler particle model 4a has not been previously determined, this step S23 is positive. This step will be described later.

  Next, in this embodiment, a bond definition process is performed (step S25). In the bond definition step, a bond 7 is defined between the determined filler particle model 4a and the polymer particle model 3a located closest to the filler particle model 4a. FIG. 9 visualizes the second simulation model 10 in which such a bond definition process has been performed. Bond 7 is visualized as an arm connecting two particle models 3a, 4a. The bond 7 is a numerical information stored in a computer that uses a potential function to constrain the relative positions of the two particle models 3a and 4a within a certain distance. In FIG. 9, three bonds 7 are shown.

  Next, in the present embodiment, the computer determines whether or not the number of defined bonds 7 has reached a predetermined number (upper limit) (step S26). When the number of bonds has reached the upper limit (Y in step S26), the computer stores the current arrangement of the polymer model 3, the filler model 4, and the yobo bond 7 as the second simulation model 10 (step S27).

  On the other hand, if the computer determines that the number of bonds has not reached the upper limit (N in step S26), the computer repeats the determination process (step S23) and subsequent steps. Thereby, the determination process (step S23) and the bond definition process (S25) are repeatedly performed until the number of bonds 7 reaches a predetermined upper limit.

  In the second and subsequent loops, in step S24, it is determined whether or not the distance between the determined filler particle model 4a and the previously determined filler particle model 4a is equal to or greater than a predetermined distance Rmin. Is done. When the distance between the determined filler particle model 4a and the previously determined filler particle model 4a is less than the predetermined distance Rmin, the determined filler particle model 4A is canceled (step S28). A new determination step is performed.

  By including such a step, in the determination step, the next filler particle model 4a can be determined so that the distance from the filler particle model 4a that has already been determined does not fall below a predetermined value. This can prevent the bond 7 from being biased to a specific location when the bond 7 is defined in the simulation model.

  Through the above processing, for example, the second simulation model 10 as shown in FIG. 9 is created. Various physical properties can be analyzed using the second simulation model 10. According to the method of the present embodiment, the second simulation model 10 is efficiently created. Further, according to the method of the present embodiment, a simulation model in which the definition and number of bonds can be arbitrarily set and changed can be created.

  10A and 10B show the result of specifying the filler particle model located on the surface of the filler model 4 from the first simulation model 2 under the same conditions. FIG. 10A shows the result obtained according to the above embodiment. In the filler model 4, the particles visualized with white circles are the filler particle models extracted in the extraction process assuming that the particles are located on the surface of the filler model 4, and 1292 particles were extracted.

  On the other hand, the result of FIG. 10B is the result obtained according to the related technique 2 described in the background art section. Similarly to FIG. 10A, in the filler model 4, the particles visualized with white circles are the filler particle models extracted as those positioned on the surface of the filler model 4. In FIG. 10B, the number of extracted filler particle models is 391, which is clearly smaller than that of the present embodiment. This number can be increased to some extent by variously changing the distance R between the particles, but requires a lot of trial and error.

  FIGS. 11A and 11B show the results of defining a bond with the upper limit being 100 based on the first simulation model of FIGS. 10A and 10B, respectively. FIG. 11A shows the result obtained according to the above embodiment. In the filler model 4, the filler particle model 4 visualized with black circles is a polymer particle model (not shown) coupled with a bond (distance Rmin is set to 2.5. This length. It is made dimensionless by the parameter σ of the Leonard Jones potential, which is one of the interparticle interaction potential functions widely used in molecular simulations). Since particles on the surface of the filler model are extracted in a wide range, the degree of freedom at the time of bond definition is increased, and it can be confirmed that the bond is defined evenly in a balanced manner.

  On the other hand, the result of FIG. 11B is a result obtained in accordance with Related Technology 2 described in the Background Art section. It is clear that the bond is defined biased.

  Although the embodiments of the present invention have been described above, the present invention can be implemented with various modifications. For example, in order to obtain a 1st simulation model, although the molecular dynamics method is employ | adopted in the said embodiment, for example, a Monte Carlo method or molecular dynamics calculation may be employ | adopted.

2 First simulation model 3 Polymer model 3a Polymer particle model 3b Chain model 4a Filler particle model 4b Chain model 5 First polyhedron 6 Second polyhedron 7 Bond 10 Second simulation model

Claims (5)

A method for creating a simulation model of a composite material in which fillers are dispersed in a polymer material using a computer,
The computer may include any three of a string-like polymer model obtained by discretizing the polymer material with a finite number of polymer particle models and a bulk filler model obtained by discretizing the filler with a finite number of filler particle models. A first step of setting a first simulation model arranged in a dimensional space;
The computer couples both particle models between at least one filler particle model located on a surface of the filler model of the first simulation model and the polymer particle model located near the filler particle model. A second step of defining a bond to set and setting a second simulation model,
The second step includes
A dividing step of dividing the three-dimensional space into a plurality of regions using a first polyhedron including one of the polymer particle models and a second polyhedron including one of the filler particle models;
The bond is defined between the polymer particle model and the filler particle model included in at least one pair of the first polyhedron and the second polyhedron that are adjacent to each other in the three-dimensional space. A method for creating a simulation model of a composite material, comprising:   The method for creating a simulation model for a composite material according to claim 1, wherein the first polyhedron and the second polyhedron are Voronoi-divided polyhedrons. The combining step is an extraction step of extracting all filler particle models belonging to the second polyhedron in contact with the first polyhedron;
A determining step of determining at least one filler particle model from the extracted filler particle models;
The composite material simulation according to claim 1, further comprising a bond definition step of defining the bond between the determined filler particle model and the polymer particle model located closest to the filler particle model. How to create a model.   The composite material simulation model creation method according to claim 3, wherein the determination step and the bond definition step are repeatedly performed until the number of bonds reaches a predetermined upper limit.   The method for creating a simulation model for a composite material according to claim 3 or 4, wherein the determining step determines the next filler particle model so that the distance from the filler particle model that has already been determined does not fall below a predetermined value. .

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