How to create a filler model

Abstract

To provide a filler model creation method that can properly represent an exterior surface of a filler.SOLUTION: The present invention is a method for creating a filler model for a numeric analysis of a filler. This creation method includes: a step S1 of inputting to a computer a filler area serving as an area where a filler exists; and a step S2 of inputting to the computer an amorphous structure model having a plurality of particle models irregularly arranged. Further, the computer includes: a step S3 of defining a filler virtual space including an entire filler area; a step S4 of arranging a plurality of amorphous structure models inside the filler virtual space; and a step S5 of deleting the particle model existing outside the filler area to create the filler model.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present invention relates to a method for creating a filler model. [Background technology]

[0002] In recent years, various simulation methods (numerical calculations) have been proposed for evaluating the properties of composite materials consisting of fillers and polymeric materials using a computer in order to develop polymeric materials for rubber compounds, etc. In this type of simulation method, a filler model is created in which the filler is modeled (for example, see Patent Document 1 below). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Patent No. 5913260 Summary of the Invention [Problem to be solved by the invention]

[0004] In the method of Patent Document 1, a filler model is created by arranging a plurality of filler particle models in a crystal lattice such as a face-centered cubic lattice based on a three-dimensional image of a polymer material and bonding them together. This causes a problem that the outer surface of the filler model is formed in a regular stepped pattern, and behavior that does not occur in the original filler occurs in the simulation. In order to solve this problem, it is possible to arrange the filler particle models that constitute the outer surface of the filler model irregularly, but there is a problem that creating such a filler model requires a long calculation time.

[0005] The present invention has been devised in view of the above-mentioned circumstances, and has as its main object to provide a method capable of creating, in a short period of time, a filler model that can appropriately represent the outer surface of the filler. [Means for solving the problem]

[0006] The present invention is a method for creating a filler model for numerical analysis of a filler, comprising the steps of inputting a filler region, which is a region in which the filler exists, into a computer, and inputting an amorphous structure model in which a plurality of particle models are irregularly arranged into the computer, wherein the method comprises the steps of: defining a virtual space for filler including the entire filler region; arranging the plurality of amorphous structure models inside the virtual space for filler; and deleting the particle models existing outside the filler region to create the filler model.

[0007] In the filler model creating method according to the present invention, after the step of creating the filler model, the computer may further include a step of modifying the filler model so that a filling rate of the particle model inside the filler model is smaller than a filling rate of the particle model in an outer layer of the filler model.

[0008] In the method for creating a filler model according to the present invention, the step of modifying the filler model may include a step of arranging the particle model inside the filler model based on a crystal structure having a filling rate smaller than that of an outer layer of the filler model.

[0009] In the filler model creating method according to the present invention, the step of creating the filler model may include a step of deleting the particle models protruding from the filler region and then combining adjacent particle models. Effect of the Invention

[0010] The filler model creating method of the present invention, having the above-mentioned configuration, makes it possible to create a filler model that appropriately represents the outer surface of the filler in a short period of time. [Brief description of the drawings]

[0011] [Figure 1] FIG. 1 is a perspective view showing an example of a computer used in a method for creating a filler model. [Diagram 2] 13 is a flowchart showing an example of a processing procedure of a filler model creating method. [Diagram 3] 13A and 13B are conceptual diagrams showing an example of a filler region and a filler virtual space. [Figure 4] FIG. 2 is a conceptual diagram showing an example of an amorphous structure model. [Diagram 5] FIG. 13 is a conceptual diagram showing an example of a virtual space for a filler in which a plurality of amorphous structure models are arranged. [Figure 6] FIG. 1 is a conceptual diagram illustrating an example of a filler model. [Figure 7] 13 is a flowchart showing an example of a processing procedure of a filler model creation method according to another embodiment of the present invention. [Figure 8] FIG. 11 is a cross-sectional view showing an example of a filler model according to another embodiment of the present invention. [Figure 9] This is the structural formula of polybutadiene. [Figure 10] 1 is a flowchart showing an example of a processing procedure of a simulation method for a polymer material. [Figure 11] FIG. 2 is a conceptual diagram showing an example of a polymer material model. [Figure 12] FIG. 1 is a conceptual diagram showing an example of a filler model whose outer surface is formed in a regular stepped pattern. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. In the filler model creation method of this embodiment (hereinafter, sometimes simply referred to as the "creation method"), a model for numerical analysis of the filler (filler model) is created. The filler model created by this creation method is used in the polymer material simulation method described below (hereinafter, sometimes simply referred to as the "simulation method"). In this embodiment, a computer is used in the creation method and simulation method.

[0013] 1 is a perspective view showing an example of a computer 1 used in the filler model creation method. The computer 1 includes a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main body 1a is provided with a central processing unit (CPU), a ROM, a working memory, a storage device such as a magnetic disk, and disk drive devices 1a1 and 1a2. The storage device stores in advance a processing procedure (program) for executing the creation method and simulation method of this embodiment.

[0014] The filler is, for example, silica, carbon black, alumina, etc. In the present embodiment, the filler is, for example, spherical. The filler is dispersed in the polymer material, for example, as an aggregate in which a plurality of spherical primary particles are bonded together, or as an aggregate in which these particles are aggregated.

[0015] Fig. 2 is a flow chart showing an example of a processing procedure of a filler model creation method. In the creation method of this embodiment, first, a filler region 17, which is a region where a filler exists, is input to a computer 1 (step S1). The filler region 17 corresponds to a region in which a particle model 11, which will be described later, can be placed in a filler model 10 created by the creation method of this embodiment. Figs. 3(a) and (b) are conceptual diagrams showing an example of the filler region 17 and a virtual space 6 for filler.

[0016] The shape of the filler region 17 can be set as appropriate. The shape of the filler region 17 may be set based on the actual three-dimensional structure of the filler identified by, for example, 3DTEM observation. In step S1, for example, from a collection of partial regions obtained by dividing the three-dimensional structure so that the length, width, and height are equally spaced, all sets of partial regions in which the filler exists may be selected, and the entire set may be input as the filler region 17. Note that the filler region 17 does not need to be a single continuous mass, and may include a higher-order structure such as a plurality of isolated aggregates or aggregates.

[0017] As shown in Fig. 3, in this embodiment, the filler region 17 is represented as an arrangement of one or more primary particles (primary particle model 5 modeling the primary particles) having a certain particle size. As shown in Fig. 3(a), for example, when the filler model 10 is composed of one primary particle model 5, the filler region 17 is defined as one spherical region. On the other hand, as shown in Fig. 3(b), for example, when the filler model 10 is composed of multiple primary particle models 5, the filler region 17 is defined as multiple isolated aggregates formed by bonding multiple primary particles.

[0018] The filler region 17 of this embodiment is input as a pair of the particle diameter D1 of the primary particle model 5 shown in FIG. 3 and the center of gravity position of each primary particle model 5. In this case, the filler region 17 is defined as a region including, for all primary particle models 5, a spherical region in which the distance from the center of gravity of each primary particle model 5 is half or less of the particle diameter D1. The filler region 17 may include overlapping spherical regions of a plurality of primary particle models 5. In such a case, the primary particle models 5 are regarded as an aggregate in which the primary particle models 5 are bonded to each other. If the overlapping is too small, a problem may occur in which the particle models 11, 11 are not adjacent to each other (are spaced apart) between the primary particle models 5, 5 bonded to each other after the particle models 11 are placed in the filler region 17. In order to avoid such a problem, it is desirable that the size (thickness) of the overlapping between the bonded primary particle models 5, 5 is sufficiently larger than the diameter of the particle model 11.

[0019] The filler model 10 of this embodiment is exemplified as being mainly composed of one primary particle model 5 shown in Fig. 3(a). For this reason, in step S1, a filler region 17 composed of one primary particle model 5 is defined inside the filler virtual space 6. In the filler region 17 of this embodiment, the particle diameter D1 of the spherical primary particle model 5 and the position of the center of gravity of the primary particle model 5 are defined. The filler region 17 is stored in the computer 1.

[0020] Next, in the creation method of this embodiment, an amorphous structure model 22 is input to the computer 1 (step S2). The amorphous structure model 22 is a model in which a plurality of particle models 11 are irregularly arranged (filled) in an amorphous virtual space 19 described below. FIG. 4 is a conceptual diagram showing an example of the amorphous structure model 22.

[0021] In step S2 of this embodiment, first, a diameter D2 of the particle model (coarse-grained particle model) 11 to be placed inside the amorphous structure model 22 is input to the computer 1. The particle model 11 can be appropriately defined based on this diameter D2.

[0022] The particle model 11 of this embodiment is a coarse-grained group of atoms constituting the filler. The particle model 11 is treated as a mass point of the equation of motion in the molecular dynamics calculation described below. That is, parameters such as mass, volume, diameter D2, charge, and initial coordinates are defined in the particle model 11. The particle model 11 (diameter D2) is input to the computer 1.

[0023] Next, in step S2 of this embodiment, an amorphous virtual space 19 is input to the computer 1. In the amorphous virtual space 19, for example, a periodic boundary condition is defined, and a three-dimensional shape that can be filled in the space without gaps is appropriately defined.

[0024] The amorphous virtual space 19 in this embodiment is defined as a cube having three pairs of amorphous planes 20, 20 facing each other. A periodic boundary condition is defined for each of the amorphous planes 20. Therefore, the amorphous virtual space 19 is treated as one amorphous plane 20 being continuous (connected) with the opposite amorphous plane 20.

[0025] The length of one side of the amorphous virtual space 19 (amorphous length) Lc can be set appropriately. Note that the larger the amorphous length Lc, the more the number of particle models 11 placed in the amorphous virtual space 19 increases, and the longer the time required to create the amorphous structure model 22 tends to be. For this reason, it is desirable to set the amorphous length Lc to a sufficiently small value that is equal to or less than half the size of the filler length La (shown in FIGS. 3(a) and (b)). This makes it possible to shorten the time required to create the amorphous structure model 22 input in step S2, and therefore to shorten the time required to create the filler model 10.

[0026] On the other hand, the shorter the amorphous length Lc is, the smaller the number of particle models 11 that can be arranged becomes. In particular, when the amorphous length Lc is extremely short, it becomes difficult to arrange the particle models 11 irregularly. In this case, when such amorphous structure models 22 are repeatedly (multiplely) arranged in the step S4 (shown in FIG. 2) of arranging the amorphous structure models described later, the outer surface of the filler model 10 (shown in FIG. 6) may become more regular. From this viewpoint, it is desirable to set the amorphous length Lc to a sufficiently large value so that the number of particle models 11 is 50 or more at a predetermined filling rate of the amorphous structure (for example, 60% to 68%).

[0027] By setting the amorphous length Lc to such a value, it is possible to prevent the amorphous length Lc from becoming smaller than necessary. This makes it easy to create an amorphous structure model 22 in which particle models 11 are irregularly arranged inside the amorphous virtual space 19 in step S2. Furthermore, it is possible to sufficiently reduce the effect of the outer surface of the filler model 10 (shown in FIG. 6) becoming regular, which is caused by the repeated arrangement of the amorphous structure models 22.

[0028] Furthermore, when a periodic boundary condition is defined on the filler plane 7 (shown in FIG. 3(a)), in step S4 (shown in FIG. 2) of arranging the amorphous structure models 22 described below, it is desirable to set the amorphous length Lc so that the size of the assembly (filler model 10) in which the amorphous structure models 22 are arranged one-dimensionally an integer number of times is sufficiently close to the filler length La. For this reason, it is desirable to set the amorphous length Lc to a value obtained by dividing the filler length La by an integer of 2 or more.

[0029] Next, in step S2 of this embodiment, a plurality of particle models 11 are arranged in the amorphous virtual space 19. The number of particles in the particle model 11 is appropriately defined. For example, the number of particles in the particle model 11 may be selected so as to be the filling rate of the amorphous structure (for example, 60% to 68%).

[0030] The particle models 11 are appropriately arranged. In this embodiment, first, a plurality of particle models 11 are randomly arranged in the amorphous virtual space 19, allowing overlap between the particle models 11. Next, in this embodiment, a constant volume molecular dynamics calculation is performed using the force field of formula 2.4 described in Paper 1 (Kurt Kremer & Gary S. Grest, "Dynamics of entangled linear polymer melts: A molecular-dynamics simulation", J. Chem Phys. vol.92, No.8, 15 April 1990), and then the overlap between the particle models (coarse-grained particle models) 11 is removed.

[0031] Next, in step S2 of this embodiment, a constant volume molecular dynamics calculation is performed using the force field of formula A1 described in Paper 1. Then, a liquid state of the particle model (coarse-grained particle model) 11 is created, and further, a potential energy minimization calculation is performed using the same force field, so that the arrangement of the particle model 11 can be created. Note that, instead of using the above-mentioned method, the arrangement of the particle model 11 may be created by performing calculations using a molecular dynamics method of hard spheres or a Monte Carlo method.

[0032] Molecular mechanics calculations (molecular dynamics calculations) can be processed using, for example, COGNAC included in the Soft Material Integrated Simulator (J-OCTA) manufactured by JSOL Corporation.

[0033] In step S2 of this embodiment, based on the above-mentioned method, a plurality of particle models 11 are irregularly arranged in the amorphous virtual space 19 to input an amorphous structure model 22. The amorphous virtual space 19 and the amorphous structure model 22 are stored in the computer 1.

[0034] Next, in the creation method of this embodiment, a filler virtual space (virtual space) 6 for creating a filler model is input to the computer 1 (step S3). As shown in Fig. 3, the filler virtual space 6 of this embodiment is defined so as to include the entire filler region 17. Note that the shape and size of the filler virtual space 6 can be defined appropriately as long as the entire filler region 17 is included.

[0035] The filler virtual space 6 in this embodiment may be defined as a rectangular parallelepiped region having a length obtained by adding the particle diameter D1 of two primary particle models 5 to the length in the x-axis direction, the length in the y-axis direction, and the length in the z-axis direction of the filler region 17, respectively (i.e., the upper and lower limit values ​​of the x-coordinate, the y-coordinate, and the z-coordinate of the filler region 17 are each expanded by the width of the particle diameter D1 of the primary particle model 5). In addition, when a periodic boundary condition is imposed on the coordinate system in which the primary particle model 5 of the filler region 17 is arranged, the entire coordinate system to which the periodic boundary condition is imposed may be defined as the filler virtual space 6. At this time, the periodic boundary condition required to define the filler virtual space 6 may be input together with the input of the filler region 17.

[0036] In this embodiment, the virtual space 6 for filler is exemplified as being defined as a cube having three pairs of planes 7, 7 facing each other. A periodic boundary condition is defined for each plane 7. Therefore, the virtual space 6 for filler is treated as one plane 7 being continuous (connected) with the opposite plane 7.

[0037] The length of one side of the virtual space for filler 6 (length for filler) La can be set appropriately. In this embodiment, the length for filler La is desirably set so as to include the entirety of the filler region 17 while making the volume as small as possible. This allows the particle model 11 described below to be filled into the filler region 17 without gaps, and furthermore, in step S4 described below, the time required to place the amorphous structure model 22 (shown in FIG. 4) can be reduced. The virtual space for filler 6 is stored in the computer 1.

[0038] Next, in the creation method of this embodiment, the computer 1 arranges a plurality of amorphous structure models 22 inside the filler virtual space 6 (step S4). In step S4, the plurality of amorphous structure models 22 are arranged so that the particle models 11 are filled in the filler region 17. Fig. 5 is a conceptual diagram showing an example of the filler virtual space 6 in which the plurality of amorphous structure models 22 are arranged.

[0039] In step S4 of the present embodiment, first, the number of times N for repeatedly arranging the amorphous structure model 22 in each of the x-axis direction, y-axis direction, and z-axis direction in the virtual space for filler 6 is determined. The number of times N can be appropriately determined once the particle models 11 are filled in the filler region 17. The number of times N is obtained, for example, by rounding off (rounding off the decimal point) a value obtained by dividing the length for filler La by the length for amorphous Lc. In order to arrange the amorphous structure model 22 without dividing it, the number of times N is preferably an integer of 2 or more. Note that, if the obtained number of times N is not an integer of 2 or more, the values ​​of the length for amorphous Lc and the like may be changed, and then the steps S2 to S4 may be performed again. The number of times N is stored in the computer 1.

[0040] Next, in step S4 of this embodiment, the computer 1 performs the following in the filler virtual space 6: The amorphous structure models 22 are repeatedly arranged in the x-axis direction, the y-axis direction, and the z-axis direction. In this embodiment, the arrangement of the amorphous structure models 22 is determined based on the determined number of times N (in FIG. 5, the number of times N=3). Within the virtual space 6 for filler, a three-dimensional vector R indicating the coordinates of each particle model 11 included in each amorphous structure model 22 is i (i x ,i y ,i z ) is defined by the following equation (1).

[0041]

number

[0042] In the above formula (1), R i (i x ,i y ,i z ) indicates the three-dimensional vector of the coordinates of the i-th particle model 11 of the amorphous structure model 22 arranged at the ix-th position in the x-axis direction, the iy-th position in the y-axis direction, and the iz-th position in the z-axis direction in the virtual space 6 for the filler.

[0043] In this embodiment, the three-dimensional vector R i (i x ,i y ,i z ), the coordinates of the particle model 11 are determined based on the above, so that the arrangement of the amorphous structure models 22 repeatedly arranged inside the virtual space 6 for the filler (in the x-axis direction, y-axis direction, and z-axis direction) can be determined.

[0044] According to the above formula (1), the amorphous structure model 22 is enlarged or reduced in each of the x-axis direction, y-axis direction, and z-axis direction based on a magnification equal to the value obtained by dividing the length for filler La by the product of the number of times N and the length for amorphous Lc. This corrects the "deviation" caused by rounding performed when the number of times N is calculated, so that the amorphous structure models 22 are arranged in the virtual space for filler 6 with almost no gaps.

[0045] In the creation method of this embodiment, the amorphous structure model 22 of the particle model 11 is input in the virtual space for amorphous 19, which is smaller than the virtual space for filler 6 shown in FIG. 4. Therefore, in this embodiment, the number of particles of the particle model 11 for which the amorphous structure model 22 is created can be reduced compared to the case where the amorphous structure model (not shown) of the particle model 11 is calculated in the virtual space for filler 6, which is larger than the virtual space for amorphous 19. Note that the calculation of repeatedly arranging the amorphous structure model 22 as in this embodiment is so small that the calculation time can be ignored compared to molecular dynamics calculations, etc. Therefore, in step S4 of this embodiment, the calculation time can be significantly reduced. The virtual space for filler 6 in which the multiple amorphous structure models 22 are arranged is stored in the computer 1.

[0046] Next, in the creation method of this embodiment, the computer 1 deletes the particle model 11 protruding from the filler region 17 (shown by a two-dot chain line in FIG. 5) to create a filler model 10 (shown in FIG. 6) (step S5). The determination of whether the particle model 11 protrudes from the filler region 17 can be defined appropriately. In this embodiment, when a part of the particle model 11 exists outside the filler region 17, it is determined that the particle model 11 protrudes from the filler region 17. As a specific example of such a determination, the particle model 11 may be determined to protrude when the center coordinates of the particle model 11 exist outside the filler region 17 or when the shortest distance between the center coordinates of the particle model 11 and the outer surface of the filler region 17 is smaller than the value obtained by dividing the diameter D2 (shown in FIG. 4) of the particle model 11 by 2.

[0047] In step S5 of this embodiment, the particle models 11 protruding from the filler region 17 are deleted, and a filler model 10 in which the primary particle model 5 is defined is created based on the particle models 11 filled in the filler region 17. FIG. 6 is a conceptual diagram showing an example of the filler model 10. The filler model 10 is stored in the computer 1.

[0048] Next, in the creation method of this embodiment, the computer 1 combines adjacent particle models 11, 11 (step S6). Step S6 in this embodiment is performed after deleting the particle models 11 protruding from the filler region 17 (shown in FIG. 5).

[0049] In step S6 of this embodiment, adjacent particle models 11, 11 are bonded to each other at a predetermined distance (hereinafter, sometimes simply referred to as "bond distance"). The bond distance can be set appropriately. The bond distance in this embodiment can be set, for example, in the range of 1.0 to 1.5 times (1.1 times in this example) the diameter D2 (shown in FIG. 4) of the particle model 11.

[0050] In step S6 of the present embodiment, as shown in Fig. 6, adjacent particle models 11, 11 that are equal to or less than the bond distance are bonded by a bond chain model 8. As a result, in step S6, a filler model 10 in which a plurality of particle models 11 are bonded is created. The rigidity of such a filler model 10 can be increased by the bond chain model 8. The filler model 10 is stored in the computer 1.

[0051] In the creation process of this embodiment, the filler model 10 in which the particle models 11, 11 are bonded is created using the bond chain model 8, but the invention is not limited to this embodiment. For example, step S6 may be omitted to create a filler model 10 in which the particle models 11, 11 are not bonded. In this case, the coordinates of all the particle models 11 constituting the filler model 10 may be fixed, or a constraint condition such as making each aggregate a rigid body may be defined.

[0052] In the creation method of this embodiment, unlike the filler particle model of Patent Document 1 (i.e., the coarse-grained particle model of this embodiment) arranged in a crystal lattice pattern, the particle model 11 of the filler model 10 is arranged in an irregular amorphous (non-crystalline) state. As a result, in the creation method of this embodiment, the outer surface of the filler model 10 becomes irregular as shown in FIG. 6, and it is possible to prevent it from being formed in a regular step shape as shown in FIG. 12. Note that, in the case of silica produced by, for example, a sintering method or a precipitation method, the outer surface of an actual filler is not formed in a regular step shape as shown in FIG. 12. Therefore, in the creation method of this embodiment, it is possible to create a filler model 10 in which the outer surface of the actual filler is appropriately expressed.

[0053] Next, in the creation method of this embodiment, in order to use the created filler model 10 in a molecular dynamics calculation, a force field (not shown) for molecular dynamics calculation may be set between the particle models 11, 11 (step S7). The force field may be, for example, the following formula (2) described in Paper 1, and a cutoff distance r c =2 1 / 6 An LJ potential in which the repulsive force between the particle models 11, 11 is expressed by σ, and a bonding potential in which the bond between the particle models 11, 11 is expressed by the following formula (3) may be used.

[0054]

number

[0055]

number

[0056] In this embodiment, the distance between adjacent particle models 11, 11 of the filler model 10 is created so as to be close to a diameter D2 (shown in FIG. 4). The diameter D2 is also determined by the cutoff distance r c =2 1 / 6 Therefore, if the bond potential shown in the above formula (3) is used as is in the bond chain model 8, the bond length before the bond potential of the above formula (3) is used is about 1.122σ, whereas the equilibrium length of the bond potential is about 0.961σ. This may cause relaxation due to molecular dynamics calculations, resulting in the entire filler model shrinking. To avoid this problem, the equilibrium length of the bond potential is set equal to the cutoff distance r c For example, the parameter σ(U LJ The (r) term and the stretched length R0 may both be multiplied by 1.168.

[0057] Incidentally, in the simulation method described later, molecular dynamics calculation is performed on all particle models 11 constituting the filler model 10 shown in FIG. 6. Therefore, if the filling rate (number) of the particle models 11 is large, the calculation time tends to increase. Therefore, in the creation method, the filler model 10 may be modified so that the filling rate of the particle models 11 is small. FIG. 7 is a flowchart showing an example of a processing procedure of a filler model creation method according to another embodiment of the present invention. FIG. 8 is a cross-sectional view showing an example of a filler model 10 according to another embodiment of the present invention. In FIG. 8, the virtual space 6 for filler is omitted. In this embodiment, the same components as those in the previous embodiments are given the same reference numerals, and the description may be omitted.

[0058] In the production method of this embodiment, the filler model 10 is modified so that the filling rate of the particle models 11 inside the filler model 10 is smaller than the filling rate of the particle models 11 in the outer layer 21 of the filler model 10. This modification process includes a step S8 of making the filler model 10 hollow, and a step S9 of filling the hollow filler model 10 with particle models 11 of a crystalline structure having a filling rate lower than that of an amorphous structure.

[0059] In step S8, the particle models 11 inside the outer layer 21 of the filler model 10 are deleted while maintaining the particle models 11 in the outer layer 21. In this embodiment, among the particle models 11 in the virtual space 6 for filler, all the particle models 11 that are not included in the outer layer 21 are deleted.

[0060] The outer layer 21 may be defined as appropriate. The outer layer 21 of this embodiment is defined as a region within a predetermined thickness r1 from the outer surface of the filler region 17 toward the inside. The thickness r1 may be defined as appropriate. The thickness r1 of this embodiment is set to 5% to 20% (10% in this example) of the particle diameter D1 (shown in FIG. 3(a)) of the primary particle model 5.

[0061] The determination of whether or not the particle model 11 is included in the outer layer 21 can be performed appropriately. In this embodiment, when at least a part of the particle model 11 exists outside the outer layer 21, it is determined that the particle model is not included in the outer layer 21. More specifically, when the central coordinates of the particle model 11 exist outside the outer layer 21, or when the shortest distance between the central coordinates of the particle model 11 and the outer surface of the outer layer 21 is smaller than a value obtained by dividing the diameter D2 (shown in FIG. 4) of the particle model 11 by 2, it is determined that the particle model is not included in the outer layer 21.

[0062] In step S9, the particle models 11 having a crystalline structure with a filling rate lower (smaller) than that of the amorphous structure are filled in the inner region of the outer layer 21 of the filler model 10. Any crystalline structure can be appropriately adopted as long as it has a filling rate smaller than that of the outer layer 21 (for example, 60% to 68%). In this embodiment, a diamond structure (filling rate of 34%) is adopted.

[0063] In the creation method of this embodiment, the amorphous arrangement of the particle models 11 constituting the outer layer 21 is maintained, so that the filler model 10 that can more appropriately express the outer surface of the filler can be created, as in the previous embodiments. Furthermore, in the creation method of this embodiment, the packing rate of the particle models 11 inside the filler model 10 can be reduced while suppressing a decrease in the strength of the entire filler model 10, so that the number of particle models 11 to be calculated in the simulation method described below can be reduced. Therefore, the creation method of this embodiment makes it possible to shorten the calculation time while maintaining the calculation accuracy in the simulation method (molecular dynamics calculation) described below.

[0064] In this embodiment, for the crystal structure filled inside the filler model 10, adjacent particle models 11 may be bonded by a bond chain model 8 (shown in FIG. 6). Furthermore, the particle model 11 constituting the crystal structure and the particle model 11 constituting the outer layer 21 may be bonded by a bond chain model 8. This makes it possible to reduce the number of particle models 11 inside the filler model 10 while suppressing a decrease in the strength of the filler model 10.

[0065] Next, a method for simulating a polymer material using the filler model 10 obtained by the above-mentioned creation method will be described. In the simulation method of the present embodiment, a computer 1 is used to calculate the performance of a polymer material containing a filler and a polymer component.

[0066] The polymer component includes, for example, natural rubber, synthetic rubber, and resin. An example of the polymer component of this embodiment is cis-1,4 polybutadiene (hereinafter, sometimes simply referred to as "polybutadiene"). Figure 9 shows the structural formula of polybutadiene.

[0067] The molecular chain 12 constituting polybutadiene is composed of monomers 13 {-[CH2-CH=CH-CH2]-} consisting of a methylene group (-CH2-) and a methine group (-CH-) linked with a degree of polymerization n. A methyl group (-CH3) is linked to the end of the polymer material instead of the methylene group (-CH2). The polymer component may be something other than polybutadiene. The filler is as described above. FIG. 10 is a flow chart showing an example of the processing procedure of the simulation method for polymer material.

[0068] In the simulation method of this embodiment, first, a cell, which is a virtual space corresponding to a part of a polymer material (not shown), is input to a computer 1 (step S10). Fig. 11 is a conceptual diagram showing an example of a polymer material model. In Fig. 11, only a part of a filler model 10 and a molecular chain model 15 are representatively shown.

[0069] The cell 14 is a region to be calculated in a molecular dynamics calculation described later. The cell 14 in this embodiment can be set in the same manner as the filler virtual space 6 shown in Fig. 3(a), for example. At least one filler model 10 and a plurality of molecular chain models 15 are arranged inside the cell 14.

[0070] The length Lb of one side of the cell 14 can be set appropriately. In this embodiment, the length Lb is preferably three times or more the radius of gyration (not shown), which is an amount indicating the spread of the molecular chain model 15 described later. This allows the cell 14 to prevent collisions with itself (image) arranged periodically due to the periodic boundary condition in the molecular dynamics calculation, and to properly calculate the spatial spread of the molecular chain model 15. In addition, the size of the cell 14 is set to a stable volume at, for example, 1 atmosphere. This allows the cell 14 to define at least a part of the volume of the polymer material to be analyzed. The cell 14 is stored in the computer 1.

[0071] Next, in the simulation method of this embodiment, a molecular chain model 15, which is a model of a molecular chain 12 (shown in FIG. 9) of a polymer material, is input to the computer 1 (step S11). The molecular chain model 15 of this embodiment is defined as a coarse-grained molecular model.

[0072] The molecular chain model 15 is represented by using a number of particles 16 which is less than the number of atoms constituting the molecular chain 12 (shown in FIG. 9). These particles 16, 16 are connected by a bonding chain (not shown). The molecular chain model 15 of this embodiment is exemplified as a Kremer-Grest model, but is not particularly limited thereto. The molecular chain model 15 may be, for example, a model based on DPD (Dissipative Particle Dynamics).

[0073] Each particle 16 in this embodiment corresponds to, for example, a monomer 13 of the molecular chain 12 shown in FIG. 9. When the molecular chain 12 is polybutadiene, for example, 1.10 monomers 13 are used as a structural unit, and the structural unit is replaced with one particle 16. As a result, a plurality of particles 16 (for example, 10 to 5000 particles) are set in the molecular chain model 15 in this embodiment. The particles 16 are treated as mass points in the equation of motion in the molecular dynamics calculation described later. That is, parameters such as mass, diameter, charge, and initial coordinates are defined for the particles 16. Each of these parameters is stored in the computer 1 as numerical information.

[0074] The bonding chain (not shown) is defined as a bonding potential that defines an equilibrium length between the particles 16, 16. Here, the "equilibrium length" is defined as the bond distance between the particles 16, 16 at which the value of the bonding potential is smallest. The bonding potential of the bonding chain (not shown) can be set, for example, based on the above-mentioned paper 1. Such a molecular chain model 15 is numerical data for handling polymeric materials in molecular dynamics calculations, and is input to the computer 1.

[0075] Next, in the simulation method of the present embodiment, the computer 1 acquires a filler model 10 (step S12). In step S12, the processing procedure of the above-mentioned creation method is performed to acquire at least one filler model 10. The filler model 10 is stored in the computer 1.

[0076] Next, in the simulation method of this embodiment, the computer 1 places the molecular chain model 15 and the filler model 10 inside the cell 14 (step S13). In step S13 of this embodiment, first, the filler model 10 is placed inside the cell 14. The position at which the filler model is placed can be set appropriately. For example, the filler model 10 may be placed in an area where the filler is placed in an electron beam transmission image of the polymer material. Thereby, in step S13, the filler model 10 can be placed inside the cell 14 based on the relative position of the filler in the actual polymer material.

[0077] Next, in step S13, a plurality of molecular-chain models 15 are placed in the region where no filler model 10 is placed. Thereby, in step S13, the molecular-chain models 15 can be placed in the cells 14 so as to approximate the distribution of the actual molecular chains 12.

[0078] Next, in the simulation method of this embodiment, a potential P3 in which an attractive force and a repulsive force act between the particles 16, 16 of the adjacent molecular chain models 15, 15 and between the particle 16 of the molecular chain model 15 and the particle model 11 of the filler model 10 is defined (step S14). As this potential P3, the LJ potential expressing the repulsive force described in the above Patent Document 1 is adopted. Each variable of the LJ potential can be appropriately set based on, for example, the above Paper 1.

[0079] Next, in the simulation method of this embodiment, the computer 1 performs molecular dynamics calculations on the molecular chain model 15 and the filler model 10 (step S15). In the molecular dynamics calculations, for example, Newton's equation of motion is applied to the cell 14 for a predetermined time, assuming that the particle model 11 of the filler model 10 and the particle 16 of the molecular chain model 15 follow classical mechanics. Then, the movements of the particle model 11 and the particle 16 at each time are tracked for each unit time.

[0080] In step S15, first, the structural relaxation of the molecular chain model 15 is calculated. In this case, the pressure and temperature are kept constant, or the volume and temperature are kept constant, in the cell 14. By calculating this structural relaxation, in step S15, a polymer material model 18 that models a polymer material (not shown) is created.

[0081] Next, in step S15 of this embodiment, a deformation calculation (e.g., elongation deformation) is performed on the created polymer material model 18. Then, a physical quantity (e.g., stress, etc.) acquired by the deformation calculation of the polymer material model 18 is stored in the computer 1.

[0082] In the simulation method of this embodiment, since the filler model 10 having a surface structure approximating the microstructure of the filler is used, the effect of the filler surface structure on the physical properties of the polymer material (molecular chain model 15) can be evaluated with high accuracy. Therefore, in the simulation method of this embodiment, the physical quantities obtained by deformation calculation of the polymer material model 18 can be calculated with high accuracy.

[0083] Next, in the simulation method of this embodiment, it is determined whether the physical properties of the polymer material model 18 are good or not (step S16). The determination of whether the physical properties are good or not is appropriately performed based on the strength, durability, etc. required for the polymer material.

[0084] If the physical properties are good in step S16 ("Y" in step S16), a polymer material is produced (step S17) based on the structures of the filler and molecular chains 12 (shown in FIG. 9). The produced polymer material is used in the production of industrial products such as tires. On the other hand, if the physical properties are not good in step S16 ("N" in step S16), the structure of at least one of the filler and the molecular chains 12 is changed (step S18), and steps S10 to S16 are carried out again. As a result, the simulation method of this embodiment makes it possible to produce a polymer material having good physical properties and an industrial product using that polymer material.

[0085] Although a particularly preferred embodiment of the present invention has been described in detail above, the present invention is not limited to the illustrated embodiment and can be modified and carried out in various forms. EXAMPLES

[0086] A model for numerical analysis of the filler was created based on the processing procedure shown in Fig. 2 (Example 1). Furthermore, a model for numerical analysis of the filler was created based on the processing procedure shown in Fig. 7 (Example 2). In Example 2, unlike Example 1, a step of modifying the filler model was carried out so that the packing rate of the particle model inside the filler model was smaller than the packing rate of the particle model of the outer layer of the filler model. In Example 2, the crystal structure of the particle model inside the filler model is a diamond structure.

[0087] For the purpose of comparing the calculation times of Example 1 and Example 2, a filler model was created by calculating structural relaxation by molecular dynamics calculations for a particle model placed inside a virtual space for a filler without using an amorphous structure model (Comparative Example 1). In Comparative Example 1, for the particle model after structural relaxation, the particle model outside the filler region was removed, and adjacent particle models were bonded to each other.

[0088] Furthermore, for comparison of the filler surface structure, a filler model was created by arranging a plurality of particle models in a crystal lattice pattern such as a face-centered cubic lattice pattern, and then deleting the particle model arranged outside the filler region corresponding to one spherical primary particle, as in the above-mentioned Patent Document 1. Fig. 12 is a conceptual diagram showing an example of the filler model of Comparative Example 2.

[0089] Then, the time required for creating the filler model was obtained for Example 1, Example 2, Comparative Example 1, and Comparative Example 2. Furthermore, based on the processing procedure shown in Fig. 10, a simulation was performed using the filler models of Example 1, Example 2, Comparative Example 1, and Comparative Example 2, and the time required for the simulation was obtained. The common specifications are as follows. Filler model (before modification process of Example 2): Number of primary particle models: 1 Number of particle models: 10,000 Amorphous structure model: Number of particle models: 80 Length of virtual space for filler La: 32.3σ Filler volumetric filling rate: 30% Structural relaxation calculations for amorphous structure model: Unit time: 0.001τ Structural relaxation calculation using the potential shown in equation 2.4 of paper 1 Number of steps: 10,000 steps Structural relaxation calculations using the LJ potential shown in equation A1 of paper 1 Number of steps: 10,000 steps Potential energy minimization with the above LJ potential Number of steps: Within 1,000 steps Structural relaxation calculations for polymer material models: Unit time: 0.006τ Number of steps: 1,000,000 steps

[0090] As a result of the test, the time required to create the filler models in Examples 1 and 2 was 0.3% of the time required to create the filler model in Comparative Example 1. Therefore, in Examples 1 and 2, the filler models could be created in a short time.

[0091] Furthermore, in Example 2, the filling rate of the particle model inside the filler model can be made smaller than the filling rate of the particle model in the outer layer of the filler model, so that the simulation calculation time can be reduced to 89% compared to Example 1 and Comparative Example 1.

[0092] In addition, the outer surfaces of the filler models of Examples 1 and 2 could be prevented from being formed in a regular stepped shape as in Comparative Example 2 shown in Fig. 12, and a filler model capable of more appropriately expressing the outer surface of the filler could be created. In the simulations of Examples 1 and 2, the behavior of the original filler could be reproduced with higher accuracy than in the simulation of Comparative Example 2. [Explanation of symbols]

[0093] S1 Step of inputting filler area S2 Step to input the amorphous structure model S3 The process of inputting virtual space for fillers S4 A process of arranging multiple amorphous structure models inside the virtual space for filler. S5: The process of deleting particle models that protrude from the filler area

Claims

1. A method for creating a filler model for numerical analysis of a filler, comprising the steps of: A step of inputting a filler region, which is a region where the filler exists, into a computer; and inputting an amorphous structure model in which a plurality of particle models are irregularly arranged into the computer, The computer, defining a virtual space for filler that includes the entire filler region; Arranging a plurality of the amorphous structure models inside the virtual space for filler; and creating the filler model by deleting the particle model that exists outside the filler region. How to create a filler model.

2. 2. The method for creating a filler model according to claim 1, further comprising, after the step of creating the filler model, a step in which the computer modifies the filler model so that a filling rate of the particle model inside the filler model is smaller than a filling rate of the particle model in an outer layer of the filler model.

3. The method for creating a filler model according to claim 2 , wherein the step of modifying the filler model includes a step of arranging the particle model inside the filler model based on a crystal structure having a smaller filling rate than an outer layer of the filler model.

4. 4. The filler model creating method according to claim 1, wherein the step of creating the filler model includes a step of deleting the particle models protruding from the filler region, and then combining adjacent particle models.

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