Creation method and simulation method for polymer material model

Abstract

To provide a method enabling creation of a polymer material model having a crosslinked structure close to reality.SOLUTION: A method for creating a polymer material model is provided. The creation method includes: a first step S1 of inputting, to a computer, a pre-crosslinking coarse grained molecular model in which a structural unit of a molecular chain before crosslinking is substituted with coarse grained particles; a second step S2 of analyzing the molecular chain after crosslinking; a third step S3 of inputting, to the computer, a chemical structure of the structural unit after crosslinking on the basis of a result of the analysis; a fourth step S4 of inputting, to the computer, a post-crosslinking structural unit model in which the chemical structure of the structural unit after crosslinking is modeled as an entire atomic model or a united atom model; a fifth step S5 of the computer calculating structural relaxation based on a molecular dynamics method for the pre-crosslinking coarse grained molecular model; and a sixth step S6 of the computer allocating a post-crosslinking structural unit model to the coarse grained particles of the pre-crosslinking coarse grained molecular model after the structural relaxation, to create a post-crosslinking molecular model in which the molecular chain after crosslinking is modeled as the entire atomic model or the united atom model.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to a method for creating a polymer material model and a simulation method. [Background technology]

[0002] The following Patent Document 1 describes a method for efficiently creating an equilibrium all-atom model configuration for any homopolymer polymer chain. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Laid-Open No. 2014-225226 Summary of the Invention [Problem to be solved by the invention]

[0004] However, the above method did not focus on creating a model for numerical analysis of polymer materials that include cross-linked molecular chains, making it difficult to create a polymer material model with a cross-linked structure that is close to reality.

[0005] The present invention has been devised in view of the above circumstances, and its main object is to provide a method capable of creating a polymer material model having a cross-linked structure that is close to reality. [Means for solving the problem]

[0006] The present invention is a method for creating a numerical analysis model of a polymer material including a cross-linked molecular chain, the method comprising the following steps: a first step of inputting a pre-cross-linking coarse-grained molecular model, in which structural units within a predetermined range of the molecular chain before cross-linking are substituted with coarse-grained particles, into a computer; a second step of analyzing the molecular chain after cross-linking; a third step of inputting a chemical structure of the structural unit after cross-linking, including at least a cross-linked portion, into the computer based on the analysis results of the molecular chain after cross-linking; a fourth step of inputting a post-cross-linking structural unit model, in which the chemical structure of the structural unit after cross-linking is modeled as an all-atom model or a united-atom model, into the computer; a fifth step of calculating structural relaxation based on a molecular dynamics method for the pre-cross-linking coarse-grained molecular model; and a sixth step of creating a post-cross-linking molecular model in which the molecular chain after cross-linking is modeled as the all-atom model or the united-atom model by assigning the post-cross-linking structural unit model to the coarse-grained particles of the pre-cross-linking coarse-grained molecular model after the structural relaxation. [Effects of the Invention]

[0007] By employing the above steps, the method for creating a polymer material model of the present invention makes it possible to create a polymer material model having a cross-linked structure that is close to reality. [Brief explanation of the drawings]

[0008] [Figure 1] FIG. 1 is a perspective view showing an example of a computer for executing a polymer material model creation method and a simulation method. [Figure 2] This is the structural formula of polybutadiene. [Figure 3] 10 is a flowchart showing an example of a processing procedure of a polymer material model creation method. [Figure 4] FIG. 1 is a conceptual diagram showing an example of a pre-crosslinking coarse-grained molecular model. [Figure 5]1 shows an example of the chemical structure of a structural unit after crosslinking, where (a) is the chemical structure of a first structural unit after crosslinking, and (b) is the chemical structure of a second structural unit after crosslinking. [Figure 6] 10 is a flowchart showing an example of a processing procedure of a fourth step. [Figure 7] FIG. 2 is a diagram showing an example of a first post-crosslinking structural unit model. [Figure 8] FIG. 10 is a diagram showing an example of a second post-crosslinking structural unit model. [Figure 9] FIG. 2(a) is a diagram illustrating a third size of the first crosslinked structure, and FIG. 2(b) is a diagram illustrating a fourth size of the second crosslinked structure. [Figure 10] 13 is a flowchart showing an example of a processing procedure of a seventh step. [Figure 11] FIG. 2 is a diagram showing an example of a pre-crosslinking structural unit model. [Figure 12] 10 is a flowchart showing an example of a processing procedure of a fifth step. [Figure 13] FIG. 1 is a conceptual diagram illustrating an example of a cell in which a pre-crosslinking coarse-grained molecular model is arranged. [Figure 14] 10 is a flowchart showing an example of a processing procedure of a sixth step. [Figure 15] FIG. 1 is a partial conceptual diagram of a coarse-grained molecular model before crosslinking after structural relaxation. [Figure 16] FIG. 1 is a partial conceptual diagram of a cross-linked molecular model. [Figure 17] FIG. 1 is a conceptual diagram showing an example of a polymer material model in which a cross-linked molecular model is placed inside a cell. [Figure 18] 1 is a flowchart showing an example of a processing procedure of a simulation method for a polymer material. DETAILED DESCRIPTION OF THE INVENTION

[0009] Hereinafter, embodiments of the present invention will be described with reference to the drawings. It should be understood that the drawings include exaggerated representations and representations that differ from the dimensional ratios of actual structures in order to facilitate understanding of the contents of the invention. Furthermore, identical or common elements are designated by the same reference numerals throughout the embodiments, and redundant explanations will be omitted. Furthermore, the specific configurations shown in the embodiments and drawings are for the purpose of understanding the contents of the present invention, and the present invention is not limited to the specific configurations shown in the drawings.

[0010] In the method for creating a polymer material model (hereinafter sometimes referred to as the "creation method") of this embodiment, a numerical analysis model of a polymer material including cross-linked molecular chains (hereinafter sometimes referred to as the "polymer material model") is created. This polymer material model is used in a simulation method for a polymer material (hereinafter sometimes referred to as the "simulation method") described below, to evaluate, for example, the performance of the polymer material. These creation methods and simulation methods use a computer.

[0011] [computer] 1 is a perspective view showing an example of a computer for executing the polymer material model creation method and simulation method. The computer 1 of this embodiment is configured to include a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main body 1a is provided with, for example, 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 has software and the like stored in advance for executing the creation method and simulation method of this embodiment.

[0012] [Polymer materials] The polymer material is not particularly limited as long as it contains crosslinkable molecular chains, and examples thereof include rubber, resin, and elastomer. An example of the polymer material of this embodiment is cis-1,4 polybutadiene (hereinafter, sometimes simply referred to as "polybutadiene"). Figure 2 shows the structural formula of polybutadiene.

[0013] The molecular chain 2 that constitutes polybutadiene is composed of monomers 3 {-[CH2-CH=CH-CH2]-} consisting of a methylene group (-CH2-) and a methine group (-CH-) linked together at a certain degree of polymerization. In addition, a methyl group (-CH3) is linked to the end of the polymer material instead of the methylene group (-CH2).

[0014] Incidentally, in the above-mentioned Patent Document 1, it is possible to create an equilibrium all-atom model arrangement for a homopolymer polymer chain. However, in the above-mentioned Patent Document 1, no attention is paid to creating a polymer material model including cross-linked molecular chains 2, so it has been difficult to create a polymer material model having a cross-linked structure close to reality.

[0015] Furthermore, there is currently no clear evidence of the cross-linking structure connecting molecular chains 2 and 2. For this reason, it is possible to assume the most plausible cross-linking structure and create a polymer material model that includes molecular chain 2 after cross-linking, but this poses the problem of the cross-linking structure deviating from reality.

[0016] As a result of extensive research, the inventors have found that the crosslinked structure can be clearly identified by analyzing the crosslinked molecular chain 2 based on the procedures described below.

[0017] [Method for creating a polymer material model (first embodiment)] In the creation method of this embodiment, a polymer material model having a cross-linked structure close to reality is created based on the above findings. Fig. 3 is a flowchart showing an example of the processing procedure of the polymer material model creation method.

[0018] [Input the pre-crosslinking coarse-grained molecular model (Step 1)] In the preparation method of this embodiment, first, a pre-crosslinking coarse-grained molecular model is input into a computer 1 (shown in FIG. 1) (first step S1). The pre-crosslinking coarse-grained molecular model is obtained by replacing structural units within a predetermined range of the pre-crosslinking molecular chain 2 shown in FIG. 2 with coarse-grained particles. Fig. 4 is a conceptual diagram showing an example of a pre-crosslinking coarse-grained molecular model 5.

[0019] The structural unit can be appropriately specified depending on, for example, the calculation performance of a computer 1 (shown in FIG. 1). As shown in FIG. 2, the structural unit 4 of this embodiment is defined as a monomer 3 of a molecular chain 2. By defining such a monomer 3 as the structural unit 4, it is possible to easily associate the coarse-grained particle 7 shown in FIG. 4 with a structural unit model (for example, shown in FIG. 7, which will be described later) in which the structural unit 4 is modeled as an all-atom model or united atoms. This allows reverse mapping to be performed efficiently. Details of reverse mapping are as described, for example, in Patent Document 1, etc.

[0020] In the first step S1 of this embodiment, the structural units 4 (monomers 3) of the molecular chains 2 before cross-linking shown in Fig. 2 are replaced with the coarse-grained particles 7 shown in Fig. 4. As a result, the coarse-grained molecular model 5 before cross-linking can be expressed using coarse-grained particles 7 whose number is less than the number of atoms constituting the molecular chains 2 shown in Fig. 2.

[0021] The coarse-grained particle 7 is represented as a sphere with a diameter. The coarse-grained particle 7 is treated as a mass point in the equation of motion in the molecular dynamics calculation described below. That is, parameters such as mass, diameter, charge, and initial coordinates are defined for the coarse-grained particle 7.

[0022] The number of coarse-grained particles 7 can be appropriately set based on, for example, the structure of the molecular chain 2 shown in Fig. 2 and the performance of the computer 1 (shown in Fig. 1) that performs the molecular dynamics calculation described below. In this embodiment, the number can be, for example, 5 to 1000.

[0023] A potential (hereinafter sometimes referred to as "first potential") P1 with a defined equilibrium length is set between adjacent coarse-grained particles 7, 7. This allows a bonding chain 8 that binds the coarse-grained particles 7, 7 to be defined between the coarse-grained particles 7, 7. Details of the equilibrium length and the first potential P1 are described in the above-mentioned Patent Document 1, etc.

[0024] In the first step S1 of this embodiment, the coarse-grained particles 7 and the bonding chains 8 are defined, thereby making it possible to create a pre-crosslinking coarse-grained molecular model 5 that models the molecular chains 2 (shown in FIG. 2) before crosslinking. The pre-crosslinking coarse-grained molecular model 5 of this embodiment is exemplified by a Kremer-Grest model, but is not particularly limited thereto.

[0025] For example, commercially available simulation software (for example, J-OCTA manufactured by JSOL Corporation) is used to create the pre-crosslinking coarse-grained molecular model 5. The pre-crosslinking coarse-grained molecular model 5 is numerical data that can be handled by a computer 1 (shown in FIG. 1 ) and is stored in the computer 1.

[0026] [Analysis of molecular chains after crosslinking (second step)] Next, in the production method of this embodiment, the cross-linked molecular chain 2 (shown in FIGS. 5(a) and 5(b) described later) is analyzed (second step S2). The analysis results in the second step S2 are used in the third step S3 described later to identify the chemical structure of the cross-linked structural unit 4 (monomer 3) including the cross-linked portion of the cross-linked molecular chain.

[0027] In the second step S2 of this embodiment, a polymer material including the cross-linked molecular chains 2 (hereinafter sometimes referred to as a "vulcanized polymer material") is targeted, and the cross-linked molecular chains 2 are analyzed. The vulcanized polymer material may be an existing one, or may be a prototype made by newly vulcanizing a polymer material including the pre-cross-linked molecular chains 2 shown in FIG. 2.

[0028] The crosslinked molecular chains 2 can be analyzed as appropriate as long as the chemical structure of the crosslinked structural units 4 can be clearly identified. An example of such an analysis is nuclear magnetic resonance (NMR) analysis. In this embodiment, nuclear magnetic resonance analysis is performed.

[0029] In nuclear magnetic resonance (NMR) analysis, a resonance phenomenon is observed when a magnetic field is applied to atomic nuclei and electromagnetic waves are irradiated. By performing such nuclear magnetic resonance analysis on molecular chains after crosslinking, the chemical structure of the molecular chains including the crosslinked structure can be obtained with high accuracy. Nuclear magnetic resonance analysis is performed based on known procedures, and for example, a nuclear magnetic resonance spectrometer (Avance 400) manufactured by Bruker can be used.

[0030] In the nuclear magnetic resonance (NMR) analysis of this embodiment, for example, one-dimensional measurement data and two-dimensional measurement data are acquired for the crosslinked molecular chain 2. The one-dimensional measurement data acquires the chemical state of a single nuclide. On the other hand, the two-dimensional measurement data acquires the correlation between the same nuclide and the correlation between different nuclide. The one-dimensional measurement data and the two-dimensional measurement data are stored in a computer 1 (shown in FIG. 1).

[0031] [Enter the chemical structure of the crosslinked structural unit (Step 3)] Next, in the production method of this embodiment, based on the analysis results of the cross-linked molecular chain 2 (shown in Figures 5(a) and 5(b) described later), the chemical structure of the cross-linked structural unit 4 including at least the cross-linked portion is input into the computer 1 (shown in Figure 1) (third step S3).

[0032] In this embodiment, nuclear magnetic resonance analysis is performed on the cross-linked molecular chains 2, and one-dimensional measurement data and two-dimensional measurement data are obtained as the analysis results of the cross-linked molecular chains 2.

[0033] In the one-dimensional measurement data, the chemical state of a single nuclide is acquired. By performing nuclear magnetic resonance analysis on the crosslinked molecular chain 2 as in the present embodiment, the presence or absence of sulfur atoms constituting the crosslinked structure, the state of atoms adjacent to the sulfur atoms (e.g., carbon atoms, sulfur atoms, etc.), etc. can be ascertained.

[0034] In the two-dimensional measurement data, correlations between the same kind of nuclides and correlations between different kinds of nuclides are obtained. By performing nuclear magnetic resonance analysis on the crosslinked molecular chain 2 as in this embodiment, more detailed information can be obtained regarding the chemical state of atoms (e.g., carbon atoms, sulfur atoms, etc.) to which the sulfur atoms constituting the crosslinked structure are bonded.

[0035] From these one-dimensional measurement data and two-dimensional measurement data, the chemical structure of the structural unit 4 after crosslinking, including at least the crosslinked portion, can be estimated. In this embodiment, the chemical structure of the structural unit 4 after crosslinking, including at least the crosslinked portion, is estimated from the one-dimensional measurement data and two-dimensional measurement data. As a result, the chemical structure of the structural unit 4 after crosslinking, including at least the crosslinked portion, can be clearly obtained.

[0036] In this embodiment, an example of the cross-linked structural unit 4 (monomer 3 shown in FIG. 2) includes a first cross-linked structural unit and a second cross-linked structural unit. FIGS. 5(a) and 5(b) are diagrams showing an example of the chemical structure of the cross-linked structural unit 4. FIG. 5(a) shows first cross-linked structural units 10A, 10A. FIG. 5(b) shows second cross-linked structural unit 10B.

[0037] As shown in FIG. 5(a), the chemical structure of the first post-crosslinking structural unit 10A of this embodiment shows a crosslinked structure 12 in which one end of a sulfur chain 11 is bonded to the chemical structure of the structural unit 4 (monomer 3) before crosslinking shown in FIG. 2. In FIG. 5(a), for two non-adjacent (separated from each other) structural units 4, 4, a first post-crosslinking structural unit 10A in which one end of the sulfur chain 11 is bonded and a second post-crosslinking structural unit 10A in which the other end of the sulfur chain 11 is bonded are shown. In addition, although a case in which the sulfur chain 11 is a tetrasulfide is illustrated, the sulfur chain 11 is not particularly limited and may be, for example, a monosulfide or a disulfide depending on the type of molecular chain 2, vulcanization conditions, etc.

[0038] As shown in FIG. 5(b), the chemical structure of the second post-crosslinking structural unit 10B is a crosslinked structure 12 in which both ends of a sulfur chain 11 are bonded in a ring shape to the chemical structure of the structural unit 4 (monomer 3) before crosslinking shown in FIG. 2. FIG. 5(b) shows the second post-crosslinking structural unit 10B in which both ends of a sulfur chain 11 are bonded in a ring shape to two adjacent structural units 4, 4. In addition, although a case in which the sulfur chain 11 is a disulfide is exemplified, this is not particularly limited, and the sulfur chain 11 may be, for example, a monosulfide or a trisulfide depending on the type of molecular chain 2, vulcanization conditions, etc.

[0039] The crosslinked structural unit 4 is not limited to an embodiment including the first post-crosslinking structural unit 10A shown in FIG. 5(a) and the second post-crosslinking structural unit 10B shown in FIG. 5(b). For example, depending on the type of molecular chain 2, vulcanization conditions, etc., it may be either the first post-crosslinking structural unit 10A or the second post-crosslinking structural unit 10B, or it may include a post-crosslinking structural unit 4 different from the first post-crosslinking structural unit 10A and the second post-crosslinking structural unit 10B. The chemical structure of the post-crosslinked structural unit 4 (in this example, the first post-crosslinking structural unit 10A and the second post-crosslinking structural unit 10B) is stored in a computer 1 (shown in FIG. 1).

[0040] [Enter the post-crosslinking structural unit model (Step 4)] Next, in the production method of this embodiment, a post-crosslinking structural unit model, which is a model of the chemical structure of the post-crosslinking structural unit 4, is input to the computer 1 (shown in FIG. 1) (fourth step S4).

[0041] In this embodiment, the post-crosslinking structural unit model is modeled as an all-atom model or a united atom model. The all-atom model is a model in which all atoms are modeled based on an actual chemical structure. On the other hand, the united atom model differs from the all-atom model in that a carbon atom and a hydrogen atom bonded to the carbon atom are treated as a single particle. These all-atom models and united atom models can handle finer structures and movements than, for example, the pre-crosslinking coarse-grained molecular model 5 shown in FIG. 4, and therefore can improve simulation accuracy. FIG. 6 is a flowchart showing an example of the processing procedure of the fourth step S4.

[0042] [Define post-bridge structural unit model] In the fourth step S4 of this embodiment, first, a post-crosslinking structural unit model is defined by modeling the chemical structure of the structural unit 4 (shown in FIGS. 5(a) and 5(b)) after crosslinking (step S41). The post-crosslinking structural unit model of this embodiment is modeled as an all-atom model, but may also be modeled as a united-atom model.

[0043] In this embodiment, examples of post-crosslinking structural units include the first post-crosslinking structural unit 10A shown in FIG. 5(a) and the second post-crosslinking structural unit 10B shown in FIG. 5(b). Therefore, in step S41 of this embodiment, the chemical structures of these post-crosslinking structural units are modeled, and a first post-crosslinking structural unit model and a second post-crosslinking structural unit model are defined as post-crosslinking structural unit models. FIG. 7 is a diagram showing an example of the first post-crosslinking structural unit model 13A. FIG. 8 is a diagram showing an example of the second post-crosslinking structural unit model 13B.

[0044] As shown in Fig. 7, the first post-crosslinking structural unit models 13A and 13A are obtained by modeling, as an all-atom model, the chemical structures of the first post-crosslinking structural units 10A and 10A shown in Fig. 5(a). As shown in Fig. 8, the second post-crosslinking structural unit model 13B is obtained by modeling, as an all-atom model, the chemical structure of the second post-crosslinking structural unit 10B shown in Fig. 5(b).

[0045] 7 and 8, the first post-crosslinking structural unit model 13A and the second post-crosslinking structural unit model 13B are configured to include a plurality of particle models 15 and bonds 16 that bond the particle models 15, 15. These particle models 15 and bonds 16 are set based on the chemical structures of the first post-crosslinking structural unit 10A and the second post-crosslinking structural unit 10B shown in FIGS. 5(a) and 5(b).

[0046] The particle model 15 is treated as a mass point in the equation of motion during molecular dynamics calculations, which will be described later. That is, parameters such as mass, diameter, charge, and initial coordinates are defined for the particle model 15.

[0047] The particle model 15 is a model of the atoms included in the chemical structure of the structural unit 4 after crosslinking shown in Figures 5(a) and 5(b). Therefore, the particle model 15 includes a carbon particle model 15c that models a carbon atom, a hydrogen particle model 15h that models a hydrogen atom, and a sulfur particle model 15s that models a sulfur atom.

[0048] The bond 16 binds the particle models 15, 15 together. In this embodiment, the bond 16 includes a main chain 16a connecting the carbon particle models 15c, 15c and a side chain 16b connecting the carbon particle model 15c and the hydrogen particle model 15h. The main chain 16a and the side chain 16b are treated as springs with defined equilibrium lengths and spring constants, for example.

[0049] In the first post-crosslinking structural unit model 13A and the second post-crosslinking structural unit model 13B, bond lengths, bond angles, dihedral angles, etc. are defined in the same manner as in conventional all-atom models, so that the first post-crosslinking structural unit model 13A and the second post-crosslinking structural unit model 13B have three-dimensional structures.

[0050] In accordance with convention, the bond lengths, bond angles, and dihedral angles of the first post-crosslinking structural unit model 13A and the second post-crosslinking structural unit model 13B change when subjected to an external or internal force, which changes the three-dimensional structures of the first post-crosslinking structural unit model 13A and the second post-crosslinking structural unit model 13B.

[0051] The bond length, bond angle, and dihedral angle can be defined by a potential (GAFF) set based on, for example, Paper 1 (J. Comput. Chem. 25, 1157-1174 (2004)). The potential is desirably set based on the chemical structures of the first post-crosslinking structural unit model 13A and the second post-crosslinking structural unit model 13B.

[0052] The first post-crosslinking structural unit 10A and the second post-crosslinking structural unit 10B shown in FIGS. 5(a) and 5(b) are extracted from the molecular chain 2 after crosslinking. Therefore, if the first post-crosslinking structural unit 10A and the second post-crosslinking structural unit 10B are simply modeled, a chemically unstable model will be created. In this embodiment, as shown in FIGS. 7 and 8, the ends of the first post-crosslinking structural unit model 13A and the second post-crosslinking structural unit model 13B are capped with methyl groups 17, respectively. This makes the first post-crosslinking structural unit model 13A and the second post-crosslinking structural unit model 13B chemically stable during molecular dynamics calculations, which will be described later.

[0053] The above-mentioned simulation software, etc., is used to create the first post-crosslinking structural unit model 13A and the second post-crosslinking structural unit model 13B. The first post-crosslinking structural unit model 13A and the second post-crosslinking structural unit model 13B are numerical data that can be handled by a computer 1 (shown in FIG. 1 ) and are stored in the computer 1.

[0054] [Get size of post-bridge structural unit model] Next, in a fourth step S4 of this embodiment, the size of the post-crosslinking structural unit model 13 is acquired (step S42). In this embodiment, the size of the post-crosslinking structural unit model 13 is used for adjusting the potential (third potential) P3 between the particle models 15, 15 in a sixth step S6 described later.

[0055] In the present embodiment, examples of the post-crosslinking structural unit model 13 include the first post-crosslinking structural unit model 13A shown in Fig. 7 and the second post-crosslinking structural unit model 13B shown in Fig. 8. Therefore, in step S42, as the size of the post-crosslinking structural unit model 13, a first size D1 (shown in Fig. 7) which is the size of the first post-crosslinking structural unit model 13A and a second size D2 (shown in Fig. 8) which is the size of the second post-crosslinking structural unit model 13B are acquired.

[0056] 7, the first size D1 is specified as the distance between the carbon particle models 15c, 15c at the ends of the first post-crosslinking structural unit model 13A (between the centers of the carbon particle models 15c, 15c). In the present embodiment, when the first post-crosslinking structural unit model 13A is capped with a methyl group 17, the first size D1 can be specified to include the methyl group 17. In order to eliminate variation in the first size D1, it is preferable to calculate structural relaxation based on molecular dynamics calculations for a plurality of first post-crosslinking structural unit models 13A, and then determine the average of the first sizes D1 of the plurality of first post-crosslinking structural unit models 13A.

[0057] Molecular dynamics calculations can be performed based on the same procedures as conventional ones. In this embodiment, first, a plurality of first post-crosslinking structural unit models 13A are arranged in a cell (not shown), which is a virtual space to be analyzed. The number of first post-crosslinking structural unit models 13A is set to, for example, 100 to 1000. Then, Newton's equation of motion is applied to the cell for a predetermined time, assuming that all first post-crosslinking structural unit models 13A follow classical mechanics. Then, the movements of all particle models 15 at each time (unit time) are tracked and stored in a computer 1 (shown in FIG. 1). Furthermore, the conditions for the molecular dynamics calculations are constant, for example, the number of particle models 15 in the system, the volume (e.g., 1 atmosphere), and the temperature (e.g., 300 K). In this embodiment, the calculations are performed until the initial arrangement of the first post-crosslinking structural unit models 13A is sufficiently relaxed. For example, the above-mentioned simulation software or the like is used for the molecular dynamics calculations.

[0058] As shown in FIG. 8, the second size D2 is specified as the distance between the carbon particle models 15c, 15c at the ends of the second post-crosslinking structural unit model 13B (between the centers of the carbon particle models 15c, 15c). When the second post-crosslinking structural unit model 13B is capped with a methyl group 17, as in this embodiment, the second size D2 can be specified to include the methyl group 17. To eliminate variations in the second size D2, it is preferable to calculate the structural relaxation based on the molecular dynamics calculation described above for a plurality of second post-crosslinking structural unit models 13B, and then calculate the average of the second sizes D2 of the plurality of second post-crosslinking structural unit models 13B. The number of second post-crosslinking structural unit models 13B is set to, for example, 100 to 1000. The first size D1 and the second size D2 are stored in the computer 1 (shown in FIG. 1).

[0059] [Get size of bridge structure] Next, in a fourth step S4 of this embodiment, the size of the cross-linked structure 12 of the post-cross-linked structural unit model 13 is acquired (step S43). The size of this cross-linked structure 12 is used in a sixth step S6 described later to identify an assignment target of the post-cross-linked structural unit model 13 shown in FIGS. 7 and 8 from the pre-cross-linking coarse-grained molecular model 5 shown in FIG. 4.

[0060] The cross-linked structure 12 of this embodiment includes a first cross-linked structure 12A provided in the first post-cross-linked structural unit model 13A and a second cross-linked structure 12B provided in the second post-cross-linked structural unit model 13B. Therefore, in step S43 of this embodiment, a third size which is the size of the first cross-linked structure 12A and a fourth size which is the size of the second cross-linked structure 12B are obtained.

[0061] 9(a) is a diagram illustrating the third size D3 of the first crosslinked structure 12A. This first crosslinked structure 12A is obtained by extracting (modeling) the sulfur chain (tetrasulfide) of the first crosslinked structural unit model 13A shown in FIG. 7. The ends of the first crosslinked structure 12A are capped with methyl groups 17, 17. This makes the first crosslinked structure 12A chemically stable during molecular dynamics calculations.

[0062] The third size D3 is specified as the distance between the carbon particle models 15c, 15c (between the centers of the carbon particle models 15c, 15c) of the methyl groups 17, 17 arranged at the ends of the first crosslinked structures 12A. To eliminate variations in the third size D3, it is preferable to calculate the structural relaxation of a plurality of first crosslinked structures 12A based on the above-mentioned molecular dynamics calculation, and then determine the average of the third sizes D3 of the plurality of first crosslinked structures 12A. The number of first crosslinked structures 12A is set to, for example, 100 to 1000.

[0063] 9(b) is a diagram illustrating the fourth size D4 of the second crosslinked structure 12B. This second crosslinked structure 12B is obtained by extracting (modeling) the sulfur chain (disulfide) of the second crosslinked structural unit model 13B shown in FIG. 8. The ends of the second crosslinked structure 12B are capped with methyl groups 17, 17. This makes the second crosslinked structure 12B chemically stable in the molecular dynamics calculations described below.

[0064] The fourth size D4 is specified as the distance between the carbon particle models 15c, 15c (between the centers of the carbon particle models 15c, 15c) of the methyl groups 17, 17 arranged at the ends of the second crosslinked structures 12B. To eliminate variations in the fourth size D4, it is preferable to calculate the structural relaxation of a plurality of second crosslinked structures 12B based on the molecular dynamics calculation described above, and then determine the average of the fourth sizes D4 of the plurality of second crosslinked structures 12B. The number of second crosslinked structures 12B is set to, for example, 100 to 1000. The third size D3 and the fourth size D4 are stored in the computer 1 (shown in FIG. 1).

[0065] [Enter the pre-crosslinking structural unit model (7th step)] Next, in the preparation method of this embodiment, a pre-crosslinking structural unit model, which is a model of the chemical structure of the pre-crosslinking structural unit 4 (monomer 3) shown in Figure 2, is input to the computer 1 (shown in Figure 1) (seventh step S7). In this embodiment, the pre-crosslinking structural unit model is input as an all-atom model or a united-atom model. Figure 10 is a flowchart showing an example of the processing procedure of the seventh step S7.

[0066] [Define pre-bridge structural unit model] In the seventh step S7 of this embodiment, first, a pre-crosslinking structural unit model is defined by modeling the chemical structure of the pre-crosslinking structural unit 4 shown in Figure 2 (step S71). The pre-crosslinking structural unit model of this embodiment is modeled as an all-atom model, but may also be modeled as a united-atom model. Figure 11 is a diagram showing an example of a pre-crosslinking structural unit model 18.

[0067] The pre-crosslinking structural unit model 18 is configured to include a plurality of particle models 15 and bonds 16 that connect the particle models 15, 15. These particle models 15 and bonds 16 are set based on the chemical structure of the pre-crosslinking structural unit 4 (monomer 3) shown in FIG.

[0068] Details of the particle model 15 and the bond 16 are as described above. In addition, in the pre-crosslinking structural unit model 18, the bond length, bond angle, dihedral angle, etc. are defined based on the chemical structure of the structural unit 4 before crosslinking.

[0069] As shown in FIG. 2, the pre-crosslinking structural unit 4 is extracted from the pre-crosslinking molecular chain 2. Therefore, if the pre-crosslinking structural unit 4 is simply modeled, a chemically unstable model will be created. In this embodiment, as shown in FIG. 11, the end of the pre-crosslinking structural unit model 18 is capped with a methyl group 17. This makes the pre-crosslinking structural unit model 18 chemically stable in the molecular dynamics calculation described below.

[0070] The above-mentioned simulation software or the like is used to create the pre-crosslinking structural unit model 18. The pre-crosslinking structural unit model 18 is numerical data that can be handled by the computer 1 (shown in FIG. 1), and is stored in the computer 1.

[0071] [Get the size of the pre-bridge structural unit model] Next, in a seventh step S7 of this embodiment, the size of the pre-crosslinking structural unit model 18 is acquired (step S72). In this embodiment, the size D5 of the pre-crosslinking structural unit model 18 (hereinafter, sometimes referred to as the "fifth size") is used for adjusting the potential (third potential) P3 between the particle models 15, 15 in a sixth step S6 described later.

[0072] The fifth size D5 in this embodiment is specified as the distance between the carbon particle models 15c, 15c at the ends of the pre-crosslinking structural unit model 18 (between the centers of the carbon particle models 15c, 15c). When the pre-crosslinking structural unit model 18 is capped with a methyl group 17, as in this embodiment, the fifth size D5 can be specified to include the methyl group 17. In order to eliminate variation in the fifth size D5, it is preferable to calculate the structural relaxation based on the above-mentioned molecular dynamics calculation for multiple pre-crosslinking structural unit models 18, and then calculate the average of the fifth sizes D5 of the multiple pre-crosslinking structural unit models 18. The number of pre-crosslinking structural unit models 18 is set to, for example, 100 to 1000. The fifth size D5 is stored in the computer 1 (shown in FIG. 1).

[0073] [Calculating the structural relaxation of the coarse-grained molecular model before cross-linking (step 5)] Next, in the creation method of this embodiment, the computer 1 (shown in FIG. 1) calculates structural relaxation based on the molecular dynamics method for the pre-crosslinking coarse-grained molecular model 5 (fifth step S5). Fig. 12 is a flowchart showing an example of the processing procedure of the fifth step S5.

[0074] Cell Input In the fifth step S5 of this embodiment, first, a cell, which is a virtual space corresponding to a part of the polymer material, is input (step S51). Fig. 13 is a conceptual diagram showing an example of a cell 19 in which a pre-crosslinking coarse-grained molecular model 5 is arranged. In Fig. 13, a part of the pre-crosslinking coarse-grained molecular model 5 is representatively shown.

[0075] The cell 19 of this embodiment has at least one pair of surfaces 20, 20 facing each other (three pairs of surfaces 20, 20 facing each other in this embodiment). The cell 19 of this embodiment is defined as a rectangular parallelepiped or a cube (a cube in this embodiment).

[0076] A periodic boundary condition is defined for each face 20, 20 of the cell 19. The length L1 of each side of the cell 19 is preferably, for example, at least twice the radius of gyration (not shown), which is an amount indicating the extent of the pre-crosslinking coarse-grained molecular model 5. This makes it possible to prevent collisions with self-images due to the periodic boundary condition in the structural relaxation calculation based on molecular dynamics described below.

[0077] [Multiple pre-crosslinked coarse-grained molecular models are placed inside the cell] Next, in a fifth step S5 of this embodiment, a plurality of pre-crosslinking coarse-grained molecular models 5 are arranged inside the cell 19 (step S52). In step S52 of this embodiment, for example, based on the Monte Carlo method, a plurality of pre-crosslinking coarse-grained molecular models 5 are randomly arranged inside the cell 19. The number of pre-crosslinking coarse-grained molecular models 5 can be set appropriately based on the calculation capacity of the computer 1, the size of the cell 19, the size of the pre-crosslinking coarse-grained molecular models 5, and the like. For example, the above-mentioned simulation software or the like is used for such arrangement.

[0078] [Define interactions between coarse-grained particles] Next, in the fifth step S5 of this embodiment, an interaction is defined between the coarse-grained particles 7, 7 (step S53). The interaction in this embodiment is defined as a potential P2 (hereinafter sometimes referred to as the "second potential") acting between the coarse-grained particle 7 of one pre-crosslinking coarse-grained molecular model 5 and the coarse-grained particle 7 of the other pre-crosslinking coarse-grained molecular model 5 for a pair of pre-crosslinking coarse-grained molecular models 5, 5. The second potential P2 can be set appropriately, and for example, an attractive force and a repulsive force are defined. The second potential P2 in this embodiment can be defined, for example, as an LJ potential. Details of the LJ potential, constants, etc. are as described in Patent Document 1 above.

[0079] [Structural relaxation calculations based on molecular dynamics for a coarse-grained molecular model before cross-linking] Next, in a fifth step S5 of this embodiment, the computer 1 (shown in FIG. 1) calculates structural relaxation based on molecular dynamics for a plurality of pre-crosslinking coarse-grained molecular models 5 arranged inside the cell 19 (step S54). In the structural relaxation calculation of this embodiment, for example, Newton's equation of motion or the Langevin equation is applied, assuming that the coarse-grained particles 7 of the pre-crosslinking coarse-grained molecular model 5 follow classical mechanics for a predetermined time in the cell 19. Then, the movement of the coarse-grained particles 7 at each time is tracked for each unit time step.

[0080] In the molecular dynamics calculation, the pressure and temperature or the volume and temperature are kept constant in the cell 19. As a result, in the fifth step S5, the initial configuration of the pre-crosslinking coarse-grained molecular model 5 is relaxed so as to approximate the molecular motion of an actual polymer material. In this embodiment, this is performed until the initial configuration of the pre-crosslinking coarse-grained molecular model 5 is sufficiently relaxed.

[0081] The calculation of the structural relaxation can be performed using, for example, the above-mentioned simulation software, etc. The pre-crosslinking coarse-grained molecular model 5 after the structural relaxation is stored in a computer 1 (shown in FIG. 1).

[0082] [Creating a molecular model after cross-linking (step 6)] Next, in the creation method of this embodiment, a computer 1 (shown in FIG. 1) creates a post-crosslinked molecular model by modeling the molecular chain after crosslinking (sixth step S6). In the sixth step S6, a post-crosslinked structural unit model 13 (shown in FIGS. 7 and 8) is assigned to a coarse-grained particle 7 (shown in FIG. 13) of the pre-crosslinked coarse-grained molecular model 5 after structural relaxation. By such reverse mapping, a post-crosslinked molecular model is created as an all-atom model or a united-atom model. Reverse mapping can be easily performed using the above-mentioned simulation software or the like.

[0083] Note that crosslinking does not necessarily occur in all structural units 4 constituting the molecular chain 2 shown in Fig. 2. In order to model such structural units 4 as all-atom models or united-atom models, in the sixth step S6 of this embodiment, pre-crosslinking structural unit models 18 (shown in Fig. 11 ) are assigned to the coarse-grained particles 7 of the pre-crosslinking coarse-grained molecular model 5 after the structural relaxation.

[0084] Fig. 14 is a flowchart showing an example of the processing procedure of the sixth step S6. Fig. 15 is a partial conceptual diagram of the pre-crosslinking coarse-grained molecular model 5 after the structure has been relaxed.

[0085] [Identify the first and second coarse-grained particles] 15, in the sixth step S6 of this embodiment, first, a first coarse-grained particle 7A and a second coarse-grained particle 7B are identified from the pre-crosslinking coarse-grained molecular model 5 after structural relaxation (step S61). In step S61 of this embodiment, the first coarse-grained particle 7A and the second coarse-grained particle 7B are identified based on the distance L2 between adjacent coarse-grained particles 7, 7 after structural relaxation (i.e., between the centers of the coarse-grained particles 7, 7 that are not connected by the bonding chains 8).

[0086] The first coarse-grained particle 7A is the coarse-grained particle 7 to be assigned to the pre-crosslinking structural unit model 18 (shown in FIG. 11 ). The second coarse-grained particle 7B is the coarse-grained particle 7 to be assigned to the post-crosslinking structural unit model 13 (shown in FIGS. 7 and 8 ).

[0087] The first coarse-grained particle 7A and the second coarse-grained particle 7B can be appropriately identified based on the distance L2 between adjacent coarse-grained particles 7, 7 after structural relaxation. It is generally believed that crosslinking is more likely to occur when the distance between carbon atoms constituting the molecular chain 2 shown in FIG. 2 approaches a predetermined range. Therefore, in this embodiment, it is assumed that crosslinking occurs between a pair of coarse-grained particles 7, 7 whose distance L2 is within a predetermined range, and the second coarse-grained particles 7B, 7B to be assigned to the crosslinked structural unit model 13 are identified. These identified second coarse-grained particles 7B, 7B are the second coarse-grained particles (hereinafter sometimes referred to as "one second coarse-grained particle") 7Ba, 7Ba to be assigned to the first crosslinked structural unit models 13A, 13A shown in FIG. 7. On the other hand, the second coarse-grained particles 7Bb, 7Bb (hereinafter sometimes referred to as the "other second coarse-grained particles") to be assigned to the second post-crosslinking structural unit model 13B shown in FIG. 8 are crosslinked structures formed between adjacent first coarse-grained particles 7, 7, and therefore cannot be identified based on the distance L2. Therefore, among the multiple coarse-grained particles 7 that are not identified as one of the second coarse-grained particles 7Ba, 7Ba based on the distance L2, a predetermined number of coarse-grained particles 7 (two consecutive coarse-grained particles 7, 7 in this example) that are randomly determined can be identified as the other second coarse-grained particles 7Bb, 7Bb. Note that the coarse-grained particles 7 that are not identified as one of the second coarse-grained particles 7Ba and the other second coarse-grained particle 7Bb are considered not to be crosslinked, and are therefore identified as the first coarse-grained particles 7A to be assigned to the pre-crosslinking structural unit model 18 (shown in FIG. 11).

[0088] The range of the distance L2 can be set as appropriate. The first cross-linked structural unit model 13A shown in Fig. 7 is provided with a first cross-linked structure 12A. It is preferable to specify a first range, which is the range of the distance L2 for identifying the coarse-grained particle 7 to be assigned to the first cross-linked structural unit model 13A, based on the third size D3 (shown in Fig. 9(a)) of this first cross-linked structure 12A.

[0089] The first post-crosslinking structural unit model 13A (shown in FIG. 7), modeled as an all-atom model or a united-atom model, and the pre-crosslinking coarse-grained molecular model 5 (shown in FIG. 13) have different spatial units. Therefore, it is preferable to set the value obtained by converting the third size D3 (shown in FIG. 9(a)) into the unit of the pre-crosslinking coarse-grained molecular model 5 as the median of the first range. In this case, the first range can be set, for example, to a range of 0.5 to 2.0 times the median.

[0090] The above conversion can be performed appropriately, for example, based on the structural unit 4. In this embodiment, the above conversion can be performed based on the ratio between the size of one coarse-grained particle 7 (shown in FIG. 13) substituted with the structural unit 4 shown in FIG. 2 and the fifth size D5 (shown in FIG. 11) of the pre-crosslinking structural unit model 18 obtained by modeling the chemical structure of the structural unit 4.

[0091] The second post-crosslinking structural unit model 13B shown in FIG. 8 forms a cyclic structure with the second crosslinked structure 12B. When the crosslinked structure is a cyclic structure like this, it is preferable to determine the number of coarse-grained particles 7 to be assigned to the second post-crosslinking structural unit model 13B based on the second size D2, which is the size of the second post-crosslinking structural unit model 13B. In this case, it is preferable to set the value obtained by converting the second size D2 into units of the pre-crosslinking coarse-grained molecular model 5 as the number of coarse-grained particles 7 to be assigned. Such conversion can be performed based on the above-mentioned procedure. Furthermore, the number of coarse-grained particles 7 to be assigned can be set to, for example, 1 to 3 (2 in this example).

[0092] In step S61 of this embodiment, in the pre-crosslinking coarse-grained molecular model 5 after structural relaxation shown in Fig. 15, coarse-grained particles 7, 7 for which the distance L2 between adjacent coarse-grained particles 7, 7 is within a first range, and coarse-grained particles 7, 7 randomly determined based on the above number are identified. Then, the coarse-grained particles 7, 7 for which the distance L2 is within the first range are identified as second coarse-grained particles 7Ba, 7Ba to be assigned to the first post-crosslinking structural unit model 13A, 13A shown in Fig. 7. Furthermore, of the multiple coarse-grained particles 7 not identified based on the distance L2, the coarse-grained particles 7, 7 randomly determined based on the above number are identified as second coarse-grained particles 7Bb, 7Bb to be assigned to the second post-crosslinking structural unit model 13B shown in Fig. 8. Furthermore, the coarse-grained particles 7 that are not identified as one second coarse-grained particle 7Ba and the other second coarse-grained particle 7Bb are identified as first coarse-grained particles 7A, which are to be assigned to the pre-crosslinking structural unit model 18 (shown in Figure 11).

[0093] The total number of the second coarse-grained particles 7B (one second coarse-grained particle 7Ba and the other second coarse-grained particle 7Bb) is preferably determined to be equal to or close to a predetermined threshold value. The threshold value may be set, for example, based on the number of crosslinking points or crosslinking density of the crosslinked molecular chains 2 (shown in FIGS. 5(a) and 5(b)). The number of crosslinking points can be determined from the analysis results of the second step S2. The crosslinking density can be obtained using a known swelling and compression method. Note that if the total number of the second coarse-grained particles 7B is smaller than the threshold value, the range used to determine the second coarse-grained particles 7B (in this example, the first range) may be adjusted to be larger. This allows the total number of the second coarse-grained particles 7B to be increased to be equal to or close to the threshold value. Therefore, it is possible to create a polymer material model having a crosslinked structure closer to reality. The determined first coarse-grained particles 7A and second coarse-grained particles 7B are stored in the computer 1 (shown in FIG. 1).

[0094] [Assign the pre-crosslinking structural unit model to the first coarse-grained particle] Next, in the sixth step S6 of this embodiment, the pre-crosslinking structural unit model 18 shown in FIG. 11 is assigned to the first coarse-grained particle 7A shown in FIG. 15 (step S62). The assignment of the pre-crosslinking structural unit model 18 to the first coarse-grained particle 7A is appropriately set based on conventional reverse mapping. FIG. 16 is a partial conceptual diagram of a post-crosslinking molecular model 21. In FIG. 16, the regions corresponding to the first coarse-grained particle 7A and the second coarse-grained particle 7B are indicated by two-dot chain lines.

[0095] In this embodiment, as shown in Fig. 11, the end of the pre-crosslinking structural unit model 18 is capped with a methyl group 17. In this case, the pre-crosslinking structural unit model 18 from which the methyl group 17 is omitted is assigned to the first coarse-grained particle 7A shown in Fig. 15. Then, as shown in Fig. 16, the pre-crosslinking structural unit models 18, 18 arranged on adjacent first coarse-grained particles 7A, 7A are bonded by a bond 16. The pre-crosslinking structural unit model 18 assigned to the first coarse-grained particle 7A is stored in the computer 1 (shown in Fig. 1).

[0096] [Assign the post-crosslinking structural unit model to the second coarse-grained particle] Next, in the sixth step S6 of this embodiment, the post-crosslinking structural unit models 13, 13 shown in FIGS. 7 and 8 are assigned to the second coarse-grained particles 7B, 7B shown in FIG. 15 (step S63). The assignment of the post-crosslinking structural unit model 13 to the second coarse-grained particle 7B is appropriately set based on conventional reverse mapping. In this embodiment, the first post-crosslinking structural unit models 13A, 13A shown in FIG. 7 are assigned to one of the second coarse-grained particles 7Ba, 7Ba. The single second post-crosslinking structural unit model 13B shown in FIG. 8 is assigned to the other second coarse-grained particles 7Bb, 7Bb. At this time, the assignment of the second post-crosslinking structural unit model 13B to the other second coarse-grained particles 7Bb, 7Bb is appropriately set based on conventional reverse mapping (for example, the two other second coarse-grained particles 7Bb, 7Bb are treated as a single elliptical coarse-grained particle).

[0097] 7 and 8, the ends of the first post-crosslinking structural unit model 13A and the second post-crosslinking structural unit model 13B are each capped with a methyl group 17. In this case, the first post-crosslinking structural unit model 13A from which the methyl group 17 is omitted is assigned to one second coarse-grained particle 7Ba, and the second post-crosslinking structural unit model 13B is assigned to the other second coarse-grained particle 7Bb. Then, as shown in FIG. 16, the adjacent first post-crosslinking structural unit model 13A, second post-crosslinking structural unit model 13B, and pre-crosslinking structural unit model 18 are bonded by a bond 16. The post-crosslinking structural unit model 13 assigned to the second coarse-grained particle 7B is stored in the computer 1 (shown in FIG. 1).

[0098] 16, in the sixth step S6 of this embodiment, the pre-crosslinking structural unit model 18 and the post-crosslinking structural unit model 13 are assigned to the coarse-grained particles 7 of the pre-crosslinking coarse-grained molecular model 5 after structural relaxation. As a result, a post-crosslinking molecular model 21 is created in which the molecular chain after crosslinking is modeled as an all-atom model or a united-atom model.

[0099] In this embodiment, for all pre-crosslinking coarse-grained molecular models 5 after structural relaxation shown in FIG. 13, pre-crosslinking structural unit models 18 and post-crosslinking structural unit models 13 are assigned to the coarse-grained particles 7. This creates a polymer material model in which a plurality of post-crosslinking molecular models 21 (shown in FIG. 16) are arranged inside a cell 19. FIG. 17 is a conceptual diagram showing an example of a polymer material model 22 in which post-crosslinking molecular models 21 are arranged inside a cell 19. In FIG. 17, some of the post-crosslinking molecular models 21 are shown as representatives.

[0100] The post-crosslinking structural unit model 13 shown in Figures 7 and 8 is input based on the analysis results in the second step S2. By assigning such a post-crosslinking structural unit model 13 to the coarse-grained particles 7 of the pre-crosslinking coarse-grained molecular model 5 after structural relaxation shown in Figure 15, a polymer material model 22 having a realistic crosslinked structure 12 can be created, as shown in Figures 16 and 17.

[0101] In this embodiment, for example, the pre-crosslinking structural unit model 18 shown in FIG. 11 and the post-crosslinking structural unit model 13 shown in FIGS. 7 and 8 are assigned to the coarse-grained particle 7 of the pre-crosslinking coarse-grained molecular model 5 after structural relaxation shown in FIG. 13. As a result, a post-crosslinking molecular model 21 in an equilibrium state is created as shown in FIGS. 16 and 17. Therefore, the time required for modeling can be shortened compared to, for example, creating a post-crosslinking molecular model (not shown) in which the post-crosslinking molecular chain 2 (shown in FIGS. 5(a) and (b)) is modeled as an all-atom model, and then calculating the structural relaxation of the post-crosslinking molecular model from scratch.

[0102] If there is a large difference in size between the post-crosslinking structural unit model 13 shown in Figures 7 and 8 and the pre-crosslinking structural unit model 18 shown in Figure 11, there may be a deviation in size between the pre-crosslinking coarse-grained molecular model 5 shown in Figure 13 and the post-crosslinking molecular model 21 shown in Figure 16. To prevent such a deviation, it is preferable to adjust the parameter σ (corresponding to the diameter of the particle model 15) of the LJ potential of the bond 16 of the post-crosslinking structural unit model 13.

[0103] The parameter σ can be adjusted as appropriate. For example, when the first size D1 shown in FIG. 7 is larger than the fifth size D5 shown in FIG. 11, it is preferable to multiply the parameter σ of the bond 16 of the cross-linked structural unit model 13 shown in FIG. 16 by the value obtained by dividing the fifth size D5 by the first size D1. Similarly, when the value obtained by dividing the second size D2 shown in FIG. 8 by the fifth size D5 shown in FIG. 11 is larger than the number of replaced coarse-grained particles 7, it is preferable to multiply the parameter σ of the bond 16 of the cross-linked structural unit model 13 shown in FIG. 16 by the value obtained by dividing the fifth size D5 by the second size D2 and then further dividing the value by the number of replaced coarse-grained particles 7.

[0104] On the other hand, when the first size D1 is smaller than the fifth size D5, it is preferable to multiply the parameter σ of the bond 16 of the cross-linked structural unit model 13 shown in Fig. 16 by the value obtained by dividing the fifth size D5 by the first size D1. Similarly, when the value obtained by dividing the second size D2 by the fifth size D5 is smaller than the number of replaced coarse-grained particles 7, it is preferable to multiply the parameter σ of the bond 16 of the cross-linked structural unit model 13 shown in Fig. 16 by the value obtained by dividing the fifth size D5 by the second size D2, which is further divided by the number of replaced coarse-grained particles 7.

[0105] In this way, by adjusting the parameter σ, the sizes (first size D1 and second size D2) of the post-crosslinking structural unit model 13 can be made to approximate the fifth size D5 of the pre-crosslinking structural unit model 18. Therefore, it is possible to prevent the sizes of the pre-crosslinking coarse-grained molecular model 5 and the post-crosslinking molecular model 21 from diverging.

[0106] [Define Potential] Next, in a sixth step S6 of this embodiment, as shown in FIG. 17, a potential (hereinafter sometimes referred to as a "third potential") P3 is defined between adjacent particle models 15, 15 without a bond 16 in between (step S64). An LJ potential is adopted as the third potential P3 of this embodiment. Details of the LJ potential are as described above. The third potential P3 is stored in the computer 1 (shown in FIG. 1).

[0107] Incidentally, if the pre-crosslinking structural unit model 18 shown in Fig. 11 and the post-crosslinking structural unit model 13 shown in Fig. 7 and Fig. 8 are simply assigned to the coarse-grained particle 7 of the pre-crosslinking coarse-grained molecular model 5 after structural relaxation shown in Fig. 13, the post-crosslinking molecular model 21 may become unstable. For this reason, in the next step S65, it is preferable to obtain a stable structure of the post-crosslinking molecular model 21 shown in Fig. 17.

[0108] [Molecular dynamics calculations were performed on the cross-linked molecular model] Next, in a sixth step S6 of this embodiment, a molecular dynamics calculation is performed on the cross-linked molecular model 21 (step S65). In step S65 of this embodiment, a stable structure of the cross-linked molecular model 21 can be obtained by performing a molecular dynamics calculation on the cross-linked molecular model 21.

[0109] In step S65 of this embodiment, the potential defining the bonds 16 (shown in FIG. 16) constituting the cross-linked molecular model 21 is changed from a FENE-type potential to a Harmonic-type potential. Details of the FENE-type potential and the Harmonic-type potential are as described in patent documents (JP 2017-224202 A, JP 2015-094750 A, etc.). Then, structural relaxation based on molecular dynamics calculation is calculated for the cross-linked molecular model 21. Details of the structural relaxation are as described above.

[0110] Since a linear spring is defined by a harmonic potential for the bond 16 that constitutes the cross-linked molecular model 21, it is possible to suppress calculation of a large force due to entanglement between the particle models 15, 15. Therefore, a stable structure of the cross-linked molecular model 21 can be reliably obtained.

[0111] In this embodiment, the equilibrium lengths of the harmonic bond potentials of the SS bonds and CS bonds constituting the first crosslinked structure 12A shown in Fig. 9(a) and the second crosslinked structure 12B shown in Fig. 9(b) are set to values ​​defined in GAFF, etc. The crosslinked molecular model 21 and polymer material model 22 shown in Fig. 17 are stored in the computer 1 (shown in Fig. 1).

[0112] [Method for creating a polymer material model (second embodiment)] In the embodiments described above, as shown in Fig. 3, the seventh step S7 of inputting a pre-crosslinking structural unit model 18 (shown in Fig. 11) that models the chemical structure of the structural unit 4 before crosslinking shown in Fig. 2 has been performed, but this is not a limitation. For example, if crosslinking occurs in all of the structural units 4 that make up the molecular chain 2 shown in Fig. 2, the seventh step S7 of inputting the pre-crosslinking structural unit model 18 (shown in Fig. 11) may be omitted. In this case, the sixth step S may omit step S62 (shown in Fig. 14) of assigning the pre-crosslinking structural unit model 18 to the first coarse-grained particle 7A (shown in Fig. 15) of the pre-crosslinking coarse-grained molecular model after structural relaxation.

[0113] [Simulation method for polymer materials] Next, a simulation method of this embodiment will be described. This simulation method uses a polymer material model 22 created by the creation method of the previous embodiments. Figure 18 is a flowchart showing an example of the processing procedure of the simulation method of a polymer material.

[0114] [Create a polymer material model] In the simulation method of this embodiment, first, the computer 1 (shown in FIG. 1) creates the polymer material model 22 shown in FIG. 17 (step S8). In step S8 of this embodiment, the polymer material model 22 is created based on the processing procedure of the creation method shown in FIG. 3. This polymer material model 22 has the post-crosslinking structural unit model 13 input based on the analysis results in the second step S2, so that a polymer material model 22 having a crosslinked structure close to reality can be created. The polymer material model 22 is stored in the computer 1.

[0115] [Calculate deformation of polymer material model] Next, in the simulation method of this embodiment, the computer 1 (shown in FIG. 1) performs a deformation calculation on the polymer material model 22 (step S9).

[0116] The deformation calculation of the polymer material model 22 can be performed as appropriate. For example, based on the procedure described in Japanese Patent No. 6408856, the extension of the polymer material model 22 may be calculated so that one end (the surface 20a on one side) and the other end (the surface 20b on the other side) of the polymer material model 22 move away from each other. Furthermore, a periodic strain may be applied to the polymer material model 22. The above-mentioned simulation software may be used for such deformation calculation.

[0117] In step S9 of this embodiment, physical quantities (stress, energy loss, etc.) of the polymer material model 22 can be calculated by calculating the deformation of the polymer material model 22. In this embodiment, a polymer material model 22 having a cross-linking structure close to reality is used, so physical quantities (stress, energy loss, etc.) that significantly affect the cross-linking structure can be calculated with high accuracy. The deformation calculation results are stored in computer 1 (shown in FIG. 1).

[0118] Next, in step S9 of this embodiment, the computer 1 (shown in FIG. 1) may output the calculation results of the deformation. The calculation results may be output as appropriate. For example, the calculation results may be displayed on a display device 1d (shown in FIG. 1) or may be printed on a printer (not shown) or the like. This makes it possible to notify an operator or the like of the calculation results of the deformation of the polymer material model 22.

[0119] [Evaluate the deformation calculation results] Next, in the simulation method of this embodiment, the performance of the polymer material is evaluated (step S10). The evaluation of the calculation results may be performed by the computer 1 (shown in FIG. 1) or by an operator.

[0120] In step S10 of this embodiment, it is evaluated whether the result of the deformation calculation (in this example, the physical quantity of the polymer material model 22) satisfies a predetermined standard. The standard can be set appropriately depending on the performance required of the polymer material and the product using the polymer material (for example, a tire, etc.).

[0121] In this embodiment, if the result of the deformation calculation is determined to satisfy the criteria ("Yes" in step S10), the performance of the polymer material is determined to be good. In this case, the polymer material is manufactured based on the structure of the molecular chain 2 shown in Figure 2, the crosslinking conditions, etc. (step S11).

[0122] On the other hand, if the result of the deformation calculation is judged not to satisfy the criteria ("No" in step S10), the performance of the polymer material is evaluated as not being good. In this case, the structure of the molecular chain 2 shown in Figure 2 and the crosslinking conditions are changed (step S12), and steps S8 to S10 are performed again.

[0123] In this way, in the simulation method of this embodiment, the structure of the molecular chain 2, crosslinking conditions, etc. are changed until the performance of the polymer material is improved, so that a polymer material with good performance can be efficiently produced.

[0124] 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 implemented in various ways. [Example]

[0125] A numerical analysis model of a polymer material including a molecular chain after crosslinking was created based on the processing procedure shown in Figure 3 (Example). In this example, first, a pre-crosslinking coarse-grained molecular model in which a predetermined range of structural units of the molecular chain before crosslinking shown in Figure 2 were replaced with coarse-grained particles was input into a computer (first step). The structural units were identified as monomers of the molecular chain. The pre-crosslinking coarse-grained molecular model is as shown in Figure 4.

[0126] Next, in the examples, the crosslinked molecular chains were analyzed (second step). In the second step, nuclear magnetic resonance analysis was performed on the crosslinked molecular chains to identify the chemical structure of the crosslinked molecular chains.

[0127] Next, in the examples, based on the analysis results of the molecular chains after crosslinking, the chemical structure of the structural unit after crosslinking (shown in FIGS. 5(a) and 5(b)), including at least the crosslinked portion, was input into a computer (third step). Furthermore, in the examples, a post-crosslinking structural unit model (shown in FIGS. 7 and 8) and a pre-crosslinking structural unit model (shown in FIG. 11), which respectively model the chemical structure of the structural unit after crosslinking and the chemical structure of the structural unit before crosslinking, were input into a computer (fourth and seventh steps). These post-crosslinking structural unit models and pre-crosslinking structural unit models were modeled as all-atom models.

[0128] Next, in the examples, structural relaxation was calculated based on the molecular dynamics method for the pre-crosslinking coarse-grained molecular model (step 5). Then, in the examples, a post-crosslinking molecular model in which the molecular chain after crosslinking was modeled as an all-atom model was created by assigning the post-crosslinking structural unit model and the pre-crosslinking structural unit model to the coarse-grained particles of the pre-crosslinking coarse-grained molecular model after structural relaxation (step 6).

[0129] In the sixth step, a first coarse-grained particle and a second coarse-grained particle were identified from the pre-crosslinking coarse-grained molecular model after the structural relaxation based on the distance between adjacent coarse-grained particles after the structural relaxation. Then, a pre-crosslinking structural unit model was assigned to the first coarse-grained particle, and a post-crosslinking structural unit model was assigned to the second coarse-grained particle, thereby creating a post-crosslinking molecular model and a polymer material model including multiple post-crosslinking molecular models.

[0130] For comparison, without analyzing the molecular chains after crosslinking, an operator assumed the most plausible crosslinked structure, and a post-crosslinked molecular model modeled as an all-atom model and a polymer material model including multiple post-crosslinked molecular models were created (Comparative Example).In the Comparative Example, the structural relaxation of the post-crosslinked molecular model was calculated from the beginning, unlike the Example in which a post-crosslinked structural unit model was assigned to a pre-crosslinking coarse-grained molecular model after structural relaxation.

[0131] Deformation calculations were performed on the polymer material model of the example and the polymer material model of the comparative example, and stresses in the polymer material models were calculated.

[0132] In addition, to evaluate the stress of the examples and comparative examples, the actual polymer material used for analysis in the second step was deformed and the stress was measured (experimental example).The stress of the examples and comparative examples was then compared with the stress of the experimental example.The common specifications are as follows: Molecular chain: Polybutadiene Number of coarse-grained molecular models before cross-linking (molecular models after cross-linking): 100,000 Number of second coarse-grained particles (crosslinking points): 300

[0133] As a result of the test, the stress of the Example was closer to that of the Experimental Example than that of the Comparative Example. Therefore, the Example was able to create a polymer material model with a more realistic cross-linked structure than the Comparative Example.

[0134] Furthermore, in the Example, unlike the Comparative Example in which the structural relaxation of the molecular model after cross-linking was calculated from the beginning, the post-cross-linking structural unit model is assigned to the pre-cross-linking coarse-grained molecular model after structural relaxation. Therefore, the time required for modeling in the Example was reduced to 0.001% compared to the Comparative Example in which the structural relaxation of the molecular model after cross-linking was calculated from the beginning.

[0135] [Note] The present invention includes the following aspects.

[0136] [Invention 1] A method for creating a model for numerical analysis of a polymeric material including crosslinked molecular chains, comprising: a first step of inputting a pre-crosslinking coarse-grained molecular model in which structural units within a predetermined range of the molecular chain before crosslinking are replaced with coarse-grained particles into a computer; a second step of analyzing the molecular chains after crosslinking; a third step of inputting into the computer a chemical structure of the structural unit after crosslinking, the chemical structure including at least a crosslinked portion, based on the analysis result of the molecular chain after crosslinking; a fourth step of inputting a post-crosslinking structural unit model, which is obtained by modeling the chemical structure of the structural unit after crosslinking as an all-atom model or a united-atom model, into the computer; a fifth step in which the computer calculates structural relaxation based on a molecular dynamics method for the pre-crosslinking coarse-grained molecular model; a sixth step in which the computer creates a post-crosslinked molecular model in which the molecular chain after crosslinking is modeled as the all-atom model or the united-atom model by assigning the post-crosslinked structural unit model to the coarse-grained particles of the pre-crosslinking coarse-grained molecular model after the structural relaxation; Including, How to create a polymer material model. [Invention 2] The method for creating a polymer material model according to aspect 1, wherein the second step includes nuclear magnetic resonance analysis of the molecular chains after crosslinking. [Invention 3] A seventh step of inputting a pre-crosslinking structural unit model, which is obtained by modeling the chemical structure of the structural unit before crosslinking using an all-atom model or a united atom model, into the computer, The method for creating a polymer material model according to invention 1 or 2, wherein the sixth step includes a step of assigning the pre-crosslinking structural unit model to the coarse-grained particles of the pre-crosslinking coarse-grained molecular model after the structural relaxation. [Invention 4] The sixth step comprises: a step of identifying, from the pre-crosslinking coarse-grained molecular model after the structural relaxation, a first coarse-grained particle to which the pre-crosslinking structural unit model is to be assigned and a second coarse-grained particle to which the post-crosslinking structural unit model is to be assigned, based on a distance between adjacent coarse-grained particles after the structural relaxation; assigning the pre-crosslinking structural unit model to the first coarse-grained particle; A method for creating a polymer material model according to aspect 3, comprising the step of assigning the post-crosslinking structural unit model to the second coarse-grained particles. [Invention 5] The chemical structure of the structural unit after crosslinking includes a first crosslinked structural unit in which one end of a sulfur chain is bonded to the chemical structure of the structural unit before crosslinking, 5. The method for creating a polymer material model according to any one of aspects 1 to 4, wherein the post-crosslinking structural unit model includes a first post-crosslinking structural unit model that models the first post-crosslinking structural unit. [Invention 6] the chemical structure of the structural unit after crosslinking includes a second crosslinked structural unit in which both ends of a sulfur chain are bonded in a ring shape in addition to the chemical structure of the structural unit before crosslinking, 6. The method for creating a polymer material model according to any one of aspects 1 to 5, wherein the post-crosslinking structural unit model includes a second post-crosslinking structural unit model that models the second post-crosslinking structural unit. [Invention 7] The fifth step is a step of arranging a plurality of the pre-crosslinking coarse-grained molecular models inside a cell that is a virtual space corresponding to a portion of the polymer material; A method for creating a polymer material model according to any one of the present inventions 1 to 6, comprising a step of calculating structural relaxation based on molecular dynamics calculations for a plurality of the pre-crosslinking coarse-grained molecular models arranged inside the cell. [Invention 8] A method for simulating a polymeric material, comprising: The computer A step of carrying out the method for creating a polymer material model according to any one of the first to seventh aspects of the present invention to create the polymer material model; and performing a deformation calculation on the polymer material model to evaluate the performance of the polymer material. Simulation methods for polymeric materials. [Explanation of symbols]

[0137] S1 1st process S2 2nd process S3 3rd process S4 4th process S5 5th process S6 6th process

Claims

1. A method for creating a model for numerical analysis of a polymeric material including crosslinked molecular chains, comprising: a first step of inputting a pre-crosslinking coarse-grained molecular model in which structural units within a predetermined range of the molecular chain before crosslinking are replaced with coarse-grained particles into a computer; a second step of analyzing the molecular chains after crosslinking; a third step of inputting into the computer a chemical structure of the structural unit after crosslinking, the chemical structure including at least a crosslinked portion, based on the analysis result of the molecular chain after crosslinking; a fourth step of inputting a post-crosslinked structural unit model, which is obtained by modeling the chemical structure of the structural unit after crosslinking as an all-atom model or a united-atom model, into the computer; a fifth step in which the computer calculates structural relaxation based on a molecular dynamics method for the pre-crosslinking coarse-grained molecular model; a sixth step in which the computer creates a post-crosslinked molecular model in which the molecular chain after crosslinking is modeled as the all-atom model or the united-atom model by assigning the post-crosslinked structural unit model to the coarse-grained particles of the pre-crosslinking coarse-grained molecular model after the structural relaxation; Including, How to create a polymer material model.

2. The method for creating a polymer material model according to claim 1 , wherein the second step includes nuclear magnetic resonance analysis of the molecular chains after crosslinking.

3. a seventh step of inputting a pre-crosslinking structural unit model, which is obtained by modeling the chemical structure of the structural unit before crosslinking using an all-atom model or a united atom model, into the computer; 2. The method for creating a polymer material model according to claim 1, wherein the sixth step includes a step of assigning the pre-crosslinking structural unit model to the coarse-grained particles of the pre-crosslinking coarse-grained molecular model after the structural relaxation.

4. The sixth step comprises: a step of identifying, from the pre-crosslinking coarse-grained molecular model after the structural relaxation, a first coarse-grained particle to which the pre-crosslinking structural unit model is to be assigned and a second coarse-grained particle to which the post-crosslinking structural unit model is to be assigned, based on a distance between adjacent coarse-grained particles after the structural relaxation; assigning the pre-crosslinking structural unit model to the first coarse-grained particle; The method for creating a polymer material model according to claim 3 , further comprising the step of assigning the post-crosslinking structural unit model to the second coarse-grained particles.

5. the chemical structure of the structural unit after crosslinking includes a first crosslinked structural unit in which one end of a sulfur chain is bonded to the chemical structure of the structural unit before crosslinking, The polymer material model creation method according to claim 1 , wherein the post-crosslinking structural unit model includes a first post-crosslinking structural unit model that models the first post-crosslinking structural unit.

6. the chemical structure of the structural unit after crosslinking includes a second crosslinked structural unit in which both ends of a sulfur chain are bonded in a ring shape in addition to the chemical structure of the structural unit before crosslinking, The polymer material model creation method according to claim 1 , wherein the post-crosslinking structural unit model includes a second post-crosslinking structural unit model that models the second post-crosslinking structural unit.

7. The fifth step is a step of arranging a plurality of the pre-crosslinking coarse-grained molecular models inside a cell that is a virtual space corresponding to a portion of the polymer material; The method for creating a polymer material model according to claim 1, further comprising a step of calculating structural relaxation based on molecular dynamics calculations for the plurality of pre-crosslinking coarse-grained molecular models arranged inside the cell.

8. A method for simulating a polymeric material, comprising: The computer a step of carrying out the polymer material model creation method according to any one of claims 1 to 7 to create the polymer material model; and performing a deformation calculation on the polymer material model to evaluate the performance of the polymer material. Simulation methods for polymeric materials.

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